LMFDB - Embedded newform 4334.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.21770$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.21770 q^{3} +1.00000 q^{4} -0.358958 q^{5} +2.21770 q^{6} +1.80298 q^{7} -1.00000 q^{8} +1.91818 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.21770 q^{3} +1.00000 q^{4} -0.358958 q^{5} +2.21770 q^{6} +1.80298 q^{7} -1.00000 q^{8} +1.91818 q^{9} +0.358958 q^{10} -1.00000 q^{11} -2.21770 q^{12} -2.88908 q^{13} -1.80298 q^{14} +0.796060 q^{15} +1.00000 q^{16} +2.70076 q^{17} -1.91818 q^{18} -0.369372 q^{19} -0.358958 q^{20} -3.99846 q^{21} +1.00000 q^{22} -1.60927 q^{23} +2.21770 q^{24} -4.87115 q^{25} +2.88908 q^{26} +2.39916 q^{27} +1.80298 q^{28} +8.74542 q^{29} -0.796060 q^{30} +3.27641 q^{31} -1.00000 q^{32} +2.21770 q^{33} -2.70076 q^{34} -0.647195 q^{35} +1.91818 q^{36} +5.82623 q^{37} +0.369372 q^{38} +6.40709 q^{39} +0.358958 q^{40} -10.2786 q^{41} +3.99846 q^{42} -11.5572 q^{43} -1.00000 q^{44} -0.688545 q^{45} +1.60927 q^{46} +9.37166 q^{47} -2.21770 q^{48} -3.74926 q^{49} +4.87115 q^{50} -5.98947 q^{51} -2.88908 q^{52} -6.63384 q^{53} -2.39916 q^{54} +0.358958 q^{55} -1.80298 q^{56} +0.819155 q^{57} -8.74542 q^{58} -4.15752 q^{59} +0.796060 q^{60} +9.42164 q^{61} -3.27641 q^{62} +3.45843 q^{63} +1.00000 q^{64} +1.03706 q^{65} -2.21770 q^{66} +4.38026 q^{67} +2.70076 q^{68} +3.56886 q^{69} +0.647195 q^{70} -7.97236 q^{71} -1.91818 q^{72} -1.81186 q^{73} -5.82623 q^{74} +10.8027 q^{75} -0.369372 q^{76} -1.80298 q^{77} -6.40709 q^{78} -8.23558 q^{79} -0.358958 q^{80} -11.0751 q^{81} +10.2786 q^{82} +16.2211 q^{83} -3.99846 q^{84} -0.969461 q^{85} +11.5572 q^{86} -19.3947 q^{87} +1.00000 q^{88} +5.27809 q^{89} +0.688545 q^{90} -5.20895 q^{91} -1.60927 q^{92} -7.26608 q^{93} -9.37166 q^{94} +0.132589 q^{95} +2.21770 q^{96} +7.39981 q^{97} +3.74926 q^{98} -1.91818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.21770	−1.28039	−0.640194	−	0.768214i	$-0.721146\pi$
$3$	−2.21770	−1.28039	−0.640194	+	0.768214i	$0.721146\pi$
$4$	1.00000	0.500000
$5$	−0.358958	−0.160531	−0.0802655	−	0.996774i	$-0.525577\pi$
$5$	−0.358958	−0.160531	−0.0802655	+	0.996774i	$0.525577\pi$
$6$	2.21770	0.905371
$7$	1.80298	0.681463	0.340731	−	0.940161i	$-0.389325\pi$
$7$	1.80298	0.681463	0.340731	+	0.940161i	$0.389325\pi$
$8$	−1.00000	−0.353553
$9$	1.91818	0.639392
$10$	0.358958	0.113513
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.21770	−0.640194
$13$	−2.88908	−0.801285	−0.400643	−	0.916234i	$-0.631213\pi$
$13$	−2.88908	−0.801285	−0.400643	+	0.916234i	$0.631213\pi$
$14$	−1.80298	−0.481867
$15$	0.796060	0.205542
$16$	1.00000	0.250000
$17$	2.70076	0.655031	0.327516	−	0.944846i	$-0.393789\pi$
$17$	2.70076	0.655031	0.327516	+	0.944846i	$0.393789\pi$
$18$	−1.91818	−0.452118
$19$	−0.369372	−0.0847398	−0.0423699	−	0.999102i	$-0.513491\pi$
$19$	−0.369372	−0.0847398	−0.0423699	+	0.999102i	$0.513491\pi$
$20$	−0.358958	−0.0802655
$21$	−3.99846	−0.872536
$22$	1.00000	0.213201
$23$	−1.60927	−0.335555	−0.167778	−	0.985825i	$-0.553659\pi$
$23$	−1.60927	−0.335555	−0.167778	+	0.985825i	$0.553659\pi$
$24$	2.21770	0.452685
$25$	−4.87115	−0.974230
$26$	2.88908	0.566594
$27$	2.39916	0.461718
$28$	1.80298	0.340731
$29$	8.74542	1.62398	0.811992	−	0.583668i	$-0.198383\pi$
$29$	8.74542	1.62398	0.811992	+	0.583668i	$0.198383\pi$
$30$	−0.796060	−0.145340
$31$	3.27641	0.588461	0.294230	−	0.955735i	$-0.404937\pi$
$31$	3.27641	0.588461	0.294230	+	0.955735i	$0.404937\pi$
$32$	−1.00000	−0.176777
$33$	2.21770	0.386051
$34$	−2.70076	−0.463177
$35$	−0.647195	−0.109396
$36$	1.91818	0.319696
$37$	5.82623	0.957826	0.478913	−	0.877862i	$-0.341031\pi$
$37$	5.82623	0.957826	0.478913	+	0.877862i	$0.341031\pi$
$38$	0.369372	0.0599201
$39$	6.40709	1.02596
$40$	0.358958	0.0567563
$41$	−10.2786	−1.60524	−0.802622	−	0.596488i	$-0.796562\pi$
$41$	−10.2786	−1.60524	−0.802622	+	0.596488i	$0.796562\pi$
$42$	3.99846	0.616976
$43$	−11.5572	−1.76246	−0.881230	−	0.472688i	$-0.843284\pi$
$43$	−11.5572	−1.76246	−0.881230	+	0.472688i	$0.843284\pi$
$44$	−1.00000	−0.150756
$45$	−0.688545	−0.102642
$46$	1.60927	0.237273
$47$	9.37166	1.36700	0.683498	−	0.729952i	$-0.260458\pi$
$47$	9.37166	1.36700	0.683498	+	0.729952i	$0.260458\pi$
$48$	−2.21770	−0.320097
$49$	−3.74926	−0.535608
$50$	4.87115	0.688884
$51$	−5.98947	−0.838694
$52$	−2.88908	−0.400643
$53$	−6.63384	−0.911229	−0.455614	−	0.890177i	$-0.650580\pi$
$53$	−6.63384	−0.911229	−0.455614	+	0.890177i	$0.650580\pi$
$54$	−2.39916	−0.326484
$55$	0.358958	0.0484019
$56$	−1.80298	−0.240934
$57$	0.819155	0.108500
$58$	−8.74542	−1.14833
$59$	−4.15752	−0.541263	−0.270631	−	0.962683i	$-0.587232\pi$
$59$	−4.15752	−0.541263	−0.270631	+	0.962683i	$0.587232\pi$
$60$	0.796060	0.102771
$61$	9.42164	1.20632	0.603159	−	0.797621i	$-0.293908\pi$
$61$	9.42164	1.20632	0.603159	+	0.797621i	$0.293908\pi$
$62$	−3.27641	−0.416105
$63$	3.45843	0.435722
$64$	1.00000	0.125000
$65$	1.03706	0.128631
$66$	−2.21770	−0.272980
$67$	4.38026	0.535134	0.267567	−	0.963539i	$-0.413780\pi$
$67$	4.38026	0.535134	0.267567	+	0.963539i	$0.413780\pi$
$68$	2.70076	0.327516
$69$	3.56886	0.429640
$70$	0.647195	0.0773546
$71$	−7.97236	−0.946145	−0.473073	−	0.881023i	$-0.656855\pi$
$71$	−7.97236	−0.946145	−0.473073	+	0.881023i	$0.656855\pi$
$72$	−1.91818	−0.226059
$73$	−1.81186	−0.212063	−0.106031	−	0.994363i	$-0.533814\pi$
$73$	−1.81186	−0.212063	−0.106031	+	0.994363i	$0.533814\pi$
$74$	−5.82623	−0.677285
$75$	10.8027	1.24739
$76$	−0.369372	−0.0423699
$77$	−1.80298	−0.205469
$78$	−6.40709	−0.725460
$79$	−8.23558	−0.926575	−0.463288	−	0.886208i	$-0.653330\pi$
$79$	−8.23558	−0.926575	−0.463288	+	0.886208i	$0.653330\pi$
$80$	−0.358958	−0.0401328
$81$	−11.0751	−1.23057
$82$	10.2786	1.13508
$83$	16.2211	1.78050	0.890248	−	0.455476i	$-0.150531\pi$
$83$	16.2211	1.78050	0.890248	+	0.455476i	$0.150531\pi$
$84$	−3.99846	−0.436268
$85$	−0.969461	−0.105153
$86$	11.5572	1.24625
$87$	−19.3947	−2.07933
$88$	1.00000	0.106600
$89$	5.27809	0.559477	0.279738	−	0.960076i	$-0.409752\pi$
$89$	5.27809	0.559477	0.279738	+	0.960076i	$0.409752\pi$
$90$	0.688545	0.0725790
$91$	−5.20895	−0.546046
$92$	−1.60927	−0.167778
$93$	−7.26608	−0.753458
$94$	−9.37166	−0.966613
$95$	0.132589	0.0136034
$96$	2.21770	0.226343
$97$	7.39981	0.751337	0.375668	−	0.926754i	$-0.377413\pi$
$97$	7.39981	0.751337	0.375668	+	0.926754i	$0.377413\pi$
$98$	3.74926	0.378732
$99$	−1.91818	−0.192784
$100$	−4.87115	−0.487115
$101$	−0.744429	−0.0740734	−0.0370367	−	0.999314i	$-0.511792\pi$
$101$	−0.744429	−0.0740734	−0.0370367	+	0.999314i	$0.511792\pi$
$102$	5.98947	0.593046
$103$	3.56061	0.350838	0.175419	−	0.984494i	$-0.443872\pi$
$103$	3.56061	0.350838	0.175419	+	0.984494i	$0.443872\pi$
$104$	2.88908	0.283297
$105$	1.43528	0.140069
$106$	6.63384	0.644336
$107$	3.45646	0.334148	0.167074	−	0.985944i	$-0.446568\pi$
$107$	3.45646	0.334148	0.167074	+	0.985944i	$0.446568\pi$
$108$	2.39916	0.230859
$109$	11.4228	1.09410	0.547051	−	0.837099i	$-0.315750\pi$
$109$	11.4228	1.09410	0.547051	+	0.837099i	$0.315750\pi$
$110$	−0.358958	−0.0342253
$111$	−12.9208	−1.22639
$112$	1.80298	0.170366
$113$	−0.564380	−0.0530924	−0.0265462	−	0.999648i	$-0.508451\pi$
$113$	−0.564380	−0.0530924	−0.0265462	+	0.999648i	$0.508451\pi$
$114$	−0.819155	−0.0767209
$115$	0.577659	0.0538670
$116$	8.74542	0.811992
$117$	−5.54175	−0.512335
$118$	4.15752	0.382730
$119$	4.86943	0.446379
$120$	−0.796060	−0.0726700
$121$	1.00000	0.0909091
$122$	−9.42164	−0.852996
$123$	22.7947	2.05533
$124$	3.27641	0.294230
$125$	3.54333	0.316925
$126$	−3.45843	−0.308102
$127$	−4.33585	−0.384744	−0.192372	−	0.981322i	$-0.561618\pi$
$127$	−4.33585	−0.384744	−0.192372	+	0.981322i	$0.561618\pi$
$128$	−1.00000	−0.0883883
$129$	25.6304	2.25663
$130$	−1.03706	−0.0909560
$131$	−7.39120	−0.645772	−0.322886	−	0.946438i	$-0.604653\pi$
$131$	−7.39120	−0.645772	−0.322886	+	0.946438i	$0.604653\pi$
$132$	2.21770	0.193026
$133$	−0.665971	−0.0577470
$134$	−4.38026	−0.378397
$135$	−0.861198	−0.0741201
$136$	−2.70076	−0.231589
$137$	15.1205	1.29183	0.645915	−	0.763410i	$-0.276476\pi$
$137$	15.1205	1.29183	0.645915	+	0.763410i	$0.276476\pi$
$138$	−3.56886	−0.303802
$139$	8.46160	0.717703	0.358852	−	0.933395i	$-0.383168\pi$
$139$	8.46160	0.717703	0.358852	+	0.933395i	$0.383168\pi$
$140$	−0.647195	−0.0546980
$141$	−20.7835	−1.75029
$142$	7.97236	0.669026
$143$	2.88908	0.241597
$144$	1.91818	0.159848
$145$	−3.13924	−0.260700
$146$	1.81186	0.149951
$147$	8.31472	0.685786
$148$	5.82623	0.478913
$149$	3.63963	0.298170	0.149085	−	0.988824i	$-0.452367\pi$
$149$	3.63963	0.298170	0.149085	+	0.988824i	$0.452367\pi$
$150$	−10.8027	−0.882039
$151$	6.02197	0.490061	0.245030	−	0.969515i	$-0.421202\pi$
$151$	6.02197	0.490061	0.245030	+	0.969515i	$0.421202\pi$
$152$	0.369372	0.0299600
$153$	5.18054	0.418822
$154$	1.80298	0.145288
$155$	−1.17610	−0.0944662
$156$	6.40709	0.512978
$157$	−17.4137	−1.38976	−0.694881	−	0.719125i	$-0.744543\pi$
$157$	−17.4137	−1.38976	−0.694881	+	0.719125i	$0.744543\pi$
$158$	8.23558	0.655187
$159$	14.7118	1.16673
$160$	0.358958	0.0283781
$161$	−2.90148	−0.228668
$162$	11.0751	0.870144
$163$	13.1311	1.02851	0.514253	−	0.857639i	$-0.328069\pi$
$163$	13.1311	1.02851	0.514253	+	0.857639i	$0.328069\pi$
$164$	−10.2786	−0.802622
$165$	−0.796060	−0.0619732
$166$	−16.2211	−1.25900
$167$	8.18834	0.633633	0.316816	−	0.948487i	$-0.397386\pi$
$167$	8.18834	0.633633	0.316816	+	0.948487i	$0.397386\pi$
$168$	3.99846	0.308488
$169$	−4.65324	−0.357942
$170$	0.969461	0.0743543
$171$	−0.708521	−0.0541819
$172$	−11.5572	−0.881230
$173$	−24.4586	−1.85955	−0.929777	−	0.368124i	$-0.880000\pi$
$173$	−24.4586	−1.85955	−0.929777	+	0.368124i	$0.880000\pi$
$174$	19.3947	1.47031
$175$	−8.78259	−0.663901
$176$	−1.00000	−0.0753778
$177$	9.22011	0.693026
$178$	−5.27809	−0.395610
$179$	10.1417	0.758030	0.379015	−	0.925391i	$-0.376263\pi$
$179$	10.1417	0.758030	0.379015	+	0.925391i	$0.376263\pi$
$180$	−0.688545	−0.0513211
$181$	−20.1249	−1.49587	−0.747936	−	0.663771i	$-0.768955\pi$
$181$	−20.1249	−1.49587	−0.747936	+	0.663771i	$0.768955\pi$
$182$	5.20895	0.386113
$183$	−20.8943	−1.54455
$184$	1.60927	0.118637
$185$	−2.09137	−0.153761
$186$	7.26608	0.532775
$187$	−2.70076	−0.197499
$188$	9.37166	0.683498
$189$	4.32564	0.314644
$190$	−0.132589	−0.00961904
$191$	−0.755966	−0.0546998	−0.0273499	−	0.999626i	$-0.508707\pi$
$191$	−0.755966	−0.0546998	−0.0273499	+	0.999626i	$0.508707\pi$
$192$	−2.21770	−0.160048
$193$	−20.3064	−1.46168	−0.730842	−	0.682546i	$-0.760873\pi$
$193$	−20.3064	−1.46168	−0.730842	+	0.682546i	$0.760873\pi$
$194$	−7.39981	−0.531275
$195$	−2.29988	−0.164698
$196$	−3.74926	−0.267804
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	1.91818	0.136319
$199$	−19.7942	−1.40317	−0.701587	−	0.712584i	$-0.747525\pi$
$199$	−19.7942	−1.40317	−0.701587	+	0.712584i	$0.747525\pi$
$200$	4.87115	0.344442
$201$	−9.71409	−0.685179
$202$	0.744429	0.0523778
$203$	15.7678	1.10669
$204$	−5.98947	−0.419347
$205$	3.68958	0.257691
$206$	−3.56061	−0.248080
$207$	−3.08685	−0.214551
$208$	−2.88908	−0.200321
$209$	0.369372	0.0255500
$210$	−1.43528	−0.0990439
$211$	−22.4085	−1.54266	−0.771332	−	0.636433i	$-0.780409\pi$
$211$	−22.4085	−1.54266	−0.771332	+	0.636433i	$0.780409\pi$
$212$	−6.63384	−0.455614
$213$	17.6803	1.21143
$214$	−3.45646	−0.236278
$215$	4.14856	0.282929
$216$	−2.39916	−0.163242
$217$	5.90731	0.401014
$218$	−11.4228	−0.773647
$219$	4.01816	0.271522
$220$	0.358958	0.0242010
$221$	−7.80271	−0.524867
$222$	12.9208	0.867187
$223$	−23.2153	−1.55461	−0.777307	−	0.629122i	$-0.783415\pi$
$223$	−23.2153	−1.55461	−0.777307	+	0.629122i	$0.783415\pi$
$224$	−1.80298	−0.120467
$225$	−9.34372	−0.622915
$226$	0.564380	0.0375420
$227$	21.8369	1.44937	0.724683	−	0.689082i	$-0.241986\pi$
$227$	21.8369	1.44937	0.724683	+	0.689082i	$0.241986\pi$
$228$	0.819155	0.0542499
$229$	−8.37251	−0.553271	−0.276635	−	0.960975i	$-0.589219\pi$
$229$	−8.37251	−0.553271	−0.276635	+	0.960975i	$0.589219\pi$
$230$	−0.577659	−0.0380897
$231$	3.99846	0.263080
$232$	−8.74542	−0.574165
$233$	−17.5989	−1.15294	−0.576471	−	0.817118i	$-0.695571\pi$
$233$	−17.5989	−1.15294	−0.576471	+	0.817118i	$0.695571\pi$
$234$	5.54175	0.362276
$235$	−3.36403	−0.219445
$236$	−4.15752	−0.270631
$237$	18.2640	1.18637
$238$	−4.86943	−0.315638
$239$	19.1350	1.23774	0.618869	−	0.785494i	$-0.287591\pi$
$239$	19.1350	1.23774	0.618869	+	0.785494i	$0.287591\pi$
$240$	0.796060	0.0513855
$241$	10.0593	0.647974	0.323987	−	0.946062i	$-0.394977\pi$
$241$	10.0593	0.647974	0.323987	+	0.946062i	$0.394977\pi$
$242$	−1.00000	−0.0642824
$243$	17.3638	1.11389
$244$	9.42164	0.603159
$245$	1.34583	0.0859818
$246$	−22.7947	−1.45334
$247$	1.06714	0.0679008
$248$	−3.27641	−0.208052
$249$	−35.9734	−2.27972
$250$	−3.54333	−0.224100
$251$	−16.6229	−1.04923	−0.524614	−	0.851340i	$-0.675790\pi$
$251$	−16.6229	−1.04923	−0.524614	+	0.851340i	$0.675790\pi$
$252$	3.45843	0.217861
$253$	1.60927	0.101174
$254$	4.33585	0.272055
$255$	2.14997	0.134636
$256$	1.00000	0.0625000
$257$	2.87775	0.179509	0.0897545	−	0.995964i	$-0.471392\pi$
$257$	2.87775	0.179509	0.0897545	+	0.995964i	$0.471392\pi$
$258$	−25.6304	−1.59568
$259$	10.5046	0.652723
$260$	1.03706	0.0643156
$261$	16.7753	1.03836
$262$	7.39120	0.456630
$263$	1.11056	0.0684800	0.0342400	−	0.999414i	$-0.489099\pi$
$263$	1.11056	0.0684800	0.0342400	+	0.999414i	$0.489099\pi$
$264$	−2.21770	−0.136490
$265$	2.38127	0.146280
$266$	0.665971	0.0408333
$267$	−11.7052	−0.716347
$268$	4.38026	0.267567
$269$	−14.6941	−0.895912	−0.447956	−	0.894056i	$-0.647848\pi$
$269$	−14.6941	−0.895912	−0.447956	+	0.894056i	$0.647848\pi$
$270$	0.861198	0.0524108
$271$	−17.4874	−1.06228	−0.531141	−	0.847283i	$-0.678237\pi$
$271$	−17.4874	−1.06228	−0.531141	+	0.847283i	$0.678237\pi$
$272$	2.70076	0.163758
$273$	11.5519	0.699151
$274$	−15.1205	−0.913461
$275$	4.87115	0.293741
$276$	3.56886	0.214820
$277$	−14.9118	−0.895962	−0.447981	−	0.894043i	$-0.647857\pi$
$277$	−14.9118	−0.895962	−0.447981	+	0.894043i	$0.647857\pi$
$278$	−8.46160	−0.507493
$279$	6.28473	0.376257
$280$	0.647195	0.0386773
$281$	18.6144	1.11044	0.555222	−	0.831702i	$-0.312633\pi$
$281$	18.6144	1.11044	0.555222	+	0.831702i	$0.312633\pi$
$282$	20.7835	1.23764
$283$	9.87892	0.587241	0.293621	−	0.955922i	$-0.405140\pi$
$283$	9.87892	0.587241	0.293621	+	0.955922i	$0.405140\pi$
$284$	−7.97236	−0.473073
$285$	−0.294043	−0.0174176
$286$	−2.88908	−0.170835
$287$	−18.5321	−1.09391
$288$	−1.91818	−0.113030
$289$	−9.70588	−0.570934
$290$	3.13924	0.184343
$291$	−16.4105	−0.962002
$292$	−1.81186	−0.106031
$293$	−23.3926	−1.36661	−0.683305	−	0.730133i	$-0.739458\pi$
$293$	−23.3926	−1.36661	−0.683305	+	0.730133i	$0.739458\pi$
$294$	−8.31472	−0.484924
$295$	1.49238	0.0868894
$296$	−5.82623	−0.338643
$297$	−2.39916	−0.139213
$298$	−3.63963	−0.210838
$299$	4.64929	0.268875
$300$	10.8027	0.623696
$301$	−20.8375	−1.20105
$302$	−6.02197	−0.346525
$303$	1.65092	0.0948427
$304$	−0.369372	−0.0211850
$305$	−3.38198	−0.193651
$306$	−5.18054	−0.296152
$307$	26.1406	1.49192	0.745961	−	0.665990i	$-0.231991\pi$
$307$	26.1406	1.49192	0.745961	+	0.665990i	$0.231991\pi$
$308$	−1.80298	−0.102734
$309$	−7.89636	−0.449208
$310$	1.17610	0.0667977
$311$	−16.1102	−0.913525	−0.456763	−	0.889589i	$-0.650991\pi$
$311$	−16.1102	−0.913525	−0.456763	+	0.889589i	$0.650991\pi$
$312$	−6.40709	−0.362730
$313$	−10.3291	−0.583838	−0.291919	−	0.956443i	$-0.594294\pi$
$313$	−10.3291	−0.583838	−0.291919	+	0.956443i	$0.594294\pi$
$314$	17.4137	0.982710
$315$	−1.24143	−0.0699469
$316$	−8.23558	−0.463288
$317$	14.0155	0.787188	0.393594	−	0.919284i	$-0.371232\pi$
$317$	14.0155	0.787188	0.393594	+	0.919284i	$0.371232\pi$
$318$	−14.7118	−0.824999
$319$	−8.74542	−0.489650
$320$	−0.358958	−0.0200664
$321$	−7.66537	−0.427839
$322$	2.90148	0.161693
$323$	−0.997587	−0.0555072
$324$	−11.0751	−0.615285
$325$	14.0731	0.780636
$326$	−13.1311	−0.727263
$327$	−25.3322	−1.40087
$328$	10.2786	0.567539
$329$	16.8969	0.931557
$330$	0.796060	0.0438217
$331$	1.94241	0.106765	0.0533823	−	0.998574i	$-0.483000\pi$
$331$	1.94241	0.106765	0.0533823	+	0.998574i	$0.483000\pi$
$332$	16.2211	0.890248
$333$	11.1757	0.612426
$334$	−8.18834	−0.448046
$335$	−1.57233	−0.0859056
$336$	−3.99846	−0.218134
$337$	−24.0109	−1.30796	−0.653979	−	0.756513i	$-0.726901\pi$
$337$	−24.0109	−1.30796	−0.653979	+	0.756513i	$0.726901\pi$
$338$	4.65324	0.253103
$339$	1.25162	0.0679788
$340$	−0.969461	−0.0525764
$341$	−3.27641	−0.177428
$342$	0.708521	0.0383124
$343$	−19.3807	−1.04646
$344$	11.5572	0.623123
$345$	−1.28107	−0.0689706
$346$	24.4586	1.31490
$347$	−3.70553	−0.198923	−0.0994617	−	0.995041i	$-0.531712\pi$
$347$	−3.70553	−0.198923	−0.0994617	+	0.995041i	$0.531712\pi$
$348$	−19.3947	−1.03966
$349$	−24.6050	−1.31708	−0.658539	−	0.752547i	$-0.728825\pi$
$349$	−24.6050	−1.31708	−0.658539	+	0.752547i	$0.728825\pi$
$350$	8.78259	0.469449
$351$	−6.93135	−0.369968
$352$	1.00000	0.0533002
$353$	13.0292	0.693474	0.346737	−	0.937962i	$-0.387290\pi$
$353$	13.0292	0.693474	0.346737	+	0.937962i	$0.387290\pi$
$354$	−9.22011	−0.490043
$355$	2.86175	0.151886
$356$	5.27809	0.279738
$357$	−10.7989	−0.571539
$358$	−10.1417	−0.536008
$359$	−36.0246	−1.90131	−0.950653	−	0.310257i	$-0.899585\pi$
$359$	−36.0246	−1.90131	−0.950653	+	0.310257i	$0.899585\pi$
$360$	0.688545	0.0362895
$361$	−18.8636	−0.992819
$362$	20.1249	1.05774
$363$	−2.21770	−0.116399
$364$	−5.20895	−0.273023
$365$	0.650384	0.0340426
$366$	20.8943	1.09216
$367$	8.27867	0.432143	0.216071	−	0.976378i	$-0.430676\pi$
$367$	8.27867	0.432143	0.216071	+	0.976378i	$0.430676\pi$
$368$	−1.60927	−0.0838888
$369$	−19.7161	−1.02638
$370$	2.09137	0.108725
$371$	−11.9607	−0.620968
$372$	−7.26608	−0.376729
$373$	−19.3331	−1.00103	−0.500516	−	0.865727i	$-0.666856\pi$
$373$	−19.3331	−1.00103	−0.500516	+	0.865727i	$0.666856\pi$
$374$	2.70076	0.139653
$375$	−7.85803	−0.405787
$376$	−9.37166	−0.483306
$377$	−25.2662	−1.30127
$378$	−4.32564	−0.222487
$379$	4.80131	0.246627	0.123313	−	0.992368i	$-0.460648\pi$
$379$	4.80131	0.246627	0.123313	+	0.992368i	$0.460648\pi$
$380$	0.132589	0.00680169
$381$	9.61559	0.492622
$382$	0.755966	0.0386786
$383$	13.5359	0.691654	0.345827	−	0.938298i	$-0.387598\pi$
$383$	13.5359	0.691654	0.345827	+	0.938298i	$0.387598\pi$
$384$	2.21770	0.113171
$385$	0.647195	0.0329841
$386$	20.3064	1.03357
$387$	−22.1688	−1.12690
$388$	7.39981	0.375668
$389$	−7.33032	−0.371662	−0.185831	−	0.982582i	$-0.559498\pi$
$389$	−7.33032	−0.371662	−0.185831	+	0.982582i	$0.559498\pi$
$390$	2.29988	0.116459
$391$	−4.34624	−0.219799
$392$	3.74926	0.189366
$393$	16.3914	0.826838
$394$	1.00000	0.0503793
$395$	2.95623	0.148744
$396$	−1.91818	−0.0963919
$397$	−1.68196	−0.0844150	−0.0422075	−	0.999109i	$-0.513439\pi$
$397$	−1.68196	−0.0844150	−0.0422075	+	0.999109i	$0.513439\pi$
$398$	19.7942	0.992193
$399$	1.47692	0.0739386
$400$	−4.87115	−0.243557
$401$	1.23325	0.0615856	0.0307928	−	0.999526i	$-0.490197\pi$
$401$	1.23325	0.0615856	0.0307928	+	0.999526i	$0.490197\pi$
$402$	9.71409	0.484495
$403$	−9.46580	−0.471525
$404$	−0.744429	−0.0370367
$405$	3.97551	0.197545
$406$	−15.7678	−0.782545
$407$	−5.82623	−0.288795
$408$	5.98947	0.296523
$409$	−31.4641	−1.55580	−0.777899	−	0.628389i	$-0.783715\pi$
$409$	−31.4641	−1.55580	−0.777899	+	0.628389i	$0.783715\pi$
$410$	−3.68958	−0.182215
$411$	−33.5326	−1.65404
$412$	3.56061	0.175419
$413$	−7.49593	−0.368850
$414$	3.08685	0.151711
$415$	−5.82269	−0.285825
$416$	2.88908	0.141649
$417$	−18.7652	−0.918938
$418$	−0.369372	−0.0180666
$419$	27.7653	1.35642	0.678212	−	0.734866i	$-0.262755\pi$
$419$	27.7653	1.35642	0.678212	+	0.734866i	$0.262755\pi$
$420$	1.43528	0.0700346
$421$	−23.4471	−1.14274	−0.571371	−	0.820692i	$-0.693588\pi$
$421$	−23.4471	−1.14274	−0.571371	+	0.820692i	$0.693588\pi$
$422$	22.4085	1.09083
$423$	17.9765	0.874046
$424$	6.63384	0.322168
$425$	−13.1558	−0.638151
$426$	−17.6803	−0.856612
$427$	16.9870	0.822061
$428$	3.45646	0.167074
$429$	−6.40709	−0.309337
$430$	−4.14856	−0.200061
$431$	−3.82614	−0.184299	−0.0921494	−	0.995745i	$-0.529374\pi$
$431$	−3.82614	−0.184299	−0.0921494	+	0.995745i	$0.529374\pi$
$432$	2.39916	0.115430
$433$	−26.8077	−1.28830	−0.644148	−	0.764901i	$-0.722788\pi$
$433$	−26.8077	−1.28830	−0.644148	+	0.764901i	$0.722788\pi$
$434$	−5.90731	−0.283560
$435$	6.96189	0.333797
$436$	11.4228	0.547051
$437$	0.594418	0.0284349
$438$	−4.01816	−0.191995
$439$	−33.8585	−1.61598	−0.807989	−	0.589198i	$-0.799444\pi$
$439$	−33.8585	−1.61598	−0.807989	+	0.589198i	$0.799444\pi$
$440$	−0.358958	−0.0171127
$441$	−7.19173	−0.342464
$442$	7.80271	0.371137
$443$	4.99621	0.237377	0.118688	−	0.992932i	$-0.462131\pi$
$443$	4.99621	0.237377	0.118688	+	0.992932i	$0.462131\pi$
$444$	−12.9208	−0.613194
$445$	−1.89461	−0.0898134
$446$	23.2153	1.09928
$447$	−8.07159	−0.381773
$448$	1.80298	0.0851829
$449$	−17.6696	−0.833879	−0.416940	−	0.908934i	$-0.636897\pi$
$449$	−17.6696	−0.833879	−0.416940	+	0.908934i	$0.636897\pi$
$450$	9.34372	0.440467
$451$	10.2786	0.483999
$452$	−0.564380	−0.0265462
$453$	−13.3549	−0.627468
$454$	−21.8369	−1.02486
$455$	1.86980	0.0876574
$456$	−0.819155	−0.0383605
$457$	4.62618	0.216403	0.108202	−	0.994129i	$-0.465491\pi$
$457$	4.62618	0.216403	0.108202	+	0.994129i	$0.465491\pi$
$458$	8.37251	0.391222
$459$	6.47956	0.302440
$460$	0.577659	0.0269335
$461$	26.5328	1.23575	0.617877	−	0.786275i	$-0.287993\pi$
$461$	26.5328	1.23575	0.617877	+	0.786275i	$0.287993\pi$
$462$	−3.99846	−0.186025
$463$	10.5581	0.490678	0.245339	−	0.969437i	$-0.421101\pi$
$463$	10.5581	0.490678	0.245339	+	0.969437i	$0.421101\pi$
$464$	8.74542	0.405996
$465$	2.60822	0.120953
$466$	17.5989	0.815253
$467$	10.9019	0.504481	0.252240	−	0.967665i	$-0.418833\pi$
$467$	10.9019	0.504481	0.252240	+	0.967665i	$0.418833\pi$
$468$	−5.54175	−0.256168
$469$	7.89753	0.364674
$470$	3.36403	0.155171
$471$	38.6182	1.77943
$472$	4.15752	0.191365
$473$	11.5572	0.531402
$474$	−18.2640	−0.838894
$475$	1.79927	0.0825561
$476$	4.86943	0.223190
$477$	−12.7249	−0.582632
$478$	−19.1350	−0.875213
$479$	−9.08182	−0.414959	−0.207479	−	0.978239i	$-0.566526\pi$
$479$	−9.08182	−0.414959	−0.207479	+	0.978239i	$0.566526\pi$
$480$	−0.796060	−0.0363350
$481$	−16.8324	−0.767492
$482$	−10.0593	−0.458187
$483$	6.43459	0.292784
$484$	1.00000	0.0454545
$485$	−2.65622	−0.120613
$486$	−17.3638	−0.787638
$487$	−12.1481	−0.550481	−0.275241	−	0.961375i	$-0.588758\pi$
$487$	−12.1481	−0.550481	−0.275241	+	0.961375i	$0.588758\pi$
$488$	−9.42164	−0.426498
$489$	−29.1207	−1.31688
$490$	−1.34583	−0.0607983
$491$	−7.76850	−0.350588	−0.175294	−	0.984516i	$-0.556088\pi$
$491$	−7.76850	−0.350588	−0.175294	+	0.984516i	$0.556088\pi$
$492$	22.7947	1.02767
$493$	23.6193	1.06376
$494$	−1.06714	−0.0480131
$495$	0.688545	0.0309478
$496$	3.27641	0.147115
$497$	−14.3740	−0.644763
$498$	35.9734	1.61201
$499$	−42.3457	−1.89565	−0.947827	−	0.318785i	$-0.896725\pi$
$499$	−42.3457	−1.89565	−0.947827	+	0.318785i	$0.896725\pi$
$500$	3.54333	0.158463
$501$	−18.1593	−0.811296
$502$	16.6229	0.741916
$503$	−18.0464	−0.804651	−0.402325	−	0.915497i	$-0.631798\pi$
$503$	−18.0464	−0.804651	−0.402325	+	0.915497i	$0.631798\pi$
$504$	−3.45843	−0.154051
$505$	0.267219	0.0118911
$506$	−1.60927	−0.0715406
$507$	10.3195	0.458304
$508$	−4.33585	−0.192372
$509$	28.5247	1.26434	0.632169	−	0.774831i	$-0.282165\pi$
$509$	28.5247	1.26434	0.632169	+	0.774831i	$0.282165\pi$
$510$	−2.14997	−0.0952023
$511$	−3.26676	−0.144513
$512$	−1.00000	−0.0441942
$513$	−0.886183	−0.0391259
$514$	−2.87775	−0.126932
$515$	−1.27811	−0.0563204
$516$	25.6304	1.12832
$517$	−9.37166	−0.412165
$518$	−10.5046	−0.461545
$519$	54.2417	2.38095
$520$	−1.03706	−0.0454780
$521$	−15.6418	−0.685278	−0.342639	−	0.939467i	$-0.611321\pi$
$521$	−15.6418	−0.685278	−0.342639	+	0.939467i	$0.611321\pi$
$522$	−16.7753	−0.734233
$523$	36.7413	1.60659	0.803293	−	0.595584i	$-0.203079\pi$
$523$	36.7413	1.60659	0.803293	+	0.595584i	$0.203079\pi$
$524$	−7.39120	−0.322886
$525$	19.4771	0.850051
$526$	−1.11056	−0.0484227
$527$	8.84881	0.385460
$528$	2.21770	0.0965128
$529$	−20.4103	−0.887403
$530$	−2.38127	−0.103436
$531$	−7.97485	−0.346079
$532$	−0.665971	−0.0288735
$533$	29.6956	1.28626
$534$	11.7052	0.506534
$535$	−1.24072	−0.0536412
$536$	−4.38026	−0.189198
$537$	−22.4913	−0.970572
$538$	14.6941	0.633506
$539$	3.74926	0.161492
$540$	−0.861198	−0.0370601
$541$	21.2140	0.912060	0.456030	−	0.889964i	$-0.349271\pi$
$541$	21.2140	0.912060	0.456030	+	0.889964i	$0.349271\pi$
$542$	17.4874	0.751147
$543$	44.6309	1.91530
$544$	−2.70076	−0.115794
$545$	−4.10030	−0.175637
$546$	−11.5519	−0.494374
$547$	12.9645	0.554320	0.277160	−	0.960824i	$-0.410607\pi$
$547$	12.9645	0.554320	0.277160	+	0.960824i	$0.410607\pi$
$548$	15.1205	0.645915
$549$	18.0724	0.771310
$550$	−4.87115	−0.207706
$551$	−3.23032	−0.137616
$552$	−3.56886	−0.151901
$553$	−14.8486	−0.631426
$554$	14.9118	0.633541
$555$	4.63803	0.196873
$556$	8.46160	0.358852
$557$	6.56414	0.278132	0.139066	−	0.990283i	$-0.455590\pi$
$557$	6.56414	0.278132	0.139066	+	0.990283i	$0.455590\pi$
$558$	−6.28473	−0.266054
$559$	33.3897	1.41223
$560$	−0.647195	−0.0273490
$561$	5.98947	0.252876
$562$	−18.6144	−0.785202
$563$	−21.8545	−0.921056	−0.460528	−	0.887645i	$-0.652340\pi$
$563$	−21.8545	−0.921056	−0.460528	+	0.887645i	$0.652340\pi$
$564$	−20.7835	−0.875143
$565$	0.202589	0.00852297
$566$	−9.87892	−0.415242
$567$	−19.9683	−0.838588
$568$	7.97236	0.334513
$569$	−6.63468	−0.278140	−0.139070	−	0.990283i	$-0.544411\pi$
$569$	−6.63468	−0.278140	−0.139070	+	0.990283i	$0.544411\pi$
$570$	0.294043	0.0123161
$571$	1.51560	0.0634258	0.0317129	−	0.999497i	$-0.489904\pi$
$571$	1.51560	0.0634258	0.0317129	+	0.999497i	$0.489904\pi$
$572$	2.88908	0.120798
$573$	1.67650	0.0700369
$574$	18.5321	0.773514
$575$	7.83897	0.326908
$576$	1.91818	0.0799240
$577$	−18.7079	−0.778821	−0.389411	−	0.921064i	$-0.627321\pi$
$577$	−18.7079	−0.778821	−0.389411	+	0.921064i	$0.627321\pi$
$578$	9.70588	0.403711
$579$	45.0334	1.87152
$580$	−3.13924	−0.130350
$581$	29.2463	1.21334
$582$	16.4105	0.680238
$583$	6.63384	0.274746
$584$	1.81186	0.0749755
$585$	1.98926	0.0822457
$586$	23.3926	0.966339
$587$	19.2305	0.793728	0.396864	−	0.917878i	$-0.370099\pi$
$587$	19.2305	0.793728	0.396864	+	0.917878i	$0.370099\pi$
$588$	8.31472	0.342893
$589$	−1.21022	−0.0498661
$590$	−1.49238	−0.0614401
$591$	2.21770	0.0912238
$592$	5.82623	0.239456
$593$	−41.0904	−1.68738	−0.843691	−	0.536829i	$-0.819622\pi$
$593$	−41.0904	−1.68738	−0.843691	+	0.536829i	$0.819622\pi$
$594$	2.39916	0.0984387
$595$	−1.74792	−0.0716578
$596$	3.63963	0.149085
$597$	43.8975	1.79661
$598$	−4.64929	−0.190124
$599$	7.17435	0.293136	0.146568	−	0.989201i	$-0.453177\pi$
$599$	7.17435	0.293136	0.146568	+	0.989201i	$0.453177\pi$
$600$	−10.8027	−0.441019
$601$	−23.1093	−0.942649	−0.471325	−	0.881960i	$-0.656224\pi$
$601$	−23.1093	−0.942649	−0.471325	+	0.881960i	$0.656224\pi$
$602$	20.8375	0.849271
$603$	8.40211	0.342160
$604$	6.02197	0.245030
$605$	−0.358958	−0.0145937
$606$	−1.65092	−0.0670639
$607$	24.7321	1.00385	0.501923	−	0.864912i	$-0.332626\pi$
$607$	24.7321	1.00385	0.501923	+	0.864912i	$0.332626\pi$
$608$	0.369372	0.0149800
$609$	−34.9683	−1.41699
$610$	3.38198	0.136932
$611$	−27.0754	−1.09535
$612$	5.18054	0.209411
$613$	44.0088	1.77750	0.888750	−	0.458393i	$-0.151575\pi$
$613$	44.0088	1.77750	0.888750	+	0.458393i	$0.151575\pi$
$614$	−26.1406	−1.05495
$615$	−8.18236	−0.329945
$616$	1.80298	0.0726442
$617$	−28.2878	−1.13882	−0.569411	−	0.822053i	$-0.692829\pi$
$617$	−28.2878	−1.13882	−0.569411	+	0.822053i	$0.692829\pi$
$618$	7.89636	0.317638
$619$	−43.7924	−1.76016	−0.880082	−	0.474822i	$-0.842512\pi$
$619$	−43.7924	−1.76016	−0.880082	+	0.474822i	$0.842512\pi$
$620$	−1.17610	−0.0472331
$621$	−3.86088	−0.154932
$622$	16.1102	0.645960
$623$	9.51630	0.381263
$624$	6.40709	0.256489
$625$	23.0838	0.923353
$626$	10.3291	0.412836
$627$	−0.819155	−0.0327139
$628$	−17.4137	−0.694881
$629$	15.7353	0.627406
$630$	1.24143	0.0494599
$631$	4.61853	0.183861	0.0919303	−	0.995765i	$-0.470696\pi$
$631$	4.61853	0.183861	0.0919303	+	0.995765i	$0.470696\pi$
$632$	8.23558	0.327594
$633$	49.6952	1.97521
$634$	−14.0155	−0.556626
$635$	1.55639	0.0617634
$636$	14.7118	0.583363
$637$	10.8319	0.429175
$638$	8.74542	0.346235
$639$	−15.2924	−0.604957
$640$	0.358958	0.0141891
$641$	23.0500	0.910418	0.455209	−	0.890384i	$-0.349564\pi$
$641$	23.0500	0.910418	0.455209	+	0.890384i	$0.349564\pi$
$642$	7.66537	0.302528
$643$	−14.5506	−0.573820	−0.286910	−	0.957958i	$-0.592628\pi$
$643$	−14.5506	−0.573820	−0.286910	+	0.957958i	$0.592628\pi$
$644$	−2.90148	−0.114334
$645$	−9.20024	−0.362259
$646$	0.997587	0.0392495
$647$	−30.0804	−1.18258	−0.591292	−	0.806458i	$-0.701382\pi$
$647$	−30.0804	−1.18258	−0.591292	+	0.806458i	$0.701382\pi$
$648$	11.0751	0.435072
$649$	4.15752	0.163197
$650$	−14.0731	−0.551993
$651$	−13.1006	−0.513454
$652$	13.1311	0.514253
$653$	7.78653	0.304711	0.152355	−	0.988326i	$-0.451314\pi$
$653$	7.78653	0.304711	0.152355	+	0.988326i	$0.451314\pi$
$654$	25.3322	0.990568
$655$	2.65313	0.103666
$656$	−10.2786	−0.401311
$657$	−3.47547	−0.135591
$658$	−16.8969	−0.658711
$659$	0.268615	0.0104638	0.00523188	−	0.999986i	$-0.498335\pi$
$659$	0.268615	0.0104638	0.00523188	+	0.999986i	$0.498335\pi$
$660$	−0.796060	−0.0309866
$661$	34.6432	1.34746	0.673732	−	0.738976i	$-0.264690\pi$
$661$	34.6432	1.34746	0.673732	+	0.738976i	$0.264690\pi$
$662$	−1.94241	−0.0754940
$663$	17.3040	0.672033
$664$	−16.2211	−0.629500
$665$	0.239056	0.00927019
$666$	−11.1757	−0.433051
$667$	−14.0737	−0.544936
$668$	8.18834	0.316816
$669$	51.4845	1.99051
$670$	1.57233	0.0607444
$671$	−9.42164	−0.363719
$672$	3.99846	0.154244
$673$	16.6290	0.641002	0.320501	−	0.947248i	$-0.396149\pi$
$673$	16.6290	0.641002	0.320501	+	0.947248i	$0.396149\pi$
$674$	24.0109	0.924865
$675$	−11.6867	−0.449820
$676$	−4.65324	−0.178971
$677$	−46.7065	−1.79507	−0.897537	−	0.440938i	$-0.854646\pi$
$677$	−46.7065	−1.79507	−0.897537	+	0.440938i	$0.854646\pi$
$678$	−1.25162	−0.0480683
$679$	13.3417	0.512008
$680$	0.969461	0.0371771
$681$	−48.4276	−1.85575
$682$	3.27641	0.125460
$683$	30.7487	1.17656	0.588282	−	0.808656i	$-0.299804\pi$
$683$	30.7487	1.17656	0.588282	+	0.808656i	$0.299804\pi$
$684$	−0.708521	−0.0270910
$685$	−5.42762	−0.207379
$686$	19.3807	0.739959
$687$	18.5677	0.708401
$688$	−11.5572	−0.440615
$689$	19.1657	0.730154
$690$	1.28107	0.0487696
$691$	−28.3094	−1.07694	−0.538471	−	0.842644i	$-0.680998\pi$
$691$	−28.3094	−1.07694	−0.538471	+	0.842644i	$0.680998\pi$
$692$	−24.4586	−0.929777
$693$	−3.45843	−0.131375
$694$	3.70553	0.140660
$695$	−3.03736	−0.115214
$696$	19.3947	0.735154
$697$	−27.7600	−1.05148
$698$	24.6050	0.931315
$699$	39.0290	1.47621
$700$	−8.78259	−0.331951
$701$	−14.6144	−0.551977	−0.275989	−	0.961161i	$-0.589005\pi$
$701$	−14.6144	−0.551977	−0.275989	+	0.961161i	$0.589005\pi$
$702$	6.93135	0.261607
$703$	−2.15205	−0.0811660
$704$	−1.00000	−0.0376889
$705$	7.46041	0.280975
$706$	−13.0292	−0.490360
$707$	−1.34219	−0.0504783
$708$	9.22011	0.346513
$709$	−3.06395	−0.115069	−0.0575346	−	0.998344i	$-0.518324\pi$
$709$	−3.06395	−0.115069	−0.0575346	+	0.998344i	$0.518324\pi$
$710$	−2.86175	−0.107399
$711$	−15.7973	−0.592444
$712$	−5.27809	−0.197805
$713$	−5.27261	−0.197461
$714$	10.7989	0.404139
$715$	−1.03706	−0.0387838
$716$	10.1417	0.379015
$717$	−42.4355	−1.58478
$718$	36.0246	1.34443
$719$	−2.82091	−0.105202	−0.0526011	−	0.998616i	$-0.516751\pi$
$719$	−2.82091	−0.105202	−0.0526011	+	0.998616i	$0.516751\pi$
$720$	−0.688545	−0.0256606
$721$	6.41972	0.239083
$722$	18.8636	0.702029
$723$	−22.3084	−0.829658
$724$	−20.1249	−0.747936
$725$	−42.6003	−1.58213
$726$	2.21770	0.0823064
$727$	−16.6990	−0.619330	−0.309665	−	0.950846i	$-0.600217\pi$
$727$	−16.6990	−0.619330	−0.309665	+	0.950846i	$0.600217\pi$
$728$	5.20895	0.193056
$729$	−5.28223	−0.195638
$730$	−0.650384	−0.0240718
$731$	−31.2133	−1.15447
$732$	−20.8943	−0.772277
$733$	−48.2137	−1.78081	−0.890406	−	0.455166i	$-0.849580\pi$
$733$	−48.2137	−1.78081	−0.890406	+	0.455166i	$0.849580\pi$
$734$	−8.27867	−0.305571
$735$	−2.98464	−0.110090
$736$	1.60927	0.0593183
$737$	−4.38026	−0.161349
$738$	19.7161	0.725760
$739$	16.5734	0.609662	0.304831	−	0.952406i	$-0.401400\pi$
$739$	16.5734	0.609662	0.304831	+	0.952406i	$0.401400\pi$
$740$	−2.09137	−0.0768804
$741$	−2.36660	−0.0869393
$742$	11.9607	0.439091
$743$	37.0662	1.35983	0.679914	−	0.733292i	$-0.262017\pi$
$743$	37.0662	1.35983	0.679914	+	0.733292i	$0.262017\pi$
$744$	7.26608	0.266388
$745$	−1.30648	−0.0478656
$746$	19.3331	0.707836
$747$	31.1149	1.13843
$748$	−2.70076	−0.0987497
$749$	6.23193	0.227710
$750$	7.85803	0.286935
$751$	21.3452	0.778897	0.389448	−	0.921048i	$-0.372666\pi$
$751$	21.3452	0.778897	0.389448	+	0.921048i	$0.372666\pi$
$752$	9.37166	0.341749
$753$	36.8645	1.34342
$754$	25.2662	0.920140
$755$	−2.16164	−0.0786700
$756$	4.32564	0.157322
$757$	−21.2694	−0.773050	−0.386525	−	0.922279i	$-0.626325\pi$
$757$	−21.2694	−0.773050	−0.386525	+	0.922279i	$0.626325\pi$
$758$	−4.80131	−0.174391
$759$	−3.56886	−0.129541
$760$	−0.132589	−0.00480952
$761$	−19.5106	−0.707260	−0.353630	−	0.935385i	$-0.615053\pi$
$761$	−19.5106	−0.707260	−0.353630	+	0.935385i	$0.615053\pi$
$762$	−9.61559	−0.348336
$763$	20.5950	0.745590
$764$	−0.755966	−0.0273499
$765$	−1.85960	−0.0672339
$766$	−13.5359	−0.489074
$767$	12.0114	0.433706
$768$	−2.21770	−0.0800242
$769$	−40.1209	−1.44680	−0.723399	−	0.690430i	$-0.757421\pi$
$769$	−40.1209	−1.44680	−0.723399	+	0.690430i	$0.757421\pi$
$770$	−0.647195	−0.0233233
$771$	−6.38197	−0.229841
$772$	−20.3064	−0.730842
$773$	−13.9455	−0.501584	−0.250792	−	0.968041i	$-0.580691\pi$
$773$	−13.9455	−0.501584	−0.250792	+	0.968041i	$0.580691\pi$
$774$	22.1688	0.796840
$775$	−15.9599	−0.573296
$776$	−7.39981	−0.265638
$777$	−23.2960	−0.835738
$778$	7.33032	0.262805
$779$	3.79662	0.136028
$780$	−2.29988	−0.0823489
$781$	7.97236	0.285274
$782$	4.34624	0.155421
$783$	20.9817	0.749823
$784$	−3.74926	−0.133902
$785$	6.25078	0.223100
$786$	−16.3914	−0.584663
$787$	46.1739	1.64592	0.822960	−	0.568099i	$-0.192321\pi$
$787$	46.1739	1.64592	0.822960	+	0.568099i	$0.192321\pi$
$788$	−1.00000	−0.0356235
$789$	−2.46288	−0.0876809
$790$	−2.95623	−0.105178
$791$	−1.01757	−0.0361805
$792$	1.91818	0.0681594
$793$	−27.2198	−0.966605
$794$	1.68196	0.0596904
$795$	−5.28094	−0.187296
$796$	−19.7942	−0.701587
$797$	21.7658	0.770983	0.385491	−	0.922711i	$-0.374032\pi$
$797$	21.7658	0.770983	0.385491	+	0.922711i	$0.374032\pi$
$798$	−1.47692	−0.0522825
$799$	25.3106	0.895425
$800$	4.87115	0.172221
$801$	10.1243	0.357725
$802$	−1.23325	−0.0435476
$803$	1.81186	0.0639393
$804$	−9.71409	−0.342589
$805$	1.04151	0.0367084
$806$	9.46580	0.333419
$807$	32.5869	1.14711
$808$	0.744429	0.0261889
$809$	33.8044	1.18850	0.594249	−	0.804281i	$-0.297449\pi$
$809$	33.8044	1.18850	0.594249	+	0.804281i	$0.297449\pi$
$810$	−3.97551	−0.139685
$811$	−23.4498	−0.823434	−0.411717	−	0.911312i	$-0.635071\pi$
$811$	−23.4498	−0.823434	−0.411717	+	0.911312i	$0.635071\pi$
$812$	15.7678	0.553343
$813$	38.7817	1.36013
$814$	5.82623	0.204209
$815$	−4.71351	−0.165107
$816$	−5.98947	−0.209673
$817$	4.26892	0.149350
$818$	31.4641	1.10012
$819$	−9.99168	−0.349137
$820$	3.68958	0.128846
$821$	−14.4656	−0.504853	−0.252426	−	0.967616i	$-0.581229\pi$
$821$	−14.4656	−0.504853	−0.252426	+	0.967616i	$0.581229\pi$
$822$	33.5326	1.16958
$823$	10.1711	0.354543	0.177272	−	0.984162i	$-0.443273\pi$
$823$	10.1711	0.354543	0.177272	+	0.984162i	$0.443273\pi$
$824$	−3.56061	−0.124040
$825$	−10.8027	−0.376103
$826$	7.49593	0.260817
$827$	11.6009	0.403403	0.201702	−	0.979447i	$-0.435353\pi$
$827$	11.6009	0.403403	0.201702	+	0.979447i	$0.435353\pi$
$828$	−3.08685	−0.107276
$829$	3.40147	0.118138	0.0590690	−	0.998254i	$-0.481187\pi$
$829$	3.40147	0.118138	0.0590690	+	0.998254i	$0.481187\pi$
$830$	5.82269	0.202109
$831$	33.0698	1.14718
$832$	−2.88908	−0.100161
$833$	−10.1259	−0.350840
$834$	18.7652	0.649787
$835$	−2.93927	−0.101718
$836$	0.369372	0.0127750
$837$	7.86063	0.271703
$838$	−27.7653	−0.959137
$839$	17.5511	0.605931	0.302965	−	0.953002i	$-0.402023\pi$
$839$	17.5511	0.605931	0.302965	+	0.953002i	$0.402023\pi$
$840$	−1.43528	−0.0495219
$841$	47.4824	1.63733
$842$	23.4471	0.808040
$843$	−41.2811	−1.42180
$844$	−22.4085	−0.771332
$845$	1.67032	0.0574608
$846$	−17.9765	−0.618044
$847$	1.80298	0.0619512
$848$	−6.63384	−0.227807
$849$	−21.9084	−0.751896
$850$	13.1558	0.451241
$851$	−9.37595	−0.321403
$852$	17.6803	0.605716
$853$	7.58940	0.259856	0.129928	−	0.991523i	$-0.458525\pi$
$853$	7.58940	0.259856	0.129928	+	0.991523i	$0.458525\pi$
$854$	−16.9870	−0.581285
$855$	0.254329	0.00869788
$856$	−3.45646	−0.118139
$857$	41.1117	1.40435	0.702174	−	0.712006i	$-0.252213\pi$
$857$	41.1117	1.40435	0.702174	+	0.712006i	$0.252213\pi$
$858$	6.40709	0.218734
$859$	−38.9348	−1.32844	−0.664219	−	0.747538i	$-0.731236\pi$
$859$	−38.9348	−1.32844	−0.664219	+	0.747538i	$0.731236\pi$
$860$	4.14856	0.141465
$861$	41.0985	1.40063
$862$	3.82614	0.130319
$863$	−56.6124	−1.92711	−0.963554	−	0.267514i	$-0.913798\pi$
$863$	−56.6124	−1.92711	−0.963554	+	0.267514i	$0.913798\pi$
$864$	−2.39916	−0.0816210
$865$	8.77962	0.298516
$866$	26.8077	0.910963
$867$	21.5247	0.731017
$868$	5.90731	0.200507
$869$	8.23558	0.279373
$870$	−6.96189	−0.236030
$871$	−12.6549	−0.428795
$872$	−11.4228	−0.386823
$873$	14.1941	0.480399
$874$	−0.594418	−0.0201065
$875$	6.38856	0.215973
$876$	4.01816	0.135761
$877$	−29.0370	−0.980508	−0.490254	−	0.871580i	$-0.663096\pi$
$877$	−29.0370	−0.980508	−0.490254	+	0.871580i	$0.663096\pi$
$878$	33.8585	1.14267
$879$	51.8776	1.74979
$880$	0.358958	0.0121005
$881$	−24.6904	−0.831842	−0.415921	−	0.909401i	$-0.636541\pi$
$881$	−24.6904	−0.831842	−0.415921	+	0.909401i	$0.636541\pi$
$882$	7.19173	0.242158
$883$	13.4616	0.453019	0.226510	−	0.974009i	$-0.427268\pi$
$883$	13.4616	0.453019	0.226510	+	0.974009i	$0.427268\pi$
$884$	−7.80271	−0.262433
$885$	−3.30963	−0.111252
$886$	−4.99621	−0.167851
$887$	−50.6070	−1.69922	−0.849608	−	0.527414i	$-0.823162\pi$
$887$	−50.6070	−1.69922	−0.849608	+	0.527414i	$0.823162\pi$
$888$	12.9208	0.433594
$889$	−7.81745	−0.262189
$890$	1.89461	0.0635076
$891$	11.0751	0.371031
$892$	−23.2153	−0.777307
$893$	−3.46163	−0.115839
$894$	8.07159	0.269954
$895$	−3.64047	−0.121687
$896$	−1.80298	−0.0602334
$897$	−10.3107	−0.344265
$898$	17.6696	0.589642
$899$	28.6536	0.955651
$900$	−9.34372	−0.311457
$901$	−17.9164	−0.596883
$902$	−10.2786	−0.342239
$903$	46.2111	1.53781
$904$	0.564380	0.0187710
$905$	7.22400	0.240134
$906$	13.3549	0.443687
$907$	53.4861	1.77598	0.887989	−	0.459866i	$-0.152102\pi$
$907$	53.4861	1.77598	0.887989	+	0.459866i	$0.152102\pi$
$908$	21.8369	0.724683
$909$	−1.42794	−0.0473619
$910$	−1.86980	−0.0619831
$911$	29.6426	0.982104	0.491052	−	0.871130i	$-0.336613\pi$
$911$	29.6426	0.982104	0.491052	+	0.871130i	$0.336613\pi$
$912$	0.819155	0.0271249
$913$	−16.2211	−0.536840
$914$	−4.62618	−0.153020
$915$	7.50020	0.247949
$916$	−8.37251	−0.276635
$917$	−13.3262	−0.440070
$918$	−6.47956	−0.213857
$919$	−7.98563	−0.263421	−0.131711	−	0.991288i	$-0.542047\pi$
$919$	−7.98563	−0.263421	−0.131711	+	0.991288i	$0.542047\pi$
$920$	−0.577659	−0.0190449
$921$	−57.9718	−1.91024
$922$	−26.5328	−0.873810
$923$	23.0328	0.758132
$924$	3.99846	0.131540
$925$	−28.3804	−0.933142
$926$	−10.5581	−0.346962
$927$	6.82988	0.224323
$928$	−8.74542	−0.287083
$929$	13.7534	0.451236	0.225618	−	0.974216i	$-0.427560\pi$
$929$	13.7534	0.451236	0.225618	+	0.974216i	$0.427560\pi$
$930$	−2.60822	−0.0855269
$931$	1.38487	0.0453874
$932$	−17.5989	−0.576471
$933$	35.7275	1.16967
$934$	−10.9019	−0.356722
$935$	0.969461	0.0317048
$936$	5.54175	0.181138
$937$	−5.84816	−0.191051	−0.0955255	−	0.995427i	$-0.530453\pi$
$937$	−5.84816	−0.191051	−0.0955255	+	0.995427i	$0.530453\pi$
$938$	−7.89753	−0.257863
$939$	22.9069	0.747538
$940$	−3.36403	−0.109723
$941$	−57.2992	−1.86790	−0.933951	−	0.357402i	$-0.883663\pi$
$941$	−57.2992	−1.86790	−0.933951	+	0.357402i	$0.883663\pi$
$942$	−38.6182	−1.25825
$943$	16.5409	0.538647
$944$	−4.15752	−0.135316
$945$	−1.55272	−0.0505101
$946$	−11.5572	−0.375758
$947$	−3.55658	−0.115573	−0.0577867	−	0.998329i	$-0.518404\pi$
$947$	−3.55658	−0.115573	−0.0577867	+	0.998329i	$0.518404\pi$
$948$	18.2640	0.593187
$949$	5.23461	0.169923
$950$	−1.79927	−0.0583759
$951$	−31.0821	−1.00791
$952$	−4.86943	−0.157819
$953$	−42.8845	−1.38916	−0.694582	−	0.719413i	$-0.744411\pi$
$953$	−42.8845	−1.38916	−0.694582	+	0.719413i	$0.744411\pi$
$954$	12.7249	0.411983
$955$	0.271360	0.00878102
$956$	19.1350	0.618869
$957$	19.3947	0.626941
$958$	9.08182	0.293420
$959$	27.2619	0.880334
$960$	0.796060	0.0256927
$961$	−20.2651	−0.653714
$962$	16.8324	0.542699
$963$	6.63009	0.213652
$964$	10.0593	0.323987
$965$	7.28914	0.234646
$966$	−6.43459	−0.207030
$967$	42.3442	1.36170	0.680849	−	0.732424i	$-0.261611\pi$
$967$	42.3442	1.36170	0.680849	+	0.732424i	$0.261611\pi$
$968$	−1.00000	−0.0321412
$969$	2.21234	0.0710707
$970$	2.65622	0.0852862
$971$	22.9456	0.736360	0.368180	−	0.929754i	$-0.379981\pi$
$971$	22.9456	0.736360	0.368180	+	0.929754i	$0.379981\pi$
$972$	17.3638	0.556944
$973$	15.2561	0.489088
$974$	12.1481	0.389249
$975$	−31.2099	−0.999516
$976$	9.42164	0.301579
$977$	53.9582	1.72628	0.863138	−	0.504969i	$-0.168496\pi$
$977$	53.9582	1.72628	0.863138	+	0.504969i	$0.168496\pi$
$978$	29.1207	0.931178
$979$	−5.27809	−0.168689
$980$	1.34583	0.0429909
$981$	21.9109	0.699560
$982$	7.76850	0.247903
$983$	−16.7411	−0.533959	−0.266980	−	0.963702i	$-0.586026\pi$
$983$	−16.7411	−0.533959	−0.266980	+	0.963702i	$0.586026\pi$
$984$	−22.7947	−0.726670
$985$	0.358958	0.0114374
$986$	−23.6193	−0.752192
$987$	−37.4722	−1.19275
$988$	1.06714	0.0339504
$989$	18.5986	0.591402
$990$	−0.688545	−0.0218834
$991$	28.2950	0.898821	0.449411	−	0.893325i	$-0.351634\pi$
$991$	28.2950	0.898821	0.449411	+	0.893325i	$0.351634\pi$
$992$	−3.27641	−0.104026
$993$	−4.30768	−0.136700
$994$	14.3740	0.455916
$995$	7.10529	0.225253
$996$	−35.9734	−1.13986
$997$	47.0248	1.48929	0.744645	−	0.667461i	$-0.232619\pi$
$997$	47.0248	1.48929	0.744645	+	0.667461i	$0.232619\pi$
$998$	42.3457	1.34043
$999$	13.9780	0.442246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.2	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.2	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.21770 q^{3} +1.00000 q^{4} -0.358958 q^{5} +2.21770 q^{6} +1.80298 q^{7} -1.00000 q^{8} +1.91818 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.21770 q^{3} +1.00000 q^{4} -0.358958 q^{5} +2.21770 q^{6} +1.80298 q^{7} -1.00000 q^{8} +1.91818 q^{9} +0.358958 q^{10} -1.00000 q^{11} -2.21770 q^{12} -2.88908 q^{13} -1.80298 q^{14} +0.796060 q^{15} +1.00000 q^{16} +2.70076 q^{17} -1.91818 q^{18} -0.369372 q^{19} -0.358958 q^{20} -3.99846 q^{21} +1.00000 q^{22} -1.60927 q^{23} +2.21770 q^{24} -4.87115 q^{25} +2.88908 q^{26} +2.39916 q^{27} +1.80298 q^{28} +8.74542 q^{29} -0.796060 q^{30} +3.27641 q^{31} -1.00000 q^{32} +2.21770 q^{33} -2.70076 q^{34} -0.647195 q^{35} +1.91818 q^{36} +5.82623 q^{37} +0.369372 q^{38} +6.40709 q^{39} +0.358958 q^{40} -10.2786 q^{41} +3.99846 q^{42} -11.5572 q^{43} -1.00000 q^{44} -0.688545 q^{45} +1.60927 q^{46} +9.37166 q^{47} -2.21770 q^{48} -3.74926 q^{49} +4.87115 q^{50} -5.98947 q^{51} -2.88908 q^{52} -6.63384 q^{53} -2.39916 q^{54} +0.358958 q^{55} -1.80298 q^{56} +0.819155 q^{57} -8.74542 q^{58} -4.15752 q^{59} +0.796060 q^{60} +9.42164 q^{61} -3.27641 q^{62} +3.45843 q^{63} +1.00000 q^{64} +1.03706 q^{65} -2.21770 q^{66} +4.38026 q^{67} +2.70076 q^{68} +3.56886 q^{69} +0.647195 q^{70} -7.97236 q^{71} -1.91818 q^{72} -1.81186 q^{73} -5.82623 q^{74} +10.8027 q^{75} -0.369372 q^{76} -1.80298 q^{77} -6.40709 q^{78} -8.23558 q^{79} -0.358958 q^{80} -11.0751 q^{81} +10.2786 q^{82} +16.2211 q^{83} -3.99846 q^{84} -0.969461 q^{85} +11.5572 q^{86} -19.3947 q^{87} +1.00000 q^{88} +5.27809 q^{89} +0.688545 q^{90} -5.20895 q^{91} -1.60927 q^{92} -7.26608 q^{93} -9.37166 q^{94} +0.132589 q^{95} +2.21770 q^{96} +7.39981 q^{97} +3.74926 q^{98} -1.91818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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