LMFDB - Embedded newform 900.2.be.f.257.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [900,2,Mod(257,900)] 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("900.257"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(900, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 10, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0,0,0,0,-12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			257.8
Character	$\chi$	$=$	900.257
Dual form			900.2.be.f.893.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61701 - 0.620711i) q^{3} +(0.876983 - 3.27295i) q^{7} +(2.22943 - 2.00739i) q^{9} +(-0.419659 + 0.242290i) q^{11} +(0.693644 + 2.58871i) q^{13} +(4.14993 - 4.14993i) q^{17} +3.85410i q^{19} +(-0.613466 - 5.83674i) q^{21} +(-3.50358 + 0.938781i) q^{23} +(2.35900 - 4.62981i) q^{27} +(-3.96149 - 6.86149i) q^{29} +(1.19381 - 2.06773i) q^{31} +(-0.528200 + 0.652273i) q^{33} +(-1.09958 - 1.09958i) q^{37} +(2.72847 + 3.75542i) q^{39} +(-10.1637 - 5.86804i) q^{41} +(9.85458 + 2.64053i) q^{43} +(1.10685 + 0.296580i) q^{47} +(-3.88090 - 2.24064i) q^{49} +(4.13456 - 9.28638i) q^{51} +(7.94909 + 7.94909i) q^{53} +(2.39229 + 6.23212i) q^{57} +(-3.17605 + 5.50108i) q^{59} +(3.04683 + 5.27726i) q^{61} +(-4.61491 - 9.05727i) q^{63} +(7.53469 - 2.01891i) q^{67} +(-5.08260 + 3.69273i) q^{69} -0.601711i q^{71} +(8.84189 - 8.84189i) q^{73} +(0.424969 + 1.58601i) q^{77} +(-12.1047 + 6.98866i) q^{79} +(0.940756 - 8.95070i) q^{81} +(-3.89739 + 14.5453i) q^{83} +(-10.6648 - 8.63616i) q^{87} +13.7208 q^{89} +9.08103 q^{91} +(0.646930 - 4.08455i) q^{93} +(0.0357970 - 0.133596i) q^{97} +(-0.449231 + 1.38259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{11} + 12 q^{21} + 8 q^{31} + 60 q^{41} + 36 q^{51} + 52 q^{61} - 36 q^{81} + 120 q^{91}+O(q^{100}) $ 32 * q - 12 * q^11 + 12 * q^21 + 8 * q^31 + 60 * q^41 + 36 * q^51 + 52 * q^61 - 36 * q^81 + 120 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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			0
$2$		0			0
$3$	1.61701	−	0.620711i	0.933580	−	0.358368i
$3$	1.61701	−	0.620711i	0.933580	−	0.358368i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.876983	−	3.27295i	0.331468	−	1.23706i	−0.576179	−	0.817324i	$-0.695457\pi$
$7$	0.876983	−	3.27295i	0.331468	−	1.23706i	0.907647	−	0.419734i	$-0.137876\pi$
$8$		0			0
$9$	2.22943	−	2.00739i	0.743145	−	0.669131i
$10$		0			0
$11$	−0.419659	+	0.242290i	−0.126532	+	0.0730533i	−0.561930	−	0.827185i	$-0.689941\pi$
$11$	−0.419659	+	0.242290i	−0.126532	+	0.0730533i	0.435398	+	0.900238i	$0.356608\pi$
$12$		0			0
$13$	0.693644	+	2.58871i	0.192382	+	0.717980i	0.992929	+	0.118710i	$0.0378758\pi$
$13$	0.693644	+	2.58871i	0.192382	+	0.717980i	−0.800547	+	0.599270i	$0.795458\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.14993	−	4.14993i	1.00651	−	1.00651i	0.00652688	−	0.999979i	$-0.497922\pi$
$17$	4.14993	−	4.14993i	1.00651	−	1.00651i	0.999979	−	0.00652688i	$-0.00207758\pi$
$18$		0			0
$19$			3.85410i			0.884192i	0.896968	+	0.442096i	$0.145765\pi$
$19$			3.85410i			0.884192i	−0.896968	+	0.442096i	$0.854235\pi$
$20$		0			0
$21$	−0.613466	−	5.83674i	−0.133869	−	1.27368i
$22$		0			0
$23$	−3.50358	+	0.938781i	−0.730546	+	0.195749i	−0.604873	−	0.796322i	$-0.706776\pi$
$23$	−3.50358	+	0.938781i	−0.730546	+	0.195749i	−0.125674	+	0.992072i	$0.540109\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.35900	−	4.62981i	0.453990	−	0.891007i
$28$		0			0
$29$	−3.96149	−	6.86149i	−0.735629	−	1.27415i	−0.954447	−	0.298382i	$-0.903553\pi$
$29$	−3.96149	−	6.86149i	−0.735629	−	1.27415i	0.218817	−	0.975766i	$-0.429780\pi$
$30$		0			0
$31$	1.19381	−	2.06773i	0.214414	−	0.371376i	−0.738677	−	0.674059i	$-0.764549\pi$
$31$	1.19381	−	2.06773i	0.214414	−	0.371376i	0.953091	+	0.302683i	$0.0978825\pi$
$32$		0			0
$33$	−0.528200	+	0.652273i	−0.0919478	+	0.113546i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.09958	−	1.09958i	−0.180771	−	0.180771i	0.610921	−	0.791692i	$-0.290799\pi$
$37$	−1.09958	−	1.09958i	−0.180771	−	0.180771i	−0.791692	+	0.610921i	$0.790799\pi$
$38$		0			0
$39$	2.72847	+	3.75542i	0.436905	+	0.601348i
$40$		0			0
$41$	−10.1637	−	5.86804i	−1.58731	−	0.916434i	−0.993748	−	0.111646i	$-0.964388\pi$
$41$	−10.1637	−	5.86804i	−1.58731	−	0.916434i	−0.593562	−	0.804788i	$-0.702279\pi$
$42$		0			0
$43$	9.85458	+	2.64053i	1.50281	+	0.402677i	0.914040	−	0.405624i	$-0.132946\pi$
$43$	9.85458	+	2.64053i	1.50281	+	0.402677i	0.588770	+	0.808301i	$0.299613\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.10685	+	0.296580i	0.161451	+	0.0432607i	0.338639	−	0.940916i	$-0.390033\pi$
$47$	1.10685	+	0.296580i	0.161451	+	0.0432607i	−0.177188	+	0.984177i	$0.556700\pi$
$48$		0			0
$49$	−3.88090	−	2.24064i	−0.554414	−	0.320091i
$50$		0			0
$51$	4.13456	−	9.28638i	0.578955	−	1.30035i
$52$		0			0
$53$	7.94909	+	7.94909i	1.09189	+	1.09189i	0.995327	+	0.0965652i	$0.0307856\pi$
$53$	7.94909	+	7.94909i	1.09189	+	1.09189i	0.0965652	+	0.995327i	$0.469214\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	2.39229	+	6.23212i	0.316866	+	0.825464i
$58$		0			0
$59$	−3.17605	+	5.50108i	−0.413486	+	0.716179i	−0.995268	−	0.0971654i	$-0.969022\pi$
$59$	−3.17605	+	5.50108i	−0.413486	+	0.716179i	0.581782	+	0.813345i	$0.302356\pi$
$60$		0			0
$61$	3.04683	+	5.27726i	0.390107	+	0.675684i	0.992463	−	0.122543i	$-0.0391048\pi$
$61$	3.04683	+	5.27726i	0.390107	+	0.675684i	−0.602357	+	0.798227i	$0.705771\pi$
$62$		0			0
$63$	−4.61491	−	9.05727i	−0.581424	−	1.14111i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	7.53469	−	2.01891i	0.920509	−	0.246650i	0.232706	−	0.972547i	$-0.425242\pi$
$67$	7.53469	−	2.01891i	0.920509	−	0.246650i	0.687803	+	0.725897i	$0.258575\pi$
$68$		0			0
$69$	−5.08260	+	3.69273i	−0.611874	+	0.444552i
$70$		0			0
$71$		−	0.601711i		−	0.0714100i	−0.999362	−	0.0357050i	$-0.988632\pi$
$71$		−	0.601711i		−	0.0714100i	0.999362	−	0.0357050i	$-0.0113677\pi$
$72$		0			0
$73$	8.84189	−	8.84189i	1.03487	−	1.03487i	0.0354953	−	0.999370i	$-0.488699\pi$
$73$	8.84189	−	8.84189i	1.03487	−	1.03487i	0.999370	−	0.0354953i	$-0.0113009\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.424969	+	1.58601i	0.0484297	+	0.180742i
$78$		0			0
$79$	−12.1047	+	6.98866i	−1.36189	+	0.786286i	−0.989875	−	0.141941i	$-0.954666\pi$
$79$	−12.1047	+	6.98866i	−1.36189	+	0.786286i	−0.372013	+	0.928228i	$0.621332\pi$
$80$		0			0
$81$	0.940756	−	8.95070i	0.104528	−	0.994522i
$82$		0			0
$83$	−3.89739	+	14.5453i	−0.427794	+	1.59655i	0.329950	+	0.943998i	$0.392968\pi$
$83$	−3.89739	+	14.5453i	−0.427794	+	1.59655i	−0.757744	+	0.652551i	$0.773699\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−10.6648	−	8.63616i	−1.14338	−	0.925893i
$88$		0			0
$89$	13.7208			1.45441			0.727203	−	0.686423i	$-0.240820\pi$
$89$	13.7208			1.45441			0.727203	+	0.686423i	$0.240820\pi$
$90$		0			0
$91$	9.08103			0.951951
$92$		0			0
$93$	0.646930	−	4.08455i	0.0670835	−	0.423548i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.0357970	−	0.133596i	0.00363463	−	0.0135646i	−0.964085	−	0.265595i	$-0.914432\pi$
$97$	0.0357970	−	0.133596i	0.00363463	−	0.0135646i	0.967719	+	0.252030i	$0.0810983\pi$
$98$		0			0
$99$	−0.449231	+	1.38259i	−0.0451494	+	0.138956i
$100$		0			0
$101$	−13.1416	+	7.58729i	−1.30763	+	0.754963i	−0.981701	−	0.190429i	$-0.939012\pi$
$101$	−13.1416	+	7.58729i	−1.30763	+	0.754963i	−0.325934	+	0.945393i	$0.605679\pi$
$102$		0			0
$103$	0.0520016	+	0.194073i	0.00512387	+	0.0191225i	0.968440	−	0.249245i	$-0.0801825\pi$
$103$	0.0520016	+	0.194073i	0.00512387	+	0.0191225i	−0.963317	+	0.268368i	$0.913516\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.11849	+	8.11849i	−0.784844	+	0.784844i	−0.980644	−	0.195800i	$-0.937270\pi$
$107$	−8.11849	+	8.11849i	−0.784844	+	0.784844i	0.195800	+	0.980644i	$0.437270\pi$
$108$		0			0
$109$		−	5.49606i		−	0.526427i	−0.964738	−	0.263213i	$-0.915218\pi$
$109$		−	5.49606i		−	0.526427i	0.964738	−	0.263213i	$-0.0847823\pi$
$110$		0			0
$111$	−2.46056	−	1.09551i	−0.233546	−	0.103981i
$112$		0			0
$113$	−15.4044	+	4.12758i	−1.44912	+	0.388290i	−0.895718	−	0.444624i	$-0.853337\pi$
$113$	−15.4044	+	4.12758i	−1.44912	+	0.388290i	−0.553402	+	0.832914i	$0.686671\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	6.74300	+	4.37895i	0.623390	+	0.404834i
$118$		0			0
$119$	−9.94307	−	17.2219i	−0.911480	−	1.57873i
$120$		0			0
$121$	−5.38259	+	9.32292i	−0.489326	+	0.847538i
$122$		0			0
$123$	−20.0772	−	3.17992i	−1.81030	−	0.286724i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−0.697687	−	0.697687i	−0.0619097	−	0.0619097i	0.675474	−	0.737384i	$-0.263939\pi$
$127$	−0.697687	−	0.697687i	−0.0619097	−	0.0619097i	−0.737384	+	0.675474i	$0.763939\pi$
$128$		0			0
$129$	17.5739	−	1.84710i	1.54730	−	0.162628i
$130$		0			0
$131$	0.161760	+	0.0933923i	0.0141330	+	0.00815972i	0.507050	−	0.861917i	$-0.330736\pi$
$131$	0.161760	+	0.0933923i	0.0141330	+	0.00815972i	−0.492917	+	0.870076i	$0.664069\pi$
$132$		0			0
$133$	12.6143	+	3.37998i	1.09380	+	0.293082i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.7939	+	2.89222i	0.922187	+	0.247099i	0.688520	−	0.725217i	$-0.258261\pi$
$137$	10.7939	+	2.89222i	0.922187	+	0.247099i	0.233667	+	0.972317i	$0.424927\pi$
$138$		0			0
$139$	7.19491	+	4.15398i	0.610264	+	0.352336i	0.773069	−	0.634322i	$-0.218721\pi$
$139$	7.19491	+	4.15398i	0.610264	+	0.352336i	−0.162805	+	0.986658i	$0.552054\pi$
$140$		0			0
$141$	1.97388	−	0.207463i	0.166231	−	0.0174716i
$142$		0			0
$143$	−0.918314	−	0.918314i	−0.0767933	−	0.0767933i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.66623	−	1.21421i	−0.632300	−	0.100147i
$148$		0			0
$149$	4.09023	−	7.08448i	0.335084	−	0.580383i	−0.648417	−	0.761286i	$-0.724568\pi$
$149$	4.09023	−	7.08448i	0.335084	−	0.580383i	0.983501	+	0.180902i	$0.0579018\pi$
$150$		0			0
$151$	10.5366	+	18.2499i	0.857454	+	1.48515i	0.874349	+	0.485297i	$0.161288\pi$
$151$	10.5366	+	18.2499i	0.857454	+	1.48515i	−0.0168953	+	0.999857i	$0.505378\pi$
$152$		0			0
$153$	0.921461	−	17.5825i	0.0744957	−	1.42146i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.4202	+	3.32798i	−0.991239	+	0.265602i	−0.717771	−	0.696279i	$-0.754838\pi$
$157$	−12.4202	+	3.32798i	−0.991239	+	0.265602i	−0.273468	+	0.961881i	$0.588171\pi$
$158$		0			0
$159$	17.7878	+	7.91966i	1.41067	+	0.628070i
$160$		0			0
$161$			12.2903i			0.968613i
$162$		0			0
$163$	−1.18932	+	1.18932i	−0.0931550	+	0.0931550i	−0.752149	−	0.658994i	$-0.770982\pi$
$163$	−1.18932	+	1.18932i	−0.0931550	+	0.0931550i	0.658994	+	0.752149i	$0.270982\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.83369	−	10.5755i	−0.219277	−	0.818355i	−0.984617	−	0.174728i	$-0.944096\pi$
$167$	−2.83369	−	10.5755i	−0.219277	−	0.818355i	0.765339	−	0.643627i	$-0.222571\pi$
$168$		0			0
$169$	5.03803	−	2.90871i	0.387541	−	0.223747i
$170$		0			0
$171$	7.73669	+	8.59247i	0.591640	+	0.657082i
$172$		0			0
$173$	4.72513	−	17.6344i	0.359245	−	1.34072i	−0.515813	−	0.856701i	$-0.672510\pi$
$173$	4.72513	−	17.6344i	0.359245	−	1.34072i	0.875058	−	0.484019i	$-0.160823\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.72112	+	10.8667i	−0.129367	+	0.816791i
$178$		0			0
$179$	−5.45364			−0.407624			−0.203812	−	0.979010i	$-0.565333\pi$
$179$	−5.45364			−0.407624			−0.203812	+	0.979010i	$0.565333\pi$
$180$		0			0
$181$	19.0584			1.41660			0.708298	−	0.705913i	$-0.249463\pi$
$181$	19.0584			1.41660			0.708298	+	0.705913i	$0.249463\pi$
$182$		0			0
$183$	8.20241	+	6.64218i	0.606340	+	0.491004i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.736068	+	2.74704i	−0.0538266	+	0.200884i
$188$		0			0
$189$	−13.0843	−	11.7812i	−0.951742	−	0.856953i
$190$		0			0
$191$	−21.2673	+	12.2787i	−1.53885	+	0.888456i	−0.539944	+	0.841701i	$0.681555\pi$
$191$	−21.2673	+	12.2787i	−1.53885	+	0.888456i	−0.998906	+	0.0467550i	$0.985112\pi$
$192$		0			0
$193$	0.493662	+	1.84237i	0.0355346	+	0.132617i	0.981414	−	0.191900i	$-0.0614650\pi$
$193$	0.493662	+	1.84237i	0.0355346	+	0.132617i	−0.945880	+	0.324517i	$0.894798\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−5.35836	+	5.35836i	−0.381767	+	0.381767i	−0.871739	−	0.489971i	$-0.837007\pi$
$197$	−5.35836	+	5.35836i	−0.381767	+	0.381767i	0.489971	+	0.871739i	$0.337007\pi$
$198$		0			0
$199$			27.7151i			1.96467i	0.187127	+	0.982336i	$0.440082\pi$
$199$			27.7151i			1.96467i	−0.187127	+	0.982336i	$0.559918\pi$
$200$		0			0
$201$	10.9305	−	7.94147i	0.770978	−	0.560148i
$202$		0			0
$203$	−25.9315	+	6.94831i	−1.82003	+	0.487676i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−5.92650	+	9.12600i	−0.411920	+	0.634301i
$208$		0			0
$209$	−0.933812	−	1.61741i	−0.0645931	−	0.111879i
$210$		0			0
$211$	−7.24803	+	12.5540i	−0.498975	+	0.864250i	−0.999999	−	0.00118335i	$-0.999623\pi$
$211$	−7.24803	+	12.5540i	−0.498975	+	0.864250i	0.501024	+	0.865433i	$0.332957\pi$
$212$		0			0
$213$	−0.373489	−	0.972972i	−0.0255910	−	0.0666669i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.72063	−	5.72063i	−0.388342	−	0.388342i
$218$		0			0
$219$	8.80915	−	19.7857i	0.595267	−	1.33699i
$220$		0			0
$221$	13.6215	+	7.86441i	0.916285	+	0.529017i
$222$		0			0
$223$	−19.5772	−	5.24569i	−1.31099	−	0.351278i	−0.465392	−	0.885105i	$-0.654087\pi$
$223$	−19.5772	−	5.24569i	−1.31099	−	0.351278i	−0.845594	+	0.533827i	$0.820753\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.46194	+	2.26737i	0.561639	+	0.150491i	0.528459	−	0.848959i	$-0.322770\pi$
$227$	8.46194	+	2.26737i	0.561639	+	0.150491i	0.0331795	+	0.999449i	$0.489437\pi$
$228$		0			0
$229$	−10.2098	−	5.89462i	−0.674681	−	0.389527i	0.123167	−	0.992386i	$-0.460695\pi$
$229$	−10.2098	−	5.89462i	−0.674681	−	0.389527i	−0.797848	+	0.602859i	$0.794028\pi$
$230$		0			0
$231$	1.67163	+	2.30080i	0.109985	+	0.151382i
$232$		0			0
$233$	9.56964	+	9.56964i	0.626928	+	0.626928i	0.947294	−	0.320366i	$-0.103806\pi$
$233$	9.56964	+	9.56964i	0.626928	+	0.626928i	−0.320366	+	0.947294i	$0.603806\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−15.2355	+	18.8143i	−0.989652	+	1.22212i
$238$		0			0
$239$	−7.25108	+	12.5592i	−0.469034	+	0.812390i	−0.999373	−	0.0353952i	$-0.988731\pi$
$239$	−7.25108	+	12.5592i	−0.469034	+	0.812390i	0.530340	+	0.847785i	$0.322064\pi$
$240$		0			0
$241$	6.52918	+	11.3089i	0.420582	+	0.728469i	0.995996	−	0.0893931i	$-0.0284927\pi$
$241$	6.52918	+	11.3089i	0.420582	+	0.728469i	−0.575415	+	0.817862i	$0.695159\pi$
$242$		0			0
$243$	−4.03459	−	15.0573i	−0.258819	−	0.965926i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−9.97717	+	2.67337i	−0.634832	+	0.170103i
$248$		0			0
$249$	2.72630	+	25.9390i	0.172772	+	1.64382i
$250$		0			0
$251$		−	14.8303i		−	0.936083i	−0.883706	−	0.468042i	$-0.844960\pi$
$251$		−	14.8303i		−	0.936083i	0.883706	−	0.468042i	$-0.155040\pi$
$252$		0			0
$253$	1.24285	−	1.24285i	0.0781374	−	0.0781374i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.06717	+	3.98273i	0.0665682	+	0.248436i	0.991189	−	0.132452i	$-0.0422850\pi$
$257$	1.06717	+	3.98273i	0.0665682	+	0.248436i	−0.924621	+	0.380888i	$0.875618\pi$
$258$		0			0
$259$	−4.56320	+	2.63456i	−0.283543	+	0.163704i
$260$		0			0
$261$	−22.6056	−	7.34500i	−1.39925	−	0.454644i
$262$		0			0
$263$	2.62595	−	9.80018i	0.161923	−	0.604305i	−0.836490	−	0.547983i	$-0.815396\pi$
$263$	2.62595	−	9.80018i	0.161923	−	0.604305i	0.998413	−	0.0563224i	$-0.0179375\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	22.1867	−	8.51668i	1.35780	−	0.521212i
$268$		0			0
$269$	5.90783			0.360207			0.180103	−	0.983648i	$-0.442357\pi$
$269$	5.90783			0.360207			0.180103	+	0.983648i	$0.442357\pi$
$270$		0			0
$271$	−28.2338			−1.71508			−0.857541	−	0.514415i	$-0.828009\pi$
$271$	−28.2338			−1.71508			−0.857541	+	0.514415i	$0.828009\pi$
$272$		0			0
$273$	14.6841	−	5.63670i	0.888723	−	0.341149i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.87868	+	7.01132i	−0.112879	+	0.421269i	−0.999119	−	0.0419558i	$-0.986641\pi$
$277$	−1.87868	+	7.01132i	−0.112879	+	0.421269i	0.886241	+	0.463225i	$0.153308\pi$
$278$		0			0
$279$	−1.48924	−	7.00631i	−0.0891583	−	0.419457i
$280$		0			0
$281$	−2.97782	+	1.71925i	−0.177642	+	0.102562i	−0.586184	−	0.810178i	$-0.699371\pi$
$281$	−2.97782	+	1.71925i	−0.177642	+	0.102562i	0.408542	+	0.912739i	$0.366037\pi$
$282$		0			0
$283$	1.26988	+	4.73926i	0.0754866	+	0.281720i	0.993343	−	0.115192i	$-0.0367484\pi$
$283$	1.26988	+	4.73926i	0.0754866	+	0.281720i	−0.917857	+	0.396912i	$0.870082\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−28.1192	+	28.1192i	−1.65982	+	1.65982i
$288$		0			0
$289$		−	17.4438i		−	1.02611i
$290$		0			0
$291$	−0.0250406	−	0.238246i	−0.00146791	−	0.0139662i
$292$		0			0
$293$	−13.0724	+	3.50273i	−0.763696	+	0.204632i	−0.619585	−	0.784930i	$-0.712699\pi$
$293$	−13.0724	+	3.50273i	−0.763696	+	0.204632i	−0.144111	+	0.989562i	$0.546032\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	0.131780	+	2.51450i	0.00764663	+	0.145906i
$298$		0			0
$299$	−4.86047	−	8.41858i	−0.281088	−	0.486859i
$300$		0			0
$301$	17.2846	−	29.9378i	0.996268	−	1.72559i
$302$		0			0
$303$	−16.5405	+	20.4258i	−0.950228	+	1.17343i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	18.5221	+	18.5221i	1.05711	+	1.05711i	0.998267	+	0.0588446i	$0.0187417\pi$
$307$	18.5221	+	18.5221i	1.05711	+	1.05711i	0.0588446	+	0.998267i	$0.481258\pi$
$308$		0			0
$309$	0.204550	+	0.281539i	0.0116364	+	0.0160162i
$310$		0			0
$311$	−3.13958	−	1.81264i	−0.178030	−	0.102785i	0.408337	−	0.912831i	$-0.366109\pi$
$311$	−3.13958	−	1.81264i	−0.178030	−	0.102785i	−0.586367	+	0.810046i	$0.699442\pi$
$312$		0			0
$313$	13.7155	+	3.67507i	0.775248	+	0.207727i	0.624689	−	0.780874i	$-0.285226\pi$
$313$	13.7155	+	3.67507i	0.775248	+	0.207727i	0.150559	+	0.988601i	$0.451893\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.2621	+	3.82151i	0.801038	+	0.214637i	0.636040	−	0.771656i	$-0.280572\pi$
$317$	14.2621	+	3.82151i	0.801038	+	0.214637i	0.164998	+	0.986294i	$0.447238\pi$
$318$		0			0
$319$	3.32495	+	1.91966i	0.186161	+	0.107480i
$320$		0			0
$321$	−8.08842	+	18.1669i	−0.451452	+	1.01398i
$322$		0			0
$323$	15.9942	+	15.9942i	0.889944	+	0.889944i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−3.41147	−	8.88717i	−0.188654	−	0.491462i
$328$		0			0
$329$	1.94138	−	3.36257i	0.107032	−	0.185385i
$330$		0			0
$331$	−10.6313	−	18.4140i	−0.584350	−	1.01212i	−0.994956	−	0.100311i	$-0.968016\pi$
$331$	−10.6313	−	18.4140i	−0.584350	−	1.01212i	0.410606	−	0.911813i	$-0.365317\pi$
$332$		0			0
$333$	−4.65875	−	0.244155i	−0.255298	−	0.0133796i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	12.7121	−	3.40620i	0.692473	−	0.185548i	0.104616	−	0.994513i	$-0.466639\pi$
$337$	12.7121	−	3.40620i	0.692473	−	0.185548i	0.587857	+	0.808965i	$0.299972\pi$
$338$		0			0
$339$	−22.3469	+	16.2360i	−1.21372	+	0.881818i
$340$		0			0
$341$			1.15699i			0.0626546i
$342$		0			0
$343$	6.03478	−	6.03478i	0.325847	−	0.325847i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.38277	−	27.5529i	−0.396328	−	1.47912i	−0.819506	−	0.573070i	$-0.805752\pi$
$347$	−7.38277	−	27.5529i	−0.396328	−	1.47912i	0.423178	−	0.906046i	$-0.360914\pi$
$348$		0			0
$349$	2.40088	−	1.38615i	0.128516	−	0.0741988i	−0.434364	−	0.900738i	$-0.643027\pi$
$349$	2.40088	−	1.38615i	0.128516	−	0.0741988i	0.562880	+	0.826539i	$0.309693\pi$
$350$		0			0
$351$	13.6215	+	2.89535i	0.727065	+	0.154542i
$352$		0			0
$353$	6.66469	−	24.8730i	0.354726	−	1.32385i	−0.526103	−	0.850421i	$-0.676347\pi$
$353$	6.66469	−	24.8730i	0.354726	−	1.32385i	0.880829	−	0.473434i	$-0.156986\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−26.7679	−	21.6762i	−1.41671	−	1.14723i
$358$		0			0
$359$	8.82143			0.465577			0.232789	−	0.972527i	$-0.425215\pi$
$359$	8.82143			0.465577			0.232789	+	0.972527i	$0.425215\pi$
$360$		0			0
$361$	4.14590			0.218205
$362$		0			0
$363$	−2.91685	+	18.4163i	−0.153095	+	0.966604i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	1.08035	−	4.03193i	0.0563939	−	0.210465i	−0.931979	−	0.362511i	$-0.881920\pi$
$367$	1.08035	−	4.03193i	0.0563939	−	0.210465i	0.988373	+	0.152046i	$0.0485862\pi$
$368$		0			0
$369$	−34.4389	+	7.32020i	−1.79282	+	0.381075i
$370$		0			0
$371$	32.9882	−	19.0457i	1.71266	−	0.988805i
$372$		0			0
$373$	−4.49526	−	16.7765i	−0.232756	−	0.868656i	−0.979148	−	0.203149i	$-0.934882\pi$
$373$	−4.49526	−	16.7765i	−0.232756	−	0.868656i	0.746392	−	0.665506i	$-0.231784\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0146	−	15.0146i	0.773290	−	0.773290i
$378$		0			0
$379$		−	10.8196i		−	0.555764i	−0.960615	−	0.277882i	$-0.910368\pi$
$379$		−	10.8196i		−	0.555764i	0.960615	−	0.277882i	$-0.0896325\pi$
$380$		0			0
$381$	−1.56123	−	0.695103i	−0.0799841	−	0.0356112i
$382$		0			0
$383$	17.7173	−	4.74733i	0.905310	−	0.242577i	0.224015	−	0.974586i	$-0.428084\pi$
$383$	17.7173	−	4.74733i	0.905310	−	0.242577i	0.681295	+	0.732009i	$0.261417\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	27.2707	−	13.8951i	1.38625	−	0.706329i
$388$		0			0
$389$	13.5841	+	23.5283i	0.688740	+	1.19293i	0.972246	+	0.233962i	$0.0751690\pi$
$389$	13.5841	+	23.5283i	0.688740	+	1.19293i	−0.283506	+	0.958970i	$0.591498\pi$
$390$		0			0
$391$	−10.6437	+	18.4355i	−0.538276	+	0.932322i
$392$		0			0
$393$	0.319537	+	0.0506097i	0.0161185	+	0.00255292i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−12.7467	−	12.7467i	−0.639741	−	0.639741i	0.310751	−	0.950491i	$-0.399420\pi$
$397$	−12.7467	−	12.7467i	−0.639741	−	0.639741i	−0.950491	+	0.310751i	$0.899420\pi$
$398$		0			0
$399$	22.4954	−	2.36436i	1.12618	−	0.118366i
$400$		0			0
$401$	4.37845	+	2.52790i	0.218649	+	0.126237i	0.605325	−	0.795979i	$-0.293043\pi$
$401$	4.37845	+	2.52790i	0.218649	+	0.126237i	−0.386675	+	0.922216i	$0.626377\pi$
$402$		0			0
$403$	6.18085	+	1.65615i	0.307890	+	0.0824988i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.727869	+	0.195032i	0.0360791	+	0.00966738i
$408$		0			0
$409$	−2.02932	−	1.17163i	−0.100344	−	0.0579334i	0.448988	−	0.893538i	$-0.351784\pi$
$409$	−2.02932	−	1.17163i	−0.100344	−	0.0579334i	−0.549332	+	0.835604i	$0.685118\pi$
$410$		0			0
$411$	19.2491	−	2.02316i	0.949488	−	0.0997953i
$412$		0			0
$413$	15.2194	+	15.2194i	0.748897	+	0.748897i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	14.2127	+	2.25106i	0.695997	+	0.110235i
$418$		0			0
$419$	−15.2094	+	26.3435i	−0.743028	+	1.28696i	0.208083	+	0.978111i	$0.433278\pi$
$419$	−15.2094	+	26.3435i	−0.743028	+	1.28696i	−0.951110	+	0.308851i	$0.900056\pi$
$420$		0			0
$421$	−15.3759	−	26.6318i	−0.749375	−	1.29796i	−0.948123	−	0.317905i	$-0.897021\pi$
$421$	−15.3759	−	26.6318i	−0.749375	−	1.29796i	0.198747	−	0.980051i	$-0.436313\pi$
$422$		0			0
$423$	3.06301	−	1.56068i	0.148929	−	0.0758829i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	19.9442	−	5.34404i	0.965168	−	0.258616i
$428$		0			0
$429$	−2.05493	−	0.914914i	−0.0992130	−	0.0441725i
$430$		0			0
$431$		−	17.0019i		−	0.818952i	−0.912321	−	0.409476i	$-0.865712\pi$
$431$		−	17.0019i		−	0.818952i	0.912321	−	0.409476i	$-0.134288\pi$
$432$		0			0
$433$	−22.0907	+	22.0907i	−1.06161	+	1.06161i	−0.0636393	+	0.997973i	$0.520271\pi$
$433$	−22.0907	+	22.0907i	−1.06161	+	1.06161i	−0.997973	+	0.0636393i	$0.979729\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.61816	−	13.5031i	−0.173080	−	0.645943i
$438$		0			0
$439$	22.0369	−	12.7230i	1.05176	−	0.607235i	0.128620	−	0.991694i	$-0.458945\pi$
$439$	22.0369	−	12.7230i	1.05176	−	0.607235i	0.923142	+	0.384459i	$0.125612\pi$
$440$		0			0
$441$	−13.1500	+	2.79513i	−0.626192	+	0.133101i
$442$		0			0
$443$	1.59048	−	5.93574i	0.0755658	−	0.282015i	−0.917795	−	0.397054i	$-0.870033\pi$
$443$	1.59048	−	5.93574i	0.0755658	−	0.282015i	0.993361	+	0.115039i	$0.0366992\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	2.21651	−	13.9945i	0.104838	−	0.661918i
$448$		0			0
$449$	41.0686			1.93815			0.969073	−	0.246773i	$-0.0793701\pi$
$449$	41.0686			1.93815			0.969073	+	0.246773i	$0.0793701\pi$
$450$		0			0
$451$	5.68708			0.267794
$452$		0			0
$453$	28.3656	+	22.9700i	1.33273	+	1.07923i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	7.06463	−	26.3655i	0.330469	−	1.23333i	−0.578229	−	0.815875i	$-0.696256\pi$
$457$	7.06463	−	26.3655i	0.330469	−	1.23333i	0.908698	−	0.417454i	$-0.137077\pi$
$458$		0			0
$459$	−9.42367	−	29.0031i	−0.439859	−	1.35375i
$460$		0			0
$461$	9.54121	−	5.50862i	0.444378	−	0.256562i	−0.261075	−	0.965319i	$-0.584077\pi$
$461$	9.54121	−	5.50862i	0.444378	−	0.256562i	0.705453	+	0.708757i	$0.250744\pi$
$462$		0			0
$463$	−3.71367	−	13.8596i	−0.172589	−	0.644110i	−0.996950	−	0.0780455i	$-0.975132\pi$
$463$	−3.71367	−	13.8596i	−0.172589	−	0.644110i	0.824361	−	0.566064i	$-0.191535\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	3.87179	−	3.87179i	0.179165	−	0.179165i	−0.611827	−	0.790992i	$-0.709565\pi$
$467$	3.87179	−	3.87179i	0.179165	−	0.179165i	0.790992	+	0.611827i	$0.209565\pi$
$468$		0			0
$469$		−	26.4312i		−	1.22048i
$470$		0			0
$471$	−18.0178	+	13.0907i	−0.830219	+	0.603189i
$472$		0			0
$473$	−4.77534	+	1.27955i	−0.219570	+	0.0588337i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	33.6789	+	1.76504i	1.54205	+	0.0808155i
$478$		0			0
$479$	−18.5611	−	32.1489i	−0.848080	−	1.46892i	−0.882919	−	0.469526i	$-0.844425\pi$
$479$	−18.5611	−	32.1489i	−0.848080	−	1.46892i	0.0348384	−	0.999393i	$-0.488908\pi$
$480$		0			0
$481$	2.08379	−	3.60923i	0.0950126	−	0.164567i
$482$		0			0
$483$	7.62874	+	19.8735i	0.347120	+	0.904278i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−5.92813	−	5.92813i	−0.268629	−	0.268629i	0.559919	−	0.828548i	$-0.310832\pi$
$487$	−5.92813	−	5.92813i	−0.268629	−	0.268629i	−0.828548	+	0.559919i	$0.810832\pi$
$488$		0			0
$489$	−1.18492	+	2.66137i	−0.0535839	+	0.120351i
$490$		0			0
$491$	−5.14174	−	2.96859i	−0.232044	−	0.133970i	0.379471	−	0.925204i	$-0.376106\pi$
$491$	−5.14174	−	2.96859i	−0.232044	−	0.133970i	−0.611514	+	0.791233i	$0.709439\pi$
$492$		0			0
$493$	−44.9146	−	12.0348i	−2.02285	−	0.542021i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.96937	−	0.527690i	−0.0883382	−	0.0236701i
$498$		0			0
$499$	12.6479	+	7.30225i	0.566196	+	0.326894i	0.755629	−	0.655000i	$-0.227331\pi$
$499$	12.6479	+	7.30225i	0.566196	+	0.326894i	−0.189432	+	0.981894i	$0.560665\pi$
$500$		0			0
$501$	−11.1464	−	15.3417i	−0.497985	−	0.685418i
$502$		0			0
$503$	0.216785	+	0.216785i	0.00966595	+	0.00966595i	0.711923	−	0.702257i	$-0.247824\pi$
$503$	0.216785	+	0.216785i	0.00966595	+	0.00966595i	−0.702257	+	0.711923i	$0.747824\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.34107	−	7.83057i	0.281617	−	0.347768i
$508$		0			0
$509$	−13.5139	+	23.4067i	−0.598993	+	1.03749i	0.393977	+	0.919120i	$0.371099\pi$
$509$	−13.5139	+	23.4067i	−0.598993	+	1.03749i	−0.992970	+	0.118366i	$0.962234\pi$
$510$		0			0
$511$	−21.1848	−	36.6932i	−0.937162	−	1.62321i
$512$		0			0
$513$	17.8437	+	9.09184i	0.787821	+	0.401415i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−0.536359	+	0.143717i	−0.0235891	+	0.00632067i
$518$		0			0
$519$	−3.30531	−	31.4480i	−0.145087	−	1.38041i
$520$		0			0
$521$		−	18.7999i		−	0.823637i	−0.911266	−	0.411818i	$-0.864894\pi$
$521$		−	18.7999i		−	0.823637i	0.911266	−	0.411818i	$-0.135106\pi$
$522$		0			0
$523$	−5.36486	+	5.36486i	−0.234589	+	0.234589i	−0.814605	−	0.580016i	$-0.803046\pi$
$523$	−5.36486	+	5.36486i	−0.234589	+	0.234589i	0.580016	+	0.814605i	$0.303046\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.62673	−	13.5352i	−0.157983	−	0.589601i
$528$		0			0
$529$	−8.52484	+	4.92182i	−0.370645	+	0.213992i
$530$		0			0
$531$	3.96203	+	18.6399i	0.171937	+	0.808901i
$532$		0			0
$533$	8.14066	−	30.3814i	0.352611	−	1.31596i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−8.81858	+	3.38513i	−0.380550	+	0.146079i
$538$		0			0
$539$	2.17154			0.0935348
$540$		0			0
$541$	−39.2086			−1.68571			−0.842854	−	0.538142i	$-0.819126\pi$
$541$	−39.2086			−1.68571			−0.842854	+	0.538142i	$0.819126\pi$
$542$		0			0
$543$	30.8175	−	11.8297i	1.32251	−	0.507663i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−8.34694	+	31.1512i	−0.356890	+	1.33193i	0.521200	+	0.853434i	$0.325484\pi$
$547$	−8.34694	+	31.1512i	−0.356890	+	1.33193i	−0.878090	+	0.478496i	$0.841182\pi$
$548$		0			0
$549$	17.3862	+	5.64913i	0.742027	+	0.241099i
$550$		0			0
$551$	26.4449	−	15.2680i	1.12659	−	0.650437i
$552$		0			0
$553$	12.2579	+	45.7470i	0.521258	+	1.94536i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	25.5285	−	25.5285i	1.08168	−	1.08168i	0.0853228	−	0.996353i	$-0.472808\pi$
$557$	25.5285	−	25.5285i	1.08168	−	1.08168i	0.996353	−	0.0853228i	$-0.0271921\pi$
$558$		0			0
$559$			27.3423i			1.15645i
$560$		0			0
$561$	0.514893	+	4.89888i	0.0217388	+	0.206831i
$562$		0			0
$563$	28.0320	−	7.51116i	1.18141	−	0.316558i	0.385924	−	0.922530i	$-0.373883\pi$
$563$	28.0320	−	7.51116i	1.18141	−	0.316558i	0.795485	+	0.605973i	$0.207216\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−28.4701	−	10.9287i	−1.19563	−	0.458960i
$568$		0			0
$569$	−6.44549	−	11.1639i	−0.270209	−	0.468016i	0.698706	−	0.715409i	$-0.253759\pi$
$569$	−6.44549	−	11.1639i	−0.270209	−	0.468016i	−0.968915	+	0.247393i	$0.920426\pi$
$570$		0			0
$571$	20.9266	−	36.2459i	0.875749	−	1.51684i	0.0197865	−	0.999804i	$-0.493701\pi$
$571$	20.9266	−	36.2459i	0.875749	−	1.51684i	0.855963	−	0.517038i	$-0.172965\pi$
$572$		0			0
$573$	−26.7679	+	33.0557i	−1.11825	+	1.38092i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−1.05491	−	1.05491i	−0.0439164	−	0.0439164i	0.684808	−	0.728724i	$-0.259886\pi$
$577$	−1.05491	−	1.05491i	−0.0439164	−	0.0439164i	−0.728724	+	0.684808i	$0.759886\pi$
$578$		0			0
$579$	1.94184	+	2.67271i	0.0807000	+	0.111074i
$580$		0			0
$581$	44.1879	+	25.5119i	1.83322	+	1.05841i
$582$		0			0
$583$	−5.26190	−	1.40992i	−0.217926	−	0.0583930i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.645811	−	0.173044i	−0.0266555	−	0.00714231i	0.245467	−	0.969405i	$-0.421059\pi$
$587$	−0.645811	−	0.173044i	−0.0266555	−	0.00714231i	−0.272122	+	0.962263i	$0.587725\pi$
$588$		0			0
$589$	7.96926	+	4.60105i	0.328367	+	0.189583i
$590$		0			0
$591$	−5.33852	+	11.9905i	−0.219597	+	0.493223i
$592$		0			0
$593$	−22.6736	−	22.6736i	−0.931092	−	0.931092i	0.0666826	−	0.997774i	$-0.478758\pi$
$593$	−22.6736	−	22.6736i	−0.931092	−	0.931092i	−0.997774	+	0.0666826i	$0.978758\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	17.2031	+	44.8156i	0.704075	+	1.83418i
$598$		0			0
$599$	−19.7958	+	34.2874i	−0.808835	+	1.40094i	0.104836	+	0.994490i	$0.466568\pi$
$599$	−19.7958	+	34.2874i	−0.808835	+	1.40094i	−0.913671	+	0.406454i	$0.866765\pi$
$600$		0			0
$601$	−2.27721	−	3.94424i	−0.0928893	−	0.160889i	0.815836	−	0.578283i	$-0.196277\pi$
$601$	−2.27721	−	3.94424i	−0.0928893	−	0.160889i	−0.908726	+	0.417394i	$0.862944\pi$
$602$		0			0
$603$	12.7453	−	19.6261i	0.519031	−	0.799237i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.84249	−	2.63729i	0.399494	−	0.107044i	−0.0534774	−	0.998569i	$-0.517031\pi$
$607$	9.84249	−	2.63729i	0.399494	−	0.107044i	0.452972	+	0.891525i	$0.350364\pi$
$608$		0			0
$609$	−37.6185	+	27.3314i	−1.52438	+	1.10753i
$610$		0			0
$611$			3.07105i			0.124241i
$612$		0			0
$613$	−14.0188	+	14.0188i	−0.566214	+	0.566214i	−0.931066	−	0.364852i	$-0.881120\pi$
$613$	−14.0188	+	14.0188i	−0.566214	+	0.566214i	0.364852	+	0.931066i	$0.381120\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.91474	+	14.6100i	0.157601	+	0.588176i	0.998869	+	0.0475568i	$0.0151435\pi$
$617$	3.91474	+	14.6100i	0.157601	+	0.588176i	−0.841267	+	0.540620i	$0.818190\pi$
$618$		0			0
$619$	1.46721	−	0.847096i	0.0589723	−	0.0340477i	−0.470224	−	0.882547i	$-0.655827\pi$
$619$	1.46721	−	0.847096i	0.0589723	−	0.0340477i	0.529196	+	0.848499i	$0.322494\pi$
$620$		0			0
$621$	−3.91858	+	18.4355i	−0.157247	+	0.739790i
$622$		0			0
$623$	12.0329	−	44.9075i	0.482090	−	1.79918i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.51393	−	2.03574i	−0.100397	−	0.0812995i
$628$		0			0
$629$	−9.12639			−0.363893
$630$		0			0
$631$	−10.0584			−0.400417			−0.200209	−	0.979753i	$-0.564162\pi$
$631$	−10.0584			−0.400417			−0.200209	+	0.979753i	$0.564162\pi$
$632$		0			0
$633$	−3.92774	+	24.7988i	−0.156114	+	0.985663i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.10841	−	11.6007i	0.123160	−	0.459638i
$638$		0			0
$639$	−1.20787	−	1.34148i	−0.0477826	−	0.0530679i
$640$		0			0
$641$	−19.1025	+	11.0288i	−0.754504	+	0.435613i	−0.827319	−	0.561732i	$-0.810135\pi$
$641$	−19.1025	+	11.0288i	−0.754504	+	0.435613i	0.0728150	+	0.997345i	$0.476802\pi$
$642$		0			0
$643$	0.0363262	+	0.135571i	0.00143256	+	0.00534640i	0.966638	−	0.256145i	$-0.0824524\pi$
$643$	0.0363262	+	0.135571i	0.00143256	+	0.00534640i	−0.965206	+	0.261491i	$0.915786\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.4519	+	21.4519i	−0.843360	+	0.843360i	−0.989294	−	0.145934i	$-0.953381\pi$
$647$	−21.4519	+	21.4519i	−0.843360	+	0.843360i	0.145934	+	0.989294i	$0.453381\pi$
$648$		0			0
$649$		−	3.07810i		−	0.120826i
$650$		0			0
$651$	−12.8012	−	5.69945i	−0.501717	−	0.223379i
$652$		0			0
$653$	−9.04126	+	2.42260i	−0.353812	+	0.0948036i	−0.431347	−	0.902186i	$-0.641962\pi$
$653$	−9.04126	+	2.42260i	−0.353812	+	0.0948036i	0.0775353	+	0.996990i	$0.475295\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	1.96328	−	37.4616i	0.0765947	−	1.46151i
$658$		0			0
$659$	−4.63337	−	8.02524i	−0.180491	−	0.312619i	0.761557	−	0.648098i	$-0.224435\pi$
$659$	−4.63337	−	8.02524i	−0.180491	−	0.312619i	−0.942048	+	0.335479i	$0.891102\pi$
$660$		0			0
$661$	4.88507	−	8.46119i	0.190007	−	0.329102i	−0.755245	−	0.655442i	$-0.772482\pi$
$661$	4.88507	−	8.46119i	0.190007	−	0.329102i	0.945252	+	0.326340i	$0.105816\pi$
$662$		0			0
$663$	26.9077	+	4.26176i	1.04501	+	0.165513i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	20.3208	+	20.3208i	0.786825	+	0.786825i
$668$		0			0
$669$	−34.9126	+	3.66946i	−1.34980	+	0.141869i
$670$		0			0
$671$	−2.55726	−	1.47643i	−0.0987219	−	0.0569971i
$672$		0			0
$673$	−14.6169	−	3.91660i	−0.563442	−	0.150974i	−0.0341547	−	0.999417i	$-0.510874\pi$
$673$	−14.6169	−	3.91660i	−0.563442	−	0.150974i	−0.529287	+	0.848443i	$0.677541\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−11.7341	−	3.14415i	−0.450979	−	0.120839i	0.0261785	−	0.999657i	$-0.491666\pi$
$677$	−11.7341	−	3.14415i	−0.450979	−	0.120839i	−0.477157	+	0.878818i	$0.658333\pi$
$678$		0			0
$679$	−0.405859	−	0.234323i	−0.0155755	−	0.00899249i
$680$		0			0
$681$	15.0904	−	1.58607i	0.578266	−	0.0607782i
$682$		0			0
$683$	−0.290114	−	0.290114i	−0.0111009	−	0.0111009i	0.701535	−	0.712635i	$-0.252499\pi$
$683$	−0.290114	−	0.290114i	−0.0111009	−	0.0111009i	−0.712635	+	0.701535i	$0.752499\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−20.1682	−	3.19432i	−0.769463	−	0.121871i
$688$		0			0
$689$	−15.0641	+	26.0918i	−0.573896	+	0.994017i
$690$		0			0
$691$	2.86257	+	4.95812i	0.108897	+	0.188616i	0.915324	−	0.402719i	$-0.131935\pi$
$691$	2.86257	+	4.95812i	0.108897	+	0.188616i	−0.806426	+	0.591334i	$0.798601\pi$
$692$		0			0
$693$	4.13118	+	2.68282i	0.156930	+	0.101912i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−66.5308	+	17.8269i	−2.52003	+	0.675241i
$698$		0			0
$699$	21.4142	+	9.53420i	0.809958	+	0.360617i
$700$		0			0
$701$		−	12.5871i		−	0.475407i	−0.971338	−	0.237703i	$-0.923605\pi$
$701$		−	12.5871i		−	0.475407i	0.971338	−	0.237703i	$-0.0763946\pi$
$702$		0			0
$703$	4.23791	−	4.23791i	0.159836	−	0.159836i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	13.3078	+	49.6656i	0.500493	+	1.86787i
$708$		0			0
$709$	33.5532	−	19.3719i	1.26012	−	0.727529i	0.287020	−	0.957925i	$-0.407335\pi$
$709$	33.5532	−	19.3719i	1.26012	−	0.727529i	0.973097	+	0.230396i	$0.0740021\pi$
$710$		0			0
$711$	−12.9577	+	39.8797i	−0.485952	+	1.49561i
$712$		0			0
$713$	−2.24145	+	8.36519i	−0.0839428	+	0.313279i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−3.92940	+	24.8092i	−0.146746	+	0.926518i
$718$		0			0
$719$	18.3617			0.684776			0.342388	−	0.939559i	$-0.388764\pi$
$719$	18.3617			0.684776			0.342388	+	0.939559i	$0.388764\pi$
$720$		0			0
$721$	0.680794			0.0253541
$722$		0			0
$723$	17.5773	+	14.2338i	0.653706	+	0.529361i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−0.988143	+	3.68780i	−0.0366482	+	0.136773i	−0.981826	−	0.189783i	$-0.939222\pi$
$727$	−0.988143	+	3.68780i	−0.0366482	+	0.136773i	0.945178	+	0.326556i	$0.105888\pi$
$728$		0			0
$729$	−15.8702	−	21.8435i	−0.587785	−	0.809017i
$730$		0			0
$731$	51.8538	−	29.9378i	1.91788	−	1.10729i
$732$		0			0
$733$	−13.1700	−	49.1511i	−0.486444	−	1.81544i	−0.573466	−	0.819229i	$-0.694402\pi$
$733$	−13.1700	−	49.1511i	−0.486444	−	1.81544i	0.0870218	−	0.996206i	$-0.472265\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.67284	+	2.67284i	−0.0984553	+	0.0984553i
$738$		0			0
$739$		−	16.4016i		−	0.603344i	−0.953412	−	0.301672i	$-0.902455\pi$
$739$		−	16.4016i		−	0.603344i	0.953412	−	0.301672i	$-0.0975447\pi$
$740$		0			0
$741$	−14.4738	+	10.5158i	−0.531707	+	0.386308i
$742$		0			0
$743$	15.9128	−	4.26383i	0.583785	−	0.156425i	0.0451735	−	0.998979i	$-0.485616\pi$
$743$	15.9128	−	4.26383i	0.583785	−	0.156425i	0.538611	+	0.842555i	$0.318949\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	20.5091	+	40.2513i	0.750387	+	1.47272i
$748$		0			0
$749$	19.4516	+	33.6911i	0.710746	+	1.23105i
$750$		0			0
$751$	−14.4753	+	25.0720i	−0.528213	+	0.914892i	0.471246	+	0.882002i	$0.343804\pi$
$751$	−14.4753	+	25.0720i	−0.528213	+	0.914892i	−0.999459	+	0.0328898i	$0.989529\pi$
$752$		0			0
$753$	−9.20537	−	23.9808i	−0.335462	−	0.873909i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−5.26561	−	5.26561i	−0.191382	−	0.191382i	0.604911	−	0.796293i	$-0.293209\pi$
$757$	−5.26561	−	5.26561i	−0.191382	−	0.191382i	−0.796293	+	0.604911i	$0.793209\pi$
$758$		0			0
$759$	1.23825	−	2.78115i	0.0449456	−	0.100949i
$760$		0			0
$761$	−5.02110	−	2.89893i	−0.182015	−	0.105086i	0.406224	−	0.913773i	$-0.366845\pi$
$761$	−5.02110	−	2.89893i	−0.182015	−	0.105086i	−0.588239	+	0.808687i	$0.700179\pi$
$762$		0			0
$763$	−17.9883	−	4.81995i	−0.651220	−	0.174494i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−16.4438	−	4.40609i	−0.593750	−	0.159095i
$768$		0			0
$769$	−32.9790	−	19.0404i	−1.18925	−	0.686615i	−0.231115	−	0.972926i	$-0.574237\pi$
$769$	−32.9790	−	19.0404i	−1.18925	−	0.686615i	−0.958136	+	0.286312i	$0.907571\pi$
$770$		0			0
$771$	4.19775	+	5.77771i	0.151178	+	0.208079i
$772$		0			0
$773$	19.2745	+	19.2745i	0.693257	+	0.693257i	0.962947	−	0.269690i	$-0.0869213\pi$
$773$	19.2745	+	19.2745i	0.693257	+	0.693257i	−0.269690	+	0.962947i	$0.586921\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−5.74342	+	7.09254i	−0.206044	+	0.254443i
$778$		0			0
$779$	22.6160	−	39.1721i	0.810303	−	1.40349i
$780$		0			0
$781$	0.145789	+	0.252514i	0.00521673	+	0.00903564i
$782$		0			0
$783$	−41.1125	+	2.15462i	−1.46924	+	0.0769997i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	34.3267	−	9.19780i	1.22361	−	0.327866i	0.411524	−	0.911399i	$-0.364997\pi$
$787$	34.3267	−	9.19780i	1.22361	−	0.327866i	0.812089	+	0.583533i	$0.198330\pi$
$788$		0			0
$789$	−1.83690	−	17.4769i	−0.0653954	−	0.622196i
$790$		0			0
$791$			54.0374i			1.92135i
$792$		0			0
$793$	−11.5479	+	11.5479i	−0.410078	+	0.410078i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−10.6949	−	39.9138i	−0.378831	−	1.41382i	−0.847665	−	0.530531i	$-0.821992\pi$
$797$	−10.6949	−	39.9138i	−0.378831	−	1.41382i	0.468834	−	0.883286i	$-0.344674\pi$
$798$		0			0
$799$	5.82415	−	3.36257i	0.206043	−	0.118959i
$800$		0			0
$801$	30.5897	−	27.5431i	1.08083	−	0.973187i
$802$		0			0
$803$	−1.56828	+	5.85289i	−0.0553433	+	0.206544i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	9.55301	−	3.66706i	0.336282	−	0.129087i
$808$		0			0
$809$	41.5139			1.45955			0.729776	−	0.683687i	$-0.239625\pi$
$809$	41.5139			1.45955			0.729776	+	0.683687i	$0.239625\pi$
$810$		0			0
$811$	−42.8314			−1.50401			−0.752007	−	0.659155i	$-0.770914\pi$
$811$	−42.8314			−1.50401			−0.752007	+	0.659155i	$0.770914\pi$
$812$		0			0
$813$	−45.6543	+	17.5251i	−1.60117	+	0.614631i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−10.1769	+	37.9806i	−0.356043	+	1.32877i
$818$		0			0
$819$	20.2456	−	18.2292i	0.707437	−	0.636980i
$820$		0			0
$821$	−26.8095	+	15.4785i	−0.935659	+	0.540203i	−0.888597	−	0.458689i	$-0.848319\pi$
$821$	−26.8095	+	15.4785i	−0.935659	+	0.540203i	−0.0470622	+	0.998892i	$0.514986\pi$
$822$		0			0
$823$	−6.06293	−	22.6272i	−0.211341	−	0.788734i	−0.987423	−	0.158102i	$-0.949463\pi$
$823$	−6.06293	−	22.6272i	−0.211341	−	0.788734i	0.776082	−	0.630632i	$-0.217204\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.0194	+	22.0194i	−0.765690	+	0.765690i	−0.977345	−	0.211654i	$-0.932115\pi$
$827$	−22.0194	+	22.0194i	−0.765690	+	0.765690i	0.211654	+	0.977345i	$0.432115\pi$
$828$		0			0
$829$			6.65597i			0.231171i	0.993298	+	0.115586i	$0.0368745\pi$
$829$			6.65597i			0.231171i	−0.993298	+	0.115586i	$0.963126\pi$
$830$		0			0
$831$	1.31417	+	12.5035i	0.0455880	+	0.433741i
$832$		0			0
$833$	−25.4039	+	6.80696i	−0.880194	+	0.235847i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−6.75701	−	10.4049i	−0.233556	−	0.359645i
$838$		0			0
$839$	11.8643	+	20.5496i	0.409601	+	0.709450i	0.994845	−	0.101407i	$-0.0323346\pi$
$839$	11.8643	+	20.5496i	0.409601	+	0.709450i	−0.585244	+	0.810857i	$0.699001\pi$
$840$		0			0
$841$	−16.8867	+	29.2487i	−0.582301	+	1.00858i
$842$		0			0
$843$	−3.74801	+	4.62841i	−0.129088	+	0.159411i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	25.7930	+	25.7930i	0.886257	+	0.886257i
$848$		0			0
$849$	4.99512	+	6.87520i	0.171432	+	0.235956i
$850$		0			0
$851$	4.88475	+	2.82021i	0.167447	+	0.0966756i
$852$		0			0
$853$	−18.4649	−	4.94766i	−0.632227	−	0.169405i	−0.0715468	−	0.997437i	$-0.522794\pi$
$853$	−18.4649	−	4.94766i	−0.632227	−	0.169405i	−0.560680	+	0.828033i	$0.689460\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−30.8026	−	8.25353i	−1.05220	−	0.281935i	−0.309037	−	0.951050i	$-0.600007\pi$
$857$	−30.8026	−	8.25353i	−1.05220	−	0.281935i	−0.743159	+	0.669115i	$0.766673\pi$
$858$		0			0
$859$	14.2177	+	8.20859i	0.485101	+	0.280073i	0.722540	−	0.691329i	$-0.242974\pi$
$859$	14.2177	+	8.20859i	0.485101	+	0.280073i	−0.237439	+	0.971403i	$0.576308\pi$
$860$		0			0
$861$	−28.0151	+	62.9229i	−0.954752	+	2.14441i
$862$		0			0
$863$	−9.10066	−	9.10066i	−0.309790	−	0.309790i	0.535038	−	0.844828i	$-0.320297\pi$
$863$	−9.10066	−	9.10066i	−0.309790	−	0.309790i	−0.844828	+	0.535038i	$0.820297\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−10.8276	−	28.2068i	−0.367724	−	0.957953i
$868$		0			0
$869$	3.38657	−	5.86571i	0.114882	−	0.198981i
$870$		0			0
$871$	10.4528	+	18.1048i	0.354179	+	0.613456i
$872$		0			0
$873$	−0.188373	−	0.369702i	−0.00637545	−	0.0125125i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−14.1411	+	3.78909i	−0.477510	+	0.127948i	−0.489543	−	0.871979i	$-0.662836\pi$
$877$	−14.1411	+	3.78909i	−0.477510	+	0.127948i	0.0120331	+	0.999928i	$0.496170\pi$
$878$		0			0
$879$	−18.9639	+	13.7781i	−0.639638	+	0.464724i
$880$		0			0
$881$		−	17.7146i		−	0.596820i	−0.954438	−	0.298410i	$-0.903544\pi$
$881$		−	17.7146i		−	0.596820i	0.954438	−	0.298410i	$-0.0964563\pi$
$882$		0			0
$883$	8.62634	−	8.62634i	0.290299	−	0.290299i	−0.546899	−	0.837198i	$-0.684192\pi$
$883$	8.62634	−	8.62634i	0.290299	−	0.290299i	0.837198	+	0.546899i	$0.184192\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.907087	−	3.38530i	−0.0304570	−	0.113667i	0.949024	−	0.315204i	$-0.102073\pi$
$887$	−0.907087	−	3.38530i	−0.0304570	−	0.113667i	−0.979481	+	0.201537i	$0.935406\pi$
$888$		0			0
$889$	−2.89535	+	1.67163i	−0.0971069	+	0.0560647i
$890$		0			0
$891$	1.77387	+	3.98418i	0.0594269	+	0.133475i
$892$		0			0
$893$	−1.14305	+	4.26592i	−0.0382507	+	0.142754i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−13.0849	−	10.5960i	−0.436893	−	0.353789i
$898$		0			0
$899$	−18.9170			−0.630917
$900$		0			0
$901$	65.9763			2.19799
$902$		0			0
$903$	9.36661	−	59.1384i	0.311701	−	1.96800i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	5.03909	−	18.8061i	0.167320	−	0.624447i	−0.830413	−	0.557149i	$-0.811895\pi$
$907$	5.03909	−	18.8061i	0.167320	−	0.624447i	0.997733	−	0.0672984i	$-0.0214380\pi$
$908$		0			0
$909$	−14.0676	+	43.2956i	−0.466593	+	1.43603i
$910$		0			0
$911$	−1.48726	+	0.858672i	−0.0492753	+	0.0284491i	−0.524435	−	0.851450i	$-0.675724\pi$
$911$	−1.48726	+	0.858672i	−0.0492753	+	0.0284491i	0.475160	+	0.879899i	$0.342390\pi$
$912$		0			0
$913$	−1.88860	−	7.04835i	−0.0625035	−	0.233266i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.447529	−	0.447529i	0.0147787	−	0.0147787i
$918$		0			0
$919$		−	43.0970i		−	1.42164i	−0.703375	−	0.710819i	$-0.748324\pi$
$919$		−	43.0970i		−	1.42164i	0.703375	−	0.710819i	$-0.251676\pi$
$920$		0			0
$921$	41.4473	+	18.4535i	1.36573	+	0.608064i
$922$		0			0
$923$	1.55766	−	0.417373i	0.0512709	−	0.0137380i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.505514	+	0.328285i	0.0166033	+	0.0107823i
$928$		0			0
$929$	−3.64047	−	6.30549i	−0.119440	−	0.206876i	0.800106	−	0.599859i	$-0.204777\pi$
$929$	−3.64047	−	6.30549i	−0.119440	−	0.206876i	−0.919546	+	0.392983i	$0.871443\pi$
$930$		0			0
$931$	8.63564	−	14.9574i	0.283022	−	0.490208i
$932$		0			0
$933$	−6.20186	−	0.982278i	−0.203040	−	0.0321584i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−10.9183	−	10.9183i	−0.356685	−	0.356685i	0.505904	−	0.862590i	$-0.331159\pi$
$937$	−10.9183	−	10.9183i	−0.356685	−	0.356685i	−0.862590	+	0.505904i	$0.831159\pi$
$938$		0			0
$939$	24.4593	−	2.57078i	0.798199	−	0.0838941i
$940$		0			0
$941$	35.4650	+	20.4757i	1.15613	+	0.667490i	0.950373	−	0.311114i	$-0.100702\pi$
$941$	35.4650	+	20.4757i	1.15613	+	0.667490i	0.205754	+	0.978604i	$0.434035\pi$
$942$		0			0
$943$	41.1183	+	11.0176i	1.33900	+	0.358783i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	37.4169	+	10.0258i	1.21588	+	0.325795i	0.809068	−	0.587715i	$-0.199972\pi$
$947$	37.4169	+	10.0258i	1.21588	+	0.325795i	0.406816	+	0.913510i	$0.366639\pi$
$948$		0			0
$949$	29.0222	+	16.7560i	0.942102	+	0.543923i
$950$		0			0
$951$	25.4339	−	2.67322i	0.824752	−	0.0866850i
$952$		0			0
$953$	−9.57092	−	9.57092i	−0.310032	−	0.310032i	0.534890	−	0.844922i	$-0.320353\pi$
$953$	−9.57092	−	9.57092i	−0.310032	−	0.310032i	−0.844922	+	0.534890i	$0.820353\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	6.56802	+	1.04027i	0.212314	+	0.0336272i
$958$		0			0
$959$	18.9322	−	32.7915i	0.611352	−	1.05889i
$960$		0			0
$961$	12.6497	+	21.9098i	0.408053	+	0.706769i
$962$		0			0
$963$	−1.80265	+	34.3966i	−0.0580896	+	1.10842i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−32.6676	+	8.75325i	−1.05052	+	0.281485i	−0.742466	−	0.669884i	$-0.766344\pi$
$967$	−32.6676	+	8.75325i	−1.05052	+	0.281485i	−0.308052	+	0.951369i	$0.599677\pi$
$968$		0			0
$969$	35.7907	+	15.9350i	1.14976	+	0.511907i
$970$		0			0
$971$			30.6923i			0.984964i	0.870323	+	0.492482i	$0.163910\pi$
$971$			30.6923i			0.984964i	−0.870323	+	0.492482i	$0.836090\pi$
$972$		0			0
$973$	19.9056	−	19.9056i	0.638143	−	0.638143i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.67329	+	6.24481i	0.0535334	+	0.199789i	0.987513	−	0.157537i	$-0.0503552\pi$
$977$	1.67329	+	6.24481i	0.0535334	+	0.199789i	−0.933980	+	0.357326i	$0.883689\pi$
$978$		0			0
$979$	−5.75807	+	3.32443i	−0.184029	+	0.106249i
$980$		0			0
$981$	−11.0327	−	12.2531i	−0.352248	−	0.391211i
$982$		0			0
$983$	−1.51459	+	5.65254i	−0.0483081	+	0.180288i	−0.985864	−	0.167545i	$-0.946416\pi$
$983$	−1.51459	+	5.65254i	−0.0483081	+	0.180288i	0.937556	+	0.347834i	$0.113083\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	1.05204	−	6.64235i	0.0334869	−	0.211428i
$988$		0			0
$989$	−37.0052			−1.17670
$990$		0			0
$991$	−3.05991			−0.0972011			−0.0486006	−	0.998818i	$-0.515476\pi$
$991$	−3.05991			−0.0972011			−0.0486006	+	0.998818i	$0.515476\pi$
$992$		0			0
$993$	−28.6207	−	23.1766i	−0.908250	−	0.735486i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.556025	−	2.07511i	0.0176095	−	0.0657195i	−0.956562	−	0.291529i	$-0.905836\pi$
$997$	0.556025	−	2.07511i	0.0176095	−	0.0657195i	0.974171	+	0.225809i	$0.0725027\pi$
$998$		0			0
$999$	−7.68478	+	2.49694i	−0.243136	+	0.0789996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.be.f.257.8	yes	32
3.2	odd	2		2700.2.bf.f.557.8		32
5.2	odd	4	inner	900.2.be.f.293.4	yes	32
5.3	odd	4	inner	900.2.be.f.293.5	yes	32
5.4	even	2	inner	900.2.be.f.257.1	✓	32
9.2	odd	6	inner	900.2.be.f.857.5	yes	32
9.7	even	3		2700.2.bf.f.2357.1		32
15.2	even	4		2700.2.bf.f.2393.8		32
15.8	even	4		2700.2.bf.f.2393.1		32
15.14	odd	2		2700.2.bf.f.557.1		32
45.2	even	12	inner	900.2.be.f.893.1	yes	32
45.7	odd	12		2700.2.bf.f.1493.1		32
45.29	odd	6	inner	900.2.be.f.857.4	yes	32
45.34	even	6		2700.2.bf.f.2357.8		32
45.38	even	12	inner	900.2.be.f.893.8	yes	32
45.43	odd	12		2700.2.bf.f.1493.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.be.f.257.1	✓	32	5.4	even	2	inner
900.2.be.f.257.8	yes	32	1.1	even	1	trivial
900.2.be.f.293.4	yes	32	5.2	odd	4	inner
900.2.be.f.293.5	yes	32	5.3	odd	4	inner
900.2.be.f.857.4	yes	32	45.29	odd	6	inner
900.2.be.f.857.5	yes	32	9.2	odd	6	inner
900.2.be.f.893.1	yes	32	45.2	even	12	inner
900.2.be.f.893.8	yes	32	45.38	even	12	inner
2700.2.bf.f.557.1		32	15.14	odd	2
2700.2.bf.f.557.8		32	3.2	odd	2
2700.2.bf.f.1493.1		32	45.7	odd	12
2700.2.bf.f.1493.8		32	45.43	odd	12
2700.2.bf.f.2357.1		32	9.7	even	3
2700.2.bf.f.2357.8		32	45.34	even	6
2700.2.bf.f.2393.1		32	15.8	even	4
2700.2.bf.f.2393.8		32	15.2	even	4

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61701 - 0.620711i) q^{3} +(0.876983 - 3.27295i) q^{7} +(2.22943 - 2.00739i) q^{9} +(-0.419659 + 0.242290i) q^{11} +(0.693644 + 2.58871i) q^{13} +(4.14993 - 4.14993i) q^{17} +3.85410i q^{19} +(-0.613466 - 5.83674i) q^{21} +(-3.50358 + 0.938781i) q^{23} +(2.35900 - 4.62981i) q^{27} +(-3.96149 - 6.86149i) q^{29} +(1.19381 - 2.06773i) q^{31} +(-0.528200 + 0.652273i) q^{33} +(-1.09958 - 1.09958i) q^{37} +(2.72847 + 3.75542i) q^{39} +(-10.1637 - 5.86804i) q^{41} +(9.85458 + 2.64053i) q^{43} +(1.10685 + 0.296580i) q^{47} +(-3.88090 - 2.24064i) q^{49} +(4.13456 - 9.28638i) q^{51} +(7.94909 + 7.94909i) q^{53} +(2.39229 + 6.23212i) q^{57} +(-3.17605 + 5.50108i) q^{59} +(3.04683 + 5.27726i) q^{61} +(-4.61491 - 9.05727i) q^{63} +(7.53469 - 2.01891i) q^{67} +(-5.08260 + 3.69273i) q^{69} -0.601711i q^{71} +(8.84189 - 8.84189i) q^{73} +(0.424969 + 1.58601i) q^{77} +(-12.1047 + 6.98866i) q^{79} +(0.940756 - 8.95070i) q^{81} +(-3.89739 + 14.5453i) q^{83} +(-10.6648 - 8.63616i) q^{87} +13.7208 q^{89} +9.08103 q^{91} +(0.646930 - 4.08455i) q^{93} +(0.0357970 - 0.133596i) q^{97} +(-0.449231 + 1.38259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{11} + 12 q^{21} + 8 q^{31} + 60 q^{41} + 36 q^{51} + 52 q^{61} - 36 q^{81} + 120 q^{91}+O(q^{100}) \) 32 * q - 12 * q^11 + 12 * q^21 + 8 * q^31 + 60 * q^41 + 36 * q^51 + 52 * q^61 - 36 * q^81 + 120 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more