LMFDB - Embedded newform 925.2.o.b.174.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [925,2,Mod(174,925)] 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("925.174"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(925, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,16,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 185)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.5
Character	$\chi$	$=$	925.174
Dual form			925.2.o.b.824.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.970676 + 0.560420i) q^{2} +(-2.89252 - 1.67000i) q^{3} +(-0.371859 + 0.644078i) q^{4} +3.74360 q^{6} +(1.06017 + 0.612087i) q^{7} -3.07527i q^{8} +(4.07778 + 7.06292i) q^{9} -3.59983 q^{11} +(2.15122 - 1.24201i) q^{12} +(-0.605879 - 0.349805i) q^{13} -1.37210 q^{14} +(0.979724 + 1.69693i) q^{16} +(-0.501229 + 0.289385i) q^{17} +(-7.91640 - 4.57054i) q^{18} +(3.87804 - 6.71697i) q^{19} +(-2.04437 - 3.54094i) q^{21} +(3.49427 - 2.01742i) q^{22} -4.47887i q^{23} +(-5.13569 + 8.89527i) q^{24} +0.784150 q^{26} -17.2195i q^{27} +(-0.788464 + 0.455220i) q^{28} -3.04867 q^{29} +7.98457 q^{31} +(3.42453 + 1.97715i) q^{32} +(10.4126 + 6.01171i) q^{33} +(0.324354 - 0.561797i) q^{34} -6.06543 q^{36} +(-5.93685 + 1.32431i) q^{37} +8.69333i q^{38} +(1.16835 + 2.02363i) q^{39} +(-2.79335 + 4.83822i) q^{41} +(3.96883 + 2.29141i) q^{42} +4.02235i q^{43} +(1.33863 - 2.31857i) q^{44} +(2.51005 + 4.34753i) q^{46} +8.09571i q^{47} -6.54454i q^{48} +(-2.75070 - 4.76435i) q^{49} +1.93309 q^{51} +(0.450603 - 0.260156i) q^{52} +(-8.60794 + 4.96979i) q^{53} +(9.65017 + 16.7146i) q^{54} +(1.88233 - 3.26029i) q^{56} +(-22.4346 + 12.9526i) q^{57} +(2.95927 - 1.70853i) q^{58} +(0.242678 + 0.420330i) q^{59} +(0.459736 - 0.796287i) q^{61} +(-7.75043 + 4.47471i) q^{62} +9.98382i q^{63} -8.35104 q^{64} -13.4763 q^{66} +(9.74876 + 5.62845i) q^{67} -0.430441i q^{68} +(-7.47970 + 12.9552i) q^{69} +(0.253677 - 0.439381i) q^{71} +(21.7204 - 12.5403i) q^{72} -3.55519i q^{73} +(5.02059 - 4.61261i) q^{74} +(2.88417 + 4.99553i) q^{76} +(-3.81642 - 2.20341i) q^{77} +(-2.26817 - 1.30953i) q^{78} +(-1.90707 + 3.30314i) q^{79} +(-16.5232 + 28.6191i) q^{81} -6.26179i q^{82} +(-10.0553 + 5.80544i) q^{83} +3.04086 q^{84} +(-2.25421 - 3.90440i) q^{86} +(8.81833 + 5.09126i) q^{87} +11.0705i q^{88} +(7.19183 + 12.4566i) q^{89} +(-0.428221 - 0.741701i) q^{91} +(2.88475 + 1.66551i) q^{92} +(-23.0955 - 13.3342i) q^{93} +(-4.53700 - 7.85831i) q^{94} +(-6.60368 - 11.4379i) q^{96} +10.2579i q^{97} +(5.34008 + 3.08309i) q^{98} +(-14.6793 - 25.4253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 16 q^{4} - 8 q^{6} + 26 q^{9} - 4 q^{11} - 40 q^{14} + 4 q^{16} + 28 q^{19} + 2 q^{21} - 30 q^{24} - 44 q^{26} + 24 q^{29} - 66 q^{34} + 80 q^{36} + 50 q^{39} - 14 q^{41} + 38 q^{44} - 28 q^{46}+ \cdots - 112 q^{99}+O(q^{100}) $ 28 * q + 16 * q^4 - 8 * q^6 + 26 * q^9 - 4 * q^11 - 40 * q^14 + 4 * q^16 + 28 * q^19 + 2 * q^21 - 30 * q^24 - 44 * q^26 + 24 * q^29 - 66 * q^34 + 80 * q^36 + 50 * q^39 - 14 * q^41 + 38 * q^44 - 28 * q^46 - 10 * q^49 + 116 * q^51 + 18 * q^54 - 50 * q^56 - 4 * q^59 - 8 * q^61 + 124 * q^64 - 4 * q^66 + 22 * q^69 + 66 * q^71 - 36 * q^74 - 24 * q^76 + 18 * q^79 - 70 * q^81 + 160 * q^84 + 34 * q^86 + 24 * q^89 - 48 * q^91 - 20 * q^94 - 30 * q^96 - 112 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.970676	+	0.560420i	−0.686372	+	0.396277i	−0.802251	−	0.596986i	$-0.796365\pi$
$2$	−0.970676	+	0.560420i	−0.686372	+	0.396277i	0.115880	+	0.993263i	$0.463031\pi$
$3$	−2.89252	−	1.67000i	−1.67000	−	0.964173i	−0.967635	−	0.252353i	$-0.918796\pi$
$3$	−2.89252	−	1.67000i	−1.67000	−	0.964173i	−0.702361	−	0.711821i	$-0.747871\pi$
$4$	−0.371859	+	0.644078i	−0.185929	+	0.322039i
$5$		0			0
$5$		0			0
$6$	3.74360			1.52832
$7$	1.06017	+	0.612087i	0.400705	+	0.231347i	0.686788	−	0.726858i	$-0.259020\pi$
$7$	1.06017	+	0.612087i	0.400705	+	0.231347i	−0.286083	+	0.958205i	$0.592353\pi$
$8$		−	3.07527i		−	1.08727i
$9$	4.07778	+	7.06292i	1.35926	+	2.35431i
$10$		0			0
$11$	−3.59983			−1.08539			−0.542695	−	0.839930i	$-0.682596\pi$
$11$	−3.59983			−1.08539			−0.542695	+	0.839930i	$0.682596\pi$
$12$	2.15122	−	1.24201i	0.621003	−	0.358536i
$13$	−0.605879	−	0.349805i	−0.168041	−	0.0970183i	0.413621	−	0.910449i	$-0.364264\pi$
$13$	−0.605879	−	0.349805i	−0.168041	−	0.0970183i	−0.581662	+	0.813431i	$0.697597\pi$
$14$	−1.37210			−0.366710
$15$		0			0
$16$	0.979724	+	1.69693i	0.244931	+	0.424233i
$17$	−0.501229	+	0.289385i	−0.121566	+	0.0701861i	−0.559550	−	0.828797i	$-0.689026\pi$
$17$	−0.501229	+	0.289385i	−0.121566	+	0.0701861i	0.437984	+	0.898983i	$0.355693\pi$
$18$	−7.91640	−	4.57054i	−1.86591	−	1.07729i
$19$	3.87804	−	6.71697i	0.889684	−	1.54098i	0.0494348	−	0.998777i	$-0.484258\pi$
$19$	3.87804	−	6.71697i	0.889684	−	1.54098i	0.840249	−	0.542200i	$-0.182409\pi$
$20$		0			0
$21$	−2.04437	−	3.54094i	−0.446117	−	0.772698i
$22$	3.49427	−	2.01742i	0.744981	−	0.430115i
$23$		−	4.47887i		−	0.933910i	−0.884281	−	0.466955i	$-0.845351\pi$
$23$		−	4.47887i		−	0.933910i	0.884281	−	0.466955i	$-0.154649\pi$
$24$	−5.13569	+	8.89527i	−1.04832	+	1.81574i
$25$		0			0
$26$	0.784150			0.153784
$27$		−	17.2195i		−	3.31390i
$28$	−0.788464	+	0.455220i	−0.149006	+	0.0860284i
$29$	−3.04867			−0.566123			−0.283062	−	0.959102i	$-0.591350\pi$
$29$	−3.04867			−0.566123			−0.283062	+	0.959102i	$0.591350\pi$
$30$		0			0
$31$	7.98457			1.43407			0.717035	−	0.697037i	$-0.245499\pi$
$31$	7.98457			1.43407			0.717035	+	0.697037i	$0.245499\pi$
$32$	3.42453	+	1.97715i	0.605377	+	0.349515i
$33$	10.4126	+	6.01171i	1.81260	+	1.04650i
$34$	0.324354	−	0.561797i	0.0556262	−	0.0963474i
$35$		0			0
$36$	−6.06543			−1.01091
$37$	−5.93685	+	1.32431i	−0.976012	+	0.217715i
$37$	−5.93685	+	1.32431i	−0.976012	+	0.217715i
$38$			8.69333i			1.41024i
$39$	1.16835	+	2.02363i	0.187085	+	0.324041i
$40$		0			0
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	−0.997397	−	0.0721120i	$-0.977026\pi$
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	0.561149	+	0.827715i	$0.310359\pi$
$42$	3.96883	+	2.29141i	0.612404	+	0.353572i
$43$			4.02235i			0.613403i	0.951806	+	0.306701i	$0.0992253\pi$
$43$			4.02235i			0.613403i	−0.951806	+	0.306701i	$0.900775\pi$
$44$	1.33863	−	2.31857i	0.201806	−	0.349538i
$45$		0			0
$46$	2.51005	+	4.34753i	0.370087	+	0.641009i
$47$			8.09571i			1.18088i	0.807081	+	0.590440i	$0.201046\pi$
$47$			8.09571i			1.18088i	−0.807081	+	0.590440i	$0.798954\pi$
$48$		−	6.54454i		−	0.944624i
$49$	−2.75070	−	4.76435i	−0.392957	−	0.680622i
$50$		0			0
$51$	1.93309			0.270686
$52$	0.450603	−	0.260156i	0.0624874	−	0.0360771i
$53$	−8.60794	+	4.96979i	−1.18239	+	0.682654i	−0.956566	−	0.291514i	$-0.905841\pi$
$53$	−8.60794	+	4.96979i	−1.18239	+	0.682654i	−0.225824	+	0.974168i	$0.572508\pi$
$54$	9.65017	+	16.7146i	1.31322	+	2.27457i
$55$		0			0
$56$	1.88233	−	3.26029i	0.251537	−	0.435675i
$57$	−22.4346	+	12.9526i	−2.97154	+	1.71562i
$58$	2.95927	−	1.70853i	0.388571	−	0.224341i
$59$	0.242678	+	0.420330i	0.0315940	+	0.0547224i	0.881390	−	0.472389i	$-0.156608\pi$
$59$	0.242678	+	0.420330i	0.0315940	+	0.0547224i	−0.849796	+	0.527112i	$0.823275\pi$
$60$		0			0
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	−0.835092	−	0.550110i	$-0.814586\pi$
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	0.893955	+	0.448156i	$0.147919\pi$
$62$	−7.75043	+	4.47471i	−0.984305	+	0.568289i
$63$			9.98382i			1.25784i
$64$	−8.35104			−1.04388
$65$		0			0
$66$	−13.4763			−1.65882
$67$	9.74876	+	5.62845i	1.19100	+	0.687624i	0.958533	−	0.284980i	$-0.0919870\pi$
$67$	9.74876	+	5.62845i	1.19100	+	0.687624i	0.232467	+	0.972604i	$0.425320\pi$
$68$		−	0.430441i		−	0.0521986i
$69$	−7.47970	+	12.9552i	−0.900451	+	1.55963i
$70$		0			0
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	−0.850580	−	0.525846i	$-0.823749\pi$
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	0.880686	+	0.473701i	$0.157082\pi$
$72$	21.7204	−	12.5403i	2.55977	−	1.47788i
$73$		−	3.55519i		−	0.416104i	−0.978118	−	0.208052i	$-0.933288\pi$
$73$		−	3.55519i		−	0.416104i	0.978118	−	0.208052i	$-0.0667123\pi$
$74$	5.02059	−	4.61261i	0.583632	−	0.536204i
$75$		0			0
$76$	2.88417	+	4.99553i	0.330837	+	0.573026i
$77$	−3.81642	−	2.20341i	−0.434921	−	0.251102i
$78$	−2.26817	−	1.30953i	−0.256820	−	0.148275i
$79$	−1.90707	+	3.30314i	−0.214562	+	0.371633i	−0.953137	−	0.302539i	$-0.902166\pi$
$79$	−1.90707	+	3.30314i	−0.214562	+	0.371633i	0.738575	+	0.674172i	$0.235499\pi$
$80$		0			0
$81$	−16.5232	+	28.6191i	−1.83591	+	3.17989i
$82$		−	6.26179i		−	0.691499i
$83$	−10.0553	+	5.80544i	−1.10371	+	0.637230i	−0.937194	−	0.348808i	$-0.886587\pi$
$83$	−10.0553	+	5.80544i	−1.10371	+	0.637230i	−0.166521	+	0.986038i	$0.553253\pi$
$84$	3.04086			0.331785
$85$		0			0
$86$	−2.25421	−	3.90440i	−0.243077	−	0.421022i
$87$	8.81833	+	5.09126i	0.945424	+	0.545841i
$88$			11.0705i			1.18011i
$89$	7.19183	+	12.4566i	0.762333	+	1.32040i	0.941645	+	0.336607i	$0.109279\pi$
$89$	7.19183	+	12.4566i	0.762333	+	1.32040i	−0.179312	+	0.983792i	$0.557387\pi$
$90$		0			0
$91$	−0.428221	−	0.741701i	−0.0448898	−	0.0777514i
$92$	2.88475	+	1.66551i	0.300756	+	0.173641i
$93$	−23.0955	−	13.3342i	−2.39489	−	1.38269i
$94$	−4.53700	−	7.85831i	−0.467956	−	0.810523i
$95$		0			0
$96$	−6.60368	−	11.4379i	−0.673986	−	1.16738i
$97$			10.2579i			1.04154i	0.853698	+	0.520768i	$0.174354\pi$
$97$			10.2579i			1.04154i	−0.853698	+	0.520768i	$0.825646\pi$
$98$	5.34008	+	3.08309i	0.539429	+	0.311440i
$99$	−14.6793	−	25.4253i	−1.47533	−	2.55534i
$100$		0			0
$101$	−5.50183			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$101$	−5.50183			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$102$	−1.87640	+	1.08334i	−0.185791	+	0.107267i
$103$			6.24169i			0.615012i	0.951546	+	0.307506i	$0.0994945\pi$
$103$			6.24169i			0.615012i	−0.951546	+	0.307506i	$0.900506\pi$
$104$	−1.07574	+	1.86324i	−0.105485	+	0.182706i
$105$		0			0
$106$	5.57034	−	9.64812i	0.541040	−	0.937108i
$107$	−0.320549	−	0.185069i	−0.0309886	−	0.0178913i	0.484426	−	0.874832i	$-0.339029\pi$
$107$	−0.320549	−	0.185069i	−0.0309886	−	0.0178913i	−0.515414	+	0.856941i	$0.672362\pi$
$108$	11.0907	+	6.40323i	1.06721	+	0.616151i
$109$	1.55541	+	2.69404i	0.148981	+	0.258043i	0.930851	−	0.365399i	$-0.119067\pi$
$109$	1.55541	+	2.69404i	0.148981	+	0.258043i	−0.781870	+	0.623441i	$0.785734\pi$
$110$		0			0
$111$	19.3840	+	6.08393i	1.83985	+	0.577461i
$112$			2.39870i			0.226656i
$113$	10.1259	−	5.84618i	0.952562	−	0.549962i	0.0586863	−	0.998276i	$-0.481309\pi$
$113$	10.1259	−	5.84618i	0.952562	−	0.549962i	0.893876	+	0.448314i	$0.147975\pi$
$114$	14.5178	−	25.1456i	1.35972	−	2.35510i
$115$		0			0
$116$	1.13367	−	1.96358i	0.105259	−	0.182314i
$117$		−	5.70570i		−	0.527492i
$118$	−0.471123	−	0.272003i	−0.0433704	−	0.0250399i
$119$	−0.708514			−0.0649494
$120$		0			0
$121$	1.95880			0.178072
$122$			1.03058i			0.0933045i
$123$	16.1596	−	9.32976i	1.45706	−	0.841236i
$124$	−2.96913	+	5.14269i	−0.266636	+	0.461827i
$125$		0			0
$126$	−5.59513	−	9.69105i	−0.498454	−	0.863347i
$127$	−15.3716	+	8.87482i	−1.36401	+	0.787513i	−0.990155	−	0.139973i	$-0.955298\pi$
$127$	−15.3716	+	8.87482i	−1.36401	+	0.787513i	−0.373857	+	0.927486i	$0.621965\pi$
$128$	1.25709	−	0.725783i	0.111112	−	0.0641508i
$129$	6.71731	−	11.6347i	0.591426	−	1.02438i
$130$		0			0
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	0.890064	−	0.455836i	$-0.150660\pi$
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	−0.839797	+	0.542900i	$0.817326\pi$
$132$	−7.74402	+	4.47101i	−0.674031	+	0.389152i
$133$	8.22273	−	4.74740i	0.713001	−	0.411651i
$134$	−12.6172			−1.08996
$135$		0			0
$136$	0.889935	+	1.54141i	0.0763113	+	0.132175i
$137$		−	1.91138i		−	0.163301i	−0.996661	−	0.0816503i	$-0.973981\pi$
$137$		−	1.91138i		−	0.163301i	0.996661	−	0.0816503i	$-0.0260191\pi$
$138$		−	16.7671i		−	1.42731i
$139$	−1.89002	−	3.27360i	−0.160309	−	0.277663i	0.774670	−	0.632365i	$-0.217916\pi$
$139$	−1.89002	−	3.27360i	−0.160309	−	0.277663i	−0.934980	+	0.354702i	$0.884582\pi$
$140$		0			0
$141$	13.5198	−	23.4170i	1.13857	−	1.97207i
$142$			0.568663i			0.0477211i
$143$	2.18106	+	1.25924i	0.182390	+	0.105303i
$144$	−7.99020	+	13.8394i	−0.665850	+	1.15329i
$145$		0			0
$146$	1.99240	+	3.45094i	0.164892	+	0.285602i
$147$			18.3746i			1.51551i
$148$	1.35471	−	4.31625i	0.111357	−	0.354794i
$149$	0.552510			0.0452633			0.0226317	−	0.999744i	$-0.492795\pi$
$149$	0.552510			0.0452633			0.0226317	+	0.999744i	$0.492795\pi$
$150$		0			0
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	−0.989971	−	0.141273i	$-0.954880\pi$
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	0.617331	+	0.786703i	$0.288214\pi$
$152$	−20.6565	−	11.9260i	−1.67546	−	0.967328i
$153$	−4.08780	−	2.36009i	−0.330479	−	0.190802i
$154$	4.93934			0.398023
$155$		0			0
$156$	−1.73784			−0.139138
$157$	2.37433	−	1.37082i	0.189492	−	0.109403i	−0.402253	−	0.915529i	$-0.631773\pi$
$157$	2.37433	−	1.37082i	0.189492	−	0.109403i	0.591745	+	0.806125i	$0.298439\pi$
$158$		−	4.27504i		−	0.340104i
$159$	33.1982			2.63279
$160$		0			0
$161$	2.74146	−	4.74835i	0.216057	−	0.374222i
$162$		−	37.0398i		−	2.91012i
$163$	18.2462	−	10.5345i	1.42915	−	0.825123i	0.432100	−	0.901826i	$-0.357773\pi$
$163$	18.2462	−	10.5345i	1.42915	−	0.825123i	0.997054	+	0.0767030i	$0.0244393\pi$
$164$	−2.07746	−	3.59827i	−0.162222	−	0.280978i
$165$		0			0
$166$	6.50697	−	11.2704i	0.505039	−	0.874753i
$167$	−8.68532	−	5.01447i	−0.672090	−	0.388031i	0.124778	−	0.992185i	$-0.460178\pi$
$167$	−8.68532	−	5.01447i	−0.672090	−	0.388031i	−0.796868	+	0.604153i	$0.793511\pi$
$168$	−10.8894	+	6.28697i	−0.840132	+	0.485050i
$169$	−6.25527	−	10.8345i	−0.481175	−	0.833419i
$170$		0			0
$171$	63.2552			4.83725
$172$	−2.59071	−	1.49575i	−0.197540	−	0.114050i
$173$	−11.5209	+	6.65162i	−0.875922	+	0.505714i	−0.869312	−	0.494265i	$-0.835437\pi$
$173$	−11.5209	+	6.65162i	−0.875922	+	0.505714i	−0.00661007	+	0.999978i	$0.502104\pi$
$174$	−11.4130			−0.865216
$175$		0			0
$176$	−3.52684	−	6.10867i	−0.265846	−	0.460458i
$177$		−	1.62109i		−	0.121848i
$178$	−13.9619	−	8.06089i	−1.04649	−	0.604190i
$179$	−9.15637			−0.684379			−0.342190	−	0.939631i	$-0.611168\pi$
$179$	−9.15637			−0.684379			−0.342190	+	0.939631i	$0.611168\pi$
$180$		0			0
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	0.144986	+	0.989434i	$0.453686\pi$
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	−0.929368	+	0.369156i	$0.879647\pi$
$182$	0.831328	+	0.479968i	0.0616222	+	0.0355776i
$183$	−2.65959	+	1.53552i	−0.196603	+	0.113509i
$184$	−13.7737			−1.01541
$185$		0			0
$186$	29.8910			2.19172
$187$	1.80434	−	1.04174i	0.131946	−	0.0761793i
$188$	−5.21427	−	3.01046i	−0.380290	−	0.219561i
$189$	10.5398	−	18.2555i	0.766661	−	1.32790i
$190$		0			0
$191$	−7.51240			−0.543578			−0.271789	−	0.962357i	$-0.587615\pi$
$191$	−7.51240			−0.543578			−0.271789	+	0.962357i	$0.587615\pi$
$192$	24.1556	+	13.9462i	1.74328	+	1.00648i
$193$			16.5435i			1.19083i	0.803418	+	0.595415i	$0.203012\pi$
$193$			16.5435i			1.19083i	−0.803418	+	0.595415i	$0.796988\pi$
$194$	−5.74876	−	9.95714i	−0.412737	−	0.714881i
$195$		0			0
$196$	4.09149			0.292249
$197$	−1.51274	+	0.873381i	−0.107778	+	0.0622259i	−0.552920	−	0.833234i	$-0.686487\pi$
$197$	−1.51274	+	0.873381i	−0.107778	+	0.0622259i	0.445142	+	0.895460i	$0.353153\pi$
$198$	28.4977	+	16.4532i	2.02525	+	1.16928i
$199$	14.8223			1.05073			0.525364	−	0.850878i	$-0.323929\pi$
$199$	14.8223			1.05073			0.525364	+	0.850878i	$0.323929\pi$
$200$		0			0
$201$	−18.7990	−	32.5608i	−1.32598	−	2.29666i
$202$	5.34049	−	3.08334i	0.375756	−	0.216943i
$203$	−3.23209	−	1.86605i	−0.226848	−	0.130971i
$204$	−0.718835	+	1.24506i	−0.0503285	+	0.0871715i
$205$		0			0
$206$	−3.49797	−	6.05866i	−0.243715	−	0.422127i
$207$	31.6339	−	18.2639i	2.19871	−	1.26943i
$208$		−	1.37085i		−	0.0950512i
$209$	−13.9603	+	24.1800i	−0.965654	+	1.67256i
$210$		0			0
$211$	−18.1359			−1.24853			−0.624264	−	0.781214i	$-0.714601\pi$
$211$	−18.1359			−1.24853			−0.624264	+	0.781214i	$0.714601\pi$
$212$		−	7.39225i		−	0.507702i
$213$	−1.46753	+	0.847279i	−0.100554	+	0.0580546i
$214$	0.414866			0.0283596
$215$		0			0
$216$	−52.9547			−3.60311
$217$	8.46496	+	4.88725i	0.574639	+	0.331768i
$218$	−3.01959	−	1.74336i	−0.204513	−	0.118075i
$219$	−5.93716	+	10.2835i	−0.401196	+	0.694892i
$220$		0			0
$221$	0.404912			0.0272373
$222$	−22.2252	+	4.95768i	−1.49166	+	0.332738i
$223$		−	3.84578i		−	0.257532i	−0.991675	−	0.128766i	$-0.958898\pi$
$223$		−	3.84578i		−	0.257532i	0.991675	−	0.128766i	$-0.0411017\pi$
$224$	2.42038	+	4.19222i	0.161718	+	0.280105i
$225$		0			0
$226$	−6.55263	+	11.3495i	−0.435874	+	0.754957i
$227$	−11.9629	−	6.90676i	−0.794003	−	0.458418i	0.0473671	−	0.998878i	$-0.484917\pi$
$227$	−11.9629	−	6.90676i	−0.794003	−	0.458418i	−0.841370	+	0.540460i	$0.818250\pi$
$228$		−	19.2662i		−	1.27594i
$229$	0.301499	−	0.522211i	0.0199236	−	0.0345087i	−0.855892	−	0.517155i	$-0.826991\pi$
$229$	0.301499	−	0.522211i	0.0199236	−	0.0345087i	0.875815	+	0.482646i	$0.160324\pi$
$230$		0			0
$231$	7.35937	+	12.7468i	0.484211	+	0.838679i
$232$			9.37547i			0.615530i
$233$			23.3424i			1.52921i	0.644499	+	0.764605i	$0.277066\pi$
$233$			23.3424i			1.52921i	−0.644499	+	0.764605i	$0.722934\pi$
$234$	3.19759	+	5.53839i	0.209033	+	0.362056i
$235$		0			0
$236$	−0.360968			−0.0234970
$237$	11.0325	−	6.36961i	0.716637	−	0.413750i
$238$	0.687737	−	0.397065i	0.0445794	−	0.0257379i
$239$	−14.0468	−	24.3297i	−0.908610	−	1.57376i	−0.815997	−	0.578057i	$-0.803811\pi$
$239$	−14.0468	−	24.3297i	−0.908610	−	1.57376i	−0.0926135	−	0.995702i	$-0.529522\pi$
$240$		0			0
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	−0.866611	−	0.498984i	$-0.833707\pi$
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	0.865439	+	0.501015i	$0.167040\pi$
$242$	−1.90136	+	1.09775i	−0.122224	+	0.0705659i
$243$	50.8498	−	29.3582i	3.26202	−	1.88333i
$244$	0.341914	+	0.592213i	0.0218888	+	0.0379125i
$245$		0			0
$246$	−10.4572	+	18.1123i	−0.666725	+	1.15480i
$247$	−4.69925	+	2.71311i	−0.299006	+	0.172631i
$248$		−	24.5547i		−	1.55922i
$249$	38.7803			2.45760
$250$		0			0
$251$	−21.4173			−1.35185			−0.675924	−	0.736971i	$-0.736255\pi$
$251$	−21.4173			−1.35185			−0.675924	+	0.736971i	$0.736255\pi$
$252$	−6.43036	−	3.71257i	−0.405075	−	0.233870i
$253$			16.1232i			1.01366i
$254$	9.94726	−	17.2292i	0.624146	−	1.08105i
$255$		0			0
$256$	7.53756	−	13.0554i	0.471097	−	0.815965i
$257$	0.699538	−	0.403879i	0.0436360	−	0.0251933i	−0.478023	−	0.878347i	$-0.658647\pi$
$257$	0.699538	−	0.403879i	0.0436360	−	0.0251933i	0.521659	+	0.853154i	$0.325313\pi$
$258$			15.0581i			0.937474i
$259$	−7.10464	−	2.22988i	−0.441461	−	0.138558i
$260$		0			0
$261$	−12.4318	−	21.5325i	−0.769508	−	1.33283i
$262$	−1.11691	−	0.644851i	−0.0690032	−	0.0398390i
$263$	−2.11194	−	1.21933i	−0.130228	−	0.0751871i	0.433471	−	0.901168i	$-0.357289\pi$
$263$	−2.11194	−	1.21933i	−0.130228	−	0.0751871i	−0.563699	+	0.825981i	$0.690622\pi$
$264$	18.4876	−	32.0215i	1.13783	−	1.97079i
$265$		0			0
$266$	−5.32107	+	9.21637i	−0.326256	+	0.565092i
$267$		−	48.0414i		−	2.94008i
$268$	−7.25032	+	4.18598i	−0.442884	+	0.255699i
$269$	−12.1567			−0.741208			−0.370604	−	0.928791i	$-0.620849\pi$
$269$	−12.1567			−0.741208			−0.370604	+	0.928791i	$0.620849\pi$
$270$		0			0
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.743797	+	0.668405i	$0.233023\pi$
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.206957	+	0.978350i	$0.433644\pi$
$272$	−0.982132	−	0.567034i	−0.0595505	−	0.0343815i
$273$			2.86051i			0.173126i
$274$	1.07118	+	1.85533i	0.0647122	+	0.112085i
$275$		0			0
$276$	−5.56279	−	9.63503i	−0.334841	−	0.579961i
$277$	20.0847	+	11.5959i	1.20678	+	0.696732i	0.962053	−	0.272861i	$-0.0879700\pi$
$277$	20.0847	+	11.5959i	1.20678	+	0.696732i	0.244722	+	0.969593i	$0.421303\pi$
$278$	3.66919	+	2.11841i	0.220063	+	0.127053i
$279$	32.5593	+	56.3944i	1.94927	+	3.37624i
$280$		0			0
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	0.985655	+	0.168771i	$0.0539799\pi$
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	−0.346668	+	0.937988i	$0.612687\pi$
$282$			30.3071i			1.80476i
$283$	11.9647	+	6.90784i	0.711229	+	0.410628i	0.811516	−	0.584330i	$-0.198643\pi$
$283$	11.9647	+	6.90784i	0.711229	+	0.410628i	−0.100287	+	0.994959i	$0.531976\pi$
$284$	0.188664	+	0.326776i	0.0111952	+	0.0193906i
$285$		0			0
$286$	−2.82281			−0.166916
$287$	−5.92282	+	3.41954i	−0.349613	+	0.201849i
$288$			32.2496i			1.90033i
$289$	−8.33251	+	14.4323i	−0.490148	+	0.848961i
$290$		0			0
$291$	17.1307	−	29.6713i	1.00422	−	1.73936i
$292$	2.28982	+	1.32203i	0.134002	+	0.0773659i
$293$	6.15518	+	3.55370i	0.359589	+	0.207609i	0.668901	−	0.743352i	$-0.266765\pi$
$293$	6.15518	+	3.55370i	0.359589	+	0.207609i	−0.309311	+	0.950961i	$0.600098\pi$
$294$	−10.2975	−	17.8358i	−0.600563	−	1.04021i
$295$		0			0
$296$	4.07261	+	18.2574i	0.236715	+	1.06119i
$297$			61.9874i			3.59687i
$298$	−0.536308	+	0.309637i	−0.0310675	+	0.0179368i
$299$	−1.56673	+	2.71366i	−0.0906064	+	0.156935i
$300$		0			0
$301$	−2.46203	+	4.26436i	−0.141909	+	0.245793i
$302$		−	10.2648i		−	0.590673i
$303$	15.9141	+	9.18804i	0.914244	+	0.527839i
$304$	15.1976			0.871645
$305$		0			0
$306$	5.29057			0.302442
$307$			23.6385i			1.34912i	0.738220	+	0.674560i	$0.235667\pi$
$307$			23.6385i			1.34912i	−0.738220	+	0.674560i	$0.764333\pi$
$308$	2.83834	−	1.63871i	0.161729	−	0.0933744i
$309$	10.4236	−	18.0542i	0.592978	−	1.02707i
$310$		0			0
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	0.998348	+	0.0574494i	$0.0182968\pi$
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	−0.449422	+	0.893320i	$0.648370\pi$
$312$	6.22321	−	3.59297i	0.352320	−	0.203412i
$313$	5.29181	−	3.05523i	0.299111	−	0.172692i	−0.342932	−	0.939360i	$-0.611420\pi$
$313$	5.29181	−	3.05523i	0.299111	−	0.172692i	0.642043	+	0.766668i	$0.278087\pi$
$314$	−1.53647	+	2.66124i	−0.0867079	+	0.150183i
$315$		0			0
$316$	−1.41832	−	2.45661i	−0.0797869	−	0.138195i
$317$	28.7872	−	16.6203i	1.61685	−	0.933490i	0.629125	−	0.777304i	$-0.283414\pi$
$317$	28.7872	−	16.6203i	1.61685	−	0.933490i	0.987728	−	0.156186i	$-0.0499198\pi$
$318$	−32.2247	+	18.6049i	−1.80707	+	1.04331i
$319$	10.9747			0.614465
$320$		0			0
$321$	0.618129	+	1.07063i	0.0345006	+	0.0597568i
$322$			6.14547i			0.342474i
$323$			4.48898i			0.249774i
$324$	−12.2886	−	21.2845i	−0.682701	−	1.18247i
$325$		0			0
$326$	−11.8074	+	20.4511i	−0.653954	+	1.13268i
$327$		−	10.3901i		−	0.574574i
$328$	14.8788	+	8.59029i	0.821545	+	0.474319i
$329$	−4.95528	+	8.58279i	−0.273193	+	0.473185i
$330$		0			0
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	0.846332	−	0.532656i	$-0.178806\pi$
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	−0.884460	+	0.466617i	$0.845473\pi$
$332$		−	8.63522i		−	0.473919i
$333$	−33.5627	−	36.5313i	−1.83922	−	2.00190i
$334$	11.2408			0.615071
$335$		0			0
$336$	4.00583	−	6.93830i	0.218536	−	0.378515i
$337$	13.2587	+	7.65489i	0.722245	+	0.416989i	0.815579	−	0.578646i	$-0.196419\pi$
$337$	13.2587	+	7.65489i	0.722245	+	0.416989i	−0.0933332	+	0.995635i	$0.529752\pi$
$338$	12.1437	+	7.01116i	0.660529	+	0.381357i
$339$	−39.0524			−2.12103
$340$		0			0
$341$	−28.7431			−1.55653
$342$	−61.4003	+	35.4495i	−3.32015	+	1.91689i
$343$		−	15.3039i		−	0.826332i
$344$	12.3698			0.666935
$345$		0			0
$346$	7.45541	−	12.9131i	0.400805	−	0.694215i
$347$		−	27.0099i		−	1.44997i	−0.688767	−	0.724983i	$-0.741848\pi$
$347$		−	27.0099i		−	1.44997i	0.688767	−	0.724983i	$-0.258152\pi$
$348$	−6.55835	+	3.78646i	−0.351564	+	0.202976i
$349$	−10.1591	−	17.5961i	−0.543806	−	0.941900i	−0.998681	−	0.0513447i	$-0.983649\pi$
$349$	−10.1591	−	17.5961i	−0.543806	−	0.941900i	0.454875	−	0.890555i	$-0.349684\pi$
$350$		0			0
$351$	−6.02347	+	10.4330i	−0.321509	+	0.556870i
$352$	−12.3277	−	7.11743i	−0.657071	−	0.379360i
$353$	−3.87131	+	2.23510i	−0.206049	+	0.118962i	−0.599474	−	0.800394i	$-0.704623\pi$
$353$	−3.87131	+	2.23510i	−0.206049	+	0.118962i	0.393425	+	0.919357i	$0.371290\pi$
$354$	0.908489	+	1.57355i	0.0482856	+	0.0836332i
$355$		0			0
$356$	−10.6974			−0.566960
$357$	2.04939	+	1.18322i	0.108465	+	0.0626224i
$358$	8.88786	−	5.13141i	0.469738	−	0.271204i
$359$	31.2742			1.65059			0.825295	−	0.564702i	$-0.191009\pi$
$359$	31.2742			1.65059			0.825295	+	0.564702i	$0.191009\pi$
$360$		0			0
$361$	−20.5784	−	35.6429i	−1.08308	−	1.87594i
$362$		−	23.6560i		−	1.24333i
$363$	−5.66585	−	3.27118i	−0.297380	−	0.171693i
$364$	0.636952			0.0333853
$365$		0			0
$366$	1.72107	−	2.98098i	0.0899617	−	0.155818i
$367$	−13.9660	−	8.06325i	−0.729017	−	0.420898i	0.0890456	−	0.996028i	$-0.471618\pi$
$367$	−13.9660	−	8.06325i	−0.729017	−	0.420898i	−0.818062	+	0.575130i	$0.804952\pi$
$368$	7.60034	−	4.38806i	0.396195	−	0.228743i
$369$	−45.5626			−2.37189
$370$		0			0
$371$	−12.1678			−0.631720
$372$	17.1765	−	9.91688i	0.890562	−	0.514166i
$373$	8.86838	+	5.12016i	0.459187	+	0.265112i	0.711703	−	0.702481i	$-0.247924\pi$
$373$	8.86838	+	5.12016i	0.459187	+	0.265112i	−0.252515	+	0.967593i	$0.581258\pi$
$374$	−1.16762	+	2.02238i	−0.0603762	+	0.104575i
$375$		0			0
$376$	24.8965			1.28394
$377$	1.84712	+	1.06644i	0.0951317	+	0.0549243i
$378$			23.6270i			1.21524i
$379$	8.28107	+	14.3432i	0.425370	+	0.736763i	0.996455	−	0.0841283i	$-0.0268106\pi$
$379$	8.28107	+	14.3432i	0.425370	+	0.736763i	−0.571085	+	0.820891i	$0.693477\pi$
$380$		0			0
$381$	59.2837			3.03720
$382$	7.29211	−	4.21010i	0.373097	−	0.215408i
$383$	−15.8495	−	9.15069i	−0.809869	−	0.467578i	0.0370411	−	0.999314i	$-0.488207\pi$
$383$	−15.8495	−	9.15069i	−0.809869	−	0.467578i	−0.846911	+	0.531735i	$0.821540\pi$
$384$	−4.84822			−0.247410
$385$		0			0
$386$	−9.27133	−	16.0584i	−0.471898	−	0.817352i
$387$	−28.4095	+	16.4023i	−1.44414	+	0.833773i
$388$	−6.60692	−	3.81451i	−0.335416	−	0.193652i
$389$	−7.33608	+	12.7065i	−0.371954	+	0.644243i	−0.989866	−	0.142004i	$-0.954645\pi$
$389$	−7.33608	+	12.7065i	−0.371954	+	0.644243i	0.617912	+	0.786247i	$0.287979\pi$
$390$		0			0
$391$	1.29612	+	2.24494i	0.0655474	+	0.113532i
$392$	−14.6517	+	8.45914i	−0.740021	+	0.427251i
$393$		−	3.84319i		−	0.193863i
$394$	0.978921	−	1.69554i	0.0493173	−	0.0854201i
$395$		0			0
$396$	21.8345			1.09723
$397$			2.00229i			0.100492i	0.998737	+	0.0502460i	$0.0160005\pi$
$397$			2.00229i			0.100492i	−0.998737	+	0.0502460i	$0.983999\pi$
$398$	−14.3877	+	8.30673i	−0.721189	+	0.416379i
$399$	−31.7125			−1.58761
$400$		0			0
$401$	−22.8854			−1.14284			−0.571422	−	0.820656i	$-0.693608\pi$
$401$	−22.8854			−1.14284			−0.571422	+	0.820656i	$0.693608\pi$
$402$	36.4954	+	21.0706i	1.82023	+	1.05091i
$403$	−4.83768	−	2.79304i	−0.240982	−	0.139131i
$404$	2.04590	−	3.54361i	0.101788	−	0.176301i
$405$		0			0
$406$	4.18308			0.207603
$407$	21.3717	−	4.76729i	1.05935	−	0.236306i
$408$		−	5.94476i		−	0.294309i
$409$	4.55814	+	7.89494i	0.225386	+	0.390380i	0.956435	−	0.291945i	$-0.0943024\pi$
$409$	4.55814	+	7.89494i	0.225386	+	0.390380i	−0.731049	+	0.682325i	$0.760969\pi$
$410$		0			0
$411$	−3.19200	+	5.52871i	−0.157450	+	0.272711i
$412$	−4.02014	−	2.32103i	−0.198058	−	0.114349i
$413$			0.594160i			0.0292367i
$414$	−20.4709	+	35.4566i	−1.00609	+	1.74259i
$415$		0			0
$416$	−1.38324	−	2.39583i	−0.0678187	−	0.117465i
$417$			12.6253i			0.618263i
$418$		−	31.2945i		−	1.53067i
$419$	−4.25529	−	7.37039i	−0.207885	−	0.360067i	0.743163	−	0.669110i	$-0.233325\pi$
$419$	−4.25529	−	7.37039i	−0.207885	−	0.360067i	−0.951048	+	0.309043i	$0.899991\pi$
$420$		0			0
$421$	−8.83588			−0.430635			−0.215317	−	0.976544i	$-0.569079\pi$
$421$	−8.83588			−0.430635			−0.215317	+	0.976544i	$0.569079\pi$
$422$	17.6041	−	10.1637i	0.856953	−	0.494762i
$423$	−57.1794	+	33.0125i	−2.78016	+	1.60512i
$424$	15.2834	+	26.4717i	0.742230	+	1.28558i
$425$		0			0
$426$	0.949665	−	1.64487i	0.0460114	−	0.0796941i
$427$	0.974793	−	0.562797i	0.0471735	−	0.0272357i
$428$	0.238398	−	0.137639i	0.0115234	−	0.00665304i
$429$	−4.20585	−	7.28474i	−0.203060	−	0.351711i
$430$		0			0
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	−0.883643	−	0.468161i	$-0.844917\pi$
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	0.847261	+	0.531177i	$0.178250\pi$
$432$	29.2204	−	16.8704i	1.40587	−	0.811677i
$433$			6.85824i			0.329586i	0.986328	+	0.164793i	$0.0526956\pi$
$433$			6.85824i			0.329586i	−0.986328	+	0.164793i	$0.947304\pi$
$434$	−10.9556			−0.525888
$435$		0			0
$436$	−2.31357			−0.110800
$437$	−30.0844	−	17.3693i	−1.43913	−	0.830884i
$438$		−	13.3092i		−	0.635938i
$439$	9.56891	−	16.5738i	0.456699	−	0.791026i	−0.542085	−	0.840324i	$-0.682365\pi$
$439$	9.56891	−	16.5738i	0.456699	−	0.791026i	0.998784	+	0.0492976i	$0.0156983\pi$
$440$		0			0
$441$	22.4335	−	38.8559i	1.06826	−	1.85028i
$442$	−0.393039	+	0.226921i	−0.0186949	+	0.0107935i
$443$		−	2.25690i		−	0.107229i	−0.998562	−	0.0536144i	$-0.982926\pi$
$443$		−	2.25690i		−	0.107229i	0.998562	−	0.0536144i	$-0.0170742\pi$
$444$	−11.1267	+	10.2225i	−0.528048	+	0.485138i
$445$		0			0
$446$	2.15525	+	3.73300i	0.102054	+	0.176763i
$447$	−1.59814	−	0.922689i	−0.0755896	−	0.0436417i
$448$	−8.85349	−	5.11156i	−0.418288	−	0.241499i
$449$	−12.1889	+	21.1119i	−0.575232	+	0.996330i	0.420785	+	0.907160i	$0.361755\pi$
$449$	−12.1889	+	21.1119i	−0.575232	+	0.996330i	−0.996016	+	0.0891698i	$0.971579\pi$
$450$		0			0
$451$	10.0556	−	17.4168i	0.473499	−	0.820124i
$452$			8.69581i			0.409017i
$453$	26.4901	−	15.2941i	1.24461	−	0.718578i
$454$	15.4827			0.726641
$455$		0			0
$456$	39.8328	+	68.9925i	1.86534	+	3.23087i
$457$	−12.1699	−	7.02629i	−0.569283	−	0.328676i	0.187580	−	0.982249i	$-0.439936\pi$
$457$	−12.1699	−	7.02629i	−0.569283	−	0.328676i	−0.756863	+	0.653574i	$0.773269\pi$
$458$			0.675864i			0.0315810i
$459$	4.98307	+	8.63092i	0.232590	+	0.402857i
$460$		0			0
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	0.990350	+	0.138587i	$0.0442559\pi$
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	−0.375156	+	0.926962i	$0.622411\pi$
$462$	−14.2871	−	8.24868i	−0.664698	−	0.383763i
$463$	−21.7739	−	12.5712i	−1.01192	−	0.584233i	−0.100167	−	0.994971i	$-0.531938\pi$
$463$	−21.7739	−	12.5712i	−1.01192	−	0.584233i	−0.911753	+	0.410738i	$0.865271\pi$
$464$	−2.98685	−	5.17338i	−0.138661	−	0.240168i
$465$		0			0
$466$	−13.0815	−	22.6579i	−0.605991	−	1.04961i
$467$			14.0309i			0.649271i	0.945839	+	0.324635i	$0.105242\pi$
$467$			14.0309i			0.649271i	−0.945839	+	0.324635i	$0.894758\pi$
$468$	3.67492	+	2.12172i	0.169873	+	0.0980764i
$469$	6.89019	+	11.9342i	0.318160	+	0.551069i
$470$		0			0
$471$	−9.15705			−0.421935
$472$	1.29263	−	0.746300i	0.0594981	−	0.0343512i
$473$		−	14.4798i		−	0.665781i
$474$	−7.13931	+	12.3656i	−0.327919	+	0.567973i
$475$		0			0
$476$	0.263467	−	0.456339i	0.0120760	−	0.0209162i
$477$	−70.2025	−	40.5314i	−3.21435	−	1.85581i
$478$	27.2697	+	15.7442i	1.24729	+	0.720122i
$479$	−3.34106	−	5.78689i	−0.152657	−	0.264410i	0.779546	−	0.626344i	$-0.215450\pi$
$479$	−3.34106	−	5.78689i	−0.152657	−	0.264410i	−0.932203	+	0.361935i	$0.882116\pi$
$480$		0			0
$481$	4.06026	+	1.27437i	0.185132	+	0.0581061i
$482$		−	0.0408034i		−	0.00185854i
$483$	−15.8594	+	9.15645i	−0.721630	+	0.416633i
$484$	−0.728396	+	1.26162i	−0.0331089	+	0.0573463i
$485$		0			0
$486$	−32.9058	+	56.9945i	−1.49264	+	2.58532i
$487$			7.26544i			0.329229i	0.986358	+	0.164614i	$0.0526380\pi$
$487$			7.26544i			0.329229i	−0.986358	+	0.164614i	$0.947362\pi$
$488$	−2.44880	−	1.41381i	−0.110852	−	0.0640003i
$489$	−70.3701			−3.18224
$490$		0			0
$491$	0.446623			0.0201558			0.0100779	−	0.999949i	$-0.496792\pi$
$491$	0.446623			0.0201558			0.0100779	+	0.999949i	$0.496792\pi$
$492$			13.8774i			0.625642i
$493$	1.52808	−	0.882237i	0.0688212	−	0.0397340i
$494$	3.04097	−	5.26711i	0.136820	−	0.236978i
$495$		0			0
$496$	7.82267	+	13.5493i	0.351248	+	0.608380i
$497$	0.537879	−	0.310545i	0.0241272	−	0.0139298i
$498$	−37.6431	+	21.7332i	−1.68683	+	0.973890i
$499$	−5.30225	+	9.18376i	−0.237361	+	0.411122i	−0.959956	−	0.280150i	$-0.909616\pi$
$499$	−5.30225	+	9.18376i	−0.237361	+	0.411122i	0.722595	+	0.691272i	$0.242949\pi$
$500$		0			0
$501$	16.7483	+	29.0089i	0.748259	+	1.29602i
$502$	20.7893	−	12.0027i	0.927870	−	0.535706i
$503$	12.0980	−	6.98478i	0.539423	−	0.311436i	−0.205422	−	0.978673i	$-0.565857\pi$
$503$	12.0980	−	6.98478i	0.539423	−	0.311436i	0.744845	+	0.667237i	$0.232523\pi$
$504$	30.7029			1.36762
$505$		0			0
$506$	−9.03576	−	15.6504i	−0.401689	−	0.695745i
$507$			41.7851i			1.85574i
$508$		−	13.2007i		−	0.585687i
$509$	19.8167	+	34.3235i	0.878360	+	1.52136i	0.853140	+	0.521682i	$0.174695\pi$
$509$	19.8167	+	34.3235i	0.878360	+	1.52136i	0.0252198	+	0.999682i	$0.491971\pi$
$510$		0			0
$511$	2.17609	−	3.76909i	0.0962643	−	0.166735i
$512$			19.7999i			0.875041i
$513$	−115.663	−	66.7781i	−5.10665	−	2.94832i
$514$	−0.452683	+	0.784070i	−0.0199670	+	0.0345839i
$515$		0			0
$516$	4.99578	+	8.65295i	0.219927	+	0.380925i
$517$		−	29.1432i		−	1.28172i
$518$	8.14597	−	1.81709i	0.357913	−	0.0798383i
$519$	44.4328			1.95038
$520$		0			0
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	−0.283854	−	0.958868i	$-0.591613\pi$
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	0.972331	−	0.233609i	$-0.0750537\pi$
$522$	24.1345	+	13.9340i	1.05634	+	0.609877i
$523$	−12.4270	−	7.17472i	−0.543394	−	0.313729i	0.203059	−	0.979166i	$-0.434912\pi$
$523$	−12.4270	−	7.17472i	−0.543394	−	0.313729i	−0.746453	+	0.665438i	$0.768245\pi$
$524$	−0.855764			−0.0373842
$525$		0			0
$526$	2.73335			0.119180
$527$	−4.00210	+	2.31061i	−0.174334	+	0.100652i
$528$			23.5593i			1.02529i
$529$	2.93969			0.127813
$530$		0			0
$531$	−1.97917	+	3.42803i	−0.0858888	+	0.148764i
$532$			7.06145i			0.306153i
$533$	3.38486	−	1.95425i	0.146615	−	0.0846480i
$534$	26.9233	+	46.6326i	1.16509	+	2.01799i
$535$		0			0
$536$	17.3090	−	29.9800i	0.747634	−	1.29494i
$537$	26.4850	+	15.2911i	1.14291	+	0.659860i
$538$	11.8002	−	6.81287i	0.508744	−	0.293723i
$539$	9.90206	+	17.1509i	0.426512	+	0.738740i
$540$		0			0
$541$	14.4219			0.620046			0.310023	−	0.950729i	$-0.399663\pi$
$541$	14.4219			0.620046			0.310023	+	0.950729i	$0.399663\pi$
$542$	−30.3849	−	17.5427i	−1.30514	−	0.753524i
$543$	61.0482	−	35.2462i	2.61983	−	1.51256i
$544$	−2.28863			−0.0981243
$545$		0			0
$546$	−1.60309	−	2.77663i	−0.0686059	−	0.118829i
$547$		−	4.85582i		−	0.207620i	−0.994597	−	0.103810i	$-0.966897\pi$
$547$		−	4.85582i		−	0.207620i	0.994597	−	0.103810i	$-0.0331034\pi$
$548$	1.23108	+	0.710765i	0.0525892	+	0.0303624i
$549$	7.49881			0.320041
$550$		0			0
$551$	−11.8229	+	20.4778i	−0.503671	+	0.872383i
$552$	39.8408	+	23.0021i	1.69574	+	0.979034i
$553$	−4.04362	+	2.33459i	−0.171952	+	0.0992767i
$554$	−25.9944			−1.10439
$555$		0			0
$556$	2.81128			0.119225
$557$	4.11206	−	2.37410i	0.174233	−	0.100594i	−0.410347	−	0.911929i	$-0.634592\pi$
$557$	4.11206	−	2.37410i	0.174233	−	0.100594i	0.584581	+	0.811336i	$0.301259\pi$
$558$	−63.2091	−	36.4938i	−2.67585	−	1.54490i
$559$	1.40704	−	2.43706i	0.0595113	−	0.103077i
$560$		0			0
$561$	−6.95878			−0.293800
$562$	−20.7946	−	12.0057i	−0.877166	−	0.506432i
$563$			12.4349i			0.524069i	0.965058	+	0.262035i	$0.0843935\pi$
$563$			12.4349i			0.524069i	−0.965058	+	0.262035i	$0.915607\pi$
$564$	10.0549	+	17.4156i	0.423389	+	0.733331i
$565$		0			0
$566$	−15.4852			−0.650890
$567$	−35.0347	+	20.2273i	−1.47132	+	0.849466i
$568$	−1.35122	−	0.780125i	−0.0566958	−	0.0327333i
$569$	−11.9189			−0.499666			−0.249833	−	0.968289i	$-0.580376\pi$
$569$	−11.9189			−0.499666			−0.249833	+	0.968289i	$0.580376\pi$
$570$		0			0
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	0.996201	+	0.0870894i	$0.0277566\pi$
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	−0.422679	+	0.906280i	$0.638910\pi$
$572$	−1.62210	+	0.936518i	−0.0678232	+	0.0391578i
$573$	21.7298	+	12.5457i	0.907774	+	0.524104i
$574$	3.83276	−	6.63853i	0.159976	−	0.277087i
$575$		0			0
$576$	−34.0537	−	58.9828i	−1.41890	−	2.45761i
$577$	5.61111	−	3.23957i	0.233593	−	0.134865i	−0.378635	−	0.925546i	$-0.623607\pi$
$577$	5.61111	−	3.23957i	0.233593	−	0.134865i	0.612229	+	0.790681i	$0.290273\pi$
$578$		−	18.6788i		−	0.776937i
$579$	27.6277	−	47.8525i	1.14817	−	1.98868i
$580$		0			0
$581$	−14.2137			−0.589685
$582$			38.4016i			1.59180i
$583$	30.9871	−	17.8904i	1.28336	−	0.740946i
$584$	−10.9332			−0.452418
$585$		0			0
$586$	−7.96625			−0.329083
$587$	33.6563	+	19.4315i	1.38914	+	0.802022i	0.993219	−	0.116261i	$-0.0370910\pi$
$587$	33.6563	+	19.4315i	1.38914	+	0.802022i	0.395924	+	0.918283i	$0.370424\pi$
$588$	−11.8347	−	6.83277i	−0.488055	−	0.281779i
$589$	30.9645	−	53.6321i	1.27587	−	2.20987i
$590$		0			0
$591$	5.83418			0.239986
$592$	−8.06374	−	8.77698i	−0.331418	−	0.360731i
$593$			35.6076i			1.46223i	0.682254	+	0.731115i	$0.261000\pi$
$593$			35.6076i			1.46223i	−0.682254	+	0.731115i	$0.739000\pi$
$594$	−34.7390	−	60.1697i	−1.42536	−	2.46879i
$595$		0			0
$596$	−0.205456	+	0.355859i	−0.00841579	+	0.0145766i
$597$	−42.8739	−	24.7532i	−1.75471	−	1.01308i
$598$		−	3.51211i		−	0.143621i
$599$	8.46167	−	14.6560i	0.345735	−	0.598830i	−0.639752	−	0.768581i	$-0.720963\pi$
$599$	8.46167	−	14.6560i	0.345735	−	0.598830i	0.985487	+	0.169751i	$0.0542964\pi$
$600$		0			0
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	0.968959	−	0.247221i	$-0.0795173\pi$
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	−0.698579	+	0.715533i	$0.746184\pi$
$602$		−	5.51908i		−	0.224941i
$603$			91.8062i			3.73864i
$604$	−3.40553	−	5.89856i	−0.138569	−	0.240009i
$605$		0			0
$606$	−20.5966			−0.836681
$607$	4.98980	−	2.88086i	0.202530	−	0.116931i	−0.395305	−	0.918550i	$-0.629361\pi$
$607$	4.98980	−	2.88086i	0.202530	−	0.116931i	0.597835	+	0.801619i	$0.296028\pi$
$608$	26.5610	−	15.3350i	1.07719	−	0.621916i
$609$	6.23259	+	10.7952i	0.252557	+	0.437442i
$610$		0			0
$611$	2.83192	−	4.90502i	0.114567	−	0.198436i
$612$	3.04017	−	1.75524i	0.122892	−	0.0709515i
$613$	−28.9125	+	16.6927i	−1.16777	+	0.674210i	−0.953153	−	0.302489i	$-0.902182\pi$
$613$	−28.9125	+	16.6927i	−1.16777	+	0.674210i	−0.214613	+	0.976699i	$0.568849\pi$
$614$	−13.2475	−	22.9453i	−0.534625	−	0.925998i
$615$		0			0
$616$	−6.77608	+	11.7365i	−0.273016	+	0.472877i
$617$	29.1637	−	16.8377i	1.17409	−	0.677860i	0.219448	−	0.975624i	$-0.429574\pi$
$617$	29.1637	−	16.8377i	1.17409	−	0.677860i	0.954639	+	0.297765i	$0.0962410\pi$
$618$			23.3664i			0.939934i
$619$	−28.0530			−1.12755			−0.563774	−	0.825929i	$-0.690651\pi$
$619$	−28.0530			−1.12755			−0.563774	+	0.825929i	$0.690651\pi$
$620$		0			0
$621$	−77.1241			−3.09488
$622$	−18.7931	−	10.8502i	−0.753535	−	0.435054i
$623$			17.6081i			0.705454i
$624$	−2.28931	+	3.96520i	−0.0916458	+	0.158735i
$625$		0			0
$626$	−3.42442	+	5.93127i	−0.136867	+	0.237061i
$627$	80.7609	−	46.6273i	3.22528	−	1.86212i
$628$			2.03900i			0.0813652i
$629$	2.59249	−	2.38182i	0.103369	−	0.0949692i
$630$		0			0
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	−0.987514	−	0.157528i	$-0.949647\pi$
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	0.357334	−	0.933977i	$-0.383686\pi$
$632$	10.1581	+	5.86476i	0.404066	+	0.233288i
$633$	52.4585	+	30.2869i	2.08504	+	1.20380i
$634$	−18.6287	+	32.2659i	−0.739841	+	1.28144i
$635$		0			0
$636$	−12.3450	+	21.3822i	−0.489512	+	0.847860i
$637$			3.84883i			0.152496i
$638$	−10.6529	+	6.15044i	−0.421751	+	0.243498i
$639$	4.13775			0.163687
$640$		0			0
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	0.885897	−	0.463882i	$-0.153544\pi$
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	−0.844682	+	0.535268i	$0.820210\pi$
$642$	−1.20001	−	0.692824i	−0.0473605	−	0.0273436i
$643$			1.07099i			0.0422359i	0.999777	+	0.0211179i	$0.00672255\pi$
$643$			1.07099i			0.0422359i	−0.999777	+	0.0211179i	$0.993277\pi$
$644$	2.03887	+	3.53143i	0.0803428	+	0.139158i
$645$		0			0
$646$	−2.51572	−	4.35735i	−0.0989795	−	0.171438i
$647$	−30.2179	−	17.4463i	−1.18799	−	0.685886i	−0.230141	−	0.973157i	$-0.573919\pi$
$647$	−30.2179	−	17.4463i	−1.18799	−	0.685886i	−0.957849	+	0.287271i	$0.907252\pi$
$648$	88.0113	+	50.8133i	3.45741	+	1.99614i
$649$	−0.873600	−	1.51312i	−0.0342918	−	0.0593951i
$650$		0			0
$651$	−16.3234	−	28.2729i	−0.639764	−	1.10810i
$652$			15.6693i			0.613658i
$653$	1.70043	+	0.981744i	0.0665430	+	0.0384186i	0.532902	−	0.846177i	$-0.321101\pi$
$653$	1.70043	+	0.981744i	0.0665430	+	0.0384186i	−0.466359	+	0.884595i	$0.654435\pi$
$654$	5.82282	+	10.0854i	0.227690	+	0.394371i
$655$		0			0
$656$	−10.9468			−0.427402
$657$	25.1100	−	14.4973i	0.979635	−	0.565593i
$658$		−	11.1081i		−	0.433041i
$659$	9.77811	−	16.9362i	0.380901	−	0.659740i	−0.610290	−	0.792178i	$-0.708947\pi$
$659$	9.77811	−	16.9362i	0.380901	−	0.659740i	0.991191	+	0.132438i	$0.0422805\pi$
$660$		0			0
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	−0.884584	−	0.466381i	$-0.845557\pi$
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	0.846190	+	0.532881i	$0.178891\pi$
$662$	1.34667	+	0.777499i	0.0523397	+	0.0302184i
$663$	−1.17122	−	0.676202i	−0.0454863	−	0.0262615i
$664$	17.8533	+	30.9228i	0.692842	+	1.20004i
$665$		0			0
$666$	53.0513	+	16.6508i	2.05570	+	0.645207i
$667$			13.6546i			0.528708i
$668$	6.45942	−	3.72935i	0.249923	−	0.144293i
$669$	−6.42244	+	11.1240i	−0.248306	+	0.430078i
$670$		0			0
$671$	−1.65497	+	2.86650i	−0.0638896	+	0.110660i
$672$		−	16.1681i		−	0.623698i
$673$	−17.8966	−	10.3326i	−0.689861	−	0.398292i	0.113699	−	0.993515i	$-0.463730\pi$
$673$	−17.8966	−	10.3326i	−0.689861	−	0.398292i	−0.803560	+	0.595224i	$0.797063\pi$
$674$	−17.1598			−0.660971
$675$		0			0
$676$	9.30432			0.357858
$677$			10.7458i			0.412994i	0.978447	+	0.206497i	$0.0662064\pi$
$677$			10.7458i			0.412994i	−0.978447	+	0.206497i	$0.933794\pi$
$678$	37.9072	−	21.8857i	1.45582	−	0.840517i
$679$	−6.27875	+	10.8751i	−0.240956	+	0.417349i
$680$		0			0
$681$	23.0685	+	39.9559i	0.883988	+	1.53111i
$682$	27.9002	−	16.1082i	1.06836	−	0.616815i
$683$	10.4376	−	6.02617i	0.399385	−	0.230585i	−0.286834	−	0.957980i	$-0.592603\pi$
$683$	10.4376	−	6.02617i	0.399385	−	0.230585i	0.686218	+	0.727396i	$0.259269\pi$
$684$	−23.5220	+	40.7413i	−0.899386	+	1.55778i
$685$		0			0
$686$	8.57660	+	14.8551i	0.327456	+	0.567171i
$687$	−1.74418	+	1.00700i	−0.0665447	+	0.0384196i
$688$	−6.82565	+	3.94079i	−0.260226	+	0.150241i
$689$	6.95383			0.264920
$690$		0			0
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	0.751112	−	0.660175i	$-0.229518\pi$
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	−0.947284	+	0.320395i	$0.896184\pi$
$692$		−	9.89386i		−	0.376108i
$693$		−	35.9401i		−	1.36525i
$694$	15.1369	+	26.2178i	0.574587	+	0.995215i
$695$		0			0
$696$	15.6570	−	27.1187i	0.593477	−	1.02793i
$697$		−	3.23341i		−	0.122474i
$698$	19.7225	+	11.3868i	0.746506	+	0.430996i
$699$	38.9817	−	67.5183i	1.47442	−	2.55378i
$700$		0			0
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	−0.977706	−	0.209978i	$-0.932661\pi$
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	0.307007	−	0.951707i	$-0.400673\pi$
$702$		−	13.5027i		−	0.509626i
$703$	−14.1280	+	45.0134i	−0.532848	+	1.69771i
$704$	30.0624			1.13302
$705$		0			0
$706$	2.50519	−	4.33912i	0.0942841	−	0.163305i
$707$	−5.83285	−	3.36760i	−0.219367	−	0.126652i
$708$	1.04411	+	0.602815i	0.0392399	+	0.0226552i
$709$	32.6695			1.22693			0.613465	−	0.789722i	$-0.289775\pi$
$709$	32.6695			1.22693			0.613465	+	0.789722i	$0.289775\pi$
$710$		0			0
$711$	−31.1065			−1.16658
$712$	38.3075	−	22.1168i	1.43563	−	0.828863i
$713$		−	35.7619i		−	1.33929i
$714$	−2.65239			−0.0992632
$715$		0			0
$716$	3.40488	−	5.89742i	0.127246	−	0.220397i
$717$			93.8323i			3.50423i
$718$	−30.3571	+	17.5267i	−1.13292	+	0.654090i
$719$	16.3243	+	28.2746i	0.608794	+	1.05446i	0.991439	+	0.130567i	$0.0416799\pi$
$719$	16.3243	+	28.2746i	0.608794	+	1.05446i	−0.382645	+	0.923895i	$0.624987\pi$
$720$		0			0
$721$	−3.82046	+	6.61723i	−0.142281	+	0.246438i
$722$	39.9500	+	23.0651i	1.48678	+	0.858395i
$723$	0.105300	−	0.0607951i	0.00391615	−	0.00226099i
$724$	−7.84829	−	13.5936i	−0.291679	−	0.505204i
$725$		0			0
$726$	7.33294			0.272151
$727$	−12.2819	−	7.09098i	−0.455512	−	0.262990i	0.254643	−	0.967035i	$-0.418042\pi$
$727$	−12.2819	−	7.09098i	−0.455512	−	0.262990i	−0.710155	+	0.704045i	$0.751375\pi$
$728$	−2.28093	+	1.31690i	−0.0845369	+	0.0488074i
$729$	−96.9728			−3.59158
$730$		0			0
$731$	−1.16401	−	2.01612i	−0.0430523	−	0.0745688i
$732$		−	2.28398i		−	0.0844184i
$733$	−16.8471	−	9.72667i	−0.622261	−	0.359263i	0.155488	−	0.987838i	$-0.450305\pi$
$733$	−16.8471	−	9.72667i	−0.622261	−	0.359263i	−0.777749	+	0.628575i	$0.783638\pi$
$734$	18.0752			0.667168
$735$		0			0
$736$	8.85542	−	15.3380i	0.326415	−	0.565368i
$737$	−35.0939	−	20.2615i	−1.29270	−	0.746341i
$738$	44.2265	−	25.5342i	1.62800	−	0.939926i
$739$	52.1774			1.91938			0.959689	−	0.281063i	$-0.0906871\pi$
$739$	52.1774			1.91938			0.959689	+	0.281063i	$0.0906871\pi$
$740$		0			0
$741$	18.1236			0.665786
$742$	11.8110	−	6.81907i	0.433594	−	0.250336i
$743$	−11.5764	−	6.68363i	−0.424696	−	0.245198i	0.272388	−	0.962187i	$-0.412186\pi$
$743$	−11.5764	−	6.68363i	−0.424696	−	0.245198i	−0.697085	+	0.716989i	$0.745520\pi$
$744$	−41.0063	+	71.0249i	−1.50336	+	2.60390i
$745$		0			0
$746$	−11.4778			−0.420231
$747$	−82.0067	−	47.3466i	−3.00047	−	1.73232i
$748$			1.54952i			0.0566559i
$749$	−0.226557	−	0.392408i	−0.00827820	−	0.0143383i
$750$		0			0
$751$	16.7410			0.610887			0.305443	−	0.952210i	$-0.401195\pi$
$751$	16.7410			0.610887			0.305443	+	0.952210i	$0.401195\pi$
$752$	−13.7379	+	7.93156i	−0.500969	+	0.289234i
$753$	61.9500	+	35.7668i	2.25758	+	1.30342i
$754$	−2.39061			−0.0870609
$755$		0			0
$756$	7.83867	+	13.5770i	0.285090	+	0.493790i
$757$	9.76765	−	5.63936i	0.355011	−	0.204966i	−0.311879	−	0.950122i	$-0.600958\pi$
$757$	9.76765	−	5.63936i	0.355011	−	0.204966i	0.666890	+	0.745156i	$0.267625\pi$
$758$	−16.0765	−	9.28176i	−0.583924	−	0.337129i
$759$	26.9257	−	46.6367i	0.977340	−	1.69280i
$760$		0			0
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	0.883631	+	0.468184i	$0.155092\pi$
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	−0.0363559	+	0.999339i	$0.511575\pi$
$762$	−57.5453	+	33.2238i	−2.08464	+	1.20357i
$763$			3.80818i			0.137865i
$764$	2.79355	−	4.83858i	0.101067	−	0.175054i
$765$		0			0
$766$	20.5129			0.741162
$767$		−	0.339559i		−	0.0122608i
$768$	−43.6051	+	25.1754i	−1.57346	+	0.908439i
$769$	−37.8487			−1.36486			−0.682430	−	0.730951i	$-0.739077\pi$
$769$	−37.8487			−1.36486			−0.682430	+	0.730951i	$0.739077\pi$
$770$		0			0
$771$	−2.69790			−0.0971626
$772$	−10.6553	−	6.15186i	−0.383494	−	0.221410i
$773$	3.59297	+	2.07440i	0.129230	+	0.0746110i	0.563221	−	0.826306i	$-0.309562\pi$
$773$	3.59297	+	2.07440i	0.129230	+	0.0746110i	−0.433991	+	0.900917i	$0.642895\pi$
$774$	18.3843	−	31.8425i	0.660810	−	1.14456i
$775$		0			0
$776$	31.5459			1.13243
$777$	16.8264	+	18.3147i	0.603644	+	0.657036i
$778$		−	16.4451i		−	0.589587i
$779$	21.6654	+	37.5256i	0.776245	+	1.34450i
$780$		0			0
$781$	−0.913195	+	1.58170i	−0.0326767	+	0.0565977i
$782$	−2.51622	−	1.45274i	−0.0899798	−	0.0519499i
$783$			52.4966i			1.87608i
$784$	5.38985	−	9.33550i	0.192495	−	0.333411i
$785$		0			0
$786$	2.15380	+	3.73049i	0.0768234	+	0.133062i
$787$			42.8205i			1.52639i	0.646170	+	0.763193i	$0.276370\pi$
$787$			42.8205i			1.52639i	−0.646170	+	0.763193i	$0.723630\pi$
$788$		−	1.29910i		−	0.0462785i
$789$	4.07256	+	7.05387i	0.144987	+	0.251125i
$790$		0			0
$791$	14.3135			0.508928
$792$	−78.1897	+	45.1429i	−2.77835	+	1.60408i
$793$	−0.557089	+	0.321636i	−0.0197828	+	0.0114216i
$794$	−1.12212	−	1.94357i	−0.0398226	−	0.0689748i
$795$		0			0
$796$	−5.51182	+	9.54674i	−0.195361	+	0.338375i
$797$	32.5896	−	18.8156i	1.15438	−	0.666482i	0.204430	−	0.978881i	$-0.434466\pi$
$797$	32.5896	−	18.8156i	1.15438	−	0.666482i	0.949951	+	0.312399i	$0.101133\pi$
$798$	30.7826	−	17.7723i	1.08969	−	0.629134i
$799$	−2.34277	−	4.05780i	−0.0828814	−	0.143555i
$800$		0			0
$801$	−58.6534	+	101.591i	−2.07242	+	3.58953i
$802$	22.2143	−	12.8255i	0.784416	−	0.452883i
$803$			12.7981i			0.451635i
$804$	27.9623			0.986153
$805$		0			0
$806$	6.26110			0.220538
$807$	35.1635	+	20.3017i	1.23781	+	0.714653i
$808$			16.9196i			0.595230i
$809$	−11.7837	+	20.4099i	−0.414292	+	0.717576i	−0.995354	−	0.0962841i	$-0.969304\pi$
$809$	−11.7837	+	20.4099i	−0.414292	+	0.717576i	0.581061	+	0.813860i	$0.302638\pi$
$810$		0			0
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.00374948	−	0.999993i	$-0.498807\pi$
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.864145	−	0.503244i	$-0.167860\pi$
$812$	2.40376	−	1.38781i	0.0843555	−	0.0487027i
$813$		−	104.551i		−	3.66677i
$814$	−18.0733	+	16.6046i	−0.633468	+	0.581991i
$815$		0			0
$816$	1.89389	+	3.28031i	0.0662994	+	0.114834i
$817$	27.0180	+	15.5988i	0.945240	+	0.545734i
$818$	−8.84896	−	5.10895i	−0.309397	−	0.178630i
$819$	3.49238	−	6.04899i	0.122034	−	0.211369i
$820$		0			0
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	−0.997890	−	0.0649222i	$-0.979320\pi$
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	0.555169	+	0.831737i	$0.312653\pi$
$822$		−	7.15545i		−	0.249575i
$823$	−7.07564	+	4.08512i	−0.246641	+	0.142398i	−0.618225	−	0.786001i	$-0.712148\pi$
$823$	−7.07564	+	4.08512i	−0.246641	+	0.142398i	0.371584	+	0.928399i	$0.378815\pi$
$824$	19.1949			0.668686
$825$		0			0
$826$	−0.332979	−	0.576736i	−0.0115858	−	0.0200672i
$827$	−0.857468	−	0.495060i	−0.0298171	−	0.0172149i	0.485017	−	0.874505i	$-0.338813\pi$
$827$	−0.857468	−	0.495060i	−0.0298171	−	0.0172149i	−0.514834	+	0.857290i	$0.672147\pi$
$828$			27.1663i			0.944094i
$829$	−13.0618	−	22.6237i	−0.453654	−	0.785752i	0.544955	−	0.838465i	$-0.316547\pi$
$829$	−13.0618	−	22.6237i	−0.453654	−	0.785752i	−0.998610	+	0.0527126i	$0.983213\pi$
$830$		0			0
$831$	−38.7303	−	67.0829i	−1.34354	−	2.32708i
$832$	5.05972	+	2.92123i	0.175414	+	0.101276i
$833$	2.75746	+	1.59202i	0.0955403	+	0.0551602i
$834$	−7.07546	−	12.2551i	−0.245003	−	0.424358i
$835$		0			0
$836$	−10.3825	−	17.9831i	−0.359087	−	0.621957i
$837$		−	137.490i		−	4.75237i
$838$	8.26102	+	4.76950i	0.285372	+	0.164760i
$839$	−20.0623	−	34.7490i	−0.692629	−	1.19967i	−0.970973	−	0.239187i	$-0.923119\pi$
$839$	−20.0623	−	34.7490i	−0.692629	−	1.19967i	0.278344	−	0.960481i	$-0.410214\pi$
$840$		0			0
$841$	−19.7056			−0.679505
$842$	8.57678	−	4.95181i	0.295575	−	0.170650i
$843$		−	71.5519i		−	2.46438i
$844$	6.74400	−	11.6809i	0.232138	−	0.402075i
$845$		0			0
$846$	37.0017	−	64.0889i	1.27215	−	2.20342i
$847$	2.07665	+	1.19895i	0.0713544	+	0.0411965i
$848$	−16.8668	−	9.73805i	−0.579208	−	0.334406i
$849$	−23.0721	−	39.9621i	−0.791833	−	1.37150i
$850$		0			0
$851$	5.93141	+	26.5904i	0.203326	+	0.911507i
$852$		−	1.26027i		−	0.0431763i
$853$	−28.2985	+	16.3382i	−0.968923	+	0.559408i	−0.898908	−	0.438138i	$-0.855638\pi$
$853$	−28.2985	+	16.3382i	−0.968923	+	0.559408i	−0.0700154	+	0.997546i	$0.522305\pi$
$854$	−0.630805	+	1.09259i	−0.0215857	+	0.0373876i
$855$		0			0
$856$	−0.569137	+	0.985774i	−0.0194527	+	0.0336931i
$857$			9.95029i			0.339896i	0.985453	+	0.169948i	$0.0543599\pi$
$857$			9.95029i			0.339896i	−0.985453	+	0.169948i	$0.945640\pi$
$858$	8.16503	+	4.71408i	0.278749	+	0.160936i
$859$	−4.53739			−0.154814			−0.0774068	−	0.997000i	$-0.524664\pi$
$859$	−4.53739			−0.154814			−0.0774068	+	0.997000i	$0.524664\pi$
$860$		0			0
$861$	22.8425			0.778470
$862$		−	1.69320i		−	0.0576706i
$863$	2.99198	−	1.72742i	0.101848	−	0.0588020i	−0.448211	−	0.893928i	$-0.647939\pi$
$863$	2.99198	−	1.72742i	0.101848	−	0.0588020i	0.550059	+	0.835126i	$0.314605\pi$
$864$	34.0457	−	58.9688i	1.15826	−	2.00616i
$865$		0			0
$866$	−3.84349	−	6.65712i	−0.130607	−	0.226218i
$867$	48.2039	−	27.8305i	1.63709	−	0.945175i
$868$	−6.29554	+	3.63473i	−0.213685	+	0.123371i
$869$	6.86514	−	11.8908i	0.232884	−	0.403367i
$870$		0			0
$871$	−3.93771	−	6.82032i	−0.133424	−	0.231098i
$872$	8.28491	−	4.78330i	0.280562	−	0.161983i
$873$	−72.4510	+	41.8296i	−2.45210	+	1.41572i
$874$	38.9363			1.31704
$875$		0			0
$876$	−4.41557	−	7.64799i	−0.149188	−	0.258402i
$877$			23.2726i			0.785861i	0.919568	+	0.392931i	$0.128539\pi$
$877$			23.2726i			0.785861i	−0.919568	+	0.392931i	$0.871461\pi$
$878$			21.4504i			0.723917i
$879$	−11.8693	−	20.5583i	−0.400342	−	0.693413i
$880$		0			0
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	−0.950962	−	0.309309i	$-0.899902\pi$
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	0.743350	+	0.668903i	$0.233236\pi$
$882$			50.2887i			1.69331i
$883$	−15.2902	−	8.82778i	−0.514555	−	0.297078i	0.220149	−	0.975466i	$-0.429346\pi$
$883$	−15.2902	−	8.82778i	−0.514555	−	0.297078i	−0.734704	+	0.678388i	$0.762679\pi$
$884$	−0.150570	+	0.260795i	−0.00506422	+	0.00877149i
$885$		0			0
$886$	1.26481	+	2.19072i	0.0424922	+	0.0735987i
$887$		−	40.8268i		−	1.37083i	−0.728153	−	0.685415i	$-0.759621\pi$
$887$		−	40.8268i		−	1.37083i	0.728153	−	0.685415i	$-0.240379\pi$
$888$	18.7097	−	59.6112i	0.627857	−	2.00042i
$889$	−21.7286			−0.728755
$890$		0			0
$891$	59.4808	−	103.024i	1.99268	−	3.45143i
$892$	2.47698	+	1.43009i	0.0829355	+	0.0478828i
$893$	54.3786	+	31.3955i	1.81971	+	1.05061i
$894$	2.06837			0.0691768
$895$		0			0
$896$	1.77697			0.0593644
$897$	9.06360	−	5.23287i	0.302625	−	0.174720i
$898$		−	27.3237i		−	0.911804i
$899$	−24.3423			−0.811861
$900$		0			0
$901$	2.87636	−	4.98201i	0.0958256	−	0.165975i
$902$			22.5414i			0.750546i
$903$	14.2429	−	8.22315i	0.473975	−	0.273649i
$904$	−17.9786	−	31.1398i	−0.597958	−	1.03569i
$905$		0			0
$906$	−17.1422	+	29.6912i	−0.569511	+	0.986422i
$907$	−49.6320	−	28.6551i	−1.64800	−	0.951475i	−0.977864	−	0.209240i	$-0.932901\pi$
$907$	−49.6320	−	28.6551i	−1.64800	−	0.951475i	−0.670139	−	0.742235i	$-0.733766\pi$
$908$	8.89699	−	5.13668i	0.295257	−	0.170467i
$909$	−22.4352	−	38.8590i	−0.744130	−	1.28887i
$910$		0			0
$911$	−21.6237			−0.716426			−0.358213	−	0.933640i	$-0.616614\pi$
$911$	−21.6237			−0.716426			−0.358213	+	0.933640i	$0.616614\pi$
$912$	−43.9595	−	25.3800i	−1.45564	−	0.840417i
$913$	36.1975	−	20.8986i	1.19796	−	0.691643i
$914$	15.7507			0.520986
$915$		0			0
$916$	0.224230	+	0.388378i	0.00740877	+	0.0128324i
$917$			1.40860i			0.0465162i
$918$	−9.67388	−	5.58522i	−0.319286	−	0.184340i
$919$	−30.6901			−1.01237			−0.506186	−	0.862424i	$-0.668945\pi$
$919$	−30.6901			−1.01237			−0.506186	+	0.862424i	$0.668945\pi$
$920$		0			0
$921$	39.4762	−	68.3748i	1.30079	−	2.25303i
$922$	−25.6429	−	14.8049i	−0.844504	−	0.487575i
$923$	−0.307395	+	0.177475i	−0.0101180	+	0.00584165i
$924$	−10.9466			−0.360117
$925$		0			0
$926$	28.1806			0.926071
$927$	−44.0846	+	25.4522i	−1.44793	+	0.835961i
$928$	−10.4403	−	6.02768i	−0.342718	−	0.197868i
$929$	−4.44146	+	7.69284i	−0.145720	+	0.252394i	−0.929641	−	0.368466i	$-0.879883\pi$
$929$	−4.44146	+	7.69284i	−0.145720	+	0.252394i	0.783922	+	0.620860i	$0.213216\pi$
$930$		0			0
$931$	−42.6693			−1.39843
$932$	−15.0343	−	8.68007i	−0.492466	−	0.284325i
$933$		−	64.6652i		−	2.11704i
$934$	−7.86317	−	13.6194i	−0.257291	−	0.445641i
$935$		0			0
$936$	−17.5466			−0.573527
$937$	−0.530517	+	0.306294i	−0.0173312	+	0.0100062i	−0.508641	−	0.860979i	$-0.669852\pi$
$937$	−0.530517	+	0.306294i	−0.0173312	+	0.0100062i	0.491309	+	0.870985i	$0.336518\pi$
$938$	−13.3763	−	7.72281i	−0.436751	−	0.252159i
$939$	−20.4089			−0.666019
$940$		0			0
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	−0.998655	−	0.0518474i	$-0.983489\pi$
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	0.454426	−	0.890784i	$-0.349844\pi$
$942$	8.88853	−	5.13180i	0.289604	−	0.167203i
$943$	21.6698	+	12.5110i	0.705665	+	0.407416i
$944$	−0.475515	+	0.823616i	−0.0154767	+	0.0268064i
$945$		0			0
$946$	8.11476	+	14.0552i	0.263834	+	0.456973i
$947$	8.97566	−	5.18210i	0.291670	−	0.168396i	−0.347025	−	0.937856i	$-0.612808\pi$
$947$	8.97566	−	5.18210i	0.291670	−	0.168396i	0.638695	+	0.769460i	$0.279475\pi$
$948$			9.47438i			0.307714i
$949$	−1.24362	+	2.15402i	−0.0403697	+	0.0699223i
$950$		0			0
$951$	−111.024			−3.60018
$952$			2.17887i			0.0706176i
$953$	12.8946	−	7.44472i	0.417698	−	0.241158i	−0.276394	−	0.961044i	$-0.589139\pi$
$953$	12.8946	−	7.44472i	0.417698	−	0.241158i	0.694092	+	0.719886i	$0.255806\pi$
$954$	90.8585			2.94165
$955$		0			0
$956$	20.8937			0.675749
$957$	−31.7445	−	18.3277i	−1.02615	−	0.592450i
$958$	6.48617	+	3.74479i	0.209559	+	0.120989i
$959$	1.16993	−	2.02638i	0.0377791	−	0.0654353i
$960$		0			0
$961$	32.7533			1.05656
$962$	−4.65538	+	1.03846i	−0.150096	+	0.0334812i
$963$		−	3.01868i		−	0.0972757i
$964$	−0.0135373	−	0.0234472i	−0.000436006	−	0.000755184i
$965$		0			0
$966$	10.2629	−	17.7759i	0.330204	−	0.571930i
$967$	37.5055	+	21.6538i	1.20609	+	0.696339i	0.961904	−	0.273389i	$-0.0881445\pi$
$967$	37.5055	+	21.6538i	1.20609	+	0.696339i	0.244190	+	0.969727i	$0.421478\pi$
$968$		−	6.02382i		−	0.193613i
$969$	7.49659	−	12.9845i	0.240825	−	0.417121i
$970$		0			0
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	0.785607	−	0.618726i	$-0.212351\pi$
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	−0.928636	+	0.370992i	$0.879018\pi$
$972$			43.6684i			1.40066i
$973$		−	4.62741i		−	0.148348i
$974$	−4.07170	−	7.05239i	−0.130466	−	0.225973i
$975$		0			0
$976$	1.80166			0.0576697
$977$	−11.5810	+	6.68632i	−0.370511	+	0.213914i	−0.673681	−	0.739022i	$-0.735288\pi$
$977$	−11.5810	+	6.68632i	−0.370511	+	0.213914i	0.303171	+	0.952936i	$0.401955\pi$
$978$	68.3065	−	39.4368i	2.18420	−	1.26105i
$979$	−25.8894	−	44.8418i	−0.827429	−	1.43315i
$980$		0			0
$981$	−12.6852	+	21.9714i	−0.405008	+	0.701494i
$982$	−0.433526	+	0.250296i	−0.0138344	+	0.00798728i
$983$	−20.0327	+	11.5659i	−0.638944	+	0.368894i	−0.784208	−	0.620499i	$-0.786930\pi$
$983$	−20.0327	+	11.5659i	−0.638944	+	0.368894i	0.145264	+	0.989393i	$0.453597\pi$
$984$	−28.6915	−	49.6952i	−0.914652	−	1.58422i
$985$		0			0
$986$	−0.988847	+	1.71273i	−0.0314913	+	0.0545445i
$987$	28.6665	−	16.5506i	0.912464	−	0.526811i
$988$		−	4.03558i		−	0.128389i
$989$	18.0156			0.572863
$990$		0			0
$991$	14.4144			0.457887			0.228944	−	0.973440i	$-0.426473\pi$
$991$	14.4144			0.457887			0.228944	+	0.973440i	$0.426473\pi$
$992$	27.3434	+	15.7867i	0.868154	+	0.501229i
$993$			4.63374i			0.147047i
$994$	−0.348071	+	0.602876i	−0.0110401	+	0.0191221i
$995$		0			0
$996$	−14.4208	+	24.9775i	−0.456940	+	0.791444i
$997$	0.882439	−	0.509477i	0.0279471	−	0.0161353i	−0.485961	−	0.873980i	$-0.661530\pi$
$997$	0.882439	−	0.509477i	0.0279471	−	0.0161353i	0.513908	+	0.857845i	$0.328197\pi$
$998$		−	11.8859i		−	0.376243i
$999$	22.8040	+	102.230i	0.721486	+	3.23441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.b.174.5		28
5.2	odd	4		185.2.e.a.26.3	✓	14
5.3	odd	4		925.2.e.c.26.5		14
5.4	even	2	inner	925.2.o.b.174.10		28
37.10	even	3	inner	925.2.o.b.824.10		28
185.47	odd	12		185.2.e.a.121.3	yes	14
185.84	even	6	inner	925.2.o.b.824.5		28
185.122	odd	12		6845.2.a.k.1.3		7
185.137	odd	12		6845.2.a.l.1.5		7
185.158	odd	12		925.2.e.c.676.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.3	✓	14	5.2	odd	4
185.2.e.a.121.3	yes	14	185.47	odd	12
925.2.e.c.26.5		14	5.3	odd	4
925.2.e.c.676.5		14	185.158	odd	12
925.2.o.b.174.5		28	1.1	even	1	trivial
925.2.o.b.174.10		28	5.4	even	2	inner
925.2.o.b.824.5		28	185.84	even	6	inner
925.2.o.b.824.10		28	37.10	even	3	inner
6845.2.a.k.1.3		7	185.122	odd	12
6845.2.a.l.1.5		7	185.137	odd	12

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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.970676 + 0.560420i) q^{2} +(-2.89252 - 1.67000i) q^{3} +(-0.371859 + 0.644078i) q^{4} +3.74360 q^{6} +(1.06017 + 0.612087i) q^{7} -3.07527i q^{8} +(4.07778 + 7.06292i) q^{9} -3.59983 q^{11} +(2.15122 - 1.24201i) q^{12} +(-0.605879 - 0.349805i) q^{13} -1.37210 q^{14} +(0.979724 + 1.69693i) q^{16} +(-0.501229 + 0.289385i) q^{17} +(-7.91640 - 4.57054i) q^{18} +(3.87804 - 6.71697i) q^{19} +(-2.04437 - 3.54094i) q^{21} +(3.49427 - 2.01742i) q^{22} -4.47887i q^{23} +(-5.13569 + 8.89527i) q^{24} +0.784150 q^{26} -17.2195i q^{27} +(-0.788464 + 0.455220i) q^{28} -3.04867 q^{29} +7.98457 q^{31} +(3.42453 + 1.97715i) q^{32} +(10.4126 + 6.01171i) q^{33} +(0.324354 - 0.561797i) q^{34} -6.06543 q^{36} +(-5.93685 + 1.32431i) q^{37} +8.69333i q^{38} +(1.16835 + 2.02363i) q^{39} +(-2.79335 + 4.83822i) q^{41} +(3.96883 + 2.29141i) q^{42} +4.02235i q^{43} +(1.33863 - 2.31857i) q^{44} +(2.51005 + 4.34753i) q^{46} +8.09571i q^{47} -6.54454i q^{48} +(-2.75070 - 4.76435i) q^{49} +1.93309 q^{51} +(0.450603 - 0.260156i) q^{52} +(-8.60794 + 4.96979i) q^{53} +(9.65017 + 16.7146i) q^{54} +(1.88233 - 3.26029i) q^{56} +(-22.4346 + 12.9526i) q^{57} +(2.95927 - 1.70853i) q^{58} +(0.242678 + 0.420330i) q^{59} +(0.459736 - 0.796287i) q^{61} +(-7.75043 + 4.47471i) q^{62} +9.98382i q^{63} -8.35104 q^{64} -13.4763 q^{66} +(9.74876 + 5.62845i) q^{67} -0.430441i q^{68} +(-7.47970 + 12.9552i) q^{69} +(0.253677 - 0.439381i) q^{71} +(21.7204 - 12.5403i) q^{72} -3.55519i q^{73} +(5.02059 - 4.61261i) q^{74} +(2.88417 + 4.99553i) q^{76} +(-3.81642 - 2.20341i) q^{77} +(-2.26817 - 1.30953i) q^{78} +(-1.90707 + 3.30314i) q^{79} +(-16.5232 + 28.6191i) q^{81} -6.26179i q^{82} +(-10.0553 + 5.80544i) q^{83} +3.04086 q^{84} +(-2.25421 - 3.90440i) q^{86} +(8.81833 + 5.09126i) q^{87} +11.0705i q^{88} +(7.19183 + 12.4566i) q^{89} +(-0.428221 - 0.741701i) q^{91} +(2.88475 + 1.66551i) q^{92} +(-23.0955 - 13.3342i) q^{93} +(-4.53700 - 7.85831i) q^{94} +(-6.60368 - 11.4379i) q^{96} +10.2579i q^{97} +(5.34008 + 3.08309i) q^{98} +(-14.6793 - 25.4253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 16 q^{4} - 8 q^{6} + 26 q^{9} - 4 q^{11} - 40 q^{14} + 4 q^{16} + 28 q^{19} + 2 q^{21} - 30 q^{24} - 44 q^{26} + 24 q^{29} - 66 q^{34} + 80 q^{36} + 50 q^{39} - 14 q^{41} + 38 q^{44} - 28 q^{46}+ \cdots - 112 q^{99}+O(q^{100}) \) 28 * q + 16 * q^4 - 8 * q^6 + 26 * q^9 - 4 * q^11 - 40 * q^14 + 4 * q^16 + 28 * q^19 + 2 * q^21 - 30 * q^24 - 44 * q^26 + 24 * q^29 - 66 * q^34 + 80 * q^36 + 50 * q^39 - 14 * q^41 + 38 * q^44 - 28 * q^46 - 10 * q^49 + 116 * q^51 + 18 * q^54 - 50 * q^56 - 4 * q^59 - 8 * q^61 + 124 * q^64 - 4 * q^66 + 22 * q^69 + 66 * q^71 - 36 * q^74 - 24 * q^76 + 18 * q^79 - 70 * q^81 + 160 * q^84 + 34 * q^86 + 24 * q^89 - 48 * q^91 - 20 * q^94 - 30 * q^96 - 112 * q^99

Introduction

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