LMFDB - Embedded newform 459.2.y.a.422.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [459,2,Mod(44,459)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(459, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([40, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("459.44"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 459 = 3^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	459.y (of order $48$, degree $16$, 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:	$3.66513345278$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	no (minimal twist has level 153)
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			422.7
Character	$\chi$	$=$	459.422
Dual form			459.2.y.a.62.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.196546 + 0.256144i) q^{2} +(0.490659 + 1.83116i) q^{4} +(0.803783 - 0.0526827i) q^{5} +(0.182581 - 2.78565i) q^{7} +(-1.16205 - 0.481337i) q^{8} +(-0.144486 + 0.216239i) q^{10} +(3.20484 - 2.81057i) q^{11} +(4.89065 - 1.31045i) q^{13} +(0.677643 + 0.594277i) q^{14} +(-2.93186 + 1.69271i) q^{16} +(0.361775 + 4.10720i) q^{17} +(5.27449 - 2.18477i) q^{19} +(0.490854 + 1.44601i) q^{20} +(0.0900113 + 1.37331i) q^{22} +(-2.49870 + 7.36094i) q^{23} +(-4.31393 + 0.567940i) q^{25} +(-0.625576 + 1.51027i) q^{26} +(5.19057 - 1.03247i) q^{28} +(-0.570719 - 0.281448i) q^{29} +(-1.44065 + 1.64275i) q^{31} +(0.471019 - 3.57775i) q^{32} +(-1.12314 - 0.714589i) q^{34} -2.24868i q^{35} +(-0.897790 + 4.51350i) q^{37} +(-0.477067 + 1.78044i) q^{38} +(-0.959395 - 0.325671i) q^{40} +(1.85115 + 3.75377i) q^{41} +(-1.07042 - 8.13062i) q^{43} +(6.71909 + 4.48955i) q^{44} +(-1.39435 - 2.08679i) q^{46} +(2.96048 + 0.793260i) q^{47} +(-0.786402 - 0.103532i) q^{49} +(0.702413 - 1.21662i) q^{50} +(4.79928 + 8.31260i) q^{52} +(-3.67083 - 8.86216i) q^{53} +(2.42793 - 2.42793i) q^{55} +(-1.55301 + 3.14919i) q^{56} +(0.184264 - 0.0908689i) q^{58} +(7.79797 - 5.98360i) q^{59} +(0.312284 + 0.0204682i) q^{61} +(-0.137626 - 0.691891i) q^{62} +(-3.96387 - 3.96387i) q^{64} +(3.86198 - 1.31097i) q^{65} +(-2.17017 - 1.25295i) q^{67} +(-7.34345 + 2.67770i) q^{68} +(0.575986 + 0.441969i) q^{70} +(1.92783 + 0.383470i) q^{71} +(-4.62155 + 3.08802i) q^{73} +(-0.979648 - 1.11707i) q^{74} +(6.58864 + 8.58648i) q^{76} +(-7.24412 - 9.44072i) q^{77} +(-4.01302 - 4.57597i) q^{79} +(-2.26741 + 1.51503i) q^{80} +(-1.32534 - 0.263627i) q^{82} +(-8.53828 - 6.55165i) q^{83} +(0.507167 + 3.28224i) q^{85} +(2.29300 + 1.32386i) q^{86} +(-5.07702 + 1.72342i) q^{88} +(-9.50851 - 9.50851i) q^{89} +(-2.75750 - 13.8629i) q^{91} +(-14.7051 - 0.963823i) q^{92} +(-0.785061 + 0.602399i) q^{94} +(4.12445 - 2.03395i) q^{95} +(-5.09492 + 10.3315i) q^{97} +(0.181083 - 0.181083i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/459\mathbb{Z}\right)^\times$.

$n$	$137$	$190$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−0.196546	+	0.256144i	−0.138979	+	0.181121i	−0.857657	−	0.514222i	$-0.828081\pi$
$2$	−0.196546	+	0.256144i	−0.138979	+	0.181121i	0.718678	+	0.695343i	$0.244748\pi$
$3$		0			0
$3$		0			0
$4$	0.490659	+	1.83116i	0.245329	+	0.915582i
$5$	0.803783	−	0.0526827i	0.359463	−	0.0235604i	0.115398	−	0.993319i	$-0.463186\pi$
$5$	0.803783	−	0.0526827i	0.359463	−	0.0235604i	0.244065	+	0.969759i	$0.421519\pi$
$6$		0			0
$7$	0.182581	−	2.78565i	0.0690092	−	1.05288i	−0.813189	−	0.581999i	$-0.802271\pi$
$7$	0.182581	−	2.78565i	0.0690092	−	1.05288i	0.882198	−	0.470878i	$-0.156063\pi$
$8$	−1.16205	−	0.481337i	−0.410847	−	0.170178i
$9$		0			0
$10$	−0.144486	+	0.216239i	−0.0456906	+	0.0683807i
$11$	3.20484	−	2.81057i	0.966295	−	0.847418i	−0.0220332	−	0.999757i	$-0.507014\pi$
$11$	3.20484	−	2.81057i	0.966295	−	0.847418i	0.988328	+	0.152339i	$0.0486806\pi$
$12$		0			0
$13$	4.89065	−	1.31045i	1.35642	−	0.363452i	0.493921	−	0.869507i	$-0.335563\pi$
$13$	4.89065	−	1.31045i	1.35642	−	0.363452i	0.862501	+	0.506055i	$0.168897\pi$
$14$	0.677643	+	0.594277i	0.181108	+	0.158827i
$15$		0			0
$16$	−2.93186	+	1.69271i	−0.732966	+	0.423178i
$17$	0.361775	+	4.10720i	0.0877433	+	0.996143i
$17$	0.361775	+	4.10720i	0.0877433	+	0.996143i
$18$		0			0
$19$	5.27449	−	2.18477i	1.21005	−	0.501220i	0.315818	−	0.948820i	$-0.397721\pi$
$19$	5.27449	−	2.18477i	1.21005	−	0.501220i	0.894234	+	0.447600i	$0.147721\pi$
$20$	0.490854	+	1.44601i	0.109758	+	0.323337i
$21$		0			0
$22$	0.0900113	+	1.37331i	0.0191905	+	0.292790i
$23$	−2.49870	+	7.36094i	−0.521016	+	1.53486i	0.294223	+	0.955737i	$0.404939\pi$
$23$	−2.49870	+	7.36094i	−0.521016	+	1.53486i	−0.815238	+	0.579126i	$0.803394\pi$
$24$		0			0
$25$	−4.31393	+	0.567940i	−0.862787	+	0.113588i
$26$	−0.625576	+	1.51027i	−0.122686	+	0.296189i
$27$		0			0
$28$	5.19057	−	1.03247i	0.980925	−	0.195118i
$29$	−0.570719	−	0.281448i	−0.105980	−	0.0522635i	0.388526	−	0.921438i	$-0.372984\pi$
$29$	−0.570719	−	0.281448i	−0.105980	−	0.0522635i	−0.494506	+	0.869174i	$0.664651\pi$
$30$		0			0
$31$	−1.44065	+	1.64275i	−0.258749	+	0.295047i	−0.866599	−	0.499005i	$-0.833699\pi$
$31$	−1.44065	+	1.64275i	−0.258749	+	0.295047i	0.607850	+	0.794052i	$0.292032\pi$
$32$	0.471019	−	3.57775i	0.0832652	−	0.632462i
$33$		0			0
$34$	−1.12314	−	0.714589i	−0.192617	−	0.122551i
$35$		−	2.24868i		−	0.380096i
$36$		0			0
$37$	−0.897790	+	4.51350i	−0.147596	+	0.742014i	0.834108	+	0.551601i	$0.185983\pi$
$37$	−0.897790	+	4.51350i	−0.147596	+	0.742014i	−0.981704	+	0.190413i	$0.939017\pi$
$38$	−0.477067	+	1.78044i	−0.0773905	+	0.288825i
$39$		0			0
$40$	−0.959395	−	0.325671i	−0.151694	−	0.0514931i
$41$	1.85115	+	3.75377i	0.289101	+	0.586240i	0.992172	−	0.124881i	$-0.0398548\pi$
$41$	1.85115	+	3.75377i	0.289101	+	0.586240i	−0.703070	+	0.711120i	$0.748188\pi$
$42$		0			0
$43$	−1.07042	−	8.13062i	−0.163237	−	1.23991i	−0.855324	−	0.518093i	$-0.826642\pi$
$43$	−1.07042	−	8.13062i	−0.163237	−	1.23991i	0.692087	−	0.721814i	$-0.256691\pi$
$44$	6.71909	+	4.48955i	1.01294	+	0.676825i
$45$		0			0
$46$	−1.39435	−	2.08679i	−0.205586	−	0.307681i
$47$	2.96048	+	0.793260i	0.431831	+	0.115709i	0.468186	−	0.883630i	$-0.344908\pi$
$47$	2.96048	+	0.793260i	0.431831	+	0.115709i	−0.0363545	+	0.999339i	$0.511575\pi$
$48$		0			0
$49$	−0.786402	−	0.103532i	−0.112343	−	0.0147903i
$50$	0.702413	−	1.21662i	0.0993362	−	0.172055i
$51$		0			0
$52$	4.79928	+	8.31260i	0.665540	+	1.15275i
$53$	−3.67083	−	8.86216i	−0.504227	−	1.21731i	−0.947162	−	0.320757i	$-0.896063\pi$
$53$	−3.67083	−	8.86216i	−0.504227	−	1.21731i	0.442935	−	0.896554i	$-0.353937\pi$
$54$		0			0
$55$	2.42793	−	2.42793i	0.327381	−	0.327381i
$56$	−1.55301	+	3.14919i	−0.207529	+	0.420828i
$57$		0			0
$58$	0.184264	−	0.0908689i	0.0241950	−	0.0119317i
$59$	7.79797	−	5.98360i	1.01521	−	0.778998i	0.0397575	−	0.999209i	$-0.487341\pi$
$59$	7.79797	−	5.98360i	1.01521	−	0.778998i	0.975452	+	0.220212i	$0.0706748\pi$
$60$		0			0
$61$	0.312284	+	0.0204682i	0.0399839	+	0.00262068i	0.0853820	−	0.996348i	$-0.472789\pi$
$61$	0.312284	+	0.0204682i	0.0399839	+	0.00262068i	−0.0453980	+	0.998969i	$0.514456\pi$
$62$	−0.137626	−	0.691891i	−0.0174785	−	0.0878703i
$63$		0			0
$64$	−3.96387	−	3.96387i	−0.495484	−	0.495484i
$65$	3.86198	−	1.31097i	0.479020	−	0.162605i
$66$		0			0
$67$	−2.17017	−	1.25295i	−0.265128	−	0.153072i	0.361543	−	0.932355i	$-0.382250\pi$
$67$	−2.17017	−	1.25295i	−0.265128	−	0.153072i	−0.626672	+	0.779283i	$0.715583\pi$
$68$	−7.34345	+	2.67770i	−0.890524	+	0.324719i
$69$		0			0
$70$	0.575986	+	0.441969i	0.0688435	+	0.0528254i
$71$	1.92783	+	0.383470i	0.228792	+	0.0455095i	0.308155	−	0.951336i	$-0.400289\pi$
$71$	1.92783	+	0.383470i	0.228792	+	0.0455095i	−0.0793629	+	0.996846i	$0.525289\pi$
$72$		0			0
$73$	−4.62155	+	3.08802i	−0.540912	+	0.361426i	−0.795814	−	0.605541i	$-0.792957\pi$
$73$	−4.62155	+	3.08802i	−0.540912	+	0.361426i	0.254902	+	0.966967i	$0.417957\pi$
$74$	−0.979648	−	1.11707i	−0.113882	−	0.129857i
$75$		0			0
$76$	6.58864	+	8.58648i	0.755769	+	0.984937i
$77$	−7.24412	−	9.44072i	−0.825544	−	1.07587i
$78$		0			0
$79$	−4.01302	−	4.57597i	−0.451500	−	0.514837i	0.480649	−	0.876913i	$-0.340401\pi$
$79$	−4.01302	−	4.57597i	−0.451500	−	0.514837i	−0.932148	+	0.362076i	$0.882068\pi$
$80$	−2.26741	+	1.51503i	−0.253504	+	0.169386i
$81$		0			0
$82$	−1.32534	−	0.263627i	−0.146360	−	0.0291127i
$83$	−8.53828	−	6.55165i	−0.937198	−	0.719137i	0.0226251	−	0.999744i	$-0.492798\pi$
$83$	−8.53828	−	6.55165i	−0.937198	−	0.719137i	−0.959823	+	0.280607i	$0.909464\pi$
$84$		0			0
$85$	0.507167	+	3.28224i	0.0550100	+	0.356009i
$86$	2.29300	+	1.32386i	0.247260	+	0.142756i
$87$		0			0
$88$	−5.07702	+	1.72342i	−0.541212	+	0.183717i
$89$	−9.50851	−	9.50851i	−1.00790	−	1.00790i	−0.999969	−	0.00793097i	$-0.997475\pi$
$89$	−9.50851	−	9.50851i	−1.00790	−	1.00790i	−0.00793097	−	0.999969i	$-0.502525\pi$
$90$		0			0
$91$	−2.75750	−	13.8629i	−0.289065	−	1.45323i
$92$	−14.7051	−	0.963823i	−1.53311	−	0.100486i
$93$		0			0
$94$	−0.785061	+	0.602399i	−0.0809729	+	0.0621327i
$95$	4.12445	−	2.03395i	0.423160	−	0.208679i
$96$		0			0
$97$	−5.09492	+	10.3315i	−0.517311	+	1.04900i	0.468861	+	0.883272i	$0.344665\pi$
$97$	−5.09492	+	10.3315i	−0.517311	+	1.04900i	−0.986171	+	0.165730i	$0.947002\pi$
$98$	0.181083	−	0.181083i	0.0182922	−	0.0182922i
$99$		0			0
$100$	−3.15666	−	7.62085i	−0.315666	−	0.762085i
$101$	0.533410	+	0.923893i	0.0530762	+	0.0919307i	0.891343	−	0.453330i	$-0.149764\pi$
$101$	0.533410	+	0.923893i	0.0530762	+	0.0919307i	−0.838267	+	0.545261i	$0.816431\pi$
$102$		0			0
$103$	−6.64266	+	11.5054i	−0.654521	+	1.13366i	0.327493	+	0.944854i	$0.393796\pi$
$103$	−6.64266	+	11.5054i	−0.654521	+	1.13366i	−0.982014	+	0.188810i	$0.939537\pi$
$104$	−6.31395	−	0.831248i	−0.619134	−	0.0815105i
$105$		0			0
$106$	2.99148	+	0.801564i	0.290558	+	0.0778548i
$107$	9.57936	+	14.3365i	0.926072	+	1.38596i	0.922511	+	0.385971i	$0.126134\pi$
$107$	9.57936	+	14.3365i	0.926072	+	1.38596i	0.00356116	+	0.999994i	$0.498866\pi$
$108$		0			0
$109$	4.45912	+	2.97949i	0.427106	+	0.285383i	0.750487	−	0.660886i	$-0.229819\pi$
$109$	4.45912	+	2.97949i	0.427106	+	0.285383i	−0.323380	+	0.946269i	$0.604819\pi$
$110$	0.144699	+	1.09910i	0.0137965	+	0.104795i
$111$		0			0
$112$	4.18000	+	8.47621i	0.394973	+	0.800926i
$113$	−7.14534	−	2.42551i	−0.672177	−	0.228173i	−0.0355762	−	0.999367i	$-0.511327\pi$
$113$	−7.14534	−	2.42551i	−0.672177	−	0.228173i	−0.636601	+	0.771194i	$0.719660\pi$
$114$		0			0
$115$	−1.62062	+	6.04824i	−0.151124	+	0.564001i
$116$	0.235348	−	1.18318i	0.0218515	−	0.109855i
$117$		0			0
$118$			3.17346i			0.292141i
$119$	11.5073	−	0.257880i	1.05487	−	0.0236398i
$120$		0			0
$121$	0.935909	−	7.10893i	0.0850826	−	0.646267i
$122$	−0.0666211	+	0.0759669i	−0.00603160	+	0.00687772i
$123$		0			0
$124$	−3.71501	−	1.83204i	−0.333618	−	0.164522i
$125$	−7.38770	+	1.46950i	−0.660776	+	0.131436i
$126$		0			0
$127$	−1.70901	+	4.12592i	−0.151650	+	0.366116i	−0.981387	−	0.192038i	$-0.938490\pi$
$127$	−1.70901	+	4.12592i	−0.151650	+	0.366116i	0.829737	+	0.558154i	$0.188490\pi$
$128$	8.94990	−	1.17828i	0.791067	−	0.104146i
$129$		0			0
$130$	−0.423262	+	1.24689i	−0.0371226	+	0.109360i
$131$	−0.314129	−	4.79268i	−0.0274456	−	0.418739i	−0.989370	−	0.145422i	$-0.953546\pi$
$131$	−0.314129	−	4.79268i	−0.0274456	−	0.418739i	0.961924	−	0.273317i	$-0.0881207\pi$
$132$		0			0
$133$	−5.12297	−	15.0918i	−0.444218	−	1.30862i
$134$	0.747474	−	0.309614i	0.0645720	−	0.0267466i
$135$		0			0
$136$	1.55655	−	4.94692i	0.133473	−	0.424195i
$137$	−11.1827	+	6.45634i	−0.955403	+	0.551602i	−0.894755	−	0.446557i	$-0.852650\pi$
$137$	−11.1827	+	6.45634i	−0.955403	+	0.551602i	−0.0606478	+	0.998159i	$0.519317\pi$
$138$		0			0
$139$	−9.20744	−	8.07471i	−0.780965	−	0.684888i	0.172961	−	0.984929i	$-0.444666\pi$
$139$	−9.20744	−	8.07471i	−0.780965	−	0.684888i	−0.953926	+	0.300041i	$0.903000\pi$
$140$	4.11770	−	1.10333i	0.348009	−	0.0932487i
$141$		0			0
$142$	−0.477132	+	0.418434i	−0.0400400	+	0.0351142i
$143$	11.9906	−	17.9453i	1.00271	−	1.50066i
$144$		0			0
$145$	−0.473562	−	0.196156i	−0.0393272	−	0.0162899i
$146$	0.117370	−	1.79072i	0.00971362	−	0.148201i
$147$		0			0
$148$	−8.70546	+	0.570586i	−0.715584	+	0.0469019i
$149$	−1.85758	−	6.93257i	−0.152179	−	0.567939i	−0.999330	−	0.0365876i	$-0.988351\pi$
$149$	−1.85758	−	6.93257i	−0.152179	−	0.567939i	0.847152	−	0.531351i	$-0.178315\pi$
$150$		0			0
$151$	3.23263	−	4.21285i	0.263068	−	0.342837i	−0.643079	−	0.765800i	$-0.722343\pi$
$151$	3.23263	−	4.21285i	0.263068	−	0.342837i	0.906147	+	0.422963i	$0.139010\pi$
$152$	−7.18084			−0.582443
$153$		0			0
$154$	3.84199			0.309596
$155$	−1.07143	+	1.39631i	−0.0860591	+	0.112154i
$156$		0			0
$157$	−4.37101	−	16.3128i	−0.348844	−	1.30190i	−0.888056	−	0.459735i	$-0.847945\pi$
$157$	−4.37101	−	16.3128i	−0.348844	−	1.30190i	0.539212	−	0.842170i	$-0.318722\pi$
$158$	1.96085	−	0.128521i	0.155997	−	0.0102246i
$159$		0			0
$160$	0.190112	−	2.90055i	0.0150297	−	0.229308i
$161$	20.0488	+	8.30449i	1.58007	+	0.654485i
$162$		0			0
$163$	−5.10782	+	7.64440i	−0.400076	+	0.598755i	−0.975740	−	0.218930i	$-0.929743\pi$
$163$	−5.10782	+	7.64440i	−0.400076	+	0.598755i	0.575665	+	0.817686i	$0.304743\pi$
$164$	−5.96547	+	5.23158i	−0.465825	+	0.408518i
$165$		0			0
$166$	3.35633	−	0.899327i	0.260502	−	0.0698013i
$167$	10.2922	+	9.02598i	0.796431	+	0.698452i	0.957482	−	0.288495i	$-0.0931547\pi$
$167$	10.2922	+	9.02598i	0.796431	+	0.698452i	−0.161050	+	0.986946i	$0.551488\pi$
$168$		0			0
$169$	10.9429	−	6.31786i	0.841758	−	0.485989i
$170$	−0.940409	−	0.515205i	−0.0721261	−	0.0395144i
$171$		0			0
$172$	14.3633	−	5.94946i	1.09519	−	0.453642i
$173$	0.258251	+	0.760782i	0.0196344	+	0.0578412i	0.956306	−	0.292369i	$-0.0944435\pi$
$173$	0.258251	+	0.760782i	0.0196344	+	0.0578412i	−0.936671	+	0.350210i	$0.886110\pi$
$174$		0			0
$175$	0.794440	+	12.1208i	0.0600540	+	0.916247i
$176$	−4.63867	+	13.6651i	−0.349653	+	1.03004i
$177$		0			0
$178$	4.30441	−	0.566686i	0.322629	−	0.0424749i
$179$	−2.75669	+	6.65524i	−0.206045	+	0.497436i	−0.992794	−	0.119837i	$-0.961763\pi$
$179$	−2.75669	+	6.65524i	−0.206045	+	0.497436i	0.786749	+	0.617273i	$0.211763\pi$
$180$		0			0
$181$	−3.34914	+	0.666185i	−0.248939	+	0.0495171i	−0.317983	−	0.948097i	$-0.603005\pi$
$181$	−3.34914	+	0.666185i	−0.248939	+	0.0495171i	0.0690433	+	0.997614i	$0.478005\pi$
$182$	4.09288	+	2.01839i	0.303384	+	0.149613i
$183$		0			0
$184$	6.44672	−	7.35107i	0.475258	−	0.541928i
$185$	−0.483845	+	3.67517i	−0.0355730	+	0.270204i
$186$		0			0
$187$	12.7030	+	12.1461i	0.928935	+	0.888213i
$188$			5.81035i			0.423763i
$189$		0			0
$190$	−0.289660	+	1.45622i	−0.0210142	+	0.105645i
$191$	−2.17003	+	8.09867i	−0.157018	+	0.585999i	0.841906	+	0.539624i	$0.181434\pi$
$191$	−2.17003	+	8.09867i	−0.157018	+	0.585999i	−0.998924	+	0.0463750i	$0.985233\pi$
$192$		0			0
$193$	−9.96043	−	3.38111i	−0.716968	−	0.243378i	−0.0609689	−	0.998140i	$-0.519419\pi$
$193$	−9.96043	−	3.38111i	−0.716968	−	0.243378i	−0.655999	+	0.754762i	$0.727752\pi$
$194$	−1.64496	−	3.33565i	−0.118101	−	0.239485i
$195$		0			0
$196$	−0.196271	−	1.49083i	−0.0140194	−	0.106488i
$197$	−12.4640	−	8.32821i	−0.888027	−	0.593360i	0.0257092	−	0.999669i	$-0.491816\pi$
$197$	−12.4640	−	8.32821i	−0.888027	−	0.593360i	−0.913736	+	0.406309i	$0.866816\pi$
$198$		0			0
$199$	5.21079	+	7.79850i	0.369383	+	0.552821i	0.968872	−	0.247562i	$-0.0796295\pi$
$199$	5.21079	+	7.79850i	0.369383	+	0.552821i	−0.599489	+	0.800383i	$0.704629\pi$
$200$	5.28638	+	1.41648i	0.373804	+	0.100160i
$201$		0			0
$202$	−0.341489	−	0.0449579i	−0.0240271	−	0.00316323i
$203$	−0.888218	+	1.53844i	−0.0623407	+	0.107977i
$204$		0			0
$205$	1.68568	+	2.91969i	0.117733	+	0.203920i
$206$	−1.64146	−	3.96283i	−0.114366	−	0.276103i
$207$		0			0
$208$	−12.1205	+	12.1205i	−0.840406	+	0.840406i
$209$	10.7635	−	21.8261i	0.744524	−	1.50975i
$210$		0			0
$211$	7.47399	−	3.68576i	0.514530	−	0.253738i	−0.166437	−	0.986052i	$-0.553226\pi$
$211$	7.47399	−	3.68576i	0.514530	−	0.253738i	0.680967	+	0.732314i	$0.261560\pi$
$212$	14.4269	−	11.0702i	0.990846	−	0.760303i
$213$		0			0
$214$	−5.55501	−	0.364094i	−0.379733	−	0.0248890i
$215$	−1.28873	−	6.47886i	−0.0878903	−	0.441854i
$216$		0			0
$217$	4.31309	+	4.31309i	0.292792	+	0.292792i
$218$	−1.63960	+	0.556570i	−0.111048	+	0.0376957i
$219$		0			0
$220$	5.63721	+	3.25465i	0.380061	+	0.219428i
$221$	7.15158	+	19.6128i	0.481067	+	1.31930i
$222$		0			0
$223$	−6.06711	−	4.65546i	−0.406284	−	0.311753i	0.385325	−	0.922781i	$-0.374089\pi$
$223$	−6.06711	−	4.65546i	−0.406284	−	0.311753i	−0.791609	+	0.611028i	$0.790756\pi$
$224$	−9.88035	−	1.96532i	−0.660159	−	0.131314i
$225$		0			0
$226$	2.02567	−	1.35351i	0.134746	−	0.0900342i
$227$	−1.46020	−	1.66504i	−0.0969172	−	0.110513i	0.701348	−	0.712819i	$-0.252582\pi$
$227$	−1.46020	−	1.66504i	−0.0969172	−	0.110513i	−0.798265	+	0.602306i	$0.794249\pi$
$228$		0			0
$229$	11.9156	+	15.5287i	0.787407	+	1.02617i	0.998810	+	0.0487694i	$0.0155300\pi$
$229$	11.9156	+	15.5287i	0.787407	+	1.02617i	−0.211403	+	0.977399i	$0.567803\pi$
$230$	−1.23069	−	1.60387i	−0.0811496	−	0.105756i
$231$		0			0
$232$	0.527734	+	0.601765i	0.0346474	+	0.0395078i
$233$	−15.2210	+	10.1704i	−0.997161	+	0.666282i	−0.943188	−	0.332260i	$-0.892189\pi$
$233$	−15.2210	+	10.1704i	−0.997161	+	0.666282i	−0.0539737	+	0.998542i	$0.517189\pi$
$234$		0			0
$235$	2.42138	+	0.481642i	0.157953	+	0.0314189i
$236$	14.7831	+	11.3435i	0.962297	+	0.738396i
$237$		0			0
$238$	−2.19566	+	2.99821i	−0.142324	+	0.194345i
$239$	18.9106	+	10.9180i	1.22323	+	0.706229i	0.965604	−	0.260017i	$-0.0837281\pi$
$239$	18.9106	+	10.9180i	1.22323	+	0.706229i	0.257621	+	0.966246i	$0.417061\pi$
$240$		0			0
$241$	−7.84710	+	2.66373i	−0.505476	+	0.171586i	−0.562517	−	0.826786i	$-0.690167\pi$
$241$	−7.84710	+	2.66373i	−0.505476	+	0.171586i	0.0570406	+	0.998372i	$0.481834\pi$
$242$	1.63696	+	1.63696i	0.105228	+	0.105228i
$243$		0			0
$244$	0.115744	+	0.581886i	0.00740978	+	0.0372515i
$245$	−0.637551	−	0.0417873i	−0.0407316	−	0.00266969i
$246$		0			0
$247$	22.9327	−	17.5969i	1.45917	−	1.11966i
$248$	2.46483	−	1.21552i	0.156517	−	0.0771856i
$249$		0			0
$250$	1.07562	−	2.18114i	0.0680282	−	0.137947i
$251$	−5.47029	+	5.47029i	−0.345282	+	0.345282i	−0.858349	−	0.513067i	$-0.828509\pi$
$251$	−5.47029	+	5.47029i	−0.345282	+	0.345282i	0.513067	+	0.858349i	$0.328509\pi$
$252$		0			0
$253$	12.6805	+	30.6134i	0.797215	+	1.92465i
$254$	−0.720930	−	1.24869i	−0.0452351	−	0.0783496i
$255$		0			0
$256$	4.14850	−	7.18541i	0.259281	−	0.449088i
$257$	−27.8814	−	3.67066i	−1.73920	−	0.228970i	−0.806906	−	0.590680i	$-0.798860\pi$
$257$	−27.8814	−	3.67066i	−1.73920	−	0.228970i	−0.932290	+	0.361711i	$0.882193\pi$
$258$		0			0
$259$	12.4091	+	3.32501i	0.771064	+	0.206606i
$260$	4.29551	+	6.42868i	0.266396	+	0.398690i
$261$		0			0
$262$	1.28936	+	0.861522i	0.0796569	+	0.0532250i
$263$	−2.03175	−	15.4327i	−0.125283	−	0.951619i	−0.932451	−	0.361297i	$-0.882334\pi$
$263$	−2.03175	−	15.4327i	−0.125283	−	0.951619i	0.807168	−	0.590322i	$-0.200999\pi$
$264$		0			0
$265$	−3.41743	−	6.92986i	−0.209931	−	0.425698i
$266$	4.87258	+	1.65402i	0.298757	+	0.101414i
$267$		0			0
$268$	1.22954	−	4.58871i	0.0751061	−	0.280300i
$269$	−0.513314	+	2.58060i	−0.0312973	+	0.157342i	−0.993274	−	0.115791i	$-0.963060\pi$
$269$	−0.513314	+	2.58060i	−0.0312973	+	0.157342i	0.961976	+	0.273133i	$0.0880598\pi$
$270$		0			0
$271$		−	9.04660i		−	0.549542i	−0.961510	−	0.274771i	$-0.911398\pi$
$271$		−	9.04660i		−	0.549542i	0.961510	−	0.274771i	$-0.0886020\pi$
$272$	−8.01299	−	11.4294i	−0.485859	−	0.693008i
$273$		0			0
$274$	0.544166	−	4.13335i	0.0328743	−	0.249705i
$275$	−12.2292	+	13.9448i	−0.737450	+	0.840900i
$276$		0			0
$277$	17.6237	+	8.69103i	1.05890	+	0.522194i	0.886450	−	0.462824i	$-0.153164\pi$
$277$	17.6237	+	8.69103i	1.05890	+	0.522194i	0.172454	+	0.985018i	$0.444830\pi$
$278$	3.87798	−	0.771378i	0.232586	−	0.0462642i
$279$		0			0
$280$	−1.08237	+	2.61308i	−0.0646841	+	0.156161i
$281$	11.3949	−	1.50016i	0.679761	−	0.0894922i	0.217264	−	0.976113i	$-0.430287\pi$
$281$	11.3949	−	1.50016i	0.679761	−	0.0894922i	0.462497	+	0.886621i	$0.346954\pi$
$282$		0			0
$283$	8.91019	−	26.2486i	0.529656	−	1.56032i	−0.271857	−	0.962338i	$-0.587638\pi$
$283$	8.91019	−	26.2486i	0.529656	−	1.56032i	0.801513	−	0.597978i	$-0.204029\pi$
$284$	0.243712	+	3.71833i	0.0144617	+	0.220642i
$285$		0			0
$286$	2.23986	+	6.59841i	0.132446	+	0.390172i
$287$	10.7947	−	4.47130i	0.637189	−	0.263932i
$288$		0			0
$289$	−16.7382	+	2.97176i	−0.984602	+	0.174810i
$290$	0.143321	−	0.0827464i	0.00841610	−	0.00485904i
$291$		0			0
$292$	−7.92228	−	6.94765i	−0.463616	−	0.406580i
$293$	7.32982	−	1.96402i	0.428213	−	0.114739i	−0.0382743	−	0.999267i	$-0.512186\pi$
$293$	7.32982	−	1.96402i	0.428213	−	0.114739i	0.466487	+	0.884528i	$0.345519\pi$
$294$		0			0
$295$	5.95265	−	5.22033i	0.346576	−	0.303939i
$296$	3.21579	−	4.81277i	0.186914	−	0.279737i
$297$		0			0
$298$	2.14084	+	0.886764i	0.124015	+	0.0513689i
$299$	−2.57417	+	39.2742i	−0.148868	+	2.27129i
$300$		0			0
$301$	−22.8445	+	1.49731i	−1.31673	+	0.0863034i
$302$	0.443734	+	1.65604i	0.0255340	+	0.0952943i
$303$		0			0
$304$	−11.7659	+	15.3336i	−0.674821	+	0.879444i
$305$	0.252087			0.0144345
$306$		0			0
$307$	−17.0157			−0.971135			−0.485568	−	0.874199i	$-0.661387\pi$
$307$	−17.0157			−0.971135			−0.485568	+	0.874199i	$0.661387\pi$
$308$	13.7331	−	17.8973i	0.782516	−	1.01980i
$309$		0			0
$310$	−0.147072	−	0.548880i	−0.00835312	−	0.0311743i
$311$	−2.59171	+	0.169869i	−0.146962	+	0.00963242i	−0.138707	−	0.990334i	$-0.544295\pi$
$311$	−2.59171	+	0.169869i	−0.146962	+	0.00963242i	−0.00825557	+	0.999966i	$0.502628\pi$
$312$		0			0
$313$	0.362272	−	5.52720i	0.0204768	−	0.312416i	−0.975318	−	0.220805i	$-0.929132\pi$
$313$	0.362272	−	5.52720i	0.0204768	−	0.312416i	0.995795	−	0.0916111i	$-0.0292017\pi$
$314$	5.03754	+	2.08662i	0.284285	+	0.117755i
$315$		0			0
$316$	6.41033	−	9.59373i	0.360609	−	0.539690i
$317$	−3.91901	+	3.43688i	−0.220114	+	0.193035i	−0.762300	−	0.647224i	$-0.775930\pi$
$317$	−3.91901	+	3.43688i	−0.220114	+	0.193035i	0.542186	+	0.840258i	$0.317597\pi$
$318$		0			0
$319$	−2.62009	+	0.702051i	−0.146697	+	0.0393073i
$320$	−3.39492	−	2.97726i	−0.189782	−	0.166434i
$321$		0			0
$322$	−6.06766	+	3.50317i	−0.338138	+	0.195224i
$323$	10.8815	+	20.8730i	0.605461	+	1.16141i
$324$		0			0
$325$	−20.3537	+	8.43077i	−1.12902	+	0.467655i
$326$	−0.954144	−	2.81082i	−0.0528451	−	0.155677i
$327$		0			0
$328$	−0.344306	−	5.25310i	−0.0190111	−	0.290054i
$329$	2.75027	−	8.10204i	0.151627	−	0.446680i
$330$		0			0
$331$	26.5414	−	3.49424i	1.45884	−	0.192061i	0.641018	−	0.767525i	$-0.278512\pi$
$331$	26.5414	−	3.49424i	1.45884	−	0.192061i	0.817827	+	0.575465i	$0.195179\pi$
$332$	7.80776	−	18.8496i	0.428507	−	1.03451i
$333$		0			0
$334$	−4.33484	+	0.862253i	−0.237192	+	0.0471804i
$335$	−1.81035	−	0.892768i	−0.0989102	−	0.0487771i
$336$		0			0
$337$	−8.19640	+	9.34620i	−0.446486	+	0.509120i	−0.930677	−	0.365843i	$-0.880781\pi$
$337$	−8.19640	+	9.34620i	−0.446486	+	0.509120i	0.484190	+	0.874963i	$0.339114\pi$
$338$	−0.532495	+	4.04470i	−0.0289639	+	0.220003i
$339$		0			0
$340$	−5.76147	+	2.53917i	−0.312460	+	0.137706i
$341$			9.31380i			0.504371i
$342$		0			0
$343$	3.38035	−	16.9942i	0.182522	−	0.917599i
$344$	−2.66969	+	9.96343i	−0.143940	+	0.537192i
$345$		0			0
$346$	−0.245628	−	0.0833795i	−0.0132050	−	0.00448251i
$347$	−2.41681	−	4.90080i	−0.129741	−	0.263089i	0.822303	−	0.569050i	$-0.192689\pi$
$347$	−2.41681	−	4.90080i	−0.129741	−	0.263089i	−0.952044	+	0.305961i	$0.901022\pi$
$348$		0			0
$349$	0.0942739	+	0.716082i	0.00504637	+	0.0383310i	0.993783	−	0.111336i	$-0.0355131\pi$
$349$	0.0942739	+	0.716082i	0.00504637	+	0.0383310i	−0.988736	+	0.149667i	$0.952180\pi$
$350$	−3.26082	−	2.17881i	−0.174298	−	0.116462i
$351$		0			0
$352$	−8.54596	−	12.7899i	−0.455501	−	0.681705i
$353$	−4.90084	−	1.31318i	−0.260846	−	0.0698934i	0.126026	−	0.992027i	$-0.459778\pi$
$353$	−4.90084	−	1.31318i	−0.260846	−	0.0698934i	−0.386872	+	0.922134i	$0.626444\pi$
$354$		0			0
$355$	1.56976	+	0.206663i	0.0833143	+	0.0109685i
$356$	12.7462	−	22.0771i	0.675547	−	1.17008i
$357$		0			0
$358$	−1.16288	−	2.01417i	−0.0614603	−	0.106452i
$359$	8.31165	+	20.0661i	0.438672	+	1.05905i	0.976408	+	0.215934i	$0.0692798\pi$
$359$	8.31165	+	20.0661i	0.438672	+	1.05905i	−0.537736	+	0.843113i	$0.680720\pi$
$360$		0			0
$361$	9.61205	−	9.61205i	0.505897	−	0.505897i
$362$	0.487621	−	0.988798i	0.0256288	−	0.0519701i
$363$		0			0
$364$	24.0323	−	11.8514i	1.25963	−	0.621182i
$365$	−3.55204	+	2.72558i	−0.185922	+	0.142663i
$366$		0			0
$367$	31.0245	+	2.03345i	1.61946	+	0.106145i	0.847953	−	0.530071i	$-0.177835\pi$
$367$	31.0245	+	2.03345i	1.61946	+	0.106145i	0.771511	+	0.636217i	$0.219502\pi$
$368$	−5.13410	−	25.8109i	−0.267633	−	1.34548i
$369$		0			0
$370$	−0.846275	−	0.846275i	−0.0439958	−	0.0439958i
$371$	−25.3571	+	8.60757i	−1.31647	+	0.446883i
$372$		0			0
$373$	−13.1878	−	7.61399i	−0.682839	−	0.394237i	0.118085	−	0.993004i	$-0.462325\pi$
$373$	−13.1878	−	7.61399i	−0.682839	−	0.394237i	−0.800924	+	0.598766i	$0.795658\pi$
$374$	−5.60789	+	0.866523i	−0.289977	+	0.0448068i
$375$		0			0
$376$	−3.05841	−	2.34680i	−0.157725	−	0.121027i
$377$	−3.16001	−	0.628565i	−0.162749	−	0.0323728i
$378$		0			0
$379$	−4.09074	+	2.73335i	−0.210127	+	0.140403i	−0.656181	−	0.754604i	$-0.727829\pi$
$379$	−4.09074	+	2.73335i	−0.210127	+	0.140403i	0.446053	+	0.895006i	$0.352829\pi$
$380$	5.74820	+	6.55456i	0.294876	+	0.336242i
$381$		0			0
$382$	−1.64791	−	2.14760i	−0.0843147	−	0.109881i
$383$	−23.2804	−	30.3396i	−1.18957	−	1.55028i	−0.763806	−	0.645446i	$-0.776672\pi$
$383$	−23.2804	−	30.3396i	−1.18957	−	1.55028i	−0.425765	−	0.904834i	$-0.639995\pi$
$384$		0			0
$385$	−6.32006	−	7.20665i	−0.322100	−	0.367285i
$386$	2.82374	−	1.88676i	0.143725	−	0.0960337i
$387$		0			0
$388$	−21.4185	−	4.26040i	−1.08736	−	0.216289i
$389$	−10.3440	−	7.93725i	−0.524463	−	0.402435i	0.312314	−	0.949979i	$-0.398896\pi$
$389$	−10.3440	−	7.93725i	−0.524463	−	0.402435i	−0.836777	+	0.547545i	$0.815563\pi$
$390$		0			0
$391$	−31.1369	−	7.59968i	−1.57466	−	0.384332i
$392$	0.864006	+	0.498834i	0.0436389	+	0.0251949i
$393$		0			0
$394$	4.58298	−	1.55571i	0.230887	−	0.0783757i
$395$	−3.46667	−	3.46667i	−0.174427	−	0.174427i
$396$		0			0
$397$	5.01160	+	25.1950i	0.251525	+	1.26450i	0.875561	+	0.483107i	$0.160492\pi$
$397$	5.01160	+	25.1950i	0.251525	+	1.26450i	−0.624036	+	0.781395i	$0.714508\pi$
$398$	−3.02170	−	0.198053i	−0.151464	−	0.00992749i
$399$		0			0
$400$	11.6865	−	8.96737i	0.584325	−	0.448368i
$401$	34.8860	−	17.2039i	1.74212	−	0.859121i	0.765720	−	0.643174i	$-0.222383\pi$
$401$	34.8860	−	17.2039i	1.74212	−	0.859121i	0.976405	−	0.215947i	$-0.0692837\pi$
$402$		0			0
$403$	−4.89299	+	9.92201i	−0.243737	+	0.494251i
$404$	−1.43008	+	1.43008i	−0.0711489	+	0.0711489i
$405$		0			0
$406$	−0.219486	−	0.529886i	−0.0108929	−	0.0262978i
$407$	9.80821	+	16.9883i	0.486175	+	0.842080i
$408$		0			0
$409$	−15.8253	+	27.4102i	−0.782509	+	1.35535i	0.147967	+	0.988992i	$0.452727\pi$
$409$	−15.8253	+	27.4102i	−0.782509	+	1.35535i	−0.930476	+	0.366353i	$0.880606\pi$
$410$	−1.07918	−	0.142076i	−0.0532967	−	0.00701665i
$411$		0			0
$412$	−24.3276	−	6.51856i	−1.19853	−	0.321146i
$413$	−15.2444	−	22.8149i	−0.750130	−	1.12265i
$414$		0			0
$415$	−7.20808	−	4.81629i	−0.353831	−	0.236422i
$416$	−2.38485	−	18.1147i	−0.116927	−	0.888149i
$417$		0			0
$418$	3.47512	+	7.04685i	0.169974	+	0.344673i
$419$	−12.6991	−	4.31077i	−0.620393	−	0.210595i	−0.00649318	−	0.999979i	$-0.502067\pi$
$419$	−12.6991	−	4.31077i	−0.620393	−	0.210595i	−0.613900	+	0.789384i	$0.710400\pi$
$420$		0			0
$421$	3.72424	−	13.8990i	0.181508	−	0.677398i	−0.813843	−	0.581085i	$-0.802628\pi$
$421$	3.72424	−	13.8990i	0.181508	−	0.677398i	0.995351	−	0.0963130i	$-0.0307050\pi$
$422$	−0.524898	+	2.63884i	−0.0255516	+	0.128457i
$423$		0			0
$424$			12.0652i			0.585937i
$425$	−3.89332	−	17.5127i	−0.188854	−	0.849492i
$426$		0			0
$427$	0.114034	−	0.866178i	0.00551852	−	0.0419173i
$428$	−21.5523	+	24.5757i	−1.04177	+	1.18791i
$429$		0			0
$430$	1.91282	+	0.943296i	0.0922442	+	0.0454898i
$431$	−19.9425	+	3.96681i	−0.960596	+	0.191074i	−0.650395	−	0.759597i	$-0.725396\pi$
$431$	−19.9425	+	3.96681i	−0.960596	+	0.191074i	−0.310201	+	0.950671i	$0.600396\pi$
$432$		0			0
$433$	−4.60087	+	11.1075i	−0.221104	+	0.533792i	−0.995040	−	0.0994712i	$-0.968285\pi$
$433$	−4.60087	+	11.1075i	−0.221104	+	0.533792i	0.773937	+	0.633263i	$0.218285\pi$
$434$	−1.95250	+	0.257051i	−0.0937228	+	0.0123388i
$435$		0			0
$436$	−3.26803	+	9.62729i	−0.156510	+	0.461064i
$437$	2.90255	+	44.2843i	0.138848	+	2.11841i
$438$		0			0
$439$	13.0083	+	38.3213i	0.620854	+	1.82898i	0.556165	+	0.831072i	$0.312272\pi$
$439$	13.0083	+	38.3213i	0.620854	+	1.82898i	0.0646889	+	0.997905i	$0.479394\pi$
$440$	−3.99003	+	1.65272i	−0.190217	+	0.0787905i
$441$		0			0
$442$	−6.42932	−	2.02299i	−0.305812	−	0.0962238i
$443$	19.5513	−	11.2880i	0.928912	−	0.536308i	0.0424450	−	0.999099i	$-0.486485\pi$
$443$	19.5513	−	11.2880i	0.928912	−	0.536308i	0.886467	+	0.462791i	$0.153152\pi$
$444$		0			0
$445$	−8.14371	−	7.14184i	−0.386049	−	0.338556i
$446$	2.38494	−	0.639042i	0.112930	−	0.0302595i
$447$		0			0
$448$	−11.7657	+	10.3182i	−0.555877	+	0.487491i
$449$	16.1218	−	24.1280i	0.760836	−	1.13867i	−0.225551	−	0.974231i	$-0.572418\pi$
$449$	16.1218	−	24.1280i	0.760836	−	1.13867i	0.986387	−	0.164440i	$-0.0525817\pi$
$450$		0			0
$451$	16.4829	+	6.82742i	0.776148	+	0.321491i
$452$	0.935592	−	14.2744i	0.0440066	−	0.671410i
$453$		0			0
$454$	0.713489	−	0.0467645i	0.0334857	−	0.00219477i
$455$	−2.94677	−	10.9975i	−0.138147	−	0.515571i
$456$		0			0
$457$	20.6995	−	26.9761i	0.968282	−	1.26189i	0.00318605	−	0.999995i	$-0.498986\pi$
$457$	20.6995	−	26.9761i	0.968282	−	1.26189i	0.965096	−	0.261895i	$-0.0843475\pi$
$458$	−6.31957			−0.295294
$459$		0			0
$460$	−11.8705			−0.553464
$461$	−16.5894	+	21.6197i	−0.772646	+	1.00693i	0.226810	+	0.973939i	$0.427170\pi$
$461$	−16.5894	+	21.6197i	−0.772646	+	1.00693i	−0.999456	+	0.0329923i	$0.989496\pi$
$462$		0			0
$463$	6.69584	+	24.9892i	0.311182	+	1.16135i	0.927492	+	0.373843i	$0.121960\pi$
$463$	6.69584	+	24.9892i	0.311182	+	1.16135i	−0.616310	+	0.787504i	$0.711373\pi$
$464$	2.14968	−	0.140898i	0.0997965	−	0.00654100i
$465$		0			0
$466$	0.386557	−	5.89772i	0.0179069	−	0.273207i
$467$	28.3180	+	11.7297i	1.31040	+	0.542787i	0.925002	−	0.379962i	$-0.124063\pi$
$467$	28.3180	+	11.7297i	1.31040	+	0.542787i	0.385401	+	0.922749i	$0.374063\pi$
$468$		0			0
$469$	−3.88651	+	5.81657i	−0.179462	+	0.268584i
$470$	−0.599283	+	0.525557i	−0.0276429	+	0.0242421i
$471$		0			0
$472$	−11.9418	+	3.19979i	−0.549665	+	0.147282i
$473$	−26.2822	−	23.0488i	−1.20845	−	1.05979i
$474$		0			0
$475$	−21.5130	+	12.4205i	−0.987084	+	0.569893i
$476$	6.11837	+	20.9452i	0.280435	+	0.960021i
$477$		0			0
$478$	−6.51340	+	2.69794i	−0.297916	+	0.123401i
$479$	−8.98937	−	26.4818i	−0.410735	−	1.20999i	−0.933832	−	0.357713i	$-0.883557\pi$
$479$	−8.98937	−	26.4818i	−0.410735	−	1.20999i	0.523097	−	0.852273i	$-0.324777\pi$
$480$		0			0
$481$	1.52391	+	23.2504i	0.0694845	+	1.06013i
$482$	0.860020	−	2.53354i	0.0391728	−	0.115399i
$483$		0			0
$484$	13.4768	−	1.77426i	0.612583	−	0.0806481i
$485$	−3.55092	+	8.57268i	−0.161239	+	0.389265i
$486$		0			0
$487$	10.4183	−	2.07233i	0.472098	−	0.0939062i	0.0466932	−	0.998909i	$-0.485132\pi$
$487$	10.4183	−	2.07233i	0.472098	−	0.0939062i	0.425405	+	0.905003i	$0.360132\pi$
$488$	−0.353038	−	0.174099i	−0.0159813	−	0.00788110i
$489$		0			0
$490$	0.136012	−	0.155092i	0.00614439	−	0.00700633i
$491$	3.71899	−	28.2485i	0.167836	−	1.27484i	−0.675463	−	0.737394i	$-0.736056\pi$
$491$	3.71899	−	28.2485i	0.167836	−	1.27484i	0.843299	−	0.537445i	$-0.180610\pi$
$492$		0			0
$493$	0.949491	−	2.44588i	0.0427629	−	0.110157i
$494$			9.33267i			0.419897i
$495$		0			0
$496$	1.44309	−	7.25493i	0.0647969	−	0.325756i
$497$	1.42020	−	5.30026i	0.0637047	−	0.237749i
$498$		0			0
$499$	−13.4460	−	4.56430i	−0.601925	−	0.204326i	0.00380945	−	0.999993i	$-0.498787\pi$
$499$	−13.4460	−	4.56430i	−0.601925	−	0.204326i	−0.605735	+	0.795667i	$0.707121\pi$
$500$	−6.31574	−	12.8071i	−0.282448	−	0.572749i
$501$		0			0
$502$	−0.326017	−	2.47635i	−0.0145509	−	0.110525i
$503$	−16.9393	−	11.3185i	−0.755288	−	0.504667i	0.117317	−	0.993095i	$-0.462571\pi$
$503$	−16.9393	−	11.3185i	−0.755288	−	0.504667i	−0.872605	+	0.488427i	$0.837571\pi$
$504$		0			0
$505$	0.477419	+	0.714508i	0.0212449	+	0.0317952i
$506$	−10.3337	−	2.76892i	−0.459391	−	0.123093i
$507$		0			0
$508$	−8.39377	−	1.10506i	−0.372413	−	0.0490291i
$509$	−6.50648	+	11.2696i	−0.288395	+	0.499514i	−0.973427	−	0.228999i	$-0.926455\pi$
$509$	−6.50648	+	11.2696i	−0.288395	+	0.499514i	0.685032	+	0.728513i	$0.259788\pi$
$510$		0			0
$511$	7.75834	+	13.4378i	0.343209	+	0.594455i
$512$	7.93419	+	19.1548i	0.350645	+	0.846532i
$513$		0			0
$514$	6.42021	−	6.42021i	0.283183	−	0.283183i
$515$	−4.73312	+	9.59782i	−0.208566	+	0.422931i
$516$		0			0
$517$	11.7174	−	5.77837i	0.515330	−	0.254133i
$518$	−3.29065	+	2.52500i	−0.144583	+	0.110942i
$519$		0			0
$520$	−5.11884	−	0.335507i	−0.224476	−	0.0147129i
$521$	1.11715	+	5.61631i	0.0489434	+	0.246055i	0.997510	−	0.0705218i	$-0.0224664\pi$
$521$	1.11715	+	5.61631i	0.0489434	+	0.246055i	−0.948567	+	0.316577i	$0.897466\pi$
$522$		0			0
$523$	−3.38005	−	3.38005i	−0.147799	−	0.147799i	0.629335	−	0.777134i	$-0.283327\pi$
$523$	−3.38005	−	3.38005i	−0.147799	−	0.147799i	−0.777134	+	0.629335i	$0.783327\pi$
$524$	8.62206	−	2.92679i	0.376656	−	0.127858i
$525$		0			0
$526$	4.35232	+	2.51281i	0.189770	+	0.109564i
$527$	−7.26830	−	5.32275i	−0.316612	−	0.231863i
$528$		0			0
$529$	−29.6928	−	22.7841i	−1.29099	−	0.990614i
$530$	2.44673	+	0.486684i	0.106279	+	0.0211402i
$531$		0			0
$532$	25.1219	−	16.7859i	1.08917	−	0.727762i
$533$	13.9724	+	15.9325i	0.605214	+	0.690114i
$534$		0			0
$535$	8.45502	+	11.0188i	0.365542	+	0.476384i
$536$	1.91876	+	2.50057i	0.0828777	+	0.108008i
$537$		0			0
$538$	−0.560117	−	0.638691i	−0.0241483	−	0.0275359i
$539$	−2.81127	+	1.87843i	−0.121090	+	0.0809098i
$540$		0			0
$541$	36.6083	+	7.28184i	1.57391	+	0.313071i	0.903390	−	0.428819i	$-0.141070\pi$
$541$	36.6083	+	7.28184i	1.57391	+	0.313071i	0.670522	+	0.741890i	$0.266070\pi$
$542$	2.31723	+	1.77808i	0.0995337	+	0.0763749i
$543$		0			0
$544$	14.8649	+	0.640234i	0.637329	+	0.0274498i
$545$	3.74113	+	2.15995i	0.160253	+	0.0925219i
$546$		0			0
$547$	−1.97164	+	0.669282i	−0.0843013	+	0.0286164i	−0.363271	−	0.931683i	$-0.618340\pi$
$547$	−1.97164	+	0.669282i	−0.0843013	+	0.0286164i	0.278970	+	0.960300i	$0.410007\pi$
$548$	−17.3095	−	17.3095i	−0.739425	−	0.739425i
$549$		0			0
$550$	−1.16826	−	5.87323i	−0.0498147	−	0.250436i
$551$	−3.62515	−	0.237605i	−0.154437	−	0.0101223i
$552$		0			0
$553$	−13.4798	+	10.3434i	−0.573218	+	0.439845i
$554$	−5.69003	+	2.80601i	−0.241746	+	0.119216i
$555$		0			0
$556$	10.2684	−	20.8223i	0.435477	−	0.883060i
$557$	10.6020	−	10.6020i	0.449223	−	0.449223i	−0.445873	−	0.895096i	$-0.647107\pi$
$557$	10.6020	−	10.6020i	0.449223	−	0.449223i	0.895096	+	0.445873i	$0.147107\pi$
$558$		0			0
$559$	−15.8898	−	38.3613i	−0.672065	−	1.62251i
$560$	3.80636	+	6.59282i	0.160848	+	0.278597i
$561$		0			0
$562$	−1.85536	+	3.21358i	−0.0782637	+	0.135557i
$563$	15.8824	+	2.09096i	0.669365	+	0.0881236i	0.457547	−	0.889186i	$-0.348728\pi$
$563$	15.8824	+	2.09096i	0.669365	+	0.0881236i	0.211818	+	0.977309i	$0.432062\pi$
$564$		0			0
$565$	−5.87108	−	1.57315i	−0.246998	−	0.0661830i
$566$	4.97215	+	7.44135i	0.208995	+	0.312783i
$567$		0			0
$568$	−2.05566	−	1.37355i	−0.0862537	−	0.0576329i
$569$	5.40322	+	41.0416i	0.226515	+	1.72055i	0.606095	+	0.795393i	$0.292735\pi$
$569$	5.40322	+	41.0416i	0.226515	+	1.72055i	−0.379580	+	0.925159i	$0.623931\pi$
$570$		0			0
$571$	−7.85328	−	15.9249i	−0.328649	−	0.666435i	0.668350	−	0.743847i	$-0.267001\pi$
$571$	−7.85328	−	15.9249i	−0.328649	−	0.666435i	−0.996999	+	0.0774121i	$0.975334\pi$
$572$	38.7440	+	13.1518i	1.61997	+	0.549905i
$573$		0			0
$574$	−0.976356	+	3.64381i	−0.0407523	+	0.152090i
$575$	6.59866	−	33.1737i	0.275183	−	1.38344i
$576$		0			0
$577$		−	2.00687i		−	0.0835470i	−0.999127	−	0.0417735i	$-0.986699\pi$
$577$		−	2.00687i		−	0.0835470i	0.999127	−	0.0417735i	$-0.0133008\pi$
$578$	2.52864	−	4.87149i	0.105178	−	0.202627i
$579$		0			0
$580$	0.126836	−	0.963415i	0.00526658	−	0.0400036i
$581$	−19.8095	+	22.5885i	−0.821838	+	0.937127i
$582$		0			0
$583$	−36.6721	−	18.0847i	−1.51880	−	0.748991i
$584$	6.85686	−	1.36391i	0.283739	−	0.0564392i
$585$		0			0
$586$	−0.937577	+	2.26351i	−0.0387310	+	0.0935048i
$587$	15.3995	−	2.02738i	0.635605	−	0.0836790i	0.194164	−	0.980969i	$-0.437801\pi$
$587$	15.3995	−	2.02738i	0.635605	−	0.0836790i	0.441441	+	0.897290i	$0.354467\pi$
$588$		0			0
$589$	−4.00969	+	11.8122i	−0.165216	+	0.486712i
$590$	0.167186	+	2.55077i	0.00688296	+	0.105014i
$591$		0			0
$592$	−5.00785	−	14.7527i	−0.205821	−	0.606330i
$593$	0.256906	−	0.106414i	0.0105499	−	0.00436989i	−0.377402	−	0.926049i	$-0.623183\pi$
$593$	0.256906	−	0.106414i	0.0105499	−	0.00436989i	0.387952	+	0.921680i	$0.373183\pi$
$594$		0			0
$595$	9.23578	−	0.813515i	0.378630	−	0.0333509i
$596$	11.7832	−	6.80306i	0.482660	−	0.278664i
$597$		0			0
$598$	−9.55392	−	8.37856i	−0.390689	−	0.342625i
$599$	38.6629	−	10.3597i	1.57972	−	0.423286i	0.640884	−	0.767638i	$-0.278568\pi$
$599$	38.6629	−	10.3597i	1.57972	−	0.423286i	0.938841	+	0.344352i	$0.111901\pi$
$600$		0			0
$601$	−27.3605	+	23.9945i	−1.11606	+	0.978757i	−0.999895	−	0.0144733i	$-0.995393\pi$
$601$	−27.3605	+	23.9945i	−1.11606	+	0.978757i	−0.116163	+	0.993230i	$0.537060\pi$
$602$	4.10648	−	6.14578i	0.167367	−	0.250483i
$603$		0			0
$604$	9.30053	+	3.85240i	0.378433	+	0.156752i
$605$	0.377750	−	5.76335i	0.0153577	−	0.234313i
$606$		0			0
$607$	19.4159	−	1.27259i	0.788068	−	0.0516527i	0.333946	−	0.942592i	$-0.391620\pi$
$607$	19.4159	−	1.27259i	0.788068	−	0.0516527i	0.454122	+	0.890940i	$0.349953\pi$
$608$	−5.33215	−	19.8999i	−0.216247	−	0.807046i
$609$		0			0
$610$	−0.0495468	+	0.0645706i	−0.00200609	+	0.00261439i
$611$	15.5182			0.627800
$612$		0			0
$613$	−8.57112			−0.346184			−0.173092	−	0.984906i	$-0.555376\pi$
$613$	−8.57112			−0.346184			−0.173092	+	0.984906i	$0.555376\pi$
$614$	3.34437	−	4.35846i	0.134968	−	0.175893i
$615$		0			0
$616$	3.87387	+	14.4575i	0.156082	+	0.582508i
$617$	28.9062	−	1.89461i	1.16372	−	0.0762742i	0.528727	−	0.848792i	$-0.322670\pi$
$617$	28.9062	−	1.89461i	1.16372	−	0.0762742i	0.634993	+	0.772518i	$0.281003\pi$
$618$		0			0
$619$	−1.58675	+	24.2092i	−0.0637769	+	0.973048i	0.839327	+	0.543627i	$0.182949\pi$
$619$	−1.58675	+	24.2092i	−0.0637769	+	0.973048i	−0.903104	+	0.429422i	$0.858717\pi$
$620$	−3.08258	−	1.27685i	−0.123799	−	0.0512794i
$621$		0			0
$622$	0.465880	−	0.697238i	0.0186801	−	0.0279567i
$623$	−28.2235	+	24.7513i	−1.13075	+	0.991640i
$624$		0			0
$625$	15.1538	−	4.06045i	0.606152	−	0.162418i
$626$	1.34456	+	1.17914i	0.0537393	+	0.0471281i
$627$		0			0
$628$	27.7268	−	16.0081i	1.10642	−	0.638791i
$629$	−18.8626	−	2.05454i	−0.752103	−	0.0819198i
$630$		0			0
$631$	10.5557	−	4.37233i	0.420217	−	0.174060i	−0.162547	−	0.986701i	$-0.551971\pi$
$631$	10.5557	−	4.37233i	0.420217	−	0.174060i	0.582764	+	0.812641i	$0.301971\pi$
$632$	2.46075	+	7.24913i	0.0978833	+	0.288355i
$633$		0			0
$634$	−0.110070	−	1.67934i	−0.00437143	−	0.0666951i
$635$	−1.15631	+	3.40638i	−0.0458867	+	0.135178i
$636$		0			0
$637$	−3.98169	+	0.524199i	−0.157760	+	0.0207695i
$638$	0.335143	−	0.809107i	0.0132684	−	0.0320328i
$639$		0			0
$640$	7.13170	−	1.41858i	0.281905	−	0.0560744i
$641$	−1.10937	−	0.547079i	−0.0438174	−	0.0216083i	0.420248	−	0.907409i	$-0.361943\pi$
$641$	−1.10937	−	0.547079i	−0.0438174	−	0.0216083i	−0.464065	+	0.885801i	$0.653610\pi$
$642$		0			0
$643$	23.8732	−	27.2222i	0.941467	−	1.07354i	−0.0557101	−	0.998447i	$-0.517742\pi$
$643$	23.8732	−	27.2222i	0.941467	−	1.07354i	0.997177	−	0.0750900i	$-0.0239244\pi$
$644$	−5.36975	+	40.7873i	−0.211598	+	1.60724i
$645$		0			0
$646$	−7.48521	−	1.31529i	−0.294502	−	0.0517495i
$647$			42.3860i			1.66637i	0.552997	+	0.833183i	$0.313484\pi$
$647$			42.3860i			1.66637i	−0.552997	+	0.833183i	$0.686516\pi$
$648$		0			0
$649$	8.17394	−	41.0932i	0.320855	−	1.61305i
$650$	1.84095	−	6.87051i	0.0722079	−	0.269484i
$651$		0			0
$652$	−16.5043	−	5.60247i	−0.646360	−	0.219410i
$653$	21.0967	+	42.7798i	0.825576	+	1.67410i	0.734852	+	0.678227i	$0.237251\pi$
$653$	21.0967	+	42.7798i	0.825576	+	1.67410i	0.0907239	+	0.995876i	$0.471082\pi$
$654$		0			0
$655$	−0.504983	−	3.83573i	−0.0197313	−	0.149874i
$656$	−11.7814	−	7.87206i	−0.459985	−	0.307352i
$657$		0			0
$658$	1.53474	+	2.29689i	0.0598302	+	0.0895422i
$659$	−12.3752	−	3.31593i	−0.482070	−	0.129170i	0.00959616	−	0.999954i	$-0.496945\pi$
$659$	−12.3752	−	3.31593i	−0.482070	−	0.129170i	−0.491666	+	0.870784i	$0.663612\pi$
$660$		0			0
$661$	36.4196	+	4.79473i	1.41656	+	0.186493i	0.799614	−	0.600515i	$-0.205038\pi$
$661$	36.4196	+	4.79473i	1.41656	+	0.186493i	0.616943	+	0.787008i	$0.288371\pi$
$662$	−4.32158	+	7.48519i	−0.167963	+	0.290920i
$663$		0			0
$664$	6.76836	+	11.7231i	0.262663	+	0.454946i
$665$	−4.91284	−	11.8606i	−0.190512	−	0.459936i
$666$		0			0
$667$	3.49778	−	3.49778i	0.135435	−	0.135435i
$668$	−11.4781	+	23.2753i	−0.444101	+	0.900549i
$669$		0			0
$670$	0.584496	−	0.288241i	0.0225810	−	0.0111357i
$671$	1.05835	−	0.812099i	0.0408571	−	0.0313507i
$672$		0			0
$673$	−8.70566	−	0.570599i	−0.335578	−	0.0219950i	−0.103317	−	0.994648i	$-0.532946\pi$
$673$	−8.70566	−	0.570599i	−0.335578	−	0.0219950i	−0.232261	+	0.972653i	$0.574612\pi$
$674$	−0.783003	−	3.93642i	−0.0301602	−	0.151625i
$675$		0			0
$676$	16.9382	+	16.9382i	0.651471	+	0.651471i
$677$	18.3702	−	6.23584i	0.706024	−	0.239663i	0.0547439	−	0.998500i	$-0.482566\pi$
$677$	18.3702	−	6.23584i	0.706024	−	0.239663i	0.651280	+	0.758838i	$0.274232\pi$
$678$		0			0
$679$	27.8496	+	16.0790i	1.06877	+	0.617055i
$680$	0.990511	−	4.05825i	0.0379844	−	0.155627i
$681$		0			0
$682$	−2.38568	−	1.83059i	−0.0913522	−	0.0700970i
$683$	−21.7757	−	4.33145i	−0.833223	−	0.165738i	−0.239996	−	0.970774i	$-0.577146\pi$
$683$	−21.7757	−	4.33145i	−0.833223	−	0.165738i	−0.593227	+	0.805036i	$0.702146\pi$
$684$		0			0
$685$	−8.64833	+	5.77863i	−0.330436	+	0.220790i
$686$	3.68856	+	4.20600i	0.140830	+	0.160586i
$687$		0			0
$688$	16.9011	+	22.0259i	0.644349	+	0.839731i
$689$	−29.5661	−	38.5313i	−1.12638	−	1.46793i
$690$		0			0
$691$	2.35737	+	2.68807i	0.0896787	+	0.102259i	0.794939	−	0.606690i	$-0.207503\pi$
$691$	2.35737	+	2.68807i	0.0896787	+	0.102259i	−0.705260	+	0.708949i	$0.749170\pi$
$692$	−1.26640	+	0.846183i	−0.0481414	+	0.0321671i
$693$		0			0
$694$	1.73032	+	0.344183i	0.0656822	+	0.0130650i
$695$	−7.82618	−	6.00524i	−0.296864	−	0.227792i
$696$		0			0
$697$	−14.7478	+	8.96108i	−0.558612	+	0.339425i
$698$	−0.201949	−	0.116596i	−0.00764390	−	0.00441321i
$699$		0			0
$700$	−21.8054	+	7.40193i	−0.824166	+	0.279767i
$701$	21.3393	+	21.3393i	0.805976	+	0.805976i	0.984022	−	0.178046i	$-0.0569776\pi$
$701$	21.3393	+	21.3393i	0.805976	+	0.805976i	−0.178046	+	0.984022i	$0.556978\pi$
$702$		0			0
$703$	5.12555	+	25.7679i	0.193314	+	0.971854i
$704$	−23.8443	−	1.56284i	−0.898666	−	0.0589017i
$705$		0			0
$706$	1.29961	−	0.997222i	0.0489113	−	0.0375310i
$707$	2.67103	−	1.31721i	0.100455	−	0.0495387i
$708$		0			0
$709$	−0.645378	+	1.30870i	−0.0242377	+	0.0491491i	−0.908655	−	0.417548i	$-0.862890\pi$
$709$	−0.645378	+	1.30870i	−0.0242377	+	0.0491491i	0.884417	+	0.466697i	$0.154556\pi$
$710$	−0.361467	+	0.361467i	−0.0135656	+	0.0135656i
$711$		0			0
$712$	6.47257	+	15.6262i	0.242570	+	0.585616i
$713$	−8.49242	−	14.7093i	−0.318044	−	0.550868i
$714$		0			0
$715$	8.69247	−	15.0558i	0.325080	−	0.563055i
$716$	−13.5394	−	1.78250i	−0.505992	−	0.0666152i
$717$		0			0
$718$	−6.77344	−	1.81494i	−0.252782	−	0.0677328i
$719$	2.37660	+	3.55683i	0.0886321	+	0.132647i	0.873136	−	0.487476i	$-0.162082\pi$
$719$	2.37660	+	3.55683i	0.0886321	+	0.132647i	−0.784504	+	0.620124i	$0.787082\pi$
$720$		0			0
$721$	30.8373	+	20.6048i	1.14844	+	0.767363i
$722$	0.572857	+	4.35128i	0.0213195	+	0.161938i
$723$		0			0
$724$	−2.86318	−	5.80595i	−0.106409	−	0.215776i
$725$	2.62189	+	0.890012i	0.0973746	+	0.0330542i
$726$		0			0
$727$	−2.44443	+	9.12275i	−0.0906591	+	0.338344i	−0.996326	−	0.0856465i	$-0.972704\pi$
$727$	−2.44443	+	9.12275i	−0.0906591	+	0.338344i	0.905667	+	0.423991i	$0.139371\pi$
$728$	−3.46838	+	17.4367i	−0.128547	+	0.646247i
$729$		0			0
$730$		−	1.44554i		−	0.0535017i
$731$	33.0068	−	7.33787i	1.22080	−	0.271401i
$732$		0			0
$733$	0.0329235	−	0.250079i	0.00121606	−	0.00923686i	−0.990826	−	0.135143i	$-0.956851\pi$
$733$	0.0329235	−	0.250079i	0.00121606	−	0.00923686i	0.992042	+	0.125906i	$0.0401839\pi$
$734$	−6.61860	+	7.54707i	−0.244297	+	0.278567i
$735$		0			0
$736$	25.1586	+	12.4069i	0.927360	+	0.457323i
$737$	−10.4765	+	2.08391i	−0.385908	+	0.0767619i
$738$		0			0
$739$	5.65622	−	13.6553i	0.208067	−	0.502319i	−0.785051	−	0.619431i	$-0.787363\pi$
$739$	5.65622	−	13.6553i	0.208067	−	0.502319i	0.993119	+	0.117111i	$0.0373635\pi$
$740$	−6.96724	+	0.917254i	−0.256121	+	0.0337189i
$741$		0			0
$742$	2.77906	−	8.18686i	0.102023	−	0.300549i
$743$	0.579925	+	8.84795i	0.0212754	+	0.324600i	0.995209	+	0.0977677i	$0.0311702\pi$
$743$	0.579925	+	8.84795i	0.0212754	+	0.324600i	−0.973934	+	0.226832i	$0.927163\pi$
$744$		0			0
$745$	−1.85832	−	5.47442i	−0.0680834	−	0.200567i
$746$	4.54230	−	1.88148i	0.166305	−	0.0688859i
$747$		0			0
$748$	−16.0087	+	29.2209i	−0.585336	+	1.06842i
$749$	41.6856	−	24.0672i	1.52316	−	0.879396i
$750$		0			0
$751$	34.5661	+	30.3137i	1.26134	+	1.10616i	0.989609	+	0.143788i	$0.0459283\pi$
$751$	34.5661	+	30.3137i	1.26134	+	1.10616i	0.271728	+	0.962374i	$0.412405\pi$
$752$	−10.0225	+	2.68552i	−0.365483	+	0.0979308i
$753$		0			0
$754$	0.782092	−	0.685876i	0.0284821	−	0.0249781i
$755$	2.37639	−	3.55652i	0.0864857	−	0.129435i
$756$		0			0
$757$	−31.0055	−	12.8429i	−1.12691	−	0.466782i	−0.260182	−	0.965560i	$-0.583783\pi$
$757$	−31.0055	−	12.8429i	−1.12691	−	0.466782i	−0.866730	+	0.498777i	$0.833783\pi$
$758$	0.103890	−	1.58505i	0.00377344	−	0.0575716i
$759$		0			0
$760$	−5.77184	+	0.378306i	−0.209367	+	0.0137226i
$761$	9.36216	+	34.9400i	0.339378	+	1.26658i	0.899044	+	0.437858i	$0.144263\pi$
$761$	9.36216	+	34.9400i	0.339378	+	1.26658i	−0.559666	+	0.828718i	$0.689071\pi$
$762$		0			0
$763$	9.11397	−	11.8776i	0.329948	−	0.429997i
$764$	−15.8947			−0.575051
$765$		0			0
$766$	12.3470			0.446114
$767$	30.2960	−	39.4825i	1.09392	−	1.42563i
$768$		0			0
$769$	−5.87798	−	21.9369i	−0.211965	−	0.791065i	−0.987213	−	0.159408i	$-0.949042\pi$
$769$	−5.87798	−	21.9369i	−0.211965	−	0.791065i	0.775248	−	0.631657i	$-0.217625\pi$
$770$	3.08813	−	0.202406i	0.111288	−	0.00729422i
$771$		0			0
$772$	1.30419	−	19.8982i	0.0469390	−	0.716150i
$773$	−38.1699	−	15.8105i	−1.37288	−	0.568664i	−0.430310	−	0.902681i	$-0.641596\pi$
$773$	−38.1699	−	15.8105i	−1.37288	−	0.568664i	−0.942567	+	0.334017i	$0.891596\pi$
$774$		0			0
$775$	5.28190	−	7.90492i	0.189731	−	0.283953i
$776$	10.8935	−	9.55333i	0.391053	−	0.342944i
$777$		0			0
$778$	4.06616	−	1.08952i	0.145779	−	0.0390613i
$779$	17.9650	+	15.7549i	0.643663	+	0.564477i
$780$		0			0
$781$	7.25616	−	4.18935i	0.259646	−	0.149907i
$782$	8.06645	−	6.48184i	0.288456	−	0.231790i
$783$		0			0
$784$	2.48087	−	1.02761i	0.0886026	−	0.0367004i
$785$	−4.37274	−	12.8817i	−0.156070	−	0.459767i
$786$		0			0
$787$	−0.414301	−	6.32101i	−0.0147682	−	0.225320i	−0.998863	−	0.0476749i	$-0.984819\pi$
$787$	−0.414301	−	6.32101i	−0.0147682	−	0.225320i	0.984095	−	0.177645i	$-0.0568478\pi$
$788$	9.13472	−	26.9100i	0.325411	−	0.958629i
$789$		0			0
$790$	1.56933	−	0.206606i	0.0558342	−	0.00735071i
$791$	−8.06124	+	19.4616i	−0.286625	+	0.691973i
$792$		0			0
$793$	1.55410	−	0.309129i	0.0551876	−	0.0109775i
$794$	−7.43857	−	3.66830i	−0.263985	−	0.130183i
$795$		0			0
$796$	−11.7236	+	13.3682i	−0.415532	+	0.473824i
$797$	−0.0599584	+	0.455429i	−0.00212384	+	0.0161321i	−0.992474	−	0.122456i	$-0.960923\pi$
$797$	−0.0599584	+	0.455429i	−0.00212384	+	0.0161321i	0.990350	+	0.138588i	$0.0442564\pi$
$798$		0			0
$799$	−2.18705	+	12.4463i	−0.0773723	+	0.440318i
$800$			15.7017i			0.555138i
$801$		0			0
$802$	−2.45005	+	12.3172i	−0.0865141	+	0.434936i
$803$	−6.13223	+	22.8858i	−0.216402	+	0.807622i
$804$		0			0
$805$	16.5524	+	5.61878i	0.583395	+	0.198036i
$806$	−1.57977	−	3.20345i	−0.0556449	−	0.112837i
$807$		0			0
$808$	−0.175145	−	1.33036i	−0.00616159	−	0.0468019i
$809$	10.9710	+	7.33062i	0.385721	+	0.257731i	0.733279	−	0.679928i	$-0.237989\pi$
$809$	10.9710	+	7.33062i	0.385721	+	0.257731i	−0.347558	+	0.937659i	$0.612989\pi$
$810$		0			0
$811$	−6.77215	−	10.1352i	−0.237802	−	0.355897i	0.693303	−	0.720646i	$-0.256155\pi$
$811$	−6.77215	−	10.1352i	−0.237802	−	0.355897i	−0.931106	+	0.364749i	$0.881155\pi$
$812$	−3.25294	−	0.871623i	−0.114156	−	0.0305880i
$813$		0			0
$814$	−6.27923	−	0.826676i	−0.220087	−	0.0289750i
$815$	−3.70285	+	6.41353i	−0.129705	+	0.224656i
$816$		0			0
$817$	−23.4094	−	40.5463i	−0.818991	−	1.41853i
$818$	−3.91056	−	9.44092i	−0.136729	−	0.330094i
$819$		0			0
$820$	−4.51933	+	4.51933i	−0.157822	+	0.157822i
$821$	−8.36253	+	16.9575i	−0.291854	+	0.591822i	−0.992578	−	0.121611i	$-0.961194\pi$
$821$	−8.36253	+	16.9575i	−0.291854	+	0.591822i	0.700723	+	0.713433i	$0.252861\pi$
$822$		0			0
$823$	−33.0876	+	16.3170i	−1.15336	+	0.568774i	−0.915418	−	0.402505i	$-0.868140\pi$
$823$	−33.0876	+	16.3170i	−1.15336	+	0.568774i	−0.237942	+	0.971279i	$0.576473\pi$
$824$	13.2571	−	10.1725i	0.461833	−	0.354377i
$825$		0			0
$826$	8.84015	+	0.579414i	0.307588	+	0.0201604i
$827$	−3.07795	−	15.4739i	−0.107031	−	0.538079i	−0.996679	−	0.0814328i	$-0.974050\pi$
$827$	−3.07795	−	15.4739i	−0.107031	−	0.538079i	0.889648	−	0.456647i	$-0.150950\pi$
$828$		0			0
$829$	−11.0403	−	11.0403i	−0.383447	−	0.383447i	0.488896	−	0.872342i	$-0.337400\pi$
$829$	−11.0403	−	11.0403i	−0.383447	−	0.383447i	−0.872342	+	0.488896i	$0.837400\pi$
$830$	2.65039	−	0.899685i	0.0919962	−	0.0312285i
$831$		0			0
$832$	−24.5803	−	14.1915i	−0.852170	−	0.492001i
$833$	0.140726	−	3.26737i	0.00487586	−	0.113208i
$834$		0			0
$835$	8.74818	+	6.71271i	0.302743	+	0.232303i
$836$	45.2484	+	9.00047i	1.56495	+	0.311288i
$837$		0			0
$838$	3.60015	−	2.40554i	0.124365	−	0.0830981i
$839$	−16.5293	−	18.8481i	−0.570656	−	0.650708i	0.392469	−	0.919765i	$-0.371621\pi$
$839$	−16.5293	−	18.8481i	−0.570656	−	0.650708i	−0.963124	+	0.269057i	$0.913288\pi$
$840$		0			0
$841$	−17.4076	−	22.6860i	−0.600261	−	0.782276i
$842$	2.82817	+	3.68575i	0.0974653	+	0.127019i
$843$		0			0
$844$	10.4164	+	11.8776i	0.358548	+	0.408845i
$845$	8.46284	−	5.65469i	0.291131	−	0.194527i
$846$		0			0
$847$	−19.6321	−	3.90507i	−0.674568	−	0.134180i
$848$	25.7634	+	19.7690i	0.884720	+	0.678870i
$849$		0			0
$850$	5.25100	+	2.44481i	0.180108	+	0.0838564i
$851$	−30.9803	−	17.8865i	−1.06199	−	0.613140i
$852$		0			0
$853$	0.129609	−	0.0439962i	0.00443771	−	0.00150640i	−0.319220	−	0.947681i	$-0.603421\pi$
$853$	0.129609	−	0.0439962i	0.00443771	−	0.00150640i	0.323657	+	0.946174i	$0.395087\pi$
$854$	0.199453	+	0.199453i	0.00682515	+	0.00682515i
$855$		0			0
$856$	−4.23100	−	21.2707i	−0.144613	−	0.727017i
$857$	−40.4206	−	2.64931i	−1.38074	−	0.0904986i	−0.643147	−	0.765743i	$-0.722372\pi$
$857$	−40.4206	−	2.64931i	−1.38074	−	0.0904986i	−0.737594	+	0.675244i	$0.764038\pi$
$858$		0			0
$859$	31.0264	−	23.8074i	1.05861	−	0.812297i	0.0758341	−	0.997120i	$-0.475838\pi$
$859$	31.0264	−	23.8074i	1.05861	−	0.812297i	0.982772	+	0.184824i	$0.0591714\pi$
$860$	11.2315	−	5.53877i	0.382992	−	0.188871i
$861$		0			0
$862$	2.90355	−	5.88781i	0.0988953	−	0.200540i
$863$	30.7086	−	30.7086i	1.04533	−	1.04533i	0.0464096	−	0.998922i	$-0.485222\pi$
$863$	30.7086	−	30.7086i	1.04533	−	1.04533i	0.998922	−	0.0464096i	$-0.0147779\pi$
$864$		0			0
$865$	0.247657	+	0.597898i	0.00842061	+	0.0203291i
$866$	−1.94083	−	3.36162i	−0.0659522	−	0.114233i
$867$		0			0
$868$	−5.78172	+	10.0142i	−0.196244	+	0.339905i
$869$	−25.7222	−	3.38639i	−0.872564	−	0.114875i
$870$		0			0
$871$	−12.2555	−	3.28384i	−0.415261	−	0.111269i
$872$	−3.74759	−	5.60866i	−0.126909	−	0.189933i
$873$		0			0
$874$	−11.9137	−	7.96045i	−0.402986	−	0.269266i
$875$	2.74467	+	20.8478i	0.0927868	+	0.704786i
$876$		0			0
$877$	19.2988	+	39.1341i	0.651675	+	1.32147i	0.932313	+	0.361652i	$0.117787\pi$
$877$	19.2988	+	39.1341i	0.651675	+	1.32147i	−0.280638	+	0.959814i	$0.590546\pi$
$878$	−12.3725	−	4.19991i	−0.417553	−	0.141740i
$879$		0			0
$880$	−3.00857	+	11.2281i	−0.101419	+	0.378500i
$881$	−0.892792	+	4.48837i	−0.0300789	+	0.151217i	−0.992906	−	0.118901i	$-0.962063\pi$
$881$	−0.892792	+	4.48837i	−0.0300789	+	0.151217i	0.962827	+	0.270118i	$0.0870628\pi$
$882$		0			0
$883$		−	12.1431i		−	0.408647i	−0.978903	−	0.204324i	$-0.934500\pi$
$883$		−	12.1431i		−	0.408647i	0.978903	−	0.204324i	$-0.0654995\pi$
$884$	−32.4053	+	22.7189i	−1.08991	+	0.764120i
$885$		0			0
$886$	−0.951396	+	7.22657i	−0.0319628	+	0.242781i
$887$	3.13535	−	3.57518i	0.105275	−	0.120043i	−0.696803	−	0.717263i	$-0.745395\pi$
$887$	3.13535	−	3.57518i	0.105275	−	0.120043i	0.802077	+	0.597220i	$0.203728\pi$
$888$		0			0
$889$	11.1813	+	5.51402i	0.375010	+	0.184934i
$890$	3.42996	−	0.682261i	0.114972	−	0.0228694i
$891$		0			0
$892$	5.54802	−	13.3941i	0.185762	−	0.448468i
$893$	17.3481	−	2.28393i	0.580534	−	0.0764287i
$894$		0			0
$895$	−1.86517	+	5.49460i	−0.0623456	+	0.183664i
$896$	−1.64818	−	25.1464i	−0.0550620	−	0.840083i
$897$		0			0
$898$	3.01157	+	8.87178i	0.100497	+	0.296055i
$899$	1.28456	−	0.532081i	0.0428424	−	0.0177459i
$900$		0			0
$901$	35.0707	−	18.2829i	1.16837	−	0.609093i
$902$	−4.98845	+	2.88008i	−0.166097	+	0.0958963i
$903$		0			0
$904$	7.13576	+	6.25789i	0.237332	+	0.208134i
$905$	−2.65688	+	0.711909i	−0.0883177	+	0.0236647i
$906$		0			0
$907$	0.788543	−	0.691533i	0.0261831	−	0.0229620i	−0.646154	−	0.763207i	$-0.723624\pi$
$907$	0.788543	−	0.691533i	0.0261831	−	0.0229620i	0.672337	+	0.740245i	$0.265290\pi$
$908$	2.33251	−	3.49084i	0.0774069	−	0.115848i
$909$		0			0
$910$	3.39612	+	1.40672i	0.112580	+	0.0466323i
$911$	−1.91386	+	29.1998i	−0.0634088	+	0.967432i	0.841073	+	0.540921i	$0.181924\pi$
$911$	−1.91386	+	29.1998i	−0.0634088	+	0.967432i	−0.904482	+	0.426511i	$0.859742\pi$
$912$		0			0
$913$	−45.7777	+	3.00043i	−1.51502	+	0.0992996i
$914$	2.84137	+	10.6041i	0.0939840	+	0.350753i
$915$		0			0
$916$	−22.5892	+	29.4388i	−0.746367	+	0.972684i
$917$	−13.4081			−0.442774
$918$		0			0
$919$	1.45071			0.0478547			0.0239273	−	0.999714i	$-0.492383\pi$
$919$	1.45071			0.0478547			0.0239273	+	0.999714i	$0.492383\pi$
$920$	4.79449	−	6.24830i	0.158070	−	0.206000i
$921$		0			0
$922$	−2.27718	−	8.49856i	−0.0749950	−	0.279885i
$923$	9.93088	−	0.650904i	0.326879	−	0.0214248i
$924$		0			0
$925$	1.30961	−	19.9808i	0.0430598	−	0.656965i
$926$	−7.71688	−	3.19644i	−0.253593	−	0.105041i
$927$		0			0
$928$	−1.27577	+	1.90932i	−0.0418791	+	0.0626766i
$929$	17.9009	−	15.6987i	0.587311	−	0.515058i	−0.313317	−	0.949648i	$-0.601440\pi$
$929$	17.9009	−	15.6987i	0.587311	−	0.515058i	0.900628	+	0.434591i	$0.143107\pi$
$930$		0			0
$931$	−4.37406	+	1.17203i	−0.143354	+	0.0384116i
$932$	−26.0919	−	22.8820i	−0.854668	−	0.749524i
$933$		0			0
$934$	−8.57031	+	4.94807i	−0.280429	+	0.161906i
$935$	10.8503	+	9.09362i	0.354844	+	0.297393i
$936$		0			0
$937$	25.8156	−	10.6932i	0.843357	−	0.349330i	0.0811809	−	0.996699i	$-0.474131\pi$
$937$	25.8156	−	10.6932i	0.843357	−	0.349330i	0.762176	+	0.647369i	$0.224131\pi$
$938$	−0.726002	−	2.13873i	−0.0237048	−	0.0698321i
$939$		0			0
$940$	0.306105	+	4.67026i	0.00998405	+	0.152327i
$941$	12.0191	−	35.4071i	0.391811	−	1.15424i	−0.554834	−	0.831961i	$-0.687218\pi$
$941$	12.0191	−	35.4071i	0.391811	−	1.15424i	0.946645	−	0.322277i	$-0.104448\pi$
$942$		0			0
$943$	−32.2567	+	4.24668i	−1.05042	+	0.138291i
$944$	−12.7341	+	30.7428i	−0.414459	+	1.00059i
$945$		0			0
$946$	11.0695	−	2.20186i	0.359900	−	0.0715886i
$947$	39.7620	+	19.6085i	1.29209	+	0.637190i	0.952831	−	0.303502i	$-0.0981560\pi$
$947$	39.7620	+	19.6085i	1.29209	+	0.637190i	0.339262	+	0.940692i	$0.389823\pi$
$948$		0			0
$949$	−18.5557	+	21.1587i	−0.602344	+	0.686841i
$950$	1.04685	−	7.95164i	0.0339644	−	0.257985i
$951$		0			0
$952$	−13.4962	−	5.23922i	−0.437414	−	0.169804i
$953$			26.1473i			0.846993i	0.905898	+	0.423496i	$0.139197\pi$
$953$			26.1473i			0.846993i	−0.905898	+	0.423496i	$0.860803\pi$
$954$		0			0
$955$	−1.31757	+	6.62389i	−0.0426357	+	0.214344i
$956$	−10.7141	+	39.9854i	−0.346518	+	1.29322i
$957$		0			0
$958$	8.55000	+	2.90233i	0.276238	+	0.0937701i
$959$	15.9434	+	32.3299i	0.514838	+	1.04399i
$960$		0			0
$961$	3.42317	+	26.0015i	0.110425	+	0.838759i
$962$	−6.25498	−	4.17945i	−0.201669	−	0.134751i
$963$		0			0
$964$	−8.72798	−	13.0623i	−0.281109	−	0.420710i
$965$	−8.18415	−	2.19294i	−0.263457	−	0.0705932i
$966$		0			0
$967$	−25.3968	−	3.34356i	−0.816707	−	0.107521i	−0.289413	−	0.957204i	$-0.593460\pi$
$967$	−25.3968	−	3.34356i	−0.816707	−	0.107521i	−0.527294	+	0.849683i	$0.676793\pi$
$968$	−4.50937	+	7.81046i	−0.144937	+	0.251038i
$969$		0			0
$970$	−1.49792	−	2.59448i	−0.0480953	−	0.0833036i
$971$	−2.58935	−	6.25124i	−0.0830962	−	0.200612i	0.876870	−	0.480727i	$-0.159627\pi$
$971$	−2.58935	−	6.25124i	−0.0830962	−	0.200612i	−0.959966	+	0.280115i	$0.909627\pi$
$972$		0			0
$973$	−24.1744	+	24.1744i	−0.774997	+	0.774997i
$974$	−1.51686	+	3.07589i	−0.0486034	+	0.0985580i
$975$		0			0
$976$	−0.950222	+	0.468597i	−0.0304159	+	0.0149994i
$977$	10.8454	−	8.32199i	0.346976	−	0.266244i	−0.420540	−	0.907274i	$-0.638159\pi$
$977$	10.8454	−	8.32199i	0.346976	−	0.266244i	0.767516	+	0.641030i	$0.221493\pi$
$978$		0			0
$979$	−57.1975	−	3.74892i	−1.82804	−	0.119816i
$980$	−0.236300	−	1.18796i	−0.00754834	−	0.0379481i
$981$		0			0
$982$	6.50474	+	6.50474i	0.207575	+	0.207575i
$983$	−9.28400	+	3.15149i	−0.296114	+	0.100517i	−0.465543	−	0.885025i	$-0.654141\pi$
$983$	−9.28400	+	3.15149i	−0.296114	+	0.100517i	0.169429	+	0.985542i	$0.445808\pi$
$984$		0			0
$985$	−10.4571	−	6.03743i	−0.333192	−	0.192369i
$986$	0.439879	+	0.723936i	0.0140086	+	0.0230548i
$987$		0			0
$988$	43.4749	+	33.3594i	1.38312	+	1.06130i
$989$	62.5237	+	12.4367i	1.98814	+	0.395465i
$990$		0			0
$991$	−25.8145	+	17.2487i	−0.820024	+	0.547922i	−0.893337	−	0.449387i	$-0.851643\pi$
$991$	−25.8145	+	17.2487i	−0.820024	+	0.547922i	0.0733136	+	0.997309i	$0.476643\pi$
$992$	5.19877	+	5.92806i	0.165061	+	0.188216i
$993$		0			0
$994$	1.07849	+	1.40552i	0.0342078	+	0.0445805i
$995$	4.59919	+	5.99378i	0.145804	+	0.190016i
$996$		0			0
$997$	−18.0484	−	20.5803i	−0.571600	−	0.651784i	0.391738	−	0.920077i	$-0.371874\pi$
$997$	−18.0484	−	20.5803i	−0.571600	−	0.651784i	−0.963338	+	0.268292i	$0.913541\pi$
$998$	3.81188	−	2.54702i	0.120663	−	0.0806244i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	459.2.y.a.422.7		256
3.2	odd	2		153.2.s.a.14.10	yes	256
9.2	odd	6	inner	459.2.y.a.116.7		256
9.7	even	3		153.2.s.a.65.10	yes	256
17.11	odd	16	inner	459.2.y.a.368.7		256
51.11	even	16		153.2.s.a.113.10	yes	256
153.11	even	48	inner	459.2.y.a.62.7		256
153.79	odd	48		153.2.s.a.11.10	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.10	✓	256	153.79	odd	48
153.2.s.a.14.10	yes	256	3.2	odd	2
153.2.s.a.65.10	yes	256	9.7	even	3
153.2.s.a.113.10	yes	256	51.11	even	16
459.2.y.a.62.7		256	153.11	even	48	inner
459.2.y.a.116.7		256	9.2	odd	6	inner
459.2.y.a.368.7		256	17.11	odd	16	inner
459.2.y.a.422.7		256	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.y (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.196546 + 0.256144i) q^{2} +(0.490659 + 1.83116i) q^{4} +(0.803783 - 0.0526827i) q^{5} +(0.182581 - 2.78565i) q^{7} +(-1.16205 - 0.481337i) q^{8} +(-0.144486 + 0.216239i) q^{10} +(3.20484 - 2.81057i) q^{11} +(4.89065 - 1.31045i) q^{13} +(0.677643 + 0.594277i) q^{14} +(-2.93186 + 1.69271i) q^{16} +(0.361775 + 4.10720i) q^{17} +(5.27449 - 2.18477i) q^{19} +(0.490854 + 1.44601i) q^{20} +(0.0900113 + 1.37331i) q^{22} +(-2.49870 + 7.36094i) q^{23} +(-4.31393 + 0.567940i) q^{25} +(-0.625576 + 1.51027i) q^{26} +(5.19057 - 1.03247i) q^{28} +(-0.570719 - 0.281448i) q^{29} +(-1.44065 + 1.64275i) q^{31} +(0.471019 - 3.57775i) q^{32} +(-1.12314 - 0.714589i) q^{34} -2.24868i q^{35} +(-0.897790 + 4.51350i) q^{37} +(-0.477067 + 1.78044i) q^{38} +(-0.959395 - 0.325671i) q^{40} +(1.85115 + 3.75377i) q^{41} +(-1.07042 - 8.13062i) q^{43} +(6.71909 + 4.48955i) q^{44} +(-1.39435 - 2.08679i) q^{46} +(2.96048 + 0.793260i) q^{47} +(-0.786402 - 0.103532i) q^{49} +(0.702413 - 1.21662i) q^{50} +(4.79928 + 8.31260i) q^{52} +(-3.67083 - 8.86216i) q^{53} +(2.42793 - 2.42793i) q^{55} +(-1.55301 + 3.14919i) q^{56} +(0.184264 - 0.0908689i) q^{58} +(7.79797 - 5.98360i) q^{59} +(0.312284 + 0.0204682i) q^{61} +(-0.137626 - 0.691891i) q^{62} +(-3.96387 - 3.96387i) q^{64} +(3.86198 - 1.31097i) q^{65} +(-2.17017 - 1.25295i) q^{67} +(-7.34345 + 2.67770i) q^{68} +(0.575986 + 0.441969i) q^{70} +(1.92783 + 0.383470i) q^{71} +(-4.62155 + 3.08802i) q^{73} +(-0.979648 - 1.11707i) q^{74} +(6.58864 + 8.58648i) q^{76} +(-7.24412 - 9.44072i) q^{77} +(-4.01302 - 4.57597i) q^{79} +(-2.26741 + 1.51503i) q^{80} +(-1.32534 - 0.263627i) q^{82} +(-8.53828 - 6.55165i) q^{83} +(0.507167 + 3.28224i) q^{85} +(2.29300 + 1.32386i) q^{86} +(-5.07702 + 1.72342i) q^{88} +(-9.50851 - 9.50851i) q^{89} +(-2.75750 - 13.8629i) q^{91} +(-14.7051 - 0.963823i) q^{92} +(-0.785061 + 0.602399i) q^{94} +(4.12445 - 2.03395i) q^{95} +(-5.09492 + 10.3315i) q^{97} +(0.181083 - 0.181083i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 24 q^{2} - 8 q^{4} + 24 q^{5} - 8 q^{7} - 32 q^{10} + 24 q^{11} - 8 q^{13} + 24 q^{14} - 32 q^{19} + 24 q^{20} - 8 q^{22} + 24 q^{23} - 8 q^{25} - 32 q^{28} + 24 q^{29} - 8 q^{31} + 24 q^{32} - 56 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 256 * q + 24 * q^2 - 8 * q^4 + 24 * q^5 - 8 * q^7 - 32 * q^10 + 24 * q^11 - 8 * q^13 + 24 * q^14 - 32 * q^19 + 24 * q^20 - 8 * q^22 + 24 * q^23 - 8 * q^25 - 32 * q^28 + 24 * q^29 - 8 * q^31 + 24 * q^32 - 56 * q^34 - 32 * q^37 - 8 * q^40 + 24 * q^41 + 16 * q^43 - 32 * q^46 - 96 * q^47 - 8 * q^49 - 16 * q^52 - 32 * q^55 - 216 * q^56 - 8 * q^58 + 24 * q^59 - 8 * q^61 - 96 * q^64 - 24 * q^65 + 24 * q^68 + 8 * q^70 - 32 * q^73 + 24 * q^74 - 8 * q^76 + 24 * q^77 - 8 * q^79 + 160 * q^82 + 24 * q^83 - 8 * q^85 - 192 * q^86 - 8 * q^88 - 128 * q^91 + 24 * q^92 - 8 * q^94 - 216 * q^95 - 8 * q^97

Introduction

L-functions

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