LMFDB - Embedded newform 6026.2.a.h.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +1.62268 q^{10} +0.118061 q^{11} +2.29919 q^{12} +4.81440 q^{13} +0.601158 q^{14} -3.73086 q^{15} +1.00000 q^{16} -3.51146 q^{17} -2.28626 q^{18} -2.74780 q^{19} -1.62268 q^{20} -1.38218 q^{21} -0.118061 q^{22} -1.00000 q^{23} -2.29919 q^{24} -2.36690 q^{25} -4.81440 q^{26} -1.64101 q^{27} -0.601158 q^{28} +5.80808 q^{29} +3.73086 q^{30} -6.64833 q^{31} -1.00000 q^{32} +0.271445 q^{33} +3.51146 q^{34} +0.975490 q^{35} +2.28626 q^{36} -4.44857 q^{37} +2.74780 q^{38} +11.0692 q^{39} +1.62268 q^{40} +8.02457 q^{41} +1.38218 q^{42} +11.2206 q^{43} +0.118061 q^{44} -3.70988 q^{45} +1.00000 q^{46} +0.815901 q^{47} +2.29919 q^{48} -6.63861 q^{49} +2.36690 q^{50} -8.07350 q^{51} +4.81440 q^{52} -7.82807 q^{53} +1.64101 q^{54} -0.191576 q^{55} +0.601158 q^{56} -6.31772 q^{57} -5.80808 q^{58} -10.7632 q^{59} -3.73086 q^{60} -3.23578 q^{61} +6.64833 q^{62} -1.37441 q^{63} +1.00000 q^{64} -7.81225 q^{65} -0.271445 q^{66} -8.38187 q^{67} -3.51146 q^{68} -2.29919 q^{69} -0.975490 q^{70} +3.85349 q^{71} -2.28626 q^{72} +6.09743 q^{73} +4.44857 q^{74} -5.44194 q^{75} -2.74780 q^{76} -0.0709734 q^{77} -11.0692 q^{78} -15.8125 q^{79} -1.62268 q^{80} -10.6318 q^{81} -8.02457 q^{82} -0.448185 q^{83} -1.38218 q^{84} +5.69798 q^{85} -11.2206 q^{86} +13.3539 q^{87} -0.118061 q^{88} +10.4150 q^{89} +3.70988 q^{90} -2.89421 q^{91} -1.00000 q^{92} -15.2858 q^{93} -0.815901 q^{94} +4.45882 q^{95} -2.29919 q^{96} -4.65467 q^{97} +6.63861 q^{98} +0.269919 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.29919	1.32744	0.663718	−	0.747983i	$-0.268977\pi$
$3$	2.29919	1.32744	0.663718	+	0.747983i	$0.268977\pi$
$4$	1.00000	0.500000
$5$	−1.62268	−0.725686	−0.362843	−	0.931850i	$-0.618194\pi$
$5$	−1.62268	−0.725686	−0.362843	+	0.931850i	$0.618194\pi$
$6$	−2.29919	−0.938639
$7$	−0.601158	−0.227216	−0.113608	−	0.993526i	$-0.536241\pi$
$7$	−0.601158	−0.227216	−0.113608	+	0.993526i	$0.536241\pi$
$8$	−1.00000	−0.353553
$9$	2.28626	0.762088
$10$	1.62268	0.513138
$11$	0.118061	0.0355968	0.0177984	−	0.999842i	$-0.494334\pi$
$11$	0.118061	0.0355968	0.0177984	+	0.999842i	$0.494334\pi$
$12$	2.29919	0.663718
$13$	4.81440	1.33527	0.667637	−	0.744487i	$-0.267306\pi$
$13$	4.81440	1.33527	0.667637	+	0.744487i	$0.267306\pi$
$14$	0.601158	0.160666
$15$	−3.73086	−0.963303
$16$	1.00000	0.250000
$17$	−3.51146	−0.851653	−0.425827	−	0.904805i	$-0.640017\pi$
$17$	−3.51146	−0.851653	−0.425827	+	0.904805i	$0.640017\pi$
$18$	−2.28626	−0.538878
$19$	−2.74780	−0.630389	−0.315195	−	0.949027i	$-0.602070\pi$
$19$	−2.74780	−0.630389	−0.315195	+	0.949027i	$0.602070\pi$
$20$	−1.62268	−0.362843
$21$	−1.38218	−0.301615
$22$	−0.118061	−0.0251707
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.29919	−0.469320
$25$	−2.36690	−0.473379
$26$	−4.81440	−0.944181
$27$	−1.64101	−0.315813
$28$	−0.601158	−0.113608
$29$	5.80808	1.07853	0.539267	−	0.842135i	$-0.318701\pi$
$29$	5.80808	1.07853	0.539267	+	0.842135i	$0.318701\pi$
$30$	3.73086	0.681158
$31$	−6.64833	−1.19408	−0.597038	−	0.802213i	$-0.703656\pi$
$31$	−6.64833	−1.19408	−0.597038	+	0.802213i	$0.703656\pi$
$32$	−1.00000	−0.176777
$33$	0.271445	0.0472525
$34$	3.51146	0.602210
$35$	0.975490	0.164888
$36$	2.28626	0.381044
$37$	−4.44857	−0.731341	−0.365670	−	0.930744i	$-0.619160\pi$
$37$	−4.44857	−0.731341	−0.365670	+	0.930744i	$0.619160\pi$
$38$	2.74780	0.445753
$39$	11.0692	1.77249
$40$	1.62268	0.256569
$41$	8.02457	1.25323	0.626613	−	0.779330i	$-0.284441\pi$
$41$	8.02457	1.25323	0.626613	+	0.779330i	$0.284441\pi$
$42$	1.38218	0.213274
$43$	11.2206	1.71112	0.855562	−	0.517701i	$-0.173212\pi$
$43$	11.2206	1.71112	0.855562	+	0.517701i	$0.173212\pi$
$44$	0.118061	0.0177984
$45$	−3.70988	−0.553037
$46$	1.00000	0.147442
$47$	0.815901	0.119011	0.0595057	−	0.998228i	$-0.481048\pi$
$47$	0.815901	0.119011	0.0595057	+	0.998228i	$0.481048\pi$
$48$	2.29919	0.331859
$49$	−6.63861	−0.948373
$50$	2.36690	0.334730
$51$	−8.07350	−1.13052
$52$	4.81440	0.667637
$53$	−7.82807	−1.07527	−0.537634	−	0.843178i	$-0.680682\pi$
$53$	−7.82807	−1.07527	−0.537634	+	0.843178i	$0.680682\pi$
$54$	1.64101	0.223313
$55$	−0.191576	−0.0258321
$56$	0.601158	0.0803331
$57$	−6.31772	−0.836802
$58$	−5.80808	−0.762638
$59$	−10.7632	−1.40125	−0.700626	−	0.713528i	$-0.747096\pi$
$59$	−10.7632	−1.40125	−0.700626	+	0.713528i	$0.747096\pi$
$60$	−3.73086	−0.481651
$61$	−3.23578	−0.414300	−0.207150	−	0.978309i	$-0.566419\pi$
$61$	−3.23578	−0.414300	−0.207150	+	0.978309i	$0.566419\pi$
$62$	6.64833	0.844339
$63$	−1.37441	−0.173159
$64$	1.00000	0.125000
$65$	−7.81225	−0.968990
$66$	−0.271445	−0.0334126
$67$	−8.38187	−1.02401	−0.512004	−	0.858983i	$-0.671097\pi$
$67$	−8.38187	−1.02401	−0.512004	+	0.858983i	$0.671097\pi$
$68$	−3.51146	−0.425827
$69$	−2.29919	−0.276790
$70$	−0.975490	−0.116593
$71$	3.85349	0.457325	0.228662	−	0.973506i	$-0.426565\pi$
$71$	3.85349	0.457325	0.228662	+	0.973506i	$0.426565\pi$
$72$	−2.28626	−0.269439
$73$	6.09743	0.713650	0.356825	−	0.934171i	$-0.383859\pi$
$73$	6.09743	0.713650	0.356825	+	0.934171i	$0.383859\pi$
$74$	4.44857	0.517136
$75$	−5.44194	−0.628381
$76$	−2.74780	−0.315195
$77$	−0.0709734	−0.00808817
$78$	−11.0692	−1.25334
$79$	−15.8125	−1.77905	−0.889523	−	0.456890i	$-0.848963\pi$
$79$	−15.8125	−1.77905	−0.889523	+	0.456890i	$0.848963\pi$
$80$	−1.62268	−0.181422
$81$	−10.6318	−1.18131
$82$	−8.02457	−0.886165
$83$	−0.448185	−0.0491947	−0.0245973	−	0.999697i	$-0.507830\pi$
$83$	−0.448185	−0.0491947	−0.0245973	+	0.999697i	$0.507830\pi$
$84$	−1.38218	−0.150808
$85$	5.69798	0.618033
$86$	−11.2206	−1.20995
$87$	13.3539	1.43168
$88$	−0.118061	−0.0125854
$89$	10.4150	1.10399	0.551995	−	0.833847i	$-0.313867\pi$
$89$	10.4150	1.10399	0.551995	+	0.833847i	$0.313867\pi$
$90$	3.70988	0.391056
$91$	−2.89421	−0.303396
$92$	−1.00000	−0.104257
$93$	−15.2858	−1.58506
$94$	−0.815901	−0.0841537
$95$	4.45882	0.457465
$96$	−2.29919	−0.234660
$97$	−4.65467	−0.472610	−0.236305	−	0.971679i	$-0.575936\pi$
$97$	−4.65467	−0.472610	−0.236305	+	0.971679i	$0.575936\pi$
$98$	6.63861	0.670601
$99$	0.269919	0.0271279
$100$	−2.36690	−0.236690
$101$	10.3386	1.02873	0.514363	−	0.857573i	$-0.328029\pi$
$101$	10.3386	1.02873	0.514363	+	0.857573i	$0.328029\pi$
$102$	8.07350	0.799395
$103$	−13.5478	−1.33490	−0.667451	−	0.744654i	$-0.732615\pi$
$103$	−13.5478	−1.33490	−0.667451	+	0.744654i	$0.732615\pi$
$104$	−4.81440	−0.472090
$105$	2.24283	0.218878
$106$	7.82807	0.760330
$107$	5.10264	0.493291	0.246645	−	0.969106i	$-0.420672\pi$
$107$	5.10264	0.493291	0.246645	+	0.969106i	$0.420672\pi$
$108$	−1.64101	−0.157906
$109$	−6.01964	−0.576577	−0.288288	−	0.957544i	$-0.593086\pi$
$109$	−6.01964	−0.576577	−0.288288	+	0.957544i	$0.593086\pi$
$110$	0.191576	0.0182661
$111$	−10.2281	−0.970808
$112$	−0.601158	−0.0568041
$113$	6.58382	0.619354	0.309677	−	0.950842i	$-0.399779\pi$
$113$	6.58382	0.619354	0.309677	+	0.950842i	$0.399779\pi$
$114$	6.31772	0.591708
$115$	1.62268	0.151316
$116$	5.80808	0.539267
$117$	11.0070	1.01760
$118$	10.7632	0.990835
$119$	2.11094	0.193510
$120$	3.73086	0.340579
$121$	−10.9861	−0.998733
$122$	3.23578	0.292954
$123$	18.4500	1.66358
$124$	−6.64833	−0.597038
$125$	11.9541	1.06921
$126$	1.37441	0.122442
$127$	−6.72267	−0.596540	−0.298270	−	0.954481i	$-0.596410\pi$
$127$	−6.72267	−0.596540	−0.298270	+	0.954481i	$0.596410\pi$
$128$	−1.00000	−0.0883883
$129$	25.7982	2.27141
$130$	7.81225	0.685179
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	0.271445	0.0236262
$133$	1.65186	0.143235
$134$	8.38187	0.724083
$135$	2.66284	0.229181
$136$	3.51146	0.301105
$137$	−14.5852	−1.24609	−0.623047	−	0.782185i	$-0.714105\pi$
$137$	−14.5852	−1.24609	−0.623047	+	0.782185i	$0.714105\pi$
$138$	2.29919	0.195720
$139$	6.91226	0.586290	0.293145	−	0.956068i	$-0.405298\pi$
$139$	6.91226	0.586290	0.293145	+	0.956068i	$0.405298\pi$
$140$	0.975490	0.0824439
$141$	1.87591	0.157980
$142$	−3.85349	−0.323377
$143$	0.568393	0.0475314
$144$	2.28626	0.190522
$145$	−9.42468	−0.782677
$146$	−6.09743	−0.504627
$147$	−15.2634	−1.25890
$148$	−4.44857	−0.365670
$149$	1.01745	0.0833528	0.0416764	−	0.999131i	$-0.486730\pi$
$149$	1.01745	0.0833528	0.0416764	+	0.999131i	$0.486730\pi$
$150$	5.44194	0.444332
$151$	1.34391	0.109365	0.0546827	−	0.998504i	$-0.482585\pi$
$151$	1.34391	0.109365	0.0546827	+	0.998504i	$0.482585\pi$
$152$	2.74780	0.222876
$153$	−8.02812	−0.649035
$154$	0.0709734	0.00571920
$155$	10.7881	0.866525
$156$	11.0692	0.886246
$157$	−7.69200	−0.613888	−0.306944	−	0.951728i	$-0.599306\pi$
$157$	−7.69200	−0.613888	−0.306944	+	0.951728i	$0.599306\pi$
$158$	15.8125	1.25798
$159$	−17.9982	−1.42735
$160$	1.62268	0.128284
$161$	0.601158	0.0473779
$162$	10.6318	0.835312
$163$	−9.79436	−0.767154	−0.383577	−	0.923509i	$-0.625308\pi$
$163$	−9.79436	−0.767154	−0.383577	+	0.923509i	$0.625308\pi$
$164$	8.02457	0.626613
$165$	−0.440469	−0.0342905
$166$	0.448185	0.0347859
$167$	−16.0930	−1.24531	−0.622657	−	0.782495i	$-0.713947\pi$
$167$	−16.0930	−1.24531	−0.622657	+	0.782495i	$0.713947\pi$
$168$	1.38218	0.106637
$169$	10.1784	0.782955
$170$	−5.69798	−0.437015
$171$	−6.28220	−0.480412
$172$	11.2206	0.855562
$173$	9.80576	0.745518	0.372759	−	0.927928i	$-0.378412\pi$
$173$	9.80576	0.745518	0.372759	+	0.927928i	$0.378412\pi$
$174$	−13.3539	−1.01235
$175$	1.42288	0.107560
$176$	0.118061	0.00889920
$177$	−24.7467	−1.86007
$178$	−10.4150	−0.780639
$179$	−5.16756	−0.386242	−0.193121	−	0.981175i	$-0.561861\pi$
$179$	−5.16756	−0.386242	−0.193121	+	0.981175i	$0.561861\pi$
$180$	−3.70988	−0.276518
$181$	8.10081	0.602129	0.301064	−	0.953604i	$-0.402658\pi$
$181$	8.10081	0.602129	0.301064	+	0.953604i	$0.402658\pi$
$182$	2.89421	0.214533
$183$	−7.43968	−0.549957
$184$	1.00000	0.0737210
$185$	7.21863	0.530724
$186$	15.2858	1.12081
$187$	−0.414567	−0.0303161
$188$	0.815901	0.0595057
$189$	0.986508	0.0717579
$190$	−4.45882	−0.323477
$191$	8.70768	0.630066	0.315033	−	0.949081i	$-0.397984\pi$
$191$	8.70768	0.630066	0.315033	+	0.949081i	$0.397984\pi$
$192$	2.29919	0.165930
$193$	23.1241	1.66451	0.832256	−	0.554391i	$-0.187049\pi$
$193$	23.1241	1.66451	0.832256	+	0.554391i	$0.187049\pi$
$194$	4.65467	0.334186
$195$	−17.9618	−1.28627
$196$	−6.63861	−0.474186
$197$	−6.73646	−0.479953	−0.239977	−	0.970779i	$-0.577140\pi$
$197$	−6.73646	−0.479953	−0.239977	+	0.970779i	$0.577140\pi$
$198$	−0.269919	−0.0191823
$199$	−1.93685	−0.137300	−0.0686500	−	0.997641i	$-0.521869\pi$
$199$	−1.93685	−0.137300	−0.0686500	+	0.997641i	$0.521869\pi$
$200$	2.36690	0.167365
$201$	−19.2715	−1.35931
$202$	−10.3386	−0.727419
$203$	−3.49157	−0.245060
$204$	−8.07350	−0.565258
$205$	−13.0213	−0.909449
$206$	13.5478	0.943918
$207$	−2.28626	−0.158906
$208$	4.81440	0.333818
$209$	−0.324409	−0.0224398
$210$	−2.24283	−0.154770
$211$	−12.6938	−0.873879	−0.436940	−	0.899491i	$-0.643938\pi$
$211$	−12.6938	−0.873879	−0.436940	+	0.899491i	$0.643938\pi$
$212$	−7.82807	−0.537634
$213$	8.85989	0.607070
$214$	−5.10264	−0.348809
$215$	−18.2075	−1.24174
$216$	1.64101	0.111657
$217$	3.99670	0.271314
$218$	6.01964	0.407701
$219$	14.0191	0.947326
$220$	−0.191576	−0.0129161
$221$	−16.9055	−1.13719
$222$	10.2281	0.686465
$223$	−10.5092	−0.703749	−0.351874	−	0.936047i	$-0.614456\pi$
$223$	−10.5092	−0.703749	−0.351874	+	0.936047i	$0.614456\pi$
$224$	0.601158	0.0401666
$225$	−5.41135	−0.360757
$226$	−6.58382	−0.437949
$227$	−22.9375	−1.52242	−0.761208	−	0.648507i	$-0.775394\pi$
$227$	−22.9375	−1.52242	−0.761208	+	0.648507i	$0.775394\pi$
$228$	−6.31772	−0.418401
$229$	−24.6843	−1.63118	−0.815591	−	0.578629i	$-0.803588\pi$
$229$	−24.6843	−1.63118	−0.815591	+	0.578629i	$0.803588\pi$
$230$	−1.62268	−0.106997
$231$	−0.163181	−0.0107365
$232$	−5.80808	−0.381319
$233$	−2.94955	−0.193231	−0.0966157	−	0.995322i	$-0.530802\pi$
$233$	−2.94955	−0.193231	−0.0966157	+	0.995322i	$0.530802\pi$
$234$	−11.0070	−0.719549
$235$	−1.32395	−0.0863649
$236$	−10.7632	−0.700626
$237$	−36.3559	−2.36157
$238$	−2.11094	−0.136832
$239$	8.98230	0.581016	0.290508	−	0.956872i	$-0.406176\pi$
$239$	8.98230	0.581016	0.290508	+	0.956872i	$0.406176\pi$
$240$	−3.73086	−0.240826
$241$	−12.4279	−0.800551	−0.400276	−	0.916395i	$-0.631086\pi$
$241$	−12.4279	−0.800551	−0.400276	+	0.916395i	$0.631086\pi$
$242$	10.9861	0.706211
$243$	−19.5214	−1.25230
$244$	−3.23578	−0.207150
$245$	10.7724	0.688221
$246$	−18.4500	−1.17633
$247$	−13.2290	−0.841742
$248$	6.64833	0.422170
$249$	−1.03046	−0.0653028
$250$	−11.9541	−0.756047
$251$	−9.30722	−0.587466	−0.293733	−	0.955887i	$-0.594898\pi$
$251$	−9.30722	−0.587466	−0.293733	+	0.955887i	$0.594898\pi$
$252$	−1.37441	−0.0865795
$253$	−0.118061	−0.00742244
$254$	6.72267	0.421818
$255$	13.1007	0.820400
$256$	1.00000	0.0625000
$257$	17.1110	1.06736	0.533678	−	0.845688i	$-0.320809\pi$
$257$	17.1110	1.06736	0.533678	+	0.845688i	$0.320809\pi$
$258$	−25.7982	−1.60613
$259$	2.67430	0.166173
$260$	−7.81225	−0.484495
$261$	13.2788	0.821937
$262$	1.00000	0.0617802
$263$	1.75797	0.108401	0.0542006	−	0.998530i	$-0.482739\pi$
$263$	1.75797	0.108401	0.0542006	+	0.998530i	$0.482739\pi$
$264$	−0.271445	−0.0167063
$265$	12.7025	0.780308
$266$	−1.65186	−0.101282
$267$	23.9461	1.46548
$268$	−8.38187	−0.512004
$269$	−8.81830	−0.537661	−0.268830	−	0.963188i	$-0.586637\pi$
$269$	−8.81830	−0.537661	−0.268830	+	0.963188i	$0.586637\pi$
$270$	−2.66284	−0.162056
$271$	−11.4333	−0.694521	−0.347260	−	0.937769i	$-0.612888\pi$
$271$	−11.4333	−0.694521	−0.347260	+	0.937769i	$0.612888\pi$
$272$	−3.51146	−0.212913
$273$	−6.65434	−0.402739
$274$	14.5852	0.881121
$275$	−0.279439	−0.0168508
$276$	−2.29919	−0.138395
$277$	12.0380	0.723294	0.361647	−	0.932315i	$-0.382215\pi$
$277$	12.0380	0.723294	0.361647	+	0.932315i	$0.382215\pi$
$278$	−6.91226	−0.414570
$279$	−15.1999	−0.909991
$280$	−0.975490	−0.0582967
$281$	−13.2570	−0.790847	−0.395423	−	0.918499i	$-0.629402\pi$
$281$	−13.2570	−0.790847	−0.395423	+	0.918499i	$0.629402\pi$
$282$	−1.87591	−0.111709
$283$	−1.40466	−0.0834981	−0.0417491	−	0.999128i	$-0.513293\pi$
$283$	−1.40466	−0.0834981	−0.0417491	+	0.999128i	$0.513293\pi$
$284$	3.85349	0.228662
$285$	10.2517	0.607256
$286$	−0.568393	−0.0336098
$287$	−4.82403	−0.284754
$288$	−2.28626	−0.134719
$289$	−4.66968	−0.274687
$290$	9.42468	0.553436
$291$	−10.7020	−0.627360
$292$	6.09743	0.356825
$293$	1.08531	0.0634044	0.0317022	−	0.999497i	$-0.489907\pi$
$293$	1.08531	0.0634044	0.0317022	+	0.999497i	$0.489907\pi$
$294$	15.2634	0.890180
$295$	17.4653	1.01687
$296$	4.44857	0.258568
$297$	−0.193740	−0.0112419
$298$	−1.01745	−0.0589394
$299$	−4.81440	−0.278424
$300$	−5.44194	−0.314191
$301$	−6.74535	−0.388795
$302$	−1.34391	−0.0773331
$303$	23.7703	1.36557
$304$	−2.74780	−0.157597
$305$	5.25066	0.300652
$306$	8.02812	0.458937
$307$	−12.1620	−0.694125	−0.347062	−	0.937842i	$-0.612821\pi$
$307$	−12.1620	−0.694125	−0.347062	+	0.937842i	$0.612821\pi$
$308$	−0.0709734	−0.00404409
$309$	−31.1489	−1.77200
$310$	−10.7881	−0.612726
$311$	−3.42649	−0.194298	−0.0971491	−	0.995270i	$-0.530972\pi$
$311$	−3.42649	−0.194298	−0.0971491	+	0.995270i	$0.530972\pi$
$312$	−11.0692	−0.626670
$313$	−6.15710	−0.348020	−0.174010	−	0.984744i	$-0.555672\pi$
$313$	−6.15710	−0.348020	−0.174010	+	0.984744i	$0.555672\pi$
$314$	7.69200	0.434084
$315$	2.23023	0.125659
$316$	−15.8125	−0.889523
$317$	34.2244	1.92223	0.961117	−	0.276141i	$-0.0890556\pi$
$317$	34.2244	1.92223	0.961117	+	0.276141i	$0.0890556\pi$
$318$	17.9982	1.00929
$319$	0.685709	0.0383923
$320$	−1.62268	−0.0907108
$321$	11.7319	0.654812
$322$	−0.601158	−0.0335012
$323$	9.64879	0.536873
$324$	−10.6318	−0.590655
$325$	−11.3952	−0.632091
$326$	9.79436	0.542459
$327$	−13.8403	−0.765369
$328$	−8.02457	−0.443082
$329$	−0.490485	−0.0270413
$330$	0.440469	0.0242470
$331$	21.3451	1.17323	0.586617	−	0.809865i	$-0.300459\pi$
$331$	21.3451	1.17323	0.586617	+	0.809865i	$0.300459\pi$
$332$	−0.448185	−0.0245973
$333$	−10.1706	−0.557346
$334$	16.0930	0.880570
$335$	13.6011	0.743109
$336$	−1.38218	−0.0754039
$337$	−5.03354	−0.274194	−0.137097	−	0.990558i	$-0.543777\pi$
$337$	−5.03354	−0.274194	−0.137097	+	0.990558i	$0.543777\pi$
$338$	−10.1784	−0.553633
$339$	15.1374	0.822153
$340$	5.69798	0.309016
$341$	−0.784910	−0.0425053
$342$	6.28220	0.339703
$343$	8.19896	0.442702
$344$	−11.2206	−0.604973
$345$	3.73086	0.200863
$346$	−9.80576	−0.527161
$347$	−12.8733	−0.691075	−0.345537	−	0.938405i	$-0.612303\pi$
$347$	−12.8733	−0.691075	−0.345537	+	0.938405i	$0.612303\pi$
$348$	13.3539	0.715842
$349$	20.6690	1.10639	0.553194	−	0.833052i	$-0.313409\pi$
$349$	20.6690	1.10639	0.553194	+	0.833052i	$0.313409\pi$
$350$	−1.42288	−0.0760561
$351$	−7.90048	−0.421697
$352$	−0.118061	−0.00629268
$353$	−11.5217	−0.613240	−0.306620	−	0.951832i	$-0.599198\pi$
$353$	−11.5217	−0.613240	−0.306620	+	0.951832i	$0.599198\pi$
$354$	24.7467	1.31527
$355$	−6.25299	−0.331874
$356$	10.4150	0.551995
$357$	4.85345	0.256872
$358$	5.16756	0.273114
$359$	6.80640	0.359228	0.179614	−	0.983737i	$-0.442515\pi$
$359$	6.80640	0.359228	0.179614	+	0.983737i	$0.442515\pi$
$360$	3.70988	0.195528
$361$	−11.4496	−0.602609
$362$	−8.10081	−0.425769
$363$	−25.2590	−1.32575
$364$	−2.89421	−0.151698
$365$	−9.89421	−0.517886
$366$	7.43968	0.388878
$367$	−0.533112	−0.0278282	−0.0139141	−	0.999903i	$-0.504429\pi$
$367$	−0.533112	−0.0278282	−0.0139141	+	0.999903i	$0.504429\pi$
$368$	−1.00000	−0.0521286
$369$	18.3463	0.955069
$370$	−7.21863	−0.375279
$371$	4.70591	0.244319
$372$	−15.2858	−0.792530
$373$	13.4325	0.695508	0.347754	−	0.937586i	$-0.386944\pi$
$373$	13.4325	0.695508	0.347754	+	0.937586i	$0.386944\pi$
$374$	0.414567	0.0214367
$375$	27.4848	1.41931
$376$	−0.815901	−0.0420769
$377$	27.9624	1.44014
$378$	−0.986508	−0.0507405
$379$	0.744775	0.0382565	0.0191283	−	0.999817i	$-0.493911\pi$
$379$	0.744775	0.0382565	0.0191283	+	0.999817i	$0.493911\pi$
$380$	4.45882	0.228732
$381$	−15.4567	−0.791870
$382$	−8.70768	−0.445524
$383$	−21.5517	−1.10124	−0.550621	−	0.834755i	$-0.685609\pi$
$383$	−21.5517	−1.10124	−0.550621	+	0.834755i	$0.685609\pi$
$384$	−2.29919	−0.117330
$385$	0.115167	0.00586948
$386$	−23.1241	−1.17699
$387$	25.6532	1.30403
$388$	−4.65467	−0.236305
$389$	13.6072	0.689914	0.344957	−	0.938619i	$-0.387894\pi$
$389$	13.6072	0.689914	0.344957	+	0.938619i	$0.387894\pi$
$390$	17.9618	0.909532
$391$	3.51146	0.177582
$392$	6.63861	0.335300
$393$	−2.29919	−0.115979
$394$	6.73646	0.339378
$395$	25.6587	1.29103
$396$	0.269919	0.0135639
$397$	−22.8790	−1.14826	−0.574132	−	0.818763i	$-0.694660\pi$
$397$	−22.8790	−1.14826	−0.574132	+	0.818763i	$0.694660\pi$
$398$	1.93685	0.0970857
$399$	3.79795	0.190135
$400$	−2.36690	−0.118345
$401$	−22.9781	−1.14747	−0.573736	−	0.819041i	$-0.694506\pi$
$401$	−22.9781	−1.14747	−0.573736	+	0.819041i	$0.694506\pi$
$402$	19.2715	0.961175
$403$	−32.0077	−1.59442
$404$	10.3386	0.514363
$405$	17.2520	0.857260
$406$	3.49157	0.173284
$407$	−0.525204	−0.0260334
$408$	8.07350	0.399698
$409$	−31.4559	−1.55539	−0.777697	−	0.628639i	$-0.783612\pi$
$409$	−31.4559	−1.55539	−0.777697	+	0.628639i	$0.783612\pi$
$410$	13.0213	0.643078
$411$	−33.5340	−1.65411
$412$	−13.5478	−0.667451
$413$	6.47040	0.318388
$414$	2.28626	0.112364
$415$	0.727263	0.0356999
$416$	−4.81440	−0.236045
$417$	15.8926	0.778263
$418$	0.324409	0.0158674
$419$	−0.850397	−0.0415446	−0.0207723	−	0.999784i	$-0.506613\pi$
$419$	−0.850397	−0.0415446	−0.0207723	+	0.999784i	$0.506613\pi$
$420$	2.24283	0.109439
$421$	−1.80229	−0.0878385	−0.0439192	−	0.999035i	$-0.513984\pi$
$421$	−1.80229	−0.0878385	−0.0439192	+	0.999035i	$0.513984\pi$
$422$	12.6938	0.617926
$423$	1.86536	0.0906971
$424$	7.82807	0.380165
$425$	8.31125	0.403155
$426$	−8.85989	−0.429263
$427$	1.94522	0.0941357
$428$	5.10264	0.246645
$429$	1.30684	0.0630950
$430$	18.2075	0.878042
$431$	11.5367	0.555702	0.277851	−	0.960624i	$-0.410378\pi$
$431$	11.5367	0.555702	0.277851	+	0.960624i	$0.410378\pi$
$432$	−1.64101	−0.0789532
$433$	11.4637	0.550912	0.275456	−	0.961314i	$-0.411171\pi$
$433$	11.4637	0.550912	0.275456	+	0.961314i	$0.411171\pi$
$434$	−3.99670	−0.191848
$435$	−21.6691	−1.03895
$436$	−6.01964	−0.288288
$437$	2.74780	0.131445
$438$	−14.0191	−0.669860
$439$	17.4847	0.834501	0.417250	−	0.908792i	$-0.362994\pi$
$439$	17.4847	0.834501	0.417250	+	0.908792i	$0.362994\pi$
$440$	0.191576	0.00913303
$441$	−15.1776	−0.722744
$442$	16.9055	0.804115
$443$	23.7018	1.12611	0.563054	−	0.826420i	$-0.309626\pi$
$443$	23.7018	1.12611	0.563054	+	0.826420i	$0.309626\pi$
$444$	−10.2281	−0.485404
$445$	−16.9003	−0.801151
$446$	10.5092	0.497626
$447$	2.33931	0.110646
$448$	−0.601158	−0.0284021
$449$	−22.3938	−1.05683	−0.528414	−	0.848987i	$-0.677213\pi$
$449$	−22.3938	−1.05683	−0.528414	+	0.848987i	$0.677213\pi$
$450$	5.41135	0.255094
$451$	0.947390	0.0446108
$452$	6.58382	0.309677
$453$	3.08989	0.145176
$454$	22.9375	1.07651
$455$	4.69639	0.220170
$456$	6.31772	0.295854
$457$	−20.5209	−0.959925	−0.479963	−	0.877289i	$-0.659350\pi$
$457$	−20.5209	−0.959925	−0.479963	+	0.877289i	$0.659350\pi$
$458$	24.6843	1.15342
$459$	5.76234	0.268963
$460$	1.62268	0.0756580
$461$	−23.4636	−1.09281	−0.546405	−	0.837521i	$-0.684004\pi$
$461$	−23.4636	−1.09281	−0.546405	+	0.837521i	$0.684004\pi$
$462$	0.163181	0.00759188
$463$	−10.0337	−0.466306	−0.233153	−	0.972440i	$-0.574904\pi$
$463$	−10.0337	−0.466306	−0.233153	+	0.972440i	$0.574904\pi$
$464$	5.80808	0.269633
$465$	24.8040	1.15026
$466$	2.94955	0.136635
$467$	−3.18900	−0.147569	−0.0737847	−	0.997274i	$-0.523508\pi$
$467$	−3.18900	−0.147569	−0.0737847	+	0.997274i	$0.523508\pi$
$468$	11.0070	0.508798
$469$	5.03883	0.232672
$470$	1.32395	0.0610692
$471$	−17.6853	−0.814898
$472$	10.7632	0.495418
$473$	1.32472	0.0609105
$474$	36.3559	1.66988
$475$	6.50377	0.298413
$476$	2.11094	0.0967548
$477$	−17.8970	−0.819449
$478$	−8.98230	−0.410841
$479$	13.7447	0.628010	0.314005	−	0.949421i	$-0.398329\pi$
$479$	13.7447	0.628010	0.314005	+	0.949421i	$0.398329\pi$
$480$	3.73086	0.170289
$481$	−21.4172	−0.976540
$482$	12.4279	0.566075
$483$	1.38218	0.0628912
$484$	−10.9861	−0.499366
$485$	7.55306	0.342967
$486$	19.5214	0.885511
$487$	−34.9908	−1.58558	−0.792792	−	0.609492i	$-0.791373\pi$
$487$	−34.9908	−1.58558	−0.792792	+	0.609492i	$0.791373\pi$
$488$	3.23578	0.146477
$489$	−22.5191	−1.01835
$490$	−10.7724	−0.486646
$491$	18.4775	0.833876	0.416938	−	0.908935i	$-0.363103\pi$
$491$	18.4775	0.833876	0.416938	+	0.908935i	$0.363103\pi$
$492$	18.4500	0.831789
$493$	−20.3948	−0.918536
$494$	13.2290	0.595202
$495$	−0.437993	−0.0196863
$496$	−6.64833	−0.298519
$497$	−2.31655	−0.103912
$498$	1.03046	0.0461761
$499$	17.1021	0.765594	0.382797	−	0.923832i	$-0.374961\pi$
$499$	17.1021	0.765594	0.382797	+	0.923832i	$0.374961\pi$
$500$	11.9541	0.534606
$501$	−37.0008	−1.65308
$502$	9.30722	0.415401
$503$	−7.78887	−0.347289	−0.173644	−	0.984808i	$-0.555554\pi$
$503$	−7.78887	−0.347289	−0.173644	+	0.984808i	$0.555554\pi$
$504$	1.37441	0.0612209
$505$	−16.7762	−0.746532
$506$	0.118061	0.00524846
$507$	23.4021	1.03932
$508$	−6.72267	−0.298270
$509$	19.0632	0.844960	0.422480	−	0.906372i	$-0.361160\pi$
$509$	19.0632	0.844960	0.422480	+	0.906372i	$0.361160\pi$
$510$	−13.1007	−0.580110
$511$	−3.66552	−0.162153
$512$	−1.00000	−0.0441942
$513$	4.50918	0.199085
$514$	−17.1110	−0.754735
$515$	21.9838	0.968720
$516$	25.7982	1.13570
$517$	0.0963262	0.00423642
$518$	−2.67430	−0.117502
$519$	22.5453	0.989628
$520$	7.81225	0.342590
$521$	−7.54190	−0.330417	−0.165208	−	0.986259i	$-0.552830\pi$
$521$	−7.54190	−0.330417	−0.165208	+	0.986259i	$0.552830\pi$
$522$	−13.2788	−0.581198
$523$	17.7776	0.777360	0.388680	−	0.921373i	$-0.372931\pi$
$523$	17.7776	0.777360	0.388680	+	0.921373i	$0.372931\pi$
$524$	−1.00000	−0.0436852
$525$	3.27147	0.142778
$526$	−1.75797	−0.0766512
$527$	23.3453	1.01694
$528$	0.271445	0.0118131
$529$	1.00000	0.0434783
$530$	−12.7025	−0.551761
$531$	−24.6076	−1.06788
$532$	1.65186	0.0716174
$533$	38.6334	1.67340
$534$	−23.9461	−1.03625
$535$	−8.27997	−0.357974
$536$	8.38187	0.362042
$537$	−11.8812	−0.512711
$538$	8.81830	0.380184
$539$	−0.783762	−0.0337590
$540$	2.66284	0.114591
$541$	29.2667	1.25828	0.629138	−	0.777294i	$-0.283408\pi$
$541$	29.2667	1.25828	0.629138	+	0.777294i	$0.283408\pi$
$542$	11.4333	0.491100
$543$	18.6253	0.799288
$544$	3.51146	0.150552
$545$	9.76797	0.418414
$546$	6.65434	0.284780
$547$	−26.9384	−1.15180	−0.575902	−	0.817519i	$-0.695349\pi$
$547$	−26.9384	−1.15180	−0.575902	+	0.817519i	$0.695349\pi$
$548$	−14.5852	−0.623047
$549$	−7.39786	−0.315733
$550$	0.279439	0.0119153
$551$	−15.9595	−0.679896
$552$	2.29919	0.0978599
$553$	9.50582	0.404229
$554$	−12.0380	−0.511446
$555$	16.5970	0.704502
$556$	6.91226	0.293145
$557$	43.7703	1.85461	0.927304	−	0.374310i	$-0.122120\pi$
$557$	43.7703	1.85461	0.927304	+	0.374310i	$0.122120\pi$
$558$	15.1999	0.643461
$559$	54.0204	2.28482
$560$	0.975490	0.0412220
$561$	−0.953166	−0.0402427
$562$	13.2570	0.559213
$563$	9.44853	0.398208	0.199104	−	0.979978i	$-0.436197\pi$
$563$	9.44853	0.398208	0.199104	+	0.979978i	$0.436197\pi$
$564$	1.87591	0.0789900
$565$	−10.6835	−0.449457
$566$	1.40466	0.0590421
$567$	6.39139	0.268413
$568$	−3.85349	−0.161689
$569$	−34.3904	−1.44172	−0.720859	−	0.693081i	$-0.756253\pi$
$569$	−34.3904	−1.44172	−0.720859	+	0.693081i	$0.756253\pi$
$570$	−10.2517	−0.429395
$571$	38.8193	1.62454	0.812268	−	0.583284i	$-0.198233\pi$
$571$	38.8193	1.62454	0.812268	+	0.583284i	$0.198233\pi$
$572$	0.568393	0.0237657
$573$	20.0206	0.836372
$574$	4.82403	0.201351
$575$	2.36690	0.0987064
$576$	2.28626	0.0952610
$577$	−0.193257	−0.00804541	−0.00402270	−	0.999992i	$-0.501280\pi$
$577$	−0.193257	−0.00804541	−0.00402270	+	0.999992i	$0.501280\pi$
$578$	4.66968	0.194233
$579$	53.1667	2.20953
$580$	−9.42468	−0.391338
$581$	0.269430	0.0111778
$582$	10.7020	0.443611
$583$	−0.924192	−0.0382761
$584$	−6.09743	−0.252314
$585$	−17.8609	−0.738456
$586$	−1.08531	−0.0448337
$587$	0.471622	0.0194659	0.00973296	−	0.999953i	$-0.496902\pi$
$587$	0.471622	0.0194659	0.00973296	+	0.999953i	$0.496902\pi$
$588$	−15.2634	−0.629452
$589$	18.2683	0.752733
$590$	−17.4653	−0.719036
$591$	−15.4884	−0.637107
$592$	−4.44857	−0.182835
$593$	0.443621	0.0182173	0.00910867	−	0.999959i	$-0.497101\pi$
$593$	0.443621	0.0182173	0.00910867	+	0.999959i	$0.497101\pi$
$594$	0.193740	0.00794924
$595$	−3.42539	−0.140427
$596$	1.01745	0.0416764
$597$	−4.45319	−0.182257
$598$	4.81440	0.196875
$599$	5.57915	0.227958	0.113979	−	0.993483i	$-0.463640\pi$
$599$	5.57915	0.227958	0.113979	+	0.993483i	$0.463640\pi$
$600$	5.44194	0.222166
$601$	35.2000	1.43584	0.717920	−	0.696126i	$-0.245094\pi$
$601$	35.2000	1.43584	0.717920	+	0.696126i	$0.245094\pi$
$602$	6.74535	0.274920
$603$	−19.1632	−0.780385
$604$	1.34391	0.0546827
$605$	17.8269	0.724767
$606$	−23.7703	−0.965602
$607$	31.8953	1.29459	0.647294	−	0.762240i	$-0.275901\pi$
$607$	31.8953	1.29459	0.647294	+	0.762240i	$0.275901\pi$
$608$	2.74780	0.111438
$609$	−8.02779	−0.325302
$610$	−5.25066	−0.212593
$611$	3.92807	0.158913
$612$	−8.02812	−0.324517
$613$	10.8474	0.438124	0.219062	−	0.975711i	$-0.429700\pi$
$613$	10.8474	0.438124	0.219062	+	0.975711i	$0.429700\pi$
$614$	12.1620	0.490820
$615$	−29.9385	−1.20724
$616$	0.0709734	0.00285960
$617$	−42.3653	−1.70556	−0.852782	−	0.522267i	$-0.825087\pi$
$617$	−42.3653	−1.70556	−0.852782	+	0.522267i	$0.825087\pi$
$618$	31.1489	1.25299
$619$	−21.7581	−0.874533	−0.437266	−	0.899332i	$-0.644053\pi$
$619$	−21.7581	−0.874533	−0.437266	+	0.899332i	$0.644053\pi$
$620$	10.7881	0.433262
$621$	1.64101	0.0658516
$622$	3.42649	0.137390
$623$	−6.26108	−0.250845
$624$	11.0692	0.443123
$625$	−7.56332	−0.302533
$626$	6.15710	0.246087
$627$	−0.745877	−0.0297875
$628$	−7.69200	−0.306944
$629$	15.6210	0.622849
$630$	−2.23023	−0.0888544
$631$	−5.17826	−0.206143	−0.103072	−	0.994674i	$-0.532867\pi$
$631$	−5.17826	−0.206143	−0.103072	+	0.994674i	$0.532867\pi$
$632$	15.8125	0.628988
$633$	−29.1855	−1.16002
$634$	−34.2244	−1.35922
$635$	10.9088	0.432901
$636$	−17.9982	−0.713676
$637$	−31.9609	−1.26634
$638$	−0.685709	−0.0271475
$639$	8.81009	0.348522
$640$	1.62268	0.0641422
$641$	−4.36173	−0.172278	−0.0861390	−	0.996283i	$-0.527453\pi$
$641$	−4.36173	−0.172278	−0.0861390	+	0.996283i	$0.527453\pi$
$642$	−11.7319	−0.463022
$643$	−13.7337	−0.541604	−0.270802	−	0.962635i	$-0.587289\pi$
$643$	−13.7337	−0.541604	−0.270802	+	0.962635i	$0.587289\pi$
$644$	0.601158	0.0236889
$645$	−41.8624	−1.64833
$646$	−9.64879	−0.379626
$647$	21.3908	0.840959	0.420479	−	0.907302i	$-0.361862\pi$
$647$	21.3908	0.840959	0.420479	+	0.907302i	$0.361862\pi$
$648$	10.6318	0.417656
$649$	−1.27072	−0.0498801
$650$	11.3952	0.446956
$651$	9.18916	0.360152
$652$	−9.79436	−0.383577
$653$	−5.04152	−0.197290	−0.0986449	−	0.995123i	$-0.531451\pi$
$653$	−5.04152	−0.197290	−0.0986449	+	0.995123i	$0.531451\pi$
$654$	13.8403	0.541198
$655$	1.62268	0.0634035
$656$	8.02457	0.313307
$657$	13.9403	0.543865
$658$	0.490485	0.0191211
$659$	−15.6129	−0.608191	−0.304096	−	0.952641i	$-0.598354\pi$
$659$	−15.6129	−0.608191	−0.304096	+	0.952641i	$0.598354\pi$
$660$	−0.440469	−0.0171452
$661$	−16.7470	−0.651381	−0.325691	−	0.945476i	$-0.605597\pi$
$661$	−16.7470	−0.651381	−0.325691	+	0.945476i	$0.605597\pi$
$662$	−21.3451	−0.829602
$663$	−38.8690	−1.50955
$664$	0.448185	0.0173930
$665$	−2.68045	−0.103944
$666$	10.1706	0.394103
$667$	−5.80808	−0.224890
$668$	−16.0930	−0.622657
$669$	−24.1627	−0.934182
$670$	−13.6011	−0.525457
$671$	−0.382021	−0.0147477
$672$	1.38218	0.0533186
$673$	22.0691	0.850703	0.425351	−	0.905028i	$-0.360150\pi$
$673$	22.0691	0.850703	0.425351	+	0.905028i	$0.360150\pi$
$674$	5.03354	0.193885
$675$	3.88411	0.149499
$676$	10.1784	0.391478
$677$	0.176272	0.00677467	0.00338733	−	0.999994i	$-0.498922\pi$
$677$	0.176272	0.00677467	0.00338733	+	0.999994i	$0.498922\pi$
$678$	−15.1374	−0.581350
$679$	2.79819	0.107385
$680$	−5.69798	−0.218508
$681$	−52.7377	−2.02091
$682$	0.784910	0.0300558
$683$	46.4105	1.77585	0.887925	−	0.459988i	$-0.152146\pi$
$683$	46.4105	1.77585	0.887925	+	0.459988i	$0.152146\pi$
$684$	−6.28220	−0.240206
$685$	23.6671	0.904273
$686$	−8.19896	−0.313038
$687$	−56.7538	−2.16529
$688$	11.2206	0.427781
$689$	−37.6875	−1.43578
$690$	−3.73086	−0.142031
$691$	−1.42767	−0.0543111	−0.0271555	−	0.999631i	$-0.508645\pi$
$691$	−1.42767	−0.0543111	−0.0271555	+	0.999631i	$0.508645\pi$
$692$	9.80576	0.372759
$693$	−0.162264	−0.00616390
$694$	12.8733	0.488664
$695$	−11.2164	−0.425463
$696$	−13.3539	−0.506177
$697$	−28.1779	−1.06731
$698$	−20.6690	−0.782335
$699$	−6.78157	−0.256502
$700$	1.42288	0.0537798
$701$	26.3563	0.995464	0.497732	−	0.867331i	$-0.334166\pi$
$701$	26.3563	0.995464	0.497732	+	0.867331i	$0.334166\pi$
$702$	7.90048	0.298185
$703$	12.2238	0.461029
$704$	0.118061	0.00444960
$705$	−3.04401	−0.114644
$706$	11.5217	0.433626
$707$	−6.21511	−0.233743
$708$	−24.7467	−0.930037
$709$	−37.5284	−1.40941	−0.704703	−	0.709502i	$-0.748920\pi$
$709$	−37.5284	−1.40941	−0.704703	+	0.709502i	$0.748920\pi$
$710$	6.25299	0.234671
$711$	−36.1516	−1.35579
$712$	−10.4150	−0.390320
$713$	6.64833	0.248982
$714$	−4.85345	−0.181636
$715$	−0.922323	−0.0344929
$716$	−5.16756	−0.193121
$717$	20.6520	0.771263
$718$	−6.80640	−0.254013
$719$	31.6776	1.18138	0.590688	−	0.806900i	$-0.298856\pi$
$719$	31.6776	1.18138	0.590688	+	0.806900i	$0.298856\pi$
$720$	−3.70988	−0.138259
$721$	8.14436	0.303312
$722$	11.4496	0.426109
$723$	−28.5741	−1.06268
$724$	8.10081	0.301064
$725$	−13.7471	−0.510555
$726$	25.2590	0.937450
$727$	2.69450	0.0999335	0.0499668	−	0.998751i	$-0.484088\pi$
$727$	2.69450	0.0999335	0.0499668	+	0.998751i	$0.484088\pi$
$728$	2.89421	0.107267
$729$	−12.9881	−0.481040
$730$	9.89421	0.366201
$731$	−39.4006	−1.45728
$732$	−7.43968	−0.274978
$733$	29.8995	1.10436	0.552182	−	0.833724i	$-0.313796\pi$
$733$	29.8995	1.10436	0.552182	+	0.833724i	$0.313796\pi$
$734$	0.533112	0.0196775
$735$	24.7677	0.913570
$736$	1.00000	0.0368605
$737$	−0.989574	−0.0364514
$738$	−18.3463	−0.675336
$739$	−8.16117	−0.300214	−0.150107	−	0.988670i	$-0.547962\pi$
$739$	−8.16117	−0.300214	−0.150107	+	0.988670i	$0.547962\pi$
$740$	7.21863	0.265362
$741$	−30.4160	−1.11736
$742$	−4.70591	−0.172759
$743$	18.9856	0.696515	0.348258	−	0.937399i	$-0.386773\pi$
$743$	18.9856	0.696515	0.348258	+	0.937399i	$0.386773\pi$
$744$	15.2858	0.560403
$745$	−1.65100	−0.0604880
$746$	−13.4325	−0.491798
$747$	−1.02467	−0.0374907
$748$	−0.414567	−0.0151581
$749$	−3.06749	−0.112084
$750$	−27.4848	−1.00360
$751$	29.1539	1.06384	0.531920	−	0.846794i	$-0.321471\pi$
$751$	29.1539	1.06384	0.531920	+	0.846794i	$0.321471\pi$
$752$	0.815901	0.0297528
$753$	−21.3990	−0.779824
$754$	−27.9624	−1.01833
$755$	−2.18073	−0.0793651
$756$	0.986508	0.0358789
$757$	−3.75880	−0.136616	−0.0683080	−	0.997664i	$-0.521760\pi$
$757$	−3.75880	−0.136616	−0.0683080	+	0.997664i	$0.521760\pi$
$758$	−0.744775	−0.0270514
$759$	−0.271445	−0.00985282
$760$	−4.45882	−0.161738
$761$	−31.4160	−1.13883	−0.569415	−	0.822051i	$-0.692830\pi$
$761$	−31.4160	−1.13883	−0.569415	+	0.822051i	$0.692830\pi$
$762$	15.4567	0.559936
$763$	3.61875	0.131008
$764$	8.70768	0.315033
$765$	13.0271	0.470996
$766$	21.5517	0.778695
$767$	−51.8184	−1.87106
$768$	2.29919	0.0829648
$769$	22.3818	0.807108	0.403554	−	0.914956i	$-0.367775\pi$
$769$	22.3818	0.807108	0.403554	+	0.914956i	$0.367775\pi$
$770$	−0.115167	−0.00415035
$771$	39.3414	1.41685
$772$	23.1241	0.832256
$773$	32.6438	1.17411	0.587057	−	0.809545i	$-0.300286\pi$
$773$	32.6438	1.17411	0.587057	+	0.809545i	$0.300286\pi$
$774$	−25.6532	−0.922086
$775$	15.7359	0.565251
$776$	4.65467	0.167093
$777$	6.14871	0.220584
$778$	−13.6072	−0.487843
$779$	−22.0499	−0.790021
$780$	−17.9618	−0.643136
$781$	0.454947	0.0162793
$782$	−3.51146	−0.125569
$783$	−9.53113	−0.340615
$784$	−6.63861	−0.237093
$785$	12.4817	0.445490
$786$	2.29919	0.0820093
$787$	−14.3986	−0.513255	−0.256628	−	0.966510i	$-0.582611\pi$
$787$	−14.3986	−0.513255	−0.256628	+	0.966510i	$0.582611\pi$
$788$	−6.73646	−0.239977
$789$	4.04191	0.143896
$790$	−25.6587	−0.912896
$791$	−3.95792	−0.140727
$792$	−0.269919	−0.00959116
$793$	−15.5784	−0.553204
$794$	22.8790	0.811945
$795$	29.2054	1.03581
$796$	−1.93685	−0.0686500
$797$	5.18362	0.183613	0.0918066	−	0.995777i	$-0.470736\pi$
$797$	5.18362	0.183613	0.0918066	+	0.995777i	$0.470736\pi$
$798$	−3.79795	−0.134446
$799$	−2.86500	−0.101356
$800$	2.36690	0.0836824
$801$	23.8115	0.841338
$802$	22.9781	0.811385
$803$	0.719870	0.0254037
$804$	−19.2715	−0.679653
$805$	−0.975490	−0.0343815
$806$	32.0077	1.12742
$807$	−20.2749	−0.713711
$808$	−10.3386	−0.363709
$809$	−50.2302	−1.76600	−0.882999	−	0.469374i	$-0.844480\pi$
$809$	−50.2302	−1.76600	−0.882999	+	0.469374i	$0.844480\pi$
$810$	−17.2520	−0.606175
$811$	18.1535	0.637455	0.318728	−	0.947846i	$-0.396744\pi$
$811$	18.1535	0.637455	0.318728	+	0.947846i	$0.396744\pi$
$812$	−3.49157	−0.122530
$813$	−26.2872	−0.921933
$814$	0.525204	0.0184084
$815$	15.8932	0.556713
$816$	−8.07350	−0.282629
$817$	−30.8320	−1.07867
$818$	31.4559	1.09983
$819$	−6.61694	−0.231215
$820$	−13.0213	−0.454725
$821$	−18.4093	−0.642488	−0.321244	−	0.946996i	$-0.604101\pi$
$821$	−18.4093	−0.642488	−0.321244	+	0.946996i	$0.604101\pi$
$822$	33.5340	1.16963
$823$	−37.5643	−1.30941	−0.654704	−	0.755885i	$-0.727207\pi$
$823$	−37.5643	−1.30941	−0.654704	+	0.755885i	$0.727207\pi$
$824$	13.5478	0.471959
$825$	−0.642482	−0.0223683
$826$	−6.47040	−0.225134
$827$	−45.9054	−1.59629	−0.798143	−	0.602468i	$-0.794184\pi$
$827$	−45.9054	−1.59629	−0.798143	+	0.602468i	$0.794184\pi$
$828$	−2.28626	−0.0794532
$829$	49.2869	1.71181	0.855903	−	0.517137i	$-0.173002\pi$
$829$	49.2869	1.71181	0.855903	+	0.517137i	$0.173002\pi$
$830$	−0.727263	−0.0252437
$831$	27.6776	0.960126
$832$	4.81440	0.166909
$833$	23.3112	0.807684
$834$	−15.8926	−0.550315
$835$	26.1139	0.903708
$836$	−0.324409	−0.0112199
$837$	10.9100	0.377105
$838$	0.850397	0.0293765
$839$	−8.05676	−0.278150	−0.139075	−	0.990282i	$-0.544413\pi$
$839$	−8.05676	−0.278150	−0.139075	+	0.990282i	$0.544413\pi$
$840$	−2.24283	−0.0773851
$841$	4.73379	0.163234
$842$	1.80229	0.0621112
$843$	−30.4804	−1.04980
$844$	−12.6938	−0.436940
$845$	−16.5164	−0.568180
$846$	−1.86536	−0.0641326
$847$	6.60436	0.226929
$848$	−7.82807	−0.268817
$849$	−3.22957	−0.110838
$850$	−8.31125	−0.285074
$851$	4.44857	0.152495
$852$	8.85989	0.303535
$853$	13.2386	0.453280	0.226640	−	0.973979i	$-0.427226\pi$
$853$	13.2386	0.453280	0.226640	+	0.973979i	$0.427226\pi$
$854$	−1.94522	−0.0665640
$855$	10.1940	0.348629
$856$	−5.10264	−0.174405
$857$	−5.97496	−0.204101	−0.102050	−	0.994779i	$-0.532540\pi$
$857$	−5.97496	−0.204101	−0.102050	+	0.994779i	$0.532540\pi$
$858$	−1.30684	−0.0446149
$859$	27.5217	0.939029	0.469515	−	0.882925i	$-0.344429\pi$
$859$	27.5217	0.939029	0.469515	+	0.882925i	$0.344429\pi$
$860$	−18.2075	−0.620869
$861$	−11.0914	−0.377992
$862$	−11.5367	−0.392940
$863$	−25.5864	−0.870972	−0.435486	−	0.900195i	$-0.643424\pi$
$863$	−25.5864	−0.870972	−0.435486	+	0.900195i	$0.643424\pi$
$864$	1.64101	0.0558284
$865$	−15.9117	−0.541012
$866$	−11.4637	−0.389554
$867$	−10.7365	−0.364630
$868$	3.99670	0.135657
$869$	−1.86684	−0.0633283
$870$	21.6691	0.734651
$871$	−40.3537	−1.36733
$872$	6.01964	0.203851
$873$	−10.6418	−0.360171
$874$	−2.74780	−0.0929458
$875$	−7.18633	−0.242942
$876$	14.0191	0.473663
$877$	−51.0839	−1.72498	−0.862490	−	0.506075i	$-0.831096\pi$
$877$	−51.0839	−1.72498	−0.862490	+	0.506075i	$0.831096\pi$
$878$	−17.4847	−0.590081
$879$	2.49533	0.0841653
$880$	−0.191576	−0.00645803
$881$	2.49391	0.0840219	0.0420110	−	0.999117i	$-0.486624\pi$
$881$	2.49391	0.0840219	0.0420110	+	0.999117i	$0.486624\pi$
$882$	15.1776	0.511057
$883$	37.1651	1.25070	0.625352	−	0.780343i	$-0.284955\pi$
$883$	37.1651	1.25070	0.625352	+	0.780343i	$0.284955\pi$
$884$	−16.9055	−0.568595
$885$	40.1560	1.34983
$886$	−23.7018	−0.796278
$887$	−22.3446	−0.750258	−0.375129	−	0.926973i	$-0.622402\pi$
$887$	−22.3446	−0.750258	−0.375129	+	0.926973i	$0.622402\pi$
$888$	10.2281	0.343233
$889$	4.04139	0.135544
$890$	16.9003	0.566499
$891$	−1.25520	−0.0420508
$892$	−10.5092	−0.351874
$893$	−2.24193	−0.0750235
$894$	−2.33931	−0.0782383
$895$	8.38532	0.280290
$896$	0.601158	0.0200833
$897$	−11.0692	−0.369590
$898$	22.3938	0.747290
$899$	−38.6141	−1.28785
$900$	−5.41135	−0.180378
$901$	27.4879	0.915756
$902$	−0.947390	−0.0315446
$903$	−15.5088	−0.516101
$904$	−6.58382	−0.218975
$905$	−13.1451	−0.436957
$906$	−3.08989	−0.102655
$907$	−29.9119	−0.993209	−0.496605	−	0.867977i	$-0.665420\pi$
$907$	−29.9119	−0.993209	−0.496605	+	0.867977i	$0.665420\pi$
$908$	−22.9375	−0.761208
$909$	23.6367	0.783979
$910$	−4.69639	−0.155684
$911$	−15.7724	−0.522561	−0.261281	−	0.965263i	$-0.584145\pi$
$911$	−15.7724	−0.522561	−0.261281	+	0.965263i	$0.584145\pi$
$912$	−6.31772	−0.209200
$913$	−0.0529133	−0.00175117
$914$	20.5209	0.678770
$915$	12.0722	0.399096
$916$	−24.6843	−0.815591
$917$	0.601158	0.0198520
$918$	−5.76234	−0.190186
$919$	−31.4918	−1.03882	−0.519409	−	0.854526i	$-0.673848\pi$
$919$	−31.4918	−1.03882	−0.519409	+	0.854526i	$0.673848\pi$
$920$	−1.62268	−0.0534983
$921$	−27.9628	−0.921406
$922$	23.4636	0.772733
$923$	18.5522	0.610654
$924$	−0.163181	−0.00536827
$925$	10.5293	0.346202
$926$	10.0337	0.329728
$927$	−30.9738	−1.01731
$928$	−5.80808	−0.190660
$929$	17.8498	0.585633	0.292816	−	0.956169i	$-0.405408\pi$
$929$	17.8498	0.585633	0.292816	+	0.956169i	$0.405408\pi$
$930$	−24.8040	−0.813354
$931$	18.2416	0.597844
$932$	−2.94955	−0.0966157
$933$	−7.87814	−0.257919
$934$	3.18900	0.104347
$935$	0.672711	0.0220000
$936$	−11.0070	−0.359775
$937$	16.6891	0.545210	0.272605	−	0.962126i	$-0.412115\pi$
$937$	16.6891	0.545210	0.272605	+	0.962126i	$0.412115\pi$
$938$	−5.03883	−0.164524
$939$	−14.1563	−0.461974
$940$	−1.32395	−0.0431825
$941$	47.7185	1.55558	0.777789	−	0.628525i	$-0.216341\pi$
$941$	47.7185	1.55558	0.777789	+	0.628525i	$0.216341\pi$
$942$	17.6853	0.576220
$943$	−8.02457	−0.261316
$944$	−10.7632	−0.350313
$945$	−1.60079	−0.0520737
$946$	−1.32472	−0.0430702
$947$	3.53327	0.114816	0.0574079	−	0.998351i	$-0.481716\pi$
$947$	3.53327	0.114816	0.0574079	+	0.998351i	$0.481716\pi$
$948$	−36.3559	−1.18079
$949$	29.3555	0.952919
$950$	−6.50377	−0.211010
$951$	78.6883	2.55164
$952$	−2.11094	−0.0684160
$953$	0.182648	0.00591654	0.00295827	−	0.999996i	$-0.499058\pi$
$953$	0.182648	0.00591654	0.00295827	+	0.999996i	$0.499058\pi$
$954$	17.8970	0.579438
$955$	−14.1298	−0.457230
$956$	8.98230	0.290508
$957$	1.57657	0.0509634
$958$	−13.7447	−0.444070
$959$	8.76798	0.283133
$960$	−3.73086	−0.120413
$961$	13.2004	0.425818
$962$	21.4172	0.690518
$963$	11.6660	0.375931
$964$	−12.4279	−0.400276
$965$	−37.5232	−1.20791
$966$	−1.38218	−0.0444708
$967$	27.8245	0.894774	0.447387	−	0.894340i	$-0.352355\pi$
$967$	27.8245	0.894774	0.447387	+	0.894340i	$0.352355\pi$
$968$	10.9861	0.353105
$969$	22.1844	0.712665
$970$	−7.55306	−0.242514
$971$	−16.9958	−0.545423	−0.272711	−	0.962096i	$-0.587920\pi$
$971$	−16.9958	−0.545423	−0.272711	+	0.962096i	$0.587920\pi$
$972$	−19.5214	−0.626151
$973$	−4.15536	−0.133215
$974$	34.9908	1.12118
$975$	−26.1997	−0.839061
$976$	−3.23578	−0.103575
$977$	−23.5314	−0.752838	−0.376419	−	0.926450i	$-0.622845\pi$
$977$	−23.5314	−0.752838	−0.376419	+	0.926450i	$0.622845\pi$
$978$	22.5191	0.720081
$979$	1.22961	0.0392985
$980$	10.7724	0.344111
$981$	−13.7625	−0.439402
$982$	−18.4775	−0.589639
$983$	−25.4980	−0.813259	−0.406630	−	0.913593i	$-0.633296\pi$
$983$	−25.4980	−0.813259	−0.406630	+	0.913593i	$0.633296\pi$
$984$	−18.4500	−0.588164
$985$	10.9311	0.348295
$986$	20.3948	0.649503
$987$	−1.12772	−0.0358957
$988$	−13.2290	−0.420871
$989$	−11.2206	−0.356794
$990$	0.437993	0.0139203
$991$	42.9548	1.36450	0.682252	−	0.731117i	$-0.261001\pi$
$991$	42.9548	1.36450	0.682252	+	0.731117i	$0.261001\pi$
$992$	6.64833	0.211085
$993$	49.0764	1.55739
$994$	2.31655	0.0734766
$995$	3.14290	0.0996367
$996$	−1.03046	−0.0326514
$997$	−21.4965	−0.680802	−0.340401	−	0.940280i	$-0.610563\pi$
$997$	−21.4965	−0.680802	−0.340401	+	0.940280i	$0.610563\pi$
$998$	−17.1021	−0.541357
$999$	7.30016	0.230967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.20	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.29919 q^{3} +1.00000 q^{4} -1.62268 q^{5} -2.29919 q^{6} -0.601158 q^{7} -1.00000 q^{8} +2.28626 q^{9} +1.62268 q^{10} +0.118061 q^{11} +2.29919 q^{12} +4.81440 q^{13} +0.601158 q^{14} -3.73086 q^{15} +1.00000 q^{16} -3.51146 q^{17} -2.28626 q^{18} -2.74780 q^{19} -1.62268 q^{20} -1.38218 q^{21} -0.118061 q^{22} -1.00000 q^{23} -2.29919 q^{24} -2.36690 q^{25} -4.81440 q^{26} -1.64101 q^{27} -0.601158 q^{28} +5.80808 q^{29} +3.73086 q^{30} -6.64833 q^{31} -1.00000 q^{32} +0.271445 q^{33} +3.51146 q^{34} +0.975490 q^{35} +2.28626 q^{36} -4.44857 q^{37} +2.74780 q^{38} +11.0692 q^{39} +1.62268 q^{40} +8.02457 q^{41} +1.38218 q^{42} +11.2206 q^{43} +0.118061 q^{44} -3.70988 q^{45} +1.00000 q^{46} +0.815901 q^{47} +2.29919 q^{48} -6.63861 q^{49} +2.36690 q^{50} -8.07350 q^{51} +4.81440 q^{52} -7.82807 q^{53} +1.64101 q^{54} -0.191576 q^{55} +0.601158 q^{56} -6.31772 q^{57} -5.80808 q^{58} -10.7632 q^{59} -3.73086 q^{60} -3.23578 q^{61} +6.64833 q^{62} -1.37441 q^{63} +1.00000 q^{64} -7.81225 q^{65} -0.271445 q^{66} -8.38187 q^{67} -3.51146 q^{68} -2.29919 q^{69} -0.975490 q^{70} +3.85349 q^{71} -2.28626 q^{72} +6.09743 q^{73} +4.44857 q^{74} -5.44194 q^{75} -2.74780 q^{76} -0.0709734 q^{77} -11.0692 q^{78} -15.8125 q^{79} -1.62268 q^{80} -10.6318 q^{81} -8.02457 q^{82} -0.448185 q^{83} -1.38218 q^{84} +5.69798 q^{85} -11.2206 q^{86} +13.3539 q^{87} -0.118061 q^{88} +10.4150 q^{89} +3.70988 q^{90} -2.89421 q^{91} -1.00000 q^{92} -15.2858 q^{93} -0.815901 q^{94} +4.45882 q^{95} -2.29919 q^{96} -4.65467 q^{97} +6.63861 q^{98} +0.269919 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 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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