LMFDB - Embedded newform 680.2.l.b.101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(101,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.l (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [36,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	680.101
Dual form			680.2.l.b.101.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40871 - 0.124621i) q^{2} -0.904376 q^{3} +(1.96894 + 0.351110i) q^{4} -1.00000 q^{5} +(1.27400 + 0.112704i) q^{6} -1.75754i q^{7} +(-2.72991 - 0.739983i) q^{8} -2.18210 q^{9} +(1.40871 + 0.124621i) q^{10} +0.717225 q^{11} +(-1.78066 - 0.317535i) q^{12} +2.57144i q^{13} +(-0.219025 + 2.47586i) q^{14} +0.904376 q^{15} +(3.75344 + 1.38263i) q^{16} +(0.409071 - 4.10276i) q^{17} +(3.07396 + 0.271936i) q^{18} +6.22808i q^{19} +(-1.96894 - 0.351110i) q^{20} +1.58947i q^{21} +(-1.01036 - 0.0893812i) q^{22} -2.65384i q^{23} +(2.46887 + 0.669223i) q^{24} +1.00000 q^{25} +(0.320455 - 3.62242i) q^{26} +4.68657 q^{27} +(0.617088 - 3.46048i) q^{28} +2.07726 q^{29} +(-1.27400 - 0.112704i) q^{30} +5.63218i q^{31} +(-5.11522 - 2.41548i) q^{32} -0.648641 q^{33} +(-1.08755 + 5.72863i) q^{34} +1.75754i q^{35} +(-4.29643 - 0.766158i) q^{36} -7.18400 q^{37} +(0.776148 - 8.77357i) q^{38} -2.32555i q^{39} +(2.72991 + 0.739983i) q^{40} +5.90642i q^{41} +(0.198081 - 2.23911i) q^{42} +8.86558i q^{43} +(1.41217 + 0.251825i) q^{44} +2.18210 q^{45} +(-0.330724 + 3.73850i) q^{46} +4.38251 q^{47} +(-3.39452 - 1.25041i) q^{48} +3.91107 q^{49} +(-1.40871 - 0.124621i) q^{50} +(-0.369954 + 3.71044i) q^{51} +(-0.902856 + 5.06301i) q^{52} -2.07945i q^{53} +(-6.60203 - 0.584044i) q^{54} -0.717225 q^{55} +(-1.30055 + 4.79792i) q^{56} -5.63252i q^{57} +(-2.92627 - 0.258870i) q^{58} +4.37190i q^{59} +(1.78066 + 0.317535i) q^{60} +9.54524 q^{61} +(0.701887 - 7.93412i) q^{62} +3.83513i q^{63} +(6.90485 + 4.04018i) q^{64} -2.57144i q^{65} +(0.913748 + 0.0808341i) q^{66} +14.7376i q^{67} +(2.24595 - 7.93446i) q^{68} +2.40007i q^{69} +(0.219025 - 2.47586i) q^{70} +12.3522i q^{71} +(5.95696 + 1.61472i) q^{72} +6.23316i q^{73} +(10.1202 + 0.895276i) q^{74} -0.904376 q^{75} +(-2.18674 + 12.2627i) q^{76} -1.26055i q^{77} +(-0.289811 + 3.27602i) q^{78} -3.03636i q^{79} +(-3.75344 - 1.38263i) q^{80} +2.30790 q^{81} +(0.736063 - 8.32045i) q^{82} +9.62582i q^{83} +(-0.558079 + 3.12958i) q^{84} +(-0.409071 + 4.10276i) q^{85} +(1.10483 - 12.4890i) q^{86} -1.87863 q^{87} +(-1.95796 - 0.530734i) q^{88} +1.67001 q^{89} +(-3.07396 - 0.271936i) q^{90} +4.51940 q^{91} +(0.931790 - 5.22526i) q^{92} -5.09361i q^{93} +(-6.17369 - 0.546151i) q^{94} -6.22808i q^{95} +(4.62608 + 2.18450i) q^{96} -11.0949i q^{97} +(-5.50957 - 0.487400i) q^{98} -1.56506 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{3} + 2 q^{4} - 36 q^{5} + 36 q^{9} + 8 q^{11} + 2 q^{12} - 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} - 2 q^{20} - 26 q^{24} + 36 q^{25} + 6 q^{26} + 16 q^{27} - 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots + 40 q^{99}+O(q^{100}) $ 36 * q + 4 * q^3 + 2 * q^4 - 36 * q^5 + 36 * q^9 + 8 * q^11 + 2 * q^12 - 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 - 2 * q^20 - 26 * q^24 + 36 * q^25 + 6 * q^26 + 16 * q^27 - 14 * q^28 - 10 * q^32 - 8 * q^33 + 12 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 - 6 * q^44 - 36 * q^45 - 24 * q^46 + 20 * q^47 + 4 * q^48 - 36 * q^49 + 6 * q^52 + 56 * q^54 - 8 * q^55 - 20 * q^56 + 18 * q^58 - 2 * q^60 + 24 * q^62 + 14 * q^64 - 16 * q^66 + 16 * q^68 + 2 * q^70 - 54 * q^72 - 6 * q^74 + 4 * q^75 + 2 * q^76 + 14 * q^78 - 6 * q^80 + 44 * q^81 - 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 + 58 * q^88 + 10 * q^90 + 56 * q^91 + 12 * q^92 + 14 * q^94 + 24 * q^96 + 10 * q^98 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.40871	−	0.124621i	−0.996110	−	0.0881202i
$2$	−1.40871	−	0.124621i	−0.996110	−	0.0881202i
$3$	−0.904376			−0.522142			−0.261071	−	0.965320i	$-0.584076\pi$
$3$	−0.904376			−0.522142			−0.261071	+	0.965320i	$0.584076\pi$
$4$	1.96894	+	0.351110i	0.984470	+	0.175555i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.27400	+	0.112704i	0.520110	+	0.0460112i
$7$		−	1.75754i		−	0.664286i	−0.943229	−	0.332143i	$-0.892228\pi$
$7$		−	1.75754i		−	0.664286i	0.943229	−	0.332143i	$-0.107772\pi$
$8$	−2.72991	−	0.739983i	−0.965170	−	0.261623i
$9$	−2.18210			−0.727368
$10$	1.40871	+	0.124621i	0.445474	+	0.0394085i
$11$	0.717225			0.216252			0.108126	−	0.994137i	$-0.465515\pi$
$11$	0.717225			0.216252			0.108126	+	0.994137i	$0.465515\pi$
$12$	−1.78066	−	0.317535i	−0.514032	−	0.0916644i
$13$			2.57144i			0.713189i	0.934259	+	0.356594i	$0.116062\pi$
$13$			2.57144i			0.713189i	−0.934259	+	0.356594i	$0.883938\pi$
$14$	−0.219025	+	2.47586i	−0.0585370	+	0.661702i
$15$	0.904376			0.233509
$16$	3.75344	+	1.38263i	0.938361	+	0.345657i
$17$	0.409071	−	4.10276i	0.0992143	−	0.995066i
$17$	0.409071	−	4.10276i	0.0992143	−	0.995066i
$18$	3.07396	+	0.271936i	0.724539	+	0.0640958i
$19$			6.22808i			1.42882i	0.699728	+	0.714409i	$0.253304\pi$
$19$			6.22808i			1.42882i	−0.699728	+	0.714409i	$0.746696\pi$
$20$	−1.96894	−	0.351110i	−0.440268	−	0.0785105i
$21$			1.58947i			0.346851i
$22$	−1.01036	−	0.0893812i	−0.215410	−	0.0190561i
$23$		−	2.65384i		−	0.553365i	−0.960961	−	0.276682i	$-0.910765\pi$
$23$		−	2.65384i		−	0.553365i	0.960961	−	0.276682i	$-0.0892350\pi$
$24$	2.46887	+	0.669223i	0.503955	+	0.136604i
$25$	1.00000			0.200000
$26$	0.320455	−	3.62242i	0.0628463	−	0.710414i
$27$	4.68657			0.901931
$28$	0.617088	−	3.46048i	0.116619	−	0.653970i
$29$	2.07726			0.385738			0.192869	−	0.981225i	$-0.438221\pi$
$29$	2.07726			0.385738			0.192869	+	0.981225i	$0.438221\pi$
$30$	−1.27400	−	0.112704i	−0.232600	−	0.0205768i
$31$			5.63218i			1.01157i	0.862660	+	0.505785i	$0.168797\pi$
$31$			5.63218i			1.01157i	−0.862660	+	0.505785i	$0.831203\pi$
$32$	−5.11522	−	2.41548i	−0.904251	−	0.427001i
$33$	−0.648641			−0.112914
$34$	−1.08755	+	5.72863i	−0.186514	+	0.982452i
$35$			1.75754i			0.297078i
$36$	−4.29643	−	0.766158i	−0.716072	−	0.127693i
$37$	−7.18400			−1.18104			−0.590521	−	0.807022i	$-0.701078\pi$
$37$	−7.18400			−1.18104			−0.590521	+	0.807022i	$0.701078\pi$
$38$	0.776148	−	8.77357i	0.125908	−	1.42326i
$39$		−	2.32555i		−	0.372385i
$40$	2.72991	+	0.739983i	0.431637	+	0.117002i
$41$			5.90642i			0.922428i	0.887289	+	0.461214i	$0.152586\pi$
$41$			5.90642i			0.922428i	−0.887289	+	0.461214i	$0.847414\pi$
$42$	0.198081	−	2.23911i	0.0305646	−	0.345502i
$43$			8.86558i			1.35199i	0.736907	+	0.675994i	$0.236285\pi$
$43$			8.86558i			1.35199i	−0.736907	+	0.675994i	$0.763715\pi$
$44$	1.41217	+	0.251825i	0.212893	+	0.0379640i
$45$	2.18210			0.325289
$46$	−0.330724	+	3.73850i	−0.0487626	+	0.551212i
$47$	4.38251			0.639254			0.319627	−	0.947543i	$-0.396442\pi$
$47$	4.38251			0.639254			0.319627	+	0.947543i	$0.396442\pi$
$48$	−3.39452	−	1.25041i	−0.489957	−	0.180482i
$49$	3.91107			0.558724
$50$	−1.40871	−	0.124621i	−0.199222	−	0.0176240i
$51$	−0.369954	+	3.71044i	−0.0518039	+	0.519565i
$52$	−0.902856	+	5.06301i	−0.125204	+	0.702113i
$53$		−	2.07945i		−	0.285634i	−0.989749	−	0.142817i	$-0.954384\pi$
$53$		−	2.07945i		−	0.285634i	0.989749	−	0.142817i	$-0.0456161\pi$
$54$	−6.60203	−	0.584044i	−0.898422	−	0.0794783i
$55$	−0.717225			−0.0967106
$56$	−1.30055	+	4.79792i	−0.173793	+	0.641149i
$57$		−	5.63252i		−	0.746045i
$58$	−2.92627	−	0.258870i	−0.384237	−	0.0339913i
$59$			4.37190i			0.569173i	0.958650	+	0.284587i	$0.0918564\pi$
$59$			4.37190i			0.569173i	−0.958650	+	0.284587i	$0.908144\pi$
$60$	1.78066	+	0.317535i	0.229882	+	0.0409936i
$61$	9.54524			1.22214			0.611071	−	0.791576i	$-0.290739\pi$
$61$	9.54524			1.22214			0.611071	+	0.791576i	$0.290739\pi$
$62$	0.701887	−	7.93412i	0.0891397	−	1.00763i
$63$			3.83513i			0.483181i
$64$	6.90485	+	4.04018i	0.863106	+	0.505022i
$65$		−	2.57144i		−	0.318948i
$66$	0.913748	+	0.0808341i	0.112475	+	0.00994999i
$67$			14.7376i			1.80049i	0.435387	+	0.900244i	$0.356612\pi$
$67$			14.7376i			1.80049i	−0.435387	+	0.900244i	$0.643388\pi$
$68$	2.24595	−	7.93446i	0.272362	−	0.962195i
$69$			2.40007i			0.288935i
$70$	0.219025	−	2.47586i	0.0261786	−	0.295922i
$71$			12.3522i			1.46594i	0.680262	+	0.732969i	$0.261866\pi$
$71$			12.3522i			1.46594i	−0.680262	+	0.732969i	$0.738134\pi$
$72$	5.95696	+	1.61472i	0.702034	+	0.190297i
$73$			6.23316i			0.729536i	0.931098	+	0.364768i	$0.118852\pi$
$73$			6.23316i			0.729536i	−0.931098	+	0.364768i	$0.881148\pi$
$74$	10.1202	+	0.895276i	1.17645	+	0.104074i
$75$	−0.904376			−0.104428
$76$	−2.18674	+	12.2627i	−0.250836	+	1.40663i
$77$		−	1.26055i		−	0.143653i
$78$	−0.289811	+	3.27602i	−0.0328147	+	0.370937i
$79$		−	3.03636i		−	0.341617i	−0.985304	−	0.170808i	$-0.945362\pi$
$79$		−	3.03636i		−	0.341617i	0.985304	−	0.170808i	$-0.0546379\pi$
$80$	−3.75344	−	1.38263i	−0.419648	−	0.154582i
$81$	2.30790			0.256433
$82$	0.736063	−	8.32045i	0.0812846	−	0.918840i
$83$			9.62582i			1.05657i	0.849067	+	0.528286i	$0.177165\pi$
$83$			9.62582i			1.05657i	−0.849067	+	0.528286i	$0.822835\pi$
$84$	−0.558079	+	3.12958i	−0.0608914	+	0.341465i
$85$	−0.409071	+	4.10276i	−0.0443700	+	0.445007i
$86$	1.10483	−	12.4890i	0.119137	−	1.34673i
$87$	−1.87863			−0.201410
$88$	−1.95796	−	0.530734i	−0.208719	−	0.0565765i
$89$	1.67001			0.177021			0.0885105	−	0.996075i	$-0.471789\pi$
$89$	1.67001			0.177021			0.0885105	+	0.996075i	$0.471789\pi$
$90$	−3.07396	−	0.271936i	−0.324024	−	0.0286645i
$91$	4.51940			0.473761
$92$	0.931790	−	5.22526i	0.0971458	−	0.544771i
$93$		−	5.09361i		−	0.528183i
$94$	−6.17369	−	0.546151i	−0.636768	−	0.0563312i
$95$		−	6.22808i		−	0.638987i
$96$	4.62608	+	2.18450i	0.472147	+	0.222955i
$97$		−	11.0949i		−	1.12652i	−0.826280	−	0.563260i	$-0.809547\pi$
$97$		−	11.0949i		−	1.12652i	0.826280	−	0.563260i	$-0.190453\pi$
$98$	−5.50957	−	0.487400i	−0.556550	−	0.0492349i
$99$	−1.56506			−0.157295
$100$	1.96894	+	0.351110i	0.196894	+	0.0351110i
$101$		−	7.52075i		−	0.748343i	−0.927360	−	0.374171i	$-0.877927\pi$
$101$		−	7.52075i		−	0.748343i	0.927360	−	0.374171i	$-0.122073\pi$
$102$	0.983556	−	5.18084i	0.0973866	−	0.512979i
$103$	8.56331			0.843768			0.421884	−	0.906650i	$-0.361369\pi$
$103$	8.56331			0.843768			0.421884	+	0.906650i	$0.361369\pi$
$104$	1.90282	−	7.01980i	0.186587	−	0.688348i
$105$		−	1.58947i		−	0.155117i
$106$	−0.259143	+	2.92935i	−0.0251702	+	0.284523i
$107$	−10.6065			−1.02537			−0.512684	−	0.858578i	$-0.671349\pi$
$107$	−10.6065			−1.02537			−0.512684	+	0.858578i	$0.671349\pi$
$108$	9.22757	+	1.64550i	0.887923	+	0.158338i
$109$	−7.78258			−0.745436			−0.372718	−	0.927945i	$-0.621574\pi$
$109$	−7.78258			−0.745436			−0.372718	+	0.927945i	$0.621574\pi$
$110$	1.01036	+	0.0893812i	0.0963344	+	0.00852216i
$111$	6.49703			0.616671
$112$	2.43002	−	6.59681i	0.229615	−	0.623340i
$113$			14.8231i			1.39444i	0.716857	+	0.697220i	$0.245580\pi$
$113$			14.8231i			1.39444i	−0.716857	+	0.697220i	$0.754420\pi$
$114$	−0.701929	+	7.93460i	−0.0657417	+	0.743143i
$115$			2.65384i			0.247472i
$116$	4.09000	+	0.729347i	0.379747	+	0.0677181i
$117$		−	5.61115i		−	0.518751i
$118$	0.544830	−	6.15875i	0.0501557	−	0.566959i
$119$	−7.21075	−	0.718957i	−0.661009	−	0.0659067i
$120$	−2.46887	−	0.669223i	−0.225376	−	0.0610914i
$121$	−10.4856			−0.953235
$122$	−13.4465	−	1.18953i	−1.21739	−	0.107695i
$123$		−	5.34162i		−	0.481638i
$124$	−1.97751	+	11.0894i	−0.177586	+	0.995860i
$125$	−1.00000			−0.0894427
$126$	0.477937	−	5.40259i	0.0425780	−	0.481301i
$127$	−1.35226			−0.119993			−0.0599967	−	0.998199i	$-0.519109\pi$
$127$	−1.35226			−0.119993			−0.0599967	+	0.998199i	$0.519109\pi$
$128$	−9.22346	−	6.55194i	−0.815246	−	0.579115i
$129$		−	8.01781i		−	0.705929i
$130$	−0.320455	+	3.62242i	−0.0281057	+	0.317707i
$131$	−5.97685			−0.522200			−0.261100	−	0.965312i	$-0.584085\pi$
$131$	−5.97685			−0.522200			−0.261100	+	0.965312i	$0.584085\pi$
$132$	−1.27713	−	0.227744i	−0.111160	−	0.0198226i
$133$	10.9461			0.949144
$134$	1.83661	−	20.7611i	0.158659	−	1.79348i
$135$	−4.68657			−0.403356
$136$	−4.15270	+	10.8975i	−0.356091	+	0.934451i
$137$	−7.66306			−0.654700			−0.327350	−	0.944903i	$-0.606156\pi$
$137$	−7.66306			−0.654700			−0.327350	+	0.944903i	$0.606156\pi$
$138$	0.299099	−	3.38101i	0.0254610	−	0.287811i
$139$	5.03224			0.426829			0.213415	−	0.976962i	$-0.431542\pi$
$139$	5.03224			0.426829			0.213415	+	0.976962i	$0.431542\pi$
$140$	−0.617088	+	3.46048i	−0.0521534	+	0.292464i
$141$	−3.96343			−0.333781
$142$	1.53934	−	17.4007i	0.129179	−	1.46024i
$143$			1.84430i			0.154228i
$144$	−8.19041	−	3.01704i	−0.682534	−	0.251420i
$145$	−2.07726			−0.172507
$146$	0.776781	−	8.78072i	0.0642868	−	0.726698i
$147$	−3.53707			−0.291733
$148$	−14.1449	−	2.52237i	−1.16270	−	0.207338i
$149$		−	13.0486i		−	1.06898i	−0.845175	−	0.534490i	$-0.820504\pi$
$149$		−	13.0486i		−	1.06898i	0.845175	−	0.534490i	$-0.179496\pi$
$150$	1.27400	+	0.112704i	0.104022	+	0.00920224i
$151$	7.85674			0.639372			0.319686	−	0.947524i	$-0.396423\pi$
$151$	7.85674			0.639372			0.319686	+	0.947524i	$0.396423\pi$
$152$	4.60867	−	17.0021i	0.373813	−	1.37905i
$153$	−0.892636	+	8.95266i	−0.0721653	+	0.723779i
$154$	−0.157091	+	1.77575i	−0.0126587	+	0.143094i
$155$		−	5.63218i		−	0.452388i
$156$	0.816521	−	4.57886i	0.0653740	−	0.366602i
$157$		−	19.8136i		−	1.58129i	−0.612272	−	0.790647i	$-0.709744\pi$
$157$		−	19.8136i		−	1.58129i	0.612272	−	0.790647i	$-0.290256\pi$
$158$	−0.378393	+	4.27735i	−0.0301033	+	0.340288i
$159$			1.88060i			0.149142i
$160$	5.11522	+	2.41548i	0.404393	+	0.190960i
$161$	−4.66423			−0.367592
$162$	−3.25116	−	0.287612i	−0.255435	−	0.0225969i
$163$	22.9485			1.79747			0.898734	−	0.438494i	$-0.144488\pi$
$163$	22.9485			1.79747			0.898734	+	0.438494i	$0.144488\pi$
$164$	−2.07380	+	11.6294i	−0.161937	+	0.908103i
$165$	0.648641			0.0504966
$166$	1.19958	−	13.5600i	0.0931053	−	1.05246i
$167$		−	13.0081i		−	1.00660i	−0.864112	−	0.503299i	$-0.832119\pi$
$167$		−	13.0081i		−	1.00660i	0.864112	−	0.503299i	$-0.167881\pi$
$168$	1.17618	−	4.33912i	0.0907445	−	0.334771i
$169$	6.38771			0.491362
$170$	1.08755	−	5.72863i	0.0834115	−	0.439366i
$171$		−	13.5903i		−	1.03928i
$172$	−3.11279	+	17.4558i	−0.237348	+	1.33099i
$173$	−8.74738			−0.665051			−0.332525	−	0.943094i	$-0.607901\pi$
$173$	−8.74738			−0.665051			−0.332525	+	0.943094i	$0.607901\pi$
$174$	2.64644	+	0.234116i	0.200626	+	0.0177483i
$175$		−	1.75754i		−	0.132857i
$176$	2.69206	+	0.991655i	0.202922	+	0.0747488i
$177$		−	3.95384i		−	0.297189i
$178$	−2.35257	−	0.208118i	−0.176332	−	0.0155991i
$179$			0.482753i			0.0360827i	0.999837	+	0.0180413i	$0.00574304\pi$
$179$			0.482753i			0.0360827i	−0.999837	+	0.0180413i	$0.994257\pi$
$180$	4.29643	+	0.766158i	0.320237	+	0.0571060i
$181$	−24.8523			−1.84726			−0.923628	−	0.383290i	$-0.874791\pi$
$181$	−24.8523			−1.84726			−0.923628	+	0.383290i	$0.874791\pi$
$182$	−6.36653	−	0.563210i	−0.471918	−	0.0417479i
$183$	−8.63248			−0.638131
$184$	−1.96380	+	7.24476i	−0.144773	+	0.534091i
$185$	7.18400			0.528178
$186$	−0.634769	+	7.17543i	−0.0465435	+	0.526128i
$187$	0.293396	−	2.94260i	0.0214552	−	0.215185i
$188$	8.62889	+	1.53874i	0.629327	+	0.112224i
$189$		−	8.23681i		−	0.599140i
$190$	−0.776148	+	8.77357i	−0.0563077	+	0.636501i
$191$	−17.2186			−1.24590			−0.622948	−	0.782263i	$-0.714065\pi$
$191$	−17.2186			−1.24590			−0.622948	+	0.782263i	$0.714065\pi$
$192$	−6.24458	−	3.65384i	−0.450664	−	0.263693i
$193$			11.7447i			0.845400i	0.906270	+	0.422700i	$0.138918\pi$
$193$			11.7447i			0.845400i	−0.906270	+	0.422700i	$0.861082\pi$
$194$	−1.38266	+	15.6296i	−0.0992691	+	1.12214i
$195$			2.32555i			0.166536i
$196$	7.70065	+	1.37321i	0.550047	+	0.0980866i
$197$	16.3796			1.16700			0.583499	−	0.812114i	$-0.301683\pi$
$197$	16.3796			1.16700			0.583499	+	0.812114i	$0.301683\pi$
$198$	2.20472	+	0.195039i	0.156683	+	0.0138608i
$199$		−	0.773803i		−	0.0548534i	−0.999624	−	0.0274267i	$-0.991269\pi$
$199$		−	0.773803i		−	0.0548534i	0.999624	−	0.0274267i	$-0.00873129\pi$
$200$	−2.72991	−	0.739983i	−0.193034	−	0.0523247i
$201$		−	13.3283i		−	0.940109i
$202$	−0.937242	+	10.5946i	−0.0659441	+	0.745431i
$203$		−	3.65086i		−	0.256240i
$204$	−2.03119	+	7.17573i	−0.142212	+	0.502402i
$205$		−	5.90642i		−	0.412522i
$206$	−12.0632	−	1.06717i	−0.840485	−	0.0743530i
$207$			5.79096i			0.402500i
$208$	−3.55534	+	9.65175i	−0.246518	+	0.669228i
$209$			4.46693i			0.308984i
$210$	−0.198081	+	2.23911i	−0.0136689	+	0.154513i
$211$	8.99659			0.619351			0.309675	−	0.950842i	$-0.399780\pi$
$211$	8.99659			0.619351			0.309675	+	0.950842i	$0.399780\pi$
$212$	0.730115	−	4.09431i	0.0501445	−	0.281198i
$213$		−	11.1710i		−	0.765427i
$214$	14.9415	+	1.32179i	1.02138	+	0.0903556i
$215$		−	8.86558i		−	0.604627i
$216$	−12.7939	−	3.46798i	−0.870516	−	0.235966i
$217$	9.89876			0.671972
$218$	10.9634	+	0.969871i	0.742536	+	0.0656880i
$219$		−	5.63712i		−	0.380921i
$220$	−1.41217	−	0.251825i	−0.0952087	−	0.0169780i
$221$	10.5500	+	1.05190i	0.709670	+	0.0707585i
$222$	−9.15245	−	0.809665i	−0.614272	−	0.0543412i
$223$	7.45345			0.499120			0.249560	−	0.968359i	$-0.419714\pi$
$223$	7.45345			0.499120			0.249560	+	0.968359i	$0.419714\pi$
$224$	−4.24529	+	8.99018i	−0.283651	+	0.600682i
$225$	−2.18210			−0.145474
$226$	1.84727	−	20.8815i	0.122878	−	1.38902i
$227$	−0.132211			−0.00877512			−0.00438756	−	0.999990i	$-0.501397\pi$
$227$	−0.132211			−0.00877512			−0.00438756	+	0.999990i	$0.501397\pi$
$228$	1.97763	−	11.0901i	0.130972	−	0.734459i
$229$		−	16.9264i		−	1.11853i	−0.828989	−	0.559265i	$-0.811083\pi$
$229$		−	16.9264i		−	1.11853i	0.828989	−	0.559265i	$-0.188917\pi$
$230$	0.330724	−	3.73850i	0.0218073	−	0.246509i
$231$			1.14001i			0.0750071i
$232$	−5.67075	−	1.53714i	−0.372303	−	0.100918i
$233$			25.1111i			1.64508i	0.568704	+	0.822542i	$0.307445\pi$
$233$			25.1111i			1.64508i	−0.568704	+	0.822542i	$0.692555\pi$
$234$	−0.699265	+	7.90449i	−0.0457124	+	0.516733i
$235$	−4.38251			−0.285883
$236$	−1.53502	+	8.60801i	−0.0999211	+	0.560334i
$237$			2.74601i			0.178372i
$238$	10.0683	+	1.91141i	0.652630	+	0.123898i
$239$	−4.26360			−0.275789			−0.137895	−	0.990447i	$-0.544034\pi$
$239$	−4.26360			−0.275789			−0.137895	+	0.990447i	$0.544034\pi$
$240$	3.39452	+	1.25041i	0.219116	+	0.0807139i
$241$		−	11.2076i		−	0.721948i	−0.932576	−	0.360974i	$-0.882444\pi$
$241$		−	11.2076i		−	0.721948i	0.932576	−	0.360974i	$-0.117556\pi$
$242$	14.7712	+	1.30672i	0.949527	+	0.0839993i
$243$	−16.1469			−1.03582
$244$	18.7940	+	3.35142i	1.20316	+	0.214553i
$245$	−3.91107			−0.249869
$246$	−0.665677	+	7.52481i	−0.0424420	+	0.479764i
$247$	−16.0151			−1.01902
$248$	4.16772	−	15.3754i	0.264650	−	0.976337i
$249$		−	8.70536i		−	0.551680i
$250$	1.40871	+	0.124621i	0.0890948	+	0.00788171i
$251$		−	6.42175i		−	0.405338i	−0.979247	−	0.202669i	$-0.935039\pi$
$251$		−	6.42175i		−	0.405338i	0.979247	−	0.202669i	$-0.0649615\pi$
$252$	−1.34655	+	7.55113i	−0.0848247	+	0.475677i
$253$		−	1.90340i		−	0.119666i
$254$	1.90494	+	0.168519i	0.119527	+	0.0105738i
$255$	0.369954	−	3.71044i	0.0231674	−	0.232357i
$256$	12.1767	+	10.3792i	0.761043	+	0.648702i
$257$	−17.7073			−1.10455			−0.552275	−	0.833662i	$-0.686240\pi$
$257$	−17.7073			−1.10455			−0.552275	+	0.833662i	$0.686240\pi$
$258$	−0.999186	+	11.2948i	−0.0622066	+	0.703183i
$259$			12.6261i			0.784550i
$260$	0.902856	−	5.06301i	0.0559928	−	0.313994i
$261$	−4.53280			−0.280574
$262$	8.41966	+	0.744840i	0.520169	+	0.0460164i
$263$	10.3401			0.637600			0.318800	−	0.947822i	$-0.396720\pi$
$263$	10.3401			0.637600			0.318800	+	0.947822i	$0.396720\pi$
$264$	1.77073	+	0.479983i	0.108981	+	0.0295409i
$265$			2.07945i			0.127740i
$266$	−15.4199	−	1.36411i	−0.945452	−	0.0836388i
$267$	−1.51032			−0.0924300
$268$	−5.17452	+	29.0175i	−0.316084	+	1.77252i
$269$	8.42558			0.513717			0.256858	−	0.966449i	$-0.417313\pi$
$269$	8.42558			0.513717			0.256858	+	0.966449i	$0.417313\pi$
$270$	6.60203	+	0.584044i	0.401787	+	0.0355438i
$271$	9.28221			0.563854			0.281927	−	0.959436i	$-0.409026\pi$
$271$	9.28221			0.563854			0.281927	+	0.959436i	$0.409026\pi$
$272$	7.20801	−	14.8339i	0.437050	−	0.899437i
$273$	−4.08723			−0.247370
$274$	10.7950	+	0.954977i	0.652153	+	0.0576922i
$275$	0.717225			0.0432503
$276$	−0.842688	+	4.72560i	−0.0507239	+	0.284447i
$277$	−3.96273			−0.238097			−0.119049	−	0.992888i	$-0.537984\pi$
$277$	−3.96273			−0.238097			−0.119049	+	0.992888i	$0.537984\pi$
$278$	−7.08898	−	0.627122i	−0.425169	−	0.0376123i
$279$		−	12.2900i		−	0.735784i
$280$	1.30055	−	4.79792i	0.0777225	−	0.286731i
$281$	25.2571			1.50671			0.753355	−	0.657614i	$-0.228434\pi$
$281$	25.2571			1.50671			0.753355	+	0.657614i	$0.228434\pi$
$282$	5.58334	+	0.493926i	0.332483	+	0.0294129i
$283$	−30.7028			−1.82509			−0.912546	−	0.408974i	$-0.865887\pi$
$283$	−30.7028			−1.82509			−0.912546	+	0.408974i	$0.865887\pi$
$284$	−4.33698	+	24.3208i	−0.257353	+	1.44317i
$285$			5.63252i			0.333642i
$286$	0.229838	−	2.59809i	0.0135906	−	0.153628i
$287$	10.3808			0.612756
$288$	11.1619	+	5.27083i	0.657724	+	0.310587i
$289$	−16.6653	−	3.35664i	−0.980313	−	0.197450i
$290$	2.92627	+	0.258870i	0.171836	+	0.0152014i
$291$			10.0340i			0.588203i
$292$	−2.18852	+	12.2727i	−0.128074	+	0.718206i
$293$			21.7331i			1.26966i	0.772651	+	0.634831i	$0.218930\pi$
$293$			21.7331i			1.26966i	−0.772651	+	0.634831i	$0.781070\pi$
$294$	4.98272	+	0.440793i	0.290598	+	0.0257076i
$295$		−	4.37190i		−	0.254542i
$296$	19.6117	+	5.31604i	1.13991	+	0.308988i
$297$	3.36133			0.195044
$298$	−1.62612	+	18.3817i	−0.0941988	+	1.06482i
$299$	6.82419			0.394653
$300$	−1.78066	−	0.317535i	−0.102806	−	0.0183329i
$301$	15.5816			0.898107
$302$	−11.0679	−	0.979112i	−0.636885	−	0.0563416i
$303$			6.80158i			0.390741i
$304$	−8.61110	+	23.3767i	−0.493881	+	1.34075i
$305$	−9.54524			−0.546559
$306$	2.37315	−	12.5005i	0.135664	−	0.714605i
$307$			18.9502i			1.08154i	0.841169	+	0.540772i	$0.181868\pi$
$307$			18.9502i			1.08154i	−0.841169	+	0.540772i	$0.818132\pi$
$308$	0.442591	−	2.48194i	0.0252190	−	0.141422i
$309$	−7.74445			−0.440566
$310$	−0.701887	+	7.93412i	−0.0398645	+	0.450628i
$311$			16.5791i			0.940113i	0.882636	+	0.470057i	$0.155767\pi$
$311$			16.5791i			0.940113i	−0.882636	+	0.470057i	$0.844233\pi$
$312$	−1.72086	+	6.34854i	−0.0974248	+	0.359415i
$313$			17.0105i			0.961488i	0.876861	+	0.480744i	$0.159633\pi$
$313$			17.0105i			0.961488i	−0.876861	+	0.480744i	$0.840367\pi$
$314$	−2.46918	+	27.9116i	−0.139344	+	1.57514i
$315$		−	3.83513i		−	0.216085i
$316$	1.06609	−	5.97840i	0.0599725	−	0.336312i
$317$	−30.0644			−1.68858			−0.844292	−	0.535883i	$-0.819979\pi$
$317$	−30.0644			−1.68858			−0.844292	+	0.535883i	$0.819979\pi$
$318$	0.234362	−	2.64923i	0.0131424	−	0.148561i
$319$	1.48987			0.0834164
$320$	−6.90485	−	4.04018i	−0.385993	−	0.225853i
$321$	9.59224			0.535387
$322$	6.57055	+	0.581259i	0.366162	+	0.0323923i
$323$	25.5523	+	2.54772i	1.42177	+	0.141759i
$324$	4.54411	+	0.810324i	0.252450	+	0.0450180i
$325$			2.57144i			0.142638i
$326$	−32.3279	−	2.85986i	−1.79048	−	0.158393i
$327$	7.03838			0.389223
$328$	4.37065	−	16.1240i	0.241329	−	0.890300i
$329$		−	7.70241i		−	0.424648i
$330$	−0.913748	−	0.0808341i	−0.0503002	−	0.00444977i
$331$		−	1.30704i		−	0.0718413i	−0.999355	−	0.0359207i	$-0.988564\pi$
$331$		−	1.30704i		−	0.0718413i	0.999355	−	0.0359207i	$-0.0114364\pi$
$332$	−3.37972	+	18.9527i	−0.185486	+	1.04016i
$333$	15.6762			0.859053
$334$	−1.62108	+	18.3247i	−0.0887016	+	1.00268i
$335$		−	14.7376i		−	0.805202i
$336$	−2.19765	+	5.96600i	−0.119892	+	0.325472i
$337$			12.4553i			0.678483i	0.940699	+	0.339242i	$0.110170\pi$
$337$			12.4553i			0.678483i	−0.940699	+	0.339242i	$0.889830\pi$
$338$	−8.99844	−	0.796041i	−0.489451	−	0.0432989i
$339$		−	13.4056i		−	0.728095i
$340$	−2.24595	+	7.93446i	−0.121804	+	0.430307i
$341$			4.03954i			0.218754i
$342$	−1.69364	+	19.1448i	−0.0915813	+	1.03523i
$343$		−	19.1766i		−	1.03544i
$344$	6.56038	−	24.2023i	0.353712	−	1.30490i
$345$		−	2.40007i		−	0.129216i
$346$	12.3225	+	1.09011i	0.662464	+	0.0586044i
$347$	21.0177			1.12829			0.564144	−	0.825676i	$-0.309206\pi$
$347$	21.0177			1.12829			0.564144	+	0.825676i	$0.309206\pi$
$348$	−3.69890	−	0.659603i	−0.198282	−	0.0353585i
$349$			7.99875i			0.428163i	0.976816	+	0.214082i	$0.0686759\pi$
$349$			7.99875i			0.428163i	−0.976816	+	0.214082i	$0.931324\pi$
$350$	−0.219025	+	2.47586i	−0.0117074	+	0.132340i
$351$			12.0512i			0.643247i
$352$	−3.66876	−	1.73244i	−0.195546	−	0.0923395i
$353$	17.1563			0.913136			0.456568	−	0.889688i	$-0.349078\pi$
$353$	17.1563			0.913136			0.456568	+	0.889688i	$0.349078\pi$
$354$	−0.492731	+	5.56983i	−0.0261884	+	0.296033i
$355$		−	12.3522i		−	0.655588i
$356$	3.28815	+	0.586357i	0.174272	+	0.0310769i
$357$	6.52123	+	0.650207i	0.345140	+	0.0344126i
$358$	0.0601610	−	0.680060i	0.00317961	−	0.0359423i
$359$	37.3318			1.97030			0.985150	−	0.171697i	$-0.0549250\pi$
$359$	37.3318			1.97030			0.985150	+	0.171697i	$0.0549250\pi$
$360$	−5.95696	−	1.61472i	−0.313959	−	0.0851032i
$361$	−19.7889			−1.04152
$362$	35.0097	+	3.09711i	1.84007	+	0.162781i
$363$	9.48291			0.497724
$364$	8.89841	+	1.58680i	0.466404	+	0.0831711i
$365$		−	6.23316i		−	0.326258i
$366$	12.1607	+	1.07579i	0.635649	+	0.0562322i
$367$			9.74596i			0.508735i	0.967108	+	0.254367i	$0.0818673\pi$
$367$			9.74596i			0.508735i	−0.967108	+	0.254367i	$0.918133\pi$
$368$	3.66928	−	9.96105i	0.191274	−	0.519256i
$369$		−	12.8884i		−	0.670945i
$370$	−10.1202	−	0.895276i	−0.526124	−	0.0465432i
$371$	−3.65471			−0.189743
$372$	1.78841	−	10.0290i	0.0927250	−	0.519980i
$373$		−	15.1227i		−	0.783023i	−0.920173	−	0.391511i	$-0.871952\pi$
$373$		−	15.1227i		−	0.783023i	0.920173	−	0.391511i	$-0.128048\pi$
$374$	−0.780020	+	4.10872i	−0.0403339	+	0.212457i
$375$	0.904376			0.0467018
$376$	−11.9639	−	3.24298i	−0.616989	−	0.167244i
$377$			5.34155i			0.275104i
$378$	−1.02648	+	11.6033i	−0.0527963	+	0.596809i
$379$	−23.1594			−1.18962			−0.594810	−	0.803866i	$-0.702773\pi$
$379$	−23.1594			−1.18962			−0.594810	+	0.803866i	$0.702773\pi$
$380$	2.18674	−	12.2627i	0.112177	−	0.629063i
$381$	1.22295			0.0626535
$382$	24.2561	+	2.14580i	1.24105	+	0.109789i
$383$	−31.4086			−1.60490			−0.802452	−	0.596716i	$-0.796472\pi$
$383$	−31.4086			−1.60490			−0.802452	+	0.596716i	$0.796472\pi$
$384$	8.34147	+	5.92541i	0.425674	+	0.302380i
$385$			1.26055i			0.0642435i
$386$	1.46363	−	16.5449i	0.0744968	−	0.842112i
$387$		−	19.3456i		−	0.983393i
$388$	3.89554	−	21.8452i	0.197766	−	1.10902i
$389$			30.5468i			1.54879i	0.632705	+	0.774393i	$0.281945\pi$
$389$			30.5468i			1.54879i	−0.632705	+	0.774393i	$0.718055\pi$
$390$	0.289811	−	3.27602i	0.0146752	−	0.165888i
$391$	−10.8881	−	1.08561i	−0.550634	−	0.0549017i
$392$	−10.6769	−	2.89412i	−0.539264	−	0.146175i
$393$	5.40532			0.272662
$394$	−23.0741	−	2.04124i	−1.16246	−	0.102836i
$395$			3.03636i			0.152776i
$396$	−3.08151	−	0.549508i	−0.154852	−	0.0276138i
$397$	0.678969			0.0340765			0.0170382	−	0.999855i	$-0.494576\pi$
$397$	0.678969			0.0340765			0.0170382	+	0.999855i	$0.494576\pi$
$398$	−0.0964319	+	1.09007i	−0.00483370	+	0.0546401i
$399$	−9.89936			−0.495588
$400$	3.75344	+	1.38263i	0.187672	+	0.0691313i
$401$		−	14.3974i		−	0.718973i	−0.933150	−	0.359486i	$-0.882952\pi$
$401$		−	14.3974i		−	0.718973i	0.933150	−	0.359486i	$-0.117048\pi$
$402$	−1.66099	+	18.7758i	−0.0828426	+	0.936452i
$403$	−14.4828			−0.721440
$404$	2.64061	−	14.8079i	0.131375	−	0.736721i
$405$	−2.30790			−0.114680
$406$	−0.454973	+	5.14302i	−0.0225800	+	0.255244i
$407$	−5.15255			−0.255402
$408$	3.75560	−	9.85541i	0.185930	−	0.487916i
$409$	−9.63143			−0.476243			−0.238122	−	0.971235i	$-0.576532\pi$
$409$	−9.63143			−0.476243			−0.238122	+	0.971235i	$0.576532\pi$
$410$	−0.736063	+	8.32045i	−0.0363516	+	0.410918i
$411$	6.93029			0.341846
$412$	16.8606	+	3.00666i	0.830664	+	0.148127i
$413$	7.68378			0.378094
$414$	0.721674	−	8.15780i	0.0354684	−	0.400934i
$415$		−	9.62582i		−	0.472513i
$416$	6.21126	−	13.1535i	0.304532	−	0.644902i
$417$	−4.55104			−0.222865
$418$	0.556673	−	6.29262i	0.0272277	−	0.307782i
$419$	−27.1118			−1.32450			−0.662248	−	0.749285i	$-0.730398\pi$
$419$	−27.1118			−1.32450			−0.662248	+	0.749285i	$0.730398\pi$
$420$	0.558079	−	3.12958i	0.0272315	−	0.152708i
$421$			4.48792i			0.218728i	0.994002	+	0.109364i	$0.0348814\pi$
$421$			4.48792i			0.218728i	−0.994002	+	0.109364i	$0.965119\pi$
$422$	−12.6736	−	1.12116i	−0.616941	−	0.0545773i
$423$	−9.56309			−0.464973
$424$	−1.53876	+	5.67672i	−0.0747287	+	0.275686i
$425$	0.409071	−	4.10276i	0.0198429	−	0.199013i
$426$	−1.39214	+	15.7368i	−0.0674496	+	0.762450i
$427$		−	16.7761i		−	0.811852i
$428$	−20.8835	−	3.72404i	−1.00944	−	0.180008i
$429$		−	1.66794i		−	0.0805289i
$430$	−1.10483	+	12.4890i	−0.0532799	+	0.602275i
$431$			24.5110i			1.18065i	0.807164	+	0.590327i	$0.201001\pi$
$431$			24.5110i			1.18065i	−0.807164	+	0.590327i	$0.798999\pi$
$432$	17.5908	+	6.47978i	0.846337	+	0.311758i
$433$	25.1872			1.21042			0.605210	−	0.796066i	$-0.293089\pi$
$433$	25.1872			1.21042			0.605210	+	0.796066i	$0.293089\pi$
$434$	−13.9445	−	1.23359i	−0.669358	−	0.0592143i
$435$	1.87863			0.0900732
$436$	−15.3234	−	2.73254i	−0.733859	−	0.130865i
$437$	16.5283			0.790658
$438$	−0.702502	+	7.94107i	−0.0335668	+	0.379439i
$439$			7.47936i			0.356970i	0.983943	+	0.178485i	$0.0571197\pi$
$439$			7.47936i			0.356970i	−0.983943	+	0.178485i	$0.942880\pi$
$440$	1.95796	+	0.530734i	0.0933422	+	0.0253018i
$441$	−8.53436			−0.406398
$442$	−14.7308	−	2.79657i	−0.700674	−	0.133019i
$443$		−	20.3792i		−	0.968243i	−0.875001	−	0.484122i	$-0.839139\pi$
$443$		−	20.3792i		−	0.968243i	0.875001	−	0.484122i	$-0.160861\pi$
$444$	12.7923	+	2.28117i	0.607094	+	0.108260i
$445$	−1.67001			−0.0791662
$446$	−10.4998	−	0.928854i	−0.497178	−	0.0439825i
$447$			11.8008i			0.558159i
$448$	7.10076	−	12.1355i	0.335479	−	0.573350i
$449$		−	36.6973i		−	1.73185i	−0.500171	−	0.865927i	$-0.666730\pi$
$449$		−	36.6973i		−	1.73185i	0.500171	−	0.865927i	$-0.333270\pi$
$450$	3.07396	+	0.271936i	0.144908	+	0.0128192i
$451$			4.23624i			0.199477i
$452$	−5.20453	+	29.1858i	−0.244801	+	1.37278i
$453$	−7.10544			−0.333843
$454$	0.186247	+	0.0164762i	0.00874098	+	0.000773265i
$455$	−4.51940			−0.211873
$456$	−4.16797	+	15.3763i	−0.195183	+	0.720061i
$457$	13.1520			0.615223			0.307611	−	0.951512i	$-0.400470\pi$
$457$	13.1520			0.615223			0.307611	+	0.951512i	$0.400470\pi$
$458$	−2.10938	+	23.8445i	−0.0985651	+	1.11418i
$459$	1.91714	−	19.2279i	0.0894844	−	0.897481i
$460$	−0.931790	+	5.22526i	−0.0434449	+	0.243629i
$461$			25.5335i			1.18921i	0.804017	+	0.594607i	$0.202692\pi$
$461$			25.5335i			1.18921i	−0.804017	+	0.594607i	$0.797308\pi$
$462$	0.142069	−	1.60595i	0.00660964	−	0.0747154i
$463$	−17.3855			−0.807973			−0.403986	−	0.914765i	$-0.632376\pi$
$463$	−17.3855			−0.807973			−0.403986	+	0.914765i	$0.632376\pi$
$464$	7.79689	+	2.87208i	0.361962	+	0.133333i
$465$			5.09361i			0.236210i
$466$	3.12937	−	35.3743i	0.144965	−	1.63869i
$467$			5.00606i			0.231653i	0.993269	+	0.115826i	$0.0369516\pi$
$467$			5.00606i			0.231653i	−0.993269	+	0.115826i	$0.963048\pi$
$468$	1.97013	−	11.0480i	0.0910692	−	0.510694i
$469$	25.9019			1.19604
$470$	6.17369	+	0.546151i	0.284771	+	0.0251921i
$471$			17.9189i			0.825659i
$472$	3.23513	−	11.9349i	0.148909	−	0.549349i
$473$			6.35861i			0.292369i
$474$	0.342210	−	3.86833i	0.0157182	−	0.177678i
$475$			6.22808i			0.285764i
$476$	−13.9451	−	3.94735i	−0.639173	−	0.180926i
$477$			4.53758i			0.207761i
$478$	6.00618	+	0.531333i	0.274716	+	0.0243026i
$479$		−	16.7452i		−	0.765106i	−0.923934	−	0.382553i	$-0.875045\pi$
$479$		−	16.7452i		−	0.765106i	0.923934	−	0.382553i	$-0.124955\pi$
$480$	−4.62608	−	2.18450i	−0.211151	−	0.0997084i
$481$		−	18.4732i		−	0.842306i
$482$	−1.39671	+	15.7883i	−0.0636182	+	0.719139i
$483$	4.21821			0.191935
$484$	−20.6455	−	3.68159i	−0.938431	−	0.167345i
$485$			11.0949i			0.503795i
$486$	22.7463	+	2.01224i	1.03180	+	0.0912771i
$487$			38.5664i			1.74761i	0.486277	+	0.873804i	$0.338354\pi$
$487$			38.5664i			1.74761i	−0.486277	+	0.873804i	$0.661646\pi$
$488$	−26.0577	−	7.06331i	−1.17958	−	0.319741i
$489$	−20.7541			−0.938533
$490$	5.50957	+	0.487400i	0.248897	+	0.0220185i
$491$		−	18.7491i		−	0.846135i	−0.906098	−	0.423067i	$-0.860953\pi$
$491$		−	18.7491i		−	0.846135i	0.906098	−	0.423067i	$-0.139047\pi$
$492$	1.87550	−	10.5173i	0.0845539	−	0.474158i
$493$	0.849748	−	8.52252i	0.0382707	−	0.383835i
$494$	22.5607	+	1.99582i	1.01505	+	0.0897960i
$495$	1.56506			0.0703442
$496$	−7.78721	+	21.1401i	−0.349656	+	0.949218i
$497$	21.7095			0.973803
$498$	−1.08487	+	12.2633i	−0.0486141	+	0.549534i
$499$	28.0822			1.25713			0.628567	−	0.777756i	$-0.283642\pi$
$499$	28.0822			1.25713			0.628567	+	0.777756i	$0.283642\pi$
$500$	−1.96894	−	0.351110i	−0.0880536	−	0.0157021i
$501$			11.7642i			0.525586i
$502$	−0.800284	+	9.04640i	−0.0357184	+	0.403761i
$503$		−	20.7157i		−	0.923666i	−0.886967	−	0.461833i	$-0.847192\pi$
$503$		−	20.7157i		−	0.923666i	0.886967	−	0.461833i	$-0.152808\pi$
$504$	2.83793	−	10.4696i	0.126411	−	0.466351i
$505$			7.52075i			0.334669i
$506$	−0.237204	+	2.68135i	−0.0105450	+	0.119200i
$507$	−5.77689			−0.256560
$508$	−2.66251	−	0.474790i	−0.118130	−	0.0210654i
$509$			3.50632i			0.155415i	0.996976	+	0.0777074i	$0.0247600\pi$
$509$			3.50632i			0.155415i	−0.996976	+	0.0777074i	$0.975240\pi$
$510$	−0.983556	+	5.18084i	−0.0435526	+	0.229411i
$511$	10.9550			0.484621
$512$	−15.8600	−	16.1388i	−0.700919	−	0.713241i
$513$			29.1883i			1.28870i
$514$	24.9445	+	2.20670i	1.10025	+	0.0973331i
$515$	−8.56331			−0.377344
$516$	2.81513	−	15.7866i	0.123929	−	0.694966i
$517$	3.14324			0.138240
$518$	1.57348	−	17.7866i	0.0691347	−	0.781498i
$519$	7.91092			0.347251
$520$	−1.90282	+	7.01980i	−0.0834442	+	0.307839i
$521$			12.4668i			0.546179i	0.961989	+	0.273090i	$0.0880455\pi$
$521$			12.4668i			0.546179i	−0.961989	+	0.273090i	$0.911954\pi$
$522$	6.38542	+	0.564882i	0.279482	+	0.0247242i
$523$		−	15.3090i		−	0.669414i	−0.942322	−	0.334707i	$-0.891363\pi$
$523$		−	15.3090i		−	0.669414i	0.942322	−	0.334707i	$-0.108637\pi$
$524$	−11.7681	−	2.09853i	−0.514090	−	0.0916747i
$525$			1.58947i			0.0693703i
$526$	−14.5663	−	1.28860i	−0.635120	−	0.0561854i
$527$	23.1075	+	2.30396i	1.00658	+	0.100362i
$528$	−2.43464	−	0.896828i	−0.105954	−	0.0390294i
$529$	15.9571			0.693788
$530$	0.259143	−	2.92935i	0.0112564	−	0.127243i
$531$		−	9.53995i		−	0.413999i
$532$	21.5521	+	3.84327i	0.934404	+	0.166627i
$533$	−15.1880			−0.657865
$534$	2.12760	+	0.188217i	0.0920704	+	0.00814495i
$535$	10.6065			0.458558
$536$	10.9056	−	40.2324i	0.471050	−	1.73778i
$537$		−	0.436590i		−	0.0188403i
$538$	−11.8692	−	1.05000i	−0.511718	−	0.0452688i
$539$	2.80512			0.120825
$540$	−9.22757	−	1.64550i	−0.397091	−	0.0708110i
$541$	−25.4426			−1.09386			−0.546932	−	0.837177i	$-0.684204\pi$
$541$	−25.4426			−1.09386			−0.546932	+	0.837177i	$0.684204\pi$
$542$	−13.0760	−	1.15676i	−0.561661	−	0.0496869i
$543$	22.4758			0.964529
$544$	−12.0026	+	19.9984i	−0.514608	+	0.857425i
$545$	7.78258			0.333369
$546$	5.75773	+	0.509354i	0.246408	+	0.0217983i
$547$	21.2156			0.907113			0.453557	−	0.891227i	$-0.350155\pi$
$547$	21.2156			0.907113			0.453557	+	0.891227i	$0.350155\pi$
$548$	−15.0881	−	2.69057i	−0.644532	−	0.114936i
$549$	−20.8287			−0.888948
$550$	−1.01036	−	0.0893812i	−0.0430821	−	0.00381123i
$551$			12.9373i			0.551150i
$552$	1.77601	−	6.55199i	0.0755921	−	0.278871i
$553$	−5.33651			−0.226931
$554$	5.58235	+	0.493839i	0.237171	+	0.0209812i
$555$	−6.49703			−0.275784
$556$	9.90818	+	1.76687i	0.420200	+	0.0749319i
$557$			39.0833i			1.65601i	0.560719	+	0.828006i	$0.310525\pi$
$557$			39.0833i			1.65601i	−0.560719	+	0.828006i	$0.689475\pi$
$558$	−1.53159	+	17.3131i	−0.0648374	+	0.732921i
$559$	−22.7973			−0.964222
$560$	−2.43002	+	6.59681i	−0.102687	+	0.278766i
$561$	−0.265340	+	2.66122i	−0.0112027	+	0.112357i
$562$	−35.5799	−	3.14756i	−1.50085	−	0.132772i
$563$			2.62335i			0.110561i	0.998471	+	0.0552804i	$0.0176053\pi$
$563$			2.62335i			0.110561i	−0.998471	+	0.0552804i	$0.982395\pi$
$564$	−7.80376	−	1.39160i	−0.328597	−	0.0585969i
$565$		−	14.8231i		−	0.623612i
$566$	43.2514	+	3.82621i	1.81799	+	0.160827i
$567$		−	4.05621i		−	0.170345i
$568$	9.14043	−	33.7205i	0.383524	−	1.41488i
$569$	−17.6521			−0.740013			−0.370007	−	0.929029i	$-0.620645\pi$
$569$	−17.6521			−0.740013			−0.370007	+	0.929029i	$0.620645\pi$
$570$	0.701929	−	7.93460i	0.0294006	−	0.332344i
$571$	−21.1270			−0.884137			−0.442068	−	0.896981i	$-0.645755\pi$
$571$	−21.1270			−0.884137			−0.442068	+	0.896981i	$0.645755\pi$
$572$	−0.647551	+	3.63132i	−0.0270755	+	0.151833i
$573$	15.5721			0.650534
$574$	−14.6235	−	1.29366i	−0.610373	−	0.0539962i
$575$		−	2.65384i		−	0.110673i
$576$	−15.0671	−	8.81609i	−0.627796	−	0.367337i
$577$	−8.17093			−0.340160			−0.170080	−	0.985430i	$-0.554403\pi$
$577$	−8.17093			−0.340160			−0.170080	+	0.985430i	$0.554403\pi$
$578$	23.0583	+	6.80539i	0.959100	+	0.283067i
$579$		−	10.6216i		−	0.441419i
$580$	−4.09000	−	0.729347i	−0.169828	−	0.0302845i
$581$	16.9177			0.701866
$582$	1.25044	−	14.1350i	0.0518325	−	0.585915i
$583$		−	1.49143i		−	0.0617689i
$584$	4.61243	−	17.0160i	0.190864	−	0.704126i
$585$			5.61115i			0.231992i
$586$	2.70840	−	30.6157i	0.111883	−	1.26472i
$587$		−	0.0917506i		−	0.00378695i	−0.999998	−	0.00189348i	$-0.999397\pi$
$587$		−	0.0917506i		−	0.00378695i	0.999998	−	0.00189348i	$-0.000602713\pi$
$588$	−6.96428	−	1.24190i	−0.287202	−	0.0512151i
$589$	−35.0777			−1.44535
$590$	−0.544830	+	6.15875i	−0.0224303	+	0.253552i
$591$	−14.8133			−0.609338
$592$	−26.9647	−	9.93279i	−1.10824	−	0.408235i
$593$	−33.3289			−1.36865			−0.684327	−	0.729175i	$-0.739904\pi$
$593$	−33.3289			−1.36865			−0.684327	+	0.729175i	$0.739904\pi$
$594$	−4.73514	−	0.418891i	−0.194285	−	0.0171873i
$595$	7.21075	+	0.718957i	0.295612	+	0.0294744i
$596$	4.58148	−	25.6918i	0.187665	−	1.05238i
$597$			0.699809i			0.0286413i
$598$	−9.61333	−	0.850436i	−0.393118	−	0.0347769i
$599$	1.24959			0.0510568			0.0255284	−	0.999674i	$-0.491873\pi$
$599$	1.24959			0.0510568			0.0255284	+	0.999674i	$0.491873\pi$
$600$	2.46887	+	0.669223i	0.100791	+	0.0273209i
$601$		−	41.3209i		−	1.68551i	−0.538295	−	0.842757i	$-0.680931\pi$
$601$		−	41.3209i		−	1.68551i	0.538295	−	0.842757i	$-0.319069\pi$
$602$	−21.9499	−	1.94179i	−0.894613	−	0.0791413i
$603$		−	32.1590i		−	1.30962i
$604$	15.4694	+	2.75857i	0.629442	+	0.112245i
$605$	10.4856			0.426300
$606$	0.847618	−	9.58147i	0.0344321	−	0.389221i
$607$			18.9355i			0.768569i	0.923215	+	0.384285i	$0.125552\pi$
$607$			18.9355i			0.768569i	−0.923215	+	0.384285i	$0.874448\pi$
$608$	15.0438	−	31.8580i	0.610106	−	1.29201i
$609$			3.30175i			0.133794i
$610$	13.4465	+	1.18953i	0.544432	+	0.0481629i
$611$			11.2693i			0.455909i
$612$	−4.90091	+	17.3138i	−0.198108	+	0.699870i
$613$			20.5022i			0.828074i	0.910260	+	0.414037i	$0.135882\pi$
$613$			20.5022i			0.828074i	−0.910260	+	0.414037i	$0.864118\pi$
$614$	2.36159	−	26.6954i	0.0953059	−	1.07734i
$615$			5.34162i			0.215395i
$616$	−0.932785	+	3.44119i	−0.0375830	+	0.138649i
$617$		−	9.37330i		−	0.377355i	−0.982039	−	0.188677i	$-0.939580\pi$
$617$		−	9.37330i		−	0.377355i	0.982039	−	0.188677i	$-0.0604201\pi$
$618$	10.9097	+	0.965119i	0.438852	+	0.0388228i
$619$	27.6976			1.11326			0.556630	−	0.830760i	$-0.312094\pi$
$619$	27.6976			1.11326			0.556630	+	0.830760i	$0.312094\pi$
$620$	1.97751	−	11.0894i	0.0794188	−	0.445362i
$621$		−	12.4374i		−	0.499097i
$622$	2.06610	−	23.3551i	0.0828430	−	0.936456i
$623$		−	2.93511i		−	0.117593i
$624$	3.21536	−	8.72881i	0.128717	−	0.349432i
$625$	1.00000			0.0400000
$626$	2.11986	−	23.9628i	0.0847265	−	0.957747i
$627$		−	4.03979i		−	0.161333i
$628$	6.95673	−	39.0117i	0.277604	−	1.55674i
$629$	−2.93877	+	29.4742i	−0.117176	+	1.17522i
$630$	−0.477937	+	5.40259i	−0.0190414	+	0.215244i
$631$	6.20893			0.247174			0.123587	−	0.992334i	$-0.460560\pi$
$631$	6.20893			0.247174			0.123587	+	0.992334i	$0.460560\pi$
$632$	−2.24685	+	8.28899i	−0.0893750	+	0.329718i
$633$	−8.13630			−0.323389
$634$	42.3521	+	3.74665i	1.68202	+	0.148798i
$635$	1.35226			0.0536626
$636$	−0.660298	+	3.70280i	−0.0261825	+	0.146825i
$637$			10.0571i			0.398476i
$638$	−2.09879	−	0.185668i	−0.0830919	−	0.00735067i
$639$		−	26.9538i		−	1.06628i
$640$	9.22346	+	6.55194i	0.364589	+	0.258988i
$641$		−	12.7659i		−	0.504223i	−0.967698	−	0.252112i	$-0.918875\pi$
$641$		−	12.7659i		−	0.504223i	0.967698	−	0.252112i	$-0.0811250\pi$
$642$	−13.5127	−	1.19539i	−0.533304	−	0.0471784i
$643$	−13.2948			−0.524296			−0.262148	−	0.965028i	$-0.584431\pi$
$643$	−13.2948			−0.524296			−0.262148	+	0.965028i	$0.584431\pi$
$644$	−9.18358	−	1.63765i	−0.361884	−	0.0645326i
$645$			8.01781i			0.315701i
$646$	−35.6784	−	6.77336i	−1.40375	−	0.266494i
$647$	−13.9961			−0.550242			−0.275121	−	0.961410i	$-0.588718\pi$
$647$	−13.9961			−0.550242			−0.275121	+	0.961410i	$0.588718\pi$
$648$	−6.30035	−	1.70780i	−0.247501	−	0.0670889i
$649$			3.13564i			0.123085i
$650$	0.320455	−	3.62242i	0.0125693	−	0.142083i
$651$	−8.95220			−0.350864
$652$	45.1843	+	8.05745i	1.76955	+	0.315554i
$653$	−17.3694			−0.679717			−0.339859	−	0.940477i	$-0.610379\pi$
$653$	−17.3694			−0.679717			−0.339859	+	0.940477i	$0.610379\pi$
$654$	−9.91504	−	0.877128i	−0.387709	−	0.0342984i
$655$	5.97685			0.233535
$656$	−8.16638	+	22.1694i	−0.318844	+	0.865571i
$657$		−	13.6014i		−	0.530641i
$658$	−0.959881	+	10.8505i	−0.0374200	+	0.422996i
$659$			25.0689i			0.976546i	0.872691	+	0.488273i	$0.162373\pi$
$659$			25.0689i			0.976546i	−0.872691	+	0.488273i	$0.837627\pi$
$660$	1.27713	+	0.227744i	0.0497124	+	0.00886492i
$661$		−	29.5549i		−	1.14955i	−0.818310	−	0.574777i	$-0.805089\pi$
$661$		−	29.5549i		−	1.14955i	0.818310	−	0.574777i	$-0.194911\pi$
$662$	−0.162884	+	1.84124i	−0.00633067	+	0.0715619i
$663$	−9.54116	−	0.951313i	−0.370548	−	0.0369459i
$664$	7.12295	−	26.2777i	0.276424	−	1.01977i
$665$	−10.9461			−0.424470
$666$	−22.0833	−	1.95359i	−0.855711	−	0.0756999i
$667$		−	5.51273i		−	0.213454i
$668$	4.56727	−	25.6122i	0.176713	−	0.990965i
$669$	−6.74071			−0.260611
$670$	−1.83661	+	20.7611i	−0.0709546	+	0.802070i
$671$	6.84608			0.264290
$672$	3.83934	−	8.13050i	0.148106	−	0.313641i
$673$			23.9965i			0.924996i	0.886620	+	0.462498i	$0.153047\pi$
$673$			23.9965i			0.924996i	−0.886620	+	0.462498i	$0.846953\pi$
$674$	1.55219	−	17.5459i	0.0597881	−	0.675844i
$675$	4.68657			0.180386
$676$	12.5770	+	2.24278i	0.483731	+	0.0862609i
$677$	−3.14369			−0.120822			−0.0604109	−	0.998174i	$-0.519241\pi$
$677$	−3.14369			−0.120822			−0.0604109	+	0.998174i	$0.519241\pi$
$678$	−1.67062	+	18.8847i	−0.0641599	+	0.725262i
$679$	−19.4997			−0.748331
$680$	4.15270	−	10.8975i	0.159249	−	0.417899i
$681$	0.119568			0.00458185
$682$	0.503411	−	5.69055i	0.0192766	−	0.217903i
$683$	20.6098			0.788613			0.394306	−	0.918979i	$-0.370985\pi$
$683$	20.6098			0.788613			0.394306	+	0.918979i	$0.370985\pi$
$684$	4.77169	−	26.7585i	0.182450	−	1.02314i
$685$	7.66306			0.292791
$686$	−2.38980	+	27.0143i	−0.0912431	+	1.03141i
$687$			15.3078i			0.584031i
$688$	−12.2578	+	33.2764i	−0.467324	+	1.26865i
$689$	5.34718			0.203711
$690$	−0.299099	+	3.38101i	−0.0113865	+	0.128713i
$691$	−32.1189			−1.22186			−0.610931	−	0.791684i	$-0.709205\pi$
$691$	−32.1189			−1.22186			−0.610931	+	0.791684i	$0.709205\pi$
$692$	−17.2231	−	3.07129i	−0.654723	−	0.116753i
$693$			2.75065i			0.104489i
$694$	−29.6079	−	2.61924i	−1.12390	−	0.0994250i
$695$	−5.03224			−0.190884
$696$	5.12848	+	1.39015i	0.194395	+	0.0526935i
$697$	24.2327	+	2.41615i	0.917877	+	0.0915180i
$698$	0.996811	−	11.2679i	0.0377298	−	0.426498i
$699$		−	22.7099i		−	0.858967i
$700$	0.617088	−	3.46048i	0.0233237	−	0.130794i
$701$			40.4674i			1.52843i	0.644961	+	0.764216i	$0.276874\pi$
$701$			40.4674i			1.52843i	−0.644961	+	0.764216i	$0.723126\pi$
$702$	1.50183	−	16.9767i	0.0566830	−	0.640744i
$703$		−	44.7425i		−	1.68750i
$704$	4.95233	+	2.89772i	0.186648	+	0.109212i
$705$	3.96343			0.149272
$706$	−24.1682	−	2.13803i	−0.909584	−	0.0804657i
$707$	−13.2180			−0.497114
$708$	1.38823	−	7.78488i	0.0521730	−	0.292574i
$709$	35.1050			1.31840			0.659198	−	0.751970i	$-0.270896\pi$
$709$	35.1050			1.31840			0.659198	+	0.751970i	$0.270896\pi$
$710$	−1.53934	+	17.4007i	−0.0577705	+	0.653037i
$711$			6.62565i			0.248481i
$712$	−4.55899	−	1.23578i	−0.170855	−	0.0463129i
$713$	14.9469			0.559767
$714$	−9.10550	−	1.72864i	−0.340765	−	0.0646925i
$715$		−	1.84430i		−	0.0689729i
$716$	−0.169499	+	0.950511i	−0.00633448	+	0.0355223i
$717$	3.85589			0.144001
$718$	−52.5898	−	4.65232i	−1.96263	−	0.173623i
$719$		−	7.74025i		−	0.288663i	−0.989529	−	0.144331i	$-0.953897\pi$
$719$		−	7.74025i		−	0.288663i	0.989529	−	0.144331i	$-0.0461031\pi$
$720$	8.19041	+	3.01704i	0.305238	+	0.112438i
$721$		−	15.0503i		−	0.560503i
$722$	27.8769	+	2.46611i	1.03747	+	0.0917792i
$723$			10.1359i			0.376959i
$724$	−48.9327	−	8.72588i	−1.81857	−	0.324295i
$725$	2.07726			0.0771476
$726$	−13.3587	−	1.18177i	−0.495787	−	0.0438595i
$727$	11.3615			0.421375			0.210688	−	0.977553i	$-0.432430\pi$
$727$	11.3615			0.421375			0.210688	+	0.977553i	$0.432430\pi$
$728$	−12.3376	−	3.34428i	−0.457260	−	0.123947i
$729$	7.67919			0.284414
$730$	−0.776781	+	8.78072i	−0.0287499	+	0.324989i
$731$	36.3734	+	3.62665i	1.34532	+	0.134136i
$732$	−16.9968	−	3.03095i	−0.628221	−	0.112027i
$733$		−	17.6468i		−	0.651800i	−0.945404	−	0.325900i	$-0.894333\pi$
$733$		−	17.6468i		−	0.651800i	0.945404	−	0.325900i	$-0.105667\pi$
$734$	1.21455	−	13.7292i	0.0448298	−	0.506756i
$735$	3.53707			0.130467
$736$	−6.41031	+	13.5750i	−0.236287	+	0.500381i
$737$			10.5702i			0.389358i
$738$	−1.60617	+	18.1561i	−0.0591238	+	0.668335i
$739$			44.2571i			1.62802i	0.580848	+	0.814012i	$0.302721\pi$
$739$			44.2571i			1.62802i	−0.580848	+	0.814012i	$0.697279\pi$
$740$	14.1449	+	2.52237i	0.519975	+	0.0927242i
$741$	14.4837			0.532071
$742$	5.14843	+	0.455453i	0.189005	+	0.0167202i
$743$		−	44.8655i		−	1.64595i	−0.568075	−	0.822977i	$-0.692312\pi$
$743$		−	44.8655i		−	1.64595i	0.568075	−	0.822977i	$-0.307688\pi$
$744$	−3.76918	+	13.9051i	−0.138185	+	0.509786i
$745$			13.0486i			0.478063i
$746$	−1.88460	+	21.3035i	−0.0690001	+	0.779977i
$747$		−	21.0046i		−	0.768517i
$748$	1.61086	−	5.69080i	0.0588987	−	0.208076i
$749$			18.6413i			0.681137i
$750$	−1.27400	−	0.112704i	−0.0465201	−	0.00411537i
$751$		−	21.4310i		−	0.782028i	−0.920385	−	0.391014i	$-0.872124\pi$
$751$		−	21.4310i		−	0.782028i	0.920385	−	0.391014i	$-0.127876\pi$
$752$	16.4495	+	6.05937i	0.599851	+	0.220963i
$753$			5.80768i			0.211644i
$754$	0.665668	−	7.52471i	0.0242422	−	0.274034i
$755$	−7.85674			−0.285936
$756$	2.89202	−	16.2178i	0.105182	−	0.589835i
$757$		−	20.0107i		−	0.727300i	−0.931536	−	0.363650i	$-0.881530\pi$
$757$		−	20.0107i		−	0.727300i	0.931536	−	0.363650i	$-0.118470\pi$
$758$	32.6250	+	2.88615i	1.18499	+	0.104830i
$759$			1.72139i			0.0624826i
$760$	−4.60867	+	17.0021i	−0.167174	+	0.616731i
$761$	29.0248			1.05215			0.526075	−	0.850438i	$-0.323663\pi$
$761$	29.0248			1.05215			0.526075	+	0.850438i	$0.323663\pi$
$762$	−1.72278	−	0.152405i	−0.0624098	−	0.00552104i
$763$			13.6782i			0.495183i
$764$	−33.9024	−	6.04563i	−1.22655	−	0.218723i
$765$	0.892636	−	8.95266i	0.0322733	−	0.323684i
$766$	44.2457	+	3.91416i	1.59866	+	0.141424i
$767$	−11.2421			−0.405928
$768$	−11.0123	−	9.38672i	−0.397372	−	0.338714i
$769$	37.7396			1.36093			0.680463	−	0.732783i	$-0.261779\pi$
$769$	37.7396			1.36093			0.680463	+	0.732783i	$0.261779\pi$
$770$	0.157091	−	1.77575i	0.00566115	−	0.0639936i
$771$	16.0140			0.576731
$772$	−4.12367	+	23.1246i	−0.148414	+	0.832271i
$773$			44.6557i			1.60615i	0.595875	+	0.803077i	$0.296805\pi$
$773$			44.6557i			1.60615i	−0.595875	+	0.803077i	$0.703195\pi$
$774$	−2.41087	+	27.2524i	−0.0866568	+	0.979567i
$775$			5.63218i			0.202314i
$776$	−8.21006	+	30.2882i	−0.294724	+	1.08728i
$777$		−	11.4188i		−	0.409646i
$778$	3.80677	−	43.0317i	0.136479	−	1.54276i
$779$	−36.7856			−1.31798
$780$	−0.816521	+	4.57886i	−0.0292362	+	0.163949i
$781$			8.85932i			0.317011i
$782$	15.2029	+	2.88619i	0.543654	+	0.103210i
$783$	9.73524			0.347909
$784$	14.6800	+	5.40755i	0.524285	+	0.193127i
$785$			19.8136i			0.707176i
$786$	−7.61454	−	0.673615i	−0.271602	−	0.0240271i
$787$	−27.0086			−0.962754			−0.481377	−	0.876514i	$-0.659863\pi$
$787$	−27.0086			−0.962754			−0.481377	+	0.876514i	$0.659863\pi$
$788$	32.2504	+	5.75103i	1.14887	+	0.204872i
$789$	−9.35137			−0.332918
$790$	0.378393	−	4.27735i	0.0134626	−	0.152181i
$791$	26.0521			0.926307
$792$	4.27248	+	1.15812i	0.151816	+	0.0411519i
$793$			24.5450i			0.871618i
$794$	−0.956472	−	0.0846136i	−0.0339439	−	0.00300283i
$795$		−	1.88060i		−	0.0666982i
$796$	0.271690	−	1.52357i	0.00962978	−	0.0540016i
$797$			28.4535i			1.00787i	0.863740	+	0.503937i	$0.168116\pi$
$797$			28.4535i			1.00787i	−0.863740	+	0.503937i	$0.831884\pi$
$798$	13.9453	+	1.23367i	0.493660	+	0.0436713i
$799$	1.79276	−	17.9804i	0.0634232	−	0.636100i
$800$	−5.11522	−	2.41548i	−0.180850	−	0.0854001i
$801$	−3.64414			−0.128759
$802$	−1.79422	+	20.2818i	−0.0633560	+	0.716176i
$803$			4.47058i			0.157763i
$804$	4.67971	−	26.2427i	0.165041	−	0.925509i
$805$	4.66423			0.164392
$806$	20.4021	+	1.80486i	0.718633	+	0.0635734i
$807$	−7.61989			−0.268233
$808$	−5.56523	+	20.5310i	−0.195784	+	0.722278i
$809$		−	21.6976i		−	0.762848i	−0.924400	−	0.381424i	$-0.875434\pi$
$809$		−	21.6976i		−	0.762848i	0.924400	−	0.381424i	$-0.124566\pi$
$810$	3.25116	+	0.287612i	0.114234	+	0.0101056i
$811$	34.4705			1.21042			0.605212	−	0.796064i	$-0.293088\pi$
$811$	34.4705			1.21042			0.605212	+	0.796064i	$0.293088\pi$
$812$	1.28185	−	7.18833i	0.0449842	−	0.252261i
$813$	−8.39461			−0.294412
$814$	7.25845	+	0.642114i	0.254409	+	0.0225061i
$815$	−22.9485			−0.803852
$816$	−6.51875	+	13.4154i	−0.228202	+	0.469633i
$817$	−55.2155			−1.93175
$818$	13.5679	+	1.20028i	0.474391	+	0.0419667i
$819$	−9.86179			−0.344599
$820$	2.07380	−	11.6294i	0.0724203	−	0.406116i
$821$	34.5521			1.20588			0.602939	−	0.797787i	$-0.293996\pi$
$821$	34.5521			1.20588			0.602939	+	0.797787i	$0.293996\pi$
$822$	−9.76278	−	0.863658i	−0.340516	−	0.0301235i
$823$			0.161550i			0.00563129i	0.999996	+	0.00281564i	$0.000896248\pi$
$823$			0.161550i			0.00563129i	−0.999996	+	0.00281564i	$0.999104\pi$
$824$	−23.3771	−	6.33670i	−0.814379	−	0.220749i
$825$	−0.648641			−0.0225828
$826$	−10.8242	−	0.957558i	−0.376623	−	0.0333177i
$827$	−18.0714			−0.628403			−0.314201	−	0.949356i	$-0.601737\pi$
$827$	−18.0714			−0.628403			−0.314201	+	0.949356i	$0.601737\pi$
$828$	−2.03326	+	11.4021i	−0.0706608	+	0.396249i
$829$		−	2.09842i		−	0.0728810i	−0.999336	−	0.0364405i	$-0.988398\pi$
$829$		−	2.09842i		−	0.0728810i	0.999336	−	0.0364405i	$-0.0116019\pi$
$830$	−1.19958	+	13.5600i	−0.0416379	+	0.470675i
$831$	3.58380			0.124321
$832$	−10.3891	+	17.7554i	−0.360176	+	0.615558i
$833$	1.59990	−	16.0462i	0.0554334	−	0.555967i
$834$	6.41110	+	0.567154i	0.221998	+	0.0196389i
$835$			13.0081i			0.450164i
$836$	−1.56838	+	8.79512i	−0.0542437	+	0.304186i
$837$			26.3956i			0.912366i
$838$	38.1927	+	3.37869i	1.31934	+	0.116715i
$839$			6.97568i			0.240827i	0.992724	+	0.120414i	$0.0384221\pi$
$839$			6.97568i			0.240827i	−0.992724	+	0.120414i	$0.961578\pi$
$840$	−1.17618	+	4.33912i	−0.0405822	+	0.149714i
$841$	−24.6850			−0.851206
$842$	0.559288	−	6.32219i	0.0192744	−	0.217877i
$843$	−22.8419			−0.786716
$844$	17.7137	+	3.15879i	0.609732	+	0.108730i
$845$	−6.38771			−0.219744
$846$	13.4716	+	1.19176i	0.463164	+	0.0409735i
$847$			18.4288i			0.633221i
$848$	2.87510	−	7.80510i	0.0987315	−	0.268028i
$849$	27.7669			0.952956
$850$	−1.08755	+	5.72863i	−0.0373027	+	0.196490i
$851$			19.0652i			0.653547i
$852$	3.92226	−	21.9951i	0.134374	−	0.753540i
$853$	18.0141			0.616792			0.308396	−	0.951258i	$-0.400208\pi$
$853$	18.0141			0.616792			0.308396	+	0.951258i	$0.400208\pi$
$854$	−2.09065	+	23.6327i	−0.0715406	+	0.808694i
$855$			13.5903i			0.464779i
$856$	28.9548	+	7.84862i	0.989654	+	0.268260i
$857$			17.8746i			0.610586i	0.952259	+	0.305293i	$0.0987543\pi$
$857$			17.8746i			0.610586i	−0.952259	+	0.305293i	$0.901246\pi$
$858$	−0.207860	+	2.34965i	−0.00709622	+	0.0802156i
$859$		−	45.2623i		−	1.54433i	−0.635422	−	0.772165i	$-0.719174\pi$
$859$		−	45.2623i		−	1.54433i	0.635422	−	0.772165i	$-0.280826\pi$
$860$	3.11279	−	17.4558i	0.106145	−	0.595237i
$861$	−9.38810			−0.319946
$862$	3.05458	−	34.5289i	0.104039	−	1.17606i
$863$	42.4859			1.44624			0.723118	−	0.690725i	$-0.242708\pi$
$863$	42.4859			1.44624			0.723118	+	0.690725i	$0.242708\pi$
$864$	−23.9728	−	11.3203i	−0.815572	−	0.385125i
$865$	8.74738			0.297420
$866$	−35.4815	−	3.13885i	−1.20571	−	0.106662i
$867$	15.0717	+	3.03566i	0.511862	+	0.103097i
$868$	19.4901	+	3.47555i	0.661536	+	0.117968i
$869$		−	2.17775i		−	0.0738752i
$870$	−2.64644	−	0.234116i	−0.0897228	−	0.00793727i
$871$	−37.8969			−1.28409
$872$	21.2458	+	5.75898i	0.719472	+	0.195024i
$873$			24.2103i			0.819395i
$874$	−23.2837	−	2.05977i	−0.787582	−	0.0696729i
$875$			1.75754i			0.0594156i
$876$	1.97925	−	11.0991i	0.0668725	−	0.375005i
$877$	50.0618			1.69047			0.845234	−	0.534396i	$-0.179461\pi$
$877$	50.0618			1.69047			0.845234	+	0.534396i	$0.179461\pi$
$878$	0.932084	−	10.5363i	0.0314563	−	0.355582i
$879$		−	19.6549i		−	0.662943i
$880$	−2.69206	−	0.991655i	−0.0907495	−	0.0334287i
$881$			38.0490i			1.28190i	0.767582	+	0.640951i	$0.221460\pi$
$881$			38.0490i			1.28190i	−0.767582	+	0.640951i	$0.778540\pi$
$882$	12.0225	+	1.06356i	0.404817	+	0.0358119i
$883$			18.1342i			0.610264i	0.952310	+	0.305132i	$0.0987005\pi$
$883$			18.1342i			0.610264i	−0.952310	+	0.305132i	$0.901299\pi$
$884$	20.4030	+	5.77533i	0.686226	+	0.194246i
$885$			3.95384i			0.132907i
$886$	−2.53967	+	28.7084i	−0.0853218	+	0.964477i
$887$			4.00490i			0.134471i	0.997737	+	0.0672357i	$0.0214179\pi$
$887$			4.00490i			0.134471i	−0.997737	+	0.0672357i	$0.978582\pi$
$888$	−17.7363	−	4.80770i	−0.595193	−	0.161336i
$889$			2.37664i			0.0797099i
$890$	2.35257	+	0.208118i	0.0788582	+	0.00697614i
$891$	1.65528			0.0554540
$892$	14.6754	+	2.61698i	0.491368	+	0.0876228i
$893$			27.2946i			0.913378i
$894$	1.47063	−	16.6239i	0.0491851	−	0.555988i
$895$		−	0.482753i		−	0.0161367i
$896$	−11.5153	+	16.2106i	−0.384698	+	0.541557i
$897$	−6.17164			−0.206065
$898$	−4.57325	+	51.6959i	−0.152611	+	1.72512i
$899$			11.6995i			0.390201i
$900$	−4.29643	−	0.766158i	−0.143214	−	0.0255386i
$901$	−8.53149	−	0.850643i	−0.284225	−	0.0283390i
$902$	0.527923	−	5.96764i	0.0175779	−	0.198701i
$903$	−14.0916			−0.468939
$904$	10.9688	−	40.4658i	0.364818	−	1.34587i
$905$	24.8523			0.826118
$906$	10.0095	+	0.885485i	0.332544	+	0.0294183i
$907$	23.5118			0.780697			0.390348	−	0.920667i	$-0.372355\pi$
$907$	23.5118			0.780697			0.390348	+	0.920667i	$0.372355\pi$
$908$	−0.260315	−	0.0464204i	−0.00863884	−	0.00154051i
$909$			16.4111i			0.544321i
$910$	6.36653	+	0.563210i	0.211048	+	0.0186702i
$911$			53.7169i			1.77972i	0.456233	+	0.889861i	$0.349199\pi$
$911$			53.7169i			1.77972i	−0.456233	+	0.889861i	$0.650801\pi$
$912$	7.78767	−	21.1413i	0.257876	−	0.700060i
$913$			6.90388i			0.228485i
$914$	−18.5273	−	1.63901i	−0.612829	−	0.0542135i
$915$	8.63248			0.285381
$916$	5.94303	−	33.3271i	0.196363	−	1.10116i
$917$			10.5045i			0.346890i
$918$	−5.09689	+	26.8476i	−0.168222	+	0.886104i
$919$	5.94427			0.196084			0.0980418	−	0.995182i	$-0.468742\pi$
$919$	5.94427			0.196084			0.0980418	+	0.995182i	$0.468742\pi$
$920$	1.96380	−	7.24476i	0.0647445	−	0.238853i
$921$		−	17.1381i		−	0.564719i
$922$	3.18200	−	35.9693i	0.104794	−	1.18459i
$923$	−31.7630			−1.04549
$924$	−0.400268	+	2.24461i	−0.0131679	+	0.0738423i
$925$	−7.18400			−0.236208
$926$	24.4912	+	2.16659i	0.804830	+	0.0711987i
$927$	−18.6860			−0.613730
$928$	−10.6257	−	5.01759i	−0.348804	−	0.164710i
$929$		−	13.1296i		−	0.430768i	−0.976529	−	0.215384i	$-0.930900\pi$
$929$		−	13.1296i		−	0.430768i	0.976529	−	0.215384i	$-0.0691003\pi$
$930$	0.634769	−	7.17543i	0.0208149	−	0.235292i
$931$			24.3584i			0.798315i
$932$	−8.81676	+	49.4423i	−0.288802	+	1.61954i
$933$		−	14.9937i		−	0.490872i
$934$	0.623859	−	7.05210i	0.0204133	−	0.230752i
$935$	−0.293396	+	2.94260i	−0.00959507	+	0.0962335i
$936$	−4.15215	+	15.3179i	−0.135717	+	0.500683i
$937$	−8.76616			−0.286378			−0.143189	−	0.989695i	$-0.545736\pi$
$937$	−8.76616			−0.286378			−0.143189	+	0.989695i	$0.545736\pi$
$938$	−36.4883	−	3.22791i	−1.19139	−	0.105395i
$939$		−	15.3838i		−	0.502033i
$940$	−8.62889	−	1.53874i	−0.281443	−	0.0501882i
$941$	−50.9012			−1.65933			−0.829666	−	0.558260i	$-0.811469\pi$
$941$	−50.9012			−1.65933			−0.829666	+	0.558260i	$0.811469\pi$
$942$	2.23307	−	25.2426i	0.0727572	−	0.822447i
$943$	15.6747			0.510439
$944$	−6.04471	+	16.4097i	−0.196739	+	0.534090i
$945$			8.23681i			0.267944i
$946$	0.792415	−	8.95746i	0.0257636	−	0.291232i
$947$	−8.21859			−0.267068			−0.133534	−	0.991044i	$-0.542633\pi$
$947$	−8.21859			−0.267068			−0.133534	+	0.991044i	$0.542633\pi$
$948$	−0.964150	+	5.40672i	−0.0313141	+	0.175602i
$949$	−16.0282			−0.520297
$950$	0.776148	−	8.77357i	0.0251816	−	0.284652i
$951$	27.1895			0.881680
$952$	19.1527	+	7.29852i	0.620743	+	0.236547i
$953$	−6.78236			−0.219702			−0.109851	−	0.993948i	$-0.535037\pi$
$953$	−6.78236			−0.219702			−0.109851	+	0.993948i	$0.535037\pi$
$954$	0.565476	−	6.39214i	0.0183080	−	0.206953i
$955$	17.2186			0.557182
$956$	−8.39476	−	1.49699i	−0.271506	−	0.0484161i
$957$	−1.34740			−0.0435552
$958$	−2.08680	+	23.5891i	−0.0674213	+	0.762130i
$959$			13.4681i			0.434908i
$960$	6.24458	+	3.65384i	0.201543	+	0.117927i
$961$	−0.721472			−0.0232733
$962$	−2.30215	+	26.0234i	−0.0742242	+	0.839029i
$963$	23.1445			0.745820
$964$	3.93511	−	22.0672i	0.126741	−	0.710736i
$965$		−	11.7447i		−	0.378075i
$966$	−5.94225	−	0.525677i	−0.191189	−	0.0169134i
$967$	30.2045			0.971312			0.485656	−	0.874150i	$-0.338581\pi$
$967$	30.2045			0.971312			0.485656	+	0.874150i	$0.338581\pi$
$968$	28.6247	+	7.75916i	0.920034	+	0.249389i
$969$	−23.1089	−	2.30410i	−0.742365	−	0.0740184i
$970$	1.38266	−	15.6296i	0.0443945	−	0.501835i
$971$		−	10.6454i		−	0.341629i	−0.985303	−	0.170814i	$-0.945360\pi$
$971$		−	10.6454i		−	0.341629i	0.985303	−	0.170814i	$-0.0546398\pi$
$972$	−31.7923	−	5.66933i	−1.01974	−	0.181844i
$973$		−	8.84434i		−	0.283537i
$974$	4.80617	−	54.3289i	0.154000	−	1.74081i
$975$		−	2.32555i		−	0.0744771i
$976$	35.8275	+	13.1975i	1.14681	+	0.422442i
$977$	−1.11212			−0.0355799			−0.0177899	−	0.999842i	$-0.505663\pi$
$977$	−1.11212			−0.0355799			−0.0177899	+	0.999842i	$0.505663\pi$
$978$	29.2366	+	2.58639i	0.934882	+	0.0827037i
$979$	1.19778			0.0382811
$980$	−7.70065	−	1.37321i	−0.245988	−	0.0438657i
$981$	16.9824			0.542206
$982$	−2.33653	+	26.4121i	−0.0745616	+	0.842843i
$983$		−	43.4117i		−	1.38462i	−0.721602	−	0.692308i	$-0.756594\pi$
$983$		−	43.4117i		−	1.38462i	0.721602	−	0.692308i	$-0.243406\pi$
$984$	−3.95271	+	14.5822i	−0.126008	+	0.464863i
$985$	−16.3796			−0.521897
$986$	−2.25913	+	11.8999i	−0.0719454	+	0.378969i
$987$			6.96588i			0.221726i
$988$	−31.5328	−	5.62306i	−1.00319	−	0.178893i
$989$	23.5279			0.748142
$990$	−2.20472	−	0.195039i	−0.0700706	−	0.00619875i
$991$		−	33.0273i		−	1.04915i	−0.851366	−	0.524573i	$-0.824225\pi$
$991$		−	33.0273i		−	1.04915i	0.851366	−	0.524573i	$-0.175775\pi$
$992$	13.6044	−	28.8098i	0.431941	−	0.914713i
$993$			1.18205i			0.0375113i
$994$	−30.5824	−	2.70545i	−0.970015	−	0.0858117i
$995$			0.773803i			0.0245312i
$996$	3.05654	−	17.1403i	0.0968500	−	0.543112i
$997$	−50.1430			−1.58804			−0.794022	−	0.607889i	$-0.792017\pi$
$997$	−50.1430			−1.58804			−0.794022	+	0.607889i	$0.792017\pi$
$998$	−39.5598	−	3.49963i	−1.25224	−	0.110779i
$999$	−33.6683			−1.06522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.l.b.101.1	yes	36
4.3	odd	2		2720.2.l.a.2481.23		36
8.3	odd	2		2720.2.l.b.2481.13		36
8.5	even	2		680.2.l.a.101.2	yes	36
17.16	even	2		680.2.l.a.101.1	✓	36
68.67	odd	2		2720.2.l.b.2481.14		36
136.67	odd	2		2720.2.l.a.2481.24		36
136.101	even	2	inner	680.2.l.b.101.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.l.a.101.1	✓	36	17.16	even	2
680.2.l.a.101.2	yes	36	8.5	even	2
680.2.l.b.101.1	yes	36	1.1	even	1	trivial
680.2.l.b.101.2	yes	36	136.101	even	2	inner
2720.2.l.a.2481.23		36	4.3	odd	2
2720.2.l.a.2481.24		36	136.67	odd	2
2720.2.l.b.2481.13		36	8.3	odd	2
2720.2.l.b.2481.14		36	68.67	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40871 - 0.124621i) q^{2} -0.904376 q^{3} +(1.96894 + 0.351110i) q^{4} -1.00000 q^{5} +(1.27400 + 0.112704i) q^{6} -1.75754i q^{7} +(-2.72991 - 0.739983i) q^{8} -2.18210 q^{9} +(1.40871 + 0.124621i) q^{10} +0.717225 q^{11} +(-1.78066 - 0.317535i) q^{12} +2.57144i q^{13} +(-0.219025 + 2.47586i) q^{14} +0.904376 q^{15} +(3.75344 + 1.38263i) q^{16} +(0.409071 - 4.10276i) q^{17} +(3.07396 + 0.271936i) q^{18} +6.22808i q^{19} +(-1.96894 - 0.351110i) q^{20} +1.58947i q^{21} +(-1.01036 - 0.0893812i) q^{22} -2.65384i q^{23} +(2.46887 + 0.669223i) q^{24} +1.00000 q^{25} +(0.320455 - 3.62242i) q^{26} +4.68657 q^{27} +(0.617088 - 3.46048i) q^{28} +2.07726 q^{29} +(-1.27400 - 0.112704i) q^{30} +5.63218i q^{31} +(-5.11522 - 2.41548i) q^{32} -0.648641 q^{33} +(-1.08755 + 5.72863i) q^{34} +1.75754i q^{35} +(-4.29643 - 0.766158i) q^{36} -7.18400 q^{37} +(0.776148 - 8.77357i) q^{38} -2.32555i q^{39} +(2.72991 + 0.739983i) q^{40} +5.90642i q^{41} +(0.198081 - 2.23911i) q^{42} +8.86558i q^{43} +(1.41217 + 0.251825i) q^{44} +2.18210 q^{45} +(-0.330724 + 3.73850i) q^{46} +4.38251 q^{47} +(-3.39452 - 1.25041i) q^{48} +3.91107 q^{49} +(-1.40871 - 0.124621i) q^{50} +(-0.369954 + 3.71044i) q^{51} +(-0.902856 + 5.06301i) q^{52} -2.07945i q^{53} +(-6.60203 - 0.584044i) q^{54} -0.717225 q^{55} +(-1.30055 + 4.79792i) q^{56} -5.63252i q^{57} +(-2.92627 - 0.258870i) q^{58} +4.37190i q^{59} +(1.78066 + 0.317535i) q^{60} +9.54524 q^{61} +(0.701887 - 7.93412i) q^{62} +3.83513i q^{63} +(6.90485 + 4.04018i) q^{64} -2.57144i q^{65} +(0.913748 + 0.0808341i) q^{66} +14.7376i q^{67} +(2.24595 - 7.93446i) q^{68} +2.40007i q^{69} +(0.219025 - 2.47586i) q^{70} +12.3522i q^{71} +(5.95696 + 1.61472i) q^{72} +6.23316i q^{73} +(10.1202 + 0.895276i) q^{74} -0.904376 q^{75} +(-2.18674 + 12.2627i) q^{76} -1.26055i q^{77} +(-0.289811 + 3.27602i) q^{78} -3.03636i q^{79} +(-3.75344 - 1.38263i) q^{80} +2.30790 q^{81} +(0.736063 - 8.32045i) q^{82} +9.62582i q^{83} +(-0.558079 + 3.12958i) q^{84} +(-0.409071 + 4.10276i) q^{85} +(1.10483 - 12.4890i) q^{86} -1.87863 q^{87} +(-1.95796 - 0.530734i) q^{88} +1.67001 q^{89} +(-3.07396 - 0.271936i) q^{90} +4.51940 q^{91} +(0.931790 - 5.22526i) q^{92} -5.09361i q^{93} +(-6.17369 - 0.546151i) q^{94} -6.22808i q^{95} +(4.62608 + 2.18450i) q^{96} -11.0949i q^{97} +(-5.50957 - 0.487400i) q^{98} -1.56506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{3} + 2 q^{4} - 36 q^{5} + 36 q^{9} + 8 q^{11} + 2 q^{12} - 2 q^{14} - 4 q^{15} + 6 q^{16} - 10 q^{18} - 2 q^{20} - 26 q^{24} + 36 q^{25} + 6 q^{26} + 16 q^{27} - 14 q^{28} - 10 q^{32} - 8 q^{33}+ \cdots + 40 q^{99}+O(q^{100}) \) 36 * q + 4 * q^3 + 2 * q^4 - 36 * q^5 + 36 * q^9 + 8 * q^11 + 2 * q^12 - 2 * q^14 - 4 * q^15 + 6 * q^16 - 10 * q^18 - 2 * q^20 - 26 * q^24 + 36 * q^25 + 6 * q^26 + 16 * q^27 - 14 * q^28 - 10 * q^32 - 8 * q^33 + 12 * q^34 + 8 * q^36 - 20 * q^38 - 2 * q^42 - 6 * q^44 - 36 * q^45 - 24 * q^46 + 20 * q^47 + 4 * q^48 - 36 * q^49 + 6 * q^52 + 56 * q^54 - 8 * q^55 - 20 * q^56 + 18 * q^58 - 2 * q^60 + 24 * q^62 + 14 * q^64 - 16 * q^66 + 16 * q^68 + 2 * q^70 - 54 * q^72 - 6 * q^74 + 4 * q^75 + 2 * q^76 + 14 * q^78 - 6 * q^80 + 44 * q^81 - 22 * q^82 - 68 * q^84 - 36 * q^86 + 24 * q^87 + 58 * q^88 + 10 * q^90 + 56 * q^91 + 12 * q^92 + 14 * q^94 + 24 * q^96 + 10 * q^98 + 40 * q^99

Introduction

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