LMFDB - Embedded newform 731.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.a (trivial)

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:	yes
Analytic conductor:	$5.83706438776$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2460365.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 6x^{3} + 7x^{2} - 7x + 1 $ x^6 - x^5 - 6x^4 + 6x^3 + 7x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.178849$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +O(q^{10})$	\(q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +0.571360 q^{10} -1.62328 q^{11} -3.27827 q^{12} -2.15615 q^{13} -4.01269 q^{14} -0.508127 q^{15} -4.23774 q^{16} -1.00000 q^{17} +0.124444 q^{18} -3.82998 q^{19} +0.543797 q^{20} +3.56860 q^{21} -3.19464 q^{22} +4.47568 q^{23} +0.437186 q^{24} -4.91571 q^{25} -4.24333 q^{26} +5.13996 q^{27} -3.81911 q^{28} -3.55839 q^{29} -1.00000 q^{30} +9.03159 q^{31} -7.84035 q^{32} +2.84109 q^{33} -1.96801 q^{34} -0.591956 q^{35} +0.118441 q^{36} +4.37329 q^{37} -7.53745 q^{38} +3.77371 q^{39} -0.0725200 q^{40} -10.4363 q^{41} +7.02304 q^{42} -1.00000 q^{43} -3.04053 q^{44} +0.0183581 q^{45} +8.80820 q^{46} -10.5387 q^{47} +7.41693 q^{48} -2.84267 q^{49} -9.67419 q^{50} +1.75021 q^{51} -4.03863 q^{52} -2.68238 q^{53} +10.1155 q^{54} -0.471277 q^{55} +0.509311 q^{56} +6.70327 q^{57} -7.00296 q^{58} +8.62164 q^{59} -0.951759 q^{60} -4.69008 q^{61} +17.7743 q^{62} -0.128930 q^{63} -6.95442 q^{64} -0.625980 q^{65} +5.59130 q^{66} -11.1335 q^{67} -1.87307 q^{68} -7.83338 q^{69} -1.16498 q^{70} +9.13386 q^{71} -0.0157951 q^{72} +16.6916 q^{73} +8.60670 q^{74} +8.60353 q^{75} -7.17384 q^{76} +3.30980 q^{77} +7.42671 q^{78} +12.6668 q^{79} -1.23032 q^{80} -9.18570 q^{81} -20.5389 q^{82} +11.1971 q^{83} +6.68425 q^{84} -0.290323 q^{85} -1.96801 q^{86} +6.22793 q^{87} +0.405481 q^{88} +7.63942 q^{89} +0.0361291 q^{90} +4.39629 q^{91} +8.38329 q^{92} -15.8072 q^{93} -20.7403 q^{94} -1.11193 q^{95} +13.7222 q^{96} -13.1442 q^{97} -5.59440 q^{98} -0.102646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.96801	1.39160	0.695798	−	0.718238i	$-0.255051\pi$
$2$	1.96801	1.39160	0.695798	+	0.718238i	$0.255051\pi$
$3$	−1.75021	−1.01048	−0.505242	−	0.862978i	$-0.668597\pi$
$3$	−1.75021	−1.01048	−0.505242	+	0.862978i	$0.668597\pi$
$4$	1.87307	0.936537
$5$	0.290323	0.129837	0.0649183	−	0.997891i	$-0.479321\pi$
$5$	0.290323	0.129837	0.0649183	+	0.997891i	$0.479321\pi$
$6$	−3.44443	−1.40618
$7$	−2.03895	−0.770652	−0.385326	−	0.922780i	$-0.625911\pi$
$7$	−2.03895	−0.770652	−0.385326	+	0.922780i	$0.625911\pi$
$8$	−0.249790	−0.0883143
$9$	0.0632334	0.0210778
$10$	0.571360	0.180680
$11$	−1.62328	−0.489439	−0.244719	−	0.969594i	$-0.578696\pi$
$11$	−1.62328	−0.489439	−0.244719	+	0.969594i	$0.578696\pi$
$12$	−3.27827	−0.946356
$13$	−2.15615	−0.598008	−0.299004	−	0.954252i	$-0.596654\pi$
$13$	−2.15615	−0.598008	−0.299004	+	0.954252i	$0.596654\pi$
$14$	−4.01269	−1.07244
$15$	−0.508127	−0.131198
$16$	−4.23774	−1.05944
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.124444	0.0293318
$19$	−3.82998	−0.878657	−0.439329	−	0.898326i	$-0.644784\pi$
$19$	−3.82998	−0.878657	−0.439329	+	0.898326i	$0.644784\pi$
$20$	0.543797	0.121597
$21$	3.56860	0.778732
$22$	−3.19464	−0.681100
$23$	4.47568	0.933244	0.466622	−	0.884457i	$-0.345471\pi$
$23$	4.47568	0.933244	0.466622	+	0.884457i	$0.345471\pi$
$24$	0.437186	0.0892401
$25$	−4.91571	−0.983142
$26$	−4.24333	−0.832185
$27$	5.13996	0.989185
$28$	−3.81911	−0.721745
$29$	−3.55839	−0.660776	−0.330388	−	0.943845i	$-0.607180\pi$
$29$	−3.55839	−0.660776	−0.330388	+	0.943845i	$0.607180\pi$
$30$	−1.00000	−0.182574
$31$	9.03159	1.62212	0.811061	−	0.584962i	$-0.198891\pi$
$31$	9.03159	1.62212	0.811061	+	0.584962i	$0.198891\pi$
$32$	−7.84035	−1.38599
$33$	2.84109	0.494570
$34$	−1.96801	−0.337511
$35$	−0.591956	−0.100059
$36$	0.118441	0.0197402
$37$	4.37329	0.718965	0.359483	−	0.933152i	$-0.382953\pi$
$37$	4.37329	0.718965	0.359483	+	0.933152i	$0.382953\pi$
$38$	−7.53745	−1.22274
$39$	3.77371	0.604278
$40$	−0.0725200	−0.0114664
$41$	−10.4363	−1.62988	−0.814942	−	0.579543i	$-0.803231\pi$
$41$	−10.4363	−1.62988	−0.814942	+	0.579543i	$0.803231\pi$
$42$	7.02304	1.08368
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.04053	−0.458378
$45$	0.0183581	0.00273667
$46$	8.80820	1.29870
$47$	−10.5387	−1.53723	−0.768615	−	0.639712i	$-0.779054\pi$
$47$	−10.5387	−1.53723	−0.768615	+	0.639712i	$0.779054\pi$
$48$	7.41693	1.07054
$49$	−2.84267	−0.406095
$50$	−9.67419	−1.36814
$51$	1.75021	0.245078
$52$	−4.03863	−0.560057
$53$	−2.68238	−0.368453	−0.184226	−	0.982884i	$-0.558978\pi$
$53$	−2.68238	−0.368453	−0.184226	+	0.982884i	$0.558978\pi$
$54$	10.1155	1.37655
$55$	−0.471277	−0.0635470
$56$	0.509311	0.0680596
$57$	6.70327	0.887869
$58$	−7.00296	−0.919533
$59$	8.62164	1.12244	0.561221	−	0.827666i	$-0.310332\pi$
$59$	8.62164	1.12244	0.561221	+	0.827666i	$0.310332\pi$
$60$	−0.951759	−0.122872
$61$	−4.69008	−0.600504	−0.300252	−	0.953860i	$-0.597071\pi$
$61$	−4.69008	−0.600504	−0.300252	+	0.953860i	$0.597071\pi$
$62$	17.7743	2.25734
$63$	−0.128930	−0.0162437
$64$	−6.95442	−0.869303
$65$	−0.625980	−0.0776433
$66$	5.59130	0.688241
$67$	−11.1335	−1.36017	−0.680084	−	0.733134i	$-0.738057\pi$
$67$	−11.1335	−1.36017	−0.680084	+	0.733134i	$0.738057\pi$
$68$	−1.87307	−0.227144
$69$	−7.83338	−0.943028
$70$	−1.16498	−0.139241
$71$	9.13386	1.08399	0.541995	−	0.840382i	$-0.317669\pi$
$71$	9.13386	1.08399	0.541995	+	0.840382i	$0.317669\pi$
$72$	−0.0157951	−0.00186147
$73$	16.6916	1.95360	0.976800	−	0.214155i	$-0.0686999\pi$
$73$	16.6916	1.95360	0.976800	+	0.214155i	$0.0686999\pi$
$74$	8.60670	1.00051
$75$	8.60353	0.993450
$76$	−7.17384	−0.822896
$77$	3.30980	0.377187
$78$	7.42671	0.840910
$79$	12.6668	1.42513	0.712564	−	0.701607i	$-0.247534\pi$
$79$	12.6668	1.42513	0.712564	+	0.701607i	$0.247534\pi$
$80$	−1.23032	−0.137553
$81$	−9.18570	−1.02063
$82$	−20.5389	−2.26814
$83$	11.1971	1.22904	0.614520	−	0.788901i	$-0.289350\pi$
$83$	11.1971	1.22904	0.614520	+	0.788901i	$0.289350\pi$
$84$	6.68425	0.729311
$85$	−0.290323	−0.0314900
$86$	−1.96801	−0.212216
$87$	6.22793	0.667704
$88$	0.405481	0.0432244
$89$	7.63942	0.809777	0.404889	−	0.914366i	$-0.367310\pi$
$89$	7.63942	0.809777	0.404889	+	0.914366i	$0.367310\pi$
$90$	0.0361291	0.00380834
$91$	4.39629	0.460856
$92$	8.38329	0.874018
$93$	−15.8072	−1.63913
$94$	−20.7403	−2.13920
$95$	−1.11193	−0.114082
$96$	13.7222	1.40052
$97$	−13.1442	−1.33459	−0.667294	−	0.744794i	$-0.732548\pi$
$97$	−13.1442	−1.33459	−0.667294	+	0.744794i	$0.732548\pi$
$98$	−5.59440	−0.565120
$99$	−0.102646	−0.0103163
$100$	−9.20750	−0.920750
$101$	13.2118	1.31462	0.657309	−	0.753621i	$-0.271695\pi$
$101$	13.2118	1.31462	0.657309	+	0.753621i	$0.271695\pi$
$102$	3.44443	0.341050
$103$	12.9351	1.27454	0.637268	−	0.770642i	$-0.280065\pi$
$103$	12.9351	1.27454	0.637268	+	0.770642i	$0.280065\pi$
$104$	0.538585	0.0528126
$105$	1.03605	0.101108
$106$	−5.27895	−0.512737
$107$	−9.52343	−0.920665	−0.460332	−	0.887747i	$-0.652270\pi$
$107$	−9.52343	−0.920665	−0.460332	+	0.887747i	$0.652270\pi$
$108$	9.62752	0.926409
$109$	−13.9100	−1.33234	−0.666170	−	0.745800i	$-0.732068\pi$
$109$	−13.9100	−1.33234	−0.666170	+	0.745800i	$0.732068\pi$
$110$	−0.927480	−0.0884317
$111$	−7.65418	−0.726503
$112$	8.64056	0.816456
$113$	−16.5162	−1.55371	−0.776856	−	0.629678i	$-0.783187\pi$
$113$	−16.5162	−1.55371	−0.776856	+	0.629678i	$0.783187\pi$
$114$	13.1921	1.23555
$115$	1.29939	0.121169
$116$	−6.66513	−0.618842
$117$	−0.136341	−0.0126047
$118$	16.9675	1.56199
$119$	2.03895	0.186911
$120$	0.126925	0.0115866
$121$	−8.36495	−0.760450
$122$	−9.23014	−0.835658
$123$	18.2658	1.64697
$124$	16.9168	1.51918
$125$	−2.87876	−0.257484
$126$	−0.253736	−0.0226046
$127$	12.9951	1.15313	0.576564	−	0.817052i	$-0.304393\pi$
$127$	12.9951	1.15313	0.576564	+	0.817052i	$0.304393\pi$
$128$	1.99430	0.176273
$129$	1.75021	0.154097
$130$	−1.23194	−0.108048
$131$	−22.2129	−1.94075	−0.970375	−	0.241602i	$-0.922327\pi$
$131$	−22.2129	−1.94075	−0.970375	+	0.241602i	$0.922327\pi$
$132$	5.32157	0.463183
$133$	7.80915	0.677139
$134$	−21.9108	−1.89280
$135$	1.49225	0.128432
$136$	0.249790	0.0214194
$137$	−8.64720	−0.738780	−0.369390	−	0.929274i	$-0.620433\pi$
$137$	−8.64720	−0.738780	−0.369390	+	0.929274i	$0.620433\pi$
$138$	−15.4162	−1.31231
$139$	3.98915	0.338355	0.169178	−	0.985586i	$-0.445889\pi$
$139$	3.98915	0.338355	0.169178	+	0.985586i	$0.445889\pi$
$140$	−1.10878	−0.0937088
$141$	18.4450	1.55335
$142$	17.9756	1.50847
$143$	3.50004	0.292688
$144$	−0.267967	−0.0223306
$145$	−1.03308	−0.0857929
$146$	32.8492	2.71862
$147$	4.97526	0.410353
$148$	8.19151	0.673338
$149$	6.38854	0.523370	0.261685	−	0.965153i	$-0.415722\pi$
$149$	6.38854	0.523370	0.261685	+	0.965153i	$0.415722\pi$
$150$	16.9319	1.38248
$151$	−9.92516	−0.807698	−0.403849	−	0.914826i	$-0.632328\pi$
$151$	−9.92516	−0.807698	−0.403849	+	0.914826i	$0.632328\pi$
$152$	0.956692	0.0775980
$153$	−0.0632334	−0.00511212
$154$	6.51373	0.524892
$155$	2.62208	0.210611
$156$	7.06845	0.565929
$157$	−20.7619	−1.65698	−0.828491	−	0.560002i	$-0.810800\pi$
$157$	−20.7619	−1.65698	−0.828491	+	0.560002i	$0.810800\pi$
$158$	24.9285	1.98320
$159$	4.69472	0.372315
$160$	−2.27624	−0.179952
$161$	−9.12571	−0.719207
$162$	−18.0776	−1.42031
$163$	−10.0984	−0.790965	−0.395483	−	0.918473i	$-0.629423\pi$
$163$	−10.0984	−0.790965	−0.395483	+	0.918473i	$0.629423\pi$
$164$	−19.5481	−1.52645
$165$	0.824834	0.0642133
$166$	22.0360	1.71033
$167$	−7.23726	−0.560036	−0.280018	−	0.959995i	$-0.590340\pi$
$167$	−7.23726	−0.560036	−0.280018	+	0.959995i	$0.590340\pi$
$168$	−0.891401	−0.0687731
$169$	−8.35102	−0.642386
$170$	−0.571360	−0.0438213
$171$	−0.242183	−0.0185202
$172$	−1.87307	−0.142821
$173$	12.3178	0.936501	0.468251	−	0.883596i	$-0.344884\pi$
$173$	12.3178	0.936501	0.468251	+	0.883596i	$0.344884\pi$
$174$	12.2566	0.929174
$175$	10.0229	0.757661
$176$	6.87906	0.518528
$177$	−15.0897	−1.13421
$178$	15.0345	1.12688
$179$	0.130015	0.00971775	0.00485888	−	0.999988i	$-0.498453\pi$
$179$	0.130015	0.00971775	0.00485888	+	0.999988i	$0.498453\pi$
$180$	0.0343862	0.00256299
$181$	11.3606	0.844426	0.422213	−	0.906497i	$-0.361253\pi$
$181$	11.3606	0.844426	0.422213	+	0.906497i	$0.361253\pi$
$182$	8.65195	0.641325
$183$	8.20863	0.606799
$184$	−1.11798	−0.0824188
$185$	1.26967	0.0933479
$186$	−31.1087	−2.28100
$187$	1.62328	0.118706
$188$	−19.7398	−1.43967
$189$	−10.4801	−0.762318
$190$	−2.18830	−0.158756
$191$	−13.7029	−0.991508	−0.495754	−	0.868463i	$-0.665108\pi$
$191$	−13.7029	−0.991508	−0.495754	+	0.868463i	$0.665108\pi$
$192$	12.1717	0.878417
$193$	25.2883	1.82029	0.910146	−	0.414288i	$-0.135970\pi$
$193$	25.2883	1.82029	0.910146	+	0.414288i	$0.135970\pi$
$194$	−25.8679	−1.85721
$195$	1.09560	0.0784573
$196$	−5.32453	−0.380323
$197$	0.863989	0.0615566	0.0307783	−	0.999526i	$-0.490201\pi$
$197$	0.863989	0.0615566	0.0307783	+	0.999526i	$0.490201\pi$
$198$	−0.202008	−0.0143561
$199$	0.708054	0.0501926	0.0250963	−	0.999685i	$-0.492011\pi$
$199$	0.708054	0.0501926	0.0250963	+	0.999685i	$0.492011\pi$
$200$	1.22790	0.0868255
$201$	19.4859	1.37443
$202$	26.0009	1.82942
$203$	7.25539	0.509229
$204$	3.27827	0.229525
$205$	−3.02991	−0.211618
$206$	25.4565	1.77364
$207$	0.283013	0.0196707
$208$	9.13720	0.633551
$209$	6.21714	0.430049
$210$	2.03895	0.140701
$211$	−23.4681	−1.61561	−0.807805	−	0.589450i	$-0.799344\pi$
$211$	−23.4681	−1.61561	−0.807805	+	0.589450i	$0.799344\pi$
$212$	−5.02429	−0.345070
$213$	−15.9862	−1.09535
$214$	−18.7422	−1.28119
$215$	−0.290323	−0.0197999
$216$	−1.28391	−0.0873592
$217$	−18.4150	−1.25009
$218$	−27.3751	−1.85408
$219$	−29.2137	−1.97408
$220$	−0.882738	−0.0595142
$221$	2.15615	0.145038
$222$	−15.0635	−1.01100
$223$	6.07464	0.406788	0.203394	−	0.979097i	$-0.434803\pi$
$223$	6.07464	0.406788	0.203394	+	0.979097i	$0.434803\pi$
$224$	15.9861	1.06812
$225$	−0.310837	−0.0207225
$226$	−32.5041	−2.16214
$227$	2.33319	0.154859	0.0774297	−	0.996998i	$-0.475329\pi$
$227$	2.33319	0.154859	0.0774297	+	0.996998i	$0.475329\pi$
$228$	12.5557	0.831523
$229$	−13.0781	−0.864222	−0.432111	−	0.901820i	$-0.642231\pi$
$229$	−13.0781	−0.864222	−0.432111	+	0.901820i	$0.642231\pi$
$230$	2.55723	0.168618
$231$	−5.79285	−0.381141
$232$	0.888852	0.0583560
$233$	3.89356	0.255075	0.127538	−	0.991834i	$-0.459293\pi$
$233$	3.89356	0.255075	0.127538	+	0.991834i	$0.459293\pi$
$234$	−0.268320	−0.0175406
$235$	−3.05964	−0.199589
$236$	16.1490	1.05121
$237$	−22.1696	−1.44007
$238$	4.01269	0.260104
$239$	−26.4426	−1.71043	−0.855215	−	0.518273i	$-0.826575\pi$
$239$	−26.4426	−1.71043	−0.855215	+	0.518273i	$0.826575\pi$
$240$	2.15331	0.138996
$241$	−12.0233	−0.774489	−0.387244	−	0.921977i	$-0.626573\pi$
$241$	−12.0233	−0.774489	−0.387244	+	0.921977i	$0.626573\pi$
$242$	−16.4623	−1.05824
$243$	0.657032	0.0421486
$244$	−8.78488	−0.562394
$245$	−0.825293	−0.0527260
$246$	35.9473	2.29192
$247$	8.25800	0.525444
$248$	−2.25601	−0.143256
$249$	−19.5973	−1.24193
$250$	−5.66544	−0.358314
$251$	9.23449	0.582876	0.291438	−	0.956590i	$-0.405866\pi$
$251$	9.23449	0.582876	0.291438	+	0.956590i	$0.405866\pi$
$252$	−0.241496	−0.0152128
$253$	−7.26530	−0.456766
$254$	25.5745	1.60469
$255$	0.508127	0.0318201
$256$	17.8337	1.11460
$257$	3.17529	0.198069	0.0990347	−	0.995084i	$-0.468425\pi$
$257$	3.17529	0.198069	0.0990347	+	0.995084i	$0.468425\pi$
$258$	3.44443	0.214441
$259$	−8.91694	−0.554072
$260$	−1.17251	−0.0727159
$261$	−0.225009	−0.0139277
$262$	−43.7153	−2.70074
$263$	6.52724	0.402487	0.201244	−	0.979541i	$-0.435502\pi$
$263$	6.52724	0.402487	0.201244	+	0.979541i	$0.435502\pi$
$264$	−0.709677	−0.0436776
$265$	−0.778756	−0.0478386
$266$	15.3685	0.942304
$267$	−13.3706	−0.818267
$268$	−20.8538	−1.27385
$269$	−6.08823	−0.371206	−0.185603	−	0.982625i	$-0.559424\pi$
$269$	−6.08823	−0.371206	−0.185603	+	0.982625i	$0.559424\pi$
$270$	2.93677	0.178726
$271$	−29.2935	−1.77945	−0.889726	−	0.456494i	$-0.849105\pi$
$271$	−29.2935	−1.77945	−0.889726	+	0.456494i	$0.849105\pi$
$272$	4.23774	0.256951
$273$	−7.69443	−0.465688
$274$	−17.0178	−1.02808
$275$	7.97960	0.481188
$276$	−14.6725	−0.883181
$277$	−22.1385	−1.33018	−0.665088	−	0.746765i	$-0.731606\pi$
$277$	−22.1385	−1.33018	−0.665088	+	0.746765i	$0.731606\pi$
$278$	7.85070	0.470854
$279$	0.571098	0.0341908
$280$	0.147865	0.00883662
$281$	−6.17797	−0.368547	−0.184273	−	0.982875i	$-0.558993\pi$
$281$	−6.17797	−0.368547	−0.184273	+	0.982875i	$0.558993\pi$
$282$	36.2999	2.16163
$283$	−8.74612	−0.519903	−0.259952	−	0.965622i	$-0.583707\pi$
$283$	−8.74612	−0.519903	−0.259952	+	0.965622i	$0.583707\pi$
$284$	17.1084	1.01520
$285$	1.94611	0.115278
$286$	6.88813	0.407304
$287$	21.2792	1.25607
$288$	−0.495772	−0.0292136
$289$	1.00000	0.0588235
$290$	−2.03312	−0.119389
$291$	23.0050	1.34858
$292$	31.2645	1.82962
$293$	−5.00471	−0.292378	−0.146189	−	0.989257i	$-0.546701\pi$
$293$	−5.00471	−0.292378	−0.146189	+	0.989257i	$0.546701\pi$
$294$	9.79138	0.571045
$295$	2.50306	0.145734
$296$	−1.09241	−0.0634949
$297$	−8.34361	−0.484145
$298$	12.5727	0.728319
$299$	−9.65024	−0.558088
$300$	16.1150	0.930403
$301$	2.03895	0.117523
$302$	−19.5328	−1.12399
$303$	−23.1233	−1.32840
$304$	16.2305	0.930881
$305$	−1.36164	−0.0779673
$306$	−0.124444	−0.00711400
$307$	30.6932	1.75175	0.875877	−	0.482534i	$-0.160284\pi$
$307$	30.6932	1.75175	0.875877	+	0.482534i	$0.160284\pi$
$308$	6.19951	0.353250
$309$	−22.6392	−1.28790
$310$	5.16029	0.293085
$311$	10.8925	0.617657	0.308828	−	0.951118i	$-0.400063\pi$
$311$	10.8925	0.617657	0.308828	+	0.951118i	$0.400063\pi$
$312$	−0.942637	−0.0533663
$313$	13.8368	0.782104	0.391052	−	0.920369i	$-0.372111\pi$
$313$	13.8368	0.782104	0.391052	+	0.920369i	$0.372111\pi$
$314$	−40.8597	−2.30585
$315$	−0.0374314	−0.00210902
$316$	23.7259	1.33469
$317$	−10.4203	−0.585261	−0.292630	−	0.956226i	$-0.594531\pi$
$317$	−10.4203	−0.585261	−0.292630	+	0.956226i	$0.594531\pi$
$318$	9.23927	0.518112
$319$	5.77628	0.323410
$320$	−2.01903	−0.112867
$321$	16.6680	0.930317
$322$	−17.9595	−1.00084
$323$	3.82998	0.213106
$324$	−17.2055	−0.955861
$325$	10.5990	0.587927
$326$	−19.8737	−1.10070
$327$	24.3455	1.34631
$328$	2.60690	0.143942
$329$	21.4880	1.18467
$330$	1.62328	0.0893589
$331$	−29.7774	−1.63671	−0.818356	−	0.574711i	$-0.805114\pi$
$331$	−29.7774	−1.63671	−0.818356	+	0.574711i	$0.805114\pi$
$332$	20.9730	1.15104
$333$	0.276538	0.0151542
$334$	−14.2430	−0.779344
$335$	−3.23230	−0.176599
$336$	−15.1228	−0.825016
$337$	26.0579	1.41946	0.709732	−	0.704472i	$-0.248816\pi$
$337$	26.0579	1.41946	0.709732	+	0.704472i	$0.248816\pi$
$338$	−16.4349	−0.893942
$339$	28.9068	1.57000
$340$	−0.543797	−0.0294916
$341$	−14.6608	−0.793929
$342$	−0.476619	−0.0257726
$343$	20.0687	1.08361
$344$	0.249790	0.0134678
$345$	−2.27421	−0.122440
$346$	24.2415	1.30323
$347$	−0.450411	−0.0241793	−0.0120897	−	0.999927i	$-0.503848\pi$
$347$	−0.450411	−0.0241793	−0.0120897	+	0.999927i	$0.503848\pi$
$348$	11.6654	0.625330
$349$	−3.89246	−0.208359	−0.104179	−	0.994559i	$-0.533222\pi$
$349$	−3.89246	−0.208359	−0.104179	+	0.994559i	$0.533222\pi$
$350$	19.7252	1.05436
$351$	−11.0825	−0.591541
$352$	12.7271	0.678357
$353$	9.88564	0.526159	0.263080	−	0.964774i	$-0.415262\pi$
$353$	9.88564	0.526159	0.263080	+	0.964774i	$0.415262\pi$
$354$	−29.6967	−1.57836
$355$	2.65177	0.140741
$356$	14.3092	0.758387
$357$	−3.56860	−0.188870
$358$	0.255871	0.0135232
$359$	−6.99527	−0.369196	−0.184598	−	0.982814i	$-0.559098\pi$
$359$	−6.99527	−0.369196	−0.184598	+	0.982814i	$0.559098\pi$
$360$	−0.00458569	−0.000241687 0
$361$	−4.33126	−0.227961
$362$	22.3578	1.17510
$363$	14.6404	0.768422
$364$	8.23458	0.431609
$365$	4.84595	0.253649
$366$	16.1547	0.844419
$367$	6.14611	0.320824	0.160412	−	0.987050i	$-0.448718\pi$
$367$	6.14611	0.320824	0.160412	+	0.987050i	$0.448718\pi$
$368$	−18.9668	−0.988712
$369$	−0.659926	−0.0343544
$370$	2.49873	0.129903
$371$	5.46924	0.283949
$372$	−29.6080	−1.53510
$373$	−36.5968	−1.89491	−0.947456	−	0.319886i	$-0.896356\pi$
$373$	−36.5968	−1.89491	−0.947456	+	0.319886i	$0.896356\pi$
$374$	3.19464	0.165191
$375$	5.03844	0.260184
$376$	2.63247	0.135759
$377$	7.67242	0.395150
$378$	−20.6250	−1.06084
$379$	−3.10751	−0.159622	−0.0798110	−	0.996810i	$-0.525432\pi$
$379$	−3.10751	−0.159622	−0.0798110	+	0.996810i	$0.525432\pi$
$380$	−2.08273	−0.106842
$381$	−22.7441	−1.16522
$382$	−26.9675	−1.37978
$383$	24.4575	1.24972	0.624860	−	0.780737i	$-0.285156\pi$
$383$	24.4575	1.24972	0.624860	+	0.780737i	$0.285156\pi$
$384$	−3.49044	−0.178121
$385$	0.960913	0.0489727
$386$	49.7677	2.53311
$387$	−0.0632334	−0.00321433
$388$	−24.6200	−1.24989
$389$	9.09194	0.460980	0.230490	−	0.973075i	$-0.425967\pi$
$389$	9.09194	0.460980	0.230490	+	0.973075i	$0.425967\pi$
$390$	2.15615	0.109181
$391$	−4.47568	−0.226345
$392$	0.710071	0.0358640
$393$	38.8772	1.96110
$394$	1.70034	0.0856619
$395$	3.67747	0.185034
$396$	−0.192263	−0.00966159
$397$	−2.48190	−0.124563	−0.0622814	−	0.998059i	$-0.519838\pi$
$397$	−2.48190	−0.124563	−0.0622814	+	0.998059i	$0.519838\pi$
$398$	1.39346	0.0698478
$399$	−13.6676	−0.684238
$400$	20.8315	1.04158
$401$	−13.1073	−0.654550	−0.327275	−	0.944929i	$-0.606130\pi$
$401$	−13.1073	−0.654550	−0.327275	+	0.944929i	$0.606130\pi$
$402$	38.3485	1.91265
$403$	−19.4735	−0.970042
$404$	24.7466	1.23119
$405$	−2.66682	−0.132516
$406$	14.2787	0.708640
$407$	−7.09910	−0.351889
$408$	−0.437186	−0.0216439
$409$	−18.8328	−0.931220	−0.465610	−	0.884990i	$-0.654165\pi$
$409$	−18.8328	−0.931220	−0.465610	+	0.884990i	$0.654165\pi$
$410$	−5.96291	−0.294487
$411$	15.1344	0.746525
$412$	24.2285	1.19365
$413$	−17.5791	−0.865012
$414$	0.556972	0.0273737
$415$	3.25078	0.159574
$416$	16.9050	0.828834
$417$	−6.98185	−0.341903
$418$	12.2354	0.598454
$419$	17.6002	0.859824	0.429912	−	0.902871i	$-0.358545\pi$
$419$	17.6002	0.859824	0.429912	+	0.902871i	$0.358545\pi$
$420$	1.94059	0.0946913
$421$	8.05613	0.392632	0.196316	−	0.980541i	$-0.437102\pi$
$421$	8.05613	0.392632	0.196316	+	0.980541i	$0.437102\pi$
$422$	−46.1855	−2.24827
$423$	−0.666399	−0.0324014
$424$	0.670032	0.0325396
$425$	4.91571	0.238447
$426$	−31.4610	−1.52429
$427$	9.56286	0.462779
$428$	−17.8381	−0.862237
$429$	−6.12581	−0.295757
$430$	−0.571360	−0.0275534
$431$	22.7136	1.09407	0.547037	−	0.837109i	$-0.315756\pi$
$431$	22.7136	1.09407	0.547037	+	0.837109i	$0.315756\pi$
$432$	−21.7818	−1.04798
$433$	23.4488	1.12688	0.563439	−	0.826158i	$-0.309478\pi$
$433$	23.4488	1.12688	0.563439	+	0.826158i	$0.309478\pi$
$434$	−36.2410	−1.73962
$435$	1.80811	0.0866924
$436$	−26.0545	−1.24779
$437$	−17.1418	−0.820002
$438$	−57.4930	−2.74712
$439$	−27.1168	−1.29421	−0.647106	−	0.762400i	$-0.724021\pi$
$439$	−27.1168	−1.29421	−0.647106	+	0.762400i	$0.724021\pi$
$440$	0.117721	0.00561211
$441$	−0.179752	−0.00855960
$442$	4.24333	0.201835
$443$	15.9713	0.758820	0.379410	−	0.925229i	$-0.376127\pi$
$443$	15.9713	0.758820	0.379410	+	0.925229i	$0.376127\pi$
$444$	−14.3369	−0.680397
$445$	2.21790	0.105139
$446$	11.9550	0.566085
$447$	−11.1813	−0.528857
$448$	14.1797	0.669930
$449$	2.09305	0.0987773	0.0493887	−	0.998780i	$-0.484273\pi$
$449$	2.09305	0.0987773	0.0493887	+	0.998780i	$0.484273\pi$
$450$	−0.611732	−0.0288373
$451$	16.9412	0.797728
$452$	−30.9361	−1.45511
$453$	17.3711	0.816166
$454$	4.59175	0.215502
$455$	1.27635	0.0598360
$456$	−1.67441	−0.0784115
$457$	−31.6882	−1.48231	−0.741155	−	0.671334i	$-0.765722\pi$
$457$	−31.6882	−1.48231	−0.741155	+	0.671334i	$0.765722\pi$
$458$	−25.7378	−1.20265
$459$	−5.13996	−0.239913
$460$	2.43386	0.113479
$461$	37.8519	1.76294	0.881470	−	0.472240i	$-0.156554\pi$
$461$	37.8519	1.76294	0.881470	+	0.472240i	$0.156554\pi$
$462$	−11.4004	−0.530395
$463$	−6.58466	−0.306015	−0.153007	−	0.988225i	$-0.548896\pi$
$463$	−6.58466	−0.306015	−0.153007	+	0.988225i	$0.548896\pi$
$464$	15.0795	0.700050
$465$	−4.58919	−0.212819
$466$	7.66257	0.354962
$467$	1.76387	0.0816223	0.0408112	−	0.999167i	$-0.487006\pi$
$467$	1.76387	0.0816223	0.0408112	+	0.999167i	$0.487006\pi$
$468$	−0.255376	−0.0118048
$469$	22.7006	1.04822
$470$	−6.02140	−0.277747
$471$	36.3377	1.67435
$472$	−2.15360	−0.0991277
$473$	1.62328	0.0746387
$474$	−43.6300	−2.00399
$475$	18.8271	0.863845
$476$	3.81911	0.175049
$477$	−0.169616	−0.00776617
$478$	−52.0394	−2.38023
$479$	−19.7593	−0.902824	−0.451412	−	0.892316i	$-0.649080\pi$
$479$	−19.7593	−0.902824	−0.451412	+	0.892316i	$0.649080\pi$
$480$	3.98389	0.181839
$481$	−9.42947	−0.429947
$482$	−23.6620	−1.07777
$483$	15.9719	0.726747
$484$	−15.6682	−0.712190
$485$	−3.81606	−0.173278
$486$	1.29305	0.0586538
$487$	3.87891	0.175770	0.0878851	−	0.996131i	$-0.471989\pi$
$487$	3.87891	0.175770	0.0878851	+	0.996131i	$0.471989\pi$
$488$	1.17154	0.0530330
$489$	17.6743	0.799258
$490$	−1.62419	−0.0733733
$491$	−33.7516	−1.52319	−0.761595	−	0.648053i	$-0.775583\pi$
$491$	−33.7516	−1.52319	−0.761595	+	0.648053i	$0.775583\pi$
$492$	34.2132	1.54245
$493$	3.55839	0.160262
$494$	16.2519	0.731206
$495$	−0.0298005	−0.00133943
$496$	−38.2735	−1.71853
$497$	−18.6235	−0.835379
$498$	−38.5677	−1.72826
$499$	−24.2088	−1.08373	−0.541867	−	0.840464i	$-0.682282\pi$
$499$	−24.2088	−1.08373	−0.541867	+	0.840464i	$0.682282\pi$
$500$	−5.39214	−0.241144
$501$	12.6667	0.565908
$502$	18.1736	0.811127
$503$	37.7657	1.68389	0.841944	−	0.539565i	$-0.181411\pi$
$503$	37.7657	1.68389	0.841944	+	0.539565i	$0.181411\pi$
$504$	0.0322055	0.00143455
$505$	3.83568	0.170686
$506$	−14.2982	−0.635633
$507$	14.6160	0.649121
$508$	24.3408	1.07995
$509$	−28.6665	−1.27062	−0.635311	−	0.772256i	$-0.719128\pi$
$509$	−28.6665	−1.27062	−0.635311	+	0.772256i	$0.719128\pi$
$510$	1.00000	0.0442807
$511$	−34.0333	−1.50555
$512$	31.1083	1.37480
$513$	−19.6859	−0.869155
$514$	6.24902	0.275632
$515$	3.75537	0.165481
$516$	3.27827	0.144318
$517$	17.1073	0.752379
$518$	−17.5487	−0.771044
$519$	−21.5586	−0.946320
$520$	0.156364	0.00685701
$521$	13.7677	0.603175	0.301588	−	0.953438i	$-0.402483\pi$
$521$	13.7677	0.603175	0.301588	+	0.953438i	$0.402483\pi$
$522$	−0.442821	−0.0193817
$523$	−28.5582	−1.24876	−0.624381	−	0.781120i	$-0.714649\pi$
$523$	−28.5582	−1.24876	−0.624381	+	0.781120i	$0.714649\pi$
$524$	−41.6064	−1.81759
$525$	−17.5422	−0.765604
$526$	12.8457	0.560099
$527$	−9.03159	−0.393422
$528$	−12.0398	−0.523965
$529$	−2.96828	−0.129056
$530$	−1.53260	−0.0665720
$531$	0.545176	0.0236586
$532$	14.6271	0.634166
$533$	22.5023	0.974683
$534$	−26.3135	−1.13870
$535$	−2.76487	−0.119536
$536$	2.78103	0.120122
$537$	−0.227553	−0.00981963
$538$	−11.9817	−0.516569
$539$	4.61446	0.198759
$540$	2.79510	0.120282
$541$	26.6222	1.14458	0.572290	−	0.820052i	$-0.306055\pi$
$541$	26.6222	1.14458	0.572290	+	0.820052i	$0.306055\pi$
$542$	−57.6500	−2.47628
$543$	−19.8834	−0.853279
$544$	7.84035	0.336152
$545$	−4.03841	−0.172986
$546$	−15.1427	−0.648049
$547$	41.2606	1.76417	0.882087	−	0.471086i	$-0.156138\pi$
$547$	41.2606	1.76417	0.882087	+	0.471086i	$0.156138\pi$
$548$	−16.1969	−0.691895
$549$	−0.296570	−0.0126573
$550$	15.7040	0.669619
$551$	13.6286	0.580596
$552$	1.95670	0.0832828
$553$	−25.8271	−1.09828
$554$	−43.5689	−1.85107
$555$	−2.22219	−0.0943266
$556$	7.47197	0.316882
$557$	26.7375	1.13290	0.566451	−	0.824095i	$-0.308316\pi$
$557$	26.7375	1.13290	0.566451	+	0.824095i	$0.308316\pi$
$558$	1.12393	0.0475797
$559$	2.15615	0.0911954
$560$	2.50856	0.106006
$561$	−2.84109	−0.119951
$562$	−12.1583	−0.512868
$563$	9.49245	0.400059	0.200029	−	0.979790i	$-0.435896\pi$
$563$	9.49245	0.400059	0.200029	+	0.979790i	$0.435896\pi$
$564$	34.5488	1.45477
$565$	−4.79504	−0.201729
$566$	−17.2125	−0.723495
$567$	18.7292	0.786553
$568$	−2.28155	−0.0957318
$569$	30.1917	1.26570	0.632851	−	0.774274i	$-0.281885\pi$
$569$	30.1917	1.26570	0.632851	+	0.774274i	$0.281885\pi$
$570$	3.82998	0.160420
$571$	−15.9145	−0.666003	−0.333001	−	0.942926i	$-0.608061\pi$
$571$	−15.9145	−0.666003	−0.333001	+	0.942926i	$0.608061\pi$
$572$	6.55584	0.274114
$573$	23.9830	1.00190
$574$	41.8778	1.74795
$575$	−22.0012	−0.917512
$576$	−0.439752	−0.0183230
$577$	−14.1386	−0.588599	−0.294299	−	0.955713i	$-0.595086\pi$
$577$	−14.1386	−0.588599	−0.294299	+	0.955713i	$0.595086\pi$
$578$	1.96801	0.0818585
$579$	−44.2598	−1.83938
$580$	−1.93504	−0.0803483
$581$	−22.8304	−0.947163
$582$	45.2742	1.87668
$583$	4.35426	0.180335
$584$	−4.16939	−0.172531
$585$	−0.0395829	−0.00163655
$586$	−9.84934	−0.406872
$587$	39.1949	1.61775	0.808873	−	0.587983i	$-0.200078\pi$
$587$	39.1949	1.61775	0.808873	+	0.587983i	$0.200078\pi$
$588$	9.31904	0.384311
$589$	−34.5908	−1.42529
$590$	4.92606	0.202803
$591$	−1.51216	−0.0622020
$592$	−18.5329	−0.761697
$593$	−2.62039	−0.107607	−0.0538033	−	0.998552i	$-0.517134\pi$
$593$	−2.62039	−0.107607	−0.0538033	+	0.998552i	$0.517134\pi$
$594$	−16.4203	−0.673735
$595$	0.591956	0.0242678
$596$	11.9662	0.490155
$597$	−1.23924	−0.0507188
$598$	−18.9918	−0.776632
$599$	25.3129	1.03426	0.517128	−	0.855908i	$-0.327001\pi$
$599$	25.3129	1.03426	0.517128	+	0.855908i	$0.327001\pi$
$600$	−2.14908	−0.0877358
$601$	10.5933	0.432109	0.216055	−	0.976381i	$-0.430681\pi$
$601$	10.5933	0.432109	0.216055	+	0.976381i	$0.430681\pi$
$602$	4.01269	0.163545
$603$	−0.704006	−0.0286693
$604$	−18.5906	−0.756439
$605$	−2.42854	−0.0987342
$606$	−45.5070	−1.84860
$607$	11.3511	0.460729	0.230364	−	0.973104i	$-0.426008\pi$
$607$	11.3511	0.460729	0.230364	+	0.973104i	$0.426008\pi$
$608$	30.0284	1.21781
$609$	−12.6985	−0.514568
$610$	−2.67973	−0.108499
$611$	22.7230	0.919276
$612$	−0.118441	−0.00478769
$613$	−37.0120	−1.49490	−0.747449	−	0.664319i	$-0.768722\pi$
$613$	−37.0120	−1.49490	−0.747449	+	0.664319i	$0.768722\pi$
$614$	60.4046	2.43773
$615$	5.30299	0.213837
$616$	−0.826757	−0.0333110
$617$	35.6001	1.43321	0.716603	−	0.697482i	$-0.245696\pi$
$617$	35.6001	1.43321	0.716603	+	0.697482i	$0.245696\pi$
$618$	−44.5542	−1.79223
$619$	−36.8760	−1.48217	−0.741086	−	0.671410i	$-0.765689\pi$
$619$	−36.8760	−1.48217	−0.741086	+	0.671410i	$0.765689\pi$
$620$	4.91136	0.197245
$621$	23.0048	0.923151
$622$	21.4366	0.859528
$623$	−15.5764	−0.624057
$624$	−15.9920	−0.640193
$625$	23.7428	0.949712
$626$	27.2311	1.08837
$627$	−10.8813	−0.434557
$628$	−38.8886	−1.55183
$629$	−4.37329	−0.174375
$630$	−0.0736655	−0.00293490
$631$	37.7041	1.50098	0.750489	−	0.660883i	$-0.229818\pi$
$631$	37.7041	1.50098	0.750489	+	0.660883i	$0.229818\pi$
$632$	−3.16405	−0.125859
$633$	41.0741	1.63255
$634$	−20.5072	−0.814446
$635$	3.77278	0.149718
$636$	8.79356	0.348687
$637$	6.12921	0.242848
$638$	11.3678	0.450055
$639$	0.577565	0.0228481
$640$	0.578992	0.0228867
$641$	−22.5274	−0.889777	−0.444888	−	0.895586i	$-0.646757\pi$
$641$	−22.5274	−0.889777	−0.444888	+	0.895586i	$0.646757\pi$
$642$	32.8028	1.29462
$643$	34.1041	1.34493	0.672467	−	0.740127i	$-0.265235\pi$
$643$	34.1041	1.34493	0.672467	+	0.740127i	$0.265235\pi$
$644$	−17.0931	−0.673564
$645$	0.508127	0.0200075
$646$	7.53745	0.296557
$647$	−7.44519	−0.292700	−0.146350	−	0.989233i	$-0.546753\pi$
$647$	−7.44519	−0.292700	−0.146350	+	0.989233i	$0.546753\pi$
$648$	2.29450	0.0901365
$649$	−13.9954	−0.549367
$650$	20.8590	0.818157
$651$	32.2301	1.26320
$652$	−18.9150	−0.740769
$653$	8.06440	0.315584	0.157792	−	0.987472i	$-0.449562\pi$
$653$	8.06440	0.315584	0.157792	+	0.987472i	$0.449562\pi$
$654$	47.9122	1.87352
$655$	−6.44893	−0.251980
$656$	44.2265	1.72676
$657$	1.05546	0.0411776
$658$	42.2886	1.64858
$659$	−11.4301	−0.445254	−0.222627	−	0.974904i	$-0.571463\pi$
$659$	−11.4301	−0.445254	−0.222627	+	0.974904i	$0.571463\pi$
$660$	1.54498	0.0601381
$661$	23.6134	0.918457	0.459228	−	0.888318i	$-0.348126\pi$
$661$	23.6134	0.918457	0.459228	+	0.888318i	$0.348126\pi$
$662$	−58.6023	−2.27764
$663$	−3.77371	−0.146559
$664$	−2.79693	−0.108542
$665$	2.26718	0.0879174
$666$	0.544231	0.0210885
$667$	−15.9262	−0.616666
$668$	−13.5559	−0.524495
$669$	−10.6319	−0.411053
$670$	−6.36121	−0.245755
$671$	7.61334	0.293910
$672$	−27.9790	−1.07931
$673$	3.41852	0.131774	0.0658872	−	0.997827i	$-0.479012\pi$
$673$	3.41852	0.131774	0.0658872	+	0.997827i	$0.479012\pi$
$674$	51.2823	1.97532
$675$	−25.2665	−0.972510
$676$	−15.6421	−0.601619
$677$	41.1771	1.58257	0.791283	−	0.611450i	$-0.209414\pi$
$677$	41.1771	1.58257	0.791283	+	0.611450i	$0.209414\pi$
$678$	56.8890	2.18481
$679$	26.8004	1.02850
$680$	0.0725200	0.00278102
$681$	−4.08358	−0.156483
$682$	−28.8527	−1.10483
$683$	−3.65574	−0.139883	−0.0699415	−	0.997551i	$-0.522281\pi$
$683$	−3.65574	−0.139883	−0.0699415	+	0.997551i	$0.522281\pi$
$684$	−0.453626	−0.0173448
$685$	−2.51048	−0.0959207
$686$	39.4955	1.50795
$687$	22.8893	0.873283
$688$	4.23774	0.161562
$689$	5.78360	0.220338
$690$	−4.47568	−0.170386
$691$	−29.8410	−1.13520	−0.567602	−	0.823303i	$-0.692129\pi$
$691$	−29.8410	−1.13520	−0.567602	+	0.823303i	$0.692129\pi$
$692$	23.0721	0.877069
$693$	0.209290	0.00795027
$694$	−0.886415	−0.0336479
$695$	1.15814	0.0439309
$696$	−1.55568	−0.0589678
$697$	10.4363	0.395305
$698$	−7.66041	−0.289951
$699$	−6.81454	−0.257750
$700$	18.7737	0.709578
$701$	15.0041	0.566697	0.283348	−	0.959017i	$-0.408555\pi$
$701$	15.0041	0.566697	0.283348	+	0.959017i	$0.408555\pi$
$702$	−21.8105	−0.823185
$703$	−16.7496	−0.631724
$704$	11.2890	0.425470
$705$	5.35500	0.201681
$706$	19.4551	0.732201
$707$	−26.9382	−1.01311
$708$	−28.2641	−1.06223
$709$	−20.2740	−0.761407	−0.380703	−	0.924697i	$-0.624318\pi$
$709$	−20.2740	−0.761407	−0.380703	+	0.924697i	$0.624318\pi$
$710$	5.21872	0.195855
$711$	0.800966	0.0300386
$712$	−1.90826	−0.0715149
$713$	40.4225	1.51384
$714$	−7.02304	−0.262831
$715$	1.01614	0.0380016
$716$	0.243527	0.00910104
$717$	46.2801	1.72836
$718$	−13.7668	−0.513772
$719$	45.0527	1.68018	0.840091	−	0.542446i	$-0.182502\pi$
$719$	45.0527	1.68018	0.840091	+	0.542446i	$0.182502\pi$
$720$	−0.0777970	−0.00289932
$721$	−26.3741	−0.982224
$722$	−8.52398	−0.317230
$723$	21.0433	0.782608
$724$	21.2792	0.790836
$725$	17.4920	0.649637
$726$	28.8125	1.06933
$727$	−27.5550	−1.02196	−0.510979	−	0.859593i	$-0.670717\pi$
$727$	−27.5550	−1.02196	−0.510979	+	0.859593i	$0.670717\pi$
$728$	−1.09815	−0.0407002
$729$	26.4072	0.978043
$730$	9.53689	0.352976
$731$	1.00000	0.0369863
$732$	15.3754	0.568290
$733$	−19.7851	−0.730780	−0.365390	−	0.930854i	$-0.619064\pi$
$733$	−19.7851	−0.730780	−0.365390	+	0.930854i	$0.619064\pi$
$734$	12.0956	0.446457
$735$	1.44443	0.0532788
$736$	−35.0909	−1.29347
$737$	18.0728	0.665719
$738$	−1.29874	−0.0478074
$739$	−3.05594	−0.112415	−0.0562073	−	0.998419i	$-0.517901\pi$
$739$	−3.05594	−0.112415	−0.0562073	+	0.998419i	$0.517901\pi$
$740$	2.37819	0.0874238
$741$	−14.4532	−0.530953
$742$	10.7635	0.395142
$743$	20.2997	0.744723	0.372362	−	0.928088i	$-0.378548\pi$
$743$	20.2997	0.744723	0.372362	+	0.928088i	$0.378548\pi$
$744$	3.94848	0.144758
$745$	1.85474	0.0679525
$746$	−72.0230	−2.63695
$747$	0.708030	0.0259055
$748$	3.04053	0.111173
$749$	19.4178	0.709512
$750$	9.91571	0.362071
$751$	47.6061	1.73717	0.868586	−	0.495538i	$-0.165029\pi$
$751$	47.6061	1.73717	0.868586	+	0.495538i	$0.165029\pi$
$752$	44.6603	1.62859
$753$	−16.1623	−0.588986
$754$	15.0994	0.549888
$755$	−2.88151	−0.104869
$756$	−19.6301	−0.713939
$757$	34.0339	1.23698	0.618491	−	0.785792i	$-0.287744\pi$
$757$	34.0339	1.23698	0.618491	+	0.785792i	$0.287744\pi$
$758$	−6.11561	−0.222129
$759$	12.7158	0.461554
$760$	0.277750	0.0100751
$761$	13.9303	0.504973	0.252486	−	0.967600i	$-0.418752\pi$
$761$	13.9303	0.504973	0.252486	+	0.967600i	$0.418752\pi$
$762$	−44.7607	−1.62151
$763$	28.3619	1.02677
$764$	−25.6666	−0.928584
$765$	−0.0183581	−0.000663740 0
$766$	48.1327	1.73910
$767$	−18.5895	−0.671229
$768$	−31.2126	−1.12629
$769$	−30.3307	−1.09375	−0.546877	−	0.837213i	$-0.684183\pi$
$769$	−30.3307	−1.09375	−0.546877	+	0.837213i	$0.684183\pi$
$770$	1.89109	0.0681501
$771$	−5.55743	−0.200146
$772$	47.3669	1.70477
$773$	−46.9073	−1.68714	−0.843570	−	0.537019i	$-0.819550\pi$
$773$	−46.9073	−1.68714	−0.843570	+	0.537019i	$0.819550\pi$
$774$	−0.124444	−0.00447305
$775$	−44.3967	−1.59478
$776$	3.28329	0.117863
$777$	15.6065	0.559881
$778$	17.8931	0.641497
$779$	39.9710	1.43211
$780$	2.05213	0.0734782
$781$	−14.8269	−0.530546
$782$	−8.80820	−0.314981
$783$	−18.2900	−0.653630
$784$	12.0465	0.430232
$785$	−6.02767	−0.215137
$786$	76.5109	2.72905
$787$	11.9255	0.425097	0.212548	−	0.977151i	$-0.431824\pi$
$787$	11.9255	0.425097	0.212548	+	0.977151i	$0.431824\pi$
$788$	1.61832	0.0576501
$789$	−11.4240	−0.406707
$790$	7.23732	0.257492
$791$	33.6758	1.19737
$792$	0.0256399	0.000911076 0
$793$	10.1125	0.359106
$794$	−4.88440	−0.173341
$795$	1.36299	0.0483402
$796$	1.32624	0.0470073
$797$	−27.9547	−0.990207	−0.495103	−	0.868834i	$-0.664870\pi$
$797$	−27.9547	−0.990207	−0.495103	+	0.868834i	$0.664870\pi$
$798$	−26.8981	−0.952183
$799$	10.5387	0.372833
$800$	38.5409	1.36263
$801$	0.483067	0.0170683
$802$	−25.7954	−0.910868
$803$	−27.0951	−0.956167
$804$	36.4985	1.28720
$805$	−2.64941	−0.0933793
$806$	−38.3240	−1.34991
$807$	10.6557	0.375098
$808$	−3.30017	−0.116100
$809$	−16.3735	−0.575662	−0.287831	−	0.957681i	$-0.592934\pi$
$809$	−16.3735	−0.575662	−0.287831	+	0.957681i	$0.592934\pi$
$810$	−5.24834	−0.184408
$811$	28.0230	0.984021	0.492011	−	0.870589i	$-0.336262\pi$
$811$	28.0230	0.984021	0.492011	+	0.870589i	$0.336262\pi$
$812$	13.5899	0.476912
$813$	51.2697	1.79811
$814$	−13.9711	−0.489687
$815$	−2.93179	−0.102696
$816$	−7.41693	−0.259645
$817$	3.82998	0.133994
$818$	−37.0631	−1.29588
$819$	0.277992	0.00971384
$820$	−5.67526	−0.198189
$821$	−16.2972	−0.568778	−0.284389	−	0.958709i	$-0.591791\pi$
$821$	−16.2972	−0.568778	−0.284389	+	0.958709i	$0.591791\pi$
$822$	29.7847	1.03886
$823$	32.8529	1.14518	0.572590	−	0.819842i	$-0.305939\pi$
$823$	32.8529	1.14518	0.572590	+	0.819842i	$0.305939\pi$
$824$	−3.23107	−0.112560
$825$	−13.9660	−0.486233
$826$	−34.5960	−1.20375
$827$	8.61783	0.299671	0.149836	−	0.988711i	$-0.452126\pi$
$827$	8.61783	0.299671	0.149836	+	0.988711i	$0.452126\pi$
$828$	0.530104	0.0184224
$829$	−8.83234	−0.306760	−0.153380	−	0.988167i	$-0.549016\pi$
$829$	−8.83234	−0.306760	−0.153380	+	0.988167i	$0.549016\pi$
$830$	6.39757	0.222063
$831$	38.7471	1.34412
$832$	14.9948	0.519850
$833$	2.84267	0.0984926
$834$	−13.7404	−0.475790
$835$	−2.10115	−0.0727132
$836$	11.6452	0.402757
$837$	46.4220	1.60458
$838$	34.6374	1.19653
$839$	16.3682	0.565092	0.282546	−	0.959254i	$-0.408821\pi$
$839$	16.3682	0.565092	0.282546	+	0.959254i	$0.408821\pi$
$840$	−0.258795	−0.00892926
$841$	−16.3379	−0.563375
$842$	15.8546	0.546384
$843$	10.8127	0.372410
$844$	−43.9575	−1.51308
$845$	−2.42450	−0.0834052
$846$	−1.31148	−0.0450897
$847$	17.0557	0.586042
$848$	11.3672	0.390352
$849$	15.3076	0.525354
$850$	9.67419	0.331822
$851$	19.5735	0.670970
$852$	−29.9433	−1.02584
$853$	−35.2003	−1.20523	−0.602617	−	0.798030i	$-0.705875\pi$
$853$	−35.2003	−1.20523	−0.602617	+	0.798030i	$0.705875\pi$
$854$	18.8198	0.644002
$855$	−0.0703113	−0.00240459
$856$	2.37886	0.0813078
$857$	40.1336	1.37094	0.685469	−	0.728101i	$-0.259597\pi$
$857$	40.1336	1.37094	0.685469	+	0.728101i	$0.259597\pi$
$858$	−12.0557	−0.411574
$859$	−19.4321	−0.663016	−0.331508	−	0.943452i	$-0.607557\pi$
$859$	−19.4321	−0.663016	−0.331508	+	0.943452i	$0.607557\pi$
$860$	−0.543797	−0.0185433
$861$	−37.2431	−1.26924
$862$	44.7006	1.52251
$863$	7.90822	0.269199	0.134600	−	0.990900i	$-0.457025\pi$
$863$	7.90822	0.269199	0.134600	+	0.990900i	$0.457025\pi$
$864$	−40.2990	−1.37100
$865$	3.57613	0.121592
$866$	46.1475	1.56816
$867$	−1.75021	−0.0594402
$868$	−34.4927	−1.17076
$869$	−20.5619	−0.697513
$870$	3.55839	0.120641
$871$	24.0054	0.813391
$872$	3.47460	0.117665
$873$	−0.831150	−0.0281302
$874$	−33.7352	−1.14111
$875$	5.86967	0.198431
$876$	−54.7195	−1.84880
$877$	−27.2520	−0.920235	−0.460117	−	0.887858i	$-0.652193\pi$
$877$	−27.2520	−0.920235	−0.460117	+	0.887858i	$0.652193\pi$
$878$	−53.3661	−1.80102
$879$	8.75929	0.295444
$880$	1.99715	0.0673240
$881$	−24.4933	−0.825200	−0.412600	−	0.910912i	$-0.635379\pi$
$881$	−24.4933	−0.825200	−0.412600	+	0.910912i	$0.635379\pi$
$882$	−0.353753	−0.0119115
$883$	10.5544	0.355182	0.177591	−	0.984104i	$-0.443170\pi$
$883$	10.5544	0.355182	0.177591	+	0.984104i	$0.443170\pi$
$884$	4.03863	0.135834
$885$	−4.38089	−0.147262
$886$	31.4318	1.05597
$887$	−48.7310	−1.63623	−0.818113	−	0.575057i	$-0.804980\pi$
$887$	−48.7310	−1.63623	−0.818113	+	0.575057i	$0.804980\pi$
$888$	1.91194	0.0641605
$889$	−26.4964	−0.888660
$890$	4.36486	0.146311
$891$	14.9110	0.499537
$892$	11.3783	0.380972
$893$	40.3631	1.35070
$894$	−22.0049	−0.735955
$895$	0.0377463	0.00126172
$896$	−4.06629	−0.135845
$897$	16.8899	0.563938
$898$	4.11916	0.137458
$899$	−32.1379	−1.07186
$900$	−0.582221	−0.0194074
$901$	2.68238	0.0893629
$902$	33.3404	1.11011
$903$	−3.56860	−0.118755
$904$	4.12559	0.137215
$905$	3.29824	0.109637
$906$	34.1866	1.13577
$907$	−36.9873	−1.22814	−0.614072	−	0.789250i	$-0.710469\pi$
$907$	−36.9873	−1.22814	−0.614072	+	0.789250i	$0.710469\pi$
$908$	4.37025	0.145032
$909$	0.835424	0.0277093
$910$	2.51186	0.0832675
$911$	24.6253	0.815872	0.407936	−	0.913010i	$-0.366249\pi$
$911$	24.6253	0.815872	0.407936	+	0.913010i	$0.366249\pi$
$912$	−28.4067	−0.940640
$913$	−18.1761	−0.601540
$914$	−62.3627	−2.06278
$915$	2.38316	0.0787847
$916$	−24.4962	−0.809376
$917$	45.2911	1.49564
$918$	−10.1155	−0.333861
$919$	−29.2801	−0.965860	−0.482930	−	0.875659i	$-0.660428\pi$
$919$	−29.2801	−0.965860	−0.482930	+	0.875659i	$0.660428\pi$
$920$	−0.324576	−0.0107010
$921$	−53.7196	−1.77012
$922$	74.4931	2.45330
$923$	−19.6940	−0.648235
$924$	−10.8504	−0.356953
$925$	−21.4979	−0.706845
$926$	−12.9587	−0.425849
$927$	0.817932	0.0268644
$928$	27.8990	0.915830
$929$	18.5784	0.609537	0.304768	−	0.952426i	$-0.401421\pi$
$929$	18.5784	0.609537	0.304768	+	0.952426i	$0.401421\pi$
$930$	−9.03159	−0.296158
$931$	10.8874	0.356819
$932$	7.29292	0.238888
$933$	−19.0642	−0.624132
$934$	3.47133	0.113585
$935$	0.471277	0.0154124
$936$	0.0340566	0.00111317
$937$	−47.0951	−1.53853	−0.769265	−	0.638930i	$-0.779377\pi$
$937$	−47.0951	−1.53853	−0.769265	+	0.638930i	$0.779377\pi$
$938$	44.6751	1.45869
$939$	−24.2174	−0.790304
$940$	−5.73093	−0.186922
$941$	−16.6518	−0.542834	−0.271417	−	0.962462i	$-0.587492\pi$
$941$	−16.6518	−0.542834	−0.271417	+	0.962462i	$0.587492\pi$
$942$	71.5131	2.33002
$943$	−46.7098	−1.52108
$944$	−36.5363	−1.18915
$945$	−3.04263	−0.0989767
$946$	3.19464	0.103867
$947$	−4.33979	−0.141024	−0.0705121	−	0.997511i	$-0.522463\pi$
$947$	−4.33979	−0.141024	−0.0705121	+	0.997511i	$0.522463\pi$
$948$	−41.5253	−1.34868
$949$	−35.9895	−1.16827
$950$	37.0519	1.20212
$951$	18.2377	0.591396
$952$	−0.509311	−0.0165069
$953$	−40.9878	−1.32773	−0.663863	−	0.747854i	$-0.731084\pi$
$953$	−40.9878	−1.32773	−0.663863	+	0.747854i	$0.731084\pi$
$954$	−0.333806	−0.0108074
$955$	−3.97828	−0.128734
$956$	−49.5290	−1.60188
$957$	−10.1097	−0.326800
$958$	−38.8865	−1.25637
$959$	17.6312	0.569342
$960$	3.53373	0.114051
$961$	50.5696	1.63128
$962$	−18.5573	−0.598312
$963$	−0.602199	−0.0194056
$964$	−22.5205	−0.725337
$965$	7.34178	0.236340
$966$	31.4329	1.01134
$967$	57.1108	1.83656	0.918279	−	0.395934i	$-0.129579\pi$
$967$	57.1108	1.83656	0.918279	+	0.395934i	$0.129579\pi$
$968$	2.08948	0.0671586
$969$	−6.70327	−0.215340
$970$	−7.51005	−0.241133
$971$	6.52691	0.209459	0.104729	−	0.994501i	$-0.466602\pi$
$971$	6.52691	0.209459	0.104729	+	0.994501i	$0.466602\pi$
$972$	1.23067	0.0394738
$973$	−8.13369	−0.260754
$974$	7.63375	0.244601
$975$	−18.5505	−0.594091
$976$	19.8754	0.636195
$977$	21.7372	0.695435	0.347718	−	0.937599i	$-0.386957\pi$
$977$	21.7372	0.695435	0.347718	+	0.937599i	$0.386957\pi$
$978$	34.7832	1.11224
$979$	−12.4010	−0.396336
$980$	−1.54583	−0.0493799
$981$	−0.879579	−0.0280828
$982$	−66.4236	−2.11966
$983$	−10.4438	−0.333106	−0.166553	−	0.986033i	$-0.553264\pi$
$983$	−10.4438	−0.333106	−0.166553	+	0.986033i	$0.553264\pi$
$984$	−4.56262	−0.145451
$985$	0.250836	0.00799230
$986$	7.00296	0.223020
$987$	−37.6084	−1.19709
$988$	15.4679	0.492098
$989$	−4.47568	−0.142318
$990$	−0.0586477	−0.00186395
$991$	20.2566	0.643471	0.321735	−	0.946830i	$-0.395734\pi$
$991$	20.2566	0.643471	0.321735	+	0.946830i	$0.395734\pi$
$992$	−70.8108	−2.24825
$993$	52.1167	1.65387
$994$	−36.6513	−1.16251
$995$	0.205565	0.00651684
$996$	−36.7071	−1.16311
$997$	−53.5272	−1.69522	−0.847611	−	0.530618i	$-0.821960\pi$
$997$	−53.5272	−1.69522	−0.847611	+	0.530618i	$0.821960\pi$
$998$	−47.6432	−1.50812
$999$	22.4785	0.711190

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.c.1.6	✓	6
3.2	odd	2		6579.2.a.j.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.c.1.6	✓	6	1.1	even	1	trivial
6579.2.a.j.1.1		6	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +O(q^{10})\)	\(q+1.96801 q^{2} -1.75021 q^{3} +1.87307 q^{4} +0.290323 q^{5} -3.44443 q^{6} -2.03895 q^{7} -0.249790 q^{8} +0.0632334 q^{9} +0.571360 q^{10} -1.62328 q^{11} -3.27827 q^{12} -2.15615 q^{13} -4.01269 q^{14} -0.508127 q^{15} -4.23774 q^{16} -1.00000 q^{17} +0.124444 q^{18} -3.82998 q^{19} +0.543797 q^{20} +3.56860 q^{21} -3.19464 q^{22} +4.47568 q^{23} +0.437186 q^{24} -4.91571 q^{25} -4.24333 q^{26} +5.13996 q^{27} -3.81911 q^{28} -3.55839 q^{29} -1.00000 q^{30} +9.03159 q^{31} -7.84035 q^{32} +2.84109 q^{33} -1.96801 q^{34} -0.591956 q^{35} +0.118441 q^{36} +4.37329 q^{37} -7.53745 q^{38} +3.77371 q^{39} -0.0725200 q^{40} -10.4363 q^{41} +7.02304 q^{42} -1.00000 q^{43} -3.04053 q^{44} +0.0183581 q^{45} +8.80820 q^{46} -10.5387 q^{47} +7.41693 q^{48} -2.84267 q^{49} -9.67419 q^{50} +1.75021 q^{51} -4.03863 q^{52} -2.68238 q^{53} +10.1155 q^{54} -0.471277 q^{55} +0.509311 q^{56} +6.70327 q^{57} -7.00296 q^{58} +8.62164 q^{59} -0.951759 q^{60} -4.69008 q^{61} +17.7743 q^{62} -0.128930 q^{63} -6.95442 q^{64} -0.625980 q^{65} +5.59130 q^{66} -11.1335 q^{67} -1.87307 q^{68} -7.83338 q^{69} -1.16498 q^{70} +9.13386 q^{71} -0.0157951 q^{72} +16.6916 q^{73} +8.60670 q^{74} +8.60353 q^{75} -7.17384 q^{76} +3.30980 q^{77} +7.42671 q^{78} +12.6668 q^{79} -1.23032 q^{80} -9.18570 q^{81} -20.5389 q^{82} +11.1971 q^{83} +6.68425 q^{84} -0.290323 q^{85} -1.96801 q^{86} +6.22793 q^{87} +0.405481 q^{88} +7.63942 q^{89} +0.0361291 q^{90} +4.39629 q^{91} +8.38329 q^{92} -15.8072 q^{93} -20.7403 q^{94} -1.11193 q^{95} +13.7222 q^{96} -13.1442 q^{97} -5.59440 q^{98} -0.102646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + 5 q^{4} + 3 q^{5} - 7 q^{6} - 7 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{10} + 4 q^{11} + 11 q^{12} - 10 q^{13} - 7 q^{14} + q^{15} - q^{16} - 6 q^{17} + q^{18} - 20 q^{19} + q^{20} - 8 q^{21} + 2 q^{22} - 3 q^{23} - 9 q^{24} - 7 q^{25} - 3 q^{26} - 6 q^{27} - 11 q^{28} - 15 q^{29} - 6 q^{30} + 12 q^{31} + q^{32} - 2 q^{33} + q^{34} - 9 q^{35} - 16 q^{36} - 14 q^{37} + 27 q^{38} + 5 q^{39} - 7 q^{40} - 2 q^{41} + 19 q^{42} - 6 q^{43} - 12 q^{44} - 18 q^{45} + 14 q^{46} - 11 q^{47} - 6 q^{48} + 3 q^{49} + 7 q^{50} + 3 q^{51} - 5 q^{52} + 3 q^{53} + 25 q^{54} + 6 q^{55} + 22 q^{56} + 11 q^{57} - 21 q^{58} + 2 q^{59} - q^{60} - 20 q^{61} + 3 q^{62} + 23 q^{63} - 39 q^{64} - 34 q^{65} + 7 q^{66} - 2 q^{67} - 5 q^{68} - 17 q^{69} - q^{70} + q^{71} + 21 q^{72} + 13 q^{73} + 28 q^{74} - 5 q^{75} - 29 q^{76} - 11 q^{77} - 26 q^{79} + 12 q^{80} + 2 q^{81} - 9 q^{82} + 10 q^{83} - 3 q^{84} - 3 q^{85} + q^{86} + 12 q^{87} - 6 q^{88} - 15 q^{89} + 15 q^{90} + 8 q^{91} - 9 q^{92} - 11 q^{93} - 33 q^{94} - 21 q^{95} + 25 q^{96} - 22 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + 5 * q^4 + 3 * q^5 - 7 * q^6 - 7 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^10 + 4 * q^11 + 11 * q^12 - 10 * q^13 - 7 * q^14 + q^15 - q^16 - 6 * q^17 + q^18 - 20 * q^19 + q^20 - 8 * q^21 + 2 * q^22 - 3 * q^23 - 9 * q^24 - 7 * q^25 - 3 * q^26 - 6 * q^27 - 11 * q^28 - 15 * q^29 - 6 * q^30 + 12 * q^31 + q^32 - 2 * q^33 + q^34 - 9 * q^35 - 16 * q^36 - 14 * q^37 + 27 * q^38 + 5 * q^39 - 7 * q^40 - 2 * q^41 + 19 * q^42 - 6 * q^43 - 12 * q^44 - 18 * q^45 + 14 * q^46 - 11 * q^47 - 6 * q^48 + 3 * q^49 + 7 * q^50 + 3 * q^51 - 5 * q^52 + 3 * q^53 + 25 * q^54 + 6 * q^55 + 22 * q^56 + 11 * q^57 - 21 * q^58 + 2 * q^59 - q^60 - 20 * q^61 + 3 * q^62 + 23 * q^63 - 39 * q^64 - 34 * q^65 + 7 * q^66 - 2 * q^67 - 5 * q^68 - 17 * q^69 - q^70 + q^71 + 21 * q^72 + 13 * q^73 + 28 * q^74 - 5 * q^75 - 29 * q^76 - 11 * q^77 - 26 * q^79 + 12 * q^80 + 2 * q^81 - 9 * q^82 + 10 * q^83 - 3 * q^84 - 3 * q^85 + q^86 + 12 * q^87 - 6 * q^88 - 15 * q^89 + 15 * q^90 + 8 * q^91 - 9 * q^92 - 11 * q^93 - 33 * q^94 - 21 * q^95 + 25 * q^96 - 22 * q^97 - 3 * q^98 - 5 * q^99

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