LMFDB - Embedded newform 6026.2.a.l.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.19697 q^{3} +1.00000 q^{4} +0.174713 q^{5} +2.19697 q^{6} +3.49233 q^{7} -1.00000 q^{8} +1.82670 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.19697 q^{3} +1.00000 q^{4} +0.174713 q^{5} +2.19697 q^{6} +3.49233 q^{7} -1.00000 q^{8} +1.82670 q^{9} -0.174713 q^{10} -0.405453 q^{11} -2.19697 q^{12} +4.26710 q^{13} -3.49233 q^{14} -0.383840 q^{15} +1.00000 q^{16} -2.55126 q^{17} -1.82670 q^{18} +4.99575 q^{19} +0.174713 q^{20} -7.67256 q^{21} +0.405453 q^{22} -1.00000 q^{23} +2.19697 q^{24} -4.96948 q^{25} -4.26710 q^{26} +2.57772 q^{27} +3.49233 q^{28} +4.57933 q^{29} +0.383840 q^{30} +1.01090 q^{31} -1.00000 q^{32} +0.890769 q^{33} +2.55126 q^{34} +0.610155 q^{35} +1.82670 q^{36} +2.11562 q^{37} -4.99575 q^{38} -9.37470 q^{39} -0.174713 q^{40} +6.75236 q^{41} +7.67256 q^{42} -3.39796 q^{43} -0.405453 q^{44} +0.319147 q^{45} +1.00000 q^{46} +9.79087 q^{47} -2.19697 q^{48} +5.19636 q^{49} +4.96948 q^{50} +5.60505 q^{51} +4.26710 q^{52} -4.54058 q^{53} -2.57772 q^{54} -0.0708378 q^{55} -3.49233 q^{56} -10.9755 q^{57} -4.57933 q^{58} -7.05461 q^{59} -0.383840 q^{60} +7.13438 q^{61} -1.01090 q^{62} +6.37942 q^{63} +1.00000 q^{64} +0.745517 q^{65} -0.890769 q^{66} -1.88020 q^{67} -2.55126 q^{68} +2.19697 q^{69} -0.610155 q^{70} +6.82167 q^{71} -1.82670 q^{72} +16.3604 q^{73} -2.11562 q^{74} +10.9178 q^{75} +4.99575 q^{76} -1.41597 q^{77} +9.37470 q^{78} -9.05809 q^{79} +0.174713 q^{80} -11.1433 q^{81} -6.75236 q^{82} +3.41988 q^{83} -7.67256 q^{84} -0.445738 q^{85} +3.39796 q^{86} -10.0607 q^{87} +0.405453 q^{88} +8.83169 q^{89} -0.319147 q^{90} +14.9021 q^{91} -1.00000 q^{92} -2.22091 q^{93} -9.79087 q^{94} +0.872821 q^{95} +2.19697 q^{96} +13.4046 q^{97} -5.19636 q^{98} -0.740639 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.19697	−1.26842	−0.634212	−	0.773159i	$-0.718675\pi$
$3$	−2.19697	−1.26842	−0.634212	+	0.773159i	$0.718675\pi$
$4$	1.00000	0.500000
$5$	0.174713	0.0781340	0.0390670	−	0.999237i	$-0.487561\pi$
$5$	0.174713	0.0781340	0.0390670	+	0.999237i	$0.487561\pi$
$6$	2.19697	0.896911
$7$	3.49233	1.31998	0.659988	−	0.751276i	$-0.270561\pi$
$7$	3.49233	1.31998	0.659988	+	0.751276i	$0.270561\pi$
$8$	−1.00000	−0.353553
$9$	1.82670	0.608899
$10$	−0.174713	−0.0552491
$11$	−0.405453	−0.122249	−0.0611243	−	0.998130i	$-0.519469\pi$
$11$	−0.405453	−0.122249	−0.0611243	+	0.998130i	$0.519469\pi$
$12$	−2.19697	−0.634212
$13$	4.26710	1.18348	0.591740	−	0.806129i	$-0.298441\pi$
$13$	4.26710	1.18348	0.591740	+	0.806129i	$0.298441\pi$
$14$	−3.49233	−0.933364
$15$	−0.383840	−0.0991070
$16$	1.00000	0.250000
$17$	−2.55126	−0.618771	−0.309385	−	0.950937i	$-0.600123\pi$
$17$	−2.55126	−0.618771	−0.309385	+	0.950937i	$0.600123\pi$
$18$	−1.82670	−0.430556
$19$	4.99575	1.14610	0.573051	−	0.819519i	$-0.305760\pi$
$19$	4.99575	1.14610	0.573051	+	0.819519i	$0.305760\pi$
$20$	0.174713	0.0390670
$21$	−7.67256	−1.67429
$22$	0.405453	0.0864428
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.19697	0.448456
$25$	−4.96948	−0.993895
$26$	−4.26710	−0.836846
$27$	2.57772	0.496082
$28$	3.49233	0.659988
$29$	4.57933	0.850361	0.425180	−	0.905109i	$-0.360211\pi$
$29$	4.57933	0.850361	0.425180	+	0.905109i	$0.360211\pi$
$30$	0.383840	0.0700792
$31$	1.01090	0.181562	0.0907812	−	0.995871i	$-0.471064\pi$
$31$	1.01090	0.181562	0.0907812	+	0.995871i	$0.471064\pi$
$32$	−1.00000	−0.176777
$33$	0.890769	0.155063
$34$	2.55126	0.437537
$35$	0.610155	0.103135
$36$	1.82670	0.304449
$37$	2.11562	0.347806	0.173903	−	0.984763i	$-0.444362\pi$
$37$	2.11562	0.347806	0.173903	+	0.984763i	$0.444362\pi$
$38$	−4.99575	−0.810417
$39$	−9.37470	−1.50115
$40$	−0.174713	−0.0276245
$41$	6.75236	1.05454	0.527271	−	0.849697i	$-0.323215\pi$
$41$	6.75236	1.05454	0.527271	+	0.849697i	$0.323215\pi$
$42$	7.67256	1.18390
$43$	−3.39796	−0.518184	−0.259092	−	0.965853i	$-0.583423\pi$
$43$	−3.39796	−0.518184	−0.259092	+	0.965853i	$0.583423\pi$
$44$	−0.405453	−0.0611243
$45$	0.319147	0.0475757
$46$	1.00000	0.147442
$47$	9.79087	1.42815	0.714073	−	0.700072i	$-0.246849\pi$
$47$	9.79087	1.42815	0.714073	+	0.700072i	$0.246849\pi$
$48$	−2.19697	−0.317106
$49$	5.19636	0.742337
$50$	4.96948	0.702790
$51$	5.60505	0.784864
$52$	4.26710	0.591740
$53$	−4.54058	−0.623697	−0.311848	−	0.950132i	$-0.600948\pi$
$53$	−4.54058	−0.623697	−0.311848	+	0.950132i	$0.600948\pi$
$54$	−2.57772	−0.350783
$55$	−0.0708378	−0.00955176
$56$	−3.49233	−0.466682
$57$	−10.9755	−1.45374
$58$	−4.57933	−0.601296
$59$	−7.05461	−0.918432	−0.459216	−	0.888325i	$-0.651870\pi$
$59$	−7.05461	−0.918432	−0.459216	+	0.888325i	$0.651870\pi$
$60$	−0.383840	−0.0495535
$61$	7.13438	0.913464	0.456732	−	0.889604i	$-0.349020\pi$
$61$	7.13438	0.913464	0.456732	+	0.889604i	$0.349020\pi$
$62$	−1.01090	−0.128384
$63$	6.37942	0.803732
$64$	1.00000	0.125000
$65$	0.745517	0.0924700
$66$	−0.890769	−0.109646
$67$	−1.88020	−0.229703	−0.114852	−	0.993383i	$-0.536639\pi$
$67$	−1.88020	−0.229703	−0.114852	+	0.993383i	$0.536639\pi$
$68$	−2.55126	−0.309385
$69$	2.19697	0.264485
$70$	−0.610155	−0.0729274
$71$	6.82167	0.809583	0.404791	−	0.914409i	$-0.367344\pi$
$71$	6.82167	0.809583	0.404791	+	0.914409i	$0.367344\pi$
$72$	−1.82670	−0.215278
$73$	16.3604	1.91484	0.957418	−	0.288706i	$-0.0932251\pi$
$73$	16.3604	1.91484	0.957418	+	0.288706i	$0.0932251\pi$
$74$	−2.11562	−0.245936
$75$	10.9178	1.26068
$76$	4.99575	0.573051
$77$	−1.41597	−0.161365
$78$	9.37470	1.06148
$79$	−9.05809	−1.01911	−0.509557	−	0.860437i	$-0.670191\pi$
$79$	−9.05809	−1.01911	−0.509557	+	0.860437i	$0.670191\pi$
$80$	0.174713	0.0195335
$81$	−11.1433	−1.23814
$82$	−6.75236	−0.745674
$83$	3.41988	0.375380	0.187690	−	0.982228i	$-0.439900\pi$
$83$	3.41988	0.375380	0.187690	+	0.982228i	$0.439900\pi$
$84$	−7.67256	−0.837145
$85$	−0.445738	−0.0483470
$86$	3.39796	0.366411
$87$	−10.0607	−1.07862
$88$	0.405453	0.0432214
$89$	8.83169	0.936157	0.468079	−	0.883687i	$-0.344946\pi$
$89$	8.83169	0.936157	0.468079	+	0.883687i	$0.344946\pi$
$90$	−0.319147	−0.0336411
$91$	14.9021	1.56216
$92$	−1.00000	−0.104257
$93$	−2.22091	−0.230298
$94$	−9.79087	−1.00985
$95$	0.872821	0.0895496
$96$	2.19697	0.224228
$97$	13.4046	1.36103	0.680516	−	0.732733i	$-0.261756\pi$
$97$	13.4046	1.36103	0.680516	+	0.732733i	$0.261756\pi$
$98$	−5.19636	−0.524911
$99$	−0.740639	−0.0744370
$100$	−4.96948	−0.496948
$101$	−2.87988	−0.286558	−0.143279	−	0.989682i	$-0.545765\pi$
$101$	−2.87988	−0.286558	−0.143279	+	0.989682i	$0.545765\pi$
$102$	−5.60505	−0.554982
$103$	0.0835949	0.00823685	0.00411842	−	0.999992i	$-0.498689\pi$
$103$	0.0835949	0.00823685	0.00411842	+	0.999992i	$0.498689\pi$
$104$	−4.26710	−0.418423
$105$	−1.34049	−0.130819
$106$	4.54058	0.441020
$107$	−17.1248	−1.65551	−0.827757	−	0.561087i	$-0.810383\pi$
$107$	−17.1248	−1.65551	−0.827757	+	0.561087i	$0.810383\pi$
$108$	2.57772	0.248041
$109$	2.84631	0.272627	0.136313	−	0.990666i	$-0.456475\pi$
$109$	2.84631	0.272627	0.136313	+	0.990666i	$0.456475\pi$
$110$	0.0708378	0.00675412
$111$	−4.64797	−0.441166
$112$	3.49233	0.329994
$113$	5.86574	0.551803	0.275901	−	0.961186i	$-0.411024\pi$
$113$	5.86574	0.551803	0.275901	+	0.961186i	$0.411024\pi$
$114$	10.9755	1.02795
$115$	−0.174713	−0.0162921
$116$	4.57933	0.425180
$117$	7.79469	0.720619
$118$	7.05461	0.649430
$119$	−8.90983	−0.816763
$120$	0.383840	0.0350396
$121$	−10.8356	−0.985055
$122$	−7.13438	−0.645916
$123$	−14.8348	−1.33761
$124$	1.01090	0.0907812
$125$	−1.74180	−0.155791
$126$	−6.37942	−0.568324
$127$	−0.333261	−0.0295721	−0.0147861	−	0.999891i	$-0.504707\pi$
$127$	−0.333261	−0.0295721	−0.0147861	+	0.999891i	$0.504707\pi$
$128$	−1.00000	−0.0883883
$129$	7.46523	0.657277
$130$	−0.745517	−0.0653861
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	0.890769	0.0775315
$133$	17.4468	1.51283
$134$	1.88020	0.162425
$135$	0.450361	0.0387609
$136$	2.55126	0.218769
$137$	−17.2114	−1.47047	−0.735235	−	0.677813i	$-0.762928\pi$
$137$	−17.2114	−1.47047	−0.735235	+	0.677813i	$0.762928\pi$
$138$	−2.19697	−0.187019
$139$	10.5816	0.897519	0.448760	−	0.893652i	$-0.351866\pi$
$139$	10.5816	0.897519	0.448760	+	0.893652i	$0.351866\pi$
$140$	0.610155	0.0515675
$141$	−21.5103	−1.81149
$142$	−6.82167	−0.572462
$143$	−1.73010	−0.144679
$144$	1.82670	0.152225
$145$	0.800068	0.0664421
$146$	−16.3604	−1.35399
$147$	−11.4163	−0.941598
$148$	2.11562	0.173903
$149$	−8.23485	−0.674625	−0.337313	−	0.941393i	$-0.609518\pi$
$149$	−8.23485	−0.674625	−0.337313	+	0.941393i	$0.609518\pi$
$150$	−10.9178	−0.891435
$151$	−4.33781	−0.353006	−0.176503	−	0.984300i	$-0.556478\pi$
$151$	−4.33781	−0.353006	−0.176503	+	0.984300i	$0.556478\pi$
$152$	−4.99575	−0.405208
$153$	−4.66037	−0.376769
$154$	1.41597	0.114102
$155$	0.176617	0.0141862
$156$	−9.37470	−0.750577
$157$	−8.85717	−0.706879	−0.353440	−	0.935457i	$-0.614988\pi$
$157$	−8.85717	−0.706879	−0.353440	+	0.935457i	$0.614988\pi$
$158$	9.05809	0.720623
$159$	9.97554	0.791111
$160$	−0.174713	−0.0138123
$161$	−3.49233	−0.275234
$162$	11.1433	0.875498
$163$	2.39536	0.187619	0.0938096	−	0.995590i	$-0.470096\pi$
$163$	2.39536	0.187619	0.0938096	+	0.995590i	$0.470096\pi$
$164$	6.75236	0.527271
$165$	0.155629	0.0121157
$166$	−3.41988	−0.265434
$167$	20.3305	1.57322	0.786609	−	0.617451i	$-0.211835\pi$
$167$	20.3305	1.57322	0.786609	+	0.617451i	$0.211835\pi$
$168$	7.67256	0.591951
$169$	5.20811	0.400624
$170$	0.445738	0.0341865
$171$	9.12571	0.697860
$172$	−3.39796	−0.259092
$173$	−24.5175	−1.86403	−0.932016	−	0.362418i	$-0.881951\pi$
$173$	−24.5175	−1.86403	−0.932016	+	0.362418i	$0.881951\pi$
$174$	10.0607	0.762698
$175$	−17.3550	−1.31192
$176$	−0.405453	−0.0305621
$177$	15.4988	1.16496
$178$	−8.83169	−0.661963
$179$	−17.7639	−1.32774	−0.663869	−	0.747849i	$-0.731087\pi$
$179$	−17.7639	−1.32774	−0.663869	+	0.747849i	$0.731087\pi$
$180$	0.319147	0.0237878
$181$	18.2258	1.35471	0.677357	−	0.735655i	$-0.263125\pi$
$181$	18.2258	1.35471	0.677357	+	0.735655i	$0.263125\pi$
$182$	−14.9021	−1.10462
$183$	−15.6740	−1.15866
$184$	1.00000	0.0737210
$185$	0.369626	0.0271755
$186$	2.22091	0.162845
$187$	1.03441	0.0756438
$188$	9.79087	0.714073
$189$	9.00224	0.654817
$190$	−0.872821	−0.0633211
$191$	−12.2561	−0.886818	−0.443409	−	0.896319i	$-0.646231\pi$
$191$	−12.2561	−0.886818	−0.443409	+	0.896319i	$0.646231\pi$
$192$	−2.19697	−0.158553
$193$	−19.9080	−1.43301	−0.716506	−	0.697581i	$-0.754260\pi$
$193$	−19.9080	−1.43301	−0.716506	+	0.697581i	$0.754260\pi$
$194$	−13.4046	−0.962395
$195$	−1.63788	−0.117291
$196$	5.19636	0.371168
$197$	−17.2697	−1.23042	−0.615209	−	0.788364i	$-0.710929\pi$
$197$	−17.2697	−1.23042	−0.615209	+	0.788364i	$0.710929\pi$
$198$	0.740639	0.0526349
$199$	6.17484	0.437723	0.218861	−	0.975756i	$-0.429766\pi$
$199$	6.17484	0.437723	0.218861	+	0.975756i	$0.429766\pi$
$200$	4.96948	0.351395
$201$	4.13075	0.291361
$202$	2.87988	0.202627
$203$	15.9925	1.12246
$204$	5.60505	0.392432
$205$	1.17972	0.0823956
$206$	−0.0835949	−0.00582433
$207$	−1.82670	−0.126964
$208$	4.26710	0.295870
$209$	−2.02554	−0.140109
$210$	1.34049	0.0925029
$211$	15.6689	1.07869	0.539345	−	0.842085i	$-0.318672\pi$
$211$	15.6689	1.07869	0.539345	+	0.842085i	$0.318672\pi$
$212$	−4.54058	−0.311848
$213$	−14.9870	−1.02689
$214$	17.1248	1.17062
$215$	−0.593667	−0.0404878
$216$	−2.57772	−0.175392
$217$	3.53038	0.239658
$218$	−2.84631	−0.192776
$219$	−35.9433	−2.42882
$220$	−0.0708378	−0.00477588
$221$	−10.8865	−0.732303
$222$	4.64797	0.311951
$223$	4.71198	0.315537	0.157769	−	0.987476i	$-0.449570\pi$
$223$	4.71198	0.315537	0.157769	+	0.987476i	$0.449570\pi$
$224$	−3.49233	−0.233341
$225$	−9.07772	−0.605181
$226$	−5.86574	−0.390183
$227$	7.59302	0.503966	0.251983	−	0.967732i	$-0.418917\pi$
$227$	7.59302	0.503966	0.251983	+	0.967732i	$0.418917\pi$
$228$	−10.9755	−0.726872
$229$	−5.19255	−0.343133	−0.171567	−	0.985173i	$-0.554883\pi$
$229$	−5.19255	−0.343133	−0.171567	+	0.985173i	$0.554883\pi$
$230$	0.174713	0.0115202
$231$	3.11086	0.204679
$232$	−4.57933	−0.300648
$233$	0.300970	0.0197172	0.00985860	−	0.999951i	$-0.496862\pi$
$233$	0.300970	0.0197172	0.00985860	+	0.999951i	$0.496862\pi$
$234$	−7.79469	−0.509555
$235$	1.71059	0.111587
$236$	−7.05461	−0.459216
$237$	19.9004	1.29267
$238$	8.90983	0.577538
$239$	24.8944	1.61028	0.805142	−	0.593082i	$-0.202089\pi$
$239$	24.8944	1.61028	0.805142	+	0.593082i	$0.202089\pi$
$240$	−0.383840	−0.0247767
$241$	23.7629	1.53070	0.765352	−	0.643612i	$-0.222565\pi$
$241$	23.7629	1.53070	0.765352	+	0.643612i	$0.222565\pi$
$242$	10.8356	0.696539
$243$	16.7483	1.07441
$244$	7.13438	0.456732
$245$	0.907871	0.0580017
$246$	14.8348	0.945830
$247$	21.3173	1.35639
$248$	−1.01090	−0.0641920
$249$	−7.51338	−0.476141
$250$	1.74180	0.110161
$251$	0.0926621	0.00584878	0.00292439	−	0.999996i	$-0.499069\pi$
$251$	0.0926621	0.00584878	0.00292439	+	0.999996i	$0.499069\pi$
$252$	6.37942	0.401866
$253$	0.405453	0.0254906
$254$	0.333261	0.0209106
$255$	0.979274	0.0613245
$256$	1.00000	0.0625000
$257$	−20.8126	−1.29825	−0.649126	−	0.760681i	$-0.724865\pi$
$257$	−20.8126	−1.29825	−0.649126	+	0.760681i	$0.724865\pi$
$258$	−7.46523	−0.464765
$259$	7.38845	0.459096
$260$	0.745517	0.0462350
$261$	8.36505	0.517783
$262$	−1.00000	−0.0617802
$263$	5.67547	0.349964	0.174982	−	0.984572i	$-0.444013\pi$
$263$	5.67547	0.349964	0.174982	+	0.984572i	$0.444013\pi$
$264$	−0.890769	−0.0548230
$265$	−0.793298	−0.0487319
$266$	−17.4468	−1.06973
$267$	−19.4030	−1.18744
$268$	−1.88020	−0.114852
$269$	16.7045	1.01849	0.509246	−	0.860621i	$-0.329924\pi$
$269$	16.7045	1.01849	0.509246	+	0.860621i	$0.329924\pi$
$270$	−0.450361	−0.0274081
$271$	−24.5682	−1.49241	−0.746206	−	0.665715i	$-0.768127\pi$
$271$	−24.5682	−1.49241	−0.746206	+	0.665715i	$0.768127\pi$
$272$	−2.55126	−0.154693
$273$	−32.7395	−1.98149
$274$	17.2114	1.03978
$275$	2.01489	0.121502
$276$	2.19697	0.132242
$277$	24.3070	1.46046	0.730232	−	0.683199i	$-0.239412\pi$
$277$	24.3070	1.46046	0.730232	+	0.683199i	$0.239412\pi$
$278$	−10.5816	−0.634642
$279$	1.84660	0.110553
$280$	−0.610155	−0.0364637
$281$	−14.2464	−0.849870	−0.424935	−	0.905224i	$-0.639703\pi$
$281$	−14.2464	−0.849870	−0.424935	+	0.905224i	$0.639703\pi$
$282$	21.5103	1.28092
$283$	29.9144	1.77822	0.889112	−	0.457689i	$-0.151323\pi$
$283$	29.9144	1.77822	0.889112	+	0.457689i	$0.151323\pi$
$284$	6.82167	0.404791
$285$	−1.91757	−0.113587
$286$	1.73010	0.102303
$287$	23.5815	1.39197
$288$	−1.82670	−0.107639
$289$	−10.4911	−0.617123
$290$	−0.800068	−0.0469816
$291$	−29.4496	−1.72636
$292$	16.3604	0.957418
$293$	−15.9543	−0.932059	−0.466029	−	0.884769i	$-0.654316\pi$
$293$	−15.9543	−0.932059	−0.466029	+	0.884769i	$0.654316\pi$
$294$	11.4163	0.665810
$295$	−1.23253	−0.0717608
$296$	−2.11562	−0.122968
$297$	−1.04514	−0.0606453
$298$	8.23485	0.477032
$299$	−4.26710	−0.246773
$300$	10.9178	0.630340
$301$	−11.8668	−0.683991
$302$	4.33781	0.249613
$303$	6.32701	0.363477
$304$	4.99575	0.286526
$305$	1.24647	0.0713726
$306$	4.66037	0.266416
$307$	21.3529	1.21867	0.609337	−	0.792912i	$-0.291436\pi$
$307$	21.3529	1.21867	0.609337	+	0.792912i	$0.291436\pi$
$308$	−1.41597	−0.0806826
$309$	−0.183656	−0.0104478
$310$	−0.176617	−0.0100312
$311$	−18.0971	−1.02619	−0.513097	−	0.858331i	$-0.671502\pi$
$311$	−18.0971	−1.02619	−0.513097	+	0.858331i	$0.671502\pi$
$312$	9.37470	0.530738
$313$	−14.1917	−0.802164	−0.401082	−	0.916042i	$-0.631366\pi$
$313$	−14.1917	−0.802164	−0.401082	+	0.916042i	$0.631366\pi$
$314$	8.85717	0.499839
$315$	1.11457	0.0627988
$316$	−9.05809	−0.509557
$317$	−16.7628	−0.941493	−0.470746	−	0.882269i	$-0.656015\pi$
$317$	−16.7628	−0.941493	−0.470746	+	0.882269i	$0.656015\pi$
$318$	−9.97554	−0.559400
$319$	−1.85670	−0.103955
$320$	0.174713	0.00976675
$321$	37.6227	2.09989
$322$	3.49233	0.194620
$323$	−12.7454	−0.709175
$324$	−11.1433	−0.619071
$325$	−21.2052	−1.17625
$326$	−2.39536	−0.132667
$327$	−6.25326	−0.345806
$328$	−6.75236	−0.372837
$329$	34.1929	1.88512
$330$	−0.155629	−0.00856708
$331$	−24.9554	−1.37168	−0.685838	−	0.727755i	$-0.740564\pi$
$331$	−24.9554	−1.37168	−0.685838	+	0.727755i	$0.740564\pi$
$332$	3.41988	0.187690
$333$	3.86460	0.211779
$334$	−20.3305	−1.11243
$335$	−0.328495	−0.0179476
$336$	−7.67256	−0.418572
$337$	3.97170	0.216352	0.108176	−	0.994132i	$-0.465499\pi$
$337$	3.97170	0.216352	0.108176	+	0.994132i	$0.465499\pi$
$338$	−5.20811	−0.283284
$339$	−12.8869	−0.699920
$340$	−0.445738	−0.0241735
$341$	−0.409871	−0.0221957
$342$	−9.12571	−0.493462
$343$	−6.29891	−0.340109
$344$	3.39796	0.183206
$345$	0.383840	0.0206652
$346$	24.5175	1.31807
$347$	16.9755	0.911292	0.455646	−	0.890161i	$-0.349408\pi$
$347$	16.9755	0.911292	0.455646	+	0.890161i	$0.349408\pi$
$348$	−10.0607	−0.539309
$349$	29.0223	1.55353	0.776765	−	0.629791i	$-0.216859\pi$
$349$	29.0223	1.55353	0.776765	+	0.629791i	$0.216859\pi$
$350$	17.3550	0.927666
$351$	10.9994	0.587103
$352$	0.405453	0.0216107
$353$	−14.7393	−0.784494	−0.392247	−	0.919860i	$-0.628302\pi$
$353$	−14.7393	−0.784494	−0.392247	+	0.919860i	$0.628302\pi$
$354$	−15.4988	−0.823752
$355$	1.19183	0.0632559
$356$	8.83169	0.468079
$357$	19.5747	1.03600
$358$	17.7639	0.938853
$359$	36.0624	1.90330	0.951650	−	0.307183i	$-0.0993863\pi$
$359$	36.0624	1.90330	0.951650	+	0.307183i	$0.0993863\pi$
$360$	−0.319147	−0.0168205
$361$	5.95747	0.313551
$362$	−18.2258	−0.957927
$363$	23.8056	1.24947
$364$	14.9021	0.781082
$365$	2.85837	0.149614
$366$	15.6740	0.819296
$367$	29.3810	1.53368	0.766838	−	0.641840i	$-0.221829\pi$
$367$	29.3810	1.53368	0.766838	+	0.641840i	$0.221829\pi$
$368$	−1.00000	−0.0521286
$369$	12.3345	0.642109
$370$	−0.369626	−0.0192160
$371$	−15.8572	−0.823264
$372$	−2.22091	−0.115149
$373$	19.2796	0.998260	0.499130	−	0.866527i	$-0.333653\pi$
$373$	19.2796	0.998260	0.499130	+	0.866527i	$0.333653\pi$
$374$	−1.03441	−0.0534883
$375$	3.82668	0.197609
$376$	−9.79087	−0.504926
$377$	19.5404	1.00638
$378$	−9.00224	−0.463025
$379$	35.6077	1.82904	0.914522	−	0.404535i	$-0.132567\pi$
$379$	35.6077	1.82904	0.914522	+	0.404535i	$0.132567\pi$
$380$	0.872821	0.0447748
$381$	0.732165	0.0375100
$382$	12.2561	0.627075
$383$	−4.05526	−0.207214	−0.103607	−	0.994618i	$-0.533038\pi$
$383$	−4.05526	−0.207214	−0.103607	+	0.994618i	$0.533038\pi$
$384$	2.19697	0.112114
$385$	−0.247389	−0.0126081
$386$	19.9080	1.01329
$387$	−6.20704	−0.315522
$388$	13.4046	0.680516
$389$	13.7865	0.699003	0.349501	−	0.936936i	$-0.386351\pi$
$389$	13.7865	0.699003	0.349501	+	0.936936i	$0.386351\pi$
$390$	1.63788	0.0829373
$391$	2.55126	0.129023
$392$	−5.19636	−0.262456
$393$	−2.19697	−0.110823
$394$	17.2697	0.870037
$395$	−1.58257	−0.0796275
$396$	−0.740639	−0.0372185
$397$	7.29810	0.366281	0.183141	−	0.983087i	$-0.441374\pi$
$397$	7.29810	0.366281	0.183141	+	0.983087i	$0.441374\pi$
$398$	−6.17484	−0.309517
$399$	−38.3301	−1.91891
$400$	−4.96948	−0.248474
$401$	−8.20549	−0.409763	−0.204881	−	0.978787i	$-0.565681\pi$
$401$	−8.20549	−0.409763	−0.204881	+	0.978787i	$0.565681\pi$
$402$	−4.13075	−0.206023
$403$	4.31359	0.214875
$404$	−2.87988	−0.143279
$405$	−1.94687	−0.0967409
$406$	−15.9925	−0.793696
$407$	−0.857784	−0.0425188
$408$	−5.60505	−0.277491
$409$	−28.8079	−1.42446	−0.712230	−	0.701946i	$-0.752315\pi$
$409$	−28.8079	−1.42446	−0.712230	+	0.701946i	$0.752315\pi$
$410$	−1.17972	−0.0582625
$411$	37.8130	1.86518
$412$	0.0835949	0.00411842
$413$	−24.6370	−1.21231
$414$	1.82670	0.0897772
$415$	0.597496	0.0293299
$416$	−4.26710	−0.209212
$417$	−23.2475	−1.13843
$418$	2.02554	0.0990723
$419$	−16.1270	−0.787854	−0.393927	−	0.919142i	$-0.628884\pi$
$419$	−16.1270	−0.787854	−0.393927	+	0.919142i	$0.628884\pi$
$420$	−1.34049	−0.0654094
$421$	13.0508	0.636058	0.318029	−	0.948081i	$-0.396979\pi$
$421$	13.0508	0.636058	0.318029	+	0.948081i	$0.396979\pi$
$422$	−15.6689	−0.762750
$423$	17.8849	0.869596
$424$	4.54058	0.220510
$425$	12.6784	0.614993
$426$	14.9870	0.726124
$427$	24.9156	1.20575
$428$	−17.1248	−0.827757
$429$	3.80100	0.183514
$430$	0.593667	0.0286292
$431$	36.4160	1.75410	0.877050	−	0.480400i	$-0.159508\pi$
$431$	36.4160	1.75410	0.877050	+	0.480400i	$0.159508\pi$
$432$	2.57772	0.124021
$433$	−36.4210	−1.75028	−0.875140	−	0.483870i	$-0.839231\pi$
$433$	−36.4210	−1.75028	−0.875140	+	0.483870i	$0.839231\pi$
$434$	−3.53038	−0.169464
$435$	−1.75773	−0.0842767
$436$	2.84631	0.136313
$437$	−4.99575	−0.238979
$438$	35.9433	1.71744
$439$	39.4548	1.88308	0.941538	−	0.336906i	$-0.109380\pi$
$439$	39.4548	1.88308	0.941538	+	0.336906i	$0.109380\pi$
$440$	0.0708378	0.00337706
$441$	9.49217	0.452008
$442$	10.8865	0.517816
$443$	21.5241	1.02264	0.511319	−	0.859391i	$-0.329157\pi$
$443$	21.5241	1.02264	0.511319	+	0.859391i	$0.329157\pi$
$444$	−4.64797	−0.220583
$445$	1.54301	0.0731457
$446$	−4.71198	−0.223118
$447$	18.0918	0.855710
$448$	3.49233	0.164997
$449$	39.5870	1.86823	0.934114	−	0.356975i	$-0.116192\pi$
$449$	39.5870	1.86823	0.934114	+	0.356975i	$0.116192\pi$
$450$	9.07772	0.427928
$451$	−2.73776	−0.128916
$452$	5.86574	0.275901
$453$	9.53005	0.447761
$454$	−7.59302	−0.356358
$455$	2.60359	0.122058
$456$	10.9755	0.513976
$457$	−15.3869	−0.719767	−0.359883	−	0.932997i	$-0.617184\pi$
$457$	−15.3869	−0.719767	−0.359883	+	0.932997i	$0.617184\pi$
$458$	5.19255	0.242632
$459$	−6.57642	−0.306961
$460$	−0.174713	−0.00814603
$461$	1.49155	0.0694682	0.0347341	−	0.999397i	$-0.488942\pi$
$461$	1.49155	0.0694682	0.0347341	+	0.999397i	$0.488942\pi$
$462$	−3.11086	−0.144730
$463$	11.9241	0.554160	0.277080	−	0.960847i	$-0.410633\pi$
$463$	11.9241	0.554160	0.277080	+	0.960847i	$0.410633\pi$
$464$	4.57933	0.212590
$465$	−0.388022	−0.0179941
$466$	−0.300970	−0.0139422
$467$	9.84590	0.455614	0.227807	−	0.973706i	$-0.426844\pi$
$467$	9.84590	0.455614	0.227807	+	0.973706i	$0.426844\pi$
$468$	7.79469	0.360310
$469$	−6.56628	−0.303203
$470$	−1.71059	−0.0789037
$471$	19.4590	0.896622
$472$	7.05461	0.324715
$473$	1.37771	0.0633472
$474$	−19.9004	−0.914055
$475$	−24.8262	−1.13911
$476$	−8.90983	−0.408381
$477$	−8.29426	−0.379768
$478$	−24.8944	−1.13864
$479$	−31.4220	−1.43571	−0.717854	−	0.696194i	$-0.754875\pi$
$479$	−31.4220	−1.43571	−0.717854	+	0.696194i	$0.754875\pi$
$480$	0.383840	0.0175198
$481$	9.02756	0.411621
$482$	−23.7629	−1.08237
$483$	7.67256	0.349113
$484$	−10.8356	−0.492528
$485$	2.34196	0.106343
$486$	−16.7483	−0.759719
$487$	−20.8221	−0.943538	−0.471769	−	0.881722i	$-0.656384\pi$
$487$	−20.8221	−0.943538	−0.471769	+	0.881722i	$0.656384\pi$
$488$	−7.13438	−0.322958
$489$	−5.26255	−0.237981
$490$	−0.907871	−0.0410134
$491$	37.4246	1.68895	0.844475	−	0.535595i	$-0.179913\pi$
$491$	37.4246	1.68895	0.844475	+	0.535595i	$0.179913\pi$
$492$	−14.8348	−0.668803
$493$	−11.6831	−0.526178
$494$	−21.3173	−0.959112
$495$	−0.129399	−0.00581606
$496$	1.01090	0.0453906
$497$	23.8235	1.06863
$498$	7.51338	0.336683
$499$	−15.7518	−0.705149	−0.352575	−	0.935784i	$-0.614694\pi$
$499$	−15.7518	−0.705149	−0.352575	+	0.935784i	$0.614694\pi$
$500$	−1.74180	−0.0778955
$501$	−44.6655	−1.99551
$502$	−0.0926621	−0.00413571
$503$	−24.6215	−1.09782	−0.548908	−	0.835882i	$-0.684956\pi$
$503$	−24.6215	−1.09782	−0.548908	+	0.835882i	$0.684956\pi$
$504$	−6.37942	−0.284162
$505$	−0.503151	−0.0223899
$506$	−0.405453	−0.0180246
$507$	−11.4421	−0.508161
$508$	−0.333261	−0.0147861
$509$	38.0869	1.68817	0.844086	−	0.536207i	$-0.180143\pi$
$509$	38.0869	1.68817	0.844086	+	0.536207i	$0.180143\pi$
$510$	−0.979274	−0.0433630
$511$	57.1358	2.52754
$512$	−1.00000	−0.0441942
$513$	12.8776	0.568561
$514$	20.8126	0.918003
$515$	0.0146051	0.000643578 0
$516$	7.46523	0.328638
$517$	−3.96973	−0.174589
$518$	−7.38845	−0.324630
$519$	53.8643	2.36438
$520$	−0.745517	−0.0326931
$521$	9.95012	0.435923	0.217961	−	0.975957i	$-0.430059\pi$
$521$	9.95012	0.435923	0.217961	+	0.975957i	$0.430059\pi$
$522$	−8.36505	−0.366128
$523$	27.4046	1.19832	0.599160	−	0.800630i	$-0.295502\pi$
$523$	27.4046	1.19832	0.599160	+	0.800630i	$0.295502\pi$
$524$	1.00000	0.0436852
$525$	38.1286	1.66407
$526$	−5.67547	−0.247462
$527$	−2.57906	−0.112346
$528$	0.890769	0.0387657
$529$	1.00000	0.0434783
$530$	0.793298	0.0344586
$531$	−12.8866	−0.559232
$532$	17.4468	0.756414
$533$	28.8130	1.24803
$534$	19.4030	0.839650
$535$	−2.99192	−0.129352
$536$	1.88020	0.0812123
$537$	39.0269	1.68413
$538$	−16.7045	−0.720182
$539$	−2.10688	−0.0907496
$540$	0.450361	0.0193804
$541$	−15.2832	−0.657074	−0.328537	−	0.944491i	$-0.606556\pi$
$541$	−15.2832	−0.657074	−0.328537	+	0.944491i	$0.606556\pi$
$542$	24.5682	1.05529
$543$	−40.0416	−1.71835
$544$	2.55126	0.109384
$545$	0.497287	0.0213014
$546$	32.7395	1.40112
$547$	6.05811	0.259026	0.129513	−	0.991578i	$-0.458659\pi$
$547$	6.05811	0.259026	0.129513	+	0.991578i	$0.458659\pi$
$548$	−17.2114	−0.735235
$549$	13.0323	0.556207
$550$	−2.01489	−0.0859150
$551$	22.8772	0.974600
$552$	−2.19697	−0.0935094
$553$	−31.6338	−1.34521
$554$	−24.3070	−1.03270
$555$	−0.812060	−0.0344700
$556$	10.5816	0.448760
$557$	−10.7052	−0.453594	−0.226797	−	0.973942i	$-0.572825\pi$
$557$	−10.7052	−0.453594	−0.226797	+	0.973942i	$0.572825\pi$
$558$	−1.84660	−0.0781729
$559$	−14.4994	−0.613260
$560$	0.610155	0.0257837
$561$	−2.27258	−0.0959484
$562$	14.2464	0.600949
$563$	11.1583	0.470267	0.235134	−	0.971963i	$-0.424447\pi$
$563$	11.1583	0.470267	0.235134	+	0.971963i	$0.424447\pi$
$564$	−21.5103	−0.905747
$565$	1.02482	0.0431145
$566$	−29.9144	−1.25739
$567$	−38.9160	−1.63432
$568$	−6.82167	−0.286231
$569$	−13.0309	−0.546283	−0.273141	−	0.961974i	$-0.588063\pi$
$569$	−13.0309	−0.546283	−0.273141	+	0.961974i	$0.588063\pi$
$570$	1.91757	0.0803180
$571$	27.3324	1.14383	0.571913	−	0.820314i	$-0.306201\pi$
$571$	27.3324	1.14383	0.571913	+	0.820314i	$0.306201\pi$
$572$	−1.73010	−0.0723393
$573$	26.9263	1.12486
$574$	−23.5815	−0.984272
$575$	4.96948	0.207241
$576$	1.82670	0.0761123
$577$	−7.59123	−0.316027	−0.158014	−	0.987437i	$-0.550509\pi$
$577$	−7.59123	−0.316027	−0.158014	+	0.987437i	$0.550509\pi$
$578$	10.4911	0.436372
$579$	43.7375	1.81767
$580$	0.800068	0.0332210
$581$	11.9433	0.495493
$582$	29.4496	1.22072
$583$	1.84099	0.0762460
$584$	−16.3604	−0.676997
$585$	1.36183	0.0563048
$586$	15.9543	0.659065
$587$	−15.3156	−0.632142	−0.316071	−	0.948736i	$-0.602364\pi$
$587$	−15.3156	−0.632142	−0.316071	+	0.948736i	$0.602364\pi$
$588$	−11.4163	−0.470799
$589$	5.05018	0.208089
$590$	1.23253	0.0507425
$591$	37.9412	1.56069
$592$	2.11562	0.0869515
$593$	−14.3853	−0.590735	−0.295368	−	0.955384i	$-0.595442\pi$
$593$	−14.3853	−0.590735	−0.295368	+	0.955384i	$0.595442\pi$
$594$	1.04514	0.0428827
$595$	−1.55666	−0.0638169
$596$	−8.23485	−0.337313
$597$	−13.5660	−0.555218
$598$	4.26710	0.174495
$599$	−5.03321	−0.205651	−0.102826	−	0.994699i	$-0.532788\pi$
$599$	−5.03321	−0.205651	−0.102826	+	0.994699i	$0.532788\pi$
$600$	−10.9178	−0.445718
$601$	−10.9025	−0.444721	−0.222361	−	0.974965i	$-0.571376\pi$
$601$	−10.9025	−0.444721	−0.222361	+	0.974965i	$0.571376\pi$
$602$	11.8668	0.483654
$603$	−3.43456	−0.139866
$604$	−4.33781	−0.176503
$605$	−1.89312	−0.0769663
$606$	−6.32701	−0.257017
$607$	39.3382	1.59669	0.798344	−	0.602202i	$-0.205710\pi$
$607$	39.3382	1.59669	0.798344	+	0.602202i	$0.205710\pi$
$608$	−4.99575	−0.202604
$609$	−35.1352	−1.42375
$610$	−1.24647	−0.0504680
$611$	41.7786	1.69018
$612$	−4.66037	−0.188384
$613$	31.9888	1.29202	0.646008	−	0.763331i	$-0.276437\pi$
$613$	31.9888	1.29202	0.646008	+	0.763331i	$0.276437\pi$
$614$	−21.3529	−0.861732
$615$	−2.59183	−0.104512
$616$	1.41597	0.0570512
$617$	34.7369	1.39845	0.699227	−	0.714900i	$-0.253528\pi$
$617$	34.7369	1.39845	0.699227	+	0.714900i	$0.253528\pi$
$618$	0.183656	0.00738772
$619$	22.7627	0.914909	0.457455	−	0.889233i	$-0.348761\pi$
$619$	22.7627	0.914909	0.457455	+	0.889233i	$0.348761\pi$
$620$	0.176617	0.00709310
$621$	−2.57772	−0.103440
$622$	18.0971	0.725629
$623$	30.8432	1.23571
$624$	−9.37470	−0.375288
$625$	24.5431	0.981723
$626$	14.1917	0.567215
$627$	4.45005	0.177718
$628$	−8.85717	−0.353440
$629$	−5.39750	−0.215212
$630$	−1.11457	−0.0444054
$631$	8.26549	0.329044	0.164522	−	0.986373i	$-0.447392\pi$
$631$	8.26549	0.329044	0.164522	+	0.986373i	$0.447392\pi$
$632$	9.05809	0.360312
$633$	−34.4241	−1.36824
$634$	16.7628	0.665736
$635$	−0.0582250	−0.00231059
$636$	9.97554	0.395556
$637$	22.1734	0.878541
$638$	1.85670	0.0735075
$639$	12.4611	0.492954
$640$	−0.174713	−0.00690613
$641$	3.91432	0.154607	0.0773033	−	0.997008i	$-0.475369\pi$
$641$	3.91432	0.154607	0.0773033	+	0.997008i	$0.475369\pi$
$642$	−37.6227	−1.48485
$643$	39.9907	1.57708	0.788540	−	0.614984i	$-0.210837\pi$
$643$	39.9907	1.57708	0.788540	+	0.614984i	$0.210837\pi$
$644$	−3.49233	−0.137617
$645$	1.30427	0.0513557
$646$	12.7454	0.501462
$647$	4.78802	0.188237	0.0941183	−	0.995561i	$-0.469997\pi$
$647$	4.78802	0.188237	0.0941183	+	0.995561i	$0.469997\pi$
$648$	11.1433	0.437749
$649$	2.86031	0.112277
$650$	21.2052	0.831738
$651$	−7.75616	−0.303988
$652$	2.39536	0.0938096
$653$	−31.4604	−1.23114	−0.615570	−	0.788082i	$-0.711074\pi$
$653$	−31.4604	−1.23114	−0.615570	+	0.788082i	$0.711074\pi$
$654$	6.25326	0.244522
$655$	0.174713	0.00682660
$656$	6.75236	0.263636
$657$	29.8854	1.16594
$658$	−34.1929	−1.33298
$659$	20.2104	0.787287	0.393644	−	0.919263i	$-0.371214\pi$
$659$	20.2104	0.787287	0.393644	+	0.919263i	$0.371214\pi$
$660$	0.155629	0.00605784
$661$	−3.78275	−0.147132	−0.0735661	−	0.997290i	$-0.523438\pi$
$661$	−3.78275	−0.147132	−0.0735661	+	0.997290i	$0.523438\pi$
$662$	24.9554	0.969921
$663$	23.9173	0.928870
$664$	−3.41988	−0.132717
$665$	3.04818	0.118203
$666$	−3.86460	−0.149750
$667$	−4.57933	−0.177312
$668$	20.3305	0.786609
$669$	−10.3521	−0.400235
$670$	0.328495	0.0126909
$671$	−2.89265	−0.111670
$672$	7.67256	0.295975
$673$	−39.8219	−1.53502	−0.767511	−	0.641035i	$-0.778505\pi$
$673$	−39.8219	−1.53502	−0.767511	+	0.641035i	$0.778505\pi$
$674$	−3.97170	−0.152984
$675$	−12.8099	−0.493054
$676$	5.20811	0.200312
$677$	36.6014	1.40671	0.703354	−	0.710840i	$-0.251685\pi$
$677$	36.6014	1.40671	0.703354	+	0.710840i	$0.251685\pi$
$678$	12.8869	0.494918
$679$	46.8133	1.79653
$680$	0.445738	0.0170933
$681$	−16.6817	−0.639243
$682$	0.409871	0.0156948
$683$	40.1445	1.53609	0.768043	−	0.640399i	$-0.221231\pi$
$683$	40.1445	1.53609	0.768043	+	0.640399i	$0.221231\pi$
$684$	9.12571	0.348930
$685$	−3.00705	−0.114894
$686$	6.29891	0.240493
$687$	11.4079	0.435238
$688$	−3.39796	−0.129546
$689$	−19.3751	−0.738132
$690$	−0.383840	−0.0146125
$691$	27.8962	1.06122	0.530611	−	0.847616i	$-0.321963\pi$
$691$	27.8962	1.06122	0.530611	+	0.847616i	$0.321963\pi$
$692$	−24.5175	−0.932016
$693$	−2.58655	−0.0982550
$694$	−16.9755	−0.644381
$695$	1.84874	0.0701268
$696$	10.0607	0.381349
$697$	−17.2270	−0.652520
$698$	−29.0223	−1.09851
$699$	−0.661224	−0.0250098
$700$	−17.3550	−0.655959
$701$	−24.5714	−0.928049	−0.464024	−	0.885822i	$-0.653595\pi$
$701$	−24.5714	−0.928049	−0.464024	+	0.885822i	$0.653595\pi$
$702$	−10.9994	−0.415145
$703$	10.5691	0.398622
$704$	−0.405453	−0.0152811
$705$	−3.75812	−0.141539
$706$	14.7393	0.554721
$707$	−10.0575	−0.378250
$708$	15.4988	0.582481
$709$	44.9640	1.68866	0.844330	−	0.535824i	$-0.179999\pi$
$709$	44.9640	1.68866	0.844330	+	0.535824i	$0.179999\pi$
$710$	−1.19183	−0.0447287
$711$	−16.5464	−0.620538
$712$	−8.83169	−0.330982
$713$	−1.01090	−0.0378584
$714$	−19.5747	−0.732563
$715$	−0.302272	−0.0113043
$716$	−17.7639	−0.663869
$717$	−54.6923	−2.04252
$718$	−36.0624	−1.34584
$719$	20.9362	0.780787	0.390393	−	0.920648i	$-0.372339\pi$
$719$	20.9362	0.780787	0.390393	+	0.920648i	$0.372339\pi$
$720$	0.319147	0.0118939
$721$	0.291941	0.0108724
$722$	−5.95747	−0.221714
$723$	−52.2065	−1.94158
$724$	18.2258	0.677357
$725$	−22.7569	−0.845169
$726$	−23.8056	−0.883507
$727$	−21.7183	−0.805485	−0.402743	−	0.915313i	$-0.631943\pi$
$727$	−21.7183	−0.805485	−0.402743	+	0.915313i	$0.631943\pi$
$728$	−14.9021	−0.552309
$729$	−3.36583	−0.124660
$730$	−2.85837	−0.105793
$731$	8.66907	0.320637
$732$	−15.6740	−0.579330
$733$	−44.2534	−1.63454	−0.817268	−	0.576257i	$-0.804513\pi$
$733$	−44.2534	−1.63454	−0.817268	+	0.576257i	$0.804513\pi$
$734$	−29.3810	−1.08447
$735$	−1.99457	−0.0735708
$736$	1.00000	0.0368605
$737$	0.762332	0.0280809
$738$	−12.3345	−0.454040
$739$	−25.2976	−0.930587	−0.465294	−	0.885156i	$-0.654051\pi$
$739$	−25.2976	−0.930587	−0.465294	+	0.885156i	$0.654051\pi$
$740$	0.369626	0.0135877
$741$	−46.8336	−1.72048
$742$	15.8572	0.582136
$743$	−16.6766	−0.611804	−0.305902	−	0.952063i	$-0.598958\pi$
$743$	−16.6766	−0.611804	−0.305902	+	0.952063i	$0.598958\pi$
$744$	2.22091	0.0814227
$745$	−1.43873	−0.0527111
$746$	−19.2796	−0.705876
$747$	6.24707	0.228568
$748$	1.03441	0.0378219
$749$	−59.8053	−2.18524
$750$	−3.82668	−0.139731
$751$	−9.00991	−0.328776	−0.164388	−	0.986396i	$-0.552565\pi$
$751$	−9.00991	−0.328776	−0.164388	+	0.986396i	$0.552565\pi$
$752$	9.79087	0.357036
$753$	−0.203576	−0.00741873
$754$	−19.5404	−0.711621
$755$	−0.757871	−0.0275817
$756$	9.00224	0.327408
$757$	35.3296	1.28408	0.642038	−	0.766673i	$-0.278089\pi$
$757$	35.3296	1.28408	0.642038	+	0.766673i	$0.278089\pi$
$758$	−35.6077	−1.29333
$759$	−0.890769	−0.0323329
$760$	−0.872821	−0.0316606
$761$	−6.51273	−0.236086	−0.118043	−	0.993008i	$-0.537662\pi$
$761$	−6.51273	−0.236086	−0.118043	+	0.993008i	$0.537662\pi$
$762$	−0.732165	−0.0265236
$763$	9.94024	0.359861
$764$	−12.2561	−0.443409
$765$	−0.814227	−0.0294384
$766$	4.05526	0.146523
$767$	−30.1027	−1.08695
$768$	−2.19697	−0.0792765
$769$	−43.6877	−1.57542	−0.787710	−	0.616046i	$-0.788733\pi$
$769$	−43.6877	−1.57542	−0.787710	+	0.616046i	$0.788733\pi$
$770$	0.247389	0.00891527
$771$	45.7247	1.64673
$772$	−19.9080	−0.716506
$773$	−10.0030	−0.359782	−0.179891	−	0.983687i	$-0.557575\pi$
$773$	−10.0030	−0.359782	−0.179891	+	0.983687i	$0.557575\pi$
$774$	6.20704	0.223107
$775$	−5.02363	−0.180454
$776$	−13.4046	−0.481197
$777$	−16.2322	−0.582328
$778$	−13.7865	−0.494270
$779$	33.7331	1.20861
$780$	−1.63788	−0.0586455
$781$	−2.76586	−0.0989703
$782$	−2.55126	−0.0912328
$783$	11.8042	0.421849
$784$	5.19636	0.185584
$785$	−1.54746	−0.0552313
$786$	2.19697	0.0783635
$787$	−25.0694	−0.893629	−0.446814	−	0.894627i	$-0.647442\pi$
$787$	−25.0694	−0.893629	−0.446814	+	0.894627i	$0.647442\pi$
$788$	−17.2697	−0.615209
$789$	−12.4689	−0.443903
$790$	1.58257	0.0563051
$791$	20.4851	0.728367
$792$	0.740639	0.0263174
$793$	30.4431	1.08107
$794$	−7.29810	−0.259000
$795$	1.74285	0.0618127
$796$	6.17484	0.218861
$797$	27.4388	0.971931	0.485966	−	0.873978i	$-0.338468\pi$
$797$	27.4388	0.971931	0.485966	+	0.873978i	$0.338468\pi$
$798$	38.3301	1.35687
$799$	−24.9790	−0.883694
$800$	4.96948	0.175697
$801$	16.1328	0.570025
$802$	8.20549	0.289746
$803$	−6.63335	−0.234086
$804$	4.13075	0.145680
$805$	−0.610155	−0.0215051
$806$	−4.31359	−0.151940
$807$	−36.6994	−1.29188
$808$	2.87988	0.101314
$809$	11.2292	0.394799	0.197399	−	0.980323i	$-0.436750\pi$
$809$	11.2292	0.394799	0.197399	+	0.980323i	$0.436750\pi$
$810$	1.94687	0.0684061
$811$	−51.1827	−1.79727	−0.898634	−	0.438700i	$-0.855439\pi$
$811$	−51.1827	−1.79727	−0.898634	+	0.438700i	$0.855439\pi$
$812$	15.9925	0.561228
$813$	53.9757	1.89301
$814$	0.857784	0.0300653
$815$	0.418500	0.0146594
$816$	5.60505	0.196216
$817$	−16.9753	−0.593892
$818$	28.8079	1.00725
$819$	27.2216	0.951200
$820$	1.17972	0.0411978
$821$	21.6048	0.754012	0.377006	−	0.926211i	$-0.376954\pi$
$821$	21.6048	0.754012	0.377006	+	0.926211i	$0.376954\pi$
$822$	−37.8130	−1.31888
$823$	−11.5981	−0.404285	−0.202142	−	0.979356i	$-0.564790\pi$
$823$	−11.5981	−0.404285	−0.202142	+	0.979356i	$0.564790\pi$
$824$	−0.0835949	−0.00291217
$825$	−4.42665	−0.154116
$826$	24.6370	0.857232
$827$	−21.2261	−0.738104	−0.369052	−	0.929409i	$-0.620318\pi$
$827$	−21.2261	−0.738104	−0.369052	+	0.929409i	$0.620318\pi$
$828$	−1.82670	−0.0634821
$829$	1.40880	0.0489297	0.0244648	−	0.999701i	$-0.492212\pi$
$829$	1.40880	0.0489297	0.0244648	+	0.999701i	$0.492212\pi$
$830$	−0.597496	−0.0207394
$831$	−53.4018	−1.85249
$832$	4.26710	0.147935
$833$	−13.2572	−0.459336
$834$	23.2475	0.804995
$835$	3.55199	0.122922
$836$	−2.02554	−0.0700547
$837$	2.60581	0.0900698
$838$	16.1270	0.557097
$839$	25.5843	0.883269	0.441634	−	0.897195i	$-0.354399\pi$
$839$	25.5843	0.883269	0.441634	+	0.897195i	$0.354399\pi$
$840$	1.34049	0.0462515
$841$	−8.02972	−0.276887
$842$	−13.0508	−0.449761
$843$	31.2990	1.07799
$844$	15.6689	0.539345
$845$	0.909924	0.0313023
$846$	−17.8849	−0.614897
$847$	−37.8415	−1.30025
$848$	−4.54058	−0.155924
$849$	−65.7211	−2.25554
$850$	−12.6784	−0.434866
$851$	−2.11562	−0.0725226
$852$	−14.9870	−0.513447
$853$	−0.668096	−0.0228752	−0.0114376	−	0.999935i	$-0.503641\pi$
$853$	−0.668096	−0.0228752	−0.0114376	+	0.999935i	$0.503641\pi$
$854$	−24.9156	−0.852594
$855$	1.59438	0.0545266
$856$	17.1248	0.585312
$857$	48.5686	1.65907	0.829535	−	0.558454i	$-0.188605\pi$
$857$	48.5686	1.65907	0.829535	+	0.558454i	$0.188605\pi$
$858$	−3.80100	−0.129764
$859$	−28.9467	−0.987650	−0.493825	−	0.869561i	$-0.664402\pi$
$859$	−28.9467	−0.987650	−0.493825	+	0.869561i	$0.664402\pi$
$860$	−0.593667	−0.0202439
$861$	−51.8079	−1.76561
$862$	−36.4160	−1.24034
$863$	33.4542	1.13880	0.569398	−	0.822062i	$-0.307176\pi$
$863$	33.4542	1.13880	0.569398	+	0.822062i	$0.307176\pi$
$864$	−2.57772	−0.0876958
$865$	−4.28352	−0.145644
$866$	36.4210	1.23763
$867$	23.0486	0.782773
$868$	3.53038	0.119829
$869$	3.67263	0.124585
$870$	1.75773	0.0595926
$871$	−8.02300	−0.271849
$872$	−2.84631	−0.0963881
$873$	24.4861	0.828731
$874$	4.99575	0.168984
$875$	−6.08292	−0.205640
$876$	−35.9433	−1.21441
$877$	8.10401	0.273653	0.136826	−	0.990595i	$-0.456310\pi$
$877$	8.10401	0.273653	0.136826	+	0.990595i	$0.456310\pi$
$878$	−39.4548	−1.33154
$879$	35.0511	1.18225
$880$	−0.0708378	−0.00238794
$881$	16.4877	0.555484	0.277742	−	0.960656i	$-0.410414\pi$
$881$	16.4877	0.555484	0.277742	+	0.960656i	$0.410414\pi$
$882$	−9.49217	−0.319618
$883$	−54.5574	−1.83600	−0.918001	−	0.396578i	$-0.870198\pi$
$883$	−54.5574	−1.83600	−0.918001	+	0.396578i	$0.870198\pi$
$884$	−10.8865	−0.366151
$885$	2.70784	0.0910231
$886$	−21.5241	−0.723115
$887$	−36.7442	−1.23375	−0.616875	−	0.787061i	$-0.711601\pi$
$887$	−36.7442	−1.23375	−0.616875	+	0.787061i	$0.711601\pi$
$888$	4.64797	0.155976
$889$	−1.16386	−0.0390345
$890$	−1.54301	−0.0517218
$891$	4.51807	0.151361
$892$	4.71198	0.157769
$893$	48.9127	1.63680
$894$	−18.0918	−0.605079
$895$	−3.10359	−0.103741
$896$	−3.49233	−0.116671
$897$	9.37470	0.313012
$898$	−39.5870	−1.32104
$899$	4.62923	0.154393
$900$	−9.07772	−0.302591
$901$	11.5842	0.385925
$902$	2.73776	0.0911575
$903$	26.0710	0.867590
$904$	−5.86574	−0.195092
$905$	3.18428	0.105849
$906$	−9.53005	−0.316615
$907$	−5.89661	−0.195794	−0.0978969	−	0.995197i	$-0.531212\pi$
$907$	−5.89661	−0.195794	−0.0978969	+	0.995197i	$0.531212\pi$
$908$	7.59302	0.251983
$909$	−5.26066	−0.174485
$910$	−2.60359	−0.0863081
$911$	42.4825	1.40751	0.703754	−	0.710444i	$-0.251506\pi$
$911$	42.4825	1.40751	0.703754	+	0.710444i	$0.251506\pi$
$912$	−10.9755	−0.363436
$913$	−1.38660	−0.0458897
$914$	15.3869	0.508952
$915$	−2.73846	−0.0905306
$916$	−5.19255	−0.171567
$917$	3.49233	0.115327
$918$	6.57642	0.217054
$919$	−4.91094	−0.161997	−0.0809984	−	0.996714i	$-0.525811\pi$
$919$	−4.91094	−0.161997	−0.0809984	+	0.996714i	$0.525811\pi$
$920$	0.174713	0.00576011
$921$	−46.9117	−1.54579
$922$	−1.49155	−0.0491215
$923$	29.1087	0.958125
$924$	3.11086	0.102340
$925$	−10.5135	−0.345683
$926$	−11.9241	−0.391850
$927$	0.152702	0.00501541
$928$	−4.57933	−0.150324
$929$	−40.2763	−1.32142	−0.660712	−	0.750640i	$-0.729745\pi$
$929$	−40.2763	−1.32142	−0.660712	+	0.750640i	$0.729745\pi$
$930$	0.388022	0.0127238
$931$	25.9597	0.850794
$932$	0.300970	0.00985860
$933$	39.7589	1.30165
$934$	−9.84590	−0.322168
$935$	0.180725	0.00591035
$936$	−7.79469	−0.254777
$937$	45.5468	1.48795	0.743975	−	0.668207i	$-0.232938\pi$
$937$	45.5468	1.48795	0.743975	+	0.668207i	$0.232938\pi$
$938$	6.56628	0.214397
$939$	31.1789	1.01748
$940$	1.71059	0.0557933
$941$	−26.4540	−0.862375	−0.431188	−	0.902262i	$-0.641905\pi$
$941$	−26.4540	−0.862375	−0.431188	+	0.902262i	$0.641905\pi$
$942$	−19.4590	−0.634008
$943$	−6.75236	−0.219887
$944$	−7.05461	−0.229608
$945$	1.57281	0.0511634
$946$	−1.37771	−0.0447933
$947$	−32.9196	−1.06974	−0.534872	−	0.844933i	$-0.679640\pi$
$947$	−32.9196	−1.06974	−0.534872	+	0.844933i	$0.679640\pi$
$948$	19.9004	0.646335
$949$	69.8112	2.26617
$950$	24.8262	0.805469
$951$	36.8275	1.19421
$952$	8.90983	0.288769
$953$	−26.0941	−0.845272	−0.422636	−	0.906299i	$-0.638895\pi$
$953$	−26.0941	−0.845272	−0.422636	+	0.906299i	$0.638895\pi$
$954$	8.29426	0.268537
$955$	−2.14129	−0.0692906
$956$	24.8944	0.805142
$957$	4.07913	0.131859
$958$	31.4220	1.01520
$959$	−60.1079	−1.94098
$960$	−0.383840	−0.0123884
$961$	−29.9781	−0.967035
$962$	−9.02756	−0.291060
$963$	−31.2817	−1.00804
$964$	23.7629	0.765352
$965$	−3.47819	−0.111967
$966$	−7.67256	−0.246860
$967$	−24.8596	−0.799431	−0.399715	−	0.916639i	$-0.630891\pi$
$967$	−24.8596	−0.799431	−0.399715	+	0.916639i	$0.630891\pi$
$968$	10.8356	0.348270
$969$	28.0014	0.899534
$970$	−2.34196	−0.0751957
$971$	33.0345	1.06013	0.530063	−	0.847958i	$-0.322168\pi$
$971$	33.0345	1.06013	0.530063	+	0.847958i	$0.322168\pi$
$972$	16.7483	0.537203
$973$	36.9544	1.18470
$974$	20.8221	0.667182
$975$	46.5873	1.49199
$976$	7.13438	0.228366
$977$	−11.4380	−0.365933	−0.182967	−	0.983119i	$-0.558570\pi$
$977$	−11.4380	−0.365933	−0.182967	+	0.983119i	$0.558570\pi$
$978$	5.26255	0.168278
$979$	−3.58083	−0.114444
$980$	0.907871	0.0290009
$981$	5.19934	0.166002
$982$	−37.4246	−1.19427
$983$	−54.9296	−1.75198	−0.875991	−	0.482328i	$-0.839791\pi$
$983$	−54.9296	−1.75198	−0.875991	+	0.482328i	$0.839791\pi$
$984$	14.8348	0.472915
$985$	−3.01725	−0.0961375
$986$	11.6831	0.372064
$987$	−75.1210	−2.39113
$988$	21.3173	0.678195
$989$	3.39796	0.108049
$990$	0.129399	0.00411257
$991$	55.2418	1.75481	0.877406	−	0.479748i	$-0.159272\pi$
$991$	55.2418	1.75481	0.877406	+	0.479748i	$0.159272\pi$
$992$	−1.01090	−0.0320960
$993$	54.8265	1.73987
$994$	−23.8235	−0.755636
$995$	1.07882	0.0342010
$996$	−7.51338	−0.238071
$997$	−28.6953	−0.908789	−0.454394	−	0.890801i	$-0.650144\pi$
$997$	−28.6953	−0.908789	−0.454394	+	0.890801i	$0.650144\pi$
$998$	15.7518	0.498616
$999$	5.45348	0.172540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.19697 q^{3} +1.00000 q^{4} +0.174713 q^{5} +2.19697 q^{6} +3.49233 q^{7} -1.00000 q^{8} +1.82670 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.19697 q^{3} +1.00000 q^{4} +0.174713 q^{5} +2.19697 q^{6} +3.49233 q^{7} -1.00000 q^{8} +1.82670 q^{9} -0.174713 q^{10} -0.405453 q^{11} -2.19697 q^{12} +4.26710 q^{13} -3.49233 q^{14} -0.383840 q^{15} +1.00000 q^{16} -2.55126 q^{17} -1.82670 q^{18} +4.99575 q^{19} +0.174713 q^{20} -7.67256 q^{21} +0.405453 q^{22} -1.00000 q^{23} +2.19697 q^{24} -4.96948 q^{25} -4.26710 q^{26} +2.57772 q^{27} +3.49233 q^{28} +4.57933 q^{29} +0.383840 q^{30} +1.01090 q^{31} -1.00000 q^{32} +0.890769 q^{33} +2.55126 q^{34} +0.610155 q^{35} +1.82670 q^{36} +2.11562 q^{37} -4.99575 q^{38} -9.37470 q^{39} -0.174713 q^{40} +6.75236 q^{41} +7.67256 q^{42} -3.39796 q^{43} -0.405453 q^{44} +0.319147 q^{45} +1.00000 q^{46} +9.79087 q^{47} -2.19697 q^{48} +5.19636 q^{49} +4.96948 q^{50} +5.60505 q^{51} +4.26710 q^{52} -4.54058 q^{53} -2.57772 q^{54} -0.0708378 q^{55} -3.49233 q^{56} -10.9755 q^{57} -4.57933 q^{58} -7.05461 q^{59} -0.383840 q^{60} +7.13438 q^{61} -1.01090 q^{62} +6.37942 q^{63} +1.00000 q^{64} +0.745517 q^{65} -0.890769 q^{66} -1.88020 q^{67} -2.55126 q^{68} +2.19697 q^{69} -0.610155 q^{70} +6.82167 q^{71} -1.82670 q^{72} +16.3604 q^{73} -2.11562 q^{74} +10.9178 q^{75} +4.99575 q^{76} -1.41597 q^{77} +9.37470 q^{78} -9.05809 q^{79} +0.174713 q^{80} -11.1433 q^{81} -6.75236 q^{82} +3.41988 q^{83} -7.67256 q^{84} -0.445738 q^{85} +3.39796 q^{86} -10.0607 q^{87} +0.405453 q^{88} +8.83169 q^{89} -0.319147 q^{90} +14.9021 q^{91} -1.00000 q^{92} -2.22091 q^{93} -9.79087 q^{94} +0.872821 q^{95} +2.19697 q^{96} +13.4046 q^{97} -5.19636 q^{98} -0.740639 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 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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