LMFDB - Embedded newform 8013.2.a.a.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99976 q^{2} +1.00000 q^{3} +1.99902 q^{4} -2.89200 q^{5} -1.99976 q^{6} +2.76984 q^{7} +0.00195305 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.99976 q^{2} +1.00000 q^{3} +1.99902 q^{4} -2.89200 q^{5} -1.99976 q^{6} +2.76984 q^{7} +0.00195305 q^{8} +1.00000 q^{9} +5.78329 q^{10} +0.706943 q^{11} +1.99902 q^{12} -4.98272 q^{13} -5.53900 q^{14} -2.89200 q^{15} -4.00195 q^{16} +0.962082 q^{17} -1.99976 q^{18} -3.81419 q^{19} -5.78118 q^{20} +2.76984 q^{21} -1.41371 q^{22} +1.84815 q^{23} +0.00195305 q^{24} +3.36367 q^{25} +9.96422 q^{26} +1.00000 q^{27} +5.53697 q^{28} +1.03115 q^{29} +5.78329 q^{30} +5.04395 q^{31} +7.99902 q^{32} +0.706943 q^{33} -1.92393 q^{34} -8.01038 q^{35} +1.99902 q^{36} -5.90020 q^{37} +7.62746 q^{38} -4.98272 q^{39} -0.00564823 q^{40} +7.06161 q^{41} -5.53900 q^{42} -0.944979 q^{43} +1.41320 q^{44} -2.89200 q^{45} -3.69585 q^{46} +5.33933 q^{47} -4.00195 q^{48} +0.672012 q^{49} -6.72651 q^{50} +0.962082 q^{51} -9.96057 q^{52} -7.96055 q^{53} -1.99976 q^{54} -2.04448 q^{55} +0.00540964 q^{56} -3.81419 q^{57} -2.06205 q^{58} +8.91668 q^{59} -5.78118 q^{60} +4.77968 q^{61} -10.0867 q^{62} +2.76984 q^{63} -7.99218 q^{64} +14.4100 q^{65} -1.41371 q^{66} -5.55311 q^{67} +1.92322 q^{68} +1.84815 q^{69} +16.0188 q^{70} +8.53602 q^{71} +0.00195305 q^{72} +5.32998 q^{73} +11.7990 q^{74} +3.36367 q^{75} -7.62466 q^{76} +1.95812 q^{77} +9.96422 q^{78} +4.84263 q^{79} +11.5736 q^{80} +1.00000 q^{81} -14.1215 q^{82} -17.5005 q^{83} +5.53697 q^{84} -2.78234 q^{85} +1.88973 q^{86} +1.03115 q^{87} +0.00138070 q^{88} -15.6583 q^{89} +5.78329 q^{90} -13.8013 q^{91} +3.69450 q^{92} +5.04395 q^{93} -10.6774 q^{94} +11.0306 q^{95} +7.99902 q^{96} +5.99221 q^{97} -1.34386 q^{98} +0.706943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * 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 $

$2$	−1.99976	−1.41404	−0.707020	−	0.707193i	$-0.749961\pi$
$2$	−1.99976	−1.41404	−0.707020	+	0.707193i	$0.749961\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.99902	0.999512
$5$	−2.89200	−1.29334	−0.646671	−	0.762769i	$-0.723839\pi$
$5$	−2.89200	−1.29334	−0.646671	+	0.762769i	$0.723839\pi$
$6$	−1.99976	−0.816397
$7$	2.76984	1.04690	0.523450	−	0.852056i	$-0.324645\pi$
$7$	2.76984	1.04690	0.523450	+	0.852056i	$0.324645\pi$
$8$	0.00195305	0.000690509 0
$9$	1.00000	0.333333
$10$	5.78329	1.82884
$11$	0.706943	0.213151	0.106576	−	0.994305i	$-0.466011\pi$
$11$	0.706943	0.213151	0.106576	+	0.994305i	$0.466011\pi$
$12$	1.99902	0.577068
$13$	−4.98272	−1.38196	−0.690979	−	0.722875i	$-0.742820\pi$
$13$	−4.98272	−1.38196	−0.690979	+	0.722875i	$0.742820\pi$
$14$	−5.53900	−1.48036
$15$	−2.89200	−0.746711
$16$	−4.00195	−1.00049
$17$	0.962082	0.233339	0.116670	−	0.993171i	$-0.462778\pi$
$17$	0.962082	0.233339	0.116670	+	0.993171i	$0.462778\pi$
$18$	−1.99976	−0.471347
$19$	−3.81419	−0.875036	−0.437518	−	0.899210i	$-0.644142\pi$
$19$	−3.81419	−0.875036	−0.437518	+	0.899210i	$0.644142\pi$
$20$	−5.78118	−1.29271
$21$	2.76984	0.604429
$22$	−1.41371	−0.301405
$23$	1.84815	0.385366	0.192683	−	0.981261i	$-0.438281\pi$
$23$	1.84815	0.385366	0.192683	+	0.981261i	$0.438281\pi$
$24$	0.00195305	0.000398665 0
$25$	3.36367	0.672733
$26$	9.96422	1.95414
$27$	1.00000	0.192450
$28$	5.53697	1.04639
$29$	1.03115	0.191480	0.0957399	−	0.995406i	$-0.469478\pi$
$29$	1.03115	0.191480	0.0957399	+	0.995406i	$0.469478\pi$
$30$	5.78329	1.05588
$31$	5.04395	0.905921	0.452960	−	0.891531i	$-0.350368\pi$
$31$	5.04395	0.905921	0.452960	+	0.891531i	$0.350368\pi$
$32$	7.99902	1.41404
$33$	0.706943	0.123063
$34$	−1.92393	−0.329951
$35$	−8.01038	−1.35400
$36$	1.99902	0.333171
$37$	−5.90020	−0.969988	−0.484994	−	0.874518i	$-0.661178\pi$
$37$	−5.90020	−0.969988	−0.484994	+	0.874518i	$0.661178\pi$
$38$	7.62746	1.23734
$39$	−4.98272	−0.797874
$40$	−0.00564823	−0.000893064 0
$41$	7.06161	1.10284	0.551419	−	0.834229i	$-0.314087\pi$
$41$	7.06161	1.10284	0.551419	+	0.834229i	$0.314087\pi$
$42$	−5.53900	−0.854687
$43$	−0.944979	−0.144108	−0.0720539	−	0.997401i	$-0.522955\pi$
$43$	−0.944979	−0.144108	−0.0720539	+	0.997401i	$0.522955\pi$
$44$	1.41320	0.213047
$45$	−2.89200	−0.431114
$46$	−3.69585	−0.544923
$47$	5.33933	0.778821	0.389411	−	0.921064i	$-0.372679\pi$
$47$	5.33933	0.778821	0.389411	+	0.921064i	$0.372679\pi$
$48$	−4.00195	−0.577632
$49$	0.672012	0.0960017
$50$	−6.72651	−0.951272
$51$	0.962082	0.134718
$52$	−9.96057	−1.38128
$53$	−7.96055	−1.09347	−0.546733	−	0.837307i	$-0.684129\pi$
$53$	−7.96055	−1.09347	−0.546733	+	0.837307i	$0.684129\pi$
$54$	−1.99976	−0.272132
$55$	−2.04448	−0.275678
$56$	0.00540964	0.000722894 0
$57$	−3.81419	−0.505202
$58$	−2.06205	−0.270760
$59$	8.91668	1.16085	0.580426	−	0.814313i	$-0.302886\pi$
$59$	8.91668	1.16085	0.580426	+	0.814313i	$0.302886\pi$
$60$	−5.78118	−0.746347
$61$	4.77968	0.611975	0.305987	−	0.952036i	$-0.401013\pi$
$61$	4.77968	0.611975	0.305987	+	0.952036i	$0.401013\pi$
$62$	−10.0867	−1.28101
$63$	2.76984	0.348967
$64$	−7.99218	−0.999023
$65$	14.4100	1.78734
$66$	−1.41371	−0.174016
$67$	−5.55311	−0.678420	−0.339210	−	0.940711i	$-0.610160\pi$
$67$	−5.55311	−0.678420	−0.339210	+	0.940711i	$0.610160\pi$
$68$	1.92322	0.233225
$69$	1.84815	0.222491
$70$	16.0188	1.91461
$71$	8.53602	1.01304	0.506519	−	0.862229i	$-0.330932\pi$
$71$	8.53602	1.01304	0.506519	+	0.862229i	$0.330932\pi$
$72$	0.00195305	0.000230170 0
$73$	5.32998	0.623827	0.311914	−	0.950110i	$-0.399030\pi$
$73$	5.32998	0.623827	0.311914	+	0.950110i	$0.399030\pi$
$74$	11.7990	1.37160
$75$	3.36367	0.388403
$76$	−7.62466	−0.874609
$77$	1.95812	0.223148
$78$	9.96422	1.12823
$79$	4.84263	0.544839	0.272419	−	0.962179i	$-0.412176\pi$
$79$	4.84263	0.544839	0.272419	+	0.962179i	$0.412176\pi$
$80$	11.5736	1.29397
$81$	1.00000	0.111111
$82$	−14.1215	−1.55946
$83$	−17.5005	−1.92093	−0.960463	−	0.278408i	$-0.910193\pi$
$83$	−17.5005	−1.92093	−0.960463	+	0.278408i	$0.910193\pi$
$84$	5.53697	0.604133
$85$	−2.78234	−0.301787
$86$	1.88973	0.203774
$87$	1.03115	0.110551
$88$	0.00138070	0.000147183 0
$89$	−15.6583	−1.65977	−0.829887	−	0.557932i	$-0.811595\pi$
$89$	−15.6583	−1.65977	−0.829887	+	0.557932i	$0.811595\pi$
$90$	5.78329	0.609613
$91$	−13.8013	−1.44677
$92$	3.69450	0.385178
$93$	5.04395	0.523034
$94$	−10.6774	−1.10129
$95$	11.0306	1.13172
$96$	7.99902	0.816397
$97$	5.99221	0.608417	0.304209	−	0.952605i	$-0.401608\pi$
$97$	5.99221	0.608417	0.304209	+	0.952605i	$0.401608\pi$
$98$	−1.34386	−0.135750
$99$	0.706943	0.0710505
$100$	6.72405	0.672405
$101$	17.2470	1.71614	0.858071	−	0.513530i	$-0.171663\pi$
$101$	17.2470	1.71614	0.858071	+	0.513530i	$0.171663\pi$
$102$	−1.92393	−0.190497
$103$	−16.4756	−1.62339	−0.811694	−	0.584083i	$-0.801454\pi$
$103$	−16.4756	−1.62339	−0.811694	+	0.584083i	$0.801454\pi$
$104$	−0.00973152	−0.000954254 0
$105$	−8.01038	−0.781733
$106$	15.9192	1.54620
$107$	2.48053	0.239802	0.119901	−	0.992786i	$-0.461742\pi$
$107$	2.48053	0.239802	0.119901	+	0.992786i	$0.461742\pi$
$108$	1.99902	0.192356
$109$	−14.0850	−1.34910	−0.674550	−	0.738229i	$-0.735662\pi$
$109$	−14.0850	−1.34910	−0.674550	+	0.738229i	$0.735662\pi$
$110$	4.08846	0.389819
$111$	−5.90020	−0.560023
$112$	−11.0848	−1.04741
$113$	−10.1792	−0.957575	−0.478787	−	0.877931i	$-0.658924\pi$
$113$	−10.1792	−0.957575	−0.478787	+	0.877931i	$0.658924\pi$
$114$	7.62746	0.714377
$115$	−5.34485	−0.498410
$116$	2.06129	0.191386
$117$	−4.98272	−0.460653
$118$	−17.8312	−1.64149
$119$	2.66481	0.244283
$120$	−0.00564823	−0.000515611 0
$121$	−10.5002	−0.954566
$122$	−9.55818	−0.865357
$123$	7.06161	0.636723
$124$	10.0830	0.905478
$125$	4.73228	0.423268
$126$	−5.53900	−0.493454
$127$	10.3003	0.914002	0.457001	−	0.889466i	$-0.348924\pi$
$127$	10.3003	0.914002	0.457001	+	0.889466i	$0.348924\pi$
$128$	−0.0156244	−0.00138102
$129$	−0.944979	−0.0832007
$130$	−28.8165	−2.52738
$131$	−4.63221	−0.404718	−0.202359	−	0.979311i	$-0.564861\pi$
$131$	−4.63221	−0.404718	−0.202359	+	0.979311i	$0.564861\pi$
$132$	1.41320	0.123003
$133$	−10.5647	−0.916076
$134$	11.1049	0.959314
$135$	−2.89200	−0.248904
$136$	0.00187900	0.000161123 0
$137$	6.87654	0.587502	0.293751	−	0.955882i	$-0.405096\pi$
$137$	6.87654	0.587502	0.293751	+	0.955882i	$0.405096\pi$
$138$	−3.69585	−0.314612
$139$	−13.0856	−1.10990	−0.554951	−	0.831883i	$-0.687263\pi$
$139$	−13.0856	−1.10990	−0.554951	+	0.831883i	$0.687263\pi$
$140$	−16.0129	−1.35334
$141$	5.33933	0.449653
$142$	−17.0699	−1.43248
$143$	−3.52250	−0.294566
$144$	−4.00195	−0.333496
$145$	−2.98209	−0.247649
$146$	−10.6587	−0.882117
$147$	0.672012	0.0554266
$148$	−11.7946	−0.969514
$149$	4.08813	0.334912	0.167456	−	0.985880i	$-0.446445\pi$
$149$	4.08813	0.334912	0.167456	+	0.985880i	$0.446445\pi$
$150$	−6.72651	−0.549217
$151$	−4.80564	−0.391078	−0.195539	−	0.980696i	$-0.562646\pi$
$151$	−4.80564	−0.391078	−0.195539	+	0.980696i	$0.562646\pi$
$152$	−0.00744932	−0.000604220 0
$153$	0.962082	0.0777797
$154$	−3.91576	−0.315541
$155$	−14.5871	−1.17167
$156$	−9.96057	−0.797484
$157$	−0.199538	−0.0159248	−0.00796242	−	0.999968i	$-0.502535\pi$
$157$	−0.199538	−0.0159248	−0.00796242	+	0.999968i	$0.502535\pi$
$158$	−9.68408	−0.770424
$159$	−7.96055	−0.631313
$160$	−23.1332	−1.82884
$161$	5.11908	0.403440
$162$	−1.99976	−0.157116
$163$	10.8944	0.853317	0.426658	−	0.904413i	$-0.359691\pi$
$163$	10.8944	0.853317	0.426658	+	0.904413i	$0.359691\pi$
$164$	14.1163	1.10230
$165$	−2.04448	−0.159163
$166$	34.9967	2.71627
$167$	−3.14151	−0.243097	−0.121549	−	0.992585i	$-0.538786\pi$
$167$	−3.14151	−0.243097	−0.121549	+	0.992585i	$0.538786\pi$
$168$	0.00540964	0.000417363 0
$169$	11.8275	0.909807
$170$	5.56400	0.426740
$171$	−3.81419	−0.291679
$172$	−1.88903	−0.144038
$173$	−3.87424	−0.294553	−0.147277	−	0.989095i	$-0.547051\pi$
$173$	−3.87424	−0.294553	−0.147277	+	0.989095i	$0.547051\pi$
$174$	−2.06205	−0.156324
$175$	9.31681	0.704285
$176$	−2.82915	−0.213255
$177$	8.91668	0.670218
$178$	31.3127	2.34699
$179$	17.0911	1.27745	0.638724	−	0.769436i	$-0.279463\pi$
$179$	17.0911	1.27745	0.638724	+	0.769436i	$0.279463\pi$
$180$	−5.78118	−0.430903
$181$	−5.16308	−0.383769	−0.191884	−	0.981418i	$-0.561460\pi$
$181$	−5.16308	−0.383769	−0.191884	+	0.981418i	$0.561460\pi$
$182$	27.5993	2.04580
$183$	4.77968	0.353324
$184$	0.00360954	0.000266098 0
$185$	17.0634	1.25453
$186$	−10.0867	−0.739591
$187$	0.680137	0.0497366
$188$	10.6734	0.778441
$189$	2.76984	0.201476
$190$	−22.0586	−1.60030
$191$	6.74637	0.488150	0.244075	−	0.969756i	$-0.421516\pi$
$191$	6.74637	0.488150	0.244075	+	0.969756i	$0.421516\pi$
$192$	−7.99218	−0.576786
$193$	−18.1149	−1.30394	−0.651969	−	0.758246i	$-0.726057\pi$
$193$	−18.1149	−1.30394	−0.651969	+	0.758246i	$0.726057\pi$
$194$	−11.9830	−0.860327
$195$	14.4100	1.03192
$196$	1.34337	0.0959548
$197$	−12.0415	−0.857919	−0.428960	−	0.903324i	$-0.641120\pi$
$197$	−12.0415	−0.857919	−0.428960	+	0.903324i	$0.641120\pi$
$198$	−1.41371	−0.100468
$199$	−13.8820	−0.984070	−0.492035	−	0.870575i	$-0.663747\pi$
$199$	−13.8820	−0.984070	−0.492035	+	0.870575i	$0.663747\pi$
$200$	0.00656942	0.000464528 0
$201$	−5.55311	−0.391686
$202$	−34.4898	−2.42670
$203$	2.85612	0.200460
$204$	1.92322	0.134653
$205$	−20.4222	−1.42635
$206$	32.9471	2.29554
$207$	1.84815	0.128455
$208$	19.9406	1.38263
$209$	−2.69642	−0.186515
$210$	16.0188	1.10540
$211$	4.83472	0.332836	0.166418	−	0.986055i	$-0.446780\pi$
$211$	4.83472	0.332836	0.166418	+	0.986055i	$0.446780\pi$
$212$	−15.9133	−1.09293
$213$	8.53602	0.584878
$214$	−4.96045	−0.339089
$215$	2.73288	0.186381
$216$	0.00195305	0.000132888 0
$217$	13.9709	0.948409
$218$	28.1666	1.90768
$219$	5.32998	0.360167
$220$	−4.08696	−0.275543
$221$	−4.79378	−0.322465
$222$	11.7990	0.791895
$223$	−6.95926	−0.466027	−0.233013	−	0.972474i	$-0.574859\pi$
$223$	−6.95926	−0.466027	−0.233013	+	0.972474i	$0.574859\pi$
$224$	22.1560	1.48036
$225$	3.36367	0.224244
$226$	20.3558	1.35405
$227$	17.7523	1.17826	0.589131	−	0.808037i	$-0.299470\pi$
$227$	17.7523	1.17826	0.589131	+	0.808037i	$0.299470\pi$
$228$	−7.62466	−0.504956
$229$	−6.15898	−0.406997	−0.203498	−	0.979075i	$-0.565231\pi$
$229$	−6.15898	−0.406997	−0.203498	+	0.979075i	$0.565231\pi$
$230$	10.6884	0.704772
$231$	1.95812	0.128835
$232$	0.00201389	0.000132218 0
$233$	15.1329	0.991392	0.495696	−	0.868496i	$-0.334913\pi$
$233$	15.1329	0.991392	0.495696	+	0.868496i	$0.334913\pi$
$234$	9.96422	0.651382
$235$	−15.4413	−1.00728
$236$	17.8246	1.16029
$237$	4.84263	0.314563
$238$	−5.32897	−0.345426
$239$	17.1296	1.10802	0.554011	−	0.832509i	$-0.313096\pi$
$239$	17.1296	1.10802	0.554011	+	0.832509i	$0.313096\pi$
$240$	11.5736	0.747076
$241$	3.47131	0.223607	0.111803	−	0.993730i	$-0.464337\pi$
$241$	3.47131	0.223607	0.111803	+	0.993730i	$0.464337\pi$
$242$	20.9979	1.34980
$243$	1.00000	0.0641500
$244$	9.55468	0.611676
$245$	−1.94346	−0.124163
$246$	−14.1215	−0.900353
$247$	19.0051	1.20926
$248$	0.00985111	0.000625546 0
$249$	−17.5005	−1.10905
$250$	−9.46340	−0.598518
$251$	3.26218	0.205907	0.102953	−	0.994686i	$-0.467171\pi$
$251$	3.26218	0.205907	0.102953	+	0.994686i	$0.467171\pi$
$252$	5.53697	0.348797
$253$	1.30654	0.0821413
$254$	−20.5980	−1.29244
$255$	−2.78234	−0.174237
$256$	16.0156	1.00098
$257$	29.5355	1.84237	0.921187	−	0.389120i	$-0.127221\pi$
$257$	29.5355	1.84237	0.921187	+	0.389120i	$0.127221\pi$
$258$	1.88973	0.117649
$259$	−16.3426	−1.01548
$260$	28.8060	1.78647
$261$	1.03115	0.0638266
$262$	9.26328	0.572288
$263$	−18.2608	−1.12601	−0.563003	−	0.826455i	$-0.690354\pi$
$263$	−18.2608	−1.12601	−0.563003	+	0.826455i	$0.690354\pi$
$264$	0.00138070	8.49761e−5 0
$265$	23.0219	1.41422
$266$	21.1268	1.29537
$267$	−15.6583	−0.958271
$268$	−11.1008	−0.678089
$269$	−32.2512	−1.96639	−0.983195	−	0.182558i	$-0.941562\pi$
$269$	−32.2512	−1.96639	−0.983195	+	0.182558i	$0.941562\pi$
$270$	5.78329	0.351960
$271$	10.0497	0.610478	0.305239	−	0.952276i	$-0.401264\pi$
$271$	10.0497	0.610478	0.305239	+	0.952276i	$0.401264\pi$
$272$	−3.85021	−0.233453
$273$	−13.8013	−0.835295
$274$	−13.7514	−0.830752
$275$	2.37792	0.143394
$276$	3.69450	0.222383
$277$	17.2623	1.03719	0.518596	−	0.855020i	$-0.326455\pi$
$277$	17.2623	1.03719	0.518596	+	0.855020i	$0.326455\pi$
$278$	26.1679	1.56945
$279$	5.04395	0.301974
$280$	−0.0156447	−0.000934949 0
$281$	−17.1094	−1.02066	−0.510330	−	0.859979i	$-0.670477\pi$
$281$	−17.1094	−1.02066	−0.510330	+	0.859979i	$0.670477\pi$
$282$	−10.6774	−0.635827
$283$	30.0871	1.78849	0.894247	−	0.447575i	$-0.147712\pi$
$283$	30.0871	1.78849	0.894247	+	0.447575i	$0.147712\pi$
$284$	17.0637	1.01254
$285$	11.0306	0.653399
$286$	7.04414	0.416529
$287$	19.5595	1.15456
$288$	7.99902	0.471347
$289$	−16.0744	−0.945553
$290$	5.96345	0.350186
$291$	5.99221	0.351270
$292$	10.6548	0.623523
$293$	19.2438	1.12424	0.562118	−	0.827057i	$-0.309987\pi$
$293$	19.2438	1.12424	0.562118	+	0.827057i	$0.309987\pi$
$294$	−1.34386	−0.0783755
$295$	−25.7870	−1.50138
$296$	−0.0115234	−0.000669785 0
$297$	0.706943	0.0410210
$298$	−8.17526	−0.473580
$299$	−9.20881	−0.532560
$300$	6.72405	0.388213
$301$	−2.61744	−0.150867
$302$	9.61011	0.553000
$303$	17.2470	0.990815
$304$	15.2642	0.875463
$305$	−13.8228	−0.791493
$306$	−1.92393	−0.109984
$307$	−19.7298	−1.12604	−0.563020	−	0.826443i	$-0.690361\pi$
$307$	−19.7298	−1.12604	−0.563020	+	0.826443i	$0.690361\pi$
$308$	3.91433	0.223039
$309$	−16.4756	−0.937263
$310$	29.1707	1.65678
$311$	−13.2965	−0.753977	−0.376989	−	0.926218i	$-0.623040\pi$
$311$	−13.2965	−0.753977	−0.376989	+	0.926218i	$0.623040\pi$
$312$	−0.00973152	−0.000550939 0
$313$	−16.7866	−0.948834	−0.474417	−	0.880300i	$-0.657341\pi$
$313$	−16.7866	−0.948834	−0.474417	+	0.880300i	$0.657341\pi$
$314$	0.399027	0.0225184
$315$	−8.01038	−0.451334
$316$	9.68054	0.544573
$317$	−16.2455	−0.912438	−0.456219	−	0.889868i	$-0.650797\pi$
$317$	−16.2455	−0.912438	−0.456219	+	0.889868i	$0.650797\pi$
$318$	15.9192	0.892702
$319$	0.728965	0.0408142
$320$	23.1134	1.29208
$321$	2.48053	0.138450
$322$	−10.2369	−0.570481
$323$	−3.66957	−0.204180
$324$	1.99902	0.111057
$325$	−16.7602	−0.929689
$326$	−21.7862	−1.20662
$327$	−14.0850	−0.778903
$328$	0.0137917	0.000761519 0
$329$	14.7891	0.815349
$330$	4.08846	0.225062
$331$	22.7350	1.24963	0.624816	−	0.780772i	$-0.285174\pi$
$331$	22.7350	1.24963	0.624816	+	0.780772i	$0.285174\pi$
$332$	−34.9838	−1.91999
$333$	−5.90020	−0.323329
$334$	6.28225	0.343750
$335$	16.0596	0.877429
$336$	−11.0848	−0.604724
$337$	−15.3334	−0.835264	−0.417632	−	0.908616i	$-0.637140\pi$
$337$	−15.3334	−0.835264	−0.417632	+	0.908616i	$0.637140\pi$
$338$	−23.6521	−1.28650
$339$	−10.1792	−0.552856
$340$	−5.56196	−0.301640
$341$	3.56579	0.193098
$342$	7.62746	0.412446
$343$	−17.5275	−0.946397
$344$	−0.00184559	−9.95077e−5 0
$345$	−5.34485	−0.287757
$346$	7.74754	0.416510
$347$	−3.82442	−0.205306	−0.102653	−	0.994717i	$-0.532733\pi$
$347$	−3.82442	−0.205306	−0.102653	+	0.994717i	$0.532733\pi$
$348$	2.06129	0.110497
$349$	−4.47863	−0.239735	−0.119868	−	0.992790i	$-0.538247\pi$
$349$	−4.47863	−0.239735	−0.119868	+	0.992790i	$0.538247\pi$
$350$	−18.6314	−0.995888
$351$	−4.98272	−0.265958
$352$	5.65485	0.301405
$353$	−34.9551	−1.86047	−0.930237	−	0.366959i	$-0.880399\pi$
$353$	−34.9551	−1.86047	−0.930237	+	0.366959i	$0.880399\pi$
$354$	−17.8312	−0.947716
$355$	−24.6862	−1.31021
$356$	−31.3012	−1.65896
$357$	2.66481	0.141037
$358$	−34.1780	−1.80636
$359$	−27.6993	−1.46191	−0.730956	−	0.682424i	$-0.760926\pi$
$359$	−27.6993	−1.46191	−0.730956	+	0.682424i	$0.760926\pi$
$360$	−0.00564823	−0.000297688 0
$361$	−4.45193	−0.234312
$362$	10.3249	0.542665
$363$	−10.5002	−0.551119
$364$	−27.5892	−1.44607
$365$	−15.4143	−0.806822
$366$	−9.55818	−0.499614
$367$	−6.07260	−0.316987	−0.158494	−	0.987360i	$-0.550664\pi$
$367$	−6.07260	−0.316987	−0.158494	+	0.987360i	$0.550664\pi$
$368$	−7.39621	−0.385554
$369$	7.06161	0.367612
$370$	−34.1226	−1.77395
$371$	−22.0494	−1.14475
$372$	10.0830	0.522778
$373$	−15.1892	−0.786466	−0.393233	−	0.919439i	$-0.628643\pi$
$373$	−15.1892	−0.786466	−0.393233	+	0.919439i	$0.628643\pi$
$374$	−1.36011	−0.0703295
$375$	4.73228	0.244374
$376$	0.0104280	0.000537783 0
$377$	−5.13793	−0.264617
$378$	−5.53900	−0.284896
$379$	−2.76386	−0.141970	−0.0709849	−	0.997477i	$-0.522614\pi$
$379$	−2.76386	−0.141970	−0.0709849	+	0.997477i	$0.522614\pi$
$380$	22.0505	1.13117
$381$	10.3003	0.527699
$382$	−13.4911	−0.690265
$383$	35.7707	1.82780	0.913899	−	0.405943i	$-0.133057\pi$
$383$	35.7707	1.82780	0.913899	+	0.405943i	$0.133057\pi$
$384$	−0.0156244	−0.000797330 0
$385$	−5.66288	−0.288607
$386$	36.2253	1.84382
$387$	−0.944979	−0.0480360
$388$	11.9786	0.608120
$389$	15.5653	0.789193	0.394596	−	0.918855i	$-0.370884\pi$
$389$	15.5653	0.789193	0.394596	+	0.918855i	$0.370884\pi$
$390$	−28.8165	−1.45918
$391$	1.77807	0.0899210
$392$	0.00131247	6.62900e−5 0
$393$	−4.63221	−0.233664
$394$	24.0800	1.21313
$395$	−14.0049	−0.704663
$396$	1.41320	0.0710158
$397$	−36.4845	−1.83110	−0.915552	−	0.402200i	$-0.868246\pi$
$397$	−36.4845	−1.83110	−0.915552	+	0.402200i	$0.868246\pi$
$398$	27.7607	1.39152
$399$	−10.5647	−0.528897
$400$	−13.4612	−0.673061
$401$	8.39162	0.419058	0.209529	−	0.977802i	$-0.432807\pi$
$401$	8.39162	0.419058	0.209529	+	0.977802i	$0.432807\pi$
$402$	11.1049	0.553860
$403$	−25.1326	−1.25194
$404$	34.4772	1.71530
$405$	−2.89200	−0.143705
$406$	−5.71155	−0.283459
$407$	−4.17111	−0.206754
$408$	0.00187900	9.30242e−5 0
$409$	28.2684	1.39778	0.698890	−	0.715229i	$-0.253678\pi$
$409$	28.2684	1.39778	0.698890	+	0.715229i	$0.253678\pi$
$410$	40.8393	2.01691
$411$	6.87654	0.339195
$412$	−32.9351	−1.62259
$413$	24.6978	1.21530
$414$	−3.69585	−0.181641
$415$	50.6114	2.48441
$416$	−39.8569	−1.95414
$417$	−13.0856	−0.640803
$418$	5.39218	0.263740
$419$	−27.2612	−1.33180	−0.665899	−	0.746042i	$-0.731952\pi$
$419$	−27.2612	−1.33180	−0.665899	+	0.746042i	$0.731952\pi$
$420$	−16.0129	−0.781351
$421$	−19.6599	−0.958163	−0.479081	−	0.877771i	$-0.659030\pi$
$421$	−19.6599	−0.958163	−0.479081	+	0.877771i	$0.659030\pi$
$422$	−9.66826	−0.470644
$423$	5.33933	0.259607
$424$	−0.0155474	−0.000755047 0
$425$	3.23612	0.156975
$426$	−17.0699	−0.827042
$427$	13.2389	0.640677
$428$	4.95863	0.239685
$429$	−3.52250	−0.170068
$430$	−5.46509	−0.263550
$431$	−16.4855	−0.794079	−0.397040	−	0.917801i	$-0.629962\pi$
$431$	−16.4855	−0.794079	−0.397040	+	0.917801i	$0.629962\pi$
$432$	−4.00195	−0.192544
$433$	19.6018	0.942003	0.471001	−	0.882133i	$-0.343893\pi$
$433$	19.6018	0.942003	0.471001	+	0.882133i	$0.343893\pi$
$434$	−27.9385	−1.34109
$435$	−2.98209	−0.142980
$436$	−28.1563	−1.34844
$437$	−7.04920	−0.337209
$438$	−10.6587	−0.509291
$439$	19.3663	0.924301	0.462151	−	0.886802i	$-0.347078\pi$
$439$	19.3663	0.924301	0.462151	+	0.886802i	$0.347078\pi$
$440$	−0.00399298	−0.000190358 0
$441$	0.672012	0.0320006
$442$	9.58640	0.455978
$443$	10.2941	0.489087	0.244544	−	0.969638i	$-0.421362\pi$
$443$	10.2941	0.489087	0.244544	+	0.969638i	$0.421362\pi$
$444$	−11.7946	−0.559749
$445$	45.2837	2.14665
$446$	13.9168	0.658981
$447$	4.08813	0.193362
$448$	−22.1371	−1.04588
$449$	3.27435	0.154526	0.0772632	−	0.997011i	$-0.475382\pi$
$449$	3.27435	0.154526	0.0772632	+	0.997011i	$0.475382\pi$
$450$	−6.72651	−0.317091
$451$	4.99215	0.235071
$452$	−20.3484	−0.957107
$453$	−4.80564	−0.225789
$454$	−35.5003	−1.66611
$455$	39.9135	1.87117
$456$	−0.00744932	−0.000348847 0
$457$	−22.2079	−1.03884	−0.519422	−	0.854518i	$-0.673853\pi$
$457$	−22.2079	−1.03884	−0.519422	+	0.854518i	$0.673853\pi$
$458$	12.3165	0.575510
$459$	0.962082	0.0449061
$460$	−10.6845	−0.498167
$461$	−33.6277	−1.56620	−0.783099	−	0.621897i	$-0.786362\pi$
$461$	−33.6277	−1.56620	−0.783099	+	0.621897i	$0.786362\pi$
$462$	−3.91576	−0.182178
$463$	−15.1051	−0.701995	−0.350998	−	0.936376i	$-0.614157\pi$
$463$	−15.1051	−0.701995	−0.350998	+	0.936376i	$0.614157\pi$
$464$	−4.12662	−0.191573
$465$	−14.5871	−0.676461
$466$	−30.2622	−1.40187
$467$	−26.9991	−1.24937	−0.624684	−	0.780878i	$-0.714772\pi$
$467$	−26.9991	−1.24937	−0.624684	+	0.780878i	$0.714772\pi$
$468$	−9.96057	−0.460428
$469$	−15.3812	−0.710239
$470$	30.8789	1.42434
$471$	−0.199538	−0.00919421
$472$	0.0174147	0.000801578 0
$473$	−0.668046	−0.0307168
$474$	−9.68408	−0.444805
$475$	−12.8297	−0.588666
$476$	5.32702	0.244164
$477$	−7.96055	−0.364488
$478$	−34.2551	−1.56679
$479$	4.79335	0.219014	0.109507	−	0.993986i	$-0.465073\pi$
$479$	4.79335	0.219014	0.109507	+	0.993986i	$0.465073\pi$
$480$	−23.1332	−1.05588
$481$	29.3991	1.34048
$482$	−6.94177	−0.316189
$483$	5.11908	0.232926
$484$	−20.9902	−0.954100
$485$	−17.3295	−0.786891
$486$	−1.99976	−0.0907108
$487$	10.6727	0.483625	0.241812	−	0.970323i	$-0.422258\pi$
$487$	10.6727	0.483625	0.241812	+	0.970323i	$0.422258\pi$
$488$	0.00933496	0.000422574 0
$489$	10.8944	0.492663
$490$	3.88644	0.175572
$491$	−3.04999	−0.137644	−0.0688221	−	0.997629i	$-0.521924\pi$
$491$	−3.04999	−0.137644	−0.0688221	+	0.997629i	$0.521924\pi$
$492$	14.1163	0.636413
$493$	0.992051	0.0446797
$494$	−38.0055	−1.70995
$495$	−2.04448	−0.0918925
$496$	−20.1857	−0.906363
$497$	23.6434	1.06055
$498$	34.9967	1.56824
$499$	−18.9881	−0.850023	−0.425011	−	0.905188i	$-0.639730\pi$
$499$	−18.9881	−0.850023	−0.425011	+	0.905188i	$0.639730\pi$
$500$	9.45994	0.423061
$501$	−3.14151	−0.140352
$502$	−6.52356	−0.291161
$503$	−20.1893	−0.900198	−0.450099	−	0.892979i	$-0.648611\pi$
$503$	−20.1893	−0.900198	−0.450099	+	0.892979i	$0.648611\pi$
$504$	0.00540964	0.000240965 0
$505$	−49.8784	−2.21956
$506$	−2.61276	−0.116151
$507$	11.8275	0.525278
$508$	20.5905	0.913555
$509$	−38.8308	−1.72114	−0.860572	−	0.509329i	$-0.829894\pi$
$509$	−38.8308	−1.72114	−0.860572	+	0.509329i	$0.829894\pi$
$510$	5.56400	0.246378
$511$	14.7632	0.653085
$512$	−31.9961	−1.41404
$513$	−3.81419	−0.168401
$514$	−59.0638	−2.60519
$515$	47.6474	2.09959
$516$	−1.88903	−0.0831601
$517$	3.77460	0.166007
$518$	32.6813	1.43593
$519$	−3.87424	−0.170060
$520$	0.0281435	0.00123418
$521$	0.995143	0.0435980	0.0217990	−	0.999762i	$-0.493061\pi$
$521$	0.995143	0.0435980	0.0217990	+	0.999762i	$0.493061\pi$
$522$	−2.06205	−0.0902534
$523$	6.17321	0.269936	0.134968	−	0.990850i	$-0.456907\pi$
$523$	6.17321	0.269936	0.134968	+	0.990850i	$0.456907\pi$
$524$	−9.25989	−0.404520
$525$	9.31681	0.406619
$526$	36.5171	1.59222
$527$	4.85270	0.211387
$528$	−2.82915	−0.123123
$529$	−19.5843	−0.851493
$530$	−46.0382	−1.99977
$531$	8.91668	0.386951
$532$	−21.1191	−0.915629
$533$	−35.1860	−1.52407
$534$	31.3127	1.35503
$535$	−7.17369	−0.310146
$536$	−0.0108455	−0.000468455 0
$537$	17.0911	0.737535
$538$	64.4945	2.78056
$539$	0.475074	0.0204629
$540$	−5.78118	−0.248782
$541$	29.8674	1.28410	0.642051	−	0.766662i	$-0.278084\pi$
$541$	29.8674	1.28410	0.642051	+	0.766662i	$0.278084\pi$
$542$	−20.0970	−0.863241
$543$	−5.16308	−0.221569
$544$	7.69571	0.329951
$545$	40.7339	1.74485
$546$	27.5993	1.18114
$547$	−44.0448	−1.88322	−0.941609	−	0.336708i	$-0.890686\pi$
$547$	−44.0448	−1.88322	−0.941609	+	0.336708i	$0.890686\pi$
$548$	13.7464	0.587216
$549$	4.77968	0.203992
$550$	−4.75526	−0.202765
$551$	−3.93301	−0.167552
$552$	0.00360954	0.000153632 0
$553$	13.4133	0.570392
$554$	−34.5204	−1.46663
$555$	17.0634	0.724301
$556$	−26.1583	−1.10936
$557$	12.4278	0.526582	0.263291	−	0.964716i	$-0.415192\pi$
$557$	12.4278	0.526582	0.263291	+	0.964716i	$0.415192\pi$
$558$	−10.0867	−0.427003
$559$	4.70856	0.199151
$560$	32.0571	1.35466
$561$	0.680137	0.0287154
$562$	34.2146	1.44326
$563$	1.39293	0.0587050	0.0293525	−	0.999569i	$-0.490655\pi$
$563$	1.39293	0.0587050	0.0293525	+	0.999569i	$0.490655\pi$
$564$	10.6734	0.449433
$565$	29.4381	1.23847
$566$	−60.1669	−2.52900
$567$	2.76984	0.116322
$568$	0.0166713	0.000699512 0
$569$	−26.8197	−1.12434	−0.562171	−	0.827021i	$-0.690034\pi$
$569$	−26.8197	−1.12434	−0.562171	+	0.827021i	$0.690034\pi$
$570$	−22.0586	−0.923933
$571$	16.6047	0.694885	0.347442	−	0.937701i	$-0.387050\pi$
$571$	16.6047	0.694885	0.347442	+	0.937701i	$0.387050\pi$
$572$	−7.04156	−0.294422
$573$	6.74637	0.281834
$574$	−39.1143	−1.63260
$575$	6.21656	0.259248
$576$	−7.99218	−0.333008
$577$	32.4715	1.35181	0.675903	−	0.736991i	$-0.263754\pi$
$577$	32.4715	1.35181	0.675903	+	0.736991i	$0.263754\pi$
$578$	32.1449	1.33705
$579$	−18.1149	−0.752828
$580$	−5.96126	−0.247528
$581$	−48.4735	−2.01102
$582$	−11.9830	−0.496710
$583$	−5.62766	−0.233074
$584$	0.0104097	0.000430758 0
$585$	14.4100	0.595781
$586$	−38.4829	−1.58972
$587$	44.9069	1.85351	0.926753	−	0.375672i	$-0.122588\pi$
$587$	44.9069	1.85351	0.926753	+	0.375672i	$0.122588\pi$
$588$	1.34337	0.0553995
$589$	−19.2386	−0.792713
$590$	51.5678	2.12301
$591$	−12.0415	−0.495320
$592$	23.6123	0.970461
$593$	3.82250	0.156971	0.0784856	−	0.996915i	$-0.474992\pi$
$593$	3.82250	0.156971	0.0784856	+	0.996915i	$0.474992\pi$
$594$	−1.41371	−0.0580054
$595$	−7.70664	−0.315941
$596$	8.17226	0.334749
$597$	−13.8820	−0.568153
$598$	18.4154	0.753061
$599$	13.1104	0.535674	0.267837	−	0.963464i	$-0.413691\pi$
$599$	13.1104	0.535674	0.267837	+	0.963464i	$0.413691\pi$
$600$	0.00656942	0.000268195 0
$601$	−39.1072	−1.59522	−0.797609	−	0.603175i	$-0.793902\pi$
$601$	−39.1072	−1.59522	−0.797609	+	0.603175i	$0.793902\pi$
$602$	5.23424	0.213332
$603$	−5.55311	−0.226140
$604$	−9.60659	−0.390887
$605$	30.3667	1.23458
$606$	−34.4898	−1.40105
$607$	16.1876	0.657033	0.328516	−	0.944498i	$-0.393451\pi$
$607$	16.1876	0.657033	0.328516	+	0.944498i	$0.393451\pi$
$608$	−30.5098	−1.23734
$609$	2.85612	0.115736
$610$	27.6423	1.11920
$611$	−26.6044	−1.07630
$612$	1.92322	0.0777417
$613$	6.47220	0.261410	0.130705	−	0.991421i	$-0.458276\pi$
$613$	6.47220	0.261410	0.130705	+	0.991421i	$0.458276\pi$
$614$	39.4548	1.59227
$615$	−20.4222	−0.823501
$616$	0.00382431	0.000154086 0
$617$	13.1152	0.527996	0.263998	−	0.964523i	$-0.414959\pi$
$617$	13.1152	0.527996	0.263998	+	0.964523i	$0.414959\pi$
$618$	32.9471	1.32533
$619$	3.97762	0.159874	0.0799369	−	0.996800i	$-0.474528\pi$
$619$	3.97762	0.159874	0.0799369	+	0.996800i	$0.474528\pi$
$620$	−29.1600	−1.17109
$621$	1.84815	0.0741637
$622$	26.5898	1.06615
$623$	−43.3709	−1.73762
$624$	19.9406	0.798263
$625$	−30.5041	−1.22016
$626$	33.5691	1.34169
$627$	−2.69642	−0.107685
$628$	−0.398881	−0.0159171
$629$	−5.67648	−0.226336
$630$	16.0188	0.638204
$631$	−9.27811	−0.369356	−0.184678	−	0.982799i	$-0.559124\pi$
$631$	−9.27811	−0.369356	−0.184678	+	0.982799i	$0.559124\pi$
$632$	0.00945792	0.000376216 0
$633$	4.83472	0.192163
$634$	32.4870	1.29022
$635$	−29.7884	−1.18212
$636$	−15.9133	−0.631004
$637$	−3.34845	−0.132670
$638$	−1.45775	−0.0577129
$639$	8.53602	0.337680
$640$	0.0451858	0.00178613
$641$	4.84828	0.191495	0.0957477	−	0.995406i	$-0.469476\pi$
$641$	4.84828	0.191495	0.0957477	+	0.995406i	$0.469476\pi$
$642$	−4.96045	−0.195773
$643$	−40.2544	−1.58748	−0.793739	−	0.608258i	$-0.791868\pi$
$643$	−40.2544	−1.58748	−0.793739	+	0.608258i	$0.791868\pi$
$644$	10.2332	0.403243
$645$	2.73288	0.107607
$646$	7.33824	0.288719
$647$	−14.0038	−0.550545	−0.275273	−	0.961366i	$-0.588768\pi$
$647$	−14.0038	−0.550545	−0.275273	+	0.961366i	$0.588768\pi$
$648$	0.00195305	7.67232e−5 0
$649$	6.30358	0.247437
$650$	33.5163	1.31462
$651$	13.9709	0.547564
$652$	21.7782	0.852900
$653$	1.12398	0.0439849	0.0219925	−	0.999758i	$-0.492999\pi$
$653$	1.12398	0.0439849	0.0219925	+	0.999758i	$0.492999\pi$
$654$	28.1666	1.10140
$655$	13.3963	0.523439
$656$	−28.2602	−1.10338
$657$	5.32998	0.207942
$658$	−29.5746	−1.15294
$659$	−12.1576	−0.473594	−0.236797	−	0.971559i	$-0.576098\pi$
$659$	−12.1576	−0.473594	−0.236797	+	0.971559i	$0.576098\pi$
$660$	−4.08696	−0.159085
$661$	−2.14532	−0.0834433	−0.0417216	−	0.999129i	$-0.513284\pi$
$661$	−2.14532	−0.0834433	−0.0417216	+	0.999129i	$0.513284\pi$
$662$	−45.4645	−1.76703
$663$	−4.79378	−0.186175
$664$	−0.0341793	−0.00132642
$665$	30.5531	1.18480
$666$	11.7990	0.457201
$667$	1.90572	0.0737898
$668$	−6.27995	−0.242979
$669$	−6.95926	−0.269061
$670$	−32.1153	−1.24072
$671$	3.37896	0.130443
$672$	22.1560	0.854687
$673$	−8.43633	−0.325197	−0.162598	−	0.986692i	$-0.551987\pi$
$673$	−8.43633	−0.325197	−0.162598	+	0.986692i	$0.551987\pi$
$674$	30.6631	1.18110
$675$	3.36367	0.129468
$676$	23.6434	0.909363
$677$	−16.5368	−0.635559	−0.317779	−	0.948165i	$-0.602937\pi$
$677$	−16.5368	−0.635559	−0.317779	+	0.948165i	$0.602937\pi$
$678$	20.3558	0.781761
$679$	16.5975	0.636953
$680$	−0.00543406	−0.000208387 0
$681$	17.7523	0.680270
$682$	−7.13071	−0.273049
$683$	−15.8851	−0.607826	−0.303913	−	0.952700i	$-0.598293\pi$
$683$	−15.8851	−0.607826	−0.303913	+	0.952700i	$0.598293\pi$
$684$	−7.62466	−0.291536
$685$	−19.8870	−0.759841
$686$	35.0507	1.33824
$687$	−6.15898	−0.234980
$688$	3.78176	0.144178
$689$	39.6652	1.51112
$690$	10.6884	0.406900
$691$	20.7628	0.789852	0.394926	−	0.918713i	$-0.370770\pi$
$691$	20.7628	0.789852	0.394926	+	0.918713i	$0.370770\pi$
$692$	−7.74471	−0.294410
$693$	1.95812	0.0743828
$694$	7.64790	0.290310
$695$	37.8434	1.43548
$696$	0.00201389	7.63364e−5 0
$697$	6.79384	0.257335
$698$	8.95616	0.338996
$699$	15.1329	0.572380
$700$	18.6245	0.703941
$701$	−45.8794	−1.73284	−0.866420	−	0.499316i	$-0.833585\pi$
$701$	−45.8794	−1.73284	−0.866420	+	0.499316i	$0.833585\pi$
$702$	9.96422	0.376075
$703$	22.5045	0.848774
$704$	−5.65002	−0.212943
$705$	−15.4413	−0.581555
$706$	69.9018	2.63079
$707$	47.7715	1.79663
$708$	17.8246	0.669891
$709$	28.3261	1.06381	0.531905	−	0.846804i	$-0.321476\pi$
$709$	28.3261	1.06381	0.531905	+	0.846804i	$0.321476\pi$
$710$	49.3663	1.85268
$711$	4.84263	0.181613
$712$	−0.0305814	−0.00114609
$713$	9.32198	0.349111
$714$	−5.32897	−0.199432
$715$	10.1871	0.380975
$716$	34.1655	1.27682
$717$	17.1296	0.639717
$718$	55.3918	2.06720
$719$	13.0612	0.487099	0.243550	−	0.969888i	$-0.421688\pi$
$719$	13.0612	0.487099	0.243550	+	0.969888i	$0.421688\pi$
$720$	11.5736	0.431324
$721$	−45.6347	−1.69953
$722$	8.90276	0.331327
$723$	3.47131	0.129099
$724$	−10.3211	−0.383581
$725$	3.46845	0.128815
$726$	20.9979	0.779305
$727$	−6.00467	−0.222701	−0.111350	−	0.993781i	$-0.535518\pi$
$727$	−6.00467	−0.222701	−0.111350	+	0.993781i	$0.535518\pi$
$728$	−0.0269547	−0.000999009 0
$729$	1.00000	0.0370370
$730$	30.8249	1.14088
$731$	−0.909147	−0.0336260
$732$	9.55468	0.353151
$733$	−41.0588	−1.51654	−0.758270	−	0.651940i	$-0.773955\pi$
$733$	−41.0588	−1.51654	−0.758270	+	0.651940i	$0.773955\pi$
$734$	12.1437	0.448233
$735$	−1.94346	−0.0716855
$736$	14.7834	0.544923
$737$	−3.92573	−0.144606
$738$	−14.1215	−0.519819
$739$	24.3805	0.896852	0.448426	−	0.893820i	$-0.351985\pi$
$739$	24.3805	0.896852	0.448426	+	0.893820i	$0.351985\pi$
$740$	34.1101	1.25391
$741$	19.0051	0.698168
$742$	44.0935	1.61872
$743$	44.8268	1.64454	0.822269	−	0.569100i	$-0.192708\pi$
$743$	44.8268	1.64454	0.822269	+	0.569100i	$0.192708\pi$
$744$	0.00985111	0.000361159 0
$745$	−11.8229	−0.433156
$746$	30.3747	1.11210
$747$	−17.5005	−0.640309
$748$	1.35961	0.0497123
$749$	6.87066	0.251049
$750$	−9.46340	−0.345555
$751$	16.0222	0.584657	0.292329	−	0.956318i	$-0.405570\pi$
$751$	16.0222	0.584657	0.292329	+	0.956318i	$0.405570\pi$
$752$	−21.3677	−0.779202
$753$	3.26218	0.118880
$754$	10.2746	0.374179
$755$	13.8979	0.505797
$756$	5.53697	0.201378
$757$	−19.7995	−0.719626	−0.359813	−	0.933024i	$-0.617160\pi$
$757$	−19.7995	−0.719626	−0.359813	+	0.933024i	$0.617160\pi$
$758$	5.52704	0.200751
$759$	1.30654	0.0474243
$760$	0.0215434	0.000781463 0
$761$	−12.1144	−0.439146	−0.219573	−	0.975596i	$-0.570466\pi$
$761$	−12.1144	−0.439146	−0.219573	+	0.975596i	$0.570466\pi$
$762$	−20.5980	−0.746188
$763$	−39.0132	−1.41237
$764$	13.4862	0.487912
$765$	−2.78234	−0.100596
$766$	−71.5327	−2.58458
$767$	−44.4293	−1.60425
$768$	16.0156	0.577914
$769$	18.5941	0.670519	0.335259	−	0.942126i	$-0.391176\pi$
$769$	18.5941	0.670519	0.335259	+	0.942126i	$0.391176\pi$
$770$	11.3244	0.408102
$771$	29.5355	1.06370
$772$	−36.2121	−1.30330
$773$	−50.7419	−1.82506	−0.912529	−	0.409012i	$-0.865873\pi$
$773$	−50.7419	−1.82506	−0.912529	+	0.409012i	$0.865873\pi$
$774$	1.88973	0.0679248
$775$	16.9662	0.609443
$776$	0.0117031	0.000420117 0
$777$	−16.3426	−0.586288
$778$	−31.1268	−1.11595
$779$	−26.9343	−0.965023
$780$	28.8060	1.03142
$781$	6.03448	0.215931
$782$	−3.55571	−0.127152
$783$	1.03115	0.0368503
$784$	−2.68936	−0.0960485
$785$	0.577063	0.0205963
$786$	9.26328	0.330410
$787$	−39.8264	−1.41966	−0.709829	−	0.704374i	$-0.751228\pi$
$787$	−39.8264	−1.41966	−0.709829	+	0.704374i	$0.751228\pi$
$788$	−24.0712	−0.857500
$789$	−18.2608	−0.650100
$790$	28.0064	0.996422
$791$	−28.1946	−1.00249
$792$	0.00138070	4.90610e−5 0
$793$	−23.8158	−0.845723
$794$	72.9600	2.58926
$795$	23.0219	0.816503
$796$	−27.7505	−0.983590
$797$	−39.5471	−1.40083	−0.700415	−	0.713736i	$-0.747001\pi$
$797$	−39.5471	−1.40083	−0.700415	+	0.713736i	$0.747001\pi$
$798$	21.1268	0.747882
$799$	5.13687	0.181730
$800$	26.9060	0.951272
$801$	−15.6583	−0.553258
$802$	−16.7812	−0.592565
$803$	3.76800	0.132970
$804$	−11.1008	−0.391495
$805$	−14.8044	−0.521786
$806$	50.2591	1.77030
$807$	−32.2512	−1.13530
$808$	0.0336843	0.00118501
$809$	−33.2745	−1.16987	−0.584935	−	0.811080i	$-0.698880\pi$
$809$	−33.2745	−1.16987	−0.584935	+	0.811080i	$0.698880\pi$
$810$	5.78329	0.203204
$811$	−48.9221	−1.71789	−0.858944	−	0.512069i	$-0.828879\pi$
$811$	−48.9221	−1.71789	−0.858944	+	0.512069i	$0.828879\pi$
$812$	5.70945	0.200363
$813$	10.0497	0.352460
$814$	8.34120	0.292359
$815$	−31.5067	−1.10363
$816$	−3.85021	−0.134784
$817$	3.60433	0.126100
$818$	−56.5298	−1.97652
$819$	−13.8013	−0.482258
$820$	−40.8244	−1.42565
$821$	−33.8396	−1.18101	−0.590505	−	0.807034i	$-0.701072\pi$
$821$	−33.8396	−1.18101	−0.590505	+	0.807034i	$0.701072\pi$
$822$	−13.7514	−0.479635
$823$	29.1898	1.01749	0.508746	−	0.860917i	$-0.330109\pi$
$823$	29.1898	1.01749	0.508746	+	0.860917i	$0.330109\pi$
$824$	−0.0321777	−0.00112096
$825$	2.37792	0.0827886
$826$	−49.3895	−1.71848
$827$	−35.2188	−1.22468	−0.612339	−	0.790595i	$-0.709771\pi$
$827$	−35.2188	−1.22468	−0.612339	+	0.790595i	$0.709771\pi$
$828$	3.69450	0.128393
$829$	13.1671	0.457314	0.228657	−	0.973507i	$-0.426567\pi$
$829$	13.1671	0.457314	0.228657	+	0.973507i	$0.426567\pi$
$830$	−101.210	−3.51306
$831$	17.2623	0.598823
$832$	39.8228	1.38061
$833$	0.646530	0.0224009
$834$	26.1679	0.906121
$835$	9.08525	0.314408
$836$	−5.39020	−0.186424
$837$	5.04395	0.174345
$838$	54.5158	1.88322
$839$	−18.6076	−0.642407	−0.321203	−	0.947010i	$-0.604087\pi$
$839$	−18.6076	−0.642407	−0.321203	+	0.947010i	$0.604087\pi$
$840$	−0.0156447	−0.000539793 0
$841$	−27.9367	−0.963335
$842$	39.3149	1.35488
$843$	−17.1094	−0.589278
$844$	9.66472	0.332673
$845$	−34.2051	−1.17669
$846$	−10.6774	−0.367095
$847$	−29.0840	−0.999337
$848$	31.8577	1.09400
$849$	30.0871	1.03259
$850$	−6.47145	−0.221969
$851$	−10.9045	−0.373800
$852$	17.0637	0.584593
$853$	−15.0792	−0.516302	−0.258151	−	0.966105i	$-0.583113\pi$
$853$	−15.0792	−0.516302	−0.258151	+	0.966105i	$0.583113\pi$
$854$	−26.4746	−0.905944
$855$	11.0306	0.377240
$856$	0.00484460	0.000165585 0
$857$	−45.9094	−1.56824	−0.784118	−	0.620612i	$-0.786884\pi$
$857$	−45.9094	−1.56824	−0.784118	+	0.620612i	$0.786884\pi$
$858$	7.04414	0.240483
$859$	−17.4514	−0.595436	−0.297718	−	0.954654i	$-0.596225\pi$
$859$	−17.4514	−0.595436	−0.297718	+	0.954654i	$0.596225\pi$
$860$	5.46309	0.186290
$861$	19.5595	0.666586
$862$	32.9670	1.12286
$863$	29.0368	0.988424	0.494212	−	0.869341i	$-0.335457\pi$
$863$	29.0368	0.988424	0.494212	+	0.869341i	$0.335457\pi$
$864$	7.99902	0.272132
$865$	11.2043	0.380958
$866$	−39.1988	−1.33203
$867$	−16.0744	−0.545915
$868$	27.9282	0.947946
$869$	3.42347	0.116133
$870$	5.96345	0.202180
$871$	27.6696	0.937548
$872$	−0.0275088	−0.000931565 0
$873$	5.99221	0.202806
$874$	14.0967	0.476827
$875$	13.1077	0.443120
$876$	10.6548	0.359991
$877$	49.8609	1.68368	0.841842	−	0.539725i	$-0.181472\pi$
$877$	49.8609	1.68368	0.841842	+	0.539725i	$0.181472\pi$
$878$	−38.7278	−1.30700
$879$	19.2438	0.649078
$880$	8.18191	0.275812
$881$	−53.7241	−1.81001	−0.905005	−	0.425401i	$-0.860133\pi$
$881$	−53.7241	−1.81001	−0.905005	+	0.425401i	$0.860133\pi$
$882$	−1.34386	−0.0452501
$883$	−5.11406	−0.172102	−0.0860509	−	0.996291i	$-0.527425\pi$
$883$	−5.11406	−0.172102	−0.0860509	+	0.996291i	$0.527425\pi$
$884$	−9.58289	−0.322307
$885$	−25.7870	−0.866821
$886$	−20.5857	−0.691589
$887$	25.1670	0.845026	0.422513	−	0.906357i	$-0.361148\pi$
$887$	25.1670	0.845026	0.422513	+	0.906357i	$0.361148\pi$
$888$	−0.0115234	−0.000386700 0
$889$	28.5301	0.956869
$890$	−90.5564	−3.03546
$891$	0.706943	0.0236835
$892$	−13.9117	−0.465799
$893$	−20.3652	−0.681497
$894$	−8.17526	−0.273421
$895$	−49.4274	−1.65218
$896$	−0.0432771	−0.00144579
$897$	−9.20881	−0.307473
$898$	−6.54791	−0.218507
$899$	5.20108	0.173466
$900$	6.72405	0.224135
$901$	−7.65870	−0.255148
$902$	−9.98309	−0.332401
$903$	−2.61744	−0.0871029
$904$	−0.0198804	−0.000661214 0
$905$	14.9316	0.496344
$906$	9.61011	0.319275
$907$	50.8308	1.68781	0.843904	−	0.536495i	$-0.180252\pi$
$907$	50.8308	1.68781	0.843904	+	0.536495i	$0.180252\pi$
$908$	35.4873	1.17769
$909$	17.2470	0.572048
$910$	−79.8172	−2.64591
$911$	57.7401	1.91301	0.956507	−	0.291709i	$-0.0942238\pi$
$911$	57.7401	1.91301	0.956507	+	0.291709i	$0.0942238\pi$
$912$	15.2642	0.505449
$913$	−12.3718	−0.409448
$914$	44.4105	1.46897
$915$	−13.8228	−0.456968
$916$	−12.3119	−0.406798
$917$	−12.8305	−0.423700
$918$	−1.92393	−0.0634991
$919$	26.2274	0.865163	0.432581	−	0.901595i	$-0.357603\pi$
$919$	26.2274	0.865163	0.432581	+	0.901595i	$0.357603\pi$
$920$	−0.0104388	−0.000344156 0
$921$	−19.7298	−0.650120
$922$	67.2472	2.21467
$923$	−42.5326	−1.39998
$924$	3.91433	0.128772
$925$	−19.8463	−0.652543
$926$	30.2066	0.992650
$927$	−16.4756	−0.541129
$928$	8.24819	0.270760
$929$	7.63926	0.250636	0.125318	−	0.992117i	$-0.460005\pi$
$929$	7.63926	0.250636	0.125318	+	0.992117i	$0.460005\pi$
$930$	29.1707	0.956544
$931$	−2.56318	−0.0840049
$932$	30.2511	0.990908
$933$	−13.2965	−0.435309
$934$	53.9916	1.76666
$935$	−1.96696	−0.0643264
$936$	−0.00973152	−0.000318085 0
$937$	−18.0327	−0.589103	−0.294551	−	0.955636i	$-0.595170\pi$
$937$	−18.0327	−0.589103	−0.294551	+	0.955636i	$0.595170\pi$
$938$	30.7587	1.00431
$939$	−16.7866	−0.547810
$940$	−30.8676	−1.00679
$941$	−0.763249	−0.0248812	−0.0124406	−	0.999923i	$-0.503960\pi$
$941$	−0.763249	−0.0248812	−0.0124406	+	0.999923i	$0.503960\pi$
$942$	0.399027	0.0130010
$943$	13.0509	0.424996
$944$	−35.6841	−1.16142
$945$	−8.01038	−0.260578
$946$	1.33593	0.0434348
$947$	−44.1628	−1.43510	−0.717550	−	0.696507i	$-0.754736\pi$
$947$	−44.1628	−1.43510	−0.717550	+	0.696507i	$0.754736\pi$
$948$	9.68054	0.314409
$949$	−26.5578	−0.862103
$950$	25.6562	0.832397
$951$	−16.2455	−0.526796
$952$	0.00520452	0.000168679 0
$953$	10.0339	0.325030	0.162515	−	0.986706i	$-0.448039\pi$
$953$	10.0339	0.325030	0.162515	+	0.986706i	$0.448039\pi$
$954$	15.9192	0.515402
$955$	−19.5105	−0.631345
$956$	34.2425	1.10748
$957$	0.728965	0.0235641
$958$	−9.58553	−0.309694
$959$	19.0469	0.615057
$960$	23.1134	0.745982
$961$	−5.55853	−0.179307
$962$	−58.7910	−1.89550
$963$	2.48053	0.0799339
$964$	6.93922	0.223497
$965$	52.3882	1.68644
$966$	−10.2369	−0.329367
$967$	6.24317	0.200767	0.100383	−	0.994949i	$-0.467993\pi$
$967$	6.24317	0.200767	0.100383	+	0.994949i	$0.467993\pi$
$968$	−0.0205075	−0.000659136 0
$969$	−3.66957	−0.117883
$970$	34.6547	1.11270
$971$	13.8748	0.445264	0.222632	−	0.974903i	$-0.428535\pi$
$971$	13.8748	0.445264	0.222632	+	0.974903i	$0.428535\pi$
$972$	1.99902	0.0641187
$973$	−36.2449	−1.16196
$974$	−21.3427	−0.683866
$975$	−16.7602	−0.536756
$976$	−19.1280	−0.612273
$977$	−32.0271	−1.02464	−0.512319	−	0.858795i	$-0.671213\pi$
$977$	−32.0271	−1.02464	−0.512319	+	0.858795i	$0.671213\pi$
$978$	−21.7862	−0.696645
$979$	−11.0695	−0.353783
$980$	−3.88502	−0.124102
$981$	−14.0850	−0.449700
$982$	6.09924	0.194635
$983$	−43.6498	−1.39221	−0.696106	−	0.717939i	$-0.745086\pi$
$983$	−43.6498	−1.39221	−0.696106	+	0.717939i	$0.745086\pi$
$984$	0.0137917	0.000439663 0
$985$	34.8239	1.10958
$986$	−1.98386	−0.0631790
$987$	14.7891	0.470742
$988$	37.9916	1.20867
$989$	−1.74646	−0.0555343
$990$	4.08846	0.129940
$991$	8.77248	0.278667	0.139334	−	0.990246i	$-0.455504\pi$
$991$	8.77248	0.278667	0.139334	+	0.990246i	$0.455504\pi$
$992$	40.3467	1.28101
$993$	22.7350	0.721475
$994$	−47.2810	−1.49966
$995$	40.1468	1.27274
$996$	−34.9838	−1.10851
$997$	−25.9693	−0.822456	−0.411228	−	0.911532i	$-0.634900\pi$
$997$	−25.9693	−0.822456	−0.411228	+	0.911532i	$0.634900\pi$
$998$	37.9715	1.20197
$999$	−5.90020	−0.186674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.a.1.19	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.a.1.19	✓	94	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99976 q^{2} +1.00000 q^{3} +1.99902 q^{4} -2.89200 q^{5} -1.99976 q^{6} +2.76984 q^{7} +0.00195305 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.99976 q^{2} +1.00000 q^{3} +1.99902 q^{4} -2.89200 q^{5} -1.99976 q^{6} +2.76984 q^{7} +0.00195305 q^{8} +1.00000 q^{9} +5.78329 q^{10} +0.706943 q^{11} +1.99902 q^{12} -4.98272 q^{13} -5.53900 q^{14} -2.89200 q^{15} -4.00195 q^{16} +0.962082 q^{17} -1.99976 q^{18} -3.81419 q^{19} -5.78118 q^{20} +2.76984 q^{21} -1.41371 q^{22} +1.84815 q^{23} +0.00195305 q^{24} +3.36367 q^{25} +9.96422 q^{26} +1.00000 q^{27} +5.53697 q^{28} +1.03115 q^{29} +5.78329 q^{30} +5.04395 q^{31} +7.99902 q^{32} +0.706943 q^{33} -1.92393 q^{34} -8.01038 q^{35} +1.99902 q^{36} -5.90020 q^{37} +7.62746 q^{38} -4.98272 q^{39} -0.00564823 q^{40} +7.06161 q^{41} -5.53900 q^{42} -0.944979 q^{43} +1.41320 q^{44} -2.89200 q^{45} -3.69585 q^{46} +5.33933 q^{47} -4.00195 q^{48} +0.672012 q^{49} -6.72651 q^{50} +0.962082 q^{51} -9.96057 q^{52} -7.96055 q^{53} -1.99976 q^{54} -2.04448 q^{55} +0.00540964 q^{56} -3.81419 q^{57} -2.06205 q^{58} +8.91668 q^{59} -5.78118 q^{60} +4.77968 q^{61} -10.0867 q^{62} +2.76984 q^{63} -7.99218 q^{64} +14.4100 q^{65} -1.41371 q^{66} -5.55311 q^{67} +1.92322 q^{68} +1.84815 q^{69} +16.0188 q^{70} +8.53602 q^{71} +0.00195305 q^{72} +5.32998 q^{73} +11.7990 q^{74} +3.36367 q^{75} -7.62466 q^{76} +1.95812 q^{77} +9.96422 q^{78} +4.84263 q^{79} +11.5736 q^{80} +1.00000 q^{81} -14.1215 q^{82} -17.5005 q^{83} +5.53697 q^{84} -2.78234 q^{85} +1.88973 q^{86} +1.03115 q^{87} +0.00138070 q^{88} -15.6583 q^{89} +5.78329 q^{90} -13.8013 q^{91} +3.69450 q^{92} +5.04395 q^{93} -10.6774 q^{94} +11.0306 q^{95} +7.99902 q^{96} +5.99221 q^{97} -1.34386 q^{98} +0.706943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * q^99

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