LMFDB - Embedded newform 120.3.g.a.91.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [120,3,Mod(91,120)] 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("120.91"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	120.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.26976317232$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + x^{14} + 24 x^{13} - 44 x^{12} - 32 x^{11} + 180 x^{10} - 64 x^{9} - 352 x^{8} + \cdots + 65536 $ x^16 - 4x^15 + x^14 + 24x^13 - 44x^12 - 32x^11 + 180x^10 - 64x^9 - 352x^8 - 256x^7 + 2880x^6 - 2048x^5 - 11264x^4 + 24576x^3 + 4096x^2 - 65536x + 65536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{15} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.6
Root			$1.56126 - 1.24999i$ of defining polynomial
Character	$\chi$	$=$	120.91
Dual form			120.3.g.a.91.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.56126 + 1.24999i) q^{2} -1.73205 q^{3} +(0.875058 - 3.90311i) q^{4} +2.23607i q^{5} +(2.70418 - 2.16504i) q^{6} -7.58970i q^{7} +(3.51265 + 7.18758i) q^{8} +3.00000 q^{9} +(-2.79506 - 3.49108i) q^{10} +16.7055 q^{11} +(-1.51564 + 6.76039i) q^{12} +10.7512i q^{13} +(9.48703 + 11.8495i) q^{14} -3.87298i q^{15} +(-14.4685 - 6.83090i) q^{16} +8.61276 q^{17} +(-4.68378 + 3.74997i) q^{18} +35.6616 q^{19} +(8.72762 + 1.95669i) q^{20} +13.1457i q^{21} +(-26.0816 + 20.8817i) q^{22} +11.2913i q^{23} +(-6.08409 - 12.4493i) q^{24} -5.00000 q^{25} +(-13.4388 - 16.7854i) q^{26} -5.19615 q^{27} +(-29.6234 - 6.64142i) q^{28} -0.589229i q^{29} +(4.84118 + 6.04673i) q^{30} -45.0411i q^{31} +(31.1277 - 7.42072i) q^{32} -28.9347 q^{33} +(-13.4467 + 10.7658i) q^{34} +16.9711 q^{35} +(2.62517 - 11.7093i) q^{36} -36.6203i q^{37} +(-55.6770 + 44.5766i) q^{38} -18.6216i q^{39} +(-16.0719 + 7.85453i) q^{40} -2.44967 q^{41} +(-16.4320 - 20.5239i) q^{42} -7.91524 q^{43} +(14.6183 - 65.2033i) q^{44} +6.70820i q^{45} +(-14.1140 - 17.6286i) q^{46} -44.3755i q^{47} +(25.0603 + 11.8315i) q^{48} -8.60348 q^{49} +(7.80629 - 6.24994i) q^{50} -14.9177 q^{51} +(41.9630 + 9.40790i) q^{52} +73.3176i q^{53} +(8.11254 - 6.49513i) q^{54} +37.3546i q^{55} +(54.5515 - 26.6600i) q^{56} -61.7677 q^{57} +(0.736530 + 0.919939i) q^{58} -89.7651 q^{59} +(-15.1167 - 3.38908i) q^{60} +98.7987i q^{61} +(56.3009 + 70.3209i) q^{62} -22.7691i q^{63} +(-39.3226 + 50.4949i) q^{64} -24.0404 q^{65} +(45.1746 - 36.1681i) q^{66} +89.5013 q^{67} +(7.53666 - 33.6165i) q^{68} -19.5571i q^{69} +(-26.4962 + 21.2136i) q^{70} +90.0121i q^{71} +(10.5380 + 21.5627i) q^{72} +68.0795 q^{73} +(45.7750 + 57.1738i) q^{74} +8.66025 q^{75} +(31.2060 - 139.191i) q^{76} -126.790i q^{77} +(23.2768 + 29.0731i) q^{78} -36.2647i q^{79} +(15.2743 - 32.3527i) q^{80} +9.00000 q^{81} +(3.82457 - 3.06206i) q^{82} -95.5904 q^{83} +(51.3093 + 11.5033i) q^{84} +19.2587i q^{85} +(12.3577 - 9.89396i) q^{86} +1.02058i q^{87} +(58.6805 + 120.072i) q^{88} -7.89970 q^{89} +(-8.38518 - 10.4732i) q^{90} +81.5982 q^{91} +(44.0711 + 9.88052i) q^{92} +78.0135i q^{93} +(55.4689 + 69.2817i) q^{94} +79.7418i q^{95} +(-53.9147 + 12.8531i) q^{96} -137.133 q^{97} +(13.4323 - 10.7543i) q^{98} +50.1164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 14 q^{4} + 6 q^{6} + 20 q^{8} + 48 q^{9} + 10 q^{10} + 64 q^{11} - 20 q^{14} - 14 q^{16} - 12 q^{18} - 32 q^{19} - 40 q^{20} + 28 q^{22} - 54 q^{24} - 80 q^{25} + 36 q^{26} - 28 q^{28}+ \cdots + 192 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 14 * q^4 + 6 * q^6 + 20 * q^8 + 48 * q^9 + 10 * q^10 + 64 * q^11 - 20 * q^14 - 14 * q^16 - 12 * q^18 - 32 * q^19 - 40 * q^20 + 28 * q^22 - 54 * q^24 - 80 * q^25 + 36 * q^26 - 28 * q^28 + 36 * q^32 - 72 * q^34 + 42 * q^36 - 240 * q^38 + 10 * q^40 - 108 * q^42 - 192 * q^43 - 100 * q^44 + 212 * q^46 - 48 * q^48 - 80 * q^49 + 20 * q^50 + 96 * q^51 + 232 * q^52 + 18 * q^54 - 116 * q^56 + 96 * q^57 + 140 * q^58 + 128 * q^59 - 30 * q^60 + 104 * q^62 + 14 * q^64 - 180 * q^66 - 64 * q^67 - 576 * q^68 - 180 * q^70 + 60 * q^72 - 160 * q^73 + 300 * q^74 + 420 * q^76 - 120 * q^78 + 80 * q^80 + 144 * q^81 + 160 * q^82 + 180 * q^84 + 312 * q^86 + 604 * q^88 + 30 * q^90 - 192 * q^91 + 216 * q^92 + 460 * q^94 - 186 * q^96 - 224 * q^97 + 428 * q^98 + 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.56126	+	1.24999i	−0.780629	+	0.624994i
$2$	−1.56126	+	1.24999i	−0.780629	+	0.624994i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	0.875058	−	3.90311i	0.218764	−	0.975778i
$5$			2.23607i			0.447214i
$5$			2.23607i			0.447214i
$6$	2.70418	−	2.16504i	0.450697	−	0.360841i
$7$		−	7.58970i		−	1.08424i	−0.840300	−	0.542121i	$-0.817621\pi$
$7$		−	7.58970i		−	1.08424i	0.840300	−	0.542121i	$-0.182379\pi$
$8$	3.51265	+	7.18758i	0.439081	+	0.898447i
$9$	3.00000			0.333333
$10$	−2.79506	−	3.49108i	−0.279506	−	0.349108i
$11$	16.7055			1.51868			0.759340	−	0.650694i	$-0.225522\pi$
$11$	16.7055			1.51868			0.759340	+	0.650694i	$0.225522\pi$
$12$	−1.51564	+	6.76039i	−0.126304	+	0.563366i
$13$			10.7512i			0.827014i	0.910501	+	0.413507i	$0.135696\pi$
$13$			10.7512i			0.827014i	−0.910501	+	0.413507i	$0.864304\pi$
$14$	9.48703	+	11.8495i	0.677645	+	0.846391i
$15$		−	3.87298i		−	0.258199i
$16$	−14.4685	−	6.83090i	−0.904284	−	0.426931i
$17$	8.61276			0.506633			0.253316	−	0.967383i	$-0.418479\pi$
$17$	8.61276			0.506633			0.253316	+	0.967383i	$0.418479\pi$
$18$	−4.68378	+	3.74997i	−0.260210	+	0.208331i
$19$	35.6616			1.87693			0.938464	−	0.345378i	$-0.112249\pi$
$19$	35.6616			1.87693			0.938464	+	0.345378i	$0.112249\pi$
$20$	8.72762	+	1.95669i	0.436381	+	0.0978344i
$21$			13.1457i			0.625988i
$22$	−26.0816	+	20.8817i	−1.18553	+	0.949166i
$23$			11.2913i			0.490925i	0.969406	+	0.245462i	$0.0789398\pi$
$23$			11.2913i			0.490925i	−0.969406	+	0.245462i	$0.921060\pi$
$24$	−6.08409	−	12.4493i	−0.253504	−	0.518719i
$25$	−5.00000			−0.200000
$26$	−13.4388	−	16.7854i	−0.516879	−	0.645591i
$27$	−5.19615			−0.192450
$28$	−29.6234	−	6.64142i	−1.05798	−	0.237194i
$29$		−	0.589229i		−	0.0203183i	−0.999948	−	0.0101591i	$-0.996766\pi$
$29$		−	0.589229i		−	0.0203183i	0.999948	−	0.0101591i	$-0.00323381\pi$
$30$	4.84118	+	6.04673i	0.161373	+	0.201558i
$31$		−	45.0411i		−	1.45294i	−0.687198	−	0.726470i	$-0.741160\pi$
$31$		−	45.0411i		−	1.45294i	0.687198	−	0.726470i	$-0.258840\pi$
$32$	31.1277	−	7.42072i	0.972740	−	0.231898i
$33$	−28.9347			−0.876810
$34$	−13.4467	+	10.7658i	−0.395492	+	0.316643i
$35$	16.9711			0.484888
$36$	2.62517	−	11.7093i	0.0729215	−	0.325259i
$37$		−	36.6203i		−	0.989738i	−0.868968	−	0.494869i	$-0.835216\pi$
$37$		−	36.6203i		−	0.989738i	0.868968	−	0.494869i	$-0.164784\pi$
$38$	−55.6770	+	44.5766i	−1.46518	+	1.17307i
$39$		−	18.6216i		−	0.477477i
$40$	−16.0719	+	7.85453i	−0.401798	+	0.196363i
$41$	−2.44967			−0.0597481			−0.0298740	−	0.999554i	$-0.509511\pi$
$41$	−2.44967			−0.0597481			−0.0298740	+	0.999554i	$0.509511\pi$
$42$	−16.4320	−	20.5239i	−0.391239	−	0.488664i
$43$	−7.91524			−0.184075			−0.0920377	−	0.995756i	$-0.529338\pi$
$43$	−7.91524			−0.184075			−0.0920377	+	0.995756i	$0.529338\pi$
$44$	14.6183	−	65.2033i	0.332233	−	1.48189i
$45$			6.70820i			0.149071i
$46$	−14.1140	−	17.6286i	−0.306825	−	0.383230i
$47$		−	44.3755i		−	0.944160i	−0.881556	−	0.472080i	$-0.843503\pi$
$47$		−	44.3755i		−	0.944160i	0.881556	−	0.472080i	$-0.156497\pi$
$48$	25.0603	+	11.8315i	0.522089	+	0.246489i
$49$	−8.60348			−0.175581
$50$	7.80629	−	6.24994i	0.156126	−	0.124999i
$51$	−14.9177			−0.292505
$52$	41.9630	+	9.40790i	0.806982	+	0.180921i
$53$			73.3176i			1.38335i	0.722209	+	0.691675i	$0.243127\pi$
$53$			73.3176i			1.38335i	−0.722209	+	0.691675i	$0.756873\pi$
$54$	8.11254	−	6.49513i	0.150232	−	0.120280i
$55$			37.3546i			0.679174i
$56$	54.5515	−	26.6600i	0.974134	−	0.476071i
$57$	−61.7677			−1.08364
$58$	0.736530	+	0.919939i	0.0126988	+	0.0158610i
$59$	−89.7651			−1.52144			−0.760721	−	0.649079i	$-0.775155\pi$
$59$	−89.7651			−1.52144			−0.760721	+	0.649079i	$0.775155\pi$
$60$	−15.1167	−	3.38908i	−0.251945	−	0.0564847i
$61$			98.7987i			1.61965i	0.586671	+	0.809826i	$0.300438\pi$
$61$			98.7987i			1.61965i	−0.586671	+	0.809826i	$0.699562\pi$
$62$	56.3009	+	70.3209i	0.908079	+	1.13421i
$63$		−	22.7691i		−	0.361414i
$64$	−39.3226	+	50.4949i	−0.614415	+	0.788983i
$65$	−24.0404			−0.369852
$66$	45.1746	−	36.1681i	0.684464	−	0.548001i
$67$	89.5013			1.33584			0.667920	−	0.744233i	$-0.267185\pi$
$67$	89.5013			1.33584			0.667920	+	0.744233i	$0.267185\pi$
$68$	7.53666	−	33.6165i	0.110833	−	0.494361i
$69$		−	19.5571i		−	0.283436i
$70$	−26.4962	+	21.2136i	−0.378518	+	0.303052i
$71$			90.0121i			1.26778i	0.773425	+	0.633888i	$0.218542\pi$
$71$			90.0121i			1.26778i	−0.773425	+	0.633888i	$0.781458\pi$
$72$	10.5380	+	21.5627i	0.146360	+	0.299482i
$73$	68.0795			0.932596			0.466298	−	0.884628i	$-0.345588\pi$
$73$	68.0795			0.932596			0.466298	+	0.884628i	$0.345588\pi$
$74$	45.7750	+	57.1738i	0.618580	+	0.772618i
$75$	8.66025			0.115470
$76$	31.2060	−	139.191i	0.410605	−	1.83146i
$77$		−	126.790i		−	1.64662i
$78$	23.2768	+	29.0731i	0.298420	+	0.372732i
$79$		−	36.2647i		−	0.459046i	−0.973303	−	0.229523i	$-0.926283\pi$
$79$		−	36.2647i		−	0.459046i	0.973303	−	0.229523i	$-0.0737167\pi$
$80$	15.2743	−	32.3527i	0.190929	−	0.404408i
$81$	9.00000			0.111111
$82$	3.82457	−	3.06206i	0.0466411	−	0.0373422i
$83$	−95.5904			−1.15169			−0.575846	−	0.817558i	$-0.695327\pi$
$83$	−95.5904			−1.15169			−0.575846	+	0.817558i	$0.695327\pi$
$84$	51.3093	+	11.5033i	0.610825	+	0.136944i
$85$			19.2587i			0.226573i
$86$	12.3577	−	9.89396i	0.143695	−	0.115046i
$87$			1.02058i			0.0117307i
$88$	58.6805	+	120.072i	0.666824	+	1.36445i
$89$	−7.89970			−0.0887607			−0.0443803	−	0.999015i	$-0.514131\pi$
$89$	−7.89970			−0.0887607			−0.0443803	+	0.999015i	$0.514131\pi$
$90$	−8.38518	−	10.4732i	−0.0931686	−	0.116369i
$91$	81.5982			0.896683
$92$	44.0711	+	9.88052i	0.479034	+	0.107397i
$93$			78.0135i			0.838855i
$94$	55.4689	+	69.2817i	0.590095	+	0.737039i
$95$			79.7418i			0.839387i
$96$	−53.9147	+	12.8531i	−0.561612	+	0.133886i
$97$	−137.133			−1.41375			−0.706873	−	0.707341i	$-0.749895\pi$
$97$	−137.133			−1.41375			−0.706873	+	0.707341i	$0.749895\pi$
$98$	13.4323	−	10.7543i	0.137064	−	0.109737i
$99$	50.1164			0.506227
$100$	−4.37529	+	19.5156i	−0.0437529	+	0.195156i
$101$		−	92.4295i		−	0.915144i	−0.889173	−	0.457572i	$-0.848719\pi$
$101$		−	92.4295i		−	0.915144i	0.889173	−	0.457572i	$-0.151281\pi$
$102$	23.2904	−	18.6470i	0.228338	−	0.182814i
$103$		−	123.314i		−	1.19722i	−0.801040	−	0.598610i	$-0.795720\pi$
$103$		−	123.314i		−	1.19722i	0.801040	−	0.598610i	$-0.204280\pi$
$104$	−77.2749	+	37.7651i	−0.743028	+	0.363126i
$105$	−29.3948			−0.279950
$106$	−91.6461	−	114.468i	−0.864586	−	1.07988i
$107$	−0.240104			−0.00224396			−0.00112198	−	0.999999i	$-0.500357\pi$
$107$	−0.240104			−0.00224396			−0.00112198	+	0.999999i	$0.500357\pi$
$108$	−4.54693	+	20.2812i	−0.0421012	+	0.187789i
$109$			117.597i			1.07887i	0.842028	+	0.539435i	$0.181362\pi$
$109$			117.597i			1.07887i	−0.842028	+	0.539435i	$0.818638\pi$
$110$	−46.6928	−	58.3202i	−0.424480	−	0.530183i
$111$			63.4282i			0.571425i
$112$	−51.8444	+	109.812i	−0.462897	+	0.980463i
$113$	41.1728			0.364361			0.182180	−	0.983265i	$-0.441685\pi$
$113$	41.1728			0.364361			0.182180	+	0.983265i	$0.441685\pi$
$114$	96.4354	−	77.2090i	0.845925	−	0.677272i
$115$	−25.2481			−0.219548
$116$	−2.29983	−	0.515610i	−0.0198261	−	0.00444491i
$117$			32.2535i			0.275671i
$118$	140.147	−	112.205i	1.18768	−	0.950893i
$119$		−	65.3682i		−	0.549313i
$120$	27.8374	−	13.6044i	0.231978	−	0.113370i
$121$	158.073			1.30639
$122$	−123.497	−	154.250i	−1.01227	−	1.26435i
$123$	4.24295			0.0344956
$124$	−175.800	−	39.4136i	−1.41775	−	0.317852i
$125$		−	11.1803i		−	0.0894427i
$126$	28.4611	+	35.5484i	0.225882	+	0.282130i
$127$		−	1.15264i		−	0.00907591i	−0.999990	−	0.00453795i	$-0.998556\pi$
$127$		−	1.15264i		−	0.00907591i	0.999990	−	0.00453795i	$-0.00144448\pi$
$128$	−1.72536	−	127.988i	−0.0134794	−	0.999909i
$129$	13.7096			0.106276
$130$	37.5332	−	30.0502i	0.288717	−	0.231155i
$131$	−191.878			−1.46472			−0.732359	−	0.680919i	$-0.761581\pi$
$131$	−191.878			−1.46472			−0.732359	+	0.680919i	$0.761581\pi$
$132$	−25.3196	+	112.935i	−0.191815	+	0.855572i
$133$		−	270.661i		−	2.03504i
$134$	−139.735	+	111.876i	−1.04280	+	0.834892i
$135$		−	11.6190i		−	0.0860663i
$136$	30.2536	+	61.9049i	0.222453	+	0.455183i
$137$	17.0127			0.124180			0.0620901	−	0.998071i	$-0.480223\pi$
$137$	17.0127			0.124180			0.0620901	+	0.998071i	$0.480223\pi$
$138$	24.4461	+	30.5336i	0.177146	+	0.221258i
$139$	−176.378			−1.26890			−0.634452	−	0.772963i	$-0.718774\pi$
$139$	−176.378			−1.26890			−0.634452	+	0.772963i	$0.718774\pi$
$140$	14.8507	−	66.2400i	0.106076	−	0.473143i
$141$			76.8607i			0.545111i
$142$	−112.514	−	140.532i	−0.792353	−	0.989663i
$143$			179.604i			1.25597i
$144$	−43.4056	−	20.4927i	−0.301428	−	0.142310i
$145$	1.31756			0.00908660
$146$	−106.290	+	85.0986i	−0.728011	+	0.582867i
$147$	14.9017			0.101372
$148$	−142.933	−	32.0449i	−0.965764	−	0.216519i
$149$		−	212.046i		−	1.42313i	−0.702620	−	0.711565i	$-0.747987\pi$
$149$		−	212.046i		−	1.42313i	0.702620	−	0.711565i	$-0.252013\pi$
$150$	−13.5209	+	10.8252i	−0.0901393	+	0.0721681i
$151$			143.361i			0.949408i	0.880146	+	0.474704i	$0.157445\pi$
$151$			143.361i			0.949408i	−0.880146	+	0.474704i	$0.842555\pi$
$152$	125.267	+	256.321i	0.824124	+	1.68632i
$153$	25.8383			0.168878
$154$	158.485	+	197.951i	1.02913	+	1.28540i
$155$	100.715			0.649774
$156$	−72.6821	−	16.2950i	−0.465911	−	0.104455i
$157$		−	82.2710i		−	0.524019i	−0.965065	−	0.262009i	$-0.915615\pi$
$157$		−	82.2710i		−	0.524019i	0.965065	−	0.262009i	$-0.0843852\pi$
$158$	45.3304	+	56.6185i	0.286901	+	0.358345i
$159$		−	126.990i		−	0.798678i
$160$	16.5932	+	69.6036i	0.103708	+	0.435023i
$161$	85.6973			0.532282
$162$	−14.0513	+	11.2499i	−0.0867366	+	0.0694438i
$163$	27.8115			0.170623			0.0853113	−	0.996354i	$-0.472812\pi$
$163$	27.8115			0.170623			0.0853113	+	0.996354i	$0.472812\pi$
$164$	−2.14360	+	9.56134i	−0.0130708	+	0.0583008i
$165$		−	64.7000i		−	0.392121i
$166$	149.241	−	119.487i	0.899044	−	0.719800i
$167$			207.819i			1.24443i	0.782848	+	0.622214i	$0.213766\pi$
$167$			207.819i			1.24443i	−0.782848	+	0.622214i	$0.786234\pi$
$168$	−94.4860	+	46.1764i	−0.562417	+	0.274860i
$169$	53.4122			0.316048
$170$	−24.0732	−	30.0678i	−0.141607	−	0.176870i
$171$	106.985			0.625642
$172$	−6.92629	+	30.8941i	−0.0402692	+	0.179617i
$173$			45.7625i			0.264523i	0.991215	+	0.132262i	$0.0422239\pi$
$173$			45.7625i			0.264523i	−0.991215	+	0.132262i	$0.957776\pi$
$174$	−1.27571	−	1.59338i	−0.00733165	−	0.00915737i
$175$			37.9485i			0.216848i
$176$	−241.704	−	114.113i	−1.37332	−	0.648372i
$177$	155.478			0.878405
$178$	12.3335	−	9.87453i	0.0692892	−	0.0554749i
$179$	−33.0983			−0.184907			−0.0924533	−	0.995717i	$-0.529471\pi$
$179$	−33.0983			−0.184907			−0.0924533	+	0.995717i	$0.529471\pi$
$180$	26.1829	+	5.87007i	0.145460	+	0.0326115i
$181$			177.147i			0.978711i	0.872084	+	0.489356i	$0.162768\pi$
$181$			177.147i			0.978711i	−0.872084	+	0.489356i	$0.837232\pi$
$182$	−127.396	+	101.997i	−0.699977	+	0.560422i
$183$		−	171.124i		−	0.935106i
$184$	−81.1569	+	39.6623i	−0.441070	+	0.215556i
$185$	81.8855			0.442624
$186$	−97.5160	−	121.799i	−0.524280	−	0.654835i
$187$	143.880			0.769413
$188$	−173.203	−	38.8312i	−0.921291	−	0.206549i
$189$			39.4372i			0.208663i
$190$	−99.6763	−	124.498i	−0.524612	−	0.655250i
$191$			28.8000i			0.150785i	0.997154	+	0.0753927i	$0.0240210\pi$
$191$			28.8000i			0.150785i	−0.997154	+	0.0753927i	$0.975979\pi$
$192$	68.1087	−	87.4598i	0.354733	−	0.455520i
$193$	87.7961			0.454902			0.227451	−	0.973789i	$-0.426961\pi$
$193$	87.7961			0.454902			0.227451	+	0.973789i	$0.426961\pi$
$194$	214.101	−	171.415i	1.10361	−	0.883583i
$195$	41.6391			0.213534
$196$	−7.52855	+	33.5803i	−0.0384109	+	0.171328i
$197$		−	347.625i		−	1.76459i	−0.470696	−	0.882296i	$-0.655997\pi$
$197$		−	347.625i		−	1.76459i	0.470696	−	0.882296i	$-0.344003\pi$
$198$	−78.2447	+	62.6450i	−0.395175	+	0.316389i
$199$			129.347i			0.649985i	0.945717	+	0.324992i	$0.105362\pi$
$199$			129.347i			0.649985i	−0.945717	+	0.324992i	$0.894638\pi$
$200$	−17.5633	−	35.9379i	−0.0878163	−	0.179689i
$201$	−155.021			−0.771247
$202$	115.536	+	144.306i	0.571960	+	0.714388i
$203$	−4.47207			−0.0220299
$204$	−13.0539	+	58.2256i	−0.0639896	+	0.285419i
$205$		−	5.47763i		−	0.0267202i
$206$	154.141	+	192.525i	0.748256	+	0.934586i
$207$			33.8738i			0.163642i
$208$	73.4402	−	155.554i	0.353078	−	0.747855i
$209$	595.744			2.85045
$210$	45.8928	−	36.7431i	0.218537	−	0.174967i
$211$	−190.507			−0.902877			−0.451439	−	0.892302i	$-0.649089\pi$
$211$	−190.507			−0.902877			−0.451439	+	0.892302i	$0.649089\pi$
$212$	286.167	+	64.1571i	1.34984	+	0.302628i
$213$		−	155.905i		−	0.731951i
$214$	0.374864	−	0.300127i	0.00175170	−	0.00140246i
$215$		−	17.6990i		−	0.0823210i
$216$	−18.2523	−	37.3478i	−0.0845013	−	0.172906i
$217$	−341.848			−1.57534
$218$	−146.995	−	183.599i	−0.674287	−	0.842197i
$219$	−117.917			−0.538434
$220$	145.799	+	32.6874i	0.662723	+	0.148579i
$221$			92.5973i			0.418992i
$222$	−79.2845	−	99.0279i	−0.357138	−	0.446071i
$223$		−	211.437i		−	0.948149i	−0.880485	−	0.474075i	$-0.842783\pi$
$223$		−	211.437i		−	0.948149i	0.880485	−	0.474075i	$-0.157217\pi$
$224$	−56.3210	−	236.250i	−0.251433	−	1.05469i
$225$	−15.0000			−0.0666667
$226$	−64.2813	+	51.4655i	−0.284431	+	0.227723i
$227$	88.8880			0.391577			0.195788	−	0.980646i	$-0.437273\pi$
$227$	88.8880			0.391577			0.195788	+	0.980646i	$0.437273\pi$
$228$	−54.0503	+	241.086i	−0.237063	+	1.05740i
$229$			152.872i			0.667565i	0.942650	+	0.333782i	$0.108325\pi$
$229$			152.872i			0.667565i	−0.942650	+	0.333782i	$0.891675\pi$
$230$	39.4187	−	31.5598i	0.171386	−	0.137216i
$231$			219.606i			0.950675i
$232$	4.23513	−	2.06976i	0.0182549	−	0.00892137i
$233$	188.417			0.808656			0.404328	−	0.914614i	$-0.367505\pi$
$233$	188.417			0.808656			0.404328	+	0.914614i	$0.367505\pi$
$234$	−40.3165	−	50.3561i	−0.172293	−	0.215197i
$235$	99.2267			0.422241
$236$	−78.5497	+	350.363i	−0.332838	+	1.48459i
$237$			62.8122i			0.265030i
$238$	81.7095	+	102.057i	0.343317	+	0.428810i
$239$		−	227.979i		−	0.953888i	−0.878934	−	0.476944i	$-0.841745\pi$
$239$		−	227.979i		−	0.953888i	0.878934	−	0.476944i	$-0.158255\pi$
$240$	−26.4559	+	56.0364i	−0.110233	+	0.233485i
$241$	−265.794			−1.10288			−0.551439	−	0.834215i	$-0.685921\pi$
$241$	−265.794			−1.10288			−0.551439	+	0.834215i	$0.685921\pi$
$242$	−246.793	+	197.590i	−1.01981	+	0.816486i
$243$	−15.5885			−0.0641500
$244$	385.622	+	86.4546i	1.58042	+	0.354322i
$245$		−	19.2380i		−	0.0785223i
$246$	−6.62435	+	5.30364i	−0.0269283	+	0.0215595i
$247$			383.404i			1.55224i
$248$	323.737	−	158.214i	1.30539	−	0.637959i
$249$	165.567			0.664929
$250$	13.9753	+	17.4554i	0.0559012	+	0.0698216i
$251$	154.894			0.617106			0.308553	−	0.951207i	$-0.400155\pi$
$251$	154.894			0.617106			0.308553	+	0.951207i	$0.400155\pi$
$252$	−88.8703	−	19.9243i	−0.352660	−	0.0790646i
$253$			188.626i			0.745558i
$254$	1.44079	+	1.79957i	0.00567239	+	0.00708492i
$255$		−	33.3571i		−	0.130812i
$256$	162.678	+	197.666i	0.635460	+	0.772134i
$257$	−422.025			−1.64212			−0.821060	−	0.570842i	$-0.806617\pi$
$257$	−422.025			−1.64212			−0.821060	+	0.570842i	$0.806617\pi$
$258$	−21.4042	+	17.1368i	−0.0829621	+	0.0664219i
$259$	−277.937			−1.07312
$260$	−21.0367	+	93.8322i	−0.0809104	+	0.360893i
$261$		−	1.76769i		−	0.00677275i
$262$	299.571	−	239.845i	1.14340	−	0.915440i
$263$			118.083i			0.448983i	0.974476	+	0.224492i	$0.0720721\pi$
$263$			118.083i			0.448983i	−0.974476	+	0.224492i	$0.927928\pi$
$264$	−101.638	−	207.971i	−0.384991	−	0.787768i
$265$	−163.943			−0.618653
$266$	338.323	+	422.572i	1.27189	+	1.58862i
$267$	13.6827			0.0512460
$268$	78.3188	−	349.333i	0.292234	−	1.30348i
$269$			493.643i			1.83510i	0.397617	+	0.917551i	$0.369837\pi$
$269$			493.643i			1.83510i	−0.397617	+	0.917551i	$0.630163\pi$
$270$	14.5236	+	18.1402i	0.0537909	+	0.0671859i
$271$		−	362.955i		−	1.33932i	−0.742669	−	0.669659i	$-0.766440\pi$
$271$		−	362.955i		−	1.33932i	0.742669	−	0.669659i	$-0.233560\pi$
$272$	−124.614	−	58.8329i	−0.458140	−	0.216297i
$273$	−141.332			−0.517700
$274$	−26.5612	+	21.2657i	−0.0969387	+	0.0776119i
$275$	−83.5274			−0.303736
$276$	−76.3334	−	17.1136i	−0.276570	−	0.0620056i
$277$		−	321.011i		−	1.15888i	−0.815013	−	0.579442i	$-0.803270\pi$
$277$		−	321.011i		−	1.15888i	0.815013	−	0.579442i	$-0.196730\pi$
$278$	275.371	−	220.470i	0.990543	−	0.793057i
$279$		−	135.123i		−	0.484313i
$280$	59.6135	+	121.981i	0.212905	+	0.435646i
$281$	−185.799			−0.661206			−0.330603	−	0.943770i	$-0.607252\pi$
$281$	−185.799			−0.661206			−0.330603	+	0.943770i	$0.607252\pi$
$282$	−96.0750	−	119.999i	−0.340691	−	0.425530i
$283$	−208.628			−0.737202			−0.368601	−	0.929588i	$-0.620163\pi$
$283$	−208.628			−0.737202			−0.368601	+	0.929588i	$0.620163\pi$
$284$	351.327	+	78.7658i	1.23707	+	0.277344i
$285$		−	138.117i		−	0.484621i
$286$	−224.502	−	280.408i	−0.784974	−	0.980447i
$287$			18.5923i			0.0647814i
$288$	93.3831	−	22.2622i	0.324247	−	0.0772992i
$289$	−214.820			−0.743323
$290$	−2.05705	+	1.64693i	−0.00709327	+	0.00567907i
$291$	237.522			0.816226
$292$	59.5735	−	265.722i	0.204019	−	0.910006i
$293$			306.925i			1.04752i	0.851864	+	0.523762i	$0.175472\pi$
$293$			306.925i			1.04752i	−0.851864	+	0.523762i	$0.824528\pi$
$294$	−23.2654	+	18.6269i	−0.0791339	+	0.0633568i
$295$		−	200.721i		−	0.680410i
$296$	263.211	−	128.634i	0.889227	−	0.434576i
$297$	−86.8042			−0.292270
$298$	265.055	+	331.059i	0.889448	+	1.11094i
$299$	−121.394			−0.406002
$300$	7.57822	−	33.8019i	0.0252607	−	0.112673i
$301$			60.0743i			0.199582i
$302$	−179.199	−	223.823i	−0.593374	−	0.741136i
$303$			160.093i			0.528358i
$304$	−515.972	−	243.601i	−1.69728	−	0.801318i
$305$	−220.921			−0.724330
$306$	−40.3402	+	32.2975i	−0.131831	+	0.105548i
$307$	283.517			0.923510			0.461755	−	0.887008i	$-0.347220\pi$
$307$	283.517			0.923510			0.461755	+	0.887008i	$0.347220\pi$
$308$	−494.874	−	110.948i	−1.60673	−	0.360221i
$309$			213.586i			0.691216i
$310$	−157.242	+	125.893i	−0.507233	+	0.406105i
$311$		−	614.016i		−	1.97433i	−0.159709	−	0.987164i	$-0.551056\pi$
$311$		−	614.016i		−	1.97433i	0.159709	−	0.987164i	$-0.448944\pi$
$312$	133.844	−	65.4111i	0.428988	−	0.209651i
$313$	−511.920			−1.63553			−0.817763	−	0.575555i	$-0.804786\pi$
$313$	−511.920			−1.63553			−0.817763	+	0.575555i	$0.804786\pi$
$314$	102.838	+	128.446i	0.327509	+	0.409065i
$315$	50.9132			0.161629
$316$	−141.545	−	31.7337i	−0.447927	−	0.100423i
$317$			429.605i			1.35522i	0.735421	+	0.677611i	$0.236985\pi$
$317$			429.605i			1.35522i	−0.735421	+	0.677611i	$0.763015\pi$
$318$	158.736	+	198.264i	0.499169	+	0.623471i
$319$		−	9.84336i		−	0.0308569i
$320$	−112.910	−	87.9279i	−0.352844	−	0.274775i
$321$	0.415872			0.00129555
$322$	−133.796	+	107.121i	−0.415515	+	0.332673i
$323$	307.145			0.950913
$324$	7.87552	−	35.1280i	0.0243072	−	0.108420i
$325$		−	53.7559i		−	0.165403i
$326$	−43.4209	+	34.7640i	−0.133193	+	0.106638i
$327$		−	203.684i		−	0.622885i
$328$	−8.60484	−	17.6072i	−0.0262343	−	0.0536805i
$329$	−336.797			−1.02370
$330$	80.8743	+	101.014i	0.245074	+	0.306102i
$331$	−537.298			−1.62326			−0.811628	−	0.584175i	$-0.801418\pi$
$331$	−537.298			−1.62326			−0.811628	+	0.584175i	$0.801418\pi$
$332$	−83.6471	+	373.100i	−0.251949	+	1.12379i
$333$		−	109.861i		−	0.329913i
$334$	−259.772	−	324.460i	−0.777760	−	0.971436i
$335$			200.131i			0.597406i
$336$	89.7972	−	190.200i	0.267253	−	0.566071i
$337$	158.578			0.470559			0.235279	−	0.971928i	$-0.424400\pi$
$337$	158.578			0.470559			0.235279	+	0.971928i	$0.424400\pi$
$338$	−83.3902	+	66.7646i	−0.246717	+	0.197528i
$339$	−71.3133			−0.210364
$340$	75.1689	+	16.8525i	0.221085	+	0.0495661i
$341$		−	752.434i		−	2.20655i
$342$	−167.031	+	133.730i	−0.488395	+	0.391023i
$343$		−	306.597i		−	0.893870i
$344$	−27.8035	−	56.8914i	−0.0808241	−	0.165382i
$345$	43.7309			0.126756
$346$	−57.2026	−	71.4472i	−0.165326	−	0.206495i
$347$	169.697			0.489041			0.244520	−	0.969644i	$-0.421370\pi$
$347$	169.697			0.489041			0.244520	+	0.969644i	$0.421370\pi$
$348$	3.98342	+	0.893062i	0.0114466	+	0.00256627i
$349$			296.370i			0.849196i	0.905382	+	0.424598i	$0.139585\pi$
$349$			296.370i			0.849196i	−0.905382	+	0.424598i	$0.860415\pi$
$350$	−47.4352	−	59.2474i	−0.135529	−	0.169278i
$351$		−	55.8648i		−	0.159159i
$352$	520.003	−	123.967i	1.47728	−	0.352178i
$353$	133.075			0.376982			0.188491	−	0.982075i	$-0.439640\pi$
$353$	133.075			0.376982			0.188491	+	0.982075i	$0.439640\pi$
$354$	−242.741	+	194.345i	−0.685709	+	0.548998i
$355$	−201.273			−0.566967
$356$	−6.91269	+	30.8334i	−0.0194177	+	0.0866107i
$357$			113.221i			0.317146i
$358$	51.6750	−	41.3725i	0.144344	−	0.115566i
$359$		−	238.095i		−	0.663218i	−0.943417	−	0.331609i	$-0.892409\pi$
$359$		−	238.095i		−	0.663218i	0.943417	−	0.331609i	$-0.107591\pi$
$360$	−48.2157	+	23.5636i	−0.133933	+	0.0654544i
$361$	910.751			2.52286
$362$	−221.431	−	276.572i	−0.611689	−	0.764011i
$363$	−273.791			−0.754244
$364$	71.4031	−	318.487i	0.196162	−	0.874964i
$365$			152.230i			0.417069i
$366$	213.904	+	267.169i	0.584436	+	0.729971i
$367$			381.665i			1.03996i	0.854179	+	0.519979i	$0.174060\pi$
$367$			381.665i			1.03996i	−0.854179	+	0.519979i	$0.825940\pi$
$368$	77.1295	−	163.368i	0.209591	−	0.443936i
$369$	−7.34901			−0.0199160
$370$	−127.844	+	102.356i	−0.345525	+	0.276638i
$371$	556.458			1.49989
$372$	304.495	+	68.2663i	0.818536	+	0.183512i
$373$		−	42.2729i		−	0.113332i	−0.998393	−	0.0566661i	$-0.981953\pi$
$373$		−	42.2729i		−	0.113332i	0.998393	−	0.0566661i	$-0.0180470\pi$
$374$	−224.634	+	179.849i	−0.600626	+	0.480879i
$375$			19.3649i			0.0516398i
$376$	318.953	−	155.876i	0.848278	−	0.414563i
$377$	6.33491			0.0168035
$378$	−49.2961	−	61.5717i	−0.130413	−	0.162888i
$379$	412.302			1.08787			0.543934	−	0.839128i	$-0.316934\pi$
$379$	412.302			1.08787			0.543934	+	0.839128i	$0.316934\pi$
$380$	311.241	+	69.7787i	0.819056	+	0.183628i
$381$			1.99643i			0.00523998i
$382$	−35.9997	−	44.9643i	−0.0942400	−	0.117708i
$383$			403.711i			1.05408i	0.849842	+	0.527038i	$0.176697\pi$
$383$			403.711i			1.05408i	−0.849842	+	0.527038i	$0.823303\pi$
$384$	2.98842	+	221.682i	0.00778234	+	0.577298i
$385$	283.510			0.736390
$386$	−137.072	+	109.744i	−0.355110	+	0.284311i
$387$	−23.7457			−0.0613585
$388$	−120.000	+	535.246i	−0.309277	+	1.37950i
$389$		−	78.5053i		−	0.201813i	−0.994896	−	0.100907i	$-0.967826\pi$
$389$		−	78.5053i		−	0.201813i	0.994896	−	0.100907i	$-0.0321743\pi$
$390$	−65.0095	+	52.0484i	−0.166691	+	0.133458i
$391$			97.2490i			0.248719i
$392$	−30.2210	−	61.8382i	−0.0770945	−	0.157751i
$393$	332.342			0.845655
$394$	434.527	+	542.732i	1.10286	+	1.37749i
$395$	81.0902			0.205292
$396$	43.8548	−	195.610i	0.110744	−	0.493965i
$397$			323.080i			0.813803i	0.913472	+	0.406902i	$0.133391\pi$
$397$			323.080i			0.813803i	−0.913472	+	0.406902i	$0.866609\pi$
$398$	−161.682	−	201.944i	−0.406237	−	0.507397i
$399$			468.798i			1.17493i
$400$	72.3427	+	34.1545i	0.180857	+	0.0853862i
$401$	−621.389			−1.54960			−0.774799	−	0.632207i	$-0.782149\pi$
$401$	−621.389			−1.54960			−0.774799	+	0.632207i	$0.782149\pi$
$402$	242.027	−	193.774i	0.602058	−	0.482025i
$403$	484.245			1.20160
$404$	−360.763	−	80.8812i	−0.892977	−	0.200201i
$405$			20.1246i			0.0496904i
$406$	6.98206	−	5.59004i	0.0171972	−	0.0137686i
$407$		−	611.760i		−	1.50310i
$408$	−52.4008	−	107.222i	−0.128433	−	0.262800i
$409$	322.888			0.789458			0.394729	−	0.918798i	$-0.370839\pi$
$409$	322.888			0.789458			0.394729	+	0.918798i	$0.370839\pi$
$410$	6.84698	+	8.55200i	0.0166999	+	0.0208585i
$411$	−29.4668			−0.0716954
$412$	−481.307	−	107.907i	−1.16822	−	0.261909i
$413$			681.290i			1.64961i
$414$	−42.3419	−	52.8858i	−0.102275	−	0.127743i
$415$		−	213.747i		−	0.515052i
$416$	79.7815	+	334.659i	0.191782	+	0.804470i
$417$	305.495			0.732602
$418$	−930.111	+	744.674i	−2.22515	+	1.78152i
$419$	19.2316			0.0458988			0.0229494	−	0.999737i	$-0.492694\pi$
$419$	19.2316			0.0458988			0.0229494	+	0.999737i	$0.492694\pi$
$420$	−25.7221	+	114.731i	−0.0612431	+	0.273169i
$421$		−	312.791i		−	0.742970i	−0.928439	−	0.371485i	$-0.878849\pi$
$421$		−	312.791i		−	0.742970i	0.928439	−	0.371485i	$-0.121151\pi$
$422$	297.431	−	238.132i	0.704813	−	0.564293i
$423$		−	133.127i		−	0.314720i
$424$	−526.976	+	257.539i	−1.24287	+	0.607404i
$425$	−43.0638			−0.101327
$426$	194.880	+	243.409i	0.457465	+	0.571382i
$427$	749.852			1.75609
$428$	−0.210105	+	0.937151i	−0.000490899	+	0.00218961i
$429$		−	311.083i		−	0.725134i
$430$	22.1236	+	27.6327i	0.0514502	+	0.0642622i
$431$		−	417.415i		−	0.968479i	−0.874935	−	0.484240i	$-0.839096\pi$
$431$		−	417.415i		−	0.968479i	0.874935	−	0.484240i	$-0.160904\pi$
$432$	75.1808	+	35.4944i	0.174030	+	0.0821629i
$433$	279.474			0.645436			0.322718	−	0.946495i	$-0.395404\pi$
$433$	279.474			0.645436			0.322718	+	0.946495i	$0.395404\pi$
$434$	533.714	−	427.307i	1.22976	−	0.984577i
$435$	−2.28208			−0.00524615
$436$	458.993	+	102.904i	1.05274	+	0.236018i
$437$			402.665i			0.921430i
$438$	184.099	−	147.395i	0.420318	−	0.336518i
$439$			30.1336i			0.0686415i	0.999411	+	0.0343207i	$0.0109268\pi$
$439$			30.1336i			0.0686415i	−0.999411	+	0.0343207i	$0.989073\pi$
$440$	−268.489	+	131.214i	−0.610202	+	0.298213i
$441$	−25.8104			−0.0585271
$442$	−115.746	−	144.568i	−0.261868	−	0.327078i
$443$	−56.2858			−0.127056			−0.0635279	−	0.997980i	$-0.520235\pi$
$443$	−56.2858			−0.127056			−0.0635279	+	0.997980i	$0.520235\pi$
$444$	247.567	+	55.5034i	0.557584	+	0.125008i
$445$		−	17.6643i		−	0.0396950i
$446$	264.294	+	330.108i	0.592588	+	0.740153i
$447$			367.275i			0.821644i
$448$	383.241	+	298.446i	0.855449	+	0.666175i
$449$	−283.497			−0.631396			−0.315698	−	0.948860i	$-0.602239\pi$
$449$	−283.497			−0.631396			−0.315698	+	0.948860i	$0.602239\pi$
$450$	23.4189	−	18.7498i	0.0520420	−	0.0416663i
$451$	−40.9229			−0.0907382
$452$	36.0285	−	160.702i	0.0797092	−	0.355535i
$453$		−	248.308i		−	0.548141i
$454$	−138.777	+	111.109i	−0.305676	+	0.244733i
$455$			182.459i			0.401009i
$456$	−216.969	−	443.960i	−0.475808	−	0.973597i
$457$	−265.204			−0.580315			−0.290158	−	0.956979i	$-0.593708\pi$
$457$	−265.204			−0.580315			−0.290158	+	0.956979i	$0.593708\pi$
$458$	−191.089	−	238.673i	−0.417224	−	0.521120i
$459$	−44.7532			−0.0975015
$460$	−22.0935	+	98.5459i	−0.0480294	+	0.214230i
$461$		−	709.643i		−	1.53936i	−0.638432	−	0.769678i	$-0.720417\pi$
$461$		−	709.643i		−	1.53936i	0.638432	−	0.769678i	$-0.279583\pi$
$462$	−274.505	−	342.862i	−0.594166	−	0.742125i
$463$			417.392i			0.901495i	0.892652	+	0.450747i	$0.148843\pi$
$463$			417.392i			0.901495i	−0.892652	+	0.450747i	$0.851157\pi$
$464$	−4.02496	+	8.52529i	−0.00867449	+	0.0183735i
$465$	−174.444			−0.375147
$466$	−294.167	+	235.519i	−0.631260	+	0.505405i
$467$	−679.287			−1.45458			−0.727288	−	0.686332i	$-0.759220\pi$
$467$	−679.287			−1.45458			−0.727288	+	0.686332i	$0.759220\pi$
$468$	125.889	+	28.2237i	0.268994	+	0.0603071i
$469$		−	679.287i		−	1.44837i
$470$	−154.919	+	124.032i	−0.329614	+	0.263898i
$471$			142.498i			0.302543i
$472$	−315.313	−	645.194i	−0.668037	−	1.36694i
$473$	−132.228			−0.279552
$474$	−78.5146	−	98.0661i	−0.165643	−	0.206891i
$475$	−178.308			−0.375385
$476$	−255.139	−	57.2010i	−0.536007	−	0.120170i
$477$			219.953i			0.461117i
$478$	284.971	+	355.934i	0.596174	+	0.744633i
$479$			157.578i			0.328974i	0.986379	+	0.164487i	$0.0525968\pi$
$479$			157.578i			0.328974i	−0.986379	+	0.164487i	$0.947403\pi$
$480$	−28.7403	−	120.557i	−0.0598757	−	0.251160i
$481$	393.711			0.818527
$482$	414.973	−	332.239i	0.860939	−	0.689292i
$483$	−148.432			−0.307313
$484$	138.323	−	616.977i	0.285792	−	1.27475i
$485$		−	306.639i		−	0.632246i
$486$	24.3376	−	19.4854i	0.0500774	−	0.0400934i
$487$			736.646i			1.51262i	0.654213	+	0.756311i	$0.273000\pi$
$487$			736.646i			1.51262i	−0.654213	+	0.756311i	$0.727000\pi$
$488$	−710.123	+	347.045i	−1.45517	+	0.711159i
$489$	−48.1709			−0.0985090
$490$	24.0472	+	30.0355i	0.0490760	+	0.0612968i
$491$	−362.408			−0.738101			−0.369050	−	0.929409i	$-0.620317\pi$
$491$	−362.408			−0.738101			−0.369050	+	0.929409i	$0.620317\pi$
$492$	3.71283	−	16.5607i	0.00754640	−	0.0336600i
$493$		−	5.07489i		−	0.0102939i
$494$	−479.251	−	598.594i	−0.970144	−	1.21173i
$495$			112.064i			0.226391i
$496$	−307.671	+	651.680i	−0.620305	+	1.31387i
$497$	683.164			1.37458
$498$	−258.494	+	206.957i	−0.519063	+	0.415577i
$499$	648.812			1.30022			0.650112	−	0.759838i	$-0.274722\pi$
$499$	648.812			1.30022			0.650112	+	0.759838i	$0.274722\pi$
$500$	−43.6381	−	9.78344i	−0.0872762	−	0.0195669i
$501$		−	359.954i		−	0.718470i
$502$	−241.829	+	193.615i	−0.481731	+	0.385687i
$503$		−	402.612i		−	0.800421i	−0.916423	−	0.400210i	$-0.868937\pi$
$503$		−	402.612i		−	0.800421i	0.916423	−	0.400210i	$-0.131063\pi$
$504$	163.655	−	79.9799i	0.324711	−	0.158690i
$505$	206.679			0.409265
$506$	−235.780	−	294.494i	−0.465969	−	0.582004i
$507$	−92.5126			−0.182471
$508$	−4.49888	−	1.00863i	−0.00885607	−	0.00198549i
$509$			470.175i			0.923724i	0.886952	+	0.461862i	$0.152818\pi$
$509$			470.175i			0.923724i	−0.886952	+	0.461862i	$0.847182\pi$
$510$	41.6959	+	52.0790i	0.0817568	+	0.102116i
$511$		−	516.702i		−	1.01116i
$512$	−501.063	−	105.263i	−0.978638	−	0.205592i
$513$	−185.303			−0.361215
$514$	658.890	−	527.526i	1.28189	−	1.02632i
$515$	275.738			0.535414
$516$	11.9967	−	53.5101i	0.0232494	−	0.103702i
$517$		−	741.315i		−	1.43388i
$518$	433.931	−	347.418i	0.837706	−	0.670691i
$519$		−	79.2630i		−	0.152723i
$520$	−84.4454	−	172.792i	−0.162395	−	0.332292i
$521$	−155.978			−0.299382			−0.149691	−	0.988733i	$-0.547828\pi$
$521$	−155.978			−0.299382			−0.149691	+	0.988733i	$0.547828\pi$
$522$	2.20959	+	2.75982i	0.00423293	+	0.00528701i
$523$	−313.578			−0.599576			−0.299788	−	0.954006i	$-0.596916\pi$
$523$	−313.578			−0.599576			−0.299788	+	0.954006i	$0.596916\pi$
$524$	−167.904	+	748.921i	−0.320428	+	1.42924i
$525$		−	65.7287i		−	0.125198i
$526$	−147.602	−	184.357i	−0.280612	−	0.350489i
$527$		−	387.928i		−	0.736107i
$528$	418.644	+	197.650i	0.792886	+	0.374338i
$529$	401.507			0.758993
$530$	255.958	−	204.927i	0.482939	−	0.386655i
$531$	−269.295			−0.507147
$532$	−1056.42	−	236.844i	−1.98575	−	0.445195i
$533$		−	26.3369i		−	0.0494125i
$534$	−21.3622	+	17.1032i	−0.0400041	+	0.0320284i
$535$		−	0.536888i		−	0.00100353i
$536$	314.387	+	643.297i	0.586542	+	1.20018i
$537$	57.3279			0.106756
$538$	−617.048	−	770.704i	−1.14693	−	1.43254i
$539$	−143.725			−0.266652
$540$	−45.3500	−	10.1673i	−0.0839816	−	0.0188282i
$541$			892.335i			1.64942i	0.565557	+	0.824709i	$0.308661\pi$
$541$			892.335i			1.64942i	−0.565557	+	0.824709i	$0.691339\pi$
$542$	453.690	+	566.667i	0.837066	+	1.04551i
$543$		−	306.827i		−	0.565059i
$544$	268.095	−	63.9129i	0.492822	−	0.117487i
$545$	−262.954			−0.482485
$546$	220.656	−	176.664i	0.404132	−	0.323560i
$547$	−671.435			−1.22749			−0.613743	−	0.789506i	$-0.710337\pi$
$547$	−671.435			−1.22749			−0.613743	+	0.789506i	$0.710337\pi$
$548$	14.8871	−	66.4024i	0.0271662	−	0.121172i
$549$			296.396i			0.539884i
$550$	130.408	−	104.408i	0.237105	−	0.189833i
$551$		−	21.0129i		−	0.0381359i
$552$	140.568	−	68.6971i	0.254652	−	0.124451i
$553$	−275.238			−0.497717
$554$	401.260	+	501.181i	0.724296	+	0.904659i
$555$	−141.830			−0.255549
$556$	−154.341	+	688.421i	−0.277591	+	1.23817i
$557$			296.095i			0.531590i	0.964030	+	0.265795i	$0.0856344\pi$
$557$			296.095i			0.531590i	−0.964030	+	0.265795i	$0.914366\pi$
$558$	168.903	+	210.963i	0.302693	+	0.378069i
$559$		−	85.0982i		−	0.152233i
$560$	−245.547	−	115.928i	−0.438476	−	0.207014i
$561$	−249.208			−0.444221
$562$	290.080	−	232.247i	0.516157	−	0.413250i
$563$	−707.222			−1.25617			−0.628084	−	0.778146i	$-0.716161\pi$
$563$	−707.222			−1.25617			−0.628084	+	0.778146i	$0.716161\pi$
$564$	299.996	+	67.2576i	0.531907	+	0.119251i
$565$			92.0651i			0.162947i
$566$	325.722	−	260.783i	0.575481	−	0.460747i
$567$		−	68.3073i		−	0.120471i
$568$	−646.969	+	316.181i	−1.13903	+	0.556657i
$569$	230.263			0.404680			0.202340	−	0.979315i	$-0.435145\pi$
$569$	230.263			0.404680			0.202340	+	0.979315i	$0.435145\pi$
$570$	172.644	+	215.636i	0.302885	+	0.378309i
$571$	−439.428			−0.769575			−0.384788	−	0.923005i	$-0.625725\pi$
$571$	−439.428			−0.769575			−0.384788	+	0.923005i	$0.625725\pi$
$572$	701.013	+	157.164i	1.22555	+	0.274761i
$573$		−	49.8831i		−	0.0870560i
$574$	−23.2401	−	29.0273i	−0.0404880	−	0.0505703i
$575$		−	56.4564i		−	0.0981850i
$576$	−117.968	+	151.485i	−0.204805	+	0.262994i
$577$	−184.670			−0.320053			−0.160026	−	0.987113i	$-0.551158\pi$
$577$	−184.670			−0.320053			−0.160026	+	0.987113i	$0.551158\pi$
$578$	335.390	−	268.523i	0.580260	−	0.464573i
$579$	−152.067			−0.262638
$580$	1.15294	−	5.14257i	0.00198782	−	0.00886650i
$581$			725.502i			1.24871i
$582$	−370.833	+	296.900i	−0.637170	+	0.510137i
$583$			1224.81i			2.10087i
$584$	239.139	+	489.327i	0.409485	+	0.837888i
$585$	−72.1211			−0.123284
$586$	−383.652	−	479.189i	−0.654697	−	0.817729i
$587$	297.341			0.506543			0.253271	−	0.967395i	$-0.418493\pi$
$587$	297.341			0.506543			0.253271	+	0.967395i	$0.418493\pi$
$588$	13.0398	−	58.1629i	0.0221766	−	0.0989164i
$589$		−	1606.24i		−	2.72706i
$590$	250.899	+	313.377i	0.425252	+	0.531148i
$591$			602.103i			1.01879i
$592$	−250.149	+	529.843i	−0.422550	+	0.895004i
$593$	−607.065			−1.02372			−0.511859	−	0.859070i	$-0.671043\pi$
$593$	−607.065			−1.02372			−0.511859	+	0.859070i	$0.671043\pi$
$594$	135.524	−	108.504i	0.228155	−	0.182667i
$595$	146.168			0.245660
$596$	−827.640	−	185.553i	−1.38866	−	0.311330i
$597$		−	224.036i		−	0.375269i
$598$	189.528	−	151.742i	0.316937	−	0.253749i
$599$			448.633i			0.748970i	0.927233	+	0.374485i	$0.122180\pi$
$599$			448.633i			0.748970i	−0.927233	+	0.374485i	$0.877820\pi$
$600$	30.4205	+	62.2463i	0.0507008	+	0.103744i
$601$	580.584			0.966030			0.483015	−	0.875612i	$-0.339542\pi$
$601$	580.584			0.966030			0.483015	+	0.875612i	$0.339542\pi$
$602$	−75.0921	−	93.7915i	−0.124738	−	0.155800i
$603$	268.504			0.445280
$604$	559.552	+	125.449i	0.926411	+	0.207697i
$605$			353.462i			0.584235i
$606$	−200.114	−	249.946i	−0.330221	−	0.412452i
$607$		−	132.576i		−	0.218413i	−0.994019	−	0.109206i	$-0.965169\pi$
$607$		−	132.576i		−	0.218413i	0.994019	−	0.109206i	$-0.0348309\pi$
$608$	1110.06	−	264.635i	1.82576	−	0.435255i
$609$	7.74585			0.0127190
$610$	344.914	−	276.148i	0.565433	−	0.452702i
$611$	477.089			0.780834
$612$	22.6100	−	100.850i	0.0369444	−	0.164787i
$613$		−	175.738i		−	0.286685i	−0.989673	−	0.143343i	$-0.954215\pi$
$613$		−	175.738i		−	0.286685i	0.989673	−	0.143343i	$-0.0457851\pi$
$614$	−442.644	+	354.393i	−0.720919	+	0.577188i
$615$			9.48754i			0.0154269i
$616$	911.310	−	445.367i	1.47940	−	0.722999i
$617$	283.254			0.459082			0.229541	−	0.973299i	$-0.426277\pi$
$617$	283.254			0.459082			0.229541	+	0.973299i	$0.426277\pi$
$618$	−266.980	−	333.463i	−0.432006	−	0.539583i
$619$	−80.2105			−0.129581			−0.0647904	−	0.997899i	$-0.520638\pi$
$619$	−80.2105			−0.129581			−0.0647904	+	0.997899i	$0.520638\pi$
$620$	88.1315	−	393.102i	0.142148	−	0.634035i
$621$		−	58.6712i		−	0.0944785i
$622$	767.513	+	958.638i	1.23394	+	1.54122i
$623$			59.9563i			0.0962381i
$624$	−127.202	+	269.427i	−0.203850	+	0.431775i
$625$	25.0000			0.0400000
$626$	799.239	−	639.893i	1.27674	−	1.02219i
$627$	−1031.86			−1.64571
$628$	−321.113	−	71.9919i	−0.511326	−	0.114637i
$629$		−	315.402i		−	0.501434i
$630$	−79.4887	+	63.6409i	−0.126173	+	0.101017i
$631$		−	178.580i		−	0.283011i	−0.989937	−	0.141505i	$-0.954806\pi$
$631$		−	178.580i		−	0.283011i	0.989937	−	0.141505i	$-0.0451942\pi$
$632$	260.655	−	127.385i	0.412429	−	0.201559i
$633$	329.968			0.521277
$634$	−537.002	−	670.725i	−0.847006	−	1.05793i
$635$	2.57738			0.00405887
$636$	−495.655	−	111.123i	−0.779332	−	0.174722i
$637$		−	92.4976i		−	0.145208i
$638$	12.3041	+	15.3680i	0.0192854	+	0.0240878i
$639$			270.036i			0.422592i
$640$	286.191	−	3.85803i	0.447173	−	0.00602818i
$641$	−379.689			−0.592339			−0.296169	−	0.955135i	$-0.595709\pi$
$641$	−379.689			−0.592339			−0.296169	+	0.955135i	$0.595709\pi$
$642$	−0.649283	+	0.519835i	−0.00101134	+	0.000809712i
$643$	−847.921			−1.31869			−0.659347	−	0.751839i	$-0.729167\pi$
$643$	−847.921			−1.31869			−0.659347	+	0.751839i	$0.729167\pi$
$644$	74.9901	−	334.486i	0.116444	−	0.519388i
$645$			30.6556i			0.0475281i
$646$	−479.533	+	383.928i	−0.742311	+	0.594315i
$647$			372.369i			0.575532i	0.957701	+	0.287766i	$0.0929126\pi$
$647$			372.369i			0.575532i	−0.957701	+	0.287766i	$0.907087\pi$
$648$	31.6139	+	64.6882i	0.0487868	+	0.0998275i
$649$	−1499.57			−2.31058
$650$	67.1942	+	83.9269i	0.103376	+	0.129118i
$651$	592.099			0.909522
$652$	24.3367	−	108.551i	0.0373262	−	0.166490i
$653$		−	650.726i		−	0.996517i	−0.867028	−	0.498259i	$-0.833973\pi$
$653$		−	650.726i		−	0.996517i	0.867028	−	0.498259i	$-0.166027\pi$
$654$	254.602	+	318.003i	0.389300	+	0.486243i
$655$		−	429.052i		−	0.655042i
$656$	35.4432	+	16.7334i	0.0540292	+	0.0255083i
$657$	204.238			0.310865
$658$	525.827	−	420.992i	0.799129	−	0.639806i
$659$	589.211			0.894099			0.447049	−	0.894509i	$-0.352475\pi$
$659$	589.211			0.894099			0.447049	+	0.894509i	$0.352475\pi$
$660$	−252.531	−	56.6163i	−0.382623	−	0.0857823i
$661$			402.340i			0.608684i	0.952563	+	0.304342i	$0.0984366\pi$
$661$			402.340i			0.608684i	−0.952563	+	0.304342i	$0.901563\pi$
$662$	838.861	−	671.616i	1.26716	−	1.01453i
$663$		−	160.383i		−	0.241905i
$664$	−335.776	−	687.063i	−0.505686	−	1.03473i
$665$	605.216			0.910099
$666$	137.325	+	171.521i	0.206193	+	0.257539i
$667$	6.65315			0.00997473
$668$	811.142	+	181.854i	1.21428	+	0.272236i
$669$			366.220i			0.547414i
$670$	−250.161	−	312.456i	−0.373375	−	0.466352i
$671$			1650.48i			2.45973i
$672$	97.5509	+	409.196i	0.145165	+	0.608923i
$673$	1237.67			1.83903			0.919515	−	0.393056i	$-0.128582\pi$
$673$	1237.67			1.83903			0.919515	+	0.393056i	$0.128582\pi$
$674$	−247.582	+	198.221i	−0.367332	+	0.294096i
$675$	25.9808			0.0384900
$676$	46.7387	−	208.474i	0.0691401	−	0.308393i
$677$		−	163.462i		−	0.241451i	−0.992686	−	0.120725i	$-0.961478\pi$
$677$		−	163.462i		−	0.241451i	0.992686	−	0.120725i	$-0.0385221\pi$
$678$	111.339	−	89.1408i	0.164216	−	0.131476i
$679$			1040.80i			1.53284i
$680$	−138.423	+	67.6491i	−0.203564	+	0.0994840i
$681$	−153.958			−0.226077
$682$	940.533	+	1174.74i	1.37908	+	1.72250i
$683$	992.033			1.45246			0.726232	−	0.687449i	$-0.241270\pi$
$683$	992.033			1.45246			0.726232	+	0.687449i	$0.241270\pi$
$684$	93.6179	−	417.574i	0.136868	−	0.610488i
$685$			38.0415i			0.0555350i
$686$	383.243	+	478.678i	0.558663	+	0.697781i
$687$		−	264.783i		−	0.385419i
$688$	114.522	+	54.0682i	0.166456	+	0.0785875i
$689$	−788.250			−1.14405
$690$	−68.2753	+	54.6631i	−0.0989497	+	0.0792219i
$691$	−465.365			−0.673466			−0.336733	−	0.941600i	$-0.609322\pi$
$691$	−465.365			−0.673466			−0.336733	+	0.941600i	$0.609322\pi$
$692$	178.616	+	40.0449i	0.258116	+	0.0578683i
$693$		−	380.369i		−	0.548872i
$694$	−264.941	+	212.119i	−0.381759	+	0.305648i
$695$		−	394.392i		−	0.567471i
$696$	−7.33546	+	3.58492i	−0.0105395	+	0.00515075i
$697$	−21.0984			−0.0302703
$698$	−370.459	−	462.710i	−0.530743	−	0.662908i
$699$	−326.347			−0.466878
$700$	148.117	+	33.2071i	0.211596	+	0.0474387i
$701$		−	261.352i		−	0.372827i	−0.982471	−	0.186414i	$-0.940314\pi$
$701$		−	261.352i		−	0.372827i	0.982471	−	0.186414i	$-0.0596864\pi$
$702$	69.8303	+	87.2194i	0.0994734	+	0.124244i
$703$		−	1305.94i		−	1.85767i
$704$	−656.902	+	843.542i	−0.933100	+	1.19821i
$705$	−171.866			−0.243781
$706$	−207.764	+	166.342i	−0.294283	+	0.235611i
$707$	−701.512			−0.992238
$708$	136.052	−	606.847i	0.192164	−	0.857128i
$709$			186.604i			0.263194i	0.991303	+	0.131597i	$0.0420104\pi$
$709$			186.604i			0.263194i	−0.991303	+	0.131597i	$0.957990\pi$
$710$	314.239	−	251.589i	0.442591	−	0.354351i
$711$		−	108.794i		−	0.153015i
$712$	−27.7489	−	56.7797i	−0.0389732	−	0.0797468i
$713$	508.572			0.713284
$714$	−141.525	−	176.767i	−0.198214	−	0.247573i
$715$	−401.606			−0.561687
$716$	−28.9629	+	129.186i	−0.0404510	+	0.180428i
$717$			394.871i			0.550727i
$718$	297.616	+	371.728i	0.414507	+	0.517727i
$719$			448.275i			0.623470i	0.950169	+	0.311735i	$0.100910\pi$
$719$			448.275i			0.623470i	−0.950169	+	0.311735i	$0.899090\pi$
$720$	45.8230	−	97.0580i	0.0636431	−	0.134803i
$721$	−935.914			−1.29808
$722$	−1421.92	+	1138.43i	−1.96942	+	1.57677i
$723$	460.368			0.636747
$724$	691.423	+	155.014i	0.955005	+	0.214107i
$725$			2.94615i			0.00406365i
$726$	427.458	−	342.235i	0.588785	−	0.471398i
$727$		−	956.205i		−	1.31527i	−0.753335	−	0.657637i	$-0.771556\pi$
$727$		−	956.205i		−	1.31527i	0.753335	−	0.657637i	$-0.228444\pi$
$728$	286.626	+	586.493i	0.393717	+	0.805623i
$729$	27.0000			0.0370370
$730$	−190.286	−	237.671i	−0.260666	−	0.325577i
$731$	−68.1721			−0.0932586
$732$	−667.917	−	149.744i	−0.912456	−	0.204568i
$733$		−	398.986i		−	0.544320i	−0.962252	−	0.272160i	$-0.912262\pi$
$733$		−	398.986i		−	0.544320i	0.962252	−	0.272160i	$-0.0877379\pi$
$734$	−477.076	−	595.877i	−0.649968	−	0.811822i
$735$			33.3211i			0.0453349i
$736$	83.7894	+	351.471i	0.113844	+	0.477542i
$737$	1495.16			2.02871
$738$	11.4737	−	9.18618i	0.0155470	−	0.0124474i
$739$	1011.87			1.36924			0.684622	−	0.728899i	$-0.259967\pi$
$739$	1011.87			1.36924			0.684622	+	0.728899i	$0.259967\pi$
$740$	71.6545	−	319.608i	0.0968305	−	0.431903i
$741$		−	664.076i		−	0.896189i
$742$	−868.775	+	695.566i	−1.17086	+	0.937421i
$743$		−	346.145i		−	0.465875i	−0.972492	−	0.232938i	$-0.925166\pi$
$743$		−	346.145i		−	0.465875i	0.972492	−	0.232938i	$-0.0748338\pi$
$744$	−560.728	+	274.034i	−0.753667	+	0.368326i
$745$	474.150			0.636443
$746$	52.8406	+	65.9989i	0.0708319	+	0.0884704i
$747$	−286.771			−0.383897
$748$	125.904	−	561.581i	0.168320	−	0.750776i
$749$			1.82231i			0.00243300i
$750$	−24.2059	−	30.2336i	−0.0322746	−	0.0403115i
$751$			71.2058i			0.0948146i	0.998876	+	0.0474073i	$0.0150959\pi$
$751$			71.2058i			0.0948146i	−0.998876	+	0.0474073i	$0.984904\pi$
$752$	−303.125	+	642.050i	−0.403091	+	0.853789i
$753$	−268.283			−0.356286
$754$	−9.89043	+	7.91856i	−0.0131173	+	0.0105021i
$755$	−320.564			−0.424588
$756$	153.928	+	34.5098i	0.203608	+	0.0456479i
$757$			1452.44i			1.91867i	0.282264	+	0.959337i	$0.408915\pi$
$757$			1452.44i			1.91867i	−0.282264	+	0.959337i	$0.591085\pi$
$758$	−643.710	+	515.373i	−0.849222	+	0.679912i
$759$		−	326.710i		−	0.430448i
$760$	−573.150	+	280.105i	−0.754145	+	0.368559i
$761$	414.416			0.544567			0.272284	−	0.962217i	$-0.412221\pi$
$761$	414.416			0.544567			0.272284	+	0.962217i	$0.412221\pi$
$762$	−2.49552	−	3.11695i	−0.00327496	−	0.00409048i
$763$	892.523			1.16976
$764$	112.410	+	25.2017i	0.147133	+	0.0329865i
$765$			57.7761i			0.0755244i
$766$	−504.634	−	630.297i	−0.658791	−	0.822842i
$767$		−	965.081i		−	1.25825i
$768$	−281.766	−	342.368i	−0.366883	−	0.445792i
$769$	−132.780			−0.172665			−0.0863326	−	0.996266i	$-0.527515\pi$
$769$	−132.780			−0.172665			−0.0863326	+	0.996266i	$0.527515\pi$
$770$	−442.632	+	354.384i	−0.574847	+	0.460239i
$771$	730.968			0.948078
$772$	76.8267	−	342.678i	0.0995165	−	0.443884i
$773$			135.449i			0.175225i	0.996155	+	0.0876126i	$0.0279238\pi$
$773$			135.449i			0.175225i	−0.996155	+	0.0876126i	$0.972076\pi$
$774$	37.0732	−	29.6819i	0.0478982	−	0.0383487i
$775$			225.206i			0.290588i
$776$	−481.702	−	985.656i	−0.620749	−	1.27018i
$777$	481.401			0.619564
$778$	98.1307	+	122.567i	0.126132	+	0.157541i
$779$	−87.3592			−0.112143
$780$	36.4367	−	162.522i	0.0467137	−	0.208362i
$781$			1503.70i			1.92535i
$782$	−121.560	−	151.831i	−0.155448	−	0.194157i
$783$			3.06173i			0.00391025i
$784$	124.480	+	58.7695i	0.158775	+	0.0749611i
$785$	183.964			0.234348
$786$	−518.873	+	415.424i	−0.660143	+	0.528530i
$787$	−370.900			−0.471283			−0.235642	−	0.971840i	$-0.575719\pi$
$787$	−370.900			−0.471283			−0.235642	+	0.971840i	$0.575719\pi$
$788$	−1356.82	−	304.192i	−1.72185	−	0.386030i
$789$		−	204.525i		−	0.259220i
$790$	−126.603	+	101.362i	−0.160257	+	0.128306i
$791$		−	312.489i		−	0.395055i
$792$	176.042	+	360.216i	0.222275	+	0.454818i
$793$	−1062.20			−1.33947
$794$	−403.846	−	504.411i	−0.508622	−	0.635279i
$795$	283.958			0.357180
$796$	504.856	+	113.186i	0.634241	+	0.142194i
$797$		−	980.881i		−	1.23072i	−0.788247	−	0.615358i	$-0.789011\pi$
$797$		−	980.881i		−	1.23072i	0.788247	−	0.615358i	$-0.210989\pi$
$798$	−585.992	−	731.916i	−0.734326	−	0.917187i
$799$		−	382.196i		−	0.478343i
$800$	−155.638	+	37.1036i	−0.194548	+	0.0463795i
$801$	−23.6991			−0.0295869
$802$	970.149	−	776.729i	1.20966	−	0.968490i
$803$	1137.30			1.41631
$804$	−135.652	+	605.063i	−0.168722	+	0.752566i
$805$			191.625i			0.238044i
$806$	−756.032	+	605.301i	−0.938005	+	0.750994i
$807$		−	855.014i		−	1.05950i
$808$	664.344	−	324.673i	0.822208	−	0.401823i
$809$	−464.769			−0.574498			−0.287249	−	0.957856i	$-0.592741\pi$
$809$	−464.769			−0.574498			−0.287249	+	0.957856i	$0.592741\pi$
$810$	−25.1555	−	31.4197i	−0.0310562	−	0.0387898i
$811$	−49.1816			−0.0606431			−0.0303216	−	0.999540i	$-0.509653\pi$
$811$	−49.1816			−0.0606431			−0.0303216	+	0.999540i	$0.509653\pi$
$812$	−3.91332	+	17.4550i	−0.00481936	+	0.0214963i
$813$			628.657i			0.773255i
$814$	764.693	+	955.115i	0.939426	+	1.17336i
$815$			62.1884i			0.0763048i
$816$	215.838	+	101.901i	0.264507	+	0.124879i
$817$	−282.270			−0.345496
$818$	−504.112	+	403.607i	−0.616274	+	0.493407i
$819$	244.795			0.298894
$820$	−21.3798	−	4.79324i	−0.0260729	−	0.00584542i
$821$			911.027i			1.10965i	0.831965	+	0.554827i	$0.187216\pi$
$821$			911.027i			1.10965i	−0.831965	+	0.554827i	$0.812784\pi$
$822$	46.0053	−	36.8332i	0.0559676	−	0.0448092i
$823$			1278.02i			1.55287i	0.630195	+	0.776437i	$0.282975\pi$
$823$			1278.02i			1.55287i	−0.630195	+	0.776437i	$0.717025\pi$
$824$	886.327	−	433.158i	1.07564	−	0.525678i
$825$	144.674			0.175362
$826$	−851.604	−	1063.67i	−1.03100	−	1.28774i
$827$	−671.016			−0.811386			−0.405693	−	0.914009i	$-0.632970\pi$
$827$	−671.016			−0.811386			−0.405693	+	0.914009i	$0.632970\pi$
$828$	132.213	+	29.6416i	0.159678	+	0.0357990i
$829$		−	31.8486i		−	0.0384181i	−0.999815	−	0.0192091i	$-0.993885\pi$
$829$		−	31.8486i		−	0.0384181i	0.999815	−	0.0192091i	$-0.00611481\pi$
$830$	267.181	+	333.714i	0.321905	+	0.402065i
$831$			556.007i			0.669082i
$832$	−542.880	−	422.764i	−0.652500	−	0.508130i
$833$	−74.0997			−0.0889552
$834$	−476.957	+	381.865i	−0.571890	+	0.457872i
$835$	−464.698			−0.556525
$836$	521.311	−	2325.26i	0.623578	−	2.78141i
$837$			234.041i			0.279618i
$838$	−30.0255	+	24.0393i	−0.0358299	+	0.0286865i
$839$		−	112.707i		−	0.134335i	−0.997742	−	0.0671674i	$-0.978604\pi$
$839$		−	112.707i		−	0.134335i	0.997742	−	0.0671674i	$-0.0213961\pi$
$840$	−103.254	−	211.277i	−0.122921	−	0.251520i
$841$	840.653			0.999587
$842$	390.985	+	488.347i	0.464352	+	0.579985i
$843$	321.813			0.381748
$844$	−166.705	+	743.570i	−0.197518	+	0.881008i
$845$			119.433i			0.141341i
$846$	166.407	+	207.845i	0.196698	+	0.245680i
$847$		−	1199.73i		−	1.41644i
$848$	500.825	−	1060.80i	0.590595	−	1.25094i
$849$	361.354			0.425623
$850$	67.2337	−	53.8292i	0.0790985	−	0.0633285i
$851$	413.490			0.485887
$852$	−608.516	−	136.426i	−0.714221	−	0.160125i
$853$		−	512.714i		−	0.601072i	−0.953770	−	0.300536i	$-0.902834\pi$
$853$		−	512.714i		−	0.601072i	0.953770	−	0.300536i	$-0.0971655\pi$
$854$	−1170.71	+	937.307i	−1.37086	+	1.09755i
$855$			239.225i			0.279796i
$856$	−0.843401	−	1.72576i	−0.000985281	−	0.00201608i
$857$	−1620.81			−1.89126			−0.945631	−	0.325243i	$-0.894554\pi$
$857$	−1620.81			−1.89126			−0.945631	+	0.325243i	$0.894554\pi$
$858$	388.850	+	485.680i	0.453205	+	0.566061i
$859$	225.172			0.262132			0.131066	−	0.991374i	$-0.458160\pi$
$859$	225.172			0.262132			0.131066	+	0.991374i	$0.458160\pi$
$860$	−69.0812	−	15.4877i	−0.0803270	−	0.0180089i
$861$		−	32.2027i		−	0.0374016i
$862$	521.763	+	651.692i	0.605294	+	0.756023i
$863$		−	1029.21i		−	1.19260i	−0.802763	−	0.596299i	$-0.796637\pi$
$863$		−	1029.21i		−	1.19260i	0.802763	−	0.596299i	$-0.203363\pi$
$864$	−161.744	+	38.5592i	−0.187204	+	0.0446287i
$865$	−102.328			−0.118298
$866$	−436.331	+	349.339i	−0.503846	+	0.403394i
$867$	372.080			0.429158
$868$	−299.137	+	1334.27i	−0.344628	+	1.53718i
$869$		−	605.818i		−	0.697144i
$870$	3.56291	−	2.85257i	0.00409530	−	0.00327881i
$871$			962.244i			1.10476i
$872$	−845.236	+	413.076i	−0.969307	+	0.473711i
$873$	−411.400			−0.471248
$874$	−503.327	−	628.664i	−0.575889	−	0.719296i
$875$	−84.8554			−0.0969776
$876$	−103.184	+	460.244i	−0.117790	+	0.525392i
$877$		−	570.056i		−	0.650007i	−0.945713	−	0.325003i	$-0.894635\pi$
$877$		−	570.056i		−	0.650007i	0.945713	−	0.325003i	$-0.105365\pi$
$878$	−37.6667	−	47.0464i	−0.0429005	−	0.0535836i
$879$		−	531.609i		−	0.604789i
$880$	255.165	−	540.467i	0.289961	−	0.614167i
$881$	596.788			0.677398			0.338699	−	0.940895i	$-0.390013\pi$
$881$	596.788			0.677398			0.338699	+	0.940895i	$0.390013\pi$
$882$	40.2968	−	32.2628i	0.0456880	−	0.0365791i
$883$	856.738			0.970258			0.485129	−	0.874442i	$-0.338773\pi$
$883$	856.738			0.970258			0.485129	+	0.874442i	$0.338773\pi$
$884$	361.418	+	81.0280i	0.408843	+	0.0916606i
$885$			347.659i			0.392835i
$886$	87.8766	−	70.3565i	0.0991835	−	0.0794092i
$887$		−	1648.76i		−	1.85880i	−0.369068	−	0.929402i	$-0.620323\pi$
$887$		−	1648.76i		−	1.85880i	0.369068	−	0.929402i	$-0.379677\pi$
$888$	−455.895	+	222.801i	−0.513396	+	0.250902i
$889$	−8.74819			−0.00984048
$890$	22.0801	+	27.5785i	0.0248091	+	0.0309871i
$891$	150.349			0.168742
$892$	−825.263	−	185.020i	−0.925183	−	0.207421i
$893$		−	1582.50i		−	1.77212i
$894$	−459.089	−	573.411i	−0.513523	−	0.641400i
$895$		−	74.0100i		−	0.0826928i
$896$	−971.393	+	13.0950i	−1.08414	+	0.0146149i
$897$	210.261			0.234405
$898$	442.612	−	354.367i	0.492886	−	0.394619i
$899$	−26.5395			−0.0295212
$900$	−13.1259	+	58.5467i	−0.0145843	+	0.0650518i
$901$			631.467i			0.700851i
$902$	63.8913	−	51.1532i	0.0708329	−	0.0567109i
$903$		−	104.052i		−	0.115229i
$904$	144.626	+	295.932i	0.159984	+	0.327359i
$905$	−396.112			−0.437693
$906$	310.382	+	387.673i	0.342585	+	0.427895i
$907$	844.509			0.931101			0.465551	−	0.885021i	$-0.345856\pi$
$907$	844.509			0.931101			0.465551	+	0.885021i	$0.345856\pi$
$908$	77.7821	−	346.940i	0.0856631	−	0.382092i
$909$		−	277.289i		−	0.305048i
$910$	−228.072	−	284.866i	−0.250628	−	0.313039i
$911$			1074.78i			1.17978i	0.807483	+	0.589891i	$0.200829\pi$
$911$			1074.78i			1.17978i	−0.807483	+	0.589891i	$0.799171\pi$
$912$	893.689	+	421.929i	0.979923	+	0.462641i
$913$	−1596.88			−1.74905
$914$	414.052	−	331.502i	0.453011	−	0.362694i
$915$	382.646			0.418192
$916$	596.677	+	133.772i	0.651395	+	0.146039i
$917$			1456.30i			1.58811i
$918$	69.8713	−	55.9410i	0.0761126	−	0.0609379i
$919$		−	1142.19i		−	1.24286i	−0.783471	−	0.621428i	$-0.786553\pi$
$919$		−	1142.19i		−	1.24286i	0.783471	−	0.621428i	$-0.213447\pi$
$920$	−88.6876	−	181.472i	−0.0963996	−	0.197253i
$921$	−491.067			−0.533188
$922$	887.046	+	1107.94i	0.962089	+	1.20167i
$923$	−967.736			−1.04847
$924$	857.146	+	192.168i	0.927647	+	0.207974i
$925$			183.102i			0.197948i
$926$	−521.735	−	651.657i	−0.563429	−	0.703733i
$927$		−	369.941i		−	0.399074i
$928$	−4.37251	−	18.3413i	−0.00471175	−	0.0197644i
$929$	415.953			0.447742			0.223871	−	0.974619i	$-0.428131\pi$
$929$	415.953			0.447742			0.223871	+	0.974619i	$0.428131\pi$
$930$	272.351	−	218.052i	0.292851	−	0.234465i
$931$	−306.814			−0.329553
$932$	164.876	−	735.412i	0.176905	−	0.789068i
$933$			1063.51i			1.13988i
$934$	1060.54	−	849.101i	1.13549	−	0.909102i
$935$			321.726i			0.344092i
$936$	−231.825	+	113.295i	−0.247676	+	0.121042i
$937$	−846.979			−0.903927			−0.451963	−	0.892037i	$-0.649276\pi$
$937$	−846.979			−0.903927			−0.451963	+	0.892037i	$0.649276\pi$
$938$	849.101	+	1060.54i	0.905225	+	1.13064i
$939$	886.671			0.944271
$940$	86.8291	−	387.293i	0.0923714	−	0.412014i
$941$		−	149.279i		−	0.158638i	−0.996849	−	0.0793192i	$-0.974725\pi$
$941$		−	149.279i		−	0.158638i	0.996849	−	0.0793192i	$-0.0252746\pi$
$942$	−178.120	−	222.476i	−0.189087	−	0.236174i
$943$		−	27.6599i		−	0.0293318i
$944$	1298.77	+	613.176i	1.37582	+	0.649551i
$945$	−88.1843			−0.0933167
$946$	206.442	−	165.283i	0.218226	−	0.174718i
$947$	543.005			0.573395			0.286697	−	0.958021i	$-0.407443\pi$
$947$	543.005			0.573395			0.286697	+	0.958021i	$0.407443\pi$
$948$	245.163	+	54.9643i	0.258611	+	0.0579793i
$949$			731.935i			0.771269i
$950$	278.385	−	222.883i	0.293037	−	0.234614i
$951$		−	744.098i		−	0.782438i
$952$	469.839	−	229.616i	0.493529	−	0.241193i
$953$	−344.292			−0.361272			−0.180636	−	0.983550i	$-0.557816\pi$
$953$	−344.292			−0.361272			−0.180636	+	0.983550i	$0.557816\pi$
$954$	−274.938	−	343.403i	−0.288195	−	0.359961i
$955$	−64.3988			−0.0674333
$956$	−889.828	−	199.495i	−0.930782	−	0.208677i
$957$			17.0492i			0.0178153i
$958$	−196.971	−	246.021i	−0.205607	−	0.256807i
$959$		−	129.121i		−	0.134641i
$960$	195.566	+	152.296i	0.203715	+	0.158641i
$961$	−1067.70			−1.11103
$962$	−614.685	+	492.135i	−0.638966	+	0.511575i
$963$	−0.720311			−0.000747987
$964$	−232.585	+	1037.42i	−0.241271	+	1.07616i
$965$			196.318i			0.203438i
$966$	231.741	−	185.538i	0.239897	−	0.192069i
$967$			1044.78i			1.08044i	0.841524	+	0.540219i	$0.181659\pi$
$967$			1044.78i			1.08044i	−0.841524	+	0.540219i	$0.818341\pi$
$968$	555.256	+	1136.16i	0.573611	+	1.17372i
$969$	−531.991			−0.549010
$970$	383.296	+	478.743i	0.395150	+	0.493550i
$971$	306.656			0.315814			0.157907	−	0.987454i	$-0.449525\pi$
$971$	306.656			0.315814			0.157907	+	0.987454i	$0.449525\pi$
$972$	−13.6408	+	60.8435i	−0.0140337	+	0.0625962i
$973$			1338.65i			1.37580i
$974$	−920.800	−	1150.10i	−0.945379	−	1.18080i
$975$			93.1079i			0.0954953i
$976$	674.884	−	1429.47i	0.691479	−	1.46462i
$977$	1753.81			1.79509			0.897547	−	0.440919i	$-0.145347\pi$
$977$	1753.81			1.79509			0.897547	+	0.440919i	$0.145347\pi$
$978$	75.2073	−	60.2131i	0.0768990	−	0.0615676i
$979$	−131.968			−0.134799
$980$	−75.0879	−	16.8343i	−0.0766203	−	0.0171779i
$981$			352.790i			0.359623i
$982$	565.812	−	453.005i	0.576183	−	0.461309i
$983$			951.541i			0.967997i	0.875069	+	0.483999i	$0.160816\pi$
$983$			951.541i			0.967997i	−0.875069	+	0.483999i	$0.839184\pi$
$984$	14.9040	+	30.4966i	0.0151464	+	0.0309924i
$985$	777.312			0.789149
$986$	6.34355	+	7.92321i	0.00643362	+	0.00803571i
$987$	583.349			0.591033
$988$	1496.47	+	335.501i	1.51465	+	0.339576i
$989$		−	89.3731i		−	0.0903672i
$990$	−140.078	−	174.961i	−0.141493	−	0.176728i
$991$		−	1786.06i		−	1.80229i	−0.433523	−	0.901143i	$-0.642730\pi$
$991$		−	1786.06i		−	1.80229i	0.433523	−	0.901143i	$-0.357270\pi$
$992$	−334.238	−	1402.03i	−0.336933	−	1.41333i
$993$	930.627			0.937187
$994$	−1066.60	+	853.947i	−1.07303	+	0.859102i
$995$	−289.229			−0.290682
$996$	144.881	−	646.228i	0.145463	−	0.648823i
$997$		−	1375.80i		−	1.37994i	−0.723839	−	0.689969i	$-0.757624\pi$
$997$		−	1375.80i		−	1.37994i	0.723839	−	0.689969i	$-0.242376\pi$
$998$	−1012.96	+	811.008i	−1.01499	+	0.812633i
$999$			190.285i			0.190475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.3.g.a.91.6	yes	16
3.2	odd	2		360.3.g.c.91.11		16
4.3	odd	2		480.3.g.a.271.16		16
5.2	odd	4		600.3.p.b.499.7		32
5.3	odd	4		600.3.p.b.499.26		32
5.4	even	2		600.3.g.d.451.11		16
8.3	odd	2	inner	120.3.g.a.91.5	✓	16
8.5	even	2		480.3.g.a.271.9		16
12.11	even	2		1440.3.g.c.271.7		16
20.3	even	4		2400.3.p.b.1999.32		32
20.7	even	4		2400.3.p.b.1999.13		32
20.19	odd	2		2400.3.g.b.751.2		16
24.5	odd	2		1440.3.g.c.271.10		16
24.11	even	2		360.3.g.c.91.12		16
40.3	even	4		600.3.p.b.499.8		32
40.13	odd	4		2400.3.p.b.1999.14		32
40.19	odd	2		600.3.g.d.451.12		16
40.27	even	4		600.3.p.b.499.25		32
40.29	even	2		2400.3.g.b.751.7		16
40.37	odd	4		2400.3.p.b.1999.31		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.3.g.a.91.5	✓	16	8.3	odd	2	inner
120.3.g.a.91.6	yes	16	1.1	even	1	trivial
360.3.g.c.91.11		16	3.2	odd	2
360.3.g.c.91.12		16	24.11	even	2
480.3.g.a.271.9		16	8.5	even	2
480.3.g.a.271.16		16	4.3	odd	2
600.3.g.d.451.11		16	5.4	even	2
600.3.g.d.451.12		16	40.19	odd	2
600.3.p.b.499.7		32	5.2	odd	4
600.3.p.b.499.8		32	40.3	even	4
600.3.p.b.499.25		32	40.27	even	4
600.3.p.b.499.26		32	5.3	odd	4
1440.3.g.c.271.7		16	12.11	even	2
1440.3.g.c.271.10		16	24.5	odd	2
2400.3.g.b.751.2		16	20.19	odd	2
2400.3.g.b.751.7		16	40.29	even	2
2400.3.p.b.1999.13		32	20.7	even	4
2400.3.p.b.1999.14		32	40.13	odd	4
2400.3.p.b.1999.31		32	40.37	odd	4
2400.3.p.b.1999.32		32	20.3	even	4

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	120.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56126 + 1.24999i) q^{2} -1.73205 q^{3} +(0.875058 - 3.90311i) q^{4} +2.23607i q^{5} +(2.70418 - 2.16504i) q^{6} -7.58970i q^{7} +(3.51265 + 7.18758i) q^{8} +3.00000 q^{9} +(-2.79506 - 3.49108i) q^{10} +16.7055 q^{11} +(-1.51564 + 6.76039i) q^{12} +10.7512i q^{13} +(9.48703 + 11.8495i) q^{14} -3.87298i q^{15} +(-14.4685 - 6.83090i) q^{16} +8.61276 q^{17} +(-4.68378 + 3.74997i) q^{18} +35.6616 q^{19} +(8.72762 + 1.95669i) q^{20} +13.1457i q^{21} +(-26.0816 + 20.8817i) q^{22} +11.2913i q^{23} +(-6.08409 - 12.4493i) q^{24} -5.00000 q^{25} +(-13.4388 - 16.7854i) q^{26} -5.19615 q^{27} +(-29.6234 - 6.64142i) q^{28} -0.589229i q^{29} +(4.84118 + 6.04673i) q^{30} -45.0411i q^{31} +(31.1277 - 7.42072i) q^{32} -28.9347 q^{33} +(-13.4467 + 10.7658i) q^{34} +16.9711 q^{35} +(2.62517 - 11.7093i) q^{36} -36.6203i q^{37} +(-55.6770 + 44.5766i) q^{38} -18.6216i q^{39} +(-16.0719 + 7.85453i) q^{40} -2.44967 q^{41} +(-16.4320 - 20.5239i) q^{42} -7.91524 q^{43} +(14.6183 - 65.2033i) q^{44} +6.70820i q^{45} +(-14.1140 - 17.6286i) q^{46} -44.3755i q^{47} +(25.0603 + 11.8315i) q^{48} -8.60348 q^{49} +(7.80629 - 6.24994i) q^{50} -14.9177 q^{51} +(41.9630 + 9.40790i) q^{52} +73.3176i q^{53} +(8.11254 - 6.49513i) q^{54} +37.3546i q^{55} +(54.5515 - 26.6600i) q^{56} -61.7677 q^{57} +(0.736530 + 0.919939i) q^{58} -89.7651 q^{59} +(-15.1167 - 3.38908i) q^{60} +98.7987i q^{61} +(56.3009 + 70.3209i) q^{62} -22.7691i q^{63} +(-39.3226 + 50.4949i) q^{64} -24.0404 q^{65} +(45.1746 - 36.1681i) q^{66} +89.5013 q^{67} +(7.53666 - 33.6165i) q^{68} -19.5571i q^{69} +(-26.4962 + 21.2136i) q^{70} +90.0121i q^{71} +(10.5380 + 21.5627i) q^{72} +68.0795 q^{73} +(45.7750 + 57.1738i) q^{74} +8.66025 q^{75} +(31.2060 - 139.191i) q^{76} -126.790i q^{77} +(23.2768 + 29.0731i) q^{78} -36.2647i q^{79} +(15.2743 - 32.3527i) q^{80} +9.00000 q^{81} +(3.82457 - 3.06206i) q^{82} -95.5904 q^{83} +(51.3093 + 11.5033i) q^{84} +19.2587i q^{85} +(12.3577 - 9.89396i) q^{86} +1.02058i q^{87} +(58.6805 + 120.072i) q^{88} -7.89970 q^{89} +(-8.38518 - 10.4732i) q^{90} +81.5982 q^{91} +(44.0711 + 9.88052i) q^{92} +78.0135i q^{93} +(55.4689 + 69.2817i) q^{94} +79.7418i q^{95} +(-53.9147 + 12.8531i) q^{96} -137.133 q^{97} +(13.4323 - 10.7543i) q^{98} +50.1164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 14 q^{4} + 6 q^{6} + 20 q^{8} + 48 q^{9} + 10 q^{10} + 64 q^{11} - 20 q^{14} - 14 q^{16} - 12 q^{18} - 32 q^{19} - 40 q^{20} + 28 q^{22} - 54 q^{24} - 80 q^{25} + 36 q^{26} - 28 q^{28}+ \cdots + 192 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 14 * q^4 + 6 * q^6 + 20 * q^8 + 48 * q^9 + 10 * q^10 + 64 * q^11 - 20 * q^14 - 14 * q^16 - 12 * q^18 - 32 * q^19 - 40 * q^20 + 28 * q^22 - 54 * q^24 - 80 * q^25 + 36 * q^26 - 28 * q^28 + 36 * q^32 - 72 * q^34 + 42 * q^36 - 240 * q^38 + 10 * q^40 - 108 * q^42 - 192 * q^43 - 100 * q^44 + 212 * q^46 - 48 * q^48 - 80 * q^49 + 20 * q^50 + 96 * q^51 + 232 * q^52 + 18 * q^54 - 116 * q^56 + 96 * q^57 + 140 * q^58 + 128 * q^59 - 30 * q^60 + 104 * q^62 + 14 * q^64 - 180 * q^66 - 64 * q^67 - 576 * q^68 - 180 * q^70 + 60 * q^72 - 160 * q^73 + 300 * q^74 + 420 * q^76 - 120 * q^78 + 80 * q^80 + 144 * q^81 + 160 * q^82 + 180 * q^84 + 312 * q^86 + 604 * q^88 + 30 * q^90 - 192 * q^91 + 216 * q^92 + 460 * q^94 - 186 * q^96 - 224 * q^97 + 428 * q^98 + 192 * q^99

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