LMFDB - Embedded newform 760.2.f.b.381.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.12
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.862980 + 1.12039i) q^{2} +3.06281i q^{3} +(-0.510530 - 1.93374i) q^{4} +1.00000i q^{5} +(-3.43153 - 2.64314i) q^{6} -2.81229 q^{7} +(2.60712 + 1.09679i) q^{8} -6.38080 q^{9} +(-1.12039 - 0.862980i) q^{10} -5.05668i q^{11} +(5.92268 - 1.56366i) q^{12} -3.98012i q^{13} +(2.42695 - 3.15085i) q^{14} -3.06281 q^{15} +(-3.47872 + 1.97447i) q^{16} +1.62171 q^{17} +(5.50651 - 7.14896i) q^{18} +1.00000i q^{19} +(1.93374 - 0.510530i) q^{20} -8.61352i q^{21} +(5.66544 + 4.36382i) q^{22} +1.51916 q^{23} +(-3.35926 + 7.98510i) q^{24} -1.00000 q^{25} +(4.45928 + 3.43477i) q^{26} -10.3548i q^{27} +(1.43576 + 5.43825i) q^{28} -0.617462i q^{29} +(2.64314 - 3.43153i) q^{30} -7.37672 q^{31} +(0.789902 - 5.60143i) q^{32} +15.4877 q^{33} +(-1.39951 + 1.81694i) q^{34} -2.81229i q^{35} +(3.25759 + 12.3388i) q^{36} -6.69976i q^{37} +(-1.12039 - 0.862980i) q^{38} +12.1904 q^{39} +(-1.09679 + 2.60712i) q^{40} -10.2747 q^{41} +(9.65047 + 7.43330i) q^{42} +9.48263i q^{43} +(-9.77832 + 2.58159i) q^{44} -6.38080i q^{45} +(-1.31101 + 1.70205i) q^{46} -7.80972 q^{47} +(-6.04741 - 10.6547i) q^{48} +0.908997 q^{49} +(0.862980 - 1.12039i) q^{50} +4.96700i q^{51} +(-7.69654 + 2.03197i) q^{52} -8.96779i q^{53} +(11.6013 + 8.93595i) q^{54} +5.05668 q^{55} +(-7.33197 - 3.08450i) q^{56} -3.06281 q^{57} +(0.691796 + 0.532858i) q^{58} +1.48840i q^{59} +(1.56366 + 5.92268i) q^{60} -7.73455i q^{61} +(6.36597 - 8.26478i) q^{62} +17.9447 q^{63} +(5.59410 + 5.71892i) q^{64} +3.98012 q^{65} +(-13.3655 + 17.3522i) q^{66} +7.61986i q^{67} +(-0.827933 - 3.13597i) q^{68} +4.65290i q^{69} +(3.15085 + 2.42695i) q^{70} -1.07002 q^{71} +(-16.6355 - 6.99841i) q^{72} +10.8626 q^{73} +(7.50632 + 5.78176i) q^{74} -3.06281i q^{75} +(1.93374 - 0.510530i) q^{76} +14.2209i q^{77} +(-10.5200 + 13.6579i) q^{78} +1.37931 q^{79} +(-1.97447 - 3.47872i) q^{80} +12.5722 q^{81} +(8.86691 - 11.5117i) q^{82} +13.9294i q^{83} +(-16.6563 + 4.39746i) q^{84} +1.62171i q^{85} +(-10.6242 - 8.18332i) q^{86} +1.89117 q^{87} +(5.54613 - 13.1834i) q^{88} +0.709012 q^{89} +(7.14896 + 5.50651i) q^{90} +11.1933i q^{91} +(-0.775577 - 2.93767i) q^{92} -22.5935i q^{93} +(6.73963 - 8.74990i) q^{94} -1.00000 q^{95} +(17.1561 + 2.41932i) q^{96} +14.3906 q^{97} +(-0.784447 + 1.01843i) q^{98} +32.2657i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−0.862980	+	1.12039i	−0.610219	+	0.792233i
$2$	−0.862980	+	1.12039i	−0.610219	+	0.792233i
$3$			3.06281i			1.76831i	0.467190	+	0.884157i	$0.345266\pi$
$3$			3.06281i			1.76831i	−0.467190	+	0.884157i	$0.654734\pi$
$4$	−0.510530	−	1.93374i	−0.255265	−	0.966871i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−3.43153	−	2.64314i	−1.40092	−	1.07906i
$7$	−2.81229			−1.06295			−0.531474	−	0.847075i	$-0.678362\pi$
$7$	−2.81229			−1.06295			−0.531474	+	0.847075i	$0.678362\pi$
$8$	2.60712	+	1.09679i	0.921754	+	0.387774i
$9$	−6.38080			−2.12693
$10$	−1.12039	−	0.862980i	−0.354297	−	0.272898i
$11$		−	5.05668i		−	1.52465i	−0.647196	−	0.762324i	$-0.724058\pi$
$11$		−	5.05668i		−	1.52465i	0.647196	−	0.762324i	$-0.275942\pi$
$12$	5.92268	−	1.56366i	1.70973	−	0.451388i
$13$		−	3.98012i		−	1.10389i	−0.833881	−	0.551944i	$-0.813886\pi$
$13$		−	3.98012i		−	1.10389i	0.833881	−	0.551944i	$-0.186114\pi$
$14$	2.42695	−	3.15085i	0.648631	−	0.842101i
$15$	−3.06281			−0.790814
$16$	−3.47872	+	1.97447i	−0.869680	+	0.493616i
$17$	1.62171			0.393323			0.196662	−	0.980471i	$-0.436990\pi$
$17$	1.62171			0.393323			0.196662	+	0.980471i	$0.436990\pi$
$18$	5.50651	−	7.14896i	1.29790	−	1.68503i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.93374	−	0.510530i	0.432398	−	0.114158i
$21$		−	8.61352i		−	1.87962i
$22$	5.66544	+	4.36382i	1.20788	+	0.930369i
$23$	1.51916			0.316767			0.158384	−	0.987378i	$-0.449372\pi$
$23$	1.51916			0.316767			0.158384	+	0.987378i	$0.449372\pi$
$24$	−3.35926	+	7.98510i	−0.685707	+	1.62995i
$25$	−1.00000			−0.200000
$26$	4.45928	+	3.43477i	0.874536	+	0.673614i
$27$		−	10.3548i		−	1.99277i
$28$	1.43576	+	5.43825i	0.271333	+	1.02773i
$29$		−	0.617462i		−	0.114660i	−0.998355	−	0.0573299i	$-0.981741\pi$
$29$		−	0.617462i		−	0.114660i	0.998355	−	0.0573299i	$-0.0182587\pi$
$30$	2.64314	−	3.43153i	0.482570	−	0.626509i
$31$	−7.37672			−1.32490			−0.662449	−	0.749107i	$-0.730483\pi$
$31$	−7.37672			−1.32490			−0.662449	+	0.749107i	$0.730483\pi$
$32$	0.789902	−	5.60143i	0.139636	−	0.990203i
$33$	15.4877			2.69606
$34$	−1.39951	+	1.81694i	−0.240013	+	0.311603i
$35$		−	2.81229i		−	0.475364i
$36$	3.25759	+	12.3388i	0.542932	+	2.05647i
$37$		−	6.69976i		−	1.10143i	−0.834692	−	0.550717i	$-0.814354\pi$
$37$		−	6.69976i		−	1.10143i	0.834692	−	0.550717i	$-0.185646\pi$
$38$	−1.12039	−	0.862980i	−0.181751	−	0.139994i
$39$	12.1904			1.95202
$40$	−1.09679	+	2.60712i	−0.173418	+	0.412221i
$41$	−10.2747			−1.60465			−0.802323	−	0.596890i	$-0.796403\pi$
$41$	−10.2747			−1.60465			−0.802323	+	0.596890i	$0.796403\pi$
$42$	9.65047	+	7.43330i	1.48910	+	1.14698i
$43$			9.48263i			1.44609i	0.690802	+	0.723044i	$0.257257\pi$
$43$			9.48263i			1.44609i	−0.690802	+	0.723044i	$0.742743\pi$
$44$	−9.77832	+	2.58159i	−1.47414	+	0.389189i
$45$		−	6.38080i		−	0.951194i
$46$	−1.31101	+	1.70205i	−0.193297	+	0.250953i
$47$	−7.80972			−1.13916			−0.569582	−	0.821934i	$-0.692895\pi$
$47$	−7.80972			−1.13916			−0.569582	+	0.821934i	$0.692895\pi$
$48$	−6.04741	−	10.6547i	−0.872869	−	1.53787i
$49$	0.908997			0.129857
$50$	0.862980	−	1.12039i	0.122044	−	0.158447i
$51$			4.96700i			0.695519i
$52$	−7.69654	+	2.03197i	−1.06732	+	0.281784i
$53$		−	8.96779i		−	1.23182i	−0.787816	−	0.615910i	$-0.788788\pi$
$53$		−	8.96779i		−	1.23182i	0.787816	−	0.615910i	$-0.211212\pi$
$54$	11.6013	+	8.93595i	1.57874	+	1.21603i
$55$	5.05668			0.681843
$56$	−7.33197	−	3.08450i	−0.979776	−	0.412184i
$57$	−3.06281			−0.405679
$58$	0.691796	+	0.532858i	0.0908373	+	0.0699677i
$59$			1.48840i			0.193773i	0.995295	+	0.0968866i	$0.0308884\pi$
$59$			1.48840i			0.193773i	−0.995295	+	0.0968866i	$0.969112\pi$
$60$	1.56366	+	5.92268i	0.201867	+	0.764615i
$61$		−	7.73455i		−	0.990307i	−0.868805	−	0.495154i	$-0.835112\pi$
$61$		−	7.73455i		−	0.990307i	0.868805	−	0.495154i	$-0.164888\pi$
$62$	6.36597	−	8.26478i	0.808479	−	1.04963i
$63$	17.9447			2.26082
$64$	5.59410	+	5.71892i	0.699262	+	0.714865i
$65$	3.98012			0.493674
$66$	−13.3655	+	17.3522i	−1.64519	+	2.13590i
$67$			7.61986i			0.930914i	0.885071	+	0.465457i	$0.154110\pi$
$67$			7.61986i			0.930914i	−0.885071	+	0.465457i	$0.845890\pi$
$68$	−0.827933	−	3.13597i	−0.100402	−	0.380293i
$69$			4.65290i			0.560144i
$70$	3.15085	+	2.42695i	0.376599	+	0.290077i
$71$	−1.07002			−0.126989			−0.0634943	−	0.997982i	$-0.520224\pi$
$71$	−1.07002			−0.126989			−0.0634943	+	0.997982i	$0.520224\pi$
$72$	−16.6355	−	6.99841i	−1.96051	−	0.824770i
$73$	10.8626			1.27137			0.635685	−	0.771949i	$-0.280718\pi$
$73$	10.8626			1.27137			0.635685	+	0.771949i	$0.280718\pi$
$74$	7.50632	+	5.78176i	0.872592	+	0.672116i
$75$		−	3.06281i		−	0.353663i
$76$	1.93374	−	0.510530i	0.221815	−	0.0585618i
$77$			14.2209i			1.62062i
$78$	−10.5200	+	13.6579i	−1.19116	+	1.54645i
$79$	1.37931			0.155185			0.0775924	−	0.996985i	$-0.475277\pi$
$79$	1.37931			0.155185			0.0775924	+	0.996985i	$0.475277\pi$
$80$	−1.97447	−	3.47872i	−0.220752	−	0.388933i
$81$	12.5722			1.39691
$82$	8.86691	−	11.5117i	0.979186	−	1.27125i
$83$			13.9294i			1.52895i	0.644653	+	0.764475i	$0.277002\pi$
$83$			13.9294i			1.52895i	−0.644653	+	0.764475i	$0.722998\pi$
$84$	−16.6563	+	4.39746i	−1.81735	+	0.479802i
$85$			1.62171i			0.175899i
$86$	−10.6242	−	8.18332i	−1.14564	−	0.882430i
$87$	1.89117			0.202755
$88$	5.54613	−	13.1834i	0.591219	−	1.40535i
$89$	0.709012			0.0751551			0.0375776	−	0.999294i	$-0.488036\pi$
$89$	0.709012			0.0751551			0.0375776	+	0.999294i	$0.488036\pi$
$90$	7.14896	+	5.50651i	0.753567	+	0.580437i
$91$			11.1933i			1.17337i
$92$	−0.775577	−	2.93767i	−0.0808595	−	0.306273i
$93$		−	22.5935i		−	2.34284i
$94$	6.73963	−	8.74990i	0.695140	−	0.902483i
$95$	−1.00000			−0.102598
$96$	17.1561	+	2.41932i	1.75099	+	0.246921i
$97$	14.3906			1.46115			0.730573	−	0.682835i	$-0.239253\pi$
$97$	14.3906			1.46115			0.730573	+	0.682835i	$0.239253\pi$
$98$	−0.784447	+	1.01843i	−0.0792411	+	0.102877i
$99$			32.2657i			3.24282i
$100$	0.510530	+	1.93374i	0.0510530	+	0.193374i
$101$		−	12.0028i		−	1.19432i	−0.802121	−	0.597161i	$-0.796295\pi$
$101$		−	12.0028i		−	1.19432i	0.802121	−	0.597161i	$-0.203705\pi$
$102$	−5.56495	−	4.28642i	−0.551013	−	0.424419i
$103$	−17.9996			−1.77356			−0.886778	−	0.462195i	$-0.847062\pi$
$103$	−17.9996			−1.77356			−0.886778	+	0.462195i	$0.847062\pi$
$104$	4.36537	−	10.3766i	0.428059	−	1.01751i
$105$	8.61352			0.840594
$106$	10.0474	+	7.73903i	0.975889	+	0.751681i
$107$		−	18.2082i		−	1.76025i	−0.474738	−	0.880127i	$-0.657457\pi$
$107$		−	18.2082i		−	1.76025i	0.474738	−	0.880127i	$-0.342543\pi$
$108$	−20.0234	+	5.28641i	−1.92675	+	0.508685i
$109$		−	1.41237i		−	0.135280i	−0.997710	−	0.0676402i	$-0.978453\pi$
$109$		−	1.41237i		−	0.135280i	0.997710	−	0.0676402i	$-0.0215470\pi$
$110$	−4.36382	+	5.66544i	−0.416074	+	0.540178i
$111$	20.5201			1.94768
$112$	9.78318	−	5.55278i	0.924424	−	0.524688i
$113$	−4.53336			−0.426463			−0.213231	−	0.977002i	$-0.568399\pi$
$113$	−4.53336			−0.426463			−0.213231	+	0.977002i	$0.568399\pi$
$114$	2.64314	−	3.43153i	0.247553	−	0.321392i
$115$			1.51916i			0.141663i
$116$	−1.19401	+	0.315233i	−0.110861	+	0.0292686i
$117$			25.3964i			2.34790i
$118$	−1.66758	−	1.28446i	−0.153513	−	0.118244i
$119$	−4.56073			−0.418082
$120$	−7.98510	−	3.35926i	−0.728936	−	0.306657i
$121$	−14.5701			−1.32455
$122$	8.66568	+	6.67476i	0.784554	+	0.604305i
$123$		−	31.4696i		−	2.83752i
$124$	3.76604	+	14.2647i	0.338200	+	1.28101i
$125$		−	1.00000i		−	0.0894427i
$126$	−15.4859	+	20.1050i	−1.37960	+	1.79109i
$127$	16.3081			1.44711			0.723554	−	0.690268i	$-0.242507\pi$
$127$	16.3081			1.44711			0.723554	+	0.690268i	$0.242507\pi$
$128$	−11.2350	+	1.33223i	−0.993043	+	0.117754i
$129$	−29.0435			−2.55714
$130$	−3.43477	+	4.45928i	−0.301249	+	0.391104i
$131$		−	8.26767i		−	0.722350i	−0.932498	−	0.361175i	$-0.882376\pi$
$131$		−	8.26767i		−	0.722350i	0.932498	−	0.361175i	$-0.117624\pi$
$132$	−7.90691	−	29.9491i	−0.688208	−	2.60674i
$133$		−	2.81229i		−	0.243857i
$134$	−8.53718	−	6.57579i	−0.737500	−	0.568062i
$135$	10.3548			0.891195
$136$	4.22799	+	1.77868i	0.362547	+	0.152521i
$137$	−17.5424			−1.49875			−0.749374	−	0.662147i	$-0.769646\pi$
$137$	−17.5424			−1.49875			−0.749374	+	0.662147i	$0.769646\pi$
$138$	−5.21305	−	4.01536i	−0.443764	−	0.341811i
$139$			0.878831i			0.0745414i	0.999305	+	0.0372707i	$0.0118664\pi$
$139$			0.878831i			0.0745414i	−0.999305	+	0.0372707i	$0.988134\pi$
$140$	−5.43825	+	1.43576i	−0.459616	+	0.121344i
$141$		−	23.9197i		−	2.01440i
$142$	0.923410	−	1.19884i	0.0774909	−	0.100604i
$143$	−20.1262			−1.68304
$144$	22.1970	−	12.5987i	1.84975	−	1.04989i
$145$	0.617462			0.0512775
$146$	−9.37420	+	12.1703i	−0.775814	+	1.00722i
$147$			2.78409i			0.229627i
$148$	−12.9556	+	3.42043i	−1.06494	+	0.281157i
$149$		−	8.52396i		−	0.698310i	−0.937065	−	0.349155i	$-0.886469\pi$
$149$		−	8.52396i		−	0.698310i	0.937065	−	0.349155i	$-0.113531\pi$
$150$	3.43153	+	2.64314i	0.280183	+	0.215812i
$151$	−15.8403			−1.28906			−0.644531	−	0.764578i	$-0.722947\pi$
$151$	−15.8403			−1.28906			−0.644531	+	0.764578i	$0.722947\pi$
$152$	−1.09679	+	2.60712i	−0.0889615	+	0.211465i
$153$	−10.3478			−0.836572
$154$	−15.9329	−	12.2723i	−1.28391	−	0.988934i
$155$		−	7.37672i		−	0.592513i
$156$	−6.22354	−	23.5730i	−0.498282	−	1.88735i
$157$		−	0.882769i		−	0.0704527i	−0.999379	−	0.0352263i	$-0.988785\pi$
$157$		−	0.882769i		−	0.0704527i	0.999379	−	0.0352263i	$-0.0112152\pi$
$158$	−1.19032	+	1.54536i	−0.0946968	+	0.122942i
$159$	27.4666			2.17825
$160$	5.60143	+	0.789902i	0.442832	+	0.0624473i
$161$	−4.27233			−0.336707
$162$	−10.8496	+	14.0858i	−0.852424	+	1.10668i
$163$			8.67648i			0.679594i	0.940499	+	0.339797i	$0.110358\pi$
$163$			8.67648i			0.679594i	−0.940499	+	0.339797i	$0.889642\pi$
$164$	5.24556	+	19.8687i	0.409610	+	1.55149i
$165$			15.4877i			1.20571i
$166$	−15.6063	−	12.0208i	−1.21128	−	0.932995i
$167$	−21.7621			−1.68400			−0.842001	−	0.539476i	$-0.818622\pi$
$167$	−21.7621			−1.68400			−0.842001	+	0.539476i	$0.818622\pi$
$168$	9.44724	−	22.4564i	0.728870	−	1.73255i
$169$	−2.84139			−0.218569
$170$	−1.81694	−	1.39951i	−0.139353	−	0.107337i
$171$		−	6.38080i		−	0.487952i
$172$	18.3370	−	4.84116i	1.39818	−	0.369135i
$173$			9.66571i			0.734870i	0.930049	+	0.367435i	$0.119764\pi$
$173$			9.66571i			0.734870i	−0.930049	+	0.367435i	$0.880236\pi$
$174$	−1.63204	+	2.11884i	−0.123725	+	0.160629i
$175$	2.81229			0.212589
$176$	9.98425	+	17.5908i	0.752591	+	1.32596i
$177$	−4.55868			−0.342652
$178$	−0.611864	+	0.794367i	−0.0458611	+	0.0595404i
$179$		−	20.0228i		−	1.49657i	−0.663376	−	0.748286i	$-0.730877\pi$
$179$		−	20.0228i		−	1.49657i	0.663376	−	0.748286i	$-0.269123\pi$
$180$	−12.3388	+	3.25759i	−0.919682	+	0.242806i
$181$		−	3.56175i		−	0.264742i	−0.991200	−	0.132371i	$-0.957741\pi$
$181$		−	3.56175i		−	0.264742i	0.991200	−	0.132371i	$-0.0422591\pi$
$182$	−12.5408	−	9.65958i	−0.929586	−	0.716016i
$183$	23.6894			1.75117
$184$	3.96063	+	1.66620i	0.291982	+	0.122834i
$185$	6.69976			0.492576
$186$	25.3134	+	19.4977i	1.85607	+	1.42964i
$187$		−	8.20049i		−	0.599679i
$188$	3.98709	+	15.1020i	0.290789	+	1.10142i
$189$			29.1206i			2.11821i
$190$	0.862980	−	1.12039i	0.0626072	−	0.0812813i
$191$	18.5078			1.33918			0.669589	−	0.742732i	$-0.266470\pi$
$191$	18.5078			1.33918			0.669589	+	0.742732i	$0.266470\pi$
$192$	−17.5160	+	17.1337i	−1.26411	+	1.23652i
$193$	−0.891942			−0.0642034			−0.0321017	−	0.999485i	$-0.510220\pi$
$193$	−0.891942			−0.0642034			−0.0321017	+	0.999485i	$0.510220\pi$
$194$	−12.4188	+	16.1230i	−0.891619	+	1.15757i
$195$			12.1904i			0.872970i
$196$	−0.464070	−	1.75777i	−0.0331479	−	0.125555i
$197$			12.9518i			0.922776i	0.887198	+	0.461388i	$0.152648\pi$
$197$			12.9518i			0.922776i	−0.887198	+	0.461388i	$0.847352\pi$
$198$	−36.1500	−	27.8447i	−2.56907	−	1.97883i
$199$	6.52220			0.462347			0.231173	−	0.972913i	$-0.425744\pi$
$199$	6.52220			0.462347			0.231173	+	0.972913i	$0.425744\pi$
$200$	−2.60712	−	1.09679i	−0.184351	−	0.0775549i
$201$	−23.3382			−1.64615
$202$	13.4478	+	10.3582i	0.946181	+	0.728798i
$203$			1.73649i			0.121877i
$204$	9.60489	−	2.53580i	0.672477	−	0.177541i
$205$		−	10.2747i		−	0.717620i
$206$	15.5333	−	20.1665i	1.08226	−	1.40507i
$207$	−9.69347			−0.673743
$208$	7.85862	+	13.8457i	0.544897	+	0.960029i
$209$	5.05668			0.349778
$210$	−7.43330	+	9.65047i	−0.512946	+	0.665946i
$211$		−	26.7423i		−	1.84102i	−0.390724	−	0.920508i	$-0.627775\pi$
$211$		−	26.7423i		−	1.84102i	0.390724	−	0.920508i	$-0.372225\pi$
$212$	−17.3414	+	4.57832i	−1.19101	+	0.314441i
$213$		−	3.27728i		−	0.224556i
$214$	20.4002	+	15.7133i	1.39453	+	1.07414i
$215$	−9.48263			−0.646710
$216$	11.3570	−	26.9960i	0.772746	−	1.83685i
$217$	20.7455			1.40830
$218$	1.58240	+	1.21885i	0.107173	+	0.0825507i
$219$			33.2700i			2.24818i
$220$	−2.58159	−	9.77832i	−0.174051	−	0.659254i
$221$		−	6.45462i		−	0.434185i
$222$	−17.7084	+	22.9904i	−1.18851	+	1.54302i
$223$	−1.22439			−0.0819910			−0.0409955	−	0.999159i	$-0.513053\pi$
$223$	−1.22439			−0.0819910			−0.0409955	+	0.999159i	$0.513053\pi$
$224$	−2.22144	+	15.7529i	−0.148426	+	1.05253i
$225$	6.38080			0.425387
$226$	3.91220	−	5.07912i	0.260236	−	0.337858i
$227$			15.1423i			1.00503i	0.864568	+	0.502516i	$0.167592\pi$
$227$			15.1423i			1.00503i	−0.864568	+	0.502516i	$0.832408\pi$
$228$	1.56366	+	5.92268i	0.103556	+	0.392239i
$229$			8.06769i			0.533128i	0.963817	+	0.266564i	$0.0858884\pi$
$229$			8.06769i			0.533128i	−0.963817	+	0.266564i	$0.914112\pi$
$230$	−1.70205	−	1.31101i	−0.112230	−	0.0864452i
$231$	−43.5559			−2.86576
$232$	0.677227	−	1.60980i	0.0444622	−	0.105688i
$233$	−18.1011			−1.18584			−0.592922	−	0.805260i	$-0.702026\pi$
$233$	−18.1011			−1.18584			−0.592922	+	0.805260i	$0.702026\pi$
$234$	−28.4538	−	21.9166i	−1.86008	−	1.43273i
$235$		−	7.80972i		−	0.509450i
$236$	2.87818	−	0.759872i	0.187354	−	0.0494635i
$237$			4.22457i			0.274415i
$238$	3.93582	−	5.10978i	0.255122	−	0.331218i
$239$	−22.5877			−1.46107			−0.730537	−	0.682873i	$-0.760730\pi$
$239$	−22.5877			−1.46107			−0.730537	+	0.682873i	$0.760730\pi$
$240$	10.6547	−	6.04741i	0.687755	−	0.390359i
$241$	−1.66938			−0.107534			−0.0537671	−	0.998554i	$-0.517123\pi$
$241$	−1.66938			−0.107534			−0.0537671	+	0.998554i	$0.517123\pi$
$242$	12.5737	−	16.3241i	0.808266	−	1.04935i
$243$			7.44209i			0.477410i
$244$	−14.9566	+	3.94872i	−0.957499	+	0.252791i
$245$			0.908997i			0.0580737i
$246$	35.2581	+	27.1576i	2.24797	+	1.73151i
$247$	3.98012			0.253249
$248$	−19.2320	−	8.09073i	−1.22123	−	0.513762i
$249$	−42.6631			−2.70366
$250$	1.12039	+	0.862980i	0.0708594	+	0.0545797i
$251$		−	3.43312i		−	0.216697i	−0.994113	−	0.108348i	$-0.965444\pi$
$251$		−	3.43312i		−	0.216697i	0.994113	−	0.108348i	$-0.0345562\pi$
$252$	−9.16130	−	34.7004i	−0.577108	−	2.18592i
$253$		−	7.68192i		−	0.482958i
$254$	−14.0735	+	18.2713i	−0.883053	+	1.14645i
$255$	−4.96700			−0.311045
$256$	8.20297	−	13.7372i	0.512686	−	0.858576i
$257$	−4.54870			−0.283740			−0.141870	−	0.989885i	$-0.545312\pi$
$257$	−4.54870			−0.283740			−0.141870	+	0.989885i	$0.545312\pi$
$258$	25.0640	−	32.5399i	1.56041	−	2.02585i
$259$			18.8417i			1.17077i
$260$	−2.03197	−	7.69654i	−0.126018	−	0.477319i
$261$			3.93991i			0.243874i
$262$	9.26298	+	7.13484i	0.572269	+	0.440792i
$263$	11.0906			0.683878			0.341939	−	0.939722i	$-0.388916\pi$
$263$	11.0906			0.683878			0.341939	+	0.939722i	$0.388916\pi$
$264$	40.3781	+	16.9867i	2.48510	+	1.04546i
$265$	8.96779			0.550887
$266$	3.15085	+	2.42695i	0.193191	+	0.148806i
$267$			2.17157i			0.132898i
$268$	14.7348	−	3.89016i	0.900074	−	0.237630i
$269$			0.456872i			0.0278560i	0.999903	+	0.0139280i	$0.00443356\pi$
$269$			0.456872i			0.0278560i	−0.999903	+	0.0139280i	$0.995566\pi$
$270$	−8.93595	+	11.6013i	−0.543825	+	0.706034i
$271$	−8.24792			−0.501025			−0.250513	−	0.968113i	$-0.580599\pi$
$271$	−8.24792			−0.501025			−0.250513	+	0.968113i	$0.580599\pi$
$272$	−5.64148	+	3.20202i	−0.342065	+	0.194151i
$273$	−34.2829			−2.07489
$274$	15.1387	−	19.6543i	0.914565	−	1.18736i
$275$			5.05668i			0.304930i
$276$	8.99752	−	2.37545i	0.541587	−	0.142985i
$277$			17.0974i			1.02729i	0.858004	+	0.513643i	$0.171704\pi$
$277$			17.0974i			1.02729i	−0.858004	+	0.513643i	$0.828296\pi$
$278$	−0.984629	−	0.758413i	−0.0590541	−	0.0454866i
$279$	47.0694			2.81797
$280$	3.08450	−	7.33197i	0.184334	−	0.438169i
$281$	8.94353			0.533527			0.266763	−	0.963762i	$-0.414046\pi$
$281$	8.94353			0.533527			0.266763	+	0.963762i	$0.414046\pi$
$282$	26.7993	+	20.6422i	1.59587	+	1.22923i
$283$			32.6729i			1.94220i	0.238671	+	0.971101i	$0.423288\pi$
$283$			32.6729i			1.94220i	−0.238671	+	0.971101i	$0.576712\pi$
$284$	0.546279	+	2.06915i	0.0324157	+	0.122782i
$285$		−	3.06281i		−	0.181425i
$286$	17.3685	−	22.5491i	1.02702	−	1.33336i
$287$	28.8956			1.70565
$288$	−5.04021	+	35.7416i	−0.296997	+	2.10610i
$289$	−14.3700			−0.845297
$290$	−0.532858	+	0.691796i	−0.0312905	+	0.0406237i
$291$			44.0757i			2.58376i
$292$	−5.54567	−	21.0054i	−0.324536	−	1.22925i
$293$			27.7877i			1.62338i	0.584091	+	0.811688i	$0.301451\pi$
$293$			27.7877i			1.62338i	−0.584091	+	0.811688i	$0.698549\pi$
$294$	−3.11925	−	2.40261i	−0.181918	−	0.140123i
$295$	−1.48840			−0.0866580
$296$	7.34824	−	17.4670i	0.427108	−	1.01525i
$297$	−52.3607			−3.03828
$298$	9.55012	+	7.35601i	0.553224	+	0.426122i
$299$		−	6.04645i		−	0.349675i
$300$	−5.92268	+	1.56366i	−0.341946	+	0.0902777i
$301$		−	26.6679i		−	1.53711i
$302$	13.6698	−	17.7472i	0.786610	−	1.02124i
$303$	36.7622			2.11194
$304$	−1.97447	−	3.47872i	−0.113243	−	0.199518i
$305$	7.73455			0.442879
$306$	8.92997	−	11.5936i	0.510493	−	0.662760i
$307$		−	10.7593i		−	0.614067i	−0.951699	−	0.307034i	$-0.900664\pi$
$307$		−	10.7593i		−	0.614067i	0.951699	−	0.307034i	$-0.0993364\pi$
$308$	27.4995	−	7.26018i	1.56693	−	0.413687i
$309$		−	55.1294i		−	3.13620i
$310$	8.26478	+	6.36597i	0.469408	+	0.361563i
$311$	14.8790			0.843708			0.421854	−	0.906664i	$-0.361379\pi$
$311$	14.8790			0.843708			0.421854	+	0.906664i	$0.361379\pi$
$312$	31.7817	+	13.3703i	1.79928	+	0.756943i
$313$	−16.0734			−0.908523			−0.454261	−	0.890868i	$-0.650097\pi$
$313$	−16.0734			−0.908523			−0.454261	+	0.890868i	$0.650097\pi$
$314$	0.989042	+	0.761812i	0.0558149	+	0.0429916i
$315$			17.9447i			1.01107i
$316$	−0.704180	−	2.66724i	−0.0396132	−	0.150044i
$317$		−	29.8614i		−	1.67718i	−0.544760	−	0.838592i	$-0.683379\pi$
$317$		−	29.8614i		−	1.67718i	0.544760	−	0.838592i	$-0.316621\pi$
$318$	−23.7032	+	30.7732i	−1.32921	+	1.72568i
$319$	−3.12231			−0.174816
$320$	−5.71892	+	5.59410i	−0.319697	+	0.312720i
$321$	55.7683			3.11268
$322$	3.68694	−	4.78666i	0.205465	−	0.266750i
$323$			1.62171i			0.0902345i
$324$	−6.41850	−	24.3115i	−0.356583	−	1.35064i
$325$			3.98012i			0.220778i
$326$	−9.72101	−	7.48763i	−0.538397	−	0.414702i
$327$	4.32581			0.239218
$328$	−26.7875	−	11.2693i	−1.47909	−	0.622241i
$329$	21.9632			1.21087
$330$	−17.3522	−	13.3655i	−0.955205	−	0.735749i
$331$		−	17.6580i		−	0.970573i	−0.874355	−	0.485286i	$-0.838715\pi$
$331$		−	17.6580i		−	0.970573i	0.874355	−	0.485286i	$-0.161285\pi$
$332$	26.9359	−	7.11137i	1.47830	−	0.390287i
$333$			42.7499i			2.34268i
$334$	18.7803	−	24.3819i	1.02761	−	1.33412i
$335$	−7.61986			−0.416317
$336$	17.0071	+	29.9640i	0.927813	+	1.63467i
$337$	−17.1181			−0.932482			−0.466241	−	0.884658i	$-0.654392\pi$
$337$	−17.1181			−0.932482			−0.466241	+	0.884658i	$0.654392\pi$
$338$	2.45206	−	3.18346i	0.133375	−	0.173157i
$339$		−	13.8848i		−	0.754120i
$340$	3.13597	−	0.827933i	0.170072	−	0.0449009i
$341$			37.3018i			2.02000i
$342$	7.14896	+	5.50651i	0.386572	+	0.297758i
$343$	17.1297			0.924916
$344$	−10.4005	+	24.7223i	−0.560756	+	1.33294i
$345$	−4.65290			−0.250504
$346$	−10.8293	−	8.34132i	−0.582188	−	0.448432i
$347$		−	10.4086i		−	0.558761i	−0.960180	−	0.279381i	$-0.909871\pi$
$347$		−	10.4086i		−	0.558761i	0.960180	−	0.279381i	$-0.0901291\pi$
$348$	−0.965498	−	3.65703i	−0.0517561	−	0.196038i
$349$			22.1049i			1.18325i	0.806214	+	0.591624i	$0.201513\pi$
$349$			22.1049i			1.18325i	−0.806214	+	0.591624i	$0.798487\pi$
$350$	−2.42695	+	3.15085i	−0.129726	+	0.168420i
$351$	−41.2132			−2.19980
$352$	−28.3247	−	3.99429i	−1.50971	−	0.212896i
$353$	−7.96563			−0.423968			−0.211984	−	0.977273i	$-0.567992\pi$
$353$	−7.96563			−0.423968			−0.211984	+	0.977273i	$0.567992\pi$
$354$	3.93405	−	5.10749i	0.209093	−	0.271460i
$355$		−	1.07002i		−	0.0567910i
$356$	−0.361972	−	1.37105i	−0.0191845	−	0.0726653i
$357$		−	13.9687i		−	0.739300i
$358$	22.4332	+	17.2793i	1.18563	+	0.913238i
$359$	−32.8817			−1.73543			−0.867715	−	0.497062i	$-0.834412\pi$
$359$	−32.8817			−1.73543			−0.867715	+	0.497062i	$0.834412\pi$
$360$	6.99841	−	16.6355i	0.368849	−	0.876767i
$361$	−1.00000			−0.0526316
$362$	3.99053	+	3.07372i	0.209738	+	0.161551i
$363$		−	44.6253i		−	2.34222i
$364$	21.6449	−	5.71450i	1.13450	−	0.299521i
$365$			10.8626i			0.568574i
$366$	−20.4435	+	26.5413i	−1.06860	+	1.38734i
$367$	8.35897			0.436335			0.218167	−	0.975911i	$-0.429992\pi$
$367$	8.35897			0.436335			0.218167	+	0.975911i	$0.429992\pi$
$368$	−5.28474	+	2.99953i	−0.275486	+	0.156361i
$369$	65.5611			3.41298
$370$	−5.78176	+	7.50632i	−0.300580	+	0.390235i
$371$			25.2201i			1.30936i
$372$	−43.6900	+	11.5347i	−2.26522	+	0.598044i
$373$		−	5.73299i		−	0.296843i	−0.988924	−	0.148422i	$-0.952581\pi$
$373$		−	5.73299i		−	0.296843i	0.988924	−	0.148422i	$-0.0474192\pi$
$374$	9.18771	+	7.07686i	0.475085	+	0.365936i
$375$	3.06281			0.158163
$376$	−20.3608	−	8.56563i	−1.05003	−	0.441739i
$377$	−2.45758			−0.126572
$378$	−32.6263	−	25.1305i	−1.67812	−	1.29257i
$379$			26.5868i			1.36567i	0.730571	+	0.682836i	$0.239254\pi$
$379$			26.5868i			1.36567i	−0.730571	+	0.682836i	$0.760746\pi$
$380$	0.510530	+	1.93374i	0.0261896	+	0.0991989i
$381$			49.9485i			2.55894i
$382$	−15.9719	+	20.7359i	−0.817192	+	1.06094i
$383$	−12.1889			−0.622824			−0.311412	−	0.950275i	$-0.600802\pi$
$383$	−12.1889			−0.622824			−0.311412	+	0.950275i	$0.600802\pi$
$384$	−4.08037	−	34.4107i	−0.208225	−	1.75601i
$385$	−14.2209			−0.724763
$386$	0.769728	−	0.999319i	0.0391781	−	0.0508640i
$387$		−	60.5068i		−	3.07573i
$388$	−7.34684	−	27.8277i	−0.372979	−	1.41274i
$389$		−	17.2618i		−	0.875209i	−0.899168	−	0.437605i	$-0.855827\pi$
$389$		−	17.2618i		−	0.875209i	0.899168	−	0.437605i	$-0.144173\pi$
$390$	−13.6579	−	10.5200i	−0.691595	−	0.532703i
$391$	2.46364			0.124592
$392$	2.36986	+	0.996980i	0.119696	+	0.0503551i
$393$	25.3223			1.27734
$394$	−14.5110	−	11.1771i	−0.731053	−	0.563096i
$395$			1.37931i			0.0694008i
$396$	62.3936	−	16.4726i	3.13539	−	0.827779i
$397$			0.694542i			0.0348581i	0.999848	+	0.0174290i	$0.00554812\pi$
$397$			0.694542i			0.0348581i	−0.999848	+	0.0174290i	$0.994452\pi$
$398$	−5.62853	+	7.30739i	−0.282133	+	0.366286i
$399$	8.61352			0.431215
$400$	3.47872	−	1.97447i	0.173936	−	0.0987233i
$401$	24.2182			1.20940			0.604700	−	0.796454i	$-0.293293\pi$
$401$	24.2182			1.20940			0.604700	+	0.796454i	$0.293293\pi$
$402$	20.1404	−	26.1478i	1.00451	−	1.30413i
$403$			29.3603i			1.46254i
$404$	−23.2103	+	6.12778i	−1.15476	+	0.304868i
$405$			12.5722i			0.624719i
$406$	−1.94553	−	1.49855i	−0.0965552	−	0.0743719i
$407$	−33.8786			−1.67930
$408$	−5.44776	+	12.9495i	−0.269704	+	0.641097i
$409$	27.3171			1.35074			0.675371	−	0.737478i	$-0.263983\pi$
$409$	27.3171			1.35074			0.675371	+	0.737478i	$0.263983\pi$
$410$	11.5117	+	8.86691i	0.568522	+	0.437905i
$411$		−	53.7290i		−	2.65026i
$412$	9.18935	+	34.8067i	0.452727	+	1.71480i
$413$		−	4.18582i		−	0.205971i
$414$	8.36528	−	10.8604i	0.411131	−	0.533761i
$415$	−13.9294			−0.683767
$416$	−22.2944	−	3.14391i	−1.09307	−	0.154143i
$417$	−2.69169			−0.131813
$418$	−4.36382	+	5.66544i	−0.213441	+	0.277106i
$419$		−	7.94266i		−	0.388024i	−0.980999	−	0.194012i	$-0.937850\pi$
$419$		−	7.94266i		−	0.388024i	0.980999	−	0.194012i	$-0.0621501\pi$
$420$	−4.39746	−	16.6563i	−0.214574	−	0.812746i
$421$			24.3855i			1.18848i	0.804289	+	0.594239i	$0.202547\pi$
$421$			24.3855i			1.18848i	−0.804289	+	0.594239i	$0.797453\pi$
$422$	29.9617	+	23.0781i	1.45851	+	1.12342i
$423$	49.8322			2.42293
$424$	9.83580	−	23.3801i	0.477668	−	1.13544i
$425$	−1.62171			−0.0786646
$426$	3.67182	+	2.82823i	0.177900	+	0.137028i
$427$			21.7518i			1.05264i
$428$	−35.2100	+	9.29583i	−1.70194	+	0.449331i
$429$		−	61.6428i		−	2.97614i
$430$	8.18332	−	10.6242i	0.394635	−	0.512345i
$431$	−18.7021			−0.900850			−0.450425	−	0.892814i	$-0.648728\pi$
$431$	−18.7021			−0.900850			−0.450425	+	0.892814i	$0.648728\pi$
$432$	20.4451	+	36.0213i	0.983666	+	1.73307i
$433$	23.9396			1.15047			0.575233	−	0.817990i	$-0.304911\pi$
$433$	23.9396			1.15047			0.575233	+	0.817990i	$0.304911\pi$
$434$	−17.9030	+	23.2430i	−0.859370	+	1.11570i
$435$			1.89117i			0.0906746i
$436$	−2.73116	+	0.721056i	−0.130799	+	0.0345323i
$437$			1.51916i			0.0726714i
$438$	−37.2753	−	28.7114i	−1.78108	−	1.37188i
$439$	−7.24965			−0.346007			−0.173003	−	0.984921i	$-0.555347\pi$
$439$	−7.24965			−0.346007			−0.173003	+	0.984921i	$0.555347\pi$
$440$	13.1834	+	5.54613i	0.628492	+	0.264401i
$441$	−5.80013			−0.276197
$442$	7.23166	+	5.57021i	0.343975	+	0.264948i
$443$		−	26.9821i		−	1.28196i	−0.767558	−	0.640979i	$-0.778529\pi$
$443$		−	26.9821i		−	1.28196i	0.767558	−	0.640979i	$-0.221471\pi$
$444$	−10.4761	−	39.6806i	−0.497174	−	1.88316i
$445$			0.709012i			0.0336104i
$446$	1.05662	−	1.37179i	0.0500325	−	0.0649560i
$447$	26.1073			1.23483
$448$	−15.7322	−	16.0833i	−0.743279	−	0.759864i
$449$	16.5865			0.782767			0.391384	−	0.920228i	$-0.371997\pi$
$449$	16.5865			0.782767			0.391384	+	0.920228i	$0.371997\pi$
$450$	−5.50651	+	7.14896i	−0.259579	+	0.337005i
$451$			51.9562i			2.44652i
$452$	2.31442	+	8.76636i	0.108861	+	0.412335i
$453$		−	48.5157i		−	2.27947i
$454$	−16.9653	−	13.0675i	−0.796219	−	0.613290i
$455$	−11.1933			−0.524749
$456$	−7.98510	−	3.35926i	−0.373936	−	0.157312i
$457$	5.05916			0.236657			0.118329	−	0.992974i	$-0.462246\pi$
$457$	5.05916			0.236657			0.118329	+	0.992974i	$0.462246\pi$
$458$	−9.03893	−	6.96226i	−0.422361	−	0.325325i
$459$		−	16.7924i		−	0.783804i
$460$	2.93767	−	0.775577i	0.136969	−	0.0361615i
$461$		−	6.93588i		−	0.323036i	−0.986870	−	0.161518i	$-0.948361\pi$
$461$		−	6.93588i		−	0.323036i	0.986870	−	0.161518i	$-0.0516390\pi$
$462$	37.5878	−	48.7994i	1.74874	−	2.27035i
$463$	7.62487			0.354358			0.177179	−	0.984179i	$-0.443303\pi$
$463$	7.62487			0.354358			0.177179	+	0.984179i	$0.443303\pi$
$464$	1.21916	+	2.14798i	0.0565980	+	0.0997174i
$465$	22.5935			1.04775
$466$	15.6209	−	20.2803i	0.723625	−	0.939465i
$467$		−	3.20732i		−	0.148417i	−0.997243	−	0.0742086i	$-0.976357\pi$
$467$		−	3.20732i		−	0.148417i	0.997243	−	0.0742086i	$-0.0236431\pi$
$468$	49.1101	−	12.9656i	2.27011	−	0.599336i
$469$		−	21.4293i		−	0.989512i
$470$	8.74990	+	6.73963i	0.403603	+	0.310876i
$471$	2.70375			0.124582
$472$	−1.63246	+	3.88043i	−0.0751402	+	0.178611i
$473$	47.9507			2.20477
$474$	−4.73315	−	3.64572i	−0.217401	−	0.167454i
$475$		−	1.00000i		−	0.0458831i
$476$	2.32839	+	8.81928i	0.106722	+	0.404231i
$477$			57.2217i			2.62000i
$478$	19.4927	−	25.3069i	0.891576	−	1.15751i
$479$	7.68052			0.350932			0.175466	−	0.984486i	$-0.443857\pi$
$479$	7.68052			0.350932			0.175466	+	0.984486i	$0.443857\pi$
$480$	−2.41932	+	17.1561i	−0.110426	+	0.783066i
$481$	−26.6659			−1.21586
$482$	1.44064	−	1.87035i	0.0656194	−	0.0851921i
$483$		−	13.0853i		−	0.595403i
$484$	7.43844	+	28.1747i	0.338111	+	1.28067i
$485$			14.3906i			0.653444i
$486$	−8.33801	−	6.42238i	−0.378220	−	0.291325i
$487$	−5.35340			−0.242586			−0.121293	−	0.992617i	$-0.538704\pi$
$487$	−5.35340			−0.242586			−0.121293	+	0.992617i	$0.538704\pi$
$488$	8.48318	−	20.1649i	0.384016	−	0.912820i
$489$	−26.5744			−1.20174
$490$	−1.01843	−	0.784447i	−0.0460079	−	0.0354377i
$491$			28.4990i			1.28614i	0.765807	+	0.643070i	$0.222340\pi$
$491$			28.4990i			1.28614i	−0.765807	+	0.643070i	$0.777660\pi$
$492$	−60.8541	+	16.0662i	−2.74351	+	0.724319i
$493$		−	1.00135i		−	0.0450984i
$494$	−3.43477	+	4.45928i	−0.154538	+	0.200632i
$495$	−32.2657			−1.45024
$496$	25.6615	−	14.5651i	1.15224	−	0.653992i
$497$	3.00922			0.134982
$498$	36.8174	−	47.7991i	1.64983	−	2.14193i
$499$			7.57745i			0.339213i	0.985512	+	0.169607i	$0.0542497\pi$
$499$			7.57745i			0.339213i	−0.985512	+	0.169607i	$0.945750\pi$
$500$	−1.93374	+	0.510530i	−0.0864796	+	0.0228316i
$501$		−	66.6532i		−	2.97784i
$502$	3.84642	+	2.96272i	0.171674	+	0.132233i
$503$	3.33433			0.148670			0.0743352	−	0.997233i	$-0.476317\pi$
$503$	3.33433			0.148670			0.0743352	+	0.997233i	$0.476317\pi$
$504$	46.7839	+	19.6816i	2.08392	+	0.876687i
$505$	12.0028			0.534117
$506$	8.60672	+	6.62935i	0.382615	+	0.294710i
$507$		−	8.70264i		−	0.386498i
$508$	−8.32575	−	31.5356i	−0.369396	−	1.39917i
$509$			27.9961i			1.24091i	0.784243	+	0.620454i	$0.213051\pi$
$509$			27.9961i			1.24091i	−0.784243	+	0.620454i	$0.786949\pi$
$510$	4.28642	−	5.56495i	0.189806	−	0.246420i
$511$	−30.5488			−1.35140
$512$	8.31199	+	21.0454i	0.367342	+	0.930086i
$513$	10.3548			0.457174
$514$	3.92544	−	5.09630i	0.173144	−	0.224788i
$515$		−	17.9996i		−	0.793159i
$516$	14.8276	+	56.1626i	0.652747	+	2.47242i
$517$			39.4913i			1.73682i
$518$	−21.1100	−	16.2600i	−0.927519	−	0.714424i
$519$	−29.6042			−1.29948
$520$	10.3766	+	4.36537i	0.455046	+	0.191434i
$521$	13.5559			0.593897			0.296948	−	0.954894i	$-0.404031\pi$
$521$	13.5559			0.593897			0.296948	+	0.954894i	$0.404031\pi$
$522$	−4.41421	−	3.40006i	−0.193205	−	0.148817i
$523$		−	5.27502i		−	0.230660i	−0.993327	−	0.115330i	$-0.963207\pi$
$523$		−	5.27502i		−	0.230660i	0.993327	−	0.115330i	$-0.0367926\pi$
$524$	−15.9875	+	4.22089i	−0.698419	+	0.184390i
$525$			8.61352i			0.375925i
$526$	−9.57100	+	12.4258i	−0.417315	+	0.541790i
$527$	−11.9629			−0.521113
$528$	−53.8772	+	30.5799i	−2.34470	+	1.33082i
$529$	−20.6921			−0.899659
$530$	−7.73903	+	10.0474i	−0.336162	+	0.436431i
$531$		−	9.49718i		−	0.412143i
$532$	−5.43825	+	1.43576i	−0.235778	+	0.0622481i
$533$			40.8948i			1.77135i
$534$	−2.43300	−	1.87402i	−0.105286	−	0.0810969i
$535$	18.2082			0.787210
$536$	−8.35740	+	19.8658i	−0.360985	+	0.858074i
$537$	61.3260			2.64641
$538$	−0.511873	−	0.394272i	−0.0220684	−	0.0169983i
$539$		−	4.59651i		−	0.197986i
$540$	−5.28641	−	20.0234i	−0.227491	−	0.861671i
$541$			37.8198i			1.62600i	0.582265	+	0.812999i	$0.302167\pi$
$541$			37.8198i			1.62600i	−0.582265	+	0.812999i	$0.697833\pi$
$542$	7.11779	−	9.24085i	0.305735	−	0.396929i
$543$	10.9089			0.468148
$544$	1.28099	−	9.08392i	0.0549222	−	0.389470i
$545$	1.41237			0.0604992
$546$	29.5855	−	38.4101i	1.26614	−	1.64380i
$547$			8.20562i			0.350847i	0.984493	+	0.175423i	$0.0561295\pi$
$547$			8.20562i			0.350847i	−0.984493	+	0.175423i	$0.943871\pi$
$548$	8.95592	+	33.9225i	0.382578	+	1.44910i
$549$			49.3526i			2.10632i
$550$	−5.66544	−	4.36382i	−0.241575	−	0.186074i
$551$	0.617462			0.0263048
$552$	−5.10326	+	12.1307i	−0.217209	+	0.516315i
$553$	−3.87903			−0.164953
$554$	−19.1557	−	14.7548i	−0.813849	−	0.626869i
$555$			20.5201i			0.871029i
$556$	1.69943	−	0.448669i	0.0720720	−	0.0190278i
$557$		−	38.8646i		−	1.64675i	−0.567500	−	0.823374i	$-0.692089\pi$
$557$		−	38.8646i		−	1.64675i	0.567500	−	0.823374i	$-0.307911\pi$
$558$	−40.6200	+	52.7359i	−1.71958	+	2.23249i
$559$	37.7420			1.59632
$560$	5.55278	+	9.78318i	0.234648	+	0.413415i
$561$	25.1165			1.06042
$562$	−7.71809	+	10.0202i	−0.325568	+	0.422677i
$563$			43.2675i			1.82351i	0.410736	+	0.911754i	$0.365272\pi$
$563$			43.2675i			1.82351i	−0.410736	+	0.911754i	$0.634728\pi$
$564$	−46.2545	+	12.2117i	−1.94766	+	0.514205i
$565$		−	4.53336i		−	0.190720i
$566$	−36.6062	−	28.1961i	−1.53868	−	1.18517i
$567$	−35.3568			−1.48485
$568$	−2.78968	−	1.17359i	−0.117052	−	0.0492429i
$569$	−4.14459			−0.173750			−0.0868750	−	0.996219i	$-0.527688\pi$
$569$	−4.14459			−0.173750			−0.0868750	+	0.996219i	$0.527688\pi$
$570$	3.43153	+	2.64314i	0.143731	+	0.110709i
$571$			7.85216i			0.328603i	0.986410	+	0.164301i	$0.0525369\pi$
$571$			7.85216i			0.328603i	−0.986410	+	0.164301i	$0.947463\pi$
$572$	10.2750	+	38.9189i	0.429621	+	1.62728i
$573$			56.6859i			2.36809i
$574$	−24.9363	+	32.3742i	−1.04082	+	1.35127i
$575$	−1.51916			−0.0633534
$576$	−35.6948	−	36.4913i	−1.48728	−	1.52047i
$577$	8.01296			0.333584			0.166792	−	0.985992i	$-0.446659\pi$
$577$	8.01296			0.333584			0.166792	+	0.985992i	$0.446659\pi$
$578$	12.4011	−	16.1000i	0.515816	−	0.669672i
$579$		−	2.73185i		−	0.113532i
$580$	−0.315233	−	1.19401i	−0.0130893	−	0.0495787i
$581$		−	39.1736i		−	1.62519i
$582$	−49.3818	−	38.0365i	−2.04694	−	1.57666i
$583$	−45.3473			−1.87809
$584$	28.3200	+	11.9140i	1.17189	+	0.493004i
$585$	−25.3964			−1.05001
$586$	−31.1330	−	23.9803i	−1.28609	−	0.990616i
$587$		−	25.2668i		−	1.04287i	−0.853290	−	0.521436i	$-0.825396\pi$
$587$		−	25.2668i		−	1.04287i	0.853290	−	0.521436i	$-0.174604\pi$
$588$	5.38370	−	1.42136i	0.222020	−	0.0586158i
$589$		−	7.37672i		−	0.303953i
$590$	1.28446	−	1.66758i	0.0528804	−	0.0686533i
$591$	−39.6688			−1.63176
$592$	13.2284	+	23.3066i	0.543686	+	0.957895i
$593$	10.1106			0.415192			0.207596	−	0.978215i	$-0.433436\pi$
$593$	10.1106			0.415192			0.207596	+	0.978215i	$0.433436\pi$
$594$	45.1863	−	58.6642i	1.85402	−	2.40702i
$595$		−	4.56073i		−	0.186972i
$596$	−16.4831	+	4.35173i	−0.675175	+	0.178254i
$597$			19.9763i			0.817574i
$598$	6.77436	+	5.21797i	0.277024	+	0.213379i
$599$	−19.9087			−0.813446			−0.406723	−	0.913552i	$-0.633329\pi$
$599$	−19.9087			−0.813446			−0.406723	+	0.913552i	$0.633329\pi$
$600$	3.35926	−	7.98510i	0.137141	−	0.325990i
$601$	−25.0367			−1.02127			−0.510634	−	0.859798i	$-0.670589\pi$
$601$	−25.0367			−1.02127			−0.510634	+	0.859798i	$0.670589\pi$
$602$	29.8784	+	23.0139i	1.21775	+	0.937977i
$603$		−	48.6208i		−	1.97999i
$604$	8.08692	+	30.6310i	0.329052	+	1.24636i
$605$		−	14.5701i		−	0.592357i
$606$	−31.7251	+	41.1879i	−1.28874	+	1.67314i
$607$	−4.94906			−0.200876			−0.100438	−	0.994943i	$-0.532024\pi$
$607$	−4.94906			−0.200876			−0.100438	+	0.994943i	$0.532024\pi$
$608$	5.60143	+	0.789902i	0.227168	+	0.0320348i
$609$	−5.31852			−0.215518
$610$	−6.67476	+	8.66568i	−0.270253	+	0.350863i
$611$			31.0836i			1.25751i
$612$	5.28287	+	20.0100i	0.213548	+	0.808858i
$613$			28.5126i			1.15161i	0.817585	+	0.575807i	$0.195312\pi$
$613$			28.5126i			1.15161i	−0.817585	+	0.575807i	$0.804688\pi$
$614$	12.0546	+	9.28509i	0.486484	+	0.374716i
$615$	31.4696			1.26898
$616$	−15.5973	+	37.0755i	−0.628435	+	1.49381i
$617$	36.9906			1.48919			0.744593	−	0.667519i	$-0.232644\pi$
$617$	36.9906			1.48919			0.744593	+	0.667519i	$0.232644\pi$
$618$	61.7663	+	47.5756i	2.48460	+	1.91377i
$619$		−	14.0321i		−	0.563997i	−0.959415	−	0.281998i	$-0.909003\pi$
$619$		−	14.0321i		−	0.563997i	0.959415	−	0.281998i	$-0.0909973\pi$
$620$	−14.2647	+	3.76604i	−0.572883	+	0.151248i
$621$		−	15.7305i		−	0.631245i
$622$	−12.8402	+	16.6702i	−0.514847	+	0.668413i
$623$	−1.99395			−0.0798860
$624$	−42.4068	+	24.0695i	−1.69763	+	0.963549i
$625$	1.00000			0.0400000
$626$	13.8710	−	18.0084i	0.554398	−	0.719761i
$627$			15.4877i			0.618518i
$628$	−1.70705	+	0.450680i	−0.0681186	+	0.0179841i
$629$		−	10.8651i		−	0.433219i
$630$	−20.1050	−	15.4859i	−0.801002	−	0.616974i
$631$	−12.3580			−0.491962			−0.245981	−	0.969275i	$-0.579110\pi$
$631$	−12.3580			−0.491962			−0.245981	+	0.969275i	$0.579110\pi$
$632$	3.59603	+	1.51282i	0.143042	+	0.0601767i
$633$	81.9066			3.25549
$634$	33.4563	+	25.7698i	1.32872	+	1.02345i
$635$			16.3081i			0.647166i
$636$	−14.0225	−	53.1134i	−0.556030	−	2.10608i
$637$		−	3.61792i		−	0.143347i
$638$	2.69449	−	3.49819i	0.106676	−	0.138495i
$639$	6.82762			0.270096
$640$	−1.33223	−	11.2350i	−0.0526610	−	0.444102i
$641$	−24.6420			−0.973301			−0.486651	−	0.873597i	$-0.661782\pi$
$641$	−24.6420			−0.973301			−0.486651	+	0.873597i	$0.661782\pi$
$642$	−48.1269	+	62.4820i	−1.89942	+	2.46597i
$643$		−	19.7785i		−	0.779990i	−0.920817	−	0.389995i	$-0.872477\pi$
$643$		−	19.7785i		−	0.779990i	0.920817	−	0.389995i	$-0.127523\pi$
$644$	2.18115	+	8.26159i	0.0859494	+	0.325552i
$645$		−	29.0435i		−	1.14359i
$646$	−1.81694	−	1.39951i	−0.0714867	−	0.0550628i
$647$	−9.04173			−0.355467			−0.177734	−	0.984079i	$-0.556877\pi$
$647$	−9.04173			−0.355467			−0.177734	+	0.984079i	$0.556877\pi$
$648$	32.7773	+	13.7891i	1.28761	+	0.541688i
$649$	7.52637			0.295436
$650$	−4.45928	−	3.43477i	−0.174907	−	0.134723i
$651$			63.5396i			2.49031i
$652$	16.7781	−	4.42960i	0.657080	−	0.173477i
$653$		−	43.0547i		−	1.68486i	−0.538805	−	0.842430i	$-0.681124\pi$
$653$		−	43.0547i		−	1.68486i	0.538805	−	0.842430i	$-0.318876\pi$
$654$	−3.73309	+	4.84658i	−0.145975	+	0.189516i
$655$	8.26767			0.323045
$656$	35.7430	−	20.2871i	1.39553	−	0.792080i
$657$	−69.3120			−2.70412
$658$	−18.9538	+	24.6073i	−0.738897	+	0.959292i
$659$		−	49.7536i		−	1.93813i	−0.246814	−	0.969063i	$-0.579384\pi$
$659$		−	49.7536i		−	1.93813i	0.246814	−	0.969063i	$-0.420616\pi$
$660$	29.9491	−	7.90691i	1.16577	−	0.307776i
$661$		−	38.6735i		−	1.50423i	−0.659034	−	0.752113i	$-0.729035\pi$
$661$		−	38.6735i		−	1.50423i	0.659034	−	0.752113i	$-0.270965\pi$
$662$	19.7838	+	15.2385i	0.768919	+	0.592262i
$663$	19.7693			0.767775
$664$	−15.2776	+	36.3156i	−0.592888	+	1.40932i
$665$	2.81229			0.109056
$666$	−47.8963	−	36.8923i	−1.85595	−	1.42955i
$667$		−	0.938025i		−	0.0363205i
$668$	11.1102	+	42.0823i	0.429866	+	1.62821i
$669$		−	3.75006i		−	0.144986i
$670$	6.57579	−	8.53718i	0.254045	−	0.329820i
$671$	−39.1112			−1.50987
$672$	−48.2481	−	6.80384i	−1.86121	−	0.262464i
$673$	−30.4504			−1.17378			−0.586889	−	0.809668i	$-0.699647\pi$
$673$	−30.4504			−1.17378			−0.586889	+	0.809668i	$0.699647\pi$
$674$	14.7726	−	19.1789i	0.569018	−	0.738742i
$675$			10.3548i			0.398555i
$676$	1.45061	+	5.49452i	0.0557929	+	0.211328i
$677$		−	21.2451i		−	0.816517i	−0.912866	−	0.408259i	$-0.866136\pi$
$677$		−	21.2451i		−	0.816517i	0.912866	−	0.408259i	$-0.133864\pi$
$678$	15.5564	+	11.9823i	0.597439	+	0.460179i
$679$	−40.4706			−1.55312
$680$	−1.77868	+	4.22799i	−0.0682093	+	0.162136i
$681$	−46.3781			−1.77721
$682$	−41.7924	−	32.1907i	−1.60031	−	1.23265i
$683$			25.0990i			0.960388i	0.877162	+	0.480194i	$0.159434\pi$
$683$			25.0990i			0.960388i	−0.877162	+	0.480194i	$0.840566\pi$
$684$	−12.3388	+	3.25759i	−0.471787	+	0.124557i
$685$		−	17.5424i		−	0.670261i
$686$	−14.7826	+	19.1919i	−0.564402	+	0.732749i
$687$	−24.7098			−0.942738
$688$	−18.7231	−	32.9874i	−0.713812	−	1.25763i
$689$	−35.6929			−1.35979
$690$	4.01536	−	5.21305i	0.152862	−	0.198457i
$691$			43.6924i			1.66214i	0.556171	+	0.831068i	$0.312270\pi$
$691$			43.6924i			1.66214i	−0.556171	+	0.831068i	$0.687730\pi$
$692$	18.6910	−	4.93463i	0.710525	−	0.187587i
$693$		−	90.7406i		−	3.44695i
$694$	11.6616	+	8.98239i	0.442669	+	0.340967i
$695$	−0.878831			−0.0333359
$696$	4.93050	+	2.07422i	0.186890	+	0.0786231i
$697$	−16.6627			−0.631144
$698$	−24.7660	−	19.0761i	−0.937407	−	0.722040i
$699$		−	55.4403i		−	2.09695i
$700$	−1.43576	−	5.43825i	−0.0542666	−	0.205547i
$701$			5.13928i			0.194108i	0.995279	+	0.0970539i	$0.0309419\pi$
$701$			5.13928i			0.194108i	−0.995279	+	0.0970539i	$0.969058\pi$
$702$	35.5662	−	46.1747i	1.34236	−	1.74275i
$703$	6.69976			0.252686
$704$	28.9188	−	28.2876i	1.08992	−	1.06613i
$705$	23.9197			0.900867
$706$	6.87419	−	8.92458i	0.258713	−	0.335881i
$707$			33.7554i			1.26950i
$708$	2.32734	+	8.81532i	0.0874669	+	0.331300i
$709$		−	23.4211i		−	0.879596i	−0.898097	−	0.439798i	$-0.855050\pi$
$709$		−	23.4211i		−	0.879596i	0.898097	−	0.439798i	$-0.144950\pi$
$710$	1.19884	+	0.923410i	0.0449917	+	0.0346550i
$711$	−8.80112			−0.330068
$712$	1.84848	+	0.777639i	0.0692746	+	0.0291432i
$713$	−11.2064			−0.419684
$714$	15.6503	+	12.0547i	0.585697	+	0.451135i
$715$		−	20.1262i		−	0.752678i
$716$	−38.7189	+	10.2222i	−1.44699	+	0.382022i
$717$		−	69.1817i		−	2.58364i
$718$	28.3763	−	36.8402i	1.05899	−	1.37486i
$719$	22.6820			0.845894			0.422947	−	0.906154i	$-0.360996\pi$
$719$	22.6820			0.845894			0.422947	+	0.906154i	$0.360996\pi$
$720$	12.5987	+	22.1970i	0.469525	+	0.827234i
$721$	50.6203			1.88520
$722$	0.862980	−	1.12039i	0.0321168	−	0.0416965i
$723$		−	5.11299i		−	0.190154i
$724$	−6.88750	+	1.81838i	−0.255972	+	0.0675794i
$725$			0.617462i			0.0229320i
$726$	49.9976	+	38.5108i	1.85558	+	1.42927i
$727$	34.2340			1.26967			0.634835	−	0.772648i	$-0.281068\pi$
$727$	34.2340			1.26967			0.634835	+	0.772648i	$0.281068\pi$
$728$	−12.2767	+	29.1822i	−0.455005	+	1.08156i
$729$	14.9230			0.552704
$730$	−12.1703	−	9.37420i	−0.450443	−	0.346955i
$731$			15.3781i			0.568780i
$732$	−12.0942	−	45.8093i	−0.447013	−	1.69316i
$733$			35.0860i			1.29593i	0.761670	+	0.647965i	$0.224380\pi$
$733$			35.0860i			1.29593i	−0.761670	+	0.647965i	$0.775620\pi$
$734$	−7.21363	+	9.36527i	−0.266260	+	0.345679i
$735$	−2.78409			−0.102693
$736$	1.19999	−	8.50948i	0.0442322	−	0.313664i
$737$	38.5312			1.41932
$738$	−56.5780	+	73.4538i	−2.08266	+	2.70387i
$739$		−	6.36634i		−	0.234190i	−0.993121	−	0.117095i	$-0.962642\pi$
$739$		−	6.36634i		−	0.234190i	0.993121	−	0.117095i	$-0.0373581\pi$
$740$	−3.42043	−	12.9556i	−0.125737	−	0.476258i
$741$			12.1904i			0.447824i
$742$	−28.2562	−	21.7644i	−1.03732	−	0.798997i
$743$	−0.905818			−0.0332312			−0.0166156	−	0.999862i	$-0.505289\pi$
$743$	−0.905818			−0.0332312			−0.0166156	+	0.999862i	$0.505289\pi$
$744$	24.7804	−	58.9038i	0.908492	−	2.15952i
$745$	8.52396			0.312294
$746$	6.42316	+	4.94746i	0.235169	+	0.181139i
$747$		−	88.8808i		−	3.25198i
$748$	−15.8576	+	4.18659i	−0.579813	+	0.153077i
$749$			51.2068i			1.87106i
$750$	−2.64314	+	3.43153i	−0.0965140	+	0.125302i
$751$	−17.1561			−0.626035			−0.313018	−	0.949747i	$-0.601340\pi$
$751$	−17.1561			−0.626035			−0.313018	+	0.949747i	$0.601340\pi$
$752$	27.1678	−	15.4200i	0.990708	−	0.562310i
$753$	10.5150			0.383188
$754$	2.12084	−	2.75344i	0.0772365	−	0.100274i
$755$		−	15.8403i		−	0.576486i
$756$	56.3118	−	14.8669i	2.04804	−	0.540705i
$757$			36.1374i			1.31344i	0.754136	+	0.656718i	$0.228056\pi$
$757$			36.1374i			1.31344i	−0.754136	+	0.656718i	$0.771944\pi$
$758$	−29.7875	−	22.9439i	−1.08193	−	0.833360i
$759$	23.5283			0.854022
$760$	−2.60712	−	1.09679i	−0.0945700	−	0.0397848i
$761$	−8.20143			−0.297302			−0.148651	−	0.988890i	$-0.547493\pi$
$761$	−8.20143			−0.297302			−0.148651	+	0.988890i	$0.547493\pi$
$762$	−55.9616	−	43.1046i	−2.02728	−	1.56151i
$763$			3.97199i			0.143796i
$764$	−9.44878	−	35.7893i	−0.341845	−	1.29481i
$765$		−	10.3478i		−	0.374127i
$766$	10.5188	−	13.6563i	0.380059	−	0.493422i
$767$	5.92402			0.213904
$768$	42.0745	+	25.1241i	1.51823	+	0.906589i
$769$	18.4357			0.664810			0.332405	−	0.943137i	$-0.392140\pi$
$769$	18.4357			0.664810			0.332405	+	0.943137i	$0.392140\pi$
$770$	12.2723	−	15.9329i	0.442265	−	0.574181i
$771$		−	13.9318i		−	0.501742i
$772$	0.455363	+	1.72479i	0.0163889	+	0.0620764i
$773$			20.9082i			0.752014i	0.926617	+	0.376007i	$0.122703\pi$
$773$			20.9082i			0.752014i	−0.926617	+	0.376007i	$0.877297\pi$
$774$	67.7909	+	52.2162i	2.43670	+	1.87687i
$775$	7.37672			0.264980
$776$	37.5180	+	15.7835i	1.34682	+	0.566595i
$777$	−57.7085			−2.07028
$778$	19.3399	+	14.8966i	0.693369	+	0.534069i
$779$		−	10.2747i		−	0.368131i
$780$	23.5730	−	6.22354i	0.844050	−	0.222839i
$781$			5.41078i			0.193613i
$782$	−2.12608	+	2.76023i	−0.0760284	+	0.0987057i
$783$	−6.39367			−0.228491
$784$	−3.16215	+	1.79478i	−0.112934	+	0.0640994i
$785$	0.882769			0.0315074
$786$	−21.8526	+	28.3708i	−0.779458	+	1.01195i
$787$		−	34.8166i		−	1.24108i	−0.784176	−	0.620539i	$-0.786914\pi$
$787$		−	34.8166i		−	1.24108i	0.784176	−	0.620539i	$-0.213086\pi$
$788$	25.0454	−	6.61227i	0.892206	−	0.235552i
$789$			33.9685i			1.20931i
$790$	−1.54536	−	1.19032i	−0.0549815	−	0.0423497i
$791$	12.7492			0.453308
$792$	−35.3887	+	84.1204i	−1.25748	+	2.98909i
$793$	−30.7845			−1.09319
$794$	−0.778156	−	0.599376i	−0.0276157	−	0.0212711i
$795$			27.4666i			0.974141i
$796$	−3.32978	−	12.6123i	−0.118021	−	0.447030i
$797$		−	31.0580i		−	1.10013i	−0.835121	−	0.550066i	$-0.814603\pi$
$797$		−	31.0580i		−	1.10013i	0.835121	−	0.550066i	$-0.185397\pi$
$798$	−7.43330	+	9.65047i	−0.263136	+	0.341623i
$799$	−12.6651			−0.448060
$800$	−0.789902	+	5.60143i	−0.0279273	+	0.198041i
$801$	−4.52407			−0.159850
$802$	−20.8998	+	27.1337i	−0.737999	+	0.958126i
$803$		−	54.9287i		−	1.93839i
$804$	11.9148	+	45.1300i	0.420204	+	1.59161i
$805$		−	4.27233i		−	0.150580i
$806$	−32.8948	−	25.3373i	−1.15867	−	0.892470i
$807$	−1.39931			−0.0492582
$808$	13.1646	−	31.2926i	0.463127	−	1.10087i
$809$	−18.1110			−0.636750			−0.318375	−	0.947965i	$-0.603137\pi$
$809$	−18.1110			−0.636750			−0.318375	+	0.947965i	$0.603137\pi$
$810$	−14.0858	−	10.8496i	−0.494923	−	0.381216i
$811$			26.9319i			0.945707i	0.881141	+	0.472854i	$0.156776\pi$
$811$			26.9319i			0.945707i	−0.881141	+	0.472854i	$0.843224\pi$
$812$	3.35792	−	0.886528i	0.117840	−	0.0311110i
$813$		−	25.2618i		−	0.885970i
$814$	29.2365	−	37.9571i	1.02474	−	1.33040i
$815$	−8.67648			−0.303924
$816$	−9.80717	−	17.2788i	−0.343320	−	0.604879i
$817$	−9.48263			−0.331755
$818$	−23.5741	+	30.6057i	−0.824249	+	1.07010i
$819$		−	71.4221i		−	2.49569i
$820$	−19.8687	+	5.24556i	−0.693846	+	0.183183i
$821$		−	15.3754i		−	0.536604i	−0.963335	−	0.268302i	$-0.913537\pi$
$821$		−	15.3754i		−	0.536604i	0.963335	−	0.268302i	$-0.0864625\pi$
$822$	60.1973	+	46.3671i	2.09962	+	1.61724i
$823$	−9.79320			−0.341370			−0.170685	−	0.985326i	$-0.554598\pi$
$823$	−9.79320			−0.341370			−0.170685	+	0.985326i	$0.554598\pi$
$824$	−46.9271	−	19.7418i	−1.63478	−	0.687740i
$825$	−15.4877			−0.539211
$826$	4.68973	+	3.61228i	0.163177	+	0.125687i
$827$		−	13.5867i		−	0.472456i	−0.971698	−	0.236228i	$-0.924089\pi$
$827$		−	13.5867i		−	0.472456i	0.971698	−	0.236228i	$-0.0759113\pi$
$828$	4.94881	+	18.7447i	0.171983	+	0.651423i
$829$			4.13713i			0.143688i	0.997416	+	0.0718442i	$0.0228884\pi$
$829$			4.13713i			0.143688i	−0.997416	+	0.0718442i	$0.977112\pi$
$830$	12.0208	−	15.6063i	0.417248	−	0.541703i
$831$	−52.3662			−1.81656
$832$	22.7620	−	22.2652i	0.789131	−	0.771907i
$833$	1.47413			0.0510757
$834$	2.32288	−	3.01573i	0.0804346	−	0.104426i
$835$		−	21.7621i		−	0.753108i
$836$	−2.58159	−	9.77832i	−0.0892861	−	0.338190i
$837$			76.3841i			2.64022i
$838$	8.89885	+	6.85436i	0.307406	+	0.236780i
$839$	3.97020			0.137067			0.0685333	−	0.997649i	$-0.478168\pi$
$839$	3.97020			0.137067			0.0685333	+	0.997649i	$0.478168\pi$
$840$	22.4564	+	9.44724i	0.774821	+	0.325961i
$841$	28.6187			0.986853
$842$	−27.3212	−	21.0442i	−0.941550	−	0.725232i
$843$			27.3923i			0.943442i
$844$	−51.7127	+	13.6527i	−1.78002	+	0.469947i
$845$		−	2.84139i		−	0.0977468i
$846$	−43.0043	+	55.8314i	−1.47852	+	1.91952i
$847$	40.9753			1.40793
$848$	17.7066	+	31.1964i	0.608047	+	1.07129i
$849$	−100.071			−3.43442
$850$	1.39951	−	1.81694i	0.0480027	−	0.0623207i
$851$		−	10.1780i		−	0.348898i
$852$	−6.33742	+	1.67315i	−0.217116	+	0.0573212i
$853$			36.8510i			1.26176i	0.775882	+	0.630878i	$0.217305\pi$
$853$			36.8510i			1.26176i	−0.775882	+	0.630878i	$0.782695\pi$
$854$	−24.3704	−	18.7714i	−0.833939	−	0.642344i
$855$	6.38080			0.218219
$856$	19.9706	−	47.4709i	0.682581	−	1.62252i
$857$	−21.6000			−0.737841			−0.368921	−	0.929461i	$-0.620273\pi$
$857$	−21.6000			−0.737841			−0.368921	+	0.929461i	$0.620273\pi$
$858$	69.0637	+	53.1965i	2.35780	+	1.81610i
$859$		−	5.01717i		−	0.171184i	−0.996330	−	0.0855919i	$-0.972722\pi$
$859$		−	5.01717i		−	0.171184i	0.996330	−	0.0855919i	$-0.0272781\pi$
$860$	4.84116	+	18.3370i	0.165082	+	0.625285i
$861$			88.5018i			3.01613i
$862$	16.1396	−	20.9536i	0.549716	−	0.713683i
$863$	−48.4943			−1.65077			−0.825383	−	0.564573i	$-0.809041\pi$
$863$	−48.4943			−1.65077			−0.825383	+	0.564573i	$0.809041\pi$
$864$	−58.0015	−	8.17924i	−1.97325	−	0.278263i
$865$	−9.66571			−0.328644
$866$	−20.6594	+	26.8216i	−0.702036	+	0.911437i
$867$		−	44.0127i		−	1.49475i
$868$	−10.5912	−	40.1165i	−0.359489	−	1.36164i
$869$		−	6.97475i		−	0.236602i
$870$	−2.11884	−	1.63204i	−0.0718354	−	0.0553314i
$871$	30.3280			1.02762
$872$	1.54907	−	3.68221i	0.0524582	−	0.124695i
$873$	−91.8237			−3.10776
$874$	−1.70205	−	1.31101i	−0.0575726	−	0.0443455i
$875$			2.81229i			0.0950729i
$876$	64.3357	−	16.9853i	2.17370	−	0.573881i
$877$		−	9.26377i		−	0.312815i	−0.987693	−	0.156408i	$-0.950009\pi$
$877$		−	9.26377i		−	0.312815i	0.987693	−	0.156408i	$-0.0499913\pi$
$878$	6.25630	−	8.12240i	0.211140	−	0.274118i
$879$	−85.1085			−2.87064
$880$	−17.5908	+	9.98425i	−0.592985	+	0.336569i
$881$	14.0630			0.473793			0.236897	−	0.971535i	$-0.423870\pi$
$881$	14.0630			0.473793			0.236897	+	0.971535i	$0.423870\pi$
$882$	5.00540	−	6.49839i	0.168541	−	0.218812i
$883$		−	48.1637i		−	1.62084i	−0.585850	−	0.810419i	$-0.699239\pi$
$883$		−	48.1637i		−	1.62084i	0.585850	−	0.810419i	$-0.300761\pi$
$884$	−12.4816	+	3.29527i	−0.419801	+	0.110832i
$885$		−	4.55868i		−	0.153238i
$886$	30.2304	+	23.2850i	1.01561	+	0.782275i
$887$	36.5264			1.22644			0.613218	−	0.789914i	$-0.289875\pi$
$887$	36.5264			1.22644			0.613218	+	0.789914i	$0.289875\pi$
$888$	53.4982	+	22.5063i	1.79528	+	0.755261i
$889$	−45.8631			−1.53820
$890$	−0.794367	−	0.611864i	−0.0266273	−	0.0205097i
$891$		−	63.5738i		−	2.12980i
$892$	0.625086	+	2.36765i	0.0209294	+	0.0792748i
$893$		−	7.80972i		−	0.261342i
$894$	−22.5300	+	29.2502i	−0.753518	+	0.978273i
$895$	20.0228			0.669288
$896$	31.5961	−	3.74662i	1.05555	−	0.125166i
$897$	18.5191			0.618336
$898$	−14.3139	+	18.5833i	−0.477660	+	0.620134i
$899$			4.55485i			0.151913i
$900$	−3.25759	−	12.3388i	−0.108586	−	0.411294i
$901$		−	14.5432i		−	0.484504i
$902$	−58.2110	−	44.8371i	−1.93821	−	1.49291i
$903$	81.6788			2.71810
$904$	−11.8190	−	4.97215i	−0.393094	−	0.165371i
$905$	3.56175			0.118396
$906$	54.3563	+	41.8681i	1.80587	+	1.39097i
$907$			48.6955i			1.61691i	0.588560	+	0.808454i	$0.299695\pi$
$907$			48.6955i			1.61691i	−0.588560	+	0.808454i	$0.700305\pi$
$908$	29.2814	−	7.73061i	0.971736	−	0.256549i
$909$			76.5874i			2.54024i
$910$	9.65958	−	12.5408i	0.320212	−	0.415723i
$911$	−37.7398			−1.25038			−0.625188	−	0.780474i	$-0.714978\pi$
$911$	−37.7398			−1.25038			−0.625188	+	0.780474i	$0.714978\pi$
$912$	10.6547	−	6.04741i	0.352811	−	0.200250i
$913$	70.4366			2.33111
$914$	−4.36595	+	5.66821i	−0.144413	+	0.187488i
$915$			23.6894i			0.783149i
$916$	15.6008	−	4.11880i	0.515466	−	0.136089i
$917$			23.2511i			0.767820i
$918$	18.8140	+	14.4915i	0.620955	+	0.478292i
$919$	1.08745			0.0358718			0.0179359	−	0.999839i	$-0.494291\pi$
$919$	1.08745			0.0358718			0.0179359	+	0.999839i	$0.494291\pi$
$920$	−1.66620	+	3.96063i	−0.0549331	+	0.130578i
$921$	32.9538			1.08586
$922$	7.77086	+	5.98553i	0.255920	+	0.197123i
$923$			4.25883i			0.140181i
$924$	22.2366	+	84.2258i	0.731529	+	2.77083i
$925$			6.69976i			0.220287i
$926$	−6.58012	+	8.54280i	−0.216236	+	0.280734i
$927$	114.852			3.77224
$928$	−3.45867	−	0.487735i	−0.113537	−	0.0160107i
$929$	7.94724			0.260740			0.130370	−	0.991465i	$-0.458383\pi$
$929$	7.94724			0.260740			0.130370	+	0.991465i	$0.458383\pi$
$930$	−19.4977	+	25.3134i	−0.639356	+	0.830060i
$931$			0.908997i			0.0297912i
$932$	9.24117	+	35.0029i	0.302705	+	1.14656i
$933$			45.5714i			1.49194i
$934$	3.59344	+	2.76786i	0.117581	+	0.0905671i
$935$	8.20049			0.268185
$936$	−27.8545	+	66.2113i	−0.910454	+	2.16418i
$937$	−20.6423			−0.674356			−0.337178	−	0.941441i	$-0.609472\pi$
$937$	−20.6423			−0.674356			−0.337178	+	0.941441i	$0.609472\pi$
$938$	24.0091	+	18.4931i	0.783924	+	0.603820i
$939$		−	49.2298i		−	1.60655i
$940$	−15.1020	+	3.98709i	−0.492572	+	0.130045i
$941$			2.32808i			0.0758931i	0.999280	+	0.0379466i	$0.0120817\pi$
$941$			2.32808i			0.0758931i	−0.999280	+	0.0379466i	$0.987918\pi$
$942$	−2.33329	+	3.02925i	−0.0760226	+	0.0986982i
$943$	−15.6090			−0.508299
$944$	−2.93879	−	5.17772i	−0.0956496	−	0.168521i
$945$	−29.1206			−0.947294
$946$	−41.3805	+	53.7232i	−1.34540	+	1.74669i
$947$		−	35.7286i		−	1.16102i	−0.814252	−	0.580511i	$-0.802853\pi$
$947$		−	35.7286i		−	1.16102i	0.814252	−	0.580511i	$-0.197147\pi$
$948$	8.16923	−	2.15677i	0.265324	−	0.0700486i
$949$		−	43.2344i		−	1.40345i
$950$	1.12039	+	0.862980i	0.0363501	+	0.0279988i
$951$	91.4598			2.96579
$952$	−11.8904	−	5.00217i	−0.385369	−	0.162121i
$953$	31.4726			1.01950			0.509749	−	0.860323i	$-0.329738\pi$
$953$	31.4726			1.01950			0.509749	+	0.860323i	$0.329738\pi$
$954$	−64.1104	−	49.3812i	−2.07565	−	1.59878i
$955$			18.5078i			0.598898i
$956$	11.5317	+	43.6787i	0.372961	+	1.41267i
$957$		−	9.56305i		−	0.309129i
$958$	−6.62814	+	8.60514i	−0.214145	+	0.278020i
$959$	49.3344			1.59309
$960$	−17.1337	−	17.5160i	−0.552986	−	0.565326i
$961$	23.4160			0.755356
$962$	23.0121	−	29.8761i	0.741941	−	0.963244i
$963$			116.183i			3.74394i
$964$	0.852268	+	3.22815i	0.0274497	+	0.103972i
$965$		−	0.891942i		−	0.0287126i
$966$	14.6606	+	11.2924i	0.471698	+	0.363327i
$967$	18.4524			0.593390			0.296695	−	0.954972i	$-0.404116\pi$
$967$	18.4524			0.593390			0.296695	+	0.954972i	$0.404116\pi$
$968$	−37.9858	−	15.9803i	−1.22091	−	0.513627i
$969$	−4.96700			−0.159563
$970$	−16.1230	−	12.4188i	−0.517680	−	0.398744i
$971$		−	13.8572i		−	0.444698i	−0.974967	−	0.222349i	$-0.928628\pi$
$971$		−	13.8572i		−	0.444698i	0.974967	−	0.222349i	$-0.0713724\pi$
$972$	14.3911	−	3.79941i	0.461594	−	0.121866i
$973$		−	2.47153i		−	0.0792336i
$974$	4.61988	−	5.99787i	0.148030	−	0.192184i
$975$	−12.1904			−0.390404
$976$	15.2716	+	26.9063i	0.488832	+	0.861250i
$977$	−12.4100			−0.397032			−0.198516	−	0.980098i	$-0.563612\pi$
$977$	−12.4100			−0.397032			−0.198516	+	0.980098i	$0.563612\pi$
$978$	22.9332	−	29.7736i	0.733323	−	0.952055i
$979$		−	3.58525i		−	0.114585i
$980$	1.75777	−	0.464070i	0.0561498	−	0.0148242i
$981$			9.01204i			0.287732i
$982$	−31.9298	−	24.5940i	−1.01892	−	0.784828i
$983$	24.7262			0.788643			0.394322	−	0.918973i	$-0.370980\pi$
$983$	24.7262			0.788643			0.394322	+	0.918973i	$0.370980\pi$
$984$	34.5156	−	82.0449i	1.10032	−	2.61549i
$985$	−12.9518			−0.412678
$986$	1.12189	+	0.864143i	0.0357284	+	0.0275199i
$987$			67.2691i			2.14120i
$988$	−2.03197	−	7.69654i	−0.0646456	−	0.244859i
$989$			14.4056i			0.458073i
$990$	27.8447	−	36.1500i	0.884962	−	1.14892i
$991$	25.6353			0.814334			0.407167	−	0.913354i	$-0.366517\pi$
$991$	25.6353			0.814334			0.407167	+	0.913354i	$0.366517\pi$
$992$	−5.82689	+	41.3202i	−0.185004	+	1.31192i
$993$	54.0832			1.71628
$994$	−2.59690	+	3.37149i	−0.0823687	+	0.106937i
$995$			6.52220i			0.206768i
$996$	21.7808	+	82.4995i	0.690151	+	2.61410i
$997$			14.5038i			0.459339i	0.973269	+	0.229669i	$0.0737645\pi$
$997$			14.5038i			0.459339i	−0.973269	+	0.229669i	$0.926236\pi$
$998$	−8.48967	−	6.53919i	−0.268736	−	0.206994i
$999$	−69.3744			−2.19491

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.12	yes	44
4.3	odd	2		3040.2.f.b.1521.4		44
8.3	odd	2		3040.2.f.b.1521.41		44
8.5	even	2	inner	760.2.f.b.381.11	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.11	✓	44	8.5	even	2	inner
760.2.f.b.381.12	yes	44	1.1	even	1	trivial
3040.2.f.b.1521.4		44	4.3	odd	2
3040.2.f.b.1521.41		44	8.3	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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.862980 + 1.12039i) q^{2} +3.06281i q^{3} +(-0.510530 - 1.93374i) q^{4} +1.00000i q^{5} +(-3.43153 - 2.64314i) q^{6} -2.81229 q^{7} +(2.60712 + 1.09679i) q^{8} -6.38080 q^{9} +(-1.12039 - 0.862980i) q^{10} -5.05668i q^{11} +(5.92268 - 1.56366i) q^{12} -3.98012i q^{13} +(2.42695 - 3.15085i) q^{14} -3.06281 q^{15} +(-3.47872 + 1.97447i) q^{16} +1.62171 q^{17} +(5.50651 - 7.14896i) q^{18} +1.00000i q^{19} +(1.93374 - 0.510530i) q^{20} -8.61352i q^{21} +(5.66544 + 4.36382i) q^{22} +1.51916 q^{23} +(-3.35926 + 7.98510i) q^{24} -1.00000 q^{25} +(4.45928 + 3.43477i) q^{26} -10.3548i q^{27} +(1.43576 + 5.43825i) q^{28} -0.617462i q^{29} +(2.64314 - 3.43153i) q^{30} -7.37672 q^{31} +(0.789902 - 5.60143i) q^{32} +15.4877 q^{33} +(-1.39951 + 1.81694i) q^{34} -2.81229i q^{35} +(3.25759 + 12.3388i) q^{36} -6.69976i q^{37} +(-1.12039 - 0.862980i) q^{38} +12.1904 q^{39} +(-1.09679 + 2.60712i) q^{40} -10.2747 q^{41} +(9.65047 + 7.43330i) q^{42} +9.48263i q^{43} +(-9.77832 + 2.58159i) q^{44} -6.38080i q^{45} +(-1.31101 + 1.70205i) q^{46} -7.80972 q^{47} +(-6.04741 - 10.6547i) q^{48} +0.908997 q^{49} +(0.862980 - 1.12039i) q^{50} +4.96700i q^{51} +(-7.69654 + 2.03197i) q^{52} -8.96779i q^{53} +(11.6013 + 8.93595i) q^{54} +5.05668 q^{55} +(-7.33197 - 3.08450i) q^{56} -3.06281 q^{57} +(0.691796 + 0.532858i) q^{58} +1.48840i q^{59} +(1.56366 + 5.92268i) q^{60} -7.73455i q^{61} +(6.36597 - 8.26478i) q^{62} +17.9447 q^{63} +(5.59410 + 5.71892i) q^{64} +3.98012 q^{65} +(-13.3655 + 17.3522i) q^{66} +7.61986i q^{67} +(-0.827933 - 3.13597i) q^{68} +4.65290i q^{69} +(3.15085 + 2.42695i) q^{70} -1.07002 q^{71} +(-16.6355 - 6.99841i) q^{72} +10.8626 q^{73} +(7.50632 + 5.78176i) q^{74} -3.06281i q^{75} +(1.93374 - 0.510530i) q^{76} +14.2209i q^{77} +(-10.5200 + 13.6579i) q^{78} +1.37931 q^{79} +(-1.97447 - 3.47872i) q^{80} +12.5722 q^{81} +(8.86691 - 11.5117i) q^{82} +13.9294i q^{83} +(-16.6563 + 4.39746i) q^{84} +1.62171i q^{85} +(-10.6242 - 8.18332i) q^{86} +1.89117 q^{87} +(5.54613 - 13.1834i) q^{88} +0.709012 q^{89} +(7.14896 + 5.50651i) q^{90} +11.1933i q^{91} +(-0.775577 - 2.93767i) q^{92} -22.5935i q^{93} +(6.73963 - 8.74990i) q^{94} -1.00000 q^{95} +(17.1561 + 2.41932i) q^{96} +14.3906 q^{97} +(-0.784447 + 1.01843i) q^{98} +32.2657i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

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