LMFDB - Embedded newform 6022.2.a.d.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.23814 q^{3} +1.00000 q^{4} +3.11624 q^{5} +2.23814 q^{6} +2.78730 q^{7} -1.00000 q^{8} +2.00926 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.23814 q^{3} +1.00000 q^{4} +3.11624 q^{5} +2.23814 q^{6} +2.78730 q^{7} -1.00000 q^{8} +2.00926 q^{9} -3.11624 q^{10} +3.00372 q^{11} -2.23814 q^{12} -3.52399 q^{13} -2.78730 q^{14} -6.97457 q^{15} +1.00000 q^{16} -0.103189 q^{17} -2.00926 q^{18} -2.56484 q^{19} +3.11624 q^{20} -6.23835 q^{21} -3.00372 q^{22} -6.42490 q^{23} +2.23814 q^{24} +4.71094 q^{25} +3.52399 q^{26} +2.21741 q^{27} +2.78730 q^{28} +5.98253 q^{29} +6.97457 q^{30} +4.88575 q^{31} -1.00000 q^{32} -6.72273 q^{33} +0.103189 q^{34} +8.68588 q^{35} +2.00926 q^{36} -9.11854 q^{37} +2.56484 q^{38} +7.88717 q^{39} -3.11624 q^{40} +6.96954 q^{41} +6.23835 q^{42} -1.60810 q^{43} +3.00372 q^{44} +6.26134 q^{45} +6.42490 q^{46} -8.33330 q^{47} -2.23814 q^{48} +0.769022 q^{49} -4.71094 q^{50} +0.230951 q^{51} -3.52399 q^{52} -7.74698 q^{53} -2.21741 q^{54} +9.36030 q^{55} -2.78730 q^{56} +5.74047 q^{57} -5.98253 q^{58} -13.0083 q^{59} -6.97457 q^{60} -11.4874 q^{61} -4.88575 q^{62} +5.60041 q^{63} +1.00000 q^{64} -10.9816 q^{65} +6.72273 q^{66} -11.6913 q^{67} -0.103189 q^{68} +14.3798 q^{69} -8.68588 q^{70} +2.03734 q^{71} -2.00926 q^{72} -14.4475 q^{73} +9.11854 q^{74} -10.5437 q^{75} -2.56484 q^{76} +8.37225 q^{77} -7.88717 q^{78} +2.31889 q^{79} +3.11624 q^{80} -10.9907 q^{81} -6.96954 q^{82} -7.96686 q^{83} -6.23835 q^{84} -0.321561 q^{85} +1.60810 q^{86} -13.3897 q^{87} -3.00372 q^{88} -12.0512 q^{89} -6.26134 q^{90} -9.82239 q^{91} -6.42490 q^{92} -10.9350 q^{93} +8.33330 q^{94} -7.99267 q^{95} +2.23814 q^{96} +4.11442 q^{97} -0.769022 q^{98} +6.03526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.23814	−1.29219	−0.646095	−	0.763257i	$-0.723599\pi$
$3$	−2.23814	−1.29219	−0.646095	+	0.763257i	$0.723599\pi$
$4$	1.00000	0.500000
$5$	3.11624	1.39362	0.696812	−	0.717254i	$-0.254601\pi$
$5$	3.11624	1.39362	0.696812	+	0.717254i	$0.254601\pi$
$6$	2.23814	0.913716
$7$	2.78730	1.05350	0.526750	−	0.850021i	$-0.323411\pi$
$7$	2.78730	1.05350	0.526750	+	0.850021i	$0.323411\pi$
$8$	−1.00000	−0.353553
$9$	2.00926	0.669754
$10$	−3.11624	−0.985441
$11$	3.00372	0.905655	0.452827	−	0.891598i	$-0.350415\pi$
$11$	3.00372	0.905655	0.452827	+	0.891598i	$0.350415\pi$
$12$	−2.23814	−0.646095
$13$	−3.52399	−0.977378	−0.488689	−	0.872458i	$-0.662525\pi$
$13$	−3.52399	−0.977378	−0.488689	+	0.872458i	$0.662525\pi$
$14$	−2.78730	−0.744936
$15$	−6.97457	−1.80083
$16$	1.00000	0.250000
$17$	−0.103189	−0.0250270	−0.0125135	−	0.999922i	$-0.503983\pi$
$17$	−0.103189	−0.0250270	−0.0125135	+	0.999922i	$0.503983\pi$
$18$	−2.00926	−0.473588
$19$	−2.56484	−0.588415	−0.294208	−	0.955741i	$-0.595056\pi$
$19$	−2.56484	−0.588415	−0.294208	+	0.955741i	$0.595056\pi$
$20$	3.11624	0.696812
$21$	−6.23835	−1.36132
$22$	−3.00372	−0.640395
$23$	−6.42490	−1.33968	−0.669842	−	0.742504i	$-0.733638\pi$
$23$	−6.42490	−1.33968	−0.669842	+	0.742504i	$0.733638\pi$
$24$	2.23814	0.456858
$25$	4.71094	0.942189
$26$	3.52399	0.691110
$27$	2.21741	0.426740
$28$	2.78730	0.526750
$29$	5.98253	1.11093	0.555464	−	0.831541i	$-0.312541\pi$
$29$	5.98253	1.11093	0.555464	+	0.831541i	$0.312541\pi$
$30$	6.97457	1.27338
$31$	4.88575	0.877506	0.438753	−	0.898608i	$-0.355420\pi$
$31$	4.88575	0.877506	0.438753	+	0.898608i	$0.355420\pi$
$32$	−1.00000	−0.176777
$33$	−6.72273	−1.17028
$34$	0.103189	0.0176967
$35$	8.68588	1.46818
$36$	2.00926	0.334877
$37$	−9.11854	−1.49908	−0.749540	−	0.661960i	$-0.769725\pi$
$37$	−9.11854	−1.49908	−0.749540	+	0.661960i	$0.769725\pi$
$38$	2.56484	0.416073
$39$	7.88717	1.26296
$40$	−3.11624	−0.492721
$41$	6.96954	1.08846	0.544229	−	0.838936i	$-0.316822\pi$
$41$	6.96954	1.08846	0.544229	+	0.838936i	$0.316822\pi$
$42$	6.23835	0.962599
$43$	−1.60810	−0.245233	−0.122617	−	0.992454i	$-0.539129\pi$
$43$	−1.60810	−0.245233	−0.122617	+	0.992454i	$0.539129\pi$
$44$	3.00372	0.452827
$45$	6.26134	0.933386
$46$	6.42490	0.947299
$47$	−8.33330	−1.21554	−0.607768	−	0.794114i	$-0.707935\pi$
$47$	−8.33330	−1.21554	−0.607768	+	0.794114i	$0.707935\pi$
$48$	−2.23814	−0.323047
$49$	0.769022	0.109860
$50$	−4.71094	−0.666228
$51$	0.230951	0.0323396
$52$	−3.52399	−0.488689
$53$	−7.74698	−1.06413	−0.532065	−	0.846704i	$-0.678584\pi$
$53$	−7.74698	−1.06413	−0.532065	+	0.846704i	$0.678584\pi$
$54$	−2.21741	−0.301751
$55$	9.36030	1.26214
$56$	−2.78730	−0.372468
$57$	5.74047	0.760344
$58$	−5.98253	−0.785545
$59$	−13.0083	−1.69353	−0.846767	−	0.531965i	$-0.821454\pi$
$59$	−13.0083	−1.69353	−0.846767	+	0.531965i	$0.821454\pi$
$60$	−6.97457	−0.900413
$61$	−11.4874	−1.47081	−0.735407	−	0.677626i	$-0.763009\pi$
$61$	−11.4874	−1.47081	−0.735407	+	0.677626i	$0.763009\pi$
$62$	−4.88575	−0.620491
$63$	5.60041	0.705585
$64$	1.00000	0.125000
$65$	−10.9816	−1.36210
$66$	6.72273	0.827511
$67$	−11.6913	−1.42832	−0.714159	−	0.699983i	$-0.753191\pi$
$67$	−11.6913	−1.42832	−0.714159	+	0.699983i	$0.753191\pi$
$68$	−0.103189	−0.0125135
$69$	14.3798	1.73113
$70$	−8.68588	−1.03816
$71$	2.03734	0.241787	0.120894	−	0.992665i	$-0.461424\pi$
$71$	2.03734	0.241787	0.120894	+	0.992665i	$0.461424\pi$
$72$	−2.00926	−0.236794
$73$	−14.4475	−1.69095	−0.845474	−	0.534017i	$-0.820682\pi$
$73$	−14.4475	−1.69095	−0.845474	+	0.534017i	$0.820682\pi$
$74$	9.11854	1.06001
$75$	−10.5437	−1.21749
$76$	−2.56484	−0.294208
$77$	8.37225	0.954106
$78$	−7.88717	−0.893046
$79$	2.31889	0.260896	0.130448	−	0.991455i	$-0.458359\pi$
$79$	2.31889	0.260896	0.130448	+	0.991455i	$0.458359\pi$
$80$	3.11624	0.348406
$81$	−10.9907	−1.22118
$82$	−6.96954	−0.769657
$83$	−7.96686	−0.874476	−0.437238	−	0.899346i	$-0.644043\pi$
$83$	−7.96686	−0.874476	−0.437238	+	0.899346i	$0.644043\pi$
$84$	−6.23835	−0.680660
$85$	−0.321561	−0.0348782
$86$	1.60810	0.173406
$87$	−13.3897	−1.43553
$88$	−3.00372	−0.320197
$89$	−12.0512	−1.27743	−0.638714	−	0.769444i	$-0.720533\pi$
$89$	−12.0512	−1.27743	−0.638714	+	0.769444i	$0.720533\pi$
$90$	−6.26134	−0.660003
$91$	−9.82239	−1.02967
$92$	−6.42490	−0.669842
$93$	−10.9350	−1.13390
$94$	8.33330	0.859514
$95$	−7.99267	−0.820030
$96$	2.23814	0.228429
$97$	4.11442	0.417756	0.208878	−	0.977942i	$-0.433019\pi$
$97$	4.11442	0.417756	0.208878	+	0.977942i	$0.433019\pi$
$98$	−0.769022	−0.0776830
$99$	6.03526	0.606566
$100$	4.71094	0.471094
$101$	7.07494	0.703983	0.351991	−	0.936003i	$-0.385505\pi$
$101$	7.07494	0.703983	0.351991	+	0.936003i	$0.385505\pi$
$102$	−0.230951	−0.0228676
$103$	2.47591	0.243959	0.121979	−	0.992533i	$-0.461076\pi$
$103$	2.47591	0.243959	0.121979	+	0.992533i	$0.461076\pi$
$104$	3.52399	0.345555
$105$	−19.4402	−1.89717
$106$	7.74698	0.752454
$107$	19.9570	1.92932	0.964658	−	0.263506i	$-0.0848790\pi$
$107$	19.9570	1.92932	0.964658	+	0.263506i	$0.0848790\pi$
$108$	2.21741	0.213370
$109$	−1.05291	−0.100850	−0.0504251	−	0.998728i	$-0.516058\pi$
$109$	−1.05291	−0.100850	−0.0504251	+	0.998728i	$0.516058\pi$
$110$	−9.36030	−0.892469
$111$	20.4086	1.93709
$112$	2.78730	0.263375
$113$	−0.587019	−0.0552221	−0.0276110	−	0.999619i	$-0.508790\pi$
$113$	−0.587019	−0.0552221	−0.0276110	+	0.999619i	$0.508790\pi$
$114$	−5.74047	−0.537645
$115$	−20.0215	−1.86702
$116$	5.98253	0.555464
$117$	−7.08061	−0.654603
$118$	13.0083	1.19751
$119$	−0.287618	−0.0263659
$120$	6.97457	0.636688
$121$	−1.97769	−0.179790
$122$	11.4874	1.04002
$123$	−15.5988	−1.40650
$124$	4.88575	0.438753
$125$	−0.900769	−0.0805673
$126$	−5.60041	−0.498924
$127$	11.9060	1.05648	0.528242	−	0.849094i	$-0.322851\pi$
$127$	11.9060	1.05648	0.528242	+	0.849094i	$0.322851\pi$
$128$	−1.00000	−0.0883883
$129$	3.59915	0.316888
$130$	10.9816	0.963148
$131$	3.35007	0.292697	0.146349	−	0.989233i	$-0.453248\pi$
$131$	3.35007	0.292697	0.146349	+	0.989233i	$0.453248\pi$
$132$	−6.72273	−0.585139
$133$	−7.14898	−0.619895
$134$	11.6913	1.00997
$135$	6.90997	0.594716
$136$	0.103189	0.00884837
$137$	1.83512	0.156785	0.0783926	−	0.996923i	$-0.475021\pi$
$137$	1.83512	0.156785	0.0783926	+	0.996923i	$0.475021\pi$
$138$	−14.3798	−1.22409
$139$	0.592916	0.0502905	0.0251452	−	0.999684i	$-0.491995\pi$
$139$	0.592916	0.0502905	0.0251452	+	0.999684i	$0.491995\pi$
$140$	8.68588	0.734091
$141$	18.6511	1.57070
$142$	−2.03734	−0.170969
$143$	−10.5851	−0.885167
$144$	2.00926	0.167439
$145$	18.6430	1.54822
$146$	14.4475	1.19568
$147$	−1.72118	−0.141960
$148$	−9.11854	−0.749540
$149$	3.22994	0.264607	0.132304	−	0.991209i	$-0.457763\pi$
$149$	3.22994	0.264607	0.132304	+	0.991209i	$0.457763\pi$
$150$	10.5437	0.860893
$151$	5.92554	0.482214	0.241107	−	0.970499i	$-0.422490\pi$
$151$	5.92554	0.482214	0.241107	+	0.970499i	$0.422490\pi$
$152$	2.56484	0.208036
$153$	−0.207334	−0.0167619
$154$	−8.37225	−0.674655
$155$	15.2252	1.22291
$156$	7.88717	0.631479
$157$	−20.3326	−1.62272	−0.811361	−	0.584546i	$-0.801273\pi$
$157$	−20.3326	−1.62272	−0.811361	+	0.584546i	$0.801273\pi$
$158$	−2.31889	−0.184481
$159$	17.3388	1.37506
$160$	−3.11624	−0.246360
$161$	−17.9081	−1.41136
$162$	10.9907	0.863507
$163$	−4.21573	−0.330201	−0.165101	−	0.986277i	$-0.552795\pi$
$163$	−4.21573	−0.330201	−0.165101	+	0.986277i	$0.552795\pi$
$164$	6.96954	0.544229
$165$	−20.9496	−1.63093
$166$	7.96686	0.618348
$167$	−8.88822	−0.687791	−0.343896	−	0.939008i	$-0.611747\pi$
$167$	−8.88822	−0.687791	−0.343896	+	0.939008i	$0.611747\pi$
$168$	6.23835	0.481300
$169$	−0.581525	−0.0447327
$170$	0.321561	0.0246626
$171$	−5.15344	−0.394094
$172$	−1.60810	−0.122617
$173$	5.24274	0.398598	0.199299	−	0.979939i	$-0.436133\pi$
$173$	5.24274	0.398598	0.199299	+	0.979939i	$0.436133\pi$
$174$	13.3897	1.01507
$175$	13.1308	0.992595
$176$	3.00372	0.226414
$177$	29.1143	2.18837
$178$	12.0512	0.903278
$179$	−21.1477	−1.58065	−0.790325	−	0.612688i	$-0.790088\pi$
$179$	−21.1477	−1.58065	−0.790325	+	0.612688i	$0.790088\pi$
$180$	6.26134	0.466693
$181$	9.79613	0.728141	0.364070	−	0.931371i	$-0.381387\pi$
$181$	9.79613	0.728141	0.364070	+	0.931371i	$0.381387\pi$
$182$	9.82239	0.728084
$183$	25.7104	1.90057
$184$	6.42490	0.473650
$185$	−28.4156	−2.08915
$186$	10.9350	0.801791
$187$	−0.309950	−0.0226658
$188$	−8.33330	−0.607768
$189$	6.18057	0.449570
$190$	7.99267	0.579849
$191$	6.30844	0.456463	0.228231	−	0.973607i	$-0.426706\pi$
$191$	6.30844	0.456463	0.228231	+	0.973607i	$0.426706\pi$
$192$	−2.23814	−0.161524
$193$	23.2276	1.67196	0.835981	−	0.548759i	$-0.184900\pi$
$193$	23.2276	1.67196	0.835981	+	0.548759i	$0.184900\pi$
$194$	−4.11442	−0.295398
$195$	24.5783	1.76009
$196$	0.769022	0.0549302
$197$	−11.4968	−0.819112	−0.409556	−	0.912285i	$-0.634316\pi$
$197$	−11.4968	−0.819112	−0.409556	+	0.912285i	$0.634316\pi$
$198$	−6.03526	−0.428907
$199$	11.1866	0.792997	0.396499	−	0.918035i	$-0.370225\pi$
$199$	11.1866	0.792997	0.396499	+	0.918035i	$0.370225\pi$
$200$	−4.71094	−0.333114
$201$	26.1667	1.84566
$202$	−7.07494	−0.497791
$203$	16.6751	1.17036
$204$	0.230951	0.0161698
$205$	21.7187	1.51690
$206$	−2.47591	−0.172505
$207$	−12.9093	−0.897259
$208$	−3.52399	−0.244344
$209$	−7.70406	−0.532901
$210$	19.4402	1.34150
$211$	4.44985	0.306341	0.153170	−	0.988200i	$-0.451052\pi$
$211$	4.44985	0.306341	0.153170	+	0.988200i	$0.451052\pi$
$212$	−7.74698	−0.532065
$213$	−4.55984	−0.312435
$214$	−19.9570	−1.36423
$215$	−5.01123	−0.341763
$216$	−2.21741	−0.150875
$217$	13.6180	0.924452
$218$	1.05291	0.0713119
$219$	32.3354	2.18502
$220$	9.36030	0.631071
$221$	0.363636	0.0244608
$222$	−20.4086	−1.36973
$223$	−15.4337	−1.03352	−0.516759	−	0.856131i	$-0.672862\pi$
$223$	−15.4337	−1.03352	−0.516759	+	0.856131i	$0.672862\pi$
$224$	−2.78730	−0.186234
$225$	9.46552	0.631035
$226$	0.587019	0.0390479
$227$	1.74822	0.116033	0.0580167	−	0.998316i	$-0.481522\pi$
$227$	1.74822	0.116033	0.0580167	+	0.998316i	$0.481522\pi$
$228$	5.74047	0.380172
$229$	−19.2737	−1.27364	−0.636819	−	0.771013i	$-0.719750\pi$
$229$	−19.2737	−1.27364	−0.636819	+	0.771013i	$0.719750\pi$
$230$	20.0215	1.32018
$231$	−18.7383	−1.23289
$232$	−5.98253	−0.392772
$233$	−12.0196	−0.787431	−0.393716	−	0.919232i	$-0.628811\pi$
$233$	−12.0196	−0.787431	−0.393716	+	0.919232i	$0.628811\pi$
$234$	7.08061	0.462874
$235$	−25.9685	−1.69400
$236$	−13.0083	−0.846767
$237$	−5.19000	−0.337127
$238$	0.287618	0.0186435
$239$	6.94962	0.449533	0.224767	−	0.974413i	$-0.427838\pi$
$239$	6.94962	0.449533	0.224767	+	0.974413i	$0.427838\pi$
$240$	−6.97457	−0.450207
$241$	17.0082	1.09560	0.547798	−	0.836611i	$-0.315466\pi$
$241$	17.0082	1.09560	0.547798	+	0.836611i	$0.315466\pi$
$242$	1.97769	0.127130
$243$	17.9464	1.15126
$244$	−11.4874	−0.735407
$245$	2.39646	0.153104
$246$	15.5988	0.994542
$247$	9.03847	0.575104
$248$	−4.88575	−0.310245
$249$	17.8309	1.12999
$250$	0.900769	0.0569697
$251$	4.15785	0.262441	0.131220	−	0.991353i	$-0.458110\pi$
$251$	4.15785	0.262441	0.131220	+	0.991353i	$0.458110\pi$
$252$	5.60041	0.352793
$253$	−19.2986	−1.21329
$254$	−11.9060	−0.747047
$255$	0.719698	0.0450693
$256$	1.00000	0.0625000
$257$	−14.5142	−0.905371	−0.452685	−	0.891670i	$-0.649534\pi$
$257$	−14.5142	−0.905371	−0.452685	+	0.891670i	$0.649534\pi$
$258$	−3.59915	−0.224074
$259$	−25.4161	−1.57928
$260$	−10.9816	−0.681049
$261$	12.0205	0.744049
$262$	−3.35007	−0.206968
$263$	2.20031	0.135677	0.0678386	−	0.997696i	$-0.478390\pi$
$263$	2.20031	0.135677	0.0678386	+	0.997696i	$0.478390\pi$
$264$	6.72273	0.413756
$265$	−24.1414	−1.48300
$266$	7.14898	0.438332
$267$	26.9723	1.65068
$268$	−11.6913	−0.714159
$269$	2.70041	0.164647	0.0823233	−	0.996606i	$-0.473766\pi$
$269$	2.70041	0.164647	0.0823233	+	0.996606i	$0.473766\pi$
$270$	−6.90997	−0.420527
$271$	−22.5183	−1.36789	−0.683946	−	0.729533i	$-0.739738\pi$
$271$	−22.5183	−1.36789	−0.683946	+	0.729533i	$0.739738\pi$
$272$	−0.103189	−0.00625675
$273$	21.9839	1.33052
$274$	−1.83512	−0.110864
$275$	14.1503	0.853298
$276$	14.3798	0.865563
$277$	−13.6958	−0.822900	−0.411450	−	0.911432i	$-0.634978\pi$
$277$	−13.6958	−0.822900	−0.411450	+	0.911432i	$0.634978\pi$
$278$	−0.592916	−0.0355607
$279$	9.81675	0.587713
$280$	−8.68588	−0.519081
$281$	2.77252	0.165395	0.0826973	−	0.996575i	$-0.473647\pi$
$281$	2.77252	0.165395	0.0826973	+	0.996575i	$0.473647\pi$
$282$	−18.6511	−1.11066
$283$	15.8444	0.941851	0.470926	−	0.882173i	$-0.343920\pi$
$283$	15.8444	0.941851	0.470926	+	0.882173i	$0.343920\pi$
$284$	2.03734	0.120894
$285$	17.8887	1.05963
$286$	10.5851	0.625907
$287$	19.4262	1.14669
$288$	−2.00926	−0.118397
$289$	−16.9894	−0.999374
$290$	−18.6430	−1.09475
$291$	−9.20865	−0.539820
$292$	−14.4475	−0.845474
$293$	−2.60720	−0.152314	−0.0761572	−	0.997096i	$-0.524265\pi$
$293$	−2.60720	−0.152314	−0.0761572	+	0.997096i	$0.524265\pi$
$294$	1.72118	0.100381
$295$	−40.5369	−2.36015
$296$	9.11854	0.530004
$297$	6.66046	0.386479
$298$	−3.22994	−0.187106
$299$	22.6412	1.30938
$300$	−10.5437	−0.608743
$301$	−4.48226	−0.258353
$302$	−5.92554	−0.340977
$303$	−15.8347	−0.909679
$304$	−2.56484	−0.147104
$305$	−35.7976	−2.04976
$306$	0.207334	0.0118525
$307$	27.6148	1.57606	0.788031	−	0.615636i	$-0.211101\pi$
$307$	27.6148	1.57606	0.788031	+	0.615636i	$0.211101\pi$
$308$	8.37225	0.477053
$309$	−5.54143	−0.315241
$310$	−15.2252	−0.864731
$311$	17.5716	0.996397	0.498198	−	0.867063i	$-0.333995\pi$
$311$	17.5716	0.996397	0.498198	+	0.867063i	$0.333995\pi$
$312$	−7.88717	−0.446523
$313$	−21.2803	−1.20283	−0.601417	−	0.798935i	$-0.705397\pi$
$313$	−21.2803	−1.20283	−0.601417	+	0.798935i	$0.705397\pi$
$314$	20.3326	1.14744
$315$	17.4522	0.983321
$316$	2.31889	0.130448
$317$	15.2247	0.855105	0.427552	−	0.903991i	$-0.359376\pi$
$317$	15.2247	0.855105	0.427552	+	0.903991i	$0.359376\pi$
$318$	−17.3388	−0.972313
$319$	17.9698	1.00612
$320$	3.11624	0.174203
$321$	−44.6665	−2.49304
$322$	17.9081	0.997979
$323$	0.264663	0.0147263
$324$	−10.9907	−0.610592
$325$	−16.6013	−0.920874
$326$	4.21573	0.233487
$327$	2.35655	0.130318
$328$	−6.96954	−0.384828
$329$	−23.2274	−1.28057
$330$	20.9496	1.15324
$331$	0.398072	0.0218800	0.0109400	−	0.999940i	$-0.496518\pi$
$331$	0.398072	0.0218800	0.0109400	+	0.999940i	$0.496518\pi$
$332$	−7.96686	−0.437238
$333$	−18.3215	−1.00401
$334$	8.88822	0.486342
$335$	−36.4329	−1.99054
$336$	−6.23835	−0.340330
$337$	3.45810	0.188375	0.0941874	−	0.995554i	$-0.469975\pi$
$337$	3.45810	0.188375	0.0941874	+	0.995554i	$0.469975\pi$
$338$	0.581525	0.0316308
$339$	1.31383	0.0713574
$340$	−0.321561	−0.0174391
$341$	14.6754	0.794718
$342$	5.15344	0.278666
$343$	−17.3676	−0.937761
$344$	1.60810	0.0867030
$345$	44.8109	2.41254
$346$	−5.24274	−0.281852
$347$	20.2350	1.08627	0.543135	−	0.839645i	$-0.317237\pi$
$347$	20.2350	1.08627	0.543135	+	0.839645i	$0.317237\pi$
$348$	−13.3897	−0.717765
$349$	18.3927	0.984537	0.492269	−	0.870443i	$-0.336168\pi$
$349$	18.3927	0.984537	0.492269	+	0.870443i	$0.336168\pi$
$350$	−13.1308	−0.701871
$351$	−7.81411	−0.417086
$352$	−3.00372	−0.160099
$353$	10.0402	0.534387	0.267194	−	0.963643i	$-0.413904\pi$
$353$	10.0402	0.534387	0.267194	+	0.963643i	$0.413904\pi$
$354$	−29.1143	−1.54741
$355$	6.34882	0.336961
$356$	−12.0512	−0.638714
$357$	0.643729	0.0340697
$358$	21.1477	1.11769
$359$	30.8967	1.63067	0.815333	−	0.578992i	$-0.196554\pi$
$359$	30.8967	1.63067	0.815333	+	0.578992i	$0.196554\pi$
$360$	−6.26134	−0.330002
$361$	−12.4216	−0.653767
$362$	−9.79613	−0.514873
$363$	4.42633	0.232322
$364$	−9.82239	−0.514833
$365$	−45.0217	−2.35654
$366$	−25.7104	−1.34391
$367$	17.2719	0.901584	0.450792	−	0.892629i	$-0.351142\pi$
$367$	17.2719	0.901584	0.450792	+	0.892629i	$0.351142\pi$
$368$	−6.42490	−0.334921
$369$	14.0036	0.729000
$370$	28.4156	1.47725
$371$	−21.5931	−1.12106
$372$	−10.9350	−0.566952
$373$	19.4838	1.00883	0.504416	−	0.863461i	$-0.331708\pi$
$373$	19.4838	1.00883	0.504416	+	0.863461i	$0.331708\pi$
$374$	0.309950	0.0160271
$375$	2.01605	0.104108
$376$	8.33330	0.429757
$377$	−21.0823	−1.08580
$378$	−6.18057	−0.317894
$379$	13.0807	0.671908	0.335954	−	0.941878i	$-0.390941\pi$
$379$	13.0807	0.671908	0.335954	+	0.941878i	$0.390941\pi$
$380$	−7.99267	−0.410015
$381$	−26.6472	−1.36518
$382$	−6.30844	−0.322768
$383$	14.7984	0.756161	0.378081	−	0.925773i	$-0.376584\pi$
$383$	14.7984	0.756161	0.378081	+	0.925773i	$0.376584\pi$
$384$	2.23814	0.114215
$385$	26.0899	1.32967
$386$	−23.2276	−1.18226
$387$	−3.23110	−0.164246
$388$	4.11442	0.208878
$389$	−14.1726	−0.718580	−0.359290	−	0.933226i	$-0.616981\pi$
$389$	−14.1726	−0.718580	−0.359290	+	0.933226i	$0.616981\pi$
$390$	−24.5783	−1.24457
$391$	0.662978	0.0335282
$392$	−0.769022	−0.0388415
$393$	−7.49792	−0.378220
$394$	11.4968	0.579200
$395$	7.22622	0.363590
$396$	6.03526	0.303283
$397$	7.20961	0.361840	0.180920	−	0.983498i	$-0.442092\pi$
$397$	7.20961	0.361840	0.180920	+	0.983498i	$0.442092\pi$
$398$	−11.1866	−0.560734
$399$	16.0004	0.801022
$400$	4.71094	0.235547
$401$	−32.9213	−1.64401	−0.822006	−	0.569479i	$-0.807145\pi$
$401$	−32.9213	−1.64401	−0.822006	+	0.569479i	$0.807145\pi$
$402$	−26.1667	−1.30508
$403$	−17.2173	−0.857655
$404$	7.07494	0.351991
$405$	−34.2495	−1.70187
$406$	−16.6751	−0.827570
$407$	−27.3895	−1.35765
$408$	−0.230951	−0.0114338
$409$	14.5679	0.720334	0.360167	−	0.932888i	$-0.382720\pi$
$409$	14.5679	0.720334	0.360167	+	0.932888i	$0.382720\pi$
$410$	−21.7187	−1.07261
$411$	−4.10726	−0.202596
$412$	2.47591	0.121979
$413$	−36.2579	−1.78414
$414$	12.9093	0.634458
$415$	−24.8266	−1.21869
$416$	3.52399	0.172778
$417$	−1.32703	−0.0649848
$418$	7.70406	0.376818
$419$	36.5145	1.78385	0.891926	−	0.452181i	$-0.149354\pi$
$419$	36.5145	1.78385	0.891926	+	0.452181i	$0.149354\pi$
$420$	−19.4402	−0.948585
$421$	4.84802	0.236278	0.118139	−	0.992997i	$-0.462307\pi$
$421$	4.84802	0.236278	0.118139	+	0.992997i	$0.462307\pi$
$422$	−4.44985	−0.216616
$423$	−16.7438	−0.814111
$424$	7.74698	0.376227
$425$	−0.486117	−0.0235801
$426$	4.55984	0.220925
$427$	−32.0189	−1.54950
$428$	19.9570	0.964658
$429$	23.6908	1.14380
$430$	5.01123	0.241663
$431$	−12.7701	−0.615116	−0.307558	−	0.951529i	$-0.599512\pi$
$431$	−12.7701	−0.615116	−0.307558	+	0.951529i	$0.599512\pi$
$432$	2.21741	0.106685
$433$	22.1786	1.06583	0.532917	−	0.846167i	$-0.321096\pi$
$433$	22.1786	1.06583	0.532917	+	0.846167i	$0.321096\pi$
$434$	−13.6180	−0.653686
$435$	−41.7256	−2.00059
$436$	−1.05291	−0.0504251
$437$	16.4789	0.788291
$438$	−32.3354	−1.54505
$439$	−7.14250	−0.340893	−0.170446	−	0.985367i	$-0.554521\pi$
$439$	−7.14250	−0.340893	−0.170446	+	0.985367i	$0.554521\pi$
$440$	−9.36030	−0.446235
$441$	1.54517	0.0735794
$442$	−0.363636	−0.0172964
$443$	−38.6396	−1.83582	−0.917912	−	0.396785i	$-0.870126\pi$
$443$	−38.6396	−1.83582	−0.917912	+	0.396785i	$0.870126\pi$
$444$	20.4086	0.968547
$445$	−37.5545	−1.78026
$446$	15.4337	0.730807
$447$	−7.22906	−0.341923
$448$	2.78730	0.131687
$449$	−26.1680	−1.23495	−0.617473	−	0.786592i	$-0.711843\pi$
$449$	−26.1680	−1.23495	−0.617473	+	0.786592i	$0.711843\pi$
$450$	−9.46552	−0.446209
$451$	20.9345	0.985768
$452$	−0.587019	−0.0276110
$453$	−13.2622	−0.623111
$454$	−1.74822	−0.0820480
$455$	−30.6089	−1.43497
$456$	−5.74047	−0.268822
$457$	23.4185	1.09547	0.547736	−	0.836652i	$-0.315490\pi$
$457$	23.4185	1.09547	0.547736	+	0.836652i	$0.315490\pi$
$458$	19.2737	0.900599
$459$	−0.228812	−0.0106800
$460$	−20.0215	−0.933508
$461$	−17.6865	−0.823741	−0.411870	−	0.911242i	$-0.635124\pi$
$461$	−17.6865	−0.823741	−0.411870	+	0.911242i	$0.635124\pi$
$462$	18.7383	0.871782
$463$	−15.0850	−0.701061	−0.350531	−	0.936551i	$-0.613999\pi$
$463$	−15.0850	−0.701061	−0.350531	+	0.936551i	$0.613999\pi$
$464$	5.98253	0.277732
$465$	−34.0760	−1.58024
$466$	12.0196	0.556798
$467$	7.96041	0.368364	0.184182	−	0.982892i	$-0.441036\pi$
$467$	7.96041	0.368364	0.184182	+	0.982892i	$0.441036\pi$
$468$	−7.08061	−0.327301
$469$	−32.5871	−1.50473
$470$	25.9685	1.19784
$471$	45.5073	2.09686
$472$	13.0083	0.598754
$473$	−4.83028	−0.222097
$474$	5.19000	0.238384
$475$	−12.0828	−0.554398
$476$	−0.287618	−0.0131830
$477$	−15.5657	−0.712705
$478$	−6.94962	−0.317868
$479$	−35.5104	−1.62251	−0.811256	−	0.584691i	$-0.801216\pi$
$479$	−35.5104	−1.62251	−0.811256	+	0.584691i	$0.801216\pi$
$480$	6.97457	0.318344
$481$	32.1336	1.46517
$482$	−17.0082	−0.774703
$483$	40.0808	1.82374
$484$	−1.97769	−0.0898948
$485$	12.8215	0.582195
$486$	−17.9464	−0.814064
$487$	10.8025	0.489506	0.244753	−	0.969585i	$-0.421293\pi$
$487$	10.8025	0.489506	0.244753	+	0.969585i	$0.421293\pi$
$488$	11.4874	0.520011
$489$	9.43538	0.426682
$490$	−2.39646	−0.108261
$491$	30.7389	1.38723	0.693613	−	0.720348i	$-0.256018\pi$
$491$	30.7389	1.38723	0.693613	+	0.720348i	$0.256018\pi$
$492$	−15.5988	−0.703248
$493$	−0.617331	−0.0278032
$494$	−9.03847	−0.406660
$495$	18.8073	0.845325
$496$	4.88575	0.219377
$497$	5.67866	0.254723
$498$	−17.8309	−0.799023
$499$	30.5414	1.36722	0.683611	−	0.729847i	$-0.260408\pi$
$499$	30.5414	1.36722	0.683611	+	0.729847i	$0.260408\pi$
$500$	−0.900769	−0.0402836
$501$	19.8931	0.888757
$502$	−4.15785	−0.185574
$503$	−6.70546	−0.298981	−0.149491	−	0.988763i	$-0.547763\pi$
$503$	−6.70546	−0.298981	−0.149491	+	0.988763i	$0.547763\pi$
$504$	−5.60041	−0.249462
$505$	22.0472	0.981087
$506$	19.2986	0.857926
$507$	1.30153	0.0578031
$508$	11.9060	0.528242
$509$	−5.78860	−0.256575	−0.128288	−	0.991737i	$-0.540948\pi$
$509$	−5.78860	−0.256575	−0.128288	+	0.991737i	$0.540948\pi$
$510$	−0.719698	−0.0318688
$511$	−40.2694	−1.78141
$512$	−1.00000	−0.0441942
$513$	−5.68730	−0.251101
$514$	14.5142	0.640194
$515$	7.71553	0.339987
$516$	3.59915	0.158444
$517$	−25.0309	−1.10086
$518$	25.4161	1.11672
$519$	−11.7340	−0.515065
$520$	10.9816	0.481574
$521$	7.40994	0.324635	0.162318	−	0.986739i	$-0.448103\pi$
$521$	7.40994	0.324635	0.162318	+	0.986739i	$0.448103\pi$
$522$	−12.0205	−0.526122
$523$	−20.1527	−0.881216	−0.440608	−	0.897700i	$-0.645237\pi$
$523$	−20.1527	−0.881216	−0.440608	+	0.897700i	$0.645237\pi$
$524$	3.35007	0.146349
$525$	−29.3885	−1.28262
$526$	−2.20031	−0.0959382
$527$	−0.504155	−0.0219613
$528$	−6.72273	−0.292569
$529$	18.2793	0.794752
$530$	24.1414	1.04864
$531$	−26.1370	−1.13425
$532$	−7.14898	−0.309948
$533$	−24.5605	−1.06384
$534$	−26.9723	−1.16721
$535$	62.1908	2.68874
$536$	11.6913	0.504987
$537$	47.3314	2.04250
$538$	−2.70041	−0.116423
$539$	2.30993	0.0994955
$540$	6.90997	0.297358
$541$	−0.00519593	−0.000223390 0	−0.000111695	−	1.00000i	$-0.500036\pi$
$541$	−0.00519593	−0.000223390 0	−0.000111695		1.00000i	$0.500036\pi$
$542$	22.5183	0.967246
$543$	−21.9251	−0.940896
$544$	0.103189	0.00442419
$545$	−3.28111	−0.140547
$546$	−21.9839	−0.940823
$547$	37.8597	1.61876	0.809382	−	0.587282i	$-0.199802\pi$
$547$	37.8597	1.61876	0.809382	+	0.587282i	$0.199802\pi$
$548$	1.83512	0.0783926
$549$	−23.0813	−0.985084
$550$	−14.1503	−0.603373
$551$	−15.3443	−0.653687
$552$	−14.3798	−0.612045
$553$	6.46344	0.274853
$554$	13.6958	0.581878
$555$	63.5979	2.69958
$556$	0.592916	0.0251452
$557$	−38.3534	−1.62509	−0.812544	−	0.582900i	$-0.801918\pi$
$557$	−38.3534	−1.62509	−0.812544	+	0.582900i	$0.801918\pi$
$558$	−9.81675	−0.415576
$559$	5.66693	0.239686
$560$	8.68588	0.367045
$561$	0.693711	0.0292885
$562$	−2.77252	−0.116952
$563$	−36.8112	−1.55141	−0.775704	−	0.631097i	$-0.782605\pi$
$563$	−36.8112	−1.55141	−0.775704	+	0.631097i	$0.782605\pi$
$564$	18.6511	0.785352
$565$	−1.82929	−0.0769588
$566$	−15.8444	−0.665989
$567$	−30.6342	−1.28652
$568$	−2.03734	−0.0854847
$569$	−8.78041	−0.368094	−0.184047	−	0.982917i	$-0.558920\pi$
$569$	−8.78041	−0.368094	−0.184047	+	0.982917i	$0.558920\pi$
$570$	−17.8887	−0.749275
$571$	−35.9148	−1.50299	−0.751495	−	0.659739i	$-0.770667\pi$
$571$	−35.9148	−1.50299	−0.751495	+	0.659739i	$0.770667\pi$
$572$	−10.5851	−0.442583
$573$	−14.1192	−0.589837
$574$	−19.4262	−0.810833
$575$	−30.2673	−1.26223
$576$	2.00926	0.0837193
$577$	−25.5673	−1.06438	−0.532191	−	0.846624i	$-0.678631\pi$
$577$	−25.5673	−1.06438	−0.532191	+	0.846624i	$0.678631\pi$
$578$	16.9894	0.706664
$579$	−51.9866	−2.16049
$580$	18.6430	0.774108
$581$	−22.2060	−0.921260
$582$	9.20865	0.381711
$583$	−23.2697	−0.963734
$584$	14.4475	0.597840
$585$	−22.0649	−0.912270
$586$	2.60720	0.107703
$587$	11.9745	0.494241	0.247121	−	0.968985i	$-0.420516\pi$
$587$	11.9745	0.494241	0.247121	+	0.968985i	$0.420516\pi$
$588$	−1.72118	−0.0709802
$589$	−12.5312	−0.516338
$590$	40.5369	1.66888
$591$	25.7314	1.05845
$592$	−9.11854	−0.374770
$593$	12.9005	0.529758	0.264879	−	0.964282i	$-0.414668\pi$
$593$	12.9005	0.529758	0.264879	+	0.964282i	$0.414668\pi$
$594$	−6.66046	−0.273282
$595$	−0.896286	−0.0367442
$596$	3.22994	0.132304
$597$	−25.0372	−1.02470
$598$	−22.6412	−0.925869
$599$	−1.47495	−0.0602650	−0.0301325	−	0.999546i	$-0.509593\pi$
$599$	−1.47495	−0.0602650	−0.0301325	+	0.999546i	$0.509593\pi$
$600$	10.5437	0.430446
$601$	2.54455	0.103794	0.0518972	−	0.998652i	$-0.483473\pi$
$601$	2.54455	0.103794	0.0518972	+	0.998652i	$0.483473\pi$
$602$	4.48226	0.182683
$603$	−23.4909	−0.956622
$604$	5.92554	0.241107
$605$	−6.16294	−0.250559
$606$	15.8347	0.643240
$607$	−9.10902	−0.369724	−0.184862	−	0.982765i	$-0.559184\pi$
$607$	−9.10902	−0.369724	−0.184862	+	0.982765i	$0.559184\pi$
$608$	2.56484	0.104018
$609$	−37.3211	−1.51233
$610$	35.7976	1.44940
$611$	29.3664	1.18804
$612$	−0.207334	−0.00838096
$613$	−29.3801	−1.18665	−0.593326	−	0.804962i	$-0.702185\pi$
$613$	−29.3801	−1.18665	−0.593326	+	0.804962i	$0.702185\pi$
$614$	−27.6148	−1.11444
$615$	−48.6095	−1.96013
$616$	−8.37225	−0.337328
$617$	26.1583	1.05309	0.526546	−	0.850147i	$-0.323487\pi$
$617$	26.1583	1.05309	0.526546	+	0.850147i	$0.323487\pi$
$618$	5.54143	0.222909
$619$	−28.0118	−1.12589	−0.562945	−	0.826494i	$-0.690332\pi$
$619$	−28.0118	−1.12589	−0.562945	+	0.826494i	$0.690332\pi$
$620$	15.2252	0.611457
$621$	−14.2466	−0.571697
$622$	−17.5716	−0.704559
$623$	−33.5904	−1.34577
$624$	7.88717	0.315739
$625$	−26.3617	−1.05447
$626$	21.2803	0.850532
$627$	17.2428	0.688609
$628$	−20.3326	−0.811361
$629$	0.940932	0.0375174
$630$	−17.4522	−0.695313
$631$	3.49392	0.139091	0.0695453	−	0.997579i	$-0.477845\pi$
$631$	3.49392	0.139091	0.0695453	+	0.997579i	$0.477845\pi$
$632$	−2.31889	−0.0922405
$633$	−9.95939	−0.395850
$634$	−15.2247	−0.604651
$635$	37.1019	1.47234
$636$	17.3388	0.687529
$637$	−2.71002	−0.107375
$638$	−17.9698	−0.711432
$639$	4.09354	0.161938
$640$	−3.11624	−0.123180
$641$	−0.958899	−0.0378742	−0.0189371	−	0.999821i	$-0.506028\pi$
$641$	−0.958899	−0.0378742	−0.0189371	+	0.999821i	$0.506028\pi$
$642$	44.6665	1.76285
$643$	−17.2790	−0.681416	−0.340708	−	0.940169i	$-0.610667\pi$
$643$	−17.2790	−0.681416	−0.340708	+	0.940169i	$0.610667\pi$
$644$	−17.9081	−0.705678
$645$	11.2158	0.441623
$646$	−0.264663	−0.0104130
$647$	32.9487	1.29535	0.647673	−	0.761918i	$-0.275742\pi$
$647$	32.9487	1.29535	0.647673	+	0.761918i	$0.275742\pi$
$648$	10.9907	0.431754
$649$	−39.0732	−1.53376
$650$	16.6013	0.651156
$651$	−30.4790	−1.19457
$652$	−4.21573	−0.165101
$653$	−17.4703	−0.683666	−0.341833	−	0.939761i	$-0.611048\pi$
$653$	−17.4703	−0.683666	−0.341833	+	0.939761i	$0.611048\pi$
$654$	−2.35655	−0.0921485
$655$	10.4396	0.407910
$656$	6.96954	0.272115
$657$	−29.0287	−1.13252
$658$	23.2274	0.905497
$659$	−44.3022	−1.72577	−0.862885	−	0.505401i	$-0.831345\pi$
$659$	−44.3022	−1.72577	−0.862885	+	0.505401i	$0.831345\pi$
$660$	−20.9496	−0.815464
$661$	9.23728	0.359289	0.179644	−	0.983732i	$-0.442505\pi$
$661$	9.23728	0.359289	0.179644	+	0.983732i	$0.442505\pi$
$662$	−0.398072	−0.0154715
$663$	−0.813868	−0.0316080
$664$	7.96686	0.309174
$665$	−22.2779	−0.863901
$666$	18.3215	0.709945
$667$	−38.4371	−1.48829
$668$	−8.88822	−0.343896
$669$	34.5428	1.33550
$670$	36.4329	1.40752
$671$	−34.5050	−1.33205
$672$	6.23835	0.240650
$673$	46.4256	1.78957	0.894787	−	0.446493i	$-0.147327\pi$
$673$	46.4256	1.78957	0.894787	+	0.446493i	$0.147327\pi$
$674$	−3.45810	−0.133201
$675$	10.4461	0.402070
$676$	−0.581525	−0.0223663
$677$	−42.6222	−1.63811	−0.819053	−	0.573718i	$-0.805501\pi$
$677$	−42.6222	−1.63811	−0.819053	+	0.573718i	$0.805501\pi$
$678$	−1.31383	−0.0504573
$679$	11.4681	0.440106
$680$	0.321561	0.0123313
$681$	−3.91275	−0.149937
$682$	−14.6754	−0.561950
$683$	−15.7119	−0.601199	−0.300600	−	0.953750i	$-0.597187\pi$
$683$	−15.7119	−0.601199	−0.300600	+	0.953750i	$0.597187\pi$
$684$	−5.15344	−0.197047
$685$	5.71868	0.218500
$686$	17.3676	0.663097
$687$	43.1371	1.64578
$688$	−1.60810	−0.0613083
$689$	27.3003	1.04006
$690$	−44.8109	−1.70592
$691$	33.7833	1.28518	0.642588	−	0.766212i	$-0.277861\pi$
$691$	33.7833	1.28518	0.642588	+	0.766212i	$0.277861\pi$
$692$	5.24274	0.199299
$693$	16.8220	0.639017
$694$	−20.2350	−0.768109
$695$	1.84767	0.0700860
$696$	13.3897	0.507536
$697$	−0.719179	−0.0272408
$698$	−18.3927	−0.696173
$699$	26.9016	1.01751
$700$	13.1308	0.496297
$701$	−34.0671	−1.28669	−0.643347	−	0.765574i	$-0.722455\pi$
$701$	−34.0671	−1.28669	−0.643347	+	0.765574i	$0.722455\pi$
$702$	7.81411	0.294925
$703$	23.3876	0.882081
$704$	3.00372	0.113207
$705$	58.1212	2.18897
$706$	−10.0402	−0.377869
$707$	19.7200	0.741645
$708$	29.1143	1.09418
$709$	25.6895	0.964790	0.482395	−	0.875954i	$-0.339767\pi$
$709$	25.6895	0.964790	0.482395	+	0.875954i	$0.339767\pi$
$710$	−6.34882	−0.238267
$711$	4.65926	0.174736
$712$	12.0512	0.451639
$713$	−31.3904	−1.17558
$714$	−0.643729	−0.0240909
$715$	−32.9856	−1.23359
$716$	−21.1477	−0.790325
$717$	−15.5542	−0.580882
$718$	−30.8967	−1.15305
$719$	−24.9952	−0.932162	−0.466081	−	0.884742i	$-0.654335\pi$
$719$	−24.9952	−0.932162	−0.466081	+	0.884742i	$0.654335\pi$
$720$	6.26134	0.233346
$721$	6.90110	0.257010
$722$	12.4216	0.462283
$723$	−38.0667	−1.41572
$724$	9.79613	0.364070
$725$	28.1834	1.04670
$726$	−4.42633	−0.164277
$727$	37.0120	1.37270	0.686350	−	0.727272i	$-0.259212\pi$
$727$	37.0120	1.37270	0.686350	+	0.727272i	$0.259212\pi$
$728$	9.82239	0.364042
$729$	−7.19451	−0.266463
$730$	45.0217	1.66633
$731$	0.165938	0.00613745
$732$	25.7104	0.950285
$733$	38.8563	1.43519	0.717595	−	0.696461i	$-0.245243\pi$
$733$	38.8563	1.43519	0.717595	+	0.696461i	$0.245243\pi$
$734$	−17.2719	−0.637516
$735$	−5.36360	−0.197839
$736$	6.42490	0.236825
$737$	−35.1173	−1.29356
$738$	−14.0036	−0.515481
$739$	−19.3952	−0.713465	−0.356733	−	0.934207i	$-0.616109\pi$
$739$	−19.3952	−0.713465	−0.356733	+	0.934207i	$0.616109\pi$
$740$	−28.4156	−1.04458
$741$	−20.2294	−0.743144
$742$	21.5931	0.792709
$743$	−45.5295	−1.67031	−0.835157	−	0.550012i	$-0.814623\pi$
$743$	−45.5295	−1.67031	−0.835157	+	0.550012i	$0.814623\pi$
$744$	10.9350	0.400896
$745$	10.0653	0.368763
$746$	−19.4838	−0.713352
$747$	−16.0075	−0.585684
$748$	−0.309950	−0.0113329
$749$	55.6261	2.03253
$750$	−2.01605	−0.0736156
$751$	−34.5129	−1.25939	−0.629697	−	0.776841i	$-0.716821\pi$
$751$	−34.5129	−1.25939	−0.629697	+	0.776841i	$0.716821\pi$
$752$	−8.33330	−0.303884
$753$	−9.30584	−0.339124
$754$	21.0823	0.767774
$755$	18.4654	0.672025
$756$	6.18057	0.224785
$757$	−36.5628	−1.32890	−0.664448	−	0.747334i	$-0.731333\pi$
$757$	−36.5628	−1.32890	−0.664448	+	0.747334i	$0.731333\pi$
$758$	−13.0807	−0.475111
$759$	43.1929	1.56780
$760$	7.99267	0.289924
$761$	23.3214	0.845398	0.422699	−	0.906270i	$-0.361083\pi$
$761$	23.3214	0.845398	0.422699	+	0.906270i	$0.361083\pi$
$762$	26.6472	0.965327
$763$	−2.93477	−0.106246
$764$	6.30844	0.228231
$765$	−0.646101	−0.0233598
$766$	−14.7984	−0.534687
$767$	45.8410	1.65522
$768$	−2.23814	−0.0807619
$769$	−5.19645	−0.187389	−0.0936944	−	0.995601i	$-0.529868\pi$
$769$	−5.19645	−0.187389	−0.0936944	+	0.995601i	$0.529868\pi$
$770$	−26.0899	−0.940216
$771$	32.4848	1.16991
$772$	23.2276	0.835981
$773$	−34.8925	−1.25500	−0.627498	−	0.778618i	$-0.715921\pi$
$773$	−34.8925	−1.25500	−0.627498	+	0.778618i	$0.715921\pi$
$774$	3.23110	0.116139
$775$	23.0165	0.826776
$776$	−4.11442	−0.147699
$777$	56.8847	2.04073
$778$	14.1726	0.508113
$779$	−17.8758	−0.640466
$780$	24.5783	0.880044
$781$	6.11958	0.218976
$782$	−0.662978	−0.0237080
$783$	13.2657	0.474078
$784$	0.769022	0.0274651
$785$	−63.3614	−2.26146
$786$	7.49792	0.267442
$787$	−3.65094	−0.130142	−0.0650710	−	0.997881i	$-0.520727\pi$
$787$	−3.65094	−0.130142	−0.0650710	+	0.997881i	$0.520727\pi$
$788$	−11.4968	−0.409556
$789$	−4.92461	−0.175321
$790$	−7.22622	−0.257097
$791$	−1.63620	−0.0581764
$792$	−6.03526	−0.214453
$793$	40.4815	1.43754
$794$	−7.20961	−0.255860
$795$	54.0319	1.91631
$796$	11.1866	0.396499
$797$	26.6024	0.942305	0.471153	−	0.882052i	$-0.343838\pi$
$797$	26.6024	0.942305	0.471153	+	0.882052i	$0.343838\pi$
$798$	−16.0004	−0.566408
$799$	0.859904	0.0304212
$800$	−4.71094	−0.166557
$801$	−24.2141	−0.855563
$802$	32.9213	1.16249
$803$	−43.3961	−1.53141
$804$	26.1667	0.922829
$805$	−55.8059	−1.96690
$806$	17.2173	0.606454
$807$	−6.04388	−0.212755
$808$	−7.07494	−0.248895
$809$	−30.0003	−1.05475	−0.527377	−	0.849631i	$-0.676824\pi$
$809$	−30.0003	−1.05475	−0.527377	+	0.849631i	$0.676824\pi$
$810$	34.2495	1.20340
$811$	−25.0254	−0.878759	−0.439380	−	0.898301i	$-0.644802\pi$
$811$	−25.0254	−0.878759	−0.439380	+	0.898301i	$0.644802\pi$
$812$	16.6751	0.585181
$813$	50.3992	1.76758
$814$	27.3895	0.960002
$815$	−13.1372	−0.460176
$816$	0.230951	0.00808490
$817$	4.12453	0.144299
$818$	−14.5679	−0.509353
$819$	−19.7358	−0.689624
$820$	21.7187	0.758451
$821$	30.2557	1.05593	0.527966	−	0.849266i	$-0.322955\pi$
$821$	30.2557	1.05593	0.527966	+	0.849266i	$0.322955\pi$
$822$	4.10726	0.143257
$823$	41.7518	1.45538	0.727688	−	0.685908i	$-0.240595\pi$
$823$	41.7518	1.45538	0.727688	+	0.685908i	$0.240595\pi$
$824$	−2.47591	−0.0862524
$825$	−31.6704	−1.10262
$826$	36.2579	1.26157
$827$	−8.30872	−0.288923	−0.144461	−	0.989510i	$-0.546145\pi$
$827$	−8.30872	−0.288923	−0.144461	+	0.989510i	$0.546145\pi$
$828$	−12.9093	−0.448629
$829$	−18.3319	−0.636694	−0.318347	−	0.947974i	$-0.603128\pi$
$829$	−18.3319	−0.636694	−0.318347	+	0.947974i	$0.603128\pi$
$830$	24.8266	0.861745
$831$	30.6531	1.06334
$832$	−3.52399	−0.122172
$833$	−0.0793546	−0.00274947
$834$	1.32703	0.0459512
$835$	−27.6978	−0.958523
$836$	−7.70406	−0.266451
$837$	10.8337	0.374467
$838$	−36.5145	−1.26137
$839$	0.960462	0.0331588	0.0165794	−	0.999863i	$-0.494722\pi$
$839$	0.960462	0.0331588	0.0165794	+	0.999863i	$0.494722\pi$
$840$	19.4402	0.670751
$841$	6.79065	0.234161
$842$	−4.84802	−0.167074
$843$	−6.20528	−0.213721
$844$	4.44985	0.153170
$845$	−1.81217	−0.0623406
$846$	16.7438	0.575663
$847$	−5.51240	−0.189408
$848$	−7.74698	−0.266032
$849$	−35.4619	−1.21705
$850$	0.486117	0.0166737
$851$	58.5857	2.00829
$852$	−4.55984	−0.156217
$853$	−10.6590	−0.364958	−0.182479	−	0.983210i	$-0.558412\pi$
$853$	−10.6590	−0.364958	−0.182479	+	0.983210i	$0.558412\pi$
$854$	32.0189	1.09566
$855$	−16.0594	−0.549219
$856$	−19.9570	−0.682116
$857$	23.1644	0.791283	0.395641	−	0.918405i	$-0.370522\pi$
$857$	23.1644	0.791283	0.395641	+	0.918405i	$0.370522\pi$
$858$	−23.6908	−0.808791
$859$	−27.7993	−0.948501	−0.474251	−	0.880390i	$-0.657281\pi$
$859$	−27.7993	−0.948501	−0.474251	+	0.880390i	$0.657281\pi$
$860$	−5.01123	−0.170882
$861$	−43.4784	−1.48174
$862$	12.7701	0.434953
$863$	2.86423	0.0974996	0.0487498	−	0.998811i	$-0.484476\pi$
$863$	2.86423	0.0974996	0.0487498	+	0.998811i	$0.484476\pi$
$864$	−2.21741	−0.0754377
$865$	16.3376	0.555497
$866$	−22.1786	−0.753659
$867$	38.0245	1.29138
$868$	13.6180	0.462226
$869$	6.96529	0.236281
$870$	41.7256	1.41463
$871$	41.1999	1.39601
$872$	1.05291	0.0356560
$873$	8.26695	0.279794
$874$	−16.4789	−0.557406
$875$	−2.51071	−0.0848775
$876$	32.3354	1.09251
$877$	0.636548	0.0214947	0.0107473	−	0.999942i	$-0.496579\pi$
$877$	0.636548	0.0214947	0.0107473	+	0.999942i	$0.496579\pi$
$878$	7.14250	0.241048
$879$	5.83528	0.196819
$880$	9.36030	0.315536
$881$	−28.0664	−0.945581	−0.472790	−	0.881175i	$-0.656753\pi$
$881$	−28.0664	−0.945581	−0.472790	+	0.881175i	$0.656753\pi$
$882$	−1.54517	−0.0520285
$883$	32.7012	1.10048	0.550242	−	0.835005i	$-0.314535\pi$
$883$	32.7012	1.10048	0.550242	+	0.835005i	$0.314535\pi$
$884$	0.363636	0.0122304
$885$	90.7272	3.04976
$886$	38.6396	1.29812
$887$	−18.2589	−0.613074	−0.306537	−	0.951859i	$-0.599170\pi$
$887$	−18.2589	−0.613074	−0.306537	+	0.951859i	$0.599170\pi$
$888$	−20.4086	−0.684866
$889$	33.1855	1.11301
$890$	37.5545	1.25883
$891$	−33.0128	−1.10597
$892$	−15.4337	−0.516759
$893$	21.3736	0.715241
$894$	7.22906	0.241776
$895$	−65.9011	−2.20283
$896$	−2.78730	−0.0931170
$897$	−50.6742	−1.69196
$898$	26.1680	0.873238
$899$	29.2291	0.974846
$900$	9.46552	0.315517
$901$	0.799403	0.0266320
$902$	−20.9345	−0.697043
$903$	10.0319	0.333841
$904$	0.587019	0.0195240
$905$	30.5271	1.01475
$906$	13.2622	0.440606
$907$	−16.9466	−0.562704	−0.281352	−	0.959605i	$-0.590783\pi$
$907$	−16.9466	−0.562704	−0.281352	+	0.959605i	$0.590783\pi$
$908$	1.74822	0.0580167
$909$	14.2154	0.471495
$910$	30.6089	1.01468
$911$	11.9254	0.395107	0.197554	−	0.980292i	$-0.436700\pi$
$911$	11.9254	0.395107	0.197554	+	0.980292i	$0.436700\pi$
$912$	5.74047	0.190086
$913$	−23.9302	−0.791973
$914$	−23.4185	−0.774615
$915$	80.1199	2.64868
$916$	−19.2737	−0.636819
$917$	9.33764	0.308356
$918$	0.228812	0.00755191
$919$	52.5854	1.73463	0.867317	−	0.497756i	$-0.165843\pi$
$919$	52.5854	1.73463	0.867317	+	0.497756i	$0.165843\pi$
$920$	20.0215	0.660090
$921$	−61.8058	−2.03657
$922$	17.6865	0.582473
$923$	−7.17954	−0.236317
$924$	−18.7383	−0.616443
$925$	−42.9569	−1.41242
$926$	15.0850	0.495725
$927$	4.97475	0.163392
$928$	−5.98253	−0.196386
$929$	8.68353	0.284897	0.142449	−	0.989802i	$-0.454502\pi$
$929$	8.68353	0.284897	0.142449	+	0.989802i	$0.454502\pi$
$930$	34.0760	1.11740
$931$	−1.97242	−0.0646435
$932$	−12.0196	−0.393716
$933$	−39.3278	−1.28753
$934$	−7.96041	−0.260472
$935$	−0.965879	−0.0315876
$936$	7.08061	0.231437
$937$	−45.0222	−1.47081	−0.735406	−	0.677626i	$-0.763009\pi$
$937$	−45.0222	−1.47081	−0.735406	+	0.677626i	$0.763009\pi$
$938$	32.5871	1.06401
$939$	47.6283	1.55429
$940$	−25.9685	−0.847001
$941$	−7.54697	−0.246024	−0.123012	−	0.992405i	$-0.539255\pi$
$941$	−7.54697	−0.246024	−0.123012	+	0.992405i	$0.539255\pi$
$942$	−45.5073	−1.48271
$943$	−44.7786	−1.45819
$944$	−13.0083	−0.423383
$945$	19.2601	0.626532
$946$	4.83028	0.157046
$947$	40.6045	1.31947	0.659734	−	0.751499i	$-0.270669\pi$
$947$	40.6045	1.31947	0.659734	+	0.751499i	$0.270669\pi$
$948$	−5.19000	−0.168563
$949$	50.9126	1.65269
$950$	12.0828	0.392019
$951$	−34.0750	−1.10496
$952$	0.287618	0.00932175
$953$	−13.9407	−0.451584	−0.225792	−	0.974176i	$-0.572497\pi$
$953$	−13.9407	−0.451584	−0.225792	+	0.974176i	$0.572497\pi$
$954$	15.5657	0.503959
$955$	19.6586	0.636138
$956$	6.94962	0.224767
$957$	−40.2189	−1.30009
$958$	35.5104	1.14729
$959$	5.11503	0.165173
$960$	−6.97457	−0.225103
$961$	−7.12947	−0.229983
$962$	−32.1336	−1.03603
$963$	40.0988	1.29217
$964$	17.0082	0.547798
$965$	72.3828	2.33009
$966$	−40.0808	−1.28958
$967$	37.1969	1.19617	0.598086	−	0.801432i	$-0.295928\pi$
$967$	37.1969	1.19617	0.598086	+	0.801432i	$0.295928\pi$
$968$	1.97769	0.0635652
$969$	−0.592353	−0.0190291
$970$	−12.8215	−0.411674
$971$	−57.9810	−1.86070	−0.930349	−	0.366676i	$-0.880496\pi$
$971$	−57.9810	−1.86070	−0.930349	+	0.366676i	$0.880496\pi$
$972$	17.9464	0.575630
$973$	1.65263	0.0529810
$974$	−10.8025	−0.346133
$975$	37.1560	1.18994
$976$	−11.4874	−0.367704
$977$	−10.4793	−0.335262	−0.167631	−	0.985850i	$-0.553612\pi$
$977$	−10.4793	−0.335262	−0.167631	+	0.985850i	$0.553612\pi$
$978$	−9.43538	−0.301710
$979$	−36.1985	−1.15691
$980$	2.39646	0.0765520
$981$	−2.11557	−0.0675449
$982$	−30.7389	−0.980916
$983$	24.3533	0.776749	0.388375	−	0.921502i	$-0.373037\pi$
$983$	24.3533	0.776749	0.388375	+	0.921502i	$0.373037\pi$
$984$	15.5988	0.497271
$985$	−35.8267	−1.14153
$986$	0.617331	0.0196598
$987$	51.9861	1.65474
$988$	9.03847	0.287552
$989$	10.3319	0.328535
$990$	−18.8073	−0.597735
$991$	47.7616	1.51720	0.758599	−	0.651558i	$-0.225884\pi$
$991$	47.7616	1.51720	0.758599	+	0.651558i	$0.225884\pi$
$992$	−4.88575	−0.155123
$993$	−0.890940	−0.0282731
$994$	−5.67866	−0.180116
$995$	34.8601	1.10514
$996$	17.8309	0.564994
$997$	16.6020	0.525792	0.262896	−	0.964824i	$-0.415322\pi$
$997$	16.6020	0.525792	0.262896	+	0.964824i	$0.415322\pi$
$998$	−30.5414	−0.966772
$999$	−20.2195	−0.639717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.12	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.23814 q^{3} +1.00000 q^{4} +3.11624 q^{5} +2.23814 q^{6} +2.78730 q^{7} -1.00000 q^{8} +2.00926 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.23814 q^{3} +1.00000 q^{4} +3.11624 q^{5} +2.23814 q^{6} +2.78730 q^{7} -1.00000 q^{8} +2.00926 q^{9} -3.11624 q^{10} +3.00372 q^{11} -2.23814 q^{12} -3.52399 q^{13} -2.78730 q^{14} -6.97457 q^{15} +1.00000 q^{16} -0.103189 q^{17} -2.00926 q^{18} -2.56484 q^{19} +3.11624 q^{20} -6.23835 q^{21} -3.00372 q^{22} -6.42490 q^{23} +2.23814 q^{24} +4.71094 q^{25} +3.52399 q^{26} +2.21741 q^{27} +2.78730 q^{28} +5.98253 q^{29} +6.97457 q^{30} +4.88575 q^{31} -1.00000 q^{32} -6.72273 q^{33} +0.103189 q^{34} +8.68588 q^{35} +2.00926 q^{36} -9.11854 q^{37} +2.56484 q^{38} +7.88717 q^{39} -3.11624 q^{40} +6.96954 q^{41} +6.23835 q^{42} -1.60810 q^{43} +3.00372 q^{44} +6.26134 q^{45} +6.42490 q^{46} -8.33330 q^{47} -2.23814 q^{48} +0.769022 q^{49} -4.71094 q^{50} +0.230951 q^{51} -3.52399 q^{52} -7.74698 q^{53} -2.21741 q^{54} +9.36030 q^{55} -2.78730 q^{56} +5.74047 q^{57} -5.98253 q^{58} -13.0083 q^{59} -6.97457 q^{60} -11.4874 q^{61} -4.88575 q^{62} +5.60041 q^{63} +1.00000 q^{64} -10.9816 q^{65} +6.72273 q^{66} -11.6913 q^{67} -0.103189 q^{68} +14.3798 q^{69} -8.68588 q^{70} +2.03734 q^{71} -2.00926 q^{72} -14.4475 q^{73} +9.11854 q^{74} -10.5437 q^{75} -2.56484 q^{76} +8.37225 q^{77} -7.88717 q^{78} +2.31889 q^{79} +3.11624 q^{80} -10.9907 q^{81} -6.96954 q^{82} -7.96686 q^{83} -6.23835 q^{84} -0.321561 q^{85} +1.60810 q^{86} -13.3897 q^{87} -3.00372 q^{88} -12.0512 q^{89} -6.26134 q^{90} -9.82239 q^{91} -6.42490 q^{92} -10.9350 q^{93} +8.33330 q^{94} -7.99267 q^{95} +2.23814 q^{96} +4.11442 q^{97} -0.769022 q^{98} +6.03526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 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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