LMFDB - Embedded newform 637.2.u.d.361.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [637,2,Mod(30,637)] 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("637.30"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(637, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,-2,1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$1$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.895644 + 1.09445i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.d.30.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89564 - 1.09445i) q^{2} +1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(-1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +4.79129 q^{10} -1.27520i q^{11} +(2.50000 + 4.33013i) q^{12} +(-3.50000 - 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} +(0.895644 - 1.55130i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.395644 - 0.228425i) q^{18} -6.56670i q^{19} +(-5.29129 - 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 + 6.56670i) q^{23} -3.10260i q^{24} +(-0.104356 + 0.180750i) q^{25} +(5.68693 + 5.47225i) q^{26} -5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +8.58258 q^{30} +(-7.50000 - 4.33013i) q^{31} +(-6.39564 + 3.69253i) q^{32} -2.28425i q^{33} -6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(-7.18693 + 12.4481i) q^{38} +(-6.26951 - 1.55130i) q^{39} +(1.89564 + 3.28335i) q^{40} +(-2.20871 + 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +(3.08258 - 1.77973i) q^{44} +(-0.395644 + 0.228425i) q^{45} +(14.3739 - 8.29875i) q^{46} +(-3.70871 + 2.14123i) q^{47} +(1.60436 - 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} +(2.68693 + 4.65390i) q^{51} +(-2.79129 - 9.66930i) q^{52} +(6.08258 - 10.5353i) q^{53} +(9.47822 + 5.47225i) q^{54} +(1.39564 + 2.41733i) q^{55} -11.7629i q^{57} -4.83465i q^{58} +(-7.66515 + 4.42548i) q^{59} +(-9.47822 - 5.47225i) q^{60} -12.7477 q^{61} +(9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(7.58258 - 2.18890i) q^{65} +(-2.50000 + 4.33013i) q^{66} +11.4014i q^{67} +(-4.18693 + 7.25198i) q^{68} +(-6.79129 + 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} -0.361500i q^{72} +(3.00000 + 1.73205i) q^{73} +(7.58258 + 13.1334i) q^{74} +(-0.186932 + 0.323775i) q^{75} +(15.8739 - 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} +(3.00000 + 5.19615i) q^{79} +3.92095i q^{80} -9.58258 q^{81} +5.58258 q^{82} +3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(-8.29129 + 4.78698i) q^{86} +(1.97822 + 3.42638i) q^{87} -2.20871 q^{88} +(-2.52178 - 1.45595i) q^{89} +1.00000 q^{90} -21.1652 q^{92} +(-13.4347 - 7.75650i) q^{93} +9.37386 q^{94} +(7.18693 + 12.4481i) q^{95} +(-11.4564 + 6.61438i) q^{96} +(13.1869 + 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - 2 q^{3} + q^{4} - 3 q^{5} - 9 q^{6} + 10 q^{9} + 10 q^{10} + 10 q^{12} - 14 q^{13} - 9 q^{15} - q^{16} + 6 q^{17} + 3 q^{18} - 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} + 9 q^{26} - 20 q^{27}+ \cdots + 39 q^{97}+O(q^{100}) $ 4 * q - 3 * q^2 - 2 * q^3 + q^4 - 3 * q^5 - 9 * q^6 + 10 * q^9 + 10 * q^10 + 10 * q^12 - 14 * q^13 - 9 * q^15 - q^16 + 6 * q^17 + 3 * q^18 - 12 * q^20 - q^22 - 6 * q^23 - 5 * q^25 + 9 * q^26 - 20 * q^27 + 9 * q^29 + 16 * q^30 - 30 * q^31 - 21 * q^32 - 8 * q^36 - 24 * q^37 - 15 * q^38 + 7 * q^39 + 3 * q^40 - 18 * q^41 - 5 * q^43 - 6 * q^44 + 3 * q^45 + 30 * q^46 - 24 * q^47 + 11 * q^48 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 + 15 * q^54 + q^55 + 6 * q^59 - 15 * q^60 + 4 * q^61 + 15 * q^62 + 32 * q^64 + 12 * q^65 - 10 * q^66 - 3 * q^68 - 18 * q^69 + 6 * q^71 + 12 * q^73 + 12 * q^74 + 13 * q^75 + 36 * q^76 + 27 * q^78 + 12 * q^79 - 20 * q^81 + 4 * q^82 - 9 * q^85 - 24 * q^86 - 15 * q^87 - 18 * q^88 - 33 * q^89 + 4 * q^90 - 48 * q^92 + 15 * q^93 + 10 * q^94 + 15 * q^95 + 39 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.89564	−	1.09445i	−1.34042	−	0.773893i	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.89564	−	1.09445i	−1.34042	−	0.773893i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	1.79129			1.03420			0.517100	−	0.855925i	$-0.327011\pi$
$3$	1.79129			1.03420			0.517100	+	0.855925i	$0.327011\pi$
$4$	1.39564	+	2.41733i	0.697822	+	1.20866i
$5$	−1.89564	+	1.09445i	−0.847758	+	0.489453i	−0.859894	−	0.510473i	$-0.829470\pi$
$5$	−1.89564	+	1.09445i	−0.847758	+	0.489453i	0.0121359	+	0.999926i	$0.496137\pi$
$6$	−3.39564	−	1.96048i	−1.38627	−	0.800361i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	0.208712			0.0695707
$10$	4.79129			1.51514
$11$		−	1.27520i		−	0.384487i	−0.981347	−	0.192244i	$-0.938424\pi$
$11$		−	1.27520i		−	0.384487i	0.981347	−	0.192244i	$-0.0615764\pi$
$12$	2.50000	+	4.33013i	0.721688	+	1.25000i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$		0			0
$15$	−3.39564	+	1.96048i	−0.876751	+	0.506193i
$16$	0.895644	−	1.55130i	0.223911	−	0.387825i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	−0.395644	−	0.228425i	−0.0932542	−	0.0538403i
$19$		−	6.56670i		−	1.50651i	−0.657731	−	0.753253i	$-0.728484\pi$
$19$		−	6.56670i		−	1.50651i	0.657731	−	0.753253i	$-0.271516\pi$
$20$	−5.29129	−	3.05493i	−1.18317	−	0.683102i
$21$		0			0
$22$	−1.39564	+	2.41733i	−0.297552	+	0.515376i
$23$	−3.79129	+	6.56670i	−0.790538	+	1.36925i	0.135096	+	0.990833i	$0.456866\pi$
$23$	−3.79129	+	6.56670i	−0.790538	+	1.36925i	−0.925634	+	0.378420i	$0.876468\pi$
$24$		−	3.10260i		−	0.633316i
$25$	−0.104356	+	0.180750i	−0.0208712	+	0.0361500i
$26$	5.68693	+	5.47225i	1.11530	+	1.07320i
$27$	−5.00000			−0.962250
$28$		0			0
$29$	1.10436	+	1.91280i	0.205074	+	0.355198i	0.950156	−	0.311774i	$-0.100923\pi$
$29$	1.10436	+	1.91280i	0.205074	+	0.355198i	−0.745082	+	0.666972i	$0.767590\pi$
$30$	8.58258			1.56696
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−6.39564	+	3.69253i	−1.13060	+	0.652753i
$33$		−	2.28425i		−	0.397637i
$34$		−	6.56670i		−	1.12618i
$35$		0			0
$36$	0.291288	+	0.504525i	0.0485480	+	0.0840876i
$37$	−6.00000	−	3.46410i	−0.986394	−	0.569495i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−6.00000	−	3.46410i	−0.986394	−	0.569495i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	−7.18693	+	12.4481i	−1.16587	+	2.01935i
$39$	−6.26951	−	1.55130i	−1.00392	−	0.248407i
$40$	1.89564	+	3.28335i	0.299728	+	0.519143i
$41$	−2.20871	+	1.27520i	−0.344943	+	0.199153i	−0.662456	−	0.749101i	$-0.730486\pi$
$41$	−2.20871	+	1.27520i	−0.344943	+	0.199153i	0.317513	+	0.948254i	$0.397152\pi$
$42$		0			0
$43$	2.18693	−	3.78788i	0.333504	−	0.577646i	−0.649692	−	0.760197i	$-0.725102\pi$
$43$	2.18693	−	3.78788i	0.333504	−	0.577646i	0.983196	+	0.182551i	$0.0584356\pi$
$44$	3.08258	−	1.77973i	0.464716	−	0.268304i
$45$	−0.395644	+	0.228425i	−0.0589791	+	0.0340516i
$46$	14.3739	−	8.29875i	2.11931	−	1.22358i
$47$	−3.70871	+	2.14123i	−0.540971	+	0.312330i	−0.745472	−	0.666536i	$-0.767776\pi$
$47$	−3.70871	+	2.14123i	−0.540971	+	0.312330i	0.204501	+	0.978866i	$0.434443\pi$
$48$	1.60436	−	2.77883i	0.231569	−	0.401089i
$49$		0			0
$50$	0.395644	−	0.228425i	0.0559525	−	0.0323042i
$51$	2.68693	+	4.65390i	0.376246	+	0.651677i
$52$	−2.79129	−	9.66930i	−0.387082	−	1.34089i
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	−0.0581117	−	0.998310i	$-0.518508\pi$
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	0.893618	−	0.448829i	$-0.148159\pi$
$54$	9.47822	+	5.47225i	1.28982	+	0.744679i
$55$	1.39564	+	2.41733i	0.188189	+	0.325952i
$56$		0			0
$57$		−	11.7629i		−	1.55803i
$58$		−	4.83465i		−	0.634821i
$59$	−7.66515	+	4.42548i	−0.997918	+	0.576148i	−0.907632	−	0.419768i	$-0.862112\pi$
$59$	−7.66515	+	4.42548i	−0.997918	+	0.576148i	−0.0902862	+	0.995916i	$0.528778\pi$
$60$	−9.47822	−	5.47225i	−1.22363	−	0.706465i
$61$	−12.7477			−1.63218			−0.816090	−	0.577925i	$-0.803862\pi$
$61$	−12.7477			−1.63218			−0.816090	+	0.577925i	$0.803862\pi$
$62$	9.47822	+	16.4168i	1.20374	+	2.08493i
$63$		0			0
$64$	12.5826			1.57282
$65$	7.58258	−	2.18890i	0.940503	−	0.271500i
$66$	−2.50000	+	4.33013i	−0.307729	+	0.533002i
$67$			11.4014i			1.39290i	0.717607	+	0.696449i	$0.245238\pi$
$67$			11.4014i			1.39290i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−4.18693	+	7.25198i	−0.507740	+	0.879432i
$69$	−6.79129	+	11.7629i	−0.817575	+	1.41608i
$70$		0			0
$71$	−0.791288	−	0.456850i	−0.0939086	−	0.0542181i	0.452310	−	0.891861i	$-0.350600\pi$
$71$	−0.791288	−	0.456850i	−0.0939086	−	0.0542181i	−0.546219	+	0.837643i	$0.683933\pi$
$72$		−	0.361500i		−	0.0426032i
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	0.665180	−	0.746683i	$-0.268355\pi$
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	−0.314057	+	0.949404i	$0.601688\pi$
$74$	7.58258	+	13.1334i	0.881457	+	1.52673i
$75$	−0.186932	+	0.323775i	−0.0215850	+	0.0373864i
$76$	15.8739	−	9.16478i	1.82086	−	1.05127i
$77$		0			0
$78$	10.1869	+	9.80238i	1.15344	+	1.10990i
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$			3.92095i			0.438376i
$81$	−9.58258			−1.06473
$82$	5.58258			0.616492
$83$			3.55945i			0.390701i	0.980734	+	0.195350i	$0.0625844\pi$
$83$			3.55945i			0.390701i	−0.980734	+	0.195350i	$0.937416\pi$
$84$		0			0
$85$	−5.68693	−	3.28335i	−0.616834	−	0.356129i
$86$	−8.29129	+	4.78698i	−0.894073	+	0.516193i
$87$	1.97822	+	3.42638i	0.212087	+	0.367346i
$88$	−2.20871			−0.235450
$89$	−2.52178	−	1.45595i	−0.267308	−	0.154330i	0.360356	−	0.932815i	$-0.382655\pi$
$89$	−2.52178	−	1.45595i	−0.267308	−	0.154330i	−0.627664	+	0.778485i	$0.715989\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−21.1652			−2.20662
$93$	−13.4347	−	7.75650i	−1.39311	−	0.804312i
$94$	9.37386			0.966840
$95$	7.18693	+	12.4481i	0.737364	+	1.27715i
$96$	−11.4564	+	6.61438i	−1.16927	+	0.675077i
$97$	13.1869	+	7.61348i	1.33893	+	0.773032i	0.986649	−	0.162863i	$-0.0520727\pi$
$97$	13.1869	+	7.61348i	1.33893	+	0.773032i	0.352281	+	0.935894i	$0.385406\pi$
$98$		0			0
$99$		−	0.266150i		−	0.0267491i
$100$	−0.582576			−0.0582576
$101$	−9.79129			−0.974270			−0.487135	−	0.873327i	$-0.661958\pi$
$101$	−9.79129			−0.974270			−0.487135	+	0.873327i	$0.661958\pi$
$102$		−	11.7629i		−	1.16470i
$103$	−2.29129	−	3.96863i	−0.225767	−	0.391040i	0.730782	−	0.682611i	$-0.239156\pi$
$103$	−2.29129	−	3.96863i	−0.225767	−	0.391040i	−0.956549	+	0.291570i	$0.905822\pi$
$104$	−1.50000	+	6.06218i	−0.147087	+	0.594445i
$105$		0			0
$106$	−23.0608	+	13.3142i	−2.23986	+	1.29319i
$107$	4.89564	−	8.47950i	0.473280	−	0.819745i	−0.526252	−	0.850328i	$-0.676403\pi$
$107$	4.89564	−	8.47950i	0.473280	−	0.819745i	0.999532	+	0.0305838i	$0.00973664\pi$
$108$	−6.97822	−	12.0866i	−0.671479	−	1.16304i
$109$	6.87386	+	3.96863i	0.658397	+	0.380126i	0.791666	−	0.610954i	$-0.209214\pi$
$109$	6.87386	+	3.96863i	0.658397	+	0.380126i	−0.133269	+	0.991080i	$0.542547\pi$
$110$		−	6.10985i		−	0.582552i
$111$	−10.7477	−	6.20520i	−1.02013	−	0.588972i
$112$		0			0
$113$	−0.708712	+	1.22753i	−0.0666700	+	0.115476i	−0.897434	−	0.441150i	$-0.854571\pi$
$113$	−0.708712	+	1.22753i	−0.0666700	+	0.115476i	0.830764	+	0.556625i	$0.187904\pi$
$114$	−12.8739	+	22.2982i	−1.20575	+	2.08842i
$115$		−	16.5975i		−	1.54773i
$116$	−3.08258	+	5.33918i	−0.286210	+	0.495730i
$117$	−0.730493	−	0.180750i	−0.0675341	−	0.0167103i
$118$	19.3739			1.78351
$119$		0			0
$120$	3.39564	+	5.88143i	0.309978	+	0.536898i
$121$	9.37386			0.852169
$122$	24.1652	+	13.9518i	2.18781	+	1.26313i
$123$	−3.95644	+	2.28425i	−0.356740	+	0.205964i
$124$		−	24.1733i		−	2.17082i
$125$		−	11.4014i		−	1.01977i
$126$		0			0
$127$	7.97822	+	13.8187i	0.707953	+	1.22621i	0.965615	+	0.259975i	$0.0837143\pi$
$127$	7.97822	+	13.8187i	0.707953	+	1.22621i	−0.257663	+	0.966235i	$0.582952\pi$
$128$	−11.0608	−	6.38595i	−0.977645	−	0.564444i
$129$	3.91742	−	6.78518i	0.344910	−	0.597402i
$130$	−16.7695	−	4.14938i	−1.47078	−	0.363924i
$131$	−1.81307	−	3.14033i	−0.158409	−	0.274372i	0.775886	−	0.630873i	$-0.217303\pi$
$131$	−1.81307	−	3.14033i	−0.158409	−	0.274372i	−0.934295	+	0.356501i	$0.883970\pi$
$132$	5.52178	−	3.18800i	0.480609	−	0.277480i
$133$		0			0
$134$	12.4782	−	21.6129i	1.07795	−	1.86707i
$135$	9.47822	−	5.47225i	0.815755	−	0.470977i
$136$	4.50000	−	2.59808i	0.385872	−	0.222783i
$137$	14.8521	−	8.57485i	1.26890	−	0.732599i	0.294119	−	0.955769i	$-0.404974\pi$
$137$	14.8521	−	8.57485i	1.26890	−	0.732599i	0.974780	+	0.223169i	$0.0716403\pi$
$138$	25.7477	−	14.8655i	2.19179	−	1.26543i
$139$	−0.395644	+	0.685275i	−0.0335581	+	0.0581243i	−0.882317	−	0.470656i	$-0.844017\pi$
$139$	−0.395644	+	0.685275i	−0.0335581	+	0.0581243i	0.848759	+	0.528781i	$0.177351\pi$
$140$		0			0
$141$	−6.64337	+	3.83555i	−0.559473	+	0.323012i
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	−1.10436	+	4.46320i	−0.0923509	+	0.373232i
$144$	0.186932	−	0.323775i	0.0155776	−	0.0269813i
$145$	−4.18693	−	2.41733i	−0.347706	−	0.200748i
$146$	−3.79129	−	6.56670i	−0.313769	−	0.543464i
$147$		0			0
$148$		−	19.3386i		−	1.58962i
$149$		−	2.18890i		−	0.179322i	−0.995972	−	0.0896609i	$-0.971422\pi$
$149$		−	2.18890i		−	0.179322i	0.995972	−	0.0896609i	$-0.0285783\pi$
$150$	0.708712	−	0.409175i	0.0578661	−	0.0334090i
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	0.00768132	−	0.999970i	$-0.497555\pi$
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	−0.862159	+	0.506637i	$0.830888\pi$
$152$	−11.3739			−0.922542
$153$	0.313068	+	0.542250i	0.0253101	+	0.0438383i
$154$		0			0
$155$	18.9564			1.52262
$156$	−5.00000	−	17.3205i	−0.400320	−	1.38675i
$157$	10.9782	−	19.0148i	0.876157	−	1.51755i	0.0206325	−	0.999787i	$-0.493432\pi$
$157$	10.9782	−	19.0148i	0.876157	−	1.51755i	0.855525	−	0.517762i	$-0.173235\pi$
$158$		−	13.1334i		−	1.04484i
$159$	10.8956	−	18.8718i	0.864081	−	1.49663i
$160$	8.08258	−	13.9994i	0.638984	−	1.10675i
$161$		0			0
$162$	18.1652	+	10.4877i	1.42719	+	0.823988i
$163$		−	6.92820i		−	0.542659i	−0.962487	−	0.271329i	$-0.912537\pi$
$163$		−	6.92820i		−	0.542659i	0.962487	−	0.271329i	$-0.0874633\pi$
$164$	−6.16515	−	3.55945i	−0.481417	−	0.277946i
$165$	2.50000	+	4.33013i	0.194625	+	0.337100i
$166$	3.89564	−	6.74745i	0.302361	−	0.523704i
$167$	−17.2913	+	9.98313i	−1.33804	+	0.772518i	−0.986517	−	0.163661i	$-0.947670\pi$
$167$	−17.2913	+	9.98313i	−1.33804	+	0.772518i	−0.351523	+	0.936179i	$0.614336\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	7.18693	+	12.4481i	0.551213	+	0.954728i
$171$		−	1.37055i		−	0.104809i
$172$	12.2087			0.930906
$173$	7.74773			0.589049			0.294524	−	0.955644i	$-0.404839\pi$
$173$	7.74773			0.589049			0.294524	+	0.955644i	$0.404839\pi$
$174$		−	8.66025i		−	0.656532i
$175$		0			0
$176$	−1.97822	−	1.14213i	−0.149114	−	0.0860910i
$177$	−13.7305	+	7.92730i	−1.03205	+	0.595853i
$178$	3.18693	+	5.51993i	0.238871	+	0.413736i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	−1.10436	−	0.637600i	−0.0823138	−	0.0475239i
$181$	−9.16515			−0.681240			−0.340620	−	0.940201i	$-0.610637\pi$
$181$	−9.16515			−0.681240			−0.340620	+	0.940201i	$0.610637\pi$
$182$		0			0
$183$	−22.8348			−1.68800
$184$	11.3739	+	6.56670i	0.838492	+	0.484104i
$185$	15.1652			1.11496
$186$	16.9782	+	29.4071i	1.24490	+	2.15624i
$187$	3.31307	−	1.91280i	0.242276	−	0.139878i
$188$	−10.3521	−	5.97678i	−0.755003	−	0.435901i
$189$		0			0
$190$		−	31.4630i		−	2.28256i
$191$	−0.626136			−0.0453056			−0.0226528	−	0.999743i	$-0.507211\pi$
$191$	−0.626136			−0.0453056			−0.0226528	+	0.999743i	$0.507211\pi$
$192$	22.5390			1.62661
$193$		−	12.4104i		−	0.893321i	−0.894704	−	0.446660i	$-0.852613\pi$
$193$		−	12.4104i		−	0.893321i	0.894704	−	0.446660i	$-0.147387\pi$
$194$	−16.6652	−	28.8649i	−1.19649	−	2.07238i
$195$	13.5826	−	3.92095i	0.972668	−	0.280785i
$196$		0			0
$197$	−9.47822	+	5.47225i	−0.675295	+	0.389882i	−0.798080	−	0.602551i	$-0.794151\pi$
$197$	−9.47822	+	5.47225i	−0.675295	+	0.389882i	0.122785	+	0.992433i	$0.460817\pi$
$198$	−0.291288	+	0.504525i	−0.0207009	+	0.0358551i
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	0.313068	+	0.180750i	0.0221373	+	0.0127810i
$201$			20.4231i			1.44054i
$202$	18.5608	+	10.7161i	1.30593	+	0.753981i
$203$		0			0
$204$	−7.50000	+	12.9904i	−0.525105	+	0.909509i
$205$	2.79129	−	4.83465i	0.194952	−	0.337667i
$206$			10.0308i			0.698879i
$207$	−0.791288	+	1.37055i	−0.0549983	+	0.0952599i
$208$	−4.47822	+	4.65390i	−0.310509	+	0.322690i
$209$	−8.37386			−0.579232
$210$		0			0
$211$	−0.708712	−	1.22753i	−0.0487898	−	0.0845063i	0.840599	−	0.541658i	$-0.182203\pi$
$211$	−0.708712	−	1.22753i	−0.0487898	−	0.0845063i	−0.889389	+	0.457151i	$0.848870\pi$
$212$	33.9564			2.33214
$213$	−1.41742	−	0.818350i	−0.0971203	−	0.0560724i
$214$	−18.5608	+	10.7161i	−1.26879	+	0.732536i
$215$			9.57395i			0.652938i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−8.68693	−	15.0462i	−0.588353	−	1.01906i
$219$	5.37386	+	3.10260i	0.363132	+	0.209654i
$220$	−3.89564	+	6.74745i	−0.262644	+	0.454913i
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$	13.5826	+	23.5257i	0.911603	+	1.57894i
$223$	17.9347	−	10.3546i	1.20099	−	0.693394i	0.240217	−	0.970719i	$-0.422781\pi$
$223$	17.9347	−	10.3546i	1.20099	−	0.693394i	0.960776	+	0.277325i	$0.0894479\pi$
$224$		0			0
$225$	−0.0217804	+	0.0377247i	−0.00145203	+	0.00251498i
$226$	2.68693	−	1.55130i	0.178732	−	0.103191i
$227$	10.6652	−	6.15753i	0.707871	−	0.408689i	−0.102401	−	0.994743i	$-0.532653\pi$
$227$	10.6652	−	6.15753i	0.707871	−	0.408689i	0.810272	+	0.586054i	$0.199319\pi$
$228$	28.4347	−	16.4168i	1.88313	−	1.08723i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	−18.1652	+	31.4630i	−1.19777	+	2.07461i
$231$		0			0
$232$	3.31307	−	1.91280i	0.217514	−	0.125582i
$233$	3.47822	+	6.02445i	0.227866	+	0.394675i	0.957175	−	0.289509i	$-0.0934919\pi$
$233$	3.47822	+	6.02445i	0.227866	+	0.394675i	−0.729310	+	0.684184i	$0.760159\pi$
$234$	1.18693	+	1.14213i	0.0775922	+	0.0746631i
$235$	4.68693	−	8.11800i	0.305742	−	0.529560i
$236$	−21.3956	−	12.3528i	−1.39274	−	0.804098i
$237$	5.37386	+	9.30780i	0.349070	+	0.604607i
$238$		0			0
$239$			13.2288i			0.855697i	0.903850	+	0.427849i	$0.140728\pi$
$239$			13.2288i			0.855697i	−0.903850	+	0.427849i	$0.859272\pi$
$240$			7.02355i			0.453368i
$241$	−3.56080	+	2.05583i	−0.229371	+	0.132427i	−0.610282	−	0.792184i	$-0.708944\pi$
$241$	−3.56080	+	2.05583i	−0.229371	+	0.132427i	0.380911	+	0.924612i	$0.375610\pi$
$242$	−17.7695	−	10.2592i	−1.14227	−	0.659488i
$243$	−2.16515			−0.138895
$244$	−17.7913	−	30.8154i	−1.13897	−	1.97275i
$245$		0			0
$246$	10.0000			0.637577
$247$	−5.68693	+	22.9835i	−0.361851	+	1.46240i
$248$	−7.50000	+	12.9904i	−0.476250	+	0.824890i
$249$			6.37600i			0.404063i
$250$	−12.4782	+	21.6129i	−0.789192	+	1.36692i
$251$	10.5826	−	18.3296i	0.667966	−	1.15695i	−0.310506	−	0.950572i	$-0.600498\pi$
$251$	10.5826	−	18.3296i	0.667966	−	1.15695i	0.978472	−	0.206380i	$-0.0661683\pi$
$252$		0			0
$253$	8.37386	+	4.83465i	0.526460	+	0.303952i
$254$		−	34.9271i		−	2.19152i
$255$	−10.1869	−	5.88143i	−0.637930	−	0.368309i
$256$	1.39564	+	2.41733i	0.0872277	+	0.151083i
$257$	−13.9782	+	24.2110i	−0.871937	+	1.51024i	−0.0119476	+	0.999929i	$0.503803\pi$
$257$	−13.9782	+	24.2110i	−0.871937	+	1.51024i	−0.859990	+	0.510311i	$0.829530\pi$
$258$	−14.8521	+	8.57485i	−0.924650	+	0.533847i
$259$		0			0
$260$	15.8739	+	15.2746i	0.984455	+	0.947292i
$261$	0.230493	+	0.399225i	0.0142671	+	0.0247114i
$262$			7.93725i			0.490365i
$263$	−27.3303			−1.68526			−0.842629	−	0.538494i	$-0.818993\pi$
$263$	−27.3303			−1.68526			−0.842629	+	0.538494i	$0.818993\pi$
$264$	−3.95644			−0.243502
$265$			26.6283i			1.63576i
$266$		0			0
$267$	−4.51723	−	2.60803i	−0.276450	−	0.159609i
$268$	−27.5608	+	15.9122i	−1.68354	+	0.971994i
$269$	5.60436	+	9.70703i	0.341704	+	0.591848i	0.984749	−	0.173980i	$-0.0556628\pi$
$269$	5.60436	+	9.70703i	0.341704	+	0.591848i	−0.643046	+	0.765828i	$0.722329\pi$
$270$	−23.9564			−1.45794
$271$	24.8739	+	14.3609i	1.51098	+	0.872364i	0.999918	+	0.0128205i	$0.00408101\pi$
$271$	24.8739	+	14.3609i	1.51098	+	0.872364i	0.511062	+	0.859544i	$0.329252\pi$
$272$	5.37386			0.325838
$273$		0			0
$274$	−37.5390			−2.26781
$275$	0.230493	+	0.133075i	0.0138992	+	0.00802472i
$276$	−37.9129			−2.28209
$277$	7.87386	+	13.6379i	0.473095	+	0.819424i	0.999526	−	0.0307939i	$-0.00980354\pi$
$277$	7.87386	+	13.6379i	0.473095	+	0.819424i	−0.526431	+	0.850218i	$0.676470\pi$
$278$	1.50000	−	0.866025i	0.0899640	−	0.0519408i
$279$	−1.56534	−	0.903750i	−0.0937145	−	0.0541061i
$280$		0			0
$281$			6.39590i			0.381548i	0.981634	+	0.190774i	$0.0610997\pi$
$281$			6.39590i			0.381548i	−0.981634	+	0.190774i	$0.938900\pi$
$282$	16.7913			0.999907
$283$	−24.7477			−1.47110			−0.735550	−	0.677471i	$-0.763076\pi$
$283$	−24.7477			−1.47110			−0.735550	+	0.677471i	$0.763076\pi$
$284$		−	2.55040i		−	0.151338i
$285$	12.8739	+	22.2982i	0.762582	+	1.32083i
$286$	6.97822	−	7.25198i	0.412631	−	0.428818i
$287$		0			0
$288$	−1.33485	+	0.770675i	−0.0786567	+	0.0454125i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	5.29129	+	9.16478i	0.310715	+	0.538174i
$291$	23.6216	+	13.6379i	1.38472	+	0.799470i
$292$			9.66930i			0.565853i
$293$	6.79129	+	3.92095i	0.396751	+	0.229064i	0.685081	−	0.728467i	$-0.259767\pi$
$293$	6.79129	+	3.92095i	0.396751	+	0.229064i	−0.288330	+	0.957531i	$0.593100\pi$
$294$		0			0
$295$	9.68693	−	16.7783i	0.563995	−	0.976868i
$296$	−6.00000	+	10.3923i	−0.348743	+	0.604040i
$297$			6.37600i			0.369973i
$298$	−2.39564	+	4.14938i	−0.138776	+	0.240367i
$299$	18.9564	−	19.7001i	1.09628	−	1.13929i
$300$	−1.04356			−0.0602500
$301$		0			0
$302$	13.2695	+	22.9835i	0.763574	+	1.32255i
$303$	−17.5390			−1.00759
$304$	−10.1869	−	5.88143i	−0.584261	−	0.337323i
$305$	24.1652	−	13.9518i	1.38369	−	0.798875i
$306$		−	1.37055i		−	0.0783492i
$307$			24.1733i			1.37964i	0.723980	+	0.689820i	$0.242311\pi$
$307$			24.1733i			1.37964i	−0.723980	+	0.689820i	$0.757689\pi$
$308$		0			0
$309$	−4.10436	−	7.10895i	−0.233489	−	0.404414i
$310$	−35.9347	−	20.7469i	−2.04095	−	1.17834i
$311$	2.76951	−	4.79693i	0.157044	−	0.272009i	−0.776757	−	0.629800i	$-0.783137\pi$
$311$	2.76951	−	4.79693i	0.157044	−	0.272009i	0.933802	+	0.357791i	$0.116470\pi$
$312$	−2.68693	+	10.8591i	−0.152118	+	0.614776i
$313$	−10.3739	−	17.9681i	−0.586365	−	1.01561i	−0.994704	−	0.102784i	$-0.967225\pi$
$313$	−10.3739	−	17.9681i	−0.586365	−	1.01561i	0.408338	−	0.912831i	$-0.366108\pi$
$314$	−41.6216	+	24.0302i	−2.34884	+	1.35610i
$315$		0			0
$316$	−8.37386	+	14.5040i	−0.471067	+	0.815911i
$317$	−16.0390	+	9.26013i	−0.900841	+	0.520101i	−0.877473	−	0.479626i	$-0.840772\pi$
$317$	−16.0390	+	9.26013i	−0.900841	+	0.520101i	−0.0233679	+	0.999727i	$0.507439\pi$
$318$	−41.3085	+	23.8495i	−2.31647	+	1.33741i
$319$	2.43920	−	1.40828i	0.136569	−	0.0788483i
$320$	−23.8521	+	13.7710i	−1.33337	+	0.769823i
$321$	8.76951	−	15.1892i	0.489466	−	0.847780i
$322$		0			0
$323$	17.0608	−	9.85005i	0.949288	−	0.548072i
$324$	−13.3739	−	23.1642i	−0.742992	−	1.28690i
$325$	0.521780	−	0.542250i	0.0289432	−	0.0300786i
$326$	−7.58258	+	13.1334i	−0.419960	+	0.727392i
$327$	12.3131	+	7.10895i	0.680914	+	0.393126i
$328$	2.20871	+	3.82560i	0.121956	+	0.211234i
$329$		0			0
$330$		−	10.9445i		−	0.602475i
$331$		−	1.08450i		−	0.0596095i	−0.999556	−	0.0298048i	$-0.990511\pi$
$331$		−	1.08450i		−	0.0596095i	0.999556	−	0.0298048i	$-0.00948855\pi$
$332$	−8.60436	+	4.96773i	−0.472225	+	0.272639i
$333$	−1.25227	−	0.723000i	−0.0686241	−	0.0396202i
$334$	43.7042			2.39139
$335$	−12.4782	−	21.6129i	−0.681758	−	1.18084i
$336$		0			0
$337$	−12.9564			−0.705782			−0.352891	−	0.935664i	$-0.614801\pi$
$337$	−12.9564			−0.705782			−0.352891	+	0.935664i	$0.614801\pi$
$338$	−15.1652	−	24.0779i	−0.824875	−	1.30967i
$339$	−1.26951	+	2.19885i	−0.0689502	+	0.119425i
$340$		−	18.3296i		−	0.994060i
$341$	−5.52178	+	9.56400i	−0.299021	+	0.517920i
$342$	−1.50000	+	2.59808i	−0.0811107	+	0.140488i
$343$		0			0
$344$	−6.56080	−	3.78788i	−0.353734	−	0.204229i
$345$		−	29.7309i		−	1.60066i
$346$	−14.6869	−	8.47950i	−0.789574	−	0.455861i
$347$	2.20871	+	3.82560i	0.118570	+	0.205369i	0.919201	−	0.393788i	$-0.128836\pi$
$347$	2.20871	+	3.82560i	0.118570	+	0.205369i	−0.800631	+	0.599157i	$0.795502\pi$
$348$	−5.52178	+	9.56400i	−0.295998	+	0.512684i
$349$	9.24773	−	5.33918i	0.495019	−	0.285800i	−0.231635	−	0.972803i	$-0.574407\pi$
$349$	9.24773	−	5.33918i	0.495019	−	0.285800i	0.726654	+	0.687003i	$0.241074\pi$
$350$		0			0
$351$	17.5000	+	4.33013i	0.934081	+	0.231125i
$352$	4.70871	+	8.15573i	0.250975	+	0.434702i
$353$		−	26.8190i		−	1.42743i	−0.700435	−	0.713716i	$-0.747011\pi$
$353$		−	26.8190i		−	1.42743i	0.700435	−	0.713716i	$-0.252989\pi$
$354$	34.7042			1.84451
$355$	2.00000			0.106149
$356$		−	8.12795i		−	0.430781i
$357$		0			0
$358$	17.0608	+	9.85005i	0.901691	+	0.520592i
$359$	−10.9782	+	6.33828i	−0.579408	+	0.334522i	−0.760898	−	0.648871i	$-0.775241\pi$
$359$	−10.9782	+	6.33828i	−0.579408	+	0.334522i	0.181490	+	0.983393i	$0.441908\pi$
$360$	0.395644	+	0.685275i	0.0208523	+	0.0361172i
$361$	−24.1216			−1.26956
$362$	17.3739	+	10.0308i	0.913150	+	0.527207i
$363$	16.7913			0.881314
$364$		0			0
$365$	−7.58258			−0.396890
$366$	43.2867	+	24.9916i	2.26263	+	1.30633i
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	6.79129	+	11.7629i	0.354020	+	0.613181i
$369$	−0.460985	+	0.266150i	−0.0239979	+	0.0138552i
$370$	−28.7477	−	16.5975i	−1.49452	−	0.862863i
$371$		0			0
$372$		−	43.3013i		−	2.24507i
$373$	36.7913			1.90498			0.952490	−	0.304569i	$-0.0985124\pi$
$373$	36.7913			1.90498			0.952490	+	0.304569i	$0.0985124\pi$
$374$	−8.37386			−0.433002
$375$		−	20.4231i		−	1.05464i
$376$	3.70871	+	6.42368i	0.191262	+	0.331276i
$377$	−2.20871	−	7.65120i	−0.113754	−	0.394057i
$378$		0			0
$379$	−3.93920	+	2.27430i	−0.202343	+	0.116823i	−0.597748	−	0.801684i	$-0.703938\pi$
$379$	−3.93920	+	2.27430i	−0.202343	+	0.116823i	0.395405	+	0.918507i	$0.370604\pi$
$380$	−20.0608	+	34.7463i	−1.02910	+	1.78245i
$381$	14.2913	+	24.7532i	0.732165	+	1.26815i
$382$	1.18693	+	0.685275i	0.0607287	+	0.0350617i
$383$		−	3.92095i		−	0.200351i	−0.994970	−	0.100176i	$-0.968060\pi$
$383$		−	3.92095i		−	0.200351i	0.994970	−	0.100176i	$-0.0319405\pi$
$384$	−19.8131	−	11.4391i	−1.01108	−	0.583748i
$385$		0			0
$386$	−13.5826	+	23.5257i	−0.691335	+	1.19743i
$387$	0.456439	−	0.790576i	0.0232021	−	0.0401872i
$388$			42.5028i			2.15775i
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.123154	+	0.992388i	$0.539301\pi$
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.797856	+	0.602848i	$0.794033\pi$
$390$	−30.0390	−	7.43273i	−1.52108	−	0.376371i
$391$	−22.7477			−1.15040
$392$		0			0
$393$	−3.24773	−	5.62523i	−0.163826	−	0.283755i
$394$	23.9564			1.20691
$395$	−11.3739	−	6.56670i	−0.572281	−	0.330407i
$396$	0.643371	−	0.371450i	0.0323306	−	0.0186661i
$397$			15.1515i			0.760432i	0.924898	+	0.380216i	$0.124150\pi$
$397$			15.1515i			0.760432i	−0.924898	+	0.380216i	$0.875850\pi$
$398$			24.0779i			1.20692i
$399$		0			0
$400$	0.186932	+	0.323775i	0.00934659	+	0.0161888i
$401$	25.5998	+	14.7801i	1.27839	+	0.738081i	0.976553	−	0.215278i	$-0.0690656\pi$
$401$	25.5998	+	14.7801i	1.27839	+	0.738081i	0.301841	+	0.953358i	$0.402399\pi$
$402$	22.3521	−	38.7149i	1.11482	−	1.93093i
$403$	22.5000	+	21.6506i	1.12080	+	1.07849i
$404$	−13.6652	−	23.6687i	−0.679867	−	1.17756i
$405$	18.1652	−	10.4877i	0.902634	−	0.521136i
$406$		0			0
$407$	−4.41742	+	7.65120i	−0.218964	+	0.379256i
$408$	8.06080	−	4.65390i	0.399069	−	0.230402i
$409$	−0.313068	+	0.180750i	−0.0154802	+	0.00893751i	−0.507720	−	0.861522i	$-0.669512\pi$
$409$	−0.313068	+	0.180750i	−0.0154802	+	0.00893751i	0.492240	+	0.870460i	$0.336178\pi$
$410$	−10.5826	+	6.10985i	−0.522636	+	0.301744i
$411$	26.6044	−	15.3600i	1.31230	−	0.757655i
$412$	6.39564	−	11.0776i	0.315091	−	0.545753i
$413$		0			0
$414$	3.00000	−	1.73205i	0.147442	−	0.0851257i
$415$	−3.89564	−	6.74745i	−0.191230	−	0.331219i
$416$	25.5826	−	7.38505i	1.25429	−	0.362082i
$417$	−0.708712	+	1.22753i	−0.0347058	+	0.0601122i
$418$	15.8739	+	9.16478i	0.776416	+	0.448264i
$419$	−12.8739	−	22.2982i	−0.628929	−	1.08934i	−0.987767	−	0.155938i	$-0.950160\pi$
$419$	−12.8739	−	22.2982i	−0.628929	−	1.08934i	0.358838	−	0.933400i	$-0.383173\pi$
$420$		0			0
$421$		−	20.0616i		−	0.977743i	−0.872356	−	0.488872i	$-0.837409\pi$
$421$		−	20.0616i		−	0.977743i	0.872356	−	0.488872i	$-0.162591\pi$
$422$			3.10260i			0.151032i
$423$	−0.774053	+	0.446900i	−0.0376358	+	0.0217290i
$424$	−18.2477	−	10.5353i	−0.886188	−	0.511641i
$425$	−0.626136			−0.0303721
$426$	1.79129	+	3.10260i	0.0867882	+	0.150322i
$427$		0			0
$428$	27.3303			1.32106
$429$	−1.97822	+	7.99488i	−0.0955093	+	0.385996i
$430$	10.4782	−	18.1488i	0.505305	−	0.875213i
$431$		−	15.6084i		−	0.751828i	−0.926655	−	0.375914i	$-0.877329\pi$
$431$		−	15.6084i		−	0.751828i	0.926655	−	0.375914i	$-0.122671\pi$
$432$	−4.47822	+	7.75650i	−0.215458	+	0.373185i
$433$	−11.2477	+	19.4816i	−0.540531	+	0.936228i	0.458342	+	0.888776i	$0.348443\pi$
$433$	−11.2477	+	19.4816i	−0.540531	+	0.936228i	−0.998874	+	0.0474518i	$0.984890\pi$
$434$		0			0
$435$	−7.50000	−	4.33013i	−0.359597	−	0.207614i
$436$			22.1552i			1.06104i
$437$	43.1216	+	24.8963i	2.06279	+	1.19095i
$438$	−6.79129	−	11.7629i	−0.324500	−	0.562051i
$439$	−5.76951	+	9.99308i	−0.275364	+	0.476944i	−0.970227	−	0.242198i	$-0.922132\pi$
$439$	−5.76951	+	9.99308i	−0.275364	+	0.476944i	0.694863	+	0.719142i	$0.255465\pi$
$440$	4.18693	−	2.41733i	0.199604	−	0.115242i
$441$		0			0
$442$	−5.68693	+	22.9835i	−0.270500	+	1.09321i
$443$	−1.58258	−	2.74110i	−0.0751904	−	0.130234i	0.825979	−	0.563701i	$-0.190623\pi$
$443$	−1.58258	−	2.74110i	−0.0751904	−	0.130234i	−0.901169	+	0.433468i	$0.857290\pi$
$444$		−	34.6410i		−	1.64399i
$445$	6.37386			0.302150
$446$	−45.3303			−2.14645
$447$		−	3.92095i		−	0.185455i
$448$		0			0
$449$	−17.2087	−	9.93545i	−0.812129	−	0.468883i	0.0355654	−	0.999367i	$-0.488677\pi$
$449$	−17.2087	−	9.93545i	−0.812129	−	0.468883i	−0.847695	+	0.530484i	$0.822010\pi$
$450$	0.0825757	−	0.0476751i	0.00389266	−	0.00224743i
$451$	1.62614	+	2.81655i	0.0765718	+	0.132626i
$452$	−3.95644			−0.186095
$453$	−18.8085	−	10.8591i	−0.883701	−	0.510205i
$454$	−26.9564			−1.26513
$455$		0			0
$456$	−20.3739			−0.954094
$457$	7.74773	+	4.47315i	0.362423	+	0.209245i	0.670143	−	0.742232i	$-0.266233\pi$
$457$	7.74773	+	4.47315i	0.362423	+	0.209245i	−0.307720	+	0.951477i	$0.599566\pi$
$458$	15.1652			0.708621
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$	40.1216	−	23.1642i	1.87068	−	1.08004i
$461$	15.4782	+	8.93635i	0.720893	+	0.416208i	0.815081	−	0.579347i	$-0.196692\pi$
$461$	15.4782	+	8.93635i	0.720893	+	0.416208i	−0.0941885	+	0.995554i	$0.530026\pi$
$462$		0			0
$463$			7.93725i			0.368875i	0.982844	+	0.184438i	$0.0590464\pi$
$463$			7.93725i			0.368875i	−0.982844	+	0.184438i	$0.940954\pi$
$464$	3.95644			0.183673
$465$	33.9564			1.57469
$466$		−	15.2270i		−	0.705375i
$467$	−5.91742	−	10.2493i	−0.273826	−	0.474280i	0.696012	−	0.718030i	$-0.254956\pi$
$467$	−5.91742	−	10.2493i	−0.273826	−	0.474280i	−0.969838	+	0.243750i	$0.921622\pi$
$468$	−0.582576	−	2.01810i	−0.0269296	−	0.0932868i
$469$		0			0
$470$	−17.7695	+	10.2592i	−0.819646	+	0.473223i
$471$	19.6652	−	34.0610i	0.906122	−	1.56945i
$472$	7.66515	+	13.2764i	0.352817	+	0.611097i
$473$	−4.83030	−	2.78878i	−0.222098	−	0.128228i
$474$		−	23.5257i		−	1.08057i
$475$	1.18693	+	0.685275i	0.0544602	+	0.0314426i
$476$		0			0
$477$	1.26951	−	2.19885i	0.0581268	−	0.100678i
$478$	14.4782	−	25.0770i	0.662218	−	1.14700i
$479$			10.2215i			0.467032i	0.972353	+	0.233516i	$0.0750232\pi$
$479$			10.2215i			0.467032i	−0.972353	+	0.233516i	$0.924977\pi$
$480$	14.4782	−	25.0770i	0.660837	−	1.14460i
$481$	18.0000	+	17.3205i	0.820729	+	0.789747i
$482$	9.00000			0.409939
$483$		0			0
$484$	13.0826	+	22.6597i	0.594663	+	1.02999i
$485$	−33.3303			−1.51345
$486$	4.10436	+	2.36965i	0.186177	+	0.107490i
$487$	8.93466	−	5.15843i	0.404868	−	0.233751i	−0.283714	−	0.958909i	$-0.591567\pi$
$487$	8.93466	−	5.15843i	0.404868	−	0.233751i	0.688582	+	0.725158i	$0.258233\pi$
$488$			22.0797i			0.999502i
$489$		−	12.4104i		−	0.561218i
$490$		0			0
$491$	−18.5608	−	32.1482i	−0.837637	−	1.45083i	−0.891865	−	0.452301i	$-0.850603\pi$
$491$	−18.5608	−	32.1482i	−0.837637	−	1.45083i	0.0542283	−	0.998529i	$-0.482730\pi$
$492$	−11.0436	−	6.37600i	−0.497882	−	0.287452i
$493$	−3.31307	+	5.73840i	−0.149213	+	0.258445i
$494$	35.9347	−	37.3444i	1.61678	−	1.68020i
$495$	0.291288	+	0.504525i	0.0130924	+	0.0226767i
$496$	−13.4347	+	7.75650i	−0.603234	+	0.348277i
$497$		0			0
$498$	6.97822	−	12.0866i	0.312701	−	0.541615i
$499$	−36.5608	+	21.1084i	−1.63669	+	0.944941i	−0.654723	+	0.755869i	$0.727215\pi$
$499$	−36.5608	+	21.1084i	−1.63669	+	0.944941i	−0.981963	+	0.189072i	$0.939452\pi$
$500$	27.5608	−	15.9122i	1.23256	−	0.711617i
$501$	−30.9737	+	17.8827i	−1.38380	+	0.798938i
$502$	−40.1216	+	23.1642i	−1.79071	+	1.03387i
$503$	11.0608	−	19.1579i	0.493176	−	0.854207i	−0.506793	−	0.862068i	$-0.669169\pi$
$503$	11.0608	−	19.1579i	0.493176	−	0.854207i	0.999969	+	0.00786127i	$0.00250235\pi$
$504$		0			0
$505$	18.5608	−	10.7161i	0.825945	−	0.476859i
$506$	−10.5826	−	18.3296i	−0.470453	−	0.814848i
$507$	20.5998	+	10.8591i	0.914870	+	0.482270i
$508$	−22.2695	+	38.5719i	−0.988050	+	1.71135i
$509$	−19.0390	−	10.9922i	−0.843890	−	0.487220i	0.0146949	−	0.999892i	$-0.495322\pi$
$509$	−19.0390	−	10.9922i	−0.843890	−	0.487220i	−0.858584	+	0.512672i	$0.828656\pi$
$510$	12.8739	+	22.2982i	0.570064	+	0.987380i
$511$		0			0
$512$			19.4340i			0.858868i
$513$			32.8335i			1.44964i
$514$	52.9955	−	30.5969i	2.33753	−	1.34957i
$515$	8.68693	+	5.01540i	0.382792	+	0.221005i
$516$	21.8693			0.962743
$517$	2.73049	+	4.72935i	0.120087	+	0.207997i
$518$		0			0
$519$	13.8784			0.609195
$520$	−3.79129	−	13.1334i	−0.166259	−	0.575938i
$521$	−12.7913	+	22.1552i	−0.560396	+	0.970635i	0.437065	+	0.899430i	$0.356018\pi$
$521$	−12.7913	+	22.1552i	−0.560396	+	0.970635i	−0.997462	+	0.0712054i	$0.977315\pi$
$522$		−	1.00905i		−	0.0441649i
$523$	6.16515	−	10.6784i	0.269583	−	0.466932i	−0.699171	−	0.714954i	$-0.746447\pi$
$523$	6.16515	−	10.6784i	0.269583	−	0.466932i	0.968754	+	0.248023i	$0.0797807\pi$
$524$	5.06080	−	8.76555i	0.221082	−	0.382925i
$525$		0			0
$526$	51.8085	+	29.9117i	2.25896	+	1.30421i
$527$		−	25.9808i		−	1.13174i
$528$	−3.54356	−	2.04588i	−0.154214	−	0.0890353i
$529$	−17.2477	−	29.8739i	−0.749901	−	1.29887i
$530$	29.1434	−	50.4778i	1.26591	−	2.19262i
$531$	−1.59981	+	0.923651i	−0.0694259	+	0.0400830i
$532$		0			0
$533$	8.83485	−	2.55040i	0.382680	−	0.110470i
$534$	5.70871	+	9.88778i	0.247040	+	0.427886i
$535$			21.4322i			0.926593i
$536$	19.7477			0.852972
$537$	−16.1216			−0.695698
$538$		−	24.5348i		−	1.05777i
$539$		0			0
$540$	26.4564	+	15.2746i	1.13850	+	0.657316i
$541$	−26.0608	+	15.0462i	−1.12044	+	0.646887i	−0.941513	−	0.336975i	$-0.890596\pi$
$541$	−26.0608	+	15.0462i	−1.12044	+	0.646887i	−0.178928	+	0.983862i	$0.557263\pi$
$542$	−31.4347	−	54.4464i	−1.35023	−	2.33867i
$543$	−16.4174			−0.704539
$544$	−19.1869	−	11.0776i	−0.822633	−	0.474947i
$545$	−17.3739			−0.744215
$546$		0			0
$547$	15.7477			0.673324			0.336662	−	0.941626i	$-0.390702\pi$
$547$	15.7477			0.673324			0.336662	+	0.941626i	$0.390702\pi$
$548$	41.4564	+	23.9349i	1.77093	+	1.02245i
$549$	−2.66061			−0.113552
$550$	−0.291288	−	0.504525i	−0.0124206	−	0.0215130i
$551$	12.5608	−	7.25198i	0.535108	−	0.308945i
$552$	20.3739	+	11.7629i	0.867169	+	0.500660i
$553$		0			0
$554$		−	34.4702i		−	1.46450i
$555$	27.1652			1.15310
$556$	−2.20871			−0.0936703
$557$			27.8281i			1.17911i	0.807727	+	0.589556i	$0.200697\pi$
$557$			27.8281i			1.17911i	−0.807727	+	0.589556i	$0.799303\pi$
$558$	1.97822	+	3.42638i	0.0837447	+	0.145050i
$559$	−10.9347	+	11.3636i	−0.462487	+	0.480630i
$560$		0			0
$561$	5.93466	−	3.42638i	0.250561	−	0.144662i
$562$	7.00000	−	12.1244i	0.295277	−	0.511435i
$563$	0.165151	+	0.286051i	0.00696030	+	0.0120556i	0.869485	−	0.493960i	$-0.164451\pi$
$563$	0.165151	+	0.286051i	0.00696030	+	0.0120556i	−0.862524	+	0.506016i	$0.831118\pi$
$564$	−18.5436	−	10.7061i	−0.780825	−	0.450809i
$565$		−	3.10260i		−	0.130527i
$566$	46.9129	+	27.0852i	1.97190	+	1.13847i
$567$		0			0
$568$	−0.791288	+	1.37055i	−0.0332017	+	0.0575070i
$569$	5.37386	−	9.30780i	0.225284	−	0.390203i	−0.731121	−	0.682248i	$-0.761002\pi$
$569$	5.37386	−	9.30780i	0.225284	−	0.390203i	0.956405	+	0.292045i	$0.0943356\pi$
$570$		−	56.3592i		−	2.36063i
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	−0.477469	−	0.878648i	$-0.658446\pi$
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	0.999667	−	0.0258237i	$-0.00822085\pi$
$572$	−12.3303	+	3.55945i	−0.515556	+	0.148828i
$573$	−1.12159			−0.0468551
$574$		0			0
$575$	−0.791288	−	1.37055i	−0.0329990	−	0.0571559i
$576$	2.62614			0.109422
$577$	17.1261	+	9.88778i	0.712970	+	0.411634i	0.812160	−	0.583435i	$-0.198292\pi$
$577$	17.1261	+	9.88778i	0.712970	+	0.411634i	−0.0991895	+	0.995069i	$0.531625\pi$
$578$	−15.1652	+	8.75560i	−0.630787	+	0.364185i
$579$		−	22.2306i		−	0.923873i
$580$		−	13.4949i		−	0.560345i
$581$		0			0
$582$	−29.8521	−	51.7053i	−1.23741	−	2.14325i
$583$	−13.4347	−	7.75650i	−0.556407	−	0.321242i
$584$	3.00000	−	5.19615i	0.124141	−	0.215018i
$585$	1.58258	−	0.456850i	0.0654315	−	0.0188884i
$586$	−8.58258	−	14.8655i	−0.354543	−	0.614086i
$587$	30.7259	−	17.7396i	1.26820	−	0.732193i	0.293549	−	0.955944i	$-0.405164\pi$
$587$	30.7259	−	17.7396i	1.26820	−	0.732193i	0.974646	+	0.223751i	$0.0718302\pi$
$588$		0			0
$589$	−28.4347	+	49.2503i	−1.17163	+	2.02932i
$590$	−36.7259	+	21.2037i	−1.51198	+	0.872944i
$591$	−16.9782	+	9.80238i	−0.698391	+	0.403216i
$592$	−10.7477	+	6.20520i	−0.441729	+	0.255032i
$593$	−16.9782	+	9.80238i	−0.697212	+	0.402535i	−0.806308	−	0.591496i	$-0.798538\pi$
$593$	−16.9782	+	9.80238i	−0.697212	+	0.402535i	0.109096	+	0.994031i	$0.465204\pi$
$594$	6.97822	−	12.0866i	0.286320	−	0.495920i
$595$		0			0
$596$	5.29129	−	3.05493i	0.216740	−	0.125135i
$597$	−9.85208	−	17.0643i	−0.403219	−	0.698396i
$598$	−57.4955	+	16.5975i	−2.35116	+	0.678723i
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	−0.579330	−	0.815093i	$-0.696686\pi$
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	0.995556	+	0.0941675i	$0.0300189\pi$
$600$	0.560795	+	0.323775i	0.0228944	+	0.0132181i
$601$	−0.686932	−	1.18980i	−0.0280205	−	0.0485330i	0.851675	−	0.524070i	$-0.175587\pi$
$601$	−0.686932	−	1.18980i	−0.0280205	−	0.0485330i	−0.879696	+	0.475537i	$0.842254\pi$
$602$		0			0
$603$			2.37960i			0.0969049i
$604$		−	33.8426i		−	1.37703i
$605$	−17.7695	+	10.2592i	−0.722433	+	0.417097i
$606$	33.2477	+	19.1956i	1.35060	+	0.779767i
$607$	7.74773			0.314471			0.157235	−	0.987561i	$-0.449742\pi$
$607$	7.74773			0.314471			0.157235	+	0.987561i	$0.449742\pi$
$608$	24.2477	+	41.9983i	0.983375	+	1.70326i
$609$		0			0
$610$	−61.0780			−2.47298
$611$	14.8348	−	4.28245i	0.600154	−	0.173249i
$612$	−0.873864	+	1.51358i	−0.0353238	+	0.0611827i
$613$			37.3067i			1.50680i	0.657561	+	0.753401i	$0.271588\pi$
$613$			37.3067i			1.50680i	−0.657561	+	0.753401i	$0.728412\pi$
$614$	26.4564	−	45.8239i	1.06769	−	1.84930i
$615$	5.00000	−	8.66025i	0.201619	−	0.349215i
$616$		0			0
$617$	−24.0826	−	13.9041i	−0.969528	−	0.559757i	−0.0704357	−	0.997516i	$-0.522439\pi$
$617$	−24.0826	−	13.9041i	−0.969528	−	0.559757i	−0.899092	+	0.437759i	$0.855772\pi$
$618$			17.9681i			0.722781i
$619$	−10.7477	−	6.20520i	−0.431988	−	0.249408i	0.268205	−	0.963362i	$-0.413569\pi$
$619$	−10.7477	−	6.20520i	−0.431988	−	0.249408i	−0.700193	+	0.713954i	$0.746903\pi$
$620$	26.4564	+	45.8239i	1.06252	+	1.84033i
$621$	18.9564	−	32.8335i	0.760696	−	1.31756i
$622$	−10.5000	+	6.06218i	−0.421012	+	0.243071i
$623$		0			0
$624$	−8.02178	+	8.33648i	−0.321128	+	0.333726i
$625$	11.9564	+	20.7092i	0.478258	+	0.828366i
$626$			45.4147i			1.81514i
$627$	−15.0000			−0.599042
$628$	61.2867			2.44561
$629$		−	20.7846i		−	0.828737i
$630$		0			0
$631$	−10.4347	−	6.02445i	−0.415397	−	0.239830i	0.277709	−	0.960665i	$-0.410425\pi$
$631$	−10.4347	−	6.02445i	−0.415397	−	0.239830i	−0.693106	+	0.720836i	$0.743758\pi$
$632$	9.00000	−	5.19615i	0.358001	−	0.206692i
$633$	−1.26951	−	2.19885i	−0.0504584	−	0.0873965i
$634$	40.5390			1.61001
$635$	−30.2477	−	17.4635i	−1.20034	−	0.693019i
$636$	60.8258			2.41190
$637$		0			0
$638$	−6.16515			−0.244081
$639$	−0.165151	−	0.0953502i	−0.00653329	−	0.00377200i
$640$	27.9564			1.10508
$641$	−7.81307	−	13.5326i	−0.308598	−	0.534507i	0.669458	−	0.742850i	$-0.266526\pi$
$641$	−7.81307	−	13.5326i	−0.308598	−	0.534507i	−0.978056	+	0.208343i	$0.933193\pi$
$642$	−33.2477	+	19.1956i	−1.31218	+	0.757589i
$643$	11.7523	+	6.78518i	0.463464	+	0.267581i	0.713500	−	0.700655i	$-0.247109\pi$
$643$	11.7523	+	6.78518i	0.463464	+	0.267581i	−0.250035	+	0.968237i	$0.580442\pi$
$644$		0			0
$645$			17.1497i			0.675269i
$646$	−43.1216			−1.69660
$647$	−29.0780			−1.14318			−0.571588	−	0.820541i	$-0.693672\pi$
$647$	−29.0780			−1.14318			−0.571588	+	0.820541i	$0.693672\pi$
$648$			16.5975i			0.652012i
$649$	5.64337	+	9.77461i	0.221522	+	0.383687i
$650$	−1.58258	+	0.456850i	−0.0620737	+	0.0179191i
$651$		0			0
$652$	16.7477	−	9.66930i	0.655892	−	0.378679i
$653$	−5.60436	+	9.70703i	−0.219315	+	0.379865i	−0.954599	−	0.297894i	$-0.903716\pi$
$653$	−5.60436	+	9.70703i	−0.219315	+	0.379865i	0.735283	+	0.677760i	$0.237049\pi$
$654$	−15.5608	−	26.9521i	−0.608475	−	1.05391i
$655$	6.87386	+	3.96863i	0.268584	+	0.155067i
$656$			4.56850i			0.178370i
$657$	0.626136	+	0.361500i	0.0244279	+	0.0141035i
$658$		0			0
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	−0.918523	−	0.395367i	$-0.870617\pi$
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	0.801660	+	0.597781i	$0.203951\pi$
$660$	−6.97822	+	12.0866i	−0.271627	+	0.470471i
$661$		−	18.7665i		−	0.729933i	−0.931021	−	0.364966i	$-0.881081\pi$
$661$		−	18.7665i		−	0.729933i	0.931021	−	0.364966i	$-0.118919\pi$
$662$	−1.18693	+	2.05583i	−0.0461314	+	0.0799020i
$663$	−5.37386	−	18.6156i	−0.208704	−	0.722970i
$664$	6.16515			0.239254
$665$		0			0
$666$	1.58258	+	2.74110i	0.0613236	+	0.106216i
$667$	−16.7477			−0.648475
$668$	−48.2650	−	27.8658i	−1.86743	−	1.07816i
$669$	32.1261	−	18.5480i	1.24207	−	0.717108i
$670$			54.6272i			2.11043i
$671$			16.2559i			0.627552i
$672$		0			0
$673$	14.2477	+	24.6778i	0.549210	+	0.951259i	0.998329	+	0.0577870i	$0.0184044\pi$
$673$	14.2477	+	24.6778i	0.549210	+	0.951259i	−0.449119	+	0.893472i	$0.648262\pi$
$674$	24.5608	+	14.1802i	0.946046	+	0.546200i
$675$	0.521780	−	0.903750i	0.0200833	−	0.0347854i
$676$	1.39564	+	36.2599i	0.0536786	+	1.39461i
$677$	16.8956	+	29.2641i	0.649352	+	1.12471i	0.983278	+	0.182112i	$0.0582933\pi$
$677$	16.8956	+	29.2641i	0.649352	+	1.12471i	−0.333925	+	0.942599i	$0.608373\pi$
$678$	4.81307	−	2.77883i	0.184845	−	0.106720i
$679$		0			0
$680$	−5.68693	+	9.85005i	−0.218084	+	0.377732i
$681$	19.1044	−	11.0299i	0.732081	−	0.422667i
$682$	20.9347	−	12.0866i	0.801630	−	0.462821i
$683$	−21.7087	+	12.5335i	−0.830661	+	0.479582i	−0.854079	−	0.520144i	$-0.825878\pi$
$683$	−21.7087	+	12.5335i	−0.830661	+	0.479582i	0.0234181	+	0.999726i	$0.492545\pi$
$684$	3.31307	−	1.91280i	0.126678	−	0.0731378i
$685$	−18.7695	+	32.5097i	−0.717146	+	1.24213i
$686$		0			0
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	−3.91742	−	6.78518i	−0.149350	−	0.258682i
$689$	−30.4129	+	31.6060i	−1.15864	+	1.20409i
$690$	−32.5390	+	56.3592i	−1.23874	+	2.14556i
$691$	−25.4347	−	14.6847i	−0.967580	−	0.558633i	−0.0690824	−	0.997611i	$-0.522007\pi$
$691$	−25.4347	−	14.6847i	−0.967580	−	0.558633i	−0.898498	+	0.438978i	$0.855340\pi$
$692$	10.8131	+	18.7288i	0.411051	+	0.711962i
$693$		0			0
$694$		−	9.66930i		−	0.367042i
$695$		−	1.73205i		−	0.0657004i
$696$	5.93466	−	3.42638i	0.224953	−	0.129876i
$697$	−6.62614	−	3.82560i	−0.250983	−	0.144905i
$698$	−23.3739			−0.884714
$699$	6.23049	+	10.7915i	0.235659	+	0.408173i
$700$		0			0
$701$	31.9129			1.20533			0.602666	−	0.797993i	$-0.294105\pi$
$701$	31.9129			1.20533			0.602666	+	0.797993i	$0.294105\pi$
$702$	−28.4347	−	27.3613i	−1.07320	−	1.03268i
$703$	−22.7477	+	39.4002i	−0.857947	+	1.48601i
$704$		−	16.0453i		−	0.604730i
$705$	8.39564	−	14.5417i	0.316198	−	0.547671i
$706$	−29.3521	+	50.8393i	−1.10468	+	1.91336i
$707$		0			0
$708$	−38.3258	−	22.1274i	−1.44037	−	0.831598i
$709$			7.28970i			0.273771i	0.990587	+	0.136885i	$0.0437092\pi$
$709$			7.28970i			0.273771i	−0.990587	+	0.136885i	$0.956291\pi$
$710$	−3.79129	−	2.18890i	−0.142284	−	0.0821480i
$711$	0.626136	+	1.08450i	0.0234820	+	0.0406719i
$712$	−2.52178	+	4.36785i	−0.0945077	+	0.163692i
$713$	56.8693	−	32.8335i	2.12977	−	1.22962i
$714$		0			0
$715$	−2.79129	−	9.66930i	−0.104388	−	0.361611i
$716$	−12.5608	−	21.7559i	−0.469419	−	0.813057i
$717$			23.6965i			0.884962i
$718$	27.7477			1.03554
$719$	5.83485			0.217603			0.108802	−	0.994063i	$-0.465299\pi$
$719$	5.83485			0.217603			0.108802	+	0.994063i	$0.465299\pi$
$720$			0.818350i			0.0304981i
$721$		0			0
$722$	45.7259	+	26.3999i	1.70174	+	0.982502i
$723$	−6.37841	+	3.68258i	−0.237216	+	0.136956i
$724$	−12.7913	−	22.1552i	−0.475384	−	0.823390i
$725$	−0.460985			−0.0171206
$726$	−31.8303	−	18.3772i	−1.18133	−	0.682043i
$727$	−27.7477			−1.02911			−0.514553	−	0.857459i	$-0.672042\pi$
$727$	−27.7477			−1.02911			−0.514553	+	0.857459i	$0.672042\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$	14.3739	+	8.29875i	0.532001	+	0.307151i
$731$	13.1216			0.485320
$732$	−31.8693	−	55.1993i	−1.17792	−	2.04022i
$733$	−7.81307	+	4.51088i	−0.288582	+	0.166613i	−0.637302	−	0.770614i	$-0.719950\pi$
$733$	−7.81307	+	4.51088i	−0.288582	+	0.166613i	0.348720	+	0.937227i	$0.386616\pi$
$734$	34.1216	+	19.7001i	1.25945	+	0.727144i
$735$		0			0
$736$		−	55.9977i		−	2.06410i
$737$	14.5390			0.535551
$738$	1.16515			0.0428898
$739$		−	12.4104i		−	0.456524i	−0.973600	−	0.228262i	$-0.926696\pi$
$739$		−	12.4104i		−	0.456524i	0.973600	−	0.228262i	$-0.0733043\pi$
$740$	21.1652	+	36.6591i	0.778046	+	1.34762i
$741$	−10.1869	+	41.1700i	−0.374226	+	1.51242i
$742$		0			0
$743$	4.64792	−	2.68348i	0.170516	−	0.0984472i	−0.412313	−	0.911042i	$-0.635279\pi$
$743$	4.64792	−	2.68348i	0.170516	−	0.0984472i	0.582829	+	0.812595i	$0.301946\pi$
$744$	−13.4347	+	23.2695i	−0.492538	+	0.853102i
$745$	2.39564	+	4.14938i	0.0877696	+	0.152021i
$746$	−69.7432	−	40.2662i	−2.55348	−	1.47425i
$747$			0.742901i			0.0271813i
$748$	9.24773	+	5.33918i	0.338130	+	0.195220i
$749$		0			0
$750$	−22.3521	+	38.7149i	−0.816183	+	1.41367i
$751$	1.87386	−	3.24563i	0.0683783	−	0.118435i	−0.829809	−	0.558047i	$-0.811551\pi$
$751$	1.87386	−	3.24563i	0.0683783	−	0.118435i	0.898188	+	0.439612i	$0.144884\pi$
$752$			7.67110i			0.279736i
$753$	18.9564	−	32.8335i	0.690811	−	1.19652i
$754$	−4.18693	+	16.9213i	−0.152479	+	0.616237i
$755$	26.5390			0.965854
$756$		0			0
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	0.806343	−	0.591448i	$-0.201443\pi$
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	−0.915380	+	0.402590i	$0.868110\pi$
$758$	9.95644			0.361634
$759$	15.0000	+	8.66025i	0.544466	+	0.314347i
$760$	21.5608	−	12.4481i	0.782092	−	0.451541i
$761$			32.0152i			1.16055i	0.814421	+	0.580274i	$0.197055\pi$
$761$			32.0152i			1.16055i	−0.814421	+	0.580274i	$0.802945\pi$
$762$		−	62.5644i		−	2.26647i
$763$		0			0
$764$	−0.873864	−	1.51358i	−0.0316153	−	0.0547593i
$765$	−1.18693	−	0.685275i	−0.0429136	−	0.0247762i
$766$	−4.29129	+	7.43273i	−0.155051	+	0.268555i
$767$	30.6606	−	8.85095i	1.10709	−	0.319589i
$768$	2.50000	+	4.33013i	0.0902110	+	0.156250i
$769$	−21.8739	+	12.6289i	−0.788792	+	0.455409i	−0.839537	−	0.543303i	$-0.817174\pi$
$769$	−21.8739	+	12.6289i	−0.788792	+	0.455409i	0.0507453	+	0.998712i	$0.483840\pi$
$770$		0			0
$771$	−25.0390	+	43.3688i	−0.901758	+	1.56189i
$772$	30.0000	−	17.3205i	1.07972	−	0.623379i
$773$	19.8303	−	11.4490i	0.713246	−	0.411793i	−0.0990155	−	0.995086i	$-0.531569\pi$
$773$	19.8303	−	11.4490i	0.713246	−	0.411793i	0.812262	+	0.583293i	$0.198236\pi$
$774$	−1.73049	+	0.999100i	−0.0622013	+	0.0359119i
$775$	1.56534	−	0.903750i	0.0562287	−	0.0324637i
$776$	13.1869	−	22.8404i	0.473383	−	0.819924i
$777$		0			0
$778$	68.8693	−	39.7617i	2.46908	−	1.42553i
$779$	8.37386	+	14.5040i	0.300025	+	0.519658i
$780$	28.4347	+	27.3613i	1.01812	+	0.979690i
$781$	−0.582576	+	1.00905i	−0.0208462	+	0.0361067i
$782$	43.1216	+	24.8963i	1.54202	+	0.890289i
$783$	−5.52178	−	9.56400i	−0.197332	−	0.341790i
$784$		0			0
$785$			48.0605i			1.71535i
$786$			14.2179i			0.507136i
$787$	4.74773	−	2.74110i	0.169238	−	0.0977097i	−0.412988	−	0.910736i	$-0.635515\pi$
$787$	4.74773	−	2.74110i	0.169238	−	0.0977097i	0.582227	+	0.813027i	$0.302182\pi$
$788$	−26.4564	−	15.2746i	−0.942472	−	0.544136i
$789$	−48.9564			−1.74290
$790$	14.3739	+	24.8963i	0.511399	+	0.885769i
$791$		0			0
$792$	−0.460985			−0.0163804
$793$	44.6170	+	11.0399i	1.58440	+	0.392037i
$794$	16.5826	−	28.7219i	0.588494	−	1.01930i
$795$			47.6990i			1.69171i
$796$	15.3521	−	26.5906i	0.544140	−	0.942478i
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	−0.739975	−	0.672634i	$-0.765163\pi$
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	0.952506	+	0.304520i	$0.0984960\pi$
$798$		0			0
$799$	−11.1261	−	6.42368i	−0.393614	−	0.227253i
$800$		−	1.54135i		−	0.0544950i
$801$	−0.526326	−	0.303875i	−0.0185968	−	0.0107369i
$802$	−32.3521	−	56.0355i	−1.14239	−	1.97868i
$803$	2.20871	−	3.82560i	0.0779438	−	0.135003i
$804$	−49.3693	+	28.5034i	−1.74112	+	1.00524i
$805$		0			0
$806$	−18.9564	−	65.6670i	−0.667712	−	2.31302i
$807$	10.0390	+	17.3881i	0.353390	+	0.612090i
$808$			16.9590i			0.596616i
$809$	−29.2432			−1.02814			−0.514068	−	0.857750i	$-0.671862\pi$
$809$	−29.2432			−1.02814			−0.514068	+	0.857750i	$0.671862\pi$
$810$	−45.9129			−1.61321
$811$			12.0489i			0.423094i	0.977368	+	0.211547i	$0.0678502\pi$
$811$			12.0489i			0.423094i	−0.977368	+	0.211547i	$0.932150\pi$
$812$		0			0
$813$	44.5562	+	25.7246i	1.56266	+	0.902200i
$814$	16.7477	−	9.66930i	0.587008	−	0.338909i
$815$	7.58258	+	13.1334i	0.265606	+	0.460043i
$816$	9.62614			0.336982
$817$	−24.8739	−	14.3609i	−0.870226	−	0.502425i
$818$	0.791288			0.0276667
$819$		0			0
$820$	15.5826			0.544167
$821$	−43.0390	−	24.8486i	−1.50207	−	0.867222i	−0.999997	−	0.00239749i	$-0.999237\pi$
$821$	−43.0390	−	24.8486i	−1.50207	−	0.867222i	−0.502075	−	0.864824i	$-0.667430\pi$
$822$	−67.2432			−2.34538
$823$	−16.2477	−	28.1419i	−0.566360	−	0.980965i	−0.996922	−	0.0784034i	$-0.975018\pi$
$823$	−16.2477	−	28.1419i	−0.566360	−	0.980965i	0.430562	−	0.902561i	$-0.358316\pi$
$824$	−6.87386	+	3.96863i	−0.239462	+	0.138254i
$825$	0.412878	+	0.238375i	0.0143746	+	0.00829917i
$826$		0			0
$827$			0.989150i			0.0343961i	0.999852	+	0.0171981i	$0.00547458\pi$
$827$			0.989150i			0.0343961i	−0.999852	+	0.0171981i	$0.994525\pi$
$828$	−4.41742			−0.153516
$829$	20.6261			0.716375			0.358188	−	0.933650i	$-0.383395\pi$
$829$	20.6261			0.716375			0.358188	+	0.933650i	$0.383395\pi$
$830$			17.0544i			0.591965i
$831$	14.1044	+	24.4295i	0.489275	+	0.847449i
$832$	−44.0390	−	10.8968i	−1.52678	−	0.377780i
$833$		0			0
$834$	2.68693	−	1.55130i	0.0930408	−	0.0537172i
$835$	21.8521	−	37.8489i	0.756223	−	1.30982i
$836$	−11.6869	−	20.2424i	−0.404201	−	0.700097i
$837$	37.5000	+	21.6506i	1.29619	+	0.748355i
$838$			56.3592i			1.94690i
$839$	−40.2695	−	23.2496i	−1.39026	−	0.802666i	−0.396914	−	0.917856i	$-0.629919\pi$
$839$	−40.2695	−	23.2496i	−1.39026	−	0.802666i	−0.993343	+	0.115190i	$0.963252\pi$
$840$		0			0
$841$	12.0608	−	20.8899i	0.415889	−	0.720342i
$842$	−21.9564	+	38.0297i	−0.756669	+	1.31059i
$843$			11.4569i			0.394597i
$844$	1.97822	−	3.42638i	0.0680931	−	0.117941i
$845$	−28.4347	+	1.09445i	−0.978182	+	0.0376502i
$846$	1.95644			0.0672638
$847$		0			0
$848$	−10.8956	−	18.8718i	−0.374158	−	0.648061i
$849$	−44.3303			−1.52141
$850$	1.18693	+	0.685275i	0.0407114	+	0.0235048i
$851$	45.4955	−	26.2668i	1.55956	−	0.900415i
$852$		−	4.56850i		−	0.156514i
$853$		−	17.6066i		−	0.602837i	−0.953492	−	0.301419i	$-0.902540\pi$
$853$		−	17.6066i		−	0.602837i	0.953492	−	0.301419i	$-0.0974601\pi$
$854$		0			0
$855$	1.50000	+	2.59808i	0.0512989	+	0.0888523i
$856$	−14.6869	−	8.47950i	−0.501989	−	0.289823i
$857$	−23.7695	+	41.1700i	−0.811951	+	1.40634i	0.0995459	+	0.995033i	$0.468261\pi$
$857$	−23.7695	+	41.1700i	−0.811951	+	1.40634i	−0.911497	+	0.411307i	$0.865072\pi$
$858$	12.5000	−	12.9904i	0.426743	−	0.443484i
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	0.960381	−	0.278691i	$-0.0899005\pi$
$859$	7.00000	+	12.1244i	0.238837	+	0.413678i	−0.721544	+	0.692369i	$0.756567\pi$
$860$	−23.1434	+	13.3618i	−0.789182	+	0.455635i
$861$		0			0
$862$	−17.0826	+	29.5879i	−0.581835	+	1.00777i
$863$	−2.66970	+	1.54135i	−0.0908776	+	0.0524682i	−0.544750	−	0.838598i	$-0.683375\pi$
$863$	−2.66970	+	1.54135i	−0.0908776	+	0.0524682i	0.453873	+	0.891067i	$0.350042\pi$
$864$	31.9782	−	18.4626i	1.08792	−	0.628112i
$865$	−14.6869	+	8.47950i	−0.499371	+	0.288312i
$866$	42.6434	−	24.6202i	1.44908	−	0.836627i
$867$	7.16515	−	12.4104i	0.243341	−	0.421479i
$868$		0			0
$869$	6.62614	−	3.82560i	0.224776	−	0.129775i
$870$	9.47822	+	16.4168i	0.321342	+	0.556580i
$871$	9.87386	−	39.9047i	0.334563	−	1.35212i
$872$	6.87386	−	11.9059i	0.232778	−	0.403184i
$873$	2.75227	+	1.58903i	0.0931503	+	0.0537804i
$874$	−54.4955	−	94.3889i	−1.84334	−	3.19275i
$875$		0			0
$876$			17.3205i			0.585206i
$877$		−	34.9271i		−	1.17940i	−0.807621	−	0.589702i	$-0.799245\pi$
$877$		−	34.9271i		−	1.17940i	0.807621	−	0.589702i	$-0.200755\pi$
$878$	21.8739	−	12.6289i	0.738207	−	0.426204i
$879$	12.1652	+	7.02355i	0.410320	+	0.236899i
$880$	5.00000			0.168550
$881$	−3.70871	−	6.42368i	−0.124950	−	0.216419i	0.796764	−	0.604291i	$-0.206544\pi$
$881$	−3.70871	−	6.42368i	−0.124950	−	0.216419i	−0.921713	+	0.387872i	$0.873210\pi$
$882$		0			0
$883$	−53.2432			−1.79178			−0.895888	−	0.444280i	$-0.853459\pi$
$883$	−53.2432			−1.79178			−0.895888	+	0.444280i	$0.853459\pi$
$884$	20.9347	−	21.7559i	0.704109	−	0.731731i
$885$	17.3521	−	30.0547i	0.583284	−	1.01028i
$886$			6.92820i			0.232758i
$887$	−15.7913	+	27.3513i	−0.530220	+	0.918367i	0.469159	+	0.883114i	$0.344557\pi$
$887$	−15.7913	+	27.3513i	−0.530220	+	0.918367i	−0.999378	+	0.0352534i	$0.988776\pi$
$888$	−10.7477	+	18.6156i	−0.360670	+	0.624699i
$889$		0			0
$890$	−12.0826	−	6.97588i	−0.405009	−	0.233832i
$891$			12.2197i			0.409376i
$892$	50.0608	+	28.9026i	1.67616	+	0.967731i
$893$	14.0608	+	24.3540i	0.470527	+	0.814976i
$894$	−4.29129	+	7.43273i	−0.143522	+	0.248588i
$895$	17.0608	−	9.85005i	0.570279	−	0.329251i
$896$		0			0
$897$	33.9564	−	35.2886i	1.13377	−	1.17825i
$898$	21.7477	+	37.6682i	0.725731	+	1.25700i
$899$		−	19.1280i		−	0.637955i
$900$	−0.121591			−0.00405302
$901$	36.4955			1.21584
$902$		−	7.11890i		−	0.237034i
$903$		0			0
$904$	2.12614	+	1.22753i	0.0707142	+	0.0408269i
$905$	17.3739	−	10.0308i	0.577527	−	0.333435i
$906$	23.7695	+	41.1700i	0.789689	+	1.36778i
$907$	23.0780			0.766293			0.383147	−	0.923688i	$-0.374840\pi$
$907$	23.0780			0.766293			0.383147	+	0.923688i	$0.374840\pi$
$908$	29.7695	+	17.1874i	0.987936	+	0.570385i
$909$	−2.04356			−0.0677806
$910$		0			0
$911$	−1.87841			−0.0622345			−0.0311172	−	0.999516i	$-0.509907\pi$
$911$	−1.87841			−0.0622345			−0.0311172	+	0.999516i	$0.509907\pi$
$912$	−18.2477	−	10.5353i	−0.604243	−	0.348860i
$913$	4.53901			0.150219
$914$	−9.79129	−	16.9590i	−0.323867	−	0.560954i
$915$	43.2867	−	24.9916i	1.43102	−	0.826197i
$916$	−16.7477	−	9.66930i	−0.553360	−	0.319483i
$917$		0			0
$918$			32.8335i			1.08367i
$919$	−19.9129			−0.656865			−0.328433	−	0.944527i	$-0.606520\pi$
$919$	−19.9129			−0.656865			−0.328433	+	0.944527i	$0.606520\pi$
$920$	−28.7477			−0.947784
$921$			43.3013i			1.42683i
$922$	−19.5608	−	33.8803i	−0.644200	−	1.11579i
$923$	2.37386	+	2.28425i	0.0781367	+	0.0751870i
$924$		0			0
$925$	1.25227	−	0.723000i	0.0411745	−	0.0237721i
$926$	8.68693	−	15.0462i	0.285470	−	0.494449i
$927$	−0.478220	−	0.828301i	−0.0157068	−	0.0272050i
$928$	−14.1261	−	8.15573i	−0.463713	−	0.267725i
$929$		−	26.7436i		−	0.877428i	−0.898627	−	0.438714i	$-0.855434\pi$
$929$		−	26.7436i		−	0.877428i	0.898627	−	0.438714i	$-0.144566\pi$
$930$	−64.3693	−	37.1636i	−2.11075	−	1.21864i
$931$		0			0
$932$	−9.70871	+	16.8160i	−0.318019	+	0.550826i
$933$	4.96099	−	8.59268i	0.162415	−	0.281312i
$934$			25.9053i			0.847648i
$935$	−4.18693	+	7.25198i	−0.136927	+	0.237165i
$936$	−0.313068	+	1.26525i	−0.0102330	+	0.0413560i
$937$	−34.4955			−1.12692			−0.563459	−	0.826144i	$-0.690530\pi$
$937$	−34.4955			−1.12692			−0.563459	+	0.826144i	$0.690530\pi$
$938$		0			0
$939$	−18.5826	−	32.1860i	−0.606419	−	1.05035i
$940$	26.1652			0.853413
$941$	−1.96099	−	1.13218i	−0.0639263	−	0.0369079i	0.467696	−	0.883889i	$-0.345084\pi$
$941$	−1.96099	−	1.13218i	−0.0639263	−	0.0369079i	−0.531622	+	0.846981i	$0.678417\pi$
$942$	−74.5562	+	43.0451i	−2.42917	+	1.40248i
$943$		−	19.3386i		−	0.629752i
$944$			15.8546i			0.516024i
$945$		0			0
$946$	6.10436	+	10.5731i	0.198470	+	0.343760i
$947$	49.2695	+	28.4458i	1.60104	+	0.924363i	0.991279	+	0.131781i	$0.0420695\pi$
$947$	49.2695	+	28.4458i	1.60104	+	0.924363i	0.609765	+	0.792582i	$0.291264\pi$
$948$	−15.0000	+	25.9808i	−0.487177	+	0.843816i
$949$	−9.00000	−	8.66025i	−0.292152	−	0.281124i
$950$	−1.50000	−	2.59808i	−0.0486664	−	0.0842927i
$951$	−28.7305	+	16.5876i	−0.931650	+	0.537888i
$952$		0			0
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$	−4.81307	+	2.77883i	−0.155829	+	0.0899678i
$955$	1.18693	−	0.685275i	0.0384082	−	0.0221750i
$956$	−31.9782	+	18.4626i	−1.03425	+	0.597124i
$957$	4.36932	−	2.52263i	0.141240	−	0.0815449i
$958$	11.1869	−	19.3763i	0.361433	−	0.626021i
$959$		0			0
$960$	−42.7259	+	24.6678i	−1.37897	+	0.796151i
$961$	22.0000	+	38.1051i	0.709677	+	1.22920i
$962$	−15.1652	−	52.5336i	−0.488944	−	1.69375i
$963$	1.02178	−	1.76978i	0.0329264	−	0.0570302i
$964$	−9.93920	−	5.73840i	−0.320120	−	0.184821i
$965$	13.5826	+	23.5257i	0.437239	+	0.757319i
$966$		0			0
$967$		−	23.8118i		−	0.765735i	−0.923803	−	0.382867i	$-0.874937\pi$
$967$		−	23.8118i		−	0.765735i	0.923803	−	0.382867i	$-0.125063\pi$
$968$		−	16.2360i		−	0.521845i
$969$	30.5608	−	17.6443i	0.981754	−	0.566816i
$970$	63.1824	+	36.4784i	2.02866	+	1.17125i
$971$	49.7477			1.59648			0.798240	−	0.602339i	$-0.205765\pi$
$971$	49.7477			1.59648			0.798240	+	0.602339i	$0.205765\pi$
$972$	−3.02178	−	5.23388i	−0.0969237	−	0.167877i
$973$		0			0
$974$	−22.5826			−0.723592
$975$	0.934659	−	0.971326i	0.0299330	−	0.0311073i
$976$	−11.4174	+	19.7756i	−0.365463	+	0.633000i
$977$			56.8161i			1.81771i	0.417115	+	0.908854i	$0.363041\pi$
$977$			56.8161i			1.81771i	−0.417115	+	0.908854i	$0.636959\pi$
$978$	−13.5826	+	23.5257i	−0.434323	+	0.752269i
$979$	−1.85663	+	3.21578i	−0.0593381	+	0.102777i
$980$		0			0
$981$	1.43466	+	0.828301i	0.0458051	+	0.0264456i
$982$			81.2555i			2.59297i
$983$	−21.7259	−	12.5435i	−0.692950	−	0.400075i	0.111766	−	0.993735i	$-0.464349\pi$
$983$	−21.7259	−	12.5435i	−0.692950	−	0.400075i	−0.804716	+	0.593660i	$0.797683\pi$
$984$	3.95644	+	6.85275i	0.126127	+	0.218458i
$985$	11.9782	−	20.7469i	0.381658	−	0.661051i
$986$	12.5608	−	7.25198i	0.400017	−	0.230950i
$987$		0			0
$988$	−63.4955	+	18.3296i	−2.02006	+	0.583141i
$989$	16.5826	+	28.7219i	0.527295	+	0.913302i
$990$		−	1.27520i		−	0.0405285i
$991$	−26.6261			−0.845807			−0.422904	−	0.906175i	$-0.638989\pi$
$991$	−26.6261			−0.845807			−0.422904	+	0.906175i	$0.638989\pi$
$992$	63.9564			2.03062
$993$		−	1.94265i		−	0.0616482i
$994$		0			0
$995$	20.8521	+	12.0390i	0.661055	+	0.381661i
$996$	−15.4129	+	8.89863i	−0.488376	+	0.281964i
$997$	−25.0390	−	43.3688i	−0.792994	−	1.37351i	−0.924105	−	0.382138i	$-0.875188\pi$
$997$	−25.0390	−	43.3688i	−0.792994	−	1.37351i	0.131112	−	0.991368i	$-0.458145\pi$
$998$	92.4083			2.92513
$999$	30.0000	+	17.3205i	0.949158	+	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.u.d.361.1		4
7.2	even	3		637.2.k.f.569.2		4
7.3	odd	6		637.2.q.e.491.2	✓	4
7.4	even	3		637.2.q.f.491.2	yes	4
7.5	odd	6		637.2.k.d.569.2		4
7.6	odd	2		637.2.u.e.361.1		4
13.4	even	6		637.2.k.f.459.1		4
91.4	even	6		637.2.q.f.589.2	yes	4
91.11	odd	12		8281.2.a.bq.1.1		4
91.17	odd	6		637.2.q.e.589.2	yes	4
91.24	even	12		8281.2.a.bs.1.1		4
91.30	even	6	inner	637.2.u.d.30.1		4
91.67	odd	12		8281.2.a.bq.1.4		4
91.69	odd	6		637.2.k.d.459.1		4
91.80	even	12		8281.2.a.bs.1.4		4
91.82	odd	6		637.2.u.e.30.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.d.459.1		4	91.69	odd	6
637.2.k.d.569.2		4	7.5	odd	6
637.2.k.f.459.1		4	13.4	even	6
637.2.k.f.569.2		4	7.2	even	3
637.2.q.e.491.2	✓	4	7.3	odd	6
637.2.q.e.589.2	yes	4	91.17	odd	6
637.2.q.f.491.2	yes	4	7.4	even	3
637.2.q.f.589.2	yes	4	91.4	even	6
637.2.u.d.30.1		4	91.30	even	6	inner
637.2.u.d.361.1		4	1.1	even	1	trivial
637.2.u.e.30.1		4	91.82	odd	6
637.2.u.e.361.1		4	7.6	odd	2
8281.2.a.bq.1.1		4	91.11	odd	12
8281.2.a.bq.1.4		4	91.67	odd	12
8281.2.a.bs.1.1		4	91.24	even	12
8281.2.a.bs.1.4		4	91.80	even	12

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.89564 - 1.09445i) q^{2} +1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(-1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +4.79129 q^{10} -1.27520i q^{11} +(2.50000 + 4.33013i) q^{12} +(-3.50000 - 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} +(0.895644 - 1.55130i) q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.395644 - 0.228425i) q^{18} -6.56670i q^{19} +(-5.29129 - 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 + 6.56670i) q^{23} -3.10260i q^{24} +(-0.104356 + 0.180750i) q^{25} +(5.68693 + 5.47225i) q^{26} -5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +8.58258 q^{30} +(-7.50000 - 4.33013i) q^{31} +(-6.39564 + 3.69253i) q^{32} -2.28425i q^{33} -6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(-7.18693 + 12.4481i) q^{38} +(-6.26951 - 1.55130i) q^{39} +(1.89564 + 3.28335i) q^{40} +(-2.20871 + 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +(3.08258 - 1.77973i) q^{44} +(-0.395644 + 0.228425i) q^{45} +(14.3739 - 8.29875i) q^{46} +(-3.70871 + 2.14123i) q^{47} +(1.60436 - 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} +(2.68693 + 4.65390i) q^{51} +(-2.79129 - 9.66930i) q^{52} +(6.08258 - 10.5353i) q^{53} +(9.47822 + 5.47225i) q^{54} +(1.39564 + 2.41733i) q^{55} -11.7629i q^{57} -4.83465i q^{58} +(-7.66515 + 4.42548i) q^{59} +(-9.47822 - 5.47225i) q^{60} -12.7477 q^{61} +(9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(7.58258 - 2.18890i) q^{65} +(-2.50000 + 4.33013i) q^{66} +11.4014i q^{67} +(-4.18693 + 7.25198i) q^{68} +(-6.79129 + 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} -0.361500i q^{72} +(3.00000 + 1.73205i) q^{73} +(7.58258 + 13.1334i) q^{74} +(-0.186932 + 0.323775i) q^{75} +(15.8739 - 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} +(3.00000 + 5.19615i) q^{79} +3.92095i q^{80} -9.58258 q^{81} +5.58258 q^{82} +3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(-8.29129 + 4.78698i) q^{86} +(1.97822 + 3.42638i) q^{87} -2.20871 q^{88} +(-2.52178 - 1.45595i) q^{89} +1.00000 q^{90} -21.1652 q^{92} +(-13.4347 - 7.75650i) q^{93} +9.37386 q^{94} +(7.18693 + 12.4481i) q^{95} +(-11.4564 + 6.61438i) q^{96} +(13.1869 + 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 2 q^{3} + q^{4} - 3 q^{5} - 9 q^{6} + 10 q^{9} + 10 q^{10} + 10 q^{12} - 14 q^{13} - 9 q^{15} - q^{16} + 6 q^{17} + 3 q^{18} - 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} + 9 q^{26} - 20 q^{27}+ \cdots + 39 q^{97}+O(q^{100}) \) 4 * q - 3 * q^2 - 2 * q^3 + q^4 - 3 * q^5 - 9 * q^6 + 10 * q^9 + 10 * q^10 + 10 * q^12 - 14 * q^13 - 9 * q^15 - q^16 + 6 * q^17 + 3 * q^18 - 12 * q^20 - q^22 - 6 * q^23 - 5 * q^25 + 9 * q^26 - 20 * q^27 + 9 * q^29 + 16 * q^30 - 30 * q^31 - 21 * q^32 - 8 * q^36 - 24 * q^37 - 15 * q^38 + 7 * q^39 + 3 * q^40 - 18 * q^41 - 5 * q^43 - 6 * q^44 + 3 * q^45 + 30 * q^46 - 24 * q^47 + 11 * q^48 - 3 * q^50 - 3 * q^51 - 2 * q^52 + 6 * q^53 + 15 * q^54 + q^55 + 6 * q^59 - 15 * q^60 + 4 * q^61 + 15 * q^62 + 32 * q^64 + 12 * q^65 - 10 * q^66 - 3 * q^68 - 18 * q^69 + 6 * q^71 + 12 * q^73 + 12 * q^74 + 13 * q^75 + 36 * q^76 + 27 * q^78 + 12 * q^79 - 20 * q^81 + 4 * q^82 - 9 * q^85 - 24 * q^86 - 15 * q^87 - 18 * q^88 - 33 * q^89 + 4 * q^90 - 48 * q^92 + 15 * q^93 + 10 * q^94 + 15 * q^95 + 39 * q^97

Introduction

L-functions

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