LMFDB - Embedded newform 425.2.n.d.274.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(49,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.49"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.3
Character	$\chi$	$=$	425.274
Dual form			425.2.n.d.349.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.982785 + 0.982785i) q^{2} +(0.0424107 + 0.102388i) q^{3} +0.0682683i q^{4} +(-0.142306 - 0.0589452i) q^{6} +(1.58527 + 0.656642i) q^{7} +(-2.03266 - 2.03266i) q^{8} +(2.11264 - 2.11264i) q^{9} +(5.35924 + 2.21987i) q^{11} +(-0.00698988 + 0.00289530i) q^{12} -1.25411 q^{13} +(-2.20332 + 0.912645i) q^{14} +3.85880 q^{16} +(1.85005 + 3.68474i) q^{17} +4.15253i q^{18} +(-1.99782 - 1.99782i) q^{19} +0.190162i q^{21} +(-7.44863 + 3.08532i) q^{22} +(-0.785431 + 1.89620i) q^{23} +(0.121915 - 0.294328i) q^{24} +(1.23252 - 1.23252i) q^{26} +(0.613073 + 0.253943i) q^{27} +(-0.0448278 + 0.108224i) q^{28} +(1.99220 + 4.80961i) q^{29} +(-2.64434 + 1.09532i) q^{31} +(0.272952 - 0.272952i) q^{32} +0.642871i q^{33} +(-5.43951 - 1.80310i) q^{34} +(0.144226 + 0.144226i) q^{36} +(-2.41443 - 5.82896i) q^{37} +3.92685 q^{38} +(-0.0531875 - 0.128406i) q^{39} +(-3.61688 + 8.73191i) q^{41} +(-0.186889 - 0.186889i) q^{42} +(5.25643 + 5.25643i) q^{43} +(-0.151547 + 0.365866i) q^{44} +(-1.09165 - 2.63546i) q^{46} +7.63491 q^{47} +(0.163655 + 0.395097i) q^{48} +(-2.86784 - 2.86784i) q^{49} +(-0.298813 + 0.345696i) q^{51} -0.0856157i q^{52} +(-5.09637 + 5.09637i) q^{53} +(-0.852091 + 0.352948i) q^{54} +(-1.88759 - 4.55706i) q^{56} +(0.119825 - 0.289282i) q^{57} +(-6.68472 - 2.76890i) q^{58} +(1.54321 - 1.54321i) q^{59} +(2.19586 - 5.30128i) q^{61} +(1.52235 - 3.67528i) q^{62} +(4.73635 - 1.96186i) q^{63} +8.25411i q^{64} +(-0.631803 - 0.631803i) q^{66} -2.46660i q^{67} +(-0.251551 + 0.126300i) q^{68} -0.227460 q^{69} +(-12.4522 + 5.15787i) q^{71} -8.58855 q^{72} +(5.39319 - 2.23393i) q^{73} +(8.10148 + 3.35574i) q^{74} +(0.136388 - 0.136388i) q^{76} +(7.03820 + 7.03820i) q^{77} +(0.178467 + 0.0739236i) q^{78} +(3.62361 + 1.50095i) q^{79} -8.88961i q^{81} +(-5.02698 - 12.1362i) q^{82} +(6.29967 - 6.29967i) q^{83} -0.0129821 q^{84} -10.3319 q^{86} +(-0.407958 + 0.407958i) q^{87} +(-6.38128 - 15.4058i) q^{88} -14.3079i q^{89} +(-1.98810 - 0.823498i) q^{91} +(-0.129450 - 0.0536200i) q^{92} +(-0.224296 - 0.224296i) q^{93} +(-7.50348 + 7.50348i) q^{94} +(0.0395233 + 0.0163711i) q^{96} +(7.84699 - 3.25033i) q^{97} +5.63693 q^{98} +(16.0119 - 6.63234i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} + 20 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} - 12 q^{22} - 8 q^{23} - 16 q^{24} + 16 q^{26} - 16 q^{27} - 20 q^{28} - 4 q^{29} + 24 q^{31} - 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) $ 24 * q - 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 + 20 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 - 12 * q^22 - 8 * q^23 - 16 * q^24 + 16 * q^26 - 16 * q^27 - 20 * q^28 - 4 * q^29 + 24 * q^31 - 60 * q^32 - 16 * q^34 + 60 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 - 20 * q^41 - 12 * q^42 + 32 * q^43 - 64 * q^44 - 40 * q^46 + 88 * q^47 - 4 * q^48 - 24 * q^49 + 16 * q^51 + 12 * q^53 + 20 * q^54 - 32 * q^56 + 56 * q^57 + 28 * q^58 + 16 * q^59 - 64 * q^61 - 16 * q^62 + 40 * q^63 - 72 * q^66 - 48 * q^68 + 48 * q^69 - 24 * q^71 - 120 * q^72 - 20 * q^73 - 32 * q^74 + 52 * q^76 - 24 * q^77 + 100 * q^78 + 48 * q^79 - 8 * q^82 - 12 * q^83 + 40 * q^84 - 16 * q^86 + 24 * q^87 - 80 * q^88 + 24 * q^91 + 56 * q^92 - 32 * q^93 + 40 * q^94 + 132 * q^96 + 24 * q^97 - 48 * q^98 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

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 $

$2$	−0.982785	+	0.982785i	−0.694934	+	0.694934i	−0.963313	−	0.268380i	$-0.913512\pi$
$2$	−0.982785	+	0.982785i	−0.694934	+	0.694934i	0.268380	+	0.963313i	$0.413512\pi$
$3$	0.0424107	+	0.102388i	0.0244858	+	0.0591140i	0.935650	−	0.352931i	$-0.114815\pi$
$3$	0.0424107	+	0.102388i	0.0244858	+	0.0591140i	−0.911164	+	0.412045i	$0.864815\pi$
$4$			0.0682683i			0.0341341i
$5$		0			0
$5$		0			0
$6$	−0.142306	−	0.0589452i	−0.0580964	−	0.0240643i
$7$	1.58527	+	0.656642i	0.599177	+	0.248187i	0.661593	−	0.749863i	$-0.269881\pi$
$7$	1.58527	+	0.656642i	0.599177	+	0.248187i	−0.0624163	+	0.998050i	$0.519881\pi$
$8$	−2.03266	−	2.03266i	−0.718655	−	0.718655i
$9$	2.11264	−	2.11264i	0.704212	−	0.704212i
$10$		0			0
$11$	5.35924	+	2.21987i	1.61587	+	0.669316i	0.993545	−	0.113442i	$-0.0361876\pi$
$11$	5.35924	+	2.21987i	1.61587	+	0.669316i	0.622327	+	0.782758i	$0.286188\pi$
$12$	−0.00698988	+	0.00289530i	−0.00201781	+	0.000835803i
$13$	−1.25411			−0.347827			−0.173913	−	0.984761i	$-0.555641\pi$
$13$	−1.25411			−0.347827			−0.173913	+	0.984761i	$0.555641\pi$
$14$	−2.20332	+	0.912645i	−0.588862	+	0.243915i
$15$		0			0
$16$	3.85880			0.964701
$17$	1.85005	+	3.68474i	0.448703	+	0.893681i
$17$	1.85005	+	3.68474i	0.448703	+	0.893681i
$18$			4.15253i			0.978761i
$19$	−1.99782	−	1.99782i	−0.458331	−	0.458331i	0.439776	−	0.898107i	$-0.355058\pi$
$19$	−1.99782	−	1.99782i	−0.458331	−	0.458331i	−0.898107	+	0.439776i	$0.855058\pi$
$20$		0			0
$21$			0.190162i			0.0414968i
$22$	−7.44863	+	3.08532i	−1.58805	+	0.657793i
$23$	−0.785431	+	1.89620i	−0.163774	+	0.395385i	−0.984367	−	0.176127i	$-0.943643\pi$
$23$	−0.785431	+	1.89620i	−0.163774	+	0.395385i	0.820594	+	0.571512i	$0.193643\pi$
$24$	0.121915	−	0.294328i	0.0248857	−	0.0600794i
$25$		0			0
$26$	1.23252	−	1.23252i	0.241716	−	0.241716i
$27$	0.613073	+	0.253943i	0.117986	+	0.0488714i
$28$	−0.0448278	+	0.108224i	−0.00847165	+	0.0204524i
$29$	1.99220	+	4.80961i	0.369943	+	0.893122i	0.993759	+	0.111550i	$0.0355816\pi$
$29$	1.99220	+	4.80961i	0.369943	+	0.893122i	−0.623816	+	0.781572i	$0.714418\pi$
$30$		0			0
$31$	−2.64434	+	1.09532i	−0.474937	+	0.196725i	−0.607295	−	0.794477i	$-0.707745\pi$
$31$	−2.64434	+	1.09532i	−0.474937	+	0.196725i	0.132358	+	0.991202i	$0.457745\pi$
$32$	0.272952	−	0.272952i	0.0482516	−	0.0482516i
$33$			0.642871i			0.111909i
$34$	−5.43951	−	1.80310i	−0.932868	−	0.309230i
$35$		0			0
$36$	0.144226	+	0.144226i	0.0240377	+	0.0240377i
$37$	−2.41443	−	5.82896i	−0.396931	−	0.958275i	−0.988390	−	0.151940i	$-0.951448\pi$
$37$	−2.41443	−	5.82896i	−0.396931	−	0.958275i	0.591459	−	0.806335i	$-0.298552\pi$
$38$	3.92685			0.637019
$39$	−0.0531875	−	0.128406i	−0.00851682	−	0.0205614i
$40$		0			0
$41$	−3.61688	+	8.73191i	−0.564861	+	1.36370i	0.340977	+	0.940072i	$0.389242\pi$
$41$	−3.61688	+	8.73191i	−0.564861	+	1.36370i	−0.905838	+	0.423624i	$0.860758\pi$
$42$	−0.186889	−	0.186889i	−0.0288375	−	0.0288375i
$43$	5.25643	+	5.25643i	0.801597	+	0.801597i	0.983345	−	0.181748i	$-0.0581755\pi$
$43$	5.25643	+	5.25643i	0.801597	+	0.801597i	−0.181748	+	0.983345i	$0.558175\pi$
$44$	−0.151547	+	0.365866i	−0.0228465	+	0.0551564i
$45$		0			0
$46$	−1.09165	−	2.63546i	−0.160954	−	0.388578i
$47$	7.63491			1.11367			0.556833	−	0.830624i	$-0.312016\pi$
$47$	7.63491			1.11367			0.556833	+	0.830624i	$0.312016\pi$
$48$	0.163655	+	0.395097i	0.0236215	+	0.0570273i
$49$	−2.86784	−	2.86784i	−0.409691	−	0.409691i
$50$		0			0
$51$	−0.298813	+	0.345696i	−0.0418422	+	0.0484072i
$52$		−	0.0856157i		−	0.0118728i
$53$	−5.09637	+	5.09637i	−0.700040	+	0.700040i	−0.964419	−	0.264379i	$-0.914833\pi$
$53$	−5.09637	+	5.09637i	−0.700040	+	0.700040i	0.264379	+	0.964419i	$0.414833\pi$
$54$	−0.852091	+	0.352948i	−0.115955	+	0.0480301i
$55$		0			0
$56$	−1.88759	−	4.55706i	−0.252240	−	0.608962i
$57$	0.119825	−	0.289282i	0.0158712	−	0.0383164i
$58$	−6.68472	−	2.76890i	−0.877746	−	0.363574i
$59$	1.54321	−	1.54321i	0.200908	−	0.200908i	−0.599481	−	0.800389i	$-0.704626\pi$
$59$	1.54321	−	1.54321i	0.200908	−	0.200908i	0.800389	+	0.599481i	$0.204626\pi$
$60$		0			0
$61$	2.19586	−	5.30128i	0.281152	−	0.678760i	−0.718712	−	0.695308i	$-0.755268\pi$
$61$	2.19586	−	5.30128i	0.281152	−	0.678760i	0.999863	+	0.0165485i	$0.00526780\pi$
$62$	1.52235	−	3.67528i	0.193339	−	0.466761i
$63$	4.73635	−	1.96186i	0.596724	−	0.247171i
$64$			8.25411i			1.03176i
$65$		0			0
$66$	−0.631803	−	0.631803i	−0.0777696	−	0.0777696i
$67$		−	2.46660i		−	0.301343i	−0.988584	−	0.150672i	$-0.951856\pi$
$67$		−	2.46660i		−	0.301343i	0.988584	−	0.150672i	$-0.0481436\pi$
$68$	−0.251551	+	0.126300i	−0.0305050	+	0.0153161i
$69$	−0.227460			−0.0273829
$70$		0			0
$71$	−12.4522	+	5.15787i	−1.47780	+	0.612126i	−0.968623	−	0.248534i	$-0.920051\pi$
$71$	−12.4522	+	5.15787i	−1.47780	+	0.612126i	−0.509180	+	0.860660i	$0.670051\pi$
$72$	−8.58855			−1.01217
$73$	5.39319	−	2.23393i	0.631225	−	0.261462i	−0.0440485	−	0.999029i	$-0.514026\pi$
$73$	5.39319	−	2.23393i	0.631225	−	0.261462i	0.675273	+	0.737567i	$0.264026\pi$
$74$	8.10148	+	3.35574i	0.941778	+	0.390097i
$75$		0			0
$76$	0.136388	−	0.136388i	0.0156447	−	0.0156447i
$77$	7.03820	+	7.03820i	0.802077	+	0.802077i
$78$	0.178467	+	0.0739236i	0.0202075	+	0.00837020i
$79$	3.62361	+	1.50095i	0.407688	+	0.168870i	0.577096	−	0.816676i	$-0.304186\pi$
$79$	3.62361	+	1.50095i	0.407688	+	0.168870i	−0.169408	+	0.985546i	$0.554186\pi$
$80$		0			0
$81$		−	8.88961i		−	0.987735i
$82$	−5.02698	−	12.1362i	−0.555137	−	1.34022i
$83$	6.29967	−	6.29967i	0.691478	−	0.691478i	−0.271079	−	0.962557i	$-0.587380\pi$
$83$	6.29967	−	6.29967i	0.691478	−	0.691478i	0.962557	+	0.271079i	$0.0873804\pi$
$84$	−0.0129821			−0.00141646
$85$		0			0
$86$	−10.3319			−1.11411
$87$	−0.407958	+	0.407958i	−0.0437376	+	0.0437376i
$88$	−6.38128	−	15.4058i	−0.680247	−	1.64226i
$89$		−	14.3079i		−	1.51664i	−0.651885	−	0.758318i	$-0.726022\pi$
$89$		−	14.3079i		−	1.51664i	0.651885	−	0.758318i	$-0.273978\pi$
$90$		0			0
$91$	−1.98810	−	0.823498i	−0.208410	−	0.0863261i
$92$	−0.129450	−	0.0536200i	−0.0134961	−	0.00559027i
$93$	−0.224296	−	0.224296i	−0.0232584	−	0.0232584i
$94$	−7.50348	+	7.50348i	−0.773925	+	0.773925i
$95$		0			0
$96$	0.0395233	+	0.0163711i	0.00403383	+	0.00167087i
$97$	7.84699	−	3.25033i	0.796741	−	0.330021i	0.0530907	−	0.998590i	$-0.483093\pi$
$97$	7.84699	−	3.25033i	0.796741	−	0.330021i	0.743650	+	0.668569i	$0.233093\pi$
$98$	5.63693			0.569416
$99$	16.0119	−	6.63234i	1.60926	−	0.666576i
$100$		0			0
$101$	2.53832			0.252572			0.126286	−	0.991994i	$-0.459694\pi$
$101$	2.53832			0.252572			0.126286	+	0.991994i	$0.459694\pi$
$102$	−0.0460763	−	0.633414i	−0.00456224	−	0.0627173i
$103$		−	16.6715i		−	1.64269i	−0.570429	−	0.821347i	$-0.693223\pi$
$103$		−	16.6715i		−	1.64269i	0.570429	−	0.821347i	$-0.306777\pi$
$104$	2.54918	+	2.54918i	0.249967	+	0.249967i
$105$		0			0
$106$		−	10.0173i		−	0.972962i
$107$	8.40335	−	3.48078i	0.812382	−	0.336500i	0.0624783	−	0.998046i	$-0.480100\pi$
$107$	8.40335	−	3.48078i	0.812382	−	0.336500i	0.749904	+	0.661546i	$0.230100\pi$
$108$	−0.0173363	+	0.0418535i	−0.00166818	+	0.00402735i
$109$	−0.284608	+	0.687106i	−0.0272605	+	0.0658128i	−0.936924	−	0.349534i	$-0.886340\pi$
$109$	−0.284608	+	0.687106i	−0.0272605	+	0.0658128i	0.909663	+	0.415347i	$0.136340\pi$
$110$		0			0
$111$	0.494421	−	0.494421i	0.0469283	−	0.0469283i
$112$	6.11726	+	2.53385i	0.578026	+	0.239426i
$113$	−3.45825	+	8.34896i	−0.325325	+	0.785404i	0.673602	+	0.739094i	$0.264746\pi$
$113$	−3.45825	+	8.34896i	−0.325325	+	0.785404i	−0.998927	+	0.0463099i	$0.985254\pi$
$114$	0.166540	+	0.402064i	0.0155979	+	0.0376568i
$115$		0			0
$116$	−0.328344	+	0.136004i	−0.0304859	+	0.0126277i
$117$	−2.64947	+	2.64947i	−0.244944	+	0.244944i
$118$			3.03328i			0.279236i
$119$	0.513284	+	7.05614i	0.0470526	+	0.646835i
$120$		0			0
$121$	16.0154	+	16.0154i	1.45595	+	1.45595i
$122$	3.05196	+	7.36808i	0.276311	+	0.667075i
$123$	−1.04744			−0.0944446
$124$	−0.0747756	−	0.180524i	−0.00671505	−	0.0162116i
$125$		0			0
$126$	−2.72673	+	6.58290i	−0.242916	+	0.586451i
$127$	−10.2527	−	10.2527i	−0.909779	−	0.909779i	0.0864752	−	0.996254i	$-0.472440\pi$
$127$	−10.2527	−	10.2527i	−0.909779	−	0.909779i	−0.996254	+	0.0864752i	$0.972440\pi$
$128$	−7.56611	−	7.56611i	−0.668756	−	0.668756i
$129$	−0.315269	+	0.761126i	−0.0277579	+	0.0670134i
$130$		0			0
$131$	−6.44750	−	15.5656i	−0.563321	−	1.35998i	−0.907096	−	0.420924i	$-0.861706\pi$
$131$	−6.44750	−	15.5656i	−0.563321	−	1.35998i	0.343775	−	0.939052i	$-0.388294\pi$
$132$	−0.0438877			−0.00381993
$133$	−1.85524	−	4.47894i	−0.160869	−	0.388373i
$134$	2.42414	+	2.42414i	0.209414	+	0.209414i
$135$		0			0
$136$	3.72930	−	11.2504i	0.319785	−	0.964711i
$137$			20.2283i			1.72822i	0.503300	+	0.864111i	$0.332119\pi$
$137$			20.2283i			1.72822i	−0.503300	+	0.864111i	$0.667881\pi$
$138$	0.223544	−	0.223544i	0.0190293	−	0.0190293i
$139$	3.93292	−	1.62907i	0.333586	−	0.138176i	−0.209603	−	0.977787i	$-0.567217\pi$
$139$	3.93292	−	1.62907i	0.333586	−	0.138176i	0.543188	+	0.839611i	$0.317217\pi$
$140$		0			0
$141$	0.323802	+	0.781727i	0.0272690	+	0.0658333i
$142$	7.16875	−	17.3069i	0.601588	−	1.45236i
$143$	−6.72106	−	2.78395i	−0.562043	−	0.232806i
$144$	8.15224	−	8.15224i	0.679354	−	0.679354i
$145$		0			0
$146$	−3.10487	+	7.49582i	−0.256961	+	0.620358i
$147$	0.172006	−	0.415260i	0.0141868	−	0.0342501i
$148$	0.397933	−	0.164829i	0.0327099	−	0.0135489i
$149$		−	4.32633i		−	0.354427i	−0.984172	−	0.177213i	$-0.943292\pi$
$149$		−	4.32633i		−	0.354427i	0.984172	−	0.177213i	$-0.0567083\pi$
$150$		0			0
$151$	−14.1854	−	14.1854i	−1.15439	−	1.15439i	−0.985663	−	0.168725i	$-0.946035\pi$
$151$	−14.1854	−	14.1854i	−1.15439	−	1.15439i	−0.168725	−	0.985663i	$-0.553965\pi$
$152$			8.12178i			0.658763i
$153$	11.6930	+	3.87603i	0.945323	+	0.313358i
$154$	−13.8341			−1.11478
$155$		0			0
$156$	0.00876606	−	0.00363102i	0.000701846	−	0.000290714i
$157$	−21.7028			−1.73207			−0.866035	−	0.499983i	$-0.833339\pi$
$157$	−21.7028			−1.73207			−0.866035	+	0.499983i	$0.833339\pi$
$158$	−5.03634	+	2.08612i	−0.400669	+	0.165963i
$159$	−0.737950	−	0.305669i	−0.0585232	−	0.0242411i
$160$		0			0
$161$	−2.49025	+	2.49025i	−0.196259	+	0.196259i
$162$	8.73658	+	8.73658i	0.686410	+	0.686410i
$163$	1.22517	+	0.507480i	0.0959623	+	0.0397489i	0.430148	−	0.902758i	$-0.358461\pi$
$163$	1.22517	+	0.507480i	0.0959623	+	0.0397489i	−0.334186	+	0.942507i	$0.608461\pi$
$164$	−0.596112	−	0.246918i	−0.0465486	−	0.0192810i
$165$		0			0
$166$			12.3824i			0.961063i
$167$	−9.56366	−	23.0887i	−0.740058	−	1.78666i	−0.605647	−	0.795733i	$-0.707086\pi$
$167$	−9.56366	−	23.0887i	−0.740058	−	1.78666i	−0.134411	−	0.990926i	$-0.542914\pi$
$168$	0.386536	−	0.386536i	0.0298219	−	0.0298219i
$169$	−11.4272			−0.879017
$170$		0			0
$171$	−8.44132			−0.645524
$172$	−0.358847	+	0.358847i	−0.0273618	+	0.0273618i
$173$	6.10776	+	14.7454i	0.464364	+	1.12108i	0.966587	+	0.256337i	$0.0825157\pi$
$173$	6.10776	+	14.7454i	0.464364	+	1.12108i	−0.502223	+	0.864738i	$0.667484\pi$
$174$		−	0.801869i		−	0.0607895i
$175$		0			0
$176$	20.6802	+	8.56604i	1.55883	+	0.645689i
$177$	0.223455	+	0.0925582i	0.0167959	+	0.00695710i
$178$	14.0616	+	14.0616i	1.05396	+	1.05396i
$179$	−10.5747	+	10.5747i	−0.790389	+	0.790389i	−0.981557	−	0.191168i	$-0.938772\pi$
$179$	−10.5747	+	10.5747i	−0.790389	+	0.790389i	0.191168	+	0.981557i	$0.438772\pi$
$180$		0			0
$181$	22.6278	+	9.37275i	1.68191	+	0.696671i	0.999414	−	0.0342158i	$-0.0108933\pi$
$181$	22.6278	+	9.37275i	1.68191	+	0.696671i	0.682499	+	0.730887i	$0.260893\pi$
$182$	2.76320	−	1.14455i	0.204822	−	0.0848400i
$183$	0.635918			0.0470084
$184$	5.45085	−	2.25782i	0.401842	−	0.166448i
$185$		0			0
$186$	0.440870			0.0323262
$187$	1.73523	+	23.8543i	0.126892	+	1.74440i
$188$			0.521222i			0.0380140i
$189$	0.805139	+	0.805139i	0.0585652	+	0.0585652i
$190$		0			0
$191$		−	0.254656i		−	0.0184263i	−0.999958	−	0.00921313i	$-0.997067\pi$
$191$		−	0.254656i		−	0.0184263i	0.999958	−	0.00921313i	$-0.00293267\pi$
$192$	−0.845126	+	0.350063i	−0.0609917	+	0.0252636i
$193$	−1.13619	+	2.74301i	−0.0817848	+	0.197446i	−0.959482	−	0.281769i	$-0.909079\pi$
$193$	−1.13619	+	2.74301i	−0.0817848	+	0.197446i	0.877697	+	0.479215i	$0.159079\pi$
$194$	−4.51753	+	10.9063i	−0.324340	+	0.783025i
$195$		0			0
$196$	0.195782	−	0.195782i	0.0139844	−	0.0139844i
$197$	5.61826	+	2.32716i	0.400284	+	0.165803i	0.573738	−	0.819039i	$-0.305493\pi$
$197$	5.61826	+	2.32716i	0.400284	+	0.165803i	−0.173454	+	0.984842i	$0.555493\pi$
$198$	−9.21808	+	22.2544i	−0.655100	+	1.58155i
$199$	−4.80772	−	11.6069i	−0.340810	−	0.822789i	−0.997634	−	0.0687451i	$-0.978100\pi$
$199$	−4.80772	−	11.6069i	−0.340810	−	0.822789i	0.656824	−	0.754044i	$-0.271900\pi$
$200$		0			0
$201$	0.252552	−	0.104610i	0.0178136	−	0.00737864i
$202$	−2.49462	+	2.49462i	−0.175521	+	0.175521i
$203$			8.93271i			0.626953i
$204$	−0.0236001	−	0.0203994i	−0.00165234	−	0.00142825i
$205$		0			0
$206$	16.3845	+	16.3845i	1.14156	+	1.14156i
$207$	2.34665	+	5.66531i	0.163103	+	0.393766i
$208$	−4.83935			−0.335549
$209$	−6.27189	−	15.1417i	−0.433836	−	1.04737i
$210$		0			0
$211$	−4.60978	+	11.1290i	−0.317351	+	0.766152i	0.682042	+	0.731313i	$0.261092\pi$
$211$	−4.60978	+	11.1290i	−0.317351	+	0.766152i	−0.999393	+	0.0348394i	$0.988908\pi$
$212$	−0.347920	−	0.347920i	−0.0238953	−	0.0238953i
$213$	−1.05621	−	1.05621i	−0.0723705	−	0.0723705i
$214$	−4.83783	+	11.6795i	−0.330707	+	0.798397i
$215$		0			0
$216$	−0.729990	−	1.76235i	−0.0496695	−	0.119913i
$217$	−4.91123			−0.333396
$218$	−0.395568	−	0.954986i	−0.0267912	−	0.0646798i
$219$	0.457458	+	0.457458i	0.0309121	+	0.0309121i
$220$		0			0
$221$	−2.32016	−	4.62106i	−0.156071	−	0.310846i
$222$			0.971818i			0.0652242i
$223$	−12.5656	+	12.5656i	−0.841453	+	0.841453i	−0.989048	−	0.147595i	$-0.952847\pi$
$223$	−12.5656	+	12.5656i	−0.841453	+	0.841453i	0.147595	+	0.989048i	$0.452847\pi$
$224$	0.611936	−	0.253472i	0.0408867	−	0.0169358i
$225$		0			0
$226$	−4.80651	−	11.6039i	−0.319724	−	0.771883i
$227$	4.27575	−	10.3226i	0.283791	−	0.685133i	−0.716126	−	0.697971i	$-0.754086\pi$
$227$	4.27575	−	10.3226i	0.283791	−	0.685133i	0.999918	+	0.0128377i	$0.00408649\pi$
$228$	0.0197488	+	0.00818022i	0.00130790	+	0.000541749i
$229$	−15.0941	+	15.0941i	−0.997445	+	0.997445i	−0.999997	−	0.00255174i	$-0.999188\pi$
$229$	−15.0941	+	15.0941i	−0.997445	+	0.997445i	0.00255174	+	0.999997i	$0.499188\pi$
$230$		0			0
$231$	−0.422135	+	1.01913i	−0.0277745	+	0.0670535i
$232$	5.72683	−	13.8258i	0.375985	−	0.907708i
$233$	7.67330	−	3.17839i	0.502695	−	0.208223i	−0.116902	−	0.993143i	$-0.537296\pi$
$233$	7.67330	−	3.17839i	0.502695	−	0.208223i	0.619597	+	0.784920i	$0.287296\pi$
$234$		−	5.20772i		−	0.340439i
$235$		0			0
$236$	0.105352	+	0.105352i	0.00685784	+	0.00685784i
$237$			0.434672i			0.0282350i
$238$	−7.43911	−	6.43022i	−0.482206	−	0.416809i
$239$	3.42382			0.221468			0.110734	−	0.993850i	$-0.464680\pi$
$239$	3.42382			0.221468			0.110734	+	0.993850i	$0.464680\pi$
$240$		0			0
$241$	−5.86504	+	2.42938i	−0.377800	+	0.156490i	−0.563499	−	0.826117i	$-0.690545\pi$
$241$	−5.86504	+	2.42938i	−0.377800	+	0.156490i	0.185699	+	0.982607i	$0.440545\pi$
$242$	−31.4795			−2.02358
$243$	2.74941	−	1.13884i	0.176375	−	0.0730569i
$244$	0.361909	+	0.149908i	0.0231689	+	0.00959686i
$245$		0			0
$246$	1.02941	−	1.02941i	0.0656327	−	0.0656327i
$247$	2.50548	+	2.50548i	0.159420	+	0.159420i
$248$	7.60146	+	3.14863i	0.482693	+	0.199938i
$249$	0.912187	+	0.377840i	0.0578075	+	0.0239446i
$250$		0			0
$251$		−	5.06308i		−	0.319579i	−0.987151	−	0.159789i	$-0.948919\pi$
$251$		−	5.06308i		−	0.319579i	0.987151	−	0.159789i	$-0.0510815\pi$
$252$	0.133933	+	0.323342i	0.00843697	+	0.0203687i
$253$	−8.41863	+	8.41863i	−0.529275	+	0.529275i
$254$	20.1524			1.26447
$255$		0			0
$256$	−1.63651			−0.102282
$257$	−12.6054	+	12.6054i	−0.786305	+	0.786305i	−0.980886	−	0.194582i	$-0.937665\pi$
$257$	−12.6054	+	12.6054i	−0.786305	+	0.786305i	0.194582	+	0.980886i	$0.437665\pi$
$258$	−0.438182	−	1.05786i	−0.0272800	−	0.0658598i
$259$		−	10.8259i		−	0.672689i
$260$		0			0
$261$	14.3698	+	5.95215i	0.889465	+	0.368429i
$262$	21.6342	+	8.96117i	1.33656	+	0.553623i
$263$	−6.44016	−	6.44016i	−0.397117	−	0.397117i	0.480098	−	0.877215i	$-0.340601\pi$
$263$	−6.44016	−	6.44016i	−0.397117	−	0.397117i	−0.877215	+	0.480098i	$0.840601\pi$
$264$	1.30674	−	1.30674i	0.0804242	−	0.0804242i
$265$		0			0
$266$	6.22513	+	2.57853i	0.381687	+	0.158100i
$267$	1.46496	−	0.606808i	0.0896544	−	0.0371361i
$268$	0.168391			0.0102861
$269$	11.7926	−	4.88466i	0.719008	−	0.297823i	0.00698191	−	0.999976i	$-0.497778\pi$
$269$	11.7926	−	4.88466i	0.719008	−	0.297823i	0.712027	+	0.702153i	$0.247778\pi$
$270$		0			0
$271$	16.4128			0.997004			0.498502	−	0.866889i	$-0.333884\pi$
$271$	16.4128			0.997004			0.498502	+	0.866889i	$0.333884\pi$
$272$	7.13899	+	14.2187i	0.432865	+	0.862134i
$273$		−	0.238484i		−	0.0144337i
$274$	−19.8801	−	19.8801i	−1.20100	−	1.20100i
$275$		0			0
$276$		−	0.0155283i		−	0.000934692i
$277$	−17.0407	+	7.05850i	−1.02388	+	0.424104i	−0.830499	−	0.557020i	$-0.811945\pi$
$277$	−17.0407	+	7.05850i	−1.02388	+	0.424104i	−0.193379	+	0.981124i	$0.561945\pi$
$278$	−2.26419	+	5.46623i	−0.135797	+	0.327843i
$279$	−3.27251	+	7.90053i	−0.195920	+	0.472992i
$280$		0			0
$281$	13.2557	−	13.2557i	0.790767	−	0.790767i	−0.190852	−	0.981619i	$-0.561125\pi$
$281$	13.2557	−	13.2557i	0.790767	−	0.790767i	0.981619	+	0.190852i	$0.0611251\pi$
$282$	−1.08650	−	0.450042i	−0.0647000	−	0.0267996i
$283$	7.57337	−	18.2837i	0.450190	−	1.08686i	−0.522059	−	0.852909i	$-0.674836\pi$
$283$	7.57337	−	18.2837i	0.450190	−	1.08686i	0.972250	−	0.233946i	$-0.0751639\pi$
$284$	−0.352119	−	0.850090i	−0.0208944	−	0.0504435i
$285$		0			0
$286$	9.34138	−	3.86933i	0.552367	−	0.228798i
$287$	−11.4675	+	11.4675i	−0.676903	+	0.676903i
$288$		−	1.15330i		−	0.0679587i
$289$	−10.1546	+	13.6339i	−0.597330	+	0.801995i
$290$		0			0
$291$	0.665592	+	0.665592i	0.0390177	+	0.0390177i
$292$	0.152507	+	0.368184i	0.00892478	+	0.0215463i
$293$	14.0051			0.818189			0.409094	−	0.912492i	$-0.365845\pi$
$293$	14.0051			0.818189			0.409094	+	0.912492i	$0.365845\pi$
$294$	0.239066	+	0.577157i	0.0139426	+	0.0336605i
$295$		0			0
$296$	−6.94058	+	16.7560i	−0.403413	+	0.973925i
$297$	2.72189	+	2.72189i	0.157940	+	0.157940i
$298$	4.25185	+	4.25185i	0.246303	+	0.246303i
$299$	0.985014	−	2.37803i	0.0569648	−	0.137525i
$300$		0			0
$301$	4.88128	+	11.7845i	0.281352	+	0.679245i
$302$	27.8823			1.60445
$303$	0.107652	+	0.259895i	0.00618444	+	0.0149306i
$304$	−7.70919	−	7.70919i	−0.442152	−	0.442152i
$305$		0			0
$306$	−15.3010	+	7.68240i	−0.874700	+	0.439174i
$307$		−	13.2813i		−	0.758001i	−0.925396	−	0.379001i	$-0.876268\pi$
$307$		−	13.2813i		−	0.758001i	0.925396	−	0.379001i	$-0.123732\pi$
$308$	−0.480486	+	0.480486i	−0.0273782	+	0.0273782i
$309$	1.70697	−	0.707051i	0.0971062	−	0.0402227i
$310$		0			0
$311$	−9.01417	−	21.7621i	−0.511147	−	1.23402i	−0.943217	−	0.332178i	$-0.892217\pi$
$311$	−9.01417	−	21.7621i	−0.511147	−	1.23402i	0.432070	−	0.901840i	$-0.357783\pi$
$312$	−0.152894	+	0.369118i	−0.00865591	+	0.0208972i
$313$	−30.1714	−	12.4974i	−1.70539	−	0.706394i	−0.705389	−	0.708821i	$-0.749228\pi$
$313$	−30.1714	−	12.4974i	−1.70539	−	0.706394i	−0.999997	+	0.00242660i	$0.999228\pi$
$314$	21.3292	−	21.3292i	1.20367	−	1.20367i
$315$		0			0
$316$	−0.102467	+	0.247378i	−0.00576423	+	0.0139161i
$317$	9.72053	−	23.4674i	0.545960	−	1.31806i	−0.374501	−	0.927227i	$-0.622186\pi$
$317$	9.72053	−	23.4674i	0.545960	−	1.31806i	0.920460	−	0.390836i	$-0.127814\pi$
$318$	1.02565	−	0.424839i	0.0575157	−	0.0238238i
$319$			30.1983i			1.69078i
$320$		0			0
$321$	0.712784	+	0.712784i	0.0397837	+	0.0397837i
$322$		−	4.89475i		−	0.272774i
$323$	3.66537	−	11.0575i	0.203947	−	0.615256i
$324$	0.606878			0.0337155
$325$		0			0
$326$	−1.70282	+	0.705330i	−0.0943103	+	0.0390646i
$327$	−0.0824221			−0.00455795
$328$	25.1009	−	10.3971i	1.38597	−	0.574086i
$329$	12.1034	+	5.01340i	0.667283	+	0.276398i
$330$		0			0
$331$	13.0376	−	13.0376i	0.716613	−	0.716613i	−0.251297	−	0.967910i	$-0.580857\pi$
$331$	13.0376	−	13.0376i	0.716613	−	0.716613i	0.967910	+	0.251297i	$0.0808570\pi$
$332$	0.430067	+	0.430067i	0.0236030	+	0.0236030i
$333$	−17.4153	−	7.21365i	−0.954352	−	0.395306i
$334$	32.0903	+	13.2922i	1.75590	+	0.727318i
$335$		0			0
$336$			0.733799i			0.0400320i
$337$	−2.52852	−	6.10439i	−0.137737	−	0.332527i	0.839927	−	0.542699i	$-0.182598\pi$
$337$	−2.52852	−	6.10439i	−0.137737	−	0.332527i	−0.977664	+	0.210172i	$0.932598\pi$
$338$	11.2305	−	11.2305i	0.610858	−	0.610858i
$339$	−1.00150			−0.0543942
$340$		0			0
$341$	−16.6031			−0.899108
$342$	8.29600	−	8.29600i	0.448596	−	0.448596i
$343$	−7.25965	−	17.5264i	−0.391984	−	0.946334i
$344$		−	21.3691i		−	1.15214i
$345$		0			0
$346$	−20.4942	−	8.48898i	−1.10178	−	0.456370i
$347$	8.88319	+	3.67954i	0.476875	+	0.197528i	0.608157	−	0.793817i	$-0.291909\pi$
$347$	8.88319	+	3.67954i	0.476875	+	0.197528i	−0.131282	+	0.991345i	$0.541909\pi$
$348$	−0.0278506	−	0.0278506i	−0.00149295	−	0.00149295i
$349$	0.486525	−	0.486525i	0.0260431	−	0.0260431i	−0.693965	−	0.720008i	$-0.744138\pi$
$349$	0.486525	−	0.486525i	0.0260431	−	0.0260431i	0.720008	+	0.693965i	$0.244138\pi$
$350$		0			0
$351$	−0.768859	−	0.318472i	−0.0410387	−	0.0169988i
$352$	2.06874	−	0.856898i	0.110264	−	0.0456728i
$353$	−15.3590			−0.817475			−0.408737	−	0.912652i	$-0.634031\pi$
$353$	−15.3590			−0.817475			−0.408737	+	0.912652i	$0.634031\pi$
$354$	−0.310573	+	0.128644i	−0.0165068	+	0.00683733i
$355$		0			0
$356$	0.976776			0.0517690
$357$	−0.700699	+	0.351810i	−0.0370849	+	0.0186198i
$358$		−	20.7853i		−	1.09854i
$359$	18.0696	+	18.0696i	0.953676	+	0.953676i	0.998974	−	0.0452975i	$-0.0144236\pi$
$359$	18.0696	+	18.0696i	0.953676	+	0.953676i	−0.0452975	+	0.998974i	$0.514424\pi$
$360$		0			0
$361$		−	11.0174i		−	0.579866i
$362$	−31.4497	+	13.0269i	−1.65296	+	0.684678i
$363$	−0.960571	+	2.31902i	−0.0504169	+	0.121717i
$364$	0.0562188	−	0.135724i	0.00294667	−	0.00711388i
$365$		0			0
$366$	−0.624971	+	0.624971i	−0.0326678	+	0.0326678i
$367$	−1.06912	−	0.442844i	−0.0558076	−	0.0231163i	0.354605	−	0.935016i	$-0.384615\pi$
$367$	−1.06912	−	0.442844i	−0.0558076	−	0.0231163i	−0.410413	+	0.911900i	$0.634615\pi$
$368$	−3.03082	+	7.31706i	−0.157993	+	0.381428i
$369$	10.8062	+	26.0885i	0.562549	+	1.35811i
$370$		0			0
$371$	−11.4256	+	4.73265i	−0.593188	+	0.245707i
$372$	0.0153123	−	0.0153123i	0.000793907	−	0.000793907i
$373$			15.1464i			0.784251i	0.919912	+	0.392126i	$0.128260\pi$
$373$			15.1464i			0.784251i	−0.919912	+	0.392126i	$0.871740\pi$
$374$	−25.1490	−	21.7383i	−1.30042	−	1.12406i
$375$		0			0
$376$	−15.5192	−	15.5192i	−0.800342	−	0.800342i
$377$	−2.49844	−	6.03176i	−0.128676	−	0.310651i
$378$	−1.58256			−0.0813979
$379$	−5.98525	−	14.4497i	−0.307442	−	0.742230i	−0.999786	−	0.0206630i	$-0.993422\pi$
$379$	−5.98525	−	14.4497i	−0.307442	−	0.742230i	0.692345	−	0.721567i	$-0.256578\pi$
$380$		0			0
$381$	0.614933	−	1.48458i	0.0315040	−	0.0760574i
$382$	0.250272	+	0.250272i	0.0128050	+	0.0128050i
$383$	3.26890	+	3.26890i	0.167033	+	0.167033i	0.785674	−	0.618641i	$-0.212316\pi$
$383$	3.26890	+	3.26890i	0.167033	+	0.167033i	−0.618641	+	0.785674i	$0.712316\pi$
$384$	0.453799	−	1.09557i	0.0231578	−	0.0559079i
$385$		0			0
$386$	−1.57915	−	3.81242i	−0.0803769	−	0.194047i
$387$	22.2098			1.12899
$388$	0.221894	+	0.535700i	0.0112650	+	0.0271961i
$389$	−4.48189	−	4.48189i	−0.227241	−	0.227241i	0.584298	−	0.811539i	$-0.301370\pi$
$389$	−4.48189	−	4.48189i	−0.227241	−	0.227241i	−0.811539	+	0.584298i	$0.801370\pi$
$390$		0			0
$391$	−8.44009	+	0.613956i	−0.426834	+	0.0310491i
$392$			11.6587i			0.588852i
$393$	1.32030	−	1.32030i	0.0666003	−	0.0666003i
$394$	−7.80864	+	3.23444i	−0.393393	+	0.162949i
$395$		0			0
$396$	0.452779	+	1.09310i	0.0227530	+	0.0549306i
$397$	1.24201	−	2.99848i	0.0623348	−	0.150490i	−0.889643	−	0.456657i	$-0.849047\pi$
$397$	1.24201	−	2.99848i	0.0623348	−	0.150490i	0.951978	+	0.306167i	$0.0990467\pi$
$398$	16.1320	+	6.68210i	0.808625	+	0.334943i
$399$	0.379910	−	0.379910i	0.0190193	−	0.0190193i
$400$		0			0
$401$	4.78153	−	11.5436i	0.238778	−	0.576462i	−0.758379	−	0.651814i	$-0.774008\pi$
$401$	4.78153	−	11.5436i	0.238778	−	0.576462i	0.997157	+	0.0753522i	$0.0240081\pi$
$402$	−0.145394	+	0.351013i	−0.00725161	+	0.0175069i
$403$	3.31628	−	1.37365i	0.165196	−	0.0684263i
$404$			0.173287i			0.00862133i
$405$		0			0
$406$	−8.77893	−	8.77893i	−0.435691	−	0.435691i
$407$		−	36.5985i		−	1.81412i
$408$	1.31007	−	0.0952982i	0.0648581	−	0.00471797i
$409$	−11.7076			−0.578904			−0.289452	−	0.957192i	$-0.593473\pi$
$409$	−11.7076			−0.578904			−0.289452	+	0.957192i	$0.593473\pi$
$410$		0			0
$411$	−2.07115	+	0.857898i	−0.102162	+	0.0423170i
$412$	1.13814			0.0560719
$413$	3.45974	−	1.43307i	0.170243	−	0.0705168i
$414$	−7.87403	−	3.26153i	−0.386987	−	0.160295i
$415$		0			0
$416$	−0.342311	+	0.342311i	−0.0167832	+	0.0167832i
$417$	0.333596	+	0.333596i	0.0163362	+	0.0163362i
$418$	21.0449	+	8.71709i	1.02934	+	0.426367i
$419$	−0.503085	−	0.208385i	−0.0245773	−	0.0101803i	0.370361	−	0.928888i	$-0.379234\pi$
$419$	−0.503085	−	0.208385i	−0.0245773	−	0.0101803i	−0.394938	+	0.918708i	$0.629234\pi$
$420$		0			0
$421$			24.3097i			1.18478i	0.805651	+	0.592391i	$0.201816\pi$
$421$			24.3097i			1.18478i	−0.805651	+	0.592391i	$0.798184\pi$
$422$	−6.40699	−	15.4678i	−0.311887	−	0.752963i
$423$	16.1298	−	16.1298i	0.784257	−	0.784257i
$424$	20.7184			1.00617
$425$		0			0
$426$	2.07606			0.100585
$427$	6.96209	−	6.96209i	0.336919	−	0.336919i
$428$	0.237627	+	0.573682i	0.0114861	+	0.0277300i
$429$		−	0.806228i		−	0.0389251i
$430$		0			0
$431$	−3.92135	−	1.62428i	−0.188885	−	0.0782387i	0.286236	−	0.958159i	$-0.407596\pi$
$431$	−3.92135	−	1.62428i	−0.188885	−	0.0782387i	−0.475121	+	0.879920i	$0.657596\pi$
$432$	2.36573	+	0.979917i	0.113821	+	0.0471463i
$433$	−18.1756	−	18.1756i	−0.873464	−	0.873464i	0.119384	−	0.992848i	$-0.461908\pi$
$433$	−18.1756	−	18.1756i	−0.873464	−	0.873464i	−0.992848	+	0.119384i	$0.961908\pi$
$434$	4.82668	−	4.82668i	0.231688	−	0.231688i
$435$		0			0
$436$	−0.0469075	−	0.0194297i	−0.00224646	−	0.000930515i
$437$	5.35741	−	2.21911i	0.256280	−	0.106154i
$438$	−0.899165			−0.0429638
$439$	−2.86412	+	1.18636i	−0.136697	+	0.0566217i	−0.449983	−	0.893037i	$-0.648570\pi$
$439$	−2.86412	+	1.18636i	−0.136697	+	0.0566217i	0.313286	+	0.949659i	$0.398570\pi$
$440$		0			0
$441$	−12.1174			−0.577018
$442$	6.82172	+	2.26128i	0.324476	+	0.107558i
$443$			26.3141i			1.25022i	0.780537	+	0.625109i	$0.214946\pi$
$443$			26.3141i			1.25022i	−0.780537	+	0.625109i	$0.785054\pi$
$444$	0.0337532	+	0.0337532i	0.00160186	+	0.00160186i
$445$		0			0
$446$		−	24.6985i		−	1.16951i
$447$	0.442967	−	0.183483i	0.0209516	−	0.00867844i
$448$	−5.41999	+	13.0850i	−0.256071	+	0.618209i
$449$	−5.62744	+	13.5858i	−0.265575	+	0.641156i	−0.999265	−	0.0383289i	$-0.987797\pi$
$449$	−5.62744	+	13.5858i	−0.265575	+	0.641156i	0.733690	+	0.679485i	$0.237797\pi$
$450$		0			0
$451$	−38.7674	+	38.7674i	−1.82549	+	1.82549i
$452$	−0.569969	−	0.236089i	−0.0268091	−	0.0111047i
$453$	0.850807	−	2.05403i	0.0399744	−	0.0965067i
$454$	5.94272	+	14.3470i	0.278906	+	0.673338i
$455$		0			0
$456$	−0.831577	+	0.344450i	−0.0389421	+	0.0161304i
$457$	7.48280	−	7.48280i	0.350030	−	0.350030i	−0.510090	−	0.860121i	$-0.670388\pi$
$457$	7.48280	−	7.48280i	0.350030	−	0.350030i	0.860121	+	0.510090i	$0.170388\pi$
$458$		−	29.6685i		−	1.38632i
$459$	0.198502	+	2.72882i	0.00926530	+	0.127371i
$460$		0			0
$461$	−13.0851	−	13.0851i	−0.609433	−	0.609433i	0.333365	−	0.942798i	$-0.391816\pi$
$461$	−13.0851	−	13.0851i	−0.609433	−	0.609433i	−0.942798	+	0.333365i	$0.891816\pi$
$462$	−0.586712	−	1.41645i	−0.0272963	−	0.0658992i
$463$	37.7389			1.75387			0.876937	−	0.480605i	$-0.159583\pi$
$463$	37.7389			1.75387			0.876937	+	0.480605i	$0.159583\pi$
$464$	7.68753	+	18.5593i	0.356884	+	0.861595i
$465$		0			0
$466$	−4.41754	+	10.6649i	−0.204638	+	0.494041i
$467$	−21.3821	−	21.3821i	−0.989444	−	0.989444i	0.0105009	−	0.999945i	$-0.496657\pi$
$467$	−21.3821	−	21.3821i	−0.989444	−	0.989444i	−0.999945	+	0.0105009i	$0.996657\pi$
$468$	−0.180875	−	0.180875i	−0.00836094	−	0.00836094i
$469$	1.61967	−	3.91024i	0.0747895	−	0.180558i
$470$		0			0
$471$	−0.920430	−	2.22211i	−0.0424112	−	0.102390i
$472$	−6.27364			−0.288768
$473$	16.5019	+	39.8390i	0.758756	+	1.83180i
$474$	−0.427189	−	0.427189i	−0.0196214	−	0.0196214i
$475$		0			0
$476$	−0.481710	+	0.0350410i	−0.0220792	+	0.00160610i
$477$			21.5335i			0.985953i
$478$	−3.36487	+	3.36487i	−0.153906	+	0.153906i
$479$	−24.9054	+	10.3162i	−1.13796	+	0.471358i	−0.870479	−	0.492206i	$-0.836191\pi$
$479$	−24.9054	+	10.3162i	−1.13796	+	0.471358i	−0.267480	+	0.963563i	$0.586191\pi$
$480$		0			0
$481$	3.02796	+	7.31014i	0.138063	+	0.333314i
$482$	3.37651	−	8.15163i	0.153796	−	0.371296i
$483$	−0.360585	−	0.149359i	−0.0164072	−	0.00679609i
$484$	−1.09335	+	1.09335i	−0.0496976	+	0.0496976i
$485$		0			0
$486$	−1.58284	+	3.82132i	−0.0717992	+	0.173339i
$487$	1.46660	−	3.54069i	0.0664581	−	0.160444i	−0.887161	−	0.461460i	$-0.847326\pi$
$487$	1.46660	−	3.54069i	0.0664581	−	0.160444i	0.953619	+	0.301016i	$0.0973258\pi$
$488$	−15.2392	+	6.31227i	−0.689845	+	0.285743i
$489$			0.146965i			0.00664600i
$490$		0			0
$491$	−4.17285	−	4.17285i	−0.188318	−	0.188318i	0.606651	−	0.794969i	$-0.292513\pi$
$491$	−4.17285	−	4.17285i	−0.188318	−	0.188318i	−0.794969	+	0.606651i	$0.792513\pi$
$492$		−	0.0715070i		−	0.00322378i
$493$	−14.0365	+	16.2388i	−0.632171	+	0.731358i
$494$	−4.92469			−0.221572
$495$		0			0
$496$	−10.2040	+	4.22662i	−0.458172	+	0.189781i
$497$	−23.1270			−1.03739
$498$	−1.26782	+	0.525148i	−0.0568123	+	0.0235324i
$499$	40.7345	+	16.8728i	1.82352	+	0.755329i	0.973538	+	0.228524i	$0.0733899\pi$
$499$	40.7345	+	16.8728i	1.82352	+	0.755329i	0.849986	+	0.526805i	$0.176610\pi$
$500$		0			0
$501$	1.95842	−	1.95842i	0.0874956	−	0.0874956i
$502$	4.97592	+	4.97592i	0.222086	+	0.222086i
$503$	−32.8295	−	13.5984i	−1.46380	−	0.606324i	−0.498362	−	0.866969i	$-0.666065\pi$
$503$	−32.8295	−	13.5984i	−1.46380	−	0.606324i	−0.965435	+	0.260645i	$0.916065\pi$
$504$	−13.6152	−	5.63960i	−0.606469	−	0.251208i
$505$		0			0
$506$		−	16.5474i		−	0.735621i
$507$	−0.484636	−	1.17002i	−0.0215235	−	0.0519622i
$508$	0.699933	−	0.699933i	0.0310545	−	0.0310545i
$509$	−32.9351			−1.45982			−0.729911	−	0.683542i	$-0.760438\pi$
$509$	−32.9351			−1.45982			−0.729911	+	0.683542i	$0.760438\pi$
$510$		0			0
$511$	10.0166			0.443107
$512$	16.7406	−	16.7406i	0.739835	−	0.739835i
$513$	−0.717476	−	1.73214i	−0.0316774	−	0.0764759i
$514$		−	24.7768i		−	1.09286i
$515$		0			0
$516$	−0.0519608	−	0.0215229i	−0.00228744	−	0.000947491i
$517$	40.9173	+	16.9485i	1.79954	+	0.745395i
$518$	10.6395	+	10.6395i	0.467475	+	0.467475i
$519$	−1.25073	+	1.25073i	−0.0549009	+	0.0549009i
$520$		0			0
$521$	22.6197	+	9.36938i	0.990986	+	0.410480i	0.818484	−	0.574529i	$-0.194815\pi$
$521$	22.6197	+	9.36938i	0.990986	+	0.410480i	0.172502	+	0.985009i	$0.444815\pi$
$522$	−19.9721	+	8.27269i	−0.874153	+	0.362086i
$523$	−9.59229			−0.419442			−0.209721	−	0.977761i	$-0.567256\pi$
$523$	−9.59229			−0.419442			−0.209721	+	0.977761i	$0.567256\pi$
$524$	1.06264	−	0.440160i	0.0464216	−	0.0192285i
$525$		0			0
$526$	12.6586			0.551940
$527$	−8.92813	−	7.71729i	−0.388915	−	0.336171i
$528$			2.48071i			0.107959i
$529$	13.2848	+	13.2848i	0.577600	+	0.577600i
$530$		0			0
$531$		−	6.52047i		−	0.282964i
$532$	0.305769	−	0.126654i	0.0132568	−	0.00549114i
$533$	4.53595	−	10.9507i	0.196474	−	0.474329i
$534$	−0.843383	+	2.03611i	−0.0364968	+	0.0881110i
$535$		0			0
$536$	−5.01377	+	5.01377i	−0.216562	+	0.216562i
$537$	−1.53121	−	0.634246i	−0.0660764	−	0.0273697i
$538$	−6.78903	+	16.3902i	−0.292696	+	0.706631i
$539$	−9.00320	−	21.7356i	−0.387795	−	0.936220i
$540$		0			0
$541$	34.9482	−	14.4760i	1.50254	−	0.622373i	0.528539	−	0.848909i	$-0.322740\pi$
$541$	34.9482	−	14.4760i	1.50254	−	0.622373i	0.974003	+	0.226536i	$0.0727402\pi$
$542$	−16.1302	+	16.1302i	−0.692852	+	0.692852i
$543$			2.71433i			0.116483i
$544$	1.51073	+	0.500782i	0.0647722	+	0.0214709i
$545$		0			0
$546$	0.234378	+	0.234378i	0.0100305	+	0.0100305i
$547$	9.30496	+	22.4642i	0.397851	+	0.960498i	0.988175	+	0.153332i	$0.0490002\pi$
$547$	9.30496	+	22.4642i	0.397851	+	0.960498i	−0.590323	+	0.807167i	$0.701000\pi$
$548$	−1.38095			−0.0589914
$549$	−6.56062	−	15.8387i	−0.280000	−	0.675981i
$550$		0			0
$551$	5.62866	−	13.5888i	0.239789	−	0.578902i
$552$	0.462349	+	0.462349i	0.0196789	+	0.0196789i
$553$	4.75882	+	4.75882i	0.202366	+	0.202366i
$554$	9.81038	−	23.6844i	0.416803	−	1.00625i
$555$		0			0
$556$	0.111214	+	0.268493i	0.00471651	+	0.0113867i
$557$	−26.8276			−1.13672			−0.568360	−	0.822780i	$-0.692422\pi$
$557$	−26.8276			−1.13672			−0.568360	+	0.822780i	$0.692422\pi$
$558$	−4.54835	−	10.9807i	−0.192547	−	0.464850i
$559$	−6.59212	−	6.59212i	−0.278817	−	0.278817i
$560$		0			0
$561$	−2.36881	+	1.18934i	−0.100011	+	0.0502141i
$562$			26.0549i			1.09906i
$563$	27.7735	−	27.7735i	1.17051	−	1.17051i	0.188426	−	0.982087i	$-0.439662\pi$
$563$	27.7735	−	27.7735i	1.17051	−	1.17051i	0.982087	−	0.188426i	$-0.0603384\pi$
$564$	−0.0533672	+	0.0221054i	−0.00224716	+	0.000930805i
$565$		0			0
$566$	10.5260	+	25.4120i	0.442440	+	1.06814i
$567$	5.83729	−	14.0925i	0.245143	−	0.591828i
$568$	35.7953	+	14.8269i	1.50194	+	0.622123i
$569$	−7.03027	+	7.03027i	−0.294724	+	0.294724i	−0.838943	−	0.544219i	$-0.816826\pi$
$569$	−7.03027	+	7.03027i	−0.294724	+	0.294724i	0.544219	+	0.838943i	$0.316826\pi$
$570$		0			0
$571$	0.173542	−	0.418968i	0.00726251	−	0.0175333i	−0.920207	−	0.391433i	$-0.871980\pi$
$571$	0.173542	−	0.418968i	0.00726251	−	0.0175333i	0.927469	+	0.373900i	$0.121980\pi$
$572$	0.190056	−	0.458835i	0.00794662	−	0.0191848i
$573$	0.0260738	−	0.0108001i	0.00108925	−	0.000451182i
$574$		−	22.5401i		−	0.940806i
$575$		0			0
$576$	17.4379	+	17.4379i	0.726581	+	0.726581i
$577$			28.8048i			1.19916i	0.800316	+	0.599579i	$0.204665\pi$
$577$			28.8048i			1.19916i	−0.800316	+	0.599579i	$0.795335\pi$
$578$	−3.41941	−	23.3790i	−0.142229	−	0.972439i
$579$	−0.329039			−0.0136744
$580$		0			0
$581$	14.1233	−	5.85007i	0.585934	−	0.242702i
$582$	−1.30827			−0.0542295
$583$	−38.6259	+	15.9994i	−1.59972	+	0.662626i
$584$	−15.5034	−	6.42170i	−0.641534	−	0.265732i
$585$		0			0
$586$	−13.7640	+	13.7640i	−0.568587	+	0.568587i
$587$	14.9214	+	14.9214i	0.615871	+	0.615871i	0.944470	−	0.328599i	$-0.106576\pi$
$587$	14.9214	+	14.9214i	0.615871	+	0.615871i	−0.328599	+	0.944470i	$0.606576\pi$
$588$	0.0283491	+	0.0117426i	0.00116910	+	0.000484256i
$589$	7.47115	+	3.09465i	0.307843	+	0.127513i
$590$		0			0
$591$			0.673942i			0.0277223i
$592$	−9.31683	−	22.4928i	−0.382919	−	0.924449i
$593$	−26.9570	+	26.9570i	−1.10699	+	1.10699i	−0.113445	+	0.993544i	$0.536189\pi$
$593$	−26.9570	+	26.9570i	−1.10699	+	1.10699i	−0.993544	+	0.113445i	$0.963811\pi$
$594$	−5.35005			−0.219515
$595$		0			0
$596$	0.295351			0.0120981
$597$	0.984511	−	0.984511i	0.0402933	−	0.0402933i
$598$	1.36904	+	3.30515i	0.0559842	+	0.135158i
$599$			35.4595i			1.44884i	0.689360	+	0.724418i	$0.257892\pi$
$599$			35.4595i			1.44884i	−0.689360	+	0.724418i	$0.742108\pi$
$600$		0			0
$601$	24.4610	+	10.1321i	0.997784	+	0.413296i	0.820984	−	0.570951i	$-0.193425\pi$
$601$	24.4610	+	10.1321i	0.997784	+	0.413296i	0.176800	+	0.984247i	$0.443425\pi$
$602$	−16.3788	−	6.78433i	−0.667551	−	0.276509i
$603$	−5.21103	−	5.21103i	−0.212210	−	0.212210i
$604$	0.968410	−	0.968410i	0.0394041	−	0.0394041i
$605$		0			0
$606$	−0.361219	−	0.149622i	−0.0146735	−	0.00607797i
$607$	−22.6195	+	9.36932i	−0.918099	+	0.380289i	−0.791151	−	0.611620i	$-0.790518\pi$
$607$	−22.6195	+	9.36932i	−0.918099	+	0.380289i	−0.126948	+	0.991909i	$0.540518\pi$
$608$	−1.09062			−0.0442304
$609$	−0.914606	+	0.378842i	−0.0370617	+	0.0153515i
$610$		0			0
$611$	−9.57499			−0.387363
$612$	−0.264610	+	0.798261i	−0.0106962	+	0.0322678i
$613$		−	13.6998i		−	0.553329i	−0.960967	−	0.276665i	$-0.910771\pi$
$613$		−	13.6998i		−	0.553329i	0.960967	−	0.276665i	$-0.0892291\pi$
$614$	13.0526	+	13.0526i	0.526761	+	0.526761i
$615$		0			0
$616$		−	28.6126i		−	1.15283i
$617$	7.11117	−	2.94554i	0.286285	−	0.118583i	−0.234920	−	0.972015i	$-0.575483\pi$
$617$	7.11117	−	2.94554i	0.286285	−	0.118583i	0.521205	+	0.853432i	$0.325483\pi$
$618$	−0.982707	+	2.37247i	−0.0395303	+	0.0954345i
$619$	16.5857	−	40.0413i	0.666634	−	1.60940i	−0.120570	−	0.992705i	$-0.538472\pi$
$619$	16.5857	−	40.0413i	0.666634	−	1.60940i	0.787204	−	0.616692i	$-0.211528\pi$
$620$		0			0
$621$	−0.963054	+	0.963054i	−0.0386460	+	0.0386460i
$622$	30.2465	+	12.5285i	1.21277	+	0.502347i
$623$	9.39517	−	22.6819i	0.376409	−	0.908733i
$624$	−0.205240	−	0.495494i	−0.00821618	−	0.0198356i
$625$		0			0
$626$	41.9342	−	17.3697i	1.67603	−	0.694233i
$627$	1.28434	−	1.28434i	0.0512915	−	0.0512915i
$628$		−	1.48161i		−	0.0591227i
$629$	17.0114	−	19.6804i	0.678288	−	0.784711i
$630$		0			0
$631$	0.518808	+	0.518808i	0.0206534	+	0.0206534i	0.717358	−	0.696705i	$-0.245351\pi$
$631$	0.518808	+	0.518808i	0.0206534	+	0.0206534i	−0.696705	+	0.717358i	$0.745351\pi$
$632$	−4.31465	−	10.4165i	−0.171628	−	0.414346i
$633$	−1.33499			−0.0530609
$634$	13.5103	+	32.6166i	0.536561	+	1.29537i
$635$		0			0
$636$	0.0208675	−	0.0503785i	0.000827449	−	0.00199764i
$637$	3.59657	+	3.59657i	0.142501	+	0.142501i
$638$	−29.6784	−	29.6784i	−1.17498	−	1.17498i
$639$	−15.4103	+	37.2036i	−0.609620	+	1.47175i
$640$		0			0
$641$	10.7822	+	26.0306i	0.425872	+	1.02815i	0.980583	+	0.196103i	$0.0628287\pi$
$641$	10.7822	+	26.0306i	0.425872	+	1.02815i	−0.554711	+	0.832043i	$0.687171\pi$
$642$	−1.40103			−0.0552941
$643$	3.62487	+	8.75122i	0.142951	+	0.345114i	0.979097	−	0.203392i	$-0.0651966\pi$
$643$	3.62487	+	8.75122i	0.142951	+	0.345114i	−0.836146	+	0.548506i	$0.815197\pi$
$644$	−0.170005	−	0.170005i	−0.00669913	−	0.00669913i
$645$		0			0
$646$	7.26488	+	14.4694i	0.285833	+	0.569292i
$647$			24.3690i			0.958044i	0.877803	+	0.479022i	$0.159009\pi$
$647$			24.3690i			0.958044i	−0.877803	+	0.479022i	$0.840991\pi$
$648$	−18.0696	+	18.0696i	−0.709840	+	0.709840i
$649$	11.6961	−	4.84470i	0.459114	−	0.190171i
$650$		0			0
$651$	−0.208289	−	0.502853i	−0.00816347	−	0.0197084i
$652$	−0.0346448	+	0.0836399i	−0.00135679	+	0.00327559i
$653$	−4.66127	−	1.93076i	−0.182410	−	0.0755565i	0.289609	−	0.957145i	$-0.406475\pi$
$653$	−4.66127	−	1.93076i	−0.182410	−	0.0755565i	−0.472019	+	0.881588i	$0.656475\pi$
$654$	0.0810032	−	0.0810032i	0.00316748	−	0.00316748i
$655$		0			0
$656$	−13.9568	+	33.6947i	−0.544922	+	1.31556i
$657$	6.67436	−	16.1133i	0.260392	−	0.628641i
$658$	−16.8222	+	6.96796i	−0.655796	+	0.271640i
$659$		−	8.17372i		−	0.318403i	−0.987246	−	0.159201i	$-0.949108\pi$
$659$		−	8.17372i		−	0.318403i	0.987246	−	0.159201i	$-0.0508919\pi$
$660$		0			0
$661$	21.6693	+	21.6693i	0.842839	+	0.842839i	0.989227	−	0.146388i	$-0.0467649\pi$
$661$	21.6693	+	21.6693i	0.842839	+	0.842839i	−0.146388	+	0.989227i	$0.546765\pi$
$662$			25.6264i			0.995998i
$663$	0.374743	−	0.433540i	0.0145538	−	0.0168373i
$664$	−25.6102			−0.993869
$665$		0			0
$666$	24.2049	−	10.0260i	0.937923	−	0.388500i
$667$	−10.6847			−0.413714
$668$	1.57623	−	0.652895i	0.0609861	−	0.0252613i
$669$	−1.81948	−	0.753655i	−0.0703453	−	0.0291380i
$670$		0			0
$671$	23.5363	−	23.5363i	0.908609	−	0.908609i
$672$	0.0519053	+	0.0519053i	0.00200229	+	0.00200229i
$673$	6.11439	+	2.53266i	0.235692	+	0.0976270i	0.497404	−	0.867519i	$-0.334287\pi$
$673$	6.11439	+	2.53266i	0.235692	+	0.0976270i	−0.261711	+	0.965146i	$0.584287\pi$
$674$	8.48430	+	3.51431i	0.326803	+	0.135366i
$675$		0			0
$676$		−	0.780116i		−	0.0300045i
$677$	15.7961	+	38.1352i	0.607094	+	1.46565i	0.866146	+	0.499791i	$0.166590\pi$
$677$	15.7961	+	38.1352i	0.607094	+	1.46565i	−0.259052	+	0.965863i	$0.583410\pi$
$678$	0.984263	−	0.984263i	0.0378004	−	0.0378004i
$679$	14.5739			0.559296
$680$		0			0
$681$	1.23825			0.0474498
$682$	16.3173	−	16.3173i	0.624821	−	0.624821i
$683$	5.06249	+	12.2219i	0.193711	+	0.467659i	0.990655	−	0.136394i	$-0.0435513\pi$
$683$	5.06249	+	12.2219i	0.193711	+	0.467659i	−0.796944	+	0.604054i	$0.793551\pi$
$684$		−	0.576275i		−	0.0220344i
$685$		0			0
$686$	24.3593	+	10.0900i	0.930043	+	0.385236i
$687$	−2.18561	−	0.905310i	−0.0833862	−	0.0345397i
$688$	20.2835	+	20.2835i	0.773302	+	0.773302i
$689$	6.39139	−	6.39139i	0.243492	−	0.243492i
$690$		0			0
$691$	−31.9758	−	13.2448i	−1.21642	−	0.503856i	−0.320147	−	0.947368i	$-0.603732\pi$
$691$	−31.9758	−	13.2448i	−1.21642	−	0.503856i	−0.896269	+	0.443512i	$0.853732\pi$
$692$	−1.00665	+	0.416966i	−0.0382669	+	0.0158507i
$693$	29.7383			1.12966
$694$	−12.3465	+	5.11407i	−0.468665	+	0.194127i
$695$		0			0
$696$	1.65848			0.0628645
$697$	−38.8662	+	2.82724i	−1.47216	+	0.107089i
$698$			0.956299i			0.0361965i
$699$	0.650860	+	0.650860i	0.0246178	+	0.0246178i
$700$		0			0
$701$			15.6045i			0.589373i	0.955594	+	0.294687i	$0.0952152\pi$
$701$			15.6045i			0.589373i	−0.955594	+	0.294687i	$0.904785\pi$
$702$	1.06861	−	0.442634i	0.0403322	−	0.0167061i
$703$	−6.82160	+	16.4688i	−0.257282	+	0.621133i
$704$	−18.3231	+	44.2358i	−0.690576	+	1.66720i
$705$		0			0
$706$	15.0945	−	15.0945i	0.568091	−	0.568091i
$707$	4.02393	+	1.66677i	0.151335	+	0.0626852i
$708$	−0.00631879	+	0.0152549i	−0.000237475	+	0.000573314i
$709$	−17.9860	−	43.4221i	−0.675480	−	1.63075i	−0.772153	−	0.635437i	$-0.780820\pi$
$709$	−17.9860	−	43.4221i	−0.675480	−	1.63075i	0.0966730	−	0.995316i	$-0.469180\pi$
$710$		0			0
$711$	10.8263	−	4.48441i	0.406019	−	0.168179i
$712$	−29.0831	+	29.0831i	−1.08994	+	1.08994i
$713$		−	5.87449i		−	0.220001i
$714$	0.342882	−	1.03439i	0.0128320	−	0.0387111i
$715$		0			0
$716$	−0.721916	−	0.721916i	−0.0269793	−	0.0269793i
$717$	0.145206	+	0.350559i	0.00542283	+	0.0130919i
$718$	−35.5170			−1.32548
$719$	−14.5015	−	35.0097i	−0.540815	−	1.30564i	−0.924149	−	0.382033i	$-0.875224\pi$
$719$	−14.5015	−	35.0097i	−0.540815	−	1.30564i	0.383334	−	0.923610i	$-0.374776\pi$
$720$		0			0
$721$	10.9472	−	26.4289i	0.407696	−	0.984264i
$722$	10.8278	+	10.8278i	0.402968	+	0.402968i
$723$	−0.497481	−	0.497481i	−0.0185015	−	0.0185015i
$724$	−0.639862	+	1.54476i	−0.0237803	+	0.0574106i
$725$		0			0
$726$	−1.33507	−	3.22314i	−0.0495490	−	0.119622i
$727$	−20.6445			−0.765664			−0.382832	−	0.923818i	$-0.625051\pi$
$727$	−20.6445			−0.765664			−0.382832	+	0.923818i	$0.625051\pi$
$728$	2.36724	+	5.71503i	0.0877359	+	0.211813i
$729$	−18.6245	−	18.6245i	−0.689797	−	0.689797i
$730$		0			0
$731$	−9.64390	+	29.0932i	−0.356693	+	1.07605i
$732$			0.0434131i			0.00160459i
$733$	24.3066	−	24.3066i	0.897786	−	0.897786i	−0.0974544	−	0.995240i	$-0.531070\pi$
$733$	24.3066	−	24.3066i	0.897786	−	0.897786i	0.995240	+	0.0974544i	$0.0310700\pi$
$734$	1.48594	−	0.615494i	0.0548469	−	0.0227183i
$735$		0			0
$736$	0.303187	+	0.731957i	0.0111756	+	0.0269803i
$737$	5.47553	−	13.2191i	0.201694	−	0.486932i
$738$	−36.2595	−	15.0192i	−1.33473	−	0.552864i
$739$	12.3512	−	12.3512i	0.454347	−	0.454347i	−0.442448	−	0.896794i	$-0.645890\pi$
$739$	12.3512	−	12.3512i	0.454347	−	0.454347i	0.896794	+	0.442448i	$0.145890\pi$
$740$		0			0
$741$	−0.150273	+	0.362791i	−0.00552041	+	0.0133275i
$742$	6.57775	−	15.8801i	0.241477	−	0.582977i
$743$	−17.0027	+	7.04274i	−0.623768	+	0.258373i	−0.672102	−	0.740458i	$-0.734609\pi$
$743$	−17.0027	+	7.04274i	−0.623768	+	0.258373i	0.0483348	+	0.998831i	$0.484609\pi$
$744$			0.911837i			0.0334296i
$745$		0			0
$746$	−14.8857	−	14.8857i	−0.545003	−	0.545003i
$747$		−	26.6178i		−	0.973895i
$748$	−1.62849	+	0.118461i	−0.0595435	+	0.00433136i
$749$	15.6072			0.570276
$750$		0			0
$751$	2.79602	−	1.15815i	0.102028	−	0.0422615i	−0.331085	−	0.943601i	$-0.607415\pi$
$751$	2.79602	−	1.15815i	0.102028	−	0.0422615i	0.433114	+	0.901339i	$0.357415\pi$
$752$	29.4616			1.07436
$753$	0.518401	−	0.214729i	0.0188916	−	0.00782515i
$754$	8.38335	+	3.47250i	0.305304	+	0.126461i
$755$		0			0
$756$	−0.0549654	+	0.0549654i	−0.00199907	+	0.00199907i
$757$	−8.25327	−	8.25327i	−0.299970	−	0.299970i	0.541032	−	0.841002i	$-0.318034\pi$
$757$	−8.25327	−	8.25327i	−0.299970	−	0.299970i	−0.841002	+	0.541032i	$0.818034\pi$
$758$	20.0831	+	8.31870i	0.729452	+	0.302149i
$759$	−1.21901	−	0.504931i	−0.0442473	−	0.0183278i
$760$		0			0
$761$			1.13354i			0.0410908i	0.999789	+	0.0205454i	$0.00654027\pi$
$761$			1.13354i			0.0410908i	−0.999789	+	0.0205454i	$0.993460\pi$
$762$	0.854676	+	2.06337i	0.0309616	+	0.0747480i
$763$	−0.902364	+	0.902364i	−0.0326678	+	0.0326678i
$764$	0.0173849			0.000628964
$765$		0			0
$766$	−6.42526			−0.232154
$767$	−1.93535	+	1.93535i	−0.0698813	+	0.0698813i
$768$	−0.0694054	−	0.167560i	−0.00250445	−	0.00604628i
$769$		−	14.6207i		−	0.527235i	−0.964627	−	0.263617i	$-0.915084\pi$
$769$		−	14.6207i		−	0.527235i	0.964627	−	0.263617i	$-0.0849156\pi$
$770$		0			0
$771$	−1.82526	−	0.756045i	−0.0657350	−	0.0272283i
$772$	−0.187260	−	0.0775658i	−0.00673965	−	0.00279165i
$773$	17.5891	+	17.5891i	0.632636	+	0.632636i	0.948729	−	0.316092i	$-0.102371\pi$
$773$	17.5891	+	17.5891i	0.632636	+	0.632636i	−0.316092	+	0.948729i	$0.602371\pi$
$774$	−21.8275	+	21.8275i	−0.784572	+	0.784572i
$775$		0			0
$776$	−22.5571	−	9.34346i	−0.809753	−	0.335411i
$777$	1.10845	−	0.459134i	0.0397654	−	0.0164714i
$778$	8.80946			0.315834
$779$	24.6706	−	10.2189i	0.883917	−	0.366130i
$780$		0			0
$781$	−78.1841			−2.79765
$782$	7.69140	−	8.89818i	0.275044	−	0.318198i
$783$			3.45455i			0.123456i
$784$	−11.0664	−	11.0664i	−0.395229	−	0.395229i
$785$		0			0
$786$			2.59514i			0.0925656i
$787$	21.7614	−	9.01386i	0.775709	−	0.321309i	0.0405267	−	0.999178i	$-0.487096\pi$
$787$	21.7614	−	9.01386i	0.775709	−	0.321309i	0.735183	+	0.677869i	$0.237096\pi$
$788$	−0.158871	+	0.383549i	−0.00565955	+	0.0136634i
$789$	0.386267	−	0.932530i	0.0137515	−	0.0331989i
$790$		0			0
$791$	−10.9645	+	10.9645i	−0.389854	+	0.389854i
$792$	−46.0281	−	19.0655i	−1.63554	−	0.677462i
$793$	−2.75385	+	6.64837i	−0.0977920	+	0.236091i
$794$	1.72623	+	4.16749i	0.0612617	+	0.147899i
$795$		0			0
$796$	0.792381	−	0.328215i	0.0280852	−	0.0116333i
$797$	22.4878	−	22.4878i	0.796558	−	0.796558i	−0.185993	−	0.982551i	$-0.559550\pi$
$797$	22.4878	−	22.4878i	0.796558	−	0.796558i	0.982551	+	0.185993i	$0.0595503\pi$
$798$			0.746739i			0.0264343i
$799$	14.1250	+	28.1327i	0.499706	+	0.995262i
$800$		0			0
$801$	−30.2274	−	30.2274i	−1.06803	−	1.06803i
$802$	6.64570	+	16.0441i	0.234668	+	0.566538i
$803$	33.8624			1.19498
$804$	0.00714156	+	0.0172413i	0.000251863	+	0.000608052i
$805$		0			0
$806$	−1.90919	+	4.60919i	−0.0672483	+	0.162352i
$807$	1.00027	+	1.00027i	0.0352110	+	0.0352110i
$808$	−5.15954	−	5.15954i	−0.181512	−	0.181512i
$809$	−6.40172	+	15.4551i	−0.225072	+	0.543373i	−0.995565	−	0.0940762i	$-0.970010\pi$
$809$	−6.40172	+	15.4551i	−0.225072	+	0.543373i	0.770493	+	0.637449i	$0.220010\pi$
$810$		0			0
$811$	19.0514	+	45.9940i	0.668983	+	1.61507i	0.783314	+	0.621626i	$0.213528\pi$
$811$	19.0514	+	45.9940i	0.668983	+	1.61507i	−0.114331	+	0.993443i	$0.536472\pi$
$812$	−0.609820			−0.0214005
$813$	0.696076	+	1.68048i	0.0244125	+	0.0589369i
$814$	35.9685	+	35.9685i	1.26069	+	1.26069i
$815$		0			0
$816$	−1.15306	+	1.33397i	−0.0403652	+	0.0466984i
$817$		−	21.0028i		−	0.734794i
$818$	11.5061	−	11.5061i	0.402300	−	0.402300i
$819$	−5.93988	+	2.46038i	−0.207556	+	0.0859727i
$820$		0			0
$821$	−6.13317	−	14.8068i	−0.214049	−	0.516760i	0.779989	−	0.625793i	$-0.215225\pi$
$821$	−6.13317	−	14.8068i	−0.214049	−	0.516760i	−0.994038	+	0.109033i	$0.965225\pi$
$822$	1.19236	−	2.87862i	0.0415885	−	0.100403i
$823$	29.6365	+	12.2758i	1.03306	+	0.427909i	0.833817	−	0.552040i	$-0.186151\pi$
$823$	29.6365	+	12.2758i	1.03306	+	0.427909i	0.199247	+	0.979949i	$0.436151\pi$
$824$	−33.8876	+	33.8876i	−1.18053	+	1.18053i
$825$		0			0
$826$	−1.99178	+	4.80858i	−0.0693028	+	0.167312i
$827$	−1.46488	+	3.53653i	−0.0509389	+	0.122977i	−0.947301	−	0.320346i	$-0.896201\pi$
$827$	−1.46488	+	3.53653i	−0.0509389	+	0.122977i	0.896362	+	0.443324i	$0.146201\pi$
$828$	−0.386761	+	0.160202i	−0.0134409	+	0.00556739i
$829$			4.09989i			0.142395i	0.997462	+	0.0711976i	$0.0226821\pi$
$829$			4.09989i			0.142395i	−0.997462	+	0.0711976i	$0.977318\pi$
$830$		0			0
$831$	−1.44542	−	1.44542i	−0.0501410	−	0.0501410i
$832$		−	10.3515i		−	0.358875i
$833$	5.26158	−	15.8729i	0.182303	−	0.549962i
$834$	−0.655705			−0.0227052
$835$		0			0
$836$	1.03370	−	0.428171i	0.0357511	−	0.0148086i
$837$	−1.89932			−0.0656501
$838$	0.699221	−	0.289627i	0.0241542	−	0.0100050i
$839$	−43.0380	−	17.8269i	−1.48584	−	0.615453i	−0.515430	−	0.856932i	$-0.672368\pi$
$839$	−43.0380	−	17.8269i	−1.48584	−	0.615453i	−0.970406	+	0.241479i	$0.922368\pi$
$840$		0			0
$841$	1.34265	−	1.34265i	0.0462982	−	0.0462982i
$842$	−23.8912	−	23.8912i	−0.823345	−	0.823345i
$843$	1.91941	+	0.795045i	0.0661080	+	0.0273828i
$844$	−0.759758	−	0.314702i	−0.0261519	−	0.0108325i
$845$		0			0
$846$			31.7042i			1.09001i
$847$	14.8724	+	35.9053i	0.511023	+	1.23372i
$848$	−19.6659	+	19.6659i	−0.675329	+	0.675329i
$849$	2.19324			0.0752717
$850$		0			0
$851$	12.9492			0.443894
$852$	0.0721058	−	0.0721058i	0.00247030	−	0.00247030i
$853$	13.5400	+	32.6885i	0.463602	+	1.11923i	0.966908	+	0.255125i	$0.0821168\pi$
$853$	13.5400	+	32.6885i	0.463602	+	1.11923i	−0.503306	+	0.864108i	$0.667883\pi$
$854$			13.6845i			0.468273i
$855$		0			0
$856$	−24.1564	−	10.0059i	−0.825650	−	0.341995i
$857$	8.51086	+	3.52531i	0.290725	+	0.120422i	0.523280	−	0.852161i	$-0.324708\pi$
$857$	8.51086	+	3.52531i	0.290725	+	0.120422i	−0.232554	+	0.972583i	$0.574708\pi$
$858$	0.792349	+	0.792349i	0.0270503	+	0.0270503i
$859$	11.8621	−	11.8621i	0.404730	−	0.404730i	−0.475166	−	0.879896i	$-0.657612\pi$
$859$	11.8621	−	11.8621i	0.404730	−	0.404730i	0.879896	+	0.475166i	$0.157612\pi$
$860$		0			0
$861$	−1.66048	−	0.687793i	−0.0565890	−	0.0234399i
$862$	5.45016	−	2.25753i	0.185633	−	0.0768918i
$863$	−34.1729			−1.16326			−0.581630	−	0.813454i	$-0.697585\pi$
$863$	−34.1729			−1.16326			−0.581630	+	0.813454i	$0.697585\pi$
$864$	0.236654	−	0.0980254i	0.00805114	−	0.00333489i
$865$		0			0
$866$	35.7254			1.21400
$867$	−1.82662	−	0.461492i	−0.0620353	−	0.0156731i
$868$		−	0.335281i		−	0.0113802i
$869$	16.0879	+	16.0879i	0.545744	+	0.545744i
$870$		0			0
$871$			3.09338i			0.104815i
$872$	1.97517	−	0.818141i	0.0668876	−	0.0277057i
$873$	9.71107	−	23.4446i	0.328670	−	0.793479i
$874$	−3.08427	+	7.44609i	−0.104327	+	0.251868i
$875$		0			0
$876$	−0.0312299	+	0.0312299i	−0.00105516	+	0.00105516i
$877$	−12.1834	−	5.04652i	−0.411404	−	0.170409i	0.167376	−	0.985893i	$-0.446471\pi$
$877$	−12.1834	−	5.04652i	−0.411404	−	0.170409i	−0.578779	+	0.815484i	$0.696471\pi$
$878$	1.64888	−	3.98075i	0.0556470	−	0.134344i
$879$	0.593968	+	1.43396i	0.0200340	+	0.0483664i
$880$		0			0
$881$	−29.5578	+	12.2433i	−0.995829	+	0.412486i	−0.820266	−	0.571982i	$-0.806175\pi$
$881$	−29.5578	+	12.2433i	−0.995829	+	0.412486i	−0.175563	+	0.984468i	$0.556175\pi$
$882$	11.9088	−	11.9088i	0.400989	−	0.400989i
$883$			48.1807i			1.62141i	0.585456	+	0.810704i	$0.300915\pi$
$883$			48.1807i			1.62141i	−0.585456	+	0.810704i	$0.699085\pi$
$884$	0.315472	−	0.158393i	0.0106105	−	0.00532735i
$885$		0			0
$886$	−25.8611	−	25.8611i	−0.868819	−	0.868819i
$887$	15.6909	+	37.8812i	0.526850	+	1.27193i	0.933577	+	0.358378i	$0.116670\pi$
$887$	15.6909	+	37.8812i	0.526850	+	1.27193i	−0.406727	+	0.913550i	$0.633330\pi$
$888$	−2.00998			−0.0674505
$889$	−9.52097	−	22.9856i	−0.319323	−	0.770914i
$890$		0			0
$891$	19.7338	−	47.6416i	0.661106	−	1.59605i
$892$	−0.857830	−	0.857830i	−0.0287223	−	0.0287223i
$893$	−15.2532	−	15.2532i	−0.510428	−	0.510428i
$894$	−0.255017	+	0.615665i	−0.00852904	+	0.0205909i
$895$		0			0
$896$	−7.02613	−	16.9626i	−0.234726	−	0.566680i
$897$	0.285259			0.00952450
$898$	−7.82140	−	18.8825i	−0.261003	−	0.630118i
$899$	−10.5361	−	10.5361i	−0.351399	−	0.351399i
$900$		0			0
$901$	−28.2073	−	9.35024i	−0.939722	−	0.311502i
$902$		−	76.2000i		−	2.53718i
$903$	−0.999574	+	0.999574i	−0.0332637	+	0.0332637i
$904$	24.0001	−	9.94116i	0.798231	−	0.330638i
$905$		0			0
$906$	1.18251	+	2.85483i	0.0392862	+	0.0948453i
$907$	−21.2985	+	51.4191i	−0.707205	+	1.70734i	−0.000335808		1.00000i	$0.500107\pi$
$907$	−21.2985	+	51.4191i	−0.707205	+	1.70734i	−0.706869	+	0.707344i	$0.749893\pi$
$908$	0.704704	+	0.291898i	0.0233864	+	0.00968698i
$909$	5.36254	−	5.36254i	0.177864	−	0.177864i
$910$		0			0
$911$	5.61087	−	13.5458i	0.185897	−	0.448794i	−0.803266	−	0.595621i	$-0.796906\pi$
$911$	5.61087	−	13.5458i	0.185897	−	0.448794i	0.989162	+	0.146827i	$0.0469061\pi$
$912$	0.462380	−	1.11628i	0.0153109	−	0.0369638i
$913$	47.7459	−	19.7770i	1.58016	−	0.654523i
$914$			14.7080i			0.486496i
$915$		0			0
$916$	−1.03045	−	1.03045i	−0.0340469	−	0.0340469i
$917$		−	28.9095i		−	0.954675i
$918$	−2.87693	−	2.48676i	−0.0949529	−	0.0820754i
$919$	−1.54175			−0.0508578			−0.0254289	−	0.999677i	$-0.508095\pi$
$919$	−1.54175			−0.0508578			−0.0254289	+	0.999677i	$0.508095\pi$
$920$		0			0
$921$	1.35985	−	0.563267i	0.0448085	−	0.0185603i
$922$	25.7196			0.847031
$923$	15.6164	−	6.46851i	0.514019	−	0.212914i
$924$	−0.0695739	−	0.0288185i	−0.00228881	−	0.000948058i
$925$		0			0
$926$	−37.0892	+	37.0892i	−1.21883	+	1.21883i
$927$	−35.2209	−	35.2209i	−1.15680	−	1.15680i
$928$	1.85657	+	0.769017i	0.0609449	+	0.0252442i
$929$	12.5602	+	5.20262i	0.412088	+	0.170692i	0.579089	−	0.815264i	$-0.303408\pi$
$929$	12.5602	+	5.20262i	0.412088	+	0.170692i	−0.167001	+	0.985957i	$0.553408\pi$
$930$		0			0
$931$			11.4588i			0.375548i
$932$	0.216983	+	0.523843i	0.00710751	+	0.0171591i
$933$	1.84589	−	1.84589i	0.0604319	−	0.0604319i
$934$	42.0279			1.37520
$935$		0			0
$936$	10.7710			0.352060
$937$	11.1059	−	11.1059i	0.362815	−	0.362815i	−0.502033	−	0.864848i	$-0.667414\pi$
$937$	11.1059	−	11.1059i	0.362815	−	0.362815i	0.864848	+	0.502033i	$0.167414\pi$
$938$	2.25113	+	5.43471i	0.0735020	+	0.177450i
$939$		−	3.61922i		−	0.118109i
$940$		0			0
$941$	−39.9824	−	16.5613i	−1.30339	−	0.539882i	−0.380441	−	0.924805i	$-0.624228\pi$
$941$	−39.9824	−	16.5613i	−1.30339	−	0.539882i	−0.922948	+	0.384924i	$0.874228\pi$
$942$	3.08844	+	1.27928i	0.100627	+	0.0416810i
$943$	−13.7166	−	13.7166i	−0.446675	−	0.446675i
$944$	5.95493	−	5.95493i	0.193817	−	0.193817i
$945$		0			0
$946$	−55.3710	−	22.9354i	−1.80027	−	0.745694i
$947$	18.9459	−	7.84765i	0.615659	−	0.255014i	−0.0529869	−	0.998595i	$-0.516874\pi$
$947$	18.9459	−	7.84765i	0.615659	−	0.255014i	0.668646	+	0.743581i	$0.266874\pi$
$948$	−0.0296743			−0.000963777
$949$	−6.76363	+	2.80159i	−0.219557	+	0.0909434i
$950$		0			0
$951$	2.81505			0.0912843
$952$	13.2994	−	15.3861i	0.431037	−	0.498666i
$953$		−	5.27570i		−	0.170897i	−0.996343	−	0.0854483i	$-0.972768\pi$
$953$		−	5.27570i		−	0.170897i	0.996343	−	0.0854483i	$-0.0272322\pi$
$954$	−21.1628	−	21.1628i	−0.685172	−	0.685172i
$955$		0			0
$956$			0.233738i			0.00755963i
$957$	−3.09196	+	1.28073i	−0.0999487	+	0.0414001i
$958$	14.3381	−	34.6153i	0.463243	−	1.11837i
$959$	−13.2828	+	32.0674i	−0.428923	+	1.03551i
$960$		0			0
$961$	−16.1275	+	16.1275i	−0.520243	+	0.520243i
$962$	−10.1601	−	4.20846i	−0.327575	−	0.135686i
$963$	10.3996	−	25.1068i	0.335122	−	0.809057i
$964$	−0.165849	−	0.400396i	−0.00534165	−	0.0128959i
$965$		0			0
$966$	0.501166	−	0.207590i	0.0161248	−	0.00667909i
$967$	−4.17382	+	4.17382i	−0.134221	+	0.134221i	−0.771025	−	0.636804i	$-0.780256\pi$
$967$	−4.17382	+	4.17382i	−0.134221	+	0.134221i	0.636804	+	0.771025i	$0.280256\pi$
$968$		−	65.1080i		−	2.09265i
$969$	1.28761	−	0.0936646i	0.0413641	−	0.00300894i
$970$		0			0
$971$	1.27662	+	1.27662i	0.0409687	+	0.0409687i	0.727294	−	0.686326i	$-0.240778\pi$
$971$	1.27662	+	1.27662i	0.0409687	+	0.0409687i	−0.686326	+	0.727294i	$0.740778\pi$
$972$	0.0777469	+	0.187698i	0.00249373	+	0.00602041i
$973$	7.30446			0.234170
$974$	2.03838	+	4.92109i	0.0653140	+	0.157682i
$975$		0			0
$976$	8.47341	−	20.4566i	0.271227	−	0.654800i
$977$	6.89768	+	6.89768i	0.220676	+	0.220676i	0.808783	−	0.588107i	$-0.200127\pi$
$977$	6.89768	+	6.89768i	0.220676	+	0.220676i	−0.588107	+	0.808783i	$0.700127\pi$
$978$	−0.144435	−	0.144435i	−0.00461853	−	0.00461853i
$979$	31.7617	−	76.6795i	1.01511	−	2.45069i
$980$		0			0
$981$	0.850330	+	2.05288i	0.0271489	+	0.0655433i
$982$	8.20202			0.261737
$983$	−1.53797	−	3.71298i	−0.0490535	−	0.118426i	0.897453	−	0.441110i	$-0.145415\pi$
$983$	−1.53797	−	3.71298i	−0.0490535	−	0.118426i	−0.946507	+	0.322684i	$0.895415\pi$
$984$	2.12909	+	2.12909i	0.0678731	+	0.0678731i
$985$		0			0
$986$	−2.16440	−	29.7541i	−0.0689284	−	0.947562i
$987$			1.45187i			0.0462136i
$988$	−0.171045	+	0.171045i	−0.00544165	+	0.00544165i
$989$	−14.0958	+	5.83867i	−0.448220	+	0.185659i
$990$		0			0
$991$	−5.31652	−	12.8352i	−0.168885	−	0.407724i	0.816665	−	0.577113i	$-0.195821\pi$
$991$	−5.31652	−	12.8352i	−0.168885	−	0.407724i	−0.985549	+	0.169389i	$0.945821\pi$
$992$	−0.422808	+	1.02075i	−0.0134242	+	0.0324088i
$993$	1.88784	+	0.781969i	0.0599088	+	0.0248150i
$994$	22.7289	−	22.7289i	0.720915	−	0.720915i
$995$		0			0
$996$	−0.0257945	+	0.0622734i	−0.000817330	+	0.00197321i
$997$	−6.14934	+	14.8458i	−0.194751	+	0.470172i	−0.990845	−	0.135001i	$-0.956896\pi$
$997$	−6.14934	+	14.8458i	−0.194751	+	0.470172i	0.796094	+	0.605173i	$0.206896\pi$
$998$	−56.6155	+	23.4509i	−1.79213	+	0.742325i
$999$		−	4.18671i		−	0.132462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.d.274.3		24
5.2	odd	4		425.2.m.c.376.3	yes	24
5.3	odd	4		425.2.m.d.376.4	yes	24
5.4	even	2		425.2.n.e.274.4		24
17.9	even	8		425.2.n.e.349.4		24
85.3	even	16		7225.2.a.cb.1.17		24
85.9	even	8	inner	425.2.n.d.349.3		24
85.37	even	16		7225.2.a.bx.1.8		24
85.43	odd	8		425.2.m.d.26.4	yes	24
85.48	even	16		7225.2.a.cb.1.18		24
85.77	odd	8		425.2.m.c.26.3	✓	24
85.82	even	16		7225.2.a.bx.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.3	✓	24	85.77	odd	8
425.2.m.c.376.3	yes	24	5.2	odd	4
425.2.m.d.26.4	yes	24	85.43	odd	8
425.2.m.d.376.4	yes	24	5.3	odd	4
425.2.n.d.274.3		24	1.1	even	1	trivial
425.2.n.d.349.3		24	85.9	even	8	inner
425.2.n.e.274.4		24	5.4	even	2
425.2.n.e.349.4		24	17.9	even	8
7225.2.a.bx.1.7		24	85.82	even	16
7225.2.a.bx.1.8		24	85.37	even	16
7225.2.a.cb.1.17		24	85.3	even	16
7225.2.a.cb.1.18		24	85.48	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.982785 + 0.982785i) q^{2} +(0.0424107 + 0.102388i) q^{3} +0.0682683i q^{4} +(-0.142306 - 0.0589452i) q^{6} +(1.58527 + 0.656642i) q^{7} +(-2.03266 - 2.03266i) q^{8} +(2.11264 - 2.11264i) q^{9} +(5.35924 + 2.21987i) q^{11} +(-0.00698988 + 0.00289530i) q^{12} -1.25411 q^{13} +(-2.20332 + 0.912645i) q^{14} +3.85880 q^{16} +(1.85005 + 3.68474i) q^{17} +4.15253i q^{18} +(-1.99782 - 1.99782i) q^{19} +0.190162i q^{21} +(-7.44863 + 3.08532i) q^{22} +(-0.785431 + 1.89620i) q^{23} +(0.121915 - 0.294328i) q^{24} +(1.23252 - 1.23252i) q^{26} +(0.613073 + 0.253943i) q^{27} +(-0.0448278 + 0.108224i) q^{28} +(1.99220 + 4.80961i) q^{29} +(-2.64434 + 1.09532i) q^{31} +(0.272952 - 0.272952i) q^{32} +0.642871i q^{33} +(-5.43951 - 1.80310i) q^{34} +(0.144226 + 0.144226i) q^{36} +(-2.41443 - 5.82896i) q^{37} +3.92685 q^{38} +(-0.0531875 - 0.128406i) q^{39} +(-3.61688 + 8.73191i) q^{41} +(-0.186889 - 0.186889i) q^{42} +(5.25643 + 5.25643i) q^{43} +(-0.151547 + 0.365866i) q^{44} +(-1.09165 - 2.63546i) q^{46} +7.63491 q^{47} +(0.163655 + 0.395097i) q^{48} +(-2.86784 - 2.86784i) q^{49} +(-0.298813 + 0.345696i) q^{51} -0.0856157i q^{52} +(-5.09637 + 5.09637i) q^{53} +(-0.852091 + 0.352948i) q^{54} +(-1.88759 - 4.55706i) q^{56} +(0.119825 - 0.289282i) q^{57} +(-6.68472 - 2.76890i) q^{58} +(1.54321 - 1.54321i) q^{59} +(2.19586 - 5.30128i) q^{61} +(1.52235 - 3.67528i) q^{62} +(4.73635 - 1.96186i) q^{63} +8.25411i q^{64} +(-0.631803 - 0.631803i) q^{66} -2.46660i q^{67} +(-0.251551 + 0.126300i) q^{68} -0.227460 q^{69} +(-12.4522 + 5.15787i) q^{71} -8.58855 q^{72} +(5.39319 - 2.23393i) q^{73} +(8.10148 + 3.35574i) q^{74} +(0.136388 - 0.136388i) q^{76} +(7.03820 + 7.03820i) q^{77} +(0.178467 + 0.0739236i) q^{78} +(3.62361 + 1.50095i) q^{79} -8.88961i q^{81} +(-5.02698 - 12.1362i) q^{82} +(6.29967 - 6.29967i) q^{83} -0.0129821 q^{84} -10.3319 q^{86} +(-0.407958 + 0.407958i) q^{87} +(-6.38128 - 15.4058i) q^{88} -14.3079i q^{89} +(-1.98810 - 0.823498i) q^{91} +(-0.129450 - 0.0536200i) q^{92} +(-0.224296 - 0.224296i) q^{93} +(-7.50348 + 7.50348i) q^{94} +(0.0395233 + 0.0163711i) q^{96} +(7.84699 - 3.25033i) q^{97} +5.63693 q^{98} +(16.0119 - 6.63234i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} + 20 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} - 12 q^{22} - 8 q^{23} - 16 q^{24} + 16 q^{26} - 16 q^{27} - 20 q^{28} - 4 q^{29} + 24 q^{31} - 60 q^{32}+ \cdots + 80 q^{99}+O(q^{100}) \) 24 * q - 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 + 20 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 - 12 * q^22 - 8 * q^23 - 16 * q^24 + 16 * q^26 - 16 * q^27 - 20 * q^28 - 4 * q^29 + 24 * q^31 - 60 * q^32 - 16 * q^34 + 60 * q^36 + 16 * q^37 + 48 * q^38 - 8 * q^39 - 20 * q^41 - 12 * q^42 + 32 * q^43 - 64 * q^44 - 40 * q^46 + 88 * q^47 - 4 * q^48 - 24 * q^49 + 16 * q^51 + 12 * q^53 + 20 * q^54 - 32 * q^56 + 56 * q^57 + 28 * q^58 + 16 * q^59 - 64 * q^61 - 16 * q^62 + 40 * q^63 - 72 * q^66 - 48 * q^68 + 48 * q^69 - 24 * q^71 - 120 * q^72 - 20 * q^73 - 32 * q^74 + 52 * q^76 - 24 * q^77 + 100 * q^78 + 48 * q^79 - 8 * q^82 - 12 * q^83 + 40 * q^84 - 16 * q^86 + 24 * q^87 - 80 * q^88 + 24 * q^91 + 56 * q^92 - 32 * q^93 + 40 * q^94 + 132 * q^96 + 24 * q^97 - 48 * q^98 + 80 * q^99

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