LMFDB - Embedded newform 637.2.k.d.459.2

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			459.2
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.459
Dual form			637.2.k.d.569.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.456850i q^{2} +(-1.39564 - 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 - 0.228425i) q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.456850i			0.323042i	0.986869	+	0.161521i	$0.0516399\pi$
$2$			0.456850i			0.323042i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	−0.915766	−	0.401711i	$-0.868416\pi$
$3$	−1.39564	−	2.41733i	−0.805775	−	1.39564i	0.109991	−	0.993933i	$-0.464918\pi$
$4$	1.79129			0.895644
$5$	0.395644	−	0.228425i	0.176937	−	0.102155i	−0.408916	−	0.912572i	$-0.634093\pi$
$5$	0.395644	−	0.228425i	0.176937	−	0.102155i	0.585853	+	0.810417i	$0.300760\pi$
$6$	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	0.108616	−	0.994084i	$-0.465358\pi$
$11$	3.39564	−	1.96048i	1.02383	−	0.591106i	0.915210	+	0.402978i	$0.132025\pi$
$12$	−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	0.357632	−	0.933863i	$-0.383584\pi$
$19$	−1.18693	−	0.685275i	−0.272301	−	0.157213i	−0.629933	+	0.776650i	$0.716918\pi$
$20$	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	−0.356883	−	0.934149i	$-0.616161\pi$
$29$	3.39564	−	5.88143i	0.630555	−	1.09215i	0.987438	−	0.158005i	$-0.0505061\pi$
$30$	0.291288	−	0.504525i	0.0531816	−	0.0921133i
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−7.50000	−	4.33013i	−1.34704	−	0.777714i	−0.987829	+	0.155543i	$0.950287\pi$
$32$			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	$-0.807139\pi$
$37$		−	6.92820i		−	1.13899i	0.821995	−	0.569495i	$-0.192861\pi$
$38$	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	0.925604	−	0.378493i	$-0.123558\pi$
$41$	6.79129	+	3.92095i	1.06062	+	0.612350i	0.135017	+	0.990843i	$0.456891\pi$
$42$		0			0
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	−0.963056	−	0.269302i	$-0.913207\pi$
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	0.248305	−	0.968682i	$-0.420126\pi$
$44$	6.08258	−	3.51178i	0.916983	−	0.529420i
$45$			2.18890i			0.326302i
$46$		−	0.723000i		−	0.106601i
$47$	−8.29129	+	4.78698i	−1.20941	+	0.698252i	−0.962630	−	0.270820i	$-0.912705\pi$
$47$	−8.29129	+	4.78698i	−1.20941	+	0.698252i	−0.246778	+	0.969072i	$0.579372\pi$
$48$	−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	−0.996272	−	0.0862695i	$-0.972505\pi$
$53$	−3.08258	+	5.33918i	−0.423424	+	0.733392i	0.572848	+	0.819662i	$0.305839\pi$
$54$			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	$0.296040\pi$
$59$			12.3151i			1.60328i	−0.597805	+	0.801642i	$0.703960\pi$
$60$	−1.97822	−	1.14213i	−0.255387	−	0.147448i
$61$	7.37386	−	12.7719i	0.944126	−	1.63528i	0.186636	−	0.982429i	$-0.440242\pi$
$61$	7.37386	−	12.7719i	0.944126	−	1.63528i	0.757491	−	0.652846i	$-0.226425\pi$
$62$	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	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	3.87386	−	2.23658i	0.473268	−	0.273241i	0.717607	+	0.696449i	$0.245238\pi$
$68$	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	−0.257863	−	0.966181i	$-0.583018\pi$
$71$	3.79129	−	2.18890i	0.449943	−	0.259775i	0.707806	+	0.706407i	$0.249685\pi$
$72$	−7.18693	−	4.14938i	−0.846988	−	0.489009i
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	0.665180	−	0.746683i	$-0.268355\pi$
$73$	3.00000	+	1.73205i	0.351123	+	0.202721i	−0.314057	+	0.949404i	$0.601688\pi$
$74$	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	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	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	$-0.874040\pi$
$83$		−	7.02355i		−	0.770935i	0.922721	−	0.385468i	$-0.125960\pi$
$84$		0			0
$85$	1.18693	−	0.685275i	0.128741	−	0.0743286i
$86$	3.70871	−	2.14123i	0.399921	−	0.230894i
$87$	−18.9564			−2.03234
$88$	3.39564	+	5.88143i	0.361977	+	0.626962i
$89$			16.1407i			1.71091i	0.517880	+	0.855453i	$0.326721\pi$
$89$			16.1407i			1.71091i	−0.517880	+	0.855453i	$0.673279\pi$
$90$	−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	−0.784998	−	0.619499i	$-0.787336\pi$
$97$	−6.31307	+	3.64485i	−0.640995	+	0.370079i	0.144003	+	0.989577i	$0.454003\pi$
$98$		0			0
$99$			18.7864i			1.88811i
$100$	−4.29129	+	7.43273i	−0.429129	+	0.743273i
$101$	−2.60436	−	4.51088i	−0.259143	−	0.448849i	0.706869	−	0.707344i	$-0.250107\pi$
$101$	−2.60436	−	4.51088i	−0.259143	−	0.448849i	−0.966013	+	0.258495i	$0.916773\pi$
$102$	3.31307	−	1.91280i	0.328043	−	0.189396i
$103$	−2.29129	−	3.96863i	−0.225767	−	0.391040i	0.730782	−	0.682611i	$-0.239156\pi$
$103$	−2.29129	−	3.96863i	−0.225767	−	0.391040i	−0.956549	+	0.291570i	$0.905822\pi$
$104$	1.50000	+	6.06218i	0.147087	+	0.594445i
$105$		0			0
$106$	−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	0.791666	−	0.610954i	$-0.209214\pi$
$109$	6.87386	+	3.96863i	0.658397	+	0.380126i	−0.133269	+	0.991080i	$0.542547\pi$
$110$	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	0.502234	−	0.864732i	$-0.332512\pi$
$113$	−5.29129	−	9.16478i	−0.497762	−	0.862150i	−0.999997	+	0.00258173i	$0.999178\pi$
$114$	−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	−0.978066	−	0.208297i	$-0.933208\pi$
$127$	−3.47822	+	6.02445i	−0.308642	+	0.534584i	0.669423	+	0.742881i	$0.266541\pi$
$128$			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	0.943371	+	0.331740i	$0.107636\pi$
$131$	8.68693	+	15.0462i	0.758981	+	1.31459i	−0.184390	+	0.982853i	$0.559031\pi$
$132$	−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	$0.170588\pi$
$137$			11.9536i			1.02126i	−0.859800	+	0.510631i	$0.829412\pi$
$138$	−1.74773	+	1.00905i	−0.148776	+	0.0858961i
$139$	−1.89564	−	3.28335i	−0.160786	−	0.278490i	0.774365	−	0.632740i	$-0.218070\pi$
$139$	−1.89564	−	3.28335i	−0.160786	−	0.278490i	−0.935151	+	0.354249i	$0.884736\pi$
$140$		0			0
$141$	23.1434	+	13.3618i	1.94902	+	1.12527i
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	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	0.516119	−	0.856517i	$-0.327376\pi$
$149$	0.395644	+	0.228425i	0.0324124	+	0.0187133i	−0.483706	+	0.875230i	$0.660710\pi$
$150$			6.10985i			0.498867i
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	0.862159	−	0.506637i	$-0.169112\pi$
$151$	10.5000	+	6.06218i	0.854478	+	0.493333i	−0.00768132	+	0.999970i	$0.502445\pi$
$152$	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	−0.846311	−	0.532689i	$-0.821182\pi$
$157$	0.478220	−	0.828301i	0.0381661	−	0.0661056i	0.884477	+	0.466583i	$0.154515\pi$
$158$	−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	0.246265	−	0.969202i	$-0.420797\pi$
$163$	−6.00000	−	3.46410i	−0.469956	−	0.271329i	−0.716221	+	0.697873i	$0.754130\pi$
$164$	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	0.903304	−	0.429001i	$-0.141134\pi$
$167$	12.7087	+	7.33738i	0.983430	+	0.567783i	0.0801258	+	0.996785i	$0.474468\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	0.313068	+	0.542250i	0.0240112	+	0.0415887i
$171$	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	0.196790	+	0.980446i	$0.436948\pi$
$173$	−9.87386	+	17.1020i	−0.750696	+	1.30024i	−0.947486	+	0.319798i	$0.896385\pi$
$174$		−	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	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$			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	−0.479701	−	0.877432i	$-0.659255\pi$
$191$	7.18693	−	12.4481i	0.520028	−	0.900715i	0.999729	−	0.0232830i	$-0.00741188\pi$
$192$	−4.76951	−	8.26103i	−0.344210	−	0.596188i
$193$	−16.7477	+	9.66930i	−1.20553	+	0.696012i	−0.961779	−	0.273827i	$-0.911711\pi$
$193$	−16.7477	+	9.66930i	−1.20553	+	0.696012i	−0.243749	+	0.969838i	$0.578377\pi$
$194$	−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	$0.640736\pi$
$198$	−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	−0.988658	−	0.150183i	$-0.952014\pi$
$211$	−5.29129	+	9.16478i	−0.364267	+	0.630929i	0.624391	+	0.781112i	$0.285347\pi$
$212$	−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	0.936364	−	0.351029i	$-0.114168\pi$
$223$	16.4347	+	9.48855i	1.10055	+	0.635401i	0.164182	+	0.986430i	$0.447502\pi$
$224$		0			0
$225$	−11.4782	−	19.8809i	−0.765215	−	1.32539i
$226$	4.18693	−	2.41733i	0.278511	−	0.160798i
$227$		−	8.85095i		−	0.587458i	−0.955889	−	0.293729i	$-0.905104\pi$
$227$		−	8.85095i		−	0.587458i	0.955889	−	0.293729i	$-0.0948964\pi$
$228$			6.85275i			0.453835i
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	−0.684969	−	0.728572i	$-0.740184\pi$
$229$	−6.00000	+	3.46410i	−0.396491	+	0.228914i	0.288478	+	0.957487i	$0.406851\pi$
$230$	−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	−0.999652	−	0.0263786i	$-0.991602\pi$
$233$	−7.97822	−	13.8187i	−0.522671	−	0.905292i	0.476981	−	0.878913i	$-0.341731\pi$
$234$	−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	$0.140728\pi$
$239$			13.2288i			0.855697i	−0.903850	+	0.427849i	$0.859272\pi$
$240$	−3.08258	−	1.77973i	−0.198979	−	0.114881i
$241$			19.7001i			1.26900i	0.772925	+	0.634498i	$0.218793\pi$
$241$			19.7001i			1.26900i	−0.772925	+	0.634498i	$0.781207\pi$
$242$	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	0.817819	−	0.575476i	$-0.195183\pi$
$251$	−1.41742	−	2.45505i	−0.0894670	−	0.154961i	−0.907286	+	0.420514i	$0.861850\pi$
$252$		0			0
$253$	−5.37386	+	3.10260i	−0.337852	+	0.195059i
$254$	−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	0.685587	−	0.727991i	$-0.259546\pi$
$263$	−4.66515	−	8.08028i	−0.287666	−	0.498251i	−0.973252	+	0.229740i	$0.926212\pi$
$264$	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	$-0.872402\pi$
$271$		−	12.8474i		−	0.780421i	0.920726	−	0.390211i	$-0.127598\pi$
$272$	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	$0.367064\pi$
$281$			30.6446i			1.82810i	−0.405597	+	0.914052i	$0.632936\pi$
$282$	−6.10436	+	10.5731i	−0.363509	+	0.629616i
$283$	1.37386	+	2.37960i	0.0816677	+	0.141453i	0.903966	−	0.427603i	$-0.140642\pi$
$283$	1.37386	+	2.37960i	0.0816677	+	0.141453i	−0.822299	+	0.569056i	$0.807309\pi$
$284$	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	−0.563128	−	0.826370i	$-0.690402\pi$
$293$	−2.20871	+	1.27520i	−0.129034	+	0.0744980i	0.434093	+	0.900868i	$0.357069\pi$
$294$		0			0
$295$	2.81307	+	4.87238i	0.163783	+	0.283681i
$296$	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	$-0.854025\pi$
$307$		−	15.5130i		−	0.885374i	0.896676	−	0.442687i	$-0.145975\pi$
$308$		0			0
$309$	−6.39564	+	11.0776i	−0.363835	+	0.630182i
$310$		−	1.80750i		−	0.102659i
$311$	13.2695	−	22.9835i	0.752445	−	1.30327i	−0.194190	−	0.980964i	$-0.562208\pi$
$311$	13.2695	−	22.9835i	0.752445	−	1.30327i	0.946635	−	0.322309i	$-0.104459\pi$
$312$	12.5608	−	12.0866i	0.711115	−	0.684271i
$313$	−3.37386	−	5.84370i	−0.190702	−	0.330306i	0.754781	−	0.655977i	$-0.227743\pi$
$313$	−3.37386	−	5.84370i	−0.190702	−	0.330306i	−0.945483	+	0.325671i	$0.894410\pi$
$314$	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	$-0.840772\pi$
$317$	−16.0390	+	9.26013i	−0.900841	+	0.520101i	−0.0233679	+	0.999727i	$0.507439\pi$
$318$			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	−0.227902	−	0.973684i	$-0.573187\pi$
$331$	−21.5608	−	12.4481i	−1.18509	−	0.684211i	−0.957186	+	0.289473i	$0.906520\pi$
$332$		−	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	0.901296	−	0.433204i	$-0.142617\pi$
$349$	18.2477	+	10.5353i	0.976778	+	0.563943i	0.0754825	+	0.997147i	$0.475950\pi$
$350$		0			0
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$	9.29129	+	16.0930i	0.495227	+	0.857759i
$353$	15.7259	−	9.07938i	0.837008	−	0.483247i	−0.0192383	−	0.999815i	$-0.506124\pi$
$353$	15.7259	−	9.07938i	0.837008	−	0.483247i	0.856246	+	0.516568i	$0.172791\pi$
$354$	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	−0.512567	−	0.858647i	$-0.671305\pi$
$359$	−0.478220	+	0.276100i	−0.0252395	+	0.0145720i	0.487327	+	0.873219i	$0.337972\pi$
$360$	−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	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	−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	0.0611098	+	0.998131i	$0.480536\pi$
$373$	−16.1044	+	27.8936i	−0.833852	+	1.44427i	−0.894962	+	0.446143i	$0.852797\pi$
$374$	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	−0.288219	−	0.957565i	$-0.593063\pi$
$379$	−24.5608	−	14.1802i	−1.26160	−	0.728387i	−0.973385	+	0.229178i	$0.926396\pi$
$380$	−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	0.527950	−	0.849276i	$-0.322961\pi$
$383$	1.10436	+	0.637600i	0.0564300	+	0.0325799i	−0.471520	+	0.881856i	$0.656294\pi$
$384$	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	−0.861808	−	0.507234i	$-0.830668\pi$
$389$	0.165151	−	0.286051i	0.00837351	−	0.0145033i	0.870182	+	0.492731i	$0.164001\pi$
$390$	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	0.995519	−	0.0945652i	$-0.0301461\pi$
$397$	28.1216	+	16.2360i	1.41138	+	0.814862i	0.415864	+	0.909427i	$0.363479\pi$
$398$		−	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	$-0.714543\pi$
$401$		−	31.2922i		−	1.56266i	0.624121	−	0.781328i	$-0.285457\pi$
$402$	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	$-0.934224\pi$
$409$		−	8.29875i		−	0.410347i	0.978726	−	0.205173i	$-0.0657759\pi$
$410$			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	−0.886581	−	0.462573i	$-0.846926\pi$
$419$	−0.873864	+	1.51358i	−0.0426910	+	0.0739430i	0.843890	+	0.536516i	$0.180260\pi$
$420$		0			0
$421$			4.18710i			0.204067i	0.994781	+	0.102033i	$0.0325349\pi$
$421$			4.18710i			0.204067i	−0.994781	+	0.102033i	$0.967465\pi$
$422$	−4.18693	−	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	−0.998232	−	0.0594316i	$-0.981071\pi$
$431$	−30.0172	+	17.3305i	−1.44588	+	0.834779i	−0.447647	+	0.894210i	$0.647738\pi$
$432$	13.9564			0.671479
$433$	−16.2477	−	28.1419i	−0.780816	−	1.35241i	−0.931467	−	0.363826i	$-0.881470\pi$
$433$	−16.2477	−	28.1419i	−0.780816	−	1.35241i	0.150651	−	0.988587i	$-0.451863\pi$
$434$		0			0
$435$	−7.50000	+	4.33013i	−0.359597	+	0.207614i
$436$	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	0.988003	−	0.154433i	$-0.0493550\pi$
$443$	7.58258	+	13.1334i	0.360259	+	0.623987i	−0.627744	+	0.778420i	$0.716022\pi$
$444$	−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	−0.916524	−	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
$451$	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	$-0.820939\pi$
$457$		−	22.8027i		−	1.06667i	0.845905	−	0.533333i	$-0.179061\pi$
$458$	−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	−0.590724	−	0.806874i	$-0.701158\pi$
$461$	−4.02178	+	2.32198i	−0.187313	+	0.108145i	0.403411	+	0.915019i	$0.367824\pi$
$462$		0			0
$463$			7.93725i			0.368875i	0.982844	+	0.184438i	$0.0590464\pi$
$463$			7.93725i			0.368875i	−0.982844	+	0.184438i	$0.940954\pi$
$464$	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	0.969180	+	0.246353i	$0.0792324\pi$
$467$	15.0826	+	26.1238i	0.697938	+	1.20886i	−0.271242	+	0.962511i	$0.587434\pi$
$468$	−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	−0.824662	−	0.565626i	$-0.808634\pi$
$479$	−16.3521	+	9.44088i	−0.747146	+	0.431365i	0.0775159	+	0.996991i	$0.475301\pi$
$480$	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	$0.231751\pi$
$487$			29.3694i			1.33086i	−0.746462	+	0.665428i	$0.768249\pi$
$488$	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	−0.815771	−	0.578375i	$-0.803687\pi$
$491$	2.06080	−	3.56940i	0.0930024	−	0.161085i	0.908773	+	0.417291i	$0.137020\pi$
$492$		−	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	−0.0988324	−	0.995104i	$-0.531511\pi$
$499$	15.9392	−	9.20250i	0.713537	−	0.411961i	0.812369	+	0.583143i	$0.198177\pi$
$500$			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	0.996540	−	0.0831100i	$-0.0264853\pi$
$503$	9.56080	+	16.5598i	0.426295	+	0.738364i	−0.570246	+	0.821474i	$0.693152\pi$
$504$		0			0
$505$	−2.06080	−	1.18980i	−0.0917042	−	0.0529454i
$506$	−1.41742	−	2.45505i	−0.0630122	−	0.109140i
$507$	−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	$-0.891711\pi$
$509$		−	15.0562i		−	0.667352i	0.942688	−	0.333676i	$-0.108289\pi$
$510$	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	−0.628269	−	0.777996i	$-0.716236\pi$
$521$	8.20871	−	14.2179i	0.359630	−	0.622898i	0.987899	+	0.155099i	$0.0495695\pi$
$522$	−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	−0.378497	−	0.925602i	$-0.623559\pi$
$541$	5.43920	−	3.14033i	0.233850	−	0.135013i	0.612347	+	0.790589i	$0.290226\pi$
$542$	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	0.248659	−	0.968591i	$-0.420010\pi$
$557$	28.5998	−	16.5121i	1.21181	−	0.699640i	0.963154	+	0.268951i	$0.0866769\pi$
$558$	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	−0.843853	−	0.536574i	$-0.819718\pi$
$571$	1.02178	−	1.76978i	0.0427602	−	0.0740628i	0.886613	+	0.462511i	$0.153052\pi$
$572$	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	0.977811	−	0.209487i	$-0.0671795\pi$
$577$	30.8739	+	17.8250i	1.28530	+	0.742066i	0.307484	+	0.951553i	$0.400513\pi$
$578$		−	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	0.660060	−	0.751213i	$-0.270531\pi$
$587$	8.22595	+	4.74925i	0.339521	+	0.196023i	−0.320539	+	0.947235i	$0.603864\pi$
$588$		0			0
$589$	5.93466	+	10.2791i	0.244533	+	0.423544i
$590$	−2.22595	+	1.28515i	−0.0916408	+	0.0529088i
$591$		−	6.37600i		−	0.262274i
$592$		−	19.3386i		−	0.794812i
$593$	−5.52178	+	3.18800i	−0.226752	+	0.130916i	−0.609073	−	0.793114i	$-0.708458\pi$
$593$	−5.52178	+	3.18800i	−0.226752	+	0.130916i	0.382321	+	0.924030i	$0.375125\pi$
$594$	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	−0.790370	−	0.612630i	$-0.790112\pi$
$599$	3.31307	−	5.73840i	0.135368	−	0.234465i	0.925738	+	0.378165i	$0.123445\pi$
$600$			23.1642i			0.945675i
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	−0.964178	−	0.265256i	$-0.914543\pi$
$601$	−6.18693	+	10.7161i	−0.252370	+	0.437118i	0.711808	+	0.702374i	$0.247877\pi$
$602$		0			0
$603$			21.4322i			0.872785i
$604$	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	−0.993819	−	0.111015i	$-0.964590\pi$
$607$	−9.87386	+	17.1020i	−0.400768	+	0.694150i	0.593051	+	0.805165i	$0.297923\pi$
$608$	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	−0.145536	−	0.989353i	$-0.546491\pi$
$613$	15.8085	−	9.12705i	0.638500	−	0.368638i	0.784037	+	0.620715i	$0.213157\pi$
$614$	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	−0.769259	−	0.638937i	$-0.779374\pi$
$617$	−14.9174	+	8.61258i	−0.600553	+	0.346729i	0.168706	+	0.985666i	$0.446041\pi$
$618$	−5.06080	−	2.92185i	−0.203575	−	0.117534i
$619$	16.7477	+	9.66930i	0.673148	+	0.388642i	0.797268	−	0.603625i	$-0.206278\pi$
$619$	16.7477	+	9.66930i	0.673148	+	0.388642i	−0.124120	+	0.992267i	$0.539611\pi$
$620$	−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	0.0588668	−	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
$633$	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	−0.549468	+	0.835515i	$0.685170\pi$
$643$	−39.2477	+	22.6597i	−1.54778	+	0.893611i	−0.998311	+	0.0580962i	$0.981497\pi$
$644$		0			0
$645$			11.9536i			0.470671i
$646$	0.939205	−	1.62675i	0.0369525	−	0.0640036i
$647$	17.5390	+	30.3785i	0.689530	+	1.19430i	0.971990	+	0.235022i	$0.0755161\pi$
$647$	17.5390	+	30.3785i	0.689530	+	1.19430i	−0.282460	+	0.959279i	$0.591151\pi$
$648$	−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	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	−8.95644			−0.348629
$661$	−43.7477	+	25.2578i	−1.70159	+	0.982413i	−0.757434	+	0.652911i	$0.773547\pi$
$661$	−43.7477	+	25.2578i	−1.70159	+	0.982413i	−0.944155	+	0.329502i	$0.893119\pi$
$662$	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	0.489261	+	0.872137i	$0.337266\pi$
$673$	−13.2477	+	22.9457i	−0.510662	+	0.884493i	−0.999924	+	0.0123559i	$0.996067\pi$
$674$			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	−0.997384	−	0.0722830i	$-0.976972\pi$
$677$	−14.6044	−	25.2955i	−0.561291	−	0.972185i	0.436093	−	0.899902i	$-0.356362\pi$
$678$	−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	$0.197268\pi$
$683$			30.3586i			1.16164i	−0.814033	+	0.580819i	$0.802732\pi$
$684$	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	$-0.937128\pi$
$691$		−	10.3169i		−	0.392472i	0.980557	−	0.196236i	$-0.0628718\pi$
$692$	−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	0.726748	−	0.686904i	$-0.241031\pi$
$709$	13.1869	+	7.61348i	0.495246	+	0.285930i	−0.231502	+	0.972834i	$0.574364\pi$
$710$	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	−0.547820	−	0.836597i	$-0.684542\pi$
$719$	12.0826	−	20.9276i	0.450604	−	0.780469i	0.998424	+	0.0561274i	$0.0178753\pi$
$720$			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	−0.746081	−	0.665855i	$-0.768067\pi$
$733$	−14.6869	+	8.47950i	−0.542474	+	0.313198i	0.203607	+	0.979053i	$0.434734\pi$
$734$	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	−0.775339	−	0.631545i	$-0.782421\pi$
$739$	−16.7477	+	9.66930i	−0.616075	+	0.355691i	0.159264	+	0.987236i	$0.449088\pi$
$740$	−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	$0.448780\pi$
$744$	−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	−0.915380	−	0.402590i	$-0.868110\pi$
$757$	−3.00000	+	5.19615i	−0.109037	+	0.188857i	0.806343	+	0.591448i	$0.201443\pi$
$758$	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	0.689474	−	0.724310i	$-0.257842\pi$
$761$	11.2259	+	6.48130i	0.406940	+	0.234947i	−0.282534	+	0.959257i	$0.591175\pi$
$762$			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	0.639310	−	0.768949i	$-0.279220\pi$
$769$	8.12614	+	4.69163i	0.293036	+	0.169184i	−0.346274	+	0.938133i	$0.612553\pi$
$770$		0			0
$771$	7.03901	+	12.1919i	0.253504	+	0.439082i
$772$	−30.0000	+	17.3205i	−1.07972	+	0.623379i
$773$		−	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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