LMFDB - Embedded newform 539.2.a.g.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [539,2,Mod(1,539)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("539.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(539, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,0,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$4.30393666895$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	539.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.87939 q^{2} -0.652704 q^{3} +1.53209 q^{4} -3.53209 q^{5} -1.22668 q^{6} -0.879385 q^{8} -2.57398 q^{9} -6.63816 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.41147 q^{13} +2.30541 q^{15} -4.71688 q^{16} +5.24897 q^{17} -4.83750 q^{18} -1.81521 q^{19} -5.41147 q^{20} +1.87939 q^{22} -6.33275 q^{23} +0.573978 q^{24} +7.47565 q^{25} -8.29086 q^{26} +3.63816 q^{27} +1.92127 q^{29} +4.33275 q^{30} -1.46791 q^{31} -7.10607 q^{32} -0.652704 q^{33} +9.86484 q^{34} -3.94356 q^{36} +4.45336 q^{37} -3.41147 q^{38} +2.87939 q^{39} +3.10607 q^{40} -0.283119 q^{41} -3.41147 q^{43} +1.53209 q^{44} +9.09152 q^{45} -11.9017 q^{46} +4.55438 q^{47} +3.07873 q^{48} +14.0496 q^{50} -3.42602 q^{51} -6.75877 q^{52} -7.23442 q^{53} +6.83750 q^{54} -3.53209 q^{55} +1.18479 q^{57} +3.61081 q^{58} -9.53983 q^{59} +3.53209 q^{60} +1.14796 q^{61} -2.75877 q^{62} -3.92127 q^{64} +15.5817 q^{65} -1.22668 q^{66} -0.694593 q^{67} +8.04189 q^{68} +4.13341 q^{69} +9.46110 q^{71} +2.26352 q^{72} -2.34730 q^{73} +8.36959 q^{74} -4.87939 q^{75} -2.78106 q^{76} +5.41147 q^{78} -12.4192 q^{79} +16.6604 q^{80} +5.34730 q^{81} -0.532089 q^{82} +11.3327 q^{83} -18.5398 q^{85} -6.41147 q^{86} -1.25402 q^{87} -0.879385 q^{88} +3.46791 q^{89} +17.0865 q^{90} -9.70233 q^{92} +0.958111 q^{93} +8.55943 q^{94} +6.41147 q^{95} +4.63816 q^{96} -15.3473 q^{97} -2.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + 9 q^{15} - 6 q^{16} + 3 q^{17} - 12 q^{18} - 9 q^{19} - 6 q^{20} - 6 q^{24} + 3 q^{25} - 9 q^{26} - 6 q^{27} - 3 q^{29}+ \cdots - 45 q^{97}+O(q^{100}) $ 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + 9 * q^15 - 6 * q^16 + 3 * q^17 - 12 * q^18 - 9 * q^19 - 6 * q^20 - 6 * q^24 + 3 * q^25 - 9 * q^26 - 6 * q^27 - 3 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 - 3 * q^33 + 6 * q^34 + 3 * q^36 + 3 * q^39 - 3 * q^40 - 9 * q^41 - 3 * q^45 - 24 * q^46 + 3 * q^47 + 18 * q^48 + 15 * q^50 - 18 * q^51 - 9 * q^52 + 9 * q^53 + 18 * q^54 - 6 * q^55 + 15 * q^58 + 6 * q^60 - 12 * q^61 + 3 * q^62 - 3 * q^64 + 15 * q^65 + 3 * q^66 + 21 * q^68 - 21 * q^69 - 9 * q^71 + 12 * q^72 - 6 * q^73 + 18 * q^74 - 9 * q^75 + 9 * q^76 + 6 * q^78 - 3 * q^79 + 27 * q^80 + 15 * q^81 + 3 * q^82 + 15 * q^83 - 27 * q^85 - 9 * q^86 + 24 * q^87 + 3 * q^88 + 15 * q^89 + 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 - 3 * q^96 - 45 * q^97

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 $

$2$	1.87939	1.32893	0.664463	−	0.747321i	$-0.268660\pi$
$2$	1.87939	1.32893	0.664463	+	0.747321i	$0.268660\pi$
$3$	−0.652704	−0.376839	−0.188419	−	0.982089i	$-0.560336\pi$
$3$	−0.652704	−0.376839	−0.188419	+	0.982089i	$0.560336\pi$
$4$	1.53209	0.766044
$5$	−3.53209	−1.57960	−0.789799	−	0.613366i	$-0.789815\pi$
$5$	−3.53209	−1.57960	−0.789799	+	0.613366i	$0.789815\pi$
$6$	−1.22668	−0.500791
$7$	0	0
$7$	0	0
$8$	−0.879385	−0.310910
$9$	−2.57398	−0.857993
$10$	−6.63816	−2.09917
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−4.41147	−1.22352	−0.611761	−	0.791042i	$-0.709539\pi$
$13$	−4.41147	−1.22352	−0.611761	+	0.791042i	$0.709539\pi$
$14$	0	0
$15$	2.30541	0.595254
$16$	−4.71688	−1.17922
$17$	5.24897	1.27306	0.636531	−	0.771251i	$-0.280369\pi$
$17$	5.24897	1.27306	0.636531	+	0.771251i	$0.280369\pi$
$18$	−4.83750	−1.14021
$19$	−1.81521	−0.416437	−0.208219	−	0.978082i	$-0.566767\pi$
$19$	−1.81521	−0.416437	−0.208219	+	0.978082i	$0.566767\pi$
$20$	−5.41147	−1.21004
$21$	0	0
$22$	1.87939	0.400686
$23$	−6.33275	−1.32047	−0.660235	−	0.751059i	$-0.729543\pi$
$23$	−6.33275	−1.32047	−0.660235	+	0.751059i	$0.729543\pi$
$24$	0.573978	0.117163
$25$	7.47565	1.49513
$26$	−8.29086	−1.62597
$27$	3.63816	0.700163
$28$	0	0
$29$	1.92127	0.356772	0.178386	−	0.983961i	$-0.442912\pi$
$29$	1.92127	0.356772	0.178386	+	0.983961i	$0.442912\pi$
$30$	4.33275	0.791048
$31$	−1.46791	−0.263645	−0.131822	−	0.991273i	$-0.542083\pi$
$31$	−1.46791	−0.263645	−0.131822	+	0.991273i	$0.542083\pi$
$32$	−7.10607	−1.25619
$33$	−0.652704	−0.113621
$34$	9.86484	1.69181
$35$	0	0
$36$	−3.94356	−0.657261
$37$	4.45336	0.732128	0.366064	−	0.930590i	$-0.380705\pi$
$37$	4.45336	0.732128	0.366064	+	0.930590i	$0.380705\pi$
$38$	−3.41147	−0.553414
$39$	2.87939	0.461071
$40$	3.10607	0.491112
$41$	−0.283119	−0.0442157	−0.0221078	−	0.999756i	$-0.507038\pi$
$41$	−0.283119	−0.0442157	−0.0221078	+	0.999756i	$0.507038\pi$
$42$	0	0
$43$	−3.41147	−0.520245	−0.260122	−	0.965576i	$-0.583763\pi$
$43$	−3.41147	−0.520245	−0.260122	+	0.965576i	$0.583763\pi$
$44$	1.53209	0.230971
$45$	9.09152	1.35528
$46$	−11.9017	−1.75481
$47$	4.55438	0.664324	0.332162	−	0.943222i	$-0.392222\pi$
$47$	4.55438	0.664324	0.332162	+	0.943222i	$0.392222\pi$
$48$	3.07873	0.444376
$49$	0	0
$50$	14.0496	1.98692
$51$	−3.42602	−0.479739
$52$	−6.75877	−0.937273
$53$	−7.23442	−0.993724	−0.496862	−	0.867829i	$-0.665515\pi$
$53$	−7.23442	−0.993724	−0.496862	+	0.867829i	$0.665515\pi$
$54$	6.83750	0.930465
$55$	−3.53209	−0.476267
$56$	0	0
$57$	1.18479	0.156930
$58$	3.61081	0.474123
$59$	−9.53983	−1.24198	−0.620990	−	0.783818i	$-0.713269\pi$
$59$	−9.53983	−1.24198	−0.620990	+	0.783818i	$0.713269\pi$
$60$	3.53209	0.455991
$61$	1.14796	0.146981	0.0734903	−	0.997296i	$-0.476586\pi$
$61$	1.14796	0.146981	0.0734903	+	0.997296i	$0.476586\pi$
$62$	−2.75877	−0.350364
$63$	0	0
$64$	−3.92127	−0.490159
$65$	15.5817	1.93267
$66$	−1.22668	−0.150994
$67$	−0.694593	−0.0848580	−0.0424290	−	0.999099i	$-0.513510\pi$
$67$	−0.694593	−0.0848580	−0.0424290	+	0.999099i	$0.513510\pi$
$68$	8.04189	0.975222
$69$	4.13341	0.497604
$70$	0	0
$71$	9.46110	1.12283	0.561413	−	0.827536i	$-0.310258\pi$
$71$	9.46110	1.12283	0.561413	+	0.827536i	$0.310258\pi$
$72$	2.26352	0.266758
$73$	−2.34730	−0.274730	−0.137365	−	0.990520i	$-0.543863\pi$
$73$	−2.34730	−0.274730	−0.137365	+	0.990520i	$0.543863\pi$
$74$	8.36959	0.972945
$75$	−4.87939	−0.563423
$76$	−2.78106	−0.319009
$77$	0	0
$78$	5.41147	0.612729
$79$	−12.4192	−1.39727	−0.698635	−	0.715478i	$-0.746209\pi$
$79$	−12.4192	−1.39727	−0.698635	+	0.715478i	$0.746209\pi$
$80$	16.6604	1.86269
$81$	5.34730	0.594144
$82$	−0.532089	−0.0587594
$83$	11.3327	1.24393	0.621965	−	0.783045i	$-0.286334\pi$
$83$	11.3327	1.24393	0.621965	+	0.783045i	$0.286334\pi$
$84$	0	0
$85$	−18.5398	−2.01093
$86$	−6.41147	−0.691367
$87$	−1.25402	−0.134445
$88$	−0.879385	−0.0937428
$89$	3.46791	0.367598	0.183799	−	0.982964i	$-0.441160\pi$
$89$	3.46791	0.367598	0.183799	+	0.982964i	$0.441160\pi$
$90$	17.0865	1.80107
$91$	0	0
$92$	−9.70233	−1.01154
$93$	0.958111	0.0993515
$94$	8.55943	0.882838
$95$	6.41147	0.657803
$96$	4.63816	0.473380
$97$	−15.3473	−1.55828	−0.779141	−	0.626849i	$-0.784344\pi$
$97$	−15.3473	−1.55828	−0.779141	+	0.626849i	$0.784344\pi$
$98$	0	0
$99$	−2.57398	−0.258695
$100$	11.4534	1.14534
$101$	−6.70233	−0.666907	−0.333454	−	0.942767i	$-0.608214\pi$
$101$	−6.70233	−0.666907	−0.333454	+	0.942767i	$0.608214\pi$
$102$	−6.43882	−0.637538
$103$	−2.24897	−0.221598	−0.110799	−	0.993843i	$-0.535341\pi$
$103$	−2.24897	−0.221598	−0.110799	+	0.993843i	$0.535341\pi$
$104$	3.87939	0.380405
$105$	0	0
$106$	−13.5963	−1.32059
$107$	−11.5321	−1.11485	−0.557425	−	0.830228i	$-0.688210\pi$
$107$	−11.5321	−1.11485	−0.557425	+	0.830228i	$0.688210\pi$
$108$	5.57398	0.536356
$109$	−11.9855	−1.14800	−0.573999	−	0.818856i	$-0.694609\pi$
$109$	−11.9855	−1.14800	−0.573999	+	0.818856i	$0.694609\pi$
$110$	−6.63816	−0.632923
$111$	−2.90673	−0.275894
$112$	0	0
$113$	5.00774	0.471089	0.235544	−	0.971864i	$-0.424313\pi$
$113$	5.00774	0.471089	0.235544	+	0.971864i	$0.424313\pi$
$114$	2.22668	0.208548
$115$	22.3678	2.08581
$116$	2.94356	0.273303
$117$	11.3550	1.04977
$118$	−17.9290	−1.65050
$119$	0	0
$120$	−2.02734	−0.185070
$121$	1.00000	0.0909091
$122$	2.15745	0.195326
$123$	0.184793	0.0166622
$124$	−2.24897	−0.201963
$125$	−8.74422	−0.782107
$126$	0	0
$127$	−14.2344	−1.26310	−0.631550	−	0.775335i	$-0.717581\pi$
$127$	−14.2344	−1.26310	−0.631550	+	0.775335i	$0.717581\pi$
$128$	6.84255	0.604802
$129$	2.22668	0.196048
$130$	29.2841	2.56838
$131$	−5.11381	−0.446795	−0.223398	−	0.974727i	$-0.571715\pi$
$131$	−5.11381	−0.446795	−0.223398	+	0.974727i	$0.571715\pi$
$132$	−1.00000	−0.0870388
$133$	0	0
$134$	−1.30541	−0.112770
$135$	−12.8503	−1.10598
$136$	−4.61587	−0.395807
$137$	19.7074	1.68372	0.841858	−	0.539699i	$-0.181462\pi$
$137$	19.7074	1.68372	0.841858	+	0.539699i	$0.181462\pi$
$138$	7.76827	0.661279
$139$	5.28581	0.448336	0.224168	−	0.974550i	$-0.428034\pi$
$139$	5.28581	0.448336	0.224168	+	0.974550i	$0.428034\pi$
$140$	0	0
$141$	−2.97266	−0.250343
$142$	17.7811	1.49215
$143$	−4.41147	−0.368906
$144$	12.1411	1.01176
$145$	−6.78611	−0.563556
$146$	−4.41147	−0.365096
$147$	0	0
$148$	6.82295	0.560843
$149$	−17.0155	−1.39396	−0.696981	−	0.717089i	$-0.745474\pi$
$149$	−17.0155	−1.39396	−0.696981	+	0.717089i	$0.745474\pi$
$150$	−9.17024	−0.748747
$151$	1.30272	0.106014	0.0530069	−	0.998594i	$-0.483119\pi$
$151$	1.30272	0.106014	0.0530069	+	0.998594i	$0.483119\pi$
$152$	1.59627	0.129474
$153$	−13.5107	−1.09228
$154$	0	0
$155$	5.18479	0.416453
$156$	4.41147	0.353201
$157$	−13.6946	−1.09295	−0.546474	−	0.837476i	$-0.684030\pi$
$157$	−13.6946	−1.09295	−0.546474	+	0.837476i	$0.684030\pi$
$158$	−23.3405	−1.85687
$159$	4.72193	0.374474
$160$	25.0993	1.98427
$161$	0	0
$162$	10.0496	0.789573
$163$	16.4047	1.28491	0.642456	−	0.766322i	$-0.277915\pi$
$163$	16.4047	1.28491	0.642456	+	0.766322i	$0.277915\pi$
$164$	−0.433763	−0.0338712
$165$	2.30541	0.179476
$166$	21.2986	1.65309
$167$	8.24628	0.638116	0.319058	−	0.947735i	$-0.396633\pi$
$167$	8.24628	0.638116	0.319058	+	0.947735i	$0.396633\pi$
$168$	0	0
$169$	6.46110	0.497008
$170$	−34.8435	−2.67237
$171$	4.67230	0.357300
$172$	−5.22668	−0.398531
$173$	−19.2344	−1.46237	−0.731183	−	0.682181i	$-0.761031\pi$
$173$	−19.2344	−1.46237	−0.731183	+	0.682181i	$0.761031\pi$
$174$	−2.35679	−0.178668
$175$	0	0
$176$	−4.71688	−0.355548
$177$	6.22668	0.468026
$178$	6.51754	0.488510
$179$	−1.32770	−0.0992367	−0.0496183	−	0.998768i	$-0.515800\pi$
$179$	−1.32770	−0.0992367	−0.0496183	+	0.998768i	$0.515800\pi$
$180$	13.9290	1.03821
$181$	−17.6527	−1.31212	−0.656058	−	0.754711i	$-0.727777\pi$
$181$	−17.6527	−1.31212	−0.656058	+	0.754711i	$0.727777\pi$
$182$	0	0
$183$	−0.749275	−0.0553880
$184$	5.56893	0.410547
$185$	−15.7297	−1.15647
$186$	1.80066	0.132031
$187$	5.24897	0.383843
$188$	6.97771	0.508902
$189$	0	0
$190$	12.0496	0.874172
$191$	15.5526	1.12535	0.562674	−	0.826679i	$-0.309773\pi$
$191$	15.5526	1.12535	0.562674	+	0.826679i	$0.309773\pi$
$192$	2.55943	0.184711
$193$	−5.21894	−0.375668	−0.187834	−	0.982201i	$-0.560147\pi$
$193$	−5.21894	−0.375668	−0.187834	+	0.982201i	$0.560147\pi$
$194$	−28.8435	−2.07084
$195$	−10.1702	−0.728306
$196$	0	0
$197$	−4.61856	−0.329058	−0.164529	−	0.986372i	$-0.552610\pi$
$197$	−4.61856	−0.329058	−0.164529	+	0.986372i	$0.552610\pi$
$198$	−4.83750	−0.343786
$199$	6.04963	0.428847	0.214423	−	0.976741i	$-0.431213\pi$
$199$	6.04963	0.428847	0.214423	+	0.976741i	$0.431213\pi$
$200$	−6.57398	−0.464850
$201$	0.453363	0.0319778
$202$	−12.5963	−0.886270
$203$	0	0
$204$	−5.24897	−0.367501
$205$	1.00000	0.0698430
$206$	−4.22668	−0.294487
$207$	16.3004	1.13295
$208$	20.8084	1.44280
$209$	−1.81521	−0.125561
$210$	0	0
$211$	8.69459	0.598560	0.299280	−	0.954165i	$-0.403253\pi$
$211$	8.69459	0.598560	0.299280	+	0.954165i	$0.403253\pi$
$212$	−11.0838	−0.761237
$213$	−6.17530	−0.423124
$214$	−21.6732	−1.48155
$215$	12.0496	0.821778
$216$	−3.19934	−0.217688
$217$	0	0
$218$	−22.5253	−1.52560
$219$	1.53209	0.103529
$220$	−5.41147	−0.364842
$221$	−23.1557	−1.55762
$222$	−5.46286	−0.366643
$223$	0.221629	0.0148414	0.00742069	−	0.999972i	$-0.497638\pi$
$223$	0.221629	0.0148414	0.00742069	+	0.999972i	$0.497638\pi$
$224$	0	0
$225$	−19.2422	−1.28281
$226$	9.41147	0.626042
$227$	9.69965	0.643788	0.321894	−	0.946776i	$-0.395681\pi$
$227$	9.69965	0.643788	0.321894	+	0.946776i	$0.395681\pi$
$228$	1.81521	0.120215
$229$	−23.6946	−1.56578	−0.782891	−	0.622158i	$-0.786256\pi$
$229$	−23.6946	−1.56578	−0.782891	+	0.622158i	$0.786256\pi$
$230$	42.0378	2.77189
$231$	0	0
$232$	−1.68954	−0.110924
$233$	20.8871	1.36836	0.684181	−	0.729313i	$-0.260160\pi$
$233$	20.8871	1.36836	0.684181	+	0.729313i	$0.260160\pi$
$234$	21.3405	1.39507
$235$	−16.0865	−1.04937
$236$	−14.6159	−0.951412
$237$	8.10607	0.526546
$238$	0	0
$239$	15.0300	0.972212	0.486106	−	0.873900i	$-0.338417\pi$
$239$	15.0300	0.972212	0.486106	+	0.873900i	$0.338417\pi$
$240$	−10.8743	−0.701935
$241$	−29.5398	−1.90283	−0.951414	−	0.307915i	$-0.900369\pi$
$241$	−29.5398	−1.90283	−0.951414	+	0.307915i	$0.900369\pi$
$242$	1.87939	0.120811
$243$	−14.4047	−0.924060
$244$	1.75877	0.112594
$245$	0	0
$246$	0.347296	0.0221428
$247$	8.00774	0.509520
$248$	1.29086	0.0819697
$249$	−7.39693	−0.468761
$250$	−16.4338	−1.03936
$251$	−3.77063	−0.238000	−0.119000	−	0.992894i	$-0.537969\pi$
$251$	−3.77063	−0.238000	−0.119000	+	0.992894i	$0.537969\pi$
$252$	0	0
$253$	−6.33275	−0.398136
$254$	−26.7520	−1.67857
$255$	12.1010	0.757795
$256$	20.7023	1.29390
$257$	8.66044	0.540224	0.270112	−	0.962829i	$-0.412939\pi$
$257$	8.66044	0.540224	0.270112	+	0.962829i	$0.412939\pi$
$258$	4.18479	0.260534
$259$	0	0
$260$	23.8726	1.48051
$261$	−4.94532	−0.306107
$262$	−9.61081	−0.593758
$263$	−5.83481	−0.359790	−0.179895	−	0.983686i	$-0.557576\pi$
$263$	−5.83481	−0.359790	−0.179895	+	0.983686i	$0.557576\pi$
$264$	0.573978	0.0353259
$265$	25.5526	1.56969
$266$	0	0
$267$	−2.26352	−0.138525
$268$	−1.06418	−0.0650050
$269$	21.9813	1.34023	0.670113	−	0.742259i	$-0.266246\pi$
$269$	21.9813	1.34023	0.670113	+	0.742259i	$0.266246\pi$
$270$	−24.1506	−1.46976
$271$	−9.85204	−0.598469	−0.299235	−	0.954180i	$-0.596731\pi$
$271$	−9.85204	−0.598469	−0.299235	+	0.954180i	$0.596731\pi$
$272$	−24.7588	−1.50122
$273$	0	0
$274$	37.0378	2.23753
$275$	7.47565	0.450799
$276$	6.33275	0.381187
$277$	23.6391	1.42034	0.710168	−	0.704033i	$-0.248619\pi$
$277$	23.6391	1.42034	0.710168	+	0.704033i	$0.248619\pi$
$278$	9.93407	0.595806
$279$	3.77837	0.226205
$280$	0	0
$281$	16.2713	0.970662	0.485331	−	0.874331i	$-0.338699\pi$
$281$	16.2713	0.970662	0.485331	+	0.874331i	$0.338699\pi$
$282$	−5.58677	−0.332687
$283$	−16.9982	−1.01044	−0.505220	−	0.862990i	$-0.668589\pi$
$283$	−16.9982	−1.01044	−0.505220	+	0.862990i	$0.668589\pi$
$284$	14.4953	0.860135
$285$	−4.18479	−0.247886
$286$	−8.29086	−0.490249
$287$	0	0
$288$	18.2909	1.07780
$289$	10.5517	0.620688
$290$	−12.7537	−0.748924
$291$	10.0172	0.587221
$292$	−3.59627	−0.210456
$293$	13.7784	0.804941	0.402471	−	0.915433i	$-0.368152\pi$
$293$	13.7784	0.804941	0.402471	+	0.915433i	$0.368152\pi$
$294$	0	0
$295$	33.6955	1.96183
$296$	−3.91622	−0.227626
$297$	3.63816	0.211107
$298$	−31.9786	−1.85247
$299$	27.9368	1.61562
$300$	−7.47565	−0.431607
$301$	0	0
$302$	2.44831	0.140884
$303$	4.37464	0.251316
$304$	8.56212	0.491071
$305$	−4.05468	−0.232170
$306$	−25.3919	−1.45156
$307$	11.6159	0.662953	0.331476	−	0.943464i	$-0.392453\pi$
$307$	11.6159	0.662953	0.331476	+	0.943464i	$0.392453\pi$
$308$	0	0
$309$	1.46791	0.0835065
$310$	9.74422	0.553435
$311$	−3.44831	−0.195536	−0.0977679	−	0.995209i	$-0.531170\pi$
$311$	−3.44831	−0.195536	−0.0977679	+	0.995209i	$0.531170\pi$
$312$	−2.53209	−0.143351
$313$	19.4219	1.09779	0.548895	−	0.835891i	$-0.315049\pi$
$313$	19.4219	1.09779	0.548895	+	0.835891i	$0.315049\pi$
$314$	−25.7374	−1.45245
$315$	0	0
$316$	−19.0273	−1.07037
$317$	−32.8161	−1.84314	−0.921569	−	0.388214i	$-0.873092\pi$
$317$	−32.8161	−1.84314	−0.921569	+	0.388214i	$0.873092\pi$
$318$	8.87433	0.497648
$319$	1.92127	0.107571
$320$	13.8503	0.774255
$321$	7.52704	0.420118
$322$	0	0
$323$	−9.52797	−0.530150
$324$	8.19253	0.455141
$325$	−32.9786	−1.82933
$326$	30.8307	1.70755
$327$	7.82295	0.432610
$328$	0.248970	0.0137471
$329$	0	0
$330$	4.33275	0.238510
$331$	−6.36009	−0.349582	−0.174791	−	0.984606i	$-0.555925\pi$
$331$	−6.36009	−0.349582	−0.174791	+	0.984606i	$0.555925\pi$
$332$	17.3628	0.952906
$333$	−11.4629	−0.628161
$334$	15.4979	0.848010
$335$	2.45336	0.134042
$336$	0	0
$337$	−15.5449	−0.846784	−0.423392	−	0.905947i	$-0.639161\pi$
$337$	−15.5449	−0.846784	−0.423392	+	0.905947i	$0.639161\pi$
$338$	12.1429	0.660487
$339$	−3.26857	−0.177524
$340$	−28.4047	−1.54046
$341$	−1.46791	−0.0794918
$342$	8.78106	0.474825
$343$	0	0
$344$	3.00000	0.161749
$345$	−14.5996	−0.786014
$346$	−36.1489	−1.94338
$347$	−19.7246	−1.05887	−0.529437	−	0.848350i	$-0.677597\pi$
$347$	−19.7246	−1.05887	−0.529437	+	0.848350i	$0.677597\pi$
$348$	−1.92127	−0.102991
$349$	5.79385	0.310138	0.155069	−	0.987904i	$-0.450440\pi$
$349$	5.79385	0.310138	0.155069	+	0.987904i	$0.450440\pi$
$350$	0	0
$351$	−16.0496	−0.856666
$352$	−7.10607	−0.378755
$353$	−33.1661	−1.76525	−0.882627	−	0.470073i	$-0.844227\pi$
$353$	−33.1661	−1.76525	−0.882627	+	0.470073i	$0.844227\pi$
$354$	11.7023	0.621972
$355$	−33.4175	−1.77361
$356$	5.31315	0.281596
$357$	0	0
$358$	−2.49525	−0.131878
$359$	4.20977	0.222183	0.111092	−	0.993810i	$-0.464565\pi$
$359$	4.20977	0.222183	0.111092	+	0.993810i	$0.464565\pi$
$360$	−7.99495	−0.421371
$361$	−15.7050	−0.826580
$362$	−33.1762	−1.74370
$363$	−0.652704	−0.0342581
$364$	0	0
$365$	8.29086	0.433963
$366$	−1.40818	−0.0736066
$367$	19.4388	1.01470	0.507349	−	0.861741i	$-0.330626\pi$
$367$	19.4388	1.01470	0.507349	+	0.861741i	$0.330626\pi$
$368$	29.8708	1.55712
$369$	0.728741	0.0379367
$370$	−29.5621	−1.53686
$371$	0	0
$372$	1.46791	0.0761076
$373$	12.7142	0.658316	0.329158	−	0.944275i	$-0.393235\pi$
$373$	12.7142	0.658316	0.329158	+	0.944275i	$0.393235\pi$
$374$	9.86484	0.510099
$375$	5.70739	0.294728
$376$	−4.00505	−0.206545
$377$	−8.47565	−0.436518
$378$	0	0
$379$	−22.8111	−1.17173	−0.585863	−	0.810410i	$-0.699245\pi$
$379$	−22.8111	−1.17173	−0.585863	+	0.810410i	$0.699245\pi$
$380$	9.82295	0.503907
$381$	9.29086	0.475985
$382$	29.2294	1.49550
$383$	−8.29860	−0.424039	−0.212019	−	0.977265i	$-0.568004\pi$
$383$	−8.29860	−0.424039	−0.212019	+	0.977265i	$0.568004\pi$
$384$	−4.46616	−0.227913
$385$	0	0
$386$	−9.80840	−0.499234
$387$	8.78106	0.446366
$388$	−23.5134	−1.19371
$389$	11.3996	0.577983	0.288992	−	0.957332i	$-0.406680\pi$
$389$	11.3996	0.577983	0.288992	+	0.957332i	$0.406680\pi$
$390$	−19.1138	−0.967865
$391$	−33.2404	−1.68104
$392$	0	0
$393$	3.33780	0.168370
$394$	−8.68004	−0.437294
$395$	43.8658	2.20713
$396$	−3.94356	−0.198171
$397$	−6.58172	−0.330327	−0.165163	−	0.986266i	$-0.552815\pi$
$397$	−6.58172	−0.330327	−0.165163	+	0.986266i	$0.552815\pi$
$398$	11.3696	0.569906
$399$	0	0
$400$	−35.2618	−1.76309
$401$	4.18984	0.209231	0.104615	−	0.994513i	$-0.466639\pi$
$401$	4.18984	0.209231	0.104615	+	0.994513i	$0.466639\pi$
$402$	0.852044	0.0424961
$403$	6.47565	0.322575
$404$	−10.2686	−0.510880
$405$	−18.8871	−0.938509
$406$	0	0
$407$	4.45336	0.220745
$408$	3.01279	0.149155
$409$	−0.773318	−0.0382381	−0.0191191	−	0.999817i	$-0.506086\pi$
$409$	−0.773318	−0.0382381	−0.0191191	+	0.999817i	$0.506086\pi$
$410$	1.87939	0.0928162
$411$	−12.8631	−0.634489
$412$	−3.44562	−0.169754
$413$	0	0
$414$	30.6346	1.50561
$415$	−40.0283	−1.96491
$416$	31.3482	1.53697
$417$	−3.45007	−0.168950
$418$	−3.41147	−0.166861
$419$	−13.7547	−0.671959	−0.335979	−	0.941869i	$-0.609067\pi$
$419$	−13.7547	−0.671959	−0.335979	+	0.941869i	$0.609067\pi$
$420$	0	0
$421$	−5.80571	−0.282953	−0.141477	−	0.989942i	$-0.545185\pi$
$421$	−5.80571	−0.282953	−0.141477	+	0.989942i	$0.545185\pi$
$422$	16.3405	0.795443
$423$	−11.7229	−0.569985
$424$	6.36184	0.308958
$425$	39.2395	1.90339
$426$	−11.6058	−0.562301
$427$	0	0
$428$	−17.6682	−0.854024
$429$	2.87939	0.139018
$430$	22.6459	1.09208
$431$	−18.0060	−0.867318	−0.433659	−	0.901077i	$-0.642778\pi$
$431$	−18.0060	−0.867318	−0.433659	+	0.901077i	$0.642778\pi$
$432$	−17.1607	−0.825647
$433$	−2.34049	−0.112477	−0.0562384	−	0.998417i	$-0.517911\pi$
$433$	−2.34049	−0.112477	−0.0562384	+	0.998417i	$0.517911\pi$
$434$	0	0
$435$	4.42932	0.212370
$436$	−18.3628	−0.879418
$437$	11.4953	0.549892
$438$	2.87939	0.137582
$439$	40.0333	1.91069	0.955343	−	0.295498i	$-0.0954857\pi$
$439$	40.0333	1.91069	0.955343	+	0.295498i	$0.0954857\pi$
$440$	3.10607	0.148076
$441$	0	0
$442$	−43.5185	−2.06996
$443$	18.9760	0.901575	0.450787	−	0.892631i	$-0.351143\pi$
$443$	18.9760	0.901575	0.450787	+	0.892631i	$0.351143\pi$
$444$	−4.45336	−0.211347
$445$	−12.2490	−0.580657
$446$	0.416527	0.0197231
$447$	11.1061	0.525299
$448$	0	0
$449$	−31.5371	−1.48833	−0.744165	−	0.667996i	$-0.767152\pi$
$449$	−31.5371	−1.48833	−0.744165	+	0.667996i	$0.767152\pi$
$450$	−36.1634	−1.70476
$451$	−0.283119	−0.0133315
$452$	7.67230	0.360875
$453$	−0.850289	−0.0399501
$454$	18.2294	0.855547
$455$	0	0
$456$	−1.04189	−0.0487909
$457$	11.6186	0.543493	0.271747	−	0.962369i	$-0.412399\pi$
$457$	11.6186	0.543493	0.271747	+	0.962369i	$0.412399\pi$
$458$	−44.5313	−2.08081
$459$	19.0966	0.891352
$460$	34.2695	1.59782
$461$	12.9786	0.604476	0.302238	−	0.953233i	$-0.402266\pi$
$461$	12.9786	0.604476	0.302238	+	0.953233i	$0.402266\pi$
$462$	0	0
$463$	35.3705	1.64381	0.821904	−	0.569626i	$-0.192912\pi$
$463$	35.3705	1.64381	0.821904	+	0.569626i	$0.192912\pi$
$464$	−9.06242	−0.420712
$465$	−3.38413	−0.156935
$466$	39.2550	1.81845
$467$	39.8658	1.84477	0.922384	−	0.386274i	$-0.126238\pi$
$467$	39.8658	1.84477	0.922384	+	0.386274i	$0.126238\pi$
$468$	17.3969	0.804173
$469$	0	0
$470$	−30.2327	−1.39453
$471$	8.93851	0.411865
$472$	8.38919	0.386144
$473$	−3.41147	−0.156860
$474$	15.2344	0.699740
$475$	−13.5699	−0.622628
$476$	0	0
$477$	18.6212	0.852608
$478$	28.2472	1.29200
$479$	30.3800	1.38810	0.694049	−	0.719928i	$-0.255825\pi$
$479$	30.3800	1.38810	0.694049	+	0.719928i	$0.255825\pi$
$480$	−16.3824	−0.747750
$481$	−19.6459	−0.895776
$482$	−55.5167	−2.52872
$483$	0	0
$484$	1.53209	0.0696404
$485$	54.2080	2.46146
$486$	−27.0719	−1.22801
$487$	−10.4311	−0.472677	−0.236339	−	0.971671i	$-0.575947\pi$
$487$	−10.4311	−0.472677	−0.236339	+	0.971671i	$0.575947\pi$
$488$	−1.00950	−0.0456977
$489$	−10.7074	−0.484205
$490$	0	0
$491$	−10.2763	−0.463763	−0.231882	−	0.972744i	$-0.574488\pi$
$491$	−10.2763	−0.463763	−0.231882	+	0.972744i	$0.574488\pi$
$492$	0.283119	0.0127640
$493$	10.0847	0.454193
$494$	15.0496	0.677115
$495$	9.09152	0.408633
$496$	6.92396	0.310895
$497$	0	0
$498$	−13.9017	−0.622949
$499$	−36.5185	−1.63479	−0.817396	−	0.576077i	$-0.804583\pi$
$499$	−36.5185	−1.63479	−0.817396	+	0.576077i	$0.804583\pi$
$500$	−13.3969	−0.599129
$501$	−5.38238	−0.240467
$502$	−7.08647	−0.316284
$503$	31.3628	1.39840	0.699199	−	0.714928i	$-0.253540\pi$
$503$	31.3628	1.39840	0.699199	+	0.714928i	$0.253540\pi$
$504$	0	0
$505$	23.6732	1.05345
$506$	−11.9017	−0.529094
$507$	−4.21719	−0.187292
$508$	−21.8084	−0.967591
$509$	11.5645	0.512587	0.256293	−	0.966599i	$-0.417499\pi$
$509$	11.5645	0.512587	0.256293	+	0.966599i	$0.417499\pi$
$510$	22.7425	1.00705
$511$	0	0
$512$	25.2226	1.11469
$513$	−6.60401	−0.291574
$514$	16.2763	0.717917
$515$	7.94356	0.350035
$516$	3.41147	0.150182
$517$	4.55438	0.200301
$518$	0	0
$519$	12.5544	0.551076
$520$	−13.7023	−0.600887
$521$	30.5604	1.33887	0.669437	−	0.742869i	$-0.266535\pi$
$521$	30.5604	1.33887	0.669437	+	0.742869i	$0.266535\pi$
$522$	−9.29416	−0.406794
$523$	4.45512	0.194809	0.0974044	−	0.995245i	$-0.468946\pi$
$523$	4.45512	0.194809	0.0974044	+	0.995245i	$0.468946\pi$
$524$	−7.83481	−0.342265
$525$	0	0
$526$	−10.9659	−0.478134
$527$	−7.70502	−0.335636
$528$	3.07873	0.133984
$529$	17.1037	0.743639
$530$	48.0232	2.08600
$531$	24.5553	1.06561
$532$	0	0
$533$	1.24897	0.0540989
$534$	−4.25402	−0.184090
$535$	40.7324	1.76101
$536$	0.610815	0.0263832
$537$	0.866592	0.0373962
$538$	41.3114	1.78106
$539$	0	0
$540$	−19.6878	−0.847227
$541$	−16.6705	−0.716723	−0.358361	−	0.933583i	$-0.616664\pi$
$541$	−16.6705	−0.716723	−0.358361	+	0.933583i	$0.616664\pi$
$542$	−18.5158	−0.795321
$543$	11.5220	0.494456
$544$	−37.2995	−1.59920
$545$	42.3337	1.81338
$546$	0	0
$547$	36.2080	1.54814	0.774071	−	0.633098i	$-0.218217\pi$
$547$	36.2080	1.54814	0.774071	+	0.633098i	$0.218217\pi$
$548$	30.1935	1.28980
$549$	−2.95481	−0.126108
$550$	14.0496	0.599078
$551$	−3.48751	−0.148573
$552$	−3.63486	−0.154710
$553$	0	0
$554$	44.4270	1.88752
$555$	10.2668	0.435802
$556$	8.09833	0.343446
$557$	−0.669940	−0.0283863	−0.0141931	−	0.999899i	$-0.504518\pi$
$557$	−0.669940	−0.0283863	−0.0141931	+	0.999899i	$0.504518\pi$
$558$	7.10101	0.300610
$559$	15.0496	0.636532
$560$	0	0
$561$	−3.42602	−0.144647
$562$	30.5800	1.28994
$563$	13.0341	0.549324	0.274662	−	0.961541i	$-0.411434\pi$
$563$	13.0341	0.549324	0.274662	+	0.961541i	$0.411434\pi$
$564$	−4.55438	−0.191774
$565$	−17.6878	−0.744131
$566$	−31.9463	−1.34280
$567$	0	0
$568$	−8.31996	−0.349098
$569$	27.4415	1.15041	0.575204	−	0.818010i	$-0.304923\pi$
$569$	27.4415	1.15041	0.575204	+	0.818010i	$0.304923\pi$
$570$	−7.86484	−0.329422
$571$	16.2395	0.679601	0.339800	−	0.940498i	$-0.389640\pi$
$571$	16.2395	0.679601	0.339800	+	0.940498i	$0.389640\pi$
$572$	−6.75877	−0.282598
$573$	−10.1513	−0.424075
$574$	0	0
$575$	−47.3414	−1.97427
$576$	10.0933	0.420553
$577$	−23.7178	−0.987386	−0.493693	−	0.869636i	$-0.664353\pi$
$577$	−23.7178	−0.987386	−0.493693	+	0.869636i	$0.664353\pi$
$578$	19.8307	0.824848
$579$	3.40642	0.141566
$580$	−10.3969	−0.431709
$581$	0	0
$582$	18.8262	0.780373
$583$	−7.23442	−0.299619
$584$	2.06418	0.0854163
$585$	−40.1070	−1.65822
$586$	25.8949	1.06971
$587$	44.5904	1.84044	0.920221	−	0.391399i	$-0.128009\pi$
$587$	44.5904	1.84044	0.920221	+	0.391399i	$0.128009\pi$
$588$	0	0
$589$	2.66456	0.109791
$590$	63.3269	2.60713
$591$	3.01455	0.124002
$592$	−21.0060	−0.863341
$593$	42.8435	1.75937	0.879685	−	0.475556i	$-0.157753\pi$
$593$	42.8435	1.75937	0.879685	+	0.475556i	$0.157753\pi$
$594$	6.83750	0.280546
$595$	0	0
$596$	−26.0692	−1.06784
$597$	−3.94862	−0.161606
$598$	52.5039	2.14705
$599$	−0.633103	−0.0258679	−0.0129339	−	0.999916i	$-0.504117\pi$
$599$	−0.633103	−0.0258679	−0.0129339	+	0.999916i	$0.504117\pi$
$600$	4.29086	0.175174
$601$	3.45842	0.141072	0.0705359	−	0.997509i	$-0.477529\pi$
$601$	3.45842	0.141072	0.0705359	+	0.997509i	$0.477529\pi$
$602$	0	0
$603$	1.78787	0.0728075
$604$	1.99588	0.0812113
$605$	−3.53209	−0.143600
$606$	8.22163	0.333981
$607$	−48.2749	−1.95942	−0.979708	−	0.200428i	$-0.935767\pi$
$607$	−48.2749	−1.95942	−0.979708	+	0.200428i	$0.935767\pi$
$608$	12.8990	0.523123
$609$	0	0
$610$	−7.62031	−0.308537
$611$	−20.0915	−0.812816
$612$	−20.6996	−0.836734
$613$	−21.3155	−0.860925	−0.430463	−	0.902608i	$-0.641650\pi$
$613$	−21.3155	−0.860925	−0.430463	+	0.902608i	$0.641650\pi$
$614$	21.8307	0.881015
$615$	−0.652704	−0.0263196
$616$	0	0
$617$	−12.4243	−0.500182	−0.250091	−	0.968222i	$-0.580461\pi$
$617$	−12.4243	−0.500182	−0.250091	+	0.968222i	$0.580461\pi$
$618$	2.75877	0.110974
$619$	−36.3405	−1.46065	−0.730324	−	0.683101i	$-0.760631\pi$
$619$	−36.3405	−1.46065	−0.730324	+	0.683101i	$0.760631\pi$
$620$	7.94356	0.319021
$621$	−23.0395	−0.924544
$622$	−6.48070	−0.259853
$623$	0	0
$624$	−13.5817	−0.543704
$625$	−6.49289	−0.259716
$626$	36.5012	1.45888
$627$	1.18479	0.0473161
$628$	−20.9813	−0.837246
$629$	23.3756	0.932045
$630$	0	0
$631$	15.9195	0.633746	0.316873	−	0.948468i	$-0.397367\pi$
$631$	15.9195	0.633746	0.316873	+	0.948468i	$0.397367\pi$
$632$	10.9213	0.434425
$633$	−5.67499	−0.225561
$634$	−61.6742	−2.44939
$635$	50.2772	1.99519
$636$	7.23442	0.286864
$637$	0	0
$638$	3.61081	0.142954
$639$	−24.3527	−0.963377
$640$	−24.1685	−0.955343
$641$	−12.4739	−0.492689	−0.246345	−	0.969182i	$-0.579230\pi$
$641$	−12.4739	−0.492689	−0.246345	+	0.969182i	$0.579230\pi$
$642$	14.1462	0.558306
$643$	36.8331	1.45255	0.726277	−	0.687402i	$-0.241249\pi$
$643$	36.8331	1.45255	0.726277	+	0.687402i	$0.241249\pi$
$644$	0	0
$645$	−7.86484	−0.309678
$646$	−17.9067	−0.704531
$647$	−20.4587	−0.804316	−0.402158	−	0.915570i	$-0.631740\pi$
$647$	−20.4587	−0.804316	−0.402158	+	0.915570i	$0.631740\pi$
$648$	−4.70233	−0.184725
$649$	−9.53983	−0.374471
$650$	−61.9796	−2.43104
$651$	0	0
$652$	25.1334	0.984300
$653$	−15.5594	−0.608888	−0.304444	−	0.952530i	$-0.598471\pi$
$653$	−15.5594	−0.608888	−0.304444	+	0.952530i	$0.598471\pi$
$654$	14.7023	0.574907
$655$	18.0624	0.705757
$656$	1.33544	0.0521400
$657$	6.04189	0.235717
$658$	0	0
$659$	−23.6673	−0.921945	−0.460973	−	0.887414i	$-0.652499\pi$
$659$	−23.6673	−0.921945	−0.460973	+	0.887414i	$0.652499\pi$
$660$	3.53209	0.137486
$661$	−20.1976	−0.785595	−0.392798	−	0.919625i	$-0.628493\pi$
$661$	−20.1976	−0.785595	−0.392798	+	0.919625i	$0.628493\pi$
$662$	−11.9531	−0.464569
$663$	15.1138	0.586972
$664$	−9.96585	−0.386750
$665$	0	0
$666$	−21.5431	−0.834779
$667$	−12.1669	−0.471106
$668$	12.6340	0.488826
$669$	−0.144658	−0.00559281
$670$	4.61081	0.178131
$671$	1.14796	0.0443163
$672$	0	0
$673$	7.92633	0.305537	0.152769	−	0.988262i	$-0.451181\pi$
$673$	7.92633	0.305537	0.152769	+	0.988262i	$0.451181\pi$
$674$	−29.2148	−1.12531
$675$	27.1976	1.04684
$676$	9.89899	0.380730
$677$	−36.0564	−1.38576	−0.692881	−	0.721052i	$-0.743659\pi$
$677$	−36.0564	−1.38576	−0.692881	+	0.721052i	$0.743659\pi$
$678$	−6.14290	−0.235917
$679$	0	0
$680$	16.3037	0.625217
$681$	−6.33099	−0.242604
$682$	−2.75877	−0.105639
$683$	−12.3568	−0.472819	−0.236410	−	0.971653i	$-0.575971\pi$
$683$	−12.3568	−0.472819	−0.236410	+	0.971653i	$0.575971\pi$
$684$	7.15839	0.273708
$685$	−69.6082	−2.65959
$686$	0	0
$687$	15.4655	0.590047
$688$	16.0915	0.613483
$689$	31.9145	1.21584
$690$	−27.4382	−1.04455
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−29.4688	−1.12024
$693$	0	0
$694$	−37.0702	−1.40716
$695$	−18.6699	−0.708191
$696$	1.10277	0.0418004
$697$	−1.48608	−0.0562893
$698$	10.8889	0.412150
$699$	−13.6331	−0.515651
$700$	0	0
$701$	12.7611	0.481981	0.240991	−	0.970527i	$-0.422528\pi$
$701$	12.7611	0.481981	0.240991	+	0.970527i	$0.422528\pi$
$702$	−30.1634	−1.13845
$703$	−8.08378	−0.304885
$704$	−3.92127	−0.147789
$705$	10.4997	0.395441
$706$	−62.3319	−2.34589
$707$	0	0
$708$	9.53983	0.358529
$709$	4.70502	0.176701	0.0883504	−	0.996089i	$-0.471840\pi$
$709$	4.70502	0.176701	0.0883504	+	0.996089i	$0.471840\pi$
$710$	−62.8043	−2.35700
$711$	31.9668	1.19885
$712$	−3.04963	−0.114290
$713$	9.29591	0.348135
$714$	0	0
$715$	15.5817	0.582723
$716$	−2.03415	−0.0760197
$717$	−9.81016	−0.366367
$718$	7.91178	0.295265
$719$	−52.6219	−1.96246	−0.981232	−	0.192831i	$-0.938233\pi$
$719$	−52.6219	−1.96246	−0.981232	+	0.192831i	$0.938233\pi$
$720$	−42.8836	−1.59818
$721$	0	0
$722$	−29.5158	−1.09846
$723$	19.2808	0.717059
$724$	−27.0455	−1.00514
$725$	14.3628	0.533420
$726$	−1.22668	−0.0455264
$727$	22.3901	0.830404	0.415202	−	0.909729i	$-0.363711\pi$
$727$	22.3901	0.830404	0.415202	+	0.909729i	$0.363711\pi$
$728$	0	0
$729$	−6.63991	−0.245923
$730$	15.5817	0.576705
$731$	−17.9067	−0.662304
$732$	−1.14796	−0.0424297
$733$	30.2158	1.11604	0.558022	−	0.829826i	$-0.311560\pi$
$733$	30.2158	1.11604	0.558022	+	0.829826i	$0.311560\pi$
$734$	36.5330	1.34846
$735$	0	0
$736$	45.0009	1.65876
$737$	−0.694593	−0.0255857
$738$	1.36959	0.0504151
$739$	12.7716	0.469810	0.234905	−	0.972018i	$-0.424522\pi$
$739$	12.7716	0.469810	0.234905	+	0.972018i	$0.424522\pi$
$740$	−24.0993	−0.885906
$741$	−5.22668	−0.192007
$742$	0	0
$743$	−37.4989	−1.37570	−0.687850	−	0.725853i	$-0.741445\pi$
$743$	−37.4989	−1.37570	−0.687850	+	0.725853i	$0.741445\pi$
$744$	−0.842549	−0.0308893
$745$	60.1002	2.20190
$746$	23.8949	0.874853
$747$	−29.1702	−1.06728
$748$	8.04189	0.294041
$749$	0	0
$750$	10.7264	0.391672
$751$	36.7847	1.34229	0.671146	−	0.741325i	$-0.265802\pi$
$751$	36.7847	1.34229	0.671146	+	0.741325i	$0.265802\pi$
$752$	−21.4825	−0.783385
$753$	2.46110	0.0896876
$754$	−15.9290	−0.580101
$755$	−4.60132	−0.167459
$756$	0	0
$757$	−2.27126	−0.0825503	−0.0412752	−	0.999148i	$-0.513142\pi$
$757$	−2.27126	−0.0825503	−0.0412752	+	0.999148i	$0.513142\pi$
$758$	−42.8708	−1.55714
$759$	4.13341	0.150033
$760$	−5.63816	−0.204517
$761$	−10.1908	−0.369415	−0.184708	−	0.982793i	$-0.559134\pi$
$761$	−10.1908	−0.369415	−0.184708	+	0.982793i	$0.559134\pi$
$762$	17.4611	0.632549
$763$	0	0
$764$	23.8280	0.862067
$765$	47.7211	1.72536
$766$	−15.5963	−0.563516
$767$	42.0847	1.51959
$768$	−13.5125	−0.487590
$769$	27.7802	1.00178	0.500891	−	0.865511i	$-0.333006\pi$
$769$	27.7802	1.00178	0.500891	+	0.865511i	$0.333006\pi$
$770$	0	0
$771$	−5.65270	−0.203577
$772$	−7.99588	−0.287778
$773$	10.7820	0.387801	0.193901	−	0.981021i	$-0.437886\pi$
$773$	10.7820	0.387801	0.193901	+	0.981021i	$0.437886\pi$
$774$	16.5030	0.593188
$775$	−10.9736	−0.394183
$776$	13.4962	0.484485
$777$	0	0
$778$	21.4243	0.768097
$779$	0.513919	0.0184131
$780$	−15.5817	−0.557915
$781$	9.46110	0.338545
$782$	−62.4715	−2.23398
$783$	6.98990	0.249798
$784$	0	0
$785$	48.3705	1.72642
$786$	6.27301	0.223751
$787$	21.3473	0.760949	0.380474	−	0.924791i	$-0.375761\pi$
$787$	21.3473	0.760949	0.380474	+	0.924791i	$0.375761\pi$
$788$	−7.07604	−0.252073
$789$	3.80840	0.135583
$790$	82.4407	2.93311
$791$	0	0
$792$	2.26352	0.0804306
$793$	−5.06418	−0.179834
$794$	−12.3696	−0.438980
$795$	−16.6783	−0.591518
$796$	9.26857	0.328516
$797$	−39.3096	−1.39242	−0.696209	−	0.717839i	$-0.745132\pi$
$797$	−39.3096	−1.39242	−0.696209	+	0.717839i	$0.745132\pi$
$798$	0	0
$799$	23.9058	0.845726
$800$	−53.1225	−1.87816
$801$	−8.92633	−0.315396
$802$	7.87433	0.278052
$803$	−2.34730	−0.0828343
$804$	0.694593	0.0244964
$805$	0	0
$806$	12.1702	0.428679
$807$	−14.3473	−0.505049
$808$	5.89393	0.207348
$809$	3.24661	0.114145	0.0570723	−	0.998370i	$-0.481823\pi$
$809$	3.24661	0.114145	0.0570723	+	0.998370i	$0.481823\pi$
$810$	−35.4962	−1.24721
$811$	−33.4056	−1.17303	−0.586515	−	0.809939i	$-0.699500\pi$
$811$	−33.4056	−1.17303	−0.586515	+	0.809939i	$0.699500\pi$
$812$	0	0
$813$	6.43047	0.225526
$814$	8.36959	0.293354
$815$	−57.9427	−2.02965
$816$	16.1601	0.565718
$817$	6.19253	0.216649
$818$	−1.45336	−0.0508157
$819$	0	0
$820$	1.53209	0.0535029
$821$	−24.1976	−0.844502	−0.422251	−	0.906479i	$-0.638760\pi$
$821$	−24.1976	−0.844502	−0.422251	+	0.906479i	$0.638760\pi$
$822$	−24.1747	−0.843189
$823$	−46.7151	−1.62839	−0.814193	−	0.580594i	$-0.802821\pi$
$823$	−46.7151	−1.62839	−0.814193	+	0.580594i	$0.802821\pi$
$824$	1.97771	0.0688968
$825$	−4.87939	−0.169878
$826$	0	0
$827$	1.89992	0.0660667	0.0330333	−	0.999454i	$-0.489483\pi$
$827$	1.89992	0.0660667	0.0330333	+	0.999454i	$0.489483\pi$
$828$	24.9736	0.867892
$829$	−50.9701	−1.77026	−0.885132	−	0.465340i	$-0.845932\pi$
$829$	−50.9701	−1.77026	−0.885132	+	0.465340i	$0.845932\pi$
$830$	−75.2285	−2.61122
$831$	−15.4293	−0.535237
$832$	17.2986	0.599721
$833$	0	0
$834$	−6.48400	−0.224523
$835$	−29.1266	−1.00797
$836$	−2.78106	−0.0961849
$837$	−5.34049	−0.184594
$838$	−25.8503	−0.892983
$839$	−42.9368	−1.48234	−0.741171	−	0.671317i	$-0.765729\pi$
$839$	−42.9368	−1.48234	−0.741171	+	0.671317i	$0.765729\pi$
$840$	0	0
$841$	−25.3087	−0.872714
$842$	−10.9112	−0.376024
$843$	−10.6203	−0.365783
$844$	13.3209	0.458524
$845$	−22.8212	−0.785073
$846$	−22.0318	−0.757468
$847$	0	0
$848$	34.1239	1.17182
$849$	11.0948	0.380773
$850$	73.7461	2.52947
$851$	−28.2020	−0.966753
$852$	−9.46110	−0.324132
$853$	−52.3560	−1.79263	−0.896317	−	0.443414i	$-0.853767\pi$
$853$	−52.3560	−1.79263	−0.896317	+	0.443414i	$0.853767\pi$
$854$	0	0
$855$	−16.5030	−0.564390
$856$	10.1411	0.346617
$857$	0.978036	0.0334091	0.0167045	−	0.999860i	$-0.494683\pi$
$857$	0.978036	0.0334091	0.0167045	+	0.999860i	$0.494683\pi$
$858$	5.41147	0.184745
$859$	34.0147	1.16057	0.580283	−	0.814415i	$-0.302942\pi$
$859$	34.0147	1.16057	0.580283	+	0.814415i	$0.302942\pi$
$860$	18.4611	0.629518
$861$	0	0
$862$	−33.8402	−1.15260
$863$	−22.6955	−0.772565	−0.386282	−	0.922381i	$-0.626241\pi$
$863$	−22.6955	−0.772565	−0.386282	+	0.922381i	$0.626241\pi$
$864$	−25.8530	−0.879536
$865$	67.9377	2.30995
$866$	−4.39868	−0.149473
$867$	−6.88713	−0.233899
$868$	0	0
$869$	−12.4192	−0.421293
$870$	8.32440	0.282224
$871$	3.06418	0.103826
$872$	10.5398	0.356924
$873$	39.5036	1.33699
$874$	21.6040	0.730766
$875$	0	0
$876$	2.34730	0.0793078
$877$	−1.22844	−0.0414813	−0.0207407	−	0.999785i	$-0.506602\pi$
$877$	−1.22844	−0.0414813	−0.0207407	+	0.999785i	$0.506602\pi$
$878$	75.2380	2.53916
$879$	−8.99319	−0.303333
$880$	16.6604	0.561623
$881$	−9.13516	−0.307771	−0.153886	−	0.988089i	$-0.549179\pi$
$881$	−9.13516	−0.307771	−0.153886	+	0.988089i	$0.549179\pi$
$882$	0	0
$883$	44.8256	1.50850	0.754251	−	0.656586i	$-0.228000\pi$
$883$	44.8256	1.50850	0.754251	+	0.656586i	$0.228000\pi$
$884$	−35.4766	−1.19321
$885$	−21.9932	−0.739293
$886$	35.6631	1.19813
$887$	23.0178	0.772864	0.386432	−	0.922318i	$-0.373707\pi$
$887$	23.0178	0.772864	0.386432	+	0.922318i	$0.373707\pi$
$888$	2.55613	0.0857782
$889$	0	0
$890$	−23.0205	−0.771650
$891$	5.34730	0.179141
$892$	0.339556	0.0113692
$893$	−8.26714	−0.276649
$894$	20.8726	0.698083
$895$	4.68954	0.156754
$896$	0	0
$897$	−18.2344	−0.608830
$898$	−59.2704	−1.97788
$899$	−2.82026	−0.0940609
$900$	−29.4807	−0.982690
$901$	−37.9733	−1.26507
$902$	−0.532089	−0.0177166
$903$	0	0
$904$	−4.40373	−0.146466
$905$	62.3509	2.07261
$906$	−1.59802	−0.0530907
$907$	−28.3209	−0.940380	−0.470190	−	0.882565i	$-0.655815\pi$
$907$	−28.3209	−0.940380	−0.470190	+	0.882565i	$0.655815\pi$
$908$	14.8607	0.493170
$909$	17.2517	0.572201
$910$	0	0
$911$	2.97596	0.0985978	0.0492989	−	0.998784i	$-0.484301\pi$
$911$	2.97596	0.0985978	0.0492989	+	0.998784i	$0.484301\pi$
$912$	−5.58853	−0.185055
$913$	11.3327	0.375059
$914$	21.8357	0.722262
$915$	2.64651	0.0874908
$916$	−36.3022	−1.19946
$917$	0	0
$918$	35.8898	1.18454
$919$	21.7939	0.718913	0.359456	−	0.933162i	$-0.382962\pi$
$919$	21.7939	0.718913	0.359456	+	0.933162i	$0.382962\pi$
$920$	−19.6699	−0.648499
$921$	−7.58172	−0.249826
$922$	24.3919	0.803304
$923$	−41.7374	−1.37380
$924$	0	0
$925$	33.2918	1.09463
$926$	66.4748	2.18450
$927$	5.78880	0.190129
$928$	−13.6527	−0.448172
$929$	−37.0651	−1.21607	−0.608033	−	0.793911i	$-0.708041\pi$
$929$	−37.0651	−1.21607	−0.608033	+	0.793911i	$0.708041\pi$
$930$	−6.36009	−0.208556
$931$	0	0
$932$	32.0009	1.04823
$933$	2.25072	0.0736854
$934$	74.9231	2.45156
$935$	−18.5398	−0.606317
$936$	−9.98545	−0.326385
$937$	−39.8340	−1.30132	−0.650660	−	0.759369i	$-0.725508\pi$
$937$	−39.8340	−1.30132	−0.650660	+	0.759369i	$0.725508\pi$
$938$	0	0
$939$	−12.6767	−0.413690
$940$	−24.6459	−0.803861
$941$	−13.6919	−0.446343	−0.223172	−	0.974779i	$-0.571641\pi$
$941$	−13.6919	−0.446343	−0.223172	+	0.974779i	$0.571641\pi$
$942$	16.7989	0.547338
$943$	1.79292	0.0583855
$944$	44.9982	1.46457
$945$	0	0
$946$	−6.41147	−0.208455
$947$	−47.1334	−1.53163	−0.765815	−	0.643061i	$-0.777664\pi$
$947$	−47.1334	−1.53163	−0.765815	+	0.643061i	$0.777664\pi$
$948$	12.4192	0.403357
$949$	10.3550	0.336139
$950$	−25.5030	−0.827426
$951$	21.4192	0.694566
$952$	0	0
$953$	−26.8990	−0.871344	−0.435672	−	0.900106i	$-0.643489\pi$
$953$	−26.8990	−0.871344	−0.435672	+	0.900106i	$0.643489\pi$
$954$	34.9965	1.13305
$955$	−54.9332	−1.77760
$956$	23.0273	0.744757
$957$	−1.25402	−0.0405368
$958$	57.0958	1.84468
$959$	0	0
$960$	−9.04013	−0.291769
$961$	−28.8452	−0.930492
$962$	−36.9222	−1.19042
$963$	29.6833	0.956532
$964$	−45.2576	−1.45765
$965$	18.4338	0.593404
$966$	0	0
$967$	−39.4270	−1.26789	−0.633943	−	0.773380i	$-0.718565\pi$
$967$	−39.4270	−1.26789	−0.633943	+	0.773380i	$0.718565\pi$
$968$	−0.879385	−0.0282645
$969$	6.21894	0.199781
$970$	101.878	3.27110
$971$	−16.0814	−0.516077	−0.258039	−	0.966135i	$-0.583076\pi$
$971$	−16.0814	−0.516077	−0.258039	+	0.966135i	$0.583076\pi$
$972$	−22.0692	−0.707871
$973$	0	0
$974$	−19.6040	−0.628153
$975$	21.5253	0.689361
$976$	−5.41477	−0.173323
$977$	27.4279	0.877496	0.438748	−	0.898610i	$-0.355422\pi$
$977$	27.4279	0.877496	0.438748	+	0.898610i	$0.355422\pi$
$978$	−20.1233	−0.643472
$979$	3.46791	0.110835
$980$	0	0
$981$	30.8503	0.984974
$982$	−19.3131	−0.616307
$983$	7.46616	0.238133	0.119067	−	0.992886i	$-0.462010\pi$
$983$	7.46616	0.238133	0.119067	+	0.992886i	$0.462010\pi$
$984$	−0.162504	−0.00518043
$985$	16.3131	0.519780
$986$	18.9531	0.603588
$987$	0	0
$988$	12.2686	0.390315
$989$	21.6040	0.686967
$990$	17.0865	0.543044
$991$	−24.2704	−0.770976	−0.385488	−	0.922713i	$-0.625967\pi$
$991$	−24.2704	−0.770976	−0.385488	+	0.922713i	$0.625967\pi$
$992$	10.4311	0.331187
$993$	4.15125	0.131736
$994$	0	0
$995$	−21.3678	−0.677406
$996$	−11.3327	−0.359092
$997$	33.1162	1.04880	0.524400	−	0.851472i	$-0.324290\pi$
$997$	33.1162	1.04880	0.524400	+	0.851472i	$0.324290\pi$
$998$	−68.6323	−2.17252
$999$	16.2020	0.512610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.a.g.1.3		3
3.2	odd	2		4851.2.a.bk.1.1		3
4.3	odd	2		8624.2.a.co.1.2		3
7.2	even	3		539.2.e.m.67.1		6
7.3	odd	6		77.2.e.a.23.1	✓	6
7.4	even	3		539.2.e.m.177.1		6
7.5	odd	6		77.2.e.a.67.1	yes	6
7.6	odd	2		539.2.a.j.1.3		3
11.10	odd	2		5929.2.a.u.1.1		3
21.5	even	6		693.2.i.h.298.3		6
21.17	even	6		693.2.i.h.100.3		6
21.20	even	2		4851.2.a.bj.1.1		3
28.3	even	6		1232.2.q.m.177.2		6
28.19	even	6		1232.2.q.m.529.2		6
28.27	even	2		8624.2.a.ch.1.2		3
77.3	odd	30		847.2.n.g.9.3		24
77.5	odd	30		847.2.n.g.487.3		24
77.10	even	6		847.2.e.c.485.3		6
77.17	even	30		847.2.n.f.366.3		24
77.19	even	30		847.2.n.f.130.3		24
77.24	even	30		847.2.n.f.807.1		24
77.26	odd	30		847.2.n.g.753.3		24
77.31	odd	30		847.2.n.g.807.3		24
77.38	odd	30		847.2.n.g.366.1		24
77.40	even	30		847.2.n.f.753.1		24
77.47	odd	30		847.2.n.g.130.1		24
77.52	even	30		847.2.n.f.9.1		24
77.54	even	6		847.2.e.c.606.3		6
77.59	odd	30		847.2.n.g.632.1		24
77.61	even	30		847.2.n.f.487.1		24
77.68	even	30		847.2.n.f.81.3		24
77.73	even	30		847.2.n.f.632.3		24
77.75	odd	30		847.2.n.g.81.1		24
77.76	even	2		5929.2.a.x.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.e.a.23.1	✓	6	7.3	odd	6
77.2.e.a.67.1	yes	6	7.5	odd	6
539.2.a.g.1.3		3	1.1	even	1	trivial
539.2.a.j.1.3		3	7.6	odd	2
539.2.e.m.67.1		6	7.2	even	3
539.2.e.m.177.1		6	7.4	even	3
693.2.i.h.100.3		6	21.17	even	6
693.2.i.h.298.3		6	21.5	even	6
847.2.e.c.485.3		6	77.10	even	6
847.2.e.c.606.3		6	77.54	even	6
847.2.n.f.9.1		24	77.52	even	30
847.2.n.f.81.3		24	77.68	even	30
847.2.n.f.130.3		24	77.19	even	30
847.2.n.f.366.3		24	77.17	even	30
847.2.n.f.487.1		24	77.61	even	30
847.2.n.f.632.3		24	77.73	even	30
847.2.n.f.753.1		24	77.40	even	30
847.2.n.f.807.1		24	77.24	even	30
847.2.n.g.9.3		24	77.3	odd	30
847.2.n.g.81.1		24	77.75	odd	30
847.2.n.g.130.1		24	77.47	odd	30
847.2.n.g.366.1		24	77.38	odd	30
847.2.n.g.487.3		24	77.5	odd	30
847.2.n.g.632.1		24	77.59	odd	30
847.2.n.g.753.3		24	77.26	odd	30
847.2.n.g.807.3		24	77.31	odd	30
1232.2.q.m.177.2		6	28.3	even	6
1232.2.q.m.529.2		6	28.19	even	6
4851.2.a.bj.1.1		3	21.20	even	2
4851.2.a.bk.1.1		3	3.2	odd	2
5929.2.a.u.1.1		3	11.10	odd	2
5929.2.a.x.1.1		3	77.76	even	2
8624.2.a.ch.1.2		3	28.27	even	2
8624.2.a.co.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.a (trivial)

\(f(q)\)	\(=\)	\(q+1.87939 q^{2} -0.652704 q^{3} +1.53209 q^{4} -3.53209 q^{5} -1.22668 q^{6} -0.879385 q^{8} -2.57398 q^{9} -6.63816 q^{10} +1.00000 q^{11} -1.00000 q^{12} -4.41147 q^{13} +2.30541 q^{15} -4.71688 q^{16} +5.24897 q^{17} -4.83750 q^{18} -1.81521 q^{19} -5.41147 q^{20} +1.87939 q^{22} -6.33275 q^{23} +0.573978 q^{24} +7.47565 q^{25} -8.29086 q^{26} +3.63816 q^{27} +1.92127 q^{29} +4.33275 q^{30} -1.46791 q^{31} -7.10607 q^{32} -0.652704 q^{33} +9.86484 q^{34} -3.94356 q^{36} +4.45336 q^{37} -3.41147 q^{38} +2.87939 q^{39} +3.10607 q^{40} -0.283119 q^{41} -3.41147 q^{43} +1.53209 q^{44} +9.09152 q^{45} -11.9017 q^{46} +4.55438 q^{47} +3.07873 q^{48} +14.0496 q^{50} -3.42602 q^{51} -6.75877 q^{52} -7.23442 q^{53} +6.83750 q^{54} -3.53209 q^{55} +1.18479 q^{57} +3.61081 q^{58} -9.53983 q^{59} +3.53209 q^{60} +1.14796 q^{61} -2.75877 q^{62} -3.92127 q^{64} +15.5817 q^{65} -1.22668 q^{66} -0.694593 q^{67} +8.04189 q^{68} +4.13341 q^{69} +9.46110 q^{71} +2.26352 q^{72} -2.34730 q^{73} +8.36959 q^{74} -4.87939 q^{75} -2.78106 q^{76} +5.41147 q^{78} -12.4192 q^{79} +16.6604 q^{80} +5.34730 q^{81} -0.532089 q^{82} +11.3327 q^{83} -18.5398 q^{85} -6.41147 q^{86} -1.25402 q^{87} -0.879385 q^{88} +3.46791 q^{89} +17.0865 q^{90} -9.70233 q^{92} +0.958111 q^{93} +8.55943 q^{94} +6.41147 q^{95} +4.63816 q^{96} -15.3473 q^{97} -2.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} - 6 q^{5} + 3 q^{6} + 3 q^{8} - 3 q^{10} + 3 q^{11} - 3 q^{12} - 3 q^{13} + 9 q^{15} - 6 q^{16} + 3 q^{17} - 12 q^{18} - 9 q^{19} - 6 q^{20} - 6 q^{24} + 3 q^{25} - 9 q^{26} - 6 q^{27} - 3 q^{29}+ \cdots - 45 q^{97}+O(q^{100}) \) 3 * q - 3 * q^3 - 6 * q^5 + 3 * q^6 + 3 * q^8 - 3 * q^10 + 3 * q^11 - 3 * q^12 - 3 * q^13 + 9 * q^15 - 6 * q^16 + 3 * q^17 - 12 * q^18 - 9 * q^19 - 6 * q^20 - 6 * q^24 + 3 * q^25 - 9 * q^26 - 6 * q^27 - 3 * q^29 - 6 * q^30 - 9 * q^31 - 9 * q^32 - 3 * q^33 + 6 * q^34 + 3 * q^36 + 3 * q^39 - 3 * q^40 - 9 * q^41 - 3 * q^45 - 24 * q^46 + 3 * q^47 + 18 * q^48 + 15 * q^50 - 18 * q^51 - 9 * q^52 + 9 * q^53 + 18 * q^54 - 6 * q^55 + 15 * q^58 + 6 * q^60 - 12 * q^61 + 3 * q^62 - 3 * q^64 + 15 * q^65 + 3 * q^66 + 21 * q^68 - 21 * q^69 - 9 * q^71 + 12 * q^72 - 6 * q^73 + 18 * q^74 - 9 * q^75 + 9 * q^76 + 6 * q^78 - 3 * q^79 + 27 * q^80 + 15 * q^81 + 3 * q^82 + 15 * q^83 - 27 * q^85 - 9 * q^86 + 24 * q^87 + 3 * q^88 + 15 * q^89 + 36 * q^90 - 3 * q^92 + 6 * q^93 + 9 * q^95 - 3 * q^96 - 45 * q^97

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