LMFDB - Embedded newform 637.2.q.e.491.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - x^{2} - 2x + 4 $ x^4 - x^3 - x^2 - 2*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.2
Root			$-0.895644 - 1.09445i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.e.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})$	\(q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i 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} +5.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} +(0.895644 + 1.55130i) q^{16} +(-1.50000 + 2.59808i) q^{17} +0.456850i q^{18} +(-5.68693 - 3.28335i) q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 - 6.56670i) q^{23} +(2.68693 - 1.55130i) q^{24} +0.208712 q^{25} +(7.58258 - 2.18890i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 + 7.43273i) q^{30} -8.66025i q^{31} +(6.39564 + 3.69253i) q^{32} +(-1.97822 - 1.14213i) q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(6.00000 - 3.46410i) q^{37} -14.3739 q^{38} +(1.79129 + 6.20520i) q^{39} +3.79129 q^{40} +(2.20871 - 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +3.55945i q^{44} +(-0.395644 - 0.228425i) q^{45} +(-14.3739 - 8.29875i) q^{46} +4.28245i q^{47} +(-1.60436 + 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} -5.37386 q^{51} +(6.97822 - 7.25198i) q^{52} -12.1652 q^{53} +(9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} +(4.18693 + 2.41733i) q^{58} +(-7.66515 - 4.42548i) q^{59} +10.9445i q^{60} +(-6.37386 + 11.0399i) q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(-1.89564 + 7.66115i) q^{65} -5.00000 q^{66} +(9.87386 - 5.70068i) q^{67} +(4.18693 + 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(0.313068 + 0.180750i) q^{72} +3.46410i q^{73} +(7.58258 - 13.1334i) q^{74} +(0.186932 + 0.323775i) q^{75} +(-15.8739 + 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} -6.00000 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} -9.57395i q^{86} +(-1.97822 + 3.42638i) q^{87} +(1.10436 + 1.91280i) q^{88} +(-2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(13.4347 - 7.75650i) q^{93} +(4.68693 + 8.11800i) q^{94} +(7.18693 - 12.4481i) q^{95} +13.2288i q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9	$ 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + q^4 + 9 * q^6 - 5 * q^9 + 5 * q^10 - 9 * q^11 + 20 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 - 9 * q^19 + 12 * q^20 - q^22 - 6 * q^23 - 3 * q^24 + 10 * q^25 + 12 * q^26 + 20 * q^27 + 9 * q^29 - 8 * q^30 + 21 * q^32 + 15 * q^33 - 8 * q^36 + 24 * q^37 - 30 * q^38 - 2 * q^39 + 6 * q^40 + 18 * q^41 - 5 * q^43 + 3 * q^45 - 30 * q^46 - 11 * q^48 - 3 * q^50 + 6 * q^51 + 5 * q^52 - 12 * q^53 + 15 * q^54 - q^55 + 3 * q^58 + 6 * q^59 + 2 * q^61 - 15 * q^62 + 32 * q^64 - 3 * q^65 - 20 * q^66 + 12 * q^67 + 3 * q^68 + 18 * q^69 + 6 * q^71 + 15 * q^72 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 - 24 * q^79 - 9 * q^80 + 10 * q^81 + 2 * q^82 - 9 * q^85 + 15 * q^87 + 9 * q^88 - 33 * q^89 - 4 * q^90 - 48 * q^92 - 15 * q^93 + 5 * q^94 + 15 * q^95 - 39 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.89564	−	1.09445i	1.34042	−	0.773893i	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.89564	−	1.09445i	1.34042	−	0.773893i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	0.999803	+	0.0198595i	$0.00632191\pi$
$3$	0.895644	+	1.55130i	0.517100	+	0.895644i	−0.482703	+	0.875784i	$0.660345\pi$
$4$	1.39564	−	2.41733i	0.697822	−	1.20866i
$5$			2.18890i			0.978906i	0.872030	+	0.489453i	$0.162804\pi$
$5$			2.18890i			0.978906i	−0.872030	+	0.489453i	$0.837196\pi$
$6$	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	$-0.728243\pi$
$11$	−1.10436	+	0.637600i	−0.332976	+	0.192244i	0.324186	+	0.945993i	$0.394910\pi$
$12$	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
$15$	−3.39564	+	1.96048i	−0.876751	+	0.506193i
$16$	0.895644	+	1.55130i	0.223911	+	0.387825i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$			0.456850i			0.107681i
$19$	−5.68693	−	3.28335i	−1.30467	−	0.753253i	−0.323470	−	0.946238i	$-0.604850\pi$
$19$	−5.68693	−	3.28335i	−1.30467	−	0.753253i	−0.981202	+	0.192986i	$0.938183\pi$
$20$	5.29129	+	3.05493i	1.18317	+	0.683102i
$21$		0			0
$22$	−1.39564	+	2.41733i	−0.297552	+	0.515376i
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	−0.925634	−	0.378420i	$-0.876468\pi$
$23$	−3.79129	−	6.56670i	−0.790538	−	1.36925i	0.135096	−	0.990833i	$-0.456866\pi$
$24$	2.68693	−	1.55130i	0.548468	−	0.316658i
$25$	0.208712			0.0417424
$26$	7.58258	−	2.18890i	1.48707	−	0.429279i
$27$	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
$31$		−	8.66025i		−	1.55543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$		−	8.66025i		−	1.55543i	0.628619	−	0.777714i	$-0.283621\pi$
$32$	6.39564	+	3.69253i	1.13060	+	0.652753i
$33$	−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
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.0821995	−	0.996616i	$-0.473806\pi$
$37$	6.00000	−	3.46410i	0.986394	−	0.569495i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−14.3739			−2.33175
$39$	1.79129	+	6.20520i	0.286836	+	0.993628i
$40$	3.79129			0.599455
$41$	2.20871	−	1.27520i	0.344943	−	0.199153i	−0.317513	−	0.948254i	$-0.602848\pi$
$41$	2.20871	−	1.27520i	0.344943	−	0.199153i	0.662456	+	0.749101i	$0.269514\pi$
$42$		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	$0.0584356\pi$
$44$			3.55945i			0.536608i
$45$	−0.395644	−	0.228425i	−0.0589791	−	0.0340516i
$46$	−14.3739	−	8.29875i	−2.11931	−	1.22358i
$47$			4.28245i			0.624660i	0.949974	+	0.312330i	$0.101109\pi$
$47$			4.28245i			0.624660i	−0.949974	+	0.312330i	$0.898891\pi$
$48$	−1.60436	+	2.77883i	−0.231569	+	0.401089i
$49$		0			0
$50$	0.395644	−	0.228425i	0.0559525	−	0.0323042i
$51$	−5.37386			−0.752491
$52$	6.97822	−	7.25198i	0.967705	−	1.00567i
$53$	−12.1652			−1.67101			−0.835506	−	0.549481i	$-0.814825\pi$
$53$	−12.1652			−1.67101			−0.835506	+	0.549481i	$0.814825\pi$
$54$	9.47822	−	5.47225i	1.28982	−	0.744679i
$55$	−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
$59$	−7.66515	−	4.42548i	−0.997918	−	0.576148i	−0.0902862	−	0.995916i	$-0.528778\pi$
$59$	−7.66515	−	4.42548i	−0.997918	−	0.576148i	−0.907632	+	0.419768i	$0.862112\pi$
$60$			10.9445i			1.41293i
$61$	−6.37386	+	11.0399i	−0.816090	+	1.41351i	0.0924533	+	0.995717i	$0.470529\pi$
$61$	−6.37386	+	11.0399i	−0.816090	+	1.41351i	−0.908543	+	0.417792i	$0.862804\pi$
$62$	−9.47822	−	16.4168i	−1.20374	−	2.08493i
$63$		0			0
$64$	12.5826			1.57282
$65$	−1.89564	+	7.66115i	−0.235126	+	0.950249i
$66$	−5.00000			−0.615457
$67$	9.87386	−	5.70068i	1.20628	−	0.696449i	0.244339	−	0.969690i	$-0.421429\pi$
$67$	9.87386	−	5.70068i	1.20628	−	0.696449i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	4.18693	+	7.25198i	0.507740	+	0.879432i
$69$	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
$73$			3.46410i			0.405442i	0.979236	+	0.202721i	$0.0649785\pi$
$73$			3.46410i			0.405442i	−0.979236	+	0.202721i	$0.935021\pi$
$74$	7.58258	−	13.1334i	0.881457	−	1.52673i
$75$	0.186932	+	0.323775i	0.0215850	+	0.0373864i
$76$	−15.8739	+	9.16478i	−1.82086	+	1.05127i
$77$		0			0
$78$	10.1869	+	9.80238i	1.15344	+	1.10990i
$79$	−6.00000			−0.675053			−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000			−0.675053			−0.337526	+	0.941316i	$0.609590\pi$
$80$	−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	$-0.937416\pi$
$83$		−	3.55945i		−	0.390701i	0.980734	−	0.195350i	$-0.0625844\pi$
$84$		0			0
$85$	−5.68693	−	3.28335i	−0.616834	−	0.356129i
$86$		−	9.57395i		−	1.03239i
$87$	−1.97822	+	3.42638i	−0.212087	+	0.367346i
$88$	1.10436	+	1.91280i	0.117725	+	0.203905i
$89$	−2.52178	+	1.45595i	−0.267308	+	0.154330i	−0.627664	−	0.778485i	$-0.715989\pi$
$89$	−2.52178	+	1.45595i	−0.267308	+	0.154330i	0.360356	+	0.932815i	$0.382655\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−21.1652			−2.20662
$93$	13.4347	−	7.75650i	1.39311	−	0.804312i
$94$	4.68693	+	8.11800i	0.483420	+	0.837308i
$95$	7.18693	−	12.4481i	0.737364	−	1.27715i
$96$			13.2288i			1.35015i
$97$	−13.1869	−	7.61348i	−1.33893	−	0.773032i	−0.352281	−	0.935894i	$-0.614594\pi$
$97$	−13.1869	−	7.61348i	−1.33893	−	0.773032i	−0.986649	+	0.162863i	$0.947927\pi$
$98$		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	$-0.328625\pi$
$101$	−4.89564	−	8.47950i	−0.487135	−	0.843742i	−0.999891	+	0.0147923i	$0.995291\pi$
$102$	−10.1869	+	5.88143i	−1.00866	+	0.582348i
$103$	−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
$106$	−23.0608	+	13.3142i	−2.23986	+	1.29319i
$107$	4.89564	+	8.47950i	0.473280	+	0.819745i	0.999532	−	0.0305838i	$-0.00973664\pi$
$107$	4.89564	+	8.47950i	0.473280	+	0.819745i	−0.526252	+	0.850328i	$0.676403\pi$
$108$	6.97822	−	12.0866i	0.671479	−	1.16304i
$109$		−	7.93725i		−	0.760251i	−0.924935	−	0.380126i	$-0.875881\pi$
$109$		−	7.93725i		−	0.760251i	0.924935	−	0.380126i	$-0.124119\pi$
$110$	−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	$0.187904\pi$
$114$	−12.8739	−	22.2982i	−1.20575	−	2.08842i
$115$	14.3739	−	8.29875i	1.34037	−	0.773863i
$116$	6.16515			0.572420
$117$	−0.521780	+	0.542250i	−0.0482386	+	0.0501310i
$118$	−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
$122$			27.9035i			2.52627i
$123$	3.95644	+	2.28425i	0.356740	+	0.205964i
$124$	−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	$0.582952\pi$
$128$	11.0608	−	6.38595i	0.977645	−	0.564444i
$129$	7.83485			0.689820
$130$	4.79129	+	16.5975i	0.420224	+	1.45570i
$131$	−3.62614			−0.316817			−0.158409	−	0.987374i	$-0.550636\pi$
$131$	−3.62614			−0.316817			−0.158409	+	0.987374i	$0.550636\pi$
$132$	−5.52178	+	3.18800i	−0.480609	+	0.277480i
$133$		0			0
$134$	12.4782	−	21.6129i	1.07795	−	1.86707i
$135$			10.9445i			0.941953i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$	−14.8521	−	8.57485i	−1.26890	−	0.732599i	−0.294119	−	0.955769i	$-0.595026\pi$
$137$	−14.8521	−	8.57485i	−1.26890	−	0.732599i	−0.974780	+	0.223169i	$0.928360\pi$
$138$		−	29.7309i		−	2.53086i
$139$	0.395644	−	0.685275i	0.0335581	−	0.0581243i	−0.848759	−	0.528781i	$-0.822649\pi$
$139$	0.395644	−	0.685275i	0.0335581	−	0.0581243i	0.882317	+	0.470656i	$0.155983\pi$
$140$		0			0
$141$	−6.64337	+	3.83555i	−0.559473	+	0.323012i
$142$	−2.00000			−0.167836
$143$	−4.41742	+	1.27520i	−0.369404	+	0.106638i
$144$	−0.373864			−0.0311553
$145$	−4.18693	+	2.41733i	−0.347706	+	0.200748i
$146$	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	$-0.304755\pi$
$149$	1.89564	+	1.09445i	0.155297	+	0.0896609i	−0.420338	+	0.907368i	$0.638088\pi$
$150$	0.708712	+	0.409175i	0.0578661	+	0.0334090i
$151$			12.1244i			0.986666i	0.869841	+	0.493333i	$0.164222\pi$
$151$			12.1244i			0.986666i	−0.869841	+	0.493333i	$0.835778\pi$
$152$	−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
$156$	17.5000	+	4.33013i	1.40112	+	0.346688i
$157$	21.9564			1.75231			0.876157	−	0.482025i	$-0.160099\pi$
$157$	21.9564			1.75231			0.876157	+	0.482025i	$0.160099\pi$
$158$	−11.3739	+	6.56670i	−0.904856	+	0.522419i
$159$	−10.8956	−	18.8718i	−0.864081	−	1.49663i
$160$	−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	$-0.245870\pi$
$163$	6.00000	+	3.46410i	0.469956	+	0.271329i	−0.246265	+	0.969202i	$0.579203\pi$
$164$		−	7.11890i		−	0.555893i
$165$	2.50000	−	4.33013i	0.194625	−	0.337100i
$166$	−3.89564	−	6.74745i	−0.302361	−	0.523704i
$167$	17.2913	−	9.98313i	1.33804	−	0.772518i	0.351523	−	0.936179i	$-0.385664\pi$
$167$	17.2913	−	9.98313i	1.33804	−	0.772518i	0.986517	+	0.163661i	$0.0523304\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−14.3739			−1.10243
$171$	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	$-0.738172\pi$
$173$	3.87386	−	6.70973i	0.294524	−	0.510131i	0.974874	+	0.222756i	$0.0715054\pi$
$174$			8.66025i			0.656532i
$175$		0			0
$176$	−1.97822	−	1.14213i	−0.149114	−	0.0860910i
$177$		−	15.8546i		−	1.19171i
$178$	−3.18693	+	5.51993i	−0.238871	+	0.413736i
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$	−1.10436	+	0.637600i	−0.0823138	+	0.0475239i
$181$	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
$183$	−22.8348			−1.68800
$184$	−11.3739	+	6.56670i	−0.838492	+	0.484104i
$185$	7.58258	+	13.1334i	0.557482	+	0.965587i
$186$	16.9782	−	29.4071i	1.24490	−	2.15624i
$187$		−	3.82560i		−	0.279756i
$188$	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	−0.854477	−	0.519490i	$-0.826122\pi$
$191$	0.313068	−	0.542250i	0.0226528	−	0.0392358i	0.877130	+	0.480254i	$0.159455\pi$
$192$	11.2695	+	19.5194i	0.813307	+	1.40869i
$193$	−10.7477	+	6.20520i	−0.773638	+	0.446660i	−0.834171	−	0.551506i	$-0.814053\pi$
$193$	−10.7477	+	6.20520i	−0.773638	+	0.446660i	0.0605327	+	0.998166i	$0.480720\pi$
$194$	−33.3303			−2.39298
$195$	−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	$0.460817\pi$
$198$	−0.291288	−	0.504525i	−0.0207009	−	0.0358551i
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		−	0.361500i		−	0.0255619i
$201$	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
$205$	2.79129	+	4.83465i	0.194952	+	0.337667i
$206$	−8.68693	+	5.01540i	−0.605247	+	0.349440i
$207$	1.58258			0.109997
$208$	1.79129	+	6.20520i	0.124203	+	0.430253i
$209$	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
$213$		−	1.63670i		−	0.112145i
$214$	18.5608	+	10.7161i	1.26879	+	0.732536i
$215$	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
$219$	−5.37386	+	3.10260i	−0.363132	+	0.209654i
$220$	−7.79129			−0.525289
$221$	−7.50000	+	7.79423i	−0.504505	+	0.524297i
$222$	27.1652			1.82321
$223$	−17.9347	+	10.3546i	−1.20099	+	0.693394i	−0.960776	−	0.277325i	$-0.910552\pi$
$223$	−17.9347	+	10.3546i	−1.20099	+	0.693394i	−0.240217	+	0.970719i	$0.577219\pi$
$224$		0			0
$225$	−0.0217804	+	0.0377247i	−0.00145203	+	0.00251498i
$226$			3.10260i			0.206382i
$227$	10.6652	+	6.15753i	0.707871	+	0.408689i	0.810272	−	0.586054i	$-0.199319\pi$
$227$	10.6652	+	6.15753i	0.707871	+	0.408689i	−0.102401	+	0.994743i	$0.532653\pi$
$228$	−28.4347	−	16.4168i	−1.88313	−	1.08723i
$229$			6.92820i			0.457829i	0.973447	+	0.228914i	$0.0735176\pi$
$229$			6.92820i			0.457829i	−0.973447	+	0.228914i	$0.926482\pi$
$230$	18.1652	−	31.4630i	1.19777	−	2.07461i
$231$		0			0
$232$	3.31307	−	1.91280i	0.217514	−	0.125582i
$233$	−6.95644			−0.455731			−0.227866	−	0.973693i	$-0.573175\pi$
$233$	−6.95644			−0.455731			−0.227866	+	0.973693i	$0.573175\pi$
$234$	−0.395644	+	1.59898i	−0.0258641	+	0.104528i
$235$	−9.37386			−0.611483
$236$	−21.3956	+	12.3528i	−1.39274	+	0.804098i
$237$	−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
$241$	−3.56080	−	2.05583i	−0.229371	−	0.132427i	0.380911	−	0.924612i	$-0.375610\pi$
$241$	−3.56080	−	2.05583i	−0.229371	−	0.132427i	−0.610282	+	0.792184i	$0.708944\pi$
$242$			20.5185i			1.31898i
$243$	−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
$247$	−17.0608	−	16.4168i	−1.08555	−	1.04457i
$248$	−15.0000			−0.952501
$249$	5.52178	−	3.18800i	0.349929	−	0.202031i
$250$	12.4782	+	21.6129i	0.789192	+	1.36692i
$251$	−10.5826	+	18.3296i	−0.667966	+	1.15695i	0.310506	+	0.950572i	$0.399502\pi$
$251$	−10.5826	+	18.3296i	−0.667966	+	1.15695i	−0.978472	+	0.206380i	$0.933832\pi$
$252$		0			0
$253$	8.37386	+	4.83465i	0.526460	+	0.303952i
$254$	30.2477	+	17.4635i	1.89791	+	1.09576i
$255$		−	11.7629i		−	0.736619i
$256$	1.39564	−	2.41733i	0.0872277	−	0.151083i
$257$	13.9782	+	24.2110i	0.871937	+	1.51024i	0.859990	+	0.510311i	$0.170470\pi$
$257$	13.9782	+	24.2110i	0.871937	+	1.51024i	0.0119476	+	0.999929i	$0.496197\pi$
$258$	14.8521	−	8.57485i	0.924650	−	0.533847i
$259$		0			0
$260$	15.8739	+	15.2746i	0.984455	+	0.947292i
$261$	−0.460985			−0.0285343
$262$	−6.87386	+	3.96863i	−0.424669	+	0.245183i
$263$	13.6652	+	23.6687i	0.842629	+	1.45948i	0.887664	+	0.460491i	$0.152327\pi$
$263$	13.6652	+	23.6687i	0.842629	+	1.45948i	−0.0450348	+	0.998985i	$0.514340\pi$
$264$	−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
$268$		−	31.8245i		−	1.94399i
$269$	−5.60436	+	9.70703i	−0.341704	+	0.591848i	−0.984749	−	0.173980i	$-0.944337\pi$
$269$	−5.60436	+	9.70703i	−0.341704	+	0.591848i	0.643046	+	0.765828i	$0.277671\pi$
$270$	11.9782	+	20.7469i	0.728971	+	1.26262i
$271$	24.8739	−	14.3609i	1.51098	−	0.872364i	0.511062	−	0.859544i	$-0.329252\pi$
$271$	24.8739	−	14.3609i	1.51098	−	0.872364i	0.999918	−	0.0128205i	$-0.00408101\pi$
$272$	−5.37386			−0.325838
$273$		0			0
$274$	−37.5390			−2.26781
$275$	−0.230493	+	0.133075i	−0.0138992	+	0.00802472i
$276$	−18.9564	−	32.8335i	−1.14104	−	1.97635i
$277$	7.87386	−	13.6379i	0.473095	−	0.819424i	−0.526431	−	0.850218i	$-0.676470\pi$
$277$	7.87386	−	13.6379i	0.473095	−	0.819424i	0.999526	+	0.0307939i	$0.00980354\pi$
$278$		−	1.73205i		−	0.103882i
$279$	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	−0.954482	−	0.298270i	$-0.903591\pi$
$283$	−12.3739	−	21.4322i	−0.735550	−	1.27401i	0.218932	−	0.975740i	$-0.429743\pi$
$284$	−2.20871	+	1.27520i	−0.131063	+	0.0756692i
$285$	25.7477			1.52516
$286$	−6.97822	+	7.25198i	−0.412631	+	0.428818i
$287$		0			0
$288$	−1.33485	+	0.770675i	−0.0786567	+	0.0454125i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−5.29129	+	9.16478i	−0.310715	+	0.538174i
$291$		−	27.2759i		−	1.59894i
$292$	8.37386	+	4.83465i	0.490043	+	0.282927i
$293$	−6.79129	−	3.92095i	−0.396751	−	0.229064i	0.288330	−	0.957531i	$-0.406900\pi$
$293$	−6.79129	−	3.92095i	−0.396751	−	0.229064i	−0.685081	+	0.728467i	$0.740233\pi$
$294$		0			0
$295$	9.68693	−	16.7783i	0.563995	−	0.976868i
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	−5.52178	+	3.18800i	−0.320406	+	0.184987i
$298$	4.79129			0.277552
$299$	−7.58258	−	26.2668i	−0.438512	−	1.51905i
$300$	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
$304$		−	11.7629i		−	0.674646i
$305$	−24.1652	−	13.9518i	−1.38369	−	0.798875i
$306$	−1.18693	−	0.685275i	−0.0678524	−	0.0391746i
$307$		−	24.1733i		−	1.37964i	−0.723980	−	0.689820i	$-0.757689\pi$
$307$		−	24.1733i		−	1.37964i	0.723980	−	0.689820i	$-0.242311\pi$
$308$		0			0
$309$	−4.10436	−	7.10895i	−0.233489	−	0.404414i
$310$	35.9347	−	20.7469i	2.04095	−	1.17834i
$311$	5.53901			0.314089			0.157044	−	0.987592i	$-0.449803\pi$
$311$	5.53901			0.314089			0.157044	+	0.987592i	$0.449803\pi$
$312$	10.7477	−	3.10260i	0.608470	−	0.175650i
$313$	−20.7477			−1.17273			−0.586365	−	0.810047i	$-0.699442\pi$
$313$	−20.7477			−1.17273			−0.586365	+	0.810047i	$0.699442\pi$
$314$	41.6216	−	24.0302i	2.34884	−	1.35610i
$315$		0			0
$316$	−8.37386	+	14.5040i	−0.471067	+	0.815911i
$317$		−	18.5203i		−	1.04020i	−0.854105	−	0.520101i	$-0.825894\pi$
$317$		−	18.5203i		−	1.04020i	0.854105	−	0.520101i	$-0.174106\pi$
$318$	−41.3085	−	23.8495i	−2.31647	−	1.33741i
$319$	−2.43920	−	1.40828i	−0.136569	−	0.0788483i
$320$			27.5420i			1.53965i
$321$	−8.76951	+	15.1892i	−0.489466	+	0.847780i
$322$		0			0
$323$	17.0608	−	9.85005i	0.949288	−	0.548072i
$324$	26.7477			1.48598
$325$	0.730493	+	0.180750i	0.0405204	+	0.0100262i
$326$	15.1652			0.839920
$327$	12.3131	−	7.10895i	0.680914	−	0.393126i
$328$	−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	$-0.323845\pi$
$331$	0.939205	+	0.542250i	0.0516234	+	0.0298048i	−0.473966	+	0.880543i	$0.657178\pi$
$332$	−8.60436	−	4.96773i	−0.472225	−	0.272639i
$333$			1.44600i			0.0792403i
$334$	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	$0.614801\pi$
$338$	28.4347	−	1.09445i	1.54664	−	0.0595303i
$339$	−2.53901			−0.137900
$340$	−15.8739	+	9.16478i	−0.860881	+	0.497030i
$341$	5.52178	+	9.56400i	0.299021	+	0.517920i
$342$	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
$346$		−	16.9590i		−	0.911722i
$347$	2.20871	−	3.82560i	0.118570	−	0.205369i	−0.800631	−	0.599157i	$-0.795502\pi$
$347$	2.20871	−	3.82560i	0.118570	−	0.205369i	0.919201	+	0.393788i	$0.128836\pi$
$348$	5.52178	+	9.56400i	0.295998	+	0.512684i
$349$	−9.24773	+	5.33918i	−0.495019	+	0.285800i	−0.726654	−	0.687003i	$-0.758926\pi$
$349$	−9.24773	+	5.33918i	−0.495019	+	0.285800i	0.231635	+	0.972803i	$0.425593\pi$
$350$		0			0
$351$	17.5000	+	4.33013i	0.934081	+	0.231125i
$352$	−9.41742			−0.501950
$353$	23.2259	−	13.4095i	1.23619	−	0.713716i	0.267879	−	0.963453i	$-0.413677\pi$
$353$	23.2259	−	13.4095i	1.23619	−	0.713716i	0.968314	+	0.249737i	$0.0803441\pi$
$354$	−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
$359$		−	12.6766i		−	0.669043i	−0.942388	−	0.334522i	$-0.891425\pi$
$359$		−	12.6766i		−	0.669043i	0.942388	−	0.334522i	$-0.108575\pi$
$360$	−0.395644	+	0.685275i	−0.0208523	+	0.0361172i
$361$	12.0608	+	20.8899i	0.634779	+	1.09947i
$362$	17.3739	−	10.0308i	0.913150	−	0.527207i
$363$	−16.7913			−0.881314
$364$		0			0
$365$	−7.58258			−0.396890
$366$	−43.2867	+	24.9916i	−2.26263	+	1.30633i
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	0.529607	−	0.848243i	$-0.322339\pi$
$367$	−9.00000	−	15.5885i	−0.469796	−	0.813711i	−0.999404	+	0.0345320i	$0.989006\pi$
$368$	6.79129	−	11.7629i	0.354020	−	0.613181i
$369$			0.532300i			0.0277104i
$370$	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	−0.212481	+	0.977165i	$0.568154\pi$
$373$	−18.3956	+	31.8622i	−0.952490	+	1.64976i	−0.740009	+	0.672596i	$0.765179\pi$
$374$	−4.18693	−	7.25198i	−0.216501	−	0.374991i
$375$	−17.6869	+	10.2116i	−0.913349	+	0.527322i
$376$	7.41742			0.382524
$377$	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	$0.370604\pi$
$380$	−20.0608	−	34.7463i	−1.02910	−	1.78245i
$381$	−14.2913	+	24.7532i	−0.732165	+	1.26815i
$382$		−	1.37055i		−	0.0701235i
$383$	−3.39564	−	1.96048i	−0.173509	−	0.100176i	0.410730	−	0.911757i	$-0.365274\pi$
$383$	−3.39564	−	1.96048i	−0.173509	−	0.100176i	−0.584240	+	0.811581i	$0.698607\pi$
$384$	19.8131	+	11.4391i	1.01108	+	0.583748i
$385$		0			0
$386$	−13.5826	+	23.5257i	−0.691335	+	1.19743i
$387$	0.456439	+	0.790576i	0.0232021	+	0.0401872i
$388$	−36.8085	+	21.2514i	−1.86867	+	1.07888i
$389$	36.3303			1.84202			0.921010	−	0.389540i	$-0.127366\pi$
$389$	36.3303			1.84202			0.921010	+	0.389540i	$0.127366\pi$
$390$	−21.4564	+	22.2982i	−1.08649	+	1.12911i
$391$	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
$395$		−	13.1334i		−	0.660813i
$396$	−0.643371	−	0.371450i	−0.0323306	−	0.0186661i
$397$	13.1216	+	7.57575i	0.658554	+	0.380216i	0.791726	−	0.610877i	$-0.209183\pi$
$397$	13.1216	+	7.57575i	0.658554	+	0.380216i	−0.133172	+	0.991093i	$0.542516\pi$
$398$		−	24.0779i		−	1.20692i
$399$		0			0
$400$	0.186932	+	0.323775i	0.00934659	+	0.0161888i
$401$	−25.5998	+	14.7801i	−1.27839	+	0.738081i	−0.976553	−	0.215278i	$-0.930934\pi$
$401$	−25.5998	+	14.7801i	−1.27839	+	0.738081i	−0.301841	+	0.953358i	$0.597601\pi$
$402$	44.7042			2.22964
$403$	7.50000	−	30.3109i	0.373602	−	1.50989i
$404$	−27.3303			−1.35973
$405$	−18.1652	+	10.4877i	−0.902634	+	0.521136i
$406$		0			0
$407$	−4.41742	+	7.65120i	−0.218964	+	0.379256i
$408$			9.30780i			0.460805i
$409$	−0.313068	−	0.180750i	−0.0154802	−	0.00893751i	0.492240	−	0.870460i	$-0.336178\pi$
$409$	−0.313068	−	0.180750i	−0.0154802	−	0.00893751i	−0.507720	+	0.861522i	$0.669512\pi$
$410$	10.5826	+	6.10985i	0.522636	+	0.301744i
$411$		−	30.7201i		−	1.51531i
$412$	−6.39564	+	11.0776i	−0.315091	+	0.545753i
$413$		0			0
$414$	3.00000	−	1.73205i	0.147442	−	0.0851257i
$415$	7.79129			0.382459
$416$	19.1869	+	18.4626i	0.940717	+	0.905205i
$417$	1.41742			0.0694116
$418$	15.8739	−	9.16478i	0.776416	−	0.448264i
$419$	12.8739	+	22.2982i	0.628929	+	1.08934i	0.987767	+	0.155938i	$0.0498399\pi$
$419$	12.8739	+	22.2982i	0.628929	+	1.08934i	−0.358838	+	0.933400i	$0.616827\pi$
$420$		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
$423$	−0.774053	−	0.446900i	−0.0376358	−	0.0217290i
$424$			21.0707i			1.02328i
$425$	−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
$429$	−5.93466	−	5.71063i	−0.286528	−	0.275712i
$430$	20.9564			1.01061
$431$	−13.5172	+	7.80418i	−0.651102	+	0.375914i	−0.788878	−	0.614549i	$-0.789338\pi$
$431$	−13.5172	+	7.80418i	−0.651102	+	0.375914i	0.137776	+	0.990463i	$0.456005\pi$
$432$	4.47822	+	7.75650i	0.215458	+	0.373185i
$433$	11.2477	−	19.4816i	0.540531	−	0.936228i	−0.458342	−	0.888776i	$-0.651557\pi$
$433$	11.2477	−	19.4816i	0.540531	−	0.936228i	0.998874	−	0.0474518i	$-0.0151101\pi$
$434$		0			0
$435$	−7.50000	−	4.33013i	−0.359597	−	0.207614i
$436$	−19.1869	−	11.0776i	−0.918887	−	0.530520i
$437$			49.7925i			2.38190i
$438$	−6.79129	+	11.7629i	−0.324500	+	0.562051i
$439$	5.76951	+	9.99308i	0.275364	+	0.476944i	0.970227	−	0.242198i	$-0.0778684\pi$
$439$	5.76951	+	9.99308i	0.275364	+	0.476944i	−0.694863	+	0.719142i	$0.744535\pi$
$440$	−4.18693	+	2.41733i	−0.199604	+	0.115242i
$441$		0			0
$442$	−5.68693	+	22.9835i	−0.270500	+	1.09321i
$443$	3.16515			0.150381			0.0751904	−	0.997169i	$-0.476044\pi$
$443$	3.16515			0.150381			0.0751904	+	0.997169i	$0.476044\pi$
$444$	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	$0.822010\pi$
$450$			0.0953502i			0.00449485i
$451$	−1.62614	+	2.81655i	−0.0765718	+	0.132626i
$452$	1.97822	+	3.42638i	0.0930476	+	0.161163i
$453$	−18.8085	+	10.8591i	−0.883701	+	0.510205i
$454$	26.9564			1.26513
$455$		0			0
$456$	−20.3739			−0.954094
$457$	−7.74773	+	4.47315i	−0.362423	+	0.209245i	−0.670143	−	0.742232i	$-0.733767\pi$
$457$	−7.74773	+	4.47315i	−0.362423	+	0.209245i	0.307720	+	0.951477i	$0.400434\pi$
$458$	7.58258	+	13.1334i	0.354310	+	0.613684i
$459$	−7.50000	+	12.9904i	−0.350070	+	0.606339i
$460$		−	46.3284i		−	2.16007i
$461$	−15.4782	−	8.93635i	−0.720893	−	0.416208i	0.0941885	−	0.995554i	$-0.469974\pi$
$461$	−15.4782	−	8.93635i	−0.720893	−	0.416208i	−0.815081	+	0.579347i	$0.803308\pi$
$462$		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
$467$	−11.8348			−0.547651			−0.273826	−	0.961779i	$-0.588289\pi$
$467$	−11.8348			−0.547651			−0.273826	+	0.961779i	$0.588289\pi$
$468$	0.582576	+	2.01810i	0.0269296	+	0.0932868i
$469$		0			0
$470$	−17.7695	+	10.2592i	−0.819646	+	0.473223i
$471$	19.6652	+	34.0610i	0.906122	+	1.56945i
$472$	−7.66515	+	13.2764i	−0.352817	+	0.611097i
$473$			5.57755i			0.256456i
$474$	−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
$478$	14.4782	+	25.0770i	0.662218	+	1.14700i
$479$	−8.85208	+	5.11075i	−0.404462	+	0.233516i	−0.688407	−	0.725324i	$-0.741690\pi$
$479$	−8.85208	+	5.11075i	−0.404462	+	0.233516i	0.283945	+	0.958840i	$0.408357\pi$
$480$	−28.9564			−1.32167
$481$	24.0000	−	6.92820i	1.09431	−	0.315899i
$482$	−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
$486$			4.73930i			0.214979i
$487$	−8.93466	−	5.15843i	−0.404868	−	0.233751i	0.283714	−	0.958909i	$-0.408433\pi$
$487$	−8.93466	−	5.15843i	−0.404868	−	0.233751i	−0.688582	+	0.725158i	$0.741767\pi$
$488$	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	$-0.482730\pi$
$492$	11.0436	−	6.37600i	0.497882	−	0.287452i
$493$	−6.62614			−0.298426
$494$	−50.3085	−	12.4481i	−2.26349	−	0.560068i
$495$	0.582576			0.0261848
$496$	13.4347	−	7.75650i	0.603234	−	0.348277i
$497$		0			0
$498$	6.97822	−	12.0866i	0.312701	−	0.541615i
$499$		−	42.2168i		−	1.88988i	−0.327240	−	0.944941i	$-0.606119\pi$
$499$		−	42.2168i		−	1.88988i	0.327240	−	0.944941i	$-0.393881\pi$
$500$	27.5608	+	15.9122i	1.23256	+	0.711617i
$501$	30.9737	+	17.8827i	1.38380	+	0.798938i
$502$			46.3284i			2.06774i
$503$	−11.0608	+	19.1579i	−0.493176	+	0.854207i	−0.999969	−	0.00786127i	$-0.997498\pi$
$503$	−11.0608	+	19.1579i	−0.493176	+	0.854207i	0.506793	+	0.862068i	$0.330831\pi$
$504$		0			0
$505$	18.5608	−	10.7161i	0.825945	−	0.476859i
$506$	21.1652			0.940906
$507$	0.895644	+	23.2695i	0.0397769	+	1.03344i
$508$	44.5390			1.97610
$509$	−19.0390	+	10.9922i	−0.843890	+	0.487220i	−0.858584	−	0.512672i	$-0.828656\pi$
$509$	−19.0390	+	10.9922i	−0.843890	+	0.487220i	0.0146949	+	0.999892i	$0.495322\pi$
$510$	−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
$514$	52.9955	+	30.5969i	2.33753	+	1.34957i
$515$		−	10.0308i		−	0.442010i
$516$	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
$520$	13.2695	+	3.28335i	0.581906	+	0.143984i
$521$	−25.5826			−1.12079			−0.560396	−	0.828224i	$-0.689351\pi$
$521$	−25.5826			−1.12079			−0.560396	+	0.828224i	$0.689351\pi$
$522$	−0.873864	+	0.504525i	−0.0382480	+	0.0220825i
$523$	−6.16515	−	10.6784i	−0.269583	−	0.466932i	0.699171	−	0.714954i	$-0.253553\pi$
$523$	−6.16515	−	10.6784i	−0.269583	−	0.466932i	−0.968754	+	0.248023i	$0.920219\pi$
$524$	−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
$528$		−	4.09175i		−	0.178071i
$529$	−17.2477	+	29.8739i	−0.749901	+	1.29887i
$530$	−29.1434	−	50.4778i	−1.26591	−	2.19262i
$531$	1.59981	−	0.923651i	0.0694259	−	0.0400830i
$532$		0			0
$533$	8.83485	−	2.55040i	0.382680	−	0.110470i
$534$	−11.4174			−0.494080
$535$	−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
$541$		−	30.0924i		−	1.29377i	−0.762586	−	0.646887i	$-0.776071\pi$
$541$		−	30.0924i		−	1.29377i	0.762586	−	0.646887i	$-0.223929\pi$
$542$	31.4347	−	54.4464i	1.35023	−	2.33867i
$543$	8.20871	+	14.2179i	0.352270	+	0.610149i
$544$	−19.1869	+	11.0776i	−0.822633	+	0.474947i
$545$	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	$0.390702\pi$
$548$	−41.4564	+	23.9349i	−1.77093	+	1.02245i
$549$	−1.33030	−	2.30415i	−0.0567759	−	0.0983388i
$550$	−0.291288	+	0.504525i	−0.0124206	+	0.0215130i
$551$		−	14.5040i		−	0.617889i
$552$	−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	$-0.465969\pi$
$557$	24.0998	−	13.9140i	1.02114	−	0.589556i	0.914434	+	0.404734i	$0.132636\pi$
$558$	3.95644			0.167489
$559$	10.9347	−	11.3636i	0.462487	−	0.480630i
$560$		0			0
$561$	5.93466	−	3.42638i	0.250561	−	0.144662i
$562$	7.00000	+	12.1244i	0.295277	+	0.511435i
$563$	−0.165151	+	0.286051i	−0.00696030	+	0.0120556i	−0.869485	−	0.493960i	$-0.835549\pi$
$563$	−0.165151	+	0.286051i	−0.00696030	+	0.0120556i	0.862524	+	0.506016i	$0.168882\pi$
$564$			21.4123i			0.901619i
$565$	−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
$569$	5.37386	+	9.30780i	0.225284	+	0.390203i	0.956405	−	0.292045i	$-0.0943356\pi$
$569$	5.37386	+	9.30780i	0.225284	+	0.390203i	−0.731121	+	0.682248i	$0.761002\pi$
$570$	48.8085	−	28.1796i	2.04436	−	1.18031i
$571$	−24.9564			−1.04439			−0.522197	−	0.852825i	$-0.674888\pi$
$571$	−24.9564			−1.04439			−0.522197	+	0.852825i	$0.674888\pi$
$572$	−3.08258	+	12.4581i	−0.128889	+	0.520899i
$573$	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
$577$			19.7756i			0.823267i	0.911349	+	0.411634i	$0.135042\pi$
$577$			19.7756i			0.823267i	−0.911349	+	0.411634i	$0.864958\pi$
$578$	15.1652	+	8.75560i	0.630787	+	0.364185i
$579$	−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
$583$	13.4347	−	7.75650i	0.556407	−	0.321242i
$584$	6.00000			0.248282
$585$	−1.18693	−	1.14213i	−0.0490736	−	0.0472211i
$586$	−17.1652			−0.709086
$587$	−30.7259	+	17.7396i	−1.26820	+	0.732193i	−0.974646	−	0.223751i	$-0.928170\pi$
$587$	−30.7259	+	17.7396i	−1.26820	+	0.732193i	−0.293549	+	0.955944i	$0.594836\pi$
$588$		0			0
$589$	−28.4347	+	49.2503i	−1.17163	+	2.02932i
$590$		−	42.4075i		−	1.74589i
$591$	−16.9782	−	9.80238i	−0.698391	−	0.403216i
$592$	10.7477	+	6.20520i	0.441729	+	0.255032i
$593$			19.6048i			0.805071i	0.915404	+	0.402535i	$0.131871\pi$
$593$			19.6048i			0.805071i	−0.915404	+	0.402535i	$0.868129\pi$
$594$	−6.97822	+	12.0866i	−0.286320	+	0.495920i
$595$		0			0
$596$	5.29129	−	3.05493i	0.216740	−	0.125135i
$597$	19.7042			0.806438
$598$	−43.1216	−	41.4938i	−1.76337	−	1.69681i
$599$	−20.3739			−0.832453			−0.416227	−	0.909261i	$-0.636648\pi$
$599$	−20.3739			−0.832453			−0.416227	+	0.909261i	$0.636648\pi$
$600$	0.560795	−	0.323775i	0.0228944	−	0.0132181i
$601$	0.686932	+	1.18980i	0.0280205	+	0.0485330i	0.879696	−	0.475537i	$-0.157746\pi$
$601$	0.686932	+	1.18980i	0.0280205	+	0.0485330i	−0.851675	+	0.524070i	$0.824413\pi$
$602$		0			0
$603$			2.37960i			0.0969049i
$604$	29.3085	+	16.9213i	1.19255	+	0.688517i
$605$	−17.7695	−	10.2592i	−0.722433	−	0.417097i
$606$		−	38.3912i		−	1.55953i
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	−0.776635	−	0.629950i	$-0.783075\pi$
$607$	3.87386	−	6.70973i	0.157235	−	0.272339i	0.933871	+	0.357611i	$0.116409\pi$
$608$	−24.2477	−	41.9983i	−0.983375	−	1.70326i
$609$		0			0
$610$	−61.0780			−2.47298
$611$	−3.70871	+	14.9886i	−0.150038	+	0.606373i
$612$	−1.74773			−0.0706477
$613$	32.3085	−	18.6533i	1.30493	−	0.753401i	0.323684	−	0.946165i	$-0.395079\pi$
$613$	32.3085	−	18.6533i	1.30493	−	0.753401i	0.981245	+	0.192764i	$0.0617453\pi$
$614$	−26.4564	−	45.8239i	−1.06769	−	1.84930i
$615$	−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
$619$		−	12.4104i		−	0.498816i	−0.968398	−	0.249408i	$-0.919764\pi$
$619$		−	12.4104i		−	0.498816i	0.968398	−	0.249408i	$-0.0802361\pi$
$620$	26.4564	−	45.8239i	1.06252	−	1.84033i
$621$	−18.9564	−	32.8335i	−0.760696	−	1.31756i
$622$	10.5000	−	6.06218i	0.421012	−	0.243071i
$623$		0			0
$624$	−8.02178	+	8.33648i	−0.321128	+	0.333726i
$625$	−23.9129			−0.956515
$626$	−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	$0.743758\pi$
$632$			10.3923i			0.413384i
$633$	1.26951	−	2.19885i	0.0504584	−	0.0873965i
$634$	−20.2695	−	35.1078i	−0.805005	−	1.39431i
$635$	−30.2477	+	17.4635i	−1.20034	+	0.693019i
$636$	−60.8258			−2.41190
$637$		0			0
$638$	−6.16515			−0.244081
$639$	0.165151	−	0.0953502i	0.00653329	−	0.00377200i
$640$	13.9782	+	24.2110i	0.552538	+	0.957023i
$641$	−7.81307	+	13.5326i	−0.308598	+	0.534507i	−0.978056	−	0.208343i	$-0.933193\pi$
$641$	−7.81307	+	13.5326i	−0.308598	+	0.534507i	0.669458	+	0.742850i	$0.266526\pi$
$642$			38.3912i			1.51518i
$643$	−11.7523	−	6.78518i	−0.463464	−	0.267581i	0.250035	−	0.968237i	$-0.419558\pi$
$643$	−11.7523	−	6.78518i	−0.463464	−	0.267581i	−0.713500	+	0.700655i	$0.752891\pi$
$644$		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	−0.996403	−	0.0847389i	$-0.972994\pi$
$647$	−14.5390	−	25.1823i	−0.571588	−	0.990019i	0.424816	−	0.905280i	$-0.360339\pi$
$648$	14.3739	−	8.29875i	0.564659	−	0.326006i
$649$	11.2867			0.443043
$650$	1.58258	−	0.456850i	0.0620737	−	0.0179191i
$651$		0			0
$652$	16.7477	−	9.66930i	0.655892	−	0.378679i
$653$	−5.60436	−	9.70703i	−0.219315	−	0.379865i	0.735283	−	0.677760i	$-0.237049\pi$
$653$	−5.60436	−	9.70703i	−0.219315	−	0.379865i	−0.954599	+	0.297894i	$0.903716\pi$
$654$	15.5608	−	26.9521i	0.608475	−	1.05391i
$655$		−	7.93725i		−	0.310134i
$656$	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	$0.203951\pi$
$660$	−6.97822	−	12.0866i	−0.271627	−	0.470471i
$661$	16.2523	−	9.38325i	0.632140	−	0.364966i	−0.149440	−	0.988771i	$-0.547747\pi$
$661$	16.2523	−	9.38325i	0.632140	−	0.364966i	0.781580	+	0.623804i	$0.214414\pi$
$662$	2.37386			0.0922628
$663$	−18.8085	−	4.65390i	−0.730462	−	0.180743i
$664$	−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
$668$		−	55.7316i		−	2.15632i
$669$	−32.1261	−	18.5480i	−1.24207	−	0.717108i
$670$	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	$0.648262\pi$
$674$	−24.5608	+	14.1802i	−0.946046	+	0.546200i
$675$	1.04356			0.0401667
$676$	30.7042	−	19.3386i	1.18093	−	0.743793i
$677$	33.7913			1.29870			0.649352	−	0.760488i	$-0.275040\pi$
$677$	33.7913			1.29870			0.649352	+	0.760488i	$0.275040\pi$
$678$	−4.81307	+	2.77883i	−0.184845	+	0.106720i
$679$		0			0
$680$	−5.68693	+	9.85005i	−0.218084	+	0.377732i
$681$			22.0598i			0.845334i
$682$	20.9347	+	12.0866i	0.801630	+	0.462821i
$683$	21.7087	+	12.5335i	0.830661	+	0.479582i	0.854079	−	0.520144i	$-0.174122\pi$
$683$	21.7087	+	12.5335i	0.830661	+	0.479582i	−0.0234181	+	0.999726i	$0.507455\pi$
$684$		−	3.82560i		−	0.146276i
$685$	18.7695	−	32.5097i	0.717146	−	1.24213i
$686$		0			0
$687$	−10.7477	+	6.20520i	−0.410051	+	0.236743i
$688$	7.83485			0.298701
$689$	−42.5780	−	10.5353i	−1.62209	−	0.401364i
$690$	65.0780			2.47748
$691$	−25.4347	+	14.6847i	−0.967580	+	0.558633i	−0.898498	−	0.438978i	$-0.855340\pi$
$691$	−25.4347	+	14.6847i	−0.967580	+	0.558633i	−0.0690824	+	0.997611i	$0.522007\pi$
$692$	−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
$696$	5.93466	+	3.42638i	0.224953	+	0.129876i
$697$			7.65120i			0.289810i
$698$	−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	$0.294105\pi$
$702$	37.9129	−	10.9445i	1.43093	−	0.413074i
$703$	−45.4955			−1.71589
$704$	−13.8956	+	8.02265i	−0.523712	+	0.302365i
$705$	−8.39564	−	14.5417i	−0.316198	−	0.547671i
$706$	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	$-0.377043\pi$
$709$	−6.31307	−	3.64485i	−0.237092	−	0.136885i	−0.613840	+	0.789431i	$0.710376\pi$
$710$		−	4.37780i		−	0.164296i
$711$	0.626136	−	1.08450i	0.0234820	−	0.0406719i
$712$	2.52178	+	4.36785i	0.0945077	+	0.163692i
$713$	−56.8693	+	32.8335i	−2.12977	+	1.22962i
$714$		0			0
$715$	−2.79129	−	9.66930i	−0.104388	−	0.361611i
$716$	25.1216			0.938838
$717$	−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	$-0.798632\pi$
$719$	2.91742	−	5.05313i	0.108802	−	0.188450i	0.915285	+	0.402807i	$0.131965\pi$
$720$		−	0.818350i		−	0.0304981i
$721$		0			0
$722$	45.7259	+	26.3999i	1.70174	+	0.982502i
$723$		−	7.36515i		−	0.273913i
$724$	12.7913	−	22.1552i	0.475384	−	0.823390i
$725$	0.230493	+	0.399225i	0.00856028	+	0.0148268i
$726$	−31.8303	+	18.3772i	−1.18133	+	0.682043i
$727$	27.7477			1.02911			0.514553	−	0.857459i	$-0.327958\pi$
$727$	27.7477			1.02911			0.514553	+	0.857459i	$0.327958\pi$
$728$		0			0
$729$	24.8693			0.921086
$730$	−14.3739	+	8.29875i	−0.532001	+	0.307151i
$731$	6.56080	+	11.3636i	0.242660	+	0.420299i
$732$	−31.8693	+	55.1993i	−1.17792	+	2.04022i
$733$			9.02175i			0.333226i	0.986022	+	0.166613i	$0.0532831\pi$
$733$			9.02175i			0.333226i	−0.986022	+	0.166613i	$0.946717\pi$
$734$	−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	$-0.739971\pi$
$739$	−10.7477	+	6.20520i	−0.395362	+	0.228262i	0.289119	+	0.957293i	$0.406638\pi$
$740$	42.3303			1.55609
$741$	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	$0.301946\pi$
$744$	−13.4347	−	23.2695i	−0.492538	−	0.853102i
$745$	−2.39564	+	4.14938i	−0.0877696	+	0.152021i
$746$			80.5325i			2.94850i
$747$	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
$751$	1.87386	+	3.24563i	0.0683783	+	0.118435i	0.898188	−	0.439612i	$-0.144884\pi$
$751$	1.87386	+	3.24563i	0.0683783	+	0.118435i	−0.829809	+	0.558047i	$0.811551\pi$
$752$	−6.64337	+	3.83555i	−0.242259	+	0.139868i
$753$	−37.9129			−1.38162
$754$	12.5608	+	12.0866i	0.457437	+	0.440169i
$755$	−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
$759$			17.3205i			0.628695i
$760$	−21.5608	−	12.4481i	−0.782092	−	0.451541i
$761$	27.7259	+	16.0076i	1.00506	+	0.580274i	0.909743	−	0.415172i	$-0.136279\pi$
$761$	27.7259	+	16.0076i	1.00506	+	0.580274i	0.0953219	+	0.995447i	$0.469612\pi$
$762$			62.5644i			2.26647i
$763$		0			0
$764$	−0.873864	−	1.51358i	−0.0316153	−	0.0547593i
$765$	1.18693	−	0.685275i	0.0429136	−	0.0247762i
$766$	−8.58258			−0.310101
$767$	−22.9955	−	22.1274i	−0.830318	−	0.798974i
$768$	5.00000			0.180422
$769$	21.8739	−	12.6289i	0.788792	−	0.455409i	−0.0507453	−	0.998712i	$-0.516160\pi$
$769$	21.8739	−	12.6289i	0.788792	−	0.455409i	0.839537	+	0.543303i	$0.182826\pi$
$770$		0			0
$771$	−25.0390	+	43.3688i	−0.901758	+	1.56189i
$772$			34.6410i			1.24676i
$773$	19.8303	+	11.4490i	0.713246	+	0.411793i

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)

\(f(q)\)	\(=\)	\(q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +(-0.104356 + 0.180750i) q^{9} +O(q^{10})\)	\(q+(1.89564 - 1.09445i) q^{2} +(0.895644 + 1.55130i) q^{3} +(1.39564 - 2.41733i) q^{4} +2.18890i 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} +5.00000 q^{12} +(3.50000 + 0.866025i) q^{13} +(-3.39564 + 1.96048i) q^{15} +(0.895644 + 1.55130i) q^{16} +(-1.50000 + 2.59808i) q^{17} +0.456850i q^{18} +(-5.68693 - 3.28335i) q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 - 6.56670i) q^{23} +(2.68693 - 1.55130i) q^{24} +0.208712 q^{25} +(7.58258 - 2.18890i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +(-4.29129 + 7.43273i) q^{30} -8.66025i q^{31} +(6.39564 + 3.69253i) q^{32} +(-1.97822 - 1.14213i) q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(6.00000 - 3.46410i) q^{37} -14.3739 q^{38} +(1.79129 + 6.20520i) q^{39} +3.79129 q^{40} +(2.20871 - 1.27520i) q^{41} +(2.18693 - 3.78788i) q^{43} +3.55945i q^{44} +(-0.395644 - 0.228425i) q^{45} +(-14.3739 - 8.29875i) q^{46} +4.28245i q^{47} +(-1.60436 + 2.77883i) q^{48} +(0.395644 - 0.228425i) q^{50} -5.37386 q^{51} +(6.97822 - 7.25198i) q^{52} -12.1652 q^{53} +(9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} +(4.18693 + 2.41733i) q^{58} +(-7.66515 - 4.42548i) q^{59} +10.9445i q^{60} +(-6.37386 + 11.0399i) q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(-1.89564 + 7.66115i) q^{65} -5.00000 q^{66} +(9.87386 - 5.70068i) q^{67} +(4.18693 + 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} +(0.313068 + 0.180750i) q^{72} +3.46410i q^{73} +(7.58258 - 13.1334i) q^{74} +(0.186932 + 0.323775i) q^{75} +(-15.8739 + 9.16478i) q^{76} +(10.1869 + 9.80238i) q^{78} -6.00000 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} -9.57395i q^{86} +(-1.97822 + 3.42638i) q^{87} +(1.10436 + 1.91280i) q^{88} +(-2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(13.4347 - 7.75650i) q^{93} +(4.68693 + 8.11800i) q^{94} +(7.18693 - 12.4481i) q^{95} +13.2288i q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i 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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