LMFDB - Embedded newform 243.2.g.a.73.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [243,2,Mod(10,243)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("243.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.g (of order $27$, degree $18$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			73.4
Character	$\chi$	$=$	243.73
Dual form			243.2.g.a.10.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.507233 - 0.254742i) q^{2} +(-1.00193 + 1.34582i) q^{4} +(0.832798 - 2.78174i) q^{5} +(1.23966 - 2.87385i) q^{7} +(-0.362501 + 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(3.33963 + 0.791507i) q^{11} +(3.33176 - 2.19133i) q^{13} +(-0.103295 - 1.77350i) q^{14} +(-0.622571 - 2.07953i) q^{16} +(-0.878443 - 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(2.90932 + 3.90789i) q^{20} +(1.89560 - 0.449266i) q^{22} +(2.43678 + 5.64910i) q^{23} +(-2.86709 - 1.88571i) q^{25} +(1.13175 - 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(0.104644 - 1.79666i) q^{29} +(-0.671302 - 0.0784640i) q^{31} +(-3.71068 - 3.93309i) q^{32} +(-0.527023 + 0.0616002i) q^{34} +(-6.96191 - 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-1.88954 + 2.00280i) q^{38} +(5.41694 + 2.72049i) q^{40} +(-5.94501 - 2.98570i) q^{41} +(1.53472 - 1.62671i) q^{43} +(-4.41129 + 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(-3.14822 + 0.367974i) q^{47} +(-1.91856 - 2.03355i) q^{49} +(-1.93465 - 0.226128i) q^{50} +(-0.389036 + 6.67950i) q^{52} +(4.18963 + 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(5.45881 + 3.59032i) q^{56} +(-0.404606 - 0.937983i) q^{58} +(4.89526 - 1.16020i) q^{59} +(-0.340761 - 0.457722i) q^{61} +(-0.360495 + 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(-3.32104 - 11.0930i) q^{65} +(0.794778 + 13.6458i) q^{67} +(1.31043 - 0.861882i) q^{68} +(-5.01945 - 1.18963i) q^{70} +(2.31784 + 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-2.56230 + 5.94009i) q^{74} +(2.33432 - 7.79718i) q^{76} +(6.41467 - 8.61639i) q^{77} +(0.666057 - 0.334506i) q^{79} -6.30319 q^{80} -3.77609 q^{82} +(3.25233 - 1.63338i) q^{83} +(-1.62096 + 2.17733i) q^{85} +(0.364070 - 1.21608i) q^{86} +(-2.83784 + 6.57885i) q^{88} +(2.27781 - 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(-10.0441 - 2.38050i) q^{92} +(-1.50314 + 0.988632i) q^{94} +(0.819027 + 14.0621i) q^{95} +(-3.58656 - 11.9799i) q^{97} +(-1.49119 - 0.542748i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) $ 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.507233	−	0.254742i	0.358668	−	0.180130i	−0.260335	−	0.965518i	$-0.583833\pi$
$2$	0.507233	−	0.254742i	0.358668	−	0.180130i	0.619003	+	0.785388i	$0.287537\pi$
$3$		0			0
$3$		0			0
$4$	−1.00193	+	1.34582i	−0.500963	+	0.672910i
$5$	0.832798	−	2.78174i	0.372439	−	1.24403i	−0.542368	−	0.840141i	$-0.682472\pi$
$5$	0.832798	−	2.78174i	0.372439	−	1.24403i	0.914807	−	0.403891i	$-0.132343\pi$
$6$		0			0
$7$	1.23966	−	2.87385i	0.468546	−	1.08621i	−0.506103	−	0.862473i	$-0.668914\pi$
$7$	1.23966	−	2.87385i	0.468546	−	1.08621i	0.974649	−	0.223739i	$-0.0718263\pi$
$8$	−0.362501	+	2.05585i	−0.128164	+	0.726852i
$9$		0			0
$10$	−0.286203	−	1.62314i	−0.0905055	−	0.513282i
$11$	3.33963	+	0.791507i	1.00694	+	0.238648i	0.700814	−	0.713344i	$-0.252820\pi$
$11$	3.33963	+	0.791507i	1.00694	+	0.238648i	0.306122	+	0.951992i	$0.400968\pi$
$12$		0			0
$13$	3.33176	−	2.19133i	0.924064	−	0.607766i	0.00419461	−	0.999991i	$-0.498665\pi$
$13$	3.33176	−	2.19133i	0.924064	−	0.607766i	0.919869	+	0.392225i	$0.128294\pi$
$14$	−0.103295	−	1.77350i	−0.0276067	−	0.473989i
$15$		0			0
$16$	−0.622571	−	2.07953i	−0.155643	−	0.519883i
$17$	−0.878443	−	0.319727i	−0.213054	−	0.0775452i	0.233289	−	0.972408i	$-0.425051\pi$
$17$	−0.878443	−	0.319727i	−0.213054	−	0.0775452i	−0.446342	+	0.894862i	$0.647274\pi$
$18$		0			0
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.807068	−	0.590458i	$-0.798947\pi$
$19$	−4.55845	+	1.65914i	−1.04578	+	0.380633i	−0.238711	+	0.971091i	$0.576725\pi$
$20$	2.90932	+	3.90789i	0.650543	+	0.873831i
$21$		0			0
$22$	1.89560	−	0.449266i	0.404144	−	0.0957838i
$23$	2.43678	+	5.64910i	0.508104	+	1.17792i	0.958501	+	0.285089i	$0.0920233\pi$
$23$	2.43678	+	5.64910i	0.508104	+	1.17792i	−0.450397	+	0.892828i	$0.648717\pi$
$24$		0			0
$25$	−2.86709	−	1.88571i	−0.573417	−	0.377143i
$26$	1.13175	−	1.96026i	0.221955	−	0.384438i
$27$		0			0
$28$	2.62564	+	4.54773i	0.496198	+	0.859441i
$29$	0.104644	−	1.79666i	0.0194318	−	0.333631i	−0.974556	−	0.224143i	$-0.928042\pi$
$29$	0.104644	−	1.79666i	0.0194318	−	0.333631i	0.993988	−	0.109488i	$-0.0349212\pi$
$30$		0			0
$31$	−0.671302	−	0.0784640i	−0.120569	−	0.0140925i	0.0555942	−	0.998453i	$-0.482295\pi$
$31$	−0.671302	−	0.0784640i	−0.120569	−	0.0140925i	−0.176164	+	0.984361i	$0.556369\pi$
$32$	−3.71068	−	3.93309i	−0.655961	−	0.695278i
$33$		0			0
$34$	−0.527023	+	0.0616002i	−0.0903837	+	0.0105643i
$35$	−6.96191	−	5.84174i	−1.17678	−	0.987434i
$36$		0			0
$37$	−8.73079	+	7.32600i	−1.43533	+	1.20439i	−0.492858	+	0.870110i	$0.664048\pi$
$37$	−8.73079	+	7.32600i	−1.43533	+	1.20439i	−0.942475	+	0.334277i	$0.891508\pi$
$38$	−1.88954	+	2.00280i	−0.306524	+	0.324897i
$39$		0			0
$40$	5.41694	+	2.72049i	0.856494	+	0.430147i
$41$	−5.94501	−	2.98570i	−0.928455	−	0.466288i	−0.0807376	−	0.996735i	$-0.525728\pi$
$41$	−5.94501	−	2.98570i	−0.928455	−	0.466288i	−0.847718	+	0.530448i	$0.822024\pi$
$42$		0			0
$43$	1.53472	−	1.62671i	0.234042	−	0.248071i	−0.599699	−	0.800226i	$-0.704713\pi$
$43$	1.53472	−	1.62671i	0.234042	−	0.248071i	0.833741	+	0.552155i	$0.186194\pi$
$44$	−4.41129	+	3.70151i	−0.665026	+	0.558023i
$45$		0			0
$46$	2.67508	+	2.24466i	0.394419	+	0.330957i
$47$	−3.14822	+	0.367974i	−0.459214	+	0.0536745i	−0.342556	−	0.939498i	$-0.611293\pi$
$47$	−3.14822	+	0.367974i	−0.459214	+	0.0536745i	−0.116659	+	0.993172i	$0.537218\pi$
$48$		0			0
$49$	−1.91856	−	2.03355i	−0.274080	−	0.290508i
$50$	−1.93465	−	0.226128i	−0.273601	−	0.0319794i
$51$		0			0
$52$	−0.389036	+	6.67950i	−0.0539497	+	0.926280i
$53$	4.18963	+	7.25666i	0.575490	+	0.996779i	0.995988	+	0.0894851i	$0.0285221\pi$
$53$	4.18963	+	7.25666i	0.575490	+	0.996779i	−0.420498	+	0.907294i	$0.638145\pi$
$54$		0			0
$55$	4.98301	−	8.63082i	0.671909	−	1.16378i
$56$	5.45881	+	3.59032i	0.729464	+	0.479776i
$57$		0			0
$58$	−0.404606	−	0.937983i	−0.0531274	−	0.123163i
$59$	4.89526	−	1.16020i	0.637309	−	0.151045i	0.100755	−	0.994911i	$-0.467874\pi$
$59$	4.89526	−	1.16020i	0.637309	−	0.151045i	0.536554	+	0.843866i	$0.319726\pi$
$60$		0			0
$61$	−0.340761	−	0.457722i	−0.0436300	−	0.0586053i	0.779773	−	0.626063i	$-0.215335\pi$
$61$	−0.340761	−	0.457722i	−0.0436300	−	0.0586053i	−0.823403	+	0.567457i	$0.807927\pi$
$62$	−0.360495	+	0.131209i	−0.0457829	+	0.0166636i
$63$		0			0
$64$	1.19553	+	0.435136i	0.149441	+	0.0543920i
$65$	−3.32104	−	11.0930i	−0.411924	−	1.37592i
$66$		0			0
$67$	0.794778	+	13.6458i	0.0970975	+	1.66710i	0.597924	+	0.801553i	$0.295992\pi$
$67$	0.794778	+	13.6458i	0.0970975	+	1.66710i	−0.500826	+	0.865548i	$0.666971\pi$
$68$	1.31043	−	0.861882i	0.158913	−	0.104519i
$69$		0			0
$70$	−5.01945	−	1.18963i	−0.599939	−	0.142188i
$71$	2.31784	+	13.1452i	0.275078	+	1.56004i	0.738715	+	0.674017i	$0.235433\pi$
$71$	2.31784	+	13.1452i	0.275078	+	1.56004i	−0.463638	+	0.886025i	$0.653456\pi$
$72$		0			0
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	0.836266	+	0.548324i	$0.184734\pi$
$73$	−1.17142	+	6.64347i	−0.137105	+	0.777560i	−0.973371	+	0.229236i	$0.926377\pi$
$74$	−2.56230	+	5.94009i	−0.297862	+	0.690521i
$75$		0			0
$76$	2.33432	−	7.79718i	0.267765	−	0.894398i
$77$	6.41467	−	8.61639i	0.731019	−	0.981929i
$78$		0			0
$79$	0.666057	−	0.334506i	0.0749373	−	0.0376349i	−0.410936	−	0.911664i	$-0.634798\pi$
$79$	0.666057	−	0.334506i	0.0749373	−	0.0376349i	0.485873	+	0.874029i	$0.338502\pi$
$80$	−6.30319			−0.704718
$81$		0			0
$82$	−3.77609			−0.417000
$83$	3.25233	−	1.63338i	0.356989	−	0.179287i	−0.261261	−	0.965268i	$-0.584138\pi$
$83$	3.25233	−	1.63338i	0.356989	−	0.179287i	0.618250	+	0.785982i	$0.287842\pi$
$84$		0			0
$85$	−1.62096	+	2.17733i	−0.175818	+	0.236165i
$86$	0.364070	−	1.21608i	0.0392586	−	0.131133i
$87$		0			0
$88$	−2.83784	+	6.57885i	−0.302515	+	0.701308i
$89$	2.27781	−	12.9181i	0.241447	−	1.36931i	−0.587154	−	0.809475i	$-0.699752\pi$
$89$	2.27781	−	12.9181i	0.241447	−	1.36931i	0.828601	−	0.559839i	$-0.189137\pi$
$90$		0			0
$91$	−2.16732	−	12.2915i	−0.227197	−	1.28850i
$92$	−10.0441	−	2.38050i	−1.04717	−	0.248185i
$93$		0			0
$94$	−1.50314	+	0.988632i	−0.155037	+	0.101970i
$95$	0.819027	+	14.0621i	0.0840304	+	1.44275i
$96$		0			0
$97$	−3.58656	−	11.9799i	−0.364160	−	1.21638i	−0.922249	−	0.386597i	$-0.873650\pi$
$97$	−3.58656	−	11.9799i	−0.364160	−	1.21638i	0.558089	−	0.829781i	$-0.311535\pi$
$98$	−1.49119	−	0.542748i	−0.150633	−	0.0548258i
$99$		0			0
$100$	5.41044	−	1.96924i	0.541044	−	0.196924i
$101$	3.57328	+	4.79974i	0.355554	+	0.477592i	0.943530	−	0.331286i	$-0.107483\pi$
$101$	3.57328	+	4.79974i	0.355554	+	0.477592i	−0.587976	+	0.808878i	$0.700075\pi$
$102$		0			0
$103$	1.72093	−	0.407867i	0.169568	−	0.0401883i	−0.144955	−	0.989438i	$-0.546304\pi$
$103$	1.72093	−	0.407867i	0.169568	−	0.0401883i	0.314523	+	0.949250i	$0.398156\pi$
$104$	3.29728	+	7.64395i	0.323325	+	0.749551i
$105$		0			0
$106$	3.97370	+	2.61354i	0.385960	+	0.253850i
$107$	3.57628	−	6.19429i	0.345732	−	0.598825i	−0.639755	−	0.768579i	$-0.720964\pi$
$107$	3.57628	−	6.19429i	0.345732	−	0.598825i	0.985486	+	0.169754i	$0.0542974\pi$
$108$		0			0
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	−0.998630	−	0.0523287i	$-0.983336\pi$
$109$	−5.68613	−	9.84867i	−0.544633	−	0.943332i	0.453997	−	0.891003i	$-0.349998\pi$
$110$	0.328913	−	5.64722i	0.0313606	−	0.538441i
$111$		0			0
$112$	−6.74803	−	0.788732i	−0.637629	−	0.0745281i
$113$	−3.99674	−	4.23629i	−0.375981	−	0.398517i	0.511558	−	0.859249i	$-0.329068\pi$
$113$	−3.99674	−	4.23629i	−0.375981	−	0.398517i	−0.887539	+	0.460732i	$0.847587\pi$
$114$		0			0
$115$	17.7437	−	2.07394i	1.65461	−	0.193396i
$116$	2.31313	+	1.94095i	0.214769	+	0.180213i
$117$		0			0
$118$	2.18749	−	1.83552i	0.201375	−	0.168973i
$119$	−2.00781	+	2.12816i	−0.184056	+	0.195088i
$120$		0			0
$121$	0.696696	+	0.349894i	0.0633360	+	0.0318086i
$122$	−0.289447	−	0.145366i	−0.0262053	−	0.0131608i
$123$		0			0
$124$	0.778193	−	0.824836i	0.0698838	−	0.0740725i
$125$	3.48865	−	2.92733i	0.312034	−	0.261828i
$126$		0			0
$127$	8.22802	+	6.90413i	0.730119	+	0.612643i	0.930164	−	0.367144i	$-0.119664\pi$
$127$	8.22802	+	6.90413i	0.730119	+	0.612643i	−0.200045	+	0.979787i	$0.564109\pi$
$128$	11.4586	−	1.33932i	1.01281	−	0.118380i
$129$		0			0
$130$	−4.51040	−	4.78075i	−0.395588	−	0.419299i
$131$	−7.11419	−	0.831529i	−0.621570	−	0.0726511i	−0.200521	−	0.979689i	$-0.564264\pi$
$131$	−7.11419	−	0.831529i	−0.621570	−	0.0726511i	−0.421048	+	0.907038i	$0.638338\pi$
$132$		0			0
$133$	−0.882797	+	15.1570i	−0.0765482	+	1.31428i
$134$	3.87930	+	6.71914i	0.335120	+	0.580446i
$135$		0			0
$136$	0.975746	−	1.69004i	0.0836695	−	0.144920i
$137$	−7.20952	−	4.74178i	−0.615951	−	0.405117i	0.202838	−	0.979212i	$-0.434984\pi$
$137$	−7.20952	−	4.74178i	−0.615951	−	0.405117i	−0.818789	+	0.574095i	$0.805354\pi$
$138$		0			0
$139$	−2.33653	−	5.41669i	−0.198182	−	0.459438i	0.789925	−	0.613203i	$-0.210119\pi$
$139$	−2.33653	−	5.41669i	−0.198182	−	0.459438i	−0.988107	+	0.153765i	$0.950860\pi$
$140$	14.8372	−	3.51649i	1.25398	−	0.297198i
$141$		0			0
$142$	4.52431	+	6.07720i	0.379672	+	0.509988i
$143$	12.8613	−	4.68113i	1.07552	−	0.391456i
$144$		0			0
$145$	−4.91069	−	1.78735i	−0.407811	−	0.148431i
$146$	1.09819	+	3.66820i	0.0908866	+	0.303583i
$147$		0			0
$148$	−1.11188	−	19.0902i	−0.0913956	−	1.56920i
$149$	−11.5252	+	7.58026i	−0.944184	+	0.620999i	−0.925468	−	0.378825i	$-0.876328\pi$
$149$	−11.5252	+	7.58026i	−0.944184	+	0.620999i	−0.0187156	+	0.999825i	$0.505958\pi$
$150$		0			0
$151$	6.10780	+	1.44758i	0.497046	+	0.117802i	0.471490	−	0.881871i	$-0.343716\pi$
$151$	6.10780	+	1.44758i	0.497046	+	0.117802i	0.0255559	+	0.999673i	$0.491864\pi$
$152$	−1.75849	−	9.97291i	−0.142633	−	0.808910i
$153$		0			0
$154$	1.05877	−	6.00461i	0.0853185	−	0.483865i
$155$	−0.777326	+	1.80204i	−0.0624363	+	0.144744i
$156$		0			0
$157$	0.0476363	−	0.159116i	0.00380179	−	0.0126989i	−0.956068	−	0.293146i	$-0.905298\pi$
$157$	0.0476363	−	0.159116i	0.00380179	−	0.0126989i	0.959869	+	0.280448i	$0.0904829\pi$
$158$	0.252633	−	0.339346i	0.0200984	−	0.0269969i
$159$		0			0
$160$	−14.0311	+	7.04667i	−1.10925	+	0.557088i
$161$	19.2554			1.51754
$162$		0			0
$163$	16.2014			1.26899			0.634495	−	0.772927i	$-0.281208\pi$
$163$	16.2014			1.26899			0.634495	+	0.772927i	$0.281208\pi$
$164$	9.97467	−	5.00947i	0.778891	−	0.391174i
$165$		0			0
$166$	1.23360	−	1.65701i	0.0957457	−	0.128609i
$167$	−5.24163	+	17.5083i	−0.405610	+	1.35483i	0.474582	+	0.880211i	$0.342599\pi$
$167$	−5.24163	+	17.5083i	−0.405610	+	1.35483i	−0.880191	+	0.474619i	$0.842586\pi$
$168$		0			0
$169$	1.14965	−	2.66518i	0.0884345	−	0.205014i
$170$	−0.267548	+	1.51734i	−0.0205200	+	0.116375i
$171$		0			0
$172$	0.651580	+	3.69529i	0.0496825	+	0.281763i
$173$	−18.3456	−	4.34799i	−1.39479	−	0.330572i	−0.536572	−	0.843855i	$-0.680281\pi$
$173$	−18.3456	−	4.34799i	−1.39479	−	0.330572i	−0.858219	+	0.513283i	$0.828429\pi$
$174$		0			0
$175$	−8.97346	+	5.90193i	−0.678329	+	0.446144i
$176$	−0.433193	−	7.43764i	−0.0326532	−	0.560633i
$177$		0			0
$178$	−2.13540	−	7.13274i	−0.160055	−	0.534621i
$179$	−9.67521	−	3.52149i	−0.723159	−	0.263209i	−0.0458930	−	0.998946i	$-0.514613\pi$
$179$	−9.67521	−	3.52149i	−0.723159	−	0.263209i	−0.677266	+	0.735738i	$0.736836\pi$
$180$		0			0
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	−0.313237	−	0.949675i	$-0.601414\pi$
$181$	0.770198	−	0.280329i	0.0572484	−	0.0208367i	0.370486	+	0.928838i	$0.379191\pi$
$182$	−4.23049	−	5.68254i	−0.313585	−	0.421218i
$183$		0			0
$184$	−12.4970	+	2.96185i	−0.921292	+	0.218350i
$185$	13.1080	+	30.3879i	0.963723	+	2.23416i
$186$		0			0
$187$	−2.68061	−	1.76306i	−0.196025	−	0.128928i
$188$	2.65905	−	4.60561i	0.193931	−	0.335899i
$189$		0			0
$190$	3.99766	+	6.92415i	0.290021	+	0.502330i
$191$	−0.0444838	+	0.763757i	−0.00321873	+	0.0552635i	−0.999535	−	0.0304908i	$-0.990293\pi$
$191$	−0.0444838	+	0.763757i	−0.00321873	+	0.0552635i	0.996316	+	0.0857543i	$0.0273300\pi$
$192$		0			0
$193$	−9.29144	−	1.08601i	−0.668812	−	0.0781730i	−0.225091	−	0.974338i	$-0.572268\pi$
$193$	−9.29144	−	1.08601i	−0.668812	−	0.0781730i	−0.443721	+	0.896165i	$0.646342\pi$
$194$	−4.87102	−	5.16298i	−0.349719	−	0.370680i
$195$		0			0
$196$	4.65905	−	0.544564i	0.332789	−	0.0388975i
$197$	−0.857832	−	0.719807i	−0.0611180	−	0.0512841i	0.611717	−	0.791077i	$-0.290479\pi$
$197$	−0.857832	−	0.719807i	−0.0611180	−	0.0512841i	−0.672835	+	0.739793i	$0.734924\pi$
$198$		0			0
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	−0.409969	−	0.912099i	$-0.634461\pi$
$199$	5.88368	−	4.93699i	0.417083	−	0.349974i	0.827052	+	0.562125i	$0.190016\pi$
$200$	4.91606	−	5.21072i	0.347618	−	0.368453i
$201$		0			0
$202$	3.03518	+	1.52433i	0.213555	+	0.107251i
$203$	−5.03360	−	2.52797i	−0.353290	−	0.177429i
$204$		0			0
$205$	−13.2564	+	14.0510i	−0.925870	+	0.981365i
$206$	0.769010	−	0.645276i	0.0535794	−	0.0449585i
$207$		0			0
$208$	−6.63120	−	5.56424i	−0.459791	−	0.385811i
$209$	−16.5368	+	1.93287i	−1.14387	+	0.133699i
$210$		0			0
$211$	7.02525	+	7.44633i	0.483638	+	0.512627i	0.922536	−	0.385910i	$-0.126113\pi$
$211$	7.02525	+	7.44633i	0.483638	+	0.512627i	−0.438898	+	0.898537i	$0.644631\pi$
$212$	−13.9638	−	1.63214i	−0.959041	−	0.112096i
$213$		0			0
$214$	0.236059	−	4.05298i	0.0161367	−	0.277056i
$215$	−3.24697	−	5.62391i	−0.221441	−	0.383547i
$216$		0			0
$217$	−1.05768	+	1.83195i	−0.0717999	+	0.124361i
$218$	−5.39307	−	3.54708i	−0.365265	−	0.240238i
$219$		0			0
$220$	6.62292	+	15.3537i	0.446517	+	1.03514i
$221$	−3.62739	+	0.859707i	−0.244005	+	0.0578301i
$222$		0			0
$223$	−2.77779	−	3.73122i	−0.186014	−	0.249861i	0.699327	−	0.714802i	$-0.253483\pi$
$223$	−2.77779	−	3.73122i	−0.186014	−	0.249861i	−0.885342	+	0.464941i	$0.846076\pi$
$224$	−15.9031	+	5.78824i	−1.06257	+	0.386743i
$225$		0			0
$226$	−3.10644	−	1.13065i	−0.206637	−	0.0752098i
$227$	4.04954	+	13.5264i	0.268777	+	0.897779i	0.980700	+	0.195521i	$0.0626397\pi$
$227$	4.04954	+	13.5264i	0.268777	+	0.897779i	−0.711922	+	0.702258i	$0.752175\pi$
$228$		0			0
$229$	0.301500	+	5.17655i	0.0199237	+	0.342076i	0.993509	+	0.113753i	$0.0362872\pi$
$229$	0.301500	+	5.17655i	0.0199237	+	0.342076i	−0.973585	+	0.228323i	$0.926676\pi$
$230$	8.47186	−	5.57203i	0.558618	−	0.367409i
$231$		0			0
$232$	3.65572	+	0.866423i	0.240010	+	0.0568834i
$233$	−0.773336	−	4.38581i	−0.0506629	−	0.287324i	0.948941	−	0.315452i	$-0.102156\pi$
$233$	−0.773336	−	4.38581i	−0.0506629	−	0.287324i	−0.999604	+	0.0281287i	$0.991045\pi$
$234$		0			0
$235$	−1.59822	+	9.06397i	−0.104257	+	0.591268i
$236$	−3.34327	+	7.75057i	−0.217628	+	0.504519i
$237$		0			0
$238$	−0.476298	+	1.59095i	−0.0308738	+	0.103126i
$239$	17.3543	−	23.3108i	1.12255	−	1.50785i	0.287420	−	0.957805i	$-0.407202\pi$
$239$	17.3543	−	23.3108i	1.12255	−	1.50785i	0.835134	−	0.550047i	$-0.185390\pi$
$240$		0			0
$241$	22.3266	−	11.2128i	1.43818	−	0.722281i	0.452635	−	0.891696i	$-0.350484\pi$
$241$	22.3266	−	11.2128i	1.43818	−	0.722281i	0.985545	+	0.169415i	$0.0541877\pi$
$242$	0.442520			0.0284463
$243$		0			0
$244$	0.957429			0.0612931
$245$	−7.25459	+	3.64339i	−0.463479	+	0.232768i
$246$		0			0
$247$	−11.5519	+	15.5169i	−0.735031	+	0.987319i
$248$	0.404658	−	1.35165i	0.0256958	−	0.0858299i
$249$		0			0
$250$	1.02385	−	2.37354i	0.0647538	−	0.150116i
$251$	−2.46091	+	13.9565i	−0.155331	+	0.880926i	0.803152	+	0.595775i	$0.203155\pi$
$251$	−2.46091	+	13.9565i	−0.155331	+	0.880926i	−0.958483	+	0.285151i	$0.907956\pi$
$252$		0			0
$253$	3.66665	+	20.7946i	0.230521	+	1.30735i
$254$	5.93230	+	1.40598i	0.372226	+	0.0882191i
$255$		0			0
$256$	3.34511	−	2.20011i	0.209069	−	0.137507i
$257$	0.854668	+	14.6741i	0.0533127	+	0.915344i	0.913874	+	0.405997i	$0.133076\pi$
$257$	0.854668	+	14.6741i	0.0533127	+	0.915344i	−0.860562	+	0.509347i	$0.829887\pi$
$258$		0			0
$259$	10.2306	+	34.1727i	0.635700	+	2.12339i
$260$	18.2566	+	6.64487i	1.13223	+	0.412098i
$261$		0			0
$262$	−3.82038	+	1.39050i	−0.236024	+	0.0859056i
$263$	−9.78683	−	13.1460i	−0.603482	−	0.810617i	0.390449	−	0.920625i	$-0.372320\pi$
$263$	−9.78683	−	13.1460i	−0.603482	−	0.810617i	−0.993931	+	0.110008i	$0.964912\pi$
$264$		0			0
$265$	23.6753	−	5.61114i	1.45436	−	0.344690i
$266$	3.41335	+	7.91304i	0.209286	+	0.485180i
$267$		0			0
$268$	−19.1611	−	12.6024i	−1.17045	−	0.769817i
$269$	−5.68131	+	9.84032i	−0.346396	+	0.599975i	−0.985606	−	0.169057i	$-0.945928\pi$
$269$	−5.68131	+	9.84032i	−0.346396	+	0.599975i	0.639211	+	0.769032i	$0.279261\pi$
$270$		0			0
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	0.820970	−	0.570971i	$-0.193433\pi$
$271$	−1.38266	−	2.39483i	−0.0839903	−	0.145476i	−0.904961	+	0.425496i	$0.860100\pi$
$272$	−0.117990	+	2.02580i	−0.00715416	+	0.122832i
$273$		0			0
$274$	−4.86484	−	0.568618i	−0.293896	−	0.0343515i
$275$	−8.08246	−	8.56691i	−0.487391	−	0.516604i
$276$		0			0
$277$	−18.2717	+	2.13566i	−1.09784	+	0.128319i	−0.645673	−	0.763614i	$-0.723423\pi$
$277$	−18.2717	+	2.13566i	−1.09784	+	0.128319i	−0.452167	+	0.891933i	$0.649349\pi$
$278$	−2.56503	−	2.15231i	−0.153840	−	0.129087i
$279$		0			0
$280$	14.5334	−	12.1950i	0.868538	−	0.728790i
$281$	7.36555	−	7.80702i	0.439392	−	0.465728i	−0.469395	−	0.882988i	$-0.655528\pi$
$281$	7.36555	−	7.80702i	0.439392	−	0.465728i	0.908787	+	0.417260i	$0.137010\pi$
$282$		0			0
$283$	−12.7718	−	6.41421i	−0.759202	−	0.381285i	0.0266946	−	0.999644i	$-0.491502\pi$
$283$	−12.7718	−	6.41421i	−0.759202	−	0.381285i	−0.785896	+	0.618358i	$0.787798\pi$
$284$	−20.0133	−	10.0511i	−1.18757	−	0.596421i
$285$		0			0
$286$	5.33120	−	5.65074i	0.315241	−	0.334135i
$287$	−15.9502	+	13.3838i	−0.941512	+	0.790022i
$288$		0			0
$289$	−12.3533	−	10.3657i	−0.726666	−	0.609745i
$290$	−2.94618	+	0.344359i	−0.173006	+	0.0202215i
$291$		0			0
$292$	−7.76724	−	8.23279i	−0.454543	−	0.481787i
$293$	−21.6982	−	2.53616i	−1.26762	−	0.148164i	−0.544428	−	0.838808i	$-0.683253\pi$
$293$	−21.6982	−	2.53616i	−1.26762	−	0.148164i	−0.723195	+	0.690644i	$0.757327\pi$
$294$		0			0
$295$	0.849396	−	14.5836i	0.0494537	−	0.849088i
$296$	−11.8962	−	20.6048i	−0.691453	−	1.19763i
$297$		0			0
$298$	−3.91497	+	6.78092i	−0.226788	+	0.392808i
$299$	20.4978	+	13.4816i	1.18542	+	0.779663i
$300$		0			0
$301$	−2.77238	−	6.42711i	−0.159798	−	0.370452i
$302$	3.46684	−	0.821656i	0.199494	−	0.0472810i
$303$		0			0
$304$	6.28819	+	8.44650i	0.360652	+	0.484440i
$305$	−1.55705	+	0.566720i	−0.0891564	+	0.0324503i
$306$		0			0
$307$	−28.6368	−	10.4229i	−1.63439	−	0.594869i	−0.648344	−	0.761347i	$-0.724538\pi$
$307$	−28.6368	−	10.4229i	−1.63439	−	0.594869i	−0.986045	+	0.166478i	$0.946760\pi$
$308$	5.16909	+	17.2660i	0.294536	+	0.983820i
$309$		0			0
$310$	0.0647710	+	1.11207i	0.00367874	+	0.0631616i
$311$	22.6519	−	14.8984i	1.28447	−	0.844812i	0.290764	−	0.956795i	$-0.406091\pi$
$311$	22.6519	−	14.8984i	1.28447	−	0.844812i	0.993710	+	0.111983i	$0.0357203\pi$
$312$		0			0
$313$	−7.88787	−	1.86946i	−0.445849	−	0.105668i	0.00155774	−	0.999999i	$-0.499504\pi$
$313$	−7.88787	−	1.86946i	−0.445849	−	0.105668i	−0.447407	+	0.894331i	$0.647652\pi$
$314$	−0.0163709	−	0.0928440i	−0.000923863	−	0.00523949i
$315$		0			0
$316$	−0.217154	+	1.23154i	−0.0122159	+	0.0692797i
$317$	7.69151	−	17.8309i	0.431998	−	1.00148i	−0.553662	−	0.832742i	$-0.686770\pi$
$317$	7.69151	−	17.8309i	0.431998	−	1.00148i	0.985660	−	0.168743i	$-0.0539708\pi$
$318$		0			0
$319$	1.77154	−	5.91736i	0.0991872	−	0.331308i
$320$	2.20607	−	2.96326i	0.123323	−	0.165652i
$321$		0			0
$322$	9.76698	−	4.90516i	0.544293	−	0.273354i
$323$	4.53480			0.252323
$324$		0			0
$325$	−13.6847			−0.759089
$326$	8.21787	−	4.12717i	0.455146	−	0.228583i
$327$		0			0
$328$	8.29321	−	11.1397i	0.457916	−	0.615088i
$329$	−2.84521	+	9.50365i	−0.156861	+	0.523953i
$330$		0			0
$331$	0.786897	−	1.82423i	0.0432518	−	0.100269i	−0.895221	−	0.445623i	$-0.852982\pi$
$331$	0.786897	−	1.82423i	0.0432518	−	0.100269i	0.938472	+	0.345354i	$0.112241\pi$
$332$	−1.06035	+	6.01357i	−0.0581945	+	0.330037i
$333$		0			0
$334$	1.80136	+	10.2160i	0.0985662	+	0.558997i
$335$	38.6210	+	9.15334i	2.11009	+	0.500100i
$336$		0			0
$337$	15.3358	−	10.0865i	0.835397	−	0.549449i	−0.0582076	−	0.998304i	$-0.518539\pi$
$337$	15.3358	−	10.0865i	0.835397	−	0.549449i	0.893604	+	0.448855i	$0.148168\pi$
$338$	−0.0957949	−	1.64473i	−0.00521055	−	0.0894617i
$339$		0			0
$340$	−1.30621	−	4.36305i	−0.0708392	−	0.236619i
$341$	−2.17980	−	0.793381i	−0.118043	−	0.0429640i
$342$		0			0
$343$	12.3650	−	4.50048i	0.667646	−	0.243003i
$344$	2.78792	+	3.74483i	0.150315	+	0.201908i
$345$		0			0
$346$	−10.4131	+	2.46796i	−0.559813	+	0.132678i
$347$	−10.6086	−	24.5935i	−0.569499	−	1.32025i	−0.922995	−	0.384812i	$-0.874266\pi$
$347$	−10.6086	−	24.5935i	−0.569499	−	1.32025i	0.353496	−	0.935436i	$-0.384993\pi$
$348$		0			0
$349$	10.9528	+	7.20376i	0.586289	+	0.385608i	0.807719	−	0.589568i	$-0.200702\pi$
$349$	10.9528	+	7.20376i	0.586289	+	0.385608i	−0.221430	+	0.975176i	$0.571072\pi$
$350$	−3.04816	+	5.27957i	−0.162931	+	0.282205i
$351$		0			0
$352$	−9.27922	−	16.0721i	−0.494584	−	0.856645i
$353$	−1.13003	+	19.4019i	−0.0601456	+	1.03266i	0.824341	+	0.566094i	$0.191546\pi$
$353$	−1.13003	+	19.4019i	−0.0601456	+	1.03266i	−0.884486	+	0.466566i	$0.845491\pi$
$354$		0			0
$355$	38.4967	+	4.49962i	2.04319	+	0.238815i
$356$	15.1032	+	16.0085i	0.800469	+	0.848447i
$357$		0			0
$358$	−5.80466	+	0.678468i	−0.306786	+	0.0358581i
$359$	11.2428	+	9.43384i	0.593373	+	0.497899i	0.889308	−	0.457309i	$-0.151187\pi$
$359$	11.2428	+	9.43384i	0.593373	+	0.497899i	−0.295935	+	0.955208i	$0.595631\pi$
$360$		0			0
$361$	3.47185	−	2.91323i	0.182729	−	0.153328i
$362$	0.319258	−	0.338394i	0.0167798	−	0.0177856i
$363$		0			0
$364$	18.7136	+	9.39832i	0.980858	+	0.492606i
$365$	17.5049	+	8.79127i	0.916246	+	0.460156i
$366$		0			0
$367$	7.54456	−	7.99677i	0.393823	−	0.417428i	−0.499875	−	0.866098i	$-0.666621\pi$
$367$	7.54456	−	7.99677i	0.393823	−	0.417428i	0.893698	+	0.448670i	$0.148102\pi$
$368$	10.2304	−	8.58433i	0.533297	−	0.447489i
$369$		0			0
$370$	14.3899	+	12.0746i	0.748096	+	0.627727i
$371$	26.0482	−	3.04460i	1.35236	−	0.158068i
$372$		0			0
$373$	14.0118	+	14.8517i	0.725505	+	0.768990i	0.980195	−	0.198033i	$-0.0634552\pi$
$373$	14.0118	+	14.8517i	0.725505	+	0.768990i	−0.254691	+	0.967023i	$0.581974\pi$
$374$	−1.80882	−	0.211421i	−0.0935319	−	0.0109323i
$375$		0			0
$376$	0.384735	−	6.60564i	0.0198412	−	0.340660i
$377$	−3.58843	−	6.21535i	−0.184814	−	0.320107i
$378$		0			0
$379$	−13.0154	+	22.5433i	−0.668556	+	1.15797i	0.309753	+	0.950817i	$0.399754\pi$
$379$	−13.0154	+	22.5433i	−0.668556	+	1.15797i	−0.978308	+	0.207155i	$0.933580\pi$
$380$	−19.7457	−	12.9870i	−1.01293	−	0.666217i
$381$		0			0
$382$	0.171997	+	0.398735i	0.00880015	+	0.0204010i
$383$	22.8964	−	5.42654i	1.16995	−	0.277283i	0.400686	−	0.916215i	$-0.368772\pi$
$383$	22.8964	−	5.42654i	1.16995	−	0.277283i	0.769263	+	0.638932i	$0.220624\pi$
$384$		0			0
$385$	−18.6264	−	25.0197i	−0.949292	−	1.27512i
$386$	−4.98958	+	1.81606i	−0.253963	+	0.0924349i
$387$		0			0
$388$	19.7163	+	7.17615i	1.00094	+	0.364314i
$389$	−9.48468	−	31.6810i	−0.480892	−	1.60629i	−0.762653	−	0.646807i	$-0.776104\pi$
$389$	−9.48468	−	31.6810i	−0.480892	−	1.60629i	0.281761	−	0.959485i	$-0.409081\pi$
$390$		0			0
$391$	−0.334405	−	5.74151i	−0.0169116	−	0.290361i
$392$	4.87615	−	3.20710i	0.246283	−	0.161983i
$393$		0			0
$394$	−0.618486	−	0.146584i	−0.0311589	−	0.00738479i
$395$	−0.375819	−	2.13137i	−0.0189095	−	0.107241i
$396$		0			0
$397$	−0.00960087	+	0.0544493i	−0.000481854	+	0.00273273i	−0.985048	−	0.172282i	$-0.944886\pi$
$397$	−0.00960087	+	0.0544493i	−0.000481854	+	0.00273273i	0.984566	+	0.175014i	$0.0559972\pi$
$398$	1.72674	−	4.00303i	0.0865536	−	0.200654i
$399$		0			0
$400$	−2.13643	+	7.13619i	−0.106822	+	0.356809i
$401$	17.1048	−	22.9757i	0.854173	−	1.14735i	−0.133535	−	0.991044i	$-0.542633\pi$
$401$	17.1048	−	22.9757i	0.854173	−	1.14735i	0.987708	−	0.156310i	$-0.0499598\pi$
$402$		0			0
$403$	−2.40856	+	1.20962i	−0.119979	+	0.0602557i
$404$	−10.0397			−0.499496
$405$		0			0
$406$	−3.19719			−0.158674
$407$	−34.9562	+	17.5557i	−1.73271	+	0.870202i
$408$		0			0
$409$	18.7728	−	25.2163i	0.928255	−	1.24686i	−0.0405846	−	0.999176i	$-0.512922\pi$
$409$	18.7728	−	25.2163i	0.928255	−	1.24686i	0.968840	−	0.247687i	$-0.0796706\pi$
$410$	−3.14472	+	10.5041i	−0.155307	+	0.518761i
$411$		0			0
$412$	−1.17532	+	2.72471i	−0.0579040	+	0.134237i
$413$	2.73421	−	15.5065i	0.134542	−	0.763024i
$414$		0			0
$415$	−1.83511	−	10.4074i	−0.0900818	−	0.510879i
$416$	−20.9818	−	4.97277i	−1.02872	−	0.243810i
$417$		0			0
$418$	−7.89561	+	5.19302i	−0.386187	+	0.253999i
$419$	−0.196196	−	3.36855i	−0.00958479	−	0.164564i	−0.999704	−	0.0243352i	$-0.992253\pi$
$419$	−0.196196	−	3.36855i	−0.00958479	−	0.164564i	0.990119	−	0.140229i	$-0.0447839\pi$
$420$		0			0
$421$	−7.24567	−	24.2022i	−0.353133	−	1.17954i	−0.931492	−	0.363763i	$-0.881492\pi$
$421$	−7.24567	−	24.2022i	−0.353133	−	1.17954i	0.578359	−	0.815782i	$-0.303693\pi$
$422$	5.46033	+	1.98740i	0.265805	+	0.0967451i
$423$		0			0
$424$	−16.4373	+	5.98270i	−0.798267	+	0.290545i
$425$	1.91566	+	2.57318i	0.0929231	+	0.124817i
$426$		0			0
$427$	−1.73785	+	0.411878i	−0.0841005	+	0.0199322i
$428$	4.75324	+	11.0192i	0.229756	+	0.532635i
$429$		0			0
$430$	−3.07962	−	2.02549i	−0.148512	−	0.0976780i
$431$	−16.4068	+	28.4174i	−0.790288	+	1.36882i	0.135501	+	0.990777i	$0.456736\pi$
$431$	−16.4068	+	28.4174i	−0.790288	+	1.36882i	−0.925789	+	0.378041i	$0.876598\pi$
$432$		0			0
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	0.978472	−	0.206379i	$-0.0661680\pi$
$433$	6.46122	+	11.1912i	0.310507	+	0.537813i	−0.667966	+	0.744192i	$0.732835\pi$
$434$	−0.0698141	+	1.19866i	−0.00335118	+	0.0575376i
$435$		0			0
$436$	18.9516	+	2.21513i	0.907618	+	0.106085i
$437$	−20.4806	−	21.7081i	−0.979719	−	1.03844i
$438$		0			0
$439$	−36.6280	+	4.28120i	−1.74816	+	0.204330i	−0.929214	−	0.369542i	$-0.879515\pi$
$439$	−36.6280	+	4.28120i	−1.74816	+	0.204330i	−0.818945	+	0.573872i	$0.805441\pi$
$440$	15.9373	+	13.3730i	0.759781	+	0.637532i
$441$		0			0
$442$	−1.62093	+	1.36012i	−0.0770997	+	0.0646943i
$443$	−23.5817	+	24.9951i	−1.12040	+	1.18755i	−0.140078	+	0.990140i	$0.544735\pi$
$443$	−23.5817	+	24.9951i	−1.12040	+	1.18755i	−0.980320	+	0.197413i	$0.936746\pi$
$444$		0			0
$445$	−34.0378	−	17.0944i	−1.61355	−	0.810354i
$446$	−2.35948	−	1.18498i	−0.111725	−	0.0561103i
$447$		0			0
$448$	2.73256	−	2.89634i	0.129101	−	0.136839i
$449$	13.4520	−	11.2876i	0.634838	−	0.532693i	−0.267590	−	0.963533i	$-0.586227\pi$
$449$	13.4520	−	11.2876i	0.634838	−	0.532693i	0.902428	+	0.430840i	$0.141783\pi$
$450$		0			0
$451$	−17.4910	−	14.6767i	−0.823617	−	0.691097i
$452$	9.70571	−	1.13444i	0.456518	−	0.0533593i
$453$		0			0
$454$	5.49981	+	5.82945i	0.258119	+	0.273590i
$455$	−35.9966	−	4.20740i	−1.68755	−	0.197246i
$456$		0			0
$457$	0.485445	−	8.33476i	0.0227081	−	0.389884i	−0.967736	−	0.251967i	$-0.918922\pi$
$457$	0.485445	−	8.33476i	0.0227081	−	0.389884i	0.990444	−	0.137916i	$-0.0440405\pi$
$458$	1.47162	+	2.54891i	0.0687641	+	0.119103i
$459$		0			0
$460$	−14.9867	+	25.9577i	−0.698758	+	1.21028i
$461$	16.9937	+	11.1769i	0.791475	+	0.520561i	0.879694	−	0.475540i	$-0.157747\pi$
$461$	16.9937	+	11.1769i	0.791475	+	0.520561i	−0.0882195	+	0.996101i	$0.528118\pi$
$462$		0			0
$463$	−1.02559	−	2.37758i	−0.0476631	−	0.110496i	0.892721	−	0.450610i	$-0.148793\pi$
$463$	−1.02559	−	2.37758i	−0.0476631	−	0.110496i	−0.940384	+	0.340114i	$0.889534\pi$
$464$	−3.80136	+	0.900939i	−0.176474	+	0.0418250i
$465$		0			0
$466$	−1.50951	−	2.02763i	−0.0699268	−	0.0939279i
$467$	−11.5019	+	4.18635i	−0.532244	+	0.193721i	−0.594140	−	0.804361i	$-0.702508\pi$
$467$	−11.5019	+	4.18635i	−0.532244	+	0.193721i	0.0618958	+	0.998083i	$0.480285\pi$
$468$		0			0
$469$	40.2012	+	14.6320i	1.85632	+	0.675645i
$470$	1.49830	+	5.00468i	0.0691116	+	0.230849i
$471$		0			0
$472$	0.610652	+	10.4845i	0.0281075	+	0.482587i
$473$	6.41295	−	4.21786i	0.294868	−	0.193937i
$474$		0			0
$475$	16.1981	+	3.83903i	0.743221	+	0.176147i
$476$	−0.852437	−	4.83441i	−0.0390714	−	0.221585i
$477$		0			0
$478$	2.86441	−	16.2449i	0.131015	−	0.743024i
$479$	10.8633	−	25.1839i	0.496357	−	1.15068i	−0.467435	−	0.884027i	$-0.654822\pi$
$479$	10.8633	−	25.1839i	0.496357	−	1.15068i	0.963792	−	0.266656i	$-0.0859189\pi$
$480$		0			0
$481$	−13.0352	+	43.5405i	−0.594353	+	1.98528i
$482$	8.46840	−	11.3750i	0.385725	−	0.518118i
$483$		0			0
$484$	−1.16893	+	0.587060i	−0.0531333	+	0.0266845i
$485$	−36.3120			−1.64884
$486$		0			0
$487$	−6.02417			−0.272981			−0.136491	−	0.990641i	$-0.543582\pi$
$487$	−6.02417			−0.272981			−0.136491	+	0.990641i	$0.543582\pi$
$488$	1.06453	−	0.534628i	0.0481891	−	0.0242015i
$489$		0			0
$490$	−2.75164	+	3.69610i	−0.124307	+	0.166973i
$491$	−0.139757	+	0.466819i	−0.00630713	+	0.0210673i	−0.961085	−	0.276252i	$-0.910907\pi$
$491$	−0.139757	+	0.466819i	−0.00630713	+	0.0210673i	0.954778	+	0.297320i	$0.0960927\pi$
$492$		0			0
$493$	−0.666364	+	1.54481i	−0.0300115	+	0.0695745i
$494$	−1.90671	+	10.8135i	−0.0857867	+	0.486521i
$495$		0			0
$496$	0.254765	+	1.44484i	0.0114393	+	0.0648754i
$497$	40.6505	+	9.63434i	1.82342	+	0.432159i
$498$		0			0
$499$	−4.58242	+	3.01391i	−0.205137	+	0.134921i	−0.647921	−	0.761708i	$-0.724361\pi$
$499$	−4.58242	+	3.01391i	−0.205137	+	0.134921i	0.442784	+	0.896628i	$0.353991\pi$
$500$	0.444284	+	7.62806i	0.0198690	+	0.341137i
$501$		0			0
$502$	2.30705	+	7.70609i	0.102969	+	0.343940i
$503$	−9.93090	−	3.61455i	−0.442797	−	0.161165i	0.110993	−	0.993821i	$-0.464597\pi$
$503$	−9.93090	−	3.61455i	−0.442797	−	0.161165i	−0.553790	+	0.832656i	$0.686819\pi$
$504$		0			0
$505$	16.3275	−	5.94271i	0.726562	−	0.264447i
$506$	7.15712	+	9.61368i	0.318173	+	0.427380i
$507$		0			0
$508$	−17.5356	+	4.15601i	−0.778015	+	0.184393i
$509$	4.91402	+	11.3920i	0.217810	+	0.504940i	0.991730	−	0.128343i	$-0.0409659\pi$
$509$	4.91402	+	11.3920i	0.217810	+	0.504940i	−0.773920	+	0.633284i	$0.781707\pi$
$510$		0			0
$511$	17.6402	+	11.6021i	0.780355	+	0.513248i
$512$	−10.4003	+	18.0139i	−0.459634	+	0.796110i
$513$		0			0
$514$	4.17162	+	7.22546i	0.184002	+	0.318701i
$515$	0.298604	−	5.12684i	0.0131581	−	0.225915i
$516$		0			0
$517$	−10.8051	−	1.26294i	−0.475209	−	0.0555440i
$518$	13.8945	+	14.7273i	0.610491	+	0.647082i
$519$		0			0
$520$	24.0095	−	2.80630i	1.05288	−	0.123064i
$521$	13.6270	+	11.4344i	0.597011	+	0.500952i	0.890483	−	0.455016i	$-0.150366\pi$
$521$	13.6270	+	11.4344i	0.597011	+	0.500952i	−0.293472	+	0.955968i	$0.594811\pi$
$522$		0			0
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	−0.841202	−	0.540721i	$-0.818151\pi$
$523$	−10.4002	+	8.72680i	−0.454769	+	0.381596i	0.386433	+	0.922317i	$0.373707\pi$
$524$	8.24697	−	8.74128i	0.360271	−	0.381865i
$525$		0			0
$526$	−8.31304	−	4.17497i	−0.362466	−	0.182037i
$527$	0.564613	+	0.283560i	0.0245949	+	0.0123520i
$528$		0			0
$529$	−10.1908	+	10.8016i	−0.443079	+	0.469636i
$530$	10.5795	−	8.87724i	0.459543	−	0.385603i
$531$		0			0
$532$	−19.5141	−	16.3743i	−0.846045	−	0.709916i
$533$	−26.3500	+	3.07988i	−1.14135	+	0.133404i
$534$		0			0
$535$	−14.2526	−	15.1069i	−0.616194	−	0.653127i
$536$	−28.3418	−	3.31268i	−1.22418	−	0.143086i
$537$		0			0
$538$	−0.375006	+	6.43861i	−0.0161677	+	0.277588i
$539$	−4.79771	−	8.30987i	−0.206652	−	0.357931i
$540$		0			0
$541$	13.6538	−	23.6492i	0.587025	−	1.01676i	−0.407595	−	0.913163i	$-0.633632\pi$
$541$	13.6538	−	23.6492i	0.587025	−	1.01676i	0.994620	−	0.103594i	$-0.0330342\pi$
$542$	−1.31139	−	0.862517i	−0.0563291	−	0.0370483i
$543$		0			0
$544$	2.00210	+	4.64139i	0.0858394	+	0.198998i
$545$	−32.1319	+	7.61539i	−1.37638	+	0.326207i
$546$		0			0
$547$	7.58248	+	10.1850i	0.324204	+	0.435481i	0.934106	−	0.356995i	$-0.116199\pi$
$547$	7.58248	+	10.1850i	0.324204	+	0.435481i	−0.609903	+	0.792476i	$0.708791\pi$
$548$	13.6050	−	4.95181i	0.581176	−	0.211531i
$549$		0			0
$550$	−6.28204	−	2.28648i	−0.267867	−	0.0974957i
$551$	2.50390	+	8.36360i	0.106670	+	0.356301i
$552$		0			0
$553$	−0.135638	−	2.32882i	−0.00576793	−	0.0990315i
$554$	−8.72397	+	5.73785i	−0.370646	+	0.243778i
$555$		0			0
$556$	9.63092	+	2.28257i	0.408442	+	0.0968025i
$557$	−2.62356	−	14.8789i	−0.111164	−	0.630441i	−0.988578	−	0.150708i	$-0.951845\pi$
$557$	−2.62356	−	14.8789i	−0.111164	−	0.630441i	0.877415	−	0.479733i	$-0.159266\pi$
$558$		0			0
$559$	1.54866	−	8.78288i	0.0655013	−	0.371476i
$560$	−7.81380	+	18.1144i	−0.330193	+	0.765474i
$561$		0			0
$562$	1.74727	−	5.83630i	0.0737043	−	0.246189i
$563$	−3.66195	+	4.91886i	−0.154333	+	0.207305i	−0.872564	−	0.488499i	$-0.837545\pi$
$563$	−3.66195	+	4.91886i	−0.154333	+	0.207305i	0.718231	+	0.695804i	$0.244952\pi$
$564$		0			0
$565$	−15.1127	+	7.58990i	−0.635798	+	0.319310i
$566$	−8.11223			−0.340982
$567$		0			0
$568$	−27.8646			−1.16917
$569$	−1.32201	+	0.663940i	−0.0554217	+	0.0278338i	−0.476294	−	0.879286i	$-0.658020\pi$
$569$	−1.32201	+	0.663940i	−0.0554217	+	0.0278338i	0.420872	+	0.907120i	$0.361724\pi$
$570$		0			0
$571$	5.26460	−	7.07158i	0.220317	−	0.295936i	−0.678199	−	0.734878i	$-0.737239\pi$
$571$	5.26460	−	7.07158i	0.220317	−	0.295936i	0.898515	+	0.438942i	$0.144647\pi$
$572$	−6.58611	+	21.9991i	−0.275379	+	0.919830i
$573$		0			0
$574$	−4.68106	+	10.8519i	−0.195384	+	0.452950i
$575$	3.66611	−	20.7915i	0.152887	−	0.867066i
$576$		0			0
$577$	2.48608	+	14.0993i	0.103497	+	0.586960i	0.991810	+	0.127722i	$0.0407665\pi$
$577$	2.48608	+	14.0993i	0.103497	+	0.586960i	−0.888313	+	0.459238i	$0.848122\pi$
$578$	−8.90659	−	2.11090i	−0.370465	−	0.0878018i
$579$		0			0
$580$	7.32559	−	4.81812i	0.304179	−	0.200062i
$581$	−0.662315	−	11.3715i	−0.0274775	−	0.471770i
$582$		0			0
$583$	8.24814	+	27.5507i	0.341603	+	1.14103i
$584$	−13.2333	−	4.81654i	−0.547599	−	0.199310i
$585$		0			0
$586$	−11.6521	+	4.24102i	−0.481344	+	0.175195i
$587$	5.09890	+	6.84901i	0.210454	+	0.282689i	0.894799	−	0.446470i	$-0.147319\pi$
$587$	5.09890	+	6.84901i	0.210454	+	0.282689i	−0.684345	+	0.729159i	$0.739912\pi$
$588$		0			0
$589$	3.19028	−	0.756110i	0.131453	−	0.0311550i
$590$	−3.28421	−	7.61364i	−0.135209	−	0.313449i
$591$		0			0
$592$	20.6702	+	13.5950i	0.849539	+	0.558751i
$593$	19.8740	−	34.4227i	0.816125	−	1.41357i	−0.0923915	−	0.995723i	$-0.529451\pi$
$593$	19.8740	−	34.4227i	0.816125	−	1.41357i	0.908517	−	0.417848i	$-0.137216\pi$
$594$		0			0
$595$	4.24788	+	7.35754i	0.174146	+	0.301630i
$596$	1.34576	−	23.1057i	0.0551243	−	0.946448i
$597$		0			0
$598$	13.8315	+	1.61667i	0.565613	+	0.0661106i
$599$	−13.9840	−	14.8221i	−0.571370	−	0.605616i	0.375662	−	0.926757i	$-0.377415\pi$
$599$	−13.9840	−	14.8221i	−0.571370	−	0.605616i	−0.947032	+	0.321140i	$0.895934\pi$
$600$		0			0
$601$	13.5963	−	1.58918i	0.554604	−	0.0648239i	0.165825	−	0.986155i	$-0.446971\pi$
$601$	13.5963	−	1.58918i	0.554604	−	0.0648239i	0.388779	+	0.921331i	$0.372897\pi$
$602$	−3.04350	−	2.55380i	−0.124044	−	0.104085i
$603$		0			0
$604$	−8.06774	+	6.76964i	−0.328272	+	0.275453i
$605$	1.55352	−	1.64664i	0.0631597	−	0.0669453i
$606$		0			0
$607$	−4.02143	−	2.01964i	−0.163225	−	0.0819745i	0.365311	−	0.930885i	$-0.380963\pi$
$607$	−4.02143	−	2.01964i	−0.163225	−	0.0819745i	−0.528536	+	0.848911i	$0.677259\pi$
$608$	23.4405	+	11.7722i	0.950636	+	0.477427i
$609$		0			0
$610$	−0.645420	+	0.684105i	−0.0261323	+	0.0276986i
$611$	−9.68275	+	8.12479i	−0.391722	+	0.328694i
$612$		0			0
$613$	27.4040	+	22.9947i	1.10684	+	0.928746i	0.997866	−	0.0652986i	$-0.0208000\pi$
$613$	27.4040	+	22.9947i	1.10684	+	0.928746i	0.108971	+	0.994045i	$0.465244\pi$
$614$	−17.1807	+	2.00814i	−0.693357	+	0.0810418i
$615$		0			0
$616$	15.3887	+	16.3110i	0.620027	+	0.657190i
$617$	27.3964	+	3.20218i	1.10294	+	0.128915i	0.648023	−	0.761621i	$-0.275596\pi$
$617$	27.3964	+	3.20218i	1.10294	+	0.128915i	0.454913	+	0.890536i	$0.349670\pi$
$618$		0			0
$619$	1.94367	−	33.3715i	0.0781227	−	1.34131i	−0.700424	−	0.713727i	$-0.747006\pi$
$619$	1.94367	−	33.3715i	0.0781227	−	1.34131i	0.778546	−	0.627587i	$-0.215957\pi$
$620$	−1.64640	−	2.85165i	−0.0661211	−	0.114525i
$621$		0			0
$622$	7.69456	−	13.3274i	0.308524	−	0.534379i
$623$	−34.3009	−	22.5601i	−1.37424	−	0.903850i
$624$		0			0
$625$	−12.0337	−	27.8973i	−0.481349	−	1.11589i
$626$	−4.47722	+	1.06112i	−0.178946	+	0.0424109i
$627$		0			0
$628$	0.166414	+	0.223532i	0.00664063	+	0.00891991i
$629$	10.0118	−	3.64400i	0.399197	−	0.145296i
$630$		0			0
$631$	10.2732	+	3.73914i	0.408970	+	0.148853i	0.538309	−	0.842748i	$-0.319063\pi$
$631$	10.2732	+	3.73914i	0.408970	+	0.148853i	−0.129339	+	0.991600i	$0.541286\pi$
$632$	0.446247	+	1.49057i	0.0177508	+	0.0592917i
$633$		0			0
$634$	−0.640898	−	11.0038i	−0.0254533	−	0.437016i
$635$	26.0578	−	17.1385i	1.03407	−	0.680120i
$636$		0			0
$637$	−10.8484	−	2.57111i	−0.429828	−	0.101871i
$638$	−0.608816	−	3.45277i	−0.0241032	−	0.136696i
$639$		0			0
$640$	5.81708	−	32.9903i	0.229940	−	1.30406i
$641$	3.68962	−	8.55350i	0.145731	−	0.337843i	−0.829679	−	0.558241i	$-0.811476\pi$
$641$	3.68962	−	8.55350i	0.145731	−	0.337843i	0.975410	+	0.220398i	$0.0707357\pi$
$642$		0			0
$643$	−0.369260	+	1.23341i	−0.0145622	+	0.0486411i	−0.964962	−	0.262390i	$-0.915489\pi$
$643$	−0.369260	+	1.23341i	−0.0145622	+	0.0486411i	0.950400	+	0.311031i	$0.100674\pi$
$644$	−19.2925	+	25.9143i	−0.760230	+	1.02117i
$645$		0			0
$646$	2.30020	−	1.15521i	0.0905003	−	0.0454510i
$647$	25.7409			1.01198			0.505989	−	0.862540i	$-0.331128\pi$
$647$	25.7409			1.01198			0.505989	+	0.862540i	$0.331128\pi$
$648$		0			0
$649$	17.2667			0.677776
$650$	−6.94132	+	3.48606i	−0.272261	+	0.136735i
$651$		0			0
$652$	−16.2326	+	21.8041i	−0.635716	+	0.853915i
$653$	−11.1737	+	37.3227i	−0.437259	+	1.46055i	0.401405	+	0.915900i	$0.368522\pi$
$653$	−11.1737	+	37.3227i	−0.437259	+	1.46055i	−0.838665	+	0.544648i	$0.816663\pi$
$654$		0			0
$655$	−8.23778	+	19.0973i	−0.321877	+	0.746194i
$656$	−2.50766	+	14.2217i	−0.0979077	+	0.555262i
$657$		0			0
$658$	0.977797	+	5.54536i	0.0381185	+	0.216181i
$659$	32.6776	+	7.74473i	1.27294	+	0.301692i	0.810908	−	0.585173i	$-0.198973\pi$
$659$	32.6776	+	7.74473i	1.27294	+	0.301692i	0.462029	+	0.886865i	$0.347122\pi$
$660$		0			0
$661$	−29.6045	+	19.4712i	−1.15148	+	0.757342i	−0.973948	−	0.226773i	$-0.927183\pi$
$661$	−29.6045	+	19.4712i	−1.15148	+	0.757342i	−0.177535	+	0.984115i	$0.556812\pi$
$662$	−0.0655685	−	1.12577i	−0.00254839	−	0.0437542i
$663$		0			0
$664$	2.17901	+	7.27838i	0.0845618	+	0.282456i
$665$	41.4278	+	15.0785i	1.60650	+	0.584718i
$666$		0			0
$667$	10.4045	−	3.78693i	0.402864	−	0.146630i
$668$	−18.3112	−	24.5963i	−0.708483	−	0.951658i
$669$		0			0
$670$	21.9216	−	5.19551i	0.846905	−	0.200720i
$671$	−0.775727	−	1.79834i	−0.0299466	−	0.0694241i
$672$		0			0
$673$	−22.9529	−	15.0964i	−0.884771	−	0.581923i	0.0237705	−	0.999717i	$-0.492433\pi$
$673$	−22.9529	−	15.0964i	−0.884771	−	0.581923i	−0.908542	+	0.417794i	$0.862803\pi$
$674$	5.20938	−	9.02292i	0.200658	−	0.347550i
$675$		0			0
$676$	2.43499	+	4.21753i	0.0936536	+	0.162213i
$677$	−0.555469	+	9.53704i	−0.0213484	+	0.366538i	0.970668	+	0.240426i	$0.0772870\pi$
$677$	−0.555469	+	9.53704i	−0.0213484	+	0.366538i	−0.992016	+	0.126112i	$0.959750\pi$
$678$		0			0
$679$	−38.8746	−	4.54379i	−1.49187	−	0.174375i
$680$	−3.88866	−	4.12174i	−0.149123	−	0.158061i
$681$		0			0
$682$	−1.30777	+	0.152857i	−0.0500772	+	0.00585319i
$683$	−25.4573	−	21.3612i	−0.974095	−	0.817363i	0.00909301	−	0.999959i	$-0.497106\pi$
$683$	−25.4573	−	21.3612i	−0.974095	−	0.817363i	−0.983188	+	0.182596i	$0.941550\pi$
$684$		0			0
$685$	−19.1945	+	16.1061i	−0.733383	+	0.615381i
$686$	5.12547	−	5.43268i	0.195691	−	0.207421i
$687$		0			0
$688$	−4.33826	−	2.17876i	−0.165395	−	0.0830643i
$689$	29.8606	+	14.9966i	1.13760	+	0.571324i
$690$		0			0
$691$	3.72605	−	3.94938i	0.141746	−	0.150242i	−0.652611	−	0.757693i	$-0.726327\pi$
$691$	3.72605	−	3.94938i	0.141746	−	0.150242i	0.794357	+	0.607451i	$0.207808\pi$
$692$	24.2325	−	20.3335i	0.921183	−	0.772964i
$693$		0			0
$694$	−11.6460	−	9.77218i	−0.442077	−	0.370947i
$695$	−17.0137	+	1.98862i	−0.645366	+	0.0754325i
$696$		0			0
$697$	4.26775	+	4.52355i	0.161652	+	0.171342i
$698$	7.39072	+	0.863851i	0.279743	+	0.0326972i
$699$		0			0
$700$	1.04779	−	17.9899i	0.0396029	−	0.679956i
$701$	16.8694	+	29.2187i	0.637150	+	1.10358i	0.986055	+	0.166418i	$0.0532200\pi$
$701$	16.8694	+	29.2187i	0.637150	+	1.10358i	−0.348906	+	0.937158i	$0.613447\pi$
$702$		0			0
$703$	27.6440	−	47.8808i	1.04261	−	1.80586i
$704$	3.64821	+	2.39946i	0.137497	+	0.0904332i
$705$		0			0
$706$	4.36930	+	10.1292i	0.164441	+	0.381216i
$707$	18.2234	−	4.31902i	0.685360	−	0.162433i
$708$		0			0
$709$	−11.5762	−	15.5495i	−0.434754	−	0.583975i	0.529714	−	0.848176i	$-0.322299\pi$
$709$	−11.5762	−	15.5495i	−0.434754	−	0.583975i	−0.964468	+	0.264201i	$0.914892\pi$
$710$	20.6730	−	7.52437i	0.775846	−	0.282385i
$711$		0			0
$712$	25.7319	+	9.36564i	0.964343	+	0.350992i
$713$	−1.19257	−	3.98345i	−0.0446620	−	0.149181i
$714$		0			0
$715$	−2.31082	−	39.6753i	−0.0864198	−	1.48377i
$716$	14.4331	−	9.49282i	0.539391	−	0.354763i
$717$		0			0
$718$	8.10592	+	1.92114i	0.302510	+	0.0716963i
$719$	0.831346	+	4.71480i	0.0310040	+	0.175832i	0.996378	−	0.0850387i	$-0.0271014\pi$
$719$	0.831346	+	4.71480i	0.0310040	+	0.175832i	−0.965374	+	0.260871i	$0.915990\pi$
$720$		0			0
$721$	0.961210	−	5.45129i	0.0357973	−	0.203017i
$722$	1.01892	−	2.36211i	0.0379201	−	0.0879087i
$723$		0			0
$724$	−0.394408	+	1.31742i	−0.0146581	+	0.0489614i
$725$	−3.68801	+	4.95385i	−0.136969	+	0.183982i
$726$		0			0
$727$	−6.75608	+	3.39303i	−0.250569	+	0.125841i	−0.569651	−	0.821887i	$-0.692922\pi$
$727$	−6.75608	+	3.39303i	−0.250569	+	0.125841i	0.319082	+	0.947727i	$0.396625\pi$
$728$	26.0550			0.965664
$729$		0			0
$730$	11.1186			0.411516
$731$	−1.86826	+	0.938278i	−0.0691003	+	0.0347035i
$732$		0			0
$733$	23.0749	−	30.9950i	0.852292	−	1.14483i	−0.135766	−	0.990741i	$-0.543349\pi$
$733$	23.0749	−	30.9950i	0.852292	−	1.14483i	0.988057	−	0.154086i	$-0.0492432\pi$
$734$	1.78974	−	5.97815i	0.0660605	−	0.220657i
$735$		0			0
$736$	13.1763	−	30.5460i	0.485684	−	1.12594i
$737$	−8.14649	+	46.2010i	−0.300080	+	1.70184i
$738$		0			0
$739$	−8.79173	−	49.8604i	−0.323409	−	1.83414i	−0.520627	−	0.853784i	$-0.674302\pi$
$739$	−8.79173	−	49.8604i	−0.323409	−	1.83414i	0.197218	−	0.980360i	$-0.436809\pi$
$740$	−54.0299	−	12.8053i	−1.98618	−	0.470733i
$741$		0			0
$742$	12.4369	−	8.17991i	0.456575	−	0.300294i
$743$	0.892750	+	15.3279i	0.0327518	+	0.562327i	0.974273	+	0.225372i	$0.0723598\pi$
$743$	0.892750	+	15.3279i	0.0327518	+	0.562327i	−0.941521	+	0.336955i	$0.890603\pi$
$744$		0			0
$745$	11.4881	+	38.3730i	0.420893	+	1.40588i
$746$	10.8906	+	3.96386i	0.398733	+	0.145127i
$747$		0			0
$748$	5.05853	−	1.84116i	0.184958	−	0.0673193i
$749$	−13.3681	−	17.9565i	−0.488460	−	0.656115i
$750$		0			0
$751$	−45.3980	+	10.7595i	−1.65660	+	0.392621i	−0.949319	−	0.314314i	$-0.898225\pi$
$751$	−45.3980	+	10.7595i	−1.65660	+	0.392621i	−0.707278	+	0.706935i	$0.750077\pi$
$752$	2.72520	+	6.31772i	0.0993778	+	0.230384i
$753$		0			0
$754$	−3.40348	−	2.23851i	−0.123948	−	0.0815216i
$755$	9.11335	−	15.7848i	0.331669	−	0.574467i
$756$		0			0
$757$	5.85224	+	10.1364i	0.212703	+	0.368413i	0.952560	−	0.304352i	$-0.0984399\pi$
$757$	5.85224	+	10.1364i	0.212703	+	0.368413i	−0.739856	+	0.672765i	$0.765107\pi$
$758$	−0.859106	+	14.7503i	−0.0312041	+	0.535754i
$759$		0			0
$760$	−29.2065	−	3.41375i	−1.05943	−	0.123830i
$761$	17.9650	+	19.0418i	0.651232	+	0.690265i	0.965894	−	0.258938i	$-0.0833727\pi$
$761$	17.9650	+	19.0418i	0.651232	+	0.690265i	−0.314662	+	0.949204i	$0.601891\pi$
$762$		0			0
$763$	−35.3524	+	4.13211i	−1.27984	+	0.149592i
$764$	−0.983309	−	0.825094i	−0.0355749	−	0.0298509i
$765$		0			0
$766$	10.2314	−	8.58519i	0.369676	−	0.310195i
$767$	13.7675	−	14.5927i	0.497114	−	0.526910i
$768$		0			0
$769$	40.6989	+	20.4398i	1.46764	+	0.737077i	0.989946	−	0.141448i	$-0.0451758\pi$
$769$	40.6989	+	20.4398i	1.46764	+	0.737077i	0.477696	+	0.878525i	$0.341472\pi$
$770$	−15.8215	−	7.94586i	−0.570168	−	0.286349i
$771$		0			0
$772$	10.7709	−	11.4165i	0.387653	−	0.410889i
$773$	−10.7154	+	8.99131i	−0.385407	+	0.323395i	−0.814821	−	0.579713i	$-0.803165\pi$
$773$	−10.7154	+	8.99131i	−0.385407	+	0.323395i	0.429414	+	0.903108i	$0.358720\pi$
$774$		0			0
$775$	1.77672	+	1.49085i	0.0638217	+	0.0535528i
$776$	25.9291	−	3.03067i	0.930799	−	0.108795i
$777$		0			0
$778$	−12.8814	−	13.6535i	−0.461822	−	0.489503i
$779$	32.0537	+	3.74654i	1.14844	+	0.134234i
$780$		0			0
$781$	−2.66373	+	45.7345i	−0.0953159	+	1.63651i
$782$	−1.63223	−	2.82710i	−0.0583683	−	0.101097i
$783$		0			0
$784$	−3.03440	+	5.25573i	−0.108371	+	0.187705i
$785$	−0.402948	−	0.265023i	−0.0143818	−	0.00945909i
$786$		0			0
$787$	5.62542	+	13.0412i	0.200525	+	0.464869i	0.988573	−	0.150745i	$-0.0481674\pi$
$787$	5.62542	+	13.0412i	0.200525	+	0.464869i	−0.788048	+	0.615614i	$0.788908\pi$
$788$	1.82821	−	0.433295i	0.0651274	−	0.0154355i
$789$		0			0
$790$	−0.733578	−	0.985367i	−0.0260995	−	0.0350578i
$791$	−17.1290	+	6.23446i	−0.609039	+	0.221672i
$792$		0			0
$793$	−2.13836	−	0.778298i	−0.0759353	−	0.0276382i
$794$	0.00900064	+	0.0300642i	0.000319421	+	0.00106694i
$795$		0			0
$796$	0.749293	+	12.8649i	0.0265580	+	0.455983i
$797$	−34.5075	+	22.6959i	−1.22232	+	0.803931i	−0.985837	−	0.167705i	$-0.946364\pi$
$797$	−34.5075	+	22.6959i	−1.22232	+	0.803931i	−0.236480	+	0.971636i	$0.575994\pi$
$798$		0			0
$799$	2.88318	+	0.683326i	0.102000	+	0.0241743i
$800$	3.22216	+	18.2738i	0.113921	+	0.646075i
$801$		0			0
$802$	2.82324	−	16.0114i	0.0996920	−	0.565381i
$803$	−9.17048	+	21.2596i	−0.323619	+	0.750234i
$804$		0			0
$805$	16.0359	−	53.5636i	0.565190	−	1.88787i
$806$	−0.913559	+	1.22712i	−0.0321787	+	0.0432236i
$807$		0			0
$808$	−11.1629	+	5.60619i	−0.392708	+	0.197225i
$809$	−23.8379			−0.838097			−0.419048	−	0.907964i	$-0.637636\pi$
$809$	−23.8379			−0.838097			−0.419048	+	0.907964i	$0.637636\pi$
$810$		0			0
$811$	−3.33188			−0.116998			−0.0584991	−	0.998287i	$-0.518631\pi$
$811$	−3.33188			−0.116998			−0.0584991	+	0.998287i	$0.518631\pi$
$812$	8.44549	−	4.24148i	0.296378	−	0.148847i
$813$		0			0
$814$	−13.2588	+	17.8096i	−0.464720	+	0.624227i
$815$	13.4925	−	45.0680i	0.472621	−	1.57866i
$816$		0			0
$817$	−4.29700	+	9.96157i	−0.150333	+	0.348511i
$818$	3.09855	−	17.5727i	0.108338	−	0.614417i
$819$		0			0
$820$	−5.62815	−	31.9188i	−0.196543	−	1.11465i
$821$	−8.73468	−	2.07016i	−0.304842	−	0.0722490i	0.0753477	−	0.997157i	$-0.475993\pi$
$821$	−8.73468	−	2.07016i	−0.304842	−	0.0722490i	−0.380190	+	0.924908i	$0.624141\pi$
$822$		0			0
$823$	1.08458	−	0.713338i	0.0378060	−	0.0248654i	−0.530465	−	0.847707i	$-0.677983\pi$
$823$	1.08458	−	0.713338i	0.0378060	−	0.0248654i	0.568271	+	0.822841i	$0.307612\pi$
$824$	0.214674	+	3.68581i	0.00747852	+	0.128401i
$825$		0			0
$826$	−2.56327	−	8.56192i	−0.0891876	−	0.297907i
$827$	−29.6308	−	10.7847i	−1.03036	−	0.375022i	−0.229144	−	0.973392i	$-0.573593\pi$
$827$	−29.6308	−	10.7847i	−1.03036	−	0.375022i	−0.801219	+	0.598371i	$0.795815\pi$
$828$		0			0
$829$	−25.1437	+	9.15156i	−0.873277	+	0.317847i	−0.739493	−	0.673164i	$-0.764935\pi$
$829$	−25.1437	+	9.15156i	−0.873277	+	0.317847i	−0.133783	+	0.991011i	$0.542713\pi$
$830$	−3.58203	−	4.81150i	−0.124334	−	0.167010i
$831$		0			0
$832$	4.93674	−	1.17003i	0.171151	−	0.0405634i
$833$	1.03516	+	2.39977i	0.0358662	+	0.0831472i
$834$		0			0
$835$	44.3382	+	29.1617i	1.53439	+	1.00918i
$836$	13.9673	−	24.1921i	0.483069	−	0.836700i
$837$		0			0
$838$	−0.957629	−	1.65866i	−0.0330807	−	0.0572975i
$839$	0.225566	−	3.87282i	0.00778740	−	0.133705i	−0.992174	−	0.124867i	$-0.960150\pi$
$839$	0.225566	−	3.87282i	0.00778740	−	0.133705i	0.999961	−	0.00883795i	$-0.00281324\pi$
$840$		0			0
$841$	25.5869	+	2.99068i	0.882306	+	0.103127i
$842$	−9.84058	−	10.4304i	−0.339129	−	0.359455i
$843$		0			0
$844$	−17.0602	+	1.99405i	−0.587236	+	0.0686380i
$845$	−6.45643	−	5.41758i	−0.222108	−	0.186371i
$846$		0			0
$847$	1.86921	−	1.56845i	0.0642267	−	0.0538926i
$848$	12.4821	−	13.2303i	0.428637	−	0.454329i
$849$		0			0
$850$	1.62718	+	0.817201i	0.0558119	+	0.0280298i
$851$	−62.6603	−	31.4692i	−2.14797	−	1.07875i
$852$		0			0
$853$	2.36014	−	2.50160i	0.0808097	−	0.0856532i	−0.685707	−	0.727878i	$-0.740507\pi$
$853$	2.36014	−	2.50160i	0.0808097	−	0.0856532i	0.766517	+	0.642224i	$0.221988\pi$
$854$	−0.776573	+	0.651622i	−0.0265738	+	0.0222980i
$855$		0			0
$856$	11.4381	+	9.59772i	0.390947	+	0.328043i
$857$	14.5601	−	1.70183i	0.497362	−	0.0581333i	0.136286	−	0.990670i	$-0.456483\pi$
$857$	14.5601	−	1.70183i	0.497362	−	0.0581333i	0.361076	+	0.932536i	$0.382409\pi$
$858$		0			0
$859$	−6.54336	−	6.93555i	−0.223256	−	0.236638i	0.606058	−	0.795421i	$-0.292750\pi$
$859$	−6.54336	−	6.93555i	−0.223256	−	0.236638i	−0.829314	+	0.558783i	$0.811269\pi$
$860$	10.8220	+	1.26491i	0.369026	+	0.0431330i
$861$		0			0
$862$	−1.08296	+	18.5938i	−0.0368859	+	0.633306i
$863$	8.00876	+	13.8716i	0.272621	+	0.472194i	0.969532	−	0.244964i	$-0.0787760\pi$
$863$	8.00876	+	13.8716i	0.272621	+	0.472194i	−0.696911	+	0.717158i	$0.745443\pi$
$864$		0			0
$865$	−27.3732	+	47.4117i	−0.930716	+	1.61205i
$866$	6.12821	+	4.03059i	0.208245	+	0.136965i
$867$		0			0
$868$	−1.40576	−	3.25892i	−0.0477147	−	0.110615i
$869$	2.48915	−	0.589939i	0.0844386	−	0.0200123i
$870$		0			0
$871$	32.5505	+	43.7229i	1.10293	+	1.48150i
$872$	22.3086	−	8.11966i	0.755464	−	0.274967i
$873$		0			0
$874$	−15.9184	−	5.79383i	−0.538448	−	0.195979i
$875$	−4.08796	−	13.6547i	−0.138198	−	0.461614i
$876$		0			0
$877$	1.92577	+	33.0643i	0.0650287	+	1.11650i	0.860147	+	0.510046i	$0.170372\pi$
$877$	1.92577	+	33.0643i	0.0650287	+	1.11650i	−0.795118	+	0.606454i	$0.792591\pi$
$878$	−17.4883	+	11.5023i	−0.590203	+	0.388182i
$879$		0			0
$880$	−21.0503	−	4.98902i	−0.709607	−	0.168180i
$881$	−2.00755	−	11.3854i	−0.0676360	−	0.383583i	−0.999770	−	0.0214681i	$-0.993166\pi$
$881$	−2.00755	−	11.3854i	−0.0676360	−	0.383583i	0.932134	−	0.362115i	$-0.117945\pi$
$882$		0			0
$883$	−7.24692	+	41.0993i	−0.243878	+	1.38310i	0.579206	+	0.815182i	$0.303363\pi$
$883$	−7.24692	+	41.0993i	−0.243878	+	1.38310i	−0.823084	+	0.567920i	$0.807748\pi$
$884$	2.47736	−	5.74317i	0.0833227	−	0.193164i
$885$		0			0
$886$	−5.59410	+	18.6856i	−0.187937	+	0.627755i
$887$	−14.3927	+	19.3327i	−0.483259	+	0.649130i	−0.975155	−	0.221524i	$-0.928897\pi$
$887$	−14.3927	+	19.3327i	−0.483259	+	0.649130i	0.491895	+	0.870654i	$0.336304\pi$
$888$		0			0
$889$	30.0413	−	15.0873i	1.00755	−	0.506013i
$890$	−21.6198			−0.724697
$891$		0			0
$892$	7.80468			0.261320
$893$	13.7405	−	6.90072i	0.459807	−	0.230924i
$894$		0			0
$895$	−17.8534	+	23.9812i	−0.596772	+	0.801604i
$896$	10.3558	−	34.5906i	0.345961	−	1.15559i
$897$		0			0
$898$	3.94788	−	9.15221i	0.131742	−	0.305413i
$899$	−0.211221	+	1.19789i	−0.00704460	+	0.0399519i
$900$		0			0
$901$	−1.36020	−	7.71410i	−0.0453149	−	0.256994i
$902$	−12.6108	−	2.98880i	−0.419892	−	0.0995163i
$903$		0			0
$904$	10.1580	−	6.68102i	0.337850	−	0.222207i
$905$	−0.138383	−	2.37595i	−0.00460001	−	0.0789792i
$906$		0			0
$907$	−6.62271	−	22.1214i	−0.219904	−	0.734529i	−0.994746	−	0.102375i	$-0.967356\pi$
$907$	−6.62271	−	22.1214i	−0.219904	−	0.734529i	0.774842	−	0.632155i	$-0.217829\pi$
$908$	−22.2614	−	8.10250i	−0.738771	−	0.268891i
$909$		0			0
$910$	−19.3305	+	7.03572i	−0.640799	+	0.233232i
$911$	13.6745	+	18.3680i	0.453055	+	0.608559i	0.968697	−	0.248246i	$-0.0798540\pi$
$911$	13.6745	+	18.3680i	0.453055	+	0.608559i	−0.515642	+	0.856804i	$0.672447\pi$
$912$		0			0
$913$	12.1544	−	2.88065i	0.402252	−	0.0953355i
$914$	−1.87698	−	4.35133i	−0.0620850	−	0.143929i
$915$		0			0
$916$	−7.26878	−	4.78075i	−0.240167	−	0.157961i
$917$	−11.2088	+	19.4143i	−0.370148	+	0.641116i
$918$		0			0
$919$	−9.84136	−	17.0457i	−0.324636	−	0.562287i	0.656802	−	0.754063i	$-0.271909\pi$
$919$	−9.84136	−	17.0457i	−0.324636	−	0.562287i	−0.981439	+	0.191776i	$0.938575\pi$
$920$	−2.16840	+	37.2301i	−0.0714902	+	1.22744i
$921$		0			0
$922$	11.4670	+	1.34030i	0.377645	+	0.0441404i
$923$	36.5279	+	38.7173i	1.20233	+	1.27440i
$924$		0			0
$925$	38.8467	−	4.54052i	1.27727	−	0.149292i
$926$	−1.12588	−	0.944728i	−0.0369988	−	0.0310457i
$927$		0			0
$928$	−7.45472	+	6.25525i	−0.244713	+	0.205339i
$929$	−19.8444	+	21.0338i	−0.651074	+	0.690098i	−0.965860	−	0.259065i	$-0.916586\pi$
$929$	−19.8444	+	21.0338i	−0.651074	+	0.690098i	0.314786	+	0.949163i	$0.398067\pi$
$930$		0			0
$931$	12.1196	+	6.08669i	0.397204	+	0.199483i
$932$	6.67733	+	3.35348i	0.218723	+	0.109847i
$933$		0			0
$934$	−4.76771	+	5.05347i	−0.156004	+	0.165355i
$935$	−7.13679	+	5.98848i	−0.233398	+	0.195844i
$936$		0			0
$937$	14.9990	+	12.5856i	0.489995	+	0.411155i	0.854025	−	0.520233i	$-0.174155\pi$
$937$	14.9990	+	12.5856i	0.489995	+	0.411155i	−0.364029	+	0.931388i	$0.618599\pi$
$938$	24.1188	−	2.81908i	0.787506	−	0.0920463i
$939$		0			0
$940$	−10.5972	−	11.2323i	−0.345641	−	0.366358i
$941$	−10.0278	−	1.17209i	−0.326898	−	0.0382089i	−0.0489390	−	0.998802i	$-0.515584\pi$
$941$	−10.0278	−	1.17209i	−0.326898	−	0.0382089i	−0.277959	+	0.960593i	$0.589658\pi$
$942$		0			0
$943$	2.37979	−	40.8595i	0.0774967	−	1.33057i
$944$	−5.46032	−	9.45755i	−0.177718	−	0.307817i
$945$		0			0
$946$	2.17839	−	3.77309i	0.0708257	−	0.122674i
$947$	17.5511	+	11.5436i	0.570335	+	0.375115i	0.801677	−	0.597757i	$-0.203941\pi$
$947$	17.5511	+	11.5436i	0.570335	+	0.375115i	−0.231342	+	0.972872i	$0.574312\pi$
$948$		0			0
$949$	10.6552	+	24.7014i	0.345881	+	0.801843i
$950$	9.19419	−	2.17906i	0.298299	−	0.0706981i
$951$		0			0
$952$	−3.64733	−	4.89922i	−0.118211	−	0.158785i
$953$	−6.34571	+	2.30965i	−0.205558	+	0.0748169i	−0.442747	−	0.896647i	$-0.645996\pi$
$953$	−6.34571	+	2.30965i	−0.205558	+	0.0748169i	0.237189	+	0.971463i	$0.423774\pi$
$954$		0			0
$955$	2.08753	+	0.759798i	0.0675508	+	0.0245865i
$956$	13.9845	+	46.7114i	0.452290	+	1.51075i
$957$		0			0
$958$	−0.905188	−	15.5415i	−0.0292453	−	0.502122i
$959$	−22.5645	+	14.8409i	−0.728645	+	0.479237i
$960$		0			0
$961$	−29.7199	−	7.04375i	−0.958706	−	0.227218i
$962$	4.47973	+	25.4058i	0.144432	+	0.819117i
$963$		0			0
$964$	−7.27912	+	41.2819i	−0.234445	+	1.32960i
$965$	−10.7589	+	24.9419i	−0.346341	+	0.802909i
$966$		0			0
$967$	−3.38236	+	11.2979i	−0.108769	+	0.363315i	−0.994993	−	0.0999421i	$-0.968134\pi$
$967$	−3.38236	+	11.2979i	−0.108769	+	0.363315i	0.886224	+	0.463257i	$0.153319\pi$
$968$	−0.971882	+	1.30546i	−0.0312375	+	0.0419592i
$969$		0			0
$970$	−18.4186	+	9.25019i	−0.591387	+	0.297006i
$971$	−24.4687			−0.785239			−0.392620	−	0.919701i	$-0.628431\pi$
$971$	−24.4687			−0.785239			−0.392620	+	0.919701i	$0.628431\pi$
$972$		0			0
$973$	−18.4632			−0.591905
$974$	−3.05566	+	1.53461i	−0.0979096	+	0.0491721i
$975$		0			0
$976$	−0.739699	+	0.993589i	−0.0236772	+	0.0318040i
$977$	11.1615	−	37.2820i	0.357088	−	1.19276i	−0.571174	−	0.820829i	$-0.693512\pi$
$977$	11.1615	−	37.2820i	0.357088	−	1.19276i	0.928262	−	0.371927i	$-0.121303\pi$
$978$		0			0
$979$	17.8318	−	41.3387i	0.569907	−	1.32119i
$980$	2.36521	−	13.4138i	0.0755538	−	0.428487i
$981$		0			0
$982$	0.0480294	+	0.272388i	0.00153268	+	0.00869226i
$983$	−18.2124	−	4.31641i	−0.580885	−	0.137672i	−0.0703395	−	0.997523i	$-0.522408\pi$
$983$	−18.2124	−	4.31641i	−0.580885	−	0.137672i	−0.510545	+	0.859851i	$0.670556\pi$
$984$		0			0
$985$	−2.71672	+	1.78681i	−0.0865618	+	0.0569326i
$986$	0.0555250	+	0.953328i	0.00176828	+	0.0303601i
$987$		0			0
$988$	−9.30881	−	31.0936i	−0.296153	−	0.989219i
$989$	12.9292	+	4.70584i	0.411125	+	0.149637i
$990$		0			0
$991$	−2.15353	+	0.783819i	−0.0684090	+	0.0248988i	−0.375998	−	0.926620i	$-0.622700\pi$
$991$	−2.15353	+	0.783819i	−0.0684090	+	0.0248988i	0.307589	+	0.951519i	$0.400478\pi$
$992$	2.18238	+	2.93144i	0.0692906	+	0.0930735i
$993$		0			0
$994$	23.0736	−	5.46853i	0.731849	−	0.173451i
$995$	−8.83352	−	20.4784i	−0.280041	−	0.649209i
$996$		0			0
$997$	−26.1338	−	17.1885i	−0.827666	−	0.544365i	0.0635312	−	0.997980i	$-0.479764\pi$
$997$	−26.1338	−	17.1885i	−0.827666	−	0.544365i	−0.891198	+	0.453615i	$0.850134\pi$
$998$	−1.55659	+	2.69609i	−0.0492729	+	0.0853432i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.2.g.a.73.4		144
3.2	odd	2		81.2.g.a.25.5	yes	144
9.2	odd	6		729.2.g.c.703.4		144
9.4	even	3		729.2.g.a.217.5		144
9.5	odd	6		729.2.g.d.217.4		144
9.7	even	3		729.2.g.b.703.5		144
81.13	even	27	inner	243.2.g.a.10.4		144
81.14	odd	54		729.2.g.d.514.4		144
81.16	even	27		6561.2.a.d.1.41		72
81.40	even	27		729.2.g.b.28.5		144
81.41	odd	54		729.2.g.c.28.4		144
81.65	odd	54		6561.2.a.c.1.32		72
81.67	even	27		729.2.g.a.514.5		144
81.68	odd	54		81.2.g.a.13.5	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.13.5	✓	144	81.68	odd	54
81.2.g.a.25.5	yes	144	3.2	odd	2
243.2.g.a.10.4		144	81.13	even	27	inner
243.2.g.a.73.4		144	1.1	even	1	trivial
729.2.g.a.217.5		144	9.4	even	3
729.2.g.a.514.5		144	81.67	even	27
729.2.g.b.28.5		144	81.40	even	27
729.2.g.b.703.5		144	9.7	even	3
729.2.g.c.28.4		144	81.41	odd	54
729.2.g.c.703.4		144	9.2	odd	6
729.2.g.d.217.4		144	9.5	odd	6
729.2.g.d.514.4		144	81.14	odd	54
6561.2.a.c.1.32		72	81.65	odd	54
6561.2.a.d.1.41		72	81.16	even	27

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:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.507233 - 0.254742i) q^{2} +(-1.00193 + 1.34582i) q^{4} +(0.832798 - 2.78174i) q^{5} +(1.23966 - 2.87385i) q^{7} +(-0.362501 + 2.05585i) q^{8} +(-0.286203 - 1.62314i) q^{10} +(3.33963 + 0.791507i) q^{11} +(3.33176 - 2.19133i) q^{13} +(-0.103295 - 1.77350i) q^{14} +(-0.622571 - 2.07953i) q^{16} +(-0.878443 - 0.319727i) q^{17} +(-4.55845 + 1.65914i) q^{19} +(2.90932 + 3.90789i) q^{20} +(1.89560 - 0.449266i) q^{22} +(2.43678 + 5.64910i) q^{23} +(-2.86709 - 1.88571i) q^{25} +(1.13175 - 1.96026i) q^{26} +(2.62564 + 4.54773i) q^{28} +(0.104644 - 1.79666i) q^{29} +(-0.671302 - 0.0784640i) q^{31} +(-3.71068 - 3.93309i) q^{32} +(-0.527023 + 0.0616002i) q^{34} +(-6.96191 - 5.84174i) q^{35} +(-8.73079 + 7.32600i) q^{37} +(-1.88954 + 2.00280i) q^{38} +(5.41694 + 2.72049i) q^{40} +(-5.94501 - 2.98570i) q^{41} +(1.53472 - 1.62671i) q^{43} +(-4.41129 + 3.70151i) q^{44} +(2.67508 + 2.24466i) q^{46} +(-3.14822 + 0.367974i) q^{47} +(-1.91856 - 2.03355i) q^{49} +(-1.93465 - 0.226128i) q^{50} +(-0.389036 + 6.67950i) q^{52} +(4.18963 + 7.25666i) q^{53} +(4.98301 - 8.63082i) q^{55} +(5.45881 + 3.59032i) q^{56} +(-0.404606 - 0.937983i) q^{58} +(4.89526 - 1.16020i) q^{59} +(-0.340761 - 0.457722i) q^{61} +(-0.360495 + 0.131209i) q^{62} +(1.19553 + 0.435136i) q^{64} +(-3.32104 - 11.0930i) q^{65} +(0.794778 + 13.6458i) q^{67} +(1.31043 - 0.861882i) q^{68} +(-5.01945 - 1.18963i) q^{70} +(2.31784 + 13.1452i) q^{71} +(-1.17142 + 6.64347i) q^{73} +(-2.56230 + 5.94009i) q^{74} +(2.33432 - 7.79718i) q^{76} +(6.41467 - 8.61639i) q^{77} +(0.666057 - 0.334506i) q^{79} -6.30319 q^{80} -3.77609 q^{82} +(3.25233 - 1.63338i) q^{83} +(-1.62096 + 2.17733i) q^{85} +(0.364070 - 1.21608i) q^{86} +(-2.83784 + 6.57885i) q^{88} +(2.27781 - 12.9181i) q^{89} +(-2.16732 - 12.2915i) q^{91} +(-10.0441 - 2.38050i) q^{92} +(-1.50314 + 0.988632i) q^{94} +(0.819027 + 14.0621i) q^{95} +(-3.58656 - 11.9799i) q^{97} +(-1.49119 - 0.542748i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{2} - 18 q^{4} + 18 q^{5} - 18 q^{7} + 18 q^{8} - 18 q^{10} + 18 q^{11} - 18 q^{13} + 18 q^{14} - 18 q^{16} + 18 q^{17} - 18 q^{19} - 18 q^{20} - 18 q^{22} - 9 q^{23} - 18 q^{25} - 45 q^{26}+ \cdots - 81 q^{98}+O(q^{100}) \) 144 * q + 18 * q^2 - 18 * q^4 + 18 * q^5 - 18 * q^7 + 18 * q^8 - 18 * q^10 + 18 * q^11 - 18 * q^13 + 18 * q^14 - 18 * q^16 + 18 * q^17 - 18 * q^19 - 18 * q^20 - 18 * q^22 - 9 * q^23 - 18 * q^25 - 45 * q^26 - 9 * q^28 - 9 * q^29 - 18 * q^31 - 36 * q^32 - 18 * q^34 - 9 * q^35 - 18 * q^37 + 9 * q^38 - 18 * q^40 - 18 * q^43 - 54 * q^44 - 18 * q^46 - 36 * q^47 - 18 * q^49 - 99 * q^50 - 45 * q^53 - 9 * q^55 - 126 * q^56 - 18 * q^58 - 45 * q^59 - 18 * q^61 - 81 * q^62 - 18 * q^64 + 9 * q^67 + 99 * q^68 + 36 * q^70 + 90 * q^71 - 18 * q^73 + 162 * q^74 + 63 * q^76 + 162 * q^77 + 36 * q^79 + 288 * q^80 - 36 * q^82 + 90 * q^83 + 36 * q^85 + 162 * q^86 + 63 * q^88 + 81 * q^89 - 18 * q^91 + 144 * q^92 + 36 * q^94 - 18 * q^95 + 9 * q^97 - 81 * q^98

Introduction

L-functions

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