LMFDB - Embedded newform 637.2.k.d.569.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(459,637)]

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([4, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (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			569.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.d.459.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})$	\(q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +(0.104356 - 0.180750i) q^{10} +(3.39564 + 1.96048i) q^{11} +(-2.50000 + 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +2.79129 q^{16} +3.00000 q^{17} +(-1.89564 + 1.09445i) q^{18} +(-1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} -1.58258 q^{23} +(4.18693 + 2.41733i) q^{24} +(-2.39564 - 4.14938i) q^{25} +(0.395644 - 1.59898i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +(-7.50000 + 4.33013i) q^{31} -4.73930i q^{32} +(-9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +6.92820i q^{37} +(0.313068 + 0.542250i) q^{38} +(-6.97822 + 7.25198i) 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} -2.18890i q^{45} +0.723000i 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} +(6.26951 + 1.55130i) q^{52} +(-3.08258 - 5.33918i) q^{53} -2.28425i q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(2.68693 - 1.55130i) q^{58} -12.3151i q^{59} +(-1.97822 + 1.14213i) q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(1.18693 + 1.14213i) q^{65} +(2.50000 + 4.33013i) q^{66} +(3.87386 + 2.23658i) q^{67} +5.37386 q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(-7.18693 + 4.14938i) q^{72} +(3.00000 - 1.73205i) q^{73} +3.16515 q^{74} +13.3739 q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} +(3.00000 - 5.19615i) q^{79} +(1.10436 + 0.637600i) q^{80} +(0.208712 - 0.361500i) q^{81} +(-1.79129 - 3.10260i) q^{82} +7.02355i q^{83} +(1.18693 + 0.685275i) q^{85} +(3.70871 + 2.14123i) q^{86} -18.9564 q^{87} +(3.39564 - 5.88143i) q^{88} -16.1407i q^{89} -1.00000 q^{90} -2.83485 q^{92} -24.1733i q^{93} +(-2.18693 + 3.78788i) q^{94} -0.626136 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 - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) $ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9	$ 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) $ 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 + 5 * q^10 + 9 * q^11 - 10 * q^12 + 14 * q^13 - 9 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^18 + 9 * q^19 + 12 * q^20 - q^22 + 12 * q^23 + 3 * q^24 - 5 * q^25 - 3 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 - 30 * q^31 - 15 * q^33 - 8 * q^36 + 15 * q^38 - 5 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 + 6 * q^44 - 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 - 7 * q^52 + 6 * q^53 - q^55 - 3 * q^58 + 15 * q^60 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 9 * q^65 + 10 * q^66 - 12 * q^67 - 6 * q^68 + 18 * q^69 + 6 * q^71 - 15 * q^72 + 12 * q^73 - 24 * q^74 + 26 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 + 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 24 * q^86 - 30 * q^87 + 9 * q^88 - 4 * q^90 - 48 * q^92 + 5 * q^94 - 30 * q^95 - 39 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$		−	0.456850i		−	0.323042i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$		−	0.456850i		−	0.323042i	0.986869	−	0.161521i	$-0.0516399\pi$
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	0.109991	+	0.993933i	$0.464918\pi$
$3$	−1.39564	+	2.41733i	−0.805775	+	1.39564i	−0.915766	+	0.401711i	$0.868416\pi$
$4$	1.79129			0.895644
$5$	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
$9$	−2.39564	−	4.14938i	−0.798548	−	1.38313i
$10$	0.104356	−	0.180750i	0.0330003	−	0.0571582i
$11$	3.39564	+	1.96048i	1.02383	+	0.591106i	0.915210	−	0.402978i	$-0.132025\pi$
$11$	3.39564	+	1.96048i	1.02383	+	0.591106i	0.108616	+	0.994084i	$0.465358\pi$
$12$	−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
$16$	2.79129			0.697822
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	−1.89564	+	1.09445i	−0.446808	+	0.257964i
$19$	−1.18693	+	0.685275i	−0.272301	+	0.157213i	−0.629933	−	0.776650i	$-0.716918\pi$
$19$	−1.18693	+	0.685275i	−0.272301	+	0.157213i	0.357632	+	0.933863i	$0.383584\pi$
$20$	0.708712	+	0.409175i	0.158473	+	0.0914943i
$21$		0			0
$22$	0.895644	−	1.55130i	0.190952	−	0.330738i
$23$	−1.58258			−0.329990			−0.164995	−	0.986294i	$-0.552761\pi$
$23$	−1.58258			−0.329990			−0.164995	+	0.986294i	$0.552761\pi$
$24$	4.18693	+	2.41733i	0.854654	+	0.493435i
$25$	−2.39564	−	4.14938i	−0.479129	−	0.829875i
$26$	0.395644	−	1.59898i	0.0775922	−	0.313585i
$27$	5.00000			0.962250
$28$		0			0
$29$	3.39564	+	5.88143i	0.630555	+	1.09215i	0.987438	+	0.158005i	$0.0505061\pi$
$29$	3.39564	+	5.88143i	0.630555	+	1.09215i	−0.356883	+	0.934149i	$0.616161\pi$
$30$	0.291288	+	0.504525i	0.0531816	+	0.0921133i
$31$	−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	$0.616954\pi$
$32$		−	4.73930i		−	0.837798i
$33$	−9.47822	+	5.47225i	−1.64995	+	0.952597i
$34$		−	1.37055i		−	0.235048i
$35$		0			0
$36$	−4.29129	−	7.43273i	−0.715215	−	1.23879i
$37$			6.92820i			1.13899i	0.821995	+	0.569495i	$0.192861\pi$
$37$			6.92820i			1.13899i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	0.313068	+	0.542250i	0.0507864	+	0.0879646i
$39$	−6.97822	+	7.25198i	−1.11741	+	1.16125i
$40$	0.395644	−	0.685275i	0.0625568	−	0.108352i
$41$	6.79129	−	3.92095i	1.06062	−	0.612350i	0.135017	−	0.990843i	$-0.456891\pi$
$41$	6.79129	−	3.92095i	1.06062	−	0.612350i	0.925604	+	0.378493i	$0.123558\pi$
$42$		0			0
$43$	−4.68693	+	8.11800i	−0.714750	+	1.23798i	0.248305	+	0.968682i	$0.420126\pi$
$43$	−4.68693	+	8.11800i	−0.714750	+	1.23798i	−0.963056	+	0.269302i	$0.913207\pi$
$44$	6.08258	+	3.51178i	0.916983	+	0.529420i
$45$		−	2.18890i		−	0.326302i
$46$			0.723000i			0.106601i
$47$	−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
$52$	6.26951	+	1.55130i	0.869424	+	0.215127i
$53$	−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	$0.972505\pi$
$54$		−	2.28425i		−	0.310847i
$55$	0.895644	+	1.55130i	0.120769	+	0.209177i
$56$		0			0
$57$		−	3.82560i		−	0.506713i
$58$	2.68693	−	1.55130i	0.352811	−	0.203696i
$59$		−	12.3151i		−	1.60328i	−0.597805	−	0.801642i	$-0.703960\pi$
$59$		−	12.3151i		−	1.60328i	0.597805	−	0.801642i	$-0.296040\pi$
$60$	−1.97822	+	1.14213i	−0.255387	+	0.147448i
$61$	7.37386	+	12.7719i	0.944126	+	1.63528i	0.757491	+	0.652846i	$0.226425\pi$
$61$	7.37386	+	12.7719i	0.944126	+	1.63528i	0.186636	+	0.982429i	$0.440242\pi$
$62$	1.97822	+	3.42638i	0.251234	+	0.435150i
$63$		0			0
$64$	3.41742			0.427178
$65$	1.18693	+	1.14213i	0.147221	+	0.141663i
$66$	2.50000	+	4.33013i	0.307729	+	0.533002i
$67$	3.87386	+	2.23658i	0.473268	+	0.273241i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	3.87386	+	2.23658i	0.473268	+	0.273241i	−0.244339	+	0.969690i	$0.578571\pi$
$68$	5.37386			0.651677
$69$	2.20871	−	3.82560i	0.265898	−	0.460548i
$70$		0			0
$71$	3.79129	+	2.18890i	0.449943	+	0.259775i	0.707806	−	0.706407i	$-0.249685\pi$
$71$	3.79129	+	2.18890i	0.449943	+	0.259775i	−0.257863	+	0.966181i	$0.583018\pi$
$72$	−7.18693	+	4.14938i	−0.846988	+	0.489009i
$73$	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	$0.268355\pi$
$74$	3.16515			0.367941
$75$	13.3739			1.54428
$76$	−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	$0.0570765\pi$
$80$	1.10436	+	0.637600i	0.123471	+	0.0712859i
$81$	0.208712	−	0.361500i	0.0231902	−	0.0401667i
$82$	−1.79129	−	3.10260i	−0.197815	−	0.342625i
$83$			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
$87$	−18.9564			−2.03234
$88$	3.39564	−	5.88143i	0.361977	−	0.626962i
$89$		−	16.1407i		−	1.71091i	−0.517880	−	0.855453i	$-0.673279\pi$
$89$		−	16.1407i		−	1.71091i	0.517880	−	0.855453i	$-0.326721\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−2.83485			−0.295553
$93$		−	24.1733i		−	2.50665i
$94$	−2.18693	+	3.78788i	−0.225565	+	0.390690i
$95$	−0.626136			−0.0642402
$96$	11.4564	+	6.61438i	1.16927	+	0.675077i
$97$	−6.31307	−	3.64485i	−0.640995	−	0.370079i	0.144003	−	0.989577i	$-0.454003\pi$
$97$	−6.31307	−	3.64485i	−0.640995	−	0.370079i	−0.784998	+	0.619499i	$0.787336\pi$
$98$		0			0
$99$		−	18.7864i		−	1.88811i
$100$	−4.29129	−	7.43273i	−0.429129	−	0.743273i
$101$	−2.60436	+	4.51088i	−0.259143	+	0.448849i	−0.966013	−	0.258495i	$-0.916773\pi$
$101$	−2.60436	+	4.51088i	−0.259143	+	0.448849i	0.706869	+	0.707344i	$0.250107\pi$
$102$	3.31307	+	1.91280i	0.328043	+	0.189396i
$103$	−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
$107$	−5.20871			−0.503545			−0.251773	−	0.967786i	$-0.581014\pi$
$107$	−5.20871			−0.503545			−0.251773	+	0.967786i	$0.581014\pi$
$108$	8.95644			0.861834
$109$	6.87386	−	3.96863i	0.658397	−	0.380126i	−0.133269	−	0.991080i	$-0.542547\pi$
$109$	6.87386	−	3.96863i	0.658397	−	0.380126i	0.791666	+	0.610954i	$0.209214\pi$
$110$	0.708712	−	0.409175i	0.0675731	−	0.0390133i
$111$	−16.7477	−	9.66930i	−1.58962	−	0.917770i
$112$		0			0
$113$	−5.29129	+	9.16478i	−0.497762	+	0.862150i	−0.999997	−	0.00258173i	$-0.999178\pi$
$113$	−5.29129	+	9.16478i	−0.497762	+	0.862150i	0.502234	+	0.864732i	$0.332512\pi$
$114$	−1.74773			−0.163690
$115$	−0.626136	−	0.361500i	−0.0583875	−	0.0337101i
$116$	6.08258	+	10.5353i	0.564753	+	0.978181i
$117$	−4.79129	−	16.5975i	−0.442955	−	1.53444i
$118$	−5.62614			−0.517928
$119$		0			0
$120$	1.10436	+	1.91280i	0.100813	+	0.174614i
$121$	2.18693	+	3.78788i	0.198812	+	0.344352i
$122$	5.83485	−	3.36875i	0.528262	−	0.304992i
$123$			21.8890i			1.97367i
$124$	−13.4347	+	7.75650i	−1.20647	+	0.696555i
$125$		−	4.47315i		−	0.400091i
$126$		0			0
$127$	−3.47822	−	6.02445i	−0.308642	−	0.534584i	0.669423	−	0.742881i	$-0.266541\pi$
$127$	−3.47822	−	6.02445i	−0.308642	−	0.534584i	−0.978066	+	0.208297i	$0.933208\pi$
$128$		−	11.0399i		−	0.975795i
$129$	−13.0826	−	22.6597i	−1.15186	−	1.99507i
$130$	0.521780	−	0.542250i	0.0457632	−	0.0475585i
$131$	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
$136$		−	5.19615i		−	0.445566i
$137$		−	11.9536i		−	1.02126i	−0.859800	−	0.510631i	$-0.829412\pi$
$137$		−	11.9536i		−	1.02126i	0.859800	−	0.510631i	$-0.170588\pi$
$138$	−1.74773	−	1.00905i	−0.148776	−	0.0858961i
$139$	−1.89564	+	3.28335i	−0.160786	+	0.278490i	−0.935151	−	0.354249i	$-0.884736\pi$
$139$	−1.89564	+	3.28335i	−0.160786	+	0.278490i	0.774365	+	0.632740i	$0.218070\pi$
$140$		0			0
$141$	23.1434	−	13.3618i	1.94902	−	1.12527i
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	10.1869	+	9.80238i	0.851874	+	0.819716i
$144$	−6.68693	−	11.5821i	−0.557244	−	0.965175i
$145$			3.10260i			0.257657i
$146$	−0.791288	−	1.37055i	−0.0654874	−	0.113428i
$147$		0			0
$148$			12.4104i			1.02013i
$149$	0.395644	−	0.228425i	0.0324124	−	0.0187133i	−0.483706	−	0.875230i	$-0.660710\pi$
$149$	0.395644	−	0.228425i	0.0324124	−	0.0187133i	0.516119	+	0.856517i	$0.327376\pi$
$150$		−	6.10985i		−	0.498867i
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	−0.00768132	−	0.999970i	$-0.502445\pi$
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	0.862159	+	0.506637i	$0.169112\pi$
$152$	1.18693	+	2.05583i	0.0962729	+	0.166750i
$153$	−7.18693	−	12.4481i	−0.581029	−	1.00637i
$154$		0			0
$155$	−3.95644			−0.317789
$156$	−12.5000	+	12.9904i	−1.00080	+	1.04006i
$157$	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	$0.821182\pi$
$158$	−2.37386	−	1.37055i	−0.188854	−	0.109035i
$159$	17.2087			1.36474
$160$	1.08258	−	1.87508i	0.0855851	−	0.148238i
$161$		0			0
$162$	−0.165151	−	0.0953502i	−0.0129755	−	0.00749142i
$163$	−6.00000	+	3.46410i	−0.469956	+	0.271329i	−0.716221	−	0.697873i	$-0.754130\pi$
$163$	−6.00000	+	3.46410i	−0.469956	+	0.271329i	0.246265	+	0.969202i	$0.420797\pi$
$164$	12.1652	−	7.02355i	0.949939	−	0.548447i
$165$	−5.00000			−0.389249
$166$	3.20871			0.249044
$167$	12.7087	−	7.33738i	0.983430	−	0.567783i	0.0801258	−	0.996785i	$-0.474468\pi$
$167$	12.7087	−	7.33738i	0.983430	−	0.567783i	0.903304	+	0.429001i	$0.141134\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	0.313068	−	0.542250i	0.0240112	−	0.0415887i
$171$	5.68693	+	3.28335i	0.434891	+	0.251084i
$172$	−8.39564	+	14.5417i	−0.640162	+	1.10879i
$173$	−9.87386	−	17.1020i	−0.750696	−	1.30024i	−0.947486	−	0.319798i	$-0.896385\pi$
$173$	−9.87386	−	17.1020i	−0.750696	−	1.30024i	0.196790	−	0.980446i	$-0.436948\pi$
$174$			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
$178$	−7.37386			−0.552694
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$		−	3.92095i		−	0.292250i
$181$	−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
$184$			2.74110i			0.202077i
$185$	−1.58258	+	2.74110i	−0.116353	+	0.201530i
$186$	−11.0436			−0.809753
$187$	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
$191$	7.18693	+	12.4481i	0.520028	+	0.900715i	0.999729	+	0.0232830i	$0.00741188\pi$
$191$	7.18693	+	12.4481i	0.520028	+	0.900715i	−0.479701	+	0.877432i	$0.659255\pi$
$192$	−4.76951	+	8.26103i	−0.344210	+	0.596188i
$193$	−16.7477	−	9.66930i	−1.20553	−	0.696012i	−0.243749	−	0.969838i	$-0.578377\pi$
$193$	−16.7477	−	9.66930i	−1.20553	−	0.696012i	−0.961779	+	0.273827i	$0.911711\pi$
$194$	−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	−0.427871	−	0.903840i	$-0.640736\pi$
$197$	1.97822	−	1.14213i	0.140942	−	0.0813731i	0.568813	+	0.822467i	$0.307403\pi$
$198$	−8.58258			−0.609937
$199$	−11.0000			−0.779769			−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000			−0.779769			−0.389885	+	0.920864i	$0.627485\pi$
$200$	−7.18693	+	4.14938i	−0.508193	+	0.293405i
$201$	−10.8131	+	6.24293i	−0.762695	+	0.440342i
$202$	2.06080	+	1.18980i	0.144997	+	0.0837141i
$203$		0			0
$204$	−7.50000	+	12.9904i	−0.525105	+	0.909509i
$205$	3.58258			0.250218
$206$	1.81307	+	1.04678i	0.126322	+	0.0729323i
$207$	3.79129	+	6.56670i	0.263513	+	0.456417i
$208$	9.76951	+	2.41733i	0.677393	+	0.167611i
$209$	−5.37386			−0.371718
$210$		0			0
$211$	−5.29129	−	9.16478i	−0.364267	−	0.630929i	0.624391	−	0.781112i	$-0.285347\pi$
$211$	−5.29129	−	9.16478i	−0.364267	−	0.630929i	−0.988658	+	0.150183i	$0.952014\pi$
$212$	−5.52178	−	9.56400i	−0.379237	−	0.656859i
$213$	−10.5826	+	6.10985i	−0.725106	+	0.418640i
$214$			2.37960i			0.162666i
$215$	−3.70871	+	2.14123i	−0.252932	+	0.146030i
$216$		−	8.66025i		−	0.589256i
$217$		0			0
$218$	−1.81307	−	3.14033i	−0.122796	−	0.212690i
$219$			9.66930i			0.653391i
$220$	1.60436	+	2.77883i	0.108166	+	0.187348i
$221$	10.5000	+	2.59808i	0.706306	+	0.174766i
$222$	−4.41742	+	7.65120i	−0.296478	+	0.513515i
$223$	16.4347	−	9.48855i	1.10055	−	0.635401i	0.164182	−	0.986430i	$-0.447502\pi$
$223$	16.4347	−	9.48855i	1.10055	−	0.635401i	0.936364	+	0.351029i	$0.114168\pi$
$224$		0			0
$225$	−11.4782	+	19.8809i	−0.765215	+	1.32539i
$226$	4.18693	+	2.41733i	0.278511	+	0.160798i
$227$			8.85095i			0.587458i	0.955889	+	0.293729i	$0.0948964\pi$
$227$			8.85095i			0.587458i	−0.955889	+	0.293729i	$0.905104\pi$
$228$		−	6.85275i		−	0.453835i
$229$	−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	$0.991602\pi$
$234$	−7.58258	+	2.18890i	−0.495688	+	0.143093i
$235$	−2.18693	−	3.78788i	−0.142660	−	0.247094i
$236$		−	22.0598i		−	1.43597i
$237$	8.37386	+	14.5040i	0.543941	+	0.942133i
$238$		0			0
$239$		−	13.2288i		−	0.855697i	−0.903850	−	0.427849i	$-0.859272\pi$
$239$		−	13.2288i		−	0.855697i	0.903850	−	0.427849i	$-0.140728\pi$
$240$	−3.08258	+	1.77973i	−0.198979	+	0.114881i
$241$		−	19.7001i		−	1.26900i	−0.772925	−	0.634498i	$-0.781207\pi$
$241$		−	19.7001i		−	1.26900i	0.772925	−	0.634498i	$-0.218793\pi$
$242$	1.73049	−	0.999100i	0.111240	−	0.0642246i
$243$	8.08258	+	13.9994i	0.518497	+	0.898064i
$244$	13.2087	+	22.8782i	0.845601	+	1.46462i
$245$		0			0
$246$	10.0000			0.637577
$247$	−4.74773	+	1.37055i	−0.302091	+	0.0872061i
$248$	7.50000	+	12.9904i	0.476250	+	0.824890i
$249$	−16.9782	−	9.80238i	−1.07595	−	0.621201i
$250$	−2.04356			−0.129246
$251$	−1.41742	+	2.45505i	−0.0894670	+	0.154961i	−0.907286	−	0.420514i	$-0.861850\pi$
$251$	−1.41742	+	2.45505i	−0.0894670	+	0.154961i	0.817819	+	0.575476i	$0.195183\pi$
$252$		0			0
$253$	−5.37386	−	3.10260i	−0.337852	−	0.195059i
$254$	−2.75227	+	1.58903i	−0.172693	+	0.0997043i
$255$	−3.31307	+	1.91280i	−0.207472	+	0.119784i
$256$	1.79129			0.111955
$257$	−5.04356			−0.314609			−0.157304	−	0.987550i	$-0.550280\pi$
$257$	−5.04356			−0.314609			−0.157304	+	0.987550i	$0.550280\pi$
$258$	−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
$262$	−6.87386	−	3.96863i	−0.424669	−	0.245183i
$263$	−4.66515	+	8.08028i	−0.287666	+	0.498251i	−0.973252	−	0.229740i	$-0.926212\pi$
$263$	−4.66515	+	8.08028i	−0.287666	+	0.498251i	0.685587	+	0.727991i	$0.259546\pi$
$264$	9.47822	+	16.4168i	0.583344	+	1.01038i
$265$		−	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
$269$	15.7913			0.962812			0.481406	−	0.876498i	$-0.340126\pi$
$269$	15.7913			0.962812			0.481406	+	0.876498i	$0.340126\pi$
$270$	0.521780	−	0.903750i	0.0317545	−	0.0550005i
$271$			12.8474i			0.780421i	0.920726	+	0.390211i	$0.127598\pi$
$271$			12.8474i			0.780421i	−0.920726	+	0.390211i	$0.872402\pi$
$272$	8.37386			0.507740
$273$		0			0
$274$	−5.46099			−0.329910
$275$		−	18.7864i		−	1.13286i
$276$	3.95644	−	6.85275i	0.238150	−	0.412487i
$277$	11.7477			0.705853			0.352926	−	0.935651i	$-0.385187\pi$
$277$	11.7477			0.705853			0.352926	+	0.935651i	$0.385187\pi$
$278$	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	$-0.632936\pi$
$281$		−	30.6446i		−	1.82810i	0.405597	−	0.914052i	$-0.367064\pi$
$282$	−6.10436	−	10.5731i	−0.363509	−	0.629616i
$283$	1.37386	−	2.37960i	0.0816677	−	0.141453i	−0.822299	−	0.569056i	$-0.807309\pi$
$283$	1.37386	−	2.37960i	0.0816677	−	0.141453i	0.903966	+	0.427603i	$0.140642\pi$
$284$	6.79129	+	3.92095i	0.402989	+	0.232666i
$285$	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
$289$	−8.00000			−0.470588
$290$	1.41742			0.0832340
$291$	17.6216	−	10.1738i	1.03300	−	0.596400i
$292$	5.37386	−	3.10260i	0.314482	−	0.181566i
$293$	−2.20871	−	1.27520i	−0.129034	−	0.0744980i	0.434093	−	0.900868i	$-0.357069\pi$
$293$	−2.20871	−	1.27520i	−0.129034	−	0.0744980i	−0.563128	+	0.826370i	$0.690402\pi$
$294$		0			0
$295$	2.81307	−	4.87238i	0.163783	−	0.283681i
$296$	12.0000			0.697486
$297$	16.9782	+	9.80238i	0.985176	+	0.568792i
$298$	−0.104356	−	0.180750i	−0.00604519	−	0.0104706i
$299$	−5.53901	−	1.37055i	−0.320330	−	0.0792610i
$300$	23.9564			1.38313
$301$		0			0
$302$	−2.76951	−	4.79693i	−0.159367	−	0.276032i
$303$	−7.26951	−	12.5912i	−0.417622	−	0.723343i
$304$	−3.31307	+	1.91280i	−0.190017	+	0.109707i
$305$			6.73750i			0.385788i
$306$	−5.68693	+	3.28335i	−0.325100	+	0.187697i
$307$			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
$310$			1.80750i			0.102659i
$311$	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	$0.562208\pi$
$312$	12.5608	+	12.0866i	0.711115	+	0.684271i
$313$	−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	−0.0233679	−	0.999727i	$-0.507439\pi$
$317$	−16.0390	−	9.26013i	−0.900841	−	0.520101i	−0.877473	+	0.479626i	$0.840772\pi$
$318$		−	7.86180i		−	0.440868i
$319$			26.6283i			1.49090i
$320$	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
$325$	−4.79129	−	16.5975i	−0.265773	−	0.920664i
$326$	1.58258	+	2.74110i	0.0876508	+	0.151816i
$327$			22.1552i			1.22518i
$328$	−6.79129	−	11.7629i	−0.374986	−	0.649495i
$329$		0			0
$330$			2.28425i			0.125744i
$331$	−21.5608	+	12.4481i	−1.18509	+	0.684211i	−0.957186	−	0.289473i	$-0.906520\pi$
$331$	−21.5608	+	12.4481i	−1.18509	+	0.684211i	−0.227902	+	0.973684i	$0.573187\pi$
$332$			12.5812i			0.690483i
$333$	28.7477	−	16.5975i	1.57537	−	0.909538i
$334$	−3.35208	−	5.80598i	−0.183418	−	0.317689i
$335$	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	$0.412586\pi$
$338$	2.76951	−	5.25378i	0.150641	−	0.285768i
$339$	−14.7695	−	25.5815i	−0.802170	−	1.38940i
$340$	2.12614	+	1.22753i	0.115306	+	0.0665719i
$341$	−33.9564			−1.83884
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$		0			0
$344$	14.0608	+	8.11800i	0.758107	+	0.437693i
$345$	1.74773	−	1.00905i	0.0940945	−	0.0543255i
$346$	−7.81307	+	4.51088i	−0.420033	+	0.242506i
$347$	−13.5826			−0.729151			−0.364575	−	0.931174i	$-0.618786\pi$
$347$	−13.5826			−0.729151			−0.364575	+	0.931174i	$0.618786\pi$
$348$	−33.9564			−1.82026
$349$	18.2477	−	10.5353i	0.976778	−	0.563943i	0.0754825	−	0.997147i	$-0.475950\pi$
$349$	18.2477	−	10.5353i	0.976778	−	0.563943i	0.901296	+	0.433204i	$0.142617\pi$
$350$		0			0
$351$	17.5000	+	4.33013i	0.934081	+	0.231125i
$352$	9.29129	−	16.0930i	0.495227	−	0.857759i
$353$	15.7259	+	9.07938i	0.837008	+	0.483247i	0.856246	−	0.516568i	$-0.172791\pi$
$353$	15.7259	+	9.07938i	0.837008	+	0.483247i	−0.0192383	+	0.999815i	$0.506124\pi$
$354$	7.85208	−	13.6002i	0.417334	−	0.722843i
$355$	1.00000	+	1.73205i	0.0530745	+	0.0919277i
$356$		−	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	0.487327	−	0.873219i	$-0.337972\pi$
$359$	−0.478220	−	0.276100i	−0.0252395	−	0.0145720i	−0.512567	+	0.858647i	$0.671305\pi$
$360$	−3.79129			−0.199818
$361$	−8.56080	+	14.8277i	−0.450568	+	0.780407i
$362$			4.18710i			0.220069i
$363$	−12.2087			−0.640791
$364$		0			0
$365$	1.58258			0.0828358
$366$			18.8063i			0.983022i
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	−0.999404	−	0.0345320i	$-0.989006\pi$
$367$	−9.00000	+	15.5885i	−0.469796	+	0.813711i	0.529607	+	0.848243i	$0.322339\pi$
$368$	−4.41742			−0.230274
$369$	−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
$373$	−16.1044	−	27.8936i	−0.833852	−	1.44427i	−0.894962	−	0.446143i	$-0.852797\pi$
$373$	−16.1044	−	27.8936i	−0.833852	−	1.44427i	0.0611098	−	0.998131i	$-0.480536\pi$
$374$	2.68693	−	4.65390i	0.138938	−	0.240648i
$375$	10.8131	+	6.24293i	0.558384	+	0.322383i
$376$	−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	−0.973385	−	0.229178i	$-0.926396\pi$
$379$	−24.5608	+	14.1802i	−1.26160	+	0.728387i	−0.288219	+	0.957565i	$0.593063\pi$
$380$	−1.12159			−0.0575364
$381$	19.4174			0.994785
$382$	5.68693	−	3.28335i	0.290969	−	0.167991i
$383$	1.10436	−	0.637600i	0.0564300	−	0.0325799i	−0.471520	−	0.881856i	$-0.656294\pi$
$383$	1.10436	−	0.637600i	0.0564300	−	0.0325799i	0.527950	+	0.849276i	$0.322961\pi$
$384$	26.6869	+	15.4077i	1.36186	+	0.786271i
$385$		0			0
$386$	−4.41742	+	7.65120i	−0.224841	+	0.389436i
$387$	44.9129			2.28305
$388$	−11.3085	−	6.52898i	−0.574103	−	0.331459i
$389$	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	$0.830668\pi$
$390$	0.582576	+	2.01810i	0.0294999	+	0.102191i
$391$	−4.74773			−0.240103
$392$		0			0
$393$	24.2477	+	41.9983i	1.22314	+	2.11853i
$394$	−0.521780	−	0.903750i	−0.0262869	−	0.0455303i
$395$	2.37386	−	1.37055i	0.119442	−	0.0689599i
$396$		−	33.6519i		−	1.69107i
$397$	28.1216	−	16.2360i	1.41138	−	0.814862i	0.415864	−	0.909427i	$-0.363479\pi$
$397$	28.1216	−	16.2360i	1.41138	−	0.814862i	0.995519	+	0.0945652i	$0.0301461\pi$
$398$			5.02535i			0.251898i
$399$		0			0
$400$	−6.68693	−	11.5821i	−0.334347	−	0.579105i
$401$			31.2922i			1.56266i	0.624121	+	0.781328i	$0.285457\pi$
$401$			31.2922i			1.56266i	−0.624121	+	0.781328i	$0.714543\pi$
$402$	2.85208	+	4.93995i	0.142249	+	0.246382i
$403$	−30.0000	+	8.66025i	−1.49441	+	0.431398i
$404$	−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
$409$			8.29875i			0.410347i	0.978726	+	0.205173i	$0.0657759\pi$
$409$			8.29875i			0.410347i	−0.978726	+	0.205173i	$0.934224\pi$
$410$		−	1.63670i		−	0.0808309i
$411$	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
$416$	4.10436	−	16.5876i	0.201233	−	0.813272i
$417$	−5.29129	−	9.16478i	−0.259115	−	0.448801i
$418$			2.45505i			0.120080i
$419$	−0.873864	−	1.51358i	−0.0426910	−	0.0739430i	0.843890	−	0.536516i	$-0.180260\pi$
$419$	−0.873864	−	1.51358i	−0.0426910	−	0.0739430i	−0.886581	+	0.462573i	$0.846926\pi$
$420$		0			0
$421$		−	4.18710i		−	0.204067i	−0.994781	−	0.102033i	$-0.967465\pi$
$421$		−	4.18710i		−	0.204067i	0.994781	−	0.102033i	$-0.0325349\pi$
$422$	−4.18693	+	2.41733i	−0.203817	+	0.117674i
$423$			45.8716i			2.23035i
$424$	−9.24773	+	5.33918i	−0.449109	+	0.259293i
$425$	−7.18693	−	12.4481i	−0.348617	−	0.603823i
$426$	2.79129	+	4.83465i	0.135238	+	0.234240i
$427$		0			0
$428$	−9.33030			−0.450997
$429$	−37.9129	+	10.9445i	−1.83045	+	0.528406i
$430$	0.978220	+	1.69433i	0.0471739	+	0.0817077i
$431$	−30.0172	−	17.3305i	−1.44588	−	0.834779i	−0.447647	−	0.894210i	$-0.647738\pi$
$431$	−30.0172	−	17.3305i	−1.44588	−	0.834779i	−0.998232	+	0.0594316i	$0.981071\pi$
$432$	13.9564			0.671479
$433$	−16.2477	+	28.1419i	−0.780816	+	1.35241i	0.150651	+	0.988587i	$0.451863\pi$
$433$	−16.2477	+	28.1419i	−0.780816	+	1.35241i	−0.931467	+	0.363826i	$0.881470\pi$
$434$		0			0
$435$	−7.50000	−	4.33013i	−0.359597	−	0.207614i
$436$	12.3131	−	7.10895i	0.589689	−	0.340457i
$437$	1.87841	−	1.08450i	0.0898565	−	0.0518787i
$438$	4.41742			0.211073
$439$	20.5390			0.980274			0.490137	−	0.871645i	$-0.336947\pi$
$439$	20.5390			0.980274			0.490137	+	0.871645i	$0.336947\pi$
$440$	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	$0.0493550\pi$
$444$	−30.0000	−	17.3205i	−1.42374	−	0.821995i
$445$	3.68693	−	6.38595i	0.174777	−	0.302723i
$446$	−4.33485	−	7.50818i	−0.205261	−	0.355523i
$447$			1.27520i			0.0603149i
$448$		0			0
$449$	−21.7913	−	12.5812i	−1.02839	−	0.593744i	−0.111870	−	0.993723i	$-0.535684\pi$
$449$	−21.7913	−	12.5812i	−1.02839	−	0.593744i	−0.916524	+	0.399979i	$0.869017\pi$
$450$	9.08258	+	5.24383i	0.428157	+	0.247196i
$451$	30.7477			1.44785
$452$	−9.47822	+	16.4168i	−0.445818	+	0.772179i
$453$			33.8426i			1.59006i
$454$	4.04356			0.189774
$455$		0			0
$456$	−6.62614			−0.310297
$457$			22.8027i			1.06667i	0.845905	+	0.533333i	$0.179061\pi$
$457$			22.8027i			1.06667i	−0.845905	+	0.533333i	$0.820939\pi$
$458$	−1.58258	+	2.74110i	−0.0739489	+	0.128083i
$459$	15.0000			0.700140
$460$	−1.12159	−	0.647551i	−0.0522944	−	0.0301922i
$461$	−4.02178	−	2.32198i	−0.187313	−	0.108145i	0.403411	−	0.915019i	$-0.367824\pi$
$461$	−4.02178	−	2.32198i	−0.187313	−	0.108145i	−0.590724	+	0.806874i	$0.701158\pi$
$462$		0			0
$463$		−	7.93725i		−	0.368875i	−0.982844	−	0.184438i	$-0.940954\pi$
$463$		−	7.93725i		−	0.368875i	0.982844	−	0.184438i	$-0.0590464\pi$
$464$	9.47822	+	16.4168i	0.440015	+	0.762129i
$465$	5.52178	−	9.56400i	0.256066	−	0.443520i
$466$	6.31307	+	3.64485i	0.292447	+	0.168844i
$467$	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
$471$	−2.66970			−0.123013
$472$	−21.3303			−0.981807
$473$	−31.8303	+	18.3772i	−1.46356	+	0.844986i
$474$	6.62614	−	3.82560i	0.304349	−	0.175716i
$475$	5.68693	+	3.28335i	0.260934	+	0.150651i
$476$		0			0
$477$	−14.7695	+	25.5815i	−0.676249	+	1.17130i
$478$	−6.04356			−0.276426
$479$	−16.3521	−	9.44088i	−0.747146	−	0.431365i	0.0775159	−	0.996991i	$-0.475301\pi$
$479$	−16.3521	−	9.44088i	−0.747146	−	0.431365i	−0.824662	+	0.565626i	$0.808634\pi$
$480$	3.02178	+	5.23388i	0.137925	+	0.238893i
$481$	−6.00000	+	24.2487i	−0.273576	+	1.10565i
$482$	−9.00000			−0.409939
$483$		0			0
$484$	3.91742	+	6.78518i	0.178065	+	0.308417i
$485$	−1.66515	−	2.88413i	−0.0756106	−	0.130961i
$486$	6.39564	−	3.69253i	0.290112	−	0.167496i
$487$		−	29.3694i		−	1.33086i	−0.746462	−	0.665428i	$-0.768249\pi$
$487$		−	29.3694i		−	1.33086i	0.746462	−	0.665428i	$-0.231751\pi$
$488$	22.1216	−	12.7719i	1.00140	−	0.578157i
$489$		−	19.3386i		−	0.874522i
$490$		0			0
$491$	2.06080	+	3.56940i	0.0930024	+	0.161085i	0.908773	−	0.417291i	$-0.137020\pi$
$491$	2.06080	+	3.56940i	0.0930024	+	0.161085i	−0.815771	+	0.578375i	$0.803687\pi$
$492$			39.2095i			1.76770i
$493$	10.1869	+	17.6443i	0.458796	+	0.794659i
$494$	0.626136	+	2.16900i	0.0281712	+	0.0975879i
$495$	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	0.812369	−	0.583143i	$-0.198177\pi$
$499$	15.9392	+	9.20250i	0.713537	+	0.411961i	−0.0988324	+	0.995104i	$0.531511\pi$
$500$		−	8.01270i		−	0.358339i
$501$			40.9615i			1.83002i
$502$	1.12159	+	0.647551i	0.0500590	+	0.0289016i
$503$	9.56080	−	16.5598i	0.426295	−	0.738364i	−0.570246	−	0.821474i	$-0.693152\pi$
$503$	9.56080	−	16.5598i	0.426295	−	0.738364i	0.996540	+	0.0831100i	$0.0264853\pi$
$504$		0			0
$505$	−2.06080	+	1.18980i	−0.0917042	+	0.0529454i
$506$	−1.41742	+	2.45505i	−0.0630122	+	0.109140i
$507$	−30.7042	+	19.3386i	−1.36362	+	0.858858i
$508$	−6.23049	−	10.7915i	−0.276433	−	0.478797i
$509$			15.0562i			0.667352i	0.942688	+	0.333676i	$0.108289\pi$
$509$			15.0562i			0.667352i	−0.942688	+	0.333676i	$0.891711\pi$
$510$	0.873864	+	1.51358i	0.0386953	+	0.0670223i
$511$		0			0
$512$		−	22.8981i		−	1.01196i
$513$	−5.93466	+	3.42638i	−0.262022	+	0.151278i
$514$			2.30415i			0.101632i
$515$	−1.81307	+	1.04678i	−0.0798933	+	0.0461264i
$516$	−23.4347	−	40.5900i	−1.03165	−	1.78688i
$517$	−18.7695	−	32.5097i	−0.825482	−	1.42978i
$518$		0			0
$519$	55.1216			2.41957
$520$	1.97822	−	2.05583i	0.0867507	−	0.0901539i
$521$	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	$0.716236\pi$
$522$	−12.8739	−	7.43273i	−0.563474	−	0.325322i
$523$	−24.3303			−1.06389			−0.531945	−	0.846779i	$-0.678539\pi$
$523$	−24.3303			−1.06389			−0.531945	+	0.846779i	$0.678539\pi$
$524$	15.5608	−	26.9521i	0.679776	−	1.17741i
$525$		0			0
$526$	3.69148	+	2.13128i	0.160956	+	0.0929280i
$527$	−22.5000	+	12.9904i	−0.980115	+	0.565870i
$528$	−26.4564	+	15.2746i	−1.15137	+	0.664743i
$529$	−20.4955			−0.891107
$530$	−1.28674			−0.0558925
$531$	−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
$535$	−2.06080	−	1.18980i	−0.0890960	−	0.0514396i
$536$	3.87386	−	6.70973i	0.167325	−	0.289816i
$537$	12.5608	+	21.7559i	0.542038	+	0.938838i
$538$		−	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	0.612347	−	0.790589i	$-0.290226\pi$
$541$	5.43920	+	3.14033i	0.233850	+	0.135013i	−0.378497	+	0.925602i	$0.623559\pi$
$542$	5.86932			0.252109
$543$	12.7913	−	22.1552i	0.548927	−	0.950769i
$544$		−	14.2179i		−	0.609588i
$545$	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	$0.580808\pi$
$548$		−	21.4123i		−	0.914686i
$549$	35.3303	−	61.1939i	1.50786	−	2.61169i
$550$	−8.58258			−0.365962
$551$	−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
$555$	−4.41742	−	7.65120i	−0.187509	−	0.324775i
$556$	−3.39564	+	5.88143i	−0.144007	+	0.249428i
$557$	28.5998	+	16.5121i	1.21181	+	0.699640i	0.963154	−	0.268951i	$-0.0866769\pi$
$557$	28.5998	+	16.5121i	1.21181	+	0.699640i	0.248659	+	0.968591i	$0.420010\pi$
$558$	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
$562$	−14.0000			−0.590554
$563$	−36.3303			−1.53114			−0.765570	−	0.643353i	$-0.777543\pi$
$563$	−36.3303			−1.53114			−0.765570	+	0.643353i	$0.777543\pi$
$564$	41.4564	−	23.9349i	1.74563	−	1.00784i
$565$	−4.18693	+	2.41733i	−0.176146	+	0.101698i
$566$	−1.08712	−	0.627650i	−0.0456951	−	0.0263821i
$567$		0			0
$568$	3.79129	−	6.56670i	0.159079	−	0.275533i
$569$	16.7477			0.702101			0.351051	−	0.936356i	$-0.385825\pi$
$569$	16.7477			0.702101			0.351051	+	0.936356i	$0.385825\pi$
$570$	−0.691478	−	0.399225i	−0.0289628	−	0.0167217i
$571$	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	$0.819718\pi$
$572$	18.2477	+	17.5589i	0.762976	+	0.734174i
$573$	−40.1216			−1.67610
$574$		0			0
$575$	3.79129	+	6.56670i	0.158108	+	0.273850i
$576$	−8.18693	−	14.1802i	−0.341122	−	0.590841i
$577$	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	$0.0671795\pi$
$578$			3.65480i			0.152020i
$579$	46.7477	−	26.9898i	1.94277	−	1.12166i
$580$			5.55765i			0.230769i
$581$		0			0
$582$	−4.64792	−	8.05043i	−0.192662	−	0.333701i
$583$		−	24.1733i		−	1.00115i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$	1.89564	−	7.66115i	0.0783752	−	0.316750i
$586$	−0.582576	+	1.00905i	−0.0240660	+	0.0416835i
$587$	8.22595	−	4.74925i	0.339521	−	0.196023i	−0.320539	−	0.947235i	$-0.603864\pi$
$587$	8.22595	−	4.74925i	0.339521	−	0.196023i	0.660060	+	0.751213i	$0.270531\pi$
$588$		0			0
$589$	5.93466	−	10.2791i	0.244533	−	0.423544i
$590$	−2.22595	−	1.28515i	−0.0916408	−	0.0529088i
$591$			6.37600i			0.262274i
$592$			19.3386i			0.794812i
$593$	−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
$598$	−0.626136	+	2.53050i	−0.0256046	+	0.103480i
$599$	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	$0.790112\pi$
$600$		−	23.1642i		−	0.945675i
$601$	−6.18693	−	10.7161i	−0.252370	−	0.437118i	0.711808	−	0.702374i	$-0.247877\pi$
$601$	−6.18693	−	10.7161i	−0.252370	−	0.437118i	−0.964178	+	0.265256i	$0.914543\pi$
$602$		0			0
$603$		−	21.4322i		−	0.872785i
$604$	18.8085	−	10.8591i	0.765308	−	0.441851i
$605$			1.99820i			0.0812384i
$606$	−5.75227	+	3.32108i	−0.233670	+	0.134910i
$607$	−9.87386	−	17.1020i	−0.400768	−	0.694150i	0.593051	−	0.805165i	$-0.297923\pi$
$607$	−9.87386	−	17.1020i	−0.400768	−	0.694150i	−0.993819	+	0.111015i	$0.964590\pi$
$608$	3.24773	+	5.62523i	0.131713	+	0.228133i
$609$		0			0
$610$	3.07803			0.124626
$611$	−24.8739	−	23.9349i	−1.00629	−	0.968302i
$612$	−12.8739	−	22.2982i	−0.520395	−	0.901351i
$613$	15.8085	+	9.12705i	0.638500	+	0.368638i	0.784037	−	0.620715i	$-0.213157\pi$
$613$	15.8085	+	9.12705i	0.638500	+	0.368638i	−0.145536	+	0.989353i	$0.546491\pi$
$614$	7.08712			0.286013
$615$	−5.00000	+	8.66025i	−0.201619	+	0.349215i
$616$		0			0
$617$	−14.9174	−	8.61258i	−0.600553	−	0.346729i	0.168706	−	0.985666i	$-0.446041\pi$
$617$	−14.9174	−	8.61258i	−0.600553	−	0.346729i	−0.769259	+	0.638937i	$0.779374\pi$
$618$	−5.06080	+	2.92185i	−0.203575	+	0.117534i
$619$	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	$0.206278\pi$
$620$	−7.08712			−0.284626
$621$	−7.91288			−0.317533
$622$	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
$626$	2.66970	+	1.54135i	0.106703	+	0.0616048i
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$	0.856629	+	1.48372i	0.0341832	+	0.0592071i
$629$			20.7846i			0.828737i
$630$		0			0
$631$	23.9347	+	13.8187i	0.952824	+	0.550113i	0.893957	−	0.448153i	$-0.147918\pi$
$631$	23.9347	+	13.8187i	0.952824	+	0.550113i	0.0588668	+	0.998266i	$0.481251\pi$
$632$	−9.00000	−	5.19615i	−0.358001	−	0.206692i
$633$	29.5390			1.17407
$634$	−4.23049	+	7.32743i	−0.168014	+	0.291009i
$635$		−	3.17805i		−	0.126117i
$636$	30.8258			1.22232
$637$		0			0
$638$	12.1652			0.481623
$639$		−	20.9753i		−	0.829770i
$640$	2.52178	−	4.36785i	0.0996821	−	0.172654i
$641$	29.3739			1.16020			0.580099	−	0.814546i	$-0.303014\pi$
$641$	29.3739			1.16020			0.580099	+	0.814546i	$0.303014\pi$
$642$	−5.75227	−	3.32108i	−0.227024	−	0.131072i
$643$	−39.2477	−	22.6597i	−1.54778	−	0.893611i	−0.998311	−	0.0580962i	$-0.981497\pi$
$643$	−39.2477	−	22.6597i	−1.54778	−	0.893611i	−0.549468	−	0.835515i	$-0.685170\pi$
$644$		0			0
$645$		−	11.9536i		−	0.470671i
$646$	0.939205	+	1.62675i	0.0369525	+	0.0640036i
$647$	17.5390	−	30.3785i	0.689530	−	1.19430i	−0.282460	−	0.959279i	$-0.591151\pi$
$647$	17.5390	−	30.3785i	0.689530	−	1.19430i	0.971990	−	0.235022i	$-0.0755161\pi$
$648$	−0.626136	−	0.361500i	−0.0245970	−	0.0142011i
$649$	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
$653$	15.7913			0.617961			0.308980	−	0.951068i	$-0.400012\pi$
$653$	15.7913			0.617961			0.308980	+	0.951068i	$0.400012\pi$
$654$	10.1216			0.395786
$655$	6.87386	−	3.96863i	0.268584	−	0.155067i
$656$	18.9564	−	10.9445i	0.740125	−	0.427311i
$657$	−14.3739	−	8.29875i	−0.560778	−	0.323765i
$658$		0			0
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	−0.918523	−	0.395367i	$-0.870617\pi$
$659$	−3.00000	+	5.19615i	−0.116863	+	0.202413i	0.801660	+	0.597781i	$0.203951\pi$
$660$	−8.95644			−0.348629
$661$	−43.7477	−	25.2578i	−1.70159	−	0.982413i	−0.944155	−	0.329502i	$-0.893119\pi$
$661$	−43.7477	−	25.2578i	−1.70159	−	0.982413i	−0.757434	−	0.652911i	$-0.773547\pi$
$662$	5.68693	+	9.85005i	0.221029	+	0.382833i
$663$	−20.9347	+	21.7559i	−0.813035	+	0.844931i
$664$	12.1652			0.472099
$665$		0			0
$666$	−7.58258	−	13.1334i	−0.293819	−	0.508909i
$667$	−5.37386	−	9.30780i	−0.208077	−	0.360400i
$668$	22.7650	−	13.1434i	0.880803	−	0.508532i
$669$			52.9706i			2.04796i
$670$	0.808522	−	0.466801i	0.0312359	−	0.0180341i
$671$			57.8251i			2.23231i
$672$		0			0
$673$	−13.2477	−	22.9457i	−0.510662	−	0.884493i	−0.999924	−	0.0123559i	$-0.996067\pi$
$673$	−13.2477	−	22.9457i	−0.510662	−	0.884493i	0.489261	−	0.872137i	$-0.337266\pi$
$674$		−	4.54860i		−	0.175206i
$675$	−11.9782	−	20.7469i	−0.461042	−	0.798548i
$676$	20.5998	+	10.8591i	0.792300	+	0.417658i
$677$	−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
$682$			15.5130i			0.594024i
$683$		−	30.3586i		−	1.16164i	−0.814033	−	0.580819i	$-0.802732\pi$
$683$		−	30.3586i		−	1.16164i	0.814033	−	0.580819i	$-0.197268\pi$
$684$	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
$689$	−6.16515	−	21.3567i	−0.234874	−	0.813626i
$690$	−0.460985	−	0.798450i	−0.0175494	−	0.0303965i
$691$			10.3169i			0.392472i	0.980557	+	0.196236i	$0.0628718\pi$
$691$			10.3169i			0.392472i	−0.980557	+	0.196236i	$0.937128\pi$
$692$	−17.6869	−	30.6347i	−0.672356	−	1.16456i
$693$		0			0
$694$			6.20520i			0.235546i
$695$	−1.50000	+	0.866025i	−0.0568982	+	0.0328502i
$696$			32.8335i			1.24455i
$697$	20.3739	−	11.7629i	0.771715	−	0.445550i
$698$	−4.81307	−	8.33648i	−0.182177	−	0.315540i
$699$	−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	$0.584627\pi$
$702$	1.97822	−	7.99488i	0.0746631	−	0.301747i
$703$	−4.74773	−	8.22330i	−0.179064	−	0.310148i
$704$	11.6044	+	6.69978i	0.437356	+	0.252507i
$705$	12.2087			0.459807
$706$	4.14792	−	7.18440i	0.156109	−	0.270389i
$707$		0			0
$708$	53.3258	+	30.7876i	2.00410	+	1.15707i
$709$	13.1869	−	7.61348i	0.495246	−	0.285930i	−0.231502	−	0.972834i	$-0.574364\pi$
$709$	13.1869	−	7.61348i	0.495246	−	0.285930i	0.726748	+	0.686904i	$0.241031\pi$
$710$	0.791288	−	0.456850i	0.0296965	−	0.0171453i
$711$	−28.7477			−1.07812
$712$	−27.9564			−1.04771
$713$	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
$717$	31.9782	+	18.4626i	1.19425	+	0.689500i
$718$	−0.126136	+	0.218475i	−0.00470737	+	0.00815341i
$719$	12.0826	+	20.9276i	0.450604	+	0.780469i	0.998424	−	0.0561274i	$-0.0178753\pi$
$719$	12.0826	+	20.9276i	0.450604	+	0.780469i	−0.547820	+	0.836597i	$0.684542\pi$
$720$		−	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
$724$	−16.4174			−0.610149
$725$	16.2695	−	28.1796i	0.604234	−	1.04656i
$726$			5.57755i			0.207002i
$727$	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
$730$		−	0.723000i		−	0.0267594i
$731$	−14.0608	+	24.3540i	−0.520057	+	0.900766i
$732$	−73.7386			−2.72546
$733$	−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
$737$	8.76951	+	15.1892i	0.323029	+	0.559503i
$738$	−8.58258	+	14.8655i	−0.315929	+	0.547205i
$739$	−16.7477	−	9.66930i	−0.616075	−	0.355691i	0.159264	−	0.987236i	$-0.449088\pi$
$739$	−16.7477	−	9.66930i	−0.616075	−	0.355691i	−0.775339	+	0.631545i	$0.782421\pi$
$740$	−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	0.160219	−	0.987081i	$-0.448780\pi$
$743$	29.8521	−	17.2351i	1.09517	−	0.632295i	0.934947	+	0.354787i	$0.115446\pi$
$744$	−41.8693			−1.53500
$745$	0.208712			0.00764662
$746$	−12.7432	+	7.35728i	−0.466561	+	0.269369i
$747$	29.1434	−	16.8259i	1.06630	−	0.615629i
$748$	18.2477	+	10.5353i	0.667203	+	0.385210i
$749$		0			0
$750$	2.85208	−	4.93995i	0.104143	−	0.180382i
$751$	23.7477			0.866567			0.433283	−	0.901258i	$-0.357355\pi$
$751$	23.7477			0.866567			0.433283	+	0.901258i	$0.357355\pi$
$752$	−23.1434	−	13.3618i	−0.843952	−	0.487256i
$753$	−3.95644	−	6.85275i	−0.144181	−	0.249728i
$754$	10.7477	−	3.10260i	0.391409	−	0.112990i
$755$	5.53901			0.201585
$756$		0			0
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	0.806343	−	0.591448i	$-0.201443\pi$
$757$	−3.00000	−	5.19615i	−0.109037	−	0.188857i	−0.915380	+	0.402590i	$0.868110\pi$
$758$	6.47822	+	11.2206i	0.235300	+	0.407551i
$759$	15.0000	−	8.66025i	0.544466	−	0.314347i
$760$			1.08450i			0.0393390i
$761$	11.2259	−	6.48130i	0.406940	−	0.234947i	−0.282534	−	0.959257i	$-0.591175\pi$
$761$	11.2259	−	6.48130i	0.406940	−	0.234947i	0.689474	+	0.724310i	$0.257842\pi$
$762$		−	8.87086i		−	0.321357i
$763$		0			0
$764$	12.8739	+	22.2982i	0.465760	+	0.806720i
$765$		−	6.56670i		−	0.237420i
$766$	−0.291288	−	0.504525i	−0.0105247	−	0.0182292i
$767$	10.6652	−	43.1027i	0.385096	−	1.55635i
$768$	−2.50000	+	4.33013i	−0.0902110	+	0.156250i
$769$	8.12614	−	4.69163i	0.293036	−	0.169184i	−0.346274	−	0.938133i	$-0.612553\pi$
$769$	8.12614	−	4.69163i	0.293036	−	0.169184i	0.639310	+	0.768949i	$0.279220\pi$
$770$		0			0
$771$	7.03901	−	12.1919i	0.253504	−	0.439082i
$772$	−30.0000	−	17.3205i	−1.07972	−	0.623379i
$773$			19.4340i			0.698991i	0.936938	+	0.349495i

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.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\)	\(q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +(0.104356 - 0.180750i) q^{10} +(3.39564 + 1.96048i) q^{11} +(-2.50000 + 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +2.79129 q^{16} +3.00000 q^{17} +(-1.89564 + 1.09445i) q^{18} +(-1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} -1.58258 q^{23} +(4.18693 + 2.41733i) q^{24} +(-2.39564 - 4.14938i) q^{25} +(0.395644 - 1.59898i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +(-7.50000 + 4.33013i) q^{31} -4.73930i q^{32} +(-9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +6.92820i q^{37} +(0.313068 + 0.542250i) q^{38} +(-6.97822 + 7.25198i) 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} -2.18890i q^{45} +0.723000i 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} +(6.26951 + 1.55130i) q^{52} +(-3.08258 - 5.33918i) q^{53} -2.28425i q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(2.68693 - 1.55130i) q^{58} -12.3151i q^{59} +(-1.97822 + 1.14213i) q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(1.18693 + 1.14213i) q^{65} +(2.50000 + 4.33013i) q^{66} +(3.87386 + 2.23658i) q^{67} +5.37386 q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(-7.18693 + 4.14938i) q^{72} +(3.00000 - 1.73205i) q^{73} +3.16515 q^{74} +13.3739 q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} +(3.00000 - 5.19615i) q^{79} +(1.10436 + 0.637600i) q^{80} +(0.208712 - 0.361500i) q^{81} +(-1.79129 - 3.10260i) q^{82} +7.02355i q^{83} +(1.18693 + 0.685275i) q^{85} +(3.70871 + 2.14123i) q^{86} -18.9564 q^{87} +(3.39564 - 5.88143i) q^{88} -16.1407i q^{89} -1.00000 q^{90} -2.83485 q^{92} -24.1733i q^{93} +(-2.18693 + 3.78788i) q^{94} -0.626136 q^{95} +(11.4564 + 6.61438i) q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9	\( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) \) 4 * q - q^3 - 2 * q^4 - 3 * q^5 + 9 * q^6 - 5 * q^9 + 5 * q^10 + 9 * q^11 - 10 * q^12 + 14 * q^13 - 9 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^18 + 9 * q^19 + 12 * q^20 - q^22 + 12 * q^23 + 3 * q^24 - 5 * q^25 - 3 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 - 30 * q^31 - 15 * q^33 - 8 * q^36 + 15 * q^38 - 5 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 + 6 * q^44 - 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 - 7 * q^52 + 6 * q^53 - q^55 - 3 * q^58 + 15 * q^60 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 9 * q^65 + 10 * q^66 - 12 * q^67 - 6 * q^68 + 18 * q^69 + 6 * q^71 - 15 * q^72 + 12 * q^73 - 24 * q^74 + 26 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 + 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 24 * q^86 - 30 * q^87 + 9 * q^88 - 4 * q^90 - 48 * q^92 + 5 * q^94 - 30 * q^95 - 39 * q^97

Introduction

L-functions

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