LMFDB - Embedded newform 731.2.a.e.1.9

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:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.248120$ 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)

$f(q)$	$=$	$q-0.248120 q^{2} -2.62183 q^{3} -1.93844 q^{4} +3.83673 q^{5} +0.650531 q^{6} +2.64030 q^{7} +0.977206 q^{8} +3.87401 q^{9} +O(q^{10})$	\(q-0.248120 q^{2} -2.62183 q^{3} -1.93844 q^{4} +3.83673 q^{5} +0.650531 q^{6} +2.64030 q^{7} +0.977206 q^{8} +3.87401 q^{9} -0.951972 q^{10} -5.27591 q^{11} +5.08226 q^{12} +1.02262 q^{13} -0.655111 q^{14} -10.0593 q^{15} +3.63441 q^{16} +1.00000 q^{17} -0.961222 q^{18} -4.44085 q^{19} -7.43726 q^{20} -6.92242 q^{21} +1.30906 q^{22} -1.34728 q^{23} -2.56207 q^{24} +9.72052 q^{25} -0.253733 q^{26} -2.29152 q^{27} -5.11805 q^{28} +5.70726 q^{29} +2.49591 q^{30} +3.28571 q^{31} -2.85618 q^{32} +13.8326 q^{33} -0.248120 q^{34} +10.1301 q^{35} -7.50953 q^{36} +10.5600 q^{37} +1.10187 q^{38} -2.68114 q^{39} +3.74928 q^{40} -7.67664 q^{41} +1.71759 q^{42} -1.00000 q^{43} +10.2270 q^{44} +14.8636 q^{45} +0.334287 q^{46} +11.4830 q^{47} -9.52881 q^{48} -0.0288376 q^{49} -2.41186 q^{50} -2.62183 q^{51} -1.98228 q^{52} +4.23206 q^{53} +0.568573 q^{54} -20.2423 q^{55} +2.58011 q^{56} +11.6432 q^{57} -1.41609 q^{58} +9.75170 q^{59} +19.4993 q^{60} +5.99186 q^{61} -0.815253 q^{62} +10.2285 q^{63} -6.56014 q^{64} +3.92352 q^{65} -3.43214 q^{66} +2.35981 q^{67} -1.93844 q^{68} +3.53233 q^{69} -2.51349 q^{70} +0.0170442 q^{71} +3.78571 q^{72} -4.68100 q^{73} -2.62015 q^{74} -25.4856 q^{75} +8.60831 q^{76} -13.9300 q^{77} +0.665245 q^{78} +5.50504 q^{79} +13.9443 q^{80} -5.61406 q^{81} +1.90473 q^{82} +17.0138 q^{83} +13.4187 q^{84} +3.83673 q^{85} +0.248120 q^{86} -14.9635 q^{87} -5.15565 q^{88} +4.11273 q^{89} -3.68795 q^{90} +2.70002 q^{91} +2.61161 q^{92} -8.61460 q^{93} -2.84917 q^{94} -17.0384 q^{95} +7.48844 q^{96} -8.24476 q^{97} +0.00715519 q^{98} -20.4390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * 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 $

$2$	−0.248120	−0.175448	−0.0877238	−	0.996145i	$-0.527959\pi$
$2$	−0.248120	−0.175448	−0.0877238	+	0.996145i	$0.527959\pi$
$3$	−2.62183	−1.51372	−0.756858	−	0.653579i	$-0.773267\pi$
$3$	−2.62183	−1.51372	−0.756858	+	0.653579i	$0.773267\pi$
$4$	−1.93844	−0.969218
$5$	3.83673	1.71584	0.857920	−	0.513784i	$-0.171757\pi$
$5$	3.83673	1.71584	0.857920	+	0.513784i	$0.171757\pi$
$6$	0.650531	0.265578
$7$	2.64030	0.997938	0.498969	−	0.866620i	$-0.333712\pi$
$7$	2.64030	0.997938	0.498969	+	0.866620i	$0.333712\pi$
$8$	0.977206	0.345495
$9$	3.87401	1.29134
$10$	−0.951972	−0.301040
$11$	−5.27591	−1.59075	−0.795373	−	0.606120i	$-0.792725\pi$
$11$	−5.27591	−1.59075	−0.795373	+	0.606120i	$0.792725\pi$
$12$	5.08226	1.46712
$13$	1.02262	0.283623	0.141812	−	0.989894i	$-0.454707\pi$
$13$	1.02262	0.283623	0.141812	+	0.989894i	$0.454707\pi$
$14$	−0.655111	−0.175086
$15$	−10.0593	−2.59729
$16$	3.63441	0.908602
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.961222	−0.226562
$19$	−4.44085	−1.01880	−0.509400	−	0.860530i	$-0.670133\pi$
$19$	−4.44085	−1.01880	−0.509400	+	0.860530i	$0.670133\pi$
$20$	−7.43726	−1.66302
$21$	−6.92242	−1.51060
$22$	1.30906	0.279093
$23$	−1.34728	−0.280926	−0.140463	−	0.990086i	$-0.544859\pi$
$23$	−1.34728	−0.280926	−0.140463	+	0.990086i	$0.544859\pi$
$24$	−2.56207	−0.522981
$25$	9.72052	1.94410
$26$	−0.253733	−0.0497611
$27$	−2.29152	−0.441003
$28$	−5.11805	−0.967220
$29$	5.70726	1.05981	0.529905	−	0.848057i	$-0.322227\pi$
$29$	5.70726	1.05981	0.529905	+	0.848057i	$0.322227\pi$
$30$	2.49591	0.455689
$31$	3.28571	0.590132	0.295066	−	0.955477i	$-0.404658\pi$
$31$	3.28571	0.590132	0.295066	+	0.955477i	$0.404658\pi$
$32$	−2.85618	−0.504907
$33$	13.8326	2.40794
$34$	−0.248120	−0.0425523
$35$	10.1301	1.71230
$36$	−7.50953	−1.25159
$37$	10.5600	1.73605	0.868025	−	0.496521i	$-0.165389\pi$
$37$	10.5600	1.73605	0.868025	+	0.496521i	$0.165389\pi$
$38$	1.10187	0.178746
$39$	−2.68114	−0.429326
$40$	3.74928	0.592813
$41$	−7.67664	−1.19889	−0.599445	−	0.800416i	$-0.704612\pi$
$41$	−7.67664	−1.19889	−0.599445	+	0.800416i	$0.704612\pi$
$42$	1.71759	0.265030
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	10.2270	1.54178
$45$	14.8636	2.21573
$46$	0.334287	0.0492879
$47$	11.4830	1.67497	0.837484	−	0.546462i	$-0.184026\pi$
$47$	11.4830	1.67497	0.837484	+	0.546462i	$0.184026\pi$
$48$	−9.52881	−1.37537
$49$	−0.0288376	−0.00411965
$50$	−2.41186	−0.341088
$51$	−2.62183	−0.367130
$52$	−1.98228	−0.274893
$53$	4.23206	0.581318	0.290659	−	0.956827i	$-0.406125\pi$
$53$	4.23206	0.581318	0.290659	+	0.956827i	$0.406125\pi$
$54$	0.568573	0.0773730
$55$	−20.2423	−2.72947
$56$	2.58011	0.344782
$57$	11.6432	1.54218
$58$	−1.41609	−0.185941
$59$	9.75170	1.26956	0.634781	−	0.772692i	$-0.281090\pi$
$59$	9.75170	1.26956	0.634781	+	0.772692i	$0.281090\pi$
$60$	19.4993	2.51734
$61$	5.99186	0.767180	0.383590	−	0.923504i	$-0.374688\pi$
$61$	5.99186	0.767180	0.383590	+	0.923504i	$0.374688\pi$
$62$	−0.815253	−0.103537
$63$	10.2285	1.28868
$64$	−6.56014	−0.820017
$65$	3.92352	0.486652
$66$	−3.43214	−0.422467
$67$	2.35981	0.288296	0.144148	−	0.989556i	$-0.453956\pi$
$67$	2.35981	0.288296	0.144148	+	0.989556i	$0.453956\pi$
$68$	−1.93844	−0.235070
$69$	3.53233	0.425243
$70$	−2.51349	−0.300419
$71$	0.0170442	0.00202277	0.00101139	−	0.999999i	$-0.499678\pi$
$71$	0.0170442	0.00202277	0.00101139	+	0.999999i	$0.499678\pi$
$72$	3.78571	0.446150
$73$	−4.68100	−0.547870	−0.273935	−	0.961748i	$-0.588325\pi$
$73$	−4.68100	−0.547870	−0.273935	+	0.961748i	$0.588325\pi$
$74$	−2.62015	−0.304586
$75$	−25.4856	−2.94282
$76$	8.60831	0.987440
$77$	−13.9300	−1.58747
$78$	0.665245	0.0753241
$79$	5.50504	0.619365	0.309683	−	0.950840i	$-0.399777\pi$
$79$	5.50504	0.619365	0.309683	+	0.950840i	$0.399777\pi$
$80$	13.9443	1.55901
$81$	−5.61406	−0.623784
$82$	1.90473	0.210342
$83$	17.0138	1.86751	0.933754	−	0.357917i	$-0.116513\pi$
$83$	17.0138	1.86751	0.933754	+	0.357917i	$0.116513\pi$
$84$	13.4187	1.46410
$85$	3.83673	0.416152
$86$	0.248120	0.0267555
$87$	−14.9635	−1.60425
$88$	−5.15565	−0.549595
$89$	4.11273	0.435948	0.217974	−	0.975955i	$-0.430055\pi$
$89$	4.11273	0.435948	0.217974	+	0.975955i	$0.430055\pi$
$90$	−3.68795	−0.388744
$91$	2.70002	0.283039
$92$	2.61161	0.272279
$93$	−8.61460	−0.893292
$94$	−2.84917	−0.293869
$95$	−17.0384	−1.74810
$96$	7.48844	0.764286
$97$	−8.24476	−0.837128	−0.418564	−	0.908187i	$-0.637466\pi$
$97$	−8.24476	−0.837128	−0.418564	+	0.908187i	$0.637466\pi$
$98$	0.00715519	0.000722784 0
$99$	−20.4390	−2.05419
$100$	−18.8426	−1.88426
$101$	7.72569	0.768735	0.384367	−	0.923180i	$-0.374420\pi$
$101$	7.72569	0.768735	0.384367	+	0.923180i	$0.374420\pi$
$102$	0.650531	0.0644121
$103$	1.75406	0.172832	0.0864161	−	0.996259i	$-0.472459\pi$
$103$	1.75406	0.172832	0.0864161	+	0.996259i	$0.472459\pi$
$104$	0.999310	0.0979904
$105$	−26.5595	−2.59194
$106$	−1.05006	−0.101991
$107$	−8.56231	−0.827750	−0.413875	−	0.910334i	$-0.635825\pi$
$107$	−8.56231	−0.827750	−0.413875	+	0.910334i	$0.635825\pi$
$108$	4.44197	0.427428
$109$	15.4753	1.48226	0.741132	−	0.671359i	$-0.234289\pi$
$109$	15.4753	1.48226	0.741132	+	0.671359i	$0.234289\pi$
$110$	5.02252	0.478878
$111$	−27.6865	−2.62789
$112$	9.59591	0.906728
$113$	−17.3754	−1.63454	−0.817268	−	0.576257i	$-0.804513\pi$
$113$	−17.3754	−1.63454	−0.817268	+	0.576257i	$0.804513\pi$
$114$	−2.88891	−0.270571
$115$	−5.16914	−0.482025
$116$	−11.0632	−1.02719
$117$	3.96164	0.366254
$118$	−2.41959	−0.222742
$119$	2.64030	0.242036
$120$	−9.82999	−0.897351
$121$	16.8352	1.53048
$122$	−1.48670	−0.134600
$123$	20.1269	1.81478
$124$	−6.36915	−0.571966
$125$	18.1114	1.61993
$126$	−2.53791	−0.226095
$127$	−1.26468	−0.112222	−0.0561109	−	0.998425i	$-0.517870\pi$
$127$	−1.26468	−0.112222	−0.0561109	+	0.998425i	$0.517870\pi$
$128$	7.34007	0.648777
$129$	2.62183	0.230840
$130$	−0.973504	−0.0853820
$131$	2.42172	0.211587	0.105793	−	0.994388i	$-0.466262\pi$
$131$	2.42172	0.211587	0.105793	+	0.994388i	$0.466262\pi$
$132$	−26.8135	−2.33382
$133$	−11.7252	−1.01670
$134$	−0.585516	−0.0505809
$135$	−8.79195	−0.756691
$136$	0.977206	0.0837948
$137$	−21.2133	−1.81237	−0.906187	−	0.422877i	$-0.861020\pi$
$137$	−21.2133	−1.81237	−0.906187	+	0.422877i	$0.861020\pi$
$138$	−0.876444	−0.0746079
$139$	10.4023	0.882311	0.441155	−	0.897431i	$-0.354569\pi$
$139$	10.4023	0.882311	0.441155	+	0.897431i	$0.354569\pi$
$140$	−19.6366	−1.65959
$141$	−30.1065	−2.53543
$142$	−0.00422901	−0.000354891 0
$143$	−5.39525	−0.451173
$144$	14.0797	1.17331
$145$	21.8972	1.81847
$146$	1.16145	0.0961224
$147$	0.0756074	0.00623599
$148$	−20.4698	−1.68261
$149$	4.33577	0.355200	0.177600	−	0.984103i	$-0.443167\pi$
$149$	4.33577	0.355200	0.177600	+	0.984103i	$0.443167\pi$
$150$	6.32350	0.516311
$151$	−7.53533	−0.613216	−0.306608	−	0.951836i	$-0.599194\pi$
$151$	−7.53533	−0.613216	−0.306608	+	0.951836i	$0.599194\pi$
$152$	−4.33963	−0.351990
$153$	3.87401	0.313195
$154$	3.45631	0.278517
$155$	12.6064	1.01257
$156$	5.19721	0.416110
$157$	14.3044	1.14162	0.570809	−	0.821083i	$-0.306630\pi$
$157$	14.3044	1.14162	0.570809	+	0.821083i	$0.306630\pi$
$158$	−1.36591	−0.108666
$159$	−11.0958	−0.879951
$160$	−10.9584	−0.866339
$161$	−3.55721	−0.280347
$162$	1.39296	0.109441
$163$	3.65702	0.286440	0.143220	−	0.989691i	$-0.454254\pi$
$163$	3.65702	0.286440	0.143220	+	0.989691i	$0.454254\pi$
$164$	14.8807	1.16199
$165$	53.0719	4.13164
$166$	−4.22147	−0.327650
$167$	23.7286	1.83617	0.918087	−	0.396378i	$-0.129733\pi$
$167$	23.7286	1.83617	0.918087	+	0.396378i	$0.129733\pi$
$168$	−6.76463	−0.521903
$169$	−11.9543	−0.919558
$170$	−0.951972	−0.0730129
$171$	−17.2039	−1.31562
$172$	1.93844	0.147804
$173$	−21.6270	−1.64427	−0.822136	−	0.569291i	$-0.807218\pi$
$173$	−21.6270	−1.64427	−0.822136	+	0.569291i	$0.807218\pi$
$174$	3.71274	0.281462
$175$	25.6650	1.94010
$176$	−19.1748	−1.44536
$177$	−25.5673	−1.92176
$178$	−1.02045	−0.0764860
$179$	−13.7253	−1.02588	−0.512939	−	0.858425i	$-0.671443\pi$
$179$	−13.7253	−1.02588	−0.512939	+	0.858425i	$0.671443\pi$
$180$	−28.8121	−2.14752
$181$	17.3511	1.28969	0.644847	−	0.764312i	$-0.276921\pi$
$181$	17.3511	1.28969	0.644847	+	0.764312i	$0.276921\pi$
$182$	−0.669929	−0.0496585
$183$	−15.7097	−1.16129
$184$	−1.31657	−0.0970586
$185$	40.5158	2.97878
$186$	2.13746	0.156726
$187$	−5.27591	−0.385813
$188$	−22.2591	−1.62341
$189$	−6.05029	−0.440094
$190$	4.22756	0.306700
$191$	−11.1728	−0.808432	−0.404216	−	0.914664i	$-0.632456\pi$
$191$	−11.1728	−0.808432	−0.404216	+	0.914664i	$0.632456\pi$
$192$	17.1996	1.24127
$193$	8.14610	0.586369	0.293184	−	0.956056i	$-0.405285\pi$
$193$	8.14610	0.586369	0.293184	+	0.956056i	$0.405285\pi$
$194$	2.04569	0.146872
$195$	−10.2868	−0.736654
$196$	0.0558998	0.00399284
$197$	−2.43143	−0.173232	−0.0866160	−	0.996242i	$-0.527605\pi$
$197$	−2.43143	−0.173232	−0.0866160	+	0.996242i	$0.527605\pi$
$198$	5.07132	0.360403
$199$	6.63219	0.470143	0.235072	−	0.971978i	$-0.424468\pi$
$199$	6.63219	0.470143	0.235072	+	0.971978i	$0.424468\pi$
$200$	9.49895	0.671677
$201$	−6.18702	−0.436399
$202$	−1.91690	−0.134873
$203$	15.0688	1.05763
$204$	5.08226	0.355829
$205$	−29.4532	−2.05710
$206$	−0.435217	−0.0303230
$207$	−5.21937	−0.362771
$208$	3.71661	0.257701
$209$	23.4295	1.62065
$210$	6.58995	0.454749
$211$	7.00049	0.481934	0.240967	−	0.970533i	$-0.422535\pi$
$211$	7.00049	0.481934	0.240967	+	0.970533i	$0.422535\pi$
$212$	−8.20358	−0.563424
$213$	−0.0446870	−0.00306191
$214$	2.12448	0.145227
$215$	−3.83673	−0.261663
$216$	−2.23929	−0.152364
$217$	8.67526	0.588915
$218$	−3.83974	−0.260060
$219$	12.2728	0.829319
$220$	39.2383	2.64545
$221$	1.02262	0.0687888
$222$	6.86959	0.461057
$223$	−6.26775	−0.419719	−0.209860	−	0.977732i	$-0.567301\pi$
$223$	−6.26775	−0.419719	−0.209860	+	0.977732i	$0.567301\pi$
$224$	−7.54117	−0.503866
$225$	37.6574	2.51050
$226$	4.31118	0.286776
$227$	−0.0141620	−0.000939964 0	−0.000469982	−	1.00000i	$-0.500150\pi$
$227$	−0.0141620	−0.000939964 0	−0.000469982		1.00000i	$0.500150\pi$
$228$	−22.5696	−1.49470
$229$	−4.39136	−0.290189	−0.145094	−	0.989418i	$-0.546349\pi$
$229$	−4.39136	−0.290189	−0.145094	+	0.989418i	$0.546349\pi$
$230$	1.28257	0.0845700
$231$	36.5221	2.40298
$232$	5.57717	0.366159
$233$	19.5863	1.28314	0.641571	−	0.767064i	$-0.278283\pi$
$233$	19.5863	1.28314	0.641571	+	0.767064i	$0.278283\pi$
$234$	−0.982964	−0.0642584
$235$	44.0572	2.87398
$236$	−18.9030	−1.23048
$237$	−14.4333	−0.937543
$238$	−0.655111	−0.0424646
$239$	−1.40600	−0.0909465	−0.0454732	−	0.998966i	$-0.514480\pi$
$239$	−1.40600	−0.0909465	−0.0454732	+	0.998966i	$0.514480\pi$
$240$	−36.5595	−2.35991
$241$	−5.72796	−0.368971	−0.184485	−	0.982835i	$-0.559062\pi$
$241$	−5.72796	−0.368971	−0.184485	+	0.982835i	$0.559062\pi$
$242$	−4.17716	−0.268518
$243$	21.5937	1.38524
$244$	−11.6148	−0.743564
$245$	−0.110642	−0.00706866
$246$	−4.99389	−0.318399
$247$	−4.54130	−0.288956
$248$	3.21082	0.203887
$249$	−44.6074	−2.82688
$250$	−4.49380	−0.284213
$251$	−26.9617	−1.70181	−0.850903	−	0.525323i	$-0.823945\pi$
$251$	−26.9617	−1.70181	−0.850903	+	0.525323i	$0.823945\pi$
$252$	−19.8274	−1.24901
$253$	7.10811	0.446883
$254$	0.313792	0.0196891
$255$	−10.0593	−0.629936
$256$	11.2991	0.706191
$257$	−26.6001	−1.65927	−0.829634	−	0.558307i	$-0.811451\pi$
$257$	−26.6001	−1.65927	−0.829634	+	0.558307i	$0.811451\pi$
$258$	−0.650531	−0.0405003
$259$	27.8815	1.73247
$260$	−7.60549	−0.471672
$261$	22.1100	1.36857
$262$	−0.600878	−0.0371224
$263$	7.62364	0.470094	0.235047	−	0.971984i	$-0.424476\pi$
$263$	7.62364	0.470094	0.235047	+	0.971984i	$0.424476\pi$
$264$	13.5173	0.831930
$265$	16.2373	0.997449
$266$	2.90925	0.178378
$267$	−10.7829	−0.659902
$268$	−4.57433	−0.279422
$269$	16.6709	1.01644	0.508222	−	0.861226i	$-0.330303\pi$
$269$	16.6709	1.01644	0.508222	+	0.861226i	$0.330303\pi$
$270$	2.18146	0.132760
$271$	−22.0429	−1.33901	−0.669505	−	0.742808i	$-0.733494\pi$
$271$	−22.0429	−1.33901	−0.669505	+	0.742808i	$0.733494\pi$
$272$	3.63441	0.220368
$273$	−7.07900	−0.428440
$274$	5.26345	0.317977
$275$	−51.2846	−3.09258
$276$	−6.84720	−0.412153
$277$	17.3120	1.04018	0.520090	−	0.854112i	$-0.325898\pi$
$277$	17.3120	1.04018	0.520090	+	0.854112i	$0.325898\pi$
$278$	−2.58102	−0.154799
$279$	12.7289	0.762059
$280$	9.89921	0.591591
$281$	−6.56698	−0.391753	−0.195877	−	0.980629i	$-0.562755\pi$
$281$	−6.56698	−0.391753	−0.195877	+	0.980629i	$0.562755\pi$
$282$	7.47004	0.444835
$283$	5.25134	0.312160	0.156080	−	0.987744i	$-0.450114\pi$
$283$	5.25134	0.312160	0.156080	+	0.987744i	$0.450114\pi$
$284$	−0.0330391	−0.00196051
$285$	44.6717	2.64613
$286$	1.33867	0.0791573
$287$	−20.2686	−1.19642
$288$	−11.0649	−0.652005
$289$	1.00000	0.0588235
$290$	−5.43315	−0.319045
$291$	21.6164	1.26717
$292$	9.07382	0.531005
$293$	−29.7898	−1.74034	−0.870168	−	0.492755i	$-0.835990\pi$
$293$	−29.7898	−1.74034	−0.870168	+	0.492755i	$0.835990\pi$
$294$	−0.0187597	−0.00109409
$295$	37.4147	2.17837
$296$	10.3193	0.599796
$297$	12.0899	0.701525
$298$	−1.07579	−0.0623191
$299$	−1.37775	−0.0796773
$300$	49.4022	2.85224
$301$	−2.64030	−0.152184
$302$	1.86967	0.107587
$303$	−20.2555	−1.16365
$304$	−16.1399	−0.925685
$305$	22.9892	1.31636
$306$	−0.961222	−0.0549494
$307$	−25.8133	−1.47324	−0.736622	−	0.676305i	$-0.763580\pi$
$307$	−25.8133	−1.47324	−0.736622	+	0.676305i	$0.763580\pi$
$308$	27.0024	1.53860
$309$	−4.59884	−0.261619
$310$	−3.12791	−0.177653
$311$	−16.7769	−0.951333	−0.475666	−	0.879626i	$-0.657793\pi$
$311$	−16.7769	−0.951333	−0.475666	+	0.879626i	$0.657793\pi$
$312$	−2.62002	−0.148330
$313$	−15.3751	−0.869054	−0.434527	−	0.900659i	$-0.643085\pi$
$313$	−15.3751	−0.869054	−0.434527	+	0.900659i	$0.643085\pi$
$314$	−3.54922	−0.200294
$315$	39.2442	2.21116
$316$	−10.6712	−0.600300
$317$	−30.6427	−1.72107	−0.860534	−	0.509393i	$-0.829870\pi$
$317$	−30.6427	−1.72107	−0.860534	+	0.509393i	$0.829870\pi$
$318$	2.75309	0.154385
$319$	−30.1110	−1.68589
$320$	−25.1695	−1.40702
$321$	22.4490	1.25298
$322$	0.882615	0.0491862
$323$	−4.44085	−0.247096
$324$	10.8825	0.604583
$325$	9.94039	0.551394
$326$	−0.907380	−0.0502551
$327$	−40.5737	−2.24373
$328$	−7.50167	−0.414210
$329$	30.3185	1.67151
$330$	−13.1682	−0.724886
$331$	15.5336	0.853803	0.426902	−	0.904298i	$-0.359605\pi$
$331$	15.5336	0.853803	0.426902	+	0.904298i	$0.359605\pi$
$332$	−32.9802	−1.81002
$333$	40.9095	2.24183
$334$	−5.88755	−0.322152
$335$	9.05395	0.494670
$336$	−25.1589	−1.37253
$337$	−7.73859	−0.421548	−0.210774	−	0.977535i	$-0.567598\pi$
$337$	−7.73859	−0.421548	−0.210774	+	0.977535i	$0.567598\pi$
$338$	2.96609	0.161334
$339$	45.5553	2.47423
$340$	−7.43726	−0.403342
$341$	−17.3351	−0.938750
$342$	4.26864	0.230822
$343$	−18.5582	−1.00205
$344$	−0.977206	−0.0526874
$345$	13.5526	0.729649
$346$	5.36610	0.288484
$347$	−27.2826	−1.46461	−0.732304	−	0.680978i	$-0.761555\pi$
$347$	−27.2826	−1.46461	−0.732304	+	0.680978i	$0.761555\pi$
$348$	29.0058	1.55487
$349$	−7.60881	−0.407290	−0.203645	−	0.979045i	$-0.565279\pi$
$349$	−7.60881	−0.407290	−0.203645	+	0.979045i	$0.565279\pi$
$350$	−6.36802	−0.340385
$351$	−2.34335	−0.125079
$352$	15.0690	0.803179
$353$	1.12912	0.0600969	0.0300485	−	0.999548i	$-0.490434\pi$
$353$	1.12912	0.0600969	0.0300485	+	0.999548i	$0.490434\pi$
$354$	6.34378	0.337168
$355$	0.0653940	0.00347075
$356$	−7.97226	−0.422529
$357$	−6.92242	−0.366373
$358$	3.40553	0.179988
$359$	−6.31686	−0.333391	−0.166696	−	0.986008i	$-0.553310\pi$
$359$	−6.31686	−0.333391	−0.166696	+	0.986008i	$0.553310\pi$
$360$	14.5248	0.765522
$361$	0.721154	0.0379555
$362$	−4.30515	−0.226274
$363$	−44.1392	−2.31671
$364$	−5.23381	−0.274326
$365$	−17.9597	−0.940056
$366$	3.89789	0.203746
$367$	−37.2755	−1.94576	−0.972882	−	0.231303i	$-0.925701\pi$
$367$	−37.2755	−1.94576	−0.972882	+	0.231303i	$0.925701\pi$
$368$	−4.89655	−0.255250
$369$	−29.7394	−1.54817
$370$	−10.0528	−0.522620
$371$	11.1739	0.580120
$372$	16.6988	0.865795
$373$	3.32905	0.172372	0.0861859	−	0.996279i	$-0.472532\pi$
$373$	3.32905	0.172372	0.0861859	+	0.996279i	$0.472532\pi$
$374$	1.30906	0.0676899
$375$	−47.4850	−2.45212
$376$	11.2213	0.578692
$377$	5.83635	0.300587
$378$	1.50120	0.0772134
$379$	25.1363	1.29117	0.645583	−	0.763690i	$-0.276614\pi$
$379$	25.1363	1.29117	0.645583	+	0.763690i	$0.276614\pi$
$380$	33.0278	1.69429
$381$	3.31577	0.169872
$382$	2.77219	0.141837
$383$	15.9380	0.814396	0.407198	−	0.913340i	$-0.366506\pi$
$383$	15.9380	0.814396	0.407198	+	0.913340i	$0.366506\pi$
$384$	−19.2444	−0.982064
$385$	−53.4456	−2.72384
$386$	−2.02121	−0.102877
$387$	−3.87401	−0.196927
$388$	15.9819	0.811360
$389$	−15.6054	−0.791225	−0.395612	−	0.918418i	$-0.629468\pi$
$389$	−15.6054	−0.791225	−0.395612	+	0.918418i	$0.629468\pi$
$390$	2.55237	0.129244
$391$	−1.34728	−0.0681347
$392$	−0.0281803	−0.00142332
$393$	−6.34935	−0.320282
$394$	0.603286	0.0303931
$395$	21.1214	1.06273
$396$	39.6196	1.99096
$397$	17.4831	0.877451	0.438725	−	0.898621i	$-0.355430\pi$
$397$	17.4831	0.877451	0.438725	+	0.898621i	$0.355430\pi$
$398$	−1.64558	−0.0824855
$399$	30.7414	1.53900
$400$	35.3283	1.76642
$401$	32.7718	1.63655	0.818274	−	0.574829i	$-0.194931\pi$
$401$	32.7718	1.63655	0.818274	+	0.574829i	$0.194931\pi$
$402$	1.53513	0.0765651
$403$	3.36003	0.167375
$404$	−14.9758	−0.745072
$405$	−21.5396	−1.07031
$406$	−3.73889	−0.185558
$407$	−55.7135	−2.76162
$408$	−2.56207	−0.126842
$409$	31.0766	1.53664	0.768319	−	0.640067i	$-0.221094\pi$
$409$	31.0766	1.53664	0.768319	+	0.640067i	$0.221094\pi$
$410$	7.30795	0.360914
$411$	55.6177	2.74342
$412$	−3.40013	−0.167512
$413$	25.7474	1.26694
$414$	1.29503	0.0636473
$415$	65.2774	3.20434
$416$	−2.92079	−0.143203
$417$	−27.2731	−1.33557
$418$	−5.81334	−0.284340
$419$	−17.0374	−0.832333	−0.416167	−	0.909288i	$-0.636627\pi$
$419$	−17.0374	−0.832333	−0.416167	+	0.909288i	$0.636627\pi$
$420$	51.4838	2.51215
$421$	−2.69005	−0.131105	−0.0655526	−	0.997849i	$-0.520881\pi$
$421$	−2.69005	−0.131105	−0.0655526	+	0.997849i	$0.520881\pi$
$422$	−1.73697	−0.0845541
$423$	44.4853	2.16295
$424$	4.13560	0.200842
$425$	9.72052	0.471514
$426$	0.0110878	0.000537204 0
$427$	15.8203	0.765598
$428$	16.5975	0.802270
$429$	14.1454	0.682948
$430$	0.951972	0.0459082
$431$	−17.0547	−0.821497	−0.410748	−	0.911749i	$-0.634733\pi$
$431$	−17.0547	−0.821497	−0.410748	+	0.911749i	$0.634733\pi$
$432$	−8.32832	−0.400697
$433$	5.36629	0.257888	0.128944	−	0.991652i	$-0.458841\pi$
$433$	5.36629	0.257888	0.128944	+	0.991652i	$0.458841\pi$
$434$	−2.15251	−0.103324
$435$	−57.4109	−2.75264
$436$	−29.9979	−1.43664
$437$	5.98305	0.286208
$438$	−3.04513	−0.145502
$439$	35.8075	1.70900	0.854501	−	0.519451i	$-0.173863\pi$
$439$	35.8075	1.70900	0.854501	+	0.519451i	$0.173863\pi$
$440$	−19.7809	−0.943016
$441$	−0.111717	−0.00531987
$442$	−0.253733	−0.0120688
$443$	−5.51352	−0.261955	−0.130978	−	0.991385i	$-0.541812\pi$
$443$	−5.51352	−0.261955	−0.130978	+	0.991385i	$0.541812\pi$
$444$	53.6685	2.54700
$445$	15.7794	0.748017
$446$	1.55516	0.0736388
$447$	−11.3677	−0.537673
$448$	−17.3207	−0.818326
$449$	30.9111	1.45879	0.729393	−	0.684095i	$-0.239803\pi$
$449$	30.9111	1.45879	0.729393	+	0.684095i	$0.239803\pi$
$450$	−9.34358	−0.440460
$451$	40.5013	1.90713
$452$	33.6810	1.58422
$453$	19.7564	0.928236
$454$	0.00351388	0.000164914 0
$455$	10.3592	0.485649
$456$	11.3778	0.532814
$457$	38.8454	1.81711	0.908555	−	0.417766i	$-0.137187\pi$
$457$	38.8454	1.81711	0.908555	+	0.417766i	$0.137187\pi$
$458$	1.08958	0.0509130
$459$	−2.29152	−0.106959
$460$	10.0200	0.467187
$461$	−6.21762	−0.289583	−0.144792	−	0.989462i	$-0.546251\pi$
$461$	−6.21762	−0.289583	−0.144792	+	0.989462i	$0.546251\pi$
$462$	−9.06187	−0.421596
$463$	22.0334	1.02398	0.511990	−	0.858992i	$-0.328909\pi$
$463$	22.0334	1.02398	0.511990	+	0.858992i	$0.328909\pi$
$464$	20.7425	0.962946
$465$	−33.0519	−1.53275
$466$	−4.85976	−0.225124
$467$	−9.67826	−0.447857	−0.223928	−	0.974606i	$-0.571888\pi$
$467$	−9.67826	−0.447857	−0.223928	+	0.974606i	$0.571888\pi$
$468$	−7.67939	−0.354980
$469$	6.23059	0.287702
$470$	−10.9315	−0.504232
$471$	−37.5039	−1.72809
$472$	9.52942	0.438627
$473$	5.27591	0.242587
$474$	3.58119	0.164490
$475$	−43.1674	−1.98066
$476$	−5.11805	−0.234585
$477$	16.3951	0.750679
$478$	0.348857	0.0159563
$479$	29.2834	1.33799	0.668996	−	0.743266i	$-0.266724\pi$
$479$	29.2834	1.33799	0.668996	+	0.743266i	$0.266724\pi$
$480$	28.7311	1.31139
$481$	10.7988	0.492385
$482$	1.42122	0.0647350
$483$	9.32641	0.424366
$484$	−32.6340	−1.48336
$485$	−31.6329	−1.43638
$486$	−5.35783	−0.243036
$487$	−29.7708	−1.34904	−0.674521	−	0.738255i	$-0.735650\pi$
$487$	−29.7708	−1.34904	−0.674521	+	0.738255i	$0.735650\pi$
$488$	5.85529	0.265056
$489$	−9.58809	−0.433588
$490$	0.0274526	0.00124018
$491$	−11.2407	−0.507288	−0.253644	−	0.967298i	$-0.581629\pi$
$491$	−11.2407	−0.507288	−0.253644	+	0.967298i	$0.581629\pi$
$492$	−39.0147	−1.75892
$493$	5.70726	0.257042
$494$	1.12679	0.0506966
$495$	−78.4188	−3.52466
$496$	11.9416	0.536195
$497$	0.0450017	0.00201860
$498$	11.0680	0.495969
$499$	26.1064	1.16868	0.584341	−	0.811508i	$-0.301353\pi$
$499$	26.1064	1.16868	0.584341	+	0.811508i	$0.301353\pi$
$500$	−35.1077	−1.57007
$501$	−62.2125	−2.77945
$502$	6.68974	0.298578
$503$	−41.0130	−1.82868	−0.914340	−	0.404946i	$-0.867290\pi$
$503$	−41.0130	−1.82868	−0.914340	+	0.404946i	$0.867290\pi$
$504$	9.99540	0.445230
$505$	29.6414	1.31902
$506$	−1.76367	−0.0784045
$507$	31.3421	1.39195
$508$	2.45149	0.108767
$509$	−31.7994	−1.40948	−0.704741	−	0.709464i	$-0.748937\pi$
$509$	−31.7994	−1.40948	−0.704741	+	0.709464i	$0.748937\pi$
$510$	2.49591	0.110521
$511$	−12.3592	−0.546740
$512$	−17.4837	−0.772676
$513$	10.1763	0.449295
$514$	6.60003	0.291115
$515$	6.72984	0.296552
$516$	−5.08226	−0.223734
$517$	−60.5833	−2.66445
$518$	−6.91796	−0.303958
$519$	56.7025	2.48896
$520$	3.83408	0.168136
$521$	−10.9641	−0.480345	−0.240172	−	0.970730i	$-0.577204\pi$
$521$	−10.9641	−0.480345	−0.240172	+	0.970730i	$0.577204\pi$
$522$	−5.48594	−0.240113
$523$	−16.7375	−0.731880	−0.365940	−	0.930638i	$-0.619252\pi$
$523$	−16.7375	−0.731880	−0.365940	+	0.930638i	$0.619252\pi$
$524$	−4.69435	−0.205074
$525$	−67.2895	−2.93675
$526$	−1.89158	−0.0824768
$527$	3.28571	0.143128
$528$	50.2732	2.18786
$529$	−21.1848	−0.921080
$530$	−4.02880	−0.175000
$531$	37.7782	1.63943
$532$	22.7285	0.985404
$533$	−7.85028	−0.340033
$534$	2.67545	0.115778
$535$	−32.8513	−1.42029
$536$	2.30602	0.0996048
$537$	35.9855	1.55289
$538$	−4.13640	−0.178333
$539$	0.152145	0.00655333
$540$	17.0426	0.733398
$541$	−13.9793	−0.601017	−0.300509	−	0.953779i	$-0.597156\pi$
$541$	−13.9793	−0.601017	−0.300509	+	0.953779i	$0.597156\pi$
$542$	5.46929	0.234926
$543$	−45.4916	−1.95223
$544$	−2.85618	−0.122458
$545$	59.3746	2.54333
$546$	1.75644	0.0751688
$547$	6.51213	0.278438	0.139219	−	0.990262i	$-0.455541\pi$
$547$	6.51213	0.278438	0.139219	+	0.990262i	$0.455541\pi$
$548$	41.1206	1.75659
$549$	23.2126	0.990688
$550$	12.7248	0.542585
$551$	−25.3451	−1.07974
$552$	3.45182	0.146919
$553$	14.5349	0.618088
$554$	−4.29547	−0.182497
$555$	−106.226	−4.50903
$556$	−20.1642	−0.855151
$557$	28.8553	1.22264	0.611319	−	0.791384i	$-0.290639\pi$
$557$	28.8553	1.22264	0.611319	+	0.791384i	$0.290639\pi$
$558$	−3.15830	−0.133702
$559$	−1.02262	−0.0432522
$560$	36.8170	1.55580
$561$	13.8326	0.584011
$562$	1.62940	0.0687321
$563$	7.63249	0.321671	0.160836	−	0.986981i	$-0.448581\pi$
$563$	7.63249	0.321671	0.160836	+	0.986981i	$0.448581\pi$
$564$	58.3596	2.45738
$565$	−66.6646	−2.80460
$566$	−1.30296	−0.0547677
$567$	−14.8228	−0.622498
$568$	0.0166557	0.000698857 0
$569$	16.1421	0.676711	0.338356	−	0.941018i	$-0.390129\pi$
$569$	16.1421	0.676711	0.338356	+	0.941018i	$0.390129\pi$
$570$	−11.0840	−0.464256
$571$	−18.3263	−0.766933	−0.383466	−	0.923555i	$-0.625270\pi$
$571$	−18.3263	−0.766933	−0.383466	+	0.923555i	$0.625270\pi$
$572$	10.4583	0.437285
$573$	29.2931	1.22374
$574$	5.02906	0.209909
$575$	−13.0962	−0.546150
$576$	−25.4141	−1.05892
$577$	−40.8744	−1.70163	−0.850813	−	0.525469i	$-0.823890\pi$
$577$	−40.8744	−1.70163	−0.850813	+	0.525469i	$0.823890\pi$
$578$	−0.248120	−0.0103204
$579$	−21.3577	−0.887596
$580$	−42.4464	−1.76249
$581$	44.9215	1.86366
$582$	−5.36347	−0.222323
$583$	−22.3280	−0.924731
$584$	−4.57430	−0.189286
$585$	15.1998	0.628433
$586$	7.39145	0.305338
$587$	−6.69164	−0.276194	−0.138097	−	0.990419i	$-0.544098\pi$
$587$	−6.69164	−0.276194	−0.138097	+	0.990419i	$0.544098\pi$
$588$	−0.146560	−0.00604403
$589$	−14.5914	−0.601227
$590$	−9.28334	−0.382189
$591$	6.37480	0.262224
$592$	38.3793	1.57738
$593$	−19.7987	−0.813033	−0.406517	−	0.913643i	$-0.633257\pi$
$593$	−19.7987	−0.813033	−0.406517	+	0.913643i	$0.633257\pi$
$594$	−2.99974	−0.123081
$595$	10.1301	0.415294
$596$	−8.40462	−0.344267
$597$	−17.3885	−0.711664
$598$	0.341848	0.0139792
$599$	−16.4349	−0.671511	−0.335756	−	0.941949i	$-0.608992\pi$
$599$	−16.4349	−0.671511	−0.335756	+	0.941949i	$0.608992\pi$
$600$	−24.9047	−1.01673
$601$	40.7190	1.66096	0.830482	−	0.557046i	$-0.188065\pi$
$601$	40.7190	1.66096	0.830482	+	0.557046i	$0.188065\pi$
$602$	0.655111	0.0267003
$603$	9.14192	0.372288
$604$	14.6068	0.594340
$605$	64.5923	2.62605
$606$	5.02580	0.204159
$607$	41.6906	1.69217	0.846085	−	0.533048i	$-0.178954\pi$
$607$	41.6906	1.69217	0.846085	+	0.533048i	$0.178954\pi$
$608$	12.6839	0.514399
$609$	−39.5080	−1.60095
$610$	−5.70408	−0.230952
$611$	11.7427	0.475060
$612$	−7.50953	−0.303555
$613$	−39.4966	−1.59525	−0.797627	−	0.603151i	$-0.793911\pi$
$613$	−39.4966	−1.59525	−0.797627	+	0.603151i	$0.793911\pi$
$614$	6.40481	0.258477
$615$	77.2215	3.11387
$616$	−13.6125	−0.548461
$617$	−14.9811	−0.603116	−0.301558	−	0.953448i	$-0.597507\pi$
$617$	−14.9811	−0.603116	−0.301558	+	0.953448i	$0.597507\pi$
$618$	1.14107	0.0459004
$619$	36.2617	1.45748	0.728740	−	0.684790i	$-0.240106\pi$
$619$	36.2617	1.45748	0.728740	+	0.684790i	$0.240106\pi$
$620$	−24.4367	−0.981402
$621$	3.08731	0.123889
$622$	4.16270	0.166909
$623$	10.8588	0.435049
$624$	−9.74435	−0.390086
$625$	20.8859	0.835436
$626$	3.81489	0.152474
$627$	−61.4283	−2.45321
$628$	−27.7282	−1.10648
$629$	10.5600	0.421054
$630$	−9.73728	−0.387943
$631$	−2.75828	−0.109805	−0.0549027	−	0.998492i	$-0.517485\pi$
$631$	−2.75828	−0.109805	−0.0549027	+	0.998492i	$0.517485\pi$
$632$	5.37956	0.213987
$633$	−18.3541	−0.729511
$634$	7.60309	0.301957
$635$	−4.85223	−0.192555
$636$	21.5084	0.852865
$637$	−0.0294899	−0.00116843
$638$	7.47115	0.295786
$639$	0.0660294	0.00261208
$640$	28.1619	1.11320
$641$	46.6092	1.84095	0.920476	−	0.390800i	$-0.127802\pi$
$641$	46.6092	1.84095	0.920476	+	0.390800i	$0.127802\pi$
$642$	−5.57005	−0.219832
$643$	33.1859	1.30872	0.654362	−	0.756181i	$-0.272937\pi$
$643$	33.1859	1.30872	0.654362	+	0.756181i	$0.272937\pi$
$644$	6.89542	0.271718
$645$	10.0593	0.396084
$646$	1.10187	0.0433523
$647$	8.16310	0.320924	0.160462	−	0.987042i	$-0.448702\pi$
$647$	8.16310	0.320924	0.160462	+	0.987042i	$0.448702\pi$
$648$	−5.48609	−0.215514
$649$	−51.4491	−2.01955
$650$	−2.46641	−0.0967407
$651$	−22.7451	−0.891450
$652$	−7.08889	−0.277622
$653$	25.6565	1.00401	0.502007	−	0.864863i	$-0.332595\pi$
$653$	25.6565	1.00401	0.502007	+	0.864863i	$0.332595\pi$
$654$	10.0672	0.393657
$655$	9.29149	0.363049
$656$	−27.9001	−1.08931
$657$	−18.1343	−0.707485
$658$	−7.52264	−0.293263
$659$	10.2093	0.397696	0.198848	−	0.980030i	$-0.436280\pi$
$659$	10.2093	0.397696	0.198848	+	0.980030i	$0.436280\pi$
$660$	−102.876	−4.00446
$661$	−2.36605	−0.0920286	−0.0460143	−	0.998941i	$-0.514652\pi$
$661$	−2.36605	−0.0920286	−0.0460143	+	0.998941i	$0.514652\pi$
$662$	−3.85420	−0.149798
$663$	−2.68114	−0.104127
$664$	16.6260	0.645214
$665$	−44.9863	−1.74449
$666$	−10.1505	−0.393323
$667$	−7.68925	−0.297729
$668$	−45.9964	−1.77965
$669$	16.4330	0.635336
$670$	−2.24647	−0.0867887
$671$	−31.6125	−1.22039
$672$	19.7717	0.762710
$673$	25.9290	0.999490	0.499745	−	0.866173i	$-0.333427\pi$
$673$	25.9290	0.999490	0.499745	+	0.866173i	$0.333427\pi$
$674$	1.92010	0.0739596
$675$	−22.2748	−0.857356
$676$	23.1726	0.891252
$677$	−38.2008	−1.46818	−0.734088	−	0.679054i	$-0.762390\pi$
$677$	−38.2008	−1.46818	−0.734088	+	0.679054i	$0.762390\pi$
$678$	−11.3032	−0.434097
$679$	−21.7686	−0.835402
$680$	3.74928	0.143778
$681$	0.0371304	0.00142284
$682$	4.30120	0.164701
$683$	10.2279	0.391361	0.195680	−	0.980668i	$-0.437308\pi$
$683$	10.2279	0.391361	0.195680	+	0.980668i	$0.437308\pi$
$684$	33.3487	1.27512
$685$	−81.3897	−3.10974
$686$	4.60467	0.175807
$687$	11.5134	0.439264
$688$	−3.63441	−0.138560
$689$	4.32779	0.164876
$690$	−3.36268	−0.128015
$691$	−11.7251	−0.446045	−0.223022	−	0.974813i	$-0.571592\pi$
$691$	−11.7251	−0.446045	−0.223022	+	0.974813i	$0.571592\pi$
$692$	41.9226	1.59366
$693$	−53.9649	−2.04996
$694$	6.76938	0.256962
$695$	39.9108	1.51390
$696$	−14.6224	−0.554261
$697$	−7.67664	−0.290774
$698$	1.88790	0.0714581
$699$	−51.3520	−1.94231
$700$	−49.7501	−1.88038
$701$	29.5222	1.11504	0.557520	−	0.830164i	$-0.311753\pi$
$701$	29.5222	1.11504	0.557520	+	0.830164i	$0.311753\pi$
$702$	0.581434	0.0219448
$703$	−46.8953	−1.76869
$704$	34.6107	1.30444
$705$	−115.511	−4.35038
$706$	−0.280157	−0.0105439
$707$	20.3981	0.767150
$708$	49.5606	1.86260
$709$	−26.1151	−0.980773	−0.490387	−	0.871505i	$-0.663144\pi$
$709$	−26.1151	−0.980773	−0.490387	+	0.871505i	$0.663144\pi$
$710$	−0.0162256	−0.000608936 0
$711$	21.3266	0.799810
$712$	4.01898	0.150618
$713$	−4.42676	−0.165784
$714$	1.71759	0.0642793
$715$	−20.7001	−0.774141
$716$	26.6057	0.994301
$717$	3.68629	0.137667
$718$	1.56734	0.0584927
$719$	−45.0688	−1.68078	−0.840392	−	0.541979i	$-0.817675\pi$
$719$	−45.0688	−1.68078	−0.840392	+	0.541979i	$0.817675\pi$
$720$	54.0202	2.01322
$721$	4.63123	0.172476
$722$	−0.178933	−0.00665920
$723$	15.0178	0.558517
$724$	−33.6339	−1.25000
$725$	55.4775	2.06038
$726$	10.9518	0.406461
$727$	−14.5161	−0.538373	−0.269186	−	0.963088i	$-0.586755\pi$
$727$	−14.5161	−0.538373	−0.269186	+	0.963088i	$0.586755\pi$
$728$	2.63847	0.0977883
$729$	−39.7729	−1.47307
$730$	4.45618	0.164931
$731$	−1.00000	−0.0369863
$732$	30.4522	1.12555
$733$	5.95289	0.219875	0.109938	−	0.993938i	$-0.464935\pi$
$733$	5.95289	0.219875	0.109938	+	0.993938i	$0.464935\pi$
$734$	9.24880	0.341380
$735$	0.290085	0.0107000
$736$	3.84807	0.141842
$737$	−12.4501	−0.458606
$738$	7.37896	0.271623
$739$	1.50772	0.0554625	0.0277313	−	0.999615i	$-0.491172\pi$
$739$	1.50772	0.0554625	0.0277313	+	0.999615i	$0.491172\pi$
$740$	−78.5373	−2.88709
$741$	11.9065	0.437397
$742$	−2.77247	−0.101781
$743$	−29.6361	−1.08724	−0.543622	−	0.839330i	$-0.682947\pi$
$743$	−29.6361	−1.08724	−0.543622	+	0.839330i	$0.682947\pi$
$744$	−8.41824	−0.308628
$745$	16.6352	0.609467
$746$	−0.826006	−0.0302422
$747$	65.9117	2.41158
$748$	10.2270	0.373937
$749$	−22.6070	−0.826043
$750$	11.7820	0.430218
$751$	9.10755	0.332339	0.166170	−	0.986097i	$-0.446860\pi$
$751$	9.10755	0.332339	0.166170	+	0.986097i	$0.446860\pi$
$752$	41.7339	1.52188
$753$	70.6890	2.57605
$754$	−1.44812	−0.0527373
$755$	−28.9110	−1.05218
$756$	11.7281	0.426547
$757$	−4.63707	−0.168537	−0.0842687	−	0.996443i	$-0.526855\pi$
$757$	−4.63707	−0.168537	−0.0842687	+	0.996443i	$0.526855\pi$
$758$	−6.23684	−0.226532
$759$	−18.6363	−0.676454
$760$	−16.6500	−0.603959
$761$	10.7734	0.390536	0.195268	−	0.980750i	$-0.437442\pi$
$761$	10.7734	0.390536	0.195268	+	0.980750i	$0.437442\pi$
$762$	−0.822711	−0.0298037
$763$	40.8594	1.47921
$764$	21.6577	0.783547
$765$	14.8636	0.537393
$766$	−3.95455	−0.142884
$767$	9.97227	0.360078
$768$	−29.6242	−1.06897
$769$	−38.3561	−1.38315	−0.691577	−	0.722302i	$-0.743084\pi$
$769$	−38.3561	−1.38315	−0.691577	+	0.722302i	$0.743084\pi$
$770$	13.2609	0.477891
$771$	69.7410	2.51166
$772$	−15.7907	−0.568319
$773$	−37.0614	−1.33301	−0.666503	−	0.745503i	$-0.732209\pi$
$773$	−37.0614	−1.33301	−0.666503	+	0.745503i	$0.732209\pi$
$774$	0.961222	0.0345504
$775$	31.9388	1.14728
$776$	−8.05683	−0.289223
$777$	−73.1006	−2.62247
$778$	3.87202	0.138819
$779$	34.0908	1.22143
$780$	19.9403	0.713978
$781$	−0.0899236	−0.00321772
$782$	0.334287	0.0119541
$783$	−13.0783	−0.467380
$784$	−0.104808	−0.00374313
$785$	54.8823	1.95883
$786$	1.57540	0.0561927
$787$	16.3598	0.583162	0.291581	−	0.956546i	$-0.405819\pi$
$787$	16.3598	0.583162	0.291581	+	0.956546i	$0.405819\pi$
$788$	4.71316	0.167900
$789$	−19.9879	−0.711588
$790$	−5.24064	−0.186454
$791$	−45.8761	−1.63117
$792$	−19.9731	−0.709712
$793$	6.12739	0.217590
$794$	−4.33791	−0.153947
$795$	−42.5715	−1.50986
$796$	−12.8561	−0.455671
$797$	34.3475	1.21665	0.608326	−	0.793687i	$-0.291841\pi$
$797$	34.3475	1.21665	0.608326	+	0.793687i	$0.291841\pi$
$798$	−7.62757	−0.270013
$799$	11.4830	0.406239
$800$	−27.7636	−0.981591
$801$	15.9328	0.562956
$802$	−8.13136	−0.287128
$803$	24.6965	0.871522
$804$	11.9931	0.422966
$805$	−13.6481	−0.481031
$806$	−0.833693	−0.0293656
$807$	−43.7084	−1.53861
$808$	7.54959	0.265594
$809$	−18.2194	−0.640558	−0.320279	−	0.947323i	$-0.603777\pi$
$809$	−18.2194	−0.640558	−0.320279	+	0.947323i	$0.603777\pi$
$810$	5.34442	0.187784
$811$	9.57679	0.336286	0.168143	−	0.985763i	$-0.446223\pi$
$811$	9.57679	0.336286	0.168143	+	0.985763i	$0.446223\pi$
$812$	−29.2100	−1.02507
$813$	57.7928	2.02688
$814$	13.8237	0.484519
$815$	14.0310	0.491484
$816$	−9.52881	−0.333575
$817$	4.44085	0.155366
$818$	−7.71073	−0.269599
$819$	10.4599	0.365499
$820$	57.0932	1.99378
$821$	−26.9812	−0.941651	−0.470826	−	0.882226i	$-0.656044\pi$
$821$	−26.9812	−0.941651	−0.470826	+	0.882226i	$0.656044\pi$
$822$	−13.7999	−0.481327
$823$	36.2689	1.26426	0.632128	−	0.774864i	$-0.282182\pi$
$823$	36.2689	1.26426	0.632128	+	0.774864i	$0.282182\pi$
$824$	1.71407	0.0597126
$825$	134.460	4.68129
$826$	−6.38845	−0.222282
$827$	33.3131	1.15841	0.579204	−	0.815182i	$-0.303363\pi$
$827$	33.3131	1.15841	0.579204	+	0.815182i	$0.303363\pi$
$828$	10.1174	0.351604
$829$	−28.7627	−0.998969	−0.499485	−	0.866323i	$-0.666477\pi$
$829$	−28.7627	−0.998969	−0.499485	+	0.866323i	$0.666477\pi$
$830$	−16.1967	−0.562194
$831$	−45.3893	−1.57454
$832$	−6.70852	−0.232576
$833$	−0.0288376	−0.000999163 0
$834$	6.76701	0.234322
$835$	91.0403	3.15058
$836$	−45.4167	−1.57077
$837$	−7.52928	−0.260250
$838$	4.22734	0.146031
$839$	25.9481	0.895828	0.447914	−	0.894077i	$-0.352167\pi$
$839$	25.9481	0.895828	0.447914	+	0.894077i	$0.352167\pi$
$840$	−25.9541	−0.895501
$841$	3.57278	0.123199
$842$	0.667457	0.0230021
$843$	17.2175	0.593003
$844$	−13.5700	−0.467099
$845$	−45.8653	−1.57781
$846$	−11.0377	−0.379484
$847$	44.4500	1.52732
$848$	15.3810	0.528187
$849$	−13.7681	−0.472521
$850$	−2.41186	−0.0827261
$851$	−14.2272	−0.487702
$852$	0.0866230	0.00296765
$853$	−16.9335	−0.579793	−0.289897	−	0.957058i	$-0.593621\pi$
$853$	−16.9335	−0.579793	−0.289897	+	0.957058i	$0.593621\pi$
$854$	−3.92534	−0.134322
$855$	−66.0068	−2.25739
$856$	−8.36715	−0.285983
$857$	−2.07954	−0.0710357	−0.0355179	−	0.999369i	$-0.511308\pi$
$857$	−2.07954	−0.0710357	−0.0355179	+	0.999369i	$0.511308\pi$
$858$	−3.50977	−0.119822
$859$	11.7902	0.402276	0.201138	−	0.979563i	$-0.435536\pi$
$859$	11.7902	0.402276	0.201138	+	0.979563i	$0.435536\pi$
$860$	7.43726	0.253609
$861$	53.1409	1.81104
$862$	4.23162	0.144130
$863$	17.9519	0.611088	0.305544	−	0.952178i	$-0.401162\pi$
$863$	17.9519	0.611088	0.305544	+	0.952178i	$0.401162\pi$
$864$	6.54500	0.222666
$865$	−82.9771	−2.82131
$866$	−1.33149	−0.0452458
$867$	−2.62183	−0.0890422
$868$	−16.8164	−0.570787
$869$	−29.0441	−0.985253
$870$	14.2448	0.482944
$871$	2.41318	0.0817676
$872$	15.1226	0.512114
$873$	−31.9403	−1.08102
$874$	−1.48452	−0.0502145
$875$	47.8194	1.61659
$876$	−23.7900	−0.803791
$877$	33.3232	1.12524	0.562622	−	0.826714i	$-0.309793\pi$
$877$	33.3232	1.12524	0.562622	+	0.826714i	$0.309793\pi$
$878$	−8.88458	−0.299840
$879$	78.1038	2.63438
$880$	−73.5686	−2.48000
$881$	−43.8971	−1.47893	−0.739466	−	0.673194i	$-0.764922\pi$
$881$	−43.8971	−1.47893	−0.739466	+	0.673194i	$0.764922\pi$
$882$	0.0277193	0.000933358 0
$883$	−8.39906	−0.282651	−0.141325	−	0.989963i	$-0.545136\pi$
$883$	−8.39906	−0.282651	−0.141325	+	0.989963i	$0.545136\pi$
$884$	−1.98228	−0.0666713
$885$	−98.0950	−3.29743
$886$	1.36802	0.0459595
$887$	26.6903	0.896173	0.448087	−	0.893990i	$-0.352106\pi$
$887$	26.6903	0.896173	0.448087	+	0.893990i	$0.352106\pi$
$888$	−27.0554	−0.907921
$889$	−3.33912	−0.111990
$890$	−3.91520	−0.131238
$891$	29.6193	0.992282
$892$	12.1496	0.406800
$893$	−50.9943	−1.70646
$894$	2.82055	0.0943334
$895$	−52.6604	−1.76024
$896$	19.3800	0.647439
$897$	3.61223	0.120609
$898$	−7.66968	−0.255940
$899$	18.7524	0.625428
$900$	−72.9965	−2.43322
$901$	4.23206	0.140990
$902$	−10.0492	−0.334602
$903$	6.92242	0.230364
$904$	−16.9793	−0.564724
$905$	66.5714	2.21291
$906$	−4.90196	−0.162857
$907$	−45.9762	−1.52662	−0.763308	−	0.646035i	$-0.776426\pi$
$907$	−45.9762	−1.52662	−0.763308	+	0.646035i	$0.776426\pi$
$908$	0.0274521	0.000911030 0
$909$	29.9294	0.992696
$910$	−2.57034	−0.0852059
$911$	32.8765	1.08925	0.544623	−	0.838681i	$-0.316673\pi$
$911$	32.8765	1.08925	0.544623	+	0.838681i	$0.316673\pi$
$912$	42.3160	1.40122
$913$	−89.7633	−2.97073
$914$	−9.63833	−0.318808
$915$	−60.2738	−1.99259
$916$	8.51236	0.281256
$917$	6.39406	0.211150
$918$	0.568573	0.0187657
$919$	18.5391	0.611549	0.305774	−	0.952104i	$-0.401085\pi$
$919$	18.5391	0.611549	0.305774	+	0.952104i	$0.401085\pi$
$920$	−5.05131	−0.166537
$921$	67.6782	2.23007
$922$	1.54272	0.0508067
$923$	0.0174297	0.000573706 0
$924$	−70.7957	−2.32901
$925$	102.648	3.37506
$926$	−5.46694	−0.179655
$927$	6.79524	0.223185
$928$	−16.3010	−0.535106
$929$	−39.8116	−1.30618	−0.653089	−	0.757281i	$-0.726527\pi$
$929$	−39.8116	−1.30618	−0.653089	+	0.757281i	$0.726527\pi$
$930$	8.20085	0.268917
$931$	0.128063	0.00419711
$932$	−37.9668	−1.24364
$933$	43.9863	1.44005
$934$	2.40137	0.0785754
$935$	−20.2423	−0.661993
$936$	3.87134	0.126539
$937$	−22.2493	−0.726853	−0.363426	−	0.931623i	$-0.618393\pi$
$937$	−22.2493	−0.726853	−0.363426	+	0.931623i	$0.618393\pi$
$938$	−1.54594	−0.0504766
$939$	40.3111	1.31550
$940$	−85.4021	−2.78551
$941$	−0.516810	−0.0168475	−0.00842377	−	0.999965i	$-0.502681\pi$
$941$	−0.516810	−0.0168475	−0.00842377	+	0.999965i	$0.502681\pi$
$942$	9.30548	0.303189
$943$	10.3426	0.336800
$944$	35.4416	1.15353
$945$	−23.2134	−0.755131
$946$	−1.30906	−0.0425612
$947$	27.0079	0.877639	0.438820	−	0.898575i	$-0.355397\pi$
$947$	27.0079	0.877639	0.438820	+	0.898575i	$0.355397\pi$
$948$	27.9780	0.908684
$949$	−4.78688	−0.155389
$950$	10.7107	0.347501
$951$	80.3402	2.60521
$952$	2.58011	0.0836220
$953$	20.3300	0.658552	0.329276	−	0.944234i	$-0.393195\pi$
$953$	20.3300	0.658552	0.329276	+	0.944234i	$0.393195\pi$
$954$	−4.06795	−0.131705
$955$	−42.8669	−1.38714
$956$	2.72544	0.0881470
$957$	78.9460	2.55196
$958$	−7.26581	−0.234748
$959$	−56.0094	−1.80864
$960$	65.9903	2.12983
$961$	−20.2041	−0.651745
$962$	−2.67941	−0.0863877
$963$	−33.1705	−1.06891
$964$	11.1033	0.357613
$965$	31.2544	1.00611
$966$	−2.31407	−0.0744540
$967$	8.99782	0.289350	0.144675	−	0.989479i	$-0.453786\pi$
$967$	8.99782	0.289350	0.144675	+	0.989479i	$0.453786\pi$
$968$	16.4515	0.528771
$969$	11.6432	0.374033
$970$	7.84877	0.252009
$971$	44.5143	1.42853	0.714266	−	0.699874i	$-0.246761\pi$
$971$	44.5143	1.42853	0.714266	+	0.699874i	$0.246761\pi$
$972$	−41.8580	−1.34260
$973$	27.4651	0.880491
$974$	7.38674	0.236686
$975$	−26.0621	−0.834654
$976$	21.7769	0.697061
$977$	−32.5160	−1.04028	−0.520140	−	0.854081i	$-0.674120\pi$
$977$	−32.5160	−1.04028	−0.520140	+	0.854081i	$0.674120\pi$
$978$	2.37900	0.0760721
$979$	−21.6984	−0.693483
$980$	0.214473	0.00685108
$981$	59.9515	1.91410
$982$	2.78906	0.0890024
$983$	8.56837	0.273289	0.136644	−	0.990620i	$-0.456368\pi$
$983$	8.56837	0.273289	0.136644	+	0.990620i	$0.456368\pi$
$984$	19.6681	0.626997
$985$	−9.32873	−0.297238
$986$	−1.41609	−0.0450974
$987$	−79.4901	−2.53020
$988$	8.80302	0.280061
$989$	1.34728	0.0428409
$990$	19.4573	0.618394
$991$	21.1157	0.670762	0.335381	−	0.942083i	$-0.391135\pi$
$991$	21.1157	0.670762	0.335381	+	0.942083i	$0.391135\pi$
$992$	−9.38460	−0.297961
$993$	−40.7265	−1.29242
$994$	−0.0111658	−0.000354159 0
$995$	25.4459	0.806690
$996$	86.4685	2.73986
$997$	17.3426	0.549246	0.274623	−	0.961552i	$-0.411447\pi$
$997$	17.3426	0.549246	0.274623	+	0.961552i	$0.411447\pi$
$998$	−6.47753	−0.205043
$999$	−24.1984	−0.765604

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.9	✓	19
3.2	odd	2		6579.2.a.t.1.11		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.9	✓	19	1.1	even	1	trivial
6579.2.a.t.1.11		19	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)

\(f(q)\)	\(=\)	\(q-0.248120 q^{2} -2.62183 q^{3} -1.93844 q^{4} +3.83673 q^{5} +0.650531 q^{6} +2.64030 q^{7} +0.977206 q^{8} +3.87401 q^{9} +O(q^{10})\)	\(q-0.248120 q^{2} -2.62183 q^{3} -1.93844 q^{4} +3.83673 q^{5} +0.650531 q^{6} +2.64030 q^{7} +0.977206 q^{8} +3.87401 q^{9} -0.951972 q^{10} -5.27591 q^{11} +5.08226 q^{12} +1.02262 q^{13} -0.655111 q^{14} -10.0593 q^{15} +3.63441 q^{16} +1.00000 q^{17} -0.961222 q^{18} -4.44085 q^{19} -7.43726 q^{20} -6.92242 q^{21} +1.30906 q^{22} -1.34728 q^{23} -2.56207 q^{24} +9.72052 q^{25} -0.253733 q^{26} -2.29152 q^{27} -5.11805 q^{28} +5.70726 q^{29} +2.49591 q^{30} +3.28571 q^{31} -2.85618 q^{32} +13.8326 q^{33} -0.248120 q^{34} +10.1301 q^{35} -7.50953 q^{36} +10.5600 q^{37} +1.10187 q^{38} -2.68114 q^{39} +3.74928 q^{40} -7.67664 q^{41} +1.71759 q^{42} -1.00000 q^{43} +10.2270 q^{44} +14.8636 q^{45} +0.334287 q^{46} +11.4830 q^{47} -9.52881 q^{48} -0.0288376 q^{49} -2.41186 q^{50} -2.62183 q^{51} -1.98228 q^{52} +4.23206 q^{53} +0.568573 q^{54} -20.2423 q^{55} +2.58011 q^{56} +11.6432 q^{57} -1.41609 q^{58} +9.75170 q^{59} +19.4993 q^{60} +5.99186 q^{61} -0.815253 q^{62} +10.2285 q^{63} -6.56014 q^{64} +3.92352 q^{65} -3.43214 q^{66} +2.35981 q^{67} -1.93844 q^{68} +3.53233 q^{69} -2.51349 q^{70} +0.0170442 q^{71} +3.78571 q^{72} -4.68100 q^{73} -2.62015 q^{74} -25.4856 q^{75} +8.60831 q^{76} -13.9300 q^{77} +0.665245 q^{78} +5.50504 q^{79} +13.9443 q^{80} -5.61406 q^{81} +1.90473 q^{82} +17.0138 q^{83} +13.4187 q^{84} +3.83673 q^{85} +0.248120 q^{86} -14.9635 q^{87} -5.15565 q^{88} +4.11273 q^{89} -3.68795 q^{90} +2.70002 q^{91} +2.61161 q^{92} -8.61460 q^{93} -2.84917 q^{94} -17.0384 q^{95} +7.48844 q^{96} -8.24476 q^{97} +0.00715519 q^{98} -20.4390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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