LMFDB - Embedded newform 297.2.n.a.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(37,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			37.1
Root			$0.913545 - 0.406737i$ of defining polynomial
Character	$\chi$	$=$	297.37
Dual form			297.2.n.a.289.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.273659 + 2.60369i) q^{2} +(-4.74803 - 1.00922i) q^{4} +(0.338261 + 3.21834i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(2.30902 - 7.10642i) q^{8} -8.47214 q^{10} +(-3.19003 + 0.907591i) q^{11} +(2.25841 - 1.00551i) q^{13} +(-1.75181 - 1.94558i) q^{14} +(9.00217 + 4.00802i) q^{16} +(-1.50000 + 1.08981i) q^{17} +(0.309017 - 0.951057i) q^{19} +(1.64195 - 15.6222i) q^{20} +(-1.49011 - 8.55422i) q^{22} +(1.19098 - 2.06284i) q^{23} +(-5.35256 + 1.13772i) q^{25} +(2.00000 + 6.15537i) q^{26} +(3.92705 - 2.85317i) q^{28} +(-1.24064 + 1.37787i) q^{29} +(-1.47815 + 0.658114i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(-2.42705 - 4.20378i) q^{34} +(-2.61803 - 1.90211i) q^{35} +(1.88197 + 5.79210i) q^{37} +(2.39169 + 1.06485i) q^{38} +(23.6519 + 5.02738i) q^{40} +(7.67636 + 8.52546i) q^{41} +(2.42705 + 4.20378i) q^{43} +(16.0623 - 1.08981i) q^{44} +(5.04508 + 3.66547i) q^{46} +(-5.81438 + 1.23588i) q^{47} +(0.627171 + 5.96713i) q^{49} +(-1.49750 - 14.2478i) q^{50} +(-11.7378 + 2.49494i) q^{52} +(-5.73607 - 4.16750i) q^{53} +(-4.00000 - 9.95959i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-3.24803 - 3.60730i) q^{58} +(-0.604528 - 0.128496i) q^{59} +(3.78747 + 1.68629i) q^{61} +(-1.30902 - 4.02874i) q^{62} +(-7.04508 - 5.11855i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(8.22191 - 3.66063i) q^{68} +(5.66897 - 6.29602i) q^{70} +(-11.3992 + 8.28199i) q^{71} +(-2.11803 - 6.51864i) q^{73} +(-15.5959 + 3.31500i) q^{74} +(-2.42705 + 4.20378i) q^{76} +(1.46007 - 2.97795i) q^{77} +(0.999533 - 9.50992i) q^{79} +(-9.85410 + 30.3278i) q^{80} +(-24.2984 + 17.6538i) q^{82} +(13.0053 + 5.79033i) q^{83} +(-4.01478 - 4.45887i) q^{85} +(-11.6095 + 5.16889i) q^{86} +(-0.916102 + 24.7653i) q^{88} +11.2361 q^{89} +(-0.763932 + 2.35114i) q^{91} +(-7.73669 + 8.59247i) q^{92} +(-1.62670 - 15.4771i) q^{94} +(3.16535 + 0.672816i) q^{95} +(-0.627171 + 5.96713i) q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28}+ \cdots - 72 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.273659	+	2.60369i	−0.193506	+	1.84109i	0.279641	+	0.960105i	$0.409785\pi$
$2$	−0.273659	+	2.60369i	−0.193506	+	1.84109i	−0.473147	+	0.880984i	$0.656882\pi$
$3$		0			0
$3$		0			0
$4$	−4.74803	−	1.00922i	−2.37401	−	0.504612i
$5$	0.338261	+	3.21834i	0.151275	+	1.43929i	0.762069	+	0.647496i	$0.224184\pi$
$5$	0.338261	+	3.21834i	0.151275	+	1.43929i	−0.610794	+	0.791790i	$0.709150\pi$
$6$		0			0
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−0.669131	+	0.743145i	−0.252908	+	0.280882i	0.603300	+	0.797514i	$0.293852\pi$
$8$	2.30902	−	7.10642i	0.816361	−	2.51250i
$9$		0			0
$10$	−8.47214			−2.67912
$11$	−3.19003	+	0.907591i	−0.961830	+	0.273649i
$11$	−3.19003	+	0.907591i	−0.961830	+	0.273649i
$12$		0			0
$13$	2.25841	−	1.00551i	0.626370	−	0.278878i	−0.0689034	−	0.997623i	$-0.521950\pi$
$13$	2.25841	−	1.00551i	0.626370	−	0.278878i	0.695273	+	0.718746i	$0.255283\pi$
$14$	−1.75181	−	1.94558i	−0.468190	−	0.519978i
$15$		0			0
$16$	9.00217	+	4.00802i	2.25054	+	1.00201i
$17$	−1.50000	+	1.08981i	−0.363803	+	0.264319i	−0.754637	−	0.656143i	$-0.772187\pi$
$17$	−1.50000	+	1.08981i	−0.363803	+	0.264319i	0.390833	+	0.920461i	$0.372187\pi$
$18$		0			0
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	−0.909332	−	0.416071i	$-0.863407\pi$
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i	0.980226	+	0.197884i	$0.0634068\pi$
$20$	1.64195	−	15.6222i	0.367152	−	3.49322i
$21$		0			0
$22$	−1.49011	−	8.55422i	−0.317692	−	1.82377i
$23$	1.19098	−	2.06284i	0.248337	−	0.430133i	−0.714727	−	0.699403i	$-0.753449\pi$
$23$	1.19098	−	2.06284i	0.248337	−	0.430133i	0.963065	+	0.269271i	$0.0867826\pi$
$24$		0			0
$25$	−5.35256	+	1.13772i	−1.07051	+	0.227544i
$26$	2.00000	+	6.15537i	0.392232	+	1.20717i
$27$		0			0
$28$	3.92705	−	2.85317i	0.742143	−	0.539198i
$29$	−1.24064	+	1.37787i	−0.230380	+	0.255863i	−0.847241	−	0.531209i	$-0.821738\pi$
$29$	−1.24064	+	1.37787i	−0.230380	+	0.255863i	0.616860	+	0.787073i	$0.288404\pi$
$30$		0			0
$31$	−1.47815	+	0.658114i	−0.265483	+	0.118201i	−0.535162	−	0.844750i	$-0.679749\pi$
$31$	−1.47815	+	0.658114i	−0.265483	+	0.118201i	0.269678	+	0.962950i	$0.413083\pi$
$32$	−5.42705	+	9.39993i	−0.959376	+	1.66169i
$33$		0			0
$34$	−2.42705	−	4.20378i	−0.416236	−	0.720942i
$35$	−2.61803	−	1.90211i	−0.442529	−	0.321516i
$36$		0			0
$37$	1.88197	+	5.79210i	0.309393	+	0.952215i	0.978001	+	0.208599i	$0.0668905\pi$
$37$	1.88197	+	5.79210i	0.309393	+	0.952215i	−0.668608	+	0.743615i	$0.733109\pi$
$38$	2.39169	+	1.06485i	0.387984	+	0.172742i
$39$		0			0
$40$	23.6519	+	5.02738i	3.73970	+	0.794898i
$41$	7.67636	+	8.52546i	1.19885	+	1.33145i	0.929684	+	0.368358i	$0.120080\pi$
$41$	7.67636	+	8.52546i	1.19885	+	1.33145i	0.269162	+	0.963095i	$0.413253\pi$
$42$		0			0
$43$	2.42705	+	4.20378i	0.370122	+	0.641070i	0.989584	−	0.143957i	$-0.0459826\pi$
$43$	2.42705	+	4.20378i	0.370122	+	0.641070i	−0.619462	+	0.785027i	$0.712649\pi$
$44$	16.0623	−	1.08981i	2.42148	−	0.164296i
$45$		0			0
$46$	5.04508	+	3.66547i	0.743857	+	0.540444i
$47$	−5.81438	+	1.23588i	−0.848114	+	0.180272i	−0.611414	−	0.791311i	$-0.709399\pi$
$47$	−5.81438	+	1.23588i	−0.848114	+	0.180272i	−0.236700	+	0.971583i	$0.576066\pi$
$48$		0			0
$49$	0.627171	+	5.96713i	0.0895958	+	0.852447i
$50$	−1.49750	−	14.2478i	−0.211778	−	2.01494i
$51$		0			0
$52$	−11.7378	+	2.49494i	−1.62774	+	0.345986i
$53$	−5.73607	−	4.16750i	−0.787910	−	0.572450i	0.119433	−	0.992842i	$-0.461892\pi$
$53$	−5.73607	−	4.16750i	−0.787910	−	0.572450i	−0.907342	+	0.420393i	$0.861892\pi$
$54$		0			0
$55$	−4.00000	−	9.95959i	−0.539360	−	1.34295i
$56$	3.73607	+	6.47106i	0.499253	+	0.864732i
$57$		0			0
$58$	−3.24803	−	3.60730i	−0.426487	−	0.473662i
$59$	−0.604528	−	0.128496i	−0.0787029	−	0.0167288i	0.168392	−	0.985720i	$-0.446143\pi$
$59$	−0.604528	−	0.128496i	−0.0787029	−	0.0167288i	−0.247095	+	0.968991i	$0.579476\pi$
$60$		0			0
$61$	3.78747	+	1.68629i	0.484935	+	0.215907i	0.634617	−	0.772827i	$-0.281158\pi$
$61$	3.78747	+	1.68629i	0.484935	+	0.215907i	−0.149681	+	0.988734i	$0.547825\pi$
$62$	−1.30902	−	4.02874i	−0.166245	−	0.511650i
$63$		0			0
$64$	−7.04508	−	5.11855i	−0.880636	−	0.639819i
$65$	4.00000	+	6.92820i	0.496139	+	0.859338i
$66$		0			0
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	−0.989017	−	0.147802i	$-0.952780\pi$
$67$	−3.00000	+	5.19615i	−0.366508	+	0.634811i	0.622509	+	0.782613i	$0.286114\pi$
$68$	8.22191	−	3.66063i	0.997053	−	0.443917i
$69$		0			0
$70$	5.66897	−	6.29602i	0.677571	−	0.752519i
$71$	−11.3992	+	8.28199i	−1.35283	+	0.982892i	−0.353970	+	0.935257i	$0.615168\pi$
$71$	−11.3992	+	8.28199i	−1.35283	+	0.982892i	−0.998865	+	0.0476350i	$0.984832\pi$
$72$		0			0
$73$	−2.11803	−	6.51864i	−0.247897	−	0.762949i	−0.995146	−	0.0984051i	$-0.968626\pi$
$73$	−2.11803	−	6.51864i	−0.247897	−	0.762949i	0.747249	−	0.664544i	$-0.231374\pi$
$74$	−15.5959	+	3.31500i	−1.81298	+	0.385361i
$75$		0			0
$76$	−2.42705	+	4.20378i	−0.278402	+	0.482206i
$77$	1.46007	−	2.97795i	0.166391	−	0.339369i
$78$		0			0
$79$	0.999533	−	9.50992i	0.112456	−	1.06995i	−0.782149	−	0.623092i	$-0.785876\pi$
$79$	0.999533	−	9.50992i	0.112456	−	1.06995i	0.894605	−	0.446858i	$-0.147457\pi$
$80$	−9.85410	+	30.3278i	−1.10172	+	3.39075i
$81$		0			0
$82$	−24.2984	+	17.6538i	−2.68331	+	1.94954i
$83$	13.0053	+	5.79033i	1.42752	+	0.635571i	0.967622	−	0.252402i	$-0.0812206\pi$
$83$	13.0053	+	5.79033i	1.42752	+	0.635571i	0.459894	+	0.887974i	$0.347887\pi$
$84$		0			0
$85$	−4.01478	−	4.45887i	−0.435464	−	0.483632i
$86$	−11.6095	+	5.16889i	−1.25189	+	0.557376i
$87$		0			0
$88$	−0.916102	+	24.7653i	−0.0976568	+	2.63999i
$89$	11.2361			1.19102			0.595510	−	0.803348i	$-0.296950\pi$
$89$	11.2361			1.19102			0.595510	+	0.803348i	$0.296950\pi$
$90$		0			0
$91$	−0.763932	+	2.35114i	−0.0800818	+	0.246467i
$92$	−7.73669	+	8.59247i	−0.806606	+	0.895827i
$93$		0			0
$94$	−1.62670	−	15.4771i	−0.167782	−	1.59634i
$95$	3.16535	+	0.672816i	0.324758	+	0.0690295i
$96$		0			0
$97$	−0.627171	+	5.96713i	−0.0636795	+	0.605870i	0.915422	+	0.402496i	$0.131857\pi$
$97$	−0.627171	+	5.96713i	−0.0636795	+	0.605870i	−0.979101	+	0.203374i	$0.934809\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	26.5623			2.65623
$101$	0.0493516	−	0.469550i	0.00491067	−	0.0467219i	−0.991792	−	0.127861i	$-0.959189\pi$
$101$	0.0493516	−	0.469550i	0.00491067	−	0.0467219i	0.996703	+	0.0811387i	$0.0258557\pi$
$102$		0			0
$103$	5.63798	+	1.19839i	0.555526	+	0.118081i	0.477116	−	0.878840i	$-0.341682\pi$
$103$	5.63798	+	1.19839i	0.555526	+	0.118081i	0.0784104	+	0.996921i	$0.475016\pi$
$104$	−1.93086	−	18.3709i	−0.189337	−	1.80142i
$105$		0			0
$106$	12.4206	−	13.7945i	1.20640	−	1.33984i
$107$	4.64590	−	14.2986i	0.449136	−	1.38230i	−0.428748	−	0.903424i	$-0.641045\pi$
$107$	4.64590	−	14.2986i	0.449136	−	1.38230i	0.877884	−	0.478874i	$-0.158955\pi$
$108$		0			0
$109$	13.8541			1.32698			0.663491	−	0.748184i	$-0.269074\pi$
$109$	13.8541			1.32698			0.663491	+	0.748184i	$0.269074\pi$
$110$	27.0264	−	7.68924i	2.57686	−	0.733140i
$111$		0			0
$112$	−9.00217	+	4.00802i	−0.850625	+	0.378723i
$113$	−8.54074	−	9.48545i	−0.803445	−	0.892316i	0.192590	−	0.981279i	$-0.438311\pi$
$113$	−8.54074	−	9.48545i	−0.803445	−	0.892316i	−0.996035	+	0.0889633i	$0.971645\pi$
$114$		0			0
$115$	7.04179	+	3.13521i	0.656651	+	0.292360i
$116$	7.28115	−	5.29007i	0.676038	−	0.491170i
$117$		0			0
$118$	0.500000	−	1.53884i	0.0460287	−	0.141662i
$119$	0.193806	−	1.84395i	0.0177662	−	0.169034i
$120$		0			0
$121$	9.35256	−	5.79048i	0.850232	−	0.526407i
$122$	−5.42705	+	9.39993i	−0.491342	+	0.851029i
$123$		0			0
$124$	7.68247	−	1.63296i	0.689906	−	0.146644i
$125$	−0.472136	−	1.45309i	−0.0422291	−	0.129968i
$126$		0			0
$127$	−7.73607	+	5.62058i	−0.686465	+	0.498746i	−0.875496	−	0.483225i	$-0.839465\pi$
$127$	−7.73607	+	5.62058i	−0.686465	+	0.498746i	0.189031	+	0.981971i	$0.439465\pi$
$128$	0.729466	−	0.810154i	0.0644763	−	0.0716082i
$129$		0			0
$130$	−19.1335	+	8.51880i	−1.67812	+	0.747148i
$131$	8.38197	−	14.5180i	0.732336	−	1.26844i	−0.223547	−	0.974693i	$-0.571764\pi$
$131$	8.38197	−	14.5180i	0.732336	−	1.26844i	0.955882	−	0.293750i	$-0.0949032\pi$
$132$		0			0
$133$	0.500000	+	0.866025i	0.0433555	+	0.0750939i
$134$	−12.7082	−	9.23305i	−1.09782	−	0.797614i
$135$		0			0
$136$	4.28115	+	13.1760i	0.367106	+	1.12984i
$137$	5.83022	+	2.59578i	0.498109	+	0.221772i	0.640384	−	0.768055i	$-0.278775\pi$
$137$	5.83022	+	2.59578i	0.498109	+	0.221772i	−0.142275	+	0.989827i	$0.545442\pi$
$138$		0			0
$139$	3.62717	+	0.770979i	0.307653	+	0.0653936i	0.359151	−	0.933280i	$-0.383066\pi$
$139$	3.62717	+	0.770979i	0.307653	+	0.0653936i	−0.0514983	+	0.998673i	$0.516400\pi$
$140$	10.5108	+	11.6735i	0.888328	+	0.986588i
$141$		0			0
$142$	−18.4443	−	31.9464i	−1.54781	−	2.68088i
$143$	−6.29180	+	5.25731i	−0.526146	+	0.439638i
$144$		0			0
$145$	−4.85410	−	3.52671i	−0.403111	−	0.292877i
$146$	17.5521	−	3.73082i	1.45263	−	0.308765i
$147$		0			0
$148$	−3.09010	−	29.4004i	−0.254005	−	2.41669i
$149$	0.750550	+	7.14101i	0.0614874	+	0.585014i	0.981277	+	0.192602i	$0.0616926\pi$
$149$	0.750550	+	7.14101i	0.0614874	+	0.585014i	−0.919790	+	0.392412i	$0.871641\pi$
$150$		0			0
$151$	11.0787	−	2.35486i	0.901574	−	0.191636i	0.266271	−	0.963898i	$-0.414208\pi$
$151$	11.0787	−	2.35486i	0.901574	−	0.191636i	0.635303	+	0.772263i	$0.280875\pi$
$152$	−6.04508	−	4.39201i	−0.490321	−	0.356239i
$153$		0			0
$154$	7.35410	+	4.61653i	0.592610	+	0.372010i
$155$	−2.61803	−	4.53457i	−0.210286	−	0.364225i
$156$		0			0
$157$	9.27020	+	10.2956i	0.739843	+	0.821679i	0.989175	−	0.146739i	$-0.0468778\pi$
$157$	9.27020	+	10.2956i	0.739843	+	0.821679i	−0.249332	+	0.968418i	$0.580211\pi$
$158$	24.4874	+	5.20495i	1.94811	+	0.414084i
$159$		0			0
$160$	−32.0879	−	14.2865i	−2.53677	−	1.12944i
$161$	0.736068	+	2.26538i	0.0580103	+	0.178537i
$162$		0			0
$163$	−5.89919	−	4.28601i	−0.462060	−	0.335706i	0.332279	−	0.943181i	$-0.392182\pi$
$163$	−5.89919	−	4.28601i	−0.462060	−	0.335706i	−0.794339	+	0.607475i	$0.792182\pi$
$164$	−27.8435	−	48.2263i	−2.17421	−	3.76584i
$165$		0			0
$166$	−18.6353	+	32.2772i	−1.44638	+	2.50520i
$167$	9.35111	−	4.16338i	0.723611	−	0.322172i	−0.0116727	−	0.999932i	$-0.503716\pi$
$167$	9.35111	−	4.16338i	0.723611	−	0.322172i	0.735284	+	0.677760i	$0.237049\pi$
$168$		0			0
$169$	−4.60934	+	5.11919i	−0.354564	+	0.393784i
$170$	12.7082	−	9.23305i	0.974675	−	0.708143i
$171$		0			0
$172$	−7.28115	−	22.4091i	−0.555183	−	1.70868i
$173$	−11.6496	+	2.47619i	−0.885701	+	0.188261i	−0.628233	−	0.778025i	$-0.716221\pi$
$173$	−11.6496	+	2.47619i	−0.885701	+	0.188261i	−0.257468	+	0.966287i	$0.582888\pi$
$174$		0			0
$175$	2.73607	−	4.73901i	0.206827	−	0.358235i
$176$	−32.3548	−	4.61542i	−2.43884	−	0.347900i
$177$		0			0
$178$	−3.07485	+	29.2553i	−0.230470	+	2.19277i
$179$	7.09017	−	21.8213i	0.529944	−	1.63100i	−0.224382	−	0.974501i	$-0.572036\pi$
$179$	7.09017	−	21.8213i	0.529944	−	1.63100i	0.754327	−	0.656499i	$-0.227964\pi$
$180$		0			0
$181$	17.0623	−	12.3965i	1.26823	−	0.921424i	0.269101	−	0.963112i	$-0.413274\pi$
$181$	17.0623	−	12.3965i	1.26823	−	0.921424i	0.999131	+	0.0416882i	$0.0132736\pi$
$182$	−5.91259	−	2.63245i	−0.438270	−	0.195131i
$183$		0			0
$184$	−11.9094	−	13.2268i	−0.877975	−	0.975090i
$185$	−18.0043	+	8.01605i	−1.32371	+	0.589352i
$186$		0			0
$187$	3.79594	−	4.83792i	0.277586	−	0.353784i
$188$	28.8541			2.10440
$189$		0			0
$190$	−2.61803	+	8.05748i	−0.189932	+	0.584551i
$191$	7.99228	−	8.87632i	0.578301	−	0.642268i	−0.381026	−	0.924564i	$-0.624429\pi$
$191$	7.99228	−	8.87632i	0.578301	−	0.642268i	0.959327	+	0.282296i	$0.0910960\pi$
$192$		0			0
$193$	1.14981	+	10.9397i	0.0827654	+	0.787460i	0.954646	+	0.297742i	$0.0962335\pi$
$193$	1.14981	+	10.9397i	0.0827654	+	0.787460i	−0.871881	+	0.489718i	$0.837100\pi$
$194$	−15.3649	−	3.26592i	−1.10314	−	0.234479i
$195$		0			0
$196$	3.04435	−	28.9651i	0.217454	−	2.06893i
$197$	−3.76393			−0.268169			−0.134085	−	0.990970i	$-0.542809\pi$
$197$	−3.76393			−0.268169			−0.134085	+	0.990970i	$0.542809\pi$
$198$		0			0
$199$	−13.8541			−0.982091			−0.491046	−	0.871134i	$-0.663385\pi$
$199$	−13.8541			−0.982091			−0.491046	+	0.871134i	$0.663385\pi$
$200$	−4.27402	+	40.6646i	−0.302219	+	2.87542i
$201$		0			0
$202$	1.20906	+	0.256993i	0.0850689	+	0.0180820i
$203$	−0.193806	−	1.84395i	−0.0136025	−	0.129420i
$204$		0			0
$205$	−24.8412	+	27.5890i	−1.73499	+	1.92690i
$206$	−4.66312	+	14.3516i	−0.324895	+	0.999924i
$207$		0			0
$208$	24.3607			1.68911
$209$	−0.122602	+	3.31436i	−0.00848058	+	0.229259i
$210$		0			0
$211$	10.5312	−	4.68880i	0.725000	−	0.322791i	−0.0108449	−	0.999941i	$-0.503452\pi$
$211$	10.5312	−	4.68880i	0.725000	−	0.322791i	0.735844	+	0.677151i	$0.236785\pi$
$212$	23.0291	+	25.5764i	1.58164	+	1.75659i
$213$		0			0
$214$	35.9578	+	16.0094i	2.45802	+	1.09438i
$215$	−12.7082	+	9.23305i	−0.866692	+	0.629689i
$216$		0			0
$217$	0.500000	−	1.53884i	0.0339422	−	0.104463i
$218$	−3.79130	+	36.0718i	−0.256779	+	2.44309i
$219$		0			0
$220$	8.94065	+	51.3253i	0.602778	+	3.46035i
$221$	−2.29180	+	3.96951i	−0.154163	+	0.267018i
$222$		0			0
$223$	−22.0148	+	4.67938i	−1.47422	+	0.313355i	−0.873782	−	0.486319i	$-0.838339\pi$
$223$	−22.0148	+	4.67938i	−1.47422	+	0.313355i	−0.600436	+	0.799673i	$0.705006\pi$
$224$	−3.35410	−	10.3229i	−0.224105	−	0.689725i
$225$		0			0
$226$	27.0344	−	19.6417i	1.79830	−	1.30654i
$227$	9.62341	−	10.6879i	0.638728	−	0.709380i	−0.333674	−	0.942688i	$-0.608289\pi$
$227$	9.62341	−	10.6879i	0.638728	−	0.709380i	0.972403	+	0.233309i	$0.0749552\pi$
$228$		0			0
$229$	−11.1273	+	4.95419i	−0.735312	+	0.327382i	−0.740000	−	0.672607i	$-0.765175\pi$
$229$	−11.1273	+	4.95419i	−0.735312	+	0.327382i	0.00468769	+	0.999989i	$0.498508\pi$
$230$	−10.0902	+	17.4767i	−0.665326	+	1.15238i
$231$		0			0
$232$	6.92705	+	11.9980i	0.454783	+	0.787708i
$233$	23.5623	+	17.1190i	1.54362	+	1.12150i	0.948015	+	0.318225i	$0.103087\pi$
$233$	23.5623	+	17.1190i	1.54362	+	1.12150i	0.595603	+	0.803279i	$0.296913\pi$
$234$		0			0
$235$	−5.94427	−	18.2946i	−0.387762	−	1.19341i
$236$	2.74064	+	1.22021i	0.178400	+	0.0794289i
$237$		0			0
$238$	4.74803	+	1.00922i	0.307769	+	0.0654183i
$239$	−1.02234	−	1.13542i	−0.0661297	−	0.0734445i	0.709172	−	0.705035i	$-0.249069\pi$
$239$	−1.02234	−	1.13542i	−0.0661297	−	0.0734445i	−0.775302	+	0.631591i	$0.782402\pi$
$240$		0			0
$241$	−13.4164	−	23.2379i	−0.864227	−	1.49688i	−0.867813	−	0.496891i	$-0.834475\pi$
$241$	−13.4164	−	23.2379i	−0.864227	−	1.49688i	0.00358606	−	0.999994i	$-0.498859\pi$
$242$	12.5172	+	25.9358i	0.804637	+	1.66722i
$243$		0			0
$244$	−16.2812	−	11.8290i	−1.04229	−	0.757271i
$245$	−18.9921	+	4.03690i	−1.21336	+	0.257908i
$246$		0			0
$247$	−0.258409	−	2.45859i	−0.0164421	−	0.156437i
$248$	1.26377	+	12.0239i	0.0802493	+	0.763521i
$249$		0			0
$250$	3.91259	−	0.831647i	0.247454	−	0.0525980i
$251$	0.354102	+	0.257270i	0.0223507	+	0.0162387i	0.598905	−	0.800820i	$-0.295603\pi$
$251$	0.354102	+	0.257270i	0.0223507	+	0.0162387i	−0.576554	+	0.817059i	$0.695603\pi$
$252$		0			0
$253$	−1.92705	+	7.66145i	−0.121153	+	0.481671i
$254$	−12.5172	−	21.6805i	−0.785400	−	1.36035i
$255$		0			0
$256$	−9.74408	−	10.8219i	−0.609005	−	0.676369i
$257$	−25.5200	−	5.42445i	−1.59190	−	0.338368i	−0.675101	−	0.737725i	$-0.735900\pi$
$257$	−25.5200	−	5.42445i	−1.59190	−	0.338368i	−0.916795	+	0.399357i	$0.869233\pi$
$258$		0			0
$259$	−5.56365	−	2.47710i	−0.345708	−	0.153919i
$260$	−12.0000	−	36.9322i	−0.744208	−	2.29044i
$261$		0			0
$262$	35.5066	+	25.7970i	2.19360	+	1.59375i
$263$	0.354102	+	0.613323i	0.0218349	+	0.0378191i	0.876736	−	0.480971i	$-0.159716\pi$
$263$	0.354102	+	0.613323i	0.0218349	+	0.0378191i	−0.854902	+	0.518790i	$0.826383\pi$
$264$		0			0
$265$	11.4721	−	19.8703i	0.704728	−	1.22062i
$266$	−2.39169	+	1.06485i	−0.146644	+	0.0652902i
$267$		0			0
$268$	19.4882	−	21.6438i	1.19043	−	1.32211i
$269$	9.92705	−	7.21242i	0.605263	−	0.439749i	−0.242480	−	0.970156i	$-0.577961\pi$
$269$	9.92705	−	7.21242i	0.605263	−	0.439749i	0.847743	+	0.530407i	$0.177961\pi$
$270$		0			0
$271$	4.70820	+	14.4904i	0.286003	+	0.880227i	0.986096	+	0.166175i	$0.0531418\pi$
$271$	4.70820	+	14.4904i	0.286003	+	0.880227i	−0.700093	+	0.714051i	$0.746858\pi$
$272$	−17.8713	+	3.79865i	−1.08360	+	0.230327i
$273$		0			0
$274$	−8.35410	+	14.4697i	−0.504690	+	0.874148i
$275$	16.0422	−	8.48729i	0.967382	−	0.511803i
$276$		0			0
$277$	1.54325	−	14.6831i	0.0927250	−	0.882219i	−0.844983	−	0.534794i	$-0.820389\pi$
$277$	1.54325	−	14.6831i	0.0927250	−	0.882219i	0.937708	−	0.347425i	$-0.112944\pi$
$278$	−3.00000	+	9.23305i	−0.179928	+	0.553762i
$279$		0			0
$280$	−19.5623	+	14.2128i	−1.16907	+	0.849380i
$281$	−5.77931	−	2.57311i	−0.344764	−	0.153499i	0.227048	−	0.973884i	$-0.427093\pi$
$281$	−5.77931	−	2.57311i	−0.344764	−	0.153499i	−0.571812	+	0.820385i	$0.693759\pi$
$282$		0			0
$283$	−11.3752	−	12.6335i	−0.676187	−	0.750981i	0.303211	−	0.952924i	$-0.401941\pi$
$283$	−11.3752	−	12.6335i	−0.676187	−	0.750981i	−0.979397	+	0.201942i	$0.935275\pi$
$284$	62.4821	−	27.8188i	3.70763	−	1.65074i
$285$		0			0
$286$	−11.9666	−	17.8206i	−0.707601	−	1.05375i
$287$	−11.4721			−0.677179
$288$		0			0
$289$	−4.19098	+	12.8985i	−0.246528	+	0.758736i
$290$	10.5108	−	11.6735i	0.617218	−	0.685490i
$291$		0			0
$292$	3.47772	+	33.0883i	0.203518	+	1.93634i
$293$	−6.67063	−	1.41789i	−0.389703	−	0.0828338i	0.00889341	−	0.999960i	$-0.497169\pi$
$293$	−6.67063	−	1.41789i	−0.389703	−	0.0828338i	−0.398596	+	0.917127i	$0.630502\pi$
$294$		0			0
$295$	0.209057	−	1.98904i	0.0121718	−	0.115807i
$296$	45.5066			2.64502
$297$		0			0
$298$	−18.7984			−1.08896
$299$	0.615520	−	5.85629i	0.0355965	−	0.338678i
$300$		0			0
$301$	−4.74803	−	1.00922i	−0.273672	−	0.0581707i
$302$	3.09953	+	29.4900i	0.178358	+	1.69696i
$303$		0			0
$304$	6.59368	−	7.32302i	0.378174	−	0.420004i
$305$	−4.14590	+	12.7598i	−0.237393	+	0.730622i
$306$		0			0
$307$	1.14590			0.0653999			0.0326999	−	0.999465i	$-0.489589\pi$
$307$	1.14590			0.0653999			0.0326999	+	0.999465i	$0.489589\pi$
$308$	−9.93789	+	12.6658i	−0.566264	+	0.721704i
$309$		0			0
$310$	12.5231	−	5.57563i	0.711262	−	0.316674i
$311$	4.80459	+	5.33603i	0.272443	+	0.302579i	0.863804	−	0.503829i	$-0.168076\pi$
$311$	4.80459	+	5.33603i	0.272443	+	0.302579i	−0.591361	+	0.806407i	$0.701409\pi$
$312$		0			0
$313$	−4.99904	−	2.22572i	−0.282563	−	0.125805i	0.260562	−	0.965457i	$-0.416092\pi$
$313$	−4.99904	−	2.22572i	−0.282563	−	0.125805i	−0.543125	+	0.839652i	$0.682759\pi$
$314$	−29.3435	+	21.3193i	−1.65595	+	1.20312i
$315$		0			0
$316$	−14.3435	+	44.1446i	−0.806883	+	2.48333i
$317$	0.319411	−	3.03899i	0.0179399	−	0.170687i	−0.981883	−	0.189486i	$-0.939318\pi$
$317$	0.319411	−	3.03899i	0.0179399	−	0.170687i	0.999823	+	0.0187996i	$0.00598445\pi$
$318$		0			0
$319$	2.70713	−	5.52142i	0.151570	−	0.309140i
$320$	14.0902	−	24.4049i	0.787664	−	1.36427i
$321$		0			0
$322$	−6.09979	+	1.29655i	−0.339928	+	0.0722540i
$323$	0.572949	+	1.76336i	0.0318797	+	0.0981157i
$324$		0			0
$325$	−10.9443	+	7.95148i	−0.607079	+	0.441069i
$326$	12.7738	−	14.1868i	0.707476	−	0.785732i
$327$		0			0
$328$	78.3104	−	34.8660i	4.32397	−	1.92515i
$329$	2.97214	−	5.14789i	0.163859	−	0.283812i
$330$		0			0
$331$	6.20820	+	10.7529i	0.341234	+	0.591034i	0.984662	−	0.174472i	$-0.0558219\pi$
$331$	6.20820	+	10.7529i	0.341234	+	0.591034i	−0.643428	+	0.765506i	$0.722489\pi$
$332$	−55.9058	−	40.6179i	−3.06823	−	2.22920i
$333$		0			0
$334$	8.28115	+	25.4868i	0.453125	+	1.39457i
$335$	−17.7378	−	7.89736i	−0.969118	−	0.431479i
$336$		0			0
$337$	2.47262	+	0.525572i	0.134692	+	0.0286298i	0.274765	−	0.961512i	$-0.411400\pi$
$337$	2.47262	+	0.525572i	0.134692	+	0.0286298i	−0.140072	+	0.990141i	$0.544733\pi$
$338$	−12.0674	−	13.4022i	−0.656380	−	0.728984i
$339$		0			0
$340$	14.5623	+	25.2227i	0.789752	+	1.36789i
$341$	4.11803	−	3.44095i	0.223004	−	0.186338i
$342$		0			0
$343$	−10.5172	−	7.64121i	−0.567877	−	0.412586i
$344$	35.4779	−	7.54106i	1.91284	−	0.406587i
$345$		0			0
$346$	−3.25923	−	31.0095i	−0.175217	−	1.66708i
$347$	2.81062	+	26.7412i	0.150882	+	1.43555i	0.763828	+	0.645420i	$0.223318\pi$
$347$	2.81062	+	26.7412i	0.150882	+	1.43555i	−0.612946	+	0.790125i	$0.710016\pi$
$348$		0			0
$349$	10.6169	−	2.25669i	0.568310	−	0.120798i	0.0852099	−	0.996363i	$-0.472844\pi$
$349$	10.6169	−	2.25669i	0.568310	−	0.120798i	0.483100	+	0.875565i	$0.339511\pi$
$350$	11.5902	+	8.42075i	0.619521	+	0.450108i
$351$		0			0
$352$	8.78115	−	34.9116i	0.468037	−	1.86079i
$353$	5.20820	+	9.02087i	0.277205	+	0.480133i	0.970689	−	0.240339i	$-0.0772586\pi$
$353$	5.20820	+	9.02087i	0.277205	+	0.480133i	−0.693484	+	0.720472i	$0.743925\pi$
$354$		0			0
$355$	−30.5102	−	33.8850i	−1.61931	−	1.79843i
$356$	−53.3492	−	11.3397i	−2.82750	−	0.601004i
$357$		0			0
$358$	54.8757	+	24.4322i	2.90027	+	1.29128i
$359$	4.98936	+	15.3557i	0.263328	+	0.810441i	0.992074	+	0.125656i	$0.0401037\pi$
$359$	4.98936	+	15.3557i	0.263328	+	0.810441i	−0.728746	+	0.684784i	$0.759896\pi$
$360$		0			0
$361$	14.5623	+	10.5801i	0.766437	+	0.556849i
$362$	27.6074	+	47.8174i	1.45101	+	2.51323i
$363$		0			0
$364$	6.00000	−	10.3923i	0.314485	−	0.544705i
$365$	20.2627	−	9.02156i	1.06060	−	0.472210i
$366$		0			0
$367$	0.473881	−	0.526298i	0.0247364	−	0.0274725i	−0.730650	−	0.682753i	$-0.760783\pi$
$367$	0.473881	−	0.526298i	0.0247364	−	0.0274725i	0.755386	+	0.655280i	$0.227449\pi$
$368$	18.9894	−	13.7966i	0.989889	−	0.719196i
$369$		0			0
$370$	−15.9443	−	49.0714i	−0.828903	−	2.55110i
$371$	6.93523	−	1.47413i	0.360059	−	0.0765330i
$372$		0			0
$373$	−12.8262	+	22.2157i	−0.664117	+	1.15029i	0.315406	+	0.948957i	$0.397859\pi$
$373$	−12.8262	+	22.2157i	−0.664117	+	1.15029i	−0.979524	+	0.201328i	$0.935474\pi$
$374$	11.5577	+	11.2074i	0.597633	+	0.579520i
$375$		0			0
$376$	−4.64278	+	44.1731i	−0.239433	+	2.27805i
$377$	−1.41641	+	4.35926i	−0.0729487	+	0.224513i
$378$		0			0
$379$	7.11803	−	5.17155i	0.365629	−	0.265645i	−0.389767	−	0.920913i	$-0.627445\pi$
$379$	7.11803	−	5.17155i	0.365629	−	0.265645i	0.755396	+	0.655269i	$0.227445\pi$
$380$	−14.3502	−	6.38910i	−0.736148	−	0.327754i
$381$		0			0
$382$	20.9241	+	23.2385i	1.07057	+	1.18899i
$383$	−12.0094	+	5.34692i	−0.613650	+	0.273215i	−0.689935	−	0.723871i	$-0.742361\pi$
$383$	−12.0094	+	5.34692i	−0.613650	+	0.273215i	0.0762846	+	0.997086i	$0.475694\pi$
$384$		0			0
$385$	10.0779	+	3.69169i	0.513620	+	0.188146i
$386$	−28.7984			−1.46580
$387$		0			0
$388$	9.00000	−	27.6992i	0.456906	−	1.40621i
$389$	−5.78964	+	6.43004i	−0.293546	+	0.326016i	−0.871820	−	0.489827i	$-0.837060\pi$
$389$	−5.78964	+	6.43004i	−0.293546	+	0.326016i	0.578274	+	0.815843i	$0.303727\pi$
$390$		0			0
$391$	0.461640	+	4.39221i	0.0233462	+	0.222124i
$392$	43.8531	+	9.32127i	2.21492	+	0.470795i
$393$		0			0
$394$	1.03003	−	9.80012i	0.0518924	−	0.493723i
$395$	30.9443			1.55698
$396$		0			0
$397$	38.1246			1.91342			0.956710	−	0.291044i	$-0.0940026\pi$
$397$	38.1246			1.91342			0.956710	+	0.291044i	$0.0940026\pi$
$398$	3.79130	−	36.0718i	0.190041	−	1.80812i
$399$		0			0
$400$	−52.7446	−	11.2112i	−2.63723	−	0.560561i
$401$	−0.581419	−	5.53184i	−0.0290347	−	0.276247i	−0.999401	−	0.0346079i	$-0.988982\pi$
$401$	−0.581419	−	5.53184i	−0.0290347	−	0.276247i	0.970366	−	0.241639i	$-0.0776849\pi$
$402$		0			0
$403$	−2.67652	+	2.97258i	−0.133327	+	0.148075i
$404$	−0.708204	+	2.17963i	−0.0352345	+	0.108441i
$405$		0			0
$406$	4.85410			0.240905
$407$	−11.2604	−	16.7689i	−0.558156	−	0.831203i
$408$		0			0
$409$	7.98680	−	3.55595i	0.394922	−	0.175831i	−0.199661	−	0.979865i	$-0.563984\pi$
$409$	7.98680	−	3.55595i	0.394922	−	0.175831i	0.594583	+	0.804034i	$0.297317\pi$
$410$	−65.0351	−	72.2288i	−3.21186	−	3.56713i
$411$		0			0
$412$	−25.5598	−	11.3800i	−1.25924	−	0.560651i
$413$	0.500000	−	0.363271i	0.0246034	−	0.0178754i
$414$		0			0
$415$	−14.2361	+	43.8141i	−0.698821	+	2.15075i
$416$	−2.80479	+	26.6858i	−0.137516	+	1.30838i
$417$		0			0
$418$	−8.59602	−	1.22622i	−0.420445	−	0.0599765i
$419$	−1.54508	+	2.67617i	−0.0754823	+	0.130739i	−0.901296	−	0.433204i	$-0.857383\pi$
$419$	−1.54508	+	2.67617i	−0.0754823	+	0.130739i	0.825814	+	0.563943i	$0.190716\pi$
$420$		0			0
$421$	−5.63798	+	1.19839i	−0.274778	+	0.0584059i	−0.343240	−	0.939248i	$-0.611524\pi$
$421$	−5.63798	+	1.19839i	−0.274778	+	0.0584059i	0.0684615	+	0.997654i	$0.478191\pi$
$422$	9.32624	+	28.7032i	0.453994	+	1.39725i
$423$		0			0
$424$	−42.8607	+	31.1401i	−2.08150	+	1.51230i
$425$	6.78893	−	7.53987i	0.329312	−	0.365737i
$426$		0			0
$427$	−3.78747	+	1.68629i	−0.183288	+	0.0816052i
$428$	−36.4894	+	63.2014i	−1.76378	+	3.05496i
$429$		0			0
$430$	−20.5623	−	35.6150i	−0.991602	−	1.71751i
$431$	19.4721	+	14.1473i	0.937940	+	0.681453i	0.947924	−	0.318497i	$-0.103178\pi$
$431$	19.4721	+	14.1473i	0.937940	+	0.681453i	−0.00998408	+	0.999950i	$0.503178\pi$
$432$		0			0
$433$	−8.57295	−	26.3848i	−0.411990	−	1.26797i	−0.914916	−	0.403644i	$-0.867743\pi$
$433$	−8.57295	−	26.3848i	−0.411990	−	1.26797i	0.502926	−	0.864329i	$-0.332257\pi$
$434$	3.86984	+	1.72296i	0.185758	+	0.0827049i
$435$		0			0
$436$	−65.7797	−	13.9819i	−3.15027	−	0.669612i
$437$	−1.59385	−	1.77015i	−0.0762440	−	0.0846776i
$438$		0			0
$439$	−6.35410	−	11.0056i	−0.303265	−	0.525270i	0.673609	−	0.739088i	$-0.264743\pi$
$439$	−6.35410	−	11.0056i	−0.303265	−	0.525270i	−0.976873	+	0.213818i	$0.931410\pi$
$440$	−80.0132	+	5.42882i	−3.81448	+	0.258809i
$441$		0			0
$442$	−9.70820	−	7.05342i	−0.461772	−	0.335497i
$443$	3.16535	−	0.672816i	0.150390	−	0.0319665i	−0.132101	−	0.991236i	$-0.542172\pi$
$443$	3.16535	−	0.672816i	0.150390	−	0.0319665i	0.282492	+	0.959270i	$0.408839\pi$
$444$		0			0
$445$	3.80073	+	36.1615i	0.180172	+	1.71422i
$446$	−6.15913	−	58.6002i	−0.291643	−	2.77480i
$447$		0			0
$448$	8.51791	−	1.81054i	0.402433	−	0.0855399i
$449$	−1.19098	−	0.865300i	−0.0562060	−	0.0408360i	0.559328	−	0.828947i	$-0.311059\pi$
$449$	−1.19098	−	0.865300i	−0.0562060	−	0.0408360i	−0.615533	+	0.788111i	$0.711059\pi$
$450$		0			0
$451$	−32.2254	−	20.2295i	−1.51744	−	0.952568i
$452$	30.9787	+	53.6567i	1.45712	+	2.52380i
$453$		0			0
$454$	25.1944	+	27.9812i	1.18243	+	1.31322i
$455$	−7.82518	−	1.66329i	−0.366850	−	0.0779764i
$456$		0			0
$457$	−0.913545	−	0.406737i	−0.0427339	−	0.0190263i	0.385258	−	0.922809i	$-0.374112\pi$
$457$	−0.913545	−	0.406737i	−0.0427339	−	0.0190263i	−0.427992	+	0.903782i	$0.640779\pi$
$458$	−9.85410	−	30.3278i	−0.460452	−	1.41713i
$459$		0			0
$460$	−30.2705	−	21.9928i	−1.41137	−	1.02542i
$461$	−11.4271	−	19.7922i	−0.532211	−	0.921816i	−0.999293	−	0.0376022i	$-0.988028\pi$
$461$	−11.4271	−	19.7922i	−0.532211	−	0.921816i	0.467082	−	0.884214i	$-0.345305\pi$
$462$		0			0
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	−0.993105	−	0.117230i	$-0.962599\pi$
$463$	−8.50000	+	14.7224i	−0.395029	+	0.684209i	0.598076	+	0.801439i	$0.295932\pi$
$464$	−16.6909	+	7.43129i	−0.774857	+	0.344989i
$465$		0			0
$466$	−51.0207	+	56.6642i	−2.36349	+	2.62492i
$467$	−4.23607	+	3.07768i	−0.196022	+	0.142418i	−0.681467	−	0.731849i	$-0.738658\pi$
$467$	−4.23607	+	3.07768i	−0.196022	+	0.142418i	0.485445	+	0.874267i	$0.338658\pi$
$468$		0			0
$469$	−1.85410	−	5.70634i	−0.0856145	−	0.263494i
$470$	49.2602	−	10.4706i	2.27220	−	0.482972i
$471$		0			0
$472$	−2.30902	+	3.99933i	−0.106281	+	0.184084i
$473$	−11.5577	−	11.2074i	−0.531422	−	0.515316i
$474$		0			0
$475$	−0.571994	+	5.44216i	−0.0262449	+	0.249703i
$476$	−2.78115	+	8.55951i	−0.127474	+	0.392324i
$477$		0			0
$478$	3.23607	−	2.35114i	0.148014	−	0.107539i
$479$	14.8324	+	6.60380i	0.677709	+	0.301735i	0.716576	−	0.697509i	$-0.245708\pi$
$479$	14.8324	+	6.60380i	0.677709	+	0.301735i	−0.0388671	+	0.999244i	$0.512375\pi$
$480$		0			0
$481$	10.0742	+	11.1886i	0.459346	+	0.510156i
$482$	64.1759	−	28.5729i	2.92313	−	1.30146i
$483$		0			0
$484$	−50.2501	+	18.0545i	−2.28410	+	0.820661i
$485$	−19.4164			−0.881654
$486$		0			0
$487$	10.5000	−	32.3157i	0.475800	−	1.46436i	−0.369075	−	0.929400i	$-0.620325\pi$
$487$	10.5000	−	32.3157i	0.475800	−	1.46436i	0.844875	−	0.534963i	$-0.179675\pi$
$488$	20.7288	−	23.0217i	0.938349	−	1.04214i
$489$		0			0
$490$	−5.31348	−	50.5543i	−0.240038	−	2.28381i
$491$	−8.14429	−	1.73112i	−0.367547	−	0.0781245i	0.0204359	−	0.999791i	$-0.493495\pi$
$491$	−8.14429	−	1.73112i	−0.367547	−	0.0781245i	−0.387983	+	0.921667i	$0.626828\pi$
$492$		0			0
$493$	0.359337	−	3.41886i	0.0161837	−	0.153978i
$494$	6.47214			0.291195
$495$		0			0
$496$	−15.9443			−0.715919
$497$	1.47282	−	14.0130i	0.0660652	−	0.628568i
$498$		0			0
$499$	−11.3305	−	2.40836i	−0.507221	−	0.107813i	−0.0528088	−	0.998605i	$-0.516817\pi$
$499$	−11.3305	−	2.40836i	−0.507221	−	0.107813i	−0.454412	+	0.890791i	$0.650151\pi$
$500$	0.775226	+	7.37578i	0.0346691	+	0.329855i
$501$		0			0
$502$	−0.766755	+	0.851568i	−0.0342220	+	0.0380073i
$503$	5.70820	−	17.5680i	0.254516	−	0.783320i	−0.739408	−	0.673257i	$-0.764895\pi$
$503$	5.70820	−	17.5680i	0.254516	−	0.783320i	0.993925	−	0.110063i	$-0.0351053\pi$
$504$		0			0
$505$	1.52786			0.0679891
$506$	−19.4207	−	7.11407i	−0.863356	−	0.316259i
$507$		0			0
$508$	42.4035	−	18.8793i	1.88135	−	0.837631i
$509$	3.22498	+	3.58171i	0.142945	+	0.158756i	0.810366	−	0.585924i	$-0.199268\pi$
$509$	3.22498	+	3.58171i	0.142945	+	0.158756i	−0.667421	+	0.744681i	$0.732602\pi$
$510$		0			0
$511$	6.26153	+	2.78781i	0.276994	+	0.123326i
$512$	32.6074	−	23.6907i	1.44106	−	1.04699i
$513$		0			0
$514$	21.1074	−	64.9619i	0.931007	−	2.86535i
$515$	−1.94971	+	18.5503i	−0.0859147	+	0.817424i
$516$		0			0
$517$	17.4263	−	9.21958i	0.766410	−	0.405477i
$518$	7.97214	−	13.8081i	0.350276	−	0.606695i
$519$		0			0
$520$	58.4708	−	12.4284i	2.56411	−	0.545019i
$521$	−1.34752	−	4.14725i	−0.0590361	−	0.181694i	0.917190	−	0.398451i	$-0.130452\pi$
$521$	−1.34752	−	4.14725i	−0.0590361	−	0.181694i	−0.976226	+	0.216757i	$0.930452\pi$
$522$		0			0
$523$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$523$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$524$	−54.4497	+	60.4725i	−2.37865	+	2.64176i
$525$		0			0
$526$	−1.69381	+	0.754131i	−0.0738535	+	0.0328817i
$527$	1.50000	−	2.59808i	0.0653410	−	0.113174i
$528$		0			0
$529$	8.66312	+	15.0050i	0.376657	+	0.652390i
$530$	48.5967	+	35.3076i	2.11091	+	1.53366i
$531$		0			0
$532$	−1.50000	−	4.61653i	−0.0650332	−	0.200152i
$533$	25.9088	+	11.5353i	1.12223	+	0.499651i
$534$		0			0
$535$	47.5893	+	10.1154i	2.05746	+	0.437328i
$536$	29.9990	+	33.3173i	1.29576	+	1.43909i
$537$		0			0
$538$	16.0623	+	27.8207i	0.692495	+	1.19944i
$539$	−7.41641	−	18.4661i	−0.319447	−	0.795391i
$540$		0			0
$541$	18.6803	+	13.5721i	0.803131	+	0.583508i	0.911831	−	0.410566i	$-0.134669\pi$
$541$	18.6803	+	13.5721i	0.803131	+	0.583508i	−0.108700	+	0.994075i	$0.534669\pi$
$542$	−39.0169	+	8.29329i	−1.67592	+	0.356228i
$543$		0			0
$544$	−2.10359	−	20.0144i	−0.0901909	−	0.858109i
$545$	4.68631	+	44.5872i	0.200739	+	1.90991i
$546$		0			0
$547$	16.3094	−	3.46667i	0.697340	−	0.148224i	0.154416	−	0.988006i	$-0.450651\pi$
$547$	16.3094	−	3.46667i	0.697340	−	0.148224i	0.542924	+	0.839782i	$0.317317\pi$
$548$	−25.0623	−	18.2088i	−1.07061	−	0.777843i
$549$		0			0
$550$	17.7082	+	44.0916i	0.755080	+	1.88007i
$551$	0.927051	+	1.60570i	0.0394937	+	0.0684051i
$552$		0			0
$553$	6.39843	+	7.10618i	0.272089	+	0.302185i
$554$	37.8078	+	8.03630i	1.60630	+	0.341430i
$555$		0			0
$556$	−16.4438	−	7.32126i	−0.697373	−	0.310491i
$557$	−9.47214	−	29.1522i	−0.401347	−	1.23522i	−0.923907	−	0.382617i	$-0.875023\pi$
$557$	−9.47214	−	29.1522i	−0.401347	−	1.23522i	0.522560	−	0.852603i	$-0.324977\pi$
$558$		0			0
$559$	9.70820	+	7.05342i	0.410613	+	0.298328i
$560$	−15.9443	−	27.6163i	−0.673768	−	1.16700i
$561$		0			0
$562$	8.28115	−	14.3434i	0.349319	−	0.605039i
$563$	−38.6475	+	17.2070i	−1.62880	+	0.725187i	−0.998683	−	0.0513142i	$-0.983659\pi$
$563$	−38.6475	+	17.2070i	−1.62880	+	0.725187i	−0.630115	+	0.776502i	$0.716992\pi$
$564$		0			0
$565$	27.6384	−	30.6956i	1.16276	−	1.29137i
$566$	36.0066	−	26.1603i	1.51347	−	1.09960i
$567$		0			0
$568$	32.5344	+	100.131i	1.36511	+	4.20139i
$569$	13.8913	−	2.95268i	0.582353	−	0.123783i	0.0926905	−	0.995695i	$-0.470453\pi$
$569$	13.8913	−	2.95268i	0.582353	−	0.123783i	0.489663	+	0.871912i	$0.337120\pi$
$570$		0			0
$571$	13.7361	−	23.7916i	0.574837	−	0.995646i	−0.421223	−	0.906957i	$-0.638399\pi$
$571$	13.7361	−	23.7916i	0.574837	−	0.995646i	0.996059	−	0.0886889i	$-0.0282677\pi$
$572$	35.1794	−	18.6120i	1.47093	−	0.778208i
$573$		0			0
$574$	3.13945	−	29.8699i	0.131038	−	1.24675i
$575$	−4.02786	+	12.3965i	−0.167974	+	0.516969i
$576$		0			0
$577$	−6.94427	+	5.04531i	−0.289094	+	0.210039i	−0.722874	−	0.690980i	$-0.757179\pi$
$577$	−6.94427	+	5.04531i	−0.289094	+	0.210039i	0.433780	+	0.901019i	$0.357179\pi$
$578$	−32.4369	−	14.4418i	−1.34920	−	0.600701i
$579$		0			0
$580$	19.4882	+	21.6438i	0.809202	+	0.898710i
$581$	−13.0053	+	5.79033i	−0.539551	+	0.240223i
$582$		0			0
$583$	22.0806	+	8.08843i	0.914485	+	0.334988i
$584$	−51.2148			−2.11928
$585$		0			0
$586$	5.51722	−	16.9803i	0.227914	−	0.701448i
$587$	8.97733	−	9.97033i	0.370534	−	0.411520i	−0.528825	−	0.848731i	$-0.677367\pi$
$587$	8.97733	−	9.97033i	0.370534	−	0.411520i	0.899359	+	0.437211i	$0.144034\pi$
$588$		0			0
$589$	0.169131	+	1.60917i	0.00696891	+	0.0663047i
$590$	5.12165	+	1.08864i	0.210855	+	0.0448186i
$591$		0			0
$592$	−6.27308	+	59.6844i	−0.257822	+	2.45301i
$593$	−6.94427			−0.285167			−0.142584	−	0.989783i	$-0.545541\pi$
$593$	−6.94427			−0.285167			−0.142584	+	0.989783i	$0.545541\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	3.64325	−	34.6632i	0.149233	−	1.41986i
$597$		0			0
$598$	15.0795	+	3.20525i	0.616648	+	0.131072i
$599$	3.27808	+	31.1889i	0.133939	+	1.27434i	0.830570	+	0.556914i	$0.188015\pi$
$599$	3.27808	+	31.1889i	0.133939	+	1.27434i	−0.696631	+	0.717429i	$0.745319\pi$
$600$		0			0
$601$	−5.70625	+	6.33744i	−0.232763	+	0.258509i	−0.848199	−	0.529677i	$-0.822313\pi$
$601$	−5.70625	+	6.33744i	−0.232763	+	0.258509i	0.615436	+	0.788187i	$0.288980\pi$
$602$	3.92705	−	12.0862i	0.160055	−	0.492598i
$603$		0			0
$604$	−54.9787			−2.23705
$605$	21.7994	+	28.1410i	0.886270	+	1.14409i
$606$		0			0
$607$	−27.7868	+	12.3715i	−1.12783	+	0.502142i	−0.883912	−	0.467653i	$-0.845100\pi$
$607$	−27.7868	+	12.3715i	−1.12783	+	0.502142i	−0.243918	+	0.969796i	$0.578433\pi$
$608$	7.26281	+	8.06617i	0.294546	+	0.327126i
$609$		0			0
$610$	−32.0879	−	14.2865i	−1.29920	−	0.578442i
$611$	−11.8885	+	8.63753i	−0.480959	+	0.349437i
$612$		0			0
$613$	4.06231	−	12.5025i	0.164075	−	0.504971i	−0.834892	−	0.550414i	$-0.814470\pi$
$613$	4.06231	−	12.5025i	0.164075	−	0.504971i	0.998967	+	0.0454430i	$0.0144699\pi$
$614$	−0.313585	+	2.98357i	−0.0126553	+	0.120407i
$615$		0			0
$616$	−17.7912	−	17.2520i	−0.716829	−	0.695104i
$617$	21.0795	−	36.5108i	0.848630	−	1.46987i	−0.0338015	−	0.999429i	$-0.510761\pi$
$617$	21.0795	−	36.5108i	0.848630	−	1.46987i	0.882431	−	0.470441i	$-0.155905\pi$
$618$		0			0
$619$	−7.27516	+	1.54638i	−0.292413	+	0.0621544i	−0.351783	−	0.936082i	$-0.614424\pi$
$619$	−7.27516	+	1.54638i	−0.292413	+	0.0621544i	0.0593692	+	0.998236i	$0.481091\pi$
$620$	7.85410	+	24.1724i	0.315428	+	0.970789i
$621$		0			0
$622$	−15.2082	+	11.0494i	−0.609793	+	0.443041i
$623$	−7.51840	+	8.35003i	−0.301218	+	0.334537i
$624$		0			0
$625$	−20.4784	+	9.11757i	−0.819136	+	0.364703i
$626$	7.16312	−	12.4069i	0.286296	−	0.495879i
$627$		0			0
$628$	−33.6246	−	58.2395i	−1.34177	−	2.32401i
$629$	−9.13525	−	6.63715i	−0.364246	−	0.264641i
$630$		0			0
$631$	7.69098	+	23.6704i	0.306173	+	0.942304i	0.979237	+	0.202720i	$0.0649780\pi$
$631$	7.69098	+	23.6704i	0.306173	+	0.942304i	−0.673064	+	0.739585i	$0.735022\pi$
$632$	−65.2736	−	29.0617i	−2.59644	−	1.15601i
$633$		0			0
$634$	7.82518	+	1.66329i	0.310778	+	0.0660578i
$635$	−20.7058	−	22.9961i	−0.821683	−	0.912571i
$636$		0			0
$637$	7.41641	+	12.8456i	0.293849	+	0.508961i
$638$	13.6353	+	8.55951i	0.539825	+	0.338874i
$639$		0			0
$640$	2.85410	+	2.07363i	0.112818	+	0.0819673i
$641$	34.6762	−	7.37065i	1.36963	−	0.291123i	0.536357	−	0.843991i	$-0.319800\pi$
$641$	34.6762	−	7.37065i	1.36963	−	0.291123i	0.833269	+	0.552868i	$0.186467\pi$
$642$		0			0
$643$	0.0152505	+	0.145099i	0.000601421	+	0.00572214i	0.994818	−	0.101667i	$-0.0324176\pi$
$643$	0.0152505	+	0.145099i	0.000601421	+	0.00572214i	−0.994217	+	0.107389i	$0.965751\pi$
$644$	−1.20859	−	11.4990i	−0.0476251	−	0.453123i
$645$		0			0
$646$	−4.74803	+	1.00922i	−0.186809	+	0.0397074i
$647$	14.7082	+	10.6861i	0.578239	+	0.420115i	0.838089	−	0.545534i	$-0.183673\pi$
$647$	14.7082	+	10.6861i	0.578239	+	0.420115i	−0.259850	+	0.965649i	$0.583673\pi$
$648$		0			0
$649$	2.04508	−	0.138757i	0.0802766	−	0.00544670i
$650$	−17.7082	−	30.6715i	−0.694573	−	1.20304i
$651$		0			0
$652$	23.6840	+	26.3037i	0.927535	+	1.03013i
$653$	42.4131	+	9.01519i	1.65975	+	0.352792i	0.939931	−	0.341365i	$-0.110889\pi$
$653$	42.4131	+	9.01519i	1.65975	+	0.352792i	0.719824	+	0.694157i	$0.244223\pi$
$654$		0			0
$655$	49.5591	+	22.0651i	1.93644	+	0.862157i
$656$	34.9336	+	107.515i	1.36393	+	4.19774i
$657$		0			0
$658$	12.5902	+	9.14729i	0.490816	+	0.356599i
$659$	−18.4894	−	32.0245i	−0.720243	−	1.24750i	−0.960902	−	0.276888i	$-0.910697\pi$
$659$	−18.4894	−	32.0245i	−0.720243	−	1.24750i	0.240659	−	0.970610i	$-0.422636\pi$
$660$		0			0
$661$	8.85410	−	15.3358i	0.344385	−	0.596492i	−0.640857	−	0.767660i	$-0.721421\pi$
$661$	8.85410	−	15.3358i	0.344385	−	0.596492i	0.985242	+	0.171168i	$0.0547542\pi$
$662$	−29.6962	+	13.2216i	−1.15418	+	0.513873i
$663$		0			0
$664$	71.1780	−	79.0512i	2.76224	−	3.06778i
$665$	−2.61803	+	1.90211i	−0.101523	+	0.0737608i
$666$		0			0
$667$	1.36475	+	4.20025i	0.0528431	+	0.162634i
$668$	−48.6011	+	10.3305i	−1.88043	+	0.399699i
$669$		0			0
$670$	25.4164	−	44.0225i	0.981922	−	1.70074i
$671$	−13.6126	−	1.94184i	−0.525508	−	0.0749638i
$672$		0			0
$673$	0.986508	−	9.38599i	0.0380271	−	0.361803i	−0.958917	−	0.283686i	$-0.908443\pi$
$673$	0.986508	−	9.38599i	0.0380271	−	0.361803i	0.996944	−	0.0781171i	$-0.0248908\pi$
$674$	−2.04508	+	6.29412i	−0.0787737	+	0.242441i
$675$		0			0
$676$	27.0517	−	19.6542i	1.04045	−	0.755930i
$677$	−21.8742	−	9.73901i	−0.840693	−	0.374301i	−0.0592240	−	0.998245i	$-0.518863\pi$
$677$	−21.8742	−	9.73901i	−0.840693	−	0.374301i	−0.781469	+	0.623944i	$0.785529\pi$
$678$		0			0
$679$	−4.01478	−	4.45887i	−0.154073	−	0.171116i
$680$	−40.9568	+	18.2351i	−1.57062	+	0.699286i
$681$		0			0
$682$	7.83225	+	11.6637i	0.299912	+	0.446628i
$683$	14.4721			0.553761			0.276880	−	0.960904i	$-0.410699\pi$
$683$	14.4721			0.553761			0.276880	+	0.960904i	$0.410699\pi$
$684$		0			0
$685$	−6.38197	+	19.6417i	−0.243842	+	0.750470i
$686$	22.7735	−	25.2925i	0.869496	−	0.965673i
$687$		0			0
$688$	4.99989	+	47.5708i	0.190619	+	1.81362i
$689$	−17.1448	−	3.64425i	−0.653166	−	0.138835i
$690$		0			0
$691$	3.61634	−	34.4072i	0.137572	−	1.30891i	−0.680054	−	0.733162i	$-0.738043\pi$
$691$	3.61634	−	34.4072i	0.137572	−	1.30891i	0.817626	−	0.575750i	$-0.195290\pi$
$692$	57.8115			2.19766
$693$		0			0
$694$	−70.3951			−2.67216
$695$	−1.25434	+	11.9343i	−0.0475799	+	0.452692i
$696$		0			0
$697$	−20.8057	−	4.42239i	−0.788072	−	0.167510i
$698$	2.97032	+	28.2607i	0.112428	+	1.06968i
$699$		0			0
$700$	−17.7737	+	19.7396i	−0.671781	+	0.746088i
$701$	−12.8926	+	39.6794i	−0.486947	+	1.49867i	0.342194	+	0.939629i	$0.388830\pi$
$701$	−12.8926	+	39.6794i	−0.486947	+	1.49867i	−0.829141	+	0.559040i	$0.811170\pi$
$702$		0			0
$703$	6.09017			0.229695
$704$	27.1196	+	9.93427i	1.02211	+	0.374412i
$705$		0			0
$706$	−24.9129	+	11.0919i	−0.937607	+	0.417450i
$707$	0.315921	+	0.350865i	0.0118814	+	0.0131957i
$708$		0			0
$709$	−27.6220	−	12.2981i	−1.03737	−	0.461865i	−0.183863	−	0.982952i	$-0.558860\pi$
$709$	−27.6220	−	12.2981i	−1.03737	−	0.461865i	−0.853504	+	0.521086i	$0.825527\pi$
$710$	96.5755	−	70.1662i	3.62441	−	2.63329i
$711$		0			0
$712$	25.9443	−	79.8483i	0.972303	−	2.99244i
$713$	−0.402863	+	3.83299i	−0.0150874	+	0.143547i
$714$		0			0
$715$	−19.0481	−	18.4708i	−0.712358	−	0.690769i
$716$	−55.6869	+	96.4526i	−2.08112	+	3.60460i
$717$		0			0
$718$	−41.3468	+	8.78853i	−1.54305	+	0.327985i
$719$	−9.14590	−	28.1482i	−0.341084	−	1.04975i	−0.963647	−	0.267180i	$-0.913908\pi$
$719$	−9.14590	−	28.1482i	−0.341084	−	1.04975i	0.622562	−	0.782570i	$-0.286092\pi$
$720$		0			0
$721$	−4.66312	+	3.38795i	−0.173664	+	0.126174i
$722$	−31.5325	+	35.0204i	−1.17352	+	1.30332i
$723$		0			0
$724$	−93.5232	+	41.6392i	−3.47576	+	1.54751i
$725$	5.07295	−	8.78661i	0.188405	−	0.326326i
$726$		0			0
$727$	17.4164	+	30.1661i	0.645939	+	1.11880i	0.984084	+	0.177705i	$0.0568672\pi$
$727$	17.4164	+	30.1661i	0.645939	+	1.11880i	−0.338145	+	0.941094i	$0.609799\pi$
$728$	14.9443	+	10.8576i	0.553872	+	0.402411i
$729$		0			0
$730$	17.9443	+	55.2268i	0.664147	+	2.04404i
$731$	−8.22191	−	3.66063i	−0.304098	−	0.135393i
$732$		0			0
$733$	−38.6641	−	8.21831i	−1.42809	−	0.303550i	−0.571948	−	0.820290i	$-0.693812\pi$
$733$	−38.6641	−	8.21831i	−1.42809	−	0.303550i	−0.856142	+	0.516740i	$0.827145\pi$
$734$	1.24064	+	1.37787i	0.0457927	+	0.0508580i
$735$		0			0
$736$	12.9271	+	22.3903i	0.476497	+	0.825318i
$737$	4.85410	−	19.2986i	0.178803	−	0.710875i
$738$		0			0
$739$	19.8541	+	14.4248i	0.730345	+	0.530627i	0.889673	−	0.456599i	$-0.150933\pi$
$739$	19.8541	+	14.4248i	0.730345	+	0.530627i	−0.159328	+	0.987226i	$0.550933\pi$
$740$	93.5751	−	19.8900i	3.43989	−	0.731171i
$741$		0			0
$742$	1.94029	+	18.4606i	0.0712303	+	0.677711i
$743$	0.246758	+	2.34775i	0.00905268	+	0.0861305i	0.998115	−	0.0613652i	$-0.0195454\pi$
$743$	0.246758	+	2.34775i	0.00905268	+	0.0861305i	−0.989063	+	0.147496i	$0.952879\pi$
$744$		0			0
$745$	−22.7283	+	4.83105i	−0.832701	+	0.176996i
$746$	−54.3328	−	39.4751i	−1.98927	−	1.44529i
$747$		0			0
$748$	−22.9058	+	19.1396i	−0.837518	+	0.699815i
$749$	7.51722	+	13.0202i	0.274673	+	0.475748i
$750$		0			0
$751$	32.9542	+	36.5993i	1.20251	+	1.33553i	0.927379	+	0.374122i	$0.122056\pi$
$751$	32.9542	+	36.5993i	1.20251	+	1.33553i	0.275135	+	0.961406i	$0.411277\pi$
$752$	−57.2954	−	12.1785i	−2.08935	−	0.444105i
$753$		0			0
$754$	−10.9625	−	4.88084i	−0.399232	−	0.177750i
$755$	11.3262	+	34.8586i	0.412204	+	1.26863i
$756$		0			0
$757$	−8.89919	−	6.46564i	−0.323446	−	0.234998i	0.414198	−	0.910187i	$-0.364062\pi$
$757$	−8.89919	−	6.46564i	−0.323446	−	0.234998i	−0.737645	+	0.675189i	$0.764062\pi$
$758$	11.5172	+	19.9484i	0.418324	+	0.724559i
$759$		0			0
$760$	12.0902	−	20.9408i	0.438557	−	0.759602i
$761$	36.5224	−	16.2608i	1.32393	−	0.589454i	0.381663	−	0.924302i	$-0.375352\pi$
$761$	36.5224	−	16.2608i	1.32393	−	0.589454i	0.942272	+	0.334848i	$0.108685\pi$
$762$		0			0
$763$	−9.27020	+	10.2956i	−0.335604	+	0.372726i
$764$	−46.9058	+	34.0790i	−1.69699	+	1.23294i
$765$		0			0
$766$	−10.6353	−	32.7319i	−0.384267	−	1.18265i
$767$	−1.49448	+	0.317661i	−0.0539624	+	0.0114701i
$768$		0			0
$769$	−4.39919	+	7.61962i	−0.158639	+	0.274770i	−0.934378	−	0.356283i	$-0.884044\pi$
$769$	−4.39919	+	7.61962i	−0.158639	+	0.274770i	0.775739	+	0.631054i	$0.217377\pi$
$770$	−12.3699	+	25.2296i	−0.445782	+	0.909212i
$771$		0			0
$772$	5.58131	−	53.1026i	0.200876	−	1.91121i
$773$	2.36475	−	7.27794i	0.0850540	−	0.261769i	−0.899480	−	0.436961i	$-0.856055\pi$
$773$	2.36475	−	7.27794i	0.0850540	−	0.261769i	0.984534	+	0.175192i	$0.0560547\pi$
$774$		0			0
$775$	7.16312	−	5.20431i	0.257307	−	0.186944i
$776$	40.9568	+	18.2351i	1.47026	+	0.654604i
$777$		0			0
$778$	−15.1575	−	16.8341i	−0.543421	−	0.603531i
$779$	10.4803	−	4.66614i	0.375496	−	0.167182i
$780$		0			0
$781$	28.8471	−	36.7656i	1.03223	−	1.31558i
$782$	−11.5623			−0.413467
$783$		0			0
$784$	−18.2705	+	56.2308i	−0.652518	+	2.00824i
$785$	−29.9990	+	33.3173i	−1.07071	+	1.18914i
$786$		0			0
$787$	−3.76302	−	35.8028i	−0.134137	−	1.27623i	−0.829881	−	0.557941i	$-0.811592\pi$
$787$	−3.76302	−	35.8028i	−0.134137	−	1.27623i	0.695743	−	0.718291i	$-0.255075\pi$
$788$	17.8713	+	3.79865i	0.636637	+	0.135321i
$789$		0			0
$790$	−8.46818	+	80.5694i	−0.301284	+	2.86653i
$791$	12.7639			0.453833
$792$		0			0
$793$	10.2492			0.363961
$794$	−10.4331	+	99.2648i	−0.370258	+	3.52277i
$795$		0			0
$796$	65.7797	+	13.9819i	2.33150	+	0.495575i
$797$	−0.969032	−	9.21973i	−0.0343249	−	0.326579i	−0.998188	−	0.0601798i	$-0.980833\pi$
$797$	−0.969032	−	9.21973i	−0.0343249	−	0.326579i	0.963863	−	0.266400i	$-0.0858341\pi$
$798$		0			0
$799$	7.37468	−	8.19041i	0.260897	−	0.289756i
$800$	18.3541	−	56.4881i	0.648915	−	1.99716i
$801$		0			0
$802$	14.5623			0.514213
$803$	12.6728	+	18.8723i	0.447215	+	0.665990i
$804$		0			0
$805$	−7.04179	+	3.13521i	−0.248191	+	0.110502i
$806$	−7.00723	−	7.78231i	−0.246819	−	0.274120i
$807$		0			0
$808$	−3.22286	−	1.43491i	−0.113380	−	0.0504800i
$809$	−5.59017	+	4.06150i	−0.196540	+	0.142795i	−0.681703	−	0.731629i	$-0.738760\pi$
$809$	−5.59017	+	4.06150i	−0.196540	+	0.142795i	0.485163	+	0.874424i	$0.338760\pi$
$810$		0			0
$811$	−15.9721	+	49.1572i	−0.560858	+	1.72614i	0.119092	+	0.992883i	$0.462002\pi$
$811$	−15.9721	+	49.1572i	−0.560858	+	1.72614i	−0.679950	+	0.733259i	$0.737998\pi$
$812$	−0.940756	+	8.95070i	−0.0330141	+	0.314108i
$813$		0			0
$814$	46.7425	−	24.7296i	1.63833	−	0.866772i
$815$	11.7984	−	20.4354i	0.413279	−	0.715820i
$816$		0			0
$817$	4.74803	−	1.00922i	0.166112	−	0.0353083i
$818$	7.07295	+	21.7683i	0.247300	+	0.761111i
$819$		0			0
$820$	145.790	−	105.923i	5.09122	−	3.69899i
$821$	8.84241	−	9.82050i	0.308602	−	0.342738i	−0.568815	−	0.822466i	$-0.692598\pi$
$821$	8.84241	−	9.82050i	0.308602	−	0.342738i	0.877417	+	0.479728i	$0.159265\pi$
$822$		0			0
$823$	−50.8920	+	22.6586i	−1.77398	+	0.789828i	−0.789638	+	0.613573i	$0.789732\pi$
$823$	−50.8920	+	22.6586i	−1.77398	+	0.789828i	−0.984344	+	0.176255i	$0.943602\pi$
$824$	21.5344	−	37.2987i	0.750188	−	1.29936i
$825$		0			0
$826$	0.809017	+	1.40126i	0.0281493	+	0.0487560i
$827$	−22.6246	−	16.4377i	−0.786735	−	0.571596i	0.120258	−	0.992743i	$-0.461628\pi$
$827$	−22.6246	−	16.4377i	−0.786735	−	0.571596i	−0.906993	+	0.421146i	$0.861628\pi$
$828$		0			0
$829$	−7.27458	−	22.3888i	−0.252656	−	0.777597i	−0.994282	−	0.106783i	$-0.965945\pi$
$829$	−7.27458	−	22.3888i	−0.252656	−	0.777597i	0.741626	−	0.670814i	$-0.234055\pi$
$830$	−110.183	−	49.0565i	−3.82449	−	1.70277i
$831$		0			0
$832$	−21.0574	−	4.47589i	−0.730035	−	0.155174i
$833$	−7.44382	−	8.26720i	−0.257913	−	0.286441i
$834$		0			0
$835$	16.5623	+	28.6868i	0.573162	+	0.992746i
$836$	3.92705	−	15.6129i	0.135820	−	0.539985i
$837$		0			0
$838$	−6.54508	−	4.75528i	−0.226096	−	0.164269i
$839$	−30.0372	+	6.38459i	−1.03700	+	0.220421i	−0.694797	−	0.719206i	$-0.744506\pi$
$839$	−30.0372	+	6.38459i	−1.03700	+	0.220421i	−0.342201	+	0.939627i	$0.611172\pi$
$840$		0			0
$841$	2.67199	+	25.4223i	0.0921375	+	0.876630i
$842$	−1.57735	−	15.0075i	−0.0543591	−	0.517193i
$843$		0			0
$844$	−54.7346	+	11.6342i	−1.88404	+	0.400466i
$845$	−18.0344	−	13.1028i	−0.620404	−	0.450750i
$846$		0			0
$847$	−1.95492	+	10.8249i	−0.0671717	+	0.371948i
$848$	−34.9336	−	60.5068i	−1.19963	−	2.07781i
$849$		0			0
$850$	17.7737	+	19.7396i	0.609631	+	0.677064i
$851$	14.1896	+	3.01609i	0.486412	+	0.103390i
$852$		0			0
$853$	−50.7587	−	22.5992i	−1.73794	−	0.773783i	−0.994470	−	0.105018i	$-0.966510\pi$
$853$	−50.7587	−	22.5992i	−1.73794	−	0.773783i	−0.743474	−	0.668765i	$-0.766823\pi$
$854$	−3.35410	−	10.3229i	−0.114775	−	0.353241i
$855$		0			0
$856$	−90.8845	−	66.0314i	−3.10637	−	2.25691i
$857$	−9.68034	−	16.7668i	−0.330674	−	0.572744i	0.651970	−	0.758245i	$-0.273943\pi$
$857$	−9.68034	−	16.7668i	−0.330674	−	0.572744i	−0.982644	+	0.185500i	$0.940609\pi$
$858$		0			0
$859$	6.21885	−	10.7714i	0.212184	−	0.367514i	−0.740214	−	0.672372i	$-0.765276\pi$
$859$	6.21885	−	10.7714i	0.212184	−	0.367514i	0.952398	+	0.304858i	$0.0986089\pi$
$860$	69.6571	−	31.0134i	2.37529	−	1.05755i
$861$		0			0
$862$	−42.1640	+	46.8279i	−1.43611	+	1.59496i
$863$	−33.5344	+	24.3642i	−1.14153	+	0.829367i	−0.987331	−	0.158674i	$-0.949278\pi$
$863$	−33.5344	+	24.3642i	−1.14153	+	0.829367i	−0.154195	+	0.988041i	$0.549278\pi$
$864$		0			0
$865$	−11.9098	−	36.6547i	−0.404946	−	1.24630i
$866$	71.0440	−	15.1009i	2.41417	−	0.513149i
$867$		0			0
$868$	−3.92705	+	6.80185i	−0.133293	+	0.230870i
$869$	5.44258	+	31.2441i	0.184627	+	1.05988i
$870$		0			0
$871$	−1.55045	+	14.7516i	−0.0525350	+	0.499838i
$872$	31.9894	−	98.4531i	1.08330	−	3.33404i
$873$		0			0
$874$	5.04508	−	3.66547i	0.170653	−	0.123986i
$875$	1.39577	+	0.621438i	0.0471857	+	0.0210084i
$876$		0			0
$877$	−25.1571	−	27.9398i	−0.849496	−	0.943461i	0.149477	−	0.988765i	$-0.452241\pi$
$877$	−25.1571	−	27.9398i	−0.849496	−	0.943461i	−0.998973	+	0.0453042i	$0.985574\pi$
$878$	30.3941	−	13.5323i	1.02575	−	0.456694i
$879$		0			0
$880$	3.90961	−	105.690i	0.131793	−	3.56281i
$881$	−24.1803			−0.814656			−0.407328	−	0.913282i	$-0.633539\pi$
$881$	−24.1803			−0.814656			−0.407328	+	0.913282i	$0.633539\pi$
$882$		0			0
$883$	−1.34346	+	4.13474i	−0.0452110	+	0.139145i	−0.971114	−	0.238616i	$-0.923306\pi$
$883$	−1.34346	+	4.13474i	−0.0452110	+	0.139145i	0.925903	+	0.377762i	$0.123306\pi$
$884$	14.8876	−	16.5344i	0.500725	−	0.556112i
$885$		0			0
$886$	0.885579	+	8.42572i	0.0297516	+	0.283068i
$887$	24.4874	+	5.20495i	0.822206	+	0.174765i	0.599760	−	0.800180i	$-0.295263\pi$
$887$	24.4874	+	5.20495i	0.822206	+	0.174765i	0.222446	+	0.974945i	$0.428596\pi$
$888$		0			0
$889$	0.999533	−	9.50992i	0.0335233	−	0.318953i
$890$	−95.1935			−3.19089
$891$		0			0
$892$	109.249			3.65793
$893$	−0.621346	+	5.91171i	−0.0207925	+	0.197828i
$894$		0			0
$895$	72.6267	+	15.4373i	2.42764	+	0.516011i
$896$	0.113954	+	1.08420i	0.00380693	+	0.0362205i
$897$		0			0
$898$	2.57890	−	2.86416i	0.0860589	−	0.0955781i
$899$	0.927051	−	2.85317i	0.0309189	−	0.0951585i
$900$		0			0
$901$	13.1459			0.437953
$902$	61.4901	−	78.3691i	2.04739	−	2.60941i
$903$		0			0
$904$	−87.1283	+	38.7920i	−2.89785	+	1.29020i
$905$	45.6676	+	50.7191i	1.51804	+	1.68596i
$906$		0			0
$907$	−37.8358	−	16.8456i	−1.25632	−	0.559348i	−0.332833	−	0.942986i	$-0.608004\pi$
$907$	−37.8358	−	16.8456i	−1.25632	−	0.559348i	−0.923484	+	0.383638i	$0.874671\pi$
$908$	−56.4787	+	41.0342i	−1.87431	+	1.36177i
$909$		0			0
$910$	6.47214	−	19.9192i	0.214549	−	0.660315i
$911$	0.332436	−	3.16292i	0.0110141	−	0.104792i	−0.987634	−	0.156779i	$-0.949889\pi$
$911$	0.332436	−	3.16292i	0.0110141	−	0.104792i	0.998648	+	0.0519872i	$0.0165555\pi$
$912$		0			0
$913$	−46.7425	−	6.66783i	−1.54695	−	0.220673i
$914$	1.30902	−	2.26728i	0.0432984	−	0.0749951i
$915$		0			0
$916$	57.8326	−	12.2927i	1.91084	−	0.406162i
$917$	5.18034	+	15.9434i	0.171070	+	0.526499i
$918$		0			0
$919$	−45.1976	+	32.8380i	−1.49093	+	1.08322i	−0.517106	+	0.855922i	$0.672991\pi$
$919$	−45.1976	+	32.8380i	−1.49093	+	1.08322i	−0.973824	+	0.227303i	$0.927009\pi$
$920$	38.5397	−	42.8027i	1.27062	−	1.41116i
$921$		0			0
$922$	54.6600	−	24.3362i	1.80013	−	0.801470i
$923$	−17.4164	+	30.1661i	−0.573268	+	0.992929i
$924$		0			0
$925$	−16.6631	−	28.8614i	−0.547880	−	0.948956i
$926$	−36.0066	−	26.1603i	−1.18325	−	0.859681i
$927$		0			0
$928$	−6.21885	−	19.1396i	−0.204144	−	0.628290i
$929$	13.4561	+	5.99102i	0.441479	+	0.196559i	0.615424	−	0.788196i	$-0.288985\pi$
$929$	13.4561	+	5.99102i	0.441479	+	0.196559i	−0.173945	+	0.984755i	$0.555651\pi$
$930$		0			0
$931$	5.86889	+	1.24747i	0.192345	+	0.0408842i
$932$	−94.5976	−	105.061i	−3.09865	−	3.44140i
$933$		0			0
$934$	−6.85410	−	11.8717i	−0.224273	−	0.388452i
$935$	16.8541	+	10.5801i	0.551188	+	0.346007i
$936$		0			0
$937$	−4.88197	−	3.54696i	−0.159487	−	0.115874i	0.505179	−	0.863014i	$-0.331426\pi$
$937$	−4.88197	−	3.54696i	−0.159487	−	0.115874i	−0.664666	+	0.747140i	$0.731426\pi$
$938$	15.3649	−	3.26592i	0.501683	−	0.106636i
$939$		0			0
$940$	9.76022	+	92.8623i	0.318343	+	3.02884i
$941$	−4.40682	−	41.9281i	−0.143658	−	1.36682i	−0.794343	−	0.607469i	$-0.792185\pi$
$941$	−4.40682	−	41.9281i	−0.143658	−	1.36682i	0.650685	−	0.759348i	$-0.274482\pi$
$942$		0			0
$943$	26.7291	−	5.68144i	0.870419	−	0.185013i
$944$	−4.92705	−	3.57971i	−0.160362	−	0.116510i
$945$		0			0
$946$	32.3435	−	27.0256i	1.05158	−	0.878678i
$947$	11.6459	+	20.1713i	0.378441	+	0.655479i	0.990836	−	0.135073i	$-0.0431270\pi$
$947$	11.6459	+	20.1713i	0.378441	+	0.655479i	−0.612395	+	0.790552i	$0.709794\pi$
$948$		0			0
$949$	−11.3379	−	12.5920i	−0.368045	−	0.408755i
$950$	−14.0132	−	2.97859i	−0.454647	−	0.0966383i
$951$		0			0
$952$	−12.6564	−	5.63497i	−0.410195	−	0.182630i
$953$	14.6803	+	45.1814i	0.475543	+	1.46357i	0.845224	+	0.534412i	$0.179467\pi$
$953$	14.6803	+	45.1814i	0.475543	+	1.46357i	−0.369681	+	0.929159i	$0.620533\pi$
$954$		0			0
$955$	31.2705	+	22.7194i	1.01189	+	0.735181i
$956$	3.70820	+	6.42280i	0.119932	+	0.207728i
$957$		0			0
$958$	−21.2533	+	36.8118i	−0.686663	+	1.18933i
$959$	−5.83022	+	2.59578i	−0.188267	+	0.0838221i
$960$		0			0
$961$	−18.9912	+	21.0919i	−0.612621	+	0.680384i
$962$	−31.8885	+	23.1684i	−1.02813	+	0.746979i
$963$		0			0
$964$	40.2492	+	123.874i	1.29634	+	3.98972i
$965$	−34.8189	+	7.40098i	−1.12086	+	0.238246i
$966$		0			0
$967$	16.2426	−	28.1331i	0.522328	−	0.904699i	−0.477334	−	0.878722i	$-0.658397\pi$
$967$	16.2426	−	28.1331i	0.522328	−	0.904699i	0.999663	−	0.0259773i	$-0.00826976\pi$
$968$	−19.5544	−	79.8336i	−0.628502	−	2.56595i
$969$		0			0
$970$	5.31348	−	50.5543i	0.170605	−	1.62320i
$971$	7.50000	−	23.0826i	0.240686	−	0.740757i	−0.755630	−	0.654999i	$-0.772669\pi$
$971$	7.50000	−	23.0826i	0.240686	−	0.740757i	0.996316	−	0.0857575i	$-0.0273310\pi$
$972$		0			0
$973$	−3.00000	+	2.17963i	−0.0961756	+	0.0698757i
$974$	81.2667	+	36.1822i	2.60395	+	1.15935i
$975$		0			0
$976$	27.3367	+	30.3605i	0.875027	+	0.971816i
$977$	−18.4866	+	8.23075i	−0.591438	+	0.263325i	−0.680556	−	0.732696i	$-0.738262\pi$
$977$	−18.4866	+	8.23075i	−0.591438	+	0.263325i	0.0891184	+	0.996021i	$0.471595\pi$
$978$		0			0
$979$	−35.8434	+	10.1978i	−1.14556	+	0.325922i
$980$	94.2492			3.01068
$981$		0			0
$982$	6.73607	−	20.7315i	0.214957	−	0.661568i
$983$	−34.6226	+	38.4523i	−1.10429	+	1.22644i	−0.132350	+	0.991203i	$0.542252\pi$
$983$	−34.6226	+	38.4523i	−1.10429	+	1.22644i	−0.971939	+	0.235234i	$0.924414\pi$
$984$		0			0
$985$	−1.27319	−	12.1136i	−0.0405673	−	0.385972i
$986$	8.80333	+	1.87121i	0.280355	+	0.0595913i
$987$		0			0
$988$	−1.25434	+	11.9343i	−0.0399059	+	0.379679i
$989$	11.5623			0.367660
$990$		0			0
$991$	−28.5967			−0.908406			−0.454203	−	0.890898i	$-0.650076\pi$
$991$	−28.5967			−0.908406			−0.454203	+	0.890898i	$0.650076\pi$
$992$	1.83576	−	17.4661i	0.0582855	−	0.554549i
$993$		0			0
$994$	36.0824	+	7.66956i	1.14447	+	0.243264i
$995$	−4.68631	−	44.5872i	−0.148566	−	1.41351i
$996$		0			0
$997$	6.43572	−	7.14759i	0.203821	−	0.226367i	−0.632565	−	0.774508i	$-0.717998\pi$
$997$	6.43572	−	7.14759i	0.203821	−	0.226367i	0.836386	+	0.548141i	$0.184664\pi$
$998$	9.37132	−	28.8420i	0.296644	−	0.912976i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.a.37.1		8
3.2	odd	2		99.2.m.a.4.1	✓	8
9.2	odd	6		99.2.m.a.70.1	yes	8
9.4	even	3		891.2.f.a.730.1		4
9.5	odd	6		891.2.f.b.730.1		4
9.7	even	3	inner	297.2.n.a.235.1		8
11.3	even	5	inner	297.2.n.a.91.1		8
33.5	odd	10		1089.2.e.g.364.2		4
33.14	odd	10		99.2.m.a.58.1	yes	8
33.17	even	10		1089.2.e.d.364.1		4
99.5	odd	30		9801.2.a.n.1.1		2
99.14	odd	30		891.2.f.b.487.1		4
99.25	even	15	inner	297.2.n.a.289.1		8
99.38	odd	30		1089.2.e.g.727.2		4
99.47	odd	30		99.2.m.a.25.1	yes	8
99.49	even	15		9801.2.a.bb.1.2		2
99.50	even	30		9801.2.a.bc.1.2		2
99.58	even	15		891.2.f.a.487.1		4
99.83	even	30		1089.2.e.d.727.1		4
99.94	odd	30		9801.2.a.m.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.4.1	✓	8	3.2	odd	2
99.2.m.a.25.1	yes	8	99.47	odd	30
99.2.m.a.58.1	yes	8	33.14	odd	10
99.2.m.a.70.1	yes	8	9.2	odd	6
297.2.n.a.37.1		8	1.1	even	1	trivial
297.2.n.a.91.1		8	11.3	even	5	inner
297.2.n.a.235.1		8	9.7	even	3	inner
297.2.n.a.289.1		8	99.25	even	15	inner
891.2.f.a.487.1		4	99.58	even	15
891.2.f.a.730.1		4	9.4	even	3
891.2.f.b.487.1		4	99.14	odd	30
891.2.f.b.730.1		4	9.5	odd	6
1089.2.e.d.364.1		4	33.17	even	10
1089.2.e.d.727.1		4	99.83	even	30
1089.2.e.g.364.2		4	33.5	odd	10
1089.2.e.g.727.2		4	99.38	odd	30
9801.2.a.m.1.1		2	99.94	odd	30
9801.2.a.n.1.1		2	99.5	odd	30
9801.2.a.bb.1.2		2	99.49	even	15
9801.2.a.bc.1.2		2	99.50	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.273659 + 2.60369i) q^{2} +(-4.74803 - 1.00922i) q^{4} +(0.338261 + 3.21834i) q^{5} +(-0.669131 + 0.743145i) q^{7} +(2.30902 - 7.10642i) q^{8} -8.47214 q^{10} +(-3.19003 + 0.907591i) q^{11} +(2.25841 - 1.00551i) q^{13} +(-1.75181 - 1.94558i) q^{14} +(9.00217 + 4.00802i) q^{16} +(-1.50000 + 1.08981i) q^{17} +(0.309017 - 0.951057i) q^{19} +(1.64195 - 15.6222i) q^{20} +(-1.49011 - 8.55422i) q^{22} +(1.19098 - 2.06284i) q^{23} +(-5.35256 + 1.13772i) q^{25} +(2.00000 + 6.15537i) q^{26} +(3.92705 - 2.85317i) q^{28} +(-1.24064 + 1.37787i) q^{29} +(-1.47815 + 0.658114i) q^{31} +(-5.42705 + 9.39993i) q^{32} +(-2.42705 - 4.20378i) q^{34} +(-2.61803 - 1.90211i) q^{35} +(1.88197 + 5.79210i) q^{37} +(2.39169 + 1.06485i) q^{38} +(23.6519 + 5.02738i) q^{40} +(7.67636 + 8.52546i) q^{41} +(2.42705 + 4.20378i) q^{43} +(16.0623 - 1.08981i) q^{44} +(5.04508 + 3.66547i) q^{46} +(-5.81438 + 1.23588i) q^{47} +(0.627171 + 5.96713i) q^{49} +(-1.49750 - 14.2478i) q^{50} +(-11.7378 + 2.49494i) q^{52} +(-5.73607 - 4.16750i) q^{53} +(-4.00000 - 9.95959i) q^{55} +(3.73607 + 6.47106i) q^{56} +(-3.24803 - 3.60730i) q^{58} +(-0.604528 - 0.128496i) q^{59} +(3.78747 + 1.68629i) q^{61} +(-1.30902 - 4.02874i) q^{62} +(-7.04508 - 5.11855i) q^{64} +(4.00000 + 6.92820i) q^{65} +(-3.00000 + 5.19615i) q^{67} +(8.22191 - 3.66063i) q^{68} +(5.66897 - 6.29602i) q^{70} +(-11.3992 + 8.28199i) q^{71} +(-2.11803 - 6.51864i) q^{73} +(-15.5959 + 3.31500i) q^{74} +(-2.42705 + 4.20378i) q^{76} +(1.46007 - 2.97795i) q^{77} +(0.999533 - 9.50992i) q^{79} +(-9.85410 + 30.3278i) q^{80} +(-24.2984 + 17.6538i) q^{82} +(13.0053 + 5.79033i) q^{83} +(-4.01478 - 4.45887i) q^{85} +(-11.6095 + 5.16889i) q^{86} +(-0.916102 + 24.7653i) q^{88} +11.2361 q^{89} +(-0.763932 + 2.35114i) q^{91} +(-7.73669 + 8.59247i) q^{92} +(-1.62670 - 15.4771i) q^{94} +(3.16535 + 0.672816i) q^{95} +(-0.627171 + 5.96713i) q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 6 q^{4} - 6 q^{5} - q^{7} + 14 q^{8} - 32 q^{10} - q^{11} + 8 q^{13} + q^{14} + 14 q^{16} - 12 q^{17} - 2 q^{19} - 24 q^{20} + 11 q^{22} + 14 q^{23} - 9 q^{25} + 16 q^{26} + 18 q^{28}+ \cdots - 72 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 - 6 * q^4 - 6 * q^5 - q^7 + 14 * q^8 - 32 * q^10 - q^11 + 8 * q^13 + q^14 + 14 * q^16 - 12 * q^17 - 2 * q^19 - 24 * q^20 + 11 * q^22 + 14 * q^23 - 9 * q^25 + 16 * q^26 + 18 * q^28 + 9 * q^29 - 3 * q^31 - 30 * q^32 - 6 * q^34 - 12 * q^35 + 24 * q^37 + 4 * q^38 + 12 * q^40 - 3 * q^41 + 6 * q^43 + 48 * q^44 + 18 * q^46 - 23 * q^47 - 6 * q^49 + 24 * q^50 + 12 * q^52 - 28 * q^53 - 32 * q^55 + 12 * q^56 + 6 * q^58 - 3 * q^59 - 6 * q^62 - 34 * q^64 + 32 * q^65 - 24 * q^67 + 9 * q^68 - 6 * q^70 - 42 * q^71 - 8 * q^73 - 13 * q^74 - 6 * q^76 + 11 * q^77 - 22 * q^79 - 52 * q^80 - 96 * q^82 + 17 * q^83 - 6 * q^85 - 21 * q^86 + 37 * q^88 + 72 * q^89 - 24 * q^91 + 21 * q^92 + 28 * q^94 + 4 * q^95 + 6 * q^97 - 72 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more