LMFDB - Embedded newform 4026.2.a.u.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.9176805.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 $ x^5 - x^4 - 12x^3 + 7x^2 + 30*x - 20
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.15973$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.15973 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.53760 q^{13} +1.48663 q^{14} +2.15973 q^{15} +1.00000 q^{16} +2.33751 q^{17} -1.00000 q^{18} +3.42627 q^{19} +2.15973 q^{20} -1.48663 q^{21} +1.00000 q^{22} +3.87512 q^{23} -1.00000 q^{24} -0.335585 q^{25} -5.53760 q^{26} +1.00000 q^{27} -1.48663 q^{28} +3.49531 q^{29} -2.15973 q^{30} +3.71539 q^{31} -1.00000 q^{32} -1.00000 q^{33} -2.33751 q^{34} -3.21070 q^{35} +1.00000 q^{36} -3.86643 q^{37} -3.42627 q^{38} +5.53760 q^{39} -2.15973 q^{40} -7.21070 q^{41} +1.48663 q^{42} +8.37981 q^{43} -1.00000 q^{44} +2.15973 q^{45} -3.87512 q^{46} +6.71346 q^{47} +1.00000 q^{48} -4.78994 q^{49} +0.335585 q^{50} +2.33751 q^{51} +5.53760 q^{52} -3.82221 q^{53} -1.00000 q^{54} -2.15973 q^{55} +1.48663 q^{56} +3.42627 q^{57} -3.49531 q^{58} -13.1375 q^{59} +2.15973 q^{60} -1.00000 q^{61} -3.71539 q^{62} -1.48663 q^{63} +1.00000 q^{64} +11.9597 q^{65} +1.00000 q^{66} -4.45050 q^{67} +2.33751 q^{68} +3.87512 q^{69} +3.21070 q^{70} -5.39594 q^{71} -1.00000 q^{72} +1.17972 q^{73} +3.86643 q^{74} -0.335585 q^{75} +3.42627 q^{76} +1.48663 q^{77} -5.53760 q^{78} -11.2878 q^{79} +2.15973 q^{80} +1.00000 q^{81} +7.21070 q^{82} +4.96222 q^{83} -1.48663 q^{84} +5.04839 q^{85} -8.37981 q^{86} +3.49531 q^{87} +1.00000 q^{88} -4.59989 q^{89} -2.15973 q^{90} -8.23235 q^{91} +3.87512 q^{92} +3.71539 q^{93} -6.71346 q^{94} +7.39980 q^{95} -1.00000 q^{96} +3.58599 q^{97} +4.78994 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.15973	0.965859	0.482929	−	0.875659i	$-0.339573\pi$
$5$	2.15973	0.965859	0.482929	+	0.875659i	$0.339573\pi$
$6$	−1.00000	−0.408248
$7$	−1.48663	−0.561892	−0.280946	−	0.959724i	$-0.590648\pi$
$7$	−1.48663	−0.561892	−0.280946	+	0.959724i	$0.590648\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−2.15973	−0.682965
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	5.53760	1.53586	0.767928	−	0.640537i	$-0.221288\pi$
$13$	5.53760	1.53586	0.767928	+	0.640537i	$0.221288\pi$
$14$	1.48663	0.397317
$15$	2.15973	0.557639
$16$	1.00000	0.250000
$17$	2.33751	0.566931	0.283465	−	0.958982i	$-0.408516\pi$
$17$	2.33751	0.566931	0.283465	+	0.958982i	$0.408516\pi$
$18$	−1.00000	−0.235702
$19$	3.42627	0.786040	0.393020	−	0.919530i	$-0.371430\pi$
$19$	3.42627	0.786040	0.393020	+	0.919530i	$0.371430\pi$
$20$	2.15973	0.482929
$21$	−1.48663	−0.324408
$22$	1.00000	0.213201
$23$	3.87512	0.808018	0.404009	−	0.914755i	$-0.367616\pi$
$23$	3.87512	0.808018	0.404009	+	0.914755i	$0.367616\pi$
$24$	−1.00000	−0.204124
$25$	−0.335585	−0.0671170
$26$	−5.53760	−1.08601
$27$	1.00000	0.192450
$28$	−1.48663	−0.280946
$29$	3.49531	0.649063	0.324531	−	0.945875i	$-0.394793\pi$
$29$	3.49531	0.649063	0.324531	+	0.945875i	$0.394793\pi$
$30$	−2.15973	−0.394310
$31$	3.71539	0.667304	0.333652	−	0.942696i	$-0.391719\pi$
$31$	3.71539	0.667304	0.333652	+	0.942696i	$0.391719\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−2.33751	−0.400880
$35$	−3.21070	−0.542708
$36$	1.00000	0.166667
$37$	−3.86643	−0.635638	−0.317819	−	0.948151i	$-0.602950\pi$
$37$	−3.86643	−0.635638	−0.317819	+	0.948151i	$0.602950\pi$
$38$	−3.42627	−0.555814
$39$	5.53760	0.886726
$40$	−2.15973	−0.341483
$41$	−7.21070	−1.12612	−0.563061	−	0.826415i	$-0.690377\pi$
$41$	−7.21070	−1.12612	−0.563061	+	0.826415i	$0.690377\pi$
$42$	1.48663	0.229391
$43$	8.37981	1.27791	0.638954	−	0.769245i	$-0.279367\pi$
$43$	8.37981	1.27791	0.638954	+	0.769245i	$0.279367\pi$
$44$	−1.00000	−0.150756
$45$	2.15973	0.321953
$46$	−3.87512	−0.571355
$47$	6.71346	0.979259	0.489630	−	0.871930i	$-0.337132\pi$
$47$	6.71346	0.979259	0.489630	+	0.871930i	$0.337132\pi$
$48$	1.00000	0.144338
$49$	−4.78994	−0.684278
$50$	0.335585	0.0474589
$51$	2.33751	0.327318
$52$	5.53760	0.767928
$53$	−3.82221	−0.525021	−0.262511	−	0.964929i	$-0.584550\pi$
$53$	−3.82221	−0.525021	−0.262511	+	0.964929i	$0.584550\pi$
$54$	−1.00000	−0.136083
$55$	−2.15973	−0.291217
$56$	1.48663	0.198659
$57$	3.42627	0.453820
$58$	−3.49531	−0.458957
$59$	−13.1375	−1.71036	−0.855178	−	0.518334i	$-0.826552\pi$
$59$	−13.1375	−1.71036	−0.855178	+	0.518334i	$0.826552\pi$
$60$	2.15973	0.278819
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.71539	−0.471855
$63$	−1.48663	−0.187297
$64$	1.00000	0.125000
$65$	11.9597	1.48342
$66$	1.00000	0.123091
$67$	−4.45050	−0.543715	−0.271858	−	0.962338i	$-0.587638\pi$
$67$	−4.45050	−0.543715	−0.271858	+	0.962338i	$0.587638\pi$
$68$	2.33751	0.283465
$69$	3.87512	0.466510
$70$	3.21070	0.383753
$71$	−5.39594	−0.640381	−0.320190	−	0.947353i	$-0.603747\pi$
$71$	−5.39594	−0.640381	−0.320190	+	0.947353i	$0.603747\pi$
$72$	−1.00000	−0.117851
$73$	1.17972	0.138076	0.0690378	−	0.997614i	$-0.478007\pi$
$73$	1.17972	0.138076	0.0690378	+	0.997614i	$0.478007\pi$
$74$	3.86643	0.449464
$75$	−0.335585	−0.0387500
$76$	3.42627	0.393020
$77$	1.48663	0.169417
$78$	−5.53760	−0.627010
$79$	−11.2878	−1.26998	−0.634991	−	0.772520i	$-0.718996\pi$
$79$	−11.2878	−1.26998	−0.634991	+	0.772520i	$0.718996\pi$
$80$	2.15973	0.241465
$81$	1.00000	0.111111
$82$	7.21070	0.796289
$83$	4.96222	0.544675	0.272337	−	0.962202i	$-0.412203\pi$
$83$	4.96222	0.544675	0.272337	+	0.962202i	$0.412203\pi$
$84$	−1.48663	−0.162204
$85$	5.04839	0.547575
$86$	−8.37981	−0.903618
$87$	3.49531	0.374737
$88$	1.00000	0.106600
$89$	−4.59989	−0.487587	−0.243794	−	0.969827i	$-0.578392\pi$
$89$	−4.59989	−0.487587	−0.243794	+	0.969827i	$0.578392\pi$
$90$	−2.15973	−0.227655
$91$	−8.23235	−0.862984
$92$	3.87512	0.404009
$93$	3.71539	0.385268
$94$	−6.71346	−0.692441
$95$	7.39980	0.759204
$96$	−1.00000	−0.102062
$97$	3.58599	0.364103	0.182051	−	0.983289i	$-0.441726\pi$
$97$	3.58599	0.364103	0.182051	+	0.983289i	$0.441726\pi$
$98$	4.78994	0.483857
$99$	−1.00000	−0.100504
$100$	−0.335585	−0.0335585
$101$	14.2082	1.41377	0.706884	−	0.707330i	$-0.250100\pi$
$101$	14.2082	1.41377	0.706884	+	0.707330i	$0.250100\pi$
$102$	−2.33751	−0.231448
$103$	13.4611	1.32636	0.663181	−	0.748459i	$-0.269206\pi$
$103$	13.4611	1.32636	0.663181	+	0.748459i	$0.269206\pi$
$104$	−5.53760	−0.543007
$105$	−3.21070	−0.313333
$106$	3.82221	0.371246
$107$	20.1230	1.94536	0.972682	−	0.232140i	$-0.0745727\pi$
$107$	20.1230	1.94536	0.972682	+	0.232140i	$0.0745727\pi$
$108$	1.00000	0.0962250
$109$	12.3175	1.17980	0.589902	−	0.807475i	$-0.299166\pi$
$109$	12.3175	1.17980	0.589902	+	0.807475i	$0.299166\pi$
$110$	2.15973	0.205922
$111$	−3.86643	−0.366986
$112$	−1.48663	−0.140473
$113$	−8.93741	−0.840760	−0.420380	−	0.907348i	$-0.638103\pi$
$113$	−8.93741	−0.840760	−0.420380	+	0.907348i	$0.638103\pi$
$114$	−3.42627	−0.320899
$115$	8.36919	0.780431
$116$	3.49531	0.324531
$117$	5.53760	0.511952
$118$	13.1375	1.20940
$119$	−3.47501	−0.318554
$120$	−2.15973	−0.197155
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−7.21070	−0.650167
$124$	3.71539	0.333652
$125$	−11.5234	−1.03068
$126$	1.48663	0.132439
$127$	21.9665	1.94921	0.974604	−	0.223935i	$-0.0718903\pi$
$127$	21.9665	1.94921	0.974604	+	0.223935i	$0.0718903\pi$
$128$	−1.00000	−0.0883883
$129$	8.37981	0.737801
$130$	−11.9597	−1.04894
$131$	16.2301	1.41803	0.709016	−	0.705193i	$-0.249140\pi$
$131$	16.2301	1.41803	0.709016	+	0.705193i	$0.249140\pi$
$132$	−1.00000	−0.0870388
$133$	−5.09358	−0.441669
$134$	4.45050	0.384465
$135$	2.15973	0.185880
$136$	−2.33751	−0.200440
$137$	−5.90932	−0.504867	−0.252433	−	0.967614i	$-0.581231\pi$
$137$	−5.90932	−0.504867	−0.252433	+	0.967614i	$0.581231\pi$
$138$	−3.87512	−0.329872
$139$	1.19750	0.101571	0.0507854	−	0.998710i	$-0.483828\pi$
$139$	1.19750	0.101571	0.0507854	+	0.998710i	$0.483828\pi$
$140$	−3.21070	−0.271354
$141$	6.71346	0.565376
$142$	5.39594	0.452817
$143$	−5.53760	−0.463078
$144$	1.00000	0.0833333
$145$	7.54891	0.626903
$146$	−1.17972	−0.0976342
$147$	−4.78994	−0.395068
$148$	−3.86643	−0.317819
$149$	−19.5786	−1.60394	−0.801971	−	0.597362i	$-0.796215\pi$
$149$	−19.5786	−1.60394	−0.801971	+	0.597362i	$0.796215\pi$
$150$	0.335585	0.0274004
$151$	11.3134	0.920668	0.460334	−	0.887746i	$-0.347730\pi$
$151$	11.3134	0.920668	0.460334	+	0.887746i	$0.347730\pi$
$152$	−3.42627	−0.277907
$153$	2.33751	0.188977
$154$	−1.48663	−0.119796
$155$	8.02423	0.644522
$156$	5.53760	0.443363
$157$	1.30526	0.104171	0.0520855	−	0.998643i	$-0.483413\pi$
$157$	1.30526	0.104171	0.0520855	+	0.998643i	$0.483413\pi$
$158$	11.2878	0.898013
$159$	−3.82221	−0.303121
$160$	−2.15973	−0.170741
$161$	−5.76085	−0.454019
$162$	−1.00000	−0.0785674
$163$	−2.48979	−0.195016	−0.0975078	−	0.995235i	$-0.531087\pi$
$163$	−2.48979	−0.195016	−0.0975078	+	0.995235i	$0.531087\pi$
$164$	−7.21070	−0.563061
$165$	−2.15973	−0.168134
$166$	−4.96222	−0.385143
$167$	13.6725	1.05801	0.529005	−	0.848618i	$-0.322565\pi$
$167$	13.6725	1.05801	0.529005	+	0.848618i	$0.322565\pi$
$168$	1.48663	0.114696
$169$	17.6651	1.35885
$170$	−5.04839	−0.387194
$171$	3.42627	0.262013
$172$	8.37981	0.638954
$173$	−15.7651	−1.19860	−0.599300	−	0.800524i	$-0.704554\pi$
$173$	−15.7651	−1.19860	−0.599300	+	0.800524i	$0.704554\pi$
$174$	−3.49531	−0.264979
$175$	0.498890	0.0377125
$176$	−1.00000	−0.0753778
$177$	−13.1375	−0.987475
$178$	4.59989	0.344776
$179$	4.56376	0.341112	0.170556	−	0.985348i	$-0.445444\pi$
$179$	4.56376	0.341112	0.170556	+	0.985348i	$0.445444\pi$
$180$	2.15973	0.160976
$181$	3.21399	0.238894	0.119447	−	0.992841i	$-0.461888\pi$
$181$	3.21399	0.238894	0.119447	+	0.992841i	$0.461888\pi$
$182$	8.23235	0.610222
$183$	−1.00000	−0.0739221
$184$	−3.87512	−0.285678
$185$	−8.35044	−0.613936
$186$	−3.71539	−0.272426
$187$	−2.33751	−0.170936
$188$	6.71346	0.489630
$189$	−1.48663	−0.108136
$190$	−7.39980	−0.536838
$191$	25.8939	1.87362	0.936808	−	0.349843i	$-0.113765\pi$
$191$	25.8939	1.87362	0.936808	+	0.349843i	$0.113765\pi$
$192$	1.00000	0.0721688
$193$	−21.8610	−1.57359	−0.786794	−	0.617216i	$-0.788261\pi$
$193$	−21.8610	−1.57359	−0.786794	+	0.617216i	$0.788261\pi$
$194$	−3.58599	−0.257459
$195$	11.9597	0.856452
$196$	−4.78994	−0.342139
$197$	−11.8061	−0.841148	−0.420574	−	0.907258i	$-0.638171\pi$
$197$	−11.8061	−0.841148	−0.420574	+	0.907258i	$0.638171\pi$
$198$	1.00000	0.0710669
$199$	6.17268	0.437570	0.218785	−	0.975773i	$-0.429791\pi$
$199$	6.17268	0.437570	0.218785	+	0.975773i	$0.429791\pi$
$200$	0.335585	0.0237295
$201$	−4.45050	−0.313914
$202$	−14.2082	−0.999684
$203$	−5.19622	−0.364703
$204$	2.33751	0.163659
$205$	−15.5731	−1.08768
$206$	−13.4611	−0.937880
$207$	3.87512	0.269339
$208$	5.53760	0.383964
$209$	−3.42627	−0.237000
$210$	3.21070	0.221560
$211$	0.750581	0.0516721	0.0258361	−	0.999666i	$-0.491775\pi$
$211$	0.750581	0.0516721	0.0258361	+	0.999666i	$0.491775\pi$
$212$	−3.82221	−0.262511
$213$	−5.39594	−0.369724
$214$	−20.1230	−1.37558
$215$	18.0981	1.23428
$216$	−1.00000	−0.0680414
$217$	−5.52340	−0.374953
$218$	−12.3175	−0.834248
$219$	1.17972	0.0797180
$220$	−2.15973	−0.145609
$221$	12.9442	0.870723
$222$	3.86643	0.259498
$223$	2.07387	0.138876	0.0694382	−	0.997586i	$-0.477879\pi$
$223$	2.07387	0.138876	0.0694382	+	0.997586i	$0.477879\pi$
$224$	1.48663	0.0993294
$225$	−0.335585	−0.0223723
$226$	8.93741	0.594507
$227$	−28.5906	−1.89762	−0.948811	−	0.315843i	$-0.897713\pi$
$227$	−28.5906	−1.89762	−0.948811	+	0.315843i	$0.897713\pi$
$228$	3.42627	0.226910
$229$	−0.844512	−0.0558069	−0.0279035	−	0.999611i	$-0.508883\pi$
$229$	−0.844512	−0.0558069	−0.0279035	+	0.999611i	$0.508883\pi$
$230$	−8.36919	−0.551848
$231$	1.48663	0.0978128
$232$	−3.49531	−0.229478
$233$	0.00482589	0.000316155 0	0.000158077	−	1.00000i	$-0.499950\pi$
$233$	0.00482589	0.000316155 0	0.000158077		1.00000i	$0.499950\pi$
$234$	−5.53760	−0.362005
$235$	14.4992	0.945826
$236$	−13.1375	−0.855178
$237$	−11.2878	−0.733224
$238$	3.47501	0.225251
$239$	−15.6790	−1.01419	−0.507094	−	0.861891i	$-0.669280\pi$
$239$	−15.6790	−1.01419	−0.507094	+	0.861891i	$0.669280\pi$
$240$	2.15973	0.139410
$241$	12.5896	0.810966	0.405483	−	0.914103i	$-0.367103\pi$
$241$	12.5896	0.810966	0.405483	+	0.914103i	$0.367103\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−10.3450	−0.660915
$246$	7.21070	0.459738
$247$	18.9733	1.20724
$248$	−3.71539	−0.235928
$249$	4.96222	0.314468
$250$	11.5234	0.728804
$251$	17.7012	1.11729	0.558645	−	0.829407i	$-0.311322\pi$
$251$	17.7012	1.11729	0.558645	+	0.829407i	$0.311322\pi$
$252$	−1.48663	−0.0936486
$253$	−3.87512	−0.243627
$254$	−21.9665	−1.37830
$255$	5.04839	0.316142
$256$	1.00000	0.0625000
$257$	−12.4144	−0.774387	−0.387194	−	0.921998i	$-0.626556\pi$
$257$	−12.4144	−0.774387	−0.387194	+	0.921998i	$0.626556\pi$
$258$	−8.37981	−0.521704
$259$	5.74794	0.357160
$260$	11.9597	0.741709
$261$	3.49531	0.216354
$262$	−16.2301	−1.00270
$263$	−23.4941	−1.44871	−0.724355	−	0.689427i	$-0.757862\pi$
$263$	−23.4941	−1.44871	−0.724355	+	0.689427i	$0.757862\pi$
$264$	1.00000	0.0615457
$265$	−8.25493	−0.507096
$266$	5.09358	0.312307
$267$	−4.59989	−0.281509
$268$	−4.45050	−0.271858
$269$	18.4428	1.12447	0.562237	−	0.826976i	$-0.309941\pi$
$269$	18.4428	1.12447	0.562237	+	0.826976i	$0.309941\pi$
$270$	−2.15973	−0.131437
$271$	20.6347	1.25347	0.626735	−	0.779232i	$-0.284391\pi$
$271$	20.6347	1.25347	0.626735	+	0.779232i	$0.284391\pi$
$272$	2.33751	0.141733
$273$	−8.23235	−0.498244
$274$	5.90932	0.356995
$275$	0.335585	0.0202365
$276$	3.87512	0.233255
$277$	0.330066	0.0198317	0.00991586	−	0.999951i	$-0.496844\pi$
$277$	0.330066	0.0198317	0.00991586	+	0.999951i	$0.496844\pi$
$278$	−1.19750	−0.0718214
$279$	3.71539	0.222435
$280$	3.21070	0.191876
$281$	7.48663	0.446615	0.223307	−	0.974748i	$-0.428315\pi$
$281$	7.48663	0.446615	0.223307	+	0.974748i	$0.428315\pi$
$282$	−6.71346	−0.399781
$283$	8.98880	0.534329	0.267164	−	0.963651i	$-0.413913\pi$
$283$	8.98880	0.534329	0.267164	+	0.963651i	$0.413913\pi$
$284$	−5.39594	−0.320190
$285$	7.39980	0.438326
$286$	5.53760	0.327445
$287$	10.7196	0.632759
$288$	−1.00000	−0.0589256
$289$	−11.5360	−0.678590
$290$	−7.54891	−0.443287
$291$	3.58599	0.210215
$292$	1.17972	0.0690378
$293$	−10.0652	−0.588014	−0.294007	−	0.955803i	$-0.594989\pi$
$293$	−10.0652	−0.588014	−0.294007	+	0.955803i	$0.594989\pi$
$294$	4.78994	0.279355
$295$	−28.3734	−1.65196
$296$	3.86643	0.224732
$297$	−1.00000	−0.0580259
$298$	19.5786	1.13416
$299$	21.4589	1.24100
$300$	−0.335585	−0.0193750
$301$	−12.4576	−0.718046
$302$	−11.3134	−0.651010
$303$	14.2082	0.816239
$304$	3.42627	0.196510
$305$	−2.15973	−0.123666
$306$	−2.33751	−0.133627
$307$	10.7141	0.611489	0.305744	−	0.952114i	$-0.401095\pi$
$307$	10.7141	0.611489	0.305744	+	0.952114i	$0.401095\pi$
$308$	1.48663	0.0847084
$309$	13.4611	0.765776
$310$	−8.02423	−0.455746
$311$	−22.0204	−1.24866	−0.624330	−	0.781161i	$-0.714628\pi$
$311$	−22.0204	−1.24866	−0.624330	+	0.781161i	$0.714628\pi$
$312$	−5.53760	−0.313505
$313$	−25.5931	−1.44661	−0.723303	−	0.690530i	$-0.757377\pi$
$313$	−25.5931	−1.44661	−0.723303	+	0.690530i	$0.757377\pi$
$314$	−1.30526	−0.0736600
$315$	−3.21070	−0.180903
$316$	−11.2878	−0.634991
$317$	8.56635	0.481134	0.240567	−	0.970632i	$-0.422667\pi$
$317$	8.56635	0.481134	0.240567	+	0.970632i	$0.422667\pi$
$318$	3.82221	0.214339
$319$	−3.49531	−0.195700
$320$	2.15973	0.120732
$321$	20.1230	1.12316
$322$	5.76085	0.321040
$323$	8.00895	0.445630
$324$	1.00000	0.0555556
$325$	−1.85834	−0.103082
$326$	2.48979	0.137897
$327$	12.3175	0.681161
$328$	7.21070	0.398145
$329$	−9.98041	−0.550238
$330$	2.15973	0.118889
$331$	−18.2004	−1.00038	−0.500191	−	0.865915i	$-0.666737\pi$
$331$	−18.2004	−1.00038	−0.500191	+	0.865915i	$0.666737\pi$
$332$	4.96222	0.272337
$333$	−3.86643	−0.211879
$334$	−13.6725	−0.748127
$335$	−9.61186	−0.525152
$336$	−1.48663	−0.0811021
$337$	33.9161	1.84753	0.923765	−	0.382961i	$-0.125095\pi$
$337$	33.9161	1.84753	0.923765	+	0.382961i	$0.125095\pi$
$338$	−17.6651	−0.960853
$339$	−8.93741	−0.485413
$340$	5.04839	0.273787
$341$	−3.71539	−0.201200
$342$	−3.42627	−0.185271
$343$	17.5272	0.946382
$344$	−8.37981	−0.451809
$345$	8.36919	0.450582
$346$	15.7651	0.847538
$347$	−15.6341	−0.839285	−0.419642	−	0.907689i	$-0.637845\pi$
$347$	−15.6341	−0.839285	−0.419642	+	0.907689i	$0.637845\pi$
$348$	3.49531	0.187368
$349$	26.7325	1.43096	0.715480	−	0.698634i	$-0.246208\pi$
$349$	26.7325	1.43096	0.715480	+	0.698634i	$0.246208\pi$
$350$	−0.498890	−0.0266668
$351$	5.53760	0.295575
$352$	1.00000	0.0533002
$353$	−25.8690	−1.37687	−0.688435	−	0.725298i	$-0.741702\pi$
$353$	−25.8690	−1.37687	−0.688435	+	0.725298i	$0.741702\pi$
$354$	13.1375	0.698250
$355$	−11.6538	−0.618517
$356$	−4.59989	−0.243794
$357$	−3.47501	−0.183917
$358$	−4.56376	−0.241202
$359$	−27.5185	−1.45237	−0.726186	−	0.687498i	$-0.758709\pi$
$359$	−27.5185	−1.45237	−0.726186	+	0.687498i	$0.758709\pi$
$360$	−2.15973	−0.113828
$361$	−7.26068	−0.382141
$362$	−3.21399	−0.168923
$363$	1.00000	0.0524864
$364$	−8.23235	−0.431492
$365$	2.54787	0.133362
$366$	1.00000	0.0522708
$367$	12.9441	0.675679	0.337840	−	0.941204i	$-0.390304\pi$
$367$	12.9441	0.675679	0.337840	+	0.941204i	$0.390304\pi$
$368$	3.87512	0.202005
$369$	−7.21070	−0.375374
$370$	8.35044	0.434119
$371$	5.68220	0.295005
$372$	3.71539	0.192634
$373$	12.6002	0.652414	0.326207	−	0.945298i	$-0.394229\pi$
$373$	12.6002	0.652414	0.326207	+	0.945298i	$0.394229\pi$
$374$	2.33751	0.120870
$375$	−11.5234	−0.595066
$376$	−6.71346	−0.346220
$377$	19.3556	0.996867
$378$	1.48663	0.0764638
$379$	37.0888	1.90512	0.952562	−	0.304344i	$-0.0984372\pi$
$379$	37.0888	1.90512	0.952562	+	0.304344i	$0.0984372\pi$
$380$	7.39980	0.379602
$381$	21.9665	1.12538
$382$	−25.8939	−1.32485
$383$	0.0199579	0.00101980	0.000509902	−	1.00000i	$-0.499838\pi$
$383$	0.0199579	0.00101980	0.000509902		1.00000i	$0.499838\pi$
$384$	−1.00000	−0.0510310
$385$	3.21070	0.163633
$386$	21.8610	1.11269
$387$	8.37981	0.425970
$388$	3.58599	0.182051
$389$	−19.0988	−0.968347	−0.484173	−	0.874972i	$-0.660880\pi$
$389$	−19.0988	−0.968347	−0.484173	+	0.874972i	$0.660880\pi$
$390$	−11.9597	−0.605603
$391$	9.05815	0.458090
$392$	4.78994	0.241929
$393$	16.2301	0.818701
$394$	11.8061	0.594782
$395$	−24.3786	−1.22662
$396$	−1.00000	−0.0502519
$397$	16.5408	0.830161	0.415080	−	0.909785i	$-0.363753\pi$
$397$	16.5408	0.830161	0.415080	+	0.909785i	$0.363753\pi$
$398$	−6.17268	−0.309409
$399$	−5.09358	−0.254998
$400$	−0.335585	−0.0167793
$401$	23.7813	1.18758	0.593791	−	0.804619i	$-0.297630\pi$
$401$	23.7813	1.18758	0.593791	+	0.804619i	$0.297630\pi$
$402$	4.45050	0.221971
$403$	20.5744	1.02488
$404$	14.2082	0.706884
$405$	2.15973	0.107318
$406$	5.19622	0.257884
$407$	3.86643	0.191652
$408$	−2.33751	−0.115724
$409$	10.7147	0.529808	0.264904	−	0.964275i	$-0.414660\pi$
$409$	10.7147	0.529808	0.264904	+	0.964275i	$0.414660\pi$
$410$	15.5731	0.769103
$411$	−5.90932	−0.291485
$412$	13.4611	0.663181
$413$	19.5305	0.961035
$414$	−3.87512	−0.190452
$415$	10.7170	0.526079
$416$	−5.53760	−0.271503
$417$	1.19750	0.0586419
$418$	3.42627	0.167584
$419$	−17.9297	−0.875922	−0.437961	−	0.898994i	$-0.644299\pi$
$419$	−17.9297	−0.875922	−0.437961	+	0.898994i	$0.644299\pi$
$420$	−3.21070	−0.156666
$421$	−3.57962	−0.174460	−0.0872299	−	0.996188i	$-0.527801\pi$
$421$	−3.57962	−0.174460	−0.0872299	+	0.996188i	$0.527801\pi$
$422$	−0.750581	−0.0365377
$423$	6.71346	0.326420
$424$	3.82221	0.185623
$425$	−0.784435	−0.0380507
$426$	5.39594	0.261434
$427$	1.48663	0.0719429
$428$	20.1230	0.972682
$429$	−5.53760	−0.267358
$430$	−18.0981	−0.872767
$431$	14.2239	0.685143	0.342572	−	0.939492i	$-0.388702\pi$
$431$	14.2239	0.685143	0.342572	+	0.939492i	$0.388702\pi$
$432$	1.00000	0.0481125
$433$	−10.0910	−0.484944	−0.242472	−	0.970158i	$-0.577958\pi$
$433$	−10.0910	−0.484944	−0.242472	+	0.970158i	$0.577958\pi$
$434$	5.52340	0.265132
$435$	7.54891	0.361943
$436$	12.3175	0.589902
$437$	13.2772	0.635135
$438$	−1.17972	−0.0563691
$439$	3.97449	0.189692	0.0948460	−	0.995492i	$-0.469764\pi$
$439$	3.97449	0.189692	0.0948460	+	0.995492i	$0.469764\pi$
$440$	2.15973	0.102961
$441$	−4.78994	−0.228093
$442$	−12.9442	−0.615694
$443$	−5.56112	−0.264217	−0.132108	−	0.991235i	$-0.542175\pi$
$443$	−5.56112	−0.264217	−0.132108	+	0.991235i	$0.542175\pi$
$444$	−3.86643	−0.183493
$445$	−9.93450	−0.470941
$446$	−2.07387	−0.0982005
$447$	−19.5786	−0.926037
$448$	−1.48663	−0.0702365
$449$	17.4973	0.825749	0.412875	−	0.910788i	$-0.364525\pi$
$449$	17.4973	0.825749	0.412875	+	0.910788i	$0.364525\pi$
$450$	0.335585	0.0158196
$451$	7.21070	0.339539
$452$	−8.93741	−0.420380
$453$	11.3134	0.531548
$454$	28.5906	1.34182
$455$	−17.7796	−0.833521
$456$	−3.42627	−0.160450
$457$	31.8542	1.49008	0.745038	−	0.667022i	$-0.232431\pi$
$457$	31.8542	1.49008	0.745038	+	0.667022i	$0.232431\pi$
$458$	0.844512	0.0394614
$459$	2.33751	0.109106
$460$	8.36919	0.390216
$461$	10.9578	0.510355	0.255177	−	0.966894i	$-0.417866\pi$
$461$	10.9578	0.510355	0.255177	+	0.966894i	$0.417866\pi$
$462$	−1.48663	−0.0691641
$463$	6.73353	0.312934	0.156467	−	0.987683i	$-0.449990\pi$
$463$	6.73353	0.312934	0.156467	+	0.987683i	$0.449990\pi$
$464$	3.49531	0.162266
$465$	8.02423	0.372115
$466$	−0.00482589	−0.000223555 0
$467$	23.9352	1.10759	0.553794	−	0.832653i	$-0.313179\pi$
$467$	23.9352	1.10759	0.553794	+	0.832653i	$0.313179\pi$
$468$	5.53760	0.255976
$469$	6.61623	0.305509
$470$	−14.4992	−0.668800
$471$	1.30526	0.0601431
$472$	13.1375	0.604702
$473$	−8.37981	−0.385304
$474$	11.2878	0.518468
$475$	−1.14980	−0.0527567
$476$	−3.47501	−0.159277
$477$	−3.82221	−0.175007
$478$	15.6790	0.717139
$479$	−31.1195	−1.42189	−0.710943	−	0.703250i	$-0.751732\pi$
$479$	−31.1195	−1.42189	−0.710943	+	0.703250i	$0.751732\pi$
$480$	−2.15973	−0.0985775
$481$	−21.4108	−0.976248
$482$	−12.5896	−0.573439
$483$	−5.76085	−0.262128
$484$	1.00000	0.0454545
$485$	7.74476	0.351672
$486$	−1.00000	−0.0453609
$487$	6.69860	0.303543	0.151771	−	0.988416i	$-0.451502\pi$
$487$	6.69860	0.303543	0.151771	+	0.988416i	$0.451502\pi$
$488$	1.00000	0.0452679
$489$	−2.48979	−0.112592
$490$	10.3450	0.467338
$491$	−37.0594	−1.67247	−0.836234	−	0.548373i	$-0.815247\pi$
$491$	−37.0594	−1.67247	−0.836234	+	0.548373i	$0.815247\pi$
$492$	−7.21070	−0.325084
$493$	8.17034	0.367974
$494$	−18.9733	−0.853650
$495$	−2.15973	−0.0970724
$496$	3.71539	0.166826
$497$	8.02175	0.359825
$498$	−4.96222	−0.222363
$499$	−20.8548	−0.933590	−0.466795	−	0.884366i	$-0.654591\pi$
$499$	−20.8548	−0.933590	−0.466795	+	0.884366i	$0.654591\pi$
$500$	−11.5234	−0.515342
$501$	13.6725	0.610843
$502$	−17.7012	−0.790043
$503$	−29.1624	−1.30029	−0.650143	−	0.759812i	$-0.725291\pi$
$503$	−29.1624	−1.30029	−0.650143	+	0.759812i	$0.725291\pi$
$504$	1.48663	0.0662196
$505$	30.6858	1.36550
$506$	3.87512	0.172270
$507$	17.6651	0.784533
$508$	21.9665	0.974604
$509$	−22.7444	−1.00813	−0.504065	−	0.863666i	$-0.668163\pi$
$509$	−22.7444	−1.00813	−0.504065	+	0.863666i	$0.668163\pi$
$510$	−5.04839	−0.223546
$511$	−1.75380	−0.0775835
$512$	−1.00000	−0.0441942
$513$	3.42627	0.151273
$514$	12.4144	0.547575
$515$	29.0723	1.28108
$516$	8.37981	0.368900
$517$	−6.71346	−0.295258
$518$	−5.74794	−0.252550
$519$	−15.7651	−0.692012
$520$	−11.9597	−0.524468
$521$	13.0689	0.572557	0.286279	−	0.958146i	$-0.407582\pi$
$521$	13.0689	0.572557	0.286279	+	0.958146i	$0.407582\pi$
$522$	−3.49531	−0.152986
$523$	−10.4644	−0.457576	−0.228788	−	0.973476i	$-0.573476\pi$
$523$	−10.4644	−0.457576	−0.228788	+	0.973476i	$0.573476\pi$
$524$	16.2301	0.709016
$525$	0.498890	0.0217733
$526$	23.4941	1.02439
$527$	8.68479	0.378315
$528$	−1.00000	−0.0435194
$529$	−7.98345	−0.347107
$530$	8.25493	0.358571
$531$	−13.1375	−0.570119
$532$	−5.09358	−0.220835
$533$	−39.9300	−1.72956
$534$	4.59989	0.199057
$535$	43.4602	1.87895
$536$	4.45050	0.192232
$537$	4.56376	0.196941
$538$	−18.4428	−0.795124
$539$	4.78994	0.206317
$540$	2.15973	0.0929398
$541$	−13.5479	−0.582471	−0.291236	−	0.956651i	$-0.594066\pi$
$541$	−13.5479	−0.582471	−0.291236	+	0.956651i	$0.594066\pi$
$542$	−20.6347	−0.886338
$543$	3.21399	0.137925
$544$	−2.33751	−0.100220
$545$	26.6025	1.13952
$546$	8.23235	0.352312
$547$	−21.5744	−0.922457	−0.461228	−	0.887281i	$-0.652591\pi$
$547$	−21.5744	−0.922457	−0.461228	+	0.887281i	$0.652591\pi$
$548$	−5.90932	−0.252433
$549$	−1.00000	−0.0426790
$550$	−0.335585	−0.0143094
$551$	11.9759	0.510189
$552$	−3.87512	−0.164936
$553$	16.7808	0.713592
$554$	−0.330066	−0.0140231
$555$	−8.35044	−0.354456
$556$	1.19750	0.0507854
$557$	−27.4818	−1.16444	−0.582221	−	0.813030i	$-0.697816\pi$
$557$	−27.4818	−1.16444	−0.582221	+	0.813030i	$0.697816\pi$
$558$	−3.71539	−0.157285
$559$	46.4041	1.96268
$560$	−3.21070	−0.135677
$561$	−2.33751	−0.0986899
$562$	−7.48663	−0.315804
$563$	10.2759	0.433078	0.216539	−	0.976274i	$-0.430523\pi$
$563$	10.2759	0.433078	0.216539	+	0.976274i	$0.430523\pi$
$564$	6.71346	0.282688
$565$	−19.3023	−0.812056
$566$	−8.98880	−0.377827
$567$	−1.48663	−0.0624324
$568$	5.39594	0.226409
$569$	−25.4295	−1.06606	−0.533030	−	0.846096i	$-0.678947\pi$
$569$	−25.4295	−1.06606	−0.533030	+	0.846096i	$0.678947\pi$
$570$	−7.39980	−0.309944
$571$	−3.94939	−0.165277	−0.0826384	−	0.996580i	$-0.526335\pi$
$571$	−3.94939	−0.165277	−0.0826384	+	0.996580i	$0.526335\pi$
$572$	−5.53760	−0.231539
$573$	25.8939	1.08173
$574$	−10.7196	−0.447428
$575$	−1.30043	−0.0542318
$576$	1.00000	0.0416667
$577$	31.8791	1.32715	0.663573	−	0.748112i	$-0.269039\pi$
$577$	31.8791	1.32715	0.663573	+	0.748112i	$0.269039\pi$
$578$	11.5360	0.479835
$579$	−21.8610	−0.908512
$580$	7.54891	0.313452
$581$	−7.37697	−0.306048
$582$	−3.58599	−0.148644
$583$	3.82221	0.158300
$584$	−1.17972	−0.0488171
$585$	11.9597	0.494473
$586$	10.0652	0.415789
$587$	−26.2885	−1.08504	−0.542521	−	0.840043i	$-0.682530\pi$
$587$	−26.2885	−1.08504	−0.542521	+	0.840043i	$0.682530\pi$
$588$	−4.78994	−0.197534
$589$	12.7299	0.524528
$590$	28.3734	1.16811
$591$	−11.8061	−0.485637
$592$	−3.86643	−0.158909
$593$	7.61998	0.312915	0.156458	−	0.987685i	$-0.449993\pi$
$593$	7.61998	0.312915	0.156458	+	0.987685i	$0.449993\pi$
$594$	1.00000	0.0410305
$595$	−7.50507	−0.307678
$596$	−19.5786	−0.801971
$597$	6.17268	0.252631
$598$	−21.4589	−0.877519
$599$	17.7112	0.723661	0.361830	−	0.932244i	$-0.382152\pi$
$599$	17.7112	0.723661	0.361830	+	0.932244i	$0.382152\pi$
$600$	0.335585	0.0137002
$601$	6.47749	0.264222	0.132111	−	0.991235i	$-0.457824\pi$
$601$	6.47749	0.264222	0.132111	+	0.991235i	$0.457824\pi$
$602$	12.4576	0.507736
$603$	−4.45050	−0.181238
$604$	11.3134	0.460334
$605$	2.15973	0.0878053
$606$	−14.2082	−0.577168
$607$	−4.66958	−0.189532	−0.0947662	−	0.995500i	$-0.530210\pi$
$607$	−4.66958	−0.189532	−0.0947662	+	0.995500i	$0.530210\pi$
$608$	−3.42627	−0.138954
$609$	−5.19622	−0.210561
$610$	2.15973	0.0874447
$611$	37.1765	1.50400
$612$	2.33751	0.0944884
$613$	−25.8100	−1.04246	−0.521228	−	0.853417i	$-0.674526\pi$
$613$	−25.8100	−1.04246	−0.521228	+	0.853417i	$0.674526\pi$
$614$	−10.7141	−0.432388
$615$	−15.5731	−0.627970
$616$	−1.48663	−0.0598979
$617$	−37.1837	−1.49696	−0.748480	−	0.663157i	$-0.769216\pi$
$617$	−37.1837	−1.49696	−0.748480	+	0.663157i	$0.769216\pi$
$618$	−13.4611	−0.541485
$619$	−40.1186	−1.61250	−0.806251	−	0.591574i	$-0.798507\pi$
$619$	−40.1186	−1.61250	−0.806251	+	0.591574i	$0.798507\pi$
$620$	8.02423	0.322261
$621$	3.87512	0.155503
$622$	22.0204	0.882936
$623$	6.83832	0.273971
$624$	5.53760	0.221682
$625$	−23.2095	−0.928378
$626$	25.5931	1.02291
$627$	−3.42627	−0.136832
$628$	1.30526	0.0520855
$629$	−9.03785	−0.360363
$630$	3.21070	0.127918
$631$	34.1963	1.36133	0.680666	−	0.732594i	$-0.261690\pi$
$631$	34.1963	1.36133	0.680666	+	0.732594i	$0.261690\pi$
$632$	11.2878	0.449006
$633$	0.750581	0.0298329
$634$	−8.56635	−0.340213
$635$	47.4415	1.88266
$636$	−3.82221	−0.151561
$637$	−26.5248	−1.05095
$638$	3.49531	0.138381
$639$	−5.39594	−0.213460
$640$	−2.15973	−0.0853707
$641$	−14.1193	−0.557680	−0.278840	−	0.960338i	$-0.589950\pi$
$641$	−14.1193	−0.557680	−0.278840	+	0.960338i	$0.589950\pi$
$642$	−20.1230	−0.794192
$643$	−27.0568	−1.06702	−0.533509	−	0.845795i	$-0.679127\pi$
$643$	−27.0568	−1.06702	−0.533509	+	0.845795i	$0.679127\pi$
$644$	−5.76085	−0.227009
$645$	18.0981	0.712611
$646$	−8.00895	−0.315108
$647$	−9.17687	−0.360780	−0.180390	−	0.983595i	$-0.557736\pi$
$647$	−9.17687	−0.360780	−0.180390	+	0.983595i	$0.557736\pi$
$648$	−1.00000	−0.0392837
$649$	13.1375	0.515692
$650$	1.85834	0.0728900
$651$	−5.52340	−0.216479
$652$	−2.48979	−0.0975078
$653$	30.7912	1.20495	0.602476	−	0.798137i	$-0.294181\pi$
$653$	30.7912	1.20495	0.602476	+	0.798137i	$0.294181\pi$
$654$	−12.3175	−0.481653
$655$	35.0526	1.36962
$656$	−7.21070	−0.281531
$657$	1.17972	0.0460252
$658$	9.98041	0.389077
$659$	10.0452	0.391305	0.195652	−	0.980673i	$-0.437318\pi$
$659$	10.0452	0.391305	0.195652	+	0.980673i	$0.437318\pi$
$660$	−2.15973	−0.0840672
$661$	−42.9194	−1.66937	−0.834685	−	0.550727i	$-0.814350\pi$
$661$	−42.9194	−1.66937	−0.834685	+	0.550727i	$0.814350\pi$
$662$	18.2004	0.707377
$663$	12.9442	0.502712
$664$	−4.96222	−0.192572
$665$	−11.0007	−0.426590
$666$	3.86643	0.149821
$667$	13.5447	0.524455
$668$	13.6725	0.529005
$669$	2.07387	0.0801804
$670$	9.61186	0.371338
$671$	1.00000	0.0386046
$672$	1.48663	0.0573478
$673$	1.77188	0.0683010	0.0341505	−	0.999417i	$-0.489127\pi$
$673$	1.77188	0.0683010	0.0341505	+	0.999417i	$0.489127\pi$
$674$	−33.9161	−1.30640
$675$	−0.335585	−0.0129167
$676$	17.6651	0.679425
$677$	−25.1569	−0.966858	−0.483429	−	0.875384i	$-0.660609\pi$
$677$	−25.1569	−0.966858	−0.483429	+	0.875384i	$0.660609\pi$
$678$	8.93741	0.343239
$679$	−5.33103	−0.204586
$680$	−5.04839	−0.193597
$681$	−28.5906	−1.09559
$682$	3.71539	0.142270
$683$	−8.36659	−0.320139	−0.160069	−	0.987106i	$-0.551172\pi$
$683$	−8.36659	−0.320139	−0.160069	+	0.987106i	$0.551172\pi$
$684$	3.42627	0.131007
$685$	−12.7625	−0.487630
$686$	−17.5272	−0.669193
$687$	−0.844512	−0.0322201
$688$	8.37981	0.319477
$689$	−21.1659	−0.806356
$690$	−8.36919	−0.318610
$691$	33.1500	1.26109	0.630543	−	0.776154i	$-0.282832\pi$
$691$	33.1500	1.26109	0.630543	+	0.776154i	$0.282832\pi$
$692$	−15.7651	−0.599300
$693$	1.48663	0.0564722
$694$	15.6341	0.593464
$695$	2.58627	0.0981030
$696$	−3.49531	−0.132489
$697$	−16.8551	−0.638433
$698$	−26.7325	−1.01184
$699$	0.00482589	0.000182532 0
$700$	0.498890	0.0188563
$701$	7.39883	0.279450	0.139725	−	0.990190i	$-0.455378\pi$
$701$	7.39883	0.279450	0.139725	+	0.990190i	$0.455378\pi$
$702$	−5.53760	−0.209003
$703$	−13.2474	−0.499637
$704$	−1.00000	−0.0376889
$705$	14.4992	0.546073
$706$	25.8690	0.973594
$707$	−21.1223	−0.794384
$708$	−13.1375	−0.493737
$709$	−12.3694	−0.464544	−0.232272	−	0.972651i	$-0.574616\pi$
$709$	−12.3694	−0.464544	−0.232272	+	0.972651i	$0.574616\pi$
$710$	11.6538	0.437358
$711$	−11.2878	−0.423327
$712$	4.59989	0.172388
$713$	14.3976	0.539194
$714$	3.47501	0.130049
$715$	−11.9597	−0.447268
$716$	4.56376	0.170556
$717$	−15.6790	−0.585541
$718$	27.5185	1.02698
$719$	−3.14204	−0.117178	−0.0585892	−	0.998282i	$-0.518660\pi$
$719$	−3.14204	−0.117178	−0.0585892	+	0.998282i	$0.518660\pi$
$720$	2.15973	0.0804882
$721$	−20.0116	−0.745272
$722$	7.26068	0.270215
$723$	12.5896	0.468211
$724$	3.21399	0.119447
$725$	−1.17297	−0.0435632
$726$	−1.00000	−0.0371135
$727$	−16.1552	−0.599163	−0.299582	−	0.954071i	$-0.596847\pi$
$727$	−16.1552	−0.599163	−0.299582	+	0.954071i	$0.596847\pi$
$728$	8.23235	0.305111
$729$	1.00000	0.0370370
$730$	−2.54787	−0.0943008
$731$	19.5879	0.724486
$732$	−1.00000	−0.0369611
$733$	−22.5644	−0.833436	−0.416718	−	0.909036i	$-0.636820\pi$
$733$	−22.5644	−0.833436	−0.416718	+	0.909036i	$0.636820\pi$
$734$	−12.9441	−0.477777
$735$	−10.3450	−0.381580
$736$	−3.87512	−0.142839
$737$	4.45050	0.163936
$738$	7.21070	0.265430
$739$	−24.5883	−0.904495	−0.452248	−	0.891892i	$-0.649378\pi$
$739$	−24.5883	−0.904495	−0.452248	+	0.891892i	$0.649378\pi$
$740$	−8.35044	−0.306968
$741$	18.9733	0.697002
$742$	−5.68220	−0.208600
$743$	27.4070	1.00547	0.502733	−	0.864442i	$-0.332328\pi$
$743$	27.4070	1.00547	0.502733	+	0.864442i	$0.332328\pi$
$744$	−3.71539	−0.136213
$745$	−42.2844	−1.54918
$746$	−12.6002	−0.461326
$747$	4.96222	0.181558
$748$	−2.33751	−0.0854680
$749$	−29.9154	−1.09308
$750$	11.5234	0.420775
$751$	−11.0652	−0.403774	−0.201887	−	0.979409i	$-0.564707\pi$
$751$	−11.0652	−0.403774	−0.201887	+	0.979409i	$0.564707\pi$
$752$	6.71346	0.244815
$753$	17.7012	0.645067
$754$	−19.3556	−0.704891
$755$	24.4337	0.889235
$756$	−1.48663	−0.0540681
$757$	−15.5340	−0.564595	−0.282297	−	0.959327i	$-0.591096\pi$
$757$	−15.5340	−0.564595	−0.282297	+	0.959327i	$0.591096\pi$
$758$	−37.0888	−1.34713
$759$	−3.87512	−0.140658
$760$	−7.39980	−0.268419
$761$	11.1588	0.404506	0.202253	−	0.979333i	$-0.435174\pi$
$761$	11.1588	0.404506	0.202253	+	0.979333i	$0.435174\pi$
$762$	−21.9665	−0.795761
$763$	−18.3115	−0.662923
$764$	25.8939	0.936808
$765$	5.04839	0.182525
$766$	−0.0199579	−0.000721110 0
$767$	−72.7503	−2.62686
$768$	1.00000	0.0360844
$769$	28.2780	1.01973	0.509865	−	0.860254i	$-0.329695\pi$
$769$	28.2780	1.01973	0.509865	+	0.860254i	$0.329695\pi$
$770$	−3.21070	−0.115706
$771$	−12.4144	−0.447093
$772$	−21.8610	−0.786794
$773$	−39.5596	−1.42286	−0.711429	−	0.702758i	$-0.751952\pi$
$773$	−39.5596	−1.42286	−0.711429	+	0.702758i	$0.751952\pi$
$774$	−8.37981	−0.301206
$775$	−1.24683	−0.0447875
$776$	−3.58599	−0.128730
$777$	5.74794	0.206206
$778$	19.0988	0.684724
$779$	−24.7058	−0.885178
$780$	11.9597	0.428226
$781$	5.39594	0.193082
$782$	−9.05815	−0.323919
$783$	3.49531	0.124912
$784$	−4.78994	−0.171069
$785$	2.81900	0.100614
$786$	−16.2301	−0.578909
$787$	13.8093	0.492249	0.246125	−	0.969238i	$-0.420843\pi$
$787$	13.8093	0.492249	0.246125	+	0.969238i	$0.420843\pi$
$788$	−11.8061	−0.420574
$789$	−23.4941	−0.836413
$790$	24.3786	0.867353
$791$	13.2866	0.472416
$792$	1.00000	0.0355335
$793$	−5.53760	−0.196646
$794$	−16.5408	−0.587012
$795$	−8.25493	−0.292772
$796$	6.17268	0.218785
$797$	−35.7035	−1.26468	−0.632341	−	0.774690i	$-0.717906\pi$
$797$	−35.7035	−1.26468	−0.632341	+	0.774690i	$0.717906\pi$
$798$	5.09358	0.180311
$799$	15.6928	0.555172
$800$	0.335585	0.0118647
$801$	−4.59989	−0.162529
$802$	−23.7813	−0.839748
$803$	−1.17972	−0.0416314
$804$	−4.45050	−0.156957
$805$	−12.4419	−0.438518
$806$	−20.5744	−0.724702
$807$	18.4428	0.649216
$808$	−14.2082	−0.499842
$809$	53.4232	1.87826	0.939130	−	0.343563i	$-0.111634\pi$
$809$	53.4232	1.87826	0.939130	+	0.343563i	$0.111634\pi$
$810$	−2.15973	−0.0758850
$811$	−47.8593	−1.68057	−0.840284	−	0.542146i	$-0.817612\pi$
$811$	−47.8593	−1.68057	−0.840284	+	0.542146i	$0.817612\pi$
$812$	−5.19622	−0.182352
$813$	20.6347	0.723692
$814$	−3.86643	−0.135518
$815$	−5.37727	−0.188357
$816$	2.33751	0.0818294
$817$	28.7115	1.00449
$818$	−10.7147	−0.374631
$819$	−8.23235	−0.287661
$820$	−15.5731	−0.543838
$821$	54.3422	1.89656	0.948278	−	0.317440i	$-0.102823\pi$
$821$	54.3422	1.89656	0.948278	+	0.317440i	$0.102823\pi$
$822$	5.90932	0.206111
$823$	14.4295	0.502982	0.251491	−	0.967860i	$-0.419079\pi$
$823$	14.4295	0.502982	0.251491	+	0.967860i	$0.419079\pi$
$824$	−13.4611	−0.468940
$825$	0.335585	0.0116836
$826$	−19.5305	−0.679554
$827$	22.0919	0.768211	0.384106	−	0.923289i	$-0.374510\pi$
$827$	22.0919	0.768211	0.384106	+	0.923289i	$0.374510\pi$
$828$	3.87512	0.134670
$829$	−14.8719	−0.516522	−0.258261	−	0.966075i	$-0.583149\pi$
$829$	−14.8719	−0.516522	−0.258261	+	0.966075i	$0.583149\pi$
$830$	−10.7170	−0.371994
$831$	0.330066	0.0114498
$832$	5.53760	0.191982
$833$	−11.1966	−0.387938
$834$	−1.19750	−0.0414661
$835$	29.5289	1.02189
$836$	−3.42627	−0.118500
$837$	3.71539	0.128423
$838$	17.9297	0.619370
$839$	16.1663	0.558121	0.279061	−	0.960273i	$-0.409977\pi$
$839$	16.1663	0.558121	0.279061	+	0.960273i	$0.409977\pi$
$840$	3.21070	0.110780
$841$	−16.7828	−0.578717
$842$	3.57962	0.123362
$843$	7.48663	0.257853
$844$	0.750581	0.0258361
$845$	38.1517	1.31246
$846$	−6.71346	−0.230814
$847$	−1.48663	−0.0510811
$848$	−3.82221	−0.131255
$849$	8.98880	0.308495
$850$	0.784435	0.0269059
$851$	−14.9829	−0.513607
$852$	−5.39594	−0.184862
$853$	4.12232	0.141145	0.0705727	−	0.997507i	$-0.477517\pi$
$853$	4.12232	0.141145	0.0705727	+	0.997507i	$0.477517\pi$
$854$	−1.48663	−0.0508713
$855$	7.39980	0.253068
$856$	−20.1230	−0.687790
$857$	34.4683	1.17741	0.588707	−	0.808347i	$-0.299637\pi$
$857$	34.4683	1.17741	0.588707	+	0.808347i	$0.299637\pi$
$858$	5.53760	0.189051
$859$	−17.3245	−0.591106	−0.295553	−	0.955326i	$-0.595504\pi$
$859$	−17.3245	−0.591106	−0.295553	+	0.955326i	$0.595504\pi$
$860$	18.0981	0.617140
$861$	10.7196	0.365324
$862$	−14.2239	−0.484469
$863$	−38.4144	−1.30764	−0.653821	−	0.756649i	$-0.726835\pi$
$863$	−38.4144	−1.30764	−0.653821	+	0.756649i	$0.726835\pi$
$864$	−1.00000	−0.0340207
$865$	−34.0483	−1.15768
$866$	10.0910	0.342907
$867$	−11.5360	−0.391784
$868$	−5.52340	−0.187476
$869$	11.2878	0.382914
$870$	−7.54891	−0.255932
$871$	−24.6451	−0.835068
$872$	−12.3175	−0.417124
$873$	3.58599	0.121368
$874$	−13.2772	−0.449108
$875$	17.1310	0.579133
$876$	1.17972	0.0398590
$877$	22.8561	0.771796	0.385898	−	0.922541i	$-0.373892\pi$
$877$	22.8561	0.771796	0.385898	+	0.922541i	$0.373892\pi$
$878$	−3.97449	−0.134132
$879$	−10.0652	−0.339490
$880$	−2.15973	−0.0728043
$881$	18.9686	0.639069	0.319535	−	0.947575i	$-0.396473\pi$
$881$	18.9686	0.639069	0.319535	+	0.947575i	$0.396473\pi$
$882$	4.78994	0.161286
$883$	−30.0557	−1.01145	−0.505727	−	0.862694i	$-0.668776\pi$
$883$	−30.0557	−1.01145	−0.505727	+	0.862694i	$0.668776\pi$
$884$	12.9442	0.435362
$885$	−28.3734	−0.953761
$886$	5.56112	0.186829
$887$	−34.4479	−1.15665	−0.578323	−	0.815808i	$-0.696293\pi$
$887$	−34.4479	−1.15665	−0.578323	+	0.815808i	$0.696293\pi$
$888$	3.86643	0.129749
$889$	−32.6559	−1.09524
$890$	9.93450	0.333005
$891$	−1.00000	−0.0335013
$892$	2.07387	0.0694382
$893$	23.0021	0.769737
$894$	19.5786	0.654807
$895$	9.85648	0.329466
$896$	1.48663	0.0496647
$897$	21.4589	0.716491
$898$	−17.4973	−0.583893
$899$	12.9865	0.433123
$900$	−0.335585	−0.0111862
$901$	−8.93447	−0.297650
$902$	−7.21070	−0.240090
$903$	−12.4576	−0.414564
$904$	8.93741	0.297254
$905$	6.94133	0.230738
$906$	−11.3134	−0.375861
$907$	11.3682	0.377475	0.188737	−	0.982028i	$-0.439560\pi$
$907$	11.3682	0.377475	0.188737	+	0.982028i	$0.439560\pi$
$908$	−28.5906	−0.948811
$909$	14.2082	0.471256
$910$	17.7796	0.589388
$911$	53.6491	1.77747	0.888736	−	0.458418i	$-0.151584\pi$
$911$	53.6491	1.77747	0.888736	+	0.458418i	$0.151584\pi$
$912$	3.42627	0.113455
$913$	−4.96222	−0.164226
$914$	−31.8542	−1.05364
$915$	−2.15973	−0.0713983
$916$	−0.844512	−0.0279035
$917$	−24.1281	−0.796780
$918$	−2.33751	−0.0771495
$919$	36.5854	1.20684	0.603420	−	0.797423i	$-0.293804\pi$
$919$	36.5854	1.20684	0.603420	+	0.797423i	$0.293804\pi$
$920$	−8.36919	−0.275924
$921$	10.7141	0.353043
$922$	−10.9578	−0.360875
$923$	−29.8806	−0.983532
$924$	1.48663	0.0489064
$925$	1.29752	0.0426621
$926$	−6.73353	−0.221277
$927$	13.4611	0.442121
$928$	−3.49531	−0.114739
$929$	11.4867	0.376865	0.188433	−	0.982086i	$-0.439659\pi$
$929$	11.4867	0.376865	0.188433	+	0.982086i	$0.439659\pi$
$930$	−8.02423	−0.263125
$931$	−16.4116	−0.537870
$932$	0.00482589	0.000158077 0
$933$	−22.0204	−0.720914
$934$	−23.9352	−0.783184
$935$	−5.04839	−0.165100
$936$	−5.53760	−0.181002
$937$	−43.0161	−1.40528	−0.702638	−	0.711548i	$-0.747995\pi$
$937$	−43.0161	−1.40528	−0.702638	+	0.711548i	$0.747995\pi$
$938$	−6.61623	−0.216027
$939$	−25.5931	−0.835199
$940$	14.4992	0.472913
$941$	−24.6054	−0.802112	−0.401056	−	0.916054i	$-0.631357\pi$
$941$	−24.6054	−0.802112	−0.401056	+	0.916054i	$0.631357\pi$
$942$	−1.30526	−0.0425276
$943$	−27.9423	−0.909928
$944$	−13.1375	−0.427589
$945$	−3.21070	−0.104444
$946$	8.37981	0.272451
$947$	21.3091	0.692452	0.346226	−	0.938151i	$-0.387463\pi$
$947$	21.3091	0.692452	0.346226	+	0.938151i	$0.387463\pi$
$948$	−11.2878	−0.366612
$949$	6.53281	0.212064
$950$	1.14980	0.0373046
$951$	8.56635	0.277783
$952$	3.47501	0.112626
$953$	−12.2237	−0.395966	−0.197983	−	0.980205i	$-0.563439\pi$
$953$	−12.2237	−0.395966	−0.197983	+	0.980205i	$0.563439\pi$
$954$	3.82221	0.123749
$955$	55.9237	1.80965
$956$	−15.6790	−0.507094
$957$	−3.49531	−0.112987
$958$	31.1195	1.00543
$959$	8.78494	0.283681
$960$	2.15973	0.0697048
$961$	−17.1959	−0.554705
$962$	21.4108	0.690311
$963$	20.1230	0.648455
$964$	12.5896	0.405483
$965$	−47.2137	−1.51986
$966$	5.76085	0.185352
$967$	−52.9113	−1.70151	−0.850757	−	0.525559i	$-0.823856\pi$
$967$	−52.9113	−1.70151	−0.850757	+	0.525559i	$0.823856\pi$
$968$	−1.00000	−0.0321412
$969$	8.00895	0.257285
$970$	−7.74476	−0.248669
$971$	−37.6806	−1.20923	−0.604613	−	0.796519i	$-0.706672\pi$
$971$	−37.6806	−1.20923	−0.604613	+	0.796519i	$0.706672\pi$
$972$	1.00000	0.0320750
$973$	−1.78024	−0.0570718
$974$	−6.69860	−0.214637
$975$	−1.85834	−0.0595144
$976$	−1.00000	−0.0320092
$977$	42.6049	1.36305	0.681525	−	0.731795i	$-0.261317\pi$
$977$	42.6049	1.36305	0.681525	+	0.731795i	$0.261317\pi$
$978$	2.48979	0.0796147
$979$	4.59989	0.147013
$980$	−10.3450	−0.330458
$981$	12.3175	0.393268
$982$	37.0594	1.18261
$983$	18.8904	0.602510	0.301255	−	0.953544i	$-0.402595\pi$
$983$	18.8904	0.602510	0.301255	+	0.953544i	$0.402595\pi$
$984$	7.21070	0.229869
$985$	−25.4979	−0.812430
$986$	−8.17034	−0.260197
$987$	−9.98041	−0.317680
$988$	18.9733	0.603622
$989$	32.4728	1.03257
$990$	2.15973	0.0686406
$991$	−20.6244	−0.655155	−0.327578	−	0.944824i	$-0.606232\pi$
$991$	−20.6244	−0.655155	−0.327578	+	0.944824i	$0.606232\pi$
$992$	−3.71539	−0.117964
$993$	−18.2004	−0.577571
$994$	−8.02175	−0.254434
$995$	13.3313	0.422631
$996$	4.96222	0.157234
$997$	−38.8518	−1.23045	−0.615225	−	0.788352i	$-0.710935\pi$
$997$	−38.8518	−1.23045	−0.615225	+	0.788352i	$0.710935\pi$
$998$	20.8548	0.660148
$999$	−3.86643	−0.122329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.u.1.4	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.u.1.4	✓	5	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.15973 q^{5} -1.00000 q^{6} -1.48663 q^{7} -1.00000 q^{8} +1.00000 q^{9} -2.15973 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.53760 q^{13} +1.48663 q^{14} +2.15973 q^{15} +1.00000 q^{16} +2.33751 q^{17} -1.00000 q^{18} +3.42627 q^{19} +2.15973 q^{20} -1.48663 q^{21} +1.00000 q^{22} +3.87512 q^{23} -1.00000 q^{24} -0.335585 q^{25} -5.53760 q^{26} +1.00000 q^{27} -1.48663 q^{28} +3.49531 q^{29} -2.15973 q^{30} +3.71539 q^{31} -1.00000 q^{32} -1.00000 q^{33} -2.33751 q^{34} -3.21070 q^{35} +1.00000 q^{36} -3.86643 q^{37} -3.42627 q^{38} +5.53760 q^{39} -2.15973 q^{40} -7.21070 q^{41} +1.48663 q^{42} +8.37981 q^{43} -1.00000 q^{44} +2.15973 q^{45} -3.87512 q^{46} +6.71346 q^{47} +1.00000 q^{48} -4.78994 q^{49} +0.335585 q^{50} +2.33751 q^{51} +5.53760 q^{52} -3.82221 q^{53} -1.00000 q^{54} -2.15973 q^{55} +1.48663 q^{56} +3.42627 q^{57} -3.49531 q^{58} -13.1375 q^{59} +2.15973 q^{60} -1.00000 q^{61} -3.71539 q^{62} -1.48663 q^{63} +1.00000 q^{64} +11.9597 q^{65} +1.00000 q^{66} -4.45050 q^{67} +2.33751 q^{68} +3.87512 q^{69} +3.21070 q^{70} -5.39594 q^{71} -1.00000 q^{72} +1.17972 q^{73} +3.86643 q^{74} -0.335585 q^{75} +3.42627 q^{76} +1.48663 q^{77} -5.53760 q^{78} -11.2878 q^{79} +2.15973 q^{80} +1.00000 q^{81} +7.21070 q^{82} +4.96222 q^{83} -1.48663 q^{84} +5.04839 q^{85} -8.37981 q^{86} +3.49531 q^{87} +1.00000 q^{88} -4.59989 q^{89} -2.15973 q^{90} -8.23235 q^{91} +3.87512 q^{92} +3.71539 q^{93} -6.71346 q^{94} +7.39980 q^{95} -1.00000 q^{96} +3.58599 q^{97} +4.78994 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

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