LMFDB - Embedded newform 8018.2.a.j.1.36

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:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.36
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.24233 q^{3} +1.00000 q^{4} +3.57017 q^{5} +2.24233 q^{6} +0.516251 q^{7} +1.00000 q^{8} +2.02804 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.24233 q^{3} +1.00000 q^{4} +3.57017 q^{5} +2.24233 q^{6} +0.516251 q^{7} +1.00000 q^{8} +2.02804 q^{9} +3.57017 q^{10} +3.00236 q^{11} +2.24233 q^{12} +1.63605 q^{13} +0.516251 q^{14} +8.00549 q^{15} +1.00000 q^{16} -0.530807 q^{17} +2.02804 q^{18} -1.00000 q^{19} +3.57017 q^{20} +1.15761 q^{21} +3.00236 q^{22} -2.37767 q^{23} +2.24233 q^{24} +7.74610 q^{25} +1.63605 q^{26} -2.17946 q^{27} +0.516251 q^{28} +4.16112 q^{29} +8.00549 q^{30} -3.37427 q^{31} +1.00000 q^{32} +6.73227 q^{33} -0.530807 q^{34} +1.84310 q^{35} +2.02804 q^{36} -8.08939 q^{37} -1.00000 q^{38} +3.66856 q^{39} +3.57017 q^{40} +2.76275 q^{41} +1.15761 q^{42} -3.09244 q^{43} +3.00236 q^{44} +7.24043 q^{45} -2.37767 q^{46} -6.39982 q^{47} +2.24233 q^{48} -6.73348 q^{49} +7.74610 q^{50} -1.19024 q^{51} +1.63605 q^{52} +6.86634 q^{53} -2.17946 q^{54} +10.7189 q^{55} +0.516251 q^{56} -2.24233 q^{57} +4.16112 q^{58} +7.54745 q^{59} +8.00549 q^{60} +13.9351 q^{61} -3.37427 q^{62} +1.04698 q^{63} +1.00000 q^{64} +5.84097 q^{65} +6.73227 q^{66} -7.40499 q^{67} -0.530807 q^{68} -5.33151 q^{69} +1.84310 q^{70} +9.46877 q^{71} +2.02804 q^{72} -5.84556 q^{73} -8.08939 q^{74} +17.3693 q^{75} -1.00000 q^{76} +1.54997 q^{77} +3.66856 q^{78} +14.2713 q^{79} +3.57017 q^{80} -10.9712 q^{81} +2.76275 q^{82} -8.41550 q^{83} +1.15761 q^{84} -1.89507 q^{85} -3.09244 q^{86} +9.33059 q^{87} +3.00236 q^{88} -5.57298 q^{89} +7.24043 q^{90} +0.844613 q^{91} -2.37767 q^{92} -7.56622 q^{93} -6.39982 q^{94} -3.57017 q^{95} +2.24233 q^{96} +9.07657 q^{97} -6.73348 q^{98} +6.08889 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.24233	1.29461	0.647304	−	0.762232i	$-0.275896\pi$
$3$	2.24233	1.29461	0.647304	+	0.762232i	$0.275896\pi$
$4$	1.00000	0.500000
$5$	3.57017	1.59663	0.798314	−	0.602242i	$-0.205726\pi$
$5$	3.57017	1.59663	0.798314	+	0.602242i	$0.205726\pi$
$6$	2.24233	0.915427
$7$	0.516251	0.195125	0.0975623	−	0.995229i	$-0.468895\pi$
$7$	0.516251	0.195125	0.0975623	+	0.995229i	$0.468895\pi$
$8$	1.00000	0.353553
$9$	2.02804	0.676012
$10$	3.57017	1.12899
$11$	3.00236	0.905244	0.452622	−	0.891702i	$-0.350489\pi$
$11$	3.00236	0.905244	0.452622	+	0.891702i	$0.350489\pi$
$12$	2.24233	0.647304
$13$	1.63605	0.453758	0.226879	−	0.973923i	$-0.427148\pi$
$13$	1.63605	0.453758	0.226879	+	0.973923i	$0.427148\pi$
$14$	0.516251	0.137974
$15$	8.00549	2.06701
$16$	1.00000	0.250000
$17$	−0.530807	−0.128740	−0.0643698	−	0.997926i	$-0.520504\pi$
$17$	−0.530807	−0.128740	−0.0643698	+	0.997926i	$0.520504\pi$
$18$	2.02804	0.478013
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.57017	0.798314
$21$	1.15761	0.252610
$22$	3.00236	0.640104
$23$	−2.37767	−0.495778	−0.247889	−	0.968788i	$-0.579737\pi$
$23$	−2.37767	−0.495778	−0.247889	+	0.968788i	$0.579737\pi$
$24$	2.24233	0.457713
$25$	7.74610	1.54922
$26$	1.63605	0.320856
$27$	−2.17946	−0.419437
$28$	0.516251	0.0975623
$29$	4.16112	0.772700	0.386350	−	0.922352i	$-0.373736\pi$
$29$	4.16112	0.772700	0.386350	+	0.922352i	$0.373736\pi$
$30$	8.00549	1.46160
$31$	−3.37427	−0.606036	−0.303018	−	0.952985i	$-0.597994\pi$
$31$	−3.37427	−0.606036	−0.303018	+	0.952985i	$0.597994\pi$
$32$	1.00000	0.176777
$33$	6.73227	1.17194
$34$	−0.530807	−0.0910326
$35$	1.84310	0.311541
$36$	2.02804	0.338006
$37$	−8.08939	−1.32989	−0.664944	−	0.746893i	$-0.731545\pi$
$37$	−8.08939	−1.32989	−0.664944	+	0.746893i	$0.731545\pi$
$38$	−1.00000	−0.162221
$39$	3.66856	0.587440
$40$	3.57017	0.564493
$41$	2.76275	0.431469	0.215734	−	0.976452i	$-0.430785\pi$
$41$	2.76275	0.431469	0.215734	+	0.976452i	$0.430785\pi$
$42$	1.15761	0.178622
$43$	−3.09244	−0.471592	−0.235796	−	0.971803i	$-0.575770\pi$
$43$	−3.09244	−0.471592	−0.235796	+	0.971803i	$0.575770\pi$
$44$	3.00236	0.452622
$45$	7.24043	1.07934
$46$	−2.37767	−0.350568
$47$	−6.39982	−0.933510	−0.466755	−	0.884387i	$-0.654577\pi$
$47$	−6.39982	−0.933510	−0.466755	+	0.884387i	$0.654577\pi$
$48$	2.24233	0.323652
$49$	−6.73348	−0.961926
$50$	7.74610	1.09546
$51$	−1.19024	−0.166667
$52$	1.63605	0.226879
$53$	6.86634	0.943165	0.471582	−	0.881822i	$-0.343683\pi$
$53$	6.86634	0.943165	0.471582	+	0.881822i	$0.343683\pi$
$54$	−2.17946	−0.296587
$55$	10.7189	1.44534
$56$	0.516251	0.0689870
$57$	−2.24233	−0.297004
$58$	4.16112	0.546382
$59$	7.54745	0.982595	0.491297	−	0.870992i	$-0.336523\pi$
$59$	7.54745	0.982595	0.491297	+	0.870992i	$0.336523\pi$
$60$	8.00549	1.03350
$61$	13.9351	1.78421	0.892106	−	0.451827i	$-0.149227\pi$
$61$	13.9351	1.78421	0.892106	+	0.451827i	$0.149227\pi$
$62$	−3.37427	−0.428532
$63$	1.04698	0.131907
$64$	1.00000	0.125000
$65$	5.84097	0.724483
$66$	6.73227	0.828685
$67$	−7.40499	−0.904664	−0.452332	−	0.891850i	$-0.649408\pi$
$67$	−7.40499	−0.904664	−0.452332	+	0.891850i	$0.649408\pi$
$68$	−0.530807	−0.0643698
$69$	−5.33151	−0.641838
$70$	1.84310	0.220293
$71$	9.46877	1.12374	0.561868	−	0.827227i	$-0.310083\pi$
$71$	9.46877	1.12374	0.561868	+	0.827227i	$0.310083\pi$
$72$	2.02804	0.239006
$73$	−5.84556	−0.684171	−0.342086	−	0.939669i	$-0.611133\pi$
$73$	−5.84556	−0.684171	−0.342086	+	0.939669i	$0.611133\pi$
$74$	−8.08939	−0.940373
$75$	17.3693	2.00563
$76$	−1.00000	−0.114708
$77$	1.54997	0.176635
$78$	3.66856	0.415383
$79$	14.2713	1.60565	0.802824	−	0.596217i	$-0.203330\pi$
$79$	14.2713	1.60565	0.802824	+	0.596217i	$0.203330\pi$
$80$	3.57017	0.399157
$81$	−10.9712	−1.21902
$82$	2.76275	0.305095
$83$	−8.41550	−0.923721	−0.461861	−	0.886953i	$-0.652818\pi$
$83$	−8.41550	−0.923721	−0.461861	+	0.886953i	$0.652818\pi$
$84$	1.15761	0.126305
$85$	−1.89507	−0.205549
$86$	−3.09244	−0.333466
$87$	9.33059	1.00034
$88$	3.00236	0.320052
$89$	−5.57298	−0.590735	−0.295368	−	0.955384i	$-0.595442\pi$
$89$	−5.57298	−0.590735	−0.295368	+	0.955384i	$0.595442\pi$
$90$	7.24043	0.763209
$91$	0.844613	0.0885395
$92$	−2.37767	−0.247889
$93$	−7.56622	−0.784580
$94$	−6.39982	−0.660091
$95$	−3.57017	−0.366291
$96$	2.24233	0.228857
$97$	9.07657	0.921586	0.460793	−	0.887508i	$-0.347565\pi$
$97$	9.07657	0.921586	0.460793	+	0.887508i	$0.347565\pi$
$98$	−6.73348	−0.680185
$99$	6.08889	0.611956
$100$	7.74610	0.774610
$101$	−4.16797	−0.414729	−0.207364	−	0.978264i	$-0.566489\pi$
$101$	−4.16797	−0.414729	−0.207364	+	0.978264i	$0.566489\pi$
$102$	−1.19024	−0.117852
$103$	−10.3139	−1.01626	−0.508130	−	0.861280i	$-0.669663\pi$
$103$	−10.3139	−1.01626	−0.508130	+	0.861280i	$0.669663\pi$
$104$	1.63605	0.160428
$105$	4.13284	0.403324
$106$	6.86634	0.666918
$107$	−7.64056	−0.738640	−0.369320	−	0.929302i	$-0.620409\pi$
$107$	−7.64056	−0.738640	−0.369320	+	0.929302i	$0.620409\pi$
$108$	−2.17946	−0.209719
$109$	−10.4517	−1.00109	−0.500547	−	0.865709i	$-0.666868\pi$
$109$	−10.4517	−1.00109	−0.500547	+	0.865709i	$0.666868\pi$
$110$	10.7189	1.02201
$111$	−18.1391	−1.72169
$112$	0.516251	0.0487812
$113$	4.96457	0.467027	0.233514	−	0.972354i	$-0.424978\pi$
$113$	4.96457	0.467027	0.233514	+	0.972354i	$0.424978\pi$
$114$	−2.24233	−0.210013
$115$	−8.48867	−0.791572
$116$	4.16112	0.386350
$117$	3.31797	0.306746
$118$	7.54745	0.694799
$119$	−0.274030	−0.0251203
$120$	8.00549	0.730798
$121$	−1.98586	−0.180533
$122$	13.9351	1.26163
$123$	6.19499	0.558584
$124$	−3.37427	−0.303018
$125$	9.80403	0.876899
$126$	1.04698	0.0932721
$127$	−15.7624	−1.39869	−0.699343	−	0.714787i	$-0.746524\pi$
$127$	−15.7624	−1.39869	−0.699343	+	0.714787i	$0.746524\pi$
$128$	1.00000	0.0883883
$129$	−6.93426	−0.610528
$130$	5.84097	0.512287
$131$	−2.80572	−0.245137	−0.122568	−	0.992460i	$-0.539113\pi$
$131$	−2.80572	−0.245137	−0.122568	+	0.992460i	$0.539113\pi$
$132$	6.73227	0.585969
$133$	−0.516251	−0.0447647
$134$	−7.40499	−0.639694
$135$	−7.78104	−0.669685
$136$	−0.530807	−0.0455163
$137$	−0.489339	−0.0418071	−0.0209035	−	0.999781i	$-0.506654\pi$
$137$	−0.489339	−0.0418071	−0.0209035	+	0.999781i	$0.506654\pi$
$138$	−5.33151	−0.453848
$139$	4.56278	0.387010	0.193505	−	0.981099i	$-0.438014\pi$
$139$	4.56278	0.387010	0.193505	+	0.981099i	$0.438014\pi$
$140$	1.84310	0.155771
$141$	−14.3505	−1.20853
$142$	9.46877	0.794601
$143$	4.91200	0.410762
$144$	2.02804	0.169003
$145$	14.8559	1.23371
$146$	−5.84556	−0.483782
$147$	−15.0987	−1.24532
$148$	−8.08939	−0.664944
$149$	6.97314	0.571262	0.285631	−	0.958340i	$-0.407797\pi$
$149$	6.97314	0.571262	0.285631	+	0.958340i	$0.407797\pi$
$150$	17.3693	1.41820
$151$	−11.4365	−0.930688	−0.465344	−	0.885130i	$-0.654069\pi$
$151$	−11.4365	−0.930688	−0.465344	+	0.885130i	$0.654069\pi$
$152$	−1.00000	−0.0811107
$153$	−1.07650	−0.0870295
$154$	1.54997	0.124900
$155$	−12.0467	−0.967614
$156$	3.66856	0.293720
$157$	16.7638	1.33790	0.668950	−	0.743307i	$-0.266744\pi$
$157$	16.7638	1.33790	0.668950	+	0.743307i	$0.266744\pi$
$158$	14.2713	1.13536
$159$	15.3966	1.22103
$160$	3.57017	0.282247
$161$	−1.22747	−0.0967385
$162$	−10.9712	−0.861977
$163$	−13.6345	−1.06794	−0.533969	−	0.845504i	$-0.679300\pi$
$163$	−13.6345	−1.06794	−0.533969	+	0.845504i	$0.679300\pi$
$164$	2.76275	0.215734
$165$	24.0353	1.87115
$166$	−8.41550	−0.653169
$167$	−6.21678	−0.481069	−0.240535	−	0.970641i	$-0.577323\pi$
$167$	−6.21678	−0.481069	−0.240535	+	0.970641i	$0.577323\pi$
$168$	1.15761	0.0893112
$169$	−10.3233	−0.794103
$170$	−1.89507	−0.145345
$171$	−2.02804	−0.155088
$172$	−3.09244	−0.235796
$173$	17.8428	1.35657	0.678283	−	0.734801i	$-0.262724\pi$
$173$	17.8428	1.35657	0.678283	+	0.734801i	$0.262724\pi$
$174$	9.33059	0.707351
$175$	3.99893	0.302291
$176$	3.00236	0.226311
$177$	16.9239	1.27208
$178$	−5.57298	−0.417713
$179$	−0.509595	−0.0380889	−0.0190445	−	0.999819i	$-0.506062\pi$
$179$	−0.509595	−0.0380889	−0.0190445	+	0.999819i	$0.506062\pi$
$180$	7.24043	0.539670
$181$	−11.6170	−0.863482	−0.431741	−	0.901998i	$-0.642101\pi$
$181$	−11.6170	−0.863482	−0.431741	+	0.901998i	$0.642101\pi$
$182$	0.844613	0.0626069
$183$	31.2472	2.30986
$184$	−2.37767	−0.175284
$185$	−28.8805	−2.12334
$186$	−7.56622	−0.554782
$187$	−1.59367	−0.116541
$188$	−6.39982	−0.466755
$189$	−1.12515	−0.0818426
$190$	−3.57017	−0.259007
$191$	2.01304	0.145659	0.0728293	−	0.997344i	$-0.476797\pi$
$191$	2.01304	0.145659	0.0728293	+	0.997344i	$0.476797\pi$
$192$	2.24233	0.161826
$193$	4.13431	0.297594	0.148797	−	0.988868i	$-0.452460\pi$
$193$	4.13431	0.297594	0.148797	+	0.988868i	$0.452460\pi$
$194$	9.07657	0.651660
$195$	13.0974	0.937923
$196$	−6.73348	−0.480963
$197$	13.8820	0.989052	0.494526	−	0.869163i	$-0.335342\pi$
$197$	13.8820	0.989052	0.494526	+	0.869163i	$0.335342\pi$
$198$	6.08889	0.432718
$199$	15.9482	1.13054	0.565268	−	0.824907i	$-0.308773\pi$
$199$	15.9482	1.13054	0.565268	+	0.824907i	$0.308773\pi$
$200$	7.74610	0.547732
$201$	−16.6044	−1.17119
$202$	−4.16797	−0.293257
$203$	2.14818	0.150773
$204$	−1.19024	−0.0833337
$205$	9.86348	0.688895
$206$	−10.3139	−0.718605
$207$	−4.82200	−0.335152
$208$	1.63605	0.113440
$209$	−3.00236	−0.207677
$210$	4.13284	0.285193
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	6.86634	0.471582
$213$	21.2321	1.45480
$214$	−7.64056	−0.522298
$215$	−11.0405	−0.752957
$216$	−2.17946	−0.148294
$217$	−1.74197	−0.118253
$218$	−10.4517	−0.707880
$219$	−13.1077	−0.885734
$220$	10.7189	0.722669
$221$	−0.868426	−0.0584167
$222$	−18.1391	−1.21742
$223$	−9.11273	−0.610234	−0.305117	−	0.952315i	$-0.598695\pi$
$223$	−9.11273	−0.610234	−0.305117	+	0.952315i	$0.598695\pi$
$224$	0.516251	0.0344935
$225$	15.7094	1.04729
$226$	4.96457	0.330238
$227$	11.8238	0.784773	0.392386	−	0.919800i	$-0.371650\pi$
$227$	11.8238	0.784773	0.392386	+	0.919800i	$0.371650\pi$
$228$	−2.24233	−0.148502
$229$	−4.27345	−0.282397	−0.141199	−	0.989981i	$-0.545096\pi$
$229$	−4.27345	−0.282397	−0.141199	+	0.989981i	$0.545096\pi$
$230$	−8.48867	−0.559726
$231$	3.47554	0.228674
$232$	4.16112	0.273191
$233$	16.1518	1.05814	0.529071	−	0.848578i	$-0.322541\pi$
$233$	16.1518	1.05814	0.529071	+	0.848578i	$0.322541\pi$
$234$	3.31797	0.216902
$235$	−22.8484	−1.49047
$236$	7.54745	0.491297
$237$	32.0010	2.07869
$238$	−0.274030	−0.0177627
$239$	19.4054	1.25523	0.627615	−	0.778524i	$-0.284031\pi$
$239$	19.4054	1.25523	0.627615	+	0.778524i	$0.284031\pi$
$240$	8.00549	0.516752
$241$	−16.6409	−1.07193	−0.535966	−	0.844240i	$-0.680052\pi$
$241$	−16.6409	−1.07193	−0.535966	+	0.844240i	$0.680052\pi$
$242$	−1.98586	−0.127656
$243$	−18.0626	−1.15872
$244$	13.9351	0.892106
$245$	−24.0397	−1.53584
$246$	6.19499	0.394978
$247$	−1.63605	−0.104099
$248$	−3.37427	−0.214266
$249$	−18.8703	−1.19586
$250$	9.80403	0.620061
$251$	−4.91676	−0.310343	−0.155171	−	0.987888i	$-0.549593\pi$
$251$	−4.91676	−0.310343	−0.155171	+	0.987888i	$0.549593\pi$
$252$	1.04698	0.0659533
$253$	−7.13860	−0.448800
$254$	−15.7624	−0.989020
$255$	−4.24937	−0.266106
$256$	1.00000	0.0625000
$257$	6.27487	0.391416	0.195708	−	0.980662i	$-0.437300\pi$
$257$	6.27487	0.391416	0.195708	+	0.980662i	$0.437300\pi$
$258$	−6.93426	−0.431708
$259$	−4.17616	−0.259494
$260$	5.84097	0.362242
$261$	8.43890	0.522355
$262$	−2.80572	−0.173338
$263$	−2.84747	−0.175582	−0.0877912	−	0.996139i	$-0.527981\pi$
$263$	−2.84747	−0.175582	−0.0877912	+	0.996139i	$0.527981\pi$
$264$	6.73227	0.414342
$265$	24.5140	1.50588
$266$	−0.516251	−0.0316534
$267$	−12.4965	−0.764771
$268$	−7.40499	−0.452332
$269$	−1.63378	−0.0996133	−0.0498067	−	0.998759i	$-0.515861\pi$
$269$	−1.63378	−0.0996133	−0.0498067	+	0.998759i	$0.515861\pi$
$270$	−7.78104	−0.473539
$271$	−28.1402	−1.70939	−0.854697	−	0.519127i	$-0.826257\pi$
$271$	−28.1402	−1.70939	−0.854697	+	0.519127i	$0.826257\pi$
$272$	−0.530807	−0.0321849
$273$	1.89390	0.114624
$274$	−0.489339	−0.0295621
$275$	23.2565	1.40242
$276$	−5.33151	−0.320919
$277$	−15.4617	−0.929004	−0.464502	−	0.885572i	$-0.653767\pi$
$277$	−15.4617	−0.929004	−0.464502	+	0.885572i	$0.653767\pi$
$278$	4.56278	0.273657
$279$	−6.84314	−0.409688
$280$	1.84310	0.110147
$281$	−14.2618	−0.850789	−0.425395	−	0.905008i	$-0.639865\pi$
$281$	−14.2618	−0.850789	−0.425395	+	0.905008i	$0.639865\pi$
$282$	−14.3505	−0.854560
$283$	16.7848	0.997754	0.498877	−	0.866673i	$-0.333746\pi$
$283$	16.7848	0.997754	0.498877	+	0.866673i	$0.333746\pi$
$284$	9.46877	0.561868
$285$	−8.00549	−0.474204
$286$	4.91200	0.290453
$287$	1.42627	0.0841902
$288$	2.02804	0.119503
$289$	−16.7182	−0.983426
$290$	14.8559	0.872368
$291$	20.3527	1.19309
$292$	−5.84556	−0.342086
$293$	−25.3707	−1.48217	−0.741086	−	0.671410i	$-0.765689\pi$
$293$	−25.3707	−1.48217	−0.741086	+	0.671410i	$0.765689\pi$
$294$	−15.0987	−0.880573
$295$	26.9457	1.56884
$296$	−8.08939	−0.470186
$297$	−6.54351	−0.379693
$298$	6.97314	0.403943
$299$	−3.88998	−0.224963
$300$	17.3693	1.00282
$301$	−1.59648	−0.0920193
$302$	−11.4365	−0.658096
$303$	−9.34596	−0.536911
$304$	−1.00000	−0.0573539
$305$	49.7508	2.84872
$306$	−1.07650	−0.0615392
$307$	−2.83753	−0.161946	−0.0809732	−	0.996716i	$-0.525803\pi$
$307$	−2.83753	−0.161946	−0.0809732	+	0.996716i	$0.525803\pi$
$308$	1.54997	0.0883177
$309$	−23.1272	−1.31566
$310$	−12.0467	−0.684207
$311$	−11.4615	−0.649922	−0.324961	−	0.945727i	$-0.605351\pi$
$311$	−11.4615	−0.649922	−0.324961	+	0.945727i	$0.605351\pi$
$312$	3.66856	0.207691
$313$	18.6502	1.05417	0.527086	−	0.849812i	$-0.323285\pi$
$313$	18.6502	1.05417	0.527086	+	0.849812i	$0.323285\pi$
$314$	16.7638	0.946038
$315$	3.73788	0.210606
$316$	14.2713	0.802824
$317$	−2.83016	−0.158958	−0.0794789	−	0.996837i	$-0.525326\pi$
$317$	−2.83016	−0.158958	−0.0794789	+	0.996837i	$0.525326\pi$
$318$	15.3966	0.863398
$319$	12.4932	0.699482
$320$	3.57017	0.199578
$321$	−17.1326	−0.956251
$322$	−1.22747	−0.0684044
$323$	0.530807	0.0295349
$324$	−10.9712	−0.609510
$325$	12.6730	0.702972
$326$	−13.6345	−0.755146
$327$	−23.4362	−1.29603
$328$	2.76275	0.152547
$329$	−3.30392	−0.182151
$330$	24.0353	1.32310
$331$	−10.7144	−0.588915	−0.294457	−	0.955665i	$-0.595139\pi$
$331$	−10.7144	−0.588915	−0.294457	+	0.955665i	$0.595139\pi$
$332$	−8.41550	−0.461861
$333$	−16.4056	−0.899021
$334$	−6.21678	−0.340167
$335$	−26.4371	−1.44441
$336$	1.15761	0.0631525
$337$	24.3092	1.32421	0.662103	−	0.749412i	$-0.269664\pi$
$337$	24.3092	1.32421	0.662103	+	0.749412i	$0.269664\pi$
$338$	−10.3233	−0.561516
$339$	11.1322	0.604618
$340$	−1.89507	−0.102775
$341$	−10.1307	−0.548611
$342$	−2.02804	−0.109664
$343$	−7.08993	−0.382820
$344$	−3.09244	−0.166733
$345$	−19.0344	−1.02478
$346$	17.8428	0.959237
$347$	13.2773	0.712764	0.356382	−	0.934340i	$-0.384010\pi$
$347$	13.2773	0.712764	0.356382	+	0.934340i	$0.384010\pi$
$348$	9.33059	0.500172
$349$	−13.8783	−0.742887	−0.371443	−	0.928456i	$-0.621137\pi$
$349$	−13.8783	−0.742887	−0.371443	+	0.928456i	$0.621137\pi$
$350$	3.99893	0.213752
$351$	−3.56571	−0.190323
$352$	3.00236	0.160026
$353$	12.1037	0.644217	0.322109	−	0.946703i	$-0.395608\pi$
$353$	12.1037	0.644217	0.322109	+	0.946703i	$0.395608\pi$
$354$	16.9239	0.899494
$355$	33.8051	1.79419
$356$	−5.57298	−0.295368
$357$	−0.614465	−0.0325209
$358$	−0.509595	−0.0269329
$359$	1.23821	0.0653504	0.0326752	−	0.999466i	$-0.489597\pi$
$359$	1.23821	0.0653504	0.0326752	+	0.999466i	$0.489597\pi$
$360$	7.24043	0.381604
$361$	1.00000	0.0526316
$362$	−11.6170	−0.610574
$363$	−4.45296	−0.233720
$364$	0.844613	0.0442697
$365$	−20.8696	−1.09237
$366$	31.2472	1.63332
$367$	22.9915	1.20015	0.600074	−	0.799945i	$-0.295138\pi$
$367$	22.9915	1.20015	0.600074	+	0.799945i	$0.295138\pi$
$368$	−2.37767	−0.123944
$369$	5.60296	0.291678
$370$	−28.8805	−1.50143
$371$	3.54476	0.184035
$372$	−7.56622	−0.392290
$373$	33.8240	1.75134	0.875670	−	0.482910i	$-0.160420\pi$
$373$	33.8240	1.75134	0.875670	+	0.482910i	$0.160420\pi$
$374$	−1.59367	−0.0824068
$375$	21.9839	1.13524
$376$	−6.39982	−0.330045
$377$	6.80780	0.350619
$378$	−1.12515	−0.0578714
$379$	8.26515	0.424552	0.212276	−	0.977210i	$-0.431912\pi$
$379$	8.26515	0.424552	0.212276	+	0.977210i	$0.431912\pi$
$380$	−3.57017	−0.183146
$381$	−35.3444	−1.81075
$382$	2.01304	0.102996
$383$	7.08611	0.362083	0.181042	−	0.983475i	$-0.442053\pi$
$383$	7.08611	0.362083	0.181042	+	0.983475i	$0.442053\pi$
$384$	2.24233	0.114428
$385$	5.53365	0.282021
$386$	4.13431	0.210431
$387$	−6.27158	−0.318802
$388$	9.07657	0.460793
$389$	6.76000	0.342746	0.171373	−	0.985206i	$-0.445180\pi$
$389$	6.76000	0.342746	0.171373	+	0.985206i	$0.445180\pi$
$390$	13.0974	0.663211
$391$	1.26208	0.0638262
$392$	−6.73348	−0.340092
$393$	−6.29134	−0.317356
$394$	13.8820	0.699366
$395$	50.9510	2.56362
$396$	6.08889	0.305978
$397$	−13.3266	−0.668844	−0.334422	−	0.942423i	$-0.608541\pi$
$397$	−13.3266	−0.668844	−0.334422	+	0.942423i	$0.608541\pi$
$398$	15.9482	0.799410
$399$	−1.15761	−0.0579527
$400$	7.74610	0.387305
$401$	−16.1888	−0.808432	−0.404216	−	0.914664i	$-0.632456\pi$
$401$	−16.1888	−0.808432	−0.404216	+	0.914664i	$0.632456\pi$
$402$	−16.6044	−0.828154
$403$	−5.52047	−0.274994
$404$	−4.16797	−0.207364
$405$	−39.1689	−1.94632
$406$	2.14818	0.106613
$407$	−24.2872	−1.20387
$408$	−1.19024	−0.0589258
$409$	14.1092	0.697653	0.348826	−	0.937187i	$-0.386580\pi$
$409$	14.1092	0.697653	0.348826	+	0.937187i	$0.386580\pi$
$410$	9.86348	0.487122
$411$	−1.09726	−0.0541238
$412$	−10.3139	−0.508130
$413$	3.89638	0.191729
$414$	−4.82200	−0.236988
$415$	−30.0447	−1.47484
$416$	1.63605	0.0802139
$417$	10.2312	0.501026
$418$	−3.00236	−0.146850
$419$	−17.7997	−0.869572	−0.434786	−	0.900534i	$-0.643176\pi$
$419$	−17.7997	−0.869572	−0.434786	+	0.900534i	$0.643176\pi$
$420$	4.13284	0.201662
$421$	0.976507	0.0475920	0.0237960	−	0.999717i	$-0.492425\pi$
$421$	0.976507	0.0475920	0.0237960	+	0.999717i	$0.492425\pi$
$422$	−1.00000	−0.0486792
$423$	−12.9791	−0.631064
$424$	6.86634	0.333459
$425$	−4.11168	−0.199446
$426$	21.2321	1.02870
$427$	7.19403	0.348144
$428$	−7.64056	−0.369320
$429$	11.0143	0.531776
$430$	−11.0405	−0.532421
$431$	−32.0627	−1.54441	−0.772203	−	0.635376i	$-0.780845\pi$
$431$	−32.0627	−1.54441	−0.772203	+	0.635376i	$0.780845\pi$
$432$	−2.17946	−0.104859
$433$	17.4649	0.839308	0.419654	−	0.907684i	$-0.362151\pi$
$433$	17.4649	0.839308	0.419654	+	0.907684i	$0.362151\pi$
$434$	−1.74197	−0.0836173
$435$	33.3118	1.59718
$436$	−10.4517	−0.500547
$437$	2.37767	0.113739
$438$	−13.1077	−0.626309
$439$	5.02964	0.240051	0.120026	−	0.992771i	$-0.461702\pi$
$439$	5.02964	0.240051	0.120026	+	0.992771i	$0.461702\pi$
$440$	10.7189	0.511004
$441$	−13.6558	−0.650274
$442$	−0.868426	−0.0413068
$443$	22.1595	1.05283	0.526416	−	0.850227i	$-0.323536\pi$
$443$	22.1595	1.05283	0.526416	+	0.850227i	$0.323536\pi$
$444$	−18.1391	−0.860843
$445$	−19.8965	−0.943184
$446$	−9.11273	−0.431500
$447$	15.6361	0.739561
$448$	0.516251	0.0243906
$449$	11.1941	0.528281	0.264140	−	0.964484i	$-0.414912\pi$
$449$	11.1941	0.528281	0.264140	+	0.964484i	$0.414912\pi$
$450$	15.7094	0.740547
$451$	8.29475	0.390585
$452$	4.96457	0.233514
$453$	−25.6444	−1.20488
$454$	11.8238	0.554918
$455$	3.01541	0.141365
$456$	−2.24233	−0.105007
$457$	−19.4898	−0.911696	−0.455848	−	0.890058i	$-0.650664\pi$
$457$	−19.4898	−0.911696	−0.455848	+	0.890058i	$0.650664\pi$
$458$	−4.27345	−0.199685
$459$	1.15687	0.0539982
$460$	−8.48867	−0.395786
$461$	12.5145	0.582859	0.291429	−	0.956592i	$-0.405869\pi$
$461$	12.5145	0.582859	0.291429	+	0.956592i	$0.405869\pi$
$462$	3.47554	0.161697
$463$	−8.84896	−0.411246	−0.205623	−	0.978631i	$-0.565922\pi$
$463$	−8.84896	−0.411246	−0.205623	+	0.978631i	$0.565922\pi$
$464$	4.16112	0.193175
$465$	−27.0127	−1.25268
$466$	16.1518	0.748219
$467$	31.3190	1.44927	0.724636	−	0.689132i	$-0.242008\pi$
$467$	31.3190	1.44927	0.724636	+	0.689132i	$0.242008\pi$
$468$	3.31797	0.153373
$469$	−3.82284	−0.176522
$470$	−22.8484	−1.05392
$471$	37.5900	1.73206
$472$	7.54745	0.347400
$473$	−9.28459	−0.426906
$474$	32.0010	1.46985
$475$	−7.74610	−0.355415
$476$	−0.274030	−0.0125601
$477$	13.9252	0.637591
$478$	19.4054	0.887581
$479$	10.7934	0.493164	0.246582	−	0.969122i	$-0.420693\pi$
$479$	10.7934	0.493164	0.246582	+	0.969122i	$0.420693\pi$
$480$	8.00549	0.365399
$481$	−13.2346	−0.603448
$482$	−16.6409	−0.757970
$483$	−2.75240	−0.125238
$484$	−1.98586	−0.0902666
$485$	32.4049	1.47143
$486$	−18.0626	−0.819336
$487$	−19.7639	−0.895588	−0.447794	−	0.894137i	$-0.647790\pi$
$487$	−19.7639	−0.895588	−0.447794	+	0.894137i	$0.647790\pi$
$488$	13.9351	0.630814
$489$	−30.5731	−1.38256
$490$	−24.0397	−1.08600
$491$	30.7738	1.38880	0.694400	−	0.719589i	$-0.255670\pi$
$491$	30.7738	1.38880	0.694400	+	0.719589i	$0.255670\pi$
$492$	6.19499	0.279292
$493$	−2.20875	−0.0994771
$494$	−1.63605	−0.0736093
$495$	21.7383	0.977066
$496$	−3.37427	−0.151509
$497$	4.88826	0.219269
$498$	−18.8703	−0.845599
$499$	9.33182	0.417749	0.208875	−	0.977942i	$-0.433020\pi$
$499$	9.33182	0.417749	0.208875	+	0.977942i	$0.433020\pi$
$500$	9.80403	0.438450
$501$	−13.9401	−0.622796
$502$	−4.91676	−0.219446
$503$	−5.64999	−0.251921	−0.125960	−	0.992035i	$-0.540201\pi$
$503$	−5.64999	−0.251921	−0.125960	+	0.992035i	$0.540201\pi$
$504$	1.04698	0.0466361
$505$	−14.8804	−0.662167
$506$	−7.13860	−0.317349
$507$	−23.1483	−1.02805
$508$	−15.7624	−0.699343
$509$	−40.2327	−1.78328	−0.891642	−	0.452741i	$-0.850446\pi$
$509$	−40.2327	−1.78328	−0.891642	+	0.452741i	$0.850446\pi$
$510$	−4.24937	−0.188165
$511$	−3.01778	−0.133499
$512$	1.00000	0.0441942
$513$	2.17946	0.0962255
$514$	6.27487	0.276773
$515$	−36.8224	−1.62259
$516$	−6.93426	−0.305264
$517$	−19.2145	−0.845054
$518$	−4.17616	−0.183490
$519$	40.0095	1.75622
$520$	5.84097	0.256144
$521$	14.5958	0.639455	0.319727	−	0.947510i	$-0.396409\pi$
$521$	14.5958	0.639455	0.319727	+	0.947510i	$0.396409\pi$
$522$	8.43890	0.369361
$523$	39.7204	1.73685	0.868425	−	0.495820i	$-0.165133\pi$
$523$	39.7204	1.73685	0.868425	+	0.495820i	$0.165133\pi$
$524$	−2.80572	−0.122568
$525$	8.96692	0.391349
$526$	−2.84747	−0.124156
$527$	1.79108	0.0780209
$528$	6.73227	0.292984
$529$	−17.3467	−0.754204
$530$	24.5140	1.06482
$531$	15.3065	0.664246
$532$	−0.516251	−0.0223823
$533$	4.51999	0.195783
$534$	−12.4965	−0.540775
$535$	−27.2781	−1.17933
$536$	−7.40499	−0.319847
$537$	−1.14268	−0.0493103
$538$	−1.63378	−0.0704373
$539$	−20.2163	−0.870778
$540$	−7.78104	−0.334843
$541$	8.94072	0.384392	0.192196	−	0.981357i	$-0.438439\pi$
$541$	8.94072	0.384392	0.192196	+	0.981357i	$0.438439\pi$
$542$	−28.1402	−1.20872
$543$	−26.0491	−1.11787
$544$	−0.530807	−0.0227582
$545$	−37.3144	−1.59837
$546$	1.89390	0.0810514
$547$	7.34911	0.314225	0.157113	−	0.987581i	$-0.449781\pi$
$547$	7.34911	0.314225	0.157113	+	0.987581i	$0.449781\pi$
$548$	−0.489339	−0.0209035
$549$	28.2610	1.20615
$550$	23.2565	0.991662
$551$	−4.16112	−0.177270
$552$	−5.33151	−0.226924
$553$	7.36758	0.313301
$554$	−15.4617	−0.656905
$555$	−64.7596	−2.74889
$556$	4.56278	0.193505
$557$	37.3857	1.58408	0.792041	−	0.610467i	$-0.209018\pi$
$557$	37.3857	1.58408	0.792041	+	0.610467i	$0.209018\pi$
$558$	−6.84314	−0.289693
$559$	−5.05938	−0.213989
$560$	1.84310	0.0778854
$561$	−3.57353	−0.150875
$562$	−14.2618	−0.601599
$563$	−8.67347	−0.365543	−0.182772	−	0.983155i	$-0.558507\pi$
$563$	−8.67347	−0.365543	−0.182772	+	0.983155i	$0.558507\pi$
$564$	−14.3505	−0.604265
$565$	17.7243	0.745668
$566$	16.7848	0.705518
$567$	−5.66389	−0.237861
$568$	9.46877	0.397301
$569$	−29.7036	−1.24524	−0.622620	−	0.782524i	$-0.713932\pi$
$569$	−29.7036	−1.24524	−0.622620	+	0.782524i	$0.713932\pi$
$570$	−8.00549	−0.335313
$571$	−26.9928	−1.12961	−0.564807	−	0.825223i	$-0.691049\pi$
$571$	−26.9928	−1.12961	−0.564807	+	0.825223i	$0.691049\pi$
$572$	4.91200	0.205381
$573$	4.51390	0.188571
$574$	1.42627	0.0595315
$575$	−18.4176	−0.768069
$576$	2.02804	0.0845015
$577$	19.0499	0.793057	0.396529	−	0.918022i	$-0.370215\pi$
$577$	19.0499	0.793057	0.396529	+	0.918022i	$0.370215\pi$
$578$	−16.7182	−0.695387
$579$	9.27049	0.385268
$580$	14.8559	0.616857
$581$	−4.34451	−0.180241
$582$	20.3527	0.843645
$583$	20.6152	0.853794
$584$	−5.84556	−0.241891
$585$	11.8457	0.489760
$586$	−25.3707	−1.04805
$587$	−25.2932	−1.04396	−0.521981	−	0.852957i	$-0.674807\pi$
$587$	−25.2932	−1.04396	−0.521981	+	0.852957i	$0.674807\pi$
$588$	−15.0987	−0.622659
$589$	3.37427	0.139034
$590$	26.9457	1.10934
$591$	31.1280	1.28044
$592$	−8.08939	−0.332472
$593$	−17.3254	−0.711471	−0.355735	−	0.934587i	$-0.615770\pi$
$593$	−17.3254	−0.711471	−0.355735	+	0.934587i	$0.615770\pi$
$594$	−6.54351	−0.268484
$595$	−0.978332	−0.0401077
$596$	6.97314	0.285631
$597$	35.7610	1.46360
$598$	−3.88998	−0.159073
$599$	11.7854	0.481537	0.240768	−	0.970583i	$-0.422601\pi$
$599$	11.7854	0.481537	0.240768	+	0.970583i	$0.422601\pi$
$600$	17.3693	0.709099
$601$	−1.69207	−0.0690210	−0.0345105	−	0.999404i	$-0.510987\pi$
$601$	−1.69207	−0.0690210	−0.0345105	+	0.999404i	$0.510987\pi$
$602$	−1.59648	−0.0650675
$603$	−15.0176	−0.611564
$604$	−11.4365	−0.465344
$605$	−7.08987	−0.288244
$606$	−9.34596	−0.379654
$607$	−14.9782	−0.607946	−0.303973	−	0.952681i	$-0.598313\pi$
$607$	−14.9782	−0.607946	−0.303973	+	0.952681i	$0.598313\pi$
$608$	−1.00000	−0.0405554
$609$	4.81693	0.195192
$610$	49.7508	2.01435
$611$	−10.4704	−0.423588
$612$	−1.07650	−0.0435148
$613$	−22.2419	−0.898343	−0.449171	−	0.893446i	$-0.648281\pi$
$613$	−22.2419	−0.898343	−0.449171	+	0.893446i	$0.648281\pi$
$614$	−2.83753	−0.114513
$615$	22.1172	0.891850
$616$	1.54997	0.0624501
$617$	−16.7094	−0.672694	−0.336347	−	0.941738i	$-0.609192\pi$
$617$	−16.7094	−0.672694	−0.336347	+	0.941738i	$0.609192\pi$
$618$	−23.1272	−0.930312
$619$	−41.8035	−1.68023	−0.840113	−	0.542411i	$-0.817511\pi$
$619$	−41.8035	−1.68023	−0.840113	+	0.542411i	$0.817511\pi$
$620$	−12.0467	−0.483807
$621$	5.18203	0.207948
$622$	−11.4615	−0.459564
$623$	−2.87706	−0.115267
$624$	3.66856	0.146860
$625$	−3.72846	−0.149138
$626$	18.6502	0.745412
$627$	−6.73227	−0.268861
$628$	16.7638	0.668950
$629$	4.29391	0.171209
$630$	3.73788	0.148921
$631$	33.9541	1.35169	0.675845	−	0.737044i	$-0.263779\pi$
$631$	33.9541	1.35169	0.675845	+	0.737044i	$0.263779\pi$
$632$	14.2713	0.567682
$633$	−2.24233	−0.0891246
$634$	−2.83016	−0.112400
$635$	−56.2743	−2.23318
$636$	15.3966	0.610515
$637$	−11.0163	−0.436482
$638$	12.4932	0.494609
$639$	19.2030	0.759659
$640$	3.57017	0.141123
$641$	−35.8861	−1.41742	−0.708708	−	0.705502i	$-0.750721\pi$
$641$	−35.8861	−1.41742	−0.708708	+	0.705502i	$0.750721\pi$
$642$	−17.1326	−0.676171
$643$	15.3857	0.606753	0.303376	−	0.952871i	$-0.401886\pi$
$643$	15.3857	0.606753	0.303376	+	0.952871i	$0.401886\pi$
$644$	−1.22747	−0.0483692
$645$	−24.7565	−0.974785
$646$	0.530807	0.0208843
$647$	−18.3563	−0.721661	−0.360831	−	0.932631i	$-0.617507\pi$
$647$	−18.3563	−0.721661	−0.360831	+	0.932631i	$0.617507\pi$
$648$	−10.9712	−0.430989
$649$	22.6601	0.889488
$650$	12.6730	0.497076
$651$	−3.90607	−0.153091
$652$	−13.6345	−0.533969
$653$	8.65871	0.338841	0.169421	−	0.985544i	$-0.445810\pi$
$653$	8.65871	0.338841	0.169421	+	0.985544i	$0.445810\pi$
$654$	−23.4362	−0.916428
$655$	−10.0169	−0.391392
$656$	2.76275	0.107867
$657$	−11.8550	−0.462508
$658$	−3.30392	−0.128800
$659$	10.8836	0.423963	0.211982	−	0.977274i	$-0.432008\pi$
$659$	10.8836	0.423963	0.211982	+	0.977274i	$0.432008\pi$
$660$	24.0353	0.935574
$661$	39.7868	1.54753	0.773763	−	0.633475i	$-0.218372\pi$
$661$	39.7868	1.54753	0.773763	+	0.633475i	$0.218372\pi$
$662$	−10.7144	−0.416425
$663$	−1.94730	−0.0756268
$664$	−8.41550	−0.326585
$665$	−1.84310	−0.0714725
$666$	−16.4056	−0.635704
$667$	−9.89375	−0.383088
$668$	−6.21678	−0.240535
$669$	−20.4337	−0.790014
$670$	−26.4371	−1.02135
$671$	41.8382	1.61515
$672$	1.15761	0.0446556
$673$	11.3182	0.436283	0.218141	−	0.975917i	$-0.430001\pi$
$673$	11.3182	0.436283	0.218141	+	0.975917i	$0.430001\pi$
$674$	24.3092	0.936356
$675$	−16.8823	−0.649801
$676$	−10.3233	−0.397052
$677$	4.55119	0.174916	0.0874582	−	0.996168i	$-0.472126\pi$
$677$	4.55119	0.174916	0.0874582	+	0.996168i	$0.472126\pi$
$678$	11.1322	0.427529
$679$	4.68579	0.179824
$680$	−1.89507	−0.0726726
$681$	26.5128	1.01597
$682$	−10.1307	−0.387926
$683$	36.6080	1.40077	0.700383	−	0.713767i	$-0.253013\pi$
$683$	36.6080	1.40077	0.700383	+	0.713767i	$0.253013\pi$
$684$	−2.02804	−0.0775439
$685$	−1.74702	−0.0667503
$686$	−7.08993	−0.270695
$687$	−9.58247	−0.365594
$688$	−3.09244	−0.117898
$689$	11.2337	0.427969
$690$	−19.0344	−0.724627
$691$	−34.7528	−1.32206	−0.661030	−	0.750360i	$-0.729880\pi$
$691$	−34.7528	−1.32206	−0.661030	+	0.750360i	$0.729880\pi$
$692$	17.8428	0.678283
$693$	3.14340	0.119408
$694$	13.2773	0.504000
$695$	16.2899	0.617910
$696$	9.33059	0.353675
$697$	−1.46649	−0.0555471
$698$	−13.8783	−0.525300
$699$	36.2177	1.36988
$700$	3.99893	0.151145
$701$	31.7612	1.19960	0.599801	−	0.800149i	$-0.295246\pi$
$701$	31.7612	1.19960	0.599801	+	0.800149i	$0.295246\pi$
$702$	−3.56571	−0.134579
$703$	8.08939	0.305097
$704$	3.00236	0.113156
$705$	−51.2337	−1.92957
$706$	12.1037	0.455530
$707$	−2.15172	−0.0809238
$708$	16.9239	0.636038
$709$	32.1588	1.20775	0.603875	−	0.797079i	$-0.293623\pi$
$709$	32.1588	1.20775	0.603875	+	0.797079i	$0.293623\pi$
$710$	33.8051	1.26868
$711$	28.9427	1.08544
$712$	−5.57298	−0.208856
$713$	8.02288	0.300459
$714$	−0.614465	−0.0229958
$715$	17.5367	0.655834
$716$	−0.509595	−0.0190445
$717$	43.5132	1.62503
$718$	1.23821	0.0462097
$719$	1.70019	0.0634063	0.0317032	−	0.999497i	$-0.489907\pi$
$719$	1.70019	0.0634063	0.0317032	+	0.999497i	$0.489907\pi$
$720$	7.24043	0.269835
$721$	−5.32458	−0.198298
$722$	1.00000	0.0372161
$723$	−37.3143	−1.38773
$724$	−11.6170	−0.431741
$725$	32.2324	1.19708
$726$	−4.45296	−0.165265
$727$	−11.8653	−0.440060	−0.220030	−	0.975493i	$-0.570616\pi$
$727$	−11.8653	−0.440060	−0.220030	+	0.975493i	$0.570616\pi$
$728$	0.844613	0.0313034
$729$	−7.58875	−0.281065
$730$	−20.8696	−0.772420
$731$	1.64149	0.0607126
$732$	31.2472	1.15493
$733$	−47.9485	−1.77102	−0.885509	−	0.464622i	$-0.846190\pi$
$733$	−47.9485	−1.77102	−0.885509	+	0.464622i	$0.846190\pi$
$734$	22.9915	0.848632
$735$	−53.9048	−1.98831
$736$	−2.37767	−0.0876419
$737$	−22.2324	−0.818942
$738$	5.60296	0.206248
$739$	−45.1239	−1.65991	−0.829954	−	0.557831i	$-0.811634\pi$
$739$	−45.1239	−1.65991	−0.829954	+	0.557831i	$0.811634\pi$
$740$	−28.8805	−1.06167
$741$	−3.66856	−0.134768
$742$	3.54476	0.130132
$743$	40.3946	1.48193	0.740967	−	0.671542i	$-0.234368\pi$
$743$	40.3946	1.48193	0.740967	+	0.671542i	$0.234368\pi$
$744$	−7.56622	−0.277391
$745$	24.8953	0.912093
$746$	33.8240	1.23838
$747$	−17.0669	−0.624447
$748$	−1.59367	−0.0582704
$749$	−3.94445	−0.144127
$750$	21.9839	0.802737
$751$	−35.6525	−1.30098	−0.650489	−	0.759516i	$-0.725436\pi$
$751$	−35.6525	−1.30098	−0.650489	+	0.759516i	$0.725436\pi$
$752$	−6.39982	−0.233377
$753$	−11.0250	−0.401773
$754$	6.80780	0.247925
$755$	−40.8302	−1.48596
$756$	−1.12515	−0.0409213
$757$	33.9411	1.23361	0.616805	−	0.787116i	$-0.288427\pi$
$757$	33.9411	1.23361	0.616805	+	0.787116i	$0.288427\pi$
$758$	8.26515	0.300204
$759$	−16.0071	−0.581020
$760$	−3.57017	−0.129504
$761$	18.0404	0.653963	0.326982	−	0.945031i	$-0.393969\pi$
$761$	18.0404	0.653963	0.326982	+	0.945031i	$0.393969\pi$
$762$	−35.3444	−1.28039
$763$	−5.39572	−0.195338
$764$	2.01304	0.0728293
$765$	−3.84327	−0.138954
$766$	7.08611	0.256031
$767$	12.3480	0.445861
$768$	2.24233	0.0809131
$769$	−13.5549	−0.488801	−0.244400	−	0.969674i	$-0.578591\pi$
$769$	−13.5549	−0.488801	−0.244400	+	0.969674i	$0.578591\pi$
$770$	5.53365	0.199419
$771$	14.0703	0.506730
$772$	4.13431	0.148797
$773$	6.30395	0.226737	0.113369	−	0.993553i	$-0.463836\pi$
$773$	6.30395	0.226737	0.113369	+	0.993553i	$0.463836\pi$
$774$	−6.27158	−0.225427
$775$	−26.1374	−0.938883
$776$	9.07657	0.325830
$777$	−9.36433	−0.335943
$778$	6.76000	0.242358
$779$	−2.76275	−0.0989858
$780$	13.0974	0.468961
$781$	28.4286	1.01726
$782$	1.26208	0.0451319
$783$	−9.06899	−0.324099
$784$	−6.73348	−0.240482
$785$	59.8497	2.13613
$786$	−6.29134	−0.224405
$787$	−45.6892	−1.62864	−0.814322	−	0.580414i	$-0.802891\pi$
$787$	−45.6892	−1.62864	−0.814322	+	0.580414i	$0.802891\pi$
$788$	13.8820	0.494526
$789$	−6.38496	−0.227311
$790$	50.9510	1.81275
$791$	2.56296	0.0911285
$792$	6.08889	0.216359
$793$	22.7986	0.809601
$794$	−13.3266	−0.472944
$795$	54.9684	1.94953
$796$	15.9482	0.565268
$797$	26.4268	0.936086	0.468043	−	0.883706i	$-0.344959\pi$
$797$	26.4268	0.936086	0.468043	+	0.883706i	$0.344959\pi$
$798$	−1.15761	−0.0409788
$799$	3.39707	0.120180
$800$	7.74610	0.273866
$801$	−11.3022	−0.399344
$802$	−16.1888	−0.571648
$803$	−17.5504	−0.619342
$804$	−16.6044	−0.585593
$805$	−4.38229	−0.154455
$806$	−5.52047	−0.194450
$807$	−3.66347	−0.128960
$808$	−4.16797	−0.146629
$809$	16.0674	0.564901	0.282451	−	0.959282i	$-0.408853\pi$
$809$	16.0674	0.564901	0.282451	+	0.959282i	$0.408853\pi$
$810$	−39.1689	−1.37626
$811$	−46.7927	−1.64311	−0.821556	−	0.570127i	$-0.806894\pi$
$811$	−46.7927	−1.64311	−0.821556	+	0.570127i	$0.806894\pi$
$812$	2.14818	0.0753865
$813$	−63.0995	−2.21300
$814$	−24.2872	−0.851267
$815$	−48.6775	−1.70510
$816$	−1.19024	−0.0416669
$817$	3.09244	0.108191
$818$	14.1092	0.493315
$819$	1.71291	0.0598538
$820$	9.86348	0.344448
$821$	−10.2326	−0.357119	−0.178560	−	0.983929i	$-0.557144\pi$
$821$	−10.2326	−0.357119	−0.178560	+	0.983929i	$0.557144\pi$
$822$	−1.09726	−0.0382713
$823$	−5.67988	−0.197988	−0.0989940	−	0.995088i	$-0.531562\pi$
$823$	−5.67988	−0.197988	−0.0989940	+	0.995088i	$0.531562\pi$
$824$	−10.3139	−0.359302
$825$	52.1488	1.81559
$826$	3.89638	0.135573
$827$	20.3749	0.708506	0.354253	−	0.935150i	$-0.384735\pi$
$827$	20.3749	0.708506	0.354253	+	0.935150i	$0.384735\pi$
$828$	−4.82200	−0.167576
$829$	−23.9530	−0.831923	−0.415961	−	0.909382i	$-0.636555\pi$
$829$	−23.9530	−0.831923	−0.415961	+	0.909382i	$0.636555\pi$
$830$	−30.0447	−1.04287
$831$	−34.6702	−1.20270
$832$	1.63605	0.0567198
$833$	3.57418	0.123838
$834$	10.2312	0.354279
$835$	−22.1950	−0.768088
$836$	−3.00236	−0.103839
$837$	7.35408	0.254194
$838$	−17.7997	−0.614880
$839$	52.8527	1.82468	0.912339	−	0.409435i	$-0.134274\pi$
$839$	52.8527	1.82468	0.912339	+	0.409435i	$0.134274\pi$
$840$	4.13284	0.142597
$841$	−11.6851	−0.402934
$842$	0.976507	0.0336527
$843$	−31.9797	−1.10144
$844$	−1.00000	−0.0344214
$845$	−36.8561	−1.26789
$846$	−12.9791	−0.446230
$847$	−1.02521	−0.0352265
$848$	6.86634	0.235791
$849$	37.6371	1.29170
$850$	−4.11168	−0.141030
$851$	19.2339	0.659329
$852$	21.2321	0.727399
$853$	5.67670	0.194366	0.0971832	−	0.995267i	$-0.469017\pi$
$853$	5.67670	0.194366	0.0971832	+	0.995267i	$0.469017\pi$
$854$	7.19403	0.246175
$855$	−7.24043	−0.247618
$856$	−7.64056	−0.261149
$857$	31.8023	1.08635	0.543174	−	0.839620i	$-0.317223\pi$
$857$	31.8023	1.08635	0.543174	+	0.839620i	$0.317223\pi$
$858$	11.0143	0.376023
$859$	16.2251	0.553593	0.276796	−	0.960929i	$-0.410727\pi$
$859$	16.2251	0.553593	0.276796	+	0.960929i	$0.410727\pi$
$860$	−11.0405	−0.376479
$861$	3.19817	0.108993
$862$	−32.0627	−1.09206
$863$	−26.4078	−0.898933	−0.449466	−	0.893297i	$-0.648386\pi$
$863$	−26.4078	−0.898933	−0.449466	+	0.893297i	$0.648386\pi$
$864$	−2.17946	−0.0741468
$865$	63.7019	2.16593
$866$	17.4649	0.593480
$867$	−37.4878	−1.27315
$868$	−1.74197	−0.0591263
$869$	42.8475	1.45350
$870$	33.3118	1.12938
$871$	−12.1149	−0.410499
$872$	−10.4517	−0.353940
$873$	18.4076	0.623004
$874$	2.37767	0.0804258
$875$	5.06134	0.171105
$876$	−13.1077	−0.442867
$877$	12.9251	0.436449	0.218225	−	0.975899i	$-0.429973\pi$
$877$	12.9251	0.436449	0.218225	+	0.975899i	$0.429973\pi$
$878$	5.02964	0.169742
$879$	−56.8894	−1.91883
$880$	10.7189	0.361334
$881$	30.3898	1.02386	0.511929	−	0.859028i	$-0.328931\pi$
$881$	30.3898	1.02386	0.511929	+	0.859028i	$0.328931\pi$
$882$	−13.6558	−0.459813
$883$	51.9333	1.74770	0.873848	−	0.486200i	$-0.161617\pi$
$883$	51.9333	1.74770	0.873848	+	0.486200i	$0.161617\pi$
$884$	−0.868426	−0.0292083
$885$	60.4211	2.03103
$886$	22.1595	0.744464
$887$	48.9521	1.64365	0.821825	−	0.569740i	$-0.192956\pi$
$887$	48.9521	1.64365	0.821825	+	0.569740i	$0.192956\pi$
$888$	−18.1391	−0.608708
$889$	−8.13735	−0.272918
$890$	−19.8965	−0.666932
$891$	−32.9394	−1.10351
$892$	−9.11273	−0.305117
$893$	6.39982	0.214162
$894$	15.6361	0.522949
$895$	−1.81934	−0.0608138
$896$	0.516251	0.0172467
$897$	−8.72261	−0.291240
$898$	11.1941	0.373551
$899$	−14.0407	−0.468284
$900$	15.7094	0.523646
$901$	−3.64470	−0.121423
$902$	8.29475	0.276185
$903$	−3.57982	−0.119129
$904$	4.96457	0.165119
$905$	−41.4745	−1.37866
$906$	−25.6444	−0.851977
$907$	−15.4135	−0.511798	−0.255899	−	0.966704i	$-0.582371\pi$
$907$	−15.4135	−0.511798	−0.255899	+	0.966704i	$0.582371\pi$
$908$	11.8238	0.392386
$909$	−8.45280	−0.280362
$910$	3.01541	0.0999599
$911$	−19.7514	−0.654393	−0.327196	−	0.944956i	$-0.606104\pi$
$911$	−19.7514	−0.654393	−0.327196	+	0.944956i	$0.606104\pi$
$912$	−2.24233	−0.0742509
$913$	−25.2663	−0.836193
$914$	−19.4898	−0.644667
$915$	111.558	3.68798
$916$	−4.27345	−0.141199
$917$	−1.44846	−0.0478322
$918$	1.15687	0.0381825
$919$	−12.2666	−0.404639	−0.202319	−	0.979320i	$-0.564848\pi$
$919$	−12.2666	−0.404639	−0.202319	+	0.979320i	$0.564848\pi$
$920$	−8.48867	−0.279863
$921$	−6.36268	−0.209657
$922$	12.5145	0.412143
$923$	15.4914	0.509905
$924$	3.47554	0.114337
$925$	−62.6612	−2.06029
$926$	−8.84896	−0.290795
$927$	−20.9170	−0.687005
$928$	4.16112	0.136595
$929$	6.09420	0.199944	0.0999721	−	0.994990i	$-0.468125\pi$
$929$	6.09420	0.199944	0.0999721	+	0.994990i	$0.468125\pi$
$930$	−27.0127	−0.885780
$931$	6.73348	0.220681
$932$	16.1518	0.529071
$933$	−25.7004	−0.841394
$934$	31.3190	1.02479
$935$	−5.68967	−0.186072
$936$	3.31797	0.108451
$937$	24.4502	0.798754	0.399377	−	0.916787i	$-0.369226\pi$
$937$	24.4502	0.798754	0.399377	+	0.916787i	$0.369226\pi$
$938$	−3.82284	−0.124820
$939$	41.8199	1.36474
$940$	−22.8484	−0.745234
$941$	−15.7224	−0.512537	−0.256268	−	0.966606i	$-0.582493\pi$
$941$	−15.7224	−0.512537	−0.256268	+	0.966606i	$0.582493\pi$
$942$	37.5900	1.22475
$943$	−6.56890	−0.213913
$944$	7.54745	0.245649
$945$	−4.01697	−0.130672
$946$	−9.28459	−0.301868
$947$	42.0196	1.36545	0.682727	−	0.730673i	$-0.260794\pi$
$947$	42.0196	1.36545	0.682727	+	0.730673i	$0.260794\pi$
$948$	32.0010	1.03934
$949$	−9.56363	−0.310448
$950$	−7.74610	−0.251317
$951$	−6.34616	−0.205788
$952$	−0.274030	−0.00888136
$953$	7.88359	0.255375	0.127687	−	0.991814i	$-0.459245\pi$
$953$	7.88359	0.255375	0.127687	+	0.991814i	$0.459245\pi$
$954$	13.9252	0.450845
$955$	7.18690	0.232563
$956$	19.4054	0.627615
$957$	28.0138	0.905556
$958$	10.7934	0.348720
$959$	−0.252622	−0.00815759
$960$	8.00549	0.258376
$961$	−19.6143	−0.632720
$962$	−13.2346	−0.426702
$963$	−15.4953	−0.499330
$964$	−16.6409	−0.535966
$965$	14.7602	0.475147
$966$	−2.75240	−0.0885570
$967$	27.9837	0.899894	0.449947	−	0.893055i	$-0.351443\pi$
$967$	27.9837	0.899894	0.449947	+	0.893055i	$0.351443\pi$
$968$	−1.98586	−0.0638281
$969$	1.19024	0.0382361
$970$	32.4049	1.04046
$971$	−50.4192	−1.61803	−0.809015	−	0.587788i	$-0.799999\pi$
$971$	−50.4192	−1.61803	−0.809015	+	0.587788i	$0.799999\pi$
$972$	−18.0626	−0.579358
$973$	2.35554	0.0755151
$974$	−19.7639	−0.633276
$975$	28.4170	0.910073
$976$	13.9351	0.446053
$977$	40.3434	1.29070	0.645350	−	0.763887i	$-0.276712\pi$
$977$	40.3434	1.29070	0.645350	+	0.763887i	$0.276712\pi$
$978$	−30.5731	−0.977618
$979$	−16.7321	−0.534760
$980$	−24.0397	−0.767919
$981$	−21.1965	−0.676752
$982$	30.7738	0.982030
$983$	−17.8944	−0.570743	−0.285372	−	0.958417i	$-0.592117\pi$
$983$	−17.8944	−0.570743	−0.285372	+	0.958417i	$0.592117\pi$
$984$	6.19499	0.197489
$985$	49.5611	1.57915
$986$	−2.20875	−0.0703409
$987$	−7.40846	−0.235814
$988$	−1.63605	−0.0520497
$989$	7.35278	0.233805
$990$	21.7383	0.690890
$991$	39.8586	1.26615	0.633075	−	0.774090i	$-0.281792\pi$
$991$	39.8586	1.26615	0.633075	+	0.774090i	$0.281792\pi$
$992$	−3.37427	−0.107133
$993$	−24.0251	−0.762414
$994$	4.88826	0.155046
$995$	56.9377	1.80505
$996$	−18.8703	−0.597929
$997$	−60.2890	−1.90937	−0.954686	−	0.297614i	$-0.903809\pi$
$997$	−60.2890	−1.90937	−0.954686	+	0.297614i	$0.903809\pi$
$998$	9.33182	0.295393
$999$	17.6305	0.557805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.36	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.36	✓	47	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.24233 q^{3} +1.00000 q^{4} +3.57017 q^{5} +2.24233 q^{6} +0.516251 q^{7} +1.00000 q^{8} +2.02804 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.24233 q^{3} +1.00000 q^{4} +3.57017 q^{5} +2.24233 q^{6} +0.516251 q^{7} +1.00000 q^{8} +2.02804 q^{9} +3.57017 q^{10} +3.00236 q^{11} +2.24233 q^{12} +1.63605 q^{13} +0.516251 q^{14} +8.00549 q^{15} +1.00000 q^{16} -0.530807 q^{17} +2.02804 q^{18} -1.00000 q^{19} +3.57017 q^{20} +1.15761 q^{21} +3.00236 q^{22} -2.37767 q^{23} +2.24233 q^{24} +7.74610 q^{25} +1.63605 q^{26} -2.17946 q^{27} +0.516251 q^{28} +4.16112 q^{29} +8.00549 q^{30} -3.37427 q^{31} +1.00000 q^{32} +6.73227 q^{33} -0.530807 q^{34} +1.84310 q^{35} +2.02804 q^{36} -8.08939 q^{37} -1.00000 q^{38} +3.66856 q^{39} +3.57017 q^{40} +2.76275 q^{41} +1.15761 q^{42} -3.09244 q^{43} +3.00236 q^{44} +7.24043 q^{45} -2.37767 q^{46} -6.39982 q^{47} +2.24233 q^{48} -6.73348 q^{49} +7.74610 q^{50} -1.19024 q^{51} +1.63605 q^{52} +6.86634 q^{53} -2.17946 q^{54} +10.7189 q^{55} +0.516251 q^{56} -2.24233 q^{57} +4.16112 q^{58} +7.54745 q^{59} +8.00549 q^{60} +13.9351 q^{61} -3.37427 q^{62} +1.04698 q^{63} +1.00000 q^{64} +5.84097 q^{65} +6.73227 q^{66} -7.40499 q^{67} -0.530807 q^{68} -5.33151 q^{69} +1.84310 q^{70} +9.46877 q^{71} +2.02804 q^{72} -5.84556 q^{73} -8.08939 q^{74} +17.3693 q^{75} -1.00000 q^{76} +1.54997 q^{77} +3.66856 q^{78} +14.2713 q^{79} +3.57017 q^{80} -10.9712 q^{81} +2.76275 q^{82} -8.41550 q^{83} +1.15761 q^{84} -1.89507 q^{85} -3.09244 q^{86} +9.33059 q^{87} +3.00236 q^{88} -5.57298 q^{89} +7.24043 q^{90} +0.844613 q^{91} -2.37767 q^{92} -7.56622 q^{93} -6.39982 q^{94} -3.57017 q^{95} +2.24233 q^{96} +9.07657 q^{97} -6.73348 q^{98} +6.08889 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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