LMFDB - Embedded newform 8018.2.a.f.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.39250 q^{3} +1.00000 q^{4} +3.35741 q^{5} +1.39250 q^{6} -0.849778 q^{7} -1.00000 q^{8} -1.06096 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.39250 q^{3} +1.00000 q^{4} +3.35741 q^{5} +1.39250 q^{6} -0.849778 q^{7} -1.00000 q^{8} -1.06096 q^{9} -3.35741 q^{10} -2.14482 q^{11} -1.39250 q^{12} -0.777327 q^{13} +0.849778 q^{14} -4.67518 q^{15} +1.00000 q^{16} +4.54820 q^{17} +1.06096 q^{18} -1.00000 q^{19} +3.35741 q^{20} +1.18331 q^{21} +2.14482 q^{22} -6.97945 q^{23} +1.39250 q^{24} +6.27221 q^{25} +0.777327 q^{26} +5.65486 q^{27} -0.849778 q^{28} -0.251361 q^{29} +4.67518 q^{30} -8.19038 q^{31} -1.00000 q^{32} +2.98666 q^{33} -4.54820 q^{34} -2.85305 q^{35} -1.06096 q^{36} +7.04638 q^{37} +1.00000 q^{38} +1.08242 q^{39} -3.35741 q^{40} +3.52467 q^{41} -1.18331 q^{42} +7.32249 q^{43} -2.14482 q^{44} -3.56206 q^{45} +6.97945 q^{46} -4.32443 q^{47} -1.39250 q^{48} -6.27788 q^{49} -6.27221 q^{50} -6.33335 q^{51} -0.777327 q^{52} +11.9004 q^{53} -5.65486 q^{54} -7.20106 q^{55} +0.849778 q^{56} +1.39250 q^{57} +0.251361 q^{58} -3.78474 q^{59} -4.67518 q^{60} +7.33146 q^{61} +8.19038 q^{62} +0.901576 q^{63} +1.00000 q^{64} -2.60981 q^{65} -2.98666 q^{66} -6.16364 q^{67} +4.54820 q^{68} +9.71886 q^{69} +2.85305 q^{70} +11.0621 q^{71} +1.06096 q^{72} +10.9956 q^{73} -7.04638 q^{74} -8.73403 q^{75} -1.00000 q^{76} +1.82262 q^{77} -1.08242 q^{78} -3.21842 q^{79} +3.35741 q^{80} -4.69151 q^{81} -3.52467 q^{82} -11.3967 q^{83} +1.18331 q^{84} +15.2702 q^{85} -7.32249 q^{86} +0.350019 q^{87} +2.14482 q^{88} +3.27588 q^{89} +3.56206 q^{90} +0.660555 q^{91} -6.97945 q^{92} +11.4051 q^{93} +4.32443 q^{94} -3.35741 q^{95} +1.39250 q^{96} -7.35547 q^{97} +6.27788 q^{98} +2.27556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.39250	−0.803958	−0.401979	−	0.915649i	$-0.631677\pi$
$3$	−1.39250	−0.803958	−0.401979	+	0.915649i	$0.631677\pi$
$4$	1.00000	0.500000
$5$	3.35741	1.50148	0.750740	−	0.660598i	$-0.229697\pi$
$5$	3.35741	1.50148	0.750740	+	0.660598i	$0.229697\pi$
$6$	1.39250	0.568484
$7$	−0.849778	−0.321186	−0.160593	−	0.987021i	$-0.551341\pi$
$7$	−0.849778	−0.321186	−0.160593	+	0.987021i	$0.551341\pi$
$8$	−1.00000	−0.353553
$9$	−1.06096	−0.353652
$10$	−3.35741	−1.06171
$11$	−2.14482	−0.646689	−0.323344	−	0.946281i	$-0.604807\pi$
$11$	−2.14482	−0.646689	−0.323344	+	0.946281i	$0.604807\pi$
$12$	−1.39250	−0.401979
$13$	−0.777327	−0.215592	−0.107796	−	0.994173i	$-0.534379\pi$
$13$	−0.777327	−0.215592	−0.107796	+	0.994173i	$0.534379\pi$
$14$	0.849778	0.227113
$15$	−4.67518	−1.20713
$16$	1.00000	0.250000
$17$	4.54820	1.10310	0.551550	−	0.834142i	$-0.314037\pi$
$17$	4.54820	1.10310	0.551550	+	0.834142i	$0.314037\pi$
$18$	1.06096	0.250070
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.35741	0.750740
$21$	1.18331	0.258220
$22$	2.14482	0.457278
$23$	−6.97945	−1.45532	−0.727658	−	0.685940i	$-0.759391\pi$
$23$	−6.97945	−1.45532	−0.727658	+	0.685940i	$0.759391\pi$
$24$	1.39250	0.284242
$25$	6.27221	1.25444
$26$	0.777327	0.152446
$27$	5.65486	1.08828
$28$	−0.849778	−0.160593
$29$	−0.251361	−0.0466766	−0.0233383	−	0.999728i	$-0.507429\pi$
$29$	−0.251361	−0.0466766	−0.0233383	+	0.999728i	$0.507429\pi$
$30$	4.67518	0.853568
$31$	−8.19038	−1.47104	−0.735518	−	0.677506i	$-0.763061\pi$
$31$	−8.19038	−1.47104	−0.735518	+	0.677506i	$0.763061\pi$
$32$	−1.00000	−0.176777
$33$	2.98666	0.519911
$34$	−4.54820	−0.780009
$35$	−2.85305	−0.482254
$36$	−1.06096	−0.176826
$37$	7.04638	1.15842	0.579209	−	0.815179i	$-0.303362\pi$
$37$	7.04638	1.15842	0.579209	+	0.815179i	$0.303362\pi$
$38$	1.00000	0.162221
$39$	1.08242	0.173327
$40$	−3.35741	−0.530853
$41$	3.52467	0.550462	0.275231	−	0.961378i	$-0.411246\pi$
$41$	3.52467	0.550462	0.275231	+	0.961378i	$0.411246\pi$
$42$	−1.18331	−0.182589
$43$	7.32249	1.11667	0.558335	−	0.829616i	$-0.311440\pi$
$43$	7.32249	1.11667	0.558335	+	0.829616i	$0.311440\pi$
$44$	−2.14482	−0.323344
$45$	−3.56206	−0.531001
$46$	6.97945	1.02906
$47$	−4.32443	−0.630783	−0.315391	−	0.948962i	$-0.602136\pi$
$47$	−4.32443	−0.630783	−0.315391	+	0.948962i	$0.602136\pi$
$48$	−1.39250	−0.200989
$49$	−6.27788	−0.896840
$50$	−6.27221	−0.887025
$51$	−6.33335	−0.886846
$52$	−0.777327	−0.107796
$53$	11.9004	1.63464	0.817321	−	0.576182i	$-0.195458\pi$
$53$	11.9004	1.63464	0.817321	+	0.576182i	$0.195458\pi$
$54$	−5.65486	−0.769529
$55$	−7.20106	−0.970990
$56$	0.849778	0.113556
$57$	1.39250	0.184441
$58$	0.251361	0.0330053
$59$	−3.78474	−0.492731	−0.246366	−	0.969177i	$-0.579236\pi$
$59$	−3.78474	−0.492731	−0.246366	+	0.969177i	$0.579236\pi$
$60$	−4.67518	−0.603563
$61$	7.33146	0.938697	0.469349	−	0.883013i	$-0.344489\pi$
$61$	7.33146	0.938697	0.469349	+	0.883013i	$0.344489\pi$
$62$	8.19038	1.04018
$63$	0.901576	0.113588
$64$	1.00000	0.125000
$65$	−2.60981	−0.323707
$66$	−2.98666	−0.367632
$67$	−6.16364	−0.753009	−0.376504	−	0.926415i	$-0.622874\pi$
$67$	−6.16364	−0.753009	−0.376504	+	0.926415i	$0.622874\pi$
$68$	4.54820	0.551550
$69$	9.71886	1.17001
$70$	2.85305	0.341005
$71$	11.0621	1.31283	0.656414	−	0.754401i	$-0.272072\pi$
$71$	11.0621	1.31283	0.656414	+	0.754401i	$0.272072\pi$
$72$	1.06096	0.125035
$73$	10.9956	1.28694	0.643470	−	0.765471i	$-0.277494\pi$
$73$	10.9956	1.28694	0.643470	+	0.765471i	$0.277494\pi$
$74$	−7.04638	−0.819125
$75$	−8.73403	−1.00852
$76$	−1.00000	−0.114708
$77$	1.82262	0.207707
$78$	−1.08242	−0.122560
$79$	−3.21842	−0.362101	−0.181051	−	0.983474i	$-0.557950\pi$
$79$	−3.21842	−0.362101	−0.181051	+	0.983474i	$0.557950\pi$
$80$	3.35741	0.375370
$81$	−4.69151	−0.521279
$82$	−3.52467	−0.389235
$83$	−11.3967	−1.25095	−0.625475	−	0.780244i	$-0.715095\pi$
$83$	−11.3967	−1.25095	−0.625475	+	0.780244i	$0.715095\pi$
$84$	1.18331	0.129110
$85$	15.2702	1.65628
$86$	−7.32249	−0.789605
$87$	0.350019	0.0375260
$88$	2.14482	0.228639
$89$	3.27588	0.347243	0.173622	−	0.984812i	$-0.444453\pi$
$89$	3.27588	0.347243	0.173622	+	0.984812i	$0.444453\pi$
$90$	3.56206	0.375474
$91$	0.660555	0.0692450
$92$	−6.97945	−0.727658
$93$	11.4051	1.18265
$94$	4.32443	0.446031
$95$	−3.35741	−0.344463
$96$	1.39250	0.142121
$97$	−7.35547	−0.746835	−0.373417	−	0.927663i	$-0.621814\pi$
$97$	−7.35547	−0.746835	−0.373417	+	0.927663i	$0.621814\pi$
$98$	6.27788	0.634161
$99$	2.27556	0.228703
$100$	6.27221	0.627221
$101$	−0.891342	−0.0886919	−0.0443459	−	0.999016i	$-0.514120\pi$
$101$	−0.891342	−0.0886919	−0.0443459	+	0.999016i	$0.514120\pi$
$102$	6.33335	0.627095
$103$	12.5025	1.23191	0.615953	−	0.787783i	$-0.288771\pi$
$103$	12.5025	1.23191	0.615953	+	0.787783i	$0.288771\pi$
$104$	0.777327	0.0762232
$105$	3.97287	0.387712
$106$	−11.9004	−1.15587
$107$	−4.18210	−0.404299	−0.202149	−	0.979355i	$-0.564793\pi$
$107$	−4.18210	−0.404299	−0.202149	+	0.979355i	$0.564793\pi$
$108$	5.65486	0.544139
$109$	−19.1368	−1.83298	−0.916488	−	0.400061i	$-0.868989\pi$
$109$	−19.1368	−1.83298	−0.916488	+	0.400061i	$0.868989\pi$
$110$	7.20106	0.686594
$111$	−9.81206	−0.931319
$112$	−0.849778	−0.0802965
$113$	−10.2146	−0.960911	−0.480456	−	0.877019i	$-0.659529\pi$
$113$	−10.2146	−0.960911	−0.480456	+	0.877019i	$0.659529\pi$
$114$	−1.39250	−0.130419
$115$	−23.4329	−2.18513
$116$	−0.251361	−0.0233383
$117$	0.824709	0.0762444
$118$	3.78474	0.348414
$119$	−3.86496	−0.354300
$120$	4.67518	0.426784
$121$	−6.39973	−0.581794
$122$	−7.33146	−0.663759
$123$	−4.90810	−0.442548
$124$	−8.19038	−0.735518
$125$	4.27135	0.382041
$126$	−0.901576	−0.0803188
$127$	2.76687	0.245520	0.122760	−	0.992436i	$-0.460826\pi$
$127$	2.76687	0.245520	0.122760	+	0.992436i	$0.460826\pi$
$128$	−1.00000	−0.0883883
$129$	−10.1965	−0.897756
$130$	2.60981	0.228895
$131$	−1.09375	−0.0955616	−0.0477808	−	0.998858i	$-0.515215\pi$
$131$	−1.09375	−0.0955616	−0.0477808	+	0.998858i	$0.515215\pi$
$132$	2.98666	0.259955
$133$	0.849778	0.0736851
$134$	6.16364	0.532458
$135$	18.9857	1.63403
$136$	−4.54820	−0.390005
$137$	6.26379	0.535152	0.267576	−	0.963537i	$-0.413777\pi$
$137$	6.26379	0.535152	0.267576	+	0.963537i	$0.413777\pi$
$138$	−9.71886	−0.827325
$139$	0.717250	0.0608364	0.0304182	−	0.999537i	$-0.490316\pi$
$139$	0.717250	0.0608364	0.0304182	+	0.999537i	$0.490316\pi$
$140$	−2.85305	−0.241127
$141$	6.02175	0.507123
$142$	−11.0621	−0.928310
$143$	1.66723	0.139421
$144$	−1.06096	−0.0884129
$145$	−0.843923	−0.0700840
$146$	−10.9956	−0.910004
$147$	8.74192	0.721021
$148$	7.04638	0.579209
$149$	−3.01148	−0.246710	−0.123355	−	0.992363i	$-0.539365\pi$
$149$	−3.01148	−0.246710	−0.123355	+	0.992363i	$0.539365\pi$
$150$	8.73403	0.713131
$151$	−24.0081	−1.95375	−0.976874	−	0.213814i	$-0.931411\pi$
$151$	−24.0081	−1.95375	−0.976874	+	0.213814i	$0.931411\pi$
$152$	1.00000	0.0811107
$153$	−4.82543	−0.390113
$154$	−1.82262	−0.146871
$155$	−27.4985	−2.20873
$156$	1.08242	0.0866633
$157$	6.15466	0.491196	0.245598	−	0.969372i	$-0.421016\pi$
$157$	6.15466	0.491196	0.245598	+	0.969372i	$0.421016\pi$
$158$	3.21842	0.256044
$159$	−16.5712	−1.31418
$160$	−3.35741	−0.265427
$161$	5.93099	0.467427
$162$	4.69151	0.368600
$163$	−6.53091	−0.511540	−0.255770	−	0.966738i	$-0.582329\pi$
$163$	−6.53091	−0.511540	−0.255770	+	0.966738i	$0.582329\pi$
$164$	3.52467	0.275231
$165$	10.0274	0.780635
$166$	11.3967	0.884556
$167$	−4.15551	−0.321563	−0.160781	−	0.986990i	$-0.551401\pi$
$167$	−4.15551	−0.321563	−0.160781	+	0.986990i	$0.551401\pi$
$168$	−1.18331	−0.0912945
$169$	−12.3958	−0.953520
$170$	−15.2702	−1.17117
$171$	1.06096	0.0811333
$172$	7.32249	0.558335
$173$	−25.4570	−1.93546	−0.967730	−	0.251989i	$-0.918915\pi$
$173$	−25.4570	−1.93546	−0.967730	+	0.251989i	$0.918915\pi$
$174$	−0.350019	−0.0265349
$175$	−5.32999	−0.402909
$176$	−2.14482	−0.161672
$177$	5.27024	0.396135
$178$	−3.27588	−0.245538
$179$	−7.90890	−0.591139	−0.295569	−	0.955321i	$-0.595509\pi$
$179$	−7.90890	−0.591139	−0.295569	+	0.955321i	$0.595509\pi$
$180$	−3.56206	−0.265501
$181$	−14.1270	−1.05005	−0.525027	−	0.851086i	$-0.675945\pi$
$181$	−14.1270	−1.05005	−0.525027	+	0.851086i	$0.675945\pi$
$182$	−0.660555	−0.0489636
$183$	−10.2090	−0.754673
$184$	6.97945	0.514532
$185$	23.6576	1.73934
$186$	−11.4051	−0.836260
$187$	−9.75508	−0.713362
$188$	−4.32443	−0.315391
$189$	−4.80538	−0.349540
$190$	3.35741	0.243572
$191$	10.5742	0.765120	0.382560	−	0.923931i	$-0.375043\pi$
$191$	10.5742	0.765120	0.382560	+	0.923931i	$0.375043\pi$
$192$	−1.39250	−0.100495
$193$	−9.74050	−0.701137	−0.350568	−	0.936537i	$-0.614012\pi$
$193$	−9.74050	−0.701137	−0.350568	+	0.936537i	$0.614012\pi$
$194$	7.35547	0.528092
$195$	3.63415	0.260247
$196$	−6.27788	−0.448420
$197$	3.06523	0.218389	0.109194	−	0.994020i	$-0.465173\pi$
$197$	3.06523	0.218389	0.109194	+	0.994020i	$0.465173\pi$
$198$	−2.27556	−0.161717
$199$	26.2375	1.85993	0.929964	−	0.367649i	$-0.119837\pi$
$199$	26.2375	1.85993	0.929964	+	0.367649i	$0.119837\pi$
$200$	−6.27221	−0.443513
$201$	8.58285	0.605387
$202$	0.891342	0.0627146
$203$	0.213601	0.0149919
$204$	−6.33335	−0.443423
$205$	11.8338	0.826507
$206$	−12.5025	−0.871089
$207$	7.40489	0.514675
$208$	−0.777327	−0.0538979
$209$	2.14482	0.148361
$210$	−3.97287	−0.274154
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	11.9004	0.817321
$213$	−15.4039	−1.05546
$214$	4.18210	0.285883
$215$	24.5846	1.67666
$216$	−5.65486	−0.384765
$217$	6.96000	0.472476
$218$	19.1368	1.29611
$219$	−15.3114	−1.03465
$220$	−7.20106	−0.485495
$221$	−3.53544	−0.237819
$222$	9.81206	0.658542
$223$	−6.86014	−0.459389	−0.229694	−	0.973263i	$-0.573773\pi$
$223$	−6.86014	−0.459389	−0.229694	+	0.973263i	$0.573773\pi$
$224$	0.849778	0.0567782
$225$	−6.65454	−0.443636
$226$	10.2146	0.679467
$227$	−20.4334	−1.35621	−0.678105	−	0.734965i	$-0.737198\pi$
$227$	−20.4334	−1.35621	−0.678105	+	0.734965i	$0.737198\pi$
$228$	1.39250	0.0922203
$229$	17.0542	1.12697	0.563486	−	0.826126i	$-0.309460\pi$
$229$	17.0542	1.12697	0.563486	+	0.826126i	$0.309460\pi$
$230$	23.4329	1.54512
$231$	−2.53800	−0.166988
$232$	0.251361	0.0165027
$233$	−12.4324	−0.814477	−0.407238	−	0.913322i	$-0.633508\pi$
$233$	−12.4324	−0.814477	−0.407238	+	0.913322i	$0.633508\pi$
$234$	−0.824709	−0.0539129
$235$	−14.5189	−0.947108
$236$	−3.78474	−0.246366
$237$	4.48164	0.291114
$238$	3.86496	0.250528
$239$	−13.7443	−0.889046	−0.444523	−	0.895767i	$-0.646627\pi$
$239$	−13.7443	−0.889046	−0.444523	+	0.895767i	$0.646627\pi$
$240$	−4.67518	−0.301782
$241$	16.4439	1.05924	0.529622	−	0.848234i	$-0.322334\pi$
$241$	16.4439	1.05924	0.529622	+	0.848234i	$0.322334\pi$
$242$	6.39973	0.411390
$243$	−10.4317	−0.669193
$244$	7.33146	0.469349
$245$	−21.0774	−1.34659
$246$	4.90810	0.312929
$247$	0.777327	0.0494601
$248$	8.19038	0.520089
$249$	15.8699	1.00571
$250$	−4.27135	−0.270144
$251$	6.17856	0.389987	0.194994	−	0.980805i	$-0.437531\pi$
$251$	6.17856	0.389987	0.194994	+	0.980805i	$0.437531\pi$
$252$	0.901576	0.0567940
$253$	14.9697	0.941137
$254$	−2.76687	−0.173609
$255$	−21.2636	−1.33158
$256$	1.00000	0.0625000
$257$	−10.2880	−0.641749	−0.320875	−	0.947122i	$-0.603977\pi$
$257$	−10.2880	−0.641749	−0.320875	+	0.947122i	$0.603977\pi$
$258$	10.1965	0.634809
$259$	−5.98786	−0.372067
$260$	−2.60981	−0.161853
$261$	0.266683	0.0165073
$262$	1.09375	0.0675722
$263$	17.8019	1.09771	0.548857	−	0.835916i	$-0.315063\pi$
$263$	17.8019	1.09771	0.548857	+	0.835916i	$0.315063\pi$
$264$	−2.98666	−0.183816
$265$	39.9545	2.45438
$266$	−0.849778	−0.0521032
$267$	−4.56166	−0.279169
$268$	−6.16364	−0.376504
$269$	−28.1483	−1.71623	−0.858115	−	0.513457i	$-0.828365\pi$
$269$	−28.1483	−1.71623	−0.858115	+	0.513457i	$0.828365\pi$
$270$	−18.9857	−1.15543
$271$	18.1743	1.10401	0.552005	−	0.833841i	$-0.313863\pi$
$271$	18.1743	1.10401	0.552005	+	0.833841i	$0.313863\pi$
$272$	4.54820	0.275775
$273$	−0.919821	−0.0556701
$274$	−6.26379	−0.378409
$275$	−13.4528	−0.811234
$276$	9.71886	0.585007
$277$	−12.9510	−0.778148	−0.389074	−	0.921207i	$-0.627205\pi$
$277$	−12.9510	−0.778148	−0.389074	+	0.921207i	$0.627205\pi$
$278$	−0.717250	−0.0430178
$279$	8.68962	0.520234
$280$	2.85305	0.170503
$281$	24.5209	1.46279	0.731396	−	0.681953i	$-0.238869\pi$
$281$	24.5209	1.46279	0.731396	+	0.681953i	$0.238869\pi$
$282$	−6.02175	−0.358590
$283$	21.1643	1.25809	0.629044	−	0.777370i	$-0.283447\pi$
$283$	21.1643	1.25809	0.629044	+	0.777370i	$0.283447\pi$
$284$	11.0621	0.656414
$285$	4.67518	0.276934
$286$	−1.66723	−0.0985854
$287$	−2.99519	−0.176801
$288$	1.06096	0.0625174
$289$	3.68609	0.216829
$290$	0.843923	0.0495569
$291$	10.2425	0.600424
$292$	10.9956	0.643470
$293$	−25.2265	−1.47375	−0.736873	−	0.676031i	$-0.763699\pi$
$293$	−25.2265	−1.47375	−0.736873	+	0.676031i	$0.763699\pi$
$294$	−8.74192	−0.509839
$295$	−12.7069	−0.739826
$296$	−7.04638	−0.409563
$297$	−12.1287	−0.703778
$298$	3.01148	0.174451
$299$	5.42532	0.313754
$300$	−8.73403	−0.504260
$301$	−6.22249	−0.358659
$302$	24.0081	1.38151
$303$	1.24119	0.0713045
$304$	−1.00000	−0.0573539
$305$	24.6147	1.40944
$306$	4.82543	0.275852
$307$	−21.7084	−1.23896	−0.619482	−	0.785011i	$-0.712657\pi$
$307$	−21.7084	−1.23896	−0.619482	+	0.785011i	$0.712657\pi$
$308$	1.82262	0.103854
$309$	−17.4096	−0.990400
$310$	27.4985	1.56181
$311$	−4.79442	−0.271867	−0.135933	−	0.990718i	$-0.543403\pi$
$311$	−4.79442	−0.271867	−0.135933	+	0.990718i	$0.543403\pi$
$312$	−1.08242	−0.0612802
$313$	1.43081	0.0808744	0.0404372	−	0.999182i	$-0.487125\pi$
$313$	1.43081	0.0808744	0.0404372	+	0.999182i	$0.487125\pi$
$314$	−6.15466	−0.347328
$315$	3.02696	0.170550
$316$	−3.21842	−0.181051
$317$	−24.2901	−1.36427	−0.682133	−	0.731228i	$-0.738948\pi$
$317$	−24.2901	−1.36427	−0.682133	+	0.731228i	$0.738948\pi$
$318$	16.5712	0.929268
$319$	0.539126	0.0301852
$320$	3.35741	0.187685
$321$	5.82356	0.325039
$322$	−5.93099	−0.330521
$323$	−4.54820	−0.253068
$324$	−4.69151	−0.260639
$325$	−4.87556	−0.270448
$326$	6.53091	0.361714
$327$	26.6480	1.47364
$328$	−3.52467	−0.194618
$329$	3.67480	0.202599
$330$	−10.0274	−0.551993
$331$	26.9152	1.47939	0.739695	−	0.672942i	$-0.234970\pi$
$331$	26.9152	1.47939	0.739695	+	0.672942i	$0.234970\pi$
$332$	−11.3967	−0.625475
$333$	−7.47589	−0.409677
$334$	4.15551	0.227379
$335$	−20.6939	−1.13063
$336$	1.18331	0.0645550
$337$	−33.1035	−1.80326	−0.901632	−	0.432503i	$-0.857630\pi$
$337$	−33.1035	−1.80326	−0.901632	+	0.432503i	$0.857630\pi$
$338$	12.3958	0.674241
$339$	14.2238	0.772532
$340$	15.2702	0.828141
$341$	17.5669	0.951302
$342$	−1.06096	−0.0573699
$343$	11.2832	0.609238
$344$	−7.32249	−0.394802
$345$	32.6302	1.75675
$346$	25.4570	1.36858
$347$	−3.45265	−0.185348	−0.0926741	−	0.995696i	$-0.529541\pi$
$347$	−3.45265	−0.185348	−0.0926741	+	0.995696i	$0.529541\pi$
$348$	0.350019	0.0187630
$349$	−20.8504	−1.11609	−0.558047	−	0.829809i	$-0.688449\pi$
$349$	−20.8504	−1.11609	−0.558047	+	0.829809i	$0.688449\pi$
$350$	5.32999	0.284900
$351$	−4.39568	−0.234624
$352$	2.14482	0.114320
$353$	16.1395	0.859016	0.429508	−	0.903063i	$-0.358687\pi$
$353$	16.1395	0.859016	0.429508	+	0.903063i	$0.358687\pi$
$354$	−5.27024	−0.280110
$355$	37.1400	1.97119
$356$	3.27588	0.173622
$357$	5.38194	0.284842
$358$	7.90890	0.417998
$359$	25.4051	1.34083	0.670416	−	0.741986i	$-0.266116\pi$
$359$	25.4051	1.34083	0.670416	+	0.741986i	$0.266116\pi$
$360$	3.56206	0.187737
$361$	1.00000	0.0526316
$362$	14.1270	0.742500
$363$	8.91160	0.467738
$364$	0.660555	0.0346225
$365$	36.9168	1.93232
$366$	10.2090	0.533634
$367$	−30.7769	−1.60654	−0.803271	−	0.595613i	$-0.796909\pi$
$367$	−30.7769	−1.60654	−0.803271	+	0.595613i	$0.796909\pi$
$368$	−6.97945	−0.363829
$369$	−3.73952	−0.194672
$370$	−23.6576	−1.22990
$371$	−10.1127	−0.525024
$372$	11.4051	0.591325
$373$	10.6394	0.550885	0.275442	−	0.961318i	$-0.411176\pi$
$373$	10.6394	0.550885	0.275442	+	0.961318i	$0.411176\pi$
$374$	9.75508	0.504423
$375$	−5.94783	−0.307145
$376$	4.32443	0.223015
$377$	0.195390	0.0100631
$378$	4.80538	0.247162
$379$	−0.975664	−0.0501165	−0.0250582	−	0.999686i	$-0.507977\pi$
$379$	−0.975664	−0.0501165	−0.0250582	+	0.999686i	$0.507977\pi$
$380$	−3.35741	−0.172232
$381$	−3.85285	−0.197387
$382$	−10.5742	−0.541021
$383$	−9.27974	−0.474173	−0.237086	−	0.971489i	$-0.576192\pi$
$383$	−9.27974	−0.474173	−0.237086	+	0.971489i	$0.576192\pi$
$384$	1.39250	0.0710605
$385$	6.11930	0.311868
$386$	9.74050	0.495778
$387$	−7.76884	−0.394912
$388$	−7.35547	−0.373417
$389$	−7.83048	−0.397021	−0.198511	−	0.980099i	$-0.563610\pi$
$389$	−7.83048	−0.397021	−0.198511	+	0.980099i	$0.563610\pi$
$390$	−3.63415	−0.184022
$391$	−31.7439	−1.60536
$392$	6.27788	0.317081
$393$	1.52305	0.0768275
$394$	−3.06523	−0.154424
$395$	−10.8056	−0.543688
$396$	2.27556	0.114351
$397$	17.8431	0.895519	0.447759	−	0.894154i	$-0.352222\pi$
$397$	17.8431	0.895519	0.447759	+	0.894154i	$0.352222\pi$
$398$	−26.2375	−1.31517
$399$	−1.18331	−0.0592397
$400$	6.27221	0.313611
$401$	−11.1835	−0.558477	−0.279239	−	0.960222i	$-0.590082\pi$
$401$	−11.1835	−0.558477	−0.279239	+	0.960222i	$0.590082\pi$
$402$	−8.58285	−0.428074
$403$	6.36660	0.317143
$404$	−0.891342	−0.0443459
$405$	−15.7513	−0.782690
$406$	−0.213601	−0.0106009
$407$	−15.1132	−0.749136
$408$	6.33335	0.313547
$409$	19.1858	0.948674	0.474337	−	0.880343i	$-0.342688\pi$
$409$	19.1858	0.948674	0.474337	+	0.880343i	$0.342688\pi$
$410$	−11.8338	−0.584429
$411$	−8.72230	−0.430240
$412$	12.5025	0.615953
$413$	3.21619	0.158258
$414$	−7.40489	−0.363930
$415$	−38.2634	−1.87828
$416$	0.777327	0.0381116
$417$	−0.998768	−0.0489099
$418$	−2.14482	−0.104907
$419$	12.9192	0.631142	0.315571	−	0.948902i	$-0.397804\pi$
$419$	12.9192	0.631142	0.315571	+	0.948902i	$0.397804\pi$
$420$	3.97287	0.193856
$421$	−13.5680	−0.661262	−0.330631	−	0.943760i	$-0.607262\pi$
$421$	−13.5680	−0.661262	−0.330631	+	0.943760i	$0.607262\pi$
$422$	1.00000	0.0486792
$423$	4.58803	0.223077
$424$	−11.9004	−0.577933
$425$	28.5273	1.38378
$426$	15.4039	0.746322
$427$	−6.23011	−0.301496
$428$	−4.18210	−0.202149
$429$	−2.32161	−0.112088
$430$	−24.5846	−1.18558
$431$	−21.1833	−1.02036	−0.510182	−	0.860067i	$-0.670422\pi$
$431$	−21.1833	−1.02036	−0.510182	+	0.860067i	$0.670422\pi$
$432$	5.65486	0.272070
$433$	22.9647	1.10361	0.551807	−	0.833972i	$-0.313939\pi$
$433$	22.9647	1.10361	0.551807	+	0.833972i	$0.313939\pi$
$434$	−6.96000	−0.334091
$435$	1.17516	0.0563446
$436$	−19.1368	−0.916488
$437$	6.97945	0.333873
$438$	15.3114	0.731605
$439$	−1.64684	−0.0785994	−0.0392997	−	0.999227i	$-0.512513\pi$
$439$	−1.64684	−0.0785994	−0.0392997	+	0.999227i	$0.512513\pi$
$440$	7.20106	0.343297
$441$	6.66055	0.317169
$442$	3.53544	0.168164
$443$	28.5103	1.35457	0.677283	−	0.735723i	$-0.263157\pi$
$443$	28.5103	1.35457	0.677283	+	0.735723i	$0.263157\pi$
$444$	−9.81206	−0.465660
$445$	10.9985	0.521379
$446$	6.86014	0.324837
$447$	4.19348	0.198345
$448$	−0.849778	−0.0401482
$449$	16.8172	0.793651	0.396825	−	0.917894i	$-0.370112\pi$
$449$	16.8172	0.793651	0.396825	+	0.917894i	$0.370112\pi$
$450$	6.65454	0.313698
$451$	−7.55981	−0.355977
$452$	−10.2146	−0.480456
$453$	33.4311	1.57073
$454$	20.4334	0.958985
$455$	2.21776	0.103970
$456$	−1.39250	−0.0652096
$457$	−8.86638	−0.414752	−0.207376	−	0.978261i	$-0.566492\pi$
$457$	−8.86638	−0.414752	−0.207376	+	0.978261i	$0.566492\pi$
$458$	−17.0542	−0.796889
$459$	25.7194	1.20048
$460$	−23.4329	−1.09256
$461$	21.1207	0.983689	0.491844	−	0.870683i	$-0.336323\pi$
$461$	21.1207	0.983689	0.491844	+	0.870683i	$0.336323\pi$
$462$	2.53800	0.118078
$463$	13.7115	0.637227	0.318614	−	0.947885i	$-0.396783\pi$
$463$	13.7115	0.637227	0.318614	+	0.947885i	$0.396783\pi$
$464$	−0.251361	−0.0116692
$465$	38.2915	1.77573
$466$	12.4324	0.575922
$467$	−20.4409	−0.945890	−0.472945	−	0.881092i	$-0.656809\pi$
$467$	−20.4409	−0.945890	−0.472945	+	0.881092i	$0.656809\pi$
$468$	0.824709	0.0381222
$469$	5.23773	0.241856
$470$	14.5189	0.669706
$471$	−8.57034	−0.394900
$472$	3.78474	0.174207
$473$	−15.7055	−0.722138
$474$	−4.48164	−0.205849
$475$	−6.27221	−0.287789
$476$	−3.86496	−0.177150
$477$	−12.6258	−0.578094
$478$	13.7443	0.628650
$479$	28.7313	1.31277	0.656383	−	0.754428i	$-0.272086\pi$
$479$	28.7313	1.31277	0.656383	+	0.754428i	$0.272086\pi$
$480$	4.67518	0.213392
$481$	−5.47734	−0.249745
$482$	−16.4439	−0.748999
$483$	−8.25887	−0.375792
$484$	−6.39973	−0.290897
$485$	−24.6953	−1.12136
$486$	10.4317	0.473191
$487$	−28.7492	−1.30275	−0.651375	−	0.758756i	$-0.725807\pi$
$487$	−28.7492	−1.30275	−0.651375	+	0.758756i	$0.725807\pi$
$488$	−7.33146	−0.331880
$489$	9.09426	0.411257
$490$	21.0774	0.952181
$491$	1.12776	0.0508951	0.0254475	−	0.999676i	$-0.491899\pi$
$491$	1.12776	0.0508951	0.0254475	+	0.999676i	$0.491899\pi$
$492$	−4.90810	−0.221274
$493$	−1.14324	−0.0514890
$494$	−0.777327	−0.0349736
$495$	7.64000	0.343392
$496$	−8.19038	−0.367759
$497$	−9.40032	−0.421662
$498$	−15.8699	−0.711145
$499$	−16.3458	−0.731739	−0.365870	−	0.930666i	$-0.619228\pi$
$499$	−16.3458	−0.731739	−0.365870	+	0.930666i	$0.619228\pi$
$500$	4.27135	0.191020
$501$	5.78653	0.258523
$502$	−6.17856	−0.275763
$503$	−25.6277	−1.14268	−0.571341	−	0.820713i	$-0.693577\pi$
$503$	−25.6277	−1.14268	−0.571341	+	0.820713i	$0.693577\pi$
$504$	−0.901576	−0.0401594
$505$	−2.99260	−0.133169
$506$	−14.9697	−0.665484
$507$	17.2610	0.766590
$508$	2.76687	0.122760
$509$	8.43307	0.373789	0.186895	−	0.982380i	$-0.440158\pi$
$509$	8.43307	0.373789	0.186895	+	0.982380i	$0.440158\pi$
$510$	21.2636	0.941570
$511$	−9.34384	−0.413347
$512$	−1.00000	−0.0441942
$513$	−5.65486	−0.249668
$514$	10.2880	0.453785
$515$	41.9760	1.84968
$516$	−10.1965	−0.448878
$517$	9.27514	0.407920
$518$	5.98786	0.263091
$519$	35.4488	1.55603
$520$	2.60981	0.114448
$521$	4.96436	0.217492	0.108746	−	0.994070i	$-0.465316\pi$
$521$	4.96436	0.217492	0.108746	+	0.994070i	$0.465316\pi$
$522$	−0.266683	−0.0116724
$523$	−45.0053	−1.96795	−0.983973	−	0.178318i	$-0.942935\pi$
$523$	−45.0053	−1.96795	−0.983973	+	0.178318i	$0.942935\pi$
$524$	−1.09375	−0.0477808
$525$	7.42199	0.323922
$526$	−17.8019	−0.776201
$527$	−37.2514	−1.62270
$528$	2.98666	0.129978
$529$	25.7128	1.11795
$530$	−39.9545	−1.73551
$531$	4.01544	0.174255
$532$	0.849778	0.0368425
$533$	−2.73983	−0.118675
$534$	4.56166	0.197402
$535$	−14.0410	−0.607047
$536$	6.16364	0.266229
$537$	11.0131	0.475251
$538$	28.1483	1.21356
$539$	13.4649	0.579976
$540$	18.9857	0.817015
$541$	−10.6429	−0.457573	−0.228787	−	0.973477i	$-0.573476\pi$
$541$	−10.6429	−0.457573	−0.228787	+	0.973477i	$0.573476\pi$
$542$	−18.1743	−0.780654
$543$	19.6718	0.844199
$544$	−4.54820	−0.195002
$545$	−64.2503	−2.75218
$546$	0.919821	0.0393647
$547$	11.2212	0.479784	0.239892	−	0.970800i	$-0.422888\pi$
$547$	11.2212	0.479784	0.239892	+	0.970800i	$0.422888\pi$
$548$	6.26379	0.267576
$549$	−7.77835	−0.331972
$550$	13.4528	0.573629
$551$	0.251361	0.0107083
$552$	−9.71886	−0.413662
$553$	2.73495	0.116302
$554$	12.9510	0.550233
$555$	−32.9431	−1.39836
$556$	0.717250	0.0304182
$557$	−1.66300	−0.0704634	−0.0352317	−	0.999379i	$-0.511217\pi$
$557$	−1.66300	−0.0704634	−0.0352317	+	0.999379i	$0.511217\pi$
$558$	−8.68962	−0.367861
$559$	−5.69197	−0.240745
$560$	−2.85305	−0.120564
$561$	13.5839	0.573513
$562$	−24.5209	−1.03435
$563$	29.5273	1.24443	0.622214	−	0.782847i	$-0.286233\pi$
$563$	29.5273	1.24443	0.622214	+	0.782847i	$0.286233\pi$
$564$	6.02175	0.253561
$565$	−34.2947	−1.44279
$566$	−21.1643	−0.889602
$567$	3.98674	0.167427
$568$	−11.0621	−0.464155
$569$	6.53252	0.273858	0.136929	−	0.990581i	$-0.456277\pi$
$569$	6.53252	0.273858	0.136929	+	0.990581i	$0.456277\pi$
$570$	−4.67518	−0.195822
$571$	−13.8230	−0.578474	−0.289237	−	0.957258i	$-0.593402\pi$
$571$	−13.8230	−0.578474	−0.289237	+	0.957258i	$0.593402\pi$
$572$	1.66723	0.0697104
$573$	−14.7245	−0.615124
$574$	2.99519	0.125017
$575$	−43.7766	−1.82561
$576$	−1.06096	−0.0442065
$577$	−33.2987	−1.38624	−0.693122	−	0.720820i	$-0.743765\pi$
$577$	−33.2987	−1.38624	−0.693122	+	0.720820i	$0.743765\pi$
$578$	−3.68609	−0.153321
$579$	13.5636	0.563684
$580$	−0.843923	−0.0350420
$581$	9.68467	0.401788
$582$	−10.2425	−0.424564
$583$	−25.5242	−1.05711
$584$	−10.9956	−0.455002
$585$	2.76889	0.114479
$586$	25.2265	1.04210
$587$	−35.3780	−1.46020	−0.730102	−	0.683338i	$-0.760528\pi$
$587$	−35.3780	−1.46020	−0.730102	+	0.683338i	$0.760528\pi$
$588$	8.74192	0.360511
$589$	8.19038	0.337479
$590$	12.7069	0.523136
$591$	−4.26832	−0.175575
$592$	7.04638	0.289604
$593$	−37.2644	−1.53027	−0.765133	−	0.643872i	$-0.777327\pi$
$593$	−37.2644	−1.53027	−0.765133	+	0.643872i	$0.777327\pi$
$594$	12.1287	0.497646
$595$	−12.9763	−0.531975
$596$	−3.01148	−0.123355
$597$	−36.5356	−1.49530
$598$	−5.42532	−0.221858
$599$	−42.1481	−1.72212	−0.861061	−	0.508501i	$-0.830200\pi$
$599$	−42.1481	−1.72212	−0.861061	+	0.508501i	$0.830200\pi$
$600$	8.73403	0.356565
$601$	−37.2608	−1.51990	−0.759950	−	0.649981i	$-0.774777\pi$
$601$	−37.2608	−1.51990	−0.759950	+	0.649981i	$0.774777\pi$
$602$	6.22249	0.253610
$603$	6.53935	0.266303
$604$	−24.0081	−0.976874
$605$	−21.4865	−0.873552
$606$	−1.24119	−0.0504199
$607$	−12.0230	−0.488000	−0.244000	−	0.969775i	$-0.578460\pi$
$607$	−12.0230	−0.488000	−0.244000	+	0.969775i	$0.578460\pi$
$608$	1.00000	0.0405554
$609$	−0.297439	−0.0120528
$610$	−24.6147	−0.996621
$611$	3.36150	0.135992
$612$	−4.82543	−0.195057
$613$	13.2090	0.533507	0.266753	−	0.963765i	$-0.414049\pi$
$613$	13.2090	0.533507	0.266753	+	0.963765i	$0.414049\pi$
$614$	21.7084	0.876080
$615$	−16.4785	−0.664477
$616$	−1.82262	−0.0734356
$617$	1.53422	0.0617654	0.0308827	−	0.999523i	$-0.490168\pi$
$617$	1.53422	0.0617654	0.0308827	+	0.999523i	$0.490168\pi$
$618$	17.4096	0.700319
$619$	−25.9259	−1.04205	−0.521024	−	0.853542i	$-0.674450\pi$
$619$	−25.9259	−1.04205	−0.521024	+	0.853542i	$0.674450\pi$
$620$	−27.4985	−1.10437
$621$	−39.4679	−1.58379
$622$	4.79442	0.192239
$623$	−2.78377	−0.111530
$624$	1.08242	0.0433317
$625$	−17.0204	−0.680816
$626$	−1.43081	−0.0571869
$627$	−2.98666	−0.119276
$628$	6.15466	0.245598
$629$	32.0483	1.27785
$630$	−3.02696	−0.120597
$631$	−13.2570	−0.527752	−0.263876	−	0.964557i	$-0.585001\pi$
$631$	−13.2570	−0.527752	−0.263876	+	0.964557i	$0.585001\pi$
$632$	3.21842	0.128022
$633$	1.39250	0.0553467
$634$	24.2901	0.964682
$635$	9.28951	0.368643
$636$	−16.5712	−0.657092
$637$	4.87996	0.193351
$638$	−0.539126	−0.0213442
$639$	−11.7364	−0.464284
$640$	−3.35741	−0.132713
$641$	−0.315487	−0.0124610	−0.00623049	−	0.999981i	$-0.501983\pi$
$641$	−0.315487	−0.0124610	−0.00623049	+	0.999981i	$0.501983\pi$
$642$	−5.82356	−0.229838
$643$	12.6930	0.500564	0.250282	−	0.968173i	$-0.419477\pi$
$643$	12.6930	0.500564	0.250282	+	0.968173i	$0.419477\pi$
$644$	5.93099	0.233714
$645$	−34.2340	−1.34796
$646$	4.54820	0.178946
$647$	0.454440	0.0178659	0.00893294	−	0.999960i	$-0.497157\pi$
$647$	0.454440	0.0178659	0.00893294	+	0.999960i	$0.497157\pi$
$648$	4.69151	0.184300
$649$	8.11760	0.318644
$650$	4.87556	0.191235
$651$	−9.69177	−0.379851
$652$	−6.53091	−0.255770
$653$	−22.1696	−0.867562	−0.433781	−	0.901018i	$-0.642821\pi$
$653$	−22.1696	−0.867562	−0.433781	+	0.901018i	$0.642821\pi$
$654$	−26.6480	−1.04202
$655$	−3.67218	−0.143484
$656$	3.52467	0.137615
$657$	−11.6659	−0.455129
$658$	−3.67480	−0.143259
$659$	−13.8961	−0.541315	−0.270658	−	0.962676i	$-0.587241\pi$
$659$	−13.8961	−0.541315	−0.270658	+	0.962676i	$0.587241\pi$
$660$	10.0274	0.390318
$661$	−39.2335	−1.52601	−0.763003	−	0.646394i	$-0.776276\pi$
$661$	−39.2335	−1.52601	−0.763003	+	0.646394i	$0.776276\pi$
$662$	−26.9152	−1.04609
$663$	4.92308	0.191197
$664$	11.3967	0.442278
$665$	2.85305	0.110637
$666$	7.47589	0.289685
$667$	1.75436	0.0679293
$668$	−4.15551	−0.160781
$669$	9.55271	0.369329
$670$	20.6939	0.799475
$671$	−15.7247	−0.607045
$672$	−1.18331	−0.0456473
$673$	2.02221	0.0779503	0.0389752	−	0.999240i	$-0.487591\pi$
$673$	2.02221	0.0779503	0.0389752	+	0.999240i	$0.487591\pi$
$674$	33.1035	1.27510
$675$	35.4685	1.36518
$676$	−12.3958	−0.476760
$677$	−3.13448	−0.120468	−0.0602340	−	0.998184i	$-0.519185\pi$
$677$	−3.13448	−0.120468	−0.0602340	+	0.998184i	$0.519185\pi$
$678$	−14.2238	−0.546263
$679$	6.25052	0.239873
$680$	−15.2702	−0.585584
$681$	28.4534	1.09033
$682$	−17.5669	−0.672672
$683$	−14.7763	−0.565398	−0.282699	−	0.959209i	$-0.591230\pi$
$683$	−14.7763	−0.565398	−0.282699	+	0.959209i	$0.591230\pi$
$684$	1.06096	0.0405666
$685$	21.0301	0.803520
$686$	−11.2832	−0.430796
$687$	−23.7479	−0.906038
$688$	7.32249	0.279167
$689$	−9.25049	−0.352415
$690$	−32.6302	−1.24221
$691$	33.7133	1.28251	0.641257	−	0.767326i	$-0.278413\pi$
$691$	33.7133	1.28251	0.641257	+	0.767326i	$0.278413\pi$
$692$	−25.4570	−0.967730
$693$	−1.93372	−0.0734560
$694$	3.45265	0.131061
$695$	2.40811	0.0913446
$696$	−0.350019	−0.0132675
$697$	16.0309	0.607214
$698$	20.8504	0.789198
$699$	17.3121	0.654805
$700$	−5.32999	−0.201455
$701$	−13.7241	−0.518353	−0.259176	−	0.965830i	$-0.583451\pi$
$701$	−13.7241	−0.518353	−0.259176	+	0.965830i	$0.583451\pi$
$702$	4.39568	0.165904
$703$	−7.04638	−0.265759
$704$	−2.14482	−0.0808361
$705$	20.2175	0.761435
$706$	−16.1395	−0.607416
$707$	0.757443	0.0284866
$708$	5.27024	0.198068
$709$	−1.64024	−0.0616004	−0.0308002	−	0.999526i	$-0.509806\pi$
$709$	−1.64024	−0.0616004	−0.0308002	+	0.999526i	$0.509806\pi$
$710$	−37.1400	−1.39384
$711$	3.41460	0.128058
$712$	−3.27588	−0.122769
$713$	57.1644	2.14082
$714$	−5.38194	−0.201414
$715$	5.59758	0.209337
$716$	−7.90890	−0.295569
$717$	19.1389	0.714756
$718$	−25.4051	−0.948111
$719$	0.225491	0.00840938	0.00420469	−	0.999991i	$-0.498662\pi$
$719$	0.225491	0.00840938	0.00420469	+	0.999991i	$0.498662\pi$
$720$	−3.56206	−0.132750
$721$	−10.6243	−0.395671
$722$	−1.00000	−0.0372161
$723$	−22.8980	−0.851588
$724$	−14.1270	−0.525027
$725$	−1.57659	−0.0585531
$726$	−8.91160	−0.330740
$727$	−23.2646	−0.862836	−0.431418	−	0.902152i	$-0.641987\pi$
$727$	−23.2646	−0.862836	−0.431418	+	0.902152i	$0.641987\pi$
$728$	−0.660555	−0.0244818
$729$	28.6006	1.05928
$730$	−36.9168	−1.36635
$731$	33.3041	1.23180
$732$	−10.2090	−0.377337
$733$	26.2032	0.967838	0.483919	−	0.875113i	$-0.339213\pi$
$733$	26.2032	0.967838	0.483919	+	0.875113i	$0.339213\pi$
$734$	30.7769	1.13600
$735$	29.3502	1.08260
$736$	6.97945	0.257266
$737$	13.2199	0.486962
$738$	3.73952	0.137654
$739$	32.2217	1.18529	0.592646	−	0.805463i	$-0.298083\pi$
$739$	32.2217	1.18529	0.592646	+	0.805463i	$0.298083\pi$
$740$	23.6576	0.869671
$741$	−1.08242	−0.0397639
$742$	10.1127	0.371248
$743$	41.5597	1.52468	0.762340	−	0.647177i	$-0.224051\pi$
$743$	41.5597	1.52468	0.762340	+	0.647177i	$0.224051\pi$
$744$	−11.4051	−0.418130
$745$	−10.1108	−0.370431
$746$	−10.6394	−0.389534
$747$	12.0914	0.442401
$748$	−9.75508	−0.356681
$749$	3.55386	0.129855
$750$	5.94783	0.217184
$751$	−36.8167	−1.34346	−0.671730	−	0.740796i	$-0.734448\pi$
$751$	−36.8167	−1.34346	−0.671730	+	0.740796i	$0.734448\pi$
$752$	−4.32443	−0.157696
$753$	−8.60362	−0.313533
$754$	−0.195390	−0.00711568
$755$	−80.6050	−2.93352
$756$	−4.80538	−0.174770
$757$	33.6429	1.22277	0.611385	−	0.791333i	$-0.290613\pi$
$757$	33.6429	1.22277	0.611385	+	0.791333i	$0.290613\pi$
$758$	0.975664	0.0354377
$759$	−20.8452	−0.756635
$760$	3.35741	0.121786
$761$	13.0996	0.474862	0.237431	−	0.971404i	$-0.423695\pi$
$761$	13.0996	0.474862	0.237431	+	0.971404i	$0.423695\pi$
$762$	3.85285	0.139574
$763$	16.2621	0.588726
$764$	10.5742	0.382560
$765$	−16.2010	−0.585747
$766$	9.27974	0.335291
$767$	2.94198	0.106229
$768$	−1.39250	−0.0502474
$769$	−2.82864	−0.102003	−0.0510016	−	0.998699i	$-0.516241\pi$
$769$	−2.82864	−0.102003	−0.0510016	+	0.998699i	$0.516241\pi$
$770$	−6.11930	−0.220524
$771$	14.3260	0.515939
$772$	−9.74050	−0.350568
$773$	−15.2922	−0.550023	−0.275011	−	0.961441i	$-0.588682\pi$
$773$	−15.2922	−0.550023	−0.275011	+	0.961441i	$0.588682\pi$
$774$	7.76884	0.279245
$775$	−51.3718	−1.84533
$776$	7.35547	0.264046
$777$	8.33807	0.299127
$778$	7.83048	0.280736
$779$	−3.52467	−0.126285
$780$	3.63415	0.130123
$781$	−23.7262	−0.848991
$782$	31.7439	1.13516
$783$	−1.42141	−0.0507972
$784$	−6.27788	−0.224210
$785$	20.6637	0.737520
$786$	−1.52305	−0.0543252
$787$	−25.4071	−0.905667	−0.452833	−	0.891595i	$-0.649587\pi$
$787$	−25.4071	−0.905667	−0.452833	+	0.891595i	$0.649587\pi$
$788$	3.06523	0.109194
$789$	−24.7891	−0.882516
$790$	10.8056	0.384445
$791$	8.68017	0.308631
$792$	−2.27556	−0.0808586
$793$	−5.69894	−0.202375
$794$	−17.8431	−0.633227
$795$	−55.6364	−1.97322
$796$	26.2375	0.929964
$797$	34.3776	1.21772	0.608859	−	0.793278i	$-0.291627\pi$
$797$	34.3776	1.21772	0.608859	+	0.793278i	$0.291627\pi$
$798$	1.18331	0.0418888
$799$	−19.6684	−0.695816
$800$	−6.27221	−0.221756
$801$	−3.47557	−0.122803
$802$	11.1835	0.394903
$803$	−23.5837	−0.832250
$804$	8.58285	0.302694
$805$	19.9128	0.701833
$806$	−6.36660	−0.224254
$807$	39.1964	1.37978
$808$	0.891342	0.0313573
$809$	−38.7471	−1.36228	−0.681138	−	0.732155i	$-0.738515\pi$
$809$	−38.7471	−1.36228	−0.681138	+	0.732155i	$0.738515\pi$
$810$	15.7513	0.553445
$811$	10.8228	0.380038	0.190019	−	0.981780i	$-0.439145\pi$
$811$	10.8228	0.380038	0.190019	+	0.981780i	$0.439145\pi$
$812$	0.213601	0.00749593
$813$	−25.3077	−0.887578
$814$	15.1132	0.529719
$815$	−21.9269	−0.768068
$816$	−6.33335	−0.221711
$817$	−7.32249	−0.256182
$818$	−19.1858	−0.670814
$819$	−0.700820	−0.0244886
$820$	11.8338	0.413254
$821$	−9.93060	−0.346580	−0.173290	−	0.984871i	$-0.555440\pi$
$821$	−9.93060	−0.346580	−0.173290	+	0.984871i	$0.555440\pi$
$822$	8.72230	0.304225
$823$	49.1566	1.71349	0.856746	−	0.515739i	$-0.172483\pi$
$823$	49.1566	1.71349	0.856746	+	0.515739i	$0.172483\pi$
$824$	−12.5025	−0.435544
$825$	18.7330	0.652198
$826$	−3.21619	−0.111906
$827$	−8.07138	−0.280669	−0.140335	−	0.990104i	$-0.544818\pi$
$827$	−8.07138	−0.280669	−0.140335	+	0.990104i	$0.544818\pi$
$828$	7.40489	0.257338
$829$	−35.5026	−1.23306	−0.616529	−	0.787332i	$-0.711462\pi$
$829$	−35.5026	−1.23306	−0.616529	+	0.787332i	$0.711462\pi$
$830$	38.2634	1.32814
$831$	18.0342	0.625598
$832$	−0.777327	−0.0269490
$833$	−28.5530	−0.989304
$834$	0.998768	0.0345845
$835$	−13.9518	−0.482820
$836$	2.14482	0.0741803
$837$	−46.3155	−1.60090
$838$	−12.9192	−0.446285
$839$	−34.3719	−1.18665	−0.593325	−	0.804963i	$-0.702185\pi$
$839$	−34.3719	−1.18665	−0.593325	+	0.804963i	$0.702185\pi$
$840$	−3.97287	−0.137077
$841$	−28.9368	−0.997821
$842$	13.5680	0.467583
$843$	−34.1452	−1.17602
$844$	−1.00000	−0.0344214
$845$	−41.6177	−1.43169
$846$	−4.58803	−0.157740
$847$	5.43835	0.186864
$848$	11.9004	0.408661
$849$	−29.4712	−1.01145
$850$	−28.5273	−0.978477
$851$	−49.1799	−1.68587
$852$	−15.4039	−0.527729
$853$	−39.8769	−1.36536	−0.682680	−	0.730717i	$-0.739186\pi$
$853$	−39.8769	−1.36536	−0.682680	+	0.730717i	$0.739186\pi$
$854$	6.23011	0.213190
$855$	3.56206	0.121820
$856$	4.18210	0.142941
$857$	1.92791	0.0658560	0.0329280	−	0.999458i	$-0.489517\pi$
$857$	1.92791	0.0658560	0.0329280	+	0.999458i	$0.489517\pi$
$858$	2.32161	0.0792585
$859$	29.0474	0.991085	0.495542	−	0.868584i	$-0.334969\pi$
$859$	29.0474	0.991085	0.495542	+	0.868584i	$0.334969\pi$
$860$	24.5846	0.838329
$861$	4.17079	0.142140
$862$	21.1833	0.721506
$863$	34.2769	1.16680	0.583399	−	0.812186i	$-0.301722\pi$
$863$	34.2769	1.16680	0.583399	+	0.812186i	$0.301722\pi$
$864$	−5.65486	−0.192382
$865$	−85.4696	−2.90605
$866$	−22.9647	−0.780373
$867$	−5.13287	−0.174321
$868$	6.96000	0.236238
$869$	6.90295	0.234167
$870$	−1.17516	−0.0398416
$871$	4.79117	0.162342
$872$	19.1368	0.648055
$873$	7.80383	0.264119
$874$	−6.97945	−0.236084
$875$	−3.62970	−0.122706
$876$	−15.3114	−0.517323
$877$	15.4852	0.522897	0.261449	−	0.965217i	$-0.415800\pi$
$877$	15.4852	0.522897	0.261449	+	0.965217i	$0.415800\pi$
$878$	1.64684	0.0555782
$879$	35.1278	1.18483
$880$	−7.20106	−0.242748
$881$	−48.3720	−1.62969	−0.814847	−	0.579675i	$-0.803179\pi$
$881$	−48.3720	−1.62969	−0.814847	+	0.579675i	$0.803179\pi$
$882$	−6.66055	−0.224272
$883$	−7.41026	−0.249375	−0.124688	−	0.992196i	$-0.539793\pi$
$883$	−7.41026	−0.249375	−0.124688	+	0.992196i	$0.539793\pi$
$884$	−3.53544	−0.118910
$885$	17.6944	0.594789
$886$	−28.5103	−0.957822
$887$	−0.367165	−0.0123282	−0.00616409	−	0.999981i	$-0.501962\pi$
$887$	−0.367165	−0.0123282	−0.00616409	+	0.999981i	$0.501962\pi$
$888$	9.81206	0.329271
$889$	−2.35122	−0.0788575
$890$	−10.9985	−0.368670
$891$	10.0625	0.337105
$892$	−6.86014	−0.229694
$893$	4.32443	0.144711
$894$	−4.19348	−0.140251
$895$	−26.5534	−0.887583
$896$	0.849778	0.0283891
$897$	−7.55473	−0.252245
$898$	−16.8172	−0.561196
$899$	2.05874	0.0686629
$900$	−6.65454	−0.221818
$901$	54.1253	1.80317
$902$	7.55981	0.251714
$903$	8.66480	0.288346
$904$	10.2146	0.339733
$905$	−47.4303	−1.57664
$906$	−33.4311	−1.11068
$907$	−49.7330	−1.65136	−0.825679	−	0.564141i	$-0.809208\pi$
$907$	−49.7330	−1.65136	−0.825679	+	0.564141i	$0.809208\pi$
$908$	−20.4334	−0.678105
$909$	0.945674	0.0313660
$910$	−2.21776	−0.0735179
$911$	51.6919	1.71263	0.856315	−	0.516455i	$-0.172749\pi$
$911$	51.6919	1.71263	0.856315	+	0.516455i	$0.172749\pi$
$912$	1.39250	0.0461101
$913$	24.4439	0.808976
$914$	8.86638	0.293274
$915$	−34.2759	−1.13313
$916$	17.0542	0.563486
$917$	0.929446	0.0306930
$918$	−25.7194	−0.848868
$919$	−34.8366	−1.14915	−0.574576	−	0.818451i	$-0.694833\pi$
$919$	−34.8366	−1.14915	−0.574576	+	0.818451i	$0.694833\pi$
$920$	23.4329	0.772560
$921$	30.2289	0.996075
$922$	−21.1207	−0.695573
$923$	−8.59886	−0.283035
$924$	−2.53800	−0.0834940
$925$	44.1964	1.45317
$926$	−13.7115	−0.450588
$927$	−13.2646	−0.435666
$928$	0.251361	0.00825134
$929$	32.4167	1.06356	0.531778	−	0.846884i	$-0.321524\pi$
$929$	32.4167	1.06356	0.531778	+	0.846884i	$0.321524\pi$
$930$	−38.2915	−1.25563
$931$	6.27788	0.205749
$932$	−12.4324	−0.407238
$933$	6.67621	0.218569
$934$	20.4409	0.668845
$935$	−32.7518	−1.07110
$936$	−0.824709	−0.0269565
$937$	−33.6149	−1.09815	−0.549075	−	0.835773i	$-0.685020\pi$
$937$	−33.6149	−1.09815	−0.549075	+	0.835773i	$0.685020\pi$
$938$	−5.23773	−0.171018
$939$	−1.99240	−0.0650196
$940$	−14.5189	−0.473554
$941$	47.3598	1.54388	0.771942	−	0.635693i	$-0.219285\pi$
$941$	47.3598	1.54388	0.771942	+	0.635693i	$0.219285\pi$
$942$	8.57034	0.279237
$943$	−24.6003	−0.801096
$944$	−3.78474	−0.123183
$945$	−16.1336	−0.524827
$946$	15.7055	0.510629
$947$	−16.9913	−0.552144	−0.276072	−	0.961137i	$-0.589033\pi$
$947$	−16.9913	−0.552144	−0.276072	+	0.961137i	$0.589033\pi$
$948$	4.48164	0.145557
$949$	−8.54719	−0.277454
$950$	6.27221	0.203498
$951$	33.8238	1.09681
$952$	3.86496	0.125264
$953$	49.9263	1.61727	0.808637	−	0.588309i	$-0.200206\pi$
$953$	49.9263	1.61727	0.808637	+	0.588309i	$0.200206\pi$
$954$	12.6258	0.408774
$955$	35.5018	1.14881
$956$	−13.7443	−0.444523
$957$	−0.750730	−0.0242677
$958$	−28.7313	−0.928266
$959$	−5.32283	−0.171883
$960$	−4.67518	−0.150891
$961$	36.0823	1.16394
$962$	5.47734	0.176597
$963$	4.43702	0.142981
$964$	16.4439	0.529622
$965$	−32.7029	−1.05274
$966$	8.25887	0.265725
$967$	−5.14364	−0.165408	−0.0827042	−	0.996574i	$-0.526356\pi$
$967$	−5.14364	−0.165408	−0.0827042	+	0.996574i	$0.526356\pi$
$968$	6.39973	0.205695
$969$	6.33335	0.203456
$970$	24.6953	0.792920
$971$	2.93073	0.0940517	0.0470259	−	0.998894i	$-0.485026\pi$
$971$	2.93073	0.0940517	0.0470259	+	0.998894i	$0.485026\pi$
$972$	−10.4317	−0.334596
$973$	−0.609504	−0.0195398
$974$	28.7492	0.921183
$975$	6.78920	0.217428
$976$	7.33146	0.234674
$977$	11.6691	0.373328	0.186664	−	0.982424i	$-0.440232\pi$
$977$	11.6691	0.373328	0.186664	+	0.982424i	$0.440232\pi$
$978$	−9.09426	−0.290802
$979$	−7.02620	−0.224558
$980$	−21.0774	−0.673293
$981$	20.3033	0.648235
$982$	−1.12776	−0.0359882
$983$	−4.45089	−0.141961	−0.0709806	−	0.997478i	$-0.522613\pi$
$983$	−4.45089	−0.141961	−0.0709806	+	0.997478i	$0.522613\pi$
$984$	4.90810	0.156464
$985$	10.2912	0.327906
$986$	1.14324	0.0364082
$987$	−5.11715	−0.162881
$988$	0.777327	0.0247301
$989$	−51.1070	−1.62511
$990$	−7.64000	−0.242815
$991$	47.0891	1.49583	0.747917	−	0.663793i	$-0.231054\pi$
$991$	47.0891	1.49583	0.747917	+	0.663793i	$0.231054\pi$
$992$	8.19038	0.260045
$993$	−37.4792	−1.18937
$994$	9.40032	0.298160
$995$	88.0902	2.79265
$996$	15.8699	0.502856
$997$	−44.9972	−1.42507	−0.712537	−	0.701634i	$-0.752454\pi$
$997$	−44.9972	−1.42507	−0.712537	+	0.701634i	$0.752454\pi$
$998$	16.3458	0.517418
$999$	39.8463	1.26068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.13	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.13	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.39250 q^{3} +1.00000 q^{4} +3.35741 q^{5} +1.39250 q^{6} -0.849778 q^{7} -1.00000 q^{8} -1.06096 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.39250 q^{3} +1.00000 q^{4} +3.35741 q^{5} +1.39250 q^{6} -0.849778 q^{7} -1.00000 q^{8} -1.06096 q^{9} -3.35741 q^{10} -2.14482 q^{11} -1.39250 q^{12} -0.777327 q^{13} +0.849778 q^{14} -4.67518 q^{15} +1.00000 q^{16} +4.54820 q^{17} +1.06096 q^{18} -1.00000 q^{19} +3.35741 q^{20} +1.18331 q^{21} +2.14482 q^{22} -6.97945 q^{23} +1.39250 q^{24} +6.27221 q^{25} +0.777327 q^{26} +5.65486 q^{27} -0.849778 q^{28} -0.251361 q^{29} +4.67518 q^{30} -8.19038 q^{31} -1.00000 q^{32} +2.98666 q^{33} -4.54820 q^{34} -2.85305 q^{35} -1.06096 q^{36} +7.04638 q^{37} +1.00000 q^{38} +1.08242 q^{39} -3.35741 q^{40} +3.52467 q^{41} -1.18331 q^{42} +7.32249 q^{43} -2.14482 q^{44} -3.56206 q^{45} +6.97945 q^{46} -4.32443 q^{47} -1.39250 q^{48} -6.27788 q^{49} -6.27221 q^{50} -6.33335 q^{51} -0.777327 q^{52} +11.9004 q^{53} -5.65486 q^{54} -7.20106 q^{55} +0.849778 q^{56} +1.39250 q^{57} +0.251361 q^{58} -3.78474 q^{59} -4.67518 q^{60} +7.33146 q^{61} +8.19038 q^{62} +0.901576 q^{63} +1.00000 q^{64} -2.60981 q^{65} -2.98666 q^{66} -6.16364 q^{67} +4.54820 q^{68} +9.71886 q^{69} +2.85305 q^{70} +11.0621 q^{71} +1.06096 q^{72} +10.9956 q^{73} -7.04638 q^{74} -8.73403 q^{75} -1.00000 q^{76} +1.82262 q^{77} -1.08242 q^{78} -3.21842 q^{79} +3.35741 q^{80} -4.69151 q^{81} -3.52467 q^{82} -11.3967 q^{83} +1.18331 q^{84} +15.2702 q^{85} -7.32249 q^{86} +0.350019 q^{87} +2.14482 q^{88} +3.27588 q^{89} +3.56206 q^{90} +0.660555 q^{91} -6.97945 q^{92} +11.4051 q^{93} +4.32443 q^{94} -3.35741 q^{95} +1.39250 q^{96} -7.35547 q^{97} +6.27788 q^{98} +2.27556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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