LMFDB - Embedded newform 6022.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.19043 q^{3} +1.00000 q^{4} -0.477734 q^{5} +2.19043 q^{6} -4.48401 q^{7} -1.00000 q^{8} +1.79797 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.19043 q^{3} +1.00000 q^{4} -0.477734 q^{5} +2.19043 q^{6} -4.48401 q^{7} -1.00000 q^{8} +1.79797 q^{9} +0.477734 q^{10} -4.66890 q^{11} -2.19043 q^{12} -7.00761 q^{13} +4.48401 q^{14} +1.04644 q^{15} +1.00000 q^{16} -3.04248 q^{17} -1.79797 q^{18} +7.58181 q^{19} -0.477734 q^{20} +9.82190 q^{21} +4.66890 q^{22} -6.56907 q^{23} +2.19043 q^{24} -4.77177 q^{25} +7.00761 q^{26} +2.63296 q^{27} -4.48401 q^{28} +8.59809 q^{29} -1.04644 q^{30} +4.69097 q^{31} -1.00000 q^{32} +10.2269 q^{33} +3.04248 q^{34} +2.14217 q^{35} +1.79797 q^{36} +11.3828 q^{37} -7.58181 q^{38} +15.3496 q^{39} +0.477734 q^{40} -6.74997 q^{41} -9.82190 q^{42} +3.21723 q^{43} -4.66890 q^{44} -0.858951 q^{45} +6.56907 q^{46} +1.29871 q^{47} -2.19043 q^{48} +13.1064 q^{49} +4.77177 q^{50} +6.66433 q^{51} -7.00761 q^{52} +5.98152 q^{53} -2.63296 q^{54} +2.23049 q^{55} +4.48401 q^{56} -16.6074 q^{57} -8.59809 q^{58} -1.36120 q^{59} +1.04644 q^{60} -3.57514 q^{61} -4.69097 q^{62} -8.06211 q^{63} +1.00000 q^{64} +3.34777 q^{65} -10.2269 q^{66} +13.6025 q^{67} -3.04248 q^{68} +14.3891 q^{69} -2.14217 q^{70} +13.5239 q^{71} -1.79797 q^{72} +1.65936 q^{73} -11.3828 q^{74} +10.4522 q^{75} +7.58181 q^{76} +20.9354 q^{77} -15.3496 q^{78} -4.11610 q^{79} -0.477734 q^{80} -11.1612 q^{81} +6.74997 q^{82} +3.66638 q^{83} +9.82190 q^{84} +1.45350 q^{85} -3.21723 q^{86} -18.8335 q^{87} +4.66890 q^{88} -12.1019 q^{89} +0.858951 q^{90} +31.4222 q^{91} -6.56907 q^{92} -10.2752 q^{93} -1.29871 q^{94} -3.62209 q^{95} +2.19043 q^{96} -12.2396 q^{97} -13.1064 q^{98} -8.39453 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * 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
$3$	−2.19043	−1.26464	−0.632322	−	0.774706i	$-0.717898\pi$
$3$	−2.19043	−1.26464	−0.632322	+	0.774706i	$0.717898\pi$
$4$	1.00000	0.500000
$5$	−0.477734	−0.213649	−0.106825	−	0.994278i	$-0.534068\pi$
$5$	−0.477734	−0.213649	−0.106825	+	0.994278i	$0.534068\pi$
$6$	2.19043	0.894238
$7$	−4.48401	−1.69480	−0.847399	−	0.530957i	$-0.821833\pi$
$7$	−4.48401	−1.69480	−0.847399	+	0.530957i	$0.821833\pi$
$8$	−1.00000	−0.353553
$9$	1.79797	0.599323
$10$	0.477734	0.151073
$11$	−4.66890	−1.40773	−0.703863	−	0.710336i	$-0.748543\pi$
$11$	−4.66890	−1.40773	−0.703863	+	0.710336i	$0.748543\pi$
$12$	−2.19043	−0.632322
$13$	−7.00761	−1.94356	−0.971780	−	0.235889i	$-0.924200\pi$
$13$	−7.00761	−1.94356	−0.971780	+	0.235889i	$0.924200\pi$
$14$	4.48401	1.19840
$15$	1.04644	0.270190
$16$	1.00000	0.250000
$17$	−3.04248	−0.737910	−0.368955	−	0.929447i	$-0.620284\pi$
$17$	−3.04248	−0.737910	−0.368955	+	0.929447i	$0.620284\pi$
$18$	−1.79797	−0.423785
$19$	7.58181	1.73939	0.869693	−	0.493593i	$-0.164317\pi$
$19$	7.58181	1.73939	0.869693	+	0.493593i	$0.164317\pi$
$20$	−0.477734	−0.106825
$21$	9.82190	2.14331
$22$	4.66890	0.995412
$23$	−6.56907	−1.36974	−0.684872	−	0.728663i	$-0.740142\pi$
$23$	−6.56907	−1.36974	−0.684872	+	0.728663i	$0.740142\pi$
$24$	2.19043	0.447119
$25$	−4.77177	−0.954354
$26$	7.00761	1.37430
$27$	2.63296	0.506714
$28$	−4.48401	−0.847399
$29$	8.59809	1.59662	0.798312	−	0.602244i	$-0.205726\pi$
$29$	8.59809	1.59662	0.798312	+	0.602244i	$0.205726\pi$
$30$	−1.04644	−0.191053
$31$	4.69097	0.842523	0.421261	−	0.906939i	$-0.361588\pi$
$31$	4.69097	0.842523	0.421261	+	0.906939i	$0.361588\pi$
$32$	−1.00000	−0.176777
$33$	10.2269	1.78027
$34$	3.04248	0.521781
$35$	2.14217	0.362092
$36$	1.79797	0.299661
$37$	11.3828	1.87132	0.935658	−	0.352908i	$-0.114807\pi$
$37$	11.3828	1.87132	0.935658	+	0.352908i	$0.114807\pi$
$38$	−7.58181	−1.22993
$39$	15.3496	2.45791
$40$	0.477734	0.0755364
$41$	−6.74997	−1.05417	−0.527084	−	0.849813i	$-0.676715\pi$
$41$	−6.74997	−1.05417	−0.527084	+	0.849813i	$0.676715\pi$
$42$	−9.82190	−1.51555
$43$	3.21723	0.490623	0.245311	−	0.969444i	$-0.421110\pi$
$43$	3.21723	0.490623	0.245311	+	0.969444i	$0.421110\pi$
$44$	−4.66890	−0.703863
$45$	−0.858951	−0.128045
$46$	6.56907	0.968556
$47$	1.29871	0.189436	0.0947179	−	0.995504i	$-0.469805\pi$
$47$	1.29871	0.189436	0.0947179	+	0.995504i	$0.469805\pi$
$48$	−2.19043	−0.316161
$49$	13.1064	1.87234
$50$	4.77177	0.674830
$51$	6.66433	0.933192
$52$	−7.00761	−0.971780
$53$	5.98152	0.821625	0.410812	−	0.911720i	$-0.365245\pi$
$53$	5.98152	0.821625	0.410812	+	0.911720i	$0.365245\pi$
$54$	−2.63296	−0.358301
$55$	2.23049	0.300759
$56$	4.48401	0.599201
$57$	−16.6074	−2.19970
$58$	−8.59809	−1.12898
$59$	−1.36120	−0.177213	−0.0886064	−	0.996067i	$-0.528241\pi$
$59$	−1.36120	−0.177213	−0.0886064	+	0.996067i	$0.528241\pi$
$60$	1.04644	0.135095
$61$	−3.57514	−0.457750	−0.228875	−	0.973456i	$-0.573505\pi$
$61$	−3.57514	−0.457750	−0.228875	+	0.973456i	$0.573505\pi$
$62$	−4.69097	−0.595753
$63$	−8.06211	−1.01573
$64$	1.00000	0.125000
$65$	3.34777	0.415240
$66$	−10.2269	−1.25884
$67$	13.6025	1.66182	0.830908	−	0.556410i	$-0.187822\pi$
$67$	13.6025	1.66182	0.830908	+	0.556410i	$0.187822\pi$
$68$	−3.04248	−0.368955
$69$	14.3891	1.73224
$70$	−2.14217	−0.256038
$71$	13.5239	1.60499	0.802496	−	0.596657i	$-0.203505\pi$
$71$	13.5239	1.60499	0.802496	+	0.596657i	$0.203505\pi$
$72$	−1.79797	−0.211893
$73$	1.65936	0.194214	0.0971068	−	0.995274i	$-0.469041\pi$
$73$	1.65936	0.194214	0.0971068	+	0.995274i	$0.469041\pi$
$74$	−11.3828	−1.32322
$75$	10.4522	1.20692
$76$	7.58181	0.869693
$77$	20.9354	2.38581
$78$	−15.3496	−1.73801
$79$	−4.11610	−0.463097	−0.231548	−	0.972823i	$-0.574379\pi$
$79$	−4.11610	−0.463097	−0.231548	+	0.972823i	$0.574379\pi$
$80$	−0.477734	−0.0534123
$81$	−11.1612	−1.24014
$82$	6.74997	0.745409
$83$	3.66638	0.402438	0.201219	−	0.979546i	$-0.435510\pi$
$83$	3.66638	0.402438	0.201219	+	0.979546i	$0.435510\pi$
$84$	9.82190	1.07166
$85$	1.45350	0.157654
$86$	−3.21723	−0.346923
$87$	−18.8335	−2.01916
$88$	4.66890	0.497706
$89$	−12.1019	−1.28280	−0.641400	−	0.767206i	$-0.721646\pi$
$89$	−12.1019	−1.28280	−0.641400	+	0.767206i	$0.721646\pi$
$90$	0.858951	0.0905414
$91$	31.4222	3.29394
$92$	−6.56907	−0.684872
$93$	−10.2752	−1.06549
$94$	−1.29871	−0.133951
$95$	−3.62209	−0.371618
$96$	2.19043	0.223559
$97$	−12.2396	−1.24274	−0.621372	−	0.783515i	$-0.713425\pi$
$97$	−12.2396	−1.24274	−0.621372	+	0.783515i	$0.713425\pi$
$98$	−13.1064	−1.32394
$99$	−8.39453	−0.843682
$100$	−4.77177	−0.477177
$101$	−2.65351	−0.264034	−0.132017	−	0.991247i	$-0.542145\pi$
$101$	−2.65351	−0.264034	−0.132017	+	0.991247i	$0.542145\pi$
$102$	−6.66433	−0.659867
$103$	−14.4685	−1.42562	−0.712812	−	0.701355i	$-0.752579\pi$
$103$	−14.4685	−1.42562	−0.712812	+	0.701355i	$0.752579\pi$
$104$	7.00761	0.687152
$105$	−4.69226	−0.457917
$106$	−5.98152	−0.580976
$107$	−8.10129	−0.783181	−0.391591	−	0.920140i	$-0.628075\pi$
$107$	−8.10129	−0.783181	−0.391591	+	0.920140i	$0.628075\pi$
$108$	2.63296	0.253357
$109$	−15.8461	−1.51778	−0.758890	−	0.651219i	$-0.774258\pi$
$109$	−15.8461	−1.51778	−0.758890	+	0.651219i	$0.774258\pi$
$110$	−2.23049	−0.212669
$111$	−24.9331	−2.36655
$112$	−4.48401	−0.423699
$113$	−6.35822	−0.598131	−0.299065	−	0.954233i	$-0.596675\pi$
$113$	−6.35822	−0.598131	−0.299065	+	0.954233i	$0.596675\pi$
$114$	16.6074	1.55542
$115$	3.13827	0.292645
$116$	8.59809	0.798312
$117$	−12.5995	−1.16482
$118$	1.36120	0.125308
$119$	13.6425	1.25061
$120$	−1.04644	−0.0955266
$121$	10.7986	0.981692
$122$	3.57514	0.323678
$123$	14.7853	1.33315
$124$	4.69097	0.421261
$125$	4.66831	0.417546
$126$	8.06211	0.718230
$127$	12.7910	1.13502	0.567511	−	0.823366i	$-0.307906\pi$
$127$	12.7910	1.13502	0.567511	+	0.823366i	$0.307906\pi$
$128$	−1.00000	−0.0883883
$129$	−7.04710	−0.620463
$130$	−3.34777	−0.293619
$131$	19.4565	1.69993	0.849963	−	0.526843i	$-0.176624\pi$
$131$	19.4565	1.69993	0.849963	+	0.526843i	$0.176624\pi$
$132$	10.2269	0.890136
$133$	−33.9969	−2.94791
$134$	−13.6025	−1.17508
$135$	−1.25786	−0.108259
$136$	3.04248	0.260890
$137$	−14.9172	−1.27446	−0.637230	−	0.770674i	$-0.719920\pi$
$137$	−14.9172	−1.27446	−0.637230	+	0.770674i	$0.719920\pi$
$138$	−14.3891	−1.22488
$139$	−3.90577	−0.331283	−0.165641	−	0.986186i	$-0.552969\pi$
$139$	−3.90577	−0.331283	−0.165641	+	0.986186i	$0.552969\pi$
$140$	2.14217	0.181046
$141$	−2.84472	−0.239569
$142$	−13.5239	−1.13490
$143$	32.7178	2.73600
$144$	1.79797	0.149831
$145$	−4.10760	−0.341118
$146$	−1.65936	−0.137330
$147$	−28.7085	−2.36784
$148$	11.3828	0.935658
$149$	−9.72807	−0.796954	−0.398477	−	0.917178i	$-0.630461\pi$
$149$	−9.72807	−0.796954	−0.398477	+	0.917178i	$0.630461\pi$
$150$	−10.4522	−0.853419
$151$	−3.60881	−0.293680	−0.146840	−	0.989160i	$-0.546910\pi$
$151$	−3.60881	−0.293680	−0.146840	+	0.989160i	$0.546910\pi$
$152$	−7.58181	−0.614966
$153$	−5.47028	−0.442246
$154$	−20.9354	−1.68702
$155$	−2.24104	−0.180004
$156$	15.3496	1.22896
$157$	9.55258	0.762379	0.381189	−	0.924497i	$-0.375515\pi$
$157$	9.55258	0.762379	0.381189	+	0.924497i	$0.375515\pi$
$158$	4.11610	0.327459
$159$	−13.1021	−1.03906
$160$	0.477734	0.0377682
$161$	29.4558	2.32144
$162$	11.1612	0.876908
$163$	−20.6949	−1.62095	−0.810474	−	0.585775i	$-0.800790\pi$
$163$	−20.6949	−1.62095	−0.810474	+	0.585775i	$0.800790\pi$
$164$	−6.74997	−0.527084
$165$	−4.88573	−0.380353
$166$	−3.66638	−0.284567
$167$	−6.75231	−0.522509	−0.261255	−	0.965270i	$-0.584136\pi$
$167$	−6.75231	−0.522509	−0.261255	+	0.965270i	$0.584136\pi$
$168$	−9.82190	−0.757776
$169$	36.1065	2.77743
$170$	−1.45350	−0.111478
$171$	13.6318	1.04245
$172$	3.21723	0.245311
$173$	−11.2406	−0.854607	−0.427304	−	0.904108i	$-0.640536\pi$
$173$	−11.2406	−0.854607	−0.427304	+	0.904108i	$0.640536\pi$
$174$	18.8335	1.42776
$175$	21.3967	1.61744
$176$	−4.66890	−0.351931
$177$	2.98160	0.224111
$178$	12.1019	0.907077
$179$	−0.791269	−0.0591422	−0.0295711	−	0.999563i	$-0.509414\pi$
$179$	−0.791269	−0.0591422	−0.0295711	+	0.999563i	$0.509414\pi$
$180$	−0.858951	−0.0640224
$181$	12.9115	0.959701	0.479850	−	0.877350i	$-0.340691\pi$
$181$	12.9115	0.959701	0.479850	+	0.877350i	$0.340691\pi$
$182$	−31.4222	−2.32917
$183$	7.83109	0.578890
$184$	6.56907	0.484278
$185$	−5.43794	−0.399805
$186$	10.2752	0.753416
$187$	14.2050	1.03877
$188$	1.29871	0.0947179
$189$	−11.8062	−0.858777
$190$	3.62209	0.262774
$191$	9.13689	0.661122	0.330561	−	0.943785i	$-0.392762\pi$
$191$	9.13689	0.661122	0.330561	+	0.943785i	$0.392762\pi$
$192$	−2.19043	−0.158080
$193$	20.9387	1.50720	0.753602	−	0.657331i	$-0.228315\pi$
$193$	20.9387	1.50720	0.753602	+	0.657331i	$0.228315\pi$
$194$	12.2396	0.878753
$195$	−7.33305	−0.525131
$196$	13.1064	0.936169
$197$	24.7766	1.76526	0.882630	−	0.470069i	$-0.155771\pi$
$197$	24.7766	1.76526	0.882630	+	0.470069i	$0.155771\pi$
$198$	8.39453	0.596573
$199$	11.5427	0.818242	0.409121	−	0.912480i	$-0.365835\pi$
$199$	11.5427	0.818242	0.409121	+	0.912480i	$0.365835\pi$
$200$	4.77177	0.337415
$201$	−29.7954	−2.10160
$202$	2.65351	0.186700
$203$	−38.5539	−2.70595
$204$	6.66433	0.466596
$205$	3.22469	0.225222
$206$	14.4685	1.00807
$207$	−11.8110	−0.820919
$208$	−7.00761	−0.485890
$209$	−35.3987	−2.44858
$210$	4.69226	0.323796
$211$	9.32741	0.642125	0.321063	−	0.947058i	$-0.395960\pi$
$211$	9.32741	0.642125	0.321063	+	0.947058i	$0.395960\pi$
$212$	5.98152	0.410812
$213$	−29.6231	−2.02974
$214$	8.10129	0.553793
$215$	−1.53698	−0.104821
$216$	−2.63296	−0.179150
$217$	−21.0344	−1.42791
$218$	15.8461	1.07323
$219$	−3.63471	−0.245611
$220$	2.23049	0.150380
$221$	21.3205	1.43417
$222$	24.9331	1.67340
$223$	−9.10911	−0.609991	−0.304996	−	0.952354i	$-0.598655\pi$
$223$	−9.10911	−0.609991	−0.304996	+	0.952354i	$0.598655\pi$
$224$	4.48401	0.299601
$225$	−8.57949	−0.571966
$226$	6.35822	0.422942
$227$	−2.62839	−0.174452	−0.0872261	−	0.996189i	$-0.527800\pi$
$227$	−2.62839	−0.174452	−0.0872261	+	0.996189i	$0.527800\pi$
$228$	−16.6074	−1.09985
$229$	−17.7578	−1.17347	−0.586735	−	0.809779i	$-0.699587\pi$
$229$	−17.7578	−1.17347	−0.586735	+	0.809779i	$0.699587\pi$
$230$	−3.13827	−0.206931
$231$	−45.8574	−3.01720
$232$	−8.59809	−0.564492
$233$	−15.1752	−0.994161	−0.497080	−	0.867704i	$-0.665595\pi$
$233$	−15.1752	−0.994161	−0.497080	+	0.867704i	$0.665595\pi$
$234$	12.5995	0.823652
$235$	−0.620437	−0.0404728
$236$	−1.36120	−0.0886064
$237$	9.01600	0.585652
$238$	−13.6425	−0.884313
$239$	2.74394	0.177490	0.0887452	−	0.996054i	$-0.471714\pi$
$239$	2.74394	0.177490	0.0887452	+	0.996054i	$0.471714\pi$
$240$	1.04644	0.0675475
$241$	26.3815	1.69938	0.849691	−	0.527280i	$-0.176788\pi$
$241$	26.3815	1.69938	0.849691	+	0.527280i	$0.176788\pi$
$242$	−10.7986	−0.694161
$243$	16.5489	1.06161
$244$	−3.57514	−0.228875
$245$	−6.26136	−0.400024
$246$	−14.7853	−0.942677
$247$	−53.1303	−3.38060
$248$	−4.69097	−0.297877
$249$	−8.03095	−0.508940
$250$	−4.66831	−0.295250
$251$	14.2136	0.897153	0.448577	−	0.893744i	$-0.351931\pi$
$251$	14.2136	0.897153	0.448577	+	0.893744i	$0.351931\pi$
$252$	−8.06211	−0.507865
$253$	30.6703	1.92823
$254$	−12.7910	−0.802582
$255$	−3.18378	−0.199376
$256$	1.00000	0.0625000
$257$	4.04634	0.252404	0.126202	−	0.992005i	$-0.459721\pi$
$257$	4.04634	0.252404	0.126202	+	0.992005i	$0.459721\pi$
$258$	7.04710	0.438733
$259$	−51.0405	−3.17150
$260$	3.34777	0.207620
$261$	15.4591	0.956893
$262$	−19.4565	−1.20203
$263$	19.2780	1.18873	0.594367	−	0.804194i	$-0.297403\pi$
$263$	19.2780	1.18873	0.594367	+	0.804194i	$0.297403\pi$
$264$	−10.2269	−0.629421
$265$	−2.85758	−0.175539
$266$	33.9969	2.08448
$267$	26.5084	1.62228
$268$	13.6025	0.830908
$269$	10.8645	0.662420	0.331210	−	0.943557i	$-0.392543\pi$
$269$	10.8645	0.662420	0.331210	+	0.943557i	$0.392543\pi$
$270$	1.25786	0.0765507
$271$	10.4583	0.635296	0.317648	−	0.948209i	$-0.397107\pi$
$271$	10.4583	0.635296	0.317648	+	0.948209i	$0.397107\pi$
$272$	−3.04248	−0.184477
$273$	−68.8280	−4.16566
$274$	14.9172	0.901180
$275$	22.2789	1.34347
$276$	14.3891	0.866119
$277$	−8.57442	−0.515187	−0.257594	−	0.966253i	$-0.582930\pi$
$277$	−8.57442	−0.515187	−0.257594	+	0.966253i	$0.582930\pi$
$278$	3.90577	0.234252
$279$	8.43421	0.504943
$280$	−2.14217	−0.128019
$281$	11.2164	0.669115	0.334558	−	0.942375i	$-0.391413\pi$
$281$	11.2164	0.669115	0.334558	+	0.942375i	$0.391413\pi$
$282$	2.84472	0.169401
$283$	9.49963	0.564694	0.282347	−	0.959312i	$-0.408887\pi$
$283$	9.49963	0.564694	0.282347	+	0.959312i	$0.408887\pi$
$284$	13.5239	0.802496
$285$	7.93392	0.469965
$286$	−32.7178	−1.93464
$287$	30.2669	1.78660
$288$	−1.79797	−0.105946
$289$	−7.74332	−0.455490
$290$	4.10760	0.241207
$291$	26.8100	1.57163
$292$	1.65936	0.0971068
$293$	−5.78324	−0.337860	−0.168930	−	0.985628i	$-0.554031\pi$
$293$	−5.78324	−0.337860	−0.168930	+	0.985628i	$0.554031\pi$
$294$	28.7085	1.67432
$295$	0.650290	0.0378614
$296$	−11.3828	−0.661610
$297$	−12.2930	−0.713314
$298$	9.72807	0.563532
$299$	46.0334	2.66218
$300$	10.4522	0.603459
$301$	−14.4261	−0.831506
$302$	3.60881	0.207663
$303$	5.81231	0.333909
$304$	7.58181	0.434846
$305$	1.70797	0.0977979
$306$	5.47028	0.312715
$307$	−14.6581	−0.836583	−0.418291	−	0.908313i	$-0.637371\pi$
$307$	−14.6581	−0.836583	−0.418291	+	0.908313i	$0.637371\pi$
$308$	20.9354	1.19290
$309$	31.6922	1.80291
$310$	2.24104	0.127282
$311$	8.50417	0.482227	0.241114	−	0.970497i	$-0.422487\pi$
$311$	8.50417	0.482227	0.241114	+	0.970497i	$0.422487\pi$
$312$	−15.3496	−0.869003
$313$	−33.1627	−1.87447	−0.937235	−	0.348699i	$-0.886623\pi$
$313$	−33.1627	−1.87447	−0.937235	+	0.348699i	$0.886623\pi$
$314$	−9.55258	−0.539083
$315$	3.85155	0.217010
$316$	−4.11610	−0.231548
$317$	5.59028	0.313981	0.156991	−	0.987600i	$-0.449821\pi$
$317$	5.59028	0.313981	0.156991	+	0.987600i	$0.449821\pi$
$318$	13.1021	0.734728
$319$	−40.1436	−2.24761
$320$	−0.477734	−0.0267062
$321$	17.7453	0.990445
$322$	−29.4558	−1.64151
$323$	−23.0675	−1.28351
$324$	−11.1612	−0.620068
$325$	33.4387	1.85484
$326$	20.6949	1.14618
$327$	34.7097	1.91945
$328$	6.74997	0.372705
$329$	−5.82342	−0.321055
$330$	4.88573	0.268951
$331$	−2.80590	−0.154226	−0.0771130	−	0.997022i	$-0.524570\pi$
$331$	−2.80590	−0.154226	−0.0771130	+	0.997022i	$0.524570\pi$
$332$	3.66638	0.201219
$333$	20.4659	1.12152
$334$	6.75231	0.369470
$335$	−6.49840	−0.355046
$336$	9.82190	0.535829
$337$	−15.2732	−0.831985	−0.415992	−	0.909368i	$-0.636566\pi$
$337$	−15.2732	−0.831985	−0.415992	+	0.909368i	$0.636566\pi$
$338$	−36.1065	−1.96394
$339$	13.9272	0.756422
$340$	1.45350	0.0788269
$341$	−21.9016	−1.18604
$342$	−13.6318	−0.737126
$343$	−27.3810	−1.47844
$344$	−3.21723	−0.173461
$345$	−6.87414	−0.370091
$346$	11.2406	0.604299
$347$	16.5625	0.889121	0.444561	−	0.895749i	$-0.353360\pi$
$347$	16.5625	0.889121	0.444561	+	0.895749i	$0.353360\pi$
$348$	−18.8335	−1.00958
$349$	−8.37004	−0.448038	−0.224019	−	0.974585i	$-0.571918\pi$
$349$	−8.37004	−0.448038	−0.224019	+	0.974585i	$0.571918\pi$
$350$	−21.3967	−1.14370
$351$	−18.4508	−0.984829
$352$	4.66890	0.248853
$353$	−10.5971	−0.564029	−0.282014	−	0.959410i	$-0.591003\pi$
$353$	−10.5971	−0.564029	−0.282014	+	0.959410i	$0.591003\pi$
$354$	−2.98160	−0.158470
$355$	−6.46083	−0.342905
$356$	−12.1019	−0.641400
$357$	−29.8829	−1.58157
$358$	0.791269	0.0418199
$359$	−3.52197	−0.185882	−0.0929412	−	0.995672i	$-0.529627\pi$
$359$	−3.52197	−0.185882	−0.0929412	+	0.995672i	$0.529627\pi$
$360$	0.858951	0.0452707
$361$	38.4838	2.02546
$362$	−12.9115	−0.678611
$363$	−23.6536	−1.24149
$364$	31.4222	1.64697
$365$	−0.792734	−0.0414936
$366$	−7.83109	−0.409337
$367$	35.2284	1.83891	0.919454	−	0.393199i	$-0.128632\pi$
$367$	35.2284	1.83891	0.919454	+	0.393199i	$0.128632\pi$
$368$	−6.56907	−0.342436
$369$	−12.1362	−0.631787
$370$	5.43794	0.282705
$371$	−26.8212	−1.39249
$372$	−10.2752	−0.532745
$373$	23.2208	1.20233	0.601164	−	0.799126i	$-0.294704\pi$
$373$	23.2208	1.20233	0.601164	+	0.799126i	$0.294704\pi$
$374$	−14.2050	−0.734524
$375$	−10.2256	−0.528047
$376$	−1.29871	−0.0669757
$377$	−60.2520	−3.10314
$378$	11.8062	0.607247
$379$	−0.150272	−0.00771896	−0.00385948	−	0.999993i	$-0.501229\pi$
$379$	−0.150272	−0.00771896	−0.00385948	+	0.999993i	$0.501229\pi$
$380$	−3.62209	−0.185809
$381$	−28.0179	−1.43540
$382$	−9.13689	−0.467484
$383$	10.3380	0.528245	0.264123	−	0.964489i	$-0.414918\pi$
$383$	10.3380	0.528245	0.264123	+	0.964489i	$0.414918\pi$
$384$	2.19043	0.111780
$385$	−10.0016	−0.509726
$386$	−20.9387	−1.06575
$387$	5.78447	0.294041
$388$	−12.2396	−0.621372
$389$	−15.8140	−0.801800	−0.400900	−	0.916122i	$-0.631303\pi$
$389$	−15.8140	−0.801800	−0.400900	+	0.916122i	$0.631303\pi$
$390$	7.33305	0.371323
$391$	19.9862	1.01075
$392$	−13.1064	−0.661971
$393$	−42.6181	−2.14980
$394$	−24.7766	−1.24823
$395$	1.96640	0.0989403
$396$	−8.39453	−0.421841
$397$	28.1718	1.41390	0.706950	−	0.707264i	$-0.250071\pi$
$397$	28.1718	1.41390	0.706950	+	0.707264i	$0.250071\pi$
$398$	−11.5427	−0.578585
$399$	74.4677	3.72805
$400$	−4.77177	−0.238589
$401$	−10.3710	−0.517902	−0.258951	−	0.965890i	$-0.583377\pi$
$401$	−10.3710	−0.517902	−0.258951	+	0.965890i	$0.583377\pi$
$402$	29.7954	1.48606
$403$	−32.8725	−1.63749
$404$	−2.65351	−0.132017
$405$	5.33209	0.264954
$406$	38.5539	1.91340
$407$	−53.1450	−2.63430
$408$	−6.66433	−0.329933
$409$	6.36994	0.314973	0.157487	−	0.987521i	$-0.449661\pi$
$409$	6.36994	0.314973	0.157487	+	0.987521i	$0.449661\pi$
$410$	−3.22469	−0.159256
$411$	32.6750	1.61174
$412$	−14.4685	−0.712812
$413$	6.10362	0.300340
$414$	11.8110	0.580478
$415$	−1.75156	−0.0859806
$416$	7.00761	0.343576
$417$	8.55530	0.418955
$418$	35.3987	1.73141
$419$	7.49645	0.366225	0.183113	−	0.983092i	$-0.441383\pi$
$419$	7.49645	0.366225	0.183113	+	0.983092i	$0.441383\pi$
$420$	−4.69226	−0.228959
$421$	4.78557	0.233235	0.116617	−	0.993177i	$-0.462795\pi$
$421$	4.78557	0.233235	0.116617	+	0.993177i	$0.462795\pi$
$422$	−9.32741	−0.454051
$423$	2.33503	0.113533
$424$	−5.98152	−0.290488
$425$	14.5180	0.704227
$426$	29.6231	1.43524
$427$	16.0310	0.775793
$428$	−8.10129	−0.391591
$429$	−71.6659	−3.46006
$430$	1.53698	0.0741197
$431$	−12.4914	−0.601688	−0.300844	−	0.953673i	$-0.597268\pi$
$431$	−12.4914	−0.601688	−0.300844	+	0.953673i	$0.597268\pi$
$432$	2.63296	0.126678
$433$	34.4731	1.65667	0.828336	−	0.560232i	$-0.189288\pi$
$433$	34.4731	1.65667	0.828336	+	0.560232i	$0.189288\pi$
$434$	21.0344	1.00968
$435$	8.99739	0.431392
$436$	−15.8461	−0.758890
$437$	−49.8054	−2.38251
$438$	3.63471	0.173673
$439$	−25.6605	−1.22471	−0.612354	−	0.790584i	$-0.709777\pi$
$439$	−25.6605	−1.22471	−0.612354	+	0.790584i	$0.709777\pi$
$440$	−2.23049	−0.106335
$441$	23.5648	1.12213
$442$	−21.3205	−1.01411
$443$	−28.8276	−1.36964	−0.684819	−	0.728713i	$-0.740119\pi$
$443$	−28.8276	−1.36964	−0.684819	+	0.728713i	$0.740119\pi$
$444$	−24.9331	−1.18327
$445$	5.78150	0.274069
$446$	9.10911	0.431329
$447$	21.3086	1.00786
$448$	−4.48401	−0.211850
$449$	−10.2267	−0.482626	−0.241313	−	0.970447i	$-0.577578\pi$
$449$	−10.2267	−0.482626	−0.241313	+	0.970447i	$0.577578\pi$
$450$	8.57949	0.404441
$451$	31.5149	1.48398
$452$	−6.35822	−0.299065
$453$	7.90482	0.371401
$454$	2.62839	0.123356
$455$	−15.0115	−0.703748
$456$	16.6074	0.777712
$457$	−1.77486	−0.0830245	−0.0415123	−	0.999138i	$-0.513218\pi$
$457$	−1.77486	−0.0830245	−0.0415123	+	0.999138i	$0.513218\pi$
$458$	17.7578	0.829769
$459$	−8.01073	−0.373909
$460$	3.13827	0.146322
$461$	−17.8727	−0.832412	−0.416206	−	0.909270i	$-0.636641\pi$
$461$	−17.8727	−0.832412	−0.416206	+	0.909270i	$0.636641\pi$
$462$	45.8574	2.13348
$463$	12.0765	0.561241	0.280620	−	0.959819i	$-0.409460\pi$
$463$	12.0765	0.561241	0.280620	+	0.959819i	$0.409460\pi$
$464$	8.59809	0.399156
$465$	4.90882	0.227641
$466$	15.1752	0.702978
$467$	42.8339	1.98211	0.991057	−	0.133436i	$-0.0426010\pi$
$467$	42.8339	1.98211	0.991057	+	0.133436i	$0.0426010\pi$
$468$	−12.5995	−0.582410
$469$	−60.9940	−2.81644
$470$	0.620437	0.0286186
$471$	−20.9242	−0.964137
$472$	1.36120	0.0626542
$473$	−15.0209	−0.690662
$474$	−9.01600	−0.414119
$475$	−36.1786	−1.65999
$476$	13.6425	0.625304
$477$	10.7546	0.492418
$478$	−2.74394	−0.125505
$479$	20.3886	0.931580	0.465790	−	0.884895i	$-0.345770\pi$
$479$	20.3886	0.931580	0.465790	+	0.884895i	$0.345770\pi$
$480$	−1.04644	−0.0477633
$481$	−79.7660	−3.63702
$482$	−26.3815	−1.20165
$483$	−64.5207	−2.93579
$484$	10.7986	0.490846
$485$	5.84728	0.265511
$486$	−16.5489	−0.750675
$487$	22.7947	1.03293	0.516464	−	0.856309i	$-0.327248\pi$
$487$	22.7947	1.03293	0.516464	+	0.856309i	$0.327248\pi$
$488$	3.57514	0.161839
$489$	45.3306	2.04992
$490$	6.26136	0.282859
$491$	−39.1986	−1.76901	−0.884505	−	0.466531i	$-0.845504\pi$
$491$	−39.1986	−1.76901	−0.884505	+	0.466531i	$0.845504\pi$
$492$	14.7853	0.666573
$493$	−26.1595	−1.17816
$494$	53.1303	2.39045
$495$	4.01035	0.180252
$496$	4.69097	0.210631
$497$	−60.6414	−2.72014
$498$	8.03095	0.359875
$499$	24.7566	1.10826	0.554130	−	0.832430i	$-0.313051\pi$
$499$	24.7566	1.10826	0.554130	+	0.832430i	$0.313051\pi$
$500$	4.66831	0.208773
$501$	14.7904	0.660788
$502$	−14.2136	−0.634383
$503$	−36.9726	−1.64853	−0.824264	−	0.566205i	$-0.808411\pi$
$503$	−36.9726	−1.64853	−0.824264	+	0.566205i	$0.808411\pi$
$504$	8.06211	0.359115
$505$	1.26767	0.0564106
$506$	−30.6703	−1.36346
$507$	−79.0887	−3.51245
$508$	12.7910	0.567511
$509$	−36.9208	−1.63649	−0.818243	−	0.574872i	$-0.805052\pi$
$509$	−36.9208	−1.63649	−0.818243	+	0.574872i	$0.805052\pi$
$510$	3.18378	0.140980
$511$	−7.44060	−0.329153
$512$	−1.00000	−0.0441942
$513$	19.9626	0.881371
$514$	−4.04634	−0.178476
$515$	6.91210	0.304584
$516$	−7.04710	−0.310231
$517$	−6.06353	−0.266674
$518$	51.0405	2.24259
$519$	24.6217	1.08077
$520$	−3.34777	−0.146810
$521$	15.3975	0.674577	0.337288	−	0.941401i	$-0.390490\pi$
$521$	15.3975	0.674577	0.337288	+	0.941401i	$0.390490\pi$
$522$	−15.4591	−0.676626
$523$	−13.7930	−0.603126	−0.301563	−	0.953446i	$-0.597508\pi$
$523$	−13.7930	−0.603126	−0.301563	+	0.953446i	$0.597508\pi$
$524$	19.4565	0.849963
$525$	−46.8678	−2.04548
$526$	−19.2780	−0.840561
$527$	−14.2722	−0.621705
$528$	10.2269	0.445068
$529$	20.1526	0.876201
$530$	2.85758	0.124125
$531$	−2.44739	−0.106208
$532$	−33.9969	−1.47395
$533$	47.3011	2.04884
$534$	−26.5084	−1.14713
$535$	3.87026	0.167326
$536$	−13.6025	−0.587540
$537$	1.73322	0.0747938
$538$	−10.8645	−0.468401
$539$	−61.1923	−2.63574
$540$	−1.25786	−0.0541295
$541$	7.60352	0.326901	0.163450	−	0.986552i	$-0.447738\pi$
$541$	7.60352	0.326901	0.163450	+	0.986552i	$0.447738\pi$
$542$	−10.4583	−0.449222
$543$	−28.2816	−1.21368
$544$	3.04248	0.130445
$545$	7.57022	0.324273
$546$	68.8280	2.94557
$547$	9.64289	0.412300	0.206150	−	0.978520i	$-0.433906\pi$
$547$	9.64289	0.412300	0.206150	+	0.978520i	$0.433906\pi$
$548$	−14.9172	−0.637230
$549$	−6.42799	−0.274340
$550$	−22.2789	−0.949976
$551$	65.1890	2.77715
$552$	−14.3891	−0.612439
$553$	18.4566	0.784855
$554$	8.57442	0.364292
$555$	11.9114	0.505611
$556$	−3.90577	−0.165641
$557$	−5.33371	−0.225996	−0.112998	−	0.993595i	$-0.536045\pi$
$557$	−5.33371	−0.225996	−0.112998	+	0.993595i	$0.536045\pi$
$558$	−8.43421	−0.357049
$559$	−22.5451	−0.953555
$560$	2.14217	0.0905230
$561$	−31.1151	−1.31368
$562$	−11.2164	−0.473136
$563$	−11.6359	−0.490394	−0.245197	−	0.969473i	$-0.578853\pi$
$563$	−11.6359	−0.490394	−0.245197	+	0.969473i	$0.578853\pi$
$564$	−2.84472	−0.119784
$565$	3.03754	0.127790
$566$	−9.49963	−0.399299
$567$	50.0470	2.10178
$568$	−13.5239	−0.567451
$569$	28.0953	1.17782	0.588908	−	0.808200i	$-0.299558\pi$
$569$	28.0953	1.17782	0.588908	+	0.808200i	$0.299558\pi$
$570$	−7.93392	−0.332315
$571$	7.57991	0.317210	0.158605	−	0.987342i	$-0.449300\pi$
$571$	7.57991	0.317210	0.158605	+	0.987342i	$0.449300\pi$
$572$	32.7178	1.36800
$573$	−20.0137	−0.836084
$574$	−30.2669	−1.26332
$575$	31.3461	1.30722
$576$	1.79797	0.0749153
$577$	23.1025	0.961771	0.480885	−	0.876784i	$-0.340315\pi$
$577$	23.1025	0.961771	0.480885	+	0.876784i	$0.340315\pi$
$578$	7.74332	0.322080
$579$	−45.8648	−1.90608
$580$	−4.10760	−0.170559
$581$	−16.4401	−0.682051
$582$	−26.8100	−1.11131
$583$	−27.9271	−1.15662
$584$	−1.65936	−0.0686649
$585$	6.01919	0.248863
$586$	5.78324	0.238903
$587$	−5.88809	−0.243028	−0.121514	−	0.992590i	$-0.538775\pi$
$587$	−5.88809	−0.243028	−0.121514	+	0.992590i	$0.538775\pi$
$588$	−28.7085	−1.18392
$589$	35.5660	1.46547
$590$	−0.650290	−0.0267720
$591$	−54.2713	−2.23242
$592$	11.3828	0.467829
$593$	−36.9225	−1.51622	−0.758112	−	0.652124i	$-0.773878\pi$
$593$	−36.9225	−1.51622	−0.758112	+	0.652124i	$0.773878\pi$
$594$	12.2930	0.504389
$595$	−6.51749	−0.267191
$596$	−9.72807	−0.398477
$597$	−25.2835	−1.03478
$598$	−46.0334	−1.88245
$599$	28.0411	1.14573	0.572865	−	0.819650i	$-0.305832\pi$
$599$	28.0411	1.14573	0.572865	+	0.819650i	$0.305832\pi$
$600$	−10.4522	−0.426710
$601$	28.8546	1.17700	0.588502	−	0.808496i	$-0.299718\pi$
$601$	28.8546	1.17700	0.588502	+	0.808496i	$0.299718\pi$
$602$	14.4261	0.587964
$603$	24.4569	0.995964
$604$	−3.60881	−0.146840
$605$	−5.15887	−0.209738
$606$	−5.81231	−0.236109
$607$	33.0271	1.34053	0.670265	−	0.742122i	$-0.266181\pi$
$607$	33.0271	1.34053	0.670265	+	0.742122i	$0.266181\pi$
$608$	−7.58181	−0.307483
$609$	84.4495	3.42207
$610$	−1.70797	−0.0691536
$611$	−9.10083	−0.368180
$612$	−5.47028	−0.221123
$613$	−28.8576	−1.16555	−0.582774	−	0.812634i	$-0.698033\pi$
$613$	−28.8576	−1.16555	−0.582774	+	0.812634i	$0.698033\pi$
$614$	14.6581	0.591553
$615$	−7.06345	−0.284826
$616$	−20.9354	−0.843511
$617$	30.2358	1.21725	0.608625	−	0.793458i	$-0.291722\pi$
$617$	30.2358	1.21725	0.608625	+	0.793458i	$0.291722\pi$
$618$	−31.6922	−1.27485
$619$	17.0152	0.683899	0.341949	−	0.939718i	$-0.388913\pi$
$619$	17.0152	0.683899	0.341949	+	0.939718i	$0.388913\pi$
$620$	−2.24104	−0.0900021
$621$	−17.2961	−0.694069
$622$	−8.50417	−0.340986
$623$	54.2651	2.17409
$624$	15.3496	0.614478
$625$	21.6286	0.865146
$626$	33.1627	1.32545
$627$	77.5382	3.09658
$628$	9.55258	0.381189
$629$	−34.6318	−1.38086
$630$	−3.85155	−0.153449
$631$	−25.5238	−1.01609	−0.508044	−	0.861331i	$-0.669631\pi$
$631$	−25.5238	−1.01609	−0.508044	+	0.861331i	$0.669631\pi$
$632$	4.11610	0.163729
$633$	−20.4310	−0.812060
$634$	−5.59028	−0.222018
$635$	−6.11072	−0.242497
$636$	−13.1021	−0.519531
$637$	−91.8442	−3.63900
$638$	40.1436	1.58930
$639$	24.3156	0.961908
$640$	0.477734	0.0188841
$641$	29.5560	1.16739	0.583695	−	0.811973i	$-0.301606\pi$
$641$	29.5560	1.16739	0.583695	+	0.811973i	$0.301606\pi$
$642$	−17.7453	−0.700350
$643$	25.4845	1.00501	0.502504	−	0.864575i	$-0.332412\pi$
$643$	25.4845	1.00501	0.502504	+	0.864575i	$0.332412\pi$
$644$	29.4558	1.16072
$645$	3.36664	0.132561
$646$	23.0675	0.907578
$647$	−42.0784	−1.65427	−0.827136	−	0.562002i	$-0.810031\pi$
$647$	−42.0784	−1.65427	−0.827136	+	0.562002i	$0.810031\pi$
$648$	11.1612	0.438454
$649$	6.35529	0.249467
$650$	−33.4387	−1.31157
$651$	46.0742	1.80579
$652$	−20.6949	−0.810474
$653$	−22.9030	−0.896263	−0.448131	−	0.893968i	$-0.647910\pi$
$653$	−22.9030	−0.896263	−0.448131	+	0.893968i	$0.647910\pi$
$654$	−34.7097	−1.35726
$655$	−9.29505	−0.363188
$656$	−6.74997	−0.263542
$657$	2.98348	0.116397
$658$	5.82342	0.227020
$659$	−19.9912	−0.778747	−0.389374	−	0.921080i	$-0.627308\pi$
$659$	−19.9912	−0.778747	−0.389374	+	0.921080i	$0.627308\pi$
$660$	−4.88573	−0.190177
$661$	−46.3125	−1.80135	−0.900673	−	0.434497i	$-0.856926\pi$
$661$	−46.3125	−1.80135	−0.900673	+	0.434497i	$0.856926\pi$
$662$	2.80590	0.109054
$663$	−46.7010	−1.81372
$664$	−3.66638	−0.142283
$665$	16.2415	0.629818
$666$	−20.4659	−0.793036
$667$	−56.4814	−2.18697
$668$	−6.75231	−0.261255
$669$	19.9528	0.771421
$670$	6.49840	0.251055
$671$	16.6920	0.644386
$672$	−9.82190	−0.378888
$673$	−28.2287	−1.08814	−0.544068	−	0.839041i	$-0.683117\pi$
$673$	−28.2287	−1.08814	−0.544068	+	0.839041i	$0.683117\pi$
$674$	15.2732	0.588302
$675$	−12.5639	−0.483584
$676$	36.1065	1.38871
$677$	−29.4951	−1.13359	−0.566794	−	0.823860i	$-0.691816\pi$
$677$	−29.4951	−1.13359	−0.566794	+	0.823860i	$0.691816\pi$
$678$	−13.9272	−0.534871
$679$	54.8826	2.10620
$680$	−1.45350	−0.0557390
$681$	5.75729	0.220620
$682$	21.9016	0.838658
$683$	27.4925	1.05197	0.525986	−	0.850493i	$-0.323696\pi$
$683$	27.4925	1.05197	0.525986	+	0.850493i	$0.323696\pi$
$684$	13.6318	0.521227
$685$	7.12644	0.272287
$686$	27.3810	1.04541
$687$	38.8972	1.48402
$688$	3.21723	0.122656
$689$	−41.9161	−1.59688
$690$	6.87414	0.261694
$691$	−25.7858	−0.980937	−0.490469	−	0.871459i	$-0.663174\pi$
$691$	−25.7858	−0.980937	−0.490469	+	0.871459i	$0.663174\pi$
$692$	−11.2406	−0.427304
$693$	37.6412	1.42987
$694$	−16.5625	−0.628704
$695$	1.86592	0.0707783
$696$	18.8335	0.713881
$697$	20.5366	0.777881
$698$	8.37004	0.316811
$699$	33.2402	1.25726
$700$	21.3967	0.808718
$701$	−12.7766	−0.482564	−0.241282	−	0.970455i	$-0.577568\pi$
$701$	−12.7766	−0.482564	−0.241282	+	0.970455i	$0.577568\pi$
$702$	18.4508	0.696379
$703$	86.3020	3.25494
$704$	−4.66890	−0.175966
$705$	1.35902	0.0511837
$706$	10.5971	0.398829
$707$	11.8984	0.447484
$708$	2.98160	0.112055
$709$	−39.0686	−1.46725	−0.733627	−	0.679553i	$-0.762174\pi$
$709$	−39.0686	−1.46725	−0.733627	+	0.679553i	$0.762174\pi$
$710$	6.46083	0.242471
$711$	−7.40061	−0.277544
$712$	12.1019	0.453538
$713$	−30.8153	−1.15404
$714$	29.8829	1.11834
$715$	−15.6304	−0.584544
$716$	−0.791269	−0.0295711
$717$	−6.01039	−0.224462
$718$	3.52197	0.131439
$719$	−5.11051	−0.190590	−0.0952950	−	0.995449i	$-0.530379\pi$
$719$	−5.11051	−0.190590	−0.0952950	+	0.995449i	$0.530379\pi$
$720$	−0.858951	−0.0320112
$721$	64.8770	2.41615
$722$	−38.4838	−1.43222
$723$	−57.7868	−2.14911
$724$	12.9115	0.479850
$725$	−41.0281	−1.52375
$726$	23.6536	0.877866
$727$	−10.3359	−0.383336	−0.191668	−	0.981460i	$-0.561390\pi$
$727$	−10.3359	−0.383336	−0.191668	+	0.981460i	$0.561390\pi$
$728$	−31.4222	−1.16458
$729$	−2.76558	−0.102429
$730$	0.792734	0.0293404
$731$	−9.78835	−0.362035
$732$	7.83109	0.289445
$733$	12.0811	0.446225	0.223113	−	0.974793i	$-0.428378\pi$
$733$	12.0811	0.446225	0.223113	+	0.974793i	$0.428378\pi$
$734$	−35.2284	−1.30030
$735$	13.7150	0.505887
$736$	6.56907	0.242139
$737$	−63.5089	−2.33938
$738$	12.1362	0.446741
$739$	19.5896	0.720615	0.360308	−	0.932834i	$-0.382672\pi$
$739$	19.5896	0.720615	0.360308	+	0.932834i	$0.382672\pi$
$740$	−5.43794	−0.199903
$741$	116.378	4.27525
$742$	26.8212	0.984637
$743$	16.3319	0.599159	0.299580	−	0.954071i	$-0.403154\pi$
$743$	16.3319	0.599159	0.299580	+	0.954071i	$0.403154\pi$
$744$	10.2752	0.376708
$745$	4.64743	0.170269
$746$	−23.2208	−0.850174
$747$	6.59204	0.241190
$748$	14.2050	0.519387
$749$	36.3263	1.32733
$750$	10.2256	0.373386
$751$	30.2439	1.10362	0.551809	−	0.833971i	$-0.313938\pi$
$751$	30.2439	1.10362	0.551809	+	0.833971i	$0.313938\pi$
$752$	1.29871	0.0473590
$753$	−31.1338	−1.13458
$754$	60.2520	2.19425
$755$	1.72405	0.0627446
$756$	−11.8062	−0.429389
$757$	4.49454	0.163357	0.0816784	−	0.996659i	$-0.473972\pi$
$757$	4.49454	0.163357	0.0816784	+	0.996659i	$0.473972\pi$
$758$	0.150272	0.00545813
$759$	−67.1810	−2.43852
$760$	3.62209	0.131387
$761$	−24.3893	−0.884110	−0.442055	−	0.896988i	$-0.645750\pi$
$761$	−24.3893	−0.884110	−0.442055	+	0.896988i	$0.645750\pi$
$762$	28.0179	1.01498
$763$	71.0541	2.57233
$764$	9.13689	0.330561
$765$	2.61334	0.0944855
$766$	−10.3380	−0.373526
$767$	9.53873	0.344424
$768$	−2.19043	−0.0790402
$769$	22.2189	0.801233	0.400617	−	0.916246i	$-0.368796\pi$
$769$	22.2189	0.801233	0.400617	+	0.916246i	$0.368796\pi$
$770$	10.0016	0.360431
$771$	−8.86321	−0.319201
$772$	20.9387	0.753602
$773$	15.0025	0.539601	0.269801	−	0.962916i	$-0.413042\pi$
$773$	15.0025	0.539601	0.269801	+	0.962916i	$0.413042\pi$
$774$	−5.78447	−0.207919
$775$	−22.3842	−0.804065
$776$	12.2396	0.439377
$777$	111.800	4.01082
$778$	15.8140	0.566958
$779$	−51.1770	−1.83360
$780$	−7.33305	−0.262565
$781$	−63.1417	−2.25939
$782$	−19.9862	−0.714707
$783$	22.6384	0.809032
$784$	13.1064	0.468085
$785$	−4.56359	−0.162882
$786$	42.6181	1.52014
$787$	37.2660	1.32839	0.664196	−	0.747559i	$-0.268774\pi$
$787$	37.2660	1.32839	0.664196	+	0.747559i	$0.268774\pi$
$788$	24.7766	0.882630
$789$	−42.2271	−1.50332
$790$	−1.96640	−0.0699613
$791$	28.5103	1.01371
$792$	8.39453	0.298287
$793$	25.0532	0.889665
$794$	−28.1718	−0.999778
$795$	6.25931	0.221995
$796$	11.5427	0.409121
$797$	1.09380	0.0387442	0.0193721	−	0.999812i	$-0.493833\pi$
$797$	1.09380	0.0387442	0.0193721	+	0.999812i	$0.493833\pi$
$798$	−74.4677	−2.63613
$799$	−3.95129	−0.139787
$800$	4.77177	0.168708
$801$	−21.7589	−0.768811
$802$	10.3710	0.366212
$803$	−7.74739	−0.273399
$804$	−29.7954	−1.05080
$805$	−14.0720	−0.495974
$806$	32.8725	1.15788
$807$	−23.7979	−0.837725
$808$	2.65351	0.0933500
$809$	6.89211	0.242314	0.121157	−	0.992633i	$-0.461340\pi$
$809$	6.89211	0.242314	0.121157	+	0.992633i	$0.461340\pi$
$810$	−5.33209	−0.187351
$811$	19.2784	0.676957	0.338479	−	0.940974i	$-0.390088\pi$
$811$	19.2784	0.676957	0.338479	+	0.940974i	$0.390088\pi$
$812$	−38.5539	−1.35298
$813$	−22.9081	−0.803422
$814$	53.1450	1.86273
$815$	9.88665	0.346314
$816$	6.66433	0.233298
$817$	24.3924	0.853382
$818$	−6.36994	−0.222720
$819$	56.4961	1.97413
$820$	3.22469	0.112611
$821$	33.0490	1.15342	0.576709	−	0.816950i	$-0.304337\pi$
$821$	33.0490	1.15342	0.576709	+	0.816950i	$0.304337\pi$
$822$	−32.6750	−1.13967
$823$	31.7826	1.10787	0.553936	−	0.832560i	$-0.313125\pi$
$823$	31.7826	1.10787	0.553936	+	0.832560i	$0.313125\pi$
$824$	14.4685	0.504034
$825$	−48.8003	−1.69901
$826$	−6.10362	−0.212372
$827$	33.9085	1.17912	0.589558	−	0.807726i	$-0.299302\pi$
$827$	33.9085	1.17912	0.589558	+	0.807726i	$0.299302\pi$
$828$	−11.8110	−0.410460
$829$	−43.0324	−1.49458	−0.747289	−	0.664499i	$-0.768645\pi$
$829$	−43.0324	−1.49458	−0.747289	+	0.664499i	$0.768645\pi$
$830$	1.75156	0.0607974
$831$	18.7816	0.651528
$832$	−7.00761	−0.242945
$833$	−39.8758	−1.38162
$834$	−8.55530	−0.296246
$835$	3.22581	0.111634
$836$	−35.3987	−1.22429
$837$	12.3511	0.426918
$838$	−7.49645	−0.258960
$839$	19.3411	0.667729	0.333864	−	0.942621i	$-0.391647\pi$
$839$	19.3411	0.667729	0.333864	+	0.942621i	$0.391647\pi$
$840$	4.69226	0.161898
$841$	44.9271	1.54921
$842$	−4.78557	−0.164922
$843$	−24.5687	−0.846192
$844$	9.32741	0.321063
$845$	−17.2493	−0.593395
$846$	−2.33503	−0.0802801
$847$	−48.4211	−1.66377
$848$	5.98152	0.205406
$849$	−20.8082	−0.714137
$850$	−14.5180	−0.497964
$851$	−74.7742	−2.56323
$852$	−29.6231	−1.01487
$853$	−38.4721	−1.31726	−0.658631	−	0.752466i	$-0.728864\pi$
$853$	−38.4721	−1.31726	−0.658631	+	0.752466i	$0.728864\pi$
$854$	−16.0310	−0.548569
$855$	−6.51240	−0.222719
$856$	8.10129	0.276896
$857$	−17.7123	−0.605041	−0.302520	−	0.953143i	$-0.597828\pi$
$857$	−17.7123	−0.605041	−0.302520	+	0.953143i	$0.597828\pi$
$858$	71.6659	2.44663
$859$	−44.0434	−1.50274	−0.751371	−	0.659880i	$-0.770607\pi$
$859$	−44.0434	−1.50274	−0.751371	+	0.659880i	$0.770607\pi$
$860$	−1.53698	−0.0524106
$861$	−66.2975	−2.25941
$862$	12.4914	0.425457
$863$	−30.8735	−1.05095	−0.525473	−	0.850810i	$-0.676112\pi$
$863$	−30.8735	−1.05095	−0.525473	+	0.850810i	$0.676112\pi$
$864$	−2.63296	−0.0895752
$865$	5.37002	0.182586
$866$	−34.4731	−1.17144
$867$	16.9612	0.576032
$868$	−21.0344	−0.713953
$869$	19.2176	0.651913
$870$	−8.99739	−0.305040
$871$	−95.3213	−3.22984
$872$	15.8461	0.536616
$873$	−22.0064	−0.744805
$874$	49.8054	1.68469
$875$	−20.9328	−0.707656
$876$	−3.63471	−0.122805
$877$	−7.84380	−0.264866	−0.132433	−	0.991192i	$-0.542279\pi$
$877$	−7.84380	−0.264866	−0.132433	+	0.991192i	$0.542279\pi$
$878$	25.6605	0.865999
$879$	12.6678	0.427273
$880$	2.23049	0.0751899
$881$	36.6011	1.23312	0.616561	−	0.787307i	$-0.288525\pi$
$881$	36.6011	1.23312	0.616561	+	0.787307i	$0.288525\pi$
$882$	−23.5648	−0.793469
$883$	36.3508	1.22330	0.611651	−	0.791127i	$-0.290506\pi$
$883$	36.3508	1.22330	0.611651	+	0.791127i	$0.290506\pi$
$884$	21.3205	0.717086
$885$	−1.42441	−0.0478811
$886$	28.8276	0.968481
$887$	−26.7914	−0.899569	−0.449784	−	0.893137i	$-0.648499\pi$
$887$	−26.7914	−0.899569	−0.449784	+	0.893137i	$0.648499\pi$
$888$	24.9331	0.836701
$889$	−57.3552	−1.92363
$890$	−5.78150	−0.193796
$891$	52.1106	1.74577
$892$	−9.10911	−0.304996
$893$	9.84654	0.329502
$894$	−21.3086	−0.712667
$895$	0.378016	0.0126357
$896$	4.48401	0.149800
$897$	−100.833	−3.36671
$898$	10.2267	0.341268
$899$	40.3333	1.34519
$900$	−8.57949	−0.285983
$901$	−18.1986	−0.606285
$902$	−31.5149	−1.04933
$903$	31.5993	1.05156
$904$	6.35822	0.211471
$905$	−6.16824	−0.205039
$906$	−7.90482	−0.262620
$907$	−21.6555	−0.719061	−0.359530	−	0.933133i	$-0.617063\pi$
$907$	−21.6555	−0.719061	−0.359530	+	0.933133i	$0.617063\pi$
$908$	−2.62839	−0.0872261
$909$	−4.77092	−0.158241
$910$	15.0115	0.497625
$911$	−27.8449	−0.922542	−0.461271	−	0.887259i	$-0.652606\pi$
$911$	−27.8449	−0.922542	−0.461271	+	0.887259i	$0.652606\pi$
$912$	−16.6074	−0.549926
$913$	−17.1180	−0.566522
$914$	1.77486	0.0587072
$915$	−3.74118	−0.123679
$916$	−17.7578	−0.586735
$917$	−87.2433	−2.88103
$918$	8.01073	0.264394
$919$	−58.6223	−1.93377	−0.966886	−	0.255210i	$-0.917856\pi$
$919$	−58.6223	−1.93377	−0.966886	+	0.255210i	$0.917856\pi$
$920$	−3.13827	−0.103466
$921$	32.1075	1.05798
$922$	17.8727	0.588604
$923$	−94.7702	−3.11940
$924$	−45.8574	−1.50860
$925$	−54.3160	−1.78590
$926$	−12.0765	−0.396857
$927$	−26.0139	−0.854409
$928$	−8.59809	−0.282246
$929$	53.8364	1.76632	0.883158	−	0.469075i	$-0.155413\pi$
$929$	53.8364	1.76632	0.883158	+	0.469075i	$0.155413\pi$
$930$	−4.90882	−0.160967
$931$	99.3699	3.25672
$932$	−15.1752	−0.497080
$933$	−18.6278	−0.609845
$934$	−42.8339	−1.40157
$935$	−6.78623	−0.221933
$936$	12.5995	0.411826
$937$	54.1740	1.76979	0.884893	−	0.465794i	$-0.154231\pi$
$937$	54.1740	1.76979	0.884893	+	0.465794i	$0.154231\pi$
$938$	60.9940	1.99152
$939$	72.6406	2.37054
$940$	−0.620437	−0.0202364
$941$	−32.7714	−1.06832	−0.534159	−	0.845384i	$-0.679372\pi$
$941$	−32.7714	−1.06832	−0.534159	+	0.845384i	$0.679372\pi$
$942$	20.9242	0.681748
$943$	44.3410	1.44394
$944$	−1.36120	−0.0443032
$945$	5.64024	0.183477
$946$	15.0209	0.488372
$947$	44.7820	1.45522	0.727610	−	0.685991i	$-0.240631\pi$
$947$	44.7820	1.45522	0.727610	+	0.685991i	$0.240631\pi$
$948$	9.01600	0.292826
$949$	−11.6282	−0.377466
$950$	36.1786	1.17379
$951$	−12.2451	−0.397074
$952$	−13.6425	−0.442156
$953$	−14.0946	−0.456569	−0.228284	−	0.973595i	$-0.573312\pi$
$953$	−14.0946	−0.456569	−0.228284	+	0.973595i	$0.573312\pi$
$954$	−10.7546	−0.348192
$955$	−4.36501	−0.141248
$956$	2.74394	0.0887452
$957$	87.9316	2.84242
$958$	−20.3886	−0.658726
$959$	66.8888	2.15995
$960$	1.04644	0.0337738
$961$	−8.99482	−0.290156
$962$	79.7660	2.57176
$963$	−14.5659	−0.469378
$964$	26.3815	0.849691
$965$	−10.0032	−0.322013
$966$	64.5207	2.07592
$967$	19.3380	0.621868	0.310934	−	0.950432i	$-0.399358\pi$
$967$	19.3380	0.621868	0.310934	+	0.950432i	$0.399358\pi$
$968$	−10.7986	−0.347081
$969$	50.5276	1.62318
$970$	−5.84728	−0.187745
$971$	−24.5251	−0.787048	−0.393524	−	0.919314i	$-0.628744\pi$
$971$	−24.5251	−0.787048	−0.393524	+	0.919314i	$0.628744\pi$
$972$	16.5489	0.530807
$973$	17.5135	0.561457
$974$	−22.7947	−0.730390
$975$	−73.2450	−2.34572
$976$	−3.57514	−0.114438
$977$	−1.36573	−0.0436937	−0.0218468	−	0.999761i	$-0.506955\pi$
$977$	−1.36573	−0.0436937	−0.0218468	+	0.999761i	$0.506955\pi$
$978$	−45.3306	−1.44951
$979$	56.5026	1.80583
$980$	−6.26136	−0.200012
$981$	−28.4908	−0.909640
$982$	39.1986	1.25088
$983$	−32.9794	−1.05188	−0.525940	−	0.850521i	$-0.676287\pi$
$983$	−32.9794	−1.05188	−0.525940	+	0.850521i	$0.676287\pi$
$984$	−14.7853	−0.471338
$985$	−11.8366	−0.377146
$986$	26.1595	0.833088
$987$	12.7558	0.406021
$988$	−53.1303	−1.69030
$989$	−21.1342	−0.672028
$990$	−4.01035	−0.127457
$991$	−5.18537	−0.164719	−0.0823594	−	0.996603i	$-0.526246\pi$
$991$	−5.18537	−0.164719	−0.0823594	+	0.996603i	$0.526246\pi$
$992$	−4.69097	−0.148938
$993$	6.14611	0.195041
$994$	60.6414	1.92343
$995$	−5.51436	−0.174817
$996$	−8.03095	−0.254470
$997$	48.0319	1.52119	0.760593	−	0.649229i	$-0.224908\pi$
$997$	48.0319	1.52119	0.760593	+	0.649229i	$0.224908\pi$
$998$	−24.7566	−0.783657
$999$	29.9704	0.948222

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.14	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.14	✓	64	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.19043 q^{3} +1.00000 q^{4} -0.477734 q^{5} +2.19043 q^{6} -4.48401 q^{7} -1.00000 q^{8} +1.79797 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.19043 q^{3} +1.00000 q^{4} -0.477734 q^{5} +2.19043 q^{6} -4.48401 q^{7} -1.00000 q^{8} +1.79797 q^{9} +0.477734 q^{10} -4.66890 q^{11} -2.19043 q^{12} -7.00761 q^{13} +4.48401 q^{14} +1.04644 q^{15} +1.00000 q^{16} -3.04248 q^{17} -1.79797 q^{18} +7.58181 q^{19} -0.477734 q^{20} +9.82190 q^{21} +4.66890 q^{22} -6.56907 q^{23} +2.19043 q^{24} -4.77177 q^{25} +7.00761 q^{26} +2.63296 q^{27} -4.48401 q^{28} +8.59809 q^{29} -1.04644 q^{30} +4.69097 q^{31} -1.00000 q^{32} +10.2269 q^{33} +3.04248 q^{34} +2.14217 q^{35} +1.79797 q^{36} +11.3828 q^{37} -7.58181 q^{38} +15.3496 q^{39} +0.477734 q^{40} -6.74997 q^{41} -9.82190 q^{42} +3.21723 q^{43} -4.66890 q^{44} -0.858951 q^{45} +6.56907 q^{46} +1.29871 q^{47} -2.19043 q^{48} +13.1064 q^{49} +4.77177 q^{50} +6.66433 q^{51} -7.00761 q^{52} +5.98152 q^{53} -2.63296 q^{54} +2.23049 q^{55} +4.48401 q^{56} -16.6074 q^{57} -8.59809 q^{58} -1.36120 q^{59} +1.04644 q^{60} -3.57514 q^{61} -4.69097 q^{62} -8.06211 q^{63} +1.00000 q^{64} +3.34777 q^{65} -10.2269 q^{66} +13.6025 q^{67} -3.04248 q^{68} +14.3891 q^{69} -2.14217 q^{70} +13.5239 q^{71} -1.79797 q^{72} +1.65936 q^{73} -11.3828 q^{74} +10.4522 q^{75} +7.58181 q^{76} +20.9354 q^{77} -15.3496 q^{78} -4.11610 q^{79} -0.477734 q^{80} -11.1612 q^{81} +6.74997 q^{82} +3.66638 q^{83} +9.82190 q^{84} +1.45350 q^{85} -3.21723 q^{86} -18.8335 q^{87} +4.66890 q^{88} -12.1019 q^{89} +0.858951 q^{90} +31.4222 q^{91} -6.56907 q^{92} -10.2752 q^{93} -1.29871 q^{94} -3.62209 q^{95} +2.19043 q^{96} -12.2396 q^{97} -13.1064 q^{98} -8.39453 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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