LMFDB - Embedded newform 637.2.u.d.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:	$1$
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			30.2
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.30
Dual form			637.2.u.d.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.395644 - 0.228425i) q^{2} -2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(0.395644 + 0.228425i) q^{5} +(-1.10436 + 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 4 * q - 3 * q^2 - 2 * q^3 + q^4 - 3 * q^5 - 9 * q^6 + 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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	$-0.798251\pi$
$3$	−2.79129			−1.61155			−0.805775	+	0.592221i	$0.798251\pi$
$4$	−0.895644	+	1.55130i	−0.447822	+	0.775650i
$5$	0.395644	+	0.228425i	0.176937	+	0.102155i	0.585853	−	0.810417i	$-0.300760\pi$
$5$	0.395644	+	0.228425i	0.176937	+	0.102155i	−0.408916	+	0.912572i	$0.634093\pi$
$6$	−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	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	1.89564	−	1.09445i	0.446808	−	0.257964i
$19$		−	1.37055i		−	0.314426i	−0.987565	−	0.157213i	$-0.949749\pi$
$19$		−	1.37055i		−	0.314426i	0.987565	−	0.157213i	$-0.0502509\pi$
$20$	−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	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−7.50000	+	4.33013i	−1.34704	+	0.777714i	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−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	−0.135017	−	0.990843i	$-0.543109\pi$
$41$	−6.79129	−	3.92095i	−1.06062	−	0.612350i	−0.925604	+	0.378493i	$0.876442\pi$
$42$		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	−0.246778	−	0.969072i	$-0.579372\pi$
$47$	−8.29129	−	4.78698i	−1.20941	−	0.698252i	−0.962630	+	0.270820i	$0.912705\pi$
$48$	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	0.993145	−	0.116893i	$-0.0372935\pi$
$59$	10.6652	+	6.15753i	1.38848	+	0.801642i	0.395340	+	0.918535i	$0.370627\pi$
$60$	1.97822	−	1.14213i	0.255387	−	0.147448i
$61$	14.7477			1.88825			0.944126	−	0.329583i	$-0.106908\pi$
$61$	14.7477			1.88825			0.944126	+	0.329583i	$0.106908\pi$
$62$	−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	−0.314057	−	0.949404i	$-0.601688\pi$
$73$	3.00000	−	1.73205i	0.351123	−	0.202721i	0.665180	+	0.746683i	$0.268355\pi$
$74$	−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	$0.125960\pi$
$83$			7.02355i			0.770935i	−0.922721	+	0.385468i	$0.874040\pi$
$84$		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	−0.999784	−	0.0207708i	$-0.993388\pi$
$89$	−13.9782	+	8.07033i	−1.48169	+	0.855453i	−0.481904	+	0.876224i	$0.660055\pi$
$90$	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	−0.144003	−	0.989577i	$-0.545997\pi$
$97$	6.31307	−	3.64485i	0.640995	−	0.370079i	0.784998	+	0.619499i	$0.212664\pi$
$98$		0			0
$99$			18.7864i			1.88811i
$100$	8.58258			0.858258
$101$	−5.20871			−0.518286			−0.259143	−	0.965839i	$-0.583440\pi$
$101$	−5.20871			−0.518286			−0.259143	+	0.965839i	$0.583440\pi$
$102$			3.82560i			0.378791i
$103$	2.29129	−	3.96863i	0.225767	−	0.391040i	−0.730782	−	0.682611i	$-0.760844\pi$
$103$	2.29129	−	3.96863i	0.225767	−	0.391040i	0.956549	+	0.291570i	$0.0941778\pi$
$104$	−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	$0.440969\pi$
$131$	−8.68693	+	15.0462i	−0.758981	+	1.31459i	−0.943371	+	0.331740i	$0.892364\pi$
$132$	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	0.935151	−	0.354249i	$-0.115264\pi$
$139$	1.89564	+	3.28335i	0.160786	+	0.278490i	−0.774365	+	0.632740i	$0.781930\pi$
$140$		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	0.846311	−	0.532689i	$-0.178818\pi$
$157$	−0.478220	−	0.828301i	−0.0381661	−	0.0661056i	−0.884477	+	0.466583i	$0.845485\pi$
$158$		−	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	−0.0801258	−	0.996785i	$-0.525532\pi$
$167$	−12.7087	−	7.33738i	−0.983430	−	0.567783i	−0.903304	+	0.429001i	$0.858866\pi$
$168$		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	$-0.770282\pi$
$173$	−19.7477			−1.50139			−0.750696	+	0.660648i	$0.770282\pi$
$174$			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	$-0.389363\pi$
$181$	9.16515			0.681240			0.340620	+	0.940201i	$0.389363\pi$
$182$		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	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$	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	−0.164182	−	0.986430i	$-0.552498\pi$
$223$	−16.4347	−	9.48855i	−1.10055	−	0.635401i	−0.936364	+	0.351029i	$0.885832\pi$
$224$		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	0.223567	−	0.974688i	$-0.428230\pi$
$227$	−7.66515	−	4.42548i	−0.508754	−	0.293729i	−0.732321	+	0.680959i	$0.761563\pi$
$228$	−5.93466	−	3.42638i	−0.393032	−	0.226917i
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	0.288478	−	0.957487i	$-0.406851\pi$
$229$	−6.00000	−	3.46410i	−0.396491	−	0.228914i	−0.684969	+	0.728572i	$0.740184\pi$
$230$	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	0.935954	−	0.352123i	$-0.114540\pi$
$241$	17.0608	+	9.85005i	1.09898	+	0.634498i	0.163029	+	0.986621i	$0.447874\pi$
$242$	−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	0.907286	−	0.420514i	$-0.138150\pi$
$251$	1.41742	+	2.45505i	0.0894670	+	0.154961i	−0.817819	+	0.575476i	$0.804817\pi$
$252$		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	0.776591	−	0.630005i	$-0.216947\pi$
$257$	−2.52178	−	4.36785i	−0.157304	−	0.272459i	−0.933896	+	0.357546i	$0.883614\pi$
$258$	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	−0.518366	−	0.855159i	$-0.673460\pi$
$269$	7.89564	−	13.6757i	0.481406	−	0.833819i	0.999772	+	0.0213391i	$0.00679298\pi$
$270$	−1.04356			−0.0635091
$271$	11.1261	−	6.42368i	0.675865	−	0.390211i	−0.122430	−	0.992477i	$-0.539069\pi$
$271$	11.1261	−	6.42368i	0.675865	−	0.390211i	0.798295	+	0.602266i	$0.205736\pi$
$272$	−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	$-0.473975\pi$
$283$	2.74773			0.163335			0.0816677	+	0.996660i	$0.473975\pi$
$284$			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	−0.434093	−	0.900868i	$-0.642931\pi$
$293$	2.20871	−	1.27520i	0.129034	−	0.0744980i	0.563128	+	0.826370i	$0.309598\pi$
$294$		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	$0.145975\pi$
$307$			15.5130i			0.885374i	−0.896676	+	0.442687i	$0.854025\pi$
$308$		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	$-0.895541\pi$
$311$	−13.2695	−	22.9835i	−0.752445	−	1.30327i	0.194190	−	0.980964i	$-0.437792\pi$
$312$	4.18693	+	16.9213i	0.237038	+	0.957979i
$313$	3.37386	−	5.84370i	0.190702	−	0.330306i	−0.754781	−	0.655977i	$-0.772257\pi$
$313$	3.37386	−	5.84370i	0.190702	−	0.330306i	0.945483	+	0.325671i	$0.105590\pi$
$314$	−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	−0.0754825	−	0.997147i	$-0.524050\pi$
$349$	−18.2477	−	10.5353i	−0.976778	−	0.563943i	−0.901296	+	0.433204i	$0.857383\pi$
$350$		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	$-0.839457\pi$
$353$		−	18.1588i		−	0.966493i	0.875484	−	0.483247i	$-0.160543\pi$
$354$	−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	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	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	$0.0103723\pi$
$383$			1.27520i			0.0651597i	−0.999469	+	0.0325799i	$0.989628\pi$
$384$	−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	$0.303187\pi$
$397$			32.4720i			1.62972i	−0.579655	+	0.814862i	$0.696813\pi$
$398$			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	0.311677	−	0.950188i	$-0.399109\pi$
$409$	−7.18693	−	4.14938i	−0.355371	−	0.205173i	−0.667048	+	0.745015i	$0.732443\pi$
$410$	−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	−0.843890	−	0.536516i	$-0.819740\pi$
$419$	0.873864	−	1.51358i	0.0426910	−	0.0739430i	0.886581	+	0.462573i	$0.153074\pi$
$420$		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	$0.118530\pi$
$433$	16.2477	+	28.1419i	0.780816	+	1.35241i	−0.150651	+	0.988587i	$0.548137\pi$
$434$		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	0.999936	−	0.0113518i	$-0.00361346\pi$
$439$	10.2695	+	17.7873i	0.490137	+	0.848942i	−0.509799	+	0.860294i	$0.670280\pi$
$440$	−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	−0.403411	−	0.915019i	$-0.632176\pi$
$461$	4.02178	−	2.32198i	0.187313	−	0.108145i	0.590724	+	0.806874i	$0.298842\pi$
$462$		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	$0.412566\pi$
$467$	−15.0826	+	26.1238i	−0.697938	+	1.20886i	−0.969180	+	0.246353i	$0.920768\pi$
$468$	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	$0.141968\pi$
$479$			18.8818i			0.862730i	−0.902178	+	0.431365i	$0.858032\pi$
$480$	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	0.570246	−	0.821474i	$-0.306848\pi$
$503$	−9.56080	−	16.5598i	−0.426295	−	0.738364i	−0.996540	+	0.0831100i	$0.973515\pi$
$504$		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	−0.182372	−	0.983230i	$-0.558377\pi$
$509$	13.0390	−	7.52808i	0.577944	−	0.333676i	0.760316	+	0.649553i	$0.225044\pi$
$510$	−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	0.628269	−	0.777996i	$-0.283764\pi$
$521$	−8.20871	−	14.2179i	−0.359630	−	0.622898i	−0.987899	+	0.155099i	$0.950430\pi$
$522$		−	14.8655i		−	0.650643i
$523$	−12.1652	−	21.0707i	−0.531945	−	0.921356i	−0.999305	−	0.0372883i	$-0.988128\pi$
$523$	−12.1652	−	21.0707i	−0.531945	−	0.921356i	0.467360	−	0.884067i	$-0.345205\pi$
$524$	−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	$0.444210\pi$
$563$	−18.1652	+	31.4630i	−0.765570	+	1.32601i	−0.939945	+	0.341327i	$0.889124\pi$
$564$	−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	0.307484	−	0.951553i	$-0.400513\pi$
$577$	30.8739	−	17.8250i	1.28530	−	0.742066i	0.977811	+	0.209487i	$0.0671795\pi$
$578$	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	0.320539	−	0.947235i	$-0.396136\pi$
$587$	−8.22595	−	4.74925i	−0.339521	−	0.196023i	−0.660060	+	0.751213i	$0.729469\pi$
$588$		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	0.382321	−	0.924030i	$-0.375125\pi$
$593$	−5.52178	−	3.18800i	−0.226752	−	0.130916i	−0.609073	+	0.793114i	$0.708458\pi$
$594$	−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	−0.711808	−	0.702374i	$-0.752123\pi$
$601$	6.18693	−	10.7161i	0.252370	−	0.437118i	0.964178	+	0.265256i	$0.0854566\pi$
$602$		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	$-0.631257\pi$
$607$	−19.7477			−0.801536			−0.400768	+	0.916180i	$0.631257\pi$
$608$	−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	−0.124120	−	0.992267i	$-0.539611\pi$
$619$	16.7477	−	9.66930i	0.673148	−	0.388642i	0.797268	+	0.603625i	$0.206278\pi$
$620$	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	$-0.314830\pi$
$643$	39.2477	−	22.6597i	1.54778	−	0.893611i	0.998311	−	0.0580962i	$-0.0185030\pi$
$644$		0			0
$645$			11.9536i			0.470671i
$646$	−1.87841			−0.0739050
$647$	35.0780			1.37906			0.689530	−	0.724257i	$-0.257817\pi$
$647$	35.0780			1.37906			0.689530	+	0.724257i	$0.257817\pi$
$648$		−	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	$0.440214\pi$
$661$			50.5155i			1.96483i	−0.186720	+	0.982413i	$0.559786\pi$
$662$	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	$-0.643638\pi$
$677$	14.6044	−	25.2955i	0.561291	−	0.972185i	0.997384	−	0.0722830i	$-0.0230285\pi$
$678$	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	−0.320333	−	0.947305i	$-0.603795\pi$
$691$	8.93466	−	5.15843i	0.339890	−	0.196236i	0.660224	+	0.751069i	$0.270462\pi$
$692$	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	$-0.351209\pi$
$719$	24.1652			0.901208			0.450604	+	0.892724i	$0.351209\pi$
$720$		−	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	$-0.501489\pi$
$727$	−0.252273			−0.00935628			−0.00467814	+	0.999989i	$0.501489\pi$
$728$		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	0.203607	−	0.979053i	$-0.434734\pi$
$733$	−14.6869	−	8.47950i	−0.542474	−	0.313198i	−0.746081	+	0.665855i	$0.768067\pi$
$734$	−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	$0.0754917\pi$
$761$			12.9626i			0.469894i	−0.972008	+	0.234947i	$0.924508\pi$
$762$		−	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	0.346274	−	0.938133i	$-0.387447\pi$
$769$	−8.12614	−	4.69163i	−0.293036	−	0.169184i	−0.639310	+	0.768949i	$0.720780\pi$
$770$		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	−

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)

\(f(q)\)	\(=\)	\(q+(0.395644 - 0.228425i) q^{2} -2.79129 q^{3} +(-0.895644 + 1.55130i) q^{4} +(0.395644 + 0.228425i) q^{5} +(-1.10436 + 0.637600i) q^{6} +1.73205i q^{8} +4.79129 q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - 2 q^{3} + q^{4} - 3 q^{5} - 9 q^{6} + 10 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 - 2 * q^3 + q^4 - 3 * q^5 - 9 * q^6 + 10 * q^9	\( 4 q - 3 q^{2} - 2 q^{3} + q^{4} - 3 q^{5} - 9 q^{6} + 10 q^{9} + 10 q^{10} + 10 q^{12} - 14 q^{13} - 9 q^{15} - q^{16} + 6 q^{17} + 3 q^{18} - 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} + 9 q^{26} - 20 q^{27} + 9 q^{29} + 16 q^{30} - 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} - 15 q^{38} + 7 q^{39} + 3 q^{40} - 18 q^{41} - 5 q^{43} - 6 q^{44} + 3 q^{45} + 30 q^{46} - 24 q^{47} + 11 q^{48} - 3 q^{50} - 3 q^{51} - 2 q^{52} + 6 q^{53} + 15 q^{54} + q^{55} + 6 q^{59} - 15 q^{60} + 4 q^{61} + 15 q^{62} + 32 q^{64} + 12 q^{65} - 10 q^{66} - 3 q^{68} - 18 q^{69} + 6 q^{71} + 12 q^{73} + 12 q^{74} + 13 q^{75} + 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} + 4 q^{82} - 9 q^{85} - 24 q^{86} - 15 q^{87} - 18 q^{88} - 33 q^{89} + 4 q^{90} - 48 q^{92} + 15 q^{93} + 10 q^{94} + 15 q^{95} + 39 q^{97}+O(q^{100}) \) 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

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