LMFDB - Embedded newform 637.2.u.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(30,637)]

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([2, 1]))

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

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

chi := DirichletCharacter("637.30");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.u (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			361.1
Root			$-0.895644 + 1.09445i$ of defining polynomial
Character	$\chi$	$=$	637.361
Dual form			637.2.u.e.30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +O(q^{10})$	\(q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} -4.79129 q^{10} -1.27520i q^{11} +(-2.50000 - 4.33013i) 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} +(-0.395644 - 0.228425i) q^{18} +6.56670i q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 + 6.56670i) q^{23} +3.10260i q^{24} +(-0.104356 + 0.180750i) q^{25} +(-5.68693 - 5.47225i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +8.58258 q^{30} +(7.50000 + 4.33013i) q^{31} +(-6.39564 + 3.69253i) q^{32} +2.28425i q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(7.18693 - 12.4481i) q^{38} +(-6.26951 - 1.55130i) 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} +(0.395644 - 0.228425i) q^{45} +(14.3739 - 8.29875i) 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} +(2.79129 + 9.66930i) q^{52} +(6.08258 - 10.5353i) q^{53} +(-9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} -4.83465i q^{58} +(7.66515 - 4.42548i) q^{59} +(-9.47822 - 5.47225i) q^{60} +12.7477 q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(7.58258 - 2.18890i) q^{65} +(2.50000 - 4.33013i) q^{66} +11.4014i q^{67} +(4.18693 - 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} -0.361500i q^{72} +(-3.00000 - 1.73205i) 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} +(3.00000 + 5.19615i) q^{79} -3.92095i q^{80} -9.58258 q^{81} -5.58258 q^{82} -3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(-8.29129 + 4.78698i) q^{86} +(-1.97822 - 3.42638i) q^{87} -2.20871 q^{88} +(2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(-13.4347 - 7.75650i) q^{93} -9.37386 q^{94} +(7.18693 + 12.4481i) 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 - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9}+O(q^{10}) $ 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9	$ 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9} - 10 q^{10} - 10 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} - 9 q^{26} + 20 q^{27} + 9 q^{29} + 16 q^{30} + 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} + 15 q^{38} + 7 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} - 6 q^{44} - 3 q^{45} + 30 q^{46} + 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} + 2 q^{52} + 6 q^{53} - 15 q^{54} - q^{55} - 6 q^{59} - 15 q^{60} - 4 q^{61} - 15 q^{62} + 32 q^{64} + 12 q^{65} + 10 q^{66} + 3 q^{68} + 18 q^{69} + 6 q^{71} - 12 q^{73} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} - 4 q^{82} - 9 q^{85} - 24 q^{86} + 15 q^{87} - 18 q^{88} + 33 q^{89} - 4 q^{90} - 48 q^{92} + 15 q^{93} - 10 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) $ 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9 - 10 * q^10 - 10 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 + 3 * q^18 + 12 * q^20 - q^22 - 6 * q^23 - 5 * q^25 - 9 * q^26 + 20 * q^27 + 9 * q^29 + 16 * q^30 + 30 * q^31 - 21 * q^32 - 8 * q^36 - 24 * q^37 + 15 * q^38 + 7 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 - 6 * q^44 - 3 * q^45 + 30 * q^46 + 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 + 2 * q^52 + 6 * q^53 - 15 * q^54 - q^55 - 6 * q^59 - 15 * q^60 - 4 * q^61 - 15 * q^62 + 32 * q^64 + 12 * q^65 + 10 * q^66 + 3 * q^68 + 18 * q^69 + 6 * q^71 - 12 * q^73 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 - 20 * q^81 - 4 * q^82 - 9 * q^85 - 24 * q^86 + 15 * q^87 - 18 * q^88 + 33 * q^89 - 4 * q^90 - 48 * q^92 + 15 * q^93 - 10 * q^94 + 15 * q^95 - 39 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.89564	−	1.09445i	−1.34042	−	0.773893i	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.89564	−	1.09445i	−1.34042	−	0.773893i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	−1.79129			−1.03420			−0.517100	−	0.855925i	$-0.672989\pi$
$3$	−1.79129			−1.03420			−0.517100	+	0.855925i	$0.672989\pi$
$4$	1.39564	+	2.41733i	0.697822	+	1.20866i
$5$	1.89564	−	1.09445i	0.847758	−	0.489453i	−0.0121359	−	0.999926i	$-0.503863\pi$
$5$	1.89564	−	1.09445i	0.847758	−	0.489453i	0.859894	+	0.510473i	$0.170530\pi$
$6$	3.39564	+	1.96048i	1.38627	+	0.800361i
$7$		0			0
$7$		0			0
$8$		−	1.73205i		−	0.612372i
$9$	0.208712			0.0695707
$10$	−4.79129			−1.51514
$11$		−	1.27520i		−	0.384487i	−0.981347	−	0.192244i	$-0.938424\pi$
$11$		−	1.27520i		−	0.384487i	0.981347	−	0.192244i	$-0.0615764\pi$
$12$	−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
$16$	0.895644	−	1.55130i	0.223911	−	0.387825i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−0.395644	−	0.228425i	−0.0932542	−	0.0538403i
$19$			6.56670i			1.50651i	0.657731	+	0.753253i	$0.271516\pi$
$19$			6.56670i			1.50651i	−0.657731	+	0.753253i	$0.728484\pi$
$20$	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	0.135096	+	0.990833i	$0.456866\pi$
$23$	−3.79129	+	6.56670i	−0.790538	+	1.36925i	−0.925634	+	0.378420i	$0.876468\pi$
$24$			3.10260i			0.633316i
$25$	−0.104356	+	0.180750i	−0.0208712	+	0.0361500i
$26$	−5.68693	−	5.47225i	−1.11530	−	1.07320i
$27$	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	$0.767590\pi$
$30$	8.58258			1.56696
$31$	7.50000	+	4.33013i	1.34704	+	0.777714i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	7.50000	+	4.33013i	1.34704	+	0.777714i	0.359211	+	0.933257i	$0.383046\pi$
$32$	−6.39564	+	3.69253i	−1.13060	+	0.652753i
$33$			2.28425i			0.397637i
$34$			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	$-0.526194\pi$
$37$	−6.00000	−	3.46410i	−0.986394	−	0.569495i	−0.904194	+	0.427121i	$0.859528\pi$
$38$	7.18693	−	12.4481i	1.16587	−	2.01935i
$39$	−6.26951	−	1.55130i	−1.00392	−	0.248407i
$40$	−1.89564	−	3.28335i	−0.299728	−	0.519143i
$41$	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	$0.0584356\pi$
$44$	3.08258	−	1.77973i	0.464716	−	0.268304i
$45$	0.395644	−	0.228425i	0.0589791	−	0.0340516i
$46$	14.3739	−	8.29875i	2.11931	−	1.22358i
$47$	3.70871	−	2.14123i	0.540971	−	0.312330i	−0.204501	−	0.978866i	$-0.565557\pi$
$47$	3.70871	−	2.14123i	0.540971	−	0.312330i	0.745472	+	0.666536i	$0.232224\pi$
$48$	−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
$52$	2.79129	+	9.66930i	0.387082	+	1.34089i
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	−0.0581117	−	0.998310i	$-0.518508\pi$
$53$	6.08258	−	10.5353i	0.835506	−	1.44714i	0.893618	−	0.448829i	$-0.148159\pi$
$54$	−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
$58$		−	4.83465i		−	0.634821i
$59$	7.66515	−	4.42548i	0.997918	−	0.576148i	0.0902862	−	0.995916i	$-0.471222\pi$
$59$	7.66515	−	4.42548i	0.997918	−	0.576148i	0.907632	+	0.419768i	$0.137888\pi$
$60$	−9.47822	−	5.47225i	−1.22363	−	0.706465i
$61$	12.7477			1.63218			0.816090	−	0.577925i	$-0.196138\pi$
$61$	12.7477			1.63218			0.816090	+	0.577925i	$0.196138\pi$
$62$	−9.47822	−	16.4168i	−1.20374	−	2.08493i
$63$		0			0
$64$	12.5826			1.57282
$65$	7.58258	−	2.18890i	0.940503	−	0.271500i
$66$	2.50000	−	4.33013i	0.307729	−	0.533002i
$67$			11.4014i			1.39290i	0.717607	+	0.696449i	$0.245238\pi$
$67$			11.4014i			1.39290i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	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	$0.683933\pi$
$72$		−	0.361500i		−	0.0426032i
$73$	−3.00000	−	1.73205i	−0.351123	−	0.202721i	0.314057	−	0.949404i	$-0.398312\pi$
$73$	−3.00000	−	1.73205i	−0.351123	−	0.202721i	−0.665180	+	0.746683i	$0.731645\pi$
$74$	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
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$		−	3.92095i		−	0.438376i
$81$	−9.58258			−1.06473
$82$	−5.58258			−0.616492
$83$		−	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
$86$	−8.29129	+	4.78698i	−0.894073	+	0.516193i
$87$	−1.97822	−	3.42638i	−0.212087	−	0.367346i
$88$	−2.20871			−0.235450
$89$	2.52178	+	1.45595i	0.267308	+	0.154330i	0.627664	−	0.778485i	$-0.284011\pi$
$89$	2.52178	+	1.45595i	0.267308	+	0.154330i	−0.360356	+	0.932815i	$0.617345\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−21.1652			−2.20662
$93$	−13.4347	−	7.75650i	−1.39311	−	0.804312i
$94$	−9.37386			−0.966840
$95$	7.18693	+	12.4481i	0.737364	+	1.27715i
$96$	11.4564	−	6.61438i	1.16927	−	0.675077i
$97$	−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
$100$	−0.582576			−0.0582576
$101$	9.79129			0.974270			0.487135	−	0.873327i	$-0.338042\pi$
$101$	9.79129			0.974270			0.487135	+	0.873327i	$0.338042\pi$
$102$		−	11.7629i		−	1.16470i
$103$	2.29129	+	3.96863i	0.225767	+	0.391040i	0.956549	−	0.291570i	$-0.0941778\pi$
$103$	2.29129	+	3.96863i	0.225767	+	0.391040i	−0.730782	+	0.682611i	$0.760844\pi$
$104$	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	−0.526252	−	0.850328i	$-0.676403\pi$
$107$	4.89564	−	8.47950i	0.473280	−	0.819745i	0.999532	+	0.0305838i	$0.00973664\pi$
$108$	6.97822	+	12.0866i	0.671479	+	1.16304i
$109$	6.87386	+	3.96863i	0.658397	+	0.380126i	0.791666	−	0.610954i	$-0.209214\pi$
$109$	6.87386	+	3.96863i	0.658397	+	0.380126i	−0.133269	+	0.991080i	$0.542547\pi$
$110$			6.10985i			0.582552i
$111$	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
$115$			16.5975i			1.54773i
$116$	−3.08258	+	5.33918i	−0.286210	+	0.495730i
$117$	0.730493	+	0.180750i	0.0675341	+	0.0167103i
$118$	−19.3739			−1.78351
$119$		0			0
$120$	3.39564	+	5.88143i	0.309978	+	0.536898i
$121$	9.37386			0.852169
$122$	−24.1652	−	13.9518i	−2.18781	−	1.26313i
$123$	−3.95644	+	2.28425i	−0.356740	+	0.205964i
$124$			24.1733i			2.17082i
$125$			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
$129$	−3.91742	+	6.78518i	−0.344910	+	0.597402i
$130$	−16.7695	−	4.14938i	−1.47078	−	0.363924i
$131$	1.81307	+	3.14033i	0.158409	+	0.274372i	0.934295	−	0.356501i	$-0.116030\pi$
$131$	1.81307	+	3.14033i	0.158409	+	0.274372i	−0.775886	+	0.630873i	$0.782697\pi$
$132$	−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
$136$	−4.50000	+	2.59808i	−0.385872	+	0.222783i
$137$	14.8521	−	8.57485i	1.26890	−	0.732599i	0.294119	−	0.955769i	$-0.404974\pi$
$137$	14.8521	−	8.57485i	1.26890	−	0.732599i	0.974780	+	0.223169i	$0.0716403\pi$
$138$	−25.7477	+	14.8655i	−2.19179	+	1.26543i
$139$	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
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	1.10436	−	4.46320i	0.0923509	−	0.373232i
$144$	0.186932	−	0.323775i	0.0155776	−	0.0269813i
$145$	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
$149$		−	2.18890i		−	0.179322i	−0.995972	−	0.0896609i	$-0.971422\pi$
$149$		−	2.18890i		−	0.179322i	0.995972	−	0.0896609i	$-0.0285783\pi$
$150$	−0.708712	+	0.409175i	−0.0578661	+	0.0334090i
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	0.00768132	−	0.999970i	$-0.497555\pi$
$151$	−10.5000	−	6.06218i	−0.854478	−	0.493333i	−0.862159	+	0.506637i	$0.830888\pi$
$152$	11.3739			0.922542
$153$	−0.313068	−	0.542250i	−0.0253101	−	0.0438383i
$154$		0			0
$155$	18.9564			1.52262
$156$	−5.00000	−	17.3205i	−0.400320	−	1.38675i
$157$	−10.9782	+	19.0148i	−0.876157	+	1.51755i	−0.0206325	+	0.999787i	$0.506568\pi$
$157$	−10.9782	+	19.0148i	−0.876157	+	1.51755i	−0.855525	+	0.517762i	$0.826765\pi$
$158$		−	13.1334i		−	1.04484i
$159$	−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
$163$		−	6.92820i		−	0.542659i	−0.962487	−	0.271329i	$-0.912537\pi$
$163$		−	6.92820i		−	0.542659i	0.962487	−	0.271329i	$-0.0874633\pi$
$164$	6.16515	+	3.55945i	0.481417	+	0.277946i
$165$	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
$170$	7.18693	+	12.4481i	0.551213	+	0.954728i
$171$			1.37055i			0.104809i
$172$	12.2087			0.930906
$173$	−7.74773			−0.589049			−0.294524	−	0.955644i	$-0.595161\pi$
$173$	−7.74773			−0.589049			−0.294524	+	0.955644i	$0.595161\pi$
$174$			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
$178$	−3.18693	−	5.51993i	−0.238871	−	0.413736i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	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
$185$	−15.1652			−1.11496
$186$	16.9782	+	29.4071i	1.24490	+	2.15624i
$187$	−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
$191$	−0.626136			−0.0453056			−0.0226528	−	0.999743i	$-0.507211\pi$
$191$	−0.626136			−0.0453056			−0.0226528	+	0.999743i	$0.507211\pi$
$192$	−22.5390			−1.62661
$193$		−	12.4104i		−	0.893321i	−0.894704	−	0.446660i	$-0.852613\pi$
$193$		−	12.4104i		−	0.893321i	0.894704	−	0.446660i	$-0.147387\pi$
$194$	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	$0.460817\pi$
$198$	−0.291288	+	0.504525i	−0.0207009	+	0.0358551i
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0.313068	+	0.180750i	0.0221373	+	0.0127810i
$201$		−	20.4231i		−	1.44054i
$202$	−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
$206$		−	10.0308i		−	0.698879i
$207$	−0.791288	+	1.37055i	−0.0549983	+	0.0952599i
$208$	4.47822	−	4.65390i	0.310509	−	0.322690i
$209$	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	$0.848870\pi$
$212$	33.9564			2.33214
$213$	1.41742	+	0.818350i	0.0971203	+	0.0560724i
$214$	−18.5608	+	10.7161i	−1.26879	+	0.732536i
$215$		−	9.57395i		−	0.652938i
$216$		−	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
$220$	3.89564	−	6.74745i	0.262644	−	0.454913i
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$	−13.5826	−	23.5257i	−0.911603	−	1.57894i
$223$	−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
$226$	2.68693	−	1.55130i	0.178732	−	0.103191i
$227$	−10.6652	+	6.15753i	−0.707871	+	0.408689i	−0.810272	−	0.586054i	$-0.800681\pi$
$227$	−10.6652	+	6.15753i	−0.707871	+	0.408689i	0.102401	+	0.994743i	$0.467347\pi$
$228$	28.4347	−	16.4168i	1.88313	−	1.08723i
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	−0.288478	−	0.957487i	$-0.593149\pi$
$229$	6.00000	−	3.46410i	0.396491	−	0.228914i	0.684969	+	0.728572i	$0.259816\pi$
$230$	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	0.957175	−	0.289509i	$-0.0934919\pi$
$233$	3.47822	+	6.02445i	0.227866	+	0.394675i	−0.729310	+	0.684184i	$0.760159\pi$
$234$	−1.18693	−	1.14213i	−0.0775922	−	0.0746631i
$235$	4.68693	−	8.11800i	0.305742	−	0.529560i
$236$	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	$0.859272\pi$
$240$			7.02355i			0.453368i
$241$	3.56080	−	2.05583i	0.229371	−	0.132427i	−0.380911	−	0.924612i	$-0.624390\pi$
$241$	3.56080	−	2.05583i	0.229371	−	0.132427i	0.610282	+	0.792184i	$0.291056\pi$
$242$	−17.7695	−	10.2592i	−1.14227	−	0.659488i
$243$	2.16515			0.138895
$244$	17.7913	+	30.8154i	1.13897	+	1.97275i
$245$		0			0
$246$	10.0000			0.637577
$247$	−5.68693	+	22.9835i	−0.361851	+	1.46240i
$248$	7.50000	−	12.9904i	0.476250	−	0.824890i
$249$			6.37600i			0.404063i
$250$	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
$254$		−	34.9271i		−	2.19152i
$255$	10.1869	+	5.88143i	0.637930	+	0.368309i
$256$	1.39564	+	2.41733i	0.0872277	+	0.151083i
$257$	13.9782	−	24.2110i	0.871937	−	1.51024i	0.0119476	−	0.999929i	$-0.496197\pi$
$257$	13.9782	−	24.2110i	0.871937	−	1.51024i	0.859990	−	0.510311i	$-0.170470\pi$
$258$	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
$262$		−	7.93725i		−	0.490365i
$263$	−27.3303			−1.68526			−0.842629	−	0.538494i	$-0.818993\pi$
$263$	−27.3303			−1.68526			−0.842629	+	0.538494i	$0.818993\pi$
$264$	3.95644			0.243502
$265$		−	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
$269$	−5.60436	−	9.70703i	−0.341704	−	0.591848i	0.643046	−	0.765828i	$-0.277671\pi$
$269$	−5.60436	−	9.70703i	−0.341704	−	0.591848i	−0.984749	+	0.173980i	$0.944337\pi$
$270$	−23.9564			−1.45794
$271$	−24.8739	−	14.3609i	−1.51098	−	0.872364i	−0.999918	−	0.0128205i	$-0.995919\pi$
$271$	−24.8739	−	14.3609i	−1.51098	−	0.872364i	−0.511062	−	0.859544i	$-0.670748\pi$
$272$	−5.37386			−0.325838
$273$		0			0
$274$	−37.5390			−2.26781
$275$	0.230493	+	0.133075i	0.0138992	+	0.00802472i
$276$	37.9129			2.28209
$277$	7.87386	+	13.6379i	0.473095	+	0.819424i	0.999526	−	0.0307939i	$-0.00980354\pi$
$277$	7.87386	+	13.6379i	0.473095	+	0.819424i	−0.526431	+	0.850218i	$0.676470\pi$
$278$	−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	$0.938900\pi$
$282$	16.7913			0.999907
$283$	24.7477			1.47110			0.735550	−	0.677471i	$-0.236924\pi$
$283$	24.7477			1.47110			0.735550	+	0.677471i	$0.236924\pi$
$284$		−	2.55040i		−	0.151338i
$285$	−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
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−5.29129	−	9.16478i	−0.310715	−	0.538174i
$291$	23.6216	+	13.6379i	1.38472	+	0.799470i
$292$		−	9.66930i		−	0.565853i
$293$	−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
$297$		−	6.37600i		−	0.369973i
$298$	−2.39564	+	4.14938i	−0.138776	+	0.240367i
$299$	−18.9564	+	19.7001i	−1.09628	+	1.13929i
$300$	1.04356			0.0602500
$301$		0			0
$302$	13.2695	+	22.9835i	0.763574	+	1.32255i
$303$	−17.5390			−1.00759
$304$	10.1869	+	5.88143i	0.584261	+	0.337323i
$305$	24.1652	−	13.9518i	1.38369	−	0.798875i
$306$			1.37055i			0.0783492i
$307$		−	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
$311$	−2.76951	+	4.79693i	−0.157044	+	0.272009i	−0.933802	−	0.357791i	$-0.883530\pi$
$311$	−2.76951	+	4.79693i	−0.157044	+	0.272009i	0.776757	+	0.629800i	$0.216863\pi$
$312$	−2.68693	+	10.8591i	−0.152118	+	0.614776i
$313$	10.3739	+	17.9681i	0.586365	+	1.01561i	0.994704	+	0.102784i	$0.0327751\pi$
$313$	10.3739	+	17.9681i	0.586365	+	1.01561i	−0.408338	+	0.912831i	$0.633892\pi$
$314$	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	$-0.840772\pi$
$317$	−16.0390	+	9.26013i	−0.900841	+	0.520101i	−0.0233679	+	0.999727i	$0.507439\pi$
$318$	41.3085	−	23.8495i	2.31647	−	1.33741i
$319$	2.43920	−	1.40828i	0.136569	−	0.0788483i
$320$	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
$325$	−0.521780	+	0.542250i	−0.0289432	+	0.0300786i
$326$	−7.58258	+	13.1334i	−0.419960	+	0.727392i
$327$	−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
$331$		−	1.08450i		−	0.0596095i	−0.999556	−	0.0298048i	$-0.990511\pi$
$331$		−	1.08450i		−	0.0596095i	0.999556	−	0.0298048i	$-0.00948855\pi$
$332$	8.60436	−	4.96773i	0.472225	−	0.272639i
$333$	−1.25227	−	0.723000i	−0.0686241	−	0.0396202i
$334$	−43.7042			−2.39139
$335$	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	$0.614801\pi$
$338$	−15.1652	−	24.0779i	−0.824875	−	1.30967i
$339$	1.26951	−	2.19885i	0.0689502	−	0.119425i
$340$		−	18.3296i		−	0.994060i
$341$	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
$345$		−	29.7309i		−	1.60066i
$346$	14.6869	+	8.47950i	0.789574	+	0.455861i
$347$	2.20871	+	3.82560i	0.118570	+	0.205369i	0.919201	−	0.393788i	$-0.128836\pi$
$347$	2.20871	+	3.82560i	0.118570	+	0.205369i	−0.800631	+	0.599157i	$0.795502\pi$
$348$	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
$352$	4.70871	+	8.15573i	0.250975	+	0.434702i
$353$			26.8190i			1.42743i	0.700435	+	0.713716i	$0.252989\pi$
$353$			26.8190i			1.42743i	−0.700435	+	0.713716i	$0.747011\pi$
$354$	34.7042			1.84451
$355$	−2.00000			−0.106149
$356$			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	$-0.775241\pi$
$359$	−10.9782	+	6.33828i	−0.579408	+	0.334522i	0.181490	+	0.983393i	$0.441908\pi$
$360$	−0.395644	−	0.685275i	−0.0208523	−	0.0361172i
$361$	−24.1216			−1.26956
$362$	−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
$367$	18.0000			0.939592			0.469796	−	0.882775i	$-0.344327\pi$
$367$	18.0000			0.939592			0.469796	+	0.882775i	$0.344327\pi$
$368$	6.79129	+	11.7629i	0.354020	+	0.613181i
$369$	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
$373$	36.7913			1.90498			0.952490	−	0.304569i	$-0.0985124\pi$
$373$	36.7913			1.90498			0.952490	+	0.304569i	$0.0985124\pi$
$374$	8.37386			0.433002
$375$		−	20.4231i		−	1.05464i
$376$	−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	$0.370604\pi$
$380$	−20.0608	+	34.7463i	−1.02910	+	1.78245i
$381$	−14.2913	−	24.7532i	−0.732165	−	1.26815i
$382$	1.18693	+	0.685275i	0.0607287	+	0.0350617i
$383$			3.92095i			0.200351i	0.994970	+	0.100176i	$0.0319405\pi$
$383$			3.92095i			0.200351i	−0.994970	+	0.100176i	$0.968060\pi$
$384$	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
$388$		−	42.5028i		−	2.15775i
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.123154	+	0.992388i	$0.539301\pi$
$389$	−18.1652	+	31.4630i	−0.921010	+	1.59524i	−0.797856	+	0.602848i	$0.794033\pi$
$390$	30.0390	+	7.43273i	1.52108	+	0.376371i
$391$	22.7477			1.15040
$392$		0			0
$393$	−3.24773	−	5.62523i	−0.163826	−	0.283755i
$394$	23.9564			1.20691
$395$	11.3739	+	6.56670i	0.572281	+	0.330407i
$396$	0.643371	−	0.371450i	0.0323306	−	0.0186661i
$397$		−	15.1515i		−	0.760432i	−0.924898	−	0.380216i	$-0.875850\pi$
$397$		−	15.1515i		−	0.760432i	0.924898	−	0.380216i	$-0.124150\pi$
$398$		−	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	$-0.0690656\pi$
$401$	25.5998	+	14.7801i	1.27839	+	0.738081i	0.301841	+	0.953358i	$0.402399\pi$
$402$	−22.3521	+	38.7149i	−1.11482	+	1.93093i
$403$	22.5000	+	21.6506i	1.12080	+	1.07849i
$404$	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
$409$	0.313068	−	0.180750i	0.0154802	−	0.00893751i	−0.492240	−	0.870460i	$-0.663822\pi$
$409$	0.313068	−	0.180750i	0.0154802	−	0.00893751i	0.507720	+	0.861522i	$0.330488\pi$
$410$	−10.5826	+	6.10985i	−0.522636	+	0.301744i
$411$	−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
$416$	−25.5826	+	7.38505i	−1.25429	+	0.362082i
$417$	−0.708712	+	1.22753i	−0.0347058	+	0.0601122i
$418$	−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	$-0.162591\pi$
$422$			3.10260i			0.151032i
$423$	0.774053	−	0.446900i	0.0376358	−	0.0217290i
$424$	−18.2477	−	10.5353i	−0.886188	−	0.511641i
$425$	0.626136			0.0303721
$426$	−1.79129	−	3.10260i	−0.0867882	−	0.150322i
$427$		0			0
$428$	27.3303			1.32106
$429$	−1.97822	+	7.99488i	−0.0955093	+	0.385996i
$430$	−10.4782	+	18.1488i	−0.505305	+	0.875213i
$431$		−	15.6084i		−	0.751828i	−0.926655	−	0.375914i	$-0.877329\pi$
$431$		−	15.6084i		−	0.751828i	0.926655	−	0.375914i	$-0.122671\pi$
$432$	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
$436$			22.1552i			1.06104i
$437$	−43.1216	−	24.8963i	−2.06279	−	1.19095i
$438$	−6.79129	−	11.7629i	−0.324500	−	0.562051i
$439$	5.76951	−	9.99308i	0.275364	−	0.476944i	−0.694863	−	0.719142i	$-0.744535\pi$
$439$	5.76951	−	9.99308i	0.275364	−	0.476944i	0.970227	+	0.242198i	$0.0778684\pi$
$440$	−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	0.825979	−	0.563701i	$-0.190623\pi$
$443$	−1.58258	−	2.74110i	−0.0751904	−	0.130234i	−0.901169	+	0.433468i	$0.857290\pi$
$444$			34.6410i			1.64399i
$445$	6.37386			0.302150
$446$	45.3303			2.14645
$447$			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
$451$	−1.62614	−	2.81655i	−0.0765718	−	0.132626i
$452$	−3.95644			−0.186095
$453$	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	$-0.266233\pi$
$457$	7.74773	+	4.47315i	0.362423	+	0.209245i	−0.307720	+	0.951477i	$0.599566\pi$
$458$	−15.1652			−0.708621
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$	−40.1216	+	23.1642i	−1.87068	+	1.08004i
$461$	−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	$0.940954\pi$
$464$	3.95644			0.183673
$465$	−33.9564			−1.57469
$466$		−	15.2270i		−	0.705375i
$467$	5.91742	+	10.2493i	0.273826	+	0.474280i	0.969838	−	0.243750i	$-0.0783775\pi$
$467$	5.91742	+	10.2493i	0.273826	+	0.474280i	−0.696012	+	0.718030i	$0.745044\pi$
$468$	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
$473$	−4.83030	−	2.78878i	−0.222098	−	0.128228i
$474$			23.5257i			1.08057i
$475$	−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
$479$		−	10.2215i		−	0.467032i	−0.972353	−	0.233516i	$-0.924977\pi$
$479$		−	10.2215i		−	0.467032i	0.972353	−	0.233516i	$-0.0750232\pi$
$480$	14.4782	−	25.0770i	0.660837	−	1.14460i
$481$	−18.0000	−	17.3205i	−0.820729	−	0.789747i
$482$	−9.00000			−0.409939
$483$		0			0
$484$	13.0826	+	22.6597i	0.594663	+	1.02999i
$485$	−33.3303			−1.51345
$486$	−4.10436	−	2.36965i	−0.186177	−	0.107490i
$487$	8.93466	−	5.15843i	0.404868	−	0.233751i	−0.283714	−	0.958909i	$-0.591567\pi$
$487$	8.93466	−	5.15843i	0.404868	−	0.233751i	0.688582	+	0.725158i	$0.258233\pi$
$488$		−	22.0797i		−	0.999502i
$489$			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
$493$	3.31307	−	5.73840i	0.149213	−	0.258445i
$494$	35.9347	−	37.3444i	1.61678	−	1.68020i
$495$	−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	−0.654723	+	0.755869i	$0.727215\pi$
$499$	−36.5608	+	21.1084i	−1.63669	+	0.944941i	−0.981963	+	0.189072i	$0.939452\pi$
$500$	−27.5608	+	15.9122i	−1.23256	+	0.711617i
$501$	−30.9737	+	17.8827i	−1.38380	+	0.798938i
$502$	40.1216	−	23.1642i	1.79071	−	1.03387i
$503$	−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
$506$	−10.5826	−	18.3296i	−0.470453	−	0.814848i
$507$	−20.5998	−	10.8591i	−0.914870	−	0.482270i
$508$	−22.2695	+	38.5719i	−0.988050	+	1.71135i
$509$	19.0390	+	10.9922i	0.843890	+	0.487220i	0.858584	−	0.512672i	$-0.171344\pi$
$509$	19.0390	+	10.9922i	0.843890	+	0.487220i	−0.0146949	+	0.999892i	$0.504678\pi$
$510$	−12.8739	−	22.2982i	−0.570064	−	0.987380i
$511$		0			0
$512$			19.4340i			0.858868i
$513$			32.8335i			1.44964i
$514$	−52.9955	+	30.5969i	−2.33753	+	1.34957i
$515$	8.68693	+	5.01540i	0.382792	+	0.221005i
$516$	−21.8693			−0.962743
$517$	−2.73049	−	4.72935i	−0.120087	−	0.207997i
$518$		0			0
$519$	13.8784			0.609195
$520$	−3.79129	−	13.1334i	−0.166259	−	0.575938i
$521$	12.7913	−	22.1552i	0.560396	−	0.970635i	−0.437065	−	0.899430i	$-0.643982\pi$
$521$	12.7913	−	22.1552i	0.560396	−	0.970635i	0.997462	−	0.0712054i	$-0.0226846\pi$
$522$		−	1.00905i		−	0.0441649i
$523$	−6.16515	+	10.6784i	−0.269583	+	0.466932i	−0.968754	−	0.248023i	$-0.920219\pi$
$523$	−6.16515	+	10.6784i	−0.269583	+	0.466932i	0.699171	+	0.714954i	$0.253553\pi$
$524$	−5.06080	+	8.76555i	−0.221082	+	0.382925i
$525$		0			0
$526$	51.8085	+	29.9117i	2.25896	+	1.30421i
$527$		−	25.9808i		−	1.13174i
$528$	3.54356	+	2.04588i	0.154214	+	0.0890353i
$529$	−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
$534$	5.70871	+	9.88778i	0.247040	+	0.427886i
$535$		−	21.4322i		−	0.926593i
$536$	19.7477			0.852972
$537$	16.1216			0.695698
$538$			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	$-0.890596\pi$
$541$	−26.0608	+	15.0462i	−1.12044	+	0.646887i	−0.178928	+	0.983862i	$0.557263\pi$
$542$	31.4347	+	54.4464i	1.35023	+	2.33867i
$543$	−16.4174			−0.704539
$544$	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
$549$	2.66061			0.113552
$550$	−0.291288	−	0.504525i	−0.0124206	−	0.0215130i
$551$	−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
$555$	27.1652			1.15310
$556$	2.20871			0.0936703
$557$			27.8281i			1.17911i	0.807727	+	0.589556i	$0.200697\pi$
$557$			27.8281i			1.17911i	−0.807727	+	0.589556i	$0.799303\pi$
$558$	−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
$562$	7.00000	−	12.1244i	0.295277	−	0.511435i
$563$	−0.165151	−	0.286051i	−0.00696030	−	0.0120556i	0.862524	−	0.506016i	$-0.168882\pi$
$563$	−0.165151	−	0.286051i	−0.00696030	−	0.0120556i	−0.869485	+	0.493960i	$0.835549\pi$
$564$	−18.5436	−	10.7061i	−0.780825	−	0.450809i
$565$			3.10260i			0.130527i
$566$	−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	−0.731121	−	0.682248i	$-0.761002\pi$
$569$	5.37386	−	9.30780i	0.225284	−	0.390203i	0.956405	+	0.292045i	$0.0943356\pi$
$570$			56.3592i			2.36063i
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	−0.477469	−	0.878648i	$-0.658446\pi$
$571$	12.4782	−	21.6129i	0.522197	−	0.904472i	0.999667	−	0.0258237i	$-0.00822085\pi$
$572$	12.3303	−	3.55945i	0.515556	−	0.148828i
$573$	1.12159			0.0468551
$574$		0			0
$575$	−0.791288	−	1.37055i	−0.0329990	−	0.0571559i
$576$	2.62614			0.109422
$577$	−17.1261	−	9.88778i	−0.712970	−	0.411634i	0.0991895	−	0.995069i	$-0.468375\pi$
$577$	−17.1261	−	9.88778i	−0.712970	−	0.411634i	−0.812160	+	0.583435i	$0.801708\pi$
$578$	−15.1652	+	8.75560i	−0.630787	+	0.364185i
$579$			22.2306i			0.923873i
$580$			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
$584$	−3.00000	+	5.19615i	−0.124141	+	0.215018i
$585$	1.58258	−	0.456850i	0.0654315	−	0.0188884i
$586$	8.58258	+	14.8655i	0.354543	+	0.614086i
$587$	−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
$590$	−36.7259	+	21.2037i	−1.51198	+	0.872944i
$591$	16.9782	−	9.80238i	0.698391	−	0.403216i
$592$	−10.7477	+	6.20520i	−0.441729	+	0.255032i
$593$	16.9782	−	9.80238i	0.697212	−	0.402535i	−0.109096	−	0.994031i	$-0.534796\pi$
$593$	16.9782	−	9.80238i	0.697212	−	0.402535i	0.806308	+	0.591496i	$0.201462\pi$
$594$	−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
$598$	57.4955	−	16.5975i	2.35116	−	0.678723i
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	−0.579330	−	0.815093i	$-0.696686\pi$
$599$	10.1869	−	17.6443i	0.416227	−	0.720926i	0.995556	+	0.0941675i	$0.0300189\pi$
$600$	−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
$604$		−	33.8426i		−	1.37703i
$605$	17.7695	−	10.2592i	0.722433	−	0.417097i
$606$	33.2477	+	19.1956i	1.35060	+	0.779767i
$607$	−7.74773			−0.314471			−0.157235	−	0.987561i	$-0.550258\pi$
$607$	−7.74773			−0.314471			−0.157235	+	0.987561i	$0.550258\pi$
$608$	−24.2477	−	41.9983i	−0.983375	−	1.70326i
$609$		0			0
$610$	−61.0780			−2.47298
$611$	14.8348	−	4.28245i	0.600154	−	0.173249i
$612$	0.873864	−	1.51358i	0.0353238	−	0.0611827i
$613$			37.3067i			1.50680i	0.657561	+	0.753401i	$0.271588\pi$
$613$			37.3067i			1.50680i	−0.657561	+	0.753401i	$0.728412\pi$
$614$	−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	$0.855772\pi$
$618$			17.9681i			0.722781i
$619$	10.7477	+	6.20520i	0.431988	+	0.249408i	0.700193	−	0.713954i	$-0.253097\pi$
$619$	10.7477	+	6.20520i	0.431988	+	0.249408i	−0.268205	+	0.963362i	$0.586431\pi$
$620$	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
$625$	11.9564	+	20.7092i	0.478258	+	0.828366i
$626$		−	45.4147i		−	1.81514i
$627$	−15.0000			−0.599042
$628$	−61.2867			−2.44561
$629$			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
$633$	1.26951	+	2.19885i	0.0504584	+	0.0873965i
$634$	40.5390			1.61001
$635$	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
$640$	−27.9564			−1.10508
$641$	−7.81307	−	13.5326i	−0.308598	−	0.534507i	0.669458	−	0.742850i	$-0.266526\pi$
$641$	−7.81307	−	13.5326i	−0.308598	−	0.534507i	−0.978056	+	0.208343i	$0.933193\pi$
$642$	33.2477	−	19.1956i	1.31218	−	0.757589i
$643$	−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
$646$	−43.1216			−1.69660
$647$	29.0780			1.14318			0.571588	−	0.820541i	$-0.306328\pi$
$647$	29.0780			1.14318			0.571588	+	0.820541i	$0.306328\pi$
$648$			16.5975i			0.652012i
$649$	−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
$653$	−5.60436	+	9.70703i	−0.219315	+	0.379865i	−0.954599	−	0.297894i	$-0.903716\pi$
$653$	−5.60436	+	9.70703i	−0.219315	+	0.379865i	0.735283	+	0.677760i	$0.237049\pi$
$654$	15.5608	+	26.9521i	0.608475	+	1.05391i
$655$	6.87386	+	3.96863i	0.268584	+	0.155067i
$656$		−	4.56850i		−	0.178370i
$657$	−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
$661$			18.7665i			0.729933i	0.931021	+	0.364966i	$0.118919\pi$
$661$			18.7665i			0.729933i	−0.931021	+	0.364966i	$0.881081\pi$
$662$	−1.18693	+	2.05583i	−0.0461314	+	0.0799020i
$663$	5.37386	+	18.6156i	0.208704	+	0.722970i
$664$	−6.16515			−0.239254
$665$		0			0
$666$	1.58258	+	2.74110i	0.0613236	+	0.106216i
$667$	−16.7477			−0.648475
$668$	48.2650	+	27.8658i	1.86743	+	1.07816i
$669$	32.1261	−	18.5480i	1.24207	−	0.717108i
$670$		−	54.6272i		−	2.11043i
$671$		−	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
$675$	−0.521780	+	0.903750i	−0.0200833	+	0.0347854i
$676$	1.39564	+	36.2599i	0.0536786	+	1.39461i
$677$	−16.8956	−	29.2641i	−0.649352	−	1.12471i	−0.983278	−	0.182112i	$-0.941707\pi$
$677$	−16.8956	−	29.2641i	−0.649352	−	1.12471i	0.333925	−	0.942599i	$-0.391627\pi$
$678$	−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
$682$	−20.9347	+	12.0866i	−0.801630	+	0.462821i
$683$	−21.7087	+	12.5335i	−0.830661	+	0.479582i	−0.854079	−	0.520144i	$-0.825878\pi$
$683$	−21.7087	+	12.5335i	−0.830661	+	0.479582i	0.0234181	+	0.999726i	$0.492545\pi$
$684$	−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
$689$	30.4129	−	31.6060i	1.15864	−	1.20409i
$690$	−32.5390	+	56.3592i	−1.23874	+	2.14556i
$691$	25.4347	+	14.6847i	0.967580	+	0.558633i	0.898498	−	0.438978i	$-0.144660\pi$
$691$	25.4347	+	14.6847i	0.967580	+	0.558633i	0.0690824	+	0.997611i	$0.477993\pi$
$692$	−10.8131	−	18.7288i	−0.411051	−	0.711962i
$693$		0			0
$694$		−	9.66930i		−	0.367042i
$695$		−	1.73205i		−	0.0657004i
$696$	−5.93466	+	3.42638i	−0.224953	+	0.129876i
$697$	−6.62614	−	3.82560i	−0.250983	−	0.144905i
$698$	23.3739			0.884714
$699$	−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	$0.294105\pi$
$702$	−28.4347	−	27.3613i	−1.07320	−	1.03268i
$703$	22.7477	−	39.4002i	0.857947	−	1.48601i
$704$		−	16.0453i		−	0.604730i
$705$	−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
$709$			7.28970i			0.273771i	0.990587	+	0.136885i	$0.0437092\pi$
$709$			7.28970i			0.273771i	−0.990587	+	0.136885i	$0.956291\pi$
$710$	3.79129	+	2.18890i	0.142284	+	0.0821480i
$711$	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
$716$	−12.5608	−	21.7559i	−0.469419	−	0.813057i
$717$		−	23.6965i		−	0.884962i
$718$	27.7477			1.03554
$719$	−5.83485			−0.217603			−0.108802	−	0.994063i	$-0.534701\pi$
$719$	−5.83485			−0.217603			−0.108802	+	0.994063i	$0.534701\pi$
$720$		−	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
$724$	12.7913	+	22.1552i	0.475384	+	0.823390i
$725$	−0.460985			−0.0171206
$726$	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
$731$	−13.1216			−0.485320
$732$	−31.8693	−	55.1993i	−1.17792	−	2.04022i
$733$	7.81307	−	4.51088i	0.288582	−	0.166613i	−0.348720	−	0.937227i	$-0.613384\pi$
$733$	7.81307	−	4.51088i	0.288582	−	0.166613i	0.637302	+	0.770614i	$0.280050\pi$
$734$	−34.1216	−	19.7001i	−1.25945	−	0.727144i
$735$		0			0
$736$		−	55.9977i		−	2.06410i
$737$	14.5390			0.535551
$738$	−1.16515			−0.0428898
$739$		−	12.4104i		−	0.456524i	−0.973600	−	0.228262i	$-0.926696\pi$
$739$		−	12.4104i		−	0.456524i	0.973600	−	0.228262i	$-0.0733043\pi$
$740$	−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	$0.301946\pi$
$744$	−13.4347	+	23.2695i	−0.492538	+	0.853102i
$745$	−2.39564	−	4.14938i	−0.0877696	−	0.152021i
$746$	−69.7432	−	40.2662i	−2.55348	−	1.47425i
$747$		−	0.742901i		−	0.0271813i
$748$	−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	−0.829809	−	0.558047i	$-0.811551\pi$
$751$	1.87386	−	3.24563i	0.0683783	−	0.118435i	0.898188	+	0.439612i	$0.144884\pi$
$752$		−	7.67110i		−	0.279736i
$753$	18.9564	−	32.8335i	0.690811	−	1.19652i
$754$	4.18693	−	16.9213i	0.152479	−	0.616237i
$755$	−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	$0.868110\pi$
$758$	9.95644			0.361634
$759$	−15.0000	−	8.66025i	−0.544466	−	0.314347i
$760$	21.5608	−	12.4481i	0.782092	−	0.451541i
$761$		−	32.0152i		−	1.16055i	−0.814421	−	0.580274i	$-0.802945\pi$
$761$		−	32.0152i		−	1.16055i	0.814421	−	0.580274i	$-0.197055\pi$
$762$			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
$766$	4.29129	−	7.43273i	0.155051	−	0.268555i
$767$	30.6606	−	8.85095i	1.10709	−	0.319589i
$768$	−2.50000	−	4.33013i	−0.0902110	−	0.156250i
$769$	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
$772$	30.0000	−	17.3205i	1.07972	−	0.623379i
$773$	−19.8303	+	11.4490i	−0.713246	+	0.411793i	−0.812262	−	0.583293i	$-0.801764\pi$
$773$	−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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} +O(q^{10})\)	\(q+(-1.89564 - 1.09445i) q^{2} -1.79129 q^{3} +(1.39564 + 2.41733i) q^{4} +(1.89564 - 1.09445i) q^{5} +(3.39564 + 1.96048i) q^{6} -1.73205i q^{8} +0.208712 q^{9} -4.79129 q^{10} -1.27520i q^{11} +(-2.50000 - 4.33013i) 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} +(-0.395644 - 0.228425i) q^{18} +6.56670i q^{19} +(5.29129 + 3.05493i) q^{20} +(-1.39564 + 2.41733i) q^{22} +(-3.79129 + 6.56670i) q^{23} +3.10260i q^{24} +(-0.104356 + 0.180750i) q^{25} +(-5.68693 - 5.47225i) q^{26} +5.00000 q^{27} +(1.10436 + 1.91280i) q^{29} +8.58258 q^{30} +(7.50000 + 4.33013i) q^{31} +(-6.39564 + 3.69253i) q^{32} +2.28425i q^{33} +6.56670i q^{34} +(0.291288 + 0.504525i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(7.18693 - 12.4481i) q^{38} +(-6.26951 - 1.55130i) 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} +(0.395644 - 0.228425i) q^{45} +(14.3739 - 8.29875i) 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} +(2.79129 + 9.66930i) q^{52} +(6.08258 - 10.5353i) q^{53} +(-9.47822 - 5.47225i) q^{54} +(-1.39564 - 2.41733i) q^{55} -11.7629i q^{57} -4.83465i q^{58} +(7.66515 - 4.42548i) q^{59} +(-9.47822 - 5.47225i) q^{60} +12.7477 q^{61} +(-9.47822 - 16.4168i) q^{62} +12.5826 q^{64} +(7.58258 - 2.18890i) q^{65} +(2.50000 - 4.33013i) q^{66} +11.4014i q^{67} +(4.18693 - 7.25198i) q^{68} +(6.79129 - 11.7629i) q^{69} +(-0.791288 - 0.456850i) q^{71} -0.361500i q^{72} +(-3.00000 - 1.73205i) 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} +(3.00000 + 5.19615i) q^{79} -3.92095i q^{80} -9.58258 q^{81} -5.58258 q^{82} -3.55945i q^{83} +(-5.68693 - 3.28335i) q^{85} +(-8.29129 + 4.78698i) q^{86} +(-1.97822 - 3.42638i) q^{87} -2.20871 q^{88} +(2.52178 + 1.45595i) q^{89} -1.00000 q^{90} -21.1652 q^{92} +(-13.4347 - 7.75650i) q^{93} -9.37386 q^{94} +(7.18693 + 12.4481i) q^{95} +(11.4564 - 6.61438i) q^{96} +(-13.1869 - 7.61348i) q^{97} -0.266150i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9}+O(q^{10}) \) 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9	\( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9} - 10 q^{10} - 10 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} - 9 q^{26} + 20 q^{27} + 9 q^{29} + 16 q^{30} + 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} + 15 q^{38} + 7 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} - 6 q^{44} - 3 q^{45} + 30 q^{46} + 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} + 2 q^{52} + 6 q^{53} - 15 q^{54} - q^{55} - 6 q^{59} - 15 q^{60} - 4 q^{61} - 15 q^{62} + 32 q^{64} + 12 q^{65} + 10 q^{66} + 3 q^{68} + 18 q^{69} + 6 q^{71} - 12 q^{73} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} - 4 q^{82} - 9 q^{85} - 24 q^{86} + 15 q^{87} - 18 q^{88} + 33 q^{89} - 4 q^{90} - 48 q^{92} + 15 q^{93} - 10 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) 4 * q - 3 * q^2 + 2 * q^3 + q^4 + 3 * q^5 + 9 * q^6 + 10 * q^9 - 10 * q^10 - 10 * q^12 + 14 * q^13 - 9 * q^15 - q^16 - 6 * q^17 + 3 * q^18 + 12 * q^20 - q^22 - 6 * q^23 - 5 * q^25 - 9 * q^26 + 20 * q^27 + 9 * q^29 + 16 * q^30 + 30 * q^31 - 21 * q^32 - 8 * q^36 - 24 * q^37 + 15 * q^38 + 7 * q^39 - 3 * q^40 + 18 * q^41 - 5 * q^43 - 6 * q^44 - 3 * q^45 + 30 * q^46 + 24 * q^47 - 11 * q^48 - 3 * q^50 - 3 * q^51 + 2 * q^52 + 6 * q^53 - 15 * q^54 - q^55 - 6 * q^59 - 15 * q^60 - 4 * q^61 - 15 * q^62 + 32 * q^64 + 12 * q^65 + 10 * q^66 + 3 * q^68 + 18 * q^69 + 6 * q^71 - 12 * q^73 + 12 * q^74 - 13 * q^75 - 36 * q^76 + 27 * q^78 + 12 * q^79 - 20 * q^81 - 4 * q^82 - 9 * q^85 - 24 * q^86 + 15 * q^87 - 18 * q^88 + 33 * q^89 - 4 * q^90 - 48 * q^92 + 15 * q^93 - 10 * q^94 + 15 * q^95 - 39 * q^97

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