LMFDB - Embedded newform 3721.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3721,2,Mod(1,3721)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3721, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3721.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3721 = 61^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3721.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:	$29.7123345921$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.966125.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 4x^{3} + 8x^{2} - 1 $ x^6 - x^5 - 6x^4 + 4x^3 + 8*x^2 - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.852692$ of defining polynomial
Character	$\chi$	$=$	3721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.852692 q^{2} -2.79079 q^{3} -1.27292 q^{4} +0.420224 q^{5} -2.37969 q^{6} -3.40882 q^{7} -2.79079 q^{8} +4.78851 q^{9} +O(q^{10})$	\(q+0.852692 q^{2} -2.79079 q^{3} -1.27292 q^{4} +0.420224 q^{5} -2.37969 q^{6} -3.40882 q^{7} -2.79079 q^{8} +4.78851 q^{9} +0.358321 q^{10} -2.79991 q^{11} +3.55244 q^{12} +5.47505 q^{13} -2.90668 q^{14} -1.17276 q^{15} +0.166147 q^{16} +3.82127 q^{17} +4.08312 q^{18} -5.68198 q^{19} -0.534909 q^{20} +9.51331 q^{21} -2.38746 q^{22} +3.05123 q^{23} +7.78851 q^{24} -4.82341 q^{25} +4.66854 q^{26} -4.99135 q^{27} +4.33915 q^{28} -1.66543 q^{29} -1.00000 q^{30} +5.39021 q^{31} +5.72325 q^{32} +7.81396 q^{33} +3.25837 q^{34} -1.43247 q^{35} -6.09537 q^{36} -0.900940 q^{37} -4.84498 q^{38} -15.2797 q^{39} -1.17276 q^{40} +11.0504 q^{41} +8.11193 q^{42} +2.23068 q^{43} +3.56405 q^{44} +2.01224 q^{45} +2.60176 q^{46} -0.616624 q^{47} -0.463681 q^{48} +4.62008 q^{49} -4.11289 q^{50} -10.6644 q^{51} -6.96928 q^{52} +2.24374 q^{53} -4.25609 q^{54} -1.17659 q^{55} +9.51331 q^{56} +15.8572 q^{57} -1.42010 q^{58} +14.9326 q^{59} +1.49282 q^{60} +4.59619 q^{62} -16.3232 q^{63} +4.54788 q^{64} +2.30075 q^{65} +6.66290 q^{66} -4.66833 q^{67} -4.86416 q^{68} -8.51535 q^{69} -1.22145 q^{70} +1.32949 q^{71} -13.3637 q^{72} -7.37278 q^{73} -0.768224 q^{74} +13.4611 q^{75} +7.23269 q^{76} +9.54440 q^{77} -13.0289 q^{78} -2.70014 q^{79} +0.0698188 q^{80} -0.435708 q^{81} +9.42261 q^{82} -10.1903 q^{83} -12.1096 q^{84} +1.60579 q^{85} +1.90208 q^{86} +4.64785 q^{87} +7.81396 q^{88} -12.4293 q^{89} +1.71583 q^{90} -18.6635 q^{91} -3.88396 q^{92} -15.0430 q^{93} -0.525791 q^{94} -2.38770 q^{95} -15.9724 q^{96} -11.9355 q^{97} +3.93951 q^{98} -13.4074 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 3 q^{3} + q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - q^2 - 3 * q^3 + q^4 - 3 * q^6 - 3 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{9} - 8 q^{10} - 3 q^{11} + 3 q^{12} + q^{13} - q^{14} - 5 q^{16} + 8 q^{17} + 5 q^{18} + 2 q^{19} - 16 q^{20} + 16 q^{21} + 5 q^{22} + 14 q^{23} + 15 q^{24} - 6 q^{25} + 11 q^{26} - 6 q^{27} + 6 q^{28} - 4 q^{29} - 6 q^{30} + 7 q^{31} + 13 q^{32} + 2 q^{33} + 15 q^{34} - 5 q^{35} - 16 q^{36} - 22 q^{37} - 9 q^{38} - 14 q^{39} - 8 q^{41} - 2 q^{42} - 7 q^{43} + 25 q^{44} + 11 q^{45} - 16 q^{46} - 11 q^{47} - 4 q^{48} - 16 q^{49} + 37 q^{50} + 5 q^{51} + 12 q^{52} + 25 q^{53} - 3 q^{54} - 30 q^{55} + 16 q^{56} + 2 q^{57} + 12 q^{58} + 11 q^{59} + q^{60} - 26 q^{62} - 24 q^{63} - 27 q^{64} - 23 q^{65} + 23 q^{66} - 7 q^{67} - 19 q^{68} - 35 q^{69} - 20 q^{70} - 22 q^{71} - 15 q^{72} - 17 q^{73} - 10 q^{74} + 20 q^{75} - 3 q^{76} + 3 q^{77} - 14 q^{78} + 12 q^{79} + 26 q^{80} - 6 q^{81} + 39 q^{82} - 36 q^{83} - 4 q^{84} + 4 q^{85} - 30 q^{86} - 8 q^{87} + 2 q^{88} - 21 q^{89} + 27 q^{90} - 11 q^{91} + 16 q^{92} + 5 q^{93} - 16 q^{94} + 12 q^{95} - 31 q^{96} - 24 q^{97} + 2 q^{98} - 23 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + q^4 - 3 * q^6 - 3 * q^8 - 3 * q^9 - 8 * q^10 - 3 * q^11 + 3 * q^12 + q^13 - q^14 - 5 * q^16 + 8 * q^17 + 5 * q^18 + 2 * q^19 - 16 * q^20 + 16 * q^21 + 5 * q^22 + 14 * q^23 + 15 * q^24 - 6 * q^25 + 11 * q^26 - 6 * q^27 + 6 * q^28 - 4 * q^29 - 6 * q^30 + 7 * q^31 + 13 * q^32 + 2 * q^33 + 15 * q^34 - 5 * q^35 - 16 * q^36 - 22 * q^37 - 9 * q^38 - 14 * q^39 - 8 * q^41 - 2 * q^42 - 7 * q^43 + 25 * q^44 + 11 * q^45 - 16 * q^46 - 11 * q^47 - 4 * q^48 - 16 * q^49 + 37 * q^50 + 5 * q^51 + 12 * q^52 + 25 * q^53 - 3 * q^54 - 30 * q^55 + 16 * q^56 + 2 * q^57 + 12 * q^58 + 11 * q^59 + q^60 - 26 * q^62 - 24 * q^63 - 27 * q^64 - 23 * q^65 + 23 * q^66 - 7 * q^67 - 19 * q^68 - 35 * q^69 - 20 * q^70 - 22 * q^71 - 15 * q^72 - 17 * q^73 - 10 * q^74 + 20 * q^75 - 3 * q^76 + 3 * q^77 - 14 * q^78 + 12 * q^79 + 26 * q^80 - 6 * q^81 + 39 * q^82 - 36 * q^83 - 4 * q^84 + 4 * q^85 - 30 * q^86 - 8 * q^87 + 2 * q^88 - 21 * q^89 + 27 * q^90 - 11 * q^91 + 16 * q^92 + 5 * q^93 - 16 * q^94 + 12 * q^95 - 31 * q^96 - 24 * q^97 + 2 * q^98 - 23 * 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 $

$2$	0.852692	0.602944	0.301472	−	0.953475i	$-0.402522\pi$
$2$	0.852692	0.602944	0.301472	+	0.953475i	$0.402522\pi$
$3$	−2.79079	−1.61126	−0.805632	−	0.592417i	$-0.798174\pi$
$3$	−2.79079	−1.61126	−0.805632	+	0.592417i	$0.798174\pi$
$4$	−1.27292	−0.636458
$5$	0.420224	0.187930	0.0939649	−	0.995576i	$-0.470046\pi$
$5$	0.420224	0.187930	0.0939649	+	0.995576i	$0.470046\pi$
$6$	−2.37969	−0.971502
$7$	−3.40882	−1.28841	−0.644207	−	0.764851i	$-0.722813\pi$
$7$	−3.40882	−1.28841	−0.644207	+	0.764851i	$0.722813\pi$
$8$	−2.79079	−0.986693
$9$	4.78851	1.59617
$10$	0.358321	0.113311
$11$	−2.79991	−0.844204	−0.422102	−	0.906548i	$-0.638708\pi$
$11$	−2.79991	−0.844204	−0.422102	+	0.906548i	$0.638708\pi$
$12$	3.55244	1.02550
$13$	5.47505	1.51851	0.759253	−	0.650795i	$-0.225564\pi$
$13$	5.47505	1.51851	0.759253	+	0.650795i	$0.225564\pi$
$14$	−2.90668	−0.776842
$15$	−1.17276	−0.302804
$16$	0.166147	0.0415367
$17$	3.82127	0.926795	0.463397	−	0.886151i	$-0.346630\pi$
$17$	3.82127	0.926795	0.463397	+	0.886151i	$0.346630\pi$
$18$	4.08312	0.962402
$19$	−5.68198	−1.30354	−0.651768	−	0.758418i	$-0.725973\pi$
$19$	−5.68198	−1.30354	−0.651768	+	0.758418i	$0.725973\pi$
$20$	−0.534909	−0.119609
$21$	9.51331	2.07597
$22$	−2.38746	−0.509008
$23$	3.05123	0.636226	0.318113	−	0.948053i	$-0.396951\pi$
$23$	3.05123	0.636226	0.318113	+	0.948053i	$0.396951\pi$
$24$	7.78851	1.58982
$25$	−4.82341	−0.964682
$26$	4.66854	0.915575
$27$	−4.99135	−0.960586
$28$	4.33915	0.820022
$29$	−1.66543	−0.309262	−0.154631	−	0.987972i	$-0.549419\pi$
$29$	−1.66543	−0.309262	−0.154631	+	0.987972i	$0.549419\pi$
$30$	−1.00000	−0.182574
$31$	5.39021	0.968111	0.484055	−	0.875037i	$-0.339163\pi$
$31$	5.39021	0.968111	0.484055	+	0.875037i	$0.339163\pi$
$32$	5.72325	1.01174
$33$	7.81396	1.36024
$34$	3.25837	0.558806
$35$	−1.43247	−0.242131
$36$	−6.09537	−1.01589
$37$	−0.900940	−0.148114	−0.0740568	−	0.997254i	$-0.523595\pi$
$37$	−0.900940	−0.148114	−0.0740568	+	0.997254i	$0.523595\pi$
$38$	−4.84498	−0.785960
$39$	−15.2797	−2.44671
$40$	−1.17276	−0.185429
$41$	11.0504	1.72579	0.862893	−	0.505387i	$-0.168650\pi$
$41$	11.0504	1.72579	0.862893	+	0.505387i	$0.168650\pi$
$42$	8.11193	1.25170
$43$	2.23068	0.340175	0.170087	−	0.985429i	$-0.445595\pi$
$43$	2.23068	0.340175	0.170087	+	0.985429i	$0.445595\pi$
$44$	3.56405	0.537301
$45$	2.01224	0.299968
$46$	2.60176	0.383609
$47$	−0.616624	−0.0899439	−0.0449719	−	0.998988i	$-0.514320\pi$
$47$	−0.616624	−0.0899439	−0.0449719	+	0.998988i	$0.514320\pi$
$48$	−0.463681	−0.0669266
$49$	4.62008	0.660012
$50$	−4.11289	−0.581650
$51$	−10.6644	−1.49331
$52$	−6.96928	−0.966466
$53$	2.24374	0.308202	0.154101	−	0.988055i	$-0.450752\pi$
$53$	2.24374	0.308202	0.154101	+	0.988055i	$0.450752\pi$
$54$	−4.25609	−0.579180
$55$	−1.17659	−0.158651
$56$	9.51331	1.27127
$57$	15.8572	2.10034
$58$	−1.42010	−0.186468
$59$	14.9326	1.94406	0.972031	−	0.234853i	$-0.0754608\pi$
$59$	14.9326	1.94406	0.972031	+	0.234853i	$0.0754608\pi$
$60$	1.49282	0.192722
$61$	0	0
$61$	0	0
$62$	4.59619	0.583717
$63$	−16.3232	−2.05653
$64$	4.54788	0.568485
$65$	2.30075	0.285373
$66$	6.66290	0.820146
$67$	−4.66833	−0.570327	−0.285164	−	0.958479i	$-0.592048\pi$
$67$	−4.66833	−0.570327	−0.285164	+	0.958479i	$0.592048\pi$
$68$	−4.86416	−0.589866
$69$	−8.51535	−1.02513
$70$	−1.22145	−0.145992
$71$	1.32949	0.157782	0.0788909	−	0.996883i	$-0.474862\pi$
$71$	1.32949	0.157782	0.0788909	+	0.996883i	$0.474862\pi$
$72$	−13.3637	−1.57493
$73$	−7.37278	−0.862919	−0.431460	−	0.902132i	$-0.642001\pi$
$73$	−7.37278	−0.862919	−0.431460	+	0.902132i	$0.642001\pi$
$74$	−0.768224	−0.0893043
$75$	13.4611	1.55436
$76$	7.23269	0.829646
$77$	9.54440	1.08768
$78$	−13.0289	−1.47523
$79$	−2.70014	−0.303790	−0.151895	−	0.988397i	$-0.548538\pi$
$79$	−2.70014	−0.303790	−0.151895	+	0.988397i	$0.548538\pi$
$80$	0.0698188	0.00780598
$81$	−0.435708	−0.0484120
$82$	9.42261	1.04055
$83$	−10.1903	−1.11854	−0.559268	−	0.828987i	$-0.688918\pi$
$83$	−10.1903	−1.11854	−0.559268	+	0.828987i	$0.688918\pi$
$84$	−12.1096	−1.32127
$85$	1.60579	0.174172
$86$	1.90208	0.205107
$87$	4.64785	0.498302
$88$	7.81396	0.832971
$89$	−12.4293	−1.31750	−0.658752	−	0.752360i	$-0.728916\pi$
$89$	−12.4293	−1.31750	−0.658752	+	0.752360i	$0.728916\pi$
$90$	1.71583	0.180864
$91$	−18.6635	−1.95647
$92$	−3.88396	−0.404931
$93$	−15.0430	−1.55988
$94$	−0.525791	−0.0542312
$95$	−2.38770	−0.244973
$96$	−15.9724	−1.63018
$97$	−11.9355	−1.21186	−0.605932	−	0.795516i	$-0.707200\pi$
$97$	−11.9355	−1.21186	−0.605932	+	0.795516i	$0.707200\pi$
$98$	3.93951	0.397950
$99$	−13.4074	−1.34749
$100$	6.13980	0.613980
$101$	15.9052	1.58263	0.791313	−	0.611411i	$-0.209398\pi$
$101$	15.9052	1.58263	0.791313	+	0.611411i	$0.209398\pi$
$102$	−9.09342	−0.900383
$103$	2.76484	0.272428	0.136214	−	0.990679i	$-0.456507\pi$
$103$	2.76484	0.272428	0.136214	+	0.990679i	$0.456507\pi$
$104$	−15.2797	−1.49830
$105$	3.99772	0.390137
$106$	1.91322	0.185828
$107$	−8.05322	−0.778534	−0.389267	−	0.921125i	$-0.627272\pi$
$107$	−8.05322	−0.778534	−0.389267	+	0.921125i	$0.627272\pi$
$108$	6.35357	0.611373
$109$	7.13460	0.683371	0.341685	−	0.939814i	$-0.389002\pi$
$109$	7.13460	0.683371	0.341685	+	0.939814i	$0.389002\pi$
$110$	−1.00327	−0.0956578
$111$	2.51433	0.238650
$112$	−0.566365	−0.0535165
$113$	−5.77252	−0.543033	−0.271517	−	0.962434i	$-0.587525\pi$
$113$	−5.77252	−0.543033	−0.271517	+	0.962434i	$0.587525\pi$
$114$	13.5213	1.26639
$115$	1.28220	0.119566
$116$	2.11995	0.196832
$117$	26.2173	2.42379
$118$	12.7329	1.17216
$119$	−13.0260	−1.19410
$120$	3.27292	0.298775
$121$	−3.16051	−0.287319
$122$	0	0
$123$	−30.8394	−2.78070
$124$	−6.86129	−0.616162
$125$	−4.12803	−0.369222
$126$	−13.9187	−1.23997
$127$	2.07780	0.184375	0.0921875	−	0.995742i	$-0.470614\pi$
$127$	2.07780	0.184375	0.0921875	+	0.995742i	$0.470614\pi$
$128$	−7.56856	−0.668973
$129$	−6.22535	−0.548111
$130$	1.96183	0.172064
$131$	1.04774	0.0915410	0.0457705	−	0.998952i	$-0.485426\pi$
$131$	1.04774	0.0915410	0.0457705	+	0.998952i	$0.485426\pi$
$132$	−9.94651	−0.865733
$133$	19.3689	1.67950
$134$	−3.98065	−0.343876
$135$	−2.09748	−0.180523
$136$	−10.6644	−0.914462
$137$	3.43498	0.293470	0.146735	−	0.989176i	$-0.453124\pi$
$137$	3.43498	0.293470	0.146735	+	0.989176i	$0.453124\pi$
$138$	−7.26097	−0.618095
$139$	3.19777	0.271231	0.135616	−	0.990762i	$-0.456699\pi$
$139$	3.19777	0.271231	0.135616	+	0.990762i	$0.456699\pi$
$140$	1.82341	0.154106
$141$	1.72087	0.144923
$142$	1.13365	0.0951336
$143$	−15.3297	−1.28193
$144$	0.795596	0.0662996
$145$	−0.699851	−0.0581195
$146$	−6.28672	−0.520292
$147$	−12.8937	−1.06345
$148$	1.14682	0.0942681
$149$	−18.2013	−1.49111	−0.745553	−	0.666446i	$-0.767815\pi$
$149$	−18.2013	−1.49111	−0.745553	+	0.666446i	$0.767815\pi$
$150$	11.4782	0.937191
$151$	−6.46079	−0.525772	−0.262886	−	0.964827i	$-0.584674\pi$
$151$	−6.46079	−0.525772	−0.262886	+	0.964827i	$0.584674\pi$
$152$	15.8572	1.28619
$153$	18.2982	1.47932
$154$	8.13843	0.655814
$155$	2.26510	0.181937
$156$	19.4498	1.55723
$157$	−0.165417	−0.0132017	−0.00660085	−	0.999978i	$-0.502101\pi$
$157$	−0.165417	−0.0132017	−0.00660085	+	0.999978i	$0.502101\pi$
$158$	−2.30239	−0.183168
$159$	−6.26181	−0.496594
$160$	2.40505	0.190136
$161$	−10.4011	−0.819723
$162$	−0.371525	−0.0291898
$163$	−13.9500	−1.09265	−0.546326	−	0.837573i	$-0.683974\pi$
$163$	−13.9500	−1.09265	−0.546326	+	0.837573i	$0.683974\pi$
$164$	−14.0663	−1.09839
$165$	3.28361	0.255629
$166$	−8.68923	−0.674415
$167$	1.18916	0.0920202	0.0460101	−	0.998941i	$-0.485349\pi$
$167$	1.18916	0.0920202	0.0460101	+	0.998941i	$0.485349\pi$
$168$	−26.5497	−2.04835
$169$	16.9762	1.30586
$170$	1.36924	0.105016
$171$	−27.2082	−2.08067
$172$	−2.83946	−0.216507
$173$	18.8015	1.42945	0.714727	−	0.699404i	$-0.246551\pi$
$173$	18.8015	1.42945	0.714727	+	0.699404i	$0.246551\pi$
$174$	3.96319	0.300449
$175$	16.4422	1.24291
$176$	−0.465196	−0.0350655
$177$	−41.6738	−3.13240
$178$	−10.5984	−0.794382
$179$	−3.82954	−0.286233	−0.143117	−	0.989706i	$-0.545712\pi$
$179$	−3.82954	−0.286233	−0.143117	+	0.989706i	$0.545712\pi$
$180$	−2.56142	−0.190917
$181$	−9.29296	−0.690740	−0.345370	−	0.938467i	$-0.612247\pi$
$181$	−9.29296	−0.690740	−0.345370	+	0.938467i	$0.612247\pi$
$182$	−15.9142	−1.17964
$183$	0	0
$184$	−8.51535	−0.627760
$185$	−0.378596	−0.0278350
$186$	−12.8270	−0.940522
$187$	−10.6992	−0.782404
$188$	0.784911	0.0572455
$189$	17.0146	1.23763
$190$	−2.03598	−0.147705
$191$	−9.72488	−0.703668	−0.351834	−	0.936062i	$-0.614442\pi$
$191$	−9.72488	−0.703668	−0.351834	+	0.936062i	$0.614442\pi$
$192$	−12.6922	−0.915979
$193$	5.14964	0.370679	0.185340	−	0.982675i	$-0.440661\pi$
$193$	5.14964	0.370679	0.185340	+	0.982675i	$0.440661\pi$
$194$	−10.1773	−0.730687
$195$	−6.42090	−0.459810
$196$	−5.88098	−0.420070
$197$	11.0144	0.784740	0.392370	−	0.919807i	$-0.371655\pi$
$197$	11.0144	0.784740	0.392370	+	0.919807i	$0.371655\pi$
$198$	−11.4324	−0.812464
$199$	−7.02844	−0.498233	−0.249117	−	0.968473i	$-0.580140\pi$
$199$	−7.02844	−0.498233	−0.249117	+	0.968473i	$0.580140\pi$
$200$	13.4611	0.951846
$201$	13.0283	0.918947
$202$	13.5622	0.954236
$203$	5.67714	0.398457
$204$	13.5748	0.950429
$205$	4.64365	0.324326
$206$	2.35756	0.164259
$207$	14.6109	1.01552
$208$	0.909663	0.0630738
$209$	15.9090	1.10045
$210$	3.40882	0.235231
$211$	−13.4958	−0.929092	−0.464546	−	0.885549i	$-0.653782\pi$
$211$	−13.4958	−0.929092	−0.464546	+	0.885549i	$0.653782\pi$
$212$	−2.85609	−0.196157
$213$	−3.71033	−0.254228
$214$	−6.86692	−0.469413
$215$	0.937383	0.0639290
$216$	13.9298	0.947804
$217$	−18.3743	−1.24733
$218$	6.08362	0.412035
$219$	20.5759	1.39039
$220$	1.49770	0.100975
$221$	20.9217	1.40734
$222$	2.14395	0.143893
$223$	−6.18406	−0.414116	−0.207058	−	0.978329i	$-0.566389\pi$
$223$	−6.18406	−0.414116	−0.207058	+	0.978329i	$0.566389\pi$
$224$	−19.5096	−1.30354
$225$	−23.0970	−1.53980
$226$	−4.92219	−0.327419
$227$	−4.05517	−0.269151	−0.134575	−	0.990903i	$-0.542967\pi$
$227$	−4.05517	−0.269151	−0.134575	+	0.990903i	$0.542967\pi$
$228$	−20.1849	−1.33678
$229$	26.4785	1.74975	0.874875	−	0.484350i	$-0.160944\pi$
$229$	26.4785	1.74975	0.874875	+	0.484350i	$0.160944\pi$
$230$	1.09332	0.0720915
$231$	−26.6364	−1.75255
$232$	4.64785	0.305146
$233$	−11.8475	−0.776153	−0.388077	−	0.921627i	$-0.626860\pi$
$233$	−11.8475	−0.776153	−0.388077	+	0.921627i	$0.626860\pi$
$234$	22.3553	1.46141
$235$	−0.259120	−0.0169031
$236$	−19.0080	−1.23731
$237$	7.53553	0.489485
$238$	−11.1072	−0.719973
$239$	−26.8822	−1.73887	−0.869433	−	0.494051i	$-0.835516\pi$
$239$	−26.8822	−1.73887	−0.869433	+	0.494051i	$0.835516\pi$
$240$	−0.194850	−0.0125775
$241$	13.7786	0.887555	0.443778	−	0.896137i	$-0.353638\pi$
$241$	13.7786	0.887555	0.443778	+	0.896137i	$0.353638\pi$
$242$	−2.69494	−0.173238
$243$	16.1900	1.03859
$244$	0	0
$245$	1.94147	0.124036
$246$	−26.2965	−1.67660
$247$	−31.1092	−1.97943
$248$	−15.0430	−0.955229
$249$	28.4391	1.80226
$250$	−3.51994	−0.222621
$251$	−21.1308	−1.33376	−0.666882	−	0.745163i	$-0.732372\pi$
$251$	−21.1308	−1.33376	−0.666882	+	0.745163i	$0.732372\pi$
$252$	20.7780	1.30889
$253$	−8.54317	−0.537105
$254$	1.77172	0.111168
$255$	−4.48142	−0.280637
$256$	−15.5494	−0.971838
$257$	−11.8528	−0.739359	−0.369680	−	0.929159i	$-0.620533\pi$
$257$	−11.8528	−0.739359	−0.369680	+	0.929159i	$0.620533\pi$
$258$	−5.30831	−0.330481
$259$	3.07115	0.190832
$260$	−2.92866	−0.181628
$261$	−7.97490	−0.493634
$262$	0.893396	0.0551942
$263$	26.4070	1.62832	0.814162	−	0.580638i	$-0.197197\pi$
$263$	26.4070	1.62832	0.814162	+	0.580638i	$0.197197\pi$
$264$	−21.8071	−1.34214
$265$	0.942873	0.0579202
$266$	16.5157	1.01264
$267$	34.6876	2.12285
$268$	5.94239	0.362989
$269$	−2.78833	−0.170007	−0.0850037	−	0.996381i	$-0.527090\pi$
$269$	−2.78833	−0.170007	−0.0850037	+	0.996381i	$0.527090\pi$
$270$	−1.78851	−0.108845
$271$	−17.2265	−1.04644	−0.523218	−	0.852199i	$-0.675268\pi$
$271$	−17.2265	−1.04644	−0.523218	+	0.852199i	$0.675268\pi$
$272$	0.634892	0.0384960
$273$	52.0859	3.15238
$274$	2.92898	0.176946
$275$	13.5051	0.814389
$276$	10.8393	0.652451
$277$	−25.5102	−1.53276	−0.766379	−	0.642388i	$-0.777944\pi$
$277$	−25.5102	−1.53276	−0.766379	+	0.642388i	$0.777944\pi$
$278$	2.72671	0.163537
$279$	25.8111	1.54527
$280$	3.99772	0.238909
$281$	11.8178	0.704992	0.352496	−	0.935813i	$-0.385333\pi$
$281$	11.8178	0.704992	0.352496	+	0.935813i	$0.385333\pi$
$282$	1.46737	0.0873807
$283$	12.5631	0.746801	0.373401	−	0.927670i	$-0.378192\pi$
$283$	12.5631	0.746801	0.373401	+	0.927670i	$0.378192\pi$
$284$	−1.69233	−0.100421
$285$	6.66358	0.394716
$286$	−13.0715	−0.772933
$287$	−37.6689	−2.22353
$288$	27.4058	1.61490
$289$	−2.39788	−0.141052
$290$	−0.596758	−0.0350428
$291$	33.3094	1.95263
$292$	9.38493	0.549212
$293$	25.9849	1.51805	0.759027	−	0.651059i	$-0.225675\pi$
$293$	25.9849	1.51805	0.759027	+	0.651059i	$0.225675\pi$
$294$	−10.9943	−0.641203
$295$	6.27504	0.365347
$296$	2.51433	0.146143
$297$	13.9753	0.810931
$298$	−15.5201	−0.899055
$299$	16.7057	0.966114
$300$	−17.1349	−0.989283
$301$	−7.60398	−0.438286
$302$	−5.50907	−0.317011
$303$	−44.3881	−2.55003
$304$	−0.944043	−0.0541446
$305$	0	0
$306$	15.6027	0.891949
$307$	14.5951	0.832986	0.416493	−	0.909139i	$-0.363259\pi$
$307$	14.5951	0.832986	0.416493	+	0.909139i	$0.363259\pi$
$308$	−12.1492	−0.692266
$309$	−7.71610	−0.438954
$310$	1.93143	0.109698
$311$	26.8507	1.52256	0.761281	−	0.648422i	$-0.224571\pi$
$311$	26.8507	1.52256	0.761281	+	0.648422i	$0.224571\pi$
$312$	42.6425	2.41416
$313$	−1.10224	−0.0623024	−0.0311512	−	0.999515i	$-0.509917\pi$
$313$	−1.10224	−0.0623024	−0.0311512	+	0.999515i	$0.509917\pi$
$314$	−0.141050	−0.00795989
$315$	−6.85939	−0.386483
$316$	3.43705	0.193349
$317$	−8.53744	−0.479511	−0.239755	−	0.970833i	$-0.577067\pi$
$317$	−8.53744	−0.479511	−0.239755	+	0.970833i	$0.577067\pi$
$318$	−5.33940	−0.299419
$319$	4.66304	0.261080
$320$	1.91113	0.106835
$321$	22.4748	1.25442
$322$	−8.86895	−0.494247
$323$	−21.7124	−1.20811
$324$	0.554620	0.0308122
$325$	−26.4084	−1.46488
$326$	−11.8951	−0.658808
$327$	−19.9112	−1.10109
$328$	−30.8394	−1.70282
$329$	2.10196	0.115885
$330$	2.79991	0.154130
$331$	−8.05798	−0.442907	−0.221453	−	0.975171i	$-0.571080\pi$
$331$	−8.05798	−0.442907	−0.221453	+	0.975171i	$0.571080\pi$
$332$	12.9715	0.711901
$333$	−4.31416	−0.236414
$334$	1.01399	0.0554831
$335$	−1.96174	−0.107181
$336$	1.58061	0.0862292
$337$	0.000980689 0	5.34215e−5 0	2.67108e−5	−	1.00000i	$-0.499991\pi$
$337$	0.000980689 0	5.34215e−5 0	2.67108e−5		1.00000i	$0.499991\pi$
$338$	14.4755	0.787363
$339$	16.1099	0.874970
$340$	−2.04403	−0.110853
$341$	−15.0921	−0.817283
$342$	−23.2002	−1.25453
$343$	8.11272	0.438046
$344$	−6.22535	−0.335648
$345$	−3.57835	−0.192652
$346$	16.0319	0.861881
$347$	12.5587	0.674186	0.337093	−	0.941471i	$-0.390556\pi$
$347$	12.5587	0.674186	0.337093	+	0.941471i	$0.390556\pi$
$348$	−5.91633	−0.317148
$349$	3.12172	0.167102	0.0835509	−	0.996504i	$-0.473374\pi$
$349$	3.12172	0.167102	0.0835509	+	0.996504i	$0.473374\pi$
$350$	14.0201	0.749406
$351$	−27.3279	−1.45866
$352$	−16.0246	−0.854113
$353$	−20.6386	−1.09848	−0.549241	−	0.835664i	$-0.685083\pi$
$353$	−20.6386	−1.09848	−0.549241	+	0.835664i	$0.685083\pi$
$354$	−35.5349	−1.88866
$355$	0.558684	0.0296519
$356$	15.8215	0.838536
$357$	36.3530	1.92400
$358$	−3.26542	−0.172583
$359$	13.5092	0.712987	0.356494	−	0.934298i	$-0.383972\pi$
$359$	13.5092	0.712987	0.356494	+	0.934298i	$0.383972\pi$
$360$	−5.61575	−0.295976
$361$	13.2849	0.699207
$362$	−7.92404	−0.416478
$363$	8.82032	0.462947
$364$	23.7571	1.24521
$365$	−3.09822	−0.162168
$366$	0	0
$367$	−24.8273	−1.29597	−0.647987	−	0.761652i	$-0.724389\pi$
$367$	−24.8273	−1.29597	−0.647987	+	0.761652i	$0.724389\pi$
$368$	0.506953	0.0264267
$369$	52.9150	2.75465
$370$	−0.322826	−0.0167829
$371$	−7.64852	−0.397091
$372$	19.1484	0.992799
$373$	7.26110	0.375966	0.187983	−	0.982172i	$-0.439805\pi$
$373$	7.26110	0.375966	0.187983	+	0.982172i	$0.439805\pi$
$374$	−9.12314	−0.471746
$375$	11.5205	0.594914
$376$	1.72087	0.0887470
$377$	−9.11829	−0.469616
$378$	14.5083	0.746224
$379$	−19.1437	−0.983347	−0.491673	−	0.870780i	$-0.663615\pi$
$379$	−19.1437	−0.983347	−0.491673	+	0.870780i	$0.663615\pi$
$380$	3.03935	0.155915
$381$	−5.79871	−0.297077
$382$	−8.29233	−0.424273
$383$	9.46801	0.483793	0.241896	−	0.970302i	$-0.422231\pi$
$383$	9.46801	0.483793	0.241896	+	0.970302i	$0.422231\pi$
$384$	21.1223	1.07789
$385$	4.01078	0.204408
$386$	4.39106	0.223499
$387$	10.6816	0.542977
$388$	15.1929	0.771301
$389$	−18.1913	−0.922333	−0.461167	−	0.887314i	$-0.652569\pi$
$389$	−18.1913	−0.922333	−0.461167	+	0.887314i	$0.652569\pi$
$390$	−5.47505	−0.277240
$391$	11.6596	0.589651
$392$	−12.8937	−0.651229
$393$	−2.92401	−0.147497
$394$	9.39186	0.473155
$395$	−1.13466	−0.0570911
$396$	17.0665	0.857623
$397$	20.6379	1.03579	0.517894	−	0.855445i	$-0.326716\pi$
$397$	20.6379	1.03579	0.517894	+	0.855445i	$0.326716\pi$
$398$	−5.99310	−0.300407
$399$	−54.0545	−2.70611
$400$	−0.801395	−0.0400697
$401$	7.94504	0.396756	0.198378	−	0.980126i	$-0.436433\pi$
$401$	7.94504	0.396756	0.198378	+	0.980126i	$0.436433\pi$
$402$	11.1092	0.554074
$403$	29.5117	1.47008
$404$	−20.2460	−1.00728
$405$	−0.183095	−0.00909806
$406$	4.84086	0.240248
$407$	2.52255	0.125038
$408$	29.7620	1.47344
$409$	17.2064	0.850802	0.425401	−	0.905005i	$-0.360133\pi$
$409$	17.2064	0.850802	0.425401	+	0.905005i	$0.360133\pi$
$410$	3.95960	0.195551
$411$	−9.58630	−0.472857
$412$	−3.51941	−0.173389
$413$	−50.9027	−2.50476
$414$	12.4586	0.612305
$415$	−4.28222	−0.210206
$416$	31.3351	1.53633
$417$	−8.92430	−0.437025
$418$	13.5655	0.663511
$419$	25.4400	1.24282	0.621412	−	0.783484i	$-0.286559\pi$
$419$	25.4400	1.24282	0.621412	+	0.783484i	$0.286559\pi$
$420$	−5.08876	−0.248306
$421$	11.8575	0.577900	0.288950	−	0.957344i	$-0.406694\pi$
$421$	11.8575	0.577900	0.288950	+	0.957344i	$0.406694\pi$
$422$	−11.5078	−0.560191
$423$	−2.95271	−0.143566
$424$	−6.26181	−0.304100
$425$	−18.4316	−0.894063
$426$	−3.16377	−0.153285
$427$	0	0
$428$	10.2511	0.495504
$429$	42.7818	2.06553
$430$	0.799299	0.0385456
$431$	5.77315	0.278083	0.139041	−	0.990287i	$-0.455598\pi$
$431$	5.77315	0.278083	0.139041	+	0.990287i	$0.455598\pi$
$432$	−0.829297	−0.0398996
$433$	−22.0053	−1.05751	−0.528755	−	0.848775i	$-0.677341\pi$
$433$	−22.0053	−1.05751	−0.528755	+	0.848775i	$0.677341\pi$
$434$	−15.6676	−0.752070
$435$	1.95314	0.0936458
$436$	−9.08175	−0.434937
$437$	−17.3371	−0.829344
$438$	17.5449	0.838328
$439$	−29.5892	−1.41222	−0.706108	−	0.708104i	$-0.749551\pi$
$439$	−29.5892	−1.41222	−0.706108	+	0.708104i	$0.749551\pi$
$440$	3.28361	0.156540
$441$	22.1233	1.05349
$442$	17.8397	0.848550
$443$	−23.9222	−1.13658	−0.568289	−	0.822829i	$-0.692394\pi$
$443$	−23.9222	−1.13658	−0.568289	+	0.822829i	$0.692394\pi$
$444$	−3.20054	−0.151891
$445$	−5.22309	−0.247598
$446$	−5.27310	−0.249689
$447$	50.7959	2.40257
$448$	−15.5029	−0.732444
$449$	0.529659	0.0249962	0.0124981	−	0.999922i	$-0.496022\pi$
$449$	0.529659	0.0249962	0.0124981	+	0.999922i	$0.496022\pi$
$450$	−19.6946	−0.928412
$451$	−30.9402	−1.45692
$452$	7.34794	0.345618
$453$	18.0307	0.847157
$454$	−3.45781	−0.162283
$455$	−7.84284	−0.367678
$456$	−44.2542	−2.07239
$457$	−13.2454	−0.619593	−0.309796	−	0.950803i	$-0.600261\pi$
$457$	−13.2454	−0.619593	−0.309796	+	0.950803i	$0.600261\pi$
$458$	22.5780	1.05500
$459$	−19.0733	−0.890266
$460$	−1.63213	−0.0760986
$461$	−9.36619	−0.436227	−0.218113	−	0.975923i	$-0.569990\pi$
$461$	−9.36619	−0.436227	−0.218113	+	0.975923i	$0.569990\pi$
$462$	−22.7127	−1.05669
$463$	9.63194	0.447634	0.223817	−	0.974631i	$-0.428148\pi$
$463$	9.63194	0.447634	0.223817	+	0.974631i	$0.428148\pi$
$464$	−0.276705	−0.0128457
$465$	−6.32141	−0.293148
$466$	−10.1022	−0.467977
$467$	17.0209	0.787633	0.393817	−	0.919189i	$-0.371155\pi$
$467$	17.0209	0.787633	0.393817	+	0.919189i	$0.371155\pi$
$468$	−33.3725	−1.54264
$469$	15.9135	0.734818
$470$	−0.220950	−0.0101917
$471$	0.461643	0.0212714
$472$	−41.6738	−1.91819
$473$	−6.24569	−0.287177
$474$	6.42549	0.295133
$475$	27.4065	1.25750
$476$	16.5811	0.759992
$477$	10.7442	0.491942
$478$	−22.9223	−1.04844
$479$	−33.3380	−1.52325	−0.761627	−	0.648016i	$-0.775599\pi$
$479$	−33.3380	−1.52325	−0.761627	+	0.648016i	$0.775599\pi$
$480$	−6.71198	−0.306359
$481$	−4.93269	−0.224912
$482$	11.7489	0.535146
$483$	29.0273	1.32079
$484$	4.02306	0.182867
$485$	−5.01557	−0.227745
$486$	13.8051	0.626213
$487$	5.23231	0.237099	0.118549	−	0.992948i	$-0.462176\pi$
$487$	5.23231	0.237099	0.118549	+	0.992948i	$0.462176\pi$
$488$	0	0
$489$	38.9316	1.76055
$490$	1.65547	0.0747867
$491$	−15.3077	−0.690827	−0.345413	−	0.938451i	$-0.612261\pi$
$491$	−15.3077	−0.690827	−0.345413	+	0.938451i	$0.612261\pi$
$492$	39.2560	1.76980
$493$	−6.36404	−0.286622
$494$	−26.5265	−1.19349
$495$	−5.63410	−0.253234
$496$	0.895567	0.0402121
$497$	−4.53201	−0.203288
$498$	24.2498	1.08666
$499$	8.39563	0.375840	0.187920	−	0.982184i	$-0.439825\pi$
$499$	8.39563	0.375840	0.187920	+	0.982184i	$0.439825\pi$
$500$	5.25464	0.234994
$501$	−3.31870	−0.148269
$502$	−18.0181	−0.804186
$503$	−0.958686	−0.0427457	−0.0213729	−	0.999772i	$-0.506804\pi$
$503$	−0.958686	−0.0427457	−0.0213729	+	0.999772i	$0.506804\pi$
$504$	45.5546	2.02916
$505$	6.68374	0.297423
$506$	−7.28470	−0.323844
$507$	−47.3771	−2.10409
$508$	−2.64487	−0.117347
$509$	1.62117	0.0718571	0.0359286	−	0.999354i	$-0.488561\pi$
$509$	1.62117	0.0718571	0.0359286	+	0.999354i	$0.488561\pi$
$510$	−3.82127	−0.169209
$511$	25.1325	1.11180
$512$	1.87826	0.0830082
$513$	28.3608	1.25216
$514$	−10.1068	−0.445793
$515$	1.16185	0.0511974
$516$	7.92434	0.348850
$517$	1.72649	0.0759310
$518$	2.61874	0.115061
$519$	−52.4711	−2.30323
$520$	−6.42090	−0.281575
$521$	19.5755	0.857618	0.428809	−	0.903395i	$-0.358933\pi$
$521$	19.5755	0.857618	0.428809	+	0.903395i	$0.358933\pi$
$522$	−6.80014	−0.297634
$523$	−38.7577	−1.69476	−0.847378	−	0.530990i	$-0.821820\pi$
$523$	−38.7577	−1.69476	−0.847378	+	0.530990i	$0.821820\pi$
$524$	−1.33368	−0.0582620
$525$	−45.8866	−2.00266
$526$	22.5170	0.981789
$527$	20.5975	0.897240
$528$	1.29826	0.0564997
$529$	−13.6900	−0.595217
$530$	0.803981	0.0349227
$531$	71.5050	3.10305
$532$	−24.6550	−1.06893
$533$	60.5016	2.62062
$534$	29.5779	1.27996
$535$	−3.38415	−0.146310
$536$	13.0283	0.562738
$537$	10.6874	0.461197
$538$	−2.37759	−0.102505
$539$	−12.9358	−0.557185
$540$	2.66992	0.114895
$541$	−31.3968	−1.34985	−0.674927	−	0.737885i	$-0.735825\pi$
$541$	−31.3968	−1.34985	−0.674927	+	0.737885i	$0.735825\pi$
$542$	−14.6889	−0.630942
$543$	25.9347	1.11296
$544$	21.8701	0.937673
$545$	2.99813	0.128426
$546$	44.4132	1.90071
$547$	35.0033	1.49663	0.748317	−	0.663341i	$-0.230862\pi$
$547$	35.0033	1.49663	0.748317	+	0.663341i	$0.230862\pi$
$548$	−4.37244	−0.186781
$549$	0	0
$550$	11.5157	0.491031
$551$	9.46292	0.403134
$552$	23.7646	1.01149
$553$	9.20431	0.391407
$554$	−21.7523	−0.924168
$555$	1.05658	0.0448494
$556$	−4.07049	−0.172627
$557$	−9.49279	−0.402222	−0.201111	−	0.979568i	$-0.564455\pi$
$557$	−9.49279	−0.402222	−0.201111	+	0.979568i	$0.564455\pi$
$558$	22.0089	0.931712
$559$	12.2131	0.516558
$560$	−0.238000	−0.0100573
$561$	29.8593	1.26066
$562$	10.0770	0.425071
$563$	−34.2346	−1.44282	−0.721408	−	0.692511i	$-0.756505\pi$
$563$	−34.2346	−1.44282	−0.721408	+	0.692511i	$0.756505\pi$
$564$	−2.19052	−0.0922376
$565$	−2.42575	−0.102052
$566$	10.7125	0.450280
$567$	1.48525	0.0623747
$568$	−3.71033	−0.155682
$569$	−36.4753	−1.52912	−0.764562	−	0.644550i	$-0.777045\pi$
$569$	−36.4753	−1.52912	−0.764562	+	0.644550i	$0.777045\pi$
$570$	5.68198	0.237992
$571$	−44.9847	−1.88255	−0.941276	−	0.337637i	$-0.890372\pi$
$571$	−44.9847	−1.88255	−0.941276	+	0.337637i	$0.890372\pi$
$572$	19.5134	0.815895
$573$	27.1401	1.13379
$574$	−32.1200	−1.34066
$575$	−14.7174	−0.613756
$576$	21.7776	0.907398
$577$	−37.6571	−1.56769	−0.783844	−	0.620958i	$-0.786744\pi$
$577$	−37.6571	−1.56769	−0.783844	+	0.620958i	$0.786744\pi$
$578$	−2.04465	−0.0850463
$579$	−14.3716	−0.597262
$580$	0.890852	0.0369906
$581$	34.7371	1.44114
$582$	28.4027	1.17733
$583$	−6.28227	−0.260185
$584$	20.5759	0.851436
$585$	11.0172	0.455503
$586$	22.1571	0.915303
$587$	−30.0336	−1.23962	−0.619810	−	0.784752i	$-0.712790\pi$
$587$	−30.0336	−1.23962	−0.619810	+	0.784752i	$0.712790\pi$
$588$	16.4126	0.676843
$589$	−30.6271	−1.26197
$590$	5.35068	0.220284
$591$	−30.7388	−1.26442
$592$	−0.149688	−0.00615215
$593$	−6.01907	−0.247173	−0.123587	−	0.992334i	$-0.539440\pi$
$593$	−6.01907	−0.247173	−0.123587	+	0.992334i	$0.539440\pi$
$594$	11.9167	0.488946
$595$	−5.47385	−0.224406
$596$	23.1687	0.949027
$597$	19.6149	0.802785
$598$	14.2448	0.582513
$599$	20.3589	0.831842	0.415921	−	0.909401i	$-0.363459\pi$
$599$	20.3589	0.831842	0.415921	+	0.909401i	$0.363459\pi$
$600$	−37.5672	−1.53367
$601$	−8.58916	−0.350359	−0.175180	−	0.984536i	$-0.556051\pi$
$601$	−8.58916	−0.350359	−0.175180	+	0.984536i	$0.556051\pi$
$602$	−6.48386	−0.264262
$603$	−22.3543	−0.910339
$604$	8.22405	0.334632
$605$	−1.32812	−0.0539958
$606$	−37.8494	−1.53753
$607$	12.5254	0.508390	0.254195	−	0.967153i	$-0.418190\pi$
$607$	12.5254	0.508390	0.254195	+	0.967153i	$0.418190\pi$
$608$	−32.5194	−1.31884
$609$	−15.8437	−0.642020
$610$	0	0
$611$	−3.37605	−0.136580
$612$	−23.2921	−0.941526
$613$	33.6555	1.35933	0.679666	−	0.733522i	$-0.262125\pi$
$613$	33.6555	1.35933	0.679666	+	0.733522i	$0.262125\pi$
$614$	12.4451	0.502245
$615$	−12.9594	−0.522575
$616$	−26.6364	−1.07321
$617$	−24.1833	−0.973585	−0.486792	−	0.873518i	$-0.661833\pi$
$617$	−24.1833	−0.973585	−0.486792	+	0.873518i	$0.661833\pi$
$618$	−6.57946	−0.264665
$619$	−30.8516	−1.24003	−0.620016	−	0.784590i	$-0.712874\pi$
$619$	−30.8516	−1.24003	−0.620016	+	0.784590i	$0.712874\pi$
$620$	−2.88328	−0.115795
$621$	−15.2298	−0.611150
$622$	22.8954	0.918021
$623$	42.3694	1.69749
$624$	−2.53868	−0.101628
$625$	22.3824	0.895295
$626$	−0.939873	−0.0375649
$627$	−44.3988	−1.77312
$628$	0.210562	0.00840232
$629$	−3.44274	−0.137271
$630$	−5.84895	−0.233028
$631$	−7.90779	−0.314804	−0.157402	−	0.987535i	$-0.550312\pi$
$631$	−7.90779	−0.314804	−0.157402	+	0.987535i	$0.550312\pi$
$632$	7.53553	0.299747
$633$	37.6641	1.49701
$634$	−7.27981	−0.289118
$635$	0.873141	0.0346495
$636$	7.97076	0.316061
$637$	25.2952	1.00223
$638$	3.97614	0.157417
$639$	6.36629	0.251846
$640$	−3.18049	−0.125720
$641$	−22.2302	−0.878040	−0.439020	−	0.898477i	$-0.644674\pi$
$641$	−22.2302	−0.878040	−0.439020	+	0.898477i	$0.644674\pi$
$642$	19.1641	0.756348
$643$	34.1133	1.34530	0.672649	−	0.739962i	$-0.265157\pi$
$643$	34.1133	1.34530	0.672649	+	0.739962i	$0.265157\pi$
$644$	13.2397	0.521719
$645$	−2.61604	−0.103006
$646$	−18.5140	−0.728424
$647$	−4.24338	−0.166825	−0.0834123	−	0.996515i	$-0.526582\pi$
$647$	−4.24338	−0.166825	−0.0834123	+	0.996515i	$0.526582\pi$
$648$	1.21597	0.0477678
$649$	−41.8100	−1.64119
$650$	−22.5183	−0.883239
$651$	51.2788	2.00977
$652$	17.7572	0.695427
$653$	39.6201	1.55045	0.775227	−	0.631683i	$-0.217636\pi$
$653$	39.6201	1.55045	0.775227	+	0.631683i	$0.217636\pi$
$654$	−16.9781	−0.663896
$655$	0.440283	0.0172033
$656$	1.83599	0.0716834
$657$	−35.3046	−1.37737
$658$	1.79233	0.0698722
$659$	22.3139	0.869225	0.434613	−	0.900618i	$-0.356885\pi$
$659$	22.3139	0.869225	0.434613	+	0.900618i	$0.356885\pi$
$660$	−4.17976	−0.162697
$661$	−41.1331	−1.59989	−0.799946	−	0.600072i	$-0.795138\pi$
$661$	−41.1331	−1.59989	−0.799946	+	0.600072i	$0.795138\pi$
$662$	−6.87098	−0.267048
$663$	−58.3880	−2.26760
$664$	28.4391	1.10365
$665$	8.13926	0.315627
$666$	−3.67865	−0.142545
$667$	−5.08160	−0.196760
$668$	−1.51370	−0.0585670
$669$	17.2584	0.667249
$670$	−1.67276	−0.0646245
$671$	0	0
$672$	54.4471	2.10034
$673$	46.6298	1.79745	0.898724	−	0.438515i	$-0.144495\pi$
$673$	46.6298	1.79745	0.898724	+	0.438515i	$0.144495\pi$
$674$	0.000836226 0	3.22102e−5 0
$675$	24.0754	0.926661
$676$	−21.6093	−0.831127
$677$	−7.51148	−0.288689	−0.144345	−	0.989527i	$-0.546107\pi$
$677$	−7.51148	−0.288689	−0.144345	+	0.989527i	$0.546107\pi$
$678$	13.7368	0.527558
$679$	40.6860	1.56138
$680$	−4.48142	−0.171855
$681$	11.3171	0.433673
$682$	−12.8689	−0.492776
$683$	27.3521	1.04660	0.523299	−	0.852149i	$-0.324701\pi$
$683$	27.3521	1.04660	0.523299	+	0.852149i	$0.324701\pi$
$684$	34.6338	1.32426
$685$	1.44346	0.0551517
$686$	6.91766	0.264117
$687$	−73.8960	−2.81931
$688$	0.370620	0.0141297
$689$	12.2846	0.468006
$690$	−3.05123	−0.116158
$691$	48.1967	1.83349	0.916744	−	0.399476i	$-0.130808\pi$
$691$	48.1967	1.83349	0.916744	+	0.399476i	$0.130808\pi$
$692$	−23.9328	−0.909787
$693$	45.7034	1.73613
$694$	10.7087	0.406497
$695$	1.34378	0.0509724
$696$	−12.9712	−0.491671
$697$	42.2267	1.59945
$698$	2.66187	0.100753
$699$	33.0638	1.25059
$700$	−20.9295	−0.791060
$701$	22.9609	0.867222	0.433611	−	0.901100i	$-0.357239\pi$
$701$	22.9609	0.867222	0.433611	+	0.901100i	$0.357239\pi$
$702$	−23.3023	−0.879489
$703$	5.11913	0.193071
$704$	−12.7336	−0.479917
$705$	0.723150	0.0272354
$706$	−17.5984	−0.662324
$707$	−54.2180	−2.03908
$708$	53.0473	1.99364
$709$	−39.1957	−1.47203	−0.736013	−	0.676967i	$-0.763294\pi$
$709$	−39.1957	−1.47203	−0.736013	+	0.676967i	$0.763294\pi$
$710$	0.476386	0.0178784
$711$	−12.9297	−0.484900
$712$	34.6876	1.29997
$713$	16.4468	0.615937
$714$	30.9979	1.16007
$715$	−6.44188	−0.240913
$716$	4.87468	0.182175
$717$	75.0226	2.80177
$718$	11.5192	0.429892
$719$	−24.2070	−0.902770	−0.451385	−	0.892329i	$-0.649070\pi$
$719$	−24.2070	−0.902770	−0.451385	+	0.892329i	$0.649070\pi$
$720$	0.334328	0.0124597
$721$	−9.42487	−0.351000
$722$	11.3280	0.421583
$723$	−38.4531	−1.43009
$724$	11.8292	0.439627
$725$	8.03303	0.298339
$726$	7.52102	0.279131
$727$	−16.7402	−0.620859	−0.310429	−	0.950596i	$-0.600473\pi$
$727$	−16.7402	−0.620859	−0.310429	+	0.950596i	$0.600473\pi$
$728$	52.0859	1.93043
$729$	−43.8758	−1.62503
$730$	−2.64183	−0.0977784
$731$	8.52402	0.315272
$732$	0	0
$733$	−5.57781	−0.206021	−0.103011	−	0.994680i	$-0.532848\pi$
$733$	−5.57781	−0.206021	−0.103011	+	0.994680i	$0.532848\pi$
$734$	−21.1700	−0.781400
$735$	−5.41823	−0.199854
$736$	17.4630	0.643694
$737$	13.0709	0.481473
$738$	45.1202	1.66090
$739$	−1.02509	−0.0377085	−0.0188543	−	0.999822i	$-0.506002\pi$
$739$	−1.02509	−0.0377085	−0.0188543	+	0.999822i	$0.506002\pi$
$740$	0.481921	0.0177158
$741$	86.8192	3.18938
$742$	−6.52183	−0.239424
$743$	52.8258	1.93799	0.968995	−	0.247082i	$-0.0794717\pi$
$743$	52.8258	1.93799	0.968995	+	0.247082i	$0.0794717\pi$
$744$	41.9817	1.53912
$745$	−7.64861	−0.280223
$746$	6.19148	0.226686
$747$	−48.7966	−1.78537
$748$	13.6192	0.497967
$749$	27.4520	1.00307
$750$	9.82341	0.358700
$751$	6.62976	0.241923	0.120962	−	0.992657i	$-0.461402\pi$
$751$	6.62976	0.241923	0.120962	+	0.992657i	$0.461402\pi$
$752$	−0.102450	−0.00373597
$753$	58.9716	2.14905
$754$	−7.77510	−0.283152
$755$	−2.71498	−0.0988082
$756$	−21.6582	−0.787702
$757$	30.3686	1.10377	0.551883	−	0.833922i	$-0.313910\pi$
$757$	30.3686	1.10377	0.551883	+	0.833922i	$0.313910\pi$
$758$	−16.3237	−0.592903
$759$	23.8422	0.865417
$760$	6.66358	0.241713
$761$	−20.2716	−0.734845	−0.367422	−	0.930054i	$-0.619760\pi$
$761$	−20.2716	−0.734845	−0.367422	+	0.930054i	$0.619760\pi$
$762$	−4.94451	−0.179121
$763$	−24.3206	−0.880465
$764$	12.3790	0.447855
$765$	7.68934	0.278009
$766$	8.07330	0.291700
$767$	81.7569	2.95207
$768$	43.3951	1.56589
$769$	−43.5961	−1.57211	−0.786057	−	0.618154i	$-0.787881\pi$
$769$	−43.5961	−1.57211	−0.786057	+	0.618154i	$0.787881\pi$
$770$	3.41996	0.123247
$771$	33.0788	1.19130
$772$	−6.55506	−0.235922
$773$	38.2470	1.37565	0.687825	−	0.725877i	$-0.258566\pi$
$773$	38.2470	1.37565	0.687825	+	0.725877i	$0.258566\pi$
$774$	9.10813	0.327385
$775$	−25.9992	−0.933920
$776$	33.3094	1.19574
$777$	−8.57092	−0.307480
$778$	−15.5115	−0.556116
$779$	−62.7883	−2.24962
$780$	8.17327	0.292650
$781$	−3.72246	−0.133200
$782$	9.94204	0.355527
$783$	8.31273	0.297073
$784$	0.767612	0.0274147
$785$	−0.0695120	−0.00248099
$786$	−2.49328	−0.0889323
$787$	27.6602	0.985981	0.492990	−	0.870035i	$-0.335904\pi$
$787$	27.6602	0.985981	0.492990	+	0.870035i	$0.335904\pi$
$788$	−14.0203	−0.499454
$789$	−73.6963	−2.62366
$790$	−0.967519	−0.0344228
$791$	19.6775	0.699652
$792$	37.4172	1.32956
$793$	0	0
$794$	17.5978	0.624522
$795$	−2.63136	−0.0933248
$796$	8.94662	0.317104
$797$	25.5435	0.904796	0.452398	−	0.891816i	$-0.350569\pi$
$797$	25.5435	0.904796	0.452398	+	0.891816i	$0.350569\pi$
$798$	−46.0918	−1.63163
$799$	−2.35629	−0.0833595
$800$	−27.6056	−0.976005
$801$	−59.5179	−2.10296
$802$	6.77467	0.239222
$803$	20.6431	0.728480
$804$	−16.5840	−0.584871
$805$	−4.37079	−0.154050
$806$	25.1644	0.886378
$807$	7.78164	0.273927
$808$	−44.3881	−1.56157
$809$	30.0256	1.05564	0.527822	−	0.849355i	$-0.323009\pi$
$809$	30.0256	1.05564	0.527822	+	0.849355i	$0.323009\pi$
$810$	−0.156124	−0.00548562
$811$	1.69488	0.0595151	0.0297576	−	0.999557i	$-0.490526\pi$
$811$	1.69488	0.0595151	0.0297576	+	0.999557i	$0.490526\pi$
$812$	−7.22652	−0.253601
$813$	48.0755	1.68608
$814$	2.15096	0.0753910
$815$	−5.86214	−0.205342
$816$	−1.77185	−0.0620272
$817$	−12.6747	−0.443430
$818$	14.6718	0.512986
$819$	−89.3703	−3.12285
$820$	−5.91097	−0.206420
$821$	17.0356	0.594547	0.297273	−	0.954792i	$-0.403923\pi$
$821$	17.0356	0.594547	0.297273	+	0.954792i	$0.403923\pi$
$822$	−8.17417	−0.285107
$823$	29.7174	1.03588	0.517942	−	0.855416i	$-0.326698\pi$
$823$	29.7174	1.03588	0.517942	+	0.855416i	$0.326698\pi$
$824$	−7.71610	−0.268803
$825$	−37.6899	−1.31220
$826$	−43.4043	−1.51023
$827$	−1.34329	−0.0467108	−0.0233554	−	0.999727i	$-0.507435\pi$
$827$	−1.34329	−0.0467108	−0.0233554	+	0.999727i	$0.507435\pi$
$828$	−18.5984	−0.646339
$829$	10.3614	0.359868	0.179934	−	0.983679i	$-0.442412\pi$
$829$	10.3614	0.359868	0.179934	+	0.983679i	$0.442412\pi$
$830$	−3.65142	−0.126743
$831$	71.1936	2.46968
$832$	24.8999	0.863248
$833$	17.6546	0.611695
$834$	−7.60968	−0.263502
$835$	0.499714	0.0172933
$836$	−20.2509	−0.700391
$837$	−26.9045	−0.929954
$838$	21.6925	0.749354
$839$	−24.2269	−0.836406	−0.418203	−	0.908354i	$-0.637340\pi$
$839$	−24.2269	−0.836406	−0.418203	+	0.908354i	$0.637340\pi$
$840$	−11.1568	−0.384946
$841$	−26.2264	−0.904357
$842$	10.1108	0.348442
$843$	−32.9811	−1.13593
$844$	17.1791	0.591328
$845$	7.13381	0.245411
$846$	−2.51775	−0.0865622
$847$	10.7736	0.370186
$848$	0.372790	0.0128017
$849$	−35.0611	−1.20329
$850$	−15.7165	−0.539070
$851$	−2.74898	−0.0942337
$852$	4.72294	0.161805
$853$	11.6307	0.398228	0.199114	−	0.979976i	$-0.436194\pi$
$853$	11.6307	0.398228	0.199114	+	0.979976i	$0.436194\pi$
$854$	0	0
$855$	−11.4335	−0.391019
$856$	22.4748	0.768174
$857$	−37.2375	−1.27201	−0.636004	−	0.771685i	$-0.719414\pi$
$857$	−37.2375	−1.27201	−0.636004	+	0.771685i	$0.719414\pi$
$858$	36.4797	1.24540
$859$	−21.6104	−0.737339	−0.368669	−	0.929561i	$-0.620187\pi$
$859$	−21.6104	−0.737339	−0.368669	+	0.929561i	$0.620187\pi$
$860$	−1.19321	−0.0406881
$861$	105.126	3.58269
$862$	4.92272	0.167668
$863$	−29.1085	−0.990865	−0.495432	−	0.868647i	$-0.664990\pi$
$863$	−29.1085	−0.990865	−0.495432	+	0.868647i	$0.664990\pi$
$864$	−28.5668	−0.971861
$865$	7.90084	0.268637
$866$	−18.7638	−0.637620
$867$	6.69197	0.227271
$868$	23.3889	0.793872
$869$	7.56015	0.256461
$870$	1.66543	0.0564632
$871$	−25.5594	−0.866046
$872$	−19.9112	−0.674277
$873$	−57.1532	−1.93434
$874$	−14.7832	−0.500048
$875$	14.0717	0.475711
$876$	−26.1914	−0.884925
$877$	−41.5427	−1.40280	−0.701398	−	0.712769i	$-0.747441\pi$
$877$	−41.5427	−1.40280	−0.701398	+	0.712769i	$0.747441\pi$
$878$	−25.2305	−0.851488
$879$	−72.5184	−2.44599
$880$	−0.195486	−0.00658984
$881$	−14.7515	−0.496991	−0.248496	−	0.968633i	$-0.579936\pi$
$881$	−14.7515	−0.496991	−0.248496	+	0.968633i	$0.579936\pi$
$882$	18.8644	0.635196
$883$	−30.0584	−1.01155	−0.505773	−	0.862667i	$-0.668793\pi$
$883$	−30.0584	−1.01155	−0.505773	+	0.862667i	$0.668793\pi$
$884$	−26.6315	−0.895715
$885$	−17.5123	−0.588670
$886$	−20.3983	−0.685293
$887$	9.11929	0.306196	0.153098	−	0.988211i	$-0.451075\pi$
$887$	9.11929	0.306196	0.153098	+	0.988211i	$0.451075\pi$
$888$	−7.01698	−0.235474
$889$	−7.08286	−0.237551
$890$	−4.45369	−0.149288
$891$	1.21994	0.0408696
$892$	7.87179	0.263567
$893$	3.50365	0.117245
$894$	43.3133	1.44861
$895$	−1.60926	−0.0537918
$896$	25.7999	0.861914
$897$	−46.6220	−1.55666
$898$	0.451637	0.0150713
$899$	−8.97700	−0.299400
$900$	29.4005	0.980016
$901$	8.57395	0.285640
$902$	−26.3824	−0.878439
$903$	21.2211	0.706195
$904$	16.1099	0.535807
$905$	−3.90512	−0.129811
$906$	15.3747	0.510789
$907$	−19.1590	−0.636164	−0.318082	−	0.948063i	$-0.603039\pi$
$907$	−19.1590	−0.636164	−0.318082	+	0.948063i	$0.603039\pi$
$908$	5.16189	0.171303
$909$	76.1622	2.52614
$910$	−6.68753	−0.221690
$911$	31.8469	1.05513	0.527567	−	0.849513i	$-0.323104\pi$
$911$	31.8469	1.05513	0.527567	+	0.849513i	$0.323104\pi$
$912$	2.63463	0.0872412
$913$	28.5320	0.944273
$914$	−11.2942	−0.373580
$915$	0	0
$916$	−33.7049	−1.11364
$917$	−3.57154	−0.117943
$918$	−16.2637	−0.536781
$919$	−58.5854	−1.93255	−0.966277	−	0.257506i	$-0.917099\pi$
$919$	−58.5854	−1.93255	−0.966277	+	0.257506i	$0.917099\pi$
$920$	−3.57835	−0.117975
$921$	−40.7319	−1.34216
$922$	−7.98647	−0.263020
$923$	7.27904	0.239593
$924$	33.9059	1.11542
$925$	4.34560	0.142883
$926$	8.21308	0.269899
$927$	13.2395	0.434842
$928$	−9.53165	−0.312892
$929$	−49.6851	−1.63012	−0.815058	−	0.579379i	$-0.803295\pi$
$929$	−49.6851	−1.63012	−0.815058	+	0.579379i	$0.803295\pi$
$930$	−5.39021	−0.176752
$931$	−26.2512	−0.860349
$932$	15.0808	0.493989
$933$	−74.9346	−2.45325
$934$	14.5136	0.474899
$935$	−4.49606	−0.147037
$936$	−73.1671	−2.39154
$937$	22.5609	0.737031	0.368516	−	0.929622i	$-0.379866\pi$
$937$	22.5609	0.737031	0.368516	+	0.929622i	$0.379866\pi$
$938$	13.5693	0.443054
$939$	3.07612	0.100386
$940$	0.329838	0.0107581
$941$	−23.3181	−0.760149	−0.380074	−	0.924956i	$-0.624102\pi$
$941$	−23.3181	−0.760149	−0.380074	+	0.924956i	$0.624102\pi$
$942$	0.393640	0.0128255
$943$	33.7174	1.09799
$944$	2.48101	0.0807499
$945$	7.14996	0.232588
$946$	−5.32565	−0.173152
$947$	−21.3146	−0.692631	−0.346316	−	0.938118i	$-0.612567\pi$
$947$	−21.3146	−0.692631	−0.346316	+	0.938118i	$0.612567\pi$
$948$	−9.59210	−0.311537
$949$	−40.3664	−1.31035
$950$	23.3694	0.758202
$951$	23.8262	0.772618
$952$	36.3530	1.17821
$953$	37.0813	1.20118	0.600591	−	0.799557i	$-0.294932\pi$
$953$	37.0813	1.20118	0.600591	+	0.799557i	$0.294932\pi$
$954$	9.16147	0.296614
$955$	−4.08663	−0.132240
$956$	34.2188	1.10672
$957$	−13.0136	−0.420669
$958$	−28.4271	−0.918438
$959$	−11.7092	−0.378111
$960$	−5.33355	−0.172140
$961$	−1.94560	−0.0627613
$962$	−4.20607	−0.135609
$963$	−38.5629	−1.24267
$964$	−17.5389	−0.564892
$965$	2.16400	0.0696617
$966$	24.7514	0.796363
$967$	45.8076	1.47307	0.736537	−	0.676398i	$-0.236460\pi$
$967$	45.8076	1.47307	0.736537	+	0.676398i	$0.236460\pi$
$968$	8.82032	0.283496
$969$	60.5948	1.94658
$970$	−4.27674	−0.137318
$971$	−18.1020	−0.580922	−0.290461	−	0.956887i	$-0.593809\pi$
$971$	−18.1020	−0.580922	−0.290461	+	0.956887i	$0.593809\pi$
$972$	−20.6085	−0.661019
$973$	−10.9006	−0.349458
$974$	4.46155	0.142957
$975$	73.7004	2.36030
$976$	0	0
$977$	−1.81750	−0.0581469	−0.0290734	−	0.999577i	$-0.509256\pi$
$977$	−1.81750	−0.0581469	−0.0290734	+	0.999577i	$0.509256\pi$
$978$	33.1967	1.06151
$979$	34.8010	1.11224
$980$	−2.47132	−0.0789436
$981$	34.1641	1.09078
$982$	−13.0528	−0.416530
$983$	42.8855	1.36784	0.683918	−	0.729559i	$-0.260274\pi$
$983$	42.8855	1.36784	0.683918	+	0.729559i	$0.260274\pi$
$984$	86.0663	2.74369
$985$	4.62849	0.147476
$986$	−5.42657	−0.172817
$987$	−5.86614	−0.186721
$988$	39.5994	1.25982
$989$	6.80631	0.216428
$990$	−4.80416	−0.152686
$991$	51.4815	1.63536	0.817682	−	0.575670i	$-0.195259\pi$
$991$	51.4815	1.63536	0.817682	+	0.575670i	$0.195259\pi$
$992$	30.8496	0.979474
$993$	22.4881	0.713640
$994$	−3.86441	−0.122572
$995$	−2.95352	−0.0936328
$996$	−36.2006	−1.14706
$997$	−58.1323	−1.84107	−0.920534	−	0.390663i	$-0.872246\pi$
$997$	−58.1323	−1.84107	−0.920534	+	0.390663i	$0.872246\pi$
$998$	7.15889	0.226611
$999$	4.49691	0.142276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3721.2.a.g.1.5		6
61.9	even	5		61.2.e.a.20.3	✓	12
61.34	even	5		61.2.e.a.58.3	yes	12
61.60	even	2		3721.2.a.h.1.2		6
183.95	odd	10		549.2.k.a.424.1		12
183.131	odd	10		549.2.k.a.325.1		12
244.95	odd	10		976.2.v.a.241.3		12
244.131	odd	10		976.2.v.a.81.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.e.a.20.3	✓	12	61.9	even	5
61.2.e.a.58.3	yes	12	61.34	even	5
549.2.k.a.325.1		12	183.131	odd	10
549.2.k.a.424.1		12	183.95	odd	10
976.2.v.a.81.3		12	244.131	odd	10
976.2.v.a.241.3		12	244.95	odd	10
3721.2.a.g.1.5		6	1.1	even	1	trivial
3721.2.a.h.1.2		6	61.60	even	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:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.a (trivial)

\(f(q)\)	\(=\)	\(q+0.852692 q^{2} -2.79079 q^{3} -1.27292 q^{4} +0.420224 q^{5} -2.37969 q^{6} -3.40882 q^{7} -2.79079 q^{8} +4.78851 q^{9} +O(q^{10})\)	\(q+0.852692 q^{2} -2.79079 q^{3} -1.27292 q^{4} +0.420224 q^{5} -2.37969 q^{6} -3.40882 q^{7} -2.79079 q^{8} +4.78851 q^{9} +0.358321 q^{10} -2.79991 q^{11} +3.55244 q^{12} +5.47505 q^{13} -2.90668 q^{14} -1.17276 q^{15} +0.166147 q^{16} +3.82127 q^{17} +4.08312 q^{18} -5.68198 q^{19} -0.534909 q^{20} +9.51331 q^{21} -2.38746 q^{22} +3.05123 q^{23} +7.78851 q^{24} -4.82341 q^{25} +4.66854 q^{26} -4.99135 q^{27} +4.33915 q^{28} -1.66543 q^{29} -1.00000 q^{30} +5.39021 q^{31} +5.72325 q^{32} +7.81396 q^{33} +3.25837 q^{34} -1.43247 q^{35} -6.09537 q^{36} -0.900940 q^{37} -4.84498 q^{38} -15.2797 q^{39} -1.17276 q^{40} +11.0504 q^{41} +8.11193 q^{42} +2.23068 q^{43} +3.56405 q^{44} +2.01224 q^{45} +2.60176 q^{46} -0.616624 q^{47} -0.463681 q^{48} +4.62008 q^{49} -4.11289 q^{50} -10.6644 q^{51} -6.96928 q^{52} +2.24374 q^{53} -4.25609 q^{54} -1.17659 q^{55} +9.51331 q^{56} +15.8572 q^{57} -1.42010 q^{58} +14.9326 q^{59} +1.49282 q^{60} +4.59619 q^{62} -16.3232 q^{63} +4.54788 q^{64} +2.30075 q^{65} +6.66290 q^{66} -4.66833 q^{67} -4.86416 q^{68} -8.51535 q^{69} -1.22145 q^{70} +1.32949 q^{71} -13.3637 q^{72} -7.37278 q^{73} -0.768224 q^{74} +13.4611 q^{75} +7.23269 q^{76} +9.54440 q^{77} -13.0289 q^{78} -2.70014 q^{79} +0.0698188 q^{80} -0.435708 q^{81} +9.42261 q^{82} -10.1903 q^{83} -12.1096 q^{84} +1.60579 q^{85} +1.90208 q^{86} +4.64785 q^{87} +7.81396 q^{88} -12.4293 q^{89} +1.71583 q^{90} -18.6635 q^{91} -3.88396 q^{92} -15.0430 q^{93} -0.525791 q^{94} -2.38770 q^{95} -15.9724 q^{96} -11.9355 q^{97} +3.93951 q^{98} -13.4074 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 3 q^{3} + q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - q^2 - 3 * q^3 + q^4 - 3 * q^6 - 3 * q^8 - 3 * q^9	\( 6 q - q^{2} - 3 q^{3} + q^{4} - 3 q^{6} - 3 q^{8} - 3 q^{9} - 8 q^{10} - 3 q^{11} + 3 q^{12} + q^{13} - q^{14} - 5 q^{16} + 8 q^{17} + 5 q^{18} + 2 q^{19} - 16 q^{20} + 16 q^{21} + 5 q^{22} + 14 q^{23} + 15 q^{24} - 6 q^{25} + 11 q^{26} - 6 q^{27} + 6 q^{28} - 4 q^{29} - 6 q^{30} + 7 q^{31} + 13 q^{32} + 2 q^{33} + 15 q^{34} - 5 q^{35} - 16 q^{36} - 22 q^{37} - 9 q^{38} - 14 q^{39} - 8 q^{41} - 2 q^{42} - 7 q^{43} + 25 q^{44} + 11 q^{45} - 16 q^{46} - 11 q^{47} - 4 q^{48} - 16 q^{49} + 37 q^{50} + 5 q^{51} + 12 q^{52} + 25 q^{53} - 3 q^{54} - 30 q^{55} + 16 q^{56} + 2 q^{57} + 12 q^{58} + 11 q^{59} + q^{60} - 26 q^{62} - 24 q^{63} - 27 q^{64} - 23 q^{65} + 23 q^{66} - 7 q^{67} - 19 q^{68} - 35 q^{69} - 20 q^{70} - 22 q^{71} - 15 q^{72} - 17 q^{73} - 10 q^{74} + 20 q^{75} - 3 q^{76} + 3 q^{77} - 14 q^{78} + 12 q^{79} + 26 q^{80} - 6 q^{81} + 39 q^{82} - 36 q^{83} - 4 q^{84} + 4 q^{85} - 30 q^{86} - 8 q^{87} + 2 q^{88} - 21 q^{89} + 27 q^{90} - 11 q^{91} + 16 q^{92} + 5 q^{93} - 16 q^{94} + 12 q^{95} - 31 q^{96} - 24 q^{97} + 2 q^{98} - 23 q^{99}+O(q^{100}) \) 6 * q - q^2 - 3 * q^3 + q^4 - 3 * q^6 - 3 * q^8 - 3 * q^9 - 8 * q^10 - 3 * q^11 + 3 * q^12 + q^13 - q^14 - 5 * q^16 + 8 * q^17 + 5 * q^18 + 2 * q^19 - 16 * q^20 + 16 * q^21 + 5 * q^22 + 14 * q^23 + 15 * q^24 - 6 * q^25 + 11 * q^26 - 6 * q^27 + 6 * q^28 - 4 * q^29 - 6 * q^30 + 7 * q^31 + 13 * q^32 + 2 * q^33 + 15 * q^34 - 5 * q^35 - 16 * q^36 - 22 * q^37 - 9 * q^38 - 14 * q^39 - 8 * q^41 - 2 * q^42 - 7 * q^43 + 25 * q^44 + 11 * q^45 - 16 * q^46 - 11 * q^47 - 4 * q^48 - 16 * q^49 + 37 * q^50 + 5 * q^51 + 12 * q^52 + 25 * q^53 - 3 * q^54 - 30 * q^55 + 16 * q^56 + 2 * q^57 + 12 * q^58 + 11 * q^59 + q^60 - 26 * q^62 - 24 * q^63 - 27 * q^64 - 23 * q^65 + 23 * q^66 - 7 * q^67 - 19 * q^68 - 35 * q^69 - 20 * q^70 - 22 * q^71 - 15 * q^72 - 17 * q^73 - 10 * q^74 + 20 * q^75 - 3 * q^76 + 3 * q^77 - 14 * q^78 + 12 * q^79 + 26 * q^80 - 6 * q^81 + 39 * q^82 - 36 * q^83 - 4 * q^84 + 4 * q^85 - 30 * q^86 - 8 * q^87 + 2 * q^88 - 21 * q^89 + 27 * q^90 - 11 * q^91 + 16 * q^92 + 5 * q^93 - 16 * q^94 + 12 * q^95 - 31 * q^96 - 24 * q^97 + 2 * q^98 - 23 * q^99

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