LMFDB - Embedded newform 507.2.f.g.239.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [507,2,Mod(239,507)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("507.239"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(507, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			239.14
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.249216 + 0.249216i) q^{2} +(0.892053 + 1.48467i) q^{3} -1.87578i q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.147689 + 0.592316i) q^{6} +(0.821655 + 0.821655i) q^{7} +(0.965906 - 0.965906i) q^{8} +(-1.40848 + 2.64881i) q^{9} +1.22474i q^{10} +(1.32603 - 1.32603i) q^{11} +(2.78492 - 1.67330i) q^{12} +0.409539i q^{14} +(-1.45617 + 5.84006i) q^{15} -3.27013 q^{16} -5.90167 q^{17} +(-1.01114 + 0.309108i) q^{18} +(3.48387 - 3.48387i) q^{19} +(4.60916 - 4.60916i) q^{20} +(-0.486926 + 1.95284i) q^{21} +0.660937 q^{22} +2.70965 q^{23} +(2.29569 + 0.572412i) q^{24} +7.07560i q^{25} +(-5.18904 + 0.271740i) q^{27} +(1.54125 - 1.54125i) q^{28} -2.68706i q^{29} +(-1.81834 + 1.09253i) q^{30} +(-3.22500 + 3.22500i) q^{31} +(-2.74678 - 2.74678i) q^{32} +(3.15161 + 0.785829i) q^{33} +(-1.47079 - 1.47079i) q^{34} +4.03793i q^{35} +(4.96858 + 2.64201i) q^{36} +(1.52785 + 1.52785i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(4.81276 + 4.81276i) q^{41} +(-0.608029 + 0.365330i) q^{42} -5.55122i q^{43} +(-2.48735 - 2.48735i) q^{44} +(-9.96955 + 3.04771i) q^{45} +(0.675287 + 0.675287i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(-2.91713 - 4.85506i) q^{48} -5.64977i q^{49} +(-1.76335 + 1.76335i) q^{50} +(-5.26460 - 8.76202i) q^{51} -2.46136i q^{53} +(-1.36091 - 1.22547i) q^{54} +6.51664 q^{55} +1.58728 q^{56} +(8.28020 + 2.06460i) q^{57} +(0.669659 - 0.669659i) q^{58} +(-7.07657 + 7.07657i) q^{59} +(10.9547 + 2.73147i) q^{60} -2.66269 q^{61} -1.60744 q^{62} +(-3.33369 + 1.01912i) q^{63} +5.17117i q^{64} +(0.589590 + 0.981273i) q^{66} +(4.81080 - 4.81080i) q^{67} +11.0702i q^{68} +(2.41715 + 4.02293i) q^{69} +(-1.00632 + 1.00632i) q^{70} +(8.20749 + 8.20749i) q^{71} +(1.19803 + 3.91896i) q^{72} +(-9.13263 - 9.13263i) q^{73} +0.761529i q^{74} +(-10.5049 + 6.31180i) q^{75} +(-6.53499 - 6.53499i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(-8.03534 - 8.03534i) q^{80} +(-5.03234 - 7.46160i) q^{81} +2.39883i q^{82} +(-4.58922 - 4.58922i) q^{83} +(3.66311 + 0.913368i) q^{84} +(-14.5015 - 14.5015i) q^{85} +(1.38345 - 1.38345i) q^{86} +(3.98940 - 2.39700i) q^{87} -2.56165i q^{88} +(3.02216 - 3.02216i) q^{89} +(-3.24410 - 1.72503i) q^{90} -5.08271i q^{92} +(-7.66492 - 1.91119i) q^{93} -1.11246 q^{94} +17.1211 q^{95} +(1.62779 - 6.52833i) q^{96} +(8.67443 - 8.67443i) q^{97} +(1.40801 - 1.40801i) q^{98} +(1.64471 + 5.38010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) $ 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.249216	+	0.249216i	0.176222	+	0.176222i	0.789707	−	0.613485i	$-0.210233\pi$
$2$	0.249216	+	0.249216i	0.176222	+	0.176222i	−0.613485	+	0.789707i	$0.710233\pi$
$3$	0.892053	+	1.48467i	0.515027	+	0.857174i
$3$	0.892053	+	1.48467i	0.515027	+	0.857174i
$4$		−	1.87578i		−	0.937892i
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.994541	+	0.104350i	$0.0332761\pi$
$5$	2.45719	+	2.45719i	1.09889	+	1.09889i	0.104350	+	0.994541i	$0.466724\pi$
$6$	−0.147689	+	0.592316i	−0.0602939	+	0.241812i
$7$	0.821655	+	0.821655i	0.310556	+	0.310556i	0.845125	−	0.534569i	$-0.179526\pi$
$7$	0.821655	+	0.821655i	0.310556	+	0.310556i	−0.534569	+	0.845125i	$0.679526\pi$
$8$	0.965906	−	0.965906i	0.341499	−	0.341499i
$9$	−1.40848	+	2.64881i	−0.469495	+	0.882935i
$10$			1.22474i			0.387298i
$11$	1.32603	−	1.32603i	0.399814	−	0.399814i	−0.478353	−	0.878167i	$-0.658766\pi$
$11$	1.32603	−	1.32603i	0.399814	−	0.399814i	0.878167	+	0.478353i	$0.158766\pi$
$12$	2.78492	−	1.67330i	0.803936	−	0.483039i
$13$		0			0
$13$		0			0
$14$			0.409539i			0.109454i
$15$	−1.45617	+	5.84006i	−0.375982	+	1.50790i
$16$	−3.27013			−0.817532
$17$	−5.90167			−1.43136			−0.715682	−	0.698426i	$-0.753884\pi$
$17$	−5.90167			−1.43136			−0.715682	+	0.698426i	$0.753884\pi$
$18$	−1.01114	+	0.309108i	−0.238328	+	0.0728573i
$19$	3.48387	−	3.48387i	0.799255	−	0.799255i	−0.183723	−	0.982978i	$-0.558815\pi$
$19$	3.48387	−	3.48387i	0.799255	−	0.799255i	0.982978	+	0.183723i	$0.0588148\pi$
$20$	4.60916	−	4.60916i	1.03064	−	1.03064i
$21$	−0.486926	+	1.95284i	−0.106256	+	0.426146i
$22$	0.660937			0.140912
$23$	2.70965			0.565001			0.282500	−	0.959267i	$-0.408836\pi$
$23$	2.70965			0.565001			0.282500	+	0.959267i	$0.408836\pi$
$24$	2.29569	+	0.572412i	0.468606	+	0.116843i
$25$			7.07560i			1.41512i
$26$		0			0
$27$	−5.18904	+	0.271740i	−0.998632	+	0.0522964i
$28$	1.54125	−	1.54125i	0.291268	−	0.291268i
$29$		−	2.68706i		−	0.498975i	−0.968378	−	0.249488i	$-0.919738\pi$
$29$		−	2.68706i		−	0.498975i	0.968378	−	0.249488i	$-0.0802622\pi$
$30$	−1.81834	+	1.09253i	−0.331981	+	0.199469i
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	−0.934690	−	0.355463i	$-0.884323\pi$
$31$	−3.22500	+	3.22500i	−0.579227	+	0.579227i	0.355463	+	0.934690i	$0.384323\pi$
$32$	−2.74678	−	2.74678i	−0.485567	−	0.485567i
$33$	3.15161	+	0.785829i	0.548625	+	0.136795i
$34$	−1.47079	−	1.47079i	−0.252238	−	0.252238i
$35$			4.03793i			0.682535i
$36$	4.96858	+	2.64201i	0.828097	+	0.440335i
$37$	1.52785	+	1.52785i	0.251177	+	0.251177i	0.821453	−	0.570276i	$-0.193164\pi$
$37$	1.52785	+	1.52785i	0.251177	+	0.251177i	−0.570276	+	0.821453i	$0.693164\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	4.81276	+	4.81276i	0.751627	+	0.751627i	0.974783	−	0.223156i	$-0.0716358\pi$
$41$	4.81276	+	4.81276i	0.751627	+	0.751627i	−0.223156	+	0.974783i	$0.571636\pi$
$42$	−0.608029	+	0.365330i	−0.0938210	+	0.0563716i
$43$		−	5.55122i		−	0.846553i	−0.906001	−	0.423276i	$-0.860880\pi$
$43$		−	5.55122i		−	0.846553i	0.906001	−	0.423276i	$-0.139120\pi$
$44$	−2.48735	−	2.48735i	−0.374982	−	0.374982i
$45$	−9.96955	+	3.04771i	−1.48617	+	0.454326i
$46$	0.675287	+	0.675287i	0.0995657	+	0.0995657i
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	−0.850895	−	0.525336i	$-0.823940\pi$
$47$	−2.23192	+	2.23192i	−0.325559	+	0.325559i	0.525336	+	0.850895i	$0.323940\pi$
$48$	−2.91713	−	4.85506i	−0.421051	−	0.700767i
$49$		−	5.64977i		−	0.807110i
$50$	−1.76335	+	1.76335i	−0.249375	+	0.249375i
$51$	−5.26460	−	8.76202i	−0.737191	−	1.22693i
$52$		0			0
$53$		−	2.46136i		−	0.338093i	−0.985608	−	0.169047i	$-0.945931\pi$
$53$		−	2.46136i		−	0.338093i	0.985608	−	0.169047i	$-0.0540689\pi$
$54$	−1.36091	−	1.22547i	−0.185197	−	0.166765i
$55$	6.51664			0.878704
$56$	1.58728			0.212110
$57$	8.28020	+	2.06460i	1.09674	+	0.273463i
$58$	0.669659	−	0.669659i	0.0879305	−	0.0879305i
$59$	−7.07657	+	7.07657i	−0.921291	+	0.921291i	−0.997121	−	0.0758301i	$-0.975839\pi$
$59$	−7.07657	+	7.07657i	−0.921291	+	0.921291i	0.0758301	+	0.997121i	$0.475839\pi$
$60$	10.9547	+	2.73147i	1.41424	+	0.352631i
$61$	−2.66269			−0.340922			−0.170461	−	0.985364i	$-0.554526\pi$
$61$	−2.66269			−0.340922			−0.170461	+	0.985364i	$0.554526\pi$
$62$	−1.60744			−0.204145
$63$	−3.33369	+	1.01912i	−0.420006	+	0.128397i
$64$			5.17117i			0.646397i
$65$		0			0
$66$	0.589590	+	0.981273i	0.0725736	+	0.120786i
$67$	4.81080	−	4.81080i	0.587732	−	0.587732i	−0.349284	−	0.937017i	$-0.613575\pi$
$67$	4.81080	−	4.81080i	0.587732	−	0.587732i	0.937017	+	0.349284i	$0.113575\pi$
$68$			11.0702i			1.34246i
$69$	2.41715	+	4.02293i	0.290991	+	0.484304i
$70$	−1.00632	+	1.00632i	−0.120278	+	0.120278i
$71$	8.20749	+	8.20749i	0.974050	+	0.974050i	0.999672	−	0.0256220i	$-0.00815664\pi$
$71$	8.20749	+	8.20749i	0.974050	+	0.974050i	−0.0256220	+	0.999672i	$0.508157\pi$
$72$	1.19803	+	3.91896i	0.141190	+	0.461854i
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.997444	−	0.0714492i	$-0.977238\pi$
$73$	−9.13263	−	9.13263i	−1.06889	−	1.06889i	−0.0714492	−	0.997444i	$-0.522762\pi$
$74$			0.761529i			0.0885259i
$75$	−10.5049	+	6.31180i	−1.21300	+	0.728824i
$76$	−6.53499	−	6.53499i	−0.749615	−	0.749615i
$77$	2.17908			0.248330
$78$		0			0
$79$	1.10008			0.123769			0.0618844	−	0.998083i	$-0.480289\pi$
$79$	1.10008			0.123769			0.0618844	+	0.998083i	$0.480289\pi$
$80$	−8.03534	−	8.03534i	−0.898378	−	0.898378i
$81$	−5.03234	−	7.46160i	−0.559149	−	0.829067i
$82$			2.39883i			0.264907i
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	0.408864	−	0.912596i	$-0.365925\pi$
$83$	−4.58922	−	4.58922i	−0.503732	−	0.503732i	−0.912596	+	0.408864i	$0.865925\pi$
$84$	3.66311	+	0.913368i	0.399678	+	0.0996566i
$85$	−14.5015	−	14.5015i	−1.57291	−	1.57291i
$86$	1.38345	−	1.38345i	0.149181	−	0.149181i
$87$	3.98940	−	2.39700i	0.427709	−	0.256986i
$88$		−	2.56165i		−	0.273073i
$89$	3.02216	−	3.02216i	0.320348	−	0.320348i	−0.528553	−	0.848901i	$-0.677265\pi$
$89$	3.02216	−	3.02216i	0.320348	−	0.320348i	0.848901	+	0.528553i	$0.177265\pi$
$90$	−3.24410	−	1.72503i	−0.341959	−	0.181834i
$91$		0			0
$92$		−	5.08271i		−	0.529909i
$93$	−7.66492	−	1.91119i	−0.794815	−	0.198181i
$94$	−1.11246			−0.114742
$95$	17.1211			1.75659
$96$	1.62779	−	6.52833i	0.166135	−	0.666295i
$97$	8.67443	−	8.67443i	0.880755	−	0.880755i	−0.112856	−	0.993611i	$-0.536000\pi$
$97$	8.67443	−	8.67443i	0.880755	−	0.880755i	0.993611	+	0.112856i	$0.0359999\pi$
$98$	1.40801	−	1.40801i	0.142231	−	0.142231i
$99$	1.64471	+	5.38010i	0.165299	+	0.540721i
$100$	13.2723			1.32723
$101$	−11.0956			−1.10405			−0.552026	−	0.833827i	$-0.686145\pi$
$101$	−11.0956			−1.10405			−0.552026	+	0.833827i	$0.686145\pi$
$102$	0.871614	−	3.49565i	0.0863026	−	0.346121i
$103$		−	4.43285i		−	0.436782i	−0.975861	−	0.218391i	$-0.929919\pi$
$103$		−	4.43285i		−	0.436782i	0.975861	−	0.218391i	$-0.0700808\pi$
$104$		0			0
$105$	−5.99499	+	3.60205i	−0.585051	+	0.351524i
$106$	0.613409	−	0.613409i	0.0595796	−	0.0595796i
$107$		−	13.0554i		−	1.26211i	−0.775738	−	0.631055i	$-0.782622\pi$
$107$		−	13.0554i		−	1.26211i	0.775738	−	0.631055i	$-0.217378\pi$
$108$	0.509725	+	9.73352i	0.0490484	+	0.936608i
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	−0.458694	−	0.888594i	$-0.651682\pi$
$109$	4.48829	−	4.48829i	0.429901	−	0.429901i	0.888594	+	0.458694i	$0.151682\pi$
$110$	1.62405	+	1.62405i	0.154847	+	0.154847i
$111$	−0.905429	+	3.63127i	−0.0859396	+	0.344665i
$112$	−2.68692	−	2.68692i	−0.253890	−	0.253890i
$113$		−	13.0126i		−	1.22413i	−0.790809	−	0.612063i	$-0.790340\pi$
$113$		−	13.0126i		−	1.22413i	0.790809	−	0.612063i	$-0.209660\pi$
$114$	1.54902	+	2.57809i	0.145079	+	0.241460i
$115$	6.65813	+	6.65813i	0.620874	+	0.620874i
$116$	−5.04035			−0.467985
$117$		0			0
$118$	−3.52718			−0.324704
$119$	−4.84913	−	4.84913i	−0.444519	−	0.444519i
$120$	4.23443	+	7.04748i	0.386549	+	0.643344i
$121$			7.48327i			0.680297i
$122$	−0.663584	−	0.663584i	−0.0600781	−	0.0600781i
$123$	−2.85212	+	11.4386i	−0.257167	+	1.03138i
$124$	6.04940	+	6.04940i	0.543252	+	0.543252i
$125$	−5.10014	+	5.10014i	−0.456171	+	0.456171i
$126$	−1.08479	−	0.576829i	−0.0966406	−	0.0513880i
$127$		−	7.79402i		−	0.691607i	−0.938307	−	0.345804i	$-0.887606\pi$
$127$		−	7.79402i		−	0.691607i	0.938307	−	0.345804i	$-0.112394\pi$
$128$	−6.78230	+	6.78230i	−0.599476	+	0.599476i
$129$	8.24172	−	4.95198i	0.725643	−	0.435997i
$130$		0			0
$131$			18.5420i			1.62003i	0.586412	+	0.810013i	$0.300540\pi$
$131$			18.5420i			1.62003i	−0.586412	+	0.810013i	$0.699460\pi$
$132$	1.47405	−	5.91174i	0.128299	−	0.514551i
$133$	5.72508			0.496428
$134$	2.39785			0.207143
$135$	−13.4182	−	12.0828i	−1.15485	−	1.03992i
$136$	−5.70046	+	5.70046i	−0.488810	+	0.488810i
$137$	−5.32795	+	5.32795i	−0.455197	+	0.455197i	−0.897075	−	0.441878i	$-0.854312\pi$
$137$	−5.32795	+	5.32795i	−0.455197	+	0.455197i	0.441878	+	0.897075i	$0.354312\pi$
$138$	−0.400186	+	1.60497i	−0.0340661	+	0.136624i
$139$	−5.39232			−0.457371			−0.228685	−	0.973500i	$-0.573443\pi$
$139$	−5.39232			−0.457371			−0.228685	+	0.973500i	$0.573443\pi$
$140$	7.57428			0.640143
$141$	−5.30466	−	1.32267i	−0.446733	−	0.111389i
$142$			4.09087i			0.343298i
$143$		0			0
$144$	4.60592	−	8.66193i	0.383827	−	0.721828i
$145$	6.60264	−	6.60264i	0.548319	−	0.548319i
$146$		−	4.55199i		−	0.376725i
$147$	8.38803	−	5.03989i	0.691833	−	0.415683i
$148$	2.86592	−	2.86592i	0.235577	−	0.235577i
$149$	−16.1312	−	16.1312i	−1.32152	−	1.32152i	−0.912545	−	0.408977i	$-0.865886\pi$
$149$	−16.1312	−	16.1312i	−1.32152	−	1.32152i	−0.408977	−	0.912545i	$-0.634114\pi$
$150$	−4.19099	−	1.04499i	−0.342193	−	0.0853231i
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	0.923125	−	0.384500i	$-0.125626\pi$
$151$	6.61873	+	6.61873i	0.538625	+	0.538625i	−0.384500	+	0.923125i	$0.625626\pi$
$152$		−	6.73019i		−	0.545891i
$153$	8.31241	−	15.6324i	0.672018	−	1.26380i
$154$	0.543062	+	0.543062i	0.0437612	+	0.0437612i
$155$	−15.8489			−1.27301
$156$		0			0
$157$	15.6785			1.25128			0.625640	−	0.780112i	$-0.284838\pi$
$157$	15.6785			1.25128			0.625640	+	0.780112i	$0.284838\pi$
$158$	0.274158	+	0.274158i	0.0218108	+	0.0218108i
$159$	3.65430	−	2.19566i	0.289805	−	0.174127i
$160$		−	13.4987i		−	1.06717i
$161$	2.22640	+	2.22640i	0.175465	+	0.175465i
$162$	0.605410	−	3.11369i	0.0475655	−	0.244634i
$163$	2.44403	+	2.44403i	0.191432	+	0.191432i	0.796314	−	0.604883i	$-0.206780\pi$
$163$	2.44403	+	2.44403i	0.191432	+	0.191432i	−0.604883	+	0.796314i	$0.706780\pi$
$164$	9.02770	−	9.02770i	0.704945	−	0.704945i
$165$	5.81319	+	9.67506i	0.452556	+	0.753202i
$166$		−	2.28741i		−	0.177537i
$167$	−3.70756	+	3.70756i	−0.286899	+	0.286899i	−0.835853	−	0.548954i	$-0.815026\pi$
$167$	−3.70756	+	3.70756i	−0.286899	+	0.286899i	0.548954	+	0.835853i	$0.315026\pi$
$168$	1.41594	+	2.35659i	0.109242	+	0.181815i
$169$		0			0
$170$		−	7.22802i		−	0.554364i
$171$	4.32112	+	14.1351i	0.330444	+	1.08094i
$172$	−10.4129			−0.793975
$173$	−14.2512			−1.08350			−0.541751	−	0.840539i	$-0.682238\pi$
$173$	−14.2512			−1.08350			−0.541751	+	0.840539i	$0.682238\pi$
$174$	1.59159	+	0.396851i	0.120658	+	0.0300852i
$175$	−5.81370	+	5.81370i	−0.439474	+	0.439474i
$176$	−4.33630	+	4.33630i	−0.326861	+	0.326861i
$177$	−16.8190	−	4.19369i	−1.26420	−	0.315217i
$178$	1.50634			0.112905
$179$	4.36667			0.326381			0.163190	−	0.986595i	$-0.447822\pi$
$179$	4.36667			0.326381			0.163190	+	0.986595i	$0.447822\pi$
$180$	5.71684	+	18.7007i	0.426108	+	1.39387i
$181$			2.10738i			0.156640i	0.996928	+	0.0783201i	$0.0249556\pi$
$181$			2.10738i			0.156640i	−0.996928	+	0.0783201i	$0.975044\pi$
$182$		0			0
$183$	−2.37526	−	3.95321i	−0.175584	−	0.292230i
$184$	2.61727	−	2.61727i	0.192947	−	0.192947i
$185$			7.50845i			0.552032i
$186$	−1.43392	−	2.38652i	−0.105140	−	0.174988i
$187$	−7.82581	+	7.82581i	−0.572280	+	0.572280i
$188$	4.18660	+	4.18660i	0.305339	+	0.305339i
$189$	−4.48688	−	4.04033i	−0.326372	−	0.293890i
$190$	4.26685	+	4.26685i	0.309550	+	0.309550i
$191$			6.79779i			0.491871i	0.969286	+	0.245935i	$0.0790951\pi$
$191$			6.79779i			0.491871i	−0.969286	+	0.245935i	$0.920905\pi$
$192$	−7.67748	+	4.61296i	−0.554075	+	0.332912i
$193$	−7.86036	−	7.86036i	−0.565801	−	0.565801i	0.365148	−	0.930949i	$-0.381018\pi$
$193$	−7.86036	−	7.86036i	−0.565801	−	0.565801i	−0.930949	+	0.365148i	$0.881018\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	1.61492	+	1.61492i	0.115058	+	0.115058i	0.762292	−	0.647233i	$-0.224074\pi$
$197$	1.61492	+	1.61492i	0.115058	+	0.115058i	−0.647233	+	0.762292i	$0.724074\pi$
$198$	−0.930919	+	1.75069i	−0.0661576	+	0.124416i
$199$			18.3431i			1.30031i	0.759801	+	0.650155i	$0.225296\pi$
$199$			18.3431i			1.30031i	−0.759801	+	0.650155i	$0.774704\pi$
$200$	6.83436	+	6.83436i	0.483262	+	0.483262i
$201$	11.4339	+	2.85096i	0.806487	+	0.201091i
$202$	−2.76519	−	2.76519i	−0.194558	−	0.194558i
$203$	2.20784	−	2.20784i	0.154960	−	0.154960i
$204$	−16.4357	+	9.87524i	−1.15073	+	0.691405i
$205$			23.6518i			1.65191i
$206$	1.10474	−	1.10474i	0.0769706	−	0.0769706i
$207$	−3.81650	+	7.17733i	−0.265265	+	0.498859i
$208$		0			0
$209$		−	9.23947i		−	0.639107i
$210$	−2.39173	−	0.596359i	−0.165045	−	0.0411527i
$211$	−8.00723			−0.551241			−0.275620	−	0.961267i	$-0.588883\pi$
$211$	−8.00723			−0.551241			−0.275620	+	0.961267i	$0.588883\pi$
$212$	−4.61697			−0.317095
$213$	−4.86389	+	19.5069i	−0.333269	+	1.33659i
$214$	3.25361	−	3.25361i	0.222412	−	0.222412i
$215$	13.6404	−	13.6404i	0.930269	−	0.930269i
$216$	−4.74965	+	5.27460i	−0.323173	+	0.358891i
$217$	−5.29967			−0.359765
$218$	2.23711			0.151516
$219$	5.41215	−	21.7057i	0.365719	−	1.46674i
$220$		−	12.2238i		−	0.824129i
$221$		0			0
$222$	−1.13062	+	0.679324i	−0.0758821	+	0.0455932i
$223$	−20.0214	+	20.0214i	−1.34073	+	1.34073i	−0.445400	+	0.895332i	$0.646938\pi$
$223$	−20.0214	+	20.0214i	−1.34073	+	1.34073i	−0.895332	+	0.445400i	$0.853062\pi$
$224$		−	4.51381i		−	0.301592i
$225$	−18.7419	−	9.96587i	−1.24946	−	0.664391i
$226$	3.24295	−	3.24295i	0.215718	−	0.215718i
$227$	5.20089	+	5.20089i	0.345195	+	0.345195i	0.858316	−	0.513121i	$-0.171511\pi$
$227$	5.20089	+	5.20089i	0.345195	+	0.345195i	−0.513121	+	0.858316i	$0.671511\pi$
$228$	3.87274	−	15.5319i	0.256479	−	1.02862i
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	0.975214	−	0.221263i	$-0.0710179\pi$
$229$	11.4094	+	11.4094i	0.753951	+	0.753951i	−0.221263	+	0.975214i	$0.571018\pi$
$230$			3.31862i			0.218823i
$231$	1.94386	+	3.23522i	0.127896	+	0.212862i
$232$	−2.59545	−	2.59545i	−0.170400	−	0.170400i
$233$	18.1554			1.18940			0.594700	−	0.803947i	$-0.297271\pi$
$233$	18.1554			1.18940			0.594700	+	0.803947i	$0.297271\pi$
$234$		0			0
$235$	−10.9685			−0.715508
$236$	13.2741	+	13.2741i	0.864071	+	0.864071i
$237$	0.981330	+	1.63326i	0.0637442	+	0.106091i
$238$		−	2.41696i		−	0.156668i
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	0.886306	−	0.463099i	$-0.153263\pi$
$239$	6.54262	+	6.54262i	0.423207	+	0.423207i	−0.463099	+	0.886306i	$0.653263\pi$
$240$	4.76187	−	19.0978i	0.307378	−	1.23275i
$241$	19.5707	+	19.5707i	1.26066	+	1.26066i	0.950775	+	0.309883i	$0.100290\pi$
$241$	19.5707	+	19.5707i	1.26066	+	1.26066i	0.309883	+	0.950775i	$0.399710\pi$
$242$	−1.86495	+	1.86495i	−0.119883	+	0.119883i
$243$	6.58890	−	14.1275i	0.422678	−	0.906280i
$244$			4.99463i			0.319748i
$245$	13.8826	−	13.8826i	0.886925	−	0.886925i
$246$	−3.56147	+	2.13988i	−0.227071	+	0.136434i
$247$		0			0
$248$			6.23009i			0.395611i
$249$	2.71965	−	10.9073i	0.172351	−	0.691221i
$250$	−2.54207			−0.160775
$251$	−5.60006			−0.353473			−0.176736	−	0.984258i	$-0.556554\pi$
$251$	−5.60006			−0.353473			−0.176736	+	0.984258i	$0.556554\pi$
$252$	1.91164	+	6.25328i	0.120422	+	0.393920i
$253$	3.59308	−	3.59308i	0.225895	−	0.225895i
$254$	1.94239	−	1.94239i	0.121877	−	0.121877i
$255$	8.59385	−	34.4661i	0.538168	−	2.15835i
$256$	6.96184			0.435115
$257$	−6.81357			−0.425019			−0.212510	−	0.977159i	$-0.568164\pi$
$257$	−6.81357			−0.425019			−0.212510	+	0.977159i	$0.568164\pi$
$258$	3.28808	+	0.819856i	0.204707	+	0.0510420i
$259$			2.51073i			0.156009i
$260$		0			0
$261$	7.11751	+	3.78469i	0.440563	+	0.234266i
$262$	−4.62097	+	4.62097i	−0.285485	+	0.285485i
$263$			22.6317i			1.39553i	0.716326	+	0.697765i	$0.245822\pi$
$263$			22.6317i			1.39553i	−0.716326	+	0.697765i	$0.754178\pi$
$264$	3.80320	−	2.28512i	0.234071	−	0.140640i
$265$	6.04803	−	6.04803i	0.371528	−	0.371528i
$266$	1.42678	+	1.42678i	0.0874816	+	0.0874816i
$267$	7.18283	+	1.79098i	0.439582	+	0.109606i
$268$	−9.02401	−	9.02401i	−0.551229	−	0.551229i
$269$			26.1029i			1.59152i	0.605610	+	0.795762i	$0.292929\pi$
$269$			26.1029i			1.59152i	−0.605610	+	0.795762i	$0.707071\pi$
$270$	−0.332812	−	6.35524i	−0.0202543	−	0.386768i
$271$	12.5033	+	12.5033i	0.759521	+	0.759521i	0.976235	−	0.216714i	$-0.0695339\pi$
$271$	12.5033	+	12.5033i	0.759521	+	0.759521i	−0.216714	+	0.976235i	$0.569534\pi$
$272$	19.2992			1.17019
$273$		0			0
$274$	−2.65562			−0.160432
$275$	9.38248	+	9.38248i	0.565785	+	0.565785i
$276$	7.54615	−	4.53405i	0.454225	−	0.272918i
$277$		−	22.7007i		−	1.36395i	−0.731375	−	0.681975i	$-0.761121\pi$
$277$		−	22.7007i		−	1.36395i	0.731375	−	0.681975i	$-0.238879\pi$
$278$	−1.34385	−	1.34385i	−0.0805989	−	0.0805989i
$279$	−4.00003	−	13.0848i	−0.239476	−	0.783364i
$280$	3.90026	+	3.90026i	0.233085	+	0.233085i
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	−0.914679	−	0.404181i	$-0.867557\pi$
$281$	−8.55751	+	8.55751i	−0.510498	+	0.510498i	0.404181	+	0.914679i	$0.367557\pi$
$282$	−0.992373	−	1.65164i	−0.0590950	−	0.0983535i
$283$			7.10558i			0.422383i	0.977445	+	0.211192i	$0.0677344\pi$
$283$			7.10558i			0.422383i	−0.977445	+	0.211192i	$0.932266\pi$
$284$	15.3955	−	15.3955i	0.913553	−	0.913553i
$285$	15.2729	+	25.4192i	0.904690	+	1.50570i
$286$		0			0
$287$			7.90886i			0.466845i
$288$	11.1445	−	3.40689i	0.656695	−	0.200753i
$289$	17.8297			1.04880
$290$	3.29096			0.193252
$291$	20.6167	+	5.14061i	1.20857	+	0.301348i
$292$	−17.1308	+	17.1308i	−1.00251	+	1.00251i
$293$	11.2394	−	11.2394i	0.656615	−	0.656615i	−0.297963	−	0.954578i	$-0.596307\pi$
$293$	11.2394	−	11.2394i	0.656615	−	0.656615i	0.954578	+	0.297963i	$0.0963071\pi$
$294$	3.34645	+	0.834411i	0.195169	+	0.0486638i
$295$	−34.7770			−2.02479
$296$	2.95152			0.171554
$297$	−6.52051	+	7.24118i	−0.378358	+	0.420176i
$298$		−	8.04031i		−	0.465763i
$299$		0			0
$300$	11.8396	+	19.7050i	0.683558	+	1.13767i
$301$	4.56119	−	4.56119i	0.262902	−	0.262902i
$302$			3.29899i			0.189835i
$303$	−9.89784	−	16.4733i	−0.568616	−	0.946364i
$304$	−11.3927	+	11.3927i	−0.653417	+	0.653417i
$305$	−6.54274	−	6.54274i	−0.374636	−	0.374636i
$306$	5.96742	−	1.82425i	0.341134	−	0.104285i
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	0.986247	−	0.165277i	$-0.0528518\pi$
$307$	14.3846	+	14.3846i	0.820970	+	0.820970i	−0.165277	+	0.986247i	$0.552852\pi$
$308$		−	4.08749i		−	0.232906i
$309$	6.58132	−	3.95433i	0.374398	−	0.224954i
$310$	−3.94979	−	3.94979i	−0.224333	−	0.224333i
$311$	−7.62181			−0.432193			−0.216097	−	0.976372i	$-0.569333\pi$
$311$	−7.62181			−0.432193			−0.216097	+	0.976372i	$0.569333\pi$
$312$		0			0
$313$	−6.51488			−0.368243			−0.184121	−	0.982904i	$-0.558944\pi$
$313$	−6.51488			−0.368243			−0.184121	+	0.982904i	$0.558944\pi$
$314$	3.90733	+	3.90733i	0.220503	+	0.220503i
$315$	−10.6957	−	5.68736i	−0.602634	−	0.320447i
$316$		−	2.06351i		−	0.116082i
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	0.507901	−	0.861416i	$-0.330422\pi$
$317$	−6.29415	−	6.29415i	−0.353515	−	0.353515i	−0.861416	+	0.507901i	$0.830422\pi$
$318$	1.45790	+	0.363516i	0.0817551	+	0.0203850i
$319$	−3.56314	−	3.56314i	−0.199497	−	0.199497i
$320$	−12.7066	+	12.7066i	−0.710319	+	0.710319i
$321$	19.3829	−	11.6461i	1.08185	−	0.650021i
$322$			1.10971i			0.0618415i
$323$	−20.5607	+	20.5607i	−1.14403	+	1.14403i
$324$	−13.9963	+	9.43958i	−0.777575	+	0.524421i
$325$		0			0
$326$			1.21818i			0.0674689i
$327$	10.6674	+	2.65984i	0.589910	+	0.147089i
$328$	9.29736			0.513361
$329$	−3.66774			−0.202209
$330$	−0.962439	+	3.85991i	−0.0529805	+	0.212481i
$331$	−11.3679	+	11.3679i	−0.624836	+	0.624836i	−0.946764	−	0.321928i	$-0.895669\pi$
$331$	−11.3679	+	11.3679i	−0.624836	+	0.624836i	0.321928	+	0.946764i	$0.395669\pi$
$332$	−8.60838	+	8.60838i	−0.472446	+	0.472446i
$333$	−6.19893	+	1.89502i	−0.339699	+	0.103847i
$334$	−1.84796			−0.101116
$335$	23.6421			1.29171
$336$	1.59231	−	6.38605i	0.0868677	−	0.348388i
$337$		−	28.3556i		−	1.54463i	−0.635243	−	0.772313i	$-0.719100\pi$
$337$		−	28.3556i		−	1.54463i	0.635243	−	0.772313i	$-0.280900\pi$
$338$		0			0
$339$	19.3195	−	11.6080i	1.04929	−	0.630457i
$340$	−27.2017	+	27.2017i	−1.47522	+	1.47522i
$341$			8.55291i			0.463166i
$342$	−2.44579	+	4.59958i	−0.132253	+	0.248717i
$343$	10.3937	−	10.3937i	0.561209	−	0.561209i
$344$	−5.36196	−	5.36196i	−0.289097	−	0.289097i
$345$	−3.94572	+	15.8245i	−0.212430	+	0.851964i
$346$	−3.55163	−	3.55163i	−0.190937	−	0.190937i
$347$			11.0739i			0.594476i	0.954803	+	0.297238i	$0.0960655\pi$
$347$			11.0739i			0.594476i	−0.954803	+	0.297238i	$0.903935\pi$
$348$	−4.49626	−	7.48325i	−0.241025	−	0.401144i
$349$	21.1548	+	21.1548i	1.13239	+	1.13239i	0.989779	+	0.142610i	$0.0455496\pi$
$349$	21.1548	+	21.1548i	1.13239	+	1.13239i	0.142610	+	0.989779i	$0.454450\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	−8.96336	−	8.96336i	−0.477072	−	0.477072i	0.427122	−	0.904194i	$-0.359527\pi$
$353$	−8.96336	−	8.96336i	−0.477072	−	0.477072i	−0.904194	+	0.427122i	$0.859527\pi$
$354$	−3.14643	−	5.23670i	−0.167231	−	0.278328i
$355$			40.3348i			2.14075i
$356$	−5.66891	−	5.66891i	−0.300452	−	0.300452i
$357$	2.87368	−	11.5250i	0.152091	−	0.609970i
$358$	1.08824	+	1.08824i	0.0575155	+	0.0575155i
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.0790589	−	0.996870i	$-0.474808\pi$
$359$	20.3859	−	20.3859i	1.07593	−	1.07593i	0.996870	−	0.0790589i	$-0.0251915\pi$
$360$	−6.68585	+	12.5734i	−0.352375	+	0.662679i
$361$		−	5.27475i		−	0.277619i
$362$	−0.525192	+	0.525192i	−0.0276035	+	0.0276035i
$363$	−11.1102	+	6.67547i	−0.583133	+	0.350371i
$364$		0			0
$365$		−	44.8813i		−	2.34919i
$366$	0.393251	−	1.57715i	0.0205556	−	0.0824392i
$367$	−23.1390			−1.20784			−0.603922	−	0.797043i	$-0.706396\pi$
$367$	−23.1390			−1.20784			−0.603922	+	0.797043i	$0.706396\pi$
$368$	−8.86090			−0.461906
$369$	−19.5268	+	5.96937i	−1.01652	+	0.310753i
$370$	−1.87122	+	1.87122i	−0.0972803	+	0.0972803i
$371$	2.02239	−	2.02239i	0.104997	−	0.104997i
$372$	−3.58497	+	14.3777i	−0.185872	+	0.745451i
$373$	20.4816			1.06050			0.530249	−	0.847842i	$-0.322098\pi$
$373$	20.4816			1.06050			0.530249	+	0.847842i	$0.322098\pi$
$374$	−3.90063			−0.201697
$375$	−12.1216	−	3.02243i	−0.625958	−	0.156078i
$376$			4.31166i			0.222357i
$377$		0			0
$378$	−0.111288	−	2.12511i	−0.00572404	−	0.109304i
$379$	2.80816	−	2.80816i	0.144246	−	0.144246i	−0.631296	−	0.775542i	$-0.717477\pi$
$379$	2.80816	−	2.80816i	0.144246	−	0.144246i	0.775542	+	0.631296i	$0.217477\pi$
$380$		−	32.1155i		−	1.64749i
$381$	11.5715	−	6.95267i	0.592828	−	0.356196i
$382$	−1.69412	+	1.69412i	−0.0866785	+	0.0866785i
$383$	18.8170	+	18.8170i	0.961502	+	0.961502i	0.999286	−	0.0377843i	$-0.0120300\pi$
$383$	18.8170	+	18.8170i	0.961502	+	0.961502i	−0.0377843	+	0.999286i	$0.512030\pi$
$384$	−16.1196	−	4.01930i	−0.822602	−	0.205109i
$385$	5.35443	+	5.35443i	0.272887	+	0.272887i
$386$		−	3.91785i		−	0.199413i
$387$	14.7041	+	7.81881i	0.747451	+	0.397452i
$388$	−16.2714	−	16.2714i	−0.826053	−	0.826053i
$389$	−6.17335			−0.313001			−0.156501	−	0.987678i	$-0.550021\pi$
$389$	−6.17335			−0.313001			−0.156501	+	0.987678i	$0.550021\pi$
$390$		0			0
$391$	−15.9914			−0.808722
$392$	−5.45714	−	5.45714i	−0.275627	−	0.275627i
$393$	−27.5288	+	16.5405i	−1.38864	+	0.834357i
$394$			0.804928i			0.0405517i
$395$	2.70311	+	2.70311i	0.136008	+	0.136008i
$396$	10.0919	−	3.08511i	0.507137	−	0.155033i
$397$	−16.8721	−	16.8721i	−0.846785	−	0.846785i	0.142946	−	0.989731i	$-0.454343\pi$
$397$	−16.8721	−	16.8721i	−0.846785	−	0.846785i	−0.989731	+	0.142946i	$0.954343\pi$
$398$	−4.57140	+	4.57140i	−0.229143	+	0.229143i
$399$	5.10708	+	8.49985i	0.255674	+	0.425525i
$400$		−	23.1381i		−	1.15691i
$401$	−16.4059	+	16.4059i	−0.819274	+	0.819274i	−0.986003	−	0.166729i	$-0.946679\pi$
$401$	−16.4059	+	16.4059i	−0.819274	+	0.819274i	0.166729	+	0.986003i	$0.446679\pi$
$402$	2.13901	+	3.56002i	0.106684	+	0.177558i
$403$		0			0
$404$			20.8129i			1.03548i
$405$	5.96917	−	30.7000i	0.296610	−	1.52550i
$406$	1.10046			0.0546147
$407$	4.05196			0.200848
$408$	−13.5484	−	3.37818i	−0.670746	−	0.167245i
$409$	8.88715	−	8.88715i	0.439441	−	0.439441i	−0.452383	−	0.891824i	$-0.649426\pi$
$409$	8.88715	−	8.88715i	0.439441	−	0.439441i	0.891824	+	0.452383i	$0.149426\pi$
$410$	−5.89440	+	5.89440i	−0.291103	+	0.291103i
$411$	−12.6630	−	3.15743i	−0.624622	−	0.155744i
$412$	−8.31506			−0.409654
$413$	−11.6290			−0.572225
$414$	−2.73984	+	0.837573i	−0.134656	+	0.0411645i
$415$		−	22.5532i		−	1.10709i
$416$		0			0
$417$	−4.81024	−	8.00582i	−0.235558	−	0.392047i
$418$	2.30262	−	2.30262i	0.112625	−	0.112625i
$419$		−	26.8089i		−	1.30970i	−0.755758	−	0.654851i	$-0.772731\pi$
$419$		−	26.8089i		−	1.30970i	0.755758	−	0.654851i	$-0.227269\pi$
$420$	6.75666	+	11.2453i	0.329691	+	0.548714i
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	−0.890471	−	0.455040i	$-0.849625\pi$
$421$	−8.93430	+	8.93430i	−0.435431	+	0.435431i	0.455040	+	0.890471i	$0.349625\pi$
$422$	−1.99553	−	1.99553i	−0.0971408	−	0.0971408i
$423$	−2.76830	−	9.05556i	−0.134599	−	0.440296i
$424$	−2.37744	−	2.37744i	−0.115459	−	0.115459i
$425$		−	41.7578i		−	2.02555i
$426$	−6.07359	+	3.64927i	−0.294266	+	0.176808i
$427$	−2.18781	−	2.18781i	−0.105876	−	0.105876i
$428$	−24.4891			−1.18372
$429$		0			0
$430$	6.79881			0.327868
$431$	−15.0091	−	15.0091i	−0.722961	−	0.722961i	0.246246	−	0.969207i	$-0.420803\pi$
$431$	−15.0091	−	15.0091i	−0.722961	−	0.722961i	−0.969207	+	0.246246i	$0.920803\pi$
$432$	16.9688	−	0.888625i	0.816413	−	0.0427540i
$433$			1.85372i			0.0890840i	0.999008	+	0.0445420i	$0.0141828\pi$
$433$			1.85372i			0.0890840i	−0.999008	+	0.0445420i	$0.985817\pi$
$434$	−1.32076	−	1.32076i	−0.0633986	−	0.0633986i
$435$	15.6926	+	3.91283i	0.752404	+	0.187606i
$436$	−8.41907	−	8.41907i	−0.403200	−	0.403200i
$437$	9.44007	−	9.44007i	0.451580	−	0.451580i
$438$	6.75820	−	4.06061i	0.322919	−	0.194024i
$439$			14.4053i			0.687526i	0.939056	+	0.343763i	$0.111702\pi$
$439$			14.4053i			0.687526i	−0.939056	+	0.343763i	$0.888298\pi$
$440$	6.29446	−	6.29446i	0.300077	−	0.300077i
$441$	14.9651	+	7.95761i	0.712625	+	0.378934i
$442$		0			0
$443$			22.2330i			1.05632i	0.849144	+	0.528162i	$0.177119\pi$
$443$			22.2330i			1.05632i	−0.849144	+	0.528162i	$0.822881\pi$
$444$	6.81148	+	1.69839i	0.323259	+	0.0806020i
$445$	14.8521			0.704055
$446$	−9.97929			−0.472533
$447$	9.55963	−	38.3394i	0.452155	−	1.81339i
$448$	−4.24892	+	4.24892i	−0.200743	+	0.200743i
$449$	−17.3832	+	17.3832i	−0.820362	+	0.820362i	−0.986160	−	0.165798i	$-0.946980\pi$
$449$	−17.3832	+	17.3832i	−0.820362	+	0.820362i	0.165798	+	0.986160i	$0.446980\pi$
$450$	−2.18712	−	7.15442i	−0.103102	−	0.337263i
$451$	12.7638			0.601022
$452$	−24.4089			−1.14810
$453$	−3.92237	+	15.7309i	−0.184289	+	0.739102i
$454$			2.59229i			0.121662i
$455$		0			0
$456$	9.99211	−	6.00368i	0.467923	−	0.281148i
$457$	−4.78633	+	4.78633i	−0.223895	+	0.223895i	−0.810136	−	0.586241i	$-0.800607\pi$
$457$	−4.78633	+	4.78633i	−0.223895	+	0.223895i	0.586241	+	0.810136i	$0.300607\pi$
$458$			5.68678i			0.265726i
$459$	30.6240	−	1.60372i	1.42941	−	0.0748552i
$460$	12.4892	−	12.4892i	0.582312	−	0.582312i
$461$	−8.76156	−	8.76156i	−0.408067	−	0.408067i	0.472997	−	0.881064i	$-0.343172\pi$
$461$	−8.76156	−	8.76156i	−0.408067	−	0.408067i	−0.881064	+	0.472997i	$0.843172\pi$
$462$	−0.321828	+	1.29071i	−0.0149728	+	0.0600491i
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	0.850339	−	0.526236i	$-0.176397\pi$
$463$	6.97385	+	6.97385i	0.324102	+	0.324102i	−0.526236	+	0.850339i	$0.676397\pi$
$464$			8.78704i			0.407928i
$465$	−14.1380	−	23.5304i	−0.655636	−	1.09119i
$466$	4.52462	+	4.52462i	0.209599	+	0.209599i
$467$	−9.19934			−0.425695			−0.212847	−	0.977085i	$-0.568274\pi$
$467$	−9.19934			−0.425695			−0.212847	+	0.977085i	$0.568274\pi$
$468$		0			0
$469$	7.90563			0.365048
$470$	−2.73353	−	2.73353i	−0.126088	−	0.126088i
$471$	13.9860	+	23.2774i	0.644443	+	1.07257i
$472$			13.6706i			0.629240i
$473$	−7.36110	−	7.36110i	−0.338464	−	0.338464i
$474$	−0.162470	+	0.651596i	−0.00746251	+	0.0299288i
$475$	24.6505	+	24.6505i	1.13104	+	1.13104i
$476$	−9.09592	+	9.09592i	−0.416911	+	0.416911i
$477$	6.51966	+	3.46678i	0.298515	+	0.158733i
$478$			3.26105i			0.149157i
$479$	16.2278	−	16.2278i	0.741469	−	0.741469i	−0.231392	−	0.972861i	$-0.574328\pi$
$479$	16.2278	−	16.2278i	0.741469	−	0.741469i	0.972861	+	0.231392i	$0.0743279\pi$
$480$	20.0412	−	12.0416i	0.914750	−	0.549621i
$481$		0			0
$482$			9.75464i			0.444312i
$483$	−1.31940	+	5.29152i	−0.0600347	+	0.240773i
$484$	14.0370			0.638045
$485$	42.6295			1.93571
$486$	5.16285	−	1.87874i	0.234192	−	0.0852213i
$487$	−20.8383	+	20.8383i	−0.944271	+	0.944271i	−0.998527	−	0.0542557i	$-0.982721\pi$
$487$	−20.8383	+	20.8383i	−0.944271	+	0.944271i	0.0542557	+	0.998527i	$0.482721\pi$
$488$	−2.57191	+	2.57191i	−0.116425	+	0.116425i
$489$	−1.44838	+	5.80879i	−0.0654978	+	0.262682i
$490$	6.91951			0.312592
$491$	−15.3239			−0.691558			−0.345779	−	0.938316i	$-0.612385\pi$
$491$	−15.3239			−0.691558			−0.345779	+	0.938316i	$0.612385\pi$
$492$	21.4563	+	5.34996i	0.967326	+	0.241195i
$493$			15.8582i			0.714215i
$494$		0			0
$495$	−9.17859	+	17.2613i	−0.412547	+	0.775838i
$496$	10.5462	−	10.5462i	0.473536	−	0.473536i
$497$			13.4874i			0.604995i
$498$	3.39605	−	2.04049i	0.152181	−	0.0914365i
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.410004	−	0.912084i	$-0.365527\pi$
$499$	29.5332	−	29.5332i	1.32209	−	1.32209i	0.912084	−	0.410004i	$-0.134473\pi$
$500$	9.56676	+	9.56676i	0.427839	+	0.427839i
$501$	−8.81183	−	2.19716i	−0.393683	−	0.0981618i
$502$	−1.39562	−	1.39562i	−0.0622897	−	0.0622897i
$503$		−	34.7649i		−	1.55009i	−0.631905	−	0.775046i	$-0.717727\pi$
$503$		−	34.7649i		−	1.55009i	0.631905	−	0.775046i	$-0.282273\pi$
$504$	−2.23566	+	4.20440i	−0.0995844	+	0.187279i
$505$	−27.2640	−	27.2640i	−1.21323	−	1.21323i
$506$	1.79091			0.0796155
$507$		0			0
$508$	−14.6199			−0.648653
$509$	−31.3223	−	31.3223i	−1.38834	−	1.38834i	−0.828814	−	0.559525i	$-0.810984\pi$
$509$	−31.3223	−	31.3223i	−1.38834	−	1.38834i	−0.559525	−	0.828814i	$-0.689016\pi$
$510$	10.7312	−	6.44778i	0.475186	−	0.285512i
$511$		−	15.0077i		−	0.663903i
$512$	15.2996	+	15.2996i	0.676153	+	0.676153i
$513$	−17.1313	+	19.0247i	−0.756364	+	0.839960i
$514$	−1.69805	−	1.69805i	−0.0748978	−	0.0748978i
$515$	10.8924	−	10.8924i	0.479975	−	0.479975i
$516$	−9.28884	−	15.4597i	−0.408918	−	0.680575i
$517$			5.91921i			0.260326i
$518$	−0.625714	+	0.625714i	−0.0274923	+	0.0274923i
$519$	−12.7128	−	21.1584i	−0.558032	−	0.928749i
$520$		0			0
$521$			1.93372i			0.0847179i	0.999102	+	0.0423590i	$0.0134873\pi$
$521$			1.93372i			0.0847179i	−0.999102	+	0.0423590i	$0.986513\pi$
$522$	0.830592	+	2.71700i	0.0363540	+	0.118920i
$523$	1.50610			0.0658572			0.0329286	−	0.999458i	$-0.489517\pi$
$523$	1.50610			0.0658572			0.0329286	+	0.999458i	$0.489517\pi$
$524$	34.7809			1.51941
$525$	−13.8175	−	3.44529i	−0.603047	−	0.150365i
$526$	−5.64018	+	5.64018i	−0.245923	+	0.245923i
$527$	19.0329	−	19.0329i	0.829085	−	0.829085i
$528$	−10.3062	−	2.56976i	−0.448519	−	0.111835i
$529$	−15.6578			−0.680774
$530$	3.01453			0.130943
$531$	−8.77722	−	28.7117i	−0.380899	−	1.24598i
$532$		−	10.7390i		−	0.465595i
$533$		0			0
$534$	1.34373	+	2.23641i	0.0581490	+	0.0967791i
$535$	32.0796	−	32.0796i	1.38692	−	1.38692i
$536$		−	9.29356i		−	0.401421i
$537$	3.89530	+	6.48307i	0.168095	+	0.279765i
$538$	−6.50526	+	6.50526i	−0.280462	+	0.280462i
$539$	−7.49178	−	7.49178i	−0.322694	−	0.322694i
$540$	−22.6646	+	25.1696i	−0.975331	+	1.08313i
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	0.649844	−	0.760068i	$-0.274834\pi$
$541$	−2.56375	−	2.56375i	−0.110224	−	0.110224i	−0.760068	+	0.649844i	$0.774834\pi$
$542$			6.23204i			0.267689i
$543$	−3.12876	+	1.87989i	−0.134268	+	0.0806739i
$544$	16.2106	+	16.2106i	0.695023	+	0.695023i
$545$	22.0572			0.944827
$546$		0			0
$547$	23.1549			0.990030			0.495015	−	0.868884i	$-0.335163\pi$
$547$	23.1549			0.990030			0.495015	+	0.868884i	$0.335163\pi$
$548$	9.99407	+	9.99407i	0.426926	+	0.426926i
$549$	3.75036	−	7.05295i	0.160061	−	0.301012i
$550$			4.67652i			0.199408i
$551$	−9.36139	−	9.36139i	−0.398809	−	0.398809i
$552$	6.22051	+	1.55104i	0.264763	+	0.0660165i
$553$	0.903887	+	0.903887i	0.0384372	+	0.0384372i
$554$	5.65736	−	5.65736i	0.240358	−	0.240358i
$555$	−11.1476	+	6.69793i	−0.473188	+	0.284311i
$556$			10.1148i			0.428964i
$557$	−2.53023	+	2.53023i	−0.107209	+	0.107209i	−0.758677	−	0.651467i	$-0.774154\pi$
$557$	−2.53023	+	2.53023i	−0.107209	+	0.107209i	0.651467	+	0.758677i	$0.274154\pi$
$558$	2.26406	−	4.25780i	0.0958451	−	0.180247i
$559$		0			0
$560$		−	13.2045i		−	0.557994i
$561$	−18.5998	−	4.63770i	−0.785283	−	0.195804i
$562$	−4.26533			−0.179922
$563$	−19.6742			−0.829169			−0.414585	−	0.910011i	$-0.636073\pi$
$563$	−19.6742			−0.829169			−0.414585	+	0.910011i	$0.636073\pi$
$564$	−2.48105	+	9.95039i	−0.104471	+	0.418987i
$565$	31.9746	−	31.9746i	1.34518	−	1.34518i
$566$	−1.77082	+	1.77082i	−0.0744332	+	0.0744332i
$567$	1.99601	−	10.2657i	0.0838247	−	0.431119i
$568$	15.8553			0.665275
$569$	9.56462			0.400970			0.200485	−	0.979697i	$-0.435748\pi$
$569$	9.56462			0.400970			0.200485	+	0.979697i	$0.435748\pi$
$570$	−2.52861	+	10.1411i	−0.105912	+	0.424764i
$571$			17.9785i			0.752375i	0.926544	+	0.376187i	$0.122765\pi$
$571$			17.9785i			0.752375i	−0.926544	+	0.376187i	$0.877235\pi$
$572$		0			0
$573$	−10.0925	+	6.06399i	−0.421619	+	0.253327i
$574$	−1.97101	+	1.97101i	−0.0822685	+	0.0822685i
$575$			19.1724i			0.799544i
$576$	−13.6974	−	7.28352i	−0.570726	−	0.303480i
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	−0.827243	−	0.561844i	$-0.810092\pi$
$577$	−6.37509	+	6.37509i	−0.265398	+	0.265398i	0.561844	+	0.827243i	$0.310092\pi$
$578$	4.44343	+	4.44343i	0.184823	+	0.184823i
$579$	4.65818	−	18.6819i	0.193587	−	0.776393i
$580$	−12.3851	−	12.3851i	−0.514264	−	0.514264i
$581$		−	7.54150i		−	0.312874i
$582$	3.85689	+	6.41913i	0.159873	+	0.266082i
$583$	−3.26384	−	3.26384i	−0.135175	−	0.135175i
$584$	−17.6425			−0.730053
$585$		0			0
$586$	5.60209			0.231420
$587$	22.1906	+	22.1906i	0.915902	+	0.915902i	0.996728	−	0.0808262i	$-0.0257559\pi$
$587$	22.1906	+	22.1906i	0.915902	+	0.915902i	−0.0808262	+	0.996728i	$0.525756\pi$
$588$	−9.45374	−	15.7341i	−0.389866	−	0.648865i
$589$			22.4710i			0.925900i
$590$	−8.66697	−	8.66697i	−0.356814	−	0.356814i
$591$	−0.957029	+	3.83822i	−0.0393669	+	0.157883i
$592$	−4.99627	−	4.99627i	−0.205345	−	0.205345i
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	−0.999673	−	0.0255650i	$-0.991862\pi$
$593$	−23.7211	+	23.7211i	−0.974108	+	0.974108i	0.0255650	+	0.999673i	$0.491862\pi$
$594$	−3.42963	+	0.179603i	−0.140719	+	0.00736920i
$595$		−	23.8305i		−	0.976956i
$596$	−30.2587	+	30.2587i	−1.23944	+	1.23944i
$597$	−27.2335	+	16.3630i	−1.11459	+	0.669695i
$598$		0			0
$599$		−	33.7915i		−	1.38068i	−0.723484	−	0.690341i	$-0.757460\pi$
$599$		−	33.7915i		−	1.38068i	0.723484	−	0.690341i	$-0.242540\pi$
$600$	−4.05016	+	16.2434i	−0.165347	+	0.663133i
$601$	−30.1484			−1.22978			−0.614888	−	0.788614i	$-0.710799\pi$
$601$	−30.1484			−1.22978			−0.614888	+	0.788614i	$0.710799\pi$
$602$	2.27344			0.0926584
$603$	5.96693	+	19.5188i	0.242992	+	0.794867i
$604$	12.4153	−	12.4153i	0.505172	−	0.505172i
$605$	−18.3878	+	18.3878i	−0.747572	+	0.747572i
$606$	1.63870	−	6.57209i	0.0665676	−	0.266973i
$607$	22.0396			0.894561			0.447281	−	0.894394i	$-0.352392\pi$
$607$	22.0396			0.894561			0.447281	+	0.894394i	$0.352392\pi$
$608$	−19.1389			−0.776184
$609$	5.24742	+	1.30840i	0.212636	+	0.0530191i
$610$		−	3.26111i		−	0.132038i
$611$		0			0
$612$	−29.3229	−	15.5923i	−1.18531	−	0.630280i
$613$	0.418180	−	0.418180i	0.0168901	−	0.0168901i	−0.698611	−	0.715501i	$-0.746198\pi$
$613$	0.418180	−	0.418180i	0.0168901	−	0.0168901i	0.715501	+	0.698611i	$0.246198\pi$
$614$			7.16972i			0.289346i
$615$	−35.1151	+	21.0986i	−1.41598	+	0.850779i
$616$	2.10479	−	2.10479i	0.0848044	−	0.0848044i
$617$	20.5560	+	20.5560i	0.827552	+	0.827552i	0.987178	−	0.159626i	$-0.0510288\pi$
$617$	20.5560	+	20.5560i	0.827552	+	0.827552i	−0.159626	+	0.987178i	$0.551029\pi$
$618$	2.62565	+	0.654685i	0.105619	+	0.0263353i
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	0.996727	−	0.0808459i	$-0.0257622\pi$
$619$	22.7868	+	22.7868i	0.915881	+	0.915881i	−0.0808459	+	0.996727i	$0.525762\pi$
$620$			29.7291i			1.19395i
$621$	−14.0605	+	0.736320i	−0.564228	+	0.0295475i
$622$	−1.89948	−	1.89948i	−0.0761620	−	0.0761620i
$623$	4.96634			0.198972
$624$		0			0
$625$	10.3139			0.412556
$626$	−1.62361	−	1.62361i	−0.0648925	−	0.0648925i
$627$	13.7175	−	8.24209i	0.547826	−	0.329157i
$628$		−	29.4095i		−	1.17357i
$629$	−9.01686	−	9.01686i	−0.359526	−	0.359526i
$630$	−1.24815	−	4.08291i	−0.0497277	−	0.162667i
$631$	−28.6918	−	28.6918i	−1.14220	−	1.14220i	−0.988047	−	0.154155i	$-0.950734\pi$
$631$	−28.6918	−	28.6918i	−1.14220	−	1.14220i	−0.154155	−	0.988047i	$-0.549266\pi$
$632$	1.06258	−	1.06258i	0.0422670	−	0.0422670i
$633$	−7.14287	−	11.8881i	−0.283904	−	0.472509i
$634$		−	3.13720i		−	0.124594i
$635$	19.1514	−	19.1514i	0.760001	−	0.760001i
$636$	−4.11858	−	6.85468i	−0.163312	−	0.271806i
$637$		0			0
$638$		−	1.77598i		−	0.0703117i
$639$	−33.3002	+	10.1799i	−1.31733	+	0.402711i
$640$	−33.3308			−1.31752
$641$	−25.7121			−1.01557			−0.507783	−	0.861485i	$-0.669535\pi$
$641$	−25.7121			−1.01557			−0.507783	+	0.861485i	$0.669535\pi$
$642$	7.73291	+	1.92814i	0.305194	+	0.0760976i
$643$	−0.448106	+	0.448106i	−0.0176716	+	0.0176716i	−0.715887	−	0.698216i	$-0.753978\pi$
$643$	−0.448106	+	0.448106i	−0.0176716	+	0.0176716i	0.698216	+	0.715887i	$0.253978\pi$
$644$	4.17624	−	4.17624i	0.164567	−	0.164567i
$645$	32.4195	+	8.08354i	1.27652	+	0.318289i
$646$	−10.2481			−0.403205
$647$	47.0248			1.84874			0.924368	−	0.381501i	$-0.124593\pi$
$647$	47.0248			1.84874			0.924368	+	0.381501i	$0.124593\pi$
$648$	−12.0680	−	2.34644i	−0.474075	−	0.0921768i
$649$			18.7675i			0.736690i
$650$		0			0
$651$	−4.72758	−	7.86826i	−0.185289	−	0.308381i
$652$	4.58448	−	4.58448i	0.179542	−	0.179542i
$653$		−	28.9755i		−	1.13390i	−0.823753	−	0.566949i	$-0.808124\pi$
$653$		−	28.9755i		−	1.13390i	0.823753	−	0.566949i	$-0.191876\pi$
$654$	1.99562	+	3.32136i	0.0780348	+	0.129876i
$655$	−45.5614	+	45.5614i	−1.78023	+	1.78023i
$656$	−15.7384	−	15.7384i	−0.614479	−	0.614479i
$657$	37.0537	−	11.3274i	1.44560	−	0.441924i
$658$	−0.914059	−	0.914059i	−0.0356337	−	0.0356337i
$659$			46.6822i			1.81848i	0.416271	+	0.909241i	$0.363337\pi$
$659$			46.6822i			1.81848i	−0.416271	+	0.909241i	$0.636663\pi$
$660$	18.1483	−	10.9043i	0.706422	−	0.424448i
$661$	−4.90953	−	4.90953i	−0.190959	−	0.190959i	0.605152	−	0.796110i	$-0.293113\pi$
$661$	−4.90953	−	4.90953i	−0.190959	−	0.190959i	−0.796110	+	0.605152i	$0.793113\pi$
$662$	−5.66611			−0.220220
$663$		0			0
$664$	−8.86551			−0.344048
$665$	14.0676	+	14.0676i	0.545520	+	0.545520i
$666$	−2.01714	−	1.07260i	−0.0781627	−	0.0415625i
$667$		−	7.28100i		−	0.281921i
$668$	6.95457	+	6.95457i	0.269080	+	0.269080i
$669$	−47.5853	−	11.8650i	−1.83975	−	0.458728i
$670$	5.89199	+	5.89199i	0.227627	+	0.227627i
$671$	−3.53081	+	3.53081i	−0.136306	+	0.136306i
$672$	6.70151	−	4.02656i	0.258517	−	0.155328i
$673$			26.1949i			1.00974i	0.863196	+	0.504870i	$0.168459\pi$
$673$			26.1949i			1.00974i	−0.863196	+	0.504870i	$0.831541\pi$
$674$	7.06665	−	7.06665i	0.272197	−	0.272197i
$675$	−1.92272	−	36.7156i	−0.0740057	−	1.41318i
$676$		0			0
$677$			21.9298i			0.842829i	0.906868	+	0.421415i	$0.138466\pi$
$677$			21.9298i			0.842829i	−0.906868	+	0.421415i	$0.861534\pi$
$678$	7.70760	+	1.92183i	0.296008	+	0.0738074i
$679$	14.2548			0.547048
$680$	−28.0142			−1.07430
$681$	−3.08213	+	12.3611i	−0.118108	+	0.473677i
$682$	−2.13152	+	2.13152i	−0.0816201	+	0.0816201i
$683$	−5.39035	+	5.39035i	−0.206256	+	0.206256i	−0.802674	−	0.596418i	$-0.796590\pi$
$683$	−5.39035	+	5.39035i	−0.206256	+	0.206256i	0.596418	+	0.802674i	$0.296590\pi$
$684$	26.5144	−	8.10549i	1.01380	−	0.309921i
$685$	−26.1836			−1.00042
$686$	5.18057			0.197795
$687$	−6.76137	+	27.1169i	−0.257962	+	1.03457i
$688$			18.1532i			0.692084i
$689$		0			0
$690$	−4.92706	+	2.96039i	−0.187570	+	0.112700i
$691$	−11.2800	+	11.2800i	−0.429113	+	0.429113i	−0.888326	−	0.459213i	$-0.848131\pi$
$691$	−11.2800	+	11.2800i	−0.429113	+	0.429113i	0.459213	+	0.888326i	$0.348131\pi$
$692$			26.7322i			1.01621i
$693$	−3.06921	+	5.77197i	−0.116589	+	0.219259i
$694$	−2.75978	+	2.75978i	−0.104760	+	0.104760i
$695$	−13.2500	−	13.2500i	−0.502600	−	0.502600i
$696$	1.53811	−	6.16867i	0.0583018	−	0.233823i
$697$	−28.4033	−	28.4033i	−1.07585	−	1.07585i
$698$			10.5442i			0.399104i
$699$	16.1956	+	26.9548i	0.612573	+	1.01952i
$700$	10.9052	+	10.9052i	0.412179	+	0.412179i
$701$	30.3059			1.14464			0.572319	−	0.820031i	$-0.306044\pi$
$701$	30.3059			1.14464			0.572319	+	0.820031i	$0.306044\pi$
$702$		0			0
$703$	10.6457			0.401509
$704$	6.85715	+	6.85715i	0.258439	+	0.258439i
$705$	−9.78451	−	16.2846i	−0.368506	−	0.613315i
$706$		−	4.46762i		−	0.168141i
$707$	−9.11674	−	9.11674i	−0.342870	−	0.342870i
$708$	−7.86646	+	31.5489i	−0.295639	+	1.18568i
$709$	24.0489	+	24.0489i	0.903174	+	0.903174i	0.995709	−	0.0925354i	$-0.0294971\pi$
$709$	24.0489	+	24.0489i	0.903174	+	0.903174i	−0.0925354	+	0.995709i	$0.529497\pi$
$710$	−10.0521	+	10.0521i	−0.377247	+	0.377247i
$711$	−1.54945	+	2.91390i	−0.0581088	+	0.109280i
$712$		−	5.83824i		−	0.218797i
$713$	−8.73861	+	8.73861i	−0.327264	+	0.327264i
$714$	3.58839	−	2.15606i	0.134292	−	0.0806884i
$715$		0			0
$716$		−	8.19093i		−	0.306110i
$717$	−3.87727	+	15.5500i	−0.144799	+	0.580725i
$718$	10.1610			0.379205
$719$	7.89679			0.294500			0.147250	−	0.989099i	$-0.452958\pi$
$719$	7.89679			0.294500			0.147250	+	0.989099i	$0.452958\pi$
$720$	32.6017	−	9.96640i	1.21499	−	0.371426i
$721$	3.64227	−	3.64227i	0.135645	−	0.135645i
$722$	1.31455	−	1.31455i	0.0489225	−	0.0489225i
$723$	−11.5979	+	46.5140i	−0.431331	+	1.72988i
$724$	3.95299			0.146912
$725$	19.0126			0.706110
$726$	−4.43246	−	1.10520i	−0.164504	−	0.0410178i
$727$			24.6824i			0.915420i	0.889102	+	0.457710i	$0.151330\pi$
$727$			24.6824i			0.915420i	−0.889102	+	0.457710i	$0.848670\pi$
$728$		0			0
$729$	26.8523	−	2.82014i	0.994530	−	0.104450i
$730$	11.1851	−	11.1851i	0.413980	−	0.413980i
$731$			32.7614i			1.21173i
$732$	−7.41537	+	4.45547i	−0.274080	+	0.164679i
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.321476	−	0.946918i	$-0.395821\pi$
$733$	34.3405	−	34.3405i	1.26839	−	1.26839i	0.946918	−	0.321476i	$-0.104179\pi$
$734$	−5.76659	−	5.76659i	−0.212849	−	0.212849i
$735$	32.9950	+	8.22704i	1.21704	+	0.303459i
$736$	−7.44281	−	7.44281i	−0.274346	−	0.274346i
$737$		−	12.7586i		−	0.469967i
$738$	−6.35404	−	3.37872i	−0.233896	−	0.124372i
$739$	27.4710	+	27.4710i	1.01054	+	1.01054i	0.999944	+	0.0105933i	$0.00337201\pi$
$739$	27.4710	+	27.4710i	1.01054	+	1.01054i	0.0105933	+	0.999944i	$0.496628\pi$
$740$	14.0842			0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	36.8590	+	36.8590i	1.35223	+	1.35223i	0.883167	+	0.469058i	$0.155407\pi$
$743$	36.8590	+	36.8590i	1.35223	+	1.35223i	0.469058	+	0.883167i	$0.344593\pi$
$744$	−9.24962	+	5.55757i	−0.339108	+	0.203750i
$745$		−	79.2751i		−	2.90441i
$746$	5.10435	+	5.10435i	0.186883	+	0.186883i
$747$	18.6198	−	5.69210i	0.681262	−	0.208263i
$748$	14.6795	+	14.6795i	0.536736	+	0.536736i
$749$	10.7270	−	10.7270i	0.391957	−	0.391957i
$750$	−2.26766	−	3.77414i	−0.0828033	−	0.137812i
$751$		−	49.3601i		−	1.80118i	−0.434674	−	0.900588i	$-0.643136\pi$
$751$		−	49.3601i		−	1.80118i	0.434674	−	0.900588i	$-0.356864\pi$
$752$	7.29867	−	7.29867i	0.266155	−	0.266155i
$753$	−4.99555	−	8.31423i	−0.182048	−	0.302987i
$754$		0			0
$755$			32.5270i			1.18378i
$756$	−7.57877	+	8.41641i	−0.275637	+	0.306102i
$757$	18.8564			0.685346			0.342673	−	0.939455i	$-0.388668\pi$
$757$	18.8564			0.685346			0.342673	+	0.939455i	$0.388668\pi$
$758$	1.39968			0.0508385
$759$	8.53976	+	2.12932i	0.309974	+	0.0772895i
$760$	16.5374	−	16.5374i	0.599874	−	0.599874i
$761$	27.2152	−	27.2152i	0.986549	−	0.986549i	−0.0133615	−	0.999911i	$-0.504253\pi$
$761$	27.2152	−	27.2152i	0.986549	−	0.986549i	0.999911	+	0.0133615i	$0.00425321\pi$
$762$	4.61653	+	1.15109i	0.167239	+	0.0416997i
$763$	7.37566			0.267017
$764$	12.7512			0.461321
$765$	58.8369	−	17.9866i	2.12725	−	0.650305i
$766$			9.37896i			0.338876i
$767$		0			0
$768$	6.21032	+	10.3360i	0.224096	+	0.372969i
$769$	−2.01778	+	2.01778i	−0.0727631	+	0.0727631i	−0.742552	−	0.669789i	$-0.766385\pi$
$769$	−2.01778	+	2.01778i	−0.0727631	+	0.0727631i	0.669789	+	0.742552i	$0.266385\pi$
$770$			2.66882i			0.0961775i
$771$	−6.07807	−	10.1159i	−0.218896	−	0.364315i
$772$	−14.7443	+	14.7443i	−0.530660	+	0.530660i
$773$	−4.54435	−	4.54435i	−0.163449	−	0.163449i	0.620644	−	0.784093i	$-0.286871\pi$
$773$	−4.54435	−	4.54435i	−0.163449	−	0.163449i	−0.784093	+	0.620644i	$0.786871\pi$
$774$	1.71592	+	5.61306i	0.0616776	+	0.201757i
$775$	−22.8188	−	22.8188i	−0.819675	−	0.819675i
$776$		−	16.7574i		−	0.601555i
$777$	−3.72761	+	2.23970i	−0.133727	+	0.0803489i
$778$	−1.53850	−	1.53850i	−0.0551578	−	0.0551578i
$779$	33.5341			1.20148
$780$		0			0
$781$	21.7668			0.778878
$782$	−3.98532	−	3.98532i	−0.142515	−	0.142515i
$783$	0.730183	+	13.9433i	0.0260946	+	0.498292i
$784$			18.4755i			0.659838i
$785$	38.5251	+	38.5251i	1.37502	+	1.37502i
$786$	−10.9828	−	2.73846i	−0.391742	−	0.0976778i
$787$	−10.7255	−	10.7255i	−0.382322	−	0.382322i	0.489616	−	0.871938i	$-0.337137\pi$
$787$	−10.7255	−	10.7255i	−0.382322	−	0.382322i	−0.871938	+	0.489616i	$0.837137\pi$
$788$	3.02924	−	3.02924i	0.107912	−	0.107912i
$789$	−33.6006	+	20.1887i	−1.19621	+	0.718736i
$790$			1.34732i			0.0479354i
$791$	10.6919	−	10.6919i	0.380160	−	0.380160i
$792$	6.78531	+	3.60804i	0.241105	+	0.128206i
$793$		0			0
$794$		−	8.40957i		−	0.298444i
$795$	14.3745	+	3.58416i	0.509811	+	0.127117i
$796$	34.4077			1.21955
$797$	−1.57925			−0.0559399			−0.0279700	−	0.999609i	$-0.508904\pi$
$797$	−1.57925			−0.0559399			−0.0279700	+	0.999609i	$0.508904\pi$
$798$	−0.845534	+	3.39106i	−0.0299316	+	0.120042i
$799$	13.1721	−	13.1721i	0.465994	−	0.465994i
$800$	19.4351	−	19.4351i	0.687135	−	0.687135i
$801$	3.74845	+	12.2618i	0.132445	+	0.433248i
$802$	−8.17724			−0.288748
$803$	−24.2203			−0.854717
$804$	5.34778	−	21.4476i	0.188602	−	0.756397i
$805$			10.9414i			0.385633i
$806$		0			0
$807$	−38.7542	+	23.2852i	−1.36421	+	0.819677i
$808$	−10.7173	+	10.7173i	−0.377033	+	0.377033i
$809$		−	12.2119i		−	0.429348i	−0.976686	−	0.214674i	$-0.931131\pi$
$809$		−	12.2119i		−	0.429348i	0.976686	−	0.214674i	$-0.0688689\pi$
$810$	9.13854	−	6.16332i	0.321096	−	0.216557i
$811$	−29.6037	+	29.6037i	−1.03952	+	1.03952i	−0.0403387	+	0.999186i	$0.512844\pi$
$811$	−29.6037	+	29.6037i	−1.03952	+	1.03952i	−0.999186	+	0.0403387i	$0.987156\pi$
$812$	−4.14143	−	4.14143i	−0.145336	−	0.145336i
$813$	−7.40966	+	29.7169i	−0.259868	+	1.04222i
$814$	1.00981	+	1.00981i	0.0353939	+	0.0353939i
$815$			12.0109i			0.420724i
$816$	17.2159	+	28.6529i	0.602677	+	1.00305i
$817$	−19.3397	−	19.3397i	−0.676612	−	0.676612i
$818$	4.42964			0.154879
$819$		0			0
$820$	44.3656			1.54931
$821$	−13.1586	−	13.1586i	−0.459237	−	0.459237i	0.439168	−	0.898405i	$-0.355273\pi$
$821$	−13.1586	−	13.1586i	−0.459237	−	0.459237i	−0.898405	+	0.439168i	$0.855273\pi$
$822$	−2.36895	−	3.94271i	−0.0826266	−	0.137518i
$823$			0.516417i			0.0180012i	0.999959	+	0.00900059i	$0.00286501\pi$
$823$			0.516417i			0.0180012i	−0.999959	+	0.00900059i	$0.997135\pi$
$824$	−4.28172	−	4.28172i	−0.149161	−	0.149161i
$825$	−5.56021	+	22.2995i	−0.193582	+	0.776370i
$826$	−2.89813	−	2.89813i	−0.100839	−	0.100839i
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	−0.238472	−	0.971149i	$-0.576646\pi$
$827$	21.0701	−	21.0701i	0.732678	−	0.732678i	0.971149	+	0.238472i	$0.0766464\pi$
$828$	13.4631	+	7.15892i	0.467876	+	0.248790i
$829$			1.68723i			0.0586000i	0.999571	+	0.0293000i	$0.00932781\pi$
$829$			1.68723i			0.0586000i	−0.999571	+	0.0293000i	$0.990672\pi$
$830$	5.62061	−	5.62061i	0.195094	−	0.195094i
$831$	33.7030	−	20.2502i	1.16914	−	0.702471i
$832$		0			0
$833$			33.3430i			1.15527i
$834$	0.796389	−	3.19396i	0.0275767	−	0.110598i
$835$	−18.2204			−0.630542
$836$	−17.3312			−0.599413
$837$	15.8583	−	17.6110i	0.548143	−	0.608726i
$838$	6.68121	−	6.68121i	0.230799	−	0.230799i
$839$	7.66187	−	7.66187i	0.264517	−	0.264517i	−0.562369	−	0.826886i	$-0.690110\pi$
$839$	7.66187	−	7.66187i	0.264517	−	0.264517i	0.826886	+	0.562369i	$0.190110\pi$
$840$	−2.31136	+	9.26984i	−0.0797495	+	0.319840i
$841$	21.7797			0.751024
$842$	−4.45314			−0.153465
$843$	−20.3388	−	5.07132i	−0.700506	−	0.174666i
$844$			15.0198i			0.517004i
$845$		0			0
$846$	1.56688	−	2.94669i	0.0538706	−	0.101309i
$847$	−6.14867	+	6.14867i	−0.211271	+	0.211271i
$848$			8.04895i			0.276402i
$849$	−10.5494	+	6.33855i	−0.362056	+	0.217539i
$850$	10.4067	−	10.4067i	0.356947	−	0.356947i
$851$	4.13994	+	4.13994i	0.141915	+	0.141915i
$852$	36.5907	+	9.12361i	1.25358	+	0.312570i
$853$	−30.1644	−	30.1644i	−1.03281	−	1.03281i	−0.999443	−	0.0333670i	$-0.989377\pi$
$853$	−30.1644	−	30.1644i	−1.03281	−	1.03281i	−0.0333670	−	0.999443i	$-0.510623\pi$
$854$		−	1.09047i		−	0.0373153i
$855$	−24.1148	+	45.3505i	−0.824709	+	1.55095i
$856$	−12.6103	−	12.6103i	−0.431010	−	0.431010i
$857$	−36.7949			−1.25689			−0.628444	−	0.777855i	$-0.716308\pi$
$857$	−36.7949			−1.25689			−0.628444	+	0.777855i	$0.716308\pi$
$858$		0			0
$859$	−48.7044			−1.66177			−0.830886	−	0.556442i	$-0.812166\pi$
$859$	−48.7044			−1.66177			−0.830886	+	0.556442i	$0.812166\pi$
$860$	−25.5865	−	25.5865i	−0.872491	−	0.872491i
$861$	−11.7420	+	7.05512i	−0.400168	+	0.240438i
$862$		−	7.48099i		−	0.254803i
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	0.991931	−	0.126779i	$-0.0404637\pi$
$863$	25.4155	+	25.4155i	0.865153	+	0.865153i	−0.126779	+	0.991931i	$0.540464\pi$
$864$	14.9996	+	13.5067i	0.510296	+	0.459509i
$865$	−35.0180	−	35.0180i	−1.19065	−	1.19065i
$866$	−0.461976	+	0.461976i	−0.0156986	+	0.0156986i
$867$	15.9050	+	26.4712i	0.540162	+	0.899008i
$868$			9.94103i			0.337421i
$869$	1.45874	−	1.45874i	0.0494845	−	0.0494845i
$870$	2.93571	+	4.88599i	0.0995299	+	0.165651i
$871$		0			0
$872$		−	8.67054i		−	0.293622i
$873$	10.7591	+	35.1947i	0.364140	+	1.19116i
$874$	4.70523			0.159157
$875$	−8.38112			−0.283333
$876$	−40.7152	−	10.1520i	−1.37564	−	0.343005i
$877$	12.9567	−	12.9567i	0.437516	−	0.437516i	−0.453659	−	0.891175i	$-0.649882\pi$
$877$	12.9567	−	12.9567i	0.437516	−	0.437516i	0.891175	+	0.453659i	$0.149882\pi$
$878$	−3.59002	+	3.59002i	−0.121157	+	0.121157i
$879$	26.7130	+	6.66068i	0.901007	+	0.224659i
$880$	−21.3102			−0.718368
$881$	−31.1077			−1.04805			−0.524023	−	0.851704i	$-0.675569\pi$
$881$	−31.1077			−1.04805			−0.524023	+	0.851704i	$0.675569\pi$
$882$	1.74639	+	5.71271i	0.0588039	+	0.192357i
$883$		−	9.56660i		−	0.321942i	−0.986959	−	0.160971i	$-0.948537\pi$
$883$		−	9.56660i		−	0.321942i	0.986959	−	0.160971i	$-0.0514625\pi$
$884$		0			0
$885$	−31.0229	−	51.6323i	−1.04282	−	1.73560i
$886$	−5.54082	+	5.54082i	−0.186148	+	0.186148i
$887$		−	24.6546i		−	0.827819i	−0.910318	−	0.413910i	$-0.864163\pi$
$887$		−	24.6546i		−	0.827819i	0.910318	−	0.413910i	$-0.135837\pi$
$888$	2.63291	+	4.38203i	0.0883547	+	0.147051i
$889$	6.40399	−	6.40399i	0.214783	−	0.214783i
$890$	3.70137	+	3.70137i	0.124070	+	0.124070i
$891$	−16.5674	−	3.22128i	−0.555028	−	0.107917i
$892$	37.5558	+	37.5558i	1.25746	+	1.25746i
$893$			15.5515i			0.520410i
$894$	11.9372	−	7.17238i	0.399240	−	0.239880i
$895$	10.7298	+	10.7298i	0.358656	+	0.358656i
$896$	−11.1454			−0.372342
$897$		0			0
$898$	−8.66432			−0.289132
$899$	8.66578	+	8.66578i	0.289020	+	0.289020i
$900$	−18.6938	+	35.1557i	−0.623127	+	1.17186i
$901$			14.5261i			0.483935i
$902$	3.18093	+	3.18093i	0.105913	+	0.105913i
$903$	10.8407	+	2.70303i	0.360755	+	0.0899513i
$904$	−12.5690	−	12.5690i	−0.418038	−	0.418038i
$905$	−5.17824	+	5.17824i	−0.172130	+	0.172130i
$906$	−4.89790	+	2.94287i	−0.162722	+	0.0977703i
$907$		−	1.68516i		−	0.0559549i	−0.999609	−	0.0279775i	$-0.991093\pi$
$907$		−	1.68516i		−	0.0559549i	0.999609	−	0.0279775i	$-0.00890666\pi$
$908$	9.75575	−	9.75575i	0.323756	−	0.323756i
$909$	15.6280	−	29.3900i	0.518346	−	0.974806i
$910$		0			0
$911$		−	43.9421i		−	1.45587i	−0.685648	−	0.727933i	$-0.740481\pi$
$911$		−	43.9421i		−	1.45587i	0.685648	−	0.727933i	$-0.259519\pi$
$912$	−27.0773	−	6.75151i	−0.896619	−	0.223565i
$913$	−12.1709			−0.402798
$914$	−2.38566			−0.0789106
$915$	3.87734	−	15.5503i	0.128181	−	0.514076i
$916$	21.4015	−	21.4015i	0.707124	−	0.707124i
$917$	−15.2352	+	15.2352i	−0.503109	+	0.503109i
$918$	8.03165	+	7.23231i	0.265084	+	0.238702i
$919$	8.41429			0.277562			0.138781	−	0.990323i	$-0.455682\pi$
$919$	8.41429			0.277562			0.138781	+	0.990323i	$0.455682\pi$
$920$	12.8623			0.424056
$921$	−8.52453	+	34.1881i	−0.280893	+	1.12654i
$922$		−	4.36704i		−	0.143821i
$923$		0			0
$924$	6.06857	−	3.64625i	0.199641	−	0.119953i
$925$	−10.8105	+	10.8105i	−0.355446	+	0.355446i
$926$			3.47599i			0.114228i
$927$	11.7418	+	6.24360i	0.385650	+	0.205067i
$928$	−7.38077	+	7.38077i	−0.242286	+	0.242286i
$929$	1.62237	+	1.62237i	0.0532282	+	0.0532282i	0.733220	−	0.679992i	$-0.238017\pi$
$929$	1.62237	+	1.62237i	0.0532282	+	0.0532282i	−0.679992	+	0.733220i	$0.738017\pi$
$930$	2.34071	−	9.38756i	0.0767550	−	0.307830i
$931$	−19.6831	−	19.6831i	−0.645087	−	0.645087i
$932$		−	34.0556i		−	1.11553i
$933$	−6.79906	−	11.3159i	−0.222591	−	0.370465i
$934$	−2.29262	−	2.29262i	−0.0750168	−	0.0750168i
$935$	−38.4590			−1.25775
$936$		0			0
$937$	7.10985			0.232269			0.116134	−	0.993234i	$-0.462950\pi$
$937$	7.10985			0.232269			0.116134	+	0.993234i	$0.462950\pi$
$938$	1.97021	+	1.97021i	0.0643296	+	0.0643296i
$939$	−5.81161	−	9.67244i	−0.189655	−	0.315648i
$940$			20.5746i			0.671069i
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	0.972266	−	0.233877i	$-0.0751412\pi$
$941$	22.6506	+	22.6506i	0.738390	+	0.738390i	−0.233877	+	0.972266i	$0.575141\pi$
$942$	−2.31555	+	9.28664i	−0.0754447	+	0.302575i
$943$	13.0409	+	13.0409i	0.424670	+	0.424670i
$944$	23.1413	−	23.1413i	0.753185	−	0.753185i
$945$	−1.09727	−	20.9530i	−0.0356941	−	0.681601i
$946$		−	3.66900i		−	0.119290i
$947$	−9.45582	+	9.45582i	−0.307273	+	0.307273i	−0.843851	−	0.536578i	$-0.819717\pi$
$947$	−9.45582	+	9.45582i	−0.307273	+	0.307273i	0.536578	+	0.843851i	$0.319717\pi$
$948$	3.06363	−	1.84076i	0.0995022	−	0.0597852i
$949$		0			0
$950$			12.2866i			0.398629i
$951$	3.73002	−	14.9594i	0.120954	−	0.485093i
$952$	−9.36762			−0.303606
$953$	−17.7883			−0.576219			−0.288110	−	0.957597i	$-0.593027\pi$
$953$	−17.7883			−0.576219			−0.288110	+	0.957597i	$0.593027\pi$
$954$	0.760824	+	2.48878i	0.0246326	+	0.0805772i
$955$	−16.7035	+	16.7035i	−0.540512	+	0.540512i
$956$	12.2725	−	12.2725i	0.396922	−	0.396922i
$957$	2.11157	−	8.46858i	0.0682575	−	0.273750i
$958$	8.08847			0.261327
$959$	−8.75547			−0.282729
$960$	−30.2000	−	7.53013i	−0.974700	−	0.243034i
$961$			10.1988i			0.328993i
$962$		0			0
$963$	34.5812	+	18.3883i	1.11436	+	0.592555i
$964$	36.7103	−	36.7103i	1.18236	−	1.18236i
$965$		−	38.6288i		−	1.24351i
$966$	−1.64755	+	0.989916i	−0.0530089	+	0.0318500i
$967$	−29.0154	+	29.0154i	−0.933072	+	0.933072i	−0.997897	−	0.0648250i	$-0.979351\pi$
$967$	−29.0154	+	29.0154i	−0.933072	+	0.933072i	0.0648250	+	0.997897i	$0.479351\pi$
$968$	7.22814	+	7.22814i	0.232321	+	0.232321i
$969$	−48.8670	−	12.1846i	−1.56983	−	0.391425i
$970$	10.6239	+	10.6239i	0.341114	+	0.341114i
$971$		−	22.5895i		−	0.724933i	−0.931997	−	0.362466i	$-0.881935\pi$
$971$		−	22.5895i		−	0.724933i	0.931997	−	0.362466i	$-0.118065\pi$
$972$	−26.5001	−	12.3593i	−0.849992	−	0.396426i
$973$	−4.43063	−	4.43063i	−0.142039	−	0.142039i
$974$	−10.3864			−0.332803
$975$		0			0
$976$	8.70733			0.278715
$977$	−1.88475	−	1.88475i	−0.0602986	−	0.0602986i	0.676314	−	0.736613i	$-0.263576\pi$
$977$	−1.88475	−	1.88475i	−0.0602986	−	0.0602986i	−0.736613	+	0.676314i	$0.763576\pi$
$978$	−1.80860	+	1.08668i	−0.0578326	+	0.0347483i
$979$		−	8.01496i		−	0.256159i
$980$	−26.0407	−	26.0407i	−0.831839	−	0.831839i
$981$	5.56693	+	18.2103i	0.177738	+	0.581411i
$982$	−3.81896	−	3.81896i	−0.121868	−	0.121868i
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.263440	+	0.964676i	$0.584857\pi$
$983$	−38.5049	+	38.5049i	−1.22812	+	1.22812i	−0.964676	+	0.263440i	$0.915143\pi$
$984$	8.29373	+	13.8035i	0.264394	+	0.440039i
$985$			7.93635i			0.252873i
$986$	−3.95210	+	3.95210i	−0.125861	+	0.125861i
$987$	−3.27182	−	5.44538i	−0.104143	−	0.173328i
$988$		0			0
$989$		−	15.0419i		−	0.478303i
$990$	−6.58924	+	2.01434i	−0.209420	+	0.0640200i
$991$	13.2443			0.420720			0.210360	−	0.977624i	$-0.432536\pi$
$991$	13.2443			0.420720			0.210360	+	0.977624i	$0.432536\pi$
$992$	17.7167			0.562506
$993$	−27.0183	−	6.73680i	−0.857400	−	0.213786i
$994$	−3.36128	+	3.36128i	−0.106613	+	0.106613i
$995$	−45.0726	+	45.0726i	−1.42890	+	1.42890i
$996$	−20.4597	−	5.10147i	−0.648291	−	0.161646i
$997$	−31.5812			−1.00019			−0.500093	−	0.865972i	$-0.666701\pi$
$997$	−31.5812			−1.00019			−0.500093	+	0.865972i	$0.666701\pi$
$998$	14.7203			0.465962
$999$	−8.34326	−	7.51290i	−0.263969	−	0.237698i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.f.g.239.14	yes	48
3.2	odd	2	inner	507.2.f.g.239.11	✓	48
13.2	odd	12		507.2.k.k.488.13		96
13.3	even	3		507.2.k.k.188.11		96
13.4	even	6		507.2.k.k.80.12		96
13.5	odd	4	inner	507.2.f.g.437.14	yes	48
13.6	odd	12		507.2.k.k.89.12		96
13.7	odd	12		507.2.k.k.89.14		96
13.8	odd	4	inner	507.2.f.g.437.12	yes	48
13.9	even	3		507.2.k.k.80.14		96
13.10	even	6		507.2.k.k.188.13		96
13.11	odd	12		507.2.k.k.488.11		96
13.12	even	2	inner	507.2.f.g.239.12	yes	48
39.2	even	12		507.2.k.k.488.12		96
39.5	even	4	inner	507.2.f.g.437.11	yes	48
39.8	even	4	inner	507.2.f.g.437.13	yes	48
39.11	even	12		507.2.k.k.488.14		96
39.17	odd	6		507.2.k.k.80.13		96
39.20	even	12		507.2.k.k.89.11		96
39.23	odd	6		507.2.k.k.188.12		96
39.29	odd	6		507.2.k.k.188.14		96
39.32	even	12		507.2.k.k.89.13		96
39.35	odd	6		507.2.k.k.80.11		96
39.38	odd	2	inner	507.2.f.g.239.13	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.f.g.239.11	✓	48	3.2	odd	2	inner
507.2.f.g.239.12	yes	48	13.12	even	2	inner
507.2.f.g.239.13	yes	48	39.38	odd	2	inner
507.2.f.g.239.14	yes	48	1.1	even	1	trivial
507.2.f.g.437.11	yes	48	39.5	even	4	inner
507.2.f.g.437.12	yes	48	13.8	odd	4	inner
507.2.f.g.437.13	yes	48	39.8	even	4	inner
507.2.f.g.437.14	yes	48	13.5	odd	4	inner
507.2.k.k.80.11		96	39.35	odd	6
507.2.k.k.80.12		96	13.4	even	6
507.2.k.k.80.13		96	39.17	odd	6
507.2.k.k.80.14		96	13.9	even	3
507.2.k.k.89.11		96	39.20	even	12
507.2.k.k.89.12		96	13.6	odd	12
507.2.k.k.89.13		96	39.32	even	12
507.2.k.k.89.14		96	13.7	odd	12
507.2.k.k.188.11		96	13.3	even	3
507.2.k.k.188.12		96	39.23	odd	6
507.2.k.k.188.13		96	13.10	even	6
507.2.k.k.188.14		96	39.29	odd	6
507.2.k.k.488.11		96	13.11	odd	12
507.2.k.k.488.12		96	39.2	even	12
507.2.k.k.488.13		96	13.2	odd	12
507.2.k.k.488.14		96	39.11	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.249216 + 0.249216i) q^{2} +(0.892053 + 1.48467i) q^{3} -1.87578i q^{4} +(2.45719 + 2.45719i) q^{5} +(-0.147689 + 0.592316i) q^{6} +(0.821655 + 0.821655i) q^{7} +(0.965906 - 0.965906i) q^{8} +(-1.40848 + 2.64881i) q^{9} +1.22474i q^{10} +(1.32603 - 1.32603i) q^{11} +(2.78492 - 1.67330i) q^{12} +0.409539i q^{14} +(-1.45617 + 5.84006i) q^{15} -3.27013 q^{16} -5.90167 q^{17} +(-1.01114 + 0.309108i) q^{18} +(3.48387 - 3.48387i) q^{19} +(4.60916 - 4.60916i) q^{20} +(-0.486926 + 1.95284i) q^{21} +0.660937 q^{22} +2.70965 q^{23} +(2.29569 + 0.572412i) q^{24} +7.07560i q^{25} +(-5.18904 + 0.271740i) q^{27} +(1.54125 - 1.54125i) q^{28} -2.68706i q^{29} +(-1.81834 + 1.09253i) q^{30} +(-3.22500 + 3.22500i) q^{31} +(-2.74678 - 2.74678i) q^{32} +(3.15161 + 0.785829i) q^{33} +(-1.47079 - 1.47079i) q^{34} +4.03793i q^{35} +(4.96858 + 2.64201i) q^{36} +(1.52785 + 1.52785i) q^{37} +1.73647 q^{38} +4.74684 q^{40} +(4.81276 + 4.81276i) q^{41} +(-0.608029 + 0.365330i) q^{42} -5.55122i q^{43} +(-2.48735 - 2.48735i) q^{44} +(-9.96955 + 3.04771i) q^{45} +(0.675287 + 0.675287i) q^{46} +(-2.23192 + 2.23192i) q^{47} +(-2.91713 - 4.85506i) q^{48} -5.64977i q^{49} +(-1.76335 + 1.76335i) q^{50} +(-5.26460 - 8.76202i) q^{51} -2.46136i q^{53} +(-1.36091 - 1.22547i) q^{54} +6.51664 q^{55} +1.58728 q^{56} +(8.28020 + 2.06460i) q^{57} +(0.669659 - 0.669659i) q^{58} +(-7.07657 + 7.07657i) q^{59} +(10.9547 + 2.73147i) q^{60} -2.66269 q^{61} -1.60744 q^{62} +(-3.33369 + 1.01912i) q^{63} +5.17117i q^{64} +(0.589590 + 0.981273i) q^{66} +(4.81080 - 4.81080i) q^{67} +11.0702i q^{68} +(2.41715 + 4.02293i) q^{69} +(-1.00632 + 1.00632i) q^{70} +(8.20749 + 8.20749i) q^{71} +(1.19803 + 3.91896i) q^{72} +(-9.13263 - 9.13263i) q^{73} +0.761529i q^{74} +(-10.5049 + 6.31180i) q^{75} +(-6.53499 - 6.53499i) q^{76} +2.17908 q^{77} +1.10008 q^{79} +(-8.03534 - 8.03534i) q^{80} +(-5.03234 - 7.46160i) q^{81} +2.39883i q^{82} +(-4.58922 - 4.58922i) q^{83} +(3.66311 + 0.913368i) q^{84} +(-14.5015 - 14.5015i) q^{85} +(1.38345 - 1.38345i) q^{86} +(3.98940 - 2.39700i) q^{87} -2.56165i q^{88} +(3.02216 - 3.02216i) q^{89} +(-3.24410 - 1.72503i) q^{90} -5.08271i q^{92} +(-7.66492 - 1.91119i) q^{93} -1.11246 q^{94} +17.1211 q^{95} +(1.62779 - 6.52833i) q^{96} +(8.67443 - 8.67443i) q^{97} +(1.40801 - 1.40801i) q^{98} +(1.64471 + 5.38010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{9} - 8 q^{16} + 112 q^{22} - 84 q^{27} + 128 q^{40} - 56 q^{42} - 188 q^{48} + 8 q^{55} + 56 q^{61} - 92 q^{66} - 72 q^{81} - 112 q^{87} + 296 q^{94}+O(q^{100}) \) 48 * q - 24 * q^9 - 8 * q^16 + 112 * q^22 - 84 * q^27 + 128 * q^40 - 56 * q^42 - 188 * q^48 + 8 * q^55 + 56 * q^61 - 92 * q^66 - 72 * q^81 - 112 * q^87 + 296 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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