LMFDB - Embedded newform 726.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [726,2,Mod(1,726)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(726, 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("726.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 726 = 2 \cdot 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	726.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.79713918674$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 66)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	726.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.85410 q^{5} +1.00000 q^{6} -4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.85410 q^{5} +1.00000 q^{6} -4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.85410 q^{10} -1.00000 q^{12} +3.23607 q^{13} +4.61803 q^{14} -2.85410 q^{15} +1.00000 q^{16} +2.47214 q^{17} -1.00000 q^{18} +3.23607 q^{19} +2.85410 q^{20} +4.61803 q^{21} -3.23607 q^{23} +1.00000 q^{24} +3.14590 q^{25} -3.23607 q^{26} -1.00000 q^{27} -4.61803 q^{28} +0.381966 q^{29} +2.85410 q^{30} +8.61803 q^{31} -1.00000 q^{32} -2.47214 q^{34} -13.1803 q^{35} +1.00000 q^{36} +1.52786 q^{37} -3.23607 q^{38} -3.23607 q^{39} -2.85410 q^{40} +3.23607 q^{41} -4.61803 q^{42} +3.23607 q^{43} +2.85410 q^{45} +3.23607 q^{46} +2.47214 q^{47} -1.00000 q^{48} +14.3262 q^{49} -3.14590 q^{50} -2.47214 q^{51} +3.23607 q^{52} -3.85410 q^{53} +1.00000 q^{54} +4.61803 q^{56} -3.23607 q^{57} -0.381966 q^{58} -3.85410 q^{59} -2.85410 q^{60} +6.76393 q^{61} -8.61803 q^{62} -4.61803 q^{63} +1.00000 q^{64} +9.23607 q^{65} +4.00000 q^{67} +2.47214 q^{68} +3.23607 q^{69} +13.1803 q^{70} +12.4721 q^{71} -1.00000 q^{72} +11.3262 q^{73} -1.52786 q^{74} -3.14590 q^{75} +3.23607 q^{76} +3.23607 q^{78} +9.32624 q^{79} +2.85410 q^{80} +1.00000 q^{81} -3.23607 q^{82} +0.673762 q^{83} +4.61803 q^{84} +7.05573 q^{85} -3.23607 q^{86} -0.381966 q^{87} -11.7082 q^{89} -2.85410 q^{90} -14.9443 q^{91} -3.23607 q^{92} -8.61803 q^{93} -2.47214 q^{94} +9.23607 q^{95} +1.00000 q^{96} +11.3262 q^{97} -14.3262 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} - 2 q^{12} + 2 q^{13} + 7 q^{14} + q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} + 7 q^{21} - 2 q^{23} + 2 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} - 7 q^{28} + 3 q^{29} - q^{30} + 15 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{37} - 2 q^{38} - 2 q^{39} + q^{40} + 2 q^{41} - 7 q^{42} + 2 q^{43} - q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} + 13 q^{49} - 13 q^{50} + 4 q^{51} + 2 q^{52} - q^{53} + 2 q^{54} + 7 q^{56} - 2 q^{57} - 3 q^{58} - q^{59} + q^{60} + 18 q^{61} - 15 q^{62} - 7 q^{63} + 2 q^{64} + 14 q^{65} + 8 q^{67} - 4 q^{68} + 2 q^{69} + 4 q^{70} + 16 q^{71} - 2 q^{72} + 7 q^{73} - 12 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{78} + 3 q^{79} - q^{80} + 2 q^{81} - 2 q^{82} + 17 q^{83} + 7 q^{84} + 32 q^{85} - 2 q^{86} - 3 q^{87} - 10 q^{89} + q^{90} - 12 q^{91} - 2 q^{92} - 15 q^{93} + 4 q^{94} + 14 q^{95} + 2 q^{96} + 7 q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 + 2 * q^9 + q^10 - 2 * q^12 + 2 * q^13 + 7 * q^14 + q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 - q^20 + 7 * q^21 - 2 * q^23 + 2 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 - 7 * q^28 + 3 * q^29 - q^30 + 15 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^37 - 2 * q^38 - 2 * q^39 + q^40 + 2 * q^41 - 7 * q^42 + 2 * q^43 - q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 + 13 * q^49 - 13 * q^50 + 4 * q^51 + 2 * q^52 - q^53 + 2 * q^54 + 7 * q^56 - 2 * q^57 - 3 * q^58 - q^59 + q^60 + 18 * q^61 - 15 * q^62 - 7 * q^63 + 2 * q^64 + 14 * q^65 + 8 * q^67 - 4 * q^68 + 2 * q^69 + 4 * q^70 + 16 * q^71 - 2 * q^72 + 7 * q^73 - 12 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^78 + 3 * q^79 - q^80 + 2 * q^81 - 2 * q^82 + 17 * q^83 + 7 * q^84 + 32 * q^85 - 2 * q^86 - 3 * q^87 - 10 * q^89 + q^90 - 12 * q^91 - 2 * q^92 - 15 * q^93 + 4 * q^94 + 14 * q^95 + 2 * q^96 + 7 * q^97 - 13 * q^98

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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	2.85410	1.27639	0.638197	−	0.769873i	$-0.279681\pi$
$5$	2.85410	1.27639	0.638197	+	0.769873i	$0.279681\pi$
$6$	1.00000	0.408248
$7$	−4.61803	−1.74545	−0.872726	−	0.488210i	$-0.837650\pi$
$7$	−4.61803	−1.74545	−0.872726	+	0.488210i	$0.837650\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.85410	−0.902546
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	3.23607	0.897524	0.448762	−	0.893651i	$-0.351865\pi$
$13$	3.23607	0.897524	0.448762	+	0.893651i	$0.351865\pi$
$14$	4.61803	1.23422
$15$	−2.85410	−0.736926
$16$	1.00000	0.250000
$17$	2.47214	0.599581	0.299791	−	0.954005i	$-0.403083\pi$
$17$	2.47214	0.599581	0.299791	+	0.954005i	$0.403083\pi$
$18$	−1.00000	−0.235702
$19$	3.23607	0.742405	0.371202	−	0.928552i	$-0.378946\pi$
$19$	3.23607	0.742405	0.371202	+	0.928552i	$0.378946\pi$
$20$	2.85410	0.638197
$21$	4.61803	1.00774
$22$	0	0
$23$	−3.23607	−0.674767	−0.337383	−	0.941367i	$-0.609542\pi$
$23$	−3.23607	−0.674767	−0.337383	+	0.941367i	$0.609542\pi$
$24$	1.00000	0.204124
$25$	3.14590	0.629180
$26$	−3.23607	−0.634645
$27$	−1.00000	−0.192450
$28$	−4.61803	−0.872726
$29$	0.381966	0.0709293	0.0354647	−	0.999371i	$-0.488709\pi$
$29$	0.381966	0.0709293	0.0354647	+	0.999371i	$0.488709\pi$
$30$	2.85410	0.521085
$31$	8.61803	1.54784	0.773922	−	0.633281i	$-0.218292\pi$
$31$	8.61803	1.54784	0.773922	+	0.633281i	$0.218292\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−2.47214	−0.423968
$35$	−13.1803	−2.22788
$36$	1.00000	0.166667
$37$	1.52786	0.251179	0.125590	−	0.992082i	$-0.459918\pi$
$37$	1.52786	0.251179	0.125590	+	0.992082i	$0.459918\pi$
$38$	−3.23607	−0.524960
$39$	−3.23607	−0.518186
$40$	−2.85410	−0.451273
$41$	3.23607	0.505389	0.252694	−	0.967546i	$-0.418683\pi$
$41$	3.23607	0.505389	0.252694	+	0.967546i	$0.418683\pi$
$42$	−4.61803	−0.712578
$43$	3.23607	0.493496	0.246748	−	0.969080i	$-0.420638\pi$
$43$	3.23607	0.493496	0.246748	+	0.969080i	$0.420638\pi$
$44$	0	0
$45$	2.85410	0.425464
$46$	3.23607	0.477132
$47$	2.47214	0.360598	0.180299	−	0.983612i	$-0.442293\pi$
$47$	2.47214	0.360598	0.180299	+	0.983612i	$0.442293\pi$
$48$	−1.00000	−0.144338
$49$	14.3262	2.04661
$50$	−3.14590	−0.444897
$51$	−2.47214	−0.346168
$52$	3.23607	0.448762
$53$	−3.85410	−0.529402	−0.264701	−	0.964331i	$-0.585273\pi$
$53$	−3.85410	−0.529402	−0.264701	+	0.964331i	$0.585273\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.61803	0.617111
$57$	−3.23607	−0.428628
$58$	−0.381966	−0.0501546
$59$	−3.85410	−0.501761	−0.250881	−	0.968018i	$-0.580720\pi$
$59$	−3.85410	−0.501761	−0.250881	+	0.968018i	$0.580720\pi$
$60$	−2.85410	−0.368463
$61$	6.76393	0.866033	0.433016	−	0.901386i	$-0.357449\pi$
$61$	6.76393	0.866033	0.433016	+	0.901386i	$0.357449\pi$
$62$	−8.61803	−1.09449
$63$	−4.61803	−0.581818
$64$	1.00000	0.125000
$65$	9.23607	1.14559
$66$	0	0
$67$	4.00000	0.488678	0.244339	−	0.969690i	$-0.421429\pi$
$67$	4.00000	0.488678	0.244339	+	0.969690i	$0.421429\pi$
$68$	2.47214	0.299791
$69$	3.23607	0.389577
$70$	13.1803	1.57535
$71$	12.4721	1.48017	0.740085	−	0.672513i	$-0.234785\pi$
$71$	12.4721	1.48017	0.740085	+	0.672513i	$0.234785\pi$
$72$	−1.00000	−0.117851
$73$	11.3262	1.32564	0.662818	−	0.748781i	$-0.269360\pi$
$73$	11.3262	1.32564	0.662818	+	0.748781i	$0.269360\pi$
$74$	−1.52786	−0.177611
$75$	−3.14590	−0.363257
$76$	3.23607	0.371202
$77$	0	0
$78$	3.23607	0.366413
$79$	9.32624	1.04928	0.524642	−	0.851323i	$-0.324199\pi$
$79$	9.32624	1.04928	0.524642	+	0.851323i	$0.324199\pi$
$80$	2.85410	0.319098
$81$	1.00000	0.111111
$82$	−3.23607	−0.357364
$83$	0.673762	0.0739550	0.0369775	−	0.999316i	$-0.488227\pi$
$83$	0.673762	0.0739550	0.0369775	+	0.999316i	$0.488227\pi$
$84$	4.61803	0.503869
$85$	7.05573	0.765301
$86$	−3.23607	−0.348954
$87$	−0.381966	−0.0409511
$88$	0	0
$89$	−11.7082	−1.24107	−0.620534	−	0.784180i	$-0.713084\pi$
$89$	−11.7082	−1.24107	−0.620534	+	0.784180i	$0.713084\pi$
$90$	−2.85410	−0.300849
$91$	−14.9443	−1.56659
$92$	−3.23607	−0.337383
$93$	−8.61803	−0.893648
$94$	−2.47214	−0.254981
$95$	9.23607	0.947601
$96$	1.00000	0.102062
$97$	11.3262	1.15001	0.575003	−	0.818152i	$-0.305001\pi$
$97$	11.3262	1.15001	0.575003	+	0.818152i	$0.305001\pi$
$98$	−14.3262	−1.44717
$99$	0	0
$100$	3.14590	0.314590
$101$	12.3820	1.23205	0.616026	−	0.787726i	$-0.288742\pi$
$101$	12.3820	1.23205	0.616026	+	0.787726i	$0.288742\pi$
$102$	2.47214	0.244778
$103$	12.0344	1.18579	0.592894	−	0.805280i	$-0.297985\pi$
$103$	12.0344	1.18579	0.592894	+	0.805280i	$0.297985\pi$
$104$	−3.23607	−0.317323
$105$	13.1803	1.28627
$106$	3.85410	0.374343
$107$	−5.38197	−0.520294	−0.260147	−	0.965569i	$-0.583771\pi$
$107$	−5.38197	−0.520294	−0.260147	+	0.965569i	$0.583771\pi$
$108$	−1.00000	−0.0962250
$109$	−17.4164	−1.66819	−0.834095	−	0.551621i	$-0.814009\pi$
$109$	−17.4164	−1.66819	−0.834095	+	0.551621i	$0.814009\pi$
$110$	0	0
$111$	−1.52786	−0.145018
$112$	−4.61803	−0.436363
$113$	−12.4721	−1.17328	−0.586640	−	0.809848i	$-0.699550\pi$
$113$	−12.4721	−1.17328	−0.586640	+	0.809848i	$0.699550\pi$
$114$	3.23607	0.303086
$115$	−9.23607	−0.861268
$116$	0.381966	0.0354647
$117$	3.23607	0.299175
$118$	3.85410	0.354799
$119$	−11.4164	−1.04654
$120$	2.85410	0.260543
$121$	0	0
$122$	−6.76393	−0.612378
$123$	−3.23607	−0.291786
$124$	8.61803	0.773922
$125$	−5.29180	−0.473313
$126$	4.61803	0.411407
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−1.00000	−0.0883883
$129$	−3.23607	−0.284920
$130$	−9.23607	−0.810057
$131$	15.2705	1.33419	0.667095	−	0.744972i	$-0.267537\pi$
$131$	15.2705	1.33419	0.667095	+	0.744972i	$0.267537\pi$
$132$	0	0
$133$	−14.9443	−1.29583
$134$	−4.00000	−0.345547
$135$	−2.85410	−0.245642
$136$	−2.47214	−0.211984
$137$	−23.1246	−1.97567	−0.987834	−	0.155509i	$-0.950298\pi$
$137$	−23.1246	−1.97567	−0.987834	+	0.155509i	$0.950298\pi$
$138$	−3.23607	−0.275472
$139$	−13.2361	−1.12267	−0.561334	−	0.827589i	$-0.689712\pi$
$139$	−13.2361	−1.12267	−0.561334	+	0.827589i	$0.689712\pi$
$140$	−13.1803	−1.11394
$141$	−2.47214	−0.208191
$142$	−12.4721	−1.04664
$143$	0	0
$144$	1.00000	0.0833333
$145$	1.09017	0.0905337
$146$	−11.3262	−0.937366
$147$	−14.3262	−1.18161
$148$	1.52786	0.125590
$149$	−1.38197	−0.113215	−0.0566075	−	0.998397i	$-0.518028\pi$
$149$	−1.38197	−0.113215	−0.0566075	+	0.998397i	$0.518028\pi$
$150$	3.14590	0.256861
$151$	−9.32624	−0.758958	−0.379479	−	0.925200i	$-0.623897\pi$
$151$	−9.32624	−0.758958	−0.379479	+	0.925200i	$0.623897\pi$
$152$	−3.23607	−0.262480
$153$	2.47214	0.199860
$154$	0	0
$155$	24.5967	1.97566
$156$	−3.23607	−0.259093
$157$	4.47214	0.356915	0.178458	−	0.983948i	$-0.442889\pi$
$157$	4.47214	0.356915	0.178458	+	0.983948i	$0.442889\pi$
$158$	−9.32624	−0.741956
$159$	3.85410	0.305650
$160$	−2.85410	−0.225637
$161$	14.9443	1.17777
$162$	−1.00000	−0.0785674
$163$	−13.4164	−1.05085	−0.525427	−	0.850839i	$-0.676094\pi$
$163$	−13.4164	−1.05085	−0.525427	+	0.850839i	$0.676094\pi$
$164$	3.23607	0.252694
$165$	0	0
$166$	−0.673762	−0.0522941
$167$	−7.23607	−0.559944	−0.279972	−	0.960008i	$-0.590325\pi$
$167$	−7.23607	−0.559944	−0.279972	+	0.960008i	$0.590325\pi$
$168$	−4.61803	−0.356289
$169$	−2.52786	−0.194451
$170$	−7.05573	−0.541150
$171$	3.23607	0.247468
$172$	3.23607	0.246748
$173$	4.14590	0.315207	0.157603	−	0.987502i	$-0.449623\pi$
$173$	4.14590	0.315207	0.157603	+	0.987502i	$0.449623\pi$
$174$	0.381966	0.0289568
$175$	−14.5279	−1.09820
$176$	0	0
$177$	3.85410	0.289692
$178$	11.7082	0.877567
$179$	−6.38197	−0.477011	−0.238505	−	0.971141i	$-0.576657\pi$
$179$	−6.38197	−0.477011	−0.238505	+	0.971141i	$0.576657\pi$
$180$	2.85410	0.212732
$181$	−16.4721	−1.22436	−0.612182	−	0.790717i	$-0.709708\pi$
$181$	−16.4721	−1.22436	−0.612182	+	0.790717i	$0.709708\pi$
$182$	14.9443	1.10774
$183$	−6.76393	−0.500004
$184$	3.23607	0.238566
$185$	4.36068	0.320604
$186$	8.61803	0.631905
$187$	0	0
$188$	2.47214	0.180299
$189$	4.61803	0.335913
$190$	−9.23607	−0.670055
$191$	22.4721	1.62603	0.813013	−	0.582245i	$-0.197826\pi$
$191$	22.4721	1.62603	0.813013	+	0.582245i	$0.197826\pi$
$192$	−1.00000	−0.0721688
$193$	−0.326238	−0.0234831	−0.0117416	−	0.999931i	$-0.503738\pi$
$193$	−0.326238	−0.0234831	−0.0117416	+	0.999931i	$0.503738\pi$
$194$	−11.3262	−0.813176
$195$	−9.23607	−0.661409
$196$	14.3262	1.02330
$197$	−6.09017	−0.433907	−0.216953	−	0.976182i	$-0.569612\pi$
$197$	−6.09017	−0.433907	−0.216953	+	0.976182i	$0.569612\pi$
$198$	0	0
$199$	13.1459	0.931888	0.465944	−	0.884814i	$-0.345715\pi$
$199$	13.1459	0.931888	0.465944	+	0.884814i	$0.345715\pi$
$200$	−3.14590	−0.222449
$201$	−4.00000	−0.282138
$202$	−12.3820	−0.871192
$203$	−1.76393	−0.123804
$204$	−2.47214	−0.173084
$205$	9.23607	0.645075
$206$	−12.0344	−0.838479
$207$	−3.23607	−0.224922
$208$	3.23607	0.224381
$209$	0	0
$210$	−13.1803	−0.909530
$211$	4.65248	0.320290	0.160145	−	0.987094i	$-0.448804\pi$
$211$	4.65248	0.320290	0.160145	+	0.987094i	$0.448804\pi$
$212$	−3.85410	−0.264701
$213$	−12.4721	−0.854577
$214$	5.38197	0.367904
$215$	9.23607	0.629895
$216$	1.00000	0.0680414
$217$	−39.7984	−2.70169
$218$	17.4164	1.17959
$219$	−11.3262	−0.765356
$220$	0	0
$221$	8.00000	0.538138
$222$	1.52786	0.102544
$223$	−1.90983	−0.127892	−0.0639458	−	0.997953i	$-0.520368\pi$
$223$	−1.90983	−0.127892	−0.0639458	+	0.997953i	$0.520368\pi$
$224$	4.61803	0.308555
$225$	3.14590	0.209727
$226$	12.4721	0.829634
$227$	7.14590	0.474290	0.237145	−	0.971474i	$-0.423788\pi$
$227$	7.14590	0.474290	0.237145	+	0.971474i	$0.423788\pi$
$228$	−3.23607	−0.214314
$229$	22.9443	1.51620	0.758100	−	0.652138i	$-0.226128\pi$
$229$	22.9443	1.51620	0.758100	+	0.652138i	$0.226128\pi$
$230$	9.23607	0.609008
$231$	0	0
$232$	−0.381966	−0.0250773
$233$	8.94427	0.585959	0.292979	−	0.956119i	$-0.405353\pi$
$233$	8.94427	0.585959	0.292979	+	0.956119i	$0.405353\pi$
$234$	−3.23607	−0.211548
$235$	7.05573	0.460265
$236$	−3.85410	−0.250881
$237$	−9.32624	−0.605804
$238$	11.4164	0.740016
$239$	16.4721	1.06549	0.532747	−	0.846275i	$-0.321160\pi$
$239$	16.4721	1.06549	0.532747	+	0.846275i	$0.321160\pi$
$240$	−2.85410	−0.184231
$241$	2.43769	0.157026	0.0785128	−	0.996913i	$-0.474983\pi$
$241$	2.43769	0.157026	0.0785128	+	0.996913i	$0.474983\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	6.76393	0.433016
$245$	40.8885	2.61227
$246$	3.23607	0.206324
$247$	10.4721	0.666326
$248$	−8.61803	−0.547246
$249$	−0.673762	−0.0426979
$250$	5.29180	0.334683
$251$	−19.3262	−1.21986	−0.609931	−	0.792455i	$-0.708803\pi$
$251$	−19.3262	−1.21986	−0.609931	+	0.792455i	$0.708803\pi$
$252$	−4.61803	−0.290909
$253$	0	0
$254$	12.0000	0.752947
$255$	−7.05573	−0.441847
$256$	1.00000	0.0625000
$257$	−1.81966	−0.113507	−0.0567536	−	0.998388i	$-0.518075\pi$
$257$	−1.81966	−0.113507	−0.0567536	+	0.998388i	$0.518075\pi$
$258$	3.23607	0.201469
$259$	−7.05573	−0.438422
$260$	9.23607	0.572797
$261$	0.381966	0.0236431
$262$	−15.2705	−0.943415
$263$	−7.70820	−0.475308	−0.237654	−	0.971350i	$-0.576378\pi$
$263$	−7.70820	−0.475308	−0.237654	+	0.971350i	$0.576378\pi$
$264$	0	0
$265$	−11.0000	−0.675725
$266$	14.9443	0.916292
$267$	11.7082	0.716530
$268$	4.00000	0.244339
$269$	−2.94427	−0.179515	−0.0897577	−	0.995964i	$-0.528609\pi$
$269$	−2.94427	−0.179515	−0.0897577	+	0.995964i	$0.528609\pi$
$270$	2.85410	0.173695
$271$	−23.4164	−1.42245	−0.711223	−	0.702967i	$-0.751858\pi$
$271$	−23.4164	−1.42245	−0.711223	+	0.702967i	$0.751858\pi$
$272$	2.47214	0.149895
$273$	14.9443	0.904468
$274$	23.1246	1.39701
$275$	0	0
$276$	3.23607	0.194788
$277$	−11.1246	−0.668413	−0.334207	−	0.942500i	$-0.608468\pi$
$277$	−11.1246	−0.668413	−0.334207	+	0.942500i	$0.608468\pi$
$278$	13.2361	0.793847
$279$	8.61803	0.515948
$280$	13.1803	0.787676
$281$	−23.1246	−1.37950	−0.689749	−	0.724048i	$-0.742279\pi$
$281$	−23.1246	−1.37950	−0.689749	+	0.724048i	$0.742279\pi$
$282$	2.47214	0.147214
$283$	23.8885	1.42003	0.710013	−	0.704188i	$-0.248689\pi$
$283$	23.8885	1.42003	0.710013	+	0.704188i	$0.248689\pi$
$284$	12.4721	0.740085
$285$	−9.23607	−0.547097
$286$	0	0
$287$	−14.9443	−0.882132
$288$	−1.00000	−0.0589256
$289$	−10.8885	−0.640503
$290$	−1.09017	−0.0640170
$291$	−11.3262	−0.663956
$292$	11.3262	0.662818
$293$	−22.9787	−1.34243	−0.671215	−	0.741262i	$-0.734227\pi$
$293$	−22.9787	−1.34243	−0.671215	+	0.741262i	$0.734227\pi$
$294$	14.3262	0.835523
$295$	−11.0000	−0.640445
$296$	−1.52786	−0.0888053
$297$	0	0
$298$	1.38197	0.0800551
$299$	−10.4721	−0.605619
$300$	−3.14590	−0.181629
$301$	−14.9443	−0.861374
$302$	9.32624	0.536665
$303$	−12.3820	−0.711325
$304$	3.23607	0.185601
$305$	19.3050	1.10540
$306$	−2.47214	−0.141323
$307$	16.6525	0.950407	0.475203	−	0.879876i	$-0.342374\pi$
$307$	16.6525	0.950407	0.475203	+	0.879876i	$0.342374\pi$
$308$	0	0
$309$	−12.0344	−0.684615
$310$	−24.5967	−1.39700
$311$	−23.8885	−1.35460	−0.677298	−	0.735709i	$-0.736849\pi$
$311$	−23.8885	−1.35460	−0.677298	+	0.735709i	$0.736849\pi$
$312$	3.23607	0.183206
$313$	15.1459	0.856097	0.428048	−	0.903756i	$-0.359201\pi$
$313$	15.1459	0.856097	0.428048	+	0.903756i	$0.359201\pi$
$314$	−4.47214	−0.252377
$315$	−13.1803	−0.742628
$316$	9.32624	0.524642
$317$	−19.8885	−1.11705	−0.558526	−	0.829487i	$-0.688633\pi$
$317$	−19.8885	−1.11705	−0.558526	+	0.829487i	$0.688633\pi$
$318$	−3.85410	−0.216127
$319$	0	0
$320$	2.85410	0.159549
$321$	5.38197	0.300392
$322$	−14.9443	−0.832812
$323$	8.00000	0.445132
$324$	1.00000	0.0555556
$325$	10.1803	0.564704
$326$	13.4164	0.743066
$327$	17.4164	0.963130
$328$	−3.23607	−0.178682
$329$	−11.4164	−0.629407
$330$	0	0
$331$	8.94427	0.491622	0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427	0.491622	0.245811	+	0.969318i	$0.420946\pi$
$332$	0.673762	0.0369775
$333$	1.52786	0.0837264
$334$	7.23607	0.395940
$335$	11.4164	0.623745
$336$	4.61803	0.251934
$337$	−6.94427	−0.378279	−0.189139	−	0.981950i	$-0.560570\pi$
$337$	−6.94427	−0.378279	−0.189139	+	0.981950i	$0.560570\pi$
$338$	2.52786	0.137498
$339$	12.4721	0.677393
$340$	7.05573	0.382651
$341$	0	0
$342$	−3.23607	−0.174987
$343$	−33.8328	−1.82680
$344$	−3.23607	−0.174477
$345$	9.23607	0.497253
$346$	−4.14590	−0.222885
$347$	−11.8541	−0.636362	−0.318181	−	0.948030i	$-0.603072\pi$
$347$	−11.8541	−0.636362	−0.318181	+	0.948030i	$0.603072\pi$
$348$	−0.381966	−0.0204755
$349$	13.2361	0.708510	0.354255	−	0.935149i	$-0.384734\pi$
$349$	13.2361	0.708510	0.354255	+	0.935149i	$0.384734\pi$
$350$	14.5279	0.776547
$351$	−3.23607	−0.172729
$352$	0	0
$353$	−21.5967	−1.14948	−0.574739	−	0.818336i	$-0.694897\pi$
$353$	−21.5967	−1.14948	−0.574739	+	0.818336i	$0.694897\pi$
$354$	−3.85410	−0.204843
$355$	35.5967	1.88928
$356$	−11.7082	−0.620534
$357$	11.4164	0.604220
$358$	6.38197	0.337297
$359$	−12.7639	−0.673655	−0.336827	−	0.941566i	$-0.609354\pi$
$359$	−12.7639	−0.673655	−0.336827	+	0.941566i	$0.609354\pi$
$360$	−2.85410	−0.150424
$361$	−8.52786	−0.448835
$362$	16.4721	0.865756
$363$	0	0
$364$	−14.9443	−0.783293
$365$	32.3262	1.69203
$366$	6.76393	0.353556
$367$	−37.5066	−1.95783	−0.978914	−	0.204274i	$-0.934517\pi$
$367$	−37.5066	−1.95783	−0.978914	+	0.204274i	$0.934517\pi$
$368$	−3.23607	−0.168692
$369$	3.23607	0.168463
$370$	−4.36068	−0.226701
$371$	17.7984	0.924046
$372$	−8.61803	−0.446824
$373$	9.52786	0.493334	0.246667	−	0.969100i	$-0.420665\pi$
$373$	9.52786	0.493334	0.246667	+	0.969100i	$0.420665\pi$
$374$	0	0
$375$	5.29180	0.273267
$376$	−2.47214	−0.127491
$377$	1.23607	0.0636607
$378$	−4.61803	−0.237526
$379$	3.70820	0.190478	0.0952388	−	0.995454i	$-0.469639\pi$
$379$	3.70820	0.190478	0.0952388	+	0.995454i	$0.469639\pi$
$380$	9.23607	0.473800
$381$	12.0000	0.614779
$382$	−22.4721	−1.14977
$383$	13.2361	0.676331	0.338166	−	0.941087i	$-0.390194\pi$
$383$	13.2361	0.676331	0.338166	+	0.941087i	$0.390194\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	0.326238	0.0166051
$387$	3.23607	0.164499
$388$	11.3262	0.575003
$389$	38.9443	1.97455	0.987276	−	0.159013i	$-0.0508312\pi$
$389$	38.9443	1.97455	0.987276	+	0.159013i	$0.0508312\pi$
$390$	9.23607	0.467686
$391$	−8.00000	−0.404577
$392$	−14.3262	−0.723584
$393$	−15.2705	−0.770295
$394$	6.09017	0.306818
$395$	26.6180	1.33930
$396$	0	0
$397$	9.88854	0.496292	0.248146	−	0.968723i	$-0.420179\pi$
$397$	9.88854	0.496292	0.248146	+	0.968723i	$0.420179\pi$
$398$	−13.1459	−0.658944
$399$	14.9443	0.748149
$400$	3.14590	0.157295
$401$	10.2918	0.513948	0.256974	−	0.966418i	$-0.417275\pi$
$401$	10.2918	0.513948	0.256974	+	0.966418i	$0.417275\pi$
$402$	4.00000	0.199502
$403$	27.8885	1.38923
$404$	12.3820	0.616026
$405$	2.85410	0.141821
$406$	1.76393	0.0875425
$407$	0	0
$408$	2.47214	0.122389
$409$	12.0902	0.597820	0.298910	−	0.954281i	$-0.403377\pi$
$409$	12.0902	0.597820	0.298910	+	0.954281i	$0.403377\pi$
$410$	−9.23607	−0.456137
$411$	23.1246	1.14065
$412$	12.0344	0.592894
$413$	17.7984	0.875801
$414$	3.23607	0.159044
$415$	1.92299	0.0943957
$416$	−3.23607	−0.158661
$417$	13.2361	0.648173
$418$	0	0
$419$	−17.9787	−0.878318	−0.439159	−	0.898409i	$-0.644723\pi$
$419$	−17.9787	−0.878318	−0.439159	+	0.898409i	$0.644723\pi$
$420$	13.1803	0.643135
$421$	35.1246	1.71187	0.855934	−	0.517084i	$-0.172983\pi$
$421$	35.1246	1.71187	0.855934	+	0.517084i	$0.172983\pi$
$422$	−4.65248	−0.226479
$423$	2.47214	0.120199
$424$	3.85410	0.187172
$425$	7.77709	0.377244
$426$	12.4721	0.604277
$427$	−31.2361	−1.51162
$428$	−5.38197	−0.260147
$429$	0	0
$430$	−9.23607	−0.445403
$431$	7.23607	0.348549	0.174275	−	0.984697i	$-0.444242\pi$
$431$	7.23607	0.348549	0.174275	+	0.984697i	$0.444242\pi$
$432$	−1.00000	−0.0481125
$433$	12.3262	0.592361	0.296181	−	0.955132i	$-0.404287\pi$
$433$	12.3262	0.592361	0.296181	+	0.955132i	$0.404287\pi$
$434$	39.7984	1.91038
$435$	−1.09017	−0.0522696
$436$	−17.4164	−0.834095
$437$	−10.4721	−0.500950
$438$	11.3262	0.541189
$439$	−16.0344	−0.765282	−0.382641	−	0.923897i	$-0.624985\pi$
$439$	−16.0344	−0.765282	−0.382641	+	0.923897i	$0.624985\pi$
$440$	0	0
$441$	14.3262	0.682202
$442$	−8.00000	−0.380521
$443$	−1.67376	−0.0795228	−0.0397614	−	0.999209i	$-0.512660\pi$
$443$	−1.67376	−0.0795228	−0.0397614	+	0.999209i	$0.512660\pi$
$444$	−1.52786	−0.0725092
$445$	−33.4164	−1.58409
$446$	1.90983	0.0904331
$447$	1.38197	0.0653647
$448$	−4.61803	−0.218182
$449$	35.8885	1.69369	0.846843	−	0.531844i	$-0.178501\pi$
$449$	35.8885	1.69369	0.846843	+	0.531844i	$0.178501\pi$
$450$	−3.14590	−0.148299
$451$	0	0
$452$	−12.4721	−0.586640
$453$	9.32624	0.438185
$454$	−7.14590	−0.335374
$455$	−42.6525	−1.99958
$456$	3.23607	0.151543
$457$	21.9787	1.02812	0.514060	−	0.857754i	$-0.328141\pi$
$457$	21.9787	1.02812	0.514060	+	0.857754i	$0.328141\pi$
$458$	−22.9443	−1.07212
$459$	−2.47214	−0.115389
$460$	−9.23607	−0.430634
$461$	−40.8328	−1.90177	−0.950887	−	0.309538i	$-0.899825\pi$
$461$	−40.8328	−1.90177	−0.950887	+	0.309538i	$0.899825\pi$
$462$	0	0
$463$	19.0902	0.887195	0.443598	−	0.896226i	$-0.353702\pi$
$463$	19.0902	0.887195	0.443598	+	0.896226i	$0.353702\pi$
$464$	0.381966	0.0177323
$465$	−24.5967	−1.14065
$466$	−8.94427	−0.414335
$467$	19.5623	0.905236	0.452618	−	0.891705i	$-0.350490\pi$
$467$	19.5623	0.905236	0.452618	+	0.891705i	$0.350490\pi$
$468$	3.23607	0.149587
$469$	−18.4721	−0.852964
$470$	−7.05573	−0.325456
$471$	−4.47214	−0.206065
$472$	3.85410	0.177399
$473$	0	0
$474$	9.32624	0.428368
$475$	10.1803	0.467106
$476$	−11.4164	−0.523270
$477$	−3.85410	−0.176467
$478$	−16.4721	−0.753418
$479$	7.23607	0.330624	0.165312	−	0.986241i	$-0.447137\pi$
$479$	7.23607	0.330624	0.165312	+	0.986241i	$0.447137\pi$
$480$	2.85410	0.130271
$481$	4.94427	0.225439
$482$	−2.43769	−0.111034
$483$	−14.9443	−0.679988
$484$	0	0
$485$	32.3262	1.46786
$486$	1.00000	0.0453609
$487$	24.9787	1.13189	0.565947	−	0.824442i	$-0.308511\pi$
$487$	24.9787	1.13189	0.565947	+	0.824442i	$0.308511\pi$
$488$	−6.76393	−0.306189
$489$	13.4164	0.606711
$490$	−40.8885	−1.84716
$491$	−42.2492	−1.90668	−0.953340	−	0.301898i	$-0.902380\pi$
$491$	−42.2492	−1.90668	−0.953340	+	0.301898i	$0.902380\pi$
$492$	−3.23607	−0.145893
$493$	0.944272	0.0425279
$494$	−10.4721	−0.471164
$495$	0	0
$496$	8.61803	0.386961
$497$	−57.5967	−2.58357
$498$	0.673762	0.0301920
$499$	−7.41641	−0.332004	−0.166002	−	0.986125i	$-0.553086\pi$
$499$	−7.41641	−0.332004	−0.166002	+	0.986125i	$0.553086\pi$
$500$	−5.29180	−0.236656
$501$	7.23607	0.323284
$502$	19.3262	0.862572
$503$	−4.36068	−0.194433	−0.0972166	−	0.995263i	$-0.530994\pi$
$503$	−4.36068	−0.194433	−0.0972166	+	0.995263i	$0.530994\pi$
$504$	4.61803	0.205704
$505$	35.3394	1.57258
$506$	0	0
$507$	2.52786	0.112266
$508$	−12.0000	−0.532414
$509$	3.20163	0.141910	0.0709548	−	0.997480i	$-0.477395\pi$
$509$	3.20163	0.141910	0.0709548	+	0.997480i	$0.477395\pi$
$510$	7.05573	0.312433
$511$	−52.3050	−2.31383
$512$	−1.00000	−0.0441942
$513$	−3.23607	−0.142876
$514$	1.81966	0.0802618
$515$	34.3475	1.51353
$516$	−3.23607	−0.142460
$517$	0	0
$518$	7.05573	0.310011
$519$	−4.14590	−0.181985
$520$	−9.23607	−0.405028
$521$	31.4164	1.37638	0.688189	−	0.725532i	$-0.258406\pi$
$521$	31.4164	1.37638	0.688189	+	0.725532i	$0.258406\pi$
$522$	−0.381966	−0.0167182
$523$	−19.5967	−0.856906	−0.428453	−	0.903564i	$-0.640941\pi$
$523$	−19.5967	−0.856906	−0.428453	+	0.903564i	$0.640941\pi$
$524$	15.2705	0.667095
$525$	14.5279	0.634048
$526$	7.70820	0.336094
$527$	21.3050	0.928058
$528$	0	0
$529$	−12.5279	−0.544690
$530$	11.0000	0.477809
$531$	−3.85410	−0.167254
$532$	−14.9443	−0.647916
$533$	10.4721	0.453599
$534$	−11.7082	−0.506664
$535$	−15.3607	−0.664100
$536$	−4.00000	−0.172774
$537$	6.38197	0.275402
$538$	2.94427	0.126937
$539$	0	0
$540$	−2.85410	−0.122821
$541$	−7.52786	−0.323648	−0.161824	−	0.986820i	$-0.551738\pi$
$541$	−7.52786	−0.323648	−0.161824	+	0.986820i	$0.551738\pi$
$542$	23.4164	1.00582
$543$	16.4721	0.706887
$544$	−2.47214	−0.105992
$545$	−49.7082	−2.12927
$546$	−14.9443	−0.639556
$547$	−18.1803	−0.777335	−0.388668	−	0.921378i	$-0.627065\pi$
$547$	−18.1803	−0.777335	−0.388668	+	0.921378i	$0.627065\pi$
$548$	−23.1246	−0.987834
$549$	6.76393	0.288678
$550$	0	0
$551$	1.23607	0.0526583
$552$	−3.23607	−0.137736
$553$	−43.0689	−1.83148
$554$	11.1246	0.472639
$555$	−4.36068	−0.185101
$556$	−13.2361	−0.561334
$557$	42.0344	1.78106	0.890528	−	0.454928i	$-0.150335\pi$
$557$	42.0344	1.78106	0.890528	+	0.454928i	$0.150335\pi$
$558$	−8.61803	−0.364830
$559$	10.4721	0.442924
$560$	−13.1803	−0.556971
$561$	0	0
$562$	23.1246	0.975453
$563$	46.8328	1.97377	0.986884	−	0.161431i	$-0.0516111\pi$
$563$	46.8328	1.97377	0.986884	+	0.161431i	$0.0516111\pi$
$564$	−2.47214	−0.104096
$565$	−35.5967	−1.49757
$566$	−23.8885	−1.00411
$567$	−4.61803	−0.193939
$568$	−12.4721	−0.523319
$569$	−36.8328	−1.54411	−0.772056	−	0.635555i	$-0.780772\pi$
$569$	−36.8328	−1.54411	−0.772056	+	0.635555i	$0.780772\pi$
$570$	9.23607	0.386856
$571$	−9.59675	−0.401611	−0.200806	−	0.979631i	$-0.564356\pi$
$571$	−9.59675	−0.401611	−0.200806	+	0.979631i	$0.564356\pi$
$572$	0	0
$573$	−22.4721	−0.938787
$574$	14.9443	0.623762
$575$	−10.1803	−0.424550
$576$	1.00000	0.0416667
$577$	7.09017	0.295168	0.147584	−	0.989050i	$-0.452850\pi$
$577$	7.09017	0.295168	0.147584	+	0.989050i	$0.452850\pi$
$578$	10.8885	0.452904
$579$	0.326238	0.0135580
$580$	1.09017	0.0452668
$581$	−3.11146	−0.129085
$582$	11.3262	0.469488
$583$	0	0
$584$	−11.3262	−0.468683
$585$	9.23607	0.381864
$586$	22.9787	0.949242
$587$	−24.0902	−0.994308	−0.497154	−	0.867662i	$-0.665622\pi$
$587$	−24.0902	−0.994308	−0.497154	+	0.867662i	$0.665622\pi$
$588$	−14.3262	−0.590804
$589$	27.8885	1.14913
$590$	11.0000	0.452863
$591$	6.09017	0.250516
$592$	1.52786	0.0627948
$593$	−24.4721	−1.00495	−0.502475	−	0.864592i	$-0.667577\pi$
$593$	−24.4721	−1.00495	−0.502475	+	0.864592i	$0.667577\pi$
$594$	0	0
$595$	−32.5836	−1.33580
$596$	−1.38197	−0.0566075
$597$	−13.1459	−0.538026
$598$	10.4721	0.428237
$599$	8.36068	0.341608	0.170804	−	0.985305i	$-0.445363\pi$
$599$	8.36068	0.341608	0.170804	+	0.985305i	$0.445363\pi$
$600$	3.14590	0.128431
$601$	23.7426	0.968483	0.484241	−	0.874934i	$-0.339096\pi$
$601$	23.7426	0.968483	0.484241	+	0.874934i	$0.339096\pi$
$602$	14.9443	0.609083
$603$	4.00000	0.162893
$604$	−9.32624	−0.379479
$605$	0	0
$606$	12.3820	0.502983
$607$	−23.7771	−0.965082	−0.482541	−	0.875873i	$-0.660286\pi$
$607$	−23.7771	−0.965082	−0.482541	+	0.875873i	$0.660286\pi$
$608$	−3.23607	−0.131240
$609$	1.76393	0.0714781
$610$	−19.3050	−0.781635
$611$	8.00000	0.323645
$612$	2.47214	0.0999302
$613$	14.2918	0.577240	0.288620	−	0.957444i	$-0.406804\pi$
$613$	14.2918	0.577240	0.288620	+	0.957444i	$0.406804\pi$
$614$	−16.6525	−0.672039
$615$	−9.23607	−0.372434
$616$	0	0
$617$	−30.2918	−1.21950	−0.609751	−	0.792593i	$-0.708731\pi$
$617$	−30.2918	−1.21950	−0.609751	+	0.792593i	$0.708731\pi$
$618$	12.0344	0.484096
$619$	−25.3050	−1.01709	−0.508546	−	0.861035i	$-0.669817\pi$
$619$	−25.3050	−1.01709	−0.508546	+	0.861035i	$0.669817\pi$
$620$	24.5967	0.987829
$621$	3.23607	0.129859
$622$	23.8885	0.957843
$623$	54.0689	2.16622
$624$	−3.23607	−0.129546
$625$	−30.8328	−1.23331
$626$	−15.1459	−0.605352
$627$	0	0
$628$	4.47214	0.178458
$629$	3.77709	0.150602
$630$	13.1803	0.525117
$631$	−17.1459	−0.682567	−0.341284	−	0.939960i	$-0.610862\pi$
$631$	−17.1459	−0.682567	−0.341284	+	0.939960i	$0.610862\pi$
$632$	−9.32624	−0.370978
$633$	−4.65248	−0.184919
$634$	19.8885	0.789875
$635$	−34.2492	−1.35914
$636$	3.85410	0.152825
$637$	46.3607	1.83688
$638$	0	0
$639$	12.4721	0.493390
$640$	−2.85410	−0.112818
$641$	47.1246	1.86131	0.930655	−	0.365898i	$-0.119238\pi$
$641$	47.1246	1.86131	0.930655	+	0.365898i	$0.119238\pi$
$642$	−5.38197	−0.212409
$643$	10.9443	0.431600	0.215800	−	0.976438i	$-0.430764\pi$
$643$	10.9443	0.431600	0.215800	+	0.976438i	$0.430764\pi$
$644$	14.9443	0.588887
$645$	−9.23607	−0.363670
$646$	−8.00000	−0.314756
$647$	−2.87539	−0.113043	−0.0565216	−	0.998401i	$-0.518001\pi$
$647$	−2.87539	−0.113043	−0.0565216	+	0.998401i	$0.518001\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−10.1803	−0.399306
$651$	39.7984	1.55982
$652$	−13.4164	−0.525427
$653$	−21.1459	−0.827503	−0.413751	−	0.910390i	$-0.635782\pi$
$653$	−21.1459	−0.827503	−0.413751	+	0.910390i	$0.635782\pi$
$654$	−17.4164	−0.681035
$655$	43.5836	1.70295
$656$	3.23607	0.126347
$657$	11.3262	0.441879
$658$	11.4164	0.445058
$659$	−43.1459	−1.68073	−0.840363	−	0.542024i	$-0.817658\pi$
$659$	−43.1459	−1.68073	−0.840363	+	0.542024i	$0.817658\pi$
$660$	0	0
$661$	5.81966	0.226359	0.113179	−	0.993575i	$-0.463897\pi$
$661$	5.81966	0.226359	0.113179	+	0.993575i	$0.463897\pi$
$662$	−8.94427	−0.347629
$663$	−8.00000	−0.310694
$664$	−0.673762	−0.0261470
$665$	−42.6525	−1.65399
$666$	−1.52786	−0.0592035
$667$	−1.23607	−0.0478607
$668$	−7.23607	−0.279972
$669$	1.90983	0.0738383
$670$	−11.4164	−0.441054
$671$	0	0
$672$	−4.61803	−0.178145
$673$	6.96556	0.268503	0.134251	−	0.990947i	$-0.457137\pi$
$673$	6.96556	0.268503	0.134251	+	0.990947i	$0.457137\pi$
$674$	6.94427	0.267483
$675$	−3.14590	−0.121086
$676$	−2.52786	−0.0972255
$677$	40.5066	1.55679	0.778397	−	0.627772i	$-0.216033\pi$
$677$	40.5066	1.55679	0.778397	+	0.627772i	$0.216033\pi$
$678$	−12.4721	−0.478989
$679$	−52.3050	−2.00728
$680$	−7.05573	−0.270575
$681$	−7.14590	−0.273831
$682$	0	0
$683$	45.7426	1.75029	0.875147	−	0.483857i	$-0.160765\pi$
$683$	45.7426	1.75029	0.875147	+	0.483857i	$0.160765\pi$
$684$	3.23607	0.123734
$685$	−66.0000	−2.52173
$686$	33.8328	1.29174
$687$	−22.9443	−0.875379
$688$	3.23607	0.123374
$689$	−12.4721	−0.475151
$690$	−9.23607	−0.351611
$691$	−0.291796	−0.0111004	−0.00555022	−	0.999985i	$-0.501767\pi$
$691$	−0.291796	−0.0111004	−0.00555022	+	0.999985i	$0.501767\pi$
$692$	4.14590	0.157603
$693$	0	0
$694$	11.8541	0.449976
$695$	−37.7771	−1.43297
$696$	0.381966	0.0144784
$697$	8.00000	0.303022
$698$	−13.2361	−0.500993
$699$	−8.94427	−0.338303
$700$	−14.5279	−0.549102
$701$	−1.05573	−0.0398743	−0.0199371	−	0.999801i	$-0.506347\pi$
$701$	−1.05573	−0.0398743	−0.0199371	+	0.999801i	$0.506347\pi$
$702$	3.23607	0.122138
$703$	4.94427	0.186477
$704$	0	0
$705$	−7.05573	−0.265734
$706$	21.5967	0.812804
$707$	−57.1803	−2.15049
$708$	3.85410	0.144846
$709$	35.0132	1.31495	0.657473	−	0.753478i	$-0.271625\pi$
$709$	35.0132	1.31495	0.657473	+	0.753478i	$0.271625\pi$
$710$	−35.5967	−1.33592
$711$	9.32624	0.349761
$712$	11.7082	0.438783
$713$	−27.8885	−1.04443
$714$	−11.4164	−0.427248
$715$	0	0
$716$	−6.38197	−0.238505
$717$	−16.4721	−0.615163
$718$	12.7639	0.476346
$719$	10.9443	0.408152	0.204076	−	0.978955i	$-0.434581\pi$
$719$	10.9443	0.408152	0.204076	+	0.978955i	$0.434581\pi$
$720$	2.85410	0.106366
$721$	−55.5755	−2.06974
$722$	8.52786	0.317374
$723$	−2.43769	−0.0906588
$724$	−16.4721	−0.612182
$725$	1.20163	0.0446273
$726$	0	0
$727$	3.41641	0.126708	0.0633538	−	0.997991i	$-0.479820\pi$
$727$	3.41641	0.126708	0.0633538	+	0.997991i	$0.479820\pi$
$728$	14.9443	0.553872
$729$	1.00000	0.0370370
$730$	−32.3262	−1.19645
$731$	8.00000	0.295891
$732$	−6.76393	−0.250002
$733$	43.7082	1.61440	0.807200	−	0.590278i	$-0.200982\pi$
$733$	43.7082	1.61440	0.807200	+	0.590278i	$0.200982\pi$
$734$	37.5066	1.38439
$735$	−40.8885	−1.50820
$736$	3.23607	0.119283
$737$	0	0
$738$	−3.23607	−0.119121
$739$	−15.0557	−0.553834	−0.276917	−	0.960894i	$-0.589313\pi$
$739$	−15.0557	−0.553834	−0.276917	+	0.960894i	$0.589313\pi$
$740$	4.36068	0.160302
$741$	−10.4721	−0.384704
$742$	−17.7984	−0.653399
$743$	37.7771	1.38591	0.692953	−	0.720982i	$-0.256309\pi$
$743$	37.7771	1.38591	0.692953	+	0.720982i	$0.256309\pi$
$744$	8.61803	0.315952
$745$	−3.94427	−0.144507
$746$	−9.52786	−0.348840
$747$	0.673762	0.0246517
$748$	0	0
$749$	24.8541	0.908149
$750$	−5.29180	−0.193229
$751$	−10.1115	−0.368972	−0.184486	−	0.982835i	$-0.559062\pi$
$751$	−10.1115	−0.368972	−0.184486	+	0.982835i	$0.559062\pi$
$752$	2.47214	0.0901495
$753$	19.3262	0.704287
$754$	−1.23607	−0.0450149
$755$	−26.6180	−0.968729
$756$	4.61803	0.167956
$757$	−30.5410	−1.11003	−0.555016	−	0.831840i	$-0.687288\pi$
$757$	−30.5410	−1.11003	−0.555016	+	0.831840i	$0.687288\pi$
$758$	−3.70820	−0.134688
$759$	0	0
$760$	−9.23607	−0.335027
$761$	−10.2918	−0.373077	−0.186539	−	0.982448i	$-0.559727\pi$
$761$	−10.2918	−0.373077	−0.186539	+	0.982448i	$0.559727\pi$
$762$	−12.0000	−0.434714
$763$	80.4296	2.91175
$764$	22.4721	0.813013
$765$	7.05573	0.255100
$766$	−13.2361	−0.478239
$767$	−12.4721	−0.450343
$768$	−1.00000	−0.0360844
$769$	4.27051	0.153999	0.0769993	−	0.997031i	$-0.475466\pi$
$769$	4.27051	0.153999	0.0769993	+	0.997031i	$0.475466\pi$
$770$	0	0
$771$	1.81966	0.0655335
$772$	−0.326238	−0.0117416
$773$	9.50658	0.341928	0.170964	−	0.985277i	$-0.445312\pi$
$773$	9.50658	0.341928	0.170964	+	0.985277i	$0.445312\pi$
$774$	−3.23607	−0.116318
$775$	27.1115	0.973872
$776$	−11.3262	−0.406588
$777$	7.05573	0.253123
$778$	−38.9443	−1.39622
$779$	10.4721	0.375203
$780$	−9.23607	−0.330704
$781$	0	0
$782$	8.00000	0.286079
$783$	−0.381966	−0.0136504
$784$	14.3262	0.511651
$785$	12.7639	0.455564
$786$	15.2705	0.544681
$787$	37.4853	1.33621	0.668103	−	0.744069i	$-0.267106\pi$
$787$	37.4853	1.33621	0.668103	+	0.744069i	$0.267106\pi$
$788$	−6.09017	−0.216953
$789$	7.70820	0.274419
$790$	−26.6180	−0.947027
$791$	57.5967	2.04790
$792$	0	0
$793$	21.8885	0.777285
$794$	−9.88854	−0.350931
$795$	11.0000	0.390130
$796$	13.1459	0.465944
$797$	−22.6180	−0.801172	−0.400586	−	0.916259i	$-0.631193\pi$
$797$	−22.6180	−0.801172	−0.400586	+	0.916259i	$0.631193\pi$
$798$	−14.9443	−0.529021
$799$	6.11146	0.216208
$800$	−3.14590	−0.111224
$801$	−11.7082	−0.413689
$802$	−10.2918	−0.363416
$803$	0	0
$804$	−4.00000	−0.141069
$805$	42.6525	1.50330
$806$	−27.8885	−0.982332
$807$	2.94427	0.103643
$808$	−12.3820	−0.435596
$809$	−30.2492	−1.06351	−0.531753	−	0.846899i	$-0.678467\pi$
$809$	−30.2492	−1.06351	−0.531753	+	0.846899i	$0.678467\pi$
$810$	−2.85410	−0.100283
$811$	40.7639	1.43142	0.715708	−	0.698400i	$-0.246104\pi$
$811$	40.7639	1.43142	0.715708	+	0.698400i	$0.246104\pi$
$812$	−1.76393	−0.0619019
$813$	23.4164	0.821249
$814$	0	0
$815$	−38.2918	−1.34130
$816$	−2.47214	−0.0865421
$817$	10.4721	0.366374
$818$	−12.0902	−0.422723
$819$	−14.9443	−0.522195
$820$	9.23607	0.322537
$821$	−21.0902	−0.736052	−0.368026	−	0.929815i	$-0.619966\pi$
$821$	−21.0902	−0.736052	−0.368026	+	0.929815i	$0.619966\pi$
$822$	−23.1246	−0.806563
$823$	−3.21478	−0.112060	−0.0560301	−	0.998429i	$-0.517844\pi$
$823$	−3.21478	−0.112060	−0.0560301	+	0.998429i	$0.517844\pi$
$824$	−12.0344	−0.419240
$825$	0	0
$826$	−17.7984	−0.619285
$827$	−10.6869	−0.371621	−0.185810	−	0.982586i	$-0.559491\pi$
$827$	−10.6869	−0.371621	−0.185810	+	0.982586i	$0.559491\pi$
$828$	−3.23607	−0.112461
$829$	7.30495	0.253711	0.126856	−	0.991921i	$-0.459511\pi$
$829$	7.30495	0.253711	0.126856	+	0.991921i	$0.459511\pi$
$830$	−1.92299	−0.0667478
$831$	11.1246	0.385909
$832$	3.23607	0.112190
$833$	35.4164	1.22711
$834$	−13.2361	−0.458328
$835$	−20.6525	−0.714708
$836$	0	0
$837$	−8.61803	−0.297883
$838$	17.9787	0.621064
$839$	−3.12461	−0.107874	−0.0539368	−	0.998544i	$-0.517177\pi$
$839$	−3.12461	−0.107874	−0.0539368	+	0.998544i	$0.517177\pi$
$840$	−13.1803	−0.454765
$841$	−28.8541	−0.994969
$842$	−35.1246	−1.21047
$843$	23.1246	0.796454
$844$	4.65248	0.160145
$845$	−7.21478	−0.248196
$846$	−2.47214	−0.0849938
$847$	0	0
$848$	−3.85410	−0.132350
$849$	−23.8885	−0.819853
$850$	−7.77709	−0.266752
$851$	−4.94427	−0.169487
$852$	−12.4721	−0.427288
$853$	−15.0557	−0.515498	−0.257749	−	0.966212i	$-0.582981\pi$
$853$	−15.0557	−0.515498	−0.257749	+	0.966212i	$0.582981\pi$
$854$	31.2361	1.06888
$855$	9.23607	0.315867
$856$	5.38197	0.183952
$857$	−8.76393	−0.299370	−0.149685	−	0.988734i	$-0.547826\pi$
$857$	−8.76393	−0.299370	−0.149685	+	0.988734i	$0.547826\pi$
$858$	0	0
$859$	4.40325	0.150237	0.0751185	−	0.997175i	$-0.476066\pi$
$859$	4.40325	0.150237	0.0751185	+	0.997175i	$0.476066\pi$
$860$	9.23607	0.314947
$861$	14.9443	0.509299
$862$	−7.23607	−0.246461
$863$	2.76393	0.0940853	0.0470427	−	0.998893i	$-0.485020\pi$
$863$	2.76393	0.0940853	0.0470427	+	0.998893i	$0.485020\pi$
$864$	1.00000	0.0340207
$865$	11.8328	0.402328
$866$	−12.3262	−0.418863
$867$	10.8885	0.369794
$868$	−39.7984	−1.35084
$869$	0	0
$870$	1.09017	0.0369602
$871$	12.9443	0.438600
$872$	17.4164	0.589794
$873$	11.3262	0.383335
$874$	10.4721	0.354225
$875$	24.4377	0.826145
$876$	−11.3262	−0.382678
$877$	30.3607	1.02521	0.512604	−	0.858625i	$-0.328681\pi$
$877$	30.3607	1.02521	0.512604	+	0.858625i	$0.328681\pi$
$878$	16.0344	0.541136
$879$	22.9787	0.775053
$880$	0	0
$881$	−12.2918	−0.414121	−0.207061	−	0.978328i	$-0.566390\pi$
$881$	−12.2918	−0.414121	−0.207061	+	0.978328i	$0.566390\pi$
$882$	−14.3262	−0.482390
$883$	27.8197	0.936206	0.468103	−	0.883674i	$-0.344938\pi$
$883$	27.8197	0.936206	0.468103	+	0.883674i	$0.344938\pi$
$884$	8.00000	0.269069
$885$	11.0000	0.369761
$886$	1.67376	0.0562311
$887$	28.5410	0.958314	0.479157	−	0.877729i	$-0.340943\pi$
$887$	28.5410	0.958314	0.479157	+	0.877729i	$0.340943\pi$
$888$	1.52786	0.0512718
$889$	55.4164	1.85861
$890$	33.4164	1.12012
$891$	0	0
$892$	−1.90983	−0.0639458
$893$	8.00000	0.267710
$894$	−1.38197	−0.0462199
$895$	−18.2148	−0.608853
$896$	4.61803	0.154278
$897$	10.4721	0.349654
$898$	−35.8885	−1.19762
$899$	3.29180	0.109788
$900$	3.14590	0.104863
$901$	−9.52786	−0.317419
$902$	0	0
$903$	14.9443	0.497314
$904$	12.4721	0.414817
$905$	−47.0132	−1.56277
$906$	−9.32624	−0.309844
$907$	−8.18034	−0.271624	−0.135812	−	0.990735i	$-0.543364\pi$
$907$	−8.18034	−0.271624	−0.135812	+	0.990735i	$0.543364\pi$
$908$	7.14590	0.237145
$909$	12.3820	0.410684
$910$	42.6525	1.41392
$911$	43.7082	1.44812	0.724059	−	0.689738i	$-0.242274\pi$
$911$	43.7082	1.44812	0.724059	+	0.689738i	$0.242274\pi$
$912$	−3.23607	−0.107157
$913$	0	0
$914$	−21.9787	−0.726991
$915$	−19.3050	−0.638202
$916$	22.9443	0.758100
$917$	−70.5197	−2.32877
$918$	2.47214	0.0815926
$919$	−50.2705	−1.65827	−0.829136	−	0.559048i	$-0.811167\pi$
$919$	−50.2705	−1.65827	−0.829136	+	0.559048i	$0.811167\pi$
$920$	9.23607	0.304504
$921$	−16.6525	−0.548718
$922$	40.8328	1.34476
$923$	40.3607	1.32849
$924$	0	0
$925$	4.80650	0.158037
$926$	−19.0902	−0.627342
$927$	12.0344	0.395263
$928$	−0.381966	−0.0125386
$929$	−23.1246	−0.758694	−0.379347	−	0.925255i	$-0.623851\pi$
$929$	−23.1246	−0.758694	−0.379347	+	0.925255i	$0.623851\pi$
$930$	24.5967	0.806559
$931$	46.3607	1.51941
$932$	8.94427	0.292979
$933$	23.8885	0.782076
$934$	−19.5623	−0.640098
$935$	0	0
$936$	−3.23607	−0.105774
$937$	−27.4508	−0.896780	−0.448390	−	0.893838i	$-0.648002\pi$
$937$	−27.4508	−0.896780	−0.448390	+	0.893838i	$0.648002\pi$
$938$	18.4721	0.603137
$939$	−15.1459	−0.494268
$940$	7.05573	0.230132
$941$	8.83282	0.287942	0.143971	−	0.989582i	$-0.454013\pi$
$941$	8.83282	0.287942	0.143971	+	0.989582i	$0.454013\pi$
$942$	4.47214	0.145710
$943$	−10.4721	−0.341020
$944$	−3.85410	−0.125440
$945$	13.1803	0.428756
$946$	0	0
$947$	2.32624	0.0755926	0.0377963	−	0.999285i	$-0.487966\pi$
$947$	2.32624	0.0755926	0.0377963	+	0.999285i	$0.487966\pi$
$948$	−9.32624	−0.302902
$949$	36.6525	1.18979
$950$	−10.1803	−0.330294
$951$	19.8885	0.644930
$952$	11.4164	0.370008
$953$	−48.7214	−1.57824	−0.789120	−	0.614239i	$-0.789463\pi$
$953$	−48.7214	−1.57824	−0.789120	+	0.614239i	$0.789463\pi$
$954$	3.85410	0.124781
$955$	64.1378	2.07545
$956$	16.4721	0.532747
$957$	0	0
$958$	−7.23607	−0.233787
$959$	106.790	3.44844
$960$	−2.85410	−0.0921157
$961$	43.2705	1.39582
$962$	−4.94427	−0.159410
$963$	−5.38197	−0.173431
$964$	2.43769	0.0785128
$965$	−0.931116	−0.0299737
$966$	14.9443	0.480824
$967$	−13.6869	−0.440142	−0.220071	−	0.975484i	$-0.570629\pi$
$967$	−13.6869	−0.440142	−0.220071	+	0.975484i	$0.570629\pi$
$968$	0	0
$969$	−8.00000	−0.256997
$970$	−32.3262	−1.03793
$971$	−9.30495	−0.298610	−0.149305	−	0.988791i	$-0.547704\pi$
$971$	−9.30495	−0.298610	−0.149305	+	0.988791i	$0.547704\pi$
$972$	−1.00000	−0.0320750
$973$	61.1246	1.95957
$974$	−24.9787	−0.800370
$975$	−10.1803	−0.326032
$976$	6.76393	0.216508
$977$	−36.7639	−1.17618	−0.588091	−	0.808795i	$-0.700120\pi$
$977$	−36.7639	−1.17618	−0.588091	+	0.808795i	$0.700120\pi$
$978$	−13.4164	−0.429009
$979$	0	0
$980$	40.8885	1.30614
$981$	−17.4164	−0.556063
$982$	42.2492	1.34823
$983$	−9.12461	−0.291030	−0.145515	−	0.989356i	$-0.546484\pi$
$983$	−9.12461	−0.291030	−0.145515	+	0.989356i	$0.546484\pi$
$984$	3.23607	0.103162
$985$	−17.3820	−0.553835
$986$	−0.944272	−0.0300717
$987$	11.4164	0.363388
$988$	10.4721	0.333163
$989$	−10.4721	−0.332995
$990$	0	0
$991$	−45.6869	−1.45129	−0.725646	−	0.688068i	$-0.758459\pi$
$991$	−45.6869	−1.45129	−0.725646	+	0.688068i	$0.758459\pi$
$992$	−8.61803	−0.273623
$993$	−8.94427	−0.283838
$994$	57.5967	1.82686
$995$	37.5197	1.18946
$996$	−0.673762	−0.0213490
$997$	−57.9574	−1.83553	−0.917765	−	0.397124i	$-0.870008\pi$
$997$	−57.9574	−1.83553	−0.917765	+	0.397124i	$0.870008\pi$
$998$	7.41641	0.234762
$999$	−1.52786	−0.0483395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	726.2.a.j.1.2		2
3.2	odd	2		2178.2.a.bb.1.1		2
4.3	odd	2		5808.2.a.cg.1.2		2
11.2	odd	10		726.2.e.f.565.1		4
11.3	even	5		726.2.e.r.493.1		4
11.4	even	5		726.2.e.r.511.1		4
11.5	even	5		726.2.e.n.487.1		4
11.6	odd	10		726.2.e.f.487.1		4
11.7	odd	10		66.2.e.a.49.1	yes	4
11.8	odd	10		66.2.e.a.31.1	✓	4
11.9	even	5		726.2.e.n.565.1		4
11.10	odd	2		726.2.a.l.1.2		2
33.8	even	10		198.2.f.c.163.1		4
33.29	even	10		198.2.f.c.181.1		4
33.32	even	2		2178.2.a.t.1.1		2
44.7	even	10		528.2.y.d.49.1		4
44.19	even	10		528.2.y.d.97.1		4
44.43	even	2		5808.2.a.cb.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
66.2.e.a.31.1	✓	4	11.8	odd	10
66.2.e.a.49.1	yes	4	11.7	odd	10
198.2.f.c.163.1		4	33.8	even	10
198.2.f.c.181.1		4	33.29	even	10
528.2.y.d.49.1		4	44.7	even	10
528.2.y.d.97.1		4	44.19	even	10
726.2.a.j.1.2		2	1.1	even	1	trivial
726.2.a.l.1.2		2	11.10	odd	2
726.2.e.f.487.1		4	11.6	odd	10
726.2.e.f.565.1		4	11.2	odd	10
726.2.e.n.487.1		4	11.5	even	5
726.2.e.n.565.1		4	11.9	even	5
726.2.e.r.493.1		4	11.3	even	5
726.2.e.r.511.1		4	11.4	even	5
2178.2.a.t.1.1		2	33.32	even	2
2178.2.a.bb.1.1		2	3.2	odd	2
5808.2.a.cb.1.2		2	44.43	even	2
5808.2.a.cg.1.2		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	726.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.85410 q^{5} +1.00000 q^{6} -4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +2.85410 q^{5} +1.00000 q^{6} -4.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.85410 q^{10} -1.00000 q^{12} +3.23607 q^{13} +4.61803 q^{14} -2.85410 q^{15} +1.00000 q^{16} +2.47214 q^{17} -1.00000 q^{18} +3.23607 q^{19} +2.85410 q^{20} +4.61803 q^{21} -3.23607 q^{23} +1.00000 q^{24} +3.14590 q^{25} -3.23607 q^{26} -1.00000 q^{27} -4.61803 q^{28} +0.381966 q^{29} +2.85410 q^{30} +8.61803 q^{31} -1.00000 q^{32} -2.47214 q^{34} -13.1803 q^{35} +1.00000 q^{36} +1.52786 q^{37} -3.23607 q^{38} -3.23607 q^{39} -2.85410 q^{40} +3.23607 q^{41} -4.61803 q^{42} +3.23607 q^{43} +2.85410 q^{45} +3.23607 q^{46} +2.47214 q^{47} -1.00000 q^{48} +14.3262 q^{49} -3.14590 q^{50} -2.47214 q^{51} +3.23607 q^{52} -3.85410 q^{53} +1.00000 q^{54} +4.61803 q^{56} -3.23607 q^{57} -0.381966 q^{58} -3.85410 q^{59} -2.85410 q^{60} +6.76393 q^{61} -8.61803 q^{62} -4.61803 q^{63} +1.00000 q^{64} +9.23607 q^{65} +4.00000 q^{67} +2.47214 q^{68} +3.23607 q^{69} +13.1803 q^{70} +12.4721 q^{71} -1.00000 q^{72} +11.3262 q^{73} -1.52786 q^{74} -3.14590 q^{75} +3.23607 q^{76} +3.23607 q^{78} +9.32624 q^{79} +2.85410 q^{80} +1.00000 q^{81} -3.23607 q^{82} +0.673762 q^{83} +4.61803 q^{84} +7.05573 q^{85} -3.23607 q^{86} -0.381966 q^{87} -11.7082 q^{89} -2.85410 q^{90} -14.9443 q^{91} -3.23607 q^{92} -8.61803 q^{93} -2.47214 q^{94} +9.23607 q^{95} +1.00000 q^{96} +11.3262 q^{97} -14.3262 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} + 2 q^{6} - 7 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} - 2 q^{12} + 2 q^{13} + 7 q^{14} + q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} + 7 q^{21} - 2 q^{23} + 2 q^{24} + 13 q^{25} - 2 q^{26} - 2 q^{27} - 7 q^{28} + 3 q^{29} - q^{30} + 15 q^{31} - 2 q^{32} + 4 q^{34} - 4 q^{35} + 2 q^{36} + 12 q^{37} - 2 q^{38} - 2 q^{39} + q^{40} + 2 q^{41} - 7 q^{42} + 2 q^{43} - q^{45} + 2 q^{46} - 4 q^{47} - 2 q^{48} + 13 q^{49} - 13 q^{50} + 4 q^{51} + 2 q^{52} - q^{53} + 2 q^{54} + 7 q^{56} - 2 q^{57} - 3 q^{58} - q^{59} + q^{60} + 18 q^{61} - 15 q^{62} - 7 q^{63} + 2 q^{64} + 14 q^{65} + 8 q^{67} - 4 q^{68} + 2 q^{69} + 4 q^{70} + 16 q^{71} - 2 q^{72} + 7 q^{73} - 12 q^{74} - 13 q^{75} + 2 q^{76} + 2 q^{78} + 3 q^{79} - q^{80} + 2 q^{81} - 2 q^{82} + 17 q^{83} + 7 q^{84} + 32 q^{85} - 2 q^{86} - 3 q^{87} - 10 q^{89} + q^{90} - 12 q^{91} - 2 q^{92} - 15 q^{93} + 4 q^{94} + 14 q^{95} + 2 q^{96} + 7 q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - q^5 + 2 * q^6 - 7 * q^7 - 2 * q^8 + 2 * q^9 + q^10 - 2 * q^12 + 2 * q^13 + 7 * q^14 + q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 + 2 * q^19 - q^20 + 7 * q^21 - 2 * q^23 + 2 * q^24 + 13 * q^25 - 2 * q^26 - 2 * q^27 - 7 * q^28 + 3 * q^29 - q^30 + 15 * q^31 - 2 * q^32 + 4 * q^34 - 4 * q^35 + 2 * q^36 + 12 * q^37 - 2 * q^38 - 2 * q^39 + q^40 + 2 * q^41 - 7 * q^42 + 2 * q^43 - q^45 + 2 * q^46 - 4 * q^47 - 2 * q^48 + 13 * q^49 - 13 * q^50 + 4 * q^51 + 2 * q^52 - q^53 + 2 * q^54 + 7 * q^56 - 2 * q^57 - 3 * q^58 - q^59 + q^60 + 18 * q^61 - 15 * q^62 - 7 * q^63 + 2 * q^64 + 14 * q^65 + 8 * q^67 - 4 * q^68 + 2 * q^69 + 4 * q^70 + 16 * q^71 - 2 * q^72 + 7 * q^73 - 12 * q^74 - 13 * q^75 + 2 * q^76 + 2 * q^78 + 3 * q^79 - q^80 + 2 * q^81 - 2 * q^82 + 17 * q^83 + 7 * q^84 + 32 * q^85 - 2 * q^86 - 3 * q^87 - 10 * q^89 + q^90 - 12 * q^91 - 2 * q^92 - 15 * q^93 + 4 * q^94 + 14 * q^95 + 2 * q^96 + 7 * q^97 - 13 * q^98

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