LMFDB - Embedded newform 4022.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.82634 q^{3} +1.00000 q^{4} +2.27969 q^{5} +2.82634 q^{6} -0.755653 q^{7} -1.00000 q^{8} +4.98821 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.82634 q^{3} +1.00000 q^{4} +2.27969 q^{5} +2.82634 q^{6} -0.755653 q^{7} -1.00000 q^{8} +4.98821 q^{9} -2.27969 q^{10} +1.66633 q^{11} -2.82634 q^{12} -0.423112 q^{13} +0.755653 q^{14} -6.44320 q^{15} +1.00000 q^{16} -4.17115 q^{17} -4.98821 q^{18} -0.322325 q^{19} +2.27969 q^{20} +2.13573 q^{21} -1.66633 q^{22} +5.28854 q^{23} +2.82634 q^{24} +0.197007 q^{25} +0.423112 q^{26} -5.61936 q^{27} -0.755653 q^{28} +3.29496 q^{29} +6.44320 q^{30} +5.47613 q^{31} -1.00000 q^{32} -4.70963 q^{33} +4.17115 q^{34} -1.72266 q^{35} +4.98821 q^{36} -9.38152 q^{37} +0.322325 q^{38} +1.19586 q^{39} -2.27969 q^{40} -6.84829 q^{41} -2.13573 q^{42} +2.13202 q^{43} +1.66633 q^{44} +11.3716 q^{45} -5.28854 q^{46} -11.3071 q^{47} -2.82634 q^{48} -6.42899 q^{49} -0.197007 q^{50} +11.7891 q^{51} -0.423112 q^{52} -12.0539 q^{53} +5.61936 q^{54} +3.79873 q^{55} +0.755653 q^{56} +0.911001 q^{57} -3.29496 q^{58} +8.17921 q^{59} -6.44320 q^{60} -2.64920 q^{61} -5.47613 q^{62} -3.76936 q^{63} +1.00000 q^{64} -0.964567 q^{65} +4.70963 q^{66} +12.2877 q^{67} -4.17115 q^{68} -14.9472 q^{69} +1.72266 q^{70} -4.51547 q^{71} -4.98821 q^{72} +4.24126 q^{73} +9.38152 q^{74} -0.556808 q^{75} -0.322325 q^{76} -1.25917 q^{77} -1.19586 q^{78} -0.712037 q^{79} +2.27969 q^{80} +0.917597 q^{81} +6.84829 q^{82} -1.59908 q^{83} +2.13573 q^{84} -9.50896 q^{85} -2.13202 q^{86} -9.31267 q^{87} -1.66633 q^{88} +14.7741 q^{89} -11.3716 q^{90} +0.319726 q^{91} +5.28854 q^{92} -15.4774 q^{93} +11.3071 q^{94} -0.734803 q^{95} +2.82634 q^{96} +9.98515 q^{97} +6.42899 q^{98} +8.31202 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) $ 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * 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
$3$	−2.82634	−1.63179	−0.815895	−	0.578201i	$-0.803755\pi$
$3$	−2.82634	−1.63179	−0.815895	+	0.578201i	$0.803755\pi$
$4$	1.00000	0.500000
$5$	2.27969	1.01951	0.509755	−	0.860320i	$-0.329736\pi$
$5$	2.27969	1.01951	0.509755	+	0.860320i	$0.329736\pi$
$6$	2.82634	1.15385
$7$	−0.755653	−0.285610	−0.142805	−	0.989751i	$-0.545612\pi$
$7$	−0.755653	−0.285610	−0.142805	+	0.989751i	$0.545612\pi$
$8$	−1.00000	−0.353553
$9$	4.98821	1.66274
$10$	−2.27969	−0.720903
$11$	1.66633	0.502419	0.251209	−	0.967933i	$-0.419172\pi$
$11$	1.66633	0.502419	0.251209	+	0.967933i	$0.419172\pi$
$12$	−2.82634	−0.815895
$13$	−0.423112	−0.117350	−0.0586751	−	0.998277i	$-0.518688\pi$
$13$	−0.423112	−0.117350	−0.0586751	+	0.998277i	$0.518688\pi$
$14$	0.755653	0.201957
$15$	−6.44320	−1.66363
$16$	1.00000	0.250000
$17$	−4.17115	−1.01165	−0.505827	−	0.862635i	$-0.668812\pi$
$17$	−4.17115	−1.01165	−0.505827	+	0.862635i	$0.668812\pi$
$18$	−4.98821	−1.17573
$19$	−0.322325	−0.0739465	−0.0369732	−	0.999316i	$-0.511772\pi$
$19$	−0.322325	−0.0739465	−0.0369732	+	0.999316i	$0.511772\pi$
$20$	2.27969	0.509755
$21$	2.13573	0.466055
$22$	−1.66633	−0.355264
$23$	5.28854	1.10274	0.551368	−	0.834262i	$-0.314106\pi$
$23$	5.28854	1.10274	0.551368	+	0.834262i	$0.314106\pi$
$24$	2.82634	0.576925
$25$	0.197007	0.0394013
$26$	0.423112	0.0829792
$27$	−5.61936	−1.08145
$28$	−0.755653	−0.142805
$29$	3.29496	0.611858	0.305929	−	0.952054i	$-0.401033\pi$
$29$	3.29496	0.611858	0.305929	+	0.952054i	$0.401033\pi$
$30$	6.44320	1.17636
$31$	5.47613	0.983543	0.491771	−	0.870724i	$-0.336350\pi$
$31$	5.47613	0.983543	0.491771	+	0.870724i	$0.336350\pi$
$32$	−1.00000	−0.176777
$33$	−4.70963	−0.819841
$34$	4.17115	0.715347
$35$	−1.72266	−0.291182
$36$	4.98821	0.831368
$37$	−9.38152	−1.54231	−0.771156	−	0.636646i	$-0.780321\pi$
$37$	−9.38152	−1.54231	−0.771156	+	0.636646i	$0.780321\pi$
$38$	0.322325	0.0522881
$39$	1.19586	0.191491
$40$	−2.27969	−0.360451
$41$	−6.84829	−1.06952	−0.534761	−	0.845003i	$-0.679599\pi$
$41$	−6.84829	−1.06952	−0.534761	+	0.845003i	$0.679599\pi$
$42$	−2.13573	−0.329551
$43$	2.13202	0.325130	0.162565	−	0.986698i	$-0.448023\pi$
$43$	2.13202	0.325130	0.162565	+	0.986698i	$0.448023\pi$
$44$	1.66633	0.251209
$45$	11.3716	1.69518
$46$	−5.28854	−0.779752
$47$	−11.3071	−1.64931	−0.824657	−	0.565633i	$-0.808632\pi$
$47$	−11.3071	−1.64931	−0.824657	+	0.565633i	$0.808632\pi$
$48$	−2.82634	−0.407947
$49$	−6.42899	−0.918427
$50$	−0.197007	−0.0278610
$51$	11.7891	1.65081
$52$	−0.423112	−0.0586751
$53$	−12.0539	−1.65574	−0.827868	−	0.560923i	$-0.810446\pi$
$53$	−12.0539	−1.65574	−0.827868	+	0.560923i	$0.810446\pi$
$54$	5.61936	0.764698
$55$	3.79873	0.512221
$56$	0.755653	0.100978
$57$	0.911001	0.120665
$58$	−3.29496	−0.432649
$59$	8.17921	1.06484	0.532421	−	0.846480i	$-0.321282\pi$
$59$	8.17921	1.06484	0.532421	+	0.846480i	$0.321282\pi$
$60$	−6.44320	−0.831813
$61$	−2.64920	−0.339195	−0.169598	−	0.985513i	$-0.554247\pi$
$61$	−2.64920	−0.339195	−0.169598	+	0.985513i	$0.554247\pi$
$62$	−5.47613	−0.695470
$63$	−3.76936	−0.474894
$64$	1.00000	0.125000
$65$	−0.964567	−0.119640
$66$	4.70963	0.579715
$67$	12.2877	1.50118	0.750589	−	0.660770i	$-0.229770\pi$
$67$	12.2877	1.50118	0.750589	+	0.660770i	$0.229770\pi$
$68$	−4.17115	−0.505827
$69$	−14.9472	−1.79943
$70$	1.72266	0.205897
$71$	−4.51547	−0.535887	−0.267944	−	0.963435i	$-0.586344\pi$
$71$	−4.51547	−0.535887	−0.267944	+	0.963435i	$0.586344\pi$
$72$	−4.98821	−0.587866
$73$	4.24126	0.496402	0.248201	−	0.968709i	$-0.420161\pi$
$73$	4.24126	0.496402	0.248201	+	0.968709i	$0.420161\pi$
$74$	9.38152	1.09058
$75$	−0.556808	−0.0642947
$76$	−0.322325	−0.0369732
$77$	−1.25917	−0.143496
$78$	−1.19586	−0.135405
$79$	−0.712037	−0.0801105	−0.0400552	−	0.999197i	$-0.512753\pi$
$79$	−0.712037	−0.0801105	−0.0400552	+	0.999197i	$0.512753\pi$
$80$	2.27969	0.254878
$81$	0.917597	0.101955
$82$	6.84829	0.756267
$83$	−1.59908	−0.175521	−0.0877607	−	0.996142i	$-0.527971\pi$
$83$	−1.59908	−0.175521	−0.0877607	+	0.996142i	$0.527971\pi$
$84$	2.13573	0.233028
$85$	−9.50896	−1.03139
$86$	−2.13202	−0.229902
$87$	−9.31267	−0.998423
$88$	−1.66633	−0.177632
$89$	14.7741	1.56605	0.783023	−	0.621993i	$-0.213677\pi$
$89$	14.7741	1.56605	0.783023	+	0.621993i	$0.213677\pi$
$90$	−11.3716	−1.19867
$91$	0.319726	0.0335164
$92$	5.28854	0.551368
$93$	−15.4774	−1.60493
$94$	11.3071	1.16624
$95$	−0.734803	−0.0753892
$96$	2.82634	0.288462
$97$	9.98515	1.01384	0.506919	−	0.861994i	$-0.330784\pi$
$97$	9.98515	1.01384	0.506919	+	0.861994i	$0.330784\pi$
$98$	6.42899	0.649426
$99$	8.31202	0.835390
$100$	0.197007	0.0197007
$101$	6.05637	0.602631	0.301316	−	0.953524i	$-0.402574\pi$
$101$	6.05637	0.602631	0.301316	+	0.953524i	$0.402574\pi$
$102$	−11.7891	−1.16730
$103$	−16.0297	−1.57945	−0.789727	−	0.613458i	$-0.789778\pi$
$103$	−16.0297	−1.57945	−0.789727	+	0.613458i	$0.789778\pi$
$104$	0.423112	0.0414896
$105$	4.86882	0.475148
$106$	12.0539	1.17078
$107$	−9.59554	−0.927636	−0.463818	−	0.885931i	$-0.653521\pi$
$107$	−9.59554	−0.927636	−0.463818	+	0.885931i	$0.653521\pi$
$108$	−5.61936	−0.540723
$109$	7.76087	0.743356	0.371678	−	0.928362i	$-0.378782\pi$
$109$	7.76087	0.743356	0.371678	+	0.928362i	$0.378782\pi$
$110$	−3.79873	−0.362195
$111$	26.5154	2.51673
$112$	−0.755653	−0.0714025
$113$	9.66967	0.909646	0.454823	−	0.890582i	$-0.349702\pi$
$113$	9.66967	0.909646	0.454823	+	0.890582i	$0.349702\pi$
$114$	−0.911001	−0.0853231
$115$	12.0562	1.12425
$116$	3.29496	0.305929
$117$	−2.11057	−0.195123
$118$	−8.17921	−0.752957
$119$	3.15195	0.288938
$120$	6.44320	0.588181
$121$	−8.22333	−0.747575
$122$	2.64920	0.239847
$123$	19.3556	1.74524
$124$	5.47613	0.491771
$125$	−10.9494	−0.979340
$126$	3.76936	0.335801
$127$	−3.90341	−0.346372	−0.173186	−	0.984889i	$-0.555406\pi$
$127$	−3.90341	−0.346372	−0.173186	+	0.984889i	$0.555406\pi$
$128$	−1.00000	−0.0883883
$129$	−6.02582	−0.530544
$130$	0.964567	0.0845981
$131$	12.0711	1.05465	0.527327	−	0.849662i	$-0.323194\pi$
$131$	12.0711	1.05465	0.527327	+	0.849662i	$0.323194\pi$
$132$	−4.70963	−0.409921
$133$	0.243566	0.0211199
$134$	−12.2877	−1.06149
$135$	−12.8104	−1.10254
$136$	4.17115	0.357674
$137$	−5.02909	−0.429664	−0.214832	−	0.976651i	$-0.568920\pi$
$137$	−5.02909	−0.429664	−0.214832	+	0.976651i	$0.568920\pi$
$138$	14.9472	1.27239
$139$	15.9973	1.35688	0.678438	−	0.734658i	$-0.262657\pi$
$139$	15.9973	1.35688	0.678438	+	0.734658i	$0.262657\pi$
$140$	−1.72266	−0.145591
$141$	31.9578	2.69133
$142$	4.51547	0.378929
$143$	−0.705047	−0.0589590
$144$	4.98821	0.415684
$145$	7.51149	0.623796
$146$	−4.24126	−0.351009
$147$	18.1705	1.49868
$148$	−9.38152	−0.771156
$149$	−11.0573	−0.905853	−0.452926	−	0.891548i	$-0.649620\pi$
$149$	−11.0573	−0.905853	−0.452926	+	0.891548i	$0.649620\pi$
$150$	0.556808	0.0454632
$151$	6.65431	0.541520	0.270760	−	0.962647i	$-0.412725\pi$
$151$	6.65431	0.541520	0.270760	+	0.962647i	$0.412725\pi$
$152$	0.322325	0.0261440
$153$	−20.8066	−1.68211
$154$	1.25917	0.101467
$155$	12.4839	1.00273
$156$	1.19586	0.0957455
$157$	−12.8879	−1.02857	−0.514284	−	0.857620i	$-0.671942\pi$
$157$	−12.8879	−1.02857	−0.514284	+	0.857620i	$0.671942\pi$
$158$	0.712037	0.0566467
$159$	34.0685	2.70181
$160$	−2.27969	−0.180226
$161$	−3.99630	−0.314952
$162$	−0.917597	−0.0720932
$163$	16.9351	1.32646	0.663228	−	0.748417i	$-0.269186\pi$
$163$	16.9351	1.32646	0.663228	+	0.748417i	$0.269186\pi$
$164$	−6.84829	−0.534761
$165$	−10.7365	−0.835837
$166$	1.59908	0.124112
$167$	−0.0822773	−0.00636681	−0.00318341	−	0.999995i	$-0.501013\pi$
$167$	−0.0822773	−0.00636681	−0.00318341	+	0.999995i	$0.501013\pi$
$168$	−2.13573	−0.164775
$169$	−12.8210	−0.986229
$170$	9.50896	0.729304
$171$	−1.60783	−0.122953
$172$	2.13202	0.162565
$173$	7.31902	0.556455	0.278228	−	0.960515i	$-0.410253\pi$
$173$	7.31902	0.556455	0.278228	+	0.960515i	$0.410253\pi$
$174$	9.31267	0.705992
$175$	−0.148869	−0.0112534
$176$	1.66633	0.125605
$177$	−23.1172	−1.73760
$178$	−14.7741	−1.10736
$179$	−0.775960	−0.0579980	−0.0289990	−	0.999579i	$-0.509232\pi$
$179$	−0.775960	−0.0579980	−0.0289990	+	0.999579i	$0.509232\pi$
$180$	11.3716	0.847588
$181$	−14.2560	−1.05964	−0.529820	−	0.848110i	$-0.677740\pi$
$181$	−14.2560	−1.05964	−0.529820	+	0.848110i	$0.677740\pi$
$182$	−0.319726	−0.0236997
$183$	7.48755	0.553496
$184$	−5.28854	−0.389876
$185$	−21.3870	−1.57240
$186$	15.4774	1.13486
$187$	−6.95054	−0.508274
$188$	−11.3071	−0.824657
$189$	4.24628	0.308872
$190$	0.734803	0.0533082
$191$	7.60207	0.550067	0.275033	−	0.961435i	$-0.411311\pi$
$191$	7.60207	0.550067	0.275033	+	0.961435i	$0.411311\pi$
$192$	−2.82634	−0.203974
$193$	11.0528	0.795598	0.397799	−	0.917473i	$-0.369774\pi$
$193$	11.0528	0.795598	0.397799	+	0.917473i	$0.369774\pi$
$194$	−9.98515	−0.716892
$195$	2.72620	0.195227
$196$	−6.42899	−0.459213
$197$	−11.3550	−0.809007	−0.404504	−	0.914536i	$-0.632556\pi$
$197$	−11.3550	−0.809007	−0.404504	+	0.914536i	$0.632556\pi$
$198$	−8.31202	−0.590710
$199$	−7.35662	−0.521497	−0.260749	−	0.965407i	$-0.583969\pi$
$199$	−7.35662	−0.521497	−0.260749	+	0.965407i	$0.583969\pi$
$200$	−0.197007	−0.0139305
$201$	−34.7291	−2.44961
$202$	−6.05637	−0.426125
$203$	−2.48984	−0.174753
$204$	11.7891	0.825403
$205$	−15.6120	−1.09039
$206$	16.0297	1.11684
$207$	26.3803	1.83356
$208$	−0.423112	−0.0293376
$209$	−0.537102	−0.0371521
$210$	−4.86882	−0.335981
$211$	−23.4718	−1.61586	−0.807932	−	0.589276i	$-0.799413\pi$
$211$	−23.4718	−1.61586	−0.807932	+	0.589276i	$0.799413\pi$
$212$	−12.0539	−0.827868
$213$	12.7622	0.874455
$214$	9.59554	0.655938
$215$	4.86035	0.331473
$216$	5.61936	0.382349
$217$	−4.13806	−0.280910
$218$	−7.76087	−0.525632
$219$	−11.9872	−0.810023
$220$	3.79873	0.256111
$221$	1.76487	0.118718
$222$	−26.5154	−1.77960
$223$	11.2688	0.754617	0.377308	−	0.926088i	$-0.376850\pi$
$223$	11.2688	0.754617	0.377308	+	0.926088i	$0.376850\pi$
$224$	0.755653	0.0504892
$225$	0.982710	0.0655140
$226$	−9.66967	−0.643217
$227$	−12.4177	−0.824195	−0.412097	−	0.911140i	$-0.635204\pi$
$227$	−12.4177	−0.824195	−0.412097	+	0.911140i	$0.635204\pi$
$228$	0.911001	0.0603325
$229$	−4.75404	−0.314156	−0.157078	−	0.987586i	$-0.550207\pi$
$229$	−4.75404	−0.314156	−0.157078	+	0.987586i	$0.550207\pi$
$230$	−12.0562	−0.794965
$231$	3.55885	0.234155
$232$	−3.29496	−0.216324
$233$	5.79050	0.379348	0.189674	−	0.981847i	$-0.439257\pi$
$233$	5.79050	0.379348	0.189674	+	0.981847i	$0.439257\pi$
$234$	2.11057	0.137972
$235$	−25.7768	−1.68149
$236$	8.17921	0.532421
$237$	2.01246	0.130723
$238$	−3.15195	−0.204310
$239$	−11.5047	−0.744178	−0.372089	−	0.928197i	$-0.621358\pi$
$239$	−11.5047	−0.744178	−0.372089	+	0.928197i	$0.621358\pi$
$240$	−6.44320	−0.415906
$241$	−18.9424	−1.22019	−0.610095	−	0.792328i	$-0.708869\pi$
$241$	−18.9424	−1.22019	−0.610095	+	0.792328i	$0.708869\pi$
$242$	8.22333	0.528616
$243$	14.2646	0.915076
$244$	−2.64920	−0.169598
$245$	−14.6561	−0.936346
$246$	−19.3556	−1.23407
$247$	0.136380	0.00867764
$248$	−5.47613	−0.347735
$249$	4.51953	0.286414
$250$	10.9494	0.692498
$251$	−23.8810	−1.50735	−0.753677	−	0.657245i	$-0.771722\pi$
$251$	−23.8810	−1.50735	−0.753677	+	0.657245i	$0.771722\pi$
$252$	−3.76936	−0.237447
$253$	8.81247	0.554035
$254$	3.90341	0.244922
$255$	26.8756	1.68301
$256$	1.00000	0.0625000
$257$	−8.90842	−0.555692	−0.277846	−	0.960626i	$-0.589621\pi$
$257$	−8.90842	−0.555692	−0.277846	+	0.960626i	$0.589621\pi$
$258$	6.02582	0.375151
$259$	7.08917	0.440500
$260$	−0.964567	−0.0598199
$261$	16.4359	1.01736
$262$	−12.0711	−0.745754
$263$	1.59760	0.0985121	0.0492561	−	0.998786i	$-0.484315\pi$
$263$	1.59760	0.0985121	0.0492561	+	0.998786i	$0.484315\pi$
$264$	4.70963	0.289858
$265$	−27.4793	−1.68804
$266$	−0.243566	−0.0149340
$267$	−41.7565	−2.55546
$268$	12.2877	0.750589
$269$	−26.8650	−1.63799	−0.818994	−	0.573802i	$-0.805468\pi$
$269$	−26.8650	−1.63799	−0.818994	+	0.573802i	$0.805468\pi$
$270$	12.8104	0.779617
$271$	−0.354087	−0.0215093	−0.0107546	−	0.999942i	$-0.503423\pi$
$271$	−0.354087	−0.0215093	−0.0107546	+	0.999942i	$0.503423\pi$
$272$	−4.17115	−0.252913
$273$	−0.903656	−0.0546917
$274$	5.02909	0.303818
$275$	0.328279	0.0197960
$276$	−14.9472	−0.899716
$277$	−20.5633	−1.23553	−0.617766	−	0.786362i	$-0.711962\pi$
$277$	−20.5633	−1.23553	−0.617766	+	0.786362i	$0.711962\pi$
$278$	−15.9973	−0.959456
$279$	27.3161	1.63537
$280$	1.72266	0.102949
$281$	28.9350	1.72612	0.863059	−	0.505104i	$-0.168546\pi$
$281$	28.9350	1.72612	0.863059	+	0.505104i	$0.168546\pi$
$282$	−31.9578	−1.90306
$283$	−30.4277	−1.80874	−0.904370	−	0.426750i	$-0.859658\pi$
$283$	−30.4277	−1.80874	−0.904370	+	0.426750i	$0.859658\pi$
$284$	−4.51547	−0.267944
$285$	2.07680	0.123019
$286$	0.705047	0.0416903
$287$	5.17493	0.305466
$288$	−4.98821	−0.293933
$289$	0.398525	0.0234427
$290$	−7.51149	−0.441090
$291$	−28.2214	−1.65437
$292$	4.24126	0.248201
$293$	−4.71020	−0.275173	−0.137586	−	0.990490i	$-0.543934\pi$
$293$	−4.71020	−0.275173	−0.137586	+	0.990490i	$0.543934\pi$
$294$	−18.1705	−1.05973
$295$	18.6461	1.08562
$296$	9.38152	0.545290
$297$	−9.36373	−0.543338
$298$	11.0573	0.640535
$299$	−2.23765	−0.129406
$300$	−0.556808	−0.0321473
$301$	−1.61107	−0.0928604
$302$	−6.65431	−0.382912
$303$	−17.1174	−0.983367
$304$	−0.322325	−0.0184866
$305$	−6.03937	−0.345813
$306$	20.8066	1.18943
$307$	21.8539	1.24727	0.623635	−	0.781716i	$-0.285655\pi$
$307$	21.8539	1.24727	0.623635	+	0.781716i	$0.285655\pi$
$308$	−1.25917	−0.0717479
$309$	45.3054	2.57734
$310$	−12.4839	−0.709039
$311$	−18.2017	−1.03212	−0.516060	−	0.856552i	$-0.672602\pi$
$311$	−18.2017	−1.03212	−0.516060	+	0.856552i	$0.672602\pi$
$312$	−1.19586	−0.0677023
$313$	6.84842	0.387095	0.193548	−	0.981091i	$-0.438001\pi$
$313$	6.84842	0.387095	0.193548	+	0.981091i	$0.438001\pi$
$314$	12.8879	0.727307
$315$	−8.59298	−0.484159
$316$	−0.712037	−0.0400552
$317$	28.4018	1.59520	0.797601	−	0.603185i	$-0.206102\pi$
$317$	28.4018	1.59520	0.797601	+	0.603185i	$0.206102\pi$
$318$	−34.0685	−1.91047
$319$	5.49050	0.307409
$320$	2.27969	0.127439
$321$	27.1203	1.51371
$322$	3.99630	0.222705
$323$	1.34447	0.0748082
$324$	0.917597	0.0509776
$325$	−0.0833560	−0.00462376
$326$	−16.9351	−0.937947
$327$	−21.9349	−1.21300
$328$	6.84829	0.378133
$329$	8.54427	0.471061
$330$	10.7365	0.591026
$331$	−21.5756	−1.18590	−0.592951	−	0.805239i	$-0.702037\pi$
$331$	−21.5756	−1.18590	−0.592951	+	0.805239i	$0.702037\pi$
$332$	−1.59908	−0.0877607
$333$	−46.7970	−2.56446
$334$	0.0822773	0.00450202
$335$	28.0121	1.53047
$336$	2.13573	0.116514
$337$	−8.43770	−0.459631	−0.229815	−	0.973234i	$-0.573812\pi$
$337$	−8.43770	−0.459631	−0.229815	+	0.973234i	$0.573812\pi$
$338$	12.8210	0.697369
$339$	−27.3298	−1.48435
$340$	−9.50896	−0.515696
$341$	9.12507	0.494150
$342$	1.60783	0.0869412
$343$	10.1477	0.547922
$344$	−2.13202	−0.114951
$345$	−34.0751	−1.83454
$346$	−7.31902	−0.393473
$347$	24.3110	1.30508	0.652542	−	0.757752i	$-0.273703\pi$
$347$	24.3110	1.30508	0.652542	+	0.757752i	$0.273703\pi$
$348$	−9.31267	−0.499212
$349$	−8.50864	−0.455457	−0.227729	−	0.973725i	$-0.573130\pi$
$349$	−8.50864	−0.455457	−0.227729	+	0.973725i	$0.573130\pi$
$350$	0.148869	0.00795737
$351$	2.37762	0.126908
$352$	−1.66633	−0.0888159
$353$	−18.8475	−1.00315	−0.501576	−	0.865114i	$-0.667246\pi$
$353$	−18.8475	−1.00315	−0.501576	+	0.865114i	$0.667246\pi$
$354$	23.1172	1.22867
$355$	−10.2939	−0.546343
$356$	14.7741	0.783023
$357$	−8.90848	−0.471487
$358$	0.775960	0.0410107
$359$	1.90761	0.100680	0.0503398	−	0.998732i	$-0.483970\pi$
$359$	1.90761	0.100680	0.0503398	+	0.998732i	$0.483970\pi$
$360$	−11.3716	−0.599335
$361$	−18.8961	−0.994532
$362$	14.2560	0.749279
$363$	23.2419	1.21989
$364$	0.319726	0.0167582
$365$	9.66877	0.506087
$366$	−7.48755	−0.391380
$367$	−28.6836	−1.49727	−0.748635	−	0.662982i	$-0.769291\pi$
$367$	−28.6836	−1.49727	−0.748635	+	0.662982i	$0.769291\pi$
$368$	5.28854	0.275684
$369$	−34.1607	−1.77833
$370$	21.3870	1.11186
$371$	9.10860	0.472895
$372$	−15.4774	−0.802467
$373$	−32.8348	−1.70012	−0.850062	−	0.526683i	$-0.823436\pi$
$373$	−32.8348	−1.70012	−0.850062	+	0.526683i	$0.823436\pi$
$374$	6.95054	0.359404
$375$	30.9466	1.59808
$376$	11.3071	0.583120
$377$	−1.39414	−0.0718017
$378$	−4.24628	−0.218405
$379$	−3.29480	−0.169243	−0.0846213	−	0.996413i	$-0.526968\pi$
$379$	−3.29480	−0.169243	−0.0846213	+	0.996413i	$0.526968\pi$
$380$	−0.734803	−0.0376946
$381$	11.0324	0.565206
$382$	−7.60207	−0.388956
$383$	−24.0520	−1.22900	−0.614501	−	0.788916i	$-0.710643\pi$
$383$	−24.0520	−1.22900	−0.614501	+	0.788916i	$0.710643\pi$
$384$	2.82634	0.144231
$385$	−2.87052	−0.146295
$386$	−11.0528	−0.562573
$387$	10.6350	0.540605
$388$	9.98515	0.506919
$389$	−0.343566	−0.0174195	−0.00870974	−	0.999962i	$-0.502772\pi$
$389$	−0.343566	−0.0174195	−0.00870974	+	0.999962i	$0.502772\pi$
$390$	−2.72620	−0.138046
$391$	−22.0593	−1.11559
$392$	6.42899	0.324713
$393$	−34.1170	−1.72097
$394$	11.3550	0.572055
$395$	−1.62323	−0.0816735
$396$	8.31202	0.417695
$397$	4.26421	0.214015	0.107007	−	0.994258i	$-0.465873\pi$
$397$	4.26421	0.214015	0.107007	+	0.994258i	$0.465873\pi$
$398$	7.35662	0.368754
$399$	−0.688401	−0.0344632
$400$	0.197007	0.00985034
$401$	6.65302	0.332236	0.166118	−	0.986106i	$-0.446877\pi$
$401$	6.65302	0.332236	0.166118	+	0.986106i	$0.446877\pi$
$402$	34.7291	1.73213
$403$	−2.31702	−0.115419
$404$	6.05637	0.301316
$405$	2.09184	0.103944
$406$	2.48984	0.123569
$407$	−15.6327	−0.774886
$408$	−11.7891	−0.583648
$409$	13.9495	0.689757	0.344879	−	0.938647i	$-0.387920\pi$
$409$	13.9495	0.689757	0.344879	+	0.938647i	$0.387920\pi$
$410$	15.6120	0.771022
$411$	14.2139	0.701121
$412$	−16.0297	−0.789727
$413$	−6.18064	−0.304130
$414$	−26.3803	−1.29652
$415$	−3.64540	−0.178946
$416$	0.423112	0.0207448
$417$	−45.2139	−2.21413
$418$	0.537102	0.0262705
$419$	8.69103	0.424584	0.212292	−	0.977206i	$-0.431907\pi$
$419$	8.69103	0.424584	0.212292	+	0.977206i	$0.431907\pi$
$420$	4.86882	0.237574
$421$	32.2163	1.57013	0.785063	−	0.619416i	$-0.212630\pi$
$421$	32.2163	1.57013	0.785063	+	0.619416i	$0.212630\pi$
$422$	23.4718	1.14259
$423$	−56.4023	−2.74237
$424$	12.0539	0.585391
$425$	−0.821745	−0.0398605
$426$	−12.7622	−0.618333
$427$	2.00188	0.0968776
$428$	−9.59554	−0.463818
$429$	1.99270	0.0962086
$430$	−4.86035	−0.234387
$431$	35.2666	1.69873	0.849365	−	0.527805i	$-0.176985\pi$
$431$	35.2666	1.69873	0.849365	+	0.527805i	$0.176985\pi$
$432$	−5.61936	−0.270361
$433$	−24.8495	−1.19419	−0.597095	−	0.802170i	$-0.703679\pi$
$433$	−24.8495	−1.19419	−0.597095	+	0.802170i	$0.703679\pi$
$434$	4.13806	0.198633
$435$	−21.2301	−1.01790
$436$	7.76087	0.371678
$437$	−1.70463	−0.0815434
$438$	11.9872	0.572773
$439$	−15.1376	−0.722481	−0.361240	−	0.932473i	$-0.617647\pi$
$439$	−15.1376	−0.722481	−0.361240	+	0.932473i	$0.617647\pi$
$440$	−3.79873	−0.181097
$441$	−32.0691	−1.52710
$442$	−1.76487	−0.0839462
$443$	−1.44665	−0.0687325	−0.0343663	−	0.999409i	$-0.510941\pi$
$443$	−1.44665	−0.0687325	−0.0343663	+	0.999409i	$0.510941\pi$
$444$	26.5154	1.25836
$445$	33.6803	1.59660
$446$	−11.2688	−0.533595
$447$	31.2518	1.47816
$448$	−0.755653	−0.0357013
$449$	35.6919	1.68440	0.842201	−	0.539163i	$-0.181259\pi$
$449$	35.6919	1.68440	0.842201	+	0.539163i	$0.181259\pi$
$450$	−0.982710	−0.0463254
$451$	−11.4115	−0.537348
$452$	9.66967	0.454823
$453$	−18.8073	−0.883646
$454$	12.4177	0.582794
$455$	0.728878	0.0341703
$456$	−0.911001	−0.0426615
$457$	−8.80114	−0.411700	−0.205850	−	0.978584i	$-0.565996\pi$
$457$	−8.80114	−0.411700	−0.205850	+	0.978584i	$0.565996\pi$
$458$	4.75404	0.222142
$459$	23.4392	1.09405
$460$	12.0562	0.562125
$461$	−19.5369	−0.909926	−0.454963	−	0.890510i	$-0.650348\pi$
$461$	−19.5369	−0.909926	−0.454963	+	0.890510i	$0.650348\pi$
$462$	−3.55885	−0.165573
$463$	12.2651	0.570008	0.285004	−	0.958526i	$-0.408005\pi$
$463$	12.2651	0.570008	0.285004	+	0.958526i	$0.408005\pi$
$464$	3.29496	0.152965
$465$	−35.2838	−1.63625
$466$	−5.79050	−0.268240
$467$	1.90509	0.0881569	0.0440785	−	0.999028i	$-0.485965\pi$
$467$	1.90509	0.0881569	0.0440785	+	0.999028i	$0.485965\pi$
$468$	−2.11057	−0.0975613
$469$	−9.28521	−0.428751
$470$	25.7768	1.18899
$471$	36.4257	1.67841
$472$	−8.17921	−0.376479
$473$	3.55266	0.163351
$474$	−2.01246	−0.0924354
$475$	−0.0635002	−0.00291359
$476$	3.15195	0.144469
$477$	−60.1275	−2.75305
$478$	11.5047	0.526213
$479$	3.34150	0.152677	0.0763384	−	0.997082i	$-0.475677\pi$
$479$	3.34150	0.152677	0.0763384	+	0.997082i	$0.475677\pi$
$480$	6.44320	0.294090
$481$	3.96944	0.180991
$482$	18.9424	0.862804
$483$	11.2949	0.513936
$484$	−8.22333	−0.373788
$485$	22.7631	1.03362
$486$	−14.2646	−0.647057
$487$	−6.05038	−0.274169	−0.137084	−	0.990559i	$-0.543773\pi$
$487$	−6.05038	−0.274169	−0.137084	+	0.990559i	$0.543773\pi$
$488$	2.64920	0.119924
$489$	−47.8643	−2.16450
$490$	14.6561	0.662096
$491$	7.33359	0.330960	0.165480	−	0.986213i	$-0.447083\pi$
$491$	7.33359	0.330960	0.165480	+	0.986213i	$0.447083\pi$
$492$	19.3556	0.872618
$493$	−13.7438	−0.618988
$494$	−0.136380	−0.00613602
$495$	18.9489	0.851688
$496$	5.47613	0.245886
$497$	3.41213	0.153055
$498$	−4.51953	−0.202525
$499$	−22.3079	−0.998639	−0.499320	−	0.866418i	$-0.666417\pi$
$499$	−22.3079	−0.998639	−0.499320	+	0.866418i	$0.666417\pi$
$500$	−10.9494	−0.489670
$501$	0.232544	0.0103893
$502$	23.8810	1.06586
$503$	−42.6451	−1.90145	−0.950726	−	0.310034i	$-0.899660\pi$
$503$	−42.6451	−1.90145	−0.950726	+	0.310034i	$0.899660\pi$
$504$	3.76936	0.167900
$505$	13.8067	0.614389
$506$	−8.81247	−0.391762
$507$	36.2365	1.60932
$508$	−3.90341	−0.173186
$509$	−25.5982	−1.13462	−0.567309	−	0.823505i	$-0.692016\pi$
$509$	−25.5982	−1.13462	−0.567309	+	0.823505i	$0.692016\pi$
$510$	−26.8756	−1.19007
$511$	−3.20492	−0.141777
$512$	−1.00000	−0.0441942
$513$	1.81126	0.0799691
$514$	8.90842	0.392934
$515$	−36.5428	−1.61027
$516$	−6.02582	−0.265272
$517$	−18.8415	−0.828646
$518$	−7.08917	−0.311480
$519$	−20.6861	−0.908017
$520$	0.964567	0.0422991
$521$	−10.2782	−0.450298	−0.225149	−	0.974324i	$-0.572287\pi$
$521$	−10.2782	−0.450298	−0.225149	+	0.974324i	$0.572287\pi$
$522$	−16.4359	−0.719381
$523$	−2.07506	−0.0907360	−0.0453680	−	0.998970i	$-0.514446\pi$
$523$	−2.07506	−0.0907360	−0.0453680	+	0.998970i	$0.514446\pi$
$524$	12.0711	0.527327
$525$	0.420754	0.0183632
$526$	−1.59760	−0.0696586
$527$	−22.8418	−0.995004
$528$	−4.70963	−0.204960
$529$	4.96862	0.216027
$530$	27.4793	1.19362
$531$	40.7996	1.77055
$532$	0.243566	0.0105599
$533$	2.89760	0.125509
$534$	41.7565	1.80698
$535$	−21.8749	−0.945734
$536$	−12.2877	−0.530746
$537$	2.19313	0.0946404
$538$	26.8650	1.15823
$539$	−10.7128	−0.461435
$540$	−12.8104	−0.551272
$541$	−2.80995	−0.120809	−0.0604046	−	0.998174i	$-0.519239\pi$
$541$	−2.80995	−0.120809	−0.0604046	+	0.998174i	$0.519239\pi$
$542$	0.354087	0.0152093
$543$	40.2923	1.72911
$544$	4.17115	0.178837
$545$	17.6924	0.757859
$546$	0.903656	0.0386729
$547$	−17.2165	−0.736126	−0.368063	−	0.929801i	$-0.619979\pi$
$547$	−17.2165	−0.736126	−0.368063	+	0.929801i	$0.619979\pi$
$548$	−5.02909	−0.214832
$549$	−13.2148	−0.563993
$550$	−0.328279	−0.0139979
$551$	−1.06205	−0.0452447
$552$	14.9472	0.636196
$553$	0.538053	0.0228804
$554$	20.5633	0.873652
$555$	60.4469	2.56583
$556$	15.9973	0.678438
$557$	−44.1225	−1.86953	−0.934766	−	0.355265i	$-0.884391\pi$
$557$	−44.1225	−1.86953	−0.934766	+	0.355265i	$0.884391\pi$
$558$	−27.3161	−1.15638
$559$	−0.902084	−0.0381541
$560$	−1.72266	−0.0727956
$561$	19.6446	0.829395
$562$	−28.9350	−1.22055
$563$	−42.4924	−1.79084	−0.895420	−	0.445222i	$-0.853125\pi$
$563$	−42.4924	−1.79084	−0.895420	+	0.445222i	$0.853125\pi$
$564$	31.9578	1.34567
$565$	22.0439	0.927394
$566$	30.4277	1.27897
$567$	−0.693385	−0.0291194
$568$	4.51547	0.189465
$569$	37.5864	1.57570	0.787852	−	0.615864i	$-0.211193\pi$
$569$	37.5864	1.57570	0.787852	+	0.615864i	$0.211193\pi$
$570$	−2.07680	−0.0869878
$571$	−10.3669	−0.433841	−0.216921	−	0.976189i	$-0.569601\pi$
$571$	−10.3669	−0.433841	−0.216921	+	0.976189i	$0.569601\pi$
$572$	−0.705047	−0.0294795
$573$	−21.4861	−0.897593
$574$	−5.17493	−0.215997
$575$	1.04188	0.0434493
$576$	4.98821	0.207842
$577$	−41.9960	−1.74831	−0.874157	−	0.485643i	$-0.838586\pi$
$577$	−41.9960	−1.74831	−0.874157	+	0.485643i	$0.838586\pi$
$578$	−0.398525	−0.0165765
$579$	−31.2390	−1.29825
$580$	7.51149	0.311898
$581$	1.20835	0.0501306
$582$	28.2214	1.16982
$583$	−20.0859	−0.831873
$584$	−4.24126	−0.175504
$585$	−4.81146	−0.198929
$586$	4.71020	0.194577
$587$	15.8165	0.652817	0.326408	−	0.945229i	$-0.394162\pi$
$587$	15.8165	0.652817	0.326408	+	0.945229i	$0.394162\pi$
$588$	18.1705	0.749340
$589$	−1.76510	−0.0727295
$590$	−18.6461	−0.767648
$591$	32.0930	1.32013
$592$	−9.38152	−0.385578
$593$	−41.0346	−1.68509	−0.842545	−	0.538627i	$-0.818943\pi$
$593$	−41.0346	−1.68509	−0.842545	+	0.538627i	$0.818943\pi$
$594$	9.36373	0.384198
$595$	7.18547	0.294576
$596$	−11.0573	−0.452926
$597$	20.7923	0.850974
$598$	2.23765	0.0915041
$599$	−19.5279	−0.797890	−0.398945	−	0.916975i	$-0.630624\pi$
$599$	−19.5279	−0.797890	−0.398945	+	0.916975i	$0.630624\pi$
$600$	0.556808	0.0227316
$601$	21.4682	0.875705	0.437852	−	0.899047i	$-0.355739\pi$
$601$	21.4682	0.875705	0.437852	+	0.899047i	$0.355739\pi$
$602$	1.61107	0.0656622
$603$	61.2934	2.49606
$604$	6.65431	0.270760
$605$	−18.7467	−0.762161
$606$	17.1174	0.695345
$607$	−38.0999	−1.54643	−0.773214	−	0.634146i	$-0.781352\pi$
$607$	−38.0999	−1.54643	−0.773214	+	0.634146i	$0.781352\pi$
$608$	0.322325	0.0130720
$609$	7.03715	0.285160
$610$	6.03937	0.244527
$611$	4.78419	0.193547
$612$	−20.8066	−0.841056
$613$	−1.67278	−0.0675631	−0.0337815	−	0.999429i	$-0.510755\pi$
$613$	−1.67278	−0.0675631	−0.0337815	+	0.999429i	$0.510755\pi$
$614$	−21.8539	−0.881953
$615$	44.1249	1.77929
$616$	1.25917	0.0507334
$617$	26.0454	1.04855	0.524273	−	0.851550i	$-0.324337\pi$
$617$	26.0454	1.04855	0.524273	+	0.851550i	$0.324337\pi$
$618$	−45.3054	−1.82245
$619$	3.92355	0.157701	0.0788504	−	0.996886i	$-0.474875\pi$
$619$	3.92355	0.157701	0.0788504	+	0.996886i	$0.474875\pi$
$620$	12.4839	0.501366
$621$	−29.7182	−1.19255
$622$	18.2017	0.729820
$623$	−11.1641	−0.447279
$624$	1.19586	0.0478727
$625$	−25.9462	−1.03785
$626$	−6.84842	−0.273718
$627$	1.51803	0.0606244
$628$	−12.8879	−0.514284
$629$	39.1318	1.56029
$630$	8.59298	0.342352
$631$	−18.2082	−0.724857	−0.362428	−	0.932012i	$-0.618052\pi$
$631$	−18.2082	−0.724857	−0.362428	+	0.932012i	$0.618052\pi$
$632$	0.712037	0.0283233
$633$	66.3393	2.63675
$634$	−28.4018	−1.12798
$635$	−8.89859	−0.353130
$636$	34.0685	1.35091
$637$	2.72019	0.107778
$638$	−5.49050	−0.217371
$639$	−22.5241	−0.891039
$640$	−2.27969	−0.0901128
$641$	−2.46521	−0.0973700	−0.0486850	−	0.998814i	$-0.515503\pi$
$641$	−2.46521	−0.0973700	−0.0486850	+	0.998814i	$0.515503\pi$
$642$	−27.1203	−1.07035
$643$	10.5245	0.415046	0.207523	−	0.978230i	$-0.433460\pi$
$643$	10.5245	0.415046	0.207523	+	0.978230i	$0.433460\pi$
$644$	−3.99630	−0.157476
$645$	−13.7370	−0.540895
$646$	−1.34447	−0.0528974
$647$	41.2498	1.62170	0.810849	−	0.585255i	$-0.199006\pi$
$647$	41.2498	1.62170	0.810849	+	0.585255i	$0.199006\pi$
$648$	−0.917597	−0.0360466
$649$	13.6293	0.534997
$650$	0.0833560	0.00326949
$651$	11.6956	0.458385
$652$	16.9351	0.663228
$653$	8.81824	0.345085	0.172542	−	0.985002i	$-0.444802\pi$
$653$	8.81824	0.345085	0.172542	+	0.985002i	$0.444802\pi$
$654$	21.9349	0.857721
$655$	27.5184	1.07523
$656$	−6.84829	−0.267381
$657$	21.1563	0.825385
$658$	−8.54427	−0.333090
$659$	44.0979	1.71781	0.858906	−	0.512133i	$-0.171145\pi$
$659$	44.0979	1.71781	0.858906	+	0.512133i	$0.171145\pi$
$660$	−10.7365	−0.417918
$661$	8.72960	0.339542	0.169771	−	0.985484i	$-0.445697\pi$
$661$	8.72960	0.339542	0.169771	+	0.985484i	$0.445697\pi$
$662$	21.5756	0.838559
$663$	−4.98812	−0.193722
$664$	1.59908	0.0620562
$665$	0.555256	0.0215319
$666$	46.7970	1.81335
$667$	17.4255	0.674718
$668$	−0.0822773	−0.00318341
$669$	−31.8496	−1.23138
$670$	−28.0121	−1.08220
$671$	−4.41446	−0.170418
$672$	−2.13573	−0.0823877
$673$	31.9066	1.22991	0.614954	−	0.788563i	$-0.289174\pi$
$673$	31.9066	1.22991	0.614954	+	0.788563i	$0.289174\pi$
$674$	8.43770	0.325008
$675$	−1.10705	−0.0426104
$676$	−12.8210	−0.493114
$677$	11.2228	0.431329	0.215665	−	0.976468i	$-0.430808\pi$
$677$	11.2228	0.431329	0.215665	+	0.976468i	$0.430808\pi$
$678$	27.3298	1.04959
$679$	−7.54531	−0.289562
$680$	9.50896	0.364652
$681$	35.0968	1.34491
$682$	−9.12507	−0.349417
$683$	−39.1209	−1.49692	−0.748459	−	0.663181i	$-0.769206\pi$
$683$	−39.1209	−1.49692	−0.748459	+	0.663181i	$0.769206\pi$
$684$	−1.60783	−0.0614767
$685$	−11.4648	−0.438047
$686$	−10.1477	−0.387439
$687$	13.4366	0.512636
$688$	2.13202	0.0812825
$689$	5.10017	0.194301
$690$	34.0751	1.29722
$691$	−38.1365	−1.45078	−0.725390	−	0.688338i	$-0.758341\pi$
$691$	−38.1365	−1.45078	−0.725390	+	0.688338i	$0.758341\pi$
$692$	7.31902	0.278228
$693$	−6.28101	−0.238596
$694$	−24.3110	−0.922834
$695$	36.4690	1.38335
$696$	9.31267	0.352996
$697$	28.5653	1.08199
$698$	8.50864	0.322057
$699$	−16.3659	−0.619016
$700$	−0.148869	−0.00562671
$701$	−21.5059	−0.812266	−0.406133	−	0.913814i	$-0.633123\pi$
$701$	−21.5059	−0.812266	−0.406133	+	0.913814i	$0.633123\pi$
$702$	−2.37762	−0.0897375
$703$	3.02390	0.114049
$704$	1.66633	0.0628023
$705$	72.8540	2.74384
$706$	18.8475	0.709336
$707$	−4.57651	−0.172117
$708$	−23.1172	−0.868799
$709$	−4.98188	−0.187099	−0.0935493	−	0.995615i	$-0.529821\pi$
$709$	−4.98188	−0.187099	−0.0935493	+	0.995615i	$0.529821\pi$
$710$	10.2939	0.386323
$711$	−3.55179	−0.133203
$712$	−14.7741	−0.553681
$713$	28.9607	1.08459
$714$	8.90848	0.333391
$715$	−1.60729	−0.0601093
$716$	−0.775960	−0.0289990
$717$	32.5163	1.21434
$718$	−1.90761	−0.0711913
$719$	18.6887	0.696972	0.348486	−	0.937314i	$-0.386696\pi$
$719$	18.6887	0.696972	0.348486	+	0.937314i	$0.386696\pi$
$720$	11.3716	0.423794
$721$	12.1129	0.451108
$722$	18.8961	0.703240
$723$	53.5378	1.99109
$724$	−14.2560	−0.529820
$725$	0.649129	0.0241080
$726$	−23.2419	−0.862589
$727$	43.1566	1.60059	0.800295	−	0.599606i	$-0.204676\pi$
$727$	43.1566	1.60059	0.800295	+	0.599606i	$0.204676\pi$
$728$	−0.319726	−0.0118498
$729$	−43.0695	−1.59517
$730$	−9.66877	−0.357857
$731$	−8.89298	−0.328919
$732$	7.48755	0.276748
$733$	−7.20368	−0.266074	−0.133037	−	0.991111i	$-0.542473\pi$
$733$	−7.20368	−0.266074	−0.133037	+	0.991111i	$0.542473\pi$
$734$	28.6836	1.05873
$735$	41.4232	1.52792
$736$	−5.28854	−0.194938
$737$	20.4754	0.754220
$738$	34.1607	1.25747
$739$	−17.4844	−0.643173	−0.321587	−	0.946880i	$-0.604216\pi$
$739$	−17.4844	−0.643173	−0.321587	+	0.946880i	$0.604216\pi$
$740$	−21.3870	−0.786201
$741$	−0.385456	−0.0141601
$742$	−9.10860	−0.334387
$743$	−37.0249	−1.35831	−0.679155	−	0.733995i	$-0.737654\pi$
$743$	−37.0249	−1.35831	−0.679155	+	0.733995i	$0.737654\pi$
$744$	15.4774	0.567430
$745$	−25.2074	−0.923526
$746$	32.8348	1.20217
$747$	−7.97652	−0.291846
$748$	−6.95054	−0.254137
$749$	7.25090	0.264942
$750$	−30.9466	−1.13001
$751$	39.6320	1.44619	0.723096	−	0.690747i	$-0.242718\pi$
$751$	39.6320	1.44619	0.723096	+	0.690747i	$0.242718\pi$
$752$	−11.3071	−0.412328
$753$	67.4958	2.45968
$754$	1.39414	0.0507715
$755$	15.1698	0.552085
$756$	4.24628	0.154436
$757$	13.4038	0.487168	0.243584	−	0.969880i	$-0.421677\pi$
$757$	13.4038	0.487168	0.243584	+	0.969880i	$0.421677\pi$
$758$	3.29480	0.119673
$759$	−24.9071	−0.904069
$760$	0.734803	0.0266541
$761$	−7.50662	−0.272115	−0.136057	−	0.990701i	$-0.543443\pi$
$761$	−7.50662	−0.272115	−0.136057	+	0.990701i	$0.543443\pi$
$762$	−11.0324	−0.399661
$763$	−5.86452	−0.212310
$764$	7.60207	0.275033
$765$	−47.4327	−1.71493
$766$	24.0520	0.869035
$767$	−3.46072	−0.124960
$768$	−2.82634	−0.101987
$769$	7.18087	0.258949	0.129474	−	0.991583i	$-0.458671\pi$
$769$	7.18087	0.258949	0.129474	+	0.991583i	$0.458671\pi$
$770$	2.87052	0.103447
$771$	25.1782	0.906772
$772$	11.0528	0.397799
$773$	−10.2831	−0.369857	−0.184929	−	0.982752i	$-0.559205\pi$
$773$	−10.2831	−0.369857	−0.184929	+	0.982752i	$0.559205\pi$
$774$	−10.6350	−0.382266
$775$	1.07884	0.0387529
$776$	−9.98515	−0.358446
$777$	−20.0364	−0.718803
$778$	0.343566	0.0123174
$779$	2.20738	0.0790874
$780$	2.72620	0.0976135
$781$	−7.52428	−0.269240
$782$	22.0593	0.788839
$783$	−18.5155	−0.661691
$784$	−6.42899	−0.229607
$785$	−29.3805	−1.04864
$786$	34.1170	1.21691
$787$	13.7708	0.490874	0.245437	−	0.969412i	$-0.421068\pi$
$787$	13.7708	0.490874	0.245437	+	0.969412i	$0.421068\pi$
$788$	−11.3550	−0.404504
$789$	−4.51536	−0.160751
$790$	1.62323	0.0577519
$791$	−7.30692	−0.259804
$792$	−8.31202	−0.295355
$793$	1.12091	0.0398047
$794$	−4.26421	−0.151331
$795$	77.6659	2.75452
$796$	−7.35662	−0.260749
$797$	15.3237	0.542794	0.271397	−	0.962467i	$-0.412514\pi$
$797$	15.3237	0.542794	0.271397	+	0.962467i	$0.412514\pi$
$798$	0.688401	0.0243691
$799$	47.1638	1.66853
$800$	−0.197007	−0.00696524
$801$	73.6960	2.60392
$802$	−6.65302	−0.234926
$803$	7.06735	0.249401
$804$	−34.7291	−1.22480
$805$	−9.11034	−0.321097
$806$	2.31702	0.0816136
$807$	75.9297	2.67285
$808$	−6.05637	−0.213062
$809$	−12.8391	−0.451399	−0.225700	−	0.974197i	$-0.572467\pi$
$809$	−12.8391	−0.451399	−0.225700	+	0.974197i	$0.572467\pi$
$810$	−2.09184	−0.0734998
$811$	−36.7927	−1.29196	−0.645982	−	0.763352i	$-0.723552\pi$
$811$	−36.7927	−1.29196	−0.645982	+	0.763352i	$0.723552\pi$
$812$	−2.48984	−0.0873764
$813$	1.00077	0.0350986
$814$	15.6327	0.547927
$815$	38.6068	1.35234
$816$	11.7891	0.412701
$817$	−0.687204	−0.0240422
$818$	−13.9495	−0.487732
$819$	1.59486	0.0557290
$820$	−15.6120	−0.545195
$821$	33.9062	1.18333	0.591667	−	0.806182i	$-0.298470\pi$
$821$	33.9062	1.18333	0.591667	+	0.806182i	$0.298470\pi$
$822$	−14.2139	−0.495768
$823$	−36.5693	−1.27473	−0.637364	−	0.770563i	$-0.719975\pi$
$823$	−36.5693	−1.27473	−0.637364	+	0.770563i	$0.719975\pi$
$824$	16.0297	0.558421
$825$	−0.927829	−0.0323029
$826$	6.18064	0.215052
$827$	53.4127	1.85734	0.928670	−	0.370906i	$-0.120953\pi$
$827$	53.4127	1.85734	0.928670	+	0.370906i	$0.120953\pi$
$828$	26.3803	0.916779
$829$	8.06769	0.280203	0.140101	−	0.990137i	$-0.455257\pi$
$829$	8.06769	0.280203	0.140101	+	0.990137i	$0.455257\pi$
$830$	3.64540	0.126534
$831$	58.1190	2.01613
$832$	−0.423112	−0.0146688
$833$	26.8163	0.929130
$834$	45.2139	1.56563
$835$	−0.187567	−0.00649103
$836$	−0.537102	−0.0185760
$837$	−30.7724	−1.06365
$838$	−8.69103	−0.300227
$839$	19.4162	0.670322	0.335161	−	0.942161i	$-0.391209\pi$
$839$	19.4162	0.670322	0.335161	+	0.942161i	$0.391209\pi$
$840$	−4.86882	−0.167990
$841$	−18.1433	−0.625630
$842$	−32.2163	−1.11025
$843$	−81.7802	−2.81666
$844$	−23.4718	−0.807932
$845$	−29.2279	−1.00547
$846$	56.4023	1.93915
$847$	6.21399	0.213515
$848$	−12.0539	−0.413934
$849$	85.9991	2.95148
$850$	0.821745	0.0281856
$851$	−49.6145	−1.70076
$852$	12.7622	0.437227
$853$	−20.2521	−0.693420	−0.346710	−	0.937972i	$-0.612701\pi$
$853$	−20.2521	−0.693420	−0.346710	+	0.937972i	$0.612701\pi$
$854$	−2.00188	−0.0685028
$855$	−3.66535	−0.125352
$856$	9.59554	0.327969
$857$	−0.549909	−0.0187845	−0.00939226	−	0.999956i	$-0.502990\pi$
$857$	−0.549909	−0.0187845	−0.00939226	+	0.999956i	$0.502990\pi$
$858$	−1.99270	−0.0680298
$859$	−17.4450	−0.595215	−0.297607	−	0.954688i	$-0.596189\pi$
$859$	−17.4450	−0.595215	−0.297607	+	0.954688i	$0.596189\pi$
$860$	4.86035	0.165737
$861$	−14.6261	−0.498457
$862$	−35.2666	−1.20118
$863$	20.2943	0.690827	0.345414	−	0.938451i	$-0.387739\pi$
$863$	20.2943	0.690827	0.345414	+	0.938451i	$0.387739\pi$
$864$	5.61936	0.191174
$865$	16.6851	0.567312
$866$	24.8495	0.844420
$867$	−1.12637	−0.0382535
$868$	−4.13806	−0.140455
$869$	−1.18649	−0.0402490
$870$	21.2301	0.719766
$871$	−5.19907	−0.176164
$872$	−7.76087	−0.262816
$873$	49.8080	1.68575
$874$	1.70463	0.0576599
$875$	8.27392	0.279709
$876$	−11.9872	−0.405011
$877$	48.2849	1.63047	0.815233	−	0.579134i	$-0.196609\pi$
$877$	48.2849	1.63047	0.815233	+	0.579134i	$0.196609\pi$
$878$	15.1376	0.510871
$879$	13.3126	0.449024
$880$	3.79873	0.128055
$881$	53.8401	1.81392	0.906959	−	0.421220i	$-0.138398\pi$
$881$	53.8401	1.81392	0.906959	+	0.421220i	$0.138398\pi$
$882$	32.0691	1.07982
$883$	−14.1361	−0.475719	−0.237860	−	0.971300i	$-0.576446\pi$
$883$	−14.1361	−0.475719	−0.237860	+	0.971300i	$0.576446\pi$
$884$	1.76487	0.0593589
$885$	−52.7002	−1.77150
$886$	1.44665	0.0486012
$887$	52.7882	1.77245	0.886227	−	0.463251i	$-0.153317\pi$
$887$	52.7882	1.77245	0.886227	+	0.463251i	$0.153317\pi$
$888$	−26.5154	−0.889798
$889$	2.94963	0.0989273
$890$	−33.6803	−1.12897
$891$	1.52902	0.0512242
$892$	11.2688	0.377308
$893$	3.64457	0.121961
$894$	−31.2518	−1.04522
$895$	−1.76895	−0.0591295
$896$	0.755653	0.0252446
$897$	6.32435	0.211164
$898$	−35.6919	−1.19105
$899$	18.0436	0.601789
$900$	0.982710	0.0327570
$901$	50.2788	1.67503
$902$	11.4115	0.379963
$903$	4.55343	0.151529
$904$	−9.66967	−0.321609
$905$	−32.4993	−1.08031
$906$	18.8073	0.624832
$907$	−9.18037	−0.304829	−0.152415	−	0.988317i	$-0.548705\pi$
$907$	−9.18037	−0.304829	−0.152415	+	0.988317i	$0.548705\pi$
$908$	−12.4177	−0.412097
$909$	30.2104	1.00202
$910$	−0.728878	−0.0241621
$911$	−21.1054	−0.699252	−0.349626	−	0.936889i	$-0.613691\pi$
$911$	−21.1054	−0.699252	−0.349626	+	0.936889i	$0.613691\pi$
$912$	0.911001	0.0301663
$913$	−2.66459	−0.0881852
$914$	8.80114	0.291116
$915$	17.0693	0.564294
$916$	−4.75404	−0.157078
$917$	−9.12155	−0.301220
$918$	−23.4392	−0.773609
$919$	−42.6348	−1.40639	−0.703197	−	0.710995i	$-0.748245\pi$
$919$	−42.6348	−1.40639	−0.703197	+	0.710995i	$0.748245\pi$
$920$	−12.0562	−0.397483
$921$	−61.7667	−2.03528
$922$	19.5369	0.643415
$923$	1.91055	0.0628865
$924$	3.55885	0.117077
$925$	−1.84822	−0.0607692
$926$	−12.2651	−0.403057
$927$	−79.9595	−2.62622
$928$	−3.29496	−0.108162
$929$	20.9318	0.686751	0.343376	−	0.939198i	$-0.388430\pi$
$929$	20.9318	0.686751	0.343376	+	0.939198i	$0.388430\pi$
$930$	35.2838	1.15700
$931$	2.07222	0.0679144
$932$	5.79050	0.189674
$933$	51.4441	1.68420
$934$	−1.90509	−0.0623364
$935$	−15.8451	−0.518190
$936$	2.11057	0.0689862
$937$	−10.0126	−0.327099	−0.163549	−	0.986535i	$-0.552294\pi$
$937$	−10.0126	−0.327099	−0.163549	+	0.986535i	$0.552294\pi$
$938$	9.28521	0.303173
$939$	−19.3560	−0.631658
$940$	−25.7768	−0.840746
$941$	−32.9504	−1.07415	−0.537076	−	0.843534i	$-0.680471\pi$
$941$	−32.9504	−1.07415	−0.537076	+	0.843534i	$0.680471\pi$
$942$	−36.4257	−1.18681
$943$	−36.2174	−1.17940
$944$	8.17921	0.266211
$945$	9.68023	0.314898
$946$	−3.55266	−0.115507
$947$	47.5397	1.54483	0.772416	−	0.635117i	$-0.219048\pi$
$947$	47.5397	1.54483	0.772416	+	0.635117i	$0.219048\pi$
$948$	2.01246	0.0653617
$949$	−1.79453	−0.0582529
$950$	0.0635002	0.00206022
$951$	−80.2731	−2.60304
$952$	−3.15195	−0.102155
$953$	−57.9169	−1.87611	−0.938056	−	0.346484i	$-0.887375\pi$
$953$	−57.9169	−1.87611	−0.938056	+	0.346484i	$0.887375\pi$
$954$	60.1275	1.94670
$955$	17.3304	0.560799
$956$	−11.5047	−0.372089
$957$	−15.5180	−0.501627
$958$	−3.34150	−0.107959
$959$	3.80025	0.122716
$960$	−6.44320	−0.207953
$961$	−1.01195	−0.0326435
$962$	−3.96944	−0.127980
$963$	−47.8645	−1.54241
$964$	−18.9424	−0.610095
$965$	25.1970	0.811121
$966$	−11.2949	−0.363408
$967$	−11.2314	−0.361177	−0.180588	−	0.983559i	$-0.557800\pi$
$967$	−11.2314	−0.361177	−0.180588	+	0.983559i	$0.557800\pi$
$968$	8.22333	0.264308
$969$	−3.79993	−0.122071
$970$	−22.7631	−0.730879
$971$	53.8582	1.72839	0.864196	−	0.503155i	$-0.167827\pi$
$971$	53.8582	1.72839	0.864196	+	0.503155i	$0.167827\pi$
$972$	14.2646	0.457538
$973$	−12.0884	−0.387537
$974$	6.05038	0.193867
$975$	0.235593	0.00754500
$976$	−2.64920	−0.0847989
$977$	−29.0786	−0.930306	−0.465153	−	0.885230i	$-0.654001\pi$
$977$	−29.0786	−0.930306	−0.465153	+	0.885230i	$0.654001\pi$
$978$	47.8643	1.53053
$979$	24.6185	0.786811
$980$	−14.6561	−0.468173
$981$	38.7128	1.23601
$982$	−7.33359	−0.234024
$983$	−7.21588	−0.230151	−0.115075	−	0.993357i	$-0.536711\pi$
$983$	−7.21588	−0.230151	−0.115075	+	0.993357i	$0.536711\pi$
$984$	−19.3556	−0.617034
$985$	−25.8858	−0.824791
$986$	13.7438	0.437691
$987$	−24.1490	−0.768672
$988$	0.136380	0.00433882
$989$	11.2753	0.358533
$990$	−18.9489	−0.602235
$991$	−19.4531	−0.617950	−0.308975	−	0.951070i	$-0.599986\pi$
$991$	−19.4531	−0.617950	−0.308975	+	0.951070i	$0.599986\pi$
$992$	−5.47613	−0.173867
$993$	60.9800	1.93514
$994$	−3.41213	−0.108226
$995$	−16.7709	−0.531672
$996$	4.51953	0.143207
$997$	45.8402	1.45177	0.725887	−	0.687814i	$-0.241429\pi$
$997$	45.8402	1.45177	0.725887	+	0.687814i	$0.241429\pi$
$998$	22.3079	0.706144
$999$	52.7181	1.66793

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.d.1.4	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.d.1.4	✓	37	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.82634 q^{3} +1.00000 q^{4} +2.27969 q^{5} +2.82634 q^{6} -0.755653 q^{7} -1.00000 q^{8} +4.98821 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.82634 q^{3} +1.00000 q^{4} +2.27969 q^{5} +2.82634 q^{6} -0.755653 q^{7} -1.00000 q^{8} +4.98821 q^{9} -2.27969 q^{10} +1.66633 q^{11} -2.82634 q^{12} -0.423112 q^{13} +0.755653 q^{14} -6.44320 q^{15} +1.00000 q^{16} -4.17115 q^{17} -4.98821 q^{18} -0.322325 q^{19} +2.27969 q^{20} +2.13573 q^{21} -1.66633 q^{22} +5.28854 q^{23} +2.82634 q^{24} +0.197007 q^{25} +0.423112 q^{26} -5.61936 q^{27} -0.755653 q^{28} +3.29496 q^{29} +6.44320 q^{30} +5.47613 q^{31} -1.00000 q^{32} -4.70963 q^{33} +4.17115 q^{34} -1.72266 q^{35} +4.98821 q^{36} -9.38152 q^{37} +0.322325 q^{38} +1.19586 q^{39} -2.27969 q^{40} -6.84829 q^{41} -2.13573 q^{42} +2.13202 q^{43} +1.66633 q^{44} +11.3716 q^{45} -5.28854 q^{46} -11.3071 q^{47} -2.82634 q^{48} -6.42899 q^{49} -0.197007 q^{50} +11.7891 q^{51} -0.423112 q^{52} -12.0539 q^{53} +5.61936 q^{54} +3.79873 q^{55} +0.755653 q^{56} +0.911001 q^{57} -3.29496 q^{58} +8.17921 q^{59} -6.44320 q^{60} -2.64920 q^{61} -5.47613 q^{62} -3.76936 q^{63} +1.00000 q^{64} -0.964567 q^{65} +4.70963 q^{66} +12.2877 q^{67} -4.17115 q^{68} -14.9472 q^{69} +1.72266 q^{70} -4.51547 q^{71} -4.98821 q^{72} +4.24126 q^{73} +9.38152 q^{74} -0.556808 q^{75} -0.322325 q^{76} -1.25917 q^{77} -1.19586 q^{78} -0.712037 q^{79} +2.27969 q^{80} +0.917597 q^{81} +6.84829 q^{82} -1.59908 q^{83} +2.13573 q^{84} -9.50896 q^{85} -2.13202 q^{86} -9.31267 q^{87} -1.66633 q^{88} +14.7741 q^{89} -11.3716 q^{90} +0.319726 q^{91} +5.28854 q^{92} -15.4774 q^{93} +11.3071 q^{94} -0.734803 q^{95} +2.82634 q^{96} +9.98515 q^{97} +6.42899 q^{98} +8.31202 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9}+O(q^{10}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9	\( 37 q - 37 q^{2} - 5 q^{3} + 37 q^{4} - 13 q^{5} + 5 q^{6} - 22 q^{7} - 37 q^{8} + 32 q^{9} + 13 q^{10} + 12 q^{11} - 5 q^{12} - 36 q^{13} + 22 q^{14} - 7 q^{15} + 37 q^{16} + 4 q^{17} - 32 q^{18} - 10 q^{19} - 13 q^{20} - 11 q^{21} - 12 q^{22} - q^{23} + 5 q^{24} + 8 q^{25} + 36 q^{26} - 20 q^{27} - 22 q^{28} - 6 q^{29} + 7 q^{30} - 23 q^{31} - 37 q^{32} - 27 q^{33} - 4 q^{34} + 24 q^{35} + 32 q^{36} - 46 q^{37} + 10 q^{38} + 5 q^{39} + 13 q^{40} + 11 q^{41} + 11 q^{42} - 22 q^{43} + 12 q^{44} - 57 q^{45} + q^{46} - 18 q^{47} - 5 q^{48} - q^{49} - 8 q^{50} + 18 q^{51} - 36 q^{52} - 25 q^{53} + 20 q^{54} - 25 q^{55} + 22 q^{56} - 25 q^{57} + 6 q^{58} + 24 q^{59} - 7 q^{60} - 40 q^{61} + 23 q^{62} - 38 q^{63} + 37 q^{64} + 14 q^{65} + 27 q^{66} - 49 q^{67} + 4 q^{68} - 19 q^{69} - 24 q^{70} + 27 q^{71} - 32 q^{72} - 87 q^{73} + 46 q^{74} - 5 q^{75} - 10 q^{76} - 50 q^{77} - 5 q^{78} + 11 q^{79} - 13 q^{80} + 5 q^{81} - 11 q^{82} - 9 q^{83} - 11 q^{84} - 68 q^{85} + 22 q^{86} - 12 q^{87} - 12 q^{88} - 3 q^{89} + 57 q^{90} - 19 q^{91} - q^{92} - 69 q^{93} + 18 q^{94} + 27 q^{95} + 5 q^{96} - 98 q^{97} + q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q - 37 * q^2 - 5 * q^3 + 37 * q^4 - 13 * q^5 + 5 * q^6 - 22 * q^7 - 37 * q^8 + 32 * q^9 + 13 * q^10 + 12 * q^11 - 5 * q^12 - 36 * q^13 + 22 * q^14 - 7 * q^15 + 37 * q^16 + 4 * q^17 - 32 * q^18 - 10 * q^19 - 13 * q^20 - 11 * q^21 - 12 * q^22 - q^23 + 5 * q^24 + 8 * q^25 + 36 * q^26 - 20 * q^27 - 22 * q^28 - 6 * q^29 + 7 * q^30 - 23 * q^31 - 37 * q^32 - 27 * q^33 - 4 * q^34 + 24 * q^35 + 32 * q^36 - 46 * q^37 + 10 * q^38 + 5 * q^39 + 13 * q^40 + 11 * q^41 + 11 * q^42 - 22 * q^43 + 12 * q^44 - 57 * q^45 + q^46 - 18 * q^47 - 5 * q^48 - q^49 - 8 * q^50 + 18 * q^51 - 36 * q^52 - 25 * q^53 + 20 * q^54 - 25 * q^55 + 22 * q^56 - 25 * q^57 + 6 * q^58 + 24 * q^59 - 7 * q^60 - 40 * q^61 + 23 * q^62 - 38 * q^63 + 37 * q^64 + 14 * q^65 + 27 * q^66 - 49 * q^67 + 4 * q^68 - 19 * q^69 - 24 * q^70 + 27 * q^71 - 32 * q^72 - 87 * q^73 + 46 * q^74 - 5 * q^75 - 10 * q^76 - 50 * q^77 - 5 * q^78 + 11 * q^79 - 13 * q^80 + 5 * q^81 - 11 * q^82 - 9 * q^83 - 11 * q^84 - 68 * q^85 + 22 * q^86 - 12 * q^87 - 12 * q^88 - 3 * q^89 + 57 * q^90 - 19 * q^91 - q^92 - 69 * q^93 + 18 * q^94 + 27 * q^95 + 5 * q^96 - 98 * q^97 + q^98 + 33 * q^99

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