LMFDB - Embedded newform 507.2.f.g.239.12

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			239.12
Character	$\chi$	$=$	507.239
Dual form			507.2.f.g.437.11

$q$-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	0.613485	−	0.789707i	$-0.289767\pi$
$2$	−0.249216	−	0.249216i	−0.176222	−	0.176222i	−0.789707	+	0.613485i	$0.789767\pi$
$3$	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	$-0.966724\pi$
$5$	−2.45719	−	2.45719i	−1.09889	−	1.09889i	−0.104350	−	0.994541i	$-0.533276\pi$
$6$	0.147689	−	0.592316i	0.0602939	−	0.241812i
$7$	−0.821655	−	0.821655i	−0.310556	−	0.310556i	0.534569	−	0.845125i	$-0.320474\pi$
$7$	−0.821655	−	0.821655i	−0.310556	−	0.310556i	−0.845125	+	0.534569i	$0.820474\pi$
$8$	−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	−0.878167	−	0.478353i	$-0.841234\pi$
$11$	−1.32603	+	1.32603i	−0.399814	+	0.399814i	0.478353	+	0.878167i	$0.341234\pi$
$12$	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	−0.982978	−	0.183723i	$-0.941185\pi$
$19$	−3.48387	+	3.48387i	−0.799255	+	0.799255i	0.183723	+	0.982978i	$0.441185\pi$
$20$	−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	−0.355463	−	0.934690i	$-0.615677\pi$
$31$	3.22500	−	3.22500i	0.579227	−	0.579227i	0.934690	+	0.355463i	$0.115677\pi$
$32$	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	0.570276	−	0.821453i	$-0.306836\pi$
$37$	−1.52785	−	1.52785i	−0.251177	−	0.251177i	−0.821453	+	0.570276i	$0.806836\pi$
$38$	1.73647			0.281693
$39$		0			0
$40$	4.74684			0.750541
$41$	−4.81276	−	4.81276i	−0.751627	−	0.751627i	0.223156	−	0.974783i	$-0.428364\pi$
$41$	−4.81276	−	4.81276i	−0.751627	−	0.751627i	−0.974783	+	0.223156i	$0.928364\pi$
$42$	−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	−0.525336	−	0.850895i	$-0.676060\pi$
$47$	2.23192	−	2.23192i	0.325559	−	0.325559i	0.850895	+	0.525336i	$0.176060\pi$
$48$	−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	−0.0758301	−	0.997121i	$-0.524161\pi$
$59$	7.07657	−	7.07657i	0.921291	−	0.921291i	0.997121	+	0.0758301i	$0.0241607\pi$
$60$	−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	−0.937017	−	0.349284i	$-0.886425\pi$
$67$	−4.81080	+	4.81080i	−0.587732	+	0.587732i	0.349284	+	0.937017i	$0.386425\pi$
$68$			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	0.0256220	−	0.999672i	$-0.491843\pi$
$71$	−8.20749	−	8.20749i	−0.974050	−	0.974050i	−0.999672	+	0.0256220i	$0.991843\pi$
$72$	−1.19803	−	3.91896i	−0.141190	−	0.461854i
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.997444	+	0.0714492i	$0.0227624\pi$
$73$	9.13263	+	9.13263i	1.06889	+	1.06889i	0.0714492	+	0.997444i	$0.477238\pi$
$74$			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	0.912596	−	0.408864i	$-0.134075\pi$
$83$	4.58922	+	4.58922i	0.503732	+	0.503732i	−0.408864	+	0.912596i	$0.634075\pi$
$84$	−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	−0.848901	−	0.528553i	$-0.822735\pi$
$89$	−3.02216	+	3.02216i	−0.320348	+	0.320348i	0.528553	+	0.848901i	$0.322735\pi$
$90$	−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	−0.993611	−	0.112856i	$-0.964000\pi$
$97$	−8.67443	+	8.67443i	−0.880755	+	0.880755i	0.112856	+	0.993611i	$0.464000\pi$
$98$	−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	−0.888594	−	0.458694i	$-0.848318\pi$
$109$	−4.48829	+	4.48829i	−0.429901	+	0.429901i	0.458694	+	0.888594i	$0.348318\pi$
$110$	−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	−0.441878	−	0.897075i	$-0.645688\pi$
$137$	5.32795	−	5.32795i	0.455197	−	0.455197i	0.897075	+	0.441878i	$0.145688\pi$
$138$	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	$0.134114\pi$
$149$	16.1312	+	16.1312i	1.32152	+	1.32152i	0.408977	+	0.912545i	$0.365886\pi$
$150$	4.19099	+	1.04499i	0.342193	+	0.0853231i
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	0.384500	−	0.923125i	$-0.374374\pi$
$151$	−6.61873	−	6.61873i	−0.538625	−	0.538625i	−0.923125	+	0.384500i	$0.874374\pi$
$152$		−	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	0.604883	−	0.796314i	$-0.293220\pi$
$163$	−2.44403	−	2.44403i	−0.191432	−	0.191432i	−0.796314	+	0.604883i	$0.793220\pi$
$164$	−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	−0.548954	−	0.835853i	$-0.684974\pi$
$167$	3.70756	−	3.70756i	0.286899	−	0.286899i	0.835853	+	0.548954i	$0.184974\pi$
$168$	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	0.930949	−	0.365148i	$-0.118982\pi$
$193$	7.86036	+	7.86036i	0.565801	+	0.565801i	−0.365148	+	0.930949i	$0.618982\pi$
$194$	4.32361			0.310417
$195$		0			0
$196$	−10.5977			−0.756981
$197$	−1.61492	−	1.61492i	−0.115058	−	0.115058i	0.647233	−	0.762292i	$-0.275926\pi$
$197$	−1.61492	−	1.61492i	−0.115058	−	0.115058i	−0.762292	+	0.647233i	$0.775926\pi$
$198$	−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	$-0.353062\pi$
$223$	20.0214	−	20.0214i	1.34073	−	1.34073i	0.895332	−	0.445400i	$-0.146938\pi$
$224$		−	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	0.513121	−	0.858316i	$-0.328489\pi$
$227$	−5.20089	−	5.20089i	−0.345195	−	0.345195i	−0.858316	+	0.513121i	$0.828489\pi$
$228$	−3.87274	+	15.5319i	−0.256479	+	1.02862i
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	0.221263	−	0.975214i	$-0.428982\pi$
$229$	−11.4094	−	11.4094i	−0.753951	−	0.753951i	−0.975214	+	0.221263i	$0.928982\pi$
$230$			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	0.463099	−	0.886306i	$-0.346737\pi$
$239$	−6.54262	−	6.54262i	−0.423207	−	0.423207i	−0.886306	+	0.463099i	$0.846737\pi$
$240$	−4.76187	+	19.0978i	−0.307378	+	1.23275i
$241$	−19.5707	−	19.5707i	−1.26066	−	1.26066i	−0.950775	−	0.309883i	$-0.899710\pi$
$241$	−19.5707	−	19.5707i	−1.26066	−	1.26066i	−0.309883	−	0.950775i	$-0.600290\pi$
$242$	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	0.216714	−	0.976235i	$-0.430466\pi$
$271$	−12.5033	−	12.5033i	−0.759521	−	0.759521i	−0.976235	+	0.216714i	$0.930466\pi$
$272$	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	−0.404181	−	0.914679i	$-0.632443\pi$
$281$	8.55751	−	8.55751i	0.510498	−	0.510498i	0.914679	+	0.404181i	$0.132443\pi$
$282$	−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	−0.954578	−	0.297963i	$-0.903693\pi$
$293$	−11.2394	+	11.2394i	−0.656615	+	0.656615i	0.297963	+	0.954578i	$0.403693\pi$
$294$	−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	0.165277	−	0.986247i	$-0.447148\pi$
$307$	−14.3846	−	14.3846i	−0.820970	−	0.820970i	−0.986247	+	0.165277i	$0.947148\pi$
$308$		−	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	0.861416	−	0.507901i	$-0.169578\pi$
$317$	6.29415	+	6.29415i	0.353515	+	0.353515i	−0.507901	+	0.861416i	$0.669578\pi$
$318$	−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	−0.321928	−	0.946764i	$-0.604331\pi$
$331$	11.3679	−	11.3679i	0.624836	−	0.624836i	0.946764	+	0.321928i	$0.104331\pi$
$332$	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	$-0.954450\pi$
$349$	−21.1548	−	21.1548i	−1.13239	−	1.13239i	−0.142610	−	0.989779i	$-0.545550\pi$
$350$	−2.89773			−0.154890
$351$		0			0
$352$	−7.28464			−0.388273
$353$	8.96336	+	8.96336i	0.477072	+	0.477072i	0.904194	−	0.427122i	$-0.140473\pi$
$353$	8.96336	+	8.96336i	0.477072	+	0.477072i	−0.427122	+	0.904194i	$0.640473\pi$
$354$	−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	$0.525192\pi$
$359$	−20.3859	+	20.3859i	−1.07593	+	1.07593i	−0.996870	+	0.0790589i	$0.974808\pi$
$360$	−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	−0.775542	−	0.631296i	$-0.782523\pi$
$379$	−2.80816	+	2.80816i	−0.144246	+	0.144246i	0.631296	+	0.775542i	$0.282523\pi$
$380$		−	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	0.0377843	−	0.999286i	$-0.487970\pi$
$383$	−18.8170	−	18.8170i	−0.961502	−	0.961502i	−0.999286	+	0.0377843i	$0.987970\pi$
$384$	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	0.989731	−	0.142946i	$-0.0456575\pi$
$397$	16.8721	+	16.8721i	0.846785	+	0.846785i	−0.142946	+	0.989731i	$0.545657\pi$
$398$	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	−0.166729	−	0.986003i	$-0.553321\pi$
$401$	16.4059	−	16.4059i	0.819274	−	0.819274i	0.986003	+	0.166729i	$0.0533205\pi$
$402$	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	−0.891824	−	0.452383i	$-0.850574\pi$
$409$	−8.88715	+	8.88715i	−0.439441	+	0.439441i	0.452383	+	0.891824i	$0.350574\pi$
$410$	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	−0.455040	−	0.890471i	$-0.650375\pi$
$421$	8.93430	−	8.93430i	0.435431	−	0.435431i	0.890471	+	0.455040i	$0.150375\pi$
$422$	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	0.969207	−	0.246246i	$-0.0791973\pi$
$431$	15.0091	+	15.0091i	0.722961	+	0.722961i	−0.246246	+	0.969207i	$0.579197\pi$
$432$	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	−0.165798	−	0.986160i	$-0.553020\pi$
$449$	17.3832	−	17.3832i	0.820362	−	0.820362i	0.986160	+	0.165798i	$0.0530198\pi$
$450$	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	−0.586241	−	0.810136i	$-0.699393\pi$
$457$	4.78633	−	4.78633i	0.223895	−	0.223895i	0.810136	+	0.586241i	$0.199393\pi$
$458$			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	0.881064	−	0.472997i	$-0.156828\pi$
$461$	8.76156	+	8.76156i	0.408067	+	0.408067i	−0.472997	+	0.881064i	$0.656828\pi$
$462$	0.321828	−	1.29071i	0.0149728	−	0.0600491i
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	0.526236	−	0.850339i	$-0.323603\pi$
$463$	−6.97385	−	6.97385i	−0.324102	−	0.324102i	−0.850339	+	0.526236i	$0.823603\pi$
$464$			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	−0.972861	−	0.231392i	$-0.925672\pi$
$479$	−16.2278	+	16.2278i	−0.741469	+	0.741469i	0.231392	+	0.972861i	$0.425672\pi$
$480$	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	−0.0542557	−	0.998527i	$-0.517279\pi$
$487$	20.8383	−	20.8383i	0.944271	−	0.944271i	0.998527	+	0.0542557i	$0.0172786\pi$
$488$	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	$0.634473\pi$
$499$	−29.5332	+	29.5332i	−1.32209	+	1.32209i	−0.912084	+	0.410004i	$0.865527\pi$
$500$	−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	$0.189016\pi$
$509$	31.3223	+	31.3223i	1.38834	+	1.38834i	0.559525	+	0.828814i	$0.310984\pi$
$510$	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	0.760068	−	0.649844i	$-0.225166\pi$
$541$	2.56375	+	2.56375i	0.110224	+	0.110224i	−0.649844	+	0.760068i	$0.725166\pi$
$542$			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	−0.651467	−	0.758677i	$-0.725846\pi$
$557$	2.53023	−	2.53023i	0.107209	−	0.107209i	0.758677	+	0.651467i	$0.225846\pi$
$558$	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	−0.561844	−	0.827243i	$-0.689908\pi$
$577$	6.37509	−	6.37509i	0.265398	−	0.265398i	0.827243	+	0.561844i	$0.189908\pi$
$578$	−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	0.0808262	−	0.996728i	$-0.474244\pi$
$587$	−22.1906	−	22.1906i	−0.915902	−	0.915902i	−0.996728	+	0.0808262i	$0.974244\pi$
$588$	−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	−0.0255650	−	0.999673i	$-0.508138\pi$
$593$	23.7211	−	23.7211i	0.974108	−	0.974108i	0.999673	+	0.0255650i	$0.00813848\pi$
$594$	−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	−0.715501	−	0.698611i	$-0.753802\pi$
$613$	−0.418180	+	0.418180i	−0.0168901	+	0.0168901i	0.698611	+	0.715501i	$0.253802\pi$
$614$			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	0.159626	−	0.987178i	$-0.448971\pi$
$617$	−20.5560	−	20.5560i	−0.827552	−	0.827552i	−0.987178	+	0.159626i	$0.948971\pi$
$618$	−2.62565	−	0.654685i	−0.105619	−	0.0263353i
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	0.0808459	−	0.996727i	$-0.474238\pi$
$619$	−22.7868	−	22.7868i	−0.915881	−	0.915881i	−0.996727	+	0.0808459i	$0.974238\pi$
$620$			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	$0.0492656\pi$
$631$	28.6918	+	28.6918i	1.14220	+	1.14220i	0.154155	+	0.988047i	$0.450734\pi$
$632$	−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	−0.698216	−	0.715887i	$-0.746022\pi$
$643$	0.448106	−	0.448106i	0.0176716	−	0.0176716i	0.715887	+	0.698216i	$0.246022\pi$
$644$	−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	0.796110	−	0.605152i	$-0.206887\pi$
$661$	4.90953	+	4.90953i	0.190959	+	0.190959i	−0.605152	+	0.796110i	$0.706887\pi$
$662$	−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	−0.596418	−	0.802674i	$-0.703410\pi$
$683$	5.39035	−	5.39035i	0.206256	−	0.206256i	0.802674	+	0.596418i	$0.203410\pi$
$684$	−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	−0.459213	−	0.888326i	$-0.651869\pi$
$691$	11.2800	−	11.2800i	0.429113	−	0.429113i	0.888326	+	0.459213i	$0.151869\pi$
$692$			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	0.0925354	−	0.995709i	$-0.470503\pi$
$709$	−24.0489	−	24.0489i	−0.903174	−	0.903174i	−0.995709	+	0.0925354i	$0.970503\pi$
$710$	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	$0.604179\pi$
$733$	−34.3405	+	34.3405i	−1.26839	+	1.26839i	−0.946918	+	0.321476i	$0.895821\pi$
$734$	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	$-0.996628\pi$
$739$	−27.4710	−	27.4710i	−1.01054	−	1.01054i	−0.0105933	−	0.999944i	$-0.503372\pi$
$740$	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	$-0.844593\pi$
$743$	−36.8590	−	36.8590i	−1.35223	−	1.35223i	−0.469058	−	0.883167i	$-0.655407\pi$
$744$	−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	−0.999911	−	0.0133615i	$-0.995747\pi$
$761$	−27.2152	+	27.2152i	−0.986549	+	0.986549i	0.0133615	+	0.999911i	$0.495747\pi$
$762$	−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	−0.669789	−	0.742552i	$-0.733615\pi$
$769$	2.01778	−	2.01778i	0.0727631	−	0.0727631i	0.742552	+	0.669789i	$0.233615\pi$
$770$			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	0.784093	−	0.620644i	$-0.213129\pi$
$773$	4.54435	+	4.54435i	0.163449	+	0.163449i	−0.620644	+	0.784093i	$0.713129\pi$
$774$	−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	0.871938	−	0.489616i	$-0.162863\pi$
$787$	10.7255	+	10.7255i	0.382322	+	0.382322i	−0.489616	+	0.871938i	$0.662863\pi$
$788$	−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	$-0.487156\pi$
$811$	29.6037	−	29.6037i	1.03952	−	1.03952i	0.999186	−	0.0403387i	$-0.0128437\pi$
$812$	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	0.898405	−	0.439168i	$-0.144727\pi$
$821$	13.1586	+	13.1586i	0.459237	+	0.459237i	−0.439168	+	0.898405i	$0.644727\pi$
$822$	−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	−0.971149	−	0.238472i	$-0.923354\pi$
$827$	−21.0701	+	21.0701i	−0.732678	+	0.732678i	0.238472	+	0.971149i	$0.423354\pi$
$828$	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	−0.826886	−	0.562369i	$-0.809890\pi$
$839$	−7.66187	+	7.66187i	−0.264517	+	0.264517i	0.562369	+	0.826886i	$0.309890\pi$
$840$	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	$0.0106230\pi$
$853$	30.1644	+	30.1644i	1.03281	+	1.03281i	0.0333670	+	0.999443i	$0.489377\pi$
$854$		−	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	0.126779	−	0.991931i	$-0.459536\pi$
$863$	−25.4155	−	25.4155i	−0.865153	−	0.865153i	−0.991931	+	0.126779i	$0.959536\pi$
$864$	−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	−0.891175	−	0.453659i	$-0.850118\pi$
$877$	−12.9567	+	12.9567i	−0.437516	+	0.437516i	0.453659	+	0.891175i	$0.350118\pi$
$878$	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	0.679992	−	0.733220i	$-0.261983\pi$
$929$	−1.62237	−	1.62237i	−0.0532282	−	0.0532282i	−0.733220	+	0.679992i	$0.761983\pi$
$930$	−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	0.233877	−	0.972266i	$-0.424859\pi$
$941$	−22.6506	−	22.6506i	−0.738390	−	0.738390i	−0.972266	+	0.233877i	$0.924859\pi$
$942$	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	−0.536578	−	0.843851i	$-0.680283\pi$
$947$	9.45582	−	9.45582i	0.307273	−	0.307273i	0.843851	+	0.536578i	$0.180283\pi$
$948$	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	−0.0648250	−	0.997897i	$-0.520649\pi$
$967$	29.0154	−	29.0154i	0.933072	−	0.933072i	0.997897	+	0.0648250i	$0.0206489\pi$
$968$	−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	0.736613	−	0.676314i	$-0.236424\pi$
$977$	1.88475	+	1.88475i	0.0602986	+	0.0602986i	−0.676314	+	0.736613i	$0.736424\pi$
$978$	−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	$-0.415143\pi$
$983$	38.5049	−	38.5049i	1.22812	−	1.22812i	0.964676	−	0.263440i	$-0.0848571\pi$
$984$	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.239.12	yes	48
3.2	odd	2	inner	507.2.f.g.239.13	yes	48
13.2	odd	12		507.2.k.k.488.11		96
13.3	even	3		507.2.k.k.188.13		96
13.4	even	6		507.2.k.k.80.14		96
13.5	odd	4	inner	507.2.f.g.437.12	yes	48
13.6	odd	12		507.2.k.k.89.14		96
13.7	odd	12		507.2.k.k.89.12		96
13.8	odd	4	inner	507.2.f.g.437.14	yes	48
13.9	even	3		507.2.k.k.80.12		96
13.10	even	6		507.2.k.k.188.11		96
13.11	odd	12		507.2.k.k.488.13		96
13.12	even	2	inner	507.2.f.g.239.14	yes	48
39.2	even	12		507.2.k.k.488.14		96
39.5	even	4	inner	507.2.f.g.437.13	yes	48
39.8	even	4	inner	507.2.f.g.437.11	yes	48
39.11	even	12		507.2.k.k.488.12		96
39.17	odd	6		507.2.k.k.80.11		96
39.20	even	12		507.2.k.k.89.13		96
39.23	odd	6		507.2.k.k.188.14		96
39.29	odd	6		507.2.k.k.188.12		96
39.32	even	12		507.2.k.k.89.11		96
39.35	odd	6		507.2.k.k.80.13		96
39.38	odd	2	inner	507.2.f.g.239.11	✓	48

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

Groups

Database

Properties

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