LMFDB - Embedded newform 525.2.i.a.226.1

Error: no document with id 250969025 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,2,Mod(151,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.151"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.i (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.19214610612$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	525.226
Dual form			525.2.i.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)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} -12.0000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} -8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} +8.00000 q^{34} +2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(-1.00000 - 5.19615i) q^{42} -1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(8.00000 - 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +(-2.50000 - 0.866025i) q^{63} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} -4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} +8.00000 q^{92} +(0.500000 - 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{6} + q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 6 q^{13} - 10 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{18} - q^{19} - 4 q^{21} - 24 q^{22} - 4 q^{23} - 6 q^{26} - 2 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 4 * q^6 + q^7 - q^9 + 6 * q^11 + 2 * q^12 + 6 * q^13 - 10 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^18 - q^19 - 4 * q^21 - 24 * q^22 - 4 * q^23 - 6 * q^26 - 2 * q^27 + 8 * q^28 - 16 * q^29 - q^31 + 8 * q^32 - 6 * q^33 + 16 * q^34 + 4 * q^36 + 7 * q^37 - 2 * q^38 + 3 * q^39 - 12 * q^41 - 2 * q^42 - 2 * q^43 + 12 * q^44 - 8 * q^46 + 2 * q^47 + 8 * q^48 - 13 * q^49 + 4 * q^51 - 6 * q^52 + 4 * q^53 + 2 * q^54 - 2 * q^57 + 16 * q^58 + 8 * q^59 + 14 * q^61 + 4 * q^62 - 5 * q^63 - 16 * q^64 - 12 * q^66 + 7 * q^67 - 8 * q^68 - 8 * q^69 + 12 * q^71 + q^73 + 14 * q^74 + 4 * q^76 - 24 * q^77 - 12 * q^78 + q^79 - q^81 + 12 * q^82 - 4 * q^83 + 10 * q^84 + 2 * q^86 - 8 * q^87 + 12 * q^89 + 3 * q^91 + 16 * q^92 + q^93 + 4 * q^94 - 8 * q^96 + 12 * q^97 + 4 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$2$	−1.00000	+	1.73205i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$		0			0
$5$		0			0
$6$	−2.00000			−0.816497
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$	3.00000			0.832050			0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000			0.832050			0.416025	+	0.909353i	$0.363423\pi$
$14$	−5.00000	−	1.73205i	−1.33631	−	0.462910i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	−1.00000	−	1.73205i	−0.235702	−	0.408248i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−12.0000			−2.55841
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$		0			0
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−1.00000			−0.192450
$28$	4.00000	−	3.46410i	0.755929	−	0.654654i
$29$	−8.00000			−1.48556			−0.742781	−	0.669534i	$-0.766494\pi$
$29$	−8.00000			−1.48556			−0.742781	+	0.669534i	$0.766494\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$	4.00000	+	6.92820i	0.707107	+	1.22474i
$33$	−3.00000	+	5.19615i	−0.522233	+	0.904534i
$34$	8.00000			1.37199
$35$		0			0
$36$	2.00000			0.333333
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$	1.50000	+	2.59808i	0.240192	+	0.416025i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	−1.00000	−	5.19615i	−0.154303	−	0.801784i
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	6.00000	−	10.3923i	0.904534	−	1.56670i
$45$		0			0
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	4.00000			0.577350
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$	1.00000	−	1.73205i	0.136083	−	0.235702i
$55$		0			0
$56$		0			0
$57$	−1.00000			−0.132453
$58$	8.00000	−	13.8564i	1.05045	−	1.81944i
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	0.999709	+	0.0241347i	$0.00768307\pi$
$59$	4.00000	+	6.92820i	0.520756	+	0.901975i	−0.478953	+	0.877841i	$0.658984\pi$
$60$		0			0
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	2.00000			0.254000
$63$	−2.50000	−	0.866025i	−0.314970	−	0.109109i
$64$	−8.00000			−1.00000
$65$		0			0
$66$	−6.00000	−	10.3923i	−0.738549	−	1.27920i
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$	−4.00000	+	6.92820i	−0.485071	+	0.840168i
$69$	−4.00000			−0.481543
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	0.893801	−	0.448463i	$-0.148028\pi$
$73$	0.500000	+	0.866025i	0.0585206	+	0.101361i	−0.835281	+	0.549823i	$0.814695\pi$
$74$	7.00000	+	12.1244i	0.813733	+	1.40943i
$75$		0			0
$76$	2.00000			0.229416
$77$	−12.0000	+	10.3923i	−1.36753	+	1.18431i
$78$	−6.00000			−0.679366
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$	−2.00000			−0.219529			−0.109764	−	0.993958i	$-0.535010\pi$
$83$	−2.00000			−0.219529			−0.109764	+	0.993958i	$0.535010\pi$
$84$	5.00000	+	1.73205i	0.545545	+	0.188982i
$85$		0			0
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	−4.00000	−	6.92820i	−0.428845	−	0.742781i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$		0			0
$91$	1.50000	+	7.79423i	0.157243	+	0.817057i
$92$	8.00000			0.834058
$93$	0.500000	−	0.866025i	0.0518476	−	0.0898027i
$94$	2.00000	+	3.46410i	0.206284	+	0.357295i
$95$		0			0
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$	6.00000			0.609208			0.304604	−	0.952479i	$-0.401476\pi$
$97$	6.00000			0.609208			0.304604	+	0.952479i	$0.401476\pi$
$98$	2.00000	−	13.8564i	0.202031	−	1.39971i
$99$	−6.00000			−0.603023
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.163335	+	0.986571i	$0.552225\pi$
$103$	−9.50000	+	16.4545i	−0.936063	+	1.62131i	−0.772728	+	0.634738i	$0.781108\pi$
$104$		0			0
$105$		0			0
$106$	−8.00000			−0.777029
$107$	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	$-0.0302972\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	0.961645	+	0.274296i	$0.0884447\pi$
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	−0.243276	+	0.969957i	$0.578222\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$	10.0000	+	3.46410i	0.944911	+	0.327327i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	8.00000	+	13.8564i	0.742781	+	1.28654i
$117$	−1.50000	+	2.59808i	−0.138675	+	0.240192i
$118$	−16.0000			−1.47292
$119$	8.00000	−	6.92820i	0.733359	−	0.635107i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	14.0000	+	24.2487i	1.26750	+	2.19538i
$123$	−3.00000	−	5.19615i	−0.270501	−	0.468521i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	4.00000	−	3.46410i	0.356348	−	0.308607i
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$		0			0
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$		0			0
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$	12.0000			1.04447
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$	−14.0000			−1.20942
$135$		0			0
$136$		0			0
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	0.984757	−	0.173939i	$-0.0556494\pi$
$137$	4.00000	+	6.92820i	0.341743	+	0.591916i	−0.643013	+	0.765855i	$0.722316\pi$
$138$	4.00000	−	6.92820i	0.340503	−	0.589768i
$139$	21.0000			1.78120			0.890598	−	0.454791i	$-0.150286\pi$
$139$	21.0000			1.78120			0.890598	+	0.454791i	$0.150286\pi$
$140$		0			0
$141$	2.00000			0.168430
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	9.00000	+	15.5885i	0.752618	+	1.30357i
$144$	2.00000	+	3.46410i	0.166667	+	0.288675i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	−5.50000	−	4.33013i	−0.453632	−	0.357143i
$148$	−14.0000			−1.15079
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	4.00000			0.323381
$154$	−6.00000	−	31.1769i	−0.483494	−	2.51231i
$155$		0			0
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	−2.00000	+	3.46410i	−0.158610	+	0.274721i
$160$		0			0
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$	2.00000			0.157135
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	−0.999410	−	0.0343508i	$-0.989064\pi$
$163$	−6.00000	+	10.3923i	−0.469956	+	0.813988i	0.529454	+	0.848339i	$0.322397\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$		0			0
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	10.0000			0.773823			0.386912	−	0.922117i	$-0.373542\pi$
$167$	10.0000			0.773823			0.386912	+	0.922117i	$0.373542\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.101598	−	0.994826i	$-0.467605\pi$
$173$	12.0000	−	20.7846i	0.912343	−	1.58022i	0.810745	−	0.585399i	$-0.199062\pi$
$174$	16.0000			1.21296
$175$		0			0
$176$	24.0000			1.80907
$177$	−4.00000	+	6.92820i	−0.300658	+	0.520756i
$178$	12.0000	+	20.7846i	0.899438	+	1.55787i
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	−15.0000	−	5.19615i	−1.11187	−	0.385164i
$183$	14.0000			1.03491
$184$		0			0
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	12.0000	−	20.7846i	0.877527	−	1.51992i
$188$	−4.00000			−0.291730
$189$	−0.500000	−	2.59808i	−0.0363696	−	0.188982i
$190$		0			0
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	−4.00000	−	6.92820i	−0.288675	−	0.500000i
$193$	−4.50000	−	7.79423i	−0.323917	−	0.561041i	0.657376	−	0.753563i	$-0.271667\pi$
$193$	−4.50000	−	7.79423i	−0.323917	−	0.561041i	−0.981293	+	0.192522i	$0.938333\pi$
$194$	−6.00000	+	10.3923i	−0.430775	+	0.746124i
$195$		0			0
$196$	11.0000	+	8.66025i	0.785714	+	0.618590i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	−3.50000	+	6.06218i	−0.246871	+	0.427593i
$202$	−20.0000			−1.40720
$203$	−4.00000	−	20.7846i	−0.280745	−	1.45879i
$204$	−8.00000			−0.560112
$205$		0			0
$206$	−19.0000	−	32.9090i	−1.32379	−	2.29288i
$207$	−2.00000	−	3.46410i	−0.139010	−	0.240772i
$208$	6.00000	−	10.3923i	0.416025	−	0.720577i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	4.00000	−	6.92820i	0.274721	−	0.475831i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	12.0000	+	20.7846i	0.820303	+	1.42081i
$215$		0			0
$216$		0			0
$217$	2.00000	−	1.73205i	0.135769	−	0.117579i
$218$	−30.0000			−2.03186
$219$	−0.500000	+	0.866025i	−0.0337869	+	0.0585206i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−7.00000	+	12.1244i	−0.469809	+	0.813733i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$	−16.0000	+	13.8564i	−1.06904	+	0.925820i
$225$		0			0
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	−5.00000	−	8.66025i	−0.331862	−	0.574801i	0.651015	−	0.759065i	$-0.274343\pi$
$227$	−5.00000	−	8.66025i	−0.331862	−	0.574801i	−0.982877	+	0.184263i	$0.941010\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	−0.996832	−	0.0795401i	$-0.974655\pi$
$229$	−6.50000	+	11.2583i	−0.429532	+	0.743971i	0.567300	+	0.823511i	$0.307988\pi$
$230$		0			0
$231$	−15.0000	−	5.19615i	−0.986928	−	0.341882i
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$		0			0
$236$	8.00000	−	13.8564i	0.520756	−	0.901975i
$237$	1.00000			0.0649570
$238$	4.00000	+	20.7846i	0.259281	+	1.34727i
$239$	14.0000			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$239$	14.0000			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$240$		0			0
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	−25.0000	−	43.3013i	−1.60706	−	2.78351i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−28.0000			−1.79252
$245$		0			0
$246$	12.0000			0.765092
$247$	−1.50000	+	2.59808i	−0.0954427	+	0.165312i
$248$		0			0
$249$	−1.00000	−	1.73205i	−0.0633724	−	0.109764i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	1.00000	+	5.19615i	0.0629941	+	0.327327i
$253$	−24.0000			−1.50887
$254$	5.00000	−	8.66025i	0.313728	−	0.543393i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	0.435970	+	0.899961i	$0.356405\pi$
$257$	−9.00000	+	15.5885i	−0.561405	+	0.972381i	−0.997374	+	0.0724199i	$0.976928\pi$
$258$	2.00000			0.124515
$259$	17.5000	+	6.06218i	1.08740	+	0.376685i
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	0.921077	−	0.389380i	$-0.127311\pi$
$263$	2.00000	+	3.46410i	0.123325	+	0.213606i	−0.797752	+	0.602986i	$0.793977\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$	12.0000			0.734388
$268$	7.00000	−	12.1244i	0.427593	−	0.740613i
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	0.977229	−	0.212187i	$-0.0680585\pi$
$269$	5.00000	+	8.66025i	0.304855	+	0.528025i	−0.672374	+	0.740212i	$0.734725\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$	−16.0000			−0.970143
$273$	−6.00000	+	5.19615i	−0.363137	+	0.314485i
$274$	−16.0000			−0.966595
$275$		0			0
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	0.741512	−	0.670940i	$-0.234109\pi$
$277$	−3.50000	−	6.06218i	−0.210295	−	0.364241i	−0.951807	+	0.306699i	$0.900776\pi$
$278$	−21.0000	+	36.3731i	−1.25950	+	2.18151i
$279$	1.00000			0.0598684
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	0.743048	−	0.669238i	$-0.233379\pi$
$283$	−3.50000	−	6.06218i	−0.208053	−	0.360359i	−0.951101	+	0.308879i	$0.900046\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	−36.0000			−2.12872
$287$	−3.00000	−	15.5885i	−0.177084	−	0.920158i
$288$	−8.00000			−0.471405
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$	13.0000	−	5.19615i	0.758175	−	0.303046i
$295$		0			0
$296$		0			0
$297$	−3.00000	−	5.19615i	−0.174078	−	0.301511i
$298$	4.00000	+	6.92820i	0.231714	+	0.401340i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	16.0000			0.920697
$303$	−5.00000	+	8.66025i	−0.287242	+	0.497519i
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$		0			0
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$	30.0000	+	10.3923i	1.70941	+	0.592157i
$309$	−19.0000			−1.08087
$310$		0			0
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	5.50000	−	9.52628i	0.310878	−	0.538457i	−0.667674	−	0.744453i	$-0.732710\pi$
$313$	5.50000	−	9.52628i	0.310878	−	0.538457i	0.978553	+	0.205996i	$0.0660435\pi$
$314$	−20.0000			−1.12867
$315$		0			0
$316$	−2.00000			−0.112509
$317$	10.0000	−	17.3205i	0.561656	−	0.972817i	−0.435696	−	0.900094i	$-0.643498\pi$
$317$	10.0000	−	17.3205i	0.561656	−	0.972817i	0.997352	−	0.0727229i	$-0.0231689\pi$
$318$	−4.00000	−	6.92820i	−0.224309	−	0.388514i
$319$	−24.0000	−	41.5692i	−1.34374	−	2.32743i
$320$		0			0
$321$	12.0000			0.669775
$322$	16.0000	−	13.8564i	0.891645	−	0.772187i
$323$	4.00000			0.222566
$324$	−1.00000	+	1.73205i	−0.0555556	+	0.0962250i
$325$		0			0
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	−7.50000	+	12.9904i	−0.414751	+	0.718370i
$328$		0			0
$329$	5.00000	+	1.73205i	0.275659	+	0.0954911i
$330$		0			0
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	2.00000	+	3.46410i	0.109764	+	0.190117i
$333$	3.50000	+	6.06218i	0.191799	+	0.332205i
$334$	−10.0000	+	17.3205i	−0.547176	+	0.947736i
$335$		0			0
$336$	2.00000	+	10.3923i	0.109109	+	0.566947i
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$	4.00000	−	6.92820i	0.217571	−	0.376845i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$	2.00000			0.108148
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$		0			0
$346$	24.0000	+	41.5692i	1.29025	+	2.23478i
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	0.996826	−	0.0796169i	$-0.0253697\pi$
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	−0.567363	+	0.823468i	$0.692036\pi$
$348$	−8.00000	+	13.8564i	−0.428845	+	0.742781i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$	−24.0000	+	41.5692i	−1.27920	+	2.21565i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$	−8.00000	−	13.8564i	−0.425195	−	0.736460i
$355$		0			0
$356$	−24.0000			−1.27200
$357$	10.0000	+	3.46410i	0.529256	+	0.183340i
$358$	36.0000			1.90266
$359$	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
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−13.0000	+	22.5167i	−0.683265	+	1.18345i
$363$	−25.0000			−1.31216
$364$	12.0000	−	10.3923i	0.628971	−	0.544705i
$365$		0			0
$366$	−14.0000	+	24.2487i	−0.731792	+	1.26750i
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	8.00000	+	13.8564i	0.417029	+	0.722315i
$369$	3.00000	−	5.19615i	0.156174	−	0.270501i
$370$		0			0
$371$	−8.00000	+	6.92820i	−0.415339	+	0.359694i
$372$	−2.00000			−0.103695
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	−0.687776	−	0.725923i	$-0.741413\pi$
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	0.972556	+	0.232671i	$0.0747464\pi$
$374$	24.0000	+	41.5692i	1.24101	+	2.14949i
$375$		0			0
$376$		0			0
$377$	−24.0000			−1.23606
$378$	5.00000	+	1.73205i	0.257172	+	0.0890871i
$379$	11.0000			0.565032			0.282516	−	0.959263i	$-0.408831\pi$
$379$	11.0000			0.565032			0.282516	+	0.959263i	$0.408831\pi$
$380$		0			0
$381$	−2.50000	−	4.33013i	−0.128079	−	0.221839i
$382$	−10.0000	−	17.3205i	−0.511645	−	0.886194i
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	−0.247451	−	0.968900i	$-0.579593\pi$
$383$	14.0000	−	24.2487i	0.715367	−	1.23905i	0.962818	−	0.270151i	$-0.0870736\pi$
$384$		0			0
$385$		0			0
$386$	18.0000			0.916176
$387$	0.500000	−	0.866025i	0.0254164	−	0.0440225i
$388$	−6.00000	−	10.3923i	−0.304604	−	0.527589i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$	−2.00000			−0.100887
$394$	12.0000	−	20.7846i	0.604551	−	1.04711i
$395$		0			0
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−18.5000	+	32.0429i	−0.928488	+	1.60819i	−0.142636	+	0.989775i	$0.545558\pi$
$397$	−18.5000	+	32.0429i	−0.928488	+	1.60819i	−0.785853	+	0.618414i	$0.787776\pi$
$398$	16.0000			0.802008
$399$	−0.500000	−	2.59808i	−0.0250313	−	0.130066i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	−7.00000	−	12.1244i	−0.349128	−	0.604708i
$403$	−1.50000	−	2.59808i	−0.0747203	−	0.129419i
$404$	10.0000	−	17.3205i	0.497519	−	0.861727i
$405$		0			0
$406$	40.0000	+	13.8564i	1.98517	+	0.687682i
$407$	42.0000			2.08186
$408$		0			0
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	0.797574	−	0.603220i	$-0.206116\pi$
$409$	−2.50000	−	4.33013i	−0.123617	−	0.214111i	−0.921192	+	0.389109i	$0.872783\pi$
$410$		0			0
$411$	−4.00000	+	6.92820i	−0.197305	+	0.341743i
$412$	38.0000			1.87213
$413$	−16.0000	+	13.8564i	−0.787309	+	0.681829i
$414$	8.00000			0.393179
$415$		0			0
$416$	12.0000	+	20.7846i	0.588348	+	1.01905i
$417$	10.5000	+	18.1865i	0.514187	+	0.890598i
$418$	6.00000	−	10.3923i	0.293470	−	0.508304i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	20.0000	−	34.6410i	0.973585	−	1.68630i
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	35.0000	+	12.1244i	1.69377	+	0.586739i
$428$	−24.0000			−1.16008
$429$	−9.00000	+	15.5885i	−0.434524	+	0.752618i
$430$		0			0
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	−2.00000	+	3.46410i	−0.0962250	+	0.166667i
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	1.00000	+	5.19615i	0.0480015	+	0.249423i
$435$		0			0
$436$	15.0000	−	25.9808i	0.718370	−	1.24425i
$437$	−2.00000	−	3.46410i	−0.0956730	−	0.165710i
$438$	−1.00000	−	1.73205i	−0.0477818	−	0.0827606i
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	−0.991322	−	0.131453i	$-0.958036\pi$
$439$	−8.00000	+	13.8564i	−0.381819	+	0.661330i	0.609503	+	0.792784i	$0.291369\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	24.0000			1.14156
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	0.0212481	+	0.999774i	$0.493236\pi$
$443$	−18.0000	+	31.1769i	−0.855206	+	1.48126i	−0.876454	+	0.481486i	$0.840097\pi$
$444$	−7.00000	−	12.1244i	−0.332205	−	0.575396i
$445$		0			0
$446$	−24.0000	+	41.5692i	−1.13643	+	1.96836i
$447$	4.00000			0.189194
$448$	−4.00000	−	20.7846i	−0.188982	−	0.981981i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$	−6.00000	−	10.3923i	−0.282216	−	0.488813i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	20.0000			0.938647
$455$		0			0
$456$		0			0
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	−0.986396	−	0.164386i	$-0.947436\pi$
$457$	−7.50000	+	12.9904i	−0.350835	+	0.607664i	0.635561	+	0.772051i	$0.280769\pi$
$458$	−13.0000	−	22.5167i	−0.607450	−	1.05213i
$459$	2.00000	+	3.46410i	0.0933520	+	0.161690i
$460$		0			0
$461$	−8.00000			−0.372597			−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000			−0.372597			−0.186299	+	0.982493i	$0.559649\pi$
$462$	24.0000	−	20.7846i	1.11658	−	0.966988i
$463$	−3.00000			−0.139422			−0.0697109	−	0.997567i	$-0.522208\pi$
$463$	−3.00000			−0.139422			−0.0697109	+	0.997567i	$0.522208\pi$
$464$	−16.0000	+	27.7128i	−0.742781	+	1.28654i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	−0.490926	−	0.871201i	$-0.663342\pi$
$467$	11.0000	−	19.0526i	0.509019	−	0.881647i	0.999945	−	0.0104461i	$-0.00332515\pi$
$468$	6.00000			0.277350
$469$	−14.0000	+	12.1244i	−0.646460	+	0.559851i
$470$		0			0
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$		0			0
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$		0			0
$476$	−20.0000	−	6.92820i	−0.916698	−	0.317554i
$477$	−4.00000			−0.183147
$478$	−14.0000	+	24.2487i	−0.640345	+	1.10911i
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	0.908093	−	0.418769i	$-0.137538\pi$
$479$	2.00000	+	3.46410i	0.0913823	+	0.158279i	−0.816711	+	0.577047i	$0.804205\pi$
$480$		0			0
$481$	10.5000	−	18.1865i	0.478759	−	0.829235i
$482$	−36.0000			−1.63976
$483$	−2.00000	−	10.3923i	−0.0910032	−	0.472866i
$484$	50.0000			2.27273
$485$		0			0
$486$	1.00000	+	1.73205i	0.0453609	+	0.0785674i
$487$	−6.50000	−	11.2583i	−0.294543	−	0.510164i	0.680335	−	0.732901i	$-0.261834\pi$
$487$	−6.50000	−	11.2583i	−0.294543	−	0.510164i	−0.974879	+	0.222737i	$0.928501\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−6.00000	+	10.3923i	−0.270501	+	0.468521i
$493$	16.0000	+	27.7128i	0.720604	+	1.24812i
$494$	−3.00000	−	5.19615i	−0.134976	−	0.233786i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	3.00000	+	15.5885i	0.134568	+	0.699238i
$498$	4.00000			0.179244
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$		0			0
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$	−12.0000	+	20.7846i	−0.535586	+	0.927663i
$503$	2.00000			0.0891756			0.0445878	−	0.999005i	$-0.485803\pi$
$503$	2.00000			0.0891756			0.0445878	+	0.999005i	$0.485803\pi$
$504$		0			0
$505$		0			0
$506$	24.0000	−	41.5692i	1.06693	−	1.84798i
$507$	−2.00000	−	3.46410i	−0.0888231	−	0.153846i
$508$	5.00000	+	8.66025i	0.221839	+	0.384237i
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	−0.955300	−	0.295637i	$-0.904468\pi$
$509$	−5.00000	+	8.66025i	−0.221621	+	0.383859i	0.733679	+	0.679496i	$0.237801\pi$
$510$		0			0
$511$	−2.00000	+	1.73205i	−0.0884748	+	0.0766214i
$512$	32.0000			1.41421
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	−18.0000	−	31.1769i	−0.793946	−	1.37515i
$515$		0			0
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	12.0000			0.527759
$518$	−28.0000	+	24.2487i	−1.23025	+	1.06543i
$519$	24.0000			1.05348
$520$		0			0
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	0.818884	−	0.573959i	$-0.194593\pi$
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	−0.906505	+	0.422194i	$0.861260\pi$
$522$	8.00000	+	13.8564i	0.350150	+	0.606478i
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	−0.720358	−	0.693602i	$-0.756023\pi$
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	0.960856	+	0.277047i	$0.0893559\pi$
$524$	4.00000			0.174741
$525$		0			0
$526$	−8.00000			−0.348817
$527$	−2.00000	+	3.46410i	−0.0871214	+	0.150899i
$528$	12.0000	+	20.7846i	0.522233	+	0.904534i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	−8.00000			−0.347170
$532$	1.00000	+	5.19615i	0.0433555	+	0.225282i
$533$	−18.0000			−0.779667
$534$	−12.0000	+	20.7846i	−0.519291	+	0.899438i
$535$		0			0
$536$		0			0
$537$	9.00000	−	15.5885i	0.388379	−	0.672692i
$538$	−20.0000			−0.862261
$539$	−33.0000	−	25.9808i	−1.42141	−	1.11907i
$540$		0			0
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	24.0000	+	41.5692i	1.03089	+	1.78555i
$543$	6.50000	+	11.2583i	0.278942	+	0.483141i
$544$	16.0000	−	27.7128i	0.685994	−	1.18818i
$545$		0			0
$546$	−3.00000	−	15.5885i	−0.128388	−	0.667124i
$547$	−36.0000			−1.53925			−0.769624	−	0.638497i	$-0.779557\pi$
$547$	−36.0000			−1.53925			−0.769624	+	0.638497i	$0.779557\pi$
$548$	8.00000	−	13.8564i	0.341743	−	0.591916i
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$	2.50000	+	0.866025i	0.106311	+	0.0368271i
$554$	14.0000			0.594803
$555$		0			0
$556$	−21.0000	−	36.3731i	−0.890598	−	1.54256i
$557$	−5.00000	−	8.66025i	−0.211857	−	0.366947i	0.740439	−	0.672124i	$-0.234618\pi$
$557$	−5.00000	−	8.66025i	−0.211857	−	0.366947i	−0.952296	+	0.305177i	$0.901284\pi$
$558$	−1.00000	+	1.73205i	−0.0423334	+	0.0733236i
$559$	−3.00000			−0.126886
$560$		0			0
$561$	24.0000			1.01328
$562$	12.0000	−	20.7846i	0.506189	−	0.876746i
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	−0.998419	−	0.0562051i	$-0.982100\pi$
$563$	−13.0000	−	22.5167i	−0.547885	−	0.948964i	0.450535	−	0.892759i	$-0.351233\pi$
$564$	−2.00000	−	3.46410i	−0.0842152	−	0.145865i
$565$		0			0
$566$	14.0000			0.588464
$567$	2.00000	−	1.73205i	0.0839921	−	0.0727393i
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$	18.0000	−	31.1769i	0.752618	−	1.30357i
$573$	−10.0000			−0.417756
$574$	30.0000	+	10.3923i	1.25218	+	0.433766i
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	−14.5000	−	25.1147i	−0.603643	−	1.04554i	−0.992264	−	0.124143i	$-0.960382\pi$
$577$	−14.5000	−	25.1147i	−0.603643	−	1.04554i	0.388621	−	0.921397i	$-0.372951\pi$
$578$	1.00000	+	1.73205i	0.0415945	+	0.0720438i
$579$	4.50000	−	7.79423i	0.187014	−	0.323917i
$580$		0			0
$581$	−1.00000	−	5.19615i	−0.0414870	−	0.215573i
$582$	−12.0000			−0.497416
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$		0			0
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$	−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
$589$	1.00000			0.0412043
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−14.0000	−	24.2487i	−0.575396	−	0.996616i
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	−0.989501	−	0.144528i	$-0.953834\pi$
$593$	−9.00000	+	15.5885i	−0.369586	+	0.640141i	0.619915	+	0.784669i	$0.287167\pi$
$594$	12.0000			0.492366
$595$		0			0
$596$	−8.00000			−0.327693
$597$	4.00000	−	6.92820i	0.163709	−	0.283552i
$598$	−12.0000	−	20.7846i	−0.490716	−	0.849946i
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	0.903988	−	0.427558i	$-0.140626\pi$
$599$	2.00000	+	3.46410i	0.0817178	+	0.141539i	−0.822270	+	0.569097i	$0.807293\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$	5.00000	+	1.73205i	0.203785	+	0.0705931i
$603$	−7.00000			−0.285062
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$	−10.0000	−	17.3205i	−0.406222	−	0.703598i
$607$	17.5000	−	30.3109i	0.710303	−	1.23028i	−0.254440	−	0.967088i	$-0.581891\pi$
$607$	17.5000	−	30.3109i	0.710303	−	1.23028i	0.964743	−	0.263193i	$-0.0847754\pi$
$608$	−8.00000			−0.324443
$609$	16.0000	−	13.8564i	0.648353	−	0.561490i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	−4.00000	−	6.92820i	−0.161690	−	0.280056i
$613$	−15.0000	−	25.9808i	−0.605844	−	1.04935i	−0.991917	−	0.126885i	$-0.959502\pi$
$613$	−15.0000	−	25.9808i	−0.605844	−	1.04935i	0.386073	−	0.922468i	$-0.373831\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$		0			0
$616$		0			0
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$	19.0000	−	32.9090i	0.764292	−	1.32379i
$619$	−1.50000	−	2.59808i	−0.0602901	−	0.104425i	0.834305	−	0.551303i	$-0.185869\pi$
$619$	−1.50000	−	2.59808i	−0.0602901	−	0.104425i	−0.894595	+	0.446878i	$0.852536\pi$
$620$		0			0
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$	12.0000			0.481156
$623$	30.0000	+	10.3923i	1.20192	+	0.416359i
$624$	12.0000			0.480384
$625$		0			0
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$	−3.00000	−	5.19615i	−0.119808	−	0.207514i
$628$	10.0000	−	17.3205i	0.399043	−	0.691164i
$629$	−28.0000			−1.11643
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	20.0000	+	34.6410i	0.794301	+	1.37577i
$635$		0			0
$636$	8.00000			0.317221
$637$	−19.5000	+	7.79423i	−0.772618	+	0.308819i
$638$	96.0000			3.80068
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$	4.00000	+	20.7846i	0.157622	+	0.819028i
$645$		0			0
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	0.994270	+	0.106897i	$0.0340916\pi$
$647$	15.0000	+	25.9808i	0.589711	+	1.02141i	−0.404559	+	0.914512i	$0.632575\pi$
$648$		0			0
$649$	−24.0000	+	41.5692i	−0.942082	+	1.63173i
$650$		0			0
$651$	2.50000	+	0.866025i	0.0979827	+	0.0339422i
$652$	24.0000			0.939913
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	−0.695934	−	0.718106i	$-0.745009\pi$
$653$	7.00000	−	12.1244i	0.273931	−	0.474463i	0.969865	+	0.243643i	$0.0783426\pi$
$654$	−15.0000	−	25.9808i	−0.586546	−	1.01593i
$655$		0			0
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	−1.00000			−0.0390137
$658$	−8.00000	+	6.92820i	−0.311872	+	0.270089i
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$662$	9.00000	+	15.5885i	0.349795	+	0.605863i
$663$	6.00000	−	10.3923i	0.233021	−	0.403604i
$664$		0			0
$665$		0			0
$666$	−14.0000			−0.542489
$667$	16.0000	−	27.7128i	0.619522	−	1.07304i
$668$	−10.0000	−	17.3205i	−0.386912	−	0.670151i
$669$	12.0000	+	20.7846i	0.463947	+	0.803579i
$670$		0			0
$671$	84.0000			3.24278
$672$	−20.0000	−	6.92820i	−0.771517	−	0.267261i
$673$	37.0000			1.42625			0.713123	−	0.701039i	$-0.247280\pi$
$673$	37.0000			1.42625			0.713123	+	0.701039i	$0.247280\pi$
$674$	25.0000	−	43.3013i	0.962964	−	1.66790i
$675$		0			0
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	−0.670342	−	0.742052i	$-0.733853\pi$
$677$	8.00000	−	13.8564i	0.307465	−	0.532545i	0.977807	+	0.209507i	$0.0671860\pi$
$678$	−12.0000			−0.460857
$679$	3.00000	+	15.5885i	0.115129	+	0.598230i
$680$		0			0
$681$	5.00000	−	8.66025i	0.191600	−	0.331862i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.801945	−	0.597398i	$-0.796201\pi$
$683$	−24.0000	−	41.5692i	−0.918334	−	1.59060i	−0.116390	−	0.993204i	$-0.537132\pi$
$684$	−1.00000	+	1.73205i	−0.0382360	+	0.0662266i
$685$		0			0
$686$	37.0000	−	1.73205i	1.41267	−	0.0661300i
$687$	−13.0000			−0.495981
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	0.486312	+	0.873785i	$0.338342\pi$
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	−0.999876	+	0.0157341i	$0.994991\pi$
$692$	−48.0000			−1.82469
$693$	−3.00000	−	15.5885i	−0.113961	−	0.592157i
$694$	−32.0000			−1.21470
$695$		0			0
$696$		0			0
$697$	12.0000	+	20.7846i	0.454532	+	0.787273i
$698$	−2.00000	+	3.46410i	−0.0757011	+	0.131118i
$699$	6.00000			0.226941
$700$		0			0
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$	3.00000	−	5.19615i	0.113228	−	0.196116i
$703$	3.50000	+	6.06218i	0.132005	+	0.228639i
$704$	−24.0000	−	41.5692i	−0.904534	−	1.56670i
$705$		0			0
$706$	36.0000			1.35488
$707$	−20.0000	+	17.3205i	−0.752177	+	0.651405i
$708$	16.0000			0.601317
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$	4.00000			0.149801
$714$	−16.0000	+	13.8564i	−0.598785	+	0.518563i
$715$		0			0
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	7.00000	+	12.1244i	0.261420	+	0.452792i
$718$	24.0000	+	41.5692i	0.895672	+	1.55135i
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	−0.352735	−	0.935723i	$-0.614748\pi$
$719$	17.0000	−	29.4449i	0.633993	−	1.09811i	0.986728	−	0.162385i	$-0.0519185\pi$
$720$		0			0
$721$	−47.5000	−	16.4545i	−1.76899	−	0.612797i
$722$	−36.0000			−1.33978
$723$	−9.00000	+	15.5885i	−0.334714	+	0.579741i
$724$	−13.0000	−	22.5167i	−0.483141	−	0.836825i
$725$		0			0
$726$	25.0000	−	43.3013i	0.927837	−	1.60706i
$727$	−7.00000			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$727$	−7.00000			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$	−14.0000	−	24.2487i	−0.517455	−	0.896258i
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	0.129275	+	0.991609i	$0.458735\pi$
$733$	−21.5000	+	37.2391i	−0.794121	+	1.37546i	−0.923396	+	0.383849i	$0.874598\pi$
$734$	−38.0000			−1.40261
$735$		0			0
$736$	−32.0000			−1.17954
$737$	−21.0000	+	36.3731i	−0.773545	+	1.33982i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	−0.945818	−	0.324697i	$-0.894738\pi$
$739$	−20.5000	−	35.5070i	−0.754105	−	1.30615i	0.191714	−	0.981451i	$-0.438596\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$	−4.00000	−	20.7846i	−0.146845	−	0.763027i
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$		0			0
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	1.00000	−	1.73205i	0.0365881	−	0.0633724i
$748$	−48.0000			−1.75505
$749$	30.0000	+	10.3923i	1.09618	+	0.379727i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$	24.0000	−	41.5692i	0.874028	−	1.51386i
$755$		0			0
$756$	−4.00000	+	3.46410i	−0.145479	+	0.125988i
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−11.0000	+	19.0526i	−0.399538	+	0.692020i
$759$	−12.0000	−	20.7846i	−0.435572	−	0.754434i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	10.0000			0.362262
$763$	−30.0000	+	25.9808i	−1.08607	+	0.940567i
$764$	20.0000			0.723575
$765$		0			0
$766$	28.0000	+	48.4974i	1.01168	+	1.75228i
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	8.00000	−	13.8564i	0.288675	−	0.500000i
$769$	−49.0000			−1.76699			−0.883493	−	0.468445i	$-0.844814\pi$
$769$	−49.0000			−1.76699			−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	−9.00000	+	15.5885i	−0.323917	+	0.561041i
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	0.981250	−	0.192740i	$-0.0617373\pi$
$773$	9.00000	+	15.5885i	0.323708	+	0.560678i	−0.657542	+	0.753418i	$0.728404\pi$
$774$	1.00000	+	1.73205i	0.0359443	+	0.0622573i
$775$		0			0
$776$		0			0
$777$	3.50000	+	18.1865i	0.125562	+	0.652438i
$778$	12.0000			0.430221
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	−16.0000	+	27.7128i	−0.572159	+	0.991008i
$783$	8.00000			0.285897
$784$	−4.00000	+	27.7128i	−0.142857	+	0.989743i
$785$		0			0
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	12.0000	+	20.7846i	0.427482	+	0.740421i
$789$	−2.00000	+	3.46410i	−0.0712019	+	0.123325i
$790$		0			0
$791$	3.00000	+	15.5885i	0.106668	+	0.554262i
$792$		0			0
$793$	21.0000	−	36.3731i	0.745732	−	1.29165i
$794$	−37.0000	−	64.0859i	−1.31308	−	2.27432i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	36.0000			1.27519			0.637593	−	0.770374i	$-0.279930\pi$
$797$	36.0000			1.27519			0.637593	+	0.770374i	$0.279930\pi$
$798$	5.00000	+	1.73205i	0.176998	+	0.0613139i
$799$	−8.00000			−0.283020
$800$		0			0
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	12.0000	+	20.7846i	0.423735	+	0.733930i
$803$	−3.00000	+	5.19615i	−0.105868	+	0.183368i
$804$	14.0000			0.493742
$805$		0			0
$806$	6.00000			0.211341
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$		0			0
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$		0			0
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$	−32.0000	+	27.7128i	−1.12298	+	0.972529i
$813$	24.0000			0.841717
$814$	−42.0000	+	72.7461i	−1.47210	+	2.54975i
$815$		0			0
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	0.500000	−	0.866025i	0.0174928	−	0.0302984i
$818$	10.0000			0.349642
$819$	−7.50000	−	2.59808i	−0.262071	−	0.0907841i
$820$		0			0
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$	−8.00000	−	13.8564i	−0.279032	−	0.483298i
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$		0			0
$825$		0			0
$826$	−8.00000	−	41.5692i	−0.278356	−	1.44638i
$827$	30.0000			1.04320			0.521601	−	0.853189i	$-0.325335\pi$
$827$	30.0000			1.04320			0.521601	+	0.853189i	$0.325335\pi$
$828$	−4.00000	+	6.92820i	−0.139010	+	0.240772i
$829$	−28.5000	−	49.3634i	−0.989846	−	1.71446i	−0.618024	−	0.786159i	$-0.712066\pi$
$829$	−28.5000	−	49.3634i	−0.989846	−	1.71446i	−0.371822	−	0.928304i	$-0.621267\pi$
$830$		0			0
$831$	3.50000	−	6.06218i	0.121414	−	0.210295i
$832$	−24.0000			−0.832050
$833$	22.0000	+	17.3205i	0.762255	+	0.600120i
$834$	−42.0000			−1.45434
$835$		0			0
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	0.500000	+	0.866025i	0.0172825	+	0.0299342i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−1.00000	+	1.73205i	−0.0344623	+	0.0596904i
$843$	−6.00000	−	10.3923i	−0.206651	−	0.357930i
$844$	20.0000	+	34.6410i	0.688428	+	1.19239i
$845$		0			0
$846$	−4.00000			−0.137523
$847$	−62.5000	−	21.6506i	−2.14753	−	0.743925i
$848$	16.0000			0.549442
$849$	3.50000	−	6.06218i	0.120120	−	0.208053i
$850$		0			0
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	9.00000			0.308154			0.154077	−	0.988059i	$-0.450760\pi$
$853$	9.00000			0.308154			0.154077	+	0.988059i	$0.450760\pi$
$854$	−56.0000	+	48.4974i	−1.91628	+	1.65955i
$855$		0			0
$856$		0			0
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	0.745163	−	0.666883i	$-0.232372\pi$
$857$	−6.00000	−	10.3923i	−0.204956	−	0.354994i	−0.950119	+	0.311888i	$0.899038\pi$
$858$	−18.0000	−	31.1769i	−0.614510	−	1.06436i
$859$	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
$862$	−4.00000			−0.136241
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	−0.912558	−	0.408946i	$-0.865896\pi$
$863$	−3.00000	+	5.19615i	−0.102121	+	0.176879i	0.810437	+	0.585826i	$0.199230\pi$
$864$	−4.00000	−	6.92820i	−0.136083	−	0.235702i
$865$		0			0
$866$	−5.00000	+	8.66025i	−0.169907	+	0.294287i
$867$	1.00000			0.0339618
$868$	−5.00000	−	1.73205i	−0.169711	−	0.0587896i
$869$	6.00000			0.203536
$870$		0			0
$871$	10.5000	+	18.1865i	0.355779	+	0.616227i
$872$		0			0
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$	8.00000			0.270604
$875$		0			0
$876$	2.00000			0.0675737
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$	−16.0000	−	27.7128i	−0.539974	−	0.935262i
$879$	8.00000	+	13.8564i	0.269833	+	0.467365i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	11.0000	+	8.66025i	0.370389	+	0.291606i
$883$	−7.00000			−0.235569			−0.117784	−	0.993039i	$-0.537579\pi$
$883$	−7.00000			−0.235569			−0.117784	+	0.993039i	$0.537579\pi$
$884$	−12.0000	+	20.7846i	−0.403604	+	0.699062i
$885$		0			0
$886$	−36.0000	−	62.3538i	−1.20944	−	2.09482i
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	−0.769792	−	0.638295i	$-0.779640\pi$
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	0.937676	+	0.347512i	$0.112973\pi$
$888$		0			0
$889$	−2.50000	−	12.9904i	−0.0838473	−	0.435683i
$890$		0			0
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	−24.0000	−	41.5692i	−0.803579	−	1.39184i
$893$	1.00000	+	1.73205i	0.0334637	+	0.0579609i
$894$	−4.00000	+	6.92820i	−0.133780	+	0.231714i
$895$		0			0
$896$		0			0
$897$	−12.0000			−0.400668
$898$	−30.0000	+	51.9615i	−1.00111	+	1.73398i
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$		0			0
$901$	8.00000	−	13.8564i	0.266519	−	0.461624i
$902$	72.0000			2.39734
$903$	2.00000	−	1.73205i	0.0665558	−	0.0576390i
$904$		0			0
$905$		0			0
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	0.999855	+	0.0170220i	$0.00541854\pi$
$907$	15.5000	+	26.8468i	0.514669	+	0.891433i	−0.485186	+	0.874411i	$0.661248\pi$
$908$	−10.0000	+	17.3205i	−0.331862	+	0.574801i
$909$	−10.0000			−0.331679
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	−6.00000	−	10.3923i	−0.198571	−	0.343935i
$914$	−15.0000	−	25.9808i	−0.496156	−	0.859367i
$915$		0			0
$916$	26.0000			0.859064
$917$	−5.00000	−	1.73205i	−0.165115	−	0.0571974i
$918$	−8.00000			−0.264039
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	−0.782210	−	0.623015i	$-0.785908\pi$
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	0.930652	+	0.365907i	$0.119241\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$	8.00000	−	13.8564i	0.263466	−	0.456336i
$923$	18.0000			0.592477
$924$	6.00000	+	31.1769i	0.197386	+	1.02565i
$925$		0			0
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$	−9.50000	−	16.4545i	−0.312021	−	0.540436i
$928$	−32.0000	−	55.4256i	−1.05045	−	1.81944i
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	−0.728046	−	0.685529i	$-0.759571\pi$
$929$	7.00000	−	12.1244i	0.229663	−	0.397787i	0.957708	+	0.287742i	$0.0929044\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$	−12.0000			−0.393073
$933$	3.00000	−	5.19615i	0.0982156	−	0.170114i
$934$	22.0000	+	38.1051i	0.719862	+	1.24684i
$935$		0			0
$936$		0			0
$937$	29.0000			0.947389			0.473694	−	0.880689i	$-0.342920\pi$
$937$	29.0000			0.947389			0.473694	+	0.880689i	$0.342920\pi$
$938$	−7.00000	−	36.3731i	−0.228558	−	1.18762i
$939$	11.0000			0.358971
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	−10.0000	−	17.3205i	−0.325818	−	0.564333i
$943$	12.0000	−	20.7846i	0.390774	−	0.676840i
$944$	32.0000			1.04151
$945$		0			0
$946$	12.0000			0.390154
$947$	13.0000	−	22.5167i	0.422443	−	0.731693i	−0.573735	−	0.819041i	$-0.694506\pi$
$947$	13.0000	−	22.5167i	0.422443	−	0.731693i	0.996178	+	0.0873481i	$0.0278392\pi$
$948$	−1.00000	−	1.73205i	−0.0324785	−	0.0562544i
$949$	1.50000	+	2.59808i	0.0486921	+	0.0843371i
$950$		0			0
$951$	20.0000			0.648544
$952$		0			0
$953$	−4.00000			−0.129573			−0.0647864	−	0.997899i	$-0.520637\pi$
$953$	−4.00000			−0.129573			−0.0647864	+	0.997899i	$0.520637\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$		0			0
$956$	−14.0000	−	24.2487i	−0.452792	−	0.784259i
$957$	24.0000	−	41.5692i	0.775810	−	1.34374i
$958$	−8.00000			−0.258468
$959$	−16.0000	+	13.8564i	−0.516667	+	0.447447i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	21.0000	+	36.3731i	0.677067	+	1.17271i
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	18.0000	−	31.1769i	0.579741	−	1.00414i
$965$		0			0
$966$	20.0000	+	6.92820i	0.643489	+	0.222911i
$967$	−55.0000			−1.76868			−0.884340	−	0.466843i	$-0.845391\pi$
$967$	−55.0000			−1.76868			−0.884340	+	0.466843i	$0.845391\pi$
$968$		0			0
$969$	2.00000	+	3.46410i	0.0642493	+	0.111283i
$970$		0			0
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	−0.0601548	−	0.998189i	$-0.519159\pi$
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	0.894534	−	0.446999i	$-0.147507\pi$
$972$	−2.00000			−0.0641500
$973$	10.5000	+	54.5596i	0.336615	+	1.74910i
$974$	26.0000			0.833094
$975$		0			0
$976$	−28.0000	−	48.4974i	−0.896258	−	1.55236i
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	0.634665	−	0.772787i	$-0.281138\pi$
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	−0.986586	+	0.163242i	$0.947805\pi$
$978$	12.0000	−	20.7846i	0.383718	−	0.664619i
$979$	72.0000			2.30113
$980$		0			0
$981$	−15.0000			−0.478913
$982$	12.0000	−	20.7846i	0.382935	−	0.663264i
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	0.999928	+	0.0119587i	$0.00380665\pi$
$983$	16.0000	+	27.7128i	0.510321	+	0.883901i	−0.489608	+	0.871943i	$0.662860\pi$
$984$		0			0
$985$		0			0
$986$	−64.0000			−2.03818
$987$	1.00000	+	5.19615i	0.0318304	+	0.165395i
$988$	6.00000			0.190885
$989$	2.00000	−	3.46410i	0.0635963	−	0.110152i
$990$		0			0
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	0.960211	−	0.279276i	$-0.0900944\pi$
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	−0.721966	+	0.691929i	$0.756761\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$	9.00000			0.285606
$994$	−30.0000	−	10.3923i	−0.951542	−	0.329624i
$995$		0			0
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	−12.5000	−	21.6506i	−0.395879	−	0.685682i	0.597334	−	0.801993i	$-0.296227\pi$
$997$	−12.5000	−	21.6506i	−0.395879	−	0.685682i	−0.993213	+	0.116310i	$0.962893\pi$
$998$	−29.0000	−	50.2295i	−0.917979	−	1.58999i
$999$	−3.50000	+	6.06218i	−0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.i.a.226.1		2
5.2	odd	4		525.2.r.d.499.1		4
5.3	odd	4		525.2.r.d.499.2		4
5.4	even	2		105.2.i.b.16.1	✓	2
7.2	even	3		3675.2.a.o.1.1		1
7.4	even	3	inner	525.2.i.a.151.1		2
7.5	odd	6		3675.2.a.p.1.1		1
15.14	odd	2		315.2.j.a.226.1		2
20.19	odd	2		1680.2.bg.l.961.1		2
35.4	even	6		105.2.i.b.46.1	yes	2
35.9	even	6		735.2.a.b.1.1		1
35.18	odd	12		525.2.r.d.424.1		4
35.19	odd	6		735.2.a.a.1.1		1
35.24	odd	6		735.2.i.f.361.1		2
35.32	odd	12		525.2.r.d.424.2		4
35.34	odd	2		735.2.i.f.226.1		2
105.44	odd	6		2205.2.a.k.1.1		1
105.74	odd	6		315.2.j.a.46.1		2
105.89	even	6		2205.2.a.m.1.1		1
140.39	odd	6		1680.2.bg.l.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	5.4	even	2
105.2.i.b.46.1	yes	2	35.4	even	6
315.2.j.a.46.1		2	105.74	odd	6
315.2.j.a.226.1		2	15.14	odd	2
525.2.i.a.151.1		2	7.4	even	3	inner
525.2.i.a.226.1		2	1.1	even	1	trivial
525.2.r.d.424.1		4	35.18	odd	12
525.2.r.d.424.2		4	35.32	odd	12
525.2.r.d.499.1		4	5.2	odd	4
525.2.r.d.499.2		4	5.3	odd	4
735.2.a.a.1.1		1	35.19	odd	6
735.2.a.b.1.1		1	35.9	even	6
735.2.i.f.226.1		2	35.34	odd	2
735.2.i.f.361.1		2	35.24	odd	6
1680.2.bg.l.961.1		2	20.19	odd	2
1680.2.bg.l.1201.1		2	140.39	odd	6
2205.2.a.k.1.1		1	105.44	odd	6
2205.2.a.m.1.1		1	105.89	even	6
3675.2.a.o.1.1		1	7.2	even	3
3675.2.a.p.1.1		1	7.5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} -2.00000 q^{6} +(0.500000 + 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(1.00000 - 1.73205i) q^{12} +3.00000 q^{13} +(-5.00000 - 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(-1.00000 - 1.73205i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} -12.0000 q^{22} +(-2.00000 + 3.46410i) q^{23} +(-3.00000 + 5.19615i) q^{26} -1.00000 q^{27} +(4.00000 - 3.46410i) q^{28} -8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(4.00000 + 6.92820i) q^{32} +(-3.00000 + 5.19615i) q^{33} +8.00000 q^{34} +2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(-1.00000 - 1.73205i) q^{38} +(1.50000 + 2.59808i) q^{39} -6.00000 q^{41} +(-1.00000 - 5.19615i) q^{42} -1.00000 q^{43} +(6.00000 - 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(1.00000 - 1.73205i) q^{47} +4.00000 q^{48} +(-6.50000 + 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(-3.00000 - 5.19615i) q^{52} +(2.00000 + 3.46410i) q^{53} +(1.00000 - 1.73205i) q^{54} -1.00000 q^{57} +(8.00000 - 13.8564i) q^{58} +(4.00000 + 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000 q^{62} +(-2.50000 - 0.866025i) q^{63} -8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(3.50000 + 6.06218i) q^{67} +(-4.00000 + 6.92820i) q^{68} -4.00000 q^{69} +6.00000 q^{71} +(0.500000 + 0.866025i) q^{73} +(7.00000 + 12.1244i) q^{74} +2.00000 q^{76} +(-12.0000 + 10.3923i) q^{77} -6.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} -2.00000 q^{83} +(5.00000 + 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(-4.00000 - 6.92820i) q^{87} +(6.00000 - 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} +8.00000 q^{92} +(0.500000 - 0.866025i) q^{93} +(2.00000 + 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} +6.00000 q^{97} +(2.00000 - 13.8564i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} - 2 q^{4} - 4 q^{6} + q^{7} - q^{9} + 6 q^{11} + 2 q^{12} + 6 q^{13} - 10 q^{14} + 4 q^{16} - 4 q^{17} - 2 q^{18} - q^{19} - 4 q^{21} - 24 q^{22} - 4 q^{23} - 6 q^{26} - 2 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 - 2 * q^4 - 4 * q^6 + q^7 - q^9 + 6 * q^11 + 2 * q^12 + 6 * q^13 - 10 * q^14 + 4 * q^16 - 4 * q^17 - 2 * q^18 - q^19 - 4 * q^21 - 24 * q^22 - 4 * q^23 - 6 * q^26 - 2 * q^27 + 8 * q^28 - 16 * q^29 - q^31 + 8 * q^32 - 6 * q^33 + 16 * q^34 + 4 * q^36 + 7 * q^37 - 2 * q^38 + 3 * q^39 - 12 * q^41 - 2 * q^42 - 2 * q^43 + 12 * q^44 - 8 * q^46 + 2 * q^47 + 8 * q^48 - 13 * q^49 + 4 * q^51 - 6 * q^52 + 4 * q^53 + 2 * q^54 - 2 * q^57 + 16 * q^58 + 8 * q^59 + 14 * q^61 + 4 * q^62 - 5 * q^63 - 16 * q^64 - 12 * q^66 + 7 * q^67 - 8 * q^68 - 8 * q^69 + 12 * q^71 + q^73 + 14 * q^74 + 4 * q^76 - 24 * q^77 - 12 * q^78 + q^79 - q^81 + 12 * q^82 - 4 * q^83 + 10 * q^84 + 2 * q^86 - 8 * q^87 + 12 * q^89 + 3 * q^91 + 16 * q^92 + q^93 + 4 * q^94 - 8 * q^96 + 12 * q^97 + 4 * q^98 - 12 * q^99

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