LMFDB - Embedded newform 507.2.f.g.437.12

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			437.12
Character	$\chi$	$=$	507.437
Dual form			507.2.f.g.239.11

$q$-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} +(-0.592316 - 0.147689i) 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} +(-5.84006 - 1.45617i) q^{15} -3.27013 q^{16} +5.90167 q^{17} +(-0.309108 - 1.01114i) q^{18} +(3.48387 + 3.48387i) q^{19} +(-4.60916 - 4.60916i) q^{20} +(1.95284 + 0.486926i) q^{21} +0.660937 q^{22} -2.70965 q^{23} +(0.572412 - 2.29569i) 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} +(0.785829 - 3.15161i) 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} +(-3.04771 - 9.96955i) 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} +(1.22547 - 1.36091i) q^{54} +6.51664 q^{55} -1.58728 q^{56} +(-2.06460 + 8.28020i) q^{57} +(0.669659 + 0.669659i) q^{58} +(7.07657 + 7.07657i) q^{59} +(2.73147 - 10.9547i) q^{60} -2.66269 q^{61} +1.60744 q^{62} +(1.01912 + 3.33369i) 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} +(3.91896 - 1.19803i) 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} +(-0.913368 + 3.66311i) 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} +(1.91119 - 7.66492i) q^{93} -1.11246 q^{94} -17.1211 q^{95} +(6.52833 + 1.62779i) q^{96} +(8.67443 + 8.67443i) q^{97} +(-1.40801 - 1.40801i) q^{98} +(5.38010 - 1.64471i) 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 $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

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

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	$-0.789767\pi$
$2$	−0.249216	+	0.249216i	−0.176222	+	0.176222i	0.613485	+	0.789707i	$0.289767\pi$
$3$	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	−0.104350	+	0.994541i	$0.533276\pi$
$5$	−2.45719	+	2.45719i	−1.09889	+	1.09889i	−0.994541	+	0.104350i	$0.966724\pi$
$6$	−0.592316	−	0.147689i	−0.241812	−	0.0602939i
$7$	0.821655	−	0.821655i	0.310556	−	0.310556i	−0.534569	−	0.845125i	$-0.679526\pi$
$7$	0.821655	−	0.821655i	0.310556	−	0.310556i	0.845125	+	0.534569i	$0.179526\pi$
$8$	−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	$-0.341234\pi$
$11$	−1.32603	−	1.32603i	−0.399814	−	0.399814i	−0.878167	+	0.478353i	$0.841234\pi$
$12$	−2.78492	+	1.67330i	−0.803936	+	0.483039i
$13$		0			0
$13$		0			0
$14$			0.409539i			0.109454i
$15$	−5.84006	−	1.45617i	−1.50790	−	0.375982i
$16$	−3.27013			−0.817532
$17$	5.90167			1.43136			0.715682	−	0.698426i	$-0.246116\pi$
$17$	5.90167			1.43136			0.715682	+	0.698426i	$0.246116\pi$
$18$	−0.309108	−	1.01114i	−0.0728573	−	0.238328i
$19$	3.48387	+	3.48387i	0.799255	+	0.799255i	0.982978	−	0.183723i	$-0.0588148\pi$
$19$	3.48387	+	3.48387i	0.799255	+	0.799255i	−0.183723	+	0.982978i	$0.558815\pi$
$20$	−4.60916	−	4.60916i	−1.03064	−	1.03064i
$21$	1.95284	+	0.486926i	0.426146	+	0.106256i
$22$	0.660937			0.140912
$23$	−2.70965			−0.565001			−0.282500	−	0.959267i	$-0.591164\pi$
$23$	−2.70965			−0.565001			−0.282500	+	0.959267i	$0.591164\pi$
$24$	0.572412	−	2.29569i	0.116843	−	0.468606i
$25$		−	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	$-0.384323\pi$
$31$	−3.22500	−	3.22500i	−0.579227	−	0.579227i	−0.934690	+	0.355463i	$0.884323\pi$
$32$	2.74678	−	2.74678i	0.485567	−	0.485567i
$33$	0.785829	−	3.15161i	0.136795	−	0.548625i
$34$	−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	$-0.693164\pi$
$37$	1.52785	−	1.52785i	0.251177	−	0.251177i	0.821453	+	0.570276i	$0.193164\pi$
$38$	−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	$-0.928364\pi$
$41$	−4.81276	+	4.81276i	−0.751627	+	0.751627i	0.223156	+	0.974783i	$0.428364\pi$
$42$	−0.608029	+	0.365330i	−0.0938210	+	0.0563716i
$43$			5.55122i			0.846553i	0.906001	+	0.423276i	$0.139120\pi$
$43$			5.55122i			0.846553i	−0.906001	+	0.423276i	$0.860880\pi$
$44$	2.48735	−	2.48735i	0.374982	−	0.374982i
$45$	−3.04771	−	9.96955i	−0.454326	−	1.48617i
$46$	0.675287	−	0.675287i	0.0995657	−	0.0995657i
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	0.850895	−	0.525336i	$-0.176060\pi$
$47$	2.23192	+	2.23192i	0.325559	+	0.325559i	−0.525336	+	0.850895i	$0.676060\pi$
$48$	−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	$-0.0540689\pi$
$54$	1.22547	−	1.36091i	0.166765	−	0.185197i
$55$	6.51664			0.878704
$56$	−1.58728			−0.212110
$57$	−2.06460	+	8.28020i	−0.273463	+	1.09674i
$58$	0.669659	+	0.669659i	0.0879305	+	0.0879305i
$59$	7.07657	+	7.07657i	0.921291	+	0.921291i	0.997121	−	0.0758301i	$-0.0241607\pi$
$59$	7.07657	+	7.07657i	0.921291	+	0.921291i	−0.0758301	+	0.997121i	$0.524161\pi$
$60$	2.73147	−	10.9547i	0.352631	−	1.41424i
$61$	−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
$63$	1.01912	+	3.33369i	0.128397	+	0.420006i
$64$		−	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	$-0.113575\pi$
$67$	4.81080	+	4.81080i	0.587732	+	0.587732i	−0.349284	+	0.937017i	$0.613575\pi$
$68$			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	$-0.991843\pi$
$71$	−8.20749	+	8.20749i	−0.974050	+	0.974050i	0.0256220	+	0.999672i	$0.491843\pi$
$72$	3.91896	−	1.19803i	0.461854	−	0.141190i
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.0714492	+	0.997444i	$0.522762\pi$
$73$	−9.13263	+	9.13263i	−1.06889	+	1.06889i	−0.997444	+	0.0714492i	$0.977238\pi$
$74$			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	$-0.634075\pi$
$83$	4.58922	−	4.58922i	0.503732	−	0.503732i	0.912596	+	0.408864i	$0.134075\pi$
$84$	−0.913368	+	3.66311i	−0.0996566	+	0.399678i
$85$	−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	$-0.322735\pi$
$89$	−3.02216	−	3.02216i	−0.320348	−	0.320348i	−0.848901	+	0.528553i	$0.822735\pi$
$90$	3.24410	+	1.72503i	0.341959	+	0.181834i
$91$		0			0
$92$		−	5.08271i		−	0.529909i
$93$	1.91119	−	7.66492i	0.198181	−	0.794815i
$94$	−1.11246			−0.114742
$95$	−17.1211			−1.75659
$96$	6.52833	+	1.62779i	0.666295	+	0.166135i
$97$	8.67443	+	8.67443i	0.880755	+	0.880755i	0.993611	−	0.112856i	$-0.0359999\pi$
$97$	8.67443	+	8.67443i	0.880755	+	0.880755i	−0.112856	+	0.993611i	$0.536000\pi$
$98$	−1.40801	−	1.40801i	−0.142231	−	0.142231i
$99$	5.38010	−	1.64471i	0.540721	−	0.165299i
$100$	13.2723			1.32723
$101$	11.0956			1.10405			0.552026	−	0.833827i	$-0.313855\pi$
$101$	11.0956			1.10405			0.552026	+	0.833827i	$0.313855\pi$
$102$	−3.49565	−	0.871614i	−0.346121	−	0.0863026i
$103$			4.43285i			0.436782i	0.975861	+	0.218391i	$0.0700808\pi$
$103$			4.43285i			0.436782i	−0.975861	+	0.218391i	$0.929919\pi$
$104$		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	$-0.151682\pi$
$109$	4.48829	+	4.48829i	0.429901	+	0.429901i	−0.458694	+	0.888594i	$0.651682\pi$
$110$	−1.62405	+	1.62405i	−0.154847	+	0.154847i
$111$	3.63127	+	0.905429i	0.344665	+	0.0859396i
$112$	−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
$123$	−11.4386	−	2.85212i	−1.03138	−	0.257167i
$124$	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	$0.112394\pi$
$127$			7.79402i			0.691607i	−0.938307	+	0.345804i	$0.887606\pi$
$128$	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	$0.699460\pi$
$132$	5.91174	+	1.47405i	0.514551	+	0.128299i
$133$	5.72508			0.496428
$134$	−2.39785			−0.207143
$135$	12.0828	−	13.4182i	1.03992	−	1.15485i
$136$	−5.70046	−	5.70046i	−0.488810	−	0.488810i
$137$	5.32795	+	5.32795i	0.455197	+	0.455197i	0.897075	−	0.441878i	$-0.145688\pi$
$137$	5.32795	+	5.32795i	0.455197	+	0.455197i	−0.441878	+	0.897075i	$0.645688\pi$
$138$	1.60497	+	0.400186i	0.136624	+	0.0340661i
$139$	−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
$141$	−1.32267	+	5.30466i	−0.111389	+	0.446733i
$142$		−	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	0.408977	−	0.912545i	$-0.365886\pi$
$149$	16.1312	−	16.1312i	1.32152	−	1.32152i	0.912545	−	0.408977i	$-0.134114\pi$
$150$	−1.04499	+	4.19099i	−0.0853231	+	0.342193i
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	−0.384500	−	0.923125i	$-0.625626\pi$
$151$	6.61873	−	6.61873i	0.538625	−	0.538625i	0.923125	+	0.384500i	$0.125626\pi$
$152$		−	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
$162$	3.11369	+	0.605410i	0.244634	+	0.0475655i
$163$	2.44403	−	2.44403i	0.191432	−	0.191432i	−0.604883	−	0.796314i	$-0.706780\pi$
$163$	2.44403	−	2.44403i	0.191432	−	0.191432i	0.796314	+	0.604883i	$0.206780\pi$
$164$	−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	$-0.184974\pi$
$167$	3.70756	+	3.70756i	0.286899	+	0.286899i	−0.548954	+	0.835853i	$0.684974\pi$
$168$	−1.41594	−	2.35659i	−0.109242	−	0.181815i
$169$		0			0
$170$		−	7.22802i		−	0.554364i
$171$	−14.1351	+	4.32112i	−1.08094	+	0.330444i
$172$	−10.4129			−0.793975
$173$	14.2512			1.08350			0.541751	−	0.840539i	$-0.317762\pi$
$173$	14.2512			1.08350			0.541751	+	0.840539i	$0.317762\pi$
$174$	−0.396851	+	1.59159i	−0.0300852	+	0.120658i
$175$	−5.81370	−	5.81370i	−0.439474	−	0.439474i
$176$	4.33630	+	4.33630i	0.326861	+	0.326861i
$177$	−4.19369	+	16.8190i	−0.315217	+	1.26420i
$178$	1.50634			0.112905
$179$	−4.36667			−0.326381			−0.163190	−	0.986595i	$-0.552178\pi$
$179$	−4.36667			−0.326381			−0.163190	+	0.986595i	$0.552178\pi$
$180$	18.7007	−	5.71684i	1.39387	−	0.426108i
$181$		−	2.10738i		−	0.156640i	−0.996928	−	0.0783201i	$-0.975044\pi$
$181$		−	2.10738i		−	0.156640i	0.996928	−	0.0783201i	$-0.0249556\pi$
$182$		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
$189$	−4.04033	+	4.48688i	−0.293890	+	0.326372i
$190$	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	$-0.881018\pi$
$193$	−7.86036	+	7.86036i	−0.565801	+	0.565801i	0.365148	+	0.930949i	$0.381018\pi$
$194$	−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	$-0.775926\pi$
$197$	−1.61492	+	1.61492i	−0.115058	+	0.115058i	0.647233	+	0.762292i	$0.275926\pi$
$198$	−0.930919	+	1.75069i	−0.0661576	+	0.124416i
$199$		−	18.3431i		−	1.30031i	−0.759801	−	0.650155i	$-0.774704\pi$
$199$		−	18.3431i		−	1.30031i	0.759801	−	0.650155i	$-0.225296\pi$
$200$	−6.83436	+	6.83436i	−0.483262	+	0.483262i
$201$	−2.85096	+	11.4339i	−0.201091	+	0.806487i
$202$	−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
$210$	0.596359	−	2.39173i	0.0411527	−	0.165045i
$211$	−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
$213$	−19.5069	−	4.86389i	−1.33659	−	0.333269i
$214$	3.25361	+	3.25361i	0.222412	+	0.222412i
$215$	−13.6404	−	13.6404i	−0.930269	−	0.930269i
$216$	5.27460	+	4.74965i	0.358891	+	0.323173i
$217$	−5.29967			−0.359765
$218$	−2.23711			−0.151516
$219$	−21.7057	−	5.41215i	−1.46674	−	0.365719i
$220$			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	−0.895332	−	0.445400i	$-0.853062\pi$
$223$	−20.0214	−	20.0214i	−1.34073	−	1.34073i	−0.445400	−	0.895332i	$-0.646938\pi$
$224$		−	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	$-0.828489\pi$
$227$	−5.20089	+	5.20089i	−0.345195	+	0.345195i	0.513121	+	0.858316i	$0.328489\pi$
$228$	−15.5319	−	3.87274i	−1.02862	−	0.256479i
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	−0.221263	−	0.975214i	$-0.571018\pi$
$229$	11.4094	−	11.4094i	0.753951	−	0.753951i	0.975214	+	0.221263i	$0.0710179\pi$
$230$			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	$-0.702729\pi$
$233$	−18.1554			−1.18940			−0.594700	+	0.803947i	$0.702729\pi$
$234$		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	$-0.846737\pi$
$239$	−6.54262	+	6.54262i	−0.423207	+	0.423207i	0.463099	+	0.886306i	$0.346737\pi$
$240$	19.0978	+	4.76187i	1.23275	+	0.307378i
$241$	19.5707	−	19.5707i	1.26066	−	1.26066i	0.309883	−	0.950775i	$-0.399710\pi$
$241$	19.5707	−	19.5707i	1.26066	−	1.26066i	0.950775	−	0.309883i	$-0.100290\pi$
$242$	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
$249$	10.9073	+	2.71965i	0.691221	+	0.172351i
$250$	−2.54207			−0.160775
$251$	5.60006			0.353473			0.176736	−	0.984258i	$-0.443446\pi$
$251$	5.60006			0.353473			0.176736	+	0.984258i	$0.443446\pi$
$252$	−6.25328	+	1.91164i	−0.393920	+	0.120422i
$253$	3.59308	+	3.59308i	0.225895	+	0.225895i
$254$	−1.94239	−	1.94239i	−0.121877	−	0.121877i
$255$	−34.4661	−	8.59385i	−2.15835	−	0.538168i
$256$	6.96184			0.435115
$257$	6.81357			0.425019			0.212510	−	0.977159i	$-0.431836\pi$
$257$	6.81357			0.425019			0.212510	+	0.977159i	$0.431836\pi$
$258$	0.819856	−	3.28808i	0.0510420	−	0.204707i
$259$		−	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
$267$	1.79098	−	7.18283i	0.109606	−	0.439582i
$268$	−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	$-0.569534\pi$
$271$	12.5033	−	12.5033i	0.759521	−	0.759521i	0.976235	+	0.216714i	$0.0695339\pi$
$272$	−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	$0.238879\pi$
$277$			22.7007i			1.36395i	−0.731375	+	0.681975i	$0.761121\pi$
$278$	1.34385	−	1.34385i	0.0805989	−	0.0805989i
$279$	13.0848	−	4.00003i	0.783364	−	0.239476i
$280$	3.90026	−	3.90026i	0.233085	−	0.233085i
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	0.914679	−	0.404181i	$-0.132443\pi$
$281$	8.55751	+	8.55751i	0.510498	+	0.510498i	−0.404181	+	0.914679i	$0.632443\pi$
$282$	−0.992373	−	1.65164i	−0.0590950	−	0.0983535i
$283$		−	7.10558i		−	0.422383i	−0.977445	−	0.211192i	$-0.932266\pi$
$283$		−	7.10558i		−	0.422383i	0.977445	−	0.211192i	$-0.0677344\pi$
$284$	−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
$288$	3.40689	+	11.1445i	0.200753	+	0.656695i
$289$	17.8297			1.04880
$290$	−3.29096			−0.193252
$291$	−5.14061	+	20.6167i	−0.301348	+	1.20857i
$292$	−17.1308	−	17.1308i	−1.00251	−	1.00251i
$293$	−11.2394	−	11.2394i	−0.656615	−	0.656615i	0.297963	−	0.954578i	$-0.403693\pi$
$293$	−11.2394	−	11.2394i	−0.656615	−	0.656615i	−0.954578	+	0.297963i	$0.903693\pi$
$294$	0.834411	−	3.34645i	0.0486638	−	0.195169i
$295$	−34.7770			−2.02479
$296$	−2.95152			−0.171554
$297$	7.24118	+	6.52051i	0.420176	+	0.378358i
$298$			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
$306$	−1.82425	−	5.96742i	−0.104285	−	0.341134i
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	−0.165277	−	0.986247i	$-0.552852\pi$
$307$	14.3846	−	14.3846i	0.820970	−	0.820970i	0.986247	+	0.165277i	$0.0528518\pi$
$308$		−	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	$-0.430667\pi$
$311$	7.62181			0.432193			0.216097	+	0.976372i	$0.430667\pi$
$312$		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	$-0.669578\pi$
$317$	6.29415	−	6.29415i	0.353515	−	0.353515i	0.861416	+	0.507901i	$0.169578\pi$
$318$	−0.363516	+	1.45790i	−0.0203850	+	0.0817551i
$319$	−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
$327$	−2.65984	+	10.6674i	−0.147089	+	0.589910i
$328$	9.29736			0.513361
$329$	3.66774			0.202209
$330$	−3.85991	−	0.962439i	−0.212481	−	0.0529805i
$331$	−11.3679	−	11.3679i	−0.624836	−	0.624836i	0.321928	−	0.946764i	$-0.395669\pi$
$331$	−11.3679	−	11.3679i	−0.624836	−	0.624836i	−0.946764	+	0.321928i	$0.895669\pi$
$332$	8.60838	+	8.60838i	0.472446	+	0.472446i
$333$	1.89502	+	6.19893i	0.103847	+	0.339699i
$334$	−1.84796			−0.101116
$335$	−23.6421			−1.29171
$336$	−6.38605	−	1.59231i	−0.348388	−	0.0868677i
$337$			28.3556i			1.54463i	0.635243	+	0.772313i	$0.280900\pi$
$337$			28.3556i			1.54463i	−0.635243	+	0.772313i	$0.719100\pi$
$338$		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
$345$	15.8245	+	3.94572i	0.851964	+	0.212430i
$346$	−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	0.142610	−	0.989779i	$-0.454450\pi$
$349$	21.1548	−	21.1548i	1.13239	−	1.13239i	0.989779	−	0.142610i	$-0.0455496\pi$
$350$	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	$-0.640473\pi$
$353$	8.96336	−	8.96336i	0.477072	−	0.477072i	0.904194	+	0.427122i	$0.140473\pi$
$354$	−3.14643	−	5.23670i	−0.167231	−	0.278328i
$355$		−	40.3348i		−	2.14075i
$356$	5.66891	−	5.66891i	0.300452	−	0.300452i
$357$	11.5250	+	2.87368i	0.609970	+	0.152091i
$358$	1.08824	−	1.08824i	0.0575155	−	0.0575155i
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.996870	−	0.0790589i	$-0.974808\pi$
$359$	−20.3859	−	20.3859i	−1.07593	−	1.07593i	−0.0790589	−	0.996870i	$-0.525192\pi$
$360$	−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
$366$	1.57715	+	0.393251i	0.0824392	+	0.0205556i
$367$	−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
$369$	−5.96937	−	19.5268i	−0.310753	−	1.01652i
$370$	−1.87122	−	1.87122i	−0.0972803	−	0.0972803i
$371$	−2.02239	−	2.02239i	−0.104997	−	0.104997i
$372$	14.3777	+	3.58497i	0.745451	+	0.185872i
$373$	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
$375$	−3.02243	+	12.1216i	−0.156078	+	0.625958i
$376$		−	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	$-0.217477\pi$
$379$	2.80816	+	2.80816i	0.144246	+	0.144246i	−0.631296	+	0.775542i	$0.717477\pi$
$380$		−	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	$-0.987970\pi$
$383$	−18.8170	+	18.8170i	−0.961502	+	0.961502i	0.0377843	+	0.999286i	$0.487970\pi$
$384$	−4.01930	+	16.1196i	−0.205109	+	0.822602i
$385$	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	$-0.449979\pi$
$389$	6.17335			0.313001			0.156501	+	0.987678i	$0.449979\pi$
$390$		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
$396$	3.08511	+	10.0919i	0.155033	+	0.507137i
$397$	−16.8721	+	16.8721i	−0.846785	+	0.846785i	−0.989731	−	0.142946i	$-0.954343\pi$
$397$	−16.8721	+	16.8721i	−0.846785	+	0.846785i	0.142946	+	0.989731i	$0.454343\pi$
$398$	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	$-0.0533205\pi$
$401$	16.4059	+	16.4059i	0.819274	+	0.819274i	−0.166729	+	0.986003i	$0.553321\pi$
$402$	−2.13901	−	3.56002i	−0.106684	−	0.177558i
$403$		0			0
$404$			20.8129i			1.03548i
$405$	30.7000	+	5.96917i	1.52550	+	0.296610i
$406$	1.10046			0.0546147
$407$	−4.05196			−0.200848
$408$	3.37818	−	13.5484i	0.167245	−	0.670746i
$409$	8.88715	+	8.88715i	0.439441	+	0.439441i	0.891824	−	0.452383i	$-0.149426\pi$
$409$	8.88715	+	8.88715i	0.439441	+	0.439441i	−0.452383	+	0.891824i	$0.649426\pi$
$410$	5.89440	+	5.89440i	0.291103	+	0.291103i
$411$	−3.15743	+	12.6630i	−0.155744	+	0.624622i
$412$	−8.31506			−0.409654
$413$	11.6290			0.572225
$414$	0.837573	+	2.73984i	0.0411645	+	0.134656i
$415$			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	$-0.349625\pi$
$421$	−8.93430	−	8.93430i	−0.435431	−	0.435431i	−0.890471	+	0.455040i	$0.849625\pi$
$422$	1.99553	−	1.99553i	0.0971408	−	0.0971408i
$423$	−9.05556	+	2.76830i	−0.440296	+	0.134599i
$424$	−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	$-0.579197\pi$
$431$	15.0091	−	15.0091i	0.722961	−	0.722961i	0.969207	+	0.246246i	$0.0791973\pi$
$432$	16.9688	−	0.888625i	0.816413	−	0.0427540i
$433$		−	1.85372i		−	0.0890840i	−0.999008	−	0.0445420i	$-0.985817\pi$
$433$		−	1.85372i		−	0.0890840i	0.999008	−	0.0445420i	$-0.0141828\pi$
$434$	1.32076	−	1.32076i	0.0633986	−	0.0633986i
$435$	−3.91283	+	15.6926i	−0.187606	+	0.752404i
$436$	−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	$-0.888298\pi$
$439$		−	14.4053i		−	0.687526i	0.939056	−	0.343763i	$-0.111702\pi$
$440$	−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	$0.822881\pi$
$444$	−1.69839	+	6.81148i	−0.0806020	+	0.323259i
$445$	14.8521			0.704055
$446$	9.97929			0.472533
$447$	38.3394	+	9.55963i	1.81339	+	0.452155i
$448$	−4.24892	−	4.24892i	−0.200743	−	0.200743i
$449$	17.3832	+	17.3832i	0.820362	+	0.820362i	0.986160	−	0.165798i	$-0.0530198\pi$
$449$	17.3832	+	17.3832i	0.820362	+	0.820362i	−0.165798	+	0.986160i	$0.553020\pi$
$450$	−7.15442	+	2.18712i	−0.337263	+	0.103102i
$451$	12.7638			0.601022
$452$	24.4089			1.14810
$453$	15.7309	+	3.92237i	0.739102	+	0.184289i
$454$		−	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	$-0.300607\pi$
$457$	−4.78633	−	4.78633i	−0.223895	−	0.223895i	−0.810136	+	0.586241i	$0.800607\pi$
$458$			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	$-0.656828\pi$
$461$	8.76156	−	8.76156i	0.408067	−	0.408067i	0.881064	+	0.472997i	$0.156828\pi$
$462$	1.29071	+	0.321828i	0.0600491	+	0.0149728i
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	−0.526236	−	0.850339i	$-0.676397\pi$
$463$	6.97385	−	6.97385i	0.324102	−	0.324102i	0.850339	+	0.526236i	$0.176397\pi$
$464$			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	$-0.431726\pi$
$467$	9.19934			0.425695			0.212847	+	0.977085i	$0.431726\pi$
$468$		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
$474$	−0.651596	−	0.162470i	−0.0299288	−	0.00746251i
$475$	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	$-0.425672\pi$
$479$	−16.2278	−	16.2278i	−0.741469	−	0.741469i	−0.972861	+	0.231392i	$0.925672\pi$
$480$	−20.0412	+	12.0416i	−0.914750	+	0.549621i
$481$		0			0
$482$			9.75464i			0.444312i
$483$	−5.29152	−	1.31940i	−0.240773	−	0.0600347i
$484$	14.0370			0.638045
$485$	−42.6295			−1.93571
$486$	1.87874	+	5.16285i	0.0852213	+	0.234192i
$487$	−20.8383	−	20.8383i	−0.944271	−	0.944271i	0.0542557	−	0.998527i	$-0.482721\pi$
$487$	−20.8383	−	20.8383i	−0.944271	−	0.944271i	−0.998527	+	0.0542557i	$0.982721\pi$
$488$	2.57191	+	2.57191i	0.116425	+	0.116425i
$489$	5.80879	+	1.44838i	0.262682	+	0.0654978i
$490$	6.91951			0.312592
$491$	15.3239			0.691558			0.345779	−	0.938316i	$-0.387615\pi$
$491$	15.3239			0.691558			0.345779	+	0.938316i	$0.387615\pi$
$492$	5.34996	−	21.4563i	0.241195	−	0.967326i
$493$		−	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	0.912084	+	0.410004i	$0.134473\pi$
$499$	29.5332	+	29.5332i	1.32209	+	1.32209i	0.410004	+	0.912084i	$0.365527\pi$
$500$	−9.56676	+	9.56676i	−0.427839	+	0.427839i
$501$	−2.19716	+	8.81183i	−0.0981618	+	0.393683i
$502$	−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	0.559525	−	0.828814i	$-0.310984\pi$
$509$	31.3223	−	31.3223i	1.38834	−	1.38834i	0.828814	−	0.559525i	$-0.189016\pi$
$510$	10.7312	−	6.44778i	0.475186	−	0.285512i
$511$			15.0077i			0.663903i
$512$	−15.2996	+	15.2996i	−0.676153	+	0.676153i
$513$	−19.0247	−	17.1313i	−0.839960	−	0.756364i
$514$	−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	$0.986513\pi$
$522$	−2.71700	+	0.830592i	−0.118920	+	0.0363540i
$523$	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
$525$	3.44529	−	13.8175i	0.150365	−	0.603047i
$526$	−5.64018	−	5.64018i	−0.245923	−	0.245923i
$527$	−19.0329	−	19.0329i	−0.829085	−	0.829085i
$528$	−2.56976	+	10.3062i	−0.111835	+	0.448519i
$529$	−15.6578			−0.680774
$530$	−3.01453			−0.130943
$531$	−28.7117	+	8.77722i	−1.24598	+	0.380899i
$532$			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
$540$	25.1696	+	22.6646i	1.08313	+	0.975331i
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	−0.760068	−	0.649844i	$-0.774834\pi$
$541$	−2.56375	+	2.56375i	−0.110224	+	0.110224i	0.649844	+	0.760068i	$0.274834\pi$
$542$			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
$552$	−1.55104	+	6.22051i	−0.0660165	+	0.264763i
$553$	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	$-0.225846\pi$
$557$	2.53023	+	2.53023i	0.107209	+	0.107209i	−0.651467	+	0.758677i	$0.725846\pi$
$558$	−2.26406	+	4.25780i	−0.0958451	+	0.180247i
$559$		0			0
$560$		−	13.2045i		−	0.557994i
$561$	4.63770	−	18.5998i	0.195804	−	0.785283i
$562$	−4.26533			−0.179922
$563$	19.6742			0.829169			0.414585	−	0.910011i	$-0.363927\pi$
$563$	19.6742			0.829169			0.414585	+	0.910011i	$0.363927\pi$
$564$	−9.95039	−	2.48105i	−0.418987	−	0.104471i
$565$	31.9746	+	31.9746i	1.34518	+	1.34518i
$566$	1.77082	+	1.77082i	0.0744332	+	0.0744332i
$567$	−10.2657	−	1.99601i	−0.431119	−	0.0838247i
$568$	15.8553			0.665275
$569$	−9.56462			−0.400970			−0.200485	−	0.979697i	$-0.564252\pi$
$569$	−9.56462			−0.400970			−0.200485	+	0.979697i	$0.564252\pi$
$570$	10.1411	+	2.52861i	0.424764	+	0.105912i
$571$		−	17.9785i		−	0.752375i	−0.926544	−	0.376187i	$-0.877235\pi$
$571$		−	17.9785i		−	0.752375i	0.926544	−	0.376187i	$-0.122765\pi$
$572$		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	$-0.310092\pi$
$577$	−6.37509	−	6.37509i	−0.265398	−	0.265398i	−0.827243	+	0.561844i	$0.810092\pi$
$578$	−4.44343	+	4.44343i	−0.184823	+	0.184823i
$579$	−18.6819	−	4.65818i	−0.776393	−	0.193587i
$580$	−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	$-0.974244\pi$
$587$	−22.1906	+	22.1906i	−0.915902	+	0.915902i	0.0808262	+	0.996728i	$0.474244\pi$
$588$	−9.45374	−	15.7341i	−0.389866	−	0.648865i
$589$		−	22.4710i		−	0.925900i
$590$	8.66697	−	8.66697i	0.356814	−	0.356814i
$591$	−3.83822	−	0.957029i	−0.157883	−	0.0393669i
$592$	−4.99627	+	4.99627i	−0.205345	+	0.205345i
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	0.999673	−	0.0255650i	$-0.00813848\pi$
$593$	23.7211	+	23.7211i	0.974108	+	0.974108i	−0.0255650	+	0.999673i	$0.508138\pi$
$594$	−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	$-0.242540\pi$
$600$	−16.2434	−	4.05016i	−0.663133	−	0.165347i
$601$	−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
$603$	−19.5188	+	5.96693i	−0.794867	+	0.242992i
$604$	12.4153	+	12.4153i	0.505172	+	0.505172i
$605$	18.3878	+	18.3878i	0.747572	+	0.747572i
$606$	−6.57209	−	1.63870i	−0.266973	−	0.0665676i
$607$	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
$609$	1.30840	−	5.24742i	0.0530191	−	0.212636i
$610$			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	$-0.246198\pi$
$613$	0.418180	+	0.418180i	0.0168901	+	0.0168901i	−0.698611	+	0.715501i	$0.746198\pi$
$614$			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	$-0.948971\pi$
$617$	−20.5560	+	20.5560i	−0.827552	+	0.827552i	0.159626	+	0.987178i	$0.448971\pi$
$618$	0.654685	−	2.62565i	0.0263353	−	0.105619i
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	−0.0808459	−	0.996727i	$-0.525762\pi$
$619$	22.7868	−	22.7868i	0.915881	−	0.915881i	0.996727	+	0.0808459i	$0.0257622\pi$
$620$			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
$630$	4.08291	−	1.24815i	0.162667	−	0.0497277i
$631$	−28.6918	+	28.6918i	−1.14220	+	1.14220i	−0.154155	+	0.988047i	$0.549266\pi$
$631$	−28.6918	+	28.6918i	−1.14220	+	1.14220i	−0.988047	+	0.154155i	$0.950734\pi$
$632$	−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
$639$	−10.1799	−	33.3002i	−0.402711	−	1.31733i
$640$	−33.3308			−1.31752
$641$	25.7121			1.01557			0.507783	−	0.861485i	$-0.330465\pi$
$641$	25.7121			1.01557			0.507783	+	0.861485i	$0.330465\pi$
$642$	−1.92814	+	7.73291i	−0.0760976	+	0.305194i
$643$	−0.448106	−	0.448106i	−0.0176716	−	0.0176716i	0.698216	−	0.715887i	$-0.253978\pi$
$643$	−0.448106	−	0.448106i	−0.0176716	−	0.0176716i	−0.715887	+	0.698216i	$0.753978\pi$
$644$	−4.17624	−	4.17624i	−0.164567	−	0.164567i
$645$	8.08354	−	32.4195i	0.318289	−	1.27652i
$646$	−10.2481			−0.403205
$647$	−47.0248			−1.84874			−0.924368	−	0.381501i	$-0.875407\pi$
$647$	−47.0248			−1.84874			−0.924368	+	0.381501i	$0.875407\pi$
$648$	−2.34644	+	12.0680i	−0.0921768	+	0.474075i
$649$		−	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
$657$	−11.3274	−	37.0537i	−0.441924	−	1.44560i
$658$	−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	$-0.793113\pi$
$661$	−4.90953	+	4.90953i	−0.190959	+	0.190959i	0.605152	+	0.796110i	$0.293113\pi$
$662$	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
$669$	11.8650	−	47.5853i	0.458728	−	1.83975i
$670$	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	$-0.831541\pi$
$673$		−	26.1949i		−	1.00974i	0.863196	−	0.504870i	$-0.168459\pi$
$674$	−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	$0.861534\pi$
$678$	−1.92183	+	7.70760i	−0.0738074	+	0.296008i
$679$	14.2548			0.547048
$680$	28.0142			1.07430
$681$	−12.3611	−	3.08213i	−0.473677	−	0.118108i
$682$	−2.13152	−	2.13152i	−0.0816201	−	0.0816201i
$683$	5.39035	+	5.39035i	0.206256	+	0.206256i	0.802674	−	0.596418i	$-0.203410\pi$
$683$	5.39035	+	5.39035i	0.206256	+	0.206256i	−0.596418	+	0.802674i	$0.703410\pi$
$684$	−8.10549	−	26.5144i	−0.309921	−	1.01380i
$685$	−26.1836			−1.00042
$686$	−5.18057			−0.197795
$687$	27.1169	+	6.76137i	1.03457	+	0.257962i
$688$		−	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	$-0.348131\pi$
$691$	−11.2800	−	11.2800i	−0.429113	−	0.429113i	−0.888326	+	0.459213i	$0.848131\pi$
$692$			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
$696$	−6.16867	−	1.53811i	−0.233823	−	0.0583018i
$697$	−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	$-0.693956\pi$
$701$	−30.3059			−1.14464			−0.572319	+	0.820031i	$0.693956\pi$
$702$		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
$708$	−31.5489	−	7.86646i	−1.18568	−	0.295639i
$709$	24.0489	−	24.0489i	0.903174	−	0.903174i	−0.0925354	−	0.995709i	$-0.529497\pi$
$709$	24.0489	−	24.0489i	0.903174	−	0.903174i	0.995709	+	0.0925354i	$0.0294971\pi$
$710$	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
$717$	−15.5500	−	3.87727i	−0.580725	−	0.144799i
$718$	10.1610			0.379205
$719$	−7.89679			−0.294500			−0.147250	−	0.989099i	$-0.547042\pi$
$719$	−7.89679			−0.294500			−0.147250	+	0.989099i	$0.547042\pi$
$720$	9.96640	+	32.6017i	0.371426	+	1.21499i
$721$	3.64227	+	3.64227i	0.135645	+	0.135645i
$722$	−1.31455	−	1.31455i	−0.0489225	−	0.0489225i
$723$	46.5140	+	11.5979i	1.72988	+	0.431331i
$724$	3.95299			0.146912
$725$	−19.0126			−0.706110
$726$	−1.10520	+	4.43246i	−0.0410178	+	0.164504i
$727$		−	24.6824i		−	0.915420i	−0.889102	−	0.457710i	$-0.848670\pi$
$727$		−	24.6824i		−	0.915420i	0.889102	−	0.457710i	$-0.151330\pi$
$728$		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	0.946918	+	0.321476i	$0.104179\pi$
$733$	34.3405	+	34.3405i	1.26839	+	1.26839i	0.321476	+	0.946918i	$0.395821\pi$
$734$	5.76659	−	5.76659i	0.212849	−	0.212849i
$735$	8.22704	−	32.9950i	0.303459	−	1.21704i
$736$	−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	0.0105933	−	0.999944i	$-0.496628\pi$
$739$	27.4710	−	27.4710i	1.01054	−	1.01054i	0.999944	−	0.0105933i	$-0.00337201\pi$
$740$	−14.0842			−0.517746
$741$		0			0
$742$	1.00802			0.0370056
$743$	−36.8590	+	36.8590i	−1.35223	+	1.35223i	−0.469058	+	0.883167i	$0.655407\pi$
$743$	−36.8590	+	36.8590i	−1.35223	+	1.35223i	−0.883167	+	0.469058i	$0.844593\pi$
$744$	−9.24962	+	5.55757i	−0.339108	+	0.203750i
$745$			79.2751i			2.90441i
$746$	−5.10435	+	5.10435i	−0.186883	+	0.186883i
$747$	5.69210	+	18.6198i	0.208263	+	0.681262i
$748$	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	$0.356864\pi$
$751$			49.3601i			1.80118i	−0.434674	+	0.900588i	$0.643136\pi$
$752$	−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
$756$	−8.41641	−	7.57877i	−0.306102	−	0.275637i
$757$	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
$759$	−2.12932	+	8.53976i	−0.0772895	+	0.309974i
$760$	16.5374	+	16.5374i	0.599874	+	0.599874i
$761$	−27.2152	−	27.2152i	−0.986549	−	0.986549i	0.0133615	−	0.999911i	$-0.495747\pi$
$761$	−27.2152	−	27.2152i	−0.986549	−	0.986549i	−0.999911	+	0.0133615i	$0.995747\pi$
$762$	1.15109	−	4.61653i	0.0416997	−	0.167239i
$763$	7.37566			0.267017
$764$	−12.7512			−0.461321
$765$	−17.9866	−	58.8369i	−0.650305	−	2.12725i
$766$		−	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	$-0.266385\pi$
$769$	−2.01778	−	2.01778i	−0.0727631	−	0.0727631i	−0.742552	+	0.669789i	$0.766385\pi$
$770$			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	$-0.713129\pi$
$773$	4.54435	−	4.54435i	0.163449	−	0.163449i	0.784093	+	0.620644i	$0.213129\pi$
$774$	5.61306	−	1.71592i	0.201757	−	0.0616776i
$775$	−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
$786$	2.73846	−	10.9828i	0.0976778	−	0.391742i
$787$	−10.7255	+	10.7255i	−0.382322	+	0.382322i	−0.871938	−	0.489616i	$-0.837137\pi$
$787$	−10.7255	+	10.7255i	−0.382322	+	0.382322i	0.489616	+	0.871938i	$0.337137\pi$
$788$	−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
$795$	−3.58416	+	14.3745i	−0.127117	+	0.509811i
$796$	34.4077			1.21955
$797$	1.57925			0.0559399			0.0279700	−	0.999609i	$-0.491096\pi$
$797$	1.57925			0.0559399			0.0279700	+	0.999609i	$0.491096\pi$
$798$	−3.39106	−	0.845534i	−0.120042	−	0.0299316i
$799$	13.1721	+	13.1721i	0.465994	+	0.465994i
$800$	−19.4351	−	19.4351i	−0.687135	−	0.687135i
$801$	12.2618	−	3.74845i	0.433248	−	0.132445i
$802$	−8.17724			−0.288748
$803$	24.2203			0.854717
$804$	−21.4476	−	5.34778i	−0.756397	−	0.188602i
$805$		−	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	−0.999186	−	0.0403387i	$-0.987156\pi$
$811$	−29.6037	−	29.6037i	−1.03952	−	1.03952i	−0.0403387	−	0.999186i	$-0.512844\pi$
$812$	4.14143	−	4.14143i	0.145336	−	0.145336i
$813$	29.7169	+	7.40966i	1.04222	+	0.259868i
$814$	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	$-0.644727\pi$
$821$	13.1586	−	13.1586i	0.459237	−	0.459237i	0.898405	+	0.439168i	$0.144727\pi$
$822$	−2.36895	−	3.94271i	−0.0826266	−	0.137518i
$823$		−	0.516417i		−	0.0180012i	−0.999959	−	0.00900059i	$-0.997135\pi$
$823$		−	0.516417i		−	0.0180012i	0.999959	−	0.00900059i	$-0.00286501\pi$
$824$	4.28172	−	4.28172i	0.149161	−	0.149161i
$825$	−22.2995	−	5.56021i	−0.776370	−	0.193582i
$826$	−2.89813	+	2.89813i	−0.100839	+	0.100839i
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	0.238472	−	0.971149i	$-0.423354\pi$
$827$	−21.0701	−	21.0701i	−0.732678	−	0.732678i	−0.971149	+	0.238472i	$0.923354\pi$
$828$	13.4631	+	7.15892i	0.467876	+	0.248790i
$829$		−	1.68723i		−	0.0586000i	−0.999571	−	0.0293000i	$-0.990672\pi$
$829$		−	1.68723i		−	0.0586000i	0.999571	−	0.0293000i	$-0.00932781\pi$
$830$	−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
$834$	3.19396	+	0.796389i	0.110598	+	0.0275767i
$835$	−18.2204			−0.630542
$836$	17.3312			0.599413
$837$	17.6110	+	15.8583i	0.608726	+	0.548143i
$838$	6.68121	+	6.68121i	0.230799	+	0.230799i
$839$	−7.66187	−	7.66187i	−0.264517	−	0.264517i	0.562369	−	0.826886i	$-0.309890\pi$
$839$	−7.66187	−	7.66187i	−0.264517	−	0.264517i	−0.826886	+	0.562369i	$0.809890\pi$
$840$	9.26984	+	2.31136i	0.319840	+	0.0797495i
$841$	21.7797			0.751024
$842$	4.45314			0.153465
$843$	−5.07132	+	20.3388i	−0.174666	+	0.700506i
$844$		−	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
$852$	9.12361	−	36.5907i	0.312570	−	1.25358i
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.0333670	+	0.999443i	$0.510623\pi$
$853$	−30.1644	+	30.1644i	−1.03281	+	1.03281i	−0.999443	+	0.0333670i	$0.989377\pi$
$854$		−	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	$-0.283692\pi$
$857$	36.7949			1.25689			0.628444	+	0.777855i	$0.283692\pi$
$858$		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	$-0.959536\pi$
$863$	−25.4155	+	25.4155i	−0.865153	+	0.865153i	0.126779	+	0.991931i	$0.459536\pi$
$864$	−13.5067	+	14.9996i	−0.459509	+	0.510296i
$865$	−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
$873$	−35.1947	+	10.7591i	−1.19116	+	0.364140i
$874$	4.70523			0.159157
$875$	8.38112			0.283333
$876$	10.1520	−	40.7152i	0.343005	−	1.37564i
$877$	12.9567	+	12.9567i	0.437516	+	0.437516i	0.891175	−	0.453659i	$-0.149882\pi$
$877$	12.9567	+	12.9567i	0.437516	+	0.437516i	−0.453659	+	0.891175i	$0.649882\pi$
$878$	3.59002	+	3.59002i	0.121157	+	0.121157i
$879$	6.66068	−	26.7130i	0.224659	−	0.901007i
$880$	−21.3102			−0.718368
$881$	31.1077			1.04805			0.524023	−	0.851704i	$-0.324431\pi$
$881$	31.1077			1.04805			0.524023	+	0.851704i	$0.324431\pi$
$882$	5.71271	−	1.74639i	0.192357	−	0.0588039i
$883$			9.56660i			0.321942i	0.986959	+	0.160971i	$0.0514625\pi$
$883$			9.56660i			0.321942i	−0.986959	+	0.160971i	$0.948537\pi$
$884$		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
$891$	−3.22128	+	16.5674i	−0.107917	+	0.555028i
$892$	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
$903$	−2.70303	+	10.8407i	−0.0899513	+	0.360755i
$904$	−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	$0.00890666\pi$
$907$			1.68516i			0.0559549i	−0.999609	+	0.0279775i	$0.991093\pi$
$908$	−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	$-0.259519\pi$
$912$	6.75151	−	27.0773i	0.223565	−	0.896619i
$913$	−12.1709			−0.402798
$914$	2.38566			0.0789106
$915$	15.5503	+	3.87734i	0.514076	+	0.128181i
$916$	21.4015	+	21.4015i	0.707124	+	0.707124i
$917$	15.2352	+	15.2352i	0.503109	+	0.503109i
$918$	7.23231	−	8.03165i	0.238702	−	0.265084i
$919$	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
$921$	34.1881	+	8.52453i	1.12654	+	0.280893i
$922$			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	$-0.761983\pi$
$929$	−1.62237	+	1.62237i	−0.0532282	+	0.0532282i	0.679992	+	0.733220i	$0.261983\pi$
$930$	−9.38756	−	2.34071i	−0.307830	−	0.0767550i
$931$	−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	$-0.924859\pi$
$941$	−22.6506	+	22.6506i	−0.738390	+	0.738390i	0.233877	+	0.972266i	$0.424859\pi$
$942$	−9.28664	−	2.31555i	−0.302575	−	0.0754447i
$943$	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	$-0.180283\pi$
$947$	9.45582	+	9.45582i	0.307273	+	0.307273i	−0.536578	+	0.843851i	$0.680283\pi$
$948$	−3.06363	+	1.84076i	−0.0995022	+	0.0597852i
$949$		0			0
$950$			12.2866i			0.398629i
$951$	14.9594	+	3.73002i	0.485093	+	0.120954i
$952$	−9.36762			−0.303606
$953$	17.7883			0.576219			0.288110	−	0.957597i	$-0.406973\pi$
$953$	17.7883			0.576219			0.288110	+	0.957597i	$0.406973\pi$
$954$	−2.48878	+	0.760824i	−0.0805772	+	0.0246326i
$955$	−16.7035	−	16.7035i	−0.540512	−	0.540512i
$956$	−12.2725	−	12.2725i	−0.396922	−	0.396922i
$957$	−8.46858	−	2.11157i	−0.273750	−	0.0682575i
$958$	8.08847			0.261327
$959$	8.75547			0.282729
$960$	−7.53013	+	30.2000i	−0.243034	+	0.974700i
$961$		−	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	$-0.479351\pi$
$967$	−29.0154	−	29.0154i	−0.933072	−	0.933072i	−0.997897	+	0.0648250i	$0.979351\pi$
$968$	−7.22814	+	7.22814i	−0.232321	+	0.232321i
$969$	−12.1846	+	48.8670i	−0.391425	+	1.56983i
$970$	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	$-0.736424\pi$
$977$	1.88475	−	1.88475i	0.0602986	−	0.0602986i	0.736613	+	0.676314i	$0.236424\pi$
$978$	−1.80860	+	1.08668i	−0.0578326	+	0.0347483i
$979$			8.01496i			0.256159i
$980$	26.0407	−	26.0407i	0.831839	−	0.831839i
$981$	−18.2103	+	5.56693i	−0.581411	+	0.177738i
$982$	−3.81896	+	3.81896i	−0.121868	+	0.121868i
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.964676	+	0.263440i	$0.0848571\pi$
$983$	38.5049	+	38.5049i	1.22812	+	1.22812i	0.263440	+	0.964676i	$0.415143\pi$
$984$	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
$990$	−2.01434	−	6.58924i	−0.0640200	−	0.209420i
$991$	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
$993$	6.73680	−	27.0183i	0.213786	−	0.857400i
$994$	−3.36128	−	3.36128i	−0.106613	−	0.106613i
$995$	45.0726	+	45.0726i	1.42890	+	1.42890i
$996$	−5.10147	+	20.4597i	−0.161646	+	0.648291i
$997$	−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
$999$	−7.51290	+	8.34326i	−0.237698	+	0.263969i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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} +(-0.592316 - 0.147689i) 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} +(-5.84006 - 1.45617i) q^{15} -3.27013 q^{16} +5.90167 q^{17} +(-0.309108 - 1.01114i) q^{18} +(3.48387 + 3.48387i) q^{19} +(-4.60916 - 4.60916i) q^{20} +(1.95284 + 0.486926i) q^{21} +0.660937 q^{22} -2.70965 q^{23} +(0.572412 - 2.29569i) 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} +(0.785829 - 3.15161i) 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} +(-3.04771 - 9.96955i) 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} +(1.22547 - 1.36091i) q^{54} +6.51664 q^{55} -1.58728 q^{56} +(-2.06460 + 8.28020i) q^{57} +(0.669659 + 0.669659i) q^{58} +(7.07657 + 7.07657i) q^{59} +(2.73147 - 10.9547i) q^{60} -2.66269 q^{61} +1.60744 q^{62} +(1.01912 + 3.33369i) 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} +(3.91896 - 1.19803i) 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} +(-0.913368 + 3.66311i) 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} +(1.91119 - 7.66492i) q^{93} -1.11246 q^{94} -17.1211 q^{95} +(6.52833 + 1.62779i) q^{96} +(8.67443 + 8.67443i) q^{97} +(-1.40801 - 1.40801i) q^{98} +(5.38010 - 1.64471i) 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

Related objects

Downloads

Learn more