LMFDB - Embedded newform 1050.2.i.i.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 210)
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.i.751.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} -5.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(-0.500000 - 2.59808i) q^{21} +3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} -1.00000 q^{27} +(0.500000 + 2.59808i) q^{28} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +1.00000 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-2.50000 + 4.33013i) q^{39} +9.00000 q^{41} +(-2.00000 + 1.73205i) q^{42} -8.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.00000 - 1.73205i) q^{56} -5.00000 q^{57} +(-6.00000 + 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} -10.0000 q^{62} +(-2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(4.00000 - 6.92820i) q^{67} -9.00000 q^{69} -6.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{74} +5.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +5.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(2.50000 + 0.866025i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} +9.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(1.50000 - 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + q^{12} - 10 q^{13} - 5 q^{14} - q^{16} - q^{18} - 5 q^{19} - q^{21} + 6 q^{22} - 9 q^{23} + q^{24} + 5 q^{26} - 2 q^{27} + q^{28} + 10 q^{31} - q^{32} + 3 q^{33} + 2 q^{36} - q^{37} - 5 q^{38} - 5 q^{39} + 18 q^{41} - 4 q^{42} - 16 q^{43} - 3 q^{44} - 9 q^{46} + 3 q^{47} - 2 q^{48} + 2 q^{49} + 5 q^{52} - 3 q^{53} + q^{54} + 4 q^{56} - 10 q^{57} - 12 q^{59} - 8 q^{61} - 20 q^{62} - 5 q^{63} + 2 q^{64} + 3 q^{66} + 8 q^{67} - 18 q^{69} - 12 q^{71} - q^{72} + 2 q^{73} - q^{74} + 10 q^{76} + 3 q^{77} + 10 q^{78} - 8 q^{79} - q^{81} - 9 q^{82} + 5 q^{84} + 8 q^{86} - 3 q^{88} - 6 q^{89} - 20 q^{91} + 18 q^{92} - 10 q^{93} + 3 q^{94} + q^{96} - 16 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9 - 3 * q^11 + q^12 - 10 * q^13 - 5 * q^14 - q^16 - q^18 - 5 * q^19 - q^21 + 6 * q^22 - 9 * q^23 + q^24 + 5 * q^26 - 2 * q^27 + q^28 + 10 * q^31 - q^32 + 3 * q^33 + 2 * q^36 - q^37 - 5 * q^38 - 5 * q^39 + 18 * q^41 - 4 * q^42 - 16 * q^43 - 3 * q^44 - 9 * q^46 + 3 * q^47 - 2 * q^48 + 2 * q^49 + 5 * q^52 - 3 * q^53 + q^54 + 4 * q^56 - 10 * q^57 - 12 * q^59 - 8 * q^61 - 20 * q^62 - 5 * q^63 + 2 * q^64 + 3 * q^66 + 8 * q^67 - 18 * q^69 - 12 * q^71 - q^72 + 2 * q^73 - q^74 + 10 * q^76 + 3 * q^77 + 10 * q^78 - 8 * q^79 - q^81 - 9 * q^82 + 5 * q^84 + 8 * q^86 - 3 * q^88 - 6 * q^89 - 20 * q^91 + 18 * q^92 - 10 * q^93 + 3 * q^94 + q^96 - 16 * 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
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$7$	2.00000	−	1.73205i	0.755929	−	0.654654i
$8$	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
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$	−2.50000	−	0.866025i	−0.668153	−	0.231455i
$15$		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
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$	−0.500000	−	2.59808i	−0.109109	−	0.566947i
$22$	3.00000			0.639602
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.768613	−	0.639713i	$-0.779053\pi$
$23$	−4.50000	−	7.79423i	−0.938315	−	1.62521i	−0.169701	−	0.985496i	$-0.554280\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−1.00000			−0.192450
$28$	0.500000	+	2.59808i	0.0944911	+	0.490990i
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	−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
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−2.50000	+	4.33013i	−0.405554	+	0.702439i
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$		0			0
$41$	9.00000			1.40556			0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000			1.40556			0.702782	+	0.711405i	$0.251941\pi$
$42$	−2.00000	+	1.73205i	−0.308607	+	0.267261i
$43$	−8.00000			−1.21999			−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000			−1.21999			−0.609994	+	0.792406i	$0.708828\pi$
$44$	−1.50000	−	2.59808i	−0.226134	−	0.391675i
$45$		0			0
$46$	−4.50000	+	7.79423i	−0.663489	+	1.14920i
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	0.954441	−	0.298401i	$-0.0964533\pi$
$47$	1.50000	+	2.59808i	0.218797	+	0.378968i	−0.735643	+	0.677369i	$0.763120\pi$
$48$	−1.00000			−0.144338
$49$	1.00000	−	6.92820i	0.142857	−	0.989743i
$50$		0			0
$51$		0			0
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−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
$56$	2.00000	−	1.73205i	0.267261	−	0.231455i
$57$	−5.00000			−0.662266
$58$		0			0
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−10.0000			−1.27000
$63$	−2.50000	−	0.866025i	−0.314970	−	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	1.50000	−	2.59808i	0.184637	−	0.319801i
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$		0			0
$69$	−9.00000			−1.08347
$70$		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	$0.129326\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		0			0
$76$	5.00000			0.573539
$77$	1.50000	+	7.79423i	0.170941	+	0.888235i
$78$	5.00000			0.566139
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.50000	−	7.79423i	−0.496942	−	0.860729i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	2.50000	+	0.866025i	0.272772	+	0.0944911i
$85$		0			0
$86$	4.00000	+	6.92820i	0.431331	+	0.747087i
$87$		0			0
$88$	−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	+	8.66025i	−1.04828	+	0.907841i
$92$	9.00000			0.938315
$93$	−5.00000	−	8.66025i	−0.518476	−	0.898027i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.00000			−0.812277			−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000			−0.812277			−0.406138	+	0.913812i	$0.633125\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$	3.00000			0.301511
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		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	$0.704379\pi$
$104$	−5.00000			−0.490290
$105$		0			0
$106$	3.00000			0.291386
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	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
$111$	−1.00000			−0.0949158
$112$	−2.50000	−	0.866025i	−0.236228	−	0.0818317i
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$		0			0
$116$		0			0
$117$	2.50000	+	4.33013i	0.231125	+	0.400320i
$118$	12.0000			1.10469
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.00000	+	6.92820i	−0.362143	+	0.627250i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$		0			0
$126$	0.500000	+	2.59808i	0.0445435	+	0.231455i
$127$	13.0000			1.15356			0.576782	−	0.816898i	$-0.304308\pi$
$127$	13.0000			1.15356			0.576782	+	0.816898i	$0.304308\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000	+	6.92820i	−0.352180	+	0.609994i
$130$		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
$133$	−12.5000	−	4.33013i	−1.08389	−	0.375470i
$134$	−8.00000			−0.691095
$135$		0			0
$136$		0			0
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	4.50000	+	7.79423i	0.383065	+	0.663489i
$139$	20.0000			1.69638			0.848189	−	0.529694i	$-0.177693\pi$
$139$	20.0000			1.69638			0.848189	+	0.529694i	$0.177693\pi$
$140$		0			0
$141$	3.00000			0.252646
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	7.50000	−	12.9904i	0.627182	−	1.08631i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−5.50000	−	4.33013i	−0.453632	−	0.357143i
$148$	1.00000			0.0821995
$149$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$149$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$		0			0
$154$	6.00000	−	5.19615i	0.483494	−	0.418718i
$155$		0			0
$156$	−2.50000	−	4.33013i	−0.200160	−	0.346688i
$157$	2.50000	−	4.33013i	0.199522	−	0.345582i	−0.748852	−	0.662738i	$-0.769394\pi$
$157$	2.50000	−	4.33013i	0.199522	−	0.345582i	0.948373	+	0.317156i	$0.102728\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−22.5000	−	7.79423i	−1.77325	−	0.614271i
$162$	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	$-0.382224\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$		0			0
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$	−0.500000	−	2.59808i	−0.0385758	−	0.200446i
$169$	12.0000			0.923077
$170$		0			0
$171$	−2.50000	+	4.33013i	−0.191180	+	0.331133i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	0.984828	−	0.173534i	$-0.0555188\pi$
$173$	4.50000	+	7.79423i	0.342129	+	0.592584i	−0.642699	+	0.766119i	$0.722185\pi$
$174$		0			0
$175$		0			0
$176$	3.00000			0.226134
$177$	6.00000	+	10.3923i	0.450988	+	0.781133i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	−0.436870	−	0.899525i	$-0.643913\pi$
$179$	7.50000	−	12.9904i	0.560576	−	0.970947i	0.997446	−	0.0714220i	$-0.0227537\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$	12.5000	+	4.33013i	0.926562	+	0.320970i
$183$	−8.00000			−0.591377
$184$	−4.50000	−	7.79423i	−0.331744	−	0.574598i
$185$		0			0
$186$	−5.00000	+	8.66025i	−0.366618	+	0.635001i
$187$		0			0
$188$	−3.00000			−0.218797
$189$	−2.00000	+	1.73205i	−0.145479	+	0.125988i
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	4.00000	+	6.92820i	0.287183	+	0.497416i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−15.0000			−1.06871			−0.534353	−	0.845262i	$-0.679445\pi$
$197$	−15.0000			−1.06871			−0.534353	+	0.845262i	$0.679445\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	−0.429745	−	0.902950i	$-0.641397\pi$
$199$	8.00000	−	13.8564i	0.567105	−	0.982255i	0.996850	−	0.0793045i	$-0.0252700\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$	4.00000	−	6.92820i	0.278693	−	0.482711i
$207$	−4.50000	+	7.79423i	−0.312772	+	0.541736i
$208$	2.50000	+	4.33013i	0.173344	+	0.300240i
$209$	15.0000			1.03757
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	−1.50000	−	2.59808i	−0.103020	−	0.178437i
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−5.00000	−	25.9808i	−0.339422	−	1.76369i
$218$	14.0000			0.948200
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$		0			0
$222$	0.500000	+	0.866025i	0.0335578	+	0.0581238i
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$	0.500000	+	2.59808i	0.0334077	+	0.173591i
$225$		0			0
$226$	−9.00000	−	15.5885i	−0.598671	−	1.03693i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	2.50000	−	4.33013i	0.165567	−	0.286770i
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	0.536515	−	0.843891i	$-0.319740\pi$
$229$	−7.00000	−	12.1244i	−0.462573	−	0.801200i	−0.999088	+	0.0426906i	$0.986407\pi$
$230$		0			0
$231$	7.50000	+	2.59808i	0.493464	+	0.170941i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$	2.50000	−	4.33013i	0.163430	−	0.283069i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−8.00000			−0.519656
$238$		0			0
$239$	30.0000			1.94054			0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000			1.94054			0.970269	+	0.242028i	$0.0778125\pi$
$240$		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
$244$	8.00000			0.512148
$245$		0			0
$246$	−9.00000			−0.573819
$247$	12.5000	+	21.6506i	0.795356	+	1.37760i
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$		0			0
$250$		0			0
$251$	9.00000			0.568075			0.284037	−	0.958813i	$-0.408326\pi$
$251$	9.00000			0.568075			0.284037	+	0.958813i	$0.408326\pi$
$252$	2.00000	−	1.73205i	0.125988	−	0.109109i
$253$	27.0000			1.69748
$254$	−6.50000	−	11.2583i	−0.407846	−	0.706410i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	0.615948	−	0.787787i	$-0.288773\pi$
$257$	−6.00000	−	10.3923i	−0.374270	−	0.648254i	−0.990217	+	0.139533i	$0.955440\pi$
$258$	8.00000			0.498058
$259$	−2.50000	−	0.866025i	−0.155342	−	0.0538122i
$260$		0			0
$261$		0			0
$262$	4.50000	−	7.79423i	0.278011	−	0.481529i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	2.50000	+	12.9904i	0.153285	+	0.796491i
$267$	−6.00000			−0.367194
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$		0			0
$273$	2.50000	+	12.9904i	0.151307	+	0.786214i
$274$	18.0000			1.08742
$275$		0			0
$276$	4.50000	−	7.79423i	0.270868	−	0.469157i
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	13.0000	−	22.5167i	0.781094	−	1.35290i	0.931305	−	0.364241i	$-0.118672\pi$
$278$	−10.0000	−	17.3205i	−0.599760	−	1.03882i
$279$	−10.0000			−0.598684
$280$		0			0
$281$	−21.0000			−1.25275			−0.626377	−	0.779520i	$-0.715463\pi$
$281$	−21.0000			−1.25275			−0.626377	+	0.779520i	$0.715463\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	0.328291	+	0.944577i	$0.393527\pi$
$283$	−11.0000	+	19.0526i	−0.653882	+	1.13256i	−0.982173	+	0.187980i	$0.939806\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−15.0000			−0.886969
$287$	18.0000	−	15.5885i	1.06251	−	0.920158i
$288$	1.00000			0.0589256
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	1.50000	−	2.59808i	0.0870388	−	0.150756i
$298$		0			0
$299$	22.5000	+	38.9711i	1.30121	+	2.25376i
$300$		0			0
$301$	−16.0000	+	13.8564i	−0.922225	+	0.798670i
$302$	−10.0000			−0.575435
$303$		0			0
$304$	−2.50000	+	4.33013i	−0.143385	+	0.248350i
$305$		0			0
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	−7.50000	−	2.59808i	−0.427352	−	0.148039i
$309$	8.00000			0.455104
$310$		0			0
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$	−2.50000	+	4.33013i	−0.141535	+	0.245145i
$313$	−2.00000	−	3.46410i	−0.113047	−	0.195803i	0.803951	−	0.594696i	$-0.202728\pi$
$313$	−2.00000	−	3.46410i	−0.113047	−	0.195803i	−0.916997	+	0.398894i	$0.869394\pi$
$314$	−5.00000			−0.282166
$315$		0			0
$316$	8.00000			0.450035
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	1.50000	−	2.59808i	0.0841158	−	0.145693i
$319$		0			0
$320$		0			0
$321$	6.00000			0.334887
$322$	4.50000	+	23.3827i	0.250775	+	1.30307i
$323$		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
$328$	9.00000			0.496942
$329$	7.50000	+	2.59808i	0.413488	+	0.143237i
$330$		0			0
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	0.674351	−	0.738411i	$-0.264424\pi$
$331$	−5.50000	−	9.52628i	−0.302307	−	0.523612i	−0.976658	+	0.214799i	$0.931090\pi$
$332$		0			0
$333$	−0.500000	+	0.866025i	−0.0273998	+	0.0474579i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$		0			0
$336$	−2.00000	+	1.73205i	−0.109109	+	0.0944911i
$337$	−20.0000			−1.08947			−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000			−1.08947			−0.544735	+	0.838608i	$0.683370\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	9.00000	−	15.5885i	0.488813	−	0.846649i
$340$		0			0
$341$	15.0000	+	25.9808i	0.812296	+	1.40694i
$342$	5.00000			0.270369
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	4.50000	−	7.79423i	0.241921	−	0.419020i
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	−0.110885	−	0.993833i	$-0.535369\pi$
$347$	15.0000	−	25.9808i	0.805242	−	1.39472i	0.916127	−	0.400887i	$-0.131298\pi$
$348$		0			0
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$		0			0
$351$	5.00000			0.266880
$352$	−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	$-0.0538590\pi$
$354$	6.00000	−	10.3923i	0.318896	−	0.552345i
$355$		0			0
$356$	6.00000			0.317999
$357$		0			0
$358$	−15.0000			−0.792775
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	0.663123	−	0.748511i	$-0.269231\pi$
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	−0.979791	+	0.200026i	$0.935897\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	2.00000			0.104973
$364$	−2.50000	−	12.9904i	−0.131036	−	0.680881i
$365$		0			0
$366$	4.00000	+	6.92820i	0.209083	+	0.362143i
$367$	−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	$0.331827\pi$
$368$	−4.50000	+	7.79423i	−0.234579	+	0.406302i
$369$	−4.50000	−	7.79423i	−0.234261	−	0.405751i
$370$		0			0
$371$	1.50000	+	7.79423i	0.0778761	+	0.404656i
$372$	10.0000			0.518476
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$		0			0
$375$		0			0
$376$	1.50000	+	2.59808i	0.0773566	+	0.133986i
$377$		0			0
$378$	2.50000	+	0.866025i	0.128586	+	0.0445435i
$379$	−19.0000			−0.975964			−0.487982	−	0.872854i	$-0.662267\pi$
$379$	−19.0000			−0.975964			−0.487982	+	0.872854i	$0.662267\pi$
$380$		0			0
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$	−9.00000	+	15.5885i	−0.460480	+	0.797575i
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	0.971897	+	0.235408i	$0.0756427\pi$
$383$	13.5000	+	23.3827i	0.689818	+	1.19480i	−0.282079	+	0.959391i	$0.591024\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	10.0000			0.508987
$387$	4.00000	+	6.92820i	0.203331	+	0.352180i
$388$	4.00000	−	6.92820i	0.203069	−	0.351726i
$389$	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
$392$	1.00000	−	6.92820i	0.0505076	−	0.349927i
$393$	9.00000			0.453990
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	0.986481	−	0.163876i	$-0.0523996\pi$
$397$	7.00000	+	12.1244i	0.351320	+	0.608504i	−0.635161	+	0.772380i	$0.719066\pi$
$398$	−16.0000			−0.802008
$399$	−10.0000	+	8.66025i	−0.500626	+	0.433555i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$	−4.00000	+	6.92820i	−0.199502	+	0.345547i
$403$	−25.0000	+	43.3013i	−1.24534	+	2.15699i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.00000			0.148704
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$		0			0
$411$	9.00000	+	15.5885i	0.443937	+	0.768922i
$412$	−8.00000			−0.394132
$413$	6.00000	+	31.1769i	0.295241	+	1.53412i
$414$	9.00000			0.442326
$415$		0			0
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$	10.0000	−	17.3205i	0.489702	−	0.848189i
$418$	−7.50000	−	12.9904i	−0.366837	−	0.635380i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		0			0
$421$	14.0000			0.682318			0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000			0.682318			0.341159	+	0.940006i	$0.389181\pi$
$422$	−2.50000	−	4.33013i	−0.121698	−	0.210787i
$423$	1.50000	−	2.59808i	0.0729325	−	0.126323i
$424$	−1.50000	+	2.59808i	−0.0728464	+	0.126174i
$425$		0			0
$426$	6.00000			0.290701
$427$	−20.0000	−	6.92820i	−0.967868	−	0.335279i
$428$	−6.00000			−0.290021
$429$	−7.50000	−	12.9904i	−0.362103	−	0.627182i
$430$		0			0
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	−0.417687	−	0.908591i	$-0.637159\pi$
$431$	12.0000	−	20.7846i	0.578020	−	1.00116i	0.995706	−	0.0925683i	$-0.0295076\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$	−20.0000	+	17.3205i	−0.960031	+	0.831411i
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−22.5000	+	38.9711i	−1.07632	+	1.86424i
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$		0			0
$441$	−6.50000	+	2.59808i	−0.309524	+	0.123718i
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$	0.500000	−	0.866025i	0.0237289	−	0.0410997i
$445$		0			0
$446$	−14.0000	−	24.2487i	−0.662919	−	1.14821i
$447$		0			0
$448$	2.00000	−	1.73205i	0.0944911	−	0.0818317i
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	−13.5000	+	23.3827i	−0.635690	+	1.10105i
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$	−5.00000	−	8.66025i	−0.234920	−	0.406894i
$454$		0			0
$455$		0			0
$456$	−5.00000			−0.234146
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$		0			0
$460$		0			0
$461$	12.0000			0.558896			0.279448	−	0.960161i	$-0.409849\pi$
$461$	12.0000			0.558896			0.279448	+	0.960161i	$0.409849\pi$
$462$	−1.50000	−	7.79423i	−0.0697863	−	0.362620i
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$		0			0
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$467$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$468$	−5.00000			−0.231125
$469$	−4.00000	−	20.7846i	−0.184703	−	0.959744i
$470$		0			0
$471$	−2.50000	−	4.33013i	−0.115194	−	0.199522i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	12.0000	−	20.7846i	0.551761	−	0.955677i
$474$	4.00000	+	6.92820i	0.183726	+	0.318223i
$475$		0			0
$476$		0			0
$477$	3.00000			0.137361
$478$	−15.0000	−	25.9808i	−0.686084	−	1.18833i
$479$	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
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$	−1.00000			−0.0455488
$483$	−18.0000	+	15.5885i	−0.819028	+	0.709299i
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−20.0000	+	34.6410i	−0.906287	+	1.56973i	−0.0871056	+	0.996199i	$0.527762\pi$
$487$	−20.0000	+	34.6410i	−0.906287	+	1.56973i	−0.819181	+	0.573535i	$0.805572\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	4.50000	+	7.79423i	0.202876	+	0.351391i
$493$		0			0
$494$	12.5000	−	21.6506i	0.562402	−	0.974108i
$495$		0			0
$496$	−10.0000			−0.449013
$497$	−12.0000	+	10.3923i	−0.538274	+	0.466159i
$498$		0			0
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	0.987648	−	0.156687i	$-0.0500814\pi$
$499$	8.00000	+	13.8564i	0.358129	+	0.620298i	−0.629519	+	0.776985i	$0.716748\pi$
$500$		0			0
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$	−4.50000	−	7.79423i	−0.200845	−	0.347873i
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$	−2.50000	−	0.866025i	−0.111359	−	0.0385758i
$505$		0			0
$506$	−13.5000	−	23.3827i	−0.600148	−	1.03949i
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	−6.50000	+	11.2583i	−0.288391	+	0.499508i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	−1.00000	−	5.19615i	−0.0442374	−	0.229864i
$512$	1.00000			0.0441942
$513$	2.50000	+	4.33013i	0.110378	+	0.191180i
$514$	−6.00000	+	10.3923i	−0.264649	+	0.458385i
$515$		0			0
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	−9.00000			−0.395820
$518$	0.500000	+	2.59808i	0.0219687	+	0.114153i
$519$	9.00000			0.395056
$520$		0			0
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	0.402592	+	0.915379i	$0.368109\pi$
$521$	−13.5000	+	23.3827i	−0.591446	+	1.02441i	−0.994038	+	0.109035i	$0.965224\pi$
$522$		0			0
$523$	−11.0000	−	19.0526i	−0.480996	−	0.833110i	0.518766	−	0.854916i	$-0.326392\pi$
$523$	−11.0000	−	19.0526i	−0.480996	−	0.833110i	−0.999762	+	0.0218062i	$0.993058\pi$
$524$	−9.00000			−0.393167
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	1.50000	−	2.59808i	0.0652791	−	0.113067i
$529$	−29.0000	+	50.2295i	−1.26087	+	2.18389i
$530$		0			0
$531$	12.0000			0.520756
$532$	10.0000	−	8.66025i	0.433555	−	0.375470i
$533$	−45.0000			−1.94917
$534$	3.00000	+	5.19615i	0.129823	+	0.224860i
$535$		0			0
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$	−7.50000	−	12.9904i	−0.323649	−	0.560576i
$538$	12.0000			0.517357
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$	4.00000	−	6.92820i	0.171656	−	0.297318i
$544$		0			0
$545$		0			0
$546$	10.0000	−	8.66025i	0.427960	−	0.370625i
$547$	−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
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$		0			0
$552$	−9.00000			−0.383065
$553$	−20.0000	−	6.92820i	−0.850487	−	0.294617i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	−10.0000	+	17.3205i	−0.424094	+	0.734553i
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$	5.00000	+	8.66025i	0.211667	+	0.366618i
$559$	40.0000			1.69182
$560$		0			0
$561$		0			0
$562$	10.5000	+	18.1865i	0.442916	+	0.767153i
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	−0.922293	−	0.386492i	$-0.873687\pi$
$563$	−3.00000	+	5.19615i	−0.126435	+	0.218992i	0.795858	+	0.605483i	$0.207020\pi$
$564$	−1.50000	+	2.59808i	−0.0631614	+	0.109399i
$565$		0			0
$566$	22.0000			0.924729
$567$	0.500000	+	2.59808i	0.0209980	+	0.109109i
$568$	−6.00000			−0.251754
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	−0.996961	−	0.0779066i	$-0.975176\pi$
$569$	−13.5000	−	23.3827i	−0.565949	−	0.980253i	0.431011	−	0.902347i	$-0.358157\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	7.50000	+	12.9904i	0.313591	+	0.543155i
$573$	−18.0000			−0.751961
$574$	−22.5000	−	7.79423i	−0.939132	−	0.325325i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	−0.998852	−	0.0479084i	$-0.984744\pi$
$577$	−11.0000	+	19.0526i	−0.457936	+	0.793168i	0.540916	+	0.841077i	$0.318078\pi$
$578$	8.50000	−	14.7224i	0.353553	−	0.612372i
$579$	5.00000	+	8.66025i	0.207793	+	0.359908i
$580$		0			0
$581$		0			0
$582$	8.00000			0.331611
$583$	−4.50000	−	7.79423i	−0.186371	−	0.322804i
$584$	1.00000	−	1.73205i	0.0413803	−	0.0716728i
$585$		0			0
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$	6.50000	−	2.59808i	0.268055	−	0.107143i
$589$	−50.0000			−2.06021
$590$		0			0
$591$	−7.50000	+	12.9904i	−0.308509	+	0.534353i
$592$	−0.500000	+	0.866025i	−0.0205499	+	0.0355934i
$593$	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
$596$		0			0
$597$	−8.00000	−	13.8564i	−0.327418	−	0.567105i
$598$	22.5000	−	38.9711i	0.920093	−	1.59365i
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	20.0000	+	6.92820i	0.815139	+	0.282372i
$603$	−8.00000			−0.325785
$604$	5.00000	+	8.66025i	0.203447	+	0.352381i
$605$		0			0
$606$		0			0
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	−0.999964	−	0.00851879i	$-0.997288\pi$
$607$	−12.5000	−	21.6506i	−0.507359	−	0.878772i	0.492604	−	0.870253i	$-0.336045\pi$
$608$	5.00000			0.202777
$609$		0			0
$610$		0			0
$611$	−7.50000	−	12.9904i	−0.303418	−	0.525535i
$612$		0			0
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	−0.733316	−	0.679888i	$-0.762028\pi$
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	0.955458	+	0.295126i	$0.0953615\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	1.50000	+	7.79423i	0.0604367	+	0.314038i
$617$	−12.0000			−0.483102			−0.241551	−	0.970388i	$-0.577656\pi$
$617$	−12.0000			−0.483102			−0.241551	+	0.970388i	$0.577656\pi$
$618$	−4.00000	−	6.92820i	−0.160904	−	0.278693i
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	0.412341	+	0.911030i	$0.364711\pi$
$619$	−14.5000	+	25.1147i	−0.582804	+	1.00945i	−0.995145	+	0.0984169i	$0.968622\pi$
$620$		0			0
$621$	4.50000	+	7.79423i	0.180579	+	0.312772i
$622$	−12.0000			−0.481156
$623$	−15.0000	−	5.19615i	−0.600962	−	0.208179i
$624$	5.00000			0.200160
$625$		0			0
$626$	−2.00000	+	3.46410i	−0.0799361	+	0.138453i
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$	2.50000	+	4.33013i	0.0997609	+	0.172791i
$629$		0			0
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	2.50000	−	4.33013i	0.0993661	−	0.172107i
$634$	−9.00000	+	15.5885i	−0.357436	+	0.619097i
$635$		0			0
$636$	−3.00000			−0.118958
$637$	−5.00000	+	34.6410i	−0.198107	+	1.37253i
$638$		0			0
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$	−3.00000	−	5.19615i	−0.118401	−	0.205076i
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$	18.0000	−	15.5885i	0.709299	−	0.614271i
$645$		0			0
$646$		0			0
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	−0.940822	−	0.338902i	$-0.889945\pi$
$647$	−4.50000	+	7.79423i	−0.176913	+	0.306423i	0.763908	+	0.645325i	$0.223278\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−18.0000	−	31.1769i	−0.706562	−	1.22380i
$650$		0			0
$651$	−25.0000	−	8.66025i	−0.979827	−	0.339422i
$652$	16.0000			0.626608
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$	−2.00000			−0.0780274
$658$	−1.50000	−	7.79423i	−0.0584761	−	0.303851i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	−0.155235	−	0.987878i	$-0.549613\pi$
$661$	20.0000	−	34.6410i	0.777910	−	1.34738i	0.933144	−	0.359502i	$-0.117053\pi$
$662$	−5.50000	+	9.52628i	−0.213764	+	0.370249i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.00000			0.0387492
$667$		0			0
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$	14.0000	−	24.2487i	0.541271	−	0.937509i
$670$		0			0
$671$	24.0000			0.926510
$672$	2.50000	+	0.866025i	0.0964396	+	0.0334077i
$673$	−20.0000			−0.770943			−0.385472	−	0.922720i	$-0.625961\pi$
$673$	−20.0000			−0.770943			−0.385472	+	0.922720i	$0.625961\pi$
$674$	10.0000	+	17.3205i	0.385186	+	0.667161i
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	0.893410	−	0.449242i	$-0.148306\pi$
$677$	1.50000	+	2.59808i	0.0576497	+	0.0998522i	−0.835760	+	0.549095i	$0.814973\pi$
$678$	−18.0000			−0.691286
$679$	−16.0000	+	13.8564i	−0.614024	+	0.531760i
$680$		0			0
$681$		0			0
$682$	15.0000	−	25.9808i	0.574380	−	0.994855i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	−2.50000	−	4.33013i	−0.0955899	−	0.165567i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−14.0000			−0.534133
$688$	4.00000	+	6.92820i	0.152499	+	0.264135i
$689$	7.50000	−	12.9904i	0.285727	−	0.494894i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−9.00000			−0.342129
$693$	6.00000	−	5.19615i	0.227921	−	0.197386i
$694$	−30.0000			−1.13878
$695$		0			0
$696$		0			0
$697$		0			0
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$	−2.50000	−	4.33013i	−0.0943564	−	0.163430i
$703$	−2.50000	+	4.33013i	−0.0942893	+	0.163314i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	−24.0000			−0.903252
$707$		0			0
$708$	−12.0000			−0.450988
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$	−90.0000			−3.37053
$714$		0			0
$715$		0			0
$716$	7.50000	+	12.9904i	0.280288	+	0.485473i
$717$	15.0000	−	25.9808i	0.560185	−	0.970269i
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	0.647965	−	0.761670i	$-0.275620\pi$
$719$	−9.00000	−	15.5885i	−0.335643	−	0.581351i	−0.983608	+	0.180319i	$0.942287\pi$
$720$		0			0
$721$	20.0000	+	6.92820i	0.744839	+	0.258020i
$722$	6.00000			0.223297
$723$	−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
$727$	−23.0000			−0.853023			−0.426511	−	0.904482i	$-0.640258\pi$
$727$	−23.0000			−0.853023			−0.426511	+	0.904482i	$0.640258\pi$
$728$	−10.0000	+	8.66025i	−0.370625	+	0.320970i
$729$	1.00000			0.0370370
$730$		0			0
$731$		0			0
$732$	4.00000	−	6.92820i	0.147844	−	0.256074i
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	0.856644	−	0.515908i	$-0.172546\pi$
$733$	−0.500000	−	0.866025i	−0.0184679	−	0.0319874i	−0.875112	+	0.483921i	$0.839212\pi$
$734$	19.0000			0.701303
$735$		0			0
$736$	9.00000			0.331744
$737$	12.0000	+	20.7846i	0.442026	+	0.765611i
$738$	−4.50000	+	7.79423i	−0.165647	+	0.286910i
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	−0.908337	−	0.418238i	$-0.862648\pi$
$739$	−2.50000	+	4.33013i	−0.0919640	+	0.159286i	0.816373	+	0.577524i	$0.195981\pi$
$740$		0			0
$741$	25.0000			0.918398
$742$	6.00000	−	5.19615i	0.220267	−	0.190757i
$743$	39.0000			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$744$	−5.00000	−	8.66025i	−0.183309	−	0.317500i
$745$		0			0
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$		0			0
$748$		0			0
$749$	15.0000	+	5.19615i	0.548088	+	0.189863i
$750$		0			0
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	0.847203	−	0.531269i	$-0.178285\pi$
$751$	−1.00000	−	1.73205i	−0.0364905	−	0.0632034i	−0.883694	+	0.468065i	$0.844951\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	4.50000	−	7.79423i	0.163989	−	0.284037i
$754$		0			0
$755$		0			0
$756$	−0.500000	−	2.59808i	−0.0181848	−	0.0944911i
$757$	−2.00000			−0.0726912			−0.0363456	−	0.999339i	$-0.511572\pi$
$757$	−2.00000			−0.0726912			−0.0363456	+	0.999339i	$0.511572\pi$
$758$	9.50000	+	16.4545i	0.345056	+	0.597654i
$759$	13.5000	−	23.3827i	0.490019	−	0.848738i
$760$		0			0
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	0.993098	+	0.117289i	$0.0374205\pi$
$761$	16.5000	+	28.5788i	0.598125	+	1.03598i	−0.394973	+	0.918693i	$0.629246\pi$
$762$	−13.0000			−0.470940
$763$	7.00000	+	36.3731i	0.253417	+	1.31679i
$764$	18.0000			0.651217
$765$		0			0
$766$	13.5000	−	23.3827i	0.487775	−	0.844851i
$767$	30.0000	−	51.9615i	1.08324	−	1.87622i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	35.0000			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$769$	35.0000			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	−0.400298	−	0.916385i	$-0.631093\pi$
$773$	16.5000	−	28.5788i	0.593464	−	1.02791i	0.993762	−	0.111524i	$-0.0355733\pi$
$774$	4.00000	−	6.92820i	0.143777	−	0.249029i
$775$		0			0
$776$	−8.00000			−0.287183
$777$	−2.00000	+	1.73205i	−0.0717496	+	0.0621370i
$778$	−6.00000			−0.215110
$779$	−22.5000	−	38.9711i	−0.806146	−	1.39629i
$780$		0			0
$781$	9.00000	−	15.5885i	0.322045	−	0.557799i
$782$		0			0
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$		0			0
$786$	−4.50000	−	7.79423i	−0.160510	−	0.278011i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	7.50000	−	12.9904i	0.267176	−	0.462763i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$		0			0
$791$	36.0000	−	31.1769i	1.28001	−	1.10852i
$792$	3.00000			0.106600
$793$	20.0000	+	34.6410i	0.710221	+	1.23014i
$794$	7.00000	−	12.1244i	0.248421	−	0.430277i
$795$		0			0
$796$	8.00000	+	13.8564i	0.283552	+	0.491127i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$	12.5000	+	4.33013i	0.442495	+	0.153285i
$799$		0			0
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	−7.50000	+	12.9904i	−0.264834	+	0.458706i
$803$	3.00000	+	5.19615i	0.105868	+	0.183368i
$804$	8.00000			0.282138
$805$		0			0
$806$	50.0000			1.76117
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$		0			0
$809$	13.5000	−	23.3827i	0.474635	−	0.822091i	−0.524943	−	0.851137i	$-0.675914\pi$
$809$	13.5000	−	23.3827i	0.474635	−	0.822091i	0.999578	+	0.0290457i	$0.00924684\pi$
$810$		0			0
$811$	−7.00000			−0.245803			−0.122902	−	0.992419i	$-0.539220\pi$
$811$	−7.00000			−0.245803			−0.122902	+	0.992419i	$0.539220\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$	−1.50000	−	2.59808i	−0.0525750	−	0.0910625i
$815$		0			0
$816$		0			0
$817$	20.0000	+	34.6410i	0.699711	+	1.21194i
$818$	2.00000			0.0699284
$819$	12.5000	+	4.33013i	0.436785	+	0.151307i
$820$		0			0
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$	9.00000	−	15.5885i	0.313911	−	0.543710i
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	−0.439961	−	0.898017i	$-0.645008\pi$
$823$	16.0000	−	27.7128i	0.557725	−	0.966008i	0.997686	−	0.0679910i	$-0.0216589\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	24.0000	−	20.7846i	0.835067	−	0.723189i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	−4.50000	−	7.79423i	−0.156386	−	0.270868i
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	−0.275677	−	0.961250i	$-0.588902\pi$
$829$	20.0000	−	34.6410i	0.694629	−	1.20313i	0.970306	−	0.241882i	$-0.0777647\pi$
$830$		0			0
$831$	−13.0000	−	22.5167i	−0.450965	−	0.781094i
$832$	−5.00000			−0.173344
$833$		0			0
$834$	−20.0000			−0.692543
$835$		0			0
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	−5.00000	+	8.66025i	−0.172825	+	0.299342i
$838$	4.50000	+	7.79423i	0.155450	+	0.269247i
$839$	−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
$841$	−29.0000			−1.00000
$842$	−7.00000	−	12.1244i	−0.241236	−	0.417833i
$843$	−10.5000	+	18.1865i	−0.361639	+	0.626377i
$844$	−2.50000	+	4.33013i	−0.0860535	+	0.149049i
$845$		0			0
$846$	−3.00000			−0.103142
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$	3.00000			0.103020
$849$	11.0000	+	19.0526i	0.377519	+	0.653882i
$850$		0			0
$851$	−4.50000	+	7.79423i	−0.154258	+	0.267183i
$852$	−3.00000	−	5.19615i	−0.102778	−	0.178017i
$853$	37.0000			1.26686			0.633428	−	0.773802i	$-0.281647\pi$
$853$	37.0000			1.26686			0.633428	+	0.773802i	$0.281647\pi$
$854$	4.00000	+	20.7846i	0.136877	+	0.711235i
$855$		0			0
$856$	3.00000	+	5.19615i	0.102538	+	0.177601i
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	−0.912705	−	0.408619i	$-0.866010\pi$
$857$	−3.00000	+	5.19615i	−0.102478	+	0.177497i	0.810227	+	0.586116i	$0.199344\pi$
$858$	−7.50000	+	12.9904i	−0.256046	+	0.443484i
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	0.898126	−	0.439738i	$-0.144929\pi$
$859$	2.00000	+	3.46410i	0.0682391	+	0.118194i	−0.829887	+	0.557931i	$0.811595\pi$
$860$		0			0
$861$	−4.50000	−	23.3827i	−0.153360	−	0.796880i
$862$	−24.0000			−0.817443
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	0.630106	−	0.776509i	$-0.283012\pi$
$863$	−10.5000	−	18.1865i	−0.357424	−	0.619077i	−0.987530	+	0.157433i	$0.949678\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−8.00000	−	13.8564i	−0.271851	−	0.470860i
$867$	17.0000			0.577350
$868$	25.0000	+	8.66025i	0.848555	+	0.293948i
$869$	24.0000			0.814144
$870$		0			0
$871$	−20.0000	+	34.6410i	−0.677674	+	1.17377i
$872$	−7.00000	+	12.1244i	−0.237050	+	0.410582i
$873$	4.00000	+	6.92820i	0.135379	+	0.234484i
$874$	45.0000			1.52215
$875$		0			0
$876$	2.00000			0.0675737
$877$	2.50000	+	4.33013i	0.0844190	+	0.146218i	0.905143	−	0.425106i	$-0.139763\pi$
$877$	2.50000	+	4.33013i	0.0844190	+	0.146218i	−0.820724	+	0.571324i	$0.806430\pi$
$878$	−4.00000	+	6.92820i	−0.134993	+	0.233816i
$879$	10.5000	−	18.1865i	0.354156	−	0.613417i
$880$		0			0
$881$	−33.0000			−1.11180			−0.555899	−	0.831250i	$-0.687626\pi$
$881$	−33.0000			−1.11180			−0.555899	+	0.831250i	$0.687626\pi$
$882$	5.50000	+	4.33013i	0.185195	+	0.145803i
$883$	−14.0000			−0.471138			−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000			−0.471138			−0.235569	+	0.971858i	$0.575695\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	0.948999	−	0.315279i	$-0.102098\pi$
$887$	6.00000	+	10.3923i	0.201460	+	0.348939i	−0.747539	+	0.664218i	$0.768765\pi$
$888$	−1.00000			−0.0335578
$889$	26.0000	−	22.5167i	0.872012	−	0.755185i
$890$		0			0
$891$	−1.50000	−	2.59808i	−0.0502519	−	0.0870388i
$892$	−14.0000	+	24.2487i	−0.468755	+	0.811907i
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$		0			0
$895$		0			0
$896$	−2.50000	−	0.866025i	−0.0835191	−	0.0289319i
$897$	45.0000			1.50251
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$		0			0
$900$		0			0
$901$		0			0
$902$	27.0000			0.899002
$903$	4.00000	+	20.7846i	0.133112	+	0.691669i
$904$	18.0000			0.598671
$905$		0			0
$906$	−5.00000	+	8.66025i	−0.166114	+	0.287718i
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	2.50000	+	4.33013i	0.0827833	+	0.143385i
$913$		0			0
$914$	−5.00000	+	8.66025i	−0.165385	+	0.286456i
$915$		0			0
$916$	14.0000			0.462573
$917$	22.5000	+	7.79423i	0.743015	+	0.257388i
$918$		0			0
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	0.999052	−	0.0435419i	$-0.0138642\pi$
$919$	14.0000	+	24.2487i	0.461817	+	0.799891i	−0.537234	+	0.843433i	$0.680531\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	−6.00000	−	10.3923i	−0.197599	−	0.342252i
$923$	30.0000			0.987462
$924$	−6.00000	+	5.19615i	−0.197386	+	0.170941i
$925$		0			0
$926$	−0.500000	−	0.866025i	−0.0164310	−	0.0284594i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$		0			0
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$		0			0
$931$	−32.5000	+	12.9904i	−1.06514	+	0.425743i
$932$	6.00000			0.196537
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$		0			0
$935$		0			0
$936$	2.50000	+	4.33013i	0.0817151	+	0.141535i
$937$	−44.0000			−1.43742			−0.718709	−	0.695311i	$-0.755266\pi$
$937$	−44.0000			−1.43742			−0.718709	+	0.695311i	$0.755266\pi$
$938$	−16.0000	+	13.8564i	−0.522419	+	0.452428i
$939$	−4.00000			−0.130535
$940$		0			0
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	−0.681218	−	0.732081i	$-0.738549\pi$
$941$	9.00000	−	15.5885i	0.293392	−	0.508169i	0.974609	+	0.223912i	$0.0718827\pi$
$942$	−2.50000	+	4.33013i	−0.0814544	+	0.141083i
$943$	−40.5000	−	70.1481i	−1.31886	−	2.28434i
$944$	12.0000			0.390567
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$	4.00000	−	6.92820i	0.129914	−	0.225018i
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		0			0
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$	−1.50000	−	2.59808i	−0.0485643	−	0.0841158i
$955$		0			0
$956$	−15.0000	+	25.9808i	−0.485135	+	0.840278i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	9.00000	+	46.7654i	0.290625	+	1.51013i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	2.50000	−	4.33013i	0.0806032	−	0.139609i
$963$	3.00000	−	5.19615i	0.0966736	−	0.167444i
$964$	0.500000	+	0.866025i	0.0161039	+	0.0278928i
$965$		0			0
$966$	22.5000	+	7.79423i	0.723926	+	0.250775i
$967$	28.0000			0.900419			0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000			0.900419			0.450210	+	0.892923i	$0.351349\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$		0			0
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$	−1.00000			−0.0320750
$973$	40.0000	−	34.6410i	1.28234	−	1.11054i
$974$	40.0000			1.28168
$975$		0			0
$976$	−4.00000	+	6.92820i	−0.128037	+	0.221766i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$	18.0000			0.575282
$980$		0			0
$981$	14.0000			0.446986
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	−0.785295	−	0.619122i	$-0.787489\pi$
$983$	4.50000	−	7.79423i	0.143528	−	0.248597i	0.928823	+	0.370525i	$0.120822\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$		0			0
$986$		0			0
$987$	6.00000	−	5.19615i	0.190982	−	0.165395i
$988$	−25.0000			−0.795356
$989$	36.0000	+	62.3538i	1.14473	+	1.98274i
$990$		0			0
$991$	29.0000	−	50.2295i	0.921215	−	1.59559i	0.123678	−	0.992322i	$-0.460531\pi$
$991$	29.0000	−	50.2295i	0.921215	−	1.59559i	0.797537	−	0.603269i	$-0.206136\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$	−11.0000			−0.349074
$994$	15.0000	+	5.19615i	0.475771	+	0.164812i
$995$		0			0
$996$		0			0
$997$	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	$0.0955086\pi$
$998$	8.00000	−	13.8564i	0.253236	−	0.438617i
$999$	0.500000	+	0.866025i	0.0158193	+	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.i.i.151.1		2
5.2	odd	4		1050.2.o.c.949.2		4
5.3	odd	4		1050.2.o.c.949.1		4
5.4	even	2		210.2.i.c.151.1	yes	2
7.2	even	3	inner	1050.2.i.i.751.1		2
7.3	odd	6		7350.2.a.cx.1.1		1
7.4	even	3		7350.2.a.cd.1.1		1
15.14	odd	2		630.2.k.a.361.1		2
20.19	odd	2		1680.2.bg.n.1201.1		2
35.2	odd	12		1050.2.o.c.499.1		4
35.4	even	6		1470.2.a.f.1.1		1
35.9	even	6		210.2.i.c.121.1	✓	2
35.19	odd	6		1470.2.i.p.961.1		2
35.23	odd	12		1050.2.o.c.499.2		4
35.24	odd	6		1470.2.a.e.1.1		1
35.34	odd	2		1470.2.i.p.361.1		2
105.44	odd	6		630.2.k.a.541.1		2
105.59	even	6		4410.2.a.w.1.1		1
105.74	odd	6		4410.2.a.bh.1.1		1
140.79	odd	6		1680.2.bg.n.961.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.i.c.121.1	✓	2	35.9	even	6
210.2.i.c.151.1	yes	2	5.4	even	2
630.2.k.a.361.1		2	15.14	odd	2
630.2.k.a.541.1		2	105.44	odd	6
1050.2.i.i.151.1		2	1.1	even	1	trivial
1050.2.i.i.751.1		2	7.2	even	3	inner
1050.2.o.c.499.1		4	35.2	odd	12
1050.2.o.c.499.2		4	35.23	odd	12
1050.2.o.c.949.1		4	5.3	odd	4
1050.2.o.c.949.2		4	5.2	odd	4
1470.2.a.e.1.1		1	35.24	odd	6
1470.2.a.f.1.1		1	35.4	even	6
1470.2.i.p.361.1		2	35.34	odd	2
1470.2.i.p.961.1		2	35.19	odd	6
1680.2.bg.n.961.1		2	140.79	odd	6
1680.2.bg.n.1201.1		2	20.19	odd	2
4410.2.a.w.1.1		1	105.59	even	6
4410.2.a.bh.1.1		1	105.74	odd	6
7350.2.a.cd.1.1		1	7.4	even	3
7350.2.a.cx.1.1		1	7.3	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.00000 q^{6} +(2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} -5.00000 q^{13} +(-2.50000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{18} +(-2.50000 - 4.33013i) q^{19} +(-0.500000 - 2.59808i) q^{21} +3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{26} -1.00000 q^{27} +(0.500000 + 2.59808i) q^{28} +(5.00000 - 8.66025i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.50000 + 2.59808i) q^{33} +1.00000 q^{36} +(-0.500000 - 0.866025i) q^{37} +(-2.50000 + 4.33013i) q^{38} +(-2.50000 + 4.33013i) q^{39} +9.00000 q^{41} +(-2.00000 + 1.73205i) q^{42} -8.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(-4.50000 + 7.79423i) q^{46} +(1.50000 + 2.59808i) q^{47} -1.00000 q^{48} +(1.00000 - 6.92820i) q^{49} +(2.50000 - 4.33013i) q^{52} +(-1.50000 + 2.59808i) q^{53} +(0.500000 + 0.866025i) q^{54} +(2.00000 - 1.73205i) q^{56} -5.00000 q^{57} +(-6.00000 + 10.3923i) q^{59} +(-4.00000 - 6.92820i) q^{61} -10.0000 q^{62} +(-2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{66} +(4.00000 - 6.92820i) q^{67} -9.00000 q^{69} -6.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{74} +5.00000 q^{76} +(1.50000 + 7.79423i) q^{77} +5.00000 q^{78} +(-4.00000 - 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-4.50000 - 7.79423i) q^{82} +(2.50000 + 0.866025i) q^{84} +(4.00000 + 6.92820i) q^{86} +(-1.50000 + 2.59808i) q^{88} +(-3.00000 - 5.19615i) q^{89} +(-10.0000 + 8.66025i) q^{91} +9.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(1.50000 - 2.59808i) q^{94} +(0.500000 + 0.866025i) q^{96} -8.00000 q^{97} +(-6.50000 + 2.59808i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 4 q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + q^{12} - 10 q^{13} - 5 q^{14} - q^{16} - q^{18} - 5 q^{19} - q^{21} + 6 q^{22} - 9 q^{23} + q^{24} + 5 q^{26} - 2 q^{27} + q^{28} + 10 q^{31} - q^{32} + 3 q^{33} + 2 q^{36} - q^{37} - 5 q^{38} - 5 q^{39} + 18 q^{41} - 4 q^{42} - 16 q^{43} - 3 q^{44} - 9 q^{46} + 3 q^{47} - 2 q^{48} + 2 q^{49} + 5 q^{52} - 3 q^{53} + q^{54} + 4 q^{56} - 10 q^{57} - 12 q^{59} - 8 q^{61} - 20 q^{62} - 5 q^{63} + 2 q^{64} + 3 q^{66} + 8 q^{67} - 18 q^{69} - 12 q^{71} - q^{72} + 2 q^{73} - q^{74} + 10 q^{76} + 3 q^{77} + 10 q^{78} - 8 q^{79} - q^{81} - 9 q^{82} + 5 q^{84} + 8 q^{86} - 3 q^{88} - 6 q^{89} - 20 q^{91} + 18 q^{92} - 10 q^{93} + 3 q^{94} + q^{96} - 16 q^{97} - 13 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 4 * q^7 + 2 * q^8 - q^9 - 3 * q^11 + q^12 - 10 * q^13 - 5 * q^14 - q^16 - q^18 - 5 * q^19 - q^21 + 6 * q^22 - 9 * q^23 + q^24 + 5 * q^26 - 2 * q^27 + q^28 + 10 * q^31 - q^32 + 3 * q^33 + 2 * q^36 - q^37 - 5 * q^38 - 5 * q^39 + 18 * q^41 - 4 * q^42 - 16 * q^43 - 3 * q^44 - 9 * q^46 + 3 * q^47 - 2 * q^48 + 2 * q^49 + 5 * q^52 - 3 * q^53 + q^54 + 4 * q^56 - 10 * q^57 - 12 * q^59 - 8 * q^61 - 20 * q^62 - 5 * q^63 + 2 * q^64 + 3 * q^66 + 8 * q^67 - 18 * q^69 - 12 * q^71 - q^72 + 2 * q^73 - q^74 + 10 * q^76 + 3 * q^77 + 10 * q^78 - 8 * q^79 - q^81 - 9 * q^82 + 5 * q^84 + 8 * q^86 - 3 * q^88 - 6 * q^89 - 20 * q^91 + 18 * q^92 - 10 * q^93 + 3 * q^94 + q^96 - 16 * q^97 - 13 * q^98 + 6 * q^99

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