LMFDB - Embedded newform 637.2.k.f.569.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("637.459");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.k (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			569.2
Root			$-0.895644 + 1.09445i$ of defining polynomial
Character	$\chi$	$=$	637.569
Dual form			637.2.k.f.459.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.18890i q^{2} +(-0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})$	\(q+2.18890i q^{2} +(-0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +(-2.39564 + 4.14938i) q^{10} +(1.10436 + 0.637600i) q^{11} +(2.50000 - 4.33013i) q^{12} +(-3.50000 - 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} -1.79129 q^{16} -3.00000 q^{17} +(0.395644 - 0.228425i) q^{18} +(-5.68693 + 3.28335i) q^{19} +(-5.29129 - 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +7.58258 q^{23} +(2.68693 + 1.55130i) q^{24} +(-0.104356 - 0.180750i) q^{25} +(1.89564 - 7.66115i) q^{26} -5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 - 7.43273i) q^{30} +(7.50000 - 4.33013i) q^{31} -7.38505i q^{32} +(-1.97822 + 1.14213i) q^{33} -6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +6.92820i q^{37} +(-7.18693 - 12.4481i) q^{38} +(4.47822 - 4.65390i) q^{39} +(1.89564 - 3.28335i) q^{40} +(-2.20871 + 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +(-3.08258 - 1.77973i) q^{44} -0.456850i q^{45} +16.5975i q^{46} +(3.70871 + 2.14123i) q^{47} +(1.60436 - 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} +(2.68693 - 4.65390i) q^{51} +(9.76951 + 2.41733i) q^{52} +(6.08258 + 10.5353i) q^{53} -10.9445i q^{54} +(1.39564 + 2.41733i) q^{55} -11.7629i q^{57} +(-4.18693 + 2.41733i) q^{58} -8.85095i q^{59} +(9.47822 - 5.47225i) q^{60} +(6.37386 + 11.0399i) q^{61} +(9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(-5.68693 - 5.47225i) q^{65} +(-2.50000 - 4.33013i) q^{66} +(-9.87386 - 5.70068i) q^{67} +8.37386 q^{68} +(-6.79129 + 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(-0.313068 + 0.180750i) q^{72} +(-3.00000 + 1.73205i) q^{73} -15.1652 q^{74} +0.373864 q^{75} +(15.8739 - 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} +(3.00000 - 5.19615i) q^{79} +(-3.39564 - 1.96048i) q^{80} +(4.79129 - 8.29875i) q^{81} +(-2.79129 - 4.83465i) q^{82} +3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(8.29129 + 4.78698i) q^{86} -3.95644 q^{87} +(1.10436 - 1.91280i) q^{88} +2.91190i q^{89} +1.00000 q^{90} -21.1652 q^{92} +15.5130i q^{93} +(-4.68693 + 8.11800i) q^{94} -14.3739 q^{95} +(11.4564 + 6.61438i) q^{96} +(13.1869 + 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{3} - 2 q^{4} + 3 q^{5} - 9 q^{6} - 5 q^{9}+O(q^{10}) $ 4 * q + q^3 - 2 * q^4 + 3 * q^5 - 9 * q^6 - 5 * q^9	$ 4 q + q^{3} - 2 q^{4} + 3 q^{5} - 9 q^{6} - 5 q^{9} - 5 q^{10} + 9 q^{11} + 10 q^{12} - 14 q^{13} - 9 q^{15} + 2 q^{16} - 12 q^{17} - 3 q^{18} - 9 q^{19} - 12 q^{20} - q^{22} + 12 q^{23} - 3 q^{24} - 5 q^{25} + 3 q^{26} - 20 q^{27} + 9 q^{29} - 8 q^{30} + 30 q^{31} + 15 q^{33} - 8 q^{36} - 15 q^{38} - 5 q^{39} + 3 q^{40} - 18 q^{41} - 5 q^{43} + 6 q^{44} + 24 q^{47} + 11 q^{48} - 3 q^{50} - 3 q^{51} + 7 q^{52} + 6 q^{53} + q^{55} - 3 q^{58} + 15 q^{60} - 2 q^{61} + 15 q^{62} + 32 q^{64} - 9 q^{65} - 10 q^{66} - 12 q^{67} + 6 q^{68} - 18 q^{69} + 6 q^{71} - 15 q^{72} - 12 q^{73} - 24 q^{74} - 26 q^{75} + 36 q^{76} + 27 q^{78} + 12 q^{79} - 9 q^{80} + 10 q^{81} - 2 q^{82} - 9 q^{85} + 24 q^{86} + 30 q^{87} + 9 q^{88} + 4 q^{90} - 48 q^{92} - 5 q^{94} - 30 q^{95} + 39 q^{97}+O(q^{100}) $ 4 * q + q^3 - 2 * q^4 + 3 * q^5 - 9 * q^6 - 5 * q^9 - 5 * q^10 + 9 * q^11 + 10 * q^12 - 14 * q^13 - 9 * q^15 + 2 * q^16 - 12 * q^17 - 3 * q^18 - 9 * q^19 - 12 * q^20 - q^22 + 12 * q^23 - 3 * q^24 - 5 * q^25 + 3 * q^26 - 20 * q^27 + 9 * q^29 - 8 * q^30 + 30 * q^31 + 15 * q^33 - 8 * q^36 - 15 * q^38 - 5 * q^39 + 3 * q^40 - 18 * q^41 - 5 * q^43 + 6 * q^44 + 24 * q^47 + 11 * q^48 - 3 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + q^55 - 3 * q^58 + 15 * q^60 - 2 * q^61 + 15 * q^62 + 32 * q^64 - 9 * q^65 - 10 * q^66 - 12 * q^67 + 6 * q^68 - 18 * q^69 + 6 * q^71 - 15 * q^72 - 12 * q^73 - 24 * q^74 - 26 * q^75 + 36 * q^76 + 27 * q^78 + 12 * q^79 - 9 * q^80 + 10 * q^81 - 2 * q^82 - 9 * q^85 + 24 * q^86 + 30 * q^87 + 9 * q^88 + 4 * q^90 - 48 * q^92 - 5 * q^94 - 30 * q^95 + 39 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$			2.18890i			1.54779i	0.633316	+	0.773893i	$0.281693\pi$
$2$			2.18890i			1.54779i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	−0.895644	+	1.55130i	−0.517100	+	0.895644i	0.482703	+	0.875784i	$0.339655\pi$
$3$	−0.895644	+	1.55130i	−0.517100	+	0.895644i	−0.999803	+	0.0198595i	$0.993678\pi$
$4$	−2.79129			−1.39564
$5$	1.89564	+	1.09445i	0.847758	+	0.489453i	0.859894	−	0.510473i	$-0.170530\pi$
$5$	1.89564	+	1.09445i	0.847758	+	0.489453i	−0.0121359	+	0.999926i	$0.503863\pi$
$6$	−3.39564	−	1.96048i	−1.38627	−	0.800361i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	−0.104356	−	0.180750i	−0.0347854	−	0.0602500i
$10$	−2.39564	+	4.14938i	−0.757569	+	1.31215i
$11$	1.10436	+	0.637600i	0.332976	+	0.192244i	0.657162	−	0.753750i	$-0.271757\pi$
$11$	1.10436	+	0.637600i	0.332976	+	0.192244i	−0.324186	+	0.945993i	$0.605090\pi$
$12$	2.50000	−	4.33013i	0.721688	−	1.25000i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$		0			0
$15$	−3.39564	+	1.96048i	−0.876751	+	0.506193i
$16$	−1.79129			−0.447822
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	0.395644	−	0.228425i	0.0932542	−	0.0538403i
$19$	−5.68693	+	3.28335i	−1.30467	+	0.753253i	−0.981202	−	0.192986i	$-0.938183\pi$
$19$	−5.68693	+	3.28335i	−1.30467	+	0.753253i	−0.323470	+	0.946238i	$0.604850\pi$
$20$	−5.29129	−	3.05493i	−1.18317	−	0.683102i
$21$		0			0
$22$	−1.39564	+	2.41733i	−0.297552	+	0.515376i
$23$	7.58258			1.58108			0.790538	−	0.612413i	$-0.209801\pi$
$23$	7.58258			1.58108			0.790538	+	0.612413i	$0.209801\pi$
$24$	2.68693	+	1.55130i	0.548468	+	0.316658i
$25$	−0.104356	−	0.180750i	−0.0208712	−	0.0361500i
$26$	1.89564	−	7.66115i	0.371766	−	1.50248i
$27$	−5.00000			−0.962250
$28$		0			0
$29$	1.10436	+	1.91280i	0.205074	+	0.355198i	0.950156	−	0.311774i	$-0.100923\pi$
$29$	1.10436	+	1.91280i	0.205074	+	0.355198i	−0.745082	+	0.666972i	$0.767590\pi$
$30$	−4.29129	−	7.43273i	−0.783478	−	1.35702i
$31$	7.50000	−	4.33013i	1.34704	−	0.777714i	0.359211	−	0.933257i	$-0.383046\pi$
$31$	7.50000	−	4.33013i	1.34704	−	0.777714i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		−	7.38505i		−	1.30551i
$33$	−1.97822	+	1.14213i	−0.344364	+	0.198819i
$34$		−	6.56670i		−	1.12618i
$35$		0			0
$36$	0.291288	+	0.504525i	0.0485480	+	0.0840876i
$37$			6.92820i			1.13899i	0.821995	+	0.569495i	$0.192861\pi$
$37$			6.92820i			1.13899i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−7.18693	−	12.4481i	−1.16587	−	2.01935i
$39$	4.47822	−	4.65390i	0.717089	−	0.745221i
$40$	1.89564	−	3.28335i	0.299728	−	0.519143i
$41$	−2.20871	+	1.27520i	−0.344943	+	0.199153i	−0.662456	−	0.749101i	$-0.730486\pi$
$41$	−2.20871	+	1.27520i	−0.344943	+	0.199153i	0.317513	+	0.948254i	$0.397152\pi$
$42$		0			0
$43$	2.18693	−	3.78788i	0.333504	−	0.577646i	−0.649692	−	0.760197i	$-0.725102\pi$
$43$	2.18693	−	3.78788i	0.333504	−	0.577646i	0.983196	+	0.182551i	$0.0584356\pi$
$44$	−3.08258	−	1.77973i	−0.464716	−	0.268304i
$45$		−	0.456850i		−	0.0681032i
$46$			16.5975i			2.44717i
$47$	3.70871	+	2.14123i	0.540971	+	0.312330i	0.745472	−	0.666536i	$-0.232224\pi$
$47$	3.70871	+	2.14123i	0.540971	+	0.312330i	−0.204501	+	0.978866i	$0.565557\pi$
$48$	1.60436	−	2.77883i	0.231569	−	0.401089i
$49$		0			0
$50$	0.395644	−	0.228425i	0.0559525	−	0.0323042i
$51$	2.68693	−	4.65390i	0.376246	−	0.651677i
$52$	9.76951	+	2.41733i	1.35479	+	0.335223i
$53$	6.08258	+	10.5353i	0.835506	+	1.44714i	0.893618	+	0.448829i	$0.148159\pi$
$53$	6.08258	+	10.5353i	0.835506	+	1.44714i	−0.0581117	+	0.998310i	$0.518508\pi$
$54$		−	10.9445i		−	1.48936i
$55$	1.39564	+	2.41733i	0.188189	+	0.325952i
$56$		0			0
$57$		−	11.7629i		−	1.55803i
$58$	−4.18693	+	2.41733i	−0.549771	+	0.317410i
$59$		−	8.85095i		−	1.15230i	−0.817345	−	0.576148i	$-0.804555\pi$
$59$		−	8.85095i		−	1.15230i	0.817345	−	0.576148i	$-0.195445\pi$
$60$	9.47822	−	5.47225i	1.22363	−	0.706465i
$61$	6.37386	+	11.0399i	0.816090	+	1.41351i	0.908543	+	0.417792i	$0.137196\pi$
$61$	6.37386	+	11.0399i	0.816090	+	1.41351i	−0.0924533	+	0.995717i	$0.529471\pi$
$62$	9.47822	+	16.4168i	1.20374	+	2.08493i
$63$		0			0
$64$	12.5826			1.57282
$65$	−5.68693	−	5.47225i	−0.705377	−	0.678749i
$66$	−2.50000	−	4.33013i	−0.307729	−	0.533002i
$67$	−9.87386	−	5.70068i	−1.20628	−	0.696449i	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−9.87386	−	5.70068i	−1.20628	−	0.696449i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	8.37386			1.01548
$69$	−6.79129	+	11.7629i	−0.817575	+	1.41608i
$70$		0			0
$71$	−0.791288	−	0.456850i	−0.0939086	−	0.0542181i	0.452310	−	0.891861i	$-0.350600\pi$
$71$	−0.791288	−	0.456850i	−0.0939086	−	0.0542181i	−0.546219	+	0.837643i	$0.683933\pi$
$72$	−0.313068	+	0.180750i	−0.0368954	+	0.0213016i
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	−0.665180	−	0.746683i	$-0.731645\pi$
$73$	−3.00000	+	1.73205i	−0.351123	+	0.202721i	0.314057	+	0.949404i	$0.398312\pi$
$74$	−15.1652			−1.76291
$75$	0.373864			0.0431700
$76$	15.8739	−	9.16478i	1.82086	−	1.05127i
$77$		0			0
$78$	10.1869	+	9.80238i	1.15344	+	1.10990i
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	−3.39564	−	1.96048i	−0.379645	−	0.219188i
$81$	4.79129	−	8.29875i	0.532365	−	0.922084i
$82$	−2.79129	−	4.83465i	−0.308246	−	0.533898i
$83$			3.55945i			0.390701i	0.980734	+	0.195350i	$0.0625844\pi$
$83$			3.55945i			0.390701i	−0.980734	+	0.195350i	$0.937416\pi$
$84$		0			0
$85$	−5.68693	−	3.28335i	−0.616834	−	0.356129i
$86$	8.29129	+	4.78698i	0.894073	+	0.516193i
$87$	−3.95644			−0.424175
$88$	1.10436	−	1.91280i	0.117725	−	0.203905i
$89$			2.91190i			0.308661i	0.988019	+	0.154330i	$0.0493220\pi$
$89$			2.91190i			0.308661i	−0.988019	+	0.154330i	$0.950678\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	−21.1652			−2.20662
$93$			15.5130i			1.60862i
$94$	−4.68693	+	8.11800i	−0.483420	+	0.837308i
$95$	−14.3739			−1.47473
$96$	11.4564	+	6.61438i	1.16927	+	0.675077i
$97$	13.1869	+	7.61348i	1.33893	+	0.773032i	0.986649	−	0.162863i	$-0.0520727\pi$
$97$	13.1869	+	7.61348i	1.33893	+	0.773032i	0.352281	+	0.935894i	$0.385406\pi$
$98$		0			0
$99$		−	0.266150i		−	0.0267491i
$100$	0.291288	+	0.504525i	0.0291288	+	0.0504525i
$101$	4.89564	−	8.47950i	0.487135	−	0.843742i	−0.512756	−	0.858534i	$-0.671375\pi$
$101$	4.89564	−	8.47950i	0.487135	−	0.843742i	0.999891	+	0.0147923i	$0.00470871\pi$
$102$	10.1869	+	5.88143i	1.00866	+	0.582348i
$103$	−2.29129	+	3.96863i	−0.225767	+	0.391040i	−0.956549	−	0.291570i	$-0.905822\pi$
$103$	−2.29129	+	3.96863i	−0.225767	+	0.391040i	0.730782	+	0.682611i	$0.239156\pi$
$104$	−1.50000	+	6.06218i	−0.147087	+	0.594445i
$105$		0			0
$106$	−23.0608	+	13.3142i	−2.23986	+	1.29319i
$107$	−9.79129			−0.946560			−0.473280	−	0.880912i	$-0.656930\pi$
$107$	−9.79129			−0.946560			−0.473280	+	0.880912i	$0.656930\pi$
$108$	13.9564			1.34296
$109$	−6.87386	+	3.96863i	−0.658397	+	0.380126i	−0.791666	−	0.610954i	$-0.790786\pi$
$109$	−6.87386	+	3.96863i	−0.658397	+	0.380126i	0.133269	+	0.991080i	$0.457453\pi$
$110$	−5.29129	+	3.05493i	−0.504505	+	0.291276i
$111$	−10.7477	−	6.20520i	−1.02013	−	0.588972i
$112$		0			0
$113$	−0.708712	+	1.22753i	−0.0666700	+	0.115476i	−0.897434	−	0.441150i	$-0.854571\pi$
$113$	−0.708712	+	1.22753i	−0.0666700	+	0.115476i	0.830764	+	0.556625i	$0.187904\pi$
$114$	25.7477			2.41150
$115$	14.3739	+	8.29875i	1.34037	+	0.773863i
$116$	−3.08258	−	5.33918i	−0.286210	−	0.495730i
$117$	0.208712	+	0.723000i	0.0192954	+	0.0668414i
$118$	19.3739			1.78351
$119$		0			0
$120$	3.39564	+	5.88143i	0.309978	+	0.536898i
$121$	−4.68693	−	8.11800i	−0.426085	−	0.738000i
$122$	−24.1652	+	13.9518i	−2.18781	+	1.26313i
$123$		−	4.56850i		−	0.411928i
$124$	−20.9347	+	12.0866i	−1.87999	+	1.08541i
$125$		−	11.4014i		−	1.01977i
$126$		0			0
$127$	7.97822	+	13.8187i	0.707953	+	1.22621i	0.965615	+	0.259975i	$0.0837143\pi$
$127$	7.97822	+	13.8187i	0.707953	+	1.22621i	−0.257663	+	0.966235i	$0.582952\pi$
$128$			12.7719i			1.12889i
$129$	3.91742	+	6.78518i	0.344910	+	0.597402i
$130$	11.9782	−	12.4481i	1.05056	−	1.09177i
$131$	−1.81307	+	3.14033i	−0.158409	+	0.274372i	−0.934295	−	0.356501i	$-0.883970\pi$
$131$	−1.81307	+	3.14033i	−0.158409	+	0.274372i	0.775886	+	0.630873i	$0.217303\pi$
$132$	5.52178	−	3.18800i	0.480609	−	0.277480i
$133$		0			0
$134$	12.4782	−	21.6129i	1.07795	−	1.86707i
$135$	−9.47822	−	5.47225i	−0.815755	−	0.470977i
$136$			5.19615i			0.445566i
$137$			17.1497i			1.46520i	0.680660	+	0.732599i	$0.261693\pi$
$137$			17.1497i			1.46520i	−0.680660	+	0.732599i	$0.738307\pi$
$138$	−25.7477	−	14.8655i	−2.19179	−	1.26543i
$139$	−0.395644	+	0.685275i	−0.0335581	+	0.0581243i	−0.882317	−	0.470656i	$-0.844017\pi$
$139$	−0.395644	+	0.685275i	−0.0335581	+	0.0581243i	0.848759	+	0.528781i	$0.177351\pi$
$140$		0			0
$141$	−6.64337	+	3.83555i	−0.559473	+	0.323012i
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	−3.31307	−	3.18800i	−0.277053	−	0.266594i
$144$	0.186932	+	0.323775i	0.0155776	+	0.0269813i
$145$			4.83465i			0.401496i
$146$	−3.79129	−	6.56670i	−0.313769	−	0.543464i
$147$		0			0
$148$		−	19.3386i		−	1.58962i
$149$	−1.89564	+	1.09445i	−0.155297	+	0.0896609i	−0.575635	−	0.817707i	$-0.695245\pi$
$149$	−1.89564	+	1.09445i	−0.155297	+	0.0896609i	0.420338	+	0.907368i	$0.361912\pi$
$150$			0.818350i			0.0668180i
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	−0.00768132	−	0.999970i	$-0.502445\pi$
$151$	10.5000	−	6.06218i	0.854478	−	0.493333i	0.862159	+	0.506637i	$0.169112\pi$
$152$	5.68693	+	9.85005i	0.461271	+	0.798945i
$153$	0.313068	+	0.542250i	0.0253101	+	0.0438383i
$154$		0			0
$155$	18.9564			1.52262
$156$	−12.5000	+	12.9904i	−1.00080	+	1.04006i
$157$	10.9782	+	19.0148i	0.876157	+	1.51755i	0.855525	+	0.517762i	$0.173235\pi$
$157$	10.9782	+	19.0148i	0.876157	+	1.51755i	0.0206325	+	0.999787i	$0.493432\pi$
$158$	11.3739	+	6.56670i	0.904856	+	0.522419i
$159$	−21.7913			−1.72816
$160$	8.08258	−	13.9994i	0.638984	−	1.10675i
$161$		0			0
$162$	18.1652	+	10.4877i	1.42719	+	0.823988i
$163$	−6.00000	+	3.46410i	−0.469956	+	0.271329i	−0.716221	−	0.697873i	$-0.754130\pi$
$163$	−6.00000	+	3.46410i	−0.469956	+	0.271329i	0.246265	+	0.969202i	$0.420797\pi$
$164$	6.16515	−	3.55945i	0.481417	−	0.277946i
$165$	−5.00000			−0.389249
$166$	−7.79129			−0.604721
$167$	−17.2913	+	9.98313i	−1.33804	+	0.772518i	−0.986517	−	0.163661i	$-0.947670\pi$
$167$	−17.2913	+	9.98313i	−1.33804	+	0.772518i	−0.351523	+	0.936179i	$0.614336\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	7.18693	−	12.4481i	0.551213	−	0.954728i
$171$	1.18693	+	0.685275i	0.0907669	+	0.0524043i
$172$	−6.10436	+	10.5731i	−0.465453	+	0.806188i
$173$	−3.87386	−	6.70973i	−0.294524	−	0.510131i	0.680350	−	0.732888i	$-0.261828\pi$
$173$	−3.87386	−	6.70973i	−0.294524	−	0.510131i	−0.974874	+	0.222756i	$0.928495\pi$
$174$		−	8.66025i		−	0.656532i
$175$		0			0
$176$	−1.97822	−	1.14213i	−0.149114	−	0.0860910i
$177$	13.7305	+	7.92730i	1.03205	+	0.595853i
$178$	−6.37386			−0.477741
$179$	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	$0.0574756\pi$
$180$			1.27520i			0.0950478i
$181$	−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
$183$	−22.8348			−1.68800
$184$		−	13.1334i		−	0.968208i
$185$	−7.58258	+	13.1334i	−0.557482	+	0.965587i
$186$	−33.9564			−2.48981
$187$	−3.31307	−	1.91280i	−0.242276	−	0.139878i
$188$	−10.3521	−	5.97678i	−0.755003	−	0.435901i
$189$		0			0
$190$		−	31.4630i		−	2.28256i
$191$	0.313068	+	0.542250i	0.0226528	+	0.0392358i	0.877130	−	0.480254i	$-0.159455\pi$
$191$	0.313068	+	0.542250i	0.0226528	+	0.0392358i	−0.854477	+	0.519490i	$0.826122\pi$
$192$	−11.2695	+	19.5194i	−0.813307	+	1.40869i
$193$	10.7477	+	6.20520i	0.773638	+	0.446660i	0.834171	−	0.551506i	$-0.185947\pi$
$193$	10.7477	+	6.20520i	0.773638	+	0.446660i	−0.0605327	+	0.998166i	$0.519280\pi$
$194$	−16.6652	+	28.8649i	−1.19649	+	2.07238i
$195$	13.5826	−	3.92095i	0.972668	−	0.280785i
$196$		0			0
$197$	−9.47822	+	5.47225i	−0.675295	+	0.389882i	−0.798080	−	0.602551i	$-0.794151\pi$
$197$	−9.47822	+	5.47225i	−0.675295	+	0.389882i	0.122785	+	0.992433i	$0.460817\pi$
$198$	0.582576			0.0414019
$199$	11.0000			0.779769			0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000			0.779769			0.389885	+	0.920864i	$0.372515\pi$
$200$	−0.313068	+	0.180750i	−0.0221373	+	0.0127810i
$201$	17.6869	−	10.2116i	1.24754	−	0.720268i
$202$	18.5608	+	10.7161i	1.30593	+	0.753981i
$203$		0			0
$204$	−7.50000	+	12.9904i	−0.525105	+	0.909509i
$205$	−5.58258			−0.389904
$206$	−8.68693	−	5.01540i	−0.605247	−	0.349440i
$207$	−0.791288	−	1.37055i	−0.0549983	−	0.0952599i
$208$	6.26951	+	1.55130i	0.434712	+	0.107563i
$209$	−8.37386			−0.579232
$210$		0			0
$211$	−0.708712	−	1.22753i	−0.0487898	−	0.0845063i	0.840599	−	0.541658i	$-0.182203\pi$
$211$	−0.708712	−	1.22753i	−0.0487898	−	0.0845063i	−0.889389	+	0.457151i	$0.848870\pi$
$212$	−16.9782	−	29.4071i	−1.16607	−	2.01969i
$213$	1.41742	−	0.818350i	0.0971203	−	0.0560724i
$214$		−	21.4322i		−	1.46507i
$215$	8.29129	−	4.78698i	0.565461	−	0.326469i
$216$			8.66025i			0.589256i
$217$		0			0
$218$	−8.68693	−	15.0462i	−0.588353	−	1.01906i
$219$		−	6.20520i		−	0.419309i
$220$	−3.89564	−	6.74745i	−0.262644	−	0.454913i
$221$	10.5000	+	2.59808i	0.706306	+	0.174766i
$222$	13.5826	−	23.5257i	0.911603	−	1.57894i
$223$	17.9347	−	10.3546i	1.20099	−	0.693394i	0.240217	−	0.970719i	$-0.422781\pi$
$223$	17.9347	−	10.3546i	1.20099	−	0.693394i	0.960776	+	0.277325i	$0.0894479\pi$
$224$		0			0
$225$	−0.0217804	+	0.0377247i	−0.00145203	+	0.00251498i
$226$	−2.68693	−	1.55130i	−0.178732	−	0.103191i
$227$			12.3151i			0.817379i	0.912673	+	0.408689i	$0.134014\pi$
$227$			12.3151i			0.817379i	−0.912673	+	0.408689i	$0.865986\pi$
$228$			32.8335i			2.17445i
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	0.684969	−	0.728572i	$-0.259816\pi$
$229$	6.00000	+	3.46410i	0.396491	+	0.228914i	−0.288478	+	0.957487i	$0.593149\pi$
$230$	−18.1652	+	31.4630i	−1.19777	+	2.07461i
$231$		0			0
$232$	3.31307	−	1.91280i	0.217514	−	0.125582i
$233$	3.47822	−	6.02445i	0.227866	−	0.394675i	−0.729310	−	0.684184i	$-0.760159\pi$
$233$	3.47822	−	6.02445i	0.227866	−	0.394675i	0.957175	+	0.289509i	$0.0934919\pi$
$234$	−1.58258	+	0.456850i	−0.103456	+	0.0298652i
$235$	4.68693	+	8.11800i	0.305742	+	0.529560i
$236$			24.7056i			1.60820i
$237$	5.37386	+	9.30780i	0.349070	+	0.604607i
$238$		0			0
$239$			13.2288i			0.855697i	0.903850	+	0.427849i	$0.140728\pi$
$239$			13.2288i			0.855697i	−0.903850	+	0.427849i	$0.859272\pi$
$240$	6.08258	−	3.51178i	0.392629	−	0.226684i
$241$		−	4.11165i		−	0.264855i	−0.991193	−	0.132427i	$-0.957723\pi$
$241$		−	4.11165i		−	0.264855i	0.991193	−	0.132427i	$-0.0422771\pi$
$242$	17.7695	−	10.2592i	1.14227	−	0.659488i
$243$	1.08258	+	1.87508i	0.0694473	+	0.120286i
$244$	−17.7913	−	30.8154i	−1.13897	−	1.97275i
$245$		0			0
$246$	10.0000			0.637577
$247$	22.7477	−	6.56670i	1.44740	−	0.417829i
$248$	−7.50000	−	12.9904i	−0.476250	−	0.824890i
$249$	−5.52178	−	3.18800i	−0.349929	−	0.202031i
$250$	24.9564			1.57838
$251$	10.5826	−	18.3296i	0.667966	−	1.15695i	−0.310506	−	0.950572i	$-0.600498\pi$
$251$	10.5826	−	18.3296i	0.667966	−	1.15695i	0.978472	−	0.206380i	$-0.0661683\pi$
$252$		0			0
$253$	8.37386	+	4.83465i	0.526460	+	0.303952i
$254$	−30.2477	+	17.4635i	−1.89791	+	1.09576i
$255$	10.1869	−	5.88143i	0.637930	−	0.368309i
$256$	−2.79129			−0.174455
$257$	27.9564			1.74387			0.871937	−	0.489617i	$-0.162864\pi$
$257$	27.9564			1.74387			0.871937	+	0.489617i	$0.162864\pi$
$258$	−14.8521	+	8.57485i	−0.924650	+	0.533847i
$259$		0			0
$260$	15.8739	+	15.2746i	0.984455	+	0.947292i
$261$	0.230493	−	0.399225i	0.0142671	−	0.0247114i
$262$	−6.87386	−	3.96863i	−0.424669	−	0.245183i
$263$	13.6652	−	23.6687i	0.842629	−	1.45948i	−0.0450348	−	0.998985i	$-0.514340\pi$
$263$	13.6652	−	23.6687i	0.842629	−	1.45948i	0.887664	−	0.460491i	$-0.152327\pi$
$264$	1.97822	+	3.42638i	0.121751	+	0.210879i
$265$			26.6283i			1.63576i
$266$		0			0
$267$	−4.51723	−	2.60803i	−0.276450	−	0.159609i
$268$	27.5608	+	15.9122i	1.68354	+	0.971994i
$269$	−11.2087			−0.683407			−0.341704	−	0.939808i	$-0.611004\pi$
$269$	−11.2087			−0.683407			−0.341704	+	0.939808i	$0.611004\pi$
$270$	11.9782	−	20.7469i	0.728971	−	1.26262i
$271$		−	28.7219i		−	1.74473i	−0.488856	−	0.872364i	$-0.662586\pi$
$271$		−	28.7219i		−	1.74473i	0.488856	−	0.872364i	$-0.337414\pi$
$272$	5.37386			0.325838
$273$		0			0
$274$	−37.5390			−2.26781
$275$		−	0.266150i		−	0.0160494i
$276$	18.9564	−	32.8335i	1.14104	−	1.97635i
$277$	−15.7477			−0.946189			−0.473095	−	0.881012i	$-0.656863\pi$
$277$	−15.7477			−0.946189			−0.473095	+	0.881012i	$0.656863\pi$
$278$	−1.50000	−	0.866025i	−0.0899640	−	0.0519408i
$279$	−1.56534	−	0.903750i	−0.0937145	−	0.0541061i
$280$		0			0
$281$			6.39590i			0.381548i	0.981634	+	0.190774i	$0.0610997\pi$
$281$			6.39590i			0.381548i	−0.981634	+	0.190774i	$0.938900\pi$
$282$	−8.39564	−	14.5417i	−0.499953	−	0.865945i
$283$	12.3739	−	21.4322i	0.735550	−	1.27401i	−0.218932	−	0.975740i	$-0.570257\pi$
$283$	12.3739	−	21.4322i	0.735550	−	1.27401i	0.954482	−	0.298270i	$-0.0964094\pi$
$284$	2.20871	+	1.27520i	0.131063	+	0.0756692i
$285$	12.8739	−	22.2982i	0.762582	−	1.32083i
$286$	6.97822	−	7.25198i	0.412631	−	0.428818i
$287$		0			0
$288$	−1.33485	+	0.770675i	−0.0786567	+	0.0454125i
$289$	−8.00000			−0.470588
$290$	−10.5826			−0.621430
$291$	−23.6216	+	13.6379i	−1.38472	+	0.799470i
$292$	8.37386	−	4.83465i	0.490043	−	0.282927i
$293$	6.79129	+	3.92095i	0.396751	+	0.229064i	0.685081	−	0.728467i	$-0.259767\pi$
$293$	6.79129	+	3.92095i	0.396751	+	0.229064i	−0.288330	+	0.957531i	$0.593100\pi$
$294$		0			0
$295$	9.68693	−	16.7783i	0.563995	−	0.976868i
$296$	12.0000			0.697486
$297$	−5.52178	−	3.18800i	−0.320406	−	0.184987i
$298$	−2.39564	−	4.14938i	−0.138776	−	0.240367i
$299$	−26.5390	−	6.56670i	−1.53479	−	0.379762i
$300$	−1.04356			−0.0602500
$301$		0			0
$302$	13.2695	+	22.9835i	0.763574	+	1.32255i
$303$	8.76951	+	15.1892i	0.503795	+	0.872599i
$304$	10.1869	−	5.88143i	0.584261	−	0.337323i
$305$			27.9035i			1.59775i
$306$	−1.18693	+	0.685275i	−0.0678524	+	0.0391746i
$307$			24.1733i			1.37964i	0.723980	+	0.689820i	$0.242311\pi$
$307$			24.1733i			1.37964i	−0.723980	+	0.689820i	$0.757689\pi$
$308$		0			0
$309$	−4.10436	−	7.10895i	−0.233489	−	0.404414i
$310$			41.4938i			2.35669i
$311$	2.76951	+	4.79693i	0.157044	+	0.272009i	0.933802	−	0.357791i	$-0.116470\pi$
$311$	2.76951	+	4.79693i	0.157044	+	0.272009i	−0.776757	+	0.629800i	$0.783137\pi$
$312$	−8.06080	−	7.75650i	−0.456353	−	0.439126i
$313$	−10.3739	+	17.9681i	−0.586365	+	1.01561i	0.408338	+	0.912831i	$0.366108\pi$
$313$	−10.3739	+	17.9681i	−0.586365	+	1.01561i	−0.994704	+	0.102784i	$0.967225\pi$
$314$	−41.6216	+	24.0302i	−2.34884	+	1.35610i
$315$		0			0
$316$	−8.37386	+	14.5040i	−0.471067	+	0.815911i
$317$	16.0390	+	9.26013i	0.900841	+	0.520101i	0.877473	−	0.479626i	$-0.159228\pi$
$317$	16.0390	+	9.26013i	0.900841	+	0.520101i	0.0233679	+	0.999727i	$0.492561\pi$
$318$		−	47.6990i		−	2.67483i
$319$			2.81655i			0.157697i
$320$	23.8521	+	13.7710i	1.33337	+	0.769823i
$321$	8.76951	−	15.1892i	0.489466	−	0.847780i
$322$		0			0
$323$	17.0608	−	9.85005i	0.949288	−	0.548072i
$324$	−13.3739	+	23.1642i	−0.742992	+	1.28690i
$325$	0.208712	+	0.723000i	0.0115773	+	0.0401048i
$326$	−7.58258	−	13.1334i	−0.419960	−	0.727392i
$327$		−	14.2179i		−	0.786252i
$328$	2.20871	+	3.82560i	0.121956	+	0.211234i
$329$		0			0
$330$		−	10.9445i		−	0.602475i
$331$	−0.939205	+	0.542250i	−0.0516234	+	0.0298048i	−0.525590	−	0.850738i	$-0.676155\pi$
$331$	−0.939205	+	0.542250i	−0.0516234	+	0.0298048i	0.473966	+	0.880543i	$0.342822\pi$
$332$		−	9.93545i		−	0.545279i
$333$	1.25227	−	0.723000i	0.0686241	−	0.0396202i
$334$	−21.8521	−	37.8489i	−1.19569	−	2.07100i
$335$	−12.4782	−	21.6129i	−0.681758	−	1.18084i
$336$		0			0
$337$	−12.9564			−0.705782			−0.352891	−	0.935664i	$-0.614801\pi$
$337$	−12.9564			−0.705782			−0.352891	+	0.935664i	$0.614801\pi$
$338$	−13.2695	+	25.1724i	−0.721766	+	1.36920i
$339$	−1.26951	−	2.19885i	−0.0689502	−	0.119425i
$340$	15.8739	+	9.16478i	0.860881	+	0.497030i
$341$	11.0436			0.598042
$342$	−1.50000	+	2.59808i	−0.0811107	+	0.140488i
$343$		0			0
$344$	−6.56080	−	3.78788i	−0.353734	−	0.204229i
$345$	−25.7477	+	14.8655i	−1.38621	+	0.800329i
$346$	14.6869	−	8.47950i	0.789574	−	0.455861i
$347$	−4.41742			−0.237140			−0.118570	−	0.992946i	$-0.537831\pi$
$347$	−4.41742			−0.237140			−0.118570	+	0.992946i	$0.537831\pi$
$348$	11.0436			0.591997
$349$	9.24773	−	5.33918i	0.495019	−	0.285800i	−0.231635	−	0.972803i	$-0.574407\pi$
$349$	9.24773	−	5.33918i	0.495019	−	0.285800i	0.726654	+	0.687003i	$0.241074\pi$
$350$		0			0
$351$	17.5000	+	4.33013i	0.934081	+	0.231125i
$352$	4.70871	−	8.15573i	0.250975	−	0.434702i
$353$	23.2259	+	13.4095i	1.23619	+	0.713716i	0.968314	−	0.249737i	$-0.0803441\pi$
$353$	23.2259	+	13.4095i	1.23619	+	0.713716i	0.267879	+	0.963453i	$0.413677\pi$
$354$	−17.3521	+	30.0547i	−0.922253	+	1.59739i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$		−	8.12795i		−	0.430781i
$357$		0			0
$358$	17.0608	+	9.85005i	0.901691	+	0.520592i
$359$	10.9782	+	6.33828i	0.579408	+	0.334522i	0.760898	−	0.648871i	$-0.224759\pi$
$359$	10.9782	+	6.33828i	0.579408	+	0.334522i	−0.181490	+	0.983393i	$0.558092\pi$
$360$	−0.791288			−0.0417045
$361$	12.0608	−	20.8899i	0.634779	−	1.09947i
$362$		−	20.0616i		−	1.05441i
$363$	16.7913			0.881314
$364$		0			0
$365$	−7.58258			−0.396890
$366$		−	49.9832i		−	2.61266i
$367$	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	$0.0109941\pi$
$368$	−13.5826			−0.708041
$369$	0.460985	+	0.266150i	0.0239979	+	0.0138552i
$370$	−28.7477	−	16.5975i	−1.49452	−	0.862863i
$371$		0			0
$372$		−	43.3013i		−	2.24507i
$373$	−18.3956	−	31.8622i	−0.952490	−	1.64976i	−0.740009	−	0.672596i	$-0.765179\pi$
$373$	−18.3956	−	31.8622i	−0.952490	−	1.64976i	−0.212481	−	0.977165i	$-0.568154\pi$
$374$	4.18693	−	7.25198i	0.216501	−	0.374991i
$375$	17.6869	+	10.2116i	0.913349	+	0.527322i
$376$	3.70871	−	6.42368i	0.191262	−	0.331276i
$377$	−2.20871	−	7.65120i	−0.113754	−	0.394057i
$378$		0			0
$379$	−3.93920	+	2.27430i	−0.202343	+	0.116823i	−0.597748	−	0.801684i	$-0.703938\pi$
$379$	−3.93920	+	2.27430i	−0.202343	+	0.116823i	0.395405	+	0.918507i	$0.370604\pi$
$380$	40.1216			2.05819
$381$	−28.5826			−1.46433
$382$	−1.18693	+	0.685275i	−0.0607287	+	0.0350617i
$383$	−3.39564	+	1.96048i	−0.173509	+	0.100176i	−0.584240	−	0.811581i	$-0.698607\pi$
$383$	−3.39564	+	1.96048i	−0.173509	+	0.100176i	0.410730	+	0.911757i	$0.365274\pi$
$384$	−19.8131	−	11.4391i	−1.01108	−	0.583748i
$385$		0			0
$386$	−13.5826	+	23.5257i	−0.691335	+	1.19743i
$387$	−0.912878			−0.0464042
$388$	−36.8085	−	21.2514i	−1.86867	−	1.07888i
$389$	−18.1652	−	31.4630i	−0.921010	−	1.59524i	−0.797856	−	0.602848i	$-0.794033\pi$
$389$	−18.1652	−	31.4630i	−0.921010	−	1.59524i	−0.123154	−	0.992388i	$-0.539301\pi$
$390$	8.58258	+	29.7309i	0.434596	+	1.50548i
$391$	−22.7477			−1.15040
$392$		0			0
$393$	−3.24773	−	5.62523i	−0.163826	−	0.283755i
$394$	−11.9782	−	20.7469i	−0.603454	−	1.04521i
$395$	11.3739	−	6.56670i	0.572281	−	0.330407i
$396$			0.742901i			0.0373322i
$397$	13.1216	−	7.57575i	0.658554	−	0.380216i	−0.133172	−	0.991093i	$-0.542516\pi$
$397$	13.1216	−	7.57575i	0.658554	−	0.380216i	0.791726	+	0.610877i	$0.209183\pi$
$398$			24.0779i			1.20692i
$399$		0			0
$400$	0.186932	+	0.323775i	0.00934659	+	0.0161888i
$401$		−	29.5601i		−	1.47616i	−0.674712	−	0.738081i	$-0.735732\pi$
$401$		−	29.5601i		−	1.47616i	0.674712	−	0.738081i	$-0.264268\pi$
$402$	22.3521	+	38.7149i	1.11482	+	1.93093i
$403$	−30.0000	+	8.66025i	−1.49441	+	0.431398i
$404$	−13.6652	+	23.6687i	−0.679867	+	1.17756i
$405$	18.1652	−	10.4877i	0.902634	−	0.521136i
$406$		0			0
$407$	−4.41742	+	7.65120i	−0.218964	+	0.379256i
$408$	−8.06080	−	4.65390i	−0.399069	−	0.230402i
$409$		−	0.361500i		−	0.0178750i	−0.999960	−	0.00893751i	$-0.997155\pi$
$409$		−	0.361500i		−	0.0178750i	0.999960	−	0.00893751i	$-0.00284494\pi$
$410$		−	12.2197i		−	0.603488i
$411$	−26.6044	−	15.3600i	−1.31230	−	0.757655i
$412$	6.39564	−	11.0776i	0.315091	−	0.545753i
$413$		0			0
$414$	3.00000	−	1.73205i	0.147442	−	0.0851257i
$415$	−3.89564	+	6.74745i	−0.191230	+	0.331219i
$416$	−6.39564	+	25.8477i	−0.313572	+	1.26729i
$417$	−0.708712	−	1.22753i	−0.0347058	−	0.0601122i
$418$		−	18.3296i		−	0.896528i
$419$	−12.8739	−	22.2982i	−0.628929	−	1.08934i	−0.987767	−	0.155938i	$-0.950160\pi$
$419$	−12.8739	−	22.2982i	−0.628929	−	1.08934i	0.358838	−	0.933400i	$-0.383173\pi$
$420$		0			0
$421$		−	20.0616i		−	0.977743i	−0.872356	−	0.488872i	$-0.837409\pi$
$421$		−	20.0616i		−	0.977743i	0.872356	−	0.488872i	$-0.162591\pi$
$422$	2.68693	−	1.55130i	0.130798	−	0.0755161i
$423$		−	0.893800i		−	0.0434580i
$424$	18.2477	−	10.5353i	0.886188	−	0.511641i
$425$	0.313068	+	0.542250i	0.0151860	+	0.0263030i
$426$	1.79129	+	3.10260i	0.0867882	+	0.150322i
$427$		0			0
$428$	27.3303			1.32106
$429$	7.91288	−	2.28425i	0.382037	−	0.110285i
$430$	10.4782	+	18.1488i	0.505305	+	0.875213i
$431$	13.5172	+	7.80418i	0.651102	+	0.375914i	0.788878	−	0.614549i	$-0.210662\pi$
$431$	13.5172	+	7.80418i	0.651102	+	0.375914i	−0.137776	+	0.990463i	$0.543995\pi$
$432$	8.95644			0.430917
$433$	−11.2477	+	19.4816i	−0.540531	+	0.936228i	0.458342	+	0.888776i	$0.348443\pi$
$433$	−11.2477	+	19.4816i	−0.540531	+	0.936228i	−0.998874	+	0.0474518i	$0.984890\pi$
$434$		0			0
$435$	−7.50000	−	4.33013i	−0.359597	−	0.207614i
$436$	19.1869	−	11.0776i	0.918887	−	0.530520i
$437$	−43.1216	+	24.8963i	−2.06279	+	1.19095i
$438$	13.5826			0.649001
$439$	11.5390			0.550727			0.275364	−	0.961340i	$-0.411202\pi$
$439$	11.5390			0.550727			0.275364	+	0.961340i	$0.411202\pi$
$440$	4.18693	−	2.41733i	0.199604	−	0.115242i
$441$		0			0
$442$	−5.68693	+	22.9835i	−0.270500	+	1.09321i
$443$	−1.58258	+	2.74110i	−0.0751904	+	0.130234i	−0.901169	−	0.433468i	$-0.857290\pi$
$443$	−1.58258	+	2.74110i	−0.0751904	+	0.130234i	0.825979	+	0.563701i	$0.190623\pi$
$444$	30.0000	+	17.3205i	1.42374	+	0.821995i
$445$	−3.18693	+	5.51993i	−0.151075	+	0.261670i
$446$	22.6652	+	39.2572i	1.07323	+	1.85888i
$447$		−	3.92095i		−	0.185455i
$448$		0			0
$449$	−17.2087	−	9.93545i	−0.812129	−	0.468883i	0.0355654	−	0.999367i	$-0.488677\pi$
$449$	−17.2087	−	9.93545i	−0.812129	−	0.468883i	−0.847695	+	0.530484i	$0.822010\pi$
$450$	−0.0825757	−	0.0476751i	−0.00389266	−	0.00224743i
$451$	−3.25227			−0.153144
$452$	1.97822	−	3.42638i	0.0930476	−	0.161163i
$453$			21.7182i			1.02041i
$454$	−26.9564			−1.26513
$455$		0			0
$456$	−20.3739			−0.954094
$457$		−	8.94630i		−	0.418490i	−0.977863	−	0.209245i	$-0.932899\pi$
$457$		−	8.94630i		−	0.418490i	0.977863	−	0.209245i	$-0.0671007\pi$
$458$	−7.58258	+	13.1334i	−0.354310	+	0.613684i
$459$	15.0000			0.700140
$460$	−40.1216	−	23.1642i	−1.87068	−	1.08004i
$461$	15.4782	+	8.93635i	0.720893	+	0.416208i	0.815081	−	0.579347i	$-0.196692\pi$
$461$	15.4782	+	8.93635i	0.720893	+	0.416208i	−0.0941885	+	0.995554i	$0.530026\pi$
$462$		0			0
$463$			7.93725i			0.368875i	0.982844	+	0.184438i	$0.0590464\pi$
$463$			7.93725i			0.368875i	−0.982844	+	0.184438i	$0.940954\pi$
$464$	−1.97822	−	3.42638i	−0.0918365	−	0.159066i
$465$	−16.9782	+	29.4071i	−0.787346	+	1.36372i
$466$	13.1869	+	7.61348i	0.610873	+	0.352688i
$467$	−5.91742	+	10.2493i	−0.273826	+	0.474280i	−0.969838	−	0.243750i	$-0.921622\pi$
$467$	−5.91742	+	10.2493i	−0.273826	+	0.474280i	0.696012	+	0.718030i	$0.254956\pi$
$468$	−0.582576	−	2.01810i	−0.0269296	−	0.0932868i
$469$		0			0
$470$	−17.7695	+	10.2592i	−0.819646	+	0.473223i
$471$	−39.3303			−1.81224
$472$	−15.3303			−0.705634
$473$	4.83030	−	2.78878i	0.222098	−	0.128228i
$474$	−20.3739	+	11.7629i	−0.935803	+	0.540286i
$475$	1.18693	+	0.685275i	0.0544602	+	0.0314426i
$476$		0			0
$477$	1.26951	−	2.19885i	0.0581268	−	0.100678i
$478$	−28.9564			−1.32444
$479$	−8.85208	−	5.11075i	−0.404462	−	0.233516i	0.283945	−	0.958840i	$-0.408357\pi$
$479$	−8.85208	−	5.11075i	−0.404462	−	0.233516i	−0.688407	+	0.725324i	$0.741690\pi$
$480$	14.4782	+	25.0770i	0.660837	+	1.14460i
$481$	6.00000	−	24.2487i	0.273576	−	1.10565i
$482$	9.00000			0.409939
$483$		0			0
$484$	13.0826	+	22.6597i	0.594663	+	1.02999i
$485$	16.6652	+	28.8649i	0.756726	+	1.31069i
$486$	−4.10436	+	2.36965i	−0.186177	+	0.107490i
$487$			10.3169i			0.467501i	0.972297	+	0.233751i	$0.0750999\pi$
$487$			10.3169i			0.467501i	−0.972297	+	0.233751i	$0.924900\pi$
$488$	19.1216	−	11.0399i	0.865594	−	0.499751i
$489$		−	12.4104i		−	0.561218i
$490$		0			0
$491$	−18.5608	−	32.1482i	−0.837637	−	1.45083i	−0.891865	−	0.452301i	$-0.850603\pi$
$491$	−18.5608	−	32.1482i	−0.837637	−	1.45083i	0.0542283	−	0.998529i	$-0.482730\pi$
$492$			12.7520i			0.574905i
$493$	−3.31307	−	5.73840i	−0.149213	−	0.258445i
$494$	14.3739	+	49.7925i	0.646711	+	2.24027i
$495$	0.291288	−	0.504525i	0.0130924	−	0.0226767i
$496$	−13.4347	+	7.75650i	−0.603234	+	0.348277i
$497$		0			0
$498$	6.97822	−	12.0866i	0.312701	−	0.541615i
$499$	36.5608	+	21.1084i	1.63669	+	0.944941i	0.981963	+	0.189072i	$0.0605479\pi$
$499$	36.5608	+	21.1084i	1.63669	+	0.944941i	0.654723	+	0.755869i	$0.272785\pi$
$500$			31.8245i			1.42323i
$501$		−	35.7653i		−	1.59788i
$502$	40.1216	+	23.1642i	1.79071	+	1.03387i
$503$	11.0608	−	19.1579i	0.493176	−	0.854207i	−0.506793	−	0.862068i	$-0.669169\pi$
$503$	11.0608	−	19.1579i	0.493176	−	0.854207i	0.999969	+	0.00786127i	$0.00250235\pi$
$504$		0			0
$505$	18.5608	−	10.7161i	0.825945	−	0.476859i
$506$	−10.5826	+	18.3296i	−0.470453	+	0.814848i
$507$	−19.7042	+	12.4104i	−0.875093	+	0.551165i
$508$	−22.2695	−	38.5719i	−0.988050	−	1.71135i
$509$			21.9844i			0.974440i	0.873279	+	0.487220i	$0.161989\pi$
$509$			21.9844i			0.974440i	−0.873279	+	0.487220i	$0.838011\pi$
$510$	12.8739	+	22.2982i	0.570064	+	0.987380i
$511$		0			0
$512$			19.4340i			0.858868i
$513$	28.4347	−	16.4168i	1.25542	−	0.724818i
$514$			61.1939i			2.69915i
$515$	−8.68693	+	5.01540i	−0.382792	+	0.221005i
$516$	−10.9347	−	18.9394i	−0.481372	−	0.833760i
$517$	2.73049	+	4.72935i	0.120087	+	0.207997i
$518$		0			0
$519$	13.8784			0.609195
$520$	−9.47822	+	9.85005i	−0.415647	+	0.431953i
$521$	−12.7913	−	22.1552i	−0.560396	−	0.970635i	−0.997462	−	0.0712054i	$-0.977315\pi$
$521$	−12.7913	−	22.1552i	−0.560396	−	0.970635i	0.437065	−	0.899430i	$-0.356018\pi$
$522$	0.873864	+	0.504525i	0.0382480	+	0.0220825i
$523$	−12.3303			−0.539166			−0.269583	−	0.962977i	$-0.586886\pi$
$523$	−12.3303			−0.539166			−0.269583	+	0.962977i	$0.586886\pi$
$524$	5.06080	−	8.76555i	0.221082	−	0.382925i
$525$		0			0
$526$	51.8085	+	29.9117i	2.25896	+	1.30421i
$527$	−22.5000	+	12.9904i	−0.980115	+	0.565870i
$528$	3.54356	−	2.04588i	0.154214	−	0.0890353i
$529$	34.4955			1.49980
$530$	−58.2867			−2.53181
$531$	−1.59981	+	0.923651i	−0.0694259	+	0.0400830i
$532$		0			0
$533$	8.83485	−	2.55040i	0.382680	−	0.110470i
$534$	5.70871	−	9.88778i	0.247040	−	0.427886i
$535$	−18.5608	−	10.7161i	−0.802453	−	0.463297i
$536$	−9.87386	+	17.1020i	−0.426486	+	0.738695i
$537$	8.06080	+	13.9617i	0.347849	+	0.602492i
$538$		−	24.5348i		−	1.05777i
$539$		0			0
$540$	26.4564	+	15.2746i	1.13850	+	0.657316i
$541$	26.0608	+	15.0462i	1.12044	+	0.646887i	0.941513	−	0.336975i	$-0.109404\pi$
$541$	26.0608	+	15.0462i	1.12044	+	0.646887i	0.178928	+	0.983862i	$0.442737\pi$
$542$	62.8693			2.70047
$543$	8.20871	−	14.2179i	0.352270	−	0.610149i
$544$			22.1552i			0.949895i
$545$	−17.3739			−0.744215
$546$		0			0
$547$	15.7477			0.673324			0.336662	−	0.941626i	$-0.390702\pi$
$547$	15.7477			0.673324			0.336662	+	0.941626i	$0.390702\pi$
$548$		−	47.8698i		−	2.04490i
$549$	1.33030	−	2.30415i	0.0567759	−	0.0983388i
$550$	0.582576			0.0248411
$551$	−12.5608	−	7.25198i	−0.535108	−	0.308945i
$552$	20.3739	+	11.7629i	0.867169	+	0.500660i
$553$		0			0
$554$		−	34.4702i		−	1.46450i
$555$	−13.5826	−	23.5257i	−0.576548	−	0.998611i
$556$	1.10436	−	1.91280i	0.0468351	−	0.0811208i
$557$	−24.0998	−	13.9140i	−1.02114	−	0.589556i	−0.106707	−	0.994290i	$-0.534031\pi$
$557$	−24.0998	−	13.9140i	−1.02114	−	0.589556i	−0.914434	+	0.404734i	$0.867364\pi$
$558$	1.97822	−	3.42638i	0.0837447	−	0.145050i
$559$	−10.9347	+	11.3636i	−0.462487	+	0.480630i
$560$		0			0
$561$	5.93466	−	3.42638i	0.250561	−	0.144662i
$562$	−14.0000			−0.590554
$563$	−0.330303			−0.0139206			−0.00696030	−	0.999976i	$-0.502216\pi$
$563$	−0.330303			−0.0139206			−0.00696030	+	0.999976i	$0.502216\pi$
$564$	18.5436	−	10.7061i	0.780825	−	0.450809i
$565$	−2.68693	+	1.55130i	−0.113040	+	0.0652637i
$566$	46.9129	+	27.0852i	1.97190	+	1.13847i
$567$		0			0
$568$	−0.791288	+	1.37055i	−0.0332017	+	0.0575070i
$569$	−10.7477			−0.450568			−0.225284	−	0.974293i	$-0.572331\pi$
$569$	−10.7477			−0.450568			−0.225284	+	0.974293i	$0.572331\pi$
$570$	48.8085	+	28.1796i	2.04436	+	1.18031i
$571$	12.4782	+	21.6129i	0.522197	+	0.904472i	0.999667	+	0.0258237i	$0.00822085\pi$
$571$	12.4782	+	21.6129i	0.522197	+	0.904472i	−0.477469	+	0.878648i	$0.658446\pi$
$572$	9.24773	+	8.89863i	0.386667	+	0.372070i
$573$	−1.12159			−0.0468551
$574$		0			0
$575$	−0.791288	−	1.37055i	−0.0329990	−	0.0571559i
$576$	−1.31307	−	2.27430i	−0.0547112	−	0.0947625i
$577$	−17.1261	+	9.88778i	−0.712970	+	0.411634i	−0.812160	−	0.583435i	$-0.801708\pi$
$577$	−17.1261	+	9.88778i	−0.712970	+	0.411634i	0.0991895	+	0.995069i	$0.468375\pi$
$578$		−	17.5112i		−	0.728370i
$579$	−19.2523	+	11.1153i	−0.800097	+	0.461936i
$580$		−	13.4949i		−	0.560345i
$581$		0			0
$582$	−29.8521	−	51.7053i	−1.23741	−	2.14325i
$583$			15.5130i			0.642483i
$584$	3.00000	+	5.19615i	0.124141	+	0.215018i
$585$	−0.395644	+	1.59898i	−0.0163579	+	0.0661095i
$586$	−8.58258	+	14.8655i	−0.354543	+	0.614086i
$587$	30.7259	−	17.7396i	1.26820	−	0.732193i	0.293549	−	0.955944i	$-0.405164\pi$
$587$	30.7259	−	17.7396i	1.26820	−	0.732193i	0.974646	+	0.223751i	$0.0718302\pi$
$588$		0			0
$589$	−28.4347	+	49.2503i	−1.17163	+	2.02932i
$590$	36.7259	+	21.2037i	1.51198	+	0.872944i
$591$		−	19.6048i		−	0.806432i
$592$		−	12.4104i		−	0.510065i
$593$	16.9782	+	9.80238i	0.697212	+	0.402535i	0.806308	−	0.591496i	$-0.201462\pi$
$593$	16.9782	+	9.80238i	0.697212	+	0.402535i	−0.109096	+	0.994031i	$0.534796\pi$
$594$	6.97822	−	12.0866i	0.286320	−	0.495920i
$595$		0			0
$596$	5.29129	−	3.05493i	0.216740	−	0.125135i
$597$	−9.85208	+	17.0643i	−0.403219	+	0.698396i
$598$	14.3739	−	58.0913i	0.587791	−	2.37553i
$599$	10.1869	+	17.6443i	0.416227	+	0.720926i	0.995556	−	0.0941675i	$-0.0300189\pi$
$599$	10.1869	+	17.6443i	0.416227	+	0.720926i	−0.579330	+	0.815093i	$0.696686\pi$
$600$		−	0.647551i		−	0.0264361i
$601$	−0.686932	−	1.18980i	−0.0280205	−	0.0485330i	0.851675	−	0.524070i	$-0.175587\pi$
$601$	−0.686932	−	1.18980i	−0.0280205	−	0.0485330i	−0.879696	+	0.475537i	$0.842254\pi$
$602$		0			0
$603$			2.37960i			0.0969049i
$604$	−29.3085	+	16.9213i	−1.19255	+	0.688517i
$605$		−	20.5185i		−	0.834194i
$606$	−33.2477	+	19.1956i	−1.35060	+	0.779767i
$607$	−3.87386	−	6.70973i	−0.157235	−	0.272339i	0.776635	−	0.629950i	$-0.216925\pi$
$607$	−3.87386	−	6.70973i	−0.157235	−	0.272339i	−0.933871	+	0.357611i	$0.883591\pi$
$608$	24.2477	+	41.9983i	0.983375	+	1.70326i
$609$		0			0
$610$	−61.0780			−2.47298
$611$	−11.1261	−	10.7061i	−0.450115	−	0.433124i
$612$	−0.873864	−	1.51358i	−0.0353238	−	0.0611827i
$613$	−32.3085	−	18.6533i	−1.30493	−	0.753401i	−0.323684	−	0.946165i	$-0.604921\pi$
$613$	−32.3085	−	18.6533i	−1.30493	−	0.753401i	−0.981245	+	0.192764i	$0.938255\pi$
$614$	−52.9129			−2.13539
$615$	5.00000	−	8.66025i	0.201619	−	0.349215i
$616$		0			0
$617$	−24.0826	−	13.9041i	−0.969528	−	0.559757i	−0.0704357	−	0.997516i	$-0.522439\pi$
$617$	−24.0826	−	13.9041i	−0.969528	−	0.559757i	−0.899092	+	0.437759i	$0.855772\pi$
$618$	15.5608	−	8.98403i	0.625947	−	0.361391i
$619$	10.7477	−	6.20520i	0.431988	−	0.249408i	−0.268205	−	0.963362i	$-0.586431\pi$
$619$	10.7477	−	6.20520i	0.431988	−	0.249408i	0.700193	+	0.713954i	$0.253097\pi$
$620$	−52.9129			−2.12503
$621$	−37.9129			−1.52139
$622$	−10.5000	+	6.06218i	−0.421012	+	0.243071i
$623$		0			0
$624$	−8.02178	+	8.33648i	−0.321128	+	0.333726i
$625$	11.9564	−	20.7092i	0.478258	−	0.828366i
$626$	−39.3303	−	22.7074i	−1.57196	−	0.907569i
$627$	7.50000	−	12.9904i	0.299521	−	0.518786i
$628$	−30.6434	−	53.0759i	−1.22280	−	2.11796i
$629$		−	20.7846i		−	0.828737i
$630$		0			0
$631$	−10.4347	−	6.02445i	−0.415397	−	0.239830i	0.277709	−	0.960665i	$-0.410425\pi$
$631$	−10.4347	−	6.02445i	−0.415397	−	0.239830i	−0.693106	+	0.720836i	$0.743758\pi$
$632$	−9.00000	−	5.19615i	−0.358001	−	0.206692i
$633$	2.53901			0.100917
$634$	−20.2695	+	35.1078i	−0.805005	+	1.39431i
$635$			34.9271i			1.38604i
$636$	60.8258			2.41190
$637$		0			0
$638$	−6.16515			−0.244081
$639$			0.190700i			0.00754399i
$640$	−13.9782	+	24.2110i	−0.552538	+	0.957023i
$641$	15.6261			0.617195			0.308598	−	0.951193i	$-0.400140\pi$
$641$	15.6261			0.617195			0.308598	+	0.951193i	$0.400140\pi$
$642$	33.2477	+	19.1956i	1.31218	+	0.757589i
$643$	11.7523	+	6.78518i	0.463464	+	0.267581i	0.713500	−	0.700655i	$-0.247109\pi$
$643$	11.7523	+	6.78518i	0.463464	+	0.267581i	−0.250035	+	0.968237i	$0.580442\pi$
$644$		0			0
$645$			17.1497i			0.675269i
$646$	21.5608	+	37.3444i	0.848298	+	1.46930i
$647$	14.5390	−	25.1823i	0.571588	−	0.990019i	−0.424816	−	0.905280i	$-0.639661\pi$
$647$	14.5390	−	25.1823i	0.571588	−	0.990019i	0.996403	−	0.0847389i	$-0.0270056\pi$
$648$	−14.3739	−	8.29875i	−0.564659	−	0.326006i
$649$	5.64337	−	9.77461i	0.221522	−	0.383687i
$650$	−1.58258	+	0.456850i	−0.0620737	+	0.0179191i
$651$		0			0
$652$	16.7477	−	9.66930i	0.655892	−	0.378679i
$653$	11.2087			0.438631			0.219315	−	0.975654i	$-0.429618\pi$
$653$	11.2087			0.438631			0.219315	+	0.975654i	$0.429618\pi$
$654$	31.1216			1.21695
$655$	−6.87386	+	3.96863i	−0.268584	+	0.155067i
$656$	3.95644	−	2.28425i	0.154473	−	0.0891850i
$657$	0.626136	+	0.361500i	0.0244279	+	0.0141035i
$658$		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	$0.203951\pi$
$660$	13.9564			0.543254
$661$	16.2523	+	9.38325i	0.632140	+	0.364966i	0.781580	−	0.623804i	$-0.214414\pi$
$661$	16.2523	+	9.38325i	0.632140	+	0.364966i	−0.149440	+	0.988771i	$0.547747\pi$
$662$	−1.18693	−	2.05583i	−0.0461314	−	0.0799020i
$663$	−13.4347	+	13.9617i	−0.521759	+	0.542228i
$664$	6.16515			0.239254
$665$		0			0
$666$	1.58258	+	2.74110i	0.0613236	+	0.106216i
$667$	8.37386	+	14.5040i	0.324237	+	0.561595i
$668$	48.2650	−	27.8658i	1.86743	−	1.07816i
$669$			37.0961i			1.43422i
$670$	47.3085	−	27.3136i	1.82769	−	1.05522i
$671$			16.2559i			0.627552i
$672$		0			0
$673$	14.2477	+	24.6778i	0.549210	+	0.951259i	0.998329	+	0.0577870i	$0.0184044\pi$
$673$	14.2477	+	24.6778i	0.549210	+	0.951259i	−0.449119	+	0.893472i	$0.648262\pi$
$674$		−	28.3604i		−	1.09240i
$675$	0.521780	+	0.903750i	0.0200833	+	0.0347854i
$676$	−32.0998	−	16.9213i	−1.23461	−	0.650819i
$677$	16.8956	−	29.2641i	0.649352	−	1.12471i	−0.333925	−	0.942599i	$-0.608373\pi$
$677$	16.8956	−	29.2641i	0.649352	−	1.12471i	0.983278	−	0.182112i	$-0.0582933\pi$
$678$	4.81307	−	2.77883i	0.184845	−	0.106720i
$679$		0			0
$680$	−5.68693	+	9.85005i	−0.218084	+	0.377732i
$681$	−19.1044	−	11.0299i	−0.732081	−	0.422667i
$682$			24.1733i			0.925642i
$683$		−	25.0671i		−	0.959164i	−0.877497	−	0.479582i	$-0.840788\pi$
$683$		−	25.0671i		−	0.959164i	0.877497	−	0.479582i	$-0.159212\pi$
$684$	−3.31307	−	1.91280i	−0.126678	−	0.0731378i
$685$	−18.7695	+	32.5097i	−0.717146	+	1.24213i
$686$		0			0
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	−3.91742	+	6.78518i	−0.149350	+	0.258682i
$689$	−12.1652	−	42.1413i	−0.463455	−	1.60546i
$690$	−32.5390	−	56.3592i	−1.23874	−	2.14556i
$691$			29.3694i			1.11727i	0.829415	+	0.558633i	$0.188674\pi$
$691$			29.3694i			1.11727i	−0.829415	+	0.558633i	$0.811326\pi$
$692$	10.8131	+	18.7288i	0.411051	+	0.711962i
$693$		0			0
$694$		−	9.66930i		−	0.367042i
$695$	−1.50000	+	0.866025i	−0.0568982	+	0.0328502i
$696$			6.85275i			0.259753i
$697$	6.62614	−	3.82560i	0.250983	−	0.144905i
$698$	11.6869	+	20.2424i	0.442357	+	0.766185i
$699$	6.23049	+	10.7915i	0.235659	+	0.408173i
$700$		0			0
$701$	31.9129			1.20533			0.602666	−	0.797993i	$-0.294105\pi$
$701$	31.9129			1.20533			0.602666	+	0.797993i	$0.294105\pi$
$702$	−9.47822	+	38.3058i	−0.357732	+	1.44576i
$703$	−22.7477	−	39.4002i	−0.857947	−	1.48601i
$704$	13.8956	+	8.02265i	0.523712	+	0.302365i
$705$	−16.7913			−0.632396
$706$	−29.3521	+	50.8393i	−1.10468	+	1.91336i
$707$		0			0
$708$	−38.3258	−	22.1274i	−1.44037	−	0.831598i
$709$	6.31307	−	3.64485i	0.237092	−	0.136885i	−0.376747	−	0.926316i	$-0.622957\pi$
$709$	6.31307	−	3.64485i	0.237092	−	0.136885i	0.613840	+	0.789431i	$0.289624\pi$
$710$	3.79129	−	2.18890i	0.142284	−	0.0821480i
$711$	−1.25227			−0.0469639
$712$	5.04356			0.189015
$713$	56.8693	−	32.8335i	2.12977	−	1.22962i
$714$		0			0
$715$	−2.79129	−	9.66930i	−0.104388	−	0.361611i
$716$	−12.5608	+	21.7559i	−0.469419	+	0.813057i
$717$	−20.5218	−	11.8483i	−0.766400	−	0.442481i
$718$	−13.8739	+	24.0302i	−0.517768	+	0.896800i
$719$	−2.91742	−	5.05313i	−0.108802	−	0.188450i	0.806483	−	0.591257i	$-0.201368\pi$
$719$	−2.91742	−	5.05313i	−0.108802	−	0.188450i	−0.915285	+	0.402807i	$0.868035\pi$
$720$			0.818350i			0.0304981i
$721$		0			0
$722$	45.7259	+	26.3999i	1.70174	+	0.982502i
$723$	6.37841	+	3.68258i	0.237216	+	0.136956i
$724$	25.5826			0.950769
$725$	0.230493	−	0.399225i	0.00856028	−	0.0148268i
$726$			36.7545i			1.36409i
$727$	−27.7477			−1.02911			−0.514553	−	0.857459i	$-0.672042\pi$
$727$	−27.7477			−1.02911			−0.514553	+	0.857459i	$0.672042\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$		−	16.5975i		−	0.614301i
$731$	−6.56080	+	11.3636i	−0.242660	+	0.420299i
$732$	63.7386			2.35585
$733$	7.81307	+	4.51088i	0.288582	+	0.166613i	0.637302	−	0.770614i	$-0.280050\pi$
$733$	7.81307	+	4.51088i	0.288582	+	0.166613i	−0.348720	+	0.937227i	$0.613384\pi$
$734$	34.1216	+	19.7001i	1.25945	+	0.727144i
$735$		0			0
$736$		−	55.9977i		−	2.06410i
$737$	−7.26951	−	12.5912i	−0.267776	−	0.463801i
$738$	−0.582576	+	1.00905i	−0.0214449	+	0.0371437i
$739$	10.7477	+	6.20520i	0.395362	+	0.228262i	0.684481	−	0.729031i	$-0.260029\pi$
$739$	10.7477	+	6.20520i	0.395362	+	0.228262i	−0.289119	+	0.957293i	$0.593362\pi$
$740$	21.1652	−	36.6591i	0.778046	−	1.34762i
$741$	−10.1869	+	41.1700i	−0.374226	+	1.51242i
$742$		0			0
$743$	4.64792	−	2.68348i	0.170516	−	0.0984472i	−0.412313	−	0.911042i	$-0.635279\pi$
$743$	4.64792	−	2.68348i	0.170516	−	0.0984472i	0.582829	+	0.812595i	$0.301946\pi$
$744$	26.8693			0.985077
$745$	−4.79129			−0.175539
$746$	69.7432	−	40.2662i	2.55348	−	1.47425i
$747$	0.643371	−	0.371450i	0.0235397	−	0.0135907i
$748$	9.24773	+	5.33918i	0.338130	+	0.195220i
$749$		0			0
$750$	−22.3521	+	38.7149i	−0.816183	+	1.41367i
$751$	−3.74773			−0.136757			−0.0683783	−	0.997659i	$-0.521782\pi$
$751$	−3.74773			−0.136757			−0.0683783	+	0.997659i	$0.521782\pi$
$752$	−6.64337	−	3.83555i	−0.242259	−	0.139868i
$753$	18.9564	+	32.8335i	0.690811	+	1.19652i
$754$	16.7477	−	4.83465i	0.609916	−	0.176068i
$755$	26.5390			0.965854
$756$		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	$0.868110\pi$
$758$	−4.97822	−	8.62253i	−0.180817	−	0.313184i
$759$	−15.0000	+	8.66025i	−0.544466	+	0.314347i
$760$			24.8963i			0.903082i
$761$	27.7259	−	16.0076i	1.00506	−	0.580274i	0.0953219	−	0.995447i	$-0.469612\pi$
$761$	27.7259	−	16.0076i	1.00506	−	0.580274i	0.909743	+	0.415172i	$0.136279\pi$
$762$		−	62.5644i		−	2.26647i
$763$		0			0
$764$	−0.873864	−	1.51358i	−0.0316153	−	0.0547593i
$765$			1.37055i			0.0495524i
$766$	−4.29129	−	7.43273i	−0.155051	−	0.268555i
$767$	−7.66515	+	30.9783i	−0.276773	+	1.11856i
$768$	2.50000	−	4.33013i	0.0902110	−	0.156250i
$769$	−21.8739	+	12.6289i	−0.788792	+	0.455409i	−0.839537	−	0.543303i	$-0.817174\pi$
$769$	−21.8739	+	12.6289i	−0.788792	+	0.455409i	0.0507453	+	0.998712i	$0.483840\pi$
$770$		0			0
$771$	−25.0390	+	43.3688i	−0.901758	+	1.56189i
$772$	−30.0000	−	17.3205i	−1.07972	−	0.623379i
$773$			22.8981i			0.823586i	0.911277	+	0.411793i	$0.135097\pi$
$773$			22.8981i			0.823586i	−0.911277	+

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.18890i q^{2} +(-0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +O(q^{10})\)	\(q+2.18890i q^{2} +(-0.895644 + 1.55130i) q^{3} -2.79129 q^{4} +(1.89564 + 1.09445i) q^{5} +(-3.39564 - 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 - 0.180750i) q^{9} +(-2.39564 + 4.14938i) q^{10} +(1.10436 + 0.637600i) q^{11} +(2.50000 - 4.33013i) q^{12} +(-3.50000 - 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} -1.79129 q^{16} -3.00000 q^{17} +(0.395644 - 0.228425i) q^{18} +(-5.68693 + 3.28335i) q^{19} +(-5.29129 - 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +7.58258 q^{23} +(2.68693 + 1.55130i) q^{24} +(-0.104356 - 0.180750i) q^{25} +(1.89564 - 7.66115i) q^{26} -5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 - 7.43273i) q^{30} +(7.50000 - 4.33013i) q^{31} -7.38505i q^{32} +(-1.97822 + 1.14213i) q^{33} -6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +6.92820i q^{37} +(-7.18693 - 12.4481i) q^{38} +(4.47822 - 4.65390i) q^{39} +(1.89564 - 3.28335i) q^{40} +(-2.20871 + 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +(-3.08258 - 1.77973i) q^{44} -0.456850i q^{45} +16.5975i q^{46} +(3.70871 + 2.14123i) q^{47} +(1.60436 - 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} +(2.68693 - 4.65390i) q^{51} +(9.76951 + 2.41733i) q^{52} +(6.08258 + 10.5353i) q^{53} -10.9445i q^{54} +(1.39564 + 2.41733i) q^{55} -11.7629i q^{57} +(-4.18693 + 2.41733i) q^{58} -8.85095i q^{59} +(9.47822 - 5.47225i) q^{60} +(6.37386 + 11.0399i) q^{61} +(9.47822 + 16.4168i) q^{62} +12.5826 q^{64} +(-5.68693 - 5.47225i) q^{65} +(-2.50000 - 4.33013i) q^{66} +(-9.87386 - 5.70068i) q^{67} +8.37386 q^{68} +(-6.79129 + 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(-0.313068 + 0.180750i) q^{72} +(-3.00000 + 1.73205i) q^{73} -15.1652 q^{74} +0.373864 q^{75} +(15.8739 - 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} +(3.00000 - 5.19615i) q^{79} +(-3.39564 - 1.96048i) q^{80} +(4.79129 - 8.29875i) q^{81} +(-2.79129 - 4.83465i) q^{82} +3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(8.29129 + 4.78698i) q^{86} -3.95644 q^{87} +(1.10436 - 1.91280i) q^{88} +2.91190i q^{89} +1.00000 q^{90} -21.1652 q^{92} +15.5130i q^{93} +(-4.68693 + 8.11800i) q^{94} -14.3739 q^{95} +(11.4564 + 6.61438i) q^{96} +(13.1869 + 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{3} - 2 q^{4} + 3 q^{5} - 9 q^{6} - 5 q^{9}+O(q^{10}) \) 4 * q + q^3 - 2 * q^4 + 3 * q^5 - 9 * q^6 - 5 * q^9	\( 4 q + q^{3} - 2 q^{4} + 3 q^{5} - 9 q^{6} - 5 q^{9} - 5 q^{10} + 9 q^{11} + 10 q^{12} - 14 q^{13} - 9 q^{15} + 2 q^{16} - 12 q^{17} - 3 q^{18} - 9 q^{19} - 12 q^{20} - q^{22} + 12 q^{23} - 3 q^{24} - 5 q^{25} + 3 q^{26} - 20 q^{27} + 9 q^{29} - 8 q^{30} + 30 q^{31} + 15 q^{33} - 8 q^{36} - 15 q^{38} - 5 q^{39} + 3 q^{40} - 18 q^{41} - 5 q^{43} + 6 q^{44} + 24 q^{47} + 11 q^{48} - 3 q^{50} - 3 q^{51} + 7 q^{52} + 6 q^{53} + q^{55} - 3 q^{58} + 15 q^{60} - 2 q^{61} + 15 q^{62} + 32 q^{64} - 9 q^{65} - 10 q^{66} - 12 q^{67} + 6 q^{68} - 18 q^{69} + 6 q^{71} - 15 q^{72} - 12 q^{73} - 24 q^{74} - 26 q^{75} + 36 q^{76} + 27 q^{78} + 12 q^{79} - 9 q^{80} + 10 q^{81} - 2 q^{82} - 9 q^{85} + 24 q^{86} + 30 q^{87} + 9 q^{88} + 4 q^{90} - 48 q^{92} - 5 q^{94} - 30 q^{95} + 39 q^{97}+O(q^{100}) \) 4 * q + q^3 - 2 * q^4 + 3 * q^5 - 9 * q^6 - 5 * q^9 - 5 * q^10 + 9 * q^11 + 10 * q^12 - 14 * q^13 - 9 * q^15 + 2 * q^16 - 12 * q^17 - 3 * q^18 - 9 * q^19 - 12 * q^20 - q^22 + 12 * q^23 - 3 * q^24 - 5 * q^25 + 3 * q^26 - 20 * q^27 + 9 * q^29 - 8 * q^30 + 30 * q^31 + 15 * q^33 - 8 * q^36 - 15 * q^38 - 5 * q^39 + 3 * q^40 - 18 * q^41 - 5 * q^43 + 6 * q^44 + 24 * q^47 + 11 * q^48 - 3 * q^50 - 3 * q^51 + 7 * q^52 + 6 * q^53 + q^55 - 3 * q^58 + 15 * q^60 - 2 * q^61 + 15 * q^62 + 32 * q^64 - 9 * q^65 - 10 * q^66 - 12 * q^67 + 6 * q^68 - 18 * q^69 + 6 * q^71 - 15 * q^72 - 12 * q^73 - 24 * q^74 - 26 * q^75 + 36 * q^76 + 27 * q^78 + 12 * q^79 - 9 * q^80 + 10 * q^81 - 2 * q^82 - 9 * q^85 + 24 * q^86 + 30 * q^87 + 9 * q^88 + 4 * q^90 - 48 * q^92 - 5 * q^94 - 30 * q^95 + 39 * q^97

Introduction

L-functions

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