LMFDB - Embedded newform 731.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.48303$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48303 q^{2} +1.10293 q^{3} +4.16544 q^{4} -3.73374 q^{5} -2.73861 q^{6} -2.89905 q^{7} -5.37685 q^{8} -1.78354 q^{9} +O(q^{10})$	\(q-2.48303 q^{2} +1.10293 q^{3} +4.16544 q^{4} -3.73374 q^{5} -2.73861 q^{6} -2.89905 q^{7} -5.37685 q^{8} -1.78354 q^{9} +9.27098 q^{10} -5.24858 q^{11} +4.59420 q^{12} -2.10553 q^{13} +7.19842 q^{14} -4.11806 q^{15} +5.02000 q^{16} +1.00000 q^{17} +4.42859 q^{18} +4.79318 q^{19} -15.5526 q^{20} -3.19745 q^{21} +13.0324 q^{22} +5.89086 q^{23} -5.93030 q^{24} +8.94078 q^{25} +5.22810 q^{26} -5.27592 q^{27} -12.0758 q^{28} +7.20505 q^{29} +10.2253 q^{30} +4.25412 q^{31} -1.71111 q^{32} -5.78882 q^{33} -2.48303 q^{34} +10.8243 q^{35} -7.42923 q^{36} +10.0416 q^{37} -11.9016 q^{38} -2.32226 q^{39} +20.0757 q^{40} -7.38412 q^{41} +7.93937 q^{42} -1.00000 q^{43} -21.8626 q^{44} +6.65927 q^{45} -14.6272 q^{46} -11.0405 q^{47} +5.53672 q^{48} +1.40448 q^{49} -22.2002 q^{50} +1.10293 q^{51} -8.77047 q^{52} -9.45938 q^{53} +13.1003 q^{54} +19.5968 q^{55} +15.5877 q^{56} +5.28655 q^{57} -17.8904 q^{58} +3.18824 q^{59} -17.1535 q^{60} +4.67100 q^{61} -10.5631 q^{62} +5.17057 q^{63} -5.79125 q^{64} +7.86151 q^{65} +14.3738 q^{66} -3.98228 q^{67} +4.16544 q^{68} +6.49722 q^{69} -26.8770 q^{70} +6.94579 q^{71} +9.58983 q^{72} -2.14240 q^{73} -24.9336 q^{74} +9.86107 q^{75} +19.9657 q^{76} +15.2159 q^{77} +5.76624 q^{78} +6.32969 q^{79} -18.7434 q^{80} -0.468358 q^{81} +18.3350 q^{82} -7.79387 q^{83} -13.3188 q^{84} -3.73374 q^{85} +2.48303 q^{86} +7.94668 q^{87} +28.2208 q^{88} +13.1696 q^{89} -16.5352 q^{90} +6.10404 q^{91} +24.5380 q^{92} +4.69200 q^{93} +27.4139 q^{94} -17.8965 q^{95} -1.88724 q^{96} -17.0924 q^{97} -3.48736 q^{98} +9.36105 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.48303	−1.75577	−0.877884	−	0.478874i	$-0.841045\pi$
$2$	−2.48303	−1.75577	−0.877884	+	0.478874i	$0.841045\pi$
$3$	1.10293	0.636778	0.318389	−	0.947960i	$-0.396858\pi$
$3$	1.10293	0.636778	0.318389	+	0.947960i	$0.396858\pi$
$4$	4.16544	2.08272
$5$	−3.73374	−1.66978	−0.834889	−	0.550419i	$-0.814468\pi$
$5$	−3.73374	−1.66978	−0.834889	+	0.550419i	$0.814468\pi$
$6$	−2.73861	−1.11803
$7$	−2.89905	−1.09574	−0.547869	−	0.836564i	$-0.684561\pi$
$7$	−2.89905	−1.09574	−0.547869	+	0.836564i	$0.684561\pi$
$8$	−5.37685	−1.90100
$9$	−1.78354	−0.594514
$10$	9.27098	2.93174
$11$	−5.24858	−1.58251	−0.791253	−	0.611489i	$-0.790571\pi$
$11$	−5.24858	−1.58251	−0.791253	+	0.611489i	$0.790571\pi$
$12$	4.59420	1.32623
$13$	−2.10553	−0.583970	−0.291985	−	0.956423i	$-0.594316\pi$
$13$	−2.10553	−0.583970	−0.291985	+	0.956423i	$0.594316\pi$
$14$	7.19842	1.92386
$15$	−4.11806	−1.06328
$16$	5.02000	1.25500
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.42859	1.04383
$19$	4.79318	1.09963	0.549815	−	0.835286i	$-0.314698\pi$
$19$	4.79318	1.09963	0.549815	+	0.835286i	$0.314698\pi$
$20$	−15.5526	−3.47768
$21$	−3.19745	−0.697741
$22$	13.0324	2.77851
$23$	5.89086	1.22833	0.614165	−	0.789178i	$-0.289493\pi$
$23$	5.89086	1.22833	0.614165	+	0.789178i	$0.289493\pi$
$24$	−5.93030	−1.21052
$25$	8.94078	1.78816
$26$	5.22810	1.02532
$27$	−5.27592	−1.01535
$28$	−12.0758	−2.28211
$29$	7.20505	1.33794	0.668972	−	0.743288i	$-0.266735\pi$
$29$	7.20505	1.33794	0.668972	+	0.743288i	$0.266735\pi$
$30$	10.2253	1.86687
$31$	4.25412	0.764062	0.382031	−	0.924149i	$-0.375225\pi$
$31$	4.25412	0.764062	0.382031	+	0.924149i	$0.375225\pi$
$32$	−1.71111	−0.302485
$33$	−5.78882	−1.00770
$34$	−2.48303	−0.425836
$35$	10.8243	1.82964
$36$	−7.42923	−1.23821
$37$	10.0416	1.65083	0.825416	−	0.564525i	$-0.190941\pi$
$37$	10.0416	1.65083	0.825416	+	0.564525i	$0.190941\pi$
$38$	−11.9016	−1.93070
$39$	−2.32226	−0.371859
$40$	20.0757	3.17425
$41$	−7.38412	−1.15321	−0.576603	−	0.817024i	$-0.695622\pi$
$41$	−7.38412	−1.15321	−0.576603	+	0.817024i	$0.695622\pi$
$42$	7.93937	1.22507
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−21.8626	−3.29591
$45$	6.65927	0.992705
$46$	−14.6272	−2.15666
$47$	−11.0405	−1.61043	−0.805213	−	0.592986i	$-0.797949\pi$
$47$	−11.0405	−1.61043	−0.805213	+	0.592986i	$0.797949\pi$
$48$	5.53672	0.799156
$49$	1.40448	0.200640
$50$	−22.2002	−3.13959
$51$	1.10293	0.154441
$52$	−8.77047	−1.21625
$53$	−9.45938	−1.29935	−0.649673	−	0.760214i	$-0.725094\pi$
$53$	−9.45938	−1.29935	−0.649673	+	0.760214i	$0.725094\pi$
$54$	13.1003	1.78272
$55$	19.5968	2.64243
$56$	15.5877	2.08300
$57$	5.28655	0.700221
$58$	−17.8904	−2.34912
$59$	3.18824	0.415074	0.207537	−	0.978227i	$-0.433455\pi$
$59$	3.18824	0.415074	0.207537	+	0.978227i	$0.433455\pi$
$60$	−17.1535	−2.21451
$61$	4.67100	0.598060	0.299030	−	0.954244i	$-0.403337\pi$
$61$	4.67100	0.598060	0.299030	+	0.954244i	$0.403337\pi$
$62$	−10.5631	−1.34152
$63$	5.17057	0.651431
$64$	−5.79125	−0.723907
$65$	7.86151	0.975100
$66$	14.3738	1.76930
$67$	−3.98228	−0.486513	−0.243256	−	0.969962i	$-0.578216\pi$
$67$	−3.98228	−0.486513	−0.243256	+	0.969962i	$0.578216\pi$
$68$	4.16544	0.505134
$69$	6.49722	0.782174
$70$	−26.8770	−3.21242
$71$	6.94579	0.824314	0.412157	−	0.911113i	$-0.364776\pi$
$71$	6.94579	0.824314	0.412157	+	0.911113i	$0.364776\pi$
$72$	9.58983	1.13017
$73$	−2.14240	−0.250749	−0.125375	−	0.992109i	$-0.540013\pi$
$73$	−2.14240	−0.250749	−0.125375	+	0.992109i	$0.540013\pi$
$74$	−24.9336	−2.89848
$75$	9.86107	1.13866
$76$	19.9657	2.29022
$77$	15.2159	1.73401
$78$	5.76624	0.652898
$79$	6.32969	0.712146	0.356073	−	0.934458i	$-0.384115\pi$
$79$	6.32969	0.712146	0.356073	+	0.934458i	$0.384115\pi$
$80$	−18.7434	−2.09557
$81$	−0.468358	−0.0520398
$82$	18.3350	2.02476
$83$	−7.79387	−0.855489	−0.427744	−	0.903900i	$-0.640692\pi$
$83$	−7.79387	−0.855489	−0.427744	+	0.903900i	$0.640692\pi$
$84$	−13.3188	−1.45320
$85$	−3.73374	−0.404980
$86$	2.48303	0.267752
$87$	7.94668	0.851973
$88$	28.2208	3.00835
$89$	13.1696	1.39597	0.697987	−	0.716110i	$-0.254079\pi$
$89$	13.1696	1.39597	0.697987	+	0.716110i	$0.254079\pi$
$90$	−16.5352	−1.74296
$91$	6.10404	0.639878
$92$	24.5380	2.55827
$93$	4.69200	0.486538
$94$	27.4139	2.82753
$95$	−17.8965	−1.83614
$96$	−1.88724	−0.192616
$97$	−17.0924	−1.73547	−0.867737	−	0.497023i	$-0.834426\pi$
$97$	−17.0924	−1.73547	−0.867737	+	0.497023i	$0.834426\pi$
$98$	−3.48736	−0.352277
$99$	9.36105	0.940821
$100$	37.2423	3.72423
$101$	−6.46694	−0.643485	−0.321742	−	0.946827i	$-0.604268\pi$
$101$	−6.46694	−0.643485	−0.321742	+	0.946827i	$0.604268\pi$
$102$	−2.73861	−0.271163
$103$	0.333796	0.0328899	0.0164449	−	0.999865i	$-0.494765\pi$
$103$	0.333796	0.0328899	0.0164449	+	0.999865i	$0.494765\pi$
$104$	11.3211	1.11013
$105$	11.9384	1.16507
$106$	23.4879	2.28135
$107$	16.1810	1.56428	0.782138	−	0.623105i	$-0.214129\pi$
$107$	16.1810	1.56428	0.782138	+	0.623105i	$0.214129\pi$
$108$	−21.9765	−2.11469
$109$	2.79226	0.267450	0.133725	−	0.991018i	$-0.457306\pi$
$109$	2.79226	0.267450	0.133725	+	0.991018i	$0.457306\pi$
$110$	−48.6594	−4.63950
$111$	11.0752	1.05121
$112$	−14.5532	−1.37515
$113$	−5.23619	−0.492580	−0.246290	−	0.969196i	$-0.579211\pi$
$113$	−5.23619	−0.492580	−0.246290	+	0.969196i	$0.579211\pi$
$114$	−13.1267	−1.22942
$115$	−21.9949	−2.05104
$116$	30.0122	2.78656
$117$	3.75531	0.347178
$118$	−7.91651	−0.728774
$119$	−2.89905	−0.265755
$120$	22.1422	2.02129
$121$	16.5476	1.50432
$122$	−11.5982	−1.05005
$123$	−8.14419	−0.734337
$124$	17.7203	1.59133
$125$	−14.7138	−1.31605
$126$	−12.8387	−1.14376
$127$	−6.36680	−0.564962	−0.282481	−	0.959273i	$-0.591157\pi$
$127$	−6.36680	−0.564962	−0.282481	+	0.959273i	$0.591157\pi$
$128$	17.8021	1.57350
$129$	−1.10293	−0.0971077
$130$	−19.5204	−1.71205
$131$	6.58609	0.575429	0.287715	−	0.957716i	$-0.407105\pi$
$131$	6.58609	0.575429	0.287715	+	0.957716i	$0.407105\pi$
$132$	−24.1130	−2.09877
$133$	−13.8957	−1.20491
$134$	9.88811	0.854203
$135$	19.6989	1.69541
$136$	−5.37685	−0.461061
$137$	18.9424	1.61836	0.809179	−	0.587562i	$-0.199912\pi$
$137$	18.9424	1.61836	0.809179	+	0.587562i	$0.199912\pi$
$138$	−16.1328	−1.37331
$139$	11.1156	0.942812	0.471406	−	0.881916i	$-0.343747\pi$
$139$	11.1156	0.942812	0.471406	+	0.881916i	$0.343747\pi$
$140$	45.0879	3.81062
$141$	−12.1769	−1.02548
$142$	−17.2466	−1.44730
$143$	11.0511	0.924136
$144$	−8.95337	−0.746115
$145$	−26.9017	−2.23407
$146$	5.31965	0.440257
$147$	1.54904	0.127763
$148$	41.8277	3.43822
$149$	−5.33805	−0.437310	−0.218655	−	0.975802i	$-0.570167\pi$
$149$	−5.33805	−0.437310	−0.218655	+	0.975802i	$0.570167\pi$
$150$	−24.4853	−1.99922
$151$	−3.89448	−0.316928	−0.158464	−	0.987365i	$-0.550654\pi$
$151$	−3.89448	−0.316928	−0.158464	+	0.987365i	$0.550654\pi$
$152$	−25.7722	−2.09040
$153$	−1.78354	−0.144191
$154$	−37.7815	−3.04452
$155$	−15.8838	−1.27581
$156$	−9.67323	−0.774478
$157$	−18.1031	−1.44479	−0.722393	−	0.691483i	$-0.756958\pi$
$157$	−18.1031	−1.44479	−0.722393	+	0.691483i	$0.756958\pi$
$158$	−15.7168	−1.25036
$159$	−10.4331	−0.827395
$160$	6.38884	0.505082
$161$	−17.0779	−1.34593
$162$	1.16295	0.0913698
$163$	−9.90070	−0.775483	−0.387741	−	0.921768i	$-0.626745\pi$
$163$	−9.90070	−0.775483	−0.387741	+	0.921768i	$0.626745\pi$
$164$	−30.7581	−2.40180
$165$	21.6139	1.68264
$166$	19.3524	1.50204
$167$	5.07573	0.392772	0.196386	−	0.980527i	$-0.437079\pi$
$167$	5.07573	0.392772	0.196386	+	0.980527i	$0.437079\pi$
$168$	17.1922	1.32641
$169$	−8.56673	−0.658979
$170$	9.27098	0.711052
$171$	−8.54883	−0.653745
$172$	−4.16544	−0.317612
$173$	11.4702	0.872065	0.436033	−	0.899931i	$-0.356383\pi$
$173$	11.4702	0.872065	0.436033	+	0.899931i	$0.356383\pi$
$174$	−19.7318	−1.49587
$175$	−25.9198	−1.95935
$176$	−26.3479	−1.98604
$177$	3.51642	0.264310
$178$	−32.7005	−2.45101
$179$	−7.95513	−0.594594	−0.297297	−	0.954785i	$-0.596085\pi$
$179$	−7.95513	−0.594594	−0.297297	+	0.954785i	$0.596085\pi$
$180$	27.7388	2.06753
$181$	22.5233	1.67414	0.837071	−	0.547095i	$-0.184266\pi$
$181$	22.5233	1.67414	0.837071	+	0.547095i	$0.184266\pi$
$182$	−15.1565	−1.12348
$183$	5.15179	0.380831
$184$	−31.6743	−2.33506
$185$	−37.4927	−2.75652
$186$	−11.6504	−0.854248
$187$	−5.24858	−0.383814
$188$	−45.9886	−3.35406
$189$	15.2951	1.11256
$190$	44.4375	3.22383
$191$	15.9366	1.15313	0.576566	−	0.817050i	$-0.304392\pi$
$191$	15.9366	1.15313	0.576566	+	0.817050i	$0.304392\pi$
$192$	−6.38736	−0.460968
$193$	7.48700	0.538926	0.269463	−	0.963011i	$-0.413154\pi$
$193$	7.48700	0.538926	0.269463	+	0.963011i	$0.413154\pi$
$194$	42.4410	3.04709
$195$	8.67071	0.620922
$196$	5.85027	0.417876
$197$	24.4292	1.74051	0.870255	−	0.492602i	$-0.163954\pi$
$197$	24.4292	1.74051	0.870255	+	0.492602i	$0.163954\pi$
$198$	−23.2438	−1.65186
$199$	−4.41253	−0.312796	−0.156398	−	0.987694i	$-0.549988\pi$
$199$	−4.41253	−0.312796	−0.156398	+	0.987694i	$0.549988\pi$
$200$	−48.0732	−3.39929
$201$	−4.39218	−0.309800
$202$	16.0576	1.12981
$203$	−20.8878	−1.46603
$204$	4.59420	0.321658
$205$	27.5704	1.92560
$206$	−0.828826	−0.0577470
$207$	−10.5066	−0.730259
$208$	−10.5698	−0.732882
$209$	−25.1574	−1.74017
$210$	−29.6435	−2.04560
$211$	7.20284	0.495864	0.247932	−	0.968777i	$-0.420249\pi$
$211$	7.20284	0.495864	0.247932	+	0.968777i	$0.420249\pi$
$212$	−39.4025	−2.70617
$213$	7.66074	0.524905
$214$	−40.1779	−2.74651
$215$	3.73374	0.254639
$216$	28.3678	1.93019
$217$	−12.3329	−0.837211
$218$	−6.93327	−0.469580
$219$	−2.36292	−0.159672
$220$	81.6293	5.50344
$221$	−2.10553	−0.141634
$222$	−27.5001	−1.84569
$223$	−13.5125	−0.904865	−0.452432	−	0.891799i	$-0.649444\pi$
$223$	−13.5125	−0.904865	−0.452432	+	0.891799i	$0.649444\pi$
$224$	4.96060	0.331444
$225$	−15.9463	−1.06308
$226$	13.0016	0.864855
$227$	9.40679	0.624350	0.312175	−	0.950025i	$-0.398942\pi$
$227$	9.40679	0.624350	0.312175	+	0.950025i	$0.398942\pi$
$228$	22.0208	1.45836
$229$	26.5418	1.75393	0.876965	−	0.480554i	$-0.159565\pi$
$229$	26.5418	1.75393	0.876965	+	0.480554i	$0.159565\pi$
$230$	54.6141	3.60114
$231$	16.7821	1.10418
$232$	−38.7405	−2.54344
$233$	−14.1518	−0.927113	−0.463557	−	0.886067i	$-0.653427\pi$
$233$	−14.1518	−0.927113	−0.463557	+	0.886067i	$0.653427\pi$
$234$	−9.32454	−0.609564
$235$	41.2224	2.68905
$236$	13.2804	0.864483
$237$	6.98122	0.453479
$238$	7.19842	0.466604
$239$	21.2848	1.37680	0.688400	−	0.725331i	$-0.258313\pi$
$239$	21.2848	1.37680	0.688400	+	0.725331i	$0.258313\pi$
$240$	−20.6726	−1.33441
$241$	−5.21334	−0.335821	−0.167910	−	0.985802i	$-0.553702\pi$
$241$	−5.21334	−0.335821	−0.167910	+	0.985802i	$0.553702\pi$
$242$	−41.0881	−2.64124
$243$	15.3112	0.982214
$244$	19.4568	1.24559
$245$	−5.24395	−0.335024
$246$	20.2223	1.28932
$247$	−10.0922	−0.642151
$248$	−22.8738	−1.45248
$249$	−8.59611	−0.544757
$250$	36.5349	2.31067
$251$	13.9416	0.879986	0.439993	−	0.898001i	$-0.354981\pi$
$251$	13.9416	0.879986	0.439993	+	0.898001i	$0.354981\pi$
$252$	21.5377	1.35675
$253$	−30.9187	−1.94384
$254$	15.8089	0.991942
$255$	−4.11806	−0.257883
$256$	−32.6206	−2.03879
$257$	−20.9233	−1.30516	−0.652581	−	0.757719i	$-0.726314\pi$
$257$	−20.9233	−1.30516	−0.652581	+	0.757719i	$0.726314\pi$
$258$	2.73861	0.170499
$259$	−29.1111	−1.80888
$260$	32.7466	2.03086
$261$	−12.8505	−0.795426
$262$	−16.3535	−1.01032
$263$	−2.71526	−0.167430	−0.0837149	−	0.996490i	$-0.526679\pi$
$263$	−2.71526	−0.167430	−0.0837149	+	0.996490i	$0.526679\pi$
$264$	31.1256	1.91565
$265$	35.3188	2.16962
$266$	34.5033	2.11553
$267$	14.5252	0.888926
$268$	−16.5879	−1.01327
$269$	13.5472	0.825990	0.412995	−	0.910733i	$-0.364483\pi$
$269$	13.5472	0.825990	0.412995	+	0.910733i	$0.364483\pi$
$270$	−48.9129	−2.97675
$271$	13.4674	0.818087	0.409044	−	0.912515i	$-0.365862\pi$
$271$	13.4674	0.818087	0.409044	+	0.912515i	$0.365862\pi$
$272$	5.02000	0.304382
$273$	6.73234	0.407460
$274$	−47.0346	−2.84146
$275$	−46.9264	−2.82977
$276$	27.0638	1.62905
$277$	31.1590	1.87216	0.936082	−	0.351782i	$-0.114424\pi$
$277$	31.1590	1.87216	0.936082	+	0.351782i	$0.114424\pi$
$278$	−27.6004	−1.65536
$279$	−7.58740	−0.454246
$280$	−58.2005	−3.47815
$281$	−16.7994	−1.00217	−0.501084	−	0.865399i	$-0.667065\pi$
$281$	−16.7994	−1.00217	−0.501084	+	0.865399i	$0.667065\pi$
$282$	30.2357	1.80051
$283$	17.2067	1.02283	0.511417	−	0.859333i	$-0.329121\pi$
$283$	17.2067	1.02283	0.511417	+	0.859333i	$0.329121\pi$
$284$	28.9323	1.71681
$285$	−19.7386	−1.16921
$286$	−27.4401	−1.62257
$287$	21.4069	1.26361
$288$	3.05184	0.179831
$289$	1.00000	0.0588235
$290$	66.7978	3.92250
$291$	−18.8518	−1.10511
$292$	−8.92405	−0.522240
$293$	2.17110	0.126837	0.0634185	−	0.997987i	$-0.479800\pi$
$293$	2.17110	0.126837	0.0634185	+	0.997987i	$0.479800\pi$
$294$	−3.84632	−0.224322
$295$	−11.9041	−0.693081
$296$	−53.9923	−3.13824
$297$	27.6911	1.60680
$298$	13.2545	0.767815
$299$	−12.4034	−0.717308
$300$	41.0757	2.37151
$301$	2.89905	0.167098
$302$	9.67011	0.556453
$303$	−7.13259	−0.409757
$304$	24.0618	1.38004
$305$	−17.4403	−0.998627
$306$	4.42859	0.253165
$307$	−18.5525	−1.05885	−0.529424	−	0.848357i	$-0.677592\pi$
$307$	−18.5525	−1.05885	−0.529424	+	0.848357i	$0.677592\pi$
$308$	63.3808	3.61146
$309$	0.368154	0.0209436
$310$	39.4398	2.24003
$311$	24.1577	1.36986	0.684928	−	0.728611i	$-0.259834\pi$
$311$	24.1577	1.36986	0.684928	+	0.728611i	$0.259834\pi$
$312$	12.4864	0.706906
$313$	6.56000	0.370793	0.185397	−	0.982664i	$-0.440643\pi$
$313$	6.56000	0.370793	0.185397	+	0.982664i	$0.440643\pi$
$314$	44.9506	2.53671
$315$	−19.3055	−1.08774
$316$	26.3659	1.48320
$317$	15.9186	0.894076	0.447038	−	0.894515i	$-0.352479\pi$
$317$	15.9186	0.894076	0.447038	+	0.894515i	$0.352479\pi$
$318$	25.9056	1.45271
$319$	−37.8163	−2.11730
$320$	21.6230	1.20876
$321$	17.8465	0.996097
$322$	42.4049	2.36313
$323$	4.79318	0.266700
$324$	−1.95092	−0.108384
$325$	−18.8251	−1.04423
$326$	24.5837	1.36157
$327$	3.07967	0.170306
$328$	39.7033	2.19225
$329$	32.0070	1.76460
$330$	−53.6681	−2.95433
$331$	−1.30472	−0.0717140	−0.0358570	−	0.999357i	$-0.511416\pi$
$331$	−1.30472	−0.0717140	−0.0358570	+	0.999357i	$0.511416\pi$
$332$	−32.4649	−1.78174
$333$	−17.9096	−0.981442
$334$	−12.6032	−0.689616
$335$	14.8688	0.812368
$336$	−16.0512	−0.875665
$337$	−18.9400	−1.03173	−0.515864	−	0.856671i	$-0.672529\pi$
$337$	−18.9400	−1.03173	−0.515864	+	0.856671i	$0.672529\pi$
$338$	21.2714	1.15701
$339$	−5.77516	−0.313664
$340$	−15.5526	−0.843461
$341$	−22.3281	−1.20913
$342$	21.2270	1.14782
$343$	16.2217	0.875889
$344$	5.37685	0.289900
$345$	−24.2589	−1.30606
$346$	−28.4809	−1.53114
$347$	5.92811	0.318237	0.159119	−	0.987259i	$-0.449135\pi$
$347$	5.92811	0.318237	0.159119	+	0.987259i	$0.449135\pi$
$348$	33.1014	1.77442
$349$	1.25124	0.0669773	0.0334886	−	0.999439i	$-0.489338\pi$
$349$	1.25124	0.0669773	0.0334886	+	0.999439i	$0.489338\pi$
$350$	64.3595	3.44016
$351$	11.1086	0.592935
$352$	8.98091	0.478684
$353$	8.22754	0.437908	0.218954	−	0.975735i	$-0.429736\pi$
$353$	8.22754	0.437908	0.218954	+	0.975735i	$0.429736\pi$
$354$	−8.73137	−0.464067
$355$	−25.9338	−1.37642
$356$	54.8571	2.90742
$357$	−3.19745	−0.169227
$358$	19.7528	1.04397
$359$	−5.56939	−0.293941	−0.146971	−	0.989141i	$-0.546952\pi$
$359$	−5.56939	−0.293941	−0.146971	+	0.989141i	$0.546952\pi$
$360$	−35.8059	−1.88714
$361$	3.97456	0.209187
$362$	−55.9260	−2.93940
$363$	18.2508	0.957920
$364$	25.4260	1.33269
$365$	7.99917	0.418695
$366$	−12.7921	−0.668652
$367$	−21.9324	−1.14486	−0.572430	−	0.819954i	$-0.693999\pi$
$367$	−21.9324	−1.14486	−0.572430	+	0.819954i	$0.693999\pi$
$368$	29.5721	1.54155
$369$	13.1699	0.685597
$370$	93.0956	4.83981
$371$	27.4232	1.42374
$372$	19.5443	1.01332
$373$	15.9409	0.825391	0.412695	−	0.910869i	$-0.364587\pi$
$373$	15.9409	0.825391	0.412695	+	0.910869i	$0.364587\pi$
$374$	13.0324	0.673888
$375$	−16.2284	−0.838029
$376$	59.3632	3.06142
$377$	−15.1705	−0.781319
$378$	−37.9783	−1.95339
$379$	−5.55551	−0.285368	−0.142684	−	0.989768i	$-0.545573\pi$
$379$	−5.55551	−0.285368	−0.142684	+	0.989768i	$0.545573\pi$
$380$	−74.5466	−3.82416
$381$	−7.02214	−0.359755
$382$	−39.5711	−2.02463
$383$	6.46880	0.330540	0.165270	−	0.986248i	$-0.447150\pi$
$383$	6.46880	0.330540	0.165270	+	0.986248i	$0.447150\pi$
$384$	19.6345	1.00197
$385$	−56.8121	−2.89541
$386$	−18.5904	−0.946229
$387$	1.78354	0.0906625
$388$	−71.1975	−3.61451
$389$	−1.44264	−0.0731446	−0.0365723	−	0.999331i	$-0.511644\pi$
$389$	−1.44264	−0.0731446	−0.0365723	+	0.999331i	$0.511644\pi$
$390$	−21.5296	−1.09019
$391$	5.89086	0.297914
$392$	−7.55167	−0.381417
$393$	7.26401	0.366421
$394$	−60.6585	−3.05593
$395$	−23.6334	−1.18912
$396$	38.9929	1.95947
$397$	−21.7105	−1.08962	−0.544810	−	0.838559i	$-0.683398\pi$
$397$	−21.7105	−1.08962	−0.544810	+	0.838559i	$0.683398\pi$
$398$	10.9565	0.549197
$399$	−15.3260	−0.767258
$400$	44.8827	2.24414
$401$	20.1290	1.00519	0.502597	−	0.864521i	$-0.332378\pi$
$401$	20.1290	1.00519	0.502597	+	0.864521i	$0.332378\pi$
$402$	10.9059	0.543938
$403$	−8.95719	−0.446190
$404$	−26.9376	−1.34020
$405$	1.74873	0.0868949
$406$	51.8650	2.57402
$407$	−52.7042	−2.61245
$408$	−5.93030	−0.293593
$409$	10.4642	0.517423	0.258712	−	0.965955i	$-0.416702\pi$
$409$	10.4642	0.517423	0.258712	+	0.965955i	$0.416702\pi$
$410$	−68.4580	−3.38090
$411$	20.8922	1.03054
$412$	1.39041	0.0685004
$413$	−9.24287	−0.454812
$414$	26.0882	1.28216
$415$	29.1003	1.42848
$416$	3.60281	0.176642
$417$	12.2597	0.600362
$418$	62.4665	3.05534
$419$	−0.222710	−0.0108801	−0.00544005	−	0.999985i	$-0.501732\pi$
$419$	−0.222710	−0.0108801	−0.00544005	+	0.999985i	$0.501732\pi$
$420$	49.7288	2.42652
$421$	21.0554	1.02618	0.513089	−	0.858335i	$-0.328501\pi$
$421$	21.0554	1.02618	0.513089	+	0.858335i	$0.328501\pi$
$422$	−17.8849	−0.870622
$423$	19.6912	0.957420
$424$	50.8616	2.47006
$425$	8.94078	0.433692
$426$	−19.0218	−0.921611
$427$	−13.5414	−0.655317
$428$	67.4010	3.25795
$429$	12.1886	0.588469
$430$	−9.27098	−0.447086
$431$	−23.3186	−1.12322	−0.561609	−	0.827403i	$-0.689817\pi$
$431$	−23.3186	−1.12322	−0.561609	+	0.827403i	$0.689817\pi$
$432$	−26.4851	−1.27427
$433$	10.9526	0.526348	0.263174	−	0.964748i	$-0.415231\pi$
$433$	10.9526	0.526348	0.263174	+	0.964748i	$0.415231\pi$
$434$	30.6229	1.46995
$435$	−29.6708	−1.42261
$436$	11.6310	0.557023
$437$	28.2360	1.35071
$438$	5.86721	0.280346
$439$	−35.1971	−1.67987	−0.839934	−	0.542688i	$-0.817406\pi$
$439$	−35.1971	−1.67987	−0.839934	+	0.542688i	$0.817406\pi$
$440$	−105.369	−5.02327
$441$	−2.50494	−0.119283
$442$	5.22810	0.248676
$443$	−33.0032	−1.56803	−0.784013	−	0.620744i	$-0.786831\pi$
$443$	−33.0032	−1.56803	−0.784013	+	0.620744i	$0.786831\pi$
$444$	46.1331	2.18938
$445$	−49.1718	−2.33097
$446$	33.5520	1.58873
$447$	−5.88751	−0.278470
$448$	16.7891	0.793212
$449$	−13.9175	−0.656806	−0.328403	−	0.944538i	$-0.606510\pi$
$449$	−13.9175	−0.656806	−0.328403	+	0.944538i	$0.606510\pi$
$450$	39.5950	1.86653
$451$	38.7561	1.82496
$452$	−21.8110	−1.02590
$453$	−4.29535	−0.201813
$454$	−23.3573	−1.09621
$455$	−22.7909	−1.06845
$456$	−28.4250	−1.33112
$457$	29.0436	1.35860	0.679300	−	0.733861i	$-0.262283\pi$
$457$	29.0436	1.35860	0.679300	+	0.733861i	$0.262283\pi$
$458$	−65.9040	−3.07949
$459$	−5.27592	−0.246259
$460$	−91.6185	−4.27174
$461$	9.21552	0.429209	0.214605	−	0.976701i	$-0.431154\pi$
$461$	9.21552	0.429209	0.214605	+	0.976701i	$0.431154\pi$
$462$	−41.6704	−1.93868
$463$	10.8082	0.502299	0.251149	−	0.967948i	$-0.419191\pi$
$463$	10.8082	0.502299	0.251149	+	0.967948i	$0.419191\pi$
$464$	36.1693	1.67912
$465$	−17.5187	−0.812410
$466$	35.1393	1.62780
$467$	−11.1493	−0.515926	−0.257963	−	0.966155i	$-0.583051\pi$
$467$	−11.1493	−0.515926	−0.257963	+	0.966155i	$0.583051\pi$
$468$	15.6425	0.723075
$469$	11.5448	0.533090
$470$	−102.356	−4.72135
$471$	−19.9665	−0.920008
$472$	−17.1427	−0.789057
$473$	5.24858	0.241330
$474$	−17.3346	−0.796203
$475$	42.8548	1.96631
$476$	−12.0758	−0.553494
$477$	16.8712	0.772479
$478$	−52.8509	−2.41734
$479$	21.1676	0.967174	0.483587	−	0.875296i	$-0.339334\pi$
$479$	21.1676	0.967174	0.483587	+	0.875296i	$0.339334\pi$
$480$	7.04646	0.321625
$481$	−21.1430	−0.964036
$482$	12.9449	0.589623
$483$	−18.8358	−0.857057
$484$	68.9278	3.13308
$485$	63.8186	2.89786
$486$	−38.0182	−1.72454
$487$	−23.0411	−1.04409	−0.522046	−	0.852918i	$-0.674831\pi$
$487$	−23.0411	−1.04409	−0.522046	+	0.852918i	$0.674831\pi$
$488$	−25.1152	−1.13691
$489$	−10.9198	−0.493810
$490$	13.0209	0.588224
$491$	−10.7845	−0.486699	−0.243349	−	0.969939i	$-0.578246\pi$
$491$	−10.7845	−0.486699	−0.243349	+	0.969939i	$0.578246\pi$
$492$	−33.9241	−1.52942
$493$	7.20505	0.324499
$494$	25.0592	1.12747
$495$	−34.9517	−1.57096
$496$	21.3557	0.958898
$497$	−20.1362	−0.903231
$498$	21.3444	0.956466
$499$	−41.1827	−1.84359	−0.921795	−	0.387678i	$-0.873277\pi$
$499$	−41.1827	−1.84359	−0.921795	+	0.387678i	$0.873277\pi$
$500$	−61.2896	−2.74095
$501$	5.59818	0.250108
$502$	−34.6174	−1.54505
$503$	19.3374	0.862212	0.431106	−	0.902301i	$-0.358123\pi$
$503$	19.3374	0.862212	0.431106	+	0.902301i	$0.358123\pi$
$504$	−27.8014	−1.23837
$505$	24.1458	1.07448
$506$	76.7719	3.41293
$507$	−9.44852	−0.419623
$508$	−26.5205	−1.17666
$509$	2.50526	0.111044	0.0555219	−	0.998457i	$-0.482318\pi$
$509$	2.50526	0.111044	0.0555219	+	0.998457i	$0.482318\pi$
$510$	10.2253	0.452782
$511$	6.21093	0.274755
$512$	45.3938	2.00614
$513$	−25.2884	−1.11651
$514$	51.9533	2.29156
$515$	−1.24631	−0.0549188
$516$	−4.59420	−0.202248
$517$	57.9470	2.54851
$518$	72.2838	3.17597
$519$	12.6509	0.555312
$520$	−42.2701	−1.85367
$521$	3.63655	0.159320	0.0796600	−	0.996822i	$-0.474617\pi$
$521$	3.63655	0.159320	0.0796600	+	0.996822i	$0.474617\pi$
$522$	31.9082	1.39658
$523$	−4.42182	−0.193353	−0.0966763	−	0.995316i	$-0.530821\pi$
$523$	−4.42182	−0.193353	−0.0966763	+	0.995316i	$0.530821\pi$
$524$	27.4339	1.19846
$525$	−28.5877	−1.24767
$526$	6.74206	0.293968
$527$	4.25412	0.185312
$528$	−29.0599	−1.26467
$529$	11.7023	0.508795
$530$	−87.6977	−3.80934
$531$	−5.68637	−0.246767
$532$	−57.8815	−2.50948
$533$	15.5475	0.673438
$534$	−36.0664	−1.56075
$535$	−60.4156	−2.61199
$536$	21.4121	0.924862
$537$	−8.77397	−0.378625
$538$	−33.6382	−1.45025
$539$	−7.37151	−0.317513
$540$	82.0545	3.53106
$541$	38.8114	1.66863	0.834317	−	0.551285i	$-0.185862\pi$
$541$	38.8114	1.66863	0.834317	+	0.551285i	$0.185862\pi$
$542$	−33.4400	−1.43637
$543$	24.8416	1.06606
$544$	−1.71111	−0.0733634
$545$	−10.4256	−0.446582
$546$	−16.7166	−0.715405
$547$	30.0079	1.28304	0.641522	−	0.767105i	$-0.278303\pi$
$547$	30.0079	1.28304	0.641522	+	0.767105i	$0.278303\pi$
$548$	78.9034	3.37059
$549$	−8.33092	−0.355555
$550$	116.520	4.96841
$551$	34.5351	1.47124
$552$	−34.9346	−1.48691
$553$	−18.3501	−0.780324
$554$	−77.3688	−3.28708
$555$	−41.3519	−1.75529
$556$	46.3013	1.96361
$557$	1.26983	0.0538045	0.0269022	−	0.999638i	$-0.491436\pi$
$557$	1.26983	0.0538045	0.0269022	+	0.999638i	$0.491436\pi$
$558$	18.8397	0.797550
$559$	2.10553	0.0890546
$560$	54.3379	2.29619
$561$	−5.78882	−0.244404
$562$	41.7134	1.75957
$563$	12.9251	0.544727	0.272363	−	0.962194i	$-0.412195\pi$
$563$	12.9251	0.544727	0.272363	+	0.962194i	$0.412195\pi$
$564$	−50.7223	−2.13579
$565$	19.5506	0.822498
$566$	−42.7248	−1.79586
$567$	1.35779	0.0570219
$568$	−37.3465	−1.56702
$569$	31.7808	1.33232	0.666160	−	0.745809i	$-0.267937\pi$
$569$	31.7808	1.33232	0.666160	+	0.745809i	$0.267937\pi$
$570$	49.0115	2.05287
$571$	−29.0170	−1.21432	−0.607162	−	0.794578i	$-0.707692\pi$
$571$	−29.0170	−1.21432	−0.607162	+	0.794578i	$0.707692\pi$
$572$	46.0325	1.92472
$573$	17.5770	0.734289
$574$	−53.1540	−2.21861
$575$	52.6689	2.19645
$576$	10.3289	0.430372
$577$	19.3667	0.806245	0.403123	−	0.915146i	$-0.367925\pi$
$577$	19.3667	0.806245	0.403123	+	0.915146i	$0.367925\pi$
$578$	−2.48303	−0.103280
$579$	8.25765	0.343176
$580$	−112.058	−4.65294
$581$	22.5948	0.937391
$582$	46.8096	1.94032
$583$	49.6483	2.05622
$584$	11.5194	0.476675
$585$	−14.0213	−0.579710
$586$	−5.39090	−0.222696
$587$	−10.5817	−0.436755	−0.218378	−	0.975864i	$-0.570076\pi$
$587$	−10.5817	−0.436755	−0.218378	+	0.975864i	$0.570076\pi$
$588$	6.45245	0.266094
$589$	20.3908	0.840186
$590$	29.5581	1.21689
$591$	26.9438	1.10832
$592$	50.4089	2.07179
$593$	24.7891	1.01797	0.508983	−	0.860777i	$-0.330022\pi$
$593$	24.7891	1.01797	0.508983	+	0.860777i	$0.330022\pi$
$594$	−68.7578	−2.82117
$595$	10.8243	0.443752
$596$	−22.2353	−0.910794
$597$	−4.86672	−0.199182
$598$	30.7980	1.25943
$599$	−36.9287	−1.50887	−0.754433	−	0.656377i	$-0.772088\pi$
$599$	−36.9287	−1.50887	−0.754433	+	0.656377i	$0.772088\pi$
$600$	−53.0215	−2.16459
$601$	32.7020	1.33394	0.666971	−	0.745083i	$-0.267590\pi$
$601$	32.7020	1.33394	0.666971	+	0.745083i	$0.267590\pi$
$602$	−7.19842	−0.293386
$603$	7.10255	0.289238
$604$	−16.2222	−0.660073
$605$	−61.7842	−2.51189
$606$	17.7104	0.719438
$607$	−10.9211	−0.443273	−0.221636	−	0.975129i	$-0.571140\pi$
$607$	−10.9211	−0.443273	−0.221636	+	0.975129i	$0.571140\pi$
$608$	−8.20167	−0.332622
$609$	−23.0378	−0.933539
$610$	43.3047	1.75336
$611$	23.2462	0.940440
$612$	−7.42923	−0.300309
$613$	34.5229	1.39437	0.697184	−	0.716892i	$-0.254436\pi$
$613$	34.5229	1.39437	0.697184	+	0.716892i	$0.254436\pi$
$614$	46.0665	1.85909
$615$	30.4082	1.22618
$616$	−81.8135	−3.29636
$617$	29.6912	1.19532	0.597662	−	0.801748i	$-0.296097\pi$
$617$	29.6912	1.19532	0.597662	+	0.801748i	$0.296097\pi$
$618$	−0.914138	−0.0367720
$619$	−33.7639	−1.35709	−0.678544	−	0.734560i	$-0.737389\pi$
$619$	−33.7639	−1.35709	−0.678544	+	0.734560i	$0.737389\pi$
$620$	−66.1628	−2.65716
$621$	−31.0797	−1.24719
$622$	−59.9842	−2.40515
$623$	−38.1793	−1.52962
$624$	−11.6577	−0.466683
$625$	10.2337	0.409347
$626$	−16.2887	−0.651027
$627$	−27.7469	−1.10810
$628$	−75.4074	−3.00908
$629$	10.0416	0.400385
$630$	47.9362	1.90983
$631$	−11.5560	−0.460038	−0.230019	−	0.973186i	$-0.573879\pi$
$631$	−11.5560	−0.460038	−0.230019	+	0.973186i	$0.573879\pi$
$632$	−34.0338	−1.35379
$633$	7.94425	0.315755
$634$	−39.5263	−1.56979
$635$	23.7719	0.943361
$636$	−43.4582	−1.72323
$637$	−2.95718	−0.117168
$638$	93.8989	3.71749
$639$	−12.3881	−0.490066
$640$	−66.4683	−2.62739
$641$	−9.48585	−0.374669	−0.187334	−	0.982296i	$-0.559985\pi$
$641$	−9.48585	−0.374669	−0.187334	+	0.982296i	$0.559985\pi$
$642$	−44.3135	−1.74891
$643$	−48.3241	−1.90572	−0.952858	−	0.303416i	$-0.901873\pi$
$643$	−48.3241	−1.90572	−0.952858	+	0.303416i	$0.901873\pi$
$644$	−71.1369	−2.80319
$645$	4.11806	0.162148
$646$	−11.9016	−0.468262
$647$	37.2131	1.46300	0.731500	−	0.681842i	$-0.238821\pi$
$647$	37.2131	1.46300	0.731500	+	0.681842i	$0.238821\pi$
$648$	2.51829	0.0989278
$649$	−16.7337	−0.656857
$650$	46.7433	1.83342
$651$	−13.6023	−0.533118
$652$	−41.2408	−1.61511
$653$	4.28947	0.167860	0.0839299	−	0.996472i	$-0.473253\pi$
$653$	4.28947	0.167860	0.0839299	+	0.996472i	$0.473253\pi$
$654$	−7.64692	−0.299018
$655$	−24.5907	−0.960839
$656$	−37.0683	−1.44727
$657$	3.82106	0.149074
$658$	−79.4743	−3.09823
$659$	−23.2327	−0.905018	−0.452509	−	0.891760i	$-0.649471\pi$
$659$	−23.2327	−0.905018	−0.452509	+	0.891760i	$0.649471\pi$
$660$	90.0315	3.50447
$661$	−32.1230	−1.24944	−0.624721	−	0.780848i	$-0.714787\pi$
$661$	−32.1230	−1.24944	−0.624721	+	0.780848i	$0.714787\pi$
$662$	3.23966	0.125913
$663$	−2.32226	−0.0901891
$664$	41.9065	1.62629
$665$	51.8827	2.01192
$666$	44.4702	1.72318
$667$	42.4440	1.64344
$668$	21.1426	0.818033
$669$	−14.9034	−0.576198
$670$	−36.9196	−1.42633
$671$	−24.5161	−0.946433
$672$	5.47120	0.211056
$673$	−28.9871	−1.11737	−0.558685	−	0.829380i	$-0.688694\pi$
$673$	−28.9871	−1.11737	−0.558685	+	0.829380i	$0.688694\pi$
$674$	47.0286	1.81147
$675$	−47.1709	−1.81561
$676$	−35.6842	−1.37247
$677$	−12.4469	−0.478374	−0.239187	−	0.970974i	$-0.576881\pi$
$677$	−12.4469	−0.478374	−0.239187	+	0.970974i	$0.576881\pi$
$678$	14.3399	0.550721
$679$	49.5518	1.90162
$680$	20.0757	0.769869
$681$	10.3750	0.397573
$682$	55.4413	2.12296
$683$	−34.8683	−1.33420	−0.667100	−	0.744968i	$-0.732464\pi$
$683$	−34.8683	−1.33420	−0.667100	+	0.744968i	$0.732464\pi$
$684$	−35.6096	−1.36157
$685$	−70.7259	−2.70230
$686$	−40.2789	−1.53786
$687$	29.2738	1.11686
$688$	−5.02000	−0.191386
$689$	19.9170	0.758779
$690$	60.2356	2.29313
$691$	2.64606	0.100661	0.0503305	−	0.998733i	$-0.483973\pi$
$691$	2.64606	0.100661	0.0503305	+	0.998733i	$0.483973\pi$
$692$	47.7785	1.81627
$693$	−27.1381	−1.03089
$694$	−14.7197	−0.558751
$695$	−41.5027	−1.57429
$696$	−42.7281	−1.61960
$697$	−7.38412	−0.279694
$698$	−3.10686	−0.117596
$699$	−15.6084	−0.590365
$700$	−107.967	−4.08077
$701$	25.9422	0.979822	0.489911	−	0.871772i	$-0.337029\pi$
$701$	25.9422	0.979822	0.489911	+	0.871772i	$0.337029\pi$
$702$	−27.5831	−1.04106
$703$	48.1313	1.81530
$704$	30.3958	1.14559
$705$	45.4655	1.71233
$706$	−20.4292	−0.768865
$707$	18.7480	0.705090
$708$	14.6474	0.550484
$709$	32.4709	1.21947	0.609735	−	0.792605i	$-0.291276\pi$
$709$	32.4709	1.21947	0.609735	+	0.792605i	$0.291276\pi$
$710$	64.3943	2.41667
$711$	−11.2893	−0.423380
$712$	−70.8109	−2.65375
$713$	25.0604	0.938521
$714$	7.93937	0.297123
$715$	−41.2617	−1.54310
$716$	−33.1366	−1.23837
$717$	23.4757	0.876717
$718$	13.8290	0.516092
$719$	−39.2066	−1.46216	−0.731080	−	0.682292i	$-0.760983\pi$
$719$	−39.2066	−1.46216	−0.731080	+	0.682292i	$0.760983\pi$
$720$	33.4295	1.24585
$721$	−0.967691	−0.0360387
$722$	−9.86896	−0.367284
$723$	−5.74996	−0.213843
$724$	93.8193	3.48677
$725$	64.4188	2.39245
$726$	−45.3174	−1.68189
$727$	−16.1489	−0.598931	−0.299466	−	0.954107i	$-0.596808\pi$
$727$	−16.1489	−0.598931	−0.299466	+	0.954107i	$0.596808\pi$
$728$	−32.8205	−1.21641
$729$	18.2923	0.677492
$730$	−19.8622	−0.735132
$731$	−1.00000	−0.0369863
$732$	21.4595	0.793165
$733$	52.1551	1.92639	0.963196	−	0.268798i	$-0.0866265\pi$
$733$	52.1551	1.92639	0.963196	+	0.268798i	$0.0866265\pi$
$734$	54.4587	2.01011
$735$	−5.78372	−0.213336
$736$	−10.0799	−0.371551
$737$	20.9013	0.769909
$738$	−32.7012	−1.20375
$739$	18.9727	0.697923	0.348961	−	0.937137i	$-0.386534\pi$
$739$	18.9727	0.697923	0.348961	+	0.937137i	$0.386534\pi$
$740$	−156.174	−5.74106
$741$	−11.1310	−0.408908
$742$	−68.0926	−2.49976
$743$	−15.1312	−0.555111	−0.277555	−	0.960710i	$-0.589524\pi$
$743$	−15.1312	−0.555111	−0.277555	+	0.960710i	$0.589524\pi$
$744$	−25.2282	−0.924910
$745$	19.9309	0.730211
$746$	−39.5818	−1.44919
$747$	13.9007	0.508600
$748$	−21.8626	−0.799377
$749$	−46.9095	−1.71404
$750$	40.2955	1.47138
$751$	−6.07538	−0.221694	−0.110847	−	0.993837i	$-0.535356\pi$
$751$	−6.07538	−0.221694	−0.110847	+	0.993837i	$0.535356\pi$
$752$	−55.4234	−2.02108
$753$	15.3766	0.560356
$754$	37.6687	1.37181
$755$	14.5410	0.529200
$756$	63.7110	2.31715
$757$	−20.9641	−0.761955	−0.380977	−	0.924584i	$-0.624412\pi$
$757$	−20.9641	−0.761955	−0.380977	+	0.924584i	$0.624412\pi$
$758$	13.7945	0.501039
$759$	−34.1012	−1.23779
$760$	96.2266	3.49050
$761$	1.78017	0.0645312	0.0322656	−	0.999479i	$-0.489728\pi$
$761$	1.78017	0.0645312	0.0322656	+	0.999479i	$0.489728\pi$
$762$	17.4362	0.631647
$763$	−8.09490	−0.293055
$764$	66.3830	2.40165
$765$	6.65927	0.240766
$766$	−16.0622	−0.580352
$767$	−6.71296	−0.242391
$768$	−35.9783	−1.29826
$769$	1.10944	0.0400075	0.0200038	−	0.999800i	$-0.493632\pi$
$769$	1.10944	0.0400075	0.0200038	+	0.999800i	$0.493632\pi$
$770$	141.066	5.08367
$771$	−23.0770	−0.831098
$772$	31.1866	1.12243
$773$	9.68588	0.348377	0.174188	−	0.984712i	$-0.444270\pi$
$773$	9.68588	0.348377	0.174188	+	0.984712i	$0.444270\pi$
$774$	−4.42859	−0.159182
$775$	38.0352	1.36626
$776$	91.9035	3.29914
$777$	−32.1076	−1.15185
$778$	3.58211	0.128425
$779$	−35.3934	−1.26810
$780$	36.1173	1.29321
$781$	−36.4555	−1.30448
$782$	−14.6272	−0.523067
$783$	−38.0133	−1.35848
$784$	7.05048	0.251803
$785$	67.5922	2.41247
$786$	−18.0367	−0.643349
$787$	−20.3631	−0.725865	−0.362932	−	0.931815i	$-0.618224\pi$
$787$	−20.3631	−0.725865	−0.362932	+	0.931815i	$0.618224\pi$
$788$	101.758	3.62499
$789$	−2.99474	−0.106616
$790$	58.6824	2.08783
$791$	15.1800	0.539738
$792$	−50.3330	−1.78850
$793$	−9.83494	−0.349249
$794$	53.9079	1.91312
$795$	38.9543	1.38157
$796$	−18.3801	−0.651467
$797$	−20.3068	−0.719303	−0.359651	−	0.933087i	$-0.617104\pi$
$797$	−20.3068	−0.719303	−0.359651	+	0.933087i	$0.617104\pi$
$798$	38.0548	1.34713
$799$	−11.0405	−0.390586
$800$	−15.2987	−0.540890
$801$	−23.4885	−0.829926
$802$	−49.9809	−1.76489
$803$	11.2446	0.396812
$804$	−18.2954	−0.645227
$805$	63.7643	2.24740
$806$	22.2410	0.783405
$807$	14.9417	0.525973
$808$	34.7718	1.22327
$809$	−14.5663	−0.512123	−0.256062	−	0.966660i	$-0.582425\pi$
$809$	−14.5663	−0.512123	−0.256062	+	0.966660i	$0.582425\pi$
$810$	−4.34214	−0.152567
$811$	14.0121	0.492033	0.246016	−	0.969266i	$-0.420878\pi$
$811$	14.0121	0.492033	0.246016	+	0.969266i	$0.420878\pi$
$812$	−87.0068	−3.05334
$813$	14.8536	0.520940
$814$	130.866	4.58685
$815$	36.9666	1.29488
$816$	5.53672	0.193824
$817$	−4.79318	−0.167692
$818$	−25.9830	−0.908475
$819$	−10.8868	−0.380416
$820$	114.843	4.01048
$821$	6.26833	0.218766	0.109383	−	0.994000i	$-0.465112\pi$
$821$	6.26833	0.218766	0.109383	+	0.994000i	$0.465112\pi$
$822$	−51.8759	−1.80938
$823$	17.7633	0.619189	0.309595	−	0.950869i	$-0.399807\pi$
$823$	17.7633	0.619189	0.309595	+	0.950869i	$0.399807\pi$
$824$	−1.79477	−0.0625238
$825$	−51.7566	−1.80193
$826$	22.9503	0.798544
$827$	13.3481	0.464160	0.232080	−	0.972697i	$-0.425447\pi$
$827$	13.3481	0.464160	0.232080	+	0.972697i	$0.425447\pi$
$828$	−43.7646	−1.52092
$829$	27.8583	0.967558	0.483779	−	0.875190i	$-0.339264\pi$
$829$	27.8583	0.967558	0.483779	+	0.875190i	$0.339264\pi$
$830$	−72.2568	−2.50807
$831$	34.3663	1.19215
$832$	12.1937	0.422740
$833$	1.40448	0.0486623
$834$	−30.4413	−1.05410
$835$	−18.9514	−0.655841
$836$	−104.791	−3.62429
$837$	−22.4444	−0.775792
$838$	0.552996	0.0191029
$839$	−5.04719	−0.174248	−0.0871241	−	0.996197i	$-0.527768\pi$
$839$	−5.04719	−0.174248	−0.0871241	+	0.996197i	$0.527768\pi$
$840$	−64.1912	−2.21481
$841$	22.9127	0.790094
$842$	−52.2813	−1.80173
$843$	−18.5286	−0.638158
$844$	30.0030	1.03275
$845$	31.9859	1.10035
$846$	−48.8939	−1.68101
$847$	−47.9722	−1.64834
$848$	−47.4861	−1.63068
$849$	18.9778	0.651318
$850$	−22.2002	−0.761462
$851$	59.1538	2.02777
$852$	31.9103	1.09323
$853$	−49.6200	−1.69896	−0.849478	−	0.527624i	$-0.823083\pi$
$853$	−49.6200	−1.69896	−0.849478	+	0.527624i	$0.823083\pi$
$854$	33.6238	1.15058
$855$	31.9191	1.09161
$856$	−87.0028	−2.97369
$857$	−5.03551	−0.172010	−0.0860049	−	0.996295i	$-0.527410\pi$
$857$	−5.03551	−0.172010	−0.0860049	+	0.996295i	$0.527410\pi$
$858$	−30.2646	−1.03322
$859$	22.3089	0.761171	0.380586	−	0.924746i	$-0.375722\pi$
$859$	22.3089	0.761171	0.380586	+	0.924746i	$0.375722\pi$
$860$	15.5526	0.530341
$861$	23.6104	0.804640
$862$	57.9008	1.97211
$863$	−33.9134	−1.15443	−0.577214	−	0.816593i	$-0.695860\pi$
$863$	−33.9134	−1.15443	−0.577214	+	0.816593i	$0.695860\pi$
$864$	9.02769	0.307128
$865$	−42.8268	−1.45616
$866$	−27.1956	−0.924145
$867$	1.10293	0.0374575
$868$	−51.3719	−1.74368
$869$	−33.2219	−1.12697
$870$	73.6735	2.49776
$871$	8.38482	0.284109
$872$	−15.0136	−0.508423
$873$	30.4851	1.03176
$874$	−70.1107	−2.37153
$875$	42.6561	1.44204
$876$	−9.84262	−0.332551
$877$	44.7321	1.51049	0.755247	−	0.655440i	$-0.227517\pi$
$877$	44.7321	1.51049	0.755247	+	0.655440i	$0.227517\pi$
$878$	87.3956	2.94946
$879$	2.39457	0.0807670
$880$	98.3759	3.31625
$881$	−13.4180	−0.452064	−0.226032	−	0.974120i	$-0.572575\pi$
$881$	−13.4180	−0.452064	−0.226032	+	0.974120i	$0.572575\pi$
$882$	6.21985	0.209433
$883$	25.8417	0.869642	0.434821	−	0.900517i	$-0.356812\pi$
$883$	25.8417	0.869642	0.434821	+	0.900517i	$0.356812\pi$
$884$	−8.77047	−0.294983
$885$	−13.1294	−0.441339
$886$	81.9478	2.75309
$887$	5.45803	0.183263	0.0916314	−	0.995793i	$-0.470792\pi$
$887$	5.45803	0.183263	0.0916314	+	0.995793i	$0.470792\pi$
$888$	−59.5498	−1.99836
$889$	18.4576	0.619050
$890$	122.095	4.09263
$891$	2.45821	0.0823533
$892$	−56.2855	−1.88458
$893$	−52.9192	−1.77087
$894$	14.6189	0.488928
$895$	29.7024	0.992840
$896$	−51.6091	−1.72414
$897$	−13.6801	−0.456766
$898$	34.5575	1.15320
$899$	30.6511	1.02227
$900$	−66.4231	−2.21410
$901$	−9.45938	−0.315138
$902$	−96.2327	−3.20420
$903$	3.19745	0.106405
$904$	28.1542	0.936395
$905$	−84.0959	−2.79544
$906$	10.6655	0.354337
$907$	2.56975	0.0853272	0.0426636	−	0.999089i	$-0.486416\pi$
$907$	2.56975	0.0853272	0.0426636	+	0.999089i	$0.486416\pi$
$908$	39.1834	1.30035
$909$	11.5341	0.382560
$910$	56.5904	1.87596
$911$	0.704453	0.0233396	0.0116698	−	0.999932i	$-0.496285\pi$
$911$	0.704453	0.0233396	0.0116698	+	0.999932i	$0.496285\pi$
$912$	26.5385	0.878777
$913$	40.9067	1.35382
$914$	−72.1160	−2.38539
$915$	−19.2354	−0.635904
$916$	110.558	3.65294
$917$	−19.0934	−0.630519
$918$	13.1003	0.432373
$919$	32.0951	1.05872	0.529360	−	0.848397i	$-0.322432\pi$
$919$	32.0951	1.05872	0.529360	+	0.848397i	$0.322432\pi$
$920$	118.263	3.89903
$921$	−20.4622	−0.674252
$922$	−22.8824	−0.753592
$923$	−14.6246	−0.481375
$924$	69.9047	2.29970
$925$	89.7799	2.95194
$926$	−26.8370	−0.881920
$927$	−0.595339	−0.0195535
$928$	−12.3286	−0.404708
$929$	−12.8948	−0.423066	−0.211533	−	0.977371i	$-0.567846\pi$
$929$	−12.8948	−0.423066	−0.211533	+	0.977371i	$0.567846\pi$
$930$	43.4995	1.42640
$931$	6.73191	0.220630
$932$	−58.9483	−1.93092
$933$	26.6443	0.872294
$934$	27.6839	0.905846
$935$	19.5968	0.640884
$936$	−20.1917	−0.659987
$937$	41.9355	1.36997	0.684987	−	0.728555i	$-0.259808\pi$
$937$	41.9355	1.36997	0.684987	+	0.728555i	$0.259808\pi$
$938$	−28.6661	−0.935982
$939$	7.23523	0.236113
$940$	171.709	5.60054
$941$	−1.22427	−0.0399102	−0.0199551	−	0.999801i	$-0.506352\pi$
$941$	−1.22427	−0.0399102	−0.0199551	+	0.999801i	$0.506352\pi$
$942$	49.5774	1.61532
$943$	−43.4989	−1.41652
$944$	16.0050	0.520918
$945$	−57.1080	−1.85772
$946$	−13.0324	−0.423719
$947$	28.3500	0.921250	0.460625	−	0.887595i	$-0.347625\pi$
$947$	28.3500	0.921250	0.460625	+	0.887595i	$0.347625\pi$
$948$	29.0798	0.944469
$949$	4.51090	0.146430
$950$	−106.410	−3.45239
$951$	17.5571	0.569328
$952$	15.5877	0.505202
$953$	−46.0640	−1.49216	−0.746079	−	0.665857i	$-0.768066\pi$
$953$	−46.0640	−1.49216	−0.746079	+	0.665857i	$0.768066\pi$
$954$	−41.8917	−1.35629
$955$	−59.5031	−1.92547
$956$	88.6606	2.86749
$957$	−41.7088	−1.34825
$958$	−52.5599	−1.69813
$959$	−54.9149	−1.77330
$960$	23.8487	0.769714
$961$	−12.9025	−0.416209
$962$	52.4986	1.69262
$963$	−28.8595	−0.929984
$964$	−21.7158	−0.699420
$965$	−27.9545	−0.899886
$966$	46.7697	1.50479
$967$	−28.1322	−0.904672	−0.452336	−	0.891848i	$-0.649409\pi$
$967$	−28.1322	−0.904672	−0.452336	+	0.891848i	$0.649409\pi$
$968$	−88.9737	−2.85972
$969$	5.28655	0.169828
$970$	−158.464	−5.08796
$971$	−47.2547	−1.51647	−0.758237	−	0.651979i	$-0.773939\pi$
$971$	−47.2547	−1.51647	−0.758237	+	0.651979i	$0.773939\pi$
$972$	63.7778	2.04567
$973$	−32.2246	−1.03307
$974$	57.2117	1.83318
$975$	−20.7628	−0.664943
$976$	23.4484	0.750565
$977$	11.1535	0.356833	0.178416	−	0.983955i	$-0.442903\pi$
$977$	11.1535	0.356833	0.178416	+	0.983955i	$0.442903\pi$
$978$	27.1142	0.867016
$979$	−69.1216	−2.20914
$980$	−21.8433	−0.697760
$981$	−4.98011	−0.159003
$982$	26.7783	0.854530
$983$	−48.8894	−1.55933	−0.779665	−	0.626197i	$-0.784611\pi$
$983$	−48.8894	−1.55933	−0.779665	+	0.626197i	$0.784611\pi$
$984$	43.7901	1.39598
$985$	−91.2122	−2.90626
$986$	−17.8904	−0.569745
$987$	35.3015	1.12366
$988$	−42.0384	−1.33742
$989$	−5.89086	−0.187319
$990$	86.7861	2.75824
$991$	37.0459	1.17680	0.588401	−	0.808570i	$-0.299758\pi$
$991$	37.0459	1.17680	0.588401	+	0.808570i	$0.299758\pi$
$992$	−7.27928	−0.231117
$993$	−1.43902	−0.0456659
$994$	49.9987	1.58586
$995$	16.4752	0.522300
$996$	−35.8066	−1.13457
$997$	−32.7001	−1.03562	−0.517812	−	0.855495i	$-0.673253\pi$
$997$	−32.7001	−1.03562	−0.517812	+	0.855495i	$0.673253\pi$
$998$	102.258	3.23691
$999$	−52.9788	−1.67617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.2	✓	19
3.2	odd	2		6579.2.a.t.1.18		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.2	✓	19	1.1	even	1	trivial
6579.2.a.t.1.18		19	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48303 q^{2} +1.10293 q^{3} +4.16544 q^{4} -3.73374 q^{5} -2.73861 q^{6} -2.89905 q^{7} -5.37685 q^{8} -1.78354 q^{9} +O(q^{10})\)	\(q-2.48303 q^{2} +1.10293 q^{3} +4.16544 q^{4} -3.73374 q^{5} -2.73861 q^{6} -2.89905 q^{7} -5.37685 q^{8} -1.78354 q^{9} +9.27098 q^{10} -5.24858 q^{11} +4.59420 q^{12} -2.10553 q^{13} +7.19842 q^{14} -4.11806 q^{15} +5.02000 q^{16} +1.00000 q^{17} +4.42859 q^{18} +4.79318 q^{19} -15.5526 q^{20} -3.19745 q^{21} +13.0324 q^{22} +5.89086 q^{23} -5.93030 q^{24} +8.94078 q^{25} +5.22810 q^{26} -5.27592 q^{27} -12.0758 q^{28} +7.20505 q^{29} +10.2253 q^{30} +4.25412 q^{31} -1.71111 q^{32} -5.78882 q^{33} -2.48303 q^{34} +10.8243 q^{35} -7.42923 q^{36} +10.0416 q^{37} -11.9016 q^{38} -2.32226 q^{39} +20.0757 q^{40} -7.38412 q^{41} +7.93937 q^{42} -1.00000 q^{43} -21.8626 q^{44} +6.65927 q^{45} -14.6272 q^{46} -11.0405 q^{47} +5.53672 q^{48} +1.40448 q^{49} -22.2002 q^{50} +1.10293 q^{51} -8.77047 q^{52} -9.45938 q^{53} +13.1003 q^{54} +19.5968 q^{55} +15.5877 q^{56} +5.28655 q^{57} -17.8904 q^{58} +3.18824 q^{59} -17.1535 q^{60} +4.67100 q^{61} -10.5631 q^{62} +5.17057 q^{63} -5.79125 q^{64} +7.86151 q^{65} +14.3738 q^{66} -3.98228 q^{67} +4.16544 q^{68} +6.49722 q^{69} -26.8770 q^{70} +6.94579 q^{71} +9.58983 q^{72} -2.14240 q^{73} -24.9336 q^{74} +9.86107 q^{75} +19.9657 q^{76} +15.2159 q^{77} +5.76624 q^{78} +6.32969 q^{79} -18.7434 q^{80} -0.468358 q^{81} +18.3350 q^{82} -7.79387 q^{83} -13.3188 q^{84} -3.73374 q^{85} +2.48303 q^{86} +7.94668 q^{87} +28.2208 q^{88} +13.1696 q^{89} -16.5352 q^{90} +6.10404 q^{91} +24.5380 q^{92} +4.69200 q^{93} +27.4139 q^{94} -17.8965 q^{95} -1.88724 q^{96} -17.0924 q^{97} -3.48736 q^{98} +9.36105 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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