LMFDB - Embedded newform 1274.2.v.d.361.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(361,1274)] 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("1274.361"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.v (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-4,6,0,-6,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.4
Root			$0.500000 + 2.47866i$ of defining polynomial
Character	$\chi$	$=$	1274.361
Dual form			1274.2.v.d.667.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} -3.34469 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.35408 - 0.781779i) q^{5} +(-2.89658 - 1.67234i) q^{6} +1.00000i q^{8} +8.18694 q^{9} +1.56356 q^{10} -2.86614i q^{11} +(-1.67234 - 2.89658i) q^{12} +(-2.99598 + 2.00602i) q^{13} +(-4.52898 + 2.61481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.11481 + 1.93090i) q^{17} +(7.09010 + 4.09347i) q^{18} -7.23602i q^{19} +(1.35408 + 0.781779i) q^{20} +(1.43307 - 2.48215i) q^{22} +(-0.833676 + 1.44397i) q^{23} -3.34469i q^{24} +(-1.27764 + 2.21294i) q^{25} +(-3.59760 + 0.239275i) q^{26} -17.3487 q^{27} +(-2.41379 - 4.18080i) q^{29} -5.22961 q^{30} +(0.517851 + 0.298982i) q^{31} +(-0.866025 + 0.500000i) q^{32} +9.58634i q^{33} +2.22961i q^{34} +(4.09347 + 7.09010i) q^{36} +(-0.0333971 - 0.0192818i) q^{37} +(3.61801 - 6.26657i) q^{38} +(10.0206 - 6.70951i) q^{39} +(0.781779 + 1.35408i) q^{40} +(6.88896 - 3.97734i) q^{41} +(5.04571 - 8.73942i) q^{43} +(2.48215 - 1.43307i) q^{44} +(11.0858 - 6.40037i) q^{45} +(-1.44397 + 0.833676i) q^{46} +(6.08501 - 3.51318i) q^{47} +(1.67234 - 2.89658i) q^{48} +(-2.21294 + 1.27764i) q^{50} +(-3.72868 - 6.45826i) q^{51} +(-3.23525 - 1.59158i) q^{52} +(2.99202 - 5.18233i) q^{53} +(-15.0244 - 8.67434i) q^{54} +(-2.24069 - 3.88098i) q^{55} +24.2022i q^{57} -4.82757i q^{58} +(0.776138 - 0.448103i) q^{59} +(-4.52898 - 2.61481i) q^{60} +14.2569 q^{61} +(0.298982 + 0.517851i) q^{62} -1.00000 q^{64} +(-2.48853 + 5.05850i) q^{65} +(-4.79317 + 8.30201i) q^{66} -1.64086i q^{67} +(-1.11481 + 1.93090i) q^{68} +(2.78838 - 4.82962i) q^{69} +(-1.98724 - 1.14733i) q^{71} +8.18694i q^{72} +(-9.72351 - 5.61387i) q^{73} +(-0.0192818 - 0.0333971i) q^{74} +(4.27332 - 7.40161i) q^{75} +(6.26657 - 3.61801i) q^{76} +(12.0329 - 0.800299i) q^{78} +(-2.13049 - 3.69011i) q^{79} +1.56356i q^{80} +33.4651 q^{81} +7.95469 q^{82} -4.94829i q^{83} +(3.01907 + 1.74306i) q^{85} +(8.73942 - 5.04571i) q^{86} +(8.07337 + 13.9835i) q^{87} +2.86614 q^{88} +(2.09682 + 1.21060i) q^{89} +12.8007 q^{90} -1.66735 q^{92} +(-1.73205 - 1.00000i) q^{93} +7.02636 q^{94} +(-5.65696 - 9.79815i) q^{95} +(2.89658 - 1.67234i) q^{96} +(4.23338 + 2.44414i) q^{97} -23.4649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{3} + 6 q^{4} - 6 q^{6} + 12 q^{9} - 4 q^{10} - 2 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} - 16 q^{26} - 40 q^{27} - 10 q^{29} - 28 q^{30} + 18 q^{31}+ \cdots - 60 q^{97}+O(q^{100}) $ 12 * q - 4 * q^3 + 6 * q^4 - 6 * q^6 + 12 * q^9 - 4 * q^10 - 2 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 - 16 * q^26 - 40 * q^27 - 10 * q^29 - 28 * q^30 + 18 * q^31 + 6 * q^36 + 6 * q^37 + 4 * q^38 + 30 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 + 18 * q^44 + 72 * q^45 + 6 * q^46 + 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 + 4 * q^52 - 18 * q^53 - 36 * q^54 + 6 * q^55 + 6 * q^59 - 6 * q^60 - 56 * q^61 + 2 * q^62 - 12 * q^64 + 38 * q^65 + 4 * q^68 - 32 * q^69 + 48 * q^71 - 48 * q^73 + 48 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 + 12 * q^82 + 54 * q^85 - 6 * q^86 - 2 * q^87 - 4 * q^88 + 12 * q^89 - 12 * q^90 - 12 * q^92 + 16 * q^94 + 32 * q^95 + 6 * q^96 - 60 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−3.34469			−1.93106			−0.965528	−	0.260298i	$-0.916179\pi$
$3$	−3.34469			−1.93106			−0.965528	+	0.260298i	$0.916179\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.35408	−	0.781779i	0.605563	−	0.349622i	−0.165664	−	0.986182i	$-0.552977\pi$
$5$	1.35408	−	0.781779i	0.605563	−	0.349622i	0.771227	+	0.636560i	$0.219643\pi$
$6$	−2.89658	−	1.67234i	−1.18253	−	0.682732i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	8.18694			2.72898
$10$	1.56356			0.494440
$11$		−	2.86614i		−	0.864173i	−0.901832	−	0.432087i	$-0.857777\pi$
$11$		−	2.86614i		−	0.864173i	0.901832	−	0.432087i	$-0.142223\pi$
$12$	−1.67234	−	2.89658i	−0.482764	−	0.836172i
$13$	−2.99598	+	2.00602i	−0.830935	+	0.556370i
$13$	−2.99598	+	2.00602i	−0.830935	+	0.556370i
$14$		0			0
$15$	−4.52898	+	2.61481i	−1.16938	+	0.675140i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.11481	+	1.93090i	0.270380	+	0.468312i	0.968959	−	0.247221i	$-0.0795173\pi$
$17$	1.11481	+	1.93090i	0.270380	+	0.468312i	−0.698579	+	0.715533i	$0.746184\pi$
$18$	7.09010	+	4.09347i	1.67115	+	0.964840i
$19$		−	7.23602i		−	1.66006i	−0.557722	−	0.830028i	$-0.688324\pi$
$19$		−	7.23602i		−	1.66006i	0.557722	−	0.830028i	$-0.311676\pi$
$20$	1.35408	+	0.781779i	0.302782	+	0.174811i
$21$		0			0
$22$	1.43307	−	2.48215i	0.305531	−	0.529196i
$23$	−0.833676	+	1.44397i	−0.173833	+	0.301088i	−0.939757	−	0.341843i	$-0.888949\pi$
$23$	−0.833676	+	1.44397i	−0.173833	+	0.301088i	0.765924	+	0.642932i	$0.222282\pi$
$24$		−	3.34469i		−	0.682732i
$25$	−1.27764	+	2.21294i	−0.255529	+	0.442589i
$26$	−3.59760	+	0.239275i	−0.705548	+	0.0469256i
$27$	−17.3487			−3.33876
$28$		0			0
$29$	−2.41379	−	4.18080i	−0.448229	−	0.776356i	0.550042	−	0.835137i	$-0.314612\pi$
$29$	−2.41379	−	4.18080i	−0.448229	−	0.776356i	−0.998271	+	0.0587816i	$0.981278\pi$
$30$	−5.22961			−0.954792
$31$	0.517851	+	0.298982i	0.0930088	+	0.0536987i	0.545783	−	0.837927i	$-0.316232\pi$
$31$	0.517851	+	0.298982i	0.0930088	+	0.0536987i	−0.452774	+	0.891625i	$0.649566\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$			9.58634i			1.66877i
$34$			2.22961i			0.382375i
$35$		0			0
$36$	4.09347	+	7.09010i	0.682245	+	1.18168i
$37$	−0.0333971	−	0.0192818i	−0.00549045	−	0.00316991i	0.497252	−	0.867606i	$-0.334342\pi$
$37$	−0.0333971	−	0.0192818i	−0.00549045	−	0.00316991i	−0.502743	+	0.864436i	$0.667676\pi$
$38$	3.61801	−	6.26657i	0.586918	−	1.01657i
$39$	10.0206	−	6.70951i	1.60458	−	1.07438i
$40$	0.781779	+	1.35408i	0.123610	+	0.214099i
$41$	6.88896	−	3.97734i	1.07588	−	0.621157i	0.146095	−	0.989271i	$-0.453330\pi$
$41$	6.88896	−	3.97734i	1.07588	−	0.621157i	0.929781	+	0.368114i	$0.119996\pi$
$42$		0			0
$43$	5.04571	−	8.73942i	0.769463	−	1.33275i	−0.168391	−	0.985720i	$-0.553857\pi$
$43$	5.04571	−	8.73942i	0.769463	−	1.33275i	0.937854	−	0.347029i	$-0.112809\pi$
$44$	2.48215	−	1.43307i	0.374198	−	0.216043i
$45$	11.0858	−	6.40037i	1.65257	−	0.954111i
$46$	−1.44397	+	0.833676i	−0.212902	+	0.122919i
$47$	6.08501	−	3.51318i	0.887590	−	0.512450i	0.0144363	−	0.999896i	$-0.495405\pi$
$47$	6.08501	−	3.51318i	0.887590	−	0.512450i	0.873153	+	0.487446i	$0.162071\pi$
$48$	1.67234	−	2.89658i	0.241382	−	0.418086i
$49$		0			0
$50$	−2.21294	+	1.27764i	−0.312958	+	0.180686i
$51$	−3.72868	−	6.45826i	−0.522119	−	0.904337i
$52$	−3.23525	−	1.59158i	−0.448649	−	0.220713i
$53$	2.99202	−	5.18233i	0.410985	−	0.711848i	−0.584012	−	0.811745i	$-0.698518\pi$
$53$	2.99202	−	5.18233i	0.410985	−	0.711848i	0.994998	+	0.0998972i	$0.0318514\pi$
$54$	−15.0244	−	8.67434i	−2.04456	−	1.18043i
$55$	−2.24069	−	3.88098i	−0.302134	−	0.523312i
$56$		0			0
$57$			24.2022i			3.20566i
$58$		−	4.82757i		−	0.633892i
$59$	0.776138	−	0.448103i	0.101044	−	0.0583381i	−0.448626	−	0.893719i	$-0.648087\pi$
$59$	0.776138	−	0.448103i	0.101044	−	0.0583381i	0.549671	+	0.835381i	$0.314753\pi$
$60$	−4.52898	−	2.61481i	−0.584688	−	0.337570i
$61$	14.2569			1.82541			0.912706	−	0.408616i	$-0.133989\pi$
$61$	14.2569			1.82541			0.912706	+	0.408616i	$0.133989\pi$
$62$	0.298982	+	0.517851i	0.0379707	+	0.0657672i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−2.48853	+	5.05850i	−0.308664	+	0.627430i
$66$	−4.79317	+	8.30201i	−0.589998	+	1.02191i
$67$		−	1.64086i		−	0.200464i	−0.994964	−	0.100232i	$-0.968042\pi$
$67$		−	1.64086i		−	0.200464i	0.994964	−	0.100232i	$-0.0319584\pi$
$68$	−1.11481	+	1.93090i	−0.135190	+	0.234156i
$69$	2.78838	−	4.82962i	0.335682	−	0.581418i
$70$		0			0
$71$	−1.98724	−	1.14733i	−0.235841	−	0.136163i	0.377422	−	0.926041i	$-0.376810\pi$
$71$	−1.98724	−	1.14733i	−0.235841	−	0.136163i	−0.613264	+	0.789878i	$0.710144\pi$
$72$			8.18694i			0.964840i
$73$	−9.72351	−	5.61387i	−1.13805	−	0.657054i	−0.192104	−	0.981375i	$-0.561531\pi$
$73$	−9.72351	−	5.61387i	−1.13805	−	0.657054i	−0.945947	+	0.324321i	$0.894864\pi$
$74$	−0.0192818	−	0.0333971i	−0.00224147	−	0.00388233i
$75$	4.27332	−	7.40161i	0.493441	−	0.854664i
$76$	6.26657	−	3.61801i	0.718825	−	0.415014i
$77$		0			0
$78$	12.0329	−	0.800299i	1.36245	−	0.0906160i
$79$	−2.13049	−	3.69011i	−0.239699	−	0.415170i	0.720929	−	0.693009i	$-0.243715\pi$
$79$	−2.13049	−	3.69011i	−0.239699	−	0.415170i	−0.960628	+	0.277839i	$0.910382\pi$
$80$			1.56356i			0.174811i
$81$	33.4651			3.71835
$82$	7.95469			0.878449
$83$		−	4.94829i		−	0.543145i	−0.962418	−	0.271572i	$-0.912456\pi$
$83$		−	4.94829i		−	0.543145i	0.962418	−	0.271572i	$-0.0875437\pi$
$84$		0			0
$85$	3.01907	+	1.74306i	0.327465	+	0.189062i
$86$	8.73942	−	5.04571i	0.942396	−	0.544092i
$87$	8.07337	+	13.9835i	0.865556	+	1.49919i
$88$	2.86614			0.305531
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	0.606997	−	0.794704i	$-0.292374\pi$
$89$	2.09682	+	1.21060i	0.222263	+	0.128323i	−0.384735	+	0.923027i	$0.625707\pi$
$90$	12.8007			1.34932
$91$		0			0
$92$	−1.66735			−0.173833
$93$	−1.73205	−	1.00000i	−0.179605	−	0.103695i
$94$	7.02636			0.724714
$95$	−5.65696	−	9.79815i	−0.580392	−	1.00527i
$96$	2.89658	−	1.67234i	0.295631	−	0.170683i
$97$	4.23338	+	2.44414i	0.429835	+	0.248165i	0.699276	−	0.714852i	$-0.253506\pi$
$97$	4.23338	+	2.44414i	0.429835	+	0.248165i	−0.269442	+	0.963017i	$0.586839\pi$
$98$		0			0
$99$		−	23.4649i		−	2.35831i
$100$	−2.55529			−0.255529
$101$	7.36747			0.733091			0.366545	−	0.930400i	$-0.380540\pi$
$101$	7.36747			0.733091			0.366545	+	0.930400i	$0.380540\pi$
$102$		−	7.45736i		−	0.738388i
$103$	−2.89263	−	5.01017i	−0.285019	−	0.493667i	0.687595	−	0.726094i	$-0.258667\pi$
$103$	−2.89263	−	5.01017i	−0.285019	−	0.493667i	−0.972614	+	0.232427i	$0.925333\pi$
$104$	−2.00602	−	2.99598i	−0.196706	−	0.293780i
$105$		0			0
$106$	5.18233	−	2.99202i	0.503352	−	0.290611i
$107$	0.514478	−	0.891102i	0.0497365	−	0.0861461i	−0.840085	−	0.542454i	$-0.817495\pi$
$107$	0.514478	−	0.891102i	0.0497365	−	0.0861461i	0.889822	+	0.456308i	$0.150829\pi$
$108$	−8.67434	−	15.0244i	−0.834689	−	1.44572i
$109$	−12.2573	−	7.07674i	−1.17403	−	0.677829i	−0.219407	−	0.975633i	$-0.570412\pi$
$109$	−12.2573	−	7.07674i	−1.17403	−	0.677829i	−0.954627	+	0.297805i	$0.903746\pi$
$110$		−	4.48137i		−	0.427282i
$111$	0.111703	+	0.0644917i	0.0106024	+	0.00612128i
$112$		0			0
$113$	6.77051	−	11.7269i	0.636916	−	1.10317i	−0.349189	−	0.937052i	$-0.613543\pi$
$113$	6.77051	−	11.7269i	0.636916	−	1.10317i	0.986106	−	0.166119i	$-0.0531237\pi$
$114$	−12.1011	+	20.9597i	−1.13337	+	1.96306i
$115$			2.60700i			0.243104i
$116$	2.41379	−	4.18080i	0.224115	−	0.388178i
$117$	−24.5279	+	16.4232i	−2.26760	+	1.51832i
$118$	0.896206			0.0825025
$119$		0			0
$120$	−2.61481	−	4.52898i	−0.238698	−	0.413437i
$121$	2.78525			0.253205
$122$	12.3469	+	7.12846i	1.11783	+	0.645381i
$123$	−23.0414	+	13.3030i	−2.07758	+	1.19949i
$124$			0.597963i			0.0536987i
$125$			11.8131i			1.05660i
$126$		0			0
$127$	4.92583	+	8.53178i	0.437096	+	0.757073i	0.997464	−	0.0711707i	$-0.0226735\pi$
$127$	4.92583	+	8.53178i	0.437096	+	0.757073i	−0.560368	+	0.828244i	$0.689340\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−16.8763	+	29.2306i	−1.48588	+	2.57361i
$130$	−4.68438	+	3.13653i	−0.410848	+	0.275092i
$131$	7.39614	+	12.8105i	0.646204	+	1.11926i	0.984022	+	0.178047i	$0.0569778\pi$
$131$	7.39614	+	12.8105i	0.646204	+	1.11926i	−0.337818	+	0.941211i	$0.609689\pi$
$132$	−8.30201	+	4.79317i	−0.722597	+	0.417192i
$133$		0			0
$134$	0.820432	−	1.42103i	0.0708746	−	0.122758i
$135$	−23.4915	+	13.5628i	−2.02183	+	1.16730i
$136$	−1.93090	+	1.11481i	−0.165573	+	0.0955938i
$137$	−0.397503	+	0.229499i	−0.0339610	+	0.0196074i	−0.516884	−	0.856055i	$-0.672908\pi$
$137$	−0.397503	+	0.229499i	−0.0339610	+	0.0196074i	0.482923	+	0.875663i	$0.339575\pi$
$138$	4.82962	−	2.78838i	0.411125	−	0.237363i
$139$	7.65731	−	13.2628i	0.649485	−	1.12494i	−0.333762	−	0.942658i	$-0.608318\pi$
$139$	7.65731	−	13.2628i	0.649485	−	1.12494i	0.983246	−	0.182283i	$-0.0583486\pi$
$140$		0			0
$141$	−20.3525	+	11.7505i	−1.71399	+	0.989570i
$142$	−1.14733	−	1.98724i	−0.0962819	−	0.166765i
$143$	5.74953	+	8.58689i	0.480800	+	0.718072i
$144$	−4.09347	+	7.09010i	−0.341122	+	0.590841i
$145$	−6.53693	−	3.77410i	−0.542862	−	0.313422i
$146$	−5.61387	−	9.72351i	−0.464607	−	0.804723i
$147$		0			0
$148$		−	0.0385636i		−	0.00316991i
$149$		−	10.2372i		−	0.838660i	−0.907834	−	0.419330i	$-0.862265\pi$
$149$		−	10.2372i		−	0.838660i	0.907834	−	0.419330i	$-0.137735\pi$
$150$	7.40161	−	4.27332i	0.604339	−	0.348915i
$151$	−13.1731	−	7.60551i	−1.07201	−	0.618927i	−0.143283	−	0.989682i	$-0.545766\pi$
$151$	−13.1731	−	7.60551i	−1.07201	−	0.618927i	−0.928731	+	0.370754i	$0.879099\pi$
$152$	7.23602			0.586918
$153$	9.12684	+	15.8082i	0.737862	+	1.27801i
$154$		0			0
$155$	0.934950			0.0750970
$156$	10.8209	+	5.32335i	0.866366	+	0.426209i
$157$	−1.13709	+	1.96950i	−0.0907500	+	0.157184i	−0.907827	−	0.419345i	$-0.862260\pi$
$157$	−1.13709	+	1.96950i	−0.0907500	+	0.157184i	0.817077	+	0.576529i	$0.195593\pi$
$158$		−	4.26098i		−	0.338985i
$159$	−10.0074	+	17.3333i	−0.793636	+	1.37462i
$160$	−0.781779	+	1.35408i	−0.0618050	+	0.107049i
$161$		0			0
$162$	28.9816	+	16.7326i	2.27701	+	1.31463i
$163$		−	0.00979262i		−	0.000767017i	−1.00000		0.000383509i	$-0.999878\pi$
$163$		−	0.00979262i		−	0.000767017i	1.00000		0.000383509i	$-0.000122075\pi$
$164$	6.88896	+	3.97734i	0.537938	+	0.310578i
$165$	7.49440	+	12.9807i	0.583438	+	1.01054i
$166$	2.47414	−	4.28534i	0.192031	−	0.332607i
$167$	−21.6080	+	12.4754i	−1.67208	+	0.965376i	−0.705608	+	0.708603i	$0.749326\pi$
$167$	−21.6080	+	12.4754i	−1.67208	+	0.965376i	−0.966472	+	0.256773i	$0.917341\pi$
$168$		0			0
$169$	4.95177	−	12.0200i	0.380906	−	0.924614i
$170$	1.74306	+	3.01907i	0.133687	+	0.231552i
$171$		−	59.2408i		−	4.53026i
$172$	10.0914			0.769463
$173$	−3.20550			−0.243709			−0.121855	−	0.992548i	$-0.538884\pi$
$173$	−3.20550			−0.243709			−0.121855	+	0.992548i	$0.538884\pi$
$174$			16.1467i			1.22408i
$175$		0			0
$176$	2.48215	+	1.43307i	0.187099	+	0.108022i
$177$	−2.59594	+	1.49877i	−0.195123	+	0.112654i
$178$	1.21060	+	2.09682i	0.0907383	+	0.157163i
$179$	15.8000			1.18094			0.590472	−	0.807058i	$-0.298942\pi$
$179$	15.8000			1.18094			0.590472	+	0.807058i	$0.298942\pi$
$180$	11.0858	+	6.40037i	0.826285	+	0.477056i
$181$	−9.11907			−0.677815			−0.338908	−	0.940820i	$-0.610057\pi$
$181$	−9.11907			−0.677815			−0.338908	+	0.940820i	$0.610057\pi$
$182$		0			0
$183$	−47.6850			−3.52497
$184$	−1.44397	−	0.833676i	−0.106451	−	0.0614594i
$185$	−0.0602965			−0.00443308
$186$	−1.00000	−	1.73205i	−0.0733236	−	0.127000i
$187$	5.53423	−	3.19519i	0.404703	−	0.233655i
$188$	6.08501	+	3.51318i	0.443795	+	0.256225i
$189$		0			0
$190$		−	11.3139i		−	0.820799i
$191$	−3.26137			−0.235984			−0.117992	−	0.993015i	$-0.537646\pi$
$191$	−3.26137			−0.235984			−0.117992	+	0.993015i	$0.537646\pi$
$192$	3.34469			0.241382
$193$			22.0730i			1.58885i	0.607361	+	0.794426i	$0.292228\pi$
$193$			22.0730i			1.58885i	−0.607361	+	0.794426i	$0.707772\pi$
$194$	2.44414	+	4.23338i	0.175479	+	0.303939i
$195$	8.32336	−	16.9191i	0.596048	−	1.21160i
$196$		0			0
$197$	−4.56660	+	2.63653i	−0.325357	+	0.187845i	−0.653778	−	0.756687i	$-0.726817\pi$
$197$	−4.56660	+	2.63653i	−0.325357	+	0.187845i	0.328421	+	0.944531i	$0.393484\pi$
$198$	11.7324	−	20.3212i	0.833789	−	1.44416i
$199$	−4.43381	−	7.67958i	−0.314304	−	0.544391i	0.664985	−	0.746857i	$-0.268438\pi$
$199$	−4.43381	−	7.67958i	−0.314304	−	0.544391i	−0.979289	+	0.202466i	$0.935105\pi$
$200$	−2.21294	−	1.27764i	−0.156479	−	0.0903431i
$201$			5.48818i			0.387106i
$202$	6.38042	+	3.68373i	0.448924	+	0.259187i
$203$		0			0
$204$	3.72868	−	6.45826i	0.261060	−	0.452169i
$205$	6.21881	−	10.7713i	0.434340	−	0.752300i
$206$		−	5.78525i		−	0.403077i
$207$	−6.82525	+	11.8217i	−0.474388	+	0.821663i
$208$	−0.239275	−	3.59760i	−0.0165907	−	0.249449i
$209$	−20.7394			−1.43458
$210$		0			0
$211$	−3.28453	−	5.68898i	−0.226117	−	0.391646i	0.730537	−	0.682873i	$-0.239270\pi$
$211$	−3.28453	−	5.68898i	−0.226117	−	0.391646i	−0.956654	+	0.291227i	$0.905936\pi$
$212$	5.98404			0.410985
$213$	6.64668	+	3.83746i	0.455423	+	0.262939i
$214$	0.891102	−	0.514478i	0.0609145	−	0.0351690i
$215$		−	15.7785i		−	1.07609i
$216$		−	17.3487i		−	1.18043i
$217$		0			0
$218$	−7.07674	−	12.2573i	−0.479297	−	0.830167i
$219$	32.5221	+	18.7766i	2.19764	+	1.26881i
$220$	2.24069	−	3.88098i	0.151067	−	0.261656i
$221$	−7.21336	−	3.54861i	−0.485223	−	0.238706i
$222$	0.0644917	+	0.111703i	0.00432840	+	0.00749700i
$223$	14.6463	−	8.45606i	0.980790	−	0.566260i	0.0782817	−	0.996931i	$-0.475057\pi$
$223$	14.6463	−	8.45606i	0.980790	−	0.566260i	0.902509	+	0.430672i	$0.141723\pi$
$224$		0			0
$225$	−10.4600	+	18.1172i	−0.697333	+	1.20782i
$226$	11.7269	−	6.77051i	0.780060	−	0.450368i
$227$	−13.9709	+	8.06611i	−0.927282	+	0.535367i	−0.885951	−	0.463779i	$-0.846493\pi$
$227$	−13.9709	+	8.06611i	−0.927282	+	0.535367i	−0.0413312	+	0.999146i	$0.513160\pi$
$228$	−20.9597	+	12.1011i	−1.38809	+	0.801415i
$229$	−5.98583	+	3.45592i	−0.395555	+	0.228374i	−0.684564	−	0.728953i	$-0.740007\pi$
$229$	−5.98583	+	3.45592i	−0.395555	+	0.228374i	0.289009	+	0.957326i	$0.406674\pi$
$230$	−1.30350	+	2.25773i	−0.0859502	+	0.148870i
$231$		0			0
$232$	4.18080	−	2.41379i	0.274483	−	0.158473i
$233$	−3.73702	−	6.47272i	−0.244821	−	0.424042i	0.717261	−	0.696805i	$-0.245396\pi$
$233$	−3.73702	−	6.47272i	−0.244821	−	0.424042i	−0.962081	+	0.272763i	$0.912062\pi$
$234$	−29.4533	+	1.95893i	−1.92543	+	0.128059i
$235$	5.49306	−	9.51426i	0.358328	−	0.620642i
$236$	0.776138	+	0.448103i	0.0505222	+	0.0291690i
$237$	7.12582	+	12.3423i	0.462872	+	0.801717i
$238$		0			0
$239$			19.8696i			1.28526i	0.766179	+	0.642628i	$0.222156\pi$
$239$			19.8696i			1.28526i	−0.766179	+	0.642628i	$0.777844\pi$
$240$		−	5.22961i		−	0.337570i
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	−0.766603	−	0.642121i	$-0.778054\pi$
$241$	−9.21842	+	5.32226i	−0.593811	+	0.342837i	0.172792	+	0.984958i	$0.444721\pi$
$242$	2.41210	+	1.39263i	0.155055	+	0.0895213i
$243$	−59.8843			−3.84158
$244$	7.12846	+	12.3469i	0.456353	+	0.790427i
$245$		0			0
$246$	−26.6060			−1.69633
$247$	14.5156	+	21.6789i	0.923605	+	1.37940i
$248$	−0.298982	+	0.517851i	−0.0189853	+	0.0328836i
$249$			16.5505i			1.04884i
$250$	−5.90656	+	10.2305i	−0.373564	+	0.647032i
$251$	−7.95696	+	13.7819i	−0.502239	+	0.869904i	0.497757	+	0.867316i	$0.334157\pi$
$251$	−7.95696	+	13.7819i	−0.502239	+	0.869904i	−0.999997	+	0.00258749i	$0.999176\pi$
$252$		0			0
$253$	4.13861	+	2.38943i	0.260192	+	0.150222i
$254$			9.85165i			0.618148i
$255$	−10.0979	−	5.83000i	−0.632352	−	0.365089i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.5509	−	26.9350i	0.970039	−	1.68016i	0.274619	−	0.961553i	$-0.411448\pi$
$257$	15.5509	−	26.9350i	0.970039	−	1.68016i	0.695420	−	0.718603i	$-0.255218\pi$
$258$	−29.2306	+	16.8763i	−1.81982	+	1.05067i
$259$		0			0
$260$	−5.62506	+	0.374120i	−0.348851	+	0.0232019i
$261$	−19.7615	−	34.2280i	−1.22321	−	2.11866i
$262$			14.7923i			0.913871i
$263$	−28.3747			−1.74966			−0.874829	−	0.484432i	$-0.839026\pi$
$263$	−28.3747			−1.74966			−0.874829	+	0.484432i	$0.839026\pi$
$264$	−9.58634			−0.589998
$265$		−	9.35639i		−	0.574758i
$266$		0			0
$267$	−7.01321	−	4.04908i	−0.429202	−	0.247800i
$268$	1.42103	−	0.820432i	0.0868032	−	0.0501159i
$269$	−10.7008	−	18.5344i	−0.652441	−	1.13006i	−0.982529	−	0.186111i	$-0.940412\pi$
$269$	−10.7008	−	18.5344i	−0.652441	−	1.13006i	0.330088	−	0.943950i	$-0.392922\pi$
$270$	−27.1257			−1.65082
$271$	4.97667	+	2.87328i	0.302311	+	0.174539i	0.643481	−	0.765462i	$-0.277490\pi$
$271$	4.97667	+	2.87328i	0.302311	+	0.174539i	−0.341170	+	0.940002i	$0.610823\pi$
$272$	−2.22961			−0.135190
$273$		0			0
$274$	−0.458997			−0.0277290
$275$	6.34260	+	3.66190i	0.382473	+	0.220821i
$276$	5.57677			0.335682
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	0.920151	+	0.391564i	$0.128066\pi$
$277$	13.3010	+	23.0380i	0.799180	+	1.38422i	−0.120971	+	0.992656i	$0.538601\pi$
$278$	13.2628	−	7.65731i	0.795453	−	0.459255i
$279$	4.23962	+	2.44774i	0.253819	+	0.146543i
$280$		0			0
$281$			6.69143i			0.399177i	0.979880	+	0.199589i	$0.0639606\pi$
$281$			6.69143i			0.399177i	−0.979880	+	0.199589i	$0.936039\pi$
$282$	−23.5010			−1.39946
$283$	19.9338			1.18494			0.592472	−	0.805591i	$-0.298152\pi$
$283$	19.9338			1.18494			0.592472	+	0.805591i	$0.298152\pi$
$284$		−	2.29466i		−	0.136163i
$285$	18.9208	+	32.7717i	1.12077	+	1.94123i
$286$	0.685794	+	10.3112i	0.0405519	+	0.609716i
$287$		0			0
$288$	−7.09010	+	4.09347i	−0.417788	+	0.241210i
$289$	6.01442	−	10.4173i	0.353789	−	0.612781i
$290$	−3.77410	−	6.53693i	−0.221623	−	0.383861i
$291$	−14.1593	−	8.17490i	−0.830035	−	0.479221i
$292$		−	11.2277i		−	0.657054i
$293$	7.67375	+	4.43044i	0.448305	+	0.258829i	0.707114	−	0.707099i	$-0.249997\pi$
$293$	7.67375	+	4.43044i	0.448305	+	0.258829i	−0.258809	+	0.965929i	$0.583330\pi$
$294$		0			0
$295$	0.700635	−	1.21354i	0.0407926	−	0.0706548i
$296$	0.0192818	−	0.0333971i	0.00112073	−	0.00194117i
$297$			49.7237i			2.88526i
$298$	5.11858	−	8.86563i	0.296511	−	0.513572i
$299$	−0.398955	−	5.99847i	−0.0230722	−	0.346900i
$300$	8.54664			0.493441
$301$		0			0
$302$	−7.60551	−	13.1731i	−0.437648	−	0.758028i
$303$	−24.6419			−1.41564
$304$	6.26657	+	3.61801i	0.359413	+	0.207507i
$305$	19.3050	−	11.1458i	1.10540	−	0.638205i
$306$			18.2537i			1.04349i
$307$			8.34636i			0.476352i	0.971222	+	0.238176i	$0.0765495\pi$
$307$			8.34636i			0.476352i	−0.971222	+	0.238176i	$0.923450\pi$
$308$		0			0
$309$	9.67493	+	16.7575i	0.550387	+	0.953299i
$310$	0.809690	+	0.467475i	0.0459873	+	0.0265508i
$311$	−3.34448	+	5.79281i	−0.189648	+	0.328480i	−0.945133	−	0.326686i	$-0.894068\pi$
$311$	−3.34448	+	5.79281i	−0.189648	+	0.328480i	0.755485	+	0.655166i	$0.227401\pi$
$312$	6.70951	+	10.0206i	0.379851	+	0.567305i
$313$	−10.6894	−	18.5145i	−0.604199	−	1.04650i	−0.992177	−	0.124835i	$-0.960160\pi$
$313$	−10.6894	−	18.5145i	−0.604199	−	1.04650i	0.387978	−	0.921669i	$-0.373174\pi$
$314$	−1.96950	+	1.13709i	−0.111146	+	0.0641699i
$315$		0			0
$316$	2.13049	−	3.69011i	0.119849	−	0.207585i
$317$	−27.4336	+	15.8388i	−1.54083	+	0.889596i	−0.542039	+	0.840353i	$0.682348\pi$
$317$	−27.4336	+	15.8388i	−1.54083	+	0.889596i	−0.998787	+	0.0492433i	$0.984319\pi$
$318$	−17.3333	+	10.0074i	−0.972002	+	0.561185i
$319$	−11.9828	+	6.91825i	−0.670906	+	0.387348i
$320$	−1.35408	+	0.781779i	−0.0756954	+	0.0437028i
$321$	−1.72077	+	2.98046i	−0.0960439	+	0.166353i
$322$		0			0
$323$	13.9720	−	8.06675i	0.777424	−	0.448846i
$324$	16.7326	+	28.9816i	0.929587	+	1.61009i
$325$	−0.611416	−	9.19291i	−0.0339152	−	0.509931i
$326$	0.00489631	−	0.00848066i	0.000271182	−	0.000469700i
$327$	40.9967	+	23.6695i	2.26713	+	1.30893i
$328$	3.97734	+	6.88896i	0.219612	+	0.380379i
$329$		0			0
$330$			14.9888i			0.825106i
$331$			24.6695i			1.35596i	0.735081	+	0.677979i	$0.237144\pi$
$331$			24.6695i			1.35596i	−0.735081	+	0.677979i	$0.762856\pi$
$332$	4.28534	−	2.47414i	0.235189	−	0.135786i
$333$	−0.273420	−	0.157859i	−0.0149833	−	0.00865062i
$334$	−24.9508			−1.36525
$335$	−1.28279	−	2.22186i	−0.0700865	−	0.121393i
$336$		0			0
$337$	28.0871			1.53000			0.765002	−	0.644028i	$-0.222738\pi$
$337$	28.0871			1.53000			0.765002	+	0.644028i	$0.222738\pi$
$338$	10.2984	−	7.93372i	0.560156	−	0.431538i
$339$	−22.6453	+	39.2227i	−1.22992	+	2.13029i
$340$			3.48613i			0.189062i
$341$	0.856923	−	1.48423i	0.0464050	−	0.0803757i
$342$	29.6204	−	51.3040i	1.60169	−	2.77420i
$343$		0			0
$344$	8.73942	+	5.04571i	0.471198	+	0.272046i
$345$		−	8.71960i		−	0.469447i
$346$	−2.77604	−	1.60275i	−0.149241	−	0.0861643i
$347$	5.05398	+	8.75374i	0.271312	+	0.469926i	0.969198	−	0.246283i	$-0.0792093\pi$
$347$	5.05398	+	8.75374i	0.271312	+	0.469926i	−0.697886	+	0.716209i	$0.745876\pi$
$348$	−8.07337	+	13.9835i	−0.432778	+	0.749593i
$349$	15.0596	−	8.69465i	0.806121	−	0.465414i	−0.0394863	−	0.999220i	$-0.512572\pi$
$349$	15.0596	−	8.69465i	0.806121	−	0.465414i	0.845607	+	0.533806i	$0.179239\pi$
$350$		0			0
$351$	51.9763	−	34.8018i	2.77429	−	1.85758i
$352$	1.43307	+	2.48215i	0.0763828	+	0.132299i
$353$		−	3.32659i		−	0.177056i	−0.996074	−	0.0885282i	$-0.971784\pi$
$353$		−	3.32659i		−	0.177056i	0.996074	−	0.0885282i	$-0.0282163\pi$
$354$	−2.99753			−0.159317
$355$	−3.58784			−0.190423
$356$			2.42120i			0.128323i
$357$		0			0
$358$	13.6832	+	7.89998i	0.723177	+	0.417527i
$359$	6.94911	−	4.01207i	0.366760	−	0.211749i	−0.305282	−	0.952262i	$-0.598751\pi$
$359$	6.94911	−	4.01207i	0.366760	−	0.211749i	0.672042	+	0.740513i	$0.265417\pi$
$360$	6.40037	+	11.0858i	0.337329	+	0.584271i
$361$	−33.3599			−1.75579
$362$	−7.89735	−	4.55954i	−0.415075	−	0.239644i
$363$	−9.31579			−0.488952
$364$		0			0
$365$	−17.5552			−0.918882
$366$	−41.2964	−	23.8425i	−2.15860	−	1.24627i
$367$	−1.03908			−0.0542395			−0.0271198	−	0.999632i	$-0.508634\pi$
$367$	−1.03908			−0.0542395			−0.0271198	+	0.999632i	$0.508634\pi$
$368$	−0.833676	−	1.44397i	−0.0434583	−	0.0752721i
$369$	56.3995	−	32.5623i	2.93604	−	1.69512i
$370$	−0.0522183	−	0.0301482i	−0.00271470	−	0.00156733i
$371$		0			0
$372$		−	2.00000i		−	0.103695i
$373$	27.3124			1.41418			0.707092	−	0.707122i	$-0.250007\pi$
$373$	27.3124			1.41418			0.707092	+	0.707122i	$0.250007\pi$
$374$	6.39038			0.330438
$375$		−	39.5112i		−	2.04035i
$376$	3.51318	+	6.08501i	0.181178	+	0.313810i
$377$	15.6184	+	7.68349i	0.804390	+	0.395720i
$378$		0			0
$379$	−1.91535	+	1.10583i	−0.0983850	+	0.0568026i	−0.548385	−	0.836226i	$-0.684757\pi$
$379$	−1.91535	+	1.10583i	−0.0983850	+	0.0568026i	0.450000	+	0.893028i	$0.351424\pi$
$380$	5.65696	−	9.79815i	0.290196	−	0.502634i
$381$	−16.4754	−	28.5361i	−0.844058	−	1.46195i
$382$	−2.82443	−	1.63068i	−0.144510	−	0.0834331i
$383$			22.3386i			1.14145i	0.821142	+	0.570724i	$0.193337\pi$
$383$			22.3386i			1.14145i	−0.821142	+	0.570724i	$0.806663\pi$
$384$	2.89658	+	1.67234i	0.147816	+	0.0853414i
$385$		0			0
$386$	−11.0365	+	19.1158i	−0.561744	+	0.972969i
$387$	41.3089	−	71.5491i	2.09985	−	3.63704i
$388$			4.88829i			0.248165i
$389$	6.13022	−	10.6178i	0.310814	−	0.538346i	−0.667725	−	0.744408i	$-0.732732\pi$
$389$	6.13022	−	10.6178i	0.310814	−	0.538346i	0.978539	+	0.206062i	$0.0660649\pi$
$390$	15.6678	−	10.4907i	0.793370	−	0.531217i
$391$	−3.71755			−0.188004
$392$		0			0
$393$	−24.7378	−	42.8471i	−1.24786	−	2.16135i
$394$	−5.27305			−0.265653
$395$	−5.76971	−	3.33114i	−0.290305	−	0.167608i
$396$	20.3212	−	11.7324i	1.02118	−	0.589578i
$397$			2.93517i			0.147312i	0.997284	+	0.0736561i	$0.0234667\pi$
$397$			2.93517i			0.147312i	−0.997284	+	0.0736561i	$0.976533\pi$
$398$		−	8.86762i		−	0.444493i
$399$		0			0
$400$	−1.27764	−	2.21294i	−0.0638822	−	0.110647i
$401$	−18.9229	−	10.9251i	−0.944963	−	0.545575i	−0.0534502	−	0.998571i	$-0.517022\pi$
$401$	−18.9229	−	10.9251i	−0.944963	−	0.545575i	−0.891513	+	0.452996i	$0.850355\pi$
$402$	−2.74409	+	4.75290i	−0.136863	+	0.237053i
$403$	−2.15123	+	0.143077i	−0.107161	+	0.00712719i
$404$	3.68373	+	6.38042i	0.183273	+	0.317438i
$405$	45.3145	−	26.1623i	2.25169	−	1.30002i
$406$		0			0
$407$	−0.0552644	+	0.0957207i	−0.00273935	+	0.00474470i
$408$	6.45826	−	3.72868i	0.319731	−	0.184597i
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	−0.649657	−	0.760227i	$-0.725088\pi$
$409$	−6.39292	+	3.69095i	−0.316109	+	0.182506i	0.333548	+	0.942733i	$0.391754\pi$
$410$	10.7713	−	6.21881i	0.531956	−	0.307125i
$411$	1.32952	−	0.767601i	0.0655806	−	0.0378630i
$412$	2.89263	−	5.01017i	0.142509	−	0.246834i
$413$		0			0
$414$	−11.8217	+	6.82525i	−0.581004	+	0.335443i
$415$	−3.86846	−	6.70038i	−0.189895	−	0.328909i
$416$	1.59158	−	3.23525i	0.0780338	−	0.158621i
$417$	−25.6113	+	44.3601i	−1.25419	+	2.17232i
$418$	−17.9609	−	10.3697i	−0.878495	−	0.507199i
$419$	−4.29137	−	7.43287i	−0.209647	−	0.363119i	0.741956	−	0.670448i	$-0.233898\pi$
$419$	−4.29137	−	7.43287i	−0.209647	−	0.363119i	−0.951603	+	0.307329i	$0.900565\pi$
$420$		0			0
$421$		−	7.49525i		−	0.365296i	−0.983178	−	0.182648i	$-0.941533\pi$
$421$		−	7.49525i		−	0.365296i	0.983178	−	0.182648i	$-0.0584669\pi$
$422$		−	6.56907i		−	0.319777i
$423$	49.8176	−	28.7622i	2.42221	−	1.39847i
$424$	5.18233	+	2.99202i	0.251676	+	0.145305i
$425$	−5.69730			−0.276360
$426$	3.83746	+	6.64668i	0.185926	+	0.322033i
$427$		0			0
$428$	1.02896			0.0497365
$429$	−19.2304	−	28.7205i	−0.928452	−	1.38664i
$430$	7.88925	−	13.6646i	0.380454	−	0.658965i
$431$		−	16.4791i		−	0.793772i	−0.917868	−	0.396886i	$-0.870091\pi$
$431$		−	16.4791i		−	0.793772i	0.917868	−	0.396886i	$-0.129909\pi$
$432$	8.67434	−	15.0244i	0.417344	−	0.722862i
$433$	12.7805	−	22.1365i	0.614192	−	1.06381i	−0.376333	−	0.926484i	$-0.622815\pi$
$433$	12.7805	−	22.1365i	0.614192	−	1.06381i	0.990526	−	0.137328i	$-0.0438515\pi$
$434$		0			0
$435$	21.8640	+	12.6232i	1.04830	+	0.605235i
$436$		−	14.1535i		−	0.677829i
$437$	10.4486	+	6.03249i	0.499823	+	0.288573i
$438$	18.7766	+	32.5221i	0.897183	+	1.55397i
$439$	−4.60420	+	7.97470i	−0.219746	+	0.380612i	−0.954730	−	0.297473i	$-0.903856\pi$
$439$	−4.60420	+	7.97470i	−0.219746	+	0.380612i	0.734984	+	0.678084i	$0.237190\pi$
$440$	3.88098	−	2.24069i	0.185019	−	0.106821i
$441$		0			0
$442$	−4.47264	−	6.67987i	−0.212742	−	0.317729i
$443$	3.10379	+	5.37593i	0.147466	+	0.255418i	0.930290	−	0.366825i	$-0.119555\pi$
$443$	3.10379	+	5.37593i	0.147466	+	0.255418i	−0.782824	+	0.622243i	$0.786222\pi$
$444$			0.128983i			0.00612128i
$445$	3.78569			0.179459
$446$	16.9121			0.800812
$447$			34.2401i			1.61950i
$448$		0			0
$449$	4.51968	+	2.60944i	0.213297	+	0.123147i	0.602843	−	0.797860i	$-0.294035\pi$
$449$	4.51968	+	2.60944i	0.213297	+	0.123147i	−0.389546	+	0.921007i	$0.627368\pi$
$450$	−18.1172	+	10.4600i	−0.854055	+	0.493089i
$451$	−11.3996	−	19.7447i	−0.536787	−	0.929743i
$452$	13.5410			0.636916
$453$	44.0600	+	25.4380i	2.07012	+	1.19518i
$454$	−16.1322			−0.757123
$455$		0			0
$456$	−24.2022			−1.13337
$457$	29.3870	+	16.9666i	1.37467	+	0.793664i	0.991511	−	0.130021i	$-0.0415043\pi$
$457$	29.3870	+	16.9666i	1.37467	+	0.793664i	0.383155	+	0.923684i	$0.374838\pi$
$458$	−6.91184			−0.322969
$459$	−19.3404	−	33.4986i	−0.902733	−	1.56358i
$460$	−2.25773	+	1.30350i	−0.105267	+	0.0607760i
$461$	−0.731583	−	0.422380i	−0.0340732	−	0.0196722i	0.482867	−	0.875694i	$-0.339596\pi$
$461$	−0.731583	−	0.422380i	−0.0340732	−	0.0196722i	−0.516940	+	0.856022i	$0.672929\pi$
$462$		0			0
$463$			6.50221i			0.302183i	0.988520	+	0.151092i	$0.0482789\pi$
$463$			6.50221i			0.302183i	−0.988520	+	0.151092i	$0.951721\pi$
$464$	4.82757			0.224115
$465$	−3.12712			−0.145016
$466$		−	7.47405i		−	0.346229i
$467$	4.76379	+	8.25113i	0.220442	+	0.381817i	0.954942	−	0.296792i	$-0.0959167\pi$
$467$	4.76379	+	8.25113i	0.220442	+	0.381817i	−0.734500	+	0.678608i	$0.762583\pi$
$468$	−26.4868	−	13.0302i	−1.22435	−	0.602321i
$469$		0			0
$470$	9.51426	−	5.49306i	0.438860	−	0.253376i
$471$	3.80322	−	6.58738i	0.175243	−	0.303530i
$472$	0.448103	+	0.776138i	0.0206256	+	0.0357246i
$473$	−25.0484	−	14.4617i	−1.15173	−	0.664949i
$474$			14.2516i			0.654599i
$475$	16.0129	+	9.24505i	0.734722	+	0.424192i
$476$		0			0
$477$	24.4955	−	42.4274i	1.12157	−	1.94262i
$478$	−9.93478	+	17.2075i	−0.454406	+	0.787055i
$479$			2.84198i			0.129854i	0.997890	+	0.0649268i	$0.0206814\pi$
$479$			2.84198i			0.129854i	−0.997890	+	0.0649268i	$0.979319\pi$
$480$	2.61481	−	4.52898i	0.119349	−	0.206719i
$481$	0.138737	−	0.00922730i	0.00632585	−	0.000420729i
$482$	−10.6445			−0.484844
$483$		0			0
$484$	1.39263	+	2.41210i	0.0633011	+	0.109641i
$485$	7.64312			0.347056
$486$	−51.8613	−	29.9422i	−2.35248	−	1.35820i
$487$	4.55853	−	2.63187i	0.206567	−	0.119261i	−0.393148	−	0.919475i	$-0.628614\pi$
$487$	4.55853	−	2.63187i	0.206567	−	0.119261i	0.599715	+	0.800214i	$0.295281\pi$
$488$			14.2569i			0.645381i
$489$			0.0327533i			0.00148115i
$490$		0			0
$491$	11.4457	+	19.8245i	0.516536	+	0.894666i	0.999816	+	0.0192004i	$0.00611205\pi$
$491$	11.4457	+	19.8245i	0.516536	+	0.894666i	−0.483280	+	0.875466i	$0.660555\pi$
$492$	−23.0414	−	13.3030i	−1.03879	−	0.599745i
$493$	5.38181	−	9.32157i	0.242384	−	0.419822i
$494$	1.73140	+	26.0323i	0.0778992	+	1.17125i
$495$	−18.3444	−	31.7734i	−0.824517	−	1.42811i
$496$	−0.517851	+	0.298982i	−0.0232522	+	0.0134247i
$497$		0			0
$498$	−8.27524	+	14.3331i	−0.370822	+	0.642283i
$499$	−5.88791	+	3.39938i	−0.263579	+	0.152177i	−0.625966	−	0.779850i	$-0.715295\pi$
$499$	−5.88791	+	3.39938i	−0.263579	+	0.152177i	0.362387	+	0.932028i	$0.381962\pi$
$500$	−10.2305	+	5.90656i	−0.457520	+	0.264150i
$501$	72.2721	−	41.7263i	3.22888	−	1.86419i
$502$	−13.7819	+	7.95696i	−0.615115	+	0.355137i
$503$	5.40300	−	9.35827i	0.240908	−	0.417265i	−0.720065	−	0.693906i	$-0.755888\pi$
$503$	5.40300	−	9.35827i	0.240908	−	0.417265i	0.960973	+	0.276642i	$0.0892215\pi$
$504$		0			0
$505$	9.97615	−	5.75973i	0.443933	−	0.256305i
$506$	2.38943	+	4.13861i	0.106223	+	0.183984i
$507$	−16.5621	+	40.2031i	−0.735550	+	1.78548i
$508$	−4.92583	+	8.53178i	−0.218548	+	0.378537i
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.126400	−	0.991979i	$-0.540342\pi$
$509$	−23.6593	−	13.6597i	−1.04868	−	0.605455i	−0.922279	+	0.386524i	$0.873676\pi$
$510$	−5.83000	−	10.0979i	−0.258157	−	0.447141i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$			125.535i			5.54252i
$514$	26.9350	−	15.5509i	1.18805	−	0.685921i
$515$	−7.83369	−	4.52279i	−0.345194	−	0.199298i
$516$	−33.7526			−1.48588
$517$	−10.0693	−	17.4405i	−0.442846	−	0.767031i
$518$		0			0
$519$	10.7214			0.470616
$520$	−5.05850	−	2.48853i	−0.221830	−	0.109129i
$521$	−1.81790	+	3.14870i	−0.0796437	+	0.137947i	−0.903096	−	0.429438i	$-0.858712\pi$
$521$	−1.81790	+	3.14870i	−0.0796437	+	0.137947i	0.823453	+	0.567385i	$0.192045\pi$
$522$		−	39.5230i		−	1.72988i
$523$	−3.59223	+	6.22193i	−0.157077	+	0.272066i	−0.933813	−	0.357760i	$-0.883541\pi$
$523$	−3.59223	+	6.22193i	−0.157077	+	0.272066i	0.776736	+	0.629826i	$0.216874\pi$
$524$	−7.39614	+	12.8105i	−0.323102	+	0.559629i
$525$		0			0
$526$	−24.5732	−	14.1873i	−1.07144	−	0.618597i
$527$			1.33323i			0.0580762i
$528$	−8.30201	−	4.79317i	−0.361299	−	0.208596i
$529$	10.1100	+	17.5110i	0.439564	+	0.761347i
$530$	4.67819	−	8.10287i	0.203208	−	0.351966i
$531$	6.35419	−	3.66859i	0.275748	−	0.159203i
$532$		0			0
$533$	−12.6606	+	25.7354i	−0.548389	+	1.11473i
$534$	−4.04908	−	7.01321i	−0.175221	−	0.303491i
$535$		−	1.60883i		−	0.0695559i
$536$	1.64086			0.0708746
$537$	−52.8459			−2.28047
$538$		−	21.4017i		−	0.922691i
$539$		0			0
$540$	−23.4915	−	13.5628i	−1.01091	−	0.583651i
$541$	−0.385436	+	0.222531i	−0.0165712	+	0.00956737i	−0.508263	−	0.861202i	$-0.669712\pi$
$541$	−0.385436	+	0.222531i	−0.0165712	+	0.00956737i	0.491692	+	0.870769i	$0.336379\pi$
$542$	2.87328	+	4.97667i	0.123418	+	0.213766i
$543$	30.5004			1.30890
$544$	−1.93090	−	1.11481i	−0.0827867	−	0.0477969i
$545$	−22.1298			−0.947935
$546$		0			0
$547$	−5.67129			−0.242487			−0.121243	−	0.992623i	$-0.538688\pi$
$547$	−5.67129			−0.242487			−0.121243	+	0.992623i	$0.538688\pi$
$548$	−0.397503	−	0.229499i	−0.0169805	−	0.00980370i
$549$	116.721			4.98151
$550$	3.66190	+	6.34260i	0.156144	+	0.270450i
$551$	−30.2524	+	17.4662i	−1.28879	+	0.744085i
$552$	4.82962	+	2.78838i	0.205562	+	0.118682i
$553$		0			0
$554$			26.6020i			1.13021i
$555$	0.201673			0.00856054
$556$	15.3146			0.649485
$557$			26.5075i			1.12316i	0.827423	+	0.561579i	$0.189806\pi$
$557$			26.5075i			1.12316i	−0.827423	+	0.561579i	$0.810194\pi$
$558$	2.44774	+	4.23962i	0.103621	+	0.179477i
$559$	2.41462	+	36.3049i	0.102128	+	1.53553i
$560$		0			0
$561$	−18.5103	+	10.6869i	−0.781504	+	0.451202i
$562$	−3.34571	+	5.79495i	−0.141130	+	0.244445i
$563$	5.76880	+	9.99186i	0.243126	+	0.421107i	0.961603	−	0.274444i	$-0.0884938\pi$
$563$	5.76880	+	9.99186i	0.243126	+	0.421107i	−0.718477	+	0.695551i	$0.755160\pi$
$564$	−20.3525	−	11.7505i	−0.856993	−	0.494785i
$565$		−	21.1722i		−	0.890720i
$566$	17.2632	+	9.96692i	0.725627	+	0.418941i
$567$		0			0
$568$	1.14733	−	1.98724i	0.0481409	−	0.0833826i
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	0.302671	+	0.953095i	$0.402122\pi$
$569$	−16.0791	+	27.8497i	−0.674069	+	1.16752i	−0.976740	+	0.214427i	$0.931212\pi$
$570$			37.8416i			1.58501i
$571$	5.77702	−	10.0061i	0.241761	−	0.418742i	−0.719455	−	0.694539i	$-0.755608\pi$
$571$	5.77702	−	10.0061i	0.241761	−	0.418742i	0.961216	+	0.275797i	$0.0889418\pi$
$572$	−4.56170	+	9.27268i	−0.190734	+	0.387710i
$573$	10.9083			0.455699
$574$		0			0
$575$	−2.13028	−	3.68976i	−0.0888389	−	0.153873i
$576$	−8.18694			−0.341122
$577$	7.91591	+	4.57025i	0.329543	+	0.190262i	0.655638	−	0.755075i	$-0.272400\pi$
$577$	7.91591	+	4.57025i	0.329543	+	0.190262i	−0.326095	+	0.945337i	$0.605733\pi$
$578$	10.4173	−	6.01442i	0.433301	−	0.250167i
$579$		−	73.8274i		−	3.06816i
$580$		−	7.54819i		−	0.313422i
$581$		0			0
$582$	−8.17490	−	14.1593i	−0.338860	−	0.586923i
$583$	−14.8533	−	8.57554i	−0.615160	−	0.355163i
$584$	5.61387	−	9.72351i	0.232304	−	0.402362i
$585$	−20.3735	+	41.4137i	−0.842339	+	1.71224i
$586$	4.43044	+	7.67375i	0.183020	+	0.317000i
$587$	−37.0629	+	21.3983i	−1.52975	+	0.883201i	−0.530378	+	0.847761i	$0.677950\pi$
$587$	−37.0629	+	21.3983i	−1.52975	+	0.883201i	−0.999372	+	0.0354398i	$0.988717\pi$
$588$		0			0
$589$	2.16344	−	3.74718i	0.0891428	−	0.154400i
$590$	1.21354	−	0.700635i	0.0499605	−	0.0288447i
$591$	15.2738	−	8.81836i	0.628282	−	0.362739i
$592$	0.0333971	−	0.0192818i	0.00137261	−	0.000792478i
$593$	12.3356	−	7.12195i	0.506561	−	0.292463i	−0.224858	−	0.974392i	$-0.572192\pi$
$593$	12.3356	−	7.12195i	0.506561	−	0.292463i	0.731419	+	0.681928i	$0.238858\pi$
$594$	−24.8619	+	43.0620i	−1.02009	+	1.76686i
$595$		0			0
$596$	8.86563	−	5.11858i	0.363150	−	0.209665i
$597$	14.8297	+	25.6858i	0.606939	+	1.05125i
$598$	2.65373	−	5.39430i	0.108519	−	0.220589i
$599$	−1.87367	+	3.24530i	−0.0765563	+	0.132599i	−0.901762	−	0.432233i	$-0.857726\pi$
$599$	−1.87367	+	3.24530i	−0.0765563	+	0.132599i	0.825206	+	0.564832i	$0.191059\pi$
$600$	7.40161	+	4.27332i	0.302169	+	0.174458i
$601$	5.33462	+	9.23984i	0.217604	+	0.376901i	0.954075	−	0.299568i	$-0.0968426\pi$
$601$	5.33462	+	9.23984i	0.217604	+	0.376901i	−0.736471	+	0.676469i	$0.763509\pi$
$602$		0			0
$603$		−	13.4337i		−	0.547061i
$604$		−	15.2110i		−	0.618927i
$605$	3.77145	−	2.17745i	0.153331	−	0.0885259i
$606$	−21.3405	−	12.3209i	−0.866898	−	0.500504i
$607$	−9.65256			−0.391785			−0.195893	−	0.980625i	$-0.562760\pi$
$607$	−9.65256			−0.391785			−0.195893	+	0.980625i	$0.562760\pi$
$608$	3.61801	+	6.26657i	0.146730	+	0.254143i
$609$		0			0
$610$	22.2915			0.902558
$611$	−11.1830	+	22.7321i	−0.452417	+	0.919641i
$612$	−9.12684	+	15.8082i	−0.368931	+	0.639007i
$613$		−	3.99489i		−	0.161352i	−0.996740	−	0.0806761i	$-0.974292\pi$
$613$		−	3.99489i		−	0.161352i	0.996740	−	0.0806761i	$-0.0257079\pi$
$614$	−4.17318	+	7.22816i	−0.168416	+	0.291705i
$615$	−20.8000	+	36.0266i	−0.838736	+	1.45273i
$616$		0			0
$617$	2.80199	+	1.61773i	0.112804	+	0.0651273i	0.555340	−	0.831623i	$-0.312588\pi$
$617$	2.80199	+	1.61773i	0.112804	+	0.0651273i	−0.442537	+	0.896750i	$0.645921\pi$
$618$			19.3499i			0.778365i
$619$	−34.0070	−	19.6340i	−1.36686	−	0.789156i	−0.376333	−	0.926485i	$-0.622815\pi$
$619$	−34.0070	−	19.6340i	−1.36686	−	0.789156i	−0.990526	+	0.137329i	$0.956148\pi$
$620$	0.467475	+	0.809690i	0.0187742	+	0.0325179i
$621$	14.4632	−	25.0510i	0.580387	−	1.00526i
$622$	−5.79281	+	3.34448i	−0.232270	+	0.134101i
$623$		0			0
$624$	0.800299	+	12.0329i	0.0320376	+	0.481700i
$625$	2.84703	+	4.93120i	0.113881	+	0.197248i
$626$		−	21.3788i		−	0.854467i
$627$	69.3669			2.77025
$628$	−2.27419			−0.0907500
$629$		−	0.0859819i		−	0.00342832i
$630$		0			0
$631$	25.4983	+	14.7215i	1.01507	+	0.586052i	0.912673	−	0.408691i	$-0.134015\pi$
$631$	25.4983	+	14.7215i	1.01507	+	0.586052i	0.102400	+	0.994743i	$0.467348\pi$
$632$	3.69011	−	2.13049i	0.146785	−	0.0847463i
$633$	10.9857	+	19.0279i	0.436644	+	0.756290i
$634$	−31.6776			−1.25808
$635$	13.3399	+	7.70181i	0.529379	+	0.305637i
$636$	−20.0147			−0.793636
$637$		0			0
$638$	−13.8365			−0.547792
$639$	−16.2694	−	9.39313i	−0.643606	−	0.371586i
$640$	−1.56356			−0.0618050
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	0.903592	−	0.428394i	$-0.140920\pi$
$641$	2.04559	+	3.54307i	0.0807961	+	0.139943i	−0.822796	+	0.568337i	$0.807587\pi$
$642$	−2.98046	+	1.72077i	−0.117629	+	0.0679133i
$643$	−19.2672	−	11.1239i	−0.759825	−	0.438685i	0.0694080	−	0.997588i	$-0.477889\pi$
$643$	−19.2672	−	11.1239i	−0.759825	−	0.438685i	−0.829233	+	0.558903i	$0.811222\pi$
$644$		0			0
$645$			52.7742i			2.07798i
$646$	16.1335			0.634764
$647$	−49.8583			−1.96013			−0.980066	−	0.198670i	$-0.936338\pi$
$647$	−49.8583			−1.96013			−0.980066	+	0.198670i	$0.936338\pi$
$648$			33.4651i			1.31463i
$649$	−1.28433	−	2.22452i	−0.0504142	−	0.0873200i
$650$	4.06695	−	8.26700i	0.159519	−	0.324259i
$651$		0			0
$652$	0.00848066	−	0.00489631i	0.000332128	−	0.000191754i
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	−0.929321	−	0.369272i	$-0.879607\pi$
$653$	−3.70177	+	6.41165i	−0.144861	+	0.250907i	0.784460	+	0.620180i	$0.212940\pi$
$654$	23.6695	+	40.9967i	0.925550	+	1.60310i
$655$	20.0299	+	11.5643i	0.782635	+	0.451854i
$656$			7.95469i			0.310578i
$657$	−79.6058	−	45.9604i	−3.10572	−	1.79309i
$658$		0			0
$659$	−15.0410	+	26.0518i	−0.585914	+	1.01483i	0.408847	+	0.912603i	$0.365931\pi$
$659$	−15.0410	+	26.0518i	−0.585914	+	1.01483i	−0.994761	+	0.102230i	$0.967402\pi$
$660$	−7.49440	+	12.9807i	−0.291719	+	0.505272i
$661$		−	26.6319i		−	1.03586i	−0.855423	−	0.517931i	$-0.826702\pi$
$661$		−	26.6319i		−	1.03586i	0.855423	−	0.517931i	$-0.173298\pi$
$662$	−12.3347	+	21.3644i	−0.479404	+	0.830351i
$663$	24.1264	+	11.8690i	0.936993	+	0.460954i
$664$	4.94829			0.192031
$665$		0			0
$666$	−0.157859	−	0.273420i	−0.00611691	−	0.0105948i
$667$	8.04926			0.311669
$668$	−21.6080	−	12.4754i	−0.836040	−	0.482688i
$669$	−48.9874	+	28.2829i	−1.89396	+	1.09348i
$670$		−	2.56559i		−	0.0991172i
$671$		−	40.8623i		−	1.57747i
$672$		0			0
$673$	−1.84652	−	3.19827i	−0.0711783	−	0.123284i	0.828240	−	0.560374i	$-0.189343\pi$
$673$	−1.84652	−	3.19827i	−0.0711783	−	0.123284i	−0.899418	+	0.437090i	$0.856009\pi$
$674$	24.3242	+	14.0436i	0.936932	+	0.540938i
$675$	22.1654	−	38.3917i	0.853148	−	1.47770i
$676$	12.8855	−	1.72163i	0.495596	−	0.0662166i
$677$	−17.8266	−	30.8767i	−0.685134	−	1.18669i	−0.973395	−	0.229134i	$-0.926410\pi$
$677$	−17.8266	−	30.8767i	−0.685134	−	1.18669i	0.288261	−	0.957552i	$-0.406923\pi$
$678$	−39.2227	+	22.6453i	−1.50634	+	0.869686i
$679$		0			0
$680$	−1.74306	+	3.01907i	−0.0668434	+	0.115776i
$681$	46.7283	−	26.9786i	1.79063	−	1.03382i
$682$	1.48423	−	0.856923i	0.0568342	−	0.0328133i
$683$	26.2105	−	15.1326i	1.00292	−	0.579034i	0.0938062	−	0.995590i	$-0.470097\pi$
$683$	26.2105	−	15.1326i	1.00292	−	0.579034i	0.909110	+	0.416557i	$0.136763\pi$
$684$	51.3040	−	29.6204i	1.96166	−	1.13256i
$685$	−0.358834	+	0.621519i	−0.0137104	+	0.0237470i
$686$		0			0
$687$	20.0207	−	11.5590i	0.763838	−	0.441002i
$688$	5.04571	+	8.73942i	0.192366	+	0.333187i
$689$	1.43183	+	21.5282i	0.0545483	+	0.820159i
$690$	4.35980	−	7.55139i	0.165975	−	0.287477i
$691$	3.03377	+	1.75155i	0.115410	+	0.0666320i	0.556594	−	0.830785i	$-0.312108\pi$
$691$	3.03377	+	1.75155i	0.115410	+	0.0666320i	−0.441184	+	0.897417i	$0.645441\pi$
$692$	−1.60275	−	2.77604i	−0.0609273	−	0.105529i
$693$		0			0
$694$			10.1080i			0.383693i
$695$		−	23.9453i		−	0.908297i
$696$	−13.9835	+	8.07337i	−0.530042	+	0.306020i
$697$	15.3597	+	8.86793i	0.581791	+	0.335897i
$698$	17.3893			0.658195
$699$	12.4992	+	21.6492i	0.472762	+	0.818849i
$700$		0			0
$701$	−45.2243			−1.70810			−0.854048	−	0.520194i	$-0.825860\pi$
$701$	−45.2243			−1.70810			−0.854048	+	0.520194i	$0.825860\pi$
$702$	62.4137	−	4.15110i	2.35565	−	0.156673i
$703$	−0.139524	+	0.241662i	−0.00526223	+	0.00911445i
$704$			2.86614i			0.108022i
$705$	−18.3726	+	31.8222i	−0.691951	+	1.19849i
$706$	1.66329	−	2.88091i	0.0625989	−	0.108424i
$707$		0			0
$708$	−2.59594	−	1.49877i	−0.0975613	−	0.0563270i
$709$		−	2.99826i		−	0.112602i	−0.998414	−	0.0563009i	$-0.982069\pi$
$709$		−	2.99826i		−	0.112602i	0.998414	−	0.0563009i	$-0.0179306\pi$
$710$	−3.10716	−	1.79392i	−0.116610	−	0.0673245i
$711$	−17.4422	−	30.2107i	−0.654133	−	1.13299i
$712$	−1.21060	+	2.09682i	−0.0453692	+	0.0785817i
$713$	−0.863440	+	0.498507i	−0.0323361	+	0.0186692i
$714$		0			0
$715$	14.4984	+	7.13248i	0.542208	+	0.266740i
$716$	7.89998	+	13.6832i	0.295236	+	0.511364i
$717$		−	66.4575i		−	2.48190i
$718$	8.02414			0.299458
$719$	−20.0794			−0.748834			−0.374417	−	0.927260i	$-0.622157\pi$
$719$	−20.0794			−0.748834			−0.374417	+	0.927260i	$0.622157\pi$
$720$			12.8007i			0.477056i
$721$		0			0
$722$	−28.8905	−	16.6800i	−1.07519	−	0.620764i
$723$	30.8327	−	17.8013i	1.14668	−	0.662037i
$724$	−4.55954	−	7.89735i	−0.169454	−	0.293503i
$725$	12.3358			0.458142
$726$	−8.06771	−	4.65790i	−0.299421	−	0.172871i
$727$	32.5895			1.20868			0.604338	−	0.796728i	$-0.293438\pi$
$727$	32.5895			1.20868			0.604338	+	0.796728i	$0.293438\pi$
$728$		0			0
$729$	99.8990			3.69996
$730$	−15.2033	−	8.77761i	−0.562698	−	0.324874i
$731$	22.4999			0.832190
$732$	−23.8425	−	41.2964i	−0.881244	−	1.52636i
$733$	−16.0380	+	9.25952i	−0.592376	+	0.342008i	−0.766036	−	0.642797i	$-0.777774\pi$
$733$	−16.0380	+	9.25952i	−0.592376	+	0.342008i	0.173661	+	0.984806i	$0.444440\pi$
$734$	−0.899869	−	0.519540i	−0.0332148	−	0.0191766i
$735$		0			0
$736$		−	1.66735i		−	0.0614594i
$737$	−4.70294			−0.173235
$738$	65.1245			2.39727
$739$			15.9312i			0.586038i	0.956107	+	0.293019i	$0.0946600\pi$
$739$			15.9312i			0.586038i	−0.956107	+	0.293019i	$0.905340\pi$
$740$	−0.0301482	−	0.0522183i	−0.00110827	−	0.00191958i
$741$	−48.5501	−	72.5093i	−1.78353	−	2.66370i
$742$		0			0
$743$	10.5962	−	6.11773i	0.388738	−	0.224438i	−0.292875	−	0.956151i	$-0.594612\pi$
$743$	10.5962	−	6.11773i	0.388738	−	0.224438i	0.681613	+	0.731713i	$0.261279\pi$
$744$	1.00000	−	1.73205i	0.0366618	−	0.0635001i
$745$	−8.00319	−	13.8619i	−0.293214	−	0.507862i
$746$	23.6532	+	13.6562i	0.866007	+	0.499989i
$747$		−	40.5113i		−	1.48223i
$748$	5.53423	+	3.19519i	0.202351	+	0.116828i
$749$		0			0
$750$	19.7556	−	34.2177i	0.721373	−	1.24945i
$751$	−10.4107	+	18.0318i	−0.379891	+	0.657990i	−0.991046	−	0.133521i	$-0.957372\pi$
$751$	−10.4107	+	18.0318i	−0.379891	+	0.657990i	0.611155	+	0.791511i	$0.290705\pi$
$752$			7.02636i			0.256225i
$753$	26.6136	−	46.0960i	0.969852	−	1.67983i
$754$	9.68421	+	14.4633i	0.352678	+	0.526723i
$755$	−23.7833			−0.865563
$756$		0			0
$757$	−13.5575	−	23.4823i	−0.492757	−	0.853480i	0.507208	−	0.861824i	$-0.330678\pi$
$757$	−13.5575	−	23.4823i	−0.492757	−	0.853480i	−0.999965	+	0.00834344i	$0.997344\pi$
$758$	−2.21166			−0.0803310
$759$	−13.8424	−	7.99190i	−0.502446	−	0.290087i
$760$	9.79815	−	5.65696i	0.355416	−	0.205200i
$761$			48.3727i			1.75351i	0.480937	+	0.876755i	$0.340297\pi$
$761$			48.3727i			1.75351i	−0.480937	+	0.876755i	$0.659703\pi$
$762$		−	32.9507i		−	1.19368i
$763$		0			0
$764$	−1.63068	−	2.82443i	−0.0589961	−	0.102184i
$765$	24.7170	+	14.2703i	0.893644	+	0.515945i
$766$	−11.1693	+	19.3458i	−0.403563	+	0.698991i
$767$	−1.42639	+	2.89945i	−0.0515039	+	0.104693i
$768$	1.67234	+	2.89658i	0.0603455	+	0.104521i
$769$	15.0214	−	8.67264i	0.541687	−	0.312743i	−0.204075	−	0.978955i	$-0.565419\pi$
$769$	15.0214	−	8.67264i	0.541687	−	0.312743i	0.745762	+	0.666212i	$0.232085\pi$
$770$		0			0
$771$	−52.0129	+	90.0890i	−1.87320	+	3.24448i
$772$	−19.1158	+	11.0365i	−0.687993	+	0.397213i
$773$	−12.1659	+	7.02398i	−0.437576	+	0.252635i	−0.702569	−	0.711616i	$-0.747964\pi$
$773$	−12.1659	+	7.02398i	−0.437576	+	0.252635i	0.264993	+	0.964250i	$0.414630\pi$
$774$	71.5491	−	41.3089i	2.57178	−	1.48482i
$775$	−1.32326	+	0.763984i	−0.0475329	+	0.0274431i
$776$	−2.44414	+	4.23338i	−0.0877396	+	0.151970i
$777$		0			0
$778$	10.6178	−	6.13022i	0.380668	−	0.219779i
$779$	−28.7801	−	49.8487i	−1.03116	−	1.78601i
$780$	18.8141	−	1.25131i	0.673652	−	0.0448042i
$781$	−3.28841	+	5.69569i	−0.117669	+	0.203808i
$782$	−3.21949	−	1.85877i	−0.115129	−	0.0664696i
$783$	41.8760	+	72.5314i	1.49653	+	2.59206i
$784$		0			0
$785$			3.55582i			0.126913i
$786$		−	49.4756i		−	1.76474i
$787$	−6.71670	+	3.87789i	−0.239424	+	0.138232i	−0.614912	−	0.788596i	$-0.710809\pi$
$787$	−6.71670	+	3.87789i	−0.239424	+	0.138232i	0.375488	+	0.926827i	$0.377475\pi$
$788$	−4.56660	−	2.63653i	−0.162678	−	0.0939224i
$789$	94.9044			3.37869
$790$	−3.33114	−	5.76971i	−0.118517	−	0.205277i
$791$		0			0
$792$	23.4649			0.833789
$793$	−42.7134	+	28.5997i	−1.51680	+	1.01560i
$794$	−1.46759	+	2.54193i	−0.0520827	+	0.0902099i
$795$			31.2942i			1.10989i
$796$	4.43381	−	7.67958i	0.157152	−	0.272195i
$797$	16.9246	−	29.3143i	0.599500	−	1.03836i	−0.393395	−	0.919370i	$-0.628699\pi$
$797$	16.9246	−	29.3143i	0.599500	−	1.03836i	0.992895	−	0.118995i	$-0.0379673\pi$
$798$		0			0
$799$	13.5672	+	7.83303i	0.479973	+	0.277113i
$800$		−	2.55529i		−	0.0903431i
$801$	17.1665	+	9.91111i	0.606550	+	0.350192i
$802$	−10.9251	−	18.9229i	−0.385779	−	0.668190i
$803$	−16.0901	+	27.8689i	−0.567808	+	0.983473i
$804$	−4.75290	+	2.74409i	−0.167622	+	0.0967766i
$805$		0			0
$806$	−1.93456	−	0.951708i	−0.0681420	−	0.0335225i
$807$	35.7909	+	61.9917i	1.25990	+	2.18221i
$808$			7.36747i			0.259187i
$809$	−32.8340			−1.15438			−0.577191	−	0.816609i	$-0.695851\pi$
$809$	−32.8340			−1.15438			−0.577191	+	0.816609i	$0.695851\pi$
$810$	52.3246			1.83850
$811$			12.2083i			0.428690i	0.976758	+	0.214345i	$0.0687617\pi$
$811$			12.2083i			0.428690i	−0.976758	+	0.214345i	$0.931238\pi$
$812$		0			0
$813$	−16.6454	−	9.61023i	−0.583780	−	0.337045i
$814$	−0.0957207	+	0.0552644i	−0.00335501	+	0.00193701i
$815$	−0.00765566	−	0.0132600i	−0.000268166	−	0.000464477i
$816$	7.45736			0.261060
$817$	−63.2386	−	36.5108i	−2.21244	−	1.27735i
$818$	−7.38191			−0.258102
$819$		0			0
$820$	12.4376			0.434340
$821$	−41.1248	−	23.7434i	−1.43526	−	0.828650i	−0.437749	−	0.899097i	$-0.644224\pi$
$821$	−41.1248	−	23.7434i	−1.43526	−	0.828650i	−0.997516	+	0.0704470i	$0.977557\pi$
$822$	1.53520			0.0535463
$823$	11.0229	+	19.0923i	0.384235	+	0.665515i	0.991663	−	0.128860i	$-0.0411317\pi$
$823$	11.0229	+	19.0923i	0.384235	+	0.665515i	−0.607427	+	0.794375i	$0.707798\pi$
$824$	5.01017	−	2.89263i	0.174538	−	0.100769i
$825$	−21.2140	−	12.2479i	−0.738578	−	0.426418i
$826$		0			0
$827$		−	45.9092i		−	1.59642i	−0.602380	−	0.798209i	$-0.705781\pi$
$827$		−	45.9092i		−	1.59642i	0.602380	−	0.798209i	$-0.294219\pi$
$828$	−13.6505			−0.474388
$829$	26.7766			0.929991			0.464996	−	0.885313i	$-0.346056\pi$
$829$	26.7766			0.929991			0.464996	+	0.885313i	$0.346056\pi$
$830$		−	7.73693i		−	0.268553i
$831$	−44.4877	−	77.0550i	−1.54326	−	2.67301i
$832$	2.99598	−	2.00602i	0.103867	−	0.0695462i
$833$		0			0
$834$	−44.3601	+	25.6113i	−1.53606	+	0.886847i
$835$	−19.5060	+	33.7854i	−0.675033	+	1.16919i
$836$	−10.3697	−	17.9609i	−0.358644	−	0.621190i
$837$	−8.98404	−	5.18694i	−0.310534	−	0.179287i
$838$		−	8.58273i		−	0.296486i
$839$	24.5960	+	14.2005i	0.849147	+	0.490255i	0.860363	−	0.509682i	$-0.170237\pi$
$839$	24.5960	+	14.2005i	0.849147	+	0.490255i	−0.0112158	+	0.999937i	$0.503570\pi$
$840$		0			0
$841$	2.84726	−	4.93160i	0.0981814	−	0.170055i
$842$	3.74763	−	6.49108i	0.129152	−	0.223697i
$843$		−	22.3807i		−	0.770834i
$844$	3.28453	−	5.68898i	0.113058	−	0.195823i
$845$	−2.69187	−	20.1472i	−0.0926031	−	0.693085i
$846$	57.5244			1.97773
$847$		0			0
$848$	2.99202	+	5.18233i	0.102746	+	0.177962i
$849$	−66.6725			−2.28819
$850$	−4.93401	−	2.84865i	−0.169235	−	0.0977079i
$851$	0.0556847	−	0.0321496i	0.00190885	−	0.00110207i
$852$			7.67493i			0.262939i
$853$			21.3316i			0.730379i	0.930933	+	0.365189i	$0.118996\pi$
$853$			21.3316i			0.730379i	−0.930933	+	0.365189i	$0.881004\pi$
$854$		0			0
$855$	−46.3132	−	80.2168i	−1.58388	−	2.74336i
$856$	0.891102	+	0.514478i	0.0304572	+	0.0175845i
$857$	−20.5412	+	35.5784i	−0.701673	+	1.21533i	0.266206	+	0.963916i	$0.414230\pi$
$857$	−20.5412	+	35.5784i	−0.701673	+	1.21533i	−0.967879	+	0.251417i	$0.919103\pi$
$858$	−2.29377	−	34.4878i	−0.0783079	−	1.17740i
$859$	14.4309	+	24.9951i	0.492376	+	0.852820i	0.999961	−	0.00878126i	$-0.00279520\pi$
$859$	14.4309	+	24.9951i	0.492376	+	0.852820i	−0.507586	+	0.861601i	$0.669462\pi$
$860$	13.6646	−	7.88925i	0.465958	−	0.269021i
$861$		0			0
$862$	8.23956	−	14.2713i	0.280641	−	0.486084i
$863$	−19.6875	+	11.3666i	−0.670171	+	0.386923i	−0.796141	−	0.605111i	$-0.793129\pi$
$863$	−19.6875	+	11.3666i	−0.670171	+	0.386923i	0.125970	+	0.992034i	$0.459796\pi$
$864$	15.0244	−	8.67434i	0.511140	−	0.295107i
$865$	−4.34050	+	2.50599i	−0.147581	+	0.0852062i
$866$	22.1365	−	12.7805i	0.752229	−	0.434300i
$867$	−20.1163	+	34.8425i	−0.683187	+	1.18331i
$868$		0			0
$869$	−10.5764	+	6.10627i	−0.358779	+	0.207141i
$870$	12.6232	+	21.8640i	0.427966	+	0.741258i
$871$	3.29161	+	4.91599i	0.111532	+	0.166572i
$872$	7.07674	−	12.2573i	0.239649	−	0.415084i
$873$	34.6584	+	20.0100i	1.17301	+	0.677238i
$874$	6.03249	+	10.4486i	0.204052	+	0.353428i
$875$		0			0
$876$			37.5533i			1.26881i
$877$		−	29.4178i		−	0.993368i	−0.867932	−	0.496684i	$-0.834551\pi$
$877$		−	29.4178i		−	0.993368i	0.867932	−	0.496684i	$-0.165449\pi$
$878$	−7.97470	+	4.60420i	−0.269133	+	0.155384i
$879$	−25.6663	−	14.8184i	−0.865703	−	0.499814i
$880$	4.48137			0.151067
$881$	−2.11104	−	3.65644i	−0.0711229	−	0.123188i	0.828271	−	0.560328i	$-0.189325\pi$
$881$	−2.11104	−	3.65644i	−0.0711229	−	0.123188i	−0.899394	+	0.437140i	$0.855992\pi$
$882$		0			0
$883$	37.1982			1.25182			0.625910	−	0.779895i	$-0.284728\pi$
$883$	37.1982			1.25182			0.625910	+	0.779895i	$0.284728\pi$
$884$	−0.533490	−	8.02126i	−0.0179432	−	0.269784i
$885$	−2.34341	+	4.05890i	−0.0787727	+	0.136438i
$886$			6.20759i			0.208548i
$887$	−28.0947	+	48.6614i	−0.943327	+	1.63389i	−0.184260	+	0.982878i	$0.558989\pi$
$887$	−28.0947	+	48.6614i	−0.943327	+	1.63389i	−0.759067	+	0.651013i	$0.774344\pi$
$888$	−0.0644917	+	0.111703i	−0.00216420	+	0.00374850i
$889$		0			0
$890$	3.27850	+	1.89284i	0.109896	+	0.0634482i
$891$		−	95.9157i		−	3.21330i
$892$	14.6463	+	8.45606i	0.490395	+	0.283130i
$893$	−25.4214	−	44.0312i	−0.850696	−	1.47345i
$894$	−17.1200	+	29.6528i	−0.572580	+	0.991737i
$895$	21.3944	−	12.3521i	0.715136	−	0.412884i
$896$		0			0
$897$	1.33438	+	20.0630i	0.0445536	+	0.669884i
$898$	2.60944	+	4.51968i	0.0870781	+	0.150824i
$899$		−	2.88671i		−	0.0962772i
$900$	−20.9200			−0.697333
$901$	13.3421			0.444489
$902$		−	22.7992i		−	0.759132i
$903$		0			0
$904$	11.7269	+	6.77051i	0.390030	+	0.225184i
$905$	−12.3480	+	7.12910i	−0.410460	+	0.236979i
$906$	25.4380	+	44.0600i	0.845123	+	1.46380i
$907$	0.653612			0.0217028			0.0108514	−	0.999941i	$-0.496546\pi$
$907$	0.653612			0.0217028			0.0108514	+	0.999941i	$0.496546\pi$
$908$	−13.9709	−	8.06611i	−0.463641	−	0.267683i
$909$	60.3170			2.00059
$910$		0			0
$911$	39.7806			1.31799			0.658995	−	0.752147i	$-0.270982\pi$
$911$	39.7806			1.31799			0.658995	+	0.752147i	$0.270982\pi$
$912$	−20.9597	−	12.1011i	−0.694046	−	0.400708i
$913$	−14.1825			−0.469371
$914$	16.9666	+	29.3870i	0.561205	+	0.972036i
$915$	−64.5693	+	37.2791i	−2.13460	+	1.23241i
$916$	−5.98583	−	3.45592i	−0.197777	−	0.114187i
$917$		0			0
$918$		−	38.6808i		−	1.27666i
$919$	34.6056			1.14153			0.570767	−	0.821112i	$-0.306646\pi$
$919$	34.6056			1.14153			0.570767	+	0.821112i	$0.306646\pi$
$920$	−2.60700			−0.0859502
$921$		−	27.9160i		−	0.919863i
$922$	−0.422380	−	0.731583i	−0.0139103	−	0.0240934i
$923$	8.25528	−	0.549054i	0.271726	−	0.0180723i
$924$		0			0
$925$	0.0853392	−	0.0492706i	0.00280593	−	0.00162001i
$926$	−3.25111	+	5.63108i	−0.106838	+	0.185049i
$927$	−23.6817	−	41.0180i	−0.777810	−	1.34721i
$928$	4.18080	+	2.41379i	0.137242	+	0.0792365i
$929$			19.2707i			0.632252i	0.948717	+	0.316126i	$0.102382\pi$
$929$			19.2707i			0.632252i	−0.948717	+	0.316126i	$0.897618\pi$
$930$	−2.70816	−	1.56356i	−0.0888041	−	0.0512711i
$931$		0			0
$932$	3.73702	−	6.47272i	0.122410	−	0.212021i
$933$	11.1862	−	19.3751i	0.366221	−	0.634314i
$934$			9.52759i			0.311752i
$935$	4.99586	−	8.65308i	0.163382	−	0.282986i
$936$	−16.4232	−	24.5279i	−0.536808	−	0.801719i
$937$	50.9507			1.66449			0.832244	−	0.554410i	$-0.187056\pi$
$937$	50.9507			1.66449			0.832244	+	0.554410i	$0.187056\pi$
$938$		0			0
$939$	35.7526	+	61.9254i	1.16674	+	2.02086i
$940$	10.9861			0.358328
$941$	21.0456	+	12.1507i	0.686068	+	0.396102i	0.802138	−	0.597139i	$-0.203696\pi$
$941$	21.0456	+	12.1507i	0.686068	+	0.396102i	−0.116069	+	0.993241i	$0.537029\pi$
$942$	6.58738	−	3.80322i	0.214628	−	0.123916i
$943$			13.2633i			0.431911i
$944$			0.896206i			0.0291690i
$945$		0			0
$946$	−14.4617	−	25.0484i	−0.470190	−	0.814393i
$947$	−22.2278	−	12.8332i	−0.722307	−	0.417024i	0.0932940	−	0.995639i	$-0.470260\pi$
$947$	−22.2278	−	12.8332i	−0.722307	−	0.417024i	−0.815601	+	0.578614i	$0.803594\pi$
$948$	−7.12582	+	12.3423i	−0.231436	+	0.400859i
$949$	40.3930	−	2.68651i	1.31121	−	0.0872080i
$950$	9.24505	+	16.0129i	0.299949	+	0.519527i
$951$	91.7569	−	52.9759i	2.97542	−	1.71786i
$952$		0			0
$953$	2.40492	−	4.16544i	0.0779029	−	0.134932i	−0.824442	−	0.565946i	$-0.808511\pi$
$953$	2.40492	−	4.16544i	0.0779029	−	0.134932i	0.902345	+	0.431015i	$0.141844\pi$
$954$	42.4274	−	24.4955i	1.37364	−	0.793070i
$955$	−4.41616	+	2.54967i	−0.142903	+	0.0825053i
$956$	−17.2075	+	9.93478i	−0.556532	+	0.321314i
$957$	40.0786	−	23.1394i	1.29556	−	0.747990i
$958$	−1.42099	+	2.46123i	−0.0459102	+	0.0795188i
$959$		0			0
$960$	4.52898	−	2.61481i	0.146172	−	0.0843925i
$961$	−15.3212	−	26.5371i	−0.494233	−	0.856037i
$962$	0.124763	+	0.0613773i	0.00402252	+	0.00197888i
$963$	4.21200	−	7.29540i	0.135730	−	0.235091i
$964$	−9.21842	−	5.32226i	−0.296905	−	0.171418i
$965$	17.2562	+	29.8887i	0.555498	+	0.962150i
$966$		0			0
$967$		−	58.2044i		−	1.87173i	−0.352362	−	0.935864i	$-0.614622\pi$
$967$		−	58.2044i		−	1.87173i	0.352362	−	0.935864i	$-0.385378\pi$
$968$			2.78525i			0.0895213i
$969$	−46.7321	+	26.9808i	−1.50125	+	0.866747i
$970$	6.61913	+	3.82156i	0.212528	+	0.122703i
$971$	36.1337			1.15959			0.579793	−	0.814764i	$-0.303133\pi$
$971$	36.1337			1.15959			0.579793	+	0.814764i	$0.303133\pi$
$972$	−29.9422	−	51.8613i	−0.960395	−	1.66345i
$973$		0			0
$974$	5.26374			0.168661
$975$	2.04499	+	30.7474i	0.0654922	+	0.984706i
$976$	−7.12846	+	12.3469i	−0.228177	+	0.395213i
$977$			16.7194i			0.534901i	0.963572	+	0.267451i	$0.0861812\pi$
$977$			16.7194i			0.534901i	−0.963572	+	0.267451i	$0.913819\pi$
$978$	−0.0163766	+	0.0283652i	−0.000523667	+	0.000907018i
$979$	3.46975	−	6.00978i	0.110894	−	0.192073i
$980$		0			0
$981$	−100.349	−	57.9368i	−3.20391	−	1.84978i
$982$			22.8913i			0.730492i
$983$	40.2497	+	23.2382i	1.28377	+	0.741183i	0.977535	−	0.210774i	$-0.0675984\pi$
$983$	40.2497	+	23.2382i	1.28377	+	0.741183i	0.306232	+	0.951957i	$0.400932\pi$
$984$	−13.3030	−	23.0414i	−0.424083	−	0.734534i
$985$	−4.12236	+	7.14014i	−0.131349	+	0.227504i
$986$	9.32157	−	5.38181i	0.296859	−	0.171392i
$987$		0			0
$988$	−11.5167	+	23.4103i	−0.366396	+	0.744782i
$989$	8.41296	+	14.5717i	0.267517	+	0.463352i
$990$		−	36.6887i		−	1.16604i
$991$	35.3510			1.12296			0.561480	−	0.827490i	$-0.310232\pi$
$991$	35.3510			1.12296			0.561480	+	0.827490i	$0.310232\pi$
$992$	−0.597963			−0.0189853
$993$		−	82.5118i		−	2.61843i
$994$		0			0
$995$	−12.0075	−	6.93251i	−0.380662	−	0.219775i
$996$	−14.3331	+	8.27524i	−0.454163	+	0.262211i
$997$	0.743899	+	1.28847i	0.0235595	+	0.0408063i	0.877565	−	0.479458i	$-0.159167\pi$
$997$	0.743899	+	1.28847i	0.0235595	+	0.0408063i	−0.854005	+	0.520264i	$0.825833\pi$
$998$	−6.79877			−0.215211
$999$	0.579396	+	0.334514i	0.0183313	+	0.0105836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.v.d.361.4		12
7.2	even	3		1274.2.o.e.569.3		12
7.3	odd	6		182.2.m.b.127.1	yes	12
7.4	even	3		1274.2.m.c.491.3		12
7.5	odd	6		1274.2.o.d.569.1		12
7.6	odd	2		1274.2.v.e.361.6		12
13.4	even	6		1274.2.o.e.459.6		12
21.17	even	6		1638.2.bj.g.127.6		12
28.3	even	6		1456.2.cc.d.673.6		12
91.3	odd	6		2366.2.d.r.337.6		12
91.4	even	6		1274.2.m.c.589.3		12
91.10	odd	6		2366.2.d.r.337.12		12
91.17	odd	6		182.2.m.b.43.1	✓	12
91.24	even	12		2366.2.a.bh.1.6		6
91.30	even	6	inner	1274.2.v.d.667.4		12
91.69	odd	6		1274.2.o.d.459.4		12
91.80	even	12		2366.2.a.bf.1.6		6
91.82	odd	6		1274.2.v.e.667.6		12
273.17	even	6		1638.2.bj.g.1135.4		12
364.199	even	6		1456.2.cc.d.225.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.1	✓	12	91.17	odd	6
182.2.m.b.127.1	yes	12	7.3	odd	6
1274.2.m.c.491.3		12	7.4	even	3
1274.2.m.c.589.3		12	91.4	even	6
1274.2.o.d.459.4		12	91.69	odd	6
1274.2.o.d.569.1		12	7.5	odd	6
1274.2.o.e.459.6		12	13.4	even	6
1274.2.o.e.569.3		12	7.2	even	3
1274.2.v.d.361.4		12	1.1	even	1	trivial
1274.2.v.d.667.4		12	91.30	even	6	inner
1274.2.v.e.361.6		12	7.6	odd	2
1274.2.v.e.667.6		12	91.82	odd	6
1456.2.cc.d.225.6		12	364.199	even	6
1456.2.cc.d.673.6		12	28.3	even	6
1638.2.bj.g.127.6		12	21.17	even	6
1638.2.bj.g.1135.4		12	273.17	even	6
2366.2.a.bf.1.6		6	91.80	even	12
2366.2.a.bh.1.6		6	91.24	even	12
2366.2.d.r.337.6		12	91.3	odd	6
2366.2.d.r.337.12		12	91.10	odd	6

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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.v (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} -3.34469 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.35408 - 0.781779i) q^{5} +(-2.89658 - 1.67234i) q^{6} +1.00000i q^{8} +8.18694 q^{9} +1.56356 q^{10} -2.86614i q^{11} +(-1.67234 - 2.89658i) q^{12} +(-2.99598 + 2.00602i) q^{13} +(-4.52898 + 2.61481i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.11481 + 1.93090i) q^{17} +(7.09010 + 4.09347i) q^{18} -7.23602i q^{19} +(1.35408 + 0.781779i) q^{20} +(1.43307 - 2.48215i) q^{22} +(-0.833676 + 1.44397i) q^{23} -3.34469i q^{24} +(-1.27764 + 2.21294i) q^{25} +(-3.59760 + 0.239275i) q^{26} -17.3487 q^{27} +(-2.41379 - 4.18080i) q^{29} -5.22961 q^{30} +(0.517851 + 0.298982i) q^{31} +(-0.866025 + 0.500000i) q^{32} +9.58634i q^{33} +2.22961i q^{34} +(4.09347 + 7.09010i) q^{36} +(-0.0333971 - 0.0192818i) q^{37} +(3.61801 - 6.26657i) q^{38} +(10.0206 - 6.70951i) q^{39} +(0.781779 + 1.35408i) q^{40} +(6.88896 - 3.97734i) q^{41} +(5.04571 - 8.73942i) q^{43} +(2.48215 - 1.43307i) q^{44} +(11.0858 - 6.40037i) q^{45} +(-1.44397 + 0.833676i) q^{46} +(6.08501 - 3.51318i) q^{47} +(1.67234 - 2.89658i) q^{48} +(-2.21294 + 1.27764i) q^{50} +(-3.72868 - 6.45826i) q^{51} +(-3.23525 - 1.59158i) q^{52} +(2.99202 - 5.18233i) q^{53} +(-15.0244 - 8.67434i) q^{54} +(-2.24069 - 3.88098i) q^{55} +24.2022i q^{57} -4.82757i q^{58} +(0.776138 - 0.448103i) q^{59} +(-4.52898 - 2.61481i) q^{60} +14.2569 q^{61} +(0.298982 + 0.517851i) q^{62} -1.00000 q^{64} +(-2.48853 + 5.05850i) q^{65} +(-4.79317 + 8.30201i) q^{66} -1.64086i q^{67} +(-1.11481 + 1.93090i) q^{68} +(2.78838 - 4.82962i) q^{69} +(-1.98724 - 1.14733i) q^{71} +8.18694i q^{72} +(-9.72351 - 5.61387i) q^{73} +(-0.0192818 - 0.0333971i) q^{74} +(4.27332 - 7.40161i) q^{75} +(6.26657 - 3.61801i) q^{76} +(12.0329 - 0.800299i) q^{78} +(-2.13049 - 3.69011i) q^{79} +1.56356i q^{80} +33.4651 q^{81} +7.95469 q^{82} -4.94829i q^{83} +(3.01907 + 1.74306i) q^{85} +(8.73942 - 5.04571i) q^{86} +(8.07337 + 13.9835i) q^{87} +2.86614 q^{88} +(2.09682 + 1.21060i) q^{89} +12.8007 q^{90} -1.66735 q^{92} +(-1.73205 - 1.00000i) q^{93} +7.02636 q^{94} +(-5.65696 - 9.79815i) q^{95} +(2.89658 - 1.67234i) q^{96} +(4.23338 + 2.44414i) q^{97} -23.4649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{3} + 6 q^{4} - 6 q^{6} + 12 q^{9} - 4 q^{10} - 2 q^{12} + 8 q^{13} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 2 q^{22} - 6 q^{23} + 12 q^{25} - 16 q^{26} - 40 q^{27} - 10 q^{29} - 28 q^{30} + 18 q^{31}+ \cdots - 60 q^{97}+O(q^{100}) \) 12 * q - 4 * q^3 + 6 * q^4 - 6 * q^6 + 12 * q^9 - 4 * q^10 - 2 * q^12 + 8 * q^13 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 2 * q^22 - 6 * q^23 + 12 * q^25 - 16 * q^26 - 40 * q^27 - 10 * q^29 - 28 * q^30 + 18 * q^31 + 6 * q^36 + 6 * q^37 + 4 * q^38 + 30 * q^39 - 2 * q^40 + 24 * q^41 + 26 * q^43 + 18 * q^44 + 72 * q^45 + 6 * q^46 + 48 * q^47 + 2 * q^48 - 12 * q^50 + 18 * q^51 + 4 * q^52 - 18 * q^53 - 36 * q^54 + 6 * q^55 + 6 * q^59 - 6 * q^60 - 56 * q^61 + 2 * q^62 - 12 * q^64 + 38 * q^65 + 4 * q^68 - 32 * q^69 + 48 * q^71 - 48 * q^73 + 48 * q^75 - 12 * q^76 - 8 * q^78 - 22 * q^79 + 68 * q^81 + 12 * q^82 + 54 * q^85 - 6 * q^86 - 2 * q^87 - 4 * q^88 + 12 * q^89 - 12 * q^90 - 12 * q^92 + 16 * q^94 + 32 * q^95 + 6 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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