LMFDB - Embedded newform 891.2.n.k.784.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [891,2,Mod(136,891)] 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("891.136"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(891, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([20, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,2,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			784.1
Character	$\chi$	$=$	891.784
Dual form			891.2.n.k.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.274837 - 2.61490i) q^{2} +(-4.80585 + 1.02151i) q^{4} +(0.0250408 - 0.238247i) q^{5} +(-0.793477 - 0.881245i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(-2.79995 + 1.77771i) q^{11} +(-5.51506 - 2.45546i) q^{13} +(-2.08629 + 2.31706i) q^{14} +(9.42161 - 4.19477i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(0.123031 + 1.17056i) q^{20} +(5.41806 + 6.83301i) q^{22} +(2.77520 + 4.80679i) q^{23} +(4.83460 + 1.02763i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(4.16541 + 4.62616i) q^{29} +(3.61535 + 1.60966i) q^{31} +(-5.89858 - 10.2166i) q^{32} +(2.41154 - 4.17691i) q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(-7.83020 + 3.48623i) q^{38} +(1.79486 - 0.381509i) q^{40} +(-7.13663 + 7.92603i) q^{41} +(-6.07195 + 10.5169i) q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(-1.61859 - 0.344042i) q^{47} +(0.584711 - 5.56316i) q^{49} +(1.35841 - 12.9244i) q^{50} +(29.0128 + 6.16687i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} +(4.54157 - 7.86622i) q^{56} +(10.9521 - 12.1636i) q^{58} +(3.84199 - 0.816641i) q^{59} +(-9.79858 + 4.36261i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +(-0.723109 + 1.25246i) q^{65} +(-4.61051 - 7.98564i) q^{67} +(-8.23341 - 3.66575i) q^{68} +(0.499790 + 0.555073i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(13.9735 + 2.97015i) q^{74} +(8.00827 + 13.8707i) q^{76} +(3.78830 + 1.05687i) q^{77} +(-0.462326 - 4.39874i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(-14.0859 + 6.27144i) q^{83} +(0.294041 - 0.326566i) q^{85} +(29.1695 + 12.9871i) q^{86} +(-19.5777 - 16.1893i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(-18.2474 - 20.2658i) q^{92} +(-0.454786 + 4.32700i) q^{94} +(-0.763872 + 0.162366i) q^{95} +(-0.636901 - 6.05971i) q^{97} -14.7078 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} + 8 q^{4} - 4 q^{5} - 7 q^{7} + 20 q^{8} - 32 q^{10} - 5 q^{11} - 7 q^{13} - 13 q^{14} - 2 q^{16} - 10 q^{17} + 8 q^{19} - 27 q^{20} + 2 q^{22} - 6 q^{23} + 2 q^{25} - 68 q^{26} - 18 q^{28}+ \cdots + 136 q^{98}+O(q^{100}) $ 48 * q + 2 * q^2 + 8 * q^4 - 4 * q^5 - 7 * q^7 + 20 * q^8 - 32 * q^10 - 5 * q^11 - 7 * q^13 - 13 * q^14 - 2 * q^16 - 10 * q^17 + 8 * q^19 - 27 * q^20 + 2 * q^22 - 6 * q^23 + 2 * q^25 - 68 * q^26 - 18 * q^28 - 22 * q^29 - 2 * q^31 - 18 * q^32 + 42 * q^34 + 12 * q^37 + 5 * q^38 - 53 * q^40 - 10 * q^41 + 30 * q^43 + 118 * q^44 + 62 * q^46 - 4 * q^47 + 3 * q^49 - 9 * q^50 + 26 * q^52 + 34 * q^53 + 24 * q^55 + 48 * q^56 - 53 * q^58 - 11 * q^59 - 3 * q^61 - 4 * q^62 + 76 * q^64 + 68 * q^65 + 14 * q^67 - 22 * q^68 + 20 * q^70 - 72 * q^71 + 70 * q^73 - 3 * q^74 + 102 * q^76 + 88 * q^77 + 9 * q^79 - 74 * q^80 - 12 * q^82 - 32 * q^83 + 45 * q^85 + 110 * q^86 - 54 * q^88 + 68 * q^89 + 26 * q^91 + q^92 + 25 * q^94 + 84 * q^95 - 15 * q^97 + 136 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.274837	−	2.61490i	−0.194339	−	1.84901i	−0.463726	−	0.885978i	$-0.653488\pi$
$2$	−0.274837	−	2.61490i	−0.194339	−	1.84901i	0.269388	−	0.963032i	$-0.413179\pi$
$3$		0			0
$3$		0			0
$4$	−4.80585	+	1.02151i	−2.40292	+	0.510757i
$5$	0.0250408	−	0.238247i	0.0111986	−	0.106547i	−0.987495	−	0.157652i	$-0.949608\pi$
$5$	0.0250408	−	0.238247i	0.0111986	−	0.106547i	0.998693	+	0.0511047i	$0.0162742\pi$
$6$		0			0
$7$	−0.793477	−	0.881245i	−0.299906	−	0.333079i	0.574291	−	0.818652i	$-0.305278\pi$
$7$	−0.793477	−	0.881245i	−0.299906	−	0.333079i	−0.874197	+	0.485572i	$0.838611\pi$
$8$	2.36698	+	7.28482i	0.836854	+	2.57557i
$9$		0			0
$10$	−0.629874			−0.199184
$11$	−2.79995	+	1.77771i	−0.844218	+	0.536000i
$11$	−2.79995	+	1.77771i	−0.844218	+	0.536000i
$12$		0			0
$13$	−5.51506	−	2.45546i	−1.52960	−	0.681023i	−0.542346	−	0.840155i	$-0.682464\pi$
$13$	−5.51506	−	2.45546i	−1.52960	−	0.681023i	−0.987257	+	0.159132i	$0.949131\pi$
$14$	−2.08629	+	2.31706i	−0.557584	+	0.619260i
$15$		0			0
$16$	9.42161	−	4.19477i	2.35540	−	1.04869i
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	0.753023	−	0.657995i	$-0.228595\pi$
$17$	1.48403	+	1.07821i	0.359929	+	0.261504i	−0.393093	+	0.919499i	$0.628595\pi$
$18$		0			0
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	−0.997614	−	0.0690339i	$-0.978008\pi$
$19$	−1.00736	−	3.10034i	−0.231105	−	0.711267i	0.766510	−	0.642233i	$-0.221992\pi$
$20$	0.123031	+	1.17056i	0.0275105	+	0.261745i
$21$		0			0
$22$	5.41806	+	6.83301i	1.15513	+	1.45680i
$23$	2.77520	+	4.80679i	0.578670	+	1.00229i	0.995632	+	0.0933616i	$0.0297613\pi$
$23$	2.77520	+	4.80679i	0.578670	+	1.00229i	−0.416963	+	0.908924i	$0.636905\pi$
$24$		0			0
$25$	4.83460	+	1.02763i	0.966921	+	0.205525i
$26$	−4.90504	+	15.0962i	−0.961958	+	2.96060i
$27$		0			0
$28$	4.71353	+	3.42458i	0.890774	+	0.647185i
$29$	4.16541	+	4.62616i	0.773498	+	0.859056i	0.993189	−	0.116513i	$-0.0371717\pi$
$29$	4.16541	+	4.62616i	0.773498	+	0.859056i	−0.219692	+	0.975569i	$0.570505\pi$
$30$		0			0
$31$	3.61535	+	1.60966i	0.649336	+	0.289103i	0.704852	−	0.709355i	$-0.251014\pi$
$31$	3.61535	+	1.60966i	0.649336	+	0.289103i	−0.0555153	+	0.998458i	$0.517680\pi$
$32$	−5.89858	−	10.2166i	−1.04273	−	1.80607i
$33$		0			0
$34$	2.41154	−	4.17691i	0.413575	−	0.716333i
$35$	−0.229824	+	0.166977i	−0.0388473	+	0.0282242i
$36$		0			0
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	0.712927	+	0.701238i	$0.247369\pi$
$37$	−1.67897	+	5.16733i	−0.276020	+	0.849504i	−0.988948	+	0.148265i	$0.952631\pi$
$38$	−7.83020	+	3.48623i	−1.27023	+	0.565541i
$39$		0			0
$40$	1.79486	−	0.381509i	0.283792	−	0.0603218i
$41$	−7.13663	+	7.92603i	−1.11455	+	1.23784i	−0.145934	+	0.989294i	$0.546619\pi$
$41$	−7.13663	+	7.92603i	−1.11455	+	1.23784i	−0.968621	+	0.248544i	$0.920048\pi$
$42$		0			0
$43$	−6.07195	+	10.5169i	−0.925964	+	1.60382i	−0.135961	+	0.990714i	$0.543412\pi$
$43$	−6.07195	+	10.5169i	−0.925964	+	1.60382i	−0.790003	+	0.613103i	$0.789921\pi$
$44$	11.6402	−	11.4036i	1.75482	−	1.71916i
$45$		0			0
$46$	11.8065	−	8.57795i	1.74078	−	1.26475i
$47$	−1.61859	−	0.344042i	−0.236095	−	0.0501836i	0.0883443	−	0.996090i	$-0.471842\pi$
$47$	−1.61859	−	0.344042i	−0.236095	−	0.0501836i	−0.324440	+	0.945906i	$0.605176\pi$
$48$		0			0
$49$	0.584711	−	5.56316i	0.0835302	−	0.794737i
$50$	1.35841	−	12.9244i	0.192108	−	1.82779i
$51$		0			0
$52$	29.0128	+	6.16687i	4.02336	+	0.855191i
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.00711436	−	0.999975i	$-0.497735\pi$
$53$	6.99142	−	5.07956i	0.960345	−	0.697732i	0.953231	+	0.302243i	$0.0977354\pi$
$54$		0			0
$55$	0.353422	+	0.711596i	0.0476554	+	0.0959516i
$56$	4.54157	−	7.86622i	0.606892	−	1.05117i
$57$		0			0
$58$	10.9521	−	12.1636i	1.43808	−	1.59715i
$59$	3.84199	−	0.816641i	0.500185	−	0.106318i	0.0490914	−	0.998794i	$-0.484367\pi$
$59$	3.84199	−	0.816641i	0.500185	−	0.106318i	0.451093	+	0.892477i	$0.351034\pi$
$60$		0			0
$61$	−9.79858	+	4.36261i	−1.25458	+	0.558575i	−0.922981	−	0.384846i	$-0.874255\pi$
$61$	−9.79858	+	4.36261i	−1.25458	+	0.558575i	−0.331599	+	0.943421i	$0.607588\pi$
$62$	3.21546	−	9.89616i	0.408364	−	1.25681i
$63$		0			0
$64$	−8.40715	+	6.10815i	−1.05089	+	0.763519i
$65$	−0.723109	+	1.25246i	−0.0896907	+	0.155349i
$66$		0			0
$67$	−4.61051	−	7.98564i	−0.563263	−	0.975601i	−0.997209	−	0.0746617i	$-0.976212\pi$
$67$	−4.61051	−	7.98564i	−0.563263	−	0.975601i	0.433946	−	0.900939i	$-0.357121\pi$
$68$	−8.23341	−	3.66575i	−0.998448	−	0.444538i
$69$		0			0
$70$	0.499790	+	0.555073i	0.0597363	+	0.0663439i
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	0.189603	−	0.981861i	$-0.439280\pi$
$71$	−5.77707	−	4.19728i	−0.685612	−	0.498126i	−0.875215	+	0.483735i	$0.839280\pi$
$72$		0			0
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	−0.960655	−	0.277745i	$-0.910413\pi$
$73$	−0.172710	+	0.531546i	−0.0202141	+	0.0622127i	0.940441	+	0.339958i	$0.110413\pi$
$74$	13.9735	+	2.97015i	1.62438	+	0.345273i
$75$		0			0
$76$	8.00827	+	13.8707i	0.918611	+	1.59108i
$77$	3.78830	+	1.05687i	0.431717	+	0.120442i
$78$		0			0
$79$	−0.462326	−	4.39874i	−0.0520157	−	0.494897i	−0.989254	−	0.146207i	$-0.953293\pi$
$79$	−0.462326	−	4.39874i	−0.0520157	−	0.494897i	0.937238	−	0.348690i	$-0.113373\pi$
$80$	−0.763468	−	2.34971i	−0.0853583	−	0.262706i
$81$		0			0
$82$	22.6872	+	16.4832i	2.50538	+	1.82026i
$83$	−14.0859	+	6.27144i	−1.54613	+	0.688380i	−0.989784	−	0.142572i	$-0.954463\pi$
$83$	−14.0859	+	6.27144i	−1.54613	+	0.688380i	−0.556343	+	0.830953i	$0.687796\pi$
$84$		0			0
$85$	0.294041	−	0.326566i	0.0318933	−	0.0354211i
$86$	29.1695	+	12.9871i	3.14542	+	1.40043i
$87$		0			0
$88$	−19.5777	−	16.1893i	−2.08699	−	1.72579i
$89$	−0.0625956			−0.00663512			−0.00331756	−	0.999994i	$-0.501056\pi$
$89$	−0.0625956			−0.00663512			−0.00331756	+	0.999994i	$0.501056\pi$
$90$		0			0
$91$	2.21221	+	6.80848i	0.231902	+	0.713722i
$92$	−18.2474	−	20.2658i	−1.90242	−	2.11286i
$93$		0			0
$94$	−0.454786	+	4.32700i	−0.0469076	+	0.446296i
$95$	−0.763872	+	0.162366i	−0.0783716	+	0.0166584i
$96$		0			0
$97$	−0.636901	−	6.05971i	−0.0646675	−	0.615270i	−0.978079	−	0.208233i	$-0.933229\pi$
$97$	−0.636901	−	6.05971i	−0.0646675	−	0.615270i	0.913412	−	0.407037i	$-0.133438\pi$
$98$	−14.7078			−1.48571
$99$		0			0
$100$	−24.2841			−2.42841
$101$	1.59485	+	15.1740i	0.158693	+	1.50986i	0.726765	+	0.686886i	$0.241023\pi$
$101$	1.59485	+	15.1740i	0.158693	+	1.50986i	−0.568072	+	0.822979i	$0.692311\pi$
$102$		0			0
$103$	−12.2234	+	2.59816i	−1.20441	+	0.256005i	−0.766041	−	0.642792i	$-0.777776\pi$
$103$	−12.2234	+	2.59816i	−1.20441	+	0.256005i	−0.438366	+	0.898797i	$0.644443\pi$
$104$	4.83356	−	45.9883i	0.473970	−	4.50952i
$105$		0			0
$106$	−15.2040	−	16.8858i	−1.47675	−	1.64009i
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	0.972621	+	0.232399i	$0.0746574\pi$
$107$	3.33446	+	10.2624i	0.322354	+	0.992105i	−0.650266	+	0.759706i	$0.725343\pi$
$108$		0			0
$109$	−5.16947			−0.495146			−0.247573	−	0.968869i	$-0.579633\pi$
$109$	−5.16947			−0.495146			−0.247573	+	0.968869i	$0.579633\pi$
$110$	1.76362	−	1.11973i	0.168154	−	0.106762i
$111$		0			0
$112$	−11.1725	−	4.97430i	−1.05570	−	0.470027i
$113$	1.36365	−	1.51448i	0.128281	−	0.142471i	−0.675582	−	0.737285i	$-0.736108\pi$
$113$	1.36365	−	1.51448i	0.128281	−	0.142471i	0.803863	+	0.594814i	$0.202774\pi$
$114$		0			0
$115$	1.21470	−	0.540818i	0.113271	−	0.0504316i
$116$	−24.7440	−	17.9776i	−2.29743	−	1.66918i
$117$		0			0
$118$	−3.19135	−	9.82197i	−0.293788	−	0.904185i
$119$	−0.227375	−	2.16332i	−0.0208434	−	0.198312i
$120$		0			0
$121$	4.67948	−	9.95502i	0.425407	−	0.905002i
$122$	14.1008	+	24.4233i	1.27662	+	2.21118i
$123$		0			0
$124$	−19.0191	−	4.04264i	−1.70797	−	0.363040i
$125$	0.736031	−	2.26527i	0.0658326	−	0.202612i
$126$		0			0
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	0.629953	−	0.776633i	$-0.283074\pi$
$127$	0.969141	+	0.704122i	0.0859974	+	0.0624808i	−0.543956	+	0.839114i	$0.683074\pi$
$128$	2.49507	+	2.77106i	0.220536	+	0.244929i
$129$		0			0
$130$	3.47379	+	1.54663i	0.304672	+	0.135649i
$131$	2.88350	+	4.99436i	0.251932	+	0.436359i	0.964058	−	0.265693i	$-0.0856007\pi$
$131$	2.88350	+	4.99436i	0.251932	+	0.436359i	−0.712126	+	0.702052i	$0.752267\pi$
$132$		0			0
$133$	−1.93284	+	3.34778i	−0.167599	+	0.290289i
$134$	−19.6145	+	14.2507i	−1.69443	+	1.23108i
$135$		0			0
$136$	−4.34189	+	13.3630i	−0.372314	+	1.14586i
$137$	0.122192	−	0.0544033i	0.0104396	−	0.00464799i	−0.401510	−	0.915855i	$-0.631515\pi$
$137$	0.122192	−	0.0544033i	0.0104396	−	0.00464799i	0.411950	+	0.911207i	$0.364848\pi$
$138$		0			0
$139$	−10.9016	+	2.31721i	−0.924663	+	0.196543i	−0.645552	−	0.763716i	$-0.723373\pi$
$139$	−10.9016	+	2.31721i	−0.924663	+	0.196543i	−0.279110	+	0.960259i	$0.590039\pi$
$140$	0.933928	−	1.03723i	0.0789313	−	0.0876621i
$141$		0			0
$142$	−9.38771	+	16.2600i	−0.787799	+	1.36451i
$143$	19.8070	−	2.92901i	1.65635	−	0.244936i
$144$		0			0
$145$	1.20647	−	0.876555i	0.100192	−	0.0727939i
$146$	1.43740	+	0.305530i	0.118960	+	0.0252858i
$147$		0			0
$148$	2.79036	−	26.5485i	0.229366	−	2.18227i
$149$	−0.412353	+	3.92327i	−0.0337813	+	0.321407i	0.964561	+	0.263858i	$0.0849951\pi$
$149$	−0.412353	+	3.92327i	−0.0337813	+	0.321407i	−0.998343	+	0.0575488i	$0.981672\pi$
$150$		0			0
$151$	2.61865	+	0.556611i	0.213102	+	0.0452963i	0.313226	−	0.949679i	$-0.398590\pi$
$151$	2.61865	+	0.556611i	0.213102	+	0.0452963i	−0.100123	+	0.994975i	$0.531924\pi$
$152$	20.2010	−	14.6769i	1.63852	−	1.19045i
$153$		0			0
$154$	1.72245	−	10.1965i	0.138799	−	0.821655i
$155$	0.474028	−	0.821040i	0.0380748	−	0.0659476i
$156$		0			0
$157$	−7.14294	+	7.93304i	−0.570069	+	0.633125i	−0.957383	−	0.288822i	$-0.906736\pi$
$157$	−7.14294	+	7.93304i	−0.570069	+	0.633125i	0.387314	+	0.921948i	$0.373403\pi$
$158$	−11.3752	+	2.41787i	−0.904960	+	0.192355i
$159$		0			0
$160$	−2.58179	+	1.14949i	−0.204109	+	0.0908750i
$161$	2.03390	−	6.25971i	0.160294	−	0.493334i
$162$		0			0
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	−0.796614	−	0.604489i	$-0.793378\pi$
$163$	−5.97347	+	4.33998i	−0.467878	+	0.339933i	0.328736	+	0.944422i	$0.393378\pi$
$164$	26.2010	−	45.3815i	2.04596	−	3.54370i
$165$		0			0
$166$	20.2705	+	35.1095i	1.57329	+	2.72503i
$167$	−9.42949	−	4.19828i	−0.729676	−	0.324873i	0.00805508	−	0.999968i	$-0.497436\pi$
$167$	−9.42949	−	4.19828i	−0.729676	−	0.324873i	−0.737731	+	0.675095i	$0.764103\pi$
$168$		0			0
$169$	15.6879	+	17.4232i	1.20676	+	1.34025i
$170$	−0.934749	−	0.679135i	−0.0716920	−	0.0520873i
$171$		0			0
$172$	18.4377	−	56.7454i	1.40586	−	4.32679i
$173$	−15.7199	−	3.34137i	−1.19516	−	0.254040i	−0.432982	−	0.901403i	$-0.642539\pi$
$173$	−15.7199	−	3.34137i	−1.19516	−	0.254040i	−0.762182	+	0.647363i	$0.775872\pi$
$174$		0			0
$175$	−2.93055	−	5.07587i	−0.221529	−	0.383700i
$176$	−18.9230	+	28.4941i	−1.42637	+	2.14782i
$177$		0			0
$178$	0.0172036	+	0.163681i	0.00128946	+	0.0122684i
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	0.898933	−	0.438085i	$-0.144343\pi$
$179$	−1.14818	−	3.53374i	−0.0858191	−	0.264124i	−0.984752	+	0.173961i	$0.944343\pi$
$180$		0			0
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	0.940674	−	0.339313i	$-0.110195\pi$
$181$	12.2247	+	8.88174i	0.908652	+	0.660174i	−0.0320216	+	0.999487i	$0.510195\pi$
$182$	17.1955	−	7.65591i	1.27461	−	0.567494i
$183$		0			0
$184$	−28.4477	+	31.5944i	−2.09720	+	2.32917i
$185$	1.18906	+	0.529403i	0.0874213	+	0.0389225i
$186$		0			0
$187$	−6.07195	−	0.380761i	−0.444025	−	0.0278440i
$188$	8.13014			0.592951
$189$		0			0
$190$	0.634510	+	1.95282i	0.0460322	+	0.141673i
$191$	8.01880	+	8.90578i	0.580220	+	0.644399i	0.959775	−	0.280770i	$-0.0905897\pi$
$191$	8.01880	+	8.90578i	0.580220	+	0.644399i	−0.379555	+	0.925169i	$0.623923\pi$
$192$		0			0
$193$	2.35538	−	22.4099i	0.169544	−	1.61310i	−0.497079	−	0.867705i	$-0.665594\pi$
$193$	2.35538	−	22.4099i	0.169544	−	1.61310i	0.666623	−	0.745395i	$-0.267739\pi$
$194$	−15.6705	+	3.33086i	−1.12507	+	0.239142i
$195$		0			0
$196$	2.87281	+	27.3330i	0.205201	+	1.95236i
$197$	−9.95308			−0.709127			−0.354564	−	0.935032i	$-0.615371\pi$
$197$	−9.95308			−0.709127			−0.354564	+	0.935032i	$0.615371\pi$
$198$		0			0
$199$	−15.5617			−1.10314			−0.551570	−	0.834128i	$-0.685971\pi$
$199$	−15.5617			−1.10314			−0.551570	+	0.834128i	$0.685971\pi$
$200$	3.95734	+	37.6516i	0.279826	+	2.66237i
$201$		0			0
$202$	39.2400	−	8.34071i	2.76091	−	0.586851i
$203$	0.771623	−	7.34150i	0.0541573	−	0.515272i
$204$		0			0
$205$	1.70965	+	1.89876i	0.119407	+	0.132615i
$206$	10.1534	+	31.2488i	0.707418	+	2.17721i
$207$		0			0
$208$	−62.2609			−4.31702
$209$	8.33207	+	6.89001i	0.576342	+	0.476592i
$210$		0			0
$211$	−2.18783	−	0.974086i	−0.150617	−	0.0670588i	0.330044	−	0.943966i	$-0.392936\pi$
$211$	−2.18783	−	0.974086i	−0.150617	−	0.0670588i	−0.480661	+	0.876907i	$0.659603\pi$
$212$	−28.4108	+	31.5534i	−1.95127	+	2.16710i
$213$		0			0
$214$	25.9187	−	11.5398i	1.77177	−	0.788841i
$215$	2.35358	+	1.70998i	0.160513	+	0.116620i
$216$		0			0
$217$	−1.45019	−	4.46324i	−0.0984456	−	0.302984i
$218$	1.42076	+	13.5176i	0.0962260	+	0.915529i
$219$		0			0
$220$	−2.42540	−	3.05880i	−0.163520	−	0.206224i
$221$	−5.53700	−	9.59036i	−0.372459	−	0.645118i
$222$		0			0
$223$	−12.7001	−	2.69950i	−0.850465	−	0.180772i	−0.237995	−	0.971266i	$-0.576490\pi$
$223$	−12.7001	−	2.69950i	−0.850465	−	0.180772i	−0.612469	+	0.790494i	$0.709824\pi$
$224$	−4.32298	+	13.3048i	−0.288841	+	0.888962i
$225$		0			0
$226$	−4.33500	−	3.14956i	−0.288360	−	0.209506i
$227$	12.3459	+	13.7115i	0.819425	+	0.910064i	0.997258	−	0.0739970i	$-0.0235755\pi$
$227$	12.3459	+	13.7115i	0.819425	+	0.910064i	−0.177834	+	0.984061i	$0.556909\pi$
$228$		0			0
$229$	18.3986	+	8.19158i	1.21581	+	0.541315i	0.911517	−	0.411263i	$-0.134912\pi$
$229$	18.3986	+	8.19158i	1.21581	+	0.541315i	0.304296	+	0.952577i	$0.401579\pi$
$230$	−1.74803	−	3.02767i	−0.115261	−	0.199639i
$231$		0			0
$232$	−23.8413	+	41.2943i	−1.56526	+	2.71110i
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	−0.375433	−	0.926850i	$-0.622506\pi$
$233$	5.95367	−	4.32560i	0.390038	−	0.283379i	0.765471	+	0.643470i	$0.222506\pi$
$234$		0			0
$235$	−0.122498	+	0.377009i	−0.00799087	+	0.0245934i
$236$	−17.6298	+	7.84930i	−1.14760	+	0.510946i
$237$		0			0
$238$	−5.59438	+	1.18912i	−0.362630	+	0.0770793i
$239$	6.44093	−	7.15338i	0.416629	−	0.462714i	−0.497899	−	0.867235i	$-0.665895\pi$
$239$	6.44093	−	7.15338i	0.416629	−	0.462714i	0.914529	+	0.404521i	$0.132562\pi$
$240$		0			0
$241$	13.2816	−	23.0043i	0.855540	−	1.48184i	−0.0206023	−	0.999788i	$-0.506558\pi$
$241$	13.2816	−	23.0043i	0.855540	−	1.48184i	0.876143	−	0.482052i	$-0.160108\pi$
$242$	−27.3174	−	9.50034i	−1.75603	−	0.610705i
$243$		0			0
$244$	42.6340	−	30.9754i	2.72936	−	1.98300i
$245$	−1.31077	−	0.278612i	−0.0837417	−	0.0177999i
$246$		0			0
$247$	−2.05711	+	19.5721i	−0.130891	+	1.24534i
$248$	−3.16860	+	30.1472i	−0.201206	+	1.91435i
$249$		0			0
$250$	−6.12574	−	1.30207i	−0.387426	−	0.0823499i
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.999185	−	0.0403590i	$-0.987150\pi$
$251$	−20.1137	+	14.6135i	−1.26957	+	0.922394i	−0.270382	+	0.962753i	$0.587150\pi$
$252$		0			0
$253$	−16.3155	−	8.52528i	−1.02575	−	0.535980i
$254$	1.57485	−	2.72772i	0.0988149	−	0.171152i
$255$		0			0
$256$	−7.34665	+	8.15929i	−0.459166	+	0.509955i
$257$	−13.1170	+	2.78811i	−0.818218	+	0.173918i	−0.597962	−	0.801525i	$-0.704023\pi$
$257$	−13.1170	+	2.78811i	−0.818218	+	0.173918i	−0.220256	+	0.975442i	$0.570689\pi$
$258$		0			0
$259$	5.88590	−	2.62057i	0.365732	−	0.162835i
$260$	2.19574	−	6.75781i	0.136174	−	0.419101i
$261$		0			0
$262$	12.2672	−	8.91267i	0.757873	−	0.550627i
$263$	0.390951	−	0.677147i	0.0241071	−	0.0417546i	−0.853720	−	0.520732i	$-0.825659\pi$
$263$	0.390951	−	0.677147i	0.0241071	−	0.0417546i	0.877827	+	0.478977i	$0.158992\pi$
$264$		0			0
$265$	−1.03512	−	1.79288i	−0.0635870	−	0.110136i
$266$	9.28531	+	4.13409i	0.569319	+	0.253477i
$267$		0			0
$268$	30.3149	+	33.6681i	1.85177	+	2.05660i
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	0.818884	−	0.573958i	$-0.194593\pi$
$269$	8.62814	+	6.26871i	0.526067	+	0.382210i	−0.292818	+	0.956168i	$0.594593\pi$
$270$		0			0
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	0.401268	+	0.915961i	$0.368570\pi$
$271$	−7.60141	+	23.3947i	−0.461753	+	1.42113i	−0.863021	+	0.505168i	$0.831430\pi$
$272$	18.5048	+	3.93331i	1.12202	+	0.238492i
$273$		0			0
$274$	−0.175842	−	0.304567i	−0.0106230	−	0.0183996i
$275$	−15.3635	+	5.71723i	−0.926453	+	0.344762i
$276$		0			0
$277$	0.937853	+	8.92308i	0.0563501	+	0.536136i	0.985888	+	0.167408i	$0.0535398\pi$
$277$	0.937853	+	8.92308i	0.0563501	+	0.536136i	−0.929538	+	0.368728i	$0.879794\pi$
$278$	9.05542	+	27.8697i	0.543108	+	1.67151i
$279$		0			0
$280$	−1.76038	−	1.27899i	−0.105203	−	0.0764344i
$281$	15.2801	−	6.80312i	0.911532	−	0.405840i	0.103263	−	0.994654i	$-0.467072\pi$
$281$	15.2801	−	6.80312i	0.911532	−	0.405840i	0.808269	+	0.588814i	$0.200405\pi$
$282$		0			0
$283$	−3.91573	+	4.34886i	−0.232766	+	0.258513i	−0.848201	−	0.529675i	$-0.822314\pi$
$283$	−3.91573	+	4.34886i	−0.232766	+	0.258513i	0.615434	+	0.788188i	$0.288981\pi$
$284$	32.0513	+	14.2702i	1.90189	+	0.846778i
$285$		0			0
$286$	−13.1027	−	50.9883i	−0.774782	−	3.01500i
$287$	12.6475			0.746560
$288$		0			0
$289$	−4.21349	−	12.9678i	−0.247852	−	0.762811i
$290$	−2.62368	−	2.91390i	−0.154068	−	0.171110i
$291$		0			0
$292$	0.287035	−	2.73095i	0.0167974	−	0.159817i
$293$	−14.6554	+	3.11511i	−0.856180	+	0.181987i	−0.615033	−	0.788502i	$-0.710857\pi$
$293$	−14.6554	+	3.11511i	−0.856180	+	0.181987i	−0.241148	+	0.970488i	$0.577524\pi$
$294$		0			0
$295$	−0.0983559	−	0.935793i	−0.00572650	−	0.0544840i
$296$	−41.6171			−2.41895
$297$		0			0
$298$	10.3723			0.600850
$299$	−3.50251	−	33.3242i	−0.202555	−	1.92719i
$300$		0			0
$301$	14.0859	−	2.99406i	0.811901	−	0.172575i
$302$	0.735778	−	7.00046i	0.0423393	−	0.402831i
$303$		0			0
$304$	−22.4962	−	24.9845i	−1.29024	−	1.43296i
$305$	0.794015	+	2.44373i	0.0454652	+	0.139927i
$306$		0			0
$307$	6.52424			0.372358			0.186179	−	0.982516i	$-0.440390\pi$
$307$	6.52424			0.372358			0.186179	+	0.982516i	$0.440390\pi$
$308$	−19.2856	−	1.20937i	−1.09890	−	0.0689100i
$309$		0			0
$310$	−2.27722	−	1.01388i	−0.129337	−	0.0575846i
$311$	9.64547	−	10.7124i	0.546945	−	0.607443i	−0.404774	−	0.914417i	$-0.632650\pi$
$311$	9.64547	−	10.7124i	0.546945	−	0.607443i	0.951718	+	0.306974i	$0.0993163\pi$
$312$		0			0
$313$	14.3778	−	6.40139i	0.812679	−	0.361828i	0.0420530	−	0.999115i	$-0.486610\pi$
$313$	14.3778	−	6.40139i	0.812679	−	0.361828i	0.770626	+	0.637287i	$0.219943\pi$
$314$	22.7072	+	16.4978i	1.28144	+	0.931022i
$315$		0			0
$316$	6.71524	+	20.6674i	0.377762	+	1.16263i
$317$	−3.06452	−	29.1570i	−0.172121	−	1.63762i	−0.650528	−	0.759482i	$-0.725453\pi$
$317$	−3.06452	−	29.1570i	−0.172121	−	1.63762i	0.478408	−	0.878138i	$-0.341214\pi$
$318$		0			0
$319$	−19.8869	−	5.54813i	−1.11345	−	0.310635i
$320$	1.24473	+	2.15593i	0.0695824	+	0.120520i
$321$		0			0
$322$	−16.9275	−	3.59805i	−0.943332	−	0.200511i
$323$	1.84786	−	5.68713i	0.102818	−	0.316440i
$324$		0			0
$325$	−24.1398	−	17.5386i	−1.33904	−	0.972868i
$326$	12.9903	+	14.4272i	0.719467	+	0.799049i
$327$		0			0
$328$	−74.6320	−	33.2283i	−4.12086	−	1.83473i
$329$	0.981128	+	1.69936i	0.0540913	+	0.0936889i
$330$		0			0
$331$	−6.70580	+	11.6148i	−0.368584	+	0.638407i	−0.989344	−	0.145594i	$-0.953491\pi$
$331$	−6.70580	+	11.6148i	−0.368584	+	0.638407i	0.620760	+	0.784001i	$0.286824\pi$
$332$	61.2883	−	44.5285i	3.36363	−	2.44382i
$333$		0			0
$334$	−8.38649	+	25.8110i	−0.458888	+	1.41231i
$335$	−2.01801	+	0.898474i	−0.110255	+	0.0490889i
$336$		0			0
$337$	−12.6398	+	2.68668i	−0.688535	+	0.146353i	−0.538876	−	0.842385i	$-0.681151\pi$
$337$	−12.6398	+	2.68668i	−0.688535	+	0.146353i	−0.149659	+	0.988738i	$0.547818\pi$
$338$	41.2482	−	45.8108i	2.24361	−	2.49178i
$339$		0			0
$340$	−1.07953	+	1.86979i	−0.0585455	+	0.101404i
$341$	−12.9843	+	1.92009i	−0.703141	+	0.103979i
$342$		0			0
$343$	−12.0820	+	8.77807i	−0.652365	+	0.473971i
$344$	−90.9861	−	19.3397i	−4.90564	−	1.04273i
$345$		0			0
$346$	−4.41693	+	42.0243i	−0.237456	+	2.25924i
$347$	3.64762	−	34.7048i	0.195815	−	1.86305i	−0.250424	−	0.968136i	$-0.580570\pi$
$347$	3.64762	−	34.7048i	0.195815	−	1.86305i	0.446238	−	0.894914i	$-0.352763\pi$
$348$		0			0
$349$	3.63898	+	0.773489i	0.194790	+	0.0414039i	0.304273	−	0.952585i	$-0.401586\pi$
$349$	3.63898	+	0.773489i	0.194790	+	0.0414039i	−0.109483	+	0.993989i	$0.534920\pi$
$350$	−12.4674	+	9.05813i	−0.666413	+	0.484177i
$351$		0			0
$352$	34.6780	+	18.1202i	1.84834	+	0.965807i
$353$	1.97626	−	3.42298i	0.105186	−	0.182187i	−0.808628	−	0.588320i	$-0.799790\pi$
$353$	1.97626	−	3.42298i	0.105186	−	0.182187i	0.913814	+	0.406133i	$0.133123\pi$
$354$		0			0
$355$	−1.14465	+	1.27127i	−0.0607519	+	0.0674718i
$356$	0.300825	−	0.0639423i	0.0159437	−	0.00338894i
$357$		0			0
$358$	−8.92479	+	3.97357i	−0.471690	+	0.210010i
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	−0.993104	−	0.117240i	$-0.962595\pi$
$359$	−2.28796	+	7.04162i	−0.120754	+	0.371643i	0.872350	+	0.488883i	$0.162595\pi$
$360$		0			0
$361$	6.77400	−	4.92160i	0.356526	−	0.259031i
$362$	19.8650	−	34.4072i	1.04408	−	1.80840i
$363$		0			0
$364$	−17.5865	−	30.4607i	−0.921783	−	1.59657i
$365$	0.122315	+	0.0544579i	0.00640224	+	0.00285046i
$366$		0			0
$367$	−17.0066	−	18.8877i	−0.887735	−	0.985930i	0.112235	−	0.993682i	$-0.464199\pi$
$367$	−17.0066	−	18.8877i	−0.887735	−	0.985930i	−0.999970	+	0.00775198i	$0.997532\pi$
$368$	46.3103	+	33.6464i	2.41409	+	1.75394i
$369$		0			0
$370$	1.05754	−	3.25476i	0.0549787	−	0.169207i
$371$	−10.0239	−	2.13064i	−0.520413	−	0.110617i
$372$		0			0
$373$	2.38737	+	4.13505i	0.123614	+	0.214105i	0.921190	−	0.389113i	$-0.127218\pi$
$373$	2.38737	+	4.13505i	0.123614	+	0.214105i	−0.797577	+	0.603218i	$0.793885\pi$
$374$	0.673142	+	15.9822i	0.0348074	+	0.826418i
$375$		0			0
$376$	−1.32489	−	12.6055i	−0.0683259	−	0.650077i
$377$	−11.6131	−	35.7416i	−0.598107	−	1.84079i
$378$		0			0
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	0.888009	−	0.459825i	$-0.152088\pi$
$379$	14.1162	+	10.2560i	0.725100	+	0.526816i	−0.162910	+	0.986641i	$0.552088\pi$
$380$	3.50519	−	1.56061i	0.179813	−	0.0800578i
$381$		0			0
$382$	21.0838	−	23.4160i	1.07874	−	1.19806i
$383$	3.09521	+	1.37808i	0.158158	+	0.0704164i	0.484289	−	0.874908i	$-0.339078\pi$
$383$	3.09521	+	1.37808i	0.158158	+	0.0704164i	−0.326131	+	0.945325i	$0.605745\pi$
$384$		0			0
$385$	0.346659	−	0.876087i	0.0176674	−	0.0446495i
$386$	−59.2469			−3.01559
$387$		0			0
$388$	9.25093	+	28.4714i	0.469645	+	1.44542i
$389$	12.5490	+	13.9371i	0.636262	+	0.706640i	0.971911	−	0.235347i	$-0.0756226\pi$
$389$	12.5490	+	13.9371i	0.636262	+	0.706640i	−0.335650	+	0.941987i	$0.608956\pi$
$390$		0			0
$391$	−1.06425	+	10.1257i	−0.0538214	+	0.512076i
$392$	41.9106	−	8.90837i	2.11680	−	0.449941i
$393$		0			0
$394$	2.73547	+	26.0263i	0.137811	+	1.31118i
$395$	−1.05956			−0.0533125
$396$		0			0
$397$	10.7157			0.537806			0.268903	−	0.963167i	$-0.413339\pi$
$397$	10.7157			0.537806			0.268903	+	0.963167i	$0.413339\pi$
$398$	4.27693	+	40.6922i	0.214383	+	2.03972i
$399$		0			0
$400$	49.8604	−	10.5982i	2.49302	−	0.529908i
$401$	−0.296093	+	2.81713i	−0.0147862	+	0.140681i	−0.999424	−	0.0339262i	$-0.989199\pi$
$401$	−0.296093	+	2.81713i	−0.0147862	+	0.140681i	0.984638	+	0.174607i	$0.0558655\pi$
$402$		0			0
$403$	−15.9864	−	17.7547i	−0.796341	−	0.884427i
$404$	−23.1650	−	71.2945i	−1.15250	−	3.54704i
$405$		0			0
$406$	−19.4093			−0.963268
$407$	−4.48499	−	17.4530i	−0.222313	−	0.865113i
$408$		0			0
$409$	21.5083	+	9.57610i	1.06352	+	0.473508i	0.862488	−	0.506078i	$-0.168905\pi$
$409$	21.5083	+	9.57610i	1.06352	+	0.473508i	0.201028	+	0.979586i	$0.435572\pi$
$410$	4.49518	−	4.99240i	0.222001	−	0.246557i
$411$		0			0
$412$	56.0897	−	24.9727i	2.76334	−	1.23032i
$413$	−3.76819	−	2.73775i	−0.185421	−	0.134716i
$414$		0			0
$415$	1.14143	+	3.51297i	0.0560307	+	0.172445i
$416$	7.44445	+	70.8292i	0.364994	+	3.47269i
$417$		0			0
$418$	15.7267	−	23.6811i	0.769217	−	1.15828i
$419$	−10.5587	−	18.2882i	−0.515826	−	0.893437i	−0.999831	−	0.0183715i	$-0.994152\pi$
$419$	−10.5587	−	18.2882i	−0.515826	−	0.893437i	0.484005	−	0.875065i	$-0.339182\pi$
$420$		0			0
$421$	23.0033	+	4.88951i	1.12111	+	0.238300i	0.730940	−	0.682442i	$-0.239082\pi$
$421$	23.0033	+	4.88951i	1.12111	+	0.238300i	0.390173	+	0.920742i	$0.372415\pi$
$422$	−1.94584	+	5.98867i	−0.0947218	+	0.291524i
$423$		0			0
$424$	53.5522	+	38.9080i	2.60073	+	1.88954i
$425$	6.06668	+	6.73773i	0.294277	+	0.326828i
$426$		0			0
$427$	11.6195	+	5.17332i	0.562306	+	0.250355i
$428$	−26.5081	−	45.9134i	−1.28132	−	2.21931i
$429$		0			0
$430$	3.82456	−	6.62434i	0.184437	−	0.319454i
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	−0.486512	−	0.873674i	$-0.661731\pi$
$431$	4.02881	−	2.92710i	0.194061	−	0.140994i	0.680573	+	0.732680i	$0.261731\pi$
$432$		0			0
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	0.560124	+	0.828409i	$0.310753\pi$
$433$	−7.90629	+	24.3331i	−0.379952	+	1.16937i	−0.940076	+	0.340964i	$0.889247\pi$
$434$	−11.2723	+	5.01877i	−0.541089	+	0.240909i
$435$		0			0
$436$	24.8437	−	5.28069i	1.18980	−	0.252899i
$437$	12.1071	−	13.4462i	0.579159	−	0.643221i
$438$		0			0
$439$	2.33003	−	4.03572i	0.111206	−	0.192615i	−0.805051	−	0.593206i	$-0.797862\pi$
$439$	2.33003	−	4.03572i	0.111206	−	0.192615i	0.916257	+	0.400591i	$0.131195\pi$
$440$	−4.34731	+	4.25895i	−0.207250	+	0.203037i
$441$		0			0
$442$	−23.5560	+	17.1145i	−1.12045	+	0.814052i
$443$	22.6184	+	4.80769i	1.07463	+	0.228420i	0.711050	−	0.703141i	$-0.248220\pi$
$443$	22.6184	+	4.80769i	1.07463	+	0.228420i	0.363583	+	0.931562i	$0.381553\pi$
$444$		0			0
$445$	−0.00156744	+	0.0149132i	−7.43040e−5	+	0.000706955i
$446$	−3.56844	+	33.9515i	−0.168971	+	1.60765i
$447$		0			0
$448$	12.0537	+	2.56208i	0.569482	+	0.121047i
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	−0.818676	−	0.574255i	$-0.805292\pi$
$449$	−11.1354	+	8.09035i	−0.525512	+	0.381807i	0.293164	+	0.956062i	$0.405292\pi$
$450$		0			0
$451$	5.89203	−	34.8794i	0.277445	−	1.64241i
$452$	−5.00642	+	8.67137i	−0.235482	+	0.407867i
$453$		0			0
$454$	32.4610	−	36.0516i	1.52347	−	1.69199i
$455$	1.67750	−	0.356563i	0.0786422	−	0.0167159i
$456$		0			0
$457$	9.90239	−	4.40883i	0.463214	−	0.206236i	−0.161841	−	0.986817i	$-0.551743\pi$
$457$	9.90239	−	4.40883i	0.463214	−	0.206236i	0.625055	+	0.780581i	$0.285076\pi$
$458$	16.3635	−	50.3617i	0.764617	−	2.35325i
$459$		0			0
$460$	−5.28520	+	3.83992i	−0.246424	+	0.179037i
$461$	−1.46396	+	2.53565i	−0.0681833	+	0.118097i	−0.898102	−	0.439788i	$-0.855054\pi$
$461$	−1.46396	+	2.53565i	−0.0681833	+	0.118097i	0.829918	+	0.557885i	$0.188387\pi$
$462$		0			0
$463$	13.5417	+	23.4550i	0.629337	+	1.09004i	0.987685	+	0.156456i	$0.0500070\pi$
$463$	13.5417	+	23.4550i	0.629337	+	1.09004i	−0.358347	+	0.933588i	$0.616660\pi$
$464$	58.6506	+	26.1129i	2.72278	+	1.21226i
$465$		0			0
$466$	−12.9473	−	14.3794i	−0.599771	−	0.666113i
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	0.778957	−	0.627077i	$-0.215749\pi$
$467$	9.14721	+	6.64584i	0.423282	+	0.307533i	−0.355675	+	0.934610i	$0.615749\pi$
$468$		0			0
$469$	−3.37897	+	10.3994i	−0.156026	+	0.480200i
$470$	1.01951	+	0.216703i	0.0470263	+	0.00999576i
$471$		0			0
$472$	15.0430	+	26.0552i	0.692410	+	1.19929i
$473$	−1.69489	−	40.2411i	−0.0779311	−	1.85029i
$474$		0			0
$475$	−1.68420	−	16.0241i	−0.0772764	−	0.735236i
$476$	3.30259	+	10.1643i	0.151374	+	0.465882i
$477$		0			0
$478$	−20.4755	−	14.8764i	−0.936530	−	0.680429i
$479$	−27.7588	+	12.3590i	−1.26833	+	0.564698i	−0.926935	−	0.375222i	$-0.877567\pi$
$479$	−27.7588	+	12.3590i	−1.26833	+	0.564698i	−0.341396	+	0.939919i	$0.610900\pi$
$480$		0			0
$481$	21.9478	−	24.3755i	1.00073	−	1.11143i
$482$	−63.8042	−	28.4075i	−2.90620	−	1.29392i
$483$		0			0
$484$	−12.3197	+	52.6225i	−0.559985	+	2.39193i
$485$	−1.45966			−0.0662796
$486$		0			0
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	0.926152	−	0.377150i	$-0.123096\pi$
$487$	−0.988742	−	3.04303i	−0.0448042	−	0.137893i	−0.970956	+	0.239257i	$0.923096\pi$
$488$	−54.9738	−	61.0546i	−2.48855	−	2.76381i
$489$		0			0
$490$	−0.368294	+	3.50409i	−0.0166378	+	0.158299i
$491$	5.85092	−	1.24365i	0.264048	−	0.0561252i	−0.0739850	−	0.997259i	$-0.523572\pi$
$491$	5.85092	−	1.24365i	0.264048	−	0.0561252i	0.338033	+	0.941134i	$0.390238\pi$
$492$		0			0
$493$	1.19362	+	11.3565i	0.0537579	+	0.511472i
$494$	51.7444			2.32809
$495$		0			0
$496$	40.8146			1.83263
$497$	0.885131	+	8.42146i	0.0397035	+	0.377754i
$498$		0			0
$499$	−28.7353	+	6.10788i	−1.28637	+	0.273426i	−0.799827	−	0.600231i	$-0.795076\pi$
$499$	−28.7353	+	6.10788i	−1.28637	+	0.273426i	−0.486543	+	0.873657i	$0.661742\pi$
$500$	−1.22325	+	11.6384i	−0.0547053	+	0.520486i
$501$		0			0
$502$	43.7407	+	48.5790i	1.95224	+	2.16818i
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	−0.999918	−	0.0128145i	$-0.995921\pi$
$503$	−4.45188	−	13.7015i	−0.198500	−	0.610919i	0.801418	−	0.598104i	$-0.204079\pi$
$504$		0			0
$505$	3.65509			0.162649
$506$	−17.8086	+	45.0065i	−0.791689	+	2.00078i
$507$		0			0
$508$	−5.37682	−	2.39391i	−0.238558	−	0.106213i
$509$	−29.3356	+	32.5805i	−1.30028	+	1.44410i	−0.474339	+	0.880342i	$0.657313\pi$
$509$	−29.3356	+	32.5805i	−1.30028	+	1.44410i	−0.825938	+	0.563761i	$0.809354\pi$
$510$		0			0
$511$	0.605463	−	0.269570i	0.0267841	−	0.0119251i
$512$	29.3882	+	21.3518i	1.29879	+	0.943624i
$513$		0			0
$514$	10.8957	+	33.5334i	0.480587	+	1.47909i
$515$	0.312922	+	2.97725i	0.0137890	+	0.131193i
$516$		0			0
$517$	5.14358	−	1.91408i	0.226214	−	0.0841813i
$518$	−8.47019	−	14.6708i	−0.372159	−	0.644598i
$519$		0			0
$520$	−10.8355	−	2.30316i	−0.475170	−	0.101000i
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	−0.716748	−	0.697332i	$-0.754370\pi$
$521$	6.23122	−	19.1777i	0.272995	−	0.840191i	0.989743	−	0.142859i	$-0.0456296\pi$
$522$		0			0
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.996318	−	0.0857293i	$-0.972678\pi$
$523$	−31.6906	−	23.0245i	−1.38573	−	1.00679i	−0.389413	−	0.921063i	$-0.627322\pi$
$524$	−18.9595	−	21.0566i	−0.828248	−	0.919862i
$525$		0			0
$526$	−1.87811	−	0.836191i	−0.0818897	−	0.0364596i
$527$	3.62973	+	6.28688i	0.158114	+	0.273861i
$528$		0			0
$529$	−3.90349	+	6.76105i	−0.169717	+	0.293959i
$530$	−4.40371	+	3.19948i	−0.191285	+	0.138977i
$531$		0			0
$532$	5.86914	−	18.0633i	0.254459	−	0.783145i
$533$	58.8211	−	26.1888i	2.54782	−	1.13436i
$534$		0			0
$535$	2.52849	−	0.537447i	0.109316	−	0.0232359i
$536$	47.2609	−	52.4886i	2.04136	−	2.26716i
$537$		0			0
$538$	14.0207	−	24.2845i	0.604475	−	1.04698i
$539$	8.25253	+	16.6160i	0.355462	+	0.715703i
$540$		0			0
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	−0.855360	−	0.518034i	$-0.826664\pi$
$541$	−14.5837	+	10.5957i	−0.627002	+	0.455544i	0.228358	+	0.973577i	$0.426664\pi$
$542$	63.2639	+	13.4472i	2.71742	+	0.577605i
$543$		0			0
$544$	2.26202	−	21.5217i	0.0969833	−	0.922734i
$545$	−0.129448	+	1.23161i	−0.00554493	+	0.0527565i
$546$		0			0
$547$	0.0876124	+	0.0186226i	0.00374604	+	0.000796244i	0.209784	−	0.977748i	$-0.432724\pi$
$547$	0.0876124	+	0.0186226i	0.00374604	+	0.000796244i	−0.206038	+	0.978544i	$0.566057\pi$
$548$	−0.531662	+	0.386275i	−0.0227115	+	0.0165008i
$549$		0			0
$550$	19.1724	+	38.6026i	0.817514	+	1.64602i
$551$	10.1466	−	17.5744i	0.432259	−	0.748695i
$552$		0			0
$553$	−3.50952	+	3.89772i	−0.149240	+	0.165748i
$554$	23.0752	−	4.90478i	0.980370	−	0.208384i
$555$		0			0
$556$	50.0244	−	22.2723i	2.12151	−	0.944556i
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	−0.969168	−	0.246400i	$-0.920752\pi$
$557$	−0.950270	+	2.92463i	−0.0402642	+	0.123921i	0.928904	+	0.370321i	$0.120752\pi$
$558$		0			0
$559$	59.3112	−	43.0921i	2.50859	−	1.82260i
$560$	−1.46488	+	2.53725i	−0.0619024	+	0.107218i
$561$		0			0
$562$	−21.9890	−	38.0860i	−0.927548	−	1.60656i
$563$	16.2740	+	7.24565i	0.685867	+	0.305368i	0.719925	−	0.694052i	$-0.244176\pi$
$563$	16.2740	+	7.24565i	0.685867	+	0.305368i	−0.0340577	+	0.999420i	$0.510843\pi$
$564$		0			0
$565$	−0.326675	−	0.362809i	−0.0137433	−	0.0152635i
$566$	12.4480	+	9.04401i	0.523229	+	0.380148i
$567$		0			0
$568$	16.9022	−	52.0197i	0.709202	−	2.18270i
$569$	4.15614	+	0.883415i	0.174234	+	0.0370347i	0.294203	−	0.955743i	$-0.404946\pi$
$569$	4.15614	+	0.883415i	0.174234	+	0.0370347i	−0.119968	+	0.992778i	$0.538279\pi$
$570$		0			0
$571$	22.5287	+	39.0208i	0.942795	+	1.63297i	0.760107	+	0.649798i	$0.225146\pi$
$571$	22.5287	+	39.0208i	0.942795	+	1.63297i	0.182688	+	0.983171i	$0.441520\pi$
$572$	−92.1975	+	34.3095i	−3.85497	+	1.43455i
$573$		0			0
$574$	−3.47600	−	33.0720i	−0.145086	−	1.38040i
$575$	8.47741	+	26.0908i	0.353533	+	1.08806i
$576$		0			0
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	0.814513	−	0.580145i	$-0.197004\pi$
$577$	12.3578	+	8.97845i	0.514461	+	0.373778i	−0.300052	+	0.953923i	$0.597004\pi$
$578$	−32.7514	+	14.5819i	−1.36228	+	0.606525i
$579$		0			0
$580$	−4.90272	+	5.44502i	−0.203574	+	0.226092i
$581$	16.7035	+	7.43688i	0.692978	+	0.308534i
$582$		0			0
$583$	−10.5456	+	26.6513i	−0.436756	+	1.10378i
$584$	−4.28101			−0.177150
$585$		0			0
$586$	12.1735	+	37.4663i	0.502884	+	1.54772i
$587$	−28.4956	−	31.6476i	−1.17614	−	1.30624i	−0.942614	−	0.333885i	$-0.891640\pi$
$587$	−28.4956	−	31.6476i	−1.17614	−	1.30624i	−0.233526	−	0.972351i	$-0.575026\pi$
$588$		0			0
$589$	1.34852	−	12.8303i	0.0555649	−	0.528664i
$590$	−2.41997	+	0.514381i	−0.0996286	+	0.0211767i
$591$		0			0
$592$	5.85719	+	55.7274i	0.240729	+	2.29038i
$593$	−10.6230			−0.436236			−0.218118	−	0.975922i	$-0.569992\pi$
$593$	−10.6230			−0.436236			−0.218118	+	0.975922i	$0.569992\pi$
$594$		0			0
$595$	−0.521100			−0.0213630
$596$	−2.02598	−	19.2759i	−0.0829872	−	0.789571i
$597$		0			0
$598$	−86.1766	+	18.3174i	−3.52402	+	0.749054i
$599$	−3.63423	+	34.5774i	−0.148491	+	1.41280i	0.625809	+	0.779976i	$0.284769\pi$
$599$	−3.63423	+	34.5774i	−0.148491	+	1.41280i	−0.774300	+	0.632819i	$0.781898\pi$
$600$		0			0
$601$	6.08081	+	6.75343i	0.248041	+	0.275478i	0.854289	−	0.519798i	$-0.173993\pi$
$601$	6.08081	+	6.75343i	0.248041	+	0.275478i	−0.606248	+	0.795276i	$0.707326\pi$
$602$	−11.7005	−	36.0104i	−0.476876	−	1.46767i
$603$		0			0
$604$	−13.1534			−0.535204
$605$	−2.25458	−	1.36415i	−0.0916617	−	0.0554608i
$606$		0			0
$607$	−14.2478	−	6.34353i	−0.578301	−	0.257476i	0.0966749	−	0.995316i	$-0.469179\pi$
$607$	−14.2478	−	6.34353i	−0.578301	−	0.257476i	−0.674976	+	0.737840i	$0.735846\pi$
$608$	−25.7331	+	28.5795i	−1.04361	+	1.15905i
$609$		0			0
$610$	6.17187	−	2.74789i	0.249892	−	0.111259i
$611$	8.08184	+	5.87180i	0.326956	+	0.237548i
$612$		0			0
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	−0.960502	−	0.278272i	$-0.910238\pi$
$613$	−8.59141	−	26.4417i	−0.347004	−	1.06797i	0.613498	−	0.789696i	$-0.289762\pi$
$614$	−1.79310	−	17.0602i	−0.0723636	−	0.688494i
$615$		0			0
$616$	1.26771	+	30.0986i	0.0510773	+	1.21271i
$617$	4.01690	+	6.95747i	0.161714	+	0.280097i	0.935484	−	0.353370i	$-0.114964\pi$
$617$	4.01690	+	6.95747i	0.161714	+	0.280097i	−0.773769	+	0.633467i	$0.781631\pi$
$618$		0			0
$619$	−3.52144	−	0.748505i	−0.141538	−	0.0300849i	0.136598	−	0.990627i	$-0.456383\pi$
$619$	−3.52144	−	0.748505i	−0.141538	−	0.0300849i	−0.278136	+	0.960542i	$0.589717\pi$
$620$	−1.43940	+	4.43002i	−0.0578078	+	0.177914i
$621$		0			0
$622$	−30.6627	−	22.2777i	−1.22946	−	0.893256i
$623$	0.0496682	+	0.0551621i	0.00198991	+	0.00221002i
$624$		0			0
$625$	22.0552	+	9.81962i	0.882209	+	0.392785i
$626$	−20.6905	−	35.8370i	−0.826959	−	1.43234i
$627$		0			0
$628$	26.2242	−	45.4216i	1.04646	−	1.81252i
$629$	−8.06309	+	5.85818i	−0.321496	+	0.233581i
$630$		0			0
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	0.745976	+	0.665973i	$0.231984\pi$
$631$	−6.25432	+	19.2488i	−0.248981	+	0.766283i	−0.994956	+	0.100310i	$0.968016\pi$
$632$	30.9497	−	13.7797i	1.23111	−	0.548126i
$633$		0			0
$634$	−75.4002	+	16.0268i	−2.99453	+	0.636506i
$635$	0.192023	−	0.213263i	0.00762021	−	0.00846310i
$636$		0			0
$637$	−16.8849	+	29.2454i	−0.669002	+	1.15875i
$638$	−9.04211	+	53.5271i	−0.357981	+	2.11916i
$639$		0			0
$640$	0.722676	−	0.525055i	0.0285663	−	0.0207546i
$641$	−27.2695	−	5.79632i	−1.07708	−	0.228941i	−0.364979	−	0.931016i	$-0.618924\pi$
$641$	−27.2695	−	5.79632i	−1.07708	−	0.228941i	−0.712103	+	0.702075i	$0.752257\pi$
$642$		0			0
$643$	−0.00935176	+	0.0889761i	−0.000368797	+	0.00350887i	−0.994705	−	0.102774i	$-0.967228\pi$
$643$	−0.00935176	+	0.0889761i	−0.000368797	+	0.00350887i	0.994336	+	0.106283i	$0.0338949\pi$
$644$	−3.38024	+	32.1609i	−0.133200	+	1.26732i
$645$		0			0
$646$	−15.3791	−	3.26893i	−0.605083	−	0.128614i
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.530473	+	0.847702i	$0.677986\pi$
$647$	−38.1698	+	27.7320i	−1.50061	+	1.09026i	−0.970137	+	0.242556i	$0.922014\pi$
$648$		0			0
$649$	−9.30565	+	9.11651i	−0.365279	+	0.357854i
$650$	−39.2272	+	67.9434i	−1.53862	+	2.66496i
$651$		0			0
$652$	24.2742	−	26.9593i	0.950652	−	1.05581i
$653$	16.9031	−	3.59287i	0.661471	−	0.140600i	0.135070	−	0.990836i	$-0.456874\pi$
$653$	16.9031	−	3.59287i	0.661471	−	0.140600i	0.526402	+	0.850236i	$0.323541\pi$
$654$		0			0
$655$	1.26210	−	0.561922i	0.0493142	−	0.0219561i
$656$	−33.9907	+	104.613i	−1.32711	+	4.08443i
$657$		0			0
$658$	4.17401	−	3.03259i	0.162720	−	0.118223i
$659$	−6.04319	+	10.4671i	−0.235409	+	0.407741i	−0.959391	−	0.282078i	$-0.908976\pi$
$659$	−6.04319	+	10.4671i	−0.235409	+	0.407741i	0.723982	+	0.689818i	$0.242310\pi$
$660$		0			0
$661$	−19.2915	−	33.4139i	−0.750353	−	1.29965i	−0.947652	−	0.319306i	$-0.896550\pi$
$661$	−19.2915	−	33.4139i	−0.750353	−	1.29965i	0.197299	−	0.980343i	$-0.436783\pi$
$662$	32.2145	+	14.3428i	1.25205	+	0.557449i
$663$		0			0
$664$	−79.0273	−	87.7687i	−3.06686	−	3.40609i
$665$	0.749199	+	0.544325i	0.0290527	+	0.0211080i
$666$		0			0
$667$	−10.6771	+	32.8608i	−0.413420	+	1.27237i
$668$	49.6053	+	10.5439i	1.91929	+	0.407957i
$669$		0			0
$670$	2.90404	+	5.02994i	0.112193	+	0.194324i
$671$	19.6801	−	29.6342i	0.759742	−	1.14401i
$672$		0			0
$673$	−3.01487	−	28.6846i	−0.116215	−	1.10571i	−0.884803	−	0.465966i	$-0.845707\pi$
$673$	−3.01487	−	28.6846i	−0.116215	−	1.10571i	0.768588	−	0.639744i	$-0.220960\pi$
$674$	10.4993	+	32.3134i	0.404416	+	1.24467i
$675$		0			0
$676$	−93.1918	−	67.7078i	−3.58430	−	2.60415i
$677$	6.43785	−	2.86632i	0.247427	−	0.110161i	−0.279276	−	0.960211i	$-0.590095\pi$
$677$	6.43785	−	2.86632i	0.247427	−	0.110161i	0.526703	+	0.850049i	$0.323428\pi$
$678$		0			0
$679$	−4.83472	+	5.36950i	−0.185540	+	0.206063i
$680$	3.07496	+	1.36906i	0.117919	+	0.0525011i
$681$		0			0
$682$	8.58939	+	33.4249i	0.328905	+	1.27991i
$683$	−32.5733			−1.24638			−0.623191	−	0.782070i	$-0.714164\pi$
$683$	−32.5733			−1.24638			−0.623191	+	0.782070i	$0.714164\pi$
$684$		0			0
$685$	−0.00990166	−	0.0304742i	−0.000378323	−	0.00116436i
$686$	26.2743	+	29.1806i	1.00316	+	1.11412i
$687$		0			0
$688$	−13.0915	+	124.557i	−0.499107	+	4.74869i
$689$	−51.0308	+	10.8469i	−1.94412	+	0.413235i
$690$		0			0
$691$	−4.51363	−	42.9443i	−0.171707	−	1.63368i	−0.653169	−	0.757212i	$-0.726561\pi$
$691$	−4.51363	−	42.9443i	−0.171707	−	1.63368i	0.481462	−	0.876467i	$-0.340106\pi$
$692$	78.9608			3.00164
$693$		0			0
$694$	−91.7519			−3.48285
$695$	0.279084	+	2.65530i	0.0105862	+	0.100721i
$696$		0			0
$697$	−19.1369	+	4.06767i	−0.724860	+	0.154074i
$698$	1.02247	−	9.72813i	0.0387010	−	0.368215i
$699$		0			0
$700$	19.2689	+	21.4002i	0.728295	+	0.808853i
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	−0.974873	−	0.222761i	$-0.928493\pi$
$701$	−8.39620	−	25.8408i	−0.317120	−	0.975995i	0.657753	−	0.753234i	$-0.271507\pi$
$702$		0			0
$703$	17.7118			0.668013
$704$	12.6811	−	32.0480i	0.477937	−	1.20786i
$705$		0			0
$706$	−9.49389	−	4.22695i	−0.357307	−	0.159083i
$707$	12.1065	−	13.4456i	0.455312	−	0.505675i
$708$		0			0
$709$	−19.6058	+	8.72907i	−0.736312	+	0.327827i	−0.740402	−	0.672164i	$-0.765365\pi$
$709$	−19.6058	+	8.72907i	−0.736312	+	0.327827i	0.00408993	+	0.999992i	$0.498698\pi$
$710$	3.63882	+	2.64376i	0.136563	+	0.0992185i
$711$		0			0
$712$	−0.148163	−	0.455998i	−0.00555263	−	0.0170892i
$713$	2.29604	+	21.8454i	0.0859874	+	0.818116i
$714$		0			0
$715$	−0.201844	−	4.79231i	−0.00754856	−	0.179222i
$716$	9.12775	+	15.8097i	0.341120	+	0.590837i
$717$		0			0
$718$	19.0419	+	4.04749i	0.710638	+	0.151051i
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	0.790181	+	0.612874i	$0.209987\pi$
$719$	−5.61293	+	17.2748i	−0.209327	+	0.644242i	−0.999508	+	0.0313684i	$0.990013\pi$
$720$		0			0
$721$	11.9886	+	8.71023i	0.446479	+	0.324386i
$722$	−14.7312	−	16.3607i	−0.548239	−	0.608881i
$723$		0			0
$724$	−67.8227	−	30.1966i	−2.52061	−	1.12225i
$725$	15.3842	+	26.6461i	0.571353	+	0.989612i
$726$		0			0
$727$	12.7753	−	22.1275i	0.473810	−	0.820662i	−0.525741	−	0.850645i	$-0.676212\pi$
$727$	12.7753	−	22.1275i	0.473810	−	0.820662i	0.999550	+	0.0299825i	$0.00954516\pi$
$728$	−44.3622	+	32.2311i	−1.64417	+	1.19456i
$729$		0			0
$730$	0.108785	−	0.334807i	0.00402633	−	0.0123918i
$731$	−20.3504	+	9.06057i	−0.752686	+	0.335117i
$732$		0			0
$733$	39.8466	−	8.46966i	1.47177	−	0.312834i	0.598913	−	0.800814i	$-0.295599\pi$
$733$	39.8466	−	8.46966i	1.47177	−	0.312834i	0.872855	+	0.487980i	$0.162266\pi$
$734$	−44.7153	+	49.6614i	−1.65047	+	1.83304i
$735$		0			0
$736$	32.7395	−	56.7065i	1.20679	−	2.09023i
$737$	27.1054	+	14.1633i	0.998439	+	0.521710i
$738$		0			0
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.00347186	−	0.999994i	$-0.498895\pi$
$739$	25.9774	−	18.8737i	0.955596	−	0.694281i	0.952124	+	0.305713i	$0.0988949\pi$
$740$	−6.25523	−	1.32959i	−0.229947	−	0.0488767i
$741$		0			0
$742$	−2.81647	+	26.7969i	−0.103396	+	0.983747i
$743$	−1.87757	+	17.8639i	−0.0688815	+	0.655364i	0.904547	+	0.426374i	$0.140209\pi$
$743$	−1.87757	+	17.8639i	−0.0688815	+	0.655364i	−0.973429	+	0.228990i	$0.926458\pi$
$744$		0			0
$745$	0.924384	+	0.196484i	0.0338668	+	0.00719861i
$746$	10.1566	−	7.37920i	0.371859	−	0.270172i
$747$		0			0
$748$	29.5698	−	4.37270i	1.08118	−	0.159882i
$749$	6.39789	−	11.0815i	0.233774	−	0.404908i
$750$		0			0
$751$	−16.6504	+	18.4922i	−0.607583	+	0.674789i	−0.965931	−	0.258799i	$-0.916673\pi$
$751$	−16.6504	+	18.4922i	−0.607583	+	0.674789i	0.358348	+	0.933588i	$0.383340\pi$
$752$	−16.6929	+	3.54818i	−0.608727	+	0.129389i
$753$		0			0
$754$	−90.2688	+	40.1903i	−3.28740	+	1.46364i
$755$	0.198184	−	0.609947i	0.00721265	−	0.0221983i
$756$		0			0
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.00391833	−	0.999992i	$-0.498753\pi$
$757$	26.3079	−	19.1138i	0.956178	−	0.694704i	0.952260	+	0.305288i	$0.0987528\pi$
$758$	22.9387	−	39.7311i	0.833173	−	1.44310i
$759$		0			0
$760$	−2.99088	−	5.18035i	−0.108491	−	0.187911i
$761$	−8.06035	−	3.58870i	−0.292187	−	0.130090i	0.255408	−	0.966833i	$-0.417790\pi$
$761$	−8.06035	−	3.58870i	−0.292187	−	0.130090i	−0.547596	+	0.836743i	$0.684457\pi$
$762$		0			0
$763$	4.10186	+	4.55557i	0.148497	+	0.164923i
$764$	−47.6345	−	34.6085i	−1.72336	−	1.25209i
$765$		0			0
$766$	2.75285	−	8.47239i	0.0994644	−	0.306120i
$767$	−23.1941	−	4.93005i	−0.837489	−	0.178014i
$768$		0			0
$769$	13.4824	+	23.3523i	0.486189	+	0.842104i	0.999874	−	0.0158750i	$-0.00505339\pi$
$769$	13.4824	+	23.3523i	0.486189	+	0.842104i	−0.513685	+	0.857979i	$0.671720\pi$
$770$	−2.38615	−	0.665696i	−0.0859909	−	0.0239900i
$771$		0			0
$772$	11.5725	+	110.105i	0.416502	+	3.96275i
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	−0.982747	−	0.184954i	$-0.940786\pi$
$773$	−8.24081	−	25.3626i	−0.296401	−	0.912230i	0.686346	−	0.727276i	$-0.259214\pi$
$774$		0			0
$775$	15.8247	+	11.4973i	0.568439	+	0.412995i
$776$	42.6363	−	18.9829i	1.53055	−	0.681447i
$777$		0			0
$778$	32.9952	−	36.6449i	1.18293	−	1.31378i
$779$	31.7626	+	14.1416i	1.13801	+	0.506675i
$780$		0			0
$781$	23.6371	+	1.48224i	0.845801	+	0.0530387i
$782$	26.7700			0.957294
$783$		0			0
$784$	−17.8273	−	54.8666i	−0.636688	−	1.95952i
$785$	1.71116	+	1.90044i	0.0610739	+	0.0678294i
$786$		0			0
$787$	1.72947	−	16.4548i	0.0616489	−	0.586551i	−0.919472	−	0.393155i	$-0.871383\pi$
$787$	1.72947	−	16.4548i	0.0616489	−	0.586551i	0.981121	−	0.193395i	$-0.0619499\pi$
$788$	47.8330	−	10.1672i	1.70398	−	0.362192i
$789$		0			0
$790$	0.291207	+	2.77065i	0.0103607	+	0.0985753i
$791$	−2.41666			−0.0859264
$792$		0			0
$793$	64.7520			2.29941
$794$	−2.94507	−	28.0204i	−0.104516	−	0.994408i
$795$		0			0
$796$	74.7872	−	15.8965i	2.65076	−	0.563437i
$797$	−4.65345	+	44.2746i	−0.164834	+	1.56829i	0.529296	+	0.848437i	$0.322456\pi$
$797$	−4.65345	+	44.2746i	−0.164834	+	1.56829i	−0.694129	+	0.719850i	$0.744210\pi$
$798$		0			0
$799$	−2.03108	−	2.25574i	−0.0718545	−	0.0798025i
$800$	−18.0184	−	55.4550i	−0.637047	−	1.96063i
$801$		0			0
$802$	7.44789			0.262994
$803$	−0.461356	−	1.79533i	−0.0162809	−	0.0633559i
$804$		0			0
$805$	−1.44043	−	0.641320i	−0.0507684	−	0.0226036i
$806$	−42.0331	+	46.6825i	−1.48055	+	1.64432i
$807$		0			0
$808$	−106.764	+	47.5346i	−3.75596	+	1.67226i
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.995198	+	0.0978851i	$0.0312078\pi$
$809$	39.7013	+	28.8447i	1.39582	+	1.01413i	0.400627	+	0.916241i	$0.368792\pi$
$810$		0			0
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	−0.860634	−	0.509224i	$-0.829933\pi$
$811$	−13.2047	−	40.6400i	−0.463681	−	1.42706i	0.396953	−	0.917839i	$-0.370067\pi$
$812$	3.79115	+	36.0703i	0.133043	+	1.26582i
$813$		0			0
$814$	−44.4051	+	16.5245i	−1.55640	+	0.579184i
$815$	0.884408	+	1.53184i	0.0309795	+	0.0536580i
$816$		0			0
$817$	38.7227	+	8.23076i	1.35474	+	0.287958i
$818$	19.1292	−	58.8737i	0.668838	−	2.05847i
$819$		0			0
$820$	−10.1559	−	7.37871i	−0.354660	−	0.257676i
$821$	19.3894	+	21.5341i	0.676695	+	0.751546i	0.979486	−	0.201511i	$-0.0645852\pi$
$821$	19.3894	+	21.5341i	0.676695	+	0.751546i	−0.302791	+	0.953057i	$0.597919\pi$
$822$		0			0
$823$	17.5670	+	7.82134i	0.612348	+	0.272635i	0.689387	−	0.724393i	$-0.257880\pi$
$823$	17.5670	+	7.82134i	0.612348	+	0.272635i	−0.0770393	+	0.997028i	$0.524547\pi$
$824$	−47.8597	−	82.8954i	−1.66727	−	2.88780i
$825$		0			0
$826$	−6.12330	+	10.6059i	−0.213057	+	0.369025i
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.230074	−	0.973173i	$-0.426103\pi$
$827$	35.2773	−	25.6305i	1.22671	−	0.891259i	0.996639	+	0.0819138i	$0.0261032\pi$
$828$		0			0
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	−0.765417	−	0.643535i	$-0.777467\pi$
$829$	6.68209	−	20.5654i	0.232078	−	0.714264i	0.997496	−	0.0707296i	$-0.0225327\pi$
$830$	8.87233	−	3.95022i	0.307963	−	0.137114i
$831$		0			0
$832$	61.3643	−	13.0434i	2.12742	−	0.452198i
$833$	6.86597	−	7.62543i	0.237892	−	0.264206i
$834$		0			0
$835$	−1.23635	+	2.14142i	−0.0427857	+	0.0741069i
$836$	−47.0809	−	24.6010i	−1.62833	−	0.850843i
$837$		0			0
$838$	−44.9198	+	32.6361i	−1.55173	+	1.12740i
$839$	−21.7184	−	4.61639i	−0.749803	−	0.159375i	−0.182867	−	0.983138i	$-0.558538\pi$
$839$	−21.7184	−	4.61639i	−0.749803	−	0.159375i	−0.566936	+	0.823762i	$0.691871\pi$
$840$		0			0
$841$	−1.01936	+	9.69858i	−0.0351504	+	0.334434i
$842$	6.46339	−	61.4951i	0.222743	−	2.11926i
$843$		0			0
$844$	11.5094	+	2.44641i	0.396171	+	0.0842088i
$845$	4.54387	−	3.30131i	0.156314	−	0.113569i
$846$		0			0
$847$	−12.4859	+	3.77531i	−0.429020	+	0.129721i
$848$	44.5628	−	77.1851i	1.53029	−	2.65055i
$849$		0			0
$850$	15.9511	−	17.7155i	0.547119	−	0.607637i
$851$	−29.4977	+	6.26994i	−1.01117	+	0.214931i
$852$		0			0
$853$	24.0410	−	10.7037i	0.823147	−	0.366489i	0.0484535	−	0.998825i	$-0.484571\pi$
$853$	24.0410	−	10.7037i	0.823147	−	0.366489i	0.774694	+	0.632337i	$0.217904\pi$
$854$	10.3342	−	31.8055i	0.353630	−	1.08836i
$855$		0			0
$856$	−66.8672	+	48.5819i	−2.28547	+	1.66049i
$857$	−13.9851	+	24.2229i	−0.477721	+	0.827437i	−0.999674	−	0.0255371i	$-0.991870\pi$
$857$	−13.9851	+	24.2229i	−0.477721	+	0.827437i	0.521953	+	0.852974i	$0.325204\pi$
$858$		0			0
$859$	−7.69037	−	13.3201i	−0.262392	−	0.454476i	0.704485	−	0.709719i	$-0.251178\pi$
$859$	−7.69037	−	13.3201i	−0.262392	−	0.454476i	−0.966877	+	0.255243i	$0.917845\pi$
$860$	−13.0577	−	5.81368i	−0.445265	−	0.198245i
$861$		0			0
$862$	−8.76133	−	9.73045i	−0.298412	−	0.331420i
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	0.0351559	−	0.999382i	$-0.488807\pi$
$863$	−26.5699	−	19.3041i	−0.904449	−	0.657121i	−0.939605	+	0.342261i	$0.888807\pi$
$864$		0			0
$865$	−1.18971	+	3.66156i	−0.0404514	+	0.124497i
$866$	65.8014	+	13.9865i	2.23602	+	0.475281i
$867$		0			0
$868$	11.5287	+	19.9682i	0.391309	+	0.677767i
$869$	9.11418	+	11.4944i	0.309177	+	0.389920i
$870$		0			0
$871$	5.81881	+	55.3622i	0.197163	+	1.87588i
$872$	−12.2360	−	37.6586i	−0.414364	−	1.27528i
$873$		0			0
$874$	−38.4880	−	27.9632i	−1.30188	−	0.945868i
$875$	−2.58028	+	1.14882i	−0.0872295	+	0.0388371i
$876$		0			0
$877$	33.4681	−	37.1701i	1.13014	−	1.25515i	0.167053	−	0.985948i	$-0.446575\pi$
$877$	33.4681	−	37.1701i	1.13014	−	1.25515i	0.963085	−	0.269197i	$-0.0867584\pi$
$878$	−11.1934	−	4.98361i	−0.377758	−	0.168189i
$879$		0			0
$880$	6.31479	+	5.22186i	0.212871	+	0.176029i
$881$	32.0798			1.08080			0.540399	−	0.841409i	$-0.318273\pi$
$881$	32.0798			1.08080			0.540399	+	0.841409i	$0.318273\pi$
$882$		0			0
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	0.832392	+	0.554188i	$0.186971\pi$
$883$	14.4035	+	44.3294i	0.484716	+	1.49180i	−0.347676	+	0.937615i	$0.613029\pi$
$884$	36.4067	+	40.4337i	1.22449	+	1.35993i
$885$		0			0
$886$	6.35525	−	60.4661i	0.213509	−	2.03140i
$887$	28.7087	−	6.10222i	0.963943	−	0.204892i	0.301052	−	0.953608i	$-0.402662\pi$
$887$	28.7087	−	6.10222i	0.963943	−	0.204892i	0.662892	+	0.748715i	$0.269329\pi$
$888$		0			0
$889$	−0.148487	−	1.41276i	−0.00498008	−	0.0473823i
$890$	0.0394273			0.00132161
$891$		0			0
$892$	63.7925			2.13593
$893$	0.563858	+	5.36475i	0.0188688	+	0.179524i
$894$		0			0
$895$	−0.870655	+	0.185063i	−0.0291028	+	0.00618598i
$896$	0.462201	−	4.39754i	0.0154410	−	0.146912i
$897$		0			0
$898$	24.2158	+	26.8944i	0.808093	+	0.897478i
$899$	7.61290	+	23.4301i	0.253904	+	0.781437i
$900$		0			0
$901$	15.8523			0.528116
$902$	−92.8253	−	5.82092i	−3.09075	−	0.193815i
$903$		0			0
$904$	14.2605	+	6.34917i	0.474296	+	0.211170i
$905$	2.42216	−	2.69009i	0.0805155	−	0.0894215i
$906$		0			0
$907$	−22.9479	+	10.2170i	−0.761971	+	0.339251i	−0.750663	−	0.660685i	$-0.770266\pi$
$907$	−22.9479	+	10.2170i	−0.761971	+	0.339251i	−0.0113074	+	0.999936i	$0.503599\pi$
$908$	−73.3389	−	53.2838i	−2.43384	−	1.76829i
$909$		0			0
$910$	−1.39341	−	4.28848i	−0.0461912	−	0.142162i
$911$	0.289433	+	2.75378i	0.00958936	+	0.0912366i	0.998270	−	0.0588001i	$-0.0187275\pi$
$911$	0.289433	+	2.75378i	0.00958936	+	0.0912366i	−0.988680	+	0.150037i	$0.952061\pi$
$912$		0			0
$913$	28.2910	−	42.6004i	0.936296	−	1.40987i
$914$	−14.2502	−	24.6820i	−0.471354	−	0.816408i
$915$		0			0
$916$	−96.7886	−	20.5731i	−3.19799	−	0.679753i
$917$	2.11327	−	6.50398i	0.0697863	−	0.214780i
$918$		0			0
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	0.418429	−	0.908250i	$-0.362581\pi$
$919$	−9.58156	−	6.96141i	−0.316066	−	0.229636i	−0.734495	+	0.678614i	$0.762581\pi$
$920$	6.81493	+	7.56874i	0.224682	+	0.249534i
$921$		0			0
$922$	7.03281	+	3.13121i	0.231613	+	0.103121i
$923$	21.5546	+	37.3337i	0.709478	+	1.22885i
$924$		0			0
$925$	−13.4272	+	23.2566i	−0.441484	+	0.764673i
$926$	57.6105	−	41.8565i	1.89320	−	1.37549i
$927$		0			0
$928$	22.6938	−	69.8443i	0.744960	−	2.29275i
$929$	−10.2852	+	4.57925i	−0.337445	+	0.150240i	−0.568462	−	0.822709i	$-0.692461\pi$
$929$	−10.2852	+	4.57925i	−0.337445	+	0.150240i	0.231017	+	0.972950i	$0.425795\pi$
$930$		0			0
$931$	−17.8367	+	3.79131i	−0.584574	+	0.124255i
$932$	−24.1938	+	26.8699i	−0.792494	+	0.880153i
$933$		0			0
$934$	14.8642	−	25.7455i	0.486371	−	0.842419i
$935$	−0.242762	+	1.43709i	−0.00793916	+	0.0469979i
$936$		0			0
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	−0.0830022	−	0.996549i	$-0.526451\pi$
$937$	25.6860	−	18.6619i	0.839123	−	0.609659i	0.922126	+	0.386891i	$0.126451\pi$
$938$	28.1220	+	5.97752i	0.918217	+	0.195173i
$939$		0			0
$940$	0.203585	−	1.93698i	0.00664021	−	0.0631774i
$941$	1.31809	−	12.5408i	0.0429686	−	0.408819i	−0.951804	−	0.306706i	$-0.900773\pi$
$941$	1.31809	−	12.5408i	0.0429686	−	0.408819i	0.994773	−	0.102113i	$-0.0325602\pi$
$942$		0			0
$943$	−57.9044	−	12.3080i	−1.88563	−	0.400802i
$944$	32.7721	−	23.8104i	1.06664	−	0.774961i
$945$		0			0
$946$	−104.760	+	15.4917i	−3.40606	+	0.503678i
$947$	−0.184885	+	0.320230i	−0.00600796	+	0.0104061i	−0.869014	−	0.494788i	$-0.835246\pi$
$947$	−0.184885	+	0.320230i	−0.00600796	+	0.0104061i	0.863006	+	0.505194i	$0.168579\pi$
$948$		0			0
$949$	2.25770	−	2.50743i	0.0732880	−	0.0813945i
$950$	−41.4385	+	8.80802i	−1.34444	+	0.285770i
$951$		0			0
$952$	15.2212	−	6.77693i	0.493323	−	0.219641i
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	−0.999344	−	0.0362151i	$-0.988470\pi$
$953$	−5.23478	+	16.1110i	−0.169571	+	0.521886i	0.829773	+	0.558101i	$0.188470\pi$
$954$		0			0
$955$	2.32257	−	1.68745i	0.0751567	−	0.0546046i
$956$	−23.6469	+	40.9576i	−0.764794	+	1.32466i
$957$		0			0
$958$	39.9467	+	69.1896i	1.29062	+	2.23542i
$959$	−0.144899	−	0.0645132i	−0.00467903	−	0.00208324i
$960$		0			0
$961$	−10.2633	−	11.3985i	−0.331073	−	0.367694i
$962$	−69.7714	−	50.6919i	−2.24952	−	1.63437i
$963$		0			0
$964$	−40.3299	+	124.123i	−1.29894	+	3.99772i
$965$	−5.28012	−	1.12232i	−0.169973	−	0.0361289i
$966$		0			0
$967$	−12.4080	−	21.4914i	−0.399016	−	0.691115i	0.594589	−	0.804030i	$-0.297315\pi$
$967$	−12.4080	−	21.4914i	−0.399016	−	0.691115i	−0.993605	+	0.112914i	$0.963981\pi$
$968$	83.5967	+	10.5258i	2.68690	+	0.338312i
$969$		0			0
$970$	0.401167	+	3.81685i	0.0128807	+	0.122552i
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	0.872679	−	0.488294i	$-0.162381\pi$
$971$	−3.75006	−	11.5415i	−0.120345	−	0.370384i	−0.993024	+	0.117910i	$0.962381\pi$
$972$		0			0
$973$	10.6922	+	7.76834i	0.342776	+	0.249042i
$974$	−7.68548	+	3.42179i	−0.246259	+	0.109641i
$975$		0			0
$976$	−74.0183	+	82.2056i	−2.36927	+	2.63134i
$977$	32.3180	+	14.3889i	1.03394	+	0.460342i	0.852317	−	0.523026i	$-0.175197\pi$
$977$	32.3180	+	14.3889i	1.03394	+	0.460342i	0.181627	+	0.983367i	$0.441864\pi$
$978$		0			0
$979$	0.175265	−	0.111277i	0.00560149	−	0.00355643i
$980$	6.58394			0.210316
$981$		0			0
$982$	−4.86006	−	14.9577i	−0.155091	−	0.477321i
$983$	15.0460	+	16.7103i	0.479894	+	0.532976i	0.933668	−	0.358141i	$-0.116589\pi$
$983$	15.0460	+	16.7103i	0.479894	+	0.532976i	−0.453774	+	0.891117i	$0.649923\pi$
$984$		0			0
$985$	−0.249233	+	2.37129i	−0.00794122	+	0.0755557i
$986$	29.3681	−	6.24238i	0.935270	−	0.198798i
$987$		0			0
$988$	−10.1070	−	96.1619i	−0.321547	−	3.05932i
$989$	−67.4036			−2.14331
$990$		0			0
$991$	16.2761			0.517028			0.258514	−	0.966008i	$-0.416767\pi$
$991$	16.2761			0.517028			0.258514	+	0.966008i	$0.416767\pi$
$992$	−4.88015	−	46.4315i	−0.154945	−	1.47420i
$993$		0			0
$994$	21.7780	−	4.62905i	0.690755	−	0.146825i
$995$	−0.389678	+	3.70753i	−0.0123536	+	0.117537i
$996$		0			0
$997$	3.09418	+	3.43644i	0.0979937	+	0.108833i	0.790147	−	0.612918i	$-0.210004\pi$
$997$	3.09418	+	3.43644i	0.0979937	+	0.108833i	−0.692153	+	0.721751i	$0.743338\pi$
$998$	23.8690	+	73.4612i	0.755560	+	2.32537i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.k.784.1		48
3.2	odd	2		891.2.n.j.784.6		48
9.2	odd	6		891.2.f.d.487.6	yes	24
9.4	even	3	inner	891.2.n.k.190.6		48
9.5	odd	6		891.2.n.j.190.1		48
9.7	even	3		891.2.f.c.487.1	✓	24
11.4	even	5	inner	891.2.n.k.136.6		48
33.26	odd	10		891.2.n.j.136.1		48
99.2	even	30		9801.2.a.cf.1.12		12
99.4	even	15	inner	891.2.n.k.433.1		48
99.20	odd	30		9801.2.a.ck.1.1		12
99.59	odd	30		891.2.n.j.433.6		48
99.70	even	15		891.2.f.c.730.1	yes	24
99.79	odd	30		9801.2.a.cl.1.1		12
99.92	odd	30		891.2.f.d.730.6	yes	24
99.97	even	15		9801.2.a.cg.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
891.2.f.c.487.1	✓	24	9.7	even	3
891.2.f.c.730.1	yes	24	99.70	even	15
891.2.f.d.487.6	yes	24	9.2	odd	6
891.2.f.d.730.6	yes	24	99.92	odd	30
891.2.n.j.136.1		48	33.26	odd	10
891.2.n.j.190.1		48	9.5	odd	6
891.2.n.j.433.6		48	99.59	odd	30
891.2.n.j.784.6		48	3.2	odd	2
891.2.n.k.136.6		48	11.4	even	5	inner
891.2.n.k.190.6		48	9.4	even	3	inner
891.2.n.k.433.1		48	99.4	even	15	inner
891.2.n.k.784.1		48	1.1	even	1	trivial
9801.2.a.cf.1.12		12	99.2	even	30
9801.2.a.cg.1.12		12	99.97	even	15
9801.2.a.ck.1.1		12	99.20	odd	30
9801.2.a.cl.1.1		12	99.79	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.274837 - 2.61490i) q^{2} +(-4.80585 + 1.02151i) q^{4} +(0.0250408 - 0.238247i) q^{5} +(-0.793477 - 0.881245i) q^{7} +(2.36698 + 7.28482i) q^{8} -0.629874 q^{10} +(-2.79995 + 1.77771i) q^{11} +(-5.51506 - 2.45546i) q^{13} +(-2.08629 + 2.31706i) q^{14} +(9.42161 - 4.19477i) q^{16} +(1.48403 + 1.07821i) q^{17} +(-1.00736 - 3.10034i) q^{19} +(0.123031 + 1.17056i) q^{20} +(5.41806 + 6.83301i) q^{22} +(2.77520 + 4.80679i) q^{23} +(4.83460 + 1.02763i) q^{25} +(-4.90504 + 15.0962i) q^{26} +(4.71353 + 3.42458i) q^{28} +(4.16541 + 4.62616i) q^{29} +(3.61535 + 1.60966i) q^{31} +(-5.89858 - 10.2166i) q^{32} +(2.41154 - 4.17691i) q^{34} +(-0.229824 + 0.166977i) q^{35} +(-1.67897 + 5.16733i) q^{37} +(-7.83020 + 3.48623i) q^{38} +(1.79486 - 0.381509i) q^{40} +(-7.13663 + 7.92603i) q^{41} +(-6.07195 + 10.5169i) q^{43} +(11.6402 - 11.4036i) q^{44} +(11.8065 - 8.57795i) q^{46} +(-1.61859 - 0.344042i) q^{47} +(0.584711 - 5.56316i) q^{49} +(1.35841 - 12.9244i) q^{50} +(29.0128 + 6.16687i) q^{52} +(6.99142 - 5.07956i) q^{53} +(0.353422 + 0.711596i) q^{55} +(4.54157 - 7.86622i) q^{56} +(10.9521 - 12.1636i) q^{58} +(3.84199 - 0.816641i) q^{59} +(-9.79858 + 4.36261i) q^{61} +(3.21546 - 9.89616i) q^{62} +(-8.40715 + 6.10815i) q^{64} +(-0.723109 + 1.25246i) q^{65} +(-4.61051 - 7.98564i) q^{67} +(-8.23341 - 3.66575i) q^{68} +(0.499790 + 0.555073i) q^{70} +(-5.77707 - 4.19728i) q^{71} +(-0.172710 + 0.531546i) q^{73} +(13.9735 + 2.97015i) q^{74} +(8.00827 + 13.8707i) q^{76} +(3.78830 + 1.05687i) q^{77} +(-0.462326 - 4.39874i) q^{79} +(-0.763468 - 2.34971i) q^{80} +(22.6872 + 16.4832i) q^{82} +(-14.0859 + 6.27144i) q^{83} +(0.294041 - 0.326566i) q^{85} +(29.1695 + 12.9871i) q^{86} +(-19.5777 - 16.1893i) q^{88} -0.0625956 q^{89} +(2.21221 + 6.80848i) q^{91} +(-18.2474 - 20.2658i) q^{92} +(-0.454786 + 4.32700i) q^{94} +(-0.763872 + 0.162366i) q^{95} +(-0.636901 - 6.05971i) q^{97} -14.7078 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} + 8 q^{4} - 4 q^{5} - 7 q^{7} + 20 q^{8} - 32 q^{10} - 5 q^{11} - 7 q^{13} - 13 q^{14} - 2 q^{16} - 10 q^{17} + 8 q^{19} - 27 q^{20} + 2 q^{22} - 6 q^{23} + 2 q^{25} - 68 q^{26} - 18 q^{28}+ \cdots + 136 q^{98}+O(q^{100}) \) 48 * q + 2 * q^2 + 8 * q^4 - 4 * q^5 - 7 * q^7 + 20 * q^8 - 32 * q^10 - 5 * q^11 - 7 * q^13 - 13 * q^14 - 2 * q^16 - 10 * q^17 + 8 * q^19 - 27 * q^20 + 2 * q^22 - 6 * q^23 + 2 * q^25 - 68 * q^26 - 18 * q^28 - 22 * q^29 - 2 * q^31 - 18 * q^32 + 42 * q^34 + 12 * q^37 + 5 * q^38 - 53 * q^40 - 10 * q^41 + 30 * q^43 + 118 * q^44 + 62 * q^46 - 4 * q^47 + 3 * q^49 - 9 * q^50 + 26 * q^52 + 34 * q^53 + 24 * q^55 + 48 * q^56 - 53 * q^58 - 11 * q^59 - 3 * q^61 - 4 * q^62 + 76 * q^64 + 68 * q^65 + 14 * q^67 - 22 * q^68 + 20 * q^70 - 72 * q^71 + 70 * q^73 - 3 * q^74 + 102 * q^76 + 88 * q^77 + 9 * q^79 - 74 * q^80 - 12 * q^82 - 32 * q^83 + 45 * q^85 + 110 * q^86 - 54 * q^88 + 68 * q^89 + 26 * q^91 + q^92 + 25 * q^94 + 84 * q^95 - 15 * q^97 + 136 * q^98

Introduction

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