LMFDB - Embedded newform 925.2.o.d.174.9

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			174.9
Character	$\chi$	$=$	925.174
Dual form			925.2.o.d.824.9

$q$-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	−0.804296	−	0.594229i	$-0.797457\pi$
$2$	−0.978390	+	0.564874i	−0.691826	+	0.399426i	0.112470	+	0.993655i	$0.464124\pi$
$3$	2.45341	+	1.41648i	1.41648	+	0.817803i	0.995987	−	0.0894944i	$-0.0285251\pi$
$3$	2.45341	+	1.41648i	1.41648	+	0.817803i	0.420489	+	0.907298i	$0.361858\pi$
$4$	−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	0.461118	−	0.887339i	$-0.347448\pi$
$7$	−0.203143	−	0.117284i	−0.0767807	−	0.0443293i	−0.537899	+	0.843009i	$0.680782\pi$
$8$		−	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	0.995766	−	0.0919288i	$-0.0293032\pi$
$13$	5.09838	+	2.94355i	1.41404	+	0.816394i	0.418270	+	0.908323i	$0.362637\pi$
$14$	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	−0.739967	−	0.672643i	$-0.765159\pi$
$17$	−2.17462	+	1.25552i	−0.527424	+	0.304508i	0.212543	+	0.977152i	$0.431825\pi$
$18$	−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	$0.177407\pi$
$23$			5.07332i			1.05786i	−0.848665	+	0.528930i	$0.822593\pi$
$24$	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	$-0.896379\pi$
$43$		−	4.19434i		−	0.639631i	0.947480	−	0.319816i	$-0.103621\pi$
$44$	−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	$-0.945266\pi$
$47$		−	2.34607i		−	0.342209i	0.985253	−	0.171104i	$-0.0547336\pi$
$48$			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	−0.973784	−	0.227474i	$-0.926953\pi$
$53$	−9.19971	+	5.31146i	−1.26368	+	0.729585i	−0.289893	+	0.957059i	$0.593620\pi$
$54$	−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	0.460093	−	0.887871i	$-0.347816\pi$
$67$	−0.644842	−	0.372300i	−0.0787800	−	0.0454836i	−0.538873	+	0.842387i	$0.681150\pi$
$68$		−	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	$0.241134\pi$
$73$			11.7418i			1.37428i	−0.726526	+	0.687139i	$0.758866\pi$
$74$	−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	−0.499134	−	0.866525i	$-0.666348\pi$
$83$	0.0157734	−	0.00910677i	0.00173135	−	0.000999597i	0.500865	+	0.865525i	$0.333015\pi$
$84$	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	$0.189518\pi$
$97$			11.0471i			1.12166i	−0.827931	+	0.560830i	$0.810482\pi$
$98$	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	$-0.921905\pi$
$103$		−	4.93011i		−	0.485778i	0.970054	−	0.242889i	$-0.0780951\pi$
$104$	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	$-0.949183\pi$
$107$	−16.7429	−	9.66652i	−1.61860	−	0.934497i	−0.631313	−	0.775528i	$-0.717484\pi$
$108$	−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	0.0410029	−	0.999159i	$-0.486945\pi$
$113$	9.85203	−	5.68807i	0.926801	−	0.535089i	0.885799	+	0.464070i	$0.153611\pi$
$114$	−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	−0.321051	−	0.947062i	$-0.604036\pi$
$127$	3.81587	−	2.20309i	0.338603	−	0.195493i	0.659654	+	0.751569i	$0.270703\pi$
$128$	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	$0.0383872\pi$
$137$			2.81626i			0.240609i	−0.992737	+	0.120305i	$0.961613\pi$
$138$		−	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	0.101678	−	0.994817i	$-0.467579\pi$
$157$	12.7061	−	7.33585i	1.01405	−	0.585465i	0.912376	+	0.409353i	$0.134245\pi$
$158$			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	0.0339828	−	0.999422i	$-0.489181\pi$
$163$	11.7011	−	6.75562i	0.916499	−	0.529141i	0.882517	+	0.470281i	$0.155848\pi$
$164$	−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	0.947106	−	0.320921i	$-0.103992\pi$
$167$	14.7674	+	8.52594i	1.14273	+	0.659757i	0.195627	+	0.980678i	$0.437326\pi$
$168$	−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	−0.930590	−	0.366063i	$-0.880705\pi$
$173$	−14.1903	+	8.19275i	−1.07886	+	0.622883i	−0.148275	+	0.988946i	$0.547372\pi$
$174$	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	$-0.712033\pi$
$193$		−	21.8452i		−	1.57245i	0.617940	−	0.786225i	$-0.287967\pi$
$194$	−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	$0.785960\pi$
$197$	−24.0418	+	13.8805i	−1.71290	+	0.988946i	−0.930591	+	0.366060i	$0.880706\pi$
$198$	−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	$-0.951038\pi$
$223$		−	4.57593i		−	0.306427i	0.988193	−	0.153214i	$-0.0489622\pi$
$224$	−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	0.267768	−	0.963483i	$-0.413714\pi$
$227$	−6.52003	−	3.76434i	−0.432750	−	0.249848i	−0.700517	+	0.713635i	$0.747047\pi$
$228$			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	$-0.640222\pi$
$233$		−	27.6141i		−	1.80906i	0.426409	−	0.904530i	$-0.359778\pi$
$234$	−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	−0.250279	−	0.968174i	$-0.580522\pi$
$257$	7.42316	−	4.28576i	0.463044	−	0.267339i	0.713323	+	0.700835i	$0.247189\pi$
$258$			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	0.614938	−	0.788575i	$-0.289181\pi$
$263$	3.88374	+	2.24228i	0.239481	+	0.138265i	−0.375457	+	0.926840i	$0.622514\pi$
$264$	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	$0.0260550\pi$
$277$	26.0599	+	15.0457i	1.56579	+	0.904007i	0.569135	+	0.822244i	$0.307278\pi$
$278$	−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	−0.287973	−	0.957638i	$-0.592981\pi$
$283$	−21.2183	−	12.2504i	−1.26130	−	0.728211i	−0.973326	+	0.229427i	$0.926315\pi$
$284$	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	0.800394	−	0.599474i	$-0.204624\pi$
$293$	11.6642	+	6.73434i	0.681431	+	0.393424i	−0.118963	+	0.992899i	$0.537957\pi$
$294$	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	$-0.982678\pi$
$307$		−	1.90606i		−	0.108784i	0.998520	−	0.0543922i	$-0.0173221\pi$
$308$	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	−0.193478	−	0.981105i	$-0.561977\pi$
$313$	9.89759	−	5.71438i	0.559445	−	0.322996i	0.752923	+	0.658109i	$0.228643\pi$
$314$	−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	0.107529	−	0.994202i	$-0.465706\pi$
$317$	18.2015	−	10.5086i	1.02230	−	0.590224i	0.914768	+	0.403978i	$0.132373\pi$
$318$	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	0.0261702	−	0.999658i	$-0.491669\pi$
$337$	−15.1720	−	8.75958i	−0.826474	−	0.477165i	−0.852644	+	0.522493i	$0.825002\pi$
$338$	−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	$-0.863448\pi$
$347$		−	15.4967i		−	0.831905i	0.909386	−	0.415953i	$-0.136552\pi$
$348$	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	$0.677615\pi$
$353$	−28.7253	+	16.5846i	−1.52889	+	0.882708i	−0.999409	+	0.0343887i	$0.989052\pi$
$354$	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	−0.0247451	−	0.999694i	$-0.507877\pi$
$367$	−17.2967	−	9.98623i	−0.902878	−	0.521277i	−0.878133	+	0.478417i	$0.841211\pi$
$368$	−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	0.235032	−	0.971988i	$-0.424481\pi$
$373$	−9.44838	−	5.45502i	−0.489218	−	0.282450i	−0.724250	+	0.689537i	$0.757814\pi$
$374$	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	0.415671	−	0.909515i	$-0.363547\pi$
$383$	−3.21262	−	1.85481i	−0.164157	−	0.0947762i	−0.579828	+	0.814739i	$0.696880\pi$
$384$	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	$-0.955788\pi$
$397$		−	5.51724i		−	0.276902i	0.990369	−	0.138451i	$-0.0442124\pi$
$398$	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	$-0.749067\pi$
$433$		−	29.5140i		−	1.41835i	0.705032	−	0.709175i	$-0.250933\pi$
$434$	−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	$0.0724916\pi$
$443$			9.50405i			0.451551i	−0.974179	+	0.225776i	$0.927508\pi$
$444$	−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	0.819958	−	0.572424i	$-0.193997\pi$
$457$	15.6955	+	9.06179i	0.734204	+	0.423893i	−0.0857544	+	0.996316i	$0.527330\pi$
$458$			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	0.959220	−	0.282661i	$-0.0912172\pi$
$463$	25.6926	+	14.8336i	1.19404	+	0.689378i	0.234818	+	0.972039i	$0.424551\pi$
$464$	−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	$-0.828485\pi$
$467$		−	22.1778i		−	1.02627i	0.858309	−	0.513133i	$-0.171515\pi$
$468$	−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	$0.0763954\pi$
$487$			10.4914i			0.475411i	−0.971337	+	0.237706i	$0.923605\pi$
$488$	−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	−0.447838	−	0.894115i	$-0.647806\pi$
$503$	2.30040	−	1.32813i	0.102570	−	0.0592186i	0.550407	+	0.834896i	$0.314472\pi$
$504$	−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	−0.194981	−	0.980807i	$-0.562464\pi$
$523$	−26.1138	−	15.0768i	−1.14187	−	0.659262i	−0.946894	+	0.321545i	$0.895798\pi$
$524$	−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	$0.0103579\pi$
$547$			1.52183i			0.0650688i	−0.999471	+	0.0325344i	$0.989642\pi$
$548$	−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	−0.480694	−	0.876888i	$-0.659615\pi$
$557$	0.905488	−	0.522784i	0.0383668	−	0.0221511i	0.519061	+	0.854737i	$0.326282\pi$
$558$	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	$0.131535\pi$
$563$			19.0566i			0.803141i	−0.915828	+	0.401570i	$0.868465\pi$
$564$	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	0.0700563	−	0.997543i	$-0.477682\pi$
$577$	23.2757	−	13.4383i	0.968982	−	0.559442i	0.898926	+	0.438101i	$0.144349\pi$
$578$		−	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	0.349307	−	0.937008i	$-0.386417\pi$
$587$	−6.96587	−	4.02175i	−0.287512	−	0.165995i	−0.636819	+	0.771013i	$0.719750\pi$
$588$	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	$0.291178\pi$
$593$			38.5933i			1.58484i	−0.609979	+	0.792418i	$0.708822\pi$
$594$	−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	−0.116310	−	0.993213i	$-0.537107\pi$
$607$	16.8934	−	9.75341i	0.685682	−	0.395879i	0.801993	+	0.597334i	$0.203773\pi$
$608$	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	−0.888932	−	0.458039i	$-0.848552\pi$
$613$	−23.1922	+	13.3900i	−0.936725	+	0.540819i	−0.0477930	+	0.998857i	$0.515219\pi$
$614$	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	−0.867986	−	0.496589i	$-0.834586\pi$
$617$	−21.6581	+	12.5043i	−0.871920	+	0.503404i	−0.00393451	+	0.999992i	$0.501252\pi$
$618$			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	$-0.904039\pi$
$643$		−	15.0584i		−	0.593847i	0.954901	−	0.296923i	$-0.0959606\pi$
$644$	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	0.893243	−	0.449574i	$-0.148424\pi$
$647$	24.1777	+	13.9590i	0.950522	+	0.548784i	0.0572792	+	0.998358i	$0.481757\pi$
$648$	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	−0.109354	−	0.994003i	$-0.534878\pi$
$653$	−26.1892	−	15.1203i	−1.02486	−	0.591704i	−0.915509	+	0.402298i	$0.868211\pi$
$654$	−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	0.574848	−	0.818261i	$-0.305061\pi$
$673$	3.98569	+	2.30114i	0.153637	+	0.0887024i	−0.421211	+	0.906963i	$0.638395\pi$
$674$	19.7922			0.762368
$675$		0			0
$676$	−15.6732			−0.602817
$677$			26.7024i			1.02626i	0.858312	+	0.513128i	$0.171513\pi$
$677$			26.7024i			1.02626i	−0.858312	+	0.513128i	$0.828487\pi$
$678$	−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	−0.712191	−	0.701986i	$-0.752297\pi$
$683$	−12.0309	+	6.94603i	−0.460349	+	0.265782i	0.251842	+	0.967768i	$0.418964\pi$
$684$	−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	0.513618	−	0.858019i	$-0.328305\pi$
$727$	0.737713	+	0.425919i	0.0273603	+	0.0157965i	−0.486257	+	0.873816i	$0.661638\pi$
$728$	−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	−0.0388862	−	0.999244i	$-0.512381\pi$
$733$	−25.0082	−	14.4385i	−0.923700	−	0.533298i	−0.884813	+	0.465945i	$0.845714\pi$
$734$	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	0.630759	−	0.775978i	$-0.282744\pi$
$743$	7.47202	+	4.31397i	0.274122	+	0.158264i	−0.356637	+	0.934243i	$0.616077\pi$
$744$	−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	−0.920497	−	0.390751i	$-0.872216\pi$
$757$	−28.6787	+	16.5577i	−1.04235	+	0.601798i	−0.121848	+	0.992549i	$0.538882\pi$
$758$	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	0.101556	−	0.994830i	$-0.467618\pi$
$773$	−19.7182	−	11.3843i	−0.709214	−	0.409465i	−0.810770	+	0.585365i	$0.800951\pi$
$774$	−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	$-0.962690\pi$
$787$		−	6.56136i		−	0.233887i	0.993139	−	0.116944i	$-0.0373097\pi$
$788$		−	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	−0.946692	−	0.322140i	$-0.895598\pi$
$797$	−32.2134	+	18.5984i	−1.14106	+	0.658790i	−0.194365	+	0.980929i	$0.562265\pi$
$798$	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	$0.728036\pi$
$823$	−46.9950	+	27.1326i	−1.63814	+	0.945782i	−0.981472	+	0.191605i	$0.938631\pi$
$824$	−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	0.792080	−	0.610418i	$-0.208998\pi$
$827$	18.9651	+	10.9495i	0.659482	+	0.380752i	−0.132597	+	0.991170i	$0.542332\pi$
$828$		−	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	−0.630443	−	0.776236i	$-0.717127\pi$
$853$	−7.98566	+	4.61052i	−0.273424	+	0.157861i	0.357019	+	0.934097i	$0.383793\pi$
$854$	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	$0.173148\pi$
$857$			30.3008i			1.03506i	−0.855666	+	0.517529i	$0.826852\pi$
$858$	−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	−0.992542	−	0.121904i	$-0.961100\pi$
$863$	−40.6353	+	23.4608i	−1.38324	+	0.798615i	−0.390699	+	0.920518i	$0.627767\pi$
$864$	−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	$0.256568\pi$
$877$			42.7360i			1.44309i	−0.692367	+	0.721545i	$0.743432\pi$
$878$		−	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	0.811564	−	0.584264i	$-0.198617\pi$
$883$	21.1382	+	12.2042i	0.711358	+	0.410703i	−0.100206	+	0.994967i	$0.531950\pi$
$884$	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	$0.0915761\pi$
$887$			16.9011i			0.567485i	−0.958901	+	0.283742i	$0.908424\pi$
$888$	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	−0.102060	−	0.994778i	$-0.532543\pi$
$907$	−30.5560	−	17.6415i	−1.01459	−	0.585776i	−0.912533	+	0.409002i	$0.865877\pi$
$908$	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	−0.447150	−	0.894459i	$-0.647561\pi$
$937$	3.18043	−	1.83622i	0.103900	−	0.0599868i	0.551050	+	0.834472i	$0.314227\pi$
$938$	−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	−0.781953	−	0.623338i	$-0.785776\pi$
$947$	−19.4827	+	11.2483i	−0.633103	+	0.365522i	0.148850	+	0.988860i	$0.452443\pi$
$948$			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	0.185324	−	0.982677i	$-0.440667\pi$
$953$	34.8533	−	20.1226i	1.12901	−	0.651834i	0.943686	+	0.330843i	$0.107333\pi$
$954$	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	0.554776	−	0.832000i	$-0.312804\pi$
$967$	3.47135	+	2.00419i	0.111631	+	0.0644503i	−0.443145	+	0.896450i	$0.646137\pi$
$968$		−	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	−0.239636	−	0.970863i	$-0.577028\pi$
$977$	15.0452	−	8.68634i	0.481338	−	0.277901i	0.720974	+	0.692962i	$0.243695\pi$
$978$	−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	−0.189345	−	0.981911i	$-0.560637\pi$
$983$	17.7564	−	10.2517i	0.566342	−	0.326977i	0.755687	+	0.654933i	$0.227303\pi$
$984$	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	0.0277042	−	0.999616i	$-0.491180\pi$
$997$	28.6467	−	16.5392i	0.907249	−	0.523801i	0.879545	+	0.475816i	$0.157847\pi$
$998$		−	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.174.9		48
5.2	odd	4		925.2.e.e.26.5	yes	24
5.3	odd	4		925.2.e.d.26.8	✓	24
5.4	even	2	inner	925.2.o.d.174.16		48
37.10	even	3	inner	925.2.o.d.824.16		48
185.47	odd	12		925.2.e.e.676.5	yes	24
185.84	even	6	inner	925.2.o.d.824.9		48
185.158	odd	12		925.2.e.d.676.8	yes	24

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

L-functions

Modular forms

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