LMFDB - Embedded newform 6026.2.a.l.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.53570 q^{3} +1.00000 q^{4} -3.27140 q^{5} +1.53570 q^{6} +1.87914 q^{7} -1.00000 q^{8} -0.641618 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.53570 q^{3} +1.00000 q^{4} -3.27140 q^{5} +1.53570 q^{6} +1.87914 q^{7} -1.00000 q^{8} -0.641618 q^{9} +3.27140 q^{10} +3.02818 q^{11} -1.53570 q^{12} -6.24269 q^{13} -1.87914 q^{14} +5.02390 q^{15} +1.00000 q^{16} +3.72669 q^{17} +0.641618 q^{18} +7.36151 q^{19} -3.27140 q^{20} -2.88580 q^{21} -3.02818 q^{22} -1.00000 q^{23} +1.53570 q^{24} +5.70205 q^{25} +6.24269 q^{26} +5.59244 q^{27} +1.87914 q^{28} -3.73602 q^{29} -5.02390 q^{30} -1.81411 q^{31} -1.00000 q^{32} -4.65038 q^{33} -3.72669 q^{34} -6.14742 q^{35} -0.641618 q^{36} +8.08341 q^{37} -7.36151 q^{38} +9.58692 q^{39} +3.27140 q^{40} +8.26831 q^{41} +2.88580 q^{42} -10.2754 q^{43} +3.02818 q^{44} +2.09899 q^{45} +1.00000 q^{46} -11.3174 q^{47} -1.53570 q^{48} -3.46883 q^{49} -5.70205 q^{50} -5.72309 q^{51} -6.24269 q^{52} +3.78798 q^{53} -5.59244 q^{54} -9.90638 q^{55} -1.87914 q^{56} -11.3051 q^{57} +3.73602 q^{58} +5.85302 q^{59} +5.02390 q^{60} -10.0936 q^{61} +1.81411 q^{62} -1.20569 q^{63} +1.00000 q^{64} +20.4223 q^{65} +4.65038 q^{66} +14.3913 q^{67} +3.72669 q^{68} +1.53570 q^{69} +6.14742 q^{70} -13.2906 q^{71} +0.641618 q^{72} -2.48475 q^{73} -8.08341 q^{74} -8.75666 q^{75} +7.36151 q^{76} +5.69037 q^{77} -9.58692 q^{78} -0.455656 q^{79} -3.27140 q^{80} -6.66347 q^{81} -8.26831 q^{82} -4.22249 q^{83} -2.88580 q^{84} -12.1915 q^{85} +10.2754 q^{86} +5.73742 q^{87} -3.02818 q^{88} -7.83106 q^{89} -2.09899 q^{90} -11.7309 q^{91} -1.00000 q^{92} +2.78593 q^{93} +11.3174 q^{94} -24.0825 q^{95} +1.53570 q^{96} -11.2146 q^{97} +3.46883 q^{98} -1.94293 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.53570	−0.886638	−0.443319	−	0.896364i	$-0.646199\pi$
$3$	−1.53570	−0.886638	−0.443319	+	0.896364i	$0.646199\pi$
$4$	1.00000	0.500000
$5$	−3.27140	−1.46301	−0.731507	−	0.681834i	$-0.761183\pi$
$5$	−3.27140	−1.46301	−0.731507	+	0.681834i	$0.761183\pi$
$6$	1.53570	0.626948
$7$	1.87914	0.710248	0.355124	−	0.934819i	$-0.384439\pi$
$7$	1.87914	0.710248	0.355124	+	0.934819i	$0.384439\pi$
$8$	−1.00000	−0.353553
$9$	−0.641618	−0.213873
$10$	3.27140	1.03451
$11$	3.02818	0.913030	0.456515	−	0.889716i	$-0.349097\pi$
$11$	3.02818	0.913030	0.456515	+	0.889716i	$0.349097\pi$
$12$	−1.53570	−0.443319
$13$	−6.24269	−1.73141	−0.865706	−	0.500553i	$-0.833130\pi$
$13$	−6.24269	−1.73141	−0.865706	+	0.500553i	$0.833130\pi$
$14$	−1.87914	−0.502221
$15$	5.02390	1.29716
$16$	1.00000	0.250000
$17$	3.72669	0.903855	0.451928	−	0.892055i	$-0.350737\pi$
$17$	3.72669	0.903855	0.451928	+	0.892055i	$0.350737\pi$
$18$	0.641618	0.151231
$19$	7.36151	1.68885	0.844423	−	0.535676i	$-0.179943\pi$
$19$	7.36151	1.68885	0.844423	+	0.535676i	$0.179943\pi$
$20$	−3.27140	−0.731507
$21$	−2.88580	−0.629733
$22$	−3.02818	−0.645610
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.53570	0.313474
$25$	5.70205	1.14041
$26$	6.24269	1.22429
$27$	5.59244	1.07627
$28$	1.87914	0.355124
$29$	−3.73602	−0.693762	−0.346881	−	0.937909i	$-0.612759\pi$
$29$	−3.73602	−0.693762	−0.346881	+	0.937909i	$0.612759\pi$
$30$	−5.02390	−0.917234
$31$	−1.81411	−0.325824	−0.162912	−	0.986641i	$-0.552089\pi$
$31$	−1.81411	−0.325824	−0.162912	+	0.986641i	$0.552089\pi$
$32$	−1.00000	−0.176777
$33$	−4.65038	−0.809527
$34$	−3.72669	−0.639122
$35$	−6.14742	−1.03910
$36$	−0.641618	−0.106936
$37$	8.08341	1.32890	0.664452	−	0.747331i	$-0.268665\pi$
$37$	8.08341	1.32890	0.664452	+	0.747331i	$0.268665\pi$
$38$	−7.36151	−1.19420
$39$	9.58692	1.53514
$40$	3.27140	0.517254
$41$	8.26831	1.29129	0.645647	−	0.763636i	$-0.276588\pi$
$41$	8.26831	1.29129	0.645647	+	0.763636i	$0.276588\pi$
$42$	2.88580	0.445289
$43$	−10.2754	−1.56698	−0.783489	−	0.621406i	$-0.786562\pi$
$43$	−10.2754	−1.56698	−0.783489	+	0.621406i	$0.786562\pi$
$44$	3.02818	0.456515
$45$	2.09899	0.312899
$46$	1.00000	0.147442
$47$	−11.3174	−1.65081	−0.825405	−	0.564540i	$-0.809053\pi$
$47$	−11.3174	−1.65081	−0.825405	+	0.564540i	$0.809053\pi$
$48$	−1.53570	−0.221660
$49$	−3.46883	−0.495547
$50$	−5.70205	−0.806392
$51$	−5.72309	−0.801393
$52$	−6.24269	−0.865706
$53$	3.78798	0.520319	0.260160	−	0.965566i	$-0.416225\pi$
$53$	3.78798	0.520319	0.260160	+	0.965566i	$0.416225\pi$
$54$	−5.59244	−0.761035
$55$	−9.90638	−1.33578
$56$	−1.87914	−0.251111
$57$	−11.3051	−1.49740
$58$	3.73602	0.490564
$59$	5.85302	0.761999	0.380999	−	0.924575i	$-0.375580\pi$
$59$	5.85302	0.761999	0.380999	+	0.924575i	$0.375580\pi$
$60$	5.02390	0.648582
$61$	−10.0936	−1.29235	−0.646174	−	0.763190i	$-0.723632\pi$
$61$	−10.0936	−1.29235	−0.646174	+	0.763190i	$0.723632\pi$
$62$	1.81411	0.230392
$63$	−1.20569	−0.151903
$64$	1.00000	0.125000
$65$	20.4223	2.53308
$66$	4.65038	0.572422
$67$	14.3913	1.75818	0.879088	−	0.476660i	$-0.158153\pi$
$67$	14.3913	1.75818	0.879088	+	0.476660i	$0.158153\pi$
$68$	3.72669	0.451928
$69$	1.53570	0.184877
$70$	6.14742	0.734757
$71$	−13.2906	−1.57730	−0.788651	−	0.614841i	$-0.789220\pi$
$71$	−13.2906	−1.57730	−0.788651	+	0.614841i	$0.789220\pi$
$72$	0.641618	0.0756154
$73$	−2.48475	−0.290818	−0.145409	−	0.989372i	$-0.546450\pi$
$73$	−2.48475	−0.290818	−0.145409	+	0.989372i	$0.546450\pi$
$74$	−8.08341	−0.939677
$75$	−8.75666	−1.01113
$76$	7.36151	0.844423
$77$	5.69037	0.648478
$78$	−9.58692	−1.08550
$79$	−0.455656	−0.0512653	−0.0256327	−	0.999671i	$-0.508160\pi$
$79$	−0.455656	−0.0512653	−0.0256327	+	0.999671i	$0.508160\pi$
$80$	−3.27140	−0.365754
$81$	−6.66347	−0.740386
$82$	−8.26831	−0.913082
$83$	−4.22249	−0.463479	−0.231739	−	0.972778i	$-0.574442\pi$
$83$	−4.22249	−0.463479	−0.231739	+	0.972778i	$0.574442\pi$
$84$	−2.88580	−0.314867
$85$	−12.1915	−1.32235
$86$	10.2754	1.10802
$87$	5.73742	0.615116
$88$	−3.02818	−0.322805
$89$	−7.83106	−0.830091	−0.415045	−	0.909801i	$-0.636234\pi$
$89$	−7.83106	−0.830091	−0.415045	+	0.909801i	$0.636234\pi$
$90$	−2.09899	−0.221253
$91$	−11.7309	−1.22973
$92$	−1.00000	−0.104257
$93$	2.78593	0.288888
$94$	11.3174	1.16730
$95$	−24.0825	−2.47081
$96$	1.53570	0.156737
$97$	−11.2146	−1.13867	−0.569335	−	0.822105i	$-0.692799\pi$
$97$	−11.2146	−1.13867	−0.569335	+	0.822105i	$0.692799\pi$
$98$	3.46883	0.350405
$99$	−1.94293	−0.195272
$100$	5.70205	0.570205
$101$	12.7299	1.26667	0.633335	−	0.773878i	$-0.281685\pi$
$101$	12.7299	1.26667	0.633335	+	0.773878i	$0.281685\pi$
$102$	5.72309	0.566670
$103$	13.2455	1.30512	0.652560	−	0.757737i	$-0.273695\pi$
$103$	13.2455	1.30512	0.652560	+	0.757737i	$0.273695\pi$
$104$	6.24269	0.612146
$105$	9.44061	0.921309
$106$	−3.78798	−0.367921
$107$	−16.8848	−1.63231	−0.816157	−	0.577830i	$-0.803900\pi$
$107$	−16.8848	−1.63231	−0.816157	+	0.577830i	$0.803900\pi$
$108$	5.59244	0.538133
$109$	17.2831	1.65542	0.827710	−	0.561156i	$-0.189643\pi$
$109$	17.2831	1.65542	0.827710	+	0.561156i	$0.189643\pi$
$110$	9.90638	0.944536
$111$	−12.4137	−1.17826
$112$	1.87914	0.177562
$113$	2.38059	0.223947	0.111973	−	0.993711i	$-0.464283\pi$
$113$	2.38059	0.223947	0.111973	+	0.993711i	$0.464283\pi$
$114$	11.3051	1.05882
$115$	3.27140	0.305060
$116$	−3.73602	−0.346881
$117$	4.00542	0.370302
$118$	−5.85302	−0.538815
$119$	7.00298	0.641962
$120$	−5.02390	−0.458617
$121$	−1.83013	−0.166376
$122$	10.0936	0.913829
$123$	−12.6977	−1.14491
$124$	−1.81411	−0.162912
$125$	−2.29670	−0.205423
$126$	1.20569	0.107411
$127$	5.81103	0.515646	0.257823	−	0.966192i	$-0.416995\pi$
$127$	5.81103	0.515646	0.257823	+	0.966192i	$0.416995\pi$
$128$	−1.00000	−0.0883883
$129$	15.7799	1.38934
$130$	−20.4223	−1.79116
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−4.65038	−0.404764
$133$	13.8333	1.19950
$134$	−14.3913	−1.24322
$135$	−18.2951	−1.57459
$136$	−3.72669	−0.319561
$137$	−7.25369	−0.619724	−0.309862	−	0.950781i	$-0.600283\pi$
$137$	−7.25369	−0.619724	−0.309862	+	0.950781i	$0.600283\pi$
$138$	−1.53570	−0.130728
$139$	−6.21450	−0.527107	−0.263553	−	0.964645i	$-0.584895\pi$
$139$	−6.21450	−0.527107	−0.263553	+	0.964645i	$0.584895\pi$
$140$	−6.14742	−0.519552
$141$	17.3801	1.46367
$142$	13.2906	1.11532
$143$	−18.9040	−1.58083
$144$	−0.641618	−0.0534682
$145$	12.2220	1.01498
$146$	2.48475	0.205639
$147$	5.32709	0.439371
$148$	8.08341	0.664452
$149$	−8.33092	−0.682496	−0.341248	−	0.939973i	$-0.610850\pi$
$149$	−8.33092	−0.682496	−0.341248	+	0.939973i	$0.610850\pi$
$150$	8.75666	0.714978
$151$	14.5106	1.18085	0.590427	−	0.807091i	$-0.298959\pi$
$151$	14.5106	1.18085	0.590427	+	0.807091i	$0.298959\pi$
$152$	−7.36151	−0.597098
$153$	−2.39111	−0.193310
$154$	−5.69037	−0.458543
$155$	5.93468	0.476685
$156$	9.58692	0.767568
$157$	19.0481	1.52020	0.760101	−	0.649805i	$-0.225149\pi$
$157$	19.0481	1.52020	0.760101	+	0.649805i	$0.225149\pi$
$158$	0.455656	0.0362501
$159$	−5.81721	−0.461335
$160$	3.27140	0.258627
$161$	−1.87914	−0.148097
$162$	6.66347	0.523532
$163$	−13.0279	−1.02042	−0.510210	−	0.860050i	$-0.670432\pi$
$163$	−13.0279	−1.02042	−0.510210	+	0.860050i	$0.670432\pi$
$164$	8.26831	0.645647
$165$	15.2133	1.18435
$166$	4.22249	0.327729
$167$	−18.7028	−1.44727	−0.723635	−	0.690183i	$-0.757530\pi$
$167$	−18.7028	−1.44727	−0.723635	+	0.690183i	$0.757530\pi$
$168$	2.88580	0.222644
$169$	25.9712	1.99779
$170$	12.1915	0.935045
$171$	−4.72328	−0.361198
$172$	−10.2754	−0.783489
$173$	−20.6579	−1.57059	−0.785295	−	0.619122i	$-0.787489\pi$
$173$	−20.6579	−1.57059	−0.785295	+	0.619122i	$0.787489\pi$
$174$	−5.73742	−0.434952
$175$	10.7150	0.809975
$176$	3.02818	0.228258
$177$	−8.98850	−0.675617
$178$	7.83106	0.586963
$179$	13.1236	0.980905	0.490453	−	0.871468i	$-0.336832\pi$
$179$	13.1236	0.980905	0.490453	+	0.871468i	$0.336832\pi$
$180$	2.09899	0.156449
$181$	−14.5535	−1.08175	−0.540875	−	0.841103i	$-0.681907\pi$
$181$	−14.5535	−1.08175	−0.540875	+	0.841103i	$0.681907\pi$
$182$	11.7309	0.869552
$183$	15.5007	1.14585
$184$	1.00000	0.0737210
$185$	−26.4441	−1.94421
$186$	−2.78593	−0.204274
$187$	11.2851	0.825247
$188$	−11.3174	−0.825405
$189$	10.5090	0.764416
$190$	24.0825	1.74712
$191$	−24.5451	−1.77602	−0.888009	−	0.459826i	$-0.847912\pi$
$191$	−24.5451	−1.77602	−0.888009	+	0.459826i	$0.847912\pi$
$192$	−1.53570	−0.110830
$193$	2.92430	0.210495	0.105248	−	0.994446i	$-0.466436\pi$
$193$	2.92430	0.210495	0.105248	+	0.994446i	$0.466436\pi$
$194$	11.2146	0.805162
$195$	−31.3626	−2.24593
$196$	−3.46883	−0.247774
$197$	−8.82764	−0.628943	−0.314472	−	0.949267i	$-0.601827\pi$
$197$	−8.82764	−0.628943	−0.314472	+	0.949267i	$0.601827\pi$
$198$	1.94293	0.138078
$199$	8.32755	0.590325	0.295162	−	0.955447i	$-0.404626\pi$
$199$	8.32755	0.590325	0.295162	+	0.955447i	$0.404626\pi$
$200$	−5.70205	−0.403196
$201$	−22.1007	−1.55887
$202$	−12.7299	−0.895671
$203$	−7.02051	−0.492743
$204$	−5.72309	−0.400696
$205$	−27.0490	−1.88918
$206$	−13.2455	−0.922860
$207$	0.641618	0.0445955
$208$	−6.24269	−0.432853
$209$	22.2920	1.54197
$210$	−9.44061	−0.651464
$211$	22.6487	1.55920	0.779600	−	0.626278i	$-0.215422\pi$
$211$	22.6487	1.55920	0.779600	+	0.626278i	$0.215422\pi$
$212$	3.78798	0.260160
$213$	20.4104	1.39850
$214$	16.8848	1.15422
$215$	33.6148	2.29251
$216$	−5.59244	−0.380517
$217$	−3.40897	−0.231416
$218$	−17.2831	−1.17056
$219$	3.81584	0.257850
$220$	−9.90638	−0.667888
$221$	−23.2646	−1.56495
$222$	12.4137	0.833154
$223$	1.97771	0.132437	0.0662185	−	0.997805i	$-0.478907\pi$
$223$	1.97771	0.132437	0.0662185	+	0.997805i	$0.478907\pi$
$224$	−1.87914	−0.125555
$225$	−3.65854	−0.243903
$226$	−2.38059	−0.158354
$227$	−27.0931	−1.79823	−0.899116	−	0.437711i	$-0.855789\pi$
$227$	−27.0931	−1.79823	−0.899116	+	0.437711i	$0.855789\pi$
$228$	−11.3051	−0.748698
$229$	2.83543	0.187370	0.0936851	−	0.995602i	$-0.470135\pi$
$229$	2.83543	0.187370	0.0936851	+	0.995602i	$0.470135\pi$
$230$	−3.27140	−0.215710
$231$	−8.73872	−0.574966
$232$	3.73602	0.245282
$233$	18.6304	1.22052	0.610258	−	0.792203i	$-0.291066\pi$
$233$	18.6304	1.22052	0.610258	+	0.792203i	$0.291066\pi$
$234$	−4.00542	−0.261843
$235$	37.0237	2.41516
$236$	5.85302	0.380999
$237$	0.699753	0.0454538
$238$	−7.00298	−0.453936
$239$	15.1613	0.980701	0.490350	−	0.871525i	$-0.336869\pi$
$239$	15.1613	0.980701	0.490350	+	0.871525i	$0.336869\pi$
$240$	5.02390	0.324291
$241$	23.1695	1.49248	0.746239	−	0.665678i	$-0.231857\pi$
$241$	23.1695	1.49248	0.746239	+	0.665678i	$0.231857\pi$
$242$	1.83013	0.117646
$243$	−6.54421	−0.419812
$244$	−10.0936	−0.646174
$245$	11.3479	0.724993
$246$	12.6977	0.809574
$247$	−45.9557	−2.92409
$248$	1.81411	0.115196
$249$	6.48449	0.410938
$250$	2.29670	0.145256
$251$	−22.8102	−1.43977	−0.719883	−	0.694095i	$-0.755805\pi$
$251$	−22.8102	−1.43977	−0.719883	+	0.694095i	$0.755805\pi$
$252$	−1.20569	−0.0759514
$253$	−3.02818	−0.190380
$254$	−5.81103	−0.364617
$255$	18.7225	1.17245
$256$	1.00000	0.0625000
$257$	11.2673	0.702837	0.351418	−	0.936218i	$-0.385699\pi$
$257$	11.2673	0.702837	0.351418	+	0.936218i	$0.385699\pi$
$258$	−15.7799	−0.982413
$259$	15.1899	0.943852
$260$	20.4223	1.26654
$261$	2.39710	0.148377
$262$	−1.00000	−0.0617802
$263$	−13.6496	−0.841670	−0.420835	−	0.907137i	$-0.638263\pi$
$263$	−13.6496	−0.841670	−0.420835	+	0.907137i	$0.638263\pi$
$264$	4.65038	0.286211
$265$	−12.3920	−0.761234
$266$	−13.8333	−0.848175
$267$	12.0262	0.735990
$268$	14.3913	0.879088
$269$	23.5701	1.43710	0.718549	−	0.695477i	$-0.244807\pi$
$269$	23.5701	1.43710	0.718549	+	0.695477i	$0.244807\pi$
$270$	18.2951	1.11340
$271$	−5.08465	−0.308870	−0.154435	−	0.988003i	$-0.549356\pi$
$271$	−5.08465	−0.308870	−0.154435	+	0.988003i	$0.549356\pi$
$272$	3.72669	0.225964
$273$	18.0152	1.09033
$274$	7.25369	0.438211
$275$	17.2668	1.04123
$276$	1.53570	0.0924384
$277$	17.7197	1.06467	0.532337	−	0.846533i	$-0.321314\pi$
$277$	17.7197	1.06467	0.532337	+	0.846533i	$0.321314\pi$
$278$	6.21450	0.372721
$279$	1.16397	0.0696848
$280$	6.14742	0.367379
$281$	9.06892	0.541006	0.270503	−	0.962719i	$-0.412810\pi$
$281$	9.06892	0.541006	0.270503	+	0.962719i	$0.412810\pi$
$282$	−17.3801	−1.03497
$283$	30.1574	1.79267	0.896335	−	0.443377i	$-0.146220\pi$
$283$	30.1574	1.79267	0.896335	+	0.443377i	$0.146220\pi$
$284$	−13.2906	−0.788651
$285$	36.9835	2.19071
$286$	18.9040	1.11782
$287$	15.5373	0.917139
$288$	0.641618	0.0378077
$289$	−3.11177	−0.183045
$290$	−12.2220	−0.717702
$291$	17.2223	1.00959
$292$	−2.48475	−0.145409
$293$	16.2894	0.951640	0.475820	−	0.879543i	$-0.342151\pi$
$293$	16.2894	0.951640	0.475820	+	0.879543i	$0.342151\pi$
$294$	−5.32709	−0.310682
$295$	−19.1476	−1.11482
$296$	−8.08341	−0.469839
$297$	16.9349	0.982663
$298$	8.33092	0.482597
$299$	6.24269	0.361024
$300$	−8.75666	−0.505566
$301$	−19.3088	−1.11294
$302$	−14.5106	−0.834990
$303$	−19.5493	−1.12308
$304$	7.36151	0.422212
$305$	33.0201	1.89072
$306$	2.39111	0.136691
$307$	−22.5806	−1.28874	−0.644370	−	0.764714i	$-0.722880\pi$
$307$	−22.5806	−1.28874	−0.644370	+	0.764714i	$0.722880\pi$
$308$	5.69037	0.324239
$309$	−20.3412	−1.15717
$310$	−5.93468	−0.337067
$311$	16.8074	0.953058	0.476529	−	0.879159i	$-0.341895\pi$
$311$	16.8074	0.953058	0.476529	+	0.879159i	$0.341895\pi$
$312$	−9.58692	−0.542752
$313$	10.4870	0.592761	0.296381	−	0.955070i	$-0.404220\pi$
$313$	10.4870	0.592761	0.296381	+	0.955070i	$0.404220\pi$
$314$	−19.0481	−1.07495
$315$	3.94429	0.222236
$316$	−0.455656	−0.0256327
$317$	−27.2855	−1.53251	−0.766254	−	0.642538i	$-0.777881\pi$
$317$	−27.2855	−1.53251	−0.766254	+	0.642538i	$0.777881\pi$
$318$	5.81721	0.326213
$319$	−11.3133	−0.633425
$320$	−3.27140	−0.182877
$321$	25.9300	1.44727
$322$	1.87914	0.104720
$323$	27.4341	1.52647
$324$	−6.66347	−0.370193
$325$	−35.5962	−1.97452
$326$	13.0279	0.721546
$327$	−26.5417	−1.46776
$328$	−8.26831	−0.456541
$329$	−21.2670	−1.17249
$330$	−15.2133	−0.837462
$331$	1.09205	0.0600242	0.0300121	−	0.999550i	$-0.490445\pi$
$331$	1.09205	0.0600242	0.0300121	+	0.999550i	$0.490445\pi$
$332$	−4.22249	−0.231739
$333$	−5.18646	−0.284216
$334$	18.7028	1.02337
$335$	−47.0797	−2.57224
$336$	−2.88580	−0.157433
$337$	−1.73877	−0.0947171	−0.0473586	−	0.998878i	$-0.515080\pi$
$337$	−1.73877	−0.0947171	−0.0473586	+	0.998878i	$0.515080\pi$
$338$	−25.9712	−1.41265
$339$	−3.65587	−0.198560
$340$	−12.1915	−0.661177
$341$	−5.49345	−0.297487
$342$	4.72328	0.255406
$343$	−19.6724	−1.06221
$344$	10.2754	0.554010
$345$	−5.02390	−0.270477
$346$	20.6579	1.11057
$347$	9.88224	0.530507	0.265253	−	0.964179i	$-0.414544\pi$
$347$	9.88224	0.530507	0.265253	+	0.964179i	$0.414544\pi$
$348$	5.73742	0.307558
$349$	−7.49821	−0.401370	−0.200685	−	0.979656i	$-0.564317\pi$
$349$	−7.49821	−0.401370	−0.200685	+	0.979656i	$0.564317\pi$
$350$	−10.7150	−0.572739
$351$	−34.9119	−1.86346
$352$	−3.02818	−0.161402
$353$	8.67233	0.461581	0.230791	−	0.973003i	$-0.425869\pi$
$353$	8.67233	0.461581	0.230791	+	0.973003i	$0.425869\pi$
$354$	8.98850	0.477734
$355$	43.4788	2.30761
$356$	−7.83106	−0.415045
$357$	−10.7545	−0.569188
$358$	−13.1236	−0.693605
$359$	20.3887	1.07607	0.538036	−	0.842922i	$-0.319166\pi$
$359$	20.3887	1.07607	0.538036	+	0.842922i	$0.319166\pi$
$360$	−2.09899	−0.110626
$361$	35.1919	1.85220
$362$	14.5535	0.764913
$363$	2.81054	0.147515
$364$	−11.7309	−0.614866
$365$	8.12861	0.425471
$366$	−15.5007	−0.810235
$367$	−12.0873	−0.630954	−0.315477	−	0.948933i	$-0.602165\pi$
$367$	−12.0873	−0.630954	−0.315477	+	0.948933i	$0.602165\pi$
$368$	−1.00000	−0.0521286
$369$	−5.30510	−0.276172
$370$	26.4441	1.37476
$371$	7.11815	0.369556
$372$	2.78593	0.144444
$373$	3.95441	0.204752	0.102376	−	0.994746i	$-0.467356\pi$
$373$	3.95441	0.204752	0.102376	+	0.994746i	$0.467356\pi$
$374$	−11.2851	−0.583538
$375$	3.52705	0.182136
$376$	11.3174	0.583650
$377$	23.3228	1.20119
$378$	−10.5090	−0.540524
$379$	33.3891	1.71509	0.857543	−	0.514413i	$-0.171990\pi$
$379$	33.3891	1.71509	0.857543	+	0.514413i	$0.171990\pi$
$380$	−24.0825	−1.23540
$381$	−8.92402	−0.457191
$382$	24.5451	1.25583
$383$	−23.4102	−1.19621	−0.598103	−	0.801419i	$-0.704079\pi$
$383$	−23.4102	−1.19621	−0.598103	+	0.801419i	$0.704079\pi$
$384$	1.53570	0.0783685
$385$	−18.6155	−0.948733
$386$	−2.92430	−0.148843
$387$	6.59285	0.335134
$388$	−11.2146	−0.569335
$389$	23.2890	1.18080	0.590400	−	0.807110i	$-0.298970\pi$
$389$	23.2890	1.18080	0.590400	+	0.807110i	$0.298970\pi$
$390$	31.3626	1.58811
$391$	−3.72669	−0.188467
$392$	3.46883	0.175202
$393$	−1.53570	−0.0774659
$394$	8.82764	0.444730
$395$	1.49063	0.0750019
$396$	−1.94293	−0.0976361
$397$	17.4759	0.877089	0.438544	−	0.898710i	$-0.355494\pi$
$397$	17.4759	0.877089	0.438544	+	0.898710i	$0.355494\pi$
$398$	−8.32755	−0.417422
$399$	−21.2439	−1.06352
$400$	5.70205	0.285103
$401$	27.8445	1.39049	0.695244	−	0.718774i	$-0.255296\pi$
$401$	27.8445	1.39049	0.695244	+	0.718774i	$0.255296\pi$
$402$	22.1007	1.10228
$403$	11.3249	0.564135
$404$	12.7299	0.633335
$405$	21.7989	1.08320
$406$	7.02051	0.348422
$407$	24.4780	1.21333
$408$	5.72309	0.283335
$409$	−5.21129	−0.257682	−0.128841	−	0.991665i	$-0.541126\pi$
$409$	−5.21129	−0.257682	−0.128841	+	0.991665i	$0.541126\pi$
$410$	27.0490	1.33585
$411$	11.1395	0.549471
$412$	13.2455	0.652560
$413$	10.9987	0.541209
$414$	−0.641618	−0.0315338
$415$	13.8135	0.678076
$416$	6.24269	0.306073
$417$	9.54362	0.467353
$418$	−22.2920	−1.09034
$419$	22.6555	1.10679	0.553397	−	0.832917i	$-0.313331\pi$
$419$	22.6555	1.10679	0.553397	+	0.832917i	$0.313331\pi$
$420$	9.44061	0.460654
$421$	20.7466	1.01113	0.505563	−	0.862789i	$-0.331285\pi$
$421$	20.7466	1.01113	0.505563	+	0.862789i	$0.331285\pi$
$422$	−22.6487	−1.10252
$423$	7.26144	0.353063
$424$	−3.78798	−0.183961
$425$	21.2498	1.03077
$426$	−20.4104	−0.988886
$427$	−18.9672	−0.917889
$428$	−16.8848	−0.816157
$429$	29.0309	1.40163
$430$	−33.6148	−1.62105
$431$	−7.05692	−0.339920	−0.169960	−	0.985451i	$-0.554364\pi$
$431$	−7.05692	−0.339920	−0.169960	+	0.985451i	$0.554364\pi$
$432$	5.59244	0.269066
$433$	−10.3858	−0.499112	−0.249556	−	0.968360i	$-0.580285\pi$
$433$	−10.3858	−0.499112	−0.249556	+	0.968360i	$0.580285\pi$
$434$	3.40897	0.163636
$435$	−18.7694	−0.899923
$436$	17.2831	0.827710
$437$	−7.36151	−0.352149
$438$	−3.81584	−0.182328
$439$	25.5015	1.21712	0.608559	−	0.793508i	$-0.291748\pi$
$439$	25.5015	1.21712	0.608559	+	0.793508i	$0.291748\pi$
$440$	9.90638	0.472268
$441$	2.22566	0.105984
$442$	23.2646	1.10658
$443$	4.05537	0.192677	0.0963383	−	0.995349i	$-0.469287\pi$
$443$	4.05537	0.192677	0.0963383	+	0.995349i	$0.469287\pi$
$444$	−12.4137	−0.589129
$445$	25.6185	1.21443
$446$	−1.97771	−0.0936471
$447$	12.7938	0.605127
$448$	1.87914	0.0887811
$449$	−14.1547	−0.668002	−0.334001	−	0.942573i	$-0.608399\pi$
$449$	−14.1547	−0.668002	−0.334001	+	0.942573i	$0.608399\pi$
$450$	3.65854	0.172465
$451$	25.0379	1.17899
$452$	2.38059	0.111973
$453$	−22.2839	−1.04699
$454$	27.0931	1.27154
$455$	38.3765	1.79912
$456$	11.3051	0.529410
$457$	20.1520	0.942672	0.471336	−	0.881954i	$-0.343772\pi$
$457$	20.1520	0.942672	0.471336	+	0.881954i	$0.343772\pi$
$458$	−2.83543	−0.132491
$459$	20.8413	0.972789
$460$	3.27140	0.152530
$461$	14.2660	0.664433	0.332217	−	0.943203i	$-0.392203\pi$
$461$	14.2660	0.664433	0.332217	+	0.943203i	$0.392203\pi$
$462$	8.73872	0.406562
$463$	22.4608	1.04384	0.521922	−	0.852993i	$-0.325215\pi$
$463$	22.4608	1.04384	0.521922	+	0.852993i	$0.325215\pi$
$464$	−3.73602	−0.173440
$465$	−9.11390	−0.422647
$466$	−18.6304	−0.863035
$467$	40.8463	1.89014	0.945070	−	0.326869i	$-0.105994\pi$
$467$	40.8463	1.89014	0.945070	+	0.326869i	$0.105994\pi$
$468$	4.00542	0.185151
$469$	27.0433	1.24874
$470$	−37.0237	−1.70778
$471$	−29.2522	−1.34787
$472$	−5.85302	−0.269407
$473$	−31.1156	−1.43070
$474$	−0.699753	−0.0321407
$475$	41.9757	1.92598
$476$	7.00298	0.320981
$477$	−2.43044	−0.111282
$478$	−15.1613	−0.693460
$479$	8.58162	0.392104	0.196052	−	0.980593i	$-0.437188\pi$
$479$	8.58162	0.392104	0.196052	+	0.980593i	$0.437188\pi$
$480$	−5.02390	−0.229308
$481$	−50.4622	−2.30088
$482$	−23.1695	−1.05534
$483$	2.88580	0.131308
$484$	−1.83013	−0.0831879
$485$	36.6874	1.66589
$486$	6.54421	0.296852
$487$	6.16390	0.279313	0.139656	−	0.990200i	$-0.455400\pi$
$487$	6.16390	0.279313	0.139656	+	0.990200i	$0.455400\pi$
$488$	10.0936	0.456914
$489$	20.0069	0.904744
$490$	−11.3479	−0.512647
$491$	12.7792	0.576716	0.288358	−	0.957523i	$-0.406891\pi$
$491$	12.7792	0.576716	0.288358	+	0.957523i	$0.406891\pi$
$492$	−12.6977	−0.572455
$493$	−13.9230	−0.627060
$494$	45.9557	2.06764
$495$	6.35611	0.285686
$496$	−1.81411	−0.0814559
$497$	−24.9749	−1.12028
$498$	−6.48449	−0.290577
$499$	32.6454	1.46141	0.730705	−	0.682693i	$-0.239191\pi$
$499$	32.6454	1.46141	0.730705	+	0.682693i	$0.239191\pi$
$500$	−2.29670	−0.102712
$501$	28.7220	1.28320
$502$	22.8102	1.01807
$503$	−42.3855	−1.88988	−0.944938	−	0.327249i	$-0.893878\pi$
$503$	−42.3855	−1.88988	−0.944938	+	0.327249i	$0.893878\pi$
$504$	1.20569	0.0537057
$505$	−41.6445	−1.85316
$506$	3.02818	0.134619
$507$	−39.8841	−1.77131
$508$	5.81103	0.257823
$509$	15.4637	0.685418	0.342709	−	0.939442i	$-0.388655\pi$
$509$	15.4637	0.685418	0.342709	+	0.939442i	$0.388655\pi$
$510$	−18.7225	−0.829047
$511$	−4.66919	−0.206553
$512$	−1.00000	−0.0441942
$513$	41.1688	1.81765
$514$	−11.2673	−0.496981
$515$	−43.3314	−1.90941
$516$	15.7799	0.694671
$517$	−34.2711	−1.50724
$518$	−15.1899	−0.667404
$519$	31.7243	1.39254
$520$	−20.4223	−0.895579
$521$	−33.2816	−1.45809	−0.729046	−	0.684465i	$-0.760036\pi$
$521$	−33.2816	−1.45809	−0.729046	+	0.684465i	$0.760036\pi$
$522$	−2.39710	−0.104918
$523$	13.7946	0.603196	0.301598	−	0.953435i	$-0.402480\pi$
$523$	13.7946	0.603196	0.301598	+	0.953435i	$0.402480\pi$
$524$	1.00000	0.0436852
$525$	−16.4550	−0.718155
$526$	13.6496	0.595150
$527$	−6.76063	−0.294497
$528$	−4.65038	−0.202382
$529$	1.00000	0.0434783
$530$	12.3920	0.538274
$531$	−3.75541	−0.162971
$532$	13.8333	0.599750
$533$	−51.6165	−2.23576
$534$	−12.0262	−0.520424
$535$	55.2369	2.38810
$536$	−14.3913	−0.621609
$537$	−20.1540	−0.869708
$538$	−23.5701	−1.01618
$539$	−10.5042	−0.452450
$540$	−18.2951	−0.787296
$541$	−7.31878	−0.314659	−0.157329	−	0.987546i	$-0.550288\pi$
$541$	−7.31878	−0.314659	−0.157329	+	0.987546i	$0.550288\pi$
$542$	5.08465	0.218404
$543$	22.3498	0.959121
$544$	−3.72669	−0.159781
$545$	−56.5399	−2.42190
$546$	−18.0152	−0.770978
$547$	26.5372	1.13465	0.567325	−	0.823494i	$-0.307978\pi$
$547$	26.5372	1.13465	0.567325	+	0.823494i	$0.307978\pi$
$548$	−7.25369	−0.309862
$549$	6.47621	0.276398
$550$	−17.2668	−0.736260
$551$	−27.5028	−1.17166
$552$	−1.53570	−0.0653638
$553$	−0.856242	−0.0364111
$554$	−17.7197	−0.752838
$555$	40.6102	1.72381
$556$	−6.21450	−0.263553
$557$	7.50644	0.318058	0.159029	−	0.987274i	$-0.449164\pi$
$557$	7.50644	0.318058	0.159029	+	0.987274i	$0.449164\pi$
$558$	−1.16397	−0.0492746
$559$	64.1459	2.71308
$560$	−6.14742	−0.259776
$561$	−17.3305	−0.731696
$562$	−9.06892	−0.382549
$563$	35.8184	1.50957	0.754784	−	0.655974i	$-0.227742\pi$
$563$	35.8184	1.50957	0.754784	+	0.655974i	$0.227742\pi$
$564$	17.3801	0.731836
$565$	−7.78785	−0.327637
$566$	−30.1574	−1.26761
$567$	−12.5216	−0.525858
$568$	13.2906	0.557660
$569$	−33.1316	−1.38895	−0.694475	−	0.719517i	$-0.744363\pi$
$569$	−33.1316	−1.38895	−0.694475	+	0.719517i	$0.744363\pi$
$570$	−36.9835	−1.54907
$571$	20.4864	0.857329	0.428664	−	0.903464i	$-0.358984\pi$
$571$	20.4864	0.857329	0.428664	+	0.903464i	$0.358984\pi$
$572$	−18.9040	−0.790416
$573$	37.6939	1.57469
$574$	−15.5373	−0.648515
$575$	−5.70205	−0.237792
$576$	−0.641618	−0.0267341
$577$	−13.4155	−0.558494	−0.279247	−	0.960219i	$-0.590085\pi$
$577$	−13.4155	−0.558494	−0.279247	+	0.960219i	$0.590085\pi$
$578$	3.11177	0.129433
$579$	−4.49085	−0.186633
$580$	12.2220	0.507492
$581$	−7.93466	−0.329185
$582$	−17.2223	−0.713887
$583$	11.4707	0.475067
$584$	2.48475	0.102820
$585$	−13.1033	−0.541757
$586$	−16.2894	−0.672911
$587$	6.40667	0.264432	0.132216	−	0.991221i	$-0.457791\pi$
$587$	6.40667	0.264432	0.132216	+	0.991221i	$0.457791\pi$
$588$	5.32709	0.219686
$589$	−13.3546	−0.550266
$590$	19.1476	0.788293
$591$	13.5566	0.557645
$592$	8.08341	0.332226
$593$	22.2372	0.913171	0.456586	−	0.889679i	$-0.349072\pi$
$593$	22.2372	0.913171	0.456586	+	0.889679i	$0.349072\pi$
$594$	−16.9349	−0.694848
$595$	−22.9095	−0.939199
$596$	−8.33092	−0.341248
$597$	−12.7886	−0.523404
$598$	−6.24269	−0.255283
$599$	0.709157	0.0289754	0.0144877	−	0.999895i	$-0.495388\pi$
$599$	0.709157	0.0289754	0.0144877	+	0.999895i	$0.495388\pi$
$600$	8.75666	0.357489
$601$	−3.59164	−0.146506	−0.0732531	−	0.997313i	$-0.523338\pi$
$601$	−3.59164	−0.146506	−0.0732531	+	0.997313i	$0.523338\pi$
$602$	19.3088	0.786970
$603$	−9.23371	−0.376026
$604$	14.5106	0.590427
$605$	5.98710	0.243410
$606$	19.5493	0.794136
$607$	−29.1188	−1.18190	−0.590948	−	0.806710i	$-0.701246\pi$
$607$	−29.1188	−1.18190	−0.590948	+	0.806710i	$0.701246\pi$
$608$	−7.36151	−0.298549
$609$	10.7814	0.436885
$610$	−33.0201	−1.33694
$611$	70.6510	2.85823
$612$	−2.39111	−0.0966550
$613$	−17.6750	−0.713888	−0.356944	−	0.934126i	$-0.616181\pi$
$613$	−17.6750	−0.713888	−0.356944	+	0.934126i	$0.616181\pi$
$614$	22.5806	0.911277
$615$	41.5391	1.67502
$616$	−5.69037	−0.229272
$617$	0.147974	0.00595723	0.00297861	−	0.999996i	$-0.499052\pi$
$617$	0.147974	0.00595723	0.00297861	+	0.999996i	$0.499052\pi$
$618$	20.3412	0.818243
$619$	−34.3898	−1.38224	−0.691121	−	0.722739i	$-0.742883\pi$
$619$	−34.3898	−1.38224	−0.691121	+	0.722739i	$0.742883\pi$
$620$	5.93468	0.238342
$621$	−5.59244	−0.224417
$622$	−16.8074	−0.673914
$623$	−14.7157	−0.589571
$624$	9.58692	0.383784
$625$	−20.9968	−0.839874
$626$	−10.4870	−0.419146
$627$	−34.2338	−1.36717
$628$	19.0481	0.760101
$629$	30.1244	1.20114
$630$	−3.94429	−0.157144
$631$	−38.0064	−1.51301	−0.756506	−	0.653987i	$-0.773095\pi$
$631$	−38.0064	−1.51301	−0.756506	+	0.653987i	$0.773095\pi$
$632$	0.455656	0.0181250
$633$	−34.7816	−1.38245
$634$	27.2855	1.08365
$635$	−19.0102	−0.754397
$636$	−5.81721	−0.230667
$637$	21.6548	0.857996
$638$	11.3133	0.447899
$639$	8.52747	0.337342
$640$	3.27140	0.129313
$641$	−5.30529	−0.209546	−0.104773	−	0.994496i	$-0.533412\pi$
$641$	−5.30529	−0.209546	−0.104773	+	0.994496i	$0.533412\pi$
$642$	−25.9300	−1.02338
$643$	11.4506	0.451567	0.225784	−	0.974177i	$-0.427506\pi$
$643$	11.4506	0.451567	0.225784	+	0.974177i	$0.427506\pi$
$644$	−1.87914	−0.0740485
$645$	−51.6223	−2.03263
$646$	−27.4341	−1.07938
$647$	6.38942	0.251194	0.125597	−	0.992081i	$-0.459915\pi$
$647$	6.38942	0.251194	0.125597	+	0.992081i	$0.459915\pi$
$648$	6.66347	0.261766
$649$	17.7240	0.695728
$650$	35.5962	1.39620
$651$	5.23516	0.205182
$652$	−13.0279	−0.510210
$653$	1.44332	0.0564813	0.0282406	−	0.999601i	$-0.491010\pi$
$653$	1.44332	0.0564813	0.0282406	+	0.999601i	$0.491010\pi$
$654$	26.5417	1.03786
$655$	−3.27140	−0.127824
$656$	8.26831	0.322823
$657$	1.59426	0.0621980
$658$	21.2670	0.829073
$659$	1.89482	0.0738119	0.0369059	−	0.999319i	$-0.488250\pi$
$659$	1.89482	0.0738119	0.0369059	+	0.999319i	$0.488250\pi$
$660$	15.2133	0.592175
$661$	−50.3369	−1.95788	−0.978940	−	0.204149i	$-0.934557\pi$
$661$	−50.3369	−1.95788	−0.978940	+	0.204149i	$0.934557\pi$
$662$	−1.09205	−0.0424435
$663$	35.7275	1.38754
$664$	4.22249	0.163865
$665$	−45.2543	−1.75489
$666$	5.18646	0.200971
$667$	3.73602	0.144659
$668$	−18.7028	−0.723635
$669$	−3.03717	−0.117424
$670$	47.0797	1.81885
$671$	−30.5651	−1.17995
$672$	2.88580	0.111322
$673$	37.2496	1.43587	0.717934	−	0.696111i	$-0.245088\pi$
$673$	37.2496	1.43587	0.717934	+	0.696111i	$0.245088\pi$
$674$	1.73877	0.0669751
$675$	31.8884	1.22739
$676$	25.9712	0.998893
$677$	5.47281	0.210337	0.105169	−	0.994454i	$-0.466462\pi$
$677$	5.47281	0.210337	0.105169	+	0.994454i	$0.466462\pi$
$678$	3.65587	0.140403
$679$	−21.0738	−0.808739
$680$	12.1915	0.467523
$681$	41.6069	1.59438
$682$	5.49345	0.210355
$683$	14.0272	0.536734	0.268367	−	0.963317i	$-0.413516\pi$
$683$	14.0272	0.536734	0.268367	+	0.963317i	$0.413516\pi$
$684$	−4.72328	−0.180599
$685$	23.7297	0.906666
$686$	19.6724	0.751096
$687$	−4.35437	−0.166130
$688$	−10.2754	−0.391744
$689$	−23.6472	−0.900887
$690$	5.02390	0.191256
$691$	−24.3274	−0.925457	−0.462728	−	0.886500i	$-0.653129\pi$
$691$	−24.3274	−0.925457	−0.462728	+	0.886500i	$0.653129\pi$
$692$	−20.6579	−0.785295
$693$	−3.65105	−0.138692
$694$	−9.88224	−0.375125
$695$	20.3301	0.771165
$696$	−5.73742	−0.217476
$697$	30.8134	1.16714
$698$	7.49821	0.283811
$699$	−28.6107	−1.08216
$700$	10.7150	0.404988
$701$	40.9539	1.54681	0.773403	−	0.633914i	$-0.218553\pi$
$701$	40.9539	1.54681	0.773403	+	0.633914i	$0.218553\pi$
$702$	34.9119	1.31766
$703$	59.5061	2.24432
$704$	3.02818	0.114129
$705$	−56.8574	−2.14137
$706$	−8.67233	−0.326387
$707$	23.9212	0.899651
$708$	−8.98850	−0.337809
$709$	−13.4901	−0.506633	−0.253316	−	0.967383i	$-0.581521\pi$
$709$	−13.4901	−0.506633	−0.253316	+	0.967383i	$0.581521\pi$
$710$	−43.4788	−1.63173
$711$	0.292357	0.0109643
$712$	7.83106	0.293481
$713$	1.81411	0.0679389
$714$	10.7545	0.402477
$715$	61.8425	2.31278
$716$	13.1236	0.490453
$717$	−23.2832	−0.869527
$718$	−20.3887	−0.760898
$719$	−12.2476	−0.456758	−0.228379	−	0.973572i	$-0.573343\pi$
$719$	−12.2476	−0.456758	−0.228379	+	0.973572i	$0.573343\pi$
$720$	2.09899	0.0782247
$721$	24.8902	0.926960
$722$	−35.1919	−1.30971
$723$	−35.5815	−1.32329
$724$	−14.5535	−0.540875
$725$	−21.3030	−0.791173
$726$	−2.81054	−0.104309
$727$	−4.59434	−0.170395	−0.0851974	−	0.996364i	$-0.527152\pi$
$727$	−4.59434	−0.170395	−0.0851974	+	0.996364i	$0.527152\pi$
$728$	11.7309	0.434776
$729$	30.0404	1.11261
$730$	−8.12861	−0.300853
$731$	−38.2931	−1.41632
$732$	15.5007	0.572923
$733$	9.09380	0.335887	0.167944	−	0.985797i	$-0.446287\pi$
$733$	9.09380	0.335887	0.167944	+	0.985797i	$0.446287\pi$
$734$	12.0873	0.446152
$735$	−17.4270	−0.642806
$736$	1.00000	0.0368605
$737$	43.5794	1.60527
$738$	5.30510	0.195283
$739$	35.2104	1.29523	0.647617	−	0.761966i	$-0.275766\pi$
$739$	35.2104	1.29523	0.647617	+	0.761966i	$0.275766\pi$
$740$	−26.4441	−0.972103
$741$	70.5742	2.59261
$742$	−7.11815	−0.261315
$743$	29.4105	1.07897	0.539484	−	0.841996i	$-0.318619\pi$
$743$	29.4105	1.07897	0.539484	+	0.841996i	$0.318619\pi$
$744$	−2.78593	−0.102137
$745$	27.2538	0.998501
$746$	−3.95441	−0.144781
$747$	2.70923	0.0991254
$748$	11.2851	0.412624
$749$	−31.7289	−1.15935
$750$	−3.52705	−0.128790
$751$	24.3715	0.889327	0.444664	−	0.895698i	$-0.353323\pi$
$751$	24.3715	0.889327	0.444664	+	0.895698i	$0.353323\pi$
$752$	−11.3174	−0.412703
$753$	35.0297	1.27655
$754$	−23.3228	−0.849368
$755$	−47.4699	−1.72761
$756$	10.5090	0.382208
$757$	9.13120	0.331879	0.165939	−	0.986136i	$-0.446934\pi$
$757$	9.13120	0.331879	0.165939	+	0.986136i	$0.446934\pi$
$758$	−33.3891	−1.21275
$759$	4.65038	0.168798
$760$	24.0825	0.873562
$761$	−22.1282	−0.802146	−0.401073	−	0.916046i	$-0.631363\pi$
$761$	−22.1282	−0.802146	−0.401073	+	0.916046i	$0.631363\pi$
$762$	8.92402	0.323283
$763$	32.4774	1.17576
$764$	−24.5451	−0.888009
$765$	7.82228	0.282815
$766$	23.4102	0.845846
$767$	−36.5386	−1.31933
$768$	−1.53570	−0.0554149
$769$	−9.34571	−0.337015	−0.168507	−	0.985700i	$-0.553895\pi$
$769$	−9.34571	−0.337015	−0.168507	+	0.985700i	$0.553895\pi$
$770$	18.6155	0.670856
$771$	−17.3033	−0.623162
$772$	2.92430	0.105248
$773$	−41.2600	−1.48402	−0.742009	−	0.670390i	$-0.766127\pi$
$773$	−41.2600	−1.48402	−0.742009	+	0.670390i	$0.766127\pi$
$774$	−6.59285	−0.236975
$775$	−10.3442	−0.371573
$776$	11.2146	0.402581
$777$	−23.3271	−0.836855
$778$	−23.2890	−0.834952
$779$	60.8673	2.18080
$780$	−31.3626	−1.12296
$781$	−40.2462	−1.44012
$782$	3.72669	0.133266
$783$	−20.8935	−0.746672
$784$	−3.46883	−0.123887
$785$	−62.3139	−2.22408
$786$	1.53570	0.0547767
$787$	18.7881	0.669723	0.334861	−	0.942267i	$-0.391310\pi$
$787$	18.7881	0.669723	0.334861	+	0.942267i	$0.391310\pi$
$788$	−8.82764	−0.314472
$789$	20.9617	0.746257
$790$	−1.49063	−0.0530344
$791$	4.47346	0.159058
$792$	1.94293	0.0690391
$793$	63.0110	2.23759
$794$	−17.4759	−0.620195
$795$	19.0304	0.674940
$796$	8.32755	0.295162
$797$	−14.0940	−0.499233	−0.249617	−	0.968345i	$-0.580305\pi$
$797$	−14.0940	−0.499233	−0.249617	+	0.968345i	$0.580305\pi$
$798$	21.2439	0.752025
$799$	−42.1764	−1.49209
$800$	−5.70205	−0.201598
$801$	5.02455	0.177534
$802$	−27.8445	−0.983223
$803$	−7.52426	−0.265526
$804$	−22.1007	−0.779433
$805$	6.14742	0.216668
$806$	−11.3249	−0.398904
$807$	−36.1967	−1.27419
$808$	−12.7299	−0.447836
$809$	1.20860	0.0424920	0.0212460	−	0.999774i	$-0.493237\pi$
$809$	1.20860	0.0424920	0.0212460	+	0.999774i	$0.493237\pi$
$810$	−21.7989	−0.765935
$811$	43.1305	1.51452	0.757258	−	0.653116i	$-0.226539\pi$
$811$	43.1305	1.51452	0.757258	+	0.653116i	$0.226539\pi$
$812$	−7.02051	−0.246372
$813$	7.80851	0.273856
$814$	−24.4780	−0.857954
$815$	42.6193	1.49289
$816$	−5.72309	−0.200348
$817$	−75.6422	−2.64639
$818$	5.21129	0.182209
$819$	7.52676	0.263006
$820$	−27.0490	−0.944590
$821$	26.7901	0.934982	0.467491	−	0.883998i	$-0.345158\pi$
$821$	26.7901	0.934982	0.467491	+	0.883998i	$0.345158\pi$
$822$	−11.1395	−0.388535
$823$	−34.3776	−1.19833	−0.599163	−	0.800627i	$-0.704500\pi$
$823$	−34.3776	−1.19833	−0.599163	+	0.800627i	$0.704500\pi$
$824$	−13.2455	−0.461430
$825$	−26.5167	−0.923194
$826$	−10.9987	−0.382692
$827$	−20.6508	−0.718099	−0.359050	−	0.933318i	$-0.616899\pi$
$827$	−20.6508	−0.718099	−0.359050	+	0.933318i	$0.616899\pi$
$828$	0.641618	0.0222978
$829$	10.7490	0.373329	0.186665	−	0.982424i	$-0.440232\pi$
$829$	10.7490	0.373329	0.186665	+	0.982424i	$0.440232\pi$
$830$	−13.8135	−0.479472
$831$	−27.2122	−0.943980
$832$	−6.24269	−0.216426
$833$	−12.9273	−0.447903
$834$	−9.54362	−0.330469
$835$	61.1845	2.11738
$836$	22.2920	0.770984
$837$	−10.1453	−0.350673
$838$	−22.6555	−0.782622
$839$	27.0142	0.932635	0.466318	−	0.884617i	$-0.345580\pi$
$839$	27.0142	0.932635	0.466318	+	0.884617i	$0.345580\pi$
$840$	−9.44061	−0.325732
$841$	−15.0421	−0.518695
$842$	−20.7466	−0.714975
$843$	−13.9272	−0.479677
$844$	22.6487	0.779600
$845$	−84.9622	−2.92279
$846$	−7.26144	−0.249653
$847$	−3.43908	−0.118168
$848$	3.78798	0.130080
$849$	−46.3128	−1.58945
$850$	−21.2498	−0.728862
$851$	−8.08341	−0.277096
$852$	20.4104	0.699248
$853$	20.5594	0.703940	0.351970	−	0.936011i	$-0.385512\pi$
$853$	20.5594	0.703940	0.351970	+	0.936011i	$0.385512\pi$
$854$	18.9672	0.649045
$855$	15.4517	0.528438
$856$	16.8848	0.577110
$857$	−25.5497	−0.872760	−0.436380	−	0.899763i	$-0.643740\pi$
$857$	−25.5497	−0.872760	−0.436380	+	0.899763i	$0.643740\pi$
$858$	−29.0309	−0.991099
$859$	−11.6251	−0.396642	−0.198321	−	0.980137i	$-0.563549\pi$
$859$	−11.6251	−0.396642	−0.198321	+	0.980137i	$0.563549\pi$
$860$	33.6148	1.14626
$861$	−23.8607	−0.813171
$862$	7.05692	0.240360
$863$	3.30525	0.112512	0.0562560	−	0.998416i	$-0.482084\pi$
$863$	3.30525	0.112512	0.0562560	+	0.998416i	$0.482084\pi$
$864$	−5.59244	−0.190259
$865$	67.5802	2.29779
$866$	10.3858	0.352925
$867$	4.77876	0.162295
$868$	−3.40897	−0.115708
$869$	−1.37981	−0.0468068
$870$	18.7694	0.636342
$871$	−89.8404	−3.04413
$872$	−17.2831	−0.585279
$873$	7.19549	0.243530
$874$	7.36151	0.249007
$875$	−4.31582	−0.145901
$876$	3.81584	0.128925
$877$	6.13129	0.207039	0.103519	−	0.994627i	$-0.466990\pi$
$877$	6.13129	0.207039	0.103519	+	0.994627i	$0.466990\pi$
$878$	−25.5015	−0.860633
$879$	−25.0157	−0.843760
$880$	−9.90638	−0.333944
$881$	43.6287	1.46989	0.734944	−	0.678128i	$-0.237209\pi$
$881$	43.6287	1.46989	0.734944	+	0.678128i	$0.237209\pi$
$882$	−2.22566	−0.0749420
$883$	34.4777	1.16027	0.580134	−	0.814521i	$-0.303000\pi$
$883$	34.4777	1.16027	0.580134	+	0.814521i	$0.303000\pi$
$884$	−23.2646	−0.782473
$885$	29.4050	0.988438
$886$	−4.05537	−0.136243
$887$	55.2293	1.85442	0.927209	−	0.374543i	$-0.122200\pi$
$887$	55.2293	1.85442	0.927209	+	0.374543i	$0.122200\pi$
$888$	12.4137	0.416577
$889$	10.9197	0.366237
$890$	−25.6185	−0.858735
$891$	−20.1782	−0.675995
$892$	1.97771	0.0662185
$893$	−83.3131	−2.78797
$894$	−12.7938	−0.427889
$895$	−42.9326	−1.43508
$896$	−1.87914	−0.0627777
$897$	−9.58692	−0.320098
$898$	14.1547	0.472349
$899$	6.77755	0.226044
$900$	−3.65854	−0.121951
$901$	14.1166	0.470293
$902$	−25.0379	−0.833672
$903$	29.6526	0.986778
$904$	−2.38059	−0.0791771
$905$	47.6102	1.58262
$906$	22.2839	0.740334
$907$	25.7548	0.855175	0.427587	−	0.903974i	$-0.359364\pi$
$907$	25.7548	0.855175	0.427587	+	0.903974i	$0.359364\pi$
$908$	−27.0931	−0.899116
$909$	−8.16772	−0.270906
$910$	−38.3765	−1.27217
$911$	−6.74217	−0.223378	−0.111689	−	0.993743i	$-0.535626\pi$
$911$	−6.74217	−0.223378	−0.111689	+	0.993743i	$0.535626\pi$
$912$	−11.3051	−0.374349
$913$	−12.7865	−0.423170
$914$	−20.1520	−0.666570
$915$	−50.7090	−1.67639
$916$	2.83543	0.0936851
$917$	1.87914	0.0620547
$918$	−20.8413	−0.687865
$919$	20.7081	0.683096	0.341548	−	0.939864i	$-0.389049\pi$
$919$	20.7081	0.683096	0.341548	+	0.939864i	$0.389049\pi$
$920$	−3.27140	−0.107855
$921$	34.6770	1.14265
$922$	−14.2660	−0.469825
$923$	82.9690	2.73096
$924$	−8.73872	−0.287483
$925$	46.0920	1.51550
$926$	−22.4608	−0.738109
$927$	−8.49857	−0.279130
$928$	3.73602	0.122641
$929$	−28.5924	−0.938086	−0.469043	−	0.883175i	$-0.655401\pi$
$929$	−28.5924	−0.938086	−0.469043	+	0.883175i	$0.655401\pi$
$930$	9.11390	0.298856
$931$	−25.5358	−0.836903
$932$	18.6304	0.610258
$933$	−25.8111	−0.845018
$934$	−40.8463	−1.33653
$935$	−36.9180	−1.20735
$936$	−4.00542	−0.130921
$937$	−3.71532	−0.121374	−0.0606872	−	0.998157i	$-0.519329\pi$
$937$	−3.71532	−0.121374	−0.0606872	+	0.998157i	$0.519329\pi$
$938$	−27.0433	−0.882994
$939$	−16.1049	−0.525565
$940$	37.0237	1.20758
$941$	−17.1954	−0.560553	−0.280276	−	0.959919i	$-0.590426\pi$
$941$	−17.1954	−0.560553	−0.280276	+	0.959919i	$0.590426\pi$
$942$	29.2522	0.953088
$943$	−8.26831	−0.269253
$944$	5.85302	0.190500
$945$	−34.3791	−1.11835
$946$	31.1156	1.01166
$947$	36.6752	1.19178	0.595892	−	0.803065i	$-0.296799\pi$
$947$	36.6752	1.19178	0.595892	+	0.803065i	$0.296799\pi$
$948$	0.699753	0.0227269
$949$	15.5115	0.503525
$950$	−41.9757	−1.36187
$951$	41.9024	1.35878
$952$	−7.00298	−0.226968
$953$	−30.4517	−0.986427	−0.493213	−	0.869908i	$-0.664178\pi$
$953$	−30.4517	−0.986427	−0.493213	+	0.869908i	$0.664178\pi$
$954$	2.43044	0.0786883
$955$	80.2967	2.59834
$956$	15.1613	0.490350
$957$	17.3739	0.561619
$958$	−8.58162	−0.277260
$959$	−13.6307	−0.440158
$960$	5.02390	0.162146
$961$	−27.7090	−0.893839
$962$	50.4622	1.62697
$963$	10.8336	0.349108
$964$	23.1695	0.746239
$965$	−9.56654	−0.307958
$966$	−2.88580	−0.0928491
$967$	−0.440730	−0.0141729	−0.00708647	−	0.999975i	$-0.502256\pi$
$967$	−0.440730	−0.0141729	−0.00708647	+	0.999975i	$0.502256\pi$
$968$	1.83013	0.0588228
$969$	−42.1306	−1.35343
$970$	−36.6874	−1.17796
$971$	18.8136	0.603759	0.301879	−	0.953346i	$-0.402386\pi$
$971$	18.8136	0.603759	0.301879	+	0.953346i	$0.402386\pi$
$972$	−6.54421	−0.209906
$973$	−11.6779	−0.374377
$974$	−6.16390	−0.197504
$975$	54.6651	1.75069
$976$	−10.0936	−0.323087
$977$	6.77624	0.216791	0.108396	−	0.994108i	$-0.465429\pi$
$977$	6.77624	0.216791	0.108396	+	0.994108i	$0.465429\pi$
$978$	−20.0069	−0.639750
$979$	−23.7138	−0.757898
$980$	11.3479	0.362496
$981$	−11.0891	−0.354049
$982$	−12.7792	−0.407800
$983$	−56.4832	−1.80153	−0.900767	−	0.434303i	$-0.856995\pi$
$983$	−56.4832	−1.80153	−0.900767	+	0.434303i	$0.856995\pi$
$984$	12.6977	0.404787
$985$	28.8787	0.920153
$986$	13.9230	0.443399
$987$	32.6597	1.03957
$988$	−45.9557	−1.46204
$989$	10.2754	0.326737
$990$	−6.35611	−0.202011
$991$	19.0119	0.603933	0.301966	−	0.953319i	$-0.402357\pi$
$991$	19.0119	0.603933	0.301966	+	0.953319i	$0.402357\pi$
$992$	1.81411	0.0575980
$993$	−1.67706	−0.0532198
$994$	24.9749	0.792155
$995$	−27.2427	−0.863653
$996$	6.48449	0.205469
$997$	−34.6110	−1.09614	−0.548071	−	0.836432i	$-0.684638\pi$
$997$	−34.6110	−1.09614	−0.548071	+	0.836432i	$0.684638\pi$
$998$	−32.6454	−1.03337
$999$	45.2060	1.43025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.12	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.53570 q^{3} +1.00000 q^{4} -3.27140 q^{5} +1.53570 q^{6} +1.87914 q^{7} -1.00000 q^{8} -0.641618 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.53570 q^{3} +1.00000 q^{4} -3.27140 q^{5} +1.53570 q^{6} +1.87914 q^{7} -1.00000 q^{8} -0.641618 q^{9} +3.27140 q^{10} +3.02818 q^{11} -1.53570 q^{12} -6.24269 q^{13} -1.87914 q^{14} +5.02390 q^{15} +1.00000 q^{16} +3.72669 q^{17} +0.641618 q^{18} +7.36151 q^{19} -3.27140 q^{20} -2.88580 q^{21} -3.02818 q^{22} -1.00000 q^{23} +1.53570 q^{24} +5.70205 q^{25} +6.24269 q^{26} +5.59244 q^{27} +1.87914 q^{28} -3.73602 q^{29} -5.02390 q^{30} -1.81411 q^{31} -1.00000 q^{32} -4.65038 q^{33} -3.72669 q^{34} -6.14742 q^{35} -0.641618 q^{36} +8.08341 q^{37} -7.36151 q^{38} +9.58692 q^{39} +3.27140 q^{40} +8.26831 q^{41} +2.88580 q^{42} -10.2754 q^{43} +3.02818 q^{44} +2.09899 q^{45} +1.00000 q^{46} -11.3174 q^{47} -1.53570 q^{48} -3.46883 q^{49} -5.70205 q^{50} -5.72309 q^{51} -6.24269 q^{52} +3.78798 q^{53} -5.59244 q^{54} -9.90638 q^{55} -1.87914 q^{56} -11.3051 q^{57} +3.73602 q^{58} +5.85302 q^{59} +5.02390 q^{60} -10.0936 q^{61} +1.81411 q^{62} -1.20569 q^{63} +1.00000 q^{64} +20.4223 q^{65} +4.65038 q^{66} +14.3913 q^{67} +3.72669 q^{68} +1.53570 q^{69} +6.14742 q^{70} -13.2906 q^{71} +0.641618 q^{72} -2.48475 q^{73} -8.08341 q^{74} -8.75666 q^{75} +7.36151 q^{76} +5.69037 q^{77} -9.58692 q^{78} -0.455656 q^{79} -3.27140 q^{80} -6.66347 q^{81} -8.26831 q^{82} -4.22249 q^{83} -2.88580 q^{84} -12.1915 q^{85} +10.2754 q^{86} +5.73742 q^{87} -3.02818 q^{88} -7.83106 q^{89} -2.09899 q^{90} -11.7309 q^{91} -1.00000 q^{92} +2.78593 q^{93} +11.3174 q^{94} -24.0825 q^{95} +1.53570 q^{96} -11.2146 q^{97} +3.46883 q^{98} -1.94293 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 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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