LMFDB - Embedded newform 6026.2.a.i.1.14

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:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.180068 q^{3} +1.00000 q^{4} -3.11636 q^{5} -0.180068 q^{6} +2.83625 q^{7} -1.00000 q^{8} -2.96758 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.180068 q^{3} +1.00000 q^{4} -3.11636 q^{5} -0.180068 q^{6} +2.83625 q^{7} -1.00000 q^{8} -2.96758 q^{9} +3.11636 q^{10} +1.84231 q^{11} +0.180068 q^{12} -3.19934 q^{13} -2.83625 q^{14} -0.561156 q^{15} +1.00000 q^{16} +5.26163 q^{17} +2.96758 q^{18} -2.30746 q^{19} -3.11636 q^{20} +0.510718 q^{21} -1.84231 q^{22} +1.00000 q^{23} -0.180068 q^{24} +4.71170 q^{25} +3.19934 q^{26} -1.07457 q^{27} +2.83625 q^{28} -4.19619 q^{29} +0.561156 q^{30} +0.161014 q^{31} -1.00000 q^{32} +0.331740 q^{33} -5.26163 q^{34} -8.83879 q^{35} -2.96758 q^{36} +3.37004 q^{37} +2.30746 q^{38} -0.576099 q^{39} +3.11636 q^{40} +7.27050 q^{41} -0.510718 q^{42} -4.10314 q^{43} +1.84231 q^{44} +9.24803 q^{45} -1.00000 q^{46} +8.67972 q^{47} +0.180068 q^{48} +1.04433 q^{49} -4.71170 q^{50} +0.947450 q^{51} -3.19934 q^{52} -5.41261 q^{53} +1.07457 q^{54} -5.74129 q^{55} -2.83625 q^{56} -0.415500 q^{57} +4.19619 q^{58} -11.3258 q^{59} -0.561156 q^{60} +4.07919 q^{61} -0.161014 q^{62} -8.41680 q^{63} +1.00000 q^{64} +9.97030 q^{65} -0.331740 q^{66} -8.82256 q^{67} +5.26163 q^{68} +0.180068 q^{69} +8.83879 q^{70} +3.83844 q^{71} +2.96758 q^{72} -3.38686 q^{73} -3.37004 q^{74} +0.848425 q^{75} -2.30746 q^{76} +5.22525 q^{77} +0.576099 q^{78} +15.0426 q^{79} -3.11636 q^{80} +8.70923 q^{81} -7.27050 q^{82} +14.6578 q^{83} +0.510718 q^{84} -16.3971 q^{85} +4.10314 q^{86} -0.755599 q^{87} -1.84231 q^{88} +4.17165 q^{89} -9.24803 q^{90} -9.07414 q^{91} +1.00000 q^{92} +0.0289934 q^{93} -8.67972 q^{94} +7.19088 q^{95} -0.180068 q^{96} -0.272963 q^{97} -1.04433 q^{98} -5.46718 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	0.180068	0.103962	0.0519811	−	0.998648i	$-0.483446\pi$
$3$	0.180068	0.103962	0.0519811	+	0.998648i	$0.483446\pi$
$4$	1.00000	0.500000
$5$	−3.11636	−1.39368	−0.696839	−	0.717227i	$-0.745411\pi$
$5$	−3.11636	−1.39368	−0.696839	+	0.717227i	$0.745411\pi$
$6$	−0.180068	−0.0735124
$7$	2.83625	1.07200	0.536001	−	0.844217i	$-0.319934\pi$
$7$	2.83625	1.07200	0.536001	+	0.844217i	$0.319934\pi$
$8$	−1.00000	−0.353553
$9$	−2.96758	−0.989192
$10$	3.11636	0.985479
$11$	1.84231	0.555476	0.277738	−	0.960657i	$-0.410415\pi$
$11$	1.84231	0.555476	0.277738	+	0.960657i	$0.410415\pi$
$12$	0.180068	0.0519811
$13$	−3.19934	−0.887338	−0.443669	−	0.896191i	$-0.646323\pi$
$13$	−3.19934	−0.887338	−0.443669	+	0.896191i	$0.646323\pi$
$14$	−2.83625	−0.758021
$15$	−0.561156	−0.144890
$16$	1.00000	0.250000
$17$	5.26163	1.27613	0.638066	−	0.769982i	$-0.279735\pi$
$17$	5.26163	1.27613	0.638066	+	0.769982i	$0.279735\pi$
$18$	2.96758	0.699464
$19$	−2.30746	−0.529368	−0.264684	−	0.964335i	$-0.585268\pi$
$19$	−2.30746	−0.529368	−0.264684	+	0.964335i	$0.585268\pi$
$20$	−3.11636	−0.696839
$21$	0.510718	0.111448
$22$	−1.84231	−0.392781
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.180068	−0.0367562
$25$	4.71170	0.942340
$26$	3.19934	0.627443
$27$	−1.07457	−0.206801
$28$	2.83625	0.536001
$29$	−4.19619	−0.779213	−0.389606	−	0.920981i	$-0.627389\pi$
$29$	−4.19619	−0.779213	−0.389606	+	0.920981i	$0.627389\pi$
$30$	0.561156	0.102453
$31$	0.161014	0.0289189	0.0144595	−	0.999895i	$-0.495397\pi$
$31$	0.161014	0.0289189	0.0144595	+	0.999895i	$0.495397\pi$
$32$	−1.00000	−0.176777
$33$	0.331740	0.0577486
$34$	−5.26163	−0.902362
$35$	−8.83879	−1.49403
$36$	−2.96758	−0.494596
$37$	3.37004	0.554032	0.277016	−	0.960865i	$-0.410655\pi$
$37$	3.37004	0.554032	0.277016	+	0.960865i	$0.410655\pi$
$38$	2.30746	0.374320
$39$	−0.576099	−0.0922496
$40$	3.11636	0.492740
$41$	7.27050	1.13546	0.567730	−	0.823215i	$-0.307822\pi$
$41$	7.27050	1.13546	0.567730	+	0.823215i	$0.307822\pi$
$42$	−0.510718	−0.0788055
$43$	−4.10314	−0.625724	−0.312862	−	0.949799i	$-0.601288\pi$
$43$	−4.10314	−0.625724	−0.312862	+	0.949799i	$0.601288\pi$
$44$	1.84231	0.277738
$45$	9.24803	1.37862
$46$	−1.00000	−0.147442
$47$	8.67972	1.26607	0.633033	−	0.774125i	$-0.281810\pi$
$47$	8.67972	1.26607	0.633033	+	0.774125i	$0.281810\pi$
$48$	0.180068	0.0259906
$49$	1.04433	0.149190
$50$	−4.71170	−0.666335
$51$	0.947450	0.132670
$52$	−3.19934	−0.443669
$53$	−5.41261	−0.743479	−0.371740	−	0.928337i	$-0.621239\pi$
$53$	−5.41261	−0.743479	−0.371740	+	0.928337i	$0.621239\pi$
$54$	1.07457	0.146230
$55$	−5.74129	−0.774155
$56$	−2.83625	−0.379010
$57$	−0.415500	−0.0550343
$58$	4.19619	0.550987
$59$	−11.3258	−1.47449	−0.737245	−	0.675626i	$-0.763874\pi$
$59$	−11.3258	−1.47449	−0.737245	+	0.675626i	$0.763874\pi$
$60$	−0.561156	−0.0724450
$61$	4.07919	0.522287	0.261143	−	0.965300i	$-0.415900\pi$
$61$	4.07919	0.522287	0.261143	+	0.965300i	$0.415900\pi$
$62$	−0.161014	−0.0204488
$63$	−8.41680	−1.06042
$64$	1.00000	0.125000
$65$	9.97030	1.23666
$66$	−0.331740	−0.0408344
$67$	−8.82256	−1.07785	−0.538924	−	0.842355i	$-0.681169\pi$
$67$	−8.82256	−1.07785	−0.538924	+	0.842355i	$0.681169\pi$
$68$	5.26163	0.638066
$69$	0.180068	0.0216776
$70$	8.83879	1.05644
$71$	3.83844	0.455539	0.227769	−	0.973715i	$-0.426857\pi$
$71$	3.83844	0.455539	0.227769	+	0.973715i	$0.426857\pi$
$72$	2.96758	0.349732
$73$	−3.38686	−0.396402	−0.198201	−	0.980161i	$-0.563510\pi$
$73$	−3.38686	−0.396402	−0.198201	+	0.980161i	$0.563510\pi$
$74$	−3.37004	−0.391759
$75$	0.848425	0.0979677
$76$	−2.30746	−0.264684
$77$	5.22525	0.595472
$78$	0.576099	0.0652303
$79$	15.0426	1.69242	0.846210	−	0.532849i	$-0.178879\pi$
$79$	15.0426	1.69242	0.846210	+	0.532849i	$0.178879\pi$
$80$	−3.11636	−0.348420
$81$	8.70923	0.967692
$82$	−7.27050	−0.802892
$83$	14.6578	1.60891	0.804453	−	0.594016i	$-0.202458\pi$
$83$	14.6578	1.60891	0.804453	+	0.594016i	$0.202458\pi$
$84$	0.510718	0.0557239
$85$	−16.3971	−1.77852
$86$	4.10314	0.442453
$87$	−0.755599	−0.0810087
$88$	−1.84231	−0.196391
$89$	4.17165	0.442194	0.221097	−	0.975252i	$-0.429036\pi$
$89$	4.17165	0.442194	0.221097	+	0.975252i	$0.429036\pi$
$90$	−9.24803	−0.974828
$91$	−9.07414	−0.951229
$92$	1.00000	0.104257
$93$	0.0289934	0.00300648
$94$	−8.67972	−0.895244
$95$	7.19088	0.737769
$96$	−0.180068	−0.0183781
$97$	−0.272963	−0.0277152	−0.0138576	−	0.999904i	$-0.504411\pi$
$97$	−0.272963	−0.0277152	−0.0138576	+	0.999904i	$0.504411\pi$
$98$	−1.04433	−0.105494
$99$	−5.46718	−0.549473
$100$	4.71170	0.471170
$101$	−1.72561	−0.171704	−0.0858521	−	0.996308i	$-0.527361\pi$
$101$	−1.72561	−0.171704	−0.0858521	+	0.996308i	$0.527361\pi$
$102$	−0.947450	−0.0938115
$103$	−15.7235	−1.54929	−0.774643	−	0.632399i	$-0.782070\pi$
$103$	−15.7235	−1.54929	−0.774643	+	0.632399i	$0.782070\pi$
$104$	3.19934	0.313721
$105$	−1.59158	−0.155322
$106$	5.41261	0.525719
$107$	8.87665	0.858138	0.429069	−	0.903272i	$-0.358842\pi$
$107$	8.87665	0.858138	0.429069	+	0.903272i	$0.358842\pi$
$108$	−1.07457	−0.103400
$109$	−12.2645	−1.17472	−0.587361	−	0.809325i	$-0.699833\pi$
$109$	−12.2645	−1.17472	−0.587361	+	0.809325i	$0.699833\pi$
$110$	5.74129	0.547410
$111$	0.606836	0.0575984
$112$	2.83625	0.268001
$113$	−15.2526	−1.43485	−0.717424	−	0.696637i	$-0.754679\pi$
$113$	−15.2526	−1.43485	−0.717424	+	0.696637i	$0.754679\pi$
$114$	0.415500	0.0389151
$115$	−3.11636	−0.290602
$116$	−4.19619	−0.389606
$117$	9.49429	0.877747
$118$	11.3258	1.04262
$119$	14.9233	1.36802
$120$	0.561156	0.0512263
$121$	−7.60591	−0.691446
$122$	−4.07919	−0.369312
$123$	1.30918	0.118045
$124$	0.161014	0.0144595
$125$	0.898453	0.0803601
$126$	8.41680	0.749828
$127$	−3.70620	−0.328872	−0.164436	−	0.986388i	$-0.552580\pi$
$127$	−3.70620	−0.328872	−0.164436	+	0.986388i	$0.552580\pi$
$128$	−1.00000	−0.0883883
$129$	−0.738844	−0.0650516
$130$	−9.97030	−0.874453
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.331740	0.0288743
$133$	−6.54454	−0.567484
$134$	8.82256	0.762153
$135$	3.34874	0.288214
$136$	−5.26163	−0.451181
$137$	6.34452	0.542049	0.271025	−	0.962572i	$-0.412638\pi$
$137$	6.34452	0.542049	0.271025	+	0.962572i	$0.412638\pi$
$138$	−0.180068	−0.0153284
$139$	−0.627932	−0.0532605	−0.0266302	−	0.999645i	$-0.508478\pi$
$139$	−0.627932	−0.0532605	−0.0266302	+	0.999645i	$0.508478\pi$
$140$	−8.83879	−0.747014
$141$	1.56294	0.131623
$142$	−3.83844	−0.322115
$143$	−5.89417	−0.492895
$144$	−2.96758	−0.247298
$145$	13.0768	1.08597
$146$	3.38686	0.280299
$147$	0.188051	0.0155102
$148$	3.37004	0.277016
$149$	−7.01246	−0.574483	−0.287242	−	0.957858i	$-0.592738\pi$
$149$	−7.01246	−0.574483	−0.287242	+	0.957858i	$0.592738\pi$
$150$	−0.848425	−0.0692736
$151$	10.1219	0.823708	0.411854	−	0.911250i	$-0.364881\pi$
$151$	10.1219	0.823708	0.411854	+	0.911250i	$0.364881\pi$
$152$	2.30746	0.187160
$153$	−15.6143	−1.26234
$154$	−5.22525	−0.421062
$155$	−0.501777	−0.0403037
$156$	−0.576099	−0.0461248
$157$	−18.1972	−1.45230	−0.726148	−	0.687538i	$-0.758691\pi$
$157$	−18.1972	−1.45230	−0.726148	+	0.687538i	$0.758691\pi$
$158$	−15.0426	−1.19672
$159$	−0.974637	−0.0772938
$160$	3.11636	0.246370
$161$	2.83625	0.223528
$162$	−8.70923	−0.684262
$163$	1.13547	0.0889369	0.0444684	−	0.999011i	$-0.485841\pi$
$163$	1.13547	0.0889369	0.0444684	+	0.999011i	$0.485841\pi$
$164$	7.27050	0.567730
$165$	−1.03382	−0.0804829
$166$	−14.6578	−1.13767
$167$	9.90036	0.766113	0.383056	−	0.923725i	$-0.374871\pi$
$167$	9.90036	0.766113	0.383056	+	0.923725i	$0.374871\pi$
$168$	−0.510718	−0.0394028
$169$	−2.76421	−0.212632
$170$	16.3971	1.25760
$171$	6.84756	0.523646
$172$	−4.10314	−0.312862
$173$	−20.3169	−1.54466	−0.772331	−	0.635220i	$-0.780909\pi$
$173$	−20.3169	−1.54466	−0.772331	+	0.635220i	$0.780909\pi$
$174$	0.755599	0.0572818
$175$	13.3636	1.01019
$176$	1.84231	0.138869
$177$	−2.03941	−0.153291
$178$	−4.17165	−0.312678
$179$	11.1814	0.835734	0.417867	−	0.908508i	$-0.362778\pi$
$179$	11.1814	0.835734	0.417867	+	0.908508i	$0.362778\pi$
$180$	9.24803	0.689308
$181$	−2.66605	−0.198166	−0.0990828	−	0.995079i	$-0.531591\pi$
$181$	−2.66605	−0.198166	−0.0990828	+	0.995079i	$0.531591\pi$
$182$	9.07414	0.672620
$183$	0.734531	0.0542981
$184$	−1.00000	−0.0737210
$185$	−10.5023	−0.772142
$186$	−0.0289934	−0.00212590
$187$	9.69353	0.708861
$188$	8.67972	0.633033
$189$	−3.04775	−0.221691
$190$	−7.19088	−0.521681
$191$	1.79571	0.129933	0.0649665	−	0.997887i	$-0.479306\pi$
$191$	1.79571	0.129933	0.0649665	+	0.997887i	$0.479306\pi$
$192$	0.180068	0.0129953
$193$	−7.22308	−0.519929	−0.259964	−	0.965618i	$-0.583711\pi$
$193$	−7.22308	−0.519929	−0.259964	+	0.965618i	$0.583711\pi$
$194$	0.272963	0.0195976
$195$	1.79533	0.128566
$196$	1.04433	0.0745952
$197$	15.2774	1.08847	0.544233	−	0.838934i	$-0.316821\pi$
$197$	15.2774	1.08847	0.544233	+	0.838934i	$0.316821\pi$
$198$	5.46718	0.388536
$199$	−4.82621	−0.342121	−0.171060	−	0.985261i	$-0.554719\pi$
$199$	−4.82621	−0.342121	−0.171060	+	0.985261i	$0.554719\pi$
$200$	−4.71170	−0.333167
$201$	−1.58866	−0.112055
$202$	1.72561	0.121413
$203$	−11.9015	−0.835319
$204$	0.947450	0.0663348
$205$	−22.6575	−1.58247
$206$	15.7235	1.09551
$207$	−2.96758	−0.206261
$208$	−3.19934	−0.221834
$209$	−4.25105	−0.294051
$210$	1.59158	0.109830
$211$	15.1183	1.04078	0.520392	−	0.853928i	$-0.325786\pi$
$211$	15.1183	1.04078	0.520392	+	0.853928i	$0.325786\pi$
$212$	−5.41261	−0.371740
$213$	0.691180	0.0473588
$214$	−8.87665	−0.606795
$215$	12.7869	0.872058
$216$	1.07457	0.0731151
$217$	0.456676	0.0310012
$218$	12.2645	0.830654
$219$	−0.609865	−0.0412108
$220$	−5.74129	−0.387078
$221$	−16.8337	−1.13236
$222$	−0.606836	−0.0407282
$223$	6.41023	0.429261	0.214631	−	0.976695i	$-0.431145\pi$
$223$	6.41023	0.429261	0.214631	+	0.976695i	$0.431145\pi$
$224$	−2.83625	−0.189505
$225$	−13.9823	−0.932155
$226$	15.2526	1.01459
$227$	−24.4650	−1.62380	−0.811898	−	0.583799i	$-0.801566\pi$
$227$	−24.4650	−1.62380	−0.811898	+	0.583799i	$0.801566\pi$
$228$	−0.415500	−0.0275171
$229$	−28.7523	−1.90001	−0.950003	−	0.312242i	$-0.898920\pi$
$229$	−28.7523	−1.90001	−0.950003	+	0.312242i	$0.898920\pi$
$230$	3.11636	0.205487
$231$	0.940899	0.0619066
$232$	4.19619	0.275493
$233$	−15.9419	−1.04439	−0.522195	−	0.852826i	$-0.674887\pi$
$233$	−15.9419	−1.04439	−0.522195	+	0.852826i	$0.674887\pi$
$234$	−9.49429	−0.620661
$235$	−27.0491	−1.76449
$236$	−11.3258	−0.737245
$237$	2.70868	0.175948
$238$	−14.9233	−0.967335
$239$	−11.9789	−0.774852	−0.387426	−	0.921901i	$-0.626636\pi$
$239$	−11.9789	−0.774852	−0.387426	+	0.921901i	$0.626636\pi$
$240$	−0.561156	−0.0362225
$241$	−7.44765	−0.479745	−0.239873	−	0.970804i	$-0.577106\pi$
$241$	−7.44765	−0.479745	−0.239873	+	0.970804i	$0.577106\pi$
$242$	7.60591	0.488926
$243$	4.79196	0.307404
$244$	4.07919	0.261143
$245$	−3.25452	−0.207923
$246$	−1.30918	−0.0834705
$247$	7.38236	0.469728
$248$	−0.161014	−0.0102244
$249$	2.63941	0.167266
$250$	−0.898453	−0.0568232
$251$	−8.65134	−0.546068	−0.273034	−	0.962004i	$-0.588027\pi$
$251$	−8.65134	−0.546068	−0.273034	+	0.962004i	$0.588027\pi$
$252$	−8.41680	−0.530208
$253$	1.84231	0.115825
$254$	3.70620	0.232548
$255$	−2.95260	−0.184899
$256$	1.00000	0.0625000
$257$	3.12698	0.195056	0.0975279	−	0.995233i	$-0.468906\pi$
$257$	3.12698	0.195056	0.0975279	+	0.995233i	$0.468906\pi$
$258$	0.738844	0.0459984
$259$	9.55829	0.593924
$260$	9.97030	0.618332
$261$	12.4525	0.770791
$262$	−1.00000	−0.0617802
$263$	4.74709	0.292718	0.146359	−	0.989232i	$-0.453244\pi$
$263$	4.74709	0.292718	0.146359	+	0.989232i	$0.453244\pi$
$264$	−0.331740	−0.0204172
$265$	16.8676	1.03617
$266$	6.54454	0.401272
$267$	0.751179	0.0459714
$268$	−8.82256	−0.538924
$269$	14.5561	0.887504	0.443752	−	0.896150i	$-0.353647\pi$
$269$	14.5561	0.887504	0.443752	+	0.896150i	$0.353647\pi$
$270$	−3.34874	−0.203798
$271$	9.44993	0.574042	0.287021	−	0.957924i	$-0.407335\pi$
$271$	9.44993	0.574042	0.287021	+	0.957924i	$0.407335\pi$
$272$	5.26163	0.319033
$273$	−1.63396	−0.0988919
$274$	−6.34452	−0.383287
$275$	8.68039	0.523447
$276$	0.180068	0.0108388
$277$	−11.7380	−0.705265	−0.352633	−	0.935762i	$-0.614713\pi$
$277$	−11.7380	−0.705265	−0.352633	+	0.935762i	$0.614713\pi$
$278$	0.627932	0.0376608
$279$	−0.477821	−0.0286064
$280$	8.83879	0.528218
$281$	5.06304	0.302036	0.151018	−	0.988531i	$-0.451745\pi$
$281$	5.06304	0.302036	0.151018	+	0.988531i	$0.451745\pi$
$282$	−1.56294	−0.0930716
$283$	3.36418	0.199980	0.0999898	−	0.994988i	$-0.468119\pi$
$283$	3.36418	0.199980	0.0999898	+	0.994988i	$0.468119\pi$
$284$	3.83844	0.227769
$285$	1.29485	0.0767001
$286$	5.89417	0.348529
$287$	20.6210	1.21722
$288$	2.96758	0.174866
$289$	10.6847	0.628513
$290$	−13.0768	−0.767898
$291$	−0.0491518	−0.00288133
$292$	−3.38686	−0.198201
$293$	−24.6029	−1.43732	−0.718659	−	0.695363i	$-0.755244\pi$
$293$	−24.6029	−1.43732	−0.718659	+	0.695363i	$0.755244\pi$
$294$	−0.188051	−0.0109673
$295$	35.2952	2.05496
$296$	−3.37004	−0.195880
$297$	−1.97968	−0.114873
$298$	7.01246	0.406221
$299$	−3.19934	−0.185023
$300$	0.848425	0.0489839
$301$	−11.6376	−0.670778
$302$	−10.1219	−0.582449
$303$	−0.310726	−0.0178508
$304$	−2.30746	−0.132342
$305$	−12.7122	−0.727900
$306$	15.6143	0.892609
$307$	−22.2355	−1.26905	−0.634524	−	0.772903i	$-0.718804\pi$
$307$	−22.2355	−1.26905	−0.634524	+	0.772903i	$0.718804\pi$
$308$	5.22525	0.297736
$309$	−2.83130	−0.161067
$310$	0.501777	0.0284990
$311$	−21.8598	−1.23956	−0.619778	−	0.784777i	$-0.712777\pi$
$311$	−21.8598	−1.23956	−0.619778	+	0.784777i	$0.712777\pi$
$312$	0.576099	0.0326152
$313$	1.35107	0.0763670	0.0381835	−	0.999271i	$-0.487843\pi$
$313$	1.35107	0.0763670	0.0381835	+	0.999271i	$0.487843\pi$
$314$	18.1972	1.02693
$315$	26.2298	1.47788
$316$	15.0426	0.846210
$317$	13.8256	0.776525	0.388262	−	0.921549i	$-0.373075\pi$
$317$	13.8256	0.776525	0.388262	+	0.921549i	$0.373075\pi$
$318$	0.974637	0.0546549
$319$	−7.73067	−0.432834
$320$	−3.11636	−0.174210
$321$	1.59840	0.0892139
$322$	−2.83625	−0.158058
$323$	−12.1410	−0.675543
$324$	8.70923	0.483846
$325$	−15.0743	−0.836174
$326$	−1.13547	−0.0628879
$327$	−2.20843	−0.122127
$328$	−7.27050	−0.401446
$329$	24.6179	1.35723
$330$	1.03382	0.0569100
$331$	0.802881	0.0441303	0.0220652	−	0.999757i	$-0.492976\pi$
$331$	0.802881	0.0441303	0.0220652	+	0.999757i	$0.492976\pi$
$332$	14.6578	0.804453
$333$	−10.0009	−0.548044
$334$	−9.90036	−0.541724
$335$	27.4943	1.50217
$336$	0.510718	0.0278620
$337$	−20.0302	−1.09111	−0.545557	−	0.838074i	$-0.683682\pi$
$337$	−20.0302	−1.09111	−0.545557	+	0.838074i	$0.683682\pi$
$338$	2.76421	0.150353
$339$	−2.74651	−0.149170
$340$	−16.3971	−0.889259
$341$	0.296637	0.0160638
$342$	−6.84756	−0.370274
$343$	−16.8918	−0.912070
$344$	4.10314	0.221227
$345$	−0.561156	−0.0302116
$346$	20.3169	1.09224
$347$	0.578901	0.0310770	0.0155385	−	0.999879i	$-0.495054\pi$
$347$	0.578901	0.0310770	0.0155385	+	0.999879i	$0.495054\pi$
$348$	−0.755599	−0.0405044
$349$	−25.7649	−1.37916	−0.689581	−	0.724209i	$-0.742205\pi$
$349$	−25.7649	−1.37916	−0.689581	+	0.724209i	$0.742205\pi$
$350$	−13.3636	−0.714313
$351$	3.43791	0.183502
$352$	−1.84231	−0.0981953
$353$	−17.6860	−0.941332	−0.470666	−	0.882312i	$-0.655986\pi$
$353$	−17.6860	−0.941332	−0.470666	+	0.882312i	$0.655986\pi$
$354$	2.03941	0.108393
$355$	−11.9620	−0.634875
$356$	4.17165	0.221097
$357$	2.68721	0.142222
$358$	−11.1814	−0.590953
$359$	11.8894	0.627497	0.313749	−	0.949506i	$-0.398415\pi$
$359$	11.8894	0.627497	0.313749	+	0.949506i	$0.398415\pi$
$360$	−9.24803	−0.487414
$361$	−13.6756	−0.719770
$362$	2.66605	0.140124
$363$	−1.36958	−0.0718843
$364$	−9.07414	−0.475614
$365$	10.5547	0.552457
$366$	−0.734531	−0.0383945
$367$	7.26661	0.379314	0.189657	−	0.981850i	$-0.439262\pi$
$367$	7.26661	0.379314	0.189657	+	0.981850i	$0.439262\pi$
$368$	1.00000	0.0521286
$369$	−21.5757	−1.12319
$370$	10.5023	0.545987
$371$	−15.3515	−0.797012
$372$	0.0289934	0.00150324
$373$	−13.5275	−0.700430	−0.350215	−	0.936669i	$-0.613891\pi$
$373$	−13.5275	−0.700430	−0.350215	+	0.936669i	$0.613891\pi$
$374$	−9.69353	−0.501241
$375$	0.161783	0.00835442
$376$	−8.67972	−0.447622
$377$	13.4250	0.691425
$378$	3.04775	0.156759
$379$	12.8909	0.662162	0.331081	−	0.943602i	$-0.392587\pi$
$379$	12.8909	0.662162	0.331081	+	0.943602i	$0.392587\pi$
$380$	7.19088	0.368884
$381$	−0.667368	−0.0341903
$382$	−1.79571	−0.0918766
$383$	−8.96319	−0.457998	−0.228999	−	0.973427i	$-0.573545\pi$
$383$	−8.96319	−0.457998	−0.228999	+	0.973427i	$0.573545\pi$
$384$	−0.180068	−0.00918905
$385$	−16.2838	−0.829897
$386$	7.22308	0.367645
$387$	12.1764	0.618961
$388$	−0.272963	−0.0138576
$389$	−28.0289	−1.42112	−0.710560	−	0.703636i	$-0.751558\pi$
$389$	−28.0289	−1.42112	−0.710560	+	0.703636i	$0.751558\pi$
$390$	−1.79533	−0.0909101
$391$	5.26163	0.266092
$392$	−1.04433	−0.0527468
$393$	0.180068	0.00908322
$394$	−15.2774	−0.769662
$395$	−46.8780	−2.35869
$396$	−5.46718	−0.274736
$397$	20.6532	1.03656	0.518278	−	0.855212i	$-0.326573\pi$
$397$	20.6532	1.03656	0.518278	+	0.855212i	$0.326573\pi$
$398$	4.82621	0.241916
$399$	−1.17846	−0.0589969
$400$	4.71170	0.235585
$401$	−21.1495	−1.05615	−0.528077	−	0.849197i	$-0.677087\pi$
$401$	−21.1495	−1.05615	−0.528077	+	0.849197i	$0.677087\pi$
$402$	1.58866	0.0792351
$403$	−0.515139	−0.0256609
$404$	−1.72561	−0.0858521
$405$	−27.1411	−1.34865
$406$	11.9015	0.590659
$407$	6.20865	0.307751
$408$	−0.947450	−0.0469058
$409$	7.40738	0.366271	0.183136	−	0.983088i	$-0.441375\pi$
$409$	7.40738	0.366271	0.183136	+	0.983088i	$0.441375\pi$
$410$	22.6575	1.11897
$411$	1.14244	0.0563526
$412$	−15.7235	−0.774643
$413$	−32.1228	−1.58066
$414$	2.96758	0.145848
$415$	−45.6791	−2.24230
$416$	3.19934	0.156861
$417$	−0.113070	−0.00553708
$418$	4.25105	0.207926
$419$	−31.3233	−1.53024	−0.765122	−	0.643885i	$-0.777321\pi$
$419$	−31.3233	−1.53024	−0.765122	+	0.643885i	$0.777321\pi$
$420$	−1.59158	−0.0776612
$421$	−25.1680	−1.22661	−0.613305	−	0.789846i	$-0.710161\pi$
$421$	−25.1680	−1.22661	−0.613305	+	0.789846i	$0.710161\pi$
$422$	−15.1183	−0.735945
$423$	−25.7577	−1.25238
$424$	5.41261	0.262860
$425$	24.7912	1.20255
$426$	−0.691180	−0.0334878
$427$	11.5696	0.559893
$428$	8.87665	0.429069
$429$	−1.06135	−0.0512425
$430$	−12.7869	−0.616638
$431$	20.4496	0.985021	0.492511	−	0.870306i	$-0.336079\pi$
$431$	20.4496	0.985021	0.492511	+	0.870306i	$0.336079\pi$
$432$	−1.07457	−0.0517002
$433$	13.6040	0.653765	0.326882	−	0.945065i	$-0.394002\pi$
$433$	13.6040	0.653765	0.326882	+	0.945065i	$0.394002\pi$
$434$	−0.456676	−0.0219212
$435$	2.35472	0.112900
$436$	−12.2645	−0.587361
$437$	−2.30746	−0.110381
$438$	0.609865	0.0291405
$439$	−9.19695	−0.438947	−0.219473	−	0.975619i	$-0.570434\pi$
$439$	−9.19695	−0.438947	−0.219473	+	0.975619i	$0.570434\pi$
$440$	5.74129	0.273705
$441$	−3.09914	−0.147578
$442$	16.8337	0.800700
$443$	−9.54765	−0.453622	−0.226811	−	0.973939i	$-0.572830\pi$
$443$	−9.54765	−0.453622	−0.226811	+	0.973939i	$0.572830\pi$
$444$	0.606836	0.0287992
$445$	−13.0004	−0.616276
$446$	−6.41023	−0.303533
$447$	−1.26272	−0.0597245
$448$	2.83625	0.134000
$449$	2.94871	0.139158	0.0695792	−	0.997576i	$-0.477834\pi$
$449$	2.94871	0.139158	0.0695792	+	0.997576i	$0.477834\pi$
$450$	13.9823	0.659133
$451$	13.3945	0.630722
$452$	−15.2526	−0.717424
$453$	1.82263	0.0856345
$454$	24.4650	1.14820
$455$	28.2783	1.32571
$456$	0.415500	0.0194575
$457$	−27.5060	−1.28668	−0.643338	−	0.765582i	$-0.722451\pi$
$457$	−27.5060	−1.28668	−0.643338	+	0.765582i	$0.722451\pi$
$458$	28.7523	1.34351
$459$	−5.65398	−0.263905
$460$	−3.11636	−0.145301
$461$	37.7226	1.75692	0.878459	−	0.477818i	$-0.158572\pi$
$461$	37.7226	1.75692	0.878459	+	0.477818i	$0.158572\pi$
$462$	−0.940899	−0.0437746
$463$	−4.23431	−0.196785	−0.0983925	−	0.995148i	$-0.531370\pi$
$463$	−4.23431	−0.196785	−0.0983925	+	0.995148i	$0.531370\pi$
$464$	−4.19619	−0.194803
$465$	−0.0903540	−0.00419006
$466$	15.9419	0.738495
$467$	−18.2718	−0.845519	−0.422759	−	0.906242i	$-0.638938\pi$
$467$	−18.2718	−0.845519	−0.422759	+	0.906242i	$0.638938\pi$
$468$	9.49429	0.438874
$469$	−25.0230	−1.15546
$470$	27.0491	1.24768
$471$	−3.27674	−0.150984
$472$	11.3258	0.521311
$473$	−7.55925	−0.347575
$474$	−2.70868	−0.124414
$475$	−10.8721	−0.498844
$476$	14.9233	0.684009
$477$	16.0623	0.735444
$478$	11.9789	0.547903
$479$	−7.83957	−0.358199	−0.179100	−	0.983831i	$-0.557318\pi$
$479$	−7.83957	−0.358199	−0.179100	+	0.983831i	$0.557318\pi$
$480$	0.561156	0.0256132
$481$	−10.7819	−0.491613
$482$	7.44765	0.339231
$483$	0.510718	0.0232385
$484$	−7.60591	−0.345723
$485$	0.850650	0.0386260
$486$	−4.79196	−0.217368
$487$	−2.46633	−0.111760	−0.0558801	−	0.998437i	$-0.517796\pi$
$487$	−2.46633	−0.111760	−0.0558801	+	0.998437i	$0.517796\pi$
$488$	−4.07919	−0.184656
$489$	0.204462	0.00924608
$490$	3.25452	0.147024
$491$	10.0832	0.455050	0.227525	−	0.973772i	$-0.426937\pi$
$491$	10.0832	0.455050	0.227525	+	0.973772i	$0.426937\pi$
$492$	1.30918	0.0590225
$493$	−22.0788	−0.994379
$494$	−7.38236	−0.332148
$495$	17.0377	0.765788
$496$	0.161014	0.00722974
$497$	10.8868	0.488339
$498$	−2.63941	−0.118275
$499$	−26.8782	−1.20323	−0.601616	−	0.798785i	$-0.705476\pi$
$499$	−26.8782	−1.20323	−0.601616	+	0.798785i	$0.705476\pi$
$500$	0.898453	0.0401801
$501$	1.78274	0.0796468
$502$	8.65134	0.386128
$503$	14.1835	0.632412	0.316206	−	0.948691i	$-0.397591\pi$
$503$	14.1835	0.632412	0.316206	+	0.948691i	$0.397591\pi$
$504$	8.41680	0.374914
$505$	5.37761	0.239301
$506$	−1.84231	−0.0819005
$507$	−0.497746	−0.0221057
$508$	−3.70620	−0.164436
$509$	26.0094	1.15285	0.576423	−	0.817151i	$-0.304448\pi$
$509$	26.0094	1.15285	0.576423	+	0.817151i	$0.304448\pi$
$510$	2.95260	0.130743
$511$	−9.60600	−0.424944
$512$	−1.00000	−0.0441942
$513$	2.47953	0.109474
$514$	−3.12698	−0.137925
$515$	49.0002	2.15921
$516$	−0.738844	−0.0325258
$517$	15.9907	0.703270
$518$	−9.55829	−0.419967
$519$	−3.65841	−0.160586
$520$	−9.97030	−0.437227
$521$	−6.54328	−0.286666	−0.143333	−	0.989675i	$-0.545782\pi$
$521$	−6.54328	−0.286666	−0.143333	+	0.989675i	$0.545782\pi$
$522$	−12.4525	−0.545032
$523$	0.573062	0.0250583	0.0125291	−	0.999922i	$-0.496012\pi$
$523$	0.573062	0.0250583	0.0125291	+	0.999922i	$0.496012\pi$
$524$	1.00000	0.0436852
$525$	2.40635	0.105022
$526$	−4.74709	−0.206983
$527$	0.847195	0.0369044
$528$	0.331740	0.0144371
$529$	1.00000	0.0434783
$530$	−16.8676	−0.732684
$531$	33.6101	1.45855
$532$	−6.54454	−0.283742
$533$	−23.2608	−1.00754
$534$	−0.751179	−0.0325067
$535$	−27.6628	−1.19597
$536$	8.82256	0.381077
$537$	2.01340	0.0868847
$538$	−14.5561	−0.627560
$539$	1.92398	0.0828717
$540$	3.34874	0.144107
$541$	19.7449	0.848898	0.424449	−	0.905452i	$-0.360468\pi$
$541$	19.7449	0.848898	0.424449	+	0.905452i	$0.360468\pi$
$542$	−9.44993	−0.405909
$543$	−0.480069	−0.0206017
$544$	−5.26163	−0.225590
$545$	38.2204	1.63718
$546$	1.63396	0.0699271
$547$	3.22818	0.138027	0.0690134	−	0.997616i	$-0.478015\pi$
$547$	3.22818	0.138027	0.0690134	+	0.997616i	$0.478015\pi$
$548$	6.34452	0.271025
$549$	−12.1053	−0.516642
$550$	−8.68039	−0.370133
$551$	9.68255	0.412490
$552$	−0.180068	−0.00766420
$553$	42.6645	1.81428
$554$	11.7380	0.498698
$555$	−1.89112	−0.0802736
$556$	−0.627932	−0.0266302
$557$	21.9754	0.931127	0.465563	−	0.885014i	$-0.345852\pi$
$557$	21.9754	0.931127	0.465563	+	0.885014i	$0.345852\pi$
$558$	0.477821	0.0202278
$559$	13.1274	0.555228
$560$	−8.83879	−0.373507
$561$	1.74549	0.0736948
$562$	−5.06304	−0.213572
$563$	36.7629	1.54937	0.774685	−	0.632347i	$-0.217908\pi$
$563$	36.7629	1.54937	0.774685	+	0.632347i	$0.217908\pi$
$564$	1.56294	0.0658116
$565$	47.5327	1.99972
$566$	−3.36418	−0.141407
$567$	24.7016	1.03737
$568$	−3.83844	−0.161057
$569$	23.2653	0.975332	0.487666	−	0.873030i	$-0.337848\pi$
$569$	23.2653	0.975332	0.487666	+	0.873030i	$0.337848\pi$
$570$	−1.29485	−0.0542351
$571$	−24.4745	−1.02423	−0.512113	−	0.858918i	$-0.671137\pi$
$571$	−24.4745	−1.02423	−0.512113	+	0.858918i	$0.671137\pi$
$572$	−5.89417	−0.246448
$573$	0.323350	0.0135081
$574$	−20.6210	−0.860703
$575$	4.71170	0.196491
$576$	−2.96758	−0.123649
$577$	−34.8341	−1.45016	−0.725082	−	0.688662i	$-0.758198\pi$
$577$	−34.8341	−1.45016	−0.725082	+	0.688662i	$0.758198\pi$
$578$	−10.6847	−0.444426
$579$	−1.30065	−0.0540530
$580$	13.0768	0.542986
$581$	41.5733	1.72475
$582$	0.0491518	0.00203741
$583$	−9.97169	−0.412985
$584$	3.38686	0.140149
$585$	−29.5876	−1.22330
$586$	24.6029	1.01634
$587$	−40.8390	−1.68561	−0.842804	−	0.538221i	$-0.819097\pi$
$587$	−40.8390	−1.68561	−0.842804	+	0.538221i	$0.819097\pi$
$588$	0.188051	0.00775508
$589$	−0.371533	−0.0153088
$590$	−35.2952	−1.45308
$591$	2.75096	0.113159
$592$	3.37004	0.138508
$593$	−13.2205	−0.542901	−0.271451	−	0.962452i	$-0.587503\pi$
$593$	−13.2205	−0.542901	−0.271451	+	0.962452i	$0.587503\pi$
$594$	1.97968	0.0812274
$595$	−46.5064	−1.90658
$596$	−7.01246	−0.287242
$597$	−0.869045	−0.0355676
$598$	3.19934	0.130831
$599$	−2.11524	−0.0864263	−0.0432131	−	0.999066i	$-0.513759\pi$
$599$	−2.11524	−0.0864263	−0.0432131	+	0.999066i	$0.513759\pi$
$600$	−0.848425	−0.0346368
$601$	−20.1091	−0.820269	−0.410135	−	0.912025i	$-0.634518\pi$
$601$	−20.1091	−0.820269	−0.410135	+	0.912025i	$0.634518\pi$
$602$	11.6376	0.474311
$603$	26.1816	1.06620
$604$	10.1219	0.411854
$605$	23.7027	0.963653
$606$	0.310726	0.0126224
$607$	−31.9652	−1.29743	−0.648715	−	0.761032i	$-0.724693\pi$
$607$	−31.9652	−1.29743	−0.648715	+	0.761032i	$0.724693\pi$
$608$	2.30746	0.0935799
$609$	−2.14307	−0.0868416
$610$	12.7122	0.514703
$611$	−27.7694	−1.12343
$612$	−15.6143	−0.631170
$613$	23.0258	0.930003	0.465001	−	0.885310i	$-0.346054\pi$
$613$	23.0258	0.930003	0.465001	+	0.885310i	$0.346054\pi$
$614$	22.2355	0.897353
$615$	−4.07988	−0.164517
$616$	−5.22525	−0.210531
$617$	−23.0805	−0.929185	−0.464593	−	0.885524i	$-0.653799\pi$
$617$	−23.0805	−0.929185	−0.464593	+	0.885524i	$0.653799\pi$
$618$	2.83130	0.113892
$619$	−48.1720	−1.93619	−0.968097	−	0.250575i	$-0.919380\pi$
$619$	−48.1720	−1.93619	−0.968097	+	0.250575i	$0.919380\pi$
$620$	−0.501777	−0.0201519
$621$	−1.07457	−0.0431210
$622$	21.8598	0.876499
$623$	11.8318	0.474033
$624$	−0.576099	−0.0230624
$625$	−26.3584	−1.05434
$626$	−1.35107	−0.0539996
$627$	−0.765478	−0.0305702
$628$	−18.1972	−0.726148
$629$	17.7319	0.707018
$630$	−26.2298	−1.04502
$631$	27.8966	1.11055	0.555273	−	0.831668i	$-0.312614\pi$
$631$	27.8966	1.11055	0.555273	+	0.831668i	$0.312614\pi$
$632$	−15.0426	−0.598361
$633$	2.72231	0.108202
$634$	−13.8256	−0.549086
$635$	11.5499	0.458342
$636$	−0.974637	−0.0386469
$637$	−3.34118	−0.132382
$638$	7.73067	0.306060
$639$	−11.3909	−0.450615
$640$	3.11636	0.123185
$641$	0.194820	0.00769494	0.00384747	−	0.999993i	$-0.498775\pi$
$641$	0.194820	0.00769494	0.00384747	+	0.999993i	$0.498775\pi$
$642$	−1.59840	−0.0630838
$643$	−13.8637	−0.546732	−0.273366	−	0.961910i	$-0.588137\pi$
$643$	−13.8637	−0.546732	−0.273366	+	0.961910i	$0.588137\pi$
$644$	2.83625	0.111764
$645$	2.30250	0.0906610
$646$	12.1410	0.477681
$647$	16.3051	0.641019	0.320510	−	0.947245i	$-0.396146\pi$
$647$	16.3051	0.641019	0.320510	+	0.947245i	$0.396146\pi$
$648$	−8.70923	−0.342131
$649$	−20.8655	−0.819044
$650$	15.0743	0.591264
$651$	0.0822327	0.00322295
$652$	1.13547	0.0444684
$653$	−28.9898	−1.13446	−0.567229	−	0.823560i	$-0.691985\pi$
$653$	−28.9898	−1.13446	−0.567229	+	0.823560i	$0.691985\pi$
$654$	2.20843	0.0863566
$655$	−3.11636	−0.121766
$656$	7.27050	0.283865
$657$	10.0508	0.392118
$658$	−24.6179	−0.959705
$659$	11.8918	0.463239	0.231619	−	0.972806i	$-0.425598\pi$
$659$	11.8918	0.463239	0.231619	+	0.972806i	$0.425598\pi$
$660$	−1.03382	−0.0402415
$661$	−16.8772	−0.656448	−0.328224	−	0.944600i	$-0.606450\pi$
$661$	−16.8772	−0.656448	−0.328224	+	0.944600i	$0.606450\pi$
$662$	−0.802881	−0.0312049
$663$	−3.03122	−0.117723
$664$	−14.6578	−0.568834
$665$	20.3952	0.790890
$666$	10.0009	0.387525
$667$	−4.19619	−0.162477
$668$	9.90036	0.383056
$669$	1.15428	0.0446269
$670$	−27.4943	−1.06220
$671$	7.51512	0.290118
$672$	−0.510718	−0.0197014
$673$	7.74456	0.298531	0.149266	−	0.988797i	$-0.452309\pi$
$673$	7.74456	0.298531	0.149266	+	0.988797i	$0.452309\pi$
$674$	20.0302	0.771535
$675$	−5.06304	−0.194877
$676$	−2.76421	−0.106316
$677$	−7.87180	−0.302538	−0.151269	−	0.988493i	$-0.548336\pi$
$677$	−7.87180	−0.302538	−0.151269	+	0.988493i	$0.548336\pi$
$678$	2.74651	0.105479
$679$	−0.774192	−0.0297108
$680$	16.3971	0.628801
$681$	−4.40535	−0.168813
$682$	−0.296637	−0.0113588
$683$	47.6935	1.82494	0.912470	−	0.409144i	$-0.134173\pi$
$683$	47.6935	1.82494	0.912470	+	0.409144i	$0.134173\pi$
$684$	6.84756	0.261823
$685$	−19.7718	−0.755442
$686$	16.8918	0.644931
$687$	−5.17736	−0.197529
$688$	−4.10314	−0.156431
$689$	17.3168	0.659717
$690$	0.561156	0.0213629
$691$	14.8643	0.565463	0.282732	−	0.959199i	$-0.408759\pi$
$691$	14.8643	0.565463	0.282732	+	0.959199i	$0.408759\pi$
$692$	−20.3169	−0.772331
$693$	−15.5063	−0.589036
$694$	−0.578901	−0.0219748
$695$	1.95686	0.0742280
$696$	0.755599	0.0286409
$697$	38.2547	1.44900
$698$	25.7649	0.975215
$699$	−2.87063	−0.108577
$700$	13.3636	0.505095
$701$	−13.4474	−0.507900	−0.253950	−	0.967217i	$-0.581730\pi$
$701$	−13.4474	−0.507900	−0.253950	+	0.967217i	$0.581730\pi$
$702$	−3.43791	−0.129756
$703$	−7.77624	−0.293287
$704$	1.84231	0.0694345
$705$	−4.87068	−0.183440
$706$	17.6860	0.665622
$707$	−4.89426	−0.184068
$708$	−2.03941	−0.0766456
$709$	−36.2297	−1.36063	−0.680317	−	0.732918i	$-0.738158\pi$
$709$	−36.2297	−1.36063	−0.680317	+	0.732918i	$0.738158\pi$
$710$	11.9620	0.448924
$711$	−44.6399	−1.67413
$712$	−4.17165	−0.156339
$713$	0.161014	0.00603002
$714$	−2.68721	−0.100566
$715$	18.3683	0.686937
$716$	11.1814	0.417867
$717$	−2.15702	−0.0805553
$718$	−11.8894	−0.443708
$719$	−26.6363	−0.993367	−0.496684	−	0.867932i	$-0.665449\pi$
$719$	−26.6363	−0.993367	−0.496684	+	0.867932i	$0.665449\pi$
$720$	9.24803	0.344654
$721$	−44.5959	−1.66084
$722$	13.6756	0.508954
$723$	−1.34108	−0.0498754
$724$	−2.66605	−0.0990828
$725$	−19.7712	−0.734283
$726$	1.36958	0.0508299
$727$	45.2769	1.67923	0.839614	−	0.543184i	$-0.182781\pi$
$727$	45.2769	1.67923	0.839614	+	0.543184i	$0.182781\pi$
$728$	9.07414	0.336310
$729$	−25.2648	−0.935734
$730$	−10.5547	−0.390646
$731$	−21.5892	−0.798506
$732$	0.734531	0.0271490
$733$	−15.3558	−0.567181	−0.283591	−	0.958945i	$-0.591526\pi$
$733$	−15.3558	−0.567181	−0.283591	+	0.958945i	$0.591526\pi$
$734$	−7.26661	−0.268215
$735$	−0.586034	−0.0216162
$736$	−1.00000	−0.0368605
$737$	−16.2539	−0.598719
$738$	21.5757	0.794214
$739$	−21.0246	−0.773403	−0.386702	−	0.922205i	$-0.626386\pi$
$739$	−21.0246	−0.773403	−0.386702	+	0.922205i	$0.626386\pi$
$740$	−10.5023	−0.386071
$741$	1.32933	0.0488340
$742$	15.3515	0.563573
$743$	30.6421	1.12415	0.562076	−	0.827086i	$-0.310003\pi$
$743$	30.6421	1.12415	0.562076	+	0.827086i	$0.310003\pi$
$744$	−0.0289934	−0.00106295
$745$	21.8533	0.800645
$746$	13.5275	0.495278
$747$	−43.4982	−1.59152
$748$	9.69353	0.354431
$749$	25.1764	0.919926
$750$	−0.161783	−0.00590746
$751$	14.1536	0.516472	0.258236	−	0.966082i	$-0.416859\pi$
$751$	14.1536	0.516472	0.258236	+	0.966082i	$0.416859\pi$
$752$	8.67972	0.316517
$753$	−1.55783	−0.0567704
$754$	−13.4250	−0.488911
$755$	−31.5435	−1.14798
$756$	−3.04775	−0.110846
$757$	12.2832	0.446439	0.223220	−	0.974768i	$-0.428343\pi$
$757$	12.2832	0.446439	0.223220	+	0.974768i	$0.428343\pi$
$758$	−12.8909	−0.468219
$759$	0.331740	0.0120414
$760$	−7.19088	−0.260841
$761$	−33.1950	−1.20332	−0.601659	−	0.798753i	$-0.705493\pi$
$761$	−33.1950	−1.20332	−0.601659	+	0.798753i	$0.705493\pi$
$762$	0.667368	0.0241762
$763$	−34.7851	−1.25931
$764$	1.79571	0.0649665
$765$	48.6597	1.75930
$766$	8.96319	0.323853
$767$	36.2350	1.30837
$768$	0.180068	0.00649764
$769$	−5.22214	−0.188315	−0.0941577	−	0.995557i	$-0.530016\pi$
$769$	−5.22214	−0.188315	−0.0941577	+	0.995557i	$0.530016\pi$
$770$	16.2838	0.586826
$771$	0.563069	0.0202784
$772$	−7.22308	−0.259964
$773$	−3.16545	−0.113853	−0.0569267	−	0.998378i	$-0.518130\pi$
$773$	−3.16545	−0.113853	−0.0569267	+	0.998378i	$0.518130\pi$
$774$	−12.1764	−0.437671
$775$	0.758649	0.0272515
$776$	0.272963	0.00979879
$777$	1.72114	0.0617456
$778$	28.0289	1.00488
$779$	−16.7764	−0.601076
$780$	1.79533	0.0642832
$781$	7.07158	0.253041
$782$	−5.26163	−0.188155
$783$	4.50909	0.161142
$784$	1.04433	0.0372976
$785$	56.7091	2.02403
$786$	−0.180068	−0.00642281
$787$	30.8609	1.10007	0.550036	−	0.835141i	$-0.314614\pi$
$787$	30.8609	1.10007	0.550036	+	0.835141i	$0.314614\pi$
$788$	15.2774	0.544233
$789$	0.854799	0.0304317
$790$	46.8780	1.66785
$791$	−43.2604	−1.53816
$792$	5.46718	0.194268
$793$	−13.0507	−0.463445
$794$	−20.6532	−0.732955
$795$	3.03732	0.107723
$796$	−4.82621	−0.171060
$797$	−40.8799	−1.44804	−0.724020	−	0.689779i	$-0.757708\pi$
$797$	−40.8799	−1.44804	−0.724020	+	0.689779i	$0.757708\pi$
$798$	1.17846	0.0417171
$799$	45.6694	1.61567
$800$	−4.71170	−0.166584
$801$	−12.3797	−0.437414
$802$	21.1495	0.746814
$803$	−6.23964	−0.220192
$804$	−1.58866	−0.0560277
$805$	−8.83879	−0.311526
$806$	0.515139	0.0181450
$807$	2.62109	0.0922668
$808$	1.72561	0.0607066
$809$	−40.7854	−1.43394	−0.716969	−	0.697106i	$-0.754471\pi$
$809$	−40.7854	−1.43394	−0.716969	+	0.697106i	$0.754471\pi$
$810$	27.1411	0.953641
$811$	−29.2687	−1.02776	−0.513882	−	0.857861i	$-0.671793\pi$
$811$	−29.2687	−1.02776	−0.513882	+	0.857861i	$0.671793\pi$
$812$	−11.9015	−0.417659
$813$	1.70163	0.0596787
$814$	−6.20865	−0.217613
$815$	−3.53853	−0.123949
$816$	0.947450	0.0331674
$817$	9.46785	0.331238
$818$	−7.40738	−0.258993
$819$	26.9282	0.940948
$820$	−22.6575	−0.791234
$821$	−22.0476	−0.769468	−0.384734	−	0.923028i	$-0.625707\pi$
$821$	−22.0476	−0.769468	−0.384734	+	0.923028i	$0.625707\pi$
$822$	−1.14244	−0.0398473
$823$	13.1850	0.459600	0.229800	−	0.973238i	$-0.426193\pi$
$823$	13.1850	0.459600	0.229800	+	0.973238i	$0.426193\pi$
$824$	15.7235	0.547755
$825$	1.56306	0.0544187
$826$	32.1228	1.11769
$827$	21.4821	0.747006	0.373503	−	0.927629i	$-0.378156\pi$
$827$	21.4821	0.747006	0.373503	+	0.927629i	$0.378156\pi$
$828$	−2.96758	−0.103130
$829$	34.7655	1.20746	0.603728	−	0.797190i	$-0.293681\pi$
$829$	34.7655	1.20746	0.603728	+	0.797190i	$0.293681\pi$
$830$	45.6791	1.58554
$831$	−2.11363	−0.0733210
$832$	−3.19934	−0.110917
$833$	5.49489	0.190387
$834$	0.113070	0.00391531
$835$	−30.8531	−1.06772
$836$	−4.25105	−0.147026
$837$	−0.173020	−0.00598046
$838$	31.3233	1.08205
$839$	32.3696	1.11752	0.558761	−	0.829329i	$-0.311277\pi$
$839$	32.3696	1.11752	0.558761	+	0.829329i	$0.311277\pi$
$840$	1.59158	0.0549148
$841$	−11.3920	−0.392827
$842$	25.1680	0.867345
$843$	0.911692	0.0314003
$844$	15.1183	0.520392
$845$	8.61428	0.296340
$846$	25.7577	0.885568
$847$	−21.5723	−0.741232
$848$	−5.41261	−0.185870
$849$	0.605780	0.0207903
$850$	−24.7912	−0.850331
$851$	3.37004	0.115524
$852$	0.691180	0.0236794
$853$	1.09492	0.0374893	0.0187447	−	0.999824i	$-0.494033\pi$
$853$	1.09492	0.0374893	0.0187447	+	0.999824i	$0.494033\pi$
$854$	−11.5696	−0.395904
$855$	−21.3395	−0.729795
$856$	−8.87665	−0.303398
$857$	−15.3754	−0.525214	−0.262607	−	0.964903i	$-0.584582\pi$
$857$	−15.3754	−0.525214	−0.262607	+	0.964903i	$0.584582\pi$
$858$	1.06135	0.0362339
$859$	39.1222	1.33483	0.667416	−	0.744685i	$-0.267401\pi$
$859$	39.1222	1.33483	0.667416	+	0.744685i	$0.267401\pi$
$860$	12.7869	0.436029
$861$	3.71317	0.126545
$862$	−20.4496	−0.696515
$863$	−9.41233	−0.320399	−0.160200	−	0.987085i	$-0.551214\pi$
$863$	−9.41233	−0.320399	−0.160200	+	0.987085i	$0.551214\pi$
$864$	1.07457	0.0365576
$865$	63.3146	2.15276
$866$	−13.6040	−0.462281
$867$	1.92398	0.0653417
$868$	0.456676	0.0155006
$869$	27.7130	0.940099
$870$	−2.35472	−0.0798324
$871$	28.2264	0.956415
$872$	12.2645	0.415327
$873$	0.810038	0.0274156
$874$	2.30746	0.0780510
$875$	2.54824	0.0861463
$876$	−0.609865	−0.0206054
$877$	44.3929	1.49904	0.749520	−	0.661982i	$-0.230284\pi$
$877$	44.3929	1.49904	0.749520	+	0.661982i	$0.230284\pi$
$878$	9.19695	0.310382
$879$	−4.43020	−0.149427
$880$	−5.74129	−0.193539
$881$	39.9281	1.34521	0.672605	−	0.740001i	$-0.265175\pi$
$881$	39.9281	1.34521	0.672605	+	0.740001i	$0.265175\pi$
$882$	3.09914	0.104353
$883$	−13.9955	−0.470988	−0.235494	−	0.971876i	$-0.575671\pi$
$883$	−13.9955	−0.470988	−0.235494	+	0.971876i	$0.575671\pi$
$884$	−16.8337	−0.566180
$885$	6.35553	0.213639
$886$	9.54765	0.320759
$887$	−11.9828	−0.402345	−0.201172	−	0.979556i	$-0.564475\pi$
$887$	−11.9828	−0.402345	−0.201172	+	0.979556i	$0.564475\pi$
$888$	−0.606836	−0.0203641
$889$	−10.5117	−0.352552
$890$	13.0004	0.435773
$891$	16.0451	0.537530
$892$	6.41023	0.214631
$893$	−20.0281	−0.670215
$894$	1.26272	0.0422316
$895$	−34.8451	−1.16474
$896$	−2.83625	−0.0947526
$897$	−0.576099	−0.0192354
$898$	−2.94871	−0.0983999
$899$	−0.675645	−0.0225340
$900$	−13.9823	−0.466077
$901$	−28.4791	−0.948778
$902$	−13.3945	−0.445988
$903$	−2.09555	−0.0697355
$904$	15.2526	0.507295
$905$	8.30836	0.276179
$906$	−1.82263	−0.0605527
$907$	−48.0125	−1.59423	−0.797114	−	0.603828i	$-0.793641\pi$
$907$	−48.0125	−1.59423	−0.797114	+	0.603828i	$0.793641\pi$
$908$	−24.4650	−0.811898
$909$	5.12087	0.169848
$910$	−28.2783	−0.937416
$911$	0.727120	0.0240906	0.0120453	−	0.999927i	$-0.496166\pi$
$911$	0.727120	0.0240906	0.0120453	+	0.999927i	$0.496166\pi$
$912$	−0.415500	−0.0137586
$913$	27.0042	0.893710
$914$	27.5060	0.909817
$915$	−2.28906	−0.0756741
$916$	−28.7523	−0.950003
$917$	2.83625	0.0936613
$918$	5.65398	0.186609
$919$	−32.2213	−1.06288	−0.531441	−	0.847095i	$-0.678349\pi$
$919$	−32.2213	−1.06288	−0.531441	+	0.847095i	$0.678349\pi$
$920$	3.11636	0.102743
$921$	−4.00390	−0.131933
$922$	−37.7226	−1.24233
$923$	−12.2805	−0.404217
$924$	0.940899	0.0309533
$925$	15.8786	0.522086
$926$	4.23431	0.139148
$927$	46.6608	1.53254
$928$	4.19619	0.137747
$929$	−34.0838	−1.11825	−0.559126	−	0.829083i	$-0.688863\pi$
$929$	−34.0838	−1.11825	−0.559126	+	0.829083i	$0.688863\pi$
$930$	0.0903540	0.00296282
$931$	−2.40976	−0.0789766
$932$	−15.9419	−0.522195
$933$	−3.93625	−0.128867
$934$	18.2718	0.597872
$935$	−30.2085	−0.987925
$936$	−9.49429	−0.310331
$937$	8.24127	0.269231	0.134615	−	0.990898i	$-0.457020\pi$
$937$	8.24127	0.269231	0.134615	+	0.990898i	$0.457020\pi$
$938$	25.0230	0.817031
$939$	0.243284	0.00793928
$940$	−27.0491	−0.882245
$941$	−2.75065	−0.0896685	−0.0448343	−	0.998994i	$-0.514276\pi$
$941$	−2.75065	−0.0896685	−0.0448343	+	0.998994i	$0.514276\pi$
$942$	3.27674	0.106762
$943$	7.27050	0.236760
$944$	−11.3258	−0.368622
$945$	9.49788	0.308966
$946$	7.55925	0.245772
$947$	−33.4469	−1.08688	−0.543439	−	0.839449i	$-0.682878\pi$
$947$	−33.4469	−1.08688	−0.543439	+	0.839449i	$0.682878\pi$
$948$	2.70868	0.0879739
$949$	10.8357	0.351743
$950$	10.8721	0.352736
$951$	2.48955	0.0807293
$952$	−14.9233	−0.483667
$953$	38.8227	1.25759	0.628795	−	0.777571i	$-0.283549\pi$
$953$	38.8227	1.25759	0.628795	+	0.777571i	$0.283549\pi$
$954$	−16.0623	−0.520037
$955$	−5.59608	−0.181085
$956$	−11.9789	−0.387426
$957$	−1.39204	−0.0449984
$958$	7.83957	0.253285
$959$	17.9947	0.581078
$960$	−0.561156	−0.0181112
$961$	−30.9741	−0.999164
$962$	10.7819	0.347623
$963$	−26.3421	−0.848863
$964$	−7.44765	−0.239873
$965$	22.5097	0.724614
$966$	−0.510718	−0.0164321
$967$	20.7530	0.667371	0.333686	−	0.942684i	$-0.391708\pi$
$967$	20.7530	0.667371	0.333686	+	0.942684i	$0.391708\pi$
$968$	7.60591	0.244463
$969$	−2.18620	−0.0702310
$970$	−0.850650	−0.0273127
$971$	47.8740	1.53635	0.768175	−	0.640240i	$-0.221165\pi$
$971$	47.8740	1.53635	0.768175	+	0.640240i	$0.221165\pi$
$972$	4.79196	0.153702
$973$	−1.78097	−0.0570954
$974$	2.46633	0.0790265
$975$	−2.71440	−0.0869305
$976$	4.07919	0.130572
$977$	1.85090	0.0592155	0.0296077	−	0.999562i	$-0.490574\pi$
$977$	1.85090	0.0592155	0.0296077	+	0.999562i	$0.490574\pi$
$978$	−0.204462	−0.00653796
$979$	7.68545	0.245628
$980$	−3.25452	−0.103962
$981$	36.3957	1.16202
$982$	−10.0832	−0.321769
$983$	−32.3375	−1.03141	−0.515703	−	0.856767i	$-0.672469\pi$
$983$	−32.3375	−1.03141	−0.515703	+	0.856767i	$0.672469\pi$
$984$	−1.30918	−0.0417352
$985$	−47.6097	−1.51697
$986$	22.0788	0.703132
$987$	4.43289	0.141100
$988$	7.38236	0.234864
$989$	−4.10314	−0.130472
$990$	−17.0377	−0.541494
$991$	−35.5786	−1.13019	−0.565096	−	0.825025i	$-0.691161\pi$
$991$	−35.5786	−1.13019	−0.565096	+	0.825025i	$0.691161\pi$
$992$	−0.161014	−0.00511220
$993$	0.144573	0.00458789
$994$	−10.8868	−0.345308
$995$	15.0402	0.476806
$996$	2.63941	0.0836328
$997$	11.6446	0.368790	0.184395	−	0.982852i	$-0.440968\pi$
$997$	11.6446	0.368790	0.184395	+	0.982852i	$0.440968\pi$
$998$	26.8782	0.850814
$999$	−3.62134	−0.114574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.14	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.14	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.180068 q^{3} +1.00000 q^{4} -3.11636 q^{5} -0.180068 q^{6} +2.83625 q^{7} -1.00000 q^{8} -2.96758 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.180068 q^{3} +1.00000 q^{4} -3.11636 q^{5} -0.180068 q^{6} +2.83625 q^{7} -1.00000 q^{8} -2.96758 q^{9} +3.11636 q^{10} +1.84231 q^{11} +0.180068 q^{12} -3.19934 q^{13} -2.83625 q^{14} -0.561156 q^{15} +1.00000 q^{16} +5.26163 q^{17} +2.96758 q^{18} -2.30746 q^{19} -3.11636 q^{20} +0.510718 q^{21} -1.84231 q^{22} +1.00000 q^{23} -0.180068 q^{24} +4.71170 q^{25} +3.19934 q^{26} -1.07457 q^{27} +2.83625 q^{28} -4.19619 q^{29} +0.561156 q^{30} +0.161014 q^{31} -1.00000 q^{32} +0.331740 q^{33} -5.26163 q^{34} -8.83879 q^{35} -2.96758 q^{36} +3.37004 q^{37} +2.30746 q^{38} -0.576099 q^{39} +3.11636 q^{40} +7.27050 q^{41} -0.510718 q^{42} -4.10314 q^{43} +1.84231 q^{44} +9.24803 q^{45} -1.00000 q^{46} +8.67972 q^{47} +0.180068 q^{48} +1.04433 q^{49} -4.71170 q^{50} +0.947450 q^{51} -3.19934 q^{52} -5.41261 q^{53} +1.07457 q^{54} -5.74129 q^{55} -2.83625 q^{56} -0.415500 q^{57} +4.19619 q^{58} -11.3258 q^{59} -0.561156 q^{60} +4.07919 q^{61} -0.161014 q^{62} -8.41680 q^{63} +1.00000 q^{64} +9.97030 q^{65} -0.331740 q^{66} -8.82256 q^{67} +5.26163 q^{68} +0.180068 q^{69} +8.83879 q^{70} +3.83844 q^{71} +2.96758 q^{72} -3.38686 q^{73} -3.37004 q^{74} +0.848425 q^{75} -2.30746 q^{76} +5.22525 q^{77} +0.576099 q^{78} +15.0426 q^{79} -3.11636 q^{80} +8.70923 q^{81} -7.27050 q^{82} +14.6578 q^{83} +0.510718 q^{84} -16.3971 q^{85} +4.10314 q^{86} -0.755599 q^{87} -1.84231 q^{88} +4.17165 q^{89} -9.24803 q^{90} -9.07414 q^{91} +1.00000 q^{92} +0.0289934 q^{93} -8.67972 q^{94} +7.19088 q^{95} -0.180068 q^{96} -0.272963 q^{97} -1.04433 q^{98} -5.46718 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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