LMFDB - Embedded newform 637.2.q.e.491.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, degree $2$, 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.1
Root			$1.39564 + 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.e.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.395644 + 0.228425i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.895644 + 1.55130i) q^{4} -0.456850i q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +O(q^{10})$	\(q+(-0.395644 + 0.228425i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.895644 + 1.55130i) q^{4} -0.456850i 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} +5.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-1.50000 + 2.59808i) q^{17} -2.18890i q^{18} +(1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} +(0.791288 + 1.37055i) q^{23} +(-4.18693 + 2.41733i) q^{24} +4.79129 q^{25} +(-1.58258 + 0.456850i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 - 0.504525i) q^{30} -8.66025i q^{31} +(4.10436 + 2.36965i) q^{32} +(9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +(6.00000 - 3.46410i) q^{37} -0.626136 q^{38} +(-2.79129 - 9.66930i) q^{39} -0.791288 q^{40} +(6.79129 - 3.92095i) q^{41} +(-4.68693 + 8.11800i) q^{43} -7.02355i q^{44} +(1.89564 + 1.09445i) q^{45} +(-0.626136 - 0.361500i) q^{46} +9.57395i q^{47} +(-3.89564 + 6.74745i) q^{48} +(-1.89564 + 1.09445i) q^{50} +8.37386 q^{51} +(-4.47822 + 4.65390i) q^{52} +6.16515 q^{53} +(-1.97822 + 1.14213i) q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(-2.68693 - 1.55130i) q^{58} +(10.6652 + 6.15753i) q^{59} -2.28425i q^{60} +(7.37386 - 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(0.395644 - 1.59898i) q^{65} -5.00000 q^{66} +(-3.87386 + 2.23658i) q^{67} +(-2.68693 - 4.65390i) q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(7.18693 + 4.14938i) q^{72} +3.46410i q^{73} +(-1.58258 + 2.74110i) q^{74} +(-6.68693 - 11.5821i) q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} -6.00000 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} -4.28245i q^{86} +(9.47822 - 16.4168i) q^{87} +(3.39564 + 5.88143i) q^{88} +(-13.9782 + 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(-20.9347 + 12.0866i) q^{93} +(-2.18693 - 3.78788i) q^{94} +(0.313068 - 0.542250i) q^{95} -13.2288i q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9	$ 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9 + 5 * q^10 - 9 * q^11 + 20 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 - 9 * q^19 + 12 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 10 * q^25 + 12 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 + 21 * q^32 + 15 * q^33 - 8 * q^36 + 24 * q^37 - 30 * q^38 - 2 * q^39 + 6 * q^40 + 18 * q^41 - 5 * q^43 + 3 * q^45 - 30 * q^46 - 11 * q^48 - 3 * q^50 + 6 * q^51 + 5 * q^52 - 12 * q^53 + 15 * q^54 - q^55 + 3 * q^58 + 6 * q^59 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 3 * q^65 - 20 * q^66 + 12 * q^67 + 3 * q^68 + 18 * q^69 + 6 * q^71 + 15 * q^72 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 - 24 * q^79 - 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 15 * q^87 + 9 * q^88 - 33 * q^89 - 4 * q^90 - 48 * q^92 - 15 * q^93 + 5 * q^94 + 15 * q^95 - 39 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.395644	+	0.228425i	−0.279763	+	0.161521i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	−0.395644	+	0.228425i	−0.279763	+	0.161521i	0.353553	+	0.935414i	$0.384973\pi$
$3$	−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	$-0.464918\pi$
$4$	−0.895644	+	1.55130i	−0.447822	+	0.775650i
$5$		−	0.456850i		−	0.204310i	−0.994769	−	0.102155i	$-0.967426\pi$
$5$		−	0.456850i		−	0.204310i	0.994769	−	0.102155i	$-0.0325737\pi$
$6$	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	$-0.867975\pi$
$11$	−3.39564	+	1.96048i	−1.02383	+	0.591106i	−0.108616	+	0.994084i	$0.534642\pi$
$12$	5.00000			1.44338
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$		0			0
$15$	−1.10436	+	0.637600i	−0.285144	+	0.164628i
$16$	−1.39564	−	2.41733i	−0.348911	−	0.604332i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		−	2.18890i		−	0.515929i
$19$	1.18693	+	0.685275i	0.272301	+	0.157213i	0.629933	−	0.776650i	$-0.283082\pi$
$19$	1.18693	+	0.685275i	0.272301	+	0.157213i	−0.357632	+	0.933863i	$0.616416\pi$
$20$	0.708712	+	0.409175i	0.158473	+	0.0914943i
$21$		0			0
$22$	0.895644	−	1.55130i	0.190952	−	0.330738i
$23$	0.791288	+	1.37055i	0.164995	+	0.285780i	0.936653	−	0.350257i	$-0.113906\pi$
$23$	0.791288	+	1.37055i	0.164995	+	0.285780i	−0.771659	+	0.636037i	$0.780573\pi$
$24$	−4.18693	+	2.41733i	−0.854654	+	0.493435i
$25$	4.79129			0.958258
$26$	−1.58258	+	0.456850i	−0.310369	+	0.0895957i
$27$	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
$31$		−	8.66025i		−	1.55543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$		−	8.66025i		−	1.55543i	0.628619	−	0.777714i	$-0.283621\pi$
$32$	4.10436	+	2.36965i	0.725555	+	0.418899i
$33$	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
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−0.626136			−0.101573
$39$	−2.79129	−	9.66930i	−0.446964	−	1.54833i
$40$	−0.791288			−0.125114
$41$	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	$0.913207\pi$
$44$		−	7.02355i		−	1.05884i
$45$	1.89564	+	1.09445i	0.282586	+	0.163151i
$46$	−0.626136	−	0.361500i	−0.0923188	−	0.0533003i
$47$			9.57395i			1.39650i	0.715852	+	0.698252i	$0.246039\pi$
$47$			9.57395i			1.39650i	−0.715852	+	0.698252i	$0.753961\pi$
$48$	−3.89564	+	6.74745i	−0.562288	+	0.973911i
$49$		0			0
$50$	−1.89564	+	1.09445i	−0.268085	+	0.154779i
$51$	8.37386			1.17258
$52$	−4.47822	+	4.65390i	−0.621017	+	0.645380i
$53$	6.16515			0.846849			0.423424	−	0.905931i	$-0.360828\pi$
$53$	6.16515			0.846849			0.423424	+	0.905931i	$0.360828\pi$
$54$	−1.97822	+	1.14213i	−0.269202	+	0.155424i
$55$	0.895644	+	1.55130i	0.120769	+	0.209177i
$56$		0			0
$57$		−	3.82560i		−	0.506713i
$58$	−2.68693	−	1.55130i	−0.352811	−	0.203696i
$59$	10.6652	+	6.15753i	1.38848	+	0.801642i	0.993145	−	0.116893i	$-0.0372935\pi$
$59$	10.6652	+	6.15753i	1.38848	+	0.801642i	0.395340	+	0.918535i	$0.370627\pi$
$60$		−	2.28425i		−	0.294896i
$61$	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
$65$	0.395644	−	1.59898i	0.0490736	−	0.198329i
$66$	−5.00000			−0.615457
$67$	−3.87386	+	2.23658i	−0.473268	+	0.273241i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	−3.87386	+	2.23658i	−0.473268	+	0.273241i	0.244339	+	0.969690i	$0.421429\pi$
$68$	−2.68693	−	4.65390i	−0.325838	−	0.564369i
$69$	2.20871	−	3.82560i	0.265898	−	0.460548i
$70$		0			0
$71$	3.79129	+	2.18890i	0.449943	+	0.259775i	0.707806	−	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
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$	−1.58258	+	2.74110i	−0.183971	+	0.318647i
$75$	−6.68693	−	11.5821i	−0.772140	−	1.33739i
$76$	−2.12614	+	1.22753i	−0.243885	+	0.140807i
$77$		0			0
$78$	3.31307	+	3.18800i	0.375131	+	0.360970i
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$	−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
$86$		−	4.28245i		−	0.461789i
$87$	9.47822	−	16.4168i	1.01617	−	1.76006i
$88$	3.39564	+	5.88143i	0.361977	+	0.626962i
$89$	−13.9782	+	8.07033i	−1.48169	+	0.855453i	−0.999784	−	0.0207708i	$-0.993388\pi$
$89$	−13.9782	+	8.07033i	−1.48169	+	0.855453i	−0.481904	+	0.876224i	$0.660055\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−2.83485			−0.295553
$93$	−20.9347	+	12.0866i	−2.17082	+	1.25333i
$94$	−2.18693	−	3.78788i	−0.225565	−	0.390690i
$95$	0.313068	−	0.542250i	0.0321201	−	0.0556337i
$96$		−	13.2288i		−	1.35015i
$97$	−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	0.706869	−	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
$103$	4.58258			0.451535			0.225767	−	0.974181i	$-0.427511\pi$
$103$	4.58258			0.451535			0.225767	+	0.974181i	$0.427511\pi$
$104$	1.50000	−	6.06218i	0.147087	−	0.594445i
$105$		0			0
$106$	−2.43920	+	1.40828i	−0.236917	+	0.136784i
$107$	2.60436	+	4.51088i	0.251773	+	0.436083i	0.964014	−	0.265852i	$-0.0856532\pi$
$107$	2.60436	+	4.51088i	0.251773	+	0.436083i	−0.712241	+	0.701935i	$0.752320\pi$
$108$	−4.47822	+	7.75650i	−0.430917	+	0.746370i
$109$			7.93725i			0.760251i	0.924935	+	0.380126i	$0.124119\pi$
$109$			7.93725i			0.760251i	−0.924935	+	0.380126i	$0.875881\pi$
$110$	−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	$0.332512\pi$
$114$	0.873864	+	1.51358i	0.0818448	+	0.141759i
$115$	0.626136	−	0.361500i	0.0583875	−	0.0337101i
$116$	−12.1652			−1.12951
$117$	−11.9782	+	12.4481i	−1.10739	+	1.15083i
$118$	−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
$122$			6.73750i			0.609985i
$123$	−18.9564	−	10.9445i	−1.70924	−	0.986833i
$124$	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	$0.933208\pi$
$128$	−9.56080	+	5.51993i	−0.845063	+	0.487897i
$129$	26.1652			2.30371
$130$	0.208712	+	0.723000i	0.0183053	+	0.0634113i
$131$	−17.3739			−1.51796			−0.758981	−	0.651113i	$-0.774302\pi$
$131$	−17.3739			−1.51796			−0.758981	+	0.651113i	$0.774302\pi$
$132$	−16.9782	+	9.80238i	−1.47776	+	0.853188i
$133$		0			0
$134$	1.02178	−	1.76978i	0.0882684	−	0.152885i
$135$		−	2.28425i		−	0.196597i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	10.3521	+	5.97678i	0.884438	+	0.510631i	0.872119	−	0.489294i	$-0.162745\pi$
$137$	10.3521	+	5.97678i	0.884438	+	0.510631i	0.0123190	+	0.999924i	$0.496079\pi$
$138$			2.01810i			0.171792i
$139$	−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
$142$	−2.00000			−0.167836
$143$	−13.5826	+	3.92095i	−1.13583	+	0.327886i
$144$	13.3739			1.11449
$145$	2.68693	−	1.55130i	0.223138	−	0.128829i
$146$	−0.791288	−	1.37055i	−0.0654874	−	0.113428i
$147$		0			0
$148$			12.4104i			1.02013i
$149$	−0.395644	−	0.228425i	−0.0324124	−	0.0187133i	0.483706	−	0.875230i	$-0.339290\pi$
$149$	−0.395644	−	0.228425i	−0.0324124	−	0.0187133i	−0.516119	+	0.856517i	$0.672624\pi$
$150$	5.29129	+	3.05493i	0.432032	+	0.249434i
$151$			12.1244i			0.986666i	0.869841	+	0.493333i	$0.164222\pi$
$151$			12.1244i			0.986666i	−0.869841	+	0.493333i	$0.835778\pi$
$152$	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
$156$	17.5000	+	4.33013i	1.40112	+	0.346688i
$157$	−0.956439			−0.0763322			−0.0381661	−	0.999271i	$-0.512152\pi$
$157$	−0.956439			−0.0763322			−0.0381661	+	0.999271i	$0.512152\pi$
$158$	2.37386	−	1.37055i	0.188854	−	0.109035i
$159$	−8.60436	−	14.9032i	−0.682370	−	1.18190i
$160$	1.08258	−	1.87508i	0.0855851	−	0.148238i
$161$		0			0
$162$	−0.165151	−	0.0953502i	−0.0129755	−	0.00749142i
$163$	6.00000	+	3.46410i	0.469956	+	0.271329i	0.716221	−	0.697873i	$-0.245870\pi$
$163$	6.00000	+	3.46410i	0.469956	+	0.271329i	−0.246265	+	0.969202i	$0.579203\pi$
$164$			14.0471i			1.09689i
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	−1.60436	−	2.77883i	−0.124522	−	0.215679i
$167$	12.7087	−	7.33738i	0.983430	−	0.567783i	0.0801258	−	0.996785i	$-0.474468\pi$
$167$	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
$170$	−0.626136			−0.0480225
$171$	−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
$177$		−	34.3749i		−	2.58377i
$178$	3.68693	−	6.38595i	0.276347	−	0.478647i
$179$	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	$0.724142\pi$
$180$	−3.39564	+	1.96048i	−0.253096	+	0.146125i
$181$	−9.16515			−0.681240			−0.340620	−	0.940201i	$-0.610637\pi$
$181$	−9.16515			−0.681240			−0.340620	+	0.940201i	$0.610637\pi$
$182$		0			0
$183$	−41.1652			−3.04302
$184$	2.37386	−	1.37055i	0.175004	−	0.101038i
$185$	−1.58258	−	2.74110i	−0.116353	−	0.201530i
$186$	5.52178	−	9.56400i	0.404877	−	0.701267i
$187$		−	11.7629i		−	0.860185i
$188$	−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	0.243749	−	0.969838i	$-0.421623\pi$
$193$	16.7477	−	9.66930i	1.20553	−	0.696012i	0.961779	+	0.273827i	$0.0882895\pi$
$194$	3.33030			0.239102
$195$	−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	$0.307403\pi$
$198$	4.29129	+	7.43273i	0.304969	+	0.528221i
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		−	8.29875i		−	0.586811i
$201$	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
$205$	−1.79129	−	3.10260i	−0.125109	−	0.216695i
$206$	−1.81307	+	1.04678i	−0.126322	+	0.0729323i
$207$	−7.58258			−0.527025
$208$	−2.79129	−	9.66930i	−0.193541	−	0.670446i
$209$	−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
$213$		−	12.2197i		−	0.837280i
$214$	−2.06080	−	1.18980i	−0.140873	−	0.0813331i
$215$	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
$219$	8.37386	−	4.83465i	0.565853	−	0.326696i
$220$	−3.20871			−0.216331
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$	8.83485			0.592956
$223$	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
$226$		−	4.83465i		−	0.321596i
$227$	−7.66515	−	4.42548i	−0.508754	−	0.293729i	0.223567	−	0.974688i	$-0.428230\pi$
$227$	−7.66515	−	4.42548i	−0.508754	−	0.293729i	−0.732321	+	0.680959i	$0.761563\pi$
$228$	5.93466	+	3.42638i	0.393032	+	0.226917i
$229$			6.92820i			0.457829i	0.973447	+	0.228914i	$0.0735176\pi$
$229$			6.92820i			0.457829i	−0.973447	+	0.228914i	$0.926482\pi$
$230$	−0.165151	+	0.286051i	−0.0108898	+	0.0188616i
$231$		0			0
$232$	10.1869	−	5.88143i	0.668805	−	0.386135i
$233$	15.9564			1.04534			0.522671	−	0.852535i	$-0.324936\pi$
$233$	15.9564			1.04534			0.522671	+	0.852535i	$0.324936\pi$
$234$	1.89564	−	7.66115i	0.123922	−	0.500825i
$235$	4.37386			0.285319
$236$	−19.1044	+	11.0299i	−1.24359	+	0.717986i
$237$	8.37386	+	14.5040i	0.543941	+	0.942133i
$238$		0			0
$239$		−	13.2288i		−	0.855697i	−0.903850	−	0.427849i	$-0.859272\pi$
$239$		−	13.2288i		−	0.855697i	0.903850	−	0.427849i	$-0.140728\pi$
$240$	3.08258	+	1.77973i	0.198979	+	0.114881i
$241$	17.0608	+	9.85005i	1.09898	+	0.634498i	0.935954	−	0.352123i	$-0.114540\pi$
$241$	17.0608	+	9.85005i	1.09898	+	0.634498i	0.163029	+	0.986621i	$0.447874\pi$
$242$			1.99820i			0.128449i
$243$	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
$247$	3.56080	+	3.42638i	0.226568	+	0.218015i
$248$	−15.0000			−0.952501
$249$	16.9782	−	9.80238i	1.07595	−	0.621201i
$250$	1.02178	+	1.76978i	0.0646231	+	0.111930i
$251$	−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
$255$		−	3.82560i		−	0.239568i
$256$	−0.895644	+	1.55130i	−0.0559777	+	0.0969563i
$257$	2.52178	+	4.36785i	0.157304	+	0.272459i	0.933896	−	0.357546i	$-0.116386\pi$
$257$	2.52178	+	4.36785i	0.157304	+	0.272459i	−0.776591	+	0.630005i	$0.783053\pi$
$258$	−10.3521	+	5.97678i	−0.644493	+	0.372098i
$259$		0			0
$260$	2.12614	+	2.04588i	0.131857	+	0.126880i
$261$	−32.5390			−2.01411
$262$	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
$268$		−	8.01270i		−	0.489454i
$269$	−7.89564	+	13.6757i	−0.481406	+	0.833819i	−0.999772	−	0.0213391i	$-0.993207\pi$
$269$	−7.89564	+	13.6757i	−0.481406	+	0.833819i	0.518366	+	0.855159i	$0.326540\pi$
$270$	0.521780	+	0.903750i	0.0317545	+	0.0550005i
$271$	11.1261	−	6.42368i	0.675865	−	0.390211i	−0.122430	−	0.992477i	$-0.539069\pi$
$271$	11.1261	−	6.42368i	0.675865	−	0.390211i	0.798295	+	0.602266i	$0.205736\pi$
$272$	8.37386			0.507740
$273$		0			0
$274$	−5.46099			−0.329910
$275$	−16.2695	+	9.39320i	−0.981088	+	0.566432i
$276$	3.95644	+	6.85275i	0.238150	+	0.412487i
$277$	−5.87386	+	10.1738i	−0.352926	+	0.611286i	−0.986761	−	0.162182i	$-0.948147\pi$
$277$	−5.87386	+	10.1738i	−0.352926	+	0.611286i	0.633835	+	0.773469i	$0.281480\pi$
$278$		−	1.73205i		−	0.103882i
$279$	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	0.903966	−	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
$285$	−1.74773			−0.103526
$286$	4.47822	−	4.65390i	0.264803	−	0.275191i
$287$		0			0
$288$	−19.6652	+	11.3537i	−1.15878	+	0.669022i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−0.708712	+	1.22753i	−0.0416170	+	0.0720828i
$291$			20.3477i			1.19280i
$292$	−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
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	−16.9782	+	9.80238i	−0.985176	+	0.568792i
$298$	0.208712			0.0120904
$299$	1.58258	+	5.48220i	0.0915227	+	0.317044i
$300$	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
$304$		−	3.82560i		−	0.219413i
$305$	−5.83485	−	3.36875i	−0.334102	−	0.192894i
$306$	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
$310$	1.56534	−	0.903750i	0.0889054	−	0.0513296i
$311$	−26.5390			−1.50489			−0.752445	−	0.658655i	$-0.771126\pi$
$311$	−26.5390			−1.50489			−0.752445	+	0.658655i	$0.771126\pi$
$312$	−16.7477	+	4.83465i	−0.948153	+	0.273708i
$313$	6.74773			0.381404			0.190702	−	0.981648i	$-0.438924\pi$
$313$	6.74773			0.381404			0.190702	+	0.981648i	$0.438924\pi$
$314$	0.378409	−	0.218475i	0.0213549	−	0.0123292i
$315$		0			0
$316$	5.37386	−	9.30780i	0.302303	−	0.523605i
$317$			18.5203i			1.04020i	0.854105	+	0.520101i	$0.174106\pi$
$317$			18.5203i			1.04020i	−0.854105	+	0.520101i	$0.825894\pi$
$318$	6.80852	+	3.93090i	0.381803	+	0.220434i
$319$	−23.0608	−	13.3142i	−1.29116	−	0.745450i
$320$		−	1.56125i		−	0.0872766i
$321$	7.26951	−	12.5912i	0.405744	−	0.702770i
$322$		0			0
$323$	−3.56080	+	2.05583i	−0.198128	+	0.114389i
$324$	−0.747727			−0.0415404
$325$	16.7695	+	4.14938i	0.930205	+	0.230166i
$326$	−3.16515			−0.175302
$327$	19.1869	−	11.0776i	1.06104	−	0.612592i
$328$	−6.79129	−	11.7629i	−0.374986	−	0.649495i
$329$		0			0
$330$			2.28425i			0.125744i
$331$	21.5608	+	12.4481i	1.18509	+	0.684211i	0.957186	−	0.289473i	$-0.0934800\pi$
$331$	21.5608	+	12.4481i	1.18509	+	0.684211i	0.227902	+	0.973684i	$0.426813\pi$
$332$	−10.8956	−	6.29060i	−0.597976	−	0.345242i
$333$			33.1950i			1.81908i
$334$	−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	$0.412586\pi$
$338$	−5.93466	+	0.228425i	−0.322803	+	0.0124247i
$339$	29.5390			1.60434
$340$	−2.12614	+	1.22753i	−0.115306	+	0.0665719i
$341$	16.9782	+	29.4071i	0.919422	+	1.59249i
$342$	1.50000	−	2.59808i	0.0811107	−	0.140488i
$343$		0			0
$344$	14.0608	+	8.11800i	0.758107	+	0.437693i
$345$	−1.74773	−	1.00905i	−0.0940945	−	0.0543255i
$346$		−	9.02175i		−	0.485013i
$347$	6.79129	−	11.7629i	0.364575	−	0.631463i	−0.624132	−	0.781319i	$-0.714547\pi$
$347$	6.79129	−	11.7629i	0.364575	−	0.631463i	0.988708	+	0.149855i	$0.0478808\pi$
$348$	16.9782	+	29.4071i	0.910128	+	1.57639i
$349$	18.2477	−	10.5353i	0.976778	−	0.563943i	0.0754825	−	0.997147i	$-0.475950\pi$
$349$	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
$352$	−18.5826			−0.990455
$353$	−15.7259	+	9.07938i	−0.837008	+	0.483247i	−0.856246	−	0.516568i	$-0.827209\pi$
$353$	−15.7259	+	9.07938i	−0.837008	+	0.483247i	0.0192383	+	0.999815i	$0.493876\pi$
$354$	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
$359$			0.552200i			0.0291440i	0.999894	+	0.0145720i	$0.00463858\pi$
$359$			0.552200i			0.0291440i	−0.999894	+	0.0145720i	$0.995361\pi$
$360$	1.89564	−	3.28335i	0.0999092	−	0.173048i
$361$	−8.56080	−	14.8277i	−0.450568	−	0.780407i
$362$	3.62614	−	2.09355i	0.190586	−	0.110035i
$363$	−12.2087			−0.640791
$364$		0			0
$365$	1.58258			0.0828358
$366$	16.2867	−	9.40315i	0.851322	−	0.491511i
$367$	−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	$0.989006\pi$
$368$	2.20871	−	3.82560i	0.115137	−	0.199423i
$369$			37.5728i			1.95596i
$370$	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
$376$	16.5826			0.855181
$377$	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	$0.593063\pi$
$380$	0.560795	+	0.971326i	0.0287682	+	0.0498280i
$381$	−9.70871	+	16.8160i	−0.497392	+	0.861509i
$382$			6.56670i			0.335982i
$383$	−1.10436	−	0.637600i	−0.0564300	−	0.0325799i	0.471520	−	0.881856i	$-0.343706\pi$
$383$	−1.10436	−	0.637600i	−0.0564300	−	0.0325799i	−0.527950	+	0.849276i	$0.677039\pi$
$384$	26.6869	+	15.4077i	1.36186	+	0.786271i
$385$		0			0
$386$	−4.41742	+	7.65120i	−0.224841	+	0.389436i
$387$	−22.4564	−	38.8957i	−1.14152	−	1.97718i
$388$	11.3085	−	6.52898i	0.574103	−	0.331459i
$389$	−0.330303			−0.0167470			−0.00837351	−	0.999965i	$-0.502665\pi$
$389$	−0.330303			−0.0167470			−0.00837351	+	0.999965i	$0.502665\pi$
$390$	1.45644	−	1.51358i	0.0737497	−	0.0766429i
$391$	−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
$395$			2.74110i			0.137920i
$396$	29.1434	+	16.8259i	1.46451	+	0.845535i
$397$	−28.1216	−	16.2360i	−1.41138	−	0.814862i	−0.415864	−	0.909427i	$-0.636521\pi$
$397$	−28.1216	−	16.2360i	−1.41138	−	0.814862i	−0.995519	+	0.0945652i	$0.969854\pi$
$398$			5.02535i			0.251898i
$399$		0			0
$400$	−6.68693	−	11.5821i	−0.334347	−	0.579105i
$401$	27.0998	−	15.6461i	1.35330	−	0.781328i	0.364590	−	0.931168i	$-0.381209\pi$
$401$	27.0998	−	15.6461i	1.35330	−	0.781328i	0.988710	+	0.149840i	$0.0478759\pi$
$402$	−5.70417			−0.284498
$403$	7.50000	−	30.3109i	0.373602	−	1.50989i
$404$	9.33030			0.464200
$405$	0.165151	−	0.0953502i	0.00820644	−	0.00473799i
$406$		0			0
$407$	−13.5826	+	23.5257i	−0.673263	+	1.16613i
$408$		−	14.5040i		−	0.718053i
$409$	−7.18693	−	4.14938i	−0.355371	−	0.205173i	0.311677	−	0.950188i	$-0.399109\pi$
$409$	−7.18693	−	4.14938i	−0.355371	−	0.205173i	−0.667048	+	0.745015i	$0.732443\pi$
$410$	1.41742	+	0.818350i	0.0700016	+	0.0404154i
$411$		−	33.3658i		−	1.64581i
$412$	−4.10436	+	7.10895i	−0.202207	+	0.350233i
$413$		0			0
$414$	3.00000	−	1.73205i	0.147442	−	0.0851257i
$415$	3.20871			0.157509
$416$	12.3131	+	11.8483i	0.603698	+	0.580909i
$417$	10.5826			0.518231
$418$	2.12614	−	1.22753i	0.103993	−	0.0600402i
$419$	−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
$423$	−39.7259	−	22.9358i	−1.93154	−	1.11518i
$424$		−	10.6784i		−	0.518587i
$425$	−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
$429$	28.4347	+	27.3613i	1.37284	+	1.32101i
$430$	−1.95644			−0.0943479
$431$	30.0172	−	17.3305i	1.44588	−	0.834779i	0.447647	−	0.894210i	$-0.352262\pi$
$431$	30.0172	−	17.3305i	1.44588	−	0.834779i	0.998232	+	0.0594316i	$0.0189288\pi$
$432$	−6.97822	−	12.0866i	−0.335740	−	0.581518i
$433$	−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
$437$			2.16900i			0.103757i
$438$	−2.20871	+	3.82560i	−0.105536	+	0.182794i
$439$	−10.2695	−	17.7873i	−0.490137	−	0.848942i	0.509799	−	0.860294i	$-0.329720\pi$
$439$	−10.2695	−	17.7873i	−0.490137	−	0.848942i	−0.999936	+	0.0113518i	$0.996387\pi$
$440$	2.68693	−	1.55130i	0.128094	−	0.0739554i
$441$		0			0
$442$	1.18693	−	4.79693i	0.0564566	−	0.228167i
$443$	−15.1652			−0.720518			−0.360259	−	0.932852i	$-0.617312\pi$
$443$	−15.1652			−0.720518			−0.360259	+	0.932852i	$0.617312\pi$
$444$	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	$0.869017\pi$
$450$		−	10.4877i		−	0.494393i
$451$	−15.3739	+	26.6283i	−0.723927	+	1.25388i
$452$	−9.47822	−	16.4168i	−0.445818	−	0.772179i
$453$	29.3085	−	16.9213i	1.37703	−	0.795031i
$454$	4.04356			0.189774
$455$		0			0
$456$	−6.62614			−0.310297
$457$	19.7477	−	11.4014i	0.923760	−	0.533333i	0.0389271	−	0.999242i	$-0.487606\pi$
$457$	19.7477	−	11.4014i	0.923760	−	0.533333i	0.884833	+	0.465909i	$0.154273\pi$
$458$	−1.58258	−	2.74110i	−0.0739489	−	0.128083i
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$			1.29510i			0.0603844i
$461$	−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
$467$	−30.1652			−1.39588			−0.697938	−	0.716158i	$-0.745899\pi$
$467$	−30.1652			−1.39588			−0.697938	+	0.716158i	$0.745899\pi$
$468$	−8.58258	−	29.7309i	−0.396730	−	1.37431i
$469$		0			0
$470$	−1.73049	+	0.999100i	−0.0798217	+	0.0460851i
$471$	1.33485	+	2.31203i	0.0615066	+	0.106533i
$472$	10.6652	−	18.4726i	0.490903	−	0.850270i
$473$		−	36.7545i		−	1.68997i
$474$	−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
$478$	3.02178	+	5.23388i	0.138213	+	0.239392i
$479$	16.3521	−	9.44088i	0.747146	−	0.431365i	−0.0775159	−	0.996991i	$-0.524699\pi$
$479$	16.3521	−	9.44088i	0.747146	−	0.431365i	0.824662	+	0.565626i	$0.191366\pi$
$480$	−6.04356			−0.275850
$481$	24.0000	−	6.92820i	1.09431	−	0.315899i
$482$	−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
$486$			7.38505i			0.334993i
$487$	25.4347	+	14.6847i	1.15255	+	0.665428i	0.949508	−	0.313742i	$-0.101583\pi$
$487$	25.4347	+	14.6847i	1.15255	+	0.665428i	0.203046	+	0.979169i	$0.434916\pi$
$488$	−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	$0.803687\pi$
$492$	33.9564	−	19.6048i	1.53087	−	0.883851i
$493$	−20.3739			−0.917593
$494$	−2.19148	−	0.542250i	−0.0985992	−	0.0243970i
$495$	−8.58258			−0.385758
$496$	−20.9347	+	12.0866i	−0.939994	+	0.542706i
$497$		0			0
$498$	−4.47822	+	7.75650i	−0.200674	+	0.347577i
$499$		−	18.4050i		−	0.823921i	−0.911202	−	0.411961i	$-0.864844\pi$
$499$		−	18.4050i		−	0.823921i	0.911202	−	0.411961i	$-0.135156\pi$
$500$	6.93920	+	4.00635i	0.310331	+	0.179169i
$501$	−35.4737	−	20.4807i	−1.58485	−	0.915012i
$502$		−	1.29510i		−	0.0578032i
$503$	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
$506$	2.83485			0.126024
$507$	−1.39564	−	36.2599i	−0.0619827	−	1.61036i
$508$	12.4610			0.552867
$509$	13.0390	−	7.52808i	0.577944	−	0.333676i	−0.182372	−	0.983230i	$-0.558377\pi$
$509$	13.0390	−	7.52808i	0.577944	−	0.333676i	0.760316	+	0.649553i	$0.225044\pi$
$510$	0.873864	+	1.51358i	0.0386953	+	0.0670223i
$511$		0			0
$512$		−	22.8981i		−	1.01196i
$513$	5.93466	+	3.42638i	0.262022	+	0.151278i
$514$	−1.99545	−	1.15208i	−0.0880157	−	0.0508159i
$515$		−	2.09355i		−	0.0922529i
$516$	−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
$520$	−2.76951	−	0.685275i	−0.121451	−	0.0300513i
$521$	−16.4174			−0.719260			−0.359630	−	0.933095i	$-0.617097\pi$
$521$	−16.4174			−0.719260			−0.359630	+	0.933095i	$0.617097\pi$
$522$	12.8739	−	7.43273i	0.563474	−	0.325322i
$523$	12.1652	+	21.0707i	0.531945	+	0.921356i	0.999305	+	0.0372883i	$0.0118720\pi$
$523$	12.1652	+	21.0707i	0.531945	+	0.921356i	−0.467360	+	0.884067i	$0.654795\pi$
$524$	15.5608	−	26.9521i	0.679776	−	1.17741i
$525$		0			0
$526$	3.69148	+	2.13128i	0.160956	+	0.0929280i
$527$	22.5000	+	12.9904i	0.980115	+	0.565870i
$528$		−	30.5493i		−	1.32949i
$529$	10.2477	−	17.7496i	0.445553	−	0.771721i
$530$	0.643371	+	1.11435i	0.0279463	+	0.0484043i
$531$	−51.0998	+	29.5025i	−2.21754	+	1.28030i
$532$		0			0
$533$	27.1652	−	7.84190i	1.17665	−	0.339671i
$534$	−20.5826			−0.890695
$535$	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
$541$		−	6.28065i		−	0.270026i	−0.990844	−	0.135013i	$-0.956892\pi$
$541$		−	6.28065i		−	0.270026i	0.990844	−	0.135013i	$-0.0431077\pi$
$542$	−2.93466	+	5.08298i	−0.126054	+	0.218333i
$543$	12.7913	+	22.1552i	0.548927	+	0.950769i
$544$	−12.3131	+	7.10895i	−0.527918	+	0.304794i
$545$	3.62614			0.155327
$546$		0			0
$547$	−11.7477			−0.502297			−0.251148	−	0.967949i	$-0.580808\pi$
$547$	−11.7477			−0.502297			−0.251148	+	0.967949i	$0.580808\pi$
$548$	−18.5436	+	10.7061i	−0.792142	+	0.457343i
$549$	35.3303	+	61.1939i	1.50786	+	2.61169i
$550$	4.29129	−	7.43273i	0.182981	−	0.316933i
$551$			9.30780i			0.396526i
$552$	−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	$-0.913323\pi$
$557$	−28.5998	+	16.5121i	−1.21181	+	0.699640i	−0.248659	+	0.968591i	$0.579990\pi$
$558$	−18.9564			−0.802490
$559$	−23.4347	+	24.3540i	−0.991180	+	1.03006i
$560$		0			0
$561$	−28.4347	+	16.4168i	−1.20051	+	0.693116i
$562$	7.00000	+	12.1244i	0.295277	+	0.511435i
$563$	18.1652	−	31.4630i	0.765570	−	1.32601i	−0.174375	−	0.984679i	$-0.555790\pi$
$563$	18.1652	−	31.4630i	0.765570	−	1.32601i	0.939945	−	0.341327i	$-0.110876\pi$
$564$			47.8698i			2.01568i
$565$	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
$569$	−8.37386	−	14.5040i	−0.351051	−	0.608038i	0.635383	−	0.772197i	$-0.280842\pi$
$569$	−8.37386	−	14.5040i	−0.351051	−	0.608038i	−0.986434	+	0.164159i	$0.947509\pi$
$570$	0.691478	−	0.399225i	0.0289628	−	0.0167217i
$571$	−2.04356			−0.0855204			−0.0427602	−	0.999085i	$-0.513615\pi$
$571$	−2.04356			−0.0855204			−0.0427602	+	0.999085i	$0.513615\pi$
$572$	6.08258	−	24.5824i	0.254325	−	1.02784i
$573$	−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
$577$			35.6501i			1.48413i	0.670327	+	0.742066i	$0.266154\pi$
$577$			35.6501i			1.48413i	−0.670327	+	0.742066i	$0.733846\pi$
$578$	−3.16515	−	1.82740i	−0.131653	−	0.0760099i
$579$	−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
$583$	−20.9347	+	12.0866i	−0.867025	+	0.500577i
$584$	6.00000			0.248282
$585$	5.68693	+	5.47225i	0.235126	+	0.226250i
$586$	1.16515			0.0481320
$587$	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
$590$			2.57030i			0.105818i
$591$	−5.52178	−	3.18800i	−0.227136	−	0.131137i
$592$	−16.7477	−	9.66930i	−0.688327	−	0.397406i
$593$			6.37600i			0.261831i	0.991394	+	0.130916i	$0.0417917\pi$
$593$			6.37600i			0.261831i	−0.991394	+	0.130916i	$0.958208\pi$
$594$	4.47822	−	7.75650i	0.183744	−	0.318253i
$595$		0			0
$596$	0.708712	−	0.409175i	0.0290300	−	0.0167605i
$597$	−30.7042			−1.25664
$598$	−1.87841	−	1.80750i	−0.0768139	−	0.0739142i
$599$	−6.62614			−0.270737			−0.135368	−	0.990795i	$-0.543222\pi$
$599$	−6.62614			−0.270737			−0.135368	+	0.990795i	$0.543222\pi$
$600$	−20.0608	+	11.5821i	−0.818979	+	0.472837i
$601$	−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
$605$	−1.73049	−	0.999100i	−0.0703545	−	0.0406192i
$606$		−	6.64215i		−	0.269819i
$607$	−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
$611$	−8.29129	+	33.5088i	−0.335430	+	1.35562i
$612$	25.7477			1.04079
$613$	−15.8085	+	9.12705i	−0.638500	+	0.368638i	−0.784037	−	0.620715i	$-0.786843\pi$
$613$	−15.8085	+	9.12705i	−0.638500	+	0.368638i	0.145536	+	0.989353i	$0.453509\pi$
$614$	−3.54356	−	6.13763i	−0.143006	−	0.247694i
$615$	−5.00000	+	8.66025i	−0.201619	+	0.349215i
$616$		0			0
$617$	−14.9174	−	8.61258i	−0.600553	−	0.346729i	0.168706	−	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
$619$			19.3386i			0.777284i	0.921389	+	0.388642i	$0.127056\pi$
$619$			19.3386i			0.777284i	−0.921389	+	0.388642i	$0.872944\pi$
$620$	3.54356	−	6.13763i	0.142313	−	0.246493i
$621$	3.95644	+	6.85275i	0.158766	+	0.274992i
$622$	10.5000	−	6.06218i	0.421012	−	0.243071i
$623$		0			0
$624$	−19.4782	+	20.2424i	−0.779753	+	0.810343i
$625$	21.9129			0.876515
$626$	−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	$0.481251\pi$
$632$			10.3923i			0.413384i
$633$	−14.7695	+	25.5815i	−0.587035	+	1.01677i
$634$	−4.23049	−	7.32743i	−0.168014	−	0.291009i
$635$	−2.75227	+	1.58903i	−0.109221	+	0.0630586i
$636$	30.8258			1.22232
$637$		0			0
$638$	12.1652			0.481623
$639$	−18.1652	+	10.4877i	−0.718602	+	0.414885i
$640$	2.52178	+	4.36785i	0.0996821	+	0.172654i
$641$	−14.6869	+	25.4385i	−0.580099	+	1.00476i	0.415368	+	0.909653i	$0.363653\pi$
$641$	−14.6869	+	25.4385i	−0.580099	+	1.00476i	−0.995467	+	0.0951074i	$0.969681\pi$
$642$			6.64215i			0.262145i
$643$	−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	0.971990	+	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
$649$	−48.2867			−1.89542
$650$	−7.58258	+	2.18890i	−0.297413	+	0.0858558i
$651$		0			0
$652$	−10.7477	+	6.20520i	−0.420913	+	0.243015i
$653$	−7.89564	−	13.6757i	−0.308980	−	0.535170i	0.669159	−	0.743119i	$-0.266654\pi$
$653$	−7.89564	−	13.6757i	−0.308980	−	0.535170i	−0.978140	+	0.207949i	$0.933321\pi$
$654$	−5.06080	+	8.76555i	−0.197893	+	0.342760i
$655$			7.93725i			0.310134i
$656$	−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	$0.203951\pi$
$660$	4.47822	+	7.75650i	0.174314	+	0.301922i
$661$	43.7477	−	25.2578i	1.70159	−	0.982413i	0.757434	−	0.652911i	$-0.226453\pi$
$661$	43.7477	−	25.2578i	1.70159	−	0.982413i	0.944155	−	0.329502i	$-0.106881\pi$
$662$	−11.3739			−0.442058
$663$	29.3085	+	7.25198i	1.13825	+	0.281644i
$664$	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
$668$			26.2867i			1.01706i
$669$	−45.8739	−	26.4853i	−1.77359	−	1.02398i
$670$	−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	$-0.337266\pi$
$674$	−3.93920	+	2.27430i	−0.151732	+	0.0876028i
$675$	23.9564			0.922084
$676$	−19.7042	+	12.4104i	−0.757853	+	0.477323i
$677$	29.2087			1.12258			0.561291	−	0.827619i	$-0.310305\pi$
$677$	29.2087			1.12258			0.561291	+	0.827619i	$0.310305\pi$
$678$	−11.6869	+	6.74745i	−0.448834	+	0.259134i
$679$		0			0
$680$	1.18693	−	2.05583i	0.0455168	−	0.0788373i
$681$			24.7056i			0.946719i
$682$	−13.4347	−	7.75650i	−0.514440	−	0.297012i
$683$	26.2913	+	15.1793i	1.00601	+	0.580819i	0.910020	−	0.414563i	$-0.136066\pi$
$683$	26.2913	+	15.1793i	1.00601	+	0.580819i	0.0959878	+	0.995383i	$0.469399\pi$
$684$		−	11.7629i		−	0.449764i
$685$	2.73049	−	4.72935i	0.104327	−	0.180699i
$686$		0			0
$687$	16.7477	−	9.66930i	0.638966	−	0.368907i
$688$	26.1652			0.997537
$689$	21.5780	+	5.33918i	0.822057	+	0.203406i
$690$	0.921970			0.0350988
$691$	8.93466	−	5.15843i	0.339890	−	0.196236i	−0.320333	−	0.947305i	$-0.603795\pi$
$691$	8.93466	−	5.15843i	0.339890	−	0.196236i	0.660224	+	0.751069i	$0.270462\pi$
$692$	−17.6869	−	30.6347i	−0.672356	−	1.16456i
$693$		0			0
$694$			6.20520i			0.235546i
$695$	1.50000	+	0.866025i	0.0568982	+	0.0328502i
$696$	−28.4347	−	16.4168i	−1.07781	−	0.622276i
$697$			23.5257i			0.891100i
$698$	−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	$0.584627\pi$
$702$	−7.91288	+	2.28425i	−0.298652	+	0.0862135i
$703$	9.49545			0.358128
$704$	−11.6044	+	6.69978i	−0.437356	+	0.252507i
$705$	−6.10436	−	10.5731i	−0.229903	−	0.398204i
$706$	4.14792	−	7.18440i	0.156109	−	0.270389i
$707$		0			0
$708$	53.3258	+	30.7876i	2.00410	+	1.15707i
$709$	−13.1869	−	7.61348i	−0.495246	−	0.285930i	0.231502	−	0.972834i	$-0.425636\pi$
$709$	−13.1869	−	7.61348i	−0.495246	−	0.285930i	−0.726748	+	0.686904i	$0.758969\pi$
$710$			0.913701i			0.0342906i
$711$	14.3739	−	24.8963i	0.539062	−	0.933683i
$712$	13.9782	+	24.2110i	0.523856	+	0.907345i
$713$	11.8693	−	6.85275i	0.444509	−	0.256638i
$714$		0			0
$715$	1.79129	+	6.20520i	0.0669904	+	0.232061i
$716$	−16.1216			−0.602492
$717$	−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
$723$		−	54.9887i		−	2.04505i
$724$	8.20871	−	14.2179i	0.305074	−	0.528404i
$725$	16.2695	+	28.1796i	0.604234	+	1.04656i
$726$	4.83030	−	2.78878i	0.179269	−	0.103501i
$727$	0.252273			0.00935628			0.00467814	−	0.999989i	$-0.498511\pi$
$727$	0.252273			0.00935628			0.00467814	+	0.999989i	$0.498511\pi$
$728$		0			0
$729$	−43.8693			−1.62479
$730$	−0.626136	+	0.361500i	−0.0231744	+	0.0133797i
$731$	−14.0608	−	24.3540i	−0.520057	−	0.900766i
$732$	36.8693	−	63.8595i	1.36273	−	2.36032i
$733$			16.9590i			0.626395i	0.949688	+	0.313198i	$0.101400\pi$
$733$			16.9590i			0.626395i	−0.949688	+	0.313198i	$0.898600\pi$
$734$	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	$-0.550912\pi$
$739$	16.7477	−	9.66930i	0.616075	−	0.355691i	0.775339	+	0.631545i	$0.217579\pi$
$740$	5.66970			0.208422
$741$	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	$0.115446\pi$
$744$	20.9347	+	36.2599i	0.767502	+	1.32935i
$745$	−0.104356	+	0.180750i	−0.00382331	+	0.00662217i
$746$		−	14.7146i		−	0.538738i
$747$	−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
$751$	−11.8739	−	20.5661i	−0.433283	−	0.750469i	0.563870	−	0.825863i	$-0.309312\pi$
$751$	−11.8739	−	20.5661i	−0.433283	−	0.750469i	−0.997154	+	0.0753944i	$0.975978\pi$
$752$	23.1434	−	13.3618i	0.843952	−	0.487256i
$753$	7.91288			0.288361
$754$	−8.06080	−	7.75650i	−0.293557	−	0.282475i
$755$	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
$759$			17.3205i			0.628695i
$760$	−0.939205	−	0.542250i	−0.0340685	−	0.0196695i
$761$	−11.2259	−	6.48130i	−0.406940	−	0.234947i	0.282534	−	0.959257i	$-0.408825\pi$
$761$	−11.2259	−	6.48130i	−0.406940	−	0.234947i	−0.689474	+	0.724310i	$0.742158\pi$
$762$		−	8.87086i		−	0.321357i
$763$		0			0
$764$	12.8739	+	22.2982i	0.465760	+	0.806720i
$765$	−5.68693	+	3.28335i	−0.205611	+	0.118710i
$766$	0.582576			0.0210493
$767$	31.9955	+	30.7876i	1.15529	+	1.11168i
$768$	5.00000			0.180422
$769$	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
$772$			34.6410i			1.24676i
$773$	−16.8303	−	9.71698i	−0.605344	−	0.349495i	0.165797	−	0.986160i	$-0.446980\pi$
$773$	−16.8303	−	9.71698i	−0.605344	−	0.349495i	−0.771141	+	0.636664i	$0.780314\pi$
$774$	17.7695	+	10.2592i	0.638712	+	0.368760i
$775$		−	41.4938i		−	1.49050i
$776$	−6.31307	+	10.9346i	−0.226626	+	0.392528i
$777$		0			0
$778$	0.130682	−	0.0754495i	0.00468519	−	0.00270499i
$779$	10.7477			0.385077
$780$	1.97822	−	7.99488i	0.0708316	−	0.286263i
$781$	−17.1652			−0.614217
$782$	1.87841	−	1.08450i	0.0671718	−	0.0387816i
$783$	16.9782	+	29.4071i	0.606752	+	1.05093i
$784$		0			0
$785$			0.436950i			0.0155954i
$786$	−19.1869	−	11.0776i	−0.684375	−	0.395124i
$787$	−22.7477	−	13.1334i	−0.810869	−	0.468155i	0.0363886	−	0.999338i	$-0.488415\pi$
$787$	−22.7477	−	13.1334i	−0.810869	−	0.468155i	−0.847258	+	0.531182i	$0.821748\pi$
$788$			4.09175i			0.145763i
$789$	−13.0218	+	22.5544i	−0.463588	+	0.802957i
$790$	−0.626136	−	1.08450i	−0.0222769	−	0.0385848i
$791$		0			0
$792$	−32.5390			−1.15622
$793$	36.8693	−	38.3157i	1.30927	−	1.36063i
$794$	14.8348			0.526469
$795$	−6.80852	+	3.93090i	−0.241473	+	0.139415i
$796$	9.85208	+	17.0643i	0.349198	+	0.604828i
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$	−24.8739	−	14.3609i	−0.879974	−	0.508053i
$800$	19.6652	+	11.3537i	0.695268	+	0.401413i
$801$		−	77.3345i		−	2.73248i
$802$	−7.14792	+	12.3806i	−0.252402	+	0.437173i
$803$	−6.79129	−	11.7629i	−0.239659	−	0.415102i
$804$	−19.3693	+	11.1829i	−0.683103	+	0.394390i
$805$		0			0
$806$	3.95644	+	13.7055i	0.139360	+	0.482756i
$807$	44.0780			1.55162
$808$	−7.81307	+	4.51088i	−0.274863	+	0.158692i
$809$	−26.6216	−	46.1099i	−0.935965	−	1.62114i	−0.772904	−	0.634524i	$-0.781196\pi$
$809$	−26.6216	−	46.1099i	−0.935965	−	1.62114i	−0.163062	−	0.986616i	$-0.552137\pi$
$810$	−0.0435608	+	0.0754495i	−0.00153057	+	0.00265102i
$811$			27.6374i			0.970479i	0.874381	+	0.485240i	$0.161268\pi$
$811$			27.6374i			0.970479i	−0.874381	+	0.485240i	$0.838732\pi$
$812$		0			0
$813$	−31.0562	−	17.9303i	−1.08919	−	0.628844i
$814$		−	12.4104i		−	0.434985i
$815$	1.58258	−	2.74110i	0.0554352	−	0.0960166i
$816$	−11.6869	−	20.2424i	−0.409124	−	0.708624i
$817$	−11.1261	+	6.42368i	−0.389254	+	0.224736i
$818$	3.79129			0.132559
$819$		0			0
$820$	6.41742			0.224106
$821$	10.9610	−	6.32833i	0.382541	−	0.220860i	−0.296382	−	0.955069i	$-0.595780\pi$
$821$	10.9610	−	6.32833i	0.382541	−	0.220860i	0.678923	+	0.734209i	$0.262447\pi$
$822$	7.62159	+	13.2010i	0.265834	+	0.460437i
$823$	11.2477	−	19.4816i	0.392071	−	0.679087i	−0.600651	−	0.799511i	$-0.705092\pi$
$823$	11.2477	−	19.4816i	0.392071	−	0.679087i	0.992723	+	0.120424i	$0.0384254\pi$
$824$		−	7.93725i		−	0.276507i
$825$	45.4129	+	26.2191i	1.58107	+	0.912833i
$826$		0			0
$827$			35.3839i			1.23042i	0.788364	+	0.615210i	$0.210929\pi$
$827$			35.3839i			1.23042i	−0.788364	+	0.615210i	$0.789071\pi$
$828$	6.79129	−	11.7629i	0.236014	−	0.408787i
$829$	17.1869	+	29.7686i	0.596927	+	1.03391i	0.993272	+	0.115806i	$0.0369451\pi$
$829$	17.1869	+	29.7686i	0.596927	+	1.03391i	−0.396345	+	0.918102i	$0.629722\pi$
$830$	−1.26951	+	0.732950i	−0.0440652	+	0.0254411i
$831$	32.7913			1.13752
$832$	11.9610	+	2.95958i	0.414673	+	0.102605i
$833$		0			0
$834$	−4.18693	+	2.41733i	−0.144982	+	0.0837052i
$835$	−3.35208	−	5.80598i	−0.116004	−	0.200924i
$836$	4.81307	−	8.33648i	0.166463	−	0.288323i
$837$		−	43.3013i		−	1.49671i
$838$	0.691478	+	0.399225i	0.0238867	+	0.0137910i
$839$	24.2305	+	13.9895i	0.836530	+	0.482971i	0.856083	−	0.516838i	$-0.172891\pi$
$839$	24.2305	+	13.9895i	0.836530	+	0.482971i	−0.0195536	+	0.999809i	$0.506224\pi$
$840$		0			0
$841$	−8.56080	+	14.8277i	−0.295200	+	0.511301i
$842$	0.956439	+	1.65660i	0.0329611	+	0.0570903i
$843$	−74.0780	+	42.7690i	−2.55138	+	1.47304i
$844$	18.9564			0.652508
$845$	2.76951	−	5.25378i	0.0952740	−	0.180735i
$846$	20.9564			0.720497
$847$		0			0
$848$	−8.60436	−	14.9032i	−0.295475	−	0.511777i
$849$	3.83485	−	6.64215i	0.131612	−	0.227958i
$850$		−	6.56670i		−	0.225236i
$851$	9.49545	+	5.48220i	0.325500	+	0.187927i
$852$	18.9564	+	10.9445i	0.649437	+	0.374953i
$853$		−	14.1425i		−	0.484229i	−0.970248	−	0.242114i	$-0.922159\pi$
$853$		−	14.1425i		−	0.484229i	0.970248	−	0.242114i	$-0.0778409\pi$
$854$		0			0
$855$	1.50000	+	2.59808i	0.0512989	+	0.0888523i
$856$	7.81307	−	4.51088i	0.267045	−	0.154179i
$857$	−15.4610			−0.528137			−0.264069	−	0.964504i	$-0.585065\pi$
$857$	−15.4610			−0.528137			−0.264069	+	0.964504i	$0.585065\pi$
$858$	−17.5000	−	4.33013i	−0.597440	−	0.147828i
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−6.64337	+	3.83555i	−0.226537	+	0.130791i
$861$		0			0
$862$	−7.91742	+	13.7134i	−0.269669	+	0.467080i
$863$		−	45.4147i		−	1.54594i	−0.634446	−	0.772968i	$-0.718772\pi$
$863$		−	45.4147i		−	1.54594i	0.634446	−	0.772968i	$-0.281228\pi$
$864$	20.5218	+	11.8483i	0.698165	+	0.403086i
$865$	7.81307	+	4.51088i	0.265652	+	0.153374i
$866$		−	14.8456i		−	0.504473i
$867$	11.1652	−	19.3386i	0.379188	−	0.656774i
$868$		0			0
$869$	20.3739	−	11.7629i	0.691136	−	0.399028i
$870$	3.95644			0.134136
$871$	−15.4955	+	4.47315i	−0.525043	+	0.151567i
$872$	13.7477			0.465557
$873$	30.2477	−	17.4635i	1.02373	−	0.591051i
$874$	−0.495454	−	0.858152i	−0.0167590	−	0.0290274i
$875$		0			0
$876$			17.3205i			0.585206i
$877$	2.75227	+	1.58903i	0.0929377	+	0.0536576i	0.545749	−	0.837949i	$-0.316245\pi$
$877$	2.75227	+	1.58903i	0.0929377	+	0.0536576i	−0.452811	+	0.891607i	$0.649579\pi$
$878$	8.12614	+	4.69163i	0.274244	+	0.158335i
$879$			7.11890i			0.240115i
$880$	2.50000	−	4.33013i	0.0842750	−	0.145969i
$881$	8.29129	+	14.3609i	0.279341	+	0.483832i	0.971221	−	0.238180i	$-0.0765508\pi$
$881$	8.29129	+	14.3609i	0.279341	+	0.483832i	−0.691880	+	0.722012i	$0.743217\pi$
$882$		0			0
$883$	29.2432			0.984111			0.492056	−	0.870564i	$-0.336246\pi$
$883$	29.2432			0.984111			0.492056	+	0.870564i	$0.336246\pi$
$884$	−5.37386	−	18.6156i	−0.180743	−	0.626111i
$885$	−15.7042			−0.527890
$886$	6.00000	−	3.46410i	0.201574	−	0.116379i
$887$	11.2087	+	19.4141i	0.376352	+	0.651860i	0.990528	−	0.137308i	$-0.0438451\pi$
$887$	11.2087	+	19.4141i	0.376352	+	0.651860i	−0.614177	+	0.789169i	$0.710512\pi$
$888$	−16.7477	+	29.0079i	−0.562017	+	0.973442i
$889$		0			0
$890$	−2.91742	−	1.68438i	−0.0977923	−	0.0564604i
$891$	−1.41742	−	0.818350i	−0.0474855	−	0.0274158i
$892$			33.9935i			1.13819i
$893$	−6.56080	+	11.3636i	−0.219549	+	0.380269i
$894$	−0.291288	−	0.504525i	−0.00974212	−	0.0168739i
$895$	3.56080	−	2.05583i	0.119024	−	0.0687187i
$896$		0			0
$897$	11.0436	−	11.4768i	0.368734	−	0.383199i
$898$	11.4955			0.383608
$899$	50.9347	−	29.4071i	1.69877	−	0.980783i
$900$	−20.5608	−	35.6123i	−0.685360	−	1.18708i
$901$	−9.24773	+	16.0175i	−0.308086	+	0.533621i
$902$		−	14.0471i		−	0.467717i
$903$		0			0
$904$	15.8739	+	9.16478i	0.527957	+	0.304816i
$905$			4.18710i			0.139184i
$906$	−7.73049	+	13.3896i	−0.256828	+	0.444840i
$907$	20.5390	+	35.5746i	0.681987	+	1.18124i	0.974374	+	0.224936i	$0.0722172\pi$
$907$	20.5390	+	35.5746i	0.681987	+	1.18124i	−0.292387	+	0.956300i	$0.594449\pi$
$908$	13.7305	−	7.92730i	0.455662	−	0.263077i
$909$	24.9564			0.827753
$910$		0			0
$911$	−43.1216			−1.42868			−0.714341	−	0.699798i	$-0.753273\pi$
$911$	−43.1216			−1.42868			−0.714341	+	0.699798i	$0.753273\pi$
$912$	−9.24773	+	5.33918i	−0.306223	+	0.176798i
$913$	−13.7695	−	23.8495i	−0.455704	−	0.789303i
$914$	−5.20871	+	9.02175i	−0.172289	+	0.298413i
$915$			18.8063i			0.621717i
$916$	−10.7477	−	6.20520i	−0.355115	−	0.205026i
$917$		0			0
$918$		−	6.85275i		−	0.226175i
$919$	−12.9564	+	22.4412i	−0.427393	+	0.740267i	−0.996641	−	0.0818992i	$-0.973901\pi$
$919$	−12.9564	+	22.4412i	−0.427393	+	0.740267i	0.569247	+	0.822166i	$0.307235\pi$
$920$	−0.626136	−	1.08450i	−0.0206431	−	0.0357549i
$921$	37.5000	−	21.6506i	1.23567	−	0.713413i
$922$	2.12159			0.0698709
$923$	11.3739	+	10.9445i	0.374375	+	0.360243i
$924$		0			0
$925$	28.7477	−	16.5975i	0.945219	−	0.545723i
$926$	1.81307	+	3.14033i	0.0595811	+	0.103198i
$927$	−10.9782	+	19.0148i	−0.360572	+	0.624529i
$928$			32.1860i			1.05656i
$929$	50.1606	+	28.9602i	1.64572	+	0.950155i	0.978748	+	0.205069i	$0.0657418\pi$
$929$	50.1606	+	28.9602i	1.64572	+	0.950155i	0.666969	+	0.745086i	$0.267592\pi$
$930$	−4.36932	−	2.52263i	−0.143276	−	0.0827202i
$931$		0			0
$932$	−14.2913	+	24.7532i	−0.468127	+	0.810819i
$933$	37.0390	+	64.1535i	1.21260	+	2.10029i
$934$	11.9347	−	6.89048i	0.390514	−	0.225463i
$935$	−5.37386			−0.175744
$936$	21.5608	+	20.7469i	0.704737	+	0.678133i
$937$	−20.4955			−0.669557			−0.334779	−	0.942297i	$-0.608662\pi$
$937$	−20.4955			−0.669557			−0.334779	+	0.942297i	$0.608662\pi$
$938$		0			0
$939$	−9.41742	−	16.3115i	−0.307326	−	0.532304i
$940$	−3.91742	+	6.78518i	−0.127772	+	0.221308i
$941$		−	39.3049i		−	1.28130i	−0.767832	−	0.640651i	$-0.778665\pi$
$941$		−	39.3049i		−	1.28130i	0.767832	−	0.640651i	$-0.221335\pi$
$942$	−1.05625	−	0.609826i	−0.0344145	−	0.0198692i
$943$	10.7477	+	6.20520i	0.349994	+	0.202069i
$944$		−	34.3749i		−	1.11881i
$945$		0			0
$946$	8.39564	+	14.5417i	0.272966	+	0.472791i
$947$	−33.2305	+	19.1856i	−1.07985	+	0.623449i	−0.930855	−	0.365389i	$-0.880936\pi$
$947$	−33.2305	+	19.1856i	−1.07985	+	0.623449i	−0.148991	+	0.988839i	$0.547603\pi$
$948$	−30.0000			−0.974355
$949$	−3.00000	+	12.1244i	−0.0973841	+	0.393573i
$950$	−3.00000			−0.0973329
$951$	44.7695	−	25.8477i	1.45175	−	0.838169i
$952$		0			0
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$		−	13.4949i		−	0.436914i
$955$	−5.68693	−	3.28335i	−0.184025	−	0.106247i
$956$	20.5218	+	11.8483i	0.663722	+	0.383200i
$957$			74.3273i			2.40266i
$958$	−4.31307	+	7.47045i	−0.139349	+	0.241359i
$959$		0			0
$960$	−3.77405	+	2.17895i	−0.121807	+	0.0703253i
$961$	−44.0000			−1.41935
$962$	−7.91288	+	8.22330i	−0.255121	+	0.265130i
$963$	−24.9564			−0.804210
$964$	−30.5608	+	17.6443i	−0.984297	+	0.568284i
$965$	−4.41742	−	7.65120i	−0.142202	−	0.246301i
$966$		0			0
$967$			23.8118i			0.765735i	0.923803	+	0.382867i	$0.125063\pi$
$967$			23.8118i			0.765735i	−0.923803	+	0.382867i	$0.874937\pi$
$968$	−6.56080	−	3.78788i	−0.210872	−	0.121747i
$969$	9.93920	+	5.73840i	0.319293	+	0.184344i
$970$		−	1.52145i		−	0.0488508i
$971$	11.1261	−	19.2710i	0.357055	−	0.618437i	−0.630413	−	0.776260i	$-0.717114\pi$
$971$	11.1261	−	19.2710i	0.357055	−	0.618437i	0.987467	+	0.157823i	$0.0504476\pi$
$972$	14.4782	+	25.0770i	0.464389	+	0.804346i
$973$		0			0
$974$	−13.4174			−0.429922
$975$	−13.3739	−	46.3284i	−0.428306	−	1.48370i
$976$	−41.1652			−1.31766
$977$	−1.20417	+	0.695226i	−0.0385247	+	0.0222422i	−0.519139	−	0.854690i	$-0.673747\pi$
$977$	−1.20417	+	0.695226i	−0.0385247	+	0.0222422i	0.480614	+	0.876932i	$0.340414\pi$
$978$	4.41742	+	7.65120i	0.141254	+	0.244659i
$979$	31.6434	−	54.8079i	1.01133	−	1.75167i
$980$		0			0
$981$	−32.9347	−	19.0148i	−1.05152	−	0.607097i
$982$	−1.63068	−	0.941475i	−0.0520372	−	0.0300437i
$983$			19.8908i			0.634418i	0.948356	+	0.317209i	$0.102746\pi$
$983$			19.8908i			0.634418i	−0.948356	+	0.317209i	$0.897254\pi$
$984$	−18.9564	+	32.8335i	−0.604309	+	1.04669i
$985$	−0.521780	−	0.903750i	−0.0166253	−	0.0287959i
$986$	8.06080	−	4.65390i	0.256708	−	0.148210i
$987$		0			0
$988$	−8.50455	+	2.45505i	−0.270566	+	0.0781056i
$989$	−14.8348			−0.471721
$990$	3.39564	−	1.96048i	0.107921	−	0.0623080i
$991$	20.1869	+	34.9648i	0.641259	+	1.11069i	0.985152	+	0.171684i	$0.0549209\pi$
$991$	20.1869	+	34.9648i	0.641259	+	1.11069i	−0.343893	+	0.939009i	$0.611746\pi$
$992$	20.5218	−	35.5448i	0.651567	−	1.12855i
$993$		−	69.4926i		−	2.20528i
$994$		0			0
$995$	−4.35208	−	2.51268i	−0.137970	−	0.0796572i
$996$			35.1178i			1.11275i
$997$	−7.03901	+	12.1919i	−0.222928	+	0.386122i	−0.955696	−	0.294356i	$-0.904895\pi$
$997$	−7.03901	+	12.1919i	−0.222928	+	0.386122i	0.732768	+	0.680479i	$0.238228\pi$
$998$	4.20417	+	7.28183i	0.133081	+	0.230502i
$999$	30.0000	−	17.3205i	0.949158	−	0.547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.e.491.1	✓	4
7.2	even	3		637.2.u.e.361.2		4
7.3	odd	6		637.2.k.f.569.1		4
7.4	even	3		637.2.k.d.569.1		4
7.5	odd	6		637.2.u.d.361.2		4
7.6	odd	2		637.2.q.f.491.1	yes	4
13.2	odd	12		8281.2.a.bs.1.2		4
13.4	even	6	inner	637.2.q.e.589.1	yes	4
13.11	odd	12		8281.2.a.bs.1.3		4
91.4	even	6		637.2.u.e.30.2		4
91.17	odd	6		637.2.u.d.30.2		4
91.30	even	6		637.2.k.d.459.2		4
91.41	even	12		8281.2.a.bq.1.2		4
91.69	odd	6		637.2.q.f.589.1	yes	4
91.76	even	12		8281.2.a.bq.1.3		4
91.82	odd	6		637.2.k.f.459.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.d.459.2		4	91.30	even	6
637.2.k.d.569.1		4	7.4	even	3
637.2.k.f.459.2		4	91.82	odd	6
637.2.k.f.569.1		4	7.3	odd	6
637.2.q.e.491.1	✓	4	1.1	even	1	trivial
637.2.q.e.589.1	yes	4	13.4	even	6	inner
637.2.q.f.491.1	yes	4	7.6	odd	2
637.2.q.f.589.1	yes	4	91.69	odd	6
637.2.u.d.30.2		4	91.17	odd	6
637.2.u.d.361.2		4	7.5	odd	6
637.2.u.e.30.2		4	91.4	even	6
637.2.u.e.361.2		4	7.2	even	3
8281.2.a.bq.1.2		4	91.41	even	12
8281.2.a.bq.1.3		4	91.76	even	12
8281.2.a.bs.1.2		4	13.2	odd	12
8281.2.a.bs.1.3		4	13.11	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.395644 + 0.228425i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.895644 + 1.55130i) q^{4} -0.456850i q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 + 4.14938i) q^{9} +O(q^{10})\)	\(q+(-0.395644 + 0.228425i) q^{2} +(-1.39564 - 2.41733i) q^{3} +(-0.895644 + 1.55130i) q^{4} -0.456850i 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} +5.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +(-1.39564 - 2.41733i) q^{16} +(-1.50000 + 2.59808i) q^{17} -2.18890i q^{18} +(1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} +(0.791288 + 1.37055i) q^{23} +(-4.18693 + 2.41733i) q^{24} +4.79129 q^{25} +(-1.58258 + 0.456850i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 - 0.504525i) q^{30} -8.66025i q^{31} +(4.10436 + 2.36965i) q^{32} +(9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +(6.00000 - 3.46410i) q^{37} -0.626136 q^{38} +(-2.79129 - 9.66930i) q^{39} -0.791288 q^{40} +(6.79129 - 3.92095i) q^{41} +(-4.68693 + 8.11800i) q^{43} -7.02355i q^{44} +(1.89564 + 1.09445i) q^{45} +(-0.626136 - 0.361500i) q^{46} +9.57395i q^{47} +(-3.89564 + 6.74745i) q^{48} +(-1.89564 + 1.09445i) q^{50} +8.37386 q^{51} +(-4.47822 + 4.65390i) q^{52} +6.16515 q^{53} +(-1.97822 + 1.14213i) q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(-2.68693 - 1.55130i) q^{58} +(10.6652 + 6.15753i) q^{59} -2.28425i q^{60} +(7.37386 - 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(0.395644 - 1.59898i) q^{65} -5.00000 q^{66} +(-3.87386 + 2.23658i) q^{67} +(-2.68693 - 4.65390i) q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(7.18693 + 4.14938i) q^{72} +3.46410i q^{73} +(-1.58258 + 2.74110i) q^{74} +(-6.68693 - 11.5821i) q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} -6.00000 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} -4.28245i q^{86} +(9.47822 - 16.4168i) q^{87} +(3.39564 + 5.88143i) q^{88} +(-13.9782 + 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(-20.9347 + 12.0866i) q^{93} +(-2.18693 - 3.78788i) q^{94} +(0.313068 - 0.542250i) q^{95} -13.2288i q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9	\( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9 + 5 * q^10 - 9 * q^11 + 20 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 - 9 * q^19 + 12 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 10 * q^25 + 12 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 + 21 * q^32 + 15 * q^33 - 8 * q^36 + 24 * q^37 - 30 * q^38 - 2 * q^39 + 6 * q^40 + 18 * q^41 - 5 * q^43 + 3 * q^45 - 30 * q^46 - 11 * q^48 - 3 * q^50 + 6 * q^51 + 5 * q^52 - 12 * q^53 + 15 * q^54 - q^55 + 3 * q^58 + 6 * q^59 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 3 * q^65 - 20 * q^66 + 12 * q^67 + 3 * q^68 + 18 * q^69 + 6 * q^71 + 15 * q^72 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 - 24 * q^79 - 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 15 * q^87 + 9 * q^88 - 33 * q^89 - 4 * q^90 - 48 * q^92 - 15 * q^93 + 5 * q^94 + 15 * q^95 - 39 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more