LMFDB - Embedded newform 819.2.et.c.271.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(136,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.et (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	819.271
Dual form			819.2.et.c.136.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.74432 - 1.74432i) q^{2} +4.08534i q^{4} +(-0.130892 - 0.488495i) q^{5} +(1.09376 - 2.40909i) q^{7} +(3.63751 - 3.63751i) q^{8} +O(q^{10})$	\(q+(-1.74432 - 1.74432i) q^{2} +4.08534i q^{4} +(-0.130892 - 0.488495i) q^{5} +(1.09376 - 2.40909i) q^{7} +(3.63751 - 3.63751i) q^{8} +(-0.623777 + 1.08041i) q^{10} +(1.54092 + 5.75079i) q^{11} +(-3.50782 + 0.833795i) q^{13} +(-6.11010 + 2.29436i) q^{14} -4.51932 q^{16} -0.933228 q^{17} +(-7.66303 - 2.05330i) q^{19} +(1.99567 - 0.534738i) q^{20} +(7.34338 - 12.7191i) q^{22} -8.12427i q^{23} +(4.10863 - 2.37212i) q^{25} +(7.57318 + 4.66436i) q^{26} +(9.84193 + 4.46838i) q^{28} +(-1.96458 - 3.40276i) q^{29} +(-2.37727 - 0.636987i) q^{31} +(0.608140 + 0.608140i) q^{32} +(1.62785 + 1.62785i) q^{34} +(-1.31999 - 0.218966i) q^{35} +(0.859350 - 0.859350i) q^{37} +(9.78519 + 16.9484i) q^{38} +(-2.25303 - 1.30079i) q^{40} +(-7.84968 - 2.10332i) q^{41} +(-0.152677 - 0.0881483i) q^{43} +(-23.4939 + 6.29518i) q^{44} +(-14.1714 + 14.1714i) q^{46} +(-1.65836 + 0.444356i) q^{47} +(-4.60738 - 5.26992i) q^{49} +(-11.3045 - 3.02904i) q^{50} +(-3.40634 - 14.3306i) q^{52} +(-0.750763 - 1.30036i) q^{53} +(2.60754 - 1.50546i) q^{55} +(-4.78451 - 12.7416i) q^{56} +(-2.50865 + 9.36239i) q^{58} +(3.03017 + 3.03017i) q^{59} +(-6.74749 + 3.89567i) q^{61} +(3.03561 + 5.25784i) q^{62} +6.91705i q^{64} +(0.866450 + 1.60442i) q^{65} +(-7.37302 + 1.97559i) q^{67} -3.81255i q^{68} +(1.92055 + 2.68444i) q^{70} +(-6.54710 + 1.75429i) q^{71} +(-3.27893 + 12.2371i) q^{73} -2.99797 q^{74} +(8.38844 - 31.3061i) q^{76} +(15.5395 + 2.57777i) q^{77} +(4.64069 - 8.03790i) q^{79} +(0.591542 + 2.20767i) q^{80} +(10.0235 + 17.3613i) q^{82} +(-1.66068 + 1.66068i) q^{83} +(0.122152 + 0.455878i) q^{85} +(0.112560 + 0.420078i) q^{86} +(26.5237 + 15.3134i) q^{88} +(-3.02064 - 3.02064i) q^{89} +(-1.82802 + 9.36260i) q^{91} +33.1904 q^{92} +(3.66782 + 2.11762i) q^{94} +4.01211i q^{95} +(-0.856967 - 3.19825i) q^{97} +(-1.15567 + 17.2292i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 6 q^{7}+O(q^{10}) $ 36 * q + 6 * q^7	$ 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) $ 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.74432	−	1.74432i	−1.23342	−	1.23342i	−0.962640	−	0.270784i	$-0.912717\pi$
$2$	−1.74432	−	1.74432i	−1.23342	−	1.23342i	−0.270784	−	0.962640i	$-0.587283\pi$
$3$		0			0
$3$		0			0
$4$			4.08534i			2.04267i
$5$	−0.130892	−	0.488495i	−0.0585366	−	0.218462i	0.930461	−	0.366390i	$-0.119406\pi$
$5$	−0.130892	−	0.488495i	−0.0585366	−	0.218462i	−0.988998	+	0.147928i	$0.952740\pi$
$6$		0			0
$7$	1.09376	−	2.40909i	0.413402	−	0.910549i
$7$	1.09376	−	2.40909i	0.413402	−	0.910549i
$8$	3.63751	−	3.63751i	1.28605	−	1.28605i
$9$		0			0
$10$	−0.623777	+	1.08041i	−0.197255	+	0.341656i
$11$	1.54092	+	5.75079i	0.464605	+	1.73393i	0.658197	+	0.752846i	$0.271320\pi$
$11$	1.54092	+	5.75079i	0.464605	+	1.73393i	−0.193592	+	0.981082i	$0.562014\pi$
$12$		0			0
$13$	−3.50782	+	0.833795i	−0.972894	+	0.231253i
$13$	−3.50782	+	0.833795i	−0.972894	+	0.231253i
$14$	−6.11010	+	2.29436i	−1.63299	+	0.613193i
$15$		0			0
$16$	−4.51932			−1.12983
$17$	−0.933228			−0.226341			−0.113171	−	0.993576i	$-0.536101\pi$
$17$	−0.933228			−0.226341			−0.113171	+	0.993576i	$0.536101\pi$
$18$		0			0
$19$	−7.66303	−	2.05330i	−1.75802	−	0.471060i	−0.771711	−	0.635973i	$-0.780599\pi$
$19$	−7.66303	−	2.05330i	−1.75802	−	0.471060i	−0.986308	+	0.164913i	$0.947266\pi$
$20$	1.99567	−	0.534738i	0.446245	−	0.119571i
$21$		0			0
$22$	7.34338	−	12.7191i	1.56561	−	2.71172i
$23$		−	8.12427i		−	1.69403i	−0.531571	−	0.847014i	$-0.678398\pi$
$23$		−	8.12427i		−	1.69403i	0.531571	−	0.847014i	$-0.321602\pi$
$24$		0			0
$25$	4.10863	−	2.37212i	0.821726	−	0.474424i
$26$	7.57318	+	4.66436i	1.48522	+	0.914757i
$27$		0			0
$28$	9.84193	+	4.46838i	1.85995	+	0.844444i
$29$	−1.96458	−	3.40276i	−0.364814	−	0.631877i	0.623932	−	0.781479i	$-0.285534\pi$
$29$	−1.96458	−	3.40276i	−0.364814	−	0.631877i	−0.988746	+	0.149602i	$0.952201\pi$
$30$		0			0
$31$	−2.37727	−	0.636987i	−0.426970	−	0.114406i	0.0389336	−	0.999242i	$-0.487604\pi$
$31$	−2.37727	−	0.636987i	−0.426970	−	0.114406i	−0.465903	+	0.884836i	$0.654271\pi$
$32$	0.608140	+	0.608140i	0.107505	+	0.107505i
$33$		0			0
$34$	1.62785	+	1.62785i	0.279174	+	0.279174i
$35$	−1.31999	−	0.218966i	−0.223119	−	0.0370120i
$36$		0			0
$37$	0.859350	−	0.859350i	0.141276	−	0.141276i	−0.632932	−	0.774208i	$-0.718149\pi$
$37$	0.859350	−	0.859350i	0.141276	−	0.141276i	0.774208	+	0.632932i	$0.218149\pi$
$38$	9.78519	+	16.9484i	1.58737	+	2.74940i
$39$		0			0
$40$	−2.25303	−	1.30079i	−0.356235	−	0.205672i
$41$	−7.84968	−	2.10332i	−1.22591	−	0.328483i	−0.412927	−	0.910764i	$-0.635494\pi$
$41$	−7.84968	−	2.10332i	−1.22591	−	0.328483i	−0.812987	+	0.582281i	$0.802160\pi$
$42$		0			0
$43$	−0.152677	−	0.0881483i	−0.0232831	−	0.0134425i	0.488313	−	0.872668i	$-0.337612\pi$
$43$	−0.152677	−	0.0881483i	−0.0232831	−	0.0134425i	−0.511596	+	0.859226i	$0.670946\pi$
$44$	−23.4939	+	6.29518i	−3.54184	+	0.949034i
$45$		0			0
$46$	−14.1714	+	14.1714i	−2.08945	+	2.08945i
$47$	−1.65836	+	0.444356i	−0.241897	+	0.0648160i	−0.377730	−	0.925916i	$-0.623295\pi$
$47$	−1.65836	+	0.444356i	−0.241897	+	0.0648160i	0.135834	+	0.990732i	$0.456629\pi$
$48$		0			0
$49$	−4.60738	−	5.26992i	−0.658198	−	0.752845i
$50$	−11.3045	−	3.02904i	−1.59870	−	0.428371i
$51$		0			0
$52$	−3.40634	−	14.3306i	−0.472374	−	1.98730i
$53$	−0.750763	−	1.30036i	−0.103125	−	0.178618i	0.809845	−	0.586643i	$-0.199551\pi$
$53$	−0.750763	−	1.30036i	−0.103125	−	0.178618i	−0.912971	+	0.408025i	$0.866218\pi$
$54$		0			0
$55$	2.60754	−	1.50546i	0.351601	−	0.202997i
$56$	−4.78451	−	12.7416i	−0.639357	−	1.70267i
$57$		0			0
$58$	−2.50865	+	9.36239i	−0.329401	+	1.22934i
$59$	3.03017	+	3.03017i	0.394495	+	0.394495i	0.876286	−	0.481791i	$-0.160014\pi$
$59$	3.03017	+	3.03017i	0.394495	+	0.394495i	−0.481791	+	0.876286i	$0.660014\pi$
$60$		0			0
$61$	−6.74749	+	3.89567i	−0.863928	+	0.498789i	−0.865326	−	0.501210i	$-0.832888\pi$
$61$	−6.74749	+	3.89567i	−0.863928	+	0.498789i	0.00139788	+	0.999999i	$0.499555\pi$
$62$	3.03561	+	5.25784i	0.385523	+	0.667746i
$63$		0			0
$64$			6.91705i			0.864631i
$65$	0.866450	+	1.60442i	0.107470	+	0.199003i
$66$		0			0
$67$	−7.37302	+	1.97559i	−0.900757	+	0.241357i	−0.679341	−	0.733822i	$-0.737734\pi$
$67$	−7.37302	+	1.97559i	−0.900757	+	0.241357i	−0.221416	+	0.975179i	$0.571068\pi$
$68$		−	3.81255i		−	0.462340i
$69$		0			0
$70$	1.92055	+	2.68444i	0.229549	+	0.320852i
$71$	−6.54710	+	1.75429i	−0.776998	+	0.208196i	−0.625461	−	0.780256i	$-0.715089\pi$
$71$	−6.54710	+	1.75429i	−0.776998	+	0.208196i	−0.151537	+	0.988452i	$0.548422\pi$
$72$		0			0
$73$	−3.27893	+	12.2371i	−0.383770	+	1.43225i	0.456327	+	0.889812i	$0.349165\pi$
$73$	−3.27893	+	12.2371i	−0.383770	+	1.43225i	−0.840097	+	0.542437i	$0.817502\pi$
$74$	−2.99797			−0.348507
$75$		0			0
$76$	8.38844	−	31.3061i	0.962220	−	3.59105i
$77$	15.5395	+	2.57777i	1.77089	+	0.293764i
$78$		0			0
$79$	4.64069	−	8.03790i	0.522118	−	0.904335i	−0.477551	−	0.878604i	$-0.658475\pi$
$79$	4.64069	−	8.03790i	0.522118	−	0.904335i	0.999669	−	0.0257307i	$-0.00819123\pi$
$80$	0.591542	+	2.20767i	0.0661364	+	0.246824i
$81$		0			0
$82$	10.0235	+	17.3613i	1.10691	+	1.91723i
$83$	−1.66068	+	1.66068i	−0.182284	+	0.182284i	−0.792350	−	0.610067i	$-0.791143\pi$
$83$	−1.66068	+	1.66068i	−0.182284	+	0.182284i	0.610067	+	0.792350i	$0.291143\pi$
$84$		0			0
$85$	0.122152	+	0.455878i	0.0132492	+	0.0494469i
$86$	0.112560	+	0.420078i	0.0121376	+	0.0452982i
$87$		0			0
$88$	26.5237	+	15.3134i	2.82743	+	1.63242i
$89$	−3.02064	−	3.02064i	−0.320187	−	0.320187i	0.528652	−	0.848839i	$-0.322698\pi$
$89$	−3.02064	−	3.02064i	−0.320187	−	0.320187i	−0.848839	+	0.528652i	$0.822698\pi$
$90$		0			0
$91$	−1.82802	+	9.36260i	−0.191629	+	0.981467i
$92$	33.1904			3.46034
$93$		0			0
$94$	3.66782	+	2.11762i	0.378307	+	0.218416i
$95$			4.01211i			0.411634i
$96$		0			0
$97$	−0.856967	−	3.19825i	−0.0870119	−	0.324733i	0.908676	−	0.417503i	$-0.137095\pi$
$97$	−0.856967	−	3.19825i	−0.0870119	−	0.324733i	−0.995688	+	0.0927700i	$0.970428\pi$
$98$	−1.15567	+	17.2292i	−0.116741	+	1.74041i
$99$		0			0
$100$	9.69091	+	16.7852i	0.969091	+	1.67852i
$101$	−2.23693	+	3.87447i	−0.222583	+	0.385524i	−0.955591	−	0.294695i	$-0.904782\pi$
$101$	−2.23693	+	3.87447i	−0.222583	+	0.385524i	0.733009	+	0.680219i	$0.238115\pi$
$102$		0			0
$103$	2.07621	−	3.59610i	0.204575	−	0.354335i	−0.745422	−	0.666593i	$-0.767752\pi$
$103$	2.07621	−	3.59610i	0.204575	−	0.354335i	0.949997	+	0.312258i	$0.101085\pi$
$104$	−9.72678	+	15.7927i	−0.953789	+	1.54860i
$105$		0			0
$106$	−0.958675	+	3.57782i	−0.0931148	+	0.347509i
$107$	−9.43055			−0.911686			−0.455843	−	0.890060i	$-0.650662\pi$
$107$	−9.43055			−0.911686			−0.455843	+	0.890060i	$0.650662\pi$
$108$		0			0
$109$	1.78152	−	6.64872i	0.170638	−	0.636832i	−0.826615	−	0.562768i	$-0.809737\pi$
$109$	1.78152	−	6.64872i	0.170638	−	0.636832i	0.997254	−	0.0740637i	$-0.0235968\pi$
$110$	−7.17442	−	1.92238i	−0.684054	−	0.183292i
$111$		0			0
$112$	−4.94304	+	10.8874i	−0.467074	+	1.02876i
$113$	2.13688	−	3.70118i	0.201020	−	0.348178i	−0.747837	−	0.663882i	$-0.768908\pi$
$113$	2.13688	−	3.70118i	0.201020	−	0.348178i	0.948857	+	0.315705i	$0.102241\pi$
$114$		0			0
$115$	−3.96867	+	1.06340i	−0.370080	+	0.0991627i
$116$	13.9014	−	8.02599i	1.29072	−	0.745195i
$117$		0			0
$118$		−	10.5712i		−	0.973160i
$119$	−1.02073	+	2.24823i	−0.0935698	+	0.206095i
$120$		0			0
$121$	−21.1709	+	12.2230i	−1.92462	+	1.11118i
$122$	18.5651	+	4.97451i	1.68081	+	0.450371i
$123$		0			0
$124$	2.60231	−	9.71194i	0.233694	−	0.872158i
$125$	−3.48457	−	3.48457i	−0.311670	−	0.311670i
$126$		0			0
$127$	9.06211	−	5.23201i	0.804132	−	0.464266i	−0.0407820	−	0.999168i	$-0.512985\pi$
$127$	9.06211	−	5.23201i	0.804132	−	0.464266i	0.844914	+	0.534902i	$0.179652\pi$
$128$	13.2819	−	13.2819i	1.17396	−	1.17396i
$129$		0			0
$130$	1.28725	−	4.30999i	0.112899	−	0.378011i
$131$	13.7862	+	7.95947i	1.20451	+	0.695422i	0.961554	−	0.274617i	$-0.0885509\pi$
$131$	13.7862	+	7.95947i	1.20451	+	0.695422i	0.242952	+	0.970038i	$0.421884\pi$
$132$		0			0
$133$	−13.3281	+	16.2151i	−1.15569	+	1.40603i
$134$	16.3070	+	9.41486i	1.40871	+	0.813320i
$135$		0			0
$136$	−3.39463	+	3.39463i	−0.291087	+	0.291087i
$137$	13.6514	−	13.6514i	1.16631	−	1.16631i	0.183247	−	0.983067i	$-0.441339\pi$
$137$	13.6514	−	13.6514i	1.16631	−	1.16631i	0.983067	−	0.183247i	$-0.0586608\pi$
$138$		0			0
$139$	−6.10481	−	3.52462i	−0.517804	−	0.298954i	0.218232	−	0.975897i	$-0.429971\pi$
$139$	−6.10481	−	3.52462i	−0.517804	−	0.298954i	−0.736036	+	0.676943i	$0.763304\pi$
$140$	0.894551	−	5.39261i	0.0756034	−	0.455759i
$141$		0			0
$142$	14.4803	+	8.36022i	1.21516	+	0.701574i
$143$	−10.2002	−	18.8879i	−0.852987	−	1.57949i
$144$		0			0
$145$	−1.40508	+	1.40508i	−0.116686	+	0.116686i
$146$	27.0651	−	15.6260i	2.23992	−	1.29322i
$147$		0			0
$148$	3.51074	+	3.51074i	0.288581	+	0.288581i
$149$	−3.76840	+	14.0639i	−0.308720	+	1.15216i	0.620976	+	0.783829i	$0.286736\pi$
$149$	−3.76840	+	14.0639i	−0.308720	+	1.15216i	−0.929696	+	0.368328i	$0.879930\pi$
$150$		0			0
$151$	−4.94839	−	1.32592i	−0.402694	−	0.107902i	0.0517866	−	0.998658i	$-0.483508\pi$
$151$	−4.94839	−	1.32592i	−0.402694	−	0.107902i	−0.454481	+	0.890757i	$0.650175\pi$
$152$	−35.3432	+	20.4054i	−2.86672	+	1.65510i
$153$		0			0
$154$	−22.6095	−	31.6025i	−1.82193	−	2.54660i
$155$			1.24466i			0.0999735i
$156$		0			0
$157$	0.998876	−	0.576701i	0.0797190	−	0.0460258i	−0.459611	−	0.888121i	$-0.652011\pi$
$157$	0.998876	−	0.576701i	0.0797190	−	0.0460258i	0.539330	+	0.842095i	$0.318678\pi$
$158$	−22.1156	+	5.92585i	−1.75942	+	0.471435i
$159$		0			0
$160$	0.217473	−	0.376674i	0.0171927	−	0.0297787i
$161$	−19.5721	−	8.88599i	−1.54249	−	0.700314i
$162$		0			0
$163$	−13.2155	−	3.54108i	−1.03512	−	0.277359i	−0.299029	−	0.954244i	$-0.596663\pi$
$163$	−13.2155	−	3.54108i	−1.03512	−	0.277359i	−0.736089	+	0.676885i	$0.763329\pi$
$164$	8.59276	−	32.0686i	0.670982	−	2.50414i
$165$		0			0
$166$	5.79354			0.449666
$167$	0.561041	−	2.09383i	0.0434146	−	0.162026i	−0.940815	−	0.338920i	$-0.889938\pi$
$167$	0.561041	−	2.09383i	0.0434146	−	0.162026i	0.984230	+	0.176894i	$0.0566051\pi$
$168$		0			0
$169$	11.6096	−	5.84960i	0.893044	−	0.449970i
$170$	0.582126	−	1.00827i	0.0446470	−	0.0773309i
$171$		0			0
$172$	0.360116	−	0.623739i	0.0274586	−	0.0475596i
$173$	−1.38571	−	2.40012i	−0.105354	−	0.182478i	0.808529	−	0.588456i	$-0.200264\pi$
$173$	−1.38571	−	2.40012i	−0.105354	−	0.182478i	−0.913883	+	0.405978i	$0.866931\pi$
$174$		0			0
$175$	−1.22079	−	12.4926i	−0.0922828	−	0.944350i
$176$	−6.96390	−	25.9896i	−0.524924	−	1.95904i
$177$		0			0
$178$			10.5380i			0.789854i
$179$	−7.91226	−	4.56814i	−0.591390	−	0.341439i	0.174257	−	0.984700i	$-0.444248\pi$
$179$	−7.91226	−	4.56814i	−0.591390	−	0.341439i	−0.765647	+	0.643261i	$0.777581\pi$
$180$		0			0
$181$	12.3155			0.915405			0.457703	−	0.889105i	$-0.348672\pi$
$181$	12.3155			0.915405			0.457703	+	0.889105i	$0.348672\pi$
$182$	19.5201	−	13.1428i	1.44693	−	0.974206i
$183$		0			0
$184$	−29.5521	−	29.5521i	−2.17861	−	2.17861i
$185$	−0.532271	−	0.307307i	−0.0391333	−	0.0225936i
$186$		0			0
$187$	−1.43803	−	5.36680i	−0.105159	−	0.392459i
$188$	−1.81535	−	6.77497i	−0.132398	−	0.494115i
$189$		0			0
$190$	6.99843	−	6.99843i	0.507720	−	0.507720i
$191$	−0.267357	−	0.463075i	−0.0193452	−	0.0335069i	0.856191	−	0.516660i	$-0.172825\pi$
$191$	−0.267357	−	0.463075i	−0.0193452	−	0.0335069i	−0.875536	+	0.483153i	$0.839491\pi$
$192$		0			0
$193$	−1.74626	−	6.51711i	−0.125698	−	0.469112i	0.874165	−	0.485628i	$-0.161409\pi$
$193$	−1.74626	−	6.51711i	−0.125698	−	0.469112i	−0.999864	+	0.0165163i	$0.994742\pi$
$194$	−4.08395	+	7.07361i	−0.293211	+	0.507856i
$195$		0			0
$196$	21.5294	−	18.8227i	1.53781	−	1.34448i
$197$	0.252665	−	0.942958i	0.0180016	−	0.0671830i	−0.956341	−	0.292254i	$-0.905595\pi$
$197$	0.252665	−	0.942958i	0.0180016	−	0.0671830i	0.974342	+	0.225071i	$0.0722614\pi$
$198$		0			0
$199$	−15.1705			−1.07541			−0.537703	−	0.843134i	$-0.680708\pi$
$199$	−15.1705			−1.07541			−0.537703	+	0.843134i	$0.680708\pi$
$200$	6.31658	−	23.5738i	0.446650	−	1.66692i
$201$		0			0
$202$	10.6603	−	2.85641i	0.750053	−	0.200976i
$203$	−10.3463	+	1.01105i	−0.726169	+	0.0709620i
$204$		0			0
$205$			4.10984i			0.287044i
$206$	−9.89436	+	2.65119i	−0.689373	+	0.184717i
$207$		0			0
$208$	15.8529	−	3.76819i	1.09920	−	0.261277i
$209$		−	47.2324i		−	3.26714i
$210$		0			0
$211$	10.0981	+	17.4904i	0.695180	+	1.20409i	0.970120	+	0.242626i	$0.0780088\pi$
$211$	10.0981	+	17.4904i	0.695180	+	1.20409i	−0.274940	+	0.961461i	$0.588658\pi$
$212$	5.31241	−	3.06712i	0.364858	−	0.210651i
$213$		0			0
$214$	16.4500	+	16.4500i	1.12450	+	1.12450i
$215$	−0.0230758	+	0.0861201i	−0.00157376	+	0.00587334i
$216$		0			0
$217$	−4.13471	+	5.03033i	−0.280683	+	0.341481i
$218$	−14.7051	+	8.48998i	−0.995953	+	0.575014i
$219$		0			0
$220$	6.15033	+	10.6527i	0.414655	+	0.718204i
$221$	3.27359	−	0.778121i	0.220206	−	0.0523421i
$222$		0			0
$223$	18.5472	+	4.96970i	1.24201	+	0.332796i	0.819245	−	0.573444i	$-0.194393\pi$
$223$	18.5472	+	4.96970i	1.24201	+	0.332796i	0.422765	+	0.906239i	$0.361059\pi$
$224$	2.13022	−	0.799903i	0.142331	−	0.0534457i
$225$		0			0
$226$	−10.1835	+	2.72865i	−0.677394	+	0.181507i
$227$	−15.5280	+	15.5280i	−1.03063	+	1.03063i	−0.0311110	+	0.999516i	$0.509905\pi$
$227$	−15.5280	+	15.5280i	−1.03063	+	1.03063i	−0.999516	+	0.0311110i	$0.990095\pi$
$228$		0			0
$229$	25.3854	−	6.80200i	1.67751	−	0.449489i	0.710394	−	0.703805i	$-0.248517\pi$
$229$	25.3854	−	6.80200i	1.67751	−	0.449489i	0.967121	+	0.254316i	$0.0818503\pi$
$230$	8.77757	+	5.06773i	0.578776	+	0.334156i
$231$		0			0
$232$	−19.5238	−	5.23138i	−1.28180	−	0.343457i
$233$	8.80891	+	5.08583i	0.577091	+	0.333184i	0.759976	−	0.649951i	$-0.225210\pi$
$233$	8.80891	+	5.08583i	0.577091	+	0.333184i	−0.182886	+	0.983134i	$0.558544\pi$
$234$		0			0
$235$	0.434132	+	0.751939i	0.0283197	+	0.0490511i
$236$	−12.3793	+	12.3793i	−0.805823	+	0.805823i
$237$		0			0
$238$	5.70212	−	2.14116i	0.369613	−	0.138791i
$239$	0.836974	+	0.836974i	0.0541394	+	0.0541394i	0.733658	−	0.679519i	$-0.237811\pi$
$239$	0.836974	+	0.836974i	0.0541394	+	0.0541394i	−0.679519	+	0.733658i	$0.737811\pi$
$240$		0			0
$241$	−9.04828	−	9.04828i	−0.582851	−	0.582851i	0.352835	−	0.935686i	$-0.385218\pi$
$241$	−9.04828	−	9.04828i	−0.582851	−	0.582851i	−0.935686	+	0.352835i	$0.885218\pi$
$242$	58.2498	+	15.6080i	3.74444	+	1.00332i
$243$		0			0
$244$	−15.9151	−	27.5658i	−1.01886	−	1.76472i
$245$	−1.97126	+	2.94047i	−0.125939	+	0.187860i
$246$		0			0
$247$	28.5925	+	0.813213i	1.81930	+	0.0517435i
$248$	−10.9644	+	6.33028i	−0.696239	+	0.401973i
$249$		0			0
$250$			12.1565i			0.768842i
$251$	−7.87428	+	13.6386i	−0.497020	+	0.860864i	−0.999994	−	0.00343776i	$-0.998906\pi$
$251$	−7.87428	+	13.6386i	−0.497020	+	0.860864i	0.502974	+	0.864301i	$0.332239\pi$
$252$		0			0
$253$	46.7210	−	12.5188i	2.93732	−	0.787053i
$254$	−24.9336	−	6.68093i	−1.56447	−	0.419199i
$255$		0			0
$256$	−32.5017			−2.03135
$257$	13.0956			0.816883			0.408442	−	0.912784i	$-0.366072\pi$
$257$	13.0956			0.816883			0.408442	+	0.912784i	$0.366072\pi$
$258$		0			0
$259$	−1.13033	−	3.01017i	−0.0702350	−	0.187043i
$260$	−6.55458	+	3.53974i	−0.406498	+	0.219526i
$261$		0			0
$262$	−10.1637	−	37.9315i	−0.627917	−	2.34342i
$263$	−5.02804	+	8.70882i	−0.310042	+	0.537009i	−0.978371	−	0.206857i	$-0.933676\pi$
$263$	−5.02804	+	8.70882i	−0.310042	+	0.537009i	0.668329	+	0.743866i	$0.267010\pi$
$264$		0			0
$265$	−0.536951	+	0.536951i	−0.0329846	+	0.0329846i
$266$	51.5329	−	5.03584i	3.15968	−	0.308767i
$267$		0			0
$268$	−8.07097	−	30.1213i	−0.493013	−	1.83995i
$269$		−	29.3765i		−	1.79112i	−0.444942	−	0.895559i	$-0.646776\pi$
$269$		−	29.3765i		−	1.79112i	0.444942	−	0.895559i	$-0.353224\pi$
$270$		0			0
$271$	1.15041	+	1.15041i	0.0698825	+	0.0698825i	0.741184	−	0.671302i	$-0.234265\pi$
$271$	1.15041	+	1.15041i	0.0698825	+	0.0698825i	−0.671302	+	0.741184i	$0.734265\pi$
$272$	4.21755			0.255727
$273$		0			0
$274$	−47.6248			−2.87712
$275$	19.9726	+	19.9726i	1.20440	+	1.20440i
$276$		0			0
$277$		−	30.7313i		−	1.84647i	−0.384239	−	0.923233i	$-0.625536\pi$
$277$		−	30.7313i		−	1.84647i	0.384239	−	0.923233i	$-0.374464\pi$
$278$	4.50070	+	16.7969i	0.269934	+	1.00741i
$279$		0			0
$280$	−5.59797	+	4.00499i	−0.334543	+	0.239344i
$281$	3.89852	−	3.89852i	0.232566	−	0.232566i	−0.581197	−	0.813763i	$-0.697415\pi$
$281$	3.89852	−	3.89852i	0.232566	−	0.232566i	0.813763	+	0.581197i	$0.197415\pi$
$282$		0			0
$283$	−3.66949	+	6.35574i	−0.218128	+	0.377809i	−0.954236	−	0.299055i	$-0.903328\pi$
$283$	−3.66949	+	6.35574i	−0.218128	+	0.377809i	0.736107	+	0.676865i	$0.236662\pi$
$284$	−7.16687	−	26.7471i	−0.425276	−	1.58715i
$285$		0			0
$286$	−15.1541	+	50.7392i	−0.896081	+	3.00027i
$287$	−13.6527	+	16.6100i	−0.805895	+	0.980459i
$288$		0			0
$289$	−16.1291			−0.948770
$290$	4.90185			0.287846
$291$		0			0
$292$	−49.9929	−	13.3955i	−2.92561	−	0.783915i
$293$	−21.1201	+	5.65910i	−1.23385	+	0.330608i	−0.816076	−	0.577944i	$-0.803855\pi$
$293$	−21.1201	+	5.65910i	−1.23385	+	0.330608i	−0.417771	+	0.908552i	$0.637188\pi$
$294$		0			0
$295$	1.08360	−	1.87685i	0.0630897	−	0.109275i
$296$		−	6.25179i		−	0.363378i
$297$		0			0
$298$	31.1053	−	17.9586i	1.80188	−	1.04032i
$299$	6.77398	+	28.4985i	0.391749	+	1.64811i
$300$		0			0
$301$	−0.379349	+	0.271400i	−0.0218653	+	0.0156432i
$302$	6.31877	+	10.9444i	0.363604	+	0.629781i
$303$		0			0
$304$	34.6317	+	9.27953i	1.98626	+	0.532217i
$305$	2.78621	+	2.78621i	0.159538	+	0.159538i
$306$		0			0
$307$	2.37972	+	2.37972i	0.135818	+	0.135818i	0.771747	−	0.635929i	$-0.219383\pi$
$307$	2.37972	+	2.37972i	0.135818	+	0.135818i	−0.635929	+	0.771747i	$0.719383\pi$
$308$	−10.5311	+	63.4843i	−0.600063	+	3.61735i
$309$		0			0
$310$	2.17109	−	2.17109i	0.123310	−	0.123310i
$311$	−6.25768	−	10.8386i	−0.354841	−	0.614602i	0.632250	−	0.774764i	$-0.282132\pi$
$311$	−6.25768	−	10.8386i	−0.354841	−	0.614602i	−0.987091	+	0.160162i	$0.948798\pi$
$312$		0			0
$313$	8.39852	+	4.84889i	0.474713	+	0.274075i	0.718210	−	0.695826i	$-0.244962\pi$
$313$	8.39852	+	4.84889i	0.474713	+	0.274075i	−0.243498	+	0.969901i	$0.578295\pi$
$314$	−2.74832	−	0.736410i	−0.155097	−	0.0415580i
$315$		0			0
$316$	32.8376	+	18.9588i	1.84726	+	1.06651i
$317$	22.5235	−	6.03514i	1.26504	−	0.338967i	0.436913	−	0.899504i	$-0.356072\pi$
$317$	22.5235	−	6.03514i	1.26504	−	0.338967i	0.828130	+	0.560536i	$0.189405\pi$
$318$		0			0
$319$	16.5413	−	16.5413i	0.926135	−	0.926135i
$320$	3.37895	−	0.905386i	0.188889	−	0.0506126i
$321$		0			0
$322$	18.6400	+	49.6401i	1.03877	+	2.76633i
$323$	7.15135	+	1.91620i	0.397912	+	0.106620i
$324$		0			0
$325$	−12.4345	+	11.7467i	−0.689740	+	0.651591i
$326$	16.8753	+	29.2289i	0.934638	+	1.61884i
$327$		0			0
$328$	−36.2041	+	20.9025i	−1.99904	+	1.15414i
$329$	−0.743354	+	4.48115i	−0.0409824	+	0.247054i
$330$		0			0
$331$	6.22017	−	23.2140i	0.341892	−	1.27596i	−0.554310	−	0.832310i	$-0.687018\pi$
$331$	6.22017	−	23.2140i	0.341892	−	1.27596i	0.896202	−	0.443647i	$-0.146315\pi$
$332$	−6.78445	−	6.78445i	−0.372345	−	0.372345i
$333$		0			0
$334$	−4.63096	+	2.67369i	−0.253395	+	0.146298i
$335$	1.93014	+	3.34309i	0.105455	+	0.182653i
$336$		0			0
$337$		−	6.92235i		−	0.377085i	−0.982065	−	0.188542i	$-0.939624\pi$
$337$		−	6.92235i		−	0.377085i	0.982065	−	0.188542i	$-0.0603762\pi$
$338$	−30.4545	−	10.0473i	−1.65651	−	0.546499i
$339$		0			0
$340$	−1.86241	+	0.499032i	−0.101004	+	0.0270638i
$341$		−	14.6527i		−	0.793489i
$342$		0			0
$343$	−17.7350	+	5.33556i	−0.957602	+	0.288093i
$344$	−0.876006	+	0.234725i	−0.0472311	+	0.0126555i
$345$		0			0
$346$	−1.76946	+	6.60373i	−0.0951270	+	0.355019i
$347$	−27.6471			−1.48418			−0.742088	−	0.670302i	$-0.766165\pi$
$347$	−27.6471			−1.48418			−0.742088	+	0.670302i	$0.766165\pi$
$348$		0			0
$349$	−1.89736	+	7.08103i	−0.101563	+	0.379039i	−0.997933	−	0.0642689i	$-0.979528\pi$
$349$	−1.89736	+	7.08103i	−0.101563	+	0.379039i	0.896369	+	0.443308i	$0.146195\pi$
$350$	−19.6617	+	23.9206i	−1.05096	+	1.27861i
$351$		0			0
$352$	−2.56019	+	4.43438i	−0.136459	+	0.236353i
$353$	−6.64590	−	24.8028i	−0.353725	−	1.32012i	−0.882081	−	0.471098i	$-0.843858\pi$
$353$	−6.64590	−	24.8028i	−0.353725	−	1.32012i	0.528355	−	0.849023i	$-0.322809\pi$
$354$		0			0
$355$	1.71393	+	2.96861i	0.0909657	+	0.157557i
$356$	12.3403	−	12.3403i	0.654037	−	0.654037i
$357$		0			0
$358$	5.83322	+	21.7699i	0.308295	+	1.15057i
$359$	−0.592674	−	2.21189i	−0.0312801	−	0.116739i	0.948521	−	0.316716i	$-0.102580\pi$
$359$	−0.592674	−	2.21189i	−0.0312801	−	0.116739i	−0.979801	+	0.199977i	$0.935913\pi$
$360$		0			0
$361$	38.0515	+	21.9690i	2.00271	+	1.15626i
$362$	−21.4823	−	21.4823i	−1.12908	−	1.12908i
$363$		0			0
$364$	−38.2494	−	7.46809i	−2.00481	−	0.391434i
$365$	6.40697			0.335356
$366$		0			0
$367$	23.3720	+	13.4938i	1.22001	+	0.704371i	0.964919	−	0.262547i	$-0.0845624\pi$
$367$	23.3720	+	13.4938i	1.22001	+	0.704371i	0.255088	+	0.966918i	$0.417896\pi$
$368$			36.7162i			1.91396i
$369$		0			0
$370$	0.392410	+	1.46450i	0.0204004	+	0.0761355i
$371$	−3.95383	+	0.386372i	−0.205273	+	0.0200595i
$372$		0			0
$373$	8.38541	+	14.5240i	0.434180	+	0.752022i	0.997228	−	0.0744019i	$-0.0237048\pi$
$373$	8.38541	+	14.5240i	0.434180	+	0.752022i	−0.563048	+	0.826424i	$0.690371\pi$
$374$	−6.85305	+	11.8698i	−0.354363	+	0.613774i
$375$		0			0
$376$	−4.41595	+	7.64865i	−0.227735	+	0.394449i
$377$	9.72861	+	10.2982i	0.501049	+	0.530384i
$378$		0			0
$379$	−6.13097	+	22.8811i	−0.314927	+	1.17532i	0.609131	+	0.793070i	$0.291518\pi$
$379$	−6.13097	+	22.8811i	−0.314927	+	1.17532i	−0.924058	+	0.382253i	$0.875148\pi$
$380$	−16.3908			−0.840833
$381$		0			0
$382$	−0.341397	+	1.27411i	−0.0174674	+	0.0651892i
$383$	−19.3985	−	5.19780i	−0.991215	−	0.265595i	−0.273454	−	0.961885i	$-0.588166\pi$
$383$	−19.3985	−	5.19780i	−0.991215	−	0.265595i	−0.717761	+	0.696290i	$0.754833\pi$
$384$		0			0
$385$	−0.774771	−	7.92840i	−0.0394860	−	0.404069i
$386$	−8.32193	+	14.4140i	−0.423575	+	0.733653i
$387$		0			0
$388$	13.0659	−	3.50100i	0.663321	−	0.177736i
$389$	28.3573	−	16.3721i	1.43777	−	0.830099i	0.440078	−	0.897959i	$-0.354951\pi$
$389$	28.3573	−	16.3721i	1.43777	−	0.830099i	0.997695	+	0.0678608i	$0.0216174\pi$
$390$		0			0
$391$			7.58180i			0.383428i
$392$	−35.9288	−	2.40997i	−1.81468	−	0.121722i
$393$		0			0
$394$	−2.08555	+	1.20410i	−0.105069	+	0.0606614i
$395$	−4.53391	−	1.21486i	−0.228126	−	0.0611261i
$396$		0			0
$397$	−0.946584	+	3.53270i	−0.0475077	+	0.177301i	−0.985603	−	0.169076i	$-0.945922\pi$
$397$	−0.946584	+	3.53270i	−0.0475077	+	0.177301i	0.938095	+	0.346377i	$0.112588\pi$
$398$	26.4622	+	26.4622i	1.32643	+	1.32643i
$399$		0			0
$400$	−18.5682	+	10.7204i	−0.928411	+	0.536018i
$401$	3.97864	−	3.97864i	0.198684	−	0.198684i	−0.600752	−	0.799436i	$-0.705132\pi$
$401$	3.97864	−	3.97864i	0.198684	−	0.198684i	0.799436	+	0.600752i	$0.205132\pi$
$402$		0			0
$403$	8.87014	+	0.252279i	0.441853	+	0.0125669i
$404$	−15.8285	−	9.13860i	−0.787499	−	0.454663i
$405$		0			0
$406$	19.8110	+	16.2837i	0.983201	+	0.808149i
$407$	6.26613	+	3.61775i	0.310601	+	0.179325i
$408$		0			0
$409$	−7.22691	+	7.22691i	−0.357348	+	0.357348i	−0.862834	−	0.505487i	$-0.831313\pi$
$409$	−7.22691	+	7.22691i	−0.357348	+	0.357348i	0.505487	+	0.862834i	$0.331313\pi$
$410$	7.16890	−	7.16890i	0.354047	−	0.354047i
$411$		0			0
$412$	14.6913	+	8.48202i	0.723788	+	0.417879i
$413$	10.6142	−	3.98567i	0.522292	−	0.196122i
$414$		0			0
$415$	1.02861	+	0.593866i	0.0504923	+	0.0291517i
$416$	−2.64031	−	1.62618i	−0.129452	−	0.0797300i
$417$		0			0
$418$	−82.3887	+	82.3887i	−4.02976	+	4.02976i
$419$	12.7783	−	7.37756i	0.624261	−	0.360417i	−0.154265	−	0.988029i	$-0.549301\pi$
$419$	12.7783	−	7.37756i	0.624261	−	0.360417i	0.778526	+	0.627612i	$0.215968\pi$
$420$		0			0
$421$	−15.6726	−	15.6726i	−0.763838	−	0.763838i	0.213176	−	0.977014i	$-0.431619\pi$
$421$	−15.6726	−	15.6726i	−0.763838	−	0.763838i	−0.977014	+	0.213176i	$0.931619\pi$
$422$	12.8946	−	48.1232i	0.627698	−	2.34260i
$423$		0			0
$424$	−7.46098	−	1.99916i	−0.362337	−	0.0970879i
$425$	−3.83429	+	2.21373i	−0.185990	+	0.107382i
$426$		0			0
$427$	2.00486	+	20.5162i	0.0970222	+	0.992849i
$428$		−	38.5270i		−	1.86227i
$429$		0			0
$430$	0.190473	−	0.109970i	0.00918543	−	0.00530321i
$431$	24.3888	−	6.53496i	1.17477	−	0.314778i	0.381918	−	0.924196i	$-0.375264\pi$
$431$	24.3888	−	6.53496i	1.17477	−	0.314778i	0.792849	+	0.609418i	$0.208597\pi$
$432$		0			0
$433$	12.7247	−	22.0399i	0.611512	−	1.05917i	−0.379474	−	0.925203i	$-0.623895\pi$
$433$	12.7247	−	22.0399i	0.611512	−	1.05917i	0.990986	−	0.133967i	$-0.0427717\pi$
$434$	15.9868	−	1.56225i	0.767391	−	0.0749903i
$435$		0			0
$436$	27.1623	+	7.27811i	1.30084	+	0.348558i
$437$	−16.6816	+	62.2565i	−0.797989	+	2.97813i
$438$		0			0
$439$	−12.5999			−0.601362			−0.300681	−	0.953725i	$-0.597214\pi$
$439$	−12.5999			−0.601362			−0.300681	+	0.953725i	$0.597214\pi$
$440$	4.00881	−	14.9611i	0.191113	−	0.713242i
$441$		0			0
$442$	−7.06751	−	4.35292i	−0.336167	−	0.207047i
$443$	5.24317	−	9.08144i	0.249111	−	0.431472i	−0.714169	−	0.699974i	$-0.753195\pi$
$443$	5.24317	−	9.08144i	0.249111	−	0.431472i	0.963279	+	0.268501i	$0.0865284\pi$
$444$		0			0
$445$	−1.08019	+	1.87095i	−0.0512060	+	0.0886914i
$446$	−23.6835	−	41.0211i	−1.12145	−	1.94240i
$447$		0			0
$448$	16.6638	+	7.56558i	0.787288	+	0.357440i
$449$	1.45535	+	5.43146i	0.0686824	+	0.256326i	0.991727	−	0.128368i	$-0.0409737\pi$
$449$	1.45535	+	5.43146i	0.0686824	+	0.256326i	−0.923044	+	0.384694i	$0.874307\pi$
$450$		0			0
$451$		−	48.3829i		−	2.27826i
$452$	15.1206	+	8.72987i	0.711212	+	0.410618i
$453$		0			0
$454$	54.1716			2.54240
$455$	4.81286	−	0.332509i	0.225630	−	0.0155883i
$456$		0			0
$457$	8.37852	+	8.37852i	0.391930	+	0.391930i	0.875375	−	0.483445i	$-0.160615\pi$
$457$	8.37852	+	8.37852i	0.391930	+	0.391930i	−0.483445	+	0.875375i	$0.660615\pi$
$458$	−56.1453	−	32.4155i	−2.62350	−	1.51468i
$459$		0			0
$460$	−4.34436	−	16.2134i	−0.202557	−	0.755952i
$461$	2.12757	+	7.94019i	0.0990907	+	0.369812i	0.997608	−	0.0691268i	$-0.0220213\pi$
$461$	2.12757	+	7.94019i	0.0990907	+	0.369812i	−0.898517	+	0.438938i	$0.855355\pi$
$462$		0			0
$463$	−21.3807	+	21.3807i	−0.993646	+	0.993646i	−0.999980	−	0.00633382i	$-0.997984\pi$
$463$	−21.3807	+	21.3807i	−0.993646	+	0.993646i	0.00633382	+	0.999980i	$0.497984\pi$
$464$	8.87858	+	15.3782i	0.412178	+	0.713913i
$465$		0			0
$466$	−6.49427	−	24.2369i	−0.300841	−	1.12275i
$467$	−14.3612	+	24.8744i	−0.664559	+	1.15105i	0.314846	+	0.949143i	$0.398047\pi$
$467$	−14.3612	+	24.8744i	−0.664559	+	1.15105i	−0.979405	+	0.201907i	$0.935286\pi$
$468$		0			0
$469$	−3.30493	+	19.9230i	−0.152607	+	0.919961i
$470$	0.554358	−	2.06889i	0.0255706	−	0.0954309i
$471$		0			0
$472$	22.0446			1.01468
$473$	0.271659	−	1.01384i	0.0124909	−	0.0466166i
$474$		0			0
$475$	−36.3552	+	9.74136i	−1.66809	+	0.446964i
$476$	−9.18477	−	4.17001i	−0.420983	−	0.191132i
$477$		0			0
$478$		−	2.91991i		−	0.133554i
$479$	−16.5106	+	4.42401i	−0.754390	+	0.202138i	−0.615464	−	0.788165i	$-0.711032\pi$
$479$	−16.5106	+	4.42401i	−0.754390	+	0.202138i	−0.138925	+	0.990303i	$0.544365\pi$
$480$		0			0
$481$	−2.29792	+	3.73097i	−0.104776	+	0.170117i
$482$			31.5663i			1.43780i
$483$		0			0
$484$	−49.9351	−	86.4902i	−2.26978	−	3.93137i
$485$	−1.45016	+	0.837249i	−0.0658483	+	0.0380175i
$486$		0			0
$487$	−10.7094	−	10.7094i	−0.485290	−	0.485290i	0.421526	−	0.906816i	$-0.361494\pi$
$487$	−10.7094	−	10.7094i	−0.485290	−	0.485290i	−0.906816	+	0.421526i	$0.861494\pi$
$488$	−10.3735	+	38.7146i	−0.469588	+	1.75253i
$489$		0			0
$490$	8.56766	−	1.69063i	0.387048	−	0.0763747i
$491$	−4.15520	+	2.39900i	−0.187521	+	0.108266i	−0.590822	−	0.806802i	$-0.701196\pi$
$491$	−4.15520	+	2.39900i	−0.187521	+	0.108266i	0.403300	+	0.915068i	$0.367863\pi$
$492$		0			0
$493$	1.83341	+	3.17555i	0.0825724	+	0.143020i
$494$	−48.4562	−	51.2932i	−2.18015	−	2.30779i
$495$		0			0
$496$	10.7436	+	2.87875i	0.482403	+	0.129259i
$497$	−2.93471	+	17.6913i	−0.131640	+	0.793563i
$498$		0			0
$499$	−14.5993	+	3.91188i	−0.653556	+	0.175120i	−0.570336	−	0.821411i	$-0.693187\pi$
$499$	−14.5993	+	3.91188i	−0.653556	+	0.175120i	−0.0832201	+	0.996531i	$0.526520\pi$
$500$	14.2357	−	14.2357i	0.636638	−	0.636638i
$501$		0			0
$502$	37.5255	−	10.0549i	1.67485	−	0.448774i
$503$	13.9638	+	8.06201i	0.622615	+	0.359467i	0.777887	−	0.628405i	$-0.216292\pi$
$503$	13.9638	+	8.06201i	0.622615	+	0.359467i	−0.155271	+	0.987872i	$0.549625\pi$
$504$		0			0
$505$	2.18546	+	0.585591i	0.0972515	+	0.0260585i
$506$	−103.334	−	59.6596i	−4.59373	−	2.65219i
$507$		0			0
$508$	21.3745	+	37.0218i	0.948342	+	1.64258i
$509$	23.4399	−	23.4399i	1.03896	−	1.03896i	0.0397455	−	0.999210i	$-0.487345\pi$
$509$	23.4399	−	23.4399i	1.03896	−	1.03896i	0.999210	−	0.0397455i	$-0.0126547\pi$
$510$		0			0
$511$	25.8940	+	21.2837i	1.14548	+	0.941536i
$512$	30.1297	+	30.1297i	1.33156	+	1.33156i
$513$		0			0
$514$	−22.8430	−	22.8430i	−1.00756	−	1.00756i
$515$	−2.02844	−	0.543518i	−0.0893837	−	0.0239503i
$516$		0			0
$517$	−5.11080	−	8.85217i	−0.224773	−	0.389318i
$518$	−3.27906	+	7.22237i	−0.144074	+	0.317333i
$519$		0			0
$520$	8.98780	+	2.68436i	0.394141	+	0.117717i
$521$	8.41886	−	4.86063i	0.368837	−	0.212948i	−0.304113	−	0.952636i	$-0.598360\pi$
$521$	8.41886	−	4.86063i	0.368837	−	0.212948i	0.672950	+	0.739688i	$0.265027\pi$
$522$		0			0
$523$		−	19.4487i		−	0.850434i	−0.905091	−	0.425217i	$-0.860198\pi$
$523$		−	19.4487i		−	0.850434i	0.905091	−	0.425217i	$-0.139802\pi$
$524$	−32.5171	+	56.3213i	−1.42052	+	2.46041i
$525$		0			0
$526$	23.9615	−	6.42047i	1.04477	−	0.279946i
$527$	2.21853	+	0.594454i	0.0966408	+	0.0258948i
$528$		0			0
$529$	−43.0038			−1.86973
$530$	1.87323			0.0813681
$531$		0			0
$532$	−66.2441	−	54.4498i	−2.87204	−	2.36070i
$533$	29.2890	+	0.833021i	1.26865	+	0.0360821i
$534$		0			0
$535$	1.23438	+	4.60678i	0.0533671	+	0.199169i
$536$	−19.6332	+	34.0057i	−0.848024	+	1.46882i
$537$		0			0
$538$	−51.2422	+	51.2422i	−2.20921	+	2.20921i
$539$	23.2066	−	34.6166i	0.999578	−	1.49104i
$540$		0			0
$541$	2.74629	+	10.2493i	0.118072	+	0.440652i	0.999498	−	0.0316700i	$-0.0100826\pi$
$541$	2.74629	+	10.2493i	0.118072	+	0.440652i	−0.881426	+	0.472322i	$0.843416\pi$
$542$		−	4.01338i		−	0.172389i
$543$		0			0
$544$	−0.567533	−	0.567533i	−0.0243328	−	0.0243328i
$545$	−3.48105			−0.149112
$546$		0			0
$547$	−23.4548			−1.00285			−0.501427	−	0.865200i	$-0.667192\pi$
$547$	−23.4548			−1.00285			−0.501427	+	0.865200i	$0.667192\pi$
$548$	55.7704	+	55.7704i	2.38239	+	2.38239i
$549$		0			0
$550$		−	69.6775i		−	2.97106i
$551$	8.06777	+	30.1093i	0.343699	+	1.28270i
$552$		0			0
$553$	−14.2882	−	19.9713i	−0.607596	−	0.849267i
$554$	−53.6054	+	53.6054i	−2.27748	+	2.27748i
$555$		0			0
$556$	14.3993	−	24.9402i	0.610664	−	1.05770i
$557$	−5.18753	−	19.3601i	−0.219803	−	0.820315i	−0.984420	−	0.175831i	$-0.943739\pi$
$557$	−5.18753	−	19.3601i	−0.219803	−	0.820315i	0.764618	−	0.644484i	$-0.222928\pi$
$558$		0			0
$559$	0.609062	+	0.181907i	0.0257606	+	0.00769383i
$560$	5.96546	+	0.989578i	0.252087	+	0.0418173i
$561$		0			0
$562$	−13.6006			−0.573706
$563$	45.7544			1.92832			0.964159	−	0.265327i	$-0.0854799\pi$
$563$	45.7544			1.92832			0.964159	+	0.265327i	$0.0854799\pi$
$564$		0			0
$565$	−2.08771	−	0.559400i	−0.0878306	−	0.0235341i
$566$	17.4872	−	4.68569i	0.735044	−	0.196954i
$567$		0			0
$568$	−17.4339	+	30.1964i	−0.731510	+	1.26701i
$569$			24.1207i			1.01119i	0.862771	+	0.505595i	$0.168727\pi$
$569$			24.1207i			1.01119i	−0.862771	+	0.505595i	$0.831273\pi$
$570$		0			0
$571$	−15.0931	+	8.71402i	−0.631628	+	0.364671i	−0.781382	−	0.624053i	$-0.785485\pi$
$571$	−15.0931	+	8.71402i	−0.631628	+	0.364671i	0.149754	+	0.988723i	$0.452152\pi$
$572$	77.1635	−	41.6715i	3.22637	−	1.74237i
$573$		0			0
$574$	52.7881	−	5.15850i	2.20333	−	0.215312i
$575$	−19.2717	−	33.3796i	−0.803687	−	1.39203i
$576$		0			0
$577$	21.0789	+	5.64807i	0.877525	+	0.235132i	0.669339	−	0.742957i	$-0.266577\pi$
$577$	21.0789	+	5.64807i	0.877525	+	0.235132i	0.208186	+	0.978089i	$0.433244\pi$
$578$	28.1344	+	28.1344i	1.17024	+	1.17024i
$579$		0			0
$580$	−5.74025	−	5.74025i	−0.238351	−	0.238351i
$581$	2.18434	+	5.81711i	0.0906217	+	0.241334i
$582$		0			0
$583$	6.32123	−	6.32123i	0.261799	−	0.261799i
$584$	32.5856	+	56.4399i	1.34840	+	2.33550i
$585$		0			0
$586$	46.7116	+	26.9689i	1.92964	+	1.11408i
$587$	−13.4282	−	3.59809i	−0.554243	−	0.148509i	−0.0291829	−	0.999574i	$-0.509291\pi$
$587$	−13.4282	−	3.59809i	−0.554243	−	0.148509i	−0.525060	+	0.851065i	$0.675957\pi$
$588$		0			0
$589$	16.9091	+	9.76250i	0.696729	+	0.402257i
$590$	−5.16399	+	1.38369i	−0.212598	+	0.0569655i
$591$		0			0
$592$	−3.88368	+	3.88368i	−0.159618	+	0.159618i
$593$	32.5656	−	8.72592i	1.33731	−	0.358331i	0.481873	−	0.876241i	$-0.339957\pi$
$593$	32.5656	−	8.72592i	1.33731	−	0.358331i	0.855435	+	0.517911i	$0.173290\pi$
$594$		0			0
$595$	1.23185	+	0.204345i	0.0505010	+	0.00837735i
$596$	−57.4557	−	15.3952i	−2.35348	−	0.630612i
$597$		0			0
$598$	37.8946	−	61.5266i	1.54962	−	2.51601i
$599$	6.39544	+	11.0772i	0.261311	+	0.452603i	0.966590	−	0.256326i	$-0.0825120\pi$
$599$	6.39544	+	11.0772i	0.261311	+	0.452603i	−0.705280	+	0.708929i	$0.749179\pi$
$600$		0			0
$601$	26.5897	−	15.3516i	1.08462	−	0.626205i	0.152480	−	0.988307i	$-0.451274\pi$
$601$	26.5897	−	15.3516i	1.08462	−	0.626205i	0.932138	+	0.362102i	$0.117941\pi$
$602$	1.13512	+	0.188299i	0.0462639	+	0.00767448i
$603$		0			0
$604$	5.41682	−	20.2158i	0.220407	−	0.822571i
$605$	8.74198	+	8.74198i	0.355412	+	0.355412i
$606$		0			0
$607$	23.2575	−	13.4277i	0.943992	−	0.545014i	0.0527827	−	0.998606i	$-0.483191\pi$
$607$	23.2575	−	13.4277i	0.943992	−	0.545014i	0.891210	+	0.453592i	$0.149858\pi$
$608$	−3.41150	−	5.90889i	−0.138355	−	0.239637i
$609$		0			0
$610$		−	9.72010i		−	0.393555i
$611$	5.44672	−	2.94145i	0.220351	−	0.118999i
$612$		0			0
$613$	10.3125	−	2.76321i	0.416516	−	0.111605i	−0.0444737	−	0.999011i	$-0.514161\pi$
$613$	10.3125	−	2.76321i	0.416516	−	0.111605i	0.460990	+	0.887405i	$0.347494\pi$
$614$		−	8.30201i		−	0.335042i
$615$		0			0
$616$	65.9019	−	47.1485i	2.65526	−	1.89967i
$617$	8.37021	−	2.24279i	0.336972	−	0.0902913i	−0.0863653	−	0.996264i	$-0.527525\pi$
$617$	8.37021	−	2.24279i	0.336972	−	0.0902913i	0.423337	+	0.905972i	$0.360859\pi$
$618$		0			0
$619$	−1.40877	+	5.25761i	−0.0566233	+	0.211321i	−0.988441	−	0.151605i	$-0.951556\pi$
$619$	−1.40877	+	5.25761i	−0.0566233	+	0.211321i	0.931818	+	0.362926i	$0.118222\pi$
$620$	−5.08486			−0.204213
$621$		0			0
$622$	−7.99065	+	29.8215i	−0.320396	+	1.19573i
$623$	−10.5808	+	3.97313i	−0.423912	+	0.159180i
$624$		0			0
$625$	10.6145	−	18.3849i	0.424580	−	0.735394i
$626$	−6.19171	−	23.1078i	−0.247471	−	0.923573i
$627$		0			0
$628$	2.35602	+	4.08075i	0.0940154	+	0.162839i
$629$	−0.801970	+	0.801970i	−0.0319766	+	0.0319766i
$630$		0			0
$631$	1.72756	+	6.44735i	0.0687731	+	0.256665i	0.991749	−	0.128192i	$-0.0409174\pi$
$631$	1.72756	+	6.44735i	0.0687731	+	0.256665i	−0.922976	+	0.384857i	$0.874251\pi$
$632$	−12.3574	−	46.1185i	−0.491551	−	1.83449i
$633$		0			0
$634$	−49.8155	−	28.7610i	−1.97842	−	1.14224i
$635$	−3.74197	−	3.74197i	−0.148495	−	0.148495i
$636$		0			0
$637$	20.5559	+	14.6443i	0.814454	+	0.580228i
$638$	−57.7068			−2.28463
$639$		0			0
$640$	−8.22661	−	4.74964i	−0.325185	−	0.187746i
$641$			3.66669i			0.144826i	0.997375	+	0.0724129i	$0.0230699\pi$
$641$			3.66669i			0.144826i	−0.997375	+	0.0724129i	$0.976930\pi$
$642$		0			0
$643$	−4.98038	−	18.5870i	−0.196407	−	0.733001i	−0.991898	−	0.127036i	$-0.959454\pi$
$643$	−4.98038	−	18.5870i	−0.196407	−	0.733001i	0.795491	−	0.605965i	$-0.207213\pi$
$644$	36.3023	−	79.9585i	1.43051	−	3.15081i
$645$		0			0
$646$	−9.13181	−	15.8168i	−0.359286	−	0.622302i
$647$	−1.07235	+	1.85736i	−0.0421583	+	0.0730204i	−0.886335	−	0.463045i	$-0.846757\pi$
$647$	−1.07235	+	1.85736i	−0.0421583	+	0.0730204i	0.844176	+	0.536066i	$0.180090\pi$
$648$		0			0
$649$	−12.7566	+	22.0952i	−0.500742	+	0.867311i
$650$	42.1799	+	1.19966i	1.65443	+	0.0470544i
$651$		0			0
$652$	14.4665	−	53.9898i	0.566553	−	2.11440i
$653$	22.7955			0.892057			0.446029	−	0.895019i	$-0.352838\pi$
$653$	22.7955			0.892057			0.446029	+	0.895019i	$0.352838\pi$
$654$		0			0
$655$	2.08366	−	7.77632i	0.0814153	−	0.303846i
$656$	35.4752	+	9.50555i	1.38507	+	0.371129i
$657$		0			0
$658$	9.11323	−	6.51993i	0.355271	−	0.254173i
$659$	16.2426	−	28.1330i	0.632721	−	1.09591i	−0.354272	−	0.935142i	$-0.615271\pi$
$659$	16.2426	−	28.1330i	0.632721	−	1.09591i	0.986993	−	0.160763i	$-0.0513954\pi$
$660$		0			0
$661$	−33.3853	+	8.94556i	−1.29854	+	0.347942i	−0.840897	−	0.541195i	$-0.817972\pi$
$661$	−33.3853	+	8.94556i	−1.29854	+	0.347942i	−0.457641	+	0.889137i	$0.651305\pi$
$662$	−51.3428	+	29.6428i	−1.99549	+	1.15210i
$663$		0			0
$664$			12.0815i			0.468853i
$665$	9.66553	+	4.38829i	0.374813	+	0.170170i
$666$		0			0
$667$	−27.6450	+	15.9608i	−1.07042	+	0.618005i
$668$	8.55402	+	2.29204i	0.330965	+	0.0886818i
$669$		0			0
$670$	2.46466	−	9.19823i	0.0952180	−	0.355359i
$671$	−32.8005	−	32.8005i	−1.26625	−	1.26625i
$672$		0			0
$673$	−14.0303	+	8.10040i	−0.540828	+	0.312247i	−0.745415	−	0.666601i	$-0.767748\pi$
$673$	−14.0303	+	8.10040i	−0.540828	+	0.312247i	0.204586	+	0.978849i	$0.434415\pi$
$674$	−12.0748	+	12.0748i	−0.465105	+	0.465105i
$675$		0			0
$676$	23.8976	+	47.4290i	0.919139	+	1.82419i
$677$	−16.1987	−	9.35233i	−0.622567	−	0.359439i	0.155301	−	0.987867i	$-0.450365\pi$
$677$	−16.1987	−	9.35233i	−0.622567	−	0.359439i	−0.777868	+	0.628428i	$0.783699\pi$
$678$		0			0
$679$	−8.64216	−	1.43360i	−0.331656	−	0.0550166i
$680$	2.10259	+	1.21393i	0.0806306	+	0.0465521i
$681$		0			0
$682$	−25.5591	+	25.5591i	−0.978708	+	0.978708i
$683$	−5.04992	+	5.04992i	−0.193230	+	0.193230i	−0.797090	−	0.603860i	$-0.793628\pi$
$683$	−5.04992	+	5.04992i	−0.193230	+	0.193230i	0.603860	+	0.797090i	$0.293628\pi$
$684$		0			0
$685$	−8.45547	−	4.88177i	−0.323067	−	0.186523i
$686$	40.2426	+	21.6287i	1.53647	+	0.825788i
$687$		0			0
$688$	0.689998	+	0.398370i	0.0263059	+	0.0151877i
$689$	3.71777	+	3.93544i	0.141636	+	0.149928i
$690$		0			0
$691$	33.0564	−	33.0564i	1.25752	−	1.25752i	0.305253	−	0.952271i	$-0.401259\pi$
$691$	33.0564	−	33.0564i	1.25752	−	1.25752i	0.952271	−	0.305253i	$-0.0987412\pi$
$692$	9.80532	−	5.66110i	0.372742	−	0.215203i
$693$		0			0
$694$	48.2256	+	48.2256i	1.83062	+	1.83062i
$695$	−0.922688	+	3.44352i	−0.0349995	+	0.130620i
$696$		0			0
$697$	7.32554	+	1.96287i	0.277475	+	0.0743491i
$698$	15.6612	−	9.04201i	0.592786	−	0.342245i
$699$		0			0
$700$	51.0364	−	4.98733i	1.92899	−	0.188503i
$701$		−	12.2740i		−	0.463581i	−0.972766	−	0.231790i	$-0.925542\pi$
$701$		−	12.2740i		−	0.463581i	0.972766	−	0.231790i	$-0.0744584\pi$
$702$		0			0
$703$	−8.34973	+	4.82072i	−0.314916	+	0.181817i
$704$	−39.7785	+	10.6586i	−1.49921	+	0.401712i
$705$		0			0
$706$	−31.6716	+	54.8568i	−1.19198	+	2.06456i
$707$	6.88727	+	9.62668i	0.259023	+	0.362049i
$708$		0			0
$709$	42.5380	+	11.3980i	1.59755	+	0.428062i	0.944301	−	0.329084i	$-0.106740\pi$
$709$	42.5380	+	11.3980i	1.59755	+	0.428062i	0.653247	+	0.757145i	$0.273406\pi$
$710$	2.18857	−	8.16786i	0.0821356	−	0.306534i
$711$		0			0
$712$	−21.9752			−0.823556
$713$	−5.17505	+	19.3136i	−0.193807	+	0.723299i
$714$		0			0
$715$	−7.89153	+	7.45505i	−0.295126	+	0.278803i
$716$	18.6624	−	32.3242i	0.697447	−	1.20801i
$717$		0			0
$718$	−2.82444	+	4.89207i	−0.105407	+	0.182570i
$719$	−0.267002	−	0.462460i	−0.00995748	−	0.0172469i	0.861004	−	0.508599i	$-0.169836\pi$
$719$	−0.267002	−	0.462460i	−0.00995748	−	0.0172469i	−0.870961	+	0.491352i	$0.836503\pi$
$720$		0			0
$721$	−6.39244	−	8.93504i	−0.238067	−	0.332758i
$722$	−28.0530	−	104.695i	−1.04403	−	3.89635i
$723$		0			0
$724$			50.3131i			1.86987i
$725$	−16.1435	−	9.32046i	−0.599555	−	0.346153i
$726$		0			0
$727$	−17.0326			−0.631703			−0.315851	−	0.948809i	$-0.602290\pi$
$727$	−17.0326			−0.631703			−0.315851	+	0.948809i	$0.602290\pi$
$728$	27.4071	+	40.7060i	1.01577	+	1.50866i
$729$		0			0
$730$	−11.1758	−	11.1758i	−0.413636	−	0.413636i
$731$	0.142483	+	0.0822625i	0.00526992	+	0.00304259i
$732$		0			0
$733$	−7.48252	−	27.9251i	−0.276373	−	1.03144i	−0.954916	−	0.296877i	$-0.904055\pi$
$733$	−7.48252	−	27.9251i	−0.276373	−	1.03144i	0.678542	−	0.734561i	$-0.262612\pi$
$734$	−17.2307	−	64.3059i	−0.635997	−	2.37357i
$735$		0			0
$736$	4.94070	−	4.94070i	0.182116	−	0.182116i
$737$	−22.7224	−	39.3564i	−0.836992	−	1.44971i
$738$		0			0
$739$	−3.67777	−	13.7256i	−0.135289	−	0.504906i	−0.999997	−	0.00262992i	$-0.999163\pi$
$739$	−3.67777	−	13.7256i	−0.135289	−	0.504906i	0.864707	−	0.502276i	$-0.167504\pi$
$740$	1.25545	−	2.17451i	0.0461513	−	0.0799364i
$741$		0			0
$742$	7.57072	+	6.22281i	0.277930	+	0.228446i
$743$	−12.9109	+	48.1840i	−0.473654	+	1.76770i	0.152816	+	0.988255i	$0.451166\pi$
$743$	−12.9109	+	48.1840i	−0.473654	+	1.76770i	−0.626470	+	0.779446i	$0.715501\pi$
$744$		0			0
$745$	7.36339			0.269774
$746$	10.7076	−	39.9614i	0.392034	−	1.46309i
$747$		0			0
$748$	21.9252	−	5.87484i	0.801664	−	0.214805i
$749$	−10.3148	+	22.7190i	−0.376893	+	0.830135i
$750$		0			0
$751$			5.71485i			0.208538i	0.994549	+	0.104269i	$0.0332503\pi$
$751$			5.71485i			0.208538i	−0.994549	+	0.104269i	$0.966750\pi$
$752$	7.49466	−	2.00819i	0.273302	−	0.0732311i
$753$		0			0
$754$	0.993553	−	34.9333i	0.0361831	−	1.27219i
$755$			2.59082i			0.0942894i
$756$		0			0
$757$	−8.98844	−	15.5684i	−0.326690	−	0.565844i	0.655163	−	0.755488i	$-0.272600\pi$
$757$	−8.98844	−	15.5684i	−0.326690	−	0.565844i	−0.981853	+	0.189643i	$0.939267\pi$
$758$	50.6065	−	29.2177i	1.83811	−	1.06123i
$759$		0			0
$760$	14.5941	+	14.5941i	0.529384	+	0.529384i
$761$	−9.13126	+	34.0783i	−0.331008	+	1.23534i	0.577125	+	0.816656i	$0.304175\pi$
$761$	−9.13126	+	34.0783i	−0.331008	+	1.23534i	−0.908133	+	0.418682i	$0.862492\pi$
$762$		0			0
$763$	−14.0688	−	11.5639i	−0.509324	−	0.418642i
$764$	1.89182	−	1.09224i	0.0684436	−	0.0395159i
$765$		0			0
$766$	24.7706	+	42.9039i	0.894997	+	1.55018i
$767$	−13.1558	−	8.10275i	−0.475030	−	0.292574i
$768$		0			0
$769$	−31.5109	−	8.44333i	−1.13631	−	0.304474i	−0.358845	−	0.933397i	$-0.616829\pi$
$769$	−31.5109	−	8.44333i	−1.13631	−	0.304474i	−0.777468	+	0.628923i	$0.783496\pi$
$770$	−12.4783	+	15.1812i	−0.449685	+	0.547091i
$771$		0			0
$772$	26.6246	−	7.13404i	0.958241	−	0.256760i
$773$	−21.4303	+	21.4303i	−0.770796	+	0.770796i	−0.978246	−	0.207450i	$-0.933484\pi$
$773$	−21.4303	+	21.4303i	−0.770796	+	0.770796i	0.207450	+	0.978246i	$0.433484\pi$
$774$		0			0
$775$	−11.2783	+	3.02202i	−0.405129	+	0.108554i
$776$	−14.7509	−	8.51642i	−0.529526	−	0.305722i
$777$		0			0
$778$	−78.0226	−	20.9061i	−2.79725	−	0.749520i
$779$	55.8336	+	32.2355i	2.00045	+	1.15496i
$780$		0			0
$781$	−20.1771	−	34.9478i	−0.721994	−	1.25053i
$782$	13.2251	−	13.2251i	0.472929	−	0.472929i
$783$		0			0
$784$	20.8222	+	23.8164i	0.743651	+	0.850587i
$785$	−0.412461	−	0.412461i	−0.0147213	−	0.0147213i
$786$		0			0
$787$	8.37433	+	8.37433i	0.298513	+	0.298513i	0.840431	−	0.541918i	$-0.182302\pi$
$787$	8.37433	+	8.37433i	0.298513	+	0.298513i	−0.541918	+	0.840431i	$0.682302\pi$
$788$	3.85230	+	1.03222i	0.137233	+	0.0367714i
$789$		0			0
$790$	5.78950	+	10.0277i	0.205981	+	0.356770i
$791$	−6.57923	−	9.19612i	−0.233930	−	0.326976i
$792$		0			0
$793$	20.4208	−	19.2913i	0.725163	−	0.685055i
$794$	7.81332	−	4.51103i	0.277285	−	0.160090i
$795$		0			0
$796$		−	61.9766i		−	2.19670i
$797$	−9.50469	+	16.4626i	−0.336673	+	0.583135i	−0.983805	−	0.179243i	$-0.942635\pi$
$797$	−9.50469	+	16.4626i	−0.336673	+	0.583135i	0.647132	+	0.762378i	$0.275968\pi$
$798$		0			0
$799$	1.54763	−	0.414686i	0.0547512	−	0.0146705i
$800$	3.94120	+	1.05604i	0.139343	+	0.0373367i
$801$		0			0
$802$	−13.8801			−0.490123
$803$	−75.4258			−2.66172
$804$		0			0
$805$	−1.77894	+	10.7240i	−0.0626994	+	0.377970i
$806$	−15.0323	−	15.9125i	−0.529492	−	0.560492i
$807$		0			0
$808$	5.95658	+	22.2303i	0.209552	+	0.782058i
$809$	−18.5825	+	32.1858i	−0.653325	+	1.13159i	0.328986	+	0.944335i	$0.393293\pi$
$809$	−18.5825	+	32.1858i	−0.653325	+	1.13159i	−0.982311	+	0.187257i	$0.940040\pi$
$810$		0			0
$811$	−21.6751	+	21.6751i	−0.761116	+	0.761116i	−0.976524	−	0.215408i	$-0.930892\pi$
$811$	−21.6751	+	21.6751i	−0.761116	+	0.761116i	0.215408	+	0.976524i	$0.430892\pi$
$812$	−4.13049	−	42.2682i	−0.144952	−	1.48332i
$813$		0			0
$814$	−4.61963	−	17.2407i	−0.161918	−	0.604286i
$815$			6.91921i			0.242369i
$816$		0			0
$817$	0.988976	+	0.988976i	0.0345999	+	0.0345999i
$818$	25.2122			0.881523
$819$		0			0
$820$	−16.7901			−0.586335
$821$	−1.77293	−	1.77293i	−0.0618758	−	0.0618758i	0.675492	−	0.737368i	$-0.263931\pi$
$821$	−1.77293	−	1.77293i	−0.0618758	−	0.0618758i	−0.737368	+	0.675492i	$0.763931\pi$
$822$		0			0
$823$			20.0566i			0.699128i	0.936912	+	0.349564i	$0.113670\pi$
$823$			20.0566i			0.699128i	−0.936912	+	0.349564i	$0.886330\pi$
$824$	−5.52862	−	20.6331i	−0.192599	−	0.718788i
$825$		0			0
$826$	−25.4670	−	11.5624i	−0.886109	−	0.402306i
$827$	19.4069	−	19.4069i	0.674842	−	0.674842i	−0.283986	−	0.958828i	$-0.591657\pi$
$827$	19.4069	−	19.4069i	0.674842	−	0.674842i	0.958828	+	0.283986i	$0.0916569\pi$
$828$		0			0
$829$	−18.3383	+	31.7629i	−0.636916	+	1.10317i	0.349190	+	0.937052i	$0.386457\pi$
$829$	−18.3383	+	31.7629i	−0.636916	+	1.10317i	−0.986106	+	0.166118i	$0.946877\pi$
$830$	−0.758328	−	2.83012i	−0.0263219	−	0.0982348i
$831$		0			0
$832$	−5.76740	−	24.2637i	−0.199949	−	0.841194i
$833$	4.29974	+	4.91803i	0.148977	+	0.170400i
$834$		0			0
$835$	−1.09626			−0.0379378
$836$	192.961			6.67368
$837$		0			0
$838$	−35.1584	−	9.42066i	−1.21453	−	0.325431i
$839$	−7.31939	+	1.96122i	−0.252693	+	0.0677090i	−0.382942	−	0.923772i	$-0.625089\pi$
$839$	−7.31939	+	1.96122i	−0.252693	+	0.0677090i	0.130249	+	0.991481i	$0.458422\pi$
$840$		0			0
$841$	6.78081	−	11.7447i	0.233821	−	0.404990i
$842$			54.6764i			1.88427i
$843$		0			0
$844$	−71.4541	+	41.2541i	−2.45955	+	1.42002i
$845$	−4.37710	−	4.90556i	−0.150577	−	0.168756i
$846$		0			0
$847$	6.29044	+	64.3714i	0.216142	+	2.21183i
$848$	3.39294	+	5.87674i	0.116514	+	0.201808i
$849$		0			0
$850$	10.5497	+	2.82679i	0.361852	+	0.0969580i
$851$	−6.98159	−	6.98159i	−0.239326	−	0.239326i
$852$		0			0
$853$	30.8352	+	30.8352i	1.05578	+	1.05578i	0.998350	+	0.0574283i	$0.0182901\pi$
$853$	30.8352	+	30.8352i	1.05578	+	1.05578i	0.0574283	+	0.998350i	$0.481710\pi$
$854$	32.2898	−	39.2841i	1.10493	−	1.34427i
$855$		0			0
$856$	−34.3037	+	34.3037i	−1.17248	+	1.17248i
$857$	7.54118	+	13.0617i	0.257602	+	0.446180i	0.965599	−	0.260036i	$-0.0837344\pi$
$857$	7.54118	+	13.0617i	0.257602	+	0.446180i	−0.707997	+	0.706215i	$0.750401\pi$
$858$		0			0
$859$	39.8801	+	23.0248i	1.36069	+	0.785596i	0.989716	−	0.143047i	$-0.0456901\pi$
$859$	39.8801	+	23.0248i	1.36069	+	0.785596i	0.370975	+	0.928643i	$0.379023\pi$
$860$	−0.351830	−	0.0942725i	−0.0119973	−	0.00321467i
$861$		0			0
$862$	−53.9411	−	31.1429i	−1.83724	−	1.06073i
$863$	−25.6796	+	6.88082i	−0.874142	+	0.234226i	−0.667878	−	0.744271i	$-0.732797\pi$
$863$	−25.6796	+	6.88082i	−0.874142	+	0.234226i	−0.206264	+	0.978496i	$0.566131\pi$
$864$		0			0
$865$	−0.991071	+	0.991071i	−0.0336974	+	0.0336974i
$866$	−60.6408	+	16.2487i	−2.06066	+	0.552152i
$867$		0			0
$868$	−20.5506	−	16.8917i	−0.697533	−	0.573342i
$869$	53.3752	+	14.3018i	1.81063	+	0.485157i
$870$		0			0
$871$	24.2160	−	13.0776i	0.820526	−	0.443118i
$872$	−17.7045	−	30.6651i	−0.599549	−	1.03845i
$873$		0			0
$874$	137.694	−	79.4975i	4.65756	−	2.68904i
$875$	−12.2059	+	4.58335i	−0.412635	+	0.154946i
$876$		0			0
$877$	13.6379	−	50.8975i	0.460521	−	1.71869i	−0.210809	−	0.977527i	$-0.567610\pi$
$877$	13.6379	−	50.8975i	0.460521	−	1.71869i	0.671330	−	0.741159i	$-0.265724\pi$
$878$	21.9784	+	21.9784i	0.741734	+	0.741734i
$879$		0			0
$880$	−11.7843	+	6.80367i	−0.397249	+	0.229352i
$881$	−19.2420	−	33.3282i	−0.648280	−	1.12285i	−0.983533	−	0.180727i	$-0.942155\pi$
$881$	−19.2420	−	33.3282i	−0.648280	−	1.12285i	0.335253	−	0.942128i	$-0.391178\pi$
$882$		0			0
$883$			17.6170i			0.592859i	0.955055	+	0.296429i	$0.0957959\pi$
$883$			17.6170i			0.592859i	−0.955055	+	0.296429i	$0.904204\pi$
$884$	3.17889	+	13.3737i	0.106918	+	0.449808i
$885$		0			0
$886$	−24.9868	+	6.69518i	−0.839447	+	0.224929i
$887$			13.4178i			0.450526i	0.974298	+	0.225263i	$0.0723241\pi$
$887$			13.4178i			0.450526i	−0.974298	+	0.225263i	$0.927676\pi$
$888$		0			0
$889$	−2.69260	−	27.5539i	−0.0903069	−	0.924130i
$890$	5.14774	−	1.37933i	0.172553	−	0.0462354i
$891$		0			0
$892$	−20.3029	+	75.7715i	−0.679792	+	2.53702i
$893$	13.6205			0.455791
$894$		0			0
$895$	−1.19587	+	4.46303i	−0.0399734	+	0.149183i
$896$	−17.4700	−	46.5243i	−0.583631	−	1.55427i
$897$		0			0
$898$	6.93561	−	12.0128i	0.231444	−	0.400874i
$899$	2.50283	+	9.34068i	0.0834740	+	0.311529i
$900$		0			0
$901$	0.700633	+	1.21353i	0.0233415	+	0.0404286i
$902$	−84.3955	+	84.3955i	−2.81006	+	2.81006i
$903$		0			0
$904$	−5.69016	−	21.2360i	−0.189252	−	0.706298i
$905$	−1.61200	−	6.01607i	−0.0535848	−	0.199981i
$906$		0			0
$907$	−12.7403	−	7.35562i	−0.423035	−	0.244239i	0.273340	−	0.961917i	$-0.411872\pi$
$907$	−12.7403	−	7.35562i	−0.423035	−	0.244239i	−0.696375	+	0.717678i	$0.745205\pi$
$908$	−63.4370	−	63.4370i	−2.10523	−	2.10523i
$909$		0			0
$910$	−8.97520	−	7.81519i	−0.297525	−	0.259071i
$911$	25.5134			0.845296			0.422648	−	0.906294i	$-0.361101\pi$
$911$	25.5134			0.845296			0.422648	+	0.906294i	$0.361101\pi$
$912$		0			0
$913$	−12.1092	−	6.99126i	−0.400757	−	0.231377i
$914$		−	29.2297i		−	0.966833i
$915$		0			0
$916$	27.7885	+	103.708i	0.918157	+	3.42661i
$917$	34.2538	−	24.5064i	1.13116	−	0.809272i
$918$		0			0
$919$	17.2037	+	29.7977i	0.567498	+	0.982936i	0.996812	+	0.0797807i	$0.0254220\pi$
$919$	17.2037	+	29.7977i	0.567498	+	0.982936i	−0.429314	+	0.903155i	$0.641245\pi$
$920$	−10.5679	+	18.3042i	−0.348415	+	0.603472i
$921$		0			0
$922$	10.1391	−	17.5614i	0.333914	−	0.578355i
$923$	21.5033	−	11.6127i	0.707790	−	0.382236i
$924$		0			0
$925$	1.49227	−	5.56924i	0.0490656	−	0.183115i
$926$	74.5898			2.45117
$927$		0			0
$928$	0.874612	−	3.26410i	0.0287106	−	0.107149i
$929$	27.9132	+	7.47932i	0.915802	+	0.245388i	0.685790	−	0.727799i	$-0.259457\pi$
$929$	27.9132	+	7.47932i	0.915802	+	0.245388i	0.230012	+	0.973188i	$0.426123\pi$
$930$		0			0
$931$	24.4858	+	49.8439i	0.802489	+	1.63357i
$932$	−20.7773	+	35.9874i	−0.680584	+	1.17881i
$933$		0			0
$934$	68.4397	−	18.3384i	2.23942	−	0.600050i
$935$	−2.43343	+	1.40494i	−0.0795817	+	0.0459465i
$936$		0			0
$937$		−	49.8602i		−	1.62886i	−0.580261	−	0.814431i	$-0.697049\pi$
$937$		−	49.8602i		−	1.62886i	0.580261	−	0.814431i	$-0.302951\pi$
$938$	40.5171	−	28.9874i	1.32293	−	0.946472i
$939$		0			0
$940$	−3.07192	+	1.77358i	−0.100195	+	0.0578477i
$941$	−28.1682	−	7.54766i	−0.918258	−	0.246047i	−0.231418	−	0.972854i	$-0.574336\pi$
$941$	−28.1682	−	7.54766i	−0.918258	−	0.246047i	−0.686841	+	0.726808i	$0.741003\pi$
$942$		0			0
$943$	−17.0879	+	63.7729i	−0.556459	+	2.07673i
$944$	−13.6943	−	13.6943i	−0.445712	−	0.445712i
$945$		0			0
$946$	−2.24234	+	1.29461i	−0.0729046	+	0.0420915i
$947$	−36.5333	+	36.5333i	−1.18717	+	1.18717i	−0.209328	+	0.977845i	$0.567128\pi$
$947$	−36.5333	+	36.5333i	−1.18717	+	1.18717i	−0.977845	+	0.209328i	$0.932872\pi$
$948$		0			0
$949$	1.29863	−	45.6596i	0.0421552	−	1.48217i
$950$	80.4075	+	46.4233i	2.60876	+	1.50617i
$951$		0			0
$952$	4.46504	+	11.8908i	0.144713	+	0.385384i
$953$	4.92386	+	2.84279i	0.159500	+	0.0920871i	0.577625	−	0.816302i	$-0.303980\pi$
$953$	4.92386	+	2.84279i	0.159500	+	0.0920871i	−0.418126	+	0.908389i	$0.637313\pi$
$954$		0			0
$955$	−0.191215	+	0.191215i	−0.00618758	+	0.00618758i
$956$	−3.41932	+	3.41932i	−0.110589	+	0.110589i
$957$		0			0
$958$	36.5168	+	21.0830i	1.17980	+	0.681160i
$959$	−17.9560	−	47.8186i	−0.579829	−	1.54414i
$960$		0			0
$961$	−21.6011	−	12.4714i	−0.696811	−	0.402304i
$962$	10.5163	−	2.49969i	0.339060	−	0.0805934i
$963$		0			0
$964$	36.9653	−	36.9653i	1.19057	−	1.19057i
$965$	−2.95501	+	1.70607i	−0.0951251	+	0.0549205i
$966$		0			0
$967$	24.1174	+	24.1174i	0.775562	+	0.775562i	0.979073	−	0.203511i	$-0.0652352\pi$
$967$	24.1174	+	24.1174i	0.775562	+	0.775562i	−0.203511	+	0.979073i	$0.565235\pi$
$968$	−32.5479	+	121.471i	−1.04613	+	3.90421i
$969$		0			0
$970$	3.98998	+	1.06911i	0.128111	+	0.0343271i
$971$	−25.7950	+	14.8928i	−0.827802	+	0.477932i	−0.853100	−	0.521748i	$-0.825280\pi$
$971$	−25.7950	+	14.8928i	−0.827802	+	0.477932i	0.0252973	+	0.999680i	$0.491947\pi$
$972$		0			0
$973$	−15.1683	+	10.8519i	−0.486273	+	0.347897i
$974$			37.3614i			1.19714i
$975$		0			0
$976$	30.4941	−	17.6058i	0.976091	−	0.563546i
$977$	−25.6398	+	6.87015i	−0.820289	+	0.219796i	−0.644473	−	0.764627i	$-0.722923\pi$
$977$	−25.6398	+	6.87015i	−0.820289	+	0.219796i	−0.175816	+	0.984423i	$0.556256\pi$
$978$		0			0
$979$	12.7165	−	22.0256i	0.406421	−	0.703942i
$980$	−12.0128	−	8.05327i	−0.383736	−	0.257252i
$981$		0			0
$982$	11.4327	+	3.06337i	0.364831	+	0.0977561i
$983$	5.04516	−	18.8288i	0.160915	−	0.600545i	−0.837610	−	0.546268i	$-0.816048\pi$
$983$	5.04516	−	18.8288i	0.160915	−	0.600545i	0.998526	−	0.0542768i	$-0.0172853\pi$
$984$		0			0
$985$	−0.493702			−0.0157307
$986$	2.34114	−	8.73725i	0.0745570	−	0.278251i
$987$		0			0
$988$	−3.32225	+	116.810i	−0.105695	+	3.71623i
$989$	−0.716141	+	1.24039i	−0.0227720	+	0.0394422i
$990$		0			0
$991$	−16.5068	+	28.5907i	−0.524357	+	0.908212i	0.475241	+	0.879856i	$0.342361\pi$
$991$	−16.5068	+	28.5907i	−0.524357	+	0.908212i	−0.999598	+	0.0283567i	$0.990973\pi$
$992$	−1.05833	−	1.83309i	−0.0336021	−	0.0582006i
$993$		0			0
$994$	35.9785	−	25.7403i	1.14117	−	0.816432i
$995$	1.98569	+	7.41071i	0.0629507	+	0.234935i
$996$		0			0
$997$		−	32.8160i		−	1.03929i	−0.854382	−	0.519646i	$-0.826064\pi$
$997$		−	32.8160i		−	1.03929i	0.854382	−	0.519646i	$-0.173936\pi$
$998$	32.2896	+	18.6424i	1.02211	+	0.590115i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.et.c.271.1		36
3.2	odd	2		273.2.bt.a.271.9	yes	36
7.3	odd	6		819.2.gh.c.388.9		36
13.6	odd	12		819.2.gh.c.19.9		36
21.17	even	6		273.2.cg.a.115.1	yes	36
39.32	even	12		273.2.cg.a.19.1	yes	36
91.45	even	12	inner	819.2.et.c.136.1		36
273.227	odd	12		273.2.bt.a.136.9	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.9	✓	36	273.227	odd	12
273.2.bt.a.271.9	yes	36	3.2	odd	2
273.2.cg.a.19.1	yes	36	39.32	even	12
273.2.cg.a.115.1	yes	36	21.17	even	6
819.2.et.c.136.1		36	91.45	even	12	inner
819.2.et.c.271.1		36	1.1	even	1	trivial
819.2.gh.c.19.9		36	13.6	odd	12
819.2.gh.c.388.9		36	7.3	odd	6

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.et (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.74432 - 1.74432i) q^{2} +4.08534i q^{4} +(-0.130892 - 0.488495i) q^{5} +(1.09376 - 2.40909i) q^{7} +(3.63751 - 3.63751i) q^{8} +O(q^{10})\)	\(q+(-1.74432 - 1.74432i) q^{2} +4.08534i q^{4} +(-0.130892 - 0.488495i) q^{5} +(1.09376 - 2.40909i) q^{7} +(3.63751 - 3.63751i) q^{8} +(-0.623777 + 1.08041i) q^{10} +(1.54092 + 5.75079i) q^{11} +(-3.50782 + 0.833795i) q^{13} +(-6.11010 + 2.29436i) q^{14} -4.51932 q^{16} -0.933228 q^{17} +(-7.66303 - 2.05330i) q^{19} +(1.99567 - 0.534738i) q^{20} +(7.34338 - 12.7191i) q^{22} -8.12427i q^{23} +(4.10863 - 2.37212i) q^{25} +(7.57318 + 4.66436i) q^{26} +(9.84193 + 4.46838i) q^{28} +(-1.96458 - 3.40276i) q^{29} +(-2.37727 - 0.636987i) q^{31} +(0.608140 + 0.608140i) q^{32} +(1.62785 + 1.62785i) q^{34} +(-1.31999 - 0.218966i) q^{35} +(0.859350 - 0.859350i) q^{37} +(9.78519 + 16.9484i) q^{38} +(-2.25303 - 1.30079i) q^{40} +(-7.84968 - 2.10332i) q^{41} +(-0.152677 - 0.0881483i) q^{43} +(-23.4939 + 6.29518i) q^{44} +(-14.1714 + 14.1714i) q^{46} +(-1.65836 + 0.444356i) q^{47} +(-4.60738 - 5.26992i) q^{49} +(-11.3045 - 3.02904i) q^{50} +(-3.40634 - 14.3306i) q^{52} +(-0.750763 - 1.30036i) q^{53} +(2.60754 - 1.50546i) q^{55} +(-4.78451 - 12.7416i) q^{56} +(-2.50865 + 9.36239i) q^{58} +(3.03017 + 3.03017i) q^{59} +(-6.74749 + 3.89567i) q^{61} +(3.03561 + 5.25784i) q^{62} +6.91705i q^{64} +(0.866450 + 1.60442i) q^{65} +(-7.37302 + 1.97559i) q^{67} -3.81255i q^{68} +(1.92055 + 2.68444i) q^{70} +(-6.54710 + 1.75429i) q^{71} +(-3.27893 + 12.2371i) q^{73} -2.99797 q^{74} +(8.38844 - 31.3061i) q^{76} +(15.5395 + 2.57777i) q^{77} +(4.64069 - 8.03790i) q^{79} +(0.591542 + 2.20767i) q^{80} +(10.0235 + 17.3613i) q^{82} +(-1.66068 + 1.66068i) q^{83} +(0.122152 + 0.455878i) q^{85} +(0.112560 + 0.420078i) q^{86} +(26.5237 + 15.3134i) q^{88} +(-3.02064 - 3.02064i) q^{89} +(-1.82802 + 9.36260i) q^{91} +33.1904 q^{92} +(3.66782 + 2.11762i) q^{94} +4.01211i q^{95} +(-0.856967 - 3.19825i) q^{97} +(-1.15567 + 17.2292i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 6 q^{7}+O(q^{10}) \) 36 * q + 6 * q^7	\( 36 q + 6 q^{7} + 8 q^{11} - 42 q^{14} - 24 q^{16} + 8 q^{17} - 18 q^{19} - 14 q^{20} + 4 q^{22} + 24 q^{25} + 50 q^{26} + 34 q^{28} - 8 q^{29} + 6 q^{31} + 50 q^{32} - 24 q^{34} - 14 q^{35} - 14 q^{37} + 8 q^{38} - 30 q^{40} - 34 q^{41} + 30 q^{43} - 28 q^{44} - 32 q^{46} + 10 q^{47} + 6 q^{49} + 20 q^{50} + 4 q^{52} + 8 q^{53} - 30 q^{55} + 92 q^{56} + 72 q^{58} + 70 q^{59} - 60 q^{61} + 48 q^{62} + 44 q^{65} - 46 q^{67} + 80 q^{70} - 42 q^{71} - 56 q^{73} - 40 q^{74} + 12 q^{76} - 24 q^{77} - 170 q^{80} + 24 q^{82} + 60 q^{83} + 2 q^{85} - 12 q^{86} + 84 q^{88} - 64 q^{89} - 86 q^{91} + 100 q^{92} - 66 q^{94} + 36 q^{97} + 22 q^{98}+O(q^{100}) \) 36 * q + 6 * q^7 + 8 * q^11 - 42 * q^14 - 24 * q^16 + 8 * q^17 - 18 * q^19 - 14 * q^20 + 4 * q^22 + 24 * q^25 + 50 * q^26 + 34 * q^28 - 8 * q^29 + 6 * q^31 + 50 * q^32 - 24 * q^34 - 14 * q^35 - 14 * q^37 + 8 * q^38 - 30 * q^40 - 34 * q^41 + 30 * q^43 - 28 * q^44 - 32 * q^46 + 10 * q^47 + 6 * q^49 + 20 * q^50 + 4 * q^52 + 8 * q^53 - 30 * q^55 + 92 * q^56 + 72 * q^58 + 70 * q^59 - 60 * q^61 + 48 * q^62 + 44 * q^65 - 46 * q^67 + 80 * q^70 - 42 * q^71 - 56 * q^73 - 40 * q^74 + 12 * q^76 - 24 * q^77 - 170 * q^80 + 24 * q^82 + 60 * q^83 + 2 * q^85 - 12 * q^86 + 84 * q^88 - 64 * q^89 - 86 * q^91 + 100 * q^92 - 66 * q^94 + 36 * q^97 + 22 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more