LMFDB - Embedded newform 925.2.o.d.174.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(174,925)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			174.16
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978390 - 0.564874i) q^{2} +(-2.45341 - 1.41648i) q^{3} +(-0.361836 + 0.626718i) q^{4} -3.20052 q^{6} +(0.203143 + 0.117284i) q^{7} +3.07706i q^{8} +(2.51281 + 4.35232i) q^{9} +O(q^{10})$	\(q+(0.978390 - 0.564874i) q^{2} +(-2.45341 - 1.41648i) q^{3} +(-0.361836 + 0.626718i) q^{4} -3.20052 q^{6} +(0.203143 + 0.117284i) q^{7} +3.07706i q^{8} +(2.51281 + 4.35232i) q^{9} +3.97640 q^{11} +(1.77546 - 1.02506i) q^{12} +(-5.09838 - 2.94355i) q^{13} +0.265003 q^{14} +(1.01448 + 1.75713i) q^{16} +(2.17462 - 1.25552i) q^{17} +(4.91702 + 2.83884i) q^{18} +(2.90630 - 5.03386i) q^{19} +(-0.332261 - 0.575493i) q^{21} +(3.89047 - 2.24616i) q^{22} -5.07332i q^{23} +(4.35858 - 7.54929i) q^{24} -6.65094 q^{26} -5.73849i q^{27} +(-0.147008 + 0.0848753i) q^{28} -1.36770 q^{29} -4.89400 q^{31} +(-3.34451 - 1.93096i) q^{32} +(-9.75573 - 5.63247i) q^{33} +(1.41842 - 2.45678i) q^{34} -3.63690 q^{36} +(-0.100688 - 6.08193i) q^{37} -6.56677i q^{38} +(8.33894 + 14.4435i) q^{39} +(-3.13168 + 5.42423i) q^{41} +(-0.650162 - 0.375371i) q^{42} +4.19434i q^{43} +(-1.43880 + 2.49208i) q^{44} +(-2.86578 - 4.96368i) q^{46} +2.34607i q^{47} -5.74794i q^{48} +(-3.47249 - 6.01453i) q^{49} -7.11366 q^{51} +(3.68955 - 2.13016i) q^{52} +(9.19971 - 5.31146i) q^{53} +(-3.24152 - 5.61448i) q^{54} +(-0.360891 + 0.625082i) q^{56} +(-14.2607 + 8.23342i) q^{57} +(-1.33814 + 0.772578i) q^{58} +(-3.61066 - 6.25384i) q^{59} +(6.77145 - 11.7285i) q^{61} +(-4.78824 + 2.76449i) q^{62} +1.17885i q^{63} -8.42090 q^{64} -12.7265 q^{66} +(0.644842 + 0.372300i) q^{67} +1.81717i q^{68} +(-7.18624 + 12.4469i) q^{69} +(1.29378 - 2.24089i) q^{71} +(-13.3923 + 7.73207i) q^{72} -11.7418i q^{73} +(-3.53403 - 5.89362i) q^{74} +(2.10321 + 3.64286i) q^{76} +(0.807776 + 0.466369i) q^{77} +(16.3175 + 9.42089i) q^{78} +(4.73446 - 8.20033i) q^{79} +(-0.590008 + 1.02192i) q^{81} +7.07602i q^{82} +(-0.0157734 + 0.00910677i) q^{83} +0.480896 q^{84} +(2.36927 + 4.10370i) q^{86} +(3.35553 + 1.93732i) q^{87} +12.2356i q^{88} +(-3.76052 - 6.51341i) q^{89} +(-0.690465 - 1.19592i) q^{91} +(3.17954 + 1.83571i) q^{92} +(12.0070 + 6.93224i) q^{93} +(1.32523 + 2.29537i) q^{94} +(5.47031 + 9.47485i) q^{96} -11.0471i q^{97} +(-6.79490 - 3.92303i) q^{98} +(9.99194 + 17.3065i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) $ 48 * q + 22 * q^4 + 20 * q^9	$ 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) $ 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.978390	−	0.564874i	0.691826	−	0.399426i	−0.112470	−	0.993655i	$-0.535876\pi$
$2$	0.978390	−	0.564874i	0.691826	−	0.399426i	0.804296	+	0.594229i	$0.202543\pi$
$3$	−2.45341	−	1.41648i	−1.41648	−	0.817803i	−0.420489	−	0.907298i	$-0.638142\pi$
$3$	−2.45341	−	1.41648i	−1.41648	−	0.817803i	−0.995987	+	0.0894944i	$0.971475\pi$
$4$	−0.361836	+	0.626718i	−0.180918	+	0.313359i
$5$		0			0
$5$		0			0
$6$	−3.20052			−1.30661
$7$	0.203143	+	0.117284i	0.0767807	+	0.0443293i	0.537899	−	0.843009i	$-0.319218\pi$
$7$	0.203143	+	0.117284i	0.0767807	+	0.0443293i	−0.461118	+	0.887339i	$0.652552\pi$
$8$			3.07706i			1.08790i
$9$	2.51281	+	4.35232i	0.837604	+	1.45077i
$10$		0			0
$11$	3.97640			1.19893			0.599465	−	0.800401i	$-0.295380\pi$
$11$	3.97640			1.19893			0.599465	+	0.800401i	$0.295380\pi$
$12$	1.77546	−	1.02506i	0.512532	−	0.295910i
$13$	−5.09838	−	2.94355i	−1.41404	−	0.816394i	−0.418270	−	0.908323i	$-0.637363\pi$
$13$	−5.09838	−	2.94355i	−1.41404	−	0.816394i	−0.995766	+	0.0919288i	$0.970697\pi$
$14$	0.265003			0.0708252
$15$		0			0
$16$	1.01448	+	1.75713i	0.253620	+	0.439282i
$17$	2.17462	−	1.25552i	0.527424	−	0.304508i	−0.212543	−	0.977152i	$-0.568175\pi$
$17$	2.17462	−	1.25552i	0.527424	−	0.304508i	0.739967	+	0.672643i	$0.234841\pi$
$18$	4.91702	+	2.83884i	1.15895	+	0.669121i
$19$	2.90630	−	5.03386i	0.666751	−	1.15485i	−0.312056	−	0.950064i	$-0.601018\pi$
$19$	2.90630	−	5.03386i	0.666751	−	1.15485i	0.978807	−	0.204783i	$-0.0656490\pi$
$20$		0			0
$21$	−0.332261	−	0.575493i	−0.0725053	−	0.125583i
$22$	3.89047	−	2.24616i	0.829450	−	0.478883i
$23$		−	5.07332i		−	1.05786i	−0.848665	−	0.528930i	$-0.822593\pi$
$23$		−	5.07332i		−	1.05786i	0.848665	−	0.528930i	$-0.177407\pi$
$24$	4.35858	−	7.54929i	0.889692	−	1.54099i
$25$		0			0
$26$	−6.65094			−1.30436
$27$		−	5.73849i		−	1.10437i
$28$	−0.147008	+	0.0848753i	−0.0277820	+	0.0160399i
$29$	−1.36770			−0.253976			−0.126988	−	0.991904i	$-0.540531\pi$
$29$	−1.36770			−0.253976			−0.126988	+	0.991904i	$0.540531\pi$
$30$		0			0
$31$	−4.89400			−0.878989			−0.439494	−	0.898245i	$-0.644842\pi$
$31$	−4.89400			−0.878989			−0.439494	+	0.898245i	$0.644842\pi$
$32$	−3.34451	−	1.93096i	−0.591232	−	0.341348i
$33$	−9.75573	−	5.63247i	−1.69825	−	0.980488i
$34$	1.41842	−	2.45678i	0.243257	−	0.421334i
$35$		0			0
$36$	−3.63690			−0.606150
$37$	−0.100688	−	6.08193i	−0.0165530	−	0.999863i
$37$	−0.100688	−	6.08193i	−0.0165530	−	0.999863i
$38$		−	6.56677i		−	1.06527i
$39$	8.33894	+	14.4435i	1.33530	+	2.31281i
$40$		0			0
$41$	−3.13168	+	5.42423i	−0.489086	+	0.847122i	−0.999921	−	0.0125565i	$-0.996003\pi$
$41$	−3.13168	+	5.42423i	−0.489086	+	0.847122i	0.510835	+	0.859679i	$0.329336\pi$
$42$	−0.650162	−	0.375371i	−0.100322	−	0.0579210i
$43$			4.19434i			0.639631i	0.947480	+	0.319816i	$0.103621\pi$
$43$			4.19434i			0.639631i	−0.947480	+	0.319816i	$0.896379\pi$
$44$	−1.43880	+	2.49208i	−0.216908	+	0.375695i
$45$		0			0
$46$	−2.86578	−	4.96368i	−0.422537	−	0.731855i
$47$			2.34607i			0.342209i	0.985253	+	0.171104i	$0.0547336\pi$
$47$			2.34607i			0.342209i	−0.985253	+	0.171104i	$0.945266\pi$
$48$		−	5.74794i		−	0.829644i
$49$	−3.47249	−	6.01453i	−0.496070	−	0.859218i
$50$		0			0
$51$	−7.11366			−0.996111
$52$	3.68955	−	2.13016i	0.511648	−	0.295400i
$53$	9.19971	−	5.31146i	1.26368	−	0.729585i	0.289893	−	0.957059i	$-0.406380\pi$
$53$	9.19971	−	5.31146i	1.26368	−	0.729585i	0.973784	+	0.227474i	$0.0730468\pi$
$54$	−3.24152	−	5.61448i	−0.441116	−	0.764035i
$55$		0			0
$56$	−0.360891	+	0.625082i	−0.0482261	+	0.0835301i
$57$	−14.2607	+	8.23342i	−1.88888	+	1.09054i
$58$	−1.33814	+	0.772578i	−0.175707	+	0.101444i
$59$	−3.61066	−	6.25384i	−0.470067	−	0.814181i	0.529347	−	0.848406i	$-0.322437\pi$
$59$	−3.61066	−	6.25384i	−0.470067	−	0.814181i	−0.999414	+	0.0342249i	$0.989104\pi$
$60$		0			0
$61$	6.77145	−	11.7285i	0.866996	−	1.50168i	0.00194382	−	0.999998i	$-0.499381\pi$
$61$	6.77145	−	11.7285i	0.866996	−	1.50168i	0.865052	−	0.501682i	$-0.167285\pi$
$62$	−4.78824	+	2.76449i	−0.608107	+	0.351091i
$63$			1.17885i			0.148522i
$64$	−8.42090			−1.05261
$65$		0			0
$66$	−12.7265			−1.56653
$67$	0.644842	+	0.372300i	0.0787800	+	0.0454836i	0.538873	−	0.842387i	$-0.318850\pi$
$67$	0.644842	+	0.372300i	0.0787800	+	0.0454836i	−0.460093	+	0.887871i	$0.652184\pi$
$68$			1.81717i			0.220364i
$69$	−7.18624	+	12.4469i	−0.865121	+	1.49843i
$70$		0			0
$71$	1.29378	−	2.24089i	0.153543	−	0.265945i	−0.778984	−	0.627043i	$-0.784265\pi$
$71$	1.29378	−	2.24089i	0.153543	−	0.265945i	0.932528	+	0.361098i	$0.117598\pi$
$72$	−13.3923	+	7.73207i	−1.57830	+	0.911233i
$73$		−	11.7418i		−	1.37428i	−0.726526	−	0.687139i	$-0.758866\pi$
$73$		−	11.7418i		−	1.37428i	0.726526	−	0.687139i	$-0.241134\pi$
$74$	−3.53403	−	5.89362i	−0.410823	−	0.685120i
$75$		0			0
$76$	2.10321	+	3.64286i	0.241254	+	0.417865i
$77$	0.807776	+	0.466369i	0.0920546	+	0.0531477i
$78$	16.3175	+	9.42089i	1.84759	+	1.06671i
$79$	4.73446	−	8.20033i	0.532669	−	0.922609i	−0.466604	−	0.884466i	$-0.654523\pi$
$79$	4.73446	−	8.20033i	0.532669	−	0.922609i	0.999272	−	0.0381426i	$-0.0121441\pi$
$80$		0			0
$81$	−0.590008	+	1.02192i	−0.0655565	+	0.113547i
$82$			7.07602i			0.781415i
$83$	−0.0157734	+	0.00910677i	−0.00173135	+	0.000999597i	−0.500865	−	0.865525i	$-0.666985\pi$
$83$	−0.0157734	+	0.00910677i	−0.00173135	+	0.000999597i	0.499134	+	0.866525i	$0.333652\pi$
$84$	0.480896			0.0524700
$85$		0			0
$86$	2.36927	+	4.10370i	0.255485	+	0.442514i
$87$	3.35553	+	1.93732i	0.359751	+	0.207702i
$88$			12.2356i			1.30432i
$89$	−3.76052	−	6.51341i	−0.398614	−	0.690420i	0.594941	−	0.803769i	$-0.297175\pi$
$89$	−3.76052	−	6.51341i	−0.398614	−	0.690420i	−0.993555	+	0.113349i	$0.963842\pi$
$90$		0			0
$91$	−0.690465	−	1.19592i	−0.0723804	−	0.125367i
$92$	3.17954	+	1.83571i	0.331490	+	0.191386i
$93$	12.0070	+	6.93224i	1.24507	+	0.718840i
$94$	1.32523	+	2.29537i	0.136687	+	0.236749i
$95$		0			0
$96$	5.47031	+	9.47485i	0.558311	+	0.967023i
$97$		−	11.0471i		−	1.12166i	−0.827931	−	0.560830i	$-0.810482\pi$
$97$		−	11.0471i		−	1.12166i	0.827931	−	0.560830i	$-0.189518\pi$
$98$	−6.79490	−	3.92303i	−0.686388	−	0.396286i
$99$	9.99194	+	17.3065i	1.00423	+	1.73937i
$100$		0			0
$101$	4.82308			0.479915			0.239957	−	0.970783i	$-0.422867\pi$
$101$	4.82308			0.479915			0.239957	+	0.970783i	$0.422867\pi$
$102$	−6.95993	+	4.01832i	−0.689136	+	0.397873i
$103$			4.93011i			0.485778i	0.970054	+	0.242889i	$0.0780951\pi$
$103$			4.93011i			0.485778i	−0.970054	+	0.242889i	$0.921905\pi$
$104$	9.05748	−	15.6880i	0.888159	−	1.53834i
$105$		0			0
$106$	6.00060	−	10.3933i	0.582830	−	1.00949i
$107$	16.7429	+	9.66652i	1.61860	+	0.934497i	0.987283	+	0.158970i	$0.0508172\pi$
$107$	16.7429	+	9.66652i	1.61860	+	0.934497i	0.631313	+	0.775528i	$0.282516\pi$
$108$	3.59642	+	2.07639i	0.346065	+	0.199801i
$109$	4.70690	+	8.15260i	0.450840	+	0.780877i	0.998438	−	0.0558639i	$-0.0177913\pi$
$109$	4.70690	+	8.15260i	0.450840	+	0.780877i	−0.547599	+	0.836741i	$0.684458\pi$
$110$		0			0
$111$	−8.36788	+	15.0641i	−0.794244	+	1.42982i
$112$			0.475930i			0.0449712i
$113$	−9.85203	+	5.68807i	−0.926801	+	0.535089i	−0.885799	−	0.464070i	$-0.846389\pi$
$113$	−9.85203	+	5.68807i	−0.926801	+	0.535089i	−0.0410029	+	0.999159i	$0.513055\pi$
$114$	−9.30168	+	16.1110i	−0.871182	+	1.50893i
$115$		0			0
$116$	0.494883	−	0.857162i	0.0459487	−	0.0795855i
$117$		−	29.5863i		−	2.73526i
$118$	−7.06526	−	4.07913i	−0.650410	−	0.375514i
$119$	0.589012			0.0539946
$120$		0			0
$121$	4.81174			0.437431
$122$		−	15.3001i		−	1.38520i
$123$	15.3666	−	8.87190i	1.38556	−	0.799953i
$124$	1.77082	−	3.06716i	0.159025	−	0.275439i
$125$		0			0
$126$	0.665904	+	1.15338i	0.0593234	+	0.102751i
$127$	−3.81587	+	2.20309i	−0.338603	+	0.195493i	−0.659654	−	0.751569i	$-0.729297\pi$
$127$	−3.81587	+	2.20309i	−0.338603	+	0.195493i	0.321051	+	0.947062i	$0.395964\pi$
$128$	−1.54990	+	0.894833i	−0.136993	+	0.0790928i
$129$	5.94119	−	10.2904i	0.523093	−	0.906023i
$130$		0			0
$131$	0.945523	+	1.63769i	0.0826107	+	0.143086i	0.904371	−	0.426748i	$-0.140341\pi$
$131$	0.945523	+	1.63769i	0.0826107	+	0.143086i	−0.821760	+	0.569834i	$0.807008\pi$
$132$	7.05994	−	4.07606i	0.614489	−	0.354775i
$133$	1.18079	−	0.681728i	0.102387	−	0.0591133i
$134$	0.841209			0.0726694
$135$		0			0
$136$	3.86331	+	6.69145i	0.331276	+	0.573787i
$137$		−	2.81626i		−	0.240609i	−0.992737	−	0.120305i	$-0.961613\pi$
$137$		−	2.81626i		−	0.240609i	0.992737	−	0.120305i	$-0.0383872\pi$
$138$			16.2373i			1.38221i
$139$	10.2414	+	17.7386i	0.868664	+	1.50457i	0.863363	+	0.504584i	$0.168354\pi$
$139$	10.2414	+	17.7386i	0.868664	+	1.50457i	0.00530075	+	0.999986i	$0.498313\pi$
$140$		0			0
$141$	3.32315	−	5.75586i	0.279860	−	0.484731i
$142$		−	2.92329i		−	0.245317i
$143$	−20.2732	−	11.7047i	−1.69533	−	0.978798i
$144$	−5.09839	+	8.83067i	−0.424866	+	0.735889i
$145$		0			0
$146$	−6.63265	−	11.4881i	−0.548922	−	0.950762i
$147$			19.6748i			1.62275i
$148$	3.84808	+	2.13756i	0.316311	+	0.175706i
$149$	−4.73067			−0.387552			−0.193776	−	0.981046i	$-0.562073\pi$
$149$	−4.73067			−0.387552			−0.193776	+	0.981046i	$0.562073\pi$
$150$		0			0
$151$	−5.82315	+	10.0860i	−0.473881	+	0.820786i	−0.999553	−	0.0299016i	$-0.990481\pi$
$151$	−5.82315	+	10.0860i	−0.473881	+	0.820786i	0.525672	+	0.850687i	$0.323814\pi$
$152$	15.4895	+	8.94286i	1.25636	+	0.725362i
$153$	10.9288	+	6.30977i	0.883545	+	0.510115i
$154$	1.05376			0.0849143
$155$		0			0
$156$	−12.0693			−0.966317
$157$	−12.7061	+	7.33585i	−1.01405	+	0.585465i	−0.912376	−	0.409353i	$-0.865755\pi$
$157$	−12.7061	+	7.33585i	−1.01405	+	0.585465i	−0.101678	+	0.994817i	$0.532421\pi$
$158$		−	10.6975i		−	0.851047i
$159$	−30.0942			−2.38663
$160$		0			0
$161$	0.595021	−	1.03061i	0.0468942	−	0.0812232i
$162$			1.33312i			0.104740i
$163$	−11.7011	+	6.75562i	−0.916499	+	0.529141i	−0.882517	−	0.470281i	$-0.844152\pi$
$163$	−11.7011	+	6.75562i	−0.916499	+	0.529141i	−0.0339828	+	0.999422i	$0.510819\pi$
$164$	−2.26631	−	3.92536i	−0.176969	−	0.306519i
$165$		0			0
$166$	−0.0102883	+	0.0178199i	−0.000798530	+	0.00138310i
$167$	−14.7674	−	8.52594i	−1.14273	−	0.659757i	−0.195627	−	0.980678i	$-0.562674\pi$
$167$	−14.7674	−	8.52594i	−1.14273	−	0.659757i	−0.947106	+	0.320921i	$0.896008\pi$
$168$	1.77083	−	1.02239i	0.136622	−	0.0788789i
$169$	10.8290	+	18.7563i	0.832998	+	1.44279i
$170$		0			0
$171$	29.2120			2.23389
$172$	−2.62867	−	1.51766i	−0.200434	−	0.115721i
$173$	14.1903	−	8.19275i	1.07886	−	0.622883i	0.148275	−	0.988946i	$-0.452628\pi$
$173$	14.1903	−	8.19275i	1.07886	−	0.622883i	0.930590	+	0.366063i	$0.119295\pi$
$174$	4.37736			0.331846
$175$		0			0
$176$	4.03397	+	6.98704i	0.304072	+	0.526668i
$177$			20.4576i			1.53769i
$178$	−7.35850	−	4.24843i	−0.551543	−	0.318434i
$179$	−15.2463			−1.13956			−0.569779	−	0.821798i	$-0.692971\pi$
$179$	−15.2463			−1.13956			−0.569779	+	0.821798i	$0.692971\pi$
$180$		0			0
$181$	2.94654	−	5.10356i	0.219015	−	0.379345i	−0.735492	−	0.677533i	$-0.763049\pi$
$181$	2.94654	−	5.10356i	0.219015	−	0.379345i	0.954507	+	0.298188i	$0.0963824\pi$
$182$	−1.35109	−	0.780051i	−0.100149	−	0.0578212i
$183$	−33.2263	+	19.1832i	−2.45616	+	1.41806i
$184$	15.6109			1.15085
$185$		0			0
$186$	15.6634			1.14849
$187$	8.64717	−	4.99245i	0.632344	−	0.365084i
$188$	−1.47032	−	0.848890i	−0.107234	−	0.0619117i
$189$	0.673036	−	1.16573i	0.0489562	−	0.0847946i
$190$		0			0
$191$	24.2857			1.75725			0.878625	−	0.477513i	$-0.158461\pi$
$191$	24.2857			1.75725			0.878625	+	0.477513i	$0.158461\pi$
$192$	20.6599	+	11.9280i	1.49100	+	0.860830i
$193$			21.8452i			1.57245i	0.617940	+	0.786225i	$0.287967\pi$
$193$			21.8452i			1.57245i	−0.617940	+	0.786225i	$0.712033\pi$
$194$	−6.24020	−	10.8083i	−0.448020	−	0.775994i
$195$		0			0
$196$	5.02588			0.358991
$197$	24.0418	−	13.8805i	1.71290	−	0.988946i	0.782313	−	0.622886i	$-0.214040\pi$
$197$	24.0418	−	13.8805i	1.71290	−	0.988946i	0.930591	−	0.366060i	$-0.119294\pi$
$198$	19.5520	+	11.2884i	1.38950	+	0.802229i
$199$	−11.8091			−0.837127			−0.418564	−	0.908188i	$-0.637466\pi$
$199$	−11.8091			−0.837127			−0.418564	+	0.908188i	$0.637466\pi$
$200$		0			0
$201$	−1.05471	−	1.82681i	−0.0743933	−	0.128853i
$202$	4.71885	−	2.72443i	0.332017	−	0.191690i
$203$	−0.277838	−	0.160410i	−0.0195004	−	0.0112586i
$204$	2.57397	−	4.45826i	0.180214	−	0.312140i
$205$		0			0
$206$	2.78489	+	4.82357i	0.194032	+	0.336074i
$207$	22.0807	−	12.7483i	1.53471	−	0.886068i
$208$		−	11.9447i		−	0.828214i
$209$	11.5566	−	20.0166i	0.799388	−	1.38458i
$210$		0			0
$211$	8.81127			0.606593			0.303296	−	0.952896i	$-0.401913\pi$
$211$	8.81127			0.606593			0.303296	+	0.952896i	$0.401913\pi$
$212$			7.68750i			0.527979i
$213$	−6.34835	+	3.66522i	−0.434981	+	0.251137i
$214$	21.8414			1.49305
$215$		0			0
$216$	17.6577			1.20145
$217$	−0.994180	−	0.573990i	−0.0674893	−	0.0389650i
$218$	9.21037	+	5.31761i	0.623805	+	0.360154i
$219$	−16.6320	+	28.8075i	−1.12389	+	1.94663i
$220$		0			0
$221$	−14.7827			−0.994395
$222$	0.322254	+	19.4653i	0.0216283	+	1.30643i
$223$			4.57593i			0.306427i	0.988193	+	0.153214i	$0.0489622\pi$
$223$			4.57593i			0.306427i	−0.988193	+	0.153214i	$0.951038\pi$
$224$	−0.452942	−	0.784518i	−0.0302635	−	0.0524178i
$225$		0			0
$226$	−6.42609	+	11.1303i	−0.427457	+	0.740377i
$227$	6.52003	+	3.76434i	0.432750	+	0.249848i	0.700517	−	0.713635i	$-0.252953\pi$
$227$	6.52003	+	3.76434i	0.432750	+	0.249848i	−0.267768	+	0.963483i	$0.586286\pi$
$228$		−	11.9166i		−	0.789194i
$229$	7.18793	−	12.4499i	0.474992	−	0.822710i	−0.524598	−	0.851350i	$-0.675784\pi$
$229$	7.18793	−	12.4499i	0.474992	−	0.822710i	0.999590	+	0.0286404i	$0.00911776\pi$
$230$		0			0
$231$	−1.32120	−	2.28839i	−0.0869288	−	0.150565i
$232$		−	4.20850i		−	0.276301i
$233$			27.6141i			1.80906i	0.426409	+	0.904530i	$0.359778\pi$
$233$			27.6141i			1.80906i	−0.426409	+	0.904530i	$0.640222\pi$
$234$	−16.7125	−	28.9470i	−1.09253	−	1.89232i
$235$		0			0
$236$	5.22586			0.340174
$237$	−23.2311	+	13.4125i	−1.50903	+	0.871236i
$238$	0.576283	−	0.332717i	0.0373549	−	0.0215668i
$239$	−8.49912	−	14.7209i	−0.549762	−	0.952216i	−0.998290	−	0.0584474i	$-0.981385\pi$
$239$	−8.49912	−	14.7209i	−0.549762	−	0.952216i	0.448528	−	0.893769i	$-0.351948\pi$
$240$		0			0
$241$	14.6060	−	25.2983i	0.940854	−	1.62961i	0.177008	−	0.984209i	$-0.443358\pi$
$241$	14.6060	−	25.2983i	0.940854	−	1.62961i	0.763846	−	0.645398i	$-0.223309\pi$
$242$	4.70776	−	2.71803i	0.302626	−	0.174721i
$243$	−12.0140	+	6.93628i	−0.770697	+	0.444962i
$244$	4.90031	+	8.48758i	0.313710	+	0.543361i
$245$		0			0
$246$	10.0230	−	17.3604i	0.639044	−	1.10686i
$247$	−29.6348	+	17.1097i	−1.88562	+	1.08866i
$248$		−	15.0591i		−	0.956256i
$249$	0.0515981			0.00326990
$250$		0			0
$251$	−3.80099			−0.239916			−0.119958	−	0.992779i	$-0.538276\pi$
$251$	−3.80099			−0.239916			−0.119958	+	0.992779i	$0.538276\pi$
$252$	−0.738809	−	0.426551i	−0.0465406	−	0.0268702i
$253$		−	20.1735i		−	1.26830i
$254$	−2.48894	+	4.31097i	−0.156170	+	0.270494i
$255$		0			0
$256$	7.40996	−	12.8344i	0.463123	−	0.802152i
$257$	−7.42316	+	4.28576i	−0.463044	+	0.267339i	−0.713323	−	0.700835i	$-0.752811\pi$
$257$	−7.42316	+	4.28576i	−0.463044	+	0.267339i	0.250279	+	0.968174i	$0.419478\pi$
$258$		−	13.4241i		−	0.835747i
$259$	0.692861	−	1.24731i	0.0430523	−	0.0775039i
$260$		0			0
$261$	−3.43677	−	5.95267i	−0.212731	−	0.368461i
$262$	1.85018	+	1.06820i	0.114305	+	0.0659937i
$263$	−3.88374	−	2.24228i	−0.239481	−	0.138265i	0.375457	−	0.926840i	$-0.377486\pi$
$263$	−3.88374	−	2.24228i	−0.239481	−	0.138265i	−0.614938	+	0.788575i	$0.710819\pi$
$264$	17.3315	−	30.0190i	1.06668	−	1.84754i
$265$		0			0
$266$	0.770180	−	1.33399i	0.0472228	−	0.0817922i
$267$			21.3067i			1.30395i
$268$	−0.466653	+	0.269423i	−0.0285054	+	0.0164576i
$269$	−22.2350			−1.35569			−0.677847	−	0.735203i	$-0.737087\pi$
$269$	−22.2350			−1.35569			−0.677847	+	0.735203i	$0.737087\pi$
$270$		0			0
$271$	8.00353	+	13.8625i	0.486180	+	0.842088i	0.999874	−	0.0158853i	$-0.00505665\pi$
$271$	8.00353	+	13.8625i	0.486180	+	0.842088i	−0.513694	+	0.857973i	$0.671723\pi$
$272$	4.41222	+	2.54740i	0.267530	+	0.154459i
$273$			3.91211i			0.236772i
$274$	−1.59083	−	2.75540i	−0.0961057	−	0.166460i
$275$		0			0
$276$	−5.20047	−	9.00748i	−0.313032	−	0.542187i
$277$	−26.0599	−	15.0457i	−1.56579	−	0.904007i	−0.996652	−	0.0817629i	$-0.973945\pi$
$277$	−26.0599	−	15.0457i	−1.56579	−	0.904007i	−0.569135	−	0.822244i	$-0.692722\pi$
$278$	20.0401	+	11.5702i	1.20193	+	0.693934i
$279$	−12.2977	−	21.3002i	−0.736244	−	1.27521i
$280$		0			0
$281$	−14.1603	−	24.5264i	−0.844734	−	1.46312i	−0.885852	−	0.463967i	$-0.846426\pi$
$281$	−14.1603	−	24.5264i	−0.844734	−	1.46312i	0.0411188	−	0.999154i	$-0.486908\pi$
$282$		−	7.50863i		−	0.447133i
$283$	21.2183	+	12.2504i	1.26130	+	0.728211i	0.973326	−	0.229427i	$-0.0736853\pi$
$283$	21.2183	+	12.2504i	1.26130	+	0.728211i	0.287973	+	0.957638i	$0.407019\pi$
$284$	0.936272	+	1.62167i	0.0555575	+	0.0962284i
$285$		0			0
$286$	−26.4468			−1.56383
$287$	−1.27236	+	0.734595i	−0.0751047	+	0.0433617i
$288$		−	19.4085i		−	1.14366i
$289$	−5.34734	+	9.26186i	−0.314549	+	0.544815i
$290$		0			0
$291$	−15.6479	+	27.1030i	−0.917297	+	1.58881i
$292$	7.35882	+	4.24862i	0.430642	+	0.248631i
$293$	−11.6642	−	6.73434i	−0.681431	−	0.393424i	0.118963	−	0.992899i	$-0.462043\pi$
$293$	−11.6642	−	6.73434i	−0.681431	−	0.393424i	−0.800394	+	0.599474i	$0.795376\pi$
$294$	11.1138	+	19.2496i	0.648168	+	1.12266i
$295$		0			0
$296$	18.7145	−	0.309823i	1.08776	−	0.0180081i
$297$		−	22.8185i		−	1.32407i
$298$	−4.62844	+	2.67223i	−0.268118	+	0.154798i
$299$	−14.9336	+	25.8657i	−0.863631	+	1.49585i
$300$		0			0
$301$	−0.491931	+	0.852050i	−0.0283544	+	0.0491113i
$302$			13.1574i			0.757121i
$303$	−11.8330	−	6.83178i	−0.679788	−	0.392476i
$304$	11.7935			0.676405
$305$		0			0
$306$	14.2569			0.815012
$307$			1.90606i			0.108784i	0.998520	+	0.0543922i	$0.0173221\pi$
$307$			1.90606i			0.108784i	−0.998520	+	0.0543922i	$0.982678\pi$
$308$	−0.584564	+	0.337498i	−0.0333086	+	0.0192307i
$309$	6.98338	−	12.0956i	0.397271	−	0.688093i
$310$		0			0
$311$	−0.0415842	−	0.0720260i	−0.00235802	−	0.00408422i	0.864844	−	0.502041i	$-0.167417\pi$
$311$	−0.0415842	−	0.0720260i	−0.00235802	−	0.00408422i	−0.867202	+	0.497957i	$0.834084\pi$
$312$	−44.4434	+	25.6594i	−2.51611	+	1.45268i
$313$	−9.89759	+	5.71438i	−0.559445	+	0.322996i	−0.752923	−	0.658109i	$-0.771357\pi$
$313$	−9.89759	+	5.71438i	−0.559445	+	0.322996i	0.193478	+	0.981105i	$0.438023\pi$
$314$	−8.28766	+	14.3546i	−0.467699	+	0.810079i
$315$		0			0
$316$	3.42619	+	5.93434i	0.192738	+	0.333833i
$317$	−18.2015	+	10.5086i	−1.02230	+	0.590224i	−0.914768	−	0.403978i	$-0.867627\pi$
$317$	−18.2015	+	10.5086i	−1.02230	+	0.590224i	−0.107529	+	0.994202i	$0.534294\pi$
$318$	−29.4439	+	16.9994i	−1.65113	+	0.953280i
$319$	−5.43852			−0.304499
$320$		0			0
$321$	−27.3848	−	47.4318i	−1.52847	−	2.64739i
$322$		−	1.34445i		−	0.0749231i
$323$		−	14.5957i		−	0.812125i
$324$	−0.426972	−	0.739537i	−0.0237207	−	0.0410854i
$325$		0			0
$326$	−7.63215	+	13.2193i	−0.422705	+	0.732147i
$327$		−	26.6689i		−	1.47479i
$328$	−16.6907	−	9.63637i	−0.921589	−	0.532079i
$329$	−0.275157	+	0.476586i	−0.0151699	+	0.0262750i
$330$		0			0
$331$	1.55569	+	2.69453i	0.0855084	+	0.148105i	0.905608	−	0.424116i	$-0.139415\pi$
$331$	1.55569	+	2.69453i	0.0855084	+	0.148105i	−0.820099	+	0.572221i	$0.806082\pi$
$332$		−	0.0131806i		−	0.000723380i
$333$	26.2175	−	15.7210i	1.43671	−	0.861504i
$334$	−19.2643			−1.05410
$335$		0			0
$336$	0.674144	−	1.16765i	0.0367776	−	0.0637006i
$337$	15.1720	+	8.75958i	0.826474	+	0.477165i	0.852644	−	0.522493i	$-0.174998\pi$
$337$	15.1720	+	8.75958i	0.826474	+	0.477165i	−0.0261702	+	0.999658i	$0.508331\pi$
$338$	21.1899	+	12.2340i	1.15258	+	0.665442i
$339$	32.2281			1.75039
$340$		0			0
$341$	−19.4605			−1.05384
$342$	28.5807	−	16.5011i	1.54547	−	0.892275i
$343$		−	3.27106i		−	0.176620i
$344$	−12.9062			−0.695858
$345$		0			0
$346$	9.25573	−	16.0314i	0.497591	−	0.861853i
$347$			15.4967i			0.831905i	0.909386	+	0.415953i	$0.136552\pi$
$347$			15.4967i			0.831905i	−0.909386	+	0.415953i	$0.863448\pi$
$348$	−2.42830	+	1.40198i	−0.130171	+	0.0751540i
$349$	8.52027	+	14.7575i	0.456080	+	0.789953i	0.998750	−	0.0499930i	$-0.0159199\pi$
$349$	8.52027	+	14.7575i	0.456080	+	0.789953i	−0.542670	+	0.839946i	$0.682587\pi$
$350$		0			0
$351$	−16.8915	+	29.2570i	−0.901604	+	1.56162i
$352$	−13.2991	−	7.67825i	−0.708845	−	0.409252i
$353$	28.7253	−	16.5846i	1.52889	−	0.882708i	0.529486	−	0.848319i	$-0.322385\pi$
$353$	28.7253	−	16.5846i	1.52889	−	0.882708i	0.999409	−	0.0343887i	$-0.0109484\pi$
$354$	11.5560	+	20.0155i	0.614193	+	1.06381i
$355$		0			0
$356$	5.44276			0.288466
$357$	−1.44509	−	0.834321i	−0.0764821	−	0.0441570i
$358$	−14.9168	+	8.61221i	−0.788376	+	0.455169i
$359$	14.7760			0.779846			0.389923	−	0.920848i	$-0.372502\pi$
$359$	14.7760			0.779846			0.389923	+	0.920848i	$0.372502\pi$
$360$		0			0
$361$	−7.39318	−	12.8054i	−0.389115	−	0.673966i
$362$		−	6.65770i		−	0.349921i
$363$	−11.8052	−	6.81572i	−0.619611	−	0.357732i
$364$	0.999339			0.0523796
$365$		0			0
$366$	−21.6722	+	37.5373i	−1.13282	+	1.96211i
$367$	17.2967	+	9.98623i	0.902878	+	0.521277i	0.878133	−	0.478417i	$-0.158789\pi$
$367$	17.2967	+	9.98623i	0.902878	+	0.521277i	0.0247451	+	0.999694i	$0.492123\pi$
$368$	8.91448	−	5.14678i	0.464699	−	0.268294i
$369$	−31.4773			−1.63864
$370$		0			0
$371$	2.49180			0.129368
$372$	−8.68911	+	5.01666i	−0.450509	+	0.260102i
$373$	9.44838	+	5.45502i	0.489218	+	0.282450i	0.724250	−	0.689537i	$-0.242186\pi$
$373$	9.44838	+	5.45502i	0.489218	+	0.282450i	−0.235032	+	0.971988i	$0.575519\pi$
$374$	5.64020	−	9.76912i	0.291648	−	0.505149i
$375$		0			0
$376$	−7.21899			−0.372291
$377$	6.97306	+	4.02590i	0.359131	+	0.207344i
$378$		−	1.52072i		−	0.0782174i
$379$	−13.0181	−	22.5481i	−0.668697	−	1.15822i	−0.978269	−	0.207341i	$-0.933519\pi$
$379$	−13.0181	−	22.5481i	−0.668697	−	1.15822i	0.309572	−	0.950876i	$-0.399814\pi$
$380$		0			0
$381$	12.4825			0.639499
$382$	23.7609	−	13.7183i	1.21571	−	0.701891i
$383$	3.21262	+	1.85481i	0.164157	+	0.0947762i	0.579828	−	0.814739i	$-0.303120\pi$
$383$	3.21262	+	1.85481i	0.164157	+	0.0947762i	−0.415671	+	0.909515i	$0.636453\pi$
$384$	5.07004			0.258729
$385$		0			0
$386$	12.3398	+	21.3731i	0.628078	+	1.08786i
$387$	−18.2551	+	10.5396i	−0.927960	+	0.535758i
$388$	6.92339	+	3.99722i	0.351482	+	0.202928i
$389$	7.13810	−	12.3635i	0.361916	−	0.626857i	−0.626360	−	0.779534i	$-0.715456\pi$
$389$	7.13810	−	12.3635i	0.361916	−	0.626857i	0.988276	+	0.152677i	$0.0487894\pi$
$390$		0			0
$391$	−6.36965	−	11.0326i	−0.322127	−	0.557941i
$392$	18.5071	−	10.6851i	0.934748	−	0.539677i
$393$		−	5.35724i		−	0.270237i
$394$	15.6815	−	27.1611i	0.790021	−	1.36836i
$395$		0			0
$396$	−14.4618			−0.726731
$397$			5.51724i			0.276902i	0.990369	+	0.138451i	$0.0442124\pi$
$397$			5.51724i			0.276902i	−0.990369	+	0.138451i	$0.955788\pi$
$398$	−11.5539	+	6.67067i	−0.579146	+	0.334370i
$399$	−3.86260			−0.193372
$400$		0			0
$401$	−27.5634			−1.37645			−0.688226	−	0.725496i	$-0.741610\pi$
$401$	−27.5634			−1.37645			−0.688226	+	0.725496i	$0.741610\pi$
$402$	−2.06383	−	1.19155i	−0.102934	−	0.0594292i
$403$	24.9515	+	14.4057i	1.24292	+	0.717601i
$404$	−1.74516	+	3.02271i	−0.0868251	+	0.150385i
$405$		0			0
$406$	−0.362445			−0.0179879
$407$	−0.400376	−	24.1842i	−0.0198459	−	1.19876i
$408$		−	21.8892i		−	1.08367i
$409$	−0.738916	−	1.27984i	−0.0365370	−	0.0632840i	0.847179	−	0.531308i	$-0.178299\pi$
$409$	−0.738916	−	1.27984i	−0.0365370	−	0.0632840i	−0.883716	+	0.468024i	$0.844966\pi$
$410$		0			0
$411$	−3.98917	+	6.90944i	−0.196771	+	0.340818i
$412$	−3.08979	−	1.78389i	−0.152223	−	0.0878859i
$413$		−	1.69389i		−	0.0833511i
$414$	14.4024	−	24.9456i	0.707837	−	1.22601i
$415$		0			0
$416$	11.3677	+	19.6895i	0.557349	+	0.965356i
$417$		−	58.0268i		−	2.84158i
$418$		−	26.1121i		−	1.27718i
$419$	5.69403	+	9.86234i	0.278171	+	0.481807i	0.970930	−	0.239362i	$-0.0769383\pi$
$419$	5.69403	+	9.86234i	0.278171	+	0.481807i	−0.692759	+	0.721169i	$0.743605\pi$
$420$		0			0
$421$	7.98895			0.389358			0.194679	−	0.980867i	$-0.437634\pi$
$421$	7.98895			0.389358			0.194679	+	0.980867i	$0.437634\pi$
$422$	8.62086	−	4.97725i	0.419657	−	0.242289i
$423$	−10.2108	+	5.89522i	−0.496467	+	0.286635i
$424$	16.3437	+	28.3081i	0.793719	+	1.37476i
$425$		0			0
$426$	−4.14077	+	7.17203i	−0.200621	+	0.347486i
$427$	2.75114	−	1.58837i	0.133137	−	0.0768667i
$428$	−12.1164	+	6.99538i	−0.585666	+	0.338134i
$429$	33.1589	+	57.4330i	1.60093	+	2.77289i
$430$		0			0
$431$	−11.5222	+	19.9570i	−0.555003	+	0.961293i	0.442901	+	0.896571i	$0.353949\pi$
$431$	−11.5222	+	19.9570i	−0.555003	+	0.961293i	−0.997903	+	0.0647223i	$0.979384\pi$
$432$	10.0833	−	5.82158i	0.485132	−	0.280091i
$433$			29.5140i			1.41835i	0.705032	+	0.709175i	$0.250933\pi$
$433$			29.5140i			1.41835i	−0.705032	+	0.709175i	$0.749067\pi$
$434$	−1.29693			−0.0622545
$435$		0			0
$436$	−6.81250			−0.326260
$437$	−25.5384	−	14.7446i	−1.22167	−	0.705330i
$438$			37.5800i			1.79564i
$439$	−13.5140	+	23.4070i	−0.644989	+	1.11715i	0.339315	+	0.940673i	$0.389805\pi$
$439$	−13.5140	+	23.4070i	−0.644989	+	1.11715i	−0.984304	+	0.176481i	$0.943529\pi$
$440$		0			0
$441$	17.4514	−	30.2267i	0.831020	−	1.43937i
$442$	−14.4633	+	8.35038i	−0.687948	+	0.397187i
$443$		−	9.50405i		−	0.451551i	−0.974179	−	0.225776i	$-0.927508\pi$
$443$		−	9.50405i		−	0.451551i	0.974179	−	0.225776i	$-0.0724916\pi$
$444$	−6.41313	−	10.6950i	−0.304354	−	0.507563i
$445$		0			0
$446$	2.58482	+	4.47704i	0.122395	+	0.211994i
$447$	11.6063	+	6.70088i	0.548958	+	0.316941i
$448$	−1.71064	−	0.987640i	−0.0808203	−	0.0466616i
$449$	15.3554	−	26.5963i	0.724665	−	1.25516i	−0.234447	−	0.972129i	$-0.575328\pi$
$449$	15.3554	−	26.5963i	0.724665	−	1.25516i	0.959112	−	0.283027i	$-0.0913387\pi$
$450$		0			0
$451$	−12.4528	+	21.5689i	−0.586380	+	1.01564i
$452$		−	8.23259i		−	0.387229i
$453$	28.5731	−	16.4967i	1.34248	−	0.775083i
$454$	8.50551			0.399183
$455$		0			0
$456$	−25.3347	−	43.8810i	−1.18641	−	2.05492i
$457$	−15.6955	−	9.06179i	−0.734204	−	0.423893i	0.0857544	−	0.996316i	$-0.472670\pi$
$457$	−15.6955	−	9.06179i	−0.734204	−	0.423893i	−0.819958	+	0.572424i	$0.806003\pi$
$458$		−	16.2411i		−	0.758896i
$459$	−7.20480	−	12.4791i	−0.336291	−	0.582473i
$460$		0			0
$461$	−0.0457549	−	0.0792498i	−0.00213102	−	0.00369103i	0.864958	−	0.501844i	$-0.167345\pi$
$461$	−0.0457549	−	0.0792498i	−0.00213102	−	0.00369103i	−0.867089	+	0.498153i	$0.834012\pi$
$462$	−2.58530	−	1.49263i	−0.120279	−	0.0694432i
$463$	−25.6926	−	14.8336i	−1.19404	−	0.689378i	−0.234818	−	0.972039i	$-0.575449\pi$
$463$	−25.6926	−	14.8336i	−1.19404	−	0.689378i	−0.959220	+	0.282661i	$0.908783\pi$
$464$	−1.38750	−	2.40323i	−0.0644132	−	0.111567i
$465$		0			0
$466$	15.5985	+	27.0174i	0.722586	+	1.25156i
$467$			22.1778i			1.02627i	0.858309	+	0.513133i	$0.171515\pi$
$467$			22.1778i			1.02627i	−0.858309	+	0.513133i	$0.828485\pi$
$468$	18.5423	+	10.7054i	0.857117	+	0.494857i
$469$	0.0873299	+	0.151260i	0.00403252	+	0.00698453i
$470$		0			0
$471$	41.5642			1.91518
$472$	19.2434	−	11.1102i	0.885751	−	0.511389i
$473$			16.6784i			0.766873i
$474$	−15.1527	+	26.2453i	−0.695989	+	1.20549i
$475$		0			0
$476$	−0.213125	+	0.369144i	−0.00976859	+	0.0169197i
$477$	46.2343	+	26.6934i	2.11692	+	1.22221i
$478$	−16.6309	−	9.60185i	−0.760680	−	0.439179i
$479$	8.91754	+	15.4456i	0.407453	+	0.705729i	0.994604	−	0.103749i	$-0.0330838\pi$
$479$	8.91754	+	15.4456i	0.407453	+	0.705729i	−0.587151	+	0.809478i	$0.699750\pi$
$480$		0			0
$481$	−17.3891	+	31.3044i	−0.792875	+	1.42736i
$482$		−	33.0021i		−	1.50321i
$483$	−2.91966	+	1.68567i	−0.132849	+	0.0767005i
$484$	−1.74106	+	3.01560i	−0.0791391	+	0.137073i
$485$		0			0
$486$	−7.83624	+	13.5728i	−0.355459	+	0.615673i
$487$		−	10.4914i		−	0.475411i	−0.971337	−	0.237706i	$-0.923605\pi$
$487$		−	10.4914i		−	0.475411i	0.971337	−	0.237706i	$-0.0763954\pi$
$488$	36.0893	+	20.8362i	1.63369	+	0.943209i
$489$	38.2767			1.73093
$490$		0			0
$491$	21.2613			0.959508			0.479754	−	0.877403i	$-0.340726\pi$
$491$	21.2613			0.959508			0.479754	+	0.877403i	$0.340726\pi$
$492$			12.8407i			0.578903i
$493$	−2.97424	+	1.71718i	−0.133953	+	0.0773377i
$494$	−19.3296	+	33.4799i	−0.869681	+	1.50633i
$495$		0			0
$496$	−4.96486	−	8.59939i	−0.222929	−	0.386124i
$497$	0.525644	−	0.303480i	0.0235783	−	0.0136130i
$498$	0.0504830	−	0.0291464i	0.00226220	−	0.00130608i
$499$	−10.4492	+	18.0986i	−0.467771	+	0.810203i	−0.999322	−	0.0368231i	$-0.988276\pi$
$499$	−10.4492	+	18.0986i	−0.467771	+	0.810203i	0.531551	+	0.847027i	$0.321610\pi$
$500$		0			0
$501$	24.1536	+	41.8353i	1.07910	+	1.86906i
$502$	−3.71885	+	2.14708i	−0.165980	+	0.0958289i
$503$	−2.30040	+	1.32813i	−0.102570	+	0.0592186i	−0.550407	−	0.834896i	$-0.685528\pi$
$503$	−2.30040	+	1.32813i	−0.102570	+	0.0592186i	0.447838	+	0.894115i	$0.352194\pi$
$504$	−3.62741			−0.161577
$505$		0			0
$506$	−11.3955	−	19.7376i	−0.506592	−	0.877443i
$507$		−	61.3560i		−	2.72491i
$508$		−	3.18863i		−	0.141473i
$509$	−8.56059	−	14.8274i	−0.379442	−	0.657212i	0.611540	−	0.791214i	$-0.290551\pi$
$509$	−8.56059	−	14.8274i	−0.379442	−	0.657212i	−0.990981	+	0.134002i	$0.957217\pi$
$510$		0			0
$511$	1.37713	−	2.38527i	0.0609208	−	0.105518i
$512$		−	20.3221i		−	0.898119i
$513$	−28.8868	−	16.6778i	−1.27538	−	0.736343i
$514$	−4.84183	+	8.38629i	−0.213564	+	0.369904i
$515$		0			0
$516$	4.29947	+	7.44690i	0.189274	+	0.327831i
$517$			9.32889i			0.410284i
$518$	−0.0266827	−	1.61173i	−0.00117237	−	0.0708154i
$519$	−46.4193			−2.03758
$520$		0			0
$521$	−5.18423	+	8.97935i	−0.227125	+	0.393392i	−0.956955	−	0.290237i	$-0.906266\pi$
$521$	−5.18423	+	8.97935i	−0.227125	+	0.393392i	0.729830	+	0.683629i	$0.239599\pi$
$522$	−6.72501	−	3.88269i	−0.294346	−	0.169941i
$523$	26.1138	+	15.0768i	1.14187	+	0.659262i	0.946894	−	0.321545i	$-0.104202\pi$
$523$	26.1138	+	15.0768i	1.14187	+	0.659262i	0.194981	+	0.980807i	$0.437536\pi$
$524$	−1.36850			−0.0597830
$525$		0			0
$526$	−5.06641			−0.220906
$527$	−10.6426	+	6.14452i	−0.463600	+	0.267659i
$528$		−	22.8561i		−	0.994684i
$529$	−2.73857			−0.119068
$530$		0			0
$531$	18.1458	−	31.4294i	0.787461	−	1.36392i
$532$			0.986693i			0.0427786i
$533$	31.9330	−	18.4365i	1.38317	−	0.798574i
$534$	12.0356	+	20.8463i	0.520832	+	0.902108i
$535$		0			0
$536$	−1.14559	+	1.98422i	−0.0494819	+	0.0857051i
$537$	37.4053	+	21.5960i	1.61416	+	0.931934i
$538$	−21.7545	+	12.5600i	−0.937904	+	0.541499i
$539$	−13.8080	−	23.9162i	−0.594753	−	1.03014i
$540$		0			0
$541$	−24.8647			−1.06902			−0.534508	−	0.845163i	$-0.679503\pi$
$541$	−24.8647			−1.06902			−0.534508	+	0.845163i	$0.679503\pi$
$542$	15.6611	+	9.04197i	0.672704	+	0.388386i
$543$	−14.4581	+	8.34742i	−0.620459	+	0.358222i
$544$	−9.69741			−0.415773
$545$		0			0
$546$	2.20985	+	3.82757i	0.0945728	+	0.163805i
$547$		−	1.52183i		−	0.0650688i	−0.999471	−	0.0325344i	$-0.989642\pi$
$547$		−	1.52183i		−	0.0650688i	0.999471	−	0.0325344i	$-0.0103579\pi$
$548$	1.76500	+	1.01902i	0.0753971	+	0.0435305i
$549$	68.0615			2.90480
$550$		0			0
$551$	−3.97495	+	6.88482i	−0.169339	+	0.293303i
$552$	−38.3000	−	22.1125i	−1.63015	−	0.941170i
$553$	1.92354	−	1.11056i	0.0817973	−	0.0472257i
$554$	−33.9956			−1.44434
$555$		0			0
$556$	−14.8228			−0.628627
$557$	−0.905488	+	0.522784i	−0.0383668	+	0.0221511i	−0.519061	−	0.854737i	$-0.673718\pi$
$557$	−0.905488	+	0.522784i	−0.0383668	+	0.0221511i	0.480694	+	0.876888i	$0.340385\pi$
$558$	−24.0639	−	13.8933i	−1.01871	−	0.588150i
$559$	12.3463	−	21.3844i	0.522191	−	0.904462i
$560$		0			0
$561$	−28.2867			−1.19427
$562$	−27.7086	−	15.9976i	−1.16882	−	0.674817i
$563$		−	19.0566i		−	0.803141i	−0.915828	−	0.401570i	$-0.868465\pi$
$563$		−	19.0566i		−	0.803141i	0.915828	−	0.401570i	$-0.131535\pi$
$564$	2.40487	+	4.16535i	0.101263	+	0.175393i
$565$		0			0
$566$	27.6797			1.16347
$567$	−0.239712	+	0.138398i	−0.0100669	+	0.00581215i
$568$	6.89536	+	3.98104i	0.289323	+	0.167041i
$569$	−2.20950			−0.0926269			−0.0463134	−	0.998927i	$-0.514747\pi$
$569$	−2.20950			−0.0926269			−0.0463134	+	0.998927i	$0.514747\pi$
$570$		0			0
$571$	−15.6806	−	27.1597i	−0.656215	−	1.13660i	−0.981588	−	0.191011i	$-0.938823\pi$
$571$	−15.6806	−	27.1597i	−0.656215	−	1.13660i	0.325373	−	0.945586i	$-0.394510\pi$
$572$	14.6711	−	8.47037i	0.613430	−	0.354164i
$573$	−59.5827	−	34.4001i	−2.48910	−	1.43708i
$574$	−0.829906	+	1.43744i	−0.0346396	+	0.0599976i
$575$		0			0
$576$	−21.1601	−	36.6504i	−0.881672	−	1.52710i
$577$	−23.2757	+	13.4383i	−0.968982	+	0.559442i	−0.898926	−	0.438101i	$-0.855651\pi$
$577$	−23.2757	+	13.4383i	−0.968982	+	0.559442i	−0.0700563	+	0.997543i	$0.522318\pi$
$578$			12.0823i			0.502557i
$579$	30.9432	−	53.5952i	1.28595	−	2.22734i
$580$		0			0
$581$	−0.00427233			−0.000177246
$582$			35.3564i			1.46557i
$583$	36.5817	−	21.1205i	1.51506	−	0.874720i
$584$	36.1303			1.49508
$585$		0			0
$586$	−15.2162			−0.628575
$587$	6.96587	+	4.02175i	0.287512	+	0.165995i	0.636819	−	0.771013i	$-0.280250\pi$
$587$	6.96587	+	4.02175i	0.287512	+	0.165995i	−0.349307	+	0.937008i	$0.613583\pi$
$588$	−12.3305	−	7.11904i	−0.508503	−	0.293584i
$589$	−14.2234	+	24.6357i	−0.586067	+	1.01510i
$590$		0			0
$591$	−78.6457			−3.23505
$592$	10.5846	−	6.34691i	0.435024	−	0.260856i
$593$		−	38.5933i		−	1.58484i	−0.609979	−	0.792418i	$-0.708822\pi$
$593$		−	38.5933i		−	1.58484i	0.609979	−	0.792418i	$-0.291178\pi$
$594$	−12.8896	−	22.3254i	−0.528866	−	0.916023i
$595$		0			0
$596$	1.71172	−	2.96479i	0.0701150	−	0.121443i
$597$	28.9726	+	16.7274i	1.18577	+	0.684605i
$598$			33.7423i			1.37983i
$599$	22.4072	−	38.8105i	0.915535	−	1.58575i	0.109418	−	0.993996i	$-0.465101\pi$
$599$	22.4072	−	38.8105i	0.915535	−	1.58575i	0.806117	−	0.591757i	$-0.201565\pi$
$600$		0			0
$601$	11.9005	+	20.6123i	0.485432	+	0.840794i	0.999860	−	0.0167403i	$-0.00532886\pi$
$601$	11.9005	+	20.6123i	0.485432	+	0.840794i	−0.514427	+	0.857534i	$0.671996\pi$
$602$			1.11152i			0.0453020i
$603$			3.74208i			0.152389i
$604$	−4.21404	−	7.29894i	−0.171467	−	0.296990i
$605$		0			0
$606$	−15.4364			−0.627060
$607$	−16.8934	+	9.75341i	−0.685682	+	0.395879i	−0.801993	−	0.597334i	$-0.796227\pi$
$607$	−16.8934	+	9.75341i	−0.685682	+	0.395879i	0.116310	+	0.993213i	$0.462893\pi$
$608$	−19.4403	+	11.2239i	−0.788409	+	0.455188i
$609$	0.454434	+	0.787103i	0.0184146	+	0.0318950i
$610$		0			0
$611$	6.90576	−	11.9611i	0.279377	−	0.483896i
$612$	−7.90889	+	4.56620i	−0.319698	+	0.184578i
$613$	23.1922	−	13.3900i	0.936725	−	0.540819i	0.0477930	−	0.998857i	$-0.484781\pi$
$613$	23.1922	−	13.3900i	0.936725	−	0.540819i	0.888932	+	0.458039i	$0.151448\pi$
$614$	1.07668	+	1.86487i	0.0434513	+	0.0752598i
$615$		0			0
$616$	−1.43505	+	2.48557i	−0.0578197	+	0.100147i
$617$	21.6581	−	12.5043i	0.871920	−	0.503404i	0.00393451	−	0.999992i	$-0.498748\pi$
$617$	21.6581	−	12.5043i	0.871920	−	0.503404i	0.867986	+	0.496589i	$0.165414\pi$
$618$		−	15.7789i		−	0.634721i
$619$	10.6832			0.429393			0.214696	−	0.976681i	$-0.431124\pi$
$619$	10.6832			0.429393			0.214696	+	0.976681i	$0.431124\pi$
$620$		0			0
$621$	−29.1132			−1.16827
$622$	−0.0813711	−	0.0469797i	−0.00326269	−	0.00188371i
$623$		−	1.76420i		−	0.0706812i
$624$	−16.9194	+	29.3052i	−0.677316	+	1.17315i
$625$		0			0
$626$	−6.45580	+	11.1818i	−0.258026	+	0.446914i
$627$	−56.7062	+	32.7393i	−2.26463	+	1.30748i
$628$		−	10.6175i		−	0.423684i
$629$	−7.85494	−	13.0995i	−0.313197	−	0.522311i
$630$		0			0
$631$	12.1765	+	21.0903i	0.484739	+	0.839593i	0.999846	−	0.0175326i	$-0.00558108\pi$
$631$	12.1765	+	21.0903i	0.484739	+	0.839593i	−0.515107	+	0.857126i	$0.672248\pi$
$632$	25.2329	+	14.5682i	1.00371	+	0.579493i
$633$	−21.6176	−	12.4810i	−0.859224	−	0.496073i
$634$	−11.8721	+	20.5631i	−0.471501	+	0.816664i
$635$		0			0
$636$	10.8892	−	18.8606i	0.431783	−	0.747870i
$637$			40.8858i			1.61995i
$638$	−5.32100	+	3.07208i	−0.210660	+	0.121625i
$639$	13.0041			0.514434
$640$		0			0
$641$	13.8989	+	24.0735i	0.548972	+	0.950847i	0.998345	+	0.0575029i	$0.0183138\pi$
$641$	13.8989	+	24.0735i	0.548972	+	0.950847i	−0.449374	+	0.893344i	$0.648353\pi$
$642$	−53.5860	−	30.9379i	−2.11487	−	1.22102i
$643$			15.0584i			0.593847i	0.954901	+	0.296923i	$0.0959606\pi$
$643$			15.0584i			0.593847i	−0.954901	+	0.296923i	$0.904039\pi$
$644$	0.430600	+	0.745821i	0.0169680	+	0.0293895i
$645$		0			0
$646$	−8.24471	−	14.2803i	−0.324384	−	0.561849i
$647$	−24.1777	−	13.9590i	−0.950522	−	0.548784i	−0.0572792	−	0.998358i	$-0.518243\pi$
$647$	−24.1777	−	13.9590i	−0.950522	−	0.548784i	−0.893243	+	0.449574i	$0.851576\pi$
$648$	−3.14452	−	1.81549i	−0.123529	−	0.0713192i
$649$	−14.3574	−	24.8678i	−0.563578	−	0.976145i
$650$		0			0
$651$	1.62609	+	2.81646i	0.0637314	+	0.110386i
$652$		−	9.77770i		−	0.382924i
$653$	26.1892	+	15.1203i	1.02486	+	0.591704i	0.915509	−	0.402298i	$-0.131789\pi$
$653$	26.1892	+	15.1203i	1.02486	+	0.591704i	0.109354	+	0.994003i	$0.465122\pi$
$654$	−15.0645	−	26.0926i	−0.589070	−	1.02030i
$655$		0			0
$656$	−12.7081			−0.496168
$657$	51.1042	−	29.5050i	1.99376	−	1.15110i
$658$			0.621716i			0.0242370i
$659$	11.8169	−	20.4674i	0.460319	−	0.797296i	−0.538658	−	0.842525i	$-0.681068\pi$
$659$	11.8169	−	20.4674i	0.460319	−	0.797296i	0.998977	+	0.0452287i	$0.0144017\pi$
$660$		0			0
$661$	1.45847	−	2.52615i	0.0567280	−	0.0982558i	−0.836267	−	0.548323i	$-0.815267\pi$
$661$	1.45847	−	2.52615i	0.0567280	−	0.0982558i	0.892995	+	0.450067i	$0.148600\pi$
$662$	3.04414	+	1.75753i	0.118314	+	0.0683085i
$663$	36.2681	+	20.9394i	1.40854	+	0.813219i
$664$	−0.0280221	−	0.0485356i	−0.00108747	−	0.00188355i
$665$		0			0
$666$	16.7705	−	30.1908i	0.649846	−	1.16987i
$667$			6.93878i			0.268671i
$668$	10.6867	−	6.16998i	0.413481	−	0.238724i
$669$	6.48170	−	11.2266i	0.250597	−	0.434047i
$670$		0			0
$671$	26.9260	−	46.6372i	1.03947	−	1.80041i
$672$			2.56633i			0.0989982i
$673$	−3.98569	−	2.30114i	−0.153637	−	0.0887024i	0.421211	−	0.906963i	$-0.361605\pi$
$673$	−3.98569	−	2.30114i	−0.153637	−	0.0887024i	−0.574848	+	0.818261i	$0.694939\pi$
$674$	19.7922			0.762368
$675$		0			0
$676$	−15.6732			−0.602817
$677$		−	26.7024i		−	1.02626i	−0.858312	−	0.513128i	$-0.828487\pi$
$677$		−	26.7024i		−	1.02626i	0.858312	−	0.513128i	$-0.171513\pi$
$678$	31.5316	−	18.2048i	1.21097	−	0.699151i
$679$	1.29565	−	2.24413i	0.0497225	−	0.0861218i
$680$		0			0
$681$	−10.6642	−	18.4709i	−0.408653	−	0.707808i
$682$	−19.0400	+	10.9927i	−0.729077	+	0.420933i
$683$	12.0309	−	6.94603i	0.460349	−	0.265782i	−0.251842	−	0.967768i	$-0.581036\pi$
$683$	12.0309	−	6.94603i	0.460349	−	0.265782i	0.712191	+	0.701986i	$0.247703\pi$
$684$	−10.5699	+	18.3076i	−0.404151	+	0.700010i
$685$		0			0
$686$	−1.84773	−	3.20037i	−0.0705468	−	0.122191i
$687$	−35.2699	+	20.3631i	−1.34563	+	0.776899i
$688$	−7.37000	+	4.25507i	−0.280979	+	0.162223i
$689$	−62.5381			−2.38251
$690$		0			0
$691$	5.84533	+	10.1244i	0.222367	+	0.385150i	0.955526	−	0.294906i	$-0.0952885\pi$
$691$	5.84533	+	10.1244i	0.222367	+	0.385150i	−0.733159	+	0.680057i	$0.761955\pi$
$692$			11.8577i			0.450762i
$693$			4.68759i			0.178067i
$694$	8.75367	+	15.1618i	0.332285	+	0.575534i
$695$		0			0
$696$	−5.96124	+	10.3252i	−0.225960	+	0.391374i
$697$			15.7276i			0.595724i
$698$	16.6723	+	9.62575i	0.631056	+	0.364340i
$699$	39.1147	−	67.7487i	1.47946	−	2.56249i
$700$		0			0
$701$	−0.111315	−	0.192803i	−0.00420430	−	0.00728206i	0.863916	−	0.503637i	$-0.168005\pi$
$701$	−0.111315	−	0.192803i	−0.00420430	−	0.00728206i	−0.868120	+	0.496355i	$0.834672\pi$
$702$			38.1664i			1.44050i
$703$	−30.9082	−	17.1691i	−1.16573	−	0.647544i
$704$	−33.4848			−1.26201
$705$		0			0
$706$	18.7364	−	32.4523i	0.705153	−	1.22136i
$707$	0.979773	+	0.565672i	0.0368482	+	0.0212743i
$708$	−12.8212	−	7.40230i	−0.481849	−	0.278196i
$709$	−40.2289			−1.51083			−0.755414	−	0.655248i	$-0.772564\pi$
$709$	−40.2289			−1.51083			−0.755414	+	0.655248i	$0.772564\pi$
$710$		0			0
$711$	47.5872			1.78466
$712$	20.0421	−	11.5713i	0.751111	−	0.433654i
$713$			24.8288i			0.929847i
$714$	−1.88514			−0.0705497
$715$		0			0
$716$	5.51664	−	9.55509i	0.206166	−	0.357091i
$717$			48.1552i			1.79839i
$718$	14.4567	−	8.34655i	0.539518	−	0.311491i
$719$	−12.6624	−	21.9319i	−0.472228	−	0.817923i	0.527267	−	0.849700i	$-0.323217\pi$
$719$	−12.6624	−	21.9319i	−0.472228	−	0.817923i	−0.999495	+	0.0317770i	$0.989883\pi$
$720$		0			0
$721$	−0.578225	+	1.00151i	−0.0215342	+	0.0372984i
$722$	−14.4668	−	8.35242i	−0.538399	−	0.310845i
$723$	−71.6689	+	41.3781i	−2.66540	+	1.53887i
$724$	2.13233	+	3.69330i	0.0792473	+	0.137260i
$725$		0			0
$726$	−15.4001			−0.571551
$727$	−0.737713	−	0.425919i	−0.0273603	−	0.0157965i	0.486257	−	0.873816i	$-0.338362\pi$
$727$	−0.737713	−	0.425919i	−0.0273603	−	0.0157965i	−0.513618	+	0.858019i	$0.671695\pi$
$728$	3.67992	−	2.12460i	0.136387	−	0.0787430i
$729$	42.8403			1.58668
$730$		0			0
$731$	5.26608	+	9.12112i	0.194773	+	0.337357i
$732$		−	27.7647i		−	1.02621i
$733$	25.0082	+	14.4385i	0.923700	+	0.533298i	0.884813	−	0.465945i	$-0.154286\pi$
$733$	25.0082	+	14.4385i	0.923700	+	0.533298i	0.0388862	+	0.999244i	$0.487619\pi$
$734$	22.5638			0.832846
$735$		0			0
$736$	−9.79635	+	16.9678i	−0.361098	+	0.625441i
$737$	2.56415	+	1.48041i	0.0944516	+	0.0545317i
$738$	−30.7971	+	17.7807i	−1.13366	+	0.654516i
$739$	23.9665			0.881622			0.440811	−	0.897600i	$-0.354691\pi$
$739$	23.9665			0.881622			0.440811	+	0.897600i	$0.354691\pi$
$740$		0			0
$741$	96.9419			3.56125
$742$	2.43796	−	1.40755i	0.0895002	−	0.0516729i
$743$	−7.47202	−	4.31397i	−0.274122	−	0.158264i	0.356637	−	0.934243i	$-0.383923\pi$
$743$	−7.47202	−	4.31397i	−0.274122	−	0.158264i	−0.630759	+	0.775978i	$0.717256\pi$
$744$	−21.3309	+	36.9462i	−0.782029	+	1.35451i
$745$		0			0
$746$	12.3256			0.451272
$747$	−0.0792711	−	0.0457672i	−0.00290038	−	0.00167453i
$748$			7.22578i			0.264201i
$749$	2.26746	+	3.92736i	0.0828513	+	0.143503i
$750$		0			0
$751$	32.1516			1.17323			0.586615	−	0.809866i	$-0.300460\pi$
$751$	32.1516			1.17323			0.586615	+	0.809866i	$0.300460\pi$
$752$	−4.12234	+	2.38003i	−0.150326	+	0.0867909i
$753$	9.32539	+	5.38402i	0.339836	+	0.196204i
$754$	9.09649			0.331275
$755$		0			0
$756$	0.487057	+	0.843607i	0.0177141	+	0.0306817i
$757$	28.6787	−	16.5577i	1.04235	−	0.601798i	0.121848	−	0.992549i	$-0.461118\pi$
$757$	28.6787	−	16.5577i	1.04235	−	0.601798i	0.920497	+	0.390751i	$0.127784\pi$
$758$	−25.4736	−	14.7072i	−0.925244	−	0.534190i
$759$	−28.5753	+	49.4939i	−1.03722	+	1.79652i
$760$		0			0
$761$	−23.9402	−	41.4656i	−0.867832	−	1.50313i	−0.864208	−	0.503135i	$-0.832180\pi$
$761$	−23.9402	−	41.4656i	−0.867832	−	1.50313i	−0.00362378	−	0.999993i	$-0.501153\pi$
$762$	12.2128	−	7.05104i	0.442422	−	0.255432i
$763$			2.20819i			0.0799417i
$764$	−8.78742	+	15.2203i	−0.317918	+	0.550650i
$765$		0			0
$766$	4.19093			0.151424
$767$			42.5126i			1.53504i
$768$	−36.3593	+	20.9921i	−1.31200	+	0.757486i
$769$	−0.908207			−0.0327508			−0.0163754	−	0.999866i	$-0.505213\pi$
$769$	−0.908207			−0.0327508			−0.0163754	+	0.999866i	$0.505213\pi$
$770$		0			0
$771$	24.2827			0.874521
$772$	−13.6908	−	7.90436i	−0.492741	−	0.284484i
$773$	19.7182	+	11.3843i	0.709214	+	0.409465i	0.810770	−	0.585365i	$-0.199049\pi$
$773$	19.7182	+	11.3843i	0.709214	+	0.409465i	−0.101556	+	0.994830i	$0.532382\pi$
$774$	−11.9071	+	20.6237i	−0.427991	+	0.741302i
$775$		0			0
$776$	33.9925			1.22026
$777$	−3.46665	+	2.07873i	−0.124366	+	0.0745742i
$778$		−	16.1285i		−	0.578235i
$779$	18.2032	+	31.5289i	0.652198	+	1.12964i
$780$		0			0
$781$	5.14459	−	8.91068i	0.184088	−	0.318849i
$782$	−12.4640	−	7.19610i	−0.445712	−	0.257332i
$783$			7.84854i			0.280484i
$784$	7.04553	−	12.2032i	0.251626	−	0.435829i
$785$		0			0
$786$	−3.02617	−	5.24147i	−0.107940	−	0.186957i
$787$			6.56136i			0.233887i	0.993139	+	0.116944i	$0.0373097\pi$
$787$			6.56136i			0.233887i	−0.993139	+	0.116944i	$0.962690\pi$
$788$			20.0899i			0.715671i
$789$	6.35226	+	11.0024i	0.226147	+	0.391697i
$790$		0			0
$791$	−2.66849			−0.0948806
$792$	−53.2533	+	30.7458i	−1.89227	+	1.09250i
$793$	−69.0469	+	39.8642i	−2.45193	+	1.41562i
$794$	3.11654	+	5.39801i	0.110602	+	0.191568i
$795$		0			0
$796$	4.27296	−	7.40099i	0.151451	−	0.262321i
$797$	32.2134	−	18.5984i	1.14106	−	0.658790i	0.194365	−	0.980929i	$-0.437735\pi$
$797$	32.2134	−	18.5984i	1.14106	−	0.658790i	0.946692	+	0.322140i	$0.104402\pi$
$798$	−3.77913	+	2.18188i	−0.133780	+	0.0772378i
$799$	2.94553	+	5.10181i	0.104205	+	0.180489i
$800$		0			0
$801$	18.8989	−	32.7339i	0.667761	−	1.15660i
$802$	−26.9678	+	15.5699i	−0.952266	+	0.549791i
$803$		−	46.6902i		−	1.64766i
$804$	1.52652			0.0538363
$805$		0			0
$806$	32.5497			1.14651
$807$	54.5516	+	31.4954i	1.92031	+	1.10869i
$808$			14.8409i			0.522101i
$809$	−20.8734	+	36.1537i	−0.733868	+	1.27110i	0.221350	+	0.975194i	$0.428954\pi$
$809$	−20.8734	+	36.1537i	−0.733868	+	1.27110i	−0.955218	+	0.295902i	$0.904380\pi$
$810$		0			0
$811$	10.7895	−	18.6879i	0.378869	−	0.656221i	−0.612029	−	0.790835i	$-0.709646\pi$
$811$	10.7895	−	18.6879i	0.378869	−	0.656221i	0.990898	+	0.134615i	$0.0429797\pi$
$812$	0.201064	−	0.116084i	0.00705595	−	0.00407375i
$813$		−	45.3473i		−	1.59040i
$814$	−14.0527	−	23.4354i	−0.492548	−	0.821410i
$815$		0			0
$816$	−7.21666	−	12.4996i	−0.252633	−	0.437574i
$817$	21.1137	+	12.1900i	0.738676	+	0.426475i
$818$	−1.44590	−	0.834788i	−0.0505545	−	0.0291877i
$819$	3.47002	−	6.01025i	0.121252	−	0.210015i
$820$		0			0
$821$	−11.9136	+	20.6349i	−0.415786	+	0.720163i	−0.995511	−	0.0946495i	$-0.969827\pi$
$821$	−11.9136	+	20.6349i	−0.415786	+	0.720163i	0.579724	+	0.814813i	$0.303160\pi$
$822$			9.01350i			0.314382i
$823$	46.9950	−	27.1326i	1.63814	−	0.945782i	0.656671	−	0.754177i	$-0.271964\pi$
$823$	46.9950	−	27.1326i	1.63814	−	0.945782i	0.981472	−	0.191605i	$-0.0613694\pi$
$824$	−15.1702			−0.528480
$825$		0			0
$826$	−0.956836	−	1.65729i	−0.0332926	−	0.0576645i
$827$	−18.9651	−	10.9495i	−0.659482	−	0.380752i	0.132597	−	0.991170i	$-0.457668\pi$
$827$	−18.9651	−	10.9495i	−0.659482	−	0.380752i	−0.792080	+	0.610418i	$0.791002\pi$
$828$			18.4511i			0.641222i
$829$	3.42064	+	5.92473i	0.118804	+	0.205774i	0.919294	−	0.393572i	$-0.128761\pi$
$829$	3.42064	+	5.92473i	0.118804	+	0.205774i	−0.800490	+	0.599346i	$0.795427\pi$
$830$		0			0
$831$	42.6237	+	73.8264i	1.47860	+	2.56101i
$832$	42.9329	+	24.7873i	1.48843	+	0.859346i
$833$	−15.1027	−	8.71956i	−0.523278	−	0.302115i
$834$	−32.7778	−	56.7728i	−1.13500	−	1.96588i
$835$		0			0
$836$	8.36319	+	14.4855i	0.289247	+	0.500990i
$837$			28.0842i			0.970732i
$838$	11.1420	+	6.43281i	0.384893	+	0.222218i
$839$	1.76839	+	3.06295i	0.0610517	+	0.105745i	0.894936	−	0.446195i	$-0.147221\pi$
$839$	1.76839	+	3.06295i	0.0610517	+	0.105745i	−0.833884	+	0.551940i	$0.813888\pi$
$840$		0			0
$841$	−27.1294			−0.935496
$842$	7.81631	−	4.51275i	0.269368	−	0.155520i
$843$			80.2310i			2.76330i
$844$	−3.18823	+	5.52218i	−0.109743	+	0.190081i
$845$		0			0
$846$	−6.66011	+	11.5356i	−0.228979	+	0.396604i
$847$	0.977469	+	0.564342i	0.0335862	+	0.0193910i
$848$	18.6658	+	10.7767i	0.640987	+	0.370074i
$849$	−34.7048	−	60.1105i	−1.19107	−	2.06299i
$850$		0			0
$851$	−30.8556	+	0.510823i	−1.05772	+	0.0175108i
$852$		−	5.30483i		−	0.181740i
$853$	7.98566	−	4.61052i	0.273424	−	0.157861i	−0.357019	−	0.934097i	$-0.616207\pi$
$853$	7.98566	−	4.61052i	0.273424	−	0.157861i	0.630443	+	0.776236i	$0.282873\pi$
$854$	1.79446	−	3.10809i	0.0614051	−	0.106357i
$855$		0			0
$856$	−29.7444	+	51.5189i	−1.01664	+	1.76088i
$857$		−	30.3008i		−	1.03506i	−0.855666	−	0.517529i	$-0.826852\pi$
$857$		−	30.3008i		−	1.03506i	0.855666	−	0.517529i	$-0.173148\pi$
$858$	64.8847	+	37.4612i	2.21513	+	1.27891i
$859$	8.49624			0.289888			0.144944	−	0.989440i	$-0.453700\pi$
$859$	8.49624			0.289888			0.144944	+	0.989440i	$0.453700\pi$
$860$		0			0
$861$	4.16214			0.141845
$862$			26.0343i			0.886730i
$863$	40.6353	−	23.4608i	1.38324	−	0.798615i	0.390699	−	0.920518i	$-0.372233\pi$
$863$	40.6353	−	23.4608i	1.38324	−	0.798615i	0.992542	+	0.121904i	$0.0388999\pi$
$864$	−11.0808	+	19.1925i	−0.376976	+	0.652941i
$865$		0			0
$866$	16.6717	+	28.8762i	0.566526	+	0.981252i
$867$	26.2384	−	15.1488i	0.891103	−	0.514479i
$868$	0.719459	−	0.415380i	0.0244200	−	0.0140989i
$869$	18.8261	−	32.6078i	0.638632	−	1.10614i
$870$		0			0
$871$	−2.19177	−	3.79625i	−0.0742651	−	0.128631i
$872$	−25.0860	+	14.4834i	−0.849520	+	0.490471i
$873$	48.0804	−	27.7592i	1.62727	−	0.939507i
$874$	−33.3153			−1.12691
$875$		0			0
$876$	−12.0361	−	20.8472i	−0.406663	−	0.704361i
$877$		−	42.7360i		−	1.44309i	−0.692367	−	0.721545i	$-0.743432\pi$
$877$		−	42.7360i		−	1.44309i	0.692367	−	0.721545i	$-0.256568\pi$
$878$			30.5349i			1.03050i
$879$	19.0781	+	33.0442i	0.643487	+	1.11455i
$880$		0			0
$881$	−26.2455	+	45.4586i	−0.884235	+	1.53154i	−0.0376461	+	0.999291i	$0.511986\pi$
$881$	−26.2455	+	45.4586i	−0.884235	+	1.53154i	−0.846588	+	0.532248i	$0.821347\pi$
$882$		−	39.4314i		−	1.32772i
$883$	−21.1382	−	12.2042i	−0.711358	−	0.410703i	0.100206	−	0.994967i	$-0.468050\pi$
$883$	−21.1382	−	12.2042i	−0.711358	−	0.410703i	−0.811564	+	0.584264i	$0.801383\pi$
$884$	5.34892	−	9.26461i	0.179904	−	0.311602i
$885$		0			0
$886$	−5.36859	−	9.29867i	−0.180361	−	0.312395i
$887$		−	16.9011i		−	0.567485i	−0.958901	−	0.283742i	$-0.908424\pi$
$887$		−	16.9011i		−	0.567485i	0.958901	−	0.283742i	$-0.0915761\pi$
$888$	−46.3531	−	25.7485i	−1.55551	−	0.864062i
$889$	−1.03355			−0.0346643
$890$		0			0
$891$	−2.34611	+	4.06358i	−0.0785976	+	0.136135i
$892$	−2.86782	−	1.65573i	−0.0960216	−	0.0554381i
$893$	11.8098	+	6.81838i	0.395199	+	0.228168i
$894$	15.1406			0.506378
$895$		0			0
$896$	−0.419800			−0.0140245
$897$	73.2763	−	42.3061i	2.44663	−	1.41256i
$898$		−	34.6954i		−	1.15780i
$899$	6.69353			0.223242
$900$		0			0
$901$	13.3373	−	23.1008i	0.444329	−	0.769601i
$902$			28.1371i			0.936861i
$903$	2.41382	−	1.39362i	0.0803268	−	0.0463767i
$904$	−17.5025	−	30.3153i	−0.582126	−	1.00827i
$905$		0			0
$906$	18.6371	−	32.2804i	0.619176	−	1.07244i
$907$	30.5560	+	17.6415i	1.01459	+	0.585776i	0.912533	−	0.409002i	$-0.134123\pi$
$907$	30.5560	+	17.6415i	1.01459	+	0.585776i	0.102060	+	0.994778i	$0.467457\pi$
$908$	−4.71836	+	2.72414i	−0.156584	+	0.0904039i
$909$	12.1195	+	20.9916i	0.401978	+	0.696247i
$910$		0			0
$911$	−29.6672			−0.982920			−0.491460	−	0.870900i	$-0.663537\pi$
$911$	−29.6672			−0.982920			−0.491460	+	0.870900i	$0.663537\pi$
$912$	−28.9343	−	16.7053i	−0.958112	−	0.553166i
$913$	−0.0627212	+	0.0362121i	−0.00207577	+	0.00119845i
$914$	−20.4751			−0.677255
$915$		0			0
$916$	5.20170	+	9.00960i	0.171869	+	0.297686i
$917$			0.443580i			0.0146483i
$918$	−14.0982	−	8.13960i	−0.465310	−	0.268647i
$919$	42.4142			1.39912			0.699558	−	0.714576i	$-0.253380\pi$
$919$	42.4142			1.39912			0.699558	+	0.714576i	$0.253380\pi$
$920$		0			0
$921$	2.69988	−	4.67633i	0.0889642	−	0.154090i
$922$	−0.0895323	−	0.0516915i	−0.00294859	−	0.00170237i
$923$	−13.1924	+	7.61661i	−0.434232	+	0.250704i
$924$	1.91223			0.0629078
$925$		0			0
$926$	−33.5165			−1.10142
$927$	−21.4574	+	12.3884i	−0.704753	+	0.406890i
$928$	4.57429	+	2.64097i	0.150159	+	0.0866941i
$929$	−9.43577	+	16.3432i	−0.309578	+	0.536204i	−0.978270	−	0.207335i	$-0.933521\pi$
$929$	−9.43577	+	16.3432i	−0.309578	+	0.536204i	0.668692	+	0.743539i	$0.266854\pi$
$930$		0			0
$931$	−40.3684			−1.32302
$932$	−17.3063	−	9.99177i	−0.566885	−	0.327291i
$933$			0.235612i			0.00771360i
$934$	12.5276	+	21.6985i	0.409917	+	0.709997i
$935$		0			0
$936$	91.0390			2.97570
$937$	−3.18043	+	1.83622i	−0.103900	+	0.0599868i	−0.551050	−	0.834472i	$-0.685773\pi$
$937$	−3.18043	+	1.83622i	−0.103900	+	0.0599868i	0.447150	+	0.894459i	$0.352439\pi$
$938$	0.170885	+	0.0986607i	0.00557960	+	0.00322139i
$939$	32.3771			1.05659
$940$		0			0
$941$	8.75971	+	15.1723i	0.285559	+	0.494602i	0.972744	−	0.231880i	$-0.0744876\pi$
$941$	8.75971	+	15.1723i	0.285559	+	0.494602i	−0.687186	+	0.726482i	$0.741154\pi$
$942$	40.6660	−	23.4785i	1.32497	−	0.764972i
$943$	27.5189	+	15.8880i	0.896137	+	0.517385i
$944$	7.32587	−	12.6888i	0.238437	−	0.412985i
$945$		0			0
$946$	9.42118	+	16.3180i	0.306309	+	0.530543i
$947$	19.4827	−	11.2483i	0.633103	−	0.365522i	−0.148850	−	0.988860i	$-0.547557\pi$
$947$	19.4827	−	11.2483i	0.633103	−	0.365522i	0.781953	+	0.623338i	$0.214224\pi$
$948$		−	19.4125i		−	0.630488i
$949$	−34.5627	+	59.8643i	−1.12195	+	1.94328i
$950$		0			0
$951$	59.5409			1.93075
$952$			1.81242i			0.0587410i
$953$	−34.8533	+	20.1226i	−1.12901	+	0.651834i	−0.943686	−	0.330843i	$-0.892667\pi$
$953$	−34.8533	+	20.1226i	−1.12901	+	0.651834i	−0.185324	+	0.982677i	$0.559333\pi$
$954$	60.3135			1.95272
$955$		0			0
$956$	12.3011			0.397847
$957$	13.3429	+	7.70354i	0.431315	+	0.249020i
$958$	17.4497	+	10.0746i	0.563773	+	0.325494i
$959$	0.330304	−	0.572103i	0.0106661	−	0.0184742i
$960$		0			0
$961$	−7.04876			−0.227379
$962$	0.669670	+	40.4505i	0.0215910	+	1.30418i
$963$			97.1605i			3.13095i
$964$	10.5699	+	18.3077i	0.340435	+	0.589650i
$965$		0			0
$966$	−1.90438	+	3.29848i	−0.0612724	+	0.106127i
$967$	−3.47135	−	2.00419i	−0.111631	−	0.0644503i	0.443145	−	0.896450i	$-0.353863\pi$
$967$	−3.47135	−	2.00419i	−0.111631	−	0.0644503i	−0.554776	+	0.832000i	$0.687196\pi$
$968$			14.8060i			0.475883i
$969$	−20.6744	+	35.8092i	−0.664159	+	1.15036i
$970$		0			0
$971$	21.4168	+	37.0949i	0.687297	+	1.19043i	0.972709	+	0.232028i	$0.0745363\pi$
$971$	21.4168	+	37.0949i	0.687297	+	1.19043i	−0.285412	+	0.958405i	$0.592130\pi$
$972$		−	10.0392i		−	0.322006i
$973$			4.80462i			0.154029i
$974$	−5.92632	−	10.2647i	−0.189892	−	0.328902i
$975$		0			0
$976$	27.4780			0.879549
$977$	−15.0452	+	8.68634i	−0.481338	+	0.277901i	−0.720974	−	0.692962i	$-0.756305\pi$
$977$	−15.0452	+	8.68634i	−0.481338	+	0.277901i	0.239636	+	0.970863i	$0.422972\pi$
$978$	37.4496	−	21.6215i	1.19750	−	0.691380i
$979$	−14.9533	−	25.8999i	−0.477910	−	0.827764i
$980$		0			0
$981$	−23.6551	+	40.9719i	−0.755250	+	1.30813i
$982$	20.8018	−	12.0099i	0.663813	−	0.383253i
$983$	−17.7564	+	10.2517i	−0.566342	+	0.326977i	−0.755687	−	0.654933i	$-0.772697\pi$
$983$	−17.7564	+	10.2517i	−0.566342	+	0.326977i	0.189345	+	0.981911i	$0.439363\pi$
$984$	27.2994	+	47.2839i	0.870273	+	1.50736i
$985$		0			0
$986$	−1.93997	+	3.36013i	−0.0617814	+	0.107008i
$987$	1.35015	−	0.779507i	0.0429756	−	0.0248120i
$988$		−	24.7636i		−	0.787834i
$989$	21.2792			0.676641
$990$		0			0
$991$	8.27328			0.262810			0.131405	−	0.991329i	$-0.458051\pi$
$991$	8.27328			0.262810			0.131405	+	0.991329i	$0.458051\pi$
$992$	16.3680	+	9.45010i	0.519686	+	0.300041i
$993$		−	8.81438i		−	0.279716i
$994$	0.342856	−	0.593844i	0.0108747	−	0.0188356i
$995$		0			0
$996$	−0.0186700	+	0.0323374i	−0.000591582	+	0.00102465i
$997$	−28.6467	+	16.5392i	−0.907249	+	0.523801i	−0.879545	−	0.475816i	$-0.842153\pi$
$997$	−28.6467	+	16.5392i	−0.907249	+	0.523801i	−0.0277042	+	0.999616i	$0.508820\pi$
$998$			23.6099i			0.747360i
$999$	−34.9011	+	0.577798i	−1.10422	+	0.0182807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.o.d.174.16		48
5.2	odd	4		925.2.e.d.26.8	✓	24
5.3	odd	4		925.2.e.e.26.5	yes	24
5.4	even	2	inner	925.2.o.d.174.9		48
37.10	even	3	inner	925.2.o.d.824.9		48
185.47	odd	12		925.2.e.d.676.8	yes	24
185.84	even	6	inner	925.2.o.d.824.16		48
185.158	odd	12		925.2.e.e.676.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.e.d.26.8	✓	24	5.2	odd	4
925.2.e.d.676.8	yes	24	185.47	odd	12
925.2.e.e.26.5	yes	24	5.3	odd	4
925.2.e.e.676.5	yes	24	185.158	odd	12
925.2.o.d.174.9		48	5.4	even	2	inner
925.2.o.d.174.16		48	1.1	even	1	trivial
925.2.o.d.824.9		48	37.10	even	3	inner
925.2.o.d.824.16		48	185.84	even	6	inner

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.978390 - 0.564874i) q^{2} +(-2.45341 - 1.41648i) q^{3} +(-0.361836 + 0.626718i) q^{4} -3.20052 q^{6} +(0.203143 + 0.117284i) q^{7} +3.07706i q^{8} +(2.51281 + 4.35232i) q^{9} +O(q^{10})\)	\(q+(0.978390 - 0.564874i) q^{2} +(-2.45341 - 1.41648i) q^{3} +(-0.361836 + 0.626718i) q^{4} -3.20052 q^{6} +(0.203143 + 0.117284i) q^{7} +3.07706i q^{8} +(2.51281 + 4.35232i) q^{9} +3.97640 q^{11} +(1.77546 - 1.02506i) q^{12} +(-5.09838 - 2.94355i) q^{13} +0.265003 q^{14} +(1.01448 + 1.75713i) q^{16} +(2.17462 - 1.25552i) q^{17} +(4.91702 + 2.83884i) q^{18} +(2.90630 - 5.03386i) q^{19} +(-0.332261 - 0.575493i) q^{21} +(3.89047 - 2.24616i) q^{22} -5.07332i q^{23} +(4.35858 - 7.54929i) q^{24} -6.65094 q^{26} -5.73849i q^{27} +(-0.147008 + 0.0848753i) q^{28} -1.36770 q^{29} -4.89400 q^{31} +(-3.34451 - 1.93096i) q^{32} +(-9.75573 - 5.63247i) q^{33} +(1.41842 - 2.45678i) q^{34} -3.63690 q^{36} +(-0.100688 - 6.08193i) q^{37} -6.56677i q^{38} +(8.33894 + 14.4435i) q^{39} +(-3.13168 + 5.42423i) q^{41} +(-0.650162 - 0.375371i) q^{42} +4.19434i q^{43} +(-1.43880 + 2.49208i) q^{44} +(-2.86578 - 4.96368i) q^{46} +2.34607i q^{47} -5.74794i q^{48} +(-3.47249 - 6.01453i) q^{49} -7.11366 q^{51} +(3.68955 - 2.13016i) q^{52} +(9.19971 - 5.31146i) q^{53} +(-3.24152 - 5.61448i) q^{54} +(-0.360891 + 0.625082i) q^{56} +(-14.2607 + 8.23342i) q^{57} +(-1.33814 + 0.772578i) q^{58} +(-3.61066 - 6.25384i) q^{59} +(6.77145 - 11.7285i) q^{61} +(-4.78824 + 2.76449i) q^{62} +1.17885i q^{63} -8.42090 q^{64} -12.7265 q^{66} +(0.644842 + 0.372300i) q^{67} +1.81717i q^{68} +(-7.18624 + 12.4469i) q^{69} +(1.29378 - 2.24089i) q^{71} +(-13.3923 + 7.73207i) q^{72} -11.7418i q^{73} +(-3.53403 - 5.89362i) q^{74} +(2.10321 + 3.64286i) q^{76} +(0.807776 + 0.466369i) q^{77} +(16.3175 + 9.42089i) q^{78} +(4.73446 - 8.20033i) q^{79} +(-0.590008 + 1.02192i) q^{81} +7.07602i q^{82} +(-0.0157734 + 0.00910677i) q^{83} +0.480896 q^{84} +(2.36927 + 4.10370i) q^{86} +(3.35553 + 1.93732i) q^{87} +12.2356i q^{88} +(-3.76052 - 6.51341i) q^{89} +(-0.690465 - 1.19592i) q^{91} +(3.17954 + 1.83571i) q^{92} +(12.0070 + 6.93224i) q^{93} +(1.32523 + 2.29537i) q^{94} +(5.47031 + 9.47485i) q^{96} -11.0471i q^{97} +(-6.79490 - 3.92303i) q^{98} +(9.99194 + 17.3065i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 22 q^{4} + 20 q^{9}+O(q^{10}) \) 48 * q + 22 * q^4 + 20 * q^9	\( 48 q + 22 q^{4} + 20 q^{9} - 40 q^{14} - 26 q^{16} - 10 q^{19} - 12 q^{21} + 42 q^{24} - 40 q^{26} - 12 q^{29} + 76 q^{31} + 10 q^{34} - 4 q^{36} - 28 q^{39} - 26 q^{41} + 30 q^{44} - 26 q^{46} + 52 q^{49} - 92 q^{51} + 74 q^{54} + 14 q^{59} + 32 q^{61} - 40 q^{64} + 164 q^{66} - 42 q^{69} - 4 q^{71} - 96 q^{74} + 34 q^{76} + 42 q^{79} - 32 q^{81} - 152 q^{84} - 32 q^{86} - 58 q^{89} + 64 q^{91} + 26 q^{94} + 52 q^{96} + 30 q^{99}+O(q^{100}) \) 48 * q + 22 * q^4 + 20 * q^9 - 40 * q^14 - 26 * q^16 - 10 * q^19 - 12 * q^21 + 42 * q^24 - 40 * q^26 - 12 * q^29 + 76 * q^31 + 10 * q^34 - 4 * q^36 - 28 * q^39 - 26 * q^41 + 30 * q^44 - 26 * q^46 + 52 * q^49 - 92 * q^51 + 74 * q^54 + 14 * q^59 + 32 * q^61 - 40 * q^64 + 164 * q^66 - 42 * q^69 - 4 * q^71 - 96 * q^74 + 34 * q^76 + 42 * q^79 - 32 * q^81 - 152 * q^84 - 32 * q^86 - 58 * q^89 + 64 * q^91 + 26 * q^94 + 52 * q^96 + 30 * q^99

Introduction

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