LMFDB - Embedded newform 637.2.bc.a.619.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			619.2
Character	$\chi$	$=$	637.619
Dual form			637.2.bc.a.460.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.531325 + 1.98293i) q^{2} +(1.57586 + 0.909822i) q^{3} +(-1.91766 - 1.10716i) q^{4} +(-2.75205 - 0.737409i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 + 0.269427i) q^{9} +O(q^{10})$	\(q+(-0.531325 + 1.98293i) q^{2} +(1.57586 + 0.909822i) q^{3} +(-1.91766 - 1.10716i) q^{4} +(-2.75205 - 0.737409i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 + 0.269427i) q^{9} +(2.92446 - 5.06531i) q^{10} +(0.165299 + 0.616905i) q^{11} +(-2.01464 - 3.48946i) q^{12} +(-3.40251 + 1.19288i) q^{13} +(-3.66593 - 3.66593i) q^{15} +(-1.76271 - 3.05311i) q^{16} +(-2.16336 + 3.74705i) q^{17} +(-0.616905 + 0.165299i) q^{18} +(-4.64791 - 1.24540i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +(-0.808282 + 0.466662i) q^{23} +(0.773315 - 0.207209i) q^{24} +(2.69986 + 1.55877i) q^{25} +(-0.557554 - 7.38074i) q^{26} -4.89283i q^{27} +6.33185 q^{29} +(9.21707 - 5.32148i) q^{30} +(-2.00502 - 7.48282i) q^{31} +(7.84064 - 2.10089i) q^{32} +(-0.300786 + 1.12255i) q^{33} +(-6.28070 - 6.28070i) q^{34} -0.688892i q^{36} +(-2.92397 - 0.783477i) q^{37} +(4.93910 - 8.55477i) q^{38} +(-6.44717 - 1.21587i) q^{39} +(-1.08560 + 0.626770i) q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(0.366025 - 1.36603i) q^{44} +(-0.229414 - 0.856183i) q^{45} +(-0.495898 - 1.85072i) q^{46} +(-2.16306 + 8.07264i) q^{47} -6.41503i q^{48} +(-4.52543 + 4.52543i) q^{50} +(-6.81830 + 3.93655i) q^{51} +(7.84554 + 1.47959i) q^{52} +(-1.68098 + 2.91155i) q^{53} +(9.70214 + 2.59968i) q^{54} -1.81964i q^{55} +(-6.19135 - 6.19135i) q^{57} +(-3.36427 + 12.5556i) q^{58} +(-0.349234 + 0.0935769i) q^{59} +(2.97122 + 11.0888i) q^{60} +(6.74625 - 3.89495i) q^{61} +15.9032 q^{62} +9.61285i q^{64} +(10.2435 - 0.773811i) q^{65} +(-2.06612 - 1.19288i) q^{66} +(-9.94603 + 2.66503i) q^{67} +(8.29717 - 4.79037i) q^{68} -1.69832 q^{69} +(5.56914 + 5.56914i) q^{71} +(0.132215 + 0.0354269i) q^{72} +(-12.1050 + 3.24351i) q^{73} +(3.10716 - 5.38176i) q^{74} +(2.83640 + 4.91279i) q^{75} +(7.53424 + 7.53424i) q^{76} +(5.83654 - 12.1383i) q^{78} +(6.89853 + 11.9486i) q^{79} +(2.59968 + 9.70214i) q^{80} +(4.91827 - 8.51869i) q^{81} +(-2.64141 - 4.57505i) q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(-20.7801 - 5.56801i) q^{86} +(9.97810 + 5.76086i) q^{87} +(0.243350 + 0.140498i) q^{88} +(-2.05418 + 7.66632i) q^{89} +1.81964 q^{90} +2.06668 q^{92} +(3.64842 - 13.6161i) q^{93} +(-14.8582 - 8.57839i) q^{94} +(11.8729 + 6.85482i) q^{95} +(14.2672 + 3.82288i) q^{96} +(0.236784 - 0.236784i) q^{97} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	$ 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.531325	+	1.98293i	−0.375703	+	1.40214i	0.476611	+	0.879114i	$0.341865\pi$
$2$	−0.531325	+	1.98293i	−0.375703	+	1.40214i	−0.852315	+	0.523030i	$0.824802\pi$
$3$	1.57586	+	0.909822i	0.909822	+	0.525286i	0.880374	−	0.474280i	$-0.157292\pi$
$3$	1.57586	+	0.909822i	0.909822	+	0.525286i	0.0294485	+	0.999566i	$0.490625\pi$
$4$	−1.91766	−	1.10716i	−0.958829	−	0.553580i
$5$	−2.75205	−	0.737409i	−1.23075	−	0.329779i	−0.415880	−	0.909419i	$-0.636526\pi$
$5$	−2.75205	−	0.737409i	−1.23075	−	0.329779i	−0.814872	+	0.579640i	$0.803193\pi$
$6$	−2.64141	+	2.64141i	−1.07835	+	1.07835i
$7$		0			0
$7$		0			0
$8$	0.311108	−	0.311108i	0.109993	−	0.109993i
$9$	0.155554	+	0.269427i	0.0518513	+	0.0898091i
$10$	2.92446	−	5.06531i	0.924796	−	1.60179i
$11$	0.165299	+	0.616905i	0.0498396	+	0.186004i	0.986358	−	0.164615i	$-0.0526380\pi$
$11$	0.165299	+	0.616905i	0.0498396	+	0.186004i	−0.936518	+	0.350619i	$0.885971\pi$
$12$	−2.01464	−	3.48946i	−0.581576	−	1.00732i
$13$	−3.40251	+	1.19288i	−0.943685	+	0.330844i
$13$	−3.40251	+	1.19288i	−0.943685	+	0.330844i
$14$		0			0
$15$	−3.66593	−	3.66593i	−0.946538	−	0.946538i
$16$	−1.76271	−	3.05311i	−0.440678	−	0.763277i
$17$	−2.16336	+	3.74705i	−0.524692	+	0.908794i	0.474894	+	0.880043i	$0.342486\pi$
$17$	−2.16336	+	3.74705i	−0.524692	+	0.908794i	−0.999587	+	0.0287509i	$0.990847\pi$
$18$	−0.616905	+	0.165299i	−0.145406	+	0.0389614i
$19$	−4.64791	−	1.24540i	−1.06630	−	0.285715i	−0.317330	−	0.948315i	$-0.602786\pi$
$19$	−4.64791	−	1.24540i	−1.06630	−	0.285715i	−0.748974	+	0.662600i	$0.769453\pi$
$20$	4.46105	+	4.46105i	0.997522	+	0.997522i
$21$		0			0
$22$	−1.31111			−0.279529
$23$	−0.808282	+	0.466662i	−0.168538	+	0.0973057i	−0.581896	−	0.813263i	$-0.697689\pi$
$23$	−0.808282	+	0.466662i	−0.168538	+	0.0973057i	0.413358	+	0.910569i	$0.364356\pi$
$24$	0.773315	−	0.207209i	0.157852	−	0.0422964i
$25$	2.69986	+	1.55877i	0.539972	+	0.311753i
$26$	−0.557554	−	7.38074i	−0.109345	−	1.44748i
$27$		−	4.89283i		−	0.941625i
$28$		0			0
$29$	6.33185			1.17580			0.587898	−	0.808935i	$-0.299956\pi$
$29$	6.33185			1.17580			0.587898	+	0.808935i	$0.299956\pi$
$30$	9.21707	−	5.32148i	1.68280	−	0.971565i
$31$	−2.00502	−	7.48282i	−0.360112	−	1.34395i	−0.873928	−	0.486055i	$-0.838435\pi$
$31$	−2.00502	−	7.48282i	−0.360112	−	1.34395i	0.513817	−	0.857900i	$-0.328231\pi$
$32$	7.84064	−	2.10089i	1.38604	−	0.371389i
$33$	−0.300786	+	1.12255i	−0.0523601	+	0.195411i
$34$	−6.28070	−	6.28070i	−1.07713	−	1.07713i
$35$		0			0
$36$		−	0.688892i		−	0.114815i
$37$	−2.92397	−	0.783477i	−0.480699	−	0.128803i	0.0103293	−	0.999947i	$-0.496712\pi$
$37$	−2.92397	−	0.783477i	−0.480699	−	0.128803i	−0.491028	+	0.871144i	$0.663379\pi$
$38$	4.93910	−	8.55477i	0.801228	−	1.38777i
$39$	−6.44717	−	1.21587i	−1.03237	−	0.194696i
$40$	−1.08560	+	0.626770i	−0.171648	+	0.0991010i
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	−0.834774	−	0.550593i	$-0.814402\pi$
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	0.550593	+	0.834774i	$0.314402\pi$
$42$		0			0
$43$			10.4795i			1.59811i	0.601259	+	0.799054i	$0.294666\pi$
$43$			10.4795i			1.59811i	−0.601259	+	0.799054i	$0.705334\pi$
$44$	0.366025	−	1.36603i	0.0551804	−	0.205936i
$45$	−0.229414	−	0.856183i	−0.0341990	−	0.127632i
$46$	−0.495898	−	1.85072i	−0.0731161	−	0.272873i
$47$	−2.16306	+	8.07264i	−0.315514	+	1.17752i	0.607995	+	0.793941i	$0.291974\pi$
$47$	−2.16306	+	8.07264i	−0.315514	+	1.17752i	−0.923510	+	0.383575i	$0.874693\pi$
$48$		−	6.41503i		−	0.925929i
$49$		0			0
$50$	−4.52543	+	4.52543i	−0.639992	+	0.639992i
$51$	−6.81830	+	3.93655i	−0.954754	+	0.551227i
$52$	7.84554	+	1.47959i	1.08798	+	0.205183i
$53$	−1.68098	+	2.91155i	−0.230901	+	0.399932i	−0.958073	−	0.286523i	$-0.907501\pi$
$53$	−1.68098	+	2.91155i	−0.230901	+	0.399932i	0.727173	+	0.686454i	$0.240834\pi$
$54$	9.70214	+	2.59968i	1.32029	+	0.353772i
$55$		−	1.81964i		−	0.245361i
$56$		0			0
$57$	−6.19135	−	6.19135i	−0.820065	−	0.820065i
$58$	−3.36427	+	12.5556i	−0.441750	+	1.64863i
$59$	−0.349234	+	0.0935769i	−0.0454663	+	0.0121827i	−0.281481	−	0.959567i	$-0.590825\pi$
$59$	−0.349234	+	0.0935769i	−0.0454663	+	0.0121827i	0.236014	+	0.971750i	$0.424159\pi$
$60$	2.97122	+	11.0888i	0.383583	+	1.43155i
$61$	6.74625	−	3.89495i	0.863768	−	0.498697i	−0.00150413	−	0.999999i	$-0.500479\pi$
$61$	6.74625	−	3.89495i	0.863768	−	0.498697i	0.865272	+	0.501302i	$0.167145\pi$
$62$	15.9032			2.01971
$63$		0			0
$64$			9.61285i			1.20161i
$65$	10.2435	−	0.773811i	1.27055	−	0.0959794i
$66$	−2.06612	−	1.19288i	−0.254322	−	0.146833i
$67$	−9.94603	+	2.66503i	−1.21510	+	0.325585i	−0.808761	−	0.588137i	$-0.799862\pi$
$67$	−9.94603	+	2.66503i	−1.21510	+	0.325585i	−0.406339	+	0.913722i	$0.633195\pi$
$68$	8.29717	−	4.79037i	1.00618	−	0.580918i
$69$	−1.69832			−0.204453
$70$		0			0
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	0.955600	−	0.294665i	$-0.0952082\pi$
$71$	5.56914	+	5.56914i	0.660935	+	0.660935i	−0.294665	+	0.955600i	$0.595208\pi$
$72$	0.132215	+	0.0354269i	0.0155817	+	0.00417510i
$73$	−12.1050	+	3.24351i	−1.41678	+	0.379624i	−0.884339	−	0.466844i	$-0.845391\pi$
$73$	−12.1050	+	3.24351i	−1.41678	+	0.379624i	−0.532438	+	0.846469i	$0.678724\pi$
$74$	3.10716	−	5.38176i	0.361200	−	0.625617i
$75$	2.83640	+	4.91279i	0.327519	+	0.567280i
$76$	7.53424	+	7.53424i	0.864236	+	0.864236i
$77$		0			0
$78$	5.83654	−	12.1383i	0.660857	−	1.37439i
$79$	6.89853	+	11.9486i	0.776145	+	1.34432i	0.934149	+	0.356884i	$0.116161\pi$
$79$	6.89853	+	11.9486i	0.776145	+	1.34432i	−0.158004	+	0.987439i	$0.550506\pi$
$80$	2.59968	+	9.70214i	0.290653	+	1.08473i
$81$	4.91827	−	8.51869i	0.546474	−	0.946521i
$82$	−2.64141	−	4.57505i	−0.291695	−	0.505230i
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	−0.902835	−	0.429987i	$-0.858518\pi$
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	0.429987	+	0.902835i	$0.358518\pi$
$84$		0			0
$85$	8.71678	−	8.71678i	0.945468	−	0.945468i
$86$	−20.7801	−	5.56801i	−2.24078	−	0.600414i
$87$	9.97810	+	5.76086i	1.06976	+	0.617629i
$88$	0.243350	+	0.140498i	0.0259412	+	0.0149772i
$89$	−2.05418	+	7.66632i	−0.217743	+	0.812628i	0.767440	+	0.641121i	$0.221530\pi$
$89$	−2.05418	+	7.66632i	−0.217743	+	0.812628i	−0.985183	+	0.171507i	$0.945136\pi$
$90$	1.81964			0.191807
$91$		0			0
$92$	2.06668			0.215466
$93$	3.64842	−	13.6161i	0.378323	−	1.41192i
$94$	−14.8582	−	8.57839i	−1.53251	−	0.884793i
$95$	11.8729	+	6.85482i	1.21813	+	0.703289i
$96$	14.2672	+	3.82288i	1.45614	+	0.390171i
$97$	0.236784	−	0.236784i	0.0240417	−	0.0240417i	−0.694984	−	0.719025i	$-0.744588\pi$
$97$	0.236784	−	0.236784i	0.0240417	−	0.0240417i	0.719025	+	0.694984i	$0.244588\pi$
$98$		0			0
$99$	−0.140498	+	0.140498i	−0.0141206	+	0.0141206i
$100$	−3.45161	−	5.97836i	−0.345161	−	0.597836i
$101$	4.60978	−	7.98437i	0.458690	−	0.794474i	−0.540202	−	0.841535i	$-0.681652\pi$
$101$	4.60978	−	7.98437i	0.458690	−	0.794474i	0.998892	+	0.0470611i	$0.0149856\pi$
$102$	−4.18317	−	15.6118i	−0.414196	−	1.54580i
$103$	−1.25354	−	2.17119i	−0.123515	−	0.213934i	0.797637	−	0.603138i	$-0.206083\pi$
$103$	−1.25354	−	2.17119i	−0.123515	−	0.213934i	−0.921151	+	0.389204i	$0.872750\pi$
$104$	−0.687433	+	1.42966i	−0.0674084	+	0.140190i
$105$		0			0
$106$	−4.88025	−	4.88025i	−0.474011	−	0.474011i
$107$	−1.44123	−	2.49629i	−0.139329	−	0.241326i	0.787914	−	0.615786i	$-0.211161\pi$
$107$	−1.44123	−	2.49629i	−0.139329	−	0.241326i	−0.927243	+	0.374460i	$0.877828\pi$
$108$	−5.41714	+	9.38277i	−0.521265	+	0.902857i
$109$	4.84720	−	1.29880i	0.464277	−	0.124403i	−0.0190949	−	0.999818i	$-0.506078\pi$
$109$	4.84720	−	1.29880i	0.464277	−	0.124403i	0.483372	+	0.875415i	$0.339412\pi$
$110$	3.60823	+	0.966822i	0.344031	+	0.0921829i
$111$	−3.89495	−	3.89495i	−0.369692	−	0.369692i
$112$		0			0
$113$	−16.3526			−1.53832			−0.769161	−	0.639055i	$-0.779326\pi$
$113$	−16.3526			−1.53832			−0.769161	+	0.639055i	$0.779326\pi$
$114$	15.5666	−	8.98741i	1.45795	−	0.841748i
$115$	2.56855	−	0.688241i	0.239518	−	0.0641788i
$116$	−12.1423	−	7.01037i	−1.12739	−	0.650897i
$117$	−0.850666	−	0.731172i	−0.0786441	−	0.0675968i
$118$		−	0.742226i		−	0.0683274i
$119$		0			0
$120$	−2.28100			−0.208226
$121$	9.17303	−	5.29605i	0.833912	−	0.481459i
$122$	4.13896	+	15.4468i	0.374724	+	1.39849i
$123$	−4.52306	+	1.21195i	−0.407830	+	0.109278i
$124$	−4.43975	+	16.5694i	−0.398701	+	1.48797i
$125$	3.79249	+	3.79249i	0.339211	+	0.339211i
$126$		0			0
$127$		−	13.8272i		−	1.22696i	−0.789709	−	0.613481i	$-0.789769\pi$
$127$		−	13.8272i		−	1.22696i	0.789709	−	0.613481i	$-0.210231\pi$
$128$	−3.38033	−	0.905756i	−0.298782	−	0.0800583i
$129$	−9.53448	+	16.5142i	−0.839464	+	1.45399i
$130$	−3.90821	+	20.7233i	−0.342772	+	1.81755i
$131$	−11.1112	+	6.41503i	−0.970786	+	0.560483i	−0.899476	−	0.436971i	$-0.856051\pi$
$131$	−11.1112	+	6.41503i	−0.970786	+	0.560483i	−0.0713101	+	0.997454i	$0.522718\pi$
$132$	1.81964	−	1.81964i	0.158380	−	0.158380i
$133$		0			0
$134$		−	21.1383i		−	1.82607i
$135$	−3.60801	+	13.4653i	−0.310528	+	1.15891i
$136$	0.492699	+	1.83878i	0.0422486	+	0.157674i
$137$	0.878736	+	3.27949i	0.0750755	+	0.280185i	0.993250	−	0.115990i	$-0.0370040\pi$
$137$	0.878736	+	3.27949i	0.0750755	+	0.280185i	−0.918175	+	0.396175i	$0.870337\pi$
$138$	0.902358	−	3.36765i	0.0768138	−	0.286673i
$139$			3.34184i			0.283451i	0.989906	+	0.141726i	$0.0452651\pi$
$139$			3.34184i			0.283451i	−0.989906	+	0.141726i	$0.954735\pi$
$140$		0			0
$141$	−10.7533	+	10.7533i	−0.905595	+	0.905595i
$142$	−14.0022	+	8.08419i	−1.17504	+	0.678410i
$143$	−1.29832	−	1.90184i	−0.108571	−	0.159040i
$144$	0.548394	−	0.949846i	0.0456995	−	0.0791539i
$145$	−17.4255	−	4.66916i	−1.44711	−	0.387753i
$146$		−	25.7266i		−	2.12915i
$147$		0			0
$148$	4.73975	+	4.73975i	0.389605	+	0.389605i
$149$	0.962413	−	3.59177i	0.0788439	−	0.294250i	−0.915233	−	0.402924i	$-0.867994\pi$
$149$	0.962413	−	3.59177i	0.0788439	−	0.294250i	0.994077	+	0.108674i	$0.0346606\pi$
$150$	−11.2488	+	3.01410i	−0.918458	+	0.246100i
$151$	−1.75087	−	6.53432i	−0.142484	−	0.531756i	−0.999855	−	0.0170568i	$-0.994570\pi$
$151$	−1.75087	−	6.53432i	−0.142484	−	0.531756i	0.857371	−	0.514699i	$-0.172096\pi$
$152$	−1.83346	+	1.05855i	−0.148713	+	0.0858594i
$153$	−1.34608			−0.108824
$154$		0			0
$155$			22.0716i			1.77283i
$156$	11.0173	+	9.46968i	0.882090	+	0.758181i
$157$	−2.96650	−	1.71271i	−0.236753	−	0.136689i	0.376931	−	0.926242i	$-0.376980\pi$
$157$	−2.96650	−	1.71271i	−0.236753	−	0.136689i	−0.613683	+	0.789552i	$0.710313\pi$
$158$	−27.3586	+	7.33072i	−2.17653	+	0.583200i
$159$	−5.29798	+	3.05879i	−0.420157	+	0.242578i
$160$	−23.1270			−1.82835
$161$		0			0
$162$	14.2788	+	14.2788i	1.12185	+	1.12185i
$163$	−14.2741	−	3.82474i	−1.11804	−	0.299577i	−0.347947	−	0.937514i	$-0.613121\pi$
$163$	−14.2741	−	3.82474i	−1.11804	−	0.299577i	−0.770088	+	0.637937i	$0.779788\pi$
$164$	5.50409	−	1.47482i	0.429797	−	0.115164i
$165$	1.65555	−	2.86750i	0.128885	−	0.223235i
$166$	−6.25330	−	10.8310i	−0.485350	−	0.840651i
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.952933	+	0.303180i	$0.0980483\pi$
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.303180	+	0.952933i	$0.401952\pi$
$168$		0			0
$169$	10.1541	−	8.11753i	0.781084	−	0.624426i
$170$	12.6533	+	21.9162i	0.970466	+	1.68090i
$171$	−0.387455	−	1.44600i	−0.0296294	−	0.110578i
$172$	11.6025	−	20.0961i	0.884680	−	1.53231i
$173$	7.19052	+	12.4543i	0.546685	+	0.946886i	0.998499	+	0.0547740i	$0.0174439\pi$
$173$	7.19052	+	12.4543i	0.546685	+	0.946886i	−0.451814	+	0.892112i	$0.649223\pi$
$174$	−16.7250	+	16.7250i	−1.26792	+	1.26792i
$175$		0			0
$176$	1.59210	−	1.59210i	0.120009	−	0.120009i
$177$	−0.635481	−	0.170277i	−0.0477657	−	0.0127988i
$178$	−14.1103	−	8.14661i	−1.05762	−	0.610614i
$179$	3.56030	+	2.05554i	0.266109	+	0.153638i	0.627118	−	0.778924i	$-0.284234\pi$
$179$	3.56030	+	2.05554i	0.266109	+	0.153638i	−0.361009	+	0.932562i	$0.617568\pi$
$180$	−0.507995	+	1.89586i	−0.0378637	+	0.141309i
$181$	−21.5760			−1.60373			−0.801867	−	0.597502i	$-0.796160\pi$
$181$	−21.5760			−1.60373			−0.801867	+	0.597502i	$0.796160\pi$
$182$		0			0
$183$	14.1748			1.04783
$184$	−0.106281	+	0.396645i	−0.00783512	+	0.0292411i
$185$	7.46917	+	4.31233i	0.549144	+	0.317049i
$186$	25.0613	+	14.4691i	1.83758	+	1.06093i
$187$	−2.66918	−	0.715204i	−0.195190	−	0.0523009i
$188$	13.0857	−	13.0857i	0.954373	−	0.954373i
$189$		0			0
$190$	−19.9010	+	19.9010i	−1.44377	+	1.44377i
$191$	−5.15087	−	8.92157i	−0.372704	−	0.645542i	0.617277	−	0.786746i	$-0.288236\pi$
$191$	−5.15087	−	8.92157i	−0.372704	−	0.645542i	−0.989980	+	0.141204i	$0.954903\pi$
$192$	−8.74598	+	15.1485i	−0.631187	+	1.09325i
$193$	2.30081	+	8.58672i	0.165616	+	0.618086i	0.997961	+	0.0638284i	$0.0203310\pi$
$193$	2.30081	+	8.58672i	0.165616	+	0.618086i	−0.832345	+	0.554257i	$0.813002\pi$
$194$	0.343717	+	0.595335i	0.0246774	+	0.0427425i
$195$	16.8463	+	8.10034i	1.20639	+	0.580078i
$196$		0			0
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	0.581751	−	0.813367i	$-0.302368\pi$
$197$	−3.25088	−	3.25088i	−0.231616	−	0.231616i	−0.813367	+	0.581751i	$0.802368\pi$
$198$	−0.203948	−	0.353248i	−0.0144939	−	0.0251043i
$199$	−3.10058	+	5.37036i	−0.219794	+	0.380695i	−0.954745	−	0.297426i	$-0.903872\pi$
$199$	−3.10058	+	5.37036i	−0.219794	+	0.380695i	0.734951	+	0.678121i	$0.237205\pi$
$200$	1.32489	−	0.355004i	0.0936840	−	0.0251026i
$201$	−18.0982	−	4.84941i	−1.27655	−	0.342051i
$202$	13.3832	+	13.3832i	0.941636	+	0.941636i
$203$		0			0
$204$	17.4336			1.22059
$205$	6.34957	−	3.66593i	0.443473	−	0.256039i
$206$	4.97136	−	1.33207i	0.346371	−	0.0928099i
$207$	−0.251463	−	0.145182i	−0.0174779	−	0.0100909i
$208$	9.63962	+	8.28553i	0.668388	+	0.574498i
$209$		−	3.07318i		−	0.212577i
$210$		0			0
$211$	−9.55554			−0.657830			−0.328915	−	0.944359i	$-0.606683\pi$
$211$	−9.55554			−0.657830			−0.328915	+	0.944359i	$0.606683\pi$
$212$	6.44709	−	3.72223i	0.442788	−	0.255644i
$213$	3.70925	+	13.8431i	0.254153	+	0.948514i
$214$	5.71573	−	1.53153i	0.390720	−	0.104693i
$215$	7.72767	−	28.8401i	0.527023	−	1.96688i
$216$	−1.52220	−	1.52220i	−0.103572	−	0.103572i
$217$		0			0
$218$			10.3017i			0.697722i
$219$	−22.0267	−	5.90204i	−1.48843	−	0.398823i
$220$	−2.01464	+	3.48946i	−0.135827	+	0.235259i
$221$	2.89109	−	15.3300i	0.194475	−	1.03121i
$222$	9.79289	−	5.65393i	0.657256	−	0.379467i
$223$	2.58074	−	2.58074i	0.172819	−	0.172819i	−0.615398	−	0.788217i	$-0.711005\pi$
$223$	2.58074	−	2.58074i	0.172819	−	0.172819i	0.788217	+	0.615398i	$0.211005\pi$
$224$		0			0
$225$			0.969888i			0.0646592i
$226$	8.68854	−	32.4261i	0.577953	−	2.15695i
$227$	−1.92311	−	7.17713i	−0.127641	−	0.476363i	0.872279	−	0.489009i	$-0.162641\pi$
$227$	−1.92311	−	7.17713i	−0.127641	−	0.476363i	−0.999920	+	0.0126456i	$0.995975\pi$
$228$	5.01807	+	18.7277i	0.332330	+	1.24027i
$229$	0.266915	−	0.996139i	0.0176382	−	0.0658267i	−0.956546	−	0.291582i	$-0.905818\pi$
$229$	0.266915	−	0.996139i	0.0176382	−	0.0658267i	0.974184	+	0.225755i	$0.0724850\pi$
$230$			5.45893i			0.359952i
$231$		0			0
$232$	1.96989	−	1.96989i	0.129330	−	0.129330i
$233$	−21.3154	+	12.3064i	−1.39642	+	0.806221i	−0.994015	−	0.109243i	$-0.965157\pi$
$233$	−21.3154	+	12.3064i	−1.39642	+	0.806221i	−0.402400	+	0.915464i	$0.631824\pi$
$234$	1.90184	−	1.29832i	0.124327	−	0.0848740i
$235$	11.9057	−	20.6212i	0.776640	−	1.34518i
$236$	0.773315	+	0.207209i	0.0503385	+	0.0134882i
$237$			25.1057i			1.63079i
$238$		0			0
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	0.463830	−	0.885924i	$-0.346475\pi$
$239$	−6.52543	−	6.52543i	−0.422095	−	0.422095i	−0.885924	+	0.463830i	$0.846475\pi$
$240$	−4.73050	+	17.6545i	−0.305352	+	1.13959i
$241$	27.5340	−	7.37772i	1.77362	−	0.475240i	0.784225	−	0.620477i	$-0.213061\pi$
$241$	27.5340	−	7.37772i	1.77362	−	0.475240i	0.989397	+	0.145237i	$0.0463943\pi$
$242$	5.62785	+	21.0034i	0.361772	+	1.35015i
$243$	2.78905	−	1.61026i	0.178917	−	0.103298i
$244$	−17.2493			−1.10427
$245$		0			0
$246$		−	9.61285i		−	0.612893i
$247$	17.3002	−	1.30688i	1.10078	−	0.0831550i
$248$	−2.95174	−	1.70419i	−0.187436	−	0.108216i
$249$	−10.7079	+	2.86918i	−0.678588	+	0.181827i
$250$	−9.53529	+	5.50520i	−0.603065	+	0.348180i
$251$	14.4448			0.911747			0.455873	−	0.890045i	$-0.349327\pi$
$251$	14.4448			0.911747			0.455873	+	0.890045i	$0.349327\pi$
$252$		0			0
$253$	−0.421494	−	0.421494i	−0.0264991	−	0.0264991i
$254$	27.4183	+	7.34672i	1.72038	+	0.460974i
$255$	21.6671	−	5.80569i	1.35685	−	0.363567i
$256$	−6.02074	+	10.4282i	−0.376296	+	0.651765i
$257$	7.31185	+	12.6645i	0.456101	+	0.789989i	0.998751	−	0.0499695i	$-0.0159124\pi$
$257$	7.31185	+	12.6645i	0.456101	+	0.789989i	−0.542650	+	0.839959i	$0.682579\pi$
$258$	−27.6806	−	27.6806i	−1.72332	−	1.72332i
$259$		0			0
$260$	−20.5002	−	9.85728i	−1.27137	−	0.611322i
$261$	0.984944	+	1.70597i	0.0609665	+	0.105597i
$262$	−6.81692	−	25.4411i	−0.421151	−	1.57176i
$263$	1.30865	−	2.26664i	0.0806946	−	0.139767i	−0.822854	−	0.568253i	$-0.807619\pi$
$263$	1.30865	−	2.26664i	0.0806946	−	0.139767i	0.903548	+	0.428486i	$0.140953\pi$
$264$	0.255657	+	0.442810i	0.0157346	+	0.0272531i
$265$	6.77314	−	6.77314i	0.416071	−	0.416071i
$266$		0			0
$267$	−10.2121	+	10.2121i	−0.624970	+	0.624970i
$268$	22.0237	+	5.90123i	1.34531	+	0.360475i
$269$	−8.50732	−	4.91170i	−0.518700	−	0.299472i	0.217702	−	0.976015i	$-0.430144\pi$
$269$	−8.50732	−	4.91170i	−0.518700	−	0.299472i	−0.736403	+	0.676543i	$0.763477\pi$
$270$	−24.7837	−	14.3089i	−1.50829	−	0.870811i
$271$	1.25707	−	4.69145i	0.0763616	−	0.284985i	−0.917177	−	0.398480i	$-0.869538\pi$
$271$	1.25707	−	4.69145i	0.0763616	−	0.284985i	0.993539	+	0.113495i	$0.0362045\pi$
$272$	15.2535			0.924882
$273$		0			0
$274$	−6.96989			−0.421066
$275$	−0.515326	+	1.92322i	−0.0310753	+	0.115975i
$276$	3.25679	+	1.88031i	0.196036	+	0.113181i
$277$	−5.10848	−	2.94938i	−0.306939	−	0.177211i	0.338617	−	0.940924i	$-0.390041\pi$
$277$	−5.10848	−	2.94938i	−0.306939	−	0.177211i	−0.645556	+	0.763713i	$0.723374\pi$
$278$	−6.62664	−	1.77560i	−0.397440	−	0.106494i
$279$	1.70419	−	1.70419i	0.102027	−	0.102027i
$280$		0			0
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	−0.375694	−	0.926744i	$-0.622595\pi$
$281$	9.23729	−	9.23729i	0.551050	−	0.551050i	0.926744	+	0.375694i	$0.122595\pi$
$282$	−15.6096	−	27.0367i	−0.929539	−	1.61001i
$283$	4.16360	−	7.21158i	0.247501	−	0.428684i	−0.715331	−	0.698786i	$-0.753724\pi$
$283$	4.16360	−	7.21158i	0.247501	−	0.428684i	0.962832	+	0.270102i	$0.0870574\pi$
$284$	−4.51377	−	16.8456i	−0.267843	−	0.999604i
$285$	12.4733	+	21.6044i	0.738857	+	1.27974i
$286$	4.46105	−	1.56399i	0.263788	−	0.0924806i
$287$		0			0
$288$	1.78568	+	1.78568i	0.105222	+	0.105222i
$289$	−0.860268	−	1.49003i	−0.0506040	−	0.0876486i
$290$	18.5172	−	32.0728i	1.08737	−	1.88338i
$291$	0.588569	−	0.157707i	0.0345025	−	0.00924492i
$292$	26.8042	+	7.18217i	1.56860	+	0.420305i
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	0.0909047	−	0.995860i	$-0.471024\pi$
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	−0.995860	+	0.0909047i	$0.971024\pi$
$294$		0			0
$295$	1.03011			0.0599754
$296$	−1.15342	+	0.665926i	−0.0670410	+	0.0387061i
$297$	3.01841	−	0.808781i	0.175146	−	0.0469302i
$298$	6.61088	+	3.81680i	0.382958	+	0.221101i
$299$	2.19351	−	2.55200i	0.126854	−	0.147586i
$300$		−	12.5614i		−	0.725232i
$301$		0			0
$302$	13.8874			0.799130
$303$	14.5287	−	8.38816i	0.834653	−	0.481887i
$304$	4.39058	+	16.3859i	0.251817	+	0.939794i
$305$	−21.4381	+	5.74433i	−1.22754	+	0.328920i
$306$	0.715204	−	2.66918i	0.0408855	−	0.152587i
$307$	5.77526	+	5.77526i	0.329611	+	0.329611i	0.852439	−	0.522827i	$-0.175123\pi$
$307$	5.77526	+	5.77526i	0.329611	+	0.329611i	−0.522827	+	0.852439i	$0.675123\pi$
$308$		0			0
$309$		−	4.56199i		−	0.259523i
$310$	−43.7664	−	11.7272i	−2.48577	−	0.666059i
$311$	1.31281	−	2.27385i	0.0744426	−	0.128938i	−0.826401	−	0.563082i	$-0.809616\pi$
$311$	1.31281	−	2.27385i	0.0744426	−	0.128938i	0.900844	+	0.434143i	$0.142949\pi$
$312$	−2.38403	+	1.62750i	−0.134969	+	0.0921390i
$313$	17.1897	−	9.92447i	0.971618	−	0.560964i	0.0718889	−	0.997413i	$-0.477097\pi$
$313$	17.1897	−	9.92447i	0.971618	−	0.560964i	0.899729	+	0.436449i	$0.143764\pi$
$314$	4.97237	−	4.97237i	0.280607	−	0.280607i
$315$		0			0
$316$		−	30.5511i		−	1.71863i
$317$	0.420067	−	1.56771i	0.0235933	−	0.0880514i	−0.953125	−	0.302576i	$-0.902153\pi$
$317$	0.420067	−	1.56771i	0.0235933	−	0.0880514i	0.976719	+	0.214524i	$0.0688201\pi$
$318$	−3.25042	−	12.1307i	−0.182275	−	0.680258i
$319$	1.04665	+	3.90615i	0.0586012	+	0.218703i
$320$	7.08860	−	26.4550i	0.396265	−	1.47888i
$321$		−	5.24507i		−	0.292751i
$322$		0			0
$323$	14.7217	−	14.7217i	0.819137	−	0.819137i
$324$	−18.8631	+	10.8906i	−1.04795	+	0.605034i
$325$	−11.0457	−	2.08311i	−0.612706	−	0.115550i
$326$	15.1684	−	26.2724i	0.840099	−	1.45509i
$327$	8.82018	+	2.36336i	0.487757	+	0.130694i
$328$			1.13221i			0.0625159i
$329$		0			0
$330$	4.80642	+	4.80642i	0.264585	+	0.264585i
$331$	−1.06265	+	3.96586i	−0.0584085	+	0.217983i	−0.988961	−	0.148174i	$-0.952660\pi$
$331$	−1.06265	+	3.96586i	−0.0584085	+	0.217983i	0.930553	+	0.366158i	$0.119327\pi$
$332$	13.0305	−	3.49150i	0.715139	−	0.191621i
$333$	−0.243746	−	0.909671i	−0.0133572	−	0.0498497i
$334$	−40.8128	+	23.5633i	−2.23318	+	1.28933i
$335$	29.3371			1.60286
$336$		0			0
$337$		−	4.47304i		−	0.243662i	−0.992551	−	0.121831i	$-0.961123\pi$
$337$		−	4.47304i		−	0.243662i	0.992551	−	0.121831i	$-0.0388766\pi$
$338$	10.7014	+	24.4479i	0.582078	+	1.32979i
$339$	−25.7694	−	14.8780i	−1.39960	−	0.808060i
$340$	−26.3667	+	7.06493i	−1.42993	+	0.383149i
$341$	4.28477	−	2.47381i	0.232033	−	0.133964i
$342$	3.07318			0.166179
$343$		0			0
$344$	3.26025	+	3.26025i	0.175781	+	0.175781i
$345$	4.67385	+	1.25235i	0.251632	+	0.0674245i
$346$	−28.5166	+	7.64100i	−1.53306	+	0.410783i
$347$	−4.40567	+	7.63085i	−0.236509	+	0.409645i	−0.959710	−	0.280992i	$-0.909337\pi$
$347$	−4.40567	+	7.63085i	−0.236509	+	0.409645i	0.723201	+	0.690637i	$0.242670\pi$
$348$	−12.7564	−	22.0947i	−0.683814	−	1.18440i
$349$	−11.8133	−	11.8133i	−0.632351	−	0.632351i	0.316306	−	0.948657i	$-0.397557\pi$
$349$	−11.8133	−	11.8133i	−0.632351	−	0.632351i	−0.948657	+	0.316306i	$0.897557\pi$
$350$		0			0
$351$	5.83654	+	16.6479i	0.311531	+	0.888598i
$352$	2.59210	+	4.48966i	0.138160	+	0.239299i
$353$	−1.06516	−	3.97522i	−0.0566926	−	0.211580i	0.931769	−	0.363052i	$-0.118265\pi$
$353$	−1.06516	−	3.97522i	−0.0566926	−	0.211580i	−0.988462	+	0.151472i	$0.951599\pi$
$354$	0.675294	−	1.16964i	0.0358915	−	0.0621658i
$355$	−11.2198	−	19.4333i	−0.595485	−	1.03141i
$356$	12.4271	−	12.4271i	0.658633	−	0.658633i
$357$		0			0
$358$	−5.96767	+	5.96767i	−0.315401	+	0.315401i
$359$	−4.81279	−	1.28958i	−0.254009	−	0.0680616i	0.129567	−	0.991571i	$-0.458641\pi$
$359$	−4.81279	−	1.28958i	−0.254009	−	0.0680616i	−0.383577	+	0.923509i	$0.625308\pi$
$360$	−0.337738	−	0.194993i	−0.0178003	−	0.0102770i
$361$	3.59755	+	2.07705i	0.189345	+	0.109318i
$362$	11.4639	−	42.7838i	0.602528	−	2.24867i
$363$	19.2739			1.01162
$364$		0			0
$365$	35.7052			1.86890
$366$	−7.53144	+	28.1077i	−0.393675	+	1.46921i
$367$	17.1570	+	9.90559i	0.895588	+	0.517068i	0.875766	−	0.482736i	$-0.160357\pi$
$367$	17.1570	+	9.90559i	0.895588	+	0.517068i	0.0198215	+	0.999804i	$0.493690\pi$
$368$	2.84954	+	1.64518i	0.148542	+	0.0857610i
$369$	−0.773315	−	0.207209i	−0.0402572	−	0.0107869i
$370$	−12.5196	+	12.5196i	−0.650863	+	0.650863i
$371$		0			0
$372$	−22.0716	+	22.0716i	−1.14436	+	1.14436i
$373$	12.2684	+	21.2495i	0.635234	+	1.10026i	0.986466	+	0.163969i	$0.0524296\pi$
$373$	12.2684	+	21.2495i	0.635234	+	1.10026i	−0.351232	+	0.936289i	$0.614237\pi$
$374$	2.83640	−	4.91279i	0.146667	−	0.254034i
$375$	2.52594	+	9.42693i	0.130439	+	0.486804i
$376$	1.83852	+	3.18441i	0.0948143	+	0.164223i
$377$	−21.5442	+	7.55311i	−1.10958	+	0.389005i
$378$		0			0
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	0.444569	−	0.895745i	$-0.353357\pi$
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	−0.895745	+	0.444569i	$0.853357\pi$
$380$	−15.1788	−	26.2904i	−0.778654	−	1.34867i
$381$	12.5803	−	21.7897i	0.644507	−	1.11632i
$382$	20.4276	−	5.47357i	1.04517	−	0.280052i
$383$	24.4505	+	6.55149i	1.24936	+	0.334765i	0.822090	−	0.569358i	$-0.192808\pi$
$383$	24.4505	+	6.55149i	1.24936	+	0.334765i	0.427272	+	0.904123i	$0.359475\pi$
$384$	−4.50284	−	4.50284i	−0.229785	−	0.229785i
$385$		0			0
$386$	−18.2494			−0.928868
$387$	−2.82346	+	1.63013i	−0.143525	+	0.0828640i
$388$	−0.716228	+	0.191913i	−0.0363609	+	0.00974289i
$389$	−10.4500	−	6.03334i	−0.529838	−	0.305902i	0.211112	−	0.977462i	$-0.432291\pi$
$389$	−10.4500	−	6.03334i	−0.529838	−	0.305902i	−0.740951	+	0.671559i	$0.765625\pi$
$390$	−25.0133	+	29.1012i	−1.26660	+	1.47360i
$391$		−	4.03823i		−	0.204222i
$392$		0			0
$393$	−23.3461			−1.17766
$394$	8.17355	−	4.71900i	0.411778	−	0.237740i
$395$	−10.1741	−	37.9701i	−0.511913	−	1.91049i
$396$	0.424981	−	0.113873i	0.0213561	−	0.00572235i
$397$	2.86297	−	10.6847i	0.143688	−	0.536251i	−0.856122	−	0.516774i	$-0.827133\pi$
$397$	2.86297	−	10.6847i	0.143688	−	0.536251i	0.999810	−	0.0194779i	$-0.00620040\pi$
$398$	−9.00164	−	9.00164i	−0.451212	−	0.451212i
$399$		0			0
$400$		−	10.9906i		−	0.549532i
$401$	24.0663	+	6.44855i	1.20181	+	0.322025i	0.803546	−	0.595243i	$-0.202944\pi$
$401$	24.0663	+	6.44855i	1.20181	+	0.322025i	0.398269	+	0.917269i	$0.369611\pi$
$402$	19.2321	−	33.3109i	0.959209	−	1.66140i
$403$	15.7482	+	23.0686i	0.784472	+	1.14913i
$404$	−17.6799	+	10.2075i	−0.879610	+	0.507843i
$405$	−19.8171	+	19.8171i	−0.984717	+	0.984717i
$406$		0			0
$407$		−	1.93332i		−	0.0958313i
$408$	−0.896536	+	3.34592i	−0.0443852	+	0.165648i
$409$	8.79283	+	32.8153i	0.434777	+	1.62261i	0.741598	+	0.670844i	$0.234068\pi$
$409$	8.79283	+	32.8153i	0.434777	+	1.62261i	−0.306821	+	0.951767i	$0.599265\pi$
$410$	3.89559	+	14.5386i	0.192390	+	0.718008i
$411$	−1.59899	+	5.96750i	−0.0788722	+	0.294355i
$412$			5.55147i			0.273501i
$413$		0			0
$414$	0.421494	−	0.421494i	0.0207153	−	0.0207153i
$415$	15.0321	−	8.67876i	0.737894	−	0.426024i
$416$	−24.1717	+	16.5012i	−1.18512	+	0.809038i
$417$	−3.04048	+	5.26627i	−0.148893	+	0.257890i
$418$	6.09391	+	1.63286i	0.298063	+	0.0798657i
$419$			19.6899i			0.961912i	0.876745	+	0.480956i	$0.159710\pi$
$419$			19.6899i			0.961912i	−0.876745	+	0.480956i	$0.840290\pi$
$420$		0			0
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.930619	+	0.365989i	$0.119269\pi$
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.365989	+	0.930619i	$0.380731\pi$
$422$	5.07709	−	18.9480i	0.247149	−	0.922373i
$423$	−2.51146	+	0.672944i	−0.122111	+	0.0327197i
$424$	0.382838	+	1.42877i	0.0185923	+	0.0693873i
$425$	−11.6816	+	6.74435i	−0.566639	+	0.327149i
$426$	−29.4207			−1.42544
$427$		0			0
$428$			6.38271i			0.308520i
$429$	−0.315634	−	4.17828i	−0.0152390	−	0.201729i
$430$	53.0819	+	30.6469i	2.55984	+	1.47792i
$431$	6.57242	−	1.76107i	0.316582	−	0.0848280i	−0.0970289	−	0.995282i	$-0.530934\pi$
$431$	6.57242	−	1.76107i	0.316582	−	0.0848280i	0.413611	+	0.910454i	$0.364267\pi$
$432$	−14.9383	+	8.62466i	−0.718721	+	0.414954i
$433$	8.34704			0.401133			0.200567	−	0.979680i	$-0.435722\pi$
$433$	8.34704			0.401133			0.200567	+	0.979680i	$0.435722\pi$
$434$		0			0
$435$	−23.2121	−	23.2121i	−1.11293	−	1.11293i
$436$	−10.7332	−	2.87596i	−0.514029	−	0.137734i
$437$	4.33800	−	1.16236i	0.207515	−	0.0556034i
$438$	23.4067	−	40.5416i	1.11841	−	1.93715i
$439$	−1.21175	−	2.09881i	−0.0578336	−	0.100171i	0.835659	−	0.549248i	$-0.185086\pi$
$439$	−1.21175	−	2.09881i	−0.0578336	−	0.100171i	−0.893493	+	0.449078i	$0.851753\pi$
$440$	−0.566106	−	0.566106i	−0.0269880	−	0.0269880i
$441$		0			0
$442$	28.8622	+	13.8780i	1.37283	+	0.660110i
$443$	−6.88816	−	11.9306i	−0.327266	−	0.566842i	0.654702	−	0.755887i	$-0.272794\pi$
$443$	−6.88816	−	11.9306i	−0.327266	−	0.566842i	−0.981968	+	0.189045i	$0.939461\pi$
$444$	3.15684	+	11.7815i	0.149817	+	0.559125i
$445$	11.3064	−	19.5833i	0.535976	−	0.928337i
$446$	3.74622	+	6.48865i	0.177389	+	0.307246i
$447$	4.78450	−	4.78450i	0.226299	−	0.226299i
$448$		0			0
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.185043	+	0.982730i	$0.559242\pi$
$449$	−24.7447	+	24.7447i	−1.16777	+	1.16777i	−0.982730	+	0.185043i	$0.940758\pi$
$450$	−1.92322	−	0.515326i	−0.0906615	−	0.0242927i
$451$	−1.42333	−	0.821763i	−0.0670222	−	0.0386953i
$452$	31.3587	+	18.1049i	1.47499	+	0.851585i
$453$	3.18596	−	11.8902i	0.149689	−	0.558648i
$454$	15.2535			0.715885
$455$		0			0
$456$	−3.85236			−0.180403
$457$	−1.04142	+	3.88663i	−0.0487156	+	0.181809i	−0.985997	−	0.166766i	$-0.946668\pi$
$457$	−1.04142	+	3.88663i	−0.0487156	+	0.181809i	0.937281	+	0.348575i	$0.113334\pi$
$458$	1.83346	+	1.05855i	0.0856718	+	0.0494626i
$459$	18.3337	+	10.5850i	0.855743	+	0.494064i
$460$	−5.68759	−	1.52399i	−0.265185	−	0.0710562i
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	−0.649363	−	0.760479i	$-0.724964\pi$
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	0.760479	+	0.649363i	$0.224964\pi$
$462$		0			0
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	−0.168270	−	0.985741i	$-0.553818\pi$
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	0.985741	+	0.168270i	$0.0538180\pi$
$464$	−11.1612	−	19.3318i	−0.518148	−	0.897458i
$465$	−20.0812	+	34.7817i	−0.931245	+	1.61296i
$466$	−13.0774	−	48.8056i	−0.605799	−	2.26087i
$467$	−10.7144	−	18.5578i	−0.495801	−	0.858753i	0.504187	−	0.863594i	$-0.331792\pi$
$467$	−10.7144	−	18.5578i	−0.495801	−	0.858753i	−0.999988	+	0.00484163i	$0.998459\pi$
$468$	0.821763	+	2.34396i	0.0379860	+	0.108350i
$469$		0			0
$470$	34.5647	+	34.5647i	1.59435	+	1.59435i
$471$	−3.11653	−	5.39798i	−0.143602	−	0.248726i
$472$	−0.0795368	+	0.137762i	−0.00366098	+	0.00634100i
$473$	−6.46485	+	1.73225i	−0.297254	+	0.0796491i
$474$	−49.7829	−	13.3393i	−2.28661	−	0.612694i
$475$	−10.6074	−	10.6074i	−0.486702	−	0.486702i
$476$		0			0
$477$	−1.04593			−0.0478900
$478$	16.4066	−	9.47235i	0.750420	−	0.433255i
$479$	6.30319	−	1.68893i	0.288000	−	0.0771694i	−0.111927	−	0.993716i	$-0.535702\pi$
$479$	6.30319	−	1.68893i	0.288000	−	0.0771694i	0.399927	+	0.916547i	$0.369036\pi$
$480$	−36.4449	−	21.0415i	−1.66348	−	0.960408i
$481$	10.8834	−	0.822153i	0.496242	−	0.0374870i
$482$			58.5180i			2.66542i
$483$		0			0
$484$	−23.4543			−1.06610
$485$	−0.826246	+	0.477034i	−0.0375179	+	0.0216610i
$486$	1.71114	+	6.38606i	0.0776188	+	0.289677i
$487$	−13.1530	+	3.52434i	−0.596020	+	0.159703i	−0.544203	−	0.838954i	$-0.683168\pi$
$487$	−13.1530	+	3.52434i	−0.596020	+	0.159703i	−0.0518167	+	0.998657i	$0.516501\pi$
$488$	0.887061	−	3.31056i	0.0401554	−	0.149862i
$489$	−19.0142	−	19.0142i	−0.859850	−	0.859850i
$490$		0			0
$491$		−	9.21924i		−	0.416059i	−0.978123	−	0.208029i	$-0.933295\pi$
$491$		−	9.21924i		−	0.416059i	0.978123	−	0.208029i	$-0.0667049\pi$
$492$	10.0155	+	2.68364i	0.451533	+	0.120988i
$493$	−13.6981	+	23.7258i	−0.616931	+	1.06856i
$494$	−6.60054	+	34.9994i	−0.296972	+	1.57470i
$495$	0.490262	−	0.283053i	0.0220356	−	0.0127223i
$496$	−19.3116	+	19.3116i	−0.867117	+	0.867117i
$497$		0			0
$498$		−	22.7576i		−	1.01979i
$499$	−2.43754	+	9.09701i	−0.109119	+	0.407238i	−0.998780	−	0.0493841i	$-0.984274\pi$
$499$	−2.43754	+	9.09701i	−0.109119	+	0.407238i	0.889661	+	0.456622i	$0.150941\pi$
$500$	−3.07380	−	11.4716i	−0.137465	−	0.513025i
$501$	10.8115	+	40.3490i	0.483021	+	1.80266i
$502$	−7.67487	+	28.6430i	−0.342546	+	1.27840i
$503$			1.81069i			0.0807346i	0.999185	+	0.0403673i	$0.0128528\pi$
$503$			1.81069i			0.0807346i	−0.999185	+	0.0403673i	$0.987147\pi$
$504$		0			0
$505$	−18.5741	+	18.5741i	−0.826535	+	0.826535i
$506$	1.05974	−	0.611844i	0.0471114	−	0.0271998i
$507$	23.3869	−	3.55366i	1.03865	−	0.157823i
$508$	−15.3089	+	26.5158i	−0.679222	+	1.17645i
$509$	−30.4438	−	8.15738i	−1.34940	−	0.361570i	−0.489485	−	0.872012i	$-0.662815\pi$
$509$	−30.4438	−	8.15738i	−1.34940	−	0.361570i	−0.859912	+	0.510442i	$0.829482\pi$
$510$			46.0491i			2.03909i
$511$		0			0
$512$	−22.4286	−	22.4286i	−0.991215	−	0.991215i
$513$	−6.09355	+	22.7414i	−0.269037	+	1.00406i
$514$	−28.9978	+	7.76993i	−1.27904	+	0.342717i
$515$	1.84874	+	6.89960i	0.0814653	+	0.304033i
$516$	36.5677	−	21.1124i	1.60980	−	0.929421i
$517$	−5.33761			−0.234748
$518$		0			0
$519$			26.1684i			1.14866i
$520$	2.94609	−	3.42757i	0.129195	−	0.150309i
$521$	−13.7477	−	7.93722i	−0.602297	−	0.347736i	0.167648	−	0.985847i	$-0.446383\pi$
$521$	−13.7477	−	7.93722i	−0.602297	−	0.347736i	−0.769945	+	0.638111i	$0.779716\pi$
$522$	−3.90615	+	1.04665i	−0.170968	+	0.0458106i
$523$	3.38438	−	1.95397i	0.147989	−	0.0854413i	−0.424177	−	0.905579i	$-0.639437\pi$
$523$	3.38438	−	1.95397i	0.147989	−	0.0854413i	0.572166	+	0.820138i	$0.306103\pi$
$524$	28.4098			1.24109
$525$		0			0
$526$	3.79928	+	3.79928i	0.165656	+	0.165656i
$527$	32.3761	+	8.67515i	1.41033	+	0.377896i
$528$	3.95746	−	1.06040i	0.172226	−	0.0461479i
$529$	−11.0645	+	19.1642i	−0.481063	+	0.833226i
$530$	9.83193	+	17.0294i	0.427072	+	0.739710i
$531$	−0.0795368	−	0.0795368i	−0.00345160	−	0.00345160i
$532$		0			0
$533$	4.02074	−	8.36196i	0.174158	−	0.362197i
$534$	−14.8239	−	25.6758i	−0.641495	−	1.11110i
$535$	2.12556	+	7.93269i	0.0918958	+	0.342960i
$536$	−2.26517	+	3.92340i	−0.0978407	+	0.169465i
$537$	3.74035	+	6.47848i	0.161408	+	0.279567i
$538$	14.2597	−	14.2597i	0.614780	−	0.614780i
$539$		0			0
$540$	21.8272	−	21.8272i	0.939292	−	0.939292i
$541$	−11.7124	−	3.13832i	−0.503555	−	0.134927i	−0.00190544	−	0.999998i	$-0.500607\pi$
$541$	−11.7124	−	3.13832i	−0.503555	−	0.134927i	−0.501649	+	0.865071i	$0.667273\pi$
$542$	8.63491	+	4.98537i	0.370901	+	0.214140i
$543$	−34.0008	−	19.6304i	−1.45911	−	0.842420i
$544$	−9.08998	+	33.9243i	−0.389730	+	1.45449i
$545$	−14.2975			−0.612436
$546$		0			0
$547$	−4.72546			−0.202046			−0.101023	−	0.994884i	$-0.532212\pi$
$547$	−4.72546			−0.202046			−0.101023	+	0.994884i	$0.532212\pi$
$548$	1.94580	−	7.26183i	0.0831205	−	0.310210i
$549$	2.09881	+	1.21175i	0.0895750	+	0.0517162i
$550$	−3.53981	−	2.04371i	−0.150938	−	0.0871441i
$551$	−29.4299	−	7.88571i	−1.25375	−	0.335943i
$552$	−0.528360	+	0.528360i	−0.0224885	+	0.0224885i
$553$		0			0
$554$	8.56268	−	8.56268i	0.363794	−	0.363794i
$555$	7.84691	+	13.5912i	0.333083	+	0.576916i
$556$	3.69995	−	6.40851i	0.156913	−	0.271781i
$557$	−8.72658	−	32.5680i	−0.369757	−	1.37995i	−0.860856	−	0.508848i	$-0.830071\pi$
$557$	−8.72658	−	32.5680i	−0.369757	−	1.37995i	0.491099	−	0.871104i	$-0.336595\pi$
$558$	2.47381	+	4.28477i	0.104725	+	0.181389i
$559$	−12.5007	−	35.6565i	−0.528725	−	1.50811i
$560$		0			0
$561$	−3.55554	−	3.55554i	−0.150115	−	0.150115i
$562$	13.4089	+	23.2249i	0.565620	+	0.979683i
$563$	−20.6388	+	35.7475i	−0.869823	+	1.50658i	−0.00764487	+	0.999971i	$0.502433\pi$
$563$	−20.6388	+	35.7475i	−0.869823	+	1.50658i	−0.862178	+	0.506606i	$0.830900\pi$
$564$	32.5269	−	8.71556i	1.36963	−	0.366991i
$565$	45.0031	+	12.0585i	1.89329	+	0.507307i
$566$	12.0878	+	12.0878i	0.508089	+	0.508089i
$567$		0			0
$568$	3.46520			0.145397
$569$	−37.7069	+	21.7701i	−1.58076	+	0.912650i	−0.586007	+	0.810306i	$0.699301\pi$
$569$	−37.7069	+	21.7701i	−1.58076	+	0.912650i	−0.994749	+	0.102344i	$0.967366\pi$
$570$	−49.4675	+	13.2548i	−2.07197	+	0.555182i
$571$	−18.4204	−	10.6350i	−0.770872	−	0.445063i	0.0623138	−	0.998057i	$-0.480152\pi$
$571$	−18.4204	−	10.6350i	−0.770872	−	0.445063i	−0.833185	+	0.552994i	$0.813485\pi$
$572$	0.384094	+	5.08453i	0.0160598	+	0.212595i
$573$		−	18.7455i		−	0.783105i
$574$		0			0
$575$	−2.90967			−0.121341
$576$	−2.58996	+	1.49532i	−0.107915	+	0.0623048i
$577$	−3.19797	−	11.9350i	−0.133133	−	0.496861i	0.866865	−	0.498543i	$-0.166131\pi$
$577$	−3.19797	−	11.9350i	−0.133133	−	0.496861i	−0.999999	+	0.00168199i	$0.999465\pi$
$578$	3.41170	−	0.914163i	0.141908	−	0.0380242i
$579$	−4.18665	+	15.6248i	−0.173991	+	0.649344i
$580$	28.2467	+	28.2467i	1.17288	+	1.17288i
$581$		0			0
$582$			1.25088i			0.0518508i
$583$	−2.07401	−	0.555730i	−0.0858968	−	0.0230160i
$584$	−2.75686	+	4.77503i	−0.114080	+	0.197592i
$585$	1.80190	+	2.63951i	0.0744994	+	0.109130i
$586$	38.9467	−	22.4859i	1.60887	−	0.928882i
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.319131	−	0.947711i	$-0.396609\pi$
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.947711	−	0.319131i	$-0.103391\pi$
$588$		0			0
$589$			37.2766i			1.53595i
$590$	−0.547324	+	2.04264i	−0.0225330	+	0.0840941i
$591$	−2.16521	−	8.08066i	−0.0890647	−	0.332394i
$592$	2.76209	+	10.3083i	0.113521	+	0.423667i
$593$	1.89614	−	7.07650i	0.0778653	−	0.290597i	−0.916002	−	0.401173i	$-0.868603\pi$
$593$	1.89614	−	7.07650i	0.0778653	−	0.290597i	0.993868	+	0.110575i	$0.0352694\pi$
$594$			6.41503i			0.263212i
$595$		0			0
$596$	−5.82225	+	5.82225i	−0.238488	+	0.238488i
$597$	−9.77215	+	5.64196i	−0.399948	+	0.230910i
$598$	3.89497	+	5.70553i	0.159277	+	0.233316i
$599$	9.26271	−	16.0435i	0.378464	−	0.655519i	−0.612375	−	0.790568i	$-0.709786\pi$
$599$	9.26271	−	16.0435i	0.378464	−	0.655519i	0.990839	+	0.135048i	$0.0431190\pi$
$600$	2.41083	+	0.645981i	0.0984219	+	0.0263721i
$601$		−	30.9807i		−	1.26373i	−0.775079	−	0.631864i	$-0.782290\pi$
$601$		−	30.9807i		−	1.26373i	0.775079	−	0.631864i	$-0.217710\pi$
$602$		0			0
$603$	−2.26517	−	2.26517i	−0.0922451	−	0.0922451i
$604$	−3.87698	+	14.4691i	−0.157752	+	0.588739i
$605$	−29.1500	+	7.81071i	−1.18511	+	0.317550i
$606$	8.91367	+	33.2663i	0.362093	+	1.35135i
$607$	25.5195	−	14.7337i	1.03581	−	0.598023i	0.117164	−	0.993113i	$-0.462620\pi$
$607$	25.5195	−	14.7337i	1.03581	−	0.598023i	0.918643	+	0.395090i	$0.129286\pi$
$608$	−39.0591			−1.58405
$609$		0			0
$610$		−	45.5625i		−	1.84477i
$611$	−2.26984	−	30.0475i	−0.0918278	−	1.21559i
$612$	2.58132	+	1.49032i	0.104343	+	0.0602427i
$613$	−19.0421	+	5.10231i	−0.769103	+	0.206080i	−0.621975	−	0.783037i	$-0.713669\pi$
$613$	−19.0421	+	5.10231i	−0.769103	+	0.206080i	−0.147128	+	0.989118i	$0.547003\pi$
$614$	−14.5205	+	8.38340i	−0.585998	+	0.338326i
$615$	13.3414			0.537976
$616$		0			0
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.992412	−	0.122957i	$-0.960762\pi$
$617$	−27.7052	−	27.7052i	−1.11537	−	1.11537i	−0.122957	−	0.992412i	$-0.539238\pi$
$618$	9.04611	+	2.42390i	0.363888	+	0.0975035i
$619$	6.26517	−	1.67875i	0.251819	−	0.0674746i	−0.130701	−	0.991422i	$-0.541723\pi$
$619$	6.26517	−	1.67875i	0.251819	−	0.0674746i	0.382520	+	0.923947i	$0.375056\pi$
$620$	24.4368	−	42.3258i	0.981405	−	1.69984i
$621$	2.28330	+	3.95478i	0.0916255	+	0.158700i
$622$	3.81137	+	3.81137i	0.152822	+	0.152822i
$623$		0			0
$624$	7.65233	+	21.8272i	0.306338	+	0.873786i
$625$	−15.4343	−	26.7330i	−0.617373	−	1.06932i
$626$	10.5462	+	39.3591i	0.421512	+	1.57310i
$627$	2.79605	−	4.84290i	0.111664	−	0.193407i
$628$	3.79249	+	6.56879i	0.151337	+	0.262123i
$629$	9.26134	−	9.26134i	0.369274	−	0.369274i
$630$		0			0
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$632$	5.86349	+	1.57112i	0.233237	+	0.0624957i
$633$	−15.0582	−	8.69384i	−0.598509	−	0.345549i
$634$	2.88547	+	1.66593i	0.114597	+	0.0661624i
$635$	−10.1963	+	38.0530i	−0.404627	+	1.51009i
$636$	13.5463			0.537145
$637$		0			0
$638$	−8.30174			−0.328669
$639$	−0.634176	+	2.36678i	−0.0250876	+	0.0936283i
$640$	8.63491	+	4.98537i	0.341325	+	0.197064i
$641$	19.3635	+	11.1795i	0.764812	+	0.441565i	0.831021	−	0.556241i	$-0.187757\pi$
$641$	19.3635	+	11.1795i	0.764812	+	0.441565i	−0.0662085	+	0.997806i	$0.521090\pi$
$642$	10.4006	+	2.78683i	0.410479	+	0.109988i
$643$	5.69880	−	5.69880i	0.224739	−	0.224739i	−0.585752	−	0.810491i	$-0.699201\pi$
$643$	5.69880	−	5.69880i	0.224739	−	0.224739i	0.810491	+	0.585752i	$0.199201\pi$
$644$		0			0
$645$	38.4170	−	38.4170i	1.51267	−	1.51267i
$646$	21.3701	+	37.0141i	0.840796	+	1.45630i
$647$	3.86755	−	6.69879i	0.152049	−	0.263357i	−0.779932	−	0.625865i	$-0.784746\pi$
$647$	3.86755	−	6.69879i	0.152049	−	0.263357i	0.931981	+	0.362508i	$0.118079\pi$
$648$	−1.12012	−	4.18034i	−0.0440024	−	0.164219i
$649$	−0.115456	−	0.199976i	−0.00453205	−	0.00784974i
$650$	9.99952	−	20.7961i	0.392214	−	0.815689i
$651$		0			0
$652$	23.1383	+	23.1383i	0.906165	+	0.906165i
$653$	−10.6960	−	18.5261i	−0.418568	−	0.724982i	0.577227	−	0.816583i	$-0.304135\pi$
$653$	−10.6960	−	18.5261i	−0.418568	−	0.724982i	−0.995796	+	0.0916019i	$0.970801\pi$
$654$	−9.37275	+	16.2341i	−0.366504	+	0.634803i
$655$	35.3089	−	9.46099i	1.37963	−	0.369672i
$656$	8.76309	+	2.34806i	0.342141	+	0.0916764i
$657$	−2.75686	−	2.75686i	−0.107555	−	0.107555i
$658$		0			0
$659$	−1.68445			−0.0656167			−0.0328084	−	0.999462i	$-0.510445\pi$
$659$	−1.68445			−0.0656167			−0.0328084	+	0.999462i	$0.510445\pi$
$660$	−6.34957	+	3.66593i	−0.247157	+	0.142696i
$661$	−31.9726	+	8.56704i	−1.24359	+	0.333219i	−0.819858	−	0.572567i	$-0.805948\pi$
$661$	−31.9726	+	8.56704i	−1.24359	+	0.333219i	−0.423734	+	0.905787i	$0.639281\pi$
$662$	−7.29942	−	4.21432i	−0.283700	−	0.163794i
$663$	18.5035	−	21.5275i	0.718617	−	0.836060i
$664$			2.68041i			0.104020i
$665$		0			0
$666$	1.93332			0.0749148
$667$	−5.11792	+	2.95483i	−0.198167	+	0.114412i
$668$	−13.1564	−	49.1005i	−0.509038	−	1.89976i
$669$	6.41491	−	1.71887i	0.248015	−	0.0664553i
$670$	−15.5875	+	58.1735i	−0.602199	+	2.24744i
$671$	3.51796	+	3.51796i	0.135809	+	0.135809i
$672$		0			0
$673$			26.2464i			1.01173i	0.862614	+	0.505863i	$0.168826\pi$
$673$			26.2464i			1.01173i	−0.862614	+	0.505863i	$0.831174\pi$
$674$	8.86973	+	2.37664i	0.341649	+	0.0915446i
$675$	7.62677	−	13.2100i	0.293555	−	0.508452i
$676$	−28.4595	+	4.32443i	−1.09460	+	0.166324i
$677$	−31.8402	+	18.3829i	−1.22372	+	0.706513i	−0.965708	−	0.259630i	$-0.916399\pi$
$677$	−31.8402	+	18.3829i	−1.22372	+	0.706513i	−0.258008	+	0.966143i	$0.583066\pi$
$678$	43.1939	−	43.1939i	1.65885	−	1.65885i
$679$		0			0
$680$		−	5.42372i		−	0.207990i
$681$	3.49937	−	13.0598i	0.134096	−	0.500454i
$682$	2.62879	+	9.81079i	0.100662	+	0.375675i
$683$	−5.33709	−	19.9183i	−0.204218	−	0.762152i	−0.989686	−	0.143251i	$-0.954245\pi$
$683$	−5.33709	−	19.9183i	−0.204218	−	0.762152i	0.785468	−	0.618902i	$-0.212422\pi$
$684$	−0.857949	+	3.20191i	−0.0328045	+	0.122428i
$685$		−	9.67329i		−	0.369597i
$686$		0			0
$687$	1.32693	−	1.32693i	0.0506255	−	0.0506255i
$688$	31.9950	−	18.4723i	1.21980	−	0.704252i
$689$	2.24644	−	11.9118i	0.0855825	−	0.453802i
$690$	−4.96666	+	8.60251i	−0.189078	+	0.327492i
$691$	41.6177	+	11.1514i	1.58321	+	0.424220i	0.939918	−	0.341399i	$-0.110901\pi$
$691$	41.6177	+	11.1514i	1.58321	+	0.424220i	0.643293	+	0.765620i	$0.277568\pi$
$692$		−	31.8442i		−	1.21054i
$693$		0			0
$694$	−12.7906	−	12.7906i	−0.485525	−	0.485525i
$695$	2.46430	−	9.19691i	0.0934764	−	0.348859i
$696$	4.89651	−	1.31202i	0.185602	−	0.0497319i
$697$	−2.88175	−	10.7549i	−0.109154	−	0.407369i
$698$	29.7016	−	17.1483i	1.12422	−	0.649071i
$699$	−44.7866			−1.69399
$700$		0			0
$701$		−	17.7368i		−	0.669911i	−0.942234	−	0.334955i	$-0.891279\pi$
$701$		−	17.7368i		−	0.669911i	0.942234	−	0.334955i	$-0.108721\pi$
$702$	−36.1127	+	2.72801i	−1.36299	+	0.102962i
$703$	12.6146	+	7.28306i	0.475770	+	0.274686i
$704$	−5.93022	+	1.58900i	−0.223503	+	0.0598876i
$705$	37.5233	−	21.6641i	1.41321	−	0.815917i
$706$	8.44854			0.317965
$707$		0			0
$708$	1.03011	+	1.03011i	0.0387140	+	0.0387140i
$709$	−26.2853	−	7.04314i	−0.987167	−	0.264511i	−0.271107	−	0.962549i	$-0.587390\pi$
$709$	−26.2853	−	7.04314i	−0.987167	−	0.264511i	−0.716060	+	0.698039i	$0.754056\pi$
$710$	44.4962	−	11.9227i	1.66991	−	0.447451i
$711$	−2.14619	+	3.71730i	−0.0804883	+	0.139410i
$712$	1.74598	+	3.02413i	0.0654334	+	0.113334i
$713$	5.11257	+	5.11257i	0.191467	+	0.191467i
$714$		0			0
$715$	2.17061	+	6.19135i	0.0811762	+	0.231543i
$716$	−4.55162	−	7.88364i	−0.170102	−	0.294625i
$717$	−4.34617	−	16.2201i	−0.162311	−	0.605752i
$718$	5.11430	−	8.85824i	0.190864	−	0.330586i
$719$	21.1775	+	36.6806i	0.789789	+	1.36795i	0.926096	+	0.377287i	$0.123143\pi$
$719$	21.1775	+	36.6806i	0.789789	+	1.36795i	−0.136308	+	0.990667i	$0.543524\pi$
$720$	−2.20963	+	2.20963i	−0.0823481	+	0.0823481i
$721$		0			0
$722$	−6.03011	+	6.03011i	−0.224418	+	0.224418i
$723$	50.1021	+	13.4248i	1.86332	+	0.499275i
$724$	41.3754	+	23.8881i	1.53771	+	0.887795i
$725$	17.0951	+	9.86987i	0.634897	+	0.366558i
$726$	−10.2407	+	38.2187i	−0.380067	+	1.41843i
$727$	−23.2484			−0.862234			−0.431117	−	0.902296i	$-0.641880\pi$
$727$	−23.2484			−0.862234			−0.431117	+	0.902296i	$0.641880\pi$
$728$		0			0
$729$	−23.6494			−0.875904
$730$	−18.9710	+	70.8009i	−0.702150	+	2.62046i
$731$	−39.2672	−	22.6709i	−1.45235	−	0.838515i
$732$	−27.1825	−	15.6938i	−1.00469	−	0.580060i
$733$	32.9595	+	8.83146i	1.21739	+	0.326197i	0.809656	−	0.586905i	$-0.199654\pi$
$733$	32.9595	+	8.83146i	1.21739	+	0.326197i	0.407730	+	0.913103i	$0.366321\pi$
$734$	−28.7580	+	28.7580i	−1.06148	+	1.06148i
$735$		0			0
$736$	−5.35704	+	5.35704i	−0.197463	+	0.197463i
$737$	−3.28814	−	5.69523i	−0.121120	−	0.209786i
$738$	0.821763	−	1.42333i	0.0302495	−	0.0523937i
$739$	1.63463	+	6.10053i	0.0601309	+	0.224412i	0.989452	−	0.144861i	$-0.0462735\pi$
$739$	1.63463	+	6.10053i	0.0601309	+	0.224412i	−0.929321	+	0.369273i	$0.879607\pi$
$740$	−9.54887	−	16.5391i	−0.351024	−	0.607991i
$741$	28.4516	+	13.6806i	1.04520	+	0.502570i
$742$		0			0
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	0.866485	−	0.499203i	$-0.166374\pi$
$743$	10.0114	+	10.0114i	0.367282	+	0.367282i	−0.499203	+	0.866485i	$0.666374\pi$
$744$	−3.10102	−	5.37112i	−0.113689	−	0.196915i
$745$	−5.29721	+	9.17504i	−0.194075	+	0.336147i
$746$	−48.6548	+	13.0370i	−1.78138	+	0.477319i
$747$	−1.83076	−	0.490549i	−0.0669838	−	0.0179483i
$748$	4.32672	+	4.32672i	0.158201	+	0.158201i
$749$		0			0
$750$	−20.0350			−0.731576
$751$	7.07270	−	4.08343i	0.258087	−	0.149006i	−0.365375	−	0.930860i	$-0.619059\pi$
$751$	7.07270	−	4.08343i	0.258087	−	0.149006i	0.623461	+	0.781854i	$0.285726\pi$
$752$	28.4595	−	7.62570i	1.03781	−	0.278081i
$753$	22.7629	+	13.1422i	0.829528	+	0.478928i
$754$	−3.53035	−	46.7337i	−0.128568	−	1.70194i
$755$			19.2739i			0.701448i
$756$		0			0
$757$	10.5210			0.382392			0.191196	−	0.981552i	$-0.438763\pi$
$757$	10.5210			0.382392			0.191196	+	0.981552i	$0.438763\pi$
$758$	22.0839	−	12.7501i	0.802122	−	0.463105i
$759$	−0.280731	−	1.04770i	−0.0101899	−	0.0380291i
$760$	5.82634	−	1.56116i	0.211343	−	0.0566293i
$761$	−2.17835	+	8.12973i	−0.0789653	+	0.294702i	−0.994103	−	0.108439i	$-0.965415\pi$
$761$	−2.17835	+	8.12973i	−0.0789653	+	0.294702i	0.915138	+	0.403141i	$0.132082\pi$
$762$	36.5232	+	36.5232i	1.32310	+	1.32310i
$763$		0			0
$764$			22.8113i			0.825286i
$765$	3.70447	+	0.992609i	0.133935	+	0.0358879i
$766$	−25.9823	+	45.0027i	−0.938779	+	1.62601i
$767$	1.07664	−	0.734988i	0.0388754	−	0.0265389i
$768$	−18.9757	+	10.9556i	−0.684726	+	0.395327i
$769$	−9.73800	+	9.73800i	−0.351161	+	0.351161i	−0.860541	−	0.509380i	$-0.829875\pi$
$769$	−9.73800	+	9.73800i	−0.351161	+	0.351161i	0.509380	+	0.860541i	$0.329875\pi$
$770$		0			0
$771$			26.6099i			0.958333i
$772$	5.09472	−	19.0138i	0.183363	−	0.684320i
$773$	5.86540	+	21.8900i	0.210964	+	0.787327i	0.987549	+	0.157315i	$0.0502837\pi$
$773$	5.86540	+	21.8900i	0.210964	+	0.787327i	−0.776585	+	0.630013i	$0.783050\pi$
$774$	−1.73225	−	6.46485i	−0.0622645	−	0.232374i
$775$	6.25070	−	23.3279i	0.224532	−	0.837964i
$776$		−	0.147331i		−	0.00528886i
$777$		0			0
$778$	17.5161	−	17.5161i	0.627981	−	0.627981i
$779$	10.7237	−	6.19135i	0.384218	−	0.221828i
$780$	−23.3371	−	34.1853i	−0.835602	−	1.22403i
$781$	−2.51506	+	4.35620i	−0.0899958	+	0.155877i
$782$	8.00753	+	2.14561i	0.286349	+	0.0767269i
$783$		−	30.9807i		−	1.10716i
$784$		0			0
$785$	6.90099	+	6.90099i	0.246307	+	0.246307i
$786$	12.4044	−	46.2938i	0.442450	−	1.65124i
$787$	−24.5672	+	6.58275i	−0.875725	+	0.234650i	−0.668562	−	0.743657i	$-0.733090\pi$
$787$	−24.5672	+	6.58275i	−0.875725	+	0.234650i	−0.207163	+	0.978306i	$0.566423\pi$
$788$	2.63483	+	9.83333i	0.0938620	+	0.350298i
$789$	4.12448	−	2.38127i	0.146836	−	0.0847755i
$790$	80.6979			2.87110
$791$		0			0
$792$			0.0874201i			0.00310634i
$793$	−18.3080	+	21.3000i	−0.650135	+	0.756386i
$794$	19.6659	+	11.3541i	0.697917	+	0.402943i
$795$	16.8359	−	4.51116i	0.597106	−	0.159994i
$796$	11.8917	−	6.86568i	0.421490	−	0.243347i
$797$	−43.9698			−1.55749			−0.778745	−	0.627341i	$-0.784143\pi$
$797$	−43.9698			−1.55749			−0.778745	+	0.627341i	$0.784143\pi$
$798$		0			0
$799$	−25.5691	−	25.5691i	−0.904571	−	0.904571i
$800$	24.4434	+	6.54960i	0.864206	+	0.231563i
$801$	−2.38505	+	0.639073i	−0.0842717	+	0.0225805i
$802$	−25.5741	+	44.2956i	−0.903051	+	1.56413i
$803$	−4.00188	−	6.93146i	−0.141223	−	0.244606i
$804$	29.3371	+	29.3371i	1.03464	+	1.03464i
$805$		0			0
$806$	−54.1109	+	18.9706i	−1.90597	+	0.668210i
$807$	−8.93755	−	15.4803i	−0.314617	−	0.544932i
$808$	−1.04986	−	3.91814i	−0.0369340	−	0.137840i
$809$	−6.02543	+	10.4363i	−0.211843	+	0.366922i	−0.952291	−	0.305191i	$-0.901280\pi$
$809$	−6.02543	+	10.4363i	−0.211843	+	0.366922i	0.740449	+	0.672113i	$0.234613\pi$
$810$	−28.7666	−	49.8251i	−1.01075	−	1.75068i
$811$	1.07742	−	1.07742i	0.0378333	−	0.0378333i	−0.687937	−	0.725770i	$-0.741483\pi$
$811$	1.07742	−	1.07742i	0.0378333	−	0.0378333i	0.725770	+	0.687937i	$0.241483\pi$
$812$		0			0
$813$	6.24935	−	6.24935i	0.219174	−	0.219174i
$814$	3.83365	+	1.02722i	0.134369	+	0.0360041i
$815$	36.4627	+	21.0517i	1.27723	+	0.737410i
$816$	24.0374	+	13.8780i	0.841479	+	0.485828i
$817$	13.0512	−	48.7077i	0.456604	−	1.70407i
$818$	−69.7423			−2.43848
$819$		0			0
$820$	−16.2351			−0.566953
$821$	−12.5125	+	46.6971i	−0.436688	+	1.62974i	0.300306	+	0.953843i	$0.402911\pi$
$821$	−12.5125	+	46.6971i	−0.436688	+	1.62974i	−0.736994	+	0.675899i	$0.763756\pi$
$822$	−10.9836	−	6.34136i	−0.383096	−	0.221180i
$823$	−4.08425	−	2.35804i	−0.142368	−	0.0821963i	0.427124	−	0.904193i	$-0.359527\pi$
$823$	−4.08425	−	2.35804i	−0.142368	−	0.0821963i	−0.569492	+	0.821997i	$0.692860\pi$
$824$	−1.06546	−	0.285489i	−0.0371171	−	0.00994550i
$825$	−2.56187	+	2.56187i	−0.0891929	+	0.0891929i
$826$		0			0
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	−0.150746	−	0.988572i	$-0.548168\pi$
$827$	24.0939	−	24.0939i	0.837826	−	0.837826i	0.988572	+	0.150746i	$0.0481677\pi$
$828$	0.321480	+	0.556819i	0.0111722	+	0.0193508i
$829$	−6.23443	+	10.7983i	−0.216531	+	0.375042i	−0.953745	−	0.300617i	$-0.902807\pi$
$829$	−6.23443	+	10.7983i	−0.216531	+	0.375042i	0.737214	+	0.675659i	$0.236141\pi$
$830$	9.22248	+	34.4188i	0.320117	+	1.19469i
$831$	−5.36683	−	9.29562i	−0.186173	−	0.322462i
$832$	−11.4669	−	32.7078i	−0.397544	−	1.13394i
$833$		0			0
$834$	−8.82717	−	8.82717i	−0.305660	−	0.305660i
$835$	−32.7027	−	56.6428i	−1.13172	−	1.96020i
$836$	−3.40251	+	5.89331i	−0.117678	+	0.203825i
$837$	−36.6122	+	9.81020i	−1.26550	+	0.339090i
$838$	−39.0436	−	10.4617i	−1.34874	−	0.361394i
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	0.995664	−	0.0930239i	$-0.0296533\pi$
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	−0.0930239	+	0.995664i	$0.529653\pi$
$840$		0			0
$841$	11.0923			0.382495
$842$	−66.8897	+	38.6188i	−2.30517	+	1.33089i
$843$	22.9609	−	6.15237i	0.790817	−	0.211899i
$844$	18.3242	+	10.5795i	0.630747	+	0.364162i
$845$	−33.9305	+	14.8521i	−1.16724	+	0.510928i
$846$		−	5.33761i		−	0.183511i
$847$		0			0
$848$	11.8524			0.407012
$849$	13.1225	−	7.57628i	0.450363	−	0.260017i
$850$	−7.16688	−	26.7472i	−0.245822	−	0.917420i
$851$	2.72901	−	0.731237i	0.0935494	−	0.0250665i
$852$	8.21346	−	30.6531i	0.281389	−	1.05016i
$853$	15.4396	+	15.4396i	0.528641	+	0.528641i	0.920167	−	0.391526i	$-0.128053\pi$
$853$	15.4396	+	15.4396i	0.528641	+	0.528641i	−0.391526	+	0.920167i	$0.628053\pi$
$854$		0			0
$855$			4.26517i			0.145866i
$856$	−1.22499	−	0.328236i	−0.0418695	−	0.0112189i
$857$	17.9655	−	31.1172i	0.613691	−	1.06294i	−0.376922	−	0.926245i	$-0.623017\pi$
$857$	17.9655	−	31.1172i	0.613691	−	1.06294i	0.990613	−	0.136699i	$-0.0436493\pi$
$858$	8.45294	+	1.59414i	0.288579	+	0.0544231i
$859$	−5.24036	+	3.02552i	−0.178799	+	0.103229i	−0.586728	−	0.809784i	$-0.699584\pi$
$859$	−5.24036	+	3.02552i	−0.178799	+	0.103229i	0.407929	+	0.913013i	$0.366251\pi$
$860$	−46.7496	+	46.7496i	−1.59415	+	1.59415i
$861$		0			0
$862$			13.9684i			0.475764i
$863$	−4.33826	+	16.1906i	−0.147676	+	0.551135i	0.851945	+	0.523631i	$0.175423\pi$
$863$	−4.33826	+	16.1906i	−0.147676	+	0.551135i	−0.999622	+	0.0275046i	$0.991244\pi$
$864$	−10.2793	−	38.3629i	−0.349709	−	1.30513i
$865$	−10.6047	−	39.5773i	−0.360571	−	1.34567i
$866$	−4.43499	+	16.5516i	−0.150707	+	0.562446i
$867$		−	3.13076i		−	0.106326i
$868$		0			0
$869$	−6.23083	+	6.23083i	−0.211367	+	0.211367i
$870$	58.3611	−	33.6948i	1.97863	−	1.14236i
$871$	30.6624	−	20.9321i	1.03895	−	0.709259i
$872$	1.10393	−	1.91207i	0.0373839	−	0.0647508i
$873$	0.100629	+	0.0269634i	0.00340576	+	0.000912572i
$874$			9.21955i			0.311856i
$875$		0			0
$876$	35.7052	+	35.7052i	1.20637	+	1.20637i
$877$	10.8981	−	40.6722i	0.368002	−	1.37340i	−0.495304	−	0.868720i	$-0.664943\pi$
$877$	10.8981	−	40.6722i	0.368002	−	1.37340i	0.863306	−	0.504682i	$-0.168390\pi$
$878$	4.80563	−	1.28766i	0.162182	−	0.0434565i
$879$	−10.3171	−	38.5040i	−0.347988	−	1.29871i
$880$	−5.55558	+	3.20751i	−0.187278	+	0.108125i
$881$	−18.8928			−0.636516			−0.318258	−	0.948004i	$-0.603098\pi$
$881$	−18.8928			−0.636516			−0.318258	+	0.948004i	$0.603098\pi$
$882$		0			0
$883$			7.28391i			0.245123i	0.992461	+	0.122562i	$0.0391109\pi$
$883$			7.28391i			0.245123i	−0.992461	+	0.122562i	$0.960889\pi$
$884$	−22.5169	+	26.1968i	−0.757324	+	0.881093i
$885$	1.62331	+	0.937219i	0.0545670	+	0.0315043i
$886$	27.3175	−	7.31969i	0.917748	−	0.245910i
$887$	−31.6549	+	18.2760i	−1.06287	+	0.613648i	−0.926224	−	0.376973i	$-0.876965\pi$
$887$	−31.6549	+	18.2760i	−1.06287	+	0.613648i	−0.136644	+	0.990620i	$0.543632\pi$
$888$	−2.42350			−0.0813272
$889$		0			0
$890$	32.8249	+	32.8249i	1.10029	+	1.10029i
$891$	6.06821	+	1.62597i	0.203293	+	0.0544721i
$892$	−7.80628	+	2.09169i	−0.261373	+	0.0700348i
$893$	20.1074	−	34.8270i	0.672868	−	1.16544i
$894$	6.94521	+	12.0295i	0.232283	+	0.402325i
$895$	−8.28233	−	8.28233i	−0.276848	−	0.276848i
$896$		0			0
$897$	5.77854	−	2.02588i	0.192940	−	0.0676422i
$898$	−35.9195	−	62.2144i	−1.19865	−	2.07612i
$899$	−12.6955	−	47.3801i	−0.423418	−	1.58022i
$900$	1.07382	−	1.85991i	0.0357941	−	0.0619971i
$901$	−7.27314	−	12.5975i	−0.242303	−	0.419682i
$902$	2.38575	−	2.38575i	0.0794368	−	0.0794368i
$903$		0			0
$904$	−5.08742	+	5.08742i	−0.169205	+	0.169205i
$905$	59.3783	+	15.9104i	1.97380	+	0.528878i
$906$	21.8846	+	12.6351i	0.727066	+	0.419772i
$907$	−7.32549	−	4.22938i	−0.243239	−	0.140434i	0.373426	−	0.927660i	$-0.378183\pi$
$907$	−7.32549	−	4.22938i	−0.243239	−	0.140434i	−0.616665	+	0.787226i	$0.711516\pi$
$908$	−4.25837	+	15.8925i	−0.141319	+	0.527410i
$909$	2.86827			0.0951347
$910$		0			0
$911$	−11.0973			−0.367669			−0.183834	−	0.982957i	$-0.558851\pi$
$911$	−11.0973			−0.367669			−0.183834	+	0.982957i	$0.558851\pi$
$912$	−7.98930	+	29.8165i	−0.264552	+	0.987322i
$913$	−3.36962	−	1.94545i	−0.111518	−	0.0643850i
$914$	−7.15359	−	4.13013i	−0.236620	−	0.136612i
$915$	−39.0098	−	10.4526i	−1.28962	−	0.345554i
$916$	−1.61474	+	1.61474i	−0.0533524	+	0.0533524i
$917$		0			0
$918$	−30.7304	+	30.7304i	−1.01425	+	1.01425i
$919$	15.3613	+	26.6065i	0.506722	+	0.877668i	0.999970	+	0.00777889i	$0.00247612\pi$
$919$	15.3613	+	26.6065i	0.506722	+	0.877668i	−0.493248	+	0.869889i	$0.664191\pi$
$920$	0.584979	−	1.01321i	0.0192862	−	0.0334046i
$921$	3.84653	+	14.3554i	0.126747	+	0.473028i
$922$	3.46317	+	5.99839i	0.114053	+	0.197546i
$923$	−25.5923	−	12.3057i	−0.842381	−	0.405048i
$924$		0			0
$925$	−6.67307	−	6.67307i	−0.219409	−	0.219409i
$926$	25.5336	+	44.2255i	0.839085	+	1.45334i
$927$	0.389986	−	0.675475i	0.0128088	−	0.0221855i
$928$	49.6458	−	13.3025i	1.62970	−	0.436677i
$929$	−33.8237	−	9.06302i	−1.10972	−	0.297348i	−0.343002	−	0.939335i	$-0.611444\pi$
$929$	−33.8237	−	9.06302i	−1.10972	−	0.297348i	−0.766716	+	0.641987i	$0.778110\pi$
$930$	−58.3001	−	58.3001i	−1.91174	−	1.91174i
$931$		0			0
$932$	54.5007			1.78523
$933$	4.13761	−	2.38885i	0.135459	−	0.0782074i
$934$	42.4916	−	11.3856i	1.39037	−	0.372548i
$935$	6.81830	+	3.93655i	0.222982	+	0.128739i
$936$	−0.492122	+	0.0371758i	−0.0160855	+	0.00121513i
$937$			18.9594i			0.619376i	0.950838	+	0.309688i	$0.100225\pi$
$937$			18.9594i			0.619376i	−0.950838	+	0.309688i	$0.899775\pi$
$938$		0			0
$939$	36.1180			1.17867
$940$	−45.6620	+	26.3630i	−1.48933	+	0.859865i
$941$	11.9999	+	44.7841i	0.391184	+	1.45992i	0.828183	+	0.560457i	$0.189375\pi$
$941$	11.9999	+	44.7841i	0.391184	+	1.45992i	−0.436999	+	0.899462i	$0.643959\pi$
$942$	12.3597	−	3.31178i	0.402701	−	0.107903i
$943$	0.621627	−	2.31994i	0.0202430	−	0.0755478i
$944$	0.901299	+	0.901299i	0.0293348	+	0.0293348i
$945$		0			0
$946$		−	13.7397i		−	0.446718i
$947$	40.9464	+	10.9715i	1.33058	+	0.356527i	0.852930	−	0.522025i	$-0.174823\pi$
$947$	40.9464	+	10.9715i	1.33058	+	0.356527i	0.477647	+	0.878552i	$0.341490\pi$
$948$	27.7961	−	48.1442i	0.902774	−	1.56365i
$949$	37.3181	−	25.4758i	1.21140	−	0.826979i
$950$	26.6698	−	15.3978i	0.865281	−	0.499570i
$951$	2.08830	−	2.08830i	0.0677179	−	0.0677179i
$952$		0			0
$953$			41.0785i			1.33066i	0.746548	+	0.665332i	$0.231710\pi$
$953$			41.0785i			1.33066i	−0.746548	+	0.665332i	$0.768290\pi$
$954$	0.555730	−	2.07401i	0.0179924	−	0.0671486i
$955$	7.59659	+	28.3509i	0.245820	+	0.917413i
$956$	5.28884	+	19.7382i	0.171053	+	0.638380i
$957$	−1.90453	+	7.10781i	−0.0615648	+	0.229763i
$958$			13.3962i			0.432810i
$959$		0			0
$960$	35.2400	−	35.2400i	1.13737	−	1.13737i
$961$	−25.1258	+	14.5064i	−0.810509	+	0.467948i
$962$	−4.15236	+	22.0179i	−0.133878	+	0.709886i
$963$	0.448379	−	0.776616i	0.0144488	−	0.0250261i
$964$	−60.9691	−	16.3366i	−1.96368	−	0.526167i
$965$		−	25.3277i		−	0.815327i
$966$		0			0
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.760492	−	0.649347i	$-0.775042\pi$
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.649347	−	0.760492i	$-0.724958\pi$
$968$	1.20616	−	4.50144i	0.0387674	−	0.144682i
$969$	36.5935	−	9.80519i	1.17555	−	0.314988i
$970$	−0.506919	−	1.89185i	−0.0162762	−	0.0607436i
$971$	−38.3513	+	22.1421i	−1.23075	+	0.710575i	−0.967187	−	0.254066i	$-0.918232\pi$
$971$	−38.3513	+	22.1421i	−1.23075	+	0.710575i	−0.263566	+	0.964641i	$0.584899\pi$
$972$	−7.13125			−0.228735
$973$		0			0
$974$		−	27.9541i		−	0.895706i
$975$	−15.5112	−	13.3323i	−0.496756	−	0.426976i
$976$	−23.7834	−	13.7314i	−0.761288	−	0.439530i
$977$	−9.57866	+	2.56659i	−0.306449	+	0.0821126i	−0.408766	−	0.912639i	$-0.634041\pi$
$977$	−9.57866	+	2.56659i	−0.306449	+	0.0821126i	0.102318	+	0.994752i	$0.467374\pi$
$978$	47.8065	−	27.6011i	1.52868	−	0.882585i
$979$	−5.06895			−0.162004
$980$		0			0
$981$	1.10393	+	1.10393i	0.0352459	+	0.0352459i
$982$	18.2811	+	4.89841i	0.583374	+	0.156315i
$983$	−43.4442	+	11.6408i	−1.38566	+	0.371285i	−0.873172	−	0.487412i	$-0.837941\pi$
$983$	−43.4442	+	11.6408i	−1.38566	+	0.371285i	−0.512484	+	0.858697i	$0.671274\pi$
$984$	−1.03011	+	1.78421i	−0.0328388	+	0.0568784i
$985$	6.54936	+	11.3438i	0.208680	+	0.361444i
$986$	−39.7684	−	39.7684i	−1.26649	−	1.26649i
$987$		0			0
$988$	−34.6227	−	16.6479i	−1.10149	−	0.529640i
$989$	−4.89038	−	8.47038i	−0.155505	−	0.269343i
$990$	0.300786	+	1.12255i	0.00955961	+	0.0356769i
$991$	−21.0684	+	36.4915i	−0.669259	+	1.15919i	0.308853	+	0.951110i	$0.400055\pi$
$991$	−21.0684	+	36.4915i	−0.669259	+	1.15919i	−0.978112	+	0.208081i	$0.933278\pi$
$992$	−31.4412	−	54.4578i	−0.998260	−	1.72904i
$993$	−5.28281	+	5.28281i	−0.167645	+	0.167645i
$994$		0			0
$995$	12.4931	−	12.4931i	0.396058	−	0.396058i
$996$	23.7108	+	6.35329i	0.751306	+	0.201312i
$997$	−24.0161	−	13.8657i	−0.760596	−	0.439131i	0.0689134	−	0.997623i	$-0.478047\pi$
$997$	−24.0161	−	13.8657i	−0.760596	−	0.439131i	−0.829510	+	0.558492i	$0.811380\pi$
$998$	−16.7436	−	9.66693i	−0.530010	−	0.306001i
$999$	−3.83342	+	14.3065i	−0.121284	+	0.452638i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bc.a.619.2		24
7.2	even	3	inner	637.2.bc.a.411.5		24
7.3	odd	6		91.2.i.a.34.2	yes	12
7.4	even	3		91.2.i.a.34.1	✓	12
7.5	odd	6	inner	637.2.bc.a.411.6		24
7.6	odd	2	inner	637.2.bc.a.619.1		24
13.5	odd	4	inner	637.2.bc.a.31.6		24
21.11	odd	6		819.2.y.h.307.5		12
21.17	even	6		819.2.y.h.307.6		12
91.5	even	12	inner	637.2.bc.a.460.2		24
91.18	odd	12		91.2.i.a.83.1	yes	12
91.31	even	12		91.2.i.a.83.2	yes	12
91.44	odd	12	inner	637.2.bc.a.460.1		24
91.83	even	4	inner	637.2.bc.a.31.5		24
273.122	odd	12		819.2.y.h.811.5		12
273.200	even	12		819.2.y.h.811.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.1	✓	12	7.4	even	3
91.2.i.a.34.2	yes	12	7.3	odd	6
91.2.i.a.83.1	yes	12	91.18	odd	12
91.2.i.a.83.2	yes	12	91.31	even	12
637.2.bc.a.31.5		24	91.83	even	4	inner
637.2.bc.a.31.6		24	13.5	odd	4	inner
637.2.bc.a.411.5		24	7.2	even	3	inner
637.2.bc.a.411.6		24	7.5	odd	6	inner
637.2.bc.a.460.1		24	91.44	odd	12	inner
637.2.bc.a.460.2		24	91.5	even	12	inner
637.2.bc.a.619.1		24	7.6	odd	2	inner
637.2.bc.a.619.2		24	1.1	even	1	trivial
819.2.y.h.307.5		12	21.11	odd	6
819.2.y.h.307.6		12	21.17	even	6
819.2.y.h.811.5		12	273.122	odd	12
819.2.y.h.811.6		12	273.200	even	12

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

\(f(q)\)	\(=\)	\(q+(-0.531325 + 1.98293i) q^{2} +(1.57586 + 0.909822i) q^{3} +(-1.91766 - 1.10716i) q^{4} +(-2.75205 - 0.737409i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 + 0.269427i) q^{9} +O(q^{10})\)	\(q+(-0.531325 + 1.98293i) q^{2} +(1.57586 + 0.909822i) q^{3} +(-1.91766 - 1.10716i) q^{4} +(-2.75205 - 0.737409i) q^{5} +(-2.64141 + 2.64141i) q^{6} +(0.311108 - 0.311108i) q^{8} +(0.155554 + 0.269427i) q^{9} +(2.92446 - 5.06531i) q^{10} +(0.165299 + 0.616905i) q^{11} +(-2.01464 - 3.48946i) q^{12} +(-3.40251 + 1.19288i) q^{13} +(-3.66593 - 3.66593i) q^{15} +(-1.76271 - 3.05311i) q^{16} +(-2.16336 + 3.74705i) q^{17} +(-0.616905 + 0.165299i) q^{18} +(-4.64791 - 1.24540i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +(-0.808282 + 0.466662i) q^{23} +(0.773315 - 0.207209i) q^{24} +(2.69986 + 1.55877i) q^{25} +(-0.557554 - 7.38074i) q^{26} -4.89283i q^{27} +6.33185 q^{29} +(9.21707 - 5.32148i) q^{30} +(-2.00502 - 7.48282i) q^{31} +(7.84064 - 2.10089i) q^{32} +(-0.300786 + 1.12255i) q^{33} +(-6.28070 - 6.28070i) q^{34} -0.688892i q^{36} +(-2.92397 - 0.783477i) q^{37} +(4.93910 - 8.55477i) q^{38} +(-6.44717 - 1.21587i) q^{39} +(-1.08560 + 0.626770i) q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(0.366025 - 1.36603i) q^{44} +(-0.229414 - 0.856183i) q^{45} +(-0.495898 - 1.85072i) q^{46} +(-2.16306 + 8.07264i) q^{47} -6.41503i q^{48} +(-4.52543 + 4.52543i) q^{50} +(-6.81830 + 3.93655i) q^{51} +(7.84554 + 1.47959i) q^{52} +(-1.68098 + 2.91155i) q^{53} +(9.70214 + 2.59968i) q^{54} -1.81964i q^{55} +(-6.19135 - 6.19135i) q^{57} +(-3.36427 + 12.5556i) q^{58} +(-0.349234 + 0.0935769i) q^{59} +(2.97122 + 11.0888i) q^{60} +(6.74625 - 3.89495i) q^{61} +15.9032 q^{62} +9.61285i q^{64} +(10.2435 - 0.773811i) q^{65} +(-2.06612 - 1.19288i) q^{66} +(-9.94603 + 2.66503i) q^{67} +(8.29717 - 4.79037i) q^{68} -1.69832 q^{69} +(5.56914 + 5.56914i) q^{71} +(0.132215 + 0.0354269i) q^{72} +(-12.1050 + 3.24351i) q^{73} +(3.10716 - 5.38176i) q^{74} +(2.83640 + 4.91279i) q^{75} +(7.53424 + 7.53424i) q^{76} +(5.83654 - 12.1383i) q^{78} +(6.89853 + 11.9486i) q^{79} +(2.59968 + 9.70214i) q^{80} +(4.91827 - 8.51869i) q^{81} +(-2.64141 - 4.57505i) q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(-20.7801 - 5.56801i) q^{86} +(9.97810 + 5.76086i) q^{87} +(0.243350 + 0.140498i) q^{88} +(-2.05418 + 7.66632i) q^{89} +1.81964 q^{90} +2.06668 q^{92} +(3.64842 - 13.6161i) q^{93} +(-14.8582 - 8.57839i) q^{94} +(11.8729 + 6.85482i) q^{95} +(14.2672 + 3.82288i) q^{96} +(0.236784 - 0.236784i) q^{97} +(-0.140498 + 0.140498i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9	\( 24 q + 4 q^{2} + 8 q^{8} + 4 q^{9} + 8 q^{11} - 8 q^{15} - 16 q^{16} + 8 q^{18} - 32 q^{22} - 8 q^{29} + 16 q^{32} - 12 q^{37} - 40 q^{39} - 12 q^{44} - 24 q^{46} - 56 q^{50} + 12 q^{53} - 16 q^{57} + 44 q^{58} - 44 q^{60} + 40 q^{65} - 60 q^{67} + 28 q^{72} + 48 q^{74} + 88 q^{78} + 4 q^{79} + 92 q^{81} + 24 q^{85} - 36 q^{86} + 48 q^{92} + 28 q^{93} + 24 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 8 * q^8 + 4 * q^9 + 8 * q^11 - 8 * q^15 - 16 * q^16 + 8 * q^18 - 32 * q^22 - 8 * q^29 + 16 * q^32 - 12 * q^37 - 40 * q^39 - 12 * q^44 - 24 * q^46 - 56 * q^50 + 12 * q^53 - 16 * q^57 + 44 * q^58 - 44 * q^60 + 40 * q^65 - 60 * q^67 + 28 * q^72 + 48 * q^74 + 88 * q^78 + 4 * q^79 + 92 * q^81 + 24 * q^85 - 36 * q^86 + 48 * q^92 + 28 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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