LMFDB - Embedded newform 585.2.cf.a.388.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [585,2,Mod(163,585)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(585, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("585.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$585 = 3^{2} \cdot 5 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	585.cf (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [20,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1$ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			388.2
Root			$1.02262i$ of defining polynomial
Character	$\chi$	$=$	585.388
Dual form			585.2.cf.a.487.2

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.511309 - 0.885613i) q^{2} +(0.477126 - 0.826407i) q^{4} +(1.69584 + 1.45744i) q^{5} +(0.834479 + 0.481787i) q^{7} -3.02107 q^{8} +(0.423625 - 2.24706i) q^{10} +(-1.60661 - 0.430490i) q^{11} +(1.82127 - 3.11175i) q^{13} -0.985368i q^{14} +(0.590448 + 1.02269i) q^{16} +(7.00342 - 1.87656i) q^{17} +(-0.707496 - 2.64041i) q^{19} +(2.01357 - 0.706075i) q^{20} +(0.440226 + 1.64295i) q^{22} +(3.72214 + 0.997344i) q^{23} +(0.751762 + 4.94316i) q^{25} +(-3.68704 - 0.0218799i) q^{26} +(0.796304 - 0.459747i) q^{28} +(-0.253107 + 0.146132i) q^{29} +(-0.125649 - 0.125649i) q^{31} +(-2.41727 + 4.18683i) q^{32} +(-5.24282 - 5.24282i) q^{34} +(0.712972 + 2.03323i) q^{35} +(3.53443 - 2.04061i) q^{37} +(-1.97663 + 1.97663i) q^{38} +(-5.12326 - 4.40302i) q^{40} +(1.79277 - 6.69071i) q^{41} +(2.05706 + 7.67707i) q^{43} +(-1.12232 + 1.12232i) q^{44} +(-1.01990 - 3.80633i) q^{46} -7.84582i q^{47} +(-3.03576 - 5.25810i) q^{49} +(3.99335 - 3.19325i) q^{50} +(-1.70259 - 2.98981i) q^{52} +(1.99855 + 1.99855i) q^{53} +(-2.09714 - 3.07157i) q^{55} +(-2.52102 - 1.45551i) q^{56} +(0.258832 + 0.149437i) q^{58} +(-4.87924 + 1.30739i) q^{59} +(-1.04169 + 1.80425i) q^{61} +(-0.0470311 + 0.175522i) q^{62} +7.30568 q^{64} +(7.62376 - 2.62264i) q^{65} +(-3.64915 - 6.32050i) q^{67} +(1.79071 - 6.68304i) q^{68} +(1.43611 - 1.67103i) q^{70} +(-12.6082 + 3.37837i) q^{71} +3.22747 q^{73} +(-3.61437 - 2.08676i) q^{74} +(-2.51962 - 0.675130i) q^{76} +(-1.13328 - 1.13328i) q^{77} +13.5845i q^{79} +(-0.489192 + 2.59485i) q^{80} +(-6.84204 + 1.83332i) q^{82} +8.56854i q^{83} +(14.6117 + 7.02469i) q^{85} +(5.74712 - 5.74712i) q^{86} +(4.85368 + 1.30054i) q^{88} +(-0.134207 + 0.500868i) q^{89} +(3.01901 - 1.71922i) q^{91} +(2.60014 - 2.60014i) q^{92} +(-6.94836 + 4.01164i) q^{94} +(2.64843 - 5.50885i) q^{95} +(-3.75660 + 6.50662i) q^{97} +(-3.10442 + 5.37702i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 12 q^{8} - 10 q^{10} + 16 q^{11} + 2 q^{13} - 2 q^{16} + 10 q^{17} + 20 q^{19} - 14 q^{20} + 16 q^{22} + 2 q^{23} - 18 q^{25} + 24 q^{26} + 6 q^{28} + 6 q^{32}+ \cdots - 4 q^{98}+O(q^{100})$ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 12 * q^8 - 10 * q^10 + 16 * q^11 + 2 * q^13 - 2 * q^16 + 10 * q^17 + 20 * q^19 - 14 * q^20 + 16 * q^22 + 2 * q^23 - 18 * q^25 + 24 * q^26 + 6 * q^28 + 6 * q^32 - 2 * q^34 + 20 * q^35 + 42 * q^37 - 8 * q^38 - 16 * q^40 - 10 * q^41 - 22 * q^43 - 36 * q^44 + 4 * q^46 - 18 * q^49 - 44 * q^50 + 46 * q^52 + 10 * q^53 + 26 * q^55 - 90 * q^58 - 16 * q^59 - 16 * q^61 + 40 * q^62 - 20 * q^64 - 8 * q^65 - 58 * q^67 - 28 * q^68 + 32 * q^70 + 16 * q^71 + 72 * q^73 + 18 * q^74 - 64 * q^76 - 28 * q^77 + 34 * q^80 + 22 * q^82 - 6 * q^85 - 60 * q^86 + 50 * q^88 - 6 * q^89 + 8 * q^91 + 8 * q^92 + 48 * q^94 - 14 * q^95 - 22 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$ .

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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

)

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

$2$	−0.511309	−	0.885613i	−0.361550	−	0.626223i	0.626666	−	0.779288i	$-0.284419\pi$
$2$	−0.511309	−	0.885613i	−0.361550	−	0.626223i	−0.988216	+	0.153065i	$0.951086\pi$
$3$		0			0
$3$		0			0
$4$	0.477126	−	0.826407i	0.238563	−	0.413204i
$5$	1.69584	+	1.45744i	0.758404	+	0.651785i
$5$	1.69584	+	1.45744i	0.758404	+	0.651785i
$6$		0			0
$7$	0.834479	+	0.481787i	0.315404	+	0.182098i	0.649342	−	0.760497i	$-0.275044\pi$
$7$	0.834479	+	0.481787i	0.315404	+	0.182098i	−0.333938	+	0.942595i	$0.608378\pi$
$8$	−3.02107			−1.06811
$9$		0			0
$10$	0.423625	−	2.24706i	0.133962	−	0.710583i
$11$	−1.60661	−	0.430490i	−0.484411	−	0.129797i	0.00834492	−	0.999965i	$-0.497344\pi$
$11$	−1.60661	−	0.430490i	−0.484411	−	0.129797i	−0.492756	+	0.870168i	$0.664010\pi$
$12$		0			0
$13$	1.82127	−	3.11175i	0.505130	−	0.863043i
$13$	1.82127	−	3.11175i	0.505130	−	0.863043i
$14$		−	0.985368i		−	0.263351i
$15$		0			0
$16$	0.590448	+	1.02269i	0.147612	+	0.255671i
$17$	7.00342	−	1.87656i	1.69858	−	0.455133i	0.725998	−	0.687697i	$-0.241378\pi$
$17$	7.00342	−	1.87656i	1.69858	−	0.455133i	0.972581	+	0.232564i	$0.0747114\pi$
$18$		0			0
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	−0.998368	−	0.0571095i	$-0.981812\pi$
$19$	−0.707496	−	2.64041i	−0.162311	−	0.605752i	0.836057	−	0.548642i	$-0.184855\pi$
$20$	2.01357	−	0.706075i	0.450247	−	0.157883i
$21$		0			0
$22$	0.440226	+	1.64295i	0.0938565	+	0.350277i
$23$	3.72214	+	0.997344i	0.776120	+	0.207961i	0.625073	−	0.780566i	$-0.285069\pi$
$23$	3.72214	+	0.997344i	0.776120	+	0.207961i	0.151046	+	0.988527i	$0.451736\pi$
$24$		0			0
$25$	0.751762	+	4.94316i	0.150352	+	0.988632i
$26$	−3.68704	−	0.0218799i	−0.723087	−	0.00429099i
$27$		0			0
$28$	0.796304	−	0.459747i	0.150487	−	0.0868839i
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	−0.523316	−	0.852139i	$-0.675305\pi$
$29$	−0.253107	+	0.146132i	−0.0470008	+	0.0271360i	0.476315	+	0.879274i	$0.341972\pi$
$30$		0			0
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	0.695733	−	0.718300i	$-0.255080\pi$
$31$	−0.125649	−	0.125649i	−0.0225673	−	0.0225673i	−0.718300	+	0.695733i	$0.755080\pi$
$32$	−2.41727	+	4.18683i	−0.427317	+	0.740134i
$33$		0			0
$34$	−5.24282	−	5.24282i	−0.899136	−	0.899136i
$35$	0.712972	+	2.03323i	0.120514	+	0.343679i
$36$		0			0
$37$	3.53443	−	2.04061i	0.581057	−	0.335474i	−0.180496	−	0.983576i	$-0.557770\pi$
$37$	3.53443	−	2.04061i	0.581057	−	0.335474i	0.761553	+	0.648102i	$0.224437\pi$
$38$	−1.97663	+	1.97663i	−0.320652	+	0.320652i
$39$		0			0
$40$	−5.12326	−	4.40302i	−0.810059	−	0.696178i
$41$	1.79277	−	6.69071i	0.279984	−	1.04491i	−0.672444	−	0.740148i	$-0.734755\pi$
$41$	1.79277	−	6.69071i	0.279984	−	1.04491i	0.952427	−	0.304765i	$-0.0985780\pi$
$42$		0			0
$43$	2.05706	+	7.67707i	0.313699	+	1.17074i	0.925194	+	0.379494i	$0.123902\pi$
$43$	2.05706	+	7.67707i	0.313699	+	1.17074i	−0.611495	+	0.791248i	$0.709432\pi$
$44$	−1.12232	+	1.12232i	−0.169195	+	0.169195i
$45$		0			0
$46$	−1.01990	−	3.80633i	−0.150376	−	0.561212i
$47$		−	7.84582i		−	1.14443i	−0.820103	−	0.572215i	$-0.806084\pi$
$47$		−	7.84582i		−	1.14443i	0.820103	−	0.572215i	$-0.193916\pi$
$48$		0			0
$49$	−3.03576	−	5.25810i	−0.433680	−	0.751156i
$50$	3.99335	−	3.19325i	0.564744	−	0.451594i
$51$		0			0
$52$	−1.70259	−	2.98981i	−0.236107	−	0.414612i
$53$	1.99855	+	1.99855i	0.274522	+	0.274522i	0.830918	−	0.556395i	$-0.187816\pi$
$53$	1.99855	+	1.99855i	0.274522	+	0.274522i	−0.556395	+	0.830918i	$0.687816\pi$
$54$		0			0
$55$	−2.09714	−	3.07157i	−0.282779	−	0.414171i
$56$	−2.52102	−	1.45551i	−0.336886	−	0.194501i
$57$		0			0
$58$	0.258832	+	0.149437i	0.0339863	+	0.0196220i
$59$	−4.87924	+	1.30739i	−0.635223	+	0.170207i	−0.562039	−	0.827111i	$-0.689983\pi$
$59$	−4.87924	+	1.30739i	−0.635223	+	0.170207i	−0.0731843	+	0.997318i	$0.523316\pi$
$60$		0			0
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	−0.924975	−	0.380027i	$-0.875915\pi$
$61$	−1.04169	+	1.80425i	−0.133374	+	0.231011i	0.791601	+	0.611038i	$0.209248\pi$
$62$	−0.0470311	+	0.175522i	−0.00597296	+	0.0222914i
$63$		0			0
$64$	7.30568			0.913209
$65$	7.62376	−	2.62264i	0.945611	−	0.325299i
$66$		0			0
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	0.552294	−	0.833649i	$-0.313752\pi$
$67$	−3.64915	−	6.32050i	−0.445814	−	0.772173i	−0.998109	+	0.0614765i	$0.980419\pi$
$68$	1.79071	−	6.68304i	0.217156	−	0.810437i
$69$		0			0
$70$	1.43611	−	1.67103i	0.171648	−	0.199726i
$71$	−12.6082	+	3.37837i	−1.49632	+	0.400939i	−0.911867	−	0.410486i	$-0.865359\pi$
$71$	−12.6082	+	3.37837i	−1.49632	+	0.400939i	−0.584457	+	0.811425i	$0.698692\pi$
$72$		0			0
$73$	3.22747			0.377746			0.188873	−	0.982001i	$-0.439517\pi$
$73$	3.22747			0.377746			0.188873	+	0.982001i	$0.439517\pi$
$74$	−3.61437	−	2.08676i	−0.420163	−	0.242581i
$75$		0			0
$76$	−2.51962	−	0.675130i	−0.289020	−	0.0774427i
$77$	−1.13328	−	1.13328i	−0.129149	−	0.129149i
$78$		0			0
$79$			13.5845i			1.52838i	0.644992	+	0.764190i	$0.276861\pi$
$79$			13.5845i			1.52838i	−0.644992	+	0.764190i	$0.723139\pi$
$80$	−0.489192	+	2.59485i	−0.0546934	+	0.290113i
$81$		0			0
$82$	−6.84204	+	1.83332i	−0.755577	+	0.202456i
$83$			8.56854i			0.940519i	0.882528	+	0.470260i	$0.155840\pi$
$83$			8.56854i			0.940519i	−0.882528	+	0.470260i	$0.844160\pi$
$84$		0			0
$85$	14.6117	+	7.02469i	1.58486	+	0.761934i
$86$	5.74712	−	5.74712i	0.619728	−	0.619728i
$87$		0			0
$88$	4.85368	+	1.30054i	0.517404	+	0.138638i
$89$	−0.134207	+	0.500868i	−0.0142259	+	0.0530919i	−0.972674	−	0.232175i	$-0.925416\pi$
$89$	−0.134207	+	0.500868i	−0.0142259	+	0.0530919i	0.958448	+	0.285267i	$0.0920823\pi$
$90$		0			0
$91$	3.01901	−	1.71922i	0.316479	−	0.180223i
$92$	2.60014	−	2.60014i	0.271084	−	0.271084i
$93$		0			0
$94$	−6.94836	+	4.01164i	−0.716669	+	0.413769i
$95$	2.64843	−	5.50885i	0.271723	−	0.565196i
$96$		0			0
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	−0.991266	−	0.131876i	$-0.957900\pi$
$97$	−3.75660	+	6.50662i	−0.381425	+	0.660648i	0.609841	+	0.792524i	$0.291233\pi$
$98$	−3.10442	+	5.37702i	−0.313594	+	0.543161i
$99$		0			0
$100$	4.44375	+	1.73725i	0.444375	+	0.173725i
$101$	−8.44685	+	4.87679i	−0.840493	+	0.485259i	−0.857432	−	0.514598i	$-0.827941\pi$
$101$	−8.44685	+	4.87679i	−0.840493	+	0.485259i	0.0169388	+	0.999857i	$0.494608\pi$
$102$		0			0
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	−0.820404	−	0.571784i	$-0.806251\pi$
$103$	−2.52321	+	2.52321i	−0.248619	+	0.248619i	0.571784	+	0.820404i	$0.306251\pi$
$104$	−5.50220	+	9.40081i	−0.539535	+	0.921825i
$105$		0			0
$106$	0.748066	−	2.79182i	0.0726586	−	0.271166i
$107$	−0.429359	−	0.115046i	−0.0415077	−	0.0111220i	0.238005	−	0.971264i	$-0.423506\pi$
$107$	−0.429359	−	0.115046i	−0.0415077	−	0.0111220i	−0.279513	+	0.960142i	$0.590173\pi$
$108$		0			0
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	−0.944258	−	0.329206i	$-0.893219\pi$
$109$	−6.42134	+	6.42134i	−0.615053	+	0.615053i	0.329206	+	0.944258i	$0.393219\pi$
$110$	−1.64793	+	3.42778i	−0.157124	+	0.326826i
$111$		0			0
$112$			1.13788i			0.107520i
$113$	1.86865	−	0.500704i	0.175788	−	0.0471023i	−0.169851	−	0.985470i	$-0.554329\pi$
$113$	1.86865	−	0.500704i	0.175788	−	0.0471023i	0.345639	+	0.938367i	$0.387662\pi$
$114$		0			0
$115$	4.85860	+	7.11612i	0.453066	+	0.663581i
$116$			0.278893i			0.0258946i
$117$		0			0
$118$	3.65264	+	3.65264i	0.336253	+	0.336253i
$119$	6.74831	+	1.80821i	0.618617	+	0.165758i
$120$		0			0
$121$	−7.13041	−	4.11674i	−0.648219	−	0.374249i
$122$	2.13050			0.192886
$123$		0			0
$124$	−0.163788	+	0.0438869i	−0.0147086	+	0.00394116i
$125$	−5.92947	+	9.47847i	−0.530348	+	0.847780i
$126$		0			0
$127$	−0.562967	+	2.10102i	−0.0499553	+	0.186436i	−0.986395	−	0.164393i	$-0.947433\pi$
$127$	−0.562967	+	2.10102i	−0.0499553	+	0.186436i	0.936440	+	0.350829i	$0.114100\pi$
$128$	1.09908	+	1.90366i	0.0971460	+	0.168262i
$129$		0			0
$130$	−6.22074	−	5.41072i	−0.545595	−	0.474552i
$131$	0.0622493			0.00543874			0.00271937	−	0.999996i	$-0.499134\pi$
$131$	0.0622493			0.00543874			0.00271937	+	0.999996i	$0.499134\pi$
$132$		0			0
$133$	0.681725	−	2.54423i	0.0591130	−	0.220613i
$134$	−3.73168	+	6.46346i	−0.322368	+	0.558358i
$135$		0			0
$136$	−21.1578	+	5.66923i	−1.81427	+	0.486132i
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	0.654440	−	0.756114i	$-0.272904\pi$
$137$	3.82564	+	2.20873i	0.326846	+	0.188705i	−0.327594	+	0.944819i	$0.606238\pi$
$138$		0			0
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.911165	−	0.412043i	$-0.135184\pi$
$139$	11.9066	+	6.87430i	1.00991	+	0.583070i	0.0987430	+	0.995113i	$0.468518\pi$
$140$	2.02046	+	0.380905i	0.170760	+	0.0321923i
$141$		0			0
$142$	9.43864	+	9.43864i	0.792073	+	0.792073i
$143$	−4.26565	+	4.21532i	−0.356711	+	0.352503i
$144$		0			0
$145$	−0.642207	−	0.121072i	−0.0533324	−	0.0100544i
$146$	−1.65023	−	2.85829i	−0.136574	−	0.236553i
$147$		0			0
$148$		−	3.89451i		−	0.320127i
$149$	1.12129	+	4.18471i	0.0918596	+	0.342825i	0.996525	−	0.0832987i	$-0.0265456\pi$
$149$	1.12129	+	4.18471i	0.0918596	+	0.342825i	−0.904665	+	0.426124i	$0.859879\pi$
$150$		0			0
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	−0.486910	−	0.873452i	$-0.661876\pi$
$151$	4.74990	−	4.74990i	0.386542	−	0.386542i	0.873452	+	0.486910i	$0.161876\pi$
$152$	2.13740	+	7.97687i	0.173366	+	0.647010i
$153$		0			0
$154$	−0.424190	+	1.58310i	−0.0341822	+	0.127570i
$155$	−0.0299556	−	0.396208i	−0.00240610	−	0.0318242i
$156$		0			0
$157$	14.4488	−	14.4488i	1.15314	−	1.15314i	0.167218	−	0.985920i	$-0.446522\pi$
$157$	14.4488	−	14.4488i	1.15314	−	1.15314i	0.985920	−	0.167218i	$-0.0534784\pi$
$158$	12.0306	−	6.94589i	0.957106	−	0.552586i
$159$		0			0
$160$	−10.2013	+	3.57719i	−0.806487	+	0.282802i
$161$	2.62554	+	2.62554i	0.206922	+	0.206922i
$162$		0			0
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	0.0544633	+	0.998516i	$0.482655\pi$
$163$	−10.6926	+	18.5201i	−0.837508	+	1.45061i	−0.891972	+	0.452091i	$0.850678\pi$
$164$	−4.67387	−	4.67387i	−0.364968	−	0.364968i
$165$		0			0
$166$	7.58841	−	4.38117i	0.588975	−	0.340045i
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	−0.556345	−	0.830951i	$-0.687797\pi$
$167$	−1.48475	+	0.857220i	−0.114893	+	0.0663337i	0.441452	+	0.897285i	$0.354464\pi$
$168$		0			0
$169$	−6.36593	−	11.3347i	−0.489687	−	0.871898i
$170$	−1.24992	−	16.5321i	−0.0958646	−	1.26795i
$171$		0			0
$172$	7.32587	+	1.96296i	0.558592	+	0.149674i
$173$	3.92804	+	14.6596i	0.298643	+	1.11455i	0.938281	+	0.345875i	$0.112418\pi$
$173$	3.92804	+	14.6596i	0.298643	+	1.11455i	−0.639638	+	0.768677i	$0.720916\pi$
$174$		0			0
$175$	−1.75422	+	4.48716i	−0.132607	+	0.339197i
$176$	−0.508363	−	1.89724i	−0.0383193	−	0.143010i
$177$		0			0
$178$	0.512196	−	0.137243i	0.0383907	−	0.0102868i
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	0.809850	−	0.586637i	$-0.199548\pi$
$179$	−1.37961	−	2.38956i	−0.103117	−	0.178604i	−0.912967	+	0.408033i	$0.866215\pi$
$180$		0			0
$181$			10.3568i			0.769818i	0.922954	+	0.384909i	$0.125767\pi$
$181$			10.3568i			0.769818i	−0.922954	+	0.384909i	$0.874233\pi$
$182$	−3.06621	−	1.79462i	−0.227283	−	0.133026i
$183$		0			0
$184$	−11.2449	−	3.01305i	−0.828981	−	0.222125i
$185$	8.96789	+	1.69066i	0.659333	+	0.124300i
$186$		0			0
$187$	−12.0596			−0.881885
$188$	−6.48384	−	3.74345i	−0.472883	−	0.273019i
$189$		0			0
$190$	−6.23287	+	0.471242i	−0.452180	+	0.0341875i
$191$	9.28983	−	16.0905i	0.672189	−	1.16427i	−0.305093	−	0.952322i	$-0.598688\pi$
$191$	9.28983	−	16.0905i	0.672189	−	1.16427i	0.977282	−	0.211943i	$-0.0679790\pi$
$192$		0			0
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	0.546079	−	0.837733i	$-0.316120\pi$
$193$	−6.28576	−	10.8872i	−0.452459	−	0.783681i	−0.998538	+	0.0540520i	$0.982786\pi$
$194$	7.68313			0.551617
$195$		0			0
$196$	−5.79377			−0.413841
$197$	7.14308	+	12.3722i	0.508924	+	0.881481i	0.999947	+	0.0103349i	$0.00328975\pi$
$197$	7.14308	+	12.3722i	0.508924	+	0.881481i	−0.491023	+	0.871147i	$0.663377\pi$
$198$		0			0
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	0.477373	+	0.878701i	$0.341589\pi$
$199$	−7.36781	+	12.7614i	−0.522291	+	0.904634i	−0.999664	+	0.0259331i	$0.991744\pi$
$200$	−2.27113	−	14.9336i	−0.160593	−	1.05597i
$201$		0			0
$202$	8.63790	+	4.98709i	0.607760	+	0.350891i
$203$	−0.281617			−0.0197656
$204$		0			0
$205$	12.7915	−	8.73354i	0.893400	−	0.609977i
$206$	3.52473	+	0.944449i	0.245580	+	0.0658029i
$207$		0			0
$208$	4.25770	+	0.0252664i	0.295219	+	0.00175191i
$209$			4.54668i			0.314500i
$210$		0			0
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	0.974678	−	0.223611i	$-0.0717845\pi$
$211$	4.26604	+	7.38900i	0.293686	+	0.508680i	−0.680992	+	0.732291i	$0.738451\pi$
$212$	2.60518	−	0.698056i	0.178925	−	0.0479427i
$213$		0			0
$214$	0.117649	+	0.439070i	0.00804229	+	0.0300142i
$215$	−7.70038	+	16.0171i	−0.525161	+	1.09236i
$216$		0			0
$217$	−0.0443156	−	0.165388i	−0.00300834	−	0.0112273i
$218$	8.97011	+	2.40353i	0.607532	+	0.162788i
$219$		0			0
$220$	−3.53897	+	0.267567i	−0.238597	+	0.0180394i
$221$	6.91576	−	25.2106i	0.465205	−	1.69585i
$222$		0			0
$223$	6.11483	−	3.53040i	0.409479	−	0.236413i	−0.281087	−	0.959682i	$-0.590695\pi$
$223$	6.11483	−	3.53040i	0.409479	−	0.236413i	0.690566	+	0.723269i	$0.257362\pi$
$224$	−4.03432	+	2.32922i	−0.269555	+	0.155627i
$225$		0			0
$226$	−1.39889	−	1.39889i	−0.0930527	−	0.0930527i
$227$	−8.58775	+	14.8744i	−0.569989	+	0.987249i	0.426578	+	0.904451i	$0.359719\pi$
$227$	−8.58775	+	14.8744i	−0.569989	+	0.987249i	−0.996566	+	0.0827985i	$0.973614\pi$
$228$		0			0
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	0.937240	−	0.348684i	$-0.113371\pi$
$229$	8.90647	+	8.90647i	0.588556	+	0.588556i	−0.348684	+	0.937240i	$0.613371\pi$
$230$	3.81788	−	7.94137i	0.251744	−	0.523638i
$231$		0			0
$232$	0.764655	−	0.441474i	0.0502021	−	0.0289842i
$233$	−17.5822	+	17.5822i	−1.15185	+	1.15185i	−0.165666	+	0.986182i	$0.552977\pi$
$233$	−17.5822	+	17.5822i	−1.15185	+	1.15185i	−0.986182	+	0.165666i	$0.947023\pi$
$234$		0			0
$235$	11.4348	−	13.3053i	0.745923	−	0.867940i
$236$	−1.24758	+	4.65603i	−0.0812105	+	0.303082i
$237$		0			0
$238$	−1.84910	−	6.90095i	−0.119860	−	0.447322i
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	−0.775684	−	0.631122i	$-0.782595\pi$
$239$	−2.23488	+	2.23488i	−0.144562	+	0.144562i	0.631122	+	0.775684i	$0.282595\pi$
$240$		0			0
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	−0.936825	−	0.349797i	$-0.886250\pi$
$241$	−4.66361	−	17.4048i	−0.300409	−	1.12114i	0.636416	−	0.771346i	$-0.280416\pi$
$242$			8.41971i			0.541239i
$243$		0			0
$244$	0.994033	+	1.72172i	0.0636364	+	0.110222i
$245$	2.51516	−	13.3413i	0.160688	−	0.852346i
$246$		0			0
$247$	−9.50483	−	2.60736i	−0.604778	−	0.165902i
$248$	0.379596	+	0.379596i	0.0241044	+	0.0241044i
$249$		0			0
$250$	11.4260	+	0.404792i	0.722647	+	0.0256013i
$251$	−12.1009	−	6.98644i	−0.763800	−	0.440980i	0.0668586	−	0.997762i	$-0.478702\pi$
$251$	−12.1009	−	6.98644i	−0.763800	−	0.440980i	−0.830658	+	0.556782i	$0.812036\pi$
$252$		0			0
$253$	−5.55068	−	3.20468i	−0.348968	−	0.201477i
$254$	2.14854	−	0.575700i	0.134812	−	0.0361227i
$255$		0			0
$256$	8.42962	−	14.6005i	0.526851	−	0.912533i
$257$	5.99887	−	22.3881i	0.374199	−	1.39653i	−0.480312	−	0.877098i	$-0.659476\pi$
$257$	5.99887	−	22.3881i	0.374199	−	1.39653i	0.854511	−	0.519433i	$-0.173857\pi$
$258$		0			0
$259$	3.93255			0.244357
$260$	1.47013	−	7.55166i	0.0911735	−	0.468334i
$261$		0			0
$262$	−0.0318286	−	0.0551288i	−0.00196638	−	0.00340587i
$263$	−0.336737	+	1.25672i	−0.0207641	+	0.0774926i	−0.975530	−	0.219864i	$-0.929438\pi$
$263$	−0.336737	+	1.25672i	−0.0207641	+	0.0774926i	0.954766	+	0.297357i	$0.0961052\pi$
$264$		0			0
$265$	0.476468	+	6.30199i	0.0292692	+	0.387128i
$266$	−2.60178	+	0.697144i	−0.159525	+	0.0427446i
$267$		0			0
$268$	−6.96441			−0.425419
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	0.275574	−	0.961280i	$-0.411132\pi$
$269$	−6.87429	−	3.96887i	−0.419133	−	0.241986i	−0.694706	+	0.719294i	$0.744466\pi$
$270$		0			0
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	0.232450	−	0.972608i	$-0.425326\pi$
$271$	−0.865041	−	0.231787i	−0.0525475	−	0.0140801i	−0.284997	+	0.958528i	$0.591993\pi$
$272$	6.05429	+	6.05429i	0.367095	+	0.367095i
$273$		0			0
$274$		−	4.51738i		−	0.272905i
$275$	0.920192	−	8.26535i	0.0554897	−	0.498420i
$276$		0			0
$277$	9.22930	−	2.47298i	0.554535	−	0.148587i	0.0293404	−	0.999569i	$-0.490659\pi$
$277$	9.22930	−	2.47298i	0.554535	−	0.148587i	0.525194	+	0.850982i	$0.323993\pi$
$278$		−	14.0596i		−	0.843236i
$279$		0			0
$280$	−2.15394	−	6.14255i	−0.128723	−	0.367087i
$281$	−5.58408	+	5.58408i	−0.333118	+	0.333118i	−0.853769	−	0.520651i	$-0.825689\pi$
$281$	−5.58408	+	5.58408i	−0.333118	+	0.333118i	0.520651	+	0.853769i	$0.325689\pi$
$282$		0			0
$283$	−20.3851	−	5.46218i	−1.21177	−	0.324693i	−0.404314	−	0.914620i	$-0.632490\pi$
$283$	−20.3851	−	5.46218i	−1.21177	−	0.324693i	−0.807457	+	0.589927i	$0.799157\pi$
$284$	−3.22382	+	12.0315i	−0.191298	+	0.713936i
$285$		0			0
$286$	5.91420	+	1.62238i	0.349714	+	0.0959335i
$287$	4.71953	−	4.71953i	0.278585	−	0.278585i
$288$		0			0
$289$	30.8040	−	17.7847i	1.81200	−	1.04616i
$290$	0.221144	+	0.630652i	0.0129860	+	0.0370332i
$291$		0			0
$292$	1.53991	−	2.66720i	0.0901164	−	0.156086i
$293$	2.01079	−	3.48280i	0.117472	−	0.203467i	−0.801293	−	0.598272i	$-0.795854\pi$
$293$	2.01079	−	3.48280i	0.117472	−	0.203467i	0.918765	+	0.394805i	$0.129188\pi$
$294$		0			0
$295$	−10.1799	−	4.89405i	−0.592694	−	0.284943i
$296$	−10.6778	+	6.16482i	−0.620633	+	0.358323i
$297$		0			0
$298$	3.13271	−	3.13271i	0.181473	−	0.181473i
$299$	9.88252	−	9.76592i	0.571521	−	0.564778i
$300$		0			0
$301$	−1.98213	+	7.39742i	−0.114248	+	0.426380i
$302$	−6.63524	−	1.77791i	−0.381815	−	0.102307i
$303$		0			0
$304$	2.28257	−	2.28257i	0.130914	−	0.130914i
$305$	−4.39612	+	1.54154i	−0.251721	+	0.0882683i
$306$		0			0
$307$		−	24.2191i		−	1.38226i	−0.722732	−	0.691128i	$-0.757114\pi$
$307$		−	24.2191i		−	1.38226i	0.722732	−	0.691128i	$-0.242886\pi$
$308$	−1.47727	+	0.395832i	−0.0841750	+	0.0225546i
$309$		0			0
$310$	−0.335570	+	0.229114i	−0.0190591	+	0.0130128i
$311$			7.87243i			0.446405i	0.974772	+	0.223202i	$0.0716511\pi$
$311$			7.87243i			0.446405i	−0.974772	+	0.223202i	$0.928349\pi$
$312$		0			0
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	0.796423	−	0.604740i	$-0.206723\pi$
$313$	3.39121	+	3.39121i	0.191683	+	0.191683i	−0.604740	+	0.796423i	$0.706723\pi$
$314$	−20.1838	−	5.40824i	−1.13904	−	0.305204i
$315$		0			0
$316$	11.2264	+	6.48154i	0.631532	+	0.364615i
$317$	−22.9255			−1.28762			−0.643812	−	0.765184i	$-0.722648\pi$
$317$	−22.9255			−1.28762			−0.643812	+	0.765184i	$0.722648\pi$
$318$		0			0
$319$	0.469553	−	0.125816i	0.0262899	−	0.00704436i
$320$	12.3893	+	10.6476i	0.692581	+	0.595216i
$321$		0			0
$322$	0.982751	−	3.66768i	0.0547666	−	0.204392i
$323$	−9.90979	−	17.1643i	−0.551395	−	0.955044i
$324$		0			0
$325$	16.7510	+	6.66356i	0.929180	+	0.369628i
$326$	21.8689			1.21120
$327$		0			0
$328$	−5.41609	+	20.2131i	−0.299053	+	1.11608i
$329$	3.78001	−	6.54718i	0.208399	−	0.360958i
$330$		0			0
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.990858	−	0.134910i	$-0.956925\pi$
$331$	−32.4118	+	8.68470i	−1.78151	+	0.477354i	−0.790653	+	0.612264i	$0.790259\pi$
$332$	7.08110	+	4.08828i	0.388626	+	0.224373i
$333$		0			0
$334$	1.51833	+	0.876609i	0.0830794	+	0.0479659i
$335$	3.02336	−	16.0370i	0.165184	−	0.876194i
$336$		0			0
$337$	14.5544	+	14.5544i	0.792826	+	0.792826i	0.981953	−	0.189126i	$-0.0605656\pi$
$337$	14.5544	+	14.5544i	0.792826	+	0.792826i	−0.189126	+	0.981953i	$0.560566\pi$
$338$	−6.78318	+	11.4333i	−0.368957	+	0.621888i
$339$		0			0
$340$	12.7769	−	8.72352i	0.692923	−	0.473099i
$341$	0.147779	+	0.255960i	0.00800267	+	0.0138610i
$342$		0			0
$343$		−	12.5954i		−	0.680087i
$344$	−6.21454	−	23.1930i	−0.335065	−	1.25048i
$345$		0			0
$346$	10.9743	−	10.9743i	0.589983	−	0.589983i
$347$	−5.90442	−	22.0356i	−0.316966	−	1.18293i	−0.922145	−	0.386844i	$-0.873565\pi$
$347$	−5.90442	−	22.0356i	−0.316966	−	1.18293i	0.605179	−	0.796089i	$-0.293101\pi$
$348$		0			0
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	−0.855918	−	0.517111i	$-0.827008\pi$
$349$	2.68798	−	10.0317i	0.143884	−	0.536983i	0.999803	−	0.0198718i	$-0.00632581\pi$
$350$	4.87083	−	0.740762i	0.260357	−	0.0395954i
$351$		0			0
$352$	5.68599	−	5.68599i	0.303064	−	0.303064i
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	−0.595825	−	0.803115i	$-0.703175\pi$
$353$	−3.72420	+	2.15017i	−0.198219	+	0.114442i	0.397605	+	0.917556i	$0.369841\pi$
$354$		0			0
$355$	−26.3054	−	12.6465i	−1.39614	−	0.671208i
$356$	0.349887	+	0.349887i	0.0185440	+	0.0185440i
$357$		0			0
$358$	−1.41082	+	2.44361i	−0.0745640	+	0.129149i
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	0.376204	−	0.926537i	$-0.377229\pi$
$359$	−10.4273	−	10.4273i	−0.550333	−	0.550333i	−0.926537	+	0.376204i	$0.877229\pi$
$360$		0			0
$361$	9.98326	−	5.76384i	0.525435	−	0.303360i
$362$	9.17216	−	5.29555i	0.482078	−	0.278328i
$363$		0			0
$364$	0.0196734	−	3.31522i	0.00103117	−	0.173765i
$365$	5.47327	+	4.70382i	0.286484	+	0.246209i
$366$		0			0
$367$	−11.0341	−	2.95657i	−0.575973	−	0.154331i	−0.0409383	−	0.999162i	$-0.513035\pi$
$367$	−11.0341	−	2.95657i	−0.575973	−	0.154331i	−0.535034	+	0.844830i	$0.679701\pi$
$368$	1.17776	+	4.39546i	0.0613950	+	0.229129i
$369$		0			0
$370$	−3.08809	−	8.80653i	−0.160542	−	0.457830i
$371$	0.704874	+	2.63063i	0.0365953	+	0.136575i
$372$		0			0
$373$	−27.1975	+	7.28755i	−1.40823	+	0.377335i	−0.881294	−	0.472568i	$-0.843327\pi$
$373$	−27.1975	+	7.28755i	−1.40823	+	0.377335i	−0.526939	+	0.849903i	$0.676661\pi$
$374$	6.16618	+	10.6801i	0.318846	+	0.552257i
$375$		0			0
$376$			23.7028i			1.22238i
$377$	−0.00625324	+	1.05375i	−0.000322058	+	0.0542709i
$378$		0			0
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.186987	−	0.982362i	$-0.559872\pi$
$379$	−16.3551	−	4.38232i	−0.840103	−	0.225105i	−0.653116	+	0.757258i	$0.726539\pi$
$380$	−3.28892	−	4.81710i	−0.168718	−	0.247112i
$381$		0			0
$382$	−18.9999			−0.972119
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	0.638950	−	0.769248i	$-0.279369\pi$
$383$	5.71918	+	3.30197i	0.292236	+	0.168723i	−0.346714	+	0.937971i	$0.612702\pi$
$384$		0			0
$385$	−0.270181	−	3.57354i	−0.0137697	−	0.182124i
$386$	−6.42793	+	11.1335i	−0.327173	+	0.566680i
$387$		0			0
$388$	3.58475	+	6.20897i	0.181988	+	0.315212i
$389$	33.6949			1.70840			0.854199	−	0.519946i	$-0.174048\pi$
$389$	33.6949			1.70840			0.854199	+	0.519946i	$0.174048\pi$
$390$		0			0
$391$	27.9393			1.41295
$392$	9.17126	+	15.8851i	0.463218	+	0.802318i
$393$		0			0
$394$	7.30464	−	12.6520i	0.368003	−	0.637399i
$395$	−19.7986	+	23.0372i	−0.996175	+	1.15913i
$396$		0			0
$397$	5.04104	+	2.91045i	0.253002	+	0.146071i	0.621138	−	0.783701i	$-0.286671\pi$
$397$	5.04104	+	2.91045i	0.253002	+	0.146071i	−0.368136	+	0.929772i	$0.620004\pi$
$398$	15.0689			0.755337
$399$		0			0
$400$	−4.61142	+	3.68750i	−0.230571	+	0.184375i
$401$	−0.255004	−	0.0683280i	−0.0127343	−	0.00341214i	0.252446	−	0.967611i	$-0.418765\pi$
$401$	−0.255004	−	0.0683280i	−0.0127343	−	0.00341214i	−0.265181	+	0.964199i	$0.585432\pi$
$402$		0			0
$403$	−0.619831	+	0.162147i	−0.0308760	+	0.00807713i
$404$			9.30738i			0.463060i
$405$		0			0
$406$	0.143993	+	0.249404i	0.00714627	+	0.0123777i
$407$	−6.55691	+	1.75692i	−0.325014	+	0.0870872i
$408$		0			0
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	0.619042	+	0.785358i	$0.287521\pi$
$409$	9.61872	+	35.8975i	0.475615	+	1.77502i	−0.143427	+	0.989661i	$0.545812\pi$
$410$	−14.2750	−	6.86281i	−0.704990	−	0.338930i
$411$		0			0
$412$	0.881310	+	3.28909i	0.0434190	+	0.162042i
$413$	−4.70151	−	1.25977i	−0.231346	−	0.0619890i
$414$		0			0
$415$	−12.4881	+	14.5309i	−0.613016	+	0.713293i
$416$	8.62585	+	15.1473i	0.422917	+	0.742657i
$417$		0			0
$418$	4.02660	−	2.32476i	0.196947	−	0.113708i
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.437428	−	0.899253i	$-0.355889\pi$
$419$	29.3721	−	16.9580i	1.43492	−	0.828451i	0.997490	+	0.0708027i	$0.0225561\pi$
$420$		0			0
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.998641	−	0.0521230i	$-0.983401\pi$
$421$	−21.5599	−	21.5599i	−1.05076	−	1.05076i	−0.0521230	−	0.998641i	$-0.516599\pi$
$422$	4.36253	−	7.55613i	0.212365	−	0.367826i
$423$		0			0
$424$	−6.03777	−	6.03777i	−0.293220	−	0.293220i
$425$	14.5411	+	33.2083i	0.705345	+	1.61084i
$426$		0			0
$427$	−1.73853	+	1.00374i	−0.0841335	+	0.0485745i
$428$	−0.299934	+	0.299934i	−0.0144979	+	0.0144979i
$429$		0			0
$430$	18.1223	−	1.37015i	0.873933	−	0.0660745i
$431$	−1.19014	+	4.44167i	−0.0573271	+	0.213948i	−0.988648	−	0.150253i	$-0.951991\pi$
$431$	−1.19014	+	4.44167i	−0.0573271	+	0.213948i	0.931320	+	0.364201i	$0.118658\pi$
$432$		0			0
$433$	−1.03596	−	3.86627i	−0.0497853	−	0.185801i	0.936555	−	0.350520i	$-0.113995\pi$
$433$	−1.03596	−	3.86627i	−0.0497853	−	0.185801i	−0.986341	+	0.164719i	$0.947328\pi$
$434$	−0.123811	+	0.123811i	−0.00594311	+	0.00594311i
$435$		0			0
$436$	2.24285	+	8.37043i	0.107413	+	0.400871i
$437$		−	10.5336i		−	0.503890i
$438$		0			0
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	−0.998773	−	0.0495192i	$-0.984231\pi$
$439$	−11.3618	−	19.6793i	−0.542271	−	0.939242i	0.456502	−	0.889723i	$-0.349102\pi$
$440$	6.33562	+	9.27944i	0.302039	+	0.442380i
$441$		0			0
$442$	−25.8629	+	6.76571i	−1.23017	+	0.321812i
$443$	−1.84874	−	1.84874i	−0.0878361	−	0.0878361i	0.661824	−	0.749660i	$-0.269783\pi$
$443$	−1.84874	−	1.84874i	−0.0878361	−	0.0878361i	−0.749660	+	0.661824i	$0.769783\pi$
$444$		0			0
$445$	−0.957576	+	0.653794i	−0.0453935	+	0.0309928i
$446$	−6.25313	−	3.61025i	−0.296094	−	0.170950i
$447$		0			0
$448$	6.09644	+	3.51978i	0.288030	+	0.166294i
$449$	31.0770	−	8.32705i	1.46661	−	0.392978i	0.564845	−	0.825197i	$-0.308936\pi$
$449$	31.0770	−	8.32705i	1.46661	−	0.392978i	0.901769	+	0.432219i	$0.142269\pi$
$450$		0			0
$451$	−5.76056	+	9.97759i	−0.271254	+	0.469826i
$452$	0.477798	−	1.78317i	0.0224737	−	0.0838731i
$453$		0			0
$454$	17.5640			0.824318
$455$	7.62543	+	1.48449i	0.357486	+	0.0695939i
$456$		0			0
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	0.979693	+	0.200501i	$0.0642571\pi$
$457$	14.1837	+	24.5669i	0.663486	+	1.14919i	−0.316208	+	0.948690i	$0.602410\pi$
$458$	3.33373	−	12.4416i	0.155775	−	0.581360i
$459$		0			0
$460$	8.19898	−	0.619891i	0.382279	−	0.0289026i
$461$	11.1174	−	2.97890i	0.517790	−	0.138741i	0.00954570	−	0.999954i	$-0.496961\pi$
$461$	11.1174	−	2.97890i	0.517790	−	0.138741i	0.508244	+	0.861213i	$0.330295\pi$
$462$		0			0
$463$	29.9456			1.39169			0.695845	−	0.718192i	$-0.255030\pi$
$463$	29.9456			1.39169			0.695845	+	0.718192i	$0.255030\pi$
$464$	−0.298893	−	0.172566i	−0.0138758	−	0.00801118i
$465$		0			0
$466$	24.5609	+	6.58109i	1.13776	+	0.304863i
$467$	16.1332	+	16.1332i	0.746557	+	0.746557i	0.973831	−	0.227274i	$-0.0729812\pi$
$467$	16.1332	+	16.1332i	0.746557	+	0.746557i	−0.227274	+	0.973831i	$0.572981\pi$
$468$		0			0
$469$		−	7.03244i		−	0.324728i
$470$	−17.6300	−	3.32368i	−0.813213	−	0.153310i
$471$		0			0
$472$	14.7405	−	3.94971i	0.678488	−	0.181800i
$473$		−	13.2196i		−	0.607837i
$474$		0			0
$475$	12.5201	−	5.48223i	0.574462	−	0.251542i
$476$	4.71411	−	4.71411i	0.216071	−	0.216071i
$477$		0			0
$478$	3.12195	+	0.836524i	0.142795	+	0.0382617i
$479$	−10.0493	+	37.5043i	−0.459162	+	1.71362i	0.216393	+	0.976306i	$0.430571\pi$
$479$	−10.0493	+	37.5043i	−0.459162	+	1.71362i	−0.675555	+	0.737309i	$0.736096\pi$
$480$		0			0
$481$	0.0873213	−	14.7148i	0.00398151	−	0.670935i
$482$	−13.0294	+	13.0294i	−0.593473	+	0.593473i
$483$		0			0
$484$	−6.80421	+	3.92841i	−0.309282	+	0.178564i
$485$	−15.8536	+	5.55920i	−0.719874	+	0.252430i
$486$		0			0
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	0.325916	+	0.945399i	$0.394327\pi$
$487$	−14.4718	+	25.0660i	−0.655782	+	1.13585i	−0.981697	+	0.190448i	$0.939006\pi$
$488$	3.14701	−	5.45078i	0.142458	−	0.246745i
$489$		0			0
$490$	−13.1013	+	4.59408i	−0.591855	+	0.207539i
$491$	−6.30003	+	3.63733i	−0.284317	+	0.164150i	−0.635376	−	0.772203i	$-0.719155\pi$
$491$	−6.30003	+	3.63733i	−0.284317	+	0.164150i	0.351059	+	0.936353i	$0.385822\pi$
$492$		0			0
$493$	−1.49839	+	1.49839i	−0.0674842	+	0.0674842i
$494$	2.55079	+	9.75077i	0.114766	+	0.438708i
$495$		0			0
$496$	0.0543104	−	0.202689i	0.00243861	−	0.00910102i
$497$	−12.1490	−	3.25531i	−0.544956	−	0.146021i
$498$		0			0
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	−0.795652	−	0.605754i	$-0.792872\pi$
$499$	−4.24201	+	4.24201i	−0.189899	+	0.189899i	0.605754	+	0.795652i	$0.292872\pi$
$500$	5.00397	+	9.42259i	0.223784	+	0.421391i
$501$		0			0
$502$			14.2889i			0.637745i
$503$	3.50677	−	0.939636i	0.156359	−	0.0418963i	−0.179790	−	0.983705i	$-0.557542\pi$
$503$	3.50677	−	0.939636i	0.156359	−	0.0418963i	0.336149	+	0.941809i	$0.390875\pi$
$504$		0			0
$505$	−21.4321	−	4.04047i	−0.953717	−	0.179799i
$506$			6.55433i			0.291376i
$507$		0			0
$508$	1.46769	+	1.46769i	0.0651184	+	0.0651184i
$509$	−22.5037	−	6.02986i	−0.997460	−	0.267269i	−0.277079	−	0.960847i	$-0.589366\pi$
$509$	−22.5037	−	6.02986i	−0.997460	−	0.267269i	−0.720381	+	0.693578i	$0.756033\pi$
$510$		0			0
$511$	2.69325	+	1.55495i	0.119143	+	0.0687870i
$512$	−12.8442			−0.567640
$513$		0			0
$514$	−22.8945	+	6.13455i	−1.00983	+	0.270584i
$515$	−7.95639	+	0.601550i	−0.350600	+	0.0265075i
$516$		0			0
$517$	−3.37754	+	12.6052i	−0.148544	+	0.554375i
$518$	−2.01075	−	3.48272i	−0.0883472	−	0.153022i
$519$		0			0
$520$	−23.0319	+	7.92319i	−1.01002	+	0.347455i
$521$	13.0530			0.571862			0.285931	−	0.958250i	$-0.407697\pi$
$521$	13.0530			0.571862			0.285931	+	0.958250i	$0.407697\pi$
$522$		0			0
$523$	4.40520	−	16.4404i	0.192626	−	0.718890i	−0.800243	−	0.599677i	$-0.795296\pi$
$523$	4.40520	−	16.4404i	0.192626	−	0.718890i	0.992869	−	0.119214i	$-0.0380374\pi$
$524$	0.0297008	−	0.0514432i	0.00129748	−	0.00224731i
$525$		0			0
$526$	1.28514	−	0.344353i	0.0560349	−	0.0150145i
$527$	−1.11577	−	0.644187i	−0.0486035	−	0.0280612i
$528$		0			0
$529$	−7.05896	−	4.07549i	−0.306911	−	0.177195i
$530$	5.33750	−	3.64423i	0.231846	−	0.158295i
$531$		0			0
$532$	−1.77730	−	1.77730i	−0.0770558	−	0.0770558i
$533$	−17.5547	−	17.7643i	−0.760377	−	0.769456i
$534$		0			0
$535$	−0.560453	−	0.820864i	−0.0242305	−	0.0354891i
$536$	11.0243	+	19.0947i	0.476178	+	0.824765i
$537$		0			0
$538$			8.11728i			0.349961i
$539$	2.61373	+	9.75457i	0.112581	+	0.420159i
$540$		0			0
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	−0.902483	−	0.430727i	$-0.858257\pi$
$541$	−10.9728	+	10.9728i	−0.471756	+	0.471756i	0.430727	+	0.902483i	$0.358257\pi$
$542$	0.237029	+	0.884606i	0.0101813	+	0.0379971i
$543$		0			0
$544$	−9.07231	+	33.8583i	−0.388972	+	1.45166i
$545$	−20.2483	+	1.53089i	−0.867340	+	0.0655761i
$546$		0			0
$547$	−20.4450	+	20.4450i	−0.874167	+	0.874167i	−0.992923	−	0.118756i	$-0.962109\pi$
$547$	−20.4450	+	20.4450i	−0.874167	+	0.874167i	0.118756	+	0.992923i	$0.462109\pi$
$548$	3.65063	−	2.10769i	0.155947	−	0.0900361i
$549$		0			0
$550$	−7.79041	+	3.41121i	−0.332184	+	0.145455i
$551$	0.564920	+	0.564920i	0.0240664	+	0.0240664i
$552$		0			0
$553$	−6.54485	+	11.3360i	−0.278315	+	0.482056i
$554$	−6.90913	−	6.90913i	−0.293541	−	0.293541i
$555$		0			0
$556$	11.3619	−	6.55982i	0.481854	−	0.278198i
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	−0.728021	−	0.685555i	$-0.759560\pi$
$557$	−11.7609	+	6.79015i	−0.498324	+	0.287708i	0.229697	+	0.973262i	$0.426226\pi$
$558$		0			0
$559$	27.6356	+	7.58098i	1.16886	+	0.320641i
$560$	−1.65839	+	1.92967i	−0.0700797	+	0.0815432i
$561$		0			0
$562$	7.80052	+	2.09014i	0.329045	+	0.0881673i
$563$	−1.25538	−	4.68514i	−0.0529080	−	0.197455i	0.934413	−	0.356191i	$-0.115925\pi$
$563$	−1.25538	−	4.68514i	−0.0529080	−	0.197455i	−0.987321	+	0.158736i	$0.949258\pi$
$564$		0			0
$565$	3.89868	+	1.87433i	0.164019	+	0.0788535i
$566$	5.58573	+	20.8462i	0.234786	+	0.876232i
$567$		0			0
$568$	38.0904	−	10.2063i	1.59824	−	0.428247i
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	0.868621	−	0.495477i	$-0.165007\pi$
$569$	0.124396	+	0.215461i	0.00521497	+	0.00903259i	−0.863406	+	0.504509i	$0.831673\pi$
$570$		0			0
$571$		−	7.72842i		−	0.323424i	−0.986838	−	0.161712i	$-0.948298\pi$
$571$		−	7.72842i		−	0.323424i	0.986838	−	0.161712i	$-0.0517016\pi$
$572$	1.44832	+	5.53640i	0.0605572	+	0.231489i
$573$		0			0
$574$	−6.59281	−	1.76654i	−0.275179	−	0.0737339i
$575$	−2.13187	+	19.1489i	−0.0889052	+	0.798565i
$576$		0			0
$577$	−12.1339			−0.505141			−0.252570	−	0.967578i	$-0.581276\pi$
$577$	−12.1339			−0.505141			−0.252570	+	0.967578i	$0.581276\pi$
$578$	−31.5007	−	18.1869i	−1.31026	−	0.756477i
$579$		0			0
$580$	−0.406469	+	0.472958i	−0.0168777	+	0.0196385i
$581$	−4.12821	+	7.15027i	−0.171267	+	0.296643i
$582$		0			0
$583$	−2.35054	−	4.07125i	−0.0973492	−	0.168614i
$584$	−9.75040			−0.403475
$585$		0			0
$586$	−4.11255			−0.169888
$587$	−18.2647	−	31.6354i	−0.753865	−	1.30573i	−0.945937	−	0.324351i	$-0.894854\pi$
$587$	−18.2647	−	31.6354i	−0.753865	−	1.30573i	0.192072	−	0.981381i	$-0.438479\pi$
$588$		0			0
$589$	−0.242870	+	0.420663i	−0.0100073	+	0.0173331i
$590$	0.870813	+	11.5178i	0.0358508	+	0.474180i
$591$		0			0
$592$	4.17380	+	2.40974i	0.171542	+	0.0990398i
$593$	16.6936			0.685525			0.342762	−	0.939422i	$-0.388637\pi$
$593$	16.6936			0.685525			0.342762	+	0.939422i	$0.388637\pi$
$594$		0			0
$595$	8.80873	+	12.9017i	0.361123	+	0.528917i
$596$	3.99327	+	1.06999i	0.163571	+	0.0438287i
$597$		0			0
$598$	−13.7018	−	3.75868i	−0.560310	−	0.153704i
$599$		−	13.2549i		−	0.541579i	−0.962639	−	0.270789i	$-0.912715\pi$
$599$		−	13.2549i		−	0.541579i	0.962639	−	0.270789i	$-0.0872847\pi$
$600$		0			0
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	0.854662	−	0.519185i	$-0.173764\pi$
$601$	−0.546605	−	0.946748i	−0.0222965	−	0.0386187i	−0.876958	+	0.480566i	$0.840431\pi$
$602$	7.56474	−	2.02696i	0.308316	−	0.0826129i
$603$		0			0
$604$	−1.65905	−	6.19166i	−0.0675058	−	0.251935i
$605$	−6.09216	−	17.3735i	−0.247682	−	0.706332i
$606$		0			0
$607$	−10.8348	−	40.4361i	−0.439771	−	1.64125i	−0.729384	−	0.684105i	$-0.760193\pi$
$607$	−10.8348	−	40.4361i	−0.439771	−	1.64125i	0.289612	−	0.957144i	$-0.406474\pi$
$608$	12.7652	+	3.42042i	0.517696	+	0.138716i
$609$		0			0
$610$	3.61298	+	3.10506i	0.146285	+	0.125720i
$611$	−24.4142	−	14.2894i	−0.987693	−	0.578087i
$612$		0			0
$613$	24.1705	−	13.9548i	0.976235	−	0.563630i	0.0751039	−	0.997176i	$-0.476071\pi$
$613$	24.1705	−	13.9548i	0.976235	−	0.563630i	0.901131	+	0.433546i	$0.142738\pi$
$614$	−21.4487	+	12.3834i	−0.865601	+	0.499755i
$615$		0			0
$616$	3.42371	+	3.42371i	0.137945	+	0.137945i
$617$	2.19132	−	3.79548i	0.0882193	−	0.152800i	−0.818539	−	0.574451i	$-0.805216\pi$
$617$	2.19132	−	3.79548i	0.0882193	−	0.152800i	0.906758	+	0.421650i	$0.138549\pi$
$618$		0			0
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	0.510998	−	0.859582i	$-0.329276\pi$
$619$	−8.67268	−	8.67268i	−0.348584	−	0.348584i	−0.859582	+	0.510998i	$0.829276\pi$
$620$	−0.341722	−	0.164286i	−0.0137239	−	0.00659787i
$621$		0			0
$622$	6.97193	−	4.02525i	0.279549	−	0.161398i
$623$	−0.353304	+	0.353304i	−0.0141548	+	0.0141548i
$624$		0			0
$625$	−23.8697	+	7.43216i	−0.954788	+	0.297287i
$626$	1.26934	−	4.73726i	0.0507332	−	0.189339i
$627$		0			0
$628$	−5.04668	−	18.8345i	−0.201385	−	0.751577i
$629$	20.9238	−	20.9238i	0.834287	−	0.834287i
$630$		0			0
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	−0.964612	−	0.263673i	$-0.915066\pi$
$631$	−6.55800	−	24.4748i	−0.261070	−	0.974326i	0.703542	−	0.710653i	$-0.251601\pi$
$632$		−	41.0398i		−	1.63248i
$633$		0			0
$634$	11.7220	+	20.3031i	0.465540	+	0.806340i
$635$	−4.01681	+	2.74251i	−0.159402	+	0.108833i
$636$		0			0
$637$	−21.8908	−	0.129906i	−0.867345	−	0.00514706i
$638$	−0.351511	−	0.351511i	−0.0139164	−	0.0139164i
$639$		0			0
$640$	−0.910600	+	4.83016i	−0.0359946	+	0.190929i
$641$	1.41675	+	0.817961i	0.0559582	+	0.0323075i	0.527718	−	0.849420i	$-0.323048\pi$
$641$	1.41675	+	0.817961i	0.0559582	+	0.0323075i	−0.471760	+	0.881727i	$0.656381\pi$
$642$		0			0
$643$	34.3541	+	19.8344i	1.35479	+	0.782191i	0.988917	−	0.148472i	$-0.0474354\pi$
$643$	34.3541	+	19.8344i	1.35479	+	0.782191i	0.365878	+	0.930663i	$0.380769\pi$
$644$	3.42248	−	0.917051i	0.134865	−	0.0361369i
$645$		0			0
$646$	−10.1339	+	17.5525i	−0.398714	+	0.690593i
$647$	3.84742	−	14.3588i	0.151258	−	0.564501i	−0.848139	−	0.529773i	$-0.822277\pi$
$647$	3.84742	−	14.3588i	0.151258	−	0.564501i	0.999397	−	0.0347277i	$-0.0110564\pi$
$648$		0			0
$649$	8.40185			0.329801
$650$	−2.66362	−	18.2421i	−0.104476	−	0.715513i
$651$		0			0
$652$	10.2034	+	17.6729i	0.399597	+	0.692123i
$653$	−3.32718	+	12.4172i	−0.130203	+	0.485922i	−0.999972	−	0.00753655i	$-0.997601\pi$
$653$	−3.32718	+	12.4172i	−0.130203	+	0.485922i	0.869769	+	0.493459i	$0.164268\pi$
$654$		0			0
$655$	0.105565	+	0.0907243i	0.00412476	+	0.00354489i
$656$	7.90103	−	2.11708i	0.308483	−	0.0826579i
$657$		0			0
$658$	−7.73102			−0.301387
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	0.848047	−	0.529922i	$-0.177779\pi$
$659$	20.8742	+	12.0517i	0.813144	+	0.469469i	−0.0349025	+	0.999391i	$0.511112\pi$
$660$		0			0
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.903217	−	0.429185i	$-0.141199\pi$
$661$	37.8150	+	10.1325i	1.47083	+	0.394108i	0.567616	+	0.823293i	$0.307866\pi$
$662$	24.2637	+	24.2637i	0.943036	+	0.943036i
$663$		0			0
$664$		−	25.8862i		−	1.00458i
$665$	4.86415	−	3.32104i	0.188624	−	0.128785i
$666$		0			0
$667$	−1.08784	+	0.291487i	−0.0421215	+	0.0112864i
$668$			1.63601i			0.0632991i
$669$		0			0
$670$	−15.7484	+	5.52232i	−0.608415	+	0.213346i
$671$	2.45030	−	2.45030i	0.0945926	−	0.0945926i
$672$		0			0
$673$	−9.87723	−	2.64660i	−0.380739	−	0.102019i	0.0633730	−	0.997990i	$-0.479814\pi$
$673$	−9.87723	−	2.64660i	−0.380739	−	0.102019i	−0.444112	+	0.895971i	$0.646481\pi$
$674$	5.44776	−	20.3313i	0.209840	−	0.783132i
$675$		0			0
$676$	−12.4044	−	0.147227i	−0.477093	−	0.00566259i
$677$	−29.8933	+	29.8933i	−1.14889	+	1.14889i	−0.162121	+	0.986771i	$0.551833\pi$
$677$	−29.8933	+	29.8933i	−1.14889	+	1.14889i	−0.986771	+	0.162121i	$0.948167\pi$
$678$		0			0
$679$	−6.26961	+	3.61976i	−0.240606	+	0.138914i
$680$	−44.1429	−	21.2221i	−1.69280	−	0.813829i
$681$		0			0
$682$	0.151121	−	0.261750i	0.00578673	−	0.0100229i
$683$	10.0103	−	17.3384i	0.383035	−	0.663436i	−0.608459	−	0.793585i	$-0.708212\pi$
$683$	10.0103	−	17.3384i	0.383035	−	0.663436i	0.991494	+	0.130149i	$0.0415455\pi$
$684$		0			0
$685$	3.26859	+	9.32129i	0.124886	+	0.356148i
$686$	−11.1546	+	6.44013i	−0.425886	+	0.245885i
$687$		0			0
$688$	−6.63664	+	6.63664i	−0.253019	+	0.253019i
$689$	9.85890	−	2.57908i	0.375594	−	0.0982550i
$690$		0			0
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	0.540147	+	0.841571i	$0.318369\pi$
$691$	−9.15886	+	34.1813i	−0.348420	+	1.30032i	−0.888566	+	0.458749i	$0.848298\pi$
$692$	13.9890	+	3.74834i	0.531782	+	0.142491i
$693$		0			0
$694$	−16.4960	+	16.4960i	−0.626181	+	0.626181i
$695$	10.1729	+	29.0109i	0.385881	+	1.10045i
$696$		0			0
$697$		−	50.2221i		−	1.90230i
$698$	−10.2586	+	2.74877i	−0.388292	+	0.104043i
$699$		0			0
$700$	2.87123	+	3.59064i	0.108522	+	0.135714i
$701$		−	37.1781i		−	1.40420i	−0.712080	−	0.702098i	$-0.752247\pi$
$701$		−	37.1781i		−	1.40420i	0.712080	−	0.702098i	$-0.247753\pi$
$702$		0			0
$703$	−7.88864	−	7.88864i	−0.297526	−	0.297526i
$704$	−11.7374	−	3.14502i	−0.442368	−	0.118532i
$705$		0			0
$706$	3.80843	+	2.19880i	0.143332	+	0.0827529i
$707$	−9.39830			−0.353459
$708$		0			0
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.763994	−	0.645224i	$-0.223236\pi$
$709$	46.5506	−	12.4732i	1.74824	−	0.468440i	0.984250	+	0.176783i	$0.0565692\pi$
$710$	2.25023	+	29.7626i	0.0844497	+	1.11697i
$711$		0			0
$712$	0.405449	−	1.51316i	0.0151948	−	0.0567079i
$713$	−0.342369	−	0.593001i	−0.0128218	−	0.0222080i
$714$		0			0
$715$	−13.3774	+	0.931609i	−0.500287	+	0.0348402i
$716$	−2.63300			−0.0983998
$717$		0			0
$718$	−3.90299	+	14.5662i	−0.145658	+	0.543604i
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	0.366190	+	0.930540i	$0.380662\pi$
$719$	−16.6992	+	28.9239i	−0.622777	+	1.07868i	−0.988966	+	0.148141i	$0.952671\pi$
$720$		0			0
$721$	−3.32122	+	0.889918i	−0.123689	+	0.0331423i
$722$	−10.2091	−	5.89421i	−0.379942	−	0.219360i
$723$		0			0
$724$	8.55897	+	4.94153i	0.318092	+	0.183650i
$725$	−0.912629	−	1.14129i	−0.0338942	−	0.0423866i
$726$		0			0
$727$	−23.6487	−	23.6487i	−0.877083	−	0.877083i	0.116149	−	0.993232i	$-0.462945\pi$
$727$	−23.6487	−	23.6487i	−0.877083	−	0.877083i	−0.993232	+	0.116149i	$0.962945\pi$
$728$	−9.12066	+	5.19389i	−0.338034	+	0.192499i
$729$		0			0
$730$	1.36723	−	7.25231i	0.0506036	−	0.268420i
$731$	28.8130	+	49.9055i	1.06569	+	1.84582i
$732$		0			0
$733$		−	14.7049i		−	0.543138i	−0.962419	−	0.271569i	$-0.912458\pi$
$733$		−	14.7049i		−	0.543138i	0.962419	−	0.271569i	$-0.0875424\pi$
$734$	3.02344	+	11.2836i	0.111597	+	0.416486i
$735$		0			0
$736$	−13.1731	+	13.1731i	−0.485568	+	0.485568i
$737$	3.14184	+	11.7255i	0.115731	+	0.431914i
$738$		0			0
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	−0.796185	−	0.605054i	$-0.793152\pi$
$739$	5.32432	−	19.8706i	0.195858	−	0.730953i	0.992043	−	0.125900i	$-0.0401817\pi$
$740$	5.67600	−	6.60447i	0.208654	−	0.242785i
$741$		0			0
$742$	1.96931	−	1.96931i	0.0722956	−	0.0722956i
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.422151	−	0.906526i	$-0.361275\pi$
$743$	38.6601	−	22.3204i	1.41830	−	0.818856i	0.996150	+	0.0876692i	$0.0279419\pi$
$744$		0			0
$745$	−4.19742	+	8.73082i	−0.153781	+	0.319872i
$746$	20.3603	+	20.3603i	0.745443	+	0.745443i
$747$		0			0
$748$	−5.75395	+	9.96614i	−0.210385	+	0.364398i
$749$	−0.302864	−	0.302864i	−0.0110664	−	0.0110664i
$750$		0			0
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	−0.195804	−	0.980643i	$-0.562732\pi$
$751$	15.2247	−	8.78996i	0.555555	−	0.320750i	0.751360	+	0.659893i	$0.229398\pi$
$752$	8.02381	−	4.63255i	0.292598	−	0.168932i
$753$		0			0
$754$	0.936413	−	0.533254i	0.0341022	−	0.0194200i
$755$	14.9778	−	1.13241i	0.545097	−	0.0412125i
$756$		0			0
$757$	33.9933	+	9.10848i	1.23551	+	0.331053i	0.816722	−	0.577032i	$-0.195789\pi$
$757$	33.9933	+	9.10848i	1.23551	+	0.331053i	0.418786	+	0.908085i	$0.362456\pi$
$758$	4.48144	+	16.7250i	0.162773	+	0.607478i
$759$		0			0
$760$	−8.00109	+	16.6426i	−0.290230	+	0.603692i
$761$	3.03122	+	11.3127i	0.109882	+	0.410084i	0.998853	−	0.0478787i	$-0.0152461\pi$
$761$	3.03122	+	11.3127i	0.109882	+	0.410084i	−0.888972	+	0.457962i	$0.848579\pi$
$762$		0			0
$763$	−8.45219	+	2.26476i	−0.305990	+	0.0819897i
$764$	−8.86485	−	15.3544i	−0.320719	−	0.555502i
$765$		0			0
$766$		−	6.75331i		−	0.244007i
$767$	−4.81817	+	17.5641i	−0.173974	+	0.634202i
$768$		0			0
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.0871555	−	0.996195i	$-0.527778\pi$
$769$	−18.3227	−	4.90954i	−0.660732	−	0.177043i	−0.573576	+	0.819152i	$0.694444\pi$
$770$	−3.02663	+	2.06646i	−0.109072	+	0.0744700i
$771$		0			0
$772$	−11.9964			−0.431760
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	0.733306	−	0.679899i	$-0.237976\pi$
$773$	14.2114	+	8.20497i	0.511149	+	0.295112i	−0.222157	+	0.975011i	$0.571310\pi$
$774$		0			0
$775$	0.526647	−	0.715564i	0.0189177	−	0.0257038i
$776$	11.3490	−	19.6570i	0.407404	−	0.705644i
$777$		0			0
$778$	−17.2285	−	29.8406i	−0.617671	−	1.06984i
$779$	−18.9346			−0.678403
$780$		0			0
$781$	21.7109			0.776876
$782$	−14.2856	−	24.7434i	−0.510852	−	0.884822i
$783$		0			0
$784$	3.58492	−	6.20926i	0.128033	−	0.221759i
$785$	45.5610	−	3.44468i	1.62614	−	0.122946i
$786$		0			0
$787$	−11.7781	−	6.80008i	−0.419844	−	0.242397i	0.275167	−	0.961396i	$-0.411267\pi$
$787$	−11.7781	−	6.80008i	−0.419844	−	0.242397i	−0.695010	+	0.719000i	$0.744600\pi$
$788$	13.6326			0.485642
$789$		0			0
$790$	30.5253	+	5.75474i	1.08604	+	0.204745i
$791$	1.80058	+	0.482465i	0.0640214	+	0.0171545i
$792$		0			0
$793$	3.71719	+	6.52751i	0.132001	+	0.231799i
$794$		−	5.95255i		−	0.211248i
$795$		0			0
$796$	7.03076	+	12.1776i	0.249199	+	0.431625i
$797$	28.9148	−	7.74769i	1.02421	−	0.274437i	0.292657	−	0.956218i	$-0.405461\pi$
$797$	28.9148	−	7.74769i	1.02421	−	0.274437i	0.731557	+	0.681780i	$0.238794\pi$
$798$		0			0
$799$	−14.7232	−	54.9476i	−0.520868	−	1.94391i
$800$	−22.5134	−	8.80145i	−0.795969	−	0.311178i
$801$		0			0
$802$	0.0698734	+	0.260771i	0.00246732	+	0.00920815i
$803$	−5.18527	−	1.38939i	−0.182984	−	0.0490305i
$804$		0			0
$805$	0.625946	+	8.27906i	0.0220617	+	0.291799i
$806$	0.460525	+	0.466023i	0.0162213	+	0.0164150i
$807$		0			0
$808$	25.5185	−	14.7331i	0.897739	−	0.518310i
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	−0.544099	−	0.839021i	$-0.683128\pi$
$809$	−2.54661	+	1.47029i	−0.0895342	+	0.0516926i	0.454564	+	0.890714i	$0.349795\pi$
$810$		0			0
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	0.933148	−	0.359492i	$-0.117050\pi$
$811$	16.3366	+	16.3366i	0.573657	+	0.573657i	−0.359492	+	0.933148i	$0.617050\pi$
$812$	−0.134367	+	0.232730i	−0.00471536	+	0.00816724i
$813$		0			0
$814$	4.90856	+	4.90856i	0.172045	+	0.172045i
$815$	−45.1248	+	15.8234i	−1.58065	+	0.554270i
$816$		0			0
$817$	18.8153	−	10.8630i	0.658262	−	0.380048i
$818$	26.8732	−	26.8732i	0.939599	−	0.939599i
$819$		0			0
$820$	−1.11428	−	14.7380i	−0.0389124	−	0.514674i
$821$	−11.8735	+	44.3125i	−0.414388	+	1.54652i	0.371672	+	0.928364i	$0.378785\pi$
$821$	−11.8735	+	44.3125i	−0.414388	+	1.54652i	−0.786059	+	0.618151i	$0.787882\pi$
$822$		0			0
$823$	−4.58752	−	17.1209i	−0.159911	−	0.596796i	−0.998635	−	0.0522385i	$-0.983364\pi$
$823$	−4.58752	−	17.1209i	−0.159911	−	0.596796i	0.838724	−	0.544557i	$-0.183302\pi$
$824$	7.62280	−	7.62280i	0.265553	−	0.265553i
$825$		0			0
$826$	1.28826	+	4.80785i	0.0448242	+	0.167286i
$827$			5.79276i			0.201434i	0.994915	+	0.100717i	$0.0321137\pi$
$827$			5.79276i			0.201434i	−0.994915	+	0.100717i	$0.967886\pi$
$828$		0			0
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	−0.994717	−	0.102657i	$-0.967265\pi$
$829$	−16.8799	−	29.2368i	−0.586262	−	1.01544i	0.408454	−	0.912779i	$-0.366068\pi$
$830$	19.2540	+	3.62985i	0.668317	+	0.125994i
$831$		0			0
$832$	13.3056	−	22.7334i	0.461290	−	0.788139i
$833$	−31.1279	−	31.1279i	−1.07852	−	1.07852i
$834$		0			0
$835$	−3.76724	−	0.710216i	−0.130371	−	0.0245780i
$836$	3.75741	+	2.16934i	0.129953	+	0.0750282i
$837$		0			0
$838$	−30.0364	−	17.3415i	−1.03759	−	0.599053i
$839$	37.8626	−	10.1452i	1.30716	−	0.350253i	0.463008	−	0.886354i	$-0.346770\pi$
$839$	37.8626	−	10.1452i	1.30716	−	0.350253i	0.844154	+	0.536101i	$0.180103\pi$
$840$		0			0
$841$	−14.4573	+	25.0408i	−0.498527	+	0.863475i
$842$	−8.06995	+	30.1175i	−0.278109	+	1.03792i
$843$		0			0
$844$	8.14177			0.280251
$845$	5.72396	−	28.4998i	0.196910	−	0.980422i
$846$		0			0
$847$	−3.96679	−	6.87068i	−0.136300	−	0.236079i
$848$	−0.863850	+	3.22393i	−0.0296647	+	0.110710i
$849$		0			0
$850$	21.9748	−	29.8575i	0.753728	−	1.02410i
$851$	15.1908	−	4.07037i	0.520735	−	0.139531i
$852$		0			0
$853$	40.6417			1.39154			0.695772	−	0.718262i	$-0.255062\pi$
$853$	40.6417			1.39154			0.695772	+	0.718262i	$0.255062\pi$
$854$	1.77785	+	1.02644i	0.0608369	+	0.0351242i
$855$		0			0
$856$	1.29713	+	0.347564i	0.0443348	+	0.0118795i
$857$	−27.2327	−	27.2327i	−0.930252	−	0.930252i	0.0674695	−	0.997721i	$-0.478507\pi$
$857$	−27.2327	−	27.2327i	−0.930252	−	0.930252i	−0.997721	+	0.0674695i	$0.978507\pi$
$858$		0			0
$859$			44.5502i			1.52003i	0.649904	+	0.760016i	$0.274809\pi$
$859$			44.5502i			1.52003i	−0.649904	+	0.760016i	$0.725191\pi$
$860$	9.56262	+	14.0058i	0.326083	+	0.477595i
$861$		0			0
$862$	4.54213	−	1.21706i	0.154706	−	0.0414532i
$863$		−	55.4497i		−	1.88753i	−0.330615	−	0.943766i	$-0.607256\pi$
$863$		−	55.4497i		−	1.88753i	0.330615	−	0.943766i	$-0.392744\pi$
$864$		0			0
$865$	−14.7041	+	30.5853i	−0.499956	+	1.03993i
$866$	−2.89432	+	2.89432i	−0.0983531	+	0.0983531i
$867$		0			0
$868$	−0.157822	−	0.0422883i	−0.00535683	−	0.00143536i
$869$	5.84800	−	21.8250i	0.198380	−	0.740363i
$870$		0			0
$871$	−26.3139	−	0.156154i	−0.891612	−	0.00529107i
$872$	19.3993	−	19.3993i	0.656944	−	0.656944i
$873$		0			0
$874$	−9.32869	+	5.38592i	−0.315548	+	0.182181i
$875$	−9.51462	+	5.05285i	−0.321653	+	0.170817i
$876$		0			0
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	−0.907841	−	0.419314i	$-0.862271\pi$
$877$	−2.68849	+	4.65661i	−0.0907839	+	0.157242i	0.817057	+	0.576557i	$0.195604\pi$
$878$	−11.6188	+	20.1244i	−0.392116	+	0.679166i
$879$		0			0
$880$	1.90300	−	3.95832i	0.0641500	−	0.133435i
$881$	37.0890	−	21.4133i	1.24956	−	0.721434i	0.278538	−	0.960425i	$-0.410150\pi$
$881$	37.0890	−	21.4133i	1.24956	−	0.721434i	0.971022	+	0.238992i	$0.0768169\pi$
$882$		0			0
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.115813	+	0.993271i	$0.536947\pi$
$883$	−32.9568	+	32.9568i	−1.10908	+	1.10908i	−0.993271	+	0.115813i	$0.963053\pi$
$884$	−17.5345	−	17.7439i	−0.589750	−	0.596791i
$885$		0			0
$886$	−0.691990	+	2.58254i	−0.0232478	+	0.0867622i
$887$	−20.4194	−	5.47136i	−0.685616	−	0.183710i	−0.100837	−	0.994903i	$-0.532152\pi$
$887$	−20.4194	−	5.47136i	−0.685616	−	0.183710i	−0.584779	+	0.811193i	$0.698819\pi$
$888$		0			0
$889$	−1.48203	+	1.48203i	−0.0497057	+	0.0497057i
$890$	1.06863	+	0.513751i	0.0358204	+	0.0172210i
$891$		0			0
$892$		−	6.73778i		−	0.225598i
$893$	−20.7162	+	5.55089i	−0.693241	+	0.185753i
$894$		0			0
$895$	1.14302	−	6.06302i	0.0382071	−	0.202664i
$896$			2.11809i			0.0707605i
$897$		0			0
$898$	−23.2645	−	23.2645i	−0.776346	−	0.776346i
$899$	0.0501642	+	0.0134414i	0.00167307	+	0.000448297i
$900$		0			0
$901$	17.7471	+	10.2463i	0.591242	+	0.341354i
$902$	11.7817			0.392288
$903$		0			0
$904$	−5.64533	+	1.51266i	−0.187761	+	0.0503104i
$905$	−15.0944	+	17.5636i	−0.501756	+	0.583833i
$906$		0			0
$907$	2.86355	−	10.6869i	0.0950825	−	0.354853i	−0.901949	−	0.431842i	$-0.857864\pi$
$907$	2.86355	−	10.6869i	0.0950825	−	0.354853i	0.997032	+	0.0769889i	$0.0245306\pi$
$908$	8.19488	+	14.1940i	0.271957	+	0.471043i
$909$		0			0
$910$	−2.58427	−	7.51221i	−0.0856676	−	0.249027i
$911$	15.0479			0.498560			0.249280	−	0.968431i	$-0.419806\pi$
$911$	15.0479			0.498560			0.249280	+	0.968431i	$0.419806\pi$
$912$		0			0
$913$	3.68867	−	13.7663i	0.122077	−	0.455598i
$914$	14.5045	−	25.1226i	0.479767	−	0.830980i
$915$		0			0
$916$	11.6099	−	3.11086i	0.383602	−	0.102786i
$917$	0.0519457	+	0.0299909i	0.00171540	+	0.000990386i
$918$		0			0
$919$	10.8342	+	6.25513i	0.357388	+	0.206338i	0.667934	−	0.744220i	$-0.267179\pi$
$919$	10.8342	+	6.25513i	0.357388	+	0.206338i	−0.310547	+	0.950558i	$0.600512\pi$
$920$	−14.6782	−	21.4983i	−0.483925	−	0.708778i
$921$		0			0
$922$	−8.32259	−	8.32259i	−0.274090	−	0.274090i
$923$	−12.4504	+	45.3866i	−0.409811	+	1.49392i
$924$		0			0
$925$	12.7441	+	15.9372i	0.419023	+	0.524013i
$926$	−15.3114	−	26.5202i	−0.503165	−	0.871508i
$927$		0			0
$928$		−	1.41296i		−	0.0463826i
$929$	−12.6170	−	47.0874i	−0.413952	−	1.54489i	−0.786926	−	0.617047i	$-0.788329\pi$
$929$	−12.6170	−	47.0874i	−0.413952	−	1.54489i	0.372975	−	0.927841i	$-0.378338\pi$
$930$		0			0
$931$	−11.7357	+	11.7357i	−0.384623	+	0.384623i
$932$	6.14112	+	22.9190i	0.201159	+	0.750736i
$933$		0			0
$934$	6.03874	−	22.5369i	0.197594	−	0.737429i
$935$	−20.4512	−	17.5761i	−0.668825	−	0.574800i
$936$		0			0
$937$	7.38027	−	7.38027i	0.241103	−	0.241103i	−0.576203	−	0.817306i	$-0.695466\pi$
$937$	7.38027	−	7.38027i	0.241103	−	0.241103i	0.817306	+	0.576203i	$0.195466\pi$
$938$	−6.22802	+	3.59575i	−0.203352	+	0.117405i
$939$		0			0
$940$	−5.53974	−	15.7981i	−0.180686	−	0.515277i
$941$	1.54410	+	1.54410i	0.0503363	+	0.0503363i	0.731827	−	0.681491i	$-0.238668\pi$
$941$	1.54410	+	1.54410i	0.0503363	+	0.0503363i	−0.681491	+	0.731827i	$0.738668\pi$
$942$		0			0
$943$	13.3459	−	23.1158i	0.434602	−	0.752753i
$944$	−4.21798	−	4.21798i	−0.137284	−	0.137284i
$945$		0			0
$946$	−11.7074	+	6.75929i	−0.380642	+	0.219764i
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	−0.591522	−	0.806289i	$-0.701473\pi$
$947$	−5.81670	+	3.35827i	−0.189017	+	0.109129i	0.402505	+	0.915418i	$0.368140\pi$
$948$		0			0
$949$	5.87810	−	10.0431i	0.190811	−	0.326011i
$950$	−11.2568	−	8.28486i	−0.365218	−	0.268796i
$951$		0			0
$952$	−20.3871	−	5.46272i	−0.660751	−	0.177048i
$953$	4.67309	+	17.4402i	0.151376	+	0.564944i	0.999388	+	0.0349673i	$0.0111327\pi$
$953$	4.67309	+	17.4402i	0.151376	+	0.564944i	−0.848012	+	0.529977i	$0.822201\pi$
$954$		0			0
$955$	39.2049	−	13.7476i	1.26864	−	0.444860i
$956$	0.780600	+	2.91324i	0.0252464	+	0.0942208i
$957$		0			0
$958$	38.3526	−	10.2765i	1.23912	−	0.332020i
$959$	2.12828	+	3.68629i	0.0687257	+	0.119036i
$960$		0			0
$961$		−	30.9684i		−	0.998981i
$962$	−13.0762	+	7.44646i	−0.421595	+	0.240083i
$963$		0			0
$964$	−16.6086	−	4.45026i	−0.534927	−	0.143333i
$965$	5.20782	−	27.6241i	0.167646	−	0.889253i
$966$		0			0
$967$	60.0570			1.93130			0.965651	−	0.259841i	$-0.0836701\pi$
$967$	60.0570			1.93130			0.965651	+	0.259841i	$0.0836701\pi$
$968$	21.5415	+	12.4370i	0.692369	+	0.399740i
$969$		0			0
$970$	13.0294	+	11.1977i	0.418348	+	0.359536i
$971$	−20.4589	+	35.4359i	−0.656558	+	1.13719i	0.324942	+	0.945734i	$0.394655\pi$
$971$	−20.4589	+	35.4359i	−0.656558	+	1.13719i	−0.981501	+	0.191459i	$0.938678\pi$
$972$		0			0
$973$	6.62390	+	11.4729i	0.212352	+	0.367805i
$974$	29.5983			0.948391
$975$		0			0
$976$	−2.46025			−0.0787506
$977$	18.7479	+	32.4724i	0.599800	+	1.03888i	0.992850	+	0.119367i	$0.0380865\pi$
$977$	18.7479	+	32.4724i	0.599800	+	1.03888i	−0.393050	+	0.919517i	$0.628580\pi$
$978$		0			0
$979$	0.431236	−	0.746923i	0.0137824	−	0.0238718i
$980$	−9.82532	−	8.44405i	−0.313858	−	0.269735i
$981$		0			0
$982$	6.44253	+	3.71959i	0.205589	+	0.118697i
$983$	46.1176			1.47092			0.735461	−	0.677567i	$-0.236966\pi$
$983$	46.1176			1.47092			0.735461	+	0.677567i	$0.236966\pi$
$984$		0			0
$985$	−5.91812	+	31.3919i	−0.188567	+	1.00023i
$986$	2.09314	+	0.560854i	0.0666591	+	0.0178612i
$987$		0			0
$988$	−6.68975	+	6.61082i	−0.212829	+	0.210318i
$989$			30.6267i			0.973873i
$990$		0			0
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	0.859584	−	0.510994i	$-0.170722\pi$
$991$	−0.401099	−	0.694724i	−0.0127413	−	0.0220686i	−0.872326	+	0.488925i	$0.837389\pi$
$992$	0.829802	−	0.222345i	0.0263462	−	0.00705945i
$993$		0			0
$994$	3.32894	+	12.4238i	0.105587	+	0.394058i
$995$	−31.0936	+	10.9033i	−0.985734	+	0.345656i
$996$		0			0
$997$	4.04012	+	15.0779i	0.127952	+	0.477522i	0.999928	−	0.0120264i	$-0.00382820\pi$
$997$	4.04012	+	15.0779i	0.127952	+	0.477522i	−0.871976	+	0.489549i	$0.837162\pi$
$998$	5.92576	+	1.58780i	0.187577	+	0.0502610i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.cf.a.388.2		20
3.2	odd	2		65.2.o.a.63.4	yes	20
5.2	odd	4		585.2.dp.a.37.4		20
13.6	odd	12		585.2.dp.a.253.4		20
15.2	even	4		65.2.t.a.37.2	yes	20
15.8	even	4		325.2.x.b.232.4		20
15.14	odd	2		325.2.s.b.193.2		20
39.2	even	12		845.2.f.e.408.8		20
39.5	even	4		845.2.t.f.418.4		20
39.8	even	4		845.2.t.e.418.2		20
39.11	even	12		845.2.f.d.408.3		20
39.17	odd	6		845.2.o.f.488.2		20
39.20	even	12		845.2.t.g.188.4		20
39.23	odd	6		845.2.k.d.268.8		20
39.29	odd	6		845.2.k.e.268.3		20
39.32	even	12		65.2.t.a.58.2	yes	20
39.35	odd	6		845.2.o.e.488.4		20
39.38	odd	2		845.2.o.g.258.2		20
65.32	even	12	inner	585.2.cf.a.487.2		20
195.2	odd	12		845.2.k.e.577.3		20
195.17	even	12		845.2.t.e.657.2		20
195.32	odd	12		65.2.o.a.32.4	✓	20
195.47	odd	4		845.2.o.f.587.2		20
195.62	even	12		845.2.f.d.437.8		20
195.77	even	4		845.2.t.g.427.4		20
195.107	even	12		845.2.f.e.437.3		20
195.122	odd	4		845.2.o.e.587.4		20
195.137	odd	12		845.2.o.g.357.2		20
195.149	even	12		325.2.x.b.318.4		20
195.152	even	12		845.2.t.f.657.4		20
195.167	odd	12		845.2.k.d.577.8		20
195.188	odd	12		325.2.s.b.32.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.32.4	✓	20	195.32	odd	12
65.2.o.a.63.4	yes	20	3.2	odd	2
65.2.t.a.37.2	yes	20	15.2	even	4
65.2.t.a.58.2	yes	20	39.32	even	12
325.2.s.b.32.2		20	195.188	odd	12
325.2.s.b.193.2		20	15.14	odd	2
325.2.x.b.232.4		20	15.8	even	4
325.2.x.b.318.4		20	195.149	even	12
585.2.cf.a.388.2		20	1.1	even	1	trivial
585.2.cf.a.487.2		20	65.32	even	12	inner
585.2.dp.a.37.4		20	5.2	odd	4
585.2.dp.a.253.4		20	13.6	odd	12
845.2.f.d.408.3		20	39.11	even	12
845.2.f.d.437.8		20	195.62	even	12
845.2.f.e.408.8		20	39.2	even	12
845.2.f.e.437.3		20	195.107	even	12
845.2.k.d.268.8		20	39.23	odd	6
845.2.k.d.577.8		20	195.167	odd	12
845.2.k.e.268.3		20	39.29	odd	6
845.2.k.e.577.3		20	195.2	odd	12
845.2.o.e.488.4		20	39.35	odd	6
845.2.o.e.587.4		20	195.122	odd	4
845.2.o.f.488.2		20	39.17	odd	6
845.2.o.f.587.2		20	195.47	odd	4
845.2.o.g.258.2		20	39.38	odd	2
845.2.o.g.357.2		20	195.137	odd	12
845.2.t.e.418.2		20	39.8	even	4
845.2.t.e.657.2		20	195.17	even	12
845.2.t.f.418.4		20	39.5	even	4
845.2.t.f.657.4		20	195.152	even	12
845.2.t.g.188.4		20	39.20	even	12
845.2.t.g.427.4		20	195.77	even	4

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	585.2.cf.a.388.2

Level	$585$
Weight	$2$
Character	585.388
Analytic conductor	$4.671$
Analytic rank	$0$
Dimension	$20$
Inner twists	$2$