LMFDB - Embedded newform 2548.2.bq.e.1941.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(361,2548)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2548, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2548.361"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2548 = 2^{2} \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2548.bq (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,28,0,0,0,10] 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:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 38x^{14} + 587x^{12} + 4762x^{10} + 21849x^{8} + 56552x^{6} + 76456x^{4} + 42624x^{2} + 2704 $ x^16 + 38x^14 + 587x^12 + 4762x^10 + 21849x^8 + 56552x^6 + 76456x^4 + 42624*x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1941.8
Root			$3.23100i$ of defining polynomial
Character	$\chi$	$=$	2548.1941
Dual form			2548.2.bq.e.361.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.23100 q^{3} +(2.72598 + 1.57385i) q^{5} +7.43937 q^{9} +3.84820i q^{11} +(1.38576 - 3.32861i) q^{13} +(8.80765 + 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +6.15618i q^{19} +(-4.01081 - 6.94693i) q^{23} +(2.45398 + 4.25042i) q^{25} +14.3436 q^{27} +(1.35952 - 2.35475i) q^{29} +(-7.37569 + 4.25836i) q^{31} +12.4335i q^{33} +(-3.10928 + 1.79515i) q^{37} +(4.47739 - 10.7548i) q^{39} +(-3.44934 - 1.99148i) q^{41} +(-5.74755 - 9.95506i) q^{43} +(20.2796 + 11.7084i) q^{45} +(-3.76830 - 2.17563i) q^{47} +(0.314003 - 0.543869i) q^{51} +(0.288402 + 0.499526i) q^{53} +(-6.05647 + 10.4901i) q^{55} +19.8906i q^{57} +(-1.80715 - 1.04336i) q^{59} +3.40510 q^{61} +(9.01628 - 6.89277i) q^{65} -5.42026i q^{67} +(-12.9589 - 22.4456i) q^{69} +(-7.92574 + 4.57593i) q^{71} +(2.86835 - 1.65604i) q^{73} +(7.92882 + 13.7331i) q^{75} +(4.49376 - 7.78342i) q^{79} +24.0261 q^{81} -7.66353i q^{83} +(0.529845 - 0.305906i) q^{85} +(4.39260 - 7.60821i) q^{87} +(-4.42996 + 2.55764i) q^{89} +(-23.8309 + 13.7588i) q^{93} +(-9.68888 + 16.7816i) q^{95} +(8.33696 - 4.81334i) q^{97} +28.6282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	3.23100			1.86542			0.932710	−	0.360628i	$-0.117438\pi$
$3$	3.23100			1.86542			0.932710	+	0.360628i	$0.117438\pi$
$4$		0			0
$5$	2.72598	+	1.57385i	1.21910	+	0.703845i	0.964725	−	0.263261i	$-0.0847982\pi$
$5$	2.72598	+	1.57385i	1.21910	+	0.703845i	0.254371	+	0.967107i	$0.418131\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	7.43937			2.47979
$10$		0			0
$11$			3.84820i			1.16028i	0.814518	+	0.580138i	$0.197001\pi$
$11$			3.84820i			1.16028i	−0.814518	+	0.580138i	$0.802999\pi$
$12$		0			0
$13$	1.38576	−	3.32861i	0.384340	−	0.923191i
$13$	1.38576	−	3.32861i	0.384340	−	0.923191i
$14$		0			0
$15$	8.80765	+	5.08510i	2.27412	+	1.31297i
$16$		0			0
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	−0.853999	−	0.520274i	$-0.825830\pi$
$17$	0.0971843	−	0.168328i	0.0235707	−	0.0408256i	0.877570	+	0.479448i	$0.159163\pi$
$18$		0			0
$19$			6.15618i			1.41232i	0.708050	+	0.706162i	$0.249575\pi$
$19$			6.15618i			1.41232i	−0.708050	+	0.706162i	$0.750425\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.01081	−	6.94693i	−0.836313	−	1.44854i	−0.892957	−	0.450141i	$-0.851374\pi$
$23$	−4.01081	−	6.94693i	−0.836313	−	1.44854i	0.0566448	−	0.998394i	$-0.481960\pi$
$24$		0			0
$25$	2.45398	+	4.25042i	0.490796	+	0.850084i
$26$		0			0
$27$	14.3436			2.76043
$28$		0			0
$29$	1.35952	−	2.35475i	0.252456	−	0.437267i	−0.711745	−	0.702438i	$-0.752095\pi$
$29$	1.35952	−	2.35475i	0.252456	−	0.437267i	0.964201	+	0.265171i	$0.0854283\pi$
$30$		0			0
$31$	−7.37569	+	4.25836i	−1.32471	+	0.764823i	−0.984476	−	0.175517i	$-0.943840\pi$
$31$	−7.37569	+	4.25836i	−1.32471	+	0.764823i	−0.340236	+	0.940340i	$0.610507\pi$
$32$		0			0
$33$			12.4335i			2.16440i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.10928	+	1.79515i	−0.511163	+	0.295120i	−0.733312	−	0.679893i	$-0.762026\pi$
$37$	−3.10928	+	1.79515i	−0.511163	+	0.295120i	0.222149	+	0.975013i	$0.428693\pi$
$38$		0			0
$39$	4.47739	−	10.7548i	0.716956	−	1.72214i
$40$		0			0
$41$	−3.44934	−	1.99148i	−0.538696	−	0.311016i	0.205854	−	0.978583i	$-0.434003\pi$
$41$	−3.44934	−	1.99148i	−0.538696	−	0.311016i	−0.744550	+	0.667566i	$0.767336\pi$
$42$		0			0
$43$	−5.74755	−	9.95506i	−0.876494	−	1.51813i	−0.855163	−	0.518359i	$-0.826543\pi$
$43$	−5.74755	−	9.95506i	−0.876494	−	1.51813i	−0.0213310	−	0.999772i	$-0.506790\pi$
$44$		0			0
$45$	20.2796	+	11.7084i	3.02310	+	1.74539i
$46$		0			0
$47$	−3.76830	−	2.17563i	−0.549663	−	0.317348i	0.199323	−	0.979934i	$-0.436126\pi$
$47$	−3.76830	−	2.17563i	−0.549663	−	0.317348i	−0.748986	+	0.662586i	$0.769459\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.314003	−	0.543869i	0.0439692	−	0.0761568i
$52$		0			0
$53$	0.288402	+	0.499526i	0.0396150	+	0.0686152i	0.885153	−	0.465300i	$-0.154054\pi$
$53$	0.288402	+	0.499526i	0.0396150	+	0.0686152i	−0.845538	+	0.533915i	$0.820720\pi$
$54$		0			0
$55$	−6.05647	+	10.4901i	−0.816655	+	1.41449i
$56$		0			0
$57$			19.8906i			2.63458i
$58$		0			0
$59$	−1.80715	−	1.04336i	−0.235271	−	0.135834i	0.377730	−	0.925916i	$-0.376705\pi$
$59$	−1.80715	−	1.04336i	−0.235271	−	0.135834i	−0.613002	+	0.790082i	$0.710038\pi$
$60$		0			0
$61$	3.40510			0.435979			0.217989	−	0.975951i	$-0.430050\pi$
$61$	3.40510			0.435979			0.217989	+	0.975951i	$0.430050\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.01628	−	6.89277i	1.11833	−	0.854943i
$66$		0			0
$67$		−	5.42026i		−	0.662190i	−0.943597	−	0.331095i	$-0.892582\pi$
$67$		−	5.42026i		−	0.662190i	0.943597	−	0.331095i	$-0.107418\pi$
$68$		0			0
$69$	−12.9589	−	22.4456i	−1.56007	−	2.70213i
$70$		0			0
$71$	−7.92574	+	4.57593i	−0.940612	+	0.543063i	−0.890152	−	0.455663i	$-0.849402\pi$
$71$	−7.92574	+	4.57593i	−0.940612	+	0.543063i	−0.0504599	+	0.998726i	$0.516069\pi$
$72$		0			0
$73$	2.86835	−	1.65604i	0.335715	−	0.193825i	−0.322661	−	0.946515i	$-0.604577\pi$
$73$	2.86835	−	1.65604i	0.335715	−	0.193825i	0.658376	+	0.752690i	$0.271244\pi$
$74$		0			0
$75$	7.92882	+	13.7331i	0.915541	+	1.58576i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.49376	−	7.78342i	0.505587	−	0.875703i	−0.494392	−	0.869239i	$-0.664609\pi$
$79$	4.49376	−	7.78342i	0.505587	−	0.875703i	0.999979	−	0.00646364i	$-0.00205746\pi$
$80$		0			0
$81$	24.0261			2.66957
$82$		0			0
$83$		−	7.66353i		−	0.841181i	−0.907251	−	0.420591i	$-0.861823\pi$
$83$		−	7.66353i		−	0.841181i	0.907251	−	0.420591i	$-0.138177\pi$
$84$		0			0
$85$	0.529845	−	0.305906i	0.0574698	−	0.0331802i
$86$		0			0
$87$	4.39260	−	7.60821i	0.470936	−	0.815686i
$88$		0			0
$89$	−4.42996	+	2.55764i	−0.469574	+	0.271109i	−0.716062	−	0.698037i	$-0.754057\pi$
$89$	−4.42996	+	2.55764i	−0.469574	+	0.271109i	0.246487	+	0.969146i	$0.420724\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−23.8309	+	13.7588i	−2.47114	+	1.42672i
$94$		0			0
$95$	−9.68888	+	16.7816i	−0.994058	+	1.72176i
$96$		0			0
$97$	8.33696	−	4.81334i	0.846490	−	0.488721i	−0.0129752	−	0.999916i	$-0.504130\pi$
$97$	8.33696	−	4.81334i	0.846490	−	0.488721i	0.859465	+	0.511195i	$0.170797\pi$
$98$		0			0
$99$			28.6282i			2.87724i
$100$		0			0
$101$	2.54158			0.252896			0.126448	−	0.991973i	$-0.459642\pi$
$101$	2.54158			0.252896			0.126448	+	0.991973i	$0.459642\pi$
$102$		0			0
$103$	−1.67696	+	2.90458i	−0.165236	+	0.286197i	−0.936739	−	0.350029i	$-0.886172\pi$
$103$	−1.67696	+	2.90458i	−0.165236	+	0.286197i	0.771503	+	0.636225i	$0.219505\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.45650	+	11.1830i	0.624174	+	1.08110i	0.988700	+	0.149907i	$0.0478975\pi$
$107$	6.45650	+	11.1830i	0.624174	+	1.08110i	−0.364526	+	0.931193i	$0.618769\pi$
$108$		0			0
$109$	6.96516	−	4.02134i	0.667141	−	0.385174i	−0.127851	−	0.991793i	$-0.540808\pi$
$109$	6.96516	−	4.02134i	0.667141	−	0.385174i	0.794993	+	0.606619i	$0.207475\pi$
$110$		0			0
$111$	−10.0461	+	5.80012i	−0.953534	+	0.550523i
$112$		0			0
$113$	4.00235	+	6.93227i	0.376509	+	0.652133i	0.990552	−	0.137140i	$-0.0437910\pi$
$113$	4.00235	+	6.93227i	0.376509	+	0.652133i	−0.614043	+	0.789273i	$0.710458\pi$
$114$		0			0
$115$		−	25.2496i		−	2.35454i
$116$		0			0
$117$	10.3092	−	24.7628i	0.953083	−	2.28932i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−3.80865			−0.346241
$122$		0			0
$123$	−11.1448	−	6.43446i	−1.00489	−	0.580176i
$124$		0			0
$125$		−	0.289701i		−	0.0259116i
$126$		0			0
$127$	0.664383	−	1.15075i	0.0589545	−	0.102112i	−0.835042	−	0.550186i	$-0.814557\pi$
$127$	0.664383	−	1.15075i	0.0589545	−	0.102112i	0.893996	+	0.448074i	$0.147890\pi$
$128$		0			0
$129$	−18.5704	−	32.1648i	−1.63503	−	2.83195i
$130$		0			0
$131$	0.296380	−	0.513346i	0.0258949	−	0.0448512i	−0.852788	−	0.522258i	$-0.825090\pi$
$131$	0.296380	−	0.513346i	0.0258949	−	0.0448512i	0.878682	+	0.477407i	$0.158423\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	39.1004	+	22.5746i	3.36523	+	1.94291i
$136$		0			0
$137$	2.21732	+	1.28017i	0.189439	+	0.109372i	0.591720	−	0.806144i	$-0.298449\pi$
$137$	2.21732	+	1.28017i	0.189439	+	0.109372i	−0.402281	+	0.915516i	$0.631783\pi$
$138$		0			0
$139$	9.01150	+	15.6084i	0.764345	+	1.32388i	0.940592	+	0.339538i	$0.110271\pi$
$139$	9.01150	+	15.6084i	0.764345	+	1.32388i	−0.176247	+	0.984346i	$0.556396\pi$
$140$		0			0
$141$	−12.1754	−	7.02946i	−1.02535	−	0.591987i
$142$		0			0
$143$	12.8092	+	5.33268i	1.07116	+	0.445941i
$144$		0			0
$145$	7.41204	−	4.27934i	0.615536	−	0.355380i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			8.10789i			0.664224i	0.943240	+	0.332112i	$0.107761\pi$
$149$			8.10789i			0.664224i	−0.943240	+	0.332112i	$0.892239\pi$
$150$		0			0
$151$	3.10734	−	1.79402i	0.252872	−	0.145995i	−0.368207	−	0.929744i	$-0.620028\pi$
$151$	3.10734	−	1.79402i	0.252872	−	0.145995i	0.621078	+	0.783748i	$0.286695\pi$
$152$		0			0
$153$	0.722990	−	1.25226i	0.0584503	−	0.101239i
$154$		0			0
$155$	−26.8080			−2.15327
$156$		0			0
$157$	−7.17236	−	12.4229i	−0.572417	−	0.991455i	−0.996317	−	0.0857459i	$-0.972673\pi$
$157$	−7.17236	−	12.4229i	−0.572417	−	0.991455i	0.423900	−	0.905709i	$-0.360661\pi$
$158$		0			0
$159$	0.931826	+	1.61397i	0.0738986	+	0.127996i
$160$		0			0
$161$		0			0
$162$		0			0
$163$			0.246141i			0.0192792i	0.999954	+	0.00963961i	$0.00306843\pi$
$163$			0.246141i			0.0192792i	−0.999954	+	0.00963961i	$0.996932\pi$
$164$		0			0
$165$	−19.5685	+	33.8936i	−1.52340	+	2.63861i
$166$		0			0
$167$	1.56604	+	0.904156i	0.121184	+	0.0699657i	0.559367	−	0.828920i	$-0.311044\pi$
$167$	1.56604	+	0.904156i	0.121184	+	0.0699657i	−0.438183	+	0.898886i	$0.644378\pi$
$168$		0			0
$169$	−9.15934	−	9.22532i	−0.704565	−	0.709640i
$170$		0			0
$171$			45.7981i			3.50227i
$172$		0			0
$173$	10.7996			0.821080			0.410540	−	0.911843i	$-0.365340\pi$
$173$	10.7996			0.821080			0.410540	+	0.911843i	$0.365340\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−5.83892	−	3.37110i	−0.438880	−	0.253387i
$178$		0			0
$179$	−8.67647			−0.648510			−0.324255	−	0.945970i	$-0.605114\pi$
$179$	−8.67647			−0.648510			−0.324255	+	0.945970i	$0.605114\pi$
$180$		0			0
$181$	−10.0087			−0.743940			−0.371970	−	0.928245i	$-0.621318\pi$
$181$	−10.0087			−0.743940			−0.371970	+	0.928245i	$0.621318\pi$
$182$		0			0
$183$	11.0019			0.813283
$184$		0			0
$185$	−11.3011			−0.830876
$186$		0			0
$187$	0.647761	+	0.373985i	0.0473690	+	0.0273485i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−24.0312			−1.73884			−0.869420	−	0.494074i	$-0.835507\pi$
$191$	−24.0312			−1.73884			−0.869420	+	0.494074i	$0.835507\pi$
$192$		0			0
$193$			3.27308i			0.235601i	0.993037	+	0.117801i	$0.0375844\pi$
$193$			3.27308i			0.235601i	−0.993037	+	0.117801i	$0.962416\pi$
$194$		0			0
$195$	29.1316	−	22.2705i	2.08616	−	1.59483i
$196$		0			0
$197$	11.0439	+	6.37619i	0.786844	+	0.454285i	0.838850	−	0.544362i	$-0.183228\pi$
$197$	11.0439	+	6.37619i	0.786844	+	0.454285i	−0.0520061	+	0.998647i	$0.516562\pi$
$198$		0			0
$199$	13.6616	−	23.6625i	0.968442	−	1.67739i	0.268373	−	0.963315i	$-0.413514\pi$
$199$	13.6616	−	23.6625i	0.968442	−	1.67739i	0.700069	−	0.714076i	$-0.253153\pi$
$200$		0			0
$201$		−	17.5129i		−	1.23526i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−6.26855	−	10.8575i	−0.437815	−	0.758317i
$206$		0			0
$207$	−29.8379	−	51.6808i	−2.07388	−	3.59206i
$208$		0			0
$209$	−23.6902			−1.63869
$210$		0			0
$211$	−13.2929	+	23.0239i	−0.915118	+	1.58503i	−0.108390	+	0.994108i	$0.534570\pi$
$211$	−13.2929	+	23.0239i	−0.915118	+	1.58503i	−0.806728	+	0.590923i	$0.798764\pi$
$212$		0			0
$213$	−25.6081	+	14.7848i	−1.75464	+	1.01304i
$214$		0			0
$215$		−	36.1831i		−	2.46766i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	9.26764	−	5.35068i	0.626249	−	0.361565i
$220$		0			0
$221$	−0.425626	−	0.556751i	−0.0286307	−	0.0374512i
$222$		0			0
$223$	13.1063	+	7.56691i	0.877661	+	0.506718i	0.869887	−	0.493252i	$-0.164192\pi$
$223$	13.1063	+	7.56691i	0.877661	+	0.506718i	0.00777474	+	0.999970i	$0.497525\pi$
$224$		0			0
$225$	18.2561	+	31.6205i	1.21707	+	2.10803i
$226$		0			0
$227$	18.5376	+	10.7027i	1.23038	+	0.710362i	0.967110	−	0.254359i	$-0.0818644\pi$
$227$	18.5376	+	10.7027i	1.23038	+	0.710362i	0.263274	+	0.964721i	$0.415198\pi$
$228$		0			0
$229$	−7.24104	−	4.18062i	−0.478501	−	0.276263i	0.241290	−	0.970453i	$-0.422429\pi$
$229$	−7.24104	−	4.18062i	−0.478501	−	0.276263i	−0.719792	+	0.694190i	$0.755763\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.0832	+	22.6607i	−0.857107	+	1.48455i	0.0175695	+	0.999846i	$0.494407\pi$
$233$	−13.0832	+	22.6607i	−0.857107	+	1.48455i	−0.874676	+	0.484707i	$0.838926\pi$
$234$		0			0
$235$	−6.84821	−	11.8614i	−0.446728	−	0.773756i
$236$		0			0
$237$	14.5193	−	25.1482i	0.943132	−	1.63355i
$238$		0			0
$239$		−	18.3562i		−	1.18736i	−0.804700	−	0.593682i	$-0.797674\pi$
$239$		−	18.3562i		−	1.18736i	0.804700	−	0.593682i	$-0.202326\pi$
$240$		0			0
$241$	2.88804	+	1.66741i	0.186035	+	0.107407i	0.590125	−	0.807312i	$-0.299078\pi$
$241$	2.88804	+	1.66741i	0.186035	+	0.107407i	−0.404090	+	0.914719i	$0.632412\pi$
$242$		0			0
$243$	34.5975			2.21943
$244$		0			0
$245$		0			0
$246$		0			0
$247$	20.4915	+	8.53098i	1.30385	+	0.542813i
$248$		0			0
$249$		−	24.7609i		−	1.56916i
$250$		0			0
$251$	−6.09884	−	10.5635i	−0.384956	−	0.666763i	0.606807	−	0.794849i	$-0.292450\pi$
$251$	−6.09884	−	10.5635i	−0.384956	−	0.666763i	−0.991763	+	0.128086i	$0.959117\pi$
$252$		0			0
$253$	26.7332	−	15.4344i	1.68070	−	0.970353i
$254$		0			0
$255$	1.71193	−	0.988384i	0.107205	−	0.0618950i
$256$		0			0
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	0.999633	−	0.0270962i	$-0.00862605\pi$
$257$	7.63648	+	13.2268i	0.476350	+	0.825063i	−0.523282	+	0.852159i	$0.675293\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.1140	−	17.5179i	0.626038	−	1.08433i
$262$		0			0
$263$	24.8989			1.53533			0.767666	−	0.640850i	$-0.221418\pi$
$263$	24.8989			1.53533			0.767666	+	0.640850i	$0.221418\pi$
$264$		0			0
$265$			1.81560i			0.111531i
$266$		0			0
$267$	−14.3132	+	8.26373i	−0.875953	+	0.505732i
$268$		0			0
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	−0.721059	−	0.692874i	$-0.756344\pi$
$269$	3.92836	−	6.80413i	0.239517	−	0.414855i	0.960576	+	0.278019i	$0.0896777\pi$
$270$		0			0
$271$	−2.28514	+	1.31933i	−0.138812	+	0.0801433i	−0.567798	−	0.823168i	$-0.692204\pi$
$271$	−2.28514	+	1.31933i	−0.138812	+	0.0801433i	0.428986	+	0.903311i	$0.358871\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−16.3565	+	9.44342i	−0.986333	+	0.569459i
$276$		0			0
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	−0.636137	−	0.771576i	$-0.719469\pi$
$277$	5.82743	−	10.0934i	0.350136	−	0.606454i	0.986273	+	0.165122i	$0.0528019\pi$
$278$		0			0
$279$	−54.8705	+	31.6795i	−3.28501	+	1.89660i
$280$		0			0
$281$		−	3.86501i		−	0.230567i	−0.993333	−	0.115283i	$-0.963222\pi$
$281$		−	3.86501i		−	0.230567i	0.993333	−	0.115283i	$-0.0367776\pi$
$282$		0			0
$283$	−6.84863			−0.407109			−0.203554	−	0.979064i	$-0.565249\pi$
$283$	−6.84863			−0.407109			−0.203554	+	0.979064i	$0.565249\pi$
$284$		0			0
$285$	−31.3048	+	54.2215i	−1.85433	+	3.21180i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.48111	+	14.6897i	0.498889	+	0.864101i
$290$		0			0
$291$	26.9367	−	15.5519i	1.57906	−	0.911670i
$292$		0			0
$293$	1.28946	−	0.744468i	0.0753309	−	0.0434923i	−0.461861	−	0.886952i	$-0.652818\pi$
$293$	1.28946	−	0.744468i	0.0753309	−	0.0434923i	0.537192	+	0.843460i	$0.319485\pi$
$294$		0			0
$295$	−3.28418	−	5.68836i	−0.191212	−	0.331189i
$296$		0			0
$297$			55.1971i			3.20286i
$298$		0			0
$299$	−28.6817	+	3.72367i	−1.65870	+	0.215346i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	8.21183			0.471757
$304$		0			0
$305$	9.28225	+	5.35911i	0.531500	+	0.306862i
$306$		0			0
$307$		−	2.33128i		−	0.133053i	−0.997785	−	0.0665265i	$-0.978808\pi$
$307$		−	2.33128i		−	0.133053i	0.997785	−	0.0665265i	$-0.0211917\pi$
$308$		0			0
$309$	−5.41826	+	9.38470i	−0.308234	+	0.533877i
$310$		0			0
$311$	−5.91221	−	10.2403i	−0.335251	−	0.580672i	0.648282	−	0.761400i	$-0.275488\pi$
$311$	−5.91221	−	10.2403i	−0.335251	−	0.580672i	−0.983533	+	0.180729i	$0.942154\pi$
$312$		0			0
$313$	9.20434	−	15.9424i	0.520260	−	0.901117i	−0.479462	−	0.877563i	$-0.659168\pi$
$313$	9.20434	−	15.9424i	0.520260	−	0.901117i	0.999723	−	0.0235548i	$-0.00749841\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.29431	−	4.21137i	−0.409689	−	0.236534i	0.280967	−	0.959717i	$-0.409345\pi$
$317$	−7.29431	−	4.21137i	−0.409689	−	0.236534i	−0.690656	+	0.723183i	$0.742678\pi$
$318$		0			0
$319$	9.06156	+	5.23170i	0.507350	+	0.292919i
$320$		0			0
$321$	20.8610	+	36.1323i	1.16435	+	2.01671i
$322$		0			0
$323$	1.03626	+	0.598284i	0.0576590	+	0.0332894i
$324$		0			0
$325$	17.5486	−	2.27830i	0.973423	−	0.126377i
$326$		0			0
$327$	22.5044	−	12.9929i	1.24450	−	0.718512i
$328$		0			0
$329$		0			0
$330$		0			0
$331$			18.0566i			0.992481i	0.868185	+	0.496240i	$0.165287\pi$
$331$			18.0566i			0.992481i	−0.868185	+	0.496240i	$0.834713\pi$
$332$		0			0
$333$	−23.1311	+	13.3548i	−1.26758	+	0.731836i
$334$		0			0
$335$	8.53065	−	14.7755i	0.466079	−	0.807273i
$336$		0			0
$337$	−3.64765			−0.198700			−0.0993500	−	0.995053i	$-0.531676\pi$
$337$	−3.64765			−0.198700			−0.0993500	+	0.995053i	$0.531676\pi$
$338$		0			0
$339$	12.9316	+	22.3982i	0.702347	+	1.21650i
$340$		0			0
$341$	−16.3870	−	28.3831i	−0.887406	−	1.53703i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		−	81.5815i		−	4.39220i
$346$		0			0
$347$	−7.29727	+	12.6392i	−0.391738	+	0.678510i	−0.992679	−	0.120783i	$-0.961459\pi$
$347$	−7.29727	+	12.6392i	−0.391738	+	0.678510i	0.600941	+	0.799294i	$0.294793\pi$
$348$		0			0
$349$	−15.4877	−	8.94182i	−0.829037	−	0.478645i	0.0244861	−	0.999700i	$-0.492205\pi$
$349$	−15.4877	−	8.94182i	−0.829037	−	0.478645i	−0.853523	+	0.521056i	$0.825538\pi$
$350$		0			0
$351$	19.8768	−	47.7443i	1.06094	−	2.54840i
$352$		0			0
$353$		−	6.38272i		−	0.339718i	−0.985468	−	0.169859i	$-0.945669\pi$
$353$		−	6.38272i		−	0.339718i	0.985468	−	0.169859i	$-0.0543312\pi$
$354$		0			0
$355$	−28.8072			−1.52893
$356$		0			0
$357$		0			0
$358$		0			0
$359$	26.4089	+	15.2472i	1.39381	+	0.804717i	0.993735	−	0.111765i	$-0.0356505\pi$
$359$	26.4089	+	15.2472i	1.39381	+	0.804717i	0.400076	+	0.916482i	$0.368984\pi$
$360$		0			0
$361$	−18.8985			−0.994660
$362$		0			0
$363$	−12.3057			−0.645884
$364$		0			0
$365$	10.4254			0.545692
$366$		0			0
$367$	−7.16337			−0.373925			−0.186962	−	0.982367i	$-0.559864\pi$
$367$	−7.16337			−0.373925			−0.186962	+	0.982367i	$0.559864\pi$
$368$		0			0
$369$	−25.6609	−	14.8153i	−1.33585	−	0.771255i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.16467			−0.0603045			−0.0301523	−	0.999545i	$-0.509599\pi$
$373$	−1.16467			−0.0603045			−0.0301523	+	0.999545i	$0.509599\pi$
$374$		0			0
$375$		−	0.936023i		−	0.0483360i
$376$		0			0
$377$	−5.95410	−	7.78843i	−0.306652	−	0.401125i
$378$		0			0
$379$	−25.1318	−	14.5099i	−1.29093	−	0.745322i	−0.312115	−	0.950044i	$-0.601037\pi$
$379$	−25.1318	−	14.5099i	−1.29093	−	0.745322i	−0.978820	+	0.204723i	$0.934371\pi$
$380$		0			0
$381$	2.14662	−	3.71806i	0.109975	−	0.190482i
$382$		0			0
$383$			21.9571i			1.12196i	0.827831	+	0.560978i	$0.189575\pi$
$383$			21.9571i			1.12196i	−0.827831	+	0.560978i	$0.810425\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−42.7582	−	74.0593i	−2.17352	−	3.76465i
$388$		0			0
$389$	14.5986	+	25.2856i	0.740180	+	1.28203i	0.952413	+	0.304811i	$0.0985932\pi$
$389$	14.5986	+	25.2856i	0.740180	+	1.28203i	−0.212233	+	0.977219i	$0.568074\pi$
$390$		0			0
$391$	−1.55915			−0.0788498
$392$		0			0
$393$	0.957605	−	1.65862i	0.0483048	−	0.0836664i
$394$		0			0
$395$	24.4998	−	14.1450i	1.23272	−	0.711710i
$396$		0			0
$397$			31.9503i			1.60354i	0.597632	+	0.801771i	$0.296108\pi$
$397$			31.9503i			1.60354i	−0.597632	+	0.801771i	$0.703892\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−31.9176	+	18.4276i	−1.59389	+	0.920232i	−0.601257	+	0.799056i	$0.705333\pi$
$401$	−31.9176	+	18.4276i	−1.59389	+	0.920232i	−0.992631	+	0.121176i	$0.961334\pi$
$402$		0			0
$403$	3.95349	+	30.4519i	0.196938	+	1.51692i
$404$		0			0
$405$	65.4947	+	37.8134i	3.25446	+	1.87896i
$406$		0			0
$407$	−6.90808	−	11.9651i	−0.342421	−	0.593090i
$408$		0			0
$409$	−4.89732	−	2.82747i	−0.242157	−	0.139809i	0.374011	−	0.927424i	$-0.377982\pi$
$409$	−4.89732	−	2.82747i	−0.242157	−	0.139809i	−0.616168	+	0.787615i	$0.711316\pi$
$410$		0			0
$411$	7.16417	+	4.13623i	0.353382	+	0.204025i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	12.0612	−	20.8906i	0.592061	−	1.02548i
$416$		0			0
$417$	29.1162	+	50.4307i	1.42582	+	2.46960i
$418$		0			0
$419$	12.9031	−	22.3488i	0.630358	−	1.09181i	−0.357120	−	0.934059i	$-0.616241\pi$
$419$	12.9031	−	22.3488i	0.630358	−	1.09181i	0.987478	−	0.157754i	$-0.0504254\pi$
$420$		0			0
$421$		−	28.8606i		−	1.40658i	−0.710903	−	0.703290i	$-0.751714\pi$
$421$		−	28.8606i		−	1.40658i	0.710903	−	0.703290i	$-0.248286\pi$
$422$		0			0
$423$	−28.0338	−	16.1853i	−1.36305	−	0.786957i
$424$		0			0
$425$	0.953954			0.0462736
$426$		0			0
$427$		0			0
$428$		0			0
$429$	41.3865	+	17.2299i	1.99816	+	0.831867i
$430$		0			0
$431$			31.6712i			1.52555i	0.646665	+	0.762774i	$0.276163\pi$
$431$			31.6712i			1.52555i	−0.646665	+	0.762774i	$0.723837\pi$
$432$		0			0
$433$	15.6517	+	27.1095i	0.752172	+	1.30280i	0.946768	+	0.321916i	$0.104327\pi$
$433$	15.6517	+	27.1095i	0.752172	+	1.30280i	−0.194597	+	0.980883i	$0.562340\pi$
$434$		0			0
$435$	23.9483	−	13.8266i	1.14823	−	0.662933i
$436$		0			0
$437$	42.7666	−	24.6913i	2.04580	−	1.18114i
$438$		0			0
$439$	18.4786	+	32.0059i	0.881935	+	1.52756i	0.849187	+	0.528092i	$0.177093\pi$
$439$	18.4786	+	32.0059i	0.881935	+	1.52756i	0.0327479	+	0.999464i	$0.489574\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.1436	+	24.4974i	−0.671981	+	1.16391i	0.305360	+	0.952237i	$0.401223\pi$
$443$	−14.1436	+	24.4974i	−0.671981	+	1.16391i	−0.977341	+	0.211669i	$0.932110\pi$
$444$		0			0
$445$	−16.1013			−0.763275
$446$		0			0
$447$			26.1966i			1.23906i
$448$		0			0
$449$	21.0690	−	12.1642i	0.994308	−	0.574064i	0.0877485	−	0.996143i	$-0.472033\pi$
$449$	21.0690	−	12.1642i	0.994308	−	0.574064i	0.906559	+	0.422079i	$0.138699\pi$
$450$		0			0
$451$	7.66360	−	13.2737i	0.360865	−	0.625036i
$452$		0			0
$453$	10.0398	−	5.79649i	0.471712	−	0.272343i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.34199	−	0.774798i	0.0627756	−	0.0362435i	−0.468284	−	0.883578i	$-0.655127\pi$
$457$	1.34199	−	0.774798i	0.0627756	−	0.0362435i	0.531059	+	0.847335i	$0.321794\pi$
$458$		0			0
$459$	1.39397	−	2.41443i	0.0650651	−	0.112696i
$460$		0			0
$461$	11.2195	−	6.47760i	0.522545	−	0.301692i	−0.215430	−	0.976519i	$-0.569115\pi$
$461$	11.2195	−	6.47760i	0.522545	−	0.301692i	0.737975	+	0.674828i	$0.235782\pi$
$462$		0			0
$463$			28.1690i			1.30912i	0.756008	+	0.654562i	$0.227147\pi$
$463$			28.1690i			1.30912i	−0.756008	+	0.654562i	$0.772853\pi$
$464$		0			0
$465$	−86.6166			−4.01675
$466$		0			0
$467$	14.6454	−	25.3666i	0.677709	−	1.17383i	−0.297960	−	0.954578i	$-0.596306\pi$
$467$	14.6454	−	25.3666i	0.677709	−	1.17383i	0.975669	−	0.219248i	$-0.0703605\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−23.1739	−	40.1384i	−1.06780	−	1.84948i
$472$		0			0
$473$	38.3091	−	22.1177i	1.76145	−	1.01697i
$474$		0			0
$475$	−26.1664	+	15.1072i	−1.20059	+	0.693164i
$476$		0			0
$477$	2.14553	+	3.71616i	0.0982369	+	0.170151i
$478$		0			0
$479$			19.4711i			0.889658i	0.895616	+	0.444829i	$0.146735\pi$
$479$			19.4711i			0.889658i	−0.895616	+	0.444829i	$0.853265\pi$
$480$		0			0
$481$	1.66663	+	12.8372i	0.0759917	+	0.585328i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	30.3018			1.37594
$486$		0			0
$487$	−3.92783	−	2.26773i	−0.177987	−	0.102761i	0.408360	−	0.912821i	$-0.366101\pi$
$487$	−3.92783	−	2.26773i	−0.177987	−	0.102761i	−0.586346	+	0.810060i	$0.699434\pi$
$488$		0			0
$489$			0.795281i			0.0359638i
$490$		0			0
$491$	9.07433	−	15.7172i	0.409519	−	0.709307i	−0.585317	−	0.810804i	$-0.699030\pi$
$491$	9.07433	−	15.7172i	0.409519	−	0.709307i	0.994836	+	0.101497i	$0.0323633\pi$
$492$		0			0
$493$	−0.264248	−	0.457690i	−0.0119011	−	0.0206133i
$494$		0			0
$495$	−45.0563	+	78.0399i	−2.02513	+	3.50763i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−5.76368	−	3.32766i	−0.258018	−	0.148967i	0.365412	−	0.930846i	$-0.380928\pi$
$499$	−5.76368	−	3.32766i	−0.258018	−	0.148967i	−0.623430	+	0.781879i	$0.714261\pi$
$500$		0			0
$501$	5.05989	+	2.92133i	0.226059	+	0.130515i
$502$		0			0
$503$	−7.45978	−	12.9207i	−0.332615	−	0.576106i	0.650409	−	0.759584i	$-0.274598\pi$
$503$	−7.45978	−	12.9207i	−0.332615	−	0.576106i	−0.983024	+	0.183478i	$0.941264\pi$
$504$		0			0
$505$	6.92829	+	4.00005i	0.308305	+	0.178000i
$506$		0			0
$507$	−29.5938	−	29.8070i	−1.31431	−	1.32378i
$508$		0			0
$509$	15.3869	−	8.88365i	0.682014	−	0.393761i	−0.118599	−	0.992942i	$-0.537840\pi$
$509$	15.3869	−	8.88365i	0.682014	−	0.393761i	0.800613	+	0.599181i	$0.204507\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			88.3018i			3.89862i
$514$		0			0
$515$	−9.14272	+	5.27855i	−0.402876	+	0.232601i
$516$		0			0
$517$	8.37226	−	14.5012i	0.368211	−	0.637761i
$518$		0			0
$519$	34.8936			1.53166
$520$		0			0
$521$	−19.0289	−	32.9591i	−0.833673	−	1.44396i	−0.895106	−	0.445853i	$-0.852900\pi$
$521$	−19.0289	−	32.9591i	−0.833673	−	1.44396i	0.0614331	−	0.998111i	$-0.480433\pi$
$522$		0			0
$523$	−6.94526	−	12.0295i	−0.303695	−	0.526015i	0.673275	−	0.739392i	$-0.264887\pi$
$523$	−6.94526	−	12.0295i	−0.303695	−	0.526015i	−0.976970	+	0.213377i	$0.931554\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			1.65538i			0.0721096i
$528$		0			0
$529$	−20.6733	+	35.8071i	−0.898837	+	1.55683i
$530$		0			0
$531$	−13.4441	−	7.76195i	−0.583424	−	0.336840i
$532$		0			0
$533$	−11.4088	+	8.72181i	−0.494170	+	0.377783i
$534$		0			0
$535$			40.6462i			1.75729i
$536$		0			0
$537$	−28.0337			−1.20974
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−36.2391	−	20.9226i	−1.55804	−	0.899535i	−0.997445	−	0.0714444i	$-0.977239\pi$
$541$	−36.2391	−	20.9226i	−1.55804	−	0.899535i	−0.560595	−	0.828090i	$-0.689428\pi$
$542$		0			0
$543$	−32.3381			−1.38776
$544$		0			0
$545$	25.3159			1.08441
$546$		0			0
$547$	−22.3475			−0.955509			−0.477754	−	0.878493i	$-0.658549\pi$
$547$	−22.3475			−0.955509			−0.477754	+	0.878493i	$0.658549\pi$
$548$		0			0
$549$	25.3318			1.08114
$550$		0			0
$551$	14.4963	+	8.36943i	0.617562	+	0.356550i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−36.5140			−1.54993
$556$		0			0
$557$		−	30.6572i		−	1.29899i	−0.760368	−	0.649493i	$-0.774981\pi$
$557$		−	30.6572i		−	1.29899i	0.760368	−	0.649493i	$-0.225019\pi$
$558$		0			0
$559$	−41.1013	+	5.33608i	−1.73840	+	0.225692i
$560$		0			0
$561$	2.09292	+	1.20835i	0.0883630	+	0.0510164i
$562$		0			0
$563$	−16.6237	+	28.7930i	−0.700604	+	1.21348i	0.267651	+	0.963516i	$0.413753\pi$
$563$	−16.6237	+	28.7930i	−0.700604	+	1.21348i	−0.968255	+	0.249966i	$0.919581\pi$
$564$		0			0
$565$			25.1963i			1.06002i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	0.961670	−	0.274209i	$-0.0884161\pi$
$569$	5.80511	+	10.0547i	0.243363	+	0.421517i	−0.718307	+	0.695726i	$0.755083\pi$
$570$		0			0
$571$	−8.34968	−	14.4621i	−0.349423	−	0.605219i	0.636724	−	0.771092i	$-0.280289\pi$
$571$	−8.34968	−	14.4621i	−0.349423	−	0.605219i	−0.986147	+	0.165873i	$0.946956\pi$
$572$		0			0
$573$	−77.6450			−3.24366
$574$		0			0
$575$	19.6849	−	34.0953i	0.820918	−	1.42187i
$576$		0			0
$577$	32.2666	−	18.6291i	1.34328	−	0.775541i	0.355990	−	0.934490i	$-0.384144\pi$
$577$	32.2666	−	18.6291i	1.34328	−	0.775541i	0.987287	+	0.158948i	$0.0508103\pi$
$578$		0			0
$579$			10.5753i			0.439495i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−1.92228	+	1.10983i	−0.0796126	+	0.0459643i
$584$		0			0
$585$	67.0754	−	51.2778i	2.77323	−	2.12008i
$586$		0			0
$587$	36.1912	+	20.8950i	1.49377	+	0.862429i	0.999974	−	0.00714861i	$-0.00227549\pi$
$587$	36.1912	+	20.8950i	1.49377	+	0.862429i	0.493796	+	0.869578i	$0.335609\pi$
$588$		0			0
$589$	−26.2152	−	45.4061i	−1.08018	−	1.87092i
$590$		0			0
$591$	35.6828	+	20.6015i	1.46779	+	0.847432i
$592$		0			0
$593$	−3.75571	−	2.16836i	−0.154228	−	0.0890438i	0.420900	−	0.907107i	$-0.361714\pi$
$593$	−3.75571	−	2.16836i	−0.154228	−	0.0890438i	−0.575128	+	0.818063i	$0.695048\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	44.1405	−	76.4536i	1.80655	−	3.12904i
$598$		0			0
$599$	−11.3789	−	19.7088i	−0.464929	−	0.805280i	0.534270	−	0.845314i	$-0.320587\pi$
$599$	−11.3789	−	19.7088i	−0.464929	−	0.805280i	−0.999198	+	0.0400339i	$0.987253\pi$
$600$		0			0
$601$	13.7634	−	23.8389i	0.561421	−	0.972410i	−0.435951	−	0.899970i	$-0.643588\pi$
$601$	13.7634	−	23.8389i	0.561421	−	0.972410i	0.997373	−	0.0724402i	$-0.0230786\pi$
$602$		0			0
$603$		−	40.3233i		−	1.64209i
$604$		0			0
$605$	−10.3823	−	5.99423i	−0.422101	−	0.243700i
$606$		0			0
$607$	−9.06967			−0.368126			−0.184063	−	0.982914i	$-0.558925\pi$
$607$	−9.06967			−0.368126			−0.184063	+	0.982914i	$0.558925\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.4638	+	9.52832i	−0.504231	+	0.385475i
$612$		0			0
$613$			9.37895i			0.378812i	0.981899	+	0.189406i	$0.0606563\pi$
$613$			9.37895i			0.378812i	−0.981899	+	0.189406i	$0.939344\pi$
$614$		0			0
$615$	−20.2537	−	35.0804i	−0.816708	−	1.41458i
$616$		0			0
$617$	−26.0786	+	15.0565i	−1.04988	+	0.606151i	−0.922617	−	0.385718i	$-0.873954\pi$
$617$	−26.0786	+	15.0565i	−1.04988	+	0.606151i	−0.127267	+	0.991869i	$0.540620\pi$
$618$		0			0
$619$	−34.5494	+	19.9471i	−1.38866	+	0.801742i	−0.993164	−	0.116727i	$-0.962760\pi$
$619$	−34.5494	+	19.9471i	−1.38866	+	0.801742i	−0.395493	+	0.918469i	$0.629426\pi$
$620$		0			0
$621$	−57.5295	−	99.6441i	−2.30858	−	3.99858i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	12.7259	−	22.0418i	0.509034	−	0.881673i
$626$		0			0
$627$	−76.5431			−3.05684
$628$		0			0
$629$			0.697840i			0.0278247i
$630$		0			0
$631$	−21.3804	+	12.3440i	−0.851140	+	0.491406i	−0.861035	−	0.508545i	$-0.830184\pi$
$631$	−21.3804	+	12.3440i	−0.851140	+	0.491406i	0.00989522	+	0.999951i	$0.496850\pi$
$632$		0			0
$633$	−42.9492	+	74.3903i	−1.70708	+	2.95675i
$634$		0			0
$635$	3.62219	−	2.09127i	0.143742	−	0.0829896i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−58.9625	+	34.0420i	−2.33252	+	1.34668i
$640$		0			0
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	−0.989202	−	0.146560i	$-0.953180\pi$
$641$	−9.30883	+	16.1234i	−0.367677	+	0.636834i	0.621525	+	0.783394i	$0.286513\pi$
$642$		0			0
$643$	−27.4384	+	15.8415i	−1.08206	+	0.624729i	−0.931452	−	0.363864i	$-0.881457\pi$
$643$	−27.4384	+	15.8415i	−1.08206	+	0.624729i	−0.150611	+	0.988593i	$0.548124\pi$
$644$		0			0
$645$		−	116.908i		−	4.60323i
$646$		0			0
$647$	−29.6583			−1.16599			−0.582994	−	0.812477i	$-0.698119\pi$
$647$	−29.6583			−1.16599			−0.582994	+	0.812477i	$0.698119\pi$
$648$		0			0
$649$	4.01506	−	6.95429i	0.157605	−	0.272980i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	0.714760	−	0.699370i	$-0.246536\pi$
$653$	−6.34483	−	10.9896i	−0.248292	−	0.430055i	−0.963052	+	0.269315i	$0.913203\pi$
$654$		0			0
$655$	1.61585	−	0.932914i	0.0631367	−	0.0364520i
$656$		0			0
$657$	21.3387	−	12.3199i	0.832502	−	0.480645i
$658$		0			0
$659$	12.2763	+	21.2632i	0.478217	+	0.828296i	0.999688	−	0.0249730i	$-0.00794998\pi$
$659$	12.2763	+	21.2632i	0.478217	+	0.828296i	−0.521471	+	0.853269i	$0.674617\pi$
$660$		0			0
$661$		−	25.5574i		−	0.994067i	−0.867731	−	0.497033i	$-0.834423\pi$
$661$		−	25.5574i		−	0.994067i	0.867731	−	0.497033i	$-0.165577\pi$
$662$		0			0
$663$	−1.37520	−	1.79886i	−0.0534082	−	0.0698621i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.8111			−0.844529
$668$		0			0
$669$	42.3464	+	24.4487i	1.63721	+	0.945242i
$670$		0			0
$671$			13.1035i			0.505856i
$672$		0			0
$673$	−3.39829	+	5.88601i	−0.130994	+	0.226889i	−0.924060	−	0.382247i	$-0.875150\pi$
$673$	−3.39829	+	5.88601i	−0.130994	+	0.226889i	0.793066	+	0.609136i	$0.208484\pi$
$674$		0			0
$675$	35.1989	+	60.9664i	1.35481	+	2.34660i
$676$		0			0
$677$	13.0478	−	22.5995i	0.501468	−	0.868569i	−0.498530	−	0.866872i	$-0.666127\pi$
$677$	13.0478	−	22.5995i	0.501468	−	0.868569i	0.999999	−	0.00169631i	$-0.000539952\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	59.8950	+	34.5804i	2.29518	+	1.32512i
$682$		0			0
$683$	−42.1666	−	24.3449i	−1.61346	−	0.931532i	−0.988560	−	0.150827i	$-0.951806\pi$
$683$	−42.1666	−	24.3449i	−1.61346	−	0.931532i	−0.624900	−	0.780705i	$-0.714860\pi$
$684$		0			0
$685$	4.02958	+	6.97944i	0.153962	+	0.266671i
$686$		0			0
$687$	−23.3958	−	13.5076i	−0.892606	−	0.515346i
$688$		0			0
$689$	2.06238	−	0.267754i	0.0785706	−	0.0102006i
$690$		0			0
$691$	3.10942	−	1.79522i	0.118288	−	0.0682935i	−0.439689	−	0.898150i	$-0.644911\pi$
$691$	3.10942	−	1.79522i	0.118288	−	0.0682935i	0.557977	+	0.829857i	$0.311578\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			56.7308i			2.15192i
$696$		0			0
$697$	−0.670443	+	0.387080i	−0.0253948	+	0.0146617i
$698$		0			0
$699$	−42.2717	+	73.2168i	−1.59886	+	2.76931i
$700$		0			0
$701$	−15.8746			−0.599575			−0.299787	−	0.954006i	$-0.596916\pi$
$701$	−15.8746			−0.599575			−0.299787	+	0.954006i	$0.596916\pi$
$702$		0			0
$703$	−11.0512	−	19.1413i	−0.416805	−	0.721928i
$704$		0			0
$705$	−22.1266	−	38.3244i	−0.833335	−	1.44338i
$706$		0			0
$707$		0			0
$708$		0			0
$709$		−	22.6500i		−	0.850637i	−0.905044	−	0.425318i	$-0.860162\pi$
$709$		−	22.6500i		−	0.850637i	0.905044	−	0.425318i	$-0.139838\pi$
$710$		0			0
$711$	33.4307	−	57.9037i	1.25375	−	2.17156i
$712$		0			0
$713$	59.1650	+	34.1589i	2.21575	+	1.27926i
$714$		0			0
$715$	26.5248	+	34.6965i	0.991969	+	1.29757i
$716$		0			0
$717$		−	59.3089i		−	2.21493i
$718$		0			0
$719$	−10.2526			−0.382358			−0.191179	−	0.981555i	$-0.561231\pi$
$719$	−10.2526			−0.382358			−0.191179	+	0.981555i	$0.561231\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9.33125	+	5.38740i	0.347033	+	0.200359i
$724$		0			0
$725$	13.3449			0.495618
$726$		0			0
$727$	−5.60059			−0.207715			−0.103857	−	0.994592i	$-0.533119\pi$
$727$	−5.60059			−0.207715			−0.103857	+	0.994592i	$0.533119\pi$
$728$		0			0
$729$	39.7064			1.47061
$730$		0			0
$731$	−2.23429			−0.0826382
$732$		0			0
$733$	−35.6418	−	20.5778i	−1.31646	−	0.760058i	−0.333302	−	0.942820i	$-0.608163\pi$
$733$	−35.6418	−	20.5778i	−1.31646	−	0.760058i	−0.983157	+	0.182762i	$0.941496\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	20.8582			0.768323
$738$		0			0
$739$		−	12.1469i		−	0.446833i	−0.974723	−	0.223416i	$-0.928279\pi$
$739$		−	12.1469i		−	0.446833i	0.974723	−	0.223416i	$-0.0717209\pi$
$740$		0			0
$741$	66.2082	+	27.5636i	2.43222	+	1.01257i
$742$		0			0
$743$	0.486744	+	0.281022i	0.0178569	+	0.0103097i	0.508902	−	0.860825i	$-0.330052\pi$
$743$	0.486744	+	0.281022i	0.0178569	+	0.0103097i	−0.491045	+	0.871134i	$0.663385\pi$
$744$		0			0
$745$	−12.7606	+	22.1020i	−0.467511	+	0.809753i
$746$		0			0
$747$		−	57.0118i		−	2.08595i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−11.3569	−	19.6707i	−0.414418	−	0.717794i	0.580949	−	0.813940i	$-0.302682\pi$
$751$	−11.3569	−	19.6707i	−0.414418	−	0.717794i	−0.995367	+	0.0961463i	$0.969348\pi$
$752$		0			0
$753$	−19.7054	−	34.1307i	−0.718104	−	1.24379i
$754$		0			0
$755$	11.2941			0.411033
$756$		0			0
$757$	−9.74099	+	16.8719i	−0.354042	+	0.613219i	−0.986954	−	0.161005i	$-0.948526\pi$
$757$	−9.74099	+	16.8719i	−0.354042	+	0.613219i	0.632911	+	0.774224i	$0.281860\pi$
$758$		0			0
$759$	86.3750	−	49.8686i	3.13521	−	1.81012i
$760$		0			0
$761$			42.7334i			1.54909i	0.632522	+	0.774543i	$0.282020\pi$
$761$			42.7334i			1.54909i	−0.632522	+	0.774543i	$0.717980\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	3.94171	−	2.27575i	0.142513	−	0.0822799i
$766$		0			0
$767$	−5.97723	+	4.56947i	−0.215825	+	0.164994i
$768$		0			0
$769$	−29.5477	−	17.0593i	−1.06552	−	0.615176i	−0.138563	−	0.990354i	$-0.544248\pi$
$769$	−29.5477	−	17.0593i	−1.06552	−	0.615176i	−0.926953	+	0.375178i	$0.877582\pi$
$770$		0			0
$771$	24.6735	+	42.7357i	0.888593	+	1.53909i
$772$		0			0
$773$	25.0026	+	14.4353i	0.899281	+	0.519200i	0.876967	−	0.480551i	$-0.159563\pi$
$773$	25.0026	+	14.4353i	0.899281	+	0.519200i	0.0223144	+	0.999751i	$0.492897\pi$
$774$		0			0
$775$	−36.1996	−	20.8999i	−1.30033	−	0.750745i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.2599	−	21.2347i	0.439256	−	0.760813i
$780$		0			0
$781$	−17.6091	−	30.4998i	−0.630103	−	1.09137i
$782$		0			0
$783$	19.5004	−	33.7757i	0.696887	−	1.20704i
$784$		0			0
$785$		−	45.1528i		−	1.61157i
$786$		0			0
$787$	−38.9448	−	22.4848i	−1.38823	−	0.801497i	−0.395117	−	0.918631i	$-0.629296\pi$
$787$	−38.9448	−	22.4848i	−1.38823	−	0.801497i	−0.993116	+	0.117134i	$0.962629\pi$
$788$		0			0
$789$	80.4484			2.86404
$790$		0			0
$791$		0			0
$792$		0			0
$793$	4.71865	−	11.3343i	0.167564	−	0.402492i
$794$		0			0
$795$			5.86620i			0.208053i
$796$		0			0
$797$	−10.7092	−	18.5489i	−0.379340	−	0.657036i	0.611627	−	0.791147i	$-0.290515\pi$
$797$	−10.7092	−	18.5489i	−0.379340	−	0.657036i	−0.990966	+	0.134111i	$0.957182\pi$
$798$		0			0
$799$	−0.732440	+	0.422874i	−0.0259118	+	0.0149602i
$800$		0			0
$801$	−32.9561	+	19.0272i	−1.16445	+	0.672293i
$802$		0			0
$803$	6.37278	+	11.0380i	0.224891	+	0.389522i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.6925	−	21.9841i	0.446799	−	0.773878i
$808$		0			0
$809$	−8.25498			−0.290230			−0.145115	−	0.989415i	$-0.546355\pi$
$809$	−8.25498			−0.290230			−0.145115	+	0.989415i	$0.546355\pi$
$810$		0			0
$811$		−	43.7679i		−	1.53690i	−0.639910	−	0.768450i	$-0.721029\pi$
$811$		−	43.7679i		−	1.53690i	0.639910	−	0.768450i	$-0.278971\pi$
$812$		0			0
$813$	−7.38329	+	4.26274i	−0.258943	+	0.149501i
$814$		0			0
$815$	−0.387387	+	0.670975i	−0.0135696	+	0.0235032i
$816$		0			0
$817$	61.2851	−	35.3830i	2.14409	−	1.23789i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−19.1465	+	11.0542i	−0.668216	+	0.385795i	−0.795400	−	0.606084i	$-0.792739\pi$
$821$	−19.1465	+	11.0542i	−0.668216	+	0.385795i	0.127184	+	0.991879i	$0.459406\pi$
$822$		0			0
$823$	−21.0355	+	36.4346i	−0.733252	+	1.27003i	0.222234	+	0.974993i	$0.428665\pi$
$823$	−21.0355	+	36.4346i	−0.733252	+	1.27003i	−0.955486	+	0.295037i	$0.904668\pi$
$824$		0			0
$825$	−52.8478	+	30.5117i	−1.83992	+	1.06228i
$826$		0			0
$827$			44.4242i			1.54478i	0.635148	+	0.772390i	$0.280939\pi$
$827$			44.4242i			1.54478i	−0.635148	+	0.772390i	$0.719061\pi$
$828$		0			0
$829$	17.9479			0.623355			0.311678	−	0.950188i	$-0.399109\pi$
$829$	17.9479			0.623355			0.311678	+	0.950188i	$0.399109\pi$
$830$		0			0
$831$	18.8284	−	32.6118i	0.653151	−	1.13129i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	2.84600	+	4.92942i	0.0984900	+	0.170590i
$836$		0			0
$837$	−105.794	+	61.0802i	−3.65677	+	2.11124i
$838$		0			0
$839$	3.09534	−	1.78709i	0.106863	−	0.0616973i	−0.445616	−	0.895224i	$-0.647015\pi$
$839$	3.09534	−	1.78709i	0.106863	−	0.0616973i	0.552479	+	0.833527i	$0.313682\pi$
$840$		0			0
$841$	10.8034	+	18.7121i	0.372532	+	0.645244i
$842$		0			0
$843$		−	12.4878i		−	0.430104i
$844$		0			0
$845$	−10.4490	−	39.5634i	−0.359455	−	1.36102i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−22.1279			−0.759429
$850$		0			0
$851$	24.9415	+	14.4000i	0.854984	+	0.493625i
$852$		0			0
$853$		−	24.4780i		−	0.838111i	−0.907961	−	0.419055i	$-0.862361\pi$
$853$		−	24.4780i		−	0.838111i	0.907961	−	0.419055i	$-0.137639\pi$
$854$		0			0
$855$	−72.0791	+	124.845i	−2.46505	+	4.26960i
$856$		0			0
$857$	13.4719	+	23.3340i	0.460192	+	0.797076i	0.998970	−	0.0453720i	$-0.0144473\pi$
$857$	13.4719	+	23.3340i	0.460192	+	0.797076i	−0.538778	+	0.842448i	$0.681114\pi$
$858$		0			0
$859$	8.97686	−	15.5484i	0.306287	−	0.530504i	−0.671260	−	0.741222i	$-0.734247\pi$
$859$	8.97686	−	15.5484i	0.306287	−	0.530504i	0.977547	+	0.210718i	$0.0675801\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.59914	+	5.54206i	0.326758	+	0.188654i	0.654401	−	0.756148i	$-0.272921\pi$
$863$	9.59914	+	5.54206i	0.326758	+	0.188654i	−0.327643	+	0.944802i	$0.606254\pi$
$864$		0			0
$865$	29.4396	+	16.9969i	1.00098	+	0.577913i
$866$		0			0
$867$	27.4025	+	47.4625i	0.930637	+	1.61191i
$868$		0			0
$869$	29.9521	+	17.2929i	1.01606	+	0.586621i
$870$		0			0
$871$	−18.0420	−	7.51118i	−0.611328	−	0.254506i
$872$		0			0
$873$	62.0217	−	35.8082i	2.09912	−	1.21193i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	4.60737i		−	0.155580i	−0.996970	−	0.0777899i	$-0.975214\pi$
$877$		−	4.60737i		−	0.155580i	0.996970	−	0.0777899i	$-0.0247863\pi$
$878$		0			0
$879$	4.16624	−	2.40538i	0.140524	−	0.0811314i
$880$		0			0
$881$	−17.1554	+	29.7140i	−0.577979	+	1.00109i	0.417732	+	0.908570i	$0.362825\pi$
$881$	−17.1554	+	29.7140i	−0.577979	+	1.00109i	−0.995711	+	0.0925186i	$0.970508\pi$
$882$		0			0
$883$	42.5926			1.43336			0.716678	−	0.697404i	$-0.245662\pi$
$883$	42.5926			1.43336			0.716678	+	0.697404i	$0.245662\pi$
$884$		0			0
$885$	−10.6112	−	18.3791i	−0.356691	−	0.617807i
$886$		0			0
$887$	−20.8026	−	36.0312i	−0.698483	−	1.20981i	−0.968992	−	0.247091i	$-0.920525\pi$
$887$	−20.8026	−	36.0312i	−0.698483	−	1.20981i	0.270509	−	0.962717i	$-0.412808\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			92.4572i			3.09743i
$892$		0			0
$893$	13.3936	−	23.1983i	0.448198	−	0.776302i
$894$		0			0
$895$	−23.6519	−	13.6554i	−0.790595	−	0.456450i
$896$		0			0
$897$	−92.6706	+	12.0312i	−3.09418	+	0.401710i
$898$		0			0
$899$			23.1572i			0.772337i
$900$		0			0
$901$	0.112112			0.00373501
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−27.2835	−	15.7521i	−0.906934	−	0.523619i
$906$		0			0
$907$	−15.6716			−0.520367			−0.260183	−	0.965559i	$-0.583783\pi$
$907$	−15.6716			−0.520367			−0.260183	+	0.965559i	$0.583783\pi$
$908$		0			0
$909$	18.9077			0.627129
$910$		0			0
$911$	−33.5478			−1.11149			−0.555743	−	0.831354i	$-0.687566\pi$
$911$	−33.5478			−1.11149			−0.555743	+	0.831354i	$0.687566\pi$
$912$		0			0
$913$	29.4908			0.976002
$914$		0			0
$915$	29.9910	+	17.3153i	0.991470	+	0.572426i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	3.33761			0.110098			0.0550488	−	0.998484i	$-0.482469\pi$
$919$	3.33761			0.110098			0.0550488	+	0.998484i	$0.482469\pi$
$920$		0			0
$921$		−	7.53236i		−	0.248200i
$922$		0			0
$923$	4.24833	+	32.7229i	0.139835	+	1.07709i
$924$		0			0
$925$	−15.2603	−	8.81051i	−0.501754	−	0.289688i
$926$		0			0
$927$	−12.4755	+	21.6082i	−0.409750	+	0.709707i
$928$		0			0
$929$			9.09688i			0.298459i	0.988803	+	0.149230i	$0.0476793\pi$
$929$			9.09688i			0.298459i	−0.988803	+	0.149230i	$0.952321\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−19.1024	−	33.0863i	−0.625384	−	1.08320i
$934$		0			0
$935$	1.17719	+	2.03895i	0.0384982	+	0.0666808i
$936$		0			0
$937$	9.08442			0.296775			0.148388	−	0.988929i	$-0.452592\pi$
$937$	9.08442			0.296775			0.148388	+	0.988929i	$0.452592\pi$
$938$		0			0
$939$	29.7392	−	51.5099i	0.970504	−	1.68096i
$940$		0			0
$941$	−7.13037	+	4.11672i	−0.232444	+	0.134201i	−0.611699	−	0.791091i	$-0.709514\pi$
$941$	−7.13037	+	4.11672i	−0.232444	+	0.134201i	0.379255	+	0.925292i	$0.376180\pi$
$942$		0			0
$943$			31.9498i			1.04043i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.37804	+	2.52766i	−0.142267	+	0.0821380i	−0.569444	−	0.822030i	$-0.692841\pi$
$947$	−4.37804	+	2.52766i	−0.142267	+	0.0821380i	0.427177	+	0.904168i	$0.359508\pi$
$948$		0			0
$949$	−1.53748	−	11.8425i	−0.0499088	−	0.384424i
$950$		0			0
$951$	−23.5679	−	13.6069i	−0.764242	−	0.441235i
$952$		0			0
$953$	19.6579	+	34.0485i	0.636782	+	1.10294i	0.986135	+	0.165948i	$0.0530684\pi$
$953$	19.6579	+	34.0485i	0.636782	+	1.10294i	−0.349352	+	0.936992i	$0.613598\pi$
$954$		0			0
$955$	−65.5087	−	37.8215i	−2.11981	−	1.22387i
$956$		0			0
$957$	29.2779	+	16.9036i	0.946421	+	0.546416i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	20.7672	−	35.9698i	0.669909	−	1.16032i
$962$		0			0
$963$	48.0323	+	83.1944i	1.54782	+	2.68090i
$964$		0			0
$965$	−5.15132	+	8.92234i	−0.165827	+	0.287220i
$966$		0			0
$967$		−	21.2101i		−	0.682071i	−0.940050	−	0.341036i	$-0.889222\pi$
$967$		−	21.2101i		−	0.682071i	0.940050	−	0.341036i	$-0.110778\pi$
$968$		0			0
$969$	3.34815	+	1.93306i	0.107558	+	0.0620987i
$970$		0			0
$971$	−23.5410			−0.755466			−0.377733	−	0.925915i	$-0.623296\pi$
$971$	−23.5410			−0.755466			−0.377733	+	0.925915i	$0.623296\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	56.6997	−	7.36118i	1.81584	−	0.235747i
$976$		0			0
$977$			12.3992i			0.396684i	0.980133	+	0.198342i	$0.0635557\pi$
$977$			12.3992i			0.396684i	−0.980133	+	0.198342i	$0.936444\pi$
$978$		0			0
$979$	−9.84230	−	17.0474i	−0.314561	−	0.544836i
$980$		0			0
$981$	51.8164	−	29.9162i	1.65437	−	0.955151i
$982$		0			0
$983$	31.2516	−	18.0431i	0.996770	−	0.575486i	0.0894792	−	0.995989i	$-0.471480\pi$
$983$	31.2516	−	18.0431i	0.996770	−	0.575486i	0.907291	+	0.420503i	$0.138146\pi$
$984$		0			0
$985$	20.0703	+	34.7628i	0.639492	+	1.10763i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−46.1047	+	79.8558i	−1.46605	+	2.53927i
$990$		0			0
$991$	52.8491			1.67881			0.839403	−	0.543510i	$-0.182905\pi$
$991$	52.8491			1.67881			0.839403	+	0.543510i	$0.182905\pi$
$992$		0			0
$993$			58.3409i			1.85139i
$994$		0			0
$995$	74.4823	−	43.0024i	2.36125	−	1.36327i
$996$		0			0
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	−0.876960	−	0.480563i	$-0.840432\pi$
$997$	−0.704139	+	1.21960i	−0.0223003	+	0.0386252i	0.854660	+	0.519188i	$0.173766\pi$
$998$		0			0
$999$	−44.5983	+	25.7489i	−1.41103	+	0.814658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.e.1941.8		16
7.2	even	3		364.2.u.a.225.1	✓	16
7.3	odd	6		2548.2.bb.c.1733.8		16
7.4	even	3		2548.2.bb.d.1733.1		16
7.5	odd	6		2548.2.u.c.589.8		16
7.6	odd	2		2548.2.bq.c.1941.1		16
13.10	even	6		2548.2.bb.d.569.1		16
21.2	odd	6		3276.2.cf.c.2773.7		16
28.23	odd	6		1456.2.cc.f.225.8		16
91.9	even	3		4732.2.g.k.337.15		16
91.10	odd	6		2548.2.bq.c.361.1		16
91.23	even	6		364.2.u.a.309.1	yes	16
91.30	even	6		4732.2.g.k.337.16		16
91.58	odd	12		4732.2.a.s.1.8		8
91.62	odd	6		2548.2.bb.c.569.8		16
91.72	odd	12		4732.2.a.t.1.8		8
91.75	odd	6		2548.2.u.c.1765.8		16
91.88	even	6	inner	2548.2.bq.e.361.8		16
273.23	odd	6		3276.2.cf.c.1765.2		16
364.23	odd	6		1456.2.cc.f.673.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.1	✓	16	7.2	even	3
364.2.u.a.309.1	yes	16	91.23	even	6
1456.2.cc.f.225.8		16	28.23	odd	6
1456.2.cc.f.673.8		16	364.23	odd	6
2548.2.u.c.589.8		16	7.5	odd	6
2548.2.u.c.1765.8		16	91.75	odd	6
2548.2.bb.c.569.8		16	91.62	odd	6
2548.2.bb.c.1733.8		16	7.3	odd	6
2548.2.bb.d.569.1		16	13.10	even	6
2548.2.bb.d.1733.1		16	7.4	even	3
2548.2.bq.c.361.1		16	91.10	odd	6
2548.2.bq.c.1941.1		16	7.6	odd	2
2548.2.bq.e.361.8		16	91.88	even	6	inner
2548.2.bq.e.1941.8		16	1.1	even	1	trivial
3276.2.cf.c.1765.2		16	273.23	odd	6
3276.2.cf.c.2773.7		16	21.2	odd	6
4732.2.a.s.1.8		8	91.58	odd	12
4732.2.a.t.1.8		8	91.72	odd	12
4732.2.g.k.337.15		16	91.9	even	3
4732.2.g.k.337.16		16	91.30	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2548.bq (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+3.23100 q^{3} +(2.72598 + 1.57385i) q^{5} +7.43937 q^{9} +3.84820i q^{11} +(1.38576 - 3.32861i) q^{13} +(8.80765 + 5.08510i) q^{15} +(0.0971843 - 0.168328i) q^{17} +6.15618i q^{19} +(-4.01081 - 6.94693i) q^{23} +(2.45398 + 4.25042i) q^{25} +14.3436 q^{27} +(1.35952 - 2.35475i) q^{29} +(-7.37569 + 4.25836i) q^{31} +12.4335i q^{33} +(-3.10928 + 1.79515i) q^{37} +(4.47739 - 10.7548i) q^{39} +(-3.44934 - 1.99148i) q^{41} +(-5.74755 - 9.95506i) q^{43} +(20.2796 + 11.7084i) q^{45} +(-3.76830 - 2.17563i) q^{47} +(0.314003 - 0.543869i) q^{51} +(0.288402 + 0.499526i) q^{53} +(-6.05647 + 10.4901i) q^{55} +19.8906i q^{57} +(-1.80715 - 1.04336i) q^{59} +3.40510 q^{61} +(9.01628 - 6.89277i) q^{65} -5.42026i q^{67} +(-12.9589 - 22.4456i) q^{69} +(-7.92574 + 4.57593i) q^{71} +(2.86835 - 1.65604i) q^{73} +(7.92882 + 13.7331i) q^{75} +(4.49376 - 7.78342i) q^{79} +24.0261 q^{81} -7.66353i q^{83} +(0.529845 - 0.305906i) q^{85} +(4.39260 - 7.60821i) q^{87} +(-4.42996 + 2.55764i) q^{89} +(-23.8309 + 13.7588i) q^{93} +(-9.68888 + 16.7816i) q^{95} +(8.33696 - 4.81334i) q^{97} +28.6282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 28 q^{9} + 10 q^{13} + 6 q^{15} + 2 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} - 30 q^{31} - 12 q^{37} - 6 q^{39} + 36 q^{41} + 6 q^{43} + 30 q^{45} + 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 18 q^{59}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q + 28 * q^9 + 10 * q^13 + 6 * q^15 + 2 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 - 30 * q^31 - 12 * q^37 - 6 * q^39 + 36 * q^41 + 6 * q^43 + 30 * q^45 + 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 18 * q^59 - 8 * q^61 - 52 * q^69 + 36 * q^71 + 12 * q^73 - 10 * q^75 - 4 * q^79 + 42 * q^85 + 26 * q^87 + 36 * q^89 + 42 * q^93 - 30 * q^95 - 42 * q^97

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