LMFDB - Embedded newform 720.2.z.g.667.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(163,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("720.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.z (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			667.8
Root			$0.0376504 - 1.41371i$ of defining polynomial
Character	$\chi$	$=$	720.667
Dual form			720.2.z.g.163.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29924 + 0.558542i) q^{2} +(1.37606 + 1.45136i) q^{4} +(-1.49107 - 1.66635i) q^{5} +(2.40368 + 2.40368i) q^{7} +(0.977191 + 2.65426i) q^{8} +O(q^{10})$	\(q+(1.29924 + 0.558542i) q^{2} +(1.37606 + 1.45136i) q^{4} +(-1.49107 - 1.66635i) q^{5} +(2.40368 + 2.40368i) q^{7} +(0.977191 + 2.65426i) q^{8} +(-1.00653 - 2.99782i) q^{10} +(2.67707 - 2.67707i) q^{11} +2.40164i q^{13} +(1.78040 + 4.46551i) q^{14} +(-0.212908 + 3.99433i) q^{16} +(0.0750544 + 0.0750544i) q^{17} +(2.67236 - 2.67236i) q^{19} +(0.366678 - 4.45708i) q^{20} +(4.97342 - 1.98291i) q^{22} +(-2.12375 + 2.12375i) q^{23} +(-0.553442 + 4.96928i) q^{25} +(-1.34141 + 3.12031i) q^{26} +(-0.180999 + 6.79621i) q^{28} +(3.95795 + 3.95795i) q^{29} -1.65367i q^{31} +(-2.50762 + 5.07068i) q^{32} +(0.0555929 + 0.139435i) q^{34} +(0.421324 - 7.58941i) q^{35} -2.53082i q^{37} +(4.96467 - 1.97942i) q^{38} +(2.96587 - 5.58602i) q^{40} -1.70882i q^{41} +3.84601i q^{43} +(7.56921 + 0.201586i) q^{44} +(-3.94547 + 1.57306i) q^{46} +(-2.15264 + 2.15264i) q^{47} +4.55532i q^{49} +(-3.49460 + 6.14717i) q^{50} +(-3.48565 + 3.30480i) q^{52} +1.29475 q^{53} +(-8.45262 - 0.469246i) q^{55} +(-4.03113 + 8.72883i) q^{56} +(2.93166 + 7.35302i) q^{58} +(-5.29614 - 5.29614i) q^{59} +(10.2413 - 10.2413i) q^{61} +(0.923645 - 2.14852i) q^{62} +(-6.09020 + 5.18744i) q^{64} +(4.00197 - 3.58100i) q^{65} -10.6230i q^{67} +(-0.00565167 + 0.212211i) q^{68} +(4.78640 - 9.62515i) q^{70} -2.27322 q^{71} +(-9.99096 - 9.99096i) q^{73} +(1.41357 - 3.28815i) q^{74} +(7.55589 + 0.201231i) q^{76} +12.8696 q^{77} -8.70617 q^{79} +(6.97341 - 5.60103i) q^{80} +(0.954448 - 2.22017i) q^{82} -11.1310 q^{83} +(0.0131558 - 0.236978i) q^{85} +(-2.14816 + 4.99689i) q^{86} +(9.72165 + 4.48963i) q^{88} -15.6390 q^{89} +(-5.77276 + 5.77276i) q^{91} +(-6.00475 - 0.159920i) q^{92} +(-3.99914 + 1.59446i) q^{94} +(-8.43775 - 0.468420i) q^{95} +(5.00672 + 5.00672i) q^{97} +(-2.54434 + 5.91846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	$ 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) $ 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	1.29924	+	0.558542i	0.918703	+	0.394949i
$2$	1.29924	+	0.558542i	0.918703	+	0.394949i
$3$		0			0
$3$		0			0
$4$	1.37606	+	1.45136i	0.688031	+	0.725681i
$5$	−1.49107	−	1.66635i	−0.666825	−	0.745214i
$5$	−1.49107	−	1.66635i	−0.666825	−	0.745214i
$6$		0			0
$7$	2.40368	+	2.40368i	0.908504	+	0.908504i	0.996152	−	0.0876474i	$-0.0279349\pi$
$7$	2.40368	+	2.40368i	0.908504	+	0.908504i	−0.0876474	+	0.996152i	$0.527935\pi$
$8$	0.977191	+	2.65426i	0.345489	+	0.938423i
$9$		0			0
$10$	−1.00653	−	2.99782i	−0.318293	−	0.947992i
$11$	2.67707	−	2.67707i	0.807167	−	0.807167i	−0.177037	−	0.984204i	$-0.556651\pi$
$11$	2.67707	−	2.67707i	0.807167	−	0.807167i	0.984204	+	0.177037i	$0.0566513\pi$
$12$		0			0
$13$			2.40164i			0.666094i	0.942910	+	0.333047i	$0.108077\pi$
$13$			2.40164i			0.666094i	−0.942910	+	0.333047i	$0.891923\pi$
$14$	1.78040	+	4.46551i	0.475833	+	1.19346i
$15$		0			0
$16$	−0.212908	+	3.99433i	−0.0532269	+	0.998582i
$17$	0.0750544	+	0.0750544i	0.0182034	+	0.0182034i	0.716150	−	0.697947i	$-0.245903\pi$
$17$	0.0750544	+	0.0750544i	0.0182034	+	0.0182034i	−0.697947	+	0.716150i	$0.745903\pi$
$18$		0			0
$19$	2.67236	−	2.67236i	0.613081	−	0.613081i	−0.330666	−	0.943748i	$-0.607274\pi$
$19$	2.67236	−	2.67236i	0.613081	−	0.613081i	0.943748	+	0.330666i	$0.107274\pi$
$20$	0.366678	−	4.45708i	0.0819918	−	0.996633i
$21$		0			0
$22$	4.97342	−	1.98291i	1.06034	−	0.422757i
$23$	−2.12375	+	2.12375i	−0.442833	+	0.442833i	−0.892963	−	0.450130i	$-0.851378\pi$
$23$	−2.12375	+	2.12375i	−0.442833	+	0.442833i	0.450130	+	0.892963i	$0.351378\pi$
$24$		0			0
$25$	−0.553442	+	4.96928i	−0.110688	+	0.993855i
$26$	−1.34141	+	3.12031i	−0.263073	+	0.611943i
$27$		0			0
$28$	−0.180999	+	6.79621i	−0.0342056	+	1.28436i
$29$	3.95795	+	3.95795i	0.734974	+	0.734974i	0.971601	−	0.236627i	$-0.0760419\pi$
$29$	3.95795	+	3.95795i	0.734974	+	0.734974i	−0.236627	+	0.971601i	$0.576042\pi$
$30$		0			0
$31$		−	1.65367i		−	0.297008i	−0.988912	−	0.148504i	$-0.952554\pi$
$31$		−	1.65367i		−	0.297008i	0.988912	−	0.148504i	$-0.0474458\pi$
$32$	−2.50762	+	5.07068i	−0.443289	+	0.896379i
$33$		0			0
$34$	0.0555929	+	0.139435i	0.00953410	+	0.0239129i
$35$	0.421324	−	7.58941i	0.0712168	−	1.28284i
$36$		0			0
$37$		−	2.53082i		−	0.416064i	−0.978122	−	0.208032i	$-0.933294\pi$
$37$		−	2.53082i		−	0.416064i	0.978122	−	0.208032i	$-0.0667059\pi$
$38$	4.96467	−	1.97942i	0.805375	−	0.321104i
$39$		0			0
$40$	2.96587	−	5.58602i	0.468945	−	0.883227i
$41$		−	1.70882i		−	0.266873i	−0.991057	−	0.133436i	$-0.957399\pi$
$41$		−	1.70882i		−	0.266873i	0.991057	−	0.133436i	$-0.0426012\pi$
$42$		0			0
$43$			3.84601i			0.586510i	0.956034	+	0.293255i	$0.0947386\pi$
$43$			3.84601i			0.586510i	−0.956034	+	0.293255i	$0.905261\pi$
$44$	7.56921	+	0.201586i	1.14110	+	0.0303902i
$45$		0			0
$46$	−3.94547	+	1.57306i	−0.581728	+	0.231936i
$47$	−2.15264	+	2.15264i	−0.313995	+	0.313995i	−0.846455	−	0.532460i	$-0.821268\pi$
$47$	−2.15264	+	2.15264i	−0.313995	+	0.313995i	0.532460	+	0.846455i	$0.321268\pi$
$48$		0			0
$49$			4.55532i			0.650760i
$50$	−3.49460	+	6.14717i	−0.494212	+	0.869342i
$51$		0			0
$52$	−3.48565	+	3.30480i	−0.483372	+	0.458293i
$53$	1.29475			0.177848			0.0889239	−	0.996038i	$-0.471657\pi$
$53$	1.29475			0.177848			0.0889239	+	0.996038i	$0.471657\pi$
$54$		0			0
$55$	−8.45262	−	0.469246i	−1.13975	−	0.0632731i
$56$	−4.03113	+	8.72883i	−0.538683	+	1.16644i
$57$		0			0
$58$	2.93166	+	7.35302i	0.384946	+	0.965499i
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	0.272622	−	0.962121i	$-0.412109\pi$
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	−0.962121	+	0.272622i	$0.912109\pi$
$60$		0			0
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.390780	−	0.920484i	$-0.372205\pi$
$61$	10.2413	−	10.2413i	1.31126	−	1.31126i	0.920484	−	0.390780i	$-0.127795\pi$
$62$	0.923645	−	2.14852i	0.117303	−	0.272862i
$63$		0			0
$64$	−6.09020	+	5.18744i	−0.761274	+	0.648430i
$65$	4.00197	−	3.58100i	0.496383	−	0.444168i
$66$		0			0
$67$		−	10.6230i		−	1.29780i	−0.760873	−	0.648901i	$-0.775229\pi$
$67$		−	10.6230i		−	1.29780i	0.760873	−	0.648901i	$-0.224771\pi$
$68$	−0.00565167	+	0.212211i	−0.000685365	+	0.0257343i
$69$		0			0
$70$	4.78640	−	9.62515i	0.572085	−	1.15043i
$71$	−2.27322			−0.269781			−0.134891	−	0.990860i	$-0.543068\pi$
$71$	−2.27322			−0.269781			−0.134891	+	0.990860i	$0.543068\pi$
$72$		0			0
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.982361	−	0.186992i	$-0.940126\pi$
$73$	−9.99096	−	9.99096i	−1.16935	−	1.16935i	−0.186992	−	0.982361i	$-0.559874\pi$
$74$	1.41357	−	3.28815i	0.164324	−	0.382240i
$75$		0			0
$76$	7.55589	+	0.201231i	0.866720	+	0.0230828i
$77$	12.8696			1.46663
$78$		0			0
$79$	−8.70617			−0.979520			−0.489760	−	0.871857i	$-0.662916\pi$
$79$	−8.70617			−0.979520			−0.489760	+	0.871857i	$0.662916\pi$
$80$	6.97341	−	5.60103i	0.779651	−	0.626214i
$81$		0			0
$82$	0.954448	−	2.22017i	0.105401	−	0.245177i
$83$	−11.1310			−1.22178			−0.610890	−	0.791715i	$-0.709188\pi$
$83$	−11.1310			−1.22178			−0.610890	+	0.791715i	$0.709188\pi$
$84$		0			0
$85$	0.0131558	−	0.236978i	0.00142695	−	0.0257039i
$86$	−2.14816	+	4.99689i	−0.231642	+	0.538829i
$87$		0			0
$88$	9.72165	+	4.48963i	1.03633	+	0.478596i
$89$	−15.6390			−1.65773			−0.828866	−	0.559447i	$-0.811014\pi$
$89$	−15.6390			−1.65773			−0.828866	+	0.559447i	$0.811014\pi$
$90$		0			0
$91$	−5.77276	+	5.77276i	−0.605149	+	0.605149i
$92$	−6.00475	−	0.159920i	−0.626038	−	0.0166729i
$93$		0			0
$94$	−3.99914	+	1.59446i	−0.412480	+	0.164456i
$95$	−8.43775	−	0.468420i	−0.865695	−	0.0480589i
$96$		0			0
$97$	5.00672	+	5.00672i	0.508355	+	0.508355i	0.914021	−	0.405666i	$-0.132960\pi$
$97$	5.00672	+	5.00672i	0.508355	+	0.508355i	−0.405666	+	0.914021i	$0.632960\pi$
$98$	−2.54434	+	5.91846i	−0.257017	+	0.597855i
$99$		0			0
$100$	−7.97379	+	6.03478i	−0.797379	+	0.603478i
$101$	−6.37101	−	6.37101i	−0.633939	−	0.633939i	0.315115	−	0.949054i	$-0.397957\pi$
$101$	−6.37101	−	6.37101i	−0.633939	−	0.633939i	−0.949054	+	0.315115i	$0.897957\pi$
$102$		0			0
$103$	−1.93695	+	1.93695i	−0.190854	+	0.190854i	−0.796065	−	0.605211i	$-0.793089\pi$
$103$	−1.93695	+	1.93695i	−0.190854	+	0.190854i	0.605211	+	0.796065i	$0.293089\pi$
$104$	−6.37457	+	2.34686i	−0.625078	+	0.230128i
$105$		0			0
$106$	1.68220	+	0.723173i	0.163389	+	0.0702408i
$107$	−6.97778			−0.674568			−0.337284	−	0.941403i	$-0.609508\pi$
$107$	−6.97778			−0.674568			−0.337284	+	0.941403i	$0.609508\pi$
$108$		0			0
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	0.720283	−	0.693680i	$-0.244012\pi$
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	−0.693680	+	0.720283i	$0.744012\pi$
$110$	−10.7199	−	5.33081i	−1.02210	−	0.508273i
$111$		0			0
$112$	−10.1128	+	9.08931i	−0.955573	+	0.858859i
$113$	8.75577	−	8.75577i	0.823674	−	0.823674i	−0.162959	−	0.986633i	$-0.552104\pi$
$113$	8.75577	−	8.75577i	0.823674	−	0.823674i	0.986633	+	0.162959i	$0.0521038\pi$
$114$		0			0
$115$	6.70557	+	0.372258i	0.625298	+	0.0347133i
$116$	−0.298037	+	11.1908i	−0.0276721	+	1.03904i
$117$		0			0
$118$	−3.92286	−	9.83909i	−0.361128	−	0.905762i
$119$			0.360813i			0.0330757i
$120$		0			0
$121$		−	3.33340i		−	0.303036i
$122$	19.0261	−	7.58574i	1.72254	−	0.686780i
$123$		0			0
$124$	2.40008	−	2.27555i	0.215533	−	0.204351i
$125$	9.10577	−	6.48729i	0.814445	−	0.580241i
$126$		0			0
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	−0.736612	−	0.676316i	$-0.763576\pi$
$127$	−0.679502	+	0.679502i	−0.0602961	+	0.0602961i	0.676316	+	0.736612i	$0.263576\pi$
$128$	−10.8100	+	3.33811i	−0.955482	+	0.295050i
$129$		0			0
$130$	7.19966	−	2.41732i	0.631452	−	0.212013i
$131$	5.43859	+	5.43859i	0.475172	+	0.475172i	0.903584	−	0.428412i	$-0.140927\pi$
$131$	5.43859	+	5.43859i	0.475172	+	0.475172i	−0.428412	+	0.903584i	$0.640927\pi$
$132$		0			0
$133$	12.8470			1.11397
$134$	5.93337	−	13.8018i	0.512565	−	1.19229i
$135$		0			0
$136$	−0.125871	+	0.272557i	−0.0107934	+	0.0233715i
$137$	7.47496	−	7.47496i	0.638629	−	0.638629i	−0.311588	−	0.950217i	$-0.600861\pi$
$137$	7.47496	−	7.47496i	0.638629	−	0.638629i	0.950217	+	0.311588i	$0.100861\pi$
$138$		0			0
$139$	−11.5307	−	11.5307i	−0.978023	−	0.978023i	0.0217404	−	0.999764i	$-0.493079\pi$
$139$	−11.5307	−	11.5307i	−0.978023	−	0.978023i	−0.999764	+	0.0217404i	$0.993079\pi$
$140$	11.5947	−	9.83200i	0.979935	−	0.830955i
$141$		0			0
$142$	−2.95346	−	1.26969i	−0.247849	−	0.106550i
$143$	6.42935	+	6.42935i	0.537649	+	0.537649i
$144$		0			0
$145$	0.693763	−	12.4969i	0.0576139	−	1.03781i
$146$	−7.40031	−	18.5611i	−0.612454	−	1.53612i
$147$		0			0
$148$	3.67314	−	3.48257i	0.301930	−	0.286265i
$149$	−5.51174	+	5.51174i	−0.451539	+	0.451539i	−0.895865	−	0.444326i	$-0.853443\pi$
$149$	−5.51174	+	5.51174i	−0.451539	+	0.451539i	0.444326	+	0.895865i	$0.353443\pi$
$150$		0			0
$151$	−4.13617			−0.336597			−0.168299	−	0.985736i	$-0.553827\pi$
$151$	−4.13617			−0.336597			−0.168299	+	0.985736i	$0.553827\pi$
$152$	9.70454	+	4.48173i	0.787142	+	0.363516i
$153$		0			0
$154$	16.7207	+	7.18822i	1.34740	+	0.579243i
$155$	−2.75559	+	2.46573i	−0.221335	+	0.198052i
$156$		0			0
$157$	20.2700			1.61772			0.808861	−	0.587999i	$-0.200084\pi$
$157$	20.2700			1.61772			0.808861	+	0.587999i	$0.200084\pi$
$158$	−11.3114	−	4.86276i	−0.899889	−	0.386860i
$159$		0			0
$160$	12.1886	−	3.38216i	0.963590	−	0.267383i
$161$	−10.2096			−0.804631
$162$		0			0
$163$	−13.1835			−1.03262			−0.516308	−	0.856403i	$-0.672694\pi$
$163$	−13.1835			−1.03262			−0.516308	+	0.856403i	$0.672694\pi$
$164$	2.48012	−	2.35144i	0.193665	−	0.183617i
$165$		0			0
$166$	−14.4618	−	6.21710i	−1.12245	−	0.482541i
$167$	11.8190	+	11.8190i	0.914585	+	0.914585i	0.996629	−	0.0820441i	$-0.0261448\pi$
$167$	11.8190	+	11.8190i	0.914585	+	0.914585i	−0.0820441	+	0.996629i	$0.526145\pi$
$168$		0			0
$169$	7.23214			0.556319
$170$	0.149455	−	0.300544i	0.0114627	−	0.0230507i
$171$		0			0
$172$	−5.58195	+	5.29234i	−0.425620	+	0.403537i
$173$			15.5763i			1.18424i	0.805849	+	0.592120i	$0.201709\pi$
$173$			15.5763i			1.18424i	−0.805849	+	0.592120i	$0.798291\pi$
$174$		0			0
$175$	−13.2748	+	10.6142i	−1.00348	+	0.802361i
$176$	10.1231	+	11.2631i	0.763060	+	0.848986i
$177$		0			0
$178$	−20.3189	−	8.73505i	−1.52296	−	0.654719i
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.182523	−	0.983202i	$-0.441574\pi$
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.983202	−	0.182523i	$-0.0584265\pi$
$180$		0			0
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	0.809351	−	0.587325i	$-0.199819\pi$
$181$	2.98705	+	2.98705i	0.222026	+	0.222026i	−0.587325	+	0.809351i	$0.699819\pi$
$182$	−10.7245	+	4.27588i	−0.794955	+	0.316950i
$183$		0			0
$184$	−7.71230	−	3.56168i	−0.568559	−	0.262571i
$185$	−4.21723	+	3.77362i	−0.310057	+	0.277442i
$186$		0			0
$187$	0.401852			0.0293863
$188$	−6.08643	−	0.162096i	−0.443899	−	0.0118221i
$189$		0			0
$190$	−10.7010	−	5.32143i	−0.776336	−	0.386057i
$191$		−	6.47168i		−	0.468274i	−0.972204	−	0.234137i	$-0.924774\pi$
$191$		−	6.47168i		−	0.468274i	0.972204	−	0.234137i	$-0.0752264\pi$
$192$		0			0
$193$	−11.1131	+	11.1131i	−0.799936	+	0.799936i	−0.983085	−	0.183149i	$-0.941371\pi$
$193$	−11.1131	+	11.1131i	−0.799936	+	0.799936i	0.183149	+	0.983085i	$0.441371\pi$
$194$	3.70848	+	9.30141i	0.266253	+	0.667802i
$195$		0			0
$196$	−6.61142	+	6.26840i	−0.472244	+	0.447743i
$197$			25.0927i			1.78778i	0.448288	+	0.893889i	$0.352034\pi$
$197$			25.0927i			1.78778i	−0.448288	+	0.893889i	$0.647966\pi$
$198$		0			0
$199$		−	18.7579i		−	1.32972i	−0.746970	−	0.664858i	$-0.768492\pi$
$199$		−	18.7579i		−	1.32972i	0.746970	−	0.664858i	$-0.231508\pi$
$200$	−13.7306	+	3.38695i	−0.970898	+	0.239494i
$201$		0			0
$202$	−4.71901	−	11.8360i	−0.332028	−	0.832775i
$203$			19.0273i			1.33545i
$204$		0			0
$205$	−2.84749	+	2.54796i	−0.198877	+	0.177958i
$206$	−3.59844	+	1.43470i	−0.250715	+	0.0999604i
$207$		0			0
$208$	−9.59293	−	0.511327i	−0.665150	−	0.0354541i
$209$		−	14.3082i		−	0.989718i
$210$		0			0
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	0.891948	−	0.452137i	$-0.149338\pi$
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	−0.452137	+	0.891948i	$0.649338\pi$
$212$	1.78166	+	1.87915i	0.122365	+	0.129061i
$213$		0			0
$214$	−9.06583	−	3.89738i	−0.619727	−	0.266420i
$215$	6.40879	−	5.73465i	0.437076	−	0.391100i
$216$		0			0
$217$	3.97489	−	3.97489i	0.269833	−	0.269833i
$218$	0.205728	+	0.515996i	0.0139337	+	0.0349476i
$219$		0			0
$220$	−10.9503	−	12.9135i	−0.738268	−	0.870630i
$221$	−0.180253	+	0.180253i	−0.0121252	+	0.0121252i
$222$		0			0
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	0.548409	−	0.836210i	$-0.315234\pi$
$223$	−4.29779	−	4.29779i	−0.287801	−	0.287801i	−0.836210	+	0.548409i	$0.815234\pi$
$224$	−18.2158	+	6.16078i	−1.21709	+	0.411634i
$225$		0			0
$226$	16.2663	−	6.48541i	1.08202	−	0.431403i
$227$		−	29.1029i		−	1.93163i	−0.259241	−	0.965813i	$-0.583472\pi$
$227$		−	29.1029i		−	1.93163i	0.259241	−	0.965813i	$-0.416528\pi$
$228$		0			0
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.241600	+	0.970376i	$0.577672\pi$
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.970376	+	0.241600i	$0.922328\pi$
$230$	8.50424	+	4.22900i	0.560753	+	0.278852i
$231$		0			0
$232$	−6.63776	+	14.3731i	−0.435790	+	0.943641i
$233$	−1.46663	−	1.46663i	−0.0960824	−	0.0960824i	0.657432	−	0.753514i	$-0.271643\pi$
$233$	−1.46663	−	1.46663i	−0.0960824	−	0.0960824i	−0.753514	+	0.657432i	$0.771643\pi$
$234$		0			0
$235$	6.79678	+	0.377322i	0.443373	+	0.0246138i
$236$	0.398804	−	14.9744i	0.0259600	−	0.974754i
$237$		0			0
$238$	−0.201529	+	0.468784i	−0.0130632	+	0.0303867i
$239$	−12.5432			−0.811352			−0.405676	−	0.914017i	$-0.632964\pi$
$239$	−12.5432			−0.811352			−0.405676	+	0.914017i	$0.632964\pi$
$240$		0			0
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$	1.86184	−	4.33089i	0.119684	−	0.278400i
$243$		0			0
$244$	28.9565	+	0.771179i	1.85375	+	0.0493697i
$245$	7.59075	−	6.79228i	0.484955	−	0.433943i
$246$		0			0
$247$	6.41803	+	6.41803i	0.408370	+	0.408370i
$248$	4.38927	−	1.61595i	0.278719	−	0.102613i
$249$		0			0
$250$	15.4540	−	3.34261i	0.977399	−	0.211405i
$251$	5.38459	−	5.38459i	0.339872	−	0.339872i	−0.516447	−	0.856319i	$-0.672746\pi$
$251$	5.38459	−	5.38459i	0.339872	−	0.339872i	0.856319	+	0.516447i	$0.172746\pi$
$252$		0			0
$253$			11.3709i			0.714880i
$254$	−1.26237	+	0.503308i	−0.0792081	+	0.0315803i
$255$		0			0
$256$	−15.9093	−	1.70085i	−0.994334	−	0.106303i
$257$	3.88657	+	3.88657i	0.242437	+	0.242437i	0.817858	−	0.575420i	$-0.195162\pi$
$257$	3.88657	+	3.88657i	0.242437	+	0.242437i	−0.575420	+	0.817858i	$0.695162\pi$
$258$		0			0
$259$	6.08327	−	6.08327i	0.377996	−	0.377996i
$260$	10.7043	+	0.880628i	0.663851	+	0.0546142i
$261$		0			0
$262$	4.02836	+	10.1037i	0.248873	+	0.624210i
$263$	−16.9658	+	16.9658i	−1.04615	+	1.04615i	−0.0472716	+	0.998882i	$0.515053\pi$
$263$	−16.9658	+	16.9658i	−1.04615	+	1.04615i	−0.998882	+	0.0472716i	$0.984947\pi$
$264$		0			0
$265$	−1.93056	−	2.15751i	−0.118593	−	0.132535i
$266$	16.6913	+	7.17557i	1.02341	+	0.439963i
$267$		0			0
$268$	15.4178	−	14.6179i	0.941791	−	0.892928i
$269$	−2.55482	−	2.55482i	−0.155770	−	0.155770i	0.624919	−	0.780689i	$-0.285132\pi$
$269$	−2.55482	−	2.55482i	−0.155770	−	0.155770i	−0.780689	+	0.624919i	$0.785132\pi$
$270$		0			0
$271$		−	3.33684i		−	0.202698i	−0.994851	−	0.101349i	$-0.967684\pi$
$271$		−	3.33684i		−	0.202698i	0.994851	−	0.101349i	$-0.0323159\pi$
$272$	−0.315772	+	0.283813i	−0.0191465	+	0.0172087i
$273$		0			0
$274$	13.8869	−	5.53671i	0.838937	−	0.334485i
$275$	11.8215	+	14.7847i	0.712863	+	0.891551i
$276$		0			0
$277$			4.60736i			0.276830i	0.990374	+	0.138415i	$0.0442007\pi$
$277$			4.60736i			0.276830i	−0.990374	+	0.138415i	$0.955799\pi$
$278$	−8.54081	−	21.4216i	−0.512244	−	1.28478i
$279$		0			0
$280$	20.5560	−	6.29799i	1.22845	−	0.376377i
$281$			22.1178i			1.31944i	0.751513	+	0.659718i	$0.229324\pi$
$281$			22.1178i			1.31944i	−0.751513	+	0.659718i	$0.770676\pi$
$282$		0			0
$283$			10.8629i			0.645734i	0.946444	+	0.322867i	$0.104647\pi$
$283$			10.8629i			0.645734i	−0.946444	+	0.322867i	$0.895353\pi$
$284$	−3.12809	−	3.29926i	−0.185618	−	0.195775i
$285$		0			0
$286$	4.76222	+	11.9443i	0.281596	+	0.706284i
$287$	4.10745	−	4.10745i	0.242455	−	0.242455i
$288$		0			0
$289$		−	16.9887i		−	0.999337i
$290$	7.88141	−	15.8490i	0.462813	−	0.930686i
$291$		0			0
$292$	0.752328	−	28.2487i	0.0440267	−	1.65313i
$293$	18.4067			1.07533			0.537665	−	0.843159i	$-0.319307\pi$
$293$	18.4067			1.07533			0.537665	+	0.843159i	$0.319307\pi$
$294$		0			0
$295$	−0.928326	+	16.7221i	−0.0540492	+	0.973600i
$296$	6.71746	−	2.47309i	0.390444	−	0.143746i
$297$		0			0
$298$	−10.2396	+	4.08255i	−0.593166	+	0.236496i
$299$	−5.10048	−	5.10048i	−0.294968	−	0.294968i
$300$		0			0
$301$	−9.24455	+	9.24455i	−0.532847	+	0.532847i
$302$	−5.37389	−	2.31023i	−0.309233	−	0.132939i
$303$		0			0
$304$	10.1053	+	11.2432i	0.579580	+	0.644845i
$305$	−32.3360	−	1.79513i	−1.85156	−	0.102789i
$306$		0			0
$307$		−	6.60872i		−	0.377180i	−0.982056	−	0.188590i	$-0.939608\pi$
$307$		−	6.60872i		−	0.377180i	0.982056	−	0.188590i	$-0.0603917\pi$
$308$	17.7094	+	18.6785i	1.00909	+	1.06431i
$309$		0			0
$310$	−4.95740	+	1.66447i	−0.281561	+	0.0945356i
$311$	0.606102			0.0343689			0.0171845	−	0.999852i	$-0.494530\pi$
$311$	0.606102			0.0343689			0.0171845	+	0.999852i	$0.494530\pi$
$312$		0			0
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.994997	+	0.0999032i	$0.0318533\pi$
$313$	19.3708	+	19.3708i	1.09490	+	1.09490i	0.0999032	+	0.994997i	$0.468147\pi$
$314$	26.3357	+	11.3216i	1.48621	+	0.638918i
$315$		0			0
$316$	−11.9802	−	12.6358i	−0.673940	−	0.710820i
$317$	7.04328			0.395590			0.197795	−	0.980243i	$-0.436622\pi$
$317$	7.04328			0.395590			0.197795	+	0.980243i	$0.436622\pi$
$318$		0			0
$319$	21.1914			1.18649
$320$	17.7250	+	2.41358i	0.990856	+	0.134923i
$321$		0			0
$322$	−13.2648	−	5.70250i	−0.739217	−	0.317788i
$323$	0.401145			0.0223203
$324$		0			0
$325$	−11.9344	−	1.32917i	−0.662001	−	0.0737290i
$326$	−17.1286	−	7.36356i	−0.948667	−	0.407830i
$327$		0			0
$328$	4.53565	−	1.66984i	0.250440	−	0.0922017i
$329$	−10.3485			−0.570532
$330$		0			0
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	−0.970031	−	0.242983i	$-0.921874\pi$
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	0.242983	+	0.970031i	$0.421874\pi$
$332$	−15.3169	−	16.1550i	−0.840623	−	0.886624i
$333$		0			0
$334$	8.75437	+	21.9572i	0.479018	+	1.20145i
$335$	−17.7016	+	15.8395i	−0.967140	+	0.865407i
$336$		0			0
$337$	7.73287	+	7.73287i	0.421236	+	0.421236i	0.885629	−	0.464393i	$-0.153727\pi$
$337$	7.73287	+	7.73287i	0.421236	+	0.421236i	−0.464393	+	0.885629i	$0.653727\pi$
$338$	9.39631	+	4.03945i	0.511092	+	0.219717i
$339$		0			0
$340$	0.362044	−	0.307003i	0.0196346	−	0.0166496i
$341$	−4.42699	−	4.42699i	−0.239735	−	0.239735i
$342$		0			0
$343$	5.87623	−	5.87623i	0.317286	−	0.317286i
$344$	−10.2083	+	3.75828i	−0.550395	+	0.202633i
$345$		0			0
$346$	−8.69999	+	20.2373i	−0.467714	+	1.08797i
$347$	11.3945			0.611691			0.305845	−	0.952081i	$-0.401061\pi$
$347$	11.3945			0.611691			0.305845	+	0.952081i	$0.401061\pi$
$348$		0			0
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	0.306730	−	0.951796i	$-0.400765\pi$
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	−0.951796	+	0.306730i	$0.900765\pi$
$350$	−23.1757	+	6.37591i	−1.23879	+	0.340807i
$351$		0			0
$352$	6.86150	+	20.2876i	0.365719	+	1.08134i
$353$	6.47876	−	6.47876i	0.344830	−	0.344830i	−0.513350	−	0.858179i	$-0.671596\pi$
$353$	6.47876	−	6.47876i	0.344830	−	0.344830i	0.858179	+	0.513350i	$0.171596\pi$
$354$		0			0
$355$	3.38952	+	3.78798i	0.179897	+	0.201045i
$356$	−21.5203	−	22.6979i	−1.14057	−	1.20299i
$357$		0			0
$358$	28.9746	−	11.5522i	1.53136	−	0.610553i
$359$			3.25098i			0.171580i	0.996313	+	0.0857902i	$0.0273415\pi$
$359$			3.25098i			0.171580i	−0.996313	+	0.0857902i	$0.972659\pi$
$360$		0			0
$361$			4.71699i			0.248263i
$362$	2.21251	+	5.54929i	0.116287	+	0.291664i
$363$		0			0
$364$	−16.3220	−	0.434694i	−0.855507	−	0.0227841i
$365$	−1.75125	+	31.5456i	−0.0916646	+	1.65117i
$366$		0			0
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	−0.956117	−	0.292985i	$-0.905351\pi$
$367$	−12.7038	+	12.7038i	−0.663132	+	0.663132i	0.292985	+	0.956117i	$0.405351\pi$
$368$	−8.03080	−	8.93513i	−0.418635	−	0.465776i
$369$		0			0
$370$	−7.58693	+	2.54735i	−0.394426	+	0.132430i
$371$	3.11216	+	3.11216i	0.161575	+	0.161575i
$372$		0			0
$373$	21.9761			1.13788			0.568939	−	0.822379i	$-0.307354\pi$
$373$	21.9761			1.13788			0.568939	+	0.822379i	$0.307354\pi$
$374$	0.522103	+	0.224451i	0.0269973	+	0.0116061i
$375$		0			0
$376$	−7.81721	−	3.61013i	−0.403142	−	0.186178i
$377$	−9.50557	+	9.50557i	−0.489562	+	0.489562i
$378$		0			0
$379$	−17.0642	−	17.0642i	−0.876527	−	0.876527i	0.116646	−	0.993174i	$-0.462786\pi$
$379$	−17.0642	−	17.0642i	−0.876527	−	0.876527i	−0.993174	+	0.116646i	$0.962786\pi$
$380$	−10.9310	−	12.8908i	−0.560749	−	0.661285i
$381$		0			0
$382$	3.61470	−	8.40828i	0.184944	−	0.430205i
$383$	0.228058	+	0.228058i	0.0116532	+	0.0116532i	0.712909	−	0.701256i	$-0.247377\pi$
$383$	0.228058	+	0.228058i	0.0116532	+	0.0116532i	−0.701256	+	0.712909i	$0.747377\pi$
$384$		0			0
$385$	−19.1894	−	21.4453i	−0.977985	−	1.09295i
$386$	−20.6457	+	8.23145i	−1.05084	+	0.418970i
$387$		0			0
$388$	−0.377011	+	14.1561i	−0.0191398	+	0.718668i
$389$	14.3036	−	14.3036i	0.725221	−	0.725221i	−0.244443	−	0.969664i	$-0.578605\pi$
$389$	14.3036	−	14.3036i	0.725221	−	0.725221i	0.969664	+	0.244443i	$0.0786050\pi$
$390$		0			0
$391$	−0.318794			−0.0161221
$392$	−12.0910	+	4.45141i	−0.610688	+	0.224830i
$393$		0			0
$394$	−14.0153	+	32.6015i	−0.706081	+	1.64244i
$395$	12.9815	+	14.5075i	0.653169	+	0.729953i
$396$		0			0
$397$	5.11618			0.256774			0.128387	−	0.991724i	$-0.459020\pi$
$397$	5.11618			0.256774			0.128387	+	0.991724i	$0.459020\pi$
$398$	10.4771	−	24.3711i	0.525170	−	1.22161i
$399$		0			0
$400$	−19.7311	−	3.26863i	−0.986555	−	0.163431i
$401$	16.2837			0.813170			0.406585	−	0.913613i	$-0.366719\pi$
$401$	16.2837			0.813170			0.406585	+	0.913613i	$0.366719\pi$
$402$		0			0
$403$	3.97152			0.197835
$404$	0.479742	−	18.0135i	0.0238681	−	0.896207i
$405$		0			0
$406$	−10.6275	+	24.7210i	−0.527436	+	1.22688i
$407$	−6.77518	−	6.77518i	−0.335833	−	0.335833i
$408$		0			0
$409$	−17.4256			−0.861640			−0.430820	−	0.902438i	$-0.641776\pi$
$409$	−17.4256			−0.861640			−0.430820	+	0.902438i	$0.641776\pi$
$410$	−5.12273	+	1.71998i	−0.252993	+	0.0849438i
$411$		0			0
$412$	−5.47659	−	0.145854i	−0.269812	−	0.00718573i
$413$		−	25.4604i		−	1.25283i
$414$		0			0
$415$	16.5970	+	18.5481i	0.814714	+	0.910488i
$416$	−12.1779	−	6.02239i	−0.597073	−	0.295272i
$417$		0			0
$418$	7.99172	−	18.5898i	0.390888	−	0.909257i
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	−0.360083	−	0.932920i	$-0.617252\pi$
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	0.932920	+	0.360083i	$0.117252\pi$
$420$		0			0
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.987082	−	0.160216i	$-0.948781\pi$
$421$	−23.5406	−	23.5406i	−1.14730	−	1.14730i	−0.160216	−	0.987082i	$-0.551219\pi$
$422$	4.73206	+	11.8687i	0.230353	+	0.577759i
$423$		0			0
$424$	1.26522	+	3.43661i	0.0614445	+	0.166896i
$425$	−0.414505	+	0.331428i	−0.0201064	+	0.0160766i
$426$		0			0
$427$	49.2335			2.38258
$428$	−9.60186	−	10.1273i	−0.464123	−	0.489521i
$429$		0			0
$430$	11.5296	−	3.87112i	0.556008	−	0.186682i
$431$			35.0243i			1.68706i	0.537079	+	0.843532i	$0.319528\pi$
$431$			35.0243i			1.68706i	−0.537079	+	0.843532i	$0.680472\pi$
$432$		0			0
$433$	10.1094	−	10.1094i	0.485828	−	0.485828i	−0.421159	−	0.906987i	$-0.638376\pi$
$433$	10.1094	−	10.1094i	0.485828	−	0.485828i	0.906987	+	0.421159i	$0.138376\pi$
$434$	7.38449	−	2.94420i	0.354467	−	0.141326i
$435$		0			0
$436$	−0.0209147	+	0.785311i	−0.00100163	+	0.0376096i
$437$			11.3509i			0.542985i
$438$		0			0
$439$			22.6071i			1.07898i	0.841993	+	0.539488i	$0.181382\pi$
$439$			22.6071i			1.07898i	−0.841993	+	0.539488i	$0.818618\pi$
$440$	−7.01433	−	22.8940i	−0.334395	−	1.09143i
$441$		0			0
$442$	−0.334872	+	0.133514i	−0.0159282	+	0.00635061i
$443$		−	10.9178i		−	0.518721i	−0.965781	−	0.259360i	$-0.916488\pi$
$443$		−	10.9178i		−	0.518721i	0.965781	−	0.259360i	$-0.0835118\pi$
$444$		0			0
$445$	23.3188	+	26.0601i	1.10542	+	1.23537i
$446$	−3.18337	−	7.98436i	−0.150737	−	0.378071i
$447$		0			0
$448$	−27.1078	−	2.16993i	−1.28072	−	0.102520i
$449$			28.8112i			1.35969i	0.733358	+	0.679843i	$0.237952\pi$
$449$			28.8112i			1.35969i	−0.733358	+	0.679843i	$0.762048\pi$
$450$		0			0
$451$	−4.57463	−	4.57463i	−0.215411	−	0.215411i
$452$	24.7563	+	0.659318i	1.16444	+	0.0310117i
$453$		0			0
$454$	16.2552	−	37.8117i	0.762893	−	1.77459i
$455$	18.2270	+	1.01187i	0.854495	+	0.0474371i
$456$		0			0
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	−0.995126	−	0.0986128i	$-0.968559\pi$
$457$	−19.1653	+	19.1653i	−0.896513	+	0.896513i	0.0986128	+	0.995126i	$0.468559\pi$
$458$	−34.0727	+	13.5848i	−1.59211	+	0.634778i
$459$		0			0
$460$	8.68700	+	10.2445i	0.405033	+	0.477651i
$461$	−4.43227	+	4.43227i	−0.206431	+	0.206431i	−0.802749	−	0.596317i	$-0.796630\pi$
$461$	−4.43227	+	4.43227i	−0.206431	+	0.206431i	0.596317	+	0.802749i	$0.296630\pi$
$462$		0			0
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	0.998103	−	0.0615691i	$-0.0196105\pi$
$463$	20.1518	+	20.1518i	0.936534	+	0.936534i	−0.0615691	+	0.998103i	$0.519610\pi$
$464$	−16.6521	+	14.9667i	−0.773052	+	0.694811i
$465$		0			0
$466$	−1.08634	−	2.72469i	−0.0503236	−	0.126219i
$467$			3.89858i			0.180405i	0.995923	+	0.0902025i	$0.0287514\pi$
$467$			3.89858i			0.180405i	−0.995923	+	0.0902025i	$0.971249\pi$
$468$		0			0
$469$	25.5342	−	25.5342i	1.17906	−	1.17906i
$470$	8.61992	+	4.28652i	0.397607	+	0.197723i
$471$		0			0
$472$	8.88200	−	19.2327i	0.408827	−	0.885256i
$473$	10.2960	+	10.2960i	0.473412	+	0.473412i
$474$		0			0
$475$	11.8007	+	14.7587i	0.541453	+	0.677175i
$476$	−0.523671	+	0.496501i	−0.0240024	+	0.0227571i
$477$		0			0
$478$	−16.2967	−	7.00590i	−0.745392	−	0.320443i
$479$	−9.85299			−0.450194			−0.225097	−	0.974336i	$-0.572270\pi$
$479$	−9.85299			−0.450194			−0.225097	+	0.974336i	$0.572270\pi$
$480$		0			0
$481$	6.07811			0.277138
$482$	19.3418	+	8.31500i	0.880994	+	0.378738i
$483$		0			0
$484$	4.83797	−	4.58696i	0.219908	−	0.208498i
$485$	0.877595	−	15.8083i	0.0398495	−	0.717818i
$486$		0			0
$487$	−13.9164	−	13.9164i	−0.630611	−	0.630611i	0.317610	−	0.948221i	$-0.397120\pi$
$487$	−13.9164	−	13.9164i	−0.630611	−	0.630611i	−0.948221	+	0.317610i	$0.897120\pi$
$488$	37.1908	+	17.1754i	1.68355	+	0.777492i
$489$		0			0
$490$	13.6560	−	4.58507i	0.616915	−	0.207132i
$491$	−2.39213	+	2.39213i	−0.107955	+	0.107955i	−0.759021	−	0.651066i	$-0.774322\pi$
$491$	−2.39213	+	2.39213i	−0.107955	+	0.107955i	0.651066	+	0.759021i	$0.274322\pi$
$492$		0			0
$493$			0.594124i			0.0267580i
$494$	4.75384	+	11.9233i	0.213885	+	0.536456i
$495$		0			0
$496$	6.60531	+	0.352079i	0.296587	+	0.0158088i
$497$	−5.46408	−	5.46408i	−0.245098	−	0.245098i
$498$		0			0
$499$	−9.87034	+	9.87034i	−0.441857	+	0.441857i	−0.892636	−	0.450779i	$-0.851146\pi$
$499$	−9.87034	+	9.87034i	−0.441857	+	0.441857i	0.450779	+	0.892636i	$0.351146\pi$
$500$	21.9455	+	4.28886i	0.981433	+	0.191804i
$501$		0			0
$502$	10.0034	−	3.98837i	0.446474	−	0.178010i
$503$	−9.29035	+	9.29035i	−0.414236	+	0.414236i	−0.883211	−	0.468975i	$-0.844623\pi$
$503$	−9.29035	+	9.29035i	−0.414236	+	0.414236i	0.468975	+	0.883211i	$0.344623\pi$
$504$		0			0
$505$	−1.11673	+	20.1159i	−0.0496939	+	0.895146i
$506$	−6.35110	+	14.7735i	−0.282341	+	0.656763i
$507$		0			0
$508$	−1.92124	−	0.0511671i	−0.0852413	−	0.00227017i
$509$	6.53818	+	6.53818i	0.289800	+	0.289800i	0.837001	−	0.547201i	$-0.184307\pi$
$509$	6.53818	+	6.53818i	0.289800	+	0.289800i	−0.547201	+	0.837001i	$0.684307\pi$
$510$		0			0
$511$		−	48.0301i		−	2.12473i
$512$	−19.7201	−	11.0958i	−0.871513	−	0.490372i
$513$		0			0
$514$	2.87878	+	7.22040i	0.126978	+	0.318478i
$515$	6.11577	+	0.339516i	0.269493	+	0.0149608i
$516$		0			0
$517$			11.5255i			0.506893i
$518$	11.3014	−	4.50588i	0.496555	−	0.197977i
$519$		0			0
$520$	13.4156	+	7.12294i	0.588312	+	0.312362i
$521$		−	14.2961i		−	0.626324i	−0.949700	−	0.313162i	$-0.898612\pi$
$521$		−	14.2961i		−	0.626324i	0.949700	−	0.313162i	$-0.101388\pi$
$522$		0			0
$523$		−	16.0319i		−	0.701027i	−0.936558	−	0.350513i	$-0.886007\pi$
$523$		−	16.0319i		−	0.701027i	0.936558	−	0.350513i	$-0.113993\pi$
$524$	−0.409530	+	15.3772i	−0.0178904	+	0.671756i
$525$		0			0
$526$	−31.5187	+	12.5665i	−1.37428	+	0.547928i
$527$	0.124115	−	0.124115i	0.00540655	−	0.00540655i
$528$		0			0
$529$			13.9794i			0.607798i
$530$	−1.30321	−	3.88143i	−0.0566077	−	0.168598i
$531$		0			0
$532$	17.6782	+	18.6456i	0.766448	+	0.808390i
$533$	4.10397			0.177762
$534$		0			0
$535$	10.4043	+	11.6274i	0.449819	+	0.502697i
$536$	28.1961	−	10.3807i	1.21789	−	0.448376i
$537$		0			0
$538$	−1.89236	−	4.74631i	−0.0815854	−	0.204628i
$539$	12.1949	+	12.1949i	0.525271	+	0.525271i
$540$		0			0
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	−0.945220	−	0.326435i	$-0.894153\pi$
$541$	−14.3926	+	14.3926i	−0.618785	+	0.618785i	0.326435	+	0.945220i	$0.394153\pi$
$542$	1.86376	−	4.33536i	0.0800555	−	0.186220i
$543$		0			0
$544$	−0.568785	+	0.192369i	−0.0243865	+	0.00824777i
$545$	0.0486846	−	0.876965i	0.00208542	−	0.0375651i
$546$		0			0
$547$		−	11.6741i		−	0.499148i	−0.968356	−	0.249574i	$-0.919709\pi$
$547$		−	11.6741i		−	0.499148i	0.968356	−	0.249574i	$-0.0802905\pi$
$548$	21.1349	+	0.562871i	0.902838	+	0.0240447i
$549$		0			0
$550$	7.10111	+	25.8117i	0.302792	+	1.10061i
$551$	21.1541			0.901197
$552$		0			0
$553$	−20.9268	−	20.9268i	−0.889898	−	0.889898i
$554$	−2.57340	+	5.98608i	−0.109333	+	0.254324i
$555$		0			0
$556$	0.868274	−	32.6023i	0.0368230	−	1.38264i
$557$	39.6712			1.68092			0.840460	−	0.541873i	$-0.182285\pi$
$557$	39.6712			1.68092			0.840460	+	0.541873i	$0.182285\pi$
$558$		0			0
$559$	−9.23671			−0.390671
$560$	30.2249	+	3.29875i	1.27723	+	0.139398i
$561$		0			0
$562$	−12.3537	+	28.7364i	−0.521110	+	1.21217i
$563$	12.4534			0.524850			0.262425	−	0.964952i	$-0.415478\pi$
$563$	12.4534			0.524850			0.262425	+	0.964952i	$0.415478\pi$
$564$		0			0
$565$	−27.6456	−	1.53474i	−1.16306	−	0.0645671i
$566$	−6.06740	+	14.1136i	−0.255032	+	0.593238i
$567$		0			0
$568$	−2.22137	−	6.03371i	−0.0932066	−	0.253169i
$569$	5.62622			0.235863			0.117932	−	0.993022i	$-0.462374\pi$
$569$	5.62622			0.235863			0.117932	+	0.993022i	$0.462374\pi$
$570$		0			0
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	−0.0294797	−	0.999565i	$-0.509385\pi$
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	0.999565	+	0.0294797i	$0.00938505\pi$
$572$	−0.484136	+	18.1785i	−0.0202427	+	0.760081i
$573$		0			0
$574$	7.63076	−	3.04239i	0.318502	−	0.126987i
$575$	−9.37814	−	11.7289i	−0.391095	−	0.489128i
$576$		0			0
$577$	−25.6307	−	25.6307i	−1.06702	−	1.06702i	−0.997587	−	0.0694322i	$-0.977881\pi$
$577$	−25.6307	−	25.6307i	−1.06702	−	1.06702i	−0.0694322	−	0.997587i	$-0.522119\pi$
$578$	9.48892	−	22.0725i	0.394687	−	0.918094i
$579$		0			0
$580$	19.0922	−	16.1896i	0.792761	−	0.672237i
$581$	−26.7552	−	26.7552i	−1.10999	−	1.10999i
$582$		0			0
$583$	3.46614	−	3.46614i	0.143553	−	0.143553i
$584$	16.7555	−	36.2817i	0.693349	−	1.50135i
$585$		0			0
$586$	23.9147	+	10.2809i	0.987908	+	0.424700i
$587$	−25.5579			−1.05489			−0.527444	−	0.849590i	$-0.676849\pi$
$587$	−25.5579			−1.05489			−0.527444	+	0.849590i	$0.676849\pi$
$588$		0			0
$589$	−4.41920	−	4.41920i	−0.182090	−	0.182090i
$590$	−10.5461	+	21.2076i	−0.434177	+	0.873103i
$591$		0			0
$592$	10.1089	+	0.538831i	0.415474	+	0.0221458i
$593$	−2.96607	+	2.96607i	−0.121802	+	0.121802i	−0.765380	−	0.643578i	$-0.777449\pi$
$593$	−2.96607	+	2.96607i	−0.121802	+	0.121802i	0.643578	+	0.765380i	$0.277449\pi$
$594$		0			0
$595$	0.601241	−	0.537996i	0.0246485	−	0.0220557i
$596$	−15.5840	−	0.415039i	−0.638347	−	0.0170007i
$597$		0			0
$598$	−3.77793	−	9.47559i	−0.154491	−	0.387486i
$599$		−	5.14724i		−	0.210311i	−0.994456	−	0.105155i	$-0.966466\pi$
$599$		−	5.14724i		−	0.210311i	0.994456	−	0.105155i	$-0.0335340\pi$
$600$		0			0
$601$		−	33.5619i		−	1.36902i	−0.729005	−	0.684509i	$-0.760017\pi$
$601$		−	33.5619i		−	1.36902i	0.729005	−	0.684509i	$-0.239983\pi$
$602$	−17.1744	+	6.84745i	−0.699976	+	0.279081i
$603$		0			0
$604$	−5.69163	−	6.00309i	−0.231589	−	0.244262i
$605$	−5.55461	+	4.97032i	−0.225827	+	0.202072i
$606$		0			0
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	−0.770821	−	0.637052i	$-0.780154\pi$
$607$	−3.29572	+	3.29572i	−0.133769	+	0.133769i	0.637052	+	0.770821i	$0.280154\pi$
$608$	6.84943	+	20.2519i	0.277781	+	0.821325i
$609$		0			0
$610$	−41.0097	−	20.3933i	−1.66043	−	0.825702i
$611$	−5.16986	−	5.16986i	−0.209150	−	0.209150i
$612$		0			0
$613$	0.261903			0.0105781			0.00528907	−	0.999986i	$-0.498316\pi$
$613$	0.261903			0.0105781			0.00528907	+	0.999986i	$0.498316\pi$
$614$	3.69125	−	8.58633i	0.148967	−	0.346516i
$615$		0			0
$616$	12.5761	+	34.1593i	0.506704	+	1.37632i
$617$	−12.1529	+	12.1529i	−0.489259	+	0.489259i	−0.908072	−	0.418813i	$-0.862446\pi$
$617$	−12.1529	+	12.1529i	−0.489259	+	0.489259i	0.418813	+	0.908072i	$0.362446\pi$
$618$		0			0
$619$	−12.1134	−	12.1134i	−0.486877	−	0.486877i	0.420442	−	0.907319i	$-0.361875\pi$
$619$	−12.1134	−	12.1134i	−0.486877	−	0.486877i	−0.907319	+	0.420442i	$0.861875\pi$
$620$	−7.37054	−	0.606366i	−0.296008	−	0.0243522i
$621$		0			0
$622$	0.787474	+	0.338534i	0.0315748	+	0.0135740i
$623$	−37.5911	−	37.5911i	−1.50606	−	1.50606i
$624$		0			0
$625$	−24.3874	−	5.50042i	−0.975496	−	0.220017i
$626$	14.3479	+	35.9867i	0.573459	+	1.43832i
$627$		0			0
$628$	27.8928	+	29.4191i	1.11304	+	1.17395i
$629$	0.189949	−	0.189949i	0.00757377	−	0.00757377i
$630$		0			0
$631$	49.8568			1.98477			0.992384	−	0.123179i	$-0.0393090\pi$
$631$	49.8568			1.98477			0.992384	+	0.123179i	$0.0393090\pi$
$632$	−8.50759	−	23.1084i	−0.338414	−	0.919204i
$633$		0			0
$634$	9.15093	+	3.93397i	0.363430	+	0.156238i
$635$	2.14547	+	0.119105i	0.0851404	+	0.00472656i
$636$		0			0
$637$	−10.9402			−0.433467
$638$	27.5328	+	11.8363i	1.09003	+	0.468604i
$639$		0			0
$640$	21.6810	+	13.0360i	0.857015	+	0.515292i
$641$	4.10036			0.161954			0.0809772	−	0.996716i	$-0.474196\pi$
$641$	4.10036			0.161954			0.0809772	+	0.996716i	$0.474196\pi$
$642$		0			0
$643$	−18.7451			−0.739233			−0.369617	−	0.929184i	$-0.620511\pi$
$643$	−18.7451			−0.739233			−0.369617	+	0.929184i	$0.620511\pi$
$644$	−14.0491	−	14.8179i	−0.553611	−	0.583906i
$645$		0			0
$646$	0.521184	+	0.224056i	0.0205057	+	0.00881537i
$647$	−5.46529	−	5.46529i	−0.214863	−	0.214863i	0.591467	−	0.806330i	$-0.298549\pi$
$647$	−5.46529	−	5.46529i	−0.214863	−	0.214863i	−0.806330	+	0.591467i	$0.798549\pi$
$648$		0			0
$649$	−28.3563			−1.11308
$650$	−14.7633	−	8.39277i	−0.579063	−	0.329192i
$651$		0			0
$652$	−18.1414	−	19.1341i	−0.710471	−	0.749350i
$653$		−	33.9219i		−	1.32747i	−0.747970	−	0.663733i	$-0.768971\pi$
$653$		−	33.9219i		−	1.32747i	0.747970	−	0.663733i	$-0.231029\pi$
$654$		0			0
$655$	0.953294	−	17.1719i	0.0372483	−	0.670961i
$656$	6.82559	+	0.363821i	0.266495	+	0.0142048i
$657$		0			0
$658$	−13.4452	−	5.78007i	−0.524149	−	0.225331i
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.0326746	+	0.999466i	$0.510402\pi$
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.999466	+	0.0326746i	$0.989598\pi$
$660$		0			0
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	0.883851	−	0.467769i	$-0.154942\pi$
$661$	10.6974	+	10.6974i	0.416081	+	0.416081i	−0.467769	+	0.883851i	$0.654942\pi$
$662$	−24.5738	+	9.79759i	−0.955087	+	0.380794i
$663$		0			0
$664$	−10.8771	−	29.5444i	−0.422112	−	1.14655i
$665$	−19.1557	−	21.4075i	−0.742826	−	0.830149i
$666$		0			0
$667$	−16.8114			−0.650941
$668$	−0.889984	+	33.4174i	−0.0344345	+	1.29296i
$669$		0			0
$670$	−31.8457	+	10.6923i	−1.23031	+	0.413081i
$671$		−	54.8333i		−	2.11682i
$672$		0			0
$673$	−6.70854	+	6.70854i	−0.258595	+	0.258595i	−0.824483	−	0.565887i	$-0.808534\pi$
$673$	−6.70854	+	6.70854i	−0.258595	+	0.258595i	0.565887	+	0.824483i	$0.308534\pi$
$674$	5.72774	+	14.3660i	0.220624	+	0.553358i
$675$		0			0
$676$	9.95188	+	10.4965i	0.382764	+	0.403710i
$677$		−	13.1970i		−	0.507200i	−0.967309	−	0.253600i	$-0.918385\pi$
$677$		−	13.1970i		−	0.507200i	0.967309	−	0.253600i	$-0.0816147\pi$
$678$		0			0
$679$			24.0691i			0.923686i
$680$	0.641857	−	0.196654i	0.0246141	−	0.00754134i
$681$		0			0
$682$	−3.27908	−	8.22440i	−0.125562	−	0.314928i
$683$		−	37.9089i		−	1.45054i	−0.688462	−	0.725272i	$-0.741714\pi$
$683$		−	37.9089i		−	1.45054i	0.688462	−	0.725272i	$-0.258286\pi$
$684$		0			0
$685$	−23.6016	−	1.31024i	−0.901770	−	0.0500616i
$686$	10.9168	−	4.35252i	0.416804	−	0.166180i
$687$		0			0
$688$	−15.3622	−	0.818844i	−0.585679	−	0.0312181i
$689$			3.10952i			0.118463i
$690$		0			0
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	0.981873	−	0.189538i	$-0.0606991\pi$
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	−0.189538	+	0.981873i	$0.560699\pi$
$692$	−22.6068	+	21.4339i	−0.859382	+	0.814794i
$693$		0			0
$694$	14.8043	+	6.36433i	0.561962	+	0.241586i
$695$	−2.02114	+	36.4073i	−0.0766664	+	1.38101i
$696$		0			0
$697$	0.128255	−	0.128255i	0.00485799	−	0.00485799i
$698$	−8.92605	−	22.3878i	−0.337856	−	0.847392i
$699$		0			0
$700$	−33.6721	−	4.66075i	−1.27269	−	0.176160i
$701$	−19.9053	+	19.9053i	−0.751812	+	0.751812i	−0.974817	−	0.223005i	$-0.928413\pi$
$701$	−19.9053	+	19.9053i	−0.751812	+	0.751812i	0.223005	+	0.974817i	$0.428413\pi$
$702$		0			0
$703$	−6.76326	−	6.76326i	−0.255081	−	0.255081i
$704$	−2.41674	+	30.1910i	−0.0910844	+	1.13787i
$705$		0			0
$706$	12.0361	−	4.79882i	0.452986	−	0.180606i
$707$		−	30.6277i		−	1.15187i
$708$		0			0
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	−0.849494	−	0.527599i	$-0.823092\pi$
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	0.527599	+	0.849494i	$0.323092\pi$
$710$	2.28806	+	6.81469i	0.0858695	+	0.255751i
$711$		0			0
$712$	−15.2823	−	41.5100i	−0.572729	−	1.55565i
$713$	3.51199	+	3.51199i	0.131525	+	0.131525i
$714$		0			0
$715$	1.12696	−	20.3001i	0.0421458	−	0.759182i
$716$	44.0975	+	1.17442i	1.64800	+	0.0438901i
$717$		0			0
$718$	−1.81581	+	4.22382i	−0.0677655	+	0.157631i
$719$	33.1900			1.23778			0.618889	−	0.785478i	$-0.287583\pi$
$719$	33.1900			1.23778			0.618889	+	0.785478i	$0.287583\pi$
$720$		0			0
$721$	−9.31162			−0.346783
$722$	−2.63464	+	6.12852i	−0.0980511	+	0.228080i
$723$		0			0
$724$	−0.224927	+	8.44566i	−0.00835936	+	0.313880i
$725$	−21.8587	+	17.4777i	−0.811810	+	0.649104i
$726$		0			0
$727$	5.06503	+	5.06503i	0.187852	+	0.187852i	0.794767	−	0.606915i	$-0.207593\pi$
$727$	5.06503	+	5.06503i	0.187852	+	0.187852i	−0.606915	+	0.794767i	$0.707593\pi$
$728$	−20.9635	−	9.68131i	−0.776958	−	0.358813i
$729$		0			0
$730$	−19.8949	+	40.0073i	−0.736341	+	1.48074i
$731$	−0.288660	+	0.288660i	−0.0106765	+	0.0106765i
$732$		0			0
$733$		−	43.0744i		−	1.59099i	−0.605961	−	0.795494i	$-0.707211\pi$
$733$		−	43.0744i		−	1.59099i	0.605961	−	0.795494i	$-0.292789\pi$
$734$	−23.6009	+	9.40969i	−0.871124	+	0.347318i
$735$		0			0
$736$	−5.44332	−	16.0944i	−0.200643	−	0.593249i
$737$	−28.4384	−	28.4384i	−1.04754	−	1.04754i
$738$		0			0
$739$	11.3838	−	11.3838i	0.418762	−	0.418762i	−0.466015	−	0.884777i	$-0.654311\pi$
$739$	11.3838	−	11.3838i	0.418762	−	0.418762i	0.884777	+	0.466015i	$0.154311\pi$
$740$	−11.2801	−	0.927997i	−0.414663	−	0.0341138i
$741$		0			0
$742$	2.30518	+	5.78173i	0.0846258	+	0.212254i
$743$	−1.54795	+	1.54795i	−0.0567888	+	0.0567888i	−0.734931	−	0.678142i	$-0.762785\pi$
$743$	−1.54795	+	1.54795i	−0.0567888	+	0.0567888i	0.678142	+	0.734931i	$0.262785\pi$
$744$		0			0
$745$	17.4029	+	0.966116i	0.637591	+	0.0353958i
$746$	28.5523	+	12.2746i	1.04537	+	0.449404i
$747$		0			0
$748$	0.552973	+	0.583233i	0.0202187	+	0.0213251i
$749$	−16.7723	−	16.7723i	−0.612847	−	0.612847i
$750$		0			0
$751$			1.49244i			0.0544600i	0.999629	+	0.0272300i	$0.00866865\pi$
$751$			1.49244i			0.0544600i	−0.999629	+	0.0272300i	$0.991331\pi$
$752$	−8.14005	−	9.05667i	−0.296837	−	0.330263i
$753$		0			0
$754$	−17.6593	+	7.04078i	−0.643113	+	0.256410i
$755$	6.16731	+	6.89231i	0.224451	+	0.250837i
$756$		0			0
$757$		−	22.7030i		−	0.825154i	−0.910923	−	0.412577i	$-0.864629\pi$
$757$		−	22.7030i		−	0.825154i	0.910923	−	0.412577i	$-0.135371\pi$
$758$	−12.6394	−	31.7015i	−0.459085	−	1.15145i
$759$		0			0
$760$	−7.00198	−	22.8537i	−0.253989	−	0.828991i
$761$		−	33.6599i		−	1.22017i	−0.792335	−	0.610086i	$-0.791135\pi$
$761$		−	33.6599i		−	1.22017i	0.792335	−	0.610086i	$-0.208865\pi$
$762$		0			0
$763$			1.33523i			0.0483386i
$764$	9.39275	−	8.90543i	0.339818	−	0.322187i
$765$		0			0
$766$	0.168923	+	0.423683i	0.00610343	+	0.0153083i
$767$	12.7194	−	12.7194i	0.459271	−	0.459271i
$768$		0			0
$769$			10.1943i			0.367615i	0.982962	+	0.183808i	$0.0588423\pi$
$769$			10.1943i			0.367615i	−0.982962	+	0.183808i	$0.941158\pi$
$770$	−12.9537	−	38.5807i	−0.466817	−	1.39035i
$771$		0			0
$772$	−31.4213	−	0.836823i	−1.13088	−	0.0301179i
$773$	−7.34419			−0.264152			−0.132076	−	0.991240i	$-0.542164\pi$
$773$	−7.34419			−0.264152			−0.132076	+	0.991240i	$0.542164\pi$
$774$		0			0
$775$	8.21755	+	0.915212i	0.295183	+	0.0328754i
$776$	−8.39662	+	18.1817i	−0.301421	+	0.652684i
$777$		0			0
$778$	26.5730	−	10.5947i	0.952688	−	0.379838i
$779$	−4.56658	−	4.56658i	−0.163615	−	0.163615i
$780$		0			0
$781$	−6.08556	+	6.08556i	−0.217759	+	0.217759i
$782$	−0.414191	−	0.178060i	−0.0148114	−	0.00636741i
$783$		0			0
$784$	−18.1954	−	0.969861i	−0.649837	−	0.0346379i
$785$	−30.2239	−	33.7769i	−1.07874	−	1.20555i
$786$		0			0
$787$			29.4359i			1.04928i	0.851326	+	0.524638i	$0.175799\pi$
$787$			29.4359i			1.04928i	−0.851326	+	0.524638i	$0.824201\pi$
$788$	−36.4186	+	34.5291i	−1.29736	+	1.23005i
$789$		0			0
$790$	8.76302	+	26.0995i	0.311774	+	0.928578i
$791$	42.0921			1.49662
$792$		0			0
$793$	24.5959	+	24.5959i	0.873425	+	0.873425i
$794$	6.64715	+	2.85760i	0.235899	+	0.101412i
$795$		0			0
$796$	27.2246	−	25.8121i	0.964950	−	0.914886i
$797$	−50.3934			−1.78503			−0.892513	−	0.451022i	$-0.851060\pi$
$797$	−50.3934			−1.78503			−0.892513	+	0.451022i	$0.851060\pi$
$798$		0			0
$799$	−0.323131			−0.0114315
$800$	−23.8098	−	15.2674i	−0.841804	−	0.539784i
$801$		0			0
$802$	21.1565	+	9.09514i	0.747062	+	0.321161i
$803$	−53.4930			−1.88773
$804$		0			0
$805$	15.2232	+	17.0128i	0.536548	+	0.599623i
$806$	5.15996	+	2.21826i	0.181752	+	0.0781348i
$807$		0			0
$808$	10.6846	−	23.1360i	0.375884	−	0.813922i
$809$	27.1588			0.954851			0.477426	−	0.878672i	$-0.341570\pi$
$809$	27.1588			0.954851			0.477426	+	0.878672i	$0.341570\pi$
$810$		0			0
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	−0.880089	−	0.474809i	$-0.842517\pi$
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	0.474809	+	0.880089i	$0.342517\pi$
$812$	−27.6155	+	26.1827i	−0.969113	+	0.918833i
$813$		0			0
$814$	−5.01838	−	12.5868i	−0.175894	−	0.441168i
$815$	19.6575	+	21.9684i	0.688574	+	0.769520i
$816$		0			0
$817$	10.2779	+	10.2779i	0.359579	+	0.359579i
$818$	−22.6401	−	9.73292i	−0.791591	−	0.340304i
$819$		0			0
$820$	−7.61635	−	0.626587i	−0.265974	−	0.0218814i
$821$	20.2900	+	20.2900i	0.708126	+	0.708126i	0.966141	−	0.258015i	$-0.0830684\pi$
$821$	20.2900	+	20.2900i	0.708126	+	0.708126i	−0.258015	+	0.966141i	$0.583068\pi$
$822$		0			0
$823$	−31.4540	+	31.4540i	−1.09642	+	1.09642i	−0.101592	+	0.994826i	$0.532394\pi$
$823$	−31.4540	+	31.4540i	−1.09642	+	1.09642i	−0.994826	+	0.101592i	$0.967606\pi$
$824$	−7.03395	−	3.24840i	−0.245039	−	0.113164i
$825$		0			0
$826$	14.2207	−	33.0793i	0.494802	−	1.15098i
$827$	−15.3304			−0.533090			−0.266545	−	0.963822i	$-0.585882\pi$
$827$	−15.3304			−0.533090			−0.266545	+	0.963822i	$0.585882\pi$
$828$		0			0
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	0.691375	−	0.722496i	$-0.257005\pi$
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	−0.722496	+	0.691375i	$0.757005\pi$
$830$	11.2036	+	33.3685i	0.388884	+	1.15824i
$831$		0			0
$832$	−12.4583	−	14.6264i	−0.431915	−	0.507080i
$833$	−0.341897	+	0.341897i	−0.0118460	+	0.0118460i
$834$		0			0
$835$	2.07168	−	37.3176i	0.0716935	−	1.29143i
$836$	20.7664	−	19.6889i	0.718220	−	0.680956i
$837$		0			0
$838$	21.7838	−	8.68522i	0.752508	−	0.300026i
$839$		−	48.1891i		−	1.66367i	−0.555021	−	0.831837i	$-0.687290\pi$
$839$		−	48.1891i		−	1.66367i	0.555021	−	0.831837i	$-0.312710\pi$
$840$		0			0
$841$			2.33080i			0.0803723i
$842$	−17.4365	−	43.7333i	−0.600902	−	1.50715i
$843$		0			0
$844$	−0.481069	+	18.0634i	−0.0165591	+	0.621767i
$845$	−10.7836	−	12.0513i	−0.370967	−	0.414577i
$846$		0			0
$847$	8.01241	−	8.01241i	0.275310	−	0.275310i
$848$	−0.275662	+	5.17166i	−0.00946628	+	0.177596i
$849$		0			0
$850$	−0.723658	+	0.199087i	−0.0248213	+	0.00682863i
$851$	5.37484	+	5.37484i	0.184247	+	0.184247i
$852$		0			0
$853$	−13.7426			−0.470537			−0.235268	−	0.971930i	$-0.575597\pi$
$853$	−13.7426			−0.470537			−0.235268	+	0.971930i	$0.575597\pi$
$854$	63.9663	+	27.4990i	2.18888	+	0.940996i
$855$		0			0
$856$	−6.81862	−	18.5208i	−0.233056	−	0.633029i
$857$	13.4366	−	13.4366i	0.458986	−	0.458986i	−0.439336	−	0.898323i	$-0.644786\pi$
$857$	13.4366	−	13.4366i	0.458986	−	0.458986i	0.898323	+	0.439336i	$0.144786\pi$
$858$		0			0
$859$	7.00719	+	7.00719i	0.239082	+	0.239082i	0.816470	−	0.577388i	$-0.195928\pi$
$859$	7.00719	+	7.00719i	0.239082	+	0.239082i	−0.577388	+	0.816470i	$0.695928\pi$
$860$	17.1420	+	1.41025i	0.584536	+	0.0480890i
$861$		0			0
$862$	−19.5626	+	45.5051i	−0.666304	+	1.54991i
$863$	41.4708	+	41.4708i	1.41168	+	1.41168i	0.748123	+	0.663560i	$0.230955\pi$
$863$	41.4708	+	41.4708i	1.41168	+	1.41168i	0.663560	+	0.748123i	$0.269045\pi$
$864$		0			0
$865$	25.9555	−	23.2252i	0.882513	−	0.789682i
$866$	18.7811	−	7.48806i	0.638209	−	0.254455i
$867$		0			0
$868$	11.2387	+	0.299313i	0.381466	+	0.0101593i
$869$	−23.3070	+	23.3070i	−0.790636	+	0.790636i
$870$		0			0
$871$	25.5125			0.864458
$872$	−0.465802	+	1.00863i	−0.0157741	+	0.0341564i
$873$		0			0
$874$	−6.33993	+	14.7475i	−0.214451	+	0.498842i
$875$	37.4807	+	6.29398i	1.26708	+	0.212775i
$876$		0			0
$877$	−5.34168			−0.180376			−0.0901879	−	0.995925i	$-0.528747\pi$
$877$	−5.34168			−0.180376			−0.0901879	+	0.995925i	$0.528747\pi$
$878$	−12.6270	+	29.3721i	−0.426141	+	0.991259i
$879$		0			0
$880$	3.67395	−	33.6627i	0.123849	−	1.13477i
$881$	45.9723			1.54885			0.774423	−	0.632668i	$-0.218040\pi$
$881$	45.9723			1.54885			0.774423	+	0.632668i	$0.218040\pi$
$882$		0			0
$883$	2.64739			0.0890918			0.0445459	−	0.999007i	$-0.485816\pi$
$883$	2.64739			0.0890918			0.0445459	+	0.999007i	$0.485816\pi$
$884$	−0.509653	−	0.0135732i	−0.0171415	−	0.000456518i
$885$		0			0
$886$	6.09806	−	14.1849i	0.204868	−	0.476551i
$887$	−3.87171	−	3.87171i	−0.129999	−	0.129999i	0.639113	−	0.769113i	$-0.279301\pi$
$887$	−3.87171	−	3.87171i	−0.129999	−	0.129999i	−0.769113	+	0.639113i	$0.779301\pi$
$888$		0			0
$889$	−3.26661			−0.109558
$890$	15.7411	+	46.8829i	0.527644	+	1.57152i
$891$		0			0
$892$	0.323627	−	12.1517i	0.0108358	−	0.406868i
$893$			11.5053i			0.385009i
$894$		0			0
$895$	−49.2441	−	2.73378i	−1.64605	−	0.0913801i
$896$	−34.0076	−	17.9601i	−1.13611	−	0.600005i
$897$		0			0
$898$	−16.0923	+	37.4328i	−0.537006	+	1.24915i
$899$	6.54516	−	6.54516i	0.218293	−	0.218293i
$900$		0			0
$901$	0.0971768	+	0.0971768i	0.00323743	+	0.00323743i
$902$	−3.38843	−	8.49868i	−0.112822	−	0.282975i
$903$		0			0
$904$	31.7962	+	14.6840i	1.05752	+	0.488384i
$905$	0.523580	−	9.43136i	0.0174044	−	0.313509i
$906$		0			0
$907$	26.2062			0.870163			0.435081	−	0.900391i	$-0.356720\pi$
$907$	26.2062			0.870163			0.435081	+	0.900391i	$0.356720\pi$
$908$	42.2388	−	40.0473i	1.40174	−	1.32902i
$909$		0			0
$910$	23.1161	+	11.4952i	0.766292	+	0.381062i
$911$		−	24.2898i		−	0.804757i	−0.915473	−	0.402378i	$-0.868184\pi$
$911$		−	24.2898i		−	0.804757i	0.915473	−	0.402378i	$-0.131816\pi$
$912$		0			0
$913$	−29.7983	+	29.7983i	−0.986181	+	0.986181i
$914$	−35.6049	+	14.1957i	−1.17771	+	0.469553i
$915$		0			0
$916$	−51.8564	−	1.38106i	−1.71339	−	0.0456314i
$917$			26.1452i			0.863391i
$918$		0			0
$919$		−	41.1294i		−	1.35673i	−0.734723	−	0.678367i	$-0.762688\pi$
$919$		−	41.1294i		−	1.35673i	0.734723	−	0.678367i	$-0.237312\pi$
$920$	5.56455	+	18.1621i	0.183458	+	0.598787i
$921$		0			0
$922$	−8.23420	+	3.28298i	−0.271179	+	0.108119i
$923$		−	5.45944i		−	0.179700i
$924$		0			0
$925$	12.5763	+	1.40066i	0.413508	+	0.0460535i
$926$	14.9265	+	37.4377i	0.490514	+	1.23028i
$927$		0			0
$928$	−29.9946	+	10.1445i	−0.984620	+	0.333009i
$929$			43.4799i			1.42653i	0.700894	+	0.713265i	$0.252785\pi$
$929$			43.4799i			1.42653i	−0.700894	+	0.713265i	$0.747215\pi$
$930$		0			0
$931$	12.1734	+	12.1734i	0.398968	+	0.398968i
$932$	0.110439	−	4.14680i	0.00361754	−	0.135833i
$933$		0			0
$934$	−2.17752	+	5.06521i	−0.0712507	+	0.165739i
$935$	−0.599188	−	0.669626i	−0.0195955	−	0.0218991i
$936$		0			0
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	−0.460910	−	0.887447i	$-0.652477\pi$
$937$	13.0565	−	13.0565i	0.426537	−	0.426537i	0.887447	+	0.460910i	$0.152477\pi$
$938$	47.4370	−	18.9132i	1.54887	−	0.617537i
$939$		0			0
$940$	8.80516	+	10.3838i	0.287193	+	0.338683i
$941$	5.53494	−	5.53494i	0.180434	−	0.180434i	−0.611111	−	0.791545i	$-0.709277\pi$
$941$	5.53494	−	5.53494i	0.180434	−	0.180434i	0.791545	+	0.611111i	$0.209277\pi$
$942$		0			0
$943$	3.62911	+	3.62911i	0.118180	+	0.118180i
$944$	22.2821	−	20.0270i	0.725222	−	0.651822i
$945$		0			0
$946$	7.62627	+	19.1278i	0.247951	+	0.621898i
$947$			31.6905i			1.02980i	0.857249	+	0.514902i	$0.172172\pi$
$947$			31.6905i			1.02980i	−0.857249	+	0.514902i	$0.827828\pi$
$948$		0			0
$949$	23.9947	−	23.9947i	0.778900	−	0.778900i
$950$	7.08861	+	25.7663i	0.229985	+	0.835969i
$951$		0			0
$952$	−0.957692	+	0.352583i	−0.0310390	+	0.0114273i
$953$	−2.85543	−	2.85543i	−0.0924965	−	0.0924965i	0.659344	−	0.751841i	$-0.270834\pi$
$953$	−2.85543	−	2.85543i	−0.0924965	−	0.0924965i	−0.751841	+	0.659344i	$0.770834\pi$
$954$		0			0
$955$	−10.7841	+	9.64970i	−0.348964	+	0.312257i
$956$	−17.2602	−	18.2047i	−0.558235	−	0.588783i
$957$		0			0
$958$	−12.8014	−	5.50331i	−0.413595	−	0.177804i
$959$	35.9348			1.16039
$960$		0			0
$961$	28.2654			0.911786
$962$	7.89694	+	3.39488i	0.254608	+	0.109455i
$963$		0			0
$964$	20.4854	+	21.6064i	0.659790	+	0.695895i
$965$	35.0886	+	1.94793i	1.12954	+	0.0627062i
$966$		0			0
$967$	−40.1144	−	40.1144i	−1.28999	−	1.28999i	−0.934790	−	0.355202i	$-0.884412\pi$
$967$	−40.1144	−	40.1144i	−1.28999	−	1.28999i	−0.355202	−	0.934790i	$-0.615588\pi$
$968$	8.84771	−	3.25737i	0.284376	−	0.104696i
$969$		0			0
$970$	9.96981	−	20.0486i	0.320111	−	0.643723i
$971$	17.3439	−	17.3439i	0.556592	−	0.556592i	−0.371743	−	0.928335i	$-0.621240\pi$
$971$	17.3439	−	17.3439i	0.556592	−	0.556592i	0.928335	+	0.371743i	$0.121240\pi$
$972$		0			0
$973$		−	55.4322i		−	1.77708i
$974$	−10.3079	−	25.8536i	−0.330285	−	0.828404i
$975$		0			0
$976$	38.7267	+	43.0876i	1.23961	+	1.37920i
$977$	12.2234	+	12.2234i	0.391060	+	0.391060i	0.875065	−	0.484005i	$-0.160818\pi$
$977$	12.2234	+	12.2234i	0.391060	+	0.391060i	−0.484005	+	0.875065i	$0.660818\pi$
$978$		0			0
$979$	−41.8667	+	41.8667i	−1.33807	+	1.33807i
$980$	20.3034	+	1.67034i	0.648568	+	0.0533569i
$981$		0			0
$982$	−4.44406	+	1.77185i	−0.141816	+	0.0565421i
$983$	−13.6091	+	13.6091i	−0.434063	+	0.434063i	−0.890008	−	0.455945i	$-0.849301\pi$
$983$	−13.6091	+	13.6091i	−0.434063	+	0.434063i	0.455945	+	0.890008i	$0.349301\pi$
$984$		0			0
$985$	41.8132	−	37.4148i	1.33228	−	1.19214i
$986$	−0.331843	+	0.771911i	−0.0105680	+	0.0245827i
$987$		0			0
$988$	−0.483284	+	18.1465i	−0.0153753	+	0.577317i
$989$	−8.16797	−	8.16797i	−0.259726	−	0.259726i
$990$		0			0
$991$		−	52.9400i		−	1.68169i	−0.541273	−	0.840847i	$-0.682058\pi$
$991$		−	52.9400i		−	1.68169i	0.541273	−	0.840847i	$-0.317942\pi$
$992$	8.38525	+	4.14678i	0.266232	+	0.131660i
$993$		0			0
$994$	−4.04725	−	10.1511i	−0.128371	−	0.321973i
$995$	−31.2573	+	27.9693i	−0.990923	+	0.886688i
$996$		0			0
$997$			3.67381i			0.116351i	0.998306	+	0.0581754i	$0.0185283\pi$
$997$			3.67381i			0.116351i	−0.998306	+	0.0581754i	$0.981472\pi$
$998$	−18.3370	+	7.31097i	−0.580446	+	0.231425i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.z.g.667.8		18
3.2	odd	2		80.2.s.b.27.2	yes	18
5.3	odd	4		720.2.bd.g.523.6		18
12.11	even	2		320.2.s.b.207.8		18
15.2	even	4		400.2.j.d.43.6		18
15.8	even	4		80.2.j.b.43.4	✓	18
15.14	odd	2		400.2.s.d.107.8		18
16.3	odd	4		720.2.bd.g.307.6		18
24.5	odd	2		640.2.s.d.287.8		18
24.11	even	2		640.2.s.c.287.2		18
48.5	odd	4		640.2.j.c.607.8		18
48.11	even	4		640.2.j.d.607.2		18
48.29	odd	4		320.2.j.b.47.2		18
48.35	even	4		80.2.j.b.67.4	yes	18
60.23	odd	4		320.2.j.b.143.8		18
60.47	odd	4		1600.2.j.d.143.2		18
60.59	even	2		1600.2.s.d.207.2		18
80.3	even	4	inner	720.2.z.g.163.8		18
120.53	even	4		640.2.j.d.543.8		18
120.83	odd	4		640.2.j.c.543.2		18
240.29	odd	4		1600.2.j.d.1007.8		18
240.53	even	4		640.2.s.c.223.2		18
240.77	even	4		1600.2.s.d.943.2		18
240.83	odd	4		80.2.s.b.3.2	yes	18
240.173	even	4		320.2.s.b.303.8		18
240.179	even	4		400.2.j.d.307.6		18
240.203	odd	4		640.2.s.d.223.8		18
240.227	odd	4		400.2.s.d.243.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	15.8	even	4
80.2.j.b.67.4	yes	18	48.35	even	4
80.2.s.b.3.2	yes	18	240.83	odd	4
80.2.s.b.27.2	yes	18	3.2	odd	2
320.2.j.b.47.2		18	48.29	odd	4
320.2.j.b.143.8		18	60.23	odd	4
320.2.s.b.207.8		18	12.11	even	2
320.2.s.b.303.8		18	240.173	even	4
400.2.j.d.43.6		18	15.2	even	4
400.2.j.d.307.6		18	240.179	even	4
400.2.s.d.107.8		18	15.14	odd	2
400.2.s.d.243.8		18	240.227	odd	4
640.2.j.c.543.2		18	120.83	odd	4
640.2.j.c.607.8		18	48.5	odd	4
640.2.j.d.543.8		18	120.53	even	4
640.2.j.d.607.2		18	48.11	even	4
640.2.s.c.223.2		18	240.53	even	4
640.2.s.c.287.2		18	24.11	even	2
640.2.s.d.223.8		18	240.203	odd	4
640.2.s.d.287.8		18	24.5	odd	2
720.2.z.g.163.8		18	80.3	even	4	inner
720.2.z.g.667.8		18	1.1	even	1	trivial
720.2.bd.g.307.6		18	16.3	odd	4
720.2.bd.g.523.6		18	5.3	odd	4
1600.2.j.d.143.2		18	60.47	odd	4
1600.2.j.d.1007.8		18	240.29	odd	4
1600.2.s.d.207.2		18	60.59	even	2
1600.2.s.d.943.2		18	240.77	even	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.z (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29924 + 0.558542i) q^{2} +(1.37606 + 1.45136i) q^{4} +(-1.49107 - 1.66635i) q^{5} +(2.40368 + 2.40368i) q^{7} +(0.977191 + 2.65426i) q^{8} +O(q^{10})\)	\(q+(1.29924 + 0.558542i) q^{2} +(1.37606 + 1.45136i) q^{4} +(-1.49107 - 1.66635i) q^{5} +(2.40368 + 2.40368i) q^{7} +(0.977191 + 2.65426i) q^{8} +(-1.00653 - 2.99782i) q^{10} +(2.67707 - 2.67707i) q^{11} +2.40164i q^{13} +(1.78040 + 4.46551i) q^{14} +(-0.212908 + 3.99433i) q^{16} +(0.0750544 + 0.0750544i) q^{17} +(2.67236 - 2.67236i) q^{19} +(0.366678 - 4.45708i) q^{20} +(4.97342 - 1.98291i) q^{22} +(-2.12375 + 2.12375i) q^{23} +(-0.553442 + 4.96928i) q^{25} +(-1.34141 + 3.12031i) q^{26} +(-0.180999 + 6.79621i) q^{28} +(3.95795 + 3.95795i) q^{29} -1.65367i q^{31} +(-2.50762 + 5.07068i) q^{32} +(0.0555929 + 0.139435i) q^{34} +(0.421324 - 7.58941i) q^{35} -2.53082i q^{37} +(4.96467 - 1.97942i) q^{38} +(2.96587 - 5.58602i) q^{40} -1.70882i q^{41} +3.84601i q^{43} +(7.56921 + 0.201586i) q^{44} +(-3.94547 + 1.57306i) q^{46} +(-2.15264 + 2.15264i) q^{47} +4.55532i q^{49} +(-3.49460 + 6.14717i) q^{50} +(-3.48565 + 3.30480i) q^{52} +1.29475 q^{53} +(-8.45262 - 0.469246i) q^{55} +(-4.03113 + 8.72883i) q^{56} +(2.93166 + 7.35302i) q^{58} +(-5.29614 - 5.29614i) q^{59} +(10.2413 - 10.2413i) q^{61} +(0.923645 - 2.14852i) q^{62} +(-6.09020 + 5.18744i) q^{64} +(4.00197 - 3.58100i) q^{65} -10.6230i q^{67} +(-0.00565167 + 0.212211i) q^{68} +(4.78640 - 9.62515i) q^{70} -2.27322 q^{71} +(-9.99096 - 9.99096i) q^{73} +(1.41357 - 3.28815i) q^{74} +(7.55589 + 0.201231i) q^{76} +12.8696 q^{77} -8.70617 q^{79} +(6.97341 - 5.60103i) q^{80} +(0.954448 - 2.22017i) q^{82} -11.1310 q^{83} +(0.0131558 - 0.236978i) q^{85} +(-2.14816 + 4.99689i) q^{86} +(9.72165 + 4.48963i) q^{88} -15.6390 q^{89} +(-5.77276 + 5.77276i) q^{91} +(-6.00475 - 0.159920i) q^{92} +(-3.99914 + 1.59446i) q^{94} +(-8.43775 - 0.468420i) q^{95} +(5.00672 + 5.00672i) q^{97} +(-2.54434 + 5.91846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8}+O(q^{10}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8	\( 18 q + 4 q^{4} - 2 q^{5} + 2 q^{7} + 12 q^{8} + 2 q^{11} + 12 q^{14} + 6 q^{17} - 2 q^{19} + 12 q^{20} + 12 q^{22} + 2 q^{23} - 6 q^{25} + 16 q^{26} + 40 q^{28} - 14 q^{29} - 20 q^{32} + 28 q^{34} - 2 q^{35} - 24 q^{38} + 44 q^{40} + 44 q^{44} + 12 q^{46} - 38 q^{47} + 8 q^{50} + 8 q^{52} - 12 q^{53} - 6 q^{55} - 20 q^{56} + 20 q^{58} - 10 q^{59} + 14 q^{61} + 40 q^{62} + 16 q^{64} + 60 q^{68} - 28 q^{70} - 24 q^{71} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 44 q^{77} - 16 q^{79} + 92 q^{80} + 48 q^{82} - 40 q^{83} + 14 q^{85} + 36 q^{86} - 8 q^{88} - 12 q^{89} + 8 q^{92} - 28 q^{94} - 34 q^{95} + 18 q^{97} + 56 q^{98}+O(q^{100}) \) 18 * q + 4 * q^4 - 2 * q^5 + 2 * q^7 + 12 * q^8 + 2 * q^11 + 12 * q^14 + 6 * q^17 - 2 * q^19 + 12 * q^20 + 12 * q^22 + 2 * q^23 - 6 * q^25 + 16 * q^26 + 40 * q^28 - 14 * q^29 - 20 * q^32 + 28 * q^34 - 2 * q^35 - 24 * q^38 + 44 * q^40 + 44 * q^44 + 12 * q^46 - 38 * q^47 + 8 * q^50 + 8 * q^52 - 12 * q^53 - 6 * q^55 - 20 * q^56 + 20 * q^58 - 10 * q^59 + 14 * q^61 + 40 * q^62 + 16 * q^64 + 60 * q^68 - 28 * q^70 - 24 * q^71 - 14 * q^73 + 48 * q^74 - 16 * q^76 + 44 * q^77 - 16 * q^79 + 92 * q^80 + 48 * q^82 - 40 * q^83 + 14 * q^85 + 36 * q^86 - 8 * q^88 - 12 * q^89 + 8 * q^92 - 28 * q^94 - 34 * q^95 + 18 * q^97 + 56 * q^98

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