LMFDB - Embedded newform 5054.2.a.bk.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5054,2,Mod(1,5054)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5054, 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("5054.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.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:	$40.3563931816$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 15x^{7} + 40x^{6} + 81x^{5} - 162x^{4} - 205x^{3} + 204x^{2} + 210x + 1 $ x^9 - 3x^8 - 15x^7 + 40x^6 + 81x^5 - 162x^4 - 205x^3 + 204x^2 + 210x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 266)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.68026$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.68026 q^{3} +1.00000 q^{4} +3.48998 q^{5} +1.68026 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.176713 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.68026 q^{3} +1.00000 q^{4} +3.48998 q^{5} +1.68026 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.176713 q^{9} +3.48998 q^{10} +3.39629 q^{11} +1.68026 q^{12} -0.689655 q^{13} -1.00000 q^{14} +5.86408 q^{15} +1.00000 q^{16} +2.88746 q^{17} -0.176713 q^{18} +3.48998 q^{20} -1.68026 q^{21} +3.39629 q^{22} +4.65311 q^{23} +1.68026 q^{24} +7.17993 q^{25} -0.689655 q^{26} -5.33772 q^{27} -1.00000 q^{28} -1.60540 q^{29} +5.86408 q^{30} +7.34243 q^{31} +1.00000 q^{32} +5.70666 q^{33} +2.88746 q^{34} -3.48998 q^{35} -0.176713 q^{36} -3.01683 q^{37} -1.15880 q^{39} +3.48998 q^{40} -5.13535 q^{41} -1.68026 q^{42} -7.95466 q^{43} +3.39629 q^{44} -0.616724 q^{45} +4.65311 q^{46} +3.81955 q^{47} +1.68026 q^{48} +1.00000 q^{49} +7.17993 q^{50} +4.85170 q^{51} -0.689655 q^{52} +0.941732 q^{53} -5.33772 q^{54} +11.8530 q^{55} -1.00000 q^{56} -1.60540 q^{58} -12.1091 q^{59} +5.86408 q^{60} -7.54098 q^{61} +7.34243 q^{62} +0.176713 q^{63} +1.00000 q^{64} -2.40688 q^{65} +5.70666 q^{66} +11.8946 q^{67} +2.88746 q^{68} +7.81846 q^{69} -3.48998 q^{70} -14.4590 q^{71} -0.176713 q^{72} +9.42019 q^{73} -3.01683 q^{74} +12.0642 q^{75} -3.39629 q^{77} -1.15880 q^{78} -6.77068 q^{79} +3.48998 q^{80} -8.43863 q^{81} -5.13535 q^{82} -10.8114 q^{83} -1.68026 q^{84} +10.0772 q^{85} -7.95466 q^{86} -2.69749 q^{87} +3.39629 q^{88} +16.3262 q^{89} -0.616724 q^{90} +0.689655 q^{91} +4.65311 q^{92} +12.3372 q^{93} +3.81955 q^{94} +1.68026 q^{96} -6.89363 q^{97} +1.00000 q^{98} -0.600169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.68026	0.970101	0.485050	−	0.874486i	$-0.338801\pi$
$3$	1.68026	0.970101	0.485050	+	0.874486i	$0.338801\pi$
$4$	1.00000	0.500000
$5$	3.48998	1.56076	0.780382	−	0.625303i	$-0.215025\pi$
$5$	3.48998	1.56076	0.780382	+	0.625303i	$0.215025\pi$
$6$	1.68026	0.685965
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−0.176713	−0.0589044
$10$	3.48998	1.10363
$11$	3.39629	1.02402	0.512010	−	0.858980i	$-0.328901\pi$
$11$	3.39629	1.02402	0.512010	+	0.858980i	$0.328901\pi$
$12$	1.68026	0.485050
$13$	−0.689655	−0.191276	−0.0956379	−	0.995416i	$-0.530489\pi$
$13$	−0.689655	−0.191276	−0.0956379	+	0.995416i	$0.530489\pi$
$14$	−1.00000	−0.267261
$15$	5.86408	1.51410
$16$	1.00000	0.250000
$17$	2.88746	0.700313	0.350157	−	0.936691i	$-0.386128\pi$
$17$	2.88746	0.700313	0.350157	+	0.936691i	$0.386128\pi$
$18$	−0.176713	−0.0416517
$19$	0	0
$19$	0	0
$20$	3.48998	0.780382
$21$	−1.68026	−0.366664
$22$	3.39629	0.724091
$23$	4.65311	0.970241	0.485120	−	0.874447i	$-0.338776\pi$
$23$	4.65311	0.970241	0.485120	+	0.874447i	$0.338776\pi$
$24$	1.68026	0.342982
$25$	7.17993	1.43599
$26$	−0.689655	−0.135252
$27$	−5.33772	−1.02724
$28$	−1.00000	−0.188982
$29$	−1.60540	−0.298115	−0.149058	−	0.988829i	$-0.547624\pi$
$29$	−1.60540	−0.298115	−0.149058	+	0.988829i	$0.547624\pi$
$30$	5.86408	1.07063
$31$	7.34243	1.31874	0.659370	−	0.751819i	$-0.270823\pi$
$31$	7.34243	1.31874	0.659370	+	0.751819i	$0.270823\pi$
$32$	1.00000	0.176777
$33$	5.70666	0.993403
$34$	2.88746	0.495196
$35$	−3.48998	−0.589913
$36$	−0.176713	−0.0294522
$37$	−3.01683	−0.495964	−0.247982	−	0.968765i	$-0.579767\pi$
$37$	−3.01683	−0.495964	−0.247982	+	0.968765i	$0.579767\pi$
$38$	0	0
$39$	−1.15880	−0.185557
$40$	3.48998	0.551814
$41$	−5.13535	−0.802007	−0.401003	−	0.916077i	$-0.631338\pi$
$41$	−5.13535	−0.802007	−0.401003	+	0.916077i	$0.631338\pi$
$42$	−1.68026	−0.259270
$43$	−7.95466	−1.21307	−0.606537	−	0.795055i	$-0.707442\pi$
$43$	−7.95466	−1.21307	−0.606537	+	0.795055i	$0.707442\pi$
$44$	3.39629	0.512010
$45$	−0.616724	−0.0919359
$46$	4.65311	0.686064
$47$	3.81955	0.557138	0.278569	−	0.960416i	$-0.410140\pi$
$47$	3.81955	0.557138	0.278569	+	0.960416i	$0.410140\pi$
$48$	1.68026	0.242525
$49$	1.00000	0.142857
$50$	7.17993	1.01540
$51$	4.85170	0.679374
$52$	−0.689655	−0.0956379
$53$	0.941732	0.129357	0.0646784	−	0.997906i	$-0.479398\pi$
$53$	0.941732	0.129357	0.0646784	+	0.997906i	$0.479398\pi$
$54$	−5.33772	−0.726371
$55$	11.8530	1.59825
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−1.60540	−0.210799
$59$	−12.1091	−1.57647	−0.788237	−	0.615372i	$-0.789006\pi$
$59$	−12.1091	−1.57647	−0.788237	+	0.615372i	$0.789006\pi$
$60$	5.86408	0.757049
$61$	−7.54098	−0.965523	−0.482762	−	0.875752i	$-0.660366\pi$
$61$	−7.54098	−0.965523	−0.482762	+	0.875752i	$0.660366\pi$
$62$	7.34243	0.932490
$63$	0.176713	0.0222638
$64$	1.00000	0.125000
$65$	−2.40688	−0.298537
$66$	5.70666	0.702442
$67$	11.8946	1.45316	0.726580	−	0.687082i	$-0.241109\pi$
$67$	11.8946	1.45316	0.726580	+	0.687082i	$0.241109\pi$
$68$	2.88746	0.350157
$69$	7.81846	0.941232
$70$	−3.48998	−0.417132
$71$	−14.4590	−1.71596	−0.857982	−	0.513680i	$-0.828282\pi$
$71$	−14.4590	−1.71596	−0.857982	+	0.513680i	$0.828282\pi$
$72$	−0.176713	−0.0208258
$73$	9.42019	1.10255	0.551275	−	0.834324i	$-0.314142\pi$
$73$	9.42019	1.10255	0.551275	+	0.834324i	$0.314142\pi$
$74$	−3.01683	−0.350699
$75$	12.0642	1.39305
$76$	0	0
$77$	−3.39629	−0.387043
$78$	−1.15880	−0.131209
$79$	−6.77068	−0.761761	−0.380880	−	0.924624i	$-0.624379\pi$
$79$	−6.77068	−0.761761	−0.380880	+	0.924624i	$0.624379\pi$
$80$	3.48998	0.390191
$81$	−8.43863	−0.937626
$82$	−5.13535	−0.567104
$83$	−10.8114	−1.18671	−0.593354	−	0.804942i	$-0.702196\pi$
$83$	−10.8114	−1.18671	−0.593354	+	0.804942i	$0.702196\pi$
$84$	−1.68026	−0.183332
$85$	10.0772	1.09302
$86$	−7.95466	−0.857773
$87$	−2.69749	−0.289202
$88$	3.39629	0.362046
$89$	16.3262	1.73057	0.865286	−	0.501278i	$-0.167136\pi$
$89$	16.3262	1.73057	0.865286	+	0.501278i	$0.167136\pi$
$90$	−0.616724	−0.0650085
$91$	0.689655	0.0722955
$92$	4.65311	0.485120
$93$	12.3372	1.27931
$94$	3.81955	0.393956
$95$	0	0
$96$	1.68026	0.171491
$97$	−6.89363	−0.699942	−0.349971	−	0.936760i	$-0.613809\pi$
$97$	−6.89363	−0.699942	−0.349971	+	0.936760i	$0.613809\pi$
$98$	1.00000	0.101015
$99$	−0.600169	−0.0603193
$100$	7.17993	0.717993
$101$	16.8448	1.67612	0.838059	−	0.545579i	$-0.183690\pi$
$101$	16.8448	1.67612	0.838059	+	0.545579i	$0.183690\pi$
$102$	4.85170	0.480390
$103$	2.26179	0.222861	0.111431	−	0.993772i	$-0.464457\pi$
$103$	2.26179	0.222861	0.111431	+	0.993772i	$0.464457\pi$
$104$	−0.689655	−0.0676262
$105$	−5.86408	−0.572276
$106$	0.941732	0.0914691
$107$	6.54921	0.633136	0.316568	−	0.948570i	$-0.397469\pi$
$107$	6.54921	0.633136	0.316568	+	0.948570i	$0.397469\pi$
$108$	−5.33772	−0.513622
$109$	−11.7556	−1.12598	−0.562992	−	0.826462i	$-0.690350\pi$
$109$	−11.7556	−1.12598	−0.562992	+	0.826462i	$0.690350\pi$
$110$	11.8530	1.13014
$111$	−5.06907	−0.481135
$112$	−1.00000	−0.0944911
$113$	−9.30925	−0.875741	−0.437870	−	0.899038i	$-0.644267\pi$
$113$	−9.30925	−0.875741	−0.437870	+	0.899038i	$0.644267\pi$
$114$	0	0
$115$	16.2392	1.51432
$116$	−1.60540	−0.149058
$117$	0.121871	0.0112670
$118$	−12.1091	−1.11474
$119$	−2.88746	−0.264693
$120$	5.86408	0.535315
$121$	0.534784	0.0486168
$122$	−7.54098	−0.682728
$123$	−8.62874	−0.778028
$124$	7.34243	0.659370
$125$	7.60789	0.680471
$126$	0.176713	0.0157429
$127$	16.6108	1.47397	0.736984	−	0.675910i	$-0.236249\pi$
$127$	16.6108	1.47397	0.736984	+	0.675910i	$0.236249\pi$
$128$	1.00000	0.0883883
$129$	−13.3659	−1.17680
$130$	−2.40688	−0.211097
$131$	11.5822	1.01194	0.505970	−	0.862551i	$-0.331135\pi$
$131$	11.5822	1.01194	0.505970	+	0.862551i	$0.331135\pi$
$132$	5.70666	0.496701
$133$	0	0
$134$	11.8946	1.02754
$135$	−18.6285	−1.60329
$136$	2.88746	0.247598
$137$	21.0197	1.79583	0.897915	−	0.440168i	$-0.145081\pi$
$137$	21.0197	1.79583	0.897915	+	0.440168i	$0.145081\pi$
$138$	7.81846	0.665551
$139$	−6.52778	−0.553679	−0.276840	−	0.960916i	$-0.589287\pi$
$139$	−6.52778	−0.553679	−0.276840	+	0.960916i	$0.589287\pi$
$140$	−3.48998	−0.294957
$141$	6.41785	0.540480
$142$	−14.4590	−1.21337
$143$	−2.34227	−0.195870
$144$	−0.176713	−0.0147261
$145$	−5.60280	−0.465288
$146$	9.42019	0.779620
$147$	1.68026	0.138586
$148$	−3.01683	−0.247982
$149$	13.4227	1.09963	0.549817	−	0.835285i	$-0.314698\pi$
$149$	13.4227	1.09963	0.549817	+	0.835285i	$0.314698\pi$
$150$	12.0642	0.985036
$151$	4.76894	0.388091	0.194045	−	0.980993i	$-0.437839\pi$
$151$	4.76894	0.388091	0.194045	+	0.980993i	$0.437839\pi$
$152$	0	0
$153$	−0.510253	−0.0412515
$154$	−3.39629	−0.273681
$155$	25.6249	2.05824
$156$	−1.15880	−0.0927784
$157$	−20.9559	−1.67247	−0.836233	−	0.548374i	$-0.815247\pi$
$157$	−20.9559	−1.67247	−0.836233	+	0.548374i	$0.815247\pi$
$158$	−6.77068	−0.538646
$159$	1.58236	0.125489
$160$	3.48998	0.275907
$161$	−4.65311	−0.366717
$162$	−8.43863	−0.663002
$163$	−2.35017	−0.184080	−0.0920398	−	0.995755i	$-0.529339\pi$
$163$	−2.35017	−0.184080	−0.0920398	+	0.995755i	$0.529339\pi$
$164$	−5.13535	−0.401003
$165$	19.9161	1.55047
$166$	−10.8114	−0.839129
$167$	3.74996	0.290180	0.145090	−	0.989418i	$-0.453653\pi$
$167$	3.74996	0.290180	0.145090	+	0.989418i	$0.453653\pi$
$168$	−1.68026	−0.129635
$169$	−12.5244	−0.963414
$170$	10.0772	0.772884
$171$	0	0
$172$	−7.95466	−0.606537
$173$	6.24646	0.474910	0.237455	−	0.971399i	$-0.423687\pi$
$173$	6.24646	0.474910	0.237455	+	0.971399i	$0.423687\pi$
$174$	−2.69749	−0.204497
$175$	−7.17993	−0.542751
$176$	3.39629	0.256005
$177$	−20.3465	−1.52934
$178$	16.3262	1.22370
$179$	7.63841	0.570921	0.285461	−	0.958390i	$-0.407853\pi$
$179$	7.63841	0.570921	0.285461	+	0.958390i	$0.407853\pi$
$180$	−0.616724	−0.0459679
$181$	−22.6168	−1.68110	−0.840548	−	0.541737i	$-0.817767\pi$
$181$	−22.6168	−1.68110	−0.840548	+	0.541737i	$0.817767\pi$
$182$	0.689655	0.0511206
$183$	−12.6708	−0.936655
$184$	4.65311	0.343032
$185$	−10.5287	−0.774082
$186$	12.3372	0.904609
$187$	9.80667	0.717134
$188$	3.81955	0.278569
$189$	5.33772	0.388262
$190$	0	0
$191$	−23.7771	−1.72045	−0.860224	−	0.509916i	$-0.829677\pi$
$191$	−23.7771	−1.72045	−0.860224	+	0.509916i	$0.829677\pi$
$192$	1.68026	0.121263
$193$	15.5606	1.12007	0.560037	−	0.828467i	$-0.310787\pi$
$193$	15.5606	1.12007	0.560037	+	0.828467i	$0.310787\pi$
$194$	−6.89363	−0.494934
$195$	−4.04419	−0.289611
$196$	1.00000	0.0714286
$197$	21.8936	1.55986	0.779928	−	0.625870i	$-0.215256\pi$
$197$	21.8936	1.55986	0.779928	+	0.625870i	$0.215256\pi$
$198$	−0.600169	−0.0426522
$199$	−22.3108	−1.58157	−0.790784	−	0.612095i	$-0.790327\pi$
$199$	−22.3108	−1.58157	−0.790784	+	0.612095i	$0.790327\pi$
$200$	7.17993	0.507698
$201$	19.9861	1.40971
$202$	16.8448	1.18519
$203$	1.60540	0.112677
$204$	4.85170	0.339687
$205$	−17.9222	−1.25174
$206$	2.26179	0.157587
$207$	−0.822266	−0.0571514
$208$	−0.689655	−0.0478190
$209$	0	0
$210$	−5.86408	−0.404660
$211$	4.82440	0.332126	0.166063	−	0.986115i	$-0.446895\pi$
$211$	4.82440	0.332126	0.166063	+	0.986115i	$0.446895\pi$
$212$	0.941732	0.0646784
$213$	−24.2949	−1.66466
$214$	6.54921	0.447695
$215$	−27.7616	−1.89332
$216$	−5.33772	−0.363186
$217$	−7.34243	−0.498437
$218$	−11.7556	−0.796191
$219$	15.8284	1.06958
$220$	11.8530	0.799127
$221$	−1.99135	−0.133953
$222$	−5.06907	−0.340214
$223$	−21.9964	−1.47299	−0.736494	−	0.676444i	$-0.763520\pi$
$223$	−21.9964	−1.47299	−0.736494	+	0.676444i	$0.763520\pi$
$224$	−1.00000	−0.0668153
$225$	−1.26879	−0.0845858
$226$	−9.30925	−0.619242
$227$	3.63096	0.240995	0.120498	−	0.992714i	$-0.461551\pi$
$227$	3.63096	0.240995	0.120498	+	0.992714i	$0.461551\pi$
$228$	0	0
$229$	−0.204306	−0.0135009	−0.00675046	−	0.999977i	$-0.502149\pi$
$229$	−0.204306	−0.0135009	−0.00675046	+	0.999977i	$0.502149\pi$
$230$	16.2392	1.07078
$231$	−5.70666	−0.375471
$232$	−1.60540	−0.105400
$233$	17.8115	1.16687	0.583435	−	0.812160i	$-0.301708\pi$
$233$	17.8115	1.16687	0.583435	+	0.812160i	$0.301708\pi$
$234$	0.121871	0.00796696
$235$	13.3301	0.869562
$236$	−12.1091	−0.788237
$237$	−11.3765	−0.738985
$238$	−2.88746	−0.187167
$239$	3.97020	0.256811	0.128405	−	0.991722i	$-0.459014\pi$
$239$	3.97020	0.256811	0.128405	+	0.991722i	$0.459014\pi$
$240$	5.86408	0.378525
$241$	0.358185	0.0230727	0.0115364	−	0.999933i	$-0.496328\pi$
$241$	0.358185	0.0230727	0.0115364	+	0.999933i	$0.496328\pi$
$242$	0.534784	0.0343772
$243$	1.83402	0.117652
$244$	−7.54098	−0.482762
$245$	3.48998	0.222966
$246$	−8.62874	−0.550149
$247$	0	0
$248$	7.34243	0.466245
$249$	−18.1660	−1.15123
$250$	7.60789	0.481165
$251$	5.11467	0.322835	0.161418	−	0.986886i	$-0.448393\pi$
$251$	5.11467	0.322835	0.161418	+	0.986886i	$0.448393\pi$
$252$	0.176713	0.0111319
$253$	15.8033	0.993546
$254$	16.6108	1.04225
$255$	16.9323	1.06034
$256$	1.00000	0.0625000
$257$	4.19016	0.261375	0.130688	−	0.991424i	$-0.458282\pi$
$257$	4.19016	0.261375	0.130688	+	0.991424i	$0.458282\pi$
$258$	−13.3659	−0.832126
$259$	3.01683	0.187457
$260$	−2.40688	−0.149268
$261$	0.283695	0.0175603
$262$	11.5822	0.715549
$263$	−17.5806	−1.08407	−0.542033	−	0.840357i	$-0.682345\pi$
$263$	−17.5806	−1.08407	−0.542033	+	0.840357i	$0.682345\pi$
$264$	5.70666	0.351221
$265$	3.28662	0.201896
$266$	0	0
$267$	27.4323	1.67883
$268$	11.8946	0.726580
$269$	3.49809	0.213283	0.106641	−	0.994298i	$-0.465990\pi$
$269$	3.49809	0.213283	0.106641	+	0.994298i	$0.465990\pi$
$270$	−18.6285	−1.13369
$271$	25.5059	1.54937	0.774686	−	0.632346i	$-0.217908\pi$
$271$	25.5059	1.54937	0.774686	+	0.632346i	$0.217908\pi$
$272$	2.88746	0.175078
$273$	1.15880	0.0701339
$274$	21.0197	1.26984
$275$	24.3851	1.47048
$276$	7.81846	0.470616
$277$	−7.92644	−0.476254	−0.238127	−	0.971234i	$-0.576533\pi$
$277$	−7.92644	−0.476254	−0.238127	+	0.971234i	$0.576533\pi$
$278$	−6.52778	−0.391510
$279$	−1.29750	−0.0776795
$280$	−3.48998	−0.208566
$281$	−29.6221	−1.76710	−0.883552	−	0.468333i	$-0.844855\pi$
$281$	−29.6221	−1.76710	−0.883552	+	0.468333i	$0.844855\pi$
$282$	6.41785	0.382177
$283$	7.05452	0.419347	0.209674	−	0.977771i	$-0.432760\pi$
$283$	7.05452	0.419347	0.209674	+	0.977771i	$0.432760\pi$
$284$	−14.4590	−0.857982
$285$	0	0
$286$	−2.34227	−0.138501
$287$	5.13535	0.303130
$288$	−0.176713	−0.0104129
$289$	−8.66255	−0.509562
$290$	−5.60280	−0.329008
$291$	−11.5831	−0.679015
$292$	9.42019	0.551275
$293$	−20.1525	−1.17732	−0.588662	−	0.808380i	$-0.700345\pi$
$293$	−20.1525	−1.17732	−0.588662	+	0.808380i	$0.700345\pi$
$294$	1.68026	0.0979950
$295$	−42.2606	−2.46050
$296$	−3.01683	−0.175350
$297$	−18.1284	−1.05192
$298$	13.4227	0.777558
$299$	−3.20904	−0.185584
$300$	12.0642	0.696525
$301$	7.95466	0.458499
$302$	4.76894	0.274421
$303$	28.3037	1.62600
$304$	0	0
$305$	−26.3178	−1.50695
$306$	−0.510253	−0.0291692
$307$	1.41021	0.0804850	0.0402425	−	0.999190i	$-0.487187\pi$
$307$	1.41021	0.0804850	0.0402425	+	0.999190i	$0.487187\pi$
$308$	−3.39629	−0.193522
$309$	3.80041	0.216198
$310$	25.6249	1.45540
$311$	−14.7950	−0.838945	−0.419473	−	0.907768i	$-0.637785\pi$
$311$	−14.7950	−0.838945	−0.419473	+	0.907768i	$0.637785\pi$
$312$	−1.15880	−0.0656043
$313$	−27.1116	−1.53244	−0.766219	−	0.642579i	$-0.777864\pi$
$313$	−27.1116	−1.53244	−0.766219	+	0.642579i	$0.777864\pi$
$314$	−20.9559	−1.18261
$315$	0.616724	0.0347485
$316$	−6.77068	−0.380880
$317$	2.37051	0.133141	0.0665704	−	0.997782i	$-0.478794\pi$
$317$	2.37051	0.133141	0.0665704	+	0.997782i	$0.478794\pi$
$318$	1.58236	0.0887343
$319$	−5.45240	−0.305276
$320$	3.48998	0.195096
$321$	11.0044	0.614206
$322$	−4.65311	−0.259308
$323$	0	0
$324$	−8.43863	−0.468813
$325$	−4.95167	−0.274669
$326$	−2.35017	−0.130164
$327$	−19.7526	−1.09232
$328$	−5.13535	−0.283552
$329$	−3.81955	−0.210579
$330$	19.9161	1.09635
$331$	−25.8400	−1.42030	−0.710148	−	0.704053i	$-0.751372\pi$
$331$	−25.8400	−1.42030	−0.710148	+	0.704053i	$0.751372\pi$
$332$	−10.8114	−0.593354
$333$	0.533113	0.0292144
$334$	3.74996	0.205188
$335$	41.5120	2.26804
$336$	−1.68026	−0.0916659
$337$	−18.3868	−1.00159	−0.500797	−	0.865565i	$-0.666960\pi$
$337$	−18.3868	−1.00159	−0.500797	+	0.865565i	$0.666960\pi$
$338$	−12.5244	−0.681236
$339$	−15.6420	−0.849557
$340$	10.0772	0.546512
$341$	24.9370	1.35042
$342$	0	0
$343$	−1.00000	−0.0539949
$344$	−7.95466	−0.428886
$345$	27.2862	1.46904
$346$	6.24646	0.335812
$347$	7.13482	0.383017	0.191509	−	0.981491i	$-0.438662\pi$
$347$	7.13482	0.383017	0.191509	+	0.981491i	$0.438662\pi$
$348$	−2.69749	−0.144601
$349$	11.1665	0.597731	0.298865	−	0.954295i	$-0.403392\pi$
$349$	11.1665	0.597731	0.298865	+	0.954295i	$0.403392\pi$
$350$	−7.17993	−0.383783
$351$	3.68118	0.196487
$352$	3.39629	0.181023
$353$	−10.0350	−0.534111	−0.267056	−	0.963681i	$-0.586051\pi$
$353$	−10.0350	−0.534111	−0.267056	+	0.963681i	$0.586051\pi$
$354$	−20.3465	−1.08141
$355$	−50.4614	−2.67821
$356$	16.3262	0.865286
$357$	−4.85170	−0.256779
$358$	7.63841	0.403702
$359$	24.8227	1.31009	0.655047	−	0.755588i	$-0.272649\pi$
$359$	24.8227	1.31009	0.655047	+	0.755588i	$0.272649\pi$
$360$	−0.616724	−0.0325042
$361$	0	0
$362$	−22.6168	−1.18871
$363$	0.898579	0.0471632
$364$	0.689655	0.0361477
$365$	32.8762	1.72082
$366$	−12.6708	−0.662315
$367$	30.4226	1.58805	0.794024	−	0.607887i	$-0.207983\pi$
$367$	30.4226	1.58805	0.794024	+	0.607887i	$0.207983\pi$
$368$	4.65311	0.242560
$369$	0.907484	0.0472417
$370$	−10.5287	−0.547359
$371$	−0.941732	−0.0488923
$372$	12.3372	0.639655
$373$	−28.4573	−1.47346	−0.736731	−	0.676186i	$-0.763631\pi$
$373$	−28.4573	−1.47346	−0.736731	+	0.676186i	$0.763631\pi$
$374$	9.80667	0.507091
$375$	12.7833	0.660125
$376$	3.81955	0.196978
$377$	1.10717	0.0570222
$378$	5.33772	0.274543
$379$	−12.0271	−0.617793	−0.308896	−	0.951096i	$-0.599960\pi$
$379$	−12.0271	−0.617793	−0.308896	+	0.951096i	$0.599960\pi$
$380$	0	0
$381$	27.9105	1.42990
$382$	−23.7771	−1.21654
$383$	−29.6410	−1.51458	−0.757291	−	0.653077i	$-0.773478\pi$
$383$	−29.6410	−1.51458	−0.757291	+	0.653077i	$0.773478\pi$
$384$	1.68026	0.0857456
$385$	−11.8530	−0.604083
$386$	15.5606	0.792012
$387$	1.40569	0.0714553
$388$	−6.89363	−0.349971
$389$	20.1294	1.02060	0.510301	−	0.859996i	$-0.329534\pi$
$389$	20.1294	1.02060	0.510301	+	0.859996i	$0.329534\pi$
$390$	−4.04419	−0.204786
$391$	13.4357	0.679472
$392$	1.00000	0.0505076
$393$	19.4611	0.981683
$394$	21.8936	1.10298
$395$	−23.6295	−1.18893
$396$	−0.600169	−0.0301596
$397$	−27.2986	−1.37008	−0.685040	−	0.728506i	$-0.740215\pi$
$397$	−27.2986	−1.37008	−0.685040	+	0.728506i	$0.740215\pi$
$398$	−22.3108	−1.11834
$399$	0	0
$400$	7.17993	0.358996
$401$	−25.9371	−1.29524	−0.647619	−	0.761964i	$-0.724235\pi$
$401$	−25.9371	−1.29524	−0.647619	+	0.761964i	$0.724235\pi$
$402$	19.9861	0.996817
$403$	−5.06374	−0.252243
$404$	16.8448	0.838059
$405$	−29.4506	−1.46341
$406$	1.60540	0.0796746
$407$	−10.2460	−0.507877
$408$	4.85170	0.240195
$409$	−12.7602	−0.630950	−0.315475	−	0.948934i	$-0.602164\pi$
$409$	−12.7602	−0.630950	−0.315475	+	0.948934i	$0.602164\pi$
$410$	−17.9222	−0.885116
$411$	35.3186	1.74214
$412$	2.26179	0.111431
$413$	12.1091	0.595851
$414$	−0.822266	−0.0404122
$415$	−37.7316	−1.85217
$416$	−0.689655	−0.0338131
$417$	−10.9684	−0.537125
$418$	0	0
$419$	−0.115955	−0.00566476	−0.00283238	−	0.999996i	$-0.500902\pi$
$419$	−0.115955	−0.00566476	−0.00283238	+	0.999996i	$0.500902\pi$
$420$	−5.86408	−0.286138
$421$	10.6381	0.518468	0.259234	−	0.965815i	$-0.416530\pi$
$421$	10.6381	0.518468	0.259234	+	0.965815i	$0.416530\pi$
$422$	4.82440	0.234848
$423$	−0.674964	−0.0328179
$424$	0.941732	0.0457346
$425$	20.7318	1.00564
$426$	−24.2949	−1.17709
$427$	7.54098	0.364934
$428$	6.54921	0.316568
$429$	−3.93563	−0.190014
$430$	−27.7616	−1.33878
$431$	38.4040	1.84986	0.924928	−	0.380141i	$-0.124125\pi$
$431$	38.4040	1.84986	0.924928	+	0.380141i	$0.124125\pi$
$432$	−5.33772	−0.256811
$433$	−8.35880	−0.401698	−0.200849	−	0.979622i	$-0.564370\pi$
$433$	−8.35880	−0.401698	−0.200849	+	0.979622i	$0.564370\pi$
$434$	−7.34243	−0.352448
$435$	−9.41419	−0.451376
$436$	−11.7556	−0.562992
$437$	0	0
$438$	15.8284	0.756310
$439$	12.5914	0.600957	0.300478	−	0.953789i	$-0.402854\pi$
$439$	12.5914	0.600957	0.300478	+	0.953789i	$0.402854\pi$
$440$	11.8530	0.565068
$441$	−0.176713	−0.00841491
$442$	−1.99135	−0.0947191
$443$	−19.5771	−0.930138	−0.465069	−	0.885275i	$-0.653970\pi$
$443$	−19.5771	−0.930138	−0.465069	+	0.885275i	$0.653970\pi$
$444$	−5.06907	−0.240567
$445$	56.9780	2.70102
$446$	−21.9964	−1.04156
$447$	22.5537	1.06676
$448$	−1.00000	−0.0472456
$449$	−27.1213	−1.27993	−0.639966	−	0.768403i	$-0.721052\pi$
$449$	−27.1213	−1.27993	−0.639966	+	0.768403i	$0.721052\pi$
$450$	−1.26879	−0.0598112
$451$	−17.4411	−0.821271
$452$	−9.30925	−0.437870
$453$	8.01307	0.376487
$454$	3.63096	0.170409
$455$	2.40688	0.112836
$456$	0	0
$457$	1.11528	0.0521705	0.0260853	−	0.999660i	$-0.491696\pi$
$457$	1.11528	0.0521705	0.0260853	+	0.999660i	$0.491696\pi$
$458$	−0.204306	−0.00954660
$459$	−15.4125	−0.719392
$460$	16.2392	0.757159
$461$	−0.280736	−0.0130752	−0.00653760	−	0.999979i	$-0.502081\pi$
$461$	−0.280736	−0.0130752	−0.00653760	+	0.999979i	$0.502081\pi$
$462$	−5.70666	−0.265498
$463$	−36.2163	−1.68311	−0.841557	−	0.540168i	$-0.818361\pi$
$463$	−36.2163	−1.68311	−0.841557	+	0.540168i	$0.818361\pi$
$464$	−1.60540	−0.0745288
$465$	43.0566	1.99670
$466$	17.8115	0.825102
$467$	29.5871	1.36913	0.684564	−	0.728953i	$-0.259993\pi$
$467$	29.5871	1.36913	0.684564	+	0.728953i	$0.259993\pi$
$468$	0.121871	0.00563349
$469$	−11.8946	−0.549243
$470$	13.3301	0.614873
$471$	−35.2115	−1.62246
$472$	−12.1091	−0.557368
$473$	−27.0163	−1.24221
$474$	−11.3765	−0.522541
$475$	0	0
$476$	−2.88746	−0.132347
$477$	−0.166416	−0.00761968
$478$	3.97020	0.181593
$479$	23.7225	1.08391	0.541955	−	0.840407i	$-0.317684\pi$
$479$	23.7225	1.08391	0.541955	+	0.840407i	$0.317684\pi$
$480$	5.86408	0.267657
$481$	2.08057	0.0948659
$482$	0.358185	0.0163149
$483$	−7.81846	−0.355752
$484$	0.534784	0.0243084
$485$	−24.0586	−1.09245
$486$	1.83402	0.0831928
$487$	10.0545	0.455614	0.227807	−	0.973706i	$-0.426844\pi$
$487$	10.0545	0.455614	0.227807	+	0.973706i	$0.426844\pi$
$488$	−7.54098	−0.341364
$489$	−3.94891	−0.178576
$490$	3.48998	0.157661
$491$	3.92303	0.177044	0.0885219	−	0.996074i	$-0.471786\pi$
$491$	3.92303	0.177044	0.0885219	+	0.996074i	$0.471786\pi$
$492$	−8.62874	−0.389014
$493$	−4.63553	−0.208774
$494$	0	0
$495$	−2.09457	−0.0941441
$496$	7.34243	0.329685
$497$	14.4590	0.648573
$498$	−18.1660	−0.814039
$499$	3.44042	0.154014	0.0770072	−	0.997031i	$-0.475464\pi$
$499$	3.44042	0.154014	0.0770072	+	0.997031i	$0.475464\pi$
$500$	7.60789	0.340235
$501$	6.30091	0.281504
$502$	5.11467	0.228279
$503$	8.48714	0.378423	0.189212	−	0.981936i	$-0.439407\pi$
$503$	8.48714	0.378423	0.189212	+	0.981936i	$0.439407\pi$
$504$	0.176713	0.00787143
$505$	58.7879	2.61603
$506$	15.8033	0.702543
$507$	−21.0443	−0.934608
$508$	16.6108	0.736984
$509$	−16.1141	−0.714244	−0.357122	−	0.934058i	$-0.616242\pi$
$509$	−16.1141	−0.714244	−0.357122	+	0.934058i	$0.616242\pi$
$510$	16.9323	0.749776
$511$	−9.42019	−0.416725
$512$	1.00000	0.0441942
$513$	0	0
$514$	4.19016	0.184820
$515$	7.89360	0.347834
$516$	−13.3659	−0.588402
$517$	12.9723	0.570521
$518$	3.01683	0.132552
$519$	10.4957	0.460710
$520$	−2.40688	−0.105549
$521$	−24.2652	−1.06308	−0.531539	−	0.847034i	$-0.678386\pi$
$521$	−24.2652	−1.06308	−0.531539	+	0.847034i	$0.678386\pi$
$522$	0.283695	0.0124170
$523$	−10.5030	−0.459265	−0.229633	−	0.973277i	$-0.573752\pi$
$523$	−10.5030	−0.459265	−0.229633	+	0.973277i	$0.573752\pi$
$524$	11.5822	0.505970
$525$	−12.0642	−0.526524
$526$	−17.5806	−0.766550
$527$	21.2010	0.923531
$528$	5.70666	0.248351
$529$	−1.34855	−0.0586326
$530$	3.28662	0.142762
$531$	2.13984	0.0928612
$532$	0	0
$533$	3.54162	0.153405
$534$	27.4323	1.18711
$535$	22.8566	0.988177
$536$	11.8946	0.513770
$537$	12.8345	0.553851
$538$	3.49809	0.150814
$539$	3.39629	0.146289
$540$	−18.6285	−0.801643
$541$	20.4591	0.879607	0.439803	−	0.898094i	$-0.355048\pi$
$541$	20.4591	0.879607	0.439803	+	0.898094i	$0.355048\pi$
$542$	25.5059	1.09557
$543$	−38.0023	−1.63083
$544$	2.88746	0.123799
$545$	−41.0268	−1.75740
$546$	1.15880	0.0495922
$547$	5.46907	0.233841	0.116920	−	0.993141i	$-0.462698\pi$
$547$	5.46907	0.233841	0.116920	+	0.993141i	$0.462698\pi$
$548$	21.0197	0.897915
$549$	1.33259	0.0568736
$550$	24.3851	1.03978
$551$	0	0
$552$	7.81846	0.332776
$553$	6.77068	0.287919
$554$	−7.92644	−0.336762
$555$	−17.6909	−0.750938
$556$	−6.52778	−0.276840
$557$	14.6076	0.618944	0.309472	−	0.950908i	$-0.399848\pi$
$557$	14.6076	0.618944	0.309472	+	0.950908i	$0.399848\pi$
$558$	−1.29750	−0.0549277
$559$	5.48597	0.232032
$560$	−3.48998	−0.147478
$561$	16.4778	0.695693
$562$	−29.6221	−1.24953
$563$	29.4767	1.24229	0.621147	−	0.783694i	$-0.286667\pi$
$563$	29.4767	1.24229	0.621147	+	0.783694i	$0.286667\pi$
$564$	6.41785	0.270240
$565$	−32.4891	−1.36682
$566$	7.05452	0.296523
$567$	8.43863	0.354389
$568$	−14.4590	−0.606685
$569$	−30.0973	−1.26175	−0.630873	−	0.775886i	$-0.717303\pi$
$569$	−30.0973	−1.26175	−0.630873	+	0.775886i	$0.717303\pi$
$570$	0	0
$571$	39.6038	1.65737	0.828684	−	0.559717i	$-0.189090\pi$
$571$	39.6038	1.65737	0.828684	+	0.559717i	$0.189090\pi$
$572$	−2.34227	−0.0979352
$573$	−39.9518	−1.66901
$574$	5.13535	0.214345
$575$	33.4090	1.39325
$576$	−0.176713	−0.00736305
$577$	2.46977	0.102818	0.0514089	−	0.998678i	$-0.483629\pi$
$577$	2.46977	0.102818	0.0514089	+	0.998678i	$0.483629\pi$
$578$	−8.66255	−0.360314
$579$	26.1459	1.08659
$580$	−5.60280	−0.232644
$581$	10.8114	0.448533
$582$	−11.5831	−0.480136
$583$	3.19840	0.132464
$584$	9.42019	0.389810
$585$	0.425327	0.0175851
$586$	−20.1525	−0.832493
$587$	25.7334	1.06213	0.531065	−	0.847331i	$-0.321792\pi$
$587$	25.7334	1.06213	0.531065	+	0.847331i	$0.321792\pi$
$588$	1.68026	0.0692929
$589$	0	0
$590$	−42.2606	−1.73984
$591$	36.7871	1.51322
$592$	−3.01683	−0.123991
$593$	1.02120	0.0419355	0.0209678	−	0.999780i	$-0.493325\pi$
$593$	1.02120	0.0419355	0.0209678	+	0.999780i	$0.493325\pi$
$594$	−18.1284	−0.743819
$595$	−10.0772	−0.413124
$596$	13.4227	0.549817
$597$	−37.4880	−1.53428
$598$	−3.20904	−0.131227
$599$	25.7829	1.05346	0.526730	−	0.850032i	$-0.323418\pi$
$599$	25.7829	1.05346	0.526730	+	0.850032i	$0.323418\pi$
$600$	12.0642	0.492518
$601$	−24.3998	−0.995288	−0.497644	−	0.867381i	$-0.665801\pi$
$601$	−24.3998	−0.995288	−0.497644	+	0.867381i	$0.665801\pi$
$602$	7.95466	0.324208
$603$	−2.10194	−0.0855975
$604$	4.76894	0.194045
$605$	1.86638	0.0758793
$606$	28.3037	1.14976
$607$	−21.8819	−0.888160	−0.444080	−	0.895987i	$-0.646469\pi$
$607$	−21.8819	−0.888160	−0.444080	+	0.895987i	$0.646469\pi$
$608$	0	0
$609$	2.69749	0.109308
$610$	−26.3178	−1.06558
$611$	−2.63417	−0.106567
$612$	−0.510253	−0.0206258
$613$	−15.6713	−0.632958	−0.316479	−	0.948600i	$-0.602501\pi$
$613$	−15.6713	−0.632958	−0.316479	+	0.948600i	$0.602501\pi$
$614$	1.41021	0.0569115
$615$	−30.1141	−1.21432
$616$	−3.39629	−0.136840
$617$	−8.26343	−0.332673	−0.166337	−	0.986069i	$-0.553194\pi$
$617$	−8.26343	−0.332673	−0.166337	+	0.986069i	$0.553194\pi$
$618$	3.80041	0.152875
$619$	0.641159	0.0257704	0.0128852	−	0.999917i	$-0.495898\pi$
$619$	0.641159	0.0257704	0.0128852	+	0.999917i	$0.495898\pi$
$620$	25.6249	1.02912
$621$	−24.8370	−0.996674
$622$	−14.7950	−0.593224
$623$	−16.3262	−0.654095
$624$	−1.15880	−0.0463892
$625$	−9.34828	−0.373931
$626$	−27.1116	−1.08360
$627$	0	0
$628$	−20.9559	−0.836233
$629$	−8.71099	−0.347330
$630$	0.616724	0.0245709
$631$	22.3543	0.889910	0.444955	−	0.895553i	$-0.353220\pi$
$631$	22.3543	0.889910	0.444955	+	0.895553i	$0.353220\pi$
$632$	−6.77068	−0.269323
$633$	8.10627	0.322195
$634$	2.37051	0.0941448
$635$	57.9712	2.30052
$636$	1.58236	0.0627446
$637$	−0.689655	−0.0273251
$638$	−5.45240	−0.215863
$639$	2.55509	0.101078
$640$	3.48998	0.137953
$641$	15.7553	0.622297	0.311149	−	0.950361i	$-0.399286\pi$
$641$	15.7553	0.622297	0.311149	+	0.950361i	$0.399286\pi$
$642$	11.0044	0.434309
$643$	10.8379	0.427404	0.213702	−	0.976899i	$-0.431448\pi$
$643$	10.8379	0.427404	0.213702	+	0.976899i	$0.431448\pi$
$644$	−4.65311	−0.183358
$645$	−46.6467	−1.83671
$646$	0	0
$647$	−24.7859	−0.974433	−0.487216	−	0.873281i	$-0.661988\pi$
$647$	−24.7859	−0.974433	−0.487216	+	0.873281i	$0.661988\pi$
$648$	−8.43863	−0.331501
$649$	−41.1261	−1.61434
$650$	−4.95167	−0.194221
$651$	−12.3372	−0.483534
$652$	−2.35017	−0.0920398
$653$	−22.6663	−0.887000	−0.443500	−	0.896274i	$-0.646263\pi$
$653$	−22.6663	−0.887000	−0.443500	+	0.896274i	$0.646263\pi$
$654$	−19.7526	−0.772386
$655$	40.4215	1.57940
$656$	−5.13535	−0.200502
$657$	−1.66467	−0.0649450
$658$	−3.81955	−0.148901
$659$	−34.7770	−1.35472	−0.677360	−	0.735651i	$-0.736876\pi$
$659$	−34.7770	−1.35472	−0.677360	+	0.735651i	$0.736876\pi$
$660$	19.9161	0.775234
$661$	5.20698	0.202528	0.101264	−	0.994860i	$-0.467711\pi$
$661$	5.20698	0.202528	0.101264	+	0.994860i	$0.467711\pi$
$662$	−25.8400	−1.00430
$663$	−3.34600	−0.129948
$664$	−10.8114	−0.419564
$665$	0	0
$666$	0.533113	0.0206577
$667$	−7.47010	−0.289244
$668$	3.74996	0.145090
$669$	−36.9598	−1.42895
$670$	41.5120	1.60375
$671$	−25.6114	−0.988715
$672$	−1.68026	−0.0648176
$673$	44.3153	1.70823	0.854115	−	0.520085i	$-0.174100\pi$
$673$	44.3153	1.70823	0.854115	+	0.520085i	$0.174100\pi$
$674$	−18.3868	−0.708234
$675$	−38.3244	−1.47511
$676$	−12.5244	−0.481707
$677$	5.91698	0.227408	0.113704	−	0.993515i	$-0.463728\pi$
$677$	5.91698	0.227408	0.113704	+	0.993515i	$0.463728\pi$
$678$	−15.6420	−0.600727
$679$	6.89363	0.264553
$680$	10.0772	0.386442
$681$	6.10097	0.233790
$682$	24.9370	0.954888
$683$	30.7379	1.17615	0.588077	−	0.808805i	$-0.299885\pi$
$683$	30.7379	1.17615	0.588077	+	0.808805i	$0.299885\pi$
$684$	0	0
$685$	73.3581	2.80287
$686$	−1.00000	−0.0381802
$687$	−0.343288	−0.0130973
$688$	−7.95466	−0.303268
$689$	−0.649470	−0.0247428
$690$	27.2862	1.03877
$691$	39.3506	1.49697	0.748484	−	0.663152i	$-0.230782\pi$
$691$	39.3506	1.49697	0.748484	+	0.663152i	$0.230782\pi$
$692$	6.24646	0.237455
$693$	0.600169	0.0227985
$694$	7.13482	0.270834
$695$	−22.7818	−0.864163
$696$	−2.69749	−0.102248
$697$	−14.8281	−0.561656
$698$	11.1665	0.422659
$699$	29.9280	1.13198
$700$	−7.17993	−0.271376
$701$	−1.21837	−0.0460171	−0.0230085	−	0.999735i	$-0.507324\pi$
$701$	−1.21837	−0.0460171	−0.0230085	+	0.999735i	$0.507324\pi$
$702$	3.68118	0.138937
$703$	0	0
$704$	3.39629	0.128002
$705$	22.3981	0.843563
$706$	−10.0350	−0.377674
$707$	−16.8448	−0.633513
$708$	−20.3465	−0.764669
$709$	26.0610	0.978743	0.489372	−	0.872075i	$-0.337226\pi$
$709$	26.0610	0.978743	0.489372	+	0.872075i	$0.337226\pi$
$710$	−50.4614	−1.89378
$711$	1.19647	0.0448710
$712$	16.3262	0.611850
$713$	34.1652	1.27950
$714$	−4.85170	−0.181570
$715$	−8.17446	−0.305707
$716$	7.63841	0.285461
$717$	6.67098	0.249132
$718$	24.8227	0.926376
$719$	17.2836	0.644568	0.322284	−	0.946643i	$-0.395549\pi$
$719$	17.2836	0.644568	0.322284	+	0.946643i	$0.395549\pi$
$720$	−0.616724	−0.0229840
$721$	−2.26179	−0.0842336
$722$	0	0
$723$	0.601845	0.0223829
$724$	−22.6168	−0.840548
$725$	−11.5267	−0.428089
$726$	0.898579	0.0333494
$727$	34.1745	1.26746	0.633731	−	0.773554i	$-0.281523\pi$
$727$	34.1745	1.26746	0.633731	+	0.773554i	$0.281523\pi$
$728$	0.689655	0.0255603
$729$	28.3975	1.05176
$730$	32.8762	1.21680
$731$	−22.9688	−0.849531
$732$	−12.6708	−0.468328
$733$	−26.5053	−0.978995	−0.489498	−	0.872005i	$-0.662820\pi$
$733$	−26.5053	−0.978995	−0.489498	+	0.872005i	$0.662820\pi$
$734$	30.4226	1.12292
$735$	5.86408	0.216300
$736$	4.65311	0.171516
$737$	40.3976	1.48806
$738$	0.907484	0.0334049
$739$	−18.7405	−0.689379	−0.344689	−	0.938717i	$-0.612016\pi$
$739$	−18.7405	−0.689379	−0.344689	+	0.938717i	$0.612016\pi$
$740$	−10.5287	−0.387041
$741$	0	0
$742$	−0.941732	−0.0345721
$743$	19.1640	0.703057	0.351529	−	0.936177i	$-0.385662\pi$
$743$	19.1640	0.703057	0.351529	+	0.936177i	$0.385662\pi$
$744$	12.3372	0.452305
$745$	46.8450	1.71627
$746$	−28.4573	−1.04189
$747$	1.91052	0.0699022
$748$	9.80667	0.358567
$749$	−6.54921	−0.239303
$750$	12.7833	0.466779
$751$	−11.9599	−0.436423	−0.218212	−	0.975901i	$-0.570022\pi$
$751$	−11.9599	−0.436423	−0.218212	+	0.975901i	$0.570022\pi$
$752$	3.81955	0.139285
$753$	8.59400	0.313183
$754$	1.10717	0.0403208
$755$	16.6435	0.605718
$756$	5.33772	0.194131
$757$	−26.3942	−0.959314	−0.479657	−	0.877456i	$-0.659239\pi$
$757$	−26.3942	−0.959314	−0.479657	+	0.877456i	$0.659239\pi$
$758$	−12.0271	−0.436846
$759$	26.5537	0.963840
$760$	0	0
$761$	38.3862	1.39150	0.695749	−	0.718285i	$-0.255073\pi$
$761$	38.3862	1.39150	0.695749	+	0.718285i	$0.255073\pi$
$762$	27.9105	1.01109
$763$	11.7556	0.425582
$764$	−23.7771	−0.860224
$765$	−1.78077	−0.0643839
$766$	−29.6410	−1.07097
$767$	8.35112	0.301541
$768$	1.68026	0.0606313
$769$	−50.5607	−1.82327	−0.911633	−	0.411004i	$-0.865178\pi$
$769$	−50.5607	−1.82327	−0.911633	+	0.411004i	$0.865178\pi$
$770$	−11.8530	−0.427151
$771$	7.04058	0.253560
$772$	15.5606	0.560037
$773$	27.2357	0.979602	0.489801	−	0.871834i	$-0.337070\pi$
$773$	27.2357	0.979602	0.489801	+	0.871834i	$0.337070\pi$
$774$	1.40569	0.0505266
$775$	52.7181	1.89369
$776$	−6.89363	−0.247467
$777$	5.06907	0.181852
$778$	20.1294	0.721675
$779$	0	0
$780$	−4.04419	−0.144805
$781$	−49.1068	−1.75718
$782$	13.4357	0.480460
$783$	8.56917	0.306237
$784$	1.00000	0.0357143
$785$	−73.1357	−2.61033
$786$	19.4611	0.694155
$787$	−13.3012	−0.474138	−0.237069	−	0.971493i	$-0.576187\pi$
$787$	−13.3012	−0.474138	−0.237069	+	0.971493i	$0.576187\pi$
$788$	21.8936	0.779928
$789$	−29.5400	−1.05165
$790$	−23.6295	−0.840700
$791$	9.30925	0.330999
$792$	−0.600169	−0.0213261
$793$	5.20067	0.184681
$794$	−27.2986	−0.968792
$795$	5.52239	0.195859
$796$	−22.3108	−0.790784
$797$	−16.4985	−0.584407	−0.292203	−	0.956356i	$-0.594388\pi$
$797$	−16.4985	−0.584407	−0.292203	+	0.956356i	$0.594388\pi$
$798$	0	0
$799$	11.0288	0.390171
$800$	7.17993	0.253849
$801$	−2.88505	−0.101938
$802$	−25.9371	−0.915871
$803$	31.9937	1.12903
$804$	19.9861	0.704856
$805$	−16.2392	−0.572358
$806$	−5.06374	−0.178363
$807$	5.87772	0.206906
$808$	16.8448	0.592597
$809$	−27.5917	−0.970072	−0.485036	−	0.874494i	$-0.661193\pi$
$809$	−27.5917	−0.970072	−0.485036	+	0.874494i	$0.661193\pi$
$810$	−29.4506	−1.03479
$811$	26.0545	0.914898	0.457449	−	0.889236i	$-0.348763\pi$
$811$	26.0545	0.914898	0.457449	+	0.889236i	$0.348763\pi$
$812$	1.60540	0.0563385
$813$	42.8566	1.50305
$814$	−10.2460	−0.359123
$815$	−8.20204	−0.287305
$816$	4.85170	0.169844
$817$	0	0
$818$	−12.7602	−0.446149
$819$	−0.121871	−0.00425852
$820$	−17.9222	−0.625872
$821$	15.5586	0.542998	0.271499	−	0.962439i	$-0.412481\pi$
$821$	15.5586	0.542998	0.271499	+	0.962439i	$0.412481\pi$
$822$	35.3186	1.23188
$823$	−31.4462	−1.09615	−0.548073	−	0.836430i	$-0.684639\pi$
$823$	−31.4462	−1.09615	−0.548073	+	0.836430i	$0.684639\pi$
$824$	2.26179	0.0787933
$825$	40.9734	1.42651
$826$	12.1091	0.421330
$827$	−24.6101	−0.855777	−0.427888	−	0.903832i	$-0.640742\pi$
$827$	−24.6101	−0.855777	−0.427888	+	0.903832i	$0.640742\pi$
$828$	−0.822266	−0.0285757
$829$	12.5367	0.435419	0.217709	−	0.976014i	$-0.430142\pi$
$829$	12.5367	0.435419	0.217709	+	0.976014i	$0.430142\pi$
$830$	−37.7316	−1.30968
$831$	−13.3185	−0.462014
$832$	−0.689655	−0.0239095
$833$	2.88746	0.100045
$834$	−10.9684	−0.379805
$835$	13.0873	0.452903
$836$	0	0
$837$	−39.1918	−1.35467
$838$	−0.115955	−0.00400559
$839$	−0.582206	−0.0201000	−0.0100500	−	0.999949i	$-0.503199\pi$
$839$	−0.582206	−0.0201000	−0.0100500	+	0.999949i	$0.503199\pi$
$840$	−5.86408	−0.202330
$841$	−26.4227	−0.911127
$842$	10.6381	0.366612
$843$	−49.7729	−1.71427
$844$	4.82440	0.166063
$845$	−43.7098	−1.50366
$846$	−0.674964	−0.0232057
$847$	−0.534784	−0.0183754
$848$	0.941732	0.0323392
$849$	11.8534	0.406809
$850$	20.7318	0.711094
$851$	−14.0376	−0.481204
$852$	−24.2949	−0.832329
$853$	34.8925	1.19470	0.597348	−	0.801982i	$-0.296221\pi$
$853$	34.8925	1.19470	0.597348	+	0.801982i	$0.296221\pi$
$854$	7.54098	0.258047
$855$	0	0
$856$	6.54921	0.223847
$857$	39.2447	1.34057	0.670287	−	0.742102i	$-0.266171\pi$
$857$	39.2447	1.34057	0.670287	+	0.742102i	$0.266171\pi$
$858$	−3.93563	−0.134360
$859$	24.0746	0.821416	0.410708	−	0.911767i	$-0.365282\pi$
$859$	24.0746	0.821416	0.410708	+	0.911767i	$0.365282\pi$
$860$	−27.7616	−0.946661
$861$	8.62874	0.294067
$862$	38.4040	1.30805
$863$	29.4492	1.00246	0.501231	−	0.865314i	$-0.332881\pi$
$863$	29.4492	1.00246	0.501231	+	0.865314i	$0.332881\pi$
$864$	−5.33772	−0.181593
$865$	21.8000	0.741222
$866$	−8.35880	−0.284044
$867$	−14.5554	−0.494326
$868$	−7.34243	−0.249218
$869$	−22.9952	−0.780058
$870$	−9.41419	−0.319171
$871$	−8.20319	−0.277954
$872$	−11.7556	−0.398096
$873$	1.21820	0.0412297
$874$	0	0
$875$	−7.60789	−0.257194
$876$	15.8284	0.534792
$877$	−53.9131	−1.82052	−0.910258	−	0.414042i	$-0.864117\pi$
$877$	−53.9131	−1.82052	−0.910258	+	0.414042i	$0.864117\pi$
$878$	12.5914	0.424941
$879$	−33.8616	−1.14212
$880$	11.8530	0.399563
$881$	−53.9199	−1.81661	−0.908303	−	0.418312i	$-0.862622\pi$
$881$	−53.9199	−1.81661	−0.908303	+	0.418312i	$0.862622\pi$
$882$	−0.176713	−0.00595024
$883$	−30.7925	−1.03625	−0.518125	−	0.855305i	$-0.673370\pi$
$883$	−30.7925	−1.03625	−0.518125	+	0.855305i	$0.673370\pi$
$884$	−1.99135	−0.0669765
$885$	−71.0089	−2.38694
$886$	−19.5771	−0.657707
$887$	37.7996	1.26919	0.634593	−	0.772847i	$-0.281168\pi$
$887$	37.7996	1.26919	0.634593	+	0.772847i	$0.281168\pi$
$888$	−5.06907	−0.170107
$889$	−16.6108	−0.557107
$890$	56.9780	1.90991
$891$	−28.6600	−0.960148
$892$	−21.9964	−0.736494
$893$	0	0
$894$	22.5537	0.754310
$895$	26.6578	0.891074
$896$	−1.00000	−0.0334077
$897$	−5.39204	−0.180035
$898$	−27.1213	−0.905048
$899$	−11.7875	−0.393136
$900$	−1.26879	−0.0422929
$901$	2.71922	0.0905903
$902$	−17.4411	−0.580726
$903$	13.3659	0.444790
$904$	−9.30925	−0.309621
$905$	−78.9322	−2.62380
$906$	8.01307	0.266216
$907$	−10.9140	−0.362393	−0.181196	−	0.983447i	$-0.557997\pi$
$907$	−10.9140	−0.362393	−0.181196	+	0.983447i	$0.557997\pi$
$908$	3.63096	0.120498
$909$	−2.97669	−0.0987307
$910$	2.40688	0.0797873
$911$	2.95818	0.0980090	0.0490045	−	0.998799i	$-0.484395\pi$
$911$	2.95818	0.0980090	0.0490045	+	0.998799i	$0.484395\pi$
$912$	0	0
$913$	−36.7187	−1.21521
$914$	1.11528	0.0368901
$915$	−44.2209	−1.46190
$916$	−0.204306	−0.00675046
$917$	−11.5822	−0.382477
$918$	−15.4125	−0.508687
$919$	18.7666	0.619053	0.309526	−	0.950891i	$-0.399830\pi$
$919$	18.7666	0.619053	0.309526	+	0.950891i	$0.399830\pi$
$920$	16.2392	0.535392
$921$	2.36953	0.0780786
$922$	−0.280736	−0.00924556
$923$	9.97170	0.328222
$924$	−5.70666	−0.187735
$925$	−21.6606	−0.712197
$926$	−36.2163	−1.19014
$927$	−0.399689	−0.0131275
$928$	−1.60540	−0.0526998
$929$	−21.1530	−0.694006	−0.347003	−	0.937864i	$-0.612801\pi$
$929$	−21.1530	−0.694006	−0.347003	+	0.937864i	$0.612801\pi$
$930$	43.0566	1.41188
$931$	0	0
$932$	17.8115	0.583435
$933$	−24.8594	−0.813861
$934$	29.5871	0.968120
$935$	34.2250	1.11928
$936$	0.121871	0.00398348
$937$	46.7568	1.52748	0.763740	−	0.645524i	$-0.223361\pi$
$937$	46.7568	1.52748	0.763740	+	0.645524i	$0.223361\pi$
$938$	−11.8946	−0.388373
$939$	−45.5547	−1.48662
$940$	13.3301	0.434781
$941$	13.5928	0.443112	0.221556	−	0.975148i	$-0.428886\pi$
$941$	13.5928	0.443112	0.221556	+	0.975148i	$0.428886\pi$
$942$	−35.2115	−1.14725
$943$	−23.8954	−0.778140
$944$	−12.1091	−0.394119
$945$	18.6285	0.605985
$946$	−27.0163	−0.878376
$947$	−24.6730	−0.801763	−0.400882	−	0.916130i	$-0.631296\pi$
$947$	−24.6730	−0.801763	−0.400882	+	0.916130i	$0.631296\pi$
$948$	−11.3765	−0.369492
$949$	−6.49668	−0.210891
$950$	0	0
$951$	3.98308	0.129160
$952$	−2.88746	−0.0935833
$953$	−8.40107	−0.272137	−0.136069	−	0.990699i	$-0.543447\pi$
$953$	−8.40107	−0.272137	−0.136069	+	0.990699i	$0.543447\pi$
$954$	−0.166416	−0.00538793
$955$	−82.9814	−2.68521
$956$	3.97020	0.128405
$957$	−9.16147	−0.296148
$958$	23.7225	0.766440
$959$	−21.0197	−0.678760
$960$	5.86408	0.189262
$961$	22.9113	0.739074
$962$	2.08057	0.0670803
$963$	−1.15733	−0.0372945
$964$	0.358185	0.0115364
$965$	54.3060	1.74817
$966$	−7.81846	−0.251555
$967$	−18.0716	−0.581144	−0.290572	−	0.956853i	$-0.593846\pi$
$967$	−18.0716	−0.581144	−0.290572	+	0.956853i	$0.593846\pi$
$968$	0.534784	0.0171886
$969$	0	0
$970$	−24.0586	−0.772475
$971$	29.0402	0.931945	0.465973	−	0.884799i	$-0.345704\pi$
$971$	29.0402	0.931945	0.465973	+	0.884799i	$0.345704\pi$
$972$	1.83402	0.0588262
$973$	6.52778	0.209271
$974$	10.0545	0.322168
$975$	−8.32012	−0.266457
$976$	−7.54098	−0.241381
$977$	−13.6288	−0.436024	−0.218012	−	0.975946i	$-0.569957\pi$
$977$	−13.6288	−0.436024	−0.218012	+	0.975946i	$0.569957\pi$
$978$	−3.94891	−0.126272
$979$	55.4485	1.77214
$980$	3.48998	0.111483
$981$	2.07737	0.0663254
$982$	3.92303	0.125189
$983$	−2.63813	−0.0841433	−0.0420716	−	0.999115i	$-0.513396\pi$
$983$	−2.63813	−0.0841433	−0.0420716	+	0.999115i	$0.513396\pi$
$984$	−8.62874	−0.275074
$985$	76.4082	2.43457
$986$	−4.63553	−0.147625
$987$	−6.41785	−0.204282
$988$	0	0
$989$	−37.0139	−1.17697
$990$	−2.09457	−0.0665700
$991$	20.9202	0.664553	0.332276	−	0.943182i	$-0.392183\pi$
$991$	20.9202	0.664553	0.332276	+	0.943182i	$0.392183\pi$
$992$	7.34243	0.233122
$993$	−43.4180	−1.37783
$994$	14.4590	0.458611
$995$	−77.8640	−2.46846
$996$	−18.1660	−0.575613
$997$	34.5148	1.09309	0.546547	−	0.837428i	$-0.315942\pi$
$997$	34.5148	1.09309	0.546547	+	0.837428i	$0.315942\pi$
$998$	3.44042	0.108905
$999$	16.1030	0.509476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.bk.1.6		9
19.9	even	9		266.2.u.c.43.2	✓	18
19.17	even	9		266.2.u.c.99.2	yes	18
19.18	odd	2		5054.2.a.bj.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
266.2.u.c.43.2	✓	18	19.9	even	9
266.2.u.c.99.2	yes	18	19.17	even	9
5054.2.a.bj.1.4		9	19.18	odd	2
5054.2.a.bk.1.6		9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.68026 q^{3} +1.00000 q^{4} +3.48998 q^{5} +1.68026 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.176713 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.68026 q^{3} +1.00000 q^{4} +3.48998 q^{5} +1.68026 q^{6} -1.00000 q^{7} +1.00000 q^{8} -0.176713 q^{9} +3.48998 q^{10} +3.39629 q^{11} +1.68026 q^{12} -0.689655 q^{13} -1.00000 q^{14} +5.86408 q^{15} +1.00000 q^{16} +2.88746 q^{17} -0.176713 q^{18} +3.48998 q^{20} -1.68026 q^{21} +3.39629 q^{22} +4.65311 q^{23} +1.68026 q^{24} +7.17993 q^{25} -0.689655 q^{26} -5.33772 q^{27} -1.00000 q^{28} -1.60540 q^{29} +5.86408 q^{30} +7.34243 q^{31} +1.00000 q^{32} +5.70666 q^{33} +2.88746 q^{34} -3.48998 q^{35} -0.176713 q^{36} -3.01683 q^{37} -1.15880 q^{39} +3.48998 q^{40} -5.13535 q^{41} -1.68026 q^{42} -7.95466 q^{43} +3.39629 q^{44} -0.616724 q^{45} +4.65311 q^{46} +3.81955 q^{47} +1.68026 q^{48} +1.00000 q^{49} +7.17993 q^{50} +4.85170 q^{51} -0.689655 q^{52} +0.941732 q^{53} -5.33772 q^{54} +11.8530 q^{55} -1.00000 q^{56} -1.60540 q^{58} -12.1091 q^{59} +5.86408 q^{60} -7.54098 q^{61} +7.34243 q^{62} +0.176713 q^{63} +1.00000 q^{64} -2.40688 q^{65} +5.70666 q^{66} +11.8946 q^{67} +2.88746 q^{68} +7.81846 q^{69} -3.48998 q^{70} -14.4590 q^{71} -0.176713 q^{72} +9.42019 q^{73} -3.01683 q^{74} +12.0642 q^{75} -3.39629 q^{77} -1.15880 q^{78} -6.77068 q^{79} +3.48998 q^{80} -8.43863 q^{81} -5.13535 q^{82} -10.8114 q^{83} -1.68026 q^{84} +10.0772 q^{85} -7.95466 q^{86} -2.69749 q^{87} +3.39629 q^{88} +16.3262 q^{89} -0.616724 q^{90} +0.689655 q^{91} +4.65311 q^{92} +12.3372 q^{93} +3.81955 q^{94} +1.68026 q^{96} -6.89363 q^{97} +1.00000 q^{98} -0.600169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9	\( 9 q + 9 q^{2} + 3 q^{3} + 9 q^{4} + 3 q^{5} + 3 q^{6} - 9 q^{7} + 9 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} + 3 q^{12} + 12 q^{13} - 9 q^{14} - 6 q^{15} + 9 q^{16} + 12 q^{17} + 12 q^{18} + 3 q^{20} - 3 q^{21} - 3 q^{22} + 6 q^{23} + 3 q^{24} + 12 q^{26} + 24 q^{27} - 9 q^{28} - 6 q^{29} - 6 q^{30} + 9 q^{31} + 9 q^{32} - 3 q^{33} + 12 q^{34} - 3 q^{35} + 12 q^{36} + 9 q^{37} + 33 q^{39} + 3 q^{40} + 3 q^{41} - 3 q^{42} + 21 q^{43} - 3 q^{44} + 18 q^{45} + 6 q^{46} + 21 q^{47} + 3 q^{48} + 9 q^{49} + 39 q^{51} + 12 q^{52} + 24 q^{54} + 24 q^{55} - 9 q^{56} - 6 q^{58} - 9 q^{59} - 6 q^{60} + 6 q^{61} + 9 q^{62} - 12 q^{63} + 9 q^{64} - 3 q^{65} - 3 q^{66} + 27 q^{67} + 12 q^{68} + 6 q^{69} - 3 q^{70} + 9 q^{71} + 12 q^{72} + 51 q^{73} + 9 q^{74} - 3 q^{75} + 3 q^{77} + 33 q^{78} + 24 q^{79} + 3 q^{80} - 3 q^{81} + 3 q^{82} + 9 q^{83} - 3 q^{84} + 6 q^{85} + 21 q^{86} - 3 q^{87} - 3 q^{88} + 9 q^{89} + 18 q^{90} - 12 q^{91} + 6 q^{92} + 3 q^{93} + 21 q^{94} + 3 q^{96} - 12 q^{97} + 9 q^{98} - 15 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 3 * q^3 + 9 * q^4 + 3 * q^5 + 3 * q^6 - 9 * q^7 + 9 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 + 3 * q^12 + 12 * q^13 - 9 * q^14 - 6 * q^15 + 9 * q^16 + 12 * q^17 + 12 * q^18 + 3 * q^20 - 3 * q^21 - 3 * q^22 + 6 * q^23 + 3 * q^24 + 12 * q^26 + 24 * q^27 - 9 * q^28 - 6 * q^29 - 6 * q^30 + 9 * q^31 + 9 * q^32 - 3 * q^33 + 12 * q^34 - 3 * q^35 + 12 * q^36 + 9 * q^37 + 33 * q^39 + 3 * q^40 + 3 * q^41 - 3 * q^42 + 21 * q^43 - 3 * q^44 + 18 * q^45 + 6 * q^46 + 21 * q^47 + 3 * q^48 + 9 * q^49 + 39 * q^51 + 12 * q^52 + 24 * q^54 + 24 * q^55 - 9 * q^56 - 6 * q^58 - 9 * q^59 - 6 * q^60 + 6 * q^61 + 9 * q^62 - 12 * q^63 + 9 * q^64 - 3 * q^65 - 3 * q^66 + 27 * q^67 + 12 * q^68 + 6 * q^69 - 3 * q^70 + 9 * q^71 + 12 * q^72 + 51 * q^73 + 9 * q^74 - 3 * q^75 + 3 * q^77 + 33 * q^78 + 24 * q^79 + 3 * q^80 - 3 * q^81 + 3 * q^82 + 9 * q^83 - 3 * q^84 + 6 * q^85 + 21 * q^86 - 3 * q^87 - 3 * q^88 + 9 * q^89 + 18 * q^90 - 12 * q^91 + 6 * q^92 + 3 * q^93 + 21 * q^94 + 3 * q^96 - 12 * q^97 + 9 * q^98 - 15 * q^99

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