LMFDB - Embedded newform 6026.2.a.l.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.455108 q^{3} +1.00000 q^{4} -2.88071 q^{5} -0.455108 q^{6} -3.99338 q^{7} -1.00000 q^{8} -2.79288 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.455108 q^{3} +1.00000 q^{4} -2.88071 q^{5} -0.455108 q^{6} -3.99338 q^{7} -1.00000 q^{8} -2.79288 q^{9} +2.88071 q^{10} +2.79245 q^{11} +0.455108 q^{12} +4.19163 q^{13} +3.99338 q^{14} -1.31103 q^{15} +1.00000 q^{16} +7.24886 q^{17} +2.79288 q^{18} -3.58943 q^{19} -2.88071 q^{20} -1.81742 q^{21} -2.79245 q^{22} -1.00000 q^{23} -0.455108 q^{24} +3.29851 q^{25} -4.19163 q^{26} -2.63638 q^{27} -3.99338 q^{28} -9.12503 q^{29} +1.31103 q^{30} -10.5932 q^{31} -1.00000 q^{32} +1.27087 q^{33} -7.24886 q^{34} +11.5038 q^{35} -2.79288 q^{36} +0.209959 q^{37} +3.58943 q^{38} +1.90764 q^{39} +2.88071 q^{40} -3.08089 q^{41} +1.81742 q^{42} +3.86185 q^{43} +2.79245 q^{44} +8.04548 q^{45} +1.00000 q^{46} -3.30779 q^{47} +0.455108 q^{48} +8.94708 q^{49} -3.29851 q^{50} +3.29901 q^{51} +4.19163 q^{52} -12.0794 q^{53} +2.63638 q^{54} -8.04425 q^{55} +3.99338 q^{56} -1.63358 q^{57} +9.12503 q^{58} +7.77883 q^{59} -1.31103 q^{60} -11.1380 q^{61} +10.5932 q^{62} +11.1530 q^{63} +1.00000 q^{64} -12.0749 q^{65} -1.27087 q^{66} +8.30992 q^{67} +7.24886 q^{68} -0.455108 q^{69} -11.5038 q^{70} +1.87983 q^{71} +2.79288 q^{72} +16.7669 q^{73} -0.209959 q^{74} +1.50118 q^{75} -3.58943 q^{76} -11.1513 q^{77} -1.90764 q^{78} -12.3875 q^{79} -2.88071 q^{80} +7.17879 q^{81} +3.08089 q^{82} -7.47080 q^{83} -1.81742 q^{84} -20.8819 q^{85} -3.86185 q^{86} -4.15287 q^{87} -2.79245 q^{88} -5.06447 q^{89} -8.04548 q^{90} -16.7388 q^{91} -1.00000 q^{92} -4.82106 q^{93} +3.30779 q^{94} +10.3401 q^{95} -0.455108 q^{96} -4.43513 q^{97} -8.94708 q^{98} -7.79897 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	0.455108	0.262757	0.131378	−	0.991332i	$-0.458060\pi$
$3$	0.455108	0.262757	0.131378	+	0.991332i	$0.458060\pi$
$4$	1.00000	0.500000
$5$	−2.88071	−1.28829	−0.644147	−	0.764902i	$-0.722788\pi$
$5$	−2.88071	−1.28829	−0.644147	+	0.764902i	$0.722788\pi$
$6$	−0.455108	−0.185797
$7$	−3.99338	−1.50936	−0.754678	−	0.656096i	$-0.772207\pi$
$7$	−3.99338	−1.50936	−0.754678	+	0.656096i	$0.772207\pi$
$8$	−1.00000	−0.353553
$9$	−2.79288	−0.930959
$10$	2.88071	0.910962
$11$	2.79245	0.841955	0.420978	−	0.907071i	$-0.361687\pi$
$11$	2.79245	0.841955	0.420978	+	0.907071i	$0.361687\pi$
$12$	0.455108	0.131378
$13$	4.19163	1.16255	0.581275	−	0.813707i	$-0.302554\pi$
$13$	4.19163	1.16255	0.581275	+	0.813707i	$0.302554\pi$
$14$	3.99338	1.06728
$15$	−1.31103	−0.338508
$16$	1.00000	0.250000
$17$	7.24886	1.75811	0.879054	−	0.476723i	$-0.158176\pi$
$17$	7.24886	1.75811	0.879054	+	0.476723i	$0.158176\pi$
$18$	2.79288	0.658287
$19$	−3.58943	−0.823471	−0.411736	−	0.911303i	$-0.635077\pi$
$19$	−3.58943	−0.823471	−0.411736	+	0.911303i	$0.635077\pi$
$20$	−2.88071	−0.644147
$21$	−1.81742	−0.396593
$22$	−2.79245	−0.595352
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.455108	−0.0928985
$25$	3.29851	0.659702
$26$	−4.19163	−0.822047
$27$	−2.63638	−0.507372
$28$	−3.99338	−0.754678
$29$	−9.12503	−1.69448	−0.847238	−	0.531213i	$-0.821736\pi$
$29$	−9.12503	−1.69448	−0.847238	+	0.531213i	$0.821736\pi$
$30$	1.31103	0.239361
$31$	−10.5932	−1.90260	−0.951299	−	0.308269i	$-0.900250\pi$
$31$	−10.5932	−1.90260	−0.951299	+	0.308269i	$0.900250\pi$
$32$	−1.00000	−0.176777
$33$	1.27087	0.221229
$34$	−7.24886	−1.24317
$35$	11.5038	1.94449
$36$	−2.79288	−0.465479
$37$	0.209959	0.0345170	0.0172585	−	0.999851i	$-0.494506\pi$
$37$	0.209959	0.0345170	0.0172585	+	0.999851i	$0.494506\pi$
$38$	3.58943	0.582282
$39$	1.90764	0.305468
$40$	2.88071	0.455481
$41$	−3.08089	−0.481154	−0.240577	−	0.970630i	$-0.577337\pi$
$41$	−3.08089	−0.481154	−0.240577	+	0.970630i	$0.577337\pi$
$42$	1.81742	0.280434
$43$	3.86185	0.588927	0.294463	−	0.955663i	$-0.404859\pi$
$43$	3.86185	0.588927	0.294463	+	0.955663i	$0.404859\pi$
$44$	2.79245	0.420978
$45$	8.04548	1.19935
$46$	1.00000	0.147442
$47$	−3.30779	−0.482491	−0.241245	−	0.970464i	$-0.577556\pi$
$47$	−3.30779	−0.482491	−0.241245	+	0.970464i	$0.577556\pi$
$48$	0.455108	0.0656891
$49$	8.94708	1.27815
$50$	−3.29851	−0.466480
$51$	3.29901	0.461954
$52$	4.19163	0.581275
$53$	−12.0794	−1.65923	−0.829615	−	0.558336i	$-0.811440\pi$
$53$	−12.0794	−1.65923	−0.829615	+	0.558336i	$0.811440\pi$
$54$	2.63638	0.358766
$55$	−8.04425	−1.08469
$56$	3.99338	0.533638
$57$	−1.63358	−0.216372
$58$	9.12503	1.19818
$59$	7.77883	1.01272	0.506359	−	0.862323i	$-0.330991\pi$
$59$	7.77883	1.01272	0.506359	+	0.862323i	$0.330991\pi$
$60$	−1.31103	−0.169254
$61$	−11.1380	−1.42608	−0.713039	−	0.701125i	$-0.752682\pi$
$61$	−11.1380	−1.42608	−0.713039	+	0.701125i	$0.752682\pi$
$62$	10.5932	1.34534
$63$	11.1530	1.40515
$64$	1.00000	0.125000
$65$	−12.0749	−1.49771
$66$	−1.27087	−0.156433
$67$	8.30992	1.01522	0.507609	−	0.861587i	$-0.330529\pi$
$67$	8.30992	1.01522	0.507609	+	0.861587i	$0.330529\pi$
$68$	7.24886	0.879054
$69$	−0.455108	−0.0547885
$70$	−11.5038	−1.37496
$71$	1.87983	0.223094	0.111547	−	0.993759i	$-0.464419\pi$
$71$	1.87983	0.223094	0.111547	+	0.993759i	$0.464419\pi$
$72$	2.79288	0.329144
$73$	16.7669	1.96242	0.981208	−	0.192954i	$-0.0618068\pi$
$73$	16.7669	1.96242	0.981208	+	0.192954i	$0.0618068\pi$
$74$	−0.209959	−0.0244072
$75$	1.50118	0.173341
$76$	−3.58943	−0.411736
$77$	−11.1513	−1.27081
$78$	−1.90764	−0.215998
$79$	−12.3875	−1.39370	−0.696850	−	0.717217i	$-0.745416\pi$
$79$	−12.3875	−1.39370	−0.696850	+	0.717217i	$0.745416\pi$
$80$	−2.88071	−0.322074
$81$	7.17879	0.797644
$82$	3.08089	0.340227
$83$	−7.47080	−0.820027	−0.410014	−	0.912079i	$-0.634476\pi$
$83$	−7.47080	−0.820027	−0.410014	+	0.912079i	$0.634476\pi$
$84$	−1.81742	−0.198297
$85$	−20.8819	−2.26496
$86$	−3.86185	−0.416434
$87$	−4.15287	−0.445235
$88$	−2.79245	−0.297676
$89$	−5.06447	−0.536833	−0.268416	−	0.963303i	$-0.586500\pi$
$89$	−5.06447	−0.536833	−0.268416	+	0.963303i	$0.586500\pi$
$90$	−8.04548	−0.848068
$91$	−16.7388	−1.75470
$92$	−1.00000	−0.104257
$93$	−4.82106	−0.499920
$94$	3.30779	0.341173
$95$	10.3401	1.06087
$96$	−0.455108	−0.0464492
$97$	−4.43513	−0.450319	−0.225160	−	0.974322i	$-0.572290\pi$
$97$	−4.43513	−0.450319	−0.225160	+	0.974322i	$0.572290\pi$
$98$	−8.94708	−0.903792
$99$	−7.79897	−0.783826
$100$	3.29851	0.329851
$101$	0.656006	0.0652751	0.0326375	−	0.999467i	$-0.489609\pi$
$101$	0.656006	0.0652751	0.0326375	+	0.999467i	$0.489609\pi$
$102$	−3.29901	−0.326651
$103$	−7.02899	−0.692587	−0.346293	−	0.938126i	$-0.612560\pi$
$103$	−7.02899	−0.692587	−0.346293	+	0.938126i	$0.612560\pi$
$104$	−4.19163	−0.411023
$105$	5.23546	0.510929
$106$	12.0794	1.17325
$107$	10.1518	0.981416	0.490708	−	0.871324i	$-0.336738\pi$
$107$	10.1518	0.981416	0.490708	+	0.871324i	$0.336738\pi$
$108$	−2.63638	−0.253686
$109$	2.54167	0.243448	0.121724	−	0.992564i	$-0.461158\pi$
$109$	2.54167	0.243448	0.121724	+	0.992564i	$0.461158\pi$
$110$	8.04425	0.766989
$111$	0.0955538	0.00906957
$112$	−3.99338	−0.377339
$113$	−11.8837	−1.11792	−0.558961	−	0.829194i	$-0.688800\pi$
$113$	−11.8837	−1.11792	−0.558961	+	0.829194i	$0.688800\pi$
$114$	1.63358	0.152998
$115$	2.88071	0.268628
$116$	−9.12503	−0.847238
$117$	−11.7067	−1.08229
$118$	−7.77883	−0.716099
$119$	−28.9475	−2.65361
$120$	1.31103	0.119681
$121$	−3.20223	−0.291112
$122$	11.1380	1.00839
$123$	−1.40214	−0.126426
$124$	−10.5932	−0.951299
$125$	4.90151	0.438404
$126$	−11.1530	−0.993590
$127$	15.2801	1.35589	0.677943	−	0.735115i	$-0.262872\pi$
$127$	15.2801	1.35589	0.677943	+	0.735115i	$0.262872\pi$
$128$	−1.00000	−0.0883883
$129$	1.75756	0.154744
$130$	12.0749	1.05904
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.27087	0.110615
$133$	14.3339	1.24291
$134$	−8.30992	−0.717868
$135$	7.59466	0.653645
$136$	−7.24886	−0.621585
$137$	15.2359	1.30169	0.650845	−	0.759211i	$-0.274415\pi$
$137$	15.2359	1.30169	0.650845	+	0.759211i	$0.274415\pi$
$138$	0.455108	0.0387413
$139$	−14.9809	−1.27066	−0.635330	−	0.772241i	$-0.719136\pi$
$139$	−14.9809	−1.27066	−0.635330	+	0.772241i	$0.719136\pi$
$140$	11.5038	0.972247
$141$	−1.50540	−0.126778
$142$	−1.87983	−0.157752
$143$	11.7049	0.978815
$144$	−2.79288	−0.232740
$145$	26.2866	2.18298
$146$	−16.7669	−1.38764
$147$	4.07189	0.335843
$148$	0.209959	0.0172585
$149$	4.54583	0.372409	0.186204	−	0.982511i	$-0.440381\pi$
$149$	4.54583	0.372409	0.186204	+	0.982511i	$0.440381\pi$
$150$	−1.50118	−0.122571
$151$	12.5366	1.02022	0.510109	−	0.860110i	$-0.329605\pi$
$151$	12.5366	1.02022	0.510109	+	0.860110i	$0.329605\pi$
$152$	3.58943	0.291141
$153$	−20.2452	−1.63673
$154$	11.1513	0.898598
$155$	30.5160	2.45111
$156$	1.90764	0.152734
$157$	−8.11841	−0.647919	−0.323960	−	0.946071i	$-0.605014\pi$
$157$	−8.11841	−0.647919	−0.323960	+	0.946071i	$0.605014\pi$
$158$	12.3875	0.985495
$159$	−5.49741	−0.435973
$160$	2.88071	0.227740
$161$	3.99338	0.314722
$162$	−7.17879	−0.564019
$163$	8.91230	0.698065	0.349033	−	0.937111i	$-0.386510\pi$
$163$	8.91230	0.698065	0.349033	+	0.937111i	$0.386510\pi$
$164$	−3.08089	−0.240577
$165$	−3.66100	−0.285008
$166$	7.47080	0.579847
$167$	−10.5177	−0.813885	−0.406942	−	0.913454i	$-0.633405\pi$
$167$	−10.5177	−0.813885	−0.406942	+	0.913454i	$0.633405\pi$
$168$	1.81742	0.140217
$169$	4.56979	0.351522
$170$	20.8819	1.60157
$171$	10.0248	0.766618
$172$	3.86185	0.294463
$173$	−13.6939	−1.04113	−0.520563	−	0.853823i	$-0.674278\pi$
$173$	−13.6939	−1.04113	−0.520563	+	0.853823i	$0.674278\pi$
$174$	4.15287	0.314829
$175$	−13.1722	−0.995725
$176$	2.79245	0.210489
$177$	3.54021	0.266098
$178$	5.06447	0.379598
$179$	9.17303	0.685624	0.342812	−	0.939404i	$-0.388621\pi$
$179$	9.17303	0.685624	0.342812	+	0.939404i	$0.388621\pi$
$180$	8.04548	0.599675
$181$	7.89238	0.586636	0.293318	−	0.956015i	$-0.405241\pi$
$181$	7.89238	0.586636	0.293318	+	0.956015i	$0.405241\pi$
$182$	16.7388	1.24076
$183$	−5.06900	−0.374711
$184$	1.00000	0.0737210
$185$	−0.604831	−0.0444681
$186$	4.82106	0.353497
$187$	20.2421	1.48025
$188$	−3.30779	−0.241245
$189$	10.5281	0.765805
$190$	−10.3401	−0.750151
$191$	17.7051	1.28109	0.640547	−	0.767919i	$-0.278708\pi$
$191$	17.7051	1.28109	0.640547	+	0.767919i	$0.278708\pi$
$192$	0.455108	0.0328446
$193$	−23.1139	−1.66378	−0.831889	−	0.554942i	$-0.812741\pi$
$193$	−23.1139	−1.66378	−0.831889	+	0.554942i	$0.812741\pi$
$194$	4.43513	0.318424
$195$	−5.49538	−0.393532
$196$	8.94708	0.639077
$197$	0.475662	0.0338895	0.0169448	−	0.999856i	$-0.494606\pi$
$197$	0.475662	0.0338895	0.0169448	+	0.999856i	$0.494606\pi$
$198$	7.79897	0.554248
$199$	3.45742	0.245090	0.122545	−	0.992463i	$-0.460894\pi$
$199$	3.45742	0.245090	0.122545	+	0.992463i	$0.460894\pi$
$200$	−3.29851	−0.233240
$201$	3.78191	0.266755
$202$	−0.656006	−0.0461564
$203$	36.4397	2.55757
$204$	3.29901	0.230977
$205$	8.87516	0.619868
$206$	7.02899	0.489733
$207$	2.79288	0.194118
$208$	4.19163	0.290637
$209$	−10.0233	−0.693326
$210$	−5.23546	−0.361281
$211$	20.1988	1.39054	0.695271	−	0.718748i	$-0.255284\pi$
$211$	20.1988	1.39054	0.695271	+	0.718748i	$0.255284\pi$
$212$	−12.0794	−0.829615
$213$	0.855524	0.0586195
$214$	−10.1518	−0.693966
$215$	−11.1249	−0.758711
$216$	2.63638	0.179383
$217$	42.3028	2.87170
$218$	−2.54167	−0.172143
$219$	7.63074	0.515638
$220$	−8.04425	−0.542343
$221$	30.3846	2.04389
$222$	−0.0955538	−0.00641315
$223$	13.5714	0.908809	0.454404	−	0.890796i	$-0.349852\pi$
$223$	13.5714	0.908809	0.454404	+	0.890796i	$0.349852\pi$
$224$	3.99338	0.266819
$225$	−9.21233	−0.614155
$226$	11.8837	0.790490
$227$	25.8894	1.71834	0.859171	−	0.511688i	$-0.170980\pi$
$227$	25.8894	1.71834	0.859171	+	0.511688i	$0.170980\pi$
$228$	−1.63358	−0.108186
$229$	−4.33620	−0.286544	−0.143272	−	0.989683i	$-0.545762\pi$
$229$	−4.33620	−0.286544	−0.143272	+	0.989683i	$0.545762\pi$
$230$	−2.88071	−0.189949
$231$	−5.07505	−0.333914
$232$	9.12503	0.599088
$233$	−3.28528	−0.215226	−0.107613	−	0.994193i	$-0.534321\pi$
$233$	−3.28528	−0.215226	−0.107613	+	0.994193i	$0.534321\pi$
$234$	11.7067	0.765292
$235$	9.52880	0.621590
$236$	7.77883	0.506359
$237$	−5.63764	−0.366204
$238$	28.9475	1.87638
$239$	2.98773	0.193260	0.0966302	−	0.995320i	$-0.469194\pi$
$239$	2.98773	0.193260	0.0966302	+	0.995320i	$0.469194\pi$
$240$	−1.31103	−0.0846269
$241$	−10.0896	−0.649928	−0.324964	−	0.945726i	$-0.605352\pi$
$241$	−10.0896	−0.649928	−0.324964	+	0.945726i	$0.605352\pi$
$242$	3.20223	0.205847
$243$	11.1763	0.716958
$244$	−11.1380	−0.713039
$245$	−25.7740	−1.64664
$246$	1.40214	0.0893970
$247$	−15.0456	−0.957326
$248$	10.5932	0.672670
$249$	−3.40002	−0.215468
$250$	−4.90151	−0.309999
$251$	15.0184	0.947953	0.473976	−	0.880538i	$-0.342818\pi$
$251$	15.0184	0.947953	0.473976	+	0.880538i	$0.342818\pi$
$252$	11.1530	0.702574
$253$	−2.79245	−0.175560
$254$	−15.2801	−0.958756
$255$	−9.50351	−0.595133
$256$	1.00000	0.0625000
$257$	−31.2904	−1.95184	−0.975920	−	0.218130i	$-0.930004\pi$
$257$	−31.2904	−1.95184	−0.975920	+	0.218130i	$0.930004\pi$
$258$	−1.75756	−0.109421
$259$	−0.838445	−0.0520984
$260$	−12.0749	−0.748853
$261$	25.4851	1.57749
$262$	−1.00000	−0.0617802
$263$	1.83830	0.113355	0.0566774	−	0.998393i	$-0.481949\pi$
$263$	1.83830	0.113355	0.0566774	+	0.998393i	$0.481949\pi$
$264$	−1.27087	−0.0782163
$265$	34.7972	2.13758
$266$	−14.3339	−0.878871
$267$	−2.30488	−0.141056
$268$	8.30992	0.507609
$269$	−5.04286	−0.307468	−0.153734	−	0.988112i	$-0.549130\pi$
$269$	−5.04286	−0.307468	−0.153734	+	0.988112i	$0.549130\pi$
$270$	−7.59466	−0.462196
$271$	27.5319	1.67244	0.836220	−	0.548393i	$-0.184760\pi$
$271$	27.5319	1.67244	0.836220	+	0.548393i	$0.184760\pi$
$272$	7.24886	0.439527
$273$	−7.61795	−0.461059
$274$	−15.2359	−0.920433
$275$	9.21092	0.555439
$276$	−0.455108	−0.0273943
$277$	5.88719	0.353727	0.176864	−	0.984235i	$-0.443405\pi$
$277$	5.88719	0.353727	0.176864	+	0.984235i	$0.443405\pi$
$278$	14.9809	0.898492
$279$	29.5856	1.77124
$280$	−11.5038	−0.687482
$281$	6.58510	0.392834	0.196417	−	0.980520i	$-0.437069\pi$
$281$	6.58510	0.392834	0.196417	+	0.980520i	$0.437069\pi$
$282$	1.50540	0.0896453
$283$	28.5510	1.69718	0.848591	−	0.529049i	$-0.177451\pi$
$283$	28.5510	1.69718	0.848591	+	0.529049i	$0.177451\pi$
$284$	1.87983	0.111547
$285$	4.70586	0.278751
$286$	−11.7049	−0.692127
$287$	12.3032	0.726233
$288$	2.79288	0.164572
$289$	35.5460	2.09094
$290$	−26.2866	−1.54360
$291$	−2.01846	−0.118324
$292$	16.7669	0.981208
$293$	8.64687	0.505156	0.252578	−	0.967577i	$-0.418722\pi$
$293$	8.64687	0.505156	0.252578	+	0.967577i	$0.418722\pi$
$294$	−4.07189	−0.237477
$295$	−22.4086	−1.30468
$296$	−0.209959	−0.0122036
$297$	−7.36197	−0.427185
$298$	−4.54583	−0.263333
$299$	−4.19163	−0.242408
$300$	1.50118	0.0866705
$301$	−15.4218	−0.888900
$302$	−12.5366	−0.721403
$303$	0.298553	0.0171514
$304$	−3.58943	−0.205868
$305$	32.0855	1.83721
$306$	20.2452	1.15734
$307$	−31.1435	−1.77745	−0.888725	−	0.458440i	$-0.848408\pi$
$307$	−31.1435	−1.77745	−0.888725	+	0.458440i	$0.848408\pi$
$308$	−11.1513	−0.635405
$309$	−3.19895	−0.181982
$310$	−30.5160	−1.73319
$311$	−6.29670	−0.357053	−0.178527	−	0.983935i	$-0.557133\pi$
$311$	−6.29670	−0.357053	−0.178527	+	0.983935i	$0.557133\pi$
$312$	−1.90764	−0.107999
$313$	24.7412	1.39846	0.699229	−	0.714898i	$-0.253527\pi$
$313$	24.7412	1.39846	0.699229	+	0.714898i	$0.253527\pi$
$314$	8.11841	0.458148
$315$	−32.1286	−1.81024
$316$	−12.3875	−0.696850
$317$	7.54473	0.423754	0.211877	−	0.977296i	$-0.432042\pi$
$317$	7.54473	0.423754	0.211877	+	0.977296i	$0.432042\pi$
$318$	5.49741	0.308280
$319$	−25.4812	−1.42667
$320$	−2.88071	−0.161037
$321$	4.62018	0.257873
$322$	−3.99338	−0.222542
$323$	−26.0193	−1.44775
$324$	7.17879	0.398822
$325$	13.8261	0.766936
$326$	−8.91230	−0.493607
$327$	1.15673	0.0639674
$328$	3.08089	0.170114
$329$	13.2093	0.728250
$330$	3.66100	0.201531
$331$	−11.8140	−0.649355	−0.324677	−	0.945825i	$-0.605256\pi$
$331$	−11.8140	−0.649355	−0.324677	+	0.945825i	$0.605256\pi$
$332$	−7.47080	−0.410014
$333$	−0.586389	−0.0321339
$334$	10.5177	0.575503
$335$	−23.9385	−1.30790
$336$	−1.81742	−0.0991483
$337$	−9.77438	−0.532445	−0.266222	−	0.963912i	$-0.585776\pi$
$337$	−9.77438	−0.532445	−0.266222	+	0.963912i	$0.585776\pi$
$338$	−4.56979	−0.248564
$339$	−5.40835	−0.293741
$340$	−20.8819	−1.13248
$341$	−29.5810	−1.60190
$342$	−10.0248	−0.542081
$343$	−7.77543	−0.419834
$344$	−3.86185	−0.208217
$345$	1.31103	0.0705837
$346$	13.6939	0.736188
$347$	−16.0531	−0.861777	−0.430889	−	0.902405i	$-0.641800\pi$
$347$	−16.0531	−0.861777	−0.430889	+	0.902405i	$0.641800\pi$
$348$	−4.15287	−0.222617
$349$	10.8118	0.578743	0.289372	−	0.957217i	$-0.406554\pi$
$349$	10.8118	0.578743	0.289372	+	0.957217i	$0.406554\pi$
$350$	13.1722	0.704084
$351$	−11.0508	−0.589845
$352$	−2.79245	−0.148838
$353$	21.7504	1.15766	0.578828	−	0.815450i	$-0.303510\pi$
$353$	21.7504	1.15766	0.578828	+	0.815450i	$0.303510\pi$
$354$	−3.54021	−0.188160
$355$	−5.41524	−0.287411
$356$	−5.06447	−0.268416
$357$	−13.1742	−0.697253
$358$	−9.17303	−0.484810
$359$	−31.0311	−1.63776	−0.818879	−	0.573967i	$-0.805404\pi$
$359$	−31.0311	−1.63776	−0.818879	+	0.573967i	$0.805404\pi$
$360$	−8.04548	−0.424034
$361$	−6.11601	−0.321895
$362$	−7.89238	−0.414814
$363$	−1.45736	−0.0764915
$364$	−16.7388	−0.877351
$365$	−48.3006	−2.52817
$366$	5.06900	0.264961
$367$	14.7983	0.772467	0.386233	−	0.922401i	$-0.373776\pi$
$367$	14.7983	0.772467	0.386233	+	0.922401i	$0.373776\pi$
$368$	−1.00000	−0.0521286
$369$	8.60455	0.447935
$370$	0.604831	0.0314437
$371$	48.2375	2.50437
$372$	−4.82106	−0.249960
$373$	16.7718	0.868410	0.434205	−	0.900814i	$-0.357029\pi$
$373$	16.7718	0.868410	0.434205	+	0.900814i	$0.357029\pi$
$374$	−20.2421	−1.04669
$375$	2.23071	0.115194
$376$	3.30779	0.170586
$377$	−38.2488	−1.96991
$378$	−10.5281	−0.541506
$379$	3.72426	0.191303	0.0956513	−	0.995415i	$-0.469507\pi$
$379$	3.72426	0.191303	0.0956513	+	0.995415i	$0.469507\pi$
$380$	10.3401	0.530437
$381$	6.95407	0.356268
$382$	−17.7051	−0.905870
$383$	−5.60723	−0.286516	−0.143258	−	0.989685i	$-0.545758\pi$
$383$	−5.60723	−0.286516	−0.143258	+	0.989685i	$0.545758\pi$
$384$	−0.455108	−0.0232246
$385$	32.1237	1.63718
$386$	23.1139	1.17647
$387$	−10.7857	−0.548267
$388$	−4.43513	−0.225160
$389$	33.0803	1.67724	0.838618	−	0.544720i	$-0.183364\pi$
$389$	33.0803	1.67724	0.838618	+	0.544720i	$0.183364\pi$
$390$	5.49538	0.278269
$391$	−7.24886	−0.366591
$392$	−8.94708	−0.451896
$393$	0.455108	0.0229571
$394$	−0.475662	−0.0239635
$395$	35.6848	1.79550
$396$	−7.79897	−0.391913
$397$	19.7079	0.989109	0.494555	−	0.869147i	$-0.335331\pi$
$397$	19.7079	0.989109	0.494555	+	0.869147i	$0.335331\pi$
$398$	−3.45742	−0.173305
$399$	6.52349	0.326583
$400$	3.29851	0.164925
$401$	−6.74101	−0.336630	−0.168315	−	0.985733i	$-0.553833\pi$
$401$	−6.74101	−0.336630	−0.168315	+	0.985733i	$0.553833\pi$
$402$	−3.78191	−0.188624
$403$	−44.4029	−2.21187
$404$	0.656006	0.0326375
$405$	−20.6800	−1.02760
$406$	−36.4397	−1.80847
$407$	0.586299	0.0290618
$408$	−3.29901	−0.163325
$409$	26.3542	1.30313	0.651566	−	0.758592i	$-0.274112\pi$
$409$	26.3542	1.30313	0.651566	+	0.758592i	$0.274112\pi$
$410$	−8.87516	−0.438313
$411$	6.93397	0.342027
$412$	−7.02899	−0.346293
$413$	−31.0638	−1.52855
$414$	−2.79288	−0.137262
$415$	21.5212	1.05644
$416$	−4.19163	−0.205512
$417$	−6.81790	−0.333874
$418$	10.0233	0.490255
$419$	−32.1146	−1.56890	−0.784450	−	0.620191i	$-0.787055\pi$
$419$	−32.1146	−1.56890	−0.784450	+	0.620191i	$0.787055\pi$
$420$	5.23546	0.255464
$421$	24.0088	1.17012	0.585059	−	0.810990i	$-0.301071\pi$
$421$	24.0088	1.17012	0.585059	+	0.810990i	$0.301071\pi$
$422$	−20.1988	−0.983262
$423$	9.23825	0.449179
$424$	12.0794	0.586626
$425$	23.9104	1.15983
$426$	−0.855524	−0.0414503
$427$	44.4784	2.15246
$428$	10.1518	0.490708
$429$	5.32700	0.257190
$430$	11.1249	0.536489
$431$	7.64731	0.368358	0.184179	−	0.982893i	$-0.441037\pi$
$431$	7.64731	0.368358	0.184179	+	0.982893i	$0.441037\pi$
$432$	−2.63638	−0.126843
$433$	39.7055	1.90813	0.954063	−	0.299606i	$-0.0968552\pi$
$433$	39.7055	1.90813	0.954063	+	0.299606i	$0.0968552\pi$
$434$	−42.3028	−2.03060
$435$	11.9632	0.573593
$436$	2.54167	0.121724
$437$	3.58943	0.171706
$438$	−7.63074	−0.364611
$439$	33.5228	1.59996	0.799978	−	0.600029i	$-0.204844\pi$
$439$	33.5228	1.59996	0.799978	+	0.600029i	$0.204844\pi$
$440$	8.04425	0.383494
$441$	−24.9881	−1.18991
$442$	−30.3846	−1.44525
$443$	−30.9219	−1.46914	−0.734572	−	0.678531i	$-0.762617\pi$
$443$	−30.9219	−1.46914	−0.734572	+	0.678531i	$0.762617\pi$
$444$	0.0955538	0.00453478
$445$	14.5893	0.691598
$446$	−13.5714	−0.642625
$447$	2.06884	0.0978529
$448$	−3.99338	−0.188669
$449$	33.0386	1.55919	0.779594	−	0.626285i	$-0.215425\pi$
$449$	33.0386	1.55919	0.779594	+	0.626285i	$0.215425\pi$
$450$	9.21233	0.434273
$451$	−8.60323	−0.405110
$452$	−11.8837	−0.558961
$453$	5.70552	0.268069
$454$	−25.8894	−1.21505
$455$	48.2196	2.26057
$456$	1.63358	0.0764992
$457$	20.0861	0.939588	0.469794	−	0.882776i	$-0.344328\pi$
$457$	20.0861	0.939588	0.469794	+	0.882776i	$0.344328\pi$
$458$	4.33620	0.202617
$459$	−19.1108	−0.892015
$460$	2.88071	0.134314
$461$	−5.24747	−0.244399	−0.122200	−	0.992506i	$-0.538995\pi$
$461$	−5.24747	−0.244399	−0.122200	+	0.992506i	$0.538995\pi$
$462$	5.07505	0.236113
$463$	25.8829	1.20288	0.601441	−	0.798917i	$-0.294593\pi$
$463$	25.8829	1.20288	0.601441	+	0.798917i	$0.294593\pi$
$464$	−9.12503	−0.423619
$465$	13.8881	0.644044
$466$	3.28528	0.152188
$467$	14.2256	0.658281	0.329140	−	0.944281i	$-0.393241\pi$
$467$	14.2256	0.658281	0.329140	+	0.944281i	$0.393241\pi$
$468$	−11.7067	−0.541143
$469$	−33.1847	−1.53233
$470$	−9.52880	−0.439531
$471$	−3.69475	−0.170245
$472$	−7.77883	−0.358050
$473$	10.7840	0.495850
$474$	5.63764	0.258945
$475$	−11.8398	−0.543245
$476$	−28.9475	−1.32680
$477$	33.7362	1.54467
$478$	−2.98773	−0.136656
$479$	16.4489	0.751571	0.375786	−	0.926707i	$-0.377373\pi$
$479$	16.4489	0.751571	0.375786	+	0.926707i	$0.377373\pi$
$480$	1.31103	0.0598403
$481$	0.880070	0.0401277
$482$	10.0896	0.459569
$483$	1.81742	0.0826954
$484$	−3.20223	−0.145556
$485$	12.7763	0.580144
$486$	−11.1763	−0.506966
$487$	35.8724	1.62554	0.812768	−	0.582588i	$-0.197960\pi$
$487$	35.8724	1.62554	0.812768	+	0.582588i	$0.197960\pi$
$488$	11.1380	0.504195
$489$	4.05606	0.183421
$490$	25.7740	1.16435
$491$	−20.3645	−0.919037	−0.459519	−	0.888168i	$-0.651978\pi$
$491$	−20.3645	−0.919037	−0.459519	+	0.888168i	$0.651978\pi$
$492$	−1.40214	−0.0632132
$493$	−66.1461	−2.97907
$494$	15.0456	0.676932
$495$	22.4666	1.00980
$496$	−10.5932	−0.475650
$497$	−7.50686	−0.336729
$498$	3.40002	0.152359
$499$	−33.3758	−1.49411	−0.747054	−	0.664764i	$-0.768532\pi$
$499$	−33.3758	−1.49411	−0.747054	+	0.664764i	$0.768532\pi$
$500$	4.90151	0.219202
$501$	−4.78669	−0.213854
$502$	−15.0184	−0.670304
$503$	−3.07663	−0.137180	−0.0685902	−	0.997645i	$-0.521850\pi$
$503$	−3.07663	−0.137180	−0.0685902	+	0.997645i	$0.521850\pi$
$504$	−11.1530	−0.496795
$505$	−1.88977	−0.0840935
$506$	2.79245	0.124140
$507$	2.07975	0.0923648
$508$	15.2801	0.677943
$509$	−42.4696	−1.88243	−0.941216	−	0.337805i	$-0.890316\pi$
$509$	−42.4696	−1.88243	−0.941216	+	0.337805i	$0.890316\pi$
$510$	9.50351	0.420822
$511$	−66.9565	−2.96198
$512$	−1.00000	−0.0441942
$513$	9.46311	0.417806
$514$	31.2904	1.38016
$515$	20.2485	0.892256
$516$	1.75756	0.0773722
$517$	−9.23684	−0.406236
$518$	0.838445	0.0368392
$519$	−6.23219	−0.273563
$520$	12.0749	0.529519
$521$	23.0924	1.01169	0.505847	−	0.862623i	$-0.331180\pi$
$521$	23.0924	1.01169	0.505847	+	0.862623i	$0.331180\pi$
$522$	−25.4851	−1.11545
$523$	−8.30947	−0.363348	−0.181674	−	0.983359i	$-0.558152\pi$
$523$	−8.30947	−0.363348	−0.181674	+	0.983359i	$0.558152\pi$
$524$	1.00000	0.0436852
$525$	−5.99477	−0.261633
$526$	−1.83830	−0.0801539
$527$	−76.7888	−3.34497
$528$	1.27087	0.0553073
$529$	1.00000	0.0434783
$530$	−34.7972	−1.51149
$531$	−21.7253	−0.942798
$532$	14.3339	0.621455
$533$	−12.9140	−0.559366
$534$	2.30488	0.0997419
$535$	−29.2445	−1.26435
$536$	−8.30992	−0.358934
$537$	4.17472	0.180152
$538$	5.04286	0.217413
$539$	24.9843	1.07615
$540$	7.59466	0.326822
$541$	−31.2188	−1.34220	−0.671100	−	0.741367i	$-0.734178\pi$
$541$	−31.2188	−1.34220	−0.671100	+	0.741367i	$0.734178\pi$
$542$	−27.5319	−1.18259
$543$	3.59188	0.154142
$544$	−7.24886	−0.310792
$545$	−7.32181	−0.313632
$546$	7.61795	0.326018
$547$	−22.8234	−0.975858	−0.487929	−	0.872883i	$-0.662247\pi$
$547$	−22.8234	−0.975858	−0.487929	+	0.872883i	$0.662247\pi$
$548$	15.2359	0.650845
$549$	31.1071	1.32762
$550$	−9.21092	−0.392755
$551$	32.7536	1.39535
$552$	0.455108	0.0193707
$553$	49.4679	2.10359
$554$	−5.88719	−0.250123
$555$	−0.275263	−0.0116843
$556$	−14.9809	−0.635330
$557$	−35.7572	−1.51508	−0.757541	−	0.652788i	$-0.773599\pi$
$557$	−35.7572	−1.51508	−0.757541	+	0.652788i	$0.773599\pi$
$558$	−29.5856	−1.25246
$559$	16.1875	0.684657
$560$	11.5038	0.486124
$561$	9.21233	0.388945
$562$	−6.58510	−0.277776
$563$	10.1411	0.427398	0.213699	−	0.976900i	$-0.431449\pi$
$563$	10.1411	0.427398	0.213699	+	0.976900i	$0.431449\pi$
$564$	−1.50540	−0.0633888
$565$	34.2335	1.44021
$566$	−28.5510	−1.20009
$567$	−28.6676	−1.20393
$568$	−1.87983	−0.0788758
$569$	−31.4834	−1.31985	−0.659926	−	0.751331i	$-0.729412\pi$
$569$	−31.4834	−1.31985	−0.659926	+	0.751331i	$0.729412\pi$
$570$	−4.70586	−0.197107
$571$	15.6873	0.656492	0.328246	−	0.944592i	$-0.393542\pi$
$571$	15.6873	0.656492	0.328246	+	0.944592i	$0.393542\pi$
$572$	11.7049	0.489407
$573$	8.05771	0.336616
$574$	−12.3032	−0.513524
$575$	−3.29851	−0.137557
$576$	−2.79288	−0.116370
$577$	23.3438	0.971814	0.485907	−	0.874010i	$-0.338489\pi$
$577$	23.3438	0.971814	0.485907	+	0.874010i	$0.338489\pi$
$578$	−35.5460	−1.47852
$579$	−10.5193	−0.437169
$580$	26.2866	1.09149
$581$	29.8338	1.23771
$582$	2.01846	0.0836679
$583$	−33.7310	−1.39700
$584$	−16.7669	−0.693819
$585$	33.7237	1.39430
$586$	−8.64687	−0.357199
$587$	16.0440	0.662207	0.331104	−	0.943594i	$-0.392579\pi$
$587$	16.0440	0.662207	0.331104	+	0.943594i	$0.392579\pi$
$588$	4.07189	0.167922
$589$	38.0236	1.56674
$590$	22.4086	0.922547
$591$	0.216478	0.00890470
$592$	0.209959	0.00862925
$593$	−4.47983	−0.183965	−0.0919823	−	0.995761i	$-0.529320\pi$
$593$	−4.47983	−0.183965	−0.0919823	+	0.995761i	$0.529320\pi$
$594$	7.36197	0.302065
$595$	83.3893	3.41863
$596$	4.54583	0.186204
$597$	1.57350	0.0643990
$598$	4.19163	0.171409
$599$	−4.87861	−0.199334	−0.0996672	−	0.995021i	$-0.531778\pi$
$599$	−4.87861	−0.199334	−0.0996672	+	0.995021i	$0.531778\pi$
$600$	−1.50118	−0.0612853
$601$	45.0072	1.83588	0.917940	−	0.396718i	$-0.129851\pi$
$601$	45.0072	1.83588	0.917940	+	0.396718i	$0.129851\pi$
$602$	15.4218	0.628547
$603$	−23.2086	−0.945127
$604$	12.5366	0.510109
$605$	9.22470	0.375037
$606$	−0.298553	−0.0121279
$607$	5.86919	0.238223	0.119111	−	0.992881i	$-0.461995\pi$
$607$	5.86919	0.238223	0.119111	+	0.992881i	$0.461995\pi$
$608$	3.58943	0.145571
$609$	16.5840	0.672018
$610$	−32.0855	−1.29910
$611$	−13.8650	−0.560920
$612$	−20.2452	−0.818363
$613$	−6.49840	−0.262468	−0.131234	−	0.991351i	$-0.541894\pi$
$613$	−6.49840	−0.262468	−0.131234	+	0.991351i	$0.541894\pi$
$614$	31.1435	1.25685
$615$	4.03915	0.162874
$616$	11.1513	0.449299
$617$	−46.7567	−1.88235	−0.941176	−	0.337916i	$-0.890278\pi$
$617$	−46.7567	−1.88235	−0.941176	+	0.337916i	$0.890278\pi$
$618$	3.19895	0.128681
$619$	3.53681	0.142157	0.0710783	−	0.997471i	$-0.477356\pi$
$619$	3.53681	0.142157	0.0710783	+	0.997471i	$0.477356\pi$
$620$	30.5160	1.22555
$621$	2.63638	0.105794
$622$	6.29670	0.252475
$623$	20.2244	0.810271
$624$	1.90764	0.0763669
$625$	−30.6124	−1.22450
$626$	−24.7412	−0.988859
$627$	−4.56168	−0.182176
$628$	−8.11841	−0.323960
$629$	1.52196	0.0606846
$630$	32.1286	1.28004
$631$	20.4207	0.812935	0.406467	−	0.913665i	$-0.366760\pi$
$631$	20.4207	0.812935	0.406467	+	0.913665i	$0.366760\pi$
$632$	12.3875	0.492748
$633$	9.19262	0.365374
$634$	−7.54473	−0.299639
$635$	−44.0175	−1.74678
$636$	−5.49741	−0.217987
$637$	37.5029	1.48592
$638$	25.4812	1.00881
$639$	−5.25012	−0.207692
$640$	2.88071	0.113870
$641$	−18.7988	−0.742506	−0.371253	−	0.928532i	$-0.621072\pi$
$641$	−18.7988	−0.742506	−0.371253	+	0.928532i	$0.621072\pi$
$642$	−4.62018	−0.182344
$643$	33.5249	1.32209	0.661046	−	0.750345i	$-0.270113\pi$
$643$	33.5249	1.32209	0.661046	+	0.750345i	$0.270113\pi$
$644$	3.99338	0.157361
$645$	−5.06302	−0.199356
$646$	26.0193	1.02371
$647$	−3.83115	−0.150618	−0.0753089	−	0.997160i	$-0.523994\pi$
$647$	−3.83115	−0.150618	−0.0753089	+	0.997160i	$0.523994\pi$
$648$	−7.17879	−0.282010
$649$	21.7220	0.852663
$650$	−13.8261	−0.542306
$651$	19.2523	0.754557
$652$	8.91230	0.349033
$653$	−36.0602	−1.41114	−0.705572	−	0.708638i	$-0.749310\pi$
$653$	−36.0602	−1.41114	−0.705572	+	0.708638i	$0.749310\pi$
$654$	−1.15673	−0.0452318
$655$	−2.88071	−0.112559
$656$	−3.08089	−0.120289
$657$	−46.8279	−1.82693
$658$	−13.2093	−0.514951
$659$	−19.0321	−0.741386	−0.370693	−	0.928755i	$-0.620880\pi$
$659$	−19.0321	−0.741386	−0.370693	+	0.928755i	$0.620880\pi$
$660$	−3.66100	−0.142504
$661$	9.09543	0.353771	0.176886	−	0.984231i	$-0.443398\pi$
$661$	9.09543	0.353771	0.176886	+	0.984231i	$0.443398\pi$
$662$	11.8140	0.459163
$663$	13.8283	0.537045
$664$	7.47080	0.289923
$665$	−41.2920	−1.60123
$666$	0.586389	0.0227221
$667$	9.12503	0.353323
$668$	−10.5177	−0.406942
$669$	6.17645	0.238795
$670$	23.9385	0.924825
$671$	−31.1024	−1.20069
$672$	1.81742	0.0701084
$673$	−6.40210	−0.246783	−0.123391	−	0.992358i	$-0.539377\pi$
$673$	−6.40210	−0.246783	−0.123391	+	0.992358i	$0.539377\pi$
$674$	9.77438	0.376495
$675$	−8.69613	−0.334714
$676$	4.56979	0.175761
$677$	−23.0345	−0.885288	−0.442644	−	0.896698i	$-0.645959\pi$
$677$	−23.0345	−0.885288	−0.442644	+	0.896698i	$0.645959\pi$
$678$	5.40835	0.207706
$679$	17.7112	0.679692
$680$	20.8819	0.800784
$681$	11.7825	0.451506
$682$	29.5810	1.13272
$683$	−13.6881	−0.523762	−0.261881	−	0.965100i	$-0.584343\pi$
$683$	−13.6881	−0.523762	−0.261881	+	0.965100i	$0.584343\pi$
$684$	10.0248	0.383309
$685$	−43.8902	−1.67696
$686$	7.77543	0.296867
$687$	−1.97344	−0.0752913
$688$	3.86185	0.147232
$689$	−50.6323	−1.92894
$690$	−1.31103	−0.0499102
$691$	28.4839	1.08358	0.541789	−	0.840515i	$-0.317747\pi$
$691$	28.4839	1.08358	0.541789	+	0.840515i	$0.317747\pi$
$692$	−13.6939	−0.520563
$693$	31.1442	1.18307
$694$	16.0531	0.609368
$695$	43.1556	1.63698
$696$	4.15287	0.157414
$697$	−22.3329	−0.845921
$698$	−10.8118	−0.409233
$699$	−1.49516	−0.0565520
$700$	−13.1722	−0.497862
$701$	32.0989	1.21236	0.606179	−	0.795328i	$-0.292701\pi$
$701$	32.0989	1.21236	0.606179	+	0.795328i	$0.292701\pi$
$702$	11.0508	0.417084
$703$	−0.753632	−0.0284238
$704$	2.79245	0.105244
$705$	4.33663	0.163327
$706$	−21.7504	−0.818586
$707$	−2.61968	−0.0985233
$708$	3.54021	0.133049
$709$	19.8291	0.744697	0.372349	−	0.928093i	$-0.378553\pi$
$709$	19.8291	0.744697	0.372349	+	0.928093i	$0.378553\pi$
$710$	5.41524	0.203230
$711$	34.5967	1.29748
$712$	5.06447	0.189799
$713$	10.5932	0.396719
$714$	13.1742	0.493032
$715$	−33.7185	−1.26100
$716$	9.17303	0.342812
$717$	1.35974	0.0507804
$718$	31.0311	1.15807
$719$	−4.36069	−0.162626	−0.0813132	−	0.996689i	$-0.525911\pi$
$719$	−4.36069	−0.162626	−0.0813132	+	0.996689i	$0.525911\pi$
$720$	8.04548	0.299837
$721$	28.0694	1.04536
$722$	6.11601	0.227614
$723$	−4.59185	−0.170773
$724$	7.89238	0.293318
$725$	−30.0990	−1.11785
$726$	1.45736	0.0540876
$727$	−24.4207	−0.905712	−0.452856	−	0.891584i	$-0.649595\pi$
$727$	−24.4207	−0.905712	−0.452856	+	0.891584i	$0.649595\pi$
$728$	16.7388	0.620381
$729$	−16.4500	−0.609258
$730$	48.3006	1.78769
$731$	27.9940	1.03540
$732$	−5.06900	−0.187356
$733$	17.6260	0.651030	0.325515	−	0.945537i	$-0.394462\pi$
$733$	17.6260	0.651030	0.325515	+	0.945537i	$0.394462\pi$
$734$	−14.7983	−0.546216
$735$	−11.7299	−0.432665
$736$	1.00000	0.0368605
$737$	23.2050	0.854768
$738$	−8.60455	−0.316738
$739$	1.36413	0.0501802	0.0250901	−	0.999685i	$-0.492013\pi$
$739$	1.36413	0.0501802	0.0250901	+	0.999685i	$0.492013\pi$
$740$	−0.604831	−0.0222340
$741$	−6.84735	−0.251544
$742$	−48.2375	−1.77085
$743$	43.0561	1.57958	0.789788	−	0.613380i	$-0.210191\pi$
$743$	43.0561	1.57958	0.789788	+	0.613380i	$0.210191\pi$
$744$	4.82106	0.176749
$745$	−13.0952	−0.479772
$746$	−16.7718	−0.614058
$747$	20.8650	0.763412
$748$	20.2421	0.740124
$749$	−40.5402	−1.48131
$750$	−2.23071	−0.0814541
$751$	−23.9972	−0.875670	−0.437835	−	0.899055i	$-0.644255\pi$
$751$	−23.9972	−0.875670	−0.437835	+	0.899055i	$0.644255\pi$
$752$	−3.30779	−0.120623
$753$	6.83499	0.249081
$754$	38.2488	1.39294
$755$	−36.1145	−1.31434
$756$	10.5281	0.382902
$757$	37.0095	1.34513	0.672566	−	0.740037i	$-0.265192\pi$
$757$	37.0095	1.34513	0.672566	+	0.740037i	$0.265192\pi$
$758$	−3.72426	−0.135271
$759$	−1.27087	−0.0461295
$760$	−10.3401	−0.375075
$761$	−13.8384	−0.501641	−0.250821	−	0.968034i	$-0.580700\pi$
$761$	−13.8384	−0.501641	−0.250821	+	0.968034i	$0.580700\pi$
$762$	−6.95407	−0.251919
$763$	−10.1498	−0.367449
$764$	17.7051	0.640547
$765$	58.3206	2.10858
$766$	5.60723	0.202598
$767$	32.6060	1.17733
$768$	0.455108	0.0164223
$769$	5.28876	0.190717	0.0953587	−	0.995443i	$-0.469600\pi$
$769$	5.28876	0.190717	0.0953587	+	0.995443i	$0.469600\pi$
$770$	−32.1237	−1.15766
$771$	−14.2405	−0.512859
$772$	−23.1139	−0.831889
$773$	−5.07240	−0.182442	−0.0912208	−	0.995831i	$-0.529077\pi$
$773$	−5.07240	−0.182442	−0.0912208	+	0.995831i	$0.529077\pi$
$774$	10.7857	0.387683
$775$	−34.9418	−1.25515
$776$	4.43513	0.159212
$777$	−0.381583	−0.0136892
$778$	−33.0803	−1.18599
$779$	11.0586	0.396217
$780$	−5.49538	−0.196766
$781$	5.24932	0.187835
$782$	7.24886	0.259219
$783$	24.0571	0.859730
$784$	8.94708	0.319539
$785$	23.3868	0.834711
$786$	−0.455108	−0.0162332
$787$	−16.2855	−0.580515	−0.290257	−	0.956949i	$-0.593741\pi$
$787$	−16.2855	−0.580515	−0.290257	+	0.956949i	$0.593741\pi$
$788$	0.475662	0.0169448
$789$	0.836627	0.0297847
$790$	−35.6848	−1.26961
$791$	47.4560	1.68734
$792$	7.79897	0.277124
$793$	−46.6865	−1.65789
$794$	−19.7079	−0.699406
$795$	15.8365	0.561662
$796$	3.45742	0.122545
$797$	26.7445	0.947340	0.473670	−	0.880702i	$-0.342929\pi$
$797$	26.7445	0.947340	0.473670	+	0.880702i	$0.342929\pi$
$798$	−6.52349	−0.230929
$799$	−23.9777	−0.848271
$800$	−3.29851	−0.116620
$801$	14.1444	0.499769
$802$	6.74101	0.238033
$803$	46.8207	1.65227
$804$	3.78191	0.133378
$805$	−11.5038	−0.405455
$806$	44.4029	1.56403
$807$	−2.29504	−0.0807893
$808$	−0.656006	−0.0230782
$809$	−37.9894	−1.33564	−0.667819	−	0.744324i	$-0.732772\pi$
$809$	−37.9894	−1.33564	−0.667819	+	0.744324i	$0.732772\pi$
$810$	20.6800	0.726623
$811$	−46.9281	−1.64787	−0.823934	−	0.566686i	$-0.808225\pi$
$811$	−46.9281	−1.64787	−0.823934	+	0.566686i	$0.808225\pi$
$812$	36.4397	1.27878
$813$	12.5300	0.439445
$814$	−0.586299	−0.0205498
$815$	−25.6738	−0.899313
$816$	3.29901	0.115489
$817$	−13.8618	−0.484964
$818$	−26.3542	−0.921454
$819$	46.7494	1.63355
$820$	8.87516	0.309934
$821$	44.2310	1.54367	0.771836	−	0.635822i	$-0.219339\pi$
$821$	44.2310	1.54367	0.771836	+	0.635822i	$0.219339\pi$
$822$	−6.93397	−0.241850
$823$	19.7416	0.688150	0.344075	−	0.938942i	$-0.388193\pi$
$823$	19.7416	0.688150	0.344075	+	0.938942i	$0.388193\pi$
$824$	7.02899	0.244866
$825$	4.19196	0.145945
$826$	31.0638	1.08085
$827$	−1.85702	−0.0645749	−0.0322874	−	0.999479i	$-0.510279\pi$
$827$	−1.85702	−0.0645749	−0.0322874	+	0.999479i	$0.510279\pi$
$828$	2.79288	0.0970592
$829$	−38.3546	−1.33211	−0.666055	−	0.745903i	$-0.732018\pi$
$829$	−38.3546	−1.33211	−0.666055	+	0.745903i	$0.732018\pi$
$830$	−21.5212	−0.747013
$831$	2.67931	0.0929441
$832$	4.19163	0.145319
$833$	64.8561	2.24713
$834$	6.81790	0.236085
$835$	30.2985	1.04852
$836$	−10.0233	−0.346663
$837$	27.9278	0.965326
$838$	32.1146	1.10938
$839$	9.25594	0.319551	0.159775	−	0.987153i	$-0.448923\pi$
$839$	9.25594	0.319551	0.159775	+	0.987153i	$0.448923\pi$
$840$	−5.23546	−0.180641
$841$	54.2662	1.87125
$842$	−24.0088	−0.827399
$843$	2.99693	0.103220
$844$	20.1988	0.695271
$845$	−13.1643	−0.452864
$846$	−9.23825	−0.317618
$847$	12.7877	0.439391
$848$	−12.0794	−0.414807
$849$	12.9938	0.445946
$850$	−23.9104	−0.820121
$851$	−0.209959	−0.00719729
$852$	0.855524	0.0293098
$853$	9.45095	0.323595	0.161797	−	0.986824i	$-0.448271\pi$
$853$	9.45095	0.323595	0.161797	+	0.986824i	$0.448271\pi$
$854$	−44.4784	−1.52202
$855$	−28.8787	−0.987629
$856$	−10.1518	−0.346983
$857$	−41.4740	−1.41673	−0.708363	−	0.705848i	$-0.750566\pi$
$857$	−41.4740	−1.41673	−0.708363	+	0.705848i	$0.750566\pi$
$858$	−5.32700	−0.181861
$859$	27.8236	0.949328	0.474664	−	0.880167i	$-0.342570\pi$
$859$	27.8236	0.949328	0.474664	+	0.880167i	$0.342570\pi$
$860$	−11.1249	−0.379355
$861$	5.59926	0.190822
$862$	−7.64731	−0.260468
$863$	2.45232	0.0834780	0.0417390	−	0.999129i	$-0.486710\pi$
$863$	2.45232	0.0834780	0.0417390	+	0.999129i	$0.486710\pi$
$864$	2.63638	0.0896916
$865$	39.4482	1.34128
$866$	−39.7055	−1.34925
$867$	16.1773	0.549408
$868$	42.3028	1.43585
$869$	−34.5914	−1.17343
$870$	−11.9632	−0.405592
$871$	34.8321	1.18024
$872$	−2.54167	−0.0860717
$873$	12.3868	0.419229
$874$	−3.58943	−0.121414
$875$	−19.5736	−0.661708
$876$	7.63074	0.257819
$877$	−19.8439	−0.670080	−0.335040	−	0.942204i	$-0.608750\pi$
$877$	−19.8439	−0.670080	−0.335040	+	0.942204i	$0.608750\pi$
$878$	−33.5228	−1.13134
$879$	3.93526	0.132733
$880$	−8.04425	−0.271171
$881$	−34.9792	−1.17848	−0.589239	−	0.807959i	$-0.700572\pi$
$881$	−34.9792	−1.17848	−0.589239	+	0.807959i	$0.700572\pi$
$882$	24.9881	0.841393
$883$	−34.5668	−1.16326	−0.581632	−	0.813452i	$-0.697586\pi$
$883$	−34.5668	−1.16326	−0.581632	+	0.813452i	$0.697586\pi$
$884$	30.3846	1.02194
$885$	−10.1983	−0.342813
$886$	30.9219	1.03884
$887$	−23.6093	−0.792724	−0.396362	−	0.918094i	$-0.629727\pi$
$887$	−23.6093	−0.792724	−0.396362	+	0.918094i	$0.629727\pi$
$888$	−0.0955538	−0.00320658
$889$	−61.0191	−2.04651
$890$	−14.5893	−0.489034
$891$	20.0464	0.671580
$892$	13.5714	0.454404
$893$	11.8731	0.397317
$894$	−2.06884	−0.0691924
$895$	−26.4249	−0.883286
$896$	3.99338	0.133409
$897$	−1.90764	−0.0636944
$898$	−33.0386	−1.10251
$899$	96.6635	3.22391
$900$	−9.21233	−0.307078
$901$	−87.5617	−2.91710
$902$	8.60323	0.286456
$903$	−7.01860	−0.233564
$904$	11.8837	0.395245
$905$	−22.7357	−0.755760
$906$	−5.70552	−0.189553
$907$	−56.0662	−1.86165	−0.930824	−	0.365468i	$-0.880909\pi$
$907$	−56.0662	−1.86165	−0.930824	+	0.365468i	$0.880909\pi$
$908$	25.8894	0.859171
$909$	−1.83214	−0.0607684
$910$	−48.2196	−1.59847
$911$	−11.0467	−0.365995	−0.182997	−	0.983113i	$-0.558580\pi$
$911$	−11.0467	−0.365995	−0.182997	+	0.983113i	$0.558580\pi$
$912$	−1.63358	−0.0540931
$913$	−20.8618	−0.690426
$914$	−20.0861	−0.664389
$915$	14.6023	0.482738
$916$	−4.33620	−0.143272
$917$	−3.99338	−0.131873
$918$	19.1108	0.630750
$919$	51.3279	1.69315	0.846576	−	0.532268i	$-0.178660\pi$
$919$	51.3279	1.69315	0.846576	+	0.532268i	$0.178660\pi$
$920$	−2.88071	−0.0949743
$921$	−14.1736	−0.467037
$922$	5.24747	0.172816
$923$	7.87954	0.259358
$924$	−5.07505	−0.166957
$925$	0.692551	0.0227709
$926$	−25.8829	−0.850566
$927$	19.6311	0.644770
$928$	9.12503	0.299544
$929$	35.4756	1.16392	0.581958	−	0.813219i	$-0.302287\pi$
$929$	35.4756	1.16392	0.581958	+	0.813219i	$0.302287\pi$
$930$	−13.8881	−0.455408
$931$	−32.1149	−1.05252
$932$	−3.28528	−0.107613
$933$	−2.86568	−0.0938180
$934$	−14.2256	−0.465475
$935$	−58.3116	−1.90699
$936$	11.7067	0.382646
$937$	−9.25911	−0.302482	−0.151241	−	0.988497i	$-0.548327\pi$
$937$	−9.25911	−0.302482	−0.151241	+	0.988497i	$0.548327\pi$
$938$	33.1847	1.08352
$939$	11.2599	0.367454
$940$	9.52880	0.310795
$941$	44.0454	1.43584	0.717920	−	0.696126i	$-0.245094\pi$
$941$	44.0454	1.43584	0.717920	+	0.696126i	$0.245094\pi$
$942$	3.69475	0.120381
$943$	3.08089	0.100328
$944$	7.77883	0.253179
$945$	−30.3284	−0.986582
$946$	−10.7840	−0.350619
$947$	−45.5669	−1.48073	−0.740363	−	0.672208i	$-0.765346\pi$
$947$	−45.5669	−1.48073	−0.740363	+	0.672208i	$0.765346\pi$
$948$	−5.63764	−0.183102
$949$	70.2806	2.28141
$950$	11.8398	0.384133
$951$	3.43366	0.111344
$952$	28.9475	0.938192
$953$	−15.8162	−0.512336	−0.256168	−	0.966632i	$-0.582460\pi$
$953$	−15.8162	−0.512336	−0.256168	+	0.966632i	$0.582460\pi$
$954$	−33.7362	−1.09225
$955$	−51.0032	−1.65042
$956$	2.98773	0.0966302
$957$	−11.5967	−0.374868
$958$	−16.4489	−0.531441
$959$	−60.8427	−1.96471
$960$	−1.31103	−0.0423135
$961$	81.2163	2.61988
$962$	−0.880070	−0.0283746
$963$	−28.3528	−0.913658
$964$	−10.0896	−0.324964
$965$	66.5847	2.14344
$966$	−1.81742	−0.0584745
$967$	7.89705	0.253952	0.126976	−	0.991906i	$-0.459473\pi$
$967$	7.89705	0.253952	0.126976	+	0.991906i	$0.459473\pi$
$968$	3.20223	0.102923
$969$	−11.8416	−0.380406
$970$	−12.7763	−0.410223
$971$	32.8853	1.05534	0.527669	−	0.849450i	$-0.323066\pi$
$971$	32.8853	1.05534	0.527669	+	0.849450i	$0.323066\pi$
$972$	11.1763	0.358479
$973$	59.8243	1.91788
$974$	−35.8724	−1.14943
$975$	6.29238	0.201518
$976$	−11.1380	−0.356519
$977$	−27.5911	−0.882718	−0.441359	−	0.897331i	$-0.645504\pi$
$977$	−27.5911	−0.882718	−0.441359	+	0.897331i	$0.645504\pi$
$978$	−4.05606	−0.129698
$979$	−14.1423	−0.451989
$980$	−25.7740	−0.823319
$981$	−7.09856	−0.226640
$982$	20.3645	0.649858
$983$	−25.0324	−0.798408	−0.399204	−	0.916862i	$-0.630714\pi$
$983$	−25.0324	−0.798408	−0.399204	+	0.916862i	$0.630714\pi$
$984$	1.40214	0.0446985
$985$	−1.37025	−0.0436597
$986$	66.1461	2.10652
$987$	6.01164	0.191353
$988$	−15.0456	−0.478663
$989$	−3.86185	−0.122800
$990$	−22.4666	−0.714035
$991$	−28.3364	−0.900135	−0.450068	−	0.892994i	$-0.648600\pi$
$991$	−28.3364	−0.900135	−0.450068	+	0.892994i	$0.648600\pi$
$992$	10.5932	0.336335
$993$	−5.37663	−0.170622
$994$	7.50686	0.238103
$995$	−9.95983	−0.315748
$996$	−3.40002	−0.107734
$997$	−26.6956	−0.845457	−0.422729	−	0.906256i	$-0.638928\pi$
$997$	−26.6956	−0.845457	−0.422729	+	0.906256i	$0.638928\pi$
$998$	33.3758	1.05649
$999$	−0.553532	−0.0175130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.20	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.20	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.455108 q^{3} +1.00000 q^{4} -2.88071 q^{5} -0.455108 q^{6} -3.99338 q^{7} -1.00000 q^{8} -2.79288 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.455108 q^{3} +1.00000 q^{4} -2.88071 q^{5} -0.455108 q^{6} -3.99338 q^{7} -1.00000 q^{8} -2.79288 q^{9} +2.88071 q^{10} +2.79245 q^{11} +0.455108 q^{12} +4.19163 q^{13} +3.99338 q^{14} -1.31103 q^{15} +1.00000 q^{16} +7.24886 q^{17} +2.79288 q^{18} -3.58943 q^{19} -2.88071 q^{20} -1.81742 q^{21} -2.79245 q^{22} -1.00000 q^{23} -0.455108 q^{24} +3.29851 q^{25} -4.19163 q^{26} -2.63638 q^{27} -3.99338 q^{28} -9.12503 q^{29} +1.31103 q^{30} -10.5932 q^{31} -1.00000 q^{32} +1.27087 q^{33} -7.24886 q^{34} +11.5038 q^{35} -2.79288 q^{36} +0.209959 q^{37} +3.58943 q^{38} +1.90764 q^{39} +2.88071 q^{40} -3.08089 q^{41} +1.81742 q^{42} +3.86185 q^{43} +2.79245 q^{44} +8.04548 q^{45} +1.00000 q^{46} -3.30779 q^{47} +0.455108 q^{48} +8.94708 q^{49} -3.29851 q^{50} +3.29901 q^{51} +4.19163 q^{52} -12.0794 q^{53} +2.63638 q^{54} -8.04425 q^{55} +3.99338 q^{56} -1.63358 q^{57} +9.12503 q^{58} +7.77883 q^{59} -1.31103 q^{60} -11.1380 q^{61} +10.5932 q^{62} +11.1530 q^{63} +1.00000 q^{64} -12.0749 q^{65} -1.27087 q^{66} +8.30992 q^{67} +7.24886 q^{68} -0.455108 q^{69} -11.5038 q^{70} +1.87983 q^{71} +2.79288 q^{72} +16.7669 q^{73} -0.209959 q^{74} +1.50118 q^{75} -3.58943 q^{76} -11.1513 q^{77} -1.90764 q^{78} -12.3875 q^{79} -2.88071 q^{80} +7.17879 q^{81} +3.08089 q^{82} -7.47080 q^{83} -1.81742 q^{84} -20.8819 q^{85} -3.86185 q^{86} -4.15287 q^{87} -2.79245 q^{88} -5.06447 q^{89} -8.04548 q^{90} -16.7388 q^{91} -1.00000 q^{92} -4.82106 q^{93} +3.30779 q^{94} +10.3401 q^{95} -0.455108 q^{96} -4.43513 q^{97} -8.94708 q^{98} -7.79897 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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