LMFDB - Embedded newform 900.2.be.f.857.5

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			857.5
Character	$\chi$	$=$	900.857
Dual form			900.2.be.f.293.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.620711 - 1.61701i) q^{3} +(-3.27295 + 0.876983i) q^{7} +(-2.22943 - 2.00739i) q^{9} +(-0.419659 - 0.242290i) q^{11} +(-2.58871 - 0.693644i) q^{13} +(-4.14993 + 4.14993i) q^{17} +3.85410i q^{19} +(-0.613466 + 5.83674i) q^{21} +(-0.938781 + 3.50358i) q^{23} +(-4.62981 + 2.35900i) q^{27} +(3.96149 - 6.86149i) q^{29} +(1.19381 + 2.06773i) q^{31} +(-0.652273 + 0.528200i) q^{33} +(-1.09958 - 1.09958i) q^{37} +(-2.72847 + 3.75542i) q^{39} +(-10.1637 + 5.86804i) q^{41} +(-2.64053 - 9.85458i) q^{43} +(0.296580 + 1.10685i) q^{47} +(3.88090 - 2.24064i) q^{49} +(4.13456 + 9.28638i) q^{51} +(-7.94909 - 7.94909i) q^{53} +(6.23212 + 2.39229i) q^{57} +(3.17605 + 5.50108i) q^{59} +(3.04683 - 5.27726i) q^{61} +(9.05727 + 4.61491i) q^{63} +(-2.01891 + 7.53469i) q^{67} +(5.08260 + 3.69273i) q^{69} +0.601711i q^{71} +(8.84189 - 8.84189i) q^{73} +(1.58601 + 0.424969i) q^{77} +(12.1047 + 6.98866i) q^{79} +(0.940756 + 8.95070i) q^{81} +(-14.5453 + 3.89739i) q^{83} +(-8.63616 - 10.6648i) q^{87} -13.7208 q^{89} +9.08103 q^{91} +(4.08455 - 0.646930i) q^{93} +(-0.133596 + 0.0357970i) q^{97} +(0.449231 + 1.38259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

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
$3$	0.620711	−	1.61701i	0.358368	−	0.933580i
$3$	0.620711	−	1.61701i	0.358368	−	0.933580i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.27295	+	0.876983i	−1.23706	+	0.331468i	−0.817324	−	0.576179i	$-0.804543\pi$
$7$	−3.27295	+	0.876983i	−1.23706	+	0.331468i	−0.419734	+	0.907647i	$0.637876\pi$
$8$		0			0
$9$	−2.22943	−	2.00739i	−0.743145	−	0.669131i
$10$		0			0
$11$	−0.419659	−	0.242290i	−0.126532	−	0.0730533i	0.435398	−	0.900238i	$-0.356608\pi$
$11$	−0.419659	−	0.242290i	−0.126532	−	0.0730533i	−0.561930	+	0.827185i	$0.689941\pi$
$12$		0			0
$13$	−2.58871	−	0.693644i	−0.717980	−	0.192382i	−0.118710	−	0.992929i	$-0.537876\pi$
$13$	−2.58871	−	0.693644i	−0.717980	−	0.192382i	−0.599270	+	0.800547i	$0.704542\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.14993	+	4.14993i	−1.00651	+	1.00651i	−0.00652688	+	0.999979i	$0.502078\pi$
$17$	−4.14993	+	4.14993i	−1.00651	+	1.00651i	−0.999979	+	0.00652688i	$0.997922\pi$
$18$		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
$23$	−0.938781	+	3.50358i	−0.195749	+	0.730546i	0.796322	+	0.604873i	$0.206776\pi$
$23$	−0.938781	+	3.50358i	−0.195749	+	0.730546i	−0.992072	+	0.125674i	$0.959891\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−4.62981	+	2.35900i	−0.891007	+	0.453990i
$28$		0			0
$29$	3.96149	−	6.86149i	0.735629	−	1.27415i	−0.218817	−	0.975766i	$-0.570220\pi$
$29$	3.96149	−	6.86149i	0.735629	−	1.27415i	0.954447	−	0.298382i	$-0.0964468\pi$
$30$		0			0
$31$	1.19381	+	2.06773i	0.214414	+	0.371376i	0.953091	−	0.302683i	$-0.0978825\pi$
$31$	1.19381	+	2.06773i	0.214414	+	0.371376i	−0.738677	+	0.674059i	$0.764549\pi$
$32$		0			0
$33$	−0.652273	+	0.528200i	−0.113546	+	0.0919478i
$34$		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	−0.593562	+	0.804788i	$0.702279\pi$
$41$	−10.1637	+	5.86804i	−1.58731	+	0.916434i	−0.993748	+	0.111646i	$0.964388\pi$
$42$		0			0
$43$	−2.64053	−	9.85458i	−0.402677	−	1.50281i	−0.808301	−	0.588770i	$-0.799613\pi$
$43$	−2.64053	−	9.85458i	−0.402677	−	1.50281i	0.405624	−	0.914040i	$-0.367054\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.296580	+	1.10685i	0.0432607	+	0.161451i	0.984177	−	0.177188i	$-0.0567001\pi$
$47$	0.296580	+	1.10685i	0.0432607	+	0.161451i	−0.940916	+	0.338639i	$0.890033\pi$
$48$		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	$-0.969214\pi$
$53$	−7.94909	−	7.94909i	−1.09189	−	1.09189i	−0.0965652	−	0.995327i	$-0.530786\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	6.23212	+	2.39229i	0.825464	+	0.316866i
$58$		0			0
$59$	3.17605	+	5.50108i	0.413486	+	0.716179i	0.995268	−	0.0971654i	$-0.0309776\pi$
$59$	3.17605	+	5.50108i	0.413486	+	0.716179i	−0.581782	+	0.813345i	$0.697644\pi$
$60$		0			0
$61$	3.04683	−	5.27726i	0.390107	−	0.675684i	−0.602357	−	0.798227i	$-0.705771\pi$
$61$	3.04683	−	5.27726i	0.390107	−	0.675684i	0.992463	+	0.122543i	$0.0391048\pi$
$62$		0			0
$63$	9.05727	+	4.61491i	1.14111	+	0.581424i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.01891	+	7.53469i	−0.246650	+	0.920509i	0.725897	+	0.687803i	$0.241425\pi$
$67$	−2.01891	+	7.53469i	−0.246650	+	0.920509i	−0.972547	+	0.232706i	$0.925242\pi$
$68$		0			0
$69$	5.08260	+	3.69273i	0.611874	+	0.444552i
$70$		0			0
$71$			0.601711i			0.0714100i	0.999362	+	0.0357050i	$0.0113677\pi$
$71$			0.601711i			0.0714100i	−0.999362	+	0.0357050i	$0.988632\pi$
$72$		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
$77$	1.58601	+	0.424969i	0.180742	+	0.0484297i
$78$		0			0
$79$	12.1047	+	6.98866i	1.36189	+	0.786286i	0.989875	−	0.141941i	$-0.0453345\pi$
$79$	12.1047	+	6.98866i	1.36189	+	0.786286i	0.372013	+	0.928228i	$0.378668\pi$
$80$		0			0
$81$	0.940756	+	8.95070i	0.104528	+	0.994522i
$82$		0			0
$83$	−14.5453	+	3.89739i	−1.59655	+	0.427794i	−0.943998	−	0.329950i	$-0.892968\pi$
$83$	−14.5453	+	3.89739i	−1.59655	+	0.427794i	−0.652551	+	0.757744i	$0.726301\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−8.63616	−	10.6648i	−0.925893	−	1.14338i
$88$		0			0
$89$	−13.7208			−1.45441			−0.727203	−	0.686423i	$-0.759180\pi$
$89$	−13.7208			−1.45441			−0.727203	+	0.686423i	$0.759180\pi$
$90$		0			0
$91$	9.08103			0.951951
$92$		0			0
$93$	4.08455	−	0.646930i	0.423548	−	0.0670835i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−0.133596	+	0.0357970i	−0.0135646	+	0.00363463i	−0.265595	−	0.964085i	$-0.585568\pi$
$97$	−0.133596	+	0.0357970i	−0.0135646	+	0.00363463i	0.252030	+	0.967719i	$0.418902\pi$
$98$		0			0
$99$	0.449231	+	1.38259i	0.0451494	+	0.138956i
$100$		0			0
$101$	−13.1416	−	7.58729i	−1.30763	−	0.754963i	−0.325934	−	0.945393i	$-0.605679\pi$
$101$	−13.1416	−	7.58729i	−1.30763	−	0.754963i	−0.981701	+	0.190429i	$0.939012\pi$
$102$		0			0
$103$	−0.194073	−	0.0520016i	−0.0191225	−	0.00512387i	0.249245	−	0.968440i	$-0.419818\pi$
$103$	−0.194073	−	0.0520016i	−0.0191225	−	0.00512387i	−0.268368	+	0.963317i	$0.586484\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.11849	−	8.11849i	0.784844	−	0.784844i	−0.195800	−	0.980644i	$-0.562730\pi$
$107$	8.11849	−	8.11849i	0.784844	−	0.784844i	0.980644	+	0.195800i	$0.0627304\pi$
$108$		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
$113$	−4.12758	+	15.4044i	−0.388290	+	1.44912i	0.444624	+	0.895718i	$0.353337\pi$
$113$	−4.12758	+	15.4044i	−0.388290	+	1.44912i	−0.832914	+	0.553402i	$0.813329\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	4.37895	+	6.74300i	0.404834	+	0.623390i
$118$		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
$123$	3.17992	+	20.0772i	0.286724	+	1.81030i
$124$		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	−0.492917	−	0.870076i	$-0.664069\pi$
$131$	0.161760	−	0.0933923i	0.0141330	−	0.00815972i	0.507050	+	0.861917i	$0.330736\pi$
$132$		0			0
$133$	−3.37998	−	12.6143i	−0.293082	−	1.09380i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.89222	+	10.7939i	0.247099	+	0.922187i	0.972317	+	0.233667i	$0.0750726\pi$
$137$	2.89222	+	10.7939i	0.247099	+	0.922187i	−0.725217	+	0.688520i	$0.758261\pi$
$138$		0			0
$139$	−7.19491	+	4.15398i	−0.610264	+	0.352336i	−0.773069	−	0.634322i	$-0.781279\pi$
$139$	−7.19491	+	4.15398i	−0.610264	+	0.352336i	0.162805	+	0.986658i	$0.447946\pi$
$140$		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
$147$	−1.21421	−	7.66623i	−0.100147	−	0.632300i
$148$		0			0
$149$	−4.09023	−	7.08448i	−0.335084	−	0.580383i	0.648417	−	0.761286i	$-0.275432\pi$
$149$	−4.09023	−	7.08448i	−0.335084	−	0.580383i	−0.983501	+	0.180902i	$0.942098\pi$
$150$		0			0
$151$	10.5366	−	18.2499i	0.857454	−	1.48515i	−0.0168953	−	0.999857i	$-0.505378\pi$
$151$	10.5366	−	18.2499i	0.857454	−	1.48515i	0.874349	−	0.485297i	$-0.161288\pi$
$152$		0			0
$153$	17.5825	−	0.921461i	1.42146	−	0.0744957i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	3.32798	−	12.4202i	0.265602	−	0.991239i	−0.696279	−	0.717771i	$-0.745162\pi$
$157$	3.32798	−	12.4202i	0.265602	−	0.991239i	0.961881	−	0.273468i	$-0.0881709\pi$
$158$		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
$167$	−10.5755	−	2.83369i	−0.818355	−	0.219277i	−0.174728	−	0.984617i	$-0.555904\pi$
$167$	−10.5755	−	2.83369i	−0.818355	−	0.219277i	−0.643627	+	0.765339i	$0.722571\pi$
$168$		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
$173$	17.6344	−	4.72513i	1.34072	−	0.359245i	0.484019	−	0.875058i	$-0.339177\pi$
$173$	17.6344	−	4.72513i	1.34072	−	0.359245i	0.856701	+	0.515813i	$0.172510\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.8667	−	1.72112i	0.816791	−	0.129367i
$178$		0			0
$179$	5.45364			0.407624			0.203812	−	0.979010i	$-0.434667\pi$
$179$	5.45364			0.407624			0.203812	+	0.979010i	$0.434667\pi$
$180$		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
$183$	−6.64218	−	8.20241i	−0.491004	−	0.606340i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.74704	−	0.736068i	0.200884	−	0.0538266i
$188$		0			0
$189$	13.0843	−	11.7812i	0.951742	−	0.856953i
$190$		0			0
$191$	−21.2673	−	12.2787i	−1.53885	−	0.888456i	−0.998906	−	0.0467550i	$-0.985112\pi$
$191$	−21.2673	−	12.2787i	−1.53885	−	0.888456i	−0.539944	−	0.841701i	$-0.681555\pi$
$192$		0			0
$193$	−1.84237	−	0.493662i	−0.132617	−	0.0355346i	0.191900	−	0.981414i	$-0.438535\pi$
$193$	−1.84237	−	0.493662i	−0.132617	−	0.0355346i	−0.324517	+	0.945880i	$0.605202\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.35836	−	5.35836i	0.381767	−	0.381767i	−0.489971	−	0.871739i	$-0.662993\pi$
$197$	5.35836	−	5.35836i	0.381767	−	0.381767i	0.871739	+	0.489971i	$0.162993\pi$
$198$		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
$203$	−6.94831	+	25.9315i	−0.487676	+	1.82003i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	9.12600	−	5.92650i	0.634301	−	0.411920i
$208$		0			0
$209$	0.933812	−	1.61741i	0.0645931	−	0.111879i
$210$		0			0
$211$	−7.24803	−	12.5540i	−0.498975	−	0.864250i	0.501024	−	0.865433i	$-0.332957\pi$
$211$	−7.24803	−	12.5540i	−0.498975	−	0.864250i	−0.999999	+	0.00118335i	$0.999623\pi$
$212$		0			0
$213$	0.972972	+	0.373489i	0.0666669	+	0.0255910i
$214$		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
$223$	5.24569	+	19.5772i	0.351278	+	1.31099i	0.885105	+	0.465392i	$0.154087\pi$
$223$	5.24569	+	19.5772i	0.351278	+	1.31099i	−0.533827	+	0.845594i	$0.679247\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.26737	+	8.46194i	0.150491	+	0.561639i	0.999449	+	0.0331795i	$0.0105633\pi$
$227$	2.26737	+	8.46194i	0.150491	+	0.561639i	−0.848959	+	0.528459i	$0.822770\pi$
$228$		0			0
$229$	10.2098	−	5.89462i	0.674681	−	0.389527i	−0.123167	−	0.992386i	$-0.539305\pi$
$229$	10.2098	−	5.89462i	0.674681	−	0.389527i	0.797848	+	0.602859i	$0.205972\pi$
$230$		0			0
$231$	1.67163	−	2.30080i	0.109985	−	0.151382i
$232$		0			0
$233$	−9.56964	−	9.56964i	−0.626928	−	0.626928i	0.320366	−	0.947294i	$-0.396194\pi$
$233$	−9.56964	−	9.56964i	−0.626928	−	0.626928i	−0.947294	+	0.320366i	$0.896194\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	18.8143	−	15.2355i	1.22212	−	0.989652i
$238$		0			0
$239$	7.25108	+	12.5592i	0.469034	+	0.812390i	0.999373	−	0.0353952i	$-0.0112690\pi$
$239$	7.25108	+	12.5592i	0.469034	+	0.812390i	−0.530340	+	0.847785i	$0.677936\pi$
$240$		0			0
$241$	6.52918	−	11.3089i	0.420582	−	0.728469i	−0.575415	−	0.817862i	$-0.695159\pi$
$241$	6.52918	−	11.3089i	0.420582	−	0.728469i	0.995996	+	0.0893931i	$0.0284927\pi$
$242$		0			0
$243$	15.0573	+	4.03459i	0.965926	+	0.258819i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.67337	−	9.97717i	0.170103	−	0.634832i
$248$		0			0
$249$	−2.72630	+	25.9390i	−0.172772	+	1.64382i
$250$		0			0
$251$			14.8303i			0.936083i	0.883706	+	0.468042i	$0.155040\pi$
$251$			14.8303i			0.936083i	−0.883706	+	0.468042i	$0.844960\pi$
$252$		0			0
$253$	1.24285	−	1.24285i	0.0781374	−	0.0781374i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.98273	+	1.06717i	0.248436	+	0.0665682i	0.380888	−	0.924621i	$-0.375618\pi$
$257$	3.98273	+	1.06717i	0.248436	+	0.0665682i	−0.132452	+	0.991189i	$0.542285\pi$
$258$		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
$263$	9.80018	−	2.62595i	0.604305	−	0.161923i	0.0563224	−	0.998413i	$-0.482063\pi$
$263$	9.80018	−	2.62595i	0.604305	−	0.161923i	0.547983	+	0.836490i	$0.315396\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.51668	+	22.1867i	−0.521212	+	1.35780i
$268$		0			0
$269$	−5.90783			−0.360207			−0.180103	−	0.983648i	$-0.557643\pi$
$269$	−5.90783			−0.360207			−0.180103	+	0.983648i	$0.557643\pi$
$270$		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
$273$	5.63670	−	14.6841i	0.341149	−	0.888723i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	7.01132	−	1.87868i	0.421269	−	0.112879i	−0.0419558	−	0.999119i	$-0.513359\pi$
$277$	7.01132	−	1.87868i	0.421269	−	0.112879i	0.463225	+	0.886241i	$0.346692\pi$
$278$		0			0
$279$	1.48924	−	7.00631i	0.0891583	−	0.419457i
$280$		0			0
$281$	−2.97782	−	1.71925i	−0.177642	−	0.102562i	0.408542	−	0.912739i	$-0.366037\pi$
$281$	−2.97782	−	1.71925i	−0.177642	−	0.102562i	−0.586184	+	0.810178i	$0.699371\pi$
$282$		0			0
$283$	−4.73926	−	1.26988i	−0.281720	−	0.0754866i	0.115192	−	0.993343i	$-0.463252\pi$
$283$	−4.73926	−	1.26988i	−0.281720	−	0.0754866i	−0.396912	+	0.917857i	$0.629918\pi$
$284$		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
$293$	−3.50273	+	13.0724i	−0.204632	+	0.763696i	0.784930	+	0.619585i	$0.212699\pi$
$293$	−3.50273	+	13.0724i	−0.204632	+	0.763696i	−0.989562	+	0.144111i	$0.953968\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.51450	+	0.131780i	0.145906	+	0.00764663i
$298$		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
$303$	−20.4258	+	16.5405i	−1.17343	+	0.950228i
$304$		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	−0.586367	−	0.810046i	$-0.699442\pi$
$311$	−3.13958	+	1.81264i	−0.178030	+	0.102785i	0.408337	+	0.912831i	$0.366109\pi$
$312$		0			0
$313$	−3.67507	−	13.7155i	−0.207727	−	0.775248i	−0.988601	−	0.150559i	$-0.951893\pi$
$313$	−3.67507	−	13.7155i	−0.207727	−	0.775248i	0.780874	−	0.624689i	$-0.214774\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.82151	+	14.2621i	0.214637	+	0.801038i	0.986294	+	0.164998i	$0.0527618\pi$
$317$	3.82151	+	14.2621i	0.214637	+	0.801038i	−0.771656	+	0.636040i	$0.780572\pi$
$318$		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
$327$	−8.88717	−	3.41147i	−0.491462	−	0.188654i
$328$		0			0
$329$	−1.94138	−	3.36257i	−0.107032	−	0.185385i
$330$		0			0
$331$	−10.6313	+	18.4140i	−0.584350	+	1.01212i	0.410606	+	0.911813i	$0.365317\pi$
$331$	−10.6313	+	18.4140i	−0.584350	+	1.01212i	−0.994956	+	0.100311i	$0.968016\pi$
$332$		0			0
$333$	0.244155	+	4.65875i	0.0133796	+	0.255298i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.40620	+	12.7121i	−0.185548	+	0.692473i	0.808965	+	0.587857i	$0.200028\pi$
$337$	−3.40620	+	12.7121i	−0.185548	+	0.692473i	−0.994513	+	0.104616i	$0.966639\pi$
$338$		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
$347$	−27.5529	−	7.38277i	−1.47912	−	0.396328i	−0.573070	−	0.819506i	$-0.694248\pi$
$347$	−27.5529	−	7.38277i	−1.47912	−	0.396328i	−0.906046	+	0.423178i	$0.860914\pi$
$348$		0			0
$349$	−2.40088	−	1.38615i	−0.128516	−	0.0741988i	0.434364	−	0.900738i	$-0.356973\pi$
$349$	−2.40088	−	1.38615i	−0.128516	−	0.0741988i	−0.562880	+	0.826539i	$0.690307\pi$
$350$		0			0
$351$	13.6215	−	2.89535i	0.727065	−	0.154542i
$352$		0			0
$353$	24.8730	−	6.66469i	1.32385	−	0.354726i	0.473434	−	0.880829i	$-0.343014\pi$
$353$	24.8730	−	6.66469i	1.32385	−	0.354726i	0.850421	+	0.526103i	$0.176347\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−21.6762	−	26.7679i	−1.14723	−	1.41671i
$358$		0			0
$359$	−8.82143			−0.465577			−0.232789	−	0.972527i	$-0.574785\pi$
$359$	−8.82143			−0.465577			−0.232789	+	0.972527i	$0.574785\pi$
$360$		0			0
$361$	4.14590			0.218205
$362$		0			0
$363$	−18.4163	+	2.91685i	−0.966604	+	0.153095i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.03193	+	1.08035i	−0.210465	+	0.0563939i	−0.362511	−	0.931979i	$-0.618080\pi$
$367$	−4.03193	+	1.08035i	−0.210465	+	0.0563939i	0.152046	+	0.988373i	$0.451414\pi$
$368$		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
$373$	16.7765	+	4.49526i	0.868656	+	0.232756i	0.665506	−	0.746392i	$-0.268216\pi$
$373$	16.7765	+	4.49526i	0.868656	+	0.232756i	0.203149	+	0.979148i	$0.434882\pi$
$374$		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
$383$	4.74733	−	17.7173i	0.242577	−	0.905310i	−0.732009	−	0.681295i	$-0.761417\pi$
$383$	4.74733	−	17.7173i	0.242577	−	0.905310i	0.974586	−	0.224015i	$-0.0719164\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−13.8951	+	27.2707i	−0.706329	+	1.38625i
$388$		0			0
$389$	−13.5841	+	23.5283i	−0.688740	+	1.19293i	0.283506	+	0.958970i	$0.408502\pi$
$389$	−13.5841	+	23.5283i	−0.688740	+	1.19293i	−0.972246	+	0.233962i	$0.924831\pi$
$390$		0			0
$391$	−10.6437	−	18.4355i	−0.538276	−	0.932322i
$392$		0			0
$393$	−0.0506097	−	0.319537i	−0.00255292	−	0.0161185i
$394$		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	−0.386675	−	0.922216i	$-0.626377\pi$
$401$	4.37845	−	2.52790i	0.218649	−	0.126237i	0.605325	+	0.795979i	$0.293043\pi$
$402$		0			0
$403$	−1.65615	−	6.18085i	−0.0824988	−	0.307890i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.195032	+	0.727869i	0.00966738	+	0.0360791i
$408$		0			0
$409$	2.02932	−	1.17163i	0.100344	−	0.0579334i	−0.448988	−	0.893538i	$-0.648216\pi$
$409$	2.02932	−	1.17163i	0.100344	−	0.0579334i	0.549332	+	0.835604i	$0.314882\pi$
$410$		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
$417$	2.25106	+	14.2127i	0.110235	+	0.695997i
$418$		0			0
$419$	15.2094	+	26.3435i	0.743028	+	1.28696i	0.951110	+	0.308851i	$0.0999444\pi$
$419$	15.2094	+	26.3435i	0.743028	+	1.28696i	−0.208083	+	0.978111i	$0.566722\pi$
$420$		0			0
$421$	−15.3759	+	26.6318i	−0.749375	+	1.29796i	0.198747	+	0.980051i	$0.436313\pi$
$421$	−15.3759	+	26.6318i	−0.749375	+	1.29796i	−0.948123	+	0.317905i	$0.897021\pi$
$422$		0			0
$423$	1.56068	−	3.06301i	0.0758829	−	0.148929i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.34404	+	19.9442i	−0.258616	+	0.965168i
$428$		0			0
$429$	2.05493	−	0.914914i	0.0992130	−	0.0441725i
$430$		0			0
$431$			17.0019i			0.818952i	0.912321	+	0.409476i	$0.134288\pi$
$431$			17.0019i			0.818952i	−0.912321	+	0.409476i	$0.865712\pi$
$432$		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
$437$	−13.5031	−	3.61816i	−0.645943	−	0.173080i
$438$		0			0
$439$	−22.0369	−	12.7230i	−1.05176	−	0.607235i	−0.128620	−	0.991694i	$-0.541055\pi$
$439$	−22.0369	−	12.7230i	−1.05176	−	0.607235i	−0.923142	+	0.384459i	$0.874388\pi$
$440$		0			0
$441$	−13.1500	−	2.79513i	−0.626192	−	0.133101i
$442$		0			0
$443$	5.93574	−	1.59048i	0.282015	−	0.0755658i	−0.115039	−	0.993361i	$-0.536699\pi$
$443$	5.93574	−	1.59048i	0.282015	−	0.0755658i	0.397054	+	0.917795i	$0.370033\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−13.9945	+	2.21651i	−0.661918	+	0.104838i
$448$		0			0
$449$	−41.0686			−1.93815			−0.969073	−	0.246773i	$-0.920630\pi$
$449$	−41.0686			−1.93815			−0.969073	+	0.246773i	$0.920630\pi$
$450$		0			0
$451$	5.68708			0.267794
$452$		0			0
$453$	−22.9700	−	28.3656i	−1.07923	−	1.33273i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−26.3655	+	7.06463i	−1.23333	+	0.330469i	−0.815875	−	0.578229i	$-0.803744\pi$
$457$	−26.3655	+	7.06463i	−1.23333	+	0.330469i	−0.417454	+	0.908698i	$0.637077\pi$
$458$		0			0
$459$	9.42367	−	29.0031i	0.439859	−	1.35375i
$460$		0			0
$461$	9.54121	+	5.50862i	0.444378	+	0.256562i	0.705453	−	0.708757i	$-0.250744\pi$
$461$	9.54121	+	5.50862i	0.444378	+	0.256562i	−0.261075	+	0.965319i	$0.584077\pi$
$462$		0			0
$463$	13.8596	+	3.71367i	0.644110	+	0.172589i	0.566064	−	0.824361i	$-0.308465\pi$
$463$	13.8596	+	3.71367i	0.644110	+	0.172589i	0.0780455	+	0.996950i	$0.475132\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.87179	+	3.87179i	−0.179165	+	0.179165i	−0.790992	−	0.611827i	$-0.790435\pi$
$467$	−3.87179	+	3.87179i	−0.179165	+	0.179165i	0.611827	+	0.790992i	$0.290435\pi$
$468$		0			0
$469$		−	26.4312i		−	1.22048i
$470$		0			0
$471$	−18.0178	−	13.0907i	−0.830219	−	0.603189i
$472$		0			0
$473$	−1.27955	+	4.77534i	−0.0588337	+	0.219570i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.76504	+	33.6789i	0.0808155	+	1.54205i
$478$		0			0
$479$	18.5611	−	32.1489i	0.848080	−	1.46892i	−0.0348384	−	0.999393i	$-0.511092\pi$
$479$	18.5611	−	32.1489i	0.848080	−	1.46892i	0.882919	−	0.469526i	$-0.155575\pi$
$480$		0			0
$481$	2.08379	+	3.60923i	0.0950126	+	0.164567i
$482$		0			0
$483$	−19.8735	−	7.62874i	−0.904278	−	0.347120i
$484$		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	−0.611514	−	0.791233i	$-0.709439\pi$
$491$	−5.14174	+	2.96859i	−0.232044	+	0.133970i	0.379471	+	0.925204i	$0.376106\pi$
$492$		0			0
$493$	12.0348	+	44.9146i	0.542021	+	2.02285i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.527690	−	1.96937i	−0.0236701	−	0.0883382i
$498$		0			0
$499$	−12.6479	+	7.30225i	−0.566196	+	0.326894i	−0.755629	−	0.655000i	$-0.772669\pi$
$499$	−12.6479	+	7.30225i	−0.566196	+	0.326894i	0.189432	+	0.981894i	$0.439335\pi$
$500$		0			0
$501$	−11.1464	+	15.3417i	−0.497985	+	0.685418i
$502$		0			0
$503$	−0.216785	−	0.216785i	−0.00966595	−	0.00966595i	0.702257	−	0.711923i	$-0.252176\pi$
$503$	−0.216785	−	0.216785i	−0.00966595	−	0.00966595i	−0.711923	+	0.702257i	$0.752176\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.83057	+	6.34107i	−0.347768	+	0.281617i
$508$		0			0
$509$	13.5139	+	23.4067i	0.598993	+	1.03749i	0.992970	+	0.118366i	$0.0377655\pi$
$509$	13.5139	+	23.4067i	0.598993	+	1.03749i	−0.393977	+	0.919120i	$0.628901\pi$
$510$		0			0
$511$	−21.1848	+	36.6932i	−0.937162	+	1.62321i
$512$		0			0
$513$	−9.09184	−	17.8437i	−0.401415	−	0.787821i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	0.143717	−	0.536359i	0.00632067	−	0.0235891i
$518$		0			0
$519$	3.30531	−	31.4480i	0.145087	−	1.38041i
$520$		0			0
$521$			18.7999i			0.823637i	0.911266	+	0.411818i	$0.135106\pi$
$521$			18.7999i			0.823637i	−0.911266	+	0.411818i	$0.864894\pi$
$522$		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
$527$	−13.5352	−	3.62673i	−0.589601	−	0.157983i
$528$		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
$533$	30.3814	−	8.14066i	1.31596	−	0.352611i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	3.38513	−	8.81858i	0.146079	−	0.380550i
$538$		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
$543$	11.8297	−	30.8175i	0.507663	−	1.32251i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	31.1512	−	8.34694i	1.33193	−	0.356890i	0.478496	−	0.878090i	$-0.341182\pi$
$547$	31.1512	−	8.34694i	1.33193	−	0.356890i	0.853434	+	0.521200i	$0.174516\pi$
$548$		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
$553$	−45.7470	−	12.2579i	−1.94536	−	0.521258i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−25.5285	+	25.5285i	−1.08168	+	1.08168i	−0.0853228	+	0.996353i	$0.527192\pi$
$557$	−25.5285	+	25.5285i	−1.08168	+	1.08168i	−0.996353	+	0.0853228i	$0.972808\pi$
$558$		0			0
$559$			27.3423i			1.15645i
$560$		0			0
$561$	0.514893	−	4.89888i	0.0217388	−	0.206831i
$562$		0			0
$563$	7.51116	−	28.0320i	0.316558	−	1.18141i	−0.605973	−	0.795485i	$-0.707216\pi$
$563$	7.51116	−	28.0320i	0.316558	−	1.18141i	0.922530	−	0.385924i	$-0.126117\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−10.9287	−	28.4701i	−0.458960	−	1.19563i
$568$		0			0
$569$	6.44549	−	11.1639i	0.270209	−	0.468016i	−0.698706	−	0.715409i	$-0.746241\pi$
$569$	6.44549	−	11.1639i	0.270209	−	0.468016i	0.968915	+	0.247393i	$0.0795739\pi$
$570$		0			0
$571$	20.9266	+	36.2459i	0.875749	+	1.51684i	0.855963	+	0.517038i	$0.172965\pi$
$571$	20.9266	+	36.2459i	0.875749	+	1.51684i	0.0197865	+	0.999804i	$0.493701\pi$
$572$		0			0
$573$	−33.0557	+	26.7679i	−1.38092	+	1.11825i
$574$		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
$583$	1.40992	+	5.26190i	0.0583930	+	0.217926i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.173044	−	0.645811i	−0.00714231	−	0.0266555i	0.962263	−	0.272122i	$-0.0877255\pi$
$587$	−0.173044	−	0.645811i	−0.00714231	−	0.0266555i	−0.969405	+	0.245467i	$0.921059\pi$
$588$		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	0.997774	−	0.0666826i	$-0.0212415\pi$
$593$	22.6736	+	22.6736i	0.931092	+	0.931092i	−0.0666826	+	0.997774i	$0.521242\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	44.8156	+	17.2031i	1.83418	+	0.704075i
$598$		0			0
$599$	19.7958	+	34.2874i	0.808835	+	1.40094i	0.913671	+	0.406454i	$0.133235\pi$
$599$	19.7958	+	34.2874i	0.808835	+	1.40094i	−0.104836	+	0.994490i	$0.533432\pi$
$600$		0			0
$601$	−2.27721	+	3.94424i	−0.0928893	+	0.160889i	−0.908726	−	0.417394i	$-0.862944\pi$
$601$	−2.27721	+	3.94424i	−0.0928893	+	0.160889i	0.815836	+	0.578283i	$0.196277\pi$
$602$		0			0
$603$	19.6261	−	12.7453i	0.799237	−	0.519031i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−2.63729	+	9.84249i	−0.107044	+	0.399494i	−0.998569	−	0.0534774i	$-0.982969\pi$
$607$	−2.63729	+	9.84249i	−0.107044	+	0.399494i	0.891525	+	0.452972i	$0.149636\pi$
$608$		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
$617$	14.6100	+	3.91474i	0.588176	+	0.157601i	0.540620	−	0.841267i	$-0.318190\pi$
$617$	14.6100	+	3.91474i	0.588176	+	0.157601i	0.0475568	+	0.998869i	$0.484856\pi$
$618$		0			0
$619$	−1.46721	−	0.847096i	−0.0589723	−	0.0340477i	0.470224	−	0.882547i	$-0.344173\pi$
$619$	−1.46721	−	0.847096i	−0.0589723	−	0.0340477i	−0.529196	+	0.848499i	$0.677506\pi$
$620$		0			0
$621$	−3.91858	−	18.4355i	−0.157247	−	0.739790i
$622$		0			0
$623$	44.9075	−	12.0329i	1.79918	−	0.482090i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−2.03574	−	2.51393i	−0.0812995	−	0.100397i
$628$		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
$633$	−24.7988	+	3.92774i	−0.985663	+	0.156114i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−11.6007	+	3.10841i	−0.459638	+	0.123160i
$638$		0			0
$639$	1.20787	−	1.34148i	0.0477826	−	0.0530679i
$640$		0			0
$641$	−19.1025	−	11.0288i	−0.754504	−	0.435613i	0.0728150	−	0.997345i	$-0.476802\pi$
$641$	−19.1025	−	11.0288i	−0.754504	−	0.435613i	−0.827319	+	0.561732i	$0.810135\pi$
$642$		0			0
$643$	−0.135571	−	0.0363262i	−0.00534640	−	0.00143256i	0.256145	−	0.966638i	$-0.417548\pi$
$643$	−0.135571	−	0.0363262i	−0.00534640	−	0.00143256i	−0.261491	+	0.965206i	$0.584214\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	21.4519	−	21.4519i	0.843360	−	0.843360i	−0.145934	−	0.989294i	$-0.546619\pi$
$647$	21.4519	−	21.4519i	0.843360	−	0.843360i	0.989294	+	0.145934i	$0.0466188\pi$
$648$		0			0
$649$		−	3.07810i		−	0.120826i
$650$		0			0
$651$	−12.8012	+	5.69945i	−0.501717	+	0.223379i
$652$		0			0
$653$	−2.42260	+	9.04126i	−0.0948036	+	0.353812i	−0.996990	−	0.0775353i	$-0.975295\pi$
$653$	−2.42260	+	9.04126i	−0.0948036	+	0.353812i	0.902186	+	0.431347i	$0.141962\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−37.4616	+	1.96328i	−1.46151	+	0.0765947i
$658$		0			0
$659$	4.63337	−	8.02524i	0.180491	−	0.312619i	−0.761557	−	0.648098i	$-0.775565\pi$
$659$	4.63337	−	8.02524i	0.180491	−	0.312619i	0.942048	+	0.335479i	$0.108898\pi$
$660$		0			0
$661$	4.88507	+	8.46119i	0.190007	+	0.329102i	0.945252	−	0.326340i	$-0.105816\pi$
$661$	4.88507	+	8.46119i	0.190007	+	0.329102i	−0.755245	+	0.655442i	$0.772482\pi$
$662$		0			0
$663$	−4.26176	−	26.9077i	−0.165513	−	1.04501i
$664$		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
$673$	3.91660	+	14.6169i	0.150974	+	0.563442i	0.999417	+	0.0341547i	$0.0108739\pi$
$673$	3.91660	+	14.6169i	0.150974	+	0.563442i	−0.848443	+	0.529287i	$0.822459\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.14415	−	11.7341i	−0.120839	−	0.450979i	0.878818	−	0.477157i	$-0.158333\pi$
$677$	−3.14415	−	11.7341i	−0.120839	−	0.450979i	−0.999657	+	0.0261785i	$0.991666\pi$
$678$		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	0.712635	−	0.701535i	$-0.247501\pi$
$683$	0.290114	+	0.290114i	0.0111009	+	0.0111009i	−0.701535	+	0.712635i	$0.747501\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−3.19432	−	20.1682i	−0.121871	−	0.769463i
$688$		0			0
$689$	15.0641	+	26.0918i	0.573896	+	0.994017i
$690$		0			0
$691$	2.86257	−	4.95812i	0.108897	−	0.188616i	−0.806426	−	0.591334i	$-0.798601\pi$
$691$	2.86257	−	4.95812i	0.108897	−	0.188616i	0.915324	+	0.402719i	$0.131935\pi$
$692$		0			0
$693$	−2.68282	−	4.13118i	−0.101912	−	0.156930i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	17.8269	−	66.5308i	0.675241	−	2.52003i
$698$		0			0
$699$	−21.4142	+	9.53420i	−0.809958	+	0.360617i
$700$		0			0
$701$			12.5871i			0.475407i	0.971338	+	0.237703i	$0.0763946\pi$
$701$			12.5871i			0.475407i	−0.971338	+	0.237703i	$0.923605\pi$
$702$		0			0
$703$	4.23791	−	4.23791i	0.159836	−	0.159836i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	49.6656	+	13.3078i	1.86787	+	0.500493i
$708$		0			0
$709$	−33.5532	−	19.3719i	−1.26012	−	0.727529i	−0.287020	−	0.957925i	$-0.592665\pi$
$709$	−33.5532	−	19.3719i	−1.26012	−	0.727529i	−0.973097	+	0.230396i	$0.925998\pi$
$710$		0			0
$711$	−12.9577	−	39.8797i	−0.485952	−	1.49561i
$712$		0			0
$713$	−8.36519	+	2.24145i	−0.313279	+	0.0839428i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	24.8092	−	3.92940i	0.926518	−	0.146746i
$718$		0			0
$719$	−18.3617			−0.684776			−0.342388	−	0.939559i	$-0.611236\pi$
$719$	−18.3617			−0.684776			−0.342388	+	0.939559i	$0.611236\pi$
$720$		0			0
$721$	0.680794			0.0253541
$722$		0			0
$723$	−14.2338	−	17.5773i	−0.529361	−	0.653706i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	3.68780	−	0.988143i	0.136773	−	0.0366482i	−0.189783	−	0.981826i	$-0.560778\pi$
$727$	3.68780	−	0.988143i	0.136773	−	0.0366482i	0.326556	+	0.945178i	$0.394112\pi$
$728$		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
$733$	49.1511	+	13.1700i	1.81544	+	0.486444i	0.996206	−	0.0870218i	$-0.0277350\pi$
$733$	49.1511	+	13.1700i	1.81544	+	0.486444i	0.819229	+	0.573466i	$0.194402\pi$
$734$		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
$743$	4.26383	−	15.9128i	0.156425	−	0.583785i	−0.842555	−	0.538611i	$-0.818949\pi$
$743$	4.26383	−	15.9128i	0.156425	−	0.583785i	0.998979	−	0.0451735i	$-0.0143841\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	40.2513	+	20.5091i	1.47272	+	0.750387i
$748$		0			0
$749$	−19.4516	+	33.6911i	−0.710746	+	1.23105i
$750$		0			0
$751$	−14.4753	−	25.0720i	−0.528213	−	0.914892i	−0.999459	−	0.0328898i	$-0.989529\pi$
$751$	−14.4753	−	25.0720i	−0.528213	−	0.914892i	0.471246	−	0.882002i	$-0.343804\pi$
$752$		0			0
$753$	23.9808	+	9.20537i	0.873909	+	0.335462i
$754$		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	−0.588239	−	0.808687i	$-0.700179\pi$
$761$	−5.02110	+	2.89893i	−0.182015	+	0.105086i	0.406224	+	0.913773i	$0.366845\pi$
$762$		0			0
$763$	4.81995	+	17.9883i	0.174494	+	0.651220i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.40609	−	16.4438i	−0.159095	−	0.593750i
$768$		0			0
$769$	32.9790	−	19.0404i	1.18925	−	0.686615i	0.231115	−	0.972926i	$-0.425763\pi$
$769$	32.9790	−	19.0404i	1.18925	−	0.686615i	0.958136	+	0.286312i	$0.0924293\pi$
$770$		0			0
$771$	4.19775	−	5.77771i	0.151178	−	0.208079i
$772$		0			0
$773$	−19.2745	−	19.2745i	−0.693257	−	0.693257i	0.269690	−	0.962947i	$-0.413079\pi$
$773$	−19.2745	−	19.2745i	−0.693257	−	0.693257i	−0.962947	+	0.269690i	$0.913079\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	7.09254	−	5.74342i	0.254443	−	0.206044i
$778$		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
$783$	−2.15462	+	41.1125i	−0.0769997	+	1.46924i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−9.19780	+	34.3267i	−0.327866	+	1.22361i	0.583533	+	0.812089i	$0.301670\pi$
$787$	−9.19780	+	34.3267i	−0.327866	+	1.22361i	−0.911399	+	0.411524i	$0.864997\pi$
$788$		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
$797$	−39.9138	−	10.6949i	−1.41382	−	0.378831i	−0.530531	−	0.847665i	$-0.678008\pi$
$797$	−39.9138	−	10.6949i	−1.41382	−	0.378831i	−0.883286	+	0.468834i	$0.844674\pi$
$798$		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
$803$	−5.85289	+	1.56828i	−0.206544	+	0.0553433i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−3.66706	+	9.55301i	−0.129087	+	0.336282i
$808$		0			0
$809$	−41.5139			−1.45955			−0.729776	−	0.683687i	$-0.760375\pi$
$809$	−41.5139			−1.45955			−0.729776	+	0.683687i	$0.760375\pi$
$810$		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
$813$	−17.5251	+	45.6543i	−0.614631	+	1.60117i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	37.9806	−	10.1769i	1.32877	−	0.356043i
$818$		0			0
$819$	−20.2456	−	18.2292i	−0.707437	−	0.636980i
$820$		0			0
$821$	−26.8095	−	15.4785i	−0.935659	−	0.540203i	−0.0470622	−	0.998892i	$-0.514986\pi$
$821$	−26.8095	−	15.4785i	−0.935659	−	0.540203i	−0.888597	+	0.458689i	$0.848319\pi$
$822$		0			0
$823$	22.6272	+	6.06293i	0.788734	+	0.211341i	0.630632	−	0.776082i	$-0.282796\pi$
$823$	22.6272	+	6.06293i	0.788734	+	0.211341i	0.158102	+	0.987423i	$0.449463\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.0194	−	22.0194i	0.765690	−	0.765690i	−0.211654	−	0.977345i	$-0.567885\pi$
$827$	22.0194	−	22.0194i	0.765690	−	0.765690i	0.977345	+	0.211654i	$0.0678851\pi$
$828$		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
$833$	−6.80696	+	25.4039i	−0.235847	+	0.880194i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−10.4049	−	6.75701i	−0.359645	−	0.233556i
$838$		0			0
$839$	−11.8643	+	20.5496i	−0.409601	+	0.709450i	−0.994845	−	0.101407i	$-0.967665\pi$
$839$	−11.8643	+	20.5496i	−0.409601	+	0.709450i	0.585244	+	0.810857i	$0.300999\pi$
$840$		0			0
$841$	−16.8867	−	29.2487i	−0.582301	−	1.00858i
$842$		0			0
$843$	−4.62841	+	3.74801i	−0.159411	+	0.129088i
$844$		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
$853$	4.94766	+	18.4649i	0.169405	+	0.632227i	0.997437	+	0.0715468i	$0.0227935\pi$
$853$	4.94766	+	18.4649i	0.169405	+	0.632227i	−0.828033	+	0.560680i	$0.810540\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.25353	−	30.8026i	−0.281935	−	1.05220i	−0.951050	−	0.309037i	$-0.899993\pi$
$857$	−8.25353	−	30.8026i	−0.281935	−	1.05220i	0.669115	−	0.743159i	$-0.266673\pi$
$858$		0			0
$859$	−14.2177	+	8.20859i	−0.485101	+	0.280073i	−0.722540	−	0.691329i	$-0.757026\pi$
$859$	−14.2177	+	8.20859i	−0.485101	+	0.280073i	0.237439	+	0.971403i	$0.423692\pi$
$860$		0			0
$861$	−28.0151	−	62.9229i	−0.954752	−	2.14441i
$862$		0			0
$863$	9.10066	+	9.10066i	0.309790	+	0.309790i	0.844828	−	0.535038i	$-0.179703\pi$
$863$	9.10066	+	9.10066i	0.309790	+	0.309790i	−0.535038	+	0.844828i	$0.679703\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−28.2068	−	10.8276i	−0.957953	−	0.367724i
$868$		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
$873$	0.369702	+	0.188373i	0.0125125	+	0.00637545i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.78909	−	14.1411i	0.127948	−	0.477510i	−0.871979	−	0.489543i	$-0.837164\pi$
$877$	3.78909	−	14.1411i	0.127948	−	0.477510i	0.999928	+	0.0120331i	$0.00383036\pi$
$878$		0			0
$879$	18.9639	+	13.7781i	0.639638	+	0.464724i
$880$		0			0
$881$			17.7146i			0.596820i	0.954438	+	0.298410i	$0.0964563\pi$
$881$			17.7146i			0.596820i	−0.954438	+	0.298410i	$0.903544\pi$
$882$		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
$887$	−3.38530	−	0.907087i	−0.113667	−	0.0304570i	0.201537	−	0.979481i	$-0.435406\pi$
$887$	−3.38530	−	0.907087i	−0.113667	−	0.0304570i	−0.315204	+	0.949024i	$0.602073\pi$
$888$		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
$893$	−4.26592	+	1.14305i	−0.142754	+	0.0382507i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−10.5960	−	13.0849i	−0.353789	−	0.436893i
$898$		0			0
$899$	18.9170			0.630917
$900$		0			0
$901$	65.9763			2.19799
$902$		0			0
$903$	59.1384	−	9.36661i	1.96800	−	0.311701i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−18.8061	+	5.03909i	−0.624447	+	0.167320i	−0.557149	−	0.830413i	$-0.688105\pi$
$907$	−18.8061	+	5.03909i	−0.624447	+	0.167320i	−0.0672984	+	0.997733i	$0.521438\pi$
$908$		0			0
$909$	14.0676	+	43.2956i	0.466593	+	1.43603i
$910$		0			0
$911$	−1.48726	−	0.858672i	−0.0492753	−	0.0284491i	0.475160	−	0.879899i	$-0.342390\pi$
$911$	−1.48726	−	0.858672i	−0.0492753	−	0.0284491i	−0.524435	+	0.851450i	$0.675724\pi$
$912$		0			0
$913$	7.04835	+	1.88860i	0.233266	+	0.0625035i
$914$		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
$923$	0.417373	−	1.55766i	0.0137380	−	0.0512709i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.328285	+	0.505514i	0.0107823	+	0.0166033i
$928$		0			0
$929$	3.64047	−	6.30549i	0.119440	−	0.206876i	−0.800106	−	0.599859i	$-0.795223\pi$
$929$	3.64047	−	6.30549i	0.119440	−	0.206876i	0.919546	+	0.392983i	$0.128557\pi$
$930$		0			0
$931$	8.63564	+	14.9574i	0.283022	+	0.490208i
$932$		0			0
$933$	0.982278	+	6.20186i	0.0321584	+	0.203040i
$934$		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	0.205754	−	0.978604i	$-0.434035\pi$
$941$	35.4650	−	20.4757i	1.15613	−	0.667490i	0.950373	+	0.311114i	$0.100702\pi$
$942$		0			0
$943$	−11.0176	−	41.1183i	−0.358783	−	1.33900i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.0258	+	37.4169i	0.325795	+	1.21588i	0.913510	+	0.406816i	$0.133361\pi$
$947$	10.0258	+	37.4169i	0.325795	+	1.21588i	−0.587715	+	0.809068i	$0.699972\pi$
$948$		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	0.844922	−	0.534890i	$-0.179647\pi$
$953$	9.57092	+	9.57092i	0.310032	+	0.310032i	−0.534890	+	0.844922i	$0.679647\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1.04027	+	6.56802i	0.0336272	+	0.212314i
$958$		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
$963$	−34.3966	+	1.80265i	−1.10842	+	0.0580896i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	8.75325	−	32.6676i	0.281485	−	1.05052i	−0.669884	−	0.742466i	$-0.733656\pi$
$967$	8.75325	−	32.6676i	0.281485	−	1.05052i	0.951369	−	0.308052i	$-0.0996771\pi$
$968$		0			0
$969$	−35.7907	+	15.9350i	−1.14976	+	0.511907i
$970$		0			0
$971$		−	30.6923i		−	0.984964i	−0.870323	−	0.492482i	$-0.836090\pi$
$971$		−	30.6923i		−	0.984964i	0.870323	−	0.492482i	$-0.163910\pi$
$972$		0			0
$973$	19.9056	−	19.9056i	0.638143	−	0.638143i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	6.24481	+	1.67329i	0.199789	+	0.0535334i	0.357326	−	0.933980i	$-0.383689\pi$
$977$	6.24481	+	1.67329i	0.199789	+	0.0535334i	−0.157537	+	0.987513i	$0.550355\pi$
$978$		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
$983$	−5.65254	+	1.51459i	−0.180288	+	0.0483081i	−0.347834	−	0.937556i	$-0.613083\pi$
$983$	−5.65254	+	1.51459i	−0.180288	+	0.0483081i	0.167545	+	0.985864i	$0.446416\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−6.64235	+	1.05204i	−0.211428	+	0.0334869i
$988$		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
$993$	23.1766	+	28.6207i	0.735486	+	0.908250i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−2.07511	+	0.556025i	−0.0657195	+	0.0176095i	−0.291529	−	0.956562i	$-0.594164\pi$
$997$	−2.07511	+	0.556025i	−0.0657195	+	0.0176095i	0.225809	+	0.974171i	$0.427497\pi$
$998$		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.857.5	yes	32
3.2	odd	2		2700.2.bf.f.2357.1		32
5.2	odd	4	inner	900.2.be.f.893.1	yes	32
5.3	odd	4	inner	900.2.be.f.893.8	yes	32
5.4	even	2	inner	900.2.be.f.857.4	yes	32
9.4	even	3		2700.2.bf.f.557.8		32
9.5	odd	6	inner	900.2.be.f.257.8	yes	32
15.2	even	4		2700.2.bf.f.1493.1		32
15.8	even	4		2700.2.bf.f.1493.8		32
15.14	odd	2		2700.2.bf.f.2357.8		32
45.4	even	6		2700.2.bf.f.557.1		32
45.13	odd	12		2700.2.bf.f.2393.1		32
45.14	odd	6	inner	900.2.be.f.257.1	✓	32
45.22	odd	12		2700.2.bf.f.2393.8		32
45.23	even	12	inner	900.2.be.f.293.5	yes	32
45.32	even	12	inner	900.2.be.f.293.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
900.2.be.f.257.1	✓	32	45.14	odd	6	inner
900.2.be.f.257.8	yes	32	9.5	odd	6	inner
900.2.be.f.293.4	yes	32	45.32	even	12	inner
900.2.be.f.293.5	yes	32	45.23	even	12	inner
900.2.be.f.857.4	yes	32	5.4	even	2	inner
900.2.be.f.857.5	yes	32	1.1	even	1	trivial
900.2.be.f.893.1	yes	32	5.2	odd	4	inner
900.2.be.f.893.8	yes	32	5.3	odd	4	inner
2700.2.bf.f.557.1		32	45.4	even	6
2700.2.bf.f.557.8		32	9.4	even	3
2700.2.bf.f.1493.1		32	15.2	even	4
2700.2.bf.f.1493.8		32	15.8	even	4
2700.2.bf.f.2357.1		32	3.2	odd	2
2700.2.bf.f.2357.8		32	15.14	odd	2
2700.2.bf.f.2393.1		32	45.13	odd	12
2700.2.bf.f.2393.8		32	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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

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