LMFDB - Embedded newform 990.2.n.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [990,2,Mod(91,990)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(990, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("990.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.n (of order $5$, degree $4$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	990.361
Dual form			990.2.n.e.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.00000 - 0.726543i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.00000 - 0.726543i) q^{7} +(0.809017 - 0.587785i) q^{8} -1.00000 q^{10} +(2.54508 + 2.12663i) q^{11} +(1.73607 - 5.34307i) q^{13} +(1.00000 - 0.726543i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.57295 - 4.84104i) q^{17} +(2.61803 - 1.90211i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-2.80902 + 1.76336i) q^{22} -0.145898 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.54508 + 3.30220i) q^{26} +(0.381966 + 1.17557i) q^{28} +(-0.309017 - 0.224514i) q^{29} +(-1.11803 + 3.44095i) q^{31} -1.00000 q^{32} +5.09017 q^{34} +(0.381966 - 1.17557i) q^{35} +(6.97214 + 5.06555i) q^{37} +(1.00000 + 3.07768i) q^{38} +(0.809017 + 0.587785i) q^{40} +(-2.61803 + 1.90211i) q^{41} +11.0902 q^{43} +(-0.809017 - 3.21644i) q^{44} +(0.0450850 - 0.138757i) q^{46} +(9.16312 - 6.65740i) q^{47} +(-1.69098 - 5.20431i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-4.54508 + 3.30220i) q^{52} +(0.145898 - 0.449028i) q^{53} +(-1.23607 + 3.07768i) q^{55} -1.23607 q^{56} +(0.309017 - 0.224514i) q^{58} +(2.35410 + 1.71036i) q^{59} +(-2.92705 - 2.12663i) q^{62} +(0.309017 - 0.951057i) q^{64} +5.61803 q^{65} +6.09017 q^{67} +(-1.57295 + 4.84104i) q^{68} +(1.00000 + 0.726543i) q^{70} +(-0.472136 - 1.45309i) q^{71} +(10.8541 + 7.88597i) q^{73} +(-6.97214 + 5.06555i) q^{74} -3.23607 q^{76} +(-1.00000 - 3.97574i) q^{77} +(2.19098 - 6.74315i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-1.00000 - 3.07768i) q^{82} +(-1.23607 - 3.80423i) q^{83} +(4.11803 - 2.99193i) q^{85} +(-3.42705 + 10.5474i) q^{86} +(3.30902 + 0.224514i) q^{88} -12.7639 q^{89} +(-5.61803 + 4.08174i) q^{91} +(0.118034 + 0.0857567i) q^{92} +(3.50000 + 10.7719i) q^{94} +(2.61803 + 1.90211i) q^{95} +(-3.90983 + 12.0332i) q^{97} +5.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8}+O(q^{10}) $ 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8	$ 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8} - 4 q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 13 q^{17} + 6 q^{19} - q^{20} - 9 q^{22} - 14 q^{23} - q^{25} + 7 q^{26} + 6 q^{28} + q^{29} - 4 q^{32} - 2 q^{34} + 6 q^{35} + 10 q^{37} + 4 q^{38} + q^{40} - 6 q^{41} + 22 q^{43} - q^{44} - 11 q^{46} + 21 q^{47} - 9 q^{49} + q^{50} - 7 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} - q^{58} - 4 q^{59} - 5 q^{62} - q^{64} + 18 q^{65} + 2 q^{67} - 13 q^{68} + 4 q^{70} + 16 q^{71} + 30 q^{73} - 10 q^{74} - 4 q^{76} - 4 q^{77} + 11 q^{79} - q^{80} - 4 q^{82} + 4 q^{83} + 12 q^{85} - 7 q^{86} + 11 q^{88} - 60 q^{89} - 18 q^{91} - 4 q^{92} + 14 q^{94} + 6 q^{95} - 38 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8 - 4 * q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 13 * q^17 + 6 * q^19 - q^20 - 9 * q^22 - 14 * q^23 - q^25 + 7 * q^26 + 6 * q^28 + q^29 - 4 * q^32 - 2 * q^34 + 6 * q^35 + 10 * q^37 + 4 * q^38 + q^40 - 6 * q^41 + 22 * q^43 - q^44 - 11 * q^46 + 21 * q^47 - 9 * q^49 + q^50 - 7 * q^52 + 14 * q^53 + 4 * q^55 + 4 * q^56 - q^58 - 4 * q^59 - 5 * q^62 - q^64 + 18 * q^65 + 2 * q^67 - 13 * q^68 + 4 * q^70 + 16 * q^71 + 30 * q^73 - 10 * q^74 - 4 * q^76 - 4 * q^77 + 11 * q^79 - q^80 - 4 * q^82 + 4 * q^83 + 12 * q^85 - 7 * q^86 + 11 * q^88 - 60 * q^89 - 18 * q^91 - 4 * q^92 + 14 * q^94 + 6 * q^95 - 38 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$		0			0
$3$		0			0
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	−1.00000	−	0.726543i	−0.377964	−	0.274607i	0.382541	−	0.923938i	$-0.375049\pi$
$7$	−1.00000	−	0.726543i	−0.377964	−	0.274607i	−0.760506	+	0.649331i	$0.775049\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$11$	2.54508	+	2.12663i	0.767372	+	0.641202i
$12$		0			0
$13$	1.73607	−	5.34307i	0.481499	−	1.48190i	−0.355490	−	0.934680i	$-0.615686\pi$
$13$	1.73607	−	5.34307i	0.481499	−	1.48190i	0.836989	−	0.547220i	$-0.184314\pi$
$14$	1.00000	−	0.726543i	0.267261	−	0.194177i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−1.57295	−	4.84104i	−0.381496	−	1.17412i	−0.938990	−	0.343944i	$-0.888237\pi$
$17$	−1.57295	−	4.84104i	−0.381496	−	1.17412i	0.557494	−	0.830181i	$-0.311763\pi$
$18$		0			0
$19$	2.61803	−	1.90211i	0.600618	−	0.436375i	−0.245480	−	0.969402i	$-0.578946\pi$
$19$	2.61803	−	1.90211i	0.600618	−	0.436375i	0.846098	+	0.533027i	$0.178946\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$		0			0
$22$	−2.80902	+	1.76336i	−0.598884	+	0.375949i
$23$	−0.145898			−0.0304218			−0.0152109	−	0.999884i	$-0.504842\pi$
$23$	−0.145898			−0.0304218			−0.0152109	+	0.999884i	$0.504842\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	4.54508	+	3.30220i	0.891364	+	0.647614i
$27$		0			0
$28$	0.381966	+	1.17557i	0.0721848	+	0.222162i
$29$	−0.309017	−	0.224514i	−0.0573830	−	0.0416912i	0.558724	−	0.829354i	$-0.311291\pi$
$29$	−0.309017	−	0.224514i	−0.0573830	−	0.0416912i	−0.616107	+	0.787662i	$0.711291\pi$
$30$		0			0
$31$	−1.11803	+	3.44095i	−0.200805	+	0.618014i	0.799055	+	0.601258i	$0.205334\pi$
$31$	−1.11803	+	3.44095i	−0.200805	+	0.618014i	−0.999860	+	0.0167555i	$0.994666\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	5.09017			0.872957
$35$	0.381966	−	1.17557i	0.0645640	−	0.198708i
$36$		0			0
$37$	6.97214	+	5.06555i	1.14621	+	0.832772i	0.987973	−	0.154629i	$-0.0494182\pi$
$37$	6.97214	+	5.06555i	1.14621	+	0.832772i	0.158239	+	0.987401i	$0.449418\pi$
$38$	1.00000	+	3.07768i	0.162221	+	0.499266i
$39$		0			0
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−2.61803	+	1.90211i	−0.408868	+	0.297060i	−0.773143	−	0.634231i	$-0.781317\pi$
$41$	−2.61803	+	1.90211i	−0.408868	+	0.297060i	0.364275	+	0.931291i	$0.381317\pi$
$42$		0			0
$43$	11.0902			1.69124			0.845618	−	0.533789i	$-0.179232\pi$
$43$	11.0902			1.69124			0.845618	+	0.533789i	$0.179232\pi$
$44$	−0.809017	−	3.21644i	−0.121964	−	0.484897i
$45$		0			0
$46$	0.0450850	−	0.138757i	0.00664742	−	0.0204586i
$47$	9.16312	−	6.65740i	1.33658	−	0.971081i	0.337016	−	0.941499i	$-0.390582\pi$
$47$	9.16312	−	6.65740i	1.33658	−	0.971081i	0.999562	−	0.0295820i	$-0.00941762\pi$
$48$		0			0
$49$	−1.69098	−	5.20431i	−0.241569	−	0.743473i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$		0			0
$52$	−4.54508	+	3.30220i	−0.630290	+	0.457932i
$53$	0.145898	−	0.449028i	0.0200406	−	0.0616787i	−0.940536	−	0.339694i	$-0.889677\pi$
$53$	0.145898	−	0.449028i	0.0200406	−	0.0616787i	0.960577	+	0.278015i	$0.0896765\pi$
$54$		0			0
$55$	−1.23607	+	3.07768i	−0.166671	+	0.414995i
$56$	−1.23607			−0.165177
$57$		0			0
$58$	0.309017	−	0.224514i	0.0405759	−	0.0294801i
$59$	2.35410	+	1.71036i	0.306478	+	0.222669i	0.730384	−	0.683037i	$-0.239341\pi$
$59$	2.35410	+	1.71036i	0.306478	+	0.222669i	−0.423906	+	0.905706i	$0.639341\pi$
$60$		0			0
$61$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$61$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$62$	−2.92705	−	2.12663i	−0.371736	−	0.270082i
$63$		0			0
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	5.61803			0.696831
$66$		0			0
$67$	6.09017			0.744033			0.372016	−	0.928226i	$-0.378667\pi$
$67$	6.09017			0.744033			0.372016	+	0.928226i	$0.378667\pi$
$68$	−1.57295	+	4.84104i	−0.190748	+	0.587062i
$69$		0			0
$70$	1.00000	+	0.726543i	0.119523	+	0.0868384i
$71$	−0.472136	−	1.45309i	−0.0560322	−	0.172449i	0.919124	−	0.393969i	$-0.128898\pi$
$71$	−0.472136	−	1.45309i	−0.0560322	−	0.172449i	−0.975156	+	0.221520i	$0.928898\pi$
$72$		0			0
$73$	10.8541	+	7.88597i	1.27038	+	0.922983i	0.999218	−	0.0395520i	$-0.0125931\pi$
$73$	10.8541	+	7.88597i	1.27038	+	0.922983i	0.271159	+	0.962535i	$0.412593\pi$
$74$	−6.97214	+	5.06555i	−0.810494	+	0.588859i
$75$		0			0
$76$	−3.23607			−0.371202
$77$	−1.00000	−	3.97574i	−0.113961	−	0.453078i
$78$		0			0
$79$	2.19098	−	6.74315i	0.246505	−	0.758664i	−0.748880	−	0.662705i	$-0.769408\pi$
$79$	2.19098	−	6.74315i	0.246505	−	0.758664i	0.995385	−	0.0959588i	$-0.0305917\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$		0			0
$82$	−1.00000	−	3.07768i	−0.110432	−	0.339873i
$83$	−1.23607	−	3.80423i	−0.135676	−	0.417568i	0.860018	−	0.510263i	$-0.170452\pi$
$83$	−1.23607	−	3.80423i	−0.135676	−	0.417568i	−0.995695	+	0.0926948i	$0.970452\pi$
$84$		0			0
$85$	4.11803	−	2.99193i	0.446663	−	0.324520i
$86$	−3.42705	+	10.5474i	−0.369548	+	1.13735i
$87$		0			0
$88$	3.30902	+	0.224514i	0.352742	+	0.0239333i
$89$	−12.7639			−1.35297			−0.676487	−	0.736455i	$-0.736499\pi$
$89$	−12.7639			−1.35297			−0.676487	+	0.736455i	$0.736499\pi$
$90$		0			0
$91$	−5.61803	+	4.08174i	−0.588930	+	0.427883i
$92$	0.118034	+	0.0857567i	0.0123059	+	0.00894076i
$93$		0			0
$94$	3.50000	+	10.7719i	0.360997	+	1.11104i
$95$	2.61803	+	1.90211i	0.268605	+	0.195153i
$96$		0			0
$97$	−3.90983	+	12.0332i	−0.396983	+	1.22179i	0.530423	+	0.847733i	$0.322033\pi$
$97$	−3.90983	+	12.0332i	−0.396983	+	1.22179i	−0.927406	+	0.374055i	$0.877967\pi$
$98$	5.47214			0.552769
$99$		0			0
$100$	1.00000			0.100000
$101$	−4.13525	+	12.7270i	−0.411473	+	1.26638i	0.503894	+	0.863765i	$0.331900\pi$
$101$	−4.13525	+	12.7270i	−0.411473	+	1.26638i	−0.915368	+	0.402619i	$0.868100\pi$
$102$		0			0
$103$	−9.09017	−	6.60440i	−0.895681	−	0.650750i	0.0416720	−	0.999131i	$-0.486732\pi$
$103$	−9.09017	−	6.60440i	−0.895681	−	0.650750i	−0.937353	+	0.348381i	$0.886732\pi$
$104$	−1.73607	−	5.34307i	−0.170235	−	0.523931i
$105$		0			0
$106$	0.381966	+	0.277515i	0.0370998	+	0.0269546i
$107$	15.9443	−	11.5842i	1.54139	−	1.11989i	0.591935	−	0.805986i	$-0.298364\pi$
$107$	15.9443	−	11.5842i	1.54139	−	1.11989i	0.949456	−	0.313900i	$-0.101636\pi$
$108$		0			0
$109$	6.47214			0.619918			0.309959	−	0.950750i	$-0.399685\pi$
$109$	6.47214			0.619918			0.309959	+	0.950750i	$0.399685\pi$
$110$	−2.54508	−	2.12663i	−0.242664	−	0.202766i
$111$		0			0
$112$	0.381966	−	1.17557i	0.0360924	−	0.111081i
$113$	0.454915	−	0.330515i	0.0427948	−	0.0310922i	−0.566182	−	0.824280i	$-0.691580\pi$
$113$	0.454915	−	0.330515i	0.0427948	−	0.0310922i	0.608977	+	0.793188i	$0.291580\pi$
$114$		0			0
$115$	−0.0450850	−	0.138757i	−0.00420420	−	0.0129392i
$116$	0.118034	+	0.363271i	0.0109592	+	0.0337289i
$117$		0			0
$118$	−2.35410	+	1.71036i	−0.216713	+	0.157451i
$119$	−1.94427	+	5.98385i	−0.178231	+	0.548539i
$120$		0			0
$121$	1.95492	+	10.8249i	0.177720	+	0.984081i
$122$		0			0
$123$		0			0
$124$	2.92705	−	2.12663i	0.262857	−	0.190977i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	−5.14590	−	15.8374i	−0.456625	−	1.40535i	−0.869217	−	0.494430i	$-0.835377\pi$
$127$	−5.14590	−	15.8374i	−0.456625	−	1.40535i	0.412593	−	0.910916i	$-0.364623\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$		0			0
$130$	−1.73607	+	5.34307i	−0.152263	+	0.468618i
$131$	5.61803			0.490850			0.245425	−	0.969416i	$-0.421073\pi$
$131$	5.61803			0.490850			0.245425	+	0.969416i	$0.421073\pi$
$132$		0			0
$133$	−4.00000			−0.346844
$134$	−1.88197	+	5.79210i	−0.162577	+	0.500361i
$135$		0			0
$136$	−4.11803	−	2.99193i	−0.353119	−	0.256556i
$137$	−3.64590	−	11.2209i	−0.311490	−	0.958668i	−0.977175	−	0.212435i	$-0.931861\pi$
$137$	−3.64590	−	11.2209i	−0.311490	−	0.958668i	0.665685	−	0.746233i	$-0.268139\pi$
$138$		0			0
$139$	−10.7082	−	7.77997i	−0.908258	−	0.659888i	0.0323157	−	0.999478i	$-0.489712\pi$
$139$	−10.7082	−	7.77997i	−0.908258	−	0.659888i	−0.940574	+	0.339590i	$0.889712\pi$
$140$	−1.00000	+	0.726543i	−0.0845154	+	0.0614041i
$141$		0			0
$142$	1.52786			0.128216
$143$	15.7812	−	9.90659i	1.31969	−	0.828431i
$144$		0			0
$145$	0.118034	−	0.363271i	0.00980219	−	0.0301680i
$146$	−10.8541	+	7.88597i	−0.898292	+	0.652647i
$147$		0			0
$148$	−2.66312	−	8.19624i	−0.218907	−	0.673727i
$149$	1.66312	+	5.11855i	0.136248	+	0.419328i	0.995782	−	0.0917502i	$-0.0292461\pi$
$149$	1.66312	+	5.11855i	0.136248	+	0.419328i	−0.859534	+	0.511079i	$0.829246\pi$
$150$		0			0
$151$	−2.47214	+	1.79611i	−0.201180	+	0.146166i	−0.683814	−	0.729656i	$-0.739680\pi$
$151$	−2.47214	+	1.79611i	−0.201180	+	0.146166i	0.482634	+	0.875822i	$0.339680\pi$
$152$	1.00000	−	3.07768i	0.0811107	−	0.249633i
$153$		0			0
$154$	4.09017	+	0.277515i	0.329595	+	0.0223628i
$155$	−3.61803			−0.290607
$156$		0			0
$157$	−19.6353	+	14.2658i	−1.56706	+	1.13854i	−0.637163	+	0.770729i	$0.719892\pi$
$157$	−19.6353	+	14.2658i	−1.56706	+	1.13854i	−0.929901	+	0.367809i	$0.880108\pi$
$158$	5.73607	+	4.16750i	0.456337	+	0.331548i
$159$		0			0
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	0.145898	+	0.106001i	0.0114984	+	0.00835406i
$162$		0			0
$163$	−1.80902	+	5.56758i	−0.141693	+	0.436087i	−0.996571	−	0.0827427i	$-0.973632\pi$
$163$	−1.80902	+	5.56758i	−0.141693	+	0.436087i	0.854878	+	0.518829i	$0.173632\pi$
$164$	3.23607			0.252694
$165$		0			0
$166$	4.00000			0.310460
$167$	−6.26393	+	19.2784i	−0.484718	+	1.49181i	0.347672	+	0.937616i	$0.386972\pi$
$167$	−6.26393	+	19.2784i	−0.484718	+	1.49181i	−0.832389	+	0.554191i	$0.813028\pi$
$168$		0			0
$169$	−15.0172	−	10.9106i	−1.15517	−	0.839281i
$170$	1.57295	+	4.84104i	0.120640	+	0.371291i
$171$		0			0
$172$	−8.97214	−	6.51864i	−0.684119	−	0.497042i
$173$	−14.9443	+	10.8576i	−1.13619	+	0.825492i	−0.986584	−	0.163254i	$-0.947801\pi$
$173$	−14.9443	+	10.8576i	−1.13619	+	0.825492i	−0.149608	+	0.988745i	$0.547801\pi$
$174$		0			0
$175$	1.23607			0.0934380
$176$	−1.23607	+	3.07768i	−0.0931721	+	0.231989i
$177$		0			0
$178$	3.94427	−	12.1392i	0.295636	−	0.909873i
$179$	20.1074	−	14.6089i	1.50290	−	1.09192i	0.533687	−	0.845682i	$-0.320806\pi$
$179$	20.1074	−	14.6089i	1.50290	−	1.09192i	0.969210	−	0.246237i	$-0.0791940\pi$
$180$		0			0
$181$	−4.29180	−	13.2088i	−0.319007	−	0.981802i	−0.974074	−	0.226231i	$-0.927360\pi$
$181$	−4.29180	−	13.2088i	−0.319007	−	0.981802i	0.655067	−	0.755571i	$-0.272640\pi$
$182$	−2.14590	−	6.60440i	−0.159065	−	0.489550i
$183$		0			0
$184$	−0.118034	+	0.0857567i	−0.00870158	+	0.00632207i
$185$	−2.66312	+	8.19624i	−0.195796	+	0.602599i
$186$		0			0
$187$	6.29180	−	15.6659i	0.460102	−	1.14561i
$188$	−11.3262			−0.826051
$189$		0			0
$190$	−2.61803	+	1.90211i	−0.189932	+	0.137994i
$191$	3.85410	+	2.80017i	0.278873	+	0.202613i	0.718426	−	0.695604i	$-0.244863\pi$
$191$	3.85410	+	2.80017i	0.278873	+	0.202613i	−0.439553	+	0.898217i	$0.644863\pi$
$192$		0			0
$193$	−0.944272	−	2.90617i	−0.0679702	−	0.209191i	0.911302	−	0.411738i	$-0.135078\pi$
$193$	−0.944272	−	2.90617i	−0.0679702	−	0.209191i	−0.979273	+	0.202547i	$0.935078\pi$
$194$	−10.2361	−	7.43694i	−0.734907	−	0.533941i
$195$		0			0
$196$	−1.69098	+	5.20431i	−0.120785	+	0.371736i
$197$	6.94427			0.494759			0.247379	−	0.968919i	$-0.420431\pi$
$197$	6.94427			0.494759			0.247379	+	0.968919i	$0.420431\pi$
$198$		0			0
$199$	−20.9787			−1.48714			−0.743571	−	0.668657i	$-0.766869\pi$
$199$	−20.9787			−1.48714			−0.743571	+	0.668657i	$0.766869\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$		0			0
$202$	−10.8262	−	7.86572i	−0.761731	−	0.553430i
$203$	0.145898	+	0.449028i	0.0102400	+	0.0315156i
$204$		0			0
$205$	−2.61803	−	1.90211i	−0.182851	−	0.132849i
$206$	9.09017	−	6.60440i	0.633342	−	0.460150i
$207$		0			0
$208$	5.61803			0.389541
$209$	10.7082	+	0.726543i	0.740702	+	0.0502560i
$210$		0			0
$211$	−6.41641	+	19.7477i	−0.441724	+	1.35949i	0.444313	+	0.895871i	$0.353448\pi$
$211$	−6.41641	+	19.7477i	−0.441724	+	1.35949i	−0.886037	+	0.463614i	$0.846552\pi$
$212$	−0.381966	+	0.277515i	−0.0262335	+	0.0190598i
$213$		0			0
$214$	6.09017	+	18.7436i	0.416315	+	1.28129i
$215$	3.42705	+	10.5474i	0.233723	+	0.719325i
$216$		0			0
$217$	3.61803	−	2.62866i	0.245608	−	0.178445i
$218$	−2.00000	+	6.15537i	−0.135457	+	0.416894i
$219$		0			0
$220$	2.80902	−	1.76336i	0.189384	−	0.118885i
$221$	−28.5967			−1.92363
$222$		0			0
$223$	−2.23607	+	1.62460i	−0.149738	+	0.108791i	−0.660132	−	0.751150i	$-0.729500\pi$
$223$	−2.23607	+	1.62460i	−0.149738	+	0.108791i	0.510394	+	0.859941i	$0.329500\pi$
$224$	1.00000	+	0.726543i	0.0668153	+	0.0485442i
$225$		0			0
$226$	0.173762	+	0.534785i	0.0115585	+	0.0355733i
$227$	−19.7082	−	14.3188i	−1.30808	−	0.950375i	−0.308080	−	0.951360i	$-0.599686\pi$
$227$	−19.7082	−	14.3188i	−1.30808	−	0.950375i	−1.00000		0.000985137i	$0.999686\pi$
$228$		0			0
$229$	1.61803	−	4.97980i	0.106923	−	0.329074i	−0.883254	−	0.468894i	$-0.844652\pi$
$229$	1.61803	−	4.97980i	0.106923	−	0.329074i	0.990177	+	0.139820i	$0.0446525\pi$
$230$	0.145898			0.00962023
$231$		0			0
$232$	−0.381966			−0.0250773
$233$	7.59017	−	23.3601i	0.497249	−	1.53037i	−0.316174	−	0.948701i	$-0.602398\pi$
$233$	7.59017	−	23.3601i	0.497249	−	1.53037i	0.813423	−	0.581673i	$-0.197602\pi$
$234$		0			0
$235$	9.16312	+	6.65740i	0.597736	+	0.434281i
$236$	−0.899187	−	2.76741i	−0.0585321	−	0.180143i
$237$		0			0
$238$	−5.09017	−	3.69822i	−0.329947	−	0.239720i
$239$	1.00000	−	0.726543i	0.0646846	−	0.0469961i	−0.554973	−	0.831868i	$-0.687271\pi$
$239$	1.00000	−	0.726543i	0.0646846	−	0.0469961i	0.619658	+	0.784872i	$0.287271\pi$
$240$		0			0
$241$	11.8885			0.765808			0.382904	−	0.923788i	$-0.374924\pi$
$241$	11.8885			0.765808			0.382904	+	0.923788i	$0.374924\pi$
$242$	−10.8992	−	1.48584i	−0.700626	−	0.0955135i
$243$		0			0
$244$		0			0
$245$	4.42705	−	3.21644i	0.282834	−	0.205491i
$246$		0			0
$247$	−5.61803	−	17.2905i	−0.357467	−	1.10017i
$248$	1.11803	+	3.44095i	0.0709952	+	0.218501i
$249$		0			0
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−3.28115	+	10.0984i	−0.207105	+	0.637402i	0.792516	+	0.609851i	$0.208771\pi$
$251$	−3.28115	+	10.0984i	−0.207105	+	0.637402i	−0.999620	+	0.0275509i	$0.991229\pi$
$252$		0			0
$253$	−0.371323	−	0.310271i	−0.0233449	−	0.0195066i
$254$	16.6525			1.04487
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.6180	−	8.44100i	−0.724713	−	0.526535i	0.163173	−	0.986597i	$-0.447827\pi$
$257$	−11.6180	−	8.44100i	−0.724713	−	0.526535i	−0.887887	+	0.460063i	$0.847827\pi$
$258$		0			0
$259$	−3.29180	−	10.1311i	−0.204542	−	0.629516i
$260$	−4.54508	−	3.30220i	−0.281874	−	0.204794i
$261$		0			0
$262$	−1.73607	+	5.34307i	−0.107255	+	0.330096i
$263$	−0.145898			−0.00899646			−0.00449823	−	0.999990i	$-0.501432\pi$
$263$	−0.145898			−0.00899646			−0.00449823	+	0.999990i	$0.501432\pi$
$264$		0			0
$265$	0.472136			0.0290031
$266$	1.23607	−	3.80423i	0.0757882	−	0.233252i
$267$		0			0
$268$	−4.92705	−	3.57971i	−0.300968	−	0.218666i
$269$	−8.59017	−	26.4378i	−0.523752	−	1.61194i	−0.766771	−	0.641921i	$-0.778138\pi$
$269$	−8.59017	−	26.4378i	−0.523752	−	1.61194i	0.243019	−	0.970022i	$-0.421862\pi$
$270$		0			0
$271$	6.97214	+	5.06555i	0.423527	+	0.307710i	0.779055	−	0.626955i	$-0.215699\pi$
$271$	6.97214	+	5.06555i	0.423527	+	0.307710i	−0.355528	+	0.934666i	$0.615699\pi$
$272$	4.11803	−	2.99193i	0.249692	−	0.181412i
$273$		0			0
$274$	11.7984			0.712766
$275$	−3.30902	−	0.224514i	−0.199541	−	0.0135387i
$276$		0			0
$277$	4.48278	−	13.7966i	0.269344	−	0.828956i	−0.721317	−	0.692606i	$-0.756463\pi$
$277$	4.48278	−	13.7966i	0.269344	−	0.828956i	0.990661	−	0.136350i	$-0.0435373\pi$
$278$	10.7082	−	7.77997i	0.642235	−	0.466611i
$279$		0			0
$280$	−0.381966	−	1.17557i	−0.0228268	−	0.0702538i
$281$	5.09017	+	15.6659i	0.303654	+	0.934551i	0.980176	+	0.198129i	$0.0634864\pi$
$281$	5.09017	+	15.6659i	0.303654	+	0.934551i	−0.676522	+	0.736422i	$0.736514\pi$
$282$		0			0
$283$	5.39919	−	3.92274i	0.320948	−	0.233183i	−0.415632	−	0.909533i	$-0.636439\pi$
$283$	5.39919	−	3.92274i	0.320948	−	0.233183i	0.736580	+	0.676350i	$0.236439\pi$
$284$	−0.472136	+	1.45309i	−0.0280161	+	0.0862247i
$285$		0			0
$286$	4.54508	+	18.0701i	0.268757	+	1.06851i
$287$	4.00000			0.236113
$288$		0			0
$289$	−7.20820	+	5.23707i	−0.424012	+	0.308063i
$290$	0.309017	+	0.224514i	0.0181461	+	0.0131839i
$291$		0			0
$292$	−4.14590	−	12.7598i	−0.242620	−	0.746709i
$293$	−16.1803	−	11.7557i	−0.945266	−	0.686776i	0.00441682	−	0.999990i	$-0.498594\pi$
$293$	−16.1803	−	11.7557i	−0.945266	−	0.686776i	−0.949682	+	0.313215i	$0.898594\pi$
$294$		0			0
$295$	−0.899187	+	2.76741i	−0.0523527	+	0.161125i
$296$	8.61803			0.500913
$297$		0			0
$298$	−5.38197			−0.311769
$299$	−0.253289	+	0.779543i	−0.0146481	+	0.0450821i
$300$		0			0
$301$	−11.0902	−	8.05748i	−0.639227	−	0.464425i
$302$	−0.944272	−	2.90617i	−0.0543367	−	0.167231i
$303$		0			0
$304$	2.61803	+	1.90211i	0.150155	+	0.109094i
$305$		0			0
$306$		0			0
$307$	22.4508			1.28134			0.640669	−	0.767817i	$-0.278657\pi$
$307$	22.4508			1.28134			0.640669	+	0.767817i	$0.278657\pi$
$308$	−1.52786	+	3.80423i	−0.0870581	+	0.216766i
$309$		0			0
$310$	1.11803	−	3.44095i	0.0635001	−	0.195433i
$311$	3.85410	−	2.80017i	0.218546	−	0.158783i	−0.473126	−	0.880995i	$-0.656874\pi$
$311$	3.85410	−	2.80017i	0.218546	−	0.158783i	0.691672	+	0.722212i	$0.256874\pi$
$312$		0			0
$313$	−0.145898	−	0.449028i	−0.00824664	−	0.0253806i	0.946849	−	0.321680i	$-0.104247\pi$
$313$	−0.145898	−	0.449028i	−0.00824664	−	0.0253806i	−0.955095	+	0.296299i	$0.904247\pi$
$314$	−7.50000	−	23.0826i	−0.423249	−	1.30263i
$315$		0			0
$316$	−5.73607	+	4.16750i	−0.322679	+	0.234440i
$317$	0.180340	−	0.555029i	0.0101289	−	0.0311735i	−0.945864	−	0.324562i	$-0.894783\pi$
$317$	0.180340	−	0.555029i	0.0101289	−	0.0311735i	0.955993	+	0.293389i	$0.0947830\pi$
$318$		0			0
$319$	−0.309017	−	1.22857i	−0.0173016	−	0.0687868i
$320$	1.00000			0.0559017
$321$		0			0
$322$	−0.145898	+	0.106001i	−0.00813058	+	0.00590721i
$323$	−13.3262	−	9.68208i	−0.741492	−	0.538725i
$324$		0			0
$325$	1.73607	+	5.34307i	0.0962997	+	0.296380i
$326$	−4.73607	−	3.44095i	−0.262307	−	0.190577i
$327$		0			0
$328$	−1.00000	+	3.07768i	−0.0552158	+	0.169937i
$329$	−14.0000			−0.771845
$330$		0			0
$331$	4.76393			0.261849			0.130925	−	0.991392i	$-0.458205\pi$
$331$	4.76393			0.261849			0.130925	+	0.991392i	$0.458205\pi$
$332$	−1.23607	+	3.80423i	−0.0678380	+	0.208784i
$333$		0			0
$334$	−16.3992	−	11.9147i	−0.897324	−	0.651944i
$335$	1.88197	+	5.79210i	0.102823	+	0.316456i
$336$		0			0
$337$	8.70820	+	6.32688i	0.474366	+	0.344647i	0.799140	−	0.601144i	$-0.205288\pi$
$337$	8.70820	+	6.32688i	0.474366	+	0.344647i	−0.324774	+	0.945792i	$0.605288\pi$
$338$	15.0172	−	10.9106i	0.816829	−	0.593461i
$339$		0			0
$340$	−5.09017			−0.276053
$341$	−10.1631	+	6.37988i	−0.550364	+	0.345490i
$342$		0			0
$343$	−4.76393	+	14.6619i	−0.257228	+	0.791667i
$344$	8.97214	−	6.51864i	0.483745	−	0.351461i
$345$		0			0
$346$	−5.70820	−	17.5680i	−0.306875	−	0.944464i
$347$	−0.0344419	−	0.106001i	−0.00184894	−	0.00569044i	0.950128	−	0.311861i	$-0.100952\pi$
$347$	−0.0344419	−	0.106001i	−0.00184894	−	0.00569044i	−0.951977	+	0.306170i	$0.900952\pi$
$348$		0			0
$349$	−12.4721	+	9.06154i	−0.667618	+	0.485053i	−0.869227	−	0.494413i	$-0.835383\pi$
$349$	−12.4721	+	9.06154i	−0.667618	+	0.485053i	0.201609	+	0.979466i	$0.435383\pi$
$350$	−0.381966	+	1.17557i	−0.0204169	+	0.0628369i
$351$		0			0
$352$	−2.54508	−	2.12663i	−0.135653	−	0.113350i
$353$	−21.3820			−1.13805			−0.569024	−	0.822321i	$-0.692679\pi$
$353$	−21.3820			−1.13805			−0.569024	+	0.822321i	$0.692679\pi$
$354$		0			0
$355$	1.23607	−	0.898056i	0.0656037	−	0.0476639i
$356$	10.3262	+	7.50245i	0.547290	+	0.397629i
$357$		0			0
$358$	7.68034	+	23.6377i	0.405919	+	1.24929i
$359$	8.23607	+	5.98385i	0.434683	+	0.315816i	0.783519	−	0.621368i	$-0.213423\pi$
$359$	8.23607	+	5.98385i	0.434683	+	0.315816i	−0.348836	+	0.937184i	$0.613423\pi$
$360$		0			0
$361$	−2.63525	+	8.11048i	−0.138698	+	0.426867i
$362$	13.8885			0.729966
$363$		0			0
$364$	6.94427			0.363979
$365$	−4.14590	+	12.7598i	−0.217006	+	0.667876i
$366$		0			0
$367$	25.2705	+	18.3601i	1.31911	+	0.958389i	0.999943	+	0.0106909i	$0.00340310\pi$
$367$	25.2705	+	18.3601i	1.31911	+	0.958389i	0.319167	+	0.947698i	$0.396597\pi$
$368$	−0.0450850	−	0.138757i	−0.00235022	−	0.00723322i
$369$		0			0
$370$	−6.97214	−	5.06555i	−0.362464	−	0.263346i
$371$	−0.472136	+	0.343027i	−0.0245121	+	0.0178091i
$372$		0			0
$373$	−20.4721			−1.06001			−0.530004	−	0.847995i	$-0.677809\pi$
$373$	−20.4721			−1.06001			−0.530004	+	0.847995i	$0.677809\pi$
$374$	12.9549	+	10.8249i	0.669883	+	0.559742i
$375$		0			0
$376$	3.50000	−	10.7719i	0.180499	−	0.555518i
$377$	−1.73607	+	1.26133i	−0.0894120	+	0.0649617i
$378$		0			0
$379$	10.0000	+	30.7768i	0.513665	+	1.58090i	0.785697	+	0.618612i	$0.212304\pi$
$379$	10.0000	+	30.7768i	0.513665	+	1.58090i	−0.272032	+	0.962288i	$0.587696\pi$
$380$	−1.00000	−	3.07768i	−0.0512989	−	0.157882i
$381$		0			0
$382$	−3.85410	+	2.80017i	−0.197193	+	0.143269i
$383$	−4.73607	+	14.5761i	−0.242002	+	0.744805i	0.754113	+	0.656744i	$0.228067\pi$
$383$	−4.73607	+	14.5761i	−0.242002	+	0.744805i	−0.996115	+	0.0880606i	$0.971933\pi$
$384$		0			0
$385$	3.47214	−	2.17963i	0.176956	−	0.111084i
$386$	3.05573			0.155532
$387$		0			0
$388$	10.2361	−	7.43694i	0.519658	−	0.377553i
$389$	0.118034	+	0.0857567i	0.00598456	+	0.00434804i	0.590774	−	0.806837i	$-0.298823\pi$
$389$	0.118034	+	0.0857567i	0.00598456	+	0.00434804i	−0.584789	+	0.811185i	$0.698823\pi$
$390$		0			0
$391$	0.229490	+	0.706298i	0.0116058	+	0.0357190i
$392$	−4.42705	−	3.21644i	−0.223600	−	0.162455i
$393$		0			0
$394$	−2.14590	+	6.60440i	−0.108109	+	0.332725i
$395$	7.09017			0.356745
$396$		0			0
$397$	26.7984			1.34497			0.672486	−	0.740110i	$-0.265227\pi$
$397$	26.7984			1.34497			0.672486	+	0.740110i	$0.265227\pi$
$398$	6.48278	−	19.9519i	0.324952	−	1.00010i
$399$		0			0
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	11.1459	+	34.3035i	0.556600	+	1.71304i	0.691681	+	0.722203i	$0.256870\pi$
$401$	11.1459	+	34.3035i	0.556600	+	1.71304i	−0.135082	+	0.990834i	$0.543130\pi$
$402$		0			0
$403$	16.4443	+	11.9475i	0.819148	+	0.595146i
$404$	10.8262	−	7.86572i	0.538625	−	0.391334i
$405$		0			0
$406$	−0.472136			−0.0234317
$407$	6.97214	+	27.7194i	0.345596	+	1.37400i
$408$		0			0
$409$	−10.5000	+	32.3157i	−0.519192	+	1.59791i	0.256332	+	0.966589i	$0.417486\pi$
$409$	−10.5000	+	32.3157i	−0.519192	+	1.59791i	−0.775524	+	0.631319i	$0.782514\pi$
$410$	2.61803	−	1.90211i	0.129295	−	0.0939387i
$411$		0			0
$412$	3.47214	+	10.6861i	0.171060	+	0.526468i
$413$	−1.11146	−	3.42071i	−0.0546912	−	0.168322i
$414$		0			0
$415$	3.23607	−	2.35114i	0.158852	−	0.115413i
$416$	−1.73607	+	5.34307i	−0.0851177	+	0.261965i
$417$		0			0
$418$	−4.00000	+	9.95959i	−0.195646	+	0.487140i
$419$	−16.1459			−0.788779			−0.394389	−	0.918943i	$-0.629044\pi$
$419$	−16.1459			−0.788779			−0.394389	+	0.918943i	$0.629044\pi$
$420$		0			0
$421$	−5.23607	+	3.80423i	−0.255190	+	0.185407i	−0.708024	−	0.706188i	$-0.750413\pi$
$421$	−5.23607	+	3.80423i	−0.255190	+	0.185407i	0.452834	+	0.891595i	$0.350413\pi$
$422$	−16.7984	−	12.2047i	−0.817732	−	0.594117i
$423$		0			0
$424$	−0.145898	−	0.449028i	−0.00708543	−	0.0218067i
$425$	4.11803	+	2.99193i	0.199754	+	0.145130i
$426$		0			0
$427$		0			0
$428$	−19.7082			−0.952632
$429$		0			0
$430$	−11.0902			−0.534815
$431$	6.90983	−	21.2663i	0.332835	−	1.02436i	−0.634944	−	0.772558i	$-0.718977\pi$
$431$	6.90983	−	21.2663i	0.332835	−	1.02436i	0.967779	−	0.251802i	$-0.0810232\pi$
$432$		0			0
$433$	−24.9443	−	18.1231i	−1.19875	−	0.870939i	−0.204584	−	0.978849i	$-0.565584\pi$
$433$	−24.9443	−	18.1231i	−1.19875	−	0.870939i	−0.994161	+	0.107910i	$0.965584\pi$
$434$	1.38197	+	4.25325i	0.0663365	+	0.204163i
$435$		0			0
$436$	−5.23607	−	3.80423i	−0.250762	−	0.182189i
$437$	−0.381966	+	0.277515i	−0.0182719	+	0.0132753i
$438$		0			0
$439$	17.3262			0.826936			0.413468	−	0.910519i	$-0.364317\pi$
$439$	17.3262			0.826936			0.413468	+	0.910519i	$0.364317\pi$
$440$	0.809017	+	3.21644i	0.0385684	+	0.153338i
$441$		0			0
$442$	8.83688	−	27.1971i	0.420328	−	1.29364i
$443$	10.2361	−	7.43694i	0.486330	−	0.353340i	−0.317441	−	0.948278i	$-0.602824\pi$
$443$	10.2361	−	7.43694i	0.486330	−	0.353340i	0.803771	+	0.594938i	$0.202824\pi$
$444$		0			0
$445$	−3.94427	−	12.1392i	−0.186976	−	0.575454i
$446$	−0.854102	−	2.62866i	−0.0404429	−	0.124470i
$447$		0			0
$448$	−1.00000	+	0.726543i	−0.0472456	+	0.0343259i
$449$	−9.00000	+	27.6992i	−0.424736	+	1.30720i	0.478510	+	0.878082i	$0.341177\pi$
$449$	−9.00000	+	27.6992i	−0.424736	+	1.30720i	−0.903247	+	0.429122i	$0.858823\pi$
$450$		0			0
$451$	−10.7082	−	0.726543i	−0.504230	−	0.0342116i
$452$	−0.562306			−0.0264486
$453$		0			0
$454$	19.7082	−	14.3188i	0.924952	−	0.672017i
$455$	−5.61803	−	4.08174i	−0.263377	−	0.191355i
$456$		0			0
$457$	−8.23607	−	25.3480i	−0.385267	−	1.18573i	−0.936286	−	0.351237i	$-0.885761\pi$
$457$	−8.23607	−	25.3480i	−0.385267	−	1.18573i	0.551019	−	0.834492i	$-0.314239\pi$
$458$	4.23607	+	3.07768i	0.197938	+	0.143811i
$459$		0			0
$460$	−0.0450850	+	0.138757i	−0.00210210	+	0.00646959i
$461$	28.2148			1.31409			0.657047	−	0.753850i	$-0.271805\pi$
$461$	28.2148			1.31409			0.657047	+	0.753850i	$0.271805\pi$
$462$		0			0
$463$	−23.8885			−1.11019			−0.555097	−	0.831785i	$-0.687319\pi$
$463$	−23.8885			−1.11019			−0.555097	+	0.831785i	$0.687319\pi$
$464$	0.118034	−	0.363271i	0.00547959	−	0.0168644i
$465$		0			0
$466$	19.8713	+	14.4374i	0.920521	+	0.668798i
$467$	11.9098	+	36.6547i	0.551121	+	1.69618i	0.705973	+	0.708239i	$0.250510\pi$
$467$	11.9098	+	36.6547i	0.551121	+	1.69618i	−0.154852	+	0.987938i	$0.549490\pi$
$468$		0			0
$469$	−6.09017	−	4.42477i	−0.281218	−	0.204317i
$470$	−9.16312	+	6.65740i	−0.422663	+	0.307083i
$471$		0			0
$472$	2.90983			0.133936
$473$	28.2254	+	23.5847i	1.29781	+	1.08442i
$474$		0			0
$475$	−1.00000	+	3.07768i	−0.0458831	+	0.141214i
$476$	5.09017	−	3.69822i	0.233308	−	0.169508i
$477$		0			0
$478$	0.381966	+	1.17557i	0.0174707	+	0.0537693i
$479$	−5.32624	−	16.3925i	−0.243362	−	0.748991i	−0.995902	−	0.0904442i	$-0.971171\pi$
$479$	−5.32624	−	16.3925i	−0.243362	−	0.748991i	0.752540	−	0.658547i	$-0.228829\pi$
$480$		0			0
$481$	39.1697	−	28.4585i	1.78598	−	1.29759i
$482$	−3.67376	+	11.3067i	−0.167335	+	0.515005i
$483$		0			0
$484$	4.78115	−	9.90659i	0.217325	−	0.450300i
$485$	−12.6525			−0.574519
$486$		0			0
$487$	12.4721	−	9.06154i	0.565166	−	0.410617i	−0.268180	−	0.963369i	$-0.586422\pi$
$487$	12.4721	−	9.06154i	0.565166	−	0.410617i	0.833346	+	0.552751i	$0.186422\pi$
$488$		0			0
$489$		0			0
$490$	1.69098	+	5.20431i	0.0763908	+	0.235107i
$491$	−0.836881	−	0.608030i	−0.0377679	−	0.0274400i	0.568741	−	0.822517i	$-0.307431\pi$
$491$	−0.836881	−	0.608030i	−0.0377679	−	0.0274400i	−0.606509	+	0.795077i	$0.707431\pi$
$492$		0			0
$493$	−0.600813	+	1.84911i	−0.0270593	+	0.0832798i
$494$	18.1803			0.817972
$495$		0			0
$496$	−3.61803			−0.162455
$497$	−0.583592	+	1.79611i	−0.0261777	+	0.0805666i
$498$		0			0
$499$	19.0344	+	13.8293i	0.852099	+	0.619086i	0.925724	−	0.378200i	$-0.123457\pi$
$499$	19.0344	+	13.8293i	0.852099	+	0.619086i	−0.0736252	+	0.997286i	$0.523457\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$		0			0
$502$	−8.59017	−	6.24112i	−0.383398	−	0.278555i
$503$	−7.01722	+	5.09831i	−0.312882	+	0.227322i	−0.733132	−	0.680086i	$-0.761942\pi$
$503$	−7.01722	+	5.09831i	−0.312882	+	0.227322i	0.420250	+	0.907408i	$0.361942\pi$
$504$		0			0
$505$	−13.3820			−0.595490
$506$	0.409830	−	0.257270i	0.0182192	−	0.0114371i
$507$		0			0
$508$	−5.14590	+	15.8374i	−0.228312	+	0.702673i
$509$	−12.7812	+	9.28605i	−0.566515	+	0.411597i	−0.833837	−	0.552010i	$-0.813861\pi$
$509$	−12.7812	+	9.28605i	−0.566515	+	0.411597i	0.267323	+	0.963607i	$0.413861\pi$
$510$		0			0
$511$	−5.12461	−	15.7719i	−0.226699	−	0.697709i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$		0			0
$514$	11.6180	−	8.44100i	0.512450	−	0.372316i
$515$	3.47214	−	10.6861i	0.153001	−	0.470887i
$516$		0			0
$517$	37.4787	+	2.54290i	1.64831	+	0.111837i
$518$	10.6525			0.468043
$519$		0			0
$520$	4.54508	−	3.30220i	0.199315	−	0.144811i
$521$	34.2705	+	24.8990i	1.50142	+	1.09084i	0.969812	+	0.243852i	$0.0784113\pi$
$521$	34.2705	+	24.8990i	1.50142	+	1.09084i	0.531606	+	0.846992i	$0.321589\pi$
$522$		0			0
$523$	−4.58359	−	14.1068i	−0.200426	−	0.616849i	−0.999870	−	0.0161084i	$-0.994872\pi$
$523$	−4.58359	−	14.1068i	−0.200426	−	0.616849i	0.799444	−	0.600741i	$-0.205128\pi$
$524$	−4.54508	−	3.30220i	−0.198553	−	0.144257i
$525$		0			0
$526$	0.0450850	−	0.138757i	0.00196580	−	0.00605010i
$527$	18.4164			0.802231
$528$		0			0
$529$	−22.9787			−0.999075
$530$	−0.145898	+	0.449028i	−0.00633741	+	0.0195045i
$531$		0			0
$532$	3.23607	+	2.35114i	0.140301	+	0.101935i
$533$	5.61803	+	17.2905i	0.243344	+	0.748936i
$534$		0			0
$535$	15.9443	+	11.5842i	0.689331	+	0.500828i
$536$	4.92705	−	3.57971i	0.212816	−	0.154620i
$537$		0			0
$538$	27.7984			1.19847
$539$	6.76393	−	16.8415i	0.291343	−	0.725415i
$540$		0			0
$541$	−9.90983	+	30.4993i	−0.426057	+	1.31127i	0.475922	+	0.879488i	$0.342115\pi$
$541$	−9.90983	+	30.4993i	−0.426057	+	1.31127i	−0.901979	+	0.431781i	$0.857885\pi$
$542$	−6.97214	+	5.06555i	−0.299479	+	0.217584i
$543$		0			0
$544$	1.57295	+	4.84104i	0.0674396	+	0.207558i
$545$	2.00000	+	6.15537i	0.0856706	+	0.263667i
$546$		0			0
$547$	−15.1074	+	10.9762i	−0.645945	+	0.469307i	−0.861888	−	0.507099i	$-0.830718\pi$
$547$	−15.1074	+	10.9762i	−0.645945	+	0.469307i	0.215942	+	0.976406i	$0.430718\pi$
$548$	−3.64590	+	11.2209i	−0.155745	+	0.479334i
$549$		0			0
$550$	1.23607	−	3.07768i	0.0527061	−	0.131233i
$551$	−1.23607			−0.0526583
$552$		0			0
$553$	−7.09017	+	5.15131i	−0.301505	+	0.219056i
$554$	11.7361	+	8.52675i	0.498618	+	0.362267i
$555$		0			0
$556$	4.09017	+	12.5882i	0.173462	+	0.533861i
$557$	4.14590	+	3.01217i	0.175667	+	0.127630i	0.672145	−	0.740420i	$-0.265373\pi$
$557$	4.14590	+	3.01217i	0.175667	+	0.127630i	−0.496477	+	0.868050i	$0.665373\pi$
$558$		0			0
$559$	19.2533	−	59.2555i	0.814327	−	2.50624i
$560$	1.23607			0.0522334
$561$		0			0
$562$	−16.4721			−0.694835
$563$	−10.7984	+	33.2340i	−0.455097	+	1.40065i	0.415924	+	0.909399i	$0.363458\pi$
$563$	−10.7984	+	33.2340i	−0.455097	+	1.40065i	−0.871021	+	0.491246i	$0.836542\pi$
$564$		0			0
$565$	0.454915	+	0.330515i	0.0191384	+	0.0139049i
$566$	2.06231	+	6.34712i	0.0866852	+	0.266790i
$567$		0			0
$568$	−1.23607	−	0.898056i	−0.0518643	−	0.0376816i
$569$	1.14590	−	0.832544i	0.0480385	−	0.0349020i	−0.563507	−	0.826111i	$-0.690548\pi$
$569$	1.14590	−	0.832544i	0.0480385	−	0.0349020i	0.611545	+	0.791209i	$0.290548\pi$
$570$		0			0
$571$	16.3607			0.684673			0.342337	−	0.939577i	$-0.388782\pi$
$571$	16.3607			0.684673			0.342337	+	0.939577i	$0.388782\pi$
$572$	−18.5902	−	1.26133i	−0.777294	−	0.0527387i
$573$		0			0
$574$	−1.23607	+	3.80423i	−0.0515925	+	0.158785i
$575$	0.118034	−	0.0857567i	0.00492236	−	0.00357630i
$576$		0			0
$577$	10.7984	+	33.2340i	0.449542	+	1.38355i	0.877425	+	0.479714i	$0.159260\pi$
$577$	10.7984	+	33.2340i	0.449542	+	1.38355i	−0.427883	+	0.903834i	$0.640740\pi$
$578$	−2.75329	−	8.47375i	−0.114522	−	0.352462i
$579$		0			0
$580$	−0.309017	+	0.224514i	−0.0128312	+	0.00932244i
$581$	−1.52786	+	4.70228i	−0.0633865	+	0.195084i
$582$		0			0
$583$	1.32624	−	0.832544i	0.0549272	−	0.0344804i
$584$	13.4164			0.555175
$585$		0			0
$586$	16.1803	−	11.7557i	0.668404	−	0.485624i
$587$	−32.1246	−	23.3399i	−1.32592	−	0.963341i	−0.999838	−	0.0180007i	$-0.994270\pi$
$587$	−32.1246	−	23.3399i	−1.32592	−	0.963341i	−0.326087	−	0.945340i	$-0.605730\pi$
$588$		0			0
$589$	3.61803	+	11.1352i	0.149078	+	0.458816i
$590$	−2.35410	−	1.71036i	−0.0969168	−	0.0704142i
$591$		0			0
$592$	−2.66312	+	8.19624i	−0.109454	+	0.336863i
$593$	33.3262			1.36854			0.684272	−	0.729227i	$-0.260120\pi$
$593$	33.3262			1.36854			0.684272	+	0.729227i	$0.260120\pi$
$594$		0			0
$595$	−6.29180			−0.257938
$596$	1.66312	−	5.11855i	0.0681240	−	0.209664i
$597$		0			0
$598$	−0.663119	−	0.481784i	−0.0271170	−	0.0197016i
$599$	1.29180	+	3.97574i	0.0527814	+	0.162444i	0.973973	−	0.226666i	$-0.0727825\pi$
$599$	1.29180	+	3.97574i	0.0527814	+	0.162444i	−0.921191	+	0.389110i	$0.872783\pi$
$600$		0			0
$601$	0.854102	+	0.620541i	0.0348395	+	0.0253124i	0.605069	−	0.796173i	$-0.293146\pi$
$601$	0.854102	+	0.620541i	0.0348395	+	0.0253124i	−0.570229	+	0.821486i	$0.693146\pi$
$602$	11.0902	−	8.05748i	0.452002	−	0.328398i
$603$		0			0
$604$	3.05573			0.124336
$605$	−9.69098	+	5.20431i	−0.393994	+	0.211585i
$606$		0			0
$607$	1.38197	−	4.25325i	0.0560923	−	0.172634i	−0.919085	−	0.394059i	$-0.871071\pi$
$607$	1.38197	−	4.25325i	0.0560923	−	0.172634i	0.975178	+	0.221425i	$0.0710706\pi$
$608$	−2.61803	+	1.90211i	−0.106175	+	0.0771409i
$609$		0			0
$610$		0			0
$611$	−19.6631	−	60.5169i	−0.795485	−	2.44825i
$612$		0			0
$613$	−4.85410	+	3.52671i	−0.196055	+	0.142443i	−0.681482	−	0.731835i	$-0.738664\pi$
$613$	−4.85410	+	3.52671i	−0.196055	+	0.142443i	0.485427	+	0.874277i	$0.338664\pi$
$614$	−6.93769	+	21.3520i	−0.279983	+	0.861698i
$615$		0			0
$616$	−3.14590	−	2.62866i	−0.126752	−	0.105912i
$617$	18.3607			0.739173			0.369587	−	0.929196i	$-0.379499\pi$
$617$	18.3607			0.739173			0.369587	+	0.929196i	$0.379499\pi$
$618$		0			0
$619$	−14.9443	+	10.8576i	−0.600661	+	0.436406i	−0.846113	−	0.533003i	$-0.821063\pi$
$619$	−14.9443	+	10.8576i	−0.600661	+	0.436406i	0.245452	+	0.969409i	$0.421063\pi$
$620$	2.92705	+	2.12663i	0.117553	+	0.0854074i
$621$		0			0
$622$	1.47214	+	4.53077i	0.0590273	+	0.181667i
$623$	12.7639	+	9.27354i	0.511376	+	0.371537i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	0.472136			0.0188703
$627$		0			0
$628$	24.2705			0.968499
$629$	13.5557	−	41.7202i	0.540502	−	1.66349i
$630$		0			0
$631$	17.2533	+	12.5352i	0.686843	+	0.499020i	0.875621	−	0.482999i	$-0.160453\pi$
$631$	17.2533	+	12.5352i	0.686843	+	0.499020i	−0.188778	+	0.982020i	$0.560453\pi$
$632$	−2.19098	−	6.74315i	−0.0871526	−	0.268228i
$633$		0			0
$634$	0.472136	+	0.343027i	0.0187509	+	0.0136233i
$635$	13.4721	−	9.78808i	0.534625	−	0.388428i
$636$		0			0
$637$	−30.7426			−1.21807
$638$	1.26393	+	0.0857567i	0.0500395	+	0.00339514i
$639$		0			0
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−8.23607	+	5.98385i	−0.325305	+	0.236348i	−0.738436	−	0.674324i	$-0.764435\pi$
$641$	−8.23607	+	5.98385i	−0.325305	+	0.236348i	0.413131	+	0.910672i	$0.364435\pi$
$642$		0			0
$643$	6.11803	+	18.8294i	0.241272	+	0.742558i	0.996227	+	0.0867821i	$0.0276584\pi$
$643$	6.11803	+	18.8294i	0.241272	+	0.742558i	−0.754956	+	0.655776i	$0.772342\pi$
$644$	−0.0557281	−	0.171513i	−0.00219599	−	0.00675858i
$645$		0			0
$646$	13.3262	−	9.68208i	0.524314	−	0.380936i
$647$	4.51722	−	13.9026i	0.177590	−	0.546567i	−0.822152	−	0.569268i	$-0.807227\pi$
$647$	4.51722	−	13.9026i	0.177590	−	0.546567i	0.999742	+	0.0227013i	$0.00722668\pi$
$648$		0			0
$649$	2.35410	+	9.35930i	0.0924066	+	0.367385i
$650$	−5.61803			−0.220357
$651$		0			0
$652$	4.73607	−	3.44095i	0.185479	−	0.134758i
$653$	−34.4164	−	25.0050i	−1.34682	−	0.978521i	−0.999163	−	0.0408980i	$-0.986978\pi$
$653$	−34.4164	−	25.0050i	−1.34682	−	0.978521i	−0.347655	−	0.937623i	$-0.613022\pi$
$654$		0			0
$655$	1.73607	+	5.34307i	0.0678338	+	0.208771i
$656$	−2.61803	−	1.90211i	−0.102217	−	0.0742650i
$657$		0			0
$658$	4.32624	−	13.3148i	0.168654	−	0.519065i
$659$	−11.4164			−0.444720			−0.222360	−	0.974965i	$-0.571376\pi$
$659$	−11.4164			−0.444720			−0.222360	+	0.974965i	$0.571376\pi$
$660$		0			0
$661$	−36.3607			−1.41427			−0.707133	−	0.707080i	$-0.750012\pi$
$661$	−36.3607			−1.41427			−0.707133	+	0.707080i	$0.750012\pi$
$662$	−1.47214	+	4.53077i	−0.0572162	+	0.176093i
$663$		0			0
$664$	−3.23607	−	2.35114i	−0.125584	−	0.0912420i
$665$	−1.23607	−	3.80423i	−0.0479327	−	0.147522i
$666$		0			0
$667$	0.0450850	+	0.0327561i	0.00174570	+	0.00126832i
$668$	16.3992	−	11.9147i	0.634504	−	0.460994i
$669$		0			0
$670$	−6.09017			−0.235284
$671$		0			0
$672$		0			0
$673$	−0.708204	+	2.17963i	−0.0272993	+	0.0840185i	−0.963778	−	0.266706i	$-0.914065\pi$
$673$	−0.708204	+	2.17963i	−0.0272993	+	0.0840185i	0.936479	+	0.350725i	$0.114065\pi$
$674$	−8.70820	+	6.32688i	−0.335427	+	0.243702i
$675$		0			0
$676$	5.73607	+	17.6538i	0.220618	+	0.678992i
$677$	−7.03444	−	21.6498i	−0.270356	−	0.832069i	−0.990411	−	0.138152i	$-0.955884\pi$
$677$	−7.03444	−	21.6498i	−0.270356	−	0.832069i	0.720055	−	0.693917i	$-0.244116\pi$
$678$		0			0
$679$	12.6525	−	9.19256i	0.485557	−	0.352778i
$680$	1.57295	−	4.84104i	0.0603198	−	0.185645i
$681$		0			0
$682$	−2.92705	−	11.6372i	−0.112083	−	0.445611i
$683$	19.1246			0.731783			0.365891	−	0.930658i	$-0.380764\pi$
$683$	19.1246			0.731783			0.365891	+	0.930658i	$0.380764\pi$
$684$		0			0
$685$	9.54508	−	6.93491i	0.364699	−	0.264969i
$686$	−12.4721	−	9.06154i	−0.476188	−	0.345971i
$687$		0			0
$688$	3.42705	+	10.5474i	0.130655	+	0.402115i
$689$	−2.14590	−	1.55909i	−0.0817522	−	0.0593965i
$690$		0			0
$691$	3.29180	−	10.1311i	0.125226	−	0.385405i	−0.868716	−	0.495310i	$-0.835054\pi$
$691$	3.29180	−	10.1311i	0.125226	−	0.385405i	0.993942	+	0.109904i	$0.0350545\pi$
$692$	18.4721			0.702205
$693$		0			0
$694$	0.111456			0.00423082
$695$	4.09017	−	12.5882i	0.155149	−	0.477499i
$696$		0			0
$697$	13.3262	+	9.68208i	0.504767	+	0.366735i
$698$	−4.76393	−	14.6619i	−0.180317	−	0.554960i
$699$		0			0
$700$	−1.00000	−	0.726543i	−0.0377964	−	0.0274607i
$701$	−10.0902	+	7.33094i	−0.381100	+	0.276886i	−0.761799	−	0.647814i	$-0.775684\pi$
$701$	−10.0902	+	7.33094i	−0.381100	+	0.276886i	0.380698	+	0.924699i	$0.375684\pi$
$702$		0			0
$703$	27.8885			1.05184
$704$	2.80902	−	1.76336i	0.105869	−	0.0664590i
$705$		0			0
$706$	6.60739	−	20.3355i	0.248672	−	0.765335i
$707$	13.3820	−	9.72257i	0.503281	−	0.365655i
$708$		0			0
$709$	−11.5623	−	35.5851i	−0.434232	−	1.33643i	−0.893872	−	0.448322i	$-0.852022\pi$
$709$	−11.5623	−	35.5851i	−0.434232	−	1.33643i	0.459641	−	0.888105i	$-0.347978\pi$
$710$	0.472136	+	1.45309i	0.0177189	+	0.0545333i
$711$		0			0
$712$	−10.3262	+	7.50245i	−0.386992	+	0.281166i
$713$	0.163119	−	0.502029i	0.00610885	−	0.0188011i
$714$		0			0
$715$	14.2984	+	11.9475i	0.534729	+	0.446810i
$716$	−24.8541			−0.928841
$717$		0			0
$718$	−8.23607	+	5.98385i	−0.307367	+	0.223315i
$719$	7.56231	+	5.49434i	0.282026	+	0.204904i	0.719801	−	0.694181i	$-0.244233\pi$
$719$	7.56231	+	5.49434i	0.282026	+	0.204904i	−0.437774	+	0.899085i	$0.644233\pi$
$720$		0			0
$721$	4.29180	+	13.2088i	0.159835	+	0.491921i
$722$	−6.89919	−	5.01255i	−0.256761	−	0.186548i
$723$		0			0
$724$	−4.29180	+	13.2088i	−0.159503	+	0.490901i
$725$	0.381966			0.0141859
$726$		0			0
$727$	−27.8197			−1.03177			−0.515887	−	0.856657i	$-0.672538\pi$
$727$	−27.8197			−1.03177			−0.515887	+	0.856657i	$0.672538\pi$
$728$	−2.14590	+	6.60440i	−0.0795323	+	0.244775i
$729$		0			0
$730$	−10.8541	−	7.88597i	−0.401728	−	0.291873i
$731$	−17.4443	−	53.6879i	−0.645200	−	1.98572i
$732$		0			0
$733$	−28.8607	−	20.9685i	−1.06599	−	0.774490i	−0.0908057	−	0.995869i	$-0.528944\pi$
$733$	−28.8607	−	20.9685i	−1.06599	−	0.774490i	−0.975188	+	0.221379i	$0.928944\pi$
$734$	−25.2705	+	18.3601i	−0.932752	+	0.677684i
$735$		0			0
$736$	0.145898			0.00537787
$737$	15.5000	+	12.9515i	0.570950	+	0.477075i
$738$		0			0
$739$	−15.1459	+	46.6143i	−0.557151	+	1.71473i	0.133044	+	0.991110i	$0.457525\pi$
$739$	−15.1459	+	46.6143i	−0.557151	+	1.71473i	−0.690195	+	0.723624i	$0.742475\pi$
$740$	6.97214	−	5.06555i	0.256301	−	0.186213i
$741$		0			0
$742$	−0.180340	−	0.555029i	−0.00662049	−	0.0203758i
$743$	4.26393	+	13.1230i	0.156428	+	0.481437i	0.998303	−	0.0582362i	$-0.0185477\pi$
$743$	4.26393	+	13.1230i	0.156428	+	0.481437i	−0.841874	+	0.539674i	$0.818548\pi$
$744$		0			0
$745$	−4.35410	+	3.16344i	−0.159522	+	0.115899i
$746$	6.32624	−	19.4702i	0.231620	−	0.712853i
$747$		0			0
$748$	−14.2984	+	8.97578i	−0.522800	+	0.328187i
$749$	−24.3607			−0.890120
$750$		0			0
$751$	−0.0278640	+	0.0202444i	−0.00101677	+	0.000738729i	−0.588294	−	0.808647i	$-0.700200\pi$
$751$	−0.0278640	+	0.0202444i	−0.00101677	+	0.000738729i	0.587277	+	0.809386i	$0.300200\pi$
$752$	9.16312	+	6.65740i	0.334145	+	0.242770i
$753$		0			0
$754$	−0.663119	−	2.04087i	−0.0241494	−	0.0743241i
$755$	−2.47214	−	1.79611i	−0.0899702	−	0.0653672i
$756$		0			0
$757$	−14.5689	+	44.8384i	−0.529515	+	1.62968i	0.225696	+	0.974198i	$0.427534\pi$
$757$	−14.5689	+	44.8384i	−0.529515	+	1.62968i	−0.755211	+	0.655482i	$0.772466\pi$
$758$	−32.3607			−1.17539
$759$		0			0
$760$	3.23607			0.117385
$761$	3.09017	−	9.51057i	0.112019	−	0.344758i	−0.879295	−	0.476278i	$-0.841986\pi$
$761$	3.09017	−	9.51057i	0.112019	−	0.344758i	0.991314	+	0.131520i	$0.0419857\pi$
$762$		0			0
$763$	−6.47214	−	4.70228i	−0.234307	−	0.170234i
$764$	−1.47214	−	4.53077i	−0.0532600	−	0.163917i
$765$		0			0
$766$	−12.3992	−	9.00854i	−0.448001	−	0.325492i
$767$	13.2254	−	9.60883i	0.477542	−	0.346955i
$768$		0			0
$769$	31.4508			1.13415			0.567073	−	0.823667i	$-0.308076\pi$
$769$	31.4508			1.13415			0.567073	+	0.823667i	$0.308076\pi$
$770$	1.00000	+	3.97574i	0.0360375	+	0.143276i
$771$		0			0
$772$	−0.944272	+	2.90617i	−0.0339851	+	0.104595i
$773$	−23.9443	+	17.3965i	−0.861216	+	0.625710i	−0.928215	−	0.372043i	$-0.878657\pi$
$773$	−23.9443	+	17.3965i	−0.861216	+	0.625710i	0.0669998	+	0.997753i	$0.478657\pi$
$774$		0			0
$775$	−1.11803	−	3.44095i	−0.0401610	−	0.123603i
$776$	3.90983	+	12.0332i	0.140355	+	0.431967i
$777$		0			0
$778$	−0.118034	+	0.0857567i	−0.00423172	+	0.00307453i
$779$	−3.23607	+	9.95959i	−0.115944	+	0.356839i
$780$		0			0
$781$	1.88854	−	4.70228i	0.0675774	−	0.168261i
$782$	−0.742646			−0.0265570
$783$		0			0
$784$	4.42705	−	3.21644i	0.158109	−	0.114873i
$785$	−19.6353	−	14.2658i	−0.700812	−	0.509170i
$786$		0			0
$787$	−2.48278	−	7.64121i	−0.0885015	−	0.272380i	0.897004	−	0.442022i	$-0.145739\pi$
$787$	−2.48278	−	7.64121i	−0.0885015	−	0.272380i	−0.985506	+	0.169642i	$0.945739\pi$
$788$	−5.61803	−	4.08174i	−0.200134	−	0.145406i
$789$		0			0
$790$	−2.19098	+	6.74315i	−0.0779517	+	0.239911i
$791$	−0.695048			−0.0247131
$792$		0			0
$793$		0			0
$794$	−8.28115	+	25.4868i	−0.293887	+	0.904492i
$795$		0			0
$796$	16.9721	+	12.3310i	0.601561	+	0.437060i
$797$	2.56231	+	7.88597i	0.0907615	+	0.279335i	0.986126	−	0.165999i	$-0.0530849\pi$
$797$	2.56231	+	7.88597i	0.0907615	+	0.279335i	−0.895364	+	0.445334i	$0.853085\pi$
$798$		0			0
$799$	−46.6418	−	33.8873i	−1.65007	−	1.19885i
$800$	0.809017	−	0.587785i	0.0286031	−	0.0207813i
$801$		0			0
$802$	−36.0689			−1.27364
$803$	10.8541	+	43.1531i	0.383033	+	1.52284i
$804$		0			0
$805$	−0.0557281	+	0.171513i	−0.00196416	+	0.00604505i
$806$	−16.4443	+	11.9475i	−0.579225	+	0.420831i
$807$		0			0
$808$	4.13525	+	12.7270i	0.145478	+	0.447735i
$809$	−8.85410	−	27.2501i	−0.311294	−	0.958063i	−0.977253	−	0.212076i	$-0.931978\pi$
$809$	−8.85410	−	27.2501i	−0.311294	−	0.958063i	0.665960	−	0.745988i	$-0.268022\pi$
$810$		0			0
$811$	25.4164	−	18.4661i	0.892491	−	0.648433i	−0.0440355	−	0.999030i	$-0.514021\pi$
$811$	25.4164	−	18.4661i	0.892491	−	0.648433i	0.936526	+	0.350597i	$0.114021\pi$
$812$	0.145898	−	0.449028i	0.00512002	−	0.0157578i
$813$		0			0
$814$	−28.5172	−	1.93487i	−0.999528	−	0.0678171i
$815$	−5.85410			−0.205060
$816$		0			0
$817$	29.0344	−	21.0948i	1.01579	−	0.738012i
$818$	−27.4894	−	19.9722i	−0.961143	−	0.698311i
$819$		0			0
$820$	1.00000	+	3.07768i	0.0349215	+	0.107477i
$821$	15.6180	+	11.3472i	0.545073	+	0.396019i	0.825966	−	0.563720i	$-0.190630\pi$
$821$	15.6180	+	11.3472i	0.545073	+	0.396019i	−0.280893	+	0.959739i	$0.590630\pi$
$822$		0			0
$823$	−5.32624	+	16.3925i	−0.185661	+	0.571406i	−0.999959	−	0.00904109i	$-0.997122\pi$
$823$	−5.32624	+	16.3925i	−0.185661	+	0.571406i	0.814298	+	0.580447i	$0.197122\pi$
$824$	−11.2361			−0.391427
$825$		0			0
$826$	3.59675			0.125147
$827$	−13.5066	+	41.5690i	−0.469670	+	1.44549i	0.383344	+	0.923606i	$0.374772\pi$
$827$	−13.5066	+	41.5690i	−0.469670	+	1.44549i	−0.853013	+	0.521889i	$0.825228\pi$
$828$		0			0
$829$	11.0000	+	7.99197i	0.382046	+	0.277573i	0.762188	−	0.647355i	$-0.224125\pi$
$829$	11.0000	+	7.99197i	0.382046	+	0.277573i	−0.380142	+	0.924928i	$0.624125\pi$
$830$	1.23607	+	3.80423i	0.0429045	+	0.132047i
$831$		0			0
$832$	−4.54508	−	3.30220i	−0.157572	−	0.114483i
$833$	−22.5344	+	16.3722i	−0.780772	+	0.567264i
$834$		0			0
$835$	−20.2705			−0.701490
$836$	−8.23607	−	6.88191i	−0.284850	−	0.238016i
$837$		0			0
$838$	4.98936	−	15.3557i	0.172354	−	0.530453i
$839$	−44.2148	+	32.1239i	−1.52646	+	1.10904i	−0.568300	+	0.822822i	$0.692399\pi$
$839$	−44.2148	+	32.1239i	−1.52646	+	1.10904i	−0.958164	+	0.286219i	$0.907601\pi$
$840$		0			0
$841$	−8.91641	−	27.4419i	−0.307462	−	0.946272i
$842$	−2.00000	−	6.15537i	−0.0689246	−	0.212128i
$843$		0			0
$844$	16.7984	−	12.2047i	0.578224	−	0.420104i
$845$	5.73607	−	17.6538i	0.197327	−	0.607309i
$846$		0			0
$847$	5.90983	−	12.2452i	0.203064	−	0.420751i
$848$	0.472136			0.0162132
$849$		0			0
$850$	−4.11803	+	2.99193i	−0.141247	+	0.102622i
$851$	−1.01722	−	0.739054i	−0.0348699	−	0.0253345i
$852$		0			0
$853$	−11.2705	−	34.6871i	−0.385895	−	1.18766i	−0.935829	−	0.352454i	$-0.885347\pi$
$853$	−11.2705	−	34.6871i	−0.385895	−	1.18766i	0.549934	−	0.835208i	$-0.314653\pi$
$854$		0			0
$855$		0			0
$856$	6.09017	−	18.7436i	0.208158	−	0.640644i
$857$	45.1591			1.54260			0.771302	−	0.636469i	$-0.219606\pi$
$857$	45.1591			1.54260			0.771302	+	0.636469i	$0.219606\pi$
$858$		0			0
$859$	21.1246			0.720762			0.360381	−	0.932805i	$-0.382647\pi$
$859$	21.1246			0.720762			0.360381	+	0.932805i	$0.382647\pi$
$860$	3.42705	−	10.5474i	0.116861	−	0.359663i
$861$		0			0
$862$	18.0902	+	13.1433i	0.616154	+	0.447662i
$863$	−14.6287	−	45.0224i	−0.497966	−	1.53258i	−0.812283	−	0.583264i	$-0.801775\pi$
$863$	−14.6287	−	45.0224i	−0.497966	−	1.53258i	0.314317	−	0.949318i	$-0.398225\pi$
$864$		0			0
$865$	−14.9443	−	10.8576i	−0.508120	−	0.369171i
$866$	24.9443	−	18.1231i	0.847641	−	0.615847i
$867$		0			0
$868$	−4.47214			−0.151794
$869$	19.9164	−	12.5025i	0.675618	−	0.424118i
$870$		0			0
$871$	10.5729	−	32.5402i	0.358251	−	1.10258i
$872$	5.23607	−	3.80423i	0.177316	−	0.128827i
$873$		0			0
$874$	−0.145898	−	0.449028i	−0.00493507	−	0.0151886i
$875$	0.381966	+	1.17557i	0.0129128	+	0.0397415i
$876$		0			0
$877$	−38.8607	+	28.2339i	−1.31223	+	0.953392i	−0.312238	+	0.950004i	$0.601079\pi$
$877$	−38.8607	+	28.2339i	−1.31223	+	0.953392i	−0.999994	+	0.00338827i	$0.998921\pi$
$878$	−5.35410	+	16.4782i	−0.180692	+	0.556113i
$879$		0			0
$880$	−3.30902	−	0.224514i	−0.111547	−	0.00756837i
$881$	−8.00000			−0.269527			−0.134763	−	0.990878i	$-0.543027\pi$
$881$	−8.00000			−0.269527			−0.134763	+	0.990878i	$0.543027\pi$
$882$		0			0
$883$	16.4443	−	11.9475i	0.553394	−	0.402064i	−0.275641	−	0.961261i	$-0.588890\pi$
$883$	16.4443	−	11.9475i	0.553394	−	0.402064i	0.829035	+	0.559196i	$0.188890\pi$
$884$	23.1353	+	16.8087i	0.778123	+	0.565339i
$885$		0			0
$886$	3.90983	+	12.0332i	0.131353	+	0.404264i
$887$	10.8820	+	7.90621i	0.365381	+	0.265465i	0.755293	−	0.655387i	$-0.227495\pi$
$887$	10.8820	+	7.90621i	0.365381	+	0.265465i	−0.389912	+	0.920852i	$0.627495\pi$
$888$		0			0
$889$	−6.36068	+	19.5762i	−0.213330	+	0.656563i
$890$	12.7639			0.427848
$891$		0			0
$892$	2.76393			0.0925433
$893$	11.3262	−	34.8586i	0.379018	−	1.16650i
$894$		0			0
$895$	20.1074	+	14.6089i	0.672116	+	0.488321i
$896$	−0.381966	−	1.17557i	−0.0127606	−	0.0392731i
$897$		0			0
$898$	−23.5623	−	17.1190i	−0.786284	−	0.571269i
$899$	1.11803	−	0.812299i	0.0372885	−	0.0270917i
$900$		0			0
$901$	−2.40325			−0.0800639
$902$	4.00000	−	9.95959i	0.133185	−	0.331618i
$903$		0			0
$904$	0.173762	−	0.534785i	0.00577924	−	0.0177867i
$905$	11.2361	−	8.16348i	0.373500	−	0.271363i
$906$		0			0
$907$	4.48278	+	13.7966i	0.148848	+	0.458108i	0.997486	−	0.0708670i	$-0.0225766\pi$
$907$	4.48278	+	13.7966i	0.148848	+	0.458108i	−0.848638	+	0.528975i	$0.822577\pi$
$908$	7.52786	+	23.1684i	0.249821	+	0.768870i
$909$		0			0
$910$	5.61803	−	4.08174i	0.186236	−	0.135308i
$911$	−3.85410	+	11.8617i	−0.127692	+	0.392996i	−0.994382	−	0.105852i	$-0.966243\pi$
$911$	−3.85410	+	11.8617i	−0.127692	+	0.392996i	0.866690	+	0.498847i	$0.166243\pi$
$912$		0			0
$913$	4.94427	−	12.3107i	0.163632	−	0.407426i
$914$	26.6525			0.881586
$915$		0			0
$916$	−4.23607	+	3.07768i	−0.139964	+	0.101690i
$917$	−5.61803	−	4.08174i	−0.185524	−	0.134791i
$918$		0			0
$919$	−14.0106	−	43.1203i	−0.462168	−	1.42241i	−0.862509	−	0.506042i	$-0.831108\pi$
$919$	−14.0106	−	43.1203i	−0.462168	−	1.42241i	0.400340	−	0.916366i	$-0.368892\pi$
$920$	−0.118034	−	0.0857567i	−0.00389147	−	0.00282732i
$921$		0			0
$922$	−8.71885	+	26.8339i	−0.287140	+	0.883726i
$923$	−8.58359			−0.282532
$924$		0			0
$925$	−8.61803			−0.283359
$926$	7.38197	−	22.7194i	0.242586	−	0.746604i
$927$		0			0
$928$	0.309017	+	0.224514i	0.0101440	+	0.00737003i
$929$	6.65248	+	20.4742i	0.218261	+	0.671737i	0.998906	+	0.0467630i	$0.0148905\pi$
$929$	6.65248	+	20.4742i	0.218261	+	0.671737i	−0.780645	+	0.624974i	$0.785109\pi$
$930$		0			0
$931$	−14.3262	−	10.4086i	−0.469523	−	0.341129i
$932$	−19.8713	+	14.4374i	−0.650907	+	0.472911i
$933$		0			0
$934$	−38.5410			−1.26110
$935$	16.8435	+	1.14281i	0.550840	+	0.0373740i
$936$		0			0
$937$	−3.50658	+	10.7921i	−0.114555	+	0.352564i	−0.991854	−	0.127380i	$-0.959343\pi$
$937$	−3.50658	+	10.7921i	−0.114555	+	0.352564i	0.877299	+	0.479944i	$0.159343\pi$
$938$	6.09017	−	4.42477i	0.198851	−	0.144474i
$939$		0			0
$940$	−3.50000	−	10.7719i	−0.114157	−	0.351340i
$941$	−14.8262	−	45.6305i	−0.483322	−	1.48751i	−0.834397	−	0.551164i	$-0.814184\pi$
$941$	−14.8262	−	45.6305i	−0.483322	−	1.48751i	0.351076	−	0.936347i	$-0.385816\pi$
$942$		0			0
$943$	0.381966	−	0.277515i	0.0124385	−	0.00903712i
$944$	−0.899187	+	2.76741i	−0.0292660	+	0.0900716i
$945$		0			0
$946$	−31.1525	+	19.5559i	−1.01285	+	0.635818i
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$		0			0
$949$	60.9787	−	44.3036i	1.97945	−	1.43816i
$950$	−2.61803	−	1.90211i	−0.0849402	−	0.0617127i
$951$		0			0
$952$	1.94427	+	5.98385i	0.0630142	+	0.193938i
$953$	−6.29837	−	4.57604i	−0.204024	−	0.148232i	0.481082	−	0.876676i	$-0.340244\pi$
$953$	−6.29837	−	4.57604i	−0.204024	−	0.148232i	−0.685106	+	0.728443i	$0.740244\pi$
$954$		0			0
$955$	−1.47214	+	4.53077i	−0.0476372	+	0.146612i
$956$	−1.23607			−0.0399773
$957$		0			0
$958$	17.2361			0.556872
$959$	−4.50658	+	13.8698i	−0.145525	+	0.447880i
$960$		0			0
$961$	14.4894	+	10.5271i	0.467399	+	0.339585i
$962$	14.9615	+	46.0467i	0.482378	+	1.48461i
$963$		0			0
$964$	−9.61803	−	6.98791i	−0.309776	−	0.225065i
$965$	2.47214	−	1.79611i	0.0795809	−	0.0578189i
$966$		0			0
$967$	−9.30495			−0.299227			−0.149614	−	0.988745i	$-0.547803\pi$
$967$	−9.30495			−0.299227			−0.149614	+	0.988745i	$0.547803\pi$
$968$	7.94427	+	7.60845i	0.255339	+	0.244545i
$969$		0			0
$970$	3.90983	−	12.0332i	0.125537	−	0.386363i
$971$	−29.4164	+	21.3723i	−0.944017	+	0.685869i	−0.949384	−	0.314117i	$-0.898292\pi$
$971$	−29.4164	+	21.3723i	−0.944017	+	0.685869i	0.00536690	+	0.999986i	$0.498292\pi$
$972$		0			0
$973$	5.05573	+	15.5599i	0.162079	+	0.498828i
$974$	4.76393	+	14.6619i	0.152646	+	0.469797i
$975$		0			0
$976$		0			0
$977$	7.67376	−	23.6174i	0.245505	−	0.755588i	−0.750048	−	0.661384i	$-0.769969\pi$
$977$	7.67376	−	23.6174i	0.245505	−	0.755588i	0.995553	−	0.0942040i	$-0.0300306\pi$
$978$		0			0
$979$	−32.4853	−	27.1441i	−1.03823	−	0.867530i
$980$	−5.47214			−0.174801
$981$		0			0
$982$	0.836881	−	0.608030i	0.0267059	−	0.0194030i
$983$	38.1803	+	27.7396i	1.21776	+	0.884757i	0.995912	−	0.0903234i	$-0.0287901\pi$
$983$	38.1803	+	27.7396i	1.21776	+	0.884757i	0.221851	+	0.975081i	$0.428790\pi$
$984$		0			0
$985$	2.14590	+	6.60440i	0.0683740	+	0.210434i
$986$	−1.57295	−	1.14281i	−0.0500929	−	0.0363946i
$987$		0			0
$988$	−5.61803	+	17.2905i	−0.178733	+	0.550085i
$989$	−1.61803			−0.0514505
$990$		0			0
$991$	−59.5197			−1.89071			−0.945353	−	0.326048i	$-0.894283\pi$
$991$	−59.5197			−1.89071			−0.945353	+	0.326048i	$0.894283\pi$
$992$	1.11803	−	3.44095i	0.0354976	−	0.109250i
$993$		0			0
$994$	−1.52786	−	1.11006i	−0.0484609	−	0.0352089i
$995$	−6.48278	−	19.9519i	−0.205518	−	0.632519i
$996$		0			0
$997$	−3.26393	−	2.37139i	−0.103370	−	0.0751025i	0.534900	−	0.844916i	$-0.320349\pi$
$997$	−3.26393	−	2.37139i	−0.103370	−	0.0751025i	−0.638269	+	0.769813i	$0.720349\pi$
$998$	−19.0344	+	13.8293i	−0.602525	+	0.437760i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.n.e.361.1		4
3.2	odd	2		330.2.m.b.31.1	✓	4
11.5	even	5	inner	990.2.n.e.181.1		4
33.5	odd	10		330.2.m.b.181.1	yes	4
33.26	odd	10		3630.2.a.bj.1.2		2
33.29	even	10		3630.2.a.bb.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.31.1	✓	4	3.2	odd	2
330.2.m.b.181.1	yes	4	33.5	odd	10
990.2.n.e.181.1		4	11.5	even	5	inner
990.2.n.e.361.1		4	1.1	even	1	trivial
3630.2.a.bb.1.1		2	33.29	even	10
3630.2.a.bj.1.2		2	33.26	odd	10

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.00000 - 0.726543i) q^{7} +(0.809017 - 0.587785i) q^{8} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-1.00000 - 0.726543i) q^{7} +(0.809017 - 0.587785i) q^{8} -1.00000 q^{10} +(2.54508 + 2.12663i) q^{11} +(1.73607 - 5.34307i) q^{13} +(1.00000 - 0.726543i) q^{14} +(0.309017 + 0.951057i) q^{16} +(-1.57295 - 4.84104i) q^{17} +(2.61803 - 1.90211i) q^{19} +(0.309017 - 0.951057i) q^{20} +(-2.80902 + 1.76336i) q^{22} -0.145898 q^{23} +(-0.809017 + 0.587785i) q^{25} +(4.54508 + 3.30220i) q^{26} +(0.381966 + 1.17557i) q^{28} +(-0.309017 - 0.224514i) q^{29} +(-1.11803 + 3.44095i) q^{31} -1.00000 q^{32} +5.09017 q^{34} +(0.381966 - 1.17557i) q^{35} +(6.97214 + 5.06555i) q^{37} +(1.00000 + 3.07768i) q^{38} +(0.809017 + 0.587785i) q^{40} +(-2.61803 + 1.90211i) q^{41} +11.0902 q^{43} +(-0.809017 - 3.21644i) q^{44} +(0.0450850 - 0.138757i) q^{46} +(9.16312 - 6.65740i) q^{47} +(-1.69098 - 5.20431i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-4.54508 + 3.30220i) q^{52} +(0.145898 - 0.449028i) q^{53} +(-1.23607 + 3.07768i) q^{55} -1.23607 q^{56} +(0.309017 - 0.224514i) q^{58} +(2.35410 + 1.71036i) q^{59} +(-2.92705 - 2.12663i) q^{62} +(0.309017 - 0.951057i) q^{64} +5.61803 q^{65} +6.09017 q^{67} +(-1.57295 + 4.84104i) q^{68} +(1.00000 + 0.726543i) q^{70} +(-0.472136 - 1.45309i) q^{71} +(10.8541 + 7.88597i) q^{73} +(-6.97214 + 5.06555i) q^{74} -3.23607 q^{76} +(-1.00000 - 3.97574i) q^{77} +(2.19098 - 6.74315i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-1.00000 - 3.07768i) q^{82} +(-1.23607 - 3.80423i) q^{83} +(4.11803 - 2.99193i) q^{85} +(-3.42705 + 10.5474i) q^{86} +(3.30902 + 0.224514i) q^{88} -12.7639 q^{89} +(-5.61803 + 4.08174i) q^{91} +(0.118034 + 0.0857567i) q^{92} +(3.50000 + 10.7719i) q^{94} +(2.61803 + 1.90211i) q^{95} +(-3.90983 + 12.0332i) q^{97} +5.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8}+O(q^{10}) \) 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8	\( 4 q + q^{2} - q^{4} - q^{5} - 4 q^{7} + q^{8} - 4 q^{10} - q^{11} - 2 q^{13} + 4 q^{14} - q^{16} - 13 q^{17} + 6 q^{19} - q^{20} - 9 q^{22} - 14 q^{23} - q^{25} + 7 q^{26} + 6 q^{28} + q^{29} - 4 q^{32} - 2 q^{34} + 6 q^{35} + 10 q^{37} + 4 q^{38} + q^{40} - 6 q^{41} + 22 q^{43} - q^{44} - 11 q^{46} + 21 q^{47} - 9 q^{49} + q^{50} - 7 q^{52} + 14 q^{53} + 4 q^{55} + 4 q^{56} - q^{58} - 4 q^{59} - 5 q^{62} - q^{64} + 18 q^{65} + 2 q^{67} - 13 q^{68} + 4 q^{70} + 16 q^{71} + 30 q^{73} - 10 q^{74} - 4 q^{76} - 4 q^{77} + 11 q^{79} - q^{80} - 4 q^{82} + 4 q^{83} + 12 q^{85} - 7 q^{86} + 11 q^{88} - 60 q^{89} - 18 q^{91} - 4 q^{92} + 14 q^{94} + 6 q^{95} - 38 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + q^2 - q^4 - q^5 - 4 * q^7 + q^8 - 4 * q^10 - q^11 - 2 * q^13 + 4 * q^14 - q^16 - 13 * q^17 + 6 * q^19 - q^20 - 9 * q^22 - 14 * q^23 - q^25 + 7 * q^26 + 6 * q^28 + q^29 - 4 * q^32 - 2 * q^34 + 6 * q^35 + 10 * q^37 + 4 * q^38 + q^40 - 6 * q^41 + 22 * q^43 - q^44 - 11 * q^46 + 21 * q^47 - 9 * q^49 + q^50 - 7 * q^52 + 14 * q^53 + 4 * q^55 + 4 * q^56 - q^58 - 4 * q^59 - 5 * q^62 - q^64 + 18 * q^65 + 2 * q^67 - 13 * q^68 + 4 * q^70 + 16 * q^71 + 30 * q^73 - 10 * q^74 - 4 * q^76 - 4 * q^77 + 11 * q^79 - q^80 - 4 * q^82 + 4 * q^83 + 12 * q^85 - 7 * q^86 + 11 * q^88 - 60 * q^89 - 18 * q^91 - 4 * q^92 + 14 * q^94 + 6 * q^95 - 38 * q^97 + 4 * q^98

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