LMFDB - Embedded newform 855.2.k.g.406.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.3518667.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 7x^{4} - 8x^{3} + 43x^{2} - 42x + 49 $ x^6 - x^5 + 7x^4 - 8x^3 + 43x^2 - 42x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.2
Root			$0.610938 + 1.05818i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.g.676.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.610938 + 1.05818i) q^{2} +(0.253509 - 0.439091i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.28514 q^{7} +3.06327 q^{8} +O(q^{10})$	\(q+(0.610938 + 1.05818i) q^{2} +(0.253509 - 0.439091i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.28514 q^{7} +3.06327 q^{8} +(0.610938 - 1.05818i) q^{10} -0.285142 q^{11} +(2.50000 - 4.33013i) q^{13} +(-0.785142 - 1.35991i) q^{14} +(1.36445 + 2.36329i) q^{16} +(-3.11796 - 5.40046i) q^{17} +(2.92771 - 3.22932i) q^{19} -0.507019 q^{20} +(-0.174204 - 0.301731i) q^{22} +(-2.61796 + 4.53443i) q^{23} +(-0.500000 + 0.866025i) q^{25} +6.10938 q^{26} +(-0.325796 + 0.564295i) q^{28} +(0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(1.39608 - 2.41808i) q^{32} +(3.80976 - 6.59869i) q^{34} +(0.642571 + 1.11297i) q^{35} +10.8695 q^{37} +(5.20584 + 1.12512i) q^{38} +(-1.53163 - 2.65287i) q^{40} +(-0.420695 - 0.728665i) q^{41} +(2.47539 + 4.28749i) q^{43} +(-0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(2.86445 - 4.96137i) q^{47} -5.34841 q^{49} -1.22188 q^{50} +(-1.26755 - 2.19546i) q^{52} +(6.18122 - 10.7062i) q^{53} +(0.142571 + 0.246941i) q^{55} -3.93673 q^{56} +1.57028 q^{58} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-0.746491 - 1.29296i) q^{62} +8.86946 q^{64} -5.00000 q^{65} +(0.492981 - 0.853869i) q^{67} -3.16172 q^{68} +(-0.785142 + 1.35991i) q^{70} +(-1.46135 - 2.53113i) q^{71} +(0.382043 + 0.661718i) q^{73} +(6.64057 + 11.5018i) q^{74} +(-0.675762 - 2.10419i) q^{76} +0.366449 q^{77} +(7.72889 + 13.3868i) q^{79} +(1.36445 - 2.36329i) q^{80} +(0.514037 - 0.890339i) q^{82} -1.66563 q^{83} +(-3.11796 + 5.40046i) q^{85} +(-3.02461 + 5.23879i) q^{86} -0.873467 q^{88} +(-8.01404 + 13.8807i) q^{89} +(-3.21286 + 5.56483i) q^{91} +(1.32735 + 2.29904i) q^{92} +7.00000 q^{94} +(-4.26053 - 0.920816i) q^{95} +(-5.87147 - 10.1697i) q^{97} +(-3.26755 - 5.65956i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8	$ 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} + 10 q^{11} + 15 q^{13} + 7 q^{14} - 3 q^{16} + q^{17} + 14 q^{20} + 8 q^{22} + 4 q^{23} - 3 q^{25} + 10 q^{26} - 11 q^{28} - 2 q^{29} - 2 q^{31} - 6 q^{32} + 25 q^{34} - 2 q^{35} - 4 q^{37} + 19 q^{38} - 6 q^{40} - 2 q^{41} + q^{43} - 18 q^{44} - 48 q^{46} + 6 q^{47} - 14 q^{49} - 2 q^{50} + 35 q^{52} + 11 q^{53} - 5 q^{55} - 30 q^{56} - 14 q^{58} + 6 q^{59} + 9 q^{61} - 13 q^{62} - 16 q^{64} - 30 q^{65} + 20 q^{67} - 68 q^{68} + 7 q^{70} - 29 q^{71} + 22 q^{73} - 7 q^{74} - 19 q^{76} + 32 q^{77} + 24 q^{79} - 3 q^{80} - 31 q^{82} + 6 q^{83} + q^{85} - 32 q^{86} - 18 q^{88} - 14 q^{89} + 10 q^{91} + 41 q^{92} + 42 q^{94} - 7 q^{97} + 23 q^{98}+O(q^{100}) $ 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8 + q^10 + 10 * q^11 + 15 * q^13 + 7 * q^14 - 3 * q^16 + q^17 + 14 * q^20 + 8 * q^22 + 4 * q^23 - 3 * q^25 + 10 * q^26 - 11 * q^28 - 2 * q^29 - 2 * q^31 - 6 * q^32 + 25 * q^34 - 2 * q^35 - 4 * q^37 + 19 * q^38 - 6 * q^40 - 2 * q^41 + q^43 - 18 * q^44 - 48 * q^46 + 6 * q^47 - 14 * q^49 - 2 * q^50 + 35 * q^52 + 11 * q^53 - 5 * q^55 - 30 * q^56 - 14 * q^58 + 6 * q^59 + 9 * q^61 - 13 * q^62 - 16 * q^64 - 30 * q^65 + 20 * q^67 - 68 * q^68 + 7 * q^70 - 29 * q^71 + 22 * q^73 - 7 * q^74 - 19 * q^76 + 32 * q^77 + 24 * q^79 - 3 * q^80 - 31 * q^82 + 6 * q^83 + q^85 - 32 * q^86 - 18 * q^88 - 14 * q^89 + 10 * q^91 + 41 * q^92 + 42 * q^94 - 7 * q^97 + 23 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.610938	+	1.05818i	0.431998	+	0.748243i	0.997045	−	0.0768155i	$-0.0244753\pi$
$2$	0.610938	+	1.05818i	0.431998	+	0.748243i	−0.565047	+	0.825059i	$0.691142\pi$
$3$		0			0
$3$		0			0
$4$	0.253509	−	0.439091i	0.126755	−	0.219546i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.28514			−0.485738			−0.242869	−	0.970059i	$-0.578089\pi$
$7$	−1.28514			−0.485738			−0.242869	+	0.970059i	$0.578089\pi$
$8$	3.06327			1.08303
$9$		0			0
$10$	0.610938	−	1.05818i	0.193196	−	0.334625i
$11$	−0.285142			−0.0859737			−0.0429868	−	0.999076i	$-0.513687\pi$
$11$	−0.285142			−0.0859737			−0.0429868	+	0.999076i	$0.513687\pi$
$12$		0			0
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	−0.277350	−	0.960769i	$-0.589456\pi$
$13$	2.50000	−	4.33013i	0.693375	−	1.20096i	0.970725	−	0.240192i	$-0.0772105\pi$
$14$	−0.785142	−	1.35991i	−0.209838	−	0.363450i
$15$		0			0
$16$	1.36445	+	2.36329i	0.341112	+	0.590823i
$17$	−3.11796	−	5.40046i	−0.756216	−	1.30980i	−0.944768	−	0.327741i	$-0.893713\pi$
$17$	−3.11796	−	5.40046i	−0.756216	−	1.30980i	0.188552	−	0.982063i	$-0.439621\pi$
$18$		0			0
$19$	2.92771	−	3.22932i	0.671664	−	0.740856i
$19$	2.92771	−	3.22932i	0.671664	−	0.740856i
$20$	−0.507019			−0.113373
$21$		0			0
$22$	−0.174204	−	0.301731i	−0.0371405	−	0.0643292i
$23$	−2.61796	+	4.53443i	−0.545882	+	0.945495i	0.452669	+	0.891679i	$0.350472\pi$
$23$	−2.61796	+	4.53443i	−0.545882	+	0.945495i	−0.998551	+	0.0538163i	$0.982861\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	6.10938			1.19815
$27$		0			0
$28$	−0.325796	+	0.564295i	−0.0615696	+	0.106642i
$29$	0.642571	−	1.11297i	0.119322	−	0.206673i	−0.800177	−	0.599764i	$-0.795261\pi$
$29$	0.642571	−	1.11297i	0.119322	−	0.206673i	0.919499	+	0.393091i	$0.128594\pi$
$30$		0			0
$31$	−1.22188			−0.219455			−0.109728	−	0.993962i	$-0.534998\pi$
$31$	−1.22188			−0.219455			−0.109728	+	0.993962i	$0.534998\pi$
$32$	1.39608	−	2.41808i	0.246795	−	0.427461i
$33$		0			0
$34$	3.80976	−	6.59869i	0.653368	−	1.13167i
$35$	0.642571	+	1.11297i	0.108614	+	0.188126i
$36$		0			0
$37$	10.8695			1.78693			0.893464	−	0.449134i	$-0.148267\pi$
$37$	10.8695			1.78693			0.893464	+	0.449134i	$0.148267\pi$
$38$	5.20584	+	1.12512i	0.844498	+	0.182519i
$39$		0			0
$40$	−1.53163	−	2.65287i	−0.242172	−	0.419455i
$41$	−0.420695	−	0.728665i	−0.0657015	−	0.113798i	0.831303	−	0.555819i	$-0.187595\pi$
$41$	−0.420695	−	0.728665i	−0.0657015	−	0.113798i	−0.897005	+	0.442020i	$0.854262\pi$
$42$		0			0
$43$	2.47539	+	4.28749i	0.377493	+	0.653837i	0.990697	−	0.136088i	$-0.0434530\pi$
$43$	2.47539	+	4.28749i	0.377493	+	0.653837i	−0.613204	+	0.789925i	$0.710120\pi$
$44$	−0.0722863	+	0.125204i	−0.0108976	+	0.0188751i
$45$		0			0
$46$	−6.39764			−0.943280
$47$	2.86445	−	4.96137i	0.417823	−	0.723690i	−0.577898	−	0.816109i	$-0.696127\pi$
$47$	2.86445	−	4.96137i	0.417823	−	0.723690i	0.995720	+	0.0924193i	$0.0294600\pi$
$48$		0			0
$49$	−5.34841			−0.764058
$50$	−1.22188			−0.172799
$51$		0			0
$52$	−1.26755	−	2.19546i	−0.175777	−	0.304455i
$53$	6.18122	−	10.7062i	0.849056	−	1.47061i	−0.0329952	−	0.999456i	$-0.510505\pi$
$53$	6.18122	−	10.7062i	0.849056	−	1.47061i	0.882051	−	0.471153i	$-0.156162\pi$
$54$		0			0
$55$	0.142571	+	0.246941i	0.0192243	+	0.0332975i
$56$	−3.93673			−0.526068
$57$		0			0
$58$	1.57028			0.206189
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	0.990013	−	0.140974i	$-0.0450235\pi$
$59$	2.86445	+	4.96137i	0.372919	+	0.645915i	−0.617094	+	0.786889i	$0.711690\pi$
$60$		0			0
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	−0.972701	−	0.232060i	$-0.925453\pi$
$61$	−2.22889	+	3.86056i	−0.285381	+	0.494294i	0.687321	+	0.726354i	$0.258787\pi$
$62$	−0.746491	−	1.29296i	−0.0948044	−	0.164206i
$63$		0			0
$64$	8.86946			1.10868
$65$	−5.00000			−0.620174
$66$		0			0
$67$	0.492981	−	0.853869i	0.0602273	−	0.104317i	−0.834340	−	0.551251i	$-0.814151\pi$
$67$	0.492981	−	0.853869i	0.0602273	−	0.104317i	0.894567	+	0.446934i	$0.147484\pi$
$68$	−3.16172			−0.383415
$69$		0			0
$70$	−0.785142	+	1.35991i	−0.0938425	+	0.162540i
$71$	−1.46135	−	2.53113i	−0.173430	−	0.300390i	0.766187	−	0.642618i	$-0.222152\pi$
$71$	−1.46135	−	2.53113i	−0.173430	−	0.300390i	−0.939617	+	0.342228i	$0.888818\pi$
$72$		0			0
$73$	0.382043	+	0.661718i	0.0447148	+	0.0774483i	0.887517	−	0.460776i	$-0.152429\pi$
$73$	0.382043	+	0.661718i	0.0447148	+	0.0774483i	−0.842802	+	0.538224i	$0.819095\pi$
$74$	6.64057	+	11.5018i	0.771951	+	1.33706i
$75$		0			0
$76$	−0.675762	−	2.10419i	−0.0775152	−	0.241368i
$77$	0.366449			0.0417607
$78$		0			0
$79$	7.72889	+	13.3868i	0.869569	+	1.50614i	0.862438	+	0.506162i	$0.168936\pi$
$79$	7.72889	+	13.3868i	0.869569	+	1.50614i	0.00713043	+	0.999975i	$0.497730\pi$
$80$	1.36445	−	2.36329i	0.152550	−	0.264224i
$81$		0			0
$82$	0.514037	−	0.890339i	0.0567659	−	0.0983215i
$83$	−1.66563			−0.182826			−0.0914132	−	0.995813i	$-0.529138\pi$
$83$	−1.66563			−0.182826			−0.0914132	+	0.995813i	$0.529138\pi$
$84$		0			0
$85$	−3.11796	+	5.40046i	−0.338190	+	0.585762i
$86$	−3.02461	+	5.23879i	−0.326153	+	0.564913i
$87$		0			0
$88$	−0.873467			−0.0931119
$89$	−8.01404	+	13.8807i	−0.849486	+	1.47135i	0.0321812	+	0.999482i	$0.489755\pi$
$89$	−8.01404	+	13.8807i	−0.849486	+	1.47135i	−0.881667	+	0.471871i	$0.843579\pi$
$90$		0			0
$91$	−3.21286	+	5.56483i	−0.336799	+	0.583353i
$92$	1.32735	+	2.29904i	0.138386	+	0.239692i
$93$		0			0
$94$	7.00000			0.721995
$95$	−4.26053	−	0.920816i	−0.437121	−	0.0944737i
$96$		0			0
$97$	−5.87147	−	10.1697i	−0.596157	−	1.03257i	−0.993382	−	0.114853i	$-0.963360\pi$
$97$	−5.87147	−	10.1697i	−0.596157	−	1.03257i	0.397225	−	0.917721i	$-0.369973\pi$
$98$	−3.26755	−	5.65956i	−0.330072	−	0.571702i
$99$		0			0
$100$	0.253509	+	0.439091i	0.0253509	+	0.0439091i
$101$	−3.95935	+	6.85779i	−0.393970	+	0.682376i	−0.992969	−	0.118374i	$-0.962232\pi$
$101$	−3.95935	+	6.85779i	−0.393970	+	0.682376i	0.598999	+	0.800750i	$0.295565\pi$
$102$		0			0
$103$	−12.8202			−1.26322			−0.631608	−	0.775288i	$-0.717605\pi$
$103$	−12.8202			−1.26322			−0.631608	+	0.775288i	$0.717605\pi$
$104$	7.65817	−	13.2643i	0.750945	−	1.30067i
$105$		0			0
$106$	15.1054			1.46716
$107$	−13.8062			−1.33470			−0.667348	−	0.744746i	$-0.732571\pi$
$107$	−13.8062			−1.33470			−0.667348	+	0.744746i	$0.732571\pi$
$108$		0			0
$109$	4.60192	+	7.97076i	0.440784	+	0.763460i	0.997748	−	0.0670767i	$-0.0213672\pi$
$109$	4.60192	+	7.97076i	0.440784	+	0.763460i	−0.556964	+	0.830537i	$0.688034\pi$
$110$	−0.174204	+	0.301731i	−0.0166097	+	0.0287689i
$111$		0			0
$112$	−1.75351	−	3.03717i	−0.165691	−	0.286985i
$113$	17.3273			1.63001			0.815005	−	0.579453i	$-0.196734\pi$
$113$	17.3273			1.63001			0.815005	+	0.579453i	$0.196734\pi$
$114$		0			0
$115$	5.23591			0.488251
$116$	−0.325796	−	0.564295i	−0.0302494	−	0.0523934i
$117$		0			0
$118$	−3.50000	+	6.06218i	−0.322201	+	0.558069i
$119$	4.00702	+	6.94036i	0.367323	+	0.636222i
$120$		0			0
$121$	−10.9187			−0.992609
$122$	−5.44687			−0.493136
$123$		0			0
$124$	−0.309757	+	0.536515i	−0.0278170	+	0.0481805i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.66563	+	8.08111i	−0.414008	+	0.717082i	−0.995324	−	0.0965956i	$-0.969205\pi$
$127$	−4.66563	+	8.08111i	−0.414008	+	0.717082i	0.581316	+	0.813678i	$0.302538\pi$
$128$	2.62653	+	4.54929i	0.232155	+	0.402104i
$129$		0			0
$130$	−3.05469	−	5.29088i	−0.267914	−	0.464041i
$131$	6.21286	+	10.7610i	0.542820	+	0.940191i	0.998741	+	0.0501711i	$0.0159767\pi$
$131$	6.21286	+	10.7610i	0.542820	+	0.940191i	−0.455921	+	0.890020i	$0.650690\pi$
$132$		0			0
$133$	−3.76253	+	4.15013i	−0.326253	+	0.359862i
$134$	1.20472			0.104072
$135$		0			0
$136$	−9.55113	−	16.5430i	−0.819003	−	1.41855i
$137$	−9.26755	+	16.0519i	−0.791780	+	1.37140i	0.133084	+	0.991105i	$0.457512\pi$
$137$	−9.26755	+	16.0519i	−0.791780	+	1.37140i	−0.924864	+	0.380298i	$0.875821\pi$
$138$		0			0
$139$	3.00702	−	5.20831i	0.255052	−	0.441763i	−0.709858	−	0.704345i	$-0.751241\pi$
$139$	3.00702	−	5.20831i	0.255052	−	0.441763i	0.964910	+	0.262582i	$0.0845741\pi$
$140$	0.651591			0.0550695
$141$		0			0
$142$	1.78559	−	3.09273i	0.149843	−	0.259536i
$143$	−0.712856	+	1.23470i	−0.0596120	+	0.103251i
$144$		0			0
$145$	−1.28514			−0.106725
$146$	−0.466810	+	0.808538i	−0.0386334	+	0.0669151i
$147$		0			0
$148$	2.75551	−	4.77268i	0.226502	−	0.392312i
$149$	−3.39608	−	5.88218i	−0.278218	−	0.481887i	0.692724	−	0.721203i	$-0.256410\pi$
$149$	−3.39608	−	5.88218i	−0.278218	−	0.481887i	−0.970942	+	0.239315i	$0.923077\pi$
$150$		0			0
$151$	−15.8875			−1.29291			−0.646453	−	0.762953i	$-0.723749\pi$
$151$	−15.8875			−1.29291			−0.646453	+	0.762953i	$0.723749\pi$
$152$	8.96837	−	9.89226i	0.727431	−	0.802368i
$153$		0			0
$154$	0.223877	+	0.387767i	0.0180406	+	0.0312472i
$155$	0.610938	+	1.05818i	0.0490717	+	0.0849947i
$156$		0			0
$157$	−3.75351	−	6.50127i	−0.299563	−	0.518858i	0.676473	−	0.736467i	$-0.263507\pi$
$157$	−3.75351	−	6.50127i	−0.299563	−	0.518858i	−0.976036	+	0.217609i	$0.930174\pi$
$158$	−9.44375	+	16.3571i	−0.751305	+	1.30130i
$159$		0			0
$160$	−2.79216			−0.220740
$161$	3.36445	−	5.82739i	0.265156	−	0.459263i
$162$		0			0
$163$	21.8202			1.70909			0.854546	−	0.519375i	$-0.173835\pi$
$163$	21.8202			1.70909			0.854546	+	0.519375i	$0.173835\pi$
$164$	−0.426600			−0.0333119
$165$		0			0
$166$	−1.01760	−	1.76253i	−0.0789808	−	0.136799i
$167$	5.64257	−	9.77322i	0.436635	−	0.756274i	−0.560792	−	0.827957i	$-0.689503\pi$
$167$	5.64257	−	9.77322i	0.436635	−	0.756274i	0.997428	+	0.0716821i	$0.0228367\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$	−7.61951			−0.584390
$171$		0			0
$172$	2.51013			0.191396
$173$	−2.92771	−	5.07095i	−0.222590	−	0.385537i	0.733004	−	0.680225i	$-0.238118\pi$
$173$	−2.92771	−	5.07095i	−0.222590	−	0.385537i	−0.955594	+	0.294688i	$0.904784\pi$
$174$		0			0
$175$	0.642571	−	1.11297i	0.0485738	−	0.0841323i
$176$	−0.389062	−	0.673875i	−0.0293266	−	0.0507952i
$177$		0			0
$178$	−19.5843			−1.46791
$179$	18.7922			1.40459			0.702296	−	0.711885i	$-0.252158\pi$
$179$	18.7922			1.40459			0.702296	+	0.711885i	$0.252158\pi$
$180$		0			0
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	−0.999989	−	0.00464265i	$-0.998522\pi$
$181$	−6.67265	+	11.5574i	−0.495974	+	0.859052i	0.504015	+	0.863695i	$0.331856\pi$
$182$	−7.85142			−0.581986
$183$		0			0
$184$	−8.01950	+	13.8902i	−0.591205	+	1.02400i
$185$	−5.43473	−	9.41323i	−0.399569	−	0.692075i
$186$		0			0
$187$	0.889062	+	1.53990i	0.0650146	+	0.112609i
$188$	−1.45233	−	2.51551i	−0.105922	−	0.183462i
$189$		0			0
$190$	−1.62853	−	5.07095i	−0.118146	−	0.367885i
$191$	0.668743			0.0483885			0.0241943	−	0.999707i	$-0.492298\pi$
$191$	0.668743			0.0483885			0.0241943	+	0.999707i	$0.492298\pi$
$192$		0			0
$193$	1.88204	+	3.25979i	0.135472	+	0.234645i	0.925778	−	0.378068i	$-0.123411\pi$
$193$	1.88204	+	3.25979i	0.135472	+	0.234645i	−0.790305	+	0.612713i	$0.790078\pi$
$194$	7.17420	−	12.4261i	0.515078	−	0.892141i
$195$		0			0
$196$	−1.35587	+	2.34844i	−0.0968480	+	0.167746i
$197$	−14.6164			−1.04138			−0.520688	−	0.853747i	$-0.674324\pi$
$197$	−14.6164			−1.04138			−0.520688	+	0.853747i	$0.674324\pi$
$198$		0			0
$199$	−5.76053	+	9.97753i	−0.408353	+	0.707288i	−0.994705	−	0.102768i	$-0.967230\pi$
$199$	−5.76053	+	9.97753i	−0.408353	+	0.707288i	0.586352	+	0.810056i	$0.300563\pi$
$200$	−1.53163	+	2.65287i	−0.108303	+	0.187586i
$201$		0			0
$202$	−9.67566			−0.680777
$203$	−0.825796	+	1.43032i	−0.0579595	+	0.100389i
$204$		0			0
$205$	−0.420695	+	0.728665i	−0.0293826	+	0.0508922i
$206$	−7.83237	−	13.5661i	−0.545707	−	0.945192i
$207$		0			0
$208$	13.6445			0.946074
$209$	−0.834816	+	0.920816i	−0.0577454	+	0.0636941i
$210$		0			0
$211$	8.57028	+	14.8442i	0.590003	+	1.02191i	0.994231	+	0.107257i	$0.0342067\pi$
$211$	8.57028	+	14.8442i	0.590003	+	1.02191i	−0.404229	+	0.914658i	$0.632460\pi$
$212$	−3.13400	−	5.42824i	−0.215244	−	0.372813i
$213$		0			0
$214$	−8.43473	−	14.6094i	−0.576586	−	0.998677i
$215$	2.47539	−	4.28749i	0.168820	−	0.292405i
$216$		0			0
$217$	1.57028			0.106598
$218$	−5.62297	+	9.73928i	−0.380836	+	0.659627i
$219$		0			0
$220$	0.144573			0.00974708
$221$	−31.1796			−2.09736
$222$		0			0
$223$	−0.762085	−	1.31997i	−0.0510330	−	0.0883918i	0.839380	−	0.543544i	$-0.182918\pi$
$223$	−0.762085	−	1.31997i	−0.0510330	−	0.0883918i	−0.890413	+	0.455153i	$0.849585\pi$
$224$	−1.79416	+	3.10758i	−0.119878	+	0.207634i
$225$		0			0
$226$	10.5859	+	18.3353i	0.704162	+	1.21964i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$		0			0
$229$	18.4397			1.21853			0.609266	−	0.792966i	$-0.291464\pi$
$229$	18.4397			1.21853			0.609266	+	0.792966i	$0.291464\pi$
$230$	3.19882	+	5.54052i	0.210924	+	0.365331i
$231$		0			0
$232$	1.96837	−	3.40931i	0.129230	−	0.223832i
$233$	6.35587	+	11.0087i	0.416387	+	0.721203i	0.995573	−	0.0939920i	$-0.0299628\pi$
$233$	6.35587	+	11.0087i	0.416387	+	0.721203i	−0.579186	+	0.815195i	$0.696629\pi$
$234$		0			0
$235$	−5.72889			−0.373712
$236$	2.90466			0.189077
$237$		0			0
$238$	−4.89608	+	8.48026i	−0.317366	+	0.549694i
$239$	10.8343			0.700811			0.350405	−	0.936598i	$-0.386044\pi$
$239$	10.8343			0.700811			0.350405	+	0.936598i	$0.386044\pi$
$240$		0			0
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	−0.662068	−	0.749444i	$-0.730321\pi$
$241$	4.93673	−	8.55067i	0.318003	−	0.550797i	0.980071	+	0.198646i	$0.0636545\pi$
$242$	−6.67065	−	11.5539i	−0.428805	−	0.742713i
$243$		0			0
$244$	1.13009	+	1.95738i	0.0723467	+	0.125308i
$245$	2.67420	+	4.63186i	0.170849	+	0.295919i
$246$		0			0
$247$	−6.66407	−	20.7507i	−0.424025	−	1.32033i
$248$	−3.74293			−0.237676
$249$		0			0
$250$	0.610938	+	1.05818i	0.0386391	+	0.0669249i
$251$	8.88550	−	15.3901i	0.560848	−	0.971417i	−0.436575	−	0.899668i	$-0.643809\pi$
$251$	8.88550	−	15.3901i	0.560848	−	0.971417i	0.997423	−	0.0717492i	$-0.0228581\pi$
$252$		0			0
$253$	0.746491	−	1.29296i	0.0469315	−	0.0812877i
$254$	−11.4016			−0.715403
$255$		0			0
$256$	5.66017	−	9.80370i	0.353760	−	0.612731i
$257$	4.07930	−	7.06556i	0.254460	−	0.440738i	−0.710289	−	0.703911i	$-0.751436\pi$
$257$	4.07930	−	7.06556i	0.254460	−	0.440738i	0.964749	+	0.263173i	$0.0847689\pi$
$258$		0			0
$259$	−13.9688			−0.867980
$260$	−1.26755	+	2.19546i	−0.0786099	+	0.136156i
$261$		0			0
$262$	−7.59134	+	13.1486i	−0.468995	+	0.812322i
$263$	3.15861	+	5.47087i	0.194768	+	0.337348i	0.946825	−	0.321750i	$-0.104271\pi$
$263$	3.15861	+	5.47087i	0.194768	+	0.337348i	−0.752056	+	0.659099i	$0.770938\pi$
$264$		0			0
$265$	−12.3624			−0.759419
$266$	−6.69024	−	1.44594i	−0.410205	−	0.0886565i
$267$		0			0
$268$	−0.249951	−	0.432927i	−0.0152682	−	0.0264452i
$269$	4.11951	+	7.13521i	0.251171	+	0.435041i	0.963849	−	0.266451i	$-0.0858510\pi$
$269$	4.11951	+	7.13521i	0.251171	+	0.435041i	−0.712677	+	0.701492i	$0.752518\pi$
$270$		0			0
$271$	2.11094	+	3.65625i	0.128230	+	0.222101i	0.922991	−	0.384821i	$-0.125737\pi$
$271$	2.11094	+	3.65625i	0.128230	+	0.222101i	−0.794761	+	0.606923i	$0.792404\pi$
$272$	8.50858	−	14.7373i	0.515908	−	0.893579i
$273$		0			0
$274$	−22.6476			−1.36819
$275$	0.142571	−	0.246941i	0.00859737	−	0.0148911i
$276$		0			0
$277$	−9.83739			−0.591071			−0.295536	−	0.955332i	$-0.595498\pi$
$277$	−9.83739			−0.591071			−0.295536	+	0.955332i	$0.595498\pi$
$278$	7.34841			0.440728
$279$		0			0
$280$	1.96837	+	3.40931i	0.117632	+	0.203745i
$281$	2.69024	−	4.65964i	0.160486	−	0.277971i	−0.774557	−	0.632504i	$-0.782027\pi$
$281$	2.69024	−	4.65964i	0.160486	−	0.277971i	0.935043	+	0.354534i	$0.115360\pi$
$282$		0			0
$283$	2.48240	+	4.29965i	0.147564	+	0.255588i	0.930326	−	0.366732i	$-0.119524\pi$
$283$	2.48240	+	4.29965i	0.147564	+	0.255588i	−0.782763	+	0.622320i	$0.786190\pi$
$284$	−1.48186			−0.0879323
$285$		0			0
$286$	−1.74204			−0.103009
$287$	0.540653	+	0.936439i	0.0319137	+	0.0552762i
$288$		0			0
$289$	−10.9433	+	18.9544i	−0.643724	+	1.11496i
$290$	−0.785142	−	1.35991i	−0.0461052	−	0.0798565i
$291$		0			0
$292$	0.387406			0.0226712
$293$	3.80620			0.222360			0.111180	−	0.993800i	$-0.464537\pi$
$293$	3.80620			0.222360			0.111180	+	0.993800i	$0.464537\pi$
$294$		0			0
$295$	2.86445	−	4.96137i	0.166775	−	0.288862i
$296$	33.2961			1.93529
$297$		0			0
$298$	4.14959	−	7.18730i	0.240379	−	0.416349i
$299$	13.0898	+	22.6722i	0.757002	+	1.31117i
$300$		0			0
$301$	−3.18122	−	5.51004i	−0.183363	−	0.317593i
$302$	−9.70628	−	16.8118i	−0.558534	−	0.967409i
$303$		0			0
$304$	11.6265	+	2.51281i	0.666827	+	0.144119i
$305$	4.45779			0.255252
$306$		0			0
$307$	−0.287144	−	0.497348i	−0.0163882	−	0.0283851i	0.857715	−	0.514125i	$-0.171883\pi$
$307$	−0.287144	−	0.497348i	−0.0163882	−	0.0283851i	−0.874103	+	0.485740i	$0.838550\pi$
$308$	0.0928982	−	0.160904i	0.00529336	−	0.00916838i
$309$		0			0
$310$	−0.746491	+	1.29296i	−0.0423978	+	0.0734352i
$311$	8.61640			0.488591			0.244296	−	0.969701i	$-0.421443\pi$
$311$	8.61640			0.488591			0.244296	+	0.969701i	$0.421443\pi$
$312$		0			0
$313$	17.0617	−	29.5517i	0.964385	−	1.67036i	0.253126	−	0.967433i	$-0.418541\pi$
$313$	17.0617	−	29.5517i	0.964385	−	1.67036i	0.711259	−	0.702930i	$-0.248125\pi$
$314$	4.58632	−	7.94375i	0.258821	−	0.448291i
$315$		0			0
$316$	7.83739			0.440887
$317$	−5.53865	+	9.59323i	−0.311082	+	0.538809i	−0.978597	−	0.205787i	$-0.934025\pi$
$317$	−5.53865	+	9.59323i	−0.311082	+	0.538809i	0.667515	+	0.744596i	$0.267358\pi$
$318$		0			0
$319$	−0.183224	+	0.317354i	−0.0102586	+	0.0177684i
$320$	−4.43473	−	7.68118i	−0.247909	−	0.429391i
$321$		0			0
$322$	8.22188			0.458187
$323$	−26.5683	−	5.74213i	−1.47830	−	0.319500i
$324$		0			0
$325$	2.50000	+	4.33013i	0.138675	+	0.240192i
$326$	13.3308	+	23.0896i	0.738325	+	1.27882i
$327$		0			0
$328$	−1.28870	−	2.23210i	−0.0711566	−	0.123247i
$329$	−3.68122	+	6.37607i	−0.202952	+	0.351524i
$330$		0			0
$331$	6.41168			0.352418			0.176209	−	0.984353i	$-0.443617\pi$
$331$	6.41168			0.352418			0.176209	+	0.984353i	$0.443617\pi$
$332$	−0.422252	+	0.731363i	−0.0231741	+	0.0401387i
$333$		0			0
$334$	13.7890			0.754503
$335$	−0.985963			−0.0538689
$336$		0			0
$337$	12.6336	+	21.8820i	0.688193	+	1.19199i	0.972422	+	0.233229i	$0.0749293\pi$
$337$	12.6336	+	21.8820i	0.688193	+	1.19199i	−0.284228	+	0.958757i	$0.591737\pi$
$338$	7.33126	−	12.6981i	0.398768	−	0.690686i
$339$		0			0
$340$	1.58086	+	2.73813i	0.0857343	+	0.148496i
$341$	0.348409			0.0188674
$342$		0			0
$343$	15.8695			0.856871
$344$	7.58276	+	13.1337i	0.408835	+	0.708123i
$345$		0			0
$346$	3.57730	−	6.19607i	0.192317	−	0.333103i
$347$	6.20428	+	10.7461i	0.333063	+	0.576882i	0.983111	−	0.183011i	$-0.0585844\pi$
$347$	6.20428	+	10.7461i	0.333063	+	0.576882i	−0.650048	+	0.759893i	$0.725251\pi$
$348$		0			0
$349$	6.20384			0.332084			0.166042	−	0.986119i	$-0.446901\pi$
$349$	6.20384			0.332084			0.166042	+	0.986119i	$0.446901\pi$
$350$	1.57028			0.0839353
$351$		0			0
$352$	−0.398082	+	0.689498i	−0.0212178	+	0.0367504i
$353$	23.3484			1.24271			0.621355	−	0.783529i	$-0.286582\pi$
$353$	23.3484			1.24271			0.621355	+	0.783529i	$0.286582\pi$
$354$		0			0
$355$	−1.46135	+	2.53113i	−0.0775603	+	0.134338i
$356$	4.06327	+	7.03778i	0.215353	+	0.373002i
$357$		0			0
$358$	11.4808	+	19.8854i	0.606782	+	1.05098i
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.580333	−	0.814379i	$-0.697078\pi$
$359$	−18.8609	−	32.6680i	−0.995440	−	1.72415i	−0.415107	−	0.909773i	$-0.636256\pi$
$360$		0			0
$361$	−1.85698	−	18.9090i	−0.0977360	−	0.995212i
$362$	−16.3063			−0.857040
$363$		0			0
$364$	1.62898	+	2.82147i	0.0853816	+	0.147885i
$365$	0.382043	−	0.661718i	0.0199971	−	0.0346359i
$366$		0			0
$367$	−14.7038	+	25.4678i	−0.767534	+	1.32941i	0.171362	+	0.985208i	$0.445183\pi$
$367$	−14.7038	+	25.4678i	−0.767534	+	1.32941i	−0.938896	+	0.344200i	$0.888150\pi$
$368$	−14.2883			−0.744827
$369$		0			0
$370$	6.64057	−	11.5018i	0.345227	−	0.597950i
$371$	−7.94375	+	13.7590i	−0.412419	+	0.714331i
$372$		0			0
$373$	−21.5491			−1.11577			−0.557886	−	0.829918i	$-0.688387\pi$
$373$	−21.5491			−1.11577			−0.557886	+	0.829918i	$0.688387\pi$
$374$	−1.08632	+	1.88157i	−0.0561725	+	0.0972935i
$375$		0			0
$376$	8.77457	−	15.1980i	0.452514	−	0.783777i
$377$	−3.21286	−	5.56483i	−0.165471	−	0.286603i
$378$		0			0
$379$	−19.3945			−0.996230			−0.498115	−	0.867111i	$-0.665974\pi$
$379$	−19.3945			−0.996230			−0.498115	+	0.867111i	$0.665974\pi$
$380$	−1.48441	+	1.63732i	−0.0761484	+	0.0839930i
$381$		0			0
$382$	0.408561	+	0.707648i	0.0209038	+	0.0362064i
$383$	9.44331	+	16.3563i	0.482531	+	0.835767i	0.999799	−	0.0200559i	$-0.00638442\pi$
$383$	9.44331	+	16.3563i	0.482531	+	0.835767i	−0.517268	+	0.855823i	$0.673051\pi$
$384$		0			0
$385$	−0.183224	−	0.317354i	−0.00933798	−	0.0161739i
$386$	−2.29962	+	3.98307i	−0.117048	+	0.202733i
$387$		0			0
$388$	−5.95389			−0.302263
$389$	−4.54021	+	7.86387i	−0.230198	+	0.398714i	−0.957866	−	0.287215i	$-0.907271\pi$
$389$	−4.54021	+	7.86387i	−0.230198	+	0.398714i	0.727668	+	0.685929i	$0.240604\pi$
$390$		0			0
$391$	32.6507			1.65122
$392$	−16.3836			−0.827497
$393$		0			0
$394$	−8.92972	−	15.4667i	−0.449873	−	0.779202i
$395$	7.72889	−	13.3868i	0.388883	−	0.673565i
$396$		0			0
$397$	−8.49800	−	14.7190i	−0.426502	−	0.738724i	0.570057	−	0.821605i	$-0.306921\pi$
$397$	−8.49800	−	14.7190i	−0.426502	−	0.738724i	−0.996559	+	0.0828814i	$0.973588\pi$
$398$	−14.0773			−0.705631
$399$		0			0
$400$	−2.72889			−0.136445
$401$	0.795720	+	1.37823i	0.0397363	+	0.0688254i	0.885210	−	0.465192i	$-0.154015\pi$
$401$	0.795720	+	1.37823i	0.0397363	+	0.0688254i	−0.845473	+	0.534018i	$0.820682\pi$
$402$		0			0
$403$	−3.05469	+	5.29088i	−0.152165	+	0.263557i
$404$	2.00746	+	3.47703i	0.0998750	+	0.172989i
$405$		0			0
$406$	−2.01804			−0.100154
$407$	−3.09935			−0.153629
$408$		0			0
$409$	0.998443	−	1.72935i	0.0493698	−	0.0855110i	−0.840284	−	0.542146i	$-0.817612\pi$
$409$	0.998443	−	1.72935i	0.0493698	−	0.0855110i	0.889654	+	0.456635i	$0.150945\pi$
$410$	−1.02807			−0.0507730
$411$		0			0
$412$	−3.25005	+	5.62925i	−0.160118	+	0.277333i
$413$	−3.68122	−	6.37607i	−0.181141	−	0.313746i
$414$		0			0
$415$	0.832814	+	1.44248i	0.0408812	+	0.0708084i
$416$	−6.98040	−	12.0904i	−0.342242	−	0.592781i
$417$		0			0
$418$	−1.48441	−	0.320820i	−0.0726046	−	0.0156918i
$419$	22.7781			1.11278			0.556392	−	0.830920i	$-0.312185\pi$
$419$	22.7781			1.11278			0.556392	+	0.830920i	$0.312185\pi$
$420$		0			0
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	0.983923	−	0.178594i	$-0.0571550\pi$
$421$	6.92070	+	11.9870i	0.337294	+	0.584210i	−0.646629	+	0.762805i	$0.723822\pi$
$422$	−10.4718	+	18.1377i	−0.509761	+	0.882931i
$423$		0			0
$424$	18.9347	−	32.7959i	0.919552	−	1.59271i
$425$	6.23591			0.302486
$426$		0			0
$427$	2.86445	−	4.96137i	0.138620	−	0.240097i
$428$	−3.50000	+	6.06218i	−0.169179	+	0.293026i
$429$		0			0
$430$	6.04923			0.291720
$431$	1.71987	−	2.97891i	0.0828435	−	0.143489i	−0.821627	−	0.570026i	$-0.806933\pi$
$431$	1.71987	−	2.97891i	0.0828435	−	0.143489i	0.904470	+	0.426537i	$0.140267\pi$
$432$		0			0
$433$	4.60036	−	7.96806i	0.221079	−	0.382920i	−0.734057	−	0.679088i	$-0.762375\pi$
$433$	4.60036	−	7.96806i	0.221079	−	0.382920i	0.955136	+	0.296168i	$0.0957087\pi$
$434$	0.959347	+	1.66164i	0.0460501	+	0.0797612i
$435$		0			0
$436$	4.66652			0.223486
$437$	6.97850	+	21.7297i	0.333827	+	1.03947i
$438$		0			0
$439$	18.7550	+	32.4846i	0.895126	+	1.55040i	0.833649	+	0.552295i	$0.186248\pi$
$439$	18.7550	+	32.4846i	0.895126	+	1.55040i	0.0614769	+	0.998109i	$0.480419\pi$
$440$	0.436734	+	0.756445i	0.0208205	+	0.0360621i
$441$		0			0
$442$	−19.0488	−	32.9935i	−0.906058	−	1.56934i
$443$	7.33939	−	12.7122i	0.348705	−	0.603975i	−0.637315	−	0.770604i	$-0.719955\pi$
$443$	7.33939	−	12.7122i	0.348705	−	0.603975i	0.986020	+	0.166629i	$0.0532882\pi$
$444$		0			0
$445$	16.0281			0.759804
$446$	0.931174	−	1.61284i	0.0440924	−	0.0763702i
$447$		0			0
$448$	−11.3985			−0.538530
$449$	7.39052			0.348780			0.174390	−	0.984677i	$-0.444205\pi$
$449$	7.39052			0.348780			0.174390	+	0.984677i	$0.444205\pi$
$450$		0			0
$451$	0.119958	+	0.207773i	0.00564860	+	0.00978367i
$452$	4.39262	−	7.60824i	0.206611	−	0.357862i
$453$		0			0
$454$	−2.44375	−	4.23270i	−0.114691	−	0.198651i
$455$	6.42571			0.301242
$456$		0			0
$457$	2.30007			0.107593			0.0537963	−	0.998552i	$-0.482868\pi$
$457$	2.30007			0.107593			0.0537963	+	0.998552i	$0.482868\pi$
$458$	11.2655	+	19.5125i	0.526404	+	0.911759i
$459$		0			0
$460$	1.32735	−	2.29904i	0.0618881	−	0.107193i
$461$	9.87848	+	17.1100i	0.460087	+	0.796894i	0.998965	−	0.0454900i	$-0.0144849\pi$
$461$	9.87848	+	17.1100i	0.460087	+	0.796894i	−0.538878	+	0.842384i	$0.681152\pi$
$462$		0			0
$463$	28.9468			1.34527			0.672635	−	0.739974i	$-0.265162\pi$
$463$	28.9468			1.34527			0.672635	+	0.739974i	$0.265162\pi$
$464$	3.50702			0.162809
$465$		0			0
$466$	−7.76609	+	13.4513i	−0.359757	+	0.623118i
$467$	3.31722			0.153503			0.0767513	−	0.997050i	$-0.475545\pi$
$467$	3.31722			0.153503			0.0767513	+	0.997050i	$0.475545\pi$
$468$		0			0
$469$	−0.633551	+	1.09734i	−0.0292547	+	0.0506706i
$470$	−3.50000	−	6.06218i	−0.161443	−	0.279627i
$471$		0			0
$472$	8.77457	+	15.1980i	0.403882	+	0.699544i
$473$	−0.705838	−	1.22255i	−0.0324544	−	0.0562127i
$474$		0			0
$475$	1.33281	+	4.15013i	0.0611537	+	0.190421i
$476$	4.06327			0.186240
$477$		0			0
$478$	6.61907	+	11.4646i	0.302749	+	0.524377i
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.0784026	+	0.996922i	$0.524982\pi$
$479$	−19.7535	+	34.2141i	−0.902561	+	1.56328i	−0.824158	+	0.566360i	$0.808351\pi$
$480$		0			0
$481$	27.1737	−	47.0662i	1.23901	−	2.14603i
$482$	12.0642			0.549507
$483$		0			0
$484$	−2.76799	+	4.79430i	−0.125818	+	0.217923i
$485$	−5.87147	+	10.1697i	−0.266610	+	0.461781i
$486$		0			0
$487$	−24.7781			−1.12280			−0.561402	−	0.827543i	$-0.689738\pi$
$487$	−24.7781			−1.12280			−0.561402	+	0.827543i	$0.689738\pi$
$488$	−6.82770	+	11.8259i	−0.309075	+	0.535334i
$489$		0			0
$490$	−3.26755	+	5.65956i	−0.147613	+	0.255673i
$491$	−6.81176	−	11.7983i	−0.307410	−	0.532450i	0.670385	−	0.742014i	$-0.266129\pi$
$491$	−6.81176	−	11.7983i	−0.307410	−	0.532450i	−0.977795	+	0.209563i	$0.932796\pi$
$492$		0			0
$493$	−8.01404			−0.360934
$494$	17.8865	−	19.7291i	0.804752	−	0.887656i
$495$		0			0
$496$	−1.66719	−	2.88765i	−0.0748589	−	0.129659i
$497$	1.87804	+	3.25286i	0.0842416	+	0.145911i
$498$		0			0
$499$	−4.09490	−	7.09257i	−0.183313	−	0.317507i	0.759694	−	0.650281i	$-0.225349\pi$
$499$	−4.09490	−	7.09257i	−0.183313	−	0.317507i	−0.943007	+	0.332774i	$0.892015\pi$
$500$	0.253509	−	0.439091i	0.0113373	−	0.0196367i
$501$		0			0
$502$	21.7140			0.969142
$503$	9.14257	−	15.8354i	0.407647	−	0.706065i	−0.586978	−	0.809603i	$-0.699683\pi$
$503$	9.14257	−	15.8354i	0.407647	−	0.706065i	0.994626	+	0.103537i	$0.0330160\pi$
$504$		0			0
$505$	7.91869			0.352377
$506$	1.82424			0.0810973
$507$		0			0
$508$	2.36556	+	4.09727i	0.104955	+	0.181787i
$509$	5.94220	−	10.2922i	0.263383	−	0.456193i	−0.703756	−	0.710442i	$-0.748495\pi$
$509$	5.94220	−	10.2922i	0.263383	−	0.456193i	0.967139	+	0.254249i	$0.0818283\pi$
$510$		0			0
$511$	−0.490980	−	0.850402i	−0.0217197	−	0.0376196i
$512$	24.3382			1.07561
$513$		0			0
$514$	9.96881			0.439705
$515$	6.41012	+	11.1026i	0.282464	+	0.489241i
$516$		0			0
$517$	−0.816776	+	1.41470i	−0.0359218	+	0.0622183i
$518$	−8.53408	−	14.7815i	−0.374966	−	0.649460i
$519$		0			0
$520$	−15.3163			−0.671666
$521$	−21.3725			−0.936345			−0.468173	−	0.883637i	$-0.655087\pi$
$521$	−21.3725			−0.936345			−0.468173	+	0.883637i	$0.655087\pi$
$522$		0			0
$523$	2.88862	−	5.00323i	0.126310	−	0.218776i	−0.795934	−	0.605383i	$-0.793020\pi$
$523$	2.88862	−	5.00323i	0.126310	−	0.218776i	0.922244	+	0.386607i	$0.126353\pi$
$524$	6.30007			0.275220
$525$		0			0
$526$	−3.85943	+	6.68473i	−0.168279	+	0.291468i
$527$	3.80976	+	6.59869i	0.165956	+	0.287444i
$528$		0			0
$529$	−2.20739	−	3.82332i	−0.0959737	−	0.166231i
$530$	−7.55269	−	13.0816i	−0.328068	−	0.568230i
$531$		0			0
$532$	0.868450	+	2.70419i	0.0376521	+	0.117242i
$533$	−4.20695			−0.182223
$534$		0			0
$535$	6.90310	+	11.9565i	0.298447	+	0.516925i
$536$	1.51013	−	2.61563i	0.0652278	−	0.112978i
$537$		0			0
$538$	−5.03354	+	8.71834i	−0.217011	+	0.375874i
$539$	1.52506			0.0656889
$540$		0			0
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	−0.892943	−	0.450170i	$-0.851363\pi$
$541$	−1.31678	+	2.28072i	−0.0566126	+	0.0980559i	0.836330	+	0.548226i	$0.184697\pi$
$542$	−2.57930	+	4.46749i	−0.110791	+	0.191895i
$543$		0			0
$544$	−17.4117			−0.746519
$545$	4.60192	−	7.97076i	0.197125	−	0.341430i
$546$		0			0
$547$	18.1812	−	31.4908i	0.777373	−	1.34645i	−0.156078	−	0.987745i	$-0.549885\pi$
$547$	18.1812	−	31.4908i	0.777373	−	1.34645i	0.933451	−	0.358705i	$-0.116782\pi$
$548$	4.69882	+	8.13859i	0.200724	+	0.347663i
$549$		0			0
$550$	0.348409			0.0148562
$551$	−1.71286	−	5.33351i	−0.0729701	−	0.227215i
$552$		0			0
$553$	−9.93273	−	17.2040i	−0.422383	−	0.731588i
$554$	−6.01003	−	10.4097i	−0.255342	−	0.442265i
$555$		0			0
$556$	−1.52461	−	2.64071i	−0.0646581	−	0.111991i
$557$	11.9824	−	20.7541i	0.507711	−	0.879381i	−0.492249	−	0.870454i	$-0.663825\pi$
$557$	11.9824	−	20.7541i	0.507711	−	0.879381i	0.999960	−	0.00892662i	$-0.00284147\pi$
$558$		0			0
$559$	24.7539			1.04698
$560$	−1.75351	+	3.03717i	−0.0740993	+	0.128344i
$561$		0			0
$562$	6.57429			0.277320
$563$	8.52017			0.359082			0.179541	−	0.983750i	$-0.442539\pi$
$563$	8.52017			0.359082			0.179541	+	0.983750i	$0.442539\pi$
$564$		0			0
$565$	−8.66363	−	15.0058i	−0.364482	−	0.631301i
$566$	−3.03319	+	5.25364i	−0.127495	+	0.220827i
$567$		0			0
$568$	−4.47650	−	7.75352i	−0.187830	−	0.325331i
$569$	−16.3734			−0.686407			−0.343204	−	0.939261i	$-0.611512\pi$
$569$	−16.3734			−0.686407			−0.343204	+	0.939261i	$0.611512\pi$
$570$		0			0
$571$	−5.21876			−0.218398			−0.109199	−	0.994020i	$-0.534829\pi$
$571$	−5.21876			−0.218398			−0.109199	+	0.994020i	$0.534829\pi$
$572$	0.361431	+	0.626018i	0.0151122	+	0.0261751i
$573$		0			0
$574$	−0.660611	+	1.14421i	−0.0275734	+	0.0477585i
$575$	−2.61796	−	4.53443i	−0.109176	−	0.189099i
$576$		0			0
$577$	−32.0390			−1.33380			−0.666900	−	0.745147i	$-0.732379\pi$
$577$	−32.0390			−1.33380			−0.666900	+	0.745147i	$0.732379\pi$
$578$	−26.7427			−1.11235
$579$		0			0
$580$	−0.325796	+	0.564295i	−0.0135279	+	0.0234311i
$581$	2.14057			0.0888058
$582$		0			0
$583$	−1.76253	+	3.05279i	−0.0729965	+	0.126434i
$584$	1.17030	+	2.02702i	0.0484274	+	0.0838787i
$585$		0			0
$586$	2.32535	+	4.02763i	0.0960594	+	0.166380i
$587$	−1.67220	−	2.89634i	−0.0690192	−	0.119545i	0.829451	−	0.558580i	$-0.188654\pi$
$587$	−1.67220	−	2.89634i	−0.0690192	−	0.119545i	−0.898470	+	0.439035i	$0.855320\pi$
$588$		0			0
$589$	−3.57730	+	3.94583i	−0.147400	+	0.162585i
$590$	7.00000			0.288185
$591$		0			0
$592$	14.8308	+	25.6877i	0.609543	+	1.05576i
$593$	21.1054	−	36.5556i	0.866694	−	1.50116i	0.00133875	−	0.999999i	$-0.499574\pi$
$593$	21.1054	−	36.5556i	0.866694	−	1.50116i	0.865355	−	0.501159i	$-0.167093\pi$
$594$		0			0
$595$	4.00702	−	6.94036i	0.164272	−	0.284527i
$596$	−3.44375			−0.141062
$597$		0			0
$598$	−15.9941	+	27.7026i	−0.654047	+	1.13284i
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	−0.914397	−	0.404818i	$-0.867335\pi$
$599$	−2.60938	+	4.51958i	−0.106616	+	0.184665i	0.807781	+	0.589483i	$0.200668\pi$
$600$		0			0
$601$	−10.1546			−0.414215			−0.207108	−	0.978318i	$-0.566405\pi$
$601$	−10.1546			−0.414215			−0.207108	+	0.978318i	$0.566405\pi$
$602$	3.88706	−	6.73259i	0.158425	−	0.274400i
$603$		0			0
$604$	−4.02763	+	6.97606i	−0.163882	+	0.283852i
$605$	5.45935	+	9.45587i	0.221954	+	0.384436i
$606$		0			0
$607$	42.8764			1.74030			0.870149	−	0.492788i	$-0.164022\pi$
$607$	42.8764			1.74030			0.870149	+	0.492788i	$0.164022\pi$
$608$	−3.72143	−	11.5878i	−0.150924	−	0.469949i
$609$		0			0
$610$	2.72343	+	4.71713i	0.110269	+	0.190991i
$611$	−14.3222	−	24.8068i	−0.579416	−	1.00358i
$612$		0			0
$613$	−12.5367	−	21.7141i	−0.506351	−	0.877025i	−0.999973	−	0.00734857i	$-0.997661\pi$
$613$	−12.5367	−	21.7141i	−0.506351	−	0.877025i	0.493622	−	0.869676i	$-0.335672\pi$
$614$	0.350854	−	0.607697i	0.0141593	−	0.0245247i
$615$		0			0
$616$	1.12253			0.0452280
$617$	−2.74849	+	4.76053i	−0.110650	+	0.191652i	−0.916033	−	0.401104i	$-0.868627\pi$
$617$	−2.74849	+	4.76053i	−0.110650	+	0.191652i	0.805382	+	0.592756i	$0.201960\pi$
$618$		0			0
$619$	15.4899			0.622590			0.311295	−	0.950313i	$-0.399237\pi$
$619$	15.4899			0.622590			0.311295	+	0.950313i	$0.399237\pi$
$620$	0.619514			0.0248803
$621$		0			0
$622$	5.26409	+	9.11767i	0.211071	+	0.365585i
$623$	10.2992	−	17.8387i	0.412628	−	0.714693i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	41.6946			1.66645
$627$		0			0
$628$	−3.80620			−0.151884
$629$	−33.8905	−	58.7001i	−1.35130	−	2.34053i
$630$		0			0
$631$	−20.6616	+	35.7870i	−0.822526	+	1.42466i	0.0812689	+	0.996692i	$0.474103\pi$
$631$	−20.6616	+	35.7870i	−0.822526	+	1.42466i	−0.903795	+	0.427965i	$0.859231\pi$
$632$	23.6757	+	41.0075i	0.941767	+	1.63119i
$633$		0			0
$634$	−13.5351			−0.537547
$635$	9.33126			0.370300
$636$		0			0
$637$	−13.3710	+	23.1593i	−0.529779	+	0.917604i
$638$	−0.447755			−0.0177268
$639$		0			0
$640$	2.62653	−	4.54929i	0.103823	−	0.179826i
$641$	−15.3358	−	26.5624i	−0.605729	−	1.04915i	−0.991936	−	0.126741i	$-0.959548\pi$
$641$	−15.3358	−	26.5624i	−0.605729	−	1.04915i	0.386207	−	0.922412i	$-0.373785\pi$
$642$		0			0
$643$	4.00902	+	6.94383i	0.158100	+	0.273838i	0.934184	−	0.356793i	$-0.116130\pi$
$643$	4.00902	+	6.94383i	0.158100	+	0.273838i	−0.776083	+	0.630630i	$0.782796\pi$
$644$	−1.70584	−	2.95460i	−0.0672194	−	0.116427i
$645$		0			0
$646$	−10.1554	−	31.6220i	−0.399559	−	1.24415i
$647$	−10.0272			−0.394209			−0.197105	−	0.980382i	$-0.563154\pi$
$647$	−10.0272			−0.394209			−0.197105	+	0.980382i	$0.563154\pi$
$648$		0			0
$649$	−0.816776	−	1.41470i	−0.0320612	−	0.0555317i
$650$	−3.05469	+	5.29088i	−0.119815	+	0.207525i
$651$		0			0
$652$	5.53163	−	9.58107i	0.216635	−	0.375224i
$653$	−20.4117			−0.798771			−0.399385	−	0.916783i	$-0.630776\pi$
$653$	−20.4117			−0.798771			−0.399385	+	0.916783i	$0.630776\pi$
$654$		0			0
$655$	6.21286	−	10.7610i	0.242756	−	0.420466i
$656$	1.14803	−	1.98845i	0.0448231	−	0.0776360i
$657$		0			0
$658$	−8.99600			−0.350700
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	0.240765	+	0.970584i	$0.422602\pi$
$659$	−18.4874	+	32.0212i	−0.720168	+	1.24737i	−0.960932	+	0.276783i	$0.910732\pi$
$660$		0			0
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	−0.895402	−	0.445259i	$-0.853112\pi$
$661$	−1.59646	+	2.76514i	−0.0620950	+	0.107552i	0.833307	+	0.552811i	$0.186445\pi$
$662$	3.91714	+	6.78468i	0.152244	+	0.263694i
$663$		0			0
$664$	−5.10226			−0.198006
$665$	5.47539	+	1.18338i	0.212326	+	0.0458895i
$666$		0			0
$667$	3.36445	+	5.82739i	0.130272	+	0.225638i
$668$	−2.86089	−	4.95520i	−0.110691	−	0.191723i
$669$		0			0
$670$	−0.602362	−	1.04332i	−0.0232713	−	0.0403070i
$671$	0.635553	−	1.10081i	0.0245352	−	0.0424963i
$672$		0			0
$673$	−15.0742			−0.581067			−0.290534	−	0.956865i	$-0.593833\pi$
$673$	−15.0742			−0.581067			−0.290534	+	0.956865i	$0.593833\pi$
$674$	−15.4366	+	26.7370i	−0.594597	+	1.02987i
$675$		0			0
$676$	−6.08422			−0.234009
$677$	−17.9648			−0.690444			−0.345222	−	0.938521i	$-0.612196\pi$
$677$	−17.9648			−0.690444			−0.345222	+	0.938521i	$0.612196\pi$
$678$		0			0
$679$	7.54567	+	13.0695i	0.289576	+	0.501561i
$680$	−9.55113	+	16.5430i	−0.366269	+	0.634397i
$681$		0			0
$682$	0.212856	+	0.368678i	0.00815069	+	0.0141174i
$683$	3.78524			0.144838			0.0724191	−	0.997374i	$-0.476928\pi$
$683$	3.78524			0.144838			0.0724191	+	0.997374i	$0.476928\pi$
$684$		0			0
$685$	18.5351			0.708190
$686$	9.69526	+	16.7927i	0.370167	+	0.641148i
$687$		0			0
$688$	−6.75507	+	11.7001i	−0.257534	+	0.446063i
$689$	−30.9061	−	53.5310i	−1.17743	−	2.03937i
$690$		0			0
$691$	−10.3335			−0.393104			−0.196552	−	0.980493i	$-0.562974\pi$
$691$	−10.3335			−0.393104			−0.196552	+	0.980493i	$0.562974\pi$
$692$	−2.96881			−0.112857
$693$		0			0
$694$	−7.58086	+	13.1304i	−0.287766	+	0.498425i
$695$	−6.01404			−0.228125
$696$		0			0
$697$	−2.62342	+	4.54389i	−0.0993690	+	0.172112i
$698$	3.79016	+	6.56475i	0.143460	+	0.248479i
$699$		0			0
$700$	−0.325796	−	0.564295i	−0.0123139	−	0.0213283i
$701$	17.9980	+	31.1734i	0.679775	+	1.17740i	0.975048	+	0.221992i	$0.0712559\pi$
$701$	17.9980	+	31.1734i	0.679775	+	1.17740i	−0.295273	+	0.955413i	$0.595411\pi$
$702$		0			0
$703$	31.8227	−	35.1010i	1.20022	−	1.32386i
$704$	−2.52906			−0.0953176
$705$		0			0
$706$	14.2644	+	24.7067i	0.536849	+	0.929850i
$707$	5.08832	−	8.81324i	0.191366	−	0.331456i
$708$		0			0
$709$	−4.40266	+	7.62562i	−0.165345	+	0.286386i	−0.936778	−	0.349925i	$-0.886207\pi$
$709$	−4.40266	+	7.62562i	−0.165345	+	0.286386i	0.771433	+	0.636311i	$0.219540\pi$
$710$	−3.57117			−0.134024
$711$		0			0
$712$	−24.5491	+	42.5203i	−0.920018	+	1.59352i
$713$	3.19882	−	5.54052i	0.119797	−	0.207494i
$714$		0			0
$715$	1.42571			0.0533186
$716$	4.76399	−	8.25147i	0.178039	−	0.308372i
$717$		0			0
$718$	23.0457	−	39.9163i	0.860057	−	1.48966i
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	0.986971	−	0.160901i	$-0.0514400\pi$
$719$	9.49600	+	16.4475i	0.354141	+	0.613390i	−0.632830	+	0.774291i	$0.718107\pi$
$720$		0			0
$721$	16.4758			0.613592
$722$	18.8746	−	13.5173i	0.702439	−	0.503061i
$723$		0			0
$724$	3.38316	+	5.85980i	0.125734	+	0.217778i
$725$	0.642571	+	1.11297i	0.0238645	+	0.0413345i
$726$		0			0
$727$	−2.04567	−	3.54321i	−0.0758697	−	0.131410i	0.825594	−	0.564264i	$-0.190840\pi$
$727$	−2.04567	−	3.54321i	−0.0758697	−	0.131410i	−0.901464	+	0.432854i	$0.857507\pi$
$728$	−9.84183	+	17.0466i	−0.364763	+	0.631787i
$729$		0			0
$730$	0.933619			0.0345548
$731$	15.4363	−	26.7364i	0.570932	−	0.988883i
$732$		0			0
$733$	−50.4678			−1.86407			−0.932036	−	0.362366i	$-0.881969\pi$
$733$	−50.4678			−1.86407			−0.932036	+	0.362366i	$0.881969\pi$
$734$	−35.9325			−1.32629
$735$		0			0
$736$	7.30976	+	12.6609i	0.269441	+	0.466686i
$737$	−0.140570	+	0.243474i	−0.00517796	+	0.00896849i
$738$		0			0
$739$	−17.1148	−	29.6438i	−0.629580	−	1.09046i	−0.987636	−	0.156764i	$-0.949894\pi$
$739$	−17.1148	−	29.6438i	−0.629580	−	1.09046i	0.358056	−	0.933700i	$-0.383440\pi$
$740$	−5.51102			−0.202589
$741$		0			0
$742$	−19.4126			−0.712658
$743$	11.2996	+	19.5715i	0.414543	+	0.718010i	0.995380	−	0.0960101i	$-0.0306081\pi$
$743$	11.2996	+	19.5715i	0.414543	+	0.718010i	−0.580837	+	0.814020i	$0.697275\pi$
$744$		0			0
$745$	−3.39608	+	5.88218i	−0.124423	+	0.215507i
$746$	−13.1652	−	22.8028i	−0.482012	−	0.834869i
$747$		0			0
$748$	0.901542			0.0329636
$749$	17.7429			0.648313
$750$		0			0
$751$	12.7199	−	22.0315i	0.464155	−	0.803940i	−0.535008	−	0.844847i	$-0.679691\pi$
$751$	12.7199	−	22.0315i	0.464155	−	0.803940i	0.999163	+	0.0409072i	$0.0130248\pi$
$752$	15.6336			0.570097
$753$		0			0
$754$	3.92571	−	6.79953i	0.142966	−	0.247624i
$755$	7.94375	+	13.7590i	0.289103	+	0.500741i
$756$		0			0
$757$	−21.4015	−	37.0686i	−0.777852	−	1.34728i	−0.933177	−	0.359416i	$-0.882976\pi$
$757$	−21.4015	−	37.0686i	−0.777852	−	1.34728i	0.155325	−	0.987863i	$-0.450357\pi$
$758$	−11.8489	−	20.5228i	−0.430370	−	0.745422i
$759$		0			0
$760$	−13.0511	−	2.82070i	−0.473414	−	0.102318i
$761$	29.8944			1.08367			0.541836	−	0.840484i	$-0.317729\pi$
$761$	29.8944			1.08367			0.541836	+	0.840484i	$0.317729\pi$
$762$		0			0
$763$	−5.91412	−	10.2436i	−0.214106	−	0.370842i
$764$	0.169533	−	0.293639i	0.00613347	−	0.0106235i
$765$		0			0
$766$	−11.5386	+	19.9854i	−0.416905	+	0.722100i
$767$	28.6445			1.03429
$768$		0			0
$769$	8.32179	−	14.4138i	0.300092	−	0.519774i	−0.676065	−	0.736842i	$-0.736316\pi$
$769$	8.32179	−	14.4138i	0.300092	−	0.519774i	0.976156	+	0.217068i	$0.0696494\pi$
$770$	0.223877	−	0.387767i	0.00806798	−	0.0139742i
$771$		0			0
$772$	1.90846			0.0686871
$773$	3.05669	−	5.29435i	0.109942	−	0.190424i	−0.805805	−	0.592181i	$-0.798267\pi$
$773$	3.05669	−	5.29435i	0.109942	−	0.190424i	0.915746	+	0.401757i	$0.131600\pi$
$774$		0			0
$775$	0.610938	−	1.05818i	0.0219455	−	0.0380108i
$776$	−17.9859	−	31.1524i	−0.645655	−	1.11831i
$777$		0			0
$778$	−11.0951			−0.397780
$779$	−3.58477	−	0.774765i	−0.128438	−	0.0277588i
$780$		0			0
$781$	0.416692	+	0.721732i	0.0149104	+	0.0258256i
$782$	19.9476	+	34.5502i	0.713323	+	1.23551i
$783$

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.610938 + 1.05818i) q^{2} +(0.253509 - 0.439091i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.28514 q^{7} +3.06327 q^{8} +O(q^{10})\)	\(q+(0.610938 + 1.05818i) q^{2} +(0.253509 - 0.439091i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.28514 q^{7} +3.06327 q^{8} +(0.610938 - 1.05818i) q^{10} -0.285142 q^{11} +(2.50000 - 4.33013i) q^{13} +(-0.785142 - 1.35991i) q^{14} +(1.36445 + 2.36329i) q^{16} +(-3.11796 - 5.40046i) q^{17} +(2.92771 - 3.22932i) q^{19} -0.507019 q^{20} +(-0.174204 - 0.301731i) q^{22} +(-2.61796 + 4.53443i) q^{23} +(-0.500000 + 0.866025i) q^{25} +6.10938 q^{26} +(-0.325796 + 0.564295i) q^{28} +(0.642571 - 1.11297i) q^{29} -1.22188 q^{31} +(1.39608 - 2.41808i) q^{32} +(3.80976 - 6.59869i) q^{34} +(0.642571 + 1.11297i) q^{35} +10.8695 q^{37} +(5.20584 + 1.12512i) q^{38} +(-1.53163 - 2.65287i) q^{40} +(-0.420695 - 0.728665i) q^{41} +(2.47539 + 4.28749i) q^{43} +(-0.0722863 + 0.125204i) q^{44} -6.39764 q^{46} +(2.86445 - 4.96137i) q^{47} -5.34841 q^{49} -1.22188 q^{50} +(-1.26755 - 2.19546i) q^{52} +(6.18122 - 10.7062i) q^{53} +(0.142571 + 0.246941i) q^{55} -3.93673 q^{56} +1.57028 q^{58} +(2.86445 + 4.96137i) q^{59} +(-2.22889 + 3.86056i) q^{61} +(-0.746491 - 1.29296i) q^{62} +8.86946 q^{64} -5.00000 q^{65} +(0.492981 - 0.853869i) q^{67} -3.16172 q^{68} +(-0.785142 + 1.35991i) q^{70} +(-1.46135 - 2.53113i) q^{71} +(0.382043 + 0.661718i) q^{73} +(6.64057 + 11.5018i) q^{74} +(-0.675762 - 2.10419i) q^{76} +0.366449 q^{77} +(7.72889 + 13.3868i) q^{79} +(1.36445 - 2.36329i) q^{80} +(0.514037 - 0.890339i) q^{82} -1.66563 q^{83} +(-3.11796 + 5.40046i) q^{85} +(-3.02461 + 5.23879i) q^{86} -0.873467 q^{88} +(-8.01404 + 13.8807i) q^{89} +(-3.21286 + 5.56483i) q^{91} +(1.32735 + 2.29904i) q^{92} +7.00000 q^{94} +(-4.26053 - 0.920816i) q^{95} +(-5.87147 - 10.1697i) q^{97} +(-3.26755 - 5.65956i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8	\( 6 q + q^{2} - 7 q^{4} - 3 q^{5} + 4 q^{7} + 12 q^{8} + q^{10} + 10 q^{11} + 15 q^{13} + 7 q^{14} - 3 q^{16} + q^{17} + 14 q^{20} + 8 q^{22} + 4 q^{23} - 3 q^{25} + 10 q^{26} - 11 q^{28} - 2 q^{29} - 2 q^{31} - 6 q^{32} + 25 q^{34} - 2 q^{35} - 4 q^{37} + 19 q^{38} - 6 q^{40} - 2 q^{41} + q^{43} - 18 q^{44} - 48 q^{46} + 6 q^{47} - 14 q^{49} - 2 q^{50} + 35 q^{52} + 11 q^{53} - 5 q^{55} - 30 q^{56} - 14 q^{58} + 6 q^{59} + 9 q^{61} - 13 q^{62} - 16 q^{64} - 30 q^{65} + 20 q^{67} - 68 q^{68} + 7 q^{70} - 29 q^{71} + 22 q^{73} - 7 q^{74} - 19 q^{76} + 32 q^{77} + 24 q^{79} - 3 q^{80} - 31 q^{82} + 6 q^{83} + q^{85} - 32 q^{86} - 18 q^{88} - 14 q^{89} + 10 q^{91} + 41 q^{92} + 42 q^{94} - 7 q^{97} + 23 q^{98}+O(q^{100}) \) 6 * q + q^2 - 7 * q^4 - 3 * q^5 + 4 * q^7 + 12 * q^8 + q^10 + 10 * q^11 + 15 * q^13 + 7 * q^14 - 3 * q^16 + q^17 + 14 * q^20 + 8 * q^22 + 4 * q^23 - 3 * q^25 + 10 * q^26 - 11 * q^28 - 2 * q^29 - 2 * q^31 - 6 * q^32 + 25 * q^34 - 2 * q^35 - 4 * q^37 + 19 * q^38 - 6 * q^40 - 2 * q^41 + q^43 - 18 * q^44 - 48 * q^46 + 6 * q^47 - 14 * q^49 - 2 * q^50 + 35 * q^52 + 11 * q^53 - 5 * q^55 - 30 * q^56 - 14 * q^58 + 6 * q^59 + 9 * q^61 - 13 * q^62 - 16 * q^64 - 30 * q^65 + 20 * q^67 - 68 * q^68 + 7 * q^70 - 29 * q^71 + 22 * q^73 - 7 * q^74 - 19 * q^76 + 32 * q^77 + 24 * q^79 - 3 * q^80 - 31 * q^82 + 6 * q^83 + q^85 - 32 * q^86 - 18 * q^88 - 14 * q^89 + 10 * q^91 + 41 * q^92 + 42 * q^94 - 7 * q^97 + 23 * q^98

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