LMFDB - Embedded newform 637.2.bb.a.423.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(227,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 5]))

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

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

chi := DirichletCharacter("637.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bb (of order $12$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			423.3
Character	$\chi$	$=$	637.423
Dual form			637.2.bb.a.509.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.876516 - 0.876516i) q^{2} +(-1.92717 + 1.11265i) q^{3} -0.463441i q^{4} +(2.51660 + 0.674321i) q^{5} +(2.66446 + 0.713939i) q^{6} +(-2.15924 + 2.15924i) q^{8} +(0.975997 - 1.69048i) q^{9} +O(q^{10})$	\(q+(-0.876516 - 0.876516i) q^{2} +(-1.92717 + 1.11265i) q^{3} -0.463441i q^{4} +(2.51660 + 0.674321i) q^{5} +(2.66446 + 0.713939i) q^{6} +(-2.15924 + 2.15924i) q^{8} +(0.975997 - 1.69048i) q^{9} +(-1.61479 - 2.79689i) q^{10} +(1.36505 + 0.365763i) q^{11} +(0.515649 + 0.893131i) q^{12} +(-0.445209 + 3.57796i) q^{13} +(-5.60021 + 1.50057i) q^{15} +2.85834 q^{16} -2.82813 q^{17} +(-2.33720 + 0.626252i) q^{18} +(-1.61939 - 6.04364i) q^{19} +(0.312508 - 1.16630i) q^{20} +(-0.875887 - 1.51708i) q^{22} +1.01874i q^{23} +(1.75875 - 6.56373i) q^{24} +(1.54845 + 0.893996i) q^{25} +(3.52637 - 2.74590i) q^{26} -2.33214i q^{27} +(-2.66549 + 4.61676i) q^{29} +(6.22395 + 3.59340i) q^{30} +(1.73101 + 6.46023i) q^{31} +(1.81311 + 1.81311i) q^{32} +(-3.03765 + 0.813935i) q^{33} +(2.47890 + 2.47890i) q^{34} +(-0.783435 - 0.452317i) q^{36} +(-6.50927 + 6.50927i) q^{37} +(-3.87792 + 6.71676i) q^{38} +(-3.12303 - 7.39071i) q^{39} +(-6.88998 + 3.97793i) q^{40} +(2.51937 + 9.40242i) q^{41} +(0.850246 - 0.490890i) q^{43} +(0.169509 - 0.632618i) q^{44} +(3.59612 - 3.59612i) q^{45} +(0.892940 - 0.892940i) q^{46} +(-0.594605 + 2.21910i) q^{47} +(-5.50852 + 3.18034i) q^{48} +(-0.573636 - 2.14084i) q^{50} +(5.45029 - 3.14673i) q^{51} +(1.65817 + 0.206328i) q^{52} +(-2.52978 + 4.38171i) q^{53} +(-2.04415 + 2.04415i) q^{54} +(3.18863 + 1.84096i) q^{55} +(9.84531 + 9.84531i) q^{57} +(6.38300 - 1.71032i) q^{58} +(5.39402 + 5.39402i) q^{59} +(0.695426 + 2.59537i) q^{60} +(6.75223 + 3.89840i) q^{61} +(4.14523 - 7.17976i) q^{62} -8.89512i q^{64} +(-3.53311 + 8.70408i) q^{65} +(3.37597 + 1.94912i) q^{66} +(-3.38240 + 12.6233i) q^{67} +1.31067i q^{68} +(-1.13350 - 1.96328i) q^{69} +(2.97420 - 11.0999i) q^{71} +(1.54273 + 5.75756i) q^{72} +(-8.43566 + 2.26033i) q^{73} +11.4110 q^{74} -3.97883 q^{75} +(-2.80087 + 0.750490i) q^{76} +(-3.74068 + 9.21546i) q^{78} +(-2.78395 - 4.82194i) q^{79} +(7.19330 + 1.92744i) q^{80} +(5.52285 + 9.56586i) q^{81} +(6.03310 - 10.4496i) q^{82} +(0.445401 - 0.445401i) q^{83} +(-7.11727 - 1.90707i) q^{85} +(-1.17553 - 0.314981i) q^{86} -11.8631i q^{87} +(-3.73724 + 2.15770i) q^{88} +(-0.108264 - 0.108264i) q^{89} -6.30411 q^{90} +0.472125 q^{92} +(-10.5240 - 10.5240i) q^{93} +(2.46625 - 1.42389i) q^{94} -16.3014i q^{95} +(-5.51153 - 1.47681i) q^{96} +(2.87974 + 0.771623i) q^{97} +(1.95059 - 1.95059i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	$ 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.876516	−	0.876516i	−0.619790	−	0.619790i	0.325687	−	0.945478i	$-0.394404\pi$
$2$	−0.876516	−	0.876516i	−0.619790	−	0.619790i	−0.945478	+	0.325687i	$0.894404\pi$
$3$	−1.92717	+	1.11265i	−1.11265	+	0.642391i	−0.939515	−	0.342507i	$-0.888724\pi$
$3$	−1.92717	+	1.11265i	−1.11265	+	0.642391i	−0.173138	+	0.984898i	$0.555391\pi$
$4$		−	0.463441i		−	0.231720i
$5$	2.51660	+	0.674321i	1.12546	+	0.301566i	0.773090	−	0.634296i	$-0.218710\pi$
$5$	2.51660	+	0.674321i	1.12546	+	0.301566i	0.352368	+	0.935862i	$0.385377\pi$
$6$	2.66446	+	0.713939i	1.08776	+	0.291464i
$7$		0			0
$7$		0			0
$8$	−2.15924	+	2.15924i	−0.763408	+	0.763408i
$9$	0.975997	−	1.69048i	0.325332	−	0.563492i
$10$	−1.61479	−	2.79689i	−0.510641	−	0.884455i
$11$	1.36505	+	0.365763i	0.411577	+	0.110282i	0.458665	−	0.888609i	$-0.348328\pi$
$11$	1.36505	+	0.365763i	0.411577	+	0.110282i	−0.0470887	+	0.998891i	$0.514994\pi$
$12$	0.515649	+	0.893131i	0.148855	+	0.257825i
$13$	−0.445209	+	3.57796i	−0.123479	+	0.992347i
$13$	−0.445209	+	3.57796i	−0.123479	+	0.992347i
$14$		0			0
$15$	−5.60021	+	1.50057i	−1.44597	+	0.387446i
$16$	2.85834			0.714585
$17$	−2.82813			−0.685922			−0.342961	−	0.939350i	$-0.611430\pi$
$17$	−2.82813			−0.685922			−0.342961	+	0.939350i	$0.611430\pi$
$18$	−2.33720	+	0.626252i	−0.550884	+	0.147609i
$19$	−1.61939	−	6.04364i	−0.371513	−	1.38651i	−0.858373	−	0.513025i	$-0.828525\pi$
$19$	−1.61939	−	6.04364i	−0.371513	−	1.38651i	0.486861	−	0.873480i	$-0.338142\pi$
$20$	0.312508	−	1.16630i	0.0698789	−	0.260792i
$21$		0			0
$22$	−0.875887	−	1.51708i	−0.186740	−	0.323443i
$23$			1.01874i			0.212422i	0.994344	+	0.106211i	$0.0338718\pi$
$23$			1.01874i			0.212422i	−0.994344	+	0.106211i	$0.966128\pi$
$24$	1.75875	−	6.56373i	0.359002	−	1.33982i
$25$	1.54845	+	0.893996i	0.309689	+	0.178799i
$26$	3.52637	−	2.74590i	0.691578	−	0.538516i
$27$		−	2.33214i		−	0.448820i
$28$		0			0
$29$	−2.66549	+	4.61676i	−0.494968	+	0.857310i	−0.999983	−	0.00580039i	$-0.998154\pi$
$29$	−2.66549	+	4.61676i	−0.494968	+	0.857310i	0.505015	+	0.863111i	$0.331487\pi$
$30$	6.22395	+	3.59340i	1.13633	+	0.656062i
$31$	1.73101	+	6.46023i	0.310899	+	1.16029i	0.927747	+	0.373210i	$0.121743\pi$
$31$	1.73101	+	6.46023i	0.310899	+	1.16029i	−0.616848	+	0.787083i	$0.711591\pi$
$32$	1.81311	+	1.81311i	0.320515	+	0.320515i
$33$	−3.03765	+	0.813935i	−0.528786	+	0.141688i
$34$	2.47890	+	2.47890i	0.425128	+	0.425128i
$35$		0			0
$36$	−0.783435	−	0.452317i	−0.130573	−	0.0753861i
$37$	−6.50927	+	6.50927i	−1.07012	+	1.07012i	−0.0727687	+	0.997349i	$0.523183\pi$
$37$	−6.50927	+	6.50927i	−1.07012	+	1.07012i	−0.997349	+	0.0727687i	$0.976817\pi$
$38$	−3.87792	+	6.71676i	−0.629082	+	1.08960i
$39$	−3.12303	−	7.39071i	−0.500086	−	1.18346i
$40$	−6.88998	+	3.97793i	−1.08940	+	0.628966i
$41$	2.51937	+	9.40242i	0.393459	+	1.46841i	0.824388	+	0.566025i	$0.191519\pi$
$41$	2.51937	+	9.40242i	0.393459	+	1.46841i	−0.430929	+	0.902386i	$0.641814\pi$
$42$		0			0
$43$	0.850246	−	0.490890i	0.129661	−	0.0748600i	−0.433766	−	0.901025i	$-0.642816\pi$
$43$	0.850246	−	0.490890i	0.129661	−	0.0748600i	0.563428	+	0.826165i	$0.309482\pi$
$44$	0.169509	−	0.632618i	0.0255545	−	0.0953707i
$45$	3.59612	−	3.59612i	0.536078	−	0.536078i
$46$	0.892940	−	0.892940i	0.131657	−	0.131657i
$47$	−0.594605	+	2.21910i	−0.0867321	+	0.323688i	−0.995637	−	0.0933159i	$-0.970253\pi$
$47$	−0.594605	+	2.21910i	−0.0867321	+	0.323688i	0.908904	+	0.417004i	$0.136920\pi$
$48$	−5.50852	+	3.18034i	−0.795086	+	0.459043i
$49$		0			0
$50$	−0.573636	−	2.14084i	−0.0811244	−	0.302760i
$51$	5.45029	−	3.14673i	0.763194	−	0.440630i
$52$	1.65817	+	0.206328i	0.229947	+	0.0286126i
$53$	−2.52978	+	4.38171i	−0.347492	+	0.601875i	−0.985803	−	0.167904i	$-0.946300\pi$
$53$	−2.52978	+	4.38171i	−0.347492	+	0.601875i	0.638311	+	0.769779i	$0.279633\pi$
$54$	−2.04415	+	2.04415i	−0.278174	+	0.278174i
$55$	3.18863	+	1.84096i	0.429955	+	0.248235i
$56$		0			0
$57$	9.84531	+	9.84531i	1.30404	+	1.30404i
$58$	6.38300	−	1.71032i	0.838129	−	0.224576i
$59$	5.39402	+	5.39402i	0.702242	+	0.702242i	0.964891	−	0.262650i	$-0.0845963\pi$
$59$	5.39402	+	5.39402i	0.702242	+	0.702242i	−0.262650	+	0.964891i	$0.584596\pi$
$60$	0.695426	+	2.59537i	0.0897792	+	0.335060i
$61$	6.75223	+	3.89840i	0.864534	+	0.499139i	0.865528	−	0.500861i	$-0.166983\pi$
$61$	6.75223	+	3.89840i	0.864534	+	0.499139i	−0.000994018		1.00000i	$0.500316\pi$
$62$	4.14523	−	7.17976i	0.526445	−	0.911830i
$63$		0			0
$64$		−	8.89512i		−	1.11189i
$65$	−3.53311	+	8.70408i	−0.438228	+	1.07961i
$66$	3.37597	+	1.94912i	0.415553	+	0.239920i
$67$	−3.38240	+	12.6233i	−0.413226	+	1.54218i	0.375137	+	0.926970i	$0.377596\pi$
$67$	−3.38240	+	12.6233i	−0.413226	+	1.54218i	−0.788363	+	0.615211i	$0.789071\pi$
$68$			1.31067i			0.158942i
$69$	−1.13350	−	1.96328i	−0.136458	−	0.236352i
$70$		0			0
$71$	2.97420	−	11.0999i	0.352973	−	1.31731i	−0.530044	−	0.847970i	$-0.677825\pi$
$71$	2.97420	−	11.0999i	0.352973	−	1.31731i	0.883017	−	0.469341i	$-0.155509\pi$
$72$	1.54273	+	5.75756i	0.181813	+	0.678536i
$73$	−8.43566	+	2.26033i	−0.987320	+	0.264552i	−0.716124	−	0.697973i	$-0.754086\pi$
$73$	−8.43566	+	2.26033i	−0.987320	+	0.264552i	−0.271196	+	0.962524i	$0.587419\pi$
$74$	11.4110			1.32650
$75$	−3.97883			−0.459436
$76$	−2.80087	+	0.750490i	−0.321282	+	0.0860871i
$77$		0			0
$78$	−3.74068	+	9.21546i	−0.423549	+	1.04345i
$79$	−2.78395	−	4.82194i	−0.313219	−	0.542511i	0.665838	−	0.746096i	$-0.268074\pi$
$79$	−2.78395	−	4.82194i	−0.313219	−	0.542511i	−0.979057	+	0.203585i	$0.934741\pi$
$80$	7.19330	+	1.92744i	0.804236	+	0.215494i
$81$	5.52285	+	9.56586i	0.613650	+	1.06287i
$82$	6.03310	−	10.4496i	0.666244	−	1.15397i
$83$	0.445401	−	0.445401i	0.0488891	−	0.0488891i	−0.682240	−	0.731129i	$-0.738994\pi$
$83$	0.445401	−	0.445401i	0.0488891	−	0.0488891i	0.731129	+	0.682240i	$0.238994\pi$
$84$		0			0
$85$	−7.11727	−	1.90707i	−0.771977	−	0.206851i
$86$	−1.17553	−	0.314981i	−0.126760	−	0.0339653i
$87$		−	11.8631i		−	1.27185i
$88$	−3.73724	+	2.15770i	−0.398391	+	0.230011i
$89$	−0.108264	−	0.108264i	−0.0114760	−	0.0114760i	0.701346	−	0.712821i	$-0.252583\pi$
$89$	−0.108264	−	0.108264i	−0.0114760	−	0.0114760i	−0.712821	+	0.701346i	$0.752583\pi$
$90$	−6.30411			−0.664511
$91$		0			0
$92$	0.472125			0.0492224
$93$	−10.5240	−	10.5240i	−1.09128	−	1.09128i
$94$	2.46625	−	1.42389i	0.254375	−	0.146863i
$95$		−	16.3014i		−	1.67249i
$96$	−5.51153	−	1.47681i	−0.562519	−	0.150726i
$97$	2.87974	+	0.771623i	0.292393	+	0.0783465i	0.402034	−	0.915625i	$-0.368303\pi$
$97$	2.87974	+	0.771623i	0.292393	+	0.0783465i	−0.109641	+	0.993971i	$0.534970\pi$
$98$		0			0
$99$	1.95059	−	1.95059i	0.196042	−	0.196042i
$100$	0.414314	−	0.717613i	0.0414314	−	0.0717613i
$101$	−2.65050	−	4.59080i	−0.263735	−	0.456802i	0.703497	−	0.710699i	$-0.251621\pi$
$101$	−2.65050	−	4.59080i	−0.263735	−	0.456802i	−0.967231	+	0.253897i	$0.918288\pi$
$102$	−7.53542	−	2.01911i	−0.746118	−	0.199922i
$103$	2.40977	+	4.17384i	0.237442	+	0.411261i	0.959979	−	0.280071i	$-0.0903579\pi$
$103$	2.40977	+	4.17384i	0.237442	+	0.411261i	−0.722538	+	0.691331i	$0.757025\pi$
$104$	−6.76437	−	8.68700i	−0.663301	−	0.851831i
$105$		0			0
$106$	6.05803	−	1.62325i	0.588408	−	0.157664i
$107$	1.77743			0.171830			0.0859151	−	0.996302i	$-0.472619\pi$
$107$	1.77743			0.171830			0.0859151	+	0.996302i	$0.472619\pi$
$108$	−1.08081			−0.104001
$109$	−9.63303	+	2.58116i	−0.922677	+	0.247231i	−0.688729	−	0.725019i	$-0.741831\pi$
$109$	−9.63303	+	2.58116i	−0.922677	+	0.247231i	−0.233948	+	0.972249i	$0.575165\pi$
$110$	−1.18126	−	4.40852i	−0.112629	−	0.420336i
$111$	5.30192	−	19.7871i	0.503236	−	1.87810i
$112$		0			0
$113$	8.26089	+	14.3083i	0.777119	+	1.34601i	0.933596	+	0.358328i	$0.116653\pi$
$113$	8.26089	+	14.3083i	0.777119	+	1.34601i	−0.156477	+	0.987682i	$0.550014\pi$
$114$		−	17.2591i		−	1.61647i
$115$	−0.686957	+	2.56376i	−0.0640591	+	0.239072i
$116$	2.13959	+	1.23530i	0.198656	+	0.114694i
$117$	5.61393	+	4.24469i	0.519008	+	0.392422i
$118$		−	9.45589i		−	0.870485i
$119$		0			0
$120$	8.85212	−	15.3323i	0.808085	−	1.39964i
$121$	−7.79671	−	4.50143i	−0.708792	−	0.409221i
$122$	−2.50142	−	9.33544i	−0.226468	−	0.845191i
$123$	−15.3169	−	15.3169i	−1.38108	−	1.38108i
$124$	2.99394	−	0.802223i	0.268863	−	0.0720417i
$125$	−5.91742	−	5.91742i	−0.529270	−	0.529270i
$126$		0			0
$127$	−5.35860	−	3.09379i	−0.475499	−	0.274529i	0.243040	−	0.970016i	$-0.421855\pi$
$127$	−5.35860	−	3.09379i	−0.475499	−	0.274529i	−0.718539	+	0.695487i	$0.755189\pi$
$128$	−4.17049	+	4.17049i	−0.368623	+	0.368623i
$129$	−1.09238	+	1.89206i	−0.0961788	+	0.166587i
$130$	10.7261	−	4.53244i	0.940740	−	0.397521i
$131$	2.15037	−	1.24152i	0.187879	−	0.108472i	−0.403110	−	0.915151i	$-0.632071\pi$
$131$	2.15037	−	1.24152i	0.187879	−	0.108472i	0.590989	+	0.806680i	$0.298738\pi$
$132$	0.377211	+	1.40777i	0.0328320	+	0.122531i
$133$		0			0
$134$	14.0292	−	8.09978i	1.21194	−	0.699715i
$135$	1.57261	−	5.86906i	0.135349	−	0.505128i
$136$	6.10662	−	6.10662i	0.523639	−	0.523639i
$137$	9.30838	−	9.30838i	0.795268	−	0.795268i	−0.187077	−	0.982345i	$-0.559901\pi$
$137$	9.30838	−	9.30838i	0.795268	−	0.795268i	0.982345	+	0.187077i	$0.0599014\pi$
$138$	−0.727317	+	2.71438i	−0.0619133	+	0.231064i
$139$	−15.3254	+	8.84813i	−1.29988	+	0.750488i	−0.980384	−	0.197098i	$-0.936848\pi$
$139$	−15.3254	+	8.84813i	−1.29988	+	0.750488i	−0.319500	+	0.947586i	$0.603515\pi$
$140$		0			0
$141$	−1.32318	−	4.93817i	−0.111432	−	0.415869i
$142$	−12.3361	+	7.12227i	−1.03523	+	0.597688i
$143$	−1.91642	+	4.72124i	−0.160259	+	0.394810i
$144$	2.78973	−	4.83196i	0.232478	−	0.402663i
$145$	−9.82114	+	9.82114i	−0.815602	+	0.815602i
$146$	9.37521	+	5.41278i	0.775898	+	0.447965i
$147$		0			0
$148$	3.01666	+	3.01666i	0.247968	+	0.247968i
$149$	16.1655	−	4.33154i	1.32433	−	0.354854i	0.473733	−	0.880669i	$-0.342906\pi$
$149$	16.1655	−	4.33154i	1.32433	−	0.354854i	0.850599	+	0.525815i	$0.176240\pi$
$150$	3.48751	+	3.48751i	0.284754	+	0.284754i
$151$	−2.27755	−	8.49993i	−0.185344	−	0.691715i	−0.994557	−	0.104198i	$-0.966772\pi$
$151$	−2.27755	−	8.49993i	−0.185344	−	0.691715i	0.809212	−	0.587516i	$-0.199894\pi$
$152$	16.5463	+	9.55303i	1.34209	+	0.774853i
$153$	−2.76024	+	4.78088i	−0.223153	+	0.386512i
$154$		0			0
$155$			17.4251i			1.39962i
$156$	−3.42516	+	1.44734i	−0.274232	+	0.115880i
$157$	−4.38854	−	2.53373i	−0.350244	−	0.202213i	0.314549	−	0.949241i	$-0.398147\pi$
$157$	−4.38854	−	2.53373i	−0.350244	−	0.202213i	−0.664793	+	0.747028i	$0.731480\pi$
$158$	−1.78633	+	6.66668i	−0.142113	+	0.530373i
$159$		−	11.2591i		−	0.892904i
$160$	3.34025	+	5.78549i	0.264070	+	0.457383i
$161$		0			0
$162$	3.54376	−	13.2255i	0.278424	−	1.03909i
$163$	−0.650182	−	2.42651i	−0.0509262	−	0.190059i	0.935777	−	0.352593i	$-0.114700\pi$
$163$	−0.650182	−	2.42651i	−0.0509262	−	0.190059i	−0.986703	+	0.162534i	$0.948033\pi$
$164$	4.35746	−	1.16758i	0.340261	−	0.0911726i
$165$	−8.19340			−0.637855
$166$	−0.780801			−0.0606019
$167$	2.57849	−	0.690905i	0.199530	−	0.0534639i	−0.157670	−	0.987492i	$-0.550398\pi$
$167$	2.57849	−	0.690905i	0.199530	−	0.0534639i	0.357200	+	0.934028i	$0.383732\pi$
$168$		0			0
$169$	−12.6036	−	3.18588i	−0.969506	−	0.245068i
$170$	4.56683	+	7.90998i	0.350260	+	0.606668i
$171$	−11.7971	−	3.16103i	−0.902149	−	0.241730i
$172$	−0.227498	−	0.394039i	−0.0173466	−	0.0300452i
$173$	−0.770968	+	1.33536i	−0.0586156	+	0.101525i	−0.893844	−	0.448378i	$-0.852002\pi$
$173$	−0.770968	+	1.33536i	−0.0586156	+	0.101525i	0.835229	+	0.549903i	$0.185335\pi$
$174$	−10.3981	+	10.3981i	−0.788282	+	0.788282i
$175$		0			0
$176$	3.90177	+	1.04547i	0.294107	+	0.0788056i
$177$	−16.3969	−	4.39353i	−1.23247	−	0.330238i
$178$			0.189790i			0.0142254i
$179$	15.3074	−	8.83772i	1.14413	−	0.660562i	0.196678	−	0.980468i	$-0.436985\pi$
$179$	15.3074	−	8.83772i	1.14413	−	0.660562i	0.947449	+	0.319906i	$0.103651\pi$
$180$	−1.66659	−	1.66659i	−0.124220	−	0.124220i
$181$	−0.905550			−0.0673090			−0.0336545	−	0.999434i	$-0.510715\pi$
$181$	−0.905550			−0.0673090			−0.0336545	+	0.999434i	$0.510715\pi$
$182$		0			0
$183$	−17.3503			−1.28257
$184$	−2.19970	−	2.19970i	−0.162164	−	0.162164i
$185$	−20.7706	+	11.9919i	−1.52708	+	0.881662i
$186$			18.4488i			1.35273i
$187$	−3.86053	−	1.03442i	−0.282310	−	0.0756446i
$188$	1.02842	+	0.275564i	0.0750052	+	0.0200976i
$189$		0			0
$190$	−14.2884	+	14.2884i	−1.03659	+	1.03659i
$191$	−11.7133	+	20.2881i	−0.847546	+	1.46799i	0.0358466	+	0.999357i	$0.488587\pi$
$191$	−11.7133	+	20.2881i	−0.847546	+	1.46799i	−0.883392	+	0.468635i	$0.844746\pi$
$192$	9.89719	+	17.1424i	0.714268	+	1.23715i
$193$	11.5170	+	3.08597i	0.829011	+	0.222133i	0.648282	−	0.761400i	$-0.275488\pi$
$193$	11.5170	+	3.08597i	0.829011	+	0.222133i	0.180729	+	0.983533i	$0.442154\pi$
$194$	−1.84780	−	3.20048i	−0.132664	−	0.229781i
$195$	−2.87572	−	20.7054i	−0.205935	−	1.48274i
$196$		0			0
$197$	10.0281	−	2.68702i	0.714472	−	0.191442i	0.116768	−	0.993159i	$-0.462747\pi$
$197$	10.0281	−	2.68702i	0.714472	−	0.191442i	0.597704	+	0.801717i	$0.296080\pi$
$198$	−3.41945			−0.243010
$199$	3.97515			0.281791			0.140896	−	0.990024i	$-0.455002\pi$
$199$	3.97515			0.281791			0.140896	+	0.990024i	$0.455002\pi$
$200$	−5.27383	+	1.41312i	−0.372916	+	0.0999225i
$201$	−7.52688	−	28.0907i	−0.530905	−	1.98137i
$202$	−1.70071	+	6.34712i	−0.119661	+	0.446582i
$203$		0			0
$204$	−1.45832	−	2.52589i	−0.102103	−	0.176848i
$205$			25.3610i			1.77129i
$206$	1.54624	−	5.77064i	0.107731	−	0.402059i
$207$	1.72215	+	0.994285i	0.119698	+	0.0691076i
$208$	−1.27256	+	10.2270i	−0.0882361	+	0.709117i
$209$		−	8.84215i		−	0.611624i
$210$		0			0
$211$	2.47669	−	4.28976i	0.170503	−	0.295319i	−0.768093	−	0.640338i	$-0.778794\pi$
$211$	2.47669	−	4.28976i	0.170503	−	0.295319i	0.938596	+	0.345019i	$0.112128\pi$
$212$	2.03066	+	1.17240i	0.139467	+	0.0805211i
$213$	6.61851	+	24.7006i	0.453493	+	1.69246i
$214$	−1.55794	−	1.55794i	−0.106499	−	0.106499i
$215$	2.47075	−	0.662035i	0.168504	−	0.0451504i
$216$	5.03565	+	5.03565i	0.342633	+	0.342633i
$217$		0			0
$218$	10.7059	+	6.18107i	0.725097	+	0.418635i
$219$	13.7420	−	13.7420i	0.928600	−	0.928600i
$220$	0.853175	−	1.47774i	0.0575211	−	0.0996294i
$221$	1.25911	−	10.1189i	0.0846968	−	0.680673i
$222$	−21.9909	+	12.6964i	−1.47593	+	0.852129i
$223$	−4.57716	−	17.0822i	−0.306509	−	1.14391i	−0.931638	−	0.363387i	$-0.881620\pi$
$223$	−4.57716	−	17.0822i	−0.306509	−	1.14391i	0.625129	−	0.780521i	$-0.285046\pi$
$224$		0			0
$225$	3.02256	−	1.74507i	0.201504	−	0.116338i
$226$	5.30063	−	19.7822i	0.352593	−	1.31589i
$227$	10.7232	−	10.7232i	0.711725	−	0.711725i	−0.255171	−	0.966896i	$-0.582132\pi$
$227$	10.7232	−	10.7232i	0.711725	−	0.711725i	0.966896	+	0.255171i	$0.0821317\pi$
$228$	4.56272	−	4.56272i	0.302174	−	0.302174i
$229$	−3.87857	+	14.4750i	−0.256303	+	0.956536i	0.711058	+	0.703134i	$0.248216\pi$
$229$	−3.87857	+	14.4750i	−0.256303	+	0.956536i	−0.967361	+	0.253403i	$0.918450\pi$
$230$	2.84930	−	1.64505i	0.187877	−	0.108471i
$231$		0			0
$232$	−4.21327	−	15.7241i	−0.276615	−	1.03234i
$233$	5.38039	−	3.10637i	0.352481	−	0.203505i	−0.313297	−	0.949655i	$-0.601433\pi$
$233$	5.38039	−	3.10637i	0.352481	−	0.203505i	0.665777	+	0.746150i	$0.268100\pi$
$234$	−1.20016	−	8.64123i	−0.0784569	−	0.564895i
$235$	−2.99277	+	5.18363i	−0.195227	+	0.338142i
$236$	2.49981	−	2.49981i	0.162724	−	0.162724i
$237$	10.7303	+	6.19515i	0.697008	+	0.402418i
$238$		0			0
$239$	−14.1820	−	14.1820i	−0.917358	−	0.917358i	0.0794785	−	0.996837i	$-0.474674\pi$
$239$	−14.1820	−	14.1820i	−0.917358	−	0.917358i	−0.996837	+	0.0794785i	$0.974674\pi$
$240$	−16.0073	+	4.28915i	−1.03327	+	0.276863i
$241$	−0.812288	−	0.812288i	−0.0523241	−	0.0523241i	0.680461	−	0.732785i	$-0.261780\pi$
$241$	−0.812288	−	0.812288i	−0.0523241	−	0.0523241i	−0.732785	+	0.680461i	$0.761780\pi$
$242$	2.88836	+	10.7795i	0.185671	+	0.692934i
$243$	−15.2279	−	8.79184i	−0.976871	−	0.563996i
$244$	1.80668	−	3.12926i	0.115661	−	0.200330i
$245$		0			0
$246$			26.8510i			1.71196i
$247$	22.3448	−	3.10342i	1.42177	−	0.197466i
$248$	−17.6869	−	10.2115i	−1.12312	−	0.648433i
$249$	−0.362787	+	1.35394i	−0.0229907	+	0.0858025i
$250$			10.3734i			0.656073i
$251$	14.3378	+	24.8339i	0.904997	+	1.56750i	0.820921	+	0.571041i	$0.193460\pi$
$251$	14.3378	+	24.8339i	0.904997	+	1.56750i	0.0840758	+	0.996459i	$0.473206\pi$
$252$		0			0
$253$	−0.372617	+	1.39062i	−0.0234262	+	0.0874278i
$254$	1.98514	+	7.40865i	0.124559	+	0.464860i
$255$	15.8381	−	4.24381i	0.991822	−	0.265758i
$256$	−10.4792			−0.654952
$257$	19.6195			1.22383			0.611916	−	0.790922i	$-0.290399\pi$
$257$	19.6195			1.22383			0.611916	+	0.790922i	$0.290399\pi$
$258$	2.61591	−	0.700930i	0.162859	−	0.0436380i
$259$		0			0
$260$	4.03383	+	1.63739i	0.250167	+	0.101546i
$261$	5.20301	+	9.01188i	0.322058	+	0.557821i
$262$	−2.97304	−	0.796624i	−0.183675	−	0.0492156i
$263$	−4.04343	−	7.00342i	−0.249328	−	0.431850i	0.714011	−	0.700134i	$-0.246877\pi$
$263$	−4.04343	−	7.00342i	−0.249328	−	0.431850i	−0.963340	+	0.268285i	$0.913543\pi$
$264$	4.80154	−	8.31650i	0.295514	−	0.511845i
$265$	−9.32114	+	9.32114i	−0.572593	+	0.572593i
$266$		0			0
$267$	0.329104	+	0.0881832i	0.0201409	+	0.00539673i
$268$	5.85015	+	1.56754i	0.357355	+	0.0957529i
$269$		−	14.3415i		−	0.874415i	−0.899361	−	0.437207i	$-0.855968\pi$
$269$		−	14.3415i		−	0.874415i	0.899361	−	0.437207i	$-0.144032\pi$
$270$	−6.52274	+	3.76591i	−0.396961	+	0.229186i
$271$	−18.4862	−	18.4862i	−1.12295	−	1.12295i	−0.991295	−	0.131660i	$-0.957969\pi$
$271$	−18.4862	−	18.4862i	−1.12295	−	1.12295i	−0.131660	−	0.991295i	$-0.542031\pi$
$272$	−8.08376			−0.490150
$273$		0			0
$274$	−16.3179			−0.985799
$275$	1.78671	+	1.78671i	0.107743	+	0.107743i
$276$	−0.909866	+	0.525312i	−0.0547675	+	0.0316200i
$277$			5.86837i			0.352596i	0.984337	+	0.176298i	$0.0564123\pi$
$277$			5.86837i			0.352596i	−0.984337	+	0.176298i	$0.943588\pi$
$278$	21.1885	+	5.67744i	1.27080	+	0.340510i
$279$	12.6103	+	3.37893i	0.754961	+	0.202291i
$280$		0			0
$281$	16.4096	−	16.4096i	0.978913	−	0.978913i	−0.0208690	−	0.999782i	$-0.506643\pi$
$281$	16.4096	−	16.4096i	0.978913	−	0.978913i	0.999782	+	0.0208690i	$0.00664330\pi$
$282$	−3.16860	+	5.48817i	−0.188687	+	0.326816i
$283$	11.1979	+	19.3953i	0.665645	+	1.15293i	0.979110	+	0.203331i	$0.0651768\pi$
$283$	11.1979	+	19.3953i	0.665645	+	1.15293i	−0.313465	+	0.949600i	$0.601490\pi$
$284$	−5.14413	−	1.37837i	−0.305248	−	0.0817909i
$285$	18.1378	+	31.4156i	1.07439	+	1.86090i
$286$	5.81800	−	2.45847i	0.344026	−	0.145372i
$287$		0			0
$288$	4.83460	−	1.29543i	0.284882	−	0.0763338i
$289$	−9.00168			−0.529511
$290$	17.2168			1.01100
$291$	−6.40830	+	1.71710i	−0.375661	+	0.100658i
$292$	1.04753	+	3.90943i	0.0613020	+	0.228782i
$293$	−1.22119	+	4.55756i	−0.0713429	+	0.266255i	−0.992379	−	0.123221i	$-0.960677\pi$
$293$	−1.22119	+	4.55756i	−0.0713429	+	0.266255i	0.921036	+	0.389477i	$0.127344\pi$
$294$		0			0
$295$	9.93730	+	17.2119i	0.578572	+	1.00212i
$296$		−	28.1102i		−	1.63387i
$297$	0.853009	−	3.18347i	0.0494966	−	0.184724i
$298$	−17.9660	−	10.3727i	−1.04074	−	0.600873i
$299$	−3.64500	−	0.453552i	−0.210796	−	0.0262296i
$300$			1.84395i			0.106461i
$301$		0			0
$302$	−5.45401	+	9.44663i	−0.313843	+	0.543592i
$303$	10.2160	+	5.89818i	0.586891	+	0.338842i
$304$	−4.62876	−	17.2748i	−0.265478	−	0.990776i
$305$	14.3639	+	14.3639i	0.822474	+	0.822474i
$306$	6.60992	−	1.77112i	0.377864	−	0.101248i
$307$	−3.77977	−	3.77977i	−0.215723	−	0.215723i	0.590970	−	0.806693i	$-0.298745\pi$
$307$	−3.77977	−	3.77977i	−0.215723	−	0.215723i	−0.806693	+	0.590970i	$0.798745\pi$
$308$		0			0
$309$	−9.28808	−	5.36248i	−0.528380	−	0.305061i
$310$	15.2734	−	15.2734i	0.867469	−	0.867469i
$311$	−1.26681	+	2.19418i	−0.0718343	+	0.124421i	−0.899705	−	0.436498i	$-0.856219\pi$
$311$	−1.26681	+	2.19418i	−0.0718343	+	0.124421i	0.827871	+	0.560919i	$0.189552\pi$
$312$	22.7017	+	9.21495i	1.28523	+	0.521694i
$313$	−4.62033	+	2.66755i	−0.261157	+	0.150779i	−0.624862	−	0.780735i	$-0.714845\pi$
$313$	−4.62033	+	2.66755i	−0.261157	+	0.150779i	0.363705	+	0.931514i	$0.381511\pi$
$314$	1.62578	+	6.06748i	0.0917478	+	0.342408i
$315$		0			0
$316$	−2.23469	+	1.29020i	−0.125711	+	0.0725792i
$317$	−3.28216	+	12.2492i	−0.184344	+	0.687982i	0.810426	+	0.585841i	$0.199236\pi$
$317$	−3.28216	+	12.2492i	−0.184344	+	0.687982i	−0.994770	+	0.102141i	$0.967431\pi$
$318$	−9.86877	+	9.86877i	−0.553413	+	0.553413i
$319$	−5.32715	+	5.32715i	−0.298263	+	0.298263i
$320$	5.99817	−	22.3855i	0.335308	−	1.25139i
$321$	−3.42541	+	1.97766i	−0.191188	+	0.110382i
$322$		0			0
$323$	4.57984	+	17.0922i	0.254829	+	0.951035i
$324$	4.43321	−	2.55951i	0.246289	−	0.142195i
$325$	−3.88806	+	5.14226i	−0.215671	+	0.285241i
$326$	−1.55698	+	2.69677i	−0.0862333	+	0.149360i
$327$	15.6926	−	15.6926i	0.867802	−	0.867802i
$328$	−25.7420	−	14.8622i	−1.42137	−	0.820626i
$329$		0			0
$330$	7.18164	+	7.18164i	0.395336	+	0.395336i
$331$	−8.64629	+	2.31677i	−0.475243	+	0.127341i	−0.488487	−	0.872571i	$-0.662451\pi$
$331$	−8.64629	+	2.31677i	−0.475243	+	0.127341i	0.0132438	+	0.999912i	$0.495784\pi$
$332$	−0.206417	−	0.206417i	−0.0113286	−	0.0113286i
$333$	4.65074	+	17.3568i	0.254859	+	0.951146i
$334$	−2.86568	−	1.65450i	−0.156803	−	0.0905303i
$335$	−17.0243	+	29.4870i	−0.930137	+	1.61105i
$336$		0			0
$337$			8.38324i			0.456664i	0.973583	+	0.228332i	$0.0733272\pi$
$337$			8.38324i			0.456664i	−0.973583	+	0.228332i	$0.926673\pi$
$338$	8.25476	+	13.8397i	0.449000	+	0.752781i
$339$	−31.8403	−	18.3830i	−1.72933	−	0.998428i
$340$	−0.883813	+	3.29844i	−0.0479315	+	0.178883i
$341$			9.45165i			0.511836i
$342$	7.56968	+	13.1111i	0.409321	+	0.708965i
$343$		0			0
$344$	−0.775938	+	2.89584i	−0.0418358	+	0.156133i
$345$	−1.52869	−	5.70515i	−0.0823019	−	0.307155i
$346$	1.84623	−	0.494695i	0.0992537	−	0.0265949i
$347$	−27.5764			−1.48038			−0.740190	−	0.672398i	$-0.765265\pi$
$347$	−27.5764			−1.48038			−0.740190	+	0.672398i	$0.765265\pi$
$348$	−5.49782			−0.294714
$349$	34.2817	−	9.18577i	1.83506	−	0.491703i	0.836633	−	0.547765i	$-0.184521\pi$
$349$	34.2817	−	9.18577i	1.83506	−	0.491703i	0.998427	+	0.0560618i	$0.0178544\pi$
$350$		0			0
$351$	8.34429	+	1.03829i	0.445385	+	0.0554198i
$352$	1.81181	+	3.13814i	0.0965697	+	0.167264i
$353$	7.01577	+	1.87987i	0.373412	+	0.100055i	0.440644	−	0.897682i	$-0.354750\pi$
$353$	7.01577	+	1.87987i	0.373412	+	0.100055i	−0.0672321	+	0.997737i	$0.521417\pi$
$354$	10.5211	+	18.2231i	0.559192	+	0.968548i
$355$	14.9697	−	25.9284i	0.794512	−	1.37613i
$356$	−0.0501740	+	0.0501740i	−0.00265922	+	0.00265922i
$357$		0			0
$358$	−21.1635	−	5.67075i	−1.11853	−	0.299709i
$359$	15.2059	+	4.07442i	0.802539	+	0.215040i	0.636698	−	0.771113i	$-0.280300\pi$
$359$	15.2059	+	4.07442i	0.802539	+	0.215040i	0.165841	+	0.986153i	$0.446966\pi$
$360$			15.5298i			0.818492i
$361$	−17.4486	+	10.0740i	−0.918349	+	0.530209i
$362$	0.793728	+	0.793728i	0.0417174	+	0.0417174i
$363$	20.0341			1.05152
$364$		0			0
$365$	−22.7534			−1.19097
$366$	15.2078	+	15.2078i	0.794924	+	0.794924i
$367$	−0.280231	+	0.161792i	−0.0146280	+	0.00844546i	−0.507296	−	0.861772i	$-0.669355\pi$
$367$	−0.280231	+	0.161792i	−0.0146280	+	0.00844546i	0.492668	+	0.870217i	$0.336022\pi$
$368$			2.91190i			0.151793i
$369$	18.3534	+	4.91779i	0.955442	+	0.256010i
$370$	28.7168	+	7.69465i	1.49292	+	0.400026i
$371$		0			0
$372$	−4.87724	+	4.87724i	−0.252873	+	0.252873i
$373$	16.1440	−	27.9622i	0.835905	−	1.44783i	−0.0573868	−	0.998352i	$-0.518277\pi$
$373$	16.1440	−	27.9622i	0.835905	−	1.44783i	0.893292	−	0.449478i	$-0.148390\pi$
$374$	2.47712	+	4.29050i	0.128089	+	0.221856i
$375$	17.9879	+	4.81985i	0.928893	+	0.248896i
$376$	−3.50767	−	6.07547i	−0.180894	−	0.313318i
$377$	−15.3319	−	11.5924i	−0.789631	−	0.597040i
$378$		0			0
$379$	13.3271	−	3.57099i	0.684568	−	0.183430i	0.100260	−	0.994961i	$-0.468033\pi$
$379$	13.3271	−	3.57099i	0.684568	−	0.183430i	0.584308	+	0.811532i	$0.301366\pi$
$380$	−7.55474			−0.387550
$381$	13.7693			0.705420
$382$	28.0497	−	7.51589i	1.43515	−	0.384547i
$383$	−4.35337	−	16.2470i	−0.222447	−	0.830183i	−0.983411	−	0.181389i	$-0.941941\pi$
$383$	−4.35337	−	16.2470i	−0.222447	−	0.830183i	0.760965	−	0.648793i	$-0.224726\pi$
$384$	3.39695	−	12.6776i	0.173350	−	0.646950i
$385$		0			0
$386$	−7.38992	−	12.7997i	−0.376137	−	0.651489i
$387$		−	1.91643i		−	0.0974175i
$388$	0.357602	−	1.33459i	0.0181545	−	0.0677534i
$389$	15.4854	+	8.94050i	0.785141	+	0.453302i	0.838249	−	0.545287i	$-0.183579\pi$
$389$	15.4854	+	8.94050i	0.785141	+	0.453302i	−0.0531079	+	0.998589i	$0.516913\pi$
$390$	−15.6280	+	20.6692i	−0.791354	+	1.04663i
$391$		−	2.88112i		−	0.145705i
$392$		0			0
$393$	−2.76275	+	4.78523i	−0.139363	+	0.241383i
$394$	−11.1450	−	6.43456i	−0.561477	−	0.324169i
$395$	−3.75455	−	14.0122i	−0.188912	−	0.705030i
$396$	−0.903984	−	0.903984i	−0.0454269	−	0.0454269i
$397$	−6.40627	+	1.71656i	−0.321522	+	0.0861515i	−0.415970	−	0.909378i	$-0.636558\pi$
$397$	−6.40627	+	1.71656i	−0.321522	+	0.0861515i	0.0944484	+	0.995530i	$0.469891\pi$
$398$	−3.48428	−	3.48428i	−0.174651	−	0.174651i
$399$		0			0
$400$	4.42599	+	2.55534i	0.221299	+	0.127767i
$401$	−15.5895	+	15.5895i	−0.778503	+	0.778503i	−0.979576	−	0.201073i	$-0.935557\pi$
$401$	−15.5895	+	15.5895i	−0.778503	+	0.778503i	0.201073	+	0.979576i	$0.435557\pi$
$402$	−18.0245	+	31.2194i	−0.898981	+	1.55708i
$403$	−23.8851	+	3.31734i	−1.18980	+	0.165249i
$404$	−2.12757	+	1.22835i	−0.105850	+	0.0611127i
$405$	7.44835	+	27.7976i	0.370112	+	1.38128i
$406$		0			0
$407$	−11.2663	+	6.50460i	−0.558450	+	0.322421i
$408$	−4.97396	+	18.5631i	−0.246248	+	0.919009i
$409$	11.7049	−	11.7049i	0.578770	−	0.578770i	−0.355794	−	0.934564i	$-0.615790\pi$
$409$	11.7049	−	11.7049i	0.578770	−	0.578770i	0.934564	+	0.355794i	$0.115790\pi$
$410$	22.2293	−	22.2293i	1.09783	−	1.09783i
$411$	−7.58185	+	28.2958i	−0.373985	+	1.39573i
$412$	1.93433	−	1.11679i	0.0952975	−	0.0550201i
$413$		0			0
$414$	−0.637987	−	2.38100i	−0.0313553	−	0.117020i
$415$	1.42124	−	0.820553i	0.0697659	−	0.0402793i
$416$	−7.29444	+	5.68001i	−0.357639	+	0.278486i
$417$	19.6898	−	34.1037i	0.964214	−	1.67007i
$418$	−7.75028	+	7.75028i	−0.379079	+	0.379079i
$419$	23.3376	+	13.4740i	1.14012	+	0.658247i	0.946460	−	0.322822i	$-0.104631\pi$
$419$	23.3376	+	13.4740i	1.14012	+	0.658247i	0.193658	+	0.981069i	$0.437965\pi$
$420$		0			0
$421$	11.8511	+	11.8511i	0.577587	+	0.577587i	0.934238	−	0.356651i	$-0.116081\pi$
$421$	11.8511	+	11.8511i	0.577587	+	0.577587i	−0.356651	+	0.934238i	$0.616081\pi$
$422$	−5.93090	+	1.58918i	−0.288712	+	0.0773601i
$423$	3.17100	+	3.17100i	0.154179	+	0.154179i
$424$	−3.99877	−	14.9236i	−0.194197	−	0.724755i
$425$	−4.37921	−	2.52834i	−0.212423	−	0.122642i
$426$	15.8492	−	27.4517i	0.767898	−	1.33004i
$427$		0			0
$428$		−	0.823732i		−	0.0398166i
$429$	−1.55984	−	11.2309i	−0.0753097	−	0.542235i
$430$	−2.74593	−	1.58537i	−0.132421	−	0.0764531i
$431$	1.60974	−	6.00762i	0.0775383	−	0.289377i	−0.916259	−	0.400587i	$-0.868806\pi$
$431$	1.60974	−	6.00762i	0.0775383	−	0.289377i	0.993797	+	0.111211i	$0.0354728\pi$
$432$		−	6.66604i		−	0.320720i
$433$	−5.55807	−	9.62686i	−0.267104	−	0.462637i	0.701009	−	0.713153i	$-0.252733\pi$
$433$	−5.55807	−	9.62686i	−0.267104	−	0.462637i	−0.968113	+	0.250515i	$0.919400\pi$
$434$		0			0
$435$	7.99951	−	29.8546i	0.383547	−	1.43142i
$436$	1.19622	+	4.46434i	0.0572884	+	0.213803i
$437$	6.15688	−	1.64973i	0.294524	−	0.0789174i
$438$	−24.0902			−1.15107
$439$	−21.2653			−1.01494			−0.507470	−	0.861670i	$-0.669419\pi$
$439$	−21.2653			−1.01494			−0.507470	+	0.861670i	$0.669419\pi$
$440$	−10.8601	+	2.90996i	−0.517736	+	0.138727i
$441$		0			0
$442$	−9.97303	+	7.76577i	−0.474369	+	0.369380i
$443$	−3.28510	−	5.68996i	−0.156080	−	0.270338i	0.777372	−	0.629041i	$-0.216552\pi$
$443$	−3.28510	−	5.68996i	−0.156080	−	0.270338i	−0.933452	+	0.358703i	$0.883219\pi$
$444$	−9.17013	−	2.45713i	−0.435195	−	0.116610i
$445$	−0.199453	−	0.345463i	−0.00945497	−	0.0163765i
$446$	−10.9609	+	18.9848i	−0.519012	+	0.898955i
$447$	−26.3343	+	26.3343i	−1.24557	+	1.24557i
$448$		0			0
$449$	−19.7570	−	5.29388i	−0.932392	−	0.249834i	−0.239518	−	0.970892i	$-0.576989\pi$
$449$	−19.7570	−	5.29388i	−0.932392	−	0.249834i	−0.692874	+	0.721058i	$0.743656\pi$
$450$	−4.17890	−	1.11973i	−0.196995	−	0.0527847i
$451$			13.7562i			0.647755i
$452$	6.63104	−	3.82843i	0.311898	−	0.180074i
$453$	13.8467	+	13.8467i	0.650575	+	0.650575i
$454$	−18.7981			−0.882241
$455$		0			0
$456$	−42.5169			−1.99103
$457$	0.506232	+	0.506232i	0.0236805	+	0.0236805i	0.718848	−	0.695167i	$-0.244670\pi$
$457$	0.506232	+	0.506232i	0.0236805	+	0.0236805i	−0.695167	+	0.718848i	$0.744670\pi$
$458$	16.0872	−	9.28795i	0.751706	−	0.433998i
$459$			6.59559i			0.307856i
$460$	1.18815	+	0.318364i	0.0553978	+	0.0148438i
$461$	−18.7893	−	5.03457i	−0.875104	−	0.234484i	−0.206811	−	0.978381i	$-0.566308\pi$
$461$	−18.7893	−	5.03457i	−0.875104	−	0.234484i	−0.668294	+	0.743897i	$0.732975\pi$
$462$		0			0
$463$	23.8616	−	23.8616i	1.10894	−	1.10894i	0.115653	−	0.993290i	$-0.463104\pi$
$463$	23.8616	−	23.8616i	1.10894	−	1.10894i	0.993290	−	0.115653i	$-0.0368962\pi$
$464$	−7.61887	+	13.1963i	−0.353697	+	0.612621i
$465$	−19.3881	−	33.5812i	−0.899101	−	1.55729i
$466$	−7.43877	−	1.99321i	−0.344594	−	0.0923338i
$467$	2.96432	+	5.13436i	0.137173	+	0.237590i	0.926425	−	0.376479i	$-0.122865\pi$
$467$	2.96432	+	5.13436i	0.137173	+	0.237590i	−0.789253	+	0.614068i	$0.789532\pi$
$468$	1.96716	−	2.60172i	0.0909321	−	0.120265i
$469$		0			0
$470$	7.16674	−	1.92032i	0.330577	−	0.0885778i
$471$	11.2766			0.519600
$472$	−23.2940			−1.07219
$473$	1.34017	−	0.359099i	0.0616213	−	0.0165114i
$474$	−3.97514	−	14.8354i	−0.182584	−	0.681414i
$475$	2.89545	−	10.8060i	0.132852	−	0.495812i
$476$		0			0
$477$	4.93812	+	8.55307i	0.226101	+	0.391618i
$478$			24.8615i			1.13714i
$479$	−5.78255	+	21.5808i	−0.264211	+	0.986050i	0.698520	+	0.715590i	$0.253842\pi$
$479$	−5.78255	+	21.5808i	−0.264211	+	0.986050i	−0.962731	+	0.270459i	$0.912824\pi$
$480$	−12.8745	−	7.43309i	−0.587637	−	0.339273i
$481$	−20.3919	−	26.1879i	−0.929791	−	1.19406i
$482$			1.42397i			0.0648599i
$483$		0			0
$484$	−2.08615	+	3.61332i	−0.0948249	+	0.164242i
$485$	6.72683	+	3.88374i	0.305450	+	0.176351i
$486$	5.64132	+	21.0537i	0.255895	+	0.955014i
$487$	−3.79944	−	3.79944i	−0.172169	−	0.172169i	0.615763	−	0.787932i	$-0.288848\pi$
$487$	−3.79944	−	3.79944i	−0.172169	−	0.172169i	−0.787932	+	0.615763i	$0.788848\pi$
$488$	−22.9973	+	6.16211i	−1.04104	+	0.278946i
$489$	3.95288	+	3.95288i	0.178756	+	0.178756i
$490$		0			0
$491$	8.53958	+	4.93033i	0.385386	+	0.222503i	0.680159	−	0.733065i	$-0.261911\pi$
$491$	8.53958	+	4.93033i	0.385386	+	0.222503i	−0.294773	+	0.955567i	$0.595244\pi$
$492$	−7.09847	+	7.09847i	−0.320024	+	0.320024i
$493$	7.53834	−	13.0568i	0.339510	−	0.588048i
$494$	−22.3058	−	16.8654i	−1.00359	−	0.758811i
$495$	6.22419	−	3.59354i	0.279757	−	0.161518i
$496$	4.94783	+	18.4655i	0.222164	+	0.829128i
$497$		0			0
$498$	1.50474	−	0.868761i	0.0674289	−	0.0389301i
$499$	−0.0722859	+	0.269775i	−0.00323596	+	0.0120768i	−0.967525	−	0.252776i	$-0.918657\pi$
$499$	−0.0722859	+	0.269775i	−0.00323596	+	0.0120768i	0.964289	+	0.264852i	$0.0853232\pi$
$500$	−2.74237	+	2.74237i	−0.122643	+	0.122643i
$501$	−4.20047	+	4.20047i	−0.187663	+	0.187663i
$502$	9.19994	−	34.3346i	0.410613	−	1.53243i
$503$	−14.3969	+	8.31203i	−0.641924	+	0.370615i	−0.785355	−	0.619045i	$-0.787520\pi$
$503$	−14.3969	+	8.31203i	−0.641924	+	0.370615i	0.143431	+	0.989660i	$0.454186\pi$
$504$		0			0
$505$	−3.57458	−	13.3405i	−0.159067	−	0.593645i
$506$	1.54551	−	0.892300i	0.0687062	−	0.0396676i
$507$	27.8341	−	7.88368i	1.23615	−	0.350126i
$508$	−1.43379	+	2.48339i	−0.0636140	+	0.110183i
$509$	28.5307	−	28.5307i	1.26460	−	1.26460i	0.315761	−	0.948839i	$-0.397740\pi$
$509$	28.5307	−	28.5307i	1.26460	−	1.26460i	0.948839	−	0.315761i	$-0.102260\pi$
$510$	−17.6021	−	10.1626i	−0.779435	−	0.450007i
$511$		0			0
$512$	17.5262	+	17.5262i	0.774556	+	0.774556i
$513$	−14.0946	+	3.77663i	−0.622291	+	0.166742i
$514$	−17.1968	−	17.1968i	−0.758519	−	0.758519i
$515$	3.24992	+	12.1289i	0.143208	+	0.534461i
$516$	0.876857	+	0.506254i	0.0386015	+	0.0222866i
$517$	−1.62333	+	2.81168i	−0.0713938	+	0.123658i
$518$		0			0
$519$		−	3.43128i		−	0.150617i
$520$	−11.1654	−	26.4231i	−0.489635	−	1.15873i
$521$	15.9440	+	9.20528i	0.698520	+	0.403291i	0.806796	−	0.590830i	$-0.201200\pi$
$521$	15.9440	+	9.20528i	0.698520	+	0.403291i	−0.108276	+	0.994121i	$0.534533\pi$
$522$	3.33853	−	12.4596i	0.146124	−	0.545341i
$523$			12.5007i			0.546617i	0.961926	+	0.273308i	$0.0881180\pi$
$523$			12.5007i			0.546617i	−0.961926	+	0.273308i	$0.911882\pi$
$524$	−0.575369	−	0.996569i	−0.0251351	−	0.0435353i
$525$		0			0
$526$	−2.59448	+	9.68274i	−0.113125	+	0.422187i
$527$	−4.89553	−	18.2704i	−0.213253	−	0.795870i
$528$	−8.68263	+	2.32650i	−0.377863	+	0.101248i
$529$	21.9622			0.954877
$530$	16.3402			0.709775
$531$	14.3830	−	3.85391i	0.624169	−	0.167246i
$532$		0			0
$533$	−34.7631	+	4.82816i	−1.50576	+	0.209131i
$534$	−0.211171	−	0.365759i	−0.00913826	−	0.0158279i
$535$	4.47307	+	1.19856i	0.193388	+	0.0518181i
$536$	−19.9533	−	34.5602i	−0.861853	−	1.49277i
$537$	−19.6666	+	34.0636i	−0.848678	+	1.46995i
$538$	−12.5705	+	12.5705i	−0.541954	+	0.541954i
$539$		0			0
$540$	−2.71996	−	0.728812i	−0.117049	−	0.0313631i
$541$	2.83805	+	0.760452i	0.122017	+	0.0326944i	0.319311	−	0.947650i	$-0.396549\pi$
$541$	2.83805	+	0.760452i	0.122017	+	0.0326944i	−0.197294	+	0.980344i	$0.563215\pi$
$542$			32.4068i			1.39199i
$543$	1.74515	−	1.00756i	0.0748916	−	0.0432387i
$544$	−5.12771	−	5.12771i	−0.219849	−	0.219849i
$545$	−25.9830			−1.11299
$546$		0			0
$547$	30.4775			1.30312			0.651561	−	0.758596i	$-0.274114\pi$
$547$	30.4775			1.30312			0.651561	+	0.758596i	$0.274114\pi$
$548$	−4.31388	−	4.31388i	−0.184280	−	0.184280i
$549$	13.1803	−	7.60965i	0.562521	−	0.324772i
$550$		−	3.13216i		−	0.133556i
$551$	32.2185	+	8.63291i	1.37255	+	0.367774i
$552$	6.68672	+	1.79170i	0.284606	+	0.0762599i
$553$		0			0
$554$	5.14372	−	5.14372i	0.218536	−	0.218536i
$555$	26.6857	−	46.2209i	1.13274	−	1.96197i
$556$	4.10058	+	7.10242i	0.173904	+	0.301210i
$557$	−2.05024	−	0.549361i	−0.0868716	−	0.0232772i	0.215121	−	0.976587i	$-0.430985\pi$
$557$	−2.05024	−	0.549361i	−0.0868716	−	0.0232772i	−0.301993	+	0.953310i	$0.597652\pi$
$558$	−8.09147	−	14.0148i	−0.342539	−	0.593295i
$559$	1.37785	+	3.26069i	0.0582767	+	0.137913i
$560$		0			0
$561$	8.59086	−	2.30191i	0.362706	−	0.0971868i
$562$	−28.7665			−1.21344
$563$	2.53466			0.106823			0.0534115	−	0.998573i	$-0.482990\pi$
$563$	2.53466			0.106823			0.0534115	+	0.998573i	$0.482990\pi$
$564$	−2.28855	+	0.613215i	−0.0963653	+	0.0258210i
$565$	11.1410	+	41.5787i	0.468705	+	1.74923i
$566$	7.18516	−	26.8154i	0.302015	−	1.12714i
$567$		0			0
$568$	17.5453	+	30.3893i	0.736184	+	1.27511i
$569$			35.0697i			1.47020i	0.677960	+	0.735099i	$0.262864\pi$
$569$			35.0697i			1.47020i	−0.677960	+	0.735099i	$0.737136\pi$
$570$	11.6382	−	43.4344i	0.487471	−	1.81927i
$571$	25.0216	+	14.4462i	1.04712	+	0.604556i	0.921842	−	0.387566i	$-0.126684\pi$
$571$	25.0216	+	14.4462i	1.04712	+	0.604556i	0.125279	+	0.992122i	$0.460017\pi$
$572$	2.18801	+	0.888145i	0.0914854	+	0.0371352i
$573$		−	52.1314i		−	2.17782i
$574$		0			0
$575$	−0.910748	+	1.57746i	−0.0379808	+	0.0657847i
$576$	−15.0370	−	8.68160i	−0.626541	−	0.361733i
$577$	4.00778	+	14.9572i	0.166846	+	0.622678i	0.997798	+	0.0663329i	$0.0211299\pi$
$577$	4.00778	+	14.9572i	0.166846	+	0.622678i	−0.830952	+	0.556345i	$0.812203\pi$
$578$	7.89012	+	7.89012i	0.328186	+	0.328186i
$579$	−25.6289	+	6.86723i	−1.06510	+	0.285392i
$580$	4.55152	+	4.55152i	0.188992	+	0.188992i
$581$		0			0
$582$	7.12204	+	4.11191i	0.295218	+	0.170444i
$583$	−5.05594	+	5.05594i	−0.209396	+	0.209396i
$584$	13.3341	−	23.0953i	0.551767	−	0.955689i
$585$	11.2657	+	14.4678i	0.465781	+	0.598169i
$586$	5.06517	−	2.92438i	0.209240	−	0.120805i
$587$	−3.18544	−	11.8882i	−0.131477	−	0.490679i	0.868511	−	0.495671i	$-0.165078\pi$
$587$	−3.18544	−	11.8882i	−0.131477	−	0.490679i	−0.999988	+	0.00499189i	$0.998411\pi$
$588$		0			0
$589$	36.2401	−	20.9232i	1.49325	−	0.862127i
$590$	6.37631	−	23.7967i	0.262508	−	0.979694i
$591$	−16.3361	+	16.3361i	−0.671979	+	0.671979i
$592$	−18.6057	+	18.6057i	−0.764690	+	0.764690i
$593$	8.83310	−	32.9656i	0.362732	−	1.35373i	−0.507738	−	0.861512i	$-0.669518\pi$
$593$	8.83310	−	32.9656i	0.362732	−	1.35373i	0.870470	−	0.492222i	$-0.163815\pi$
$594$	−3.53804	+	2.04269i	−0.145168	+	0.0838125i
$595$		0			0
$596$	−2.00741	−	7.49177i	−0.0822268	−	0.306875i
$597$	−7.66081	+	4.42297i	−0.313536	+	0.181020i
$598$	2.79736	+	3.59245i	0.114392	+	0.146906i
$599$	−5.99292	+	10.3800i	−0.244864	+	0.424117i	−0.962093	−	0.272720i	$-0.912077\pi$
$599$	−5.99292	+	10.3800i	−0.244864	+	0.424117i	0.717229	+	0.696837i	$0.245410\pi$
$600$	8.59127	−	8.59127i	0.350737	−	0.350737i
$601$	−17.2242	−	9.94437i	−0.702588	−	0.405639i	0.105723	−	0.994396i	$-0.466284\pi$
$601$	−17.2242	−	9.94437i	−0.702588	−	0.405639i	−0.808311	+	0.588756i	$0.799618\pi$
$602$		0			0
$603$	18.0382	+	18.0382i	0.734570	+	0.734570i
$604$	−3.93922	+	1.05551i	−0.160284	+	0.0429481i
$605$	−16.5858	−	16.5858i	−0.674309	−	0.674309i
$606$	−3.78459	−	14.1243i	−0.153739	−	0.573760i
$607$	7.94179	+	4.58519i	0.322347	+	0.186107i	0.652438	−	0.757842i	$-0.273746\pi$
$607$	7.94179	+	4.58519i	0.322347	+	0.186107i	−0.330091	+	0.943949i	$0.607079\pi$
$608$	8.02164	−	13.8939i	0.325321	−	0.563472i
$609$		0			0
$610$		−	25.1803i		−	1.01952i
$611$	−7.67511	−	3.11543i	−0.310502	−	0.126037i
$612$	2.21566	+	1.27921i	0.0895626	+	0.0517090i
$613$	4.92157	−	18.3676i	0.198780	−	0.741859i	−0.792475	−	0.609904i	$-0.791208\pi$
$613$	4.92157	−	18.3676i	0.198780	−	0.741859i	0.991256	−	0.131955i	$-0.0421254\pi$
$614$			6.62606i			0.267406i
$615$	−28.2180	−	48.8750i	−1.13786	−	1.97083i
$616$		0			0
$617$	6.74741	−	25.1817i	0.271641	−	1.01378i	−0.686419	−	0.727207i	$-0.740818\pi$
$617$	6.74741	−	25.1817i	0.271641	−	1.01378i	0.958059	−	0.286570i	$-0.0925151\pi$
$618$	3.44085	+	12.8414i	0.138411	+	0.516558i
$619$	1.48444	−	0.397756i	0.0596649	−	0.0159872i	−0.228863	−	0.973459i	$-0.573501\pi$
$619$	1.48444	−	0.397756i	0.0596649	−	0.0159872i	0.288528	+	0.957471i	$0.406834\pi$
$620$	8.07550			0.324320
$621$	2.37584			0.0953391
$622$	3.03362	−	0.812855i	0.121637	−	0.0325925i
$623$		0			0
$624$	−8.92670	−	21.1252i	−0.357354	−	0.845683i
$625$	−15.3715	−	26.6243i	−0.614861	−	1.06497i
$626$	6.38794	+	1.71164i	0.255314	+	0.0684111i
$627$	9.83825	+	17.0404i	0.392902	+	0.680526i
$628$	−1.17423	+	2.03383i	−0.0468570	+	0.0811587i
$629$	18.4091	−	18.4091i	0.734017	−	0.734017i
$630$		0			0
$631$	5.46012	+	1.46304i	0.217364	+	0.0582425i	0.365858	−	0.930671i	$-0.380776\pi$
$631$	5.46012	+	1.46304i	0.217364	+	0.0582425i	−0.148493	+	0.988913i	$0.547442\pi$
$632$	16.4230	+	4.40053i	0.653271	+	0.175043i
$633$			11.0228i			0.438117i
$634$	13.6135	−	7.85973i	0.540659	−	0.312150i
$635$	−11.3992	−	11.3992i	−0.452365	−	0.452365i
$636$	−5.21792			−0.206904
$637$		0			0
$638$	9.33866			0.369721
$639$	−15.8612	−	15.8612i	−0.627461	−	0.627461i
$640$	−13.3077	+	7.68321i	−0.526034	+	0.303706i
$641$		−	2.17816i		−	0.0860321i	−0.999074	−	0.0430160i	$-0.986303\pi$
$641$		−	2.17816i		−	0.0860321i	0.999074	−	0.0430160i	$-0.0136967\pi$
$642$	4.73587	+	1.26897i	0.186910	+	0.0500824i
$643$	23.5550	+	6.31154i	0.928918	+	0.248903i	0.691393	−	0.722479i	$-0.256997\pi$
$643$	23.5550	+	6.31154i	0.928918	+	0.248903i	0.237525	+	0.971381i	$0.423664\pi$
$644$		0			0
$645$	−4.02494	+	4.02494i	−0.158482	+	0.158482i
$646$	10.9673	−	18.9959i	0.431501	−	0.747382i
$647$	−12.8514	−	22.2592i	−0.505239	−	0.875100i	−0.999982	−	0.00606025i	$-0.998071\pi$
$647$	−12.8514	−	22.2592i	−0.505239	−	0.875100i	0.494742	−	0.869040i	$-0.335262\pi$
$648$	−32.5802	−	8.72984i	−1.27987	−	0.342941i
$649$	5.39015	+	9.33602i	0.211582	+	0.366471i
$650$	7.91522	−	1.09932i	0.310460	−	0.0431191i
$651$		0			0
$652$	−1.12455	+	0.301321i	−0.0440406	+	0.0118006i
$653$	12.2898			0.480938			0.240469	−	0.970657i	$-0.422699\pi$
$653$	12.2898			0.480938			0.240469	+	0.970657i	$0.422699\pi$
$654$	−27.5096			−1.07571
$655$	6.24880	−	1.67436i	0.244161	−	0.0654227i
$656$	7.20122	+	26.8753i	0.281160	+	1.04930i
$657$	−4.41215	+	16.4664i	−0.172134	+	0.642414i
$658$		0			0
$659$	−22.5477	−	39.0538i	−0.878336	−	1.52132i	−0.853167	−	0.521639i	$-0.825321\pi$
$659$	−22.5477	−	39.0538i	−0.878336	−	1.52132i	−0.0251690	−	0.999683i	$-0.508012\pi$
$660$			3.79716i			0.147804i
$661$	3.90501	−	14.5737i	0.151887	−	0.566851i	−0.847465	−	0.530852i	$-0.821872\pi$
$661$	3.90501	−	14.5737i	0.151887	−	0.566851i	0.999352	−	0.0359990i	$-0.0114613\pi$
$662$	9.60929	+	5.54792i	0.373475	+	0.215626i
$663$	8.83235	+	20.9019i	0.343020	+	0.811762i
$664$			1.92346i			0.0746446i
$665$		0			0
$666$	11.1371	−	19.2899i	0.431552	−	0.747470i
$667$	−4.70327	−	2.71543i	−0.182111	−	0.105142i
$668$	−0.320194	−	1.19498i	−0.0123887	−	0.0462351i
$669$	27.8275	+	27.8275i	1.07588	+	1.07588i
$670$	40.7679	−	10.9237i	1.57500	−	0.422020i
$671$	7.79121	+	7.79121i	0.300776	+	0.300776i
$672$		0			0
$673$	10.7821	+	6.22503i	0.415618	+	0.239957i	0.693201	−	0.720744i	$-0.256200\pi$
$673$	10.7821	+	6.22503i	0.415618	+	0.239957i	−0.277582	+	0.960702i	$0.589533\pi$
$674$	7.34804	−	7.34804i	0.283036	−	0.283036i
$675$	2.08492	−	3.61119i	0.0802487	−	0.138995i
$676$	−1.47647	+	5.84101i	−0.0567872	+	0.224654i
$677$	−32.6889	+	18.8729i	−1.25634	+	0.725346i	−0.972360	−	0.233485i	$-0.924987\pi$
$677$	−32.6889	+	18.8729i	−1.25634	+	0.725346i	−0.283976	+	0.958831i	$0.591654\pi$
$678$	11.7955	+	44.0215i	0.453005	+	1.69064i
$679$		0			0
$680$	19.4858	−	11.2501i	0.747245	−	0.431422i
$681$	−8.73427	+	32.5967i	−0.334698	+	1.24911i
$682$	8.28452	−	8.28452i	0.317231	−	0.317231i
$683$	−12.7501	+	12.7501i	−0.487870	+	0.487870i	−0.907634	−	0.419763i	$-0.862113\pi$
$683$	−12.7501	+	12.7501i	−0.487870	+	0.487870i	0.419763	+	0.907634i	$0.362113\pi$
$684$	−1.46495	+	5.46727i	−0.0560138	+	0.209046i
$685$	29.7023	−	17.1486i	1.13487	−	0.655216i
$686$		0			0
$687$	−8.63101	−	32.2114i	−0.329294	−	1.22894i
$688$	2.43029	−	1.40313i	0.0926541	−	0.0534938i
$689$	−14.5513	−	11.0022i	−0.554361	−	0.419152i
$690$	−3.66073	+	6.34057i	−0.139362	+	0.241382i
$691$	13.2542	−	13.2542i	0.504212	−	0.504212i	−0.408532	−	0.912744i	$-0.633959\pi$
$691$	13.2542	−	13.2542i	0.504212	−	0.504212i	0.912744	+	0.408532i	$0.133959\pi$
$692$	0.618858	+	0.357298i	0.0235255	+	0.0135824i
$693$		0			0
$694$	24.1712	+	24.1712i	0.917525	+	0.917525i
$695$	−44.5344	+	11.9330i	−1.68929	+	0.452643i
$696$	25.6152	+	25.6152i	0.970943	+	0.970943i
$697$	−7.12510	−	26.5912i	−0.269883	−	1.00722i
$698$	−38.1000	−	21.9970i	−1.44210	−	0.832599i
$699$	−6.91262	+	11.9730i	−0.261459	+	0.452861i
$700$		0			0
$701$			12.1851i			0.460223i	0.973164	+	0.230112i	$0.0739092\pi$
$701$			12.1851i			0.460223i	−0.973164	+	0.230112i	$0.926091\pi$
$702$	−6.40383	−	8.22398i	−0.241697	−	0.310394i
$703$	49.8807	+	28.7986i	1.88129	+	1.08616i
$704$	3.25350	−	12.1422i	0.122621	−	0.457628i
$705$		−	13.3197i		−	0.501647i
$706$	−4.50170	−	7.79717i	−0.169424	−	0.293450i
$707$		0			0
$708$	−2.03614	+	7.59899i	−0.0765229	+	0.285587i
$709$	−0.401518	−	1.49849i	−0.0150793	−	0.0562768i	0.957976	−	0.286848i	$-0.0926073\pi$
$709$	−0.401518	−	1.49849i	−0.0150793	−	0.0562768i	−0.973056	+	0.230571i	$0.925941\pi$
$710$	−35.8478	+	9.60540i	−1.34535	+	0.360484i
$711$	−10.8685			−0.407601
$712$	0.467538			0.0175217
$713$	−6.58129	+	1.76345i	−0.246471	+	0.0660417i
$714$		0			0
$715$	−8.00648	+	10.5892i	−0.299425	+	0.396013i
$716$	−4.09576	−	7.09406i	−0.153066	−	0.265118i
$717$	43.1109	+	11.5515i	1.61000	+	0.431399i
$718$	−9.75695	−	16.8995i	−0.364126	−	0.630685i
$719$	−11.1032	+	19.2313i	−0.414080	+	0.717207i	−0.995331	−	0.0965166i	$-0.969230\pi$
$719$	−11.1032	+	19.2313i	−0.414080	+	0.717207i	0.581252	+	0.813724i	$0.302563\pi$
$720$	10.2789	−	10.2789i	0.383073	−	0.383073i
$721$		0			0
$722$	24.1240	+	6.46400i	0.897802	+	0.240565i
$723$	2.46922	+	0.661624i	0.0918311	+	0.0246061i
$724$			0.419669i			0.0155969i
$725$	−8.25472	+	4.76587i	−0.306573	+	0.177000i
$726$	−17.5602	−	17.5602i	−0.651722	−	0.651722i
$727$	−20.1830			−0.748547			−0.374274	−	0.927318i	$-0.622108\pi$
$727$	−20.1830			−0.748547			−0.374274	+	0.927318i	$0.622108\pi$
$728$		0			0
$729$	5.99197			0.221925
$730$	19.9437	+	19.9437i	0.738150	+	0.738150i
$731$	−2.40461	+	1.38830i	−0.0889376	+	0.0513481i
$732$			8.04083i			0.297197i
$733$	−3.63806	−	0.974815i	−0.134375	−	0.0360056i	0.191005	−	0.981589i	$-0.438825\pi$
$733$	−3.63806	−	0.974815i	−0.134375	−	0.0360056i	−0.325380	+	0.945583i	$0.605492\pi$
$734$	0.387440	+	0.103814i	0.0143007	+	0.00383185i
$735$		0			0
$736$	−1.84708	+	1.84708i	−0.0680844	+	0.0680844i
$737$	−9.23426	+	15.9942i	−0.340148	+	0.589154i
$738$	−11.7766	−	20.3976i	−0.433501	−	0.750846i
$739$	16.7825	+	4.49685i	0.617353	+	0.165419i	0.553924	−	0.832567i	$-0.313130\pi$
$739$	16.7825	+	4.49685i	0.617353	+	0.165419i	0.0634288	+	0.997986i	$0.479796\pi$
$740$	5.55754	+	9.62594i	0.204299	+	0.353856i
$741$	−39.6093	+	30.8429i	−1.45509	+	1.13304i
$742$		0			0
$743$	3.38542	−	0.907121i	0.124199	−	0.0332790i	−0.196184	−	0.980567i	$-0.562855\pi$
$743$	3.38542	−	0.907121i	0.124199	−	0.0332790i	0.320383	+	0.947288i	$0.396188\pi$
$744$	45.4476			1.66619
$745$	43.6030			1.59749
$746$	−38.6598	+	10.3589i	−1.41544	+	0.379265i
$747$	−0.318229	−	1.18765i	−0.0116434	−	0.0434538i
$748$	−0.479395	+	1.78913i	−0.0175284	+	0.0654169i
$749$		0			0
$750$	−11.5420	−	19.9914i	−0.421455	−	0.729982i
$751$			1.77791i			0.0648770i	0.999474	+	0.0324385i	$0.0103273\pi$
$751$			1.77791i			0.0648770i	−0.999474	+	0.0324385i	$0.989673\pi$
$752$	−1.69958	+	6.34293i	−0.0619774	+	0.231303i
$753$	−55.2630	−	31.9061i	−2.01390	−	1.16272i
$754$	3.27768	+	23.5996i	0.119366	+	0.859445i
$755$		−	22.9267i		−	0.834389i
$756$		0			0
$757$	−24.7027	+	42.7863i	−0.897834	+	1.55509i	−0.0675762	+	0.997714i	$0.521527\pi$
$757$	−24.7027	+	42.7863i	−0.897834	+	1.55509i	−0.830258	+	0.557380i	$0.811807\pi$
$758$	−14.8115	−	8.55140i	−0.537977	−	0.310601i
$759$	−0.829187	−	3.09457i	−0.0300976	−	0.112326i
$760$	35.1987	+	35.1987i	1.27679	+	1.27679i
$761$	−14.3625	+	3.84841i	−0.520639	+	0.139505i	−0.509562	−	0.860434i	$-0.670193\pi$
$761$	−14.3625	+	3.84841i	−0.520639	+	0.139505i	−0.0110771	+	0.999939i	$0.503526\pi$
$762$	−12.0690	−	12.0690i	−0.437213	−	0.437213i
$763$		0			0
$764$	9.40231	+	5.42843i	0.340164	+	0.196394i
$765$	−10.1703	+	10.1703i	−0.367708	+	0.367708i
$766$	−10.4249	+	18.0565i	−0.376669	+	0.652409i
$767$	−21.7011	+	16.8981i	−0.783580	+	0.610156i
$768$	20.1953	−	11.6598i	0.728735	−	0.420735i
$769$	−7.72722	−	28.8384i	−0.278651	−	1.03994i	−0.953355	−	0.301850i	$-0.902396\pi$
$769$	−7.72722	−	28.8384i	−0.278651	−	1.03994i	0.674705	−	0.738088i	$-0.264271\pi$
$770$		0			0
$771$	−37.8102	+	21.8297i	−1.36170	+	0.786179i
$772$	1.43016	−	5.33745i	0.0514727	−	0.192099i
$773$	26.2162	−	26.2162i	0.942932	−	0.942932i	−0.0555251	−	0.998457i	$-0.517683\pi$
$773$	26.2162	−	26.2162i	0.942932	−	0.942932i	0.998457	+	0.0555251i	$0.0176833\pi$
$774$	−1.67978	+	1.67978i	−0.0603784	+	0.0603784i
$775$	−3.09504	+	11.5508i	−0.111177	+	0.414919i
$776$	−7.88418	+	4.55193i	−0.283026	+	0.163405i
$777$		0			0
$778$	−5.73671	−	21.4097i	−0.205671	−	0.767575i
$779$	52.7449	−	30.4523i	1.88978	−	1.09107i
$780$	−9.59573	+	1.33273i	−0.343582	+	0.0477193i
$781$	8.11984	−	14.0640i	0.290551	−	0.503248i
$782$	−2.52535	+	2.52535i	−0.0903063	+	0.0903063i
$783$	10.7669	+	6.21628i	0.384778	+	0.222152i
$784$		0			0
$785$	−9.33567	−	9.33567i	−0.333204	−	0.333204i
$786$	6.61593	−	1.77273i	0.235982	−	0.0632313i
$787$	−32.1979	−	32.1979i	−1.14773	−	1.14773i	−0.986998	−	0.160734i	$-0.948614\pi$
$787$	−32.1979	−	32.1979i	−1.14773	−	1.14773i	−0.160734	−	0.986998i	$-0.551386\pi$
$788$	−1.24527	−	4.64743i	−0.0443611	−	0.165558i
$789$	15.5848	+	8.99787i	0.554833	+	0.320333i
$790$	−8.99097	+	15.5728i	−0.319885	+	0.554056i
$791$		0			0
$792$			8.42361i			0.299320i
$793$	−16.9545	+	22.4236i	−0.602071	+	0.796285i
$794$	7.11979	+	4.11061i	0.252672	+	0.145880i
$795$	7.59225	−	28.3346i	0.269269	−	1.00493i
$796$		−	1.84225i		−	0.0652967i
$797$	5.85462	+	10.1405i	0.207381	+	0.359195i	0.950889	−	0.309533i	$-0.100173\pi$
$797$	5.85462	+	10.1405i	0.207381	+	0.359195i	−0.743507	+	0.668728i	$0.766839\pi$
$798$		0			0
$799$	1.68162	−	6.27589i	0.0594914	−	0.222025i
$800$	1.18659	+	4.42841i	0.0419523	+	0.156568i
$801$	−0.288683	+	0.0773525i	−0.0102001	+	0.00273312i
$802$	27.3289			0.965017
$803$	−12.3418			−0.435533
$804$	−13.0184	+	3.48826i	−0.459123	+	0.123022i
$805$		0			0
$806$	23.8434	+	18.0280i	0.839847	+	0.635008i
$807$	15.9571	+	27.6385i	0.561716	+	0.972921i
$808$	15.6358	+	4.18959i	0.550064	+	0.147389i
$809$	19.8661	+	34.4091i	0.698456	+	1.20976i	0.969002	+	0.247054i	$0.0794624\pi$
$809$	19.8661	+	34.4091i	0.698456	+	1.20976i	−0.270546	+	0.962707i	$0.587204\pi$
$810$	17.8365	−	30.8937i	0.626709	−	1.08549i
$811$	−3.48546	+	3.48546i	−0.122391	+	0.122391i	−0.765649	−	0.643258i	$-0.777582\pi$
$811$	−3.48546	+	3.48546i	−0.122391	+	0.122391i	0.643258	+	0.765649i	$0.277582\pi$
$812$		0			0
$813$	56.1947	+	15.0573i	1.97084	+	0.528084i
$814$	15.5765	+	4.17370i	0.545955	+	0.146288i
$815$		−	6.54500i		−	0.229261i
$816$	15.5788	−	8.99442i	0.545367	−	0.314868i
$817$	−4.34364	−	4.34364i	−0.151965	−	0.151965i
$818$	−20.5190			−0.717432
$819$		0			0
$820$	11.7533			0.410444
$821$	20.1996	+	20.1996i	0.704971	+	0.704971i	0.965473	−	0.260502i	$-0.0838882\pi$
$821$	20.1996	+	20.1996i	0.704971	+	0.704971i	−0.260502	+	0.965473i	$0.583888\pi$
$822$	31.4474	−	18.1561i	1.09685	−	0.633268i
$823$			39.5422i			1.37835i	0.724593	+	0.689177i	$0.242028\pi$
$823$			39.5422i			1.37835i	−0.724593	+	0.689177i	$0.757972\pi$
$824$	−14.2156	−	3.80906i	−0.495225	−	0.132695i
$825$	−5.43129	−	1.45531i	−0.189093	−	0.0506673i
$826$		0			0
$827$	−30.8511	+	30.8511i	−1.07280	+	1.07280i	−0.0756634	+	0.997133i	$0.524107\pi$
$827$	−30.8511	+	30.8511i	−1.07280	+	1.07280i	−0.997133	+	0.0756634i	$0.975893\pi$
$828$	0.460792	−	0.798116i	0.0160136	−	0.0277364i
$829$	21.4990	+	37.2373i	0.746690	+	1.29330i	0.949401	+	0.314066i	$0.101691\pi$
$829$	21.4990	+	37.2373i	0.746690	+	1.29330i	−0.202711	+	0.979239i	$0.564975\pi$
$830$	−1.96497	−	0.526511i	−0.0682049	−	0.0182755i
$831$	−6.52947	−	11.3094i	−0.226505	−	0.392318i
$832$	31.8264	+	3.96019i	1.10338	+	0.137295i
$833$		0			0
$834$	−47.1509	+	12.6340i	−1.63270	+	0.437481i
$835$	6.95493			0.240685
$836$	−4.09781			−0.141726
$837$	15.0662	−	4.03696i	0.520762	−	0.139538i
$838$	−8.64564	−	32.2660i	−0.298659	−	1.11461i
$839$	−12.0010	+	44.7884i	−0.414321	+	1.54627i	0.371872	+	0.928284i	$0.378716\pi$
$839$	−12.0010	+	44.7884i	−0.414321	+	1.54627i	−0.786193	+	0.617982i	$0.787951\pi$
$840$		0			0
$841$	0.290370	+	0.502936i	0.0100128	+	0.0173426i
$842$		−	20.7753i		−	0.715965i
$843$	−13.3659	+	49.8823i	−0.460346	+	1.71804i
$844$	−1.98805	−	1.14780i	−0.0684315	−	0.0395089i
$845$	−29.5699	−	16.5165i	−1.01723	−	0.568183i
$846$		−	5.55885i		−	0.191117i
$847$		0			0
$848$	−7.23098	+	12.5244i	−0.248313	+	0.430091i
$849$	−43.1605	−	24.9187i	−1.48126	−	0.855209i
$850$	1.62232	+	6.05457i	0.0556450	+	0.207670i
$851$	−6.63124	−	6.63124i	−0.227316	−	0.227316i
$852$	11.4473	−	3.06729i	0.392177	−	0.105084i
$853$	3.22439	+	3.22439i	0.110401	+	0.110401i	0.760149	−	0.649748i	$-0.225126\pi$
$853$	3.22439	+	3.22439i	0.110401	+	0.110401i	−0.649748	+	0.760149i	$0.725126\pi$
$854$		0			0
$855$	−27.5571	−	15.9101i	−0.942434	−	0.544115i
$856$	−3.83790	+	3.83790i	−0.131177	+	0.131177i
$857$	−12.4518	+	21.5671i	−0.425345	+	0.736719i	−0.996453	−	0.0841565i	$-0.973180\pi$
$857$	−12.4518	+	21.5671i	−0.425345	+	0.736719i	0.571108	+	0.820875i	$0.306514\pi$
$858$	−8.47688	+	11.2113i	−0.289396	+	0.382748i
$859$	−25.4805	+	14.7112i	−0.869383	+	0.501939i	−0.867143	−	0.498059i	$-0.834046\pi$
$859$	−25.4805	+	14.7112i	−0.869383	+	0.501939i	−0.00224010	+	0.999997i	$0.500713\pi$
$860$	−0.306814	−	1.14505i	−0.0104623	−	0.0390457i
$861$		0			0
$862$	−6.67673	+	3.85481i	−0.227410	+	0.131295i
$863$	−4.22635	+	15.7730i	−0.143867	+	0.536918i	0.855936	+	0.517081i	$0.172981\pi$
$863$	−4.22635	+	15.7730i	−0.143867	+	0.536918i	−0.999803	+	0.0198370i	$0.993685\pi$
$864$	4.22842	−	4.22842i	0.143854	−	0.143854i
$865$	−2.84068	+	2.84068i	−0.0965859	+	0.0965859i
$866$	−3.56636	+	13.3098i	−0.121190	+	0.452286i
$867$	17.3478	−	10.0158i	0.589162	−	0.340153i
$868$		0			0
$869$	−2.03653	−	7.60044i	−0.0690846	−	0.257827i
$870$	−33.1797	+	19.1563i	−1.12490	+	0.649459i
$871$	−43.6597	−	17.7221i	−1.47935	−	0.600490i
$872$	15.2267	−	26.3734i	0.515641	−	0.893117i
$873$	4.11502	−	4.11502i	0.139272	−	0.139272i
$874$	−6.84262	−	3.95059i	−0.231455	−	0.133631i
$875$		0			0
$876$	−6.36861	−	6.36861i	−0.215175	−	0.215175i
$877$	32.8267	−	8.79590i	1.10848	−	0.297016i	0.342267	−	0.939603i	$-0.388805\pi$
$877$	32.8267	−	8.79590i	1.10848	−	0.297016i	0.766213	+	0.642587i	$0.222139\pi$
$878$	18.6394	+	18.6394i	0.629050	+	0.629050i
$879$	−2.71753	−	10.1420i	−0.0916601	−	0.342080i
$880$	9.11420	+	5.26209i	0.307240	+	0.177385i
$881$	−3.17840	+	5.50515i	−0.107083	+	0.185473i	−0.914587	−	0.404388i	$-0.867484\pi$
$881$	−3.17840	+	5.50515i	−0.107083	+	0.185473i	0.807504	+	0.589862i	$0.200818\pi$
$882$		0			0
$883$		−	19.8386i		−	0.667623i	−0.942640	−	0.333811i	$-0.891665\pi$
$883$		−	19.8386i		−	0.667623i	0.942640	−	0.333811i	$-0.108335\pi$
$884$	−4.68953	−	0.583523i	−0.157726	−	0.0196260i
$885$	−38.3018	−	22.1135i	−1.28750	−	0.743339i
$886$	−2.10790	+	7.86677i	−0.0708161	+	0.264289i
$887$			1.06844i			0.0358749i	0.999839	+	0.0179374i	$0.00570997\pi$
$887$			1.06844i			0.0358749i	−0.999839	+	0.0179374i	$0.994290\pi$
$888$	31.2769	+	54.1732i	1.04959	+	1.81793i
$889$		0			0
$890$	−0.127980	+	0.477627i	−0.00428989	+	0.0160101i
$891$	4.04011	+	15.0779i	0.135349	+	0.505128i
$892$	−7.91659	+	2.12124i	−0.265067	+	0.0710245i
$893$	14.3743			0.481018
$894$	46.1648			1.54398
$895$	44.4820	−	11.9189i	1.48687	−	0.398406i
$896$		0			0
$897$	7.52920	−	3.18155i	0.251393	−	0.106229i
$898$	12.6772	+	21.9575i	0.423043	+	0.732732i
$899$	−34.4393	−	9.22799i	−1.14862	−	0.307771i
$900$	−0.808738	−	1.40078i	−0.0269579	−	0.0466925i
$901$	7.15456	−	12.3921i	0.238353	−	0.412839i
$902$	12.0575	−	12.0575i	0.401472	−	0.401472i
$903$		0			0
$904$	−48.7323	−	13.0578i	−1.62081	−	0.434296i
$905$	−2.27891	−	0.610631i	−0.0757534	−	0.0202981i
$906$		−	24.2737i		−	0.806440i
$907$	2.07736	−	1.19936i	0.0689775	−	0.0398242i	−0.465115	−	0.885250i	$-0.653987\pi$
$907$	2.07736	−	1.19936i	0.0689775	−	0.0398242i	0.534092	+	0.845426i	$0.320654\pi$
$908$	−4.96958	−	4.96958i	−0.164921	−	0.164921i
$909$	−10.3475			−0.343206
$910$		0			0
$911$	−6.07001			−0.201108			−0.100554	−	0.994932i	$-0.532062\pi$
$911$	−6.07001			−0.201108			−0.100554	+	0.994932i	$0.532062\pi$
$912$	28.1413	+	28.1413i	0.931850	+	0.931850i
$913$	0.770903	−	0.445081i	0.0255132	−	0.0147300i
$914$		−	0.887440i		−	0.0293539i
$915$	−43.6637	−	11.6997i	−1.44348	−	0.386779i
$916$	6.70832	+	1.79749i	0.221649	+	0.0593907i
$917$		0			0
$918$	5.78113	−	5.78113i	0.190806	−	0.190806i
$919$	0.559898	−	0.969772i	0.0184693	−	0.0319898i	−0.856643	−	0.515910i	$-0.827454\pi$
$919$	0.559898	−	0.969772i	0.0184693	−	0.0319898i	0.875112	+	0.483920i	$0.160787\pi$
$920$	−4.05247	−	7.01909i	−0.133606	−	0.231412i
$921$	11.4899	+	3.07870i	0.378604	+	0.101447i
$922$	12.0562	+	20.8820i	0.397050	+	0.687712i
$923$	38.3907	+	15.5833i	1.26365	+	0.512931i
$924$		0			0
$925$	−15.8985	+	4.25999i	−0.522740	+	0.140068i
$926$	−41.8301			−1.37462
$927$	9.40770			0.308989
$928$	−13.2035	+	3.53787i	−0.433426	+	0.116136i
$929$	8.03463	+	29.9857i	0.263608	+	0.983798i	0.963097	+	0.269155i	$0.0867442\pi$
$929$	8.03463	+	29.9857i	0.263608	+	0.983798i	−0.699489	+	0.714643i	$0.746589\pi$
$930$	−12.4404	+	46.4284i	−0.407938	+	1.52245i
$931$		0			0
$932$	−1.43962	−	2.49349i	−0.0471562	−	0.0816770i
$933$		−	5.63809i		−	0.184583i
$934$	1.90207	−	7.09862i	0.0622376	−	0.232274i
$935$	−9.01787	−	5.20647i	−0.294916	−	0.170270i
$936$	−21.2872	+	2.95652i	−0.695793	+	0.0966369i
$937$			7.31506i			0.238973i	0.992836	+	0.119486i	$0.0381248\pi$
$937$			7.31506i			0.238973i	−0.992836	+	0.119486i	$0.961875\pi$
$938$		0			0
$939$	5.93612	−	10.2817i	0.193718	−	0.335529i
$940$	2.40230	+	1.38697i	0.0783545	+	0.0452380i
$941$	−0.629247	−	2.34838i	−0.0205129	−	0.0765550i	0.954911	−	0.296893i	$-0.0959506\pi$
$941$	−0.629247	−	2.34838i	−0.0205129	−	0.0765550i	−0.975424	+	0.220338i	$0.929284\pi$
$942$	−9.88415	−	9.88415i	−0.322043	−	0.322043i
$943$	−9.57860	+	2.56658i	−0.311922	+	0.0835793i
$944$	15.4179	+	15.4179i	0.501812	+	0.501812i
$945$		0			0
$946$	−1.48944	−	0.859928i	−0.0484258	−	0.0279587i
$947$	16.4252	−	16.4252i	0.533748	−	0.533748i	−0.387938	−	0.921685i	$-0.626813\pi$
$947$	16.4252	−	16.4252i	0.533748	−	0.533748i	0.921685	+	0.387938i	$0.126813\pi$
$948$	2.87108	−	4.97286i	0.0932485	−	0.161511i
$949$	−4.33173	−	31.1888i	−0.140614	−	1.01243i
$950$	−12.0095	+	6.93369i	−0.389640	+	0.224959i
$951$	−7.30381	−	27.2582i	−0.236842	−	0.883907i
$952$		0			0
$953$	−33.8286	+	19.5310i	−1.09582	+	0.632670i	−0.935119	−	0.354334i	$-0.884708\pi$
$953$	−33.8286	+	19.5310i	−1.09582	+	0.632670i	−0.160697	+	0.987004i	$0.551374\pi$
$954$	3.16856	−	11.8252i	0.102586	−	0.382856i
$955$	−43.1584	+	43.1584i	−1.39657	+	1.39657i
$956$	−6.57252	+	6.57252i	−0.212571	+	0.212571i
$957$	4.33906	−	16.1936i	0.140262	−	0.523465i
$958$	23.9844	−	13.8474i	0.774900	−	0.447388i
$959$		0			0
$960$	13.3478	+	49.8145i	0.430797	+	1.60776i
$961$	−11.8914	+	6.86551i	−0.383594	+	0.221468i
$962$	−5.08026	+	40.8279i	−0.163794	+	1.31635i
$963$	1.73476	−	3.00470i	0.0559019	−	0.0968249i
$964$	−0.376448	+	0.376448i	−0.0121246	+	0.0121246i
$965$	26.9027	+	15.5323i	0.866030	+	0.500003i
$966$		0			0
$967$	−37.5795	−	37.5795i	−1.20848	−	1.20848i	−0.971520	−	0.236956i	$-0.923850\pi$
$967$	−37.5795	−	37.5795i	−1.20848	−	1.20848i	−0.236956	−	0.971520i	$-0.576150\pi$
$968$	26.5547	−	7.11531i	0.853500	−	0.228695i
$969$	−27.8438	−	27.8438i	−0.894472	−	0.894472i
$970$	−2.49202	−	9.30033i	−0.0800138	−	0.298616i
$971$	25.4016	+	14.6656i	0.815177	+	0.470642i	0.848750	−	0.528794i	$-0.177356\pi$
$971$	25.4016	+	14.6656i	0.815177	+	0.470642i	−0.0335738	+	0.999436i	$0.510689\pi$
$972$	−4.07450	+	7.05723i	−0.130690	+	0.226361i
$973$		0			0
$974$			6.66054i			0.213417i
$975$	1.77141	−	14.2361i	0.0567306	−	0.455920i
$976$	19.3002	+	11.1430i	0.617783	+	0.356677i
$977$	−14.2072	+	53.0221i	−0.454530	+	1.69633i	0.234937	+	0.972011i	$0.424512\pi$
$977$	−14.2072	+	53.0221i	−0.454530	+	1.69633i	−0.689467	+	0.724318i	$0.742155\pi$
$978$		−	6.92953i		−	0.221582i
$979$	−0.108187	−	0.187385i	−0.00345766	−	0.00598884i
$980$		0			0
$981$	−5.03841	+	18.8036i	−0.160864	+	0.600353i
$982$	−3.16357	−	11.8066i	−0.100953	−	0.376763i
$983$	−41.7323	+	11.1821i	−1.33105	+	0.356654i	−0.853107	−	0.521735i	$-0.825285\pi$
$983$	−41.7323	+	11.1821i	−1.33105	+	0.356654i	−0.477945	+	0.878390i	$0.658618\pi$
$984$	66.1458			2.10865
$985$	27.0486			0.861841
$986$	−18.0519	+	4.83701i	−0.574891	+	0.154042i
$987$		0			0
$988$	−1.43825	−	10.3555i	−0.0457569	−	0.329453i
$989$	0.500088	+	0.866178i	0.0159019	+	0.0275429i
$990$	−8.60539	−	2.30581i	−0.273497	−	0.0732834i
$991$	−15.3304	−	26.5530i	−0.486986	−	0.843484i	0.512902	−	0.858447i	$-0.328570\pi$
$991$	−15.3304	−	26.5530i	−0.486986	−	0.843484i	−0.999888	+	0.0149629i	$0.995237\pi$
$992$	−8.57459	+	14.8516i	−0.272243	+	0.471539i
$993$	14.0851	−	14.0851i	0.446978	−	0.446978i
$994$		0			0
$995$	10.0039	+	2.68053i	0.317144	+	0.0849785i
$996$	0.627471	+	0.168130i	0.0198822	+	0.00532742i
$997$		−	32.7982i		−	1.03873i	−0.854552	−	0.519365i	$-0.826168\pi$
$997$		−	32.7982i		−	1.03873i	0.854552	−	0.519365i	$-0.173832\pi$
$998$	0.299821	−	0.173102i	0.00949068	−	0.00547944i
$999$	15.1805	+	15.1805i	0.480290	+	0.480290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bb.a.423.3		28
7.2	even	3		91.2.w.a.33.3	✓	28
7.3	odd	6		637.2.bd.b.293.5		28
7.4	even	3		637.2.bd.a.293.5		28
7.5	odd	6		637.2.x.a.215.3		28
7.6	odd	2		91.2.ba.a.59.3	yes	28
13.2	odd	12		637.2.x.a.80.3		28
21.2	odd	6		819.2.gh.b.397.5		28
21.20	even	2		819.2.et.b.514.5		28
91.2	odd	12		91.2.ba.a.54.3	yes	28
91.41	even	12		91.2.w.a.80.3	yes	28
91.54	even	12	inner	637.2.bb.a.509.3		28
91.67	odd	12		637.2.bd.b.587.5		28
91.80	even	12		637.2.bd.a.587.5		28
273.2	even	12		819.2.et.b.145.5		28
273.41	odd	12		819.2.gh.b.262.5		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.w.a.33.3	✓	28	7.2	even	3
91.2.w.a.80.3	yes	28	91.41	even	12
91.2.ba.a.54.3	yes	28	91.2	odd	12
91.2.ba.a.59.3	yes	28	7.6	odd	2
637.2.x.a.80.3		28	13.2	odd	12
637.2.x.a.215.3		28	7.5	odd	6
637.2.bb.a.423.3		28	1.1	even	1	trivial
637.2.bb.a.509.3		28	91.54	even	12	inner
637.2.bd.a.293.5		28	7.4	even	3
637.2.bd.a.587.5		28	91.80	even	12
637.2.bd.b.293.5		28	7.3	odd	6
637.2.bd.b.587.5		28	91.67	odd	12
819.2.et.b.145.5		28	273.2	even	12
819.2.et.b.514.5		28	21.20	even	2
819.2.gh.b.262.5		28	273.41	odd	12
819.2.gh.b.397.5		28	21.2	odd	6

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.876516 - 0.876516i) q^{2} +(-1.92717 + 1.11265i) q^{3} -0.463441i q^{4} +(2.51660 + 0.674321i) q^{5} +(2.66446 + 0.713939i) q^{6} +(-2.15924 + 2.15924i) q^{8} +(0.975997 - 1.69048i) q^{9} +O(q^{10})\)	\(q+(-0.876516 - 0.876516i) q^{2} +(-1.92717 + 1.11265i) q^{3} -0.463441i q^{4} +(2.51660 + 0.674321i) q^{5} +(2.66446 + 0.713939i) q^{6} +(-2.15924 + 2.15924i) q^{8} +(0.975997 - 1.69048i) q^{9} +(-1.61479 - 2.79689i) q^{10} +(1.36505 + 0.365763i) q^{11} +(0.515649 + 0.893131i) q^{12} +(-0.445209 + 3.57796i) q^{13} +(-5.60021 + 1.50057i) q^{15} +2.85834 q^{16} -2.82813 q^{17} +(-2.33720 + 0.626252i) q^{18} +(-1.61939 - 6.04364i) q^{19} +(0.312508 - 1.16630i) q^{20} +(-0.875887 - 1.51708i) q^{22} +1.01874i q^{23} +(1.75875 - 6.56373i) q^{24} +(1.54845 + 0.893996i) q^{25} +(3.52637 - 2.74590i) q^{26} -2.33214i q^{27} +(-2.66549 + 4.61676i) q^{29} +(6.22395 + 3.59340i) q^{30} +(1.73101 + 6.46023i) q^{31} +(1.81311 + 1.81311i) q^{32} +(-3.03765 + 0.813935i) q^{33} +(2.47890 + 2.47890i) q^{34} +(-0.783435 - 0.452317i) q^{36} +(-6.50927 + 6.50927i) q^{37} +(-3.87792 + 6.71676i) q^{38} +(-3.12303 - 7.39071i) q^{39} +(-6.88998 + 3.97793i) q^{40} +(2.51937 + 9.40242i) q^{41} +(0.850246 - 0.490890i) q^{43} +(0.169509 - 0.632618i) q^{44} +(3.59612 - 3.59612i) q^{45} +(0.892940 - 0.892940i) q^{46} +(-0.594605 + 2.21910i) q^{47} +(-5.50852 + 3.18034i) q^{48} +(-0.573636 - 2.14084i) q^{50} +(5.45029 - 3.14673i) q^{51} +(1.65817 + 0.206328i) q^{52} +(-2.52978 + 4.38171i) q^{53} +(-2.04415 + 2.04415i) q^{54} +(3.18863 + 1.84096i) q^{55} +(9.84531 + 9.84531i) q^{57} +(6.38300 - 1.71032i) q^{58} +(5.39402 + 5.39402i) q^{59} +(0.695426 + 2.59537i) q^{60} +(6.75223 + 3.89840i) q^{61} +(4.14523 - 7.17976i) q^{62} -8.89512i q^{64} +(-3.53311 + 8.70408i) q^{65} +(3.37597 + 1.94912i) q^{66} +(-3.38240 + 12.6233i) q^{67} +1.31067i q^{68} +(-1.13350 - 1.96328i) q^{69} +(2.97420 - 11.0999i) q^{71} +(1.54273 + 5.75756i) q^{72} +(-8.43566 + 2.26033i) q^{73} +11.4110 q^{74} -3.97883 q^{75} +(-2.80087 + 0.750490i) q^{76} +(-3.74068 + 9.21546i) q^{78} +(-2.78395 - 4.82194i) q^{79} +(7.19330 + 1.92744i) q^{80} +(5.52285 + 9.56586i) q^{81} +(6.03310 - 10.4496i) q^{82} +(0.445401 - 0.445401i) q^{83} +(-7.11727 - 1.90707i) q^{85} +(-1.17553 - 0.314981i) q^{86} -11.8631i q^{87} +(-3.73724 + 2.15770i) q^{88} +(-0.108264 - 0.108264i) q^{89} -6.30411 q^{90} +0.472125 q^{92} +(-10.5240 - 10.5240i) q^{93} +(2.46625 - 1.42389i) q^{94} -16.3014i q^{95} +(-5.51153 - 1.47681i) q^{96} +(2.87974 + 0.771623i) q^{97} +(1.95059 - 1.95059i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9	\( 28 q - 2 q^{2} + 6 q^{3} + 6 q^{5} + 12 q^{6} - 4 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 8 q^{12} + 10 q^{15} + 4 q^{16} + 12 q^{17} + 2 q^{18} - 14 q^{19} - 36 q^{20} - 8 q^{22} + 18 q^{24} - 24 q^{26} - 8 q^{29} - 30 q^{30} + 4 q^{31} + 10 q^{32} + 12 q^{33} + 12 q^{34} + 54 q^{36} - 10 q^{37} - 20 q^{39} - 48 q^{40} + 18 q^{41} + 48 q^{43} - 6 q^{44} + 6 q^{45} + 24 q^{46} + 6 q^{47} + 12 q^{48} + 10 q^{50} - 12 q^{51} + 26 q^{52} + 12 q^{53} + 30 q^{54} - 6 q^{55} + 12 q^{57} - 46 q^{58} - 42 q^{59} + 10 q^{60} - 30 q^{61} - 36 q^{62} + 28 q^{65} - 66 q^{66} - 10 q^{67} + 42 q^{69} - 42 q^{71} + 46 q^{72} - 40 q^{73} + 12 q^{74} + 40 q^{75} + 52 q^{76} - 62 q^{78} + 4 q^{79} - 30 q^{80} - 6 q^{81} + 54 q^{82} - 66 q^{83} - 54 q^{85} - 18 q^{86} - 6 q^{88} - 72 q^{90} - 156 q^{92} + 20 q^{93} + 18 q^{94} + 66 q^{96} + 62 q^{97} - 36 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 + 6 * q^3 + 6 * q^5 + 12 * q^6 - 4 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 8 * q^12 + 10 * q^15 + 4 * q^16 + 12 * q^17 + 2 * q^18 - 14 * q^19 - 36 * q^20 - 8 * q^22 + 18 * q^24 - 24 * q^26 - 8 * q^29 - 30 * q^30 + 4 * q^31 + 10 * q^32 + 12 * q^33 + 12 * q^34 + 54 * q^36 - 10 * q^37 - 20 * q^39 - 48 * q^40 + 18 * q^41 + 48 * q^43 - 6 * q^44 + 6 * q^45 + 24 * q^46 + 6 * q^47 + 12 * q^48 + 10 * q^50 - 12 * q^51 + 26 * q^52 + 12 * q^53 + 30 * q^54 - 6 * q^55 + 12 * q^57 - 46 * q^58 - 42 * q^59 + 10 * q^60 - 30 * q^61 - 36 * q^62 + 28 * q^65 - 66 * q^66 - 10 * q^67 + 42 * q^69 - 42 * q^71 + 46 * q^72 - 40 * q^73 + 12 * q^74 + 40 * q^75 + 52 * q^76 - 62 * q^78 + 4 * q^79 - 30 * q^80 - 6 * q^81 + 54 * q^82 - 66 * q^83 - 54 * q^85 - 18 * q^86 - 6 * q^88 - 72 * q^90 - 156 * q^92 + 20 * q^93 + 18 * q^94 + 66 * q^96 + 62 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more