LMFDB - Embedded newform 1050.2.i.e.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(151,1050)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1050.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.i (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:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1050.151
Dual form			1050.2.i.e.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +(2.50000 - 0.866025i) q^{42} +10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +4.00000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(-5.00000 + 8.66025i) q^{67} -6.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(1.50000 - 7.79423i) q^{77} -4.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(4.50000 - 7.79423i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 - 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + q^{12} + 8 q^{13} + 4 q^{14} - q^{16} - q^{18} + 4 q^{19} - q^{21} + 6 q^{22} + q^{24} - 4 q^{26} - 2 q^{27} + q^{28} + 18 q^{29} + q^{31} - q^{32} + 3 q^{33} + 2 q^{36} + 8 q^{37} + 4 q^{38} + 4 q^{39} + 5 q^{42} + 20 q^{43} - 3 q^{44} - 6 q^{47} - 2 q^{48} + 11 q^{49} - 4 q^{52} - 3 q^{53} + q^{54} - 5 q^{56} + 8 q^{57} - 9 q^{58} - 3 q^{59} + 10 q^{61} - 2 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{66} - 10 q^{67} - 12 q^{71} - q^{72} + 2 q^{73} + 8 q^{74} - 8 q^{76} + 3 q^{77} - 8 q^{78} + q^{79} - q^{81} + 18 q^{83} - 4 q^{84} - 10 q^{86} + 9 q^{87} - 3 q^{88} - 6 q^{89} - 20 q^{91} - q^{93} - 6 q^{94} + q^{96} + 2 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 - 5 * q^7 + 2 * q^8 - q^9 - 3 * q^11 + q^12 + 8 * q^13 + 4 * q^14 - q^16 - q^18 + 4 * q^19 - q^21 + 6 * q^22 + q^24 - 4 * q^26 - 2 * q^27 + q^28 + 18 * q^29 + q^31 - q^32 + 3 * q^33 + 2 * q^36 + 8 * q^37 + 4 * q^38 + 4 * q^39 + 5 * q^42 + 20 * q^43 - 3 * q^44 - 6 * q^47 - 2 * q^48 + 11 * q^49 - 4 * q^52 - 3 * q^53 + q^54 - 5 * q^56 + 8 * q^57 - 9 * q^58 - 3 * q^59 + 10 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^66 - 10 * q^67 - 12 * q^71 - q^72 + 2 * q^73 + 8 * q^74 - 8 * q^76 + 3 * q^77 - 8 * q^78 + q^79 - q^81 + 18 * q^83 - 4 * q^84 - 10 * q^86 + 9 * q^87 - 3 * q^88 - 6 * q^89 - 20 * q^91 - q^93 - 6 * q^94 + q^96 + 2 * q^97 - 13 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	2.00000	+	1.73205i	0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$	−0.500000	+	2.59808i	−0.109109	+	0.566947i
$22$	3.00000			0.639602
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$	−1.00000			−0.192450
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	−0.817625	−	0.575751i	$-0.804710\pi$
$31$	0.500000	−	0.866025i	0.0898027	−	0.155543i	0.907428	+	0.420208i	$0.138043\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$	1.00000			0.166667
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	2.00000	−	3.46410i	0.324443	−	0.561951i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	2.50000	−	0.866025i	0.385758	−	0.133631i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$	−1.00000			−0.144338
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$		0			0
$52$	−2.00000	+	3.46410i	−0.277350	+	0.480384i
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	4.00000			0.529813
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	−0.946993	−	0.321253i	$-0.895896\pi$
$59$	−1.50000	+	2.59808i	−0.195283	+	0.338241i	0.751710	+	0.659494i	$0.229229\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−1.00000			−0.127000
$63$	2.00000	+	1.73205i	0.251976	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	1.50000	−	7.79423i	0.170941	−	0.888235i
$78$	−4.00000			−0.452911
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$	−2.00000	−	1.73205i	−0.218218	−	0.188982i
$85$		0			0
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		0			0
$93$	−0.500000	−	0.866025i	−0.0518476	−	0.0898027i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	3.00000			0.301511
$100$		0			0
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	3.00000			0.291386
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	2.00000	+	1.73205i	0.188982	+	0.163663i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$		0			0
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	3.00000			0.276172
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$		0			0
$124$	0.500000	+	0.866025i	0.0449013	+	0.0777714i
$125$		0			0
$126$	0.500000	−	2.59808i	0.0445435	−	0.231455i
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$		0			0
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	0.992865	−	0.119241i	$-0.0380462\pi$
$131$	4.50000	+	7.79423i	0.393167	+	0.680985i	−0.599699	+	0.800226i	$0.704713\pi$
$132$	−3.00000			−0.261116
$133$	−8.00000	−	6.92820i	−0.693688	−	0.600751i
$134$	10.0000			0.863868
$135$		0			0
$136$		0			0
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	−6.00000	+	10.3923i	−0.501745	+	0.869048i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$	−8.00000			−0.657596
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$	−7.50000	+	2.59808i	−0.604367	+	0.209359i
$155$		0			0
$156$	2.00000	+	3.46410i	0.160128	+	0.277350i
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	0.500000	−	0.866025i	0.0397779	−	0.0688973i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$		0			0
$162$	1.00000			0.0785674
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$		0			0
$165$		0			0
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	−6.00000			−0.464294			−0.232147	−	0.972681i	$-0.574575\pi$
$167$	−6.00000			−0.464294			−0.232147	+	0.972681i	$0.574575\pi$
$168$	−0.500000	+	2.59808i	−0.0385758	+	0.200446i
$169$	3.00000			0.230769
$170$		0			0
$171$	2.00000	−	3.46410i	0.152944	−	0.264906i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	−9.00000			−0.682288
$175$		0			0
$176$	3.00000			0.226134
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	8.00000	+	6.92820i	0.592999	+	0.513553i
$183$	10.0000			0.739221
$184$		0			0
$185$		0			0
$186$	−0.500000	+	0.866025i	−0.0366618	+	0.0635001i
$187$		0			0
$188$	6.00000			0.437595
$189$	2.50000	−	0.866025i	0.181848	−	0.0629941i
$190$		0			0
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	0.289980	+	0.957033i	$0.406351\pi$
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	−0.973805	+	0.227387i	$0.926982\pi$
$194$	−0.500000	−	0.866025i	−0.0358979	−	0.0621770i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$		0			0
$201$	5.00000	+	8.66025i	0.352673	+	0.610847i
$202$	−18.0000			−1.26648
$203$	−22.5000	+	7.79423i	−1.57919	+	0.547048i
$204$		0			0
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$		0			0
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−0.500000	+	2.59808i	−0.0339422	+	0.176369i
$218$	14.0000			0.948200
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$		0			0
$222$	−4.00000	−	6.92820i	−0.268462	−	0.464991i
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$		0			0
$226$		0			0
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.0634974	+	0.997982i	$0.520225\pi$
$227$	−13.5000	+	23.3827i	−0.896026	+	1.55196i	−0.832529	+	0.553981i	$0.813108\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$		0			0
$231$	−6.00000	−	5.19615i	−0.394771	−	0.341882i
$232$	9.00000			0.590879
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$		0			0
$236$	−1.50000	−	2.59808i	−0.0976417	−	0.169120i
$237$	1.00000			0.0649570
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	−0.849472	−	0.527633i	$-0.823079\pi$
$241$	0.500000	−	0.866025i	0.0322078	−	0.0557856i	0.881680	+	0.471848i	$0.156413\pi$
$242$	1.00000	−	1.73205i	0.0642824	−	0.111340i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−10.0000			−0.640184
$245$		0			0
$246$		0			0
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$	0.500000	−	0.866025i	0.0317500	−	0.0549927i
$249$	4.50000	−	7.79423i	0.285176	−	0.493939i
$250$		0			0
$251$	27.0000			1.70422			0.852112	−	0.523359i	$-0.175321\pi$
$251$	27.0000			1.70422			0.852112	+	0.523359i	$0.175321\pi$
$252$	−2.50000	+	0.866025i	−0.157485	+	0.0545545i
$253$		0			0
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	−10.0000			−0.622573
$259$	−16.0000	−	13.8564i	−0.994192	−	0.860995i
$260$		0			0
$261$	−4.50000	−	7.79423i	−0.278543	−	0.482451i
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	−2.00000	+	10.3923i	−0.122628	+	0.637193i
$267$	−6.00000			−0.367194
$268$	−5.00000	−	8.66025i	−0.305424	−	0.529009i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$		0			0
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	0.649211	−	0.760609i	$-0.275099\pi$
$271$	−5.50000	−	9.52628i	−0.334101	−	0.578680i	−0.983312	+	0.181928i	$0.941766\pi$
$272$		0			0
$273$	−2.00000	+	10.3923i	−0.121046	+	0.628971i
$274$	−18.0000			−1.08742
$275$		0			0
$276$		0			0
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	−0.720473	−	0.693482i	$-0.756075\pi$
$277$	4.00000	−	6.92820i	0.240337	−	0.416275i	0.960810	+	0.277207i	$0.0894088\pi$
$278$	−1.00000	−	1.73205i	−0.0599760	−	0.103882i
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	3.00000	+	5.19615i	0.178647	+	0.309426i
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	12.0000			0.709575
$287$		0			0
$288$	1.00000			0.0589256
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	−33.0000			−1.92788			−0.963940	−	0.266119i	$-0.914259\pi$
$293$	−33.0000			−1.92788			−0.963940	+	0.266119i	$0.914259\pi$
$294$	−5.50000	+	4.33013i	−0.320767	+	0.252538i
$295$		0			0
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$		0			0
$300$		0			0
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$	−1.00000			−0.0575435
$303$	−9.00000	−	15.5885i	−0.517036	−	0.895533i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		0			0
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	6.00000	+	5.19615i	0.341882	+	0.296078i
$309$	8.00000			0.455104
$310$		0			0
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$	2.00000	−	3.46410i	0.113228	−	0.196116i
$313$	−15.5000	−	26.8468i	−0.876112	−	1.51747i	−0.855574	−	0.517681i	$-0.826795\pi$
$313$	−15.5000	−	26.8468i	−0.876112	−	1.51747i	−0.0205381	−	0.999789i	$-0.506538\pi$
$314$	4.00000			0.225733
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	0.964281	−	0.264883i	$-0.0853332\pi$
$317$	4.50000	+	7.79423i	0.252745	+	0.437767i	−0.711535	+	0.702650i	$0.752000\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$	−13.5000	+	23.3827i	−0.755855	+	1.30918i
$320$		0			0
$321$	−3.00000			−0.167444
$322$		0			0
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$		0			0
$329$	12.0000	+	10.3923i	0.661581	+	0.572946i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−4.50000	+	7.79423i	−0.246970	+	0.427764i
$333$	4.00000	−	6.92820i	0.219199	−	0.379663i
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$	7.00000			0.381314			0.190657	−	0.981657i	$-0.438938\pi$
$337$	7.00000			0.381314			0.190657	+	0.981657i	$0.438938\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$		0			0
$341$	1.50000	+	2.59808i	0.0812296	+	0.140694i
$342$	−4.00000			−0.216295
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	10.0000			0.539164
$345$		0			0
$346$	9.00000	−	15.5885i	0.483843	−	0.838041i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$	4.50000	+	7.79423i	0.241225	+	0.417815i
$349$	26.0000			1.39175			0.695874	−	0.718164i	$-0.255017\pi$
$349$	26.0000			1.39175			0.695874	+	0.718164i	$0.255017\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$	1.50000	−	2.59808i	0.0797241	−	0.138086i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$	12.0000			0.634220
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	2.00000			0.104973
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$		0			0
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.50000	−	7.79423i	0.0778761	−	0.404656i
$372$	1.00000			0.0518476
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	0.950804	−	0.309794i	$-0.100260\pi$
$373$	4.00000	+	6.92820i	0.207112	+	0.358729i	−0.743691	+	0.668523i	$0.766927\pi$
$374$		0			0
$375$		0			0
$376$	−3.00000	−	5.19615i	−0.154713	−	0.267971i
$377$	36.0000			1.85409
$378$	−2.00000	−	1.73205i	−0.102869	−	0.0890871i
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$	−2.50000	+	4.33013i	−0.128079	+	0.221839i
$382$		0			0
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	0.998954	−	0.0457244i	$-0.0145596\pi$
$383$	9.00000	+	15.5885i	0.459879	+	0.796533i	−0.539076	+	0.842257i	$0.681226\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	19.0000			0.967075
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$		0			0
$391$		0			0
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	9.00000			0.453990
$394$	3.00000	+	5.19615i	0.151138	+	0.261778i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	−2.00000	−	3.46410i	−0.100377	−	0.173858i	0.811463	−	0.584404i	$-0.198672\pi$
$397$	−2.00000	−	3.46410i	−0.100377	−	0.173858i	−0.911840	+	0.410546i	$0.865338\pi$
$398$	20.0000			1.00251
$399$	−10.0000	+	3.46410i	−0.500626	+	0.173422i
$400$		0			0
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	−0.992932	−	0.118686i	$-0.962132\pi$
$401$	−12.0000	−	20.7846i	−0.599251	−	1.03793i	0.393680	−	0.919247i	$-0.371202\pi$
$402$	5.00000	−	8.66025i	0.249377	−	0.431934i
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	9.00000	+	15.5885i	0.447767	+	0.775555i
$405$		0			0
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$	−24.0000			−1.18964
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	−9.00000	−	15.5885i	−0.443937	−	0.768922i
$412$	−8.00000			−0.394132
$413$	1.50000	−	7.79423i	0.0738102	−	0.383529i
$414$		0			0
$415$		0			0
$416$	−2.00000	+	3.46410i	−0.0980581	+	0.169842i
$417$	1.00000	−	1.73205i	0.0489702	−	0.0848189i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	−7.00000	−	12.1244i	−0.340755	−	0.590204i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$		0			0
$426$	6.00000			0.290701
$427$	−20.0000	−	17.3205i	−0.967868	−	0.838198i
$428$	3.00000			0.145010
$429$	6.00000	+	10.3923i	0.289683	+	0.501745i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	34.0000			1.63394			0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000			1.63394			0.816968	+	0.576683i	$0.195653\pi$
$434$	2.50000	−	0.866025i	0.120004	−	0.0415705i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		0			0
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	−6.50000	−	2.59808i	−0.309524	−	0.123718i
$442$		0			0
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	−0.929631	−	0.368492i	$-0.879874\pi$
$443$	−16.5000	−	28.5788i	−0.783939	−	1.35782i	0.145692	−	0.989330i	$-0.453459\pi$
$444$	−4.00000	+	6.92820i	−0.189832	+	0.328798i
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	−18.0000			−0.851371
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	12.0000			0.566315			0.283158	−	0.959073i	$-0.408618\pi$
$449$	12.0000			0.566315			0.283158	+	0.959073i	$0.408618\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	−0.500000	−	0.866025i	−0.0234920	−	0.0406894i
$454$	27.0000			1.26717
$455$		0			0
$456$	4.00000			0.187317
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	0.854094	−	0.520119i	$-0.174112\pi$
$457$	−0.500000	−	0.866025i	−0.0233890	−	0.0405110i	−0.877483	+	0.479608i	$0.840779\pi$
$458$	2.00000	−	3.46410i	0.0934539	−	0.161867i
$459$		0			0
$460$		0			0
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$	−1.50000	+	7.79423i	−0.0697863	+	0.362620i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$		0			0
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	0.895696	+	0.444667i	$0.146678\pi$
$467$	18.0000	+	31.1769i	0.832941	+	1.44270i	−0.0627555	+	0.998029i	$0.519989\pi$
$468$	4.00000			0.184900
$469$	5.00000	−	25.9808i	0.230879	−	1.19968i
$470$		0			0
$471$	2.00000	+	3.46410i	0.0921551	+	0.159617i
$472$	−1.50000	+	2.59808i	−0.0690431	+	0.119586i
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$	−0.500000	−	0.866025i	−0.0229658	−	0.0397779i
$475$		0			0
$476$		0			0
$477$	3.00000			0.137361
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	−0.583803	−	0.811895i	$-0.698436\pi$
$479$	9.00000	−	15.5885i	0.411220	−	0.712255i	0.995023	+	0.0996406i	$0.0317693\pi$
$480$		0			0
$481$	16.0000	+	27.7128i	0.729537	+	1.26360i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	20.5000	−	35.5070i	0.928944	−	1.60898i	0.143851	−	0.989599i	$-0.454051\pi$
$487$	20.5000	−	35.5070i	0.928944	−	1.60898i	0.785093	−	0.619378i	$-0.212615\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−33.0000			−1.48927			−0.744635	−	0.667472i	$-0.767376\pi$
$491$	−33.0000			−1.48927			−0.744635	+	0.667472i	$0.767376\pi$
$492$		0			0
$493$		0			0
$494$	8.00000	−	13.8564i	0.359937	−	0.623429i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	15.0000	−	5.19615i	0.672842	−	0.233079i
$498$	−9.00000			−0.403300
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	0.842774	−	0.538267i	$-0.180921\pi$
$499$	−1.00000	−	1.73205i	−0.0447661	−	0.0775372i	−0.887540	+	0.460730i	$0.847588\pi$
$500$		0			0
$501$	−3.00000	+	5.19615i	−0.134030	+	0.232147i
$502$	−13.5000	−	23.3827i	−0.602534	−	1.04362i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$		0			0
$506$		0			0
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$	2.50000	−	4.33013i	0.110920	−	0.192118i
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	0.897352	−	0.441315i	$-0.145488\pi$
$509$	1.50000	+	2.59808i	0.0664863	+	0.115158i	−0.830866	+	0.556473i	$0.812154\pi$
$510$		0			0
$511$	−1.00000	+	5.19615i	−0.0442374	+	0.229864i
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$	18.0000			0.791639
$518$	−4.00000	+	20.7846i	−0.175750	+	0.913223i
$519$	18.0000			0.790112
$520$		0			0
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	−4.50000	+	7.79423i	−0.196960	+	0.341144i
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	0.818980	−	0.573822i	$-0.194540\pi$
$523$	−2.00000	−	3.46410i	−0.0874539	−	0.151475i	−0.906434	+	0.422347i	$0.861206\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$	6.00000			0.261612
$527$		0			0
$528$	1.50000	−	2.59808i	0.0652791	−	0.113067i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	3.00000			0.130189
$532$	10.0000	−	3.46410i	0.433555	−	0.150188i
$533$		0			0
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$		0			0
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	21.0000			0.905374
$539$	3.00000	+	20.7846i	0.129219	+	0.895257i
$540$		0			0
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	−0.997587	−	0.0694205i	$-0.977885\pi$
$541$	−13.0000	−	22.5167i	−0.558914	−	0.968067i	0.438674	−	0.898646i	$-0.355448\pi$
$542$	−5.50000	+	9.52628i	−0.236245	+	0.409189i
$543$	4.00000	−	6.92820i	0.171656	−	0.297318i
$544$		0			0
$545$		0			0
$546$	10.0000	−	3.46410i	0.427960	−	0.148250i
$547$	−8.00000			−0.342055			−0.171028	−	0.985266i	$-0.554709\pi$
$547$	−8.00000			−0.342055			−0.171028	+	0.985266i	$0.554709\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$		0			0
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$		0			0
$553$	−2.00000	−	1.73205i	−0.0850487	−	0.0736543i
$554$	−8.00000			−0.339887
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$	0.500000	+	0.866025i	0.0211667	+	0.0366618i
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$		0			0
$566$	−14.0000			−0.588464
$567$	0.500000	−	2.59808i	0.0209980	−	0.109109i
$568$	−6.00000			−0.251754
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	0.945573	+	0.325409i	$0.105502\pi$
$569$	18.0000	+	31.1769i	0.754599	+	1.30700i	−0.190974	+	0.981595i	$0.561165\pi$
$570$		0			0
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	−0.252893	−	0.967494i	$-0.581382\pi$
$571$	17.0000	−	29.4449i	0.711428	−	1.23223i	0.964321	−	0.264735i	$-0.0852845\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	11.5000	−	19.9186i	0.478751	−	0.829222i	−0.520952	−	0.853586i	$-0.674423\pi$
$577$	11.5000	−	19.9186i	0.478751	−	0.829222i	0.999703	+	0.0243645i	$0.00775624\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	9.50000	+	16.4545i	0.394807	+	0.683825i
$580$		0			0
$581$	−22.5000	+	7.79423i	−0.933457	+	0.323359i
$582$	−1.00000			−0.0414513
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	16.5000	+	28.5788i	0.681609	+	1.18058i
$587$	−21.0000			−0.866763			−0.433381	−	0.901211i	$-0.642680\pi$
$587$	−21.0000			−0.866763			−0.433381	+	0.901211i	$0.642680\pi$
$588$	6.50000	+	2.59808i	0.268055	+	0.107143i
$589$	4.00000			0.164817
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	0.999965	−	0.00831589i	$-0.00264706\pi$
$593$	12.0000	+	20.7846i	0.492781	+	0.853522i	−0.507184	+	0.861838i	$0.669314\pi$
$594$	−3.00000			−0.123091
$595$		0			0
$596$	18.0000			0.737309
$597$	10.0000	+	17.3205i	0.409273	+	0.708881i
$598$		0			0
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	−0.621480	−	0.783430i	$-0.713468\pi$
$599$	9.00000	−	15.5885i	0.367730	−	0.636927i	0.989210	+	0.146503i	$0.0468017\pi$
$600$		0			0
$601$	11.0000			0.448699			0.224350	−	0.974509i	$-0.427974\pi$
$601$	11.0000			0.448699			0.224350	+	0.974509i	$0.427974\pi$
$602$	20.0000	+	17.3205i	0.815139	+	0.705931i
$603$	10.0000			0.407231
$604$	0.500000	+	0.866025i	0.0203447	+	0.0352381i
$605$		0			0
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	0.786212	−	0.617957i	$-0.212039\pi$
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	−0.928272	+	0.371901i	$0.878706\pi$
$608$	−4.00000			−0.162221
$609$	−4.50000	+	23.3827i	−0.182349	+	0.947514i
$610$		0			0
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$		0			0
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	−0.981129	−	0.193352i	$-0.938064\pi$
$613$	−8.00000	+	13.8564i	−0.323117	+	0.559655i	0.658012	+	0.753007i	$0.271397\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	1.50000	−	7.79423i	0.0604367	−	0.314038i
$617$	6.00000			0.241551			0.120775	−	0.992680i	$-0.461462\pi$
$617$	6.00000			0.241551			0.120775	+	0.992680i	$0.461462\pi$
$618$	−4.00000	−	6.92820i	−0.160904	−	0.278693i
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	−0.290684	−	0.956819i	$-0.593883\pi$
$619$	17.0000	−	29.4449i	0.683288	−	1.18349i	0.973972	−	0.226670i	$-0.0727838\pi$
$620$		0			0
$621$		0			0
$622$	24.0000			0.962312
$623$	12.0000	+	10.3923i	0.480770	+	0.416359i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	−15.5000	+	26.8468i	−0.619505	+	1.07301i
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$		0			0
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	0.500000	+	0.866025i	0.0198889	+	0.0344486i
$633$	7.00000	−	12.1244i	0.278225	−	0.481900i
$634$	4.50000	−	7.79423i	0.178718	−	0.309548i
$635$		0			0
$636$	−3.00000			−0.118958
$637$	22.0000	−	17.3205i	0.871672	−	0.686264i
$638$	27.0000			1.06894
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	1.50000	+	2.59808i	0.0592003	+	0.102538i
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	−0.986916	−	0.161233i	$-0.948453\pi$
$647$	−9.00000	+	15.5885i	−0.353827	+	0.612845i	0.633090	+	0.774078i	$0.281786\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$		0			0
$651$	2.00000	+	1.73205i	0.0783862	+	0.0678844i
$652$	16.0000			0.626608
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	0.893882	−	0.448303i	$-0.147971\pi$
$653$	1.50000	+	2.59808i	0.0586995	+	0.101671i	−0.835182	+	0.549973i	$0.814638\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$		0			0
$657$	−2.00000			−0.0780274
$658$	3.00000	−	15.5885i	0.116952	−	0.607701i
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	−10.0000	+	17.3205i	−0.388661	+	0.673181i
$663$		0			0
$664$	9.00000			0.349268
$665$		0			0
$666$	−8.00000			−0.309994
$667$		0			0
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	−30.0000			−1.15814
$672$	−2.00000	−	1.73205i	−0.0771517	−	0.0668153i
$673$	−29.0000			−1.11787			−0.558934	−	0.829212i	$-0.688789\pi$
$673$	−29.0000			−1.11787			−0.558934	+	0.829212i	$0.688789\pi$
$674$	−3.50000	−	6.06218i	−0.134815	−	0.233506i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$		0			0
$679$	−2.50000	+	0.866025i	−0.0959412	+	0.0332350i
$680$		0			0
$681$	13.5000	+	23.3827i	0.517321	+	0.896026i
$682$	1.50000	−	2.59808i	0.0574380	−	0.0994855i
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	−0.355920	−	0.934516i	$-0.615832\pi$
$683$	16.5000	−	28.5788i	0.631355	−	1.09354i	0.987275	−	0.159022i	$-0.0508342\pi$
$684$	2.00000	+	3.46410i	0.0764719	+	0.132453i
$685$		0			0
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$	4.00000			0.152610
$688$	−5.00000	−	8.66025i	−0.190623	−	0.330169i
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−18.0000			−0.684257
$693$	−7.50000	+	2.59808i	−0.284901	+	0.0986928i
$694$	−12.0000			−0.455514
$695$		0			0
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$		0			0
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$	−24.0000			−0.907763
$700$		0			0
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	−16.0000	+	27.7128i	−0.603451	+	1.04521i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	−24.0000			−0.903252
$707$	−9.00000	+	46.7654i	−0.338480	+	1.75879i
$708$	−3.00000			−0.112747
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	0.944509	−	0.328484i	$-0.106538\pi$
$709$	5.00000	+	8.66025i	0.187779	+	0.325243i	−0.756730	+	0.653727i	$0.773204\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	−12.0000	+	20.7846i	−0.448148	+	0.776215i
$718$	−15.0000	+	25.9808i	−0.559795	+	0.969593i
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	0.983608	−	0.180319i	$-0.0577130\pi$
$719$	9.00000	+	15.5885i	0.335643	+	0.581351i	−0.647965	+	0.761670i	$0.724380\pi$
$720$		0			0
$721$	−16.0000	−	13.8564i	−0.595871	−	0.516040i
$722$	−3.00000			−0.111648
$723$	−0.500000	−	0.866025i	−0.0185952	−	0.0322078i
$724$	−4.00000	+	6.92820i	−0.148659	+	0.257485i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	13.0000			0.482143			0.241072	−	0.970507i	$-0.422501\pi$
$727$	13.0000			0.482143			0.241072	+	0.970507i	$0.422501\pi$
$728$	−10.0000	+	3.46410i	−0.370625	+	0.128388i
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	−5.00000	+	8.66025i	−0.184805	+	0.320092i
$733$	−5.00000	−	8.66025i	−0.184679	−	0.319874i	0.758789	−	0.651336i	$-0.225791\pi$
$733$	−5.00000	−	8.66025i	−0.184679	−	0.319874i	−0.943468	+	0.331463i	$0.892458\pi$
$734$	19.0000			0.701303
$735$		0			0
$736$		0			0
$737$	−15.0000	−	25.9808i	−0.552532	−	0.957014i
$738$		0			0
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.119677	+	0.992813i	$0.538186\pi$
$739$	−25.0000	+	43.3013i	−0.919640	+	1.59286i	−0.799962	+	0.600050i	$0.795147\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$	−7.50000	+	2.59808i	−0.275334	+	0.0953784i
$743$	−42.0000			−1.54083			−0.770415	−	0.637542i	$-0.779951\pi$
$743$	−42.0000			−1.54083			−0.770415	+	0.637542i	$0.779951\pi$
$744$	−0.500000	−	0.866025i	−0.0183309	−	0.0317500i
$745$		0			0
$746$	4.00000	−	6.92820i	0.146450	−	0.253660i
$747$	−4.50000	−	7.79423i	−0.164646	−	0.285176i
$748$		0			0
$749$	6.00000	+	5.19615i	0.219235	+	0.189863i
$750$		0			0
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	0.922792	−	0.385299i	$-0.125902\pi$
$751$	3.50000	+	6.06218i	0.127717	+	0.221212i	−0.795075	+	0.606511i	$0.792568\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$	13.5000	−	23.3827i	0.491967	−	0.852112i
$754$	−18.0000	−	31.1769i	−0.655521	−	1.13540i
$755$		0			0
$756$	−0.500000	+	2.59808i	−0.0181848	+	0.0944911i
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$	−4.00000	−	6.92820i	−0.145287	−	0.251644i
$759$		0			0
$760$		0			0
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	0.736543	−	0.676391i	$-0.236457\pi$
$761$	−6.00000	−	10.3923i	−0.217500	−	0.376721i	−0.954043	+	0.299670i	$0.903123\pi$
$762$	5.00000			0.181131
$763$	7.00000	−	36.3731i	0.253417	−	1.31679i
$764$		0			0
$765$		0			0
$766$	9.00000	−	15.5885i	0.325183	−	0.563234i
$767$	−6.00000	+	10.3923i	−0.216647	+	0.375244i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−19.0000			−0.685158			−0.342579	−	0.939489i	$-0.611300\pi$
$769$	−19.0000			−0.685158			−0.342579	+	0.939489i	$0.611300\pi$
$770$		0			0
$771$	6.00000			0.216085
$772$	−9.50000	−	16.4545i	−0.341912	−	0.592210i
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$		0			0
$776$	1.00000			0.0358979
$777$	−20.0000	+	6.92820i	−0.717496	+	0.248548i
$778$	−6.00000			−0.215110
$779$		0			0
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$	−9.00000			−0.321634
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$	−4.50000	−	7.79423i	−0.160510	−	0.278011i
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.0526599	−	0.998613i	$-0.483230\pi$
$787$	25.0000	−	43.3013i	0.891154	−	1.54352i	0.838494	−	0.544911i	$-0.183437\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$		0			0
$791$		0			0
$792$	3.00000			0.106600
$793$	20.0000	+	34.6410i	0.710221	+	1.23014i
$794$	−2.00000	+	3.46410i	−0.0709773	+	0.122936i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	33.0000			1.16892			0.584460	−	0.811423i	$-0.301306\pi$
$797$	33.0000			1.16892			0.584460	+	0.811423i	$0.301306\pi$
$798$	8.00000	+	6.92820i	0.283197	+	0.245256i
$799$		0			0
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	−10.0000			−0.352673
$805$		0			0
$806$	−4.00000			−0.140894
$807$	10.5000	+	18.1865i	0.369618	+	0.640196i
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$809$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	4.50000	−	23.3827i	0.157919	−	0.820571i
$813$	−11.0000			−0.385787
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$		0			0
$816$		0			0
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$	−25.0000			−0.874105
$819$	8.00000	+	6.92820i	0.279543	+	0.242091i
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$	−9.00000	+	15.5885i	−0.313911	+	0.543710i
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	−7.50000	+	2.59808i	−0.260958	+	0.0903986i
$827$	−15.0000			−0.521601			−0.260801	−	0.965393i	$-0.583986\pi$
$827$	−15.0000			−0.521601			−0.260801	+	0.965393i	$0.583986\pi$
$828$		0			0
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	−0.829202	−	0.558949i	$-0.811205\pi$
$829$	2.00000	−	3.46410i	0.0694629	−	0.120313i	0.898665	+	0.438636i	$0.144538\pi$
$830$		0			0
$831$	−4.00000	−	6.92820i	−0.138758	−	0.240337i
$832$	4.00000			0.138675
$833$		0			0
$834$	−2.00000			−0.0692543
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	−0.500000	+	0.866025i	−0.0172825	+	0.0299342i
$838$		0			0
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$		0			0
$846$	6.00000			0.206284
$847$	−4.00000	−	3.46410i	−0.137442	−	0.119028i
$848$	3.00000			0.103020
$849$	−7.00000	−	12.1244i	−0.240239	−	0.416107i
$850$		0			0
$851$		0			0
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	−5.00000	+	25.9808i	−0.171096	+	0.889043i
$855$		0			0
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	0.244701	+	0.969599i	$0.421310\pi$
$857$	−21.0000	+	36.3731i	−0.717346	+	1.24248i	−0.962048	+	0.272882i	$0.912023\pi$
$858$	6.00000	−	10.3923i	0.204837	−	0.354787i
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	−0.878498	−	0.477746i	$-0.841454\pi$
$859$	−25.0000	−	43.3013i	−0.852989	−	1.47742i	0.0255092	−	0.999675i	$-0.491879\pi$
$860$		0			0
$861$		0			0
$862$	12.0000			0.408722
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−17.0000	−	29.4449i	−0.577684	−	1.00058i
$867$	17.0000			0.577350
$868$	−2.00000	−	1.73205i	−0.0678844	−	0.0587896i
$869$	−3.00000			−0.101768
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	−0.500000	−	0.866025i	−0.0169224	−	0.0293105i
$874$		0			0
$875$		0			0
$876$	2.00000			0.0675737
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	0.998888	+	0.0471555i	$0.0150156\pi$
$877$	16.0000	+	27.7128i	0.540282	+	0.935795i	−0.458606	+	0.888640i	$0.651651\pi$
$878$	−17.5000	+	30.3109i	−0.590596	+	1.02294i
$879$	−16.5000	+	28.5788i	−0.556531	+	0.963940i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$	1.00000	+	6.92820i	0.0336718	+	0.233285i
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$		0			0
$885$		0			0
$886$	−16.5000	+	28.5788i	−0.554328	+	0.960125i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$	8.00000			0.268462
$889$	12.5000	−	4.33013i	0.419237	−	0.145228i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−9.50000	+	16.4545i	−0.318084	+	0.550937i
$893$	12.0000	−	20.7846i	0.401565	−	0.695530i
$894$	9.00000	+	15.5885i	0.301005	+	0.521356i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$		0			0
$898$	−6.00000	−	10.3923i	−0.200223	−	0.346796i
$899$	4.50000	−	7.79423i	0.150083	−	0.259952i
$900$		0			0
$901$		0			0
$902$		0			0
$903$	−5.00000	+	25.9808i	−0.166390	+	0.864586i
$904$		0			0
$905$		0			0
$906$	−0.500000	+	0.866025i	−0.0166114	+	0.0287718i
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$	−13.5000	−	23.3827i	−0.448013	−	0.775982i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−13.5000	+	23.3827i	−0.446785	+	0.773854i
$914$	−0.500000	+	0.866025i	−0.0165385	+	0.0286456i
$915$		0			0
$916$	−4.00000			−0.132164
$917$	−18.0000	−	15.5885i	−0.594412	−	0.514776i
$918$		0			0
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	0.792480	−	0.609898i	$-0.208790\pi$
$919$	−4.00000	−	6.92820i	−0.131948	−	0.228540i	−0.924427	+	0.381358i	$0.875456\pi$
$920$		0			0
$921$	−4.00000	+	6.92820i	−0.131804	+	0.228292i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	−24.0000			−0.789970
$924$	7.50000	−	2.59808i	0.246732	−	0.0854704i
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	0.911034	−	0.412332i	$-0.135286\pi$
$929$	3.00000	+	5.19615i	0.0984268	+	0.170480i	−0.812607	+	0.582812i	$0.801952\pi$
$930$		0			0
$931$	26.0000	+	10.3923i	0.852116	+	0.340594i
$932$	24.0000			0.786146
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$	18.0000	−	31.1769i	0.588978	−	1.02014i
$935$		0			0
$936$	−2.00000	−	3.46410i	−0.0653720	−	0.113228i
$937$	−35.0000			−1.14340			−0.571700	−	0.820463i	$-0.693716\pi$
$937$	−35.0000			−1.14340			−0.571700	+	0.820463i	$0.693716\pi$
$938$	−25.0000	+	8.66025i	−0.816279	+	0.282767i
$939$	−31.0000			−1.01165
$940$		0			0
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	−0.783309	−	0.621633i	$-0.786469\pi$
$941$	4.50000	−	7.79423i	0.146696	−	0.254085i	0.930004	+	0.367549i	$0.119803\pi$
$942$	2.00000	−	3.46410i	0.0651635	−	0.112867i
$943$		0			0
$944$	3.00000			0.0976417
$945$		0			0
$946$	30.0000			0.975384
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	−0.500000	+	0.866025i	−0.0162392	+	0.0281272i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$		0			0
$951$	9.00000			0.291845
$952$		0			0
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	−1.50000	−	2.59808i	−0.0485643	−	0.0841158i
$955$		0			0
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$	13.5000	+	23.3827i	0.436393	+	0.755855i
$958$	−18.0000			−0.581554
$959$	−9.00000	+	46.7654i	−0.290625	+	1.51013i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	16.0000	−	27.7128i	0.515861	−	0.893497i
$963$	−1.50000	+	2.59808i	−0.0483368	+	0.0837218i
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$		0			0
$966$		0			0
$967$	1.00000			0.0321578			0.0160789	−	0.999871i	$-0.494882\pi$
$967$	1.00000			0.0321578			0.0160789	+	0.999871i	$0.494882\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$		0			0
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	0.988389	+	0.151948i	$0.0485545\pi$
$971$	19.5000	+	33.7750i	0.625785	+	1.08389i	−0.362604	+	0.931943i	$0.618112\pi$
$972$	−1.00000			−0.0320750
$973$	−5.00000	+	1.73205i	−0.160293	+	0.0555270i
$974$	−41.0000			−1.31372
$975$		0			0
$976$	5.00000	−	8.66025i	0.160046	−	0.277208i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$	18.0000			0.575282
$980$		0			0
$981$	14.0000			0.446986
$982$	16.5000	+	28.5788i	0.526536	+	0.911987i
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	−0.422027	−	0.906583i	$-0.638681\pi$
$983$	18.0000	−	31.1769i	0.574111	−	0.994389i	0.996138	−	0.0878058i	$-0.0279855\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.0000	−	5.19615i	0.477455	−	0.165395i
$988$	−16.0000			−0.509028
$989$		0			0
$990$		0			0
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	−0.744124	−	0.668042i	$-0.767133\pi$
$991$	6.50000	−	11.2583i	0.206479	−	0.357633i	0.950603	+	0.310409i	$0.100466\pi$
$992$	0.500000	+	0.866025i	0.0158750	+	0.0274963i
$993$	−20.0000			−0.634681
$994$	−12.0000	−	10.3923i	−0.380617	−	0.329624i
$995$		0			0
$996$	4.50000	+	7.79423i	0.142588	+	0.246970i
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	−0.733630	−	0.679549i	$-0.762175\pi$
$997$	7.00000	−	12.1244i	0.221692	−	0.383982i	0.955322	+	0.295567i	$0.0955086\pi$
$998$	−1.00000	+	1.73205i	−0.0316544	+	0.0548271i
$999$	−4.00000	−	6.92820i	−0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.e.151.1		2
5.2	odd	4		1050.2.o.b.949.2		4
5.3	odd	4		1050.2.o.b.949.1		4
5.4	even	2		42.2.e.b.25.1	✓	2
7.2	even	3	inner	1050.2.i.e.751.1		2
7.3	odd	6		7350.2.a.cw.1.1		1
7.4	even	3		7350.2.a.ce.1.1		1
15.14	odd	2		126.2.g.b.109.1		2
20.19	odd	2		336.2.q.d.193.1		2
35.2	odd	12		1050.2.o.b.499.1		4
35.4	even	6		294.2.a.d.1.1		1
35.9	even	6		42.2.e.b.37.1	yes	2
35.19	odd	6		294.2.e.f.79.1		2
35.23	odd	12		1050.2.o.b.499.2		4
35.24	odd	6		294.2.a.a.1.1		1
35.34	odd	2		294.2.e.f.67.1		2
40.19	odd	2		1344.2.q.j.193.1		2
40.29	even	2		1344.2.q.v.193.1		2
45.4	even	6		1134.2.e.a.865.1		2
45.14	odd	6		1134.2.e.p.865.1		2
45.29	odd	6		1134.2.h.a.109.1		2
45.34	even	6		1134.2.h.p.109.1		2
60.59	even	2		1008.2.s.n.865.1		2
105.44	odd	6		126.2.g.b.37.1		2
105.59	even	6		882.2.a.k.1.1		1
105.74	odd	6		882.2.a.g.1.1		1
105.89	even	6		882.2.g.b.667.1		2
105.104	even	2		882.2.g.b.361.1		2
140.19	even	6		2352.2.q.m.961.1		2
140.39	odd	6		2352.2.a.m.1.1		1
140.59	even	6		2352.2.a.n.1.1		1
140.79	odd	6		336.2.q.d.289.1		2
140.139	even	2		2352.2.q.m.1537.1		2
280.59	even	6		9408.2.a.bm.1.1		1
280.109	even	6		9408.2.a.d.1.1		1
280.149	even	6		1344.2.q.v.961.1		2
280.179	odd	6		9408.2.a.bu.1.1		1
280.219	odd	6		1344.2.q.j.961.1		2
280.269	odd	6		9408.2.a.db.1.1		1
315.79	even	6		1134.2.e.a.919.1		2
315.149	odd	6		1134.2.h.a.541.1		2
315.184	even	6		1134.2.h.p.541.1		2
315.254	odd	6		1134.2.e.p.919.1		2
420.59	odd	6		7056.2.a.bz.1.1		1
420.179	even	6		7056.2.a.g.1.1		1
420.359	even	6		1008.2.s.n.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.e.b.25.1	✓	2	5.4	even	2
42.2.e.b.37.1	yes	2	35.9	even	6
126.2.g.b.37.1		2	105.44	odd	6
126.2.g.b.109.1		2	15.14	odd	2
294.2.a.a.1.1		1	35.24	odd	6
294.2.a.d.1.1		1	35.4	even	6
294.2.e.f.67.1		2	35.34	odd	2
294.2.e.f.79.1		2	35.19	odd	6
336.2.q.d.193.1		2	20.19	odd	2
336.2.q.d.289.1		2	140.79	odd	6
882.2.a.g.1.1		1	105.74	odd	6
882.2.a.k.1.1		1	105.59	even	6
882.2.g.b.361.1		2	105.104	even	2
882.2.g.b.667.1		2	105.89	even	6
1008.2.s.n.289.1		2	420.359	even	6
1008.2.s.n.865.1		2	60.59	even	2
1050.2.i.e.151.1		2	1.1	even	1	trivial
1050.2.i.e.751.1		2	7.2	even	3	inner
1050.2.o.b.499.1		4	35.2	odd	12
1050.2.o.b.499.2		4	35.23	odd	12
1050.2.o.b.949.1		4	5.3	odd	4
1050.2.o.b.949.2		4	5.2	odd	4
1134.2.e.a.865.1		2	45.4	even	6
1134.2.e.a.919.1		2	315.79	even	6
1134.2.e.p.865.1		2	45.14	odd	6
1134.2.e.p.919.1		2	315.254	odd	6
1134.2.h.a.109.1		2	45.29	odd	6
1134.2.h.a.541.1		2	315.149	odd	6
1134.2.h.p.109.1		2	45.34	even	6
1134.2.h.p.541.1		2	315.184	even	6
1344.2.q.j.193.1		2	40.19	odd	2
1344.2.q.j.961.1		2	280.219	odd	6
1344.2.q.v.193.1		2	40.29	even	2
1344.2.q.v.961.1		2	280.149	even	6
2352.2.a.m.1.1		1	140.39	odd	6
2352.2.a.n.1.1		1	140.59	even	6
2352.2.q.m.961.1		2	140.19	even	6
2352.2.q.m.1537.1		2	140.139	even	2
7056.2.a.g.1.1		1	420.179	even	6
7056.2.a.bz.1.1		1	420.59	odd	6
7350.2.a.ce.1.1		1	7.4	even	3
7350.2.a.cw.1.1		1	7.3	odd	6
9408.2.a.d.1.1		1	280.109	even	6
9408.2.a.bm.1.1		1	280.59	even	6
9408.2.a.bu.1.1		1	280.179	odd	6
9408.2.a.db.1.1		1	280.269	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +4.00000 q^{13} +(2.00000 + 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(2.00000 + 3.46410i) q^{19} +(-0.500000 + 2.59808i) q^{21} +3.00000 q^{22} +(0.500000 - 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +9.00000 q^{29} +(0.500000 - 0.866025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(2.00000 - 3.46410i) q^{38} +(2.00000 - 3.46410i) q^{39} +(2.50000 - 0.866025i) q^{42} +10.0000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-3.00000 - 5.19615i) q^{47} -1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 0.866025i) q^{56} +4.00000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(-1.50000 + 2.59808i) q^{59} +(5.00000 + 8.66025i) q^{61} -1.00000 q^{62} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(-5.00000 + 8.66025i) q^{67} -6.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} -4.00000 q^{76} +(1.50000 - 7.79423i) q^{77} -4.00000 q^{78} +(0.500000 + 0.866025i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.00000 q^{83} +(-2.00000 - 1.73205i) q^{84} +(-5.00000 - 8.66025i) q^{86} +(4.50000 - 7.79423i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(-0.500000 - 0.866025i) q^{93} +(-3.00000 + 5.19615i) q^{94} +(0.500000 + 0.866025i) q^{96} +1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 - 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + q^{12} + 8 q^{13} + 4 q^{14} - q^{16} - q^{18} + 4 q^{19} - q^{21} + 6 q^{22} + q^{24} - 4 q^{26} - 2 q^{27} + q^{28} + 18 q^{29} + q^{31} - q^{32} + 3 q^{33} + 2 q^{36} + 8 q^{37} + 4 q^{38} + 4 q^{39} + 5 q^{42} + 20 q^{43} - 3 q^{44} - 6 q^{47} - 2 q^{48} + 11 q^{49} - 4 q^{52} - 3 q^{53} + q^{54} - 5 q^{56} + 8 q^{57} - 9 q^{58} - 3 q^{59} + 10 q^{61} - 2 q^{62} + 4 q^{63} + 2 q^{64} + 3 q^{66} - 10 q^{67} - 12 q^{71} - q^{72} + 2 q^{73} + 8 q^{74} - 8 q^{76} + 3 q^{77} - 8 q^{78} + q^{79} - q^{81} + 18 q^{83} - 4 q^{84} - 10 q^{86} + 9 q^{87} - 3 q^{88} - 6 q^{89} - 20 q^{91} - q^{93} - 6 q^{94} + q^{96} + 2 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 - 5 * q^7 + 2 * q^8 - q^9 - 3 * q^11 + q^12 + 8 * q^13 + 4 * q^14 - q^16 - q^18 + 4 * q^19 - q^21 + 6 * q^22 + q^24 - 4 * q^26 - 2 * q^27 + q^28 + 18 * q^29 + q^31 - q^32 + 3 * q^33 + 2 * q^36 + 8 * q^37 + 4 * q^38 + 4 * q^39 + 5 * q^42 + 20 * q^43 - 3 * q^44 - 6 * q^47 - 2 * q^48 + 11 * q^49 - 4 * q^52 - 3 * q^53 + q^54 - 5 * q^56 + 8 * q^57 - 9 * q^58 - 3 * q^59 + 10 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 + 3 * q^66 - 10 * q^67 - 12 * q^71 - q^72 + 2 * q^73 + 8 * q^74 - 8 * q^76 + 3 * q^77 - 8 * q^78 + q^79 - q^81 + 18 * q^83 - 4 * q^84 - 10 * q^86 + 9 * q^87 - 3 * q^88 - 6 * q^89 - 20 * q^91 - q^93 - 6 * q^94 + q^96 + 2 * q^97 - 13 * q^98 + 6 * q^99

Introduction

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