LMFDB - Embedded newform 2548.2.bb.d.569.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2548,2,Mod(569,2548)] 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, 2, 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("2548.569"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,-14,0,-6,0,10] 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:	$\Z[a_1, \ldots, a_{9}]$
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			569.1
Root			$-3.23100i$ of defining polynomial
Character	$\chi$	$=$	2548.569
Dual form			2548.2.bb.d.1733.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61550 + 2.79813i) q^{3} +(-2.72598 - 1.57385i) q^{5} +(-3.71968 - 6.44268i) q^{9} +(3.33264 + 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(8.80765 - 5.08510i) q^{15} -0.194369 q^{17} +(-5.33141 + 3.07809i) q^{19} +8.02163 q^{23} +(2.45398 + 4.25042i) q^{25} +14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} +(7.37569 - 4.25836i) q^{31} +(-10.7678 + 6.21677i) q^{33} +3.59029i q^{37} +(-11.5526 - 1.49984i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(-5.74755 + 9.95506i) q^{43} +23.4168i q^{45} +(3.76830 + 2.17563i) q^{47} +(0.314003 - 0.543869i) q^{51} +(0.288402 + 0.499526i) q^{53} +(-6.05647 - 10.4901i) q^{55} -19.8906i q^{57} -2.08672i q^{59} +(-1.70255 - 2.94891i) q^{61} +(1.46117 - 11.2547i) q^{65} +(-4.69408 - 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(-7.92574 - 4.57593i) q^{71} +(-2.86835 + 1.65604i) q^{73} -15.8576 q^{75} +(4.49376 - 7.78342i) q^{79} +(-12.0130 + 20.8072i) q^{81} +7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} -8.78521 q^{87} +5.11527i q^{89} +27.5175i q^{93} +19.3778 q^{95} +(8.33696 + 4.81334i) q^{97} -28.6282i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} + 6 q^{15} - 4 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} + 30 q^{31} - 42 q^{33} - 18 q^{39} + 36 q^{41} + 6 q^{43} - 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 4 q^{61}+ \cdots - 42 q^{97}+O(q^{100}) $ 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 + 6 * q^15 - 4 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 + 30 * q^31 - 42 * q^33 - 18 * q^39 + 36 * q^41 + 6 * q^43 - 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 4 * q^61 + 30 * q^65 - 24 * q^67 - 52 * q^69 + 36 * q^71 - 12 * q^73 + 20 * q^75 - 4 * q^79 + 42 * q^85 - 52 * q^87 + 60 * q^95 - 42 * q^97

Character values

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

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

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
$3$	−1.61550	+	2.79813i	−0.932710	+	1.61550i	−0.154042	+	0.988064i	$0.549229\pi$
$3$	−1.61550	+	2.79813i	−0.932710	+	1.61550i	−0.778668	+	0.627436i	$0.784104\pi$
$4$		0			0
$5$	−2.72598	−	1.57385i	−1.21910	−	0.703845i	−0.254371	−	0.967107i	$-0.581869\pi$
$5$	−2.72598	−	1.57385i	−1.21910	−	0.703845i	−0.964725	+	0.263261i	$0.915202\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.71968	−	6.44268i	−1.23989	−	2.14756i
$10$		0			0
$11$	3.33264	+	1.92410i	1.00483	+	0.580138i	0.909673	−	0.415324i	$-0.136332\pi$
$11$	3.33264	+	1.92410i	1.00483	+	0.580138i	0.0951552	+	0.995462i	$0.469665\pi$
$12$		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
$17$	−0.194369			−0.0471413			−0.0235707	−	0.999722i	$-0.507503\pi$
$17$	−0.194369			−0.0471413			−0.0235707	+	0.999722i	$0.507503\pi$
$18$		0			0
$19$	−5.33141	+	3.07809i	−1.22311	+	0.706162i	−0.965579	−	0.260108i	$-0.916242\pi$
$19$	−5.33141	+	3.07809i	−1.22311	+	0.706162i	−0.257529	+	0.966271i	$0.582908\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.02163			1.67263			0.836313	−	0.548253i	$-0.184707\pi$
$23$	8.02163			1.67263			0.836313	+	0.548253i	$0.184707\pi$
$24$		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	0.340236	−	0.940340i	$-0.389493\pi$
$31$	7.37569	−	4.25836i	1.32471	−	0.764823i	0.984476	+	0.175517i	$0.0561596\pi$
$32$		0			0
$33$	−10.7678	+	6.21677i	−1.87443	+	1.08220i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			3.59029i			0.590240i	0.955460	+	0.295120i	$0.0953597\pi$
$37$			3.59029i			0.590240i	−0.955460	+	0.295120i	$0.904640\pi$
$38$		0			0
$39$	−11.5526	−	1.49984i	−1.84989	−	0.240167i
$40$		0			0
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	−0.744550	−	0.667566i	$-0.767336\pi$
$41$	−3.44934	+	1.99148i	−0.538696	+	0.311016i	0.205854	+	0.978583i	$0.434003\pi$
$42$		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
$45$			23.4168i			3.49078i
$46$		0			0
$47$	3.76830	+	2.17563i	0.549663	+	0.317348i	0.748986	−	0.662586i	$-0.230541\pi$
$47$	3.76830	+	2.17563i	0.549663	+	0.317348i	−0.199323	+	0.979934i	$0.563874\pi$
$48$		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
$59$		−	2.08672i		−	0.271668i	−0.990732	−	0.135834i	$-0.956629\pi$
$59$		−	2.08672i		−	0.271668i	0.990732	−	0.135834i	$-0.0433714\pi$
$60$		0			0
$61$	−1.70255	−	2.94891i	−0.217989	−	0.377569i	0.736204	−	0.676760i	$-0.236617\pi$
$61$	−1.70255	−	2.94891i	−0.217989	−	0.377569i	−0.954193	+	0.299191i	$0.903283\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.46117	−	11.2547i	0.181236	−	1.39598i
$66$		0			0
$67$	−4.69408	−	2.71013i	−0.573474	−	0.331095i	0.185062	−	0.982727i	$-0.440751\pi$
$67$	−4.69408	−	2.71013i	−0.573474	−	0.331095i	−0.758535	+	0.651632i	$0.774085\pi$
$68$		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	−0.658376	−	0.752690i	$-0.728756\pi$
$73$	−2.86835	+	1.65604i	−0.335715	+	0.193825i	0.322661	+	0.946515i	$0.395423\pi$
$74$		0			0
$75$	−15.8576			−1.83108
$76$		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
$81$	−12.0130	+	20.8072i	−1.33478	+	2.31191i
$82$		0			0
$83$			7.66353i			0.841181i	0.907251	+	0.420591i	$0.138177\pi$
$83$			7.66353i			0.841181i	−0.907251	+	0.420591i	$0.861823\pi$
$84$		0			0
$85$	0.529845	+	0.305906i	0.0574698	+	0.0331802i
$86$		0			0
$87$	−8.78521			−0.941873
$88$		0			0
$89$			5.11527i			0.542218i	0.962549	+	0.271109i	$0.0873904\pi$
$89$			5.11527i			0.542218i	−0.962549	+	0.271109i	$0.912610\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$			27.5175i			2.85343i
$94$		0			0
$95$	19.3778			1.98812
$96$		0			0
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	0.859465	−	0.511195i	$-0.170797\pi$
$97$	8.33696	+	4.81334i	0.846490	+	0.488721i	−0.0129752	+	0.999916i	$0.504130\pi$
$98$		0			0
$99$		−	28.6282i		−	2.87724i
$100$		0			0
$101$	−1.27079	+	2.20107i	−0.126448	+	0.219015i	−0.922298	−	0.386479i	$-0.873691\pi$
$101$	−1.27079	+	2.20107i	−0.126448	+	0.219015i	0.795850	+	0.605494i	$0.207024\pi$
$102$		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
$107$	−12.9130			−1.24835			−0.624174	−	0.781286i	$-0.714564\pi$
$107$	−12.9130			−1.24835			−0.624174	+	0.781286i	$0.714564\pi$
$108$		0			0
$109$	−6.96516	+	4.02134i	−0.667141	+	0.385174i	−0.794993	−	0.606619i	$-0.792525\pi$
$109$	−6.96516	+	4.02134i	−0.667141	+	0.385174i	0.127851	+	0.991793i	$0.459192\pi$
$110$		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
$115$	−21.8668	−	12.6248i	−2.03909	−	1.17727i
$116$		0			0
$117$	16.2906	−	21.3094i	1.50607	−	1.97005i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.90432	+	3.29839i	0.173120	+	0.299853i
$122$		0			0
$123$		−	12.8689i		−	1.16035i
$124$		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	$-0.825090\pi$
$131$	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
$137$			2.56034i			0.218745i	0.994001	+	0.109372i	$0.0348841\pi$
$137$			2.56034i			0.218745i	−0.994001	+	0.109372i	$0.965116\pi$
$138$		0			0
$139$	9.01150	−	15.6084i	0.764345	−	1.32388i	−0.176247	−	0.984346i	$-0.556396\pi$
$139$	9.01150	−	15.6084i	0.764345	−	1.32388i	0.940592	−	0.339538i	$-0.110271\pi$
$140$		0			0
$141$	−12.1754	+	7.02946i	−1.02535	+	0.591987i
$142$		0			0
$143$	−1.78635	+	13.7594i	−0.149382	+	1.15062i
$144$		0			0
$145$		−	8.55869i		−	0.710760i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.02164	+	4.05394i	−0.575235	+	0.332112i	−0.759237	−	0.650814i	$-0.774428\pi$
$149$	−7.02164	+	4.05394i	−0.575235	+	0.332112i	0.184002	+	0.982926i	$0.441095\pi$
$150$		0			0
$151$	−3.10734	+	1.79402i	−0.252872	+	0.145995i	−0.621078	−	0.783748i	$-0.713305\pi$
$151$	−3.10734	+	1.79402i	−0.252872	+	0.145995i	0.368207	+	0.929744i	$0.379972\pi$
$152$		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
$159$	−1.86365			−0.147797
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−0.213164	+	0.123070i	−0.0166963	+	0.00963961i	−0.508325	−	0.861165i	$-0.669735\pi$
$163$	−0.213164	+	0.123070i	−0.0166963	+	0.00963961i	0.491629	+	0.870805i	$0.336402\pi$
$164$		0			0
$165$	39.1370			3.04681
$166$		0			0
$167$	1.56604	−	0.904156i	0.121184	−	0.0699657i	−0.438183	−	0.898886i	$-0.644378\pi$
$167$	1.56604	−	0.904156i	0.121184	−	0.0699657i	0.559367	+	0.828920i	$0.311044\pi$
$168$		0			0
$169$	−9.15934	+	9.22532i	−0.704565	+	0.709640i
$170$		0			0
$171$	39.6623	+	22.8990i	3.03305	+	1.75113i
$172$		0			0
$173$	−5.39981	−	9.35275i	−0.410540	−	0.711076i	0.584409	−	0.811459i	$-0.301326\pi$
$173$	−5.39981	−	9.35275i	−0.410540	−	0.711076i	−0.994949	+	0.100383i	$0.967993\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	5.83892	+	3.37110i	0.438880	+	0.253387i
$178$		0			0
$179$	4.33823	−	7.51404i	0.324255	−	0.561626i	−0.657106	−	0.753798i	$-0.728220\pi$
$179$	4.33823	−	7.51404i	0.324255	−	0.561626i	0.981361	+	0.192172i	$0.0615532\pi$
$180$		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
$185$	5.65057	−	9.78707i	0.415438	−	0.719559i
$186$		0			0
$187$	−0.647761	−	0.373985i	−0.0473690	−	0.0273485i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.0156	+	20.8117i	0.869420	+	1.50588i	0.862591	+	0.505902i	$0.168840\pi$
$191$	12.0156	+	20.8117i	0.869420	+	1.50588i	0.00682903	+	0.999977i	$0.497826\pi$
$192$		0			0
$193$	2.83457	+	1.63654i	0.204037	+	0.117801i	0.598537	−	0.801095i	$-0.295749\pi$
$193$	2.83457	+	1.63654i	0.204037	+	0.117801i	−0.394500	+	0.918896i	$0.629082\pi$
$194$		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
$199$	−27.3231			−1.93688			−0.968442	−	0.249239i	$-0.919819\pi$
$199$	−27.3231			−1.93688			−0.968442	+	0.249239i	$0.919819\pi$
$200$		0			0
$201$	15.1666	−	8.75643i	1.06977	−	0.617631i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	12.5371			0.875629
$206$		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
$215$	31.3355	−	18.0915i	2.13706	−	1.23383i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	10.7014i		−	0.723130i
$220$		0			0
$221$	−0.269348	−	0.646978i	−0.0181183	−	0.0435205i
$222$		0			0
$223$	13.1063	−	7.56691i	0.877661	−	0.506718i	0.00777474	−	0.999970i	$-0.497525\pi$
$223$	13.1063	−	7.56691i	0.877661	−	0.506718i	0.869887	+	0.493252i	$0.164192\pi$
$224$		0			0
$225$	18.2561	−	31.6205i	1.21707	−	2.10803i
$226$		0			0
$227$			21.4054i			1.42072i	0.703836	+	0.710362i	$0.251469\pi$
$227$			21.4054i			1.42072i	−0.703836	+	0.710362i	$0.748531\pi$
$228$		0			0
$229$	7.24104	+	4.18062i	0.478501	+	0.276263i	0.719792	−	0.694190i	$-0.244237\pi$
$229$	7.24104	+	4.18062i	0.478501	+	0.276263i	−0.241290	+	0.970453i	$0.577571\pi$
$230$		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	$0.202326\pi$
$239$			18.3562i			1.18736i	−0.804700	+	0.593682i	$0.797674\pi$
$240$		0			0
$241$			3.33482i			0.214814i	0.994215	+	0.107407i	$0.0342549\pi$
$241$			3.33482i			0.214814i	−0.994215	+	0.107407i	$0.965745\pi$
$242$		0			0
$243$	−17.2988	−	29.9623i	−1.10972	−	1.92209i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−17.6338	−	13.4807i	−1.12201	−	0.857757i
$248$		0			0
$249$	−21.4435	−	12.3804i	−1.35893	−	0.784578i
$250$		0			0
$251$	−6.09884	+	10.5635i	−0.384956	+	0.666763i	−0.991763	−	0.128086i	$-0.959117\pi$
$251$	−6.09884	+	10.5635i	−0.384956	+	0.666763i	0.606807	+	0.794849i	$0.292450\pi$
$252$		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
$257$	−15.2730			−0.952701			−0.476350	−	0.879256i	$-0.658041\pi$
$257$	−15.2730			−0.952701			−0.476350	+	0.879256i	$0.658041\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	10.1140	−	17.5179i	0.626038	−	1.08433i
$262$		0			0
$263$	−12.4495	+	21.5631i	−0.767666	+	1.32964i	0.171159	+	0.985243i	$0.445249\pi$
$263$	−12.4495	+	21.5631i	−0.767666	+	1.32964i	−0.938825	+	0.344394i	$0.888085\pi$
$264$		0			0
$265$		−	1.81560i		−	0.111531i
$266$		0			0
$267$	−14.3132	−	8.26373i	−0.875953	−	0.505732i
$268$		0			0
$269$	−7.85673			−0.479033			−0.239517	−	0.970892i	$-0.576989\pi$
$269$	−7.85673			−0.479033			−0.239517	+	0.970892i	$0.576989\pi$
$270$		0			0
$271$			2.63865i			0.160287i	0.996783	+	0.0801433i	$0.0255378\pi$
$271$			2.63865i			0.160287i	−0.996783	+	0.0801433i	$0.974462\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			18.8868i			1.13892i
$276$		0			0
$277$	−11.6549			−0.700273			−0.350136	−	0.936699i	$-0.613865\pi$
$277$	−11.6549			−0.700273			−0.350136	+	0.936699i	$0.613865\pi$
$278$		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
$283$	3.42431	−	5.93109i	0.203554	−	0.352566i	−0.746117	−	0.665815i	$-0.768084\pi$
$283$	3.42431	−	5.93109i	0.203554	−	0.352566i	0.949671	+	0.313249i	$0.101417\pi$
$284$		0			0
$285$	−31.3048	+	54.2215i	−1.85433	+	3.21180i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−16.9622			−0.997778
$290$		0			0
$291$	−26.9367	+	15.5519i	−1.57906	+	0.911670i
$292$		0			0
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	0.537192	−	0.843460i	$-0.319485\pi$
$293$	1.28946	+	0.744468i	0.0753309	+	0.0434923i	−0.461861	+	0.886952i	$0.652818\pi$
$294$		0			0
$295$	−3.28418	+	5.68836i	−0.191212	+	0.331189i
$296$		0			0
$297$	47.8021	+	27.5985i	2.77376	+	1.60143i
$298$		0			0
$299$	11.1160	+	26.7009i	0.642858	+	1.54415i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−4.10592	−	7.11166i	−0.235879	−	0.408554i
$304$		0			0
$305$			10.7182i			0.613723i
$306$		0			0
$307$			2.33128i			0.133053i	0.997785	+	0.0665265i	$0.0211917\pi$
$307$			2.33128i			0.133053i	−0.997785	+	0.0665265i	$0.978808\pi$
$308$		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	0.690656	−	0.723183i	$-0.257322\pi$
$317$	7.29431	+	4.21137i	0.409689	+	0.236534i	−0.280967	+	0.959717i	$0.590655\pi$
$318$		0			0
$319$			10.4634i			0.585838i
$320$		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
$325$	−10.7474	+	14.0584i	−0.596158	+	0.779821i
$326$		0			0
$327$		−	25.9859i		−	1.43702i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−15.6375	+	9.02830i	−0.859513	+	0.496240i	−0.863849	−	0.503750i	$-0.831953\pi$
$331$	−15.6375	+	9.02830i	−0.859513	+	0.496240i	0.00433587	+	0.999991i	$0.498620\pi$
$332$		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
$341$	32.7740			1.77481
$342$		0			0
$343$		0			0
$344$		0			0
$345$	70.6517	−	40.7908i	3.80376	−	2.19610i
$346$		0			0
$347$	14.5945			0.783476			0.391738	−	0.920077i	$-0.371874\pi$
$347$	14.5945			0.783476			0.391738	+	0.920077i	$0.371874\pi$
$348$		0			0
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	−0.853523	−	0.521056i	$-0.825538\pi$
$349$	−15.4877	+	8.94182i	−0.829037	+	0.478645i	0.0244861	+	0.999700i	$0.492205\pi$
$350$		0			0
$351$	19.8768	+	47.7443i	1.06094	+	2.54840i
$352$		0			0
$353$	−5.52760	−	3.19136i	−0.294204	−	0.169859i	0.345632	−	0.938370i	$-0.387665\pi$
$353$	−5.52760	−	3.19136i	−0.294204	−	0.169859i	−0.639836	+	0.768511i	$0.720998\pi$
$354$		0			0
$355$	14.4036	+	24.9478i	0.764464	+	1.32409i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−26.4089	−	15.2472i	−1.39381	−	0.804717i	−0.400076	−	0.916482i	$-0.631016\pi$
$359$	−26.4089	−	15.2472i	−1.39381	−	0.804717i	−0.993735	+	0.111765i	$0.964350\pi$
$360$		0			0
$361$	9.44927	−	16.3666i	0.497330	−	0.861400i
$362$		0			0
$363$	−12.3057			−0.645884
$364$		0			0
$365$	10.4254			0.545692
$366$		0			0
$367$	3.58169	−	6.20366i	0.186962	−	0.323829i	−0.757274	−	0.653098i	$-0.773469\pi$
$367$	3.58169	−	6.20366i	0.186962	−	0.323829i	0.944236	+	0.329269i	$0.106802\pi$
$368$		0			0
$369$	25.6609	+	14.8153i	1.33585	+	0.771255i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	0.582337	+	1.00864i	0.0301523	+	0.0522252i	0.880708	−	0.473660i	$-0.157067\pi$
$373$	0.582337	+	1.00864i	0.0301523	+	0.0522252i	−0.850556	+	0.525885i	$0.823734\pi$
$374$		0			0
$375$	−0.810620	−	0.468011i	−0.0418602	−	0.0241680i
$376$		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
$381$	−4.29325			−0.219950
$382$		0			0
$383$	−19.0154	+	10.9786i	−0.971642	+	0.560978i	−0.899737	−	0.436433i	$-0.856241\pi$
$383$	−19.0154	+	10.9786i	−0.971642	+	0.560978i	−0.0719059	+	0.997411i	$0.522908\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	85.5163			4.34704
$388$		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
$397$	−27.6698	+	15.9752i	−1.38871	+	0.801771i	−0.993170	−	0.116679i	$-0.962775\pi$
$397$	−27.6698	+	15.9752i	−1.38871	+	0.801771i	−0.395538	+	0.918450i	$0.629442\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			36.8552i			1.84046i	0.391374	+	0.920232i	$0.372000\pi$
$401$			36.8552i			1.84046i	−0.391374	+	0.920232i	$0.628000\pi$
$402$		0			0
$403$	24.3954	+	18.6498i	1.21522	+	0.929011i
$404$		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
$409$		−	5.65493i		−	0.279618i	−0.990178	−	0.139809i	$-0.955351\pi$
$409$		−	5.65493i		−	0.279618i	0.990178	−	0.139809i	$-0.0446489\pi$
$410$		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	$0.0504254\pi$
$419$	12.9031	+	22.3488i	0.630358	+	1.09181i	−0.357120	+	0.934059i	$0.616241\pi$
$420$		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
$423$		−	32.3706i		−	1.57391i
$424$		0			0
$425$	−0.476977	−	0.826149i	−0.0231368	−	0.0400741i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−35.6148	−	27.2268i	−1.71950	−	1.31452i
$430$		0			0
$431$	27.4281	+	15.8356i	1.32116	+	0.762774i	0.983914	−	0.178641i	$-0.0571702\pi$
$431$	27.4281	+	15.8356i	1.32116	+	0.762774i	0.337249	+	0.941415i	$0.390504\pi$
$432$		0			0
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	−0.194597	−	0.980883i	$-0.562340\pi$
$433$	15.6517	−	27.1095i	0.752172	−	1.30280i	0.946768	−	0.321916i	$-0.104327\pi$
$434$		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
$439$	−36.9572			−1.76387			−0.881935	−	0.471371i	$-0.843759\pi$
$439$	−36.9572			−1.76387			−0.881935	+	0.471371i	$0.843759\pi$
$440$		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
$445$	8.05065	−	13.9441i	0.381638	−	0.661016i
$446$		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
$451$	−15.3272			−0.721730
$452$		0			0
$453$		−	11.5930i		−	0.544686i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	1.54960i		−	0.0724870i	−0.999343	−	0.0362435i	$-0.988461\pi$
$457$		−	1.54960i		−	0.0724870i	0.999343	−	0.0362435i	$-0.0115392\pi$
$458$		0			0
$459$	−2.78795			−0.130130
$460$		0			0
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	0.737975	−	0.674828i	$-0.235782\pi$
$461$	11.2195	+	6.47760i	0.522545	+	0.301692i	−0.215430	+	0.976519i	$0.569115\pi$
$462$		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
$465$	43.3083	−	75.0122i	2.00837	−	3.47861i
$466$		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
$471$	46.3478			2.13559
$472$		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
$479$	16.8625	+	9.73555i	0.770466	+	0.444829i	0.833041	−	0.553211i	$-0.186598\pi$
$479$	16.8625	+	9.73555i	0.770466	+	0.444829i	−0.0625747	+	0.998040i	$0.519931\pi$
$480$		0			0
$481$	−11.9507	+	4.97528i	−0.544905	+	0.226853i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.1509	−	26.2422i	−0.687968	−	1.19160i
$486$		0			0
$487$		−	4.53546i		−	0.205521i	−0.994706	−	0.102761i	$-0.967232\pi$
$487$		−	4.53546i		−	0.205521i	0.994706	−	0.102761i	$-0.0327676\pi$
$488$		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	$-0.285739\pi$
$499$	5.76368	+	3.32766i	0.258018	+	0.148967i	−0.365412	+	0.930846i	$0.619072\pi$
$500$		0			0
$501$			5.84266i			0.261031i
$502$		0			0
$503$	−7.45978	+	12.9207i	−0.332615	+	0.576106i	−0.983024	−	0.183478i	$-0.941264\pi$
$503$	−7.45978	+	12.9207i	−0.332615	+	0.576106i	0.650409	+	0.759584i	$0.274598\pi$
$504$		0			0
$505$	6.92829	−	4.00005i	0.308305	−	0.178000i
$506$		0			0
$507$	−11.0167	−	40.5325i	−0.489269	−	1.80011i
$508$		0			0
$509$		−	17.7673i		−	0.787522i	−0.919213	−	0.393761i	$-0.871174\pi$
$509$		−	17.7673i		−	0.787522i	0.919213	−	0.393761i	$-0.128826\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−76.4716	+	44.1509i	−3.37630	+	1.94931i
$514$		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
$523$	13.8905			0.607390			0.303695	−	0.952769i	$-0.401780\pi$
$523$	13.8905			0.607390			0.303695	+	0.952769i	$0.401780\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.43360	+	0.827691i	−0.0624487	+	0.0360548i
$528$		0			0
$529$	41.3465			1.79767
$530$		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
$535$	35.2006	+	20.3231i	1.52185	+	0.878643i
$536$		0			0
$537$	14.0168	+	24.2779i	0.604871	+	1.04767i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	36.2391	+	20.9226i	1.55804	+	0.899535i	0.997445	+	0.0714444i	$0.0227608\pi$
$541$	36.2391	+	20.9226i	1.55804	+	0.899535i	0.560595	+	0.828090i	$0.310572\pi$
$542$		0			0
$543$	16.1690	−	28.0056i	0.693880	−	1.20184i
$544$		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
$549$	−12.6659	+	21.9380i	−0.540568	+	0.936291i
$550$		0			0
$551$	−14.4963	−	8.36943i	−0.617562	−	0.356550i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	18.2570	+	31.6220i	0.774966	+	1.34228i
$556$		0			0
$557$	−26.5499	−	15.3286i	−1.12495	−	0.649493i	−0.182293	−	0.983244i	$-0.558352\pi$
$557$	−26.5499	−	15.3286i	−1.12495	−	0.649493i	−0.942661	+	0.333752i	$0.891685\pi$
$558$		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
$563$	33.2473			1.40121			0.700604	−	0.713550i	$-0.252914\pi$
$563$	33.2473			1.40121			0.700604	+	0.713550i	$0.252914\pi$
$564$		0			0
$565$	−21.8206	+	12.5982i	−0.918001	+	0.530008i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−11.6102			−0.486725			−0.243363	−	0.969935i	$-0.578251\pi$
$569$	−11.6102			−0.486725			−0.243363	+	0.969935i	$0.578251\pi$
$570$		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	−0.987287	−	0.158948i	$-0.949190\pi$
$577$	−32.2666	+	18.6291i	−1.34328	+	0.775541i	−0.355990	+	0.934490i	$0.615856\pi$
$578$		0			0
$579$	−9.15849	+	5.28765i	−0.380614	+	0.219747i
$580$		0			0
$581$		0			0
$582$		0			0
$583$			2.21965i			0.0919287i
$584$		0			0
$585$	−77.9456	+	32.4501i	−3.22265	+	1.34165i
$586$		0			0
$587$	36.1912	−	20.8950i	1.49377	−	0.862429i	0.493796	−	0.869578i	$-0.335609\pi$
$587$	36.1912	−	20.8950i	1.49377	−	0.862429i	0.999974	+	0.00714861i	$0.00227549\pi$
$588$		0			0
$589$	−26.2152	+	45.4061i	−1.08018	+	1.87092i
$590$		0			0
$591$			41.2030i			1.69486i
$592$		0			0
$593$	3.75571	+	2.16836i	0.154228	+	0.0890438i	0.575128	−	0.818063i	$-0.304952\pi$
$593$	3.75571	+	2.16836i	0.154228	+	0.0890438i	−0.420900	+	0.907107i	$0.638286\pi$
$594$		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	0.997373	+	0.0724402i	$0.0230786\pi$
$601$	13.7634	+	23.8389i	0.561421	+	0.972410i	−0.435951	+	0.899970i	$0.643588\pi$
$602$		0			0
$603$			40.3233i			1.64209i
$604$		0			0
$605$		−	11.9885i		−	0.487400i
$606$		0			0
$607$	4.53483	+	7.85456i	0.184063	+	0.318807i	0.943260	−	0.332054i	$-0.107742\pi$
$607$	4.53483	+	7.85456i	0.184063	+	0.318807i	−0.759197	+	0.650861i	$0.774408\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.01987	+	15.5581i	−0.0817153	+	0.629414i
$612$		0			0
$613$	8.12241	+	4.68947i	0.328061	+	0.189406i	0.654980	−	0.755646i	$-0.272677\pi$
$613$	8.12241	+	4.68947i	0.328061	+	0.189406i	−0.326919	+	0.945052i	$0.606010\pi$
$614$		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	0.395493	−	0.918469i	$-0.370574\pi$
$619$	34.5494	−	19.9471i	1.38866	−	0.801742i	0.993164	+	0.116727i	$0.0372404\pi$
$620$		0			0
$621$	115.059			4.61716
$622$		0			0
$623$		0			0
$624$		0			0
$625$	12.7259	−	22.0418i	0.509034	−	0.881673i
$626$		0			0
$627$	38.2715	−	66.2883i	1.52842	−	2.64730i
$628$		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
$633$	85.8985			3.41416
$634$		0			0
$635$		−	4.18255i		−	0.165979i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			68.0840i			2.69336i
$640$		0			0
$641$	18.6177			0.735353			0.367677	−	0.929954i	$-0.380153\pi$
$641$	18.6177			0.735353			0.367677	+	0.929954i	$0.380153\pi$
$642$		0			0
$643$	−27.4384	−	15.8415i	−1.08206	−	0.624729i	−0.150611	−	0.988593i	$-0.548124\pi$
$643$	−27.4384	−	15.8415i	−1.08206	−	0.624729i	−0.931452	+	0.363864i	$0.881457\pi$
$644$		0			0
$645$			116.908i			4.60323i
$646$		0			0
$647$	14.8291	−	25.6848i	0.582994	−	1.00977i	−0.412129	−	0.911126i	$-0.635215\pi$
$647$	14.8291	−	25.6848i	0.582994	−	1.00977i	0.995122	−	0.0986488i	$-0.0314521\pi$
$648$		0			0
$649$	4.01506	−	6.95429i	0.157605	−	0.272980i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	12.6897			0.496585			0.248292	−	0.968685i	$-0.420131\pi$
$653$	12.6897			0.496585			0.248292	+	0.968685i	$0.420131\pi$
$654$		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
$661$	−22.1333	−	12.7787i	−0.860887	−	0.497033i	0.00342228	−	0.999994i	$-0.498911\pi$
$661$	−22.1333	−	12.7787i	−0.860887	−	0.497033i	−0.864309	+	0.502961i	$0.832244\pi$
$662$		0			0
$663$	2.24546	+	0.291523i	0.0872065	+	0.0113218i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	10.9055	+	18.8890i	0.422264	+	0.731383i
$668$		0			0
$669$			48.8974i			1.89048i
$670$		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	−0.498530	−	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
$683$		−	48.6898i		−	1.86306i	−0.363660	−	0.931532i	$-0.618473\pi$
$683$		−	48.6898i		−	1.86306i	0.363660	−	0.931532i	$-0.381527\pi$
$684$		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
$689$	−1.26307	+	1.65220i	−0.0481193	+	0.0629438i
$690$		0			0
$691$		−	3.59045i		−	0.136587i	−0.997665	−	0.0682935i	$-0.978245\pi$
$691$		−	3.59045i		−	0.136587i	0.997665	−	0.0682935i	$-0.0217554\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−49.1303	+	28.3654i	−1.86362	+	1.07596i
$696$		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
$705$	44.2532			1.66667
$706$		0			0
$707$		0			0
$708$		0			0
$709$	19.6154	−	11.3250i	0.736673	−	0.425318i	−0.0841852	−	0.996450i	$-0.526829\pi$
$709$	19.6154	−	11.3250i	0.736673	−	0.425318i	0.820858	+	0.571132i	$0.193495\pi$
$710$		0			0
$711$	−66.8614			−2.50750
$712$		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
$717$	−51.3630	−	29.6544i	−1.91819	−	1.10747i
$718$		0			0
$719$	5.12631	+	8.87903i	0.191179	+	0.331132i	0.945641	−	0.325212i	$-0.105436\pi$
$719$	5.12631	+	8.87903i	0.191179	+	0.331132i	−0.754462	+	0.656344i	$0.772102\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−9.33125	−	5.38740i	−0.347033	−	0.200359i
$724$		0			0
$725$	−6.67246	+	11.5570i	−0.247809	+	0.429218i
$726$		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
$731$	1.11714	−	1.93495i	0.0413191	−	0.0715667i
$732$		0			0
$733$	35.6418	+	20.5778i	1.31646	+	0.760058i	0.983157	−	0.182762i	$-0.0585038\pi$
$733$	35.6418	+	20.5778i	1.31646	+	0.760058i	0.333302	+	0.942820i	$0.391837\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.4291	−	18.0638i	−0.384162	−	0.665388i
$738$		0			0
$739$	−10.5196	−	6.07347i	−0.386968	−	0.223416i	0.293877	−	0.955843i	$-0.405054\pi$
$739$	−10.5196	−	6.07347i	−0.386968	−	0.223416i	−0.680846	+	0.732427i	$0.738388\pi$
$740$		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
$745$	25.5211			0.935022
$746$		0			0
$747$	49.3737	−	28.5059i	1.80649	−	1.04298i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	22.7138			0.828837			0.414418	−	0.910086i	$-0.363985\pi$
$751$	22.7138			0.828837			0.414418	+	0.910086i	$0.363985\pi$
$752$		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
$761$	−37.0082	+	21.3667i	−1.34155	+	0.774543i	−0.987034	−	0.160509i	$-0.948687\pi$
$761$	−37.0082	+	21.3667i	−1.34155	+	0.774543i	−0.354513	+	0.935051i	$0.615353\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		−	4.55150i		−	0.164560i
$766$		0			0
$767$	6.94589	−	2.89169i	0.250802	−	0.104413i
$768$		0			0
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.926953	−	0.375178i	$-0.877582\pi$
$769$	−29.5477	+	17.0593i	−1.06552	+	0.615176i	−0.138563	+	0.990354i	$0.544248\pi$
$770$		0			0
$771$	24.6735	−	42.7357i	0.888593	−	1.53909i
$772$		0			0
$773$			28.8705i			1.03840i	0.854653	+	0.519200i	$0.173770\pi$
$773$			28.8705i			1.03840i	−0.854653	+	0.519200i	$0.826230\pi$
$774$		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
$787$		−	44.9696i		−	1.60299i	−0.597999	−	0.801497i	$-0.704037\pi$
$787$		−	44.9696i		−	1.60299i	0.597999	−	0.801497i	$-0.295963\pi$
$788$		0			0
$789$	−40.2242	−	69.6704i	−1.43202	−	2.48033i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	7.45644	−	9.75361i	0.264786	−	0.346361i
$794$		0			0
$795$	5.08028	+	2.93310i	0.180179	+	0.104026i
$796$		0			0
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	−0.990966	−	0.134111i	$-0.957182\pi$
$797$	−10.7092	+	18.5489i	−0.379340	+	0.657036i	0.611627	+	0.791147i	$0.290515\pi$
$798$		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
$803$	−12.7456			−0.449781
$804$		0			0
$805$		0			0
$806$		0			0
$807$	12.6925	−	21.9841i	0.446799	−	0.773878i
$808$		0			0
$809$	4.12749	−	7.14902i	0.145115	−	0.251346i	−0.784301	−	0.620381i	$-0.786978\pi$
$809$	4.12749	−	7.14902i	0.145115	−	0.251346i	0.929416	+	0.369034i	$0.120312\pi$
$810$		0			0
$811$			43.7679i			1.53690i	0.639910	+	0.768450i	$0.278971\pi$
$811$			43.7679i			1.53690i	−0.639910	+	0.768450i	$0.721029\pi$
$812$		0			0
$813$	−7.38329	−	4.26274i	−0.258943	−	0.149501i
$814$		0			0
$815$	0.774775			0.0271392
$816$		0			0
$817$		−	70.7659i		−	2.47579i
$818$		0			0
$819$		0			0
$820$		0			0
$821$			22.1084i			0.771589i	0.922585	+	0.385795i	$0.126073\pi$
$821$			22.1084i			0.771589i	−0.922585	+	0.385795i	$0.873927\pi$
$822$		0			0
$823$	42.0711			1.46650			0.733252	−	0.679957i	$-0.238001\pi$
$823$	42.0711			1.46650			0.733252	+	0.679957i	$0.238001\pi$
$824$		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
$829$	−8.97394	+	15.5433i	−0.311678	+	0.539842i	−0.978726	−	0.205173i	$-0.934224\pi$
$829$	−8.97394	+	15.5433i	−0.311678	+	0.539842i	0.667048	+	0.745015i	$0.267558\pi$
$830$		0			0
$831$	18.8284	−	32.6118i	0.653151	−	1.13129i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−5.69201			−0.196980
$836$		0			0
$837$	105.794	−	61.0802i	3.65677	−	2.11124i
$838$		0			0
$839$	3.09534	+	1.78709i	0.106863	+	0.0616973i	0.552479	−	0.833527i	$-0.313682\pi$
$839$	3.09534	+	1.78709i	0.106863	+	0.0616973i	−0.445616	+	0.895224i	$0.647015\pi$
$840$		0			0
$841$	10.8034	−	18.7121i	0.372532	−	0.645244i
$842$		0			0
$843$	−10.8148	−	6.24392i	−0.372481	−	0.215052i
$844$		0			0
$845$	39.4874	−	10.7326i	1.35841	−	0.369214i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	11.0640	+	19.1633i	0.379714	+	0.657684i
$850$		0			0
$851$			28.8000i			0.987251i
$852$		0			0
$853$			24.4780i			0.838111i	0.907961	+	0.419055i	$0.137639\pi$
$853$			24.4780i			0.838111i	−0.907961	+	0.419055i	$0.862361\pi$
$854$		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	0.327643	−	0.944802i	$-0.393746\pi$
$863$	−9.59914	−	5.54206i	−0.326758	−	0.188654i	−0.654401	+	0.756148i	$0.727079\pi$
$864$		0			0
$865$			33.9939i			1.15583i
$866$		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
$871$	2.51611	−	19.3804i	0.0852551	−	0.656679i
$872$		0			0
$873$		−	71.6165i		−	2.42385i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	3.99010	−	2.30368i	0.134736	−	0.0777899i	−0.431117	−	0.902296i	$-0.641880\pi$
$877$	3.99010	−	2.30368i	0.134736	−	0.0777899i	0.565853	+	0.824506i	$0.308547\pi$
$878$		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	$-0.970508\pi$
$881$	−17.1554	−	29.7140i	−0.577979	−	1.00109i	0.417732	−	0.908570i	$-0.362825\pi$
$882$		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
$887$	41.6052			1.39697			0.698483	−	0.715627i	$-0.253859\pi$
$887$	41.6052			1.39697			0.698483	+	0.715627i	$0.253859\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−80.0703	+	46.2286i	−2.68246	+	1.54872i
$892$		0			0
$893$	−26.7871			−0.896397
$894$		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
$899$	20.0548	+	11.5786i	0.668864	+	0.386169i
$900$		0			0
$901$	−0.0560562	−	0.0970922i	−0.00186750	−	0.00323461i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	27.2835	+	15.7521i	0.906934	+	0.523619i
$906$		0			0
$907$	7.83580	−	13.5720i	0.260183	−	0.450651i	−0.706107	−	0.708105i	$-0.749550\pi$
$907$	7.83580	−	13.5720i	0.260183	−	0.450651i	0.966290	+	0.257454i	$0.0828837\pi$
$908$		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
$913$	−14.7454	+	25.5398i	−0.488001	+	0.845243i
$914$		0			0
$915$	−29.9910	−	17.3153i	−0.991470	−	0.572426i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.66880	−	2.89045i	−0.0550488	−	0.0953473i	0.837188	−	0.546915i	$-0.184198\pi$
$919$	−1.66880	−	2.89045i	−0.0550488	−	0.0953473i	−0.892237	+	0.451568i	$0.850865\pi$
$920$		0			0
$921$	−6.52321	−	3.76618i	−0.214947	−	0.124100i
$922$		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
$927$	24.9510			0.819499
$928$		0			0
$929$	−7.87813	+	4.54844i	−0.258473	+	0.149230i	−0.623638	−	0.781713i	$-0.714346\pi$
$929$	−7.87813	+	4.54844i	−0.258473	+	0.149230i	0.365165	+	0.930943i	$0.381013\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	38.2047			1.25077
$934$		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	−0.379255	−	0.925292i	$-0.623820\pi$
$941$	7.13037	−	4.11672i	0.232444	−	0.134201i	0.611699	+	0.791091i	$0.290486\pi$
$942$		0			0
$943$	−27.6693	+	15.9749i	−0.901036	+	0.520214i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			5.05532i			0.164276i	0.996621	+	0.0821380i	$0.0261748\pi$
$947$			5.05532i			0.164276i	−0.996621	+	0.0821380i	$0.973825\pi$
$948$		0			0
$949$	−9.48717	−	7.25275i	−0.307967	−	0.235434i
$950$		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
$955$		−	75.6429i		−	2.44775i
$956$		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
$969$			3.86611i			0.124197i
$970$		0			0
$971$	11.7705	+	20.3871i	0.377733	+	0.654252i	0.990732	−	0.135831i	$-0.0433705\pi$
$971$	11.7705	+	20.3871i	0.377733	+	0.654252i	−0.612999	+	0.790084i	$0.710037\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−21.9749	−	52.7840i	−0.703759	−	1.69044i
$976$		0			0
$977$	10.7380	+	6.19958i	0.343539	+	0.198342i	0.661836	−	0.749649i	$-0.269778\pi$
$977$	10.7380	+	6.19958i	0.343539	+	0.198342i	−0.318297	+	0.947991i	$0.603111\pi$
$978$		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	−0.907291	−	0.420503i	$-0.861854\pi$
$983$	−31.2516	+	18.0431i	−0.996770	+	0.575486i	−0.0894792	+	0.995989i	$0.528520\pi$
$984$		0			0
$985$	−40.1406			−1.27898
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−46.1047	+	79.8558i	−1.46605	+	2.53927i
$990$		0			0
$991$	−26.4245	+	45.7686i	−0.839403	+	1.45389i	0.0509920	+	0.998699i	$0.483762\pi$
$991$	−26.4245	+	45.7686i	−0.839403	+	1.45389i	−0.890395	+	0.455189i	$0.849572\pi$
$992$		0			0
$993$		−	58.3409i		−	1.85139i
$994$		0			0
$995$	74.4823	+	43.0024i	2.36125	+	1.36327i
$996$		0			0
$997$	1.40828			0.0446006			0.0223003	−	0.999751i	$-0.492901\pi$
$997$	1.40828			0.0446006			0.0223003	+	0.999751i	$0.492901\pi$
$998$		0			0
$999$			51.4977i			1.62932i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bb.d.569.1		16
7.2	even	3		364.2.u.a.309.1	yes	16
7.3	odd	6		2548.2.bq.c.361.1		16
7.4	even	3		2548.2.bq.e.361.8		16
7.5	odd	6		2548.2.u.c.1765.8		16
7.6	odd	2		2548.2.bb.c.569.8		16
13.4	even	6		2548.2.bq.e.1941.8		16
21.2	odd	6		3276.2.cf.c.1765.2		16
28.23	odd	6		1456.2.cc.f.673.8		16
91.2	odd	12		4732.2.a.t.1.8		8
91.4	even	6	inner	2548.2.bb.d.1733.1		16
91.16	even	3		4732.2.g.k.337.16		16
91.17	odd	6		2548.2.bb.c.1733.8		16
91.23	even	6		4732.2.g.k.337.15		16
91.30	even	6		364.2.u.a.225.1	✓	16
91.37	odd	12		4732.2.a.s.1.8		8
91.69	odd	6		2548.2.bq.c.1941.1		16
91.82	odd	6		2548.2.u.c.589.8		16
273.212	odd	6		3276.2.cf.c.2773.7		16
364.303	odd	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	91.30	even	6
364.2.u.a.309.1	yes	16	7.2	even	3
1456.2.cc.f.225.8		16	364.303	odd	6
1456.2.cc.f.673.8		16	28.23	odd	6
2548.2.u.c.589.8		16	91.82	odd	6
2548.2.u.c.1765.8		16	7.5	odd	6
2548.2.bb.c.569.8		16	7.6	odd	2
2548.2.bb.c.1733.8		16	91.17	odd	6
2548.2.bb.d.569.1		16	1.1	even	1	trivial
2548.2.bb.d.1733.1		16	91.4	even	6	inner
2548.2.bq.c.361.1		16	7.3	odd	6
2548.2.bq.c.1941.1		16	91.69	odd	6
2548.2.bq.e.361.8		16	7.4	even	3
2548.2.bq.e.1941.8		16	13.4	even	6
3276.2.cf.c.1765.2		16	21.2	odd	6
3276.2.cf.c.2773.7		16	273.212	odd	6
4732.2.a.s.1.8		8	91.37	odd	12
4732.2.a.t.1.8		8	91.2	odd	12
4732.2.g.k.337.15		16	91.23	even	6
4732.2.g.k.337.16		16	91.16	even	3

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.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.61550 + 2.79813i) q^{3} +(-2.72598 - 1.57385i) q^{5} +(-3.71968 - 6.44268i) q^{9} +(3.33264 + 1.92410i) q^{11} +(1.38576 + 3.32861i) q^{13} +(8.80765 - 5.08510i) q^{15} -0.194369 q^{17} +(-5.33141 + 3.07809i) q^{19} +8.02163 q^{23} +(2.45398 + 4.25042i) q^{25} +14.3436 q^{27} +(1.35952 + 2.35475i) q^{29} +(7.37569 - 4.25836i) q^{31} +(-10.7678 + 6.21677i) q^{33} +3.59029i q^{37} +(-11.5526 - 1.49984i) q^{39} +(-3.44934 + 1.99148i) q^{41} +(-5.74755 + 9.95506i) q^{43} +23.4168i q^{45} +(3.76830 + 2.17563i) q^{47} +(0.314003 - 0.543869i) q^{51} +(0.288402 + 0.499526i) q^{53} +(-6.05647 - 10.4901i) q^{55} -19.8906i q^{57} -2.08672i q^{59} +(-1.70255 - 2.94891i) q^{61} +(1.46117 - 11.2547i) q^{65} +(-4.69408 - 2.71013i) q^{67} +(-12.9589 + 22.4456i) q^{69} +(-7.92574 - 4.57593i) q^{71} +(-2.86835 + 1.65604i) q^{73} -15.8576 q^{75} +(4.49376 - 7.78342i) q^{79} +(-12.0130 + 20.8072i) q^{81} +7.66353i q^{83} +(0.529845 + 0.305906i) q^{85} -8.78521 q^{87} +5.11527i q^{89} +27.5175i q^{93} +19.3778 q^{95} +(8.33696 + 4.81334i) q^{97} -28.6282i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 14 q^{9} - 6 q^{11} + 10 q^{13} + 6 q^{15} - 4 q^{17} + 22 q^{25} - 12 q^{27} - 22 q^{29} + 30 q^{31} - 42 q^{33} - 18 q^{39} + 36 q^{41} + 6 q^{43} - 18 q^{47} + 2 q^{51} - 4 q^{53} + 2 q^{55} + 4 q^{61}+ \cdots - 42 q^{97}+O(q^{100}) \) 16 * q - 14 * q^9 - 6 * q^11 + 10 * q^13 + 6 * q^15 - 4 * q^17 + 22 * q^25 - 12 * q^27 - 22 * q^29 + 30 * q^31 - 42 * q^33 - 18 * q^39 + 36 * q^41 + 6 * q^43 - 18 * q^47 + 2 * q^51 - 4 * q^53 + 2 * q^55 + 4 * q^61 + 30 * q^65 - 24 * q^67 - 52 * q^69 + 36 * q^71 - 12 * q^73 + 20 * q^75 - 4 * q^79 + 42 * q^85 - 52 * q^87 + 60 * q^95 - 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more