LMFDB - Embedded newform 891.2.n.g.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			379.2
Character	$\chi$	$=$	891.379
Dual form			891.2.n.g.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.655019 - 0.139229i) q^{2} +(-1.41743 - 0.631078i) q^{4} +(2.70426 - 0.574808i) q^{5} +(-0.157889 - 1.50221i) q^{7} +(1.92410 + 1.39794i) q^{8} -1.85137 q^{10} +(-3.05136 - 1.29969i) q^{11} +(0.993724 - 1.10364i) q^{13} +(-0.105731 + 1.00596i) q^{14} +(1.01071 + 1.12251i) q^{16} +(1.46138 - 4.49766i) q^{17} +(2.87328 + 2.08756i) q^{19} +(-4.19583 - 0.891852i) q^{20} +(1.81775 + 1.27616i) q^{22} +(-1.04751 - 1.81434i) q^{23} +(2.41489 - 1.07518i) q^{25} +(-0.804567 + 0.584552i) q^{26} +(-0.724217 + 2.22891i) q^{28} +(-0.821016 - 7.81145i) q^{29} +(-5.86662 + 6.51554i) q^{31} +(-2.88407 - 4.99535i) q^{32} +(-1.58343 + 2.74259i) q^{34} +(-1.29045 - 3.97161i) q^{35} +(4.16960 - 3.02939i) q^{37} +(-1.59140 - 1.76743i) q^{38} +(6.00680 + 2.67440i) q^{40} +(-0.734494 + 6.98824i) q^{41} +(-1.45808 + 2.52546i) q^{43} +(3.50487 + 3.76786i) q^{44} +(0.433531 + 1.33427i) q^{46} +(1.98762 - 0.884945i) q^{47} +(4.61532 - 0.981018i) q^{49} +(-1.73149 + 0.368040i) q^{50} +(-2.10501 + 0.937212i) q^{52} +(-4.13417 - 12.7237i) q^{53} +(-8.99874 - 1.76076i) q^{55} +(1.79621 - 3.11112i) q^{56} +(-0.549796 + 5.23096i) q^{58} +(-6.14001 - 2.73371i) q^{59} +(-6.93526 - 7.70239i) q^{61} +(4.74990 - 3.45100i) q^{62} +(0.260092 + 0.800479i) q^{64} +(2.05290 - 3.55573i) q^{65} +(-6.01970 - 10.4264i) q^{67} +(-4.90977 + 5.45286i) q^{68} +(0.292311 + 2.78115i) q^{70} +(3.34410 - 10.2921i) q^{71} +(3.63900 - 2.64389i) q^{73} +(-3.15295 + 1.40378i) q^{74} +(-2.75524 - 4.77222i) q^{76} +(-1.47064 + 4.78899i) q^{77} +(15.0895 + 3.20738i) q^{79} +(3.37845 + 2.45459i) q^{80} +(1.45407 - 4.47517i) q^{82} +(2.24043 + 2.48824i) q^{83} +(1.36666 - 13.0029i) q^{85} +(1.30668 - 1.45122i) q^{86} +(-4.05422 - 6.76635i) q^{88} -10.6583 q^{89} +(-1.81480 - 1.31853i) q^{91} +(0.339776 + 3.23276i) q^{92} +(-1.42514 + 0.302923i) q^{94} +(8.97003 + 3.99371i) q^{95} +(-2.17186 - 0.461642i) q^{97} -3.15971 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100}) $ 32 * q - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

Character values

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

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

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 $

$2$	−0.655019	−	0.139229i	−0.463168	−	0.0984495i	−0.0295838	−	0.999562i	$-0.509418\pi$
$2$	−0.655019	−	0.139229i	−0.463168	−	0.0984495i	−0.433585	+	0.901113i	$0.642752\pi$
$3$		0			0
$3$		0			0
$4$	−1.41743	−	0.631078i	−0.708713	−	0.315539i
$5$	2.70426	−	0.574808i	1.20938	−	0.257062i	0.441268	−	0.897375i	$-0.354529\pi$
$5$	2.70426	−	0.574808i	1.20938	−	0.257062i	0.768114	+	0.640313i	$0.221196\pi$
$6$		0			0
$7$	−0.157889	−	1.50221i	−0.0596763	−	0.567782i	−0.982980	−	0.183712i	$-0.941189\pi$
$7$	−0.157889	−	1.50221i	−0.0596763	−	0.567782i	0.923304	−	0.384070i	$-0.125478\pi$
$8$	1.92410	+	1.39794i	0.680271	+	0.494246i
$9$		0			0
$10$	−1.85137			−0.585455
$11$	−3.05136	−	1.29969i	−0.920020	−	0.391872i
$11$	−3.05136	−	1.29969i	−0.920020	−	0.391872i
$12$		0			0
$13$	0.993724	−	1.10364i	0.275609	−	0.306095i	−0.589410	−	0.807834i	$-0.700640\pi$
$13$	0.993724	−	1.10364i	0.275609	−	0.306095i	0.865019	+	0.501739i	$0.167306\pi$
$14$	−0.105731	+	1.00596i	−0.0282577	+	0.268854i
$15$		0			0
$16$	1.01071	+	1.12251i	0.252678	+	0.280627i
$17$	1.46138	−	4.49766i	0.354436	−	1.09084i	−0.601899	−	0.798572i	$-0.705589\pi$
$17$	1.46138	−	4.49766i	0.354436	−	1.09084i	0.956336	−	0.292271i	$-0.0944109\pi$
$18$		0			0
$19$	2.87328	+	2.08756i	0.659175	+	0.478919i	0.866384	−	0.499378i	$-0.166438\pi$
$19$	2.87328	+	2.08756i	0.659175	+	0.478919i	−0.207209	+	0.978297i	$0.566438\pi$
$20$	−4.19583	−	0.891852i	−0.938217	−	0.199424i
$21$		0			0
$22$	1.81775	+	1.27616i	0.387545	+	0.272078i
$23$	−1.04751	−	1.81434i	−0.218421	−	0.378316i	0.735904	−	0.677086i	$-0.236757\pi$
$23$	−1.04751	−	1.81434i	−0.218421	−	0.378316i	−0.954325	+	0.298769i	$0.903424\pi$
$24$		0			0
$25$	2.41489	−	1.07518i	0.482977	−	0.215035i
$26$	−0.804567	+	0.584552i	−0.157788	+	0.114640i
$27$		0			0
$28$	−0.724217	+	2.22891i	−0.136864	+	0.421225i
$29$	−0.821016	−	7.81145i	−0.152459	−	1.45055i	−0.756708	−	0.653753i	$-0.773193\pi$
$29$	−0.821016	−	7.81145i	−0.152459	−	1.45055i	0.604249	−	0.796796i	$-0.293473\pi$
$30$		0			0
$31$	−5.86662	+	6.51554i	−1.05368	+	1.17023i	−0.0686815	+	0.997639i	$0.521879\pi$
$31$	−5.86662	+	6.51554i	−1.05368	+	1.17023i	−0.984994	+	0.172587i	$0.944787\pi$
$32$	−2.88407	−	4.99535i	−0.509836	−	0.883061i
$33$		0			0
$34$	−1.58343	+	2.74259i	−0.271557	+	0.470350i
$35$	−1.29045	−	3.97161i	−0.218127	−	0.671325i
$36$		0			0
$37$	4.16960	−	3.02939i	0.685478	−	0.498029i	−0.189693	−	0.981844i	$-0.560749\pi$
$37$	4.16960	−	3.02939i	0.685478	−	0.498029i	0.875170	+	0.483815i	$0.160749\pi$
$38$	−1.59140	−	1.76743i	−0.258160	−	0.286715i
$39$		0			0
$40$	6.00680	+	2.67440i	0.949759	+	0.422860i
$41$	−0.734494	+	6.98824i	−0.114709	+	1.09138i	0.774088	+	0.633078i	$0.218209\pi$
$41$	−0.734494	+	6.98824i	−0.114709	+	1.09138i	−0.888796	+	0.458302i	$0.848458\pi$
$42$		0			0
$43$	−1.45808	+	2.52546i	−0.222355	+	0.385129i	−0.955522	−	0.294918i	$-0.904708\pi$
$43$	−1.45808	+	2.52546i	−0.222355	+	0.385129i	0.733168	+	0.680048i	$0.238041\pi$
$44$	3.50487	+	3.76786i	0.528379	+	0.568027i
$45$		0			0
$46$	0.433531	+	1.33427i	0.0639207	+	0.196728i
$47$	1.98762	−	0.884945i	0.289924	−	0.129083i	−0.256621	−	0.966512i	$-0.582609\pi$
$47$	1.98762	−	0.884945i	0.289924	−	0.129083i	0.546545	+	0.837430i	$0.315943\pi$
$48$		0			0
$49$	4.61532	−	0.981018i	0.659332	−	0.140145i
$50$	−1.73149	+	0.368040i	−0.244870	+	0.0520487i
$51$		0			0
$52$	−2.10501	+	0.937212i	−0.291913	+	0.129968i
$53$	−4.13417	−	12.7237i	−0.567872	−	1.74773i	−0.659260	−	0.751915i	$-0.729130\pi$
$53$	−4.13417	−	12.7237i	−0.567872	−	1.74773i	0.0913880	−	0.995815i	$-0.470870\pi$
$54$		0			0
$55$	−8.99874	−	1.76076i	−1.21339	−	0.237421i
$56$	1.79621	−	3.11112i	0.240028	−	0.415741i
$57$		0			0
$58$	−0.549796	+	5.23096i	−0.0721917	+	0.686858i
$59$	−6.14001	−	2.73371i	−0.799361	−	0.355899i	−0.0339365	−	0.999424i	$-0.510804\pi$
$59$	−6.14001	−	2.73371i	−0.799361	−	0.355899i	−0.765425	+	0.643525i	$0.777471\pi$
$60$		0			0
$61$	−6.93526	−	7.70239i	−0.887969	−	0.986190i	0.112002	−	0.993708i	$-0.464274\pi$
$61$	−6.93526	−	7.70239i	−0.887969	−	0.986190i	−0.999972	+	0.00751803i	$0.997607\pi$
$62$	4.74990	−	3.45100i	0.603238	−	0.438278i
$63$		0			0
$64$	0.260092	+	0.800479i	0.0325114	+	0.100060i
$65$	2.05290	−	3.55573i	0.254631	−	0.441035i
$66$		0			0
$67$	−6.01970	−	10.4264i	−0.735423	−	1.27379i	−0.954538	−	0.298091i	$-0.903650\pi$
$67$	−6.01970	−	10.4264i	−0.735423	−	1.27379i	0.219115	−	0.975699i	$-0.429683\pi$
$68$	−4.90977	+	5.45286i	−0.595397	+	0.661256i
$69$		0			0
$70$	0.292311	+	2.78115i	0.0349378	+	0.332411i
$71$	3.34410	−	10.2921i	0.396872	−	1.22145i	−0.530622	−	0.847608i	$-0.678042\pi$
$71$	3.34410	−	10.2921i	0.396872	−	1.22145i	0.927494	−	0.373838i	$-0.121958\pi$
$72$		0			0
$73$	3.63900	−	2.64389i	0.425913	−	0.309444i	−0.354099	−	0.935208i	$-0.615213\pi$
$73$	3.63900	−	2.64389i	0.425913	−	0.309444i	0.780013	+	0.625764i	$0.215213\pi$
$74$	−3.15295	+	1.40378i	−0.366522	+	0.163186i
$75$		0			0
$76$	−2.75524	−	4.77222i	−0.316048	−	0.547411i
$77$	−1.47064	+	4.78899i	−0.167595	+	0.545756i
$78$		0			0
$79$	15.0895	+	3.20738i	1.69770	+	0.360858i	0.952161	−	0.305598i	$-0.0988564\pi$
$79$	15.0895	+	3.20738i	1.69770	+	0.360858i	0.745544	+	0.666456i	$0.232190\pi$
$80$	3.37845	+	2.45459i	0.377723	+	0.274432i
$81$		0			0
$82$	1.45407	−	4.47517i	0.160575	−	0.494200i
$83$	2.24043	+	2.48824i	0.245919	+	0.273120i	0.853449	−	0.521176i	$-0.174506\pi$
$83$	2.24043	+	2.48824i	0.245919	+	0.273120i	−0.607531	+	0.794296i	$0.707840\pi$
$84$		0			0
$85$	1.36666	−	13.0029i	0.148235	−	1.41036i
$86$	1.30668	−	1.45122i	0.140903	−	0.156489i
$87$		0			0
$88$	−4.05422	−	6.76635i	−0.432182	−	0.721295i
$89$	−10.6583			−1.12978			−0.564888	−	0.825167i	$-0.691081\pi$
$89$	−10.6583			−1.12978			−0.564888	+	0.825167i	$0.691081\pi$
$90$		0			0
$91$	−1.81480	−	1.31853i	−0.190243	−	0.138219i
$92$	0.339776	+	3.23276i	0.0354241	+	0.337038i
$93$		0			0
$94$	−1.42514	+	0.302923i	−0.146992	+	0.0312441i
$95$	8.97003	+	3.99371i	0.920306	+	0.409746i
$96$		0			0
$97$	−2.17186	−	0.461642i	−0.220519	−	0.0468727i	0.0963273	−	0.995350i	$-0.469290\pi$
$97$	−2.17186	−	0.461642i	−0.220519	−	0.0468727i	−0.316846	+	0.948477i	$0.602624\pi$
$98$	−3.15971			−0.319179
$99$		0			0
$100$	−4.10144			−0.410144
$101$	0.475271	+	0.101022i	0.0472912	+	0.0100521i	0.231497	−	0.972836i	$-0.425638\pi$
$101$	0.475271	+	0.101022i	0.0472912	+	0.0100521i	−0.184205	+	0.982888i	$0.558971\pi$
$102$		0			0
$103$	−5.84003	−	2.60015i	−0.575435	−	0.256200i	0.0983201	−	0.995155i	$-0.468653\pi$
$103$	−5.84003	−	2.60015i	−0.575435	−	0.256200i	−0.673755	+	0.738955i	$0.735320\pi$
$104$	3.45484	−	0.734350i	0.338775	−	0.0720089i
$105$		0			0
$106$	0.936462	+	8.90984i	0.0909572	+	0.865400i
$107$	9.78725	+	7.11085i	0.946169	+	0.687432i	0.949898	−	0.312561i	$-0.101187\pi$
$107$	9.78725	+	7.11085i	0.946169	+	0.687432i	−0.00372856	+	0.999993i	$0.501187\pi$
$108$		0			0
$109$	−4.73854			−0.453870			−0.226935	−	0.973910i	$-0.572871\pi$
$109$	−4.73854			−0.453870			−0.226935	+	0.973910i	$0.572871\pi$
$110$	5.64920	+	2.40621i	0.538630	+	0.229423i
$111$		0			0
$112$	1.52667	−	1.69553i	0.144256	−	0.160213i
$113$	1.92115	−	18.2786i	0.180727	−	1.71950i	−0.409539	−	0.912293i	$-0.634310\pi$
$113$	1.92115	−	18.2786i	0.180727	−	1.71950i	0.590266	−	0.807209i	$-0.299023\pi$
$114$		0			0
$115$	−3.87564	−	4.30433i	−0.361405	−	0.401381i
$116$	−3.76591	+	11.5903i	−0.349656	+	1.07613i
$117$		0			0
$118$	3.64121	+	2.64550i	0.335201	+	0.243538i
$119$	−6.98717	−	1.48517i	−0.640513	−	0.136145i
$120$		0			0
$121$	7.62160	+	7.93166i	0.692873	+	0.721060i
$122$	3.47034	+	6.01080i	0.314190	+	0.544192i
$123$		0			0
$124$	12.4273	−	5.53300i	1.11601	−	0.496878i
$125$	−5.27088	+	3.82952i	−0.471442	+	0.342523i
$126$		0			0
$127$	−6.90430	+	21.2493i	−0.612658	+	1.88557i	−0.181156	+	0.983454i	$0.557984\pi$
$127$	−6.90430	+	21.2493i	−0.612658	+	1.88557i	−0.431501	+	0.902112i	$0.642016\pi$
$128$	1.14695	+	10.9125i	0.101377	+	0.964540i
$129$		0			0
$130$	−1.83975	+	2.04325i	−0.161357	+	0.179205i
$131$	1.98522	+	3.43851i	0.173450	+	0.300424i	0.939624	−	0.342209i	$-0.111175\pi$
$131$	1.98522	+	3.43851i	0.173450	+	0.300424i	−0.766174	+	0.642633i	$0.777842\pi$
$132$		0			0
$133$	2.68229	−	4.64587i	0.232584	−	0.402848i
$134$	2.49136	+	7.66762i	0.215221	+	0.662381i
$135$		0			0
$136$	9.09929	−	6.61102i	0.780258	−	0.566890i
$137$	4.00879	+	4.45221i	0.342494	+	0.380378i	0.889643	−	0.456657i	$-0.150953\pi$
$137$	4.00879	+	4.45221i	0.342494	+	0.380378i	−0.547149	+	0.837035i	$0.684287\pi$
$138$		0			0
$139$	15.7023	+	6.99113i	1.33186	+	0.592980i	0.944367	−	0.328895i	$-0.106676\pi$
$139$	15.7023	+	6.99113i	1.33186	+	0.592980i	0.387488	+	0.921875i	$0.373343\pi$
$140$	−0.677275	+	6.44384i	−0.0572402	+	0.544604i
$141$		0			0
$142$	−3.62340	+	6.27592i	−0.304069	+	0.526664i
$143$	−4.46660	+	2.07607i	−0.373516	+	0.173610i
$144$		0			0
$145$	−6.71032	−	20.6522i	−0.557262	−	1.71508i
$146$	−2.75172	+	1.22515i	−0.227734	+	0.101394i
$147$		0			0
$148$	−7.82188	+	1.66259i	−0.642955	+	0.136664i
$149$	12.5939	−	2.67691i	1.03173	−	0.219301i	0.339218	−	0.940708i	$-0.389838\pi$
$149$	12.5939	−	2.67691i	1.03173	−	0.219301i	0.692511	+	0.721407i	$0.256504\pi$
$150$		0			0
$151$	−7.68194	+	3.42022i	−0.625147	+	0.278334i	−0.694761	−	0.719240i	$-0.744490\pi$
$151$	−7.68194	+	3.42022i	−0.625147	+	0.278334i	0.0696138	+	0.997574i	$0.477823\pi$
$152$	2.61019	+	8.03333i	0.211714	+	0.651589i
$153$		0			0
$154$	1.63006	−	2.93213i	0.131354	−	0.236278i
$155$	−12.1197	+	20.9919i	−0.973476	+	1.68611i
$156$		0			0
$157$	−1.23471	+	11.7475i	−0.0985406	+	0.937552i	0.827840	+	0.560964i	$0.189569\pi$
$157$	−1.23471	+	11.7475i	−0.0985406	+	0.937552i	−0.926381	+	0.376588i	$0.877097\pi$
$158$	−9.43737	−	4.20179i	−0.750797	−	0.334276i
$159$		0			0
$160$	−10.6706	−	11.8509i	−0.843587	−	0.936898i
$161$	−2.56013	+	1.86005i	−0.201767	+	0.146592i
$162$		0			0
$163$	1.42569	+	4.38781i	0.111668	+	0.343680i	0.991238	−	0.132091i	$-0.0421691\pi$
$163$	1.42569	+	4.38781i	0.111668	+	0.343680i	−0.879569	+	0.475771i	$0.842169\pi$
$164$	5.45122	−	9.44179i	0.425669	−	0.737280i
$165$		0			0
$166$	−1.12109	−	1.94178i	−0.0870132	−	0.150711i
$167$	6.58855	−	7.31732i	0.509837	−	0.566231i	−0.432184	−	0.901786i	$-0.642257\pi$
$167$	6.58855	−	7.31732i	0.509837	−	0.566231i	0.942021	+	0.335554i	$0.108924\pi$
$168$		0			0
$169$	1.12833	+	10.7354i	0.0867947	+	0.825797i
$170$	−2.70556	+	8.32684i	−0.207507	+	0.638640i
$171$		0			0
$172$	3.66048	−	2.65949i	0.279109	−	0.202785i
$173$	13.4172	−	5.97372i	1.02009	−	0.454173i	0.172604	−	0.984991i	$-0.444782\pi$
$173$	13.4172	−	5.97372i	1.02009	−	0.454173i	0.847486	+	0.530818i	$0.178115\pi$
$174$		0			0
$175$	−1.99643	−	3.45791i	−0.150916	−	0.261393i
$176$	−1.62513	−	4.73880i	−0.122499	−	0.357200i
$177$		0			0
$178$	6.98139	+	1.48394i	0.523277	+	0.111226i
$179$	9.16182	+	6.65645i	0.684787	+	0.497527i	0.874942	−	0.484227i	$-0.160899\pi$
$179$	9.16182	+	6.65645i	0.684787	+	0.497527i	−0.190156	+	0.981754i	$0.560899\pi$
$180$		0			0
$181$	−1.94459	+	5.98485i	−0.144541	+	0.444850i	−0.996952	−	0.0780221i	$-0.975140\pi$
$181$	−1.94459	+	5.98485i	−0.144541	+	0.444850i	0.852411	+	0.522872i	$0.175140\pi$
$182$	1.00515	+	1.11633i	0.0745068	+	0.0827482i
$183$		0			0
$184$	0.520826	−	4.95533i	0.0383958	−	0.365311i
$185$	9.53436	−	10.5890i	0.700980	−	0.778517i
$186$		0			0
$187$	−10.3048	+	11.8246i	−0.753559	+	0.864704i
$188$	−3.37577			−0.246204
$189$		0			0
$190$	−5.31950	−	3.86484i	−0.385917	−	0.280385i
$191$	0.383598	+	3.64969i	0.0277562	+	0.264082i	0.999596	+	0.0284381i	$0.00905335\pi$
$191$	0.383598	+	3.64969i	0.0277562	+	0.264082i	−0.971839	+	0.235644i	$0.924280\pi$
$192$		0			0
$193$	−1.37495	+	0.292255i	−0.0989711	+	0.0210370i	−0.257131	−	0.966377i	$-0.582777\pi$
$193$	−1.37495	+	0.292255i	−0.0989711	+	0.0210370i	0.158160	+	0.987414i	$0.449444\pi$
$194$	1.35833	+	0.604769i	0.0975227	+	0.0434199i
$195$		0			0
$196$	−7.16098	−	1.52211i	−0.511498	−	0.108722i
$197$	−3.38982			−0.241514			−0.120757	−	0.992682i	$-0.538532\pi$
$197$	−3.38982			−0.241514			−0.120757	+	0.992682i	$0.538532\pi$
$198$		0			0
$199$	7.38470			0.523487			0.261744	−	0.965137i	$-0.415703\pi$
$199$	7.38470			0.523487			0.261744	+	0.965137i	$0.415703\pi$
$200$	6.14951	+	1.30712i	0.434836	+	0.0924272i
$201$		0			0
$202$	−0.297246	−	0.132343i	−0.0209142	−	0.00931159i
$203$	−11.6048	+	2.46668i	−0.814498	+	0.173127i
$204$		0			0
$205$	2.03064	+	19.3202i	0.141826	+	1.34938i
$206$	3.46332	+	2.51625i	0.241301	+	0.175315i
$207$		0			0
$208$	2.24322			0.155539
$209$	−6.05422	−	10.1043i	−0.418779	−	0.698927i
$210$		0			0
$211$	−1.30097	+	1.44488i	−0.0895626	+	0.0994693i	−0.786260	−	0.617896i	$-0.787985\pi$
$211$	−1.30097	+	1.44488i	−0.0895626	+	0.0994693i	0.696697	+	0.717365i	$0.254652\pi$
$212$	−2.16975	+	20.6438i	−0.149019	+	1.41782i
$213$		0			0
$214$	−5.42080	−	6.02041i	−0.370558	−	0.411547i
$215$	−2.49136	+	7.66762i	−0.169909	+	0.522927i
$216$		0			0
$217$	10.7140	+	7.78417i	0.727313	+	0.528424i
$218$	3.10384	+	0.659741i	0.210218	+	0.0446833i
$219$		0			0
$220$	11.6439	+	8.17466i	0.785030	+	0.551135i
$221$	−3.51160	−	6.08227i	−0.236216	−	0.409138i
$222$		0			0
$223$	15.5108	−	6.90587i	1.03868	−	0.462452i	0.184723	−	0.982791i	$-0.440861\pi$
$223$	15.5108	−	6.90587i	1.03868	−	0.462452i	0.853960	+	0.520339i	$0.174194\pi$
$224$	−7.04870	+	5.12118i	−0.470961	+	0.342173i
$225$		0			0
$226$	−3.80329	+	11.7053i	−0.252991	+	0.778626i
$227$	1.70425	+	16.2149i	0.113115	+	1.07622i	0.892926	+	0.450203i	$0.148648\pi$
$227$	1.70425	+	16.2149i	0.113115	+	1.07622i	−0.779811	+	0.626015i	$0.784685\pi$
$228$		0			0
$229$	−13.5976	+	15.1017i	−0.898554	+	0.997946i	0.101441	+	0.994842i	$0.467655\pi$
$229$	−13.5976	+	15.1017i	−0.898554	+	0.997946i	−0.999995	+	0.00310418i	$0.999012\pi$
$230$	1.93933	+	3.35902i	0.127876	+	0.221487i
$231$		0			0
$232$	9.34021	−	16.1777i	0.613215	−	1.06212i
$233$	−0.139989	−	0.430843i	−0.00917101	−	0.0282255i	0.946366	−	0.323096i	$-0.104724\pi$
$233$	−0.139989	−	0.430843i	−0.00917101	−	0.0282255i	−0.955537	+	0.294870i	$0.904724\pi$
$234$		0			0
$235$	4.86637	−	3.53562i	0.317447	−	0.230639i
$236$	6.97782	+	7.74966i	0.454217	+	0.504460i
$237$		0			0
$238$	4.36995	+	1.94563i	0.283262	+	0.126116i
$239$	1.99061	−	18.9394i	0.128762	−	1.22509i	−0.719113	−	0.694893i	$-0.755452\pi$
$239$	1.99061	−	18.9394i	0.128762	−	1.22509i	0.847875	−	0.530196i	$-0.177882\pi$
$240$		0			0
$241$	8.93559	−	15.4769i	0.575592	−	0.996955i	−0.420385	−	0.907346i	$-0.638105\pi$
$241$	8.93559	−	15.4769i	0.575592	−	0.996955i	0.995977	−	0.0896090i	$-0.0285617\pi$
$242$	−3.88798	−	6.25653i	−0.249929	−	0.402185i
$243$		0			0
$244$	4.96941	+	15.2943i	0.318134	+	0.979114i
$245$	11.9171	−	5.30585i	0.761358	−	0.338978i
$246$		0			0
$247$	5.15916	−	1.09661i	0.328269	−	0.0697758i
$248$	−20.3963	+	4.33536i	−1.29516	+	0.275296i
$249$		0			0
$250$	3.98571	−	1.77455i	0.252078	−	0.112232i
$251$	−3.85401	−	11.8614i	−0.243263	−	0.748687i	−0.995917	−	0.0902709i	$-0.971227\pi$
$251$	−3.85401	−	11.8614i	−0.243263	−	0.748687i	0.752654	−	0.658416i	$-0.228773\pi$
$252$		0			0
$253$	0.838246	+	6.89765i	0.0527001	+	0.433652i
$254$	7.48095	−	12.9574i	0.469397	−	0.813019i
$255$		0			0
$256$	0.944018	−	8.98173i	0.0590011	−	0.561358i
$257$	22.0169	+	9.80254i	1.37337	+	0.611465i	0.954945	−	0.296784i	$-0.0959142\pi$
$257$	22.0169	+	9.80254i	1.37337	+	0.611465i	0.418429	+	0.908249i	$0.362581\pi$
$258$		0			0
$259$	−5.20912	−	5.78531i	−0.323679	−	0.359482i
$260$	−5.15379	+	3.74444i	−0.319624	+	0.232221i
$261$		0			0
$262$	−0.821621	−	2.52869i	−0.0507599	−	0.156223i
$263$	−9.07714	+	15.7221i	−0.559720	+	0.969464i	0.437799	+	0.899073i	$0.355758\pi$
$263$	−9.07714	+	15.7221i	−0.559720	+	0.969464i	−0.997519	+	0.0703912i	$0.977575\pi$
$264$		0			0
$265$	−18.4935	−	32.0317i	−1.13605	−	1.96769i
$266$	−2.40379	+	2.66968i	−0.147386	+	0.163689i
$267$		0			0
$268$	1.95258	+	18.5776i	0.119273	+	1.13481i
$269$	−4.12310	+	12.6896i	−0.251390	+	0.773698i	0.743130	+	0.669147i	$0.233340\pi$
$269$	−4.12310	+	12.6896i	−0.251390	+	0.773698i	−0.994520	+	0.104551i	$0.966660\pi$
$270$		0			0
$271$	5.26488	−	3.82516i	0.319819	−	0.232362i	−0.416279	−	0.909237i	$-0.636666\pi$
$271$	5.26488	−	3.82516i	0.319819	−	0.232362i	0.736098	+	0.676875i	$0.236666\pi$
$272$	6.52570	−	2.90543i	0.395679	−	0.176168i
$273$		0			0
$274$	−2.00596	−	3.47442i	−0.121184	−	0.209898i
$275$	−8.76609	+	0.142142i	−0.528615	+	0.00857148i
$276$		0			0
$277$	13.2624	+	2.81902i	0.796862	+	0.169378i	0.588313	−	0.808634i	$-0.299792\pi$
$277$	13.2624	+	2.81902i	0.796862	+	0.169378i	0.208549	+	0.978012i	$0.433126\pi$
$278$	−9.31197	−	6.76554i	−0.558495	−	0.405770i
$279$		0			0
$280$	3.06911	−	9.44574i	0.183414	−	0.564491i
$281$	20.4620	+	22.7254i	1.22066	+	1.35568i	0.914955	+	0.403556i	$0.132226\pi$
$281$	20.4620	+	22.7254i	1.22066	+	1.35568i	0.305707	+	0.952126i	$0.401107\pi$
$282$		0			0
$283$	0.0784979	−	0.746858i	0.00466622	−	0.0443961i	−0.991941	−	0.126700i	$-0.959561\pi$
$283$	0.0784979	−	0.746858i	0.00466622	−	0.0443961i	0.996607	+	0.0823044i	$0.0262280\pi$
$284$	−11.2351	+	12.4779i	−0.666682	+	0.740426i
$285$		0			0
$286$	3.21476	−	0.737989i	0.190093	−	0.0436382i
$287$	10.6138			0.626512
$288$		0			0
$289$	−4.34004	−	3.15323i	−0.255297	−	0.185484i
$290$	1.52001	+	14.4619i	0.0892578	+	0.849231i
$291$		0			0
$292$	−6.82652	+	1.45102i	−0.399492	+	0.0849146i
$293$	−13.8990	−	6.18825i	−0.811990	−	0.361521i	−0.0416320	−	0.999133i	$-0.513256\pi$
$293$	−13.8990	−	6.18825i	−0.811990	−	0.361521i	−0.770358	+	0.637612i	$0.779922\pi$
$294$		0			0
$295$	−18.1755	−	3.86333i	−1.05822	−	0.224932i
$296$	12.2576			0.712460
$297$		0			0
$298$	−8.62192			−0.499454
$299$	−3.04332	−	0.646878i	−0.176000	−	0.0374099i
$300$		0			0
$301$	4.02399	+	1.79160i	0.231939	+	0.103266i
$302$	5.50801	−	1.17076i	0.316950	−	0.0673699i
$303$		0			0
$304$	0.560752	+	5.33520i	0.0321613	+	0.305995i
$305$	−23.1821	−	16.8428i	−1.32741	−	0.964417i
$306$		0			0
$307$	2.79291			0.159400			0.0797000	−	0.996819i	$-0.474604\pi$
$307$	2.79291			0.159400			0.0797000	+	0.996819i	$0.474604\pi$
$308$	5.10675	−	5.85995i	0.290984	−	0.333902i
$309$		0			0
$310$	10.8613	−	12.0627i	0.616880	−	0.685114i
$311$	−2.43054	+	23.1250i	−0.137823	+	1.31130i	0.678883	+	0.734246i	$0.262464\pi$
$311$	−2.43054	+	23.1250i	−0.137823	+	1.31130i	−0.816706	+	0.577053i	$0.804202\pi$
$312$		0			0
$313$	−9.31595	−	10.3464i	−0.526569	−	0.584814i	0.419916	−	0.907563i	$-0.362060\pi$
$313$	−9.31595	−	10.3464i	−0.526569	−	0.584814i	−0.946485	+	0.322749i	$0.895393\pi$
$314$	2.44435	−	7.52292i	0.137942	−	0.424543i
$315$		0			0
$316$	−19.3642	−	14.0689i	−1.08932	−	0.791437i
$317$	6.35962	+	1.35178i	0.357192	+	0.0759235i	0.383013	−	0.923743i	$-0.374887\pi$
$317$	6.35962	+	1.35178i	0.357192	+	0.0759235i	−0.0258206	+	0.999667i	$0.508220\pi$
$318$		0			0
$319$	−7.64726	+	24.9026i	−0.428164	+	1.39428i
$320$	1.16348	+	2.01520i	0.0650403	+	0.112653i
$321$		0			0
$322$	1.93591	−	0.861922i	0.107884	−	0.0480330i
$323$	13.5881	−	9.87231i	0.756061	−	0.549310i
$324$		0			0
$325$	1.21312	−	3.73360i	0.0672918	−	0.207103i
$326$	−0.322943	−	3.07260i	−0.0178861	−	0.170175i
$327$		0			0
$328$	−11.1824	+	12.4193i	−0.617443	+	0.685740i
$329$	−1.64320	−	2.84610i	−0.0905924	−	0.156911i
$330$		0			0
$331$	6.50427	−	11.2657i	0.357507	−	0.619220i	−0.630037	−	0.776565i	$-0.716960\pi$
$331$	6.50427	−	11.2657i	0.357507	−	0.619220i	0.987544	+	0.157345i	$0.0502935\pi$
$332$	−1.60536	−	4.94079i	−0.0881055	−	0.271161i
$333$		0			0
$334$	−5.33441	+	3.87567i	−0.291886	+	0.212067i
$335$	−22.2720	−	24.7356i	−1.21685	−	1.35145i
$336$		0			0
$337$	26.6480	+	11.8644i	1.45161	+	0.646297i	0.972805	−	0.231626i	$-0.0744046\pi$
$337$	26.6480	+	11.8644i	1.45161	+	0.646297i	0.478802	+	0.877923i	$0.341071\pi$
$338$	0.755590	−	7.18896i	0.0410987	−	0.391028i
$339$		0			0
$340$	−10.1430	+	17.5681i	−0.550079	+	0.952765i
$341$	26.3694	−	12.2565i	1.42798	−	0.663725i
$342$		0			0
$343$	−5.46976	−	16.8342i	−0.295339	−	0.908961i
$344$	−6.33592	+	2.82093i	−0.341610	+	0.152095i
$345$		0			0
$346$	−9.62023	+	2.04484i	−0.517187	+	0.109931i
$347$	22.6451	−	4.81337i	1.21565	−	0.258395i	0.444931	−	0.895565i	$-0.353228\pi$
$347$	22.6451	−	4.81337i	1.21565	−	0.258395i	0.770724	+	0.637170i	$0.219895\pi$
$348$		0			0
$349$	−7.75634	+	3.45335i	−0.415188	+	0.184853i	−0.603690	−	0.797219i	$-0.706303\pi$
$349$	−7.75634	+	3.45335i	−0.415188	+	0.184853i	0.188502	+	0.982073i	$0.439637\pi$
$350$	0.826257	+	2.54296i	0.0441653	+	0.135927i
$351$		0			0
$352$	2.30791	+	18.9910i	0.123012	+	1.01222i
$353$	−0.687569	+	1.19090i	−0.0365956	+	0.0633854i	−0.883743	−	0.467972i	$-0.844985\pi$
$353$	−0.687569	+	1.19090i	−0.0365956	+	0.0633854i	0.847148	+	0.531358i	$0.178318\pi$
$354$		0			0
$355$	3.12734	−	29.7547i	0.165982	−	1.57922i
$356$	15.1073	+	6.72622i	0.800687	+	0.356489i
$357$		0			0
$358$	−5.07440	−	5.63569i	−0.268190	−	0.297856i
$359$	−16.8945	+	12.2746i	−0.891658	+	0.647827i	−0.936310	−	0.351175i	$-0.885782\pi$
$359$	−16.8945	+	12.2746i	−0.891658	+	0.647827i	0.0446518	+	0.999003i	$0.485782\pi$
$360$		0			0
$361$	−1.97350	−	6.07381i	−0.103868	−	0.319674i
$362$	2.10701	−	3.64945i	0.110742	−	0.191811i
$363$		0			0
$364$	1.74025	+	3.01420i	0.0912138	+	0.157987i
$365$	8.32108	−	9.24150i	0.435545	−	0.483722i
$366$		0			0
$367$	−1.30131	−	12.3811i	−0.0679276	−	0.646288i	−0.974523	−	0.224287i	$-0.927995\pi$
$367$	−1.30131	−	12.3811i	−0.0679276	−	0.646288i	0.906595	−	0.422001i	$-0.138672\pi$
$368$	0.977884	−	3.00962i	0.0509757	−	0.156887i
$369$		0			0
$370$	−7.71948	+	5.60853i	−0.401316	+	0.291574i
$371$	−18.4609	+	8.21932i	−0.958442	+	0.426726i
$372$		0			0
$373$	14.2488	+	24.6796i	0.737774	+	1.27786i	0.953496	+	0.301407i	$0.0974563\pi$
$373$	14.2488	+	24.6796i	0.737774	+	1.27786i	−0.215722	+	0.976455i	$0.569210\pi$
$374$	8.39615	−	6.31065i	0.434155	−	0.326316i
$375$		0			0
$376$	5.06147	+	1.07585i	0.261026	+	0.0554827i
$377$	−9.43690	−	6.85631i	−0.486025	−	0.353118i
$378$		0			0
$379$	−1.33092	+	4.09616i	−0.0683649	+	0.210405i	−0.979402	−	0.201918i	$-0.935283\pi$
$379$	−1.33092	+	4.09616i	−0.0683649	+	0.210405i	0.911038	+	0.412323i	$0.135283\pi$
$380$	−10.1940	−	11.3216i	−0.522941	−	0.580785i
$381$		0			0
$382$	0.256877	−	2.44403i	0.0131430	−	0.125047i
$383$	−12.0374	+	13.3688i	−0.615081	+	0.683116i	−0.967542	−	0.252710i	$-0.918678\pi$
$383$	−12.0374	+	13.3688i	−0.615081	+	0.683116i	0.352461	+	0.935826i	$0.385345\pi$
$384$		0			0
$385$	−1.22423	+	13.7960i	−0.0623926	+	0.703110i
$386$	0.941309			0.0479114
$387$		0			0
$388$	2.78711	+	2.02496i	0.141494	+	0.102802i
$389$	−3.75231	−	35.7009i	−0.190250	−	1.81011i	−0.507379	−	0.861723i	$-0.669386\pi$
$389$	−3.75231	−	35.7009i	−0.190250	−	1.81011i	0.317130	−	0.948382i	$-0.397281\pi$
$390$		0			0
$391$	−9.69111	+	2.05991i	−0.490100	+	0.104174i
$392$	10.2517	+	4.56437i	0.517791	+	0.230535i
$393$		0			0
$394$	2.22039	+	0.471959i	0.111862	+	0.0237770i
$395$	42.6496			2.14594
$396$		0			0
$397$	19.8332			0.995398			0.497699	−	0.867350i	$-0.334178\pi$
$397$	19.8332			0.995398			0.497699	+	0.867350i	$0.334178\pi$
$398$	−4.83712	−	1.02816i	−0.242463	−	0.0515371i
$399$		0			0
$400$	3.64765	+	1.62404i	0.182383	+	0.0812019i
$401$	−13.4891	+	2.86721i	−0.673616	+	0.143181i	−0.532005	−	0.846741i	$-0.678561\pi$
$401$	−13.4891	+	2.86721i	−0.673616	+	0.143181i	−0.141610	+	0.989922i	$0.545228\pi$
$402$		0			0
$403$	1.36103	+	12.9493i	0.0677975	+	0.645050i
$404$	−0.609908	−	0.443124i	−0.0303440	−	0.0220462i
$405$		0			0
$406$	7.94480			0.394294
$407$	−16.6602	+	3.82457i	−0.825817	+	0.189577i
$408$		0			0
$409$	24.6982	−	27.4302i	1.22125	−	1.35633i	0.306726	−	0.951798i	$-0.400766\pi$
$409$	24.6982	−	27.4302i	1.22125	−	1.35633i	0.914522	−	0.404536i	$-0.132567\pi$
$410$	1.35982	−	12.9378i	0.0671568	−	0.638954i
$411$		0			0
$412$	6.63691	+	7.37103i	0.326977	+	0.363145i
$413$	−3.13717	+	9.65521i	−0.154370	+	0.475102i
$414$		0			0
$415$	7.48895	+	5.44104i	0.367618	+	0.267090i
$416$	−8.37904	−	1.78102i	−0.410816	−	0.0873217i
$417$		0			0
$418$	2.55883	+	7.46141i	0.125156	+	0.364949i
$419$	1.16856	+	2.02400i	0.0570879	+	0.0988791i	0.893157	−	0.449745i	$-0.148485\pi$
$419$	1.16856	+	2.02400i	0.0570879	+	0.0988791i	−0.836069	+	0.548624i	$0.815152\pi$
$420$		0			0
$421$	−14.0095	+	6.23742i	−0.682781	+	0.303993i	−0.718659	−	0.695363i	$-0.755244\pi$
$421$	−14.0095	+	6.23742i	−0.682781	+	0.303993i	0.0358784	+	0.999356i	$0.488577\pi$
$422$	1.05333	−	0.765289i	0.0512753	−	0.0372537i
$423$		0			0
$424$	9.83236	−	30.2609i	0.477502	−	1.46960i
$425$	−1.30672	−	12.4326i	−0.0633851	−	0.603069i
$426$		0			0
$427$	−10.4756	+	11.6343i	−0.506950	+	0.563025i
$428$	−9.38519	−	16.2556i	−0.453650	−	0.785745i
$429$		0			0
$430$	2.69944	−	4.67557i	0.130179	−	0.225476i
$431$	−2.41444	−	7.43087i	−0.116299	−	0.357932i	0.875917	−	0.482463i	$-0.160258\pi$
$431$	−2.41444	−	7.43087i	−0.116299	−	0.357932i	−0.992216	+	0.124530i	$0.960258\pi$
$432$		0			0
$433$	−20.3571	+	14.7903i	−0.978301	+	0.710777i	−0.957328	−	0.289003i	$-0.906676\pi$
$433$	−20.3571	+	14.7903i	−0.978301	+	0.710777i	−0.0209724	+	0.999780i	$0.506676\pi$
$434$	−5.93409	−	6.59047i	−0.284845	−	0.316353i
$435$		0			0
$436$	6.71653	+	2.99039i	0.321664	+	0.143214i
$437$	0.777755	−	7.39984i	0.0372051	−	0.353983i
$438$		0			0
$439$	−0.492942	+	0.853801i	−0.0235268	+	0.0407497i	−0.877549	−	0.479487i	$-0.840823\pi$
$439$	−0.492942	+	0.853801i	−0.0235268	+	0.0407497i	0.854022	+	0.520236i	$0.174156\pi$
$440$	−14.8530	−	15.9676i	−0.708090	−	0.761224i
$441$		0			0
$442$	1.45334	+	4.47292i	0.0691283	+	0.212755i
$443$	9.84382	−	4.38275i	0.467694	−	0.208231i	−0.159338	−	0.987224i	$-0.550936\pi$
$443$	9.84382	−	4.38275i	0.467694	−	0.208231i	0.627032	+	0.778993i	$0.284269\pi$
$444$		0			0
$445$	−28.8228	+	6.12647i	−1.36633	+	0.290423i
$446$	−11.1214	+	2.36393i	−0.526613	+	0.111935i
$447$		0			0
$448$	1.16142	−	0.517099i	0.0548721	−	0.0244306i
$449$	7.13830	+	21.9694i	0.336877	+	1.03680i	0.965790	+	0.259326i	$0.0835003\pi$
$449$	7.13830	+	21.9694i	0.336877	+	1.03680i	−0.628913	+	0.777476i	$0.716500\pi$
$450$		0			0
$451$	11.3238	−	20.3690i	0.533216	−	0.959140i
$452$	−14.2583	+	24.6961i	−0.670654	+	1.16161i
$453$		0			0
$454$	1.14126	−	10.8583i	0.0535618	−	0.509606i
$455$	−5.66559	−	2.52248i	−0.265607	−	0.118256i
$456$		0			0
$457$	18.3131	+	20.3388i	0.856651	+	0.951407i	0.999264	−	0.0383713i	$-0.0122170\pi$
$457$	18.3131	+	20.3388i	0.856651	+	0.951407i	−0.142613	+	0.989779i	$0.545550\pi$
$458$	11.0093	−	7.99870i	0.514429	−	0.373755i
$459$		0			0
$460$	2.77706	+	8.54690i	0.129481	+	0.398501i
$461$	9.76471	−	16.9130i	0.454788	−	0.787715i	−0.543888	−	0.839158i	$-0.683048\pi$
$461$	9.76471	−	16.9130i	0.454788	−	0.787715i	0.998676	+	0.0514422i	$0.0163818\pi$
$462$		0			0
$463$	−7.29658	−	12.6380i	−0.339101	−	0.587340i	0.645163	−	0.764045i	$-0.276789\pi$
$463$	−7.29658	−	12.6380i	−0.339101	−	0.587340i	−0.984264	+	0.176705i	$0.943456\pi$
$464$	7.93861	−	8.81672i	0.368541	−	0.409306i
$465$		0			0
$466$	0.0317100	+	0.301701i	0.00146894	+	0.0139760i
$467$	1.87684	−	5.77631i	0.0868496	−	0.267296i	−0.898194	−	0.439598i	$-0.855121\pi$
$467$	1.87684	−	5.77631i	0.0868496	−	0.267296i	0.985044	+	0.172303i	$0.0551208\pi$
$468$		0			0
$469$	−14.7122	+	10.6891i	−0.679348	+	0.493575i
$470$	−3.67982	+	1.63836i	−0.169738	+	0.0755720i
$471$		0			0
$472$	−7.99242	−	13.8433i	−0.367881	−	0.637189i
$473$	7.73144	−	5.81104i	0.355492	−	0.267192i
$474$		0			0
$475$	9.18313	+	1.95193i	0.421351	+	0.0895609i
$476$	8.96654	+	6.51457i	0.410980	+	0.298595i
$477$		0			0
$478$	−3.94080	+	12.1285i	−0.180248	+	0.554746i
$479$	−27.1789	−	30.1853i	−1.24184	−	1.37920i	−0.897895	−	0.440210i	$-0.854904\pi$
$479$	−27.1789	−	30.1853i	−1.24184	−	1.37920i	−0.343943	−	0.938990i	$-0.611763\pi$
$480$		0			0
$481$	0.800066	−	7.61212i	0.0364799	−	0.347083i
$482$	−8.00781	+	8.89358i	−0.364746	+	0.405091i
$483$		0			0
$484$	−5.79755	−	16.0524i	−0.263525	−	0.729653i
$485$	−6.13862			−0.278740
$486$		0			0
$487$	−11.9767	−	8.70158i	−0.542716	−	0.394306i	0.282377	−	0.959304i	$-0.408877\pi$
$487$	−11.9767	−	8.70158i	−0.542716	−	0.394306i	−0.825093	+	0.564998i	$0.808877\pi$
$488$	−2.57665	−	24.5152i	−0.116640	−	1.10975i
$489$		0			0
$490$	−8.54468	+	1.81623i	−0.386009	+	0.0820488i
$491$	−36.0682	−	16.0586i	−1.62774	−	0.724715i	−0.629120	−	0.777308i	$-0.716585\pi$
$491$	−36.0682	−	16.0586i	−1.62774	−	0.724715i	−0.998616	+	0.0525930i	$0.983251\pi$
$492$		0			0
$493$	−36.3331	−	7.72283i	−1.63636	−	0.347819i
$494$	−3.53203			−0.158913
$495$		0			0
$496$	−13.2432			−0.594638
$497$	−15.9889	−	3.39854i	−0.717199	−	0.152445i
$498$		0			0
$499$	−2.90214	−	1.29211i	−0.129917	−	0.0578430i	0.340748	−	0.940155i	$-0.389320\pi$
$499$	−2.90214	−	1.29211i	−0.129917	−	0.0578430i	−0.470666	+	0.882312i	$0.655986\pi$
$500$	9.88781	−	2.10172i	0.442196	−	0.0939917i
$501$		0			0
$502$	0.873002	+	8.30606i	0.0389640	+	0.370717i
$503$	−14.8735	−	10.8062i	−0.663174	−	0.481824i	0.204559	−	0.978854i	$-0.434424\pi$
$503$	−14.8735	−	10.8062i	−0.663174	−	0.481824i	−0.867733	+	0.497030i	$0.834424\pi$
$504$		0			0
$505$	1.34332			0.0597771
$506$	0.411283	−	4.63480i	0.0182838	−	0.206042i
$507$		0			0
$508$	23.1963	−	25.7621i	1.02917	−	1.14301i
$509$	1.63651	−	15.5703i	0.0725370	−	0.690144i	−0.896469	−	0.443106i	$-0.853876\pi$
$509$	1.63651	−	15.5703i	0.0725370	−	0.690144i	0.969006	−	0.247037i	$-0.0794570\pi$
$510$		0			0
$511$	−4.54624	−	5.04911i	−0.201114	−	0.223360i
$512$	4.91260	−	15.1194i	0.217108	−	0.668190i
$513$		0			0
$514$	−13.0567	−	9.48623i	−0.575905	−	0.418419i
$515$	−17.2875	−	3.67458i	−0.761780	−	0.161921i
$516$		0			0
$517$	−7.21510	+	0.116993i	−0.317320	+	0.00514533i
$518$	2.60659	+	4.51475i	0.114527	+	0.198367i
$519$		0			0
$520$	8.92069	−	3.97174i	0.391198	−	0.174173i
$521$	14.6674	−	10.6565i	0.642592	−	0.466870i	−0.218148	−	0.975916i	$-0.570001\pi$
$521$	14.6674	−	10.6565i	0.642592	−	0.466870i	0.860740	+	0.509045i	$0.170001\pi$
$522$		0			0
$523$	5.24113	−	16.1305i	0.229178	−	0.705339i	−0.768662	−	0.639655i	$-0.779077\pi$
$523$	5.24113	−	16.1305i	0.229178	−	0.705339i	0.997840	−	0.0656837i	$-0.0209228\pi$
$524$	−0.643938	−	6.12666i	−0.0281306	−	0.267644i
$525$		0			0
$526$	8.13466	−	9.03446i	0.354688	−	0.393921i
$527$	20.7313	+	35.9077i	0.903071	+	1.56417i
$528$		0			0
$529$	9.30544	−	16.1175i	0.404584	−	0.700761i
$530$	7.65389	+	23.5562i	0.332464	+	1.02322i
$531$		0			0
$532$	−6.73386	+	4.89243i	−0.291950	+	0.212114i
$533$	6.98263	+	7.75500i	0.302451	+	0.335906i
$534$		0			0
$535$	30.5546	+	13.6038i	1.32099	+	0.588144i
$536$	2.99301	−	28.4766i	0.129278	−	1.23000i
$537$		0			0
$538$	4.46746	−	7.73787i	0.192606	−	0.333603i
$539$	−15.3580	−	3.00506i	−0.661518	−	0.129437i
$540$		0			0
$541$	−2.07721	−	6.39299i	−0.0893062	−	0.274856i	0.896422	−	0.443202i	$-0.146158\pi$
$541$	−2.07721	−	6.39299i	−0.0893062	−	0.274856i	−0.985728	+	0.168346i	$0.946158\pi$
$542$	−3.98117	+	1.77253i	−0.171006	+	0.0761368i
$543$		0			0
$544$	−26.6821	+	5.67145i	−1.14399	+	0.243162i
$545$	−12.8142	+	2.72375i	−0.548902	+	0.116673i
$546$		0			0
$547$	41.8550	−	18.6350i	1.78959	−	0.796777i	0.812810	−	0.582529i	$-0.197937\pi$
$547$	41.8550	−	18.6350i	1.78959	−	0.796777i	0.976779	−	0.214247i	$-0.0687299\pi$
$548$	−2.87247	−	8.84054i	−0.122706	−	0.377649i
$549$		0			0
$550$	5.76175	+	1.12738i	0.245682	+	0.0480719i
$551$	13.9478	−	24.1584i	0.594198	−	1.02918i
$552$		0			0
$553$	2.43569	−	23.1741i	0.103576	−	0.985461i
$554$	−8.29465	−	3.69302i	−0.352406	−	0.156901i
$555$		0			0
$556$	−17.8449	−	19.8188i	−0.756794	−	0.840505i
$557$	9.67054	−	7.02606i	0.409754	−	0.297704i	−0.363748	−	0.931497i	$-0.618503\pi$
$557$	9.67054	−	7.02606i	0.409754	−	0.297704i	0.773502	+	0.633794i	$0.218503\pi$
$558$		0			0
$559$	1.33828	+	4.11881i	0.0566033	+	0.174207i
$560$	3.15389	−	5.46270i	0.133276	−	0.230841i
$561$		0			0
$562$	−10.2390	−	17.7345i	−0.431906	−	0.748083i
$563$	−23.0203	+	25.5666i	−0.970190	+	1.07750i	0.0267742	+	0.999642i	$0.491476\pi$
$563$	−23.0203	+	25.5666i	−0.970190	+	1.07750i	−0.996964	+	0.0778635i	$0.975190\pi$
$564$		0			0
$565$	−5.31136	−	50.5342i	−0.223451	−	2.12599i
$566$	−0.155402	+	0.478277i	−0.00653202	+	0.0201035i
$567$		0			0
$568$	20.8221	−	15.1281i	0.873675	−	0.634762i
$569$	10.5116	−	4.68005i	0.440668	−	0.196198i	−0.174395	−	0.984676i	$-0.555797\pi$
$569$	10.5116	−	4.68005i	0.440668	−	0.196198i	0.615063	+	0.788478i	$0.289130\pi$
$570$		0			0
$571$	18.2755	+	31.6542i	0.764807	+	1.32469i	0.940348	+	0.340213i	$0.110499\pi$
$571$	18.2755	+	31.6542i	0.764807	+	1.32469i	−0.175541	+	0.984472i	$0.556167\pi$
$572$	7.64124	−	0.123903i	0.319496	−	0.00518063i
$573$		0			0
$574$	−6.95223	−	1.47774i	−0.290181	−	0.0616798i
$575$	−4.48036	−	3.25517i	−0.186844	−	0.135750i
$576$		0			0
$577$	−6.88976	+	21.2045i	−0.286824	+	0.882754i	0.699022	+	0.715101i	$0.253619\pi$
$577$	−6.88976	+	21.2045i	−0.286824	+	0.882754i	−0.985846	+	0.167654i	$0.946381\pi$
$578$	2.40379	+	2.66968i	0.0999846	+	0.111044i
$579$		0			0
$580$	−3.52181	+	33.5078i	−0.146235	+	1.39133i
$581$	3.38413	−	3.75846i	0.140397	−	0.155927i
$582$		0			0
$583$	−3.92201	+	44.1976i	−0.162433	+	1.83048i
$584$	10.6978			0.442678
$585$		0			0
$586$	8.24255	+	5.98856i	0.340497	+	0.247385i
$587$	2.45942	+	23.3998i	0.101511	+	0.965814i	0.920166	+	0.391528i	$0.128054\pi$
$587$	2.45942	+	23.3998i	0.101511	+	0.965814i	−0.818655	+	0.574286i	$0.805280\pi$
$588$		0			0
$589$	−30.4580	+	6.47404i	−1.25500	+	0.266758i
$590$	11.3674	+	5.06111i	0.467990	+	0.208363i
$591$		0			0
$592$	7.61478	+	1.61857i	0.312966	+	0.0665229i
$593$	−26.7811			−1.09977			−0.549884	−	0.835241i	$-0.685328\pi$
$593$	−26.7811			−1.09977			−0.549884	+	0.835241i	$0.685328\pi$
$594$		0			0
$595$	−19.7488			−0.809622
$596$	−19.5402	−	4.15340i	−0.800397	−	0.170130i
$597$		0			0
$598$	1.90337	+	0.847434i	0.0778345	+	0.0346542i
$599$	−10.3705	+	2.20431i	−0.423726	+	0.0900657i	−0.414839	−	0.909895i	$-0.636162\pi$
$599$	−10.3705	+	2.20431i	−0.423726	+	0.0900657i	−0.00888668	+	0.999961i	$0.502829\pi$
$600$		0			0
$601$	4.09108	+	38.9241i	0.166879	+	1.58775i	0.682472	+	0.730912i	$0.260905\pi$
$601$	4.09108	+	38.9241i	0.166879	+	1.58775i	−0.515593	+	0.856834i	$0.672428\pi$
$602$	−2.38635	−	1.73378i	−0.0972603	−	0.0706638i
$603$		0			0
$604$	13.0470			0.530875
$605$	25.1700	+	17.0683i	1.02330	+	0.693925i
$606$		0			0
$607$	5.74813	−	6.38395i	0.233309	−	0.259116i	−0.615110	−	0.788442i	$-0.710888\pi$
$607$	5.74813	−	6.38395i	0.233309	−	0.259116i	0.848419	+	0.529325i	$0.177555\pi$
$608$	2.14136	−	20.3737i	0.0868436	−	0.826261i
$609$		0			0
$610$	12.8397	+	14.2600i	0.519866	+	0.577370i
$611$	0.998482	−	3.07301i	0.0403943	−	0.124321i
$612$		0			0
$613$	8.05694	+	5.85371i	0.325417	+	0.236429i	0.738483	−	0.674272i	$-0.235542\pi$
$613$	8.05694	+	5.85371i	0.325417	+	0.236429i	−0.413067	+	0.910701i	$0.635542\pi$
$614$	−1.82941	−	0.388853i	−0.0738290	−	0.0156928i
$615$		0			0
$616$	−9.52437	+	7.15863i	−0.383748	+	0.288429i
$617$	3.64515	+	6.31358i	0.146748	+	0.254175i	0.930024	−	0.367499i	$-0.119786\pi$
$617$	3.64515	+	6.31358i	0.146748	+	0.254175i	−0.783276	+	0.621674i	$0.786453\pi$
$618$		0			0
$619$	−30.0908	+	13.3973i	−1.20945	+	0.538483i	−0.909593	−	0.415501i	$-0.863606\pi$
$619$	−30.0908	+	13.3973i	−1.20945	+	0.538483i	−0.299859	+	0.953984i	$0.596940\pi$
$620$	30.4263	−	22.1060i	1.22195	−	0.887797i
$621$		0			0
$622$	4.81171	−	14.8089i	0.192932	−	0.593784i
$623$	1.68282	+	16.0110i	0.0674209	+	0.641467i
$624$		0			0
$625$	−20.8966	+	23.2080i	−0.835863	+	0.928320i
$626$	4.66161	+	8.07415i	0.186315	+	0.322708i
$627$		0			0
$628$	9.16370	−	15.8720i	0.365671	−	0.633361i
$629$	−7.53181	−	23.1805i	−0.300313	−	0.924268i
$630$		0			0
$631$	6.31372	−	4.58719i	0.251345	−	0.182613i	−0.454978	−	0.890503i	$-0.650353\pi$
$631$	6.31372	−	4.58719i	0.251345	−	0.182613i	0.706323	+	0.707890i	$0.250353\pi$
$632$	24.5500	+	27.2655i	0.976547	+	1.08457i
$633$		0			0
$634$	−3.97747	−	1.77088i	−0.157965	−	0.0703308i
$635$	−6.45678	+	61.4321i	−0.256229	+	2.43786i
$636$		0			0
$637$	3.50367	−	6.06853i	0.138820	−	0.240444i
$638$	8.47626	−	15.2470i	0.335578	−	0.603633i
$639$		0			0
$640$	9.37426	+	28.8510i	0.370550	+	1.14044i
$641$	10.9954	−	4.89547i	0.434293	−	0.193359i	−0.177933	−	0.984043i	$-0.556941\pi$
$641$	10.9954	−	4.89547i	0.434293	−	0.193359i	0.612226	+	0.790683i	$0.290274\pi$
$642$		0			0
$643$	33.0817	−	7.03173i	1.30461	−	0.277304i	0.497378	−	0.867534i	$-0.334296\pi$
$643$	33.0817	−	7.03173i	1.30461	−	0.277304i	0.807236	+	0.590229i	$0.200963\pi$
$644$	4.80263	−	1.02083i	0.189250	−	0.0402264i
$645$		0			0
$646$	−10.2750	+	4.57471i	−0.404263	+	0.179989i
$647$	5.98134	+	18.4087i	0.235151	+	0.723719i	0.997101	+	0.0760844i	$0.0242418\pi$
$647$	5.98134	+	18.4087i	0.235151	+	0.723719i	−0.761951	+	0.647635i	$0.775758\pi$
$648$		0			0
$649$	15.1824	+	16.3217i	0.595961	+	0.640681i
$650$	−1.31444	+	2.27668i	−0.0515566	+	0.0892986i
$651$		0			0
$652$	0.748249	−	7.11911i	0.0293037	−	0.278806i
$653$	2.42243	+	1.07853i	0.0947970	+	0.0422063i	0.453587	−	0.891212i	$-0.350144\pi$
$653$	2.42243	+	1.07853i	0.0947970	+	0.0422063i	−0.358790	+	0.933418i	$0.616811\pi$
$654$		0			0
$655$	7.34504	+	8.15749i	0.286994	+	0.318740i
$656$	−8.58673	+	6.23863i	−0.335256	+	0.243577i
$657$		0			0
$658$	0.680067	+	2.09303i	0.0265118	+	0.0815948i
$659$	−1.34963	+	2.33764i	−0.0525743	+	0.0910614i	−0.891115	−	0.453778i	$-0.850076\pi$
$659$	−1.34963	+	2.33764i	−0.0525743	+	0.0910614i	0.838541	+	0.544839i	$0.183409\pi$
$660$		0			0
$661$	6.28133	+	10.8796i	0.244315	+	0.423167i	0.961939	−	0.273265i	$-0.0881035\pi$
$661$	6.28133	+	10.8796i	0.244315	+	0.423167i	−0.717624	+	0.696431i	$0.754770\pi$
$662$	−5.82893	+	6.47369i	−0.226548	+	0.251607i
$663$		0			0
$664$	0.832384	+	7.91960i	0.0323028	+	0.307340i
$665$	4.58313	−	14.1054i	0.177726	−	0.546985i
$666$		0			0
$667$	−13.3126	+	9.67218i	−0.515466	+	0.374508i
$668$	−13.9566	+	6.21387i	−0.539996	+	0.240422i
$669$		0			0
$670$	11.1447	+	19.3032i	0.430557	+	0.745747i
$671$	11.1512	+	32.5165i	0.430489	+	1.25528i
$672$		0			0
$673$	22.1705	+	4.71248i	0.854609	+	0.181653i	0.614328	−	0.789051i	$-0.289427\pi$
$673$	22.1705	+	4.71248i	0.854609	+	0.181653i	0.240281	+	0.970703i	$0.422760\pi$
$674$	−15.8031	−	11.4816i	−0.608711	−	0.442254i
$675$		0			0
$676$	5.17553	−	15.9286i	0.199059	−	0.612640i
$677$	19.7553	+	21.9404i	0.759256	+	0.843240i	0.991593	−	0.129396i	$-0.0413038\pi$
$677$	19.7553	+	21.9404i	0.759256	+	0.843240i	−0.232337	+	0.972635i	$0.574637\pi$
$678$		0			0
$679$	−0.350572	+	3.33547i	−0.0134537	+	0.128004i
$680$	20.8068	−	23.1083i	0.797903	−	0.886161i
$681$		0			0
$682$	−18.9789	+	4.35685i	−0.726739	+	0.166832i
$683$	16.5916			0.634859			0.317430	−	0.948282i	$-0.397180\pi$
$683$	16.5916			0.634859			0.317430	+	0.948282i	$0.397180\pi$
$684$		0			0
$685$	13.4000	+	9.73565i	0.511987	+	0.371980i
$686$	1.23900	+	11.7883i	0.0473051	+	0.450078i
$687$		0			0
$688$	−4.30855	+	0.915811i	−0.164262	+	0.0349150i
$689$	−18.1506	−	8.08117i	−0.691483	−	0.307868i
$690$		0			0
$691$	−23.0121	−	4.89136i	−0.875420	−	0.186076i	−0.251777	−	0.967785i	$-0.581015\pi$
$691$	−23.0121	−	4.89136i	−0.875420	−	0.186076i	−0.623643	+	0.781709i	$0.714348\pi$
$692$	−22.7877			−0.866260
$693$		0			0
$694$	−15.5032			−0.588492
$695$	46.4818	+	9.88000i	1.76315	+	0.374770i
$696$		0			0
$697$	30.3574	+	13.5160i	1.14987	+	0.511954i
$698$	5.56136	−	1.18210i	0.210501	−	0.0447433i
$699$		0			0
$700$	0.647572	+	6.16123i	0.0244759	+	0.232873i
$701$	18.3698	+	13.3465i	0.693819	+	0.504089i	0.877913	−	0.478820i	$-0.158935\pi$
$701$	18.3698	+	13.3465i	0.693819	+	0.504089i	−0.184095	+	0.982909i	$0.558935\pi$
$702$		0			0
$703$	18.3044			0.690365
$704$	0.246744	−	2.78059i	0.00929952	−	0.104797i
$705$		0			0
$706$	0.616179	−	0.684336i	0.0231902	−	0.0257553i
$707$	0.0767163	−	0.729907i	0.00288521	−	0.0274510i
$708$		0			0
$709$	−7.69668	−	8.54803i	−0.289055	−	0.321028i	0.581075	−	0.813850i	$-0.302632\pi$
$709$	−7.69668	−	8.54803i	−0.289055	−	0.321028i	−0.870130	+	0.492822i	$0.835965\pi$
$710$	−6.19118	+	19.0545i	−0.232351	+	0.715102i
$711$		0			0
$712$	−20.5076	−	14.8996i	−0.768555	−	0.558388i
$713$	17.9668	+	3.81895i	0.672861	+	0.143021i
$714$		0			0
$715$	−10.8855	+	8.18168i	−0.407095	+	0.305978i
$716$	−8.78545	−	15.2169i	−0.328328	−	0.568680i
$717$		0			0
$718$	12.7752	−	5.68789i	0.476766	−	0.212270i
$719$	−37.1445	+	26.9870i	−1.38526	+	1.00645i	−0.388888	+	0.921285i	$0.627141\pi$
$719$	−37.1445	+	26.9870i	−1.38526	+	1.00645i	−0.996367	+	0.0851620i	$0.972859\pi$
$720$		0			0
$721$	−2.98390	+	9.18349i	−0.111126	+	0.342011i
$722$	0.447033	+	4.25323i	0.0166368	+	0.158289i
$723$		0			0
$724$	6.53322	−	7.25588i	0.242805	−	0.269663i
$725$	−10.3813	−	17.9810i	−0.385554	−	0.667798i
$726$		0			0
$727$	0.417822	−	0.723690i	0.0154962	−	0.0268402i	−0.858173	−	0.513360i	$-0.828401\pi$
$727$	0.417822	−	0.723690i	0.0154962	−	0.0268402i	0.873670	+	0.486520i	$0.161734\pi$
$728$	−1.64863	−	5.07396i	−0.0611023	−	0.188053i
$729$		0			0
$730$	−6.73715	+	4.89483i	−0.249353	+	0.181166i
$731$	9.22787	+	10.2486i	0.341305	+	0.379058i
$732$		0			0
$733$	−29.1994	−	13.0004i	−1.07850	−	0.480181i	−0.210936	−	0.977500i	$-0.567651\pi$
$733$	−29.1994	−	13.0004i	−1.07850	−	0.480181i	−0.867568	+	0.497319i	$0.834318\pi$
$734$	−0.871423	+	8.29104i	−0.0321648	+	0.306028i
$735$		0			0
$736$	−6.04218	+	10.4654i	−0.222718	+	0.385758i
$737$	4.81712	+	39.6385i	0.177441	+	1.46010i
$738$		0			0
$739$	2.00537	+	6.17190i	0.0737687	+	0.227037i	0.981142	−	0.193289i	$-0.0619156\pi$
$739$	2.00537	+	6.17190i	0.0737687	+	0.227037i	−0.907373	+	0.420326i	$0.861916\pi$
$740$	−20.1967	+	8.99216i	−0.742446	+	0.330558i
$741$		0			0
$742$	13.2366	−	2.81353i	0.485931	−	0.103288i
$743$	10.8978	−	2.31639i	0.399800	−	0.0849801i	−0.00362357	−	0.999993i	$-0.501153\pi$
$743$	10.8978	−	2.31639i	0.399800	−	0.0849801i	0.403424	+	0.915013i	$0.367820\pi$
$744$		0			0
$745$	32.5183	−	14.4781i	1.19138	−	0.530437i
$746$	−5.89712	−	18.1495i	−0.215909	−	0.664499i
$747$		0			0
$748$	22.0685	−	10.2574i	0.806905	−	0.375049i
$749$	9.13670	−	15.8252i	0.333848	−	0.578242i
$750$		0			0
$751$	3.73172	−	35.5050i	0.136173	−	1.29560i	−0.686521	−	0.727110i	$-0.740863\pi$
$751$	3.73172	−	35.5050i	0.136173	−	1.29560i	0.822693	−	0.568485i	$-0.192470\pi$
$752$	3.00227	+	1.33670i	0.109482	+	0.0487443i
$753$		0			0
$754$	5.22676	+	5.80490i	0.190347	+	0.211402i
$755$	−18.8080	+	13.6648i	−0.684493	+	0.497313i
$756$		0			0
$757$	−1.57431	−	4.84524i	−0.0572194	−	0.176103i	0.918362	−	0.395741i	$-0.129512\pi$
$757$	−1.57431	−	4.84524i	−0.0572194	−	0.176103i	−0.975581	+	0.219638i	$0.929512\pi$
$758$	1.44208	−	2.49776i	0.0523788	−	0.0907227i
$759$		0			0
$760$	11.6762	+	20.2238i	0.423542	+	0.733596i
$761$	8.35928	−	9.28392i	0.303024	−	0.336542i	−0.572332	−	0.820022i	$-0.693961\pi$
$761$	8.35928	−	9.28392i	0.303024	−	0.336542i	0.875355	+	0.483481i	$0.160628\pi$
$762$		0			0
$763$	0.748162	+	7.11829i	0.0270853	+	0.257699i
$764$	1.75952	−	5.41525i	0.0636572	−	0.195917i
$765$		0			0
$766$	9.74603	−	7.08091i	0.352138	−	0.255844i
$767$	−9.11851	+	4.05982i	−0.329250	+	0.146592i
$768$		0			0
$769$	−2.74929	−	4.76192i	−0.0991421	−	0.171719i	0.812188	−	0.583396i	$-0.198277\pi$
$769$	−2.74929	−	4.76192i	−0.0991421	−	0.171719i	−0.911330	+	0.411677i	$0.864943\pi$
$770$	2.72269	−	8.86620i	0.0981191	−	0.319516i
$771$		0			0
$772$	2.13332	+	0.453452i	0.0767800	+	0.0163201i
$773$	39.4097	+	28.6328i	1.41747	+	1.02985i	0.992183	+	0.124790i	$0.0398258\pi$
$773$	39.4097	+	28.6328i	1.41747	+	1.02985i	0.425284	+	0.905060i	$0.360174\pi$
$774$		0			0
$775$	−7.16186	+	22.0419i	−0.257262	+	0.791770i
$776$	−3.53352	−	3.92437i	−0.126846	−	0.140877i
$777$		0			0
$778$	−2.51275	+	23.9072i	−0.0900863	+	0.857114i
$779$	−16.6988	+	18.5459i	−0.598295	+	0.664474i
$780$		0			0
$781$	−23.5806	+	27.0586i	−0.843781	+	0.968232i
$782$	6.63466			0.237255
$783$		0			0
$784$	5.76597	+	4.18922i	0.205927	+	0.149615i
$785$	3.41357	+	32.4780i	0.121836	+	1.15919i
$786$		0			0
$787$	−19.8941	+	4.22862i	−0.709148	+	0.150734i	−0.548345	−	0.836252i	$-0.684742\pi$
$787$	−19.8941	+	4.22862i	−0.709148	+	0.150734i	−0.160803	+	0.986986i	$0.551409\pi$
$788$	4.80481	+	2.13924i	0.171164	+	0.0762073i
$789$		0			0
$790$	−27.9363	−	5.93805i	−0.993930	−	0.211266i
$791$	−27.7616			−0.987088
$792$		0			0
$793$	−15.3924			−0.546601
$794$	−12.9911	−	2.76134i	−0.461037	−	0.0979964i
$795$		0			0
$796$	−10.4673	−	4.66032i	−0.371002	−	0.165181i
$797$	16.9058	−	3.59344i	0.598835	−	0.127286i	0.101486	−	0.994837i	$-0.467640\pi$
$797$	16.9058	−	3.59344i	0.598835	−	0.127286i	0.497349	+	0.867551i	$0.334307\pi$
$798$		0			0
$799$	−1.07552	−	10.2329i	−0.0380491	−	0.362013i
$800$	−12.3356	−	8.96232i	−0.436128	−	0.316866i
$801$		0			0
$802$	9.23484			0.326094
$803$	−14.5402	+	3.33788i	−0.513111	+	0.117791i
$804$		0			0
$805$	−5.85410	+	6.50163i	−0.206330	+	0.229152i
$806$	0.911414	−	8.67153i	0.0321032	−	0.305442i
$807$		0			0
$808$	0.773244	+	0.858775i	0.0272026	+	0.0302116i
$809$	−3.94755	+	12.1493i	−0.138789	+	0.427147i	−0.996160	−	0.0875508i	$-0.972096\pi$
$809$	−3.94755	+	12.1493i	−0.138789	+	0.427147i	0.857371	+	0.514698i	$0.172096\pi$
$810$		0			0
$811$	−14.3899	−	10.4549i	−0.505298	−	0.367121i	0.305739	−	0.952115i	$-0.401097\pi$
$811$	−14.3899	−	10.4549i	−0.505298	−	0.367121i	−0.811037	+	0.584995i	$0.801097\pi$
$812$	18.0056	+	3.82721i	0.631873	+	0.134309i
$813$		0			0
$814$	11.4453	−	0.185585i	0.401156	−	0.00650474i
$815$	6.37757	+	11.0463i	0.223397	+	0.386934i
$816$		0			0
$817$	−9.46150	+	4.21253i	−0.331016	+	0.147378i
$818$	−19.9969	+	14.5286i	−0.699174	+	0.507980i
$819$		0			0
$820$	9.31430	−	28.6665i	0.325269	−	1.00108i
$821$	−3.17615	−	30.2191i	−0.110848	−	1.05465i	−0.898633	−	0.438701i	$-0.855439\pi$
$821$	−3.17615	−	30.2191i	−0.110848	−	1.05465i	0.787784	−	0.615951i	$-0.211228\pi$
$822$		0			0
$823$	17.1549	−	19.0525i	0.597983	−	0.664128i	−0.365837	−	0.930679i	$-0.619217\pi$
$823$	17.1549	−	19.0525i	0.597983	−	0.664128i	0.963821	+	0.266551i	$0.0858841\pi$
$824$	−7.60194	−	13.1669i	−0.264826	−	0.458692i
$825$		0			0
$826$	3.39919	−	5.88756i	0.118273	−	0.204855i
$827$	3.14133	+	9.66803i	0.109235	+	0.336190i	0.990701	−	0.136057i	$-0.0434430\pi$
$827$	3.14133	+	9.66803i	0.109235	+	0.336190i	−0.881466	+	0.472247i	$0.843443\pi$
$828$		0			0
$829$	−2.17360	+	1.57922i	−0.0754924	+	0.0548484i	−0.624891	−	0.780712i	$-0.714857\pi$
$829$	−2.17360	+	1.57922i	−0.0754924	+	0.0548484i	0.549399	+	0.835560i	$0.314857\pi$
$830$	−4.14786	−	4.60667i	−0.143974	−	0.159900i
$831$		0			0
$832$	1.14190	+	0.508407i	0.0395883	+	0.0176259i
$833$	2.33245	−	22.1918i	0.0808147	−	0.768901i
$834$		0			0
$835$	13.6111	−	23.5751i	0.471031	−	0.815850i
$836$	2.20482	+	18.1427i	0.0762553	+	0.627479i
$837$		0			0
$838$	−0.483630	−	1.48846i	−0.0167067	−	0.0514180i
$839$	−11.9655	+	5.32740i	−0.413096	+	0.183922i	−0.602752	−	0.797928i	$-0.705929\pi$
$839$	−11.9655	+	5.32740i	−0.413096	+	0.183922i	0.189656	+	0.981851i	$0.439263\pi$
$840$		0			0
$841$	−31.9783	+	6.79721i	−1.10270	+	0.234386i
$842$	10.0449	−	2.13511i	0.346170	−	0.0735808i
$843$		0			0
$844$	2.75586	−	1.22699i	0.0948606	−	0.0422347i
$845$	9.22207	+	28.3826i	0.317249	+	0.976391i
$846$		0			0
$847$	10.7117	−	12.7016i	0.368057	−	0.436431i
$848$	10.1040	−	17.5006i	0.346972	−	0.600973i
$849$		0			0
$850$	−0.875047	+	8.32551i	−0.0300139	+	0.285563i
$851$	−9.86405	−	4.39176i	−0.338135	−	0.150548i
$852$		0			0
$853$	1.07948	+	1.19889i	0.0369609	+	0.0410492i	0.761342	−	0.648351i	$-0.224541\pi$
$853$	1.07948	+	1.19889i	0.0369609	+	0.0410492i	−0.724381	+	0.689400i	$0.757874\pi$
$854$	8.48156	−	6.16221i	0.290233	−	0.210867i
$855$		0			0
$856$	8.89109	+	27.3639i	0.303891	+	0.935281i
$857$	−20.7735	+	35.9807i	−0.709608	+	1.22908i	0.255395	+	0.966837i	$0.417795\pi$
$857$	−20.7735	+	35.9807i	−0.709608	+	1.22908i	−0.965003	+	0.262240i	$0.915539\pi$
$858$		0			0
$859$	−19.0349	−	32.9695i	−0.649463	−	1.12490i	−0.983251	−	0.182255i	$-0.941660\pi$
$859$	−19.0349	−	32.9695i	−0.649463	−	1.12490i	0.333788	−	0.942648i	$-0.391673\pi$
$860$	8.37019	−	9.29603i	0.285421	−	0.316992i
$861$		0			0
$862$	0.546912	+	5.20352i	0.0186279	+	0.177233i
$863$	−13.1442	+	40.4536i	−0.447433	+	1.37706i	0.432360	+	0.901701i	$0.357681\pi$
$863$	−13.1442	+	40.4536i	−0.447433	+	1.37706i	−0.879793	+	0.475357i	$0.842319\pi$
$864$		0			0
$865$	32.8498	−	23.8668i	1.11693	−	0.811495i
$866$	15.3935	−	6.85364i	0.523094	−	0.232896i
$867$		0			0
$868$	−10.2739	−	17.7948i	−0.348717	−	0.603996i
$869$	−41.8750	−	29.3986i	−1.42051	−	0.997280i
$870$		0			0
$871$	−17.4889	−	3.71739i	−0.592590	−	0.125959i
$872$	−9.11742	−	6.62419i	−0.308755	−	0.224323i
$873$		0			0
$874$	−1.53971	+	4.73875i	−0.0520816	+	0.160291i
$875$	6.58496	+	7.31334i	0.222612	+	0.247236i
$876$		0			0
$877$	0.826551	−	7.86411i	0.0279107	−	0.265552i	−0.971663	−	0.236369i	$-0.924043\pi$
$877$	0.826551	−	7.86411i	0.0279107	−	0.265552i	0.999574	−	0.0291834i	$-0.00929068\pi$
$878$	0.441760	−	0.490624i	0.0149087	−	0.0165578i
$879$		0			0
$880$	−7.11867	−	11.8808i	−0.239970	−	0.400501i
$881$	−41.5877			−1.40113			−0.700563	−	0.713591i	$-0.747068\pi$
$881$	−41.5877			−1.40113			−0.700563	+	0.713591i	$0.747068\pi$
$882$		0			0
$883$	−9.71314	−	7.05701i	−0.326873	−	0.237487i	0.412229	−	0.911080i	$-0.364750\pi$
$883$	−9.71314	−	7.05701i	−0.326873	−	0.237487i	−0.739103	+	0.673593i	$0.764750\pi$
$884$	1.13904	+	10.8373i	0.0383101	+	0.364497i
$885$		0			0
$886$	−7.05810	+	1.50024i	−0.237121	+	0.0504017i
$887$	43.5917	+	19.4083i	1.46367	+	0.651666i	0.975282	−	0.220963i	$-0.0709199\pi$
$887$	43.5917	+	19.4083i	1.46367	+	0.651666i	0.488384	+	0.872629i	$0.337587\pi$
$888$		0			0
$889$	33.0110	+	7.01670i	1.10715	+	0.235333i
$890$	19.7325			0.661434
$891$		0			0
$892$	−26.3436			−0.882050
$893$	7.55836	+	1.60658i	0.252931	+	0.0537621i
$894$		0			0
$895$	28.6021	+	12.7345i	0.956063	+	0.425667i
$896$	16.2118	−	3.44593i	0.541599	−	0.115120i
$897$		0			0
$898$	−1.61695	−	15.3843i	−0.0539583	−	0.513379i
$899$	55.7124	+	40.4774i	1.85811	+	1.35000i
$900$		0			0
$901$	−63.2683			−2.10777
$902$	−10.2532	+	11.7655i	−0.341396	+	0.391749i
$903$		0			0
$904$	29.2488	−	32.4841i	0.972800	−	1.08040i
$905$	−1.81855	+	17.3023i	−0.0604506	+	0.575149i
$906$		0			0
$907$	−1.50348	−	1.66979i	−0.0499223	−	0.0554444i	0.717666	−	0.696387i	$-0.245210\pi$
$907$	−1.50348	−	1.66979i	−0.0499223	−	0.0554444i	−0.767589	+	0.640943i	$0.778544\pi$
$908$	7.81720	−	24.0589i	0.259423	−	0.798422i
$909$		0			0
$910$	3.35987	+	2.44109i	0.111379	+	0.0809213i
$911$	12.5203	+	2.66127i	0.414816	+	0.0881719i	0.410592	−	0.911819i	$-0.365322\pi$
$911$	12.5203	+	2.66127i	0.414816	+	0.0881719i	0.00422413	+	0.999991i	$0.498655\pi$
$912$		0			0
$913$	−3.60239	−	10.5044i	−0.119222	−	0.347645i
$914$	−9.16370	−	15.8720i	−0.303108	−	0.524999i
$915$		0			0
$916$	28.8039	−	12.8243i	0.951708	−	0.423728i
$917$	4.85192	−	3.52513i	0.160224	−	0.116410i
$918$		0			0
$919$	3.53256	−	10.8721i	0.116528	−	0.358637i	−0.875734	−	0.482793i	$-0.839622\pi$
$919$	3.53256	−	10.8721i	0.116528	−	0.358637i	0.992263	+	0.124156i	$0.0396223\pi$
$920$	−1.43991	−	13.6999i	−0.0474725	−	0.451671i
$921$		0			0
$922$	−8.75084	+	9.71879i	−0.288194	+	0.320071i
$923$	−8.03567	−	13.9182i	−0.264497	−	0.458123i
$924$		0			0
$925$	6.81198	−	11.7987i	0.223976	−	0.387939i
$926$	3.01982	+	9.29405i	0.0992375	+	0.305422i
$927$		0			0
$928$	−36.6530	+	26.6300i	−1.20319	+	0.874172i
$929$	6.18101	+	6.86471i	0.202792	+	0.225224i	0.835959	−	0.548792i	$-0.184912\pi$
$929$	6.18101	+	6.86471i	0.202792	+	0.225224i	−0.633167	+	0.774015i	$0.718245\pi$
$930$		0			0
$931$	15.3090	+	6.81602i	0.501733	+	0.223386i
$932$	−0.0734712	+	0.699032i	−0.00240663	+	0.0228976i
$933$		0			0
$934$	−2.03359	+	3.52228i	−0.0665411	+	0.115253i
$935$	−21.0699	+	37.9002i	−0.689058	+	1.23947i
$936$		0			0
$937$	−10.4711	−	32.2266i	−0.342075	−	1.05280i	−0.963131	−	0.269032i	$-0.913296\pi$
$937$	−10.4711	−	32.2266i	−0.342075	−	1.05280i	0.621056	−	0.783766i	$-0.286704\pi$
$938$	11.1250	−	4.95318i	0.363245	−	0.161727i
$939$		0			0
$940$	−9.12896	+	1.94042i	−0.297754	+	0.0632896i
$941$	−10.3450	+	2.19890i	−0.337237	+	0.0716820i	−0.373418	−	0.927663i	$-0.621814\pi$
$941$	−10.3450	+	2.19890i	−0.337237	+	0.0716820i	0.0361806	+	0.999345i	$0.488481\pi$
$942$		0			0
$943$	13.4485	−	5.98764i	0.437942	−	0.194984i
$944$	−3.13717	−	9.65521i	−0.102106	−	0.314250i
$945$		0			0
$946$	−5.87331	+	2.72991i	−0.190958	+	0.0887570i
$947$	1.82612	−	3.16292i	0.0593408	−	0.102781i	−0.834829	−	0.550510i	$-0.814433\pi$
$947$	1.82612	−	3.16292i	0.0593408	−	0.102781i	0.894170	+	0.447728i	$0.147767\pi$
$948$		0			0
$949$	0.698255	−	6.64346i	0.0226663	−	0.215656i
$950$	−5.74336	−	2.55711i	−0.186339	−	0.0829636i
$951$		0			0
$952$	−11.3678	−	12.6252i	−0.368433	−	0.409187i
$953$	11.6292	−	8.44909i	0.376706	−	0.273693i	−0.383280	−	0.923632i	$-0.625206\pi$
$953$	11.6292	−	8.44909i	0.376706	−	0.273693i	0.759986	+	0.649939i	$0.225206\pi$
$954$		0			0
$955$	3.13522	+	9.64922i	0.101453	+	0.312241i
$956$	−14.7738	+	25.5890i	−0.477819	+	0.827607i
$957$		0			0
$958$	13.6001	+	23.5560i	0.439399	+	0.761061i
$959$	6.05522	−	6.72500i	0.195533	−	0.217162i
$960$		0			0
$961$	−4.79467	−	45.6182i	−0.154667	−	1.47155i
$962$	−1.58388	+	4.87469i	−0.0510665	+	0.157166i
$963$		0			0
$964$	−22.4327	+	16.2983i	−0.722508	+	0.524933i
$965$	−3.55023	+	1.58066i	−0.114286	+	0.0508834i
$966$		0			0
$967$	−17.6955	−	30.6496i	−0.569050	−	0.985623i	−0.996660	−	0.0816600i	$-0.973978\pi$
$967$	−17.6955	−	30.6496i	−0.569050	−	0.985623i	0.427610	−	0.903963i	$-0.359356\pi$
$968$	3.57673	+	25.9158i	0.114960	+	0.832966i
$969$		0			0
$970$	4.02091	+	0.854671i	0.129104	+	0.0274418i
$971$	−0.118477	−	0.0860787i	−0.00380211	−	0.00276240i	0.585883	−	0.810396i	$-0.300748\pi$
$971$	−0.118477	−	0.0860787i	−0.00380211	−	0.00276240i	−0.589685	+	0.807634i	$0.700748\pi$
$972$		0			0
$973$	8.02293	−	24.6920i	0.257203	−	0.791591i
$974$	6.63345	+	7.36720i	0.212550	+	0.236060i
$975$		0			0
$976$	1.63645	−	15.5698i	0.0523815	−	0.498377i
$977$	26.7730	−	29.7344i	0.856544	−	0.951289i	−0.142715	−	0.989764i	$-0.545583\pi$
$977$	26.7730	−	29.7344i	0.856544	−	0.951289i	0.999260	+	0.0384748i	$0.0122499\pi$
$978$		0			0
$979$	32.5223	+	13.8525i	1.03942	+	0.442728i
$980$	−20.2401			−0.646545
$981$		0			0
$982$	21.3896	+	15.5404i	0.682568	+	0.495915i
$983$	−1.59628	−	15.1876i	−0.0509134	−	0.484408i	−0.990035	−	0.140823i	$-0.955025\pi$
$983$	−1.59628	−	15.1876i	−0.0509134	−	0.484408i	0.939121	−	0.343585i	$-0.111641\pi$
$984$		0			0
$985$	−9.16694	+	1.94849i	−0.292083	+	0.0620842i
$986$	22.7236	+	10.1172i	0.723667	+	0.322197i
$987$		0			0
$988$	−8.00477	−	1.70147i	−0.254666	−	0.0541309i
$989$	6.10940			0.194268
$990$		0			0
$991$	21.5067			0.683184			0.341592	−	0.939848i	$-0.389034\pi$
$991$	21.5067			0.683184			0.341592	+	0.939848i	$0.389034\pi$
$992$	49.4671	+	10.5146i	1.57058	+	0.333838i
$993$		0			0
$994$	9.99985	+	4.45222i	0.317176	+	0.141216i
$995$	19.9701	−	4.24478i	0.633096	−	0.134569i
$996$		0			0
$997$	2.30559	+	21.9363i	0.0730189	+	0.694729i	0.968396	+	0.249419i	$0.0802397\pi$
$997$	2.30559	+	21.9363i	0.0730189	+	0.694729i	−0.895377	+	0.445309i	$0.853094\pi$
$998$	1.72106	+	1.25042i	0.0544791	+	0.0395814i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.g.379.2		32
3.2	odd	2	inner	891.2.n.g.379.3		32
9.2	odd	6		297.2.f.c.82.2	✓	16
9.4	even	3	inner	891.2.n.g.676.3		32
9.5	odd	6	inner	891.2.n.g.676.2		32
9.7	even	3		297.2.f.c.82.3	yes	16
11.9	even	5	inner	891.2.n.g.460.3		32
33.20	odd	10	inner	891.2.n.g.460.2		32
99.20	odd	30		297.2.f.c.163.2	yes	16
99.25	even	15		3267.2.a.bg.1.5		8
99.31	even	15	inner	891.2.n.g.757.2		32
99.47	odd	30		3267.2.a.bg.1.4		8
99.52	odd	30		3267.2.a.bh.1.4		8
99.74	even	30		3267.2.a.bh.1.5		8
99.86	odd	30	inner	891.2.n.g.757.3		32
99.97	even	15		297.2.f.c.163.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.c.82.2	✓	16	9.2	odd	6
297.2.f.c.82.3	yes	16	9.7	even	3
297.2.f.c.163.2	yes	16	99.20	odd	30
297.2.f.c.163.3	yes	16	99.97	even	15
891.2.n.g.379.2		32	1.1	even	1	trivial
891.2.n.g.379.3		32	3.2	odd	2	inner
891.2.n.g.460.2		32	33.20	odd	10	inner
891.2.n.g.460.3		32	11.9	even	5	inner
891.2.n.g.676.2		32	9.5	odd	6	inner
891.2.n.g.676.3		32	9.4	even	3	inner
891.2.n.g.757.2		32	99.31	even	15	inner
891.2.n.g.757.3		32	99.86	odd	30	inner
3267.2.a.bg.1.4		8	99.47	odd	30
3267.2.a.bg.1.5		8	99.25	even	15
3267.2.a.bh.1.4		8	99.52	odd	30
3267.2.a.bh.1.5		8	99.74	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.655019 - 0.139229i) q^{2} +(-1.41743 - 0.631078i) q^{4} +(2.70426 - 0.574808i) q^{5} +(-0.157889 - 1.50221i) q^{7} +(1.92410 + 1.39794i) q^{8} -1.85137 q^{10} +(-3.05136 - 1.29969i) q^{11} +(0.993724 - 1.10364i) q^{13} +(-0.105731 + 1.00596i) q^{14} +(1.01071 + 1.12251i) q^{16} +(1.46138 - 4.49766i) q^{17} +(2.87328 + 2.08756i) q^{19} +(-4.19583 - 0.891852i) q^{20} +(1.81775 + 1.27616i) q^{22} +(-1.04751 - 1.81434i) q^{23} +(2.41489 - 1.07518i) q^{25} +(-0.804567 + 0.584552i) q^{26} +(-0.724217 + 2.22891i) q^{28} +(-0.821016 - 7.81145i) q^{29} +(-5.86662 + 6.51554i) q^{31} +(-2.88407 - 4.99535i) q^{32} +(-1.58343 + 2.74259i) q^{34} +(-1.29045 - 3.97161i) q^{35} +(4.16960 - 3.02939i) q^{37} +(-1.59140 - 1.76743i) q^{38} +(6.00680 + 2.67440i) q^{40} +(-0.734494 + 6.98824i) q^{41} +(-1.45808 + 2.52546i) q^{43} +(3.50487 + 3.76786i) q^{44} +(0.433531 + 1.33427i) q^{46} +(1.98762 - 0.884945i) q^{47} +(4.61532 - 0.981018i) q^{49} +(-1.73149 + 0.368040i) q^{50} +(-2.10501 + 0.937212i) q^{52} +(-4.13417 - 12.7237i) q^{53} +(-8.99874 - 1.76076i) q^{55} +(1.79621 - 3.11112i) q^{56} +(-0.549796 + 5.23096i) q^{58} +(-6.14001 - 2.73371i) q^{59} +(-6.93526 - 7.70239i) q^{61} +(4.74990 - 3.45100i) q^{62} +(0.260092 + 0.800479i) q^{64} +(2.05290 - 3.55573i) q^{65} +(-6.01970 - 10.4264i) q^{67} +(-4.90977 + 5.45286i) q^{68} +(0.292311 + 2.78115i) q^{70} +(3.34410 - 10.2921i) q^{71} +(3.63900 - 2.64389i) q^{73} +(-3.15295 + 1.40378i) q^{74} +(-2.75524 - 4.77222i) q^{76} +(-1.47064 + 4.78899i) q^{77} +(15.0895 + 3.20738i) q^{79} +(3.37845 + 2.45459i) q^{80} +(1.45407 - 4.47517i) q^{82} +(2.24043 + 2.48824i) q^{83} +(1.36666 - 13.0029i) q^{85} +(1.30668 - 1.45122i) q^{86} +(-4.05422 - 6.76635i) q^{88} -10.6583 q^{89} +(-1.81480 - 1.31853i) q^{91} +(0.339776 + 3.23276i) q^{92} +(-1.42514 + 0.302923i) q^{94} +(8.97003 + 3.99371i) q^{95} +(-2.17186 - 0.461642i) q^{97} -3.15971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{4} - 8 q^{7} - 24 q^{10} - 8 q^{13} + 2 q^{16} + 20 q^{19} + 24 q^{22} + 16 q^{25} - 60 q^{28} + 6 q^{31} - 32 q^{34} + 24 q^{37} + 40 q^{40} + 80 q^{43} - 24 q^{46} - 40 q^{49} - 12 q^{52}+ \cdots + 46 q^{94}+O(q^{100}) \) 32 * q - 2 * q^4 - 8 * q^7 - 24 * q^10 - 8 * q^13 + 2 * q^16 + 20 * q^19 + 24 * q^22 + 16 * q^25 - 60 * q^28 + 6 * q^31 - 32 * q^34 + 24 * q^37 + 40 * q^40 + 80 * q^43 - 24 * q^46 - 40 * q^49 - 12 * q^52 + 112 * q^55 + 50 * q^58 + 6 * q^61 + 12 * q^64 - 64 * q^67 - 74 * q^70 - 64 * q^73 - 52 * q^76 + 4 * q^79 + 8 * q^82 - 70 * q^85 - 56 * q^88 - 188 * q^91 + 46 * q^94

Introduction

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