LMFDB - Embedded newform 760.2.f.b.381.11

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)

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);

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")

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

$q$-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	$-0.654734\pi$
$3$		−	3.06281i		−	1.76831i	0.467190	−	0.884157i	$-0.345266\pi$
$4$	−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	$0.275942\pi$
$11$			5.05668i			1.52465i	−0.647196	+	0.762324i	$0.724058\pi$
$12$	5.92268	+	1.56366i	1.70973	+	0.451388i
$13$			3.98012i			1.10389i	0.833881	+	0.551944i	$0.186114\pi$
$13$			3.98012i			1.10389i	−0.833881	+	0.551944i	$0.813886\pi$
$14$	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	$0.0182587\pi$
$29$			0.617462i			0.114660i	−0.998355	+	0.0573299i	$0.981741\pi$
$30$	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	$0.185646\pi$
$37$			6.69976i			1.10143i	−0.834692	+	0.550717i	$0.814354\pi$
$38$	−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	$-0.742743\pi$
$43$		−	9.48263i		−	1.44609i	0.690802	−	0.723044i	$-0.257257\pi$
$44$	−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	$0.211212\pi$
$53$			8.96779i			1.23182i	−0.787816	+	0.615910i	$0.788788\pi$
$54$	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	$-0.969112\pi$
$59$		−	1.48840i		−	0.193773i	0.995295	−	0.0968866i	$-0.0308884\pi$
$60$	1.56366	−	5.92268i	0.201867	−	0.764615i
$61$			7.73455i			0.990307i	0.868805	+	0.495154i	$0.164888\pi$
$61$			7.73455i			0.990307i	−0.868805	+	0.495154i	$0.835112\pi$
$62$	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	$-0.845890\pi$
$67$		−	7.61986i		−	0.930914i	0.885071	−	0.465457i	$-0.154110\pi$
$68$	−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	$-0.722998\pi$
$83$		−	13.9294i		−	1.52895i	0.644653	−	0.764475i	$-0.277002\pi$
$84$	−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	$0.203705\pi$
$101$			12.0028i			1.19432i	−0.802121	+	0.597161i	$0.796295\pi$
$102$	−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	$0.342543\pi$
$107$			18.2082i			1.76025i	−0.474738	+	0.880127i	$0.657457\pi$
$108$	−20.0234	−	5.28641i	−1.92675	−	0.508685i
$109$			1.41237i			0.135280i	0.997710	+	0.0676402i	$0.0215470\pi$
$109$			1.41237i			0.135280i	−0.997710	+	0.0676402i	$0.978453\pi$
$110$	−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	$0.117624\pi$
$131$			8.26767i			0.722350i	−0.932498	+	0.361175i	$0.882376\pi$
$132$	−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	$-0.988134\pi$
$139$		−	0.878831i		−	0.0745414i	0.999305	−	0.0372707i	$-0.0118664\pi$
$140$	−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	$0.113531\pi$
$149$			8.52396i			0.698310i	−0.937065	+	0.349155i	$0.886469\pi$
$150$	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	$0.0112152\pi$
$157$			0.882769i			0.0704527i	−0.999379	+	0.0352263i	$0.988785\pi$
$158$	−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	$-0.889642\pi$
$163$		−	8.67648i		−	0.679594i	0.940499	−	0.339797i	$-0.110358\pi$
$164$	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	$-0.880236\pi$
$173$		−	9.66571i		−	0.734870i	0.930049	−	0.367435i	$-0.119764\pi$
$174$	−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	$0.269123\pi$
$179$			20.0228i			1.49657i	−0.663376	+	0.748286i	$0.730877\pi$
$180$	−12.3388	−	3.25759i	−0.919682	−	0.242806i
$181$			3.56175i			0.264742i	0.991200	+	0.132371i	$0.0422591\pi$
$181$			3.56175i			0.264742i	−0.991200	+	0.132371i	$0.957741\pi$
$182$	−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	$-0.847352\pi$
$197$		−	12.9518i		−	0.922776i	0.887198	−	0.461388i	$-0.152648\pi$
$198$	−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	$0.372225\pi$
$211$			26.7423i			1.84102i	−0.390724	+	0.920508i	$0.627775\pi$
$212$	−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	$-0.832408\pi$
$227$		−	15.1423i		−	1.00503i	0.864568	−	0.502516i	$-0.167592\pi$
$228$	1.56366	−	5.92268i	0.103556	−	0.392239i
$229$		−	8.06769i		−	0.533128i	−0.963817	−	0.266564i	$-0.914112\pi$
$229$		−	8.06769i		−	0.533128i	0.963817	−	0.266564i	$-0.0858884\pi$
$230$	−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	$0.0345562\pi$
$251$			3.43312i			0.216697i	−0.994113	+	0.108348i	$0.965444\pi$
$252$	−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	$-0.995566\pi$
$269$		−	0.456872i		−	0.0278560i	0.999903	−	0.0139280i	$-0.00443356\pi$
$270$	−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	$-0.828296\pi$
$277$		−	17.0974i		−	1.02729i	0.858004	−	0.513643i	$-0.171704\pi$
$278$	−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	$-0.576712\pi$
$283$		−	32.6729i		−	1.94220i	0.238671	−	0.971101i	$-0.423288\pi$
$284$	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	$-0.698549\pi$
$293$		−	27.7877i		−	1.62338i	0.584091	−	0.811688i	$-0.301451\pi$
$294$	−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	$0.0993364\pi$
$307$			10.7593i			0.614067i	−0.951699	+	0.307034i	$0.900664\pi$
$308$	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	$0.316621\pi$
$317$			29.8614i			1.67718i	−0.544760	+	0.838592i	$0.683379\pi$
$318$	−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	$0.161285\pi$
$331$			17.6580i			0.970573i	−0.874355	+	0.485286i	$0.838715\pi$
$332$	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	$0.0901291\pi$
$347$			10.4086i			0.558761i	−0.960180	+	0.279381i	$0.909871\pi$
$348$	−0.965498	+	3.65703i	−0.0517561	+	0.196038i
$349$		−	22.1049i		−	1.18325i	−0.806214	−	0.591624i	$-0.798487\pi$
$349$		−	22.1049i		−	1.18325i	0.806214	−	0.591624i	$-0.201513\pi$
$350$	−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	$0.0474192\pi$
$373$			5.73299i			0.296843i	−0.988924	+	0.148422i	$0.952581\pi$
$374$	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	$-0.760746\pi$
$379$		−	26.5868i		−	1.36567i	0.730571	−	0.682836i	$-0.239254\pi$
$380$	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	$0.144173\pi$
$389$			17.2618i			0.875209i	−0.899168	+	0.437605i	$0.855827\pi$
$390$	−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	$-0.994452\pi$
$397$		−	0.694542i		−	0.0348581i	0.999848	−	0.0174290i	$-0.00554812\pi$
$398$	−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	$0.0621501\pi$
$419$			7.94266i			0.388024i	−0.980999	+	0.194012i	$0.937850\pi$
$420$	−4.39746	+	16.6563i	−0.214574	+	0.812746i
$421$		−	24.3855i		−	1.18848i	−0.804289	−	0.594239i	$-0.797453\pi$
$421$		−	24.3855i		−	1.18848i	0.804289	−	0.594239i	$-0.202547\pi$
$422$	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	$0.221471\pi$
$443$			26.9821i			1.28196i	−0.767558	+	0.640979i	$0.778529\pi$
$444$	−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	$0.0516390\pi$
$461$			6.93588i			0.323036i	−0.986870	+	0.161518i	$0.948361\pi$
$462$	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	$0.0236431\pi$
$467$			3.20732i			0.148417i	−0.997243	+	0.0742086i	$0.976357\pi$
$468$	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	$-0.777660\pi$
$491$		−	28.4990i		−	1.28614i	0.765807	−	0.643070i	$-0.222340\pi$
$492$	−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	$-0.945750\pi$
$499$		−	7.57745i		−	0.339213i	0.985512	−	0.169607i	$-0.0542497\pi$
$500$	−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	$-0.786949\pi$
$509$		−	27.9961i		−	1.24091i	0.784243	−	0.620454i	$-0.213051\pi$
$510$	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	$0.0367926\pi$
$523$			5.27502i			0.230660i	−0.993327	+	0.115330i	$0.963207\pi$
$524$	−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	$-0.697833\pi$
$541$		−	37.8198i		−	1.62600i	0.582265	−	0.812999i	$-0.302167\pi$
$542$	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	$-0.943871\pi$
$547$		−	8.20562i		−	0.350847i	0.984493	−	0.175423i	$-0.0561295\pi$
$548$	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	$0.307911\pi$
$557$			38.8646i			1.64675i	−0.567500	+	0.823374i	$0.692089\pi$
$558$	−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	$-0.634728\pi$
$563$		−	43.2675i		−	1.82351i	0.410736	−	0.911754i	$-0.365272\pi$
$564$	−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	$-0.947463\pi$
$571$		−	7.85216i		−	0.328603i	0.986410	−	0.164301i	$-0.0525369\pi$
$572$	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	$0.174604\pi$
$587$			25.2668i			1.04287i	−0.853290	+	0.521436i	$0.825396\pi$
$588$	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	$-0.804688\pi$
$613$		−	28.5126i		−	1.15161i	0.817585	−	0.575807i	$-0.195312\pi$
$614$	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	$0.0909973\pi$
$619$			14.0321i			0.563997i	−0.959415	+	0.281998i	$0.909003\pi$
$620$	−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	$0.127523\pi$
$643$			19.7785i			0.779990i	−0.920817	+	0.389995i	$0.872477\pi$
$644$	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	$0.318876\pi$
$653$			43.0547i			1.68486i	−0.538805	+	0.842430i	$0.681124\pi$
$654$	−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	$0.420616\pi$
$659$			49.7536i			1.93813i	−0.246814	+	0.969063i	$0.579384\pi$
$660$	29.9491	+	7.90691i	1.16577	+	0.307776i
$661$			38.6735i			1.50423i	0.659034	+	0.752113i	$0.270965\pi$
$661$			38.6735i			1.50423i	−0.659034	+	0.752113i	$0.729035\pi$
$662$	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	$0.133864\pi$
$677$			21.2451i			0.816517i	−0.912866	+	0.408259i	$0.866136\pi$
$678$	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	$-0.840566\pi$
$683$		−	25.0990i		−	0.960388i	0.877162	−	0.480194i	$-0.159434\pi$
$684$	−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	$-0.687730\pi$
$691$		−	43.6924i		−	1.66214i	0.556171	−	0.831068i	$-0.312270\pi$
$692$	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	$-0.969058\pi$
$701$		−	5.13928i		−	0.194108i	0.995279	−	0.0970539i	$-0.0309419\pi$
$702$	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	$0.144950\pi$
$709$			23.4211i			0.879596i	−0.898097	+	0.439798i	$0.855050\pi$
$710$	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	$-0.775620\pi$
$733$		−	35.0860i		−	1.29593i	0.761670	−	0.647965i	$-0.224380\pi$
$734$	−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	$0.0373581\pi$
$739$			6.36634i			0.234190i	−0.993121	+	0.117095i	$0.962642\pi$
$740$	−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	$-0.771944\pi$
$757$		−	36.1374i		−	1.31344i	0.754136	−	0.656718i	$-0.228056\pi$
$758$	−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	$-0.877297\pi$
$773$		−	20.9082i		−	0.752014i	0.926617	−	0.376007i	$-0.122703\pi$
$774$	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	$0.213086\pi$
$787$			34.8166i			1.24108i	−0.784176	+	0.620539i	$0.786914\pi$
$788$	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	$0.185397\pi$
$797$			31.0580i			1.10013i	−0.835121	+	0.550066i	$0.814603\pi$
$798$	−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	$-0.843224\pi$
$811$		−	26.9319i		−	0.945707i	0.881141	−	0.472854i	$-0.156776\pi$
$812$	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	$0.0864625\pi$
$821$			15.3754i			0.536604i	−0.963335	+	0.268302i	$0.913537\pi$
$822$	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	$0.0759113\pi$
$827$			13.5867i			0.472456i	−0.971698	+	0.236228i	$0.924089\pi$
$828$	4.94881	−	18.7447i	0.171983	−	0.651423i
$829$		−	4.13713i		−	0.143688i	−0.997416	−	0.0718442i	$-0.977112\pi$
$829$		−	4.13713i		−	0.143688i	0.997416	−	0.0718442i	$-0.0228884\pi$
$830$	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	$-0.782695\pi$
$853$		−	36.8510i		−	1.26176i	0.775882	−	0.630878i	$-0.217305\pi$
$854$	−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	$0.0272781\pi$
$859$			5.01717i			0.171184i	−0.996330	+	0.0855919i	$0.972722\pi$
$860$	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	$0.0499913\pi$
$877$			9.26377i			0.312815i	−0.987693	+	0.156408i	$0.950009\pi$
$878$	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	$0.300761\pi$
$883$			48.1637i			1.62084i	−0.585850	+	0.810419i	$0.699239\pi$
$884$	−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	$-0.700305\pi$
$907$		−	48.6955i		−	1.61691i	0.588560	−	0.808454i	$-0.299695\pi$
$908$	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	$-0.987918\pi$
$941$		−	2.32808i		−	0.0758931i	0.999280	−	0.0379466i	$-0.0120817\pi$
$942$	−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	$0.197147\pi$
$947$			35.7286i			1.16102i	−0.814252	+	0.580511i	$0.802853\pi$
$948$	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	$0.0713724\pi$
$971$			13.8572i			0.444698i	−0.974967	+	0.222349i	$0.928628\pi$
$972$	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	$-0.926236\pi$
$997$		−	14.5038i		−	0.459339i	0.973269	−	0.229669i	$-0.0737645\pi$
$998$	−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.381.11	✓	44
4.3	odd	2		3040.2.f.b.1521.41		44
8.3	odd	2		3040.2.f.b.1521.4		44
8.5	even	2	inner	760.2.f.b.381.12	yes	44

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