LMFDB - Embedded newform 153.3.p.b.73.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [153,3,Mod(10,153)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(153, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("153.10"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	153.p (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,0,-16,0,8,24,0,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$4.16894804471$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	153.73
Dual form			153.3.p.b.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841487 + 2.03153i) q^{2} +(-0.590587 + 0.590587i) q^{4} +(1.04667 - 5.26197i) q^{5} +(1.21824 + 6.12453i) q^{7} +(6.42935 + 2.66313i) q^{8} +(11.5706 - 2.30154i) q^{10} +(12.1433 + 8.11392i) q^{11} +(4.79884 + 4.79884i) q^{13} +(-11.4170 + 7.62861i) q^{14} +18.6433i q^{16} +(-6.50562 - 15.7060i) q^{17} +(-9.56175 - 23.0841i) q^{19} +(2.48950 + 3.72580i) q^{20} +(-6.26521 + 31.4973i) q^{22} +(-7.27639 + 10.8899i) q^{23} +(-3.49585 - 1.44803i) q^{25} +(-5.71082 + 13.7871i) q^{26} +(-4.33654 - 2.89759i) q^{28} +(-32.3980 - 6.44436i) q^{29} +(-1.00960 + 0.674593i) q^{31} +(-12.1570 + 5.03558i) q^{32} +(26.4327 - 26.4327i) q^{34} +33.5022 q^{35} +(-25.8238 - 38.6481i) q^{37} +(38.8500 - 38.8500i) q^{38} +(20.7427 - 31.0437i) q^{40} +(-6.13577 - 30.8466i) q^{41} +(-27.8948 + 67.3441i) q^{43} +(-11.9637 + 2.37972i) q^{44} +(-28.2461 - 5.61851i) q^{46} +(10.4882 + 10.4882i) q^{47} +(9.24438 - 3.82915i) q^{49} -8.32041i q^{50} -5.66826 q^{52} +(1.97838 + 4.77624i) q^{53} +(55.4053 - 55.4053i) q^{55} +(-8.47786 + 42.6211i) q^{56} +(-14.1706 - 71.2404i) q^{58} +(-26.1013 - 10.8115i) q^{59} +(-81.0541 + 16.1227i) q^{61} +(-2.22002 - 1.48337i) q^{62} +(32.2713 + 32.2713i) q^{64} +(30.2741 - 20.2285i) q^{65} -44.5324i q^{67} +(13.1179 + 5.43359i) q^{68} +(28.1917 + 68.0607i) q^{70} +(-32.1978 - 48.1875i) q^{71} +(-0.262865 + 1.32151i) q^{73} +(56.7843 - 84.9838i) q^{74} +(19.2802 + 7.98612i) q^{76} +(-34.9004 + 84.2570i) q^{77} +(-24.7128 - 16.5125i) q^{79} +(98.1004 + 19.5134i) q^{80} +(57.5026 - 38.4220i) q^{82} +(62.2748 - 25.7951i) q^{83} +(-89.4535 + 17.7934i) q^{85} -160.285 q^{86} +(56.4655 + 84.5065i) q^{88} +(-90.1397 + 90.1397i) q^{89} +(-23.5444 + 35.2368i) q^{91} +(-2.13408 - 10.7288i) q^{92} +(-12.4814 + 30.1327i) q^{94} +(-131.476 + 26.1522i) q^{95} +(-66.3366 - 13.1952i) q^{97} +(15.5581 + 15.5581i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8} + 16 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{14} + 80 q^{20} - 104 q^{22} + 56 q^{23} + 64 q^{25} - 176 q^{26} + 152 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32}+ \cdots + 120 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8 + 16 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^14 + 80 * q^20 - 104 * q^22 + 56 * q^23 + 64 * q^25 - 176 * q^26 + 152 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 + 160 * q^35 + 32 * q^37 + 120 * q^38 + 64 * q^40 - 48 * q^41 - 232 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 120 * q^56 + 240 * q^58 + 48 * q^59 - 160 * q^61 + 168 * q^62 - 64 * q^64 + 96 * q^65 - 272 * q^68 + 224 * q^70 - 40 * q^71 + 48 * q^73 + 160 * q^74 + 80 * q^76 + 48 * q^77 - 136 * q^79 + 240 * q^80 - 64 * q^82 + 264 * q^83 - 272 * q^85 - 832 * q^86 + 264 * q^88 - 160 * q^89 + 320 * q^91 - 24 * q^92 + 32 * q^94 - 272 * q^95 + 48 * q^97 + 120 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{5}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	0.841487	+	2.03153i	0.420744	+	1.01577i	0.982129	+	0.188210i	$0.0602687\pi$
$2$	0.841487	+	2.03153i	0.420744	+	1.01577i	−0.561385	+	0.827555i	$0.689731\pi$
$3$		0			0
$3$		0			0
$4$	−0.590587	+	0.590587i	−0.147647	+	0.147647i
$5$	1.04667	−	5.26197i	0.209334	−	1.05239i	−0.723014	−	0.690833i	$-0.757244\pi$
$5$	1.04667	−	5.26197i	0.209334	−	1.05239i	0.932348	−	0.361561i	$-0.117756\pi$
$6$		0			0
$7$	1.21824	+	6.12453i	0.174035	+	0.874933i	0.964835	+	0.262858i	$0.0846649\pi$
$7$	1.21824	+	6.12453i	0.174035	+	0.874933i	−0.790800	+	0.612075i	$0.790335\pi$
$8$	6.42935	+	2.66313i	0.803669	+	0.332891i
$9$		0			0
$10$	11.5706	−	2.30154i	1.15706	−	0.230154i
$11$	12.1433	+	8.11392i	1.10394	+	0.737629i	0.967463	−	0.253014i	$-0.0814218\pi$
$11$	12.1433	+	8.11392i	1.10394	+	0.737629i	0.136478	+	0.990643i	$0.456422\pi$
$12$		0			0
$13$	4.79884	+	4.79884i	0.369141	+	0.369141i	0.867164	−	0.498023i	$-0.165940\pi$
$13$	4.79884	+	4.79884i	0.369141	+	0.369141i	−0.498023	+	0.867164i	$0.665940\pi$
$14$	−11.4170	+	7.62861i	−0.815502	+	0.544901i
$15$		0			0
$16$			18.6433i			1.16520i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$17$	−6.50562	−	15.7060i	−0.382683	−	0.923880i
$18$		0			0
$19$	−9.56175	−	23.0841i	−0.503250	−	1.21495i	−0.947704	−	0.319151i	$-0.896602\pi$
$19$	−9.56175	−	23.0841i	−0.503250	−	1.21495i	0.444454	−	0.895802i	$-0.353398\pi$
$20$	2.48950	+	3.72580i	0.124475	+	0.186290i
$21$		0			0
$22$	−6.26521	+	31.4973i	−0.284782	+	1.43170i
$23$	−7.27639	+	10.8899i	−0.316365	+	0.473474i	−0.955238	−	0.295839i	$-0.904401\pi$
$23$	−7.27639	+	10.8899i	−0.316365	+	0.473474i	0.638873	+	0.769312i	$0.279401\pi$
$24$		0			0
$25$	−3.49585	−	1.44803i	−0.139834	−	0.0579211i
$26$	−5.71082	+	13.7871i	−0.219647	+	0.530274i
$27$		0			0
$28$	−4.33654	−	2.89759i	−0.154877	−	0.103485i
$29$	−32.3980	−	6.44436i	−1.11717	−	0.222219i	−0.398228	−	0.917287i	$-0.630375\pi$
$29$	−32.3980	−	6.44436i	−1.11717	−	0.222219i	−0.718945	+	0.695067i	$0.755375\pi$
$30$		0			0
$31$	−1.00960	+	0.674593i	−0.0325678	+	0.0217611i	−0.571748	−	0.820430i	$-0.693734\pi$
$31$	−1.00960	+	0.674593i	−0.0325678	+	0.0217611i	0.539180	+	0.842191i	$0.318734\pi$
$32$	−12.1570	+	5.03558i	−0.379905	+	0.157362i
$33$		0			0
$34$	26.4327	−	26.4327i	0.777433	−	0.777433i
$35$	33.5022			0.957206
$36$		0			0
$37$	−25.8238	−	38.6481i	−0.697941	−	1.04454i	−0.995944	−	0.0899781i	$-0.971320\pi$
$37$	−25.8238	−	38.6481i	−0.697941	−	1.04454i	0.298002	−	0.954565i	$-0.403680\pi$
$38$	38.8500	−	38.8500i	1.02237	−	1.02237i
$39$		0			0
$40$	20.7427	−	31.0437i	0.518568	−	0.776092i
$41$	−6.13577	−	30.8466i	−0.149653	−	0.752356i	−0.980602	−	0.196008i	$-0.937202\pi$
$41$	−6.13577	−	30.8466i	−0.149653	−	0.752356i	0.830949	−	0.556348i	$-0.187798\pi$
$42$		0			0
$43$	−27.8948	+	67.3441i	−0.648717	+	1.56614i	0.165901	+	0.986142i	$0.446947\pi$
$43$	−27.8948	+	67.3441i	−0.648717	+	1.56614i	−0.814617	+	0.579999i	$0.803053\pi$
$44$	−11.9637	+	2.37972i	−0.271902	+	0.0540846i
$45$		0			0
$46$	−28.2461	−	5.61851i	−0.614047	−	0.122141i
$47$	10.4882	+	10.4882i	0.223153	+	0.223153i	0.809825	−	0.586672i	$-0.199562\pi$
$47$	10.4882	+	10.4882i	0.223153	+	0.223153i	−0.586672	+	0.809825i	$0.699562\pi$
$48$		0			0
$49$	9.24438	−	3.82915i	0.188661	−	0.0781458i
$50$		−	8.32041i		−	0.166408i
$51$		0			0
$52$	−5.66826			−0.109005
$53$	1.97838	+	4.77624i	0.0373280	+	0.0901178i	0.941444	−	0.337169i	$-0.109469\pi$
$53$	1.97838	+	4.77624i	0.0373280	+	0.0901178i	−0.904116	+	0.427287i	$0.859469\pi$
$54$		0			0
$55$	55.4053	−	55.4053i	1.00737	−	1.00737i
$56$	−8.47786	+	42.6211i	−0.151390	+	0.761091i
$57$		0			0
$58$	−14.1706	−	71.2404i	−0.244321	−	1.22828i
$59$	−26.1013	−	10.8115i	−0.442394	−	0.183246i	0.150356	−	0.988632i	$-0.451958\pi$
$59$	−26.1013	−	10.8115i	−0.442394	−	0.183246i	−0.592751	+	0.805386i	$0.701958\pi$
$60$		0			0
$61$	−81.0541	+	16.1227i	−1.32876	+	0.264306i	−0.807891	−	0.589332i	$-0.799391\pi$
$61$	−81.0541	+	16.1227i	−1.32876	+	0.264306i	−0.520866	+	0.853639i	$0.674391\pi$
$62$	−2.22002	−	1.48337i	−0.0358068	−	0.0239254i
$63$		0			0
$64$	32.2713	+	32.2713i	0.504239	+	0.504239i
$65$	30.2741	−	20.2285i	0.465756	−	0.311208i
$66$		0			0
$67$		−	44.5324i		−	0.664663i	−0.943163	−	0.332332i	$-0.892165\pi$
$67$		−	44.5324i		−	0.664663i	0.943163	−	0.332332i	$-0.107835\pi$
$68$	13.1179	+	5.43359i	0.192910	+	0.0799058i
$69$		0			0
$70$	28.1917	+	68.0607i	0.402738	+	0.972296i
$71$	−32.1978	−	48.1875i	−0.453491	−	0.678697i	0.532323	−	0.846541i	$-0.321319\pi$
$71$	−32.1978	−	48.1875i	−0.453491	−	0.678697i	−0.985813	+	0.167845i	$0.946319\pi$
$72$		0			0
$73$	−0.262865	+	1.32151i	−0.00360089	+	0.0181029i	−0.982544	−	0.186031i	$-0.940438\pi$
$73$	−0.262865	+	1.32151i	−0.00360089	+	0.0181029i	0.978943	+	0.204133i	$0.0654377\pi$
$74$	56.7843	−	84.9838i	0.767356	−	1.14843i
$75$		0			0
$76$	19.2802	+	7.98612i	0.253687	+	0.105081i
$77$	−34.9004	+	84.2570i	−0.453252	+	1.09425i
$78$		0			0
$79$	−24.7128	−	16.5125i	−0.312820	−	0.209020i	0.389242	−	0.921136i	$-0.372737\pi$
$79$	−24.7128	−	16.5125i	−0.312820	−	0.209020i	−0.702062	+	0.712116i	$0.747737\pi$
$80$	98.1004	+	19.5134i	1.22626	+	0.243917i
$81$		0			0
$82$	57.5026	−	38.4220i	0.701252	−	0.468561i
$83$	62.2748	−	25.7951i	0.750298	−	0.310784i	0.0254351	−	0.999676i	$-0.491903\pi$
$83$	62.2748	−	25.7951i	0.750298	−	0.310784i	0.724863	+	0.688893i	$0.241903\pi$
$84$		0			0
$85$	−89.4535	+	17.7934i	−1.05239	+	0.209334i
$86$	−160.285			−1.86377
$87$		0			0
$88$	56.4655	+	84.5065i	0.641653	+	0.960302i
$89$	−90.1397	+	90.1397i	−1.01281	+	1.01281i	−0.0128890	+	0.999917i	$0.504103\pi$
$89$	−90.1397	+	90.1397i	−1.01281	+	1.01281i	−0.999917	+	0.0128890i	$0.995897\pi$
$90$		0			0
$91$	−23.5444	+	35.2368i	−0.258730	+	0.387217i
$92$	−2.13408	−	10.7288i	−0.0231966	−	0.116617i
$93$		0			0
$94$	−12.4814	+	30.1327i	−0.132781	+	0.320561i
$95$	−131.476	+	26.1522i	−1.38396	+	0.275286i
$96$		0			0
$97$	−66.3366	−	13.1952i	−0.683882	−	0.136033i	−0.159091	−	0.987264i	$-0.550856\pi$
$97$	−66.3366	−	13.1952i	−0.683882	−	0.136033i	−0.524791	+	0.851231i	$0.675856\pi$
$98$	15.5581	+	15.5581i	0.158756	+	0.158756i
$99$		0			0
$100$	2.91979	−	1.20941i	0.0291979	−	0.0120941i
$101$			34.6405i			0.342975i	0.985186	+	0.171488i	$0.0548573\pi$
$101$			34.6405i			0.342975i	−0.985186	+	0.171488i	$0.945143\pi$
$102$		0			0
$103$	151.166			1.46763			0.733817	−	0.679347i	$-0.237737\pi$
$103$	151.166			1.46763			0.733817	+	0.679347i	$0.237737\pi$
$104$	18.0735	+	43.6333i	0.173784	+	0.419551i
$105$		0			0
$106$	−8.03830	+	8.03830i	−0.0758330	+	0.0758330i
$107$	1.86075	−	9.35463i	0.0173902	−	0.0874264i	−0.971116	−	0.238610i	$-0.923308\pi$
$107$	1.86075	−	9.35463i	0.0173902	−	0.0874264i	0.988506	+	0.151183i	$0.0483083\pi$
$108$		0			0
$109$	22.6951	+	114.096i	0.208212	+	1.04675i	0.933574	+	0.358385i	$0.116673\pi$
$109$	22.6951	+	114.096i	0.208212	+	1.04675i	−0.725362	+	0.688368i	$0.758327\pi$
$110$	159.180	+	65.9347i	1.44710	+	0.599406i
$111$		0			0
$112$	−114.181	+	22.7121i	−1.01948	+	0.202786i
$113$	54.8360	+	36.6403i	0.485274	+	0.324250i	0.774026	−	0.633154i	$-0.218240\pi$
$113$	54.8360	+	36.6403i	0.485274	+	0.324250i	−0.288751	+	0.957404i	$0.593240\pi$
$114$		0			0
$115$	49.6863	+	49.6863i	0.432055	+	0.432055i
$116$	22.9398	−	15.3279i	0.197757	−	0.132137i
$117$		0			0
$118$		−	62.1233i		−	0.526468i
$119$	88.2661	−	58.9775i	0.741732	−	0.495609i
$120$		0			0
$121$	35.3203	+	85.2709i	0.291904	+	0.704718i
$122$	−100.960	−	151.097i	−0.827539	−	1.23850i
$123$		0			0
$124$	0.197851	−	0.994662i	0.00159557	−	0.00802147i
$125$	63.2382	−	94.6427i	0.505906	−	0.757141i
$126$		0			0
$127$	88.2580	+	36.5576i	0.694945	+	0.287855i	0.702059	−	0.712119i	$-0.252264\pi$
$127$	88.2580	+	36.5576i	0.694945	+	0.287855i	−0.00711395	+	0.999975i	$0.502264\pi$
$128$	−58.5465	+	141.344i	−0.457395	+	1.10425i
$129$		0			0
$130$	66.5702	+	44.4808i	0.512078	+	0.342160i
$131$	−42.0736	−	8.36897i	−0.321173	−	0.0638852i	0.0318711	−	0.999492i	$-0.489853\pi$
$131$	−42.0736	−	8.36897i	−0.321173	−	0.0638852i	−0.353044	+	0.935607i	$0.614853\pi$
$132$		0			0
$133$	129.731	−	86.6833i	0.975419	−	0.651754i
$134$	90.4690	−	37.4735i	0.675142	−	0.279653i
$135$		0			0
$136$		−	118.304i		−	0.869885i
$137$	63.8232			0.465863			0.232931	−	0.972493i	$-0.425168\pi$
$137$	63.8232			0.465863			0.232931	+	0.972493i	$0.425168\pi$
$138$		0			0
$139$	−145.186	−	217.286i	−1.04450	−	1.56321i	−0.805868	−	0.592095i	$-0.798301\pi$
$139$	−145.186	−	217.286i	−1.04450	−	1.56321i	−0.238632	−	0.971110i	$-0.576699\pi$
$140$	−19.7860	+	19.7860i	−0.141328	+	0.141328i
$141$		0			0
$142$	70.8002	−	105.960i	0.498593	−	0.746197i
$143$	19.3365	+	97.2113i	0.135220	+	0.679799i
$144$		0			0
$145$	−67.8201	+	163.732i	−0.467725	+	1.12919i
$146$	−2.90589	+	0.578017i	−0.0199033	+	0.00395902i
$147$		0			0
$148$	38.0763	+	7.57384i	0.257272	+	0.0511746i
$149$	83.6010	+	83.6010i	0.561080	+	0.561080i	0.929614	−	0.368534i	$-0.120140\pi$
$149$	83.6010	+	83.6010i	0.561080	+	0.561080i	−0.368534	+	0.929614i	$0.620140\pi$
$150$		0			0
$151$	25.5851	−	10.5977i	0.169437	−	0.0701833i	−0.296352	−	0.955079i	$-0.595770\pi$
$151$	25.5851	−	10.5977i	0.169437	−	0.0701833i	0.465790	+	0.884895i	$0.345770\pi$
$152$		−	173.880i		−	1.14395i
$153$		0			0
$154$	−200.539			−1.30220
$155$	2.49297	+	6.01857i	0.0160837	+	0.0388295i
$156$		0			0
$157$	−55.8958	+	55.8958i	−0.356024	+	0.356024i	−0.862345	−	0.506321i	$-0.831005\pi$
$157$	−55.8958	+	55.8958i	−0.356024	+	0.356024i	0.506321	+	0.862345i	$0.331005\pi$
$158$	12.7503	−	64.0998i	0.0806978	−	0.405695i
$159$		0			0
$160$	13.7727	+	69.2402i	0.0860796	+	0.432751i
$161$	−75.5599	−	31.2979i	−0.469316	−	0.194397i
$162$		0			0
$163$	−54.4489	+	10.8306i	−0.334042	+	0.0664451i	−0.359262	−	0.933237i	$-0.616971\pi$
$163$	−54.4489	+	10.8306i	−0.334042	+	0.0664451i	0.0252196	+	0.999682i	$0.491971\pi$
$164$	21.8413	+	14.5939i	0.133179	+	0.0889871i
$165$		0			0
$166$	104.807	+	104.807i	0.631367	+	0.631367i
$167$	42.9537	−	28.7008i	0.257208	−	0.171861i	−0.420281	−	0.907394i	$-0.638068\pi$
$167$	42.9537	−	28.7008i	0.257208	−	0.171861i	0.677489	+	0.735533i	$0.263068\pi$
$168$		0			0
$169$		−	122.942i		−	0.727470i
$170$	−111.422	−	166.755i	−0.655423	−	0.980910i
$171$		0			0
$172$	−23.2982	−	56.2468i	−0.135455	−	0.327016i
$173$	10.2620	+	15.3581i	0.0593178	+	0.0887754i	0.859943	−	0.510390i	$-0.170499\pi$
$173$	10.2620	+	15.3581i	0.0593178	+	0.0887754i	−0.800625	+	0.599166i	$0.795499\pi$
$174$		0			0
$175$	4.60969	−	23.1745i	0.0263411	−	0.132425i
$176$	−151.270	+	226.392i	−0.859489	+	1.28632i
$177$		0			0
$178$	−258.973	−	107.270i	−1.45490	−	0.602641i
$179$	−23.9825	+	57.8989i	−0.133980	+	0.323457i	−0.976604	−	0.215046i	$-0.931010\pi$
$179$	−23.9825	+	57.8989i	−0.133980	+	0.323457i	0.842624	+	0.538503i	$0.181010\pi$
$180$		0			0
$181$	86.9711	+	58.1122i	0.480503	+	0.321062i	0.772124	−	0.635472i	$-0.219194\pi$
$181$	86.9711	+	58.1122i	0.480503	+	0.321062i	−0.291621	+	0.956534i	$0.594194\pi$
$182$	−91.3969	−	18.1800i	−0.502181	−	0.0998899i
$183$		0			0
$184$	−75.7837	+	50.6370i	−0.411868	+	0.275201i
$185$	−230.394	+	95.4324i	−1.24537	+	0.515851i
$186$		0			0
$187$	48.4369	−	243.509i	0.259021	−	1.30219i
$188$	−12.3883			−0.0658954
$189$		0			0
$190$	−163.764	−	245.091i	−0.861917	−	1.28995i
$191$	137.930	−	137.930i	0.722145	−	0.722145i	−0.246897	−	0.969042i	$-0.579411\pi$
$191$	137.930	−	137.930i	0.722145	−	0.722145i	0.969042	+	0.246897i	$0.0794109\pi$
$192$		0			0
$193$	49.1142	−	73.5045i	0.254478	−	0.380853i	−0.682131	−	0.731230i	$-0.738947\pi$
$193$	49.1142	−	73.5045i	0.254478	−	0.380853i	0.936609	+	0.350377i	$0.113947\pi$
$194$	−29.0150	−	145.868i	−0.149562	−	0.751899i
$195$		0			0
$196$	−3.19816	+	7.72105i	−0.0163172	+	0.0393931i
$197$	−252.430	+	50.2114i	−1.28137	+	0.254880i	−0.788398	−	0.615165i	$-0.789089\pi$
$197$	−252.430	+	50.2114i	−1.28137	+	0.254880i	−0.492972	+	0.870045i	$0.664089\pi$
$198$		0			0
$199$	223.079	+	44.3732i	1.12100	+	0.222981i	0.720594	−	0.693357i	$-0.243869\pi$
$199$	223.079	+	44.3732i	1.12100	+	0.222981i	0.400406	+	0.916338i	$0.368869\pi$
$200$	−18.6198	−	18.6198i	−0.0930988	−	0.0930988i
$201$		0			0
$202$	−70.3732	+	29.1495i	−0.348382	+	0.144305i
$203$		−	206.273i		−	1.01612i
$204$		0			0
$205$	−168.736			−0.823103
$206$	127.204	+	307.099i	0.617498	+	1.49077i
$207$		0			0
$208$	−89.4660	+	89.4660i	−0.430125	+	0.430125i
$209$	71.1910	−	357.901i	0.340627	−	1.71245i
$210$		0			0
$211$	1.57784	+	7.93236i	0.00747794	+	0.0375941i	0.984344	−	0.176257i	$-0.0563991\pi$
$211$	1.57784	+	7.93236i	0.00747794	+	0.0375941i	−0.976866	+	0.213852i	$0.931399\pi$
$212$	−3.98919	−	1.65238i	−0.0188169	−	0.00779423i
$213$		0			0
$214$	20.5700	−	4.09163i	0.0961215	−	0.0191198i
$215$	325.166	+	217.269i	1.51240	+	1.01055i
$216$		0			0
$217$	−5.36151	−	5.36151i	−0.0247074	−	0.0247074i
$218$	−212.692	+	142.116i	−0.975651	+	0.651909i
$219$		0			0
$220$			65.4433i			0.297469i
$221$	44.1509	−	106.590i	0.199778	−	0.482306i
$222$		0			0
$223$	18.7769	+	45.3315i	0.0842014	+	0.203280i	0.960372	−	0.278720i	$-0.0899103\pi$
$223$	18.7769	+	45.3315i	0.0842014	+	0.203280i	−0.876171	+	0.482001i	$0.839910\pi$
$224$	−45.6507	−	68.3211i	−0.203798	−	0.305005i
$225$		0			0
$226$	−28.2920	+	142.233i	−0.125186	+	0.629351i
$227$	93.3694	−	139.737i	0.411319	−	0.615582i	−0.566743	−	0.823894i	$-0.691797\pi$
$227$	93.3694	−	139.737i	0.411319	−	0.615582i	0.978062	+	0.208312i	$0.0667969\pi$
$228$		0			0
$229$	114.723	+	47.5197i	0.500972	+	0.207510i	0.618836	−	0.785520i	$-0.287605\pi$
$229$	114.723	+	47.5197i	0.500972	+	0.207510i	−0.117864	+	0.993030i	$0.537605\pi$
$230$	−59.1289	+	142.750i	−0.257082	+	0.620651i
$231$		0			0
$232$	−191.136	−	127.713i	−0.823863	−	0.550487i
$233$	346.291	+	68.8815i	1.48623	+	0.295629i	0.870436	−	0.492281i	$-0.163837\pi$
$233$	346.291	+	68.8815i	1.48623	+	0.295629i	0.615791	+	0.787910i	$0.288837\pi$
$234$		0			0
$235$	66.1661	−	44.2108i	0.281558	−	0.188131i
$236$	21.8002	−	9.02993i	0.0923737	−	0.0382624i
$237$		0			0
$238$	194.089	+	129.686i	0.815502	+	0.544901i
$239$	−206.527			−0.864131			−0.432066	−	0.901842i	$-0.642215\pi$
$239$	−206.527			−0.864131			−0.432066	+	0.901842i	$0.642215\pi$
$240$		0			0
$241$	160.021	+	239.488i	0.663988	+	0.993728i	0.998678	+	0.0513996i	$0.0163682\pi$
$241$	160.021	+	239.488i	0.663988	+	0.993728i	−0.334691	+	0.942328i	$0.608632\pi$
$242$	−143.509	+	143.509i	−0.593011	+	0.593011i
$243$		0			0
$244$	38.3477	−	57.3913i	0.157163	−	0.235210i
$245$	−10.4730	−	52.6515i	−0.0427471	−	0.214904i
$246$		0			0
$247$	64.8915	−	156.662i	0.262719	−	0.634259i
$248$	−8.28761	+	1.64851i	−0.0334178	+	0.00664721i
$249$		0			0
$250$	245.484	+	48.8297i	0.981935	+	0.195319i
$251$	−191.096	−	191.096i	−0.761337	−	0.761337i	0.215227	−	0.976564i	$-0.430951\pi$
$251$	−191.096	−	191.096i	−0.761337	−	0.761337i	−0.976564	+	0.215227i	$0.930951\pi$
$252$		0			0
$253$	−176.720	+	73.1996i	−0.698496	+	0.289327i
$254$			210.062i			0.827014i
$255$		0			0
$256$	−153.856			−0.601002
$257$	20.2061	+	48.7819i	0.0786230	+	0.189813i	0.958303	−	0.285753i	$-0.0922436\pi$
$257$	20.2061	+	48.7819i	0.0786230	+	0.189813i	−0.879680	+	0.475565i	$0.842244\pi$
$258$		0			0
$259$	205.242	−	205.242i	0.792439	−	0.792439i
$260$	−5.93280	+	29.8262i	−0.0228185	+	0.114716i
$261$		0			0
$262$	−18.4026	−	92.5162i	−0.0702390	−	0.353115i
$263$	468.907	+	194.228i	1.78292	+	0.738509i	0.991947	+	0.126654i	$0.0404239\pi$
$263$	468.907	+	194.228i	1.78292	+	0.738509i	0.790970	+	0.611854i	$0.209576\pi$
$264$		0			0
$265$	27.2032	−	5.41105i	0.102654	−	0.0204191i
$266$	285.266	+	190.609i	1.07243	+	0.716575i
$267$		0			0
$268$	26.3003	+	26.3003i	0.0981353	+	0.0981353i
$269$	−146.551	+	97.9225i	−0.544801	+	0.364024i	−0.797310	−	0.603570i	$-0.793744\pi$
$269$	−146.551	+	97.9225i	−0.544801	+	0.364024i	0.252509	+	0.967595i	$0.418744\pi$
$270$		0			0
$271$			464.255i			1.71312i	0.516050	+	0.856559i	$0.327402\pi$
$271$			464.255i			1.71312i	−0.516050	+	0.856559i	$0.672598\pi$
$272$	292.810	−	121.286i	1.07651	−	0.445905i
$273$		0			0
$274$	53.7064	+	129.659i	0.196009	+	0.473207i
$275$	−30.7021	−	45.9489i	−0.111644	−	0.167087i
$276$		0			0
$277$	34.4498	−	173.191i	0.124368	−	0.625238i	−0.867445	−	0.497534i	$-0.834239\pi$
$277$	34.4498	−	173.191i	0.124368	−	0.625238i	0.991812	−	0.127704i	$-0.0407609\pi$
$278$	319.250	−	477.792i	1.14838	−	1.71868i
$279$		0			0
$280$	215.398	+	89.2206i	0.769277	+	0.318645i
$281$	−152.875	+	369.073i	−0.544040	+	1.31343i	0.377811	+	0.925883i	$0.376677\pi$
$281$	−152.875	+	369.073i	−0.544040	+	1.31343i	−0.921851	+	0.387545i	$0.873323\pi$
$282$		0			0
$283$	297.348	+	198.682i	1.05070	+	0.702055i	0.955975	−	0.293448i	$-0.0948029\pi$
$283$	297.348	+	198.682i	1.05070	+	0.702055i	0.0947249	+	0.995503i	$0.469803\pi$
$284$	47.4745	+	9.44326i	0.167164	+	0.0332509i
$285$		0			0
$286$	−181.216	+	121.085i	−0.633623	+	0.423373i
$287$	181.446	−	75.1574i	0.632216	−	0.261872i
$288$		0			0
$289$	−204.354	+	204.354i	−0.707107	+	0.707107i
$290$	−389.697			−1.34378
$291$		0			0
$292$	−0.625222	−	0.935711i	−0.00214117	−	0.00320449i
$293$	169.002	−	169.002i	0.576800	−	0.576800i	−0.357220	−	0.934020i	$-0.616275\pi$
$293$	169.002	−	169.002i	0.576800	−	0.576800i	0.934020	+	0.357220i	$0.116275\pi$
$294$		0			0
$295$	−84.2093	+	126.028i	−0.285455	+	0.427214i
$296$	−63.1058	−	317.254i	−0.213195	−	1.07181i
$297$		0			0
$298$	−99.4888	+	240.187i	−0.333855	+	0.805997i
$299$	−87.1770	+	17.3406i	−0.291562	+	0.0579953i
$300$		0			0
$301$	−446.433	−	88.8011i	−1.48317	−	0.295020i
$302$	43.0590	+	43.0590i	0.142579	+	0.142579i
$303$		0			0
$304$	430.363	−	178.262i	1.41567	−	0.586389i
$305$			443.380i			1.45370i
$306$		0			0
$307$	409.955			1.33536			0.667679	−	0.744450i	$-0.267288\pi$
$307$	409.955			1.33536			0.667679	+	0.744450i	$0.267288\pi$
$308$	−29.1493	−	70.3727i	−0.0946407	−	0.228483i
$309$		0			0
$310$	−10.1291	+	10.1291i	−0.0326745	+	0.0326745i
$311$	−42.2576	+	212.443i	−0.135877	+	0.683098i	0.851455	+	0.524428i	$0.175721\pi$
$311$	−42.2576	+	212.443i	−0.135877	+	0.683098i	−0.987332	+	0.158670i	$0.949279\pi$
$312$		0			0
$313$	−92.3584	−	464.317i	−0.295075	−	1.48344i	−0.789246	−	0.614077i	$-0.789528\pi$
$313$	−92.3584	−	464.317i	−0.295075	−	1.48344i	0.494171	−	0.869365i	$-0.335472\pi$
$314$	−160.590	−	66.5184i	−0.511432	−	0.211842i
$315$		0			0
$316$	24.3471	−	4.84294i	0.0770479	−	0.0153258i
$317$	−213.145	−	142.419i	−0.672383	−	0.449272i	0.171939	−	0.985108i	$-0.444997\pi$
$317$	−213.145	−	142.419i	−0.672383	−	0.449272i	−0.844322	+	0.535836i	$0.819997\pi$
$318$		0			0
$319$	−341.131	−	341.131i	−1.06938	−	1.06938i
$320$	203.588	−	136.033i	0.636213	−	0.425104i
$321$		0			0
$322$		−	179.839i		−	0.558506i
$323$	−300.353	+	300.353i	−0.929884	+	0.929884i
$324$		0			0
$325$	−9.82715	−	23.7248i	−0.0302374	−	0.0729995i
$326$	−67.8206	−	101.501i	−0.208039	−	0.311352i
$327$		0			0
$328$	42.6993	−	214.664i	0.130181	−	0.654464i
$329$	−51.4579	+	77.0122i	−0.156407	+	0.234080i
$330$		0			0
$331$	208.580	+	86.3966i	0.630151	+	0.261017i	0.674817	−	0.737985i	$-0.264222\pi$
$331$	208.580	+	86.3966i	0.630151	+	0.261017i	−0.0446663	+	0.999002i	$0.514222\pi$
$332$	−21.5444	+	52.0129i	−0.0648929	+	0.156665i
$333$		0			0
$334$	94.4515	+	63.1105i	0.282789	+	0.188954i
$335$	−234.328	−	46.6108i	−0.699488	−	0.139137i
$336$		0			0
$337$	−300.276	+	200.638i	−0.891027	+	0.595365i	−0.914601	−	0.404357i	$-0.867495\pi$
$337$	−300.276	+	200.638i	−0.891027	+	0.595365i	0.0235742	+	0.999722i	$0.492495\pi$
$338$	249.761	−	103.454i	0.738938	−	0.306078i
$339$		0			0
$340$	42.3215	−	63.3386i	0.124475	−	0.186290i
$341$	−17.7335			−0.0520045
$342$		0			0
$343$	204.708	+	306.367i	0.596815	+	0.893197i
$344$	−358.691	+	358.691i	−1.04271	+	1.04271i
$345$		0			0
$346$	−22.5652	+	33.7712i	−0.0652173	+	0.0976046i
$347$	−3.09377	−	15.5534i	−0.00891575	−	0.0448225i	0.976071	−	0.217451i	$-0.0697741\pi$
$347$	−3.09377	−	15.5534i	−0.00891575	−	0.0448225i	−0.984987	+	0.172628i	$0.944774\pi$
$348$		0			0
$349$	−121.062	+	292.270i	−0.346883	+	0.837448i	0.650102	+	0.759847i	$0.274726\pi$
$349$	−121.062	+	292.270i	−0.346883	+	0.837448i	−0.996984	+	0.0776015i	$0.975274\pi$
$350$	50.9586	−	10.1363i	0.145596	−	0.0289608i
$351$		0			0
$352$	−188.484	−	37.4919i	−0.535467	−	0.106511i
$353$	−191.613	−	191.613i	−0.542812	−	0.542812i	0.381540	−	0.924352i	$-0.375394\pi$
$353$	−191.613	−	191.613i	−0.542812	−	0.542812i	−0.924352	+	0.381540i	$0.875394\pi$
$354$		0			0
$355$	−287.262	+	118.988i	−0.809188	+	0.335177i
$356$		−	106.471i		−	0.299075i
$357$		0			0
$358$	−137.804			−0.384928
$359$	−60.5865	−	146.269i	−0.168765	−	0.407434i	0.816757	−	0.576981i	$-0.195769\pi$
$359$	−60.5865	−	146.269i	−0.168765	−	0.407434i	−0.985522	+	0.169547i	$0.945769\pi$
$360$		0			0
$361$	−186.183	+	186.183i	−0.515743	+	0.515743i
$362$	−44.8717	+	225.585i	−0.123955	+	0.623163i
$363$		0			0
$364$	−6.90532	−	34.7154i	−0.0189707	−	0.0953719i
$365$	6.67862	+	2.76638i	0.0182976	+	0.00757911i
$366$		0			0
$367$	−479.595	+	95.3974i	−1.30680	+	0.259938i	−0.798892	−	0.601474i	$-0.794580\pi$
$367$	−479.595	+	95.3974i	−1.30680	+	0.259938i	−0.507906	+	0.861413i	$0.669580\pi$
$368$	−203.023	−	135.656i	−0.551694	−	0.368630i
$369$		0			0
$370$	−387.748	−	387.748i	−1.04797	−	1.04797i
$371$	−26.8421	+	17.9353i	−0.0723506	+	0.0483431i
$372$		0			0
$373$		−	573.453i		−	1.53741i	−0.639605	−	0.768704i	$-0.720902\pi$
$373$		−	573.453i		−	1.53741i	0.639605	−	0.768704i	$-0.279098\pi$
$374$	535.455	−	106.509i	1.43170	−	0.284782i
$375$		0			0
$376$	39.5008	+	95.3635i	0.105055	+	0.253626i
$377$	−124.547	−	186.398i	−0.330364	−	0.494425i
$378$		0			0
$379$	136.954	−	688.516i	0.361357	−	1.81666i	−0.189284	−	0.981922i	$-0.560617\pi$
$379$	136.954	−	688.516i	0.361357	−	1.81666i	0.550641	−	0.834742i	$-0.314383\pi$
$380$	62.2028	−	93.0930i	0.163692	−	0.244982i
$381$		0			0
$382$	396.274	+	164.142i	1.03737	+	0.429692i
$383$	118.024	−	284.935i	0.308157	−	0.743956i	−0.691608	−	0.722273i	$-0.743098\pi$
$383$	118.024	−	284.935i	0.308157	−	0.743956i	0.999765	−	0.0216830i	$-0.00690247\pi$
$384$		0			0
$385$	406.829	+	271.834i	1.05670	+	0.706063i
$386$	190.656	+	37.9238i	0.493927	+	0.0982481i
$387$		0			0
$388$	46.9704	−	31.3846i	0.121058	−	0.0808882i
$389$	−263.382	+	109.097i	−0.677076	+	0.280454i	−0.694604	−	0.719392i	$-0.744420\pi$
$389$	−263.382	+	109.097i	−0.677076	+	0.280454i	0.0175282	+	0.999846i	$0.494420\pi$
$390$		0			0
$391$	218.374	+	43.4372i	0.558500	+	0.111093i
$392$	69.6329			0.177635
$393$		0			0
$394$	−314.423	−	470.567i	−0.798027	−	1.19433i
$395$	−112.755	+	112.755i	−0.285455	+	0.285455i
$396$		0			0
$397$	69.0841	−	103.392i	0.174015	−	0.260432i	−0.734202	−	0.678931i	$-0.762444\pi$
$397$	69.0841	−	103.392i	0.174015	−	0.260432i	0.908217	+	0.418499i	$0.137444\pi$
$398$	97.5727	+	490.531i	0.245158	+	1.23249i
$399$		0			0
$400$	26.9960	−	65.1740i	0.0674899	−	0.162935i
$401$	418.770	−	83.2986i	1.04432	−	0.207727i	0.357014	−	0.934099i	$-0.383795\pi$
$401$	418.770	−	83.2986i	1.04432	−	0.207727i	0.687302	+	0.726372i	$0.258795\pi$
$402$		0			0
$403$	−8.08217	−	1.60764i	−0.0200550	−	0.00398919i
$404$	−20.4582	−	20.4582i	−0.0506391	−	0.0506391i
$405$		0			0
$406$	419.050	−	173.576i	1.03214	−	0.427528i
$407$		−	678.850i		−	1.66794i
$408$		0			0
$409$	−215.550			−0.527018			−0.263509	−	0.964657i	$-0.584880\pi$
$409$	−215.550			−0.527018			−0.263509	+	0.964657i	$0.584880\pi$
$410$	−141.989	−	342.793i	−0.346315	−	0.836079i
$411$		0			0
$412$	−89.2768	+	89.2768i	−0.216691	+	0.216691i
$413$	34.4176	−	173.029i	0.0833356	−	0.418956i
$414$		0			0
$415$	−70.5517	−	354.687i	−0.170004	−	0.854668i
$416$	−82.5042	−	34.1743i	−0.198327	−	0.0821499i
$417$		0			0
$418$	786.994	−	156.543i	1.88276	−	0.374504i
$419$	517.326	+	345.666i	1.23467	+	0.824979i	0.989504	−	0.144503i	$-0.0461584\pi$
$419$	517.326	+	345.666i	1.23467	+	0.824979i	0.245164	+	0.969482i	$0.421158\pi$
$420$		0			0
$421$	−36.3708	−	36.3708i	−0.0863916	−	0.0863916i	0.662590	−	0.748982i	$-0.269457\pi$
$421$	−36.3708	−	36.3708i	−0.0863916	−	0.0863916i	−0.748982	+	0.662590i	$0.769457\pi$
$422$	−14.7871	+	9.88042i	−0.0350405	+	0.0234133i
$423$		0			0
$424$			35.9769i			0.0848511i
$425$			64.3259i			0.151355i
$426$		0			0
$427$	−197.488	−	476.777i	−0.462500	−	1.11657i
$428$	4.42578	+	6.62365i	0.0103406	+	0.0154758i
$429$		0			0
$430$	−167.765	+	843.413i	−0.390152	+	1.96143i
$431$	−261.460	+	391.302i	−0.606635	+	0.907893i	−0.999934	−	0.0115175i	$-0.996334\pi$
$431$	−261.460	+	391.302i	−0.606635	+	0.907893i	0.393299	+	0.919411i	$0.371334\pi$
$432$		0			0
$433$	−594.595	−	246.289i	−1.37320	−	0.568798i	−0.430545	−	0.902569i	$-0.641679\pi$
$433$	−594.595	−	246.289i	−1.37320	−	0.568798i	−0.942654	+	0.333772i	$0.891679\pi$
$434$	6.38042	−	15.4037i	0.0147014	−	0.0354924i
$435$		0			0
$436$	−80.7871	−	53.9802i	−0.185291	−	0.123808i
$437$	320.958	+	63.8426i	0.734459	+	0.146093i
$438$		0			0
$439$	−688.000	+	459.707i	−1.56720	+	1.04717i	−0.597809	+	0.801638i	$0.703962\pi$
$439$	−688.000	+	459.707i	−1.56720	+	1.04717i	−0.969389	+	0.245530i	$0.921038\pi$
$440$	503.772	−	208.669i	1.14494	−	0.474248i
$441$		0			0
$442$	253.693			0.573965
$443$	−354.430			−0.800068			−0.400034	−	0.916500i	$-0.631002\pi$
$443$	−354.430			−0.800068			−0.400034	+	0.916500i	$0.631002\pi$
$444$		0			0
$445$	379.966	+	568.659i	0.853856	+	1.27789i
$446$	−76.2917	+	76.2917i	−0.171058	+	0.171058i
$447$		0			0
$448$	−158.332	+	236.961i	−0.353420	+	0.528930i
$449$	−153.330	−	770.842i	−0.341492	−	1.71680i	−0.645185	−	0.764027i	$-0.723220\pi$
$449$	−153.330	−	770.842i	−0.341492	−	1.71680i	0.303692	−	0.952770i	$-0.401780\pi$
$450$		0			0
$451$	175.778	−	424.366i	0.389752	−	0.940945i
$452$	−54.0247	+	10.7462i	−0.119524	+	0.0237747i
$453$		0			0
$454$	362.450	+	72.0957i	0.798347	+	0.158801i
$455$	160.772	+	160.772i	0.353344	+	0.353344i
$456$		0			0
$457$	300.390	−	124.426i	0.657309	−	0.272266i	−0.0289968	−	0.999580i	$-0.509231\pi$
$457$	300.390	−	124.426i	0.657309	−	0.272266i	0.686306	+	0.727313i	$0.259231\pi$
$458$			273.050i			0.596178i
$459$		0			0
$460$	−58.6882			−0.127583
$461$	94.2242	+	227.477i	0.204391	+	0.493444i	0.992522	−	0.122064i	$-0.0389512\pi$
$461$	94.2242	+	227.477i	0.204391	+	0.493444i	−0.788131	+	0.615507i	$0.788951\pi$
$462$		0			0
$463$	−248.069	+	248.069i	−0.535786	+	0.535786i	−0.922288	−	0.386503i	$-0.873683\pi$
$463$	−248.069	+	248.069i	−0.535786	+	0.535786i	0.386503	+	0.922288i	$0.373683\pi$
$464$	120.144	−	604.005i	0.258931	−	1.30174i
$465$		0			0
$466$	151.464	+	761.463i	0.325031	+	1.63404i
$467$	202.212	+	83.7591i	0.433003	+	0.179356i	0.588529	−	0.808476i	$-0.299707\pi$
$467$	202.212	+	83.7591i	0.433003	+	0.179356i	−0.155526	+	0.987832i	$0.549707\pi$
$468$		0			0
$469$	272.740	−	54.2514i	0.581536	−	0.115675i
$470$	145.493	+	97.2156i	0.309561	+	0.206842i
$471$		0			0
$472$	−139.022	−	139.022i	−0.294538	−	0.294538i
$473$	−885.161	+	591.446i	−1.87138	+	1.25041i
$474$		0			0
$475$			94.5441i			0.199040i
$476$	−17.2974	+	86.9601i	−0.0363392	+	0.182689i
$477$		0			0
$478$	−173.790	−	419.566i	−0.363578	−	0.877754i
$479$	279.157	+	417.789i	0.582792	+	0.872210i	0.999318	−	0.0369135i	$-0.0117526\pi$
$479$	279.157	+	417.789i	0.582792	+	0.872210i	−0.416526	+	0.909124i	$0.636753\pi$
$480$		0			0
$481$	61.5415	−	309.390i	0.127945	−	0.643223i
$482$	−351.872	+	526.614i	−0.730025	+	1.09256i
$483$		0			0
$484$	−71.2196	−	29.5001i	−0.147148	−	0.0609506i
$485$	−138.865	+	335.250i	−0.286320	+	0.691238i
$486$		0			0
$487$	−209.352	−	139.885i	−0.429882	−	0.287238i	0.321745	−	0.946826i	$-0.395731\pi$
$487$	−209.352	−	139.885i	−0.429882	−	0.287238i	−0.751627	+	0.659589i	$0.770731\pi$
$488$	−564.063	−	112.199i	−1.15587	−	0.229916i
$489$		0			0
$490$	98.1502	−	65.5819i	0.200307	−	0.133841i
$491$	209.123	−	86.6215i	0.425912	−	0.176418i	−0.159423	−	0.987210i	$-0.550963\pi$
$491$	209.123	−	86.6215i	0.425912	−	0.176418i	0.585334	+	0.810792i	$0.300963\pi$
$492$		0			0
$493$	109.554	+	550.766i	0.222219	+	1.11717i
$494$	372.869			0.754796
$495$		0			0
$496$	−12.5766	−	18.8223i	−0.0253561	−	0.0379481i
$497$	255.901	−	255.901i	0.514891	−	0.514891i
$498$		0			0
$499$	−119.919	+	179.471i	−0.240318	+	0.359662i	−0.931949	−	0.362590i	$-0.881893\pi$
$499$	−119.919	+	179.471i	−0.240318	+	0.359662i	0.691631	+	0.722251i	$0.256893\pi$
$500$	18.5471	+	93.2423i	0.0370941	+	0.186485i
$501$		0			0
$502$	227.412	−	549.021i	0.453012	−	1.09367i
$503$	−865.523	+	172.163i	−1.72072	+	0.342273i	−0.954023	−	0.299735i	$-0.903102\pi$
$503$	−865.523	+	172.163i	−1.72072	+	0.342273i	−0.766698	+	0.642008i	$0.778102\pi$
$504$		0			0
$505$	182.277	+	36.2572i	0.360945	+	0.0717964i
$506$	−297.414	−	297.414i	−0.587776	−	0.587776i
$507$		0			0
$508$	−73.7144	+	30.5335i	−0.145107	+	0.0601053i
$509$		−	459.446i		−	0.902645i	−0.892361	−	0.451323i	$-0.850952\pi$
$509$		−	459.446i		−	0.902645i	0.892361	−	0.451323i	$-0.149048\pi$
$510$		0			0
$511$	−8.41386			−0.0164655
$512$	104.718	+	252.811i	0.204527	+	0.493772i
$513$		0			0
$514$	−82.0986	+	82.0986i	−0.159725	+	0.159725i
$515$	158.221	−	795.433i	0.307226	−	1.54453i
$516$		0			0
$517$	42.2612	+	212.462i	0.0817432	+	0.410951i
$518$	589.663	+	244.246i	1.13835	+	0.471518i
$519$		0			0
$520$	248.514	−	49.4326i	0.477912	−	0.0950626i
$521$	−84.0959	−	56.1911i	−0.161412	−	0.107852i	0.472241	−	0.881470i	$-0.343445\pi$
$521$	−84.0959	−	56.1911i	−0.161412	−	0.107852i	−0.633653	+	0.773617i	$0.718445\pi$
$522$		0			0
$523$	395.099	+	395.099i	0.755448	+	0.755448i	0.975490	−	0.220042i	$-0.0706196\pi$
$523$	395.099	+	395.099i	0.755448	+	0.755448i	−0.220042	+	0.975490i	$0.570620\pi$
$524$	29.7907	−	19.9055i	0.0568525	−	0.0379876i
$525$		0			0
$526$			1116.04i			2.12175i
$527$	17.1632	+	11.4681i	0.0325678	+	0.0217611i
$528$		0			0
$529$	136.796	+	330.254i	0.258593	+	0.624299i
$530$	33.8838	+	50.7108i	0.0639318	+	0.0956807i
$531$		0			0
$532$	−25.4232	+	127.811i	−0.0477880	+	0.240247i
$533$	118.583	−	177.472i	0.222483	−	0.332969i
$534$		0			0
$535$	−47.2762	−	19.5824i	−0.0883667	−	0.0366027i
$536$	118.596	−	286.315i	0.221260	−	0.534170i
$537$		0			0
$538$	−322.254	−	215.323i	−0.598985	−	0.400229i
$539$	143.327	+	28.5095i	0.265913	+	0.0528934i
$540$		0			0
$541$	−33.9436	+	22.6804i	−0.0627423	+	0.0419230i	−0.586546	−	0.809916i	$-0.699513\pi$
$541$	−33.9436	+	22.6804i	−0.0627423	+	0.0419230i	0.523804	+	0.851839i	$0.324513\pi$
$542$	−943.148	+	390.665i	−1.74012	+	0.720783i
$543$		0			0
$544$	158.177	+	158.177i	0.290767	+	0.290767i
$545$	624.125			1.14518
$546$		0			0
$547$	−37.8284	−	56.6142i	−0.0691562	−	0.103500i	0.795280	−	0.606243i	$-0.207324\pi$
$547$	−37.8284	−	56.6142i	−0.0691562	−	0.103500i	−0.864436	+	0.502743i	$0.832324\pi$
$548$	−37.6931	+	37.6931i	−0.0687830	+	0.0687830i
$549$		0			0
$550$	67.5112	−	101.038i	0.122748	−	0.183705i
$551$	161.019	+	809.498i	0.292231	+	1.46914i
$552$		0			0
$553$	71.0254	−	171.470i	0.128436	−	0.310073i
$554$	380.832	−	75.7521i	0.687422	−	0.136737i
$555$		0			0
$556$	214.071	+	42.5813i	0.385019	+	0.0765850i
$557$	208.814	+	208.814i	0.374890	+	0.374890i	0.869255	−	0.494365i	$-0.164599\pi$
$557$	208.814	+	208.814i	0.374890	+	0.374890i	−0.494365	+	0.869255i	$0.664599\pi$
$558$		0			0
$559$	−457.036	+	189.310i	−0.817595	+	0.338659i
$560$			624.591i			1.11534i
$561$		0			0
$562$	−878.426			−1.56304
$563$	−169.121	−	408.295i	−0.300393	−	0.725212i	−0.999944	−	0.0106294i	$-0.996616\pi$
$563$	−169.121	−	408.295i	−0.300393	−	0.725212i	0.699551	−	0.714583i	$-0.253384\pi$
$564$		0			0
$565$	250.195	−	250.195i	0.442824	−	0.442824i
$566$	−153.413	+	771.260i	−0.271048	+	1.36265i
$567$		0			0
$568$	−78.6820	−	395.561i	−0.138525	−	0.696411i
$569$	−595.479	−	246.656i	−1.04654	−	0.433490i	−0.207882	−	0.978154i	$-0.566657\pi$
$569$	−595.479	−	246.656i	−1.04654	−	0.433490i	−0.838654	+	0.544664i	$0.816657\pi$
$570$		0			0
$571$	−117.482	+	23.3687i	−0.205748	+	0.0409259i	−0.296888	−	0.954912i	$-0.595949\pi$
$571$	−117.482	+	23.3687i	−0.205748	+	0.0409259i	0.0911400	+	0.995838i	$0.470949\pi$
$572$	−68.8316	−	45.9918i	−0.120335	−	0.0804052i
$573$		0			0
$574$	305.369	+	305.369i	0.532002	+	0.532002i
$575$	41.2060	−	27.5330i	0.0716626	−	0.0478834i
$576$		0			0
$577$		−	177.008i		−	0.306773i	−0.988166	−	0.153387i	$-0.950982\pi$
$577$		−	177.008i		−	0.306773i	0.988166	−	0.153387i	$-0.0490180\pi$
$578$	−587.112	−	243.190i	−1.01577	−	0.420744i
$579$		0			0
$580$	−56.6444	−	136.752i	−0.0976628	−	0.235779i
$581$	233.848	+	349.979i	0.402493	+	0.602373i
$582$		0			0
$583$	−14.7299	+	74.0520i	−0.0252656	+	0.127019i
$584$	−5.20940	+	7.79642i	−0.00892021	+	0.0133500i
$585$		0			0
$586$	485.547	+	201.120i	0.828578	+	0.343208i
$587$	239.200	−	577.480i	0.407496	−	0.983781i	−0.578299	−	0.815825i	$-0.696283\pi$
$587$	239.200	−	577.480i	0.407496	−	0.983781i	0.985794	−	0.167956i	$-0.0537168\pi$
$588$		0			0
$589$	25.2259	+	16.8554i	0.0428284	+	0.0286170i
$590$	−326.891	−	65.0226i	−0.554052	−	0.110208i
$591$		0			0
$592$	720.527	−	481.441i	1.21711	−	0.813245i
$593$	138.551	−	57.3899i	0.233645	−	0.0967789i	−0.262789	−	0.964853i	$-0.584642\pi$
$593$	138.551	−	57.3899i	0.233645	−	0.0967789i	0.496434	+	0.868074i	$0.334642\pi$
$594$		0			0
$595$	−217.953	−	526.184i	−0.366307	−	0.884343i
$596$	−98.7472			−0.165683
$597$		0			0
$598$	−108.586	−	162.511i	−0.181582	−	0.271757i
$599$	217.159	−	217.159i	0.362536	−	0.362536i	−0.502210	−	0.864746i	$-0.667480\pi$
$599$	217.159	−	217.159i	0.362536	−	0.362536i	0.864746	+	0.502210i	$0.167480\pi$
$600$		0			0
$601$	225.714	−	337.804i	0.375564	−	0.562071i	−0.594753	−	0.803908i	$-0.702750\pi$
$601$	225.714	−	337.804i	0.375564	−	0.562071i	0.970317	+	0.241838i	$0.0777502\pi$
$602$	−195.266	−	981.668i	−0.324362	−	1.63068i
$603$		0			0
$604$	−8.85135	+	21.3690i	−0.0146545	+	0.0353792i
$605$	485.662	−	96.6041i	0.802747	−	0.159676i
$606$		0			0
$607$	1017.17	+	202.327i	1.67573	+	0.333323i	0.939274	−	0.343167i	$-0.111500\pi$
$607$	1017.17	+	202.327i	1.67573	+	0.333323i	0.736452	+	0.676490i	$0.236500\pi$
$608$	232.484	+	232.484i	0.382374	+	0.382374i
$609$		0			0
$610$	−900.740	+	373.099i	−1.47662	+	0.611637i
$611$			100.662i			0.164750i
$612$		0			0
$613$	132.402			0.215991			0.107995	−	0.994151i	$-0.465557\pi$
$613$	132.402			0.215991			0.107995	+	0.994151i	$0.465557\pi$
$614$	344.972	+	832.835i	0.561843	+	1.35641i
$615$		0			0
$616$	−448.774	+	448.774i	−0.728529	+	0.728529i
$617$	−49.9956	+	251.345i	−0.0810302	+	0.407366i	0.918887	+	0.394520i	$0.129089\pi$
$617$	−49.9956	+	251.345i	−0.0810302	+	0.407366i	−0.999917	+	0.0128460i	$0.995911\pi$
$618$		0			0
$619$	−17.9310	−	90.1450i	−0.0289676	−	0.145630i	0.963595	−	0.267367i	$-0.0861536\pi$
$619$	−17.9310	−	90.1450i	−0.0289676	−	0.145630i	−0.992562	+	0.121737i	$0.961154\pi$
$620$	−5.02680	−	2.08217i	−0.00810774	−	0.00335834i
$621$		0			0
$622$	−467.145	+	92.9208i	−0.751036	+	0.149390i
$623$	−661.875	−	442.251i	−1.06240	−	0.709873i
$624$		0			0
$625$	−498.708	−	498.708i	−0.797932	−	0.797932i
$626$	865.556	−	578.346i	1.38268	−	0.923875i
$627$		0			0
$628$		−	66.0226i		−	0.105131i
$629$	−439.005	+	657.018i	−0.697941	+	1.04454i
$630$		0			0
$631$	219.866	+	530.804i	0.348441	+	0.841210i	0.996805	+	0.0798795i	$0.0254536\pi$
$631$	219.866	+	530.804i	0.348441	+	0.841210i	−0.648364	+	0.761331i	$0.724546\pi$
$632$	−114.912	−	171.978i	−0.181823	−	0.272117i
$633$		0			0
$634$	109.970	−	552.855i	0.173454	−	0.872012i
$635$	284.742	−	426.147i	0.448413	−	0.671098i
$636$		0			0
$637$	62.7377	+	25.9868i	0.0984893	+	0.0407956i
$638$	405.961	−	980.076i	0.636302	−	1.53617i
$639$		0			0
$640$	682.468	+	456.011i	1.06636	+	0.712517i
$641$	966.275	+	192.204i	1.50745	+	0.299850i	0.878555	−	0.477641i	$-0.158508\pi$
$641$	966.275	+	192.204i	1.50745	+	0.299850i	0.628894	+	0.777491i	$0.283508\pi$
$642$		0			0
$643$	−29.4169	+	19.6558i	−0.0457495	+	0.0305688i	−0.578235	−	0.815870i	$-0.696258\pi$
$643$	−29.4169	+	19.6558i	−0.0457495	+	0.0305688i	0.532485	+	0.846439i	$0.321258\pi$
$644$	63.1088	−	26.1405i	0.0979950	−	0.0405909i
$645$		0			0
$646$	−862.919	−	357.433i	−1.33579	−	0.553301i
$647$	472.176			0.729793			0.364897	−	0.931048i	$-0.381104\pi$
$647$	472.176			0.729793			0.364897	+	0.931048i	$0.381104\pi$
$648$		0			0
$649$	−229.233	−	343.071i	−0.353210	−	0.528615i
$650$	39.9283	−	39.9283i	0.0614281	−	0.0614281i
$651$		0			0
$652$	25.7604	−	38.5532i	0.0395098	−	0.0591306i
$653$	124.126	+	624.023i	0.190086	+	0.955625i	0.951568	+	0.307439i	$0.0994720\pi$
$653$	124.126	+	624.023i	0.190086	+	0.955625i	−0.761482	+	0.648186i	$0.775528\pi$
$654$		0			0
$655$	−88.0746	+	212.631i	−0.134465	+	0.324627i
$656$	575.082	−	114.391i	0.876649	−	0.174376i
$657$		0			0
$658$	−199.754	−	39.7335i	−0.303577	−	0.0603853i
$659$	−128.530	−	128.530i	−0.195037	−	0.195037i	0.602831	−	0.797869i	$-0.294039\pi$
$659$	−128.530	−	128.530i	−0.195037	−	0.195037i	−0.797869	+	0.602831i	$0.794039\pi$
$660$		0			0
$661$	1075.49	−	445.481i	1.62706	−	0.673950i	0.632161	−	0.774837i	$-0.282168\pi$
$661$	1075.49	−	445.481i	1.62706	−	0.673950i	0.994898	+	0.100887i	$0.0321681\pi$
$662$			496.438i			0.749906i
$663$		0			0
$664$	469.082			0.706449
$665$	−320.340	−	773.368i	−0.481714	−	1.16296i
$666$		0			0
$667$	305.919	−	305.919i	0.458649	−	0.458649i
$668$	−8.41761	+	42.3182i	−0.0126012	+	0.0633506i
$669$		0			0
$670$	−102.493	−	515.268i	−0.152975	−	0.769056i
$671$	−1115.09	−	461.884i	−1.66183	−	0.688352i
$672$		0			0
$673$	105.260	−	20.9375i	0.156404	−	0.0311106i	−0.116267	−	0.993218i	$-0.537093\pi$
$673$	105.260	−	20.9375i	0.156404	−	0.0311106i	0.272671	+	0.962107i	$0.412093\pi$
$674$	−660.281	−	441.186i	−0.979645	−	0.654578i
$675$		0			0
$676$	72.6081	+	72.6081i	0.107408	+	0.107408i
$677$	876.782	−	585.847i	1.29510	−	0.865358i	0.299057	−	0.954235i	$-0.403328\pi$
$677$	876.782	−	585.847i	1.29510	−	0.865358i	0.996043	+	0.0888773i	$0.0283279\pi$
$678$		0			0
$679$		−	422.355i		−	0.622025i
$680$	−622.515	−	123.826i	−0.915463	−	0.182097i
$681$		0			0
$682$	−14.9225	−	36.0262i	−0.0218805	−	0.0528243i
$683$	339.367	+	507.899i	0.496877	+	0.743629i	0.992143	−	0.125113i	$-0.0399292\pi$
$683$	339.367	+	507.899i	0.496877	+	0.743629i	−0.495265	+	0.868742i	$0.664929\pi$
$684$		0			0
$685$	66.8019	−	335.836i	0.0975210	−	0.490271i
$686$	−450.134	+	673.673i	−0.656172	+	0.982031i
$687$		0			0
$688$	−1255.51	−	520.051i	−1.82488	−	0.755888i
$689$	−13.4265	+	32.4143i	−0.0194869	+	0.0470455i
$690$		0			0
$691$	−815.612	−	544.975i	−1.18034	−	0.788675i	−0.198816	−	0.980037i	$-0.563710\pi$
$691$	−815.612	−	544.975i	−1.18034	−	0.788675i	−0.981520	+	0.191362i	$0.938710\pi$
$692$	−15.1309	−	3.00972i	−0.0218655	−	0.00434931i
$693$		0			0
$694$	28.9939	−	19.3731i	0.0417779	−	0.0279151i
$695$	−1295.31	+	536.536i	−1.86376	+	0.771994i
$696$		0			0
$697$	−444.558	+	297.044i	−0.637817	+	0.426176i
$698$	−695.626			−0.996600
$699$		0			0
$700$	10.9641	+	16.4089i	0.0156630	+	0.0234413i
$701$	−52.7814	+	52.7814i	−0.0752944	+	0.0752944i	−0.743751	−	0.668457i	$-0.766955\pi$
$701$	−52.7814	+	52.7814i	−0.0752944	+	0.0752944i	0.668457	+	0.743751i	$0.266955\pi$
$702$		0			0
$703$	−645.236	+	965.663i	−0.917832	+	1.37363i
$704$	130.035	+	653.728i	0.184708	+	0.928591i
$705$		0			0
$706$	228.027	−	550.507i	0.322985	−	0.779755i
$707$	−212.157	+	42.2006i	−0.300080	+	0.0596896i
$708$		0			0
$709$	−752.626	−	149.707i	−1.06153	−	0.211152i	−0.366711	−	0.930335i	$-0.619516\pi$
$709$	−752.626	−	149.707i	−1.06153	−	0.211152i	−0.694821	+	0.719183i	$0.744516\pi$
$710$	−483.454	−	483.454i	−0.680921	−	0.680921i
$711$		0			0
$712$	−819.594	+	339.487i	−1.15111	+	0.476807i
$713$		−	15.9030i		−	0.0223044i
$714$		0			0
$715$	531.762			0.743723
$716$	−20.0306	−	48.3580i	−0.0279756	−	0.0675392i
$717$		0			0
$718$	246.167	−	246.167i	0.342851	−	0.342851i
$719$	−224.919	+	1130.74i	−0.312822	+	1.57266i	0.429785	+	0.902931i	$0.358590\pi$
$719$	−224.919	+	1130.74i	−0.312822	+	1.57266i	−0.742606	+	0.669729i	$0.766410\pi$
$720$		0			0
$721$	184.157	+	925.822i	0.255419	+	1.28408i
$722$	−534.907	−	221.566i	−0.740869	−	0.306878i
$723$		0			0
$724$	−85.6842	+	17.0437i	−0.118348	+	0.0235410i
$725$	103.927	+	69.4417i	0.143347	+	0.0957817i
$726$		0			0
$727$	195.955	+	195.955i	0.269539	+	0.269539i	0.828914	−	0.559376i	$-0.188959\pi$
$727$	195.955	+	195.955i	0.269539	+	0.269539i	−0.559376	+	0.828914i	$0.688959\pi$
$728$	−245.216	+	163.848i	−0.336834	+	0.225066i
$729$		0			0
$730$			15.8957i			0.0217749i
$731$	1239.18			1.69518
$732$		0			0
$733$	169.675	+	409.632i	0.231480	+	0.558843i	0.996352	−	0.0853397i	$-0.0271976\pi$
$733$	169.675	+	409.632i	0.231480	+	0.558843i	−0.764871	+	0.644183i	$0.777198\pi$
$734$	−597.376	−	894.036i	−0.813863	−	1.21803i
$735$		0			0
$736$	33.6219	−	169.029i	0.0456820	−	0.229659i
$737$	361.333	−	540.773i	0.490275	−	0.733749i
$738$		0			0
$739$	98.1432	+	40.6523i	0.132805	+	0.0550098i	0.448096	−	0.893985i	$-0.352102\pi$
$739$	98.1432	+	40.6523i	0.132805	+	0.0550098i	−0.315291	+	0.948995i	$0.602102\pi$
$740$	79.7067	−	192.429i	0.107712	−	0.260039i
$741$		0			0
$742$	−59.0234	−	39.4382i	−0.0795463	−	0.0531512i
$743$	−905.734	−	180.162i	−1.21902	−	0.242479i	−0.456668	−	0.889637i	$-0.650957\pi$
$743$	−905.734	−	180.162i	−1.21902	−	0.242479i	−0.762355	+	0.647159i	$0.775957\pi$
$744$		0			0
$745$	527.409	−	352.403i	0.707931	−	0.473025i
$746$	1164.99	−	482.554i	1.56165	−	0.646855i
$747$		0			0
$748$	115.207	+	172.419i	0.154020	+	0.230507i
$749$	59.5595			0.0795187
$750$		0			0
$751$	636.671	+	952.846i	0.847765	+	1.26877i	0.961374	+	0.275244i	$0.0887587\pi$
$751$	636.671	+	952.846i	0.847765	+	1.26877i	−0.113610	+	0.993525i	$0.536241\pi$
$752$	−195.534	+	195.534i	−0.260018	+	0.260018i
$753$		0			0
$754$	273.869	−	409.873i	0.363221	−	0.543598i
$755$	−28.9855	−	145.720i	−0.0383914	−	0.193007i
$756$		0			0
$757$	24.5973	−	59.3832i	0.0324932	−	0.0784455i	−0.906800	−	0.421561i	$-0.861482\pi$
$757$	24.5973	−	59.3832i	0.0324932	−	0.0784455i	0.939293	+	0.343116i	$0.111482\pi$
$758$	1513.99	−	301.151i	1.99734	−	0.397296i
$759$		0			0
$760$	−914.952	−	181.995i	−1.20388	−	0.239467i
$761$	173.164	+	173.164i	0.227548	+	0.227548i	0.811668	−	0.584120i	$-0.198560\pi$
$761$	173.164	+	173.164i	0.227548	+	0.227548i	−0.584120	+	0.811668i	$0.698560\pi$
$762$		0			0
$763$	−671.137	+	277.994i	−0.879602	+	0.364343i
$764$			162.919i			0.213245i
$765$		0			0
$766$	678.170			0.885339
$767$	−73.3731	−	177.138i	−0.0956624	−	0.230950i
$768$		0			0
$769$	550.339	−	550.339i	0.715655	−	0.715655i	−0.252057	−	0.967712i	$-0.581107\pi$
$769$	550.339	−	550.339i	0.715655	−	0.715655i	0.967712	+	0.252057i	$0.0811072\pi$
$770$	−209.898	+	1055.23i	−0.272595	+	1.37043i
$771$		0			0
$772$	14.4046	+	72.4170i	0.0186588	+	0.0938044i
$773$	−399.534	−	165.492i	−0.516861	−	0.214091i	0.108976	−	0.994044i	$-0.465243\pi$
$773$	−399.534	−	165.492i	−0.516861	−	0.214091i	−0.625837	+	0.779953i	$0.715243\pi$
$774$		0			0
$775$	4.50624	−	0.896346i	0.00581450	−	0.00115658i
$776$	−391.361	−	261.499i	−0.504331	−	0.336983i
$777$		0			0
$778$	−443.266	−	443.266i	−0.569751	−	0.569751i
$779$	−653.397	+	436.586i	−0.838764	+	0.560444i
$780$		0			0
$781$		−	846.408i		−	1.08375i
$782$	95.5146	+	480.184i	0.122141	+	0.614047i
$783$		0			0
$784$	71.3878	+	172.345i	0.0910559	+	0.219828i
$785$	235.617	+	352.626i	0.300150	+	0.449206i
$786$		0			0
$787$	−222.286	+	1117.51i	−0.282447	+	1.41996i	0.535437	+	0.844575i	$0.320147\pi$
$787$	−222.286	+	1117.51i	−0.282447	+	1.41996i	−0.817884	+	0.575383i	$0.804853\pi$
$788$	119.428	−	178.736i	0.151558	−	0.226822i
$789$		0			0
$790$	−323.946	−	134.183i	−0.410059	−	0.169852i
$791$	−157.601	+	380.481i	−0.199242	+	0.481013i
$792$		0			0
$793$	−466.336	−	311.595i	−0.588065	−	0.392932i
$794$	268.177	+	53.3436i	0.337754	+	0.0671834i
$795$		0			0
$796$	−157.954	+	105.541i	−0.198434	+	0.132590i
$797$	−104.084	+	43.1132i	−0.130595	+	0.0540943i	−0.447024	−	0.894522i	$-0.647516\pi$
$797$	−104.084	+	43.1132i	−0.130595	+	0.0540943i	0.316429	+	0.948616i	$0.397516\pi$
$798$		0			0
$799$	96.4946	−	232.959i	0.120769	−	0.291563i
$800$	49.7905			0.0622381
$801$		0			0
$802$	521.614	+	780.650i	0.650391	+	0.973379i
$803$	−13.9147	+	13.9147i	−0.0173284	+	0.0173284i
$804$		0			0
$805$	−243.775	+	364.835i	−0.302826	+	0.453212i
$806$	−3.53507	−	17.7720i	−0.00438594	−	0.0220496i
$807$		0			0
$808$	−92.2520	+	222.716i	−0.114173	+	0.275639i
$809$	−638.126	+	126.931i	−0.788783	+	0.156899i	−0.573014	−	0.819546i	$-0.694226\pi$
$809$	−638.126	+	126.931i	−0.788783	+	0.156899i	−0.215769	+	0.976444i	$0.569226\pi$
$810$		0			0
$811$	−631.322	−	125.578i	−0.778449	−	0.154843i	−0.210154	−	0.977668i	$-0.567397\pi$
$811$	−631.322	−	125.578i	−0.778449	−	0.154843i	−0.568294	+	0.822825i	$0.692397\pi$
$812$	121.822	+	121.822i	0.150027	+	0.150027i
$813$		0			0
$814$	1379.10	−	571.243i	1.69423	−	0.701773i
$815$			297.845i			0.365453i
$816$		0			0
$817$	1821.30			2.22925
$818$	−181.383	−	437.897i	−0.221739	−	0.535326i
$819$		0			0
$820$	99.6533	−	99.6533i	0.121528	−	0.121528i
$821$	174.401	−	876.775i	0.212426	−	1.06794i	−0.716477	−	0.697611i	$-0.754246\pi$
$821$	174.401	−	876.775i	0.212426	−	1.06794i	0.928902	−	0.370325i	$-0.120754\pi$
$822$		0			0
$823$	180.424	+	907.053i	0.219227	+	1.10213i	0.920950	+	0.389680i	$0.127414\pi$
$823$	180.424	+	907.053i	0.219227	+	1.10213i	−0.701723	+	0.712450i	$0.747586\pi$
$824$	971.901	+	402.575i	1.17949	+	0.488562i
$825$		0			0
$826$	380.476	−	75.6813i	0.460624	−	0.0916239i
$827$	704.948	+	471.032i	0.852417	+	0.569567i	0.903237	−	0.429141i	$-0.141184\pi$
$827$	704.948	+	471.032i	0.852417	+	0.569567i	−0.0508208	+	0.998708i	$0.516184\pi$
$828$		0			0
$829$	862.801	+	862.801i	1.04077	+	1.04077i	0.999133	+	0.0416400i	$0.0132583\pi$
$829$	862.801	+	862.801i	1.04077	+	1.04077i	0.0416400	+	0.999133i	$0.486742\pi$
$830$	661.189	−	441.793i	0.796614	−	0.532280i
$831$		0			0
$832$			309.729i			0.372271i
$833$	−120.281	−	120.281i	−0.144395	−	0.144395i
$834$		0			0
$835$	−106.064	−	256.062i	−0.127023	−	0.306661i
$836$	169.327	+	253.416i	0.202545	+	0.303129i
$837$		0			0
$838$	−266.908	+	1341.84i	−0.318506	+	1.60124i
$839$	213.563	−	319.620i	0.254545	−	0.380954i	−0.682085	−	0.731273i	$-0.738927\pi$
$839$	213.563	−	319.620i	0.254545	−	0.380954i	0.936631	+	0.350319i	$0.113927\pi$
$840$		0			0
$841$	231.119	+	95.7324i	0.274814	+	0.113832i
$842$	43.2829	−	104.494i	0.0514048	−	0.124102i
$843$		0			0
$844$	−5.61660	−	3.75289i	−0.00665474	−	0.00444655i
$845$	−646.919	−	128.680i	−0.765585	−	0.152284i
$846$		0			0
$847$	−479.215	+	320.201i	−0.565779	+	0.378042i
$848$	−89.0448	+	36.8836i	−0.105006	+	0.0434948i
$849$		0			0
$850$	−130.680	+	54.1294i	−0.153741	+	0.0636817i
$851$	608.778			0.715368
$852$		0			0
$853$	−485.458	−	726.539i	−0.569118	−	0.851745i	0.429566	−	0.903036i	$-0.358667\pi$
$853$	−485.458	−	726.539i	−0.569118	−	0.851745i	−0.998684	+	0.0512903i	$0.983667\pi$
$854$	802.404	−	802.404i	0.939583	−	0.939583i
$855$		0			0
$856$	36.8760	−	55.1888i	0.0430794	−	0.0644729i
$857$	262.053	+	1317.43i	0.305779	+	1.53726i	0.762111	+	0.647446i	$0.224163\pi$
$857$	262.053	+	1317.43i	0.305779	+	1.53726i	−0.456332	+	0.889810i	$0.650837\pi$
$858$		0			0
$859$	−97.9655	+	236.510i	−0.114046	+	0.275331i	−0.970588	−	0.240745i	$-0.922608\pi$
$859$	−97.9655	+	236.510i	−0.114046	+	0.275331i	0.856542	+	0.516077i	$0.172608\pi$
$860$	−320.355	+	63.7225i	−0.372506	+	0.0740960i
$861$		0			0
$862$	−1014.96	−	201.887i	−1.17744	−	0.234208i
$863$	1137.90	+	1137.90i	1.31854	+	1.31854i	0.914930	+	0.403612i	$0.132245\pi$
$863$	1137.90	+	1137.90i	1.31854	+	1.31854i	0.403612	+	0.914930i	$0.367755\pi$
$864$		0			0
$865$	91.5550	−	37.9233i	0.105844	−	0.0438420i
$866$		−	1415.19i		−	1.63417i
$867$		0			0
$868$	6.33287			0.00729593
$869$	−166.114	−	401.035i	−0.191156	−	0.461490i
$870$		0			0
$871$	213.704	−	213.704i	0.245355	−	0.245355i
$872$	−157.937	+	794.004i	−0.181121	+	0.910555i
$873$		0			0
$874$	140.384	+	705.760i	0.160623	+	0.807505i
$875$	656.681	+	272.006i	0.750493	+	0.310864i
$876$		0			0
$877$	−483.538	+	96.1816i	−0.551354	+	0.109671i	−0.462902	−	0.886409i	$-0.653192\pi$
$877$	−483.538	+	96.1816i	−0.551354	+	0.109671i	−0.0884519	+	0.996080i	$0.528192\pi$
$878$	−1512.85	−	1010.86i	−1.72307	−	1.15132i
$879$		0			0
$880$	1032.94	+	1032.94i	1.17379	+	1.17379i
$881$	334.347	−	223.404i	0.379508	−	0.253579i	−0.351155	−	0.936317i	$-0.614211\pi$
$881$	334.347	−	223.404i	0.379508	−	0.253579i	0.730663	+	0.682738i	$0.239211\pi$
$882$		0			0
$883$		−	907.327i		−	1.02755i	−0.857925	−	0.513775i	$-0.828246\pi$
$883$		−	907.327i		−	1.02755i	0.857925	−	0.513775i	$-0.171754\pi$
$884$	36.8755	+	89.0253i	0.0417144	+	0.100707i
$885$		0			0
$886$	−298.248	−	720.035i	−0.336624	−	0.812681i
$887$	705.933	+	1056.50i	0.795866	+	1.19110i	0.978160	+	0.207854i	$0.0666478\pi$
$887$	705.933	+	1056.50i	0.795866	+	1.19110i	−0.182294	+	0.983244i	$0.558352\pi$
$888$		0			0
$889$	−116.379	+	585.074i	−0.130910	+	0.658127i
$890$	−835.512	+	1250.43i	−0.938778	+	1.40498i
$891$		0			0
$892$	−37.8615	−	15.6828i	−0.0424457	−	0.0175816i
$893$	141.825	−	342.395i	0.158818	−	0.383421i
$894$		0			0
$895$	279.561	+	186.796i	0.312358	+	0.208711i
$896$	−936.988	−	186.379i	−1.04575	−	0.208012i
$897$		0			0
$898$	1436.96	−	960.148i	1.60018	−	1.06921i
$899$	37.0564	−	15.3493i	0.0412195	−	0.0170737i
$900$		0			0
$901$	62.1448	−	62.1448i	0.0689732	−	0.0689732i
$902$	1010.03			1.11976
$903$		0			0
$904$	254.983	+	381.608i	0.282060	+	0.422133i
$905$	396.815	−	396.815i	0.438470	−	0.438470i
$906$		0			0
$907$	852.359	−	1275.64i	0.939756	−	1.40644i	0.0262336	−	0.999656i	$-0.491649\pi$
$907$	852.359	−	1275.64i	0.939756	−	1.40644i	0.913522	−	0.406788i	$-0.133351\pi$
$908$	27.3842	+	137.670i	0.0301588	+	0.151619i
$909$		0			0
$910$	−191.325	+	461.899i	−0.210247	+	0.507582i
$911$	−359.228	+	71.4549i	−0.394323	+	0.0784357i	−0.388269	−	0.921546i	$-0.626927\pi$
$911$	−359.228	+	71.4549i	−0.394323	+	0.0784357i	−0.00605352	+	0.999982i	$0.501927\pi$
$912$		0			0
$913$	965.523	+	192.054i	1.05753	+	0.210355i
$914$	505.549	+	505.549i	0.553117	+	0.553117i
$915$		0			0
$916$	−95.8181	+	39.6892i	−0.104605	+	0.0433288i
$917$		−	267.877i		−	0.292123i
$918$		0			0
$919$	−944.655			−1.02792			−0.513958	−	0.857815i	$-0.671821\pi$
$919$	−944.655			−1.02792			−0.513958	+	0.857815i	$0.671821\pi$
$920$	187.130	+	451.772i	0.203402	+	0.491057i
$921$		0			0
$922$	−382.839	+	382.839i	−0.415226	+	0.415226i
$923$	76.7316	−	385.756i	0.0831328	−	0.417937i
$924$		0			0
$925$	34.3127	+	172.501i	0.0370948	+	0.186488i
$926$	−712.706	−	295.212i	−0.769661	−	0.318804i
$927$		0			0
$928$	426.312	−	84.7988i	0.459388	−	0.0913780i
$929$	−807.914	−	539.831i	−0.869660	−	0.581088i	0.0387126	−	0.999250i	$-0.487674\pi$
$929$	−807.914	−	539.831i	−0.869660	−	0.581088i	−0.908372	+	0.418162i	$0.862674\pi$
$930$		0			0
$931$	−176.785	−	176.785i	−0.189887	−	0.189887i
$932$	−245.195	+	163.834i	−0.263085	+	0.175788i
$933$		0			0
$934$			481.282i			0.515292i
$935$	−1230.64	−	509.748i	−1.31619	−	0.545184i
$936$		0			0
$937$	−229.656	−	554.438i	−0.245097	−	0.591716i	0.752678	−	0.658389i	$-0.228762\pi$
$937$	−229.656	−	554.438i	−0.245097	−	0.591716i	−0.997775	+	0.0666728i	$0.978762\pi$
$938$	339.721	+	508.428i	0.362176	+	0.542034i
$939$		0			0
$940$	−12.9665	+	65.1871i	−0.0137942	+	0.0693480i
$941$	−602.514	+	901.726i	−0.640291	+	0.958263i	0.359394	+	0.933186i	$0.382983\pi$
$941$	−602.514	+	901.726i	−0.640291	+	0.958263i	−0.999686	+	0.0250777i	$0.992017\pi$
$942$		0			0
$943$	380.563	+	157.634i	0.403566	+	0.167162i
$944$	201.562	−	486.613i	0.213519	−	0.515480i
$945$		0			0
$946$	−1946.39	−	1300.54i	−2.05750	−	1.37478i
$947$	−683.372	−	135.931i	−0.721618	−	0.143539i	−0.179400	−	0.983776i	$-0.557416\pi$
$947$	−683.372	−	135.931i	−0.721618	−	0.143539i	−0.542219	+	0.840237i	$0.682416\pi$
$948$		0			0
$949$	−7.60316	+	5.08027i	−0.00801176	+	0.00535329i
$950$	−192.069	+	79.5577i	−0.202178	+	0.0837449i
$951$		0			0
$952$	724.559	−	144.124i	0.761091	−	0.151390i
$953$	1779.95			1.86774			0.933868	−	0.357618i	$-0.116411\pi$
$953$	1779.95			1.86774			0.933868	+	0.357618i	$0.116411\pi$
$954$		0			0
$955$	−581.415	−	870.149i	−0.608812	−	0.911151i
$956$	121.972	−	121.972i	0.127586	−	0.127586i
$957$		0			0
$958$	−613.843	+	918.681i	−0.640754	+	0.958957i
$959$	77.7522	+	390.887i	0.0810763	+	0.407598i
$960$		0			0
$961$	−367.195	+	886.486i	−0.382096	+	0.922462i
$962$	680.322	−	135.324i	0.707195	−	0.140670i
$963$		0			0
$964$	−235.945	−	46.9324i	−0.244756	−	0.0486850i
$965$	−335.373	−	335.373i	−0.347536	−	0.347536i
$966$		0			0
$967$	−558.012	+	231.136i	−0.577055	+	0.239024i	−0.652071	−	0.758158i	$-0.726099\pi$
$967$	−558.012	+	231.136i	−0.577055	+	0.239024i	0.0750154	+	0.997182i	$0.476099\pi$
$968$			642.299i			0.663532i
$969$		0			0
$970$	−797.924			−0.822602
$971$	−421.281	−	1017.06i	−0.433863	−	1.04744i	−0.978031	−	0.208461i	$-0.933155\pi$
$971$	−421.281	−	1017.06i	−0.433863	−	1.04744i	0.544168	−	0.838976i	$-0.316845\pi$
$972$		0			0
$973$	1153.90	−	1153.90i	1.18592	−	1.18592i
$974$	108.013	−	543.017i	0.110896	−	0.557512i
$975$		0			0
$976$	−300.579	−	1511.11i	−0.307971	−	1.54827i
$977$	−1012.20	−	419.266i	−1.03603	−	0.429136i	−0.201142	−	0.979562i	$-0.564465\pi$
$977$	−1012.20	−	419.266i	−1.03603	−	0.429136i	−0.834884	+	0.550426i	$0.814465\pi$
$978$		0			0
$979$	−1825.98	+	363.211i	−1.86515	+	0.371002i
$980$	37.2805	+	24.9100i	0.0380413	+	0.0254184i
$981$		0			0
$982$	351.948	+	351.948i	0.358399	+	0.358399i
$983$	1021.98	−	682.863i	1.03965	−	0.694673i	0.0862178	−	0.996276i	$-0.472522\pi$
$983$	1021.98	−	682.863i	1.03965	−	0.694673i	0.953433	+	0.301604i	$0.0975219\pi$
$984$		0			0
$985$			1380.83i			1.40186i
$986$	−1026.71	+	686.025i	−1.04129	+	0.695766i
$987$		0			0
$988$	54.1984	+	130.847i	0.0548567	+	0.132436i
$989$	−530.396	−	793.794i	−0.536295	−	0.802623i
$990$		0			0
$991$	−143.735	+	722.604i	−0.145040	+	0.729167i	0.837985	+	0.545694i	$0.183734\pi$
$991$	−143.735	+	722.604i	−0.145040	+	0.729167i	−0.983025	+	0.183473i	$0.941266\pi$
$992$	8.87670	−	13.2849i	0.00894829	−	0.0133921i
$993$		0			0
$994$	735.207	+	304.533i	0.739645	+	0.306371i
$995$	466.981	−	1127.39i	0.469328	−	1.13306i
$996$		0			0
$997$	145.149	+	96.9855i	0.145586	+	0.0972774i	0.626230	−	0.779638i	$-0.284597\pi$
$997$	145.149	+	96.9855i	0.145586	+	0.0972774i	−0.480644	+	0.876916i	$0.659597\pi$
$998$	−465.511	−	92.5960i	−0.466444	−	0.0927815i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.3.p.b.73.1		8
3.2	odd	2		17.3.e.a.5.1	✓	8
12.11	even	2		272.3.bh.c.209.1		8
15.2	even	4		425.3.t.c.124.1		8
15.8	even	4		425.3.t.a.124.1		8
15.14	odd	2		425.3.u.b.226.1		8
17.7	odd	16	inner	153.3.p.b.109.1		8
51.2	odd	8		289.3.e.k.224.1		8
51.5	even	16		289.3.e.l.40.1		8
51.8	odd	8		289.3.e.b.65.1		8
51.11	even	16		289.3.e.i.214.1		8
51.14	even	16		289.3.e.d.249.1		8
51.20	even	16		289.3.e.b.249.1		8
51.23	even	16		289.3.e.m.214.1		8
51.26	odd	8		289.3.e.d.65.1		8
51.29	even	16		289.3.e.k.40.1		8
51.32	odd	8		289.3.e.l.224.1		8
51.38	odd	4		289.3.e.m.131.1		8
51.41	even	16		17.3.e.a.7.1	yes	8
51.44	even	16		289.3.e.c.75.1		8
51.47	odd	4		289.3.e.i.131.1		8
51.50	odd	2		289.3.e.c.158.1		8
204.143	odd	16		272.3.bh.c.177.1		8
255.92	odd	16		425.3.t.a.24.1		8
255.143	odd	16		425.3.t.c.24.1		8
255.194	even	16		425.3.u.b.126.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.a.5.1	✓	8	3.2	odd	2
17.3.e.a.7.1	yes	8	51.41	even	16
153.3.p.b.73.1		8	1.1	even	1	trivial
153.3.p.b.109.1		8	17.7	odd	16	inner
272.3.bh.c.177.1		8	204.143	odd	16
272.3.bh.c.209.1		8	12.11	even	2
289.3.e.b.65.1		8	51.8	odd	8
289.3.e.b.249.1		8	51.20	even	16
289.3.e.c.75.1		8	51.44	even	16
289.3.e.c.158.1		8	51.50	odd	2
289.3.e.d.65.1		8	51.26	odd	8
289.3.e.d.249.1		8	51.14	even	16
289.3.e.i.131.1		8	51.47	odd	4
289.3.e.i.214.1		8	51.11	even	16
289.3.e.k.40.1		8	51.29	even	16
289.3.e.k.224.1		8	51.2	odd	8
289.3.e.l.40.1		8	51.5	even	16
289.3.e.l.224.1		8	51.32	odd	8
289.3.e.m.131.1		8	51.38	odd	4
289.3.e.m.214.1		8	51.23	even	16
425.3.t.a.24.1		8	255.92	odd	16
425.3.t.a.124.1		8	15.8	even	4
425.3.t.c.24.1		8	255.143	odd	16
425.3.t.c.124.1		8	15.2	even	4
425.3.u.b.126.1		8	255.194	even	16
425.3.u.b.226.1		8	15.14	odd	2

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:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	153.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841487 + 2.03153i) q^{2} +(-0.590587 + 0.590587i) q^{4} +(1.04667 - 5.26197i) q^{5} +(1.21824 + 6.12453i) q^{7} +(6.42935 + 2.66313i) q^{8} +(11.5706 - 2.30154i) q^{10} +(12.1433 + 8.11392i) q^{11} +(4.79884 + 4.79884i) q^{13} +(-11.4170 + 7.62861i) q^{14} +18.6433i q^{16} +(-6.50562 - 15.7060i) q^{17} +(-9.56175 - 23.0841i) q^{19} +(2.48950 + 3.72580i) q^{20} +(-6.26521 + 31.4973i) q^{22} +(-7.27639 + 10.8899i) q^{23} +(-3.49585 - 1.44803i) q^{25} +(-5.71082 + 13.7871i) q^{26} +(-4.33654 - 2.89759i) q^{28} +(-32.3980 - 6.44436i) q^{29} +(-1.00960 + 0.674593i) q^{31} +(-12.1570 + 5.03558i) q^{32} +(26.4327 - 26.4327i) q^{34} +33.5022 q^{35} +(-25.8238 - 38.6481i) q^{37} +(38.8500 - 38.8500i) q^{38} +(20.7427 - 31.0437i) q^{40} +(-6.13577 - 30.8466i) q^{41} +(-27.8948 + 67.3441i) q^{43} +(-11.9637 + 2.37972i) q^{44} +(-28.2461 - 5.61851i) q^{46} +(10.4882 + 10.4882i) q^{47} +(9.24438 - 3.82915i) q^{49} -8.32041i q^{50} -5.66826 q^{52} +(1.97838 + 4.77624i) q^{53} +(55.4053 - 55.4053i) q^{55} +(-8.47786 + 42.6211i) q^{56} +(-14.1706 - 71.2404i) q^{58} +(-26.1013 - 10.8115i) q^{59} +(-81.0541 + 16.1227i) q^{61} +(-2.22002 - 1.48337i) q^{62} +(32.2713 + 32.2713i) q^{64} +(30.2741 - 20.2285i) q^{65} -44.5324i q^{67} +(13.1179 + 5.43359i) q^{68} +(28.1917 + 68.0607i) q^{70} +(-32.1978 - 48.1875i) q^{71} +(-0.262865 + 1.32151i) q^{73} +(56.7843 - 84.9838i) q^{74} +(19.2802 + 7.98612i) q^{76} +(-34.9004 + 84.2570i) q^{77} +(-24.7128 - 16.5125i) q^{79} +(98.1004 + 19.5134i) q^{80} +(57.5026 - 38.4220i) q^{82} +(62.2748 - 25.7951i) q^{83} +(-89.4535 + 17.7934i) q^{85} -160.285 q^{86} +(56.4655 + 84.5065i) q^{88} +(-90.1397 + 90.1397i) q^{89} +(-23.5444 + 35.2368i) q^{91} +(-2.13408 - 10.7288i) q^{92} +(-12.4814 + 30.1327i) q^{94} +(-131.476 + 26.1522i) q^{95} +(-66.3366 - 13.1952i) q^{97} +(15.5581 + 15.5581i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 16 q^{5} + 8 q^{7} + 24 q^{8} + 16 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{14} + 80 q^{20} - 104 q^{22} + 56 q^{23} + 64 q^{25} - 176 q^{26} + 152 q^{28} - 48 q^{29} + 24 q^{31} - 88 q^{32}+ \cdots + 120 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 - 16 * q^5 + 8 * q^7 + 24 * q^8 + 16 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^14 + 80 * q^20 - 104 * q^22 + 56 * q^23 + 64 * q^25 - 176 * q^26 + 152 * q^28 - 48 * q^29 + 24 * q^31 - 88 * q^32 - 136 * q^34 + 160 * q^35 + 32 * q^37 + 120 * q^38 + 64 * q^40 - 48 * q^41 - 232 * q^43 - 120 * q^44 - 88 * q^46 - 192 * q^47 + 16 * q^49 - 384 * q^52 + 32 * q^53 + 224 * q^55 + 120 * q^56 + 240 * q^58 + 48 * q^59 - 160 * q^61 + 168 * q^62 - 64 * q^64 + 96 * q^65 - 272 * q^68 + 224 * q^70 - 40 * q^71 + 48 * q^73 + 160 * q^74 + 80 * q^76 + 48 * q^77 - 136 * q^79 + 240 * q^80 - 64 * q^82 + 264 * q^83 - 272 * q^85 - 832 * q^86 + 264 * q^88 - 160 * q^89 + 320 * q^91 - 24 * q^92 + 32 * q^94 - 272 * q^95 + 48 * q^97 + 120 * q^98

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