LMFDB - Embedded newform 2548.2.bq.f.1941.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2548,2,Mod(361,2548)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.3458824350$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} + 17 x^{16} - 6 x^{15} + 188 x^{14} - 49 x^{13} + 1116 x^{12} - x^{11} + 4649 x^{10} + \cdots + 16 $ x^18 - x^17 + 17x^16 - 6x^15 + 188x^14 - 49x^13 + 1116x^12 - x^11 + 4649x^10 + 106x^9 + 9589x^8 + 3532x^7 + 12349x^6 + 753x^5 + 2622x^4 - 883x^3 + 541x^2 - 92*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 364)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1941.4
Root			$-0.302937 + 0.524702i$ of defining polynomial
Character	$\chi$	$=$	2548.1941
Dual form			2548.2.bq.f.361.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.605874 q^{3} +(-3.48722 - 2.01335i) q^{5} -2.63292 q^{9} +3.01596i q^{11} +(1.03064 + 3.45511i) q^{13} +(2.11282 + 1.21984i) q^{15} +(2.53164 - 4.38494i) q^{17} +3.31908i q^{19} +(-2.45461 - 4.25150i) q^{23} +(5.60715 + 9.71187i) q^{25} +3.41284 q^{27} +(-1.30988 + 2.26878i) q^{29} +(-8.86474 + 5.11806i) q^{31} -1.82729i q^{33} +(-1.76903 + 1.02135i) q^{37} +(-0.624435 - 2.09336i) q^{39} +(-0.252355 - 0.145697i) q^{41} +(-0.581173 - 1.00662i) q^{43} +(9.18157 + 5.30098i) q^{45} +(-3.64039 - 2.10178i) q^{47} +(-1.53386 + 2.65672i) q^{51} +(-1.74405 - 3.02079i) q^{53} +(6.07218 - 10.5173i) q^{55} -2.01094i q^{57} +(5.84388 + 3.37397i) q^{59} +13.2920 q^{61} +(3.36229 - 14.1238i) q^{65} -4.13667i q^{67} +(1.48718 + 2.57588i) q^{69} +(-1.10708 + 0.639174i) q^{71} +(12.9146 - 7.45626i) q^{73} +(-3.39722 - 5.88417i) q^{75} +(3.45991 - 5.99274i) q^{79} +5.83100 q^{81} -10.4993i q^{83} +(-17.6568 + 10.1942i) q^{85} +(0.793622 - 1.37459i) q^{87} +(-0.511598 + 0.295371i) q^{89} +(5.37092 - 3.10090i) q^{93} +(6.68246 - 11.5744i) q^{95} +(4.94617 - 2.85568i) q^{97} -7.94077i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{3} + 12 q^{9} + 4 q^{13} + 6 q^{15} + 10 q^{17} - 6 q^{23} + 5 q^{25} + 20 q^{27} + 2 q^{29} - 9 q^{31} + 18 q^{37} + 11 q^{39} + 9 q^{41} - 14 q^{43} - 30 q^{45} - 36 q^{47} + 2 q^{51} - 13 q^{53}+ \cdots + 18 q^{97}+O(q^{100}) $ 18 * q + 2 * q^3 + 12 * q^9 + 4 * q^13 + 6 * q^15 + 10 * q^17 - 6 * q^23 + 5 * q^25 + 20 * q^27 + 2 * q^29 - 9 * q^31 + 18 * q^37 + 11 * q^39 + 9 * q^41 - 14 * q^43 - 30 * q^45 - 36 * q^47 + 2 * q^51 - 13 * q^53 + q^55 + 42 * q^61 + 30 * q^65 + q^69 - 45 * q^71 + 33 * q^73 - 25 * q^75 - 14 * q^79 + 2 * q^81 - 30 * q^85 - 2 * q^87 + 9 * q^89 + 21 * q^93 + 30 * q^95 + 18 * q^97

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.605874			−0.349801			−0.174901	−	0.984586i	$-0.555960\pi$
$3$	−0.605874			−0.349801			−0.174901	+	0.984586i	$0.555960\pi$
$4$		0			0
$5$	−3.48722	−	2.01335i	−1.55953	−	0.900397i	−0.997301	−	0.0734176i	$-0.976609\pi$
$5$	−3.48722	−	2.01335i	−1.55953	−	0.900397i	−0.562232	−	0.826979i	$-0.690057\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.63292			−0.877639
$10$		0			0
$11$			3.01596i			0.909346i	0.890658	+	0.454673i	$0.150244\pi$
$11$			3.01596i			0.909346i	−0.890658	+	0.454673i	$0.849756\pi$
$12$		0			0
$13$	1.03064	+	3.45511i	0.285847	+	0.958275i
$13$	1.03064	+	3.45511i	0.285847	+	0.958275i
$14$		0			0
$15$	2.11282	+	1.21984i	0.545527	+	0.314960i
$16$		0			0
$17$	2.53164	−	4.38494i	0.614014	−	1.06350i	−0.376543	−	0.926399i	$-0.622887\pi$
$17$	2.53164	−	4.38494i	0.614014	−	1.06350i	0.990557	−	0.137104i	$-0.0437794\pi$
$18$		0			0
$19$			3.31908i			0.761449i	0.924689	+	0.380724i	$0.124325\pi$
$19$			3.31908i			0.761449i	−0.924689	+	0.380724i	$0.875675\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.45461	−	4.25150i	−0.511821	−	0.886500i	−0.999906	−	0.0137038i	$-0.995638\pi$
$23$	−2.45461	−	4.25150i	−0.511821	−	0.886500i	0.488085	−	0.872796i	$-0.337696\pi$
$24$		0			0
$25$	5.60715	+	9.71187i	1.12143	+	1.94237i
$26$		0			0
$27$	3.41284			0.656801
$28$		0			0
$29$	−1.30988	+	2.26878i	−0.243239	+	0.421302i	−0.961635	−	0.274332i	$-0.911543\pi$
$29$	−1.30988	+	2.26878i	−0.243239	+	0.421302i	0.718396	+	0.695634i	$0.244876\pi$
$30$		0			0
$31$	−8.86474	+	5.11806i	−1.59216	+	0.919231i	−0.599218	+	0.800586i	$0.704522\pi$
$31$	−8.86474	+	5.11806i	−1.59216	+	0.919231i	−0.992937	+	0.118646i	$0.962145\pi$
$32$		0			0
$33$		−	1.82729i		−	0.318090i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.76903	+	1.02135i	−0.290826	+	0.167909i	−0.638314	−	0.769776i	$-0.720368\pi$
$37$	−1.76903	+	1.02135i	−0.290826	+	0.167909i	0.347488	+	0.937684i	$0.387035\pi$
$38$		0			0
$39$	−0.624435	−	2.09336i	−0.0999897	−	0.335206i
$40$		0			0
$41$	−0.252355	−	0.145697i	−0.0394112	−	0.0227540i	0.480165	−	0.877178i	$-0.340577\pi$
$41$	−0.252355	−	0.145697i	−0.0394112	−	0.0227540i	−0.519576	+	0.854424i	$0.673910\pi$
$42$		0			0
$43$	−0.581173	−	1.00662i	−0.0886281	−	0.153508i	0.818303	−	0.574787i	$-0.194915\pi$
$43$	−0.581173	−	1.00662i	−0.0886281	−	0.153508i	−0.906931	+	0.421278i	$0.861582\pi$
$44$		0			0
$45$	9.18157	+	5.30098i	1.36871	+	0.790224i
$46$		0			0
$47$	−3.64039	−	2.10178i	−0.531006	−	0.306576i	0.210420	−	0.977611i	$-0.432517\pi$
$47$	−3.64039	−	2.10178i	−0.531006	−	0.306576i	−0.741426	+	0.671035i	$0.765850\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−1.53386	+	2.65672i	−0.214783	+	0.372015i
$52$		0			0
$53$	−1.74405	−	3.02079i	−0.239564	−	0.414937i	0.721025	−	0.692909i	$-0.243671\pi$
$53$	−1.74405	−	3.02079i	−0.239564	−	0.414937i	−0.960589	+	0.277972i	$0.910338\pi$
$54$		0			0
$55$	6.07218	−	10.5173i	0.818772	−	1.41816i
$56$		0			0
$57$		−	2.01094i		−	0.266356i
$58$		0			0
$59$	5.84388	+	3.37397i	0.760809	+	0.439253i	0.829586	−	0.558379i	$-0.188576\pi$
$59$	5.84388	+	3.37397i	0.760809	+	0.439253i	−0.0687772	+	0.997632i	$0.521910\pi$
$60$		0			0
$61$	13.2920			1.70187			0.850936	−	0.525270i	$-0.176036\pi$
$61$	13.2920			1.70187			0.850936	+	0.525270i	$0.176036\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.36229	−	14.1238i	0.417040	−	1.75184i
$66$		0			0
$67$		−	4.13667i		−	0.505375i	−0.967548	−	0.252687i	$-0.918686\pi$
$67$		−	4.13667i		−	0.505375i	0.967548	−	0.252687i	$-0.0813144\pi$
$68$		0			0
$69$	1.48718	+	2.57588i	0.179036	+	0.310099i
$70$		0			0
$71$	−1.10708	+	0.639174i	−0.131387	+	0.0758560i	−0.564253	−	0.825602i	$-0.690836\pi$
$71$	−1.10708	+	0.639174i	−0.131387	+	0.0758560i	0.432866	+	0.901458i	$0.357502\pi$
$72$		0			0
$73$	12.9146	−	7.45626i	1.51154	−	0.872690i	0.511634	−	0.859204i	$-0.329041\pi$
$73$	12.9146	−	7.45626i	1.51154	−	0.872690i	0.999909	−	0.0134859i	$-0.00429282\pi$
$74$		0			0
$75$	−3.39722	−	5.88417i	−0.392278	−	0.679445i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	3.45991	−	5.99274i	0.389270	−	0.674236i	−0.603081	−	0.797680i	$-0.706060\pi$
$79$	3.45991	−	5.99274i	0.389270	−	0.674236i	0.992352	+	0.123444i	$0.0393938\pi$
$80$		0			0
$81$	5.83100			0.647889
$82$		0			0
$83$		−	10.4993i		−	1.15245i	−0.817292	−	0.576224i	$-0.804526\pi$
$83$		−	10.4993i		−	1.15245i	0.817292	−	0.576224i	$-0.195474\pi$
$84$		0			0
$85$	−17.6568	+	10.1942i	−1.91515	+	1.10571i
$86$		0			0
$87$	0.793622	−	1.37459i	0.0850852	−	0.147372i
$88$		0			0
$89$	−0.511598	+	0.295371i	−0.0542293	+	0.0313093i	−0.526870	−	0.849946i	$-0.676634\pi$
$89$	−0.511598	+	0.295371i	−0.0542293	+	0.0313093i	0.472640	+	0.881255i	$0.343301\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	5.37092	−	3.10090i	0.556938	−	0.321548i
$94$		0			0
$95$	6.68246	−	11.5744i	0.685606	−	1.18750i
$96$		0			0
$97$	4.94617	−	2.85568i	0.502208	−	0.289950i	−0.227417	−	0.973797i	$-0.573028\pi$
$97$	4.94617	−	2.85568i	0.502208	−	0.289950i	0.729625	+	0.683848i	$0.239695\pi$
$98$		0			0
$99$		−	7.94077i		−	0.798077i
$100$		0			0
$101$	−1.62019			−0.161215			−0.0806075	−	0.996746i	$-0.525686\pi$
$101$	−1.62019			−0.161215			−0.0806075	+	0.996746i	$0.525686\pi$
$102$		0			0
$103$	−3.68130	+	6.37620i	−0.362729	+	0.628265i	−0.988409	−	0.151815i	$-0.951488\pi$
$103$	−3.68130	+	6.37620i	−0.362729	+	0.628265i	0.625680	+	0.780080i	$0.284822\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.62841	−	8.01664i	−0.447445	−	0.774998i	0.550774	−	0.834655i	$-0.314333\pi$
$107$	−4.62841	−	8.01664i	−0.447445	−	0.774998i	−0.998219	+	0.0596565i	$0.980999\pi$
$108$		0			0
$109$	9.86259	−	5.69417i	0.944665	−	0.545402i	0.0532452	−	0.998581i	$-0.483044\pi$
$109$	9.86259	−	5.69417i	0.944665	−	0.545402i	0.891420	+	0.453179i	$0.149710\pi$
$110$		0			0
$111$	1.07181	−	0.618808i	0.101731	−	0.0587347i
$112$		0			0
$113$	−7.06719	−	12.2407i	−0.664826	−	1.15151i	−0.979333	−	0.202257i	$-0.935172\pi$
$113$	−7.06719	−	12.2407i	−0.664826	−	1.15151i	0.314507	−	0.949255i	$-0.398161\pi$
$114$		0			0
$115$			19.7679i			1.84337i
$116$		0			0
$117$	−2.71358	−	9.09702i	−0.250870	−	0.841020i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.90399			0.173090
$122$		0			0
$123$	0.152895	+	0.0882740i	0.0137861	+	0.00795940i
$124$		0			0
$125$		−	25.0231i		−	2.23813i
$126$		0			0
$127$	−1.67517	+	2.90149i	−0.148648	+	0.257465i	−0.930728	−	0.365712i	$-0.880825\pi$
$127$	−1.67517	+	2.90149i	−0.148648	+	0.257465i	0.782080	+	0.623178i	$0.214159\pi$
$128$		0			0
$129$	0.352118	+	0.609886i	0.0310022	+	0.0536974i
$130$		0			0
$131$	6.08531	−	10.5401i	0.531676	−	0.920890i	−0.467640	−	0.883919i	$-0.654896\pi$
$131$	6.08531	−	10.5401i	0.531676	−	0.920890i	0.999316	−	0.0369713i	$-0.0117710\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−11.9013	−	6.87123i	−1.02430	−	0.591381i
$136$		0			0
$137$	2.99901	+	1.73148i	0.256223	+	0.147930i	0.622610	−	0.782532i	$-0.286072\pi$
$137$	2.99901	+	1.73148i	0.256223	+	0.147930i	−0.366388	+	0.930462i	$0.619406\pi$
$138$		0			0
$139$	−4.58975	−	7.94968i	−0.389297	−	0.674283i	0.603058	−	0.797697i	$-0.293949\pi$
$139$	−4.58975	−	7.94968i	−0.389297	−	0.674283i	−0.992355	+	0.123415i	$0.960615\pi$
$140$		0			0
$141$	2.20562	+	1.27341i	0.185747	+	0.107241i
$142$		0			0
$143$	−10.4205	+	3.10836i	−0.871404	+	0.259934i
$144$		0			0
$145$	9.13569	−	5.27449i	0.758678	−	0.438023i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			6.18683i			0.506845i	0.967356	+	0.253422i	$0.0815563\pi$
$149$			6.18683i			0.506845i	−0.967356	+	0.253422i	$0.918444\pi$
$150$		0			0
$151$	−17.0651	+	9.85256i	−1.38874	+	0.801790i	−0.993174	−	0.116646i	$-0.962786\pi$
$151$	−17.0651	+	9.85256i	−1.38874	+	0.801790i	−0.395568	+	0.918437i	$0.629452\pi$
$152$		0			0
$153$	−6.66561	+	11.5452i	−0.538882	+	0.933372i
$154$		0			0
$155$	41.2178			3.31069
$156$		0			0
$157$	−9.33447	−	16.1678i	−0.744972	−	1.29033i	−0.950208	−	0.311617i	$-0.899129\pi$
$157$	−9.33447	−	16.1678i	−0.744972	−	1.29033i	0.205236	−	0.978713i	$-0.434204\pi$
$158$		0			0
$159$	1.05668	+	1.83022i	0.0837998	+	0.145146i
$160$		0			0
$161$		0			0
$162$		0			0
$163$		−	18.8843i		−	1.47913i	−0.673083	−	0.739567i	$-0.735030\pi$
$163$		−	18.8843i		−	1.47913i	0.673083	−	0.739567i	$-0.264970\pi$
$164$		0			0
$165$	−3.67897	+	6.37217i	−0.286408	+	0.496073i
$166$		0			0
$167$	12.3365	+	7.12250i	0.954630	+	0.551156i	0.894516	−	0.447036i	$-0.147520\pi$
$167$	12.3365	+	7.12250i	0.954630	+	0.551156i	0.0601137	+	0.998192i	$0.480854\pi$
$168$		0			0
$169$	−10.8756	+	7.12192i	−0.836583	+	0.547840i
$170$		0			0
$171$		−	8.73886i		−	0.668277i
$172$		0			0
$173$	−19.9996			−1.52054			−0.760272	−	0.649605i	$-0.774934\pi$
$173$	−19.9996			−1.52054			−0.760272	+	0.649605i	$0.774934\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.54066	−	2.04420i	−0.266132	−	0.153651i
$178$		0			0
$179$	23.4022			1.74916			0.874580	−	0.484881i	$-0.161137\pi$
$179$	23.4022			1.74916			0.874580	+	0.484881i	$0.161137\pi$
$180$		0			0
$181$	5.15299			0.383019			0.191509	−	0.981491i	$-0.438662\pi$
$181$	5.15299			0.383019			0.191509	+	0.981491i	$0.438662\pi$
$182$		0			0
$183$	−8.05330			−0.595317
$184$		0			0
$185$	8.22532			0.604738
$186$		0			0
$187$	13.2248	+	7.63534i	0.967092	+	0.558351i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	22.3386			1.61636			0.808182	−	0.588933i	$-0.200452\pi$
$191$	22.3386			1.61636			0.808182	+	0.588933i	$0.200452\pi$
$192$		0			0
$193$		−	10.3162i		−	0.742577i	−0.928518	−	0.371288i	$-0.878916\pi$
$193$		−	10.3162i		−	0.742577i	0.928518	−	0.371288i	$-0.121084\pi$
$194$		0			0
$195$	−2.03712	+	8.55722i	−0.145881	+	0.612795i
$196$		0			0
$197$	23.1481	+	13.3646i	1.64923	+	0.952186i	0.977377	+	0.211505i	$0.0678364\pi$
$197$	23.1481	+	13.3646i	1.64923	+	0.952186i	0.671857	+	0.740681i	$0.265497\pi$
$198$		0			0
$199$	−0.0439516	+	0.0761264i	−0.00311565	+	0.00539646i	−0.867579	−	0.497299i	$-0.834325\pi$
$199$	−0.0439516	+	0.0761264i	−0.00311565	+	0.00539646i	0.864463	+	0.502696i	$0.167658\pi$
$200$		0			0
$201$			2.50630i			0.176781i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.586678	+	1.01616i	0.0409753	+	0.0709714i
$206$		0			0
$207$	6.46278	+	11.1939i	0.449194	+	0.778027i
$208$		0			0
$209$	−10.0102			−0.692420
$210$		0			0
$211$	−12.1986	+	21.1285i	−0.839783	+	1.45455i	0.0502926	+	0.998735i	$0.483985\pi$
$211$	−12.1986	+	21.1285i	−0.839783	+	1.45455i	−0.890076	+	0.455813i	$0.849349\pi$
$212$		0			0
$213$	0.670752	−	0.387259i	0.0459592	−	0.0265345i
$214$		0			0
$215$			4.68042i			0.319202i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−7.82463	+	4.51755i	−0.528740	+	0.305268i
$220$		0			0
$221$	17.7596	+	4.22784i	1.19464	+	0.284395i
$222$		0			0
$223$	2.25338	+	1.30099i	0.150897	+	0.0871206i	0.573548	−	0.819172i	$-0.305567\pi$
$223$	2.25338	+	1.30099i	0.150897	+	0.0871206i	−0.422650	+	0.906293i	$0.638900\pi$
$224$		0			0
$225$	−14.7632	−	25.5705i	−0.984210	−	1.70470i
$226$		0			0
$227$	12.8164	+	7.39957i	0.850657	+	0.491127i	0.860872	−	0.508821i	$-0.169919\pi$
$227$	12.8164	+	7.39957i	0.850657	+	0.491127i	−0.0102158	+	0.999948i	$0.503252\pi$
$228$		0			0
$229$	2.79819	+	1.61554i	0.184910	+	0.106758i	0.589597	−	0.807697i	$-0.299286\pi$
$229$	2.79819	+	1.61554i	0.184910	+	0.106758i	−0.404688	+	0.914455i	$0.632620\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.44152	−	9.42499i	0.356486	−	0.617452i	−0.630885	−	0.775876i	$-0.717308\pi$
$233$	5.44152	−	9.42499i	0.356486	−	0.617452i	0.987371	+	0.158424i	$0.0506414\pi$
$234$		0			0
$235$	8.46324	+	14.6588i	0.552081	+	0.956232i
$236$		0			0
$237$	−2.09627	+	3.63085i	−0.136167	+	0.235849i
$238$		0			0
$239$			14.2791i			0.923639i	0.886974	+	0.461819i	$0.152803\pi$
$239$			14.2791i			0.923639i	−0.886974	+	0.461819i	$0.847197\pi$
$240$		0			0
$241$	−21.9539	−	12.6751i	−1.41417	−	0.816473i	−0.418394	−	0.908266i	$-0.637407\pi$
$241$	−21.9539	−	12.6751i	−1.41417	−	0.816473i	−0.995778	+	0.0917927i	$0.970740\pi$
$242$		0			0
$243$	−13.7714			−0.883433
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−11.4678	+	3.42076i	−0.729677	+	0.217658i
$248$		0			0
$249$			6.36125i			0.403128i
$250$		0			0
$251$	10.6797	+	18.4977i	0.674094	+	1.16756i	0.976733	+	0.214460i	$0.0687991\pi$
$251$	10.6797	+	18.4977i	0.674094	+	1.16756i	−0.302639	+	0.953105i	$0.597868\pi$
$252$		0			0
$253$	12.8224	−	7.40299i	0.806135	−	0.465422i
$254$		0			0
$255$	10.6978	−	6.17638i	0.669922	−	0.386780i
$256$		0			0
$257$	−4.53161	−	7.84898i	−0.282674	−	0.489606i	0.689368	−	0.724411i	$-0.257888\pi$
$257$	−4.53161	−	7.84898i	−0.282674	−	0.489606i	−0.972042	+	0.234805i	$0.924555\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	3.44881	−	5.97351i	0.213476	−	0.369751i
$262$		0			0
$263$	−14.7945			−0.912269			−0.456134	−	0.889911i	$-0.650766\pi$
$263$	−14.7945			−0.912269			−0.456134	+	0.889911i	$0.650766\pi$
$264$		0			0
$265$			14.0455i			0.862811i
$266$		0			0
$267$	0.309964	−	0.178958i	0.0189695	−	0.0109520i
$268$		0			0
$269$	14.6738	−	25.4158i	0.894678	−	1.54963i	0.0604745	−	0.998170i	$-0.480739\pi$
$269$	14.6738	−	25.4158i	0.894678	−	1.54963i	0.834203	−	0.551457i	$-0.185928\pi$
$270$		0			0
$271$	−9.80478	+	5.66079i	−0.595598	+	0.343869i	−0.767308	−	0.641279i	$-0.778404\pi$
$271$	−9.80478	+	5.66079i	−0.595598	+	0.343869i	0.171710	+	0.985148i	$0.445071\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−29.2906	+	16.9109i	−1.76629	+	1.01977i
$276$		0			0
$277$	−9.30823	+	16.1223i	−0.559277	+	0.968697i	0.438280	+	0.898839i	$0.355588\pi$
$277$	−9.30823	+	16.1223i	−0.559277	+	0.968697i	−0.997557	+	0.0698581i	$0.977745\pi$
$278$		0			0
$279$	23.3401	−	13.4754i	1.39734	−	0.806753i
$280$		0			0
$281$		−	9.63428i		−	0.574733i	−0.957821	−	0.287366i	$-0.907220\pi$
$281$		−	9.63428i		−	0.574733i	0.957821	−	0.287366i	$-0.0927797\pi$
$282$		0			0
$283$	17.7476			1.05498			0.527492	−	0.849560i	$-0.323133\pi$
$283$	17.7476			1.05498			0.527492	+	0.849560i	$0.323133\pi$
$284$		0			0
$285$	−4.04873	+	7.01260i	−0.239826	+	0.415391i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−4.31844	−	7.47976i	−0.254026	−	0.439986i
$290$		0			0
$291$	−2.99676	+	1.73018i	−0.175673	+	0.101425i
$292$		0			0
$293$	21.2670	−	12.2785i	1.24243	−	0.717320i	0.272845	−	0.962058i	$-0.412035\pi$
$293$	21.2670	−	12.2785i	1.24243	−	0.717320i	0.969589	+	0.244738i	$0.0787021\pi$
$294$		0			0
$295$	−13.5859	−	23.5316i	−0.791005	−	1.37006i
$296$		0			0
$297$			10.2930i			0.597259i
$298$		0			0
$299$	12.1596	−	12.8627i	0.703208	−	0.743869i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	0.981632			0.0563933
$304$		0			0
$305$	−46.3523	−	26.7615i	−2.65413	−	1.53236i
$306$		0			0
$307$		−	3.59068i		−	0.204931i	−0.994737	−	0.102466i	$-0.967327\pi$
$307$		−	3.59068i		−	0.204931i	0.994737	−	0.102466i	$-0.0326731\pi$
$308$		0			0
$309$	2.23040	−	3.86317i	0.126883	−	0.219768i
$310$		0			0
$311$	−4.31915	−	7.48098i	−0.244916	−	0.424208i	0.717192	−	0.696876i	$-0.245427\pi$
$311$	−4.31915	−	7.48098i	−0.244916	−	0.424208i	−0.962108	+	0.272668i	$0.912094\pi$
$312$		0			0
$313$	−9.01786	+	15.6194i	−0.509720	+	0.882861i	0.490217	+	0.871601i	$0.336918\pi$
$313$	−9.01786	+	15.6194i	−0.509720	+	0.882861i	−0.999937	+	0.0112601i	$0.996416\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	12.6003	+	7.27477i	0.707702	+	0.408592i	0.810210	−	0.586140i	$-0.199353\pi$
$317$	12.6003	+	7.27477i	0.707702	+	0.408592i	−0.102508	+	0.994732i	$0.532687\pi$
$318$		0			0
$319$	−6.84254	−	3.95055i	−0.383109	−	0.221188i
$320$		0			0
$321$	2.80423	+	4.85707i	0.156517	+	0.271095i
$322$		0			0
$323$	14.5539	+	8.40272i	0.809803	+	0.467540i
$324$		0			0
$325$	−27.7766	+	29.3827i	−1.54077	+	1.62986i
$326$		0			0
$327$	−5.97549	+	3.44995i	−0.330445	+	0.190783i
$328$		0			0
$329$		0			0
$330$		0			0
$331$			28.5151i			1.56733i	0.621182	+	0.783666i	$0.286653\pi$
$331$			28.5151i			1.56733i	−0.621182	+	0.783666i	$0.713347\pi$
$332$		0			0
$333$	4.65770	−	2.68912i	0.255240	−	0.147363i
$334$		0			0
$335$	−8.32856	+	14.4255i	−0.455038	+	0.788149i
$336$		0			0
$337$	6.02834			0.328385			0.164192	−	0.986428i	$-0.447498\pi$
$337$	6.02834			0.328385			0.164192	+	0.986428i	$0.447498\pi$
$338$		0			0
$339$	4.28183	+	7.41634i	0.232557	+	0.402801i
$340$		0			0
$341$	−15.4359	−	26.7357i	−0.835899	−	1.44782i
$342$		0			0
$343$		0			0
$344$		0			0
$345$		−	11.9769i		−	0.644813i
$346$		0			0
$347$	2.16529	−	3.75039i	0.116239	−	0.201331i	−0.802036	−	0.597276i	$-0.796250\pi$
$347$	2.16529	−	3.75039i	0.116239	−	0.201331i	0.918274	+	0.395945i	$0.129583\pi$
$348$		0			0
$349$	2.85466	+	1.64814i	0.152806	+	0.0882228i	0.574454	−	0.818537i	$-0.305215\pi$
$349$	2.85466	+	1.64814i	0.152806	+	0.0882228i	−0.421647	+	0.906760i	$0.638548\pi$
$350$		0			0
$351$	3.51739	+	11.7917i	0.187745	+	0.629396i
$352$		0			0
$353$			20.5841i			1.09558i	0.836616	+	0.547790i	$0.184531\pi$
$353$			20.5841i			1.09558i	−0.836616	+	0.547790i	$0.815469\pi$
$354$		0			0
$355$	5.14752			0.273202
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.9348	+	7.46793i	0.682674	+	0.394142i	0.800862	−	0.598849i	$-0.204375\pi$
$359$	12.9348	+	7.46793i	0.682674	+	0.394142i	−0.118188	+	0.992991i	$0.537708\pi$
$360$		0			0
$361$	7.98372			0.420196
$362$		0			0
$363$	−1.15358			−0.0605471
$364$		0			0
$365$	−60.0482			−3.14307
$366$		0			0
$367$	5.01214			0.261631			0.130816	−	0.991407i	$-0.458240\pi$
$367$	5.01214			0.261631			0.130816	+	0.991407i	$0.458240\pi$
$368$		0			0
$369$	0.664429	+	0.383608i	0.0345888	+	0.0199698i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	17.0022			0.880338			0.440169	−	0.897915i	$-0.354918\pi$
$373$	17.0022			0.880338			0.440169	+	0.897915i	$0.354918\pi$
$374$		0			0
$375$			15.1608i			0.782902i
$376$		0			0
$377$	−9.18889	−	2.18750i	−0.473252	−	0.112662i
$378$		0			0
$379$	24.9003	+	14.3762i	1.27904	+	0.738454i	0.976672	−	0.214737i	$-0.0688894\pi$
$379$	24.9003	+	14.3762i	1.27904	+	0.738454i	0.302369	+	0.953191i	$0.402223\pi$
$380$		0			0
$381$	1.01494	−	1.75793i	0.0519972	−	0.0900617i
$382$		0			0
$383$			29.8622i			1.52589i	0.646465	+	0.762944i	$0.276247\pi$
$383$			29.8622i			1.52589i	−0.646465	+	0.762944i	$0.723753\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.53018	+	2.65035i	0.0777834	+	0.134725i
$388$		0			0
$389$	−4.17584	−	7.23276i	−0.211723	−	0.366715i	0.740531	−	0.672023i	$-0.234574\pi$
$389$	−4.17584	−	7.23276i	−0.211723	−	0.366715i	−0.952254	+	0.305307i	$0.901241\pi$
$390$		0			0
$391$	−24.8568			−1.25706
$392$		0			0
$393$	−3.68693	+	6.38595i	−0.185981	+	0.322129i
$394$		0			0
$395$	−24.1310	+	13.9320i	−1.21416	+	0.700996i
$396$		0			0
$397$			2.86213i			0.143646i	0.997417	+	0.0718232i	$0.0228817\pi$
$397$			2.86213i			0.143646i	−0.997417	+	0.0718232i	$0.977118\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−14.6879	+	8.48009i	−0.733481	+	0.423476i	−0.819694	−	0.572801i	$-0.805857\pi$
$401$	−14.6879	+	8.48009i	−0.733481	+	0.423476i	0.0862132	+	0.996277i	$0.472523\pi$
$402$		0			0
$403$	−26.8198	−	25.3538i	−1.33599	−	1.26296i
$404$		0			0
$405$	−20.3340	−	11.7398i	−1.01040	−	0.583357i
$406$		0			0
$407$	−3.08034	−	5.33531i	−0.152687	−	0.264462i
$408$		0			0
$409$	−8.05450	−	4.65027i	−0.398269	−	0.229941i	0.287468	−	0.957790i	$-0.407187\pi$
$409$	−8.05450	−	4.65027i	−0.398269	−	0.229941i	−0.685737	+	0.727849i	$0.740520\pi$
$410$		0			0
$411$	−1.81702	−	1.04906i	−0.0896270	−	0.0517462i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−21.1387	+	36.6134i	−1.03766	+	1.79728i
$416$		0			0
$417$	2.78081	+	4.81650i	0.136177	+	0.235865i
$418$		0			0
$419$	−10.1471	+	17.5753i	−0.495718	+	0.858608i	−0.999988	−	0.00493765i	$-0.998428\pi$
$419$	−10.1471	+	17.5753i	−0.495718	+	0.858608i	0.504270	+	0.863546i	$0.331762\pi$
$420$		0			0
$421$		−	6.82905i		−	0.332827i	−0.986056	−	0.166414i	$-0.946781\pi$
$421$		−	6.82905i		−	0.332827i	0.986056	−	0.166414i	$-0.0532187\pi$
$422$		0			0
$423$	9.58485	+	5.53381i	0.466031	+	0.269063i
$424$		0			0
$425$	56.7812			2.75429
$426$		0			0
$427$		0			0
$428$		0			0
$429$	6.31349	−	1.88327i	0.304818	−	0.0909252i
$430$		0			0
$431$		−	9.67781i		−	0.466164i	−0.972457	−	0.233082i	$-0.925119\pi$
$431$		−	9.67781i		−	0.466164i	0.972457	−	0.233082i	$-0.0748810\pi$
$432$		0			0
$433$	−9.67518	−	16.7579i	−0.464960	−	0.805334i	0.534240	−	0.845333i	$-0.320598\pi$
$433$	−9.67518	−	16.7579i	−0.464960	−	0.805334i	−0.999200	+	0.0399991i	$0.987264\pi$
$434$		0			0
$435$	−5.53507	+	3.19568i	−0.265386	+	0.153221i
$436$		0			0
$437$	14.1111	−	8.14703i	0.675024	−	0.389725i
$438$		0			0
$439$	8.69109	+	15.0534i	0.414803	+	0.718460i	0.995408	−	0.0957255i	$-0.0305171\pi$
$439$	8.69109	+	15.0534i	0.414803	+	0.718460i	−0.580605	+	0.814186i	$0.697184\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.61637	−	11.4599i	0.314353	−	0.544476i	−0.664946	−	0.746891i	$-0.731546\pi$
$443$	6.61637	−	11.4599i	0.314353	−	0.544476i	0.979300	+	0.202415i	$0.0648790\pi$
$444$		0			0
$445$	2.37874			0.112763
$446$		0			0
$447$		−	3.74844i		−	0.177295i
$448$		0			0
$449$	6.12896	−	3.53855i	0.289243	−	0.166995i	−0.348357	−	0.937362i	$-0.613260\pi$
$449$	6.12896	−	3.53855i	0.289243	−	0.166995i	0.637601	+	0.770367i	$0.279927\pi$
$450$		0			0
$451$	0.439416	−	0.761091i	0.0206913	−	0.0358384i
$452$		0			0
$453$	10.3393	−	5.96941i	0.485784	−	0.280467i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	28.9889	−	16.7367i	1.35604	−	0.782911i	0.366954	−	0.930239i	$-0.380401\pi$
$457$	28.9889	−	16.7367i	1.35604	−	0.782911i	0.989088	+	0.147328i	$0.0470672\pi$
$458$		0			0
$459$	8.64009	−	14.9651i	0.403285	−	0.698510i
$460$		0			0
$461$	−7.21129	+	4.16344i	−0.335863	+	0.193911i	−0.658441	−	0.752632i	$-0.728784\pi$
$461$	−7.21129	+	4.16344i	−0.335863	+	0.193911i	0.322578	+	0.946543i	$0.395451\pi$
$462$		0			0
$463$		−	4.45810i		−	0.207186i	−0.994620	−	0.103593i	$-0.966966\pi$
$463$		−	4.45810i		−	0.207186i	0.994620	−	0.103593i	$-0.0330339\pi$
$464$		0			0
$465$	−24.9728			−1.15808
$466$		0			0
$467$	16.0477	−	27.7954i	0.742599	−	1.28622i	−0.208710	−	0.977978i	$-0.566926\pi$
$467$	16.0477	−	27.7954i	0.742599	−	1.28622i	0.951308	−	0.308241i	$-0.0997403\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	5.65551	+	9.79564i	0.260592	+	0.451359i
$472$		0			0
$473$	3.03593	−	1.75279i	0.139592	−	0.0805936i
$474$		0			0
$475$	−32.2344	+	18.6106i	−1.47902	+	0.853911i
$476$		0			0
$477$	4.59195	+	7.95348i	0.210251	+	0.364165i
$478$		0			0
$479$		−	19.3554i		−	0.884371i	−0.896924	−	0.442185i	$-0.854203\pi$
$479$		−	19.3554i		−	0.884371i	0.896924	−	0.442185i	$-0.145797\pi$
$480$		0			0
$481$	−5.35209	−	5.05955i	−0.244034	−	0.230695i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−22.9979			−1.04428
$486$		0			0
$487$	5.07742	+	2.93145i	0.230080	+	0.132837i	0.610609	−	0.791932i	$-0.290925\pi$
$487$	5.07742	+	2.93145i	0.230080	+	0.132837i	−0.380529	+	0.924769i	$0.624258\pi$
$488$		0			0
$489$			11.4415i			0.517403i
$490$		0			0
$491$	5.13898	−	8.90098i	0.231919	−	0.401696i	−0.726454	−	0.687215i	$-0.758833\pi$
$491$	5.13898	−	8.90098i	0.231919	−	0.401696i	0.958373	+	0.285520i	$0.0921662\pi$
$492$		0			0
$493$	6.63230	+	11.4875i	0.298704	+	0.517370i
$494$		0			0
$495$	−15.9875	+	27.6912i	−0.718587	+	1.24463i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	26.5363	+	15.3208i	1.18793	+	0.685851i	0.957835	−	0.287317i	$-0.0927634\pi$
$499$	26.5363	+	15.3208i	1.18793	+	0.685851i	0.230094	+	0.973168i	$0.426097\pi$
$500$		0			0
$501$	−7.47438	−	4.31534i	−0.333931	−	0.192795i
$502$		0			0
$503$	−1.91528	−	3.31736i	−0.0853981	−	0.147914i	0.820163	−	0.572130i	$-0.193883\pi$
$503$	−1.91528	−	3.31736i	−0.0853981	−	0.147914i	−0.905561	+	0.424216i	$0.860550\pi$
$504$		0			0
$505$	5.64997	+	3.26201i	0.251420	+	0.145158i
$506$		0			0
$507$	6.58923	−	4.31499i	0.292638	−	0.191635i
$508$		0			0
$509$	16.3952	−	9.46577i	0.726704	−	0.419563i	−0.0905109	−	0.995895i	$-0.528850\pi$
$509$	16.3952	−	9.46577i	0.726704	−	0.419563i	0.817215	+	0.576333i	$0.195517\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$			11.3275i			0.500120i
$514$		0			0
$515$	25.6750	−	14.8235i	1.13138	−	0.653201i
$516$		0			0
$517$	6.33888	−	10.9793i	0.278784	−	0.482868i
$518$		0			0
$519$	12.1173			0.531888
$520$		0			0
$521$	−22.1534	−	38.3709i	−0.970559	−	1.68106i	−0.693873	−	0.720097i	$-0.744097\pi$
$521$	−22.1534	−	38.3709i	−0.970559	−	1.68106i	−0.276686	−	0.960960i	$-0.589236\pi$
$522$		0			0
$523$	−11.4413	−	19.8169i	−0.500293	−	0.866532i	−1.00000		0.000337913i	$-0.999892\pi$
$523$	−11.4413	−	19.8169i	−0.500293	−	0.866532i	0.499707	−	0.866194i	$-0.333441\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			51.8284i			2.25768i
$528$		0			0
$529$	−0.550191	+	0.952958i	−0.0239213	+	0.0414330i
$530$		0			0
$531$	−15.3865	−	8.88338i	−0.667716	−	0.385506i
$532$		0			0
$533$	0.243313	−	1.02207i	0.0105391	−	0.0442709i
$534$		0			0
$535$			37.2744i			1.61151i
$536$		0			0
$537$	−14.1788			−0.611859
$538$		0			0
$539$		0			0
$540$		0			0
$541$	1.49131	+	0.861006i	0.0641163	+	0.0370175i	0.531715	−	0.846923i	$-0.321548\pi$
$541$	1.49131	+	0.861006i	0.0641163	+	0.0370175i	−0.467599	+	0.883941i	$0.654881\pi$
$542$		0			0
$543$	−3.12206			−0.133981
$544$		0			0
$545$	−45.8574			−1.96432
$546$		0			0
$547$	21.7554			0.930195			0.465098	−	0.885259i	$-0.346019\pi$
$547$	21.7554			0.930195			0.465098	+	0.885259i	$0.346019\pi$
$548$		0			0
$549$	−34.9968			−1.49363
$550$		0			0
$551$	−7.53025	−	4.34759i	−0.320800	−	0.185214i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−4.98351			−0.211538
$556$		0			0
$557$		−	20.2913i		−	0.859768i	−0.902884	−	0.429884i	$-0.858554\pi$
$557$		−	20.2913i		−	0.859768i	0.902884	−	0.429884i	$-0.141446\pi$
$558$		0			0
$559$	2.87901	−	3.04548i	0.121769	−	0.128810i
$560$		0			0
$561$	−8.01255	−	4.62605i	−0.338290	−	0.195312i
$562$		0			0
$563$	6.08156	−	10.5336i	0.256307	−	0.443937i	−0.708943	−	0.705266i	$-0.750828\pi$
$563$	6.08156	−	10.5336i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841609\pi$
$564$		0			0
$565$			56.9149i			2.39443i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.60362	−	4.50961i	−0.109150	−	0.189052i	0.806276	−	0.591539i	$-0.201479\pi$
$569$	−2.60362	−	4.50961i	−0.109150	−	0.189052i	−0.915426	+	0.402486i	$0.868146\pi$
$570$		0			0
$571$	7.11158	+	12.3176i	0.297611	+	0.515477i	0.975589	−	0.219605i	$-0.0704770\pi$
$571$	7.11158	+	12.3176i	0.297611	+	0.515477i	−0.677978	+	0.735082i	$0.737144\pi$
$572$		0			0
$573$	−13.5344			−0.565406
$574$		0			0
$575$	27.5267	−	47.6776i	1.14794	−	1.98829i
$576$		0			0
$577$	−8.49045	+	4.90196i	−0.353462	+	0.204071i	−0.666209	−	0.745765i	$-0.732084\pi$
$577$	−8.49045	+	4.90196i	−0.353462	+	0.204071i	0.312747	+	0.949836i	$0.398751\pi$
$578$		0			0
$579$			6.25032i			0.259754i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	9.11057	−	5.25999i	0.377321	−	0.217847i
$584$		0			0
$585$	−8.85262	+	37.1867i	−0.366011	+	1.53748i
$586$		0			0
$587$	14.4001	+	8.31388i	0.594354	+	0.343151i	0.766817	−	0.641865i	$-0.221839\pi$
$587$	14.4001	+	8.31388i	0.594354	+	0.343151i	−0.172463	+	0.985016i	$0.555173\pi$
$588$		0			0
$589$	−16.9872	−	29.4228i	−0.699947	−	1.21234i
$590$		0			0
$591$	−14.0248	−	8.09724i	−0.576904	−	0.333076i
$592$		0			0
$593$	27.2185	+	15.7146i	1.11773	+	0.645322i	0.940821	−	0.338905i	$-0.110056\pi$
$593$	27.2185	+	15.7146i	1.11773	+	0.645322i	0.176910	+	0.984227i	$0.443390\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.0266291	−	0.0461230i	0.00108986	−	0.00188769i
$598$		0			0
$599$	−19.9208	−	34.5039i	−0.813943	−	1.40979i	−0.910084	−	0.414424i	$-0.863983\pi$
$599$	−19.9208	−	34.5039i	−0.813943	−	1.40979i	0.0961406	−	0.995368i	$-0.469350\pi$
$600$		0			0
$601$	4.75064	−	8.22836i	0.193783	−	0.335642i	−0.752718	−	0.658343i	$-0.771258\pi$
$601$	4.75064	−	8.22836i	0.193783	−	0.335642i	0.946501	+	0.322701i	$0.104591\pi$
$602$		0			0
$603$			10.8915i			0.443536i
$604$		0			0
$605$	−6.63964	−	3.83340i	−0.269940	−	0.155850i
$606$		0			0
$607$	−3.68363			−0.149514			−0.0747569	−	0.997202i	$-0.523818\pi$
$607$	−3.68363			−0.149514			−0.0747569	+	0.997202i	$0.523818\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.50997	−	14.7441i	0.141998	−	0.596483i
$612$		0			0
$613$			28.1993i			1.13896i	0.822006	+	0.569479i	$0.192855\pi$
$613$			28.1993i			1.13896i	−0.822006	+	0.569479i	$0.807145\pi$
$614$		0			0
$615$	−0.355453	−	0.615662i	−0.0143332	−	0.0248259i
$616$		0			0
$617$	−4.12127	+	2.37942i	−0.165916	+	0.0957917i	−0.580659	−	0.814147i	$-0.697205\pi$
$617$	−4.12127	+	2.37942i	−0.165916	+	0.0957917i	0.414743	+	0.909939i	$0.363872\pi$
$618$		0			0
$619$	18.7796	−	10.8424i	0.754815	−	0.435793i	−0.0726159	−	0.997360i	$-0.523135\pi$
$619$	18.7796	−	10.8424i	0.754815	−	0.435793i	0.827431	+	0.561567i	$0.189801\pi$
$620$		0			0
$621$	−8.37717	−	14.5097i	−0.336164	−	0.582254i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−22.3445	+	38.7018i	−0.893779	+	1.54807i
$626$		0			0
$627$	6.06492			0.242210
$628$		0			0
$629$			10.3428i			0.412393i
$630$		0			0
$631$	−32.0785	+	18.5205i	−1.27702	+	0.737290i	−0.976300	−	0.216421i	$-0.930562\pi$
$631$	−32.0785	+	18.5205i	−1.27702	+	0.737290i	−0.300724	+	0.953711i	$0.597228\pi$
$632$		0			0
$633$	7.39079	−	12.8012i	0.293757	−	0.508803i
$634$		0			0
$635$	11.6834	−	6.74542i	0.463642	−	0.267684i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	2.91486	−	1.68289i	0.115310	−	0.0665742i
$640$		0			0
$641$	−0.310057	+	0.537034i	−0.0122465	+	0.0212116i	−0.872084	−	0.489357i	$-0.837232\pi$
$641$	−0.310057	+	0.537034i	−0.0122465	+	0.0212116i	0.859837	+	0.510568i	$0.170565\pi$
$642$		0			0
$643$	−11.5598	+	6.67403i	−0.455872	+	0.263198i	−0.710307	−	0.703892i	$-0.751444\pi$
$643$	−11.5598	+	6.67403i	−0.455872	+	0.263198i	0.254435	+	0.967090i	$0.418111\pi$
$644$		0			0
$645$		−	2.83574i		−	0.111657i
$646$		0			0
$647$	−6.52504			−0.256526			−0.128263	−	0.991740i	$-0.540940\pi$
$647$	−6.52504			−0.256526			−0.128263	+	0.991740i	$0.540940\pi$
$648$		0			0
$649$	−10.1757	+	17.6249i	−0.399433	+	0.691838i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.15183	+	7.19118i	0.162474	+	0.281413i	0.935755	−	0.352650i	$-0.114719\pi$
$653$	4.15183	+	7.19118i	0.162474	+	0.281413i	−0.773282	+	0.634063i	$0.781386\pi$
$654$		0			0
$655$	−42.4417	+	24.5037i	−1.65833	+	0.957439i
$656$		0			0
$657$	−34.0031	+	19.6317i	−1.32659	+	0.765906i
$658$		0			0
$659$	5.41342	+	9.37632i	0.210877	+	0.365250i	0.951989	−	0.306131i	$-0.0990347\pi$
$659$	5.41342	+	9.37632i	0.210877	+	0.365250i	−0.741112	+	0.671381i	$0.765701\pi$
$660$		0			0
$661$		−	16.0233i		−	0.623236i	−0.950207	−	0.311618i	$-0.899129\pi$
$661$		−	16.0233i		−	0.623236i	0.950207	−	0.311618i	$-0.100871\pi$
$662$		0			0
$663$	−10.7601	−	2.56154i	−0.417888	−	0.0994818i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.8610			0.497978
$668$		0			0
$669$	−1.36526	−	0.788235i	−0.0527841	−	0.0304749i
$670$		0			0
$671$			40.0883i			1.54759i
$672$		0			0
$673$	7.99990	−	13.8562i	0.308373	−	0.534119i	−0.669633	−	0.742692i	$-0.733549\pi$
$673$	7.99990	−	13.8562i	0.308373	−	0.534119i	0.978007	+	0.208573i	$0.0668820\pi$
$674$		0			0
$675$	19.1363	+	33.1450i	0.736556	+	1.27575i
$676$		0			0
$677$	4.80538	−	8.32316i	0.184686	−	0.319885i	−0.758785	−	0.651341i	$-0.774207\pi$
$677$	4.80538	−	8.32316i	0.184686	−	0.319885i	0.943471	+	0.331456i	$0.107540\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−7.76514	−	4.48321i	−0.297561	−	0.171797i
$682$		0			0
$683$	−15.8268	−	9.13760i	−0.605595	−	0.349641i	0.165644	−	0.986186i	$-0.447030\pi$
$683$	−15.8268	−	9.13760i	−0.605595	−	0.349641i	−0.771240	+	0.636545i	$0.780363\pi$
$684$		0			0
$685$	−6.97214	−	12.0761i	−0.266392	−	0.461404i
$686$		0			0
$687$	−1.69535	−	0.978812i	−0.0646817	−	0.0373440i
$688$		0			0
$689$	8.63967	−	9.13923i	0.329145	−	0.348177i
$690$		0			0
$691$	19.3973	−	11.1990i	0.737908	−	0.426031i	−0.0834002	−	0.996516i	$-0.526578\pi$
$691$	19.3973	−	11.1990i	0.737908	−	0.426031i	0.821308	+	0.570485i	$0.193245\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$			36.9631i			1.40209i
$696$		0			0
$697$	−1.27774	+	0.737706i	−0.0483980	+	0.0279426i
$698$		0			0
$699$	−3.29688	+	5.71036i	−0.124699	+	0.215985i
$700$		0			0
$701$	−25.9923			−0.981715			−0.490858	−	0.871240i	$-0.663317\pi$
$701$	−25.9923			−0.981715			−0.490858	+	0.871240i	$0.663317\pi$
$702$		0			0
$703$	−3.38993	−	5.87154i	−0.127854	−	0.221449i
$704$		0			0
$705$	−5.12765	−	8.88136i	−0.193119	−	0.334491i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			1.43956i			0.0540640i	0.999635	+	0.0270320i	$0.00860560\pi$
$709$			1.43956i			0.0540640i	−0.999635	+	0.0270320i	$0.991394\pi$
$710$		0			0
$711$	−9.10966	+	15.7784i	−0.341639	+	0.591736i
$712$		0			0
$713$	43.5189	+	25.1257i	1.62980	+	0.940964i
$714$		0			0
$715$	42.5967	+	10.1405i	1.59303	+	0.379234i
$716$		0			0
$717$		−	8.65134i		−	0.323090i
$718$		0			0
$719$	−40.8771			−1.52446			−0.762228	−	0.647308i	$-0.775895\pi$
$719$	−40.8771			−1.52446			−0.762228	+	0.647308i	$0.775895\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	13.3013	+	7.67949i	0.494680	+	0.285603i
$724$		0			0
$725$	−29.3788			−1.09110
$726$		0			0
$727$	22.0673			0.818432			0.409216	−	0.912438i	$-0.365802\pi$
$727$	22.0673			0.818432			0.409216	+	0.912438i	$0.365802\pi$
$728$		0			0
$729$	−9.14930			−0.338863
$730$		0			0
$731$	−5.88529			−0.217675
$732$		0			0
$733$	10.1099	+	5.83696i	0.373418	+	0.215593i	0.674951	−	0.737863i	$-0.264165\pi$
$733$	10.1099	+	5.83696i	0.373418	+	0.215593i	−0.301533	+	0.953456i	$0.597498\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	12.4760			0.459560
$738$		0			0
$739$		−	29.1737i		−	1.07317i	−0.843846	−	0.536585i	$-0.819714\pi$
$739$		−	29.1737i		−	1.07317i	0.843846	−	0.536585i	$-0.180286\pi$
$740$		0			0
$741$	6.94803	−	2.07255i	0.255242	−	0.0761370i
$742$		0			0
$743$	20.1398	+	11.6277i	0.738858	+	0.426580i	0.821654	−	0.569987i	$-0.193052\pi$
$743$	20.1398	+	11.6277i	0.738858	+	0.426580i	−0.0827959	+	0.996567i	$0.526385\pi$
$744$		0			0
$745$	12.4562	−	21.5749i	0.456362	−	0.790441i
$746$		0			0
$747$			27.6438i			1.01143i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−16.8130	−	29.1210i	−0.613517	−	1.06264i	−0.990643	−	0.136480i	$-0.956421\pi$
$751$	−16.8130	−	29.1210i	−0.613517	−	1.06264i	0.377126	−	0.926162i	$-0.376912\pi$
$752$		0			0
$753$	−6.47052	−	11.2073i	−0.235799	−	0.408416i
$754$		0			0
$755$	79.3466			2.88772
$756$		0			0
$757$	10.7585	−	18.6343i	0.391025	−	0.677275i	−0.601560	−	0.798828i	$-0.705454\pi$
$757$	10.7585	−	18.6343i	0.391025	−	0.677275i	0.992585	+	0.121552i	$0.0387872\pi$
$758$		0			0
$759$	−7.76873	+	4.48528i	−0.281987	+	0.162805i
$760$		0			0
$761$		−	1.30767i		−	0.0474029i	−0.999719	−	0.0237014i	$-0.992455\pi$
$761$		−	1.30767i		−	0.0474029i	0.999719	−	0.0237014i	$-0.00754511\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	46.4889	−	26.8404i	1.68081	−	0.970416i
$766$		0			0
$767$	−5.63451	+	23.6686i	−0.203451	+	0.854624i
$768$		0			0
$769$	31.1392	+	17.9782i	1.12291	+	0.648312i	0.942142	−	0.335214i	$-0.108809\pi$
$769$	31.1392	+	17.9782i	1.12291	+	0.648312i	0.180767	+	0.983526i	$0.442142\pi$
$770$		0			0
$771$	2.74558	+	4.75549i	0.0988798	+	0.171265i
$772$		0			0
$773$	−37.8302	−	21.8413i	−1.36066	−	0.785576i	−0.370947	−	0.928654i	$-0.620967\pi$
$773$	−37.8302	−	21.8413i	−1.36066	−	0.785576i	−0.989711	+	0.143078i	$0.954300\pi$
$774$		0			0
$775$	−99.4119	−	57.3955i	−3.57098	−	2.06171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.483580	−	0.837584i	0.0173260	−	0.0300096i
$780$		0			0
$781$	−1.92772	−	3.33892i	−0.0689794	−	0.119476i
$782$		0			0
$783$	−4.47041	+	7.74297i	−0.159759	+	0.276711i
$784$		0			0
$785$			75.1742i			2.68308i
$786$		0			0
$787$	16.8292	+	9.71634i	0.599896	+	0.346350i	0.769001	−	0.639248i	$-0.220754\pi$
$787$	16.8292	+	9.71634i	0.599896	+	0.346350i	−0.169105	+	0.985598i	$0.554088\pi$
$788$		0			0
$789$	8.96361			0.319113
$790$		0			0
$791$		0			0
$792$		0			0
$793$	13.6993	+	45.9255i	0.486475	+	1.63086i
$794$		0			0
$795$		−	8.50983i		−	0.301813i
$796$		0			0
$797$	−8.40446	−	14.5570i	−0.297701	−	0.515634i	0.677908	−	0.735146i	$-0.262887\pi$
$797$	−8.40446	−	14.5570i	−0.297701	−	0.515634i	−0.975610	+	0.219513i	$0.929553\pi$
$798$		0			0
$799$	−18.4323	+	10.6419i	−0.652090	+	0.376484i
$800$		0			0
$801$	1.34700	−	0.777689i	0.0475938	−	0.0274783i
$802$		0			0
$803$	22.4878	+	38.9500i	0.793577	+	1.37452i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.89047	+	15.3988i	−0.312960	+	0.542062i
$808$		0			0
$809$	−19.3130			−0.679008			−0.339504	−	0.940605i	$-0.610259\pi$
$809$	−19.3130			−0.679008			−0.339504	+	0.940605i	$0.610259\pi$
$810$		0			0
$811$			21.4951i			0.754795i	0.926051	+	0.377397i	$0.123181\pi$
$811$			21.4951i			0.754795i	−0.926051	+	0.377397i	$0.876819\pi$
$812$		0			0
$813$	5.94046	−	3.42973i	0.208341	−	0.120286i
$814$		0			0
$815$	−38.0207	+	65.8538i	−1.33181	+	2.30676i
$816$		0			0
$817$	3.34105	−	1.92896i	0.116889	−	0.0674857i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−42.1884	+	24.3575i	−1.47239	+	0.850082i	−0.999518	−	0.0310515i	$-0.990114\pi$
$821$	−42.1884	+	24.3575i	−1.47239	+	0.850082i	−0.472868	+	0.881134i	$0.656781\pi$
$822$		0			0
$823$	9.05247	−	15.6793i	0.315549	−	0.546547i	−0.664005	−	0.747728i	$-0.731145\pi$
$823$	9.05247	−	15.6793i	0.315549	−	0.546547i	0.979554	+	0.201181i	$0.0644780\pi$
$824$		0			0
$825$	17.7464	−	10.2459i	0.617850	−	0.356716i
$826$		0			0
$827$		−	43.6958i		−	1.51945i	−0.650244	−	0.759726i	$-0.725333\pi$
$827$		−	43.6958i		−	1.51945i	0.650244	−	0.759726i	$-0.274667\pi$
$828$		0			0
$829$	30.4929			1.05906			0.529530	−	0.848291i	$-0.322368\pi$
$829$	30.4929			1.05906			0.529530	+	0.848291i	$0.322368\pi$
$830$		0			0
$831$	5.63961	−	9.76810i	0.195636	−	0.338852i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−28.6802	−	49.6755i	−0.992518	−	1.71909i
$836$		0			0
$837$	−30.2539	+	17.4671i	−1.04573	+	0.603752i
$838$		0			0
$839$	27.3088	−	15.7668i	0.942806	−	0.544329i	0.0519670	−	0.998649i	$-0.483451\pi$
$839$	27.3088	−	15.7668i	0.942806	−	0.544329i	0.890839	+	0.454320i	$0.150118\pi$
$840$		0			0
$841$	11.0684	+	19.1711i	0.381670	+	0.661072i
$842$		0			0
$843$			5.83716i			0.201042i
$844$		0			0
$845$	52.2645	−	2.93940i	1.79795	−	0.101118i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−10.7528			−0.369035
$850$		0			0
$851$	8.68453	+	5.01402i	0.297702	+	0.171878i
$852$		0			0
$853$			49.9618i			1.71066i	0.518085	+	0.855329i	$0.326645\pi$
$853$			49.9618i			1.71066i	−0.518085	+	0.855329i	$0.673355\pi$
$854$		0			0
$855$	−17.5944	+	30.4743i	−0.601715	+	1.04220i
$856$		0			0
$857$	20.4955	+	35.4993i	0.700113	+	1.21263i	0.968426	+	0.249300i	$0.0802006\pi$
$857$	20.4955	+	35.4993i	0.700113	+	1.21263i	−0.268313	+	0.963332i	$0.586466\pi$
$858$		0			0
$859$	−22.7071	+	39.3298i	−0.774756	+	1.34192i	0.160175	+	0.987089i	$0.448794\pi$
$859$	−22.7071	+	39.3298i	−0.774756	+	1.34192i	−0.934931	+	0.354829i	$0.884539\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−45.5827	−	26.3172i	−1.55165	−	0.895848i	−0.998007	−	0.0630969i	$-0.979902\pi$
$863$	−45.5827	−	26.3172i	−1.55165	−	0.895848i	−0.553647	−	0.832751i	$-0.686764\pi$
$864$		0			0
$865$	69.7432	+	40.2662i	2.37134	+	1.36909i
$866$		0			0
$867$	2.61643	+	4.53179i	0.0888587	+	0.153908i
$868$		0			0
$869$	18.0739	+	10.4350i	0.613114	+	0.353982i
$870$		0			0
$871$	14.2926	−	4.26340i	0.484288	−	0.144460i
$872$		0			0
$873$	−13.0229	+	7.51876i	−0.440757	+	0.254471i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	11.7224i		−	0.395838i	−0.980218	−	0.197919i	$-0.936582\pi$
$877$		−	11.7224i		−	0.395838i	0.980218	−	0.197919i	$-0.0634183\pi$
$878$		0			0
$879$	−12.8851	+	7.43924i	−0.434605	+	0.250919i
$880$		0			0
$881$	14.5273	−	25.1619i	0.489435	−	0.847727i	−0.510491	−	0.859883i	$-0.670536\pi$
$881$	14.5273	−	25.1619i	0.489435	−	0.847727i	0.999926	+	0.0121562i	$0.00386953\pi$
$882$		0			0
$883$	−41.9709			−1.41243			−0.706216	−	0.707996i	$-0.749599\pi$
$883$	−41.9709			−1.41243			−0.706216	+	0.707996i	$0.749599\pi$
$884$		0			0
$885$	8.23137	+	14.2572i	0.276695	+	0.479249i
$886$		0			0
$887$	18.4327	+	31.9265i	0.618911	+	1.07199i	0.989685	+	0.143262i	$0.0457592\pi$
$887$	18.4327	+	31.9265i	0.618911	+	1.07199i	−0.370774	+	0.928723i	$0.620907\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$			17.5861i			0.589155i
$892$		0			0
$893$	6.97597	−	12.0827i	0.233442	−	0.404333i
$894$		0			0
$895$	−81.6086	−	47.1167i	−2.72787	−	1.57494i
$896$		0			0
$897$	−7.36719	+	7.79317i	−0.245983	+	0.260206i
$898$		0			0
$899$		−	26.8162i		−	0.894370i
$900$		0			0
$901$	−17.6613			−0.588383
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−17.9696	−	10.3748i	−0.597331	−	0.344869i
$906$		0			0
$907$	31.0746			1.03181			0.515907	−	0.856645i	$-0.327455\pi$
$907$	31.0746			1.03181			0.515907	+	0.856645i	$0.327455\pi$
$908$		0			0
$909$	4.26583			0.141489
$910$		0			0
$911$	12.7180			0.421365			0.210682	−	0.977555i	$-0.432431\pi$
$911$	12.7180			0.421365			0.210682	+	0.977555i	$0.432431\pi$
$912$		0			0
$913$	31.6654			1.04797
$914$		0			0
$915$	28.0837	+	16.2141i	0.928417	+	0.536022i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−10.5876			−0.349253			−0.174627	−	0.984635i	$-0.555872\pi$
$919$	−10.5876			−0.349253			−0.174627	+	0.984635i	$0.555872\pi$
$920$		0			0
$921$			2.17550i			0.0716852i
$922$		0			0
$923$	−3.34942	−	3.16634i	−0.110247	−	0.104221i
$924$		0			0
$925$	−19.8384	−	11.4537i	−0.652282	−	0.376595i
$926$		0			0
$927$	9.69255	−	16.7880i	0.318345	−	0.551390i
$928$		0			0
$929$		−	15.4183i		−	0.505857i	−0.967485	−	0.252928i	$-0.918606\pi$
$929$		−	15.4183i		−	0.505857i	0.967485	−	0.252928i	$-0.0813937\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	2.61686	+	4.53253i	0.0856721	+	0.148388i
$934$		0			0
$935$	−30.7452	−	53.2522i	−1.00548	−	1.74153i
$936$		0			0
$937$	1.66353			0.0543452			0.0271726	−	0.999631i	$-0.491350\pi$
$937$	1.66353			0.0543452			0.0271726	+	0.999631i	$0.491350\pi$
$938$		0			0
$939$	5.46369	−	9.46339i	0.178301	−	0.308826i
$940$		0			0
$941$	25.8392	−	14.9183i	0.842335	−	0.486322i	−0.0157224	−	0.999876i	$-0.505005\pi$
$941$	25.8392	−	14.9183i	0.842335	−	0.486322i	0.858057	+	0.513554i	$0.171671\pi$
$942$		0			0
$943$			1.43052i			0.0465840i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.43043	−	3.13526i	0.176465	−	0.101882i	−0.409166	−	0.912460i	$-0.634180\pi$
$947$	5.43043	−	3.13526i	0.176465	−	0.101882i	0.585631	+	0.810578i	$0.300847\pi$
$948$		0			0
$949$	39.0725	+	36.9368i	1.26835	+	1.19902i
$950$		0			0
$951$	−7.63418	−	4.40759i	−0.247555	−	0.142926i
$952$		0			0
$953$	10.6219	+	18.3977i	0.344078	+	0.595960i	0.985186	−	0.171491i	$-0.0548583\pi$
$953$	10.6219	+	18.3977i	0.344078	+	0.595960i	−0.641108	+	0.767451i	$0.721525\pi$
$954$		0			0
$955$	−77.8996	−	44.9754i	−2.52077	−	1.45537i
$956$		0			0
$957$	4.14572	+	2.39353i	0.134012	+	0.0773719i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	36.8891	−	63.8938i	1.18997	−	2.06109i
$962$		0			0
$963$	12.1862	+	21.1072i	0.392696	+	0.680169i
$964$		0			0
$965$	−20.7701	+	35.9749i	−0.668614	+	1.15807i
$966$		0			0
$967$		−	28.1083i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$967$		−	28.1083i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$968$		0			0
$969$	−8.81785	−	5.09099i	−0.283270	−	0.163546i
$970$		0			0
$971$	−19.0275			−0.610621			−0.305310	−	0.952253i	$-0.598760\pi$
$971$	−19.0275			−0.610621			−0.305310	+	0.952253i	$0.598760\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	16.8291	−	17.8022i	0.538964	−	0.570127i
$976$		0			0
$977$		−	60.5225i		−	1.93629i	−0.250400	−	0.968143i	$-0.580562\pi$
$977$		−	60.5225i		−	1.93629i	0.250400	−	0.968143i	$-0.419438\pi$
$978$		0			0
$979$	−0.890828	−	1.54296i	−0.0284710	−	0.0493132i
$980$		0			0
$981$	−25.9674	+	14.9923i	−0.829075	+	0.478666i
$982$		0			0
$983$	−38.4381	+	22.1922i	−1.22598	+	0.707823i	−0.966188	−	0.257840i	$-0.916989\pi$
$983$	−38.4381	+	22.1922i	−1.22598	+	0.707823i	−0.259797	+	0.965663i	$0.583656\pi$
$984$		0			0
$985$	−53.8151	−	93.2104i	−1.71469	−	2.96993i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.85310	+	4.94172i	−0.0907234	+	0.157138i
$990$		0			0
$991$	45.4599			1.44408			0.722040	−	0.691851i	$-0.243205\pi$
$991$	45.4599			1.44408			0.722040	+	0.691851i	$0.243205\pi$
$992$		0			0
$993$		−	17.2766i		−	0.548255i
$994$		0			0
$995$	0.306538	−	0.176980i	0.00971791	−	0.00561064i
$996$		0			0
$997$	16.3250	−	28.2758i	0.517018	−	0.895502i	−0.482786	−	0.875738i	$-0.660375\pi$
$997$	16.3250	−	28.2758i	0.517018	−	0.895502i	0.999805	−	0.0197639i	$-0.00629145\pi$
$998$		0			0
$999$	−6.03740	+	3.48569i	−0.191015	+	0.110283i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2548.2.bq.f.1941.4		18
7.2	even	3		2548.2.u.d.589.6		18
7.3	odd	6		364.2.bb.a.277.4	yes	18
7.4	even	3		2548.2.bb.f.1733.6		18
7.5	odd	6		2548.2.u.e.589.4		18
7.6	odd	2		364.2.bq.a.121.6	yes	18
13.10	even	6		2548.2.bb.f.569.6		18
21.17	even	6		3276.2.hi.i.1369.9		18
21.20	even	2		3276.2.fe.i.2305.1		18
91.10	odd	6		364.2.bq.a.361.6	yes	18
91.23	even	6		2548.2.u.d.1765.6		18
91.62	odd	6		364.2.bb.a.205.4	✓	18
91.75	odd	6		2548.2.u.e.1765.4		18
91.88	even	6	inner	2548.2.bq.f.361.4		18
273.62	even	6		3276.2.hi.i.1297.9		18
273.101	even	6		3276.2.fe.i.361.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
364.2.bb.a.205.4	✓	18	91.62	odd	6
364.2.bb.a.277.4	yes	18	7.3	odd	6
364.2.bq.a.121.6	yes	18	7.6	odd	2
364.2.bq.a.361.6	yes	18	91.10	odd	6
2548.2.u.d.589.6		18	7.2	even	3
2548.2.u.d.1765.6		18	91.23	even	6
2548.2.u.e.589.4		18	7.5	odd	6
2548.2.u.e.1765.4		18	91.75	odd	6
2548.2.bb.f.569.6		18	13.10	even	6
2548.2.bb.f.1733.6		18	7.4	even	3
2548.2.bq.f.361.4		18	91.88	even	6	inner
2548.2.bq.f.1941.4		18	1.1	even	1	trivial
3276.2.fe.i.361.1		18	273.101	even	6
3276.2.fe.i.2305.1		18	21.20	even	2
3276.2.hi.i.1297.9		18	273.62	even	6
3276.2.hi.i.1369.9		18	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q-0.605874 q^{3} +(-3.48722 - 2.01335i) q^{5} -2.63292 q^{9} +3.01596i q^{11} +(1.03064 + 3.45511i) q^{13} +(2.11282 + 1.21984i) q^{15} +(2.53164 - 4.38494i) q^{17} +3.31908i q^{19} +(-2.45461 - 4.25150i) q^{23} +(5.60715 + 9.71187i) q^{25} +3.41284 q^{27} +(-1.30988 + 2.26878i) q^{29} +(-8.86474 + 5.11806i) q^{31} -1.82729i q^{33} +(-1.76903 + 1.02135i) q^{37} +(-0.624435 - 2.09336i) q^{39} +(-0.252355 - 0.145697i) q^{41} +(-0.581173 - 1.00662i) q^{43} +(9.18157 + 5.30098i) q^{45} +(-3.64039 - 2.10178i) q^{47} +(-1.53386 + 2.65672i) q^{51} +(-1.74405 - 3.02079i) q^{53} +(6.07218 - 10.5173i) q^{55} -2.01094i q^{57} +(5.84388 + 3.37397i) q^{59} +13.2920 q^{61} +(3.36229 - 14.1238i) q^{65} -4.13667i q^{67} +(1.48718 + 2.57588i) q^{69} +(-1.10708 + 0.639174i) q^{71} +(12.9146 - 7.45626i) q^{73} +(-3.39722 - 5.88417i) q^{75} +(3.45991 - 5.99274i) q^{79} +5.83100 q^{81} -10.4993i q^{83} +(-17.6568 + 10.1942i) q^{85} +(0.793622 - 1.37459i) q^{87} +(-0.511598 + 0.295371i) q^{89} +(5.37092 - 3.10090i) q^{93} +(6.68246 - 11.5744i) q^{95} +(4.94617 - 2.85568i) q^{97} -7.94077i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{3} + 12 q^{9} + 4 q^{13} + 6 q^{15} + 10 q^{17} - 6 q^{23} + 5 q^{25} + 20 q^{27} + 2 q^{29} - 9 q^{31} + 18 q^{37} + 11 q^{39} + 9 q^{41} - 14 q^{43} - 30 q^{45} - 36 q^{47} + 2 q^{51} - 13 q^{53}+ \cdots + 18 q^{97}+O(q^{100}) \) 18 * q + 2 * q^3 + 12 * q^9 + 4 * q^13 + 6 * q^15 + 10 * q^17 - 6 * q^23 + 5 * q^25 + 20 * q^27 + 2 * q^29 - 9 * q^31 + 18 * q^37 + 11 * q^39 + 9 * q^41 - 14 * q^43 - 30 * q^45 - 36 * q^47 + 2 * q^51 - 13 * q^53 + q^55 + 42 * q^61 + 30 * q^65 + q^69 - 45 * q^71 + 33 * q^73 - 25 * q^75 - 14 * q^79 + 2 * q^81 - 30 * q^85 - 2 * q^87 + 9 * q^89 + 21 * q^93 + 30 * q^95 + 18 * q^97

Introduction

L-functions

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