LMFDB - Embedded newform 350.2.e.a.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(51,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("350.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.e (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:	$2.79476407074$
Analytic rank:	$1$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	350.51
Dual form			350.2.e.a.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{12} -2.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +(4.00000 + 3.46410i) q^{21} +(-4.50000 + 7.79423i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(1.00000 - 1.73205i) q^{26} -4.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +1.00000 q^{36} +(4.00000 - 6.92820i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(2.00000 + 3.46410i) q^{39} -3.00000 q^{41} +(-5.00000 + 1.73205i) q^{42} +10.0000 q^{43} +(-4.50000 - 7.79423i) q^{46} +(-1.50000 + 2.59808i) q^{47} +2.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} +(-2.50000 + 0.866025i) q^{56} +16.0000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} +5.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{68} +18.0000 q^{69} -9.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(4.00000 + 6.92820i) q^{74} +8.00000 q^{76} -4.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(5.50000 + 9.52628i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(6.00000 + 10.3923i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(5.00000 - 1.73205i) q^{91} +9.00000 q^{92} +(-5.00000 + 8.66025i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-1.00000 + 1.73205i) q^{96} -5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 - 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - 2 q^{12} - 4 q^{13} + q^{14} - q^{16} - 3 q^{17} - q^{18} - 8 q^{19} + 8 q^{21} - 9 q^{23} - 2 q^{24} + 2 q^{26} - 8 q^{27} + 4 q^{28} - 12 q^{29} - 5 q^{31} - q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 8 q^{38} + 4 q^{39} - 6 q^{41} - 10 q^{42} + 20 q^{43} - 9 q^{46} - 3 q^{47} + 4 q^{48} + 11 q^{49} - 6 q^{51} + 2 q^{52} + 6 q^{53} + 4 q^{54} - 5 q^{56} + 32 q^{57} + 6 q^{58} - 12 q^{59} + 4 q^{61} + 10 q^{62} + q^{63} + 2 q^{64} + 2 q^{67} - 3 q^{68} + 36 q^{69} - 18 q^{71} - q^{72} - 10 q^{73} + 8 q^{74} + 16 q^{76} - 8 q^{78} - 5 q^{79} + 11 q^{81} + 3 q^{82} + 12 q^{83} + 2 q^{84} - 10 q^{86} + 12 q^{87} - 3 q^{89} + 10 q^{91} + 18 q^{92} - 10 q^{93} - 3 q^{94} - 2 q^{96} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 - 5 * q^7 + 2 * q^8 - q^9 - 2 * q^12 - 4 * q^13 + q^14 - q^16 - 3 * q^17 - q^18 - 8 * q^19 + 8 * q^21 - 9 * q^23 - 2 * q^24 + 2 * q^26 - 8 * q^27 + 4 * q^28 - 12 * q^29 - 5 * q^31 - q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 8 * q^38 + 4 * q^39 - 6 * q^41 - 10 * q^42 + 20 * q^43 - 9 * q^46 - 3 * q^47 + 4 * q^48 + 11 * q^49 - 6 * q^51 + 2 * q^52 + 6 * q^53 + 4 * q^54 - 5 * q^56 + 32 * q^57 + 6 * q^58 - 12 * q^59 + 4 * q^61 + 10 * q^62 + q^63 + 2 * q^64 + 2 * q^67 - 3 * q^68 + 36 * q^69 - 18 * q^71 - q^72 - 10 * q^73 + 8 * q^74 + 16 * q^76 - 8 * q^78 - 5 * q^79 + 11 * q^81 + 3 * q^82 + 12 * q^83 + 2 * q^84 - 10 * q^86 + 12 * q^87 - 3 * q^89 + 10 * q^91 + 18 * q^92 - 10 * q^93 - 3 * q^94 - 2 * q^96 - 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	2.00000			0.816497
$7$	−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
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−2.00000			−0.554700			−0.277350	−	0.960769i	$-0.589456\pi$
$13$	−2.00000			−0.554700			−0.277350	+	0.960769i	$0.589456\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.114708	+	0.993399i	$0.536593\pi$
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$	4.00000	+	3.46410i	0.872872	+	0.755929i
$22$		0			0
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.169701	+	0.985496i	$0.554280\pi$
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.768613	+	0.639713i	$0.779053\pi$
$24$	−1.00000	−	1.73205i	−0.204124	−	0.353553i
$25$		0			0
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	−4.00000			−0.769800
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	−6.00000			−1.11417			−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000			−1.11417			−0.557086	+	0.830455i	$0.688081\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	−0.323640	−	0.946180i	$-0.604907\pi$
$37$	4.00000	−	6.92820i	0.657596	−	1.13899i	0.981236	−	0.192809i	$-0.0617599\pi$
$38$	−4.00000	−	6.92820i	−0.648886	−	1.12390i
$39$	2.00000	+	3.46410i	0.320256	+	0.554700i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	−5.00000	+	1.73205i	−0.771517	+	0.267261i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$		0			0
$45$		0			0
$46$	−4.50000	−	7.79423i	−0.663489	−	1.14920i
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	2.00000			0.288675
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$		0			0
$56$	−2.50000	+	0.866025i	−0.334077	+	0.115728i
$57$	16.0000			2.11925
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$		0			0
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	−0.709113	−	0.705095i	$-0.750904\pi$
$61$	2.00000	−	3.46410i	0.256074	−	0.443533i	0.965187	+	0.261562i	$0.0842377\pi$
$62$	5.00000			0.635001
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	18.0000			2.16695
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	−0.994850	−	0.101361i	$-0.967680\pi$
$73$	−5.00000	−	8.66025i	−0.585206	−	1.01361i	0.409644	−	0.912245i	$-0.365653\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	8.00000			0.917663
$77$		0			0
$78$	−4.00000			−0.452911
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$		0			0
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	−	5.19615i	0.109109	−	0.566947i
$85$		0			0
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$	6.00000	+	10.3923i	0.643268	+	1.11417i
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	5.00000	−	1.73205i	0.524142	−	0.181568i
$92$	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
$96$	−1.00000	+	1.73205i	−0.102062	+	0.176777i
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$		0			0
$100$		0			0
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	5.50000	−	9.52628i	0.541931	−	0.938652i	−0.456862	−	0.889538i	$-0.651027\pi$
$103$	5.50000	−	9.52628i	0.541931	−	0.938652i	0.998793	−	0.0491146i	$-0.0156400\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	−6.00000			−0.582772
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$	−16.0000			−1.51865
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$	−8.00000	+	13.8564i	−0.749269	+	1.29777i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	1.00000	−	1.73205i	0.0924500	−	0.160128i
$118$	12.0000			1.10469
$119$	6.00000	+	5.19615i	0.550019	+	0.476331i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	2.00000	+	3.46410i	0.181071	+	0.313625i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$		0			0
$126$	2.00000	+	1.73205i	0.178174	+	0.154303i
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−10.0000	−	17.3205i	−0.880451	−	1.52499i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	4.00000	−	20.7846i	0.346844	−	1.80225i
$134$	−2.00000			−0.172774
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	−9.00000	+	15.5885i	−0.766131	+	1.32698i
$139$	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
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	10.0000			0.827606
$147$	−13.0000	−	5.19615i	−1.07222	−	0.428571i
$148$	−8.00000			−0.657596
$149$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$149$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$150$		0			0
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	0.935857	−	0.352381i	$-0.114628\pi$
$151$	2.00000	+	3.46410i	0.162758	+	0.281905i	−0.773099	+	0.634285i	$0.781294\pi$
$152$	−4.00000	+	6.92820i	−0.324443	+	0.561951i
$153$	3.00000			0.242536
$154$		0			0
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	0.903167	−	0.429289i	$-0.141236\pi$
$157$	1.00000	+	1.73205i	0.0798087	+	0.138233i	−0.823359	+	0.567521i	$0.807902\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$	4.50000	−	23.3827i	0.354650	−	1.84281i
$162$	−11.0000			−0.864242
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	−0.665771	−	0.746156i	$-0.731897\pi$
$163$	4.00000	−	6.92820i	0.313304	−	0.542659i	0.979076	+	0.203497i	$0.0652307\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−24.0000			−1.85718			−0.928588	−	0.371113i	$-0.878976\pi$
$167$	−24.0000			−1.85718			−0.928588	+	0.371113i	$0.878976\pi$
$168$	4.00000	+	3.46410i	0.308607	+	0.267261i
$169$	−9.00000			−0.692308
$170$		0			0
$171$	−4.00000	−	6.92820i	−0.305888	−	0.529813i
$172$	−5.00000	−	8.66025i	−0.381246	−	0.660338i
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	−0.998755	−	0.0498898i	$-0.984113\pi$
$173$	−6.00000	+	10.3923i	−0.456172	+	0.790112i	0.542583	+	0.840002i	$0.317446\pi$
$174$	−12.0000			−0.909718
$175$		0			0
$176$		0			0
$177$	−12.0000	+	20.7846i	−0.901975	+	1.56227i
$178$	−1.50000	−	2.59808i	−0.112430	−	0.194734i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−1.00000	+	5.19615i	−0.0741249	+	0.385164i
$183$	−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
$189$	10.0000	−	3.46410i	0.727393	−	0.251976i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	0.941865	−	0.335993i	$-0.109072\pi$
$193$	2.50000	+	4.33013i	0.179954	+	0.311689i	−0.761911	+	0.647682i	$0.775738\pi$
$194$	2.50000	−	4.33013i	0.179490	−	0.310885i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−8.50000	−	14.7224i	−0.602549	−	1.04365i	0.389885	−	0.920864i	$-0.372515\pi$
$200$		0			0
$201$	2.00000	−	3.46410i	0.141069	−	0.244339i
$202$		0			0
$203$	15.0000	−	5.19615i	1.05279	−	0.364698i
$204$	6.00000			0.420084
$205$		0			0
$206$	5.50000	+	9.52628i	0.383203	+	0.663727i
$207$	−4.50000	−	7.79423i	−0.312772	−	0.541736i
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$		0			0
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$	9.00000	+	15.5885i	0.616670	+	1.06810i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$		0			0
$216$	−4.00000			−0.272166
$217$	10.0000	+	8.66025i	0.678844	+	0.587896i
$218$	−10.0000			−0.677285
$219$	−10.0000	+	17.3205i	−0.675737	+	1.17041i
$220$		0			0
$221$	3.00000	+	5.19615i	0.201802	+	0.349531i
$222$	8.00000	−	13.8564i	0.536925	−	0.929981i
$223$	−23.0000			−1.54019			−0.770097	−	0.637927i	$-0.779792\pi$
$223$	−23.0000			−1.54019			−0.770097	+	0.637927i	$0.779792\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	7.50000	−	12.9904i	0.498893	−	0.864107i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$	−8.00000	−	13.8564i	−0.529813	−	0.917663i
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$		0			0
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	10.0000			0.649570
$238$	−7.50000	+	2.59808i	−0.486153	+	0.168408i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$	5.50000	+	9.52628i	0.353553	+	0.612372i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−4.00000			−0.256074
$245$		0			0
$246$	−6.00000			−0.382546
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$	−2.50000	−	4.33013i	−0.158750	−	0.274963i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−2.50000	+	0.866025i	−0.157485	+	0.0545545i
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	20.0000			1.24515
$259$	−4.00000	+	20.7846i	−0.248548	+	1.29149i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$		0			0
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$		0			0
$265$		0			0
$266$	16.0000	+	13.8564i	0.981023	+	0.849591i
$267$	6.00000			0.367194
$268$	1.00000	−	1.73205i	0.0610847	−	0.105802i
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.807535	+	0.589819i	$0.200801\pi$
$269$	15.0000	+	25.9808i	0.914566	+	1.58408i	0.107031	+	0.994256i	$0.465866\pi$
$270$		0			0
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	3.00000			0.181902
$273$	−8.00000	−	6.92820i	−0.484182	−	0.419314i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−9.00000	−	15.5885i	−0.541736	−	0.938315i
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	0.799666	−	0.600446i	$-0.205010\pi$
$277$	−2.00000	−	3.46410i	−0.120168	−	0.208138i	−0.919834	+	0.392308i	$0.871677\pi$
$278$	−1.00000	+	1.73205i	−0.0599760	+	0.103882i
$279$	5.00000			0.299342
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	1.00000	+	1.73205i	0.0594438	+	0.102960i	0.894216	−	0.447636i	$-0.147734\pi$
$283$	1.00000	+	1.73205i	0.0594438	+	0.102960i	−0.834772	+	0.550596i	$0.814401\pi$
$284$	4.50000	+	7.79423i	0.267026	+	0.462502i
$285$		0			0
$286$		0			0
$287$	7.50000	−	2.59808i	0.442711	−	0.153360i
$288$	1.00000			0.0589256
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$	5.00000	+	8.66025i	0.293105	+	0.507673i
$292$	−5.00000	+	8.66025i	−0.292603	+	0.506803i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	11.0000	−	8.66025i	0.641533	−	0.505076i
$295$		0			0
$296$	4.00000	−	6.92820i	0.232495	−	0.402694i
$297$		0			0
$298$		0			0
$299$	9.00000	−	15.5885i	0.520483	−	0.901504i
$300$		0			0
$301$	−25.0000	+	8.66025i	−1.44098	+	0.499169i
$302$	−4.00000			−0.230174
$303$		0			0
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$		0			0
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	−22.0000			−1.25154
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	2.00000	+	3.46410i	0.113228	+	0.196116i
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	−0.519300	−	0.854592i	$-0.673807\pi$
$313$	8.50000	−	14.7224i	0.480448	−	0.832161i	0.999748	+	0.0224310i	$0.00714060\pi$
$314$	−2.00000			−0.112867
$315$		0			0
$316$	5.00000			0.281272
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$		0			0
$320$		0			0
$321$	−24.0000			−1.33955
$322$	18.0000	+	15.5885i	1.00310	+	0.868711i
$323$	24.0000			1.33540
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$		0			0
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	10.0000	−	17.3205i	0.553001	−	0.957826i
$328$	−3.00000			−0.165647
$329$	1.50000	−	7.79423i	0.0826977	−	0.429710i
$330$		0			0
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	−0.991735	−	0.128302i	$-0.959047\pi$
$331$	−7.00000	+	12.1244i	−0.384755	+	0.666415i	0.606980	+	0.794717i	$0.292381\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	4.00000	+	6.92820i	0.219199	+	0.379663i
$334$	12.0000	−	20.7846i	0.656611	−	1.13728i
$335$		0			0
$336$	−5.00000	+	1.73205i	−0.272772	+	0.0944911i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	15.0000	+	25.9808i	0.814688	+	1.41108i
$340$		0			0
$341$		0			0
$342$	8.00000			0.432590
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	10.0000			0.539164
$345$		0			0
$346$	−6.00000	−	10.3923i	−0.322562	−	0.558694i
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	0.774197	−	0.632945i	$-0.218154\pi$
$347$	−3.00000	−	5.19615i	−0.161048	−	0.278944i	−0.935245	+	0.354001i	$0.884821\pi$
$348$	6.00000	−	10.3923i	0.321634	−	0.557086i
$349$	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
$351$	8.00000			0.427008
$352$		0			0
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$	−12.0000	−	20.7846i	−0.637793	−	1.10469i
$355$		0			0
$356$	3.00000			0.159000
$357$	3.00000	−	15.5885i	0.158777	−	0.825029i
$358$	24.0000			1.26844
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$	−10.0000	+	17.3205i	−0.525588	+	0.910346i
$363$	−22.0000			−1.15470
$364$	−4.00000	−	3.46410i	−0.209657	−	0.181568i
$365$		0			0
$366$	4.00000	−	6.92820i	0.209083	−	0.362143i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	−4.50000	−	7.79423i	−0.234579	−	0.406302i
$369$	1.50000	−	2.59808i	0.0780869	−	0.135250i
$370$		0			0
$371$	−12.0000	−	10.3923i	−0.623009	−	0.539542i
$372$	10.0000			0.518476
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	−0.838975	−	0.544170i	$-0.816844\pi$
$373$	1.00000	−	1.73205i	0.0517780	−	0.0896822i	0.890753	+	0.454488i	$0.150178\pi$
$374$		0			0
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	12.0000			0.618031
$378$	−2.00000	+	10.3923i	−0.102869	+	0.534522i
$379$	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
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	−7.50000	−	12.9904i	−0.383733	−	0.664646i
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	−0.727851	−	0.685736i	$-0.759481\pi$
$383$	4.50000	−	7.79423i	0.229939	−	0.398266i	0.957790	+	0.287469i	$0.0928139\pi$
$384$	2.00000			0.102062
$385$		0			0
$386$	−5.00000			−0.254493
$387$	−5.00000	+	8.66025i	−0.254164	+	0.440225i
$388$	2.50000	+	4.33013i	0.126918	+	0.219829i
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	0.998763	−	0.0497253i	$-0.0158346\pi$
$389$	9.00000	+	15.5885i	0.456318	+	0.790366i	−0.542445	+	0.840091i	$0.682501\pi$
$390$		0			0
$391$	27.0000			1.36545
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$		0			0
$396$		0			0
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	−0.839840	−	0.542834i	$-0.817351\pi$
$397$	1.00000	−	1.73205i	0.0501886	−	0.0869291i	0.890028	+	0.455905i	$0.150684\pi$
$398$	17.0000			0.852133
$399$	−40.0000	+	13.8564i	−2.00250	+	0.693688i
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	2.00000	+	3.46410i	0.0997509	+	0.172774i
$403$	5.00000	+	8.66025i	0.249068	+	0.431398i
$404$		0			0
$405$		0			0
$406$	−3.00000	+	15.5885i	−0.148888	+	0.773642i
$407$		0			0
$408$	−3.00000	+	5.19615i	−0.148522	+	0.257248i
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	9.00000	−	15.5885i	0.443937	−	0.768922i
$412$	−11.0000			−0.541931
$413$	24.0000	+	20.7846i	1.18096	+	1.02274i
$414$	9.00000			0.442326
$415$		0			0
$416$	1.00000	+	1.73205i	0.0490290	+	0.0849208i
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$		0			0
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	−1.00000	+	1.73205i	−0.0486792	+	0.0843149i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	3.00000	+	5.19615i	0.145693	+	0.252347i
$425$		0			0
$426$	−18.0000			−0.872103
$427$	−2.00000	+	10.3923i	−0.0967868	+	0.502919i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	0.899888	−	0.436121i	$-0.143648\pi$
$431$	1.50000	+	2.59808i	0.0722525	+	0.125145i	−0.827636	+	0.561266i	$0.810315\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−29.0000			−1.39365			−0.696826	−	0.717241i	$-0.745405\pi$
$433$	−29.0000			−1.39365			−0.696826	+	0.717241i	$0.745405\pi$
$434$	−12.5000	+	4.33013i	−0.600019	+	0.207853i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	−36.0000	−	62.3538i	−1.72211	−	2.98279i
$438$	−10.0000	−	17.3205i	−0.477818	−	0.827606i
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	0.449488	+	0.893287i	$0.351607\pi$
$439$	−11.5000	+	19.9186i	−0.548865	+	0.950662i	−0.998353	+	0.0573756i	$0.981727\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	−6.00000			−0.285391
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	8.00000	+	13.8564i	0.379663	+	0.657596i
$445$		0			0
$446$	11.5000	−	19.9186i	0.544541	−	0.943172i
$447$		0			0
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−27.0000			−1.27421			−0.637104	−	0.770778i	$-0.719868\pi$
$449$	−27.0000			−1.27421			−0.637104	+	0.770778i	$0.719868\pi$
$450$		0			0
$451$		0			0
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	16.0000			0.749269
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$	6.00000	+	10.3923i	0.280056	+	0.485071i
$460$		0			0
$461$	−24.0000			−1.11779			−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000			−1.11779			−0.558896	+	0.829238i	$0.688775\pi$
$462$		0			0
$463$	25.0000			1.16185			0.580924	−	0.813958i	$-0.302691\pi$
$463$	25.0000			1.16185			0.580924	+	0.813958i	$0.302691\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	−0.927052	−	0.374934i	$-0.877665\pi$
$467$	−3.00000	+	5.19615i	−0.138823	+	0.240449i	0.788228	+	0.615383i	$0.210999\pi$
$468$	−2.00000			−0.0924500
$469$	−4.00000	−	3.46410i	−0.184703	−	0.159957i
$470$		0			0
$471$	2.00000	−	3.46410i	0.0921551	−	0.159617i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$		0			0
$474$	−5.00000	+	8.66025i	−0.229658	+	0.397779i
$475$		0			0
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$	−6.00000			−0.274721
$478$	−7.50000	+	12.9904i	−0.343042	+	0.594166i
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	0.990060	+	0.140643i	$0.0449170\pi$
$479$	13.5000	+	23.3827i	0.616831	+	1.06838i	−0.373230	+	0.927739i	$0.621750\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−22.0000			−1.00207
$483$	−45.0000	+	15.5885i	−2.04757	+	0.709299i
$484$	−11.0000			−0.500000
$485$		0			0
$486$	5.00000	+	8.66025i	0.226805	+	0.392837i
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	0.963312	−	0.268384i	$-0.0864896\pi$
$487$	5.50000	+	9.52628i	0.249229	+	0.431677i	−0.714083	+	0.700061i	$0.753156\pi$
$488$	2.00000	−	3.46410i	0.0905357	−	0.156813i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	42.0000			1.89543			0.947717	−	0.319113i	$-0.103385\pi$
$491$	42.0000			1.89543			0.947717	+	0.319113i	$0.103385\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	8.00000	+	13.8564i	0.359937	+	0.623429i
$495$		0			0
$496$	5.00000			0.224507
$497$	22.5000	−	7.79423i	1.00926	−	0.349619i
$498$	12.0000			0.537733
$499$	17.0000	−	29.4449i	0.761025	−	1.31813i	−0.181298	−	0.983428i	$-0.558030\pi$
$499$	17.0000	−	29.4449i	0.761025	−	1.31813i	0.942323	−	0.334705i	$-0.108637\pi$
$500$		0			0
$501$	24.0000	+	41.5692i	1.07224	+	1.85718i
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	0.500000	−	2.59808i	0.0222718	−	0.115728i
$505$		0			0
$506$		0			0
$507$	9.00000	+	15.5885i	0.399704	+	0.692308i
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	20.0000	+	17.3205i	0.884748	+	0.766214i
$512$	1.00000			0.0441942
$513$	16.0000	−	27.7128i	0.706417	−	1.22355i
$514$	9.00000	+	15.5885i	0.396973	+	0.687577i
$515$		0			0
$516$	−10.0000	+	17.3205i	−0.440225	+	0.762493i
$517$		0			0
$518$	−16.0000	−	13.8564i	−0.703000	−	0.608816i
$519$	24.0000			1.05348
$520$		0			0
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$	3.00000	+	5.19615i	0.131306	+	0.227429i
$523$	−17.0000	+	29.4449i	−0.743358	+	1.28753i	0.207600	+	0.978214i	$0.433435\pi$
$523$	−17.0000	+	29.4449i	−0.743358	+	1.28753i	−0.950958	+	0.309320i	$0.899899\pi$
$524$		0			0
$525$		0			0
$526$	−9.00000			−0.392419
$527$	−7.50000	+	12.9904i	−0.326705	+	0.565870i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$		0			0
$531$	12.0000			0.520756
$532$	−20.0000	+	6.92820i	−0.867110	+	0.300376i
$533$	6.00000			0.259889
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	−24.0000	+	41.5692i	−1.03568	+	1.79384i
$538$	−30.0000			−1.29339
$539$		0			0
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−5.50000	−	9.52628i	−0.236245	−	0.409189i
$543$	−20.0000	−	34.6410i	−0.858282	−	1.48659i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		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	$0.554709\pi$
$548$	4.50000	−	7.79423i	0.192230	−	0.332953i
$549$	2.00000	+	3.46410i	0.0853579	+	0.147844i
$550$		0			0
$551$	24.0000	−	41.5692i	1.02243	−	1.77091i
$552$	18.0000			0.766131
$553$	2.50000	−	12.9904i	0.106311	−	0.552407i
$554$	4.00000			0.169944
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	0.999952	+	0.00979220i	$0.00311700\pi$
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	−0.491496	+	0.870880i	$0.663550\pi$
$558$	−2.50000	+	4.33013i	−0.105833	+	0.183309i
$559$	−20.0000			−0.845910
$560$		0			0
$561$		0			0
$562$	−1.50000	+	2.59808i	−0.0632737	+	0.109593i
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	0.795858	−	0.605483i	$-0.207020\pi$
$563$	−3.00000	−	5.19615i	−0.126435	−	0.218992i	−0.922293	+	0.386492i	$0.873687\pi$
$564$	−3.00000	−	5.19615i	−0.126323	−	0.218797i
$565$		0			0
$566$	−2.00000			−0.0840663
$567$	−22.0000	−	19.0526i	−0.923913	−	0.800132i
$568$	−9.00000			−0.377632
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	−0.832870	−	0.553469i	$-0.813304\pi$
$569$	1.50000	−	2.59808i	0.0628833	−	0.108917i	0.895753	+	0.444552i	$0.146637\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$		0			0
$573$	30.0000			1.25327
$574$	−1.50000	+	7.79423i	−0.0626088	+	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	−0.965701	−	0.259656i	$-0.916391\pi$
$577$	−17.0000	−	29.4449i	−0.707719	−	1.22581i	0.257982	−	0.966150i	$-0.416942\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	5.00000	−	8.66025i	0.207793	−	0.359908i
$580$		0			0
$581$	−15.0000	+	5.19615i	−0.622305	+	0.215573i
$582$	−10.0000			−0.414513
$583$		0			0
$584$	−5.00000	−	8.66025i	−0.206901	−	0.358364i
$585$		0			0
$586$	3.00000	−	5.19615i	0.123929	−	0.214651i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	2.00000	+	13.8564i	0.0824786	+	0.571429i
$589$	40.0000			1.64817
$590$		0			0
$591$	18.0000	+	31.1769i	0.740421	+	1.28245i
$592$	4.00000	+	6.92820i	0.164399	+	0.284747i
$593$	1.50000	−	2.59808i	0.0615976	−	0.106690i	−0.833582	−	0.552396i	$-0.813714\pi$
$593$	1.50000	−	2.59808i	0.0615976	−	0.106690i	0.895180	+	0.445705i	$0.147047\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−17.0000	+	29.4449i	−0.695764	+	1.20510i
$598$	9.00000	+	15.5885i	0.368037	+	0.637459i
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	0.567768	−	0.823189i	$-0.307807\pi$
$599$	−10.5000	−	18.1865i	−0.429018	−	0.743082i	−0.996786	+	0.0801071i	$0.974474\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$	5.00000	−	25.9808i	0.203785	−	1.05890i
$603$	−2.00000			−0.0814463
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$		0			0
$606$		0			0
$607$	−12.5000	+	21.6506i	−0.507359	+	0.878772i	0.492604	+	0.870253i	$0.336045\pi$
$607$	−12.5000	+	21.6506i	−0.507359	+	0.878772i	−0.999964	+	0.00851879i	$0.997288\pi$
$608$	8.00000			0.324443
$609$	−24.0000	−	20.7846i	−0.972529	−	0.842235i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−1.50000	−	2.59808i	−0.0606339	−	0.105021i
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$		0			0
$616$		0			0
$617$	−15.0000			−0.603877			−0.301939	−	0.953327i	$-0.597634\pi$
$617$	−15.0000			−0.603877			−0.301939	+	0.953327i	$0.597634\pi$
$618$	11.0000	−	19.0526i	0.442485	−	0.766406i
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	0.948840	−	0.315757i	$-0.102258\pi$
$619$	5.00000	+	8.66025i	0.200967	+	0.348085i	−0.747873	+	0.663842i	$0.768925\pi$
$620$		0			0
$621$	18.0000	−	31.1769i	0.722315	−	1.25109i
$622$	21.0000			0.842023
$623$	1.50000	−	7.79423i	0.0600962	−	0.312269i
$624$	−4.00000			−0.160128
$625$		0			0
$626$	8.50000	+	14.7224i	0.339728	+	0.588427i
$627$		0			0
$628$	1.00000	−	1.73205i	0.0399043	−	0.0691164i
$629$	−24.0000			−0.956943
$630$		0			0
$631$	−19.0000			−0.756378			−0.378189	−	0.925728i	$-0.623453\pi$
$631$	−19.0000			−0.756378			−0.378189	+	0.925728i	$0.623453\pi$
$632$	−2.50000	+	4.33013i	−0.0994447	+	0.172243i
$633$	−2.00000	−	3.46410i	−0.0794929	−	0.137686i
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$		0			0
$636$	−12.0000			−0.475831
$637$	−11.0000	+	8.66025i	−0.435836	+	0.343132i
$638$		0			0
$639$	4.50000	−	7.79423i	0.178017	−	0.308335i
$640$		0			0
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$	12.0000	−	20.7846i	0.473602	−	0.820303i
$643$	−20.0000			−0.788723			−0.394362	−	0.918955i	$-0.629034\pi$
$643$	−20.0000			−0.788723			−0.394362	+	0.918955i	$0.629034\pi$
$644$	−22.5000	+	7.79423i	−0.886624	+	0.307136i
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	5.50000	+	9.52628i	0.216060	+	0.374228i
$649$		0			0
$650$		0			0
$651$	5.00000	−	25.9808i	0.195965	−	1.01827i
$652$	−8.00000			−0.313304
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	−0.634437	−	0.772975i	$-0.718768\pi$
$653$	9.00000	−	15.5885i	0.352197	−	0.610023i	0.986634	+	0.162951i	$0.0521013\pi$
$654$	10.0000	+	17.3205i	0.391031	+	0.677285i
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	10.0000			0.390137
$658$	6.00000	+	5.19615i	0.233904	+	0.202567i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	0.978615	−	0.205702i	$-0.0659478\pi$
$661$	8.00000	+	13.8564i	0.311164	+	0.538952i	−0.667451	+	0.744654i	$0.732615\pi$
$662$	−7.00000	−	12.1244i	−0.272063	−	0.471226i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$	6.00000			0.232845
$665$		0			0
$666$	−8.00000			−0.309994
$667$	27.0000	−	46.7654i	1.04544	−	1.81076i
$668$	12.0000	+	20.7846i	0.464294	+	0.804181i
$669$	23.0000	+	39.8372i	0.889231	+	1.54019i
$670$		0			0
$671$		0			0
$672$	1.00000	−	5.19615i	0.0385758	−	0.200446i
$673$	−5.00000			−0.192736			−0.0963679	−	0.995346i	$-0.530723\pi$
$673$	−5.00000			−0.192736			−0.0963679	+	0.995346i	$0.530723\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$	−30.0000			−1.15214
$679$	12.5000	−	4.33013i	0.479706	−	0.166175i
$680$		0			0
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$		0			0
$683$	−15.0000	−	25.9808i	−0.573959	−	0.994126i	−0.996154	−	0.0876211i	$-0.972074\pi$
$683$	−15.0000	−	25.9808i	−0.573959	−	0.994126i	0.422195	−	0.906505i	$-0.361260\pi$
$684$	−4.00000	+	6.92820i	−0.152944	+	0.264906i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$	40.0000			1.52610
$688$	−5.00000	+	8.66025i	−0.190623	+	0.330169i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$	12.0000			0.456172
$693$		0			0
$694$	6.00000			0.227757
$695$		0			0
$696$	6.00000	+	10.3923i	0.227429	+	0.393919i
$697$	4.50000	+	7.79423i	0.170450	+	0.295227i
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$	12.0000			0.453882
$700$		0			0
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$	−4.00000	+	6.92820i	−0.150970	+	0.261488i
$703$	32.0000	+	55.4256i	1.20690	+	2.09042i
$704$		0			0
$705$		0			0
$706$	9.00000			0.338719
$707$		0			0
$708$	24.0000			0.901975
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	−0.826023	−	0.563636i	$-0.809402\pi$
$709$	2.00000	−	3.46410i	0.0751116	−	0.130097i	0.901135	+	0.433539i	$0.142735\pi$
$710$		0			0
$711$	−2.50000	−	4.33013i	−0.0937573	−	0.162392i
$712$	−1.50000	+	2.59808i	−0.0562149	+	0.0973670i
$713$	45.0000			1.68526
$714$	12.0000	+	10.3923i	0.449089	+	0.388922i
$715$		0			0
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$	−15.0000	−	25.9808i	−0.560185	−	0.970269i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	−5.50000	+	28.5788i	−0.204831	+	1.06433i
$722$	45.0000			1.67473
$723$	22.0000	−	38.1051i	0.818189	−	1.41714i
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$		0			0
$726$	11.0000	−	19.0526i	0.408248	−	0.707107i
$727$	31.0000			1.14973			0.574863	−	0.818250i	$-0.305055\pi$
$727$	31.0000			1.14973			0.574863	+	0.818250i	$0.305055\pi$
$728$	5.00000	−	1.73205i	0.185312	−	0.0641941i
$729$	13.0000			0.481481
$730$		0			0
$731$	−15.0000	−	25.9808i	−0.554795	−	0.960933i
$732$	4.00000	+	6.92820i	0.147844	+	0.256074i
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$	−8.00000			−0.295285
$735$		0			0
$736$	9.00000			0.331744
$737$		0			0
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	0.783028	−	0.621987i	$-0.213674\pi$
$739$	−4.00000	−	6.92820i	−0.147142	−	0.254858i	−0.930170	+	0.367129i	$0.880341\pi$
$740$		0			0
$741$	−32.0000			−1.17555
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	−33.0000			−1.21065			−0.605326	−	0.795977i	$-0.706957\pi$
$743$	−33.0000			−1.21065			−0.605326	+	0.795977i	$0.706957\pi$
$744$	−5.00000	+	8.66025i	−0.183309	+	0.317500i
$745$		0			0
$746$	1.00000	+	1.73205i	0.0366126	+	0.0634149i
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$		0			0
$749$	−6.00000	+	31.1769i	−0.219235	+	1.13918i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$		0			0
$754$	−6.00000	+	10.3923i	−0.218507	+	0.378465i
$755$		0			0
$756$	−8.00000	−	6.92820i	−0.290957	−	0.251976i
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−4.00000	+	6.92820i	−0.145287	+	0.251644i
$759$		0			0
$760$		0			0
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	0.0932544	+	0.995642i	$0.470273\pi$
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	−0.908879	+	0.417061i	$0.863060\pi$
$762$	−16.0000			−0.579619
$763$	−20.0000	−	17.3205i	−0.724049	−	0.627044i
$764$	15.0000			0.542681
$765$		0			0
$766$	4.50000	+	7.79423i	0.162592	+	0.281617i
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$	2.50000	−	4.33013i	0.0899770	−	0.155845i
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	0.737716	−	0.675111i	$-0.235904\pi$
$773$	−6.00000	−	10.3923i	−0.215805	−	0.373785i	−0.953521	+	0.301326i	$0.902571\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$		0			0
$776$	−5.00000			−0.179490
$777$	40.0000	−	13.8564i	1.43499	−	0.497096i
$778$	−18.0000			−0.645331
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$	−13.5000	+	23.3827i	−0.482759	+	0.836163i
$783$	24.0000			0.857690
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$		0			0
$786$		0			0
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	0.687481	−	0.726202i	$-0.258716\pi$
$787$	−8.00000	−	13.8564i	−0.285169	−	0.493928i	−0.972650	+	0.232275i	$0.925383\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	9.00000	−	15.5885i	0.320408	−	0.554964i
$790$		0			0
$791$	37.5000	−	12.9904i	1.33335	−	0.461885i
$792$		0			0
$793$	−4.00000	+	6.92820i	−0.142044	+	0.246028i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$		0			0
$796$	−8.50000	+	14.7224i	−0.301275	+	0.521823i
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$	8.00000	−	41.5692i	0.283197	−	1.47153i
$799$	9.00000			0.318397
$800$		0			0
$801$	−1.50000	−	2.59808i	−0.0529999	−	0.0917985i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$		0			0
$804$	−4.00000			−0.141069
$805$		0			0
$806$	−10.0000			−0.352235
$807$	30.0000	−	51.9615i	1.05605	−	1.82913i
$808$		0			0
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$		0			0
$811$	26.0000			0.912983			0.456492	−	0.889728i	$-0.349106\pi$
$811$	26.0000			0.912983			0.456492	+	0.889728i	$0.349106\pi$
$812$	−12.0000	−	10.3923i	−0.421117	−	0.364698i
$813$	22.0000			0.771574
$814$		0			0
$815$		0			0
$816$	−3.00000	−	5.19615i	−0.105021	−	0.181902i
$817$	−40.0000	+	69.2820i	−1.39942	+	2.42387i
$818$	−7.00000			−0.244749
$819$	−1.00000	+	5.19615i	−0.0349428	+	0.181568i
$820$		0			0
$821$	6.00000	−	10.3923i	0.209401	−	0.362694i	−0.742125	−	0.670262i	$-0.766182\pi$
$821$	6.00000	−	10.3923i	0.209401	−	0.362694i	0.951526	+	0.307568i	$0.0995151\pi$
$822$	9.00000	+	15.5885i	0.313911	+	0.543710i
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	0.985997	−	0.166762i	$-0.0533313\pi$
$823$	10.0000	+	17.3205i	0.348578	+	0.603755i	−0.637419	+	0.770517i	$0.719998\pi$
$824$	5.50000	−	9.52628i	0.191602	−	0.331864i
$825$		0			0
$826$	−30.0000	+	10.3923i	−1.04383	+	0.361595i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−4.50000	+	7.79423i	−0.156386	+	0.270868i
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	−0.940726	−	0.339169i	$-0.889854\pi$
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	0.176634	−	0.984277i	$-0.443479\pi$
$830$		0			0
$831$	−4.00000	+	6.92820i	−0.138758	+	0.240337i
$832$	−2.00000			−0.0693375
$833$	−19.5000	−	7.79423i	−0.675635	−	0.270054i
$834$	4.00000			0.138509
$835$		0			0
$836$		0			0
$837$	10.0000	+	17.3205i	0.345651	+	0.598684i
$838$	15.0000	−	25.9808i	0.518166	−	0.897491i
$839$	−33.0000			−1.13929			−0.569643	−	0.821892i	$-0.692919\pi$
$839$	−33.0000			−1.13929			−0.569643	+	0.821892i	$0.692919\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	2.00000	−	3.46410i	0.0689246	−	0.119381i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$		0			0
$846$	3.00000			0.103142
$847$	−5.50000	+	28.5788i	−0.188982	+	0.981981i
$848$	−6.00000			−0.206041
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$		0			0
$851$	36.0000	+	62.3538i	1.23406	+	2.13746i
$852$	9.00000	−	15.5885i	0.308335	−	0.534052i
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$	−8.00000	−	6.92820i	−0.273754	−	0.237078i
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$		0			0
$861$	−12.0000	−	10.3923i	−0.408959	−	0.354169i
$862$	−3.00000			−0.102180
$863$	10.5000	−	18.1865i	0.357424	−	0.619077i	−0.630106	−	0.776509i	$-0.716988\pi$
$863$	10.5000	−	18.1865i	0.357424	−	0.619077i	0.987530	+	0.157433i	$0.0503217\pi$
$864$	2.00000	+	3.46410i	0.0680414	+	0.117851i
$865$		0			0
$866$	14.5000	−	25.1147i	0.492730	−	0.853433i
$867$	−16.0000			−0.543388
$868$	2.50000	−	12.9904i	0.0848555	−	0.440922i
$869$		0			0
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	2.50000	−	4.33013i	0.0846122	−	0.146553i
$874$	72.0000			2.43544
$875$		0			0
$876$	20.0000			0.675737
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$	−11.5000	−	19.9186i	−0.388106	−	0.672220i
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$		0			0
$881$	27.0000			0.909653			0.454827	−	0.890580i	$-0.349701\pi$
$881$	27.0000			0.909653			0.454827	+	0.890580i	$0.349701\pi$
$882$	−6.50000	−	2.59808i	−0.218866	−	0.0874818i
$883$	−26.0000			−0.874970			−0.437485	−	0.899226i	$-0.644131\pi$
$883$	−26.0000			−0.874970			−0.437485	+	0.899226i	$0.644131\pi$
$884$	3.00000	−	5.19615i	0.100901	−	0.174766i
$885$		0			0
$886$	−6.00000	−	10.3923i	−0.201574	−	0.349136i
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	−0.387768	−	0.921757i	$-0.626754\pi$
$887$	18.0000	−	31.1769i	0.604381	−	1.04682i	0.992149	−	0.125061i	$-0.0399128\pi$
$888$	−16.0000			−0.536925
$889$	20.0000	−	6.92820i	0.670778	−	0.232364i
$890$		0			0
$891$		0			0
$892$	11.5000	+	19.9186i	0.385048	+	0.666924i
$893$	−12.0000	−	20.7846i	−0.401565	−	0.695530i
$894$		0			0
$895$		0			0
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$	−36.0000			−1.20201
$898$	13.5000	−	23.3827i	0.450501	−	0.780290i
$899$	15.0000	+	25.9808i	0.500278	+	0.866507i
$900$		0			0
$901$	9.00000	−	15.5885i	0.299833	−	0.519327i
$902$		0			0
$903$	40.0000	+	34.6410i	1.33112	+	1.15278i
$904$	−15.0000			−0.498893
$905$		0			0
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	−20.0000	−	34.6410i	−0.664089	−	1.15024i	−0.979531	−	0.201291i	$-0.935486\pi$
$907$	−20.0000	−	34.6410i	−0.664089	−	1.15024i	0.315442	−	0.948945i	$-0.397847\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$		0			0
$910$		0			0
$911$	3.00000			0.0993944			0.0496972	−	0.998764i	$-0.484174\pi$
$911$	3.00000			0.0993944			0.0496972	+	0.998764i	$0.484174\pi$
$912$	−8.00000	+	13.8564i	−0.264906	+	0.458831i
$913$		0			0
$914$	−11.0000	−	19.0526i	−0.363848	−	0.630203i
$915$		0			0
$916$	20.0000			0.660819
$917$		0			0
$918$	−12.0000			−0.396059
$919$	−5.50000	+	9.52628i	−0.181428	+	0.314243i	−0.942367	−	0.334581i	$-0.891405\pi$
$919$	−5.50000	+	9.52628i	−0.181428	+	0.314243i	0.760939	+	0.648824i	$0.224739\pi$
$920$		0			0
$921$	−16.0000	−	27.7128i	−0.527218	−	0.913168i
$922$	12.0000	−	20.7846i	0.395199	−	0.684505i
$923$	18.0000			0.592477
$924$		0			0
$925$		0			0
$926$	−12.5000	+	21.6506i	−0.410775	+	0.711484i
$927$	5.50000	+	9.52628i	0.180644	+	0.312884i
$928$	3.00000	+	5.19615i	0.0984798	+	0.170572i
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	0.283178	+	0.959067i	$0.408611\pi$
$929$	−21.0000	+	36.3731i	−0.688988	+	1.19336i	−0.972166	+	0.234294i	$0.924722\pi$
$930$		0			0
$931$	8.00000	+	55.4256i	0.262189	+	1.81650i
$932$	6.00000			0.196537
$933$	−21.0000	+	36.3731i	−0.687509	+	1.19080i
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$		0			0
$936$	1.00000	−	1.73205i	0.0326860	−	0.0566139i
$937$	34.0000			1.11073			0.555366	−	0.831606i	$-0.312578\pi$
$937$	34.0000			1.11073			0.555366	+	0.831606i	$0.312578\pi$
$938$	5.00000	−	1.73205i	0.163256	−	0.0565535i
$939$	−34.0000			−1.10955
$940$		0			0
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	0.910773	−	0.412908i	$-0.135487\pi$
$941$	3.00000	+	5.19615i	0.0977972	+	0.169390i	−0.812975	+	0.582298i	$0.802154\pi$
$942$	2.00000	+	3.46410i	0.0651635	+	0.112867i
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$	12.0000			0.390567
$945$		0			0
$946$		0			0
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−5.00000	−	8.66025i	−0.162392	−	0.281272i
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$		0			0
$951$	24.0000			0.778253
$952$	6.00000	+	5.19615i	0.194461	+	0.168408i
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$	3.00000	−	5.19615i	0.0971286	−	0.168232i
$955$		0			0
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$		0			0
$958$	−27.0000			−0.872330
$959$	−18.0000	−	15.5885i	−0.581250	−	0.503378i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	−8.00000	−	13.8564i	−0.257930	−	0.446748i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	11.0000	−	19.0526i	0.354286	−	0.613642i
$965$		0			0
$966$	9.00000	−	46.7654i	0.289570	−	1.50465i
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$	5.50000	−	9.52628i	0.176777	−	0.306186i
$969$	−24.0000	−	41.5692i	−0.770991	−	1.33540i
$970$		0			0
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	−0.999771	−	0.0213768i	$-0.993195\pi$
$971$	−15.0000	+	25.9808i	−0.481373	+	0.833762i	0.518399	+	0.855139i	$0.326528\pi$
$972$	−10.0000			−0.320750
$973$	−5.00000	+	1.73205i	−0.160293	+	0.0555270i
$974$	−11.0000			−0.352463
$975$		0			0
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	−25.5000	−	44.1673i	−0.815817	−	1.41304i	−0.908740	−	0.417364i	$-0.862954\pi$
$977$	−25.5000	−	44.1673i	−0.815817	−	1.41304i	0.0929223	−	0.995673i	$-0.470379\pi$
$978$	8.00000	−	13.8564i	0.255812	−	0.443079i
$979$		0			0
$980$		0			0
$981$	−10.0000			−0.319275
$982$	−21.0000	+	36.3731i	−0.670137	+	1.16071i
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$		0			0
$986$	−18.0000			−0.573237
$987$	−15.0000	+	5.19615i	−0.477455	+	0.165395i
$988$	−16.0000			−0.509028
$989$	−45.0000	+	77.9423i	−1.43092	+	2.47842i
$990$		0			0
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	0.538384	−	0.842700i	$-0.319035\pi$
$991$	−14.5000	−	25.1147i	−0.460608	−	0.797796i	−0.998991	+	0.0449040i	$0.985702\pi$
$992$	−2.50000	+	4.33013i	−0.0793751	+	0.137482i
$993$	28.0000			0.888553
$994$	−4.50000	+	23.3827i	−0.142731	+	0.741654i
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	−2.00000	−	3.46410i	−0.0633406	−	0.109709i	0.832616	−	0.553851i	$-0.186842\pi$
$997$	−2.00000	−	3.46410i	−0.0633406	−	0.109709i	−0.895957	+	0.444141i	$0.853509\pi$
$998$	17.0000	+	29.4449i	0.538126	+	0.932061i
$999$	−16.0000	+	27.7128i	−0.506218	+	0.876795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.e.a.51.1	✓	2
5.2	odd	4		350.2.j.e.149.1		4
5.3	odd	4		350.2.j.e.149.2		4
5.4	even	2		350.2.e.k.51.1	yes	2
7.2	even	3		2450.2.a.be.1.1		1
7.4	even	3	inner	350.2.e.a.151.1	yes	2
7.5	odd	6		2450.2.a.u.1.1		1
35.2	odd	12		2450.2.c.o.99.2		2
35.4	even	6		350.2.e.k.151.1	yes	2
35.9	even	6		2450.2.a.e.1.1		1
35.12	even	12		2450.2.c.d.99.2		2
35.18	odd	12		350.2.j.e.249.1		4
35.19	odd	6		2450.2.a.o.1.1		1
35.23	odd	12		2450.2.c.o.99.1		2
35.32	odd	12		350.2.j.e.249.2		4
35.33	even	12		2450.2.c.d.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.e.a.51.1	✓	2	1.1	even	1	trivial
350.2.e.a.151.1	yes	2	7.4	even	3	inner
350.2.e.k.51.1	yes	2	5.4	even	2
350.2.e.k.151.1	yes	2	35.4	even	6
350.2.j.e.149.1		4	5.2	odd	4
350.2.j.e.149.2		4	5.3	odd	4
350.2.j.e.249.1		4	35.18	odd	12
350.2.j.e.249.2		4	35.32	odd	12
2450.2.a.e.1.1		1	35.9	even	6
2450.2.a.o.1.1		1	35.19	odd	6
2450.2.a.u.1.1		1	7.5	odd	6
2450.2.a.be.1.1		1	7.2	even	3
2450.2.c.d.99.1		2	35.33	even	12
2450.2.c.d.99.2		2	35.12	even	12
2450.2.c.o.99.1		2	35.23	odd	12
2450.2.c.o.99.2		2	35.2	odd	12

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 + 1.73205i) q^{12} -2.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-4.00000 + 6.92820i) q^{19} +(4.00000 + 3.46410i) q^{21} +(-4.50000 + 7.79423i) q^{23} +(-1.00000 - 1.73205i) q^{24} +(1.00000 - 1.73205i) q^{26} -4.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +3.00000 q^{34} +1.00000 q^{36} +(4.00000 - 6.92820i) q^{37} +(-4.00000 - 6.92820i) q^{38} +(2.00000 + 3.46410i) q^{39} -3.00000 q^{41} +(-5.00000 + 1.73205i) q^{42} +10.0000 q^{43} +(-4.50000 - 7.79423i) q^{46} +(-1.50000 + 2.59808i) q^{47} +2.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(1.00000 + 1.73205i) q^{52} +(3.00000 + 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} +(-2.50000 + 0.866025i) q^{56} +16.0000 q^{57} +(3.00000 - 5.19615i) q^{58} +(-6.00000 - 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} +5.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{68} +18.0000 q^{69} -9.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(-5.00000 - 8.66025i) q^{73} +(4.00000 + 6.92820i) q^{74} +8.00000 q^{76} -4.00000 q^{78} +(-2.50000 + 4.33013i) q^{79} +(5.50000 + 9.52628i) q^{81} +(1.50000 - 2.59808i) q^{82} +6.00000 q^{83} +(1.00000 - 5.19615i) q^{84} +(-5.00000 + 8.66025i) q^{86} +(6.00000 + 10.3923i) q^{87} +(-1.50000 + 2.59808i) q^{89} +(5.00000 - 1.73205i) q^{91} +9.00000 q^{92} +(-5.00000 + 8.66025i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(-1.00000 + 1.73205i) q^{96} -5.00000 q^{97} +(1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 - 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + 4 q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - 2 q^{12} - 4 q^{13} + q^{14} - q^{16} - 3 q^{17} - q^{18} - 8 q^{19} + 8 q^{21} - 9 q^{23} - 2 q^{24} + 2 q^{26} - 8 q^{27} + 4 q^{28} - 12 q^{29} - 5 q^{31} - q^{32} + 6 q^{34} + 2 q^{36} + 8 q^{37} - 8 q^{38} + 4 q^{39} - 6 q^{41} - 10 q^{42} + 20 q^{43} - 9 q^{46} - 3 q^{47} + 4 q^{48} + 11 q^{49} - 6 q^{51} + 2 q^{52} + 6 q^{53} + 4 q^{54} - 5 q^{56} + 32 q^{57} + 6 q^{58} - 12 q^{59} + 4 q^{61} + 10 q^{62} + q^{63} + 2 q^{64} + 2 q^{67} - 3 q^{68} + 36 q^{69} - 18 q^{71} - q^{72} - 10 q^{73} + 8 q^{74} + 16 q^{76} - 8 q^{78} - 5 q^{79} + 11 q^{81} + 3 q^{82} + 12 q^{83} + 2 q^{84} - 10 q^{86} + 12 q^{87} - 3 q^{89} + 10 q^{91} + 18 q^{92} - 10 q^{93} - 3 q^{94} - 2 q^{96} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + 4 * q^6 - 5 * q^7 + 2 * q^8 - q^9 - 2 * q^12 - 4 * q^13 + q^14 - q^16 - 3 * q^17 - q^18 - 8 * q^19 + 8 * q^21 - 9 * q^23 - 2 * q^24 + 2 * q^26 - 8 * q^27 + 4 * q^28 - 12 * q^29 - 5 * q^31 - q^32 + 6 * q^34 + 2 * q^36 + 8 * q^37 - 8 * q^38 + 4 * q^39 - 6 * q^41 - 10 * q^42 + 20 * q^43 - 9 * q^46 - 3 * q^47 + 4 * q^48 + 11 * q^49 - 6 * q^51 + 2 * q^52 + 6 * q^53 + 4 * q^54 - 5 * q^56 + 32 * q^57 + 6 * q^58 - 12 * q^59 + 4 * q^61 + 10 * q^62 + q^63 + 2 * q^64 + 2 * q^67 - 3 * q^68 + 36 * q^69 - 18 * q^71 - q^72 - 10 * q^73 + 8 * q^74 + 16 * q^76 - 8 * q^78 - 5 * q^79 + 11 * q^81 + 3 * q^82 + 12 * q^83 + 2 * q^84 - 10 * q^86 + 12 * q^87 - 3 * q^89 + 10 * q^91 + 18 * q^92 - 10 * q^93 - 3 * q^94 - 2 * q^96 - 10 * q^97 + 2 * q^98

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