LMFDB - Embedded newform 105.2.g.a.104.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(104,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("105.104");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.g (of order $2$, degree $1$, 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:	$0.838429221223$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			104.1
Root			$0.517638i$ of defining polynomial
Character	$\chi$	$=$	105.104
Dual form			105.2.g.a.104.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.73205 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q-1.73205 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.73205 q^{8} +(-1.00000 + 2.82843i) q^{9} +(3.00000 - 2.44949i) q^{10} +2.82843i q^{11} +(-1.00000 - 1.41421i) q^{12} -4.00000 q^{13} +(-1.73205 - 4.24264i) q^{14} +(3.73205 + 1.03528i) q^{15} -5.00000 q^{16} +2.82843i q^{17} +(1.73205 - 4.89898i) q^{18} +(-1.73205 + 1.41421i) q^{20} +(2.46410 - 3.86370i) q^{21} -4.89898i q^{22} -3.46410 q^{23} +(-1.73205 - 2.44949i) q^{24} +(1.00000 - 4.89898i) q^{25} +6.92820 q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 2.44949i) q^{28} -5.65685i q^{29} +(-6.46410 - 1.79315i) q^{30} +9.79796i q^{31} +5.19615 q^{32} +(4.00000 - 2.82843i) q^{33} -4.89898i q^{34} +(-5.19615 - 2.82843i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(4.00000 + 5.65685i) q^{39} +(-3.00000 + 2.44949i) q^{40} -3.46410 q^{41} +(-4.26795 + 6.69213i) q^{42} +4.89898i q^{43} +2.82843i q^{44} +(-2.26795 - 6.31319i) q^{45} +6.00000 q^{46} +2.82843i q^{47} +(5.00000 + 7.07107i) q^{48} +(-5.00000 + 4.89898i) q^{49} +(-1.73205 + 8.48528i) q^{50} +(4.00000 - 2.82843i) q^{51} -4.00000 q^{52} +(-8.66025 + 2.44949i) q^{54} +(-4.00000 - 4.89898i) q^{55} +(1.73205 + 4.24264i) q^{56} +9.79796i q^{58} +6.92820 q^{59} +(3.73205 + 1.03528i) q^{60} -9.79796i q^{61} -16.9706i q^{62} +(-7.92820 + 0.378937i) q^{63} +1.00000 q^{64} +(6.92820 - 5.65685i) q^{65} +(-6.92820 + 4.89898i) q^{66} -4.89898i q^{67} +2.82843i q^{68} +(3.46410 + 4.89898i) q^{69} +(9.00000 + 4.89898i) q^{70} +2.82843i q^{71} +(-1.73205 + 4.89898i) q^{72} +8.00000 q^{73} +(-7.92820 + 3.48477i) q^{75} +(-6.92820 + 2.82843i) q^{77} +(-6.92820 - 9.79796i) q^{78} +8.00000 q^{79} +(8.66025 - 7.07107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +6.00000 q^{82} +2.82843i q^{83} +(2.46410 - 3.86370i) q^{84} +(-4.00000 - 4.89898i) q^{85} -8.48528i q^{86} +(-8.00000 + 5.65685i) q^{87} +4.89898i q^{88} +10.3923 q^{89} +(3.92820 + 10.9348i) q^{90} +(-4.00000 - 9.79796i) q^{91} -3.46410 q^{92} +(13.8564 - 9.79796i) q^{93} -4.89898i q^{94} +(-5.19615 - 7.34847i) q^{96} +8.00000 q^{97} +(8.66025 - 8.48528i) q^{98} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} + 4 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^7 - 4 * q^9	$ 4 q - 4 q^{3} + 4 q^{4} + 4 q^{7} - 4 q^{9} + 12 q^{10} - 4 q^{12} - 16 q^{13} + 8 q^{15} - 20 q^{16} - 4 q^{21} + 4 q^{25} + 20 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{33} - 4 q^{36} + 16 q^{39} - 12 q^{40} - 24 q^{42} - 16 q^{45} + 24 q^{46} + 20 q^{48} - 20 q^{49} + 16 q^{51} - 16 q^{52} - 16 q^{55} + 8 q^{60} - 4 q^{63} + 4 q^{64} + 36 q^{70} + 32 q^{73} - 4 q^{75} + 32 q^{79} - 28 q^{81} + 24 q^{82} - 4 q^{84} - 16 q^{85} - 32 q^{87} - 12 q^{90} - 16 q^{91} + 32 q^{97} - 32 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^7 - 4 * q^9 + 12 * q^10 - 4 * q^12 - 16 * q^13 + 8 * q^15 - 20 * q^16 - 4 * q^21 + 4 * q^25 + 20 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^33 - 4 * q^36 + 16 * q^39 - 12 * q^40 - 24 * q^42 - 16 * q^45 + 24 * q^46 + 20 * q^48 - 20 * q^49 + 16 * q^51 - 16 * q^52 - 16 * q^55 + 8 * q^60 - 4 * q^63 + 4 * q^64 + 36 * q^70 + 32 * q^73 - 4 * q^75 + 32 * q^79 - 28 * q^81 + 24 * q^82 - 4 * q^84 - 16 * q^85 - 32 * q^87 - 12 * q^90 - 16 * q^91 + 32 * q^97 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	−1.73205			−1.22474			−0.612372	−	0.790569i	$-0.709785\pi$
$2$	−1.73205			−1.22474			−0.612372	+	0.790569i	$0.709785\pi$
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$3$	−1.00000	−	1.41421i	−0.577350	−	0.816497i
$4$	1.00000			0.500000
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$6$	1.73205	+	2.44949i	0.707107	+	1.00000i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$	1.73205			0.612372
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$	3.00000	−	2.44949i	0.948683	−	0.774597i
$11$			2.82843i			0.852803i	0.904534	+	0.426401i	$0.140219\pi$
$11$			2.82843i			0.852803i	−0.904534	+	0.426401i	$0.859781\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	−1.73205	−	4.24264i	−0.462910	−	1.13389i
$15$	3.73205	+	1.03528i	0.963611	+	0.267307i
$16$	−5.00000			−1.25000
$17$			2.82843i			0.685994i	0.939336	+	0.342997i	$0.111442\pi$
$17$			2.82843i			0.685994i	−0.939336	+	0.342997i	$0.888558\pi$
$18$	1.73205	−	4.89898i	0.408248	−	1.15470i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	−1.73205	+	1.41421i	−0.387298	+	0.316228i
$21$	2.46410	−	3.86370i	0.537711	−	0.843129i
$22$		−	4.89898i		−	1.04447i
$23$	−3.46410			−0.722315			−0.361158	−	0.932505i	$-0.617618\pi$
$23$	−3.46410			−0.722315			−0.361158	+	0.932505i	$0.617618\pi$
$24$	−1.73205	−	2.44949i	−0.353553	−	0.500000i
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$	6.92820			1.35873
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	1.00000	+	2.44949i	0.188982	+	0.462910i
$29$		−	5.65685i		−	1.05045i	−0.850963	−	0.525226i	$-0.823981\pi$
$29$		−	5.65685i		−	1.05045i	0.850963	−	0.525226i	$-0.176019\pi$
$30$	−6.46410	−	1.79315i	−1.18018	−	0.327383i
$31$			9.79796i			1.75977i	0.475191	+	0.879883i	$0.342379\pi$
$31$			9.79796i			1.75977i	−0.475191	+	0.879883i	$0.657621\pi$
$32$	5.19615			0.918559
$33$	4.00000	−	2.82843i	0.696311	−	0.492366i
$34$		−	4.89898i		−	0.840168i
$35$	−5.19615	−	2.82843i	−0.878310	−	0.478091i
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$		0			0		1.00000			$0$
$37$		0			0		−1.00000			$\pi$
$38$		0			0
$39$	4.00000	+	5.65685i	0.640513	+	0.905822i
$40$	−3.00000	+	2.44949i	−0.474342	+	0.387298i
$41$	−3.46410			−0.541002			−0.270501	−	0.962720i	$-0.587189\pi$
$41$	−3.46410			−0.541002			−0.270501	+	0.962720i	$0.587189\pi$
$42$	−4.26795	+	6.69213i	−0.658559	+	1.03262i
$43$			4.89898i			0.747087i	0.927613	+	0.373544i	$0.121857\pi$
$43$			4.89898i			0.747087i	−0.927613	+	0.373544i	$0.878143\pi$
$44$			2.82843i			0.426401i
$45$	−2.26795	−	6.31319i	−0.338086	−	0.941115i
$46$	6.00000			0.884652
$47$			2.82843i			0.412568i	0.978492	+	0.206284i	$0.0661372\pi$
$47$			2.82843i			0.412568i	−0.978492	+	0.206284i	$0.933863\pi$
$48$	5.00000	+	7.07107i	0.721688	+	1.02062i
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	−1.73205	+	8.48528i	−0.244949	+	1.20000i
$51$	4.00000	−	2.82843i	0.560112	−	0.396059i
$52$	−4.00000			−0.554700
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−8.66025	+	2.44949i	−1.17851	+	0.333333i
$55$	−4.00000	−	4.89898i	−0.539360	−	0.660578i
$56$	1.73205	+	4.24264i	0.231455	+	0.566947i
$57$		0			0
$58$			9.79796i			1.28654i
$59$	6.92820			0.901975			0.450988	−	0.892530i	$-0.351072\pi$
$59$	6.92820			0.901975			0.450988	+	0.892530i	$0.351072\pi$
$60$	3.73205	+	1.03528i	0.481806	+	0.133654i
$61$		−	9.79796i		−	1.25450i	−0.778818	−	0.627250i	$-0.784180\pi$
$61$		−	9.79796i		−	1.25450i	0.778818	−	0.627250i	$-0.215820\pi$
$62$		−	16.9706i		−	2.15526i
$63$	−7.92820	+	0.378937i	−0.998860	+	0.0477416i
$64$	1.00000			0.125000
$65$	6.92820	−	5.65685i	0.859338	−	0.701646i
$66$	−6.92820	+	4.89898i	−0.852803	+	0.603023i
$67$		−	4.89898i		−	0.598506i	−0.954174	−	0.299253i	$-0.903263\pi$
$67$		−	4.89898i		−	0.598506i	0.954174	−	0.299253i	$-0.0967374\pi$
$68$			2.82843i			0.342997i
$69$	3.46410	+	4.89898i	0.417029	+	0.589768i
$70$	9.00000	+	4.89898i	1.07571	+	0.585540i
$71$			2.82843i			0.335673i	0.985815	+	0.167836i	$0.0536780\pi$
$71$			2.82843i			0.335673i	−0.985815	+	0.167836i	$0.946322\pi$
$72$	−1.73205	+	4.89898i	−0.204124	+	0.577350i
$73$	8.00000			0.936329			0.468165	−	0.883641i	$-0.344915\pi$
$73$	8.00000			0.936329			0.468165	+	0.883641i	$0.344915\pi$
$74$		0			0
$75$	−7.92820	+	3.48477i	−0.915470	+	0.402386i
$76$		0			0
$77$	−6.92820	+	2.82843i	−0.789542	+	0.322329i
$78$	−6.92820	−	9.79796i	−0.784465	−	1.10940i
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	8.66025	−	7.07107i	0.968246	−	0.790569i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	6.00000			0.662589
$83$			2.82843i			0.310460i	0.987878	+	0.155230i	$0.0496119\pi$
$83$			2.82843i			0.310460i	−0.987878	+	0.155230i	$0.950388\pi$
$84$	2.46410	−	3.86370i	0.268856	−	0.421565i
$85$	−4.00000	−	4.89898i	−0.433861	−	0.531369i
$86$		−	8.48528i		−	0.914991i
$87$	−8.00000	+	5.65685i	−0.857690	+	0.606478i
$88$			4.89898i			0.522233i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$	3.92820	+	10.9348i	0.414069	+	1.15263i
$91$	−4.00000	−	9.79796i	−0.419314	−	1.02711i
$92$	−3.46410			−0.361158
$93$	13.8564	−	9.79796i	1.43684	−	1.01600i
$94$		−	4.89898i		−	0.505291i
$95$		0			0
$96$	−5.19615	−	7.34847i	−0.530330	−	0.750000i
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$	8.66025	−	8.48528i	0.874818	−	0.857143i
$99$	−8.00000	−	2.82843i	−0.804030	−	0.284268i
$100$	1.00000	−	4.89898i	0.100000	−	0.489898i
$101$	−17.3205			−1.72345			−0.861727	−	0.507371i	$-0.830617\pi$
$101$	−17.3205			−1.72345			−0.861727	+	0.507371i	$0.830617\pi$
$102$	−6.92820	+	4.89898i	−0.685994	+	0.485071i
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	−6.92820			−0.679366
$105$	1.19615	+	10.1769i	0.116733	+	0.993163i
$106$		0			0
$107$	10.3923			1.00466			0.502331	−	0.864675i	$-0.332476\pi$
$107$	10.3923			1.00466			0.502331	+	0.864675i	$0.332476\pi$
$108$	5.00000	−	1.41421i	0.481125	−	0.136083i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	6.92820	+	8.48528i	0.660578	+	0.809040i
$111$		0			0
$112$	−5.00000	−	12.2474i	−0.472456	−	1.15728i
$113$	6.92820			0.651751			0.325875	−	0.945413i	$-0.394341\pi$
$113$	6.92820			0.651751			0.325875	+	0.945413i	$0.394341\pi$
$114$		0			0
$115$	6.00000	−	4.89898i	0.559503	−	0.456832i
$116$		−	5.65685i		−	0.525226i
$117$	4.00000	−	11.3137i	0.369800	−	1.04595i
$118$	−12.0000			−1.10469
$119$	−6.92820	+	2.82843i	−0.635107	+	0.259281i
$120$	6.46410	+	1.79315i	0.590089	+	0.163692i
$121$	3.00000			0.272727
$122$			16.9706i			1.53644i
$123$	3.46410	+	4.89898i	0.312348	+	0.441726i
$124$			9.79796i			0.879883i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$	13.7321	−	0.656339i	1.22335	−	0.0584713i
$127$			14.6969i			1.30414i	0.758158	+	0.652071i	$0.226100\pi$
$127$			14.6969i			1.30414i	−0.758158	+	0.652071i	$0.773900\pi$
$128$	−12.1244			−1.07165
$129$	6.92820	−	4.89898i	0.609994	−	0.431331i
$130$	−12.0000	+	9.79796i	−1.05247	+	0.859338i
$131$	6.92820			0.605320			0.302660	−	0.953099i	$-0.402125\pi$
$131$	6.92820			0.605320			0.302660	+	0.953099i	$0.402125\pi$
$132$	4.00000	−	2.82843i	0.348155	−	0.246183i
$133$		0			0
$134$			8.48528i			0.733017i
$135$	−6.66025	+	9.52056i	−0.573223	+	0.819399i
$136$			4.89898i			0.420084i
$137$	−6.92820			−0.591916			−0.295958	−	0.955201i	$-0.595639\pi$
$137$	−6.92820			−0.591916			−0.295958	+	0.955201i	$0.595639\pi$
$138$	−6.00000	−	8.48528i	−0.510754	−	0.722315i
$139$			9.79796i			0.831052i	0.909581	+	0.415526i	$0.136402\pi$
$139$			9.79796i			0.831052i	−0.909581	+	0.415526i	$0.863598\pi$
$140$	−5.19615	−	2.82843i	−0.439155	−	0.239046i
$141$	4.00000	−	2.82843i	0.336861	−	0.238197i
$142$		−	4.89898i		−	0.411113i
$143$		−	11.3137i		−	0.946100i
$144$	5.00000	−	14.1421i	0.416667	−	1.17851i
$145$	8.00000	+	9.79796i	0.664364	+	0.813676i
$146$	−13.8564			−1.14676
$147$	11.9282	+	2.17209i	0.983822	+	0.179151i
$148$		0			0
$149$			11.3137i			0.926855i	0.886135	+	0.463428i	$0.153381\pi$
$149$			11.3137i			0.926855i	−0.886135	+	0.463428i	$0.846619\pi$
$150$	13.7321	−	6.03579i	1.12122	−	0.492820i
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$		0			0
$153$	−8.00000	−	2.82843i	−0.646762	−	0.228665i
$154$	12.0000	−	4.89898i	0.966988	−	0.394771i
$155$	−13.8564	−	16.9706i	−1.11297	−	1.36311i
$156$	4.00000	+	5.65685i	0.320256	+	0.452911i
$157$	−4.00000			−0.319235			−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000			−0.319235			−0.159617	+	0.987179i	$0.551026\pi$
$158$	−13.8564			−1.10236
$159$		0			0
$160$	−9.00000	+	7.34847i	−0.711512	+	0.580948i
$161$	−3.46410	−	8.48528i	−0.273009	−	0.668734i
$162$	12.1244	+	9.79796i	0.952579	+	0.769800i
$163$		−	14.6969i		−	1.15115i	−0.817748	−	0.575577i	$-0.804778\pi$
$163$		−	14.6969i		−	1.15115i	0.817748	−	0.575577i	$-0.195222\pi$
$164$	−3.46410			−0.270501
$165$	−2.92820	+	10.5558i	−0.227960	+	0.821771i
$166$		−	4.89898i		−	0.380235i
$167$		−	14.1421i		−	1.09435i	−0.837018	−	0.547176i	$-0.815703\pi$
$167$		−	14.1421i		−	1.09435i	0.837018	−	0.547176i	$-0.184297\pi$
$168$	4.26795	−	6.69213i	0.329279	−	0.516309i
$169$	3.00000			0.230769
$170$	6.92820	+	8.48528i	0.531369	+	0.650791i
$171$		0			0
$172$			4.89898i			0.373544i
$173$			19.7990i			1.50529i	0.658427	+	0.752645i	$0.271222\pi$
$173$			19.7990i			1.50529i	−0.658427	+	0.752645i	$0.728778\pi$
$174$	13.8564	−	9.79796i	1.05045	−	0.742781i
$175$	13.0000	−	2.44949i	0.982708	−	0.185164i
$176$		−	14.1421i		−	1.06600i
$177$	−6.92820	−	9.79796i	−0.520756	−	0.736460i
$178$	−18.0000			−1.34916
$179$			2.82843i			0.211407i	0.994398	+	0.105703i	$0.0337094\pi$
$179$			2.82843i			0.211407i	−0.994398	+	0.105703i	$0.966291\pi$
$180$	−2.26795	−	6.31319i	−0.169043	−	0.470558i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	6.92820	+	16.9706i	0.513553	+	1.25794i
$183$	−13.8564	+	9.79796i	−1.02430	+	0.724286i
$184$	−6.00000			−0.442326
$185$		0			0
$186$	−24.0000	+	16.9706i	−1.75977	+	1.24434i
$187$	−8.00000			−0.585018
$188$			2.82843i			0.206284i
$189$	8.46410	+	10.8332i	0.615673	+	0.788002i
$190$		0			0
$191$			19.7990i			1.43260i	0.697790	+	0.716302i	$0.254167\pi$
$191$			19.7990i			1.43260i	−0.697790	+	0.716302i	$0.745833\pi$
$192$	−1.00000	−	1.41421i	−0.0721688	−	0.102062i
$193$			9.79796i			0.705273i	0.935760	+	0.352636i	$0.114715\pi$
$193$			9.79796i			0.705273i	−0.935760	+	0.352636i	$0.885285\pi$
$194$	−13.8564			−0.994832
$195$	−14.9282	−	4.14110i	−1.06903	−	0.296551i
$196$	−5.00000	+	4.89898i	−0.357143	+	0.349927i
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$	13.8564	+	4.89898i	0.984732	+	0.348155i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	1.73205	−	8.48528i	0.122474	−	0.600000i
$201$	−6.92820	+	4.89898i	−0.488678	+	0.345547i
$202$	30.0000			2.11079
$203$	13.8564	−	5.65685i	0.972529	−	0.397033i
$204$	4.00000	−	2.82843i	0.280056	−	0.198030i
$205$	6.00000	−	4.89898i	0.419058	−	0.342160i
$206$	17.3205			1.20678
$207$	3.46410	−	9.79796i	0.240772	−	0.681005i
$208$	20.0000			1.38675
$209$		0			0
$210$	−2.07180	−	17.6269i	−0.142968	−	1.21637i
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	4.00000	−	2.82843i	0.274075	−	0.193801i
$214$	−18.0000			−1.23045
$215$	−6.92820	−	8.48528i	−0.472500	−	0.578691i
$216$	8.66025	−	2.44949i	0.589256	−	0.166667i
$217$	−24.0000	+	9.79796i	−1.62923	+	0.665129i
$218$	17.3205			1.17309
$219$	−8.00000	−	11.3137i	−0.540590	−	0.764510i
$220$	−4.00000	−	4.89898i	−0.269680	−	0.330289i
$221$		−	11.3137i		−	0.761042i
$222$		0			0
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$	5.19615	+	12.7279i	0.347183	+	0.850420i
$225$	12.8564	+	7.72741i	0.857094	+	0.515160i
$226$	−12.0000			−0.798228
$227$			2.82843i			0.187729i	0.995585	+	0.0938647i	$0.0299221\pi$
$227$			2.82843i			0.187729i	−0.995585	+	0.0938647i	$0.970078\pi$
$228$		0			0
$229$		−	19.5959i		−	1.29493i	−0.762093	−	0.647467i	$-0.775828\pi$
$229$		−	19.5959i		−	1.29493i	0.762093	−	0.647467i	$-0.224172\pi$
$230$	−10.3923	+	8.48528i	−0.685248	+	0.559503i
$231$	10.9282	+	6.96953i	0.719023	+	0.458562i
$232$		−	9.79796i		−	0.643268i
$233$	−20.7846			−1.36165			−0.680823	−	0.732448i	$-0.738378\pi$
$233$	−20.7846			−1.36165			−0.680823	+	0.732448i	$0.738378\pi$
$234$	−6.92820	+	19.5959i	−0.452911	+	1.28103i
$235$	−4.00000	−	4.89898i	−0.260931	−	0.319574i
$236$	6.92820			0.450988
$237$	−8.00000	−	11.3137i	−0.519656	−	0.734904i
$238$	12.0000	−	4.89898i	0.777844	−	0.317554i
$239$			2.82843i			0.182956i	0.995807	+	0.0914779i	$0.0291591\pi$
$239$			2.82843i			0.182956i	−0.995807	+	0.0914779i	$0.970841\pi$
$240$	−18.6603	−	5.17638i	−1.20451	−	0.334134i
$241$		−	9.79796i		−	0.631142i	−0.948902	−	0.315571i	$-0.897804\pi$
$241$		−	9.79796i		−	0.631142i	0.948902	−	0.315571i	$-0.102196\pi$
$242$	−5.19615			−0.334021
$243$	−1.00000	+	15.5563i	−0.0641500	+	0.997940i
$244$		−	9.79796i		−	0.627250i
$245$	1.73205	−	15.5563i	0.110657	−	0.993859i
$246$	−6.00000	−	8.48528i	−0.382546	−	0.541002i
$247$		0			0
$248$			16.9706i			1.07763i
$249$	4.00000	−	2.82843i	0.253490	−	0.179244i
$250$	−9.00000	−	17.1464i	−0.569210	−	1.08444i
$251$	20.7846			1.31191			0.655956	−	0.754799i	$-0.272265\pi$
$251$	20.7846			1.31191			0.655956	+	0.754799i	$0.272265\pi$
$252$	−7.92820	+	0.378937i	−0.499430	+	0.0238708i
$253$		−	9.79796i		−	0.615992i
$254$		−	25.4558i		−	1.59724i
$255$	−2.92820	+	10.5558i	−0.183371	+	0.661032i
$256$	19.0000			1.18750
$257$		−	14.1421i		−	0.882162i	−0.897467	−	0.441081i	$-0.854595\pi$
$257$		−	14.1421i		−	0.882162i	0.897467	−	0.441081i	$-0.145405\pi$
$258$	−12.0000	+	8.48528i	−0.747087	+	0.528271i
$259$		0			0
$260$	6.92820	−	5.65685i	0.429669	−	0.350823i
$261$	16.0000	+	5.65685i	0.990375	+	0.350150i
$262$	−12.0000			−0.741362
$263$	3.46410			0.213606			0.106803	−	0.994280i	$-0.465939\pi$
$263$	3.46410			0.213606			0.106803	+	0.994280i	$0.465939\pi$
$264$	6.92820	−	4.89898i	0.426401	−	0.301511i
$265$		0			0
$266$		0			0
$267$	−10.3923	−	14.6969i	−0.635999	−	0.899438i
$268$		−	4.89898i		−	0.299253i
$269$	−10.3923			−0.633630			−0.316815	−	0.948487i	$-0.602613\pi$
$269$	−10.3923			−0.633630			−0.316815	+	0.948487i	$0.602613\pi$
$270$	11.5359	−	16.4901i	0.702052	−	1.00355i
$271$			29.3939i			1.78555i	0.450502	+	0.892775i	$0.351245\pi$
$271$			29.3939i			1.78555i	−0.450502	+	0.892775i	$0.648755\pi$
$272$		−	14.1421i		−	0.857493i
$273$	−9.85641	+	15.4548i	−0.596537	+	0.935368i
$274$	12.0000			0.724947
$275$	13.8564	+	2.82843i	0.835573	+	0.170561i
$276$	3.46410	+	4.89898i	0.208514	+	0.294884i
$277$			19.5959i			1.17740i	0.808350	+	0.588702i	$0.200361\pi$
$277$			19.5959i			1.17740i	−0.808350	+	0.588702i	$0.799639\pi$
$278$		−	16.9706i		−	1.01783i
$279$	−27.7128	−	9.79796i	−1.65912	−	0.586588i
$280$	−9.00000	−	4.89898i	−0.537853	−	0.292770i
$281$			28.2843i			1.68730i	0.536895	+	0.843649i	$0.319597\pi$
$281$			28.2843i			1.68730i	−0.536895	+	0.843649i	$0.680403\pi$
$282$	−6.92820	+	4.89898i	−0.412568	+	0.291730i
$283$	14.0000			0.832214			0.416107	−	0.909316i	$-0.363394\pi$
$283$	14.0000			0.832214			0.416107	+	0.909316i	$0.363394\pi$
$284$			2.82843i			0.167836i
$285$		0			0
$286$			19.5959i			1.15873i
$287$	−3.46410	−	8.48528i	−0.204479	−	0.500870i
$288$	−5.19615	+	14.6969i	−0.306186	+	0.866025i
$289$	9.00000			0.529412
$290$	−13.8564	−	16.9706i	−0.813676	−	0.996546i
$291$	−8.00000	−	11.3137i	−0.468968	−	0.663221i
$292$	8.00000			0.468165
$293$			2.82843i			0.165238i	0.996581	+	0.0826192i	$0.0263285\pi$
$293$			2.82843i			0.165238i	−0.996581	+	0.0826192i	$0.973671\pi$
$294$	−20.6603	−	3.76217i	−1.20493	−	0.219414i
$295$	−12.0000	+	9.79796i	−0.698667	+	0.570459i
$296$		0			0
$297$	4.00000	+	14.1421i	0.232104	+	0.820610i
$298$		−	19.5959i		−	1.13516i
$299$	13.8564			0.801337
$300$	−7.92820	+	3.48477i	−0.457735	+	0.201193i
$301$	−12.0000	+	4.89898i	−0.691669	+	0.282372i
$302$	−13.8564			−0.797347
$303$	17.3205	+	24.4949i	0.995037	+	1.40720i
$304$		0			0
$305$	13.8564	+	16.9706i	0.793416	+	0.971732i
$306$	13.8564	+	4.89898i	0.792118	+	0.280056i
$307$	−10.0000			−0.570730			−0.285365	−	0.958419i	$-0.592115\pi$
$307$	−10.0000			−0.570730			−0.285365	+	0.958419i	$0.592115\pi$
$308$	−6.92820	+	2.82843i	−0.394771	+	0.161165i
$309$	10.0000	+	14.1421i	0.568880	+	0.804518i
$310$	24.0000	+	29.3939i	1.36311	+	1.66946i
$311$	27.7128			1.57145			0.785725	−	0.618576i	$-0.212290\pi$
$311$	27.7128			1.57145			0.785725	+	0.618576i	$0.212290\pi$
$312$	6.92820	+	9.79796i	0.392232	+	0.554700i
$313$	−16.0000			−0.904373			−0.452187	−	0.891923i	$-0.649356\pi$
$313$	−16.0000			−0.904373			−0.452187	+	0.891923i	$0.649356\pi$
$314$	6.92820			0.390981
$315$	13.1962	−	11.8685i	0.743519	−	0.668715i
$316$	8.00000			0.450035
$317$	13.8564			0.778253			0.389127	−	0.921184i	$-0.372777\pi$
$317$	13.8564			0.778253			0.389127	+	0.921184i	$0.372777\pi$
$318$		0			0
$319$	16.0000			0.895828
$320$	−1.73205	+	1.41421i	−0.0968246	+	0.0790569i
$321$	−10.3923	−	14.6969i	−0.580042	−	0.820303i
$322$	6.00000	+	14.6969i	0.334367	+	0.819028i
$323$		0			0
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$	−4.00000	+	19.5959i	−0.221880	+	1.08699i
$326$			25.4558i			1.40987i
$327$	10.0000	+	14.1421i	0.553001	+	0.782062i
$328$	−6.00000			−0.331295
$329$	−6.92820	+	2.82843i	−0.381964	+	0.155936i
$330$	5.07180	−	18.2832i	0.279193	−	1.00646i
$331$	−28.0000			−1.53902			−0.769510	−	0.638635i	$-0.779499\pi$
$331$	−28.0000			−1.53902			−0.769510	+	0.638635i	$0.779499\pi$
$332$			2.82843i			0.155230i
$333$		0			0
$334$			24.4949i			1.34030i
$335$	6.92820	+	8.48528i	0.378528	+	0.463600i
$336$	−12.3205	+	19.3185i	−0.672139	+	1.05391i
$337$		−	19.5959i		−	1.06746i	−0.845656	−	0.533729i	$-0.820790\pi$
$337$		−	19.5959i		−	1.06746i	0.845656	−	0.533729i	$-0.179210\pi$
$338$	−5.19615			−0.282633
$339$	−6.92820	−	9.79796i	−0.376288	−	0.532152i
$340$	−4.00000	−	4.89898i	−0.216930	−	0.265684i
$341$	−27.7128			−1.50073
$342$		0			0
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$			8.48528i			0.457496i
$345$	−12.9282	−	3.58630i	−0.696031	−	0.193080i
$346$		−	34.2929i		−	1.84360i
$347$	17.3205			0.929814			0.464907	−	0.885360i	$-0.346088\pi$
$347$	17.3205			0.929814			0.464907	+	0.885360i	$0.346088\pi$
$348$	−8.00000	+	5.65685i	−0.428845	+	0.303239i
$349$			19.5959i			1.04895i	0.851427	+	0.524473i	$0.175738\pi$
$349$			19.5959i			1.04895i	−0.851427	+	0.524473i	$0.824262\pi$
$350$	−22.5167	+	4.24264i	−1.20357	+	0.226779i
$351$	−20.0000	+	5.65685i	−1.06752	+	0.301941i
$352$			14.6969i			0.783349i
$353$		−	31.1127i		−	1.65596i	−0.560756	−	0.827981i	$-0.689490\pi$
$353$		−	31.1127i		−	1.65596i	0.560756	−	0.827981i	$-0.310510\pi$
$354$	12.0000	+	16.9706i	0.637793	+	0.901975i
$355$	−4.00000	−	4.89898i	−0.212298	−	0.260011i
$356$	10.3923			0.550791
$357$	10.9282	+	6.96953i	0.578382	+	0.368867i
$358$		−	4.89898i		−	0.258919i
$359$		−	31.1127i		−	1.64207i	−0.570881	−	0.821033i	$-0.693398\pi$
$359$		−	31.1127i		−	1.64207i	0.570881	−	0.821033i	$-0.306602\pi$
$360$	−3.92820	−	10.9348i	−0.207034	−	0.576313i
$361$	19.0000			1.00000
$362$		0			0
$363$	−3.00000	−	4.24264i	−0.157459	−	0.222681i
$364$	−4.00000	−	9.79796i	−0.209657	−	0.513553i
$365$	−13.8564	+	11.3137i	−0.725277	+	0.592187i
$366$	24.0000	−	16.9706i	1.25450	−	0.887066i
$367$	−10.0000			−0.521996			−0.260998	−	0.965339i	$-0.584052\pi$
$367$	−10.0000			−0.521996			−0.260998	+	0.965339i	$0.584052\pi$
$368$	17.3205			0.902894
$369$	3.46410	−	9.79796i	0.180334	−	0.510061i
$370$		0			0
$371$		0			0
$372$	13.8564	−	9.79796i	0.718421	−	0.508001i
$373$			9.79796i			0.507319i	0.967294	+	0.253660i	$0.0816343\pi$
$373$			9.79796i			0.507319i	−0.967294	+	0.253660i	$0.918366\pi$
$374$	13.8564			0.716498
$375$	8.80385	−	17.2480i	0.454629	−	0.890681i
$376$			4.89898i			0.252646i
$377$			22.6274i			1.16537i
$378$	−14.6603	−	18.7637i	−0.754042	−	0.965101i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	20.7846	−	14.6969i	1.06483	−	0.752947i
$382$		−	34.2929i		−	1.75458i
$383$		−	14.1421i		−	0.722629i	−0.932444	−	0.361315i	$-0.882328\pi$
$383$		−	14.1421i		−	0.722629i	0.932444	−	0.361315i	$-0.117672\pi$
$384$	12.1244	+	17.1464i	0.618718	+	0.875000i
$385$	8.00000	−	14.6969i	0.407718	−	0.749025i
$386$		−	16.9706i		−	0.863779i
$387$	−13.8564	−	4.89898i	−0.704361	−	0.249029i
$388$	8.00000			0.406138
$389$		−	22.6274i		−	1.14726i	−0.819116	−	0.573628i	$-0.805536\pi$
$389$		−	22.6274i		−	1.14726i	0.819116	−	0.573628i	$-0.194464\pi$
$390$	25.8564	+	7.17260i	1.30929	+	0.363199i
$391$		−	9.79796i		−	0.495504i
$392$	−8.66025	+	8.48528i	−0.437409	+	0.428571i
$393$	−6.92820	−	9.79796i	−0.349482	−	0.494242i
$394$		0			0
$395$	−13.8564	+	11.3137i	−0.697191	+	0.569254i
$396$	−8.00000	−	2.82843i	−0.402015	−	0.142134i
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$		0			0
$399$		0			0
$400$	−5.00000	+	24.4949i	−0.250000	+	1.22474i
$401$		−	22.6274i		−	1.12996i	−0.825105	−	0.564980i	$-0.808884\pi$
$401$		−	22.6274i		−	1.12996i	0.825105	−	0.564980i	$-0.191116\pi$
$402$	12.0000	−	8.48528i	0.598506	−	0.423207i
$403$		−	39.1918i		−	1.95228i
$404$	−17.3205			−0.861727
$405$	20.1244	−	0.101536i	0.999987	−	0.00504536i
$406$	−24.0000	+	9.79796i	−1.19110	+	0.486265i
$407$		0			0
$408$	6.92820	−	4.89898i	0.342997	−	0.242536i
$409$			9.79796i			0.484478i	0.970217	+	0.242239i	$0.0778818\pi$
$409$			9.79796i			0.484478i	−0.970217	+	0.242239i	$0.922118\pi$
$410$	−10.3923	+	8.48528i	−0.513239	+	0.419058i
$411$	6.92820	+	9.79796i	0.341743	+	0.483298i
$412$	−10.0000			−0.492665
$413$	6.92820	+	16.9706i	0.340915	+	0.835067i
$414$	−6.00000	+	16.9706i	−0.294884	+	0.834058i
$415$	−4.00000	−	4.89898i	−0.196352	−	0.240481i
$416$	−20.7846			−1.01905
$417$	13.8564	−	9.79796i	0.678551	−	0.479808i
$418$		0			0
$419$	6.92820			0.338465			0.169232	−	0.985576i	$-0.445871\pi$
$419$	6.92820			0.338465			0.169232	+	0.985576i	$0.445871\pi$
$420$	1.19615	+	10.1769i	0.0583663	+	0.496582i
$421$	26.0000			1.26716			0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000			1.26716			0.633581	+	0.773676i	$0.281584\pi$
$422$	6.92820			0.337260
$423$	−8.00000	−	2.82843i	−0.388973	−	0.137523i
$424$		0			0
$425$	13.8564	+	2.82843i	0.672134	+	0.137199i
$426$	−6.92820	+	4.89898i	−0.335673	+	0.237356i
$427$	24.0000	−	9.79796i	1.16144	−	0.474156i
$428$	10.3923			0.502331
$429$	−16.0000	+	11.3137i	−0.772487	+	0.546231i
$430$	12.0000	+	14.6969i	0.578691	+	0.708749i
$431$			2.82843i			0.136241i	0.997677	+	0.0681203i	$0.0217002\pi$
$431$			2.82843i			0.136241i	−0.997677	+	0.0681203i	$0.978300\pi$
$432$	−25.0000	+	7.07107i	−1.20281	+	0.340207i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	41.5692	−	16.9706i	1.99539	−	0.814613i
$435$	5.85641	−	21.1117i	0.280793	−	1.01223i
$436$	−10.0000			−0.478913
$437$		0			0
$438$	13.8564	+	19.5959i	0.662085	+	0.936329i
$439$		−	39.1918i		−	1.87052i	−0.353956	−	0.935262i	$-0.615164\pi$
$439$		−	39.1918i		−	1.87052i	0.353956	−	0.935262i	$-0.384836\pi$
$440$	−6.92820	−	8.48528i	−0.330289	−	0.404520i
$441$	−8.85641	−	19.0411i	−0.421734	−	0.906720i
$442$			19.5959i			0.932083i
$443$	−17.3205			−0.822922			−0.411461	−	0.911427i	$-0.634981\pi$
$443$	−17.3205			−0.822922			−0.411461	+	0.911427i	$0.634981\pi$
$444$		0			0
$445$	−18.0000	+	14.6969i	−0.853282	+	0.696702i
$446$	−45.0333			−2.13239
$447$	16.0000	−	11.3137i	0.756774	−	0.535120i
$448$	1.00000	+	2.44949i	0.0472456	+	0.115728i
$449$		−	5.65685i		−	0.266963i	−0.991051	−	0.133482i	$-0.957384\pi$
$449$		−	5.65685i		−	0.266963i	0.991051	−	0.133482i	$-0.0426157\pi$
$450$	−22.2679	−	13.3843i	−1.04972	−	0.630940i
$451$		−	9.79796i		−	0.461368i
$452$	6.92820			0.325875
$453$	−8.00000	−	11.3137i	−0.375873	−	0.531564i
$454$		−	4.89898i		−	0.229920i
$455$	20.7846	+	11.3137i	0.974398	+	0.530395i
$456$		0			0
$457$			19.5959i			0.916658i	0.888783	+	0.458329i	$0.151552\pi$
$457$			19.5959i			0.916658i	−0.888783	+	0.458329i	$0.848448\pi$
$458$			33.9411i			1.58596i
$459$	4.00000	+	14.1421i	0.186704	+	0.660098i
$460$	6.00000	−	4.89898i	0.279751	−	0.228416i
$461$	3.46410			0.161339			0.0806696	−	0.996741i	$-0.474294\pi$
$461$	3.46410			0.161339			0.0806696	+	0.996741i	$0.474294\pi$
$462$	−18.9282	−	12.0716i	−0.880620	−	0.561621i
$463$		−	4.89898i		−	0.227675i	−0.993499	−	0.113837i	$-0.963686\pi$
$463$		−	4.89898i		−	0.227675i	0.993499	−	0.113837i	$-0.0363143\pi$
$464$			28.2843i			1.31306i
$465$	−10.1436	+	36.5665i	−0.470398	+	1.69573i
$466$	36.0000			1.66767
$467$			2.82843i			0.130884i	0.997856	+	0.0654420i	$0.0208457\pi$
$467$			2.82843i			0.130884i	−0.997856	+	0.0654420i	$0.979154\pi$
$468$	4.00000	−	11.3137i	0.184900	−	0.522976i
$469$	12.0000	−	4.89898i	0.554109	−	0.226214i
$470$	6.92820	+	8.48528i	0.319574	+	0.391397i
$471$	4.00000	+	5.65685i	0.184310	+	0.260654i
$472$	12.0000			0.552345
$473$	−13.8564			−0.637118
$474$	13.8564	+	19.5959i	0.636446	+	0.900070i
$475$		0			0
$476$	−6.92820	+	2.82843i	−0.317554	+	0.129641i
$477$		0			0
$478$		−	4.89898i		−	0.224074i
$479$	−27.7128			−1.26623			−0.633115	−	0.774057i	$-0.718224\pi$
$479$	−27.7128			−1.26623			−0.633115	+	0.774057i	$0.718224\pi$
$480$	19.3923	+	5.37945i	0.885134	+	0.245537i
$481$		0			0
$482$			16.9706i			0.772988i
$483$	−8.53590	+	13.3843i	−0.388397	+	0.609005i
$484$	3.00000			0.136364
$485$	−13.8564	+	11.3137i	−0.629187	+	0.513729i
$486$	1.73205	−	26.9444i	0.0785674	−	1.22222i
$487$			14.6969i			0.665982i	0.942930	+	0.332991i	$0.108058\pi$
$487$			14.6969i			0.665982i	−0.942930	+	0.332991i	$0.891942\pi$
$488$		−	16.9706i		−	0.768221i
$489$	−20.7846	+	14.6969i	−0.939913	+	0.664619i
$490$	−3.00000	+	26.9444i	−0.135526	+	1.21722i
$491$		−	14.1421i		−	0.638226i	−0.947717	−	0.319113i	$-0.896615\pi$
$491$		−	14.1421i		−	0.638226i	0.947717	−	0.319113i	$-0.103385\pi$
$492$	3.46410	+	4.89898i	0.156174	+	0.220863i
$493$	16.0000			0.720604
$494$		0			0
$495$	17.8564	−	6.41473i	0.802586	−	0.288321i
$496$		−	48.9898i		−	2.19971i
$497$	−6.92820	+	2.82843i	−0.310772	+	0.126872i
$498$	−6.92820	+	4.89898i	−0.310460	+	0.219529i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$	5.19615	+	9.89949i	0.232379	+	0.442719i
$501$	−20.0000	+	14.1421i	−0.893534	+	0.631824i
$502$	−36.0000			−1.60676
$503$			19.7990i			0.882793i	0.897312	+	0.441397i	$0.145517\pi$
$503$			19.7990i			0.882793i	−0.897312	+	0.441397i	$0.854483\pi$
$504$	−13.7321	+	0.656339i	−0.611674	+	0.0292357i
$505$	30.0000	−	24.4949i	1.33498	−	1.09001i
$506$			16.9706i			0.754434i
$507$	−3.00000	−	4.24264i	−0.133235	−	0.188422i
$508$			14.6969i			0.652071i
$509$	−3.46410			−0.153544			−0.0767718	−	0.997049i	$-0.524461\pi$
$509$	−3.46410			−0.153544			−0.0767718	+	0.997049i	$0.524461\pi$
$510$	5.07180	−	18.2832i	0.224583	−	0.809595i
$511$	8.00000	+	19.5959i	0.353899	+	0.866872i
$512$	−8.66025			−0.382733
$513$		0			0
$514$			24.4949i			1.08042i
$515$	17.3205	−	14.1421i	0.763233	−	0.623177i
$516$	6.92820	−	4.89898i	0.304997	−	0.215666i
$517$	−8.00000			−0.351840
$518$		0			0
$519$	28.0000	−	19.7990i	1.22906	−	0.869079i
$520$	12.0000	−	9.79796i	0.526235	−	0.429669i
$521$	−10.3923			−0.455295			−0.227648	−	0.973744i	$-0.573103\pi$
$521$	−10.3923			−0.455295			−0.227648	+	0.973744i	$0.573103\pi$
$522$	−27.7128	−	9.79796i	−1.21296	−	0.428845i
$523$	26.0000			1.13690			0.568450	−	0.822718i	$-0.307543\pi$
$523$	26.0000			1.13690			0.568450	+	0.822718i	$0.307543\pi$
$524$	6.92820			0.302660
$525$	−16.4641	−	15.9353i	−0.718552	−	0.695473i
$526$	−6.00000			−0.261612
$527$	−27.7128			−1.20719
$528$	−20.0000	+	14.1421i	−0.870388	+	0.615457i
$529$	−11.0000			−0.478261
$530$		0			0
$531$	−6.92820	+	19.5959i	−0.300658	+	0.850390i
$532$		0			0
$533$	13.8564			0.600188
$534$	18.0000	+	25.4558i	0.778936	+	1.10158i
$535$	−18.0000	+	14.6969i	−0.778208	+	0.635404i
$536$		−	8.48528i		−	0.366508i
$537$	4.00000	−	2.82843i	0.172613	−	0.122056i
$538$	18.0000			0.776035
$539$	−13.8564	−	14.1421i	−0.596838	−	0.609145i
$540$	−6.66025	+	9.52056i	−0.286612	+	0.409700i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$		−	50.9117i		−	2.18684i
$543$		0			0
$544$			14.6969i			0.630126i
$545$	17.3205	−	14.1421i	0.741929	−	0.605783i
$546$	17.0718	−	26.7685i	0.730605	−	1.14559i
$547$			34.2929i			1.46626i	0.680090	+	0.733128i	$0.261941\pi$
$547$			34.2929i			1.46626i	−0.680090	+	0.733128i	$0.738059\pi$
$548$	−6.92820			−0.295958
$549$	27.7128	+	9.79796i	1.18275	+	0.418167i
$550$	−24.0000	−	4.89898i	−1.02336	−	0.208893i
$551$		0			0
$552$	6.00000	+	8.48528i	0.255377	+	0.361158i
$553$	8.00000	+	19.5959i	0.340195	+	0.833303i
$554$		−	33.9411i		−	1.44202i
$555$		0			0
$556$			9.79796i			0.415526i
$557$	−41.5692			−1.76134			−0.880672	−	0.473726i	$-0.842909\pi$
$557$	−41.5692			−1.76134			−0.880672	+	0.473726i	$0.842909\pi$
$558$	48.0000	+	16.9706i	2.03200	+	0.718421i
$559$		−	19.5959i		−	0.828819i
$560$	25.9808	+	14.1421i	1.09789	+	0.597614i
$561$	8.00000	+	11.3137i	0.337760	+	0.477665i
$562$		−	48.9898i		−	2.06651i
$563$		−	14.1421i		−	0.596020i	−0.954563	−	0.298010i	$-0.903677\pi$
$563$		−	14.1421i		−	0.596020i	0.954563	−	0.298010i	$-0.0963229\pi$
$564$	4.00000	−	2.82843i	0.168430	−	0.119098i
$565$	−12.0000	+	9.79796i	−0.504844	+	0.412203i
$566$	−24.2487			−1.01925
$567$	6.85641	−	22.8033i	0.287942	−	0.957648i
$568$			4.89898i			0.205557i
$569$			28.2843i			1.18574i	0.805299	+	0.592869i	$0.202005\pi$
$569$			28.2843i			1.18574i	−0.805299	+	0.592869i	$0.797995\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$		−	11.3137i		−	0.473050i
$573$	28.0000	−	19.7990i	1.16972	−	0.827115i
$574$	6.00000	+	14.6969i	0.250435	+	0.613438i
$575$	−3.46410	+	16.9706i	−0.144463	+	0.707721i
$576$	−1.00000	+	2.82843i	−0.0416667	+	0.117851i
$577$	8.00000			0.333044			0.166522	−	0.986038i	$-0.446746\pi$
$577$	8.00000			0.333044			0.166522	+	0.986038i	$0.446746\pi$
$578$	−15.5885			−0.648394
$579$	13.8564	−	9.79796i	0.575853	−	0.407189i
$580$	8.00000	+	9.79796i	0.332182	+	0.406838i
$581$	−6.92820	+	2.82843i	−0.287430	+	0.117343i
$582$	13.8564	+	19.5959i	0.574367	+	0.812277i
$583$		0			0
$584$	13.8564			0.573382
$585$	9.07180	+	25.2528i	0.375073	+	1.04407i
$586$		−	4.89898i		−	0.202375i
$587$			19.7990i			0.817192i	0.912715	+	0.408596i	$0.133981\pi$
$587$			19.7990i			0.817192i	−0.912715	+	0.408596i	$0.866019\pi$
$588$	11.9282	+	2.17209i	0.491911	+	0.0895754i
$589$		0			0
$590$	20.7846	−	16.9706i	0.855689	−	0.698667i
$591$		0			0
$592$		0			0
$593$			19.7990i			0.813047i	0.913640	+	0.406524i	$0.133259\pi$
$593$			19.7990i			0.813047i	−0.913640	+	0.406524i	$0.866741\pi$
$594$	−6.92820	−	24.4949i	−0.284268	−	1.00504i
$595$	8.00000	−	14.6969i	0.327968	−	0.602516i
$596$			11.3137i			0.463428i
$597$		0			0
$598$	−24.0000			−0.981433
$599$			36.7696i			1.50236i	0.660096	+	0.751182i	$0.270516\pi$
$599$			36.7696i			1.50236i	−0.660096	+	0.751182i	$0.729484\pi$
$600$	−13.7321	+	6.03579i	−0.560609	+	0.246410i
$601$		−	9.79796i		−	0.399667i	−0.979830	−	0.199834i	$-0.935960\pi$
$601$		−	9.79796i		−	0.399667i	0.979830	−	0.199834i	$-0.0640401\pi$
$602$	20.7846	−	8.48528i	0.847117	−	0.345834i
$603$	13.8564	+	4.89898i	0.564276	+	0.199502i
$604$	8.00000			0.325515
$605$	−5.19615	+	4.24264i	−0.211254	+	0.172488i
$606$	−30.0000	−	42.4264i	−1.21867	−	1.72345i
$607$	−10.0000			−0.405887			−0.202944	−	0.979190i	$-0.565051\pi$
$607$	−10.0000			−0.405887			−0.202944	+	0.979190i	$0.565051\pi$
$608$		0			0
$609$	−21.8564	−	13.9391i	−0.885666	−	0.564839i
$610$	−24.0000	−	29.3939i	−0.971732	−	1.19012i
$611$		−	11.3137i		−	0.457704i
$612$	−8.00000	−	2.82843i	−0.323381	−	0.114332i
$613$			29.3939i			1.18721i	0.804757	+	0.593604i	$0.202295\pi$
$613$			29.3939i			1.18721i	−0.804757	+	0.593604i	$0.797705\pi$
$614$	17.3205			0.698999
$615$	−12.9282	−	3.58630i	−0.521315	−	0.144614i
$616$	−12.0000	+	4.89898i	−0.483494	+	0.197386i
$617$	48.4974			1.95243			0.976216	−	0.216799i	$-0.0695615\pi$
$617$	48.4974			1.95243			0.976216	+	0.216799i	$0.0695615\pi$
$618$	−17.3205	−	24.4949i	−0.696733	−	0.985329i
$619$		−	9.79796i		−	0.393813i	−0.980422	−	0.196907i	$-0.936910\pi$
$619$		−	9.79796i		−	0.393813i	0.980422	−	0.196907i	$-0.0630896\pi$
$620$	−13.8564	−	16.9706i	−0.556487	−	0.681554i
$621$	−17.3205	+	4.89898i	−0.695048	+	0.196589i
$622$	−48.0000			−1.92462
$623$	10.3923	+	25.4558i	0.416359	+	1.01987i
$624$	−20.0000	−	28.2843i	−0.800641	−	1.13228i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$	27.7128			1.10763
$627$		0			0
$628$	−4.00000			−0.159617
$629$		0			0
$630$	−22.8564	+	20.5569i	−0.910621	+	0.819005i
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	13.8564			0.551178
$633$	4.00000	+	5.65685i	0.158986	+	0.224840i
$634$	−24.0000			−0.953162
$635$	−20.7846	−	25.4558i	−0.824812	−	1.01018i
$636$		0			0
$637$	20.0000	−	19.5959i	0.792429	−	0.776419i
$638$	−27.7128			−1.09716
$639$	−8.00000	−	2.82843i	−0.316475	−	0.111891i
$640$	21.0000	−	17.1464i	0.830098	−	0.677772i
$641$		−	5.65685i		−	0.223432i	−0.993740	−	0.111716i	$-0.964365\pi$
$641$		−	5.65685i		−	0.223432i	0.993740	−	0.111716i	$-0.0356347\pi$
$642$	18.0000	+	25.4558i	0.710403	+	1.00466i
$643$	−22.0000			−0.867595			−0.433798	−	0.901010i	$-0.642827\pi$
$643$	−22.0000			−0.867595			−0.433798	+	0.901010i	$0.642827\pi$
$644$	−3.46410	−	8.48528i	−0.136505	−	0.334367i
$645$	−5.07180	+	18.2832i	−0.199702	+	0.719902i
$646$		0			0
$647$			19.7990i			0.778379i	0.921158	+	0.389189i	$0.127245\pi$
$647$			19.7990i			0.778379i	−0.921158	+	0.389189i	$0.872755\pi$
$648$	−12.1244	−	9.79796i	−0.476290	−	0.384900i
$649$			19.5959i			0.769207i
$650$	6.92820	−	33.9411i	0.271746	−	1.33128i
$651$	37.8564	+	24.1432i	1.48371	+	0.946245i
$652$		−	14.6969i		−	0.575577i
$653$	27.7128			1.08449			0.542243	−	0.840222i	$-0.317575\pi$
$653$	27.7128			1.08449			0.542243	+	0.840222i	$0.317575\pi$
$654$	−17.3205	−	24.4949i	−0.677285	−	0.957826i
$655$	−12.0000	+	9.79796i	−0.468879	+	0.382838i
$656$	17.3205			0.676252
$657$	−8.00000	+	22.6274i	−0.312110	+	0.882780i
$658$	12.0000	−	4.89898i	0.467809	−	0.190982i
$659$			2.82843i			0.110180i	0.998481	+	0.0550899i	$0.0175446\pi$
$659$			2.82843i			0.110180i	−0.998481	+	0.0550899i	$0.982455\pi$
$660$	−2.92820	+	10.5558i	−0.113980	+	0.410885i
$661$			9.79796i			0.381096i	0.981678	+	0.190548i	$0.0610266\pi$
$661$			9.79796i			0.381096i	−0.981678	+	0.190548i	$0.938973\pi$
$662$	48.4974			1.88491
$663$	−16.0000	+	11.3137i	−0.621389	+	0.439388i
$664$			4.89898i			0.190117i
$665$		0			0
$666$		0			0
$667$			19.5959i			0.758757i
$668$		−	14.1421i		−	0.547176i
$669$	−26.0000	−	36.7696i	−1.00522	−	1.42159i
$670$	−12.0000	−	14.6969i	−0.463600	−	0.567792i
$671$	27.7128			1.06984
$672$	12.8038	−	20.0764i	0.493919	−	0.774464i
$673$		−	9.79796i		−	0.377684i	−0.982008	−	0.188842i	$-0.939527\pi$
$673$		−	9.79796i		−	0.377684i	0.982008	−	0.188842i	$-0.0604733\pi$
$674$			33.9411i			1.30736i
$675$	−1.92820	−	25.9091i	−0.0742166	−	0.997242i
$676$	3.00000			0.115385
$677$			2.82843i			0.108705i	0.998522	+	0.0543526i	$0.0173095\pi$
$677$			2.82843i			0.108705i	−0.998522	+	0.0543526i	$0.982690\pi$
$678$	12.0000	+	16.9706i	0.460857	+	0.651751i
$679$	8.00000	+	19.5959i	0.307012	+	0.752022i
$680$	−6.92820	−	8.48528i	−0.265684	−	0.325396i
$681$	4.00000	−	2.82843i	0.153280	−	0.108386i
$682$	48.0000			1.83801
$683$	10.3923			0.397650			0.198825	−	0.980035i	$-0.436287\pi$
$683$	10.3923			0.397650			0.198825	+	0.980035i	$0.436287\pi$
$684$		0			0
$685$	12.0000	−	9.79796i	0.458496	−	0.374361i
$686$	29.4449	+	12.7279i	1.12421	+	0.485954i
$687$	−27.7128	+	19.5959i	−1.05731	+	0.747631i
$688$		−	24.4949i		−	0.933859i
$689$		0			0
$690$	22.3923	+	6.21166i	0.852460	+	0.236474i
$691$		−	9.79796i		−	0.372732i	−0.982480	−	0.186366i	$-0.940329\pi$
$691$		−	9.79796i		−	0.372732i	0.982480	−	0.186366i	$-0.0596710\pi$
$692$			19.7990i			0.752645i
$693$	−1.07180	−	22.4243i	−0.0407142	−	0.851830i
$694$	−30.0000			−1.13878
$695$	−13.8564	−	16.9706i	−0.525603	−	0.643730i
$696$	−13.8564	+	9.79796i	−0.525226	+	0.371391i
$697$		−	9.79796i		−	0.371124i
$698$		−	33.9411i		−	1.28469i
$699$	20.7846	+	29.3939i	0.786146	+	1.11178i
$700$	13.0000	−	2.44949i	0.491354	−	0.0925820i
$701$		−	22.6274i		−	0.854626i	−0.904104	−	0.427313i	$-0.859460\pi$
$701$		−	22.6274i		−	0.854626i	0.904104	−	0.427313i	$-0.140540\pi$
$702$	34.6410	−	9.79796i	1.30744	−	0.369800i
$703$		0			0
$704$			2.82843i			0.106600i
$705$	−2.92820	+	10.5558i	−0.110283	+	0.397556i
$706$			53.8888i			2.02813i
$707$	−17.3205	−	42.4264i	−0.651405	−	1.59561i
$708$	−6.92820	−	9.79796i	−0.260378	−	0.368230i
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	6.92820	+	8.48528i	0.260011	+	0.318447i
$711$	−8.00000	+	22.6274i	−0.300023	+	0.848594i
$712$	18.0000			0.674579
$713$		−	33.9411i		−	1.27111i
$714$	−18.9282	−	12.0716i	−0.708370	−	0.451768i
$715$	16.0000	+	19.5959i	0.598366	+	0.732846i
$716$			2.82843i			0.105703i
$717$	4.00000	−	2.82843i	0.149383	−	0.105630i
$718$			53.8888i			2.01111i
$719$	−41.5692			−1.55027			−0.775135	−	0.631795i	$-0.782318\pi$
$719$	−41.5692			−1.55027			−0.775135	+	0.631795i	$0.782318\pi$
$720$	11.3397	+	31.5660i	0.422607	+	1.17639i
$721$	−10.0000	−	24.4949i	−0.372419	−	0.912238i
$722$	−32.9090			−1.22474
$723$	−13.8564	+	9.79796i	−0.515325	+	0.364390i
$724$		0			0
$725$	−27.7128	−	5.65685i	−1.02923	−	0.210090i
$726$	5.19615	+	7.34847i	0.192847	+	0.272727i
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$	−6.92820	−	16.9706i	−0.256776	−	0.628971i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	24.0000	−	19.5959i	0.888280	−	0.725277i
$731$	−13.8564			−0.512498
$732$	−13.8564	+	9.79796i	−0.512148	+	0.362143i
$733$	−28.0000			−1.03420			−0.517102	−	0.855924i	$-0.672989\pi$
$733$	−28.0000			−1.03420			−0.517102	+	0.855924i	$0.672989\pi$
$734$	17.3205			0.639312
$735$	−23.7321	+	13.1069i	−0.875370	+	0.483454i
$736$	−18.0000			−0.663489
$737$	13.8564			0.510407
$738$	−6.00000	+	16.9706i	−0.220863	+	0.624695i
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.2487			−0.889599			−0.444799	−	0.895630i	$-0.646725\pi$
$743$	−24.2487			−0.889599			−0.444799	+	0.895630i	$0.646725\pi$
$744$	24.0000	−	16.9706i	0.879883	−	0.622171i
$745$	−16.0000	−	19.5959i	−0.586195	−	0.717939i
$746$		−	16.9706i		−	0.621336i
$747$	−8.00000	−	2.82843i	−0.292705	−	0.103487i
$748$	−8.00000			−0.292509
$749$	10.3923	+	25.4558i	0.379727	+	0.930136i
$750$	−15.2487	+	29.8744i	−0.556804	+	1.09086i
$751$	8.00000			0.291924			0.145962	−	0.989290i	$-0.453372\pi$
$751$	8.00000			0.291924			0.145962	+	0.989290i	$0.453372\pi$
$752$		−	14.1421i		−	0.515711i
$753$	−20.7846	−	29.3939i	−0.757433	−	1.07117i
$754$		−	39.1918i		−	1.42728i
$755$	−13.8564	+	11.3137i	−0.504286	+	0.411748i
$756$	8.46410	+	10.8332i	0.307836	+	0.394001i
$757$		−	29.3939i		−	1.06834i	−0.845378	−	0.534169i	$-0.820624\pi$
$757$		−	29.3939i		−	1.06834i	0.845378	−	0.534169i	$-0.179376\pi$
$758$	48.4974			1.76151
$759$	−13.8564	+	9.79796i	−0.502956	+	0.355643i
$760$		0			0
$761$	38.1051			1.38131			0.690655	−	0.723185i	$-0.257322\pi$
$761$	38.1051			1.38131			0.690655	+	0.723185i	$0.257322\pi$
$762$	−36.0000	+	25.4558i	−1.30414	+	0.922168i
$763$	−10.0000	−	24.4949i	−0.362024	−	0.886775i
$764$			19.7990i			0.716302i
$765$	17.8564	−	6.41473i	0.645600	−	0.231925i
$766$			24.4949i			0.885037i
$767$	−27.7128			−1.00065
$768$	−19.0000	−	26.8701i	−0.685603	−	0.969590i
$769$		−	19.5959i		−	0.706647i	−0.935501	−	0.353323i	$-0.885052\pi$
$769$		−	19.5959i		−	0.706647i	0.935501	−	0.353323i	$-0.114948\pi$
$770$	−13.8564	+	25.4558i	−0.499350	+	0.917365i
$771$	−20.0000	+	14.1421i	−0.720282	+	0.509317i
$772$			9.79796i			0.352636i
$773$			2.82843i			0.101731i	0.998706	+	0.0508657i	$0.0161981\pi$
$773$			2.82843i			0.101731i	−0.998706	+	0.0508657i	$0.983802\pi$
$774$	24.0000	+	8.48528i	0.862662	+	0.304997i
$775$	48.0000	+	9.79796i	1.72421	+	0.351953i
$776$	13.8564			0.497416
$777$		0			0
$778$			39.1918i			1.40510i
$779$		0			0
$780$	−14.9282	−	4.14110i	−0.534515	−	0.148275i
$781$	−8.00000			−0.286263
$782$			16.9706i			0.606866i
$783$	−8.00000	−	28.2843i	−0.285897	−	1.01080i
$784$	25.0000	−	24.4949i	0.892857	−	0.874818i
$785$	6.92820	−	5.65685i	0.247278	−	0.201902i
$786$	12.0000	+	16.9706i	0.428026	+	0.605320i
$787$	14.0000			0.499046			0.249523	−	0.968369i	$-0.419726\pi$
$787$	14.0000			0.499046			0.249523	+	0.968369i	$0.419726\pi$
$788$		0			0
$789$	−3.46410	−	4.89898i	−0.123325	−	0.174408i
$790$	24.0000	−	19.5959i	0.853882	−	0.697191i
$791$	6.92820	+	16.9706i	0.246339	+	0.603404i
$792$	−13.8564	−	4.89898i	−0.492366	−	0.174078i
$793$			39.1918i			1.39174i
$794$	−34.6410			−1.22936
$795$		0			0
$796$		0			0
$797$			36.7696i			1.30244i	0.758887	+	0.651222i	$0.225743\pi$
$797$			36.7696i			1.30244i	−0.758887	+	0.651222i	$0.774257\pi$
$798$		0			0
$799$	−8.00000			−0.283020
$800$	5.19615	−	25.4558i	0.183712	−	0.900000i
$801$	−10.3923	+	29.3939i	−0.367194	+	1.03858i
$802$			39.1918i			1.38391i
$803$			22.6274i			0.798504i
$804$	−6.92820	+	4.89898i	−0.244339	+	0.172774i
$805$	18.0000	+	9.79796i	0.634417	+	0.345333i
$806$			67.8823i			2.39105i
$807$	10.3923	+	14.6969i	0.365826	+	0.517357i
$808$	−30.0000			−1.05540
$809$		−	22.6274i		−	0.795538i	−0.917486	−	0.397769i	$-0.869785\pi$
$809$		−	22.6274i		−	0.795538i	0.917486	−	0.397769i	$-0.130215\pi$
$810$	−34.8564	+	0.175865i	−1.22473	+	0.00617928i
$811$			29.3939i			1.03216i	0.856541	+	0.516079i	$0.172609\pi$
$811$			29.3939i			1.03216i	−0.856541	+	0.516079i	$0.827391\pi$
$812$	13.8564	−	5.65685i	0.486265	−	0.198517i
$813$	41.5692	−	29.3939i	1.45790	−	1.03089i
$814$		0			0
$815$	20.7846	+	25.4558i	0.728053	+	0.891679i
$816$	−20.0000	+	14.1421i	−0.700140	+	0.495074i
$817$		0			0
$818$		−	16.9706i		−	0.593362i
$819$	31.7128	−	1.51575i	1.10814	−	0.0529646i
$820$	6.00000	−	4.89898i	0.209529	−	0.171080i
$821$		−	22.6274i		−	0.789702i	−0.918745	−	0.394851i	$-0.870796\pi$
$821$		−	22.6274i		−	0.789702i	0.918745	−	0.394851i	$-0.129204\pi$
$822$	−12.0000	−	16.9706i	−0.418548	−	0.591916i
$823$		−	4.89898i		−	0.170768i	−0.996348	−	0.0853838i	$-0.972788\pi$
$823$		−	4.89898i		−	0.170768i	0.996348	−	0.0853838i	$-0.0272117\pi$
$824$	−17.3205			−0.603388
$825$	−9.85641	−	22.4243i	−0.343156	−	0.780715i
$826$	−12.0000	−	29.3939i	−0.417533	−	1.02274i
$827$	10.3923			0.361376			0.180688	−	0.983540i	$-0.442168\pi$
$827$	10.3923			0.361376			0.180688	+	0.983540i	$0.442168\pi$
$828$	3.46410	−	9.79796i	0.120386	−	0.340503i
$829$		−	29.3939i		−	1.02089i	−0.859910	−	0.510446i	$-0.829480\pi$
$829$		−	29.3939i		−	1.02089i	0.859910	−	0.510446i	$-0.170520\pi$
$830$	6.92820	+	8.48528i	0.240481	+	0.294528i
$831$	27.7128	−	19.5959i	0.961347	−	0.679775i
$832$	−4.00000			−0.138675
$833$	−13.8564	−	14.1421i	−0.480096	−	0.489996i
$834$	−24.0000	+	16.9706i	−0.831052	+	0.587643i
$835$	20.0000	+	24.4949i	0.692129	+	0.847681i
$836$		0			0
$837$	13.8564	+	48.9898i	0.478947	+	1.69334i
$838$	−12.0000			−0.414533
$839$	−27.7128			−0.956753			−0.478376	−	0.878155i	$-0.658774\pi$
$839$	−27.7128			−0.956753			−0.478376	+	0.878155i	$0.658774\pi$
$840$	2.07180	+	17.6269i	0.0714838	+	0.608186i
$841$	−3.00000			−0.103448
$842$	−45.0333			−1.55195
$843$	40.0000	−	28.2843i	1.37767	−	0.974162i
$844$	−4.00000			−0.137686
$845$	−5.19615	+	4.24264i	−0.178753	+	0.145951i
$846$	13.8564	+	4.89898i	0.476393	+	0.168430i
$847$	3.00000	+	7.34847i	0.103081	+	0.252496i
$848$		0			0
$849$	−14.0000	−	19.7990i	−0.480479	−	0.679500i
$850$	−24.0000	−	4.89898i	−0.823193	−	0.168034i
$851$		0			0
$852$	4.00000	−	2.82843i	0.137038	−	0.0969003i
$853$	20.0000			0.684787			0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000			0.684787			0.342393	+	0.939557i	$0.388762\pi$
$854$	−41.5692	+	16.9706i	−1.42247	+	0.580721i
$855$		0			0
$856$	18.0000			0.615227
$857$		−	48.0833i		−	1.64249i	−0.570574	−	0.821246i	$-0.693279\pi$
$857$		−	48.0833i		−	1.64249i	0.570574	−	0.821246i	$-0.306721\pi$
$858$	27.7128	−	19.5959i	0.946100	−	0.668994i
$859$			39.1918i			1.33721i	0.743619	+	0.668604i	$0.233108\pi$
$859$			39.1918i			1.33721i	−0.743619	+	0.668604i	$0.766892\pi$
$860$	−6.92820	−	8.48528i	−0.236250	−	0.289346i
$861$	−8.53590	+	13.3843i	−0.290903	+	0.456134i
$862$		−	4.89898i		−	0.166860i
$863$	10.3923			0.353758			0.176879	−	0.984233i	$-0.443400\pi$
$863$	10.3923			0.353758			0.176879	+	0.984233i	$0.443400\pi$
$864$	25.9808	−	7.34847i	0.883883	−	0.250000i
$865$	−28.0000	−	34.2929i	−0.952029	−	1.16599i
$866$	27.7128			0.941720
$867$	−9.00000	−	12.7279i	−0.305656	−	0.432263i
$868$	−24.0000	+	9.79796i	−0.814613	+	0.332564i
$869$			22.6274i			0.767583i
$870$	−10.1436	+	36.5665i	−0.343900	+	1.23972i
$871$			19.5959i			0.663982i
$872$	−17.3205			−0.586546
$873$	−8.00000	+	22.6274i	−0.270759	+	0.765822i
$874$		0			0
$875$	−19.0526	+	22.6274i	−0.644094	+	0.764946i
$876$	−8.00000	−	11.3137i	−0.270295	−	0.382255i
$877$		−	48.9898i		−	1.65427i	−0.562005	−	0.827134i	$-0.689970\pi$
$877$		−	48.9898i		−	1.65427i	0.562005	−	0.827134i	$-0.310030\pi$
$878$			67.8823i			2.29092i
$879$	4.00000	−	2.82843i	0.134917	−	0.0954005i
$880$	20.0000	+	24.4949i	0.674200	+	0.825723i
$881$	−10.3923			−0.350126			−0.175063	−	0.984557i	$-0.556013\pi$
$881$	−10.3923			−0.350126			−0.175063	+	0.984557i	$0.556013\pi$
$882$	15.3397	+	32.9802i	0.516516	+	1.11050i
$883$			14.6969i			0.494591i	0.968940	+	0.247296i	$0.0795419\pi$
$883$			14.6969i			0.494591i	−0.968940	+	0.247296i	$0.920458\pi$
$884$		−	11.3137i		−	0.380521i
$885$	25.8564	+	7.17260i	0.869154	+	0.241104i
$886$	30.0000			1.00787
$887$			2.82843i			0.0949693i	0.998872	+	0.0474846i	$0.0151205\pi$
$887$			2.82843i			0.0949693i	−0.998872	+	0.0474846i	$0.984879\pi$
$888$		0			0
$889$	−36.0000	+	14.6969i	−1.20740	+	0.492919i
$890$	31.1769	−	25.4558i	1.04505	−	0.853282i
$891$	16.0000	−	19.7990i	0.536020	−	0.663291i
$892$	26.0000			0.870544
$893$		0			0
$894$	−27.7128	+	19.5959i	−0.926855	+	0.655386i
$895$	−4.00000	−	4.89898i	−0.133705	−	0.163755i
$896$	−12.1244	−	29.6985i	−0.405046	−	0.992157i
$897$	−13.8564	−	19.5959i	−0.462652	−	0.654289i
$898$			9.79796i			0.326962i
$899$	55.4256			1.84855
$900$	12.8564	+	7.72741i	0.428547	+	0.257580i
$901$		0			0
$902$			16.9706i			0.565058i
$903$	18.9282	+	12.0716i	0.629891	+	0.401717i
$904$	12.0000			0.399114
$905$		0			0
$906$	13.8564	+	19.5959i	0.460348	+	0.651031i
$907$		−	24.4949i		−	0.813340i	−0.913575	−	0.406670i	$-0.866690\pi$
$907$		−	24.4949i		−	0.813340i	0.913575	−	0.406670i	$-0.133310\pi$
$908$			2.82843i			0.0938647i
$909$	17.3205	−	48.9898i	0.574485	−	1.62489i
$910$	−36.0000	−	19.5959i	−1.19339	−	0.649598i
$911$		−	48.0833i		−	1.59307i	−0.604593	−	0.796535i	$-0.706664\pi$
$911$		−	48.0833i		−	1.59307i	0.604593	−	0.796535i	$-0.293336\pi$
$912$		0			0
$913$	−8.00000			−0.264761
$914$		−	33.9411i		−	1.12267i
$915$	10.1436	−	36.5665i	0.335337	−	1.20885i
$916$		−	19.5959i		−	0.647467i
$917$	6.92820	+	16.9706i	0.228789	+	0.560417i
$918$	−6.92820	−	24.4949i	−0.228665	−	0.808452i
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	10.3923	−	8.48528i	0.342624	−	0.279751i
$921$	10.0000	+	14.1421i	0.329511	+	0.465999i
$922$	−6.00000			−0.197599
$923$		−	11.3137i		−	0.372395i
$924$	10.9282	+	6.96953i	0.359511	+	0.229281i
$925$		0			0
$926$			8.48528i			0.278844i
$927$	10.0000	−	28.2843i	0.328443	−	0.928977i
$928$		−	29.3939i		−	0.964901i
$929$	45.0333			1.47750			0.738748	−	0.673982i	$-0.235418\pi$
$929$	45.0333			1.47750			0.738748	+	0.673982i	$0.235418\pi$
$930$	17.5692	−	63.3350i	0.576117	−	2.07684i
$931$		0			0
$932$	−20.7846			−0.680823
$933$	−27.7128	−	39.1918i	−0.907277	−	1.28308i
$934$		−	4.89898i		−	0.160300i
$935$	13.8564	−	11.3137i	0.453153	−	0.369998i
$936$	6.92820	−	19.5959i	0.226455	−	0.640513i
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	−20.7846	+	8.48528i	−0.678642	+	0.277054i
$939$	16.0000	+	22.6274i	0.522140	+	0.738418i
$940$	−4.00000	−	4.89898i	−0.130466	−	0.159787i
$941$	−24.2487			−0.790485			−0.395243	−	0.918577i	$-0.629340\pi$
$941$	−24.2487			−0.790485			−0.395243	+	0.918577i	$0.629340\pi$
$942$	−6.92820	−	9.79796i	−0.225733	−	0.319235i
$943$	12.0000			0.390774
$944$	−34.6410			−1.12747
$945$	−29.9808	−	6.79367i	−0.975274	−	0.220998i
$946$	24.0000			0.780307
$947$	3.46410			0.112568			0.0562841	−	0.998415i	$-0.482075\pi$
$947$	3.46410			0.112568			0.0562841	+	0.998415i	$0.482075\pi$
$948$	−8.00000	−	11.3137i	−0.259828	−	0.367452i
$949$	−32.0000			−1.03876
$950$		0			0
$951$	−13.8564	−	19.5959i	−0.449325	−	0.635441i
$952$	−12.0000	+	4.89898i	−0.388922	+	0.158777i
$953$	−20.7846			−0.673280			−0.336640	−	0.941634i	$-0.609290\pi$
$953$	−20.7846			−0.673280			−0.336640	+	0.941634i	$0.609290\pi$
$954$		0			0
$955$	−28.0000	−	34.2929i	−0.906059	−	1.10969i
$956$			2.82843i			0.0914779i
$957$	−16.0000	−	22.6274i	−0.517207	−	0.731441i
$958$	48.0000			1.55081
$959$	−6.92820	−	16.9706i	−0.223723	−	0.548008i
$960$	3.73205	+	1.03528i	0.120451	+	0.0334134i
$961$	−65.0000			−2.09677
$962$		0			0
$963$	−10.3923	+	29.3939i	−0.334887	+	0.947204i
$964$		−	9.79796i		−	0.315571i
$965$	−13.8564	−	16.9706i	−0.446054	−	0.546302i
$966$	14.7846	−	23.1822i	0.475687	−	0.745876i
$967$		−	34.2929i		−	1.10278i	−0.834246	−	0.551392i	$-0.814097\pi$
$967$		−	34.2929i		−	1.10278i	0.834246	−	0.551392i	$-0.185903\pi$
$968$	5.19615			0.167011
$969$		0			0
$970$	24.0000	−	19.5959i	0.770594	−	0.629187i
$971$	−20.7846			−0.667010			−0.333505	−	0.942748i	$-0.608231\pi$
$971$	−20.7846			−0.667010			−0.333505	+	0.942748i	$0.608231\pi$
$972$	−1.00000	+	15.5563i	−0.0320750	+	0.498970i
$973$	−24.0000	+	9.79796i	−0.769405	+	0.314108i
$974$		−	25.4558i		−	0.815658i
$975$	31.7128	−	13.9391i	1.01562	−	0.446407i
$976$			48.9898i			1.56813i
$977$	48.4974			1.55157			0.775785	−	0.630997i	$-0.217354\pi$
$977$	48.4974			1.55157			0.775785	+	0.630997i	$0.217354\pi$
$978$	36.0000	−	25.4558i	1.15115	−	0.813988i
$979$			29.3939i			0.939432i
$980$	1.73205	−	15.5563i	0.0553283	−	0.496929i
$981$	10.0000	−	28.2843i	0.319275	−	0.903047i
$982$			24.4949i			0.781664i
$983$			2.82843i			0.0902128i	0.998982	+	0.0451064i	$0.0143627\pi$
$983$			2.82843i			0.0902128i	−0.998982	+	0.0451064i	$0.985637\pi$
$984$	6.00000	+	8.48528i	0.191273	+	0.270501i
$985$		0			0
$986$	−27.7128			−0.882556
$987$	10.9282	+	6.96953i	0.347849	+	0.221843i
$988$		0			0
$989$		−	16.9706i		−	0.539633i
$990$	−30.9282	+	11.1106i	−0.982963	+	0.353119i
$991$	8.00000			0.254128			0.127064	−	0.991894i	$-0.459445\pi$
$991$	8.00000			0.254128			0.127064	+	0.991894i	$0.459445\pi$
$992$			50.9117i			1.61645i
$993$	28.0000	+	39.5980i	0.888553	+	1.25660i
$994$	12.0000	−	4.89898i	0.380617	−	0.155386i
$995$		0			0
$996$	4.00000	−	2.82843i	0.126745	−	0.0896221i
$997$	−52.0000			−1.64686			−0.823428	−	0.567420i	$-0.807941\pi$
$997$	−52.0000			−1.64686			−0.823428	+	0.567420i	$0.807941\pi$
$998$	6.92820			0.219308
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.g.a.104.1	✓	4
3.2	odd	2	inner	105.2.g.a.104.4	yes	4
4.3	odd	2		1680.2.k.c.209.3		4
5.2	odd	4		525.2.b.j.251.2		8
5.3	odd	4		525.2.b.j.251.7		8
5.4	even	2		105.2.g.c.104.4	yes	4
7.2	even	3		735.2.p.c.374.4		8
7.3	odd	6		735.2.p.a.509.4		8
7.4	even	3		735.2.p.c.509.3		8
7.5	odd	6		735.2.p.a.374.3		8
7.6	odd	2		105.2.g.c.104.2	yes	4
12.11	even	2		1680.2.k.c.209.2		4
15.2	even	4		525.2.b.j.251.8		8
15.8	even	4		525.2.b.j.251.1		8
15.14	odd	2		105.2.g.c.104.1	yes	4
20.19	odd	2		1680.2.k.a.209.1		4
21.2	odd	6		735.2.p.c.374.1		8
21.5	even	6		735.2.p.a.374.2		8
21.11	odd	6		735.2.p.c.509.2		8
21.17	even	6		735.2.p.a.509.1		8
21.20	even	2		105.2.g.c.104.3	yes	4
28.27	even	2		1680.2.k.a.209.2		4
35.4	even	6		735.2.p.a.509.2		8
35.9	even	6		735.2.p.a.374.1		8
35.13	even	4		525.2.b.j.251.6		8
35.19	odd	6		735.2.p.c.374.2		8
35.24	odd	6		735.2.p.c.509.1		8
35.27	even	4		525.2.b.j.251.3		8
35.34	odd	2	inner	105.2.g.a.104.3	yes	4
60.59	even	2		1680.2.k.a.209.4		4
84.83	odd	2		1680.2.k.a.209.3		4
105.44	odd	6		735.2.p.a.374.4		8
105.59	even	6		735.2.p.c.509.4		8
105.62	odd	4		525.2.b.j.251.5		8
105.74	odd	6		735.2.p.a.509.3		8
105.83	odd	4		525.2.b.j.251.4		8
105.89	even	6		735.2.p.c.374.3		8
105.104	even	2	inner	105.2.g.a.104.2	yes	4
140.139	even	2		1680.2.k.c.209.4		4
420.419	odd	2		1680.2.k.c.209.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.g.a.104.1	✓	4	1.1	even	1	trivial
105.2.g.a.104.2	yes	4	105.104	even	2	inner
105.2.g.a.104.3	yes	4	35.34	odd	2	inner
105.2.g.a.104.4	yes	4	3.2	odd	2	inner
105.2.g.c.104.1	yes	4	15.14	odd	2
105.2.g.c.104.2	yes	4	7.6	odd	2
105.2.g.c.104.3	yes	4	21.20	even	2
105.2.g.c.104.4	yes	4	5.4	even	2
525.2.b.j.251.1		8	15.8	even	4
525.2.b.j.251.2		8	5.2	odd	4
525.2.b.j.251.3		8	35.27	even	4
525.2.b.j.251.4		8	105.83	odd	4
525.2.b.j.251.5		8	105.62	odd	4
525.2.b.j.251.6		8	35.13	even	4
525.2.b.j.251.7		8	5.3	odd	4
525.2.b.j.251.8		8	15.2	even	4
735.2.p.a.374.1		8	35.9	even	6
735.2.p.a.374.2		8	21.5	even	6
735.2.p.a.374.3		8	7.5	odd	6
735.2.p.a.374.4		8	105.44	odd	6
735.2.p.a.509.1		8	21.17	even	6
735.2.p.a.509.2		8	35.4	even	6
735.2.p.a.509.3		8	105.74	odd	6
735.2.p.a.509.4		8	7.3	odd	6
735.2.p.c.374.1		8	21.2	odd	6
735.2.p.c.374.2		8	35.19	odd	6
735.2.p.c.374.3		8	105.89	even	6
735.2.p.c.374.4		8	7.2	even	3
735.2.p.c.509.1		8	35.24	odd	6
735.2.p.c.509.2		8	21.11	odd	6
735.2.p.c.509.3		8	7.4	even	3
735.2.p.c.509.4		8	105.59	even	6
1680.2.k.a.209.1		4	20.19	odd	2
1680.2.k.a.209.2		4	28.27	even	2
1680.2.k.a.209.3		4	84.83	odd	2
1680.2.k.a.209.4		4	60.59	even	2
1680.2.k.c.209.1		4	420.419	odd	2
1680.2.k.c.209.2		4	12.11	even	2
1680.2.k.c.209.3		4	4.3	odd	2
1680.2.k.c.209.4		4	140.139	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.73205 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q-1.73205 q^{2} +(-1.00000 - 1.41421i) q^{3} +1.00000 q^{4} +(-1.73205 + 1.41421i) q^{5} +(1.73205 + 2.44949i) q^{6} +(1.00000 + 2.44949i) q^{7} +1.73205 q^{8} +(-1.00000 + 2.82843i) q^{9} +(3.00000 - 2.44949i) q^{10} +2.82843i q^{11} +(-1.00000 - 1.41421i) q^{12} -4.00000 q^{13} +(-1.73205 - 4.24264i) q^{14} +(3.73205 + 1.03528i) q^{15} -5.00000 q^{16} +2.82843i q^{17} +(1.73205 - 4.89898i) q^{18} +(-1.73205 + 1.41421i) q^{20} +(2.46410 - 3.86370i) q^{21} -4.89898i q^{22} -3.46410 q^{23} +(-1.73205 - 2.44949i) q^{24} +(1.00000 - 4.89898i) q^{25} +6.92820 q^{26} +(5.00000 - 1.41421i) q^{27} +(1.00000 + 2.44949i) q^{28} -5.65685i q^{29} +(-6.46410 - 1.79315i) q^{30} +9.79796i q^{31} +5.19615 q^{32} +(4.00000 - 2.82843i) q^{33} -4.89898i q^{34} +(-5.19615 - 2.82843i) q^{35} +(-1.00000 + 2.82843i) q^{36} +(4.00000 + 5.65685i) q^{39} +(-3.00000 + 2.44949i) q^{40} -3.46410 q^{41} +(-4.26795 + 6.69213i) q^{42} +4.89898i q^{43} +2.82843i q^{44} +(-2.26795 - 6.31319i) q^{45} +6.00000 q^{46} +2.82843i q^{47} +(5.00000 + 7.07107i) q^{48} +(-5.00000 + 4.89898i) q^{49} +(-1.73205 + 8.48528i) q^{50} +(4.00000 - 2.82843i) q^{51} -4.00000 q^{52} +(-8.66025 + 2.44949i) q^{54} +(-4.00000 - 4.89898i) q^{55} +(1.73205 + 4.24264i) q^{56} +9.79796i q^{58} +6.92820 q^{59} +(3.73205 + 1.03528i) q^{60} -9.79796i q^{61} -16.9706i q^{62} +(-7.92820 + 0.378937i) q^{63} +1.00000 q^{64} +(6.92820 - 5.65685i) q^{65} +(-6.92820 + 4.89898i) q^{66} -4.89898i q^{67} +2.82843i q^{68} +(3.46410 + 4.89898i) q^{69} +(9.00000 + 4.89898i) q^{70} +2.82843i q^{71} +(-1.73205 + 4.89898i) q^{72} +8.00000 q^{73} +(-7.92820 + 3.48477i) q^{75} +(-6.92820 + 2.82843i) q^{77} +(-6.92820 - 9.79796i) q^{78} +8.00000 q^{79} +(8.66025 - 7.07107i) q^{80} +(-7.00000 - 5.65685i) q^{81} +6.00000 q^{82} +2.82843i q^{83} +(2.46410 - 3.86370i) q^{84} +(-4.00000 - 4.89898i) q^{85} -8.48528i q^{86} +(-8.00000 + 5.65685i) q^{87} +4.89898i q^{88} +10.3923 q^{89} +(3.92820 + 10.9348i) q^{90} +(-4.00000 - 9.79796i) q^{91} -3.46410 q^{92} +(13.8564 - 9.79796i) q^{93} -4.89898i q^{94} +(-5.19615 - 7.34847i) q^{96} +8.00000 q^{97} +(8.66025 - 8.48528i) q^{98} +(-8.00000 - 2.82843i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} + 4 q^{4} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^7 - 4 * q^9	\( 4 q - 4 q^{3} + 4 q^{4} + 4 q^{7} - 4 q^{9} + 12 q^{10} - 4 q^{12} - 16 q^{13} + 8 q^{15} - 20 q^{16} - 4 q^{21} + 4 q^{25} + 20 q^{27} + 4 q^{28} - 12 q^{30} + 16 q^{33} - 4 q^{36} + 16 q^{39} - 12 q^{40} - 24 q^{42} - 16 q^{45} + 24 q^{46} + 20 q^{48} - 20 q^{49} + 16 q^{51} - 16 q^{52} - 16 q^{55} + 8 q^{60} - 4 q^{63} + 4 q^{64} + 36 q^{70} + 32 q^{73} - 4 q^{75} + 32 q^{79} - 28 q^{81} + 24 q^{82} - 4 q^{84} - 16 q^{85} - 32 q^{87} - 12 q^{90} - 16 q^{91} + 32 q^{97} - 32 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 + 4 * q^4 + 4 * q^7 - 4 * q^9 + 12 * q^10 - 4 * q^12 - 16 * q^13 + 8 * q^15 - 20 * q^16 - 4 * q^21 + 4 * q^25 + 20 * q^27 + 4 * q^28 - 12 * q^30 + 16 * q^33 - 4 * q^36 + 16 * q^39 - 12 * q^40 - 24 * q^42 - 16 * q^45 + 24 * q^46 + 20 * q^48 - 20 * q^49 + 16 * q^51 - 16 * q^52 - 16 * q^55 + 8 * q^60 - 4 * q^63 + 4 * q^64 + 36 * q^70 + 32 * q^73 - 4 * q^75 + 32 * q^79 - 28 * q^81 + 24 * q^82 - 4 * q^84 - 16 * q^85 - 32 * q^87 - 12 * q^90 - 16 * q^91 + 32 * q^97 - 32 * q^99

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