LMFDB - Embedded newform 1122.2.l.f.727.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1122,2,Mod(463,1122)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1122, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1122.463");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1122 = 2 \cdot 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1122.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.95921510679$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 44x^{14} + 714x^{12} + 5412x^{10} + 20333x^{8} + 35896x^{6} + 23500x^{4} + 1152x^{2} + 4 $ x^16 + 44x^14 + 714x^12 + 5412x^10 + 20333x^8 + 35896x^6 + 23500x^4 + 1152*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			727.2
Root			$1.17550i$ of defining polynomial
Character	$\chi$	$=$	1122.727
Dual form			1122.2.l.f.463.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.896566 - 0.896566i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.18919 + 3.18919i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.896566 - 0.896566i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.18919 + 3.18919i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-0.896566 + 0.896566i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +2.51020 q^{13} +(3.18919 + 3.18919i) q^{14} +1.26794i q^{15} +1.00000 q^{16} +(3.48953 + 2.19617i) q^{17} +1.00000 q^{18} -4.85530i q^{19} +(0.896566 + 0.896566i) q^{20} +4.51020 q^{21} +(0.707107 + 0.707107i) q^{22} +(1.03000 - 1.03000i) q^{23} +(0.707107 - 0.707107i) q^{24} -3.39234i q^{25} -2.51020i q^{26} +(0.707107 - 0.707107i) q^{27} +(3.18919 - 3.18919i) q^{28} +(2.95578 + 2.95578i) q^{29} +1.26794 q^{30} +(-3.66241 - 3.66241i) q^{31} -1.00000i q^{32} +1.00000 q^{33} +(2.19617 - 3.48953i) q^{34} +5.71864 q^{35} -1.00000i q^{36} +(6.74891 + 6.74891i) q^{37} -4.85530 q^{38} +(-1.77498 - 1.77498i) q^{39} +(0.896566 - 0.896566i) q^{40} +(5.88688 - 5.88688i) q^{41} -4.51020i q^{42} -11.0762i q^{43} +(0.707107 - 0.707107i) q^{44} +(0.896566 - 0.896566i) q^{45} +(-1.03000 - 1.03000i) q^{46} -2.10192 q^{47} +(-0.707107 - 0.707107i) q^{48} -13.3419i q^{49} -3.39234 q^{50} +(-0.914546 - 4.02040i) q^{51} -2.51020 q^{52} +8.13075i q^{53} +(-0.707107 - 0.707107i) q^{54} +1.26794 q^{55} +(-3.18919 - 3.18919i) q^{56} +(-3.43321 + 3.43321i) q^{57} +(2.95578 - 2.95578i) q^{58} +3.22737i q^{59} -1.26794i q^{60} +(-9.10827 + 9.10827i) q^{61} +(-3.66241 + 3.66241i) q^{62} +(-3.18919 - 3.18919i) q^{63} -1.00000 q^{64} +(-2.25056 - 2.25056i) q^{65} -1.00000i q^{66} +7.91155 q^{67} +(-3.48953 - 2.19617i) q^{68} -1.45664 q^{69} -5.71864i q^{70} +(11.1731 + 11.1731i) q^{71} -1.00000 q^{72} +(7.53379 + 7.53379i) q^{73} +(6.74891 - 6.74891i) q^{74} +(-2.39875 + 2.39875i) q^{75} +4.85530i q^{76} -4.51020i q^{77} +(-1.77498 + 1.77498i) q^{78} +(9.01391 - 9.01391i) q^{79} +(-0.896566 - 0.896566i) q^{80} -1.00000 q^{81} +(-5.88688 - 5.88688i) q^{82} -8.36020i q^{83} -4.51020 q^{84} +(-1.15958 - 5.09761i) q^{85} -11.0762 q^{86} -4.18010i q^{87} +(-0.707107 - 0.707107i) q^{88} -13.9677 q^{89} +(-0.896566 - 0.896566i) q^{90} +(-8.00550 + 8.00550i) q^{91} +(-1.03000 + 1.03000i) q^{92} +5.17944i q^{93} +2.10192i q^{94} +(-4.35309 + 4.35309i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.75416 + 4.75416i) q^{97} -13.3419 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4} + 4 q^{5}+O(q^{10}) $ 16 * q - 16 * q^4 + 4 * q^5	$ 16 q - 16 q^{4} + 4 q^{5} + 4 q^{10} - 32 q^{13} + 16 q^{16} + 4 q^{17} + 16 q^{18} - 4 q^{20} + 8 q^{29} + 8 q^{30} - 32 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} - 32 q^{38} - 4 q^{40} + 32 q^{41} - 4 q^{45} - 40 q^{47} + 24 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{55} - 4 q^{57} + 8 q^{58} - 12 q^{61} - 32 q^{62} - 16 q^{64} - 24 q^{65} + 48 q^{67} - 4 q^{68} + 40 q^{71} - 16 q^{72} - 12 q^{73} + 32 q^{74} + 8 q^{75} + 40 q^{79} + 4 q^{80} - 16 q^{81} - 32 q^{82} + 28 q^{85} + 48 q^{86} - 72 q^{89} + 4 q^{90} - 8 q^{91} - 80 q^{95} + 72 q^{97}+O(q^{100}) $ 16 * q - 16 * q^4 + 4 * q^5 + 4 * q^10 - 32 * q^13 + 16 * q^16 + 4 * q^17 + 16 * q^18 - 4 * q^20 + 8 * q^29 + 8 * q^30 - 32 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 - 32 * q^38 - 4 * q^40 + 32 * q^41 - 4 * q^45 - 40 * q^47 + 24 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^55 - 4 * q^57 + 8 * q^58 - 12 * q^61 - 32 * q^62 - 16 * q^64 - 24 * q^65 + 48 * q^67 - 4 * q^68 + 40 * q^71 - 16 * q^72 - 12 * q^73 + 32 * q^74 + 8 * q^75 + 40 * q^79 + 4 * q^80 - 16 * q^81 - 32 * q^82 + 28 * q^85 + 48 * q^86 - 72 * q^89 + 4 * q^90 - 8 * q^91 - 80 * q^95 + 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1122\mathbb{Z}\right)^\times$.

$n$	$409$	$749$	$1057$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	−1.00000			−0.500000
$5$	−0.896566	−	0.896566i	−0.400956	−	0.400956i	0.477614	−	0.878570i	$-0.341502\pi$
$5$	−0.896566	−	0.896566i	−0.400956	−	0.400956i	−0.878570	+	0.477614i	$0.841502\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	−3.18919	+	3.18919i	−1.20540	+	1.20540i	−0.232901	+	0.972501i	$0.574822\pi$
$7$	−3.18919	+	3.18919i	−1.20540	+	1.20540i	−0.972501	+	0.232901i	$0.925178\pi$
$8$			1.00000i			0.353553i
$9$			1.00000i			0.333333i
$10$	−0.896566	+	0.896566i	−0.283519	+	0.283519i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	2.51020			0.696204			0.348102	−	0.937457i	$-0.386826\pi$
$13$	2.51020			0.696204			0.348102	+	0.937457i	$0.386826\pi$
$14$	3.18919	+	3.18919i	0.852347	+	0.852347i
$15$			1.26794i			0.327380i
$16$	1.00000			0.250000
$17$	3.48953	+	2.19617i	0.846336	+	0.532649i
$17$	3.48953	+	2.19617i	0.846336	+	0.532649i
$18$	1.00000			0.235702
$19$		−	4.85530i		−	1.11388i	−0.830552	−	0.556941i	$-0.811975\pi$
$19$		−	4.85530i		−	1.11388i	0.830552	−	0.556941i	$-0.188025\pi$
$20$	0.896566	+	0.896566i	0.200478	+	0.200478i
$21$	4.51020			0.984206
$22$	0.707107	+	0.707107i	0.150756	+	0.150756i
$23$	1.03000	−	1.03000i	0.214770	−	0.214770i	−0.591520	−	0.806290i	$-0.701472\pi$
$23$	1.03000	−	1.03000i	0.214770	−	0.214770i	0.806290	+	0.591520i	$0.201472\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$		−	3.39234i		−	0.678468i
$26$		−	2.51020i		−	0.492290i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	3.18919	−	3.18919i	0.602701	−	0.602701i
$29$	2.95578	+	2.95578i	0.548874	+	0.548874i	0.926115	−	0.377241i	$-0.123127\pi$
$29$	2.95578	+	2.95578i	0.548874	+	0.548874i	−0.377241	+	0.926115i	$0.623127\pi$
$30$	1.26794			0.231492
$31$	−3.66241	−	3.66241i	−0.657789	−	0.657789i	0.297068	−	0.954856i	$-0.403991\pi$
$31$	−3.66241	−	3.66241i	−0.657789	−	0.657789i	−0.954856	+	0.297068i	$0.903991\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.00000			0.174078
$34$	2.19617	−	3.48953i	0.376640	−	0.598450i
$35$	5.71864			0.966627
$36$		−	1.00000i		−	0.166667i
$37$	6.74891	+	6.74891i	1.10951	+	1.10951i	0.993214	+	0.116299i	$0.0371032\pi$
$37$	6.74891	+	6.74891i	1.10951	+	1.10951i	0.116299	+	0.993214i	$0.462897\pi$
$38$	−4.85530			−0.787633
$39$	−1.77498	−	1.77498i	−0.284224	−	0.284224i
$40$	0.896566	−	0.896566i	0.141759	−	0.141759i
$41$	5.88688	−	5.88688i	0.919376	−	0.919376i	−0.0776079	−	0.996984i	$-0.524728\pi$
$41$	5.88688	−	5.88688i	0.919376	−	0.919376i	0.996984	+	0.0776079i	$0.0247282\pi$
$42$		−	4.51020i		−	0.695939i
$43$		−	11.0762i		−	1.68910i	−0.535474	−	0.844552i	$-0.679867\pi$
$43$		−	11.0762i		−	1.68910i	0.535474	−	0.844552i	$-0.320133\pi$
$44$	0.707107	−	0.707107i	0.106600	−	0.106600i
$45$	0.896566	−	0.896566i	0.133652	−	0.133652i
$46$	−1.03000	−	1.03000i	−0.151865	−	0.151865i
$47$	−2.10192			−0.306597			−0.153298	−	0.988180i	$-0.548990\pi$
$47$	−2.10192			−0.306597			−0.153298	+	0.988180i	$0.548990\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$		−	13.3419i		−	1.90598i
$50$	−3.39234			−0.479749
$51$	−0.914546	−	4.02040i	−0.128062	−	0.562968i
$52$	−2.51020			−0.348102
$53$			8.13075i			1.11684i	0.829557	+	0.558422i	$0.188593\pi$
$53$			8.13075i			1.11684i	−0.829557	+	0.558422i	$0.811407\pi$
$54$	−0.707107	−	0.707107i	−0.0962250	−	0.0962250i
$55$	1.26794			0.170968
$56$	−3.18919	−	3.18919i	−0.426174	−	0.426174i
$57$	−3.43321	+	3.43321i	−0.454740	+	0.454740i
$58$	2.95578	−	2.95578i	0.388112	−	0.388112i
$59$			3.22737i			0.420168i	0.977683	+	0.210084i	$0.0673737\pi$
$59$			3.22737i			0.420168i	−0.977683	+	0.210084i	$0.932626\pi$
$60$		−	1.26794i		−	0.163690i
$61$	−9.10827	+	9.10827i	−1.16619	+	1.16619i	−0.183101	+	0.983094i	$0.558613\pi$
$61$	−9.10827	+	9.10827i	−1.16619	+	1.16619i	−0.983094	+	0.183101i	$0.941387\pi$
$62$	−3.66241	+	3.66241i	−0.465127	+	0.465127i
$63$	−3.18919	−	3.18919i	−0.401800	−	0.401800i
$64$	−1.00000			−0.125000
$65$	−2.25056	−	2.25056i	−0.279147	−	0.279147i
$66$		−	1.00000i		−	0.123091i
$67$	7.91155			0.966550			0.483275	−	0.875469i	$-0.339447\pi$
$67$	7.91155			0.966550			0.483275	+	0.875469i	$0.339447\pi$
$68$	−3.48953	−	2.19617i	−0.423168	−	0.266325i
$69$	−1.45664			−0.175359
$70$		−	5.71864i		−	0.683508i
$71$	11.1731	+	11.1731i	1.32600	+	1.32600i	0.908825	+	0.417178i	$0.136981\pi$
$71$	11.1731	+	11.1731i	1.32600	+	1.32600i	0.417178	+	0.908825i	$0.363019\pi$
$72$	−1.00000			−0.117851
$73$	7.53379	+	7.53379i	0.881764	+	0.881764i	0.993714	−	0.111950i	$-0.0357097\pi$
$73$	7.53379	+	7.53379i	0.881764	+	0.881764i	−0.111950	+	0.993714i	$0.535710\pi$
$74$	6.74891	−	6.74891i	0.784545	−	0.784545i
$75$	−2.39875	+	2.39875i	−0.276983	+	0.276983i
$76$			4.85530i			0.556941i
$77$		−	4.51020i		−	0.513985i
$78$	−1.77498	+	1.77498i	−0.200977	+	0.200977i
$79$	9.01391	−	9.01391i	1.01414	−	1.01414i	0.0142452	−	0.999899i	$-0.495465\pi$
$79$	9.01391	−	9.01391i	1.01414	−	1.01414i	0.999899	−	0.0142452i	$-0.00453455\pi$
$80$	−0.896566	−	0.896566i	−0.100239	−	0.100239i
$81$	−1.00000			−0.111111
$82$	−5.88688	−	5.88688i	−0.650097	−	0.650097i
$83$		−	8.36020i		−	0.917651i	−0.888526	−	0.458825i	$-0.848270\pi$
$83$		−	8.36020i		−	0.917651i	0.888526	−	0.458825i	$-0.151730\pi$
$84$	−4.51020			−0.492103
$85$	−1.15958	−	5.09761i	−0.125775	−	0.552913i
$86$	−11.0762			−1.19438
$87$		−	4.18010i		−	0.448154i
$88$	−0.707107	−	0.707107i	−0.0753778	−	0.0753778i
$89$	−13.9677			−1.48057			−0.740285	−	0.672293i	$-0.765309\pi$
$89$	−13.9677			−1.48057			−0.740285	+	0.672293i	$0.765309\pi$
$90$	−0.896566	−	0.896566i	−0.0945063	−	0.0945063i
$91$	−8.00550	+	8.00550i	−0.839205	+	0.839205i
$92$	−1.03000	+	1.03000i	−0.107385	+	0.107385i
$93$			5.17944i			0.537082i
$94$			2.10192i			0.216797i
$95$	−4.35309	+	4.35309i	−0.446618	+	0.446618i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	4.75416	+	4.75416i	0.482712	+	0.482712i	0.905997	−	0.423285i	$-0.139123\pi$
$97$	4.75416	+	4.75416i	0.482712	+	0.482712i	−0.423285	+	0.905997i	$0.639123\pi$
$98$	−13.3419			−1.34773
$99$	−0.707107	−	0.707107i	−0.0710669	−	0.0710669i
$100$			3.39234i			0.339234i
$101$	14.1157			1.40456			0.702282	−	0.711899i	$-0.252165\pi$
$101$	14.1157			1.40456			0.702282	+	0.711899i	$0.252165\pi$
$102$	−4.02040	+	0.914546i	−0.398079	+	0.0905535i
$103$	4.56404			0.449708			0.224854	−	0.974392i	$-0.427809\pi$
$103$	4.56404			0.449708			0.224854	+	0.974392i	$0.427809\pi$
$104$			2.51020i			0.246145i
$105$	−4.04369	−	4.04369i	−0.394624	−	0.394624i
$106$	8.13075			0.789728
$107$	−7.65610	−	7.65610i	−0.740143	−	0.740143i	0.232462	−	0.972605i	$-0.425322\pi$
$107$	−7.65610	−	7.65610i	−0.740143	−	0.740143i	−0.972605	+	0.232462i	$0.925322\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	11.0241	−	11.0241i	1.05592	−	1.05592i	0.0575810	−	0.998341i	$-0.481661\pi$
$109$	11.0241	−	11.0241i	1.05592	−	1.05592i	0.998341	−	0.0575810i	$-0.0183388\pi$
$110$		−	1.26794i		−	0.120893i
$111$		−	9.54440i		−	0.905914i
$112$	−3.18919	+	3.18919i	−0.301350	+	0.301350i
$113$	13.2261	−	13.2261i	1.24421	−	1.24421i	0.285970	−	0.958238i	$-0.407684\pi$
$113$	13.2261	−	13.2261i	1.24421	−	1.24421i	0.958238	−	0.285970i	$-0.0923159\pi$
$114$	3.43321	+	3.43321i	0.321550	+	0.321550i
$115$	−1.84693			−0.172227
$116$	−2.95578	−	2.95578i	−0.274437	−	0.274437i
$117$			2.51020i			0.232068i
$118$	3.22737			0.297103
$119$	−18.1328	+	4.12478i	−1.66223	+	0.378118i
$120$	−1.26794			−0.115746
$121$		−	1.00000i		−	0.0909091i
$122$	9.10827	+	9.10827i	0.824624	+	0.824624i
$123$	−8.32530			−0.750667
$124$	3.66241	+	3.66241i	0.328894	+	0.328894i
$125$	−7.52428	+	7.52428i	−0.672992	+	0.672992i
$126$	−3.18919	+	3.18919i	−0.284116	+	0.284116i
$127$		−	14.9754i		−	1.32885i	−0.747353	−	0.664427i	$-0.768676\pi$
$127$		−	14.9754i		−	1.32885i	0.747353	−	0.664427i	$-0.231324\pi$
$128$			1.00000i			0.0883883i
$129$	−7.83205	+	7.83205i	−0.689574	+	0.689574i
$130$	−2.25056	+	2.25056i	−0.197387	+	0.197387i
$131$	10.4360	+	10.4360i	0.911800	+	0.911800i	0.996414	−	0.0846137i	$-0.0269656\pi$
$131$	10.4360	+	10.4360i	0.911800	+	0.911800i	−0.0846137	+	0.996414i	$0.526966\pi$
$132$	−1.00000			−0.0870388
$133$	15.4845	+	15.4845i	1.34267	+	1.34267i
$134$		−	7.91155i		−	0.683454i
$135$	−1.26794			−0.109127
$136$	−2.19617	+	3.48953i	−0.188320	+	0.299225i
$137$	17.8276			1.52312			0.761558	−	0.648097i	$-0.224435\pi$
$137$	17.8276			1.52312			0.761558	+	0.648097i	$0.224435\pi$
$138$			1.45664i			0.123998i
$139$	5.79166	+	5.79166i	0.491242	+	0.491242i	0.908697	−	0.417455i	$-0.137078\pi$
$139$	5.79166	+	5.79166i	0.491242	+	0.491242i	−0.417455	+	0.908697i	$0.637078\pi$
$140$	−5.71864			−0.483313
$141$	1.48628	+	1.48628i	0.125168	+	0.125168i
$142$	11.1731	−	11.1731i	0.937626	−	0.937626i
$143$	−1.77498	+	1.77498i	−0.148431	+	0.148431i
$144$			1.00000i			0.0833333i
$145$		−	5.30010i		−	0.440149i
$146$	7.53379	−	7.53379i	0.623501	−	0.623501i
$147$	−9.43414	+	9.43414i	−0.778115	+	0.778115i
$148$	−6.74891	−	6.74891i	−0.554757	−	0.554757i
$149$	−16.4946			−1.35129			−0.675646	−	0.737227i	$-0.736135\pi$
$149$	−16.4946			−1.35129			−0.675646	+	0.737227i	$0.736135\pi$
$150$	2.39875	+	2.39875i	0.195857	+	0.195857i
$151$		−	10.8274i		−	0.881118i	−0.897724	−	0.440559i	$-0.854780\pi$
$151$		−	10.8274i		−	0.881118i	0.897724	−	0.440559i	$-0.145220\pi$
$152$	4.85530			0.393816
$153$	−2.19617	+	3.48953i	−0.177550	+	0.282112i
$154$	−4.51020			−0.363442
$155$			6.56719i			0.527489i
$156$	1.77498	+	1.77498i	0.142112	+	0.142112i
$157$	4.18290			0.333832			0.166916	−	0.985971i	$-0.446619\pi$
$157$	4.18290			0.333832			0.166916	+	0.985971i	$0.446619\pi$
$158$	−9.01391	−	9.01391i	−0.717108	−	0.717108i
$159$	5.74931	−	5.74931i	0.455950	−	0.455950i
$160$	−0.896566	+	0.896566i	−0.0708797	+	0.0708797i
$161$			6.56975i			0.517768i
$162$			1.00000i			0.0785674i
$163$	6.90776	−	6.90776i	0.541057	−	0.541057i	−0.382782	−	0.923839i	$-0.625034\pi$
$163$	6.90776	−	6.90776i	0.541057	−	0.541057i	0.923839	+	0.382782i	$0.125034\pi$
$164$	−5.88688	+	5.88688i	−0.459688	+	0.459688i
$165$	−0.896566	−	0.896566i	−0.0697975	−	0.0697975i
$166$	−8.36020			−0.648877
$167$	4.86003	+	4.86003i	0.376081	+	0.376081i	0.869686	−	0.493605i	$-0.164321\pi$
$167$	4.86003	+	4.86003i	0.376081	+	0.376081i	−0.493605	+	0.869686i	$0.664321\pi$
$168$			4.51020i			0.347969i
$169$	−6.69890			−0.515300
$170$	−5.09761	+	1.15958i	−0.390969	+	0.0889361i
$171$	4.85530			0.371294
$172$			11.0762i			0.844552i
$173$	−4.33906	−	4.33906i	−0.329892	−	0.329892i	0.522653	−	0.852545i	$-0.324942\pi$
$173$	−4.33906	−	4.33906i	−0.329892	−	0.329892i	−0.852545	+	0.522653i	$0.824942\pi$
$174$	−4.18010			−0.316893
$175$	10.8188	+	10.8188i	0.817826	+	0.817826i
$176$	−0.707107	+	0.707107i	−0.0533002	+	0.0533002i
$177$	2.28209	−	2.28209i	0.171533	−	0.171533i
$178$			13.9677i			1.04692i
$179$			26.4397i			1.97620i	0.153817	+	0.988099i	$0.450843\pi$
$179$			26.4397i			1.97620i	−0.153817	+	0.988099i	$0.549157\pi$
$180$	−0.896566	+	0.896566i	−0.0668261	+	0.0668261i
$181$	10.3815	−	10.3815i	0.771653	−	0.771653i	−0.206742	−	0.978395i	$-0.566286\pi$
$181$	10.3815	−	10.3815i	0.771653	−	0.771653i	0.978395	+	0.206742i	$0.0662862\pi$
$182$	8.00550	+	8.00550i	0.593407	+	0.593407i
$183$	12.8810			0.952194
$184$	1.03000	+	1.03000i	0.0759327	+	0.0759327i
$185$		−	12.1017i		−	0.889733i
$186$	5.17944			0.379775
$187$	−4.02040	+	0.914546i	−0.294001	+	0.0668782i
$188$	2.10192			0.153298
$189$			4.51020i			0.328069i
$190$	4.35309	+	4.35309i	0.315806	+	0.315806i
$191$	−7.07596			−0.511999			−0.255999	−	0.966677i	$-0.582404\pi$
$191$	−7.07596			−0.511999			−0.255999	+	0.966677i	$0.582404\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	1.13715	−	1.13715i	0.0818537	−	0.0818537i	−0.664995	−	0.746848i	$-0.731566\pi$
$193$	1.13715	−	1.13715i	0.0818537	−	0.0818537i	0.746848	+	0.664995i	$0.231566\pi$
$194$	4.75416	−	4.75416i	0.341329	−	0.341329i
$195$			3.18277i			0.227923i
$196$			13.3419i			0.952992i
$197$	−8.02738	+	8.02738i	−0.571927	+	0.571927i	−0.932667	−	0.360740i	$-0.882524\pi$
$197$	−8.02738	+	8.02738i	−0.571927	+	0.571927i	0.360740	+	0.932667i	$0.382524\pi$
$198$	−0.707107	+	0.707107i	−0.0502519	+	0.0502519i
$199$	−1.86648	−	1.86648i	−0.132311	−	0.132311i	0.637850	−	0.770161i	$-0.279824\pi$
$199$	−1.86648	−	1.86648i	−0.132311	−	0.132311i	−0.770161	+	0.637850i	$0.779824\pi$
$200$	3.39234			0.239875
$201$	−5.59431	−	5.59431i	−0.394592	−	0.394592i
$202$		−	14.1157i		−	0.993177i
$203$	−18.8531			−1.32323
$204$	0.914546	+	4.02040i	0.0640310	+	0.281484i
$205$	−10.5559			−0.737259
$206$		−	4.56404i		−	0.317992i
$207$	1.03000	+	1.03000i	0.0715901	+	0.0715901i
$208$	2.51020			0.174051
$209$	3.43321	+	3.43321i	0.237480	+	0.237480i
$210$	−4.04369	+	4.04369i	−0.279041	+	0.279041i
$211$	−18.7536	+	18.7536i	−1.29105	+	1.29105i	−0.356918	+	0.934136i	$0.616173\pi$
$211$	−18.7536	+	18.7536i	−1.29105	+	1.29105i	−0.934136	+	0.356918i	$0.883827\pi$
$212$		−	8.13075i		−	0.558422i
$213$		−	15.8011i		−	1.08268i
$214$	−7.65610	+	7.65610i	−0.523360	+	0.523360i
$215$	−9.93053	+	9.93053i	−0.677257	+	0.677257i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	23.3603			1.58580
$218$	−11.0241	−	11.0241i	−0.746650	−	0.746650i
$219$		−	10.6544i		−	0.719957i
$220$	−1.26794			−0.0854842
$221$	8.75942	+	5.51282i	0.589222	+	0.370833i
$222$	−9.54440			−0.640578
$223$		−	21.5950i		−	1.44611i	−0.690792	−	0.723054i	$-0.742738\pi$
$223$		−	21.5950i		−	1.44611i	0.690792	−	0.723054i	$-0.257262\pi$
$224$	3.18919	+	3.18919i	0.213087	+	0.213087i
$225$	3.39234			0.226156
$226$	−13.2261	−	13.2261i	−0.879789	−	0.879789i
$227$	−6.02484	+	6.02484i	−0.399882	+	0.399882i	−0.878192	−	0.478309i	$-0.841250\pi$
$227$	−6.02484	+	6.02484i	−0.399882	+	0.399882i	0.478309	+	0.878192i	$0.341250\pi$
$228$	3.43321	−	3.43321i	0.227370	−	0.227370i
$229$			18.6213i			1.23053i	0.788320	+	0.615266i	$0.210951\pi$
$229$			18.6213i			1.23053i	−0.788320	+	0.615266i	$0.789049\pi$
$230$			1.84693i			0.121783i
$231$	−3.18919	+	3.18919i	−0.209833	+	0.209833i
$232$	−2.95578	+	2.95578i	−0.194056	+	0.194056i
$233$	15.5225	+	15.5225i	1.01691	+	1.01691i	0.999854	+	0.0170598i	$0.00543058\pi$
$233$	15.5225	+	15.5225i	1.01691	+	1.01691i	0.0170598	+	0.999854i	$0.494569\pi$
$234$	2.51020			0.164097
$235$	1.88451	+	1.88451i	0.122932	+	0.122932i
$236$		−	3.22737i		−	0.210084i
$237$	−12.7476			−0.828045
$238$	4.12478	+	18.1328i	0.267370	+	1.17537i
$239$	14.7962			0.957089			0.478545	−	0.878063i	$-0.341165\pi$
$239$	14.7962			0.957089			0.478545	+	0.878063i	$0.341165\pi$
$240$			1.26794i			0.0818449i
$241$	−11.0753	−	11.0753i	−0.713424	−	0.713424i	0.253826	−	0.967250i	$-0.418311\pi$
$241$	−11.0753	−	11.0753i	−0.713424	−	0.713424i	−0.967250	+	0.253826i	$0.918311\pi$
$242$	−1.00000			−0.0642824
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	9.10827	−	9.10827i	0.583097	−	0.583097i
$245$	−11.9619	+	11.9619i	−0.764217	+	0.764217i
$246$			8.32530i			0.530802i
$247$		−	12.1878i		−	0.775488i
$248$	3.66241	−	3.66241i	0.232564	−	0.232564i
$249$	−5.91155	+	5.91155i	−0.374629	+	0.374629i
$250$	7.52428	+	7.52428i	0.475878	+	0.475878i
$251$	−0.920546			−0.0581043			−0.0290522	−	0.999578i	$-0.509249\pi$
$251$	−0.920546			−0.0581043			−0.0290522	+	0.999578i	$0.509249\pi$
$252$	3.18919	+	3.18919i	0.200900	+	0.200900i
$253$			1.45664i			0.0915783i
$254$	−14.9754			−0.939641
$255$	−2.78460	+	4.42450i	−0.174379	+	0.277073i
$256$	1.00000			0.0625000
$257$			4.72860i			0.294962i	0.989065	+	0.147481i	$0.0471165\pi$
$257$			4.72860i			0.294962i	−0.989065	+	0.147481i	$0.952884\pi$
$258$	7.83205	+	7.83205i	0.487602	+	0.487602i
$259$	−43.0471			−2.67482
$260$	2.25056	+	2.25056i	0.139574	+	0.139574i
$261$	−2.95578	+	2.95578i	−0.182958	+	0.182958i
$262$	10.4360	−	10.4360i	0.644740	−	0.644740i
$263$			12.2294i			0.754094i	0.926194	+	0.377047i	$0.123061\pi$
$263$			12.2294i			0.754094i	−0.926194	+	0.377047i	$0.876939\pi$
$264$			1.00000i			0.0615457i
$265$	7.28975	−	7.28975i	0.447806	−	0.447806i
$266$	15.4845	−	15.4845i	0.949414	−	0.949414i
$267$	9.87664	+	9.87664i	0.604440	+	0.604440i
$268$	−7.91155			−0.483275
$269$	−9.09765	−	9.09765i	−0.554694	−	0.554694i	0.373098	−	0.927792i	$-0.378295\pi$
$269$	−9.09765	−	9.09765i	−0.554694	−	0.554694i	−0.927792	+	0.373098i	$0.878295\pi$
$270$			1.26794i			0.0771641i
$271$	18.9280			1.14979			0.574896	−	0.818227i	$-0.305043\pi$
$271$	18.9280			1.14979			0.574896	+	0.818227i	$0.305043\pi$
$272$	3.48953	+	2.19617i	0.211584	+	0.133162i
$273$	11.3215			0.685208
$274$		−	17.8276i		−	1.07701i
$275$	2.39875	+	2.39875i	0.144650	+	0.144650i
$276$	1.45664			0.0876796
$277$	−4.03691	−	4.03691i	−0.242554	−	0.242554i	0.575352	−	0.817906i	$-0.304865\pi$
$277$	−4.03691	−	4.03691i	−0.242554	−	0.242554i	−0.817906	+	0.575352i	$0.804865\pi$
$278$	5.79166	−	5.79166i	0.347361	−	0.347361i
$279$	3.66241	−	3.66241i	0.219263	−	0.219263i
$280$			5.71864i			0.341754i
$281$		−	13.5398i		−	0.807714i	−0.914822	−	0.403857i	$-0.867669\pi$
$281$		−	13.5398i		−	0.807714i	0.914822	−	0.403857i	$-0.132331\pi$
$282$	1.48628	−	1.48628i	0.0885069	−	0.0885069i
$283$	−15.3332	+	15.3332i	−0.911461	+	0.911461i	−0.996387	−	0.0849259i	$-0.972935\pi$
$283$	−15.3332	+	15.3332i	−0.911461	+	0.911461i	0.0849259	+	0.996387i	$0.472935\pi$
$284$	−11.1731	−	11.1731i	−0.663001	−	0.663001i
$285$	6.15620			0.364662
$286$	1.77498	+	1.77498i	0.104957	+	0.104957i
$287$			37.5488i			2.21643i
$288$	1.00000			0.0589256
$289$	7.35368	+	15.3272i	0.432569	+	0.901601i
$290$	−5.30010			−0.311232
$291$		−	6.72339i		−	0.394132i
$292$	−7.53379	−	7.53379i	−0.440882	−	0.440882i
$293$	12.0620			0.704672			0.352336	−	0.935874i	$-0.385387\pi$
$293$	12.0620			0.704672			0.352336	+	0.935874i	$0.385387\pi$
$294$	9.43414	+	9.43414i	0.550210	+	0.550210i
$295$	2.89355	−	2.89355i	0.168469	−	0.168469i
$296$	−6.74891	+	6.74891i	−0.392272	+	0.392272i
$297$			1.00000i			0.0580259i
$298$			16.4946i			0.955507i
$299$	2.58551	−	2.58551i	0.149524	−	0.149524i
$300$	2.39875	−	2.39875i	0.138492	−	0.138492i
$301$	35.3241	+	35.3241i	2.03605	+	2.03605i
$302$	−10.8274			−0.623044
$303$	−9.98130	−	9.98130i	−0.573411	−	0.573411i
$304$		−	4.85530i		−	0.278470i
$305$	16.3323			0.935186
$306$	3.48953	+	2.19617i	0.199483	+	0.125547i
$307$	−12.1071			−0.690991			−0.345495	−	0.938420i	$-0.612289\pi$
$307$	−12.1071			−0.690991			−0.345495	+	0.938420i	$0.612289\pi$
$308$			4.51020i			0.256992i
$309$	−3.22727	−	3.22727i	−0.183593	−	0.183593i
$310$	6.56719			0.372991
$311$	0.249743	+	0.249743i	0.0141616	+	0.0141616i	0.714152	−	0.699991i	$-0.246812\pi$
$311$	0.249743	+	0.249743i	0.0141616	+	0.0141616i	−0.699991	+	0.714152i	$0.746812\pi$
$312$	1.77498	−	1.77498i	0.100488	−	0.100488i
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	−0.386253	−	0.922393i	$-0.626231\pi$
$313$	9.48528	−	9.48528i	0.536140	−	0.536140i	0.922393	+	0.386253i	$0.126231\pi$
$314$		−	4.18290i		−	0.236055i
$315$			5.71864i			0.322209i
$316$	−9.01391	+	9.01391i	−0.507072	+	0.507072i
$317$	4.45426	−	4.45426i	0.250176	−	0.250176i	−0.570867	−	0.821043i	$-0.693393\pi$
$317$	4.45426	−	4.45426i	0.250176	−	0.250176i	0.821043	+	0.570867i	$0.193393\pi$
$318$	−5.74931	−	5.74931i	−0.322405	−	0.322405i
$319$	−4.18010			−0.234041
$320$	0.896566	+	0.896566i	0.0501195	+	0.0501195i
$321$			10.8274i			0.604324i
$322$	6.56975			0.366118
$323$	10.6631	−	16.9427i	0.593308	−	0.942718i
$324$	1.00000			0.0555556
$325$		−	8.51545i		−	0.472352i
$326$	−6.90776	−	6.90776i	−0.382585	−	0.382585i
$327$	−15.5905			−0.862157
$328$	5.88688	+	5.88688i	0.325049	+	0.325049i
$329$	6.70343	−	6.70343i	0.369572	−	0.369572i
$330$	−0.896566	+	0.896566i	−0.0493543	+	0.0493543i
$331$			20.0783i			1.10360i	0.833976	+	0.551801i	$0.186059\pi$
$331$			20.0783i			1.10360i	−0.833976	+	0.551801i	$0.813941\pi$
$332$			8.36020i			0.458825i
$333$	−6.74891	+	6.74891i	−0.369838	+	0.369838i
$334$	4.86003	−	4.86003i	0.265929	−	0.265929i
$335$	−7.09323	−	7.09323i	−0.387544	−	0.387544i
$336$	4.51020			0.246051
$337$	−18.5542	−	18.5542i	−1.01071	−	1.01071i	−0.999942	−	0.0107691i	$-0.996572\pi$
$337$	−18.5542	−	18.5542i	−1.01071	−	1.01071i	−0.0107691	−	0.999942i	$-0.503428\pi$
$338$			6.69890i			0.364372i
$339$	−18.7046			−1.01589
$340$	1.15958	+	5.09761i	0.0628873	+	0.276457i
$341$	5.17944			0.280482
$342$		−	4.85530i		−	0.262544i
$343$	20.2255	+	20.2255i	1.09207	+	1.09207i
$344$	11.0762			0.597188
$345$	1.30598	+	1.30598i	0.0703114	+	0.0703114i
$346$	−4.33906	+	4.33906i	−0.233269	+	0.233269i
$347$	6.37447	−	6.37447i	0.342200	−	0.342200i	−0.514994	−	0.857194i	$-0.672206\pi$
$347$	6.37447	−	6.37447i	0.342200	−	0.342200i	0.857194	+	0.514994i	$0.172206\pi$
$348$			4.18010i			0.224077i
$349$			16.6931i			0.893561i	0.894644	+	0.446780i	$0.147429\pi$
$349$			16.6931i			0.893561i	−0.894644	+	0.446780i	$0.852571\pi$
$350$	10.8188	−	10.8188i	0.578290	−	0.578290i
$351$	1.77498	−	1.77498i	0.0947413	−	0.0947413i
$352$	0.707107	+	0.707107i	0.0376889	+	0.0376889i
$353$	−23.2110			−1.23540			−0.617699	−	0.786414i	$-0.711935\pi$
$353$	−23.2110			−1.23540			−0.617699	+	0.786414i	$0.711935\pi$
$354$	−2.28209	−	2.28209i	−0.121292	−	0.121292i
$355$		−	20.0348i		−	1.06334i
$356$	13.9677			0.740285
$357$	15.7385	+	9.90516i	0.832969	+	0.524237i
$358$	26.4397			1.39738
$359$			12.2743i			0.647814i	0.946089	+	0.323907i	$0.104996\pi$
$359$			12.2743i			0.647814i	−0.946089	+	0.323907i	$0.895004\pi$
$360$	0.896566	+	0.896566i	0.0472532	+	0.0472532i
$361$	−4.57389			−0.240731
$362$	−10.3815	−	10.3815i	−0.545641	−	0.545641i
$363$	−0.707107	+	0.707107i	−0.0371135	+	0.0371135i
$364$	8.00550	−	8.00550i	0.419602	−	0.419602i
$365$		−	13.5091i		−	0.707098i
$366$		−	12.8810i		−	0.673303i
$367$	−0.983344	+	0.983344i	−0.0513302	+	0.0513302i	−0.732306	−	0.680976i	$-0.761556\pi$
$367$	−0.983344	+	0.983344i	−0.0513302	+	0.0513302i	0.680976	+	0.732306i	$0.261556\pi$
$368$	1.03000	−	1.03000i	0.0536925	−	0.0536925i
$369$	5.88688	+	5.88688i	0.306459	+	0.306459i
$370$	−12.1017			−0.629136
$371$	−25.9305	−	25.9305i	−1.34625	−	1.34625i
$372$		−	5.17944i		−	0.268541i
$373$	1.70381			0.0882200			0.0441100	−	0.999027i	$-0.485955\pi$
$373$	1.70381			0.0882200			0.0441100	+	0.999027i	$0.485955\pi$
$374$	0.914546	+	4.02040i	0.0472900	+	0.207890i
$375$	10.6409			0.549496
$376$		−	2.10192i		−	0.108398i
$377$	7.41959	+	7.41959i	0.382128	+	0.382128i
$378$	4.51020			0.231980
$379$	−2.89493	−	2.89493i	−0.148703	−	0.148703i	0.628836	−	0.777538i	$-0.283532\pi$
$379$	−2.89493	−	2.89493i	−0.148703	−	0.148703i	−0.777538	+	0.628836i	$0.783532\pi$
$380$	4.35309	−	4.35309i	0.223309	−	0.223309i
$381$	−10.5892	+	10.5892i	−0.542502	+	0.542502i
$382$			7.07596i			0.362038i
$383$			34.1052i			1.74269i	0.490668	+	0.871346i	$0.336753\pi$
$383$			34.1052i			1.74269i	−0.490668	+	0.871346i	$0.663247\pi$
$384$	0.707107	−	0.707107i	0.0360844	−	0.0360844i
$385$	−4.04369	+	4.04369i	−0.206085	+	0.206085i
$386$	−1.13715	−	1.13715i	−0.0578793	−	0.0578793i
$387$	11.0762			0.563034
$388$	−4.75416	−	4.75416i	−0.241356	−	0.241356i
$389$		−	25.2068i		−	1.27804i	−0.769192	−	0.639018i	$-0.779341\pi$
$389$		−	25.2068i		−	1.27804i	0.769192	−	0.639018i	$-0.220659\pi$
$390$	3.18277			0.161166
$391$	5.85628	−	1.33217i	0.296165	−	0.0673705i
$392$	13.3419			0.673867
$393$		−	14.7588i		−	0.744482i
$394$	8.02738	+	8.02738i	0.404413	+	0.404413i
$395$	−16.1631			−0.813255
$396$	0.707107	+	0.707107i	0.0355335	+	0.0355335i
$397$	11.8505	−	11.8505i	0.594760	−	0.594760i	−0.344153	−	0.938914i	$-0.611834\pi$
$397$	11.8505	−	11.8505i	0.594760	−	0.594760i	0.938914	+	0.344153i	$0.111834\pi$
$398$	−1.86648	+	1.86648i	−0.0935581	+	0.0935581i
$399$		−	21.8983i		−	1.09629i
$400$		−	3.39234i		−	0.169617i
$401$	−10.0635	+	10.0635i	−0.502547	+	0.502547i	−0.912229	−	0.409682i	$-0.865640\pi$
$401$	−10.0635	+	10.0635i	−0.502547	+	0.502547i	0.409682	+	0.912229i	$0.365640\pi$
$402$	−5.59431	+	5.59431i	−0.279019	+	0.279019i
$403$	−9.19339	−	9.19339i	−0.457955	−	0.457955i
$404$	−14.1157			−0.702282
$405$	0.896566	+	0.896566i	0.0445507	+	0.0445507i
$406$			18.8531i			0.935663i
$407$	−9.54440			−0.473098
$408$	4.02040	−	0.914546i	0.199039	−	0.0452768i
$409$	−31.1765			−1.54158			−0.770789	−	0.637091i	$-0.780138\pi$
$409$	−31.1765			−1.54158			−0.770789	+	0.637091i	$0.780138\pi$
$410$			10.5559i			0.521321i
$411$	−12.6060	−	12.6060i	−0.621809	−	0.621809i
$412$	−4.56404			−0.224854
$413$	−10.2927	−	10.2927i	−0.506470	−	0.506470i
$414$	1.03000	−	1.03000i	0.0506218	−	0.0506218i
$415$	−7.49547	+	7.49547i	−0.367938	+	0.367938i
$416$		−	2.51020i		−	0.123073i
$417$		−	8.19064i		−	0.401097i
$418$	3.43321	−	3.43321i	0.167924	−	0.167924i
$419$	−2.84604	+	2.84604i	−0.139038	+	0.139038i	−0.773200	−	0.634162i	$-0.781345\pi$
$419$	−2.84604	+	2.84604i	−0.139038	+	0.139038i	0.634162	+	0.773200i	$0.281345\pi$
$420$	4.04369	+	4.04369i	0.197312	+	0.197312i
$421$	25.8926			1.26193			0.630964	−	0.775812i	$-0.282660\pi$
$421$	25.8926			1.26193			0.630964	+	0.775812i	$0.282660\pi$
$422$	18.7536	+	18.7536i	0.912913	+	0.912913i
$423$		−	2.10192i		−	0.102199i
$424$	−8.13075			−0.394864
$425$	7.45015	−	11.8377i	0.361386	−	0.574212i
$426$	−15.8011			−0.765568
$427$		−	58.0961i		−	2.81147i
$428$	7.65610	+	7.65610i	0.370072	+	0.370072i
$429$	2.51020			0.121194
$430$	9.93053	+	9.93053i	0.478893	+	0.478893i
$431$	−12.3947	+	12.3947i	−0.597033	+	0.597033i	−0.939522	−	0.342489i	$-0.888730\pi$
$431$	−12.3947	+	12.3947i	−0.597033	+	0.597033i	0.342489	+	0.939522i	$0.388730\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$		−	37.1758i		−	1.78655i	−0.449507	−	0.893277i	$-0.648400\pi$
$433$		−	37.1758i		−	1.78655i	0.449507	−	0.893277i	$-0.351600\pi$
$434$		−	23.3603i		−	1.12133i
$435$	−3.74773	+	3.74773i	−0.179690	+	0.179690i
$436$	−11.0241	+	11.0241i	−0.527961	+	0.527961i
$437$	−5.00096	−	5.00096i	−0.239228	−	0.239228i
$438$	−10.6544			−0.509087
$439$	−19.6255	−	19.6255i	−0.936676	−	0.936676i	0.0614355	−	0.998111i	$-0.480432\pi$
$439$	−19.6255	−	19.6255i	−0.936676	−	0.936676i	−0.998111	+	0.0614355i	$0.980432\pi$
$440$			1.26794i			0.0604464i
$441$	13.3419			0.635328
$442$	5.51282	−	8.75942i	0.262218	−	0.416643i
$443$	16.8239			0.799326			0.399663	−	0.916662i	$-0.369127\pi$
$443$	16.8239			0.799326			0.399663	+	0.916662i	$0.369127\pi$
$444$			9.54440i			0.452957i
$445$	12.5229	+	12.5229i	0.593644	+	0.593644i
$446$	−21.5950			−1.02255
$447$	11.6635	+	11.6635i	0.551662	+	0.551662i
$448$	3.18919	−	3.18919i	0.150675	−	0.150675i
$449$	1.68235	−	1.68235i	0.0793949	−	0.0793949i	−0.666294	−	0.745689i	$-0.732120\pi$
$449$	1.68235	−	1.68235i	0.0793949	−	0.0793949i	0.745689	+	0.666294i	$0.232120\pi$
$450$		−	3.39234i		−	0.159916i
$451$			8.32530i			0.392023i
$452$	−13.2261	+	13.2261i	−0.622104	+	0.622104i
$453$	−7.65610	+	7.65610i	−0.359715	+	0.359715i
$454$	6.02484	+	6.02484i	0.282760	+	0.282760i
$455$	14.3549			0.672969
$456$	−3.43321	−	3.43321i	−0.160775	−	0.160775i
$457$			9.00500i			0.421236i	0.977568	+	0.210618i	$0.0675477\pi$
$457$			9.00500i			0.421236i	−0.977568	+	0.210618i	$0.932452\pi$
$458$	18.6213			0.870118
$459$	4.02040	−	0.914546i	0.187656	−	0.0426873i
$460$	1.84693			0.0861135
$461$			2.58101i			0.120210i	0.998192	+	0.0601048i	$0.0191435\pi$
$461$			2.58101i			0.120210i	−0.998192	+	0.0601048i	$0.980857\pi$
$462$	3.18919	+	3.18919i	0.148375	+	0.148375i
$463$	15.4095			0.716142			0.358071	−	0.933694i	$-0.383435\pi$
$463$	15.4095			0.716142			0.358071	+	0.933694i	$0.383435\pi$
$464$	2.95578	+	2.95578i	0.137218	+	0.137218i
$465$	4.64370	−	4.64370i	0.215347	−	0.215347i
$466$	15.5225	−	15.5225i	0.719067	−	0.719067i
$467$		−	22.2427i		−	1.02927i	−0.857409	−	0.514635i	$-0.827927\pi$
$467$		−	22.2427i		−	1.02927i	0.857409	−	0.514635i	$-0.172073\pi$
$468$		−	2.51020i		−	0.116034i
$469$	−25.2315	+	25.2315i	−1.16508	+	1.16508i
$470$	1.88451	−	1.88451i	0.0869260	−	0.0869260i
$471$	−2.95776	−	2.95776i	−0.136286	−	0.136286i
$472$	−3.22737			−0.148552
$473$	7.83205	+	7.83205i	0.360118	+	0.360118i
$474$			12.7476i			0.585516i
$475$	−16.4708			−0.755733
$476$	18.1328	−	4.12478i	0.831115	−	0.189059i
$477$	−8.13075			−0.372281
$478$		−	14.7962i		−	0.676764i
$479$	−5.29846	−	5.29846i	−0.242093	−	0.242093i	0.575623	−	0.817716i	$-0.304760\pi$
$479$	−5.29846	−	5.29846i	−0.242093	−	0.242093i	−0.817716	+	0.575623i	$0.804760\pi$
$480$	1.26794			0.0578731
$481$	16.9411	+	16.9411i	0.772448	+	0.772448i
$482$	−11.0753	+	11.0753i	−0.504467	+	0.504467i
$483$	4.64551	−	4.64551i	0.211378	−	0.211378i
$484$			1.00000i			0.0454545i
$485$		−	8.52483i		−	0.387093i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	−14.5819	+	14.5819i	−0.660769	+	0.660769i	−0.955561	−	0.294792i	$-0.904749\pi$
$487$	−14.5819	+	14.5819i	−0.660769	+	0.660769i	0.294792	+	0.955561i	$0.404749\pi$
$488$	−9.10827	−	9.10827i	−0.412312	−	0.412312i
$489$	−9.76904			−0.441771
$490$	11.9619	+	11.9619i	0.540383	+	0.540383i
$491$		−	1.67305i		−	0.0755039i	−0.999287	−	0.0377520i	$-0.987980\pi$
$491$		−	1.67305i		−	0.0755039i	0.999287	−	0.0377520i	$-0.0120197\pi$
$492$	8.32530			0.375334
$493$	3.82289	+	16.8057i	0.172174	+	0.756889i
$494$	−12.1878			−0.548353
$495$			1.26794i			0.0569895i
$496$	−3.66241	−	3.66241i	−0.164447	−	0.164447i
$497$	−71.2663			−3.19673
$498$	5.91155	+	5.91155i	0.264903	+	0.264903i
$499$	−14.2200	+	14.2200i	−0.636573	+	0.636573i	−0.949708	−	0.313136i	$-0.898620\pi$
$499$	−14.2200	+	14.2200i	−0.636573	+	0.636573i	0.313136	+	0.949708i	$0.398620\pi$
$500$	7.52428	−	7.52428i	0.336496	−	0.336496i
$501$		−	6.87313i		−	0.307069i
$502$			0.920546i			0.0410860i
$503$	15.3345	−	15.3345i	0.683729	−	0.683729i	−0.277109	−	0.960838i	$-0.589376\pi$
$503$	15.3345	−	15.3345i	0.683729	−	0.683729i	0.960838	+	0.277109i	$0.0893763\pi$
$504$	3.18919	−	3.18919i	0.142058	−	0.142058i
$505$	−12.6556	−	12.6556i	−0.563169	−	0.563169i
$506$	1.45664			0.0647556
$507$	4.73684	+	4.73684i	0.210370	+	0.210370i
$508$			14.9754i			0.664427i
$509$	−10.9592			−0.485760			−0.242880	−	0.970056i	$-0.578092\pi$
$509$	−10.9592			−0.485760			−0.242880	+	0.970056i	$0.578092\pi$
$510$	4.42450	+	2.78460i	0.195920	+	0.123304i
$511$	−48.0534			−2.12576
$512$		−	1.00000i		−	0.0441942i
$513$	−3.43321	−	3.43321i	−0.151580	−	0.151580i
$514$	4.72860			0.208569
$515$	−4.09196	−	4.09196i	−0.180313	−	0.180313i
$516$	7.83205	−	7.83205i	0.344787	−	0.344787i
$517$	1.48628	−	1.48628i	0.0653667	−	0.0653667i
$518$			43.0471i			1.89138i
$519$			6.13635i			0.269356i
$520$	2.25056	−	2.25056i	0.0986935	−	0.0986935i
$521$	18.0276	−	18.0276i	0.789803	−	0.789803i	−0.191659	−	0.981462i	$-0.561387\pi$
$521$	18.0276	−	18.0276i	0.789803	−	0.789803i	0.981462	+	0.191659i	$0.0613868\pi$
$522$	2.95578	+	2.95578i	0.129371	+	0.129371i
$523$	12.4588			0.544787			0.272393	−	0.962186i	$-0.412185\pi$
$523$	12.4588			0.544787			0.272393	+	0.962186i	$0.412185\pi$
$524$	−10.4360	−	10.4360i	−0.455900	−	0.455900i
$525$		−	15.3001i		−	0.667752i
$526$	12.2294			0.533225
$527$	−4.73683	−	20.8234i	−0.206340	−	0.907081i
$528$	1.00000			0.0435194
$529$			20.8782i			0.907748i
$530$	−7.28975	−	7.28975i	−0.316646	−	0.316646i
$531$	−3.22737			−0.140056
$532$	−15.4845	−	15.4845i	−0.671337	−	0.671337i
$533$	14.7772	−	14.7772i	0.640073	−	0.640073i
$534$	9.87664	−	9.87664i	0.427404	−	0.427404i
$535$			13.7284i			0.593530i
$536$			7.91155i			0.341727i
$537$	18.6957	−	18.6957i	0.806780	−	0.806780i
$538$	−9.09765	+	9.09765i	−0.392228	+	0.392228i
$539$	9.43414	+	9.43414i	0.406357	+	0.406357i
$540$	1.26794			0.0545633
$541$	−18.6113	−	18.6113i	−0.800161	−	0.800161i	0.182960	−	0.983120i	$-0.441432\pi$
$541$	−18.6113	−	18.6113i	−0.800161	−	0.800161i	−0.983120	+	0.182960i	$0.941432\pi$
$542$		−	18.9280i		−	0.813025i
$543$	−14.6817			−0.630052
$544$	2.19617	−	3.48953i	0.0941600	−	0.149612i
$545$	−19.7677			−0.846757
$546$		−	11.3215i		−	0.484515i
$547$	−23.8906	−	23.8906i	−1.02149	−	1.02149i	−0.999764	−	0.0217250i	$-0.993084\pi$
$547$	−23.8906	−	23.8906i	−1.02149	−	1.02149i	−0.0217250	−	0.999764i	$-0.506916\pi$
$548$	−17.8276			−0.761558
$549$	−9.10827	−	9.10827i	−0.388732	−	0.388732i
$550$	2.39875	−	2.39875i	0.102283	−	0.102283i
$551$	14.3512	−	14.3512i	0.611380	−	0.611380i
$552$		−	1.45664i		−	0.0619988i
$553$			57.4942i			2.44490i
$554$	−4.03691	+	4.03691i	−0.171512	+	0.171512i
$555$	−8.55718	+	8.55718i	−0.363232	+	0.363232i
$556$	−5.79166	−	5.79166i	−0.245621	−	0.245621i
$557$	24.2179			1.02614			0.513072	−	0.858345i	$-0.328507\pi$
$557$	24.2179			1.02614			0.513072	+	0.858345i	$0.328507\pi$
$558$	−3.66241	−	3.66241i	−0.155042	−	0.155042i
$559$		−	27.8034i		−	1.17596i
$560$	5.71864			0.241657
$561$	3.48953	+	2.19617i	0.147328	+	0.0927224i
$562$	−13.5398			−0.571140
$563$		−	41.5939i		−	1.75297i	−0.481425	−	0.876487i	$-0.659881\pi$
$563$		−	41.5939i		−	1.75297i	0.481425	−	0.876487i	$-0.340119\pi$
$564$	−1.48628	−	1.48628i	−0.0625838	−	0.0625838i
$565$	−23.7162			−0.997747
$566$	15.3332	+	15.3332i	0.644500	+	0.644500i
$567$	3.18919	−	3.18919i	0.133933	−	0.133933i
$568$	−11.1731	+	11.1731i	−0.468813	+	0.468813i
$569$		−	24.3165i		−	1.01940i	−0.860352	−	0.509700i	$-0.829756\pi$
$569$		−	24.3165i		−	1.01940i	0.860352	−	0.509700i	$-0.170244\pi$
$570$		−	6.15620i		−	0.257855i
$571$	9.46627	−	9.46627i	0.396151	−	0.396151i	−0.480722	−	0.876873i	$-0.659625\pi$
$571$	9.46627	−	9.46627i	0.396151	−	0.396151i	0.876873	+	0.480722i	$0.159625\pi$
$572$	1.77498	−	1.77498i	0.0742156	−	0.0742156i
$573$	5.00346	+	5.00346i	0.209023	+	0.209023i
$574$	37.5488			1.56726
$575$	−3.49412	−	3.49412i	−0.145715	−	0.145715i
$576$		−	1.00000i		−	0.0416667i
$577$	16.1030			0.670378			0.335189	−	0.942151i	$-0.391200\pi$
$577$	16.1030			0.670378			0.335189	+	0.942151i	$0.391200\pi$
$578$	15.3272	−	7.35368i	0.637528	−	0.305873i
$579$	−1.60817			−0.0668333
$580$			5.30010i			0.220075i
$581$	26.6623	+	26.6623i	1.10614	+	1.10614i
$582$	−6.72339			−0.278694
$583$	−5.74931	−	5.74931i	−0.238112	−	0.238112i
$584$	−7.53379	+	7.53379i	−0.311751	+	0.311751i
$585$	2.25056	−	2.25056i	0.0930491	−	0.0930491i
$586$		−	12.0620i		−	0.498278i
$587$		−	7.98810i		−	0.329704i	−0.986318	−	0.164852i	$-0.947285\pi$
$587$		−	7.98810i		−	0.329704i	0.986318	−	0.164852i	$-0.0527147\pi$
$588$	9.43414	−	9.43414i	0.389057	−	0.389057i
$589$	−17.7821	+	17.7821i	−0.732699	+	0.732699i
$590$	−2.89355	−	2.89355i	−0.119125	−	0.119125i
$591$	11.3524			0.466976
$592$	6.74891	+	6.74891i	0.277378	+	0.277378i
$593$		−	19.7618i		−	0.811521i	−0.913979	−	0.405761i	$-0.867007\pi$
$593$		−	19.7618i		−	0.811521i	0.913979	−	0.405761i	$-0.132993\pi$
$594$	1.00000			0.0410305
$595$	19.9554	+	12.5591i	0.818091	+	0.514873i
$596$	16.4946			0.675646
$597$			2.63960i			0.108032i
$598$	−2.58551	−	2.58551i	−0.105729	−	0.105729i
$599$	1.78677			0.0730056			0.0365028	−	0.999334i	$-0.488378\pi$
$599$	1.78677			0.0730056			0.0365028	+	0.999334i	$0.488378\pi$
$600$	−2.39875	−	2.39875i	−0.0979284	−	0.0979284i
$601$	1.77235	−	1.77235i	0.0722958	−	0.0722958i	−0.670034	−	0.742330i	$-0.733721\pi$
$601$	1.77235	−	1.77235i	0.0722958	−	0.0722958i	0.742330	+	0.670034i	$0.233721\pi$
$602$	35.3241	−	35.3241i	1.43970	−	1.43970i
$603$			7.91155i			0.322183i
$604$			10.8274i			0.440559i
$605$	−0.896566	+	0.896566i	−0.0364506	+	0.0364506i
$606$	−9.98130	+	9.98130i	−0.405463	+	0.405463i
$607$	−17.5714	−	17.5714i	−0.713200	−	0.713200i	0.254003	−	0.967203i	$-0.418253\pi$
$607$	−17.5714	−	17.5714i	−0.713200	−	0.713200i	−0.967203	+	0.254003i	$0.918253\pi$
$608$	−4.85530			−0.196908
$609$	13.3311	+	13.3311i	0.540205	+	0.540205i
$610$		−	16.3323i		−	0.661277i
$611$	−5.27624			−0.213454
$612$	2.19617	−	3.48953i	0.0887749	−	0.141056i
$613$	16.4735			0.665357			0.332679	−	0.943040i	$-0.392048\pi$
$613$	16.4735			0.665357			0.332679	+	0.943040i	$0.392048\pi$
$614$			12.1071i			0.488604i
$615$	7.46418	+	7.46418i	0.300985	+	0.300985i
$616$	4.51020			0.181721
$617$	22.7300	+	22.7300i	0.915075	+	0.915075i	0.996666	−	0.0815913i	$-0.0260002\pi$
$617$	22.7300	+	22.7300i	0.915075	+	0.915075i	−0.0815913	+	0.996666i	$0.526000\pi$
$618$	−3.22727	+	3.22727i	−0.129820	+	0.129820i
$619$	11.6270	−	11.6270i	0.467330	−	0.467330i	−0.433719	−	0.901048i	$-0.642799\pi$
$619$	11.6270	−	11.6270i	0.467330	−	0.467330i	0.901048	+	0.433719i	$0.142799\pi$
$620$		−	6.56719i		−	0.263745i
$621$		−	1.45664i		−	0.0584530i
$622$	0.249743	−	0.249743i	0.0100138	−	0.0100138i
$623$	44.5456	−	44.5456i	1.78468	−	1.78468i
$624$	−1.77498	−	1.77498i	−0.0710560	−	0.0710560i
$625$	−3.46967			−0.138787
$626$	−9.48528	−	9.48528i	−0.379108	−	0.379108i
$627$		−	4.85530i		−	0.193902i
$628$	−4.18290			−0.166916
$629$	8.72879	+	38.3723i	0.348039	+	1.53000i
$630$	5.71864			0.227836
$631$			31.4127i			1.25052i	0.780416	+	0.625261i	$0.215007\pi$
$631$			31.4127i			1.25052i	−0.780416	+	0.625261i	$0.784993\pi$
$632$	9.01391	+	9.01391i	0.358554	+	0.358554i
$633$	26.5217			1.05414
$634$	−4.45426	−	4.45426i	−0.176901	−	0.176901i
$635$	−13.4264	+	13.4264i	−0.532812	+	0.532812i
$636$	−5.74931	+	5.74931i	−0.227975	+	0.227975i
$637$		−	33.4908i		−	1.32695i
$638$			4.18010i			0.165492i
$639$	−11.1731	+	11.1731i	−0.442001	+	0.442001i
$640$	0.896566	−	0.896566i	0.0354399	−	0.0354399i
$641$	13.3244	+	13.3244i	0.526284	+	0.526284i	0.919462	−	0.393179i	$-0.128625\pi$
$641$	13.3244	+	13.3244i	0.526284	+	0.526284i	−0.393179	+	0.919462i	$0.628625\pi$
$642$	10.8274			0.427322
$643$	−0.480580	−	0.480580i	−0.0189522	−	0.0189522i	0.697567	−	0.716519i	$-0.254266\pi$
$643$	−0.480580	−	0.480580i	−0.0189522	−	0.0189522i	−0.716519	+	0.697567i	$0.754266\pi$
$644$		−	6.56975i		−	0.258884i
$645$	14.0439			0.552978
$646$	−16.9427	−	10.6631i	−0.666602	−	0.419532i
$647$	5.98000			0.235098			0.117549	−	0.993067i	$-0.462496\pi$
$647$	5.98000			0.235098			0.117549	+	0.993067i	$0.462496\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−2.28209	−	2.28209i	−0.0895800	−	0.0895800i
$650$	−8.51545			−0.334003
$651$	−16.5182	−	16.5182i	−0.647400	−	0.647400i
$652$	−6.90776	+	6.90776i	−0.270529	+	0.270529i
$653$	−4.48468	+	4.48468i	−0.175499	+	0.175499i	−0.789391	−	0.613891i	$-0.789603\pi$
$653$	−4.48468	+	4.48468i	−0.175499	+	0.175499i	0.613891	+	0.789391i	$0.289603\pi$
$654$			15.5905i			0.609637i
$655$		−	18.7132i		−	0.731184i
$656$	5.88688	−	5.88688i	0.229844	−	0.229844i
$657$	−7.53379	+	7.53379i	−0.293921	+	0.293921i
$658$	−6.70343	−	6.70343i	−0.261327	−	0.261327i
$659$	13.2400			0.515757			0.257878	−	0.966177i	$-0.416977\pi$
$659$	13.2400			0.515757			0.257878	+	0.966177i	$0.416977\pi$
$660$	0.896566	+	0.896566i	0.0348988	+	0.0348988i
$661$		−	32.9569i		−	1.28188i	−0.767593	−	0.640938i	$-0.778546\pi$
$661$		−	32.9569i		−	1.28188i	0.767593	−	0.640938i	$-0.221454\pi$
$662$	20.0783			0.780364
$663$	−2.29569	−	10.0920i	−0.0891572	−	0.391941i
$664$	8.36020			0.324439
$665$		−	27.7657i		−	1.07671i
$666$	6.74891	+	6.74891i	0.261515	+	0.261515i
$667$	6.08891			0.235763
$668$	−4.86003	−	4.86003i	−0.188040	−	0.188040i
$669$	−15.2700	+	15.2700i	−0.590371	+	0.590371i
$670$	−7.09323	+	7.09323i	−0.274035	+	0.274035i
$671$		−	12.8810i		−	0.497267i
$672$		−	4.51020i		−	0.173985i
$673$	0.380958	−	0.380958i	0.0146849	−	0.0146849i	−0.699726	−	0.714411i	$-0.746695\pi$
$673$	0.380958	−	0.380958i	0.0146849	−	0.0146849i	0.714411	+	0.699726i	$0.246695\pi$
$674$	−18.5542	+	18.5542i	−0.714681	+	0.714681i
$675$	−2.39875	−	2.39875i	−0.0923278	−	0.0923278i
$676$	6.69890			0.257650
$677$	−15.8168	−	15.8168i	−0.607888	−	0.607888i	0.334506	−	0.942394i	$-0.391431\pi$
$677$	−15.8168	−	15.8168i	−0.607888	−	0.607888i	−0.942394	+	0.334506i	$0.891431\pi$
$678$			18.7046i			0.718344i
$679$	−30.3238			−1.16372
$680$	5.09761	−	1.15958i	0.195484	−	0.0444680i
$681$	8.52041			0.326503
$682$		−	5.17944i		−	0.198331i
$683$	4.73482	+	4.73482i	0.181173	+	0.181173i	0.791867	−	0.610694i	$-0.209109\pi$
$683$	4.73482	+	4.73482i	0.181173	+	0.181173i	−0.610694	+	0.791867i	$0.709109\pi$
$684$	−4.85530			−0.185647
$685$	−15.9836	−	15.9836i	−0.610703	−	0.610703i
$686$	20.2255	−	20.2255i	0.772213	−	0.772213i
$687$	13.1673	−	13.1673i	0.502363	−	0.502363i
$688$		−	11.0762i		−	0.422276i
$689$			20.4098i			0.777551i
$690$	1.30598	−	1.30598i	0.0497176	−	0.0497176i
$691$	−28.9965	+	28.9965i	−1.10308	+	1.10308i	−0.109044	+	0.994037i	$0.534779\pi$
$691$	−28.9965	+	28.9965i	−1.10308	+	1.10308i	−0.994037	+	0.109044i	$0.965221\pi$
$692$	4.33906	+	4.33906i	0.164946	+	0.164946i
$693$	4.51020			0.171328
$694$	−6.37447	−	6.37447i	−0.241972	−	0.241972i
$695$		−	10.3852i		−	0.393933i
$696$	4.18010			0.158446
$697$	33.4710	−	7.61387i	1.26781	−	0.288396i
$698$	16.6931			0.631843
$699$		−	21.9522i		−	0.830307i
$700$	−10.8188	−	10.8188i	−0.408913	−	0.408913i
$701$	14.0550			0.530851			0.265426	−	0.964131i	$-0.414488\pi$
$701$	14.0550			0.530851			0.265426	+	0.964131i	$0.414488\pi$
$702$	−1.77498	−	1.77498i	−0.0669922	−	0.0669922i
$703$	32.7679	−	32.7679i	1.23587	−	1.23587i
$704$	0.707107	−	0.707107i	0.0266501	−	0.0266501i
$705$		−	2.66510i		−	0.100374i
$706$			23.2110i			0.873559i
$707$	−45.0177	+	45.0177i	−1.69306	+	1.69306i
$708$	−2.28209	+	2.28209i	−0.0857663	+	0.0857663i
$709$	−17.7149	−	17.7149i	−0.665298	−	0.665298i	0.291326	−	0.956624i	$-0.405903\pi$
$709$	−17.7149	−	17.7149i	−0.665298	−	0.665298i	−0.956624	+	0.291326i	$0.905903\pi$
$710$	−20.0348			−0.751894
$711$	9.01391	+	9.01391i	0.338048	+	0.338048i
$712$		−	13.9677i		−	0.523461i
$713$	−7.54458			−0.282547
$714$	9.90516	−	15.7385i	0.370691	−	0.588998i
$715$	3.18277			0.119029
$716$		−	26.4397i		−	0.988099i
$717$	−10.4625	−	10.4625i	−0.390730	−	0.390730i
$718$	12.2743			0.458074
$719$	−9.99905	−	9.99905i	−0.372902	−	0.372902i	0.495631	−	0.868533i	$-0.334937\pi$
$719$	−9.99905	−	9.99905i	−0.372902	−	0.372902i	−0.868533	+	0.495631i	$0.834937\pi$
$720$	0.896566	−	0.896566i	0.0334130	−	0.0334130i
$721$	−14.5556	+	14.5556i	−0.542079	+	0.542079i
$722$			4.57389i			0.170223i
$723$			15.6629i			0.582508i
$724$	−10.3815	+	10.3815i	−0.385826	+	0.385826i
$725$	10.0270	−	10.0270i	0.372393	−	0.372393i
$726$	0.707107	+	0.707107i	0.0262432	+	0.0262432i
$727$	18.6514			0.691743			0.345872	−	0.938282i	$-0.387583\pi$
$727$	18.6514			0.691743			0.345872	+	0.938282i	$0.387583\pi$
$728$	−8.00550	−	8.00550i	−0.296704	−	0.296704i
$729$		−	1.00000i		−	0.0370370i
$730$	−13.5091			−0.499993
$731$	24.3252	−	38.6507i	0.899700	−	1.42955i
$732$	−12.8810			−0.476097
$733$		−	7.17885i		−	0.265157i	−0.991173	−	0.132579i	$-0.957674\pi$
$733$		−	7.17885i		−	0.265157i	0.991173	−	0.132579i	$-0.0423257\pi$
$734$	0.983344	+	0.983344i	0.0362959	+	0.0362959i
$735$	16.9167			0.623980
$736$	−1.03000	−	1.03000i	−0.0379664	−	0.0379664i
$737$	−5.59431	+	5.59431i	−0.206069	+	0.206069i
$738$	5.88688	−	5.88688i	0.216699	−	0.216699i
$739$		−	0.984806i		−	0.0362267i	−0.999836	−	0.0181133i	$-0.994234\pi$
$739$		−	0.984806i		−	0.0362267i	0.999836	−	0.0181133i	$-0.00576597\pi$
$740$			12.1017i			0.444867i
$741$	−8.61804	+	8.61804i	−0.316592	+	0.316592i
$742$	−25.9305	+	25.9305i	−0.951939	+	0.951939i
$743$	33.0509	+	33.0509i	1.21252	+	1.21252i	0.970195	+	0.242326i	$0.0779105\pi$
$743$	33.0509	+	33.0509i	1.21252	+	1.21252i	0.242326	+	0.970195i	$0.422090\pi$
$744$	−5.17944			−0.189887
$745$	14.7885	+	14.7885i	0.541809	+	0.541809i
$746$		−	1.70381i		−	0.0623810i
$747$	8.36020			0.305884
$748$	4.02040	−	0.914546i	0.147000	−	0.0334391i
$749$	48.8335			1.78434
$750$		−	10.6409i		−	0.388552i
$751$	10.0272	+	10.0272i	0.365897	+	0.365897i	0.865978	−	0.500082i	$-0.166697\pi$
$751$	10.0272	+	10.0272i	0.365897	+	0.365897i	−0.500082	+	0.865978i	$0.666697\pi$
$752$	−2.10192			−0.0766492
$753$	0.650924	+	0.650924i	0.0237210	+	0.0237210i
$754$	7.41959	−	7.41959i	0.270205	−	0.270205i
$755$	−9.70743	+	9.70743i	−0.353290	+	0.353290i
$756$		−	4.51020i		−	0.164034i
$757$		−	20.0762i		−	0.729683i	−0.931070	−	0.364841i	$-0.881123\pi$
$757$		−	20.0762i		−	0.729683i	0.931070	−	0.364841i	$-0.118877\pi$
$758$	−2.89493	+	2.89493i	−0.105149	+	0.105149i
$759$	1.03000	−	1.03000i	0.0373867	−	0.0373867i
$760$	−4.35309	−	4.35309i	−0.157903	−	0.157903i
$761$	18.8710			0.684074			0.342037	−	0.939686i	$-0.388883\pi$
$761$	18.8710			0.684074			0.342037	+	0.939686i	$0.388883\pi$
$762$	10.5892	+	10.5892i	0.383607	+	0.383607i
$763$			70.3162i			2.54562i
$764$	7.07596			0.255999
$765$	5.09761	−	1.15958i	0.184304	−	0.0419249i
$766$	34.1052			1.23227
$767$			8.10133i			0.292522i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$	−30.7405			−1.10853			−0.554265	−	0.832340i	$-0.687001\pi$
$769$	−30.7405			−1.10853			−0.554265	+	0.832340i	$0.687001\pi$
$770$	4.04369	+	4.04369i	0.145724	+	0.145724i
$771$	3.34362	−	3.34362i	0.120418	−	0.120418i
$772$	−1.13715	+	1.13715i	−0.0409268	+	0.0409268i
$773$			38.0732i			1.36940i	0.728826	+	0.684699i	$0.240066\pi$
$773$			38.0732i			1.36940i	−0.728826	+	0.684699i	$0.759934\pi$
$774$		−	11.0762i		−	0.398126i
$775$	−12.4242	+	12.4242i	−0.446289	+	0.446289i
$776$	−4.75416	+	4.75416i	−0.170664	+	0.170664i
$777$	30.4389	+	30.4389i	1.09199	+	1.09199i
$778$	−25.2068			−0.903708
$779$	−28.5825	−	28.5825i	−1.02408	−	1.02408i
$780$		−	3.18277i		−	0.113961i
$781$	−15.8011			−0.565409
$782$	−1.33217	−	5.85628i	−0.0476381	−	0.209420i
$783$	4.18010			0.149385
$784$		−	13.3419i		−	0.476496i
$785$	−3.75024	−	3.75024i	−0.133852	−	0.133852i
$786$	−14.7588			−0.526428
$787$	−39.3545	−	39.3545i	−1.40284	−	1.40284i	−0.790931	−	0.611905i	$-0.790403\pi$
$787$	−39.3545	−	39.3545i	−1.40284	−	1.40284i	−0.611905	−	0.790931i	$-0.709597\pi$
$788$	8.02738	−	8.02738i	0.285964	−	0.285964i
$789$	8.64746	−	8.64746i	0.307858	−	0.307858i
$790$			16.1631i			0.575058i
$791$			84.3613i			2.99954i
$792$	0.707107	−	0.707107i	0.0251259	−	0.0251259i
$793$	−22.8636	+	22.8636i	−0.811909	+	0.811909i
$794$	−11.8505	−	11.8505i	−0.420559	−	0.420559i
$795$	−10.3093			−0.365632
$796$	1.86648	+	1.86648i	0.0661556	+	0.0661556i
$797$			9.11173i			0.322754i	0.986893	+	0.161377i	$0.0515935\pi$
$797$			9.11173i			0.322754i	−0.986893	+	0.161377i	$0.948406\pi$
$798$	−21.8983			−0.775193
$799$	−7.33473	−	4.61618i	−0.259484	−	0.163309i
$800$	−3.39234			−0.119937
$801$		−	13.9677i		−	0.493523i
$802$	10.0635	+	10.0635i	0.355354	+	0.355354i
$803$	−10.6544			−0.375985
$804$	5.59431	+	5.59431i	0.197296	+	0.197296i
$805$	5.89021	−	5.89021i	0.207603	−	0.207603i
$806$	−9.19339	+	9.19339i	−0.323823	+	0.323823i
$807$			12.8660i			0.452905i
$808$			14.1157i			0.496588i
$809$	−11.0653	+	11.0653i	−0.389035	+	0.389035i	−0.874343	−	0.485308i	$-0.838707\pi$
$809$	−11.0653	+	11.0653i	−0.389035	+	0.389035i	0.485308	+	0.874343i	$0.338707\pi$
$810$	0.896566	−	0.896566i	0.0315021	−	0.0315021i
$811$	2.62695	+	2.62695i	0.0922447	+	0.0922447i	0.751723	−	0.659479i	$-0.229223\pi$
$811$	2.62695	+	2.62695i	0.0922447	+	0.0922447i	−0.659479	+	0.751723i	$0.729223\pi$
$812$	18.8531			0.661613
$813$	−13.3841	−	13.3841i	−0.469400	−	0.469400i
$814$			9.54440i			0.334531i
$815$	−12.3865			−0.433881
$816$	−0.914546	−	4.02040i	−0.0320155	−	0.140742i
$817$	−53.7782			−1.88146
$818$			31.1765i			1.09006i
$819$	−8.00550	−	8.00550i	−0.279735	−	0.279735i
$820$	10.5559			0.368630
$821$	8.93928	+	8.93928i	0.311983	+	0.311983i	0.845677	−	0.533694i	$-0.179197\pi$
$821$	8.93928	+	8.93928i	0.311983	+	0.311983i	−0.533694	+	0.845677i	$0.679197\pi$
$822$	−12.6060	+	12.6060i	−0.439686	+	0.439686i
$823$	3.14515	−	3.14515i	0.109633	−	0.109633i	−0.650162	−	0.759795i	$-0.725299\pi$
$823$	3.14515	−	3.14515i	0.109633	−	0.109633i	0.759795	+	0.650162i	$0.225299\pi$
$824$			4.56404i			0.158996i
$825$		−	3.39234i		−	0.118106i
$826$	−10.2927	+	10.2927i	−0.358129	+	0.358129i
$827$	13.3767	−	13.3767i	0.465154	−	0.465154i	−0.435186	−	0.900340i	$-0.643318\pi$
$827$	13.3767	−	13.3767i	0.465154	−	0.465154i	0.900340	+	0.435186i	$0.143318\pi$
$828$	−1.03000	−	1.03000i	−0.0357950	−	0.0357950i
$829$	−32.7185			−1.13636			−0.568179	−	0.822905i	$-0.692352\pi$
$829$	−32.7185			−1.13636			−0.568179	+	0.822905i	$0.692352\pi$
$830$	7.49547	+	7.49547i	0.260171	+	0.260171i
$831$			5.70905i			0.198045i
$832$	−2.51020			−0.0870255
$833$	29.3011	−	46.5570i	1.01522	−	1.61310i
$834$	−8.19064			−0.283619
$835$		−	8.71468i		−	0.301584i
$836$	−3.43321	−	3.43321i	−0.118740	−	0.118740i
$837$	−5.17944			−0.179027
$838$	2.84604	+	2.84604i	0.0983147	+	0.0983147i
$839$	−8.80580	+	8.80580i	−0.304010	+	0.304010i	−0.842580	−	0.538570i	$-0.818965\pi$
$839$	−8.80580	+	8.80580i	−0.304010	+	0.304010i	0.538570	+	0.842580i	$0.318965\pi$
$840$	4.04369	−	4.04369i	0.139521	−	0.139521i
$841$		−	11.5268i		−	0.397475i
$842$		−	25.8926i		−	0.892318i
$843$	−9.57405	+	9.57405i	−0.329748	+	0.329748i
$844$	18.7536	−	18.7536i	0.645527	−	0.645527i
$845$	6.00601	+	6.00601i	0.206613	+	0.206613i
$846$	−2.10192			−0.0722656
$847$	3.18919	+	3.18919i	0.109582	+	0.109582i
$848$			8.13075i			0.279211i
$849$	21.6844			0.744205
$850$	−11.8377	−	7.45015i	−0.406029	−	0.255538i
$851$	13.9028			0.476581
$852$			15.8011i			0.541338i
$853$	11.4761	+	11.4761i	0.392934	+	0.392934i	0.875732	−	0.482798i	$-0.160379\pi$
$853$	11.4761	+	11.4761i	0.392934	+	0.392934i	−0.482798	+	0.875732i	$0.660379\pi$
$854$	−58.0961			−1.98801
$855$	−4.35309	−	4.35309i	−0.148873	−	0.148873i
$856$	7.65610	−	7.65610i	0.261680	−	0.261680i
$857$	−11.7770	+	11.7770i	−0.402293	+	0.402293i	−0.879040	−	0.476747i	$-0.841816\pi$
$857$	−11.7770	+	11.7770i	−0.402293	+	0.402293i	0.476747	+	0.879040i	$0.341816\pi$
$858$		−	2.51020i		−	0.0856968i
$859$			1.21666i			0.0415120i	0.999785	+	0.0207560i	$0.00660731\pi$
$859$			1.21666i			0.0415120i	−0.999785	+	0.0207560i	$0.993393\pi$
$860$	9.93053	−	9.93053i	0.338628	−	0.338628i
$861$	26.5510	−	26.5510i	0.904855	−	0.904855i
$862$	12.3947	+	12.3947i	0.422166	+	0.422166i
$863$	40.9418			1.39367			0.696837	−	0.717229i	$-0.254590\pi$
$863$	40.9418			1.39367			0.696837	+	0.717229i	$0.254590\pi$
$864$	−0.707107	−	0.707107i	−0.0240563	−	0.0240563i
$865$			7.78050i			0.264545i
$866$	−37.1758			−1.26328
$867$	5.63814	−	16.0378i	0.191481	−	0.544673i
$868$	−23.3603			−0.792900
$869$			12.7476i			0.432432i
$870$	3.74773	+	3.74773i	0.127060	+	0.127060i
$871$	19.8596			0.672916
$872$	11.0241	+	11.0241i	0.373325	+	0.373325i
$873$	−4.75416	+	4.75416i	−0.160904	+	0.160904i
$874$	−5.00096	+	5.00096i	−0.169160	+	0.169160i
$875$		−	47.9928i		−	1.62245i
$876$			10.6544i			0.359979i
$877$	14.3075	−	14.3075i	0.483129	−	0.483129i	−0.423001	−	0.906129i	$-0.639023\pi$
$877$	14.3075	−	14.3075i	0.483129	−	0.483129i	0.906129	+	0.423001i	$0.139023\pi$
$878$	−19.6255	+	19.6255i	−0.662330	+	0.662330i
$879$	−8.52915	−	8.52915i	−0.287681	−	0.287681i
$880$	1.26794			0.0427421
$881$	20.1404	+	20.1404i	0.678547	+	0.678547i	0.959671	−	0.281125i	$-0.0907074\pi$
$881$	20.1404	+	20.1404i	0.678547	+	0.678547i	−0.281125	+	0.959671i	$0.590707\pi$
$882$		−	13.3419i		−	0.449245i
$883$	35.2752			1.18710			0.593552	−	0.804796i	$-0.297725\pi$
$883$	35.2752			1.18710			0.593552	+	0.804796i	$0.297725\pi$
$884$	−8.75942	−	5.51282i	−0.294611	−	0.185416i
$885$	−4.09209			−0.137554
$886$		−	16.8239i		−	0.565209i
$887$	8.84929	+	8.84929i	0.297130	+	0.297130i	0.839889	−	0.542759i	$-0.182620\pi$
$887$	8.84929	+	8.84929i	0.297130	+	0.297130i	−0.542759	+	0.839889i	$0.682620\pi$
$888$	9.54440			0.320289
$889$	47.7595	+	47.7595i	1.60180	+	1.60180i
$890$	12.5229	−	12.5229i	0.419770	−	0.419770i
$891$	0.707107	−	0.707107i	0.0236890	−	0.0236890i
$892$			21.5950i			0.723054i
$893$			10.2055i			0.341512i
$894$	11.6635	−	11.6635i	0.390084	−	0.390084i
$895$	23.7050	−	23.7050i	0.792369	−	0.792369i
$896$	−3.18919	−	3.18919i	−0.106543	−	0.106543i
$897$	−3.65646			−0.122086
$898$	−1.68235	−	1.68235i	−0.0561407	−	0.0561407i
$899$		−	21.6506i		−	0.722086i
$900$	−3.39234			−0.113078
$901$	−17.8565	+	28.3725i	−0.594886	+	0.945225i
$902$	8.32530			0.277202
$903$		−	49.9558i		−	1.66243i
$904$	13.2261	+	13.2261i	0.439894	+	0.439894i
$905$	−18.6154			−0.618798
$906$	7.65610	+	7.65610i	0.254357	+	0.254357i
$907$	2.95168	−	2.95168i	0.0980089	−	0.0980089i	−0.656402	−	0.754411i	$-0.727923\pi$
$907$	2.95168	−	2.95168i	0.0980089	−	0.0980089i	0.754411	+	0.656402i	$0.227923\pi$
$908$	6.02484	−	6.02484i	0.199941	−	0.199941i
$909$			14.1157i			0.468188i
$910$		−	14.3549i		−	0.475861i
$911$	8.20258	−	8.20258i	0.271764	−	0.271764i	−0.558046	−	0.829810i	$-0.688449\pi$
$911$	8.20258	−	8.20258i	0.271764	−	0.271764i	0.829810	+	0.558046i	$0.188449\pi$
$912$	−3.43321	+	3.43321i	−0.113685	+	0.113685i
$913$	5.91155	+	5.91155i	0.195644	+	0.195644i
$914$	9.00500			0.297859
$915$	−11.5487	−	11.5487i	−0.381788	−	0.381788i
$916$		−	18.6213i		−	0.615266i
$917$	−66.5650			−2.19817
$918$	−0.914546	−	4.02040i	−0.0301845	−	0.132693i
$919$	3.60242			0.118833			0.0594165	−	0.998233i	$-0.481076\pi$
$919$	3.60242			0.118833			0.0594165	+	0.998233i	$0.481076\pi$
$920$		−	1.84693i		−	0.0608914i
$921$	8.56104	+	8.56104i	0.282096	+	0.282096i
$922$	2.58101			0.0850010
$923$	28.0467	+	28.0467i	0.923168	+	0.923168i
$924$	3.18919	−	3.18919i	0.104917	−	0.104917i
$925$	22.8946	−	22.8946i	0.752769	−	0.752769i
$926$		−	15.4095i		−	0.506389i
$927$			4.56404i			0.149903i
$928$	2.95578	−	2.95578i	0.0970281	−	0.0970281i
$929$	−35.8536	+	35.8536i	−1.17632	+	1.17632i	−0.195643	+	0.980675i	$0.562679\pi$
$929$	−35.8536	+	35.8536i	−1.17632	+	1.17632i	−0.980675	+	0.195643i	$0.937321\pi$
$930$	−4.64370	−	4.64370i	−0.152273	−	0.152273i
$931$	−64.7788			−2.12304
$932$	−15.5225	−	15.5225i	−0.508457	−	0.508457i
$933$		−	0.353190i		−	0.0115629i
$934$	−22.2427			−0.727804
$935$	4.42450	+	2.78460i	0.144697	+	0.0910662i
$936$	−2.51020			−0.0820484
$937$		−	30.2377i		−	0.987821i	−0.869513	−	0.493911i	$-0.835567\pi$
$937$		−	30.2377i		−	0.987821i	0.869513	−	0.493911i	$-0.164433\pi$
$938$	25.2315	+	25.2315i	0.823836	+	0.823836i
$939$	−13.4142			−0.437756
$940$	−1.88451	−	1.88451i	−0.0614660	−	0.0614660i
$941$	−2.28058	+	2.28058i	−0.0743447	+	0.0743447i	−0.743301	−	0.668957i	$-0.766741\pi$
$941$	−2.28058	+	2.28058i	−0.0743447	+	0.0743447i	0.668957	+	0.743301i	$0.266741\pi$
$942$	−2.95776	+	2.95776i	−0.0963689	+	0.0963689i
$943$		−	12.1270i		−	0.394909i
$944$			3.22737i			0.105042i
$945$	4.04369	−	4.04369i	0.131541	−	0.131541i
$946$	7.83205	−	7.83205i	0.254642	−	0.254642i
$947$	12.0913	+	12.0913i	0.392915	+	0.392915i	0.875725	−	0.482810i	$-0.160384\pi$
$947$	12.0913	+	12.0913i	0.392915	+	0.392915i	−0.482810	+	0.875725i	$0.660384\pi$
$948$	12.7476			0.414022
$949$	18.9113	+	18.9113i	0.613887	+	0.613887i
$950$			16.4708i			0.534384i
$951$	−6.29928			−0.204268
$952$	−4.12478	−	18.1328i	−0.133685	−	0.587687i
$953$	17.4144			0.564107			0.282054	−	0.959399i	$-0.408984\pi$
$953$	17.4144			0.564107			0.282054	+	0.959399i	$0.408984\pi$
$954$			8.13075i			0.263243i
$955$	6.34406	+	6.34406i	0.205289	+	0.205289i
$956$	−14.7962			−0.478545
$957$	2.95578	+	2.95578i	0.0955467	+	0.0955467i
$958$	−5.29846	+	5.29846i	−0.171186	+	0.171186i
$959$	−56.8557	+	56.8557i	−1.83597	+	1.83597i
$960$		−	1.26794i		−	0.0409224i
$961$		−	4.17345i		−	0.134627i
$962$	16.9411	−	16.9411i	0.546203	−	0.546203i
$963$	7.65610	−	7.65610i	0.246714	−	0.246714i
$964$	11.0753	+	11.0753i	0.356712	+	0.356712i
$965$	−2.03906			−0.0656395
$966$	−4.64551	−	4.64551i	−0.149467	−	0.149467i
$967$		−	18.0191i		−	0.579455i	−0.957109	−	0.289728i	$-0.906435\pi$
$967$		−	18.0191i		−	0.579455i	0.957109	−	0.289728i	$-0.0935647\pi$
$968$	1.00000			0.0321412
$969$	−19.5202	+	4.44039i	−0.627080	+	0.142646i
$970$	−8.52483			−0.273716
$971$			24.6364i			0.790621i	0.918548	+	0.395310i	$0.129363\pi$
$971$			24.6364i			0.790621i	−0.918548	+	0.395310i	$0.870637\pi$
$972$	−0.707107	−	0.707107i	−0.0226805	−	0.0226805i
$973$	−36.9414			−1.18429
$974$	14.5819	+	14.5819i	0.467234	+	0.467234i
$975$	−6.02133	+	6.02133i	−0.192837	+	0.192837i
$976$	−9.10827	+	9.10827i	−0.291549	+	0.291549i
$977$		−	12.5426i		−	0.401274i	−0.979666	−	0.200637i	$-0.935699\pi$
$977$		−	12.5426i		−	0.401274i	0.979666	−	0.200637i	$-0.0643011\pi$
$978$			9.76904i			0.312380i
$979$	9.87664	−	9.87664i	0.315659	−	0.315659i
$980$	11.9619	−	11.9619i	0.382108	−	0.382108i
$981$	11.0241	+	11.0241i	0.351974	+	0.351974i
$982$	−1.67305			−0.0533893
$983$	23.7236	+	23.7236i	0.756666	+	0.756666i	0.975714	−	0.219048i	$-0.0702952\pi$
$983$	23.7236	+	23.7236i	0.756666	+	0.756666i	−0.219048	+	0.975714i	$0.570295\pi$
$984$		−	8.32530i		−	0.265401i
$985$	14.3941			0.458636
$986$	16.8057	−	3.82289i	0.535201	−	0.121746i
$987$	−9.48009			−0.301754
$988$			12.1878i			0.387744i
$989$	−11.4085	−	11.4085i	−0.362769	−	0.362769i
$990$	1.26794			0.0402976
$991$	−1.85332	−	1.85332i	−0.0588725	−	0.0588725i	0.677058	−	0.735930i	$-0.263255\pi$
$991$	−1.85332	−	1.85332i	−0.0588725	−	0.0588725i	−0.735930	+	0.677058i	$0.763255\pi$
$992$	−3.66241	+	3.66241i	−0.116282	+	0.116282i
$993$	14.1975	−	14.1975i	0.450543	−	0.450543i
$994$			71.2663i			2.26043i
$995$			3.34684i			0.106102i
$996$	5.91155	−	5.91155i	0.187315	−	0.187315i
$997$	−26.6720	+	26.6720i	−0.844712	+	0.844712i	−0.989467	−	0.144755i	$-0.953760\pi$
$997$	−26.6720	+	26.6720i	−0.844712	+	0.844712i	0.144755	+	0.989467i	$0.453760\pi$
$998$	14.2200	+	14.2200i	0.450125	+	0.450125i
$999$	9.54440			0.301971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1122.2.l.f.727.2	yes	16
17.4	even	4	inner	1122.2.l.f.463.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1122.2.l.f.463.2	✓	16	17.4	even	4	inner
1122.2.l.f.727.2	yes	16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1122 = 2 \cdot 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1122.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.896566 - 0.896566i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.18919 + 3.18919i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 - 0.707107i) q^{3} -1.00000 q^{4} +(-0.896566 - 0.896566i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(-3.18919 + 3.18919i) q^{7} +1.00000i q^{8} +1.00000i q^{9} +(-0.896566 + 0.896566i) q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.707107 + 0.707107i) q^{12} +2.51020 q^{13} +(3.18919 + 3.18919i) q^{14} +1.26794i q^{15} +1.00000 q^{16} +(3.48953 + 2.19617i) q^{17} +1.00000 q^{18} -4.85530i q^{19} +(0.896566 + 0.896566i) q^{20} +4.51020 q^{21} +(0.707107 + 0.707107i) q^{22} +(1.03000 - 1.03000i) q^{23} +(0.707107 - 0.707107i) q^{24} -3.39234i q^{25} -2.51020i q^{26} +(0.707107 - 0.707107i) q^{27} +(3.18919 - 3.18919i) q^{28} +(2.95578 + 2.95578i) q^{29} +1.26794 q^{30} +(-3.66241 - 3.66241i) q^{31} -1.00000i q^{32} +1.00000 q^{33} +(2.19617 - 3.48953i) q^{34} +5.71864 q^{35} -1.00000i q^{36} +(6.74891 + 6.74891i) q^{37} -4.85530 q^{38} +(-1.77498 - 1.77498i) q^{39} +(0.896566 - 0.896566i) q^{40} +(5.88688 - 5.88688i) q^{41} -4.51020i q^{42} -11.0762i q^{43} +(0.707107 - 0.707107i) q^{44} +(0.896566 - 0.896566i) q^{45} +(-1.03000 - 1.03000i) q^{46} -2.10192 q^{47} +(-0.707107 - 0.707107i) q^{48} -13.3419i q^{49} -3.39234 q^{50} +(-0.914546 - 4.02040i) q^{51} -2.51020 q^{52} +8.13075i q^{53} +(-0.707107 - 0.707107i) q^{54} +1.26794 q^{55} +(-3.18919 - 3.18919i) q^{56} +(-3.43321 + 3.43321i) q^{57} +(2.95578 - 2.95578i) q^{58} +3.22737i q^{59} -1.26794i q^{60} +(-9.10827 + 9.10827i) q^{61} +(-3.66241 + 3.66241i) q^{62} +(-3.18919 - 3.18919i) q^{63} -1.00000 q^{64} +(-2.25056 - 2.25056i) q^{65} -1.00000i q^{66} +7.91155 q^{67} +(-3.48953 - 2.19617i) q^{68} -1.45664 q^{69} -5.71864i q^{70} +(11.1731 + 11.1731i) q^{71} -1.00000 q^{72} +(7.53379 + 7.53379i) q^{73} +(6.74891 - 6.74891i) q^{74} +(-2.39875 + 2.39875i) q^{75} +4.85530i q^{76} -4.51020i q^{77} +(-1.77498 + 1.77498i) q^{78} +(9.01391 - 9.01391i) q^{79} +(-0.896566 - 0.896566i) q^{80} -1.00000 q^{81} +(-5.88688 - 5.88688i) q^{82} -8.36020i q^{83} -4.51020 q^{84} +(-1.15958 - 5.09761i) q^{85} -11.0762 q^{86} -4.18010i q^{87} +(-0.707107 - 0.707107i) q^{88} -13.9677 q^{89} +(-0.896566 - 0.896566i) q^{90} +(-8.00550 + 8.00550i) q^{91} +(-1.03000 + 1.03000i) q^{92} +5.17944i q^{93} +2.10192i q^{94} +(-4.35309 + 4.35309i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(4.75416 + 4.75416i) q^{97} -13.3419 q^{98} +(-0.707107 - 0.707107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4} + 4 q^{5}+O(q^{10}) \) 16 * q - 16 * q^4 + 4 * q^5	\( 16 q - 16 q^{4} + 4 q^{5} + 4 q^{10} - 32 q^{13} + 16 q^{16} + 4 q^{17} + 16 q^{18} - 4 q^{20} + 8 q^{29} + 8 q^{30} - 32 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} - 32 q^{38} - 4 q^{40} + 32 q^{41} - 4 q^{45} - 40 q^{47} + 24 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{55} - 4 q^{57} + 8 q^{58} - 12 q^{61} - 32 q^{62} - 16 q^{64} - 24 q^{65} + 48 q^{67} - 4 q^{68} + 40 q^{71} - 16 q^{72} - 12 q^{73} + 32 q^{74} + 8 q^{75} + 40 q^{79} + 4 q^{80} - 16 q^{81} - 32 q^{82} + 28 q^{85} + 48 q^{86} - 72 q^{89} + 4 q^{90} - 8 q^{91} - 80 q^{95} + 72 q^{97}+O(q^{100}) \) 16 * q - 16 * q^4 + 4 * q^5 + 4 * q^10 - 32 * q^13 + 16 * q^16 + 4 * q^17 + 16 * q^18 - 4 * q^20 + 8 * q^29 + 8 * q^30 - 32 * q^31 + 16 * q^33 - 4 * q^34 + 32 * q^37 - 32 * q^38 - 4 * q^40 + 32 * q^41 - 4 * q^45 - 40 * q^47 + 24 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^55 - 4 * q^57 + 8 * q^58 - 12 * q^61 - 32 * q^62 - 16 * q^64 - 24 * q^65 + 48 * q^67 - 4 * q^68 + 40 * q^71 - 16 * q^72 - 12 * q^73 + 32 * q^74 + 8 * q^75 + 40 * q^79 + 4 * q^80 - 16 * q^81 - 32 * q^82 + 28 * q^85 + 48 * q^86 - 72 * q^89 + 4 * q^90 - 8 * q^91 - 80 * q^95 + 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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