LMFDB - Embedded newform 637.2.q.f.589.1

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			589.1
Root			$1.39564 - 0.228425i$ of defining polynomial
Character	$\chi$	$=$	637.589
Dual form			637.2.q.f.491.1

$q$-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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

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

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	0.353553	−	0.935414i	$-0.384973\pi$
$2$	−0.395644	−	0.228425i	−0.279763	−	0.161521i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	1.39564	−	2.41733i	0.805775	−	1.39564i	−0.109991	−	0.993933i	$-0.535082\pi$
$3$	1.39564	−	2.41733i	0.805775	−	1.39564i	0.915766	−	0.401711i	$-0.131584\pi$
$4$	−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	−0.108616	−	0.994084i	$-0.534642\pi$
$11$	−3.39564	−	1.96048i	−1.02383	−	0.591106i	−0.915210	+	0.402978i	$0.867975\pi$
$12$	−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	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$			2.18890i			0.515929i
$19$	−1.18693	+	0.685275i	−0.272301	+	0.157213i	−0.629933	−	0.776650i	$-0.716918\pi$
$19$	−1.18693	+	0.685275i	−0.272301	+	0.157213i	0.357632	+	0.933863i	$0.383584\pi$
$20$	−0.708712	+	0.409175i	−0.158473	+	0.0914943i
$21$		0			0
$22$	0.895644	+	1.55130i	0.190952	+	0.330738i
$23$	0.791288	−	1.37055i	0.164995	−	0.285780i	−0.771659	−	0.636037i	$-0.780573\pi$
$23$	0.791288	−	1.37055i	0.164995	−	0.285780i	0.936653	+	0.350257i	$0.113906\pi$
$24$	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	−0.356883	−	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
$31$		−	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	0.904194	−	0.427121i	$-0.140472\pi$
$37$	6.00000	+	3.46410i	0.986394	+	0.569495i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	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	$-0.543109\pi$
$41$	−6.79129	−	3.92095i	−1.06062	−	0.612350i	−0.925604	+	0.378493i	$0.876442\pi$
$42$		0			0
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	−0.963056	−	0.269302i	$-0.913207\pi$
$43$	−4.68693	−	8.11800i	−0.714750	−	1.23798i	0.248305	−	0.968682i	$-0.420126\pi$
$44$			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	$-0.962707\pi$
$59$	−10.6652	+	6.15753i	−1.38848	+	0.801642i	−0.395340	+	0.918535i	$0.629373\pi$
$60$			2.28425i			0.294896i
$61$	−7.37386	−	12.7719i	−0.944126	−	1.63528i	−0.757491	−	0.652846i	$-0.773575\pi$
$61$	−7.37386	−	12.7719i	−0.944126	−	1.63528i	−0.186636	−	0.982429i	$-0.559758\pi$
$62$	−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	0.244339	−	0.969690i	$-0.421429\pi$
$67$	−3.87386	−	2.23658i	−0.473268	−	0.273241i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	2.68693	−	4.65390i	0.325838	−	0.564369i
$69$	−2.20871	−	3.82560i	−0.265898	−	0.460548i
$70$		0			0
$71$	3.79129	−	2.18890i	0.449943	−	0.259775i	−0.257863	−	0.966181i	$-0.583018\pi$
$71$	3.79129	−	2.18890i	0.449943	−	0.259775i	0.707806	+	0.706407i	$0.249685\pi$
$72$	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	$-0.00661204\pi$
$89$	13.9782	+	8.07033i	1.48169	+	0.855453i	0.481904	+	0.876224i	$0.339945\pi$
$90$	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	$-0.545997\pi$
$97$	6.31307	−	3.64485i	0.640995	−	0.370079i	0.784998	+	0.619499i	$0.212664\pi$
$98$		0			0
$99$			18.7864i			1.88811i
$100$	−4.29129	−	7.43273i	−0.429129	−	0.743273i
$101$	2.60436	−	4.51088i	0.259143	−	0.448849i	−0.706869	−	0.707344i	$-0.749893\pi$
$101$	2.60436	−	4.51088i	0.259143	−	0.448849i	0.966013	+	0.258495i	$0.0832265\pi$
$102$	−3.31307	−	1.91280i	−0.328043	−	0.189396i
$103$	−4.58258			−0.451535			−0.225767	−	0.974181i	$-0.572489\pi$
$103$	−4.58258			−0.451535			−0.225767	+	0.974181i	$0.572489\pi$
$104$	−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	−0.712241	−	0.701935i	$-0.752320\pi$
$107$	2.60436	−	4.51088i	0.251773	−	0.436083i	0.964014	+	0.265852i	$0.0856532\pi$
$108$	4.47822	+	7.75650i	0.430917	+	0.746370i
$109$		−	7.93725i		−	0.760251i	−0.924935	−	0.380126i	$-0.875881\pi$
$109$		−	7.93725i		−	0.760251i	0.924935	−	0.380126i	$-0.124119\pi$
$110$	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	$0.999178\pi$
$114$	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	−0.978066	−	0.208297i	$-0.933208\pi$
$127$	−3.47822	+	6.02445i	−0.308642	+	0.534584i	0.669423	+	0.742881i	$0.266541\pi$
$128$	−9.56080	−	5.51993i	−0.845063	−	0.487897i
$129$	−26.1652			−2.30371
$130$	0.208712	−	0.723000i	0.0183053	−	0.0634113i
$131$	17.3739			1.51796			0.758981	−	0.651113i	$-0.225698\pi$
$131$	17.3739			1.51796			0.758981	+	0.651113i	$0.225698\pi$
$132$	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	0.0123190	−	0.999924i	$-0.496079\pi$
$137$	10.3521	−	5.97678i	0.884438	−	0.510631i	0.872119	+	0.489294i	$0.162745\pi$
$138$			2.01810i			0.171792i
$139$	1.89564	+	3.28335i	0.160786	+	0.278490i	0.935151	−	0.354249i	$-0.115264\pi$
$139$	1.89564	+	3.28335i	0.160786	+	0.278490i	−0.774365	+	0.632740i	$0.781930\pi$
$140$		0			0
$141$	23.1434	+	13.3618i	1.94902	+	1.12527i
$142$	−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	−0.516119	−	0.856517i	$-0.672624\pi$
$149$	−0.395644	+	0.228425i	−0.0324124	+	0.0187133i	0.483706	+	0.875230i	$0.339290\pi$
$150$	−5.29129	+	3.05493i	−0.432032	+	0.249434i
$151$		−	12.1244i		−	0.986666i	−0.869841	−	0.493333i	$-0.835778\pi$
$151$		−	12.1244i		−	0.986666i	0.869841	−	0.493333i	$-0.164222\pi$
$152$	−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	$-0.487848\pi$
$157$	0.956439			0.0763322			0.0381661	+	0.999271i	$0.487848\pi$
$158$	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	−0.246265	−	0.969202i	$-0.579203\pi$
$163$	6.00000	−	3.46410i	0.469956	−	0.271329i	0.716221	+	0.697873i	$0.245870\pi$
$164$			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	$-0.525532\pi$
$167$	−12.7087	−	7.33738i	−0.983430	−	0.567783i	−0.903304	+	0.429001i	$0.858866\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	−0.626136			−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	0.947486	+	0.319798i	$0.103615\pi$
$173$	9.87386	+	17.1020i	0.750696	+	1.30024i	−0.196790	+	0.980446i	$0.563052\pi$
$174$			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	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$	3.39564	+	1.96048i	0.253096	+	0.146125i
$181$	9.16515			0.681240			0.340620	−	0.940201i	$-0.389363\pi$
$181$	9.16515			0.681240			0.340620	+	0.940201i	$0.389363\pi$
$182$		0			0
$183$	−41.1652			−3.04302
$184$	2.37386	+	1.37055i	0.175004	+	0.101038i
$185$	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	0.999729	+	0.0232830i	$0.00741188\pi$
$191$	7.18693	+	12.4481i	0.520028	+	0.900715i	−0.479701	+	0.877432i	$0.659255\pi$
$192$	4.76951	−	8.26103i	0.344210	−	0.596188i
$193$	16.7477	+	9.66930i	1.20553	+	0.696012i	0.961779	−	0.273827i	$-0.0882895\pi$
$193$	16.7477	+	9.66930i	1.20553	+	0.696012i	0.243749	+	0.969838i	$0.421623\pi$
$194$	−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	0.568813	−	0.822467i	$-0.307403\pi$
$197$	1.97822	+	1.14213i	0.140942	+	0.0813731i	−0.427871	+	0.903840i	$0.640736\pi$
$198$	4.29129	−	7.43273i	0.304969	−	0.528221i
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$			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	−0.988658	−	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
$213$		−	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	$-0.552498\pi$
$223$	−16.4347	−	9.48855i	−1.10055	−	0.635401i	−0.936364	+	0.351029i	$0.885832\pi$
$224$		0			0
$225$	−11.4782	−	19.8809i	−0.765215	−	1.32539i
$226$			4.83465i			0.321596i
$227$	7.66515	−	4.42548i	0.508754	−	0.293729i	−0.223567	−	0.974688i	$-0.571770\pi$
$227$	7.66515	−	4.42548i	0.508754	−	0.293729i	0.732321	+	0.680959i	$0.238437\pi$
$228$	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	$0.140728\pi$
$239$			13.2288i			0.855697i	−0.903850	+	0.427849i	$0.859272\pi$
$240$	3.08258	−	1.77973i	0.198979	−	0.114881i
$241$	−17.0608	+	9.85005i	−1.09898	+	0.634498i	−0.935954	−	0.352123i	$-0.885460\pi$
$241$	−17.0608	+	9.85005i	−1.09898	+	0.634498i	−0.163029	+	0.986621i	$0.552126\pi$
$242$		−	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	$-0.138150\pi$
$251$	1.41742	+	2.45505i	0.0894670	+	0.154961i	−0.817819	+	0.575476i	$0.804817\pi$
$252$		0			0
$253$	−5.37386	+	3.10260i	−0.337852	+	0.195059i
$254$	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	$-0.883614\pi$
$257$	−2.52178	+	4.36785i	−0.157304	+	0.272459i	0.776591	+	0.630005i	$0.216947\pi$
$258$	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	−0.973252	−	0.229740i	$-0.926212\pi$
$263$	−4.66515	+	8.08028i	−0.287666	+	0.498251i	0.685587	+	0.727991i	$0.259546\pi$
$264$	−9.47822	−	16.4168i	−0.583344	−	1.01038i
$265$		−	2.81655i		−	0.173019i
$266$		0			0
$267$	39.0172	−	22.5266i	2.38782	−	1.37861i
$268$			8.01270i			0.489454i
$269$	7.89564	+	13.6757i	0.481406	+	0.833819i	0.999772	−	0.0213391i	$-0.00679298\pi$
$269$	7.89564	+	13.6757i	0.481406	+	0.833819i	−0.518366	+	0.855159i	$0.673460\pi$
$270$	0.521780	−	0.903750i	0.0317545	−	0.0550005i
$271$	−11.1261	−	6.42368i	−0.675865	−	0.390211i	0.122430	−	0.992477i	$-0.460931\pi$
$271$	−11.1261	−	6.42368i	−0.675865	−	0.390211i	−0.798295	+	0.602266i	$0.794264\pi$
$272$	−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	0.633835	−	0.773469i	$-0.281480\pi$
$277$	−5.87386	−	10.1738i	−0.352926	−	0.611286i	−0.986761	+	0.162182i	$0.948147\pi$
$278$		−	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	$0.367064\pi$
$281$			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	$-0.859358\pi$
$283$	−1.37386	+	2.37960i	−0.0816677	+	0.141453i	0.822299	+	0.569056i	$0.192691\pi$
$284$	−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	$-0.642931\pi$
$293$	2.20871	−	1.27520i	0.129034	−	0.0744980i	0.563128	+	0.826370i	$0.309598\pi$
$294$		0			0
$295$	2.81307	+	4.87238i	0.163783	+	0.283681i
$296$	−6.00000	+	10.3923i	−0.348743	+	0.604040i
$297$	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	$-0.228874\pi$
$311$	26.5390			1.50489			0.752445	+	0.658655i	$0.228874\pi$
$312$	−16.7477	−	4.83465i	−0.948153	−	0.273708i
$313$	−6.74773			−0.381404			−0.190702	−	0.981648i	$-0.561076\pi$
$313$	−6.74773			−0.381404			−0.190702	+	0.981648i	$0.561076\pi$
$314$	−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	$-0.825894\pi$
$317$		−	18.5203i		−	1.04020i	0.854105	−	0.520101i	$-0.174106\pi$
$318$	−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	0.227902	−	0.973684i	$-0.426813\pi$
$331$	21.5608	−	12.4481i	1.18509	−	0.684211i	0.957186	+	0.289473i	$0.0934800\pi$
$332$	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	0.988708	−	0.149855i	$-0.0478808\pi$
$347$	6.79129	+	11.7629i	0.364575	+	0.631463i	−0.624132	+	0.781319i	$0.714547\pi$
$348$	−16.9782	+	29.4071i	−0.910128	+	1.57639i
$349$	−18.2477	−	10.5353i	−0.976778	−	0.563943i	−0.0754825	−	0.997147i	$-0.524050\pi$
$349$	−18.2477	−	10.5353i	−0.976778	−	0.563943i	−0.901296	+	0.433204i	$0.857383\pi$
$350$		0			0
$351$	17.5000	−	4.33013i	0.934081	−	0.231125i
$352$	−18.5826			−0.990455
$353$	15.7259	+	9.07938i	0.837008	+	0.483247i	0.856246	−	0.516568i	$-0.172791\pi$
$353$	15.7259	+	9.07938i	0.837008	+	0.483247i	−0.0192383	+	0.999815i	$0.506124\pi$
$354$	7.85208	−	13.6002i	0.417334	−	0.722843i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$		−	28.9126i		−	1.53236i
$357$		0			0
$358$	−3.56080	+	2.05583i	−0.188194	+	0.108654i
$359$		−	0.552200i		−	0.0291440i	−0.999894	−	0.0145720i	$-0.995361\pi$
$359$		−	0.552200i		−	0.0291440i	0.999894	−	0.0145720i	$-0.00463858\pi$
$360$	−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	$-0.677661\pi$
$367$	9.00000	−	15.5885i	0.469796	−	0.813711i	0.999404	+	0.0345320i	$0.0109941\pi$
$368$	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	−0.894962	−	0.446143i	$-0.852797\pi$
$373$	−16.1044	−	27.8936i	−0.833852	−	1.44427i	0.0611098	−	0.998131i	$-0.480536\pi$
$374$	−2.68693	+	4.65390i	−0.138938	+	0.240648i
$375$	−10.8131	−	6.24293i	−0.558384	−	0.322383i
$376$	−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	−0.288219	−	0.957565i	$-0.593063\pi$
$379$	−24.5608	−	14.1802i	−1.26160	−	0.728387i	−0.973385	+	0.229178i	$0.926396\pi$
$380$	0.560795	−	0.971326i	0.0287682	−	0.0498280i
$381$	9.70871	+	16.8160i	0.497392	+	0.861509i
$382$		−	6.56670i		−	0.335982i
$383$	1.10436	−	0.637600i	0.0564300	−	0.0325799i	−0.471520	−	0.881856i	$-0.656294\pi$
$383$	1.10436	−	0.637600i	0.0564300	−	0.0325799i	0.527950	+	0.849276i	$0.322961\pi$
$384$	−26.6869	+	15.4077i	−1.36186	+	0.786271i
$385$		0			0
$386$	−4.41742	−	7.65120i	−0.224841	−	0.389436i
$387$	−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	$-0.363479\pi$
$397$	28.1216	−	16.2360i	1.41138	−	0.814862i	0.995519	+	0.0945652i	$0.0301461\pi$
$398$			5.02535i			0.251898i
$399$		0			0
$400$	−6.68693	+	11.5821i	−0.334347	+	0.579105i
$401$	27.0998	+	15.6461i	1.35330	+	0.781328i	0.988710	−	0.149840i	$-0.0478759\pi$
$401$	27.0998	+	15.6461i	1.35330	+	0.781328i	0.364590	+	0.931168i	$0.381209\pi$
$402$	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	$-0.600891\pi$
$409$	7.18693	−	4.14938i	0.355371	−	0.205173i	0.667048	+	0.745015i	$0.267557\pi$
$410$	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	$-0.819740\pi$
$419$	0.873864	−	1.51358i	0.0426910	−	0.0739430i	0.886581	+	0.462573i	$0.153074\pi$
$420$		0			0
$421$			4.18710i			0.204067i	0.994781	+	0.102033i	$0.0325349\pi$
$421$			4.18710i			0.204067i	−0.994781	+	0.102033i	$0.967465\pi$
$422$	4.18693	−	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	0.998232	−	0.0594316i	$-0.0189288\pi$
$431$	30.0172	+	17.3305i	1.44588	+	0.834779i	0.447647	+	0.894210i	$0.352262\pi$
$432$	6.97822	−	12.0866i	0.335740	−	0.581518i
$433$	16.2477	+	28.1419i	0.780816	+	1.35241i	0.931467	+	0.363826i	$0.118530\pi$
$433$	16.2477	+	28.1419i	0.780816	+	1.35241i	−0.150651	+	0.988587i	$0.548137\pi$
$434$		0			0
$435$	−7.50000	+	4.33013i	−0.359597	+	0.207614i
$436$	−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	$-0.670280\pi$
$439$	10.2695	−	17.7873i	0.490137	−	0.848942i	0.999936	+	0.0113518i	$0.00361346\pi$
$440$	−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	−0.916524	−	0.399979i	$-0.869017\pi$
$449$	−21.7913	+	12.5812i	−1.02839	+	0.593744i	−0.111870	+	0.993723i	$0.535684\pi$
$450$			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	0.884833	−	0.465909i	$-0.154273\pi$
$457$	19.7477	+	11.4014i	0.923760	+	0.533333i	0.0389271	+	0.999242i	$0.487606\pi$
$458$	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	$-0.632176\pi$
$461$	4.02178	−	2.32198i	0.187313	−	0.108145i	0.590724	+	0.806874i	$0.298842\pi$
$462$		0			0
$463$			7.93725i			0.368875i	0.982844	+	0.184438i	$0.0590464\pi$
$463$			7.93725i			0.368875i	−0.982844	+	0.184438i	$0.940954\pi$
$464$	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	$-0.254101\pi$
$467$	30.1652			1.39588			0.697938	+	0.716158i	$0.254101\pi$
$468$	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	$-0.475301\pi$
$479$	−16.3521	−	9.44088i	−0.747146	−	0.431365i	−0.824662	+	0.565626i	$0.808634\pi$
$480$	−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	0.203046	−	0.979169i	$-0.434916\pi$
$487$	25.4347	−	14.6847i	1.15255	−	0.665428i	0.949508	+	0.313742i	$0.101583\pi$
$488$	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	$0.137020\pi$
$492$	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	$0.135156\pi$
$499$			18.4050i			0.823921i	−0.911202	+	0.411961i	$0.864844\pi$
$500$	−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	$-0.306848\pi$
$503$	−9.56080	−	16.5598i	−0.426295	−	0.738364i	−0.996540	+	0.0831100i	$0.973515\pi$
$504$		0			0
$505$	−2.06080	−	1.18980i	−0.0917042	−	0.0529454i
$506$	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	$-0.441623\pi$
$509$	−13.0390	−	7.52808i	−0.577944	−	0.333676i	−0.760316	+	0.649553i	$0.774956\pi$
$510$	−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	$-0.382903\pi$
$521$	16.4174			0.719260			0.359630	+	0.933095i	$0.382903\pi$
$522$	12.8739	+	7.43273i	0.563474	+	0.325322i
$523$	−12.1652	+	21.0707i	−0.531945	+	0.921356i	0.467360	+	0.884067i	$0.345205\pi$
$523$	−12.1652	+	21.0707i	−0.531945	+	0.921356i	−0.999305	+	0.0372883i	$0.988128\pi$
$524$	−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	$0.0431077\pi$
$541$			6.28065i			0.270026i	−0.990844	+	0.135013i	$0.956892\pi$
$542$	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	−0.248659	−	0.968591i	$-0.579990\pi$
$557$	−28.5998	−	16.5121i	−1.21181	−	0.699640i	−0.963154	+	0.268951i	$0.913323\pi$
$558$	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	−0.939945	−	0.341327i	$-0.889124\pi$
$563$	−18.1652	−	31.4630i	−0.765570	−	1.32601i	0.174375	−	0.984679i	$-0.444210\pi$
$564$		−	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	−0.986434	−	0.164159i	$-0.947509\pi$
$569$	−8.37386	+	14.5040i	−0.351051	+	0.608038i	0.635383	+	0.772197i	$0.280842\pi$
$570$	−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	$-0.396136\pi$
$587$	−8.22595	−	4.74925i	−0.339521	−	0.196023i	−0.660060	+	0.751213i	$0.729469\pi$
$588$		0			0
$589$	5.93466	+	10.2791i	0.244533	+	0.423544i
$590$		−	2.57030i		−	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	$-0.752123\pi$
$601$	6.18693	−	10.7161i	0.252370	−	0.437118i	0.964178	+	0.265256i	$0.0854566\pi$
$602$		0			0
$603$			21.4322i			0.872785i
$604$	−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	$-0.0354101\pi$
$607$	9.87386	+	17.1020i	0.400768	+	0.694150i	−0.593051	+	0.805165i	$0.702077\pi$
$608$	−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	0.145536	−	0.989353i	$-0.453509\pi$
$613$	−15.8085	−	9.12705i	−0.638500	−	0.368638i	−0.784037	+	0.620715i	$0.786843\pi$
$614$	3.54356	−	6.13763i	0.143006	−	0.247694i
$615$	5.00000	+	8.66025i	0.201619	+	0.349215i
$616$		0			0
$617$	−14.9174	+	8.61258i	−0.600553	+	0.346729i	−0.769259	−	0.638937i	$-0.779374\pi$
$617$	−14.9174	+	8.61258i	−0.600553	+	0.346729i	0.168706	+	0.985666i	$0.446041\pi$
$618$	5.06080	−	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	0.0588668	−	0.998266i	$-0.481251\pi$
$631$	23.9347	−	13.8187i	0.952824	−	0.550113i	0.893957	+	0.448153i	$0.147918\pi$
$632$		−	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	−0.995467	−	0.0951074i	$-0.969681\pi$
$641$	−14.6869	−	25.4385i	−0.580099	−	1.00476i	0.415368	−	0.909653i	$-0.363653\pi$
$642$			6.64215i			0.262145i
$643$	39.2477	−	22.6597i	1.54778	−	0.893611i	0.549468	−	0.835515i	$-0.314830\pi$
$643$	39.2477	−	22.6597i	1.54778	−	0.893611i	0.998311	−	0.0580962i	$-0.0185030\pi$
$644$		0			0
$645$			11.9536i			0.470671i
$646$	0.939205	+	1.62675i	0.0369525	+	0.0640036i
$647$	−17.5390	+	30.3785i	−0.689530	+	1.19430i	0.282460	+	0.959279i	$0.408849\pi$
$647$	−17.5390	+	30.3785i	−0.689530	+	1.19430i	−0.971990	+	0.235022i	$0.924484\pi$
$648$	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	−0.978140	−	0.207949i	$-0.933321\pi$
$653$	−7.89564	+	13.6757i	−0.308980	+	0.535170i	0.669159	+	0.743119i	$0.266654\pi$
$654$	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	0.801660	−	0.597781i	$-0.203951\pi$
$659$	−3.00000	−	5.19615i	−0.116863	−	0.202413i	−0.918523	+	0.395367i	$0.870617\pi$
$660$	4.47822	−	7.75650i	0.174314	−	0.301922i
$661$	−43.7477	−	25.2578i	−1.70159	−	0.982413i	−0.944155	−	0.329502i	$-0.893119\pi$
$661$	−43.7477	−	25.2578i	−1.70159	−	0.982413i	−0.757434	−	0.652911i	$-0.773547\pi$
$662$	−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	0.489261	+	0.872137i	$0.337266\pi$
$673$	−13.2477	+	22.9457i	−0.510662	+	0.884493i	−0.999924	+	0.0123559i	$0.996067\pi$
$674$	−3.93920	−	2.27430i	−0.151732	−	0.0876028i
$675$	−23.9564			−0.922084
$676$	−19.7042	−	12.4104i	−0.757853	−	0.477323i
$677$	−29.2087			−1.12258			−0.561291	−	0.827619i	$-0.689695\pi$
$677$	−29.2087			−1.12258			−0.561291	+	0.827619i	$0.689695\pi$
$678$	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	0.0959878	−	0.995383i	$-0.469399\pi$
$683$	26.2913	−	15.1793i	1.00601	−	0.580819i	0.910020	+	0.414563i	$0.136066\pi$
$684$		−	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	$-0.396205\pi$
$691$	−8.93466	−	5.15843i	−0.339890	−	0.196236i	−0.660224	+	0.751069i	$0.729538\pi$
$692$	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	−0.726748	−	0.686904i	$-0.758969\pi$
$709$	−13.1869	+	7.61348i	−0.495246	+	0.285930i	0.231502	+	0.972834i	$0.425636\pi$
$710$			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	$-0.315458\pi$
$719$	−12.0826	−	20.9276i	−0.450604	−	0.780469i	−0.998424	+	0.0561274i	$0.982125\pi$
$720$		−	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	$-0.501489\pi$
$727$	−0.252273			−0.00935628			−0.00467814	+	0.999989i	$0.501489\pi$
$728$		0			0
$729$	−43.8693			−1.62479
$730$	−0.626136	−	0.361500i	−0.0231744	−	0.0133797i
$731$	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	0.775339	−	0.631545i	$-0.217579\pi$
$739$	16.7477	+	9.66930i	0.616075	+	0.355691i	−0.159264	+	0.987236i	$0.550912\pi$
$740$	−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	0.934947	−	0.354787i	$-0.115446\pi$
$743$	29.8521	+	17.2351i	1.09517	+	0.632295i	0.160219	+	0.987081i	$0.448780\pi$
$744$	20.9347	−	36.2599i	0.767502	−	1.32935i
$745$	0.104356	+	0.180750i	0.00382331	+	0.00662217i
$746$			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	−0.997154	−	0.0753944i	$-0.975978\pi$
$751$	−11.8739	+	20.5661i	−0.433283	+	0.750469i	0.563870	+	0.825863i	$0.309312\pi$
$752$	−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	−0.915380	−	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
$759$			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	$-0.591175\pi$
$761$	11.2259	−	6.48130i	0.406940	−	0.234947i	0.689474	+	0.724310i	$0.257842\pi$
$762$		−	8.87086i		−	0.321357i
$763$		0			0
$764$	12.8739	−	22.2982i	0.465760	−	0.806720i
$765$	−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	$-0.387447\pi$
$769$	−8.12614	−	4.69163i	−0.293036	−	0.169184i	−0.639310	+	0.768949i	$0.720780\pi$
$770$		0			0
$771$	7.03901	+	12.1919i	0.253504	+	0.439082i
$772$		−	34.6410i		−	1.24676i
$773$	16.8303	−	9.71698i	0.605344	−	0.349495i	−0.165797	−	0.986160i	$-0.553020\pi$

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

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