LMFDB - Embedded newform 637.2.u.e.30.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
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			30.2
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.e.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.395644 - 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.395644 - 0.228425i) q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} -0.208712 q^{10} +3.92095i q^{11} +(-2.50000 + 4.33013i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.89564 - 1.09445i) q^{18} +1.37055i q^{19} +(0.708712 - 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 + 1.37055i) q^{23} +4.83465i q^{24} +(-2.39564 - 4.14938i) q^{25} +(1.18693 - 1.14213i) q^{26} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} -0.582576 q^{30} +(7.50000 - 4.33013i) q^{31} +(-4.10436 - 2.36965i) q^{32} +10.9445i q^{33} +1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(-6.00000 + 3.46410i) q^{37} +(0.313068 + 0.542250i) q^{38} +(9.76951 - 2.41733i) q^{39} +(0.395644 - 0.685275i) q^{40} +(6.79129 + 3.92095i) q^{41} +(-4.68693 - 8.11800i) q^{43} +(-6.08258 - 3.51178i) q^{44} +(-1.89564 - 1.09445i) q^{45} +(0.626136 + 0.361500i) q^{46} +(8.29129 + 4.78698i) q^{47} +(-3.89564 - 6.74745i) q^{48} +(-1.89564 - 1.09445i) q^{50} +(-4.18693 + 7.25198i) q^{51} +(-1.79129 + 6.20520i) q^{52} +(-3.08258 - 5.33918i) q^{53} +(1.97822 - 1.14213i) q^{54} +(0.895644 - 1.55130i) q^{55} +3.82560i q^{57} -3.10260i q^{58} +(-10.6652 - 6.15753i) q^{59} +(1.97822 - 1.14213i) q^{60} -14.7477 q^{61} +(1.97822 - 3.42638i) q^{62} +3.41742 q^{64} +(-1.58258 - 0.456850i) q^{65} +(2.50000 + 4.33013i) q^{66} +4.47315i q^{67} +(-2.68693 - 4.65390i) q^{68} +(2.20871 + 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +8.29875i q^{72} +(-3.00000 + 1.73205i) q^{73} +(-1.58258 + 2.74110i) q^{74} +(-6.68693 - 11.5821i) q^{75} +(-2.12614 - 1.22753i) q^{76} +(3.31307 - 3.18800i) q^{78} +(3.00000 - 5.19615i) q^{79} +1.27520i q^{80} -0.417424 q^{81} +3.58258 q^{82} -7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +(-3.70871 - 2.14123i) q^{86} +(9.47822 - 16.4168i) q^{87} -6.79129 q^{88} +(13.9782 - 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(20.9347 - 12.0866i) q^{93} +4.37386 q^{94} +(0.313068 - 0.542250i) q^{95} +(-11.4564 - 6.61438i) q^{96} +(-6.31307 + 3.64485i) q^{97} +18.7864i 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.395644	−	0.228425i	0.279763	−	0.161521i	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	0.395644	−	0.228425i	0.279763	−	0.161521i	0.633316	+	0.773893i	$0.281693\pi$
$3$	2.79129			1.61155			0.805775	−	0.592221i	$-0.201749\pi$
$3$	2.79129			1.61155			0.805775	+	0.592221i	$0.201749\pi$
$4$	−0.895644	+	1.55130i	−0.447822	+	0.775650i
$5$	−0.395644	−	0.228425i	−0.176937	−	0.102155i	0.408916	−	0.912572i	$-0.365907\pi$
$5$	−0.395644	−	0.228425i	−0.176937	−	0.102155i	−0.585853	+	0.810417i	$0.699240\pi$
$6$	1.10436	−	0.637600i	0.450851	−	0.260299i
$7$		0			0
$7$		0			0
$8$			1.73205i			0.612372i
$9$	4.79129			1.59710
$10$	−0.208712			−0.0660006
$11$			3.92095i			1.18221i	0.806594	+	0.591106i	$0.201308\pi$
$11$			3.92095i			1.18221i	−0.806594	+	0.591106i	$0.798692\pi$
$12$	−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
$15$	−1.10436	−	0.637600i	−0.285144	−	0.164628i
$16$	−1.39564	−	2.41733i	−0.348911	−	0.604332i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.89564	−	1.09445i	0.446808	−	0.257964i
$19$			1.37055i			0.314426i	0.987565	+	0.157213i	$0.0502509\pi$
$19$			1.37055i			0.314426i	−0.987565	+	0.157213i	$0.949749\pi$
$20$	0.708712	−	0.409175i	0.158473	−	0.0914943i
$21$		0			0
$22$	0.895644	+	1.55130i	0.190952	+	0.330738i
$23$	0.791288	+	1.37055i	0.164995	+	0.285780i	0.936653	−	0.350257i	$-0.113906\pi$
$23$	0.791288	+	1.37055i	0.164995	+	0.285780i	−0.771659	+	0.636037i	$0.780573\pi$
$24$			4.83465i			0.986869i
$25$	−2.39564	−	4.14938i	−0.479129	−	0.829875i
$26$	1.18693	−	1.14213i	0.232776	−	0.223989i
$27$	5.00000			0.962250
$28$		0			0
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	−0.356883	−	0.934149i	$-0.616161\pi$
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	0.987438	−	0.158005i	$-0.0505061\pi$
$30$	−0.582576			−0.106363
$31$	7.50000	−	4.33013i	1.34704	−	0.777714i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	7.50000	−	4.33013i	1.34704	−	0.777714i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−4.10436	−	2.36965i	−0.725555	−	0.418899i
$33$			10.9445i			1.90519i
$34$			1.37055i			0.235048i
$35$		0			0
$36$	−4.29129	+	7.43273i	−0.715215	+	1.23879i
$37$	−6.00000	+	3.46410i	−0.986394	+	0.569495i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−6.00000	+	3.46410i	−0.986394	+	0.569495i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	0.313068	+	0.542250i	0.0507864	+	0.0879646i
$39$	9.76951	−	2.41733i	1.56437	−	0.387082i
$40$	0.395644	−	0.685275i	0.0625568	−	0.108352i
$41$	6.79129	+	3.92095i	1.06062	+	0.612350i	0.925604	−	0.378493i	$-0.123558\pi$
$41$	6.79129	+	3.92095i	1.06062	+	0.612350i	0.135017	+	0.990843i	$0.456891\pi$
$42$		0			0
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	−0.963056	−	0.269302i	$-0.913207\pi$
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	0.248305	−	0.968682i	$-0.420126\pi$
$44$	−6.08258	−	3.51178i	−0.916983	−	0.529420i
$45$	−1.89564	−	1.09445i	−0.282586	−	0.163151i
$46$	0.626136	+	0.361500i	0.0923188	+	0.0533003i
$47$	8.29129	+	4.78698i	1.20941	+	0.698252i	0.962630	−	0.270820i	$-0.0872947\pi$
$47$	8.29129	+	4.78698i	1.20941	+	0.698252i	0.246778	+	0.969072i	$0.420628\pi$
$48$	−3.89564	−	6.74745i	−0.562288	−	0.973911i
$49$		0			0
$50$	−1.89564	−	1.09445i	−0.268085	−	0.154779i
$51$	−4.18693	+	7.25198i	−0.586288	+	1.01548i
$52$	−1.79129	+	6.20520i	−0.248407	+	0.860507i
$53$	−3.08258	−	5.33918i	−0.423424	−	0.733392i	0.572848	−	0.819662i	$-0.305839\pi$
$53$	−3.08258	−	5.33918i	−0.423424	−	0.733392i	−0.996272	+	0.0862695i	$0.972505\pi$
$54$	1.97822	−	1.14213i	0.269202	−	0.155424i
$55$	0.895644	−	1.55130i	0.120769	−	0.209177i
$56$		0			0
$57$			3.82560i			0.506713i
$58$		−	3.10260i		−	0.407392i
$59$	−10.6652	−	6.15753i	−1.38848	−	0.801642i	−0.395340	−	0.918535i	$-0.629373\pi$
$59$	−10.6652	−	6.15753i	−1.38848	−	0.801642i	−0.993145	+	0.116893i	$0.962707\pi$
$60$	1.97822	−	1.14213i	0.255387	−	0.147448i
$61$	−14.7477			−1.88825			−0.944126	−	0.329583i	$-0.893092\pi$
$61$	−14.7477			−1.88825			−0.944126	+	0.329583i	$0.893092\pi$
$62$	1.97822	−	3.42638i	0.251234	−	0.435150i
$63$		0			0
$64$	3.41742			0.427178
$65$	−1.58258	−	0.456850i	−0.196294	−	0.0566653i
$66$	2.50000	+	4.33013i	0.307729	+	0.533002i
$67$			4.47315i			0.546483i	0.961946	+	0.273241i	$0.0880957\pi$
$67$			4.47315i			0.546483i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−2.68693	−	4.65390i	−0.325838	−	0.564369i
$69$	2.20871	+	3.82560i	0.265898	+	0.460548i
$70$		0			0
$71$	3.79129	−	2.18890i	0.449943	−	0.259775i	−0.257863	−	0.966181i	$-0.583018\pi$
$71$	3.79129	−	2.18890i	0.449943	−	0.259775i	0.707806	+	0.706407i	$0.249685\pi$
$72$			8.29875i			0.978018i
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	−0.665180	−	0.746683i	$-0.731645\pi$
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	0.314057	+	0.949404i	$0.398312\pi$
$74$	−1.58258	+	2.74110i	−0.183971	+	0.318647i
$75$	−6.68693	−	11.5821i	−0.772140	−	1.33739i
$76$	−2.12614	−	1.22753i	−0.243885	−	0.140807i
$77$		0			0
$78$	3.31307	−	3.18800i	0.375131	−	0.360970i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$			1.27520i			0.142572i
$81$	−0.417424			−0.0463805
$82$	3.58258			0.395629
$83$		−	7.02355i		−	0.770935i	−0.922721	−	0.385468i	$-0.874040\pi$
$83$		−	7.02355i		−	0.770935i	0.922721	−	0.385468i	$-0.125960\pi$
$84$		0			0
$85$	1.18693	−	0.685275i	0.128741	−	0.0743286i
$86$	−3.70871	−	2.14123i	−0.399921	−	0.230894i
$87$	9.47822	−	16.4168i	1.01617	−	1.76006i
$88$	−6.79129			−0.723954
$89$	13.9782	−	8.07033i	1.48169	−	0.855453i	0.481904	−	0.876224i	$-0.339945\pi$
$89$	13.9782	−	8.07033i	1.48169	−	0.855453i	0.999784	+	0.0207708i	$0.00661204\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−2.83485			−0.295553
$93$	20.9347	−	12.0866i	2.17082	−	1.25333i
$94$	4.37386			0.451130
$95$	0.313068	−	0.542250i	0.0321201	−	0.0556337i
$96$	−11.4564	−	6.61438i	−1.16927	−	0.675077i
$97$	−6.31307	+	3.64485i	−0.640995	+	0.370079i	−0.784998	−	0.619499i	$-0.787336\pi$
$97$	−6.31307	+	3.64485i	−0.640995	+	0.370079i	0.144003	+	0.989577i	$0.454003\pi$
$98$		0			0
$99$			18.7864i			1.88811i
$100$	8.58258			0.858258
$101$	5.20871			0.518286			0.259143	−	0.965839i	$-0.416560\pi$
$101$	5.20871			0.518286			0.259143	+	0.965839i	$0.416560\pi$
$102$			3.82560i			0.378791i
$103$	−2.29129	+	3.96863i	−0.225767	+	0.391040i	−0.956549	−	0.291570i	$-0.905822\pi$
$103$	−2.29129	+	3.96863i	−0.225767	+	0.391040i	0.730782	+	0.682611i	$0.239156\pi$
$104$	1.50000	+	6.06218i	0.147087	+	0.594445i
$105$		0			0
$106$	−2.43920	−	1.40828i	−0.236917	−	0.136784i
$107$	2.60436	+	4.51088i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$107$	2.60436	+	4.51088i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$108$	−4.47822	+	7.75650i	−0.430917	+	0.746370i
$109$	−6.87386	+	3.96863i	−0.658397	+	0.380126i	−0.791666	−	0.610954i	$-0.790786\pi$
$109$	−6.87386	+	3.96863i	−0.658397	+	0.380126i	0.133269	+	0.991080i	$0.457453\pi$
$110$		−	0.818350i		−	0.0780266i
$111$	−16.7477	+	9.66930i	−1.58962	+	0.917770i
$112$		0			0
$113$	−5.29129	−	9.16478i	−0.497762	−	0.862150i	0.502234	−	0.864732i	$-0.332512\pi$
$113$	−5.29129	−	9.16478i	−0.497762	−	0.862150i	−0.999997	+	0.00258173i	$0.999178\pi$
$114$	0.873864	+	1.51358i	0.0818448	+	0.141759i
$115$		−	0.723000i		−	0.0674201i
$116$	6.08258	+	10.5353i	0.564753	+	0.978181i
$117$	16.7695	−	4.14938i	1.55034	−	0.383610i
$118$	−5.62614			−0.517928
$119$		0			0
$120$	1.10436	−	1.91280i	0.100813	−	0.174614i
$121$	−4.37386			−0.397624
$122$	−5.83485	+	3.36875i	−0.528262	+	0.304992i
$123$	18.9564	+	10.9445i	1.70924	+	0.986833i
$124$			15.5130i			1.39311i
$125$			4.47315i			0.400091i
$126$		0			0
$127$	−3.47822	+	6.02445i	−0.308642	+	0.534584i	−0.978066	−	0.208297i	$-0.933208\pi$
$127$	−3.47822	+	6.02445i	−0.308642	+	0.534584i	0.669423	+	0.742881i	$0.266541\pi$
$128$	9.56080	−	5.51993i	0.845063	−	0.487897i
$129$	−13.0826	−	22.6597i	−1.15186	−	1.99507i
$130$	−0.730493	+	0.180750i	−0.0640684	+	0.0158528i
$131$	8.68693	−	15.0462i	0.758981	−	1.31459i	−0.184390	−	0.982853i	$-0.559031\pi$
$131$	8.68693	−	15.0462i	0.758981	−	1.31459i	0.943371	−	0.331740i	$-0.107636\pi$
$132$	−16.9782	−	9.80238i	−1.47776	−	0.853188i
$133$		0			0
$134$	1.02178	+	1.76978i	0.0882684	+	0.152885i
$135$	−1.97822	−	1.14213i	−0.170258	−	0.0982985i
$136$	−4.50000	−	2.59808i	−0.385872	−	0.222783i
$137$	−10.3521	−	5.97678i	−0.884438	−	0.510631i	−0.0123190	−	0.999924i	$-0.503921\pi$
$137$	−10.3521	−	5.97678i	−0.884438	−	0.510631i	−0.872119	+	0.489294i	$0.837255\pi$
$138$	1.74773	+	1.00905i	0.148776	+	0.0858961i
$139$	−1.89564	−	3.28335i	−0.160786	−	0.278490i	0.774365	−	0.632740i	$-0.218070\pi$
$139$	−1.89564	−	3.28335i	−0.160786	−	0.278490i	−0.935151	+	0.354249i	$0.884736\pi$
$140$		0			0
$141$	23.1434	+	13.3618i	1.94902	+	1.12527i
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	3.39564	+	13.7233i	0.283958	+	1.14760i
$144$	−6.68693	−	11.5821i	−0.557244	−	0.965175i
$145$	−2.68693	+	1.55130i	−0.223138	+	0.128829i
$146$	−0.791288	+	1.37055i	−0.0654874	+	0.113428i
$147$		0			0
$148$		−	12.4104i		−	1.02013i
$149$		−	0.456850i		−	0.0374266i	−0.999825	−	0.0187133i	$-0.994043\pi$
$149$		−	0.456850i		−	0.0374266i	0.999825	−	0.0187133i	$-0.00595698\pi$
$150$	−5.29129	−	3.05493i	−0.432032	−	0.249434i
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	−0.862159	−	0.506637i	$-0.830888\pi$
$151$	−10.5000	+	6.06218i	−0.854478	+	0.493333i	0.00768132	+	0.999970i	$0.497555\pi$
$152$	−2.37386			−0.192546
$153$	−7.18693	+	12.4481i	−0.581029	+	1.00637i
$154$		0			0
$155$	−3.95644			−0.317789
$156$	−5.00000	+	17.3205i	−0.400320	+	1.38675i
$157$	0.478220	+	0.828301i	0.0381661	+	0.0661056i	0.884477	−	0.466583i	$-0.154515\pi$
$157$	0.478220	+	0.828301i	0.0381661	+	0.0661056i	−0.846311	+	0.532689i	$0.821182\pi$
$158$		−	2.74110i		−	0.218070i
$159$	−8.60436	−	14.9032i	−0.682370	−	1.18190i
$160$	1.08258	+	1.87508i	0.0855851	+	0.148238i
$161$		0			0
$162$	−0.165151	+	0.0953502i	−0.0129755	+	0.00749142i
$163$			6.92820i			0.542659i	0.962487	+	0.271329i	$0.0874633\pi$
$163$			6.92820i			0.542659i	−0.962487	+	0.271329i	$0.912537\pi$
$164$	−12.1652	+	7.02355i	−0.949939	+	0.548447i
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	−1.60436	−	2.77883i	−0.124522	−	0.215679i
$167$	12.7087	+	7.33738i	0.983430	+	0.567783i	0.903304	−	0.429001i	$-0.141134\pi$
$167$	12.7087	+	7.33738i	0.983430	+	0.567783i	0.0801258	+	0.996785i	$0.474468\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	0.313068	−	0.542250i	0.0240112	−	0.0415887i
$171$			6.56670i			0.502168i
$172$	16.7913			1.28032
$173$	19.7477			1.50139			0.750696	−	0.660648i	$-0.229718\pi$
$173$	19.7477			1.50139			0.750696	+	0.660648i	$0.229718\pi$
$174$		−	8.66025i		−	0.656532i
$175$		0			0
$176$	9.47822	−	5.47225i	0.714448	−	0.412487i
$177$	−29.7695	−	17.1874i	−2.23761	−	1.29189i
$178$	3.68693	−	6.38595i	0.276347	−	0.478647i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	3.39564	−	1.96048i	0.253096	−	0.146125i
$181$	−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
$183$	−41.1652			−3.04302
$184$	−2.37386	+	1.37055i	−0.175004	+	0.101038i
$185$	3.16515			0.232707
$186$	5.52178	−	9.56400i	0.404877	−	0.701267i
$187$	−10.1869	−	5.88143i	−0.744942	−	0.430093i
$188$	−14.8521	+	8.57485i	−1.08320	+	0.625386i
$189$		0			0
$190$		−	0.286051i		−	0.0207523i
$191$	−14.3739			−1.04006			−0.520028	−	0.854149i	$-0.674079\pi$
$191$	−14.3739			−1.04006			−0.520028	+	0.854149i	$0.674079\pi$
$192$	9.53901			0.688419
$193$		−	19.3386i		−	1.39202i	−0.718030	−	0.696012i	$-0.754956\pi$
$193$		−	19.3386i		−	1.39202i	0.718030	−	0.696012i	$-0.245044\pi$
$194$	−1.66515	+	2.88413i	−0.119551	+	0.207068i
$195$	−4.41742	−	1.27520i	−0.316338	−	0.0913190i
$196$		0			0
$197$	1.97822	+	1.14213i	0.140942	+	0.0813731i	0.568813	−	0.822467i	$-0.307403\pi$
$197$	1.97822	+	1.14213i	0.140942	+	0.0813731i	−0.427871	+	0.903840i	$0.640736\pi$
$198$	4.29129	+	7.43273i	0.304969	+	0.528221i
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$	7.18693	−	4.14938i	0.508193	−	0.293405i
$201$			12.4859i			0.880684i
$202$	2.06080	−	1.18980i	0.144997	−	0.0837141i
$203$		0			0
$204$	−7.50000	−	12.9904i	−0.525105	−	0.909509i
$205$	−1.79129	−	3.10260i	−0.125109	−	0.216695i
$206$			2.09355i			0.145865i
$207$	3.79129	+	6.56670i	0.263513	+	0.456417i
$208$	−6.97822	−	7.25198i	−0.483852	−	0.502834i
$209$	−5.37386			−0.371718
$210$		0			0
$211$	−5.29129	+	9.16478i	−0.364267	+	0.630929i	−0.988658	−	0.150183i	$-0.952014\pi$
$211$	−5.29129	+	9.16478i	−0.364267	+	0.630929i	0.624391	+	0.781112i	$0.285347\pi$
$212$	11.0436			0.758475
$213$	10.5826	−	6.10985i	0.725106	−	0.418640i
$214$	2.06080	+	1.18980i	0.140873	+	0.0813331i
$215$			4.28245i			0.292061i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−1.81307	+	3.14033i	−0.122796	+	0.212690i
$219$	−8.37386	+	4.83465i	−0.565853	+	0.326696i
$220$	1.60436	+	2.77883i	0.108166	+	0.187348i
$221$	−3.00000	+	10.3923i	−0.201802	+	0.699062i
$222$	−4.41742	+	7.65120i	−0.296478	+	0.513515i
$223$	16.4347	+	9.48855i	1.10055	+	0.635401i	0.936364	−	0.351029i	$-0.114168\pi$
$223$	16.4347	+	9.48855i	1.10055	+	0.635401i	0.164182	+	0.986430i	$0.447502\pi$
$224$		0			0
$225$	−11.4782	−	19.8809i	−0.765215	−	1.32539i
$226$	−4.18693	−	2.41733i	−0.278511	−	0.160798i
$227$	7.66515	+	4.42548i	0.508754	+	0.293729i	0.732321	−	0.680959i	$-0.238437\pi$
$227$	7.66515	+	4.42548i	0.508754	+	0.293729i	−0.223567	+	0.974688i	$0.571770\pi$
$228$	−5.93466	−	3.42638i	−0.393032	−	0.226917i
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	0.684969	−	0.728572i	$-0.259816\pi$
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	−0.288478	+	0.957487i	$0.593149\pi$
$230$	−0.165151	−	0.286051i	−0.0108898	−	0.0188616i
$231$		0			0
$232$	10.1869	+	5.88143i	0.668805	+	0.386135i
$233$	−7.97822	+	13.8187i	−0.522671	+	0.905292i	0.476981	+	0.878913i	$0.341731\pi$
$233$	−7.97822	+	13.8187i	−0.522671	+	0.905292i	−0.999652	+	0.0263786i	$0.991602\pi$
$234$	5.68693	−	5.47225i	0.371766	−	0.357732i
$235$	−2.18693	−	3.78788i	−0.142660	−	0.247094i
$236$	19.1044	−	11.0299i	1.24359	−	0.717986i
$237$	8.37386	−	14.5040i	0.543941	−	0.942133i
$238$		0			0
$239$			13.2288i			0.855697i	0.903850	+	0.427849i	$0.140728\pi$
$239$			13.2288i			0.855697i	−0.903850	+	0.427849i	$0.859272\pi$
$240$			3.55945i			0.229762i
$241$	−17.0608	−	9.85005i	−1.09898	−	0.634498i	−0.163029	−	0.986621i	$-0.552126\pi$
$241$	−17.0608	−	9.85005i	−1.09898	−	0.634498i	−0.935954	+	0.352123i	$0.885460\pi$
$242$	−1.73049	+	0.999100i	−0.111240	+	0.0642246i
$243$	−16.1652			−1.03699
$244$	13.2087	−	22.8782i	0.845601	−	1.46462i
$245$		0			0
$246$	10.0000			0.637577
$247$	1.18693	+	4.79693i	0.0755227	+	0.305221i
$248$	7.50000	+	12.9904i	0.476250	+	0.824890i
$249$		−	19.6048i		−	1.24240i
$250$	1.02178	+	1.76978i	0.0646231	+	0.111930i
$251$	−1.41742	−	2.45505i	−0.0894670	−	0.154961i	0.817819	−	0.575476i	$-0.195183\pi$
$251$	−1.41742	−	2.45505i	−0.0894670	−	0.154961i	−0.907286	+	0.420514i	$0.861850\pi$
$252$		0			0
$253$	−5.37386	+	3.10260i	−0.337852	+	0.195059i
$254$			3.17805i			0.199409i
$255$	3.31307	−	1.91280i	0.207472	−	0.119784i
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	2.52178	+	4.36785i	0.157304	+	0.272459i	0.933896	−	0.357546i	$-0.116386\pi$
$257$	2.52178	+	4.36785i	0.157304	+	0.272459i	−0.776591	+	0.630005i	$0.783053\pi$
$258$	−10.3521	−	5.97678i	−0.644493	−	0.372098i
$259$		0			0
$260$	2.12614	−	2.04588i	0.131857	−	0.126880i
$261$	16.2695	−	28.1796i	1.00706	−	1.74427i
$262$		−	7.93725i		−	0.490365i
$263$	9.33030			0.575331			0.287666	−	0.957731i	$-0.407121\pi$
$263$	9.33030			0.575331			0.287666	+	0.957731i	$0.407121\pi$
$264$	−18.9564			−1.16669
$265$			2.81655i			0.173019i
$266$		0			0
$267$	39.0172	−	22.5266i	2.38782	−	1.37861i
$268$	−6.93920	−	4.00635i	−0.423879	−	0.244727i
$269$	−7.89564	+	13.6757i	−0.481406	+	0.833819i	−0.999772	−	0.0213391i	$-0.993207\pi$
$269$	−7.89564	+	13.6757i	−0.481406	+	0.833819i	0.518366	+	0.855159i	$0.326540\pi$
$270$	−1.04356			−0.0635091
$271$	−11.1261	+	6.42368i	−0.675865	+	0.390211i	−0.798295	−	0.602266i	$-0.794264\pi$
$271$	−11.1261	+	6.42368i	−0.675865	+	0.390211i	0.122430	+	0.992477i	$0.460931\pi$
$272$	8.37386			0.507740
$273$		0			0
$274$	−5.46099			−0.329910
$275$	16.2695	−	9.39320i	0.981088	−	0.566432i
$276$	−7.91288			−0.476299
$277$	−5.87386	+	10.1738i	−0.352926	+	0.611286i	−0.986761	−	0.162182i	$-0.948147\pi$
$277$	−5.87386	+	10.1738i	−0.352926	+	0.611286i	0.633835	+	0.773469i	$0.281480\pi$
$278$	−1.50000	−	0.866025i	−0.0899640	−	0.0519408i
$279$	35.9347	−	20.7469i	2.15135	−	1.24208i
$280$		0			0
$281$			30.6446i			1.82810i	0.405597	+	0.914052i	$0.367064\pi$
$281$			30.6446i			1.82810i	−0.405597	+	0.914052i	$0.632936\pi$
$282$	12.2087			0.727018
$283$	−2.74773			−0.163335			−0.0816677	−	0.996660i	$-0.526025\pi$
$283$	−2.74773			−0.163335			−0.0816677	+	0.996660i	$0.526025\pi$
$284$			7.84190i			0.465331i
$285$	0.873864	−	1.51358i	0.0517632	−	0.0896565i
$286$	4.47822	+	4.65390i	0.264803	+	0.275191i
$287$		0			0
$288$	−19.6652	−	11.3537i	−1.15878	−	0.669022i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−0.708712	+	1.22753i	−0.0416170	+	0.0720828i
$291$	−17.6216	+	10.1738i	−1.03300	+	0.596400i
$292$		−	6.20520i		−	0.363132i
$293$	−2.20871	+	1.27520i	−0.129034	+	0.0744980i	−0.563128	−	0.826370i	$-0.690402\pi$
$293$	−2.20871	+	1.27520i	−0.129034	+	0.0744980i	0.434093	+	0.900868i	$0.357069\pi$
$294$		0			0
$295$	2.81307	+	4.87238i	0.163783	+	0.283681i
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$			19.6048i			1.13758i
$298$	−0.104356	−	0.180750i	−0.00604519	−	0.0104706i
$299$	3.95644	+	4.11165i	0.228807	+	0.237783i
$300$	23.9564			1.38313
$301$		0			0
$302$	−2.76951	+	4.79693i	−0.159367	+	0.276032i
$303$	14.5390			0.835245
$304$	3.31307	−	1.91280i	0.190017	−	0.109707i
$305$	5.83485	+	3.36875i	0.334102	+	0.192894i
$306$			6.56670i			0.375393i
$307$		−	15.5130i		−	0.885374i	−0.896676	−	0.442687i	$-0.854025\pi$
$307$		−	15.5130i		−	0.885374i	0.896676	−	0.442687i	$-0.145975\pi$
$308$		0			0
$309$	−6.39564	+	11.0776i	−0.363835	+	0.630182i
$310$	−1.56534	+	0.903750i	−0.0889054	+	0.0513296i
$311$	13.2695	+	22.9835i	0.752445	+	1.30327i	0.946635	+	0.322309i	$0.104459\pi$
$311$	13.2695	+	22.9835i	0.752445	+	1.30327i	−0.194190	+	0.980964i	$0.562208\pi$
$312$	4.18693	+	16.9213i	0.237038	+	0.957979i
$313$	−3.37386	+	5.84370i	−0.190702	+	0.330306i	−0.945483	−	0.325671i	$-0.894410\pi$
$313$	−3.37386	+	5.84370i	−0.190702	+	0.330306i	0.754781	+	0.655977i	$0.227743\pi$
$314$	0.378409	+	0.218475i	0.0213549	+	0.0123292i
$315$		0			0
$316$	5.37386	+	9.30780i	0.302303	+	0.523605i
$317$	16.0390	+	9.26013i	0.900841	+	0.520101i	0.877473	−	0.479626i	$-0.159228\pi$
$317$	16.0390	+	9.26013i	0.900841	+	0.520101i	0.0233679	+	0.999727i	$0.492561\pi$
$318$	−6.80852	−	3.93090i	−0.381803	−	0.220434i
$319$	23.0608	+	13.3142i	1.29116	+	0.745450i
$320$	−1.35208	−	0.780626i	−0.0755837	−	0.0436383i
$321$	7.26951	+	12.5912i	0.405744	+	0.702770i
$322$		0			0
$323$	−3.56080	−	2.05583i	−0.198128	−	0.114389i
$324$	0.373864	−	0.647551i	0.0207702	−	0.0359750i
$325$	−11.9782	−	12.4481i	−0.664432	−	0.690498i
$326$	1.58258	+	2.74110i	0.0876508	+	0.151816i
$327$	−19.1869	+	11.0776i	−1.06104	+	0.612592i
$328$	−6.79129	+	11.7629i	−0.374986	+	0.649495i
$329$		0			0
$330$		−	2.28425i		−	0.125744i
$331$			24.8963i			1.36842i	0.729284	+	0.684211i	$0.239853\pi$
$331$			24.8963i			1.36842i	−0.729284	+	0.684211i	$0.760147\pi$
$332$	10.8956	+	6.29060i	0.597976	+	0.345242i
$333$	−28.7477	+	16.5975i	−1.57537	+	0.909538i
$334$	6.70417			0.366836
$335$	1.02178	−	1.76978i	0.0558258	−	0.0966932i
$336$		0			0
$337$	9.95644			0.542362			0.271181	−	0.962528i	$-0.412586\pi$
$337$	9.95644			0.542362			0.271181	+	0.962528i	$0.412586\pi$
$338$	3.16515	−	5.02535i	0.172162	−	0.273343i
$339$	−14.7695	−	25.5815i	−0.802170	−	1.38940i
$340$			2.45505i			0.133144i
$341$	16.9782	+	29.4071i	0.919422	+	1.59249i
$342$	1.50000	+	2.59808i	0.0811107	+	0.140488i
$343$		0			0
$344$	14.0608	−	8.11800i	0.758107	−	0.437693i
$345$		−	2.01810i		−	0.108651i
$346$	7.81307	−	4.51088i	0.420033	−	0.242506i
$347$	6.79129	−	11.7629i	0.364575	−	0.631463i	−0.624132	−	0.781319i	$-0.714547\pi$
$347$	6.79129	−	11.7629i	0.364575	−	0.631463i	0.988708	+	0.149855i	$0.0478808\pi$
$348$	16.9782	+	29.4071i	0.910128	+	1.57639i
$349$	18.2477	+	10.5353i	0.976778	+	0.563943i	0.901296	−	0.433204i	$-0.142617\pi$
$349$	18.2477	+	10.5353i	0.976778	+	0.563943i	0.0754825	+	0.997147i	$0.475950\pi$
$350$		0			0
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$	9.29129	−	16.0930i	0.495227	−	0.857759i
$353$			18.1588i			0.966493i	0.875484	+	0.483247i	$0.160543\pi$
$353$			18.1588i			0.966493i	−0.875484	+	0.483247i	$0.839457\pi$
$354$	−15.7042			−0.834667
$355$	−2.00000			−0.106149
$356$			28.9126i			1.53236i
$357$		0			0
$358$	−3.56080	+	2.05583i	−0.188194	+	0.108654i
$359$	0.478220	+	0.276100i	0.0252395	+	0.0145720i	0.512567	−	0.858647i	$-0.328695\pi$
$359$	0.478220	+	0.276100i	0.0252395	+	0.0145720i	−0.487327	+	0.873219i	$0.662028\pi$
$360$	1.89564	−	3.28335i	0.0999092	−	0.173048i
$361$	17.1216			0.901136
$362$	−3.62614	+	2.09355i	−0.190586	+	0.110035i
$363$	−12.2087			−0.640791
$364$		0			0
$365$	1.58258			0.0828358
$366$	−16.2867	+	9.40315i	−0.851322	+	0.491511i
$367$	18.0000			0.939592			0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000			0.939592			0.469796	+	0.882775i	$0.344327\pi$
$368$	2.20871	−	3.82560i	0.115137	−	0.199423i
$369$	32.5390	+	18.7864i	1.69391	+	0.977981i
$370$	1.25227	−	0.723000i	0.0651026	−	0.0375870i
$371$		0			0
$372$			43.3013i			2.24507i
$373$	32.2087			1.66770			0.833852	−	0.551988i	$-0.186131\pi$
$373$	32.2087			1.66770			0.833852	+	0.551988i	$0.186131\pi$
$374$	−5.37386			−0.277876
$375$			12.4859i			0.644767i
$376$	−8.29129	+	14.3609i	−0.427591	+	0.740609i
$377$	6.79129	−	23.5257i	0.349769	−	1.21164i
$378$		0			0
$379$	−24.5608	−	14.1802i	−1.26160	−	0.728387i	−0.288219	−	0.957565i	$-0.593063\pi$
$379$	−24.5608	−	14.1802i	−1.26160	−	0.728387i	−0.973385	+	0.229178i	$0.926396\pi$
$380$	0.560795	+	0.971326i	0.0287682	+	0.0498280i
$381$	−9.70871	+	16.8160i	−0.497392	+	0.861509i
$382$	−5.68693	+	3.28335i	−0.290969	+	0.167991i
$383$		−	1.27520i		−	0.0651597i	−0.999469	−	0.0325799i	$-0.989628\pi$
$383$		−	1.27520i		−	0.0651597i	0.999469	−	0.0325799i	$-0.0103723\pi$
$384$	26.6869	−	15.4077i	1.36186	−	0.786271i
$385$		0			0
$386$	−4.41742	−	7.65120i	−0.224841	−	0.389436i
$387$	−22.4564	−	38.8957i	−1.14152	−	1.97718i
$388$		−	13.0580i		−	0.662917i
$389$	0.165151	+	0.286051i	0.00837351	+	0.0145033i	0.870182	−	0.492731i	$-0.164001\pi$
$389$	0.165151	+	0.286051i	0.00837351	+	0.0145033i	−0.861808	+	0.507234i	$0.830668\pi$
$390$	−2.03901	+	0.504525i	−0.103250	+	0.0255476i
$391$	−4.74773			−0.240103
$392$		0			0
$393$	24.2477	−	41.9983i	1.22314	−	2.11853i
$394$	1.04356			0.0525738
$395$	−2.37386	+	1.37055i	−0.119442	+	0.0689599i
$396$	−29.1434	−	16.8259i	−1.46451	−	0.845535i
$397$		−	32.4720i		−	1.62972i	−0.579655	−	0.814862i	$-0.696813\pi$
$397$		−	32.4720i		−	1.62972i	0.579655	−	0.814862i	$-0.303187\pi$
$398$		−	5.02535i		−	0.251898i
$399$		0			0
$400$	−6.68693	+	11.5821i	−0.334347	+	0.579105i
$401$	−27.0998	+	15.6461i	−1.35330	+	0.781328i	−0.988710	−	0.149840i	$-0.952124\pi$
$401$	−27.0998	+	15.6461i	−1.35330	+	0.781328i	−0.364590	+	0.931168i	$0.618791\pi$
$402$	2.85208	+	4.93995i	0.142249	+	0.246382i
$403$	22.5000	−	21.6506i	1.12080	−	1.07849i
$404$	−4.66515	+	8.08028i	−0.232100	+	0.402009i
$405$	0.165151	+	0.0953502i	0.00820644	+	0.00473799i
$406$		0			0
$407$	−13.5826	−	23.5257i	−0.673263	−	1.16613i
$408$	−12.5608	−	7.25198i	−0.621852	−	0.359026i
$409$	7.18693	+	4.14938i	0.355371	+	0.205173i	0.667048	−	0.745015i	$-0.267557\pi$
$409$	7.18693	+	4.14938i	0.355371	+	0.205173i	−0.311677	+	0.950188i	$0.600891\pi$
$410$	−1.41742	−	0.818350i	−0.0700016	−	0.0404154i
$411$	−28.8956	−	16.6829i	−1.42532	−	0.822907i
$412$	−4.10436	−	7.10895i	−0.202207	−	0.350233i
$413$		0			0
$414$	3.00000	+	1.73205i	0.147442	+	0.0851257i
$415$	−1.60436	+	2.77883i	−0.0787547	+	0.136407i
$416$	−16.4174	−	4.73930i	−0.804930	−	0.232363i
$417$	−5.29129	−	9.16478i	−0.259115	−	0.448801i
$418$	−2.12614	+	1.22753i	−0.103993	+	0.0600402i
$419$	−0.873864	+	1.51358i	−0.0426910	+	0.0739430i	−0.886581	−	0.462573i	$-0.846926\pi$
$419$	−0.873864	+	1.51358i	−0.0426910	+	0.0739430i	0.843890	+	0.536516i	$0.180260\pi$
$420$		0			0
$421$			4.18710i			0.204067i	0.994781	+	0.102033i	$0.0325349\pi$
$421$			4.18710i			0.204067i	−0.994781	+	0.102033i	$0.967465\pi$
$422$			4.83465i			0.235347i
$423$	39.7259	+	22.9358i	1.93154	+	1.11518i
$424$	9.24773	−	5.33918i	0.449109	−	0.259293i
$425$	14.3739			0.697235
$426$	2.79129	−	4.83465i	0.135238	−	0.234240i
$427$		0			0
$428$	−9.33030			−0.450997
$429$	9.47822	+	38.3058i	0.457613	+	1.84942i
$430$	0.978220	+	1.69433i	0.0471739	+	0.0817077i
$431$		−	34.6609i		−	1.66956i	−0.550585	−	0.834779i	$-0.685595\pi$
$431$		−	34.6609i		−	1.66956i	0.550585	−	0.834779i	$-0.314405\pi$
$432$	−6.97822	−	12.0866i	−0.335740	−	0.581518i
$433$	−16.2477	−	28.1419i	−0.780816	−	1.35241i	−0.931467	−	0.363826i	$-0.881470\pi$
$433$	−16.2477	−	28.1419i	−0.780816	−	1.35241i	0.150651	−	0.988587i	$-0.451863\pi$
$434$		0			0
$435$	−7.50000	+	4.33013i	−0.359597	+	0.207614i
$436$		−	14.2179i		−	0.680914i
$437$	−1.87841	+	1.08450i	−0.0898565	+	0.0518787i
$438$	−2.20871	+	3.82560i	−0.105536	+	0.182794i
$439$	−10.2695	−	17.7873i	−0.490137	−	0.848942i	0.509799	−	0.860294i	$-0.329720\pi$
$439$	−10.2695	−	17.7873i	−0.490137	−	0.848942i	−0.999936	+	0.0113518i	$0.996387\pi$
$440$	2.68693	+	1.55130i	0.128094	+	0.0739554i
$441$		0			0
$442$	1.18693	+	4.79693i	0.0564566	+	0.228167i
$443$	7.58258	−	13.1334i	0.360259	−	0.623987i	−0.627744	−	0.778420i	$-0.716022\pi$
$443$	7.58258	−	13.1334i	0.360259	−	0.623987i	0.988003	+	0.154433i	$0.0493550\pi$
$444$		−	34.6410i		−	1.64399i
$445$	−7.37386			−0.349555
$446$	8.66970			0.410522
$447$		−	1.27520i		−	0.0603149i
$448$		0			0
$449$	−21.7913	+	12.5812i	−1.02839	+	0.593744i	−0.916524	−	0.399979i	$-0.869017\pi$
$449$	−21.7913	+	12.5812i	−1.02839	+	0.593744i	−0.111870	+	0.993723i	$0.535684\pi$
$450$	−9.08258	−	5.24383i	−0.428157	−	0.247196i
$451$	−15.3739	+	26.6283i	−0.723927	+	1.25388i
$452$	18.9564			0.891636
$453$	−29.3085	+	16.9213i	−1.37703	+	0.795031i
$454$	4.04356			0.189774
$455$		0			0
$456$	−6.62614			−0.310297
$457$	−19.7477	+	11.4014i	−0.923760	+	0.533333i	−0.884833	−	0.465909i	$-0.845727\pi$
$457$	−19.7477	+	11.4014i	−0.923760	+	0.533333i	−0.0389271	+	0.999242i	$0.512394\pi$
$458$	3.16515			0.147898
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$	1.12159	+	0.647551i	0.0522944	+	0.0301922i
$461$	−4.02178	+	2.32198i	−0.187313	+	0.108145i	−0.590724	−	0.806874i	$-0.701158\pi$
$461$	−4.02178	+	2.32198i	−0.187313	+	0.108145i	0.403411	+	0.915019i	$0.367824\pi$
$462$		0			0
$463$			7.93725i			0.368875i	0.982844	+	0.184438i	$0.0590464\pi$
$463$			7.93725i			0.368875i	−0.982844	+	0.184438i	$0.940954\pi$
$464$	−18.9564			−0.880031
$465$	−11.0436			−0.512133
$466$			7.28970i			0.337689i
$467$	15.0826	−	26.1238i	0.697938	−	1.20886i	−0.271242	−	0.962511i	$-0.587434\pi$
$467$	15.0826	−	26.1238i	0.697938	−	1.20886i	0.969180	−	0.246353i	$-0.0792324\pi$
$468$	−8.58258	+	29.7309i	−0.396730	+	1.37431i
$469$		0			0
$470$	−1.73049	−	0.999100i	−0.0798217	−	0.0460851i
$471$	1.33485	+	2.31203i	0.0615066	+	0.106533i
$472$	10.6652	−	18.4726i	0.490903	−	0.850270i
$473$	31.8303	−	18.3772i	1.46356	−	0.844986i
$474$		−	7.65120i		−	0.351431i
$475$	5.68693	−	3.28335i	0.260934	−	0.150651i
$476$		0			0
$477$	−14.7695	−	25.5815i	−0.676249	−	1.17130i
$478$	3.02178	+	5.23388i	0.138213	+	0.239392i
$479$		−	18.8818i		−	0.862730i	−0.902178	−	0.431365i	$-0.858032\pi$
$479$		−	18.8818i		−	0.862730i	0.902178	−	0.431365i	$-0.141968\pi$
$480$	3.02178	+	5.23388i	0.137925	+	0.238893i
$481$	−18.0000	+	17.3205i	−0.820729	+	0.789747i
$482$	−9.00000			−0.409939
$483$		0			0
$484$	3.91742	−	6.78518i	0.178065	−	0.308417i
$485$	3.33030			0.151221
$486$	−6.39564	+	3.69253i	−0.290112	+	0.167496i
$487$	−25.4347	−	14.6847i	−1.15255	−	0.665428i	−0.203046	−	0.979169i	$-0.565084\pi$
$487$	−25.4347	−	14.6847i	−1.15255	−	0.665428i	−0.949508	+	0.313742i	$0.898417\pi$
$488$		−	25.5438i		−	1.15631i
$489$			19.3386i			0.874522i
$490$		0			0
$491$	2.06080	−	3.56940i	0.0930024	−	0.161085i	−0.815771	−	0.578375i	$-0.803687\pi$
$491$	2.06080	−	3.56940i	0.0930024	−	0.161085i	0.908773	+	0.417291i	$0.137020\pi$
$492$	−33.9564	+	19.6048i	−1.53087	+	0.883851i
$493$	10.1869	+	17.6443i	0.458796	+	0.794659i
$494$	1.56534	+	1.62675i	0.0704280	+	0.0731910i
$495$	4.29129	−	7.43273i	0.192879	−	0.334076i
$496$	−20.9347	−	12.0866i	−0.939994	−	0.542706i
$497$		0			0
$498$	−4.47822	−	7.75650i	−0.200674	−	0.347577i
$499$	−15.9392	−	9.20250i	−0.713537	−	0.411961i	0.0988324	−	0.995104i	$-0.468489\pi$
$499$	−15.9392	−	9.20250i	−0.713537	−	0.411961i	−0.812369	+	0.583143i	$0.801823\pi$
$500$	−6.93920	−	4.00635i	−0.310331	−	0.179169i
$501$	35.4737	+	20.4807i	1.58485	+	0.915012i
$502$	−1.12159	−	0.647551i	−0.0500590	−	0.0289016i
$503$	9.56080	+	16.5598i	0.426295	+	0.738364i	0.996540	−	0.0831100i	$-0.0264853\pi$
$503$	9.56080	+	16.5598i	0.426295	+	0.738364i	−0.570246	+	0.821474i	$0.693152\pi$
$504$		0			0
$505$	−2.06080	−	1.18980i	−0.0917042	−	0.0529454i
$506$	−1.41742	+	2.45505i	−0.0630122	+	0.109140i
$507$	32.0998	−	16.9213i	1.42560	−	0.751501i
$508$	−6.23049	−	10.7915i	−0.276433	−	0.478797i
$509$	−13.0390	+	7.52808i	−0.577944	+	0.333676i	−0.760316	−	0.649553i	$-0.774956\pi$
$509$	−13.0390	+	7.52808i	−0.577944	+	0.333676i	0.182372	+	0.983230i	$0.441623\pi$
$510$	0.873864	−	1.51358i	0.0386953	−	0.0670223i
$511$		0			0
$512$			22.8981i			1.01196i
$513$			6.85275i			0.302556i
$514$	1.99545	+	1.15208i	0.0880157	+	0.0508159i
$515$	1.81307	−	1.04678i	0.0798933	−	0.0461264i
$516$	46.8693			2.06331
$517$	−18.7695	+	32.5097i	−0.825482	+	1.42978i
$518$		0			0
$519$	55.1216			2.41957
$520$	0.791288	−	2.74110i	0.0347003	−	0.120205i
$521$	8.20871	+	14.2179i	0.359630	+	0.622898i	0.987899	−	0.155099i	$-0.0495695\pi$
$521$	8.20871	+	14.2179i	0.359630	+	0.622898i	−0.628269	+	0.777996i	$0.716236\pi$
$522$		−	14.8655i		−	0.650643i
$523$	12.1652	+	21.0707i	0.531945	+	0.921356i	0.999305	+	0.0372883i	$0.0118720\pi$
$523$	12.1652	+	21.0707i	0.531945	+	0.921356i	−0.467360	+	0.884067i	$0.654795\pi$
$524$	15.5608	+	26.9521i	0.679776	+	1.17741i
$525$		0			0
$526$	3.69148	−	2.13128i	0.160956	−	0.0929280i
$527$			25.9808i			1.13174i
$528$	26.4564	−	15.2746i	1.15137	−	0.664743i
$529$	10.2477	−	17.7496i	0.445553	−	0.771721i
$530$	0.643371	+	1.11435i	0.0279463	+	0.0484043i
$531$	−51.0998	−	29.5025i	−2.21754	−	1.28030i
$532$		0			0
$533$	27.1652	+	7.84190i	1.17665	+	0.339671i
$534$	10.2913	−	17.8250i	0.445348	−	0.771365i
$535$		−	2.37960i		−	0.102879i
$536$	−7.74773			−0.334651
$537$	−25.1216			−1.08408
$538$			7.21425i			0.311029i
$539$		0			0
$540$	3.54356	−	2.04588i	0.152491	−	0.0880405i
$541$	−5.43920	−	3.14033i	−0.233850	−	0.135013i	0.378497	−	0.925602i	$-0.376441\pi$
$541$	−5.43920	−	3.14033i	−0.233850	−	0.135013i	−0.612347	+	0.790589i	$0.709774\pi$
$542$	−2.93466	+	5.08298i	−0.126054	+	0.218333i
$543$	−25.5826			−1.09785
$544$	12.3131	−	7.10895i	0.527918	−	0.304794i
$545$	3.62614			0.155327
$546$		0			0
$547$	−11.7477			−0.502297			−0.251148	−	0.967949i	$-0.580808\pi$
$547$	−11.7477			−0.502297			−0.251148	+	0.967949i	$0.580808\pi$
$548$	18.5436	−	10.7061i	0.792142	−	0.457343i
$549$	−70.6606			−3.01572
$550$	4.29129	−	7.43273i	0.182981	−	0.316933i
$551$	8.06080	+	4.65390i	0.343401	+	0.198263i
$552$	−6.62614	+	3.82560i	−0.282027	+	0.162828i
$553$		0			0
$554$			5.36695i			0.228020i
$555$	8.83485			0.375018
$556$	6.79129			0.288015
$557$			33.0242i			1.39928i	0.714495	+	0.699640i	$0.246656\pi$
$557$			33.0242i			1.39928i	−0.714495	+	0.699640i	$0.753344\pi$
$558$	9.47822	−	16.4168i	0.401245	−	0.694977i
$559$	−23.4347	−	24.3540i	−0.991180	−	1.03006i
$560$		0			0
$561$	−28.4347	−	16.4168i	−1.20051	−	0.693116i
$562$	7.00000	+	12.1244i	0.295277	+	0.511435i
$563$	18.1652	−	31.4630i	0.765570	−	1.32601i	−0.174375	−	0.984679i	$-0.555790\pi$
$563$	18.1652	−	31.4630i	0.765570	−	1.32601i	0.939945	−	0.341327i	$-0.110876\pi$
$564$	−41.4564	+	23.9349i	−1.74563	+	1.00784i
$565$			4.83465i			0.203395i
$566$	−1.08712	+	0.627650i	−0.0456951	+	0.0263821i
$567$		0			0
$568$	3.79129	+	6.56670i	0.159079	+	0.275533i
$569$	−8.37386	−	14.5040i	−0.351051	−	0.608038i	0.635383	−	0.772197i	$-0.280842\pi$
$569$	−8.37386	−	14.5040i	−0.351051	−	0.608038i	−0.986434	+	0.164159i	$0.947509\pi$
$570$		−	0.798450i		−	0.0334434i
$571$	1.02178	+	1.76978i	0.0427602	+	0.0740628i	0.886613	−	0.462511i	$-0.153052\pi$
$571$	1.02178	+	1.76978i	0.0427602	+	0.0740628i	−0.843853	+	0.536574i	$0.819718\pi$
$572$	−24.3303	−	7.02355i	−1.01730	−	0.293670i
$573$	−40.1216			−1.67610
$574$		0			0
$575$	3.79129	−	6.56670i	0.158108	−	0.273850i
$576$	16.3739			0.682244
$577$	−30.8739	+	17.8250i	−1.28530	+	0.742066i	−0.977811	−	0.209487i	$-0.932821\pi$
$577$	−30.8739	+	17.8250i	−1.28530	+	0.742066i	−0.307484	+	0.951553i	$0.599487\pi$
$578$	3.16515	+	1.82740i	0.131653	+	0.0760099i
$579$		−	53.9796i		−	2.24332i
$580$		−	5.55765i		−	0.230769i
$581$		0			0
$582$	−4.64792	+	8.05043i	−0.192662	+	0.333701i
$583$	20.9347	−	12.0866i	0.867025	−	0.500577i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$	−7.58258	−	2.18890i	−0.313501	−	0.0904999i
$586$	−0.582576	+	1.00905i	−0.0240660	+	0.0416835i
$587$	8.22595	+	4.74925i	0.339521	+	0.196023i	0.660060	−	0.751213i	$-0.270531\pi$
$587$	8.22595	+	4.74925i	0.339521	+	0.196023i	−0.320539	+	0.947235i	$0.603864\pi$
$588$		0			0
$589$	5.93466	+	10.2791i	0.244533	+	0.423544i
$590$	2.22595	+	1.28515i	0.0916408	+	0.0529088i
$591$	5.52178	+	3.18800i	0.227136	+	0.131137i
$592$	16.7477	+	9.66930i	0.688327	+	0.397406i
$593$	5.52178	+	3.18800i	0.226752	+	0.130916i	0.609073	−	0.793114i	$-0.291542\pi$
$593$	5.52178	+	3.18800i	0.226752	+	0.130916i	−0.382321	+	0.924030i	$0.624875\pi$
$594$	4.47822	+	7.75650i	0.183744	+	0.318253i
$595$		0			0
$596$	0.708712	+	0.409175i	0.0290300	+	0.0167605i
$597$	15.3521	−	26.5906i	0.628319	−	1.08828i
$598$	2.50455	+	0.723000i	0.102418	+	0.0295657i
$599$	3.31307	+	5.73840i	0.135368	+	0.234465i	0.925738	−	0.378165i	$-0.123445\pi$
$599$	3.31307	+	5.73840i	0.135368	+	0.234465i	−0.790370	+	0.612630i	$0.790112\pi$
$600$	20.0608	−	11.5821i	0.818979	−	0.472837i
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	−0.964178	−	0.265256i	$-0.914543\pi$
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	0.711808	+	0.702374i	$0.247877\pi$
$602$		0			0
$603$			21.4322i			0.872785i
$604$		−	21.7182i		−	0.883701i
$605$	1.73049	+	0.999100i	0.0703545	+	0.0406192i
$606$	5.75227	−	3.32108i	0.233670	−	0.134910i
$607$	19.7477			0.801536			0.400768	−	0.916180i	$-0.368743\pi$
$607$	19.7477			0.801536			0.400768	+	0.916180i	$0.368743\pi$
$608$	3.24773	−	5.62523i	0.131713	−	0.228133i
$609$		0			0
$610$	3.07803			0.124626
$611$	33.1652	+	9.57395i	1.34172	+	0.387321i
$612$	−12.8739	−	22.2982i	−0.520395	−	0.901351i
$613$			18.2541i			0.737277i	0.929573	+	0.368638i	$0.120176\pi$
$613$			18.2541i			0.737277i	−0.929573	+	0.368638i	$0.879824\pi$
$614$	−3.54356	−	6.13763i	−0.143006	−	0.247694i
$615$	−5.00000	−	8.66025i	−0.201619	−	0.349215i
$616$		0			0
$617$	−14.9174	+	8.61258i	−0.600553	+	0.346729i	−0.769259	−	0.638937i	$-0.779374\pi$
$617$	−14.9174	+	8.61258i	−0.600553	+	0.346729i	0.168706	+	0.985666i	$0.446041\pi$
$618$			5.84370i			0.235068i
$619$	−16.7477	+	9.66930i	−0.673148	+	0.388642i	−0.797268	−	0.603625i	$-0.793722\pi$
$619$	−16.7477	+	9.66930i	−0.673148	+	0.388642i	0.124120	+	0.992267i	$0.460389\pi$
$620$	3.54356	−	6.13763i	0.142313	−	0.246493i
$621$	3.95644	+	6.85275i	0.158766	+	0.274992i
$622$	10.5000	+	6.06218i	0.421012	+	0.243071i
$623$		0			0
$624$	−19.4782	−	20.2424i	−0.779753	−	0.810343i
$625$	−10.9564	+	18.9771i	−0.438258	+	0.759084i
$626$			3.08270i			0.123210i
$627$	−15.0000			−0.599042
$628$	−1.71326			−0.0683664
$629$		−	20.7846i		−	0.828737i
$630$		0			0
$631$	23.9347	−	13.8187i	0.952824	−	0.550113i	0.0588668	−	0.998266i	$-0.481251\pi$
$631$	23.9347	−	13.8187i	0.952824	−	0.550113i	0.893957	+	0.448153i	$0.147918\pi$
$632$	9.00000	+	5.19615i	0.358001	+	0.206692i
$633$	−14.7695	+	25.5815i	−0.587035	+	1.01677i
$634$	8.46099			0.336029
$635$	2.75227	−	1.58903i	0.109221	−	0.0630586i
$636$	30.8258			1.22232
$637$		0			0
$638$	12.1652			0.481623
$639$	18.1652	−	10.4877i	0.718602	−	0.414885i
$640$	−5.04356			−0.199364
$641$	−14.6869	+	25.4385i	−0.580099	+	1.00476i	0.415368	+	0.909653i	$0.363653\pi$
$641$	−14.6869	+	25.4385i	−0.580099	+	1.00476i	−0.995467	+	0.0951074i	$0.969681\pi$
$642$	5.75227	+	3.32108i	0.227024	+	0.131072i
$643$	−39.2477	+	22.6597i	−1.54778	+	0.893611i	−0.549468	+	0.835515i	$0.685170\pi$
$643$	−39.2477	+	22.6597i	−1.54778	+	0.893611i	−0.998311	+	0.0580962i	$0.981497\pi$
$644$		0			0
$645$			11.9536i			0.470671i
$646$	−1.87841			−0.0739050
$647$	−35.0780			−1.37906			−0.689530	−	0.724257i	$-0.742183\pi$
$647$	−35.0780			−1.37906			−0.689530	+	0.724257i	$0.742183\pi$
$648$		−	0.723000i		−	0.0284021i
$649$	24.1434	−	41.8175i	0.947710	−	1.64148i
$650$	−7.58258	−	2.18890i	−0.297413	−	0.0858558i
$651$		0			0
$652$	−10.7477	−	6.20520i	−0.420913	−	0.243015i
$653$	−7.89564	−	13.6757i	−0.308980	−	0.535170i	0.669159	−	0.743119i	$-0.266654\pi$
$653$	−7.89564	−	13.6757i	−0.308980	−	0.535170i	−0.978140	+	0.207949i	$0.933321\pi$
$654$	−5.06080	+	8.76555i	−0.197893	+	0.342760i
$655$	−6.87386	+	3.96863i	−0.268584	+	0.155067i
$656$		−	21.8890i		−	0.854622i
$657$	−14.3739	+	8.29875i	−0.560778	+	0.323765i
$658$		0			0
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	4.47822	+	7.75650i	0.174314	+	0.301922i
$661$		−	50.5155i		−	1.96483i	−0.186720	−	0.982413i	$-0.559786\pi$
$661$		−	50.5155i		−	1.96483i	0.186720	−	0.982413i	$-0.440214\pi$
$662$	5.68693	+	9.85005i	0.221029	+	0.382833i
$663$	−8.37386	+	29.0079i	−0.325214	+	1.12657i
$664$	12.1652			0.472099
$665$		0			0
$666$	−7.58258	+	13.1334i	−0.293819	+	0.508909i
$667$	10.7477			0.416154
$668$	−22.7650	+	13.1434i	−0.880803	+	0.508532i
$669$	45.8739	+	26.4853i	1.77359	+	1.02398i
$670$		−	0.933601i		−	0.0360682i
$671$		−	57.8251i		−	2.23231i
$672$		0			0
$673$	−13.2477	+	22.9457i	−0.510662	+	0.884493i	0.489261	+	0.872137i	$0.337266\pi$
$673$	−13.2477	+	22.9457i	−0.510662	+	0.884493i	−0.999924	+	0.0123559i	$0.996067\pi$
$674$	3.93920	−	2.27430i	0.151732	−	0.0876028i
$675$	−11.9782	−	20.7469i	−0.461042	−	0.798548i
$676$	−0.895644	+	23.2695i	−0.0344478	+	0.894981i
$677$	−14.6044	+	25.2955i	−0.561291	+	0.972185i	0.436093	+	0.899902i	$0.356362\pi$
$677$	−14.6044	+	25.2955i	−0.561291	+	0.972185i	−0.997384	+	0.0722830i	$0.976972\pi$
$678$	−11.6869	−	6.74745i	−0.448834	−	0.259134i
$679$		0			0
$680$	1.18693	+	2.05583i	0.0455168	+	0.0788373i
$681$	21.3956	+	12.3528i	0.819883	+	0.473360i
$682$	13.4347	+	7.75650i	0.514440	+	0.297012i
$683$	−26.2913	−	15.1793i	−1.00601	−	0.580819i	−0.0959878	−	0.995383i	$-0.530601\pi$
$683$	−26.2913	−	15.1793i	−1.00601	−	0.580819i	−0.910020	+	0.414563i	$0.863934\pi$
$684$	−10.1869	−	5.88143i	−0.389507	−	0.224882i
$685$	2.73049	+	4.72935i	0.104327	+	0.180699i
$686$		0			0
$687$	16.7477	+	9.66930i	0.638966	+	0.368907i
$688$	−13.0826	+	22.6597i	−0.498769	+	0.863892i
$689$	−15.4129	−	16.0175i	−0.587184	−	0.610219i
$690$	−0.460985	−	0.798450i	−0.0175494	−	0.0303965i
$691$	−8.93466	+	5.15843i	−0.339890	+	0.196236i	−0.660224	−	0.751069i	$-0.729538\pi$
$691$	−8.93466	+	5.15843i	−0.339890	+	0.196236i	0.320333	+	0.947305i	$0.396205\pi$
$692$	−17.6869	+	30.6347i	−0.672356	+	1.16456i
$693$		0			0
$694$		−	6.20520i		−	0.235546i
$695$			1.73205i			0.0657004i
$696$	28.4347	+	16.4168i	1.07781	+	0.622276i
$697$	−20.3739	+	11.7629i	−0.771715	+	0.445550i
$698$	9.62614			0.364355
$699$	−22.2695	+	38.5719i	−0.842310	+	1.45892i
$700$		0			0
$701$	−13.9129			−0.525482			−0.262741	−	0.964866i	$-0.584627\pi$
$701$	−13.9129			−0.525482			−0.262741	+	0.964866i	$0.584627\pi$
$702$	5.93466	−	5.71063i	0.223989	−	0.215534i
$703$	−4.74773	−	8.22330i	−0.179064	−	0.310148i
$704$			13.3996i			0.505015i
$705$	−6.10436	−	10.5731i	−0.229903	−	0.398204i
$706$	4.14792	+	7.18440i	0.156109	+	0.270389i
$707$		0			0
$708$	53.3258	−	30.7876i	2.00410	−	1.15707i
$709$		−	15.2270i		−	0.571860i	−0.958250	−	0.285930i	$-0.907697\pi$
$709$		−	15.2270i		−	0.571860i	0.958250	−	0.285930i	$-0.0923025\pi$
$710$	−0.791288	+	0.456850i	−0.0296965	+	0.0171453i
$711$	14.3739	−	24.8963i	0.539062	−	0.933683i
$712$	13.9782	+	24.2110i	0.523856	+	0.907345i
$713$	11.8693	+	6.85275i	0.444509	+	0.256638i
$714$		0			0
$715$	1.79129	−	6.20520i	0.0669904	−	0.232061i
$716$	8.06080	−	13.9617i	0.301246	−	0.521773i
$717$			36.9253i			1.37900i
$718$	0.252273			0.00941474
$719$	−24.1652			−0.901208			−0.450604	−	0.892724i	$-0.648791\pi$
$719$	−24.1652			−0.901208			−0.450604	+	0.892724i	$0.648791\pi$
$720$			6.10985i			0.227701i
$721$		0			0
$722$	6.77405	−	3.91100i	0.252104	−	0.145552i
$723$	−47.6216	−	27.4943i	−1.77107	−	1.02253i
$724$	8.20871	−	14.2179i	0.305074	−	0.528404i
$725$	−32.5390			−1.20847
$726$	−4.83030	+	2.78878i	−0.179269	+	0.103501i
$727$	0.252273			0.00935628			0.00467814	−	0.999989i	$-0.498511\pi$
$727$	0.252273			0.00935628			0.00467814	+	0.999989i	$0.498511\pi$
$728$		0			0
$729$	−43.8693			−1.62479
$730$	0.626136	−	0.361500i	0.0231744	−	0.0133797i
$731$	28.1216			1.04011
$732$	36.8693	−	63.8595i	1.36273	−	2.36032i
$733$	14.6869	+	8.47950i	0.542474	+	0.313198i	0.746081	−	0.665855i	$-0.231933\pi$
$733$	14.6869	+	8.47950i	0.542474	+	0.313198i	−0.203607	+	0.979053i	$0.565266\pi$
$734$	7.12159	−	4.11165i	0.262863	−	0.151764i
$735$		0			0
$736$		−	7.50030i		−	0.276465i
$737$	−17.5390			−0.646058
$738$	17.1652			0.631858
$739$		−	19.3386i		−	0.711382i	−0.934604	−	0.355691i	$-0.884246\pi$
$739$		−	19.3386i		−	0.711382i	0.934604	−	0.355691i	$-0.115754\pi$
$740$	−2.83485	+	4.91010i	−0.104211	+	0.180499i
$741$	3.31307	+	13.3896i	0.121709	+	0.491879i
$742$		0			0
$743$	29.8521	+	17.2351i	1.09517	+	0.632295i	0.934947	−	0.354787i	$-0.115446\pi$
$743$	29.8521	+	17.2351i	1.09517	+	0.632295i	0.160219	+	0.987081i	$0.448780\pi$
$744$	20.9347	+	36.2599i	0.767502	+	1.32935i
$745$	−0.104356	+	0.180750i	−0.00382331	+	0.00662217i
$746$	12.7432	−	7.35728i	0.466561	−	0.269369i
$747$		−	33.6519i		−	1.23126i
$748$	18.2477	−	10.5353i	0.667203	−	0.385210i
$749$		0			0
$750$	2.85208	+	4.93995i	0.104143	+	0.180382i
$751$	−11.8739	−	20.5661i	−0.433283	−	0.750469i	0.563870	−	0.825863i	$-0.309312\pi$
$751$	−11.8739	−	20.5661i	−0.433283	−	0.750469i	−0.997154	+	0.0753944i	$0.975978\pi$
$752$		−	26.7237i		−	0.974512i
$753$	−3.95644	−	6.85275i	−0.144181	−	0.249728i
$754$	−2.68693	−	10.8591i	−0.0978523	−	0.395465i
$755$	5.53901			0.201585
$756$		0			0
$757$	−3.00000	+	5.19615i	−0.109037	+	0.188857i	−0.915380	−	0.402590i	$-0.868110\pi$
$757$	−3.00000	+	5.19615i	−0.109037	+	0.188857i	0.806343	+	0.591448i	$0.201443\pi$
$758$	−12.9564			−0.470599
$759$	−15.0000	+	8.66025i	−0.544466	+	0.314347i
$760$	0.939205	+	0.542250i	0.0340685	+	0.0196695i
$761$		−	12.9626i		−	0.469894i	−0.972008	−	0.234947i	$-0.924508\pi$
$761$		−	12.9626i		−	0.469894i	0.972008	−	0.234947i	$-0.0754917\pi$
$762$			8.87086i			0.321357i
$763$		0			0
$764$	12.8739	−	22.2982i	0.465760	−	0.806720i
$765$	5.68693	−	3.28335i	0.205611	−	0.118710i
$766$	−0.291288	−	0.504525i	−0.0105247	−	0.0182292i
$767$	−42.6606	−	12.3151i	−1.54039	−	0.444671i
$768$	−2.50000	+	4.33013i	−0.0902110	+	0.156250i
$769$	8.12614	+	4.69163i	0.293036	+	0.169184i	0.639310	−	0.768949i	$-0.279220\pi$
$769$	8.12614	+	4.69163i	0.293036	+	0.169184i	−0.346274	+	0.938133i	$0.612553\pi$
$770$		0			0
$771$	7.03901	+	12.1919i	0.253504	+	0.439082i
$772$	30.0000	+	17.3205i	1.07972	+	0.623379i
$773$	16.8303	+	9.71698i	0.605344	+	0.349495i	0.771141	−	0.636664i	$-0.219686\pi$
$773$	16.8303	+	9.71698i	0.605344	+	0.349495i	−0.165797	+	0.986160i	$0.553020\pi$
$774$	−17.7695	−	10.2592i	−0.638712	−	0.368760i
$775$	−35.9347	−	20.7469i	−1.29081	−	0.745250i
$776$	−6.31307	−	10.9346i	−0.226626	−	0.392528i
$777$		0			0
$778$	0.130682	+	0.0754495i	0.00468519	+	0.00270499i
$779$	−5.37386	+	9.30780i	−0.192539	+	0.333487i
$780$	5.93466	−	5.71063i	0.212495	−	0.204473i
$781$	8.58258	+	14.8655i	0.307109	+	0.531928i
$782$	−1.87841	+	1.08450i	−0.0671718	+	0.0387816i
$783$	16.9782	−	29.4071i	0.606752	−	1.05093i
$784$		0			0
$785$		−	0.436950i		−	0.0155954i
$786$		−	22.1552i		−	0.790248i
$787$	22.7477	+	13.1334i	0.810869	+	0.468155i	0.847258	−	0.531182i	$-0.178252\pi$
$787$	22.7477	+	13.1334i	0.810869	+	0.468155i	−0.0363886	+	0.999338i	$0.511585\pi$
$788$	−3.54356	+	2.04588i	−0.126234	+	0.0728813i
$789$	26.0436			0.927175
$790$	−0.626136	+	1.08450i	−0.0222769	+	0.0385848i
$791$		0			0
$792$	−32.5390			−1.15622
$793$	−51.6170	+	12.7719i	−1.83298	+	0.453544i
$794$	−7.41742	−	12.8474i	−0.263235	−	0.455936i
$795$			7.86180i			0.278829i
$796$	9.85208	+	17.0643i	0.349198	+	0.604828i
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	0.739975	−	0.672634i	$-0.234837\pi$
$797$	−6.00000	−	10.3923i	−0.212531	−	0.368114i	−0.952506	+	0.304520i	$0.901504\pi$
$798$		0			0
$799$	−24.8739	+	14.3609i	−0.879974	+	0.508053i
$800$			22.7074i			0.802826i
$801$	66.9737	−	38.6673i	2.36640	−	1.36624i
$802$	−7.14792	+	12.3806i	−0.252402	+	0.437173i
$803$	−6.79129	−	11.7629i	−0.239659	−	0.415102i
$804$	−19.3693	−	11.1829i	−0.683103	−	0.394390i
$805$		0			0
$806$	3.95644	−	13.7055i	0.139360	−	0.482756i
$807$	−22.0390	+	38.1727i	−0.775810	+	1.34374i
$808$			9.02175i			0.317384i
$809$	53.2432			1.87193			0.935965	−	0.352092i	$-0.114530\pi$
$809$	53.2432			1.87193			0.935965	+	0.352092i	$0.114530\pi$
$810$	0.0871215			0.00306114
$811$		−	27.6374i		−	0.970479i	−0.874381	−	0.485240i	$-0.838732\pi$
$811$		−	27.6374i		−	0.970479i	0.874381	−	0.485240i	$-0.161268\pi$
$812$		0			0
$813$	−31.0562	+	17.9303i	−1.08919	+	0.628844i
$814$	−10.7477	−	6.20520i	−0.376708	−	0.217492i
$815$	1.58258	−	2.74110i	0.0554352	−	0.0960166i
$816$	23.3739			0.818249
$817$	11.1261	−	6.42368i	0.389254	−	0.224736i
$818$	3.79129			0.132559
$819$		0			0
$820$	6.41742			0.224106
$821$	−10.9610	+	6.32833i	−0.382541	+	0.220860i	−0.678923	−	0.734209i	$-0.737553\pi$
$821$	−10.9610	+	6.32833i	−0.382541	+	0.220860i	0.296382	+	0.955069i	$0.404220\pi$
$822$	−15.2432			−0.531667
$823$	11.2477	−	19.4816i	0.392071	−	0.679087i	−0.600651	−	0.799511i	$-0.705092\pi$
$823$	11.2477	−	19.4816i	0.392071	−	0.679087i	0.992723	+	0.120424i	$0.0384254\pi$
$824$	−6.87386	−	3.96863i	−0.239462	−	0.138254i
$825$	45.4129	−	26.2191i	1.58107	−	0.912833i
$826$		0			0
$827$		−	35.3839i		−	1.23042i	−0.788364	−	0.615210i	$-0.789071\pi$
$827$		−	35.3839i		−	1.23042i	0.788364	−	0.615210i	$-0.210929\pi$
$828$	−13.5826			−0.472027
$829$	−34.3739			−1.19385			−0.596927	−	0.802296i	$-0.703612\pi$
$829$	−34.3739			−1.19385			−0.596927	+	0.802296i	$0.703612\pi$
$830$			1.46590i			0.0508822i
$831$	−16.3956	+	28.3981i	−0.568759	+	0.985119i
$832$	11.9610	−	2.95958i	0.414673	−	0.102605i
$833$		0			0
$834$	−4.18693	−	2.41733i	−0.144982	−	0.0837052i
$835$	−3.35208	−	5.80598i	−0.116004	−	0.200924i
$836$	4.81307	−	8.33648i	0.166463	−	0.288323i
$837$	37.5000	−	21.6506i	1.29619	−	0.748355i
$838$			0.798450i			0.0275820i
$839$	24.2305	−	13.9895i	0.836530	−	0.482971i	−0.0195536	−	0.999809i	$-0.506224\pi$
$839$	24.2305	−	13.9895i	0.836530	−	0.482971i	0.856083	+	0.516838i	$0.172891\pi$
$840$		0			0
$841$	−8.56080	−	14.8277i	−0.295200	−	0.511301i
$842$	0.956439	+	1.65660i	0.0329611	+	0.0570903i
$843$			85.5379i			2.94608i
$844$	−9.47822	−	16.4168i	−0.326254	−	0.565088i
$845$	−5.93466	−	0.228425i	−0.204158	−	0.00785806i
$846$	20.9564			0.720497
$847$		0			0
$848$	−8.60436	+	14.9032i	−0.295475	+	0.511777i
$849$	−7.66970			−0.263223
$850$	5.68693	−	3.28335i	0.195060	−	0.112618i
$851$	−9.49545	−	5.48220i	−0.325500	−	0.187927i
$852$			21.8890i			0.749905i
$853$			14.1425i			0.484229i	0.970248	+	0.242114i	$0.0778409\pi$
$853$			14.1425i			0.484229i	−0.970248	+	0.242114i	$0.922159\pi$
$854$		0			0
$855$	1.50000	−	2.59808i	0.0512989	−	0.0888523i
$856$	−7.81307	+	4.51088i	−0.267045	+	0.154179i
$857$	7.73049	+	13.3896i	0.264069	+	0.457380i	0.967319	−	0.253562i	$-0.0816021\pi$
$857$	7.73049	+	13.3896i	0.264069	+	0.457380i	−0.703251	+	0.710942i	$0.748269\pi$
$858$	12.5000	+	12.9904i	0.426743	+	0.443484i
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	−0.960381	−	0.278691i	$-0.910099\pi$
$859$	−7.00000	+	12.1244i	−0.238837	+	0.413678i	0.721544	+	0.692369i	$0.243433\pi$
$860$	−6.64337	−	3.83555i	−0.226537	−	0.130791i
$861$		0			0
$862$	−7.91742	−	13.7134i	−0.269669	−	0.467080i
$863$	−39.3303	−	22.7074i	−1.33882	−	0.772968i	−0.352187	−	0.935930i	$-0.614562\pi$
$863$	−39.3303	−	22.7074i	−1.33882	−	0.772968i	−0.986632	+	0.162962i	$0.947895\pi$
$864$	−20.5218	−	11.8483i	−0.698165	−	0.403086i
$865$	−7.81307	−	4.51088i	−0.265652	−	0.153374i
$866$	−12.8566	−	7.42278i	−0.436886	−	0.252236i
$867$	11.1652	+	19.3386i	0.379188	+	0.656774i
$868$		0			0
$869$	20.3739	+	11.7629i	0.691136	+	0.399028i
$870$	−1.97822	+	3.42638i	−0.0670679	+	0.116165i
$871$	3.87386	+	15.6560i	0.131261	+	0.530484i
$872$	−6.87386	−	11.9059i	−0.232778	−	0.403184i
$873$	−30.2477	+	17.4635i	−1.02373	+	0.591051i
$874$	−0.495454	+	0.858152i	−0.0167590	+	0.0290274i
$875$		0			0
$876$		−	17.3205i		−	0.585206i
$877$			3.17805i			0.107315i	0.998559	+	0.0536576i	$0.0170879\pi$
$877$			3.17805i			0.107315i	−0.998559	+	0.0536576i	$0.982912\pi$
$878$	−8.12614	−	4.69163i	−0.274244	−	0.158335i
$879$	−6.16515	+	3.55945i	−0.207945	+	0.120057i
$880$	−5.00000			−0.168550
$881$	8.29129	−	14.3609i	0.279341	−	0.483832i	−0.691880	−	0.722012i	$-0.743217\pi$
$881$	8.29129	−	14.3609i	0.279341	−	0.483832i	0.971221	+	0.238180i	$0.0765508\pi$
$882$		0			0
$883$	29.2432			0.984111			0.492056	−	0.870564i	$-0.336246\pi$
$883$	29.2432			0.984111			0.492056	+	0.870564i	$0.336246\pi$
$884$	−13.4347	−	13.9617i	−0.451856	−	0.469583i
$885$	7.85208	+	13.6002i	0.263945	+	0.457166i
$886$		−	6.92820i		−	0.232758i
$887$	11.2087	+	19.4141i	0.376352	+	0.651860i	0.990528	−	0.137308i	$-0.0438451\pi$
$887$	11.2087	+	19.4141i	0.376352	+	0.651860i	−0.614177	+	0.789169i	$0.710512\pi$
$888$	−16.7477	−	29.0079i	−0.562017	−	0.973442i
$889$		0			0
$890$	−2.91742	+	1.68438i	−0.0977923	+	0.0564604i
$891$		−	1.63670i		−	0.0548315i
$892$	−29.4392	+	16.9967i	−0.985697	+	0.569093i
$893$	−6.56080	+	11.3636i	−0.219549	+	0.380269i
$894$	−0.291288	−	0.504525i	−0.00974212	−	0.0168739i
$895$	3.56080	+	2.05583i	0.119024	+	0.0687187i
$896$		0			0
$897$	11.0436	+	11.4768i	0.368734	+	0.383199i
$898$	−5.74773	+	9.95536i	−0.191804	+	0.332215i
$899$		−	58.8143i		−	1.96157i
$900$	41.1216			1.37072
$901$	18.4955			0.616173
$902$			14.0471i			0.467717i
$903$		0			0
$904$	15.8739	−	9.16478i	0.527957	−	0.304816i
$905$	3.62614	+	2.09355i	0.120537	+	0.0695920i
$906$	−7.73049	+	13.3896i	−0.256828	+	0.444840i
$907$	−41.0780			−1.36397			−0.681987	−	0.731364i	$-0.738884\pi$
$907$	−41.0780			−1.36397			−0.681987	+	0.731364i	$0.738884\pi$
$908$	−13.7305	+	7.92730i	−0.455662	+	0.263077i
$909$	24.9564			0.827753
$910$		0			0
$911$	−43.1216			−1.42868			−0.714341	−	0.699798i	$-0.753273\pi$
$911$	−43.1216			−1.42868			−0.714341	+	0.699798i	$0.753273\pi$
$912$	9.24773	−	5.33918i	0.306223	−	0.176798i
$913$	27.5390			0.911408
$914$	−5.20871	+	9.02175i	−0.172289	+	0.298413i
$915$	16.2867	+	9.40315i	0.538423	+	0.310859i
$916$	−10.7477	+	6.20520i	−0.355115	+	0.205026i
$917$		0			0
$918$			6.85275i			0.226175i
$919$	25.9129			0.854787			0.427393	−	0.904066i	$-0.359432\pi$
$919$	25.9129			0.854787			0.427393	+	0.904066i	$0.359432\pi$
$920$	1.25227			0.0412862
$921$		−	43.3013i		−	1.42683i
$922$	−1.06080	+	1.83735i	−0.0349354	+	0.0605099i
$923$	11.3739	−	10.9445i	0.374375	−	0.360243i
$924$		0			0
$925$	28.7477	+	16.5975i	0.945219	+	0.545723i
$926$	1.81307	+	3.14033i	0.0595811	+	0.103198i
$927$	−10.9782	+	19.0148i	−0.360572	+	0.624529i
$928$	−27.8739	+	16.0930i	−0.915004	+	0.528278i
$929$			57.9205i			1.90031i	0.311779	+	0.950155i	$0.399075\pi$
$929$			57.9205i			1.90031i	−0.311779	+	0.950155i	$0.600925\pi$
$930$	−4.36932	+	2.52263i	−0.143276	+	0.0827202i
$931$		0			0
$932$	−14.2913	−	24.7532i	−0.468127	−	0.810819i
$933$	37.0390	+	64.1535i	1.21260	+	2.10029i
$934$		−	13.7810i		−	0.450927i
$935$	2.68693	+	4.65390i	0.0878721	+	0.152199i
$936$	7.18693	+	29.0456i	0.234912	+	0.949386i
$937$	−20.4955			−0.669557			−0.334779	−	0.942297i	$-0.608662\pi$
$937$	−20.4955			−0.669557			−0.334779	+	0.942297i	$0.608662\pi$
$938$		0			0
$939$	−9.41742	+	16.3115i	−0.307326	+	0.532304i
$940$	7.83485			0.255545
$941$	34.0390	−	19.6524i	1.10964	−	0.640651i	0.170904	−	0.985288i	$-0.445331\pi$
$941$	34.0390	−	19.6524i	1.10964	−	0.640651i	0.938736	+	0.344637i	$0.111998\pi$
$942$	1.05625	+	0.609826i	0.0344145	+	0.0198692i
$943$			12.4104i			0.404138i
$944$			34.3749i			1.11881i
$945$		0			0
$946$	8.39564	−	14.5417i	0.272966	−	0.472791i
$947$	33.2305	−	19.1856i	1.07985	−	0.623449i	0.148991	−	0.988839i	$-0.452397\pi$
$947$	33.2305	−	19.1856i	1.07985	−	0.623449i	0.930855	+	0.365389i	$0.119064\pi$
$948$	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
$951$	44.7695	+	25.8477i	1.45175	+	0.838169i
$952$		0			0
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$	−11.6869	−	6.74745i	−0.378378	−	0.218457i
$955$	5.68693	+	3.28335i	0.184025	+	0.106247i
$956$	−20.5218	−	11.8483i	−0.663722	−	0.383200i
$957$	64.3693	+	37.1636i	2.08076	+	1.20133i
$958$	−4.31307	−	7.47045i	−0.139349	−	0.241359i
$959$		0			0
$960$	−3.77405	−	2.17895i	−0.121807	−	0.0703253i
$961$	22.0000	−	38.1051i	0.709677	−	1.22920i
$962$	−3.16515	+	10.9644i	−0.102049	+	0.353507i
$963$	12.4782	+	21.6129i	0.402105	+	0.696466i
$964$	30.5608	−	17.6443i	0.984297	−	0.568284i
$965$	−4.41742	+	7.65120i	−0.142202	+	0.246301i
$966$		0			0
$967$		−	23.8118i		−	0.765735i	−0.923803	−	0.382867i	$-0.874937\pi$
$967$		−	23.8118i		−	0.765735i	0.923803	−	0.382867i	$-0.125063\pi$
$968$		−	7.57575i		−	0.243494i
$969$	−9.93920	−	5.73840i	−0.319293	−	0.184344i
$970$	1.31761	−	0.760725i	0.0423060	−	0.0244254i
$971$	−22.2523			−0.714109			−0.357055	−	0.934083i	$-0.616219\pi$
$971$	−22.2523			−0.714109			−0.357055	+	0.934083i	$0.616219\pi$
$972$	14.4782	−	25.0770i	0.464389	−	0.804346i
$973$		0			0
$974$	−13.4174			−0.429922
$975$	−33.4347	−	34.7463i	−1.07077	−	1.11277i
$976$	20.5826	+	35.6501i	0.658832	+	1.14113i
$977$			1.39045i			0.0444845i	0.999753	+	0.0222422i	$0.00708051\pi$
$977$			1.39045i			0.0444845i	−0.999753	+	0.0222422i	$0.992919\pi$
$978$	4.41742	+	7.65120i	0.141254	+	0.244659i
$979$	31.6434	+	54.8079i	1.01133	+	1.75167i
$980$		0			0
$981$	−32.9347	+	19.0148i	−1.05152	+	0.607097i
$982$		−	1.88295i		−	0.0600873i
$983$	−17.2259	+	9.94540i	−0.549422	+	0.317209i	−0.748889	−	0.662695i	$-0.769412\pi$
$983$	−17.2259	+	9.94540i	−0.549422	+	0.317209i	0.199467	+	0.979905i	$0.436079\pi$
$984$	−18.9564	+	32.8335i	−0.604309	+	1.04669i
$985$	−0.521780	−	0.903750i	−0.0166253	−	0.0287959i
$986$	8.06080	+	4.65390i	0.256708	+	0.148210i
$987$		0			0
$988$	−8.50455	−	2.45505i	−0.270566	−	0.0781056i
$989$	7.41742	−	12.8474i	0.235860	−	0.408522i
$990$		−	3.92095i		−	0.124616i
$991$	−40.3739			−1.28252			−0.641259	−	0.767324i	$-0.721588\pi$
$991$	−40.3739			−1.28252			−0.641259	+	0.767324i	$0.721588\pi$
$992$	−41.0436			−1.30313
$993$			69.4926i			2.20528i
$994$		0			0
$995$	−4.35208	+	2.51268i	−0.137970	+	0.0796572i
$996$	30.4129	+	17.5589i	0.963669	+	0.556375i
$997$	−7.03901	+	12.1919i	−0.222928	+	0.386122i	−0.955696	−	0.294356i	$-0.904895\pi$
$997$	−7.03901	+	12.1919i	−0.222928	+	0.386122i	0.732768	+	0.680479i	$0.238228\pi$
$998$	−8.40833			−0.266161
$999$	−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.e.30.2		4
7.2	even	3		637.2.q.e.589.1	yes	4
7.3	odd	6		637.2.k.f.459.2		4
7.4	even	3		637.2.k.d.459.2		4
7.5	odd	6		637.2.q.f.589.1	yes	4
7.6	odd	2		637.2.u.d.30.2		4
13.10	even	6		637.2.k.d.569.1		4
91.10	odd	6		637.2.u.d.361.2		4
91.19	even	12		8281.2.a.bq.1.3		4
91.23	even	6		637.2.q.e.491.1	✓	4
91.33	even	12		8281.2.a.bq.1.2		4
91.58	odd	12		8281.2.a.bs.1.3		4
91.62	odd	6		637.2.k.f.569.1		4
91.72	odd	12		8281.2.a.bs.1.2		4
91.75	odd	6		637.2.q.f.491.1	yes	4
91.88	even	6	inner	637.2.u.e.361.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.d.459.2		4	7.4	even	3
637.2.k.d.569.1		4	13.10	even	6
637.2.k.f.459.2		4	7.3	odd	6
637.2.k.f.569.1		4	91.62	odd	6
637.2.q.e.491.1	✓	4	91.23	even	6
637.2.q.e.589.1	yes	4	7.2	even	3
637.2.q.f.491.1	yes	4	91.75	odd	6
637.2.q.f.589.1	yes	4	7.5	odd	6
637.2.u.d.30.2		4	7.6	odd	2
637.2.u.d.361.2		4	91.10	odd	6
637.2.u.e.30.2		4	1.1	even	1	trivial
637.2.u.e.361.2		4	91.88	even	6	inner
8281.2.a.bq.1.2		4	91.33	even	12
8281.2.a.bq.1.3		4	91.19	even	12
8281.2.a.bs.1.2		4	91.72	odd	12
8281.2.a.bs.1.3		4	91.58	odd	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 $\F_{q}$

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+(0.395644 - 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(-0.395644 - 0.228425i) q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} -0.208712 q^{10} +3.92095i q^{11} +(-2.50000 + 4.33013i) q^{12} +(3.50000 - 0.866025i) q^{13} +(-1.10436 - 0.637600i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.89564 - 1.09445i) q^{18} +1.37055i q^{19} +(0.708712 - 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 + 1.37055i) q^{23} +4.83465i q^{24} +(-2.39564 - 4.14938i) q^{25} +(1.18693 - 1.14213i) q^{26} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} -0.582576 q^{30} +(7.50000 - 4.33013i) q^{31} +(-4.10436 - 2.36965i) q^{32} +10.9445i q^{33} +1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(-6.00000 + 3.46410i) q^{37} +(0.313068 + 0.542250i) q^{38} +(9.76951 - 2.41733i) q^{39} +(0.395644 - 0.685275i) q^{40} +(6.79129 + 3.92095i) q^{41} +(-4.68693 - 8.11800i) q^{43} +(-6.08258 - 3.51178i) q^{44} +(-1.89564 - 1.09445i) q^{45} +(0.626136 + 0.361500i) q^{46} +(8.29129 + 4.78698i) q^{47} +(-3.89564 - 6.74745i) q^{48} +(-1.89564 - 1.09445i) q^{50} +(-4.18693 + 7.25198i) q^{51} +(-1.79129 + 6.20520i) q^{52} +(-3.08258 - 5.33918i) q^{53} +(1.97822 - 1.14213i) q^{54} +(0.895644 - 1.55130i) q^{55} +3.82560i q^{57} -3.10260i q^{58} +(-10.6652 - 6.15753i) q^{59} +(1.97822 - 1.14213i) q^{60} -14.7477 q^{61} +(1.97822 - 3.42638i) q^{62} +3.41742 q^{64} +(-1.58258 - 0.456850i) q^{65} +(2.50000 + 4.33013i) q^{66} +4.47315i q^{67} +(-2.68693 - 4.65390i) q^{68} +(2.20871 + 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +8.29875i q^{72} +(-3.00000 + 1.73205i) q^{73} +(-1.58258 + 2.74110i) q^{74} +(-6.68693 - 11.5821i) q^{75} +(-2.12614 - 1.22753i) q^{76} +(3.31307 - 3.18800i) q^{78} +(3.00000 - 5.19615i) q^{79} +1.27520i q^{80} -0.417424 q^{81} +3.58258 q^{82} -7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +(-3.70871 - 2.14123i) q^{86} +(9.47822 - 16.4168i) q^{87} -6.79129 q^{88} +(13.9782 - 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(20.9347 - 12.0866i) q^{93} +4.37386 q^{94} +(0.313068 - 0.542250i) q^{95} +(-11.4564 - 6.61438i) q^{96} +(-6.31307 + 3.64485i) q^{97} +18.7864i 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

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