LMFDB - Embedded newform 2548.2.bq.c.361.1

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			361.1
Root			$3.23100i$ of defining polynomial
Character	$\chi$	$=$	2548.361
Dual form			2548.2.bq.c.1941.1

$q$-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 $\left(\mathbb{Z}/2548\mathbb{Z}\right)^\times$.

$n$	$197$	$885$	$1275$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

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	$-0.882562\pi$
$3$	−3.23100			−1.86542			−0.932710	+	0.360628i	$0.882562\pi$
$4$		0			0
$5$	−2.72598	+	1.57385i	−1.21910	+	0.703845i	−0.964725	−	0.263261i	$-0.915202\pi$
$5$	−2.72598	+	1.57385i	−1.21910	+	0.703845i	−0.254371	+	0.967107i	$0.581869\pi$
$6$		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	$-0.802999\pi$
$11$		−	3.84820i		−	1.16028i	0.814518	−	0.580138i	$-0.197001\pi$
$12$		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	$-0.174170\pi$
$17$	−0.0971843	−	0.168328i	−0.0235707	−	0.0408256i	−0.877570	+	0.479448i	$0.840837\pi$
$18$		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	0.0566448	+	0.998394i	$0.481960\pi$
$23$	−4.01081	+	6.94693i	−0.836313	+	1.44854i	−0.892957	+	0.450141i	$0.851374\pi$
$24$		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	0.964201	−	0.265171i	$-0.0854283\pi$
$29$	1.35952	+	2.35475i	0.252456	+	0.437267i	−0.711745	+	0.702438i	$0.752095\pi$
$30$		0			0
$31$	7.37569	+	4.25836i	1.32471	+	0.764823i	0.984476	−	0.175517i	$-0.0561596\pi$
$31$	7.37569	+	4.25836i	1.32471	+	0.764823i	0.340236	+	0.940340i	$0.389493\pi$
$32$		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	0.222149	−	0.975013i	$-0.428693\pi$
$37$	−3.10928	−	1.79515i	−0.511163	−	0.295120i	−0.733312	+	0.679893i	$0.762026\pi$
$38$		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	$-0.565997\pi$
$41$	3.44934	−	1.99148i	0.538696	−	0.311016i	0.744550	+	0.667566i	$0.232664\pi$
$42$		0			0
$43$	−5.74755	+	9.95506i	−0.876494	+	1.51813i	−0.0213310	+	0.999772i	$0.506790\pi$
$43$	−5.74755	+	9.95506i	−0.876494	+	1.51813i	−0.855163	+	0.518359i	$0.826543\pi$
$44$		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	$-0.563874\pi$
$47$	3.76830	−	2.17563i	0.549663	−	0.317348i	0.748986	+	0.662586i	$0.230541\pi$
$48$		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	−0.845538	−	0.533915i	$-0.820720\pi$
$53$	0.288402	−	0.499526i	0.0396150	−	0.0686152i	0.885153	+	0.465300i	$0.154054\pi$
$54$		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	$-0.623295\pi$
$59$	1.80715	−	1.04336i	0.235271	−	0.135834i	0.613002	+	0.790082i	$0.289962\pi$
$60$		0			0
$61$	−3.40510			−0.435979			−0.217989	−	0.975951i	$-0.569950\pi$
$61$	−3.40510			−0.435979			−0.217989	+	0.975951i	$0.569950\pi$
$62$		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	$0.107418\pi$
$67$			5.42026i			0.662190i	−0.943597	+	0.331095i	$0.892582\pi$
$68$		0			0
$69$	12.9589	−	22.4456i	1.56007	−	2.70213i
$70$		0			0
$71$	−7.92574	−	4.57593i	−0.940612	−	0.543063i	−0.0504599	−	0.998726i	$-0.516069\pi$
$71$	−7.92574	−	4.57593i	−0.940612	−	0.543063i	−0.890152	+	0.455663i	$0.849402\pi$
$72$		0			0
$73$	−2.86835	−	1.65604i	−0.335715	−	0.193825i	0.322661	−	0.946515i	$-0.395423\pi$
$73$	−2.86835	−	1.65604i	−0.335715	−	0.193825i	−0.658376	+	0.752690i	$0.728756\pi$
$74$		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	0.999979	+	0.00646364i	$0.00205746\pi$
$79$	4.49376	+	7.78342i	0.505587	+	0.875703i	−0.494392	+	0.869239i	$0.664609\pi$
$80$		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	$-0.245943\pi$
$89$	4.42996	+	2.55764i	0.469574	+	0.271109i	−0.246487	+	0.969146i	$0.579276\pi$
$90$		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	$-0.495870\pi$
$97$	−8.33696	−	4.81334i	−0.846490	−	0.488721i	−0.859465	+	0.511195i	$0.829203\pi$
$98$		0			0
$99$		−	28.6282i		−	2.87724i
$100$		0			0
$101$	−2.54158			−0.252896			−0.126448	−	0.991973i	$-0.540358\pi$
$101$	−2.54158			−0.252896			−0.126448	+	0.991973i	$0.540358\pi$
$102$		0			0
$103$	1.67696	+	2.90458i	0.165236	+	0.286197i	0.936739	−	0.350029i	$-0.113828\pi$
$103$	1.67696	+	2.90458i	0.165236	+	0.286197i	−0.771503	+	0.636225i	$0.780495\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.45650	−	11.1830i	0.624174	−	1.08110i	−0.364526	−	0.931193i	$-0.618769\pi$
$107$	6.45650	−	11.1830i	0.624174	−	1.08110i	0.988700	−	0.149907i	$-0.0478975\pi$
$108$		0			0
$109$	6.96516	+	4.02134i	0.667141	+	0.385174i	0.794993	−	0.606619i	$-0.207475\pi$
$109$	6.96516	+	4.02134i	0.667141	+	0.385174i	−0.127851	+	0.991793i	$0.540808\pi$
$110$		0			0
$111$	10.0461	+	5.80012i	0.953534	+	0.550523i
$112$		0			0
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	−0.614043	−	0.789273i	$-0.710458\pi$
$113$	4.00235	−	6.93227i	0.376509	−	0.652133i	0.990552	+	0.137140i	$0.0437910\pi$
$114$		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	0.893996	−	0.448074i	$-0.147890\pi$
$127$	0.664383	+	1.15075i	0.0589545	+	0.102112i	−0.835042	+	0.550186i	$0.814557\pi$
$128$		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	$-0.174910\pi$
$131$	−0.296380	−	0.513346i	−0.0258949	−	0.0448512i	−0.878682	+	0.477407i	$0.841577\pi$
$132$		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	−0.402281	−	0.915516i	$-0.631783\pi$
$137$	2.21732	−	1.28017i	0.189439	−	0.109372i	0.591720	+	0.806144i	$0.298449\pi$
$138$		0			0
$139$	−9.01150	+	15.6084i	−0.764345	+	1.32388i	0.176247	+	0.984346i	$0.443604\pi$
$139$	−9.01150	+	15.6084i	−0.764345	+	1.32388i	−0.940592	+	0.339538i	$0.889729\pi$
$140$		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	$-0.892239\pi$
$149$		−	8.10789i		−	0.664224i	0.943240	−	0.332112i	$-0.107761\pi$
$150$		0			0
$151$	3.10734	+	1.79402i	0.252872	+	0.145995i	0.621078	−	0.783748i	$-0.286695\pi$
$151$	3.10734	+	1.79402i	0.252872	+	0.145995i	−0.368207	+	0.929744i	$0.620028\pi$
$152$		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	−0.423900	−	0.905709i	$-0.639339\pi$
$157$	7.17236	−	12.4229i	0.572417	−	0.991455i	0.996317	−	0.0857459i	$-0.0273273\pi$
$158$		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	$-0.996932\pi$
$163$		−	0.246141i		−	0.0192792i	0.999954	−	0.00963961i	$-0.00306843\pi$
$164$		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	$-0.688956\pi$
$167$	−1.56604	+	0.904156i	−0.121184	+	0.0699657i	0.438183	+	0.898886i	$0.355622\pi$
$168$		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	$-0.634660\pi$
$173$	−10.7996			−0.821080			−0.410540	+	0.911843i	$0.634660\pi$
$174$		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	$-0.378682\pi$
$181$	10.0087			0.743940			0.371970	+	0.928245i	$0.378682\pi$
$182$		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	$-0.962416\pi$
$193$		−	3.27308i		−	0.235601i	0.993037	−	0.117801i	$-0.0375844\pi$
$194$		0			0
$195$	−29.1316	−	22.2705i	−2.08616	−	1.59483i
$196$		0			0
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	−0.0520061	−	0.998647i	$-0.516562\pi$
$197$	11.0439	−	6.37619i	0.786844	−	0.454285i	0.838850	+	0.544362i	$0.183228\pi$
$198$		0			0
$199$	−13.6616	−	23.6625i	−0.968442	−	1.67739i	−0.700069	−	0.714076i	$-0.746847\pi$
$199$	−13.6616	−	23.6625i	−0.968442	−	1.67739i	−0.268373	−	0.963315i	$-0.586486\pi$
$200$		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	−0.806728	−	0.590923i	$-0.798764\pi$
$211$	−13.2929	−	23.0239i	−0.915118	−	1.58503i	−0.108390	−	0.994108i	$-0.534570\pi$
$212$		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	$-0.835808\pi$
$223$	−13.1063	+	7.56691i	−0.877661	+	0.506718i	−0.00777474	+	0.999970i	$0.502475\pi$
$224$		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	$-0.918136\pi$
$227$	−18.5376	+	10.7027i	−1.23038	+	0.710362i	−0.263274	+	0.964721i	$0.584802\pi$
$228$		0			0
$229$	7.24104	−	4.18062i	0.478501	−	0.276263i	−0.241290	−	0.970453i	$-0.577571\pi$
$229$	7.24104	−	4.18062i	0.478501	−	0.276263i	0.719792	+	0.694190i	$0.244237\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13.0832	−	22.6607i	−0.857107	−	1.48455i	−0.874676	−	0.484707i	$-0.838926\pi$
$233$	−13.0832	−	22.6607i	−0.857107	−	1.48455i	0.0175695	−	0.999846i	$-0.494407\pi$
$234$		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	$0.202326\pi$
$239$			18.3562i			1.18736i	−0.804700	+	0.593682i	$0.797674\pi$
$240$		0			0
$241$	−2.88804	+	1.66741i	−0.186035	+	0.107407i	−0.590125	−	0.807312i	$-0.700922\pi$
$241$	−2.88804	+	1.66741i	−0.186035	+	0.107407i	0.404090	+	0.914719i	$0.367588\pi$
$242$		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	$-0.707550\pi$
$251$	6.09884	−	10.5635i	0.384956	−	0.666763i	0.991763	+	0.128086i	$0.0408834\pi$
$252$		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	$-0.991374\pi$
$257$	−7.63648	+	13.2268i	−0.476350	+	0.825063i	0.523282	+	0.852159i	$0.324707\pi$
$258$		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	$-0.243656\pi$
$269$	−3.92836	−	6.80413i	−0.239517	−	0.414855i	−0.960576	+	0.278019i	$0.910322\pi$
$270$		0			0
$271$	2.28514	+	1.31933i	0.138812	+	0.0801433i	0.567798	−	0.823168i	$-0.307796\pi$
$271$	2.28514	+	1.31933i	0.138812	+	0.0801433i	−0.428986	+	0.903311i	$0.641129\pi$
$272$		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	0.986273	−	0.165122i	$-0.0528019\pi$
$277$	5.82743	+	10.0934i	0.350136	+	0.606454i	−0.636137	+	0.771576i	$0.719469\pi$
$278$		0			0
$279$	54.8705	+	31.6795i	3.28501	+	1.89660i
$280$		0			0
$281$			3.86501i			0.230567i	0.993333	+	0.115283i	$0.0367776\pi$
$281$			3.86501i			0.230567i	−0.993333	+	0.115283i	$0.963222\pi$
$282$		0			0
$283$	6.84863			0.407109			0.203554	−	0.979064i	$-0.434751\pi$
$283$	6.84863			0.407109			0.203554	+	0.979064i	$0.434751\pi$
$284$		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	$-0.347182\pi$
$293$	−1.28946	−	0.744468i	−0.0753309	−	0.0434923i	−0.537192	+	0.843460i	$0.680515\pi$
$294$		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	$-0.724512\pi$
$311$	5.91221	−	10.2403i	0.335251	−	0.580672i	0.983533	+	0.180729i	$0.0578456\pi$
$312$		0			0
$313$	−9.20434	−	15.9424i	−0.520260	−	0.901117i	−0.999723	−	0.0235548i	$-0.992502\pi$
$313$	−9.20434	−	15.9424i	−0.520260	−	0.901117i	0.479462	−	0.877563i	$-0.340832\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.29431	+	4.21137i	−0.409689	+	0.236534i	−0.690656	−	0.723183i	$-0.742678\pi$
$317$	−7.29431	+	4.21137i	−0.409689	+	0.236534i	0.280967	+	0.959717i	$0.409345\pi$
$318$		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	$-0.834713\pi$
$331$		−	18.0566i		−	0.992481i	0.868185	−	0.496240i	$-0.165287\pi$
$332$		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	0.600941	−	0.799294i	$-0.294793\pi$
$347$	−7.29727	−	12.6392i	−0.391738	−	0.678510i	−0.992679	+	0.120783i	$0.961459\pi$
$348$		0			0
$349$	15.4877	−	8.94182i	0.829037	−	0.478645i	−0.0244861	−	0.999700i	$-0.507795\pi$
$349$	15.4877	−	8.94182i	0.829037	−	0.478645i	0.853523	+	0.521056i	$0.174462\pi$
$350$		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	0.400076	−	0.916482i	$-0.368984\pi$
$359$	26.4089	−	15.2472i	1.39381	−	0.804717i	0.993735	+	0.111765i	$0.0356505\pi$
$360$		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	$-0.440136\pi$
$367$	7.16337			0.373925			0.186962	+	0.982367i	$0.440136\pi$
$368$		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	−0.978820	−	0.204723i	$-0.934371\pi$
$379$	−25.1318	+	14.5099i	−1.29093	+	0.745322i	−0.312115	+	0.950044i	$0.601037\pi$
$380$		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	−0.212233	−	0.977219i	$-0.568074\pi$
$389$	14.5986	−	25.2856i	0.740180	−	1.28203i	0.952413	−	0.304811i	$-0.0985932\pi$
$390$		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	−0.992631	−	0.121176i	$-0.961334\pi$
$401$	−31.9176	−	18.4276i	−1.59389	−	0.920232i	−0.601257	−	0.799056i	$-0.705333\pi$
$402$		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	$-0.622018\pi$
$409$	4.89732	−	2.82747i	0.242157	−	0.139809i	0.616168	+	0.787615i	$0.288684\pi$
$410$		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	−0.987478	−	0.157754i	$-0.949575\pi$
$419$	−12.9031	−	22.3488i	−0.630358	−	1.09181i	0.357120	−	0.934059i	$-0.383759\pi$
$420$		0			0
$421$			28.8606i			1.40658i	0.710903	+	0.703290i	$0.248286\pi$
$421$			28.8606i			1.40658i	−0.710903	+	0.703290i	$0.751714\pi$
$422$		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	$-0.723837\pi$
$431$		−	31.6712i		−	1.52555i	0.646665	−	0.762774i	$-0.276163\pi$
$432$		0			0
$433$	−15.6517	+	27.1095i	−0.752172	+	1.30280i	0.194597	+	0.980883i	$0.437660\pi$
$433$	−15.6517	+	27.1095i	−0.752172	+	1.30280i	−0.946768	+	0.321916i	$0.895673\pi$
$434$		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	−0.0327479	+	0.999464i	$0.510426\pi$
$439$	−18.4786	+	32.0059i	−0.881935	+	1.52756i	−0.849187	+	0.528092i	$0.822907\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−14.1436	−	24.4974i	−0.671981	−	1.16391i	−0.977341	−	0.211669i	$-0.932110\pi$
$443$	−14.1436	−	24.4974i	−0.671981	−	1.16391i	0.305360	−	0.952237i	$-0.401223\pi$
$444$		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	0.906559	−	0.422079i	$-0.138699\pi$
$449$	21.0690	+	12.1642i	0.994308	+	0.574064i	0.0877485	+	0.996143i	$0.472033\pi$
$450$		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	0.531059	−	0.847335i	$-0.321794\pi$
$457$	1.34199	+	0.774798i	0.0627756	+	0.0362435i	−0.468284	+	0.883578i	$0.655127\pi$
$458$		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	$-0.430885\pi$
$461$	−11.2195	−	6.47760i	−0.522545	−	0.301692i	−0.737975	+	0.674828i	$0.764218\pi$
$462$		0			0
$463$		−	28.1690i		−	1.30912i	−0.756008	−	0.654562i	$-0.772853\pi$
$463$		−	28.1690i		−	1.30912i	0.756008	−	0.654562i	$-0.227147\pi$
$464$		0			0
$465$	86.6166			4.01675
$466$		0			0
$467$	−14.6454	−	25.3666i	−0.677709	−	1.17383i	−0.975669	−	0.219248i	$-0.929639\pi$
$467$	−14.6454	−	25.3666i	−0.677709	−	1.17383i	0.297960	−	0.954578i	$-0.403694\pi$
$468$		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	−0.586346	−	0.810060i	$-0.699434\pi$
$487$	−3.92783	+	2.26773i	−0.177987	+	0.102761i	0.408360	+	0.912821i	$0.366101\pi$
$488$		0			0
$489$			0.795281i			0.0359638i
$490$		0			0
$491$	9.07433	+	15.7172i	0.409519	+	0.709307i	0.994836	−	0.101497i	$-0.0323633\pi$
$491$	9.07433	+	15.7172i	0.409519	+	0.709307i	−0.585317	+	0.810804i	$0.699030\pi$
$492$		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	−0.623430	−	0.781879i	$-0.714261\pi$
$499$	−5.76368	+	3.32766i	−0.258018	+	0.148967i	0.365412	+	0.930846i	$0.380928\pi$
$500$		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	$-0.725402\pi$
$503$	7.45978	−	12.9207i	0.332615	−	0.576106i	0.983024	+	0.183478i	$0.0587357\pi$
$504$		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	$-0.462160\pi$
$509$	−15.3869	−	8.88365i	−0.682014	−	0.393761i	−0.800613	+	0.599181i	$0.795493\pi$
$510$		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	−0.0614331	−	0.998111i	$-0.519567\pi$
$521$	19.0289	−	32.9591i	0.833673	−	1.44396i	0.895106	−	0.445853i	$-0.147100\pi$
$522$		0			0
$523$	6.94526	−	12.0295i	0.303695	−	0.526015i	−0.673275	−	0.739392i	$-0.735113\pi$
$523$	6.94526	−	12.0295i	0.303695	−	0.526015i	0.976970	+	0.213377i	$0.0684463\pi$
$524$		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	−0.560595	+	0.828090i	$0.689428\pi$
$541$	−36.2391	+	20.9226i	−1.55804	+	0.899535i	−0.997445	+	0.0714444i	$0.977239\pi$
$542$		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	$0.225019\pi$
$557$			30.6572i			1.29899i	−0.760368	+	0.649493i	$0.774981\pi$
$558$		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	0.968255	+	0.249966i	$0.0804193\pi$
$563$	16.6237	+	28.7930i	0.700604	+	1.21348i	−0.267651	+	0.963516i	$0.586247\pi$
$564$		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	−0.718307	−	0.695726i	$-0.755083\pi$
$569$	5.80511	−	10.0547i	0.243363	−	0.421517i	0.961670	+	0.274209i	$0.0884161\pi$
$570$		0			0
$571$	−8.34968	+	14.4621i	−0.349423	+	0.605219i	−0.986147	−	0.165873i	$-0.946956\pi$
$571$	−8.34968	+	14.4621i	−0.349423	+	0.605219i	0.636724	+	0.771092i	$0.280289\pi$
$572$		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	$-0.615856\pi$
$577$	−32.2666	−	18.6291i	−1.34328	−	0.775541i	−0.987287	+	0.158948i	$0.949190\pi$
$578$		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	$-0.997725\pi$
$587$	−36.1912	+	20.8950i	−1.49377	+	0.862429i	−0.493796	+	0.869578i	$0.664391\pi$
$588$		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	$-0.638286\pi$
$593$	3.75571	−	2.16836i	0.154228	−	0.0890438i	0.575128	+	0.818063i	$0.304952\pi$
$594$		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	−0.999198	−	0.0400339i	$-0.987253\pi$
$599$	−11.3789	+	19.7088i	−0.464929	+	0.805280i	0.534270	+	0.845314i	$0.320587\pi$
$600$		0			0
$601$	−13.7634	−	23.8389i	−0.561421	−	0.972410i	−0.997373	−	0.0724402i	$-0.976921\pi$
$601$	−13.7634	−	23.8389i	−0.561421	−	0.972410i	0.435951	−	0.899970i	$-0.356412\pi$
$602$		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	$-0.441075\pi$
$607$	9.06967			0.368126			0.184063	+	0.982914i	$0.441075\pi$
$608$		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	$-0.939344\pi$
$613$		−	9.37895i		−	0.378812i	0.981899	−	0.189406i	$-0.0606563\pi$
$614$		0			0
$615$	20.2537	−	35.0804i	0.816708	−	1.41458i
$616$		0			0
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.127267	−	0.991869i	$-0.540620\pi$
$617$	−26.0786	−	15.0565i	−1.04988	−	0.606151i	−0.922617	+	0.385718i	$0.873954\pi$
$618$		0			0
$619$	34.5494	+	19.9471i	1.38866	+	0.801742i	0.993164	−	0.116727i	$-0.0372404\pi$
$619$	34.5494	+	19.9471i	1.38866	+	0.801742i	0.395493	+	0.918469i	$0.370574\pi$
$620$		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	0.00989522	−	0.999951i	$-0.496850\pi$
$631$	−21.3804	−	12.3440i	−0.851140	−	0.491406i	−0.861035	+	0.508545i	$0.830184\pi$
$632$		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	0.621525	−	0.783394i	$-0.286513\pi$
$641$	−9.30883	−	16.1234i	−0.367677	−	0.636834i	−0.989202	+	0.146560i	$0.953180\pi$
$642$		0			0
$643$	27.4384	+	15.8415i	1.08206	+	0.624729i	0.931452	−	0.363864i	$-0.118543\pi$
$643$	27.4384	+	15.8415i	1.08206	+	0.624729i	0.150611	+	0.988593i	$0.451876\pi$
$644$		0			0
$645$			116.908i			4.60323i
$646$		0			0
$647$	29.6583			1.16599			0.582994	−	0.812477i	$-0.301881\pi$
$647$	29.6583			1.16599			0.582994	+	0.812477i	$0.301881\pi$
$648$		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	−0.963052	−	0.269315i	$-0.913203\pi$
$653$	−6.34483	+	10.9896i	−0.248292	+	0.430055i	0.714760	+	0.699370i	$0.246536\pi$
$654$		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	−0.521471	−	0.853269i	$-0.674617\pi$
$659$	12.2763	−	21.2632i	0.478217	−	0.828296i	0.999688	+	0.0249730i	$0.00794998\pi$
$660$		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	0.793066	−	0.609136i	$-0.208484\pi$
$673$	−3.39829	−	5.88601i	−0.130994	−	0.226889i	−0.924060	+	0.382247i	$0.875150\pi$
$674$		0			0
$675$	−35.1989	+	60.9664i	−1.35481	+	2.34660i
$676$		0			0
$677$	−13.0478	−	22.5995i	−0.501468	−	0.868569i	−0.999999	−	0.00169631i	$-0.999460\pi$
$677$	−13.0478	−	22.5995i	−0.501468	−	0.868569i	0.498530	−	0.866872i	$-0.333873\pi$
$678$		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	−0.624900	+	0.780705i	$0.714860\pi$
$683$	−42.1666	+	24.3449i	−1.61346	+	0.931532i	−0.988560	+	0.150827i	$0.951806\pi$
$684$		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	$-0.355089\pi$
$691$	−3.10942	−	1.79522i	−0.118288	−	0.0682935i	−0.557977	+	0.829857i	$0.688422\pi$
$692$		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	$0.139838\pi$
$709$			22.6500i			0.850637i	−0.905044	+	0.425318i	$0.860162\pi$
$710$		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	$-0.438769\pi$
$719$	10.2526			0.382358			0.191179	+	0.981555i	$0.438769\pi$
$720$		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	$-0.466881\pi$
$727$	5.60059			0.207715			0.103857	+	0.994592i	$0.466881\pi$
$728$		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	$-0.391837\pi$
$733$	35.6418	−	20.5778i	1.31646	−	0.760058i	0.983157	+	0.182762i	$0.0585038\pi$
$734$		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	$0.0717209\pi$
$739$			12.1469i			0.446833i	−0.974723	+	0.223416i	$0.928279\pi$
$740$		0			0
$741$	−66.2082	+	27.5636i	−2.43222	+	1.01257i
$742$		0			0
$743$	0.486744	−	0.281022i	0.0178569	−	0.0103097i	−0.491045	−	0.871134i	$-0.663385\pi$
$743$	0.486744	−	0.281022i	0.0178569	−	0.0103097i	0.508902	+	0.860825i	$0.330052\pi$
$744$		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	−0.995367	−	0.0961463i	$-0.969348\pi$
$751$	−11.3569	+	19.6707i	−0.414418	+	0.717794i	0.580949	+	0.813940i	$0.302682\pi$
$752$		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	0.632911	−	0.774224i	$-0.281860\pi$
$757$	−9.74099	−	16.8719i	−0.354042	−	0.613219i	−0.986954	+	0.161005i	$0.948526\pi$
$758$		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	$-0.455752\pi$
$769$	29.5477	−	17.0593i	1.06552	−	0.615176i	0.926953	+	0.375178i	$0.122418\pi$
$770$		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	$-0.840437\pi$
$773$	−25.0026	+	14.4353i	−0.899281	+	0.519200i	−0.0223144	+	0.999751i	$0.507103\pi$
$774$		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	$-0.370704\pi$
$787$	38.9448	−	22.4848i	1.38823	−	0.801497i	0.993116	+	0.117134i	$0.0373706\pi$
$788$		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	$-0.709485\pi$
$797$	10.7092	−	18.5489i	0.379340	−	0.657036i	0.990966	+	0.134111i	$0.0428179\pi$
$798$		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	0.127184	−	0.991879i	$-0.459406\pi$
$821$	−19.1465	−	11.0542i	−0.668216	−	0.385795i	−0.795400	+	0.606084i	$0.792739\pi$
$822$		0			0
$823$	−21.0355	−	36.4346i	−0.733252	−	1.27003i	−0.955486	−	0.295037i	$-0.904668\pi$
$823$	−21.0355	−	36.4346i	−0.733252	−	1.27003i	0.222234	−	0.974993i	$-0.428665\pi$
$824$		0			0
$825$	52.8478	+	30.5117i	1.83992	+	1.06228i
$826$		0			0
$827$		−	44.4242i		−	1.54478i	−0.635148	−	0.772390i	$-0.719061\pi$
$827$		−	44.4242i		−	1.54478i	0.635148	−	0.772390i	$-0.280939\pi$
$828$		0			0
$829$	−17.9479			−0.623355			−0.311678	−	0.950188i	$-0.600891\pi$
$829$	−17.9479			−0.623355			−0.311678	+	0.950188i	$0.600891\pi$
$830$		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	$-0.352985\pi$
$839$	−3.09534	−	1.78709i	−0.106863	−	0.0616973i	−0.552479	+	0.833527i	$0.686318\pi$
$840$		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	$-0.985553\pi$
$857$	−13.4719	+	23.3340i	−0.460192	+	0.797076i	0.538778	+	0.842448i	$0.318886\pi$
$858$		0			0
$859$	−8.97686	−	15.5484i	−0.306287	−	0.530504i	0.671260	−	0.741222i	$-0.265753\pi$
$859$	−8.97686	−	15.5484i	−0.306287	−	0.530504i	−0.977547	+	0.210718i	$0.932420\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.59914	−	5.54206i	0.326758	−	0.188654i	−0.327643	−	0.944802i	$-0.606254\pi$
$863$	9.59914	−	5.54206i	0.326758	−	0.188654i	0.654401	+	0.756148i	$0.272921\pi$
$864$		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	$0.0247863\pi$
$877$			4.60737i			0.155580i	−0.996970	+	0.0777899i	$0.975214\pi$
$878$		0			0
$879$	4.16624	+	2.40538i	0.140524	+	0.0811314i
$880$		0			0
$881$	17.1554	+	29.7140i	0.577979	+	1.00109i	0.995711	+	0.0925186i	$0.0294918\pi$
$881$	17.1554	+	29.7140i	0.577979	+	1.00109i	−0.417732	+	0.908570i	$0.637175\pi$
$882$		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	−0.270509	−	0.962717i	$-0.587192\pi$
$887$	20.8026	−	36.0312i	0.698483	−	1.20981i	0.968992	−	0.247091i	$-0.0794745\pi$
$888$		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	$-0.547408\pi$
$937$	−9.08442			−0.296775			−0.148388	+	0.988929i	$0.547408\pi$
$938$		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	$-0.290486\pi$
$941$	7.13037	+	4.11672i	0.232444	+	0.134201i	−0.379255	+	0.925292i	$0.623820\pi$
$942$		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	0.427177	−	0.904168i	$-0.359508\pi$
$947$	−4.37804	−	2.52766i	−0.142267	−	0.0821380i	−0.569444	+	0.822030i	$0.692841\pi$
$948$		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	−0.349352	−	0.936992i	$-0.613598\pi$
$953$	19.6579	−	34.0485i	0.636782	−	1.10294i	0.986135	−	0.165948i	$-0.0530684\pi$
$954$		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	$0.110778\pi$
$967$			21.2101i			0.682071i	−0.940050	+	0.341036i	$0.889222\pi$
$968$		0			0
$969$	−3.34815	+	1.93306i	−0.107558	+	0.0620987i
$970$		0			0
$971$	23.5410			0.755466			0.377733	−	0.925915i	$-0.376704\pi$
$971$	23.5410			0.755466			0.377733	+	0.925915i	$0.376704\pi$
$972$		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	$-0.936444\pi$
$977$		−	12.3992i		−	0.396684i	0.980133	−	0.198342i	$-0.0635557\pi$
$978$		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	$-0.528520\pi$
$983$	−31.2516	−	18.0431i	−0.996770	−	0.575486i	−0.907291	+	0.420503i	$0.861854\pi$
$984$		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	$-0.159568\pi$
$997$	0.704139	+	1.21960i	0.0223003	+	0.0386252i	−0.854660	+	0.519188i	$0.826234\pi$
$998$		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.c.361.1		16
7.2	even	3		2548.2.bb.c.569.8		16
7.3	odd	6		364.2.u.a.309.1	yes	16
7.4	even	3		2548.2.u.c.1765.8		16
7.5	odd	6		2548.2.bb.d.569.1		16
7.6	odd	2		2548.2.bq.e.361.8		16
13.4	even	6		2548.2.bb.c.1733.8		16
21.17	even	6		3276.2.cf.c.1765.2		16
28.3	even	6		1456.2.cc.f.673.8		16
91.3	odd	6		4732.2.g.k.337.16		16
91.4	even	6		2548.2.u.c.589.8		16
91.10	odd	6		4732.2.g.k.337.15		16
91.17	odd	6		364.2.u.a.225.1	✓	16
91.24	even	12		4732.2.a.s.1.8		8
91.30	even	6	inner	2548.2.bq.c.1941.1		16
91.69	odd	6		2548.2.bb.d.1733.1		16
91.80	even	12		4732.2.a.t.1.8		8
91.82	odd	6		2548.2.bq.e.1941.8		16
273.17	even	6		3276.2.cf.c.2773.7		16
364.199	even	6		1456.2.cc.f.225.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.u.a.225.1	✓	16	91.17	odd	6
364.2.u.a.309.1	yes	16	7.3	odd	6
1456.2.cc.f.225.8		16	364.199	even	6
1456.2.cc.f.673.8		16	28.3	even	6
2548.2.u.c.589.8		16	91.4	even	6
2548.2.u.c.1765.8		16	7.4	even	3
2548.2.bb.c.569.8		16	7.2	even	3
2548.2.bb.c.1733.8		16	13.4	even	6
2548.2.bb.d.569.1		16	7.5	odd	6
2548.2.bb.d.1733.1		16	91.69	odd	6
2548.2.bq.c.361.1		16	1.1	even	1	trivial
2548.2.bq.c.1941.1		16	91.30	even	6	inner
2548.2.bq.e.361.8		16	7.6	odd	2
2548.2.bq.e.1941.8		16	91.82	odd	6
3276.2.cf.c.1765.2		16	21.17	even	6
3276.2.cf.c.2773.7		16	273.17	even	6
4732.2.a.s.1.8		8	91.24	even	12
4732.2.a.t.1.8		8	91.80	even	12
4732.2.g.k.337.15		16	91.10	odd	6
4732.2.g.k.337.16		16	91.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2548 = 2^{2} \cdot 7^{2} \cdot 13 \)
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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