LMFDB - Embedded newform 165.3.l.f.98.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [165,3,Mod(32,165)] 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("165.32"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(165, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 2])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	165.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,12,0,0,0,0,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$4.49592436194$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			98.1
Root			$-1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	165.98
Dual form			165.3.l.f.32.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 1.22474i) q^{2} +3.00000 q^{3} +1.00000i q^{4} +5.00000i q^{5} +(-3.67423 + 3.67423i) q^{6} +(4.89898 + 4.89898i) q^{7} +(-6.12372 - 6.12372i) q^{8} +9.00000 q^{9} +(-6.12372 - 6.12372i) q^{10} +(-9.79796 - 5.00000i) q^{11} +3.00000i q^{12} +(-4.89898 + 4.89898i) q^{13} -12.0000 q^{14} +15.0000i q^{15} +11.0000 q^{16} +(4.89898 - 4.89898i) q^{17} +(-11.0227 + 11.0227i) q^{18} +19.5959 q^{19} -5.00000 q^{20} +(14.6969 + 14.6969i) q^{21} +(18.1237 - 5.87628i) q^{22} +(-7.00000 + 7.00000i) q^{23} +(-18.3712 - 18.3712i) q^{24} -25.0000 q^{25} -12.0000i q^{26} +27.0000 q^{27} +(-4.89898 + 4.89898i) q^{28} +48.9898i q^{29} +(-18.3712 - 18.3712i) q^{30} -48.0000 q^{31} +(11.0227 - 11.0227i) q^{32} +(-29.3939 - 15.0000i) q^{33} +12.0000i q^{34} +(-24.4949 + 24.4949i) q^{35} +9.00000i q^{36} +(37.0000 - 37.0000i) q^{37} +(-24.0000 + 24.0000i) q^{38} +(-14.6969 + 14.6969i) q^{39} +(30.6186 - 30.6186i) q^{40} +29.3939 q^{41} -36.0000 q^{42} +(44.0908 - 44.0908i) q^{43} +(5.00000 - 9.79796i) q^{44} +45.0000i q^{45} -17.1464i q^{46} +(17.0000 + 17.0000i) q^{47} +33.0000 q^{48} -1.00000i q^{49} +(30.6186 - 30.6186i) q^{50} +(14.6969 - 14.6969i) q^{51} +(-4.89898 - 4.89898i) q^{52} +(43.0000 - 43.0000i) q^{53} +(-33.0681 + 33.0681i) q^{54} +(25.0000 - 48.9898i) q^{55} -60.0000i q^{56} +58.7878 q^{57} +(-60.0000 - 60.0000i) q^{58} +38.0000 q^{59} -15.0000 q^{60} +48.9898i q^{61} +(58.7878 - 58.7878i) q^{62} +(44.0908 + 44.0908i) q^{63} +71.0000i q^{64} +(-24.4949 - 24.4949i) q^{65} +(54.3712 - 17.6288i) q^{66} +(-13.0000 + 13.0000i) q^{67} +(4.89898 + 4.89898i) q^{68} +(-21.0000 + 21.0000i) q^{69} -60.0000i q^{70} +(-55.1135 - 55.1135i) q^{72} +(93.0806 - 93.0806i) q^{73} +90.6311i q^{74} -75.0000 q^{75} +19.5959i q^{76} +(-23.5051 - 72.4949i) q^{77} -36.0000i q^{78} -29.3939 q^{79} +55.0000i q^{80} +81.0000 q^{81} +(-36.0000 + 36.0000i) q^{82} +(-102.879 - 102.879i) q^{83} +(-14.6969 + 14.6969i) q^{84} +(24.4949 + 24.4949i) q^{85} +108.000i q^{86} +146.969i q^{87} +(29.3814 + 90.6186i) q^{88} +48.0000 q^{89} +(-55.1135 - 55.1135i) q^{90} -48.0000 q^{91} +(-7.00000 - 7.00000i) q^{92} -144.000 q^{93} -41.6413 q^{94} +97.9796i q^{95} +(33.0681 - 33.0681i) q^{96} +(47.0000 - 47.0000i) q^{97} +(1.22474 + 1.22474i) q^{98} +(-88.1816 - 45.0000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 12 q^{3} + 36 q^{9} - 48 q^{14} + 44 q^{16} - 20 q^{20} + 48 q^{22} - 28 q^{23} - 100 q^{25} + 108 q^{27} - 192 q^{31} + 148 q^{37} - 96 q^{38} - 144 q^{42} + 20 q^{44} + 68 q^{47} + 132 q^{48} + 172 q^{53}+ \cdots + 188 q^{97}+O(q^{100}) $ 4 * q + 12 * q^3 + 36 * q^9 - 48 * q^14 + 44 * q^16 - 20 * q^20 + 48 * q^22 - 28 * q^23 - 100 * q^25 + 108 * q^27 - 192 * q^31 + 148 * q^37 - 96 * q^38 - 144 * q^42 + 20 * q^44 + 68 * q^47 + 132 * q^48 + 172 * q^53 + 100 * q^55 - 240 * q^58 + 152 * q^59 - 60 * q^60 + 144 * q^66 - 52 * q^67 - 84 * q^69 - 300 * q^75 - 192 * q^77 + 324 * q^81 - 144 * q^82 + 240 * q^88 + 192 * q^89 - 192 * q^91 - 28 * q^92 - 576 * q^93 + 188 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.22474	+	1.22474i	−0.612372	+	0.612372i	−0.943564	−	0.331191i	$-0.892549\pi$
$2$	−1.22474	+	1.22474i	−0.612372	+	0.612372i	0.331191	+	0.943564i	$0.392549\pi$
$3$	3.00000			1.00000
$3$	3.00000			1.00000
$4$			1.00000i			0.250000i
$5$			5.00000i			1.00000i
$5$			5.00000i			1.00000i
$6$	−3.67423	+	3.67423i	−0.612372	+	0.612372i
$7$	4.89898	+	4.89898i	0.699854	+	0.699854i	0.964379	−	0.264525i	$-0.0852151\pi$
$7$	4.89898	+	4.89898i	0.699854	+	0.699854i	−0.264525	+	0.964379i	$0.585215\pi$
$8$	−6.12372	−	6.12372i	−0.765466	−	0.765466i
$9$	9.00000			1.00000
$10$	−6.12372	−	6.12372i	−0.612372	−	0.612372i
$11$	−9.79796	−	5.00000i	−0.890724	−	0.454545i
$11$	−9.79796	−	5.00000i	−0.890724	−	0.454545i
$12$			3.00000i			0.250000i
$13$	−4.89898	+	4.89898i	−0.376845	+	0.376845i	−0.869962	−	0.493118i	$-0.835857\pi$
$13$	−4.89898	+	4.89898i	−0.376845	+	0.376845i	0.493118	+	0.869962i	$0.335857\pi$
$14$	−12.0000			−0.857143
$15$			15.0000i			1.00000i
$16$	11.0000			0.687500
$17$	4.89898	−	4.89898i	0.288175	−	0.288175i	−0.548183	−	0.836358i	$-0.684680\pi$
$17$	4.89898	−	4.89898i	0.288175	−	0.288175i	0.836358	+	0.548183i	$0.184680\pi$
$18$	−11.0227	+	11.0227i	−0.612372	+	0.612372i
$19$	19.5959			1.03136			0.515682	−	0.856780i	$-0.327539\pi$
$19$	19.5959			1.03136			0.515682	+	0.856780i	$0.327539\pi$
$20$	−5.00000			−0.250000
$21$	14.6969	+	14.6969i	0.699854	+	0.699854i
$22$	18.1237	−	5.87628i	0.823806	−	0.267103i
$23$	−7.00000	+	7.00000i	−0.304348	+	0.304348i	−0.842712	−	0.538364i	$-0.819042\pi$
$23$	−7.00000	+	7.00000i	−0.304348	+	0.304348i	0.538364	+	0.842712i	$0.319042\pi$
$24$	−18.3712	−	18.3712i	−0.765466	−	0.765466i
$25$	−25.0000			−1.00000
$26$		−	12.0000i		−	0.461538i
$27$	27.0000			1.00000
$28$	−4.89898	+	4.89898i	−0.174964	+	0.174964i
$29$			48.9898i			1.68930i	0.535316	+	0.844652i	$0.320192\pi$
$29$			48.9898i			1.68930i	−0.535316	+	0.844652i	$0.679808\pi$
$30$	−18.3712	−	18.3712i	−0.612372	−	0.612372i
$31$	−48.0000			−1.54839			−0.774194	−	0.632949i	$-0.781844\pi$
$31$	−48.0000			−1.54839			−0.774194	+	0.632949i	$0.781844\pi$
$32$	11.0227	−	11.0227i	0.344459	−	0.344459i
$33$	−29.3939	−	15.0000i	−0.890724	−	0.454545i
$34$			12.0000i			0.352941i
$35$	−24.4949	+	24.4949i	−0.699854	+	0.699854i
$36$			9.00000i			0.250000i
$37$	37.0000	−	37.0000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$37$	37.0000	−	37.0000i	1.00000	−	1.00000i	1.00000			$0$
$38$	−24.0000	+	24.0000i	−0.631579	+	0.631579i
$39$	−14.6969	+	14.6969i	−0.376845	+	0.376845i
$40$	30.6186	−	30.6186i	0.765466	−	0.765466i
$41$	29.3939			0.716924			0.358462	−	0.933544i	$-0.383301\pi$
$41$	29.3939			0.716924			0.358462	+	0.933544i	$0.383301\pi$
$42$	−36.0000			−0.857143
$43$	44.0908	−	44.0908i	1.02537	−	1.02537i	0.0256980	−	0.999670i	$-0.491819\pi$
$43$	44.0908	−	44.0908i	1.02537	−	1.02537i	0.999670	−	0.0256980i	$-0.00818084\pi$
$44$	5.00000	−	9.79796i	0.113636	−	0.222681i
$45$			45.0000i			1.00000i
$46$		−	17.1464i		−	0.372748i
$47$	17.0000	+	17.0000i	0.361702	+	0.361702i	0.864439	−	0.502737i	$-0.167674\pi$
$47$	17.0000	+	17.0000i	0.361702	+	0.361702i	−0.502737	+	0.864439i	$0.667674\pi$
$48$	33.0000			0.687500
$49$		−	1.00000i		−	0.0204082i
$50$	30.6186	−	30.6186i	0.612372	−	0.612372i
$51$	14.6969	−	14.6969i	0.288175	−	0.288175i
$52$	−4.89898	−	4.89898i	−0.0942111	−	0.0942111i
$53$	43.0000	−	43.0000i	0.811321	−	0.811321i	−0.173511	−	0.984832i	$-0.555511\pi$
$53$	43.0000	−	43.0000i	0.811321	−	0.811321i	0.984832	+	0.173511i	$0.0555113\pi$
$54$	−33.0681	+	33.0681i	−0.612372	+	0.612372i
$55$	25.0000	−	48.9898i	0.454545	−	0.890724i
$56$		−	60.0000i		−	1.07143i
$57$	58.7878			1.03136
$58$	−60.0000	−	60.0000i	−1.03448	−	1.03448i
$59$	38.0000			0.644068			0.322034	−	0.946728i	$-0.395633\pi$
$59$	38.0000			0.644068			0.322034	+	0.946728i	$0.395633\pi$
$60$	−15.0000			−0.250000
$61$			48.9898i			0.803111i	0.915835	+	0.401556i	$0.131530\pi$
$61$			48.9898i			0.803111i	−0.915835	+	0.401556i	$0.868470\pi$
$62$	58.7878	−	58.7878i	0.948190	−	0.948190i
$63$	44.0908	+	44.0908i	0.699854	+	0.699854i
$64$			71.0000i			1.10938i
$65$	−24.4949	−	24.4949i	−0.376845	−	0.376845i
$66$	54.3712	−	17.6288i	0.823806	−	0.267103i
$67$	−13.0000	+	13.0000i	−0.194030	+	0.194030i	−0.797435	−	0.603405i	$-0.793810\pi$
$67$	−13.0000	+	13.0000i	−0.194030	+	0.194030i	0.603405	+	0.797435i	$0.293810\pi$
$68$	4.89898	+	4.89898i	0.0720438	+	0.0720438i
$69$	−21.0000	+	21.0000i	−0.304348	+	0.304348i
$70$		−	60.0000i		−	0.857143i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−55.1135	−	55.1135i	−0.765466	−	0.765466i
$73$	93.0806	−	93.0806i	1.27508	−	1.27508i	0.331688	−	0.943389i	$-0.392382\pi$
$73$	93.0806	−	93.0806i	1.27508	−	1.27508i	0.943389	−	0.331688i	$-0.107618\pi$
$74$			90.6311i			1.22474i
$75$	−75.0000			−1.00000
$76$			19.5959i			0.257841i
$77$	−23.5051	−	72.4949i	−0.305261	−	0.941492i
$78$		−	36.0000i		−	0.461538i
$79$	−29.3939			−0.372074			−0.186037	−	0.982543i	$-0.559564\pi$
$79$	−29.3939			−0.372074			−0.186037	+	0.982543i	$0.559564\pi$
$80$			55.0000i			0.687500i
$81$	81.0000			1.00000
$82$	−36.0000	+	36.0000i	−0.439024	+	0.439024i
$83$	−102.879	−	102.879i	−1.23950	−	1.23950i	−0.960205	−	0.279296i	$-0.909899\pi$
$83$	−102.879	−	102.879i	−1.23950	−	1.23950i	−0.279296	−	0.960205i	$-0.590101\pi$
$84$	−14.6969	+	14.6969i	−0.174964	+	0.174964i
$85$	24.4949	+	24.4949i	0.288175	+	0.288175i
$86$			108.000i			1.25581i
$87$			146.969i			1.68930i
$88$	29.3814	+	90.6186i	0.333879	+	1.02976i
$89$	48.0000			0.539326			0.269663	−	0.962955i	$-0.413088\pi$
$89$	48.0000			0.539326			0.269663	+	0.962955i	$0.413088\pi$
$90$	−55.1135	−	55.1135i	−0.612372	−	0.612372i
$91$	−48.0000			−0.527473
$92$	−7.00000	−	7.00000i	−0.0760870	−	0.0760870i
$93$	−144.000			−1.54839
$94$	−41.6413			−0.442993
$95$			97.9796i			1.03136i
$96$	33.0681	−	33.0681i	0.344459	−	0.344459i
$97$	47.0000	−	47.0000i	0.484536	−	0.484536i	−0.422041	−	0.906577i	$-0.638686\pi$
$97$	47.0000	−	47.0000i	0.484536	−	0.484536i	0.906577	+	0.422041i	$0.138686\pi$
$98$	1.22474	+	1.22474i	0.0124974	+	0.0124974i
$99$	−88.1816	−	45.0000i	−0.890724	−	0.454545i
$100$		−	25.0000i		−	0.250000i
$101$	−19.5959			−0.194019			−0.0970095	−	0.995283i	$-0.530928\pi$
$101$	−19.5959			−0.194019			−0.0970095	+	0.995283i	$0.530928\pi$
$102$			36.0000i			0.352941i
$103$	23.0000	+	23.0000i	0.223301	+	0.223301i	0.809887	−	0.586586i	$-0.199528\pi$
$103$	23.0000	+	23.0000i	0.223301	+	0.223301i	−0.586586	+	0.809887i	$0.699528\pi$
$104$	60.0000			0.576923
$105$	−73.4847	+	73.4847i	−0.699854	+	0.699854i
$106$			105.328i			0.993661i
$107$	4.89898	−	4.89898i	0.0457849	−	0.0457849i	−0.683844	−	0.729629i	$-0.739693\pi$
$107$	4.89898	−	4.89898i	0.0457849	−	0.0457849i	0.729629	+	0.683844i	$0.239693\pi$
$108$			27.0000i			0.250000i
$109$	−176.363			−1.61801			−0.809006	−	0.587801i	$-0.799994\pi$
$109$	−176.363			−1.61801			−0.809006	+	0.587801i	$0.799994\pi$
$110$	29.3814	+	90.6186i	0.267103	+	0.823806i
$111$	111.000	−	111.000i	1.00000	−	1.00000i
$112$	53.8888	+	53.8888i	0.481150	+	0.481150i
$113$	−127.000	+	127.000i	−1.12389	+	1.12389i	−0.132743	+	0.991150i	$0.542379\pi$
$113$	−127.000	+	127.000i	−1.12389	+	1.12389i	−0.991150	+	0.132743i	$0.957621\pi$
$114$	−72.0000	+	72.0000i	−0.631579	+	0.631579i
$115$	−35.0000	−	35.0000i	−0.304348	−	0.304348i
$116$	−48.9898			−0.422326
$117$	−44.0908	+	44.0908i	−0.376845	+	0.376845i
$118$	−46.5403	+	46.5403i	−0.394409	+	0.394409i
$119$	48.0000			0.403361
$120$	91.8559	−	91.8559i	0.765466	−	0.765466i
$121$	71.0000	+	97.9796i	0.586777	+	0.809749i
$122$	−60.0000	−	60.0000i	−0.491803	−	0.491803i
$123$	88.1816			0.716924
$124$		−	48.0000i		−	0.387097i
$125$		−	125.000i		−	1.00000i
$126$	−108.000			−0.857143
$127$	4.89898	+	4.89898i	0.0385746	+	0.0385746i	0.726131	−	0.687556i	$-0.241317\pi$
$127$	4.89898	+	4.89898i	0.0385746	+	0.0385746i	−0.687556	+	0.726131i	$0.741317\pi$
$128$	−42.8661	−	42.8661i	−0.334891	−	0.334891i
$129$	132.272	−	132.272i	1.02537	−	1.02537i
$130$	60.0000			0.461538
$131$	78.3837			0.598349			0.299174	−	0.954198i	$-0.403289\pi$
$131$	78.3837			0.598349			0.299174	+	0.954198i	$0.403289\pi$
$132$	15.0000	−	29.3939i	0.113636	−	0.222681i
$133$	96.0000	+	96.0000i	0.721805	+	0.721805i
$134$		−	31.8434i		−	0.237637i
$135$			135.000i			1.00000i
$136$	−60.0000			−0.441176
$137$	7.00000	+	7.00000i	0.0510949	+	0.0510949i	0.732193	−	0.681098i	$-0.238497\pi$
$137$	7.00000	+	7.00000i	0.0510949	+	0.0510949i	−0.681098	+	0.732193i	$0.738497\pi$
$138$		−	51.4393i		−	0.372748i
$139$	19.5959			0.140978			0.0704889	−	0.997513i	$-0.477544\pi$
$139$	19.5959			0.140978			0.0704889	+	0.997513i	$0.477544\pi$
$140$	−24.4949	−	24.4949i	−0.174964	−	0.174964i
$141$	51.0000	+	51.0000i	0.361702	+	0.361702i
$142$		0			0
$143$	72.4949	−	23.5051i	0.506957	−	0.164371i
$144$	99.0000			0.687500
$145$	−244.949			−1.68930
$146$			228.000i			1.56164i
$147$		−	3.00000i		−	0.0204082i
$148$	37.0000	+	37.0000i	0.250000	+	0.250000i
$149$			48.9898i			0.328791i	0.986395	+	0.164395i	$0.0525673\pi$
$149$			48.9898i			0.328791i	−0.986395	+	0.164395i	$0.947433\pi$
$150$	91.8559	−	91.8559i	0.612372	−	0.612372i
$151$		−	97.9796i		−	0.648871i	−0.945908	−	0.324436i	$-0.894826\pi$
$151$		−	97.9796i		−	0.648871i	0.945908	−	0.324436i	$-0.105174\pi$
$152$	−120.000	−	120.000i	−0.789474	−	0.789474i
$153$	44.0908	−	44.0908i	0.288175	−	0.288175i
$154$	117.576	+	60.0000i	0.763477	+	0.389610i
$155$		−	240.000i		−	1.54839i
$156$	−14.6969	−	14.6969i	−0.0942111	−	0.0942111i
$157$	−83.0000	+	83.0000i	−0.528662	+	0.528662i	−0.920173	−	0.391511i	$-0.871952\pi$
$157$	−83.0000	+	83.0000i	−0.528662	+	0.528662i	0.391511	+	0.920173i	$0.371952\pi$
$158$	36.0000	−	36.0000i	0.227848	−	0.227848i
$159$	129.000	−	129.000i	0.811321	−	0.811321i
$160$	55.1135	+	55.1135i	0.344459	+	0.344459i
$161$	−68.5857			−0.425998
$162$	−99.2043	+	99.2043i	−0.612372	+	0.612372i
$163$	13.0000	+	13.0000i	0.0797546	+	0.0797546i	0.745859	−	0.666104i	$-0.232039\pi$
$163$	13.0000	+	13.0000i	0.0797546	+	0.0797546i	−0.666104	+	0.745859i	$0.732039\pi$
$164$			29.3939i			0.179231i
$165$	75.0000	−	146.969i	0.454545	−	0.890724i
$166$	252.000			1.51807
$167$	102.879	−	102.879i	0.616039	−	0.616039i	−0.328474	−	0.944513i	$-0.606534\pi$
$167$	102.879	−	102.879i	0.616039	−	0.616039i	0.944513	+	0.328474i	$0.106534\pi$
$168$		−	180.000i		−	1.07143i
$169$			121.000i			0.715976i
$170$	−60.0000			−0.352941
$171$	176.363			1.03136
$172$	44.0908	+	44.0908i	0.256342	+	0.256342i
$173$	44.0908	+	44.0908i	0.254860	+	0.254860i	0.822960	−	0.568100i	$-0.192321\pi$
$173$	44.0908	+	44.0908i	0.254860	+	0.254860i	−0.568100	+	0.822960i	$0.692321\pi$
$174$	−180.000	−	180.000i	−1.03448	−	1.03448i
$175$	−122.474	−	122.474i	−0.699854	−	0.699854i
$176$	−107.778	−	55.0000i	−0.612372	−	0.312500i
$177$	114.000			0.644068
$178$	−58.7878	+	58.7878i	−0.330268	+	0.330268i
$179$	−192.000			−1.07263			−0.536313	−	0.844019i	$-0.680183\pi$
$179$	−192.000			−1.07263			−0.536313	+	0.844019i	$0.680183\pi$
$180$	−45.0000			−0.250000
$181$	−288.000			−1.59116			−0.795580	−	0.605848i	$-0.792834\pi$
$181$	−288.000			−1.59116			−0.795580	+	0.605848i	$0.792834\pi$
$182$	58.7878	−	58.7878i	0.323010	−	0.323010i
$183$			146.969i			0.803111i
$184$	85.7321			0.465936
$185$	185.000	+	185.000i	1.00000	+	1.00000i
$186$	176.363	−	176.363i	0.948190	−	0.948190i
$187$	−72.4949	+	23.5051i	−0.387673	+	0.125696i
$188$	−17.0000	+	17.0000i	−0.0904255	+	0.0904255i
$189$	132.272	+	132.272i	0.699854	+	0.699854i
$190$	−120.000	−	120.000i	−0.631579	−	0.631579i
$191$		−	110.000i		−	0.575916i	−0.957643	−	0.287958i	$-0.907024\pi$
$191$		−	110.000i		−	0.575916i	0.957643	−	0.287958i	$-0.0929764\pi$
$192$			213.000i			1.10938i
$193$	−53.8888	+	53.8888i	−0.279216	+	0.279216i	−0.832796	−	0.553580i	$-0.813261\pi$
$193$	−53.8888	+	53.8888i	−0.279216	+	0.279216i	0.553580	+	0.832796i	$0.313261\pi$
$194$			115.126i			0.593433i
$195$	−73.4847	−	73.4847i	−0.376845	−	0.376845i
$196$	1.00000			0.00510204
$197$	−93.0806	+	93.0806i	−0.472490	+	0.472490i	−0.902720	−	0.430229i	$-0.858433\pi$
$197$	−93.0806	+	93.0806i	−0.472490	+	0.472490i	0.430229	+	0.902720i	$0.358433\pi$
$198$	163.114	−	52.8865i	0.823806	−	0.267103i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	153.093	+	153.093i	0.765466	+	0.765466i
$201$	−39.0000	+	39.0000i	−0.194030	+	0.194030i
$202$	24.0000	−	24.0000i	0.118812	−	0.118812i
$203$	−240.000	+	240.000i	−1.18227	+	1.18227i
$204$	14.6969	+	14.6969i	0.0720438	+	0.0720438i
$205$			146.969i			0.716924i
$206$	−56.3383			−0.273487
$207$	−63.0000	+	63.0000i	−0.304348	+	0.304348i
$208$	−53.8888	+	53.8888i	−0.259081	+	0.259081i
$209$	−192.000	−	97.9796i	−0.918660	−	0.468802i
$210$		−	180.000i		−	0.857143i
$211$		−	244.949i		−	1.16090i	−0.814297	−	0.580448i	$-0.802878\pi$
$211$		−	244.949i		−	1.16090i	0.814297	−	0.580448i	$-0.197122\pi$
$212$	43.0000	+	43.0000i	0.202830	+	0.202830i
$213$		0			0
$214$			12.0000i			0.0560748i
$215$	220.454	+	220.454i	1.02537	+	1.02537i
$216$	−165.341	−	165.341i	−0.765466	−	0.765466i
$217$	−235.151	−	235.151i	−1.08365	−	1.08365i
$218$	216.000	−	216.000i	0.990826	−	0.990826i
$219$	279.242	−	279.242i	1.27508	−	1.27508i
$220$	48.9898	+	25.0000i	0.222681	+	0.113636i
$221$			48.0000i			0.217195i
$222$			271.893i			1.22474i
$223$	−47.0000	−	47.0000i	−0.210762	−	0.210762i	0.593829	−	0.804591i	$-0.297616\pi$
$223$	−47.0000	−	47.0000i	−0.210762	−	0.210762i	−0.804591	+	0.593829i	$0.797616\pi$
$224$	108.000			0.482143
$225$	−225.000			−1.00000
$226$		−	311.085i		−	1.37648i
$227$	200.858	−	200.858i	0.884838	−	0.884838i	−0.109184	−	0.994022i	$-0.534824\pi$
$227$	200.858	−	200.858i	0.884838	−	0.884838i	0.994022	+	0.109184i	$0.0348237\pi$
$228$			58.7878i			0.257841i
$229$		−	240.000i		−	1.04803i	−0.851708	−	0.524017i	$-0.824433\pi$
$229$		−	240.000i		−	1.04803i	0.851708	−	0.524017i	$-0.175567\pi$
$230$	85.7321			0.372748
$231$	−70.5153	−	217.485i	−0.305261	−	0.941492i
$232$	300.000	−	300.000i	1.29310	−	1.29310i
$233$	−200.858	−	200.858i	−0.862052	−	0.862052i	0.129524	−	0.991576i	$-0.458655\pi$
$233$	−200.858	−	200.858i	−0.862052	−	0.862052i	−0.991576	+	0.129524i	$0.958655\pi$
$234$		−	108.000i		−	0.461538i
$235$	−85.0000	+	85.0000i	−0.361702	+	0.361702i
$236$			38.0000i			0.161017i
$237$	−88.1816			−0.372074
$238$	−58.7878	+	58.7878i	−0.247007	+	0.247007i
$239$		−	195.959i		−	0.819913i	−0.912105	−	0.409956i	$-0.865544\pi$
$239$		−	195.959i		−	0.819913i	0.912105	−	0.409956i	$-0.134456\pi$
$240$			165.000i			0.687500i
$241$			391.918i			1.62622i	0.582112	+	0.813109i	$0.302227\pi$
$241$			391.918i			1.62622i	−0.582112	+	0.813109i	$0.697773\pi$
$242$	−206.957	−	33.0431i	−0.855194	−	0.136542i
$243$	243.000			1.00000
$244$	−48.9898			−0.200778
$245$	5.00000			0.0204082
$246$	−108.000	+	108.000i	−0.439024	+	0.439024i
$247$	−96.0000	+	96.0000i	−0.388664	+	0.388664i
$248$	293.939	+	293.939i	1.18524	+	1.18524i
$249$	−308.636	−	308.636i	−1.23950	−	1.23950i
$250$	153.093	+	153.093i	0.612372	+	0.612372i
$251$		−	240.000i		−	0.956175i	−0.878312	−	0.478088i	$-0.841330\pi$
$251$		−	240.000i		−	0.956175i	0.878312	−	0.478088i	$-0.158670\pi$
$252$	−44.0908	+	44.0908i	−0.174964	+	0.174964i
$253$	103.586	−	33.5857i	0.409430	−	0.132750i
$254$	−12.0000			−0.0472441
$255$	73.4847	+	73.4847i	0.288175	+	0.288175i
$256$	−179.000			−0.699219
$257$	127.000	+	127.000i	0.494163	+	0.494163i	0.909615	−	0.415452i	$-0.136377\pi$
$257$	127.000	+	127.000i	0.494163	+	0.494163i	−0.415452	+	0.909615i	$0.636377\pi$
$258$			324.000i			1.25581i
$259$	362.524			1.39971
$260$	24.4949	−	24.4949i	0.0942111	−	0.0942111i
$261$			440.908i			1.68930i
$262$	−96.0000	+	96.0000i	−0.366412	+	0.366412i
$263$	44.0908	+	44.0908i	0.167646	+	0.167646i	0.785944	−	0.618298i	$-0.212178\pi$
$263$	44.0908	+	44.0908i	0.167646	+	0.167646i	−0.618298	+	0.785944i	$0.712178\pi$
$264$	88.1441	+	271.856i	0.333879	+	1.02976i
$265$	215.000	+	215.000i	0.811321	+	0.811321i
$266$	−235.151			−0.884026
$267$	144.000			0.539326
$268$	−13.0000	−	13.0000i	−0.0485075	−	0.0485075i
$269$	298.000			1.10781			0.553903	−	0.832581i	$-0.313138\pi$
$269$	298.000			1.10781			0.553903	+	0.832581i	$0.313138\pi$
$270$	−165.341	−	165.341i	−0.612372	−	0.612372i
$271$		−	97.9796i		−	0.361548i	−0.983525	−	0.180774i	$-0.942140\pi$
$271$		−	97.9796i		−	0.361548i	0.983525	−	0.180774i	$-0.0578603\pi$
$272$	53.8888	−	53.8888i	0.198120	−	0.198120i
$273$	−144.000			−0.527473
$274$	−17.1464			−0.0625782
$275$	244.949	+	125.000i	0.890724	+	0.454545i
$276$	−21.0000	−	21.0000i	−0.0760870	−	0.0760870i
$277$	−44.0908	−	44.0908i	−0.159173	−	0.159173i	0.623027	−	0.782200i	$-0.285903\pi$
$277$	−44.0908	−	44.0908i	−0.159173	−	0.159173i	−0.782200	+	0.623027i	$0.785903\pi$
$278$	−24.0000	+	24.0000i	−0.0863309	+	0.0863309i
$279$	−432.000			−1.54839
$280$	300.000			1.07143
$281$	−460.504			−1.63880			−0.819402	−	0.573219i	$-0.805694\pi$
$281$	−460.504			−1.63880			−0.819402	+	0.573219i	$0.805694\pi$
$282$	−124.924			−0.442993
$283$	−151.868	+	151.868i	−0.536637	+	0.536637i	−0.922540	−	0.385902i	$-0.873890\pi$
$283$	−151.868	+	151.868i	−0.536637	+	0.536637i	0.385902	+	0.922540i	$0.373890\pi$
$284$		0			0
$285$			293.939i			1.03136i
$286$	−60.0000	+	117.576i	−0.209790	+	0.411103i
$287$	144.000	+	144.000i	0.501742	+	0.501742i
$288$	99.2043	−	99.2043i	0.344459	−	0.344459i
$289$			241.000i			0.833910i
$290$	300.000	−	300.000i	1.03448	−	1.03448i
$291$	141.000	−	141.000i	0.484536	−	0.484536i
$292$	93.0806	+	93.0806i	0.318769	+	0.318769i
$293$	−347.828	−	347.828i	−1.18712	−	1.18712i	−0.977859	−	0.209266i	$-0.932893\pi$
$293$	−347.828	−	347.828i	−1.18712	−	1.18712i	−0.209266	−	0.977859i	$-0.567107\pi$
$294$	3.67423	+	3.67423i	0.0124974	+	0.0124974i
$295$			190.000i			0.644068i
$296$	−453.156			−1.53093
$297$	−264.545	−	135.000i	−0.890724	−	0.454545i
$298$	−60.0000	−	60.0000i	−0.201342	−	0.201342i
$299$		−	68.5857i		−	0.229384i
$300$		−	75.0000i		−	0.250000i
$301$	432.000			1.43522
$302$	120.000	+	120.000i	0.397351	+	0.397351i
$303$	−58.7878			−0.194019
$304$	215.555			0.709063
$305$	−244.949			−0.803111
$306$			108.000i			0.352941i
$307$	−338.030	−	338.030i	−1.10107	−	1.10107i	−0.994281	−	0.106792i	$-0.965942\pi$
$307$	−338.030	−	338.030i	−1.10107	−	1.10107i	−0.106792	−	0.994281i	$-0.534058\pi$
$308$	72.4949	−	23.5051i	0.235373	−	0.0763153i
$309$	69.0000	+	69.0000i	0.223301	+	0.223301i
$310$	293.939	+	293.939i	0.948190	+	0.948190i
$311$			480.000i			1.54341i	0.635982	+	0.771704i	$0.280595\pi$
$311$			480.000i			1.54341i	−0.635982	+	0.771704i	$0.719405\pi$
$312$	180.000			0.576923
$313$	−217.000	−	217.000i	−0.693291	−	0.693291i	0.269664	−	0.962955i	$-0.413087\pi$
$313$	−217.000	−	217.000i	−0.693291	−	0.693291i	−0.962955	+	0.269664i	$0.913087\pi$
$314$		−	203.308i		−	0.647477i
$315$	−220.454	+	220.454i	−0.699854	+	0.699854i
$316$		−	29.3939i		−	0.0930186i
$317$	67.0000	+	67.0000i	0.211356	+	0.211356i	0.804844	−	0.593487i	$-0.202249\pi$
$317$	67.0000	+	67.0000i	0.211356	+	0.211356i	−0.593487	+	0.804844i	$0.702249\pi$
$318$			315.984i			0.993661i
$319$	244.949	−	480.000i	0.767865	−	1.50470i
$320$	−355.000			−1.10938
$321$	14.6969	−	14.6969i	0.0457849	−	0.0457849i
$322$	84.0000	−	84.0000i	0.260870	−	0.260870i
$323$	96.0000	−	96.0000i	0.297214	−	0.297214i
$324$			81.0000i			0.250000i
$325$	122.474	−	122.474i	0.376845	−	0.376845i
$326$	−31.8434			−0.0976790
$327$	−529.090			−1.61801
$328$	−180.000	−	180.000i	−0.548780	−	0.548780i
$329$			166.565i			0.506278i
$330$	88.1441	+	271.856i	0.267103	+	0.823806i
$331$	−288.000			−0.870091			−0.435045	−	0.900409i	$-0.643268\pi$
$331$	−288.000			−0.870091			−0.435045	+	0.900409i	$0.643268\pi$
$332$	102.879	−	102.879i	0.309875	−	0.309875i
$333$	333.000	−	333.000i	1.00000	−	1.00000i
$334$			252.000i			0.754491i
$335$	−65.0000	−	65.0000i	−0.194030	−	0.194030i
$336$	161.666	+	161.666i	0.481150	+	0.481150i
$337$	249.848	+	249.848i	0.741389	+	0.741389i	0.972845	−	0.231457i	$-0.0743491\pi$
$337$	249.848	+	249.848i	0.741389	+	0.741389i	−0.231457	+	0.972845i	$0.574349\pi$
$338$	−148.194	−	148.194i	−0.438444	−	0.438444i
$339$	−381.000	+	381.000i	−1.12389	+	1.12389i
$340$	−24.4949	+	24.4949i	−0.0720438	+	0.0720438i
$341$	470.302	+	240.000i	1.37918	+	0.703812i
$342$	−216.000	+	216.000i	−0.631579	+	0.631579i
$343$	244.949	−	244.949i	0.714137	−	0.714137i
$344$	−540.000			−1.56977
$345$	−105.000	−	105.000i	−0.304348	−	0.304348i
$346$	−108.000			−0.312139
$347$	−142.070	+	142.070i	−0.409425	+	0.409425i	−0.881538	−	0.472113i	$-0.843491\pi$
$347$	−142.070	+	142.070i	−0.409425	+	0.409425i	0.472113	+	0.881538i	$0.343491\pi$
$348$	−146.969			−0.422326
$349$	−274.343			−0.786083			−0.393041	−	0.919521i	$-0.628577\pi$
$349$	−274.343			−0.786083			−0.393041	+	0.919521i	$0.628577\pi$
$350$	300.000			0.857143
$351$	−132.272	+	132.272i	−0.376845	+	0.376845i
$352$	−163.114	+	52.8865i	−0.463391	+	0.150246i
$353$	−257.000	+	257.000i	−0.728045	+	0.728045i	−0.970230	−	0.242185i	$-0.922136\pi$
$353$	−257.000	+	257.000i	−0.728045	+	0.728045i	0.242185	+	0.970230i	$0.422136\pi$
$354$	−139.621	+	139.621i	−0.394409	+	0.394409i
$355$		0			0
$356$			48.0000i			0.134831i
$357$	144.000			0.403361
$358$	235.151	−	235.151i	0.656846	−	0.656846i
$359$			195.959i			0.545847i	0.962036	+	0.272924i	$0.0879906\pi$
$359$			195.959i			0.545847i	−0.962036	+	0.272924i	$0.912009\pi$
$360$	275.568	−	275.568i	0.765466	−	0.765466i
$361$	23.0000			0.0637119
$362$	352.727	−	352.727i	0.974383	−	0.974383i
$363$	213.000	+	293.939i	0.586777	+	0.809749i
$364$		−	48.0000i		−	0.131868i
$365$	465.403	+	465.403i	1.27508	+	1.27508i
$366$	−180.000	−	180.000i	−0.491803	−	0.491803i
$367$	97.0000	−	97.0000i	0.264305	−	0.264305i	−0.562495	−	0.826800i	$-0.690159\pi$
$367$	97.0000	−	97.0000i	0.264305	−	0.264305i	0.826800	+	0.562495i	$0.190159\pi$
$368$	−77.0000	+	77.0000i	−0.209239	+	0.209239i
$369$	264.545			0.716924
$370$	−453.156			−1.22474
$371$	421.312			1.13561
$372$		−	144.000i		−	0.387097i
$373$	−102.879	+	102.879i	−0.275814	+	0.275814i	−0.831435	−	0.555621i	$-0.812480\pi$
$373$	−102.879	+	102.879i	−0.275814	+	0.275814i	0.555621	+	0.831435i	$0.312480\pi$
$374$	60.0000	−	117.576i	0.160428	−	0.314373i
$375$		−	375.000i		−	1.00000i
$376$		−	208.207i		−	0.553741i
$377$	−240.000	−	240.000i	−0.636605	−	0.636605i
$378$	−324.000			−0.857143
$379$		−	720.000i		−	1.89974i	−0.312651	−	0.949868i	$-0.601217\pi$
$379$		−	720.000i		−	1.89974i	0.312651	−	0.949868i	$-0.398783\pi$
$380$	−97.9796			−0.257841
$381$	14.6969	+	14.6969i	0.0385746	+	0.0385746i
$382$	134.722	+	134.722i	0.352675	+	0.352675i
$383$	353.000	−	353.000i	0.921671	−	0.921671i	−0.0754766	−	0.997148i	$-0.524048\pi$
$383$	353.000	−	353.000i	0.921671	−	0.921671i	0.997148	+	0.0754766i	$0.0240478\pi$
$384$	−128.598	−	128.598i	−0.334891	−	0.334891i
$385$	362.474	−	117.526i	0.941492	−	0.305261i
$386$		−	132.000i		−	0.341969i
$387$	396.817	−	396.817i	1.02537	−	1.02537i
$388$	47.0000	+	47.0000i	0.121134	+	0.121134i
$389$	−422.000			−1.08483			−0.542416	−	0.840110i	$-0.682490\pi$
$389$	−422.000			−1.08483			−0.542416	+	0.840110i	$0.682490\pi$
$390$	180.000			0.461538
$391$			68.5857i			0.175411i
$392$	−6.12372	+	6.12372i	−0.0156217	+	0.0156217i
$393$	235.151			0.598349
$394$		−	228.000i		−	0.578680i
$395$		−	146.969i		−	0.372074i
$396$	45.0000	−	88.1816i	0.113636	−	0.222681i
$397$	−493.000	+	493.000i	−1.24181	+	1.24181i	−0.282566	+	0.959248i	$0.591185\pi$
$397$	−493.000	+	493.000i	−1.24181	+	1.24181i	−0.959248	+	0.282566i	$0.908815\pi$
$398$		0			0
$399$	288.000	+	288.000i	0.721805	+	0.721805i
$400$	−275.000			−0.687500
$401$		−	590.000i		−	1.47132i	−0.677350	−	0.735661i	$-0.736872\pi$
$401$		−	590.000i		−	1.47132i	0.677350	−	0.735661i	$-0.263128\pi$
$402$		−	95.5301i		−	0.237637i
$403$	235.151	−	235.151i	0.583501	−	0.583501i
$404$		−	19.5959i		−	0.0485047i
$405$			405.000i			1.00000i
$406$		−	587.878i		−	1.44797i
$407$	−547.524	+	177.524i	−1.34527	+	0.436178i
$408$	−180.000			−0.441176
$409$	−323.333			−0.790544			−0.395272	−	0.918564i	$-0.629350\pi$
$409$	−323.333			−0.790544			−0.395272	+	0.918564i	$0.629350\pi$
$410$	−180.000	−	180.000i	−0.439024	−	0.439024i
$411$	21.0000	+	21.0000i	0.0510949	+	0.0510949i
$412$	−23.0000	+	23.0000i	−0.0558252	+	0.0558252i
$413$	186.161	+	186.161i	0.450754	+	0.450754i
$414$		−	154.318i		−	0.372748i
$415$	514.393	−	514.393i	1.23950	−	1.23950i
$416$			108.000i			0.259615i
$417$	58.7878			0.140978
$418$	355.151	−	115.151i	0.849644	−	0.275481i
$419$	288.000			0.687351			0.343675	−	0.939088i	$-0.388328\pi$
$419$	288.000			0.687351			0.343675	+	0.939088i	$0.388328\pi$
$420$	−73.4847	−	73.4847i	−0.174964	−	0.174964i
$421$	672.000			1.59620			0.798100	−	0.602525i	$-0.205839\pi$
$421$	672.000			1.59620			0.798100	+	0.602525i	$0.205839\pi$
$422$	300.000	+	300.000i	0.710900	+	0.710900i
$423$	153.000	+	153.000i	0.361702	+	0.361702i
$424$	−526.640			−1.24208
$425$	−122.474	+	122.474i	−0.288175	+	0.288175i
$426$		0			0
$427$	−240.000	+	240.000i	−0.562061	+	0.562061i
$428$	4.89898	+	4.89898i	0.0114462	+	0.0114462i
$429$	217.485	−	70.5153i	0.506957	−	0.164371i
$430$	−540.000			−1.25581
$431$	29.3939			0.0681993			0.0340996	−	0.999418i	$-0.489144\pi$
$431$	29.3939			0.0681993			0.0340996	+	0.999418i	$0.489144\pi$
$432$	297.000			0.687500
$433$	−47.0000	−	47.0000i	−0.108545	−	0.108545i	0.650748	−	0.759293i	$-0.274455\pi$
$433$	−47.0000	−	47.0000i	−0.108545	−	0.108545i	−0.759293	+	0.650748i	$0.774455\pi$
$434$	576.000			1.32719
$435$	−734.847			−1.68930
$436$		−	176.363i		−	0.404503i
$437$	−137.171	+	137.171i	−0.313893	+	0.313893i
$438$			684.000i			1.56164i
$439$	754.443			1.71855			0.859274	−	0.511515i	$-0.170916\pi$
$439$	754.443			1.71855			0.859274	+	0.511515i	$0.170916\pi$
$440$	−453.093	+	146.907i	−1.02976	+	0.333879i
$441$		−	9.00000i		−	0.0204082i
$442$	−58.7878	−	58.7878i	−0.133004	−	0.133004i
$443$	43.0000	−	43.0000i	0.0970655	−	0.0970655i	−0.656907	−	0.753972i	$-0.728135\pi$
$443$	43.0000	−	43.0000i	0.0970655	−	0.0970655i	0.753972	+	0.656907i	$0.228135\pi$
$444$	111.000	+	111.000i	0.250000	+	0.250000i
$445$			240.000i			0.539326i
$446$	115.126			0.258130
$447$			146.969i			0.328791i
$448$	−347.828	+	347.828i	−0.776401	+	0.776401i
$449$	528.000			1.17595			0.587973	−	0.808880i	$-0.299926\pi$
$449$	528.000			1.17595			0.587973	+	0.808880i	$0.299926\pi$
$450$	275.568	−	275.568i	0.612372	−	0.612372i
$451$	−288.000	−	146.969i	−0.638581	−	0.325874i
$452$	−127.000	−	127.000i	−0.280973	−	0.280973i
$453$		−	293.939i		−	0.648871i
$454$			492.000i			1.08370i
$455$		−	240.000i		−	0.527473i
$456$	−360.000	−	360.000i	−0.789474	−	0.789474i
$457$	543.787	+	543.787i	1.18991	+	1.18991i	0.977093	+	0.212812i	$0.0682622\pi$
$457$	543.787	+	543.787i	1.18991	+	1.18991i	0.212812	+	0.977093i	$0.431738\pi$
$458$	293.939	+	293.939i	0.641788	+	0.641788i
$459$	132.272	−	132.272i	0.288175	−	0.288175i
$460$	35.0000	−	35.0000i	0.0760870	−	0.0760870i
$461$	274.343			0.595104			0.297552	−	0.954706i	$-0.403830\pi$
$461$	274.343			0.595104			0.297552	+	0.954706i	$0.403830\pi$
$462$	352.727	+	180.000i	0.763477	+	0.389610i
$463$	−287.000	−	287.000i	−0.619870	−	0.619870i	0.325628	−	0.945498i	$-0.394424\pi$
$463$	−287.000	−	287.000i	−0.619870	−	0.619870i	−0.945498	+	0.325628i	$0.894424\pi$
$464$			538.888i			1.16140i
$465$		−	720.000i		−	1.54839i
$466$	492.000			1.05579
$467$	−403.000	−	403.000i	−0.862955	−	0.862955i	0.128725	−	0.991680i	$-0.458911\pi$
$467$	−403.000	−	403.000i	−0.862955	−	0.862955i	−0.991680	+	0.128725i	$0.958911\pi$
$468$	−44.0908	−	44.0908i	−0.0942111	−	0.0942111i
$469$	−127.373			−0.271585
$470$		−	208.207i		−	0.442993i
$471$	−249.000	+	249.000i	−0.528662	+	0.528662i
$472$	−232.702	−	232.702i	−0.493012	−	0.493012i
$473$	−652.454	+	211.546i	−1.37940	+	0.447243i
$474$	108.000	−	108.000i	0.227848	−	0.227848i
$475$	−489.898			−1.03136
$476$			48.0000i			0.100840i
$477$	387.000	−	387.000i	0.811321	−	0.811321i
$478$	240.000	+	240.000i	0.502092	+	0.502092i
$479$			97.9796i			0.204550i	0.994756	+	0.102275i	$0.0326122\pi$
$479$			97.9796i			0.204550i	−0.994756	+	0.102275i	$0.967388\pi$
$480$	165.341	+	165.341i	0.344459	+	0.344459i
$481$			362.524i			0.753689i
$482$	−480.000	−	480.000i	−0.995851	−	0.995851i
$483$	−205.757			−0.425998
$484$	−97.9796	+	71.0000i	−0.202437	+	0.146694i
$485$	235.000	+	235.000i	0.484536	+	0.484536i
$486$	−297.613	+	297.613i	−0.612372	+	0.612372i
$487$	407.000	−	407.000i	0.835729	−	0.835729i	−0.152565	−	0.988294i	$-0.548753\pi$
$487$	407.000	−	407.000i	0.835729	−	0.835729i	0.988294	+	0.152565i	$0.0487532\pi$
$488$	300.000	−	300.000i	0.614754	−	0.614754i
$489$	39.0000	+	39.0000i	0.0797546	+	0.0797546i
$490$	−6.12372	+	6.12372i	−0.0124974	+	0.0124974i
$491$	−117.576			−0.239461			−0.119731	−	0.992806i	$-0.538203\pi$
$491$	−117.576			−0.239461			−0.119731	+	0.992806i	$0.538203\pi$
$492$			88.1816i			0.179231i
$493$	240.000	+	240.000i	0.486815	+	0.486815i
$494$		−	235.151i		−	0.476014i
$495$	225.000	−	440.908i	0.454545	−	0.890724i
$496$	−528.000			−1.06452
$497$		0			0
$498$	756.000			1.51807
$499$		−	240.000i		−	0.480962i	−0.970654	−	0.240481i	$-0.922695\pi$
$499$		−	240.000i		−	0.480962i	0.970654	−	0.240481i	$-0.0773052\pi$
$500$	125.000			0.250000
$501$	308.636	−	308.636i	0.616039	−	0.616039i
$502$	293.939	+	293.939i	0.585535	+	0.585535i
$503$	93.0806	+	93.0806i	0.185051	+	0.185051i	0.793553	−	0.608502i	$-0.208229\pi$
$503$	93.0806	+	93.0806i	0.185051	+	0.185051i	−0.608502	+	0.793553i	$0.708229\pi$
$504$		−	540.000i		−	1.07143i
$505$		−	97.9796i		−	0.194019i
$506$	−85.7321	+	168.000i	−0.169431	+	0.332016i
$507$			363.000i			0.715976i
$508$	−4.89898	+	4.89898i	−0.00964366	+	0.00964366i
$509$	−202.000			−0.396857			−0.198428	−	0.980115i	$-0.563584\pi$
$509$	−202.000			−0.396857			−0.198428	+	0.980115i	$0.563584\pi$
$510$	−180.000			−0.352941
$511$	912.000			1.78474
$512$	390.694	−	390.694i	0.763073	−	0.763073i
$513$	529.090			1.03136
$514$	−311.085			−0.605224
$515$	−115.000	+	115.000i	−0.223301	+	0.223301i
$516$	132.272	+	132.272i	0.256342	+	0.256342i
$517$	−81.5653	−	251.565i	−0.157767	−	0.486587i
$518$	−444.000	+	444.000i	−0.857143	+	0.857143i
$519$	132.272	+	132.272i	0.254860	+	0.254860i
$520$			300.000i			0.576923i
$521$			350.000i			0.671785i	0.941900	+	0.335893i	$0.109038\pi$
$521$			350.000i			0.671785i	−0.941900	+	0.335893i	$0.890962\pi$
$522$	−540.000	−	540.000i	−1.03448	−	1.03448i
$523$	−494.797	+	494.797i	−0.946074	+	0.946074i	−0.998619	−	0.0525442i	$-0.983267\pi$
$523$	−494.797	+	494.797i	−0.946074	+	0.946074i	0.0525442	+	0.998619i	$0.483267\pi$
$524$			78.3837i			0.149587i
$525$	−367.423	−	367.423i	−0.699854	−	0.699854i
$526$	−108.000			−0.205323
$527$	−235.151	+	235.151i	−0.446207	+	0.446207i
$528$	−323.333	−	165.000i	−0.612372	−	0.312500i
$529$			431.000i			0.814745i
$530$	−526.640			−0.993661
$531$	342.000			0.644068
$532$	−96.0000	+	96.0000i	−0.180451	+	0.180451i
$533$	−144.000	+	144.000i	−0.270169	+	0.270169i
$534$	−176.363	+	176.363i	−0.330268	+	0.330268i
$535$	24.4949	+	24.4949i	0.0457849	+	0.0457849i
$536$	159.217			0.297046
$537$	−576.000			−1.07263
$538$	−364.974	+	364.974i	−0.678390	+	0.678390i
$539$	−5.00000	+	9.79796i	−0.00927644	+	0.0181780i
$540$	−135.000			−0.250000
$541$			636.867i			1.17720i	0.808423	+	0.588602i	$0.200321\pi$
$541$			636.867i			1.17720i	−0.808423	+	0.588602i	$0.799679\pi$
$542$	120.000	+	120.000i	0.221402	+	0.221402i
$543$	−864.000			−1.59116
$544$		−	108.000i		−	0.198529i
$545$		−	881.816i		−	1.61801i
$546$	176.363	−	176.363i	0.323010	−	0.323010i
$547$	249.848	+	249.848i	0.456760	+	0.456760i	0.897591	−	0.440830i	$-0.145316\pi$
$547$	249.848	+	249.848i	0.456760	+	0.456760i	−0.440830	+	0.897591i	$0.645316\pi$
$548$	−7.00000	+	7.00000i	−0.0127737	+	0.0127737i
$549$			440.908i			0.803111i
$550$	−453.093	+	146.907i	−0.823806	+	0.267103i
$551$			960.000i			1.74229i
$552$	257.196			0.465936
$553$	−144.000	−	144.000i	−0.260398	−	0.260398i
$554$	108.000			0.194946
$555$	555.000	+	555.000i	1.00000	+	1.00000i
$556$			19.5959i			0.0352445i
$557$	298.838	−	298.838i	0.536513	−	0.536513i	−0.385990	−	0.922503i	$-0.626140\pi$
$557$	298.838	−	298.838i	0.536513	−	0.536513i	0.922503	+	0.385990i	$0.126140\pi$
$558$	529.090	−	529.090i	0.948190	−	0.948190i
$559$			432.000i			0.772809i
$560$	−269.444	+	269.444i	−0.481150	+	0.481150i
$561$	−217.485	+	70.5153i	−0.387673	+	0.125696i
$562$	564.000	−	564.000i	1.00356	−	1.00356i
$563$	−543.787	−	543.787i	−0.965873	−	0.965873i	0.0335632	−	0.999437i	$-0.489314\pi$
$563$	−543.787	−	543.787i	−0.965873	−	0.965873i	−0.999437	+	0.0335632i	$0.989314\pi$
$564$	−51.0000	+	51.0000i	−0.0904255	+	0.0904255i
$565$	−635.000	−	635.000i	−1.12389	−	1.12389i
$566$		−	372.000i		−	0.657244i
$567$	396.817	+	396.817i	0.699854	+	0.699854i
$568$		0			0
$569$			391.918i			0.688784i	0.938826	+	0.344392i	$0.111915\pi$
$569$			391.918i			0.688784i	−0.938826	+	0.344392i	$0.888085\pi$
$570$	−360.000	−	360.000i	−0.631579	−	0.631579i
$571$			734.847i			1.28695i	0.765468	+	0.643474i	$0.222507\pi$
$571$			734.847i			1.28695i	−0.765468	+	0.643474i	$0.777493\pi$
$572$	23.5051	+	72.4949i	0.0410928	+	0.126739i
$573$		−	330.000i		−	0.575916i
$574$	−352.727			−0.614506
$575$	175.000	−	175.000i	0.304348	−	0.304348i
$576$			639.000i			1.10938i
$577$	−433.000	+	433.000i	−0.750433	+	0.750433i	−0.974560	−	0.224127i	$-0.928047\pi$
$577$	−433.000	+	433.000i	−0.750433	+	0.750433i	0.224127	+	0.974560i	$0.428047\pi$
$578$	−295.164	−	295.164i	−0.510664	−	0.510664i
$579$	−161.666	+	161.666i	−0.279216	+	0.279216i
$580$		−	244.949i		−	0.422326i
$581$		−	1008.00i		−	1.73494i
$582$			345.378i			0.593433i
$583$	−636.312	+	206.312i	−1.09144	+	0.353880i
$584$	−1140.00			−1.95205
$585$	−220.454	−	220.454i	−0.376845	−	0.376845i
$586$	852.000			1.45392
$587$	197.000	+	197.000i	0.335605	+	0.335605i	0.854710	−	0.519105i	$-0.173735\pi$
$587$	197.000	+	197.000i	0.335605	+	0.335605i	−0.519105	+	0.854710i	$0.673735\pi$
$588$	3.00000			0.00510204
$589$	−940.604			−1.59695
$590$	−232.702	−	232.702i	−0.394409	−	0.394409i
$591$	−279.242	+	279.242i	−0.472490	+	0.472490i
$592$	407.000	−	407.000i	0.687500	−	0.687500i
$593$	−53.8888	−	53.8888i	−0.0908748	−	0.0908748i	0.660208	−	0.751083i	$-0.270468\pi$
$593$	−53.8888	−	53.8888i	−0.0908748	−	0.0908748i	−0.751083	+	0.660208i	$0.770468\pi$
$594$	489.341	−	158.659i	0.823806	−	0.267103i
$595$			240.000i			0.403361i
$596$	−48.9898			−0.0821976
$597$		0			0
$598$	84.0000	+	84.0000i	0.140468	+	0.140468i
$599$	528.000			0.881469			0.440735	−	0.897637i	$-0.354718\pi$
$599$	528.000			0.881469			0.440735	+	0.897637i	$0.354718\pi$
$600$	459.279	+	459.279i	0.765466	+	0.765466i
$601$		−	587.878i		−	0.978166i	−0.872237	−	0.489083i	$-0.837332\pi$
$601$		−	587.878i		−	0.978166i	0.872237	−	0.489083i	$-0.162668\pi$
$602$	−529.090	+	529.090i	−0.878887	+	0.878887i
$603$	−117.000	+	117.000i	−0.194030	+	0.194030i
$604$	97.9796			0.162218
$605$	−489.898	+	355.000i	−0.809749	+	0.586777i
$606$	72.0000	−	72.0000i	0.118812	−	0.118812i
$607$	739.746	+	739.746i	1.21869	+	1.21869i	0.968090	+	0.250601i	$0.0806284\pi$
$607$	739.746	+	739.746i	1.21869	+	1.21869i	0.250601	+	0.968090i	$0.419372\pi$
$608$	216.000	−	216.000i	0.355263	−	0.355263i
$609$	−720.000	+	720.000i	−1.18227	+	1.18227i
$610$	300.000	−	300.000i	0.491803	−	0.491803i
$611$	−166.565			−0.272611
$612$	44.0908	+	44.0908i	0.0720438	+	0.0720438i
$613$	191.060	−	191.060i	0.311681	−	0.311681i	−0.533880	−	0.845560i	$-0.679267\pi$
$613$	191.060	−	191.060i	0.311681	−	0.311681i	0.845560	+	0.533880i	$0.179267\pi$
$614$	828.000			1.34853
$615$			440.908i			0.716924i
$616$	−300.000	+	587.878i	−0.487013	+	0.954347i
$617$	487.000	+	487.000i	0.789303	+	0.789303i	0.981380	−	0.192077i	$-0.0615223\pi$
$617$	487.000	+	487.000i	0.789303	+	0.789303i	−0.192077	+	0.981380i	$0.561522\pi$
$618$	−169.015			−0.273487
$619$			310.000i			0.500808i	0.968141	+	0.250404i	$0.0805634\pi$
$619$			310.000i			0.500808i	−0.968141	+	0.250404i	$0.919437\pi$
$620$	240.000			0.387097
$621$	−189.000	+	189.000i	−0.304348	+	0.304348i
$622$	−587.878	−	587.878i	−0.945141	−	0.945141i
$623$	235.151	+	235.151i	0.377449	+	0.377449i
$624$	−161.666	+	161.666i	−0.259081	+	0.259081i
$625$	625.000			1.00000
$626$	531.539			0.849104
$627$	−576.000	−	293.939i	−0.918660	−	0.468802i
$628$	−83.0000	−	83.0000i	−0.132166	−	0.132166i
$629$		−	362.524i		−	0.576351i
$630$		−	540.000i		−	0.857143i
$631$	−338.000			−0.535658			−0.267829	−	0.963467i	$-0.586306\pi$
$631$	−338.000			−0.535658			−0.267829	+	0.963467i	$0.586306\pi$
$632$	180.000	+	180.000i	0.284810	+	0.284810i
$633$		−	734.847i		−	1.16090i
$634$	−164.116			−0.258858
$635$	−24.4949	+	24.4949i	−0.0385746	+	0.0385746i
$636$	129.000	+	129.000i	0.202830	+	0.202830i
$637$	4.89898	+	4.89898i	0.00769071	+	0.00769071i
$638$	287.878	+	887.878i	0.451219	+	1.39166i
$639$		0			0
$640$	214.330	−	214.330i	0.334891	−	0.334891i
$641$		−	1070.00i		−	1.66927i	−0.550806	−	0.834633i	$-0.685680\pi$
$641$		−	1070.00i		−	1.66927i	0.550806	−	0.834633i	$-0.314320\pi$
$642$			36.0000i			0.0560748i
$643$	803.000	+	803.000i	1.24883	+	1.24883i	0.956236	+	0.292598i	$0.0945198\pi$
$643$	803.000	+	803.000i	1.24883	+	1.24883i	0.292598	+	0.956236i	$0.405480\pi$
$644$		−	68.5857i		−	0.106500i
$645$	661.362	+	661.362i	1.02537	+	1.02537i
$646$			235.151i			0.364011i
$647$	617.000	+	617.000i	0.953632	+	0.953632i	0.998972	−	0.0453395i	$-0.0144370\pi$
$647$	617.000	+	617.000i	0.953632	+	0.953632i	−0.0453395	+	0.998972i	$0.514437\pi$
$648$	−496.022	−	496.022i	−0.765466	−	0.765466i
$649$	−372.322	−	190.000i	−0.573686	−	0.292758i
$650$			300.000i			0.461538i
$651$	−705.453	−	705.453i	−1.08365	−	1.08365i
$652$	−13.0000	+	13.0000i	−0.0199387	+	0.0199387i
$653$	653.000	−	653.000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$653$	653.000	−	653.000i	1.00000	−	1.00000i	1.00000			$0$
$654$	648.000	−	648.000i	0.990826	−	0.990826i
$655$			391.918i			0.598349i
$656$	323.333			0.492885
$657$	837.725	−	837.725i	1.27508	−	1.27508i
$658$	−204.000	−	204.000i	−0.310030	−	0.310030i
$659$			342.929i			0.520377i	0.965558	+	0.260189i	$0.0837847\pi$
$659$			342.929i			0.520377i	−0.965558	+	0.260189i	$0.916215\pi$
$660$	146.969	+	75.0000i	0.222681	+	0.113636i
$661$	122.000			0.184569			0.0922844	−	0.995733i	$-0.470583\pi$
$661$	122.000			0.184569			0.0922844	+	0.995733i	$0.470583\pi$
$662$	352.727	−	352.727i	0.532820	−	0.532820i
$663$			144.000i			0.217195i
$664$			1260.00i			1.89759i
$665$	−480.000	+	480.000i	−0.721805	+	0.721805i
$666$			815.680i			1.22474i
$667$	−342.929	−	342.929i	−0.514136	−	0.514136i
$668$	102.879	+	102.879i	0.154010	+	0.154010i
$669$	−141.000	−	141.000i	−0.210762	−	0.210762i
$670$	159.217			0.237637
$671$	244.949	−	480.000i	0.365051	−	0.715350i
$672$	324.000			0.482143
$673$	191.060	−	191.060i	0.283893	−	0.283893i	−0.550766	−	0.834660i	$-0.685664\pi$
$673$	191.060	−	191.060i	0.283893	−	0.283893i	0.834660	+	0.550766i	$0.185664\pi$
$674$	−612.000			−0.908012
$675$	−675.000			−1.00000
$676$	−121.000			−0.178994
$677$	4.89898	−	4.89898i	0.00723631	−	0.00723631i	−0.703479	−	0.710716i	$-0.748371\pi$
$677$	4.89898	−	4.89898i	0.00723631	−	0.00723631i	0.710716	+	0.703479i	$0.248371\pi$
$678$		−	933.256i		−	1.37648i
$679$	460.504			0.678209
$680$		−	300.000i		−	0.441176i
$681$	602.574	−	602.574i	0.884838	−	0.884838i
$682$	−869.939	+	282.061i	−1.27557	+	0.413580i
$683$	53.0000	−	53.0000i	0.0775988	−	0.0775988i	−0.667242	−	0.744841i	$-0.732525\pi$
$683$	53.0000	−	53.0000i	0.0775988	−	0.0775988i	0.744841	+	0.667242i	$0.232525\pi$
$684$			176.363i			0.257841i
$685$	−35.0000	+	35.0000i	−0.0510949	+	0.0510949i
$686$			600.000i			0.874636i
$687$		−	720.000i		−	1.04803i
$688$	484.999	−	484.999i	0.704940	−	0.704940i
$689$			421.312i			0.611484i
$690$	257.196			0.372748
$691$	−598.000			−0.865412			−0.432706	−	0.901535i	$-0.642441\pi$
$691$	−598.000			−0.865412			−0.432706	+	0.901535i	$0.642441\pi$
$692$	−44.0908	+	44.0908i	−0.0637151	+	0.0637151i
$693$	−211.546	−	652.454i	−0.305261	−	0.941492i
$694$		−	348.000i		−	0.501441i
$695$			97.9796i			0.140978i
$696$	900.000	−	900.000i	1.29310	−	1.29310i
$697$	144.000	−	144.000i	0.206600	−	0.206600i
$698$	336.000	−	336.000i	0.481375	−	0.481375i
$699$	−602.574	−	602.574i	−0.862052	−	0.862052i
$700$	122.474	−	122.474i	0.174964	−	0.174964i
$701$	862.220			1.22999			0.614993	−	0.788532i	$-0.289159\pi$
$701$	862.220			1.22999			0.614993	+	0.788532i	$0.289159\pi$
$702$		−	324.000i		−	0.461538i
$703$	725.049	−	725.049i	1.03136	−	1.03136i
$704$	355.000	−	695.655i	0.504261	−	0.988146i
$705$	−255.000	+	255.000i	−0.361702	+	0.361702i
$706$		−	629.519i		−	0.891670i
$707$	−96.0000	−	96.0000i	−0.135785	−	0.135785i
$708$			114.000i			0.161017i
$709$			170.000i			0.239774i	0.992788	+	0.119887i	$0.0382533\pi$
$709$			170.000i			0.239774i	−0.992788	+	0.119887i	$0.961747\pi$
$710$		0			0
$711$	−264.545			−0.372074
$712$	−293.939	−	293.939i	−0.412835	−	0.412835i
$713$	336.000	−	336.000i	0.471248	−	0.471248i
$714$	−176.363	+	176.363i	−0.247007	+	0.247007i
$715$	117.526	+	362.474i	0.164371	+	0.506957i
$716$		−	192.000i		−	0.268156i
$717$		−	587.878i		−	0.819913i
$718$	−240.000	−	240.000i	−0.334262	−	0.334262i
$719$	−912.000			−1.26843			−0.634214	−	0.773157i	$-0.718676\pi$
$719$	−912.000			−1.26843			−0.634214	+	0.773157i	$0.718676\pi$
$720$			495.000i			0.687500i
$721$			225.353i			0.312556i
$722$	−28.1691	+	28.1691i	−0.0390154	+	0.0390154i
$723$			1175.76i			1.62622i
$724$		−	288.000i		−	0.397790i
$725$		−	1224.74i		−	1.68930i
$726$	−620.871	−	99.1293i	−0.855194	−	0.136542i
$727$	457.000	−	457.000i	0.628611	−	0.628611i	−0.319108	−	0.947718i	$-0.603383\pi$
$727$	457.000	−	457.000i	0.628611	−	0.628611i	0.947718	+	0.319108i	$0.103383\pi$
$728$	293.939	+	293.939i	0.403762	+	0.403762i
$729$	729.000			1.00000
$730$	−1140.00			−1.56164
$731$		−	432.000i		−	0.590971i
$732$	−146.969			−0.200778
$733$	142.070	−	142.070i	0.193820	−	0.193820i	−0.603524	−	0.797345i	$-0.706237\pi$
$733$	142.070	−	142.070i	0.193820	−	0.193820i	0.797345	+	0.603524i	$0.206237\pi$
$734$			237.601i			0.323706i
$735$	15.0000			0.0204082
$736$			154.318i			0.209671i
$737$	192.373	−	62.3735i	0.261022	−	0.0846316i
$738$	−324.000	+	324.000i	−0.439024	+	0.439024i
$739$	−78.3837			−0.106067			−0.0530336	−	0.998593i	$-0.516889\pi$
$739$	−78.3837			−0.106067			−0.0530336	+	0.998593i	$0.516889\pi$
$740$	−185.000	+	185.000i	−0.250000	+	0.250000i
$741$	−288.000	+	288.000i	−0.388664	+	0.388664i
$742$	−516.000	+	516.000i	−0.695418	+	0.695418i
$743$	−102.879	−	102.879i	−0.138464	−	0.138464i	0.634478	−	0.772941i	$-0.281215\pi$
$743$	−102.879	−	102.879i	−0.138464	−	0.138464i	−0.772941	+	0.634478i	$0.781215\pi$
$744$	881.816	+	881.816i	1.18524	+	1.18524i
$745$	−244.949			−0.328791
$746$		−	252.000i		−	0.337802i
$747$	−925.907	−	925.907i	−1.23950	−	1.23950i
$748$	−23.5051	−	72.4949i	−0.0314239	−	0.0969183i
$749$	48.0000			0.0640854
$750$	459.279	+	459.279i	0.612372	+	0.612372i
$751$	−578.000			−0.769640			−0.384820	−	0.922992i	$-0.625737\pi$
$751$	−578.000			−0.769640			−0.384820	+	0.922992i	$0.625737\pi$
$752$	187.000	+	187.000i	0.248670	+	0.248670i
$753$		−	720.000i		−	0.956175i
$754$	587.878			0.779678
$755$	489.898			0.648871
$756$	−132.272	+	132.272i	−0.174964	+	0.174964i
$757$	277.000	−	277.000i	0.365918	−	0.365918i	−0.500068	−	0.865986i	$-0.666692\pi$
$757$	277.000	−	277.000i	0.365918	−	0.365918i	0.865986	+	0.500068i	$0.166692\pi$
$758$	881.816	+	881.816i	1.16335	+	1.16335i
$759$	310.757	−	100.757i	0.409430	−	0.132750i
$760$	600.000	−	600.000i	0.789474	−	0.789474i
$761$	813.231			1.06863			0.534317	−	0.845284i	$-0.320569\pi$
$761$	813.231			1.06863			0.534317	+	0.845284i	$0.320569\pi$
$762$	−36.0000			−0.0472441
$763$	−864.000	−	864.000i	−1.13237	−	1.13237i
$764$	110.000			0.143979
$765$	220.454	+	220.454i	0.288175	+	0.288175i
$766$			864.670i			1.12881i
$767$	−186.161	+	186.161i	−0.242713	+	0.242713i
$768$	−537.000			−0.699219
$769$	−617.271			−0.802694			−0.401347	−	0.915926i	$-0.631458\pi$
$769$	−617.271			−0.802694			−0.401347	+	0.915926i	$0.631458\pi$
$770$	−300.000	+	587.878i	−0.389610	+	0.763477i
$771$	381.000	+	381.000i	0.494163	+	0.494163i
$772$	−53.8888	−	53.8888i	−0.0698041	−	0.0698041i
$773$	−197.000	+	197.000i	−0.254851	+	0.254851i	−0.822956	−	0.568105i	$-0.807677\pi$
$773$	−197.000	+	197.000i	−0.254851	+	0.254851i	0.568105	+	0.822956i	$0.307677\pi$
$774$			972.000i			1.25581i
$775$	1200.00			1.54839
$776$	−575.630			−0.741791
$777$	1087.57			1.39971
$778$	516.842	−	516.842i	0.664322	−	0.664322i
$779$	576.000			0.739409
$780$	73.4847	−	73.4847i	0.0942111	−	0.0942111i
$781$		0			0
$782$	−84.0000	−	84.0000i	−0.107417	−	0.107417i
$783$			1322.72i			1.68930i
$784$		−	11.0000i		−	0.0140306i
$785$	−415.000	−	415.000i	−0.528662	−	0.528662i
$786$	−288.000	+	288.000i	−0.366412	+	0.366412i
$787$	−436.009	−	436.009i	−0.554014	−	0.554014i	0.373583	−	0.927597i	$-0.378129\pi$
$787$	−436.009	−	436.009i	−0.554014	−	0.554014i	−0.927597	+	0.373583i	$0.878129\pi$
$788$	−93.0806	−	93.0806i	−0.118123	−	0.118123i
$789$	132.272	+	132.272i	0.167646	+	0.167646i
$790$	180.000	+	180.000i	0.227848	+	0.227848i
$791$	−1244.34			−1.57312
$792$	264.432	+	815.568i	0.333879	+	1.02976i
$793$	−240.000	−	240.000i	−0.302648	−	0.302648i
$794$		−	1207.60i		−	1.52090i
$795$	645.000	+	645.000i	0.811321	+	0.811321i
$796$		0			0
$797$	−883.000	−	883.000i	−1.10790	−	1.10790i	−0.993426	−	0.114479i	$-0.963480\pi$
$797$	−883.000	−	883.000i	−1.10790	−	1.10790i	−0.114479	−	0.993426i	$-0.536520\pi$
$798$	−705.453			−0.884026
$799$	166.565			0.208467
$800$	−275.568	+	275.568i	−0.344459	+	0.344459i
$801$	432.000			0.539326
$802$	722.599	+	722.599i	0.900997	+	0.900997i
$803$	−1377.40	+	446.597i	−1.71532	+	0.556161i
$804$	−39.0000	−	39.0000i	−0.0485075	−	0.0485075i
$805$		−	342.929i		−	0.425998i
$806$			576.000i			0.714640i
$807$	894.000			1.10781
$808$	120.000	+	120.000i	0.148515	+	0.148515i
$809$			979.796i			1.21112i	0.795800	+	0.605560i	$0.207051\pi$
$809$			979.796i			1.21112i	−0.795800	+	0.605560i	$0.792949\pi$
$810$	−496.022	−	496.022i	−0.612372	−	0.612372i
$811$		−	930.806i		−	1.14773i	−0.818951	−	0.573863i	$-0.805444\pi$
$811$		−	930.806i		−	1.14773i	0.818951	−	0.573863i	$-0.194556\pi$
$812$	−240.000	−	240.000i	−0.295567	−	0.295567i
$813$		−	293.939i		−	0.361548i
$814$	453.156	−	888.000i	0.556702	−	1.09091i
$815$	−65.0000	+	65.0000i	−0.0797546	+	0.0797546i
$816$	161.666	−	161.666i	0.198120	−	0.198120i
$817$	864.000	−	864.000i	1.05753	−	1.05753i
$818$	396.000	−	396.000i	0.484108	−	0.484108i
$819$	−432.000			−0.527473
$820$	−146.969			−0.179231
$821$	−215.555			−0.262552			−0.131276	−	0.991346i	$-0.541907\pi$
$821$	−215.555			−0.262552			−0.131276	+	0.991346i	$0.541907\pi$
$822$	−51.4393			−0.0625782
$823$	743.000	+	743.000i	0.902795	+	0.902795i	0.995677	−	0.0928824i	$-0.0296081\pi$
$823$	743.000	+	743.000i	0.902795	+	0.902795i	−0.0928824	+	0.995677i	$0.529608\pi$
$824$		−	281.691i		−	0.341858i
$825$	734.847	+	375.000i	0.890724	+	0.454545i
$826$	−456.000			−0.552058
$827$	−827.928	+	827.928i	−1.00112	+	1.00112i	−0.00112219	+	0.999999i	$0.500357\pi$
$827$	−827.928	+	827.928i	−1.00112	+	1.00112i	−0.999999	+	0.00112219i	$0.999643\pi$
$828$	−63.0000	−	63.0000i	−0.0760870	−	0.0760870i
$829$		−	410.000i		−	0.494572i	−0.968943	−	0.247286i	$-0.920461\pi$
$829$		−	410.000i		−	0.494572i	0.968943	−	0.247286i	$-0.0795387\pi$
$830$			1260.00i			1.51807i
$831$	−132.272	−	132.272i	−0.159173	−	0.159173i
$832$	−347.828	−	347.828i	−0.418062	−	0.418062i
$833$	−4.89898	−	4.89898i	−0.00588113	−	0.00588113i
$834$	−72.0000	+	72.0000i	−0.0863309	+	0.0863309i
$835$	514.393	+	514.393i	0.616039	+	0.616039i
$836$	97.9796	−	192.000i	0.117200	−	0.229665i
$837$	−1296.00			−1.54839
$838$	−352.727	+	352.727i	−0.420915	+	0.420915i
$839$	−1262.00			−1.50417			−0.752086	−	0.659065i	$-0.770952\pi$
$839$	−1262.00			−1.50417			−0.752086	+	0.659065i	$0.770952\pi$
$840$	900.000			1.07143
$841$	−1559.00			−1.85375
$842$	−823.029	+	823.029i	−0.977469	+	0.977469i
$843$	−1381.51			−1.63880
$844$	244.949			0.290224
$845$	−605.000			−0.715976
$846$	−374.772			−0.442993
$847$	−132.172	+	827.828i	−0.156048	+	0.977364i
$848$	473.000	−	473.000i	0.557783	−	0.557783i
$849$	−455.605	+	455.605i	−0.536637	+	0.536637i
$850$		−	300.000i		−	0.352941i
$851$			518.000i			0.608696i
$852$		0			0
$853$	−249.848	+	249.848i	−0.292905	+	0.292905i	−0.838227	−	0.545322i	$-0.816407\pi$
$853$	−249.848	+	249.848i	−0.292905	+	0.292905i	0.545322	+	0.838227i	$0.316407\pi$
$854$		−	587.878i		−	0.688381i
$855$			881.816i			1.03136i
$856$	−60.0000			−0.0700935
$857$	−191.060	+	191.060i	−0.222941	+	0.222941i	−0.809736	−	0.586795i	$-0.800389\pi$
$857$	−191.060	+	191.060i	−0.222941	+	0.222941i	0.586795	+	0.809736i	$0.300389\pi$
$858$	−180.000	+	352.727i	−0.209790	+	0.411103i
$859$			310.000i			0.360885i	0.983586	+	0.180442i	$0.0577529\pi$
$859$			310.000i			0.360885i	−0.983586	+	0.180442i	$0.942247\pi$
$860$	−220.454	+	220.454i	−0.256342	+	0.256342i
$861$	432.000	+	432.000i	0.501742	+	0.501742i
$862$	−36.0000	+	36.0000i	−0.0417633	+	0.0417633i
$863$	833.000	−	833.000i	0.965238	−	0.965238i	−0.0341782	−	0.999416i	$-0.510881\pi$
$863$	833.000	−	833.000i	0.965238	−	0.965238i	0.999416	+	0.0341782i	$0.0108814\pi$
$864$	297.613	−	297.613i	0.344459	−	0.344459i
$865$	−220.454	+	220.454i	−0.254860	+	0.254860i
$866$	115.126			0.132940
$867$			723.000i			0.833910i
$868$	235.151	−	235.151i	0.270911	−	0.270911i
$869$	288.000	+	146.969i	0.331415	+	0.169125i
$870$	900.000	−	900.000i	1.03448	−	1.03448i
$871$		−	127.373i		−	0.146238i
$872$	1080.00	+	1080.00i	1.23853	+	1.23853i
$873$	423.000	−	423.000i	0.484536	−	0.484536i
$874$		−	336.000i		−	0.384439i
$875$	612.372	−	612.372i	0.699854	−	0.699854i
$876$	279.242	+	279.242i	0.318769	+	0.318769i
$877$	−44.0908	−	44.0908i	−0.0502746	−	0.0502746i	0.681523	−	0.731797i	$-0.261318\pi$
$877$	−44.0908	−	44.0908i	−0.0502746	−	0.0502746i	−0.731797	+	0.681523i	$0.761318\pi$
$878$	−924.000	+	924.000i	−1.05239	+	1.05239i
$879$	−1043.48	−	1043.48i	−1.18712	−	1.18712i
$880$	275.000	−	538.888i	0.312500	−	0.612372i
$881$			480.000i			0.544835i	0.962179	+	0.272418i	$0.0878233\pi$
$881$			480.000i			0.544835i	−0.962179	+	0.272418i	$0.912177\pi$
$882$	11.0227	+	11.0227i	0.0124974	+	0.0124974i
$883$	83.0000	+	83.0000i	0.0939977	+	0.0939977i	0.752542	−	0.658544i	$-0.228827\pi$
$883$	83.0000	+	83.0000i	0.0939977	+	0.0939977i	−0.658544	+	0.752542i	$0.728827\pi$
$884$	−48.0000			−0.0542986
$885$			570.000i			0.644068i
$886$			105.328i			0.118880i
$887$	−876.917	+	876.917i	−0.988633	+	0.988633i	−0.999936	−	0.0113033i	$-0.996402\pi$
$887$	−876.917	+	876.917i	−0.988633	+	0.988633i	0.0113033	+	0.999936i	$0.496402\pi$
$888$	−1359.47			−1.53093
$889$			48.0000i			0.0539933i
$890$	−293.939	−	293.939i	−0.330268	−	0.330268i
$891$	−793.635	−	405.000i	−0.890724	−	0.454545i
$892$	47.0000	−	47.0000i	0.0526906	−	0.0526906i
$893$	333.131	+	333.131i	0.373047	+	0.373047i
$894$	−180.000	−	180.000i	−0.201342	−	0.201342i
$895$		−	960.000i		−	1.07263i
$896$		−	420.000i		−	0.468750i
$897$		−	205.757i		−	0.229384i
$898$	−646.665	+	646.665i	−0.720117	+	0.720117i
$899$		−	2351.51i		−	2.61570i
$900$		−	225.000i		−	0.250000i
$901$		−	421.312i		−	0.467605i
$902$	532.727	−	172.727i	0.590606	−	0.191493i
$903$	1296.00			1.43522
$904$	1555.43			1.72060
$905$		−	1440.00i		−	1.59116i
$906$	360.000	+	360.000i	0.397351	+	0.397351i
$907$	37.0000	−	37.0000i	0.0407938	−	0.0407938i	−0.686416	−	0.727209i	$-0.740817\pi$
$907$	37.0000	−	37.0000i	0.0407938	−	0.0407938i	0.727209	+	0.686416i	$0.240817\pi$
$908$	200.858	+	200.858i	0.221209	+	0.221209i
$909$	−176.363			−0.194019
$910$	293.939	+	293.939i	0.323010	+	0.323010i
$911$		−	370.000i		−	0.406147i	−0.979163	−	0.203074i	$-0.934907\pi$
$911$		−	370.000i		−	0.406147i	0.979163	−	0.203074i	$-0.0650931\pi$
$912$	646.665			0.709063
$913$	493.607	+	1522.39i	0.540643	+	1.66746i
$914$	−1332.00			−1.45733
$915$	−734.847			−0.803111
$916$	240.000			0.262009
$917$	384.000	+	384.000i	0.418757	+	0.418757i
$918$			324.000i			0.352941i
$919$	1538.28			1.67386			0.836931	−	0.547308i	$-0.184347\pi$
$919$	1538.28			1.67386			0.836931	+	0.547308i	$0.184347\pi$
$920$			428.661i			0.465936i
$921$	−1014.09	−	1014.09i	−1.10107	−	1.10107i
$922$	−336.000	+	336.000i	−0.364425	+	0.364425i
$923$		0			0
$924$	217.485	−	70.5153i	0.235373	−	0.0763153i
$925$	−925.000	+	925.000i	−1.00000	+	1.00000i
$926$	703.004			0.759183
$927$	207.000	+	207.000i	0.223301	+	0.223301i
$928$	540.000	+	540.000i	0.581897	+	0.581897i
$929$	158.000			0.170075			0.0850377	−	0.996378i	$-0.472899\pi$
$929$	158.000			0.170075			0.0850377	+	0.996378i	$0.472899\pi$
$930$	881.816	+	881.816i	0.948190	+	0.948190i
$931$		−	19.5959i		−	0.0210482i
$932$	200.858	−	200.858i	0.215513	−	0.215513i
$933$			1440.00i			1.54341i
$934$	987.144			1.05690
$935$	−117.526	−	362.474i	−0.125696	−	0.387673i
$936$	540.000			0.576923
$937$	788.736	+	788.736i	0.841767	+	0.841767i	0.989089	−	0.147322i	$-0.0470652\pi$
$937$	788.736	+	788.736i	0.841767	+	0.841767i	−0.147322	+	0.989089i	$0.547065\pi$
$938$	156.000	−	156.000i	0.166311	−	0.166311i
$939$	−651.000	−	651.000i	−0.693291	−	0.693291i
$940$	−85.0000	−	85.0000i	−0.0904255	−	0.0904255i
$941$	176.363			0.187421			0.0937106	−	0.995599i	$-0.470127\pi$
$941$	176.363			0.187421			0.0937106	+	0.995599i	$0.470127\pi$
$942$		−	609.923i		−	0.647477i
$943$	−205.757	+	205.757i	−0.218194	+	0.218194i
$944$	418.000			0.442797
$945$	−661.362	+	661.362i	−0.699854	+	0.699854i
$946$	540.000	−	1058.18i	0.570825	−	1.11858i
$947$	−413.000	−	413.000i	−0.436114	−	0.436114i	0.454588	−	0.890702i	$-0.349787\pi$
$947$	−413.000	−	413.000i	−0.436114	−	0.436114i	−0.890702	+	0.454588i	$0.849787\pi$
$948$		−	88.1816i		−	0.0930186i
$949$			912.000i			0.961012i
$950$	600.000	−	600.000i	0.631579	−	0.631579i
$951$	201.000	+	201.000i	0.211356	+	0.211356i
$952$	−293.939	−	293.939i	−0.308759	−	0.308759i
$953$	240.050	+	240.050i	0.251889	+	0.251889i	0.821745	−	0.569856i	$-0.193001\pi$
$953$	240.050	+	240.050i	0.251889	+	0.251889i	−0.569856	+	0.821745i	$0.693001\pi$
$954$			947.953i			0.993661i
$955$	550.000			0.575916
$956$	195.959			0.204978
$957$	734.847	−	1440.00i	0.767865	−	1.50470i
$958$	−120.000	−	120.000i	−0.125261	−	0.125261i
$959$			68.5857i			0.0715179i
$960$	−1065.00			−1.10938
$961$	1343.00			1.39750
$962$	−444.000	−	444.000i	−0.461538	−	0.461538i
$963$	44.0908	−	44.0908i	0.0457849	−	0.0457849i
$964$	−391.918			−0.406554
$965$	−269.444	−	269.444i	−0.279216	−	0.279216i
$966$	252.000	−	252.000i	0.260870	−	0.260870i
$967$	592.777	+	592.777i	0.613006	+	0.613006i	0.943728	−	0.330722i	$-0.107292\pi$
$967$	592.777	+	592.777i	0.613006	+	0.613006i	−0.330722	+	0.943728i	$0.607292\pi$
$968$	165.216	−	1034.78i	0.170677	−	1.06899i
$969$	288.000	−	288.000i	0.297214	−	0.297214i
$970$	−575.630			−0.593433
$971$			1430.00i			1.47271i	0.676596	+	0.736354i	$0.263454\pi$
$971$			1430.00i			1.47271i	−0.676596	+	0.736354i	$0.736546\pi$
$972$			243.000i			0.250000i
$973$	96.0000	+	96.0000i	0.0986639	+	0.0986639i
$974$			996.942i			1.02355i
$975$	367.423	−	367.423i	0.376845	−	0.376845i
$976$			538.888i			0.552139i
$977$	1217.00	+	1217.00i	1.24565	+	1.24565i	0.957622	+	0.288028i	$0.0929996\pi$
$977$	1217.00	+	1217.00i	1.24565	+	1.24565i	0.288028	+	0.957622i	$0.407000\pi$
$978$	−95.5301			−0.0976790
$979$	−470.302	−	240.000i	−0.480390	−	0.245148i
$980$			5.00000i			0.00510204i
$981$	−1587.27			−1.61801
$982$	144.000	−	144.000i	0.146640	−	0.146640i
$983$	−137.000	+	137.000i	−0.139369	+	0.139369i	−0.773349	−	0.633980i	$-0.781420\pi$
$983$	−137.000	+	137.000i	−0.139369	+	0.139369i	0.633980	+	0.773349i	$0.281420\pi$
$984$	−540.000	−	540.000i	−0.548780	−	0.548780i
$985$	−465.403	−	465.403i	−0.472490	−	0.472490i
$986$	−587.878			−0.596225
$987$			499.696i			0.506278i
$988$	−96.0000	−	96.0000i	−0.0971660	−	0.0971660i
$989$			617.271i			0.624137i
$990$	264.432	+	815.568i	0.267103	+	0.823806i
$991$	−1008.00			−1.01715			−0.508577	−	0.861016i	$-0.669828\pi$
$991$	−1008.00			−1.01715			−0.508577	+	0.861016i	$0.669828\pi$
$992$	−529.090	+	529.090i	−0.533357	+	0.533357i
$993$	−864.000			−0.870091
$994$		0			0
$995$		0			0
$996$	308.636	−	308.636i	0.309875	−	0.309875i
$997$	−1268.84	−	1268.84i	−1.27265	−	1.27265i	−0.944691	−	0.327963i	$-0.893638\pi$
$997$	−1268.84	−	1268.84i	−1.27265	−	1.27265i	−0.327963	−	0.944691i	$-0.606362\pi$
$998$	293.939	+	293.939i	0.294528	+	0.294528i
$999$	999.000	−	999.000i	1.00000	−	1.00000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.3.l.f.98.1	yes	4
3.2	odd	2		165.3.l.b.98.2	yes	4
5.2	odd	4		165.3.l.b.32.1	✓	4
11.10	odd	2	inner	165.3.l.f.98.2	yes	4
15.2	even	4	inner	165.3.l.f.32.2	yes	4
33.32	even	2		165.3.l.b.98.1	yes	4
55.32	even	4		165.3.l.b.32.2	yes	4
165.32	odd	4	inner	165.3.l.f.32.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.3.l.b.32.1	✓	4	5.2	odd	4
165.3.l.b.32.2	yes	4	55.32	even	4
165.3.l.b.98.1	yes	4	33.32	even	2
165.3.l.b.98.2	yes	4	3.2	odd	2
165.3.l.f.32.1	yes	4	165.32	odd	4	inner
165.3.l.f.32.2	yes	4	15.2	even	4	inner
165.3.l.f.98.1	yes	4	1.1	even	1	trivial
165.3.l.f.98.2	yes	4	11.10	odd	2	inner

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	165.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 1.22474i) q^{2} +3.00000 q^{3} +1.00000i q^{4} +5.00000i q^{5} +(-3.67423 + 3.67423i) q^{6} +(4.89898 + 4.89898i) q^{7} +(-6.12372 - 6.12372i) q^{8} +9.00000 q^{9} +(-6.12372 - 6.12372i) q^{10} +(-9.79796 - 5.00000i) q^{11} +3.00000i q^{12} +(-4.89898 + 4.89898i) q^{13} -12.0000 q^{14} +15.0000i q^{15} +11.0000 q^{16} +(4.89898 - 4.89898i) q^{17} +(-11.0227 + 11.0227i) q^{18} +19.5959 q^{19} -5.00000 q^{20} +(14.6969 + 14.6969i) q^{21} +(18.1237 - 5.87628i) q^{22} +(-7.00000 + 7.00000i) q^{23} +(-18.3712 - 18.3712i) q^{24} -25.0000 q^{25} -12.0000i q^{26} +27.0000 q^{27} +(-4.89898 + 4.89898i) q^{28} +48.9898i q^{29} +(-18.3712 - 18.3712i) q^{30} -48.0000 q^{31} +(11.0227 - 11.0227i) q^{32} +(-29.3939 - 15.0000i) q^{33} +12.0000i q^{34} +(-24.4949 + 24.4949i) q^{35} +9.00000i q^{36} +(37.0000 - 37.0000i) q^{37} +(-24.0000 + 24.0000i) q^{38} +(-14.6969 + 14.6969i) q^{39} +(30.6186 - 30.6186i) q^{40} +29.3939 q^{41} -36.0000 q^{42} +(44.0908 - 44.0908i) q^{43} +(5.00000 - 9.79796i) q^{44} +45.0000i q^{45} -17.1464i q^{46} +(17.0000 + 17.0000i) q^{47} +33.0000 q^{48} -1.00000i q^{49} +(30.6186 - 30.6186i) q^{50} +(14.6969 - 14.6969i) q^{51} +(-4.89898 - 4.89898i) q^{52} +(43.0000 - 43.0000i) q^{53} +(-33.0681 + 33.0681i) q^{54} +(25.0000 - 48.9898i) q^{55} -60.0000i q^{56} +58.7878 q^{57} +(-60.0000 - 60.0000i) q^{58} +38.0000 q^{59} -15.0000 q^{60} +48.9898i q^{61} +(58.7878 - 58.7878i) q^{62} +(44.0908 + 44.0908i) q^{63} +71.0000i q^{64} +(-24.4949 - 24.4949i) q^{65} +(54.3712 - 17.6288i) q^{66} +(-13.0000 + 13.0000i) q^{67} +(4.89898 + 4.89898i) q^{68} +(-21.0000 + 21.0000i) q^{69} -60.0000i q^{70} +(-55.1135 - 55.1135i) q^{72} +(93.0806 - 93.0806i) q^{73} +90.6311i q^{74} -75.0000 q^{75} +19.5959i q^{76} +(-23.5051 - 72.4949i) q^{77} -36.0000i q^{78} -29.3939 q^{79} +55.0000i q^{80} +81.0000 q^{81} +(-36.0000 + 36.0000i) q^{82} +(-102.879 - 102.879i) q^{83} +(-14.6969 + 14.6969i) q^{84} +(24.4949 + 24.4949i) q^{85} +108.000i q^{86} +146.969i q^{87} +(29.3814 + 90.6186i) q^{88} +48.0000 q^{89} +(-55.1135 - 55.1135i) q^{90} -48.0000 q^{91} +(-7.00000 - 7.00000i) q^{92} -144.000 q^{93} -41.6413 q^{94} +97.9796i q^{95} +(33.0681 - 33.0681i) q^{96} +(47.0000 - 47.0000i) q^{97} +(1.22474 + 1.22474i) q^{98} +(-88.1816 - 45.0000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 12 q^{3} + 36 q^{9} - 48 q^{14} + 44 q^{16} - 20 q^{20} + 48 q^{22} - 28 q^{23} - 100 q^{25} + 108 q^{27} - 192 q^{31} + 148 q^{37} - 96 q^{38} - 144 q^{42} + 20 q^{44} + 68 q^{47} + 132 q^{48} + 172 q^{53}+ \cdots + 188 q^{97}+O(q^{100}) \) 4 * q + 12 * q^3 + 36 * q^9 - 48 * q^14 + 44 * q^16 - 20 * q^20 + 48 * q^22 - 28 * q^23 - 100 * q^25 + 108 * q^27 - 192 * q^31 + 148 * q^37 - 96 * q^38 - 144 * q^42 + 20 * q^44 + 68 * q^47 + 132 * q^48 + 172 * q^53 + 100 * q^55 - 240 * q^58 + 152 * q^59 - 60 * q^60 + 144 * q^66 - 52 * q^67 - 84 * q^69 - 300 * q^75 - 192 * q^77 + 324 * q^81 - 144 * q^82 + 240 * q^88 + 192 * q^89 - 192 * q^91 - 28 * q^92 - 576 * q^93 + 188 * q^97

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