LMFDB - Embedded newform 6026.2.a.h.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.41227 q^{3} +1.00000 q^{4} +0.460247 q^{5} +2.41227 q^{6} -4.49457 q^{7} -1.00000 q^{8} +2.81904 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.41227 q^{3} +1.00000 q^{4} +0.460247 q^{5} +2.41227 q^{6} -4.49457 q^{7} -1.00000 q^{8} +2.81904 q^{9} -0.460247 q^{10} -2.62582 q^{11} -2.41227 q^{12} +0.877859 q^{13} +4.49457 q^{14} -1.11024 q^{15} +1.00000 q^{16} +0.794105 q^{17} -2.81904 q^{18} +0.648378 q^{19} +0.460247 q^{20} +10.8421 q^{21} +2.62582 q^{22} -1.00000 q^{23} +2.41227 q^{24} -4.78817 q^{25} -0.877859 q^{26} +0.436529 q^{27} -4.49457 q^{28} +2.58114 q^{29} +1.11024 q^{30} -6.97168 q^{31} -1.00000 q^{32} +6.33418 q^{33} -0.794105 q^{34} -2.06861 q^{35} +2.81904 q^{36} +7.43390 q^{37} -0.648378 q^{38} -2.11763 q^{39} -0.460247 q^{40} +1.59484 q^{41} -10.8421 q^{42} -1.00435 q^{43} -2.62582 q^{44} +1.29745 q^{45} +1.00000 q^{46} -8.71767 q^{47} -2.41227 q^{48} +13.2012 q^{49} +4.78817 q^{50} -1.91559 q^{51} +0.877859 q^{52} +8.84706 q^{53} -0.436529 q^{54} -1.20853 q^{55} +4.49457 q^{56} -1.56406 q^{57} -2.58114 q^{58} +3.77789 q^{59} -1.11024 q^{60} +3.78698 q^{61} +6.97168 q^{62} -12.6704 q^{63} +1.00000 q^{64} +0.404032 q^{65} -6.33418 q^{66} +14.9876 q^{67} +0.794105 q^{68} +2.41227 q^{69} +2.06861 q^{70} -6.81686 q^{71} -2.81904 q^{72} +8.09734 q^{73} -7.43390 q^{74} +11.5504 q^{75} +0.648378 q^{76} +11.8019 q^{77} +2.11763 q^{78} -11.8233 q^{79} +0.460247 q^{80} -9.51014 q^{81} -1.59484 q^{82} +14.8328 q^{83} +10.8421 q^{84} +0.365484 q^{85} +1.00435 q^{86} -6.22639 q^{87} +2.62582 q^{88} -9.69816 q^{89} -1.29745 q^{90} -3.94560 q^{91} -1.00000 q^{92} +16.8176 q^{93} +8.71767 q^{94} +0.298414 q^{95} +2.41227 q^{96} -3.98455 q^{97} -13.2012 q^{98} -7.40229 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.41227	−1.39272	−0.696362	−	0.717691i	$-0.745199\pi$
$3$	−2.41227	−1.39272	−0.696362	+	0.717691i	$0.745199\pi$
$4$	1.00000	0.500000
$5$	0.460247	0.205829	0.102914	−	0.994690i	$-0.467183\pi$
$5$	0.460247	0.205829	0.102914	+	0.994690i	$0.467183\pi$
$6$	2.41227	0.984804
$7$	−4.49457	−1.69879	−0.849395	−	0.527758i	$-0.823033\pi$
$7$	−4.49457	−1.69879	−0.849395	+	0.527758i	$0.823033\pi$
$8$	−1.00000	−0.353553
$9$	2.81904	0.939679
$10$	−0.460247	−0.145543
$11$	−2.62582	−0.791714	−0.395857	−	0.918312i	$-0.629552\pi$
$11$	−2.62582	−0.791714	−0.395857	+	0.918312i	$0.629552\pi$
$12$	−2.41227	−0.696362
$13$	0.877859	0.243474	0.121737	−	0.992562i	$-0.461153\pi$
$13$	0.877859	0.243474	0.121737	+	0.992562i	$0.461153\pi$
$14$	4.49457	1.20123
$15$	−1.11024	−0.286662
$16$	1.00000	0.250000
$17$	0.794105	0.192599	0.0962994	−	0.995352i	$-0.469299\pi$
$17$	0.794105	0.192599	0.0962994	+	0.995352i	$0.469299\pi$
$18$	−2.81904	−0.664454
$19$	0.648378	0.148748	0.0743741	−	0.997230i	$-0.476304\pi$
$19$	0.648378	0.148748	0.0743741	+	0.997230i	$0.476304\pi$
$20$	0.460247	0.102914
$21$	10.8421	2.36594
$22$	2.62582	0.559827
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.41227	0.492402
$25$	−4.78817	−0.957635
$26$	−0.877859	−0.172162
$27$	0.436529	0.0840101
$28$	−4.49457	−0.849395
$29$	2.58114	0.479305	0.239652	−	0.970859i	$-0.422967\pi$
$29$	2.58114	0.479305	0.239652	+	0.970859i	$0.422967\pi$
$30$	1.11024	0.202701
$31$	−6.97168	−1.25215	−0.626075	−	0.779763i	$-0.715340\pi$
$31$	−6.97168	−1.25215	−0.626075	+	0.779763i	$0.715340\pi$
$32$	−1.00000	−0.176777
$33$	6.33418	1.10264
$34$	−0.794105	−0.136188
$35$	−2.06861	−0.349659
$36$	2.81904	0.469840
$37$	7.43390	1.22213	0.611063	−	0.791582i	$-0.290742\pi$
$37$	7.43390	1.22213	0.611063	+	0.791582i	$0.290742\pi$
$38$	−0.648378	−0.105181
$39$	−2.11763	−0.339093
$40$	−0.460247	−0.0727714
$41$	1.59484	0.249072	0.124536	−	0.992215i	$-0.460256\pi$
$41$	1.59484	0.249072	0.124536	+	0.992215i	$0.460256\pi$
$42$	−10.8421	−1.67298
$43$	−1.00435	−0.153161	−0.0765807	−	0.997063i	$-0.524400\pi$
$43$	−1.00435	−0.153161	−0.0765807	+	0.997063i	$0.524400\pi$
$44$	−2.62582	−0.395857
$45$	1.29745	0.193413
$46$	1.00000	0.147442
$47$	−8.71767	−1.27160	−0.635802	−	0.771853i	$-0.719330\pi$
$47$	−8.71767	−1.27160	−0.635802	+	0.771853i	$0.719330\pi$
$48$	−2.41227	−0.348181
$49$	13.2012	1.88589
$50$	4.78817	0.677150
$51$	−1.91559	−0.268237
$52$	0.877859	0.121737
$53$	8.84706	1.21524	0.607619	−	0.794229i	$-0.292125\pi$
$53$	8.84706	1.21524	0.607619	+	0.794229i	$0.292125\pi$
$54$	−0.436529	−0.0594041
$55$	−1.20853	−0.162958
$56$	4.49457	0.600613
$57$	−1.56406	−0.207165
$58$	−2.58114	−0.338920
$59$	3.77789	0.491840	0.245920	−	0.969290i	$-0.420910\pi$
$59$	3.77789	0.491840	0.245920	+	0.969290i	$0.420910\pi$
$60$	−1.11024	−0.143331
$61$	3.78698	0.484873	0.242437	−	0.970167i	$-0.422053\pi$
$61$	3.78698	0.484873	0.242437	+	0.970167i	$0.422053\pi$
$62$	6.97168	0.885404
$63$	−12.6704	−1.59632
$64$	1.00000	0.125000
$65$	0.404032	0.0501140
$66$	−6.33418	−0.779684
$67$	14.9876	1.83103	0.915515	−	0.402285i	$-0.131784\pi$
$67$	14.9876	1.83103	0.915515	+	0.402285i	$0.131784\pi$
$68$	0.794105	0.0962994
$69$	2.41227	0.290403
$70$	2.06861	0.247247
$71$	−6.81686	−0.809012	−0.404506	−	0.914535i	$-0.632557\pi$
$71$	−6.81686	−0.809012	−0.404506	+	0.914535i	$0.632557\pi$
$72$	−2.81904	−0.332227
$73$	8.09734	0.947723	0.473861	−	0.880600i	$-0.342860\pi$
$73$	8.09734	0.947723	0.473861	+	0.880600i	$0.342860\pi$
$74$	−7.43390	−0.864173
$75$	11.5504	1.33372
$76$	0.648378	0.0743741
$77$	11.8019	1.34496
$78$	2.11763	0.239775
$79$	−11.8233	−1.33022	−0.665110	−	0.746745i	$-0.731615\pi$
$79$	−11.8233	−1.33022	−0.665110	+	0.746745i	$0.731615\pi$
$80$	0.460247	0.0514572
$81$	−9.51014	−1.05668
$82$	−1.59484	−0.176121
$83$	14.8328	1.62811	0.814054	−	0.580789i	$-0.197256\pi$
$83$	14.8328	1.62811	0.814054	+	0.580789i	$0.197256\pi$
$84$	10.8421	1.18297
$85$	0.365484	0.0396423
$86$	1.00435	0.108301
$87$	−6.22639	−0.667539
$88$	2.62582	0.279913
$89$	−9.69816	−1.02800	−0.514001	−	0.857789i	$-0.671837\pi$
$89$	−9.69816	−1.02800	−0.514001	+	0.857789i	$0.671837\pi$
$90$	−1.29745	−0.136764
$91$	−3.94560	−0.413612
$92$	−1.00000	−0.104257
$93$	16.8176	1.74390
$94$	8.71767	0.899159
$95$	0.298414	0.0306166
$96$	2.41227	0.246201
$97$	−3.98455	−0.404570	−0.202285	−	0.979327i	$-0.564837\pi$
$97$	−3.98455	−0.404570	−0.202285	+	0.979327i	$0.564837\pi$
$98$	−13.2012	−1.33352
$99$	−7.40229	−0.743958
$100$	−4.78817	−0.478817
$101$	2.57846	0.256566	0.128283	−	0.991738i	$-0.459053\pi$
$101$	2.57846	0.256566	0.128283	+	0.991738i	$0.459053\pi$
$102$	1.91559	0.189672
$103$	11.5301	1.13610	0.568049	−	0.822995i	$-0.307699\pi$
$103$	11.5301	1.13610	0.568049	+	0.822995i	$0.307699\pi$
$104$	−0.877859	−0.0860812
$105$	4.99005	0.486979
$106$	−8.84706	−0.859303
$107$	−0.677536	−0.0654999	−0.0327499	−	0.999464i	$-0.510426\pi$
$107$	−0.677536	−0.0654999	−0.0327499	+	0.999464i	$0.510426\pi$
$108$	0.436529	0.0420050
$109$	13.4069	1.28415	0.642074	−	0.766643i	$-0.278074\pi$
$109$	13.4069	1.28415	0.642074	+	0.766643i	$0.278074\pi$
$110$	1.20853	0.115228
$111$	−17.9326	−1.70208
$112$	−4.49457	−0.424697
$113$	−2.04836	−0.192693	−0.0963467	−	0.995348i	$-0.530716\pi$
$113$	−2.04836	−0.192693	−0.0963467	+	0.995348i	$0.530716\pi$
$114$	1.56406	0.146488
$115$	−0.460247	−0.0429182
$116$	2.58114	0.239652
$117$	2.47472	0.228788
$118$	−3.77789	−0.347783
$119$	−3.56916	−0.327185
$120$	1.11024	0.101350
$121$	−4.10507	−0.373188
$122$	−3.78698	−0.342857
$123$	−3.84718	−0.346889
$124$	−6.97168	−0.626075
$125$	−4.50498	−0.402937
$126$	12.6704	1.12877
$127$	6.60663	0.586244	0.293122	−	0.956075i	$-0.405306\pi$
$127$	6.60663	0.586244	0.293122	+	0.956075i	$0.405306\pi$
$128$	−1.00000	−0.0883883
$129$	2.42275	0.213312
$130$	−0.404032	−0.0354359
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	6.33418	0.551320
$133$	−2.91418	−0.252692
$134$	−14.9876	−1.29473
$135$	0.200911	0.0172917
$136$	−0.794105	−0.0680939
$137$	8.31080	0.710039	0.355020	−	0.934859i	$-0.384474\pi$
$137$	8.31080	0.710039	0.355020	+	0.934859i	$0.384474\pi$
$138$	−2.41227	−0.205346
$139$	−0.604721	−0.0512918	−0.0256459	−	0.999671i	$-0.508164\pi$
$139$	−0.604721	−0.0512918	−0.0256459	+	0.999671i	$0.508164\pi$
$140$	−2.06861	−0.174830
$141$	21.0294	1.77099
$142$	6.81686	0.572058
$143$	−2.30510	−0.192762
$144$	2.81904	0.234920
$145$	1.18796	0.0986547
$146$	−8.09734	−0.670141
$147$	−31.8448	−2.62652
$148$	7.43390	0.611063
$149$	−2.18608	−0.179091	−0.0895455	−	0.995983i	$-0.528541\pi$
$149$	−2.18608	−0.179091	−0.0895455	+	0.995983i	$0.528541\pi$
$150$	−11.5504	−0.943083
$151$	−15.3419	−1.24851	−0.624253	−	0.781222i	$-0.714597\pi$
$151$	−15.3419	−1.24851	−0.624253	+	0.781222i	$0.714597\pi$
$152$	−0.648378	−0.0525904
$153$	2.23861	0.180981
$154$	−11.8019	−0.951028
$155$	−3.20869	−0.257728
$156$	−2.11763	−0.169546
$157$	−11.1164	−0.887185	−0.443593	−	0.896229i	$-0.646296\pi$
$157$	−11.1164	−0.887185	−0.443593	+	0.896229i	$0.646296\pi$
$158$	11.8233	0.940608
$159$	−21.3415	−1.69249
$160$	−0.460247	−0.0363857
$161$	4.49457	0.354222
$162$	9.51014	0.747187
$163$	12.8532	1.00674	0.503371	−	0.864070i	$-0.332093\pi$
$163$	12.8532	1.00674	0.503371	+	0.864070i	$0.332093\pi$
$164$	1.59484	0.124536
$165$	2.91529	0.226955
$166$	−14.8328	−1.15125
$167$	17.0085	1.31616	0.658080	−	0.752948i	$-0.271369\pi$
$167$	17.0085	1.31616	0.658080	+	0.752948i	$0.271369\pi$
$168$	−10.8421	−0.836488
$169$	−12.2294	−0.940720
$170$	−0.365484	−0.0280314
$171$	1.82780	0.139776
$172$	−1.00435	−0.0765807
$173$	11.7883	0.896245	0.448122	−	0.893972i	$-0.352093\pi$
$173$	11.7883	0.896245	0.448122	+	0.893972i	$0.352093\pi$
$174$	6.22639	0.472022
$175$	21.5208	1.62682
$176$	−2.62582	−0.197929
$177$	−9.11329	−0.684997
$178$	9.69816	0.726908
$179$	−20.8338	−1.55719	−0.778596	−	0.627525i	$-0.784068\pi$
$179$	−20.8338	−1.55719	−0.778596	+	0.627525i	$0.784068\pi$
$180$	1.29745	0.0967064
$181$	−6.87479	−0.510999	−0.255499	−	0.966809i	$-0.582240\pi$
$181$	−6.87479	−0.510999	−0.255499	+	0.966809i	$0.582240\pi$
$182$	3.94560	0.292468
$183$	−9.13522	−0.675295
$184$	1.00000	0.0737210
$185$	3.42143	0.251548
$186$	−16.8176	−1.23312
$187$	−2.08518	−0.152483
$188$	−8.71767	−0.635802
$189$	−1.96201	−0.142715
$190$	−0.298414	−0.0216492
$191$	17.1231	1.23898	0.619492	−	0.785003i	$-0.287339\pi$
$191$	17.1231	1.23898	0.619492	+	0.785003i	$0.287339\pi$
$192$	−2.41227	−0.174090
$193$	22.0959	1.59050	0.795250	−	0.606281i	$-0.207339\pi$
$193$	22.0959	1.59050	0.795250	+	0.606281i	$0.207339\pi$
$194$	3.98455	0.286074
$195$	−0.974634	−0.0697950
$196$	13.2012	0.942943
$197$	−4.27109	−0.304303	−0.152151	−	0.988357i	$-0.548620\pi$
$197$	−4.27109	−0.304303	−0.152151	+	0.988357i	$0.548620\pi$
$198$	7.40229	0.526058
$199$	19.0104	1.34761	0.673807	−	0.738907i	$-0.264658\pi$
$199$	19.0104	1.34761	0.673807	+	0.738907i	$0.264658\pi$
$200$	4.78817	0.338575
$201$	−36.1542	−2.55012
$202$	−2.57846	−0.181420
$203$	−11.6011	−0.814238
$204$	−1.91559	−0.134118
$205$	0.734020	0.0512662
$206$	−11.5301	−0.803342
$207$	−2.81904	−0.195937
$208$	0.877859	0.0608686
$209$	−1.70252	−0.117766
$210$	−4.99005	−0.344346
$211$	−7.08629	−0.487840	−0.243920	−	0.969795i	$-0.578433\pi$
$211$	−7.08629	−0.487840	−0.243920	+	0.969795i	$0.578433\pi$
$212$	8.84706	0.607619
$213$	16.4441	1.12673
$214$	0.677536	0.0463154
$215$	−0.462247	−0.0315250
$216$	−0.436529	−0.0297020
$217$	31.3347	2.12714
$218$	−13.4069	−0.908029
$219$	−19.5330	−1.31992
$220$	−1.20853	−0.0814788
$221$	0.697112	0.0468929
$222$	17.9326	1.20355
$223$	−26.3899	−1.76720	−0.883598	−	0.468246i	$-0.844886\pi$
$223$	−26.3899	−1.76720	−0.883598	+	0.468246i	$0.844886\pi$
$224$	4.49457	0.300306
$225$	−13.4980	−0.899869
$226$	2.04836	0.136255
$227$	12.4452	0.826015	0.413008	−	0.910728i	$-0.364478\pi$
$227$	12.4452	0.826015	0.413008	+	0.910728i	$0.364478\pi$
$228$	−1.56406	−0.103583
$229$	4.70486	0.310906	0.155453	−	0.987843i	$-0.450316\pi$
$229$	4.70486	0.310906	0.155453	+	0.987843i	$0.450316\pi$
$230$	0.460247	0.0303478
$231$	−28.4695	−1.87315
$232$	−2.58114	−0.169460
$233$	0.200287	0.0131212	0.00656061	−	0.999978i	$-0.497912\pi$
$233$	0.200287	0.0131212	0.00656061	+	0.999978i	$0.497912\pi$
$234$	−2.47472	−0.161777
$235$	−4.01228	−0.261732
$236$	3.77789	0.245920
$237$	28.5209	1.85263
$238$	3.56916	0.231355
$239$	18.1759	1.17570	0.587852	−	0.808969i	$-0.299974\pi$
$239$	18.1759	1.17570	0.587852	+	0.808969i	$0.299974\pi$
$240$	−1.11024	−0.0716656
$241$	−17.1104	−1.10218	−0.551088	−	0.834447i	$-0.685787\pi$
$241$	−17.1104	−1.10218	−0.551088	+	0.834447i	$0.685787\pi$
$242$	4.10507	0.263884
$243$	21.6314	1.38766
$244$	3.78698	0.242437
$245$	6.07581	0.388169
$246$	3.84718	0.245287
$247$	0.569185	0.0362164
$248$	6.97168	0.442702
$249$	−35.7806	−2.26750
$250$	4.50498	0.284920
$251$	−17.2290	−1.08748	−0.543741	−	0.839253i	$-0.682993\pi$
$251$	−17.2290	−1.08748	−0.543741	+	0.839253i	$0.682993\pi$
$252$	−12.6704	−0.798159
$253$	2.62582	0.165084
$254$	−6.60663	−0.414537
$255$	−0.881646	−0.0552108
$256$	1.00000	0.0625000
$257$	−16.4630	−1.02694	−0.513468	−	0.858109i	$-0.671639\pi$
$257$	−16.4630	−1.02694	−0.513468	+	0.858109i	$0.671639\pi$
$258$	−2.42275	−0.150834
$259$	−33.4122	−2.07613
$260$	0.404032	0.0250570
$261$	7.27632	0.450393
$262$	1.00000	0.0617802
$263$	14.2504	0.878719	0.439359	−	0.898311i	$-0.355205\pi$
$263$	14.2504	0.878719	0.439359	+	0.898311i	$0.355205\pi$
$264$	−6.33418	−0.389842
$265$	4.07183	0.250131
$266$	2.91418	0.178680
$267$	23.3946	1.43172
$268$	14.9876	0.915515
$269$	21.1869	1.29179	0.645895	−	0.763426i	$-0.276484\pi$
$269$	21.1869	1.29179	0.645895	+	0.763426i	$0.276484\pi$
$270$	−0.200911	−0.0122271
$271$	29.9437	1.81895	0.909474	−	0.415760i	$-0.136484\pi$
$271$	29.9437	1.81895	0.909474	+	0.415760i	$0.136484\pi$
$272$	0.794105	0.0481497
$273$	9.51786	0.576047
$274$	−8.31080	−0.502074
$275$	12.5729	0.758173
$276$	2.41227	0.145201
$277$	15.5132	0.932101	0.466050	−	0.884758i	$-0.345677\pi$
$277$	15.5132	0.932101	0.466050	+	0.884758i	$0.345677\pi$
$278$	0.604721	0.0362688
$279$	−19.6534	−1.17662
$280$	2.06861	0.123623
$281$	−18.9578	−1.13093	−0.565464	−	0.824773i	$-0.691303\pi$
$281$	−18.9578	−1.13093	−0.565464	+	0.824773i	$0.691303\pi$
$282$	−21.0294	−1.25228
$283$	1.24346	0.0739157	0.0369579	−	0.999317i	$-0.488233\pi$
$283$	1.24346	0.0739157	0.0369579	+	0.999317i	$0.488233\pi$
$284$	−6.81686	−0.404506
$285$	−0.719855	−0.0426405
$286$	2.30510	0.136303
$287$	−7.16813	−0.423121
$288$	−2.81904	−0.166113
$289$	−16.3694	−0.962906
$290$	−1.18796	−0.0697594
$291$	9.61180	0.563454
$292$	8.09734	0.473861
$293$	2.83227	0.165463	0.0827316	−	0.996572i	$-0.473636\pi$
$293$	2.83227	0.165463	0.0827316	+	0.996572i	$0.473636\pi$
$294$	31.8448	1.85723
$295$	1.73876	0.101235
$296$	−7.43390	−0.432086
$297$	−1.14625	−0.0665120
$298$	2.18608	0.126636
$299$	−0.877859	−0.0507679
$300$	11.5504	0.666860
$301$	4.51411	0.260189
$302$	15.3419	0.882827
$303$	−6.21993	−0.357326
$304$	0.648378	0.0371870
$305$	1.74295	0.0998008
$306$	−2.23861	−0.127973
$307$	−8.47363	−0.483616	−0.241808	−	0.970324i	$-0.577740\pi$
$307$	−8.47363	−0.483616	−0.241808	+	0.970324i	$0.577740\pi$
$308$	11.8019	0.672478
$309$	−27.8138	−1.58227
$310$	3.20869	0.182241
$311$	−29.8126	−1.69052	−0.845259	−	0.534357i	$-0.820554\pi$
$311$	−29.8126	−1.69052	−0.845259	+	0.534357i	$0.820554\pi$
$312$	2.11763	0.119887
$313$	11.8646	0.670624	0.335312	−	0.942107i	$-0.391158\pi$
$313$	11.8646	0.670624	0.335312	+	0.942107i	$0.391158\pi$
$314$	11.1164	0.627335
$315$	−5.83150	−0.328568
$316$	−11.8233	−0.665110
$317$	−28.4403	−1.59737	−0.798683	−	0.601752i	$-0.794470\pi$
$317$	−28.4403	−1.59737	−0.798683	+	0.601752i	$0.794470\pi$
$318$	21.3415	1.19677
$319$	−6.77760	−0.379473
$320$	0.460247	0.0257286
$321$	1.63440	0.0912233
$322$	−4.49457	−0.250473
$323$	0.514880	0.0286487
$324$	−9.51014	−0.528341
$325$	−4.20334	−0.233160
$326$	−12.8532	−0.711874
$327$	−32.3410	−1.78846
$328$	−1.59484	−0.0880603
$329$	39.1822	2.16019
$330$	−2.91529	−0.160481
$331$	17.2305	0.947077	0.473538	−	0.880773i	$-0.342977\pi$
$331$	17.2305	0.947077	0.473538	+	0.880773i	$0.342977\pi$
$332$	14.8328	0.814054
$333$	20.9564	1.14841
$334$	−17.0085	−0.930665
$335$	6.89800	0.376878
$336$	10.8421	0.591486
$337$	−29.6804	−1.61679	−0.808396	−	0.588639i	$-0.799664\pi$
$337$	−29.6804	−1.61679	−0.808396	+	0.588639i	$0.799664\pi$
$338$	12.2294	0.665190
$339$	4.94119	0.268369
$340$	0.365484	0.0198212
$341$	18.3064	0.991345
$342$	−1.82780	−0.0988363
$343$	−27.8718	−1.50493
$344$	1.00435	0.0541507
$345$	1.11024	0.0597732
$346$	−11.7883	−0.633741
$347$	17.7986	0.955479	0.477740	−	0.878501i	$-0.341456\pi$
$347$	17.7986	0.955479	0.477740	+	0.878501i	$0.341456\pi$
$348$	−6.22639	−0.333770
$349$	−18.4127	−0.985610	−0.492805	−	0.870140i	$-0.664028\pi$
$349$	−18.4127	−0.985610	−0.492805	+	0.870140i	$0.664028\pi$
$350$	−21.5208	−1.15034
$351$	0.383211	0.0204543
$352$	2.62582	0.139957
$353$	−15.5953	−0.830054	−0.415027	−	0.909809i	$-0.636228\pi$
$353$	−15.5953	−0.830054	−0.415027	+	0.909809i	$0.636228\pi$
$354$	9.11329	0.484366
$355$	−3.13744	−0.166518
$356$	−9.69816	−0.514001
$357$	8.60978	0.455678
$358$	20.8338	1.10110
$359$	−18.7690	−0.990588	−0.495294	−	0.868726i	$-0.664940\pi$
$359$	−18.7690	−0.990588	−0.495294	+	0.868726i	$0.664940\pi$
$360$	−1.29745	−0.0683818
$361$	−18.5796	−0.977874
$362$	6.87479	0.361331
$363$	9.90253	0.519748
$364$	−3.94560	−0.206806
$365$	3.72678	0.195068
$366$	9.13522	0.477505
$367$	−4.46882	−0.233271	−0.116635	−	0.993175i	$-0.537211\pi$
$367$	−4.46882	−0.233271	−0.116635	+	0.993175i	$0.537211\pi$
$368$	−1.00000	−0.0521286
$369$	4.49592	0.234048
$370$	−3.42143	−0.177872
$371$	−39.7638	−2.06443
$372$	16.8176	0.871950
$373$	−33.7315	−1.74655	−0.873277	−	0.487225i	$-0.838009\pi$
$373$	−33.7315	−1.74655	−0.873277	+	0.487225i	$0.838009\pi$
$374$	2.08518	0.107822
$375$	10.8672	0.561180
$376$	8.71767	0.449580
$377$	2.26587	0.116698
$378$	1.96201	0.100915
$379$	24.9988	1.28410	0.642050	−	0.766663i	$-0.278084\pi$
$379$	24.9988	1.28410	0.642050	+	0.766663i	$0.278084\pi$
$380$	0.298414	0.0153083
$381$	−15.9370	−0.816475
$382$	−17.1231	−0.876094
$383$	6.41793	0.327941	0.163970	−	0.986465i	$-0.447570\pi$
$383$	6.41793	0.327941	0.163970	+	0.986465i	$0.447570\pi$
$384$	2.41227	0.123101
$385$	5.43181	0.276830
$386$	−22.0959	−1.12465
$387$	−2.83129	−0.143923
$388$	−3.98455	−0.202285
$389$	27.5282	1.39573	0.697867	−	0.716228i	$-0.254133\pi$
$389$	27.5282	1.39573	0.697867	+	0.716228i	$0.254133\pi$
$390$	0.974634	0.0493525
$391$	−0.794105	−0.0401596
$392$	−13.2012	−0.666761
$393$	2.41227	0.121683
$394$	4.27109	0.215174
$395$	−5.44162	−0.273797
$396$	−7.40229	−0.371979
$397$	−13.5398	−0.679542	−0.339771	−	0.940508i	$-0.610350\pi$
$397$	−13.5398	−0.679542	−0.339771	+	0.940508i	$0.610350\pi$
$398$	−19.0104	−0.952907
$399$	7.02979	0.351930
$400$	−4.78817	−0.239409
$401$	24.2827	1.21262	0.606310	−	0.795228i	$-0.292649\pi$
$401$	24.2827	1.21262	0.606310	+	0.795228i	$0.292649\pi$
$402$	36.1542	1.80321
$403$	−6.12015	−0.304866
$404$	2.57846	0.128283
$405$	−4.37701	−0.217495
$406$	11.6011	0.575753
$407$	−19.5201	−0.967574
$408$	1.91559	0.0948360
$409$	32.3561	1.59990	0.799952	−	0.600064i	$-0.204858\pi$
$409$	32.3561	1.59990	0.799952	+	0.600064i	$0.204858\pi$
$410$	−0.734020	−0.0362507
$411$	−20.0479	−0.988889
$412$	11.5301	0.568049
$413$	−16.9800	−0.835532
$414$	2.81904	0.138548
$415$	6.82673	0.335111
$416$	−0.877859	−0.0430406
$417$	1.45875	0.0714353
$418$	1.70252	0.0832732
$419$	−4.87191	−0.238008	−0.119004	−	0.992894i	$-0.537970\pi$
$419$	−4.87191	−0.238008	−0.119004	+	0.992894i	$0.537970\pi$
$420$	4.99005	0.243490
$421$	−6.76788	−0.329847	−0.164923	−	0.986306i	$-0.552738\pi$
$421$	−6.76788	−0.329847	−0.164923	+	0.986306i	$0.552738\pi$
$422$	7.08629	0.344955
$423$	−24.5754	−1.19490
$424$	−8.84706	−0.429651
$425$	−3.80231	−0.184439
$426$	−16.4441	−0.796719
$427$	−17.0209	−0.823698
$428$	−0.677536	−0.0327499
$429$	5.56052	0.268465
$430$	0.462247	0.0222915
$431$	17.4799	0.841976	0.420988	−	0.907066i	$-0.361683\pi$
$431$	17.4799	0.841976	0.420988	+	0.907066i	$0.361683\pi$
$432$	0.436529	0.0210025
$433$	−10.8029	−0.519153	−0.259576	−	0.965723i	$-0.583583\pi$
$433$	−10.8029	−0.519153	−0.259576	+	0.965723i	$0.583583\pi$
$434$	−31.3347	−1.50411
$435$	−2.86568	−0.137399
$436$	13.4069	0.642074
$437$	−0.648378	−0.0310161
$438$	19.5330	0.933321
$439$	−25.7481	−1.22889	−0.614444	−	0.788960i	$-0.710620\pi$
$439$	−25.7481	−1.22889	−0.614444	+	0.788960i	$0.710620\pi$
$440$	1.20853	0.0576142
$441$	37.2147	1.77213
$442$	−0.697112	−0.0331583
$443$	−1.98805	−0.0944553	−0.0472277	−	0.998884i	$-0.515039\pi$
$443$	−1.98805	−0.0944553	−0.0472277	+	0.998884i	$0.515039\pi$
$444$	−17.9326	−0.851041
$445$	−4.46355	−0.211592
$446$	26.3899	1.24960
$447$	5.27342	0.249424
$448$	−4.49457	−0.212349
$449$	−30.6524	−1.44658	−0.723289	−	0.690545i	$-0.757371\pi$
$449$	−30.6524	−1.44658	−0.723289	+	0.690545i	$0.757371\pi$
$450$	13.4980	0.636304
$451$	−4.18776	−0.197194
$452$	−2.04836	−0.0963467
$453$	37.0088	1.73882
$454$	−12.4452	−0.584081
$455$	−1.81595	−0.0851331
$456$	1.56406	0.0732439
$457$	−15.4859	−0.724401	−0.362201	−	0.932100i	$-0.617975\pi$
$457$	−15.4859	−0.724401	−0.362201	+	0.932100i	$0.617975\pi$
$458$	−4.70486	−0.219844
$459$	0.346650	0.0161802
$460$	−0.460247	−0.0214591
$461$	−29.4029	−1.36943	−0.684715	−	0.728811i	$-0.740074\pi$
$461$	−29.4029	−1.36943	−0.684715	+	0.728811i	$0.740074\pi$
$462$	28.4695	1.32452
$463$	−27.9058	−1.29689	−0.648447	−	0.761260i	$-0.724581\pi$
$463$	−27.9058	−1.29689	−0.648447	+	0.761260i	$0.724581\pi$
$464$	2.58114	0.119826
$465$	7.74022	0.358944
$466$	−0.200287	−0.00927810
$467$	−20.3053	−0.939616	−0.469808	−	0.882769i	$-0.655677\pi$
$467$	−20.3053	−0.939616	−0.469808	+	0.882769i	$0.655677\pi$
$468$	2.47472	0.114394
$469$	−67.3630	−3.11053
$470$	4.01228	0.185073
$471$	26.8157	1.23560
$472$	−3.77789	−0.173892
$473$	2.63723	0.121260
$474$	−28.5209	−1.31001
$475$	−3.10455	−0.142446
$476$	−3.56916	−0.163592
$477$	24.9402	1.14193
$478$	−18.1759	−0.831348
$479$	−12.9549	−0.591925	−0.295962	−	0.955200i	$-0.595640\pi$
$479$	−12.9549	−0.591925	−0.295962	+	0.955200i	$0.595640\pi$
$480$	1.11024	0.0506752
$481$	6.52592	0.297556
$482$	17.1104	0.779356
$483$	−10.8421	−0.493334
$484$	−4.10507	−0.186594
$485$	−1.83388	−0.0832720
$486$	−21.6314	−0.981221
$487$	−27.1150	−1.22870	−0.614349	−	0.789034i	$-0.710581\pi$
$487$	−27.1150	−1.22870	−0.614349	+	0.789034i	$0.710581\pi$
$488$	−3.78698	−0.171429
$489$	−31.0054	−1.40211
$490$	−6.07581	−0.274477
$491$	−10.5565	−0.476406	−0.238203	−	0.971215i	$-0.576558\pi$
$491$	−10.5565	−0.476406	−0.238203	+	0.971215i	$0.576558\pi$
$492$	−3.84718	−0.173444
$493$	2.04969	0.0923135
$494$	−0.569185	−0.0256088
$495$	−3.40688	−0.153128
$496$	−6.97168	−0.313038
$497$	30.6389	1.37434
$498$	35.7806	1.60337
$499$	−11.9256	−0.533865	−0.266933	−	0.963715i	$-0.586010\pi$
$499$	−11.9256	−0.533865	−0.266933	+	0.963715i	$0.586010\pi$
$500$	−4.50498	−0.201469
$501$	−41.0291	−1.83305
$502$	17.2290	0.768966
$503$	−14.8762	−0.663296	−0.331648	−	0.943403i	$-0.607605\pi$
$503$	−14.8762	−0.663296	−0.331648	+	0.943403i	$0.607605\pi$
$504$	12.6704	0.564383
$505$	1.18673	0.0528087
$506$	−2.62582	−0.116732
$507$	29.5005	1.31016
$508$	6.60663	0.293122
$509$	−11.3539	−0.503255	−0.251627	−	0.967824i	$-0.580966\pi$
$509$	−11.3539	−0.503255	−0.251627	+	0.967824i	$0.580966\pi$
$510$	0.881646	0.0390399
$511$	−36.3941	−1.60998
$512$	−1.00000	−0.0441942
$513$	0.283036	0.0124963
$514$	16.4630	0.726153
$515$	5.30670	0.233841
$516$	2.42275	0.106656
$517$	22.8910	1.00675
$518$	33.4122	1.46805
$519$	−28.4364	−1.24822
$520$	−0.404032	−0.0177180
$521$	23.4108	1.02565	0.512824	−	0.858494i	$-0.328600\pi$
$521$	23.4108	1.02565	0.512824	+	0.858494i	$0.328600\pi$
$522$	−7.27632	−0.318476
$523$	−36.3521	−1.58957	−0.794783	−	0.606894i	$-0.792415\pi$
$523$	−36.3521	−1.58957	−0.794783	+	0.606894i	$0.792415\pi$
$524$	−1.00000	−0.0436852
$525$	−51.9139	−2.26571
$526$	−14.2504	−0.621348
$527$	−5.53624	−0.241163
$528$	6.33418	0.275660
$529$	1.00000	0.0434783
$530$	−4.07183	−0.176869
$531$	10.6500	0.462172
$532$	−2.91418	−0.126346
$533$	1.40005	0.0606427
$534$	−23.3946	−1.01238
$535$	−0.311834	−0.0134818
$536$	−14.9876	−0.647367
$537$	50.2567	2.16874
$538$	−21.1869	−0.913434
$539$	−34.6640	−1.49308
$540$	0.200911	0.00864584
$541$	44.6482	1.91958	0.959789	−	0.280723i	$-0.0905743\pi$
$541$	44.6482	1.91958	0.959789	+	0.280723i	$0.0905743\pi$
$542$	−29.9437	−1.28619
$543$	16.5838	0.711680
$544$	−0.794105	−0.0340470
$545$	6.17048	0.264314
$546$	−9.51786	−0.407327
$547$	−19.6844	−0.841643	−0.420821	−	0.907144i	$-0.638258\pi$
$547$	−19.6844	−0.841643	−0.420821	+	0.907144i	$0.638258\pi$
$548$	8.31080	0.355020
$549$	10.6756	0.455625
$550$	−12.5729	−0.536109
$551$	1.67355	0.0712957
$552$	−2.41227	−0.102673
$553$	53.1405	2.25976
$554$	−15.5132	−0.659095
$555$	−8.25340	−0.350337
$556$	−0.604721	−0.0256459
$557$	4.58050	0.194082	0.0970411	−	0.995280i	$-0.469062\pi$
$557$	4.58050	0.194082	0.0970411	+	0.995280i	$0.469062\pi$
$558$	19.6534	0.831996
$559$	−0.881675	−0.0372909
$560$	−2.06861	−0.0874149
$561$	5.03001	0.212367
$562$	18.9578	0.799687
$563$	−36.9245	−1.55618	−0.778092	−	0.628151i	$-0.783812\pi$
$563$	−36.9245	−1.55618	−0.778092	+	0.628151i	$0.783812\pi$
$564$	21.0294	0.885496
$565$	−0.942751	−0.0396618
$566$	−1.24346	−0.0522663
$567$	42.7440	1.79508
$568$	6.81686	0.286029
$569$	19.3897	0.812860	0.406430	−	0.913682i	$-0.366774\pi$
$569$	19.3897	0.812860	0.406430	+	0.913682i	$0.366774\pi$
$570$	0.719855	0.0301514
$571$	−8.12576	−0.340053	−0.170026	−	0.985440i	$-0.554385\pi$
$571$	−8.12576	−0.340053	−0.170026	+	0.985440i	$0.554385\pi$
$572$	−2.30510	−0.0963811
$573$	−41.3055	−1.72556
$574$	7.16813	0.299192
$575$	4.78817	0.199681
$576$	2.81904	0.117460
$577$	13.7070	0.570631	0.285315	−	0.958434i	$-0.407902\pi$
$577$	13.7070	0.570631	0.285315	+	0.958434i	$0.407902\pi$
$578$	16.3694	0.680877
$579$	−53.3013	−2.21513
$580$	1.18796	0.0493273
$581$	−66.6670	−2.76581
$582$	−9.61180	−0.398422
$583$	−23.2308	−0.962121
$584$	−8.09734	−0.335071
$585$	1.13898	0.0470911
$586$	−2.83227	−0.117000
$587$	−10.5966	−0.437370	−0.218685	−	0.975795i	$-0.570177\pi$
$587$	−10.5966	−0.437370	−0.218685	+	0.975795i	$0.570177\pi$
$588$	−31.8448	−1.31326
$589$	−4.52028	−0.186255
$590$	−1.73876	−0.0715837
$591$	10.3030	0.423809
$592$	7.43390	0.305531
$593$	10.7539	0.441610	0.220805	−	0.975318i	$-0.429132\pi$
$593$	10.7539	0.441610	0.220805	+	0.975318i	$0.429132\pi$
$594$	1.14625	0.0470311
$595$	−1.64270	−0.0673440
$596$	−2.18608	−0.0895455
$597$	−45.8583	−1.87685
$598$	0.877859	0.0358983
$599$	28.3027	1.15642	0.578208	−	0.815890i	$-0.303752\pi$
$599$	28.3027	1.15642	0.578208	+	0.815890i	$0.303752\pi$
$600$	−11.5504	−0.471541
$601$	−37.9573	−1.54831	−0.774156	−	0.632995i	$-0.781825\pi$
$601$	−37.9573	−1.54831	−0.774156	+	0.632995i	$0.781825\pi$
$602$	−4.51411	−0.183981
$603$	42.2507	1.72058
$604$	−15.3419	−0.624253
$605$	−1.88935	−0.0768128
$606$	6.21993	0.252667
$607$	−16.3774	−0.664738	−0.332369	−	0.943149i	$-0.607848\pi$
$607$	−16.3774	−0.664738	−0.332369	+	0.943149i	$0.607848\pi$
$608$	−0.648378	−0.0262952
$609$	27.9850	1.13401
$610$	−1.74295	−0.0705698
$611$	−7.65289	−0.309603
$612$	2.23861	0.0904905
$613$	−32.8644	−1.32738	−0.663690	−	0.748008i	$-0.731011\pi$
$613$	−32.8644	−1.32738	−0.663690	+	0.748008i	$0.731011\pi$
$614$	8.47363	0.341968
$615$	−1.77065	−0.0713996
$616$	−11.8019	−0.475514
$617$	10.9973	0.442734	0.221367	−	0.975191i	$-0.428948\pi$
$617$	10.9973	0.442734	0.221367	+	0.975191i	$0.428948\pi$
$618$	27.8138	1.11883
$619$	4.89692	0.196824	0.0984119	−	0.995146i	$-0.468624\pi$
$619$	4.89692	0.196824	0.0984119	+	0.995146i	$0.468624\pi$
$620$	−3.20869	−0.128864
$621$	−0.436529	−0.0175173
$622$	29.8126	1.19538
$623$	43.5891	1.74636
$624$	−2.11763	−0.0847731
$625$	21.8675	0.874699
$626$	−11.8646	−0.474203
$627$	4.10695	0.164016
$628$	−11.1164	−0.443593
$629$	5.90329	0.235380
$630$	5.83150	0.232333
$631$	−32.4013	−1.28988	−0.644938	−	0.764235i	$-0.723117\pi$
$631$	−32.4013	−1.28988	−0.644938	+	0.764235i	$0.723117\pi$
$632$	11.8233	0.470304
$633$	17.0940	0.679427
$634$	28.4403	1.12951
$635$	3.04068	0.120666
$636$	−21.3415	−0.846245
$637$	11.5888	0.459165
$638$	6.77760	0.268328
$639$	−19.2170	−0.760212
$640$	−0.460247	−0.0181929
$641$	−16.0119	−0.632431	−0.316215	−	0.948687i	$-0.602412\pi$
$641$	−16.0119	−0.632431	−0.316215	+	0.948687i	$0.602412\pi$
$642$	−1.63440	−0.0645046
$643$	7.40926	0.292193	0.146096	−	0.989270i	$-0.453329\pi$
$643$	7.40926	0.292193	0.146096	+	0.989270i	$0.453329\pi$
$644$	4.49457	0.177111
$645$	1.11506	0.0439056
$646$	−0.514880	−0.0202577
$647$	−10.2470	−0.402851	−0.201425	−	0.979504i	$-0.564557\pi$
$647$	−10.2470	−0.402851	−0.201425	+	0.979504i	$0.564557\pi$
$648$	9.51014	0.373594
$649$	−9.92007	−0.389397
$650$	4.20334	0.164869
$651$	−75.5877	−2.96252
$652$	12.8532	0.503371
$653$	38.1379	1.49245	0.746226	−	0.665693i	$-0.231864\pi$
$653$	38.1379	1.49245	0.746226	+	0.665693i	$0.231864\pi$
$654$	32.3410	1.26463
$655$	−0.460247	−0.0179833
$656$	1.59484	0.0622681
$657$	22.8267	0.890555
$658$	−39.1822	−1.52748
$659$	−40.2282	−1.56707	−0.783534	−	0.621349i	$-0.786585\pi$
$659$	−40.2282	−1.56707	−0.783534	+	0.621349i	$0.786585\pi$
$660$	2.91529	0.113477
$661$	22.8208	0.887626	0.443813	−	0.896120i	$-0.353626\pi$
$661$	22.8208	0.887626	0.443813	+	0.896120i	$0.353626\pi$
$662$	−17.2305	−0.669684
$663$	−1.68162	−0.0653088
$664$	−14.8328	−0.575623
$665$	−1.34124	−0.0520112
$666$	−20.9564	−0.812045
$667$	−2.58114	−0.0999420
$668$	17.0085	0.658080
$669$	63.6595	2.46122
$670$	−6.89800	−0.266493
$671$	−9.94393	−0.383881
$672$	−10.8421	−0.418244
$673$	−1.88147	−0.0725255	−0.0362628	−	0.999342i	$-0.511545\pi$
$673$	−1.88147	−0.0725255	−0.0362628	+	0.999342i	$0.511545\pi$
$674$	29.6804	1.14324
$675$	−2.09018	−0.0804509
$676$	−12.2294	−0.470360
$677$	23.0777	0.886949	0.443474	−	0.896287i	$-0.353746\pi$
$677$	23.0777	0.886949	0.443474	+	0.896287i	$0.353746\pi$
$678$	−4.94119	−0.189765
$679$	17.9089	0.687279
$680$	−0.365484	−0.0140157
$681$	−30.0211	−1.15041
$682$	−18.3064	−0.700987
$683$	48.0500	1.83858	0.919291	−	0.393578i	$-0.128763\pi$
$683$	48.0500	1.83858	0.919291	+	0.393578i	$0.128763\pi$
$684$	1.82780	0.0698878
$685$	3.82502	0.146146
$686$	27.8718	1.06415
$687$	−11.3494	−0.433006
$688$	−1.00435	−0.0382903
$689$	7.76648	0.295879
$690$	−1.11024	−0.0422661
$691$	−13.7851	−0.524409	−0.262204	−	0.965012i	$-0.584449\pi$
$691$	−13.7851	−0.524409	−0.262204	+	0.965012i	$0.584449\pi$
$692$	11.7883	0.448122
$693$	33.2701	1.26383
$694$	−17.7986	−0.675626
$695$	−0.278321	−0.0105573
$696$	6.22639	0.236011
$697$	1.26647	0.0479710
$698$	18.4127	0.696931
$699$	−0.483145	−0.0182742
$700$	21.5208	0.813410
$701$	51.8058	1.95668	0.978340	−	0.207005i	$-0.0663718\pi$
$701$	51.8058	1.95668	0.978340	+	0.207005i	$0.0663718\pi$
$702$	−0.383211	−0.0144634
$703$	4.81998	0.181789
$704$	−2.62582	−0.0989643
$705$	9.67870	0.364521
$706$	15.5953	0.586937
$707$	−11.5891	−0.435852
$708$	−9.11329	−0.342498
$709$	−13.6097	−0.511123	−0.255561	−	0.966793i	$-0.582260\pi$
$709$	−13.6097	−0.511123	−0.255561	+	0.966793i	$0.582260\pi$
$710$	3.13744	0.117746
$711$	−33.3302	−1.24998
$712$	9.69816	0.363454
$713$	6.97168	0.261091
$714$	−8.60978	−0.322213
$715$	−1.06092	−0.0396760
$716$	−20.8338	−0.778596
$717$	−43.8452	−1.63743
$718$	18.7690	0.700451
$719$	43.6103	1.62639	0.813194	−	0.581993i	$-0.197727\pi$
$719$	43.6103	1.62639	0.813194	+	0.581993i	$0.197727\pi$
$720$	1.29745	0.0483532
$721$	−51.8230	−1.92999
$722$	18.5796	0.691461
$723$	41.2748	1.53503
$724$	−6.87479	−0.255499
$725$	−12.3589	−0.458999
$726$	−9.90253	−0.367517
$727$	41.2105	1.52841	0.764207	−	0.644972i	$-0.223131\pi$
$727$	41.2105	1.52841	0.764207	+	0.644972i	$0.223131\pi$
$728$	3.94560	0.146234
$729$	−23.6504	−0.875939
$730$	−3.72678	−0.137934
$731$	−0.797556	−0.0294987
$732$	−9.13522	−0.337647
$733$	−27.5284	−1.01679	−0.508393	−	0.861125i	$-0.669760\pi$
$733$	−27.5284	−1.01679	−0.508393	+	0.861125i	$0.669760\pi$
$734$	4.46882	0.164947
$735$	−14.6565	−0.540613
$736$	1.00000	0.0368605
$737$	−39.3548	−1.44965
$738$	−4.49592	−0.165497
$739$	−12.9950	−0.478028	−0.239014	−	0.971016i	$-0.576824\pi$
$739$	−12.9950	−0.478028	−0.239014	+	0.971016i	$0.576824\pi$
$740$	3.42143	0.125774
$741$	−1.37303	−0.0504394
$742$	39.7638	1.45977
$743$	−23.7409	−0.870968	−0.435484	−	0.900197i	$-0.643423\pi$
$743$	−23.7409	−0.870968	−0.435484	+	0.900197i	$0.643423\pi$
$744$	−16.8176	−0.616561
$745$	−1.00614	−0.0368621
$746$	33.7315	1.23500
$747$	41.8141	1.52990
$748$	−2.08518	−0.0762416
$749$	3.04524	0.111271
$750$	−10.8672	−0.396814
$751$	5.75838	0.210126	0.105063	−	0.994466i	$-0.466496\pi$
$751$	5.75838	0.210126	0.105063	+	0.994466i	$0.466496\pi$
$752$	−8.71767	−0.317901
$753$	41.5609	1.51456
$754$	−2.26587	−0.0825183
$755$	−7.06106	−0.256978
$756$	−1.96201	−0.0713577
$757$	−19.4332	−0.706311	−0.353156	−	0.935565i	$-0.614891\pi$
$757$	−19.4332	−0.706311	−0.353156	+	0.935565i	$0.614891\pi$
$758$	−24.9988	−0.907996
$759$	−6.33418	−0.229916
$760$	−0.298414	−0.0108246
$761$	18.9672	0.687561	0.343780	−	0.939050i	$-0.388292\pi$
$761$	18.9672	0.687561	0.343780	+	0.939050i	$0.388292\pi$
$762$	15.9370	0.577335
$763$	−60.2583	−2.18150
$764$	17.1231	0.619492
$765$	1.03031	0.0372511
$766$	−6.41793	−0.231889
$767$	3.31646	0.119750
$768$	−2.41227	−0.0870452
$769$	2.24872	0.0810908	0.0405454	−	0.999178i	$-0.487090\pi$
$769$	2.24872	0.0810908	0.0405454	+	0.999178i	$0.487090\pi$
$770$	−5.43181	−0.195749
$771$	39.7133	1.43024
$772$	22.0959	0.795250
$773$	−25.4305	−0.914672	−0.457336	−	0.889294i	$-0.651196\pi$
$773$	−25.4305	−0.914672	−0.457336	+	0.889294i	$0.651196\pi$
$774$	2.83129	0.101769
$775$	33.3816	1.19910
$776$	3.98455	0.143037
$777$	80.5992	2.89148
$778$	−27.5282	−0.986932
$779$	1.03406	0.0370490
$780$	−0.974634	−0.0348975
$781$	17.8998	0.640507
$782$	0.794105	0.0283971
$783$	1.12674	0.0402664
$784$	13.2012	0.471471
$785$	−5.11629	−0.182608
$786$	−2.41227	−0.0860428
$787$	−53.0282	−1.89025	−0.945125	−	0.326708i	$-0.894061\pi$
$787$	−53.0282	−1.89025	−0.945125	+	0.326708i	$0.894061\pi$
$788$	−4.27109	−0.152151
$789$	−34.3758	−1.22381
$790$	5.44162	0.193604
$791$	9.20651	0.327346
$792$	7.40229	0.263029
$793$	3.32444	0.118054
$794$	13.5398	0.480509
$795$	−9.82235	−0.348363
$796$	19.0104	0.673807
$797$	−30.1499	−1.06797	−0.533983	−	0.845495i	$-0.679305\pi$
$797$	−30.1499	−1.06797	−0.533983	+	0.845495i	$0.679305\pi$
$798$	−7.02979	−0.248852
$799$	−6.92275	−0.244909
$800$	4.78817	0.169287
$801$	−27.3395	−0.965993
$802$	−24.2827	−0.857452
$803$	−21.2622	−0.750326
$804$	−36.1542	−1.27506
$805$	2.06861	0.0729090
$806$	6.12015	0.215573
$807$	−51.1086	−1.79911
$808$	−2.57846	−0.0907098
$809$	16.5344	0.581320	0.290660	−	0.956826i	$-0.406125\pi$
$809$	16.5344	0.581320	0.290660	+	0.956826i	$0.406125\pi$
$810$	4.37701	0.153792
$811$	−9.87120	−0.346625	−0.173312	−	0.984867i	$-0.555447\pi$
$811$	−9.87120	−0.346625	−0.173312	+	0.984867i	$0.555447\pi$
$812$	−11.6011	−0.407119
$813$	−72.2322	−2.53329
$814$	19.5201	0.684178
$815$	5.91566	0.207216
$816$	−1.91559	−0.0670592
$817$	−0.651196	−0.0227825
$818$	−32.3561	−1.13130
$819$	−11.1228	−0.388662
$820$	0.734020	0.0256331
$821$	−35.5947	−1.24226	−0.621132	−	0.783706i	$-0.713327\pi$
$821$	−35.5947	−1.24226	−0.621132	+	0.783706i	$0.713327\pi$
$822$	20.0479	0.699250
$823$	0.783110	0.0272975	0.0136488	−	0.999907i	$-0.495655\pi$
$823$	0.783110	0.0272975	0.0136488	+	0.999907i	$0.495655\pi$
$824$	−11.5301	−0.401671
$825$	−30.3292	−1.05593
$826$	16.9800	0.590811
$827$	−31.0859	−1.08096	−0.540481	−	0.841356i	$-0.681758\pi$
$827$	−31.0859	−1.08096	−0.540481	+	0.841356i	$0.681758\pi$
$828$	−2.81904	−0.0979683
$829$	0.945704	0.0328457	0.0164228	−	0.999865i	$-0.494772\pi$
$829$	0.945704	0.0328457	0.0164228	+	0.999865i	$0.494772\pi$
$830$	−6.82673	−0.236959
$831$	−37.4221	−1.29816
$832$	0.877859	0.0304343
$833$	10.4831	0.363219
$834$	−1.45875	−0.0505124
$835$	7.82812	0.270903
$836$	−1.70252	−0.0588830
$837$	−3.04334	−0.105193
$838$	4.87191	0.168297
$839$	14.8816	0.513768	0.256884	−	0.966442i	$-0.417304\pi$
$839$	14.8816	0.513768	0.256884	+	0.966442i	$0.417304\pi$
$840$	−4.99005	−0.172173
$841$	−22.3377	−0.770267
$842$	6.76788	0.233237
$843$	45.7314	1.57507
$844$	−7.08629	−0.243920
$845$	−5.62852	−0.193627
$846$	24.5754	0.844921
$847$	18.4505	0.633968
$848$	8.84706	0.303809
$849$	−2.99955	−0.102944
$850$	3.80231	0.130418
$851$	−7.43390	−0.254831
$852$	16.4441	0.563365
$853$	−15.1927	−0.520190	−0.260095	−	0.965583i	$-0.583754\pi$
$853$	−15.1927	−0.520190	−0.260095	+	0.965583i	$0.583754\pi$
$854$	17.0209	0.582442
$855$	0.841240	0.0287698
$856$	0.677536	0.0231577
$857$	−16.3065	−0.557018	−0.278509	−	0.960434i	$-0.589840\pi$
$857$	−16.3065	−0.557018	−0.278509	+	0.960434i	$0.589840\pi$
$858$	−5.56052	−0.189833
$859$	36.4736	1.24446	0.622232	−	0.782833i	$-0.286226\pi$
$859$	36.4736	1.24446	0.622232	+	0.782833i	$0.286226\pi$
$860$	−0.462247	−0.0157625
$861$	17.2914	0.589291
$862$	−17.4799	−0.595367
$863$	−35.0893	−1.19445	−0.597227	−	0.802072i	$-0.703731\pi$
$863$	−35.0893	−1.19445	−0.597227	+	0.802072i	$0.703731\pi$
$864$	−0.436529	−0.0148510
$865$	5.42551	0.184473
$866$	10.8029	0.367096
$867$	39.4874	1.34106
$868$	31.3347	1.06357
$869$	31.0457	1.05315
$870$	2.86568	0.0971556
$871$	13.1570	0.445809
$872$	−13.4069	−0.454015
$873$	−11.2326	−0.380166
$874$	0.648378	0.0219317
$875$	20.2479	0.684506
$876$	−19.5330	−0.659958
$877$	6.29673	0.212626	0.106313	−	0.994333i	$-0.466096\pi$
$877$	6.29673	0.212626	0.106313	+	0.994333i	$0.466096\pi$
$878$	25.7481	0.868956
$879$	−6.83220	−0.230444
$880$	−1.20853	−0.0407394
$881$	2.75278	0.0927434	0.0463717	−	0.998924i	$-0.485234\pi$
$881$	2.75278	0.0927434	0.0463717	+	0.998924i	$0.485234\pi$
$882$	−37.2147	−1.25308
$883$	−43.4094	−1.46084	−0.730422	−	0.682996i	$-0.760677\pi$
$883$	−43.4094	−1.46084	−0.730422	+	0.682996i	$0.760677\pi$
$884$	0.697112	0.0234464
$885$	−4.19436	−0.140992
$886$	1.98805	0.0667900
$887$	50.3513	1.69063	0.845315	−	0.534268i	$-0.179413\pi$
$887$	50.3513	1.69063	0.845315	+	0.534268i	$0.179413\pi$
$888$	17.9326	0.601777
$889$	−29.6940	−0.995905
$890$	4.46355	0.149618
$891$	24.9719	0.836591
$892$	−26.3899	−0.883598
$893$	−5.65235	−0.189149
$894$	−5.27342	−0.176370
$895$	−9.58870	−0.320515
$896$	4.49457	0.150153
$897$	2.11763	0.0707057
$898$	30.6524	1.02289
$899$	−17.9948	−0.600162
$900$	−13.4980	−0.449935
$901$	7.02549	0.234053
$902$	4.18776	0.139437
$903$	−10.8892	−0.362371
$904$	2.04836	0.0681274
$905$	−3.16410	−0.105178
$906$	−37.0088	−1.22953
$907$	29.2600	0.971562	0.485781	−	0.874080i	$-0.338535\pi$
$907$	29.2600	0.971562	0.485781	+	0.874080i	$0.338535\pi$
$908$	12.4452	0.413008
$909$	7.26877	0.241090
$910$	1.81595	0.0601982
$911$	−19.1451	−0.634307	−0.317153	−	0.948374i	$-0.602727\pi$
$911$	−19.1451	−0.634307	−0.317153	+	0.948374i	$0.602727\pi$
$912$	−1.56406	−0.0517913
$913$	−38.9482	−1.28900
$914$	15.4859	0.512229
$915$	−4.20445	−0.138995
$916$	4.70486	0.155453
$917$	4.49457	0.148424
$918$	−0.346650	−0.0114412
$919$	−24.2888	−0.801214	−0.400607	−	0.916250i	$-0.631201\pi$
$919$	−24.2888	−0.801214	−0.400607	+	0.916250i	$0.631201\pi$
$920$	0.460247	0.0151739
$921$	20.4407	0.673543
$922$	29.4029	0.968334
$923$	−5.98425	−0.196974
$924$	−28.4695	−0.936576
$925$	−35.5948	−1.17035
$926$	27.9058	0.917042
$927$	32.5039	1.06757
$928$	−2.58114	−0.0847299
$929$	−4.87805	−0.160044	−0.0800218	−	0.996793i	$-0.525499\pi$
$929$	−4.87805	−0.160044	−0.0800218	+	0.996793i	$0.525499\pi$
$930$	−7.74022	−0.253812
$931$	8.55937	0.280522
$932$	0.200287	0.00656061
$933$	71.9160	2.35442
$934$	20.3053	0.664409
$935$	−0.959696	−0.0313854
$936$	−2.47472	−0.0808887
$937$	11.8812	0.388142	0.194071	−	0.980988i	$-0.437831\pi$
$937$	11.8812	0.388142	0.194071	+	0.980988i	$0.437831\pi$
$938$	67.3630	2.19948
$939$	−28.6205	−0.933994
$940$	−4.01228	−0.130866
$941$	−8.35763	−0.272451	−0.136225	−	0.990678i	$-0.543497\pi$
$941$	−8.35763	−0.272451	−0.136225	+	0.990678i	$0.543497\pi$
$942$	−26.8157	−0.873704
$943$	−1.59484	−0.0519351
$944$	3.77789	0.122960
$945$	−0.903010	−0.0293749
$946$	−2.63723	−0.0857438
$947$	42.1854	1.37084	0.685420	−	0.728148i	$-0.259619\pi$
$947$	42.1854	1.37084	0.685420	+	0.728148i	$0.259619\pi$
$948$	28.5209	0.926315
$949$	7.10833	0.230746
$950$	3.10455	0.100725
$951$	68.6056	2.22469
$952$	3.56916	0.115677
$953$	10.8419	0.351202	0.175601	−	0.984461i	$-0.443813\pi$
$953$	10.8419	0.351202	0.175601	+	0.984461i	$0.443813\pi$
$954$	−24.9402	−0.807469
$955$	7.88085	0.255018
$956$	18.1759	0.587852
$957$	16.3494	0.528501
$958$	12.9549	0.418554
$959$	−37.3535	−1.20621
$960$	−1.11024	−0.0358328
$961$	17.6043	0.567880
$962$	−6.52592	−0.210404
$963$	−1.91000	−0.0615489
$964$	−17.1104	−0.551088
$965$	10.1696	0.327371
$966$	10.8421	0.348839
$967$	−57.4506	−1.84749	−0.923743	−	0.383014i	$-0.874886\pi$
$967$	−57.4506	−1.84749	−0.923743	+	0.383014i	$0.874886\pi$
$968$	4.10507	0.131942
$969$	−1.24203	−0.0398997
$970$	1.83388	0.0588822
$971$	−20.9322	−0.671747	−0.335874	−	0.941907i	$-0.609032\pi$
$971$	−20.9322	−0.671747	−0.335874	+	0.941907i	$0.609032\pi$
$972$	21.6314	0.693828
$973$	2.71796	0.0871339
$974$	27.1150	0.868821
$975$	10.1396	0.324727
$976$	3.78698	0.121218
$977$	−19.0775	−0.610345	−0.305172	−	0.952297i	$-0.598714\pi$
$977$	−19.0775	−0.610345	−0.305172	+	0.952297i	$0.598714\pi$
$978$	31.0054	0.991444
$979$	25.4656	0.813885
$980$	6.07581	0.194085
$981$	37.7945	1.20669
$982$	10.5565	0.336870
$983$	1.24712	0.0397768	0.0198884	−	0.999802i	$-0.493669\pi$
$983$	1.24712	0.0397768	0.0198884	+	0.999802i	$0.493669\pi$
$984$	3.84718	0.122644
$985$	−1.96576	−0.0626342
$986$	−2.04969	−0.0652755
$987$	−94.5180	−3.00854
$988$	0.569185	0.0181082
$989$	1.00435	0.0319364
$990$	3.40688	0.108278
$991$	52.3126	1.66177	0.830883	−	0.556447i	$-0.187836\pi$
$991$	52.3126	1.66177	0.830883	+	0.556447i	$0.187836\pi$
$992$	6.97168	0.221351
$993$	−41.5647	−1.31902
$994$	−30.6389	−0.971806
$995$	8.74949	0.277378
$996$	−35.7806	−1.13375
$997$	46.5551	1.47441	0.737207	−	0.675666i	$-0.236144\pi$
$997$	46.5551	1.47441	0.737207	+	0.675666i	$0.236144\pi$
$998$	11.9256	0.377500
$999$	3.24511	0.102671

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.4	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.41227 q^{3} +1.00000 q^{4} +0.460247 q^{5} +2.41227 q^{6} -4.49457 q^{7} -1.00000 q^{8} +2.81904 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.41227 q^{3} +1.00000 q^{4} +0.460247 q^{5} +2.41227 q^{6} -4.49457 q^{7} -1.00000 q^{8} +2.81904 q^{9} -0.460247 q^{10} -2.62582 q^{11} -2.41227 q^{12} +0.877859 q^{13} +4.49457 q^{14} -1.11024 q^{15} +1.00000 q^{16} +0.794105 q^{17} -2.81904 q^{18} +0.648378 q^{19} +0.460247 q^{20} +10.8421 q^{21} +2.62582 q^{22} -1.00000 q^{23} +2.41227 q^{24} -4.78817 q^{25} -0.877859 q^{26} +0.436529 q^{27} -4.49457 q^{28} +2.58114 q^{29} +1.11024 q^{30} -6.97168 q^{31} -1.00000 q^{32} +6.33418 q^{33} -0.794105 q^{34} -2.06861 q^{35} +2.81904 q^{36} +7.43390 q^{37} -0.648378 q^{38} -2.11763 q^{39} -0.460247 q^{40} +1.59484 q^{41} -10.8421 q^{42} -1.00435 q^{43} -2.62582 q^{44} +1.29745 q^{45} +1.00000 q^{46} -8.71767 q^{47} -2.41227 q^{48} +13.2012 q^{49} +4.78817 q^{50} -1.91559 q^{51} +0.877859 q^{52} +8.84706 q^{53} -0.436529 q^{54} -1.20853 q^{55} +4.49457 q^{56} -1.56406 q^{57} -2.58114 q^{58} +3.77789 q^{59} -1.11024 q^{60} +3.78698 q^{61} +6.97168 q^{62} -12.6704 q^{63} +1.00000 q^{64} +0.404032 q^{65} -6.33418 q^{66} +14.9876 q^{67} +0.794105 q^{68} +2.41227 q^{69} +2.06861 q^{70} -6.81686 q^{71} -2.81904 q^{72} +8.09734 q^{73} -7.43390 q^{74} +11.5504 q^{75} +0.648378 q^{76} +11.8019 q^{77} +2.11763 q^{78} -11.8233 q^{79} +0.460247 q^{80} -9.51014 q^{81} -1.59484 q^{82} +14.8328 q^{83} +10.8421 q^{84} +0.365484 q^{85} +1.00435 q^{86} -6.22639 q^{87} +2.62582 q^{88} -9.69816 q^{89} -1.29745 q^{90} -3.94560 q^{91} -1.00000 q^{92} +16.8176 q^{93} +8.71767 q^{94} +0.298414 q^{95} +2.41227 q^{96} -3.98455 q^{97} -13.2012 q^{98} -7.40229 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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