LMFDB - Embedded newform 8027.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53949 q^{2} -2.72406 q^{3} +4.44903 q^{4} -2.80223 q^{5} +6.91773 q^{6} -4.07042 q^{7} -6.21931 q^{8} +4.42048 q^{9} +O(q^{10})$	\(q-2.53949 q^{2} -2.72406 q^{3} +4.44903 q^{4} -2.80223 q^{5} +6.91773 q^{6} -4.07042 q^{7} -6.21931 q^{8} +4.42048 q^{9} +7.11625 q^{10} +2.99898 q^{11} -12.1194 q^{12} +1.87353 q^{13} +10.3368 q^{14} +7.63344 q^{15} +6.89584 q^{16} -0.770033 q^{17} -11.2258 q^{18} +4.38597 q^{19} -12.4672 q^{20} +11.0880 q^{21} -7.61589 q^{22} +1.00000 q^{23} +16.9418 q^{24} +2.85250 q^{25} -4.75783 q^{26} -3.86948 q^{27} -18.1094 q^{28} +6.60985 q^{29} -19.3851 q^{30} -2.52558 q^{31} -5.07333 q^{32} -8.16938 q^{33} +1.95549 q^{34} +11.4062 q^{35} +19.6669 q^{36} -8.76887 q^{37} -11.1381 q^{38} -5.10361 q^{39} +17.4279 q^{40} -12.0148 q^{41} -28.1580 q^{42} -7.51409 q^{43} +13.3425 q^{44} -12.3872 q^{45} -2.53949 q^{46} -8.94719 q^{47} -18.7847 q^{48} +9.56830 q^{49} -7.24391 q^{50} +2.09761 q^{51} +8.33541 q^{52} +2.42046 q^{53} +9.82652 q^{54} -8.40382 q^{55} +25.3152 q^{56} -11.9476 q^{57} -16.7857 q^{58} +9.72280 q^{59} +33.9614 q^{60} +13.9467 q^{61} +6.41370 q^{62} -17.9932 q^{63} -0.907990 q^{64} -5.25007 q^{65} +20.7461 q^{66} -1.90824 q^{67} -3.42590 q^{68} -2.72406 q^{69} -28.9661 q^{70} -14.6824 q^{71} -27.4924 q^{72} -3.52322 q^{73} +22.2685 q^{74} -7.77037 q^{75} +19.5133 q^{76} -12.2071 q^{77} +12.9606 q^{78} -13.5062 q^{79} -19.3237 q^{80} -2.72077 q^{81} +30.5116 q^{82} +8.94914 q^{83} +49.3311 q^{84} +2.15781 q^{85} +19.0820 q^{86} -18.0056 q^{87} -18.6516 q^{88} -3.32611 q^{89} +31.4573 q^{90} -7.62606 q^{91} +4.44903 q^{92} +6.87983 q^{93} +22.7213 q^{94} -12.2905 q^{95} +13.8200 q^{96} -12.7269 q^{97} -24.2986 q^{98} +13.2569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.53949	−1.79569	−0.897847	−	0.440307i	$-0.854869\pi$
$2$	−2.53949	−1.79569	−0.897847	+	0.440307i	$0.854869\pi$
$3$	−2.72406	−1.57273	−0.786367	−	0.617759i	$-0.788041\pi$
$3$	−2.72406	−1.57273	−0.786367	+	0.617759i	$0.788041\pi$
$4$	4.44903	2.22452
$5$	−2.80223	−1.25320	−0.626598	−	0.779343i	$-0.715553\pi$
$5$	−2.80223	−1.25320	−0.626598	+	0.779343i	$0.715553\pi$
$6$	6.91773	2.82415
$7$	−4.07042	−1.53847	−0.769237	−	0.638964i	$-0.779363\pi$
$7$	−4.07042	−1.53847	−0.769237	+	0.638964i	$0.779363\pi$
$8$	−6.21931	−2.19886
$9$	4.42048	1.47349
$10$	7.11625	2.25036
$11$	2.99898	0.904225	0.452113	−	0.891961i	$-0.350670\pi$
$11$	2.99898	0.904225	0.452113	+	0.891961i	$0.350670\pi$
$12$	−12.1194	−3.49858
$13$	1.87353	0.519625	0.259812	−	0.965659i	$-0.416339\pi$
$13$	1.87353	0.519625	0.259812	+	0.965659i	$0.416339\pi$
$14$	10.3368	2.76263
$15$	7.63344	1.97094
$16$	6.89584	1.72396
$17$	−0.770033	−0.186760	−0.0933802	−	0.995631i	$-0.529767\pi$
$17$	−0.770033	−0.186760	−0.0933802	+	0.995631i	$0.529767\pi$
$18$	−11.2258	−2.64595
$19$	4.38597	1.00621	0.503105	−	0.864225i	$-0.332191\pi$
$19$	4.38597	1.00621	0.503105	+	0.864225i	$0.332191\pi$
$20$	−12.4672	−2.78776
$21$	11.0880	2.41961
$22$	−7.61589	−1.62371
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	16.9418	3.45822
$25$	2.85250	0.570500
$26$	−4.75783	−0.933087
$27$	−3.86948	−0.744682
$28$	−18.1094	−3.42236
$29$	6.60985	1.22742	0.613709	−	0.789532i	$-0.289677\pi$
$29$	6.60985	1.22742	0.613709	+	0.789532i	$0.289677\pi$
$30$	−19.3851	−3.53921
$31$	−2.52558	−0.453608	−0.226804	−	0.973940i	$-0.572828\pi$
$31$	−2.52558	−0.453608	−0.226804	+	0.973940i	$0.572828\pi$
$32$	−5.07333	−0.896846
$33$	−8.16938	−1.42211
$34$	1.95549	0.335365
$35$	11.4062	1.92801
$36$	19.6669	3.27781
$37$	−8.76887	−1.44159	−0.720797	−	0.693146i	$-0.756224\pi$
$37$	−8.76887	−1.44159	−0.720797	+	0.693146i	$0.756224\pi$
$38$	−11.1381	−1.80684
$39$	−5.10361	−0.817232
$40$	17.4279	2.75560
$41$	−12.0148	−1.87640	−0.938200	−	0.346093i	$-0.887508\pi$
$41$	−12.0148	−1.87640	−0.938200	+	0.346093i	$0.887508\pi$
$42$	−28.1580	−4.34488
$43$	−7.51409	−1.14589	−0.572944	−	0.819594i	$-0.694199\pi$
$43$	−7.51409	−1.14589	−0.572944	+	0.819594i	$0.694199\pi$
$44$	13.3425	2.01147
$45$	−12.3872	−1.84658
$46$	−2.53949	−0.374428
$47$	−8.94719	−1.30508	−0.652541	−	0.757754i	$-0.726297\pi$
$47$	−8.94719	−1.30508	−0.652541	+	0.757754i	$0.726297\pi$
$48$	−18.7847	−2.71133
$49$	9.56830	1.36690
$50$	−7.24391	−1.02444
$51$	2.09761	0.293725
$52$	8.33541	1.15591
$53$	2.42046	0.332476	0.166238	−	0.986086i	$-0.446838\pi$
$53$	2.42046	0.332476	0.166238	+	0.986086i	$0.446838\pi$
$54$	9.82652	1.33722
$55$	−8.40382	−1.13317
$56$	25.3152	3.38288
$57$	−11.9476	−1.58250
$58$	−16.7857	−2.20407
$59$	9.72280	1.26580	0.632900	−	0.774233i	$-0.281864\pi$
$59$	9.72280	1.26580	0.632900	+	0.774233i	$0.281864\pi$
$60$	33.9614	4.38440
$61$	13.9467	1.78570	0.892848	−	0.450358i	$-0.148704\pi$
$61$	13.9467	1.78570	0.892848	+	0.450358i	$0.148704\pi$
$62$	6.41370	0.814541
$63$	−17.9932	−2.26693
$64$	−0.907990	−0.113499
$65$	−5.25007	−0.651191
$66$	20.7461	2.55367
$67$	−1.90824	−0.233129	−0.116564	−	0.993183i	$-0.537188\pi$
$67$	−1.90824	−0.233129	−0.116564	+	0.993183i	$0.537188\pi$
$68$	−3.42590	−0.415452
$69$	−2.72406	−0.327938
$70$	−28.9661	−3.46211
$71$	−14.6824	−1.74248	−0.871242	−	0.490854i	$-0.836685\pi$
$71$	−14.6824	−1.74248	−0.871242	+	0.490854i	$0.836685\pi$
$72$	−27.4924	−3.24001
$73$	−3.52322	−0.412362	−0.206181	−	0.978514i	$-0.566104\pi$
$73$	−3.52322	−0.412362	−0.206181	+	0.978514i	$0.566104\pi$
$74$	22.2685	2.58866
$75$	−7.77037	−0.897245
$76$	19.5133	2.23833
$77$	−12.2071	−1.39113
$78$	12.9606	1.46750
$79$	−13.5062	−1.51957	−0.759783	−	0.650176i	$-0.774695\pi$
$79$	−13.5062	−1.51957	−0.759783	+	0.650176i	$0.774695\pi$
$80$	−19.3237	−2.16046
$81$	−2.72077	−0.302308
$82$	30.5116	3.36944
$83$	8.94914	0.982296	0.491148	−	0.871076i	$-0.336577\pi$
$83$	8.94914	0.982296	0.491148	+	0.871076i	$0.336577\pi$
$84$	49.3311	5.38246
$85$	2.15781	0.234047
$86$	19.0820	2.05767
$87$	−18.0056	−1.93040
$88$	−18.6516	−1.98826
$89$	−3.32611	−0.352567	−0.176283	−	0.984339i	$-0.556407\pi$
$89$	−3.32611	−0.352567	−0.176283	+	0.984339i	$0.556407\pi$
$90$	31.4573	3.31589
$91$	−7.62606	−0.799428
$92$	4.44903	0.463844
$93$	6.87983	0.713405
$94$	22.7213	2.34353
$95$	−12.2905	−1.26098
$96$	13.8200	1.41050
$97$	−12.7269	−1.29222	−0.646110	−	0.763244i	$-0.723605\pi$
$97$	−12.7269	−1.29222	−0.646110	+	0.763244i	$0.723605\pi$
$98$	−24.2986	−2.45453
$99$	13.2569	1.33237
$100$	12.6909	1.26909
$101$	12.1171	1.20570	0.602848	−	0.797856i	$-0.294033\pi$
$101$	12.1171	1.20570	0.602848	+	0.797856i	$0.294033\pi$
$102$	−5.32688	−0.527440
$103$	17.9436	1.76803	0.884015	−	0.467458i	$-0.154830\pi$
$103$	17.9436	1.76803	0.884015	+	0.467458i	$0.154830\pi$
$104$	−11.6521	−1.14258
$105$	−31.0713	−3.03225
$106$	−6.14674	−0.597025
$107$	16.4173	1.58712	0.793561	−	0.608491i	$-0.208225\pi$
$107$	16.4173	1.58712	0.793561	+	0.608491i	$0.208225\pi$
$108$	−17.2155	−1.65656
$109$	−11.4688	−1.09851	−0.549255	−	0.835655i	$-0.685088\pi$
$109$	−11.4688	−1.09851	−0.549255	+	0.835655i	$0.685088\pi$
$110$	21.3415	2.03483
$111$	23.8869	2.26725
$112$	−28.0689	−2.65227
$113$	4.33876	0.408156	0.204078	−	0.978955i	$-0.434580\pi$
$113$	4.33876	0.408156	0.204078	+	0.978955i	$0.434580\pi$
$114$	30.3409	2.84169
$115$	−2.80223	−0.261309
$116$	29.4074	2.73041
$117$	8.28192	0.765664
$118$	−24.6910	−2.27299
$119$	3.13436	0.287326
$120$	−47.4747	−4.33383
$121$	−2.00614	−0.182376
$122$	−35.4177	−3.20656
$123$	32.7291	2.95108
$124$	−11.2364	−1.00906
$125$	6.01780	0.538248
$126$	45.6937	4.07072
$127$	4.35061	0.386054	0.193027	−	0.981193i	$-0.438170\pi$
$127$	4.35061	0.386054	0.193027	+	0.981193i	$0.438170\pi$
$128$	12.4525	1.10065
$129$	20.4688	1.80218
$130$	13.3325	1.16934
$131$	11.9854	1.04717	0.523585	−	0.851974i	$-0.324594\pi$
$131$	11.9854	1.04717	0.523585	+	0.851974i	$0.324594\pi$
$132$	−36.3459	−3.16350
$133$	−17.8527	−1.54803
$134$	4.84597	0.418628
$135$	10.8432	0.933232
$136$	4.78907	0.410660
$137$	13.9091	1.18833	0.594166	−	0.804342i	$-0.297482\pi$
$137$	13.9091	1.18833	0.594166	+	0.804342i	$0.297482\pi$
$138$	6.91773	0.588876
$139$	−7.65548	−0.649329	−0.324664	−	0.945829i	$-0.605251\pi$
$139$	−7.65548	−0.649329	−0.324664	+	0.945829i	$0.605251\pi$
$140$	50.7468	4.28889
$141$	24.3726	2.05255
$142$	37.2860	3.12897
$143$	5.61868	0.469858
$144$	30.4829	2.54025
$145$	−18.5223	−1.53819
$146$	8.94720	0.740475
$147$	−26.0646	−2.14977
$148$	−39.0130	−3.20685
$149$	2.04256	0.167333	0.0836663	−	0.996494i	$-0.473337\pi$
$149$	2.04256	0.167333	0.0836663	+	0.996494i	$0.473337\pi$
$150$	19.7328	1.61118
$151$	13.7482	1.11881	0.559405	−	0.828894i	$-0.311029\pi$
$151$	13.7482	1.11881	0.559405	+	0.828894i	$0.311029\pi$
$152$	−27.2777	−2.21251
$153$	−3.40392	−0.275190
$154$	30.9998	2.49804
$155$	7.07727	0.568460
$156$	−22.7061	−1.81795
$157$	−0.128169	−0.0102290	−0.00511451	−	0.999987i	$-0.501628\pi$
$157$	−0.128169	−0.0102290	−0.00511451	+	0.999987i	$0.501628\pi$
$158$	34.2989	2.72868
$159$	−6.59347	−0.522896
$160$	14.2166	1.12392
$161$	−4.07042	−0.320794
$162$	6.90938	0.542852
$163$	20.8124	1.63015	0.815076	−	0.579354i	$-0.196695\pi$
$163$	20.8124	1.63015	0.815076	+	0.579354i	$0.196695\pi$
$164$	−53.4544	−4.17408
$165$	22.8925	1.78218
$166$	−22.7263	−1.76390
$167$	−19.9700	−1.54533	−0.772663	−	0.634816i	$-0.781076\pi$
$167$	−19.9700	−1.54533	−0.772663	+	0.634816i	$0.781076\pi$
$168$	−68.9600	−5.32038
$169$	−9.48987	−0.729990
$170$	−5.47975	−0.420277
$171$	19.3881	1.48264
$172$	−33.4305	−2.54905
$173$	−13.3231	−1.01293	−0.506467	−	0.862259i	$-0.669049\pi$
$173$	−13.3231	−1.01293	−0.506467	+	0.862259i	$0.669049\pi$
$174$	45.7251	3.46641
$175$	−11.6109	−0.877698
$176$	20.6805	1.55885
$177$	−26.4855	−1.99077
$178$	8.44663	0.633102
$179$	−6.20647	−0.463893	−0.231947	−	0.972728i	$-0.574510\pi$
$179$	−6.20647	−0.463893	−0.231947	+	0.972728i	$0.574510\pi$
$180$	−55.1112	−4.10774
$181$	6.49355	0.482661	0.241331	−	0.970443i	$-0.422416\pi$
$181$	6.49355	0.482661	0.241331	+	0.970443i	$0.422416\pi$
$182$	19.3663	1.43553
$183$	−37.9917	−2.80843
$184$	−6.21931	−0.458494
$185$	24.5724	1.80660
$186$	−17.4713	−1.28106
$187$	−2.30931	−0.168874
$188$	−39.8063	−2.90318
$189$	15.7504	1.14567
$190$	31.2116	2.26433
$191$	11.5385	0.834894	0.417447	−	0.908701i	$-0.362925\pi$
$191$	11.5385	0.834894	0.417447	+	0.908701i	$0.362925\pi$
$192$	2.47342	0.178503
$193$	−24.0756	−1.73300	−0.866499	−	0.499178i	$-0.833635\pi$
$193$	−24.0756	−1.73300	−0.866499	+	0.499178i	$0.833635\pi$
$194$	32.3199	2.32043
$195$	14.3015	1.02415
$196$	42.5697	3.04069
$197$	12.9170	0.920297	0.460148	−	0.887842i	$-0.347796\pi$
$197$	12.9170	0.920297	0.460148	+	0.887842i	$0.347796\pi$
$198$	−33.6659	−2.39253
$199$	−22.2451	−1.57692	−0.788458	−	0.615089i	$-0.789120\pi$
$199$	−22.2451	−1.57692	−0.788458	+	0.615089i	$0.789120\pi$
$200$	−17.7406	−1.25445
$201$	5.19815	0.366649
$202$	−30.7713	−2.16506
$203$	−26.9048	−1.88835
$204$	9.33235	0.653395
$205$	33.6683	2.35150
$206$	−45.5676	−3.17484
$207$	4.42048	0.307245
$208$	12.9196	0.895812
$209$	13.1534	0.909840
$210$	78.9053	5.44498
$211$	17.6365	1.21415	0.607074	−	0.794645i	$-0.292343\pi$
$211$	17.6365	1.21415	0.607074	+	0.794645i	$0.292343\pi$
$212$	10.7687	0.739598
$213$	39.9958	2.74046
$214$	−41.6917	−2.84999
$215$	21.0562	1.43602
$216$	24.0655	1.63745
$217$	10.2802	0.697864
$218$	29.1249	1.97259
$219$	9.59745	0.648536
$220$	−37.3889	−2.52076
$221$	−1.44268	−0.0970453
$222$	−60.6607	−4.07128
$223$	14.7752	0.989423	0.494712	−	0.869057i	$-0.335274\pi$
$223$	14.7752	0.989423	0.494712	+	0.869057i	$0.335274\pi$
$224$	20.6506	1.37977
$225$	12.6094	0.840628
$226$	−11.0183	−0.732924
$227$	−26.5303	−1.76088	−0.880438	−	0.474161i	$-0.842751\pi$
$227$	−26.5303	−1.76088	−0.880438	+	0.474161i	$0.842751\pi$
$228$	−53.1554	−3.52030
$229$	−27.0924	−1.79032	−0.895160	−	0.445746i	$-0.852939\pi$
$229$	−27.0924	−1.79032	−0.895160	+	0.445746i	$0.852939\pi$
$230$	7.11625	0.469232
$231$	33.2528	2.18787
$232$	−41.1087	−2.69892
$233$	−7.66489	−0.502144	−0.251072	−	0.967968i	$-0.580783\pi$
$233$	−7.66489	−0.502144	−0.251072	+	0.967968i	$0.580783\pi$
$234$	−21.0319	−1.37490
$235$	25.0721	1.63552
$236$	43.2571	2.81580
$237$	36.7917	2.38988
$238$	−7.95968	−0.515949
$239$	−8.84689	−0.572258	−0.286129	−	0.958191i	$-0.592369\pi$
$239$	−8.84689	−0.572258	−0.286129	+	0.958191i	$0.592369\pi$
$240$	52.6389	3.39783
$241$	8.52195	0.548947	0.274473	−	0.961595i	$-0.411496\pi$
$241$	8.52195	0.548947	0.274473	+	0.961595i	$0.411496\pi$
$242$	5.09458	0.327492
$243$	19.0200	1.22013
$244$	62.0495	3.97231
$245$	−26.8126	−1.71299
$246$	−83.1153	−5.29924
$247$	8.21725	0.522851
$248$	15.7074	0.997420
$249$	−24.3780	−1.54489
$250$	−15.2822	−0.966529
$251$	14.7524	0.931162	0.465581	−	0.885005i	$-0.345845\pi$
$251$	14.7524	0.931162	0.465581	+	0.885005i	$0.345845\pi$
$252$	−80.0524	−5.04283
$253$	2.99898	0.188544
$254$	−11.0483	−0.693235
$255$	−5.87800	−0.368094
$256$	−29.8071	−1.86294
$257$	14.5332	0.906557	0.453278	−	0.891369i	$-0.350254\pi$
$257$	14.5332	0.906557	0.453278	+	0.891369i	$0.350254\pi$
$258$	−51.9805	−3.23616
$259$	35.6930	2.21785
$260$	−23.3578	−1.44859
$261$	29.2187	1.80859
$262$	−30.4369	−1.88040
$263$	−4.09336	−0.252407	−0.126204	−	0.992004i	$-0.540279\pi$
$263$	−4.09336	−0.252407	−0.126204	+	0.992004i	$0.540279\pi$
$264$	50.8079	3.12701
$265$	−6.78269	−0.416657
$266$	45.3369	2.77978
$267$	9.06050	0.554494
$268$	−8.48983	−0.518599
$269$	9.08735	0.554065	0.277033	−	0.960861i	$-0.410649\pi$
$269$	9.08735	0.554065	0.277033	+	0.960861i	$0.410649\pi$
$270$	−27.5362	−1.67580
$271$	−14.3007	−0.868708	−0.434354	−	0.900742i	$-0.643023\pi$
$271$	−14.3007	−0.868708	−0.434354	+	0.900742i	$0.643023\pi$
$272$	−5.31002	−0.321967
$273$	20.7738	1.25729
$274$	−35.3220	−2.13388
$275$	8.55458	0.515860
$276$	−12.1194	−0.729503
$277$	22.6976	1.36377	0.681884	−	0.731460i	$-0.261161\pi$
$277$	22.6976	1.36377	0.681884	+	0.731460i	$0.261161\pi$
$278$	19.4410	1.16600
$279$	−11.1643	−0.668389
$280$	−70.9390	−4.23942
$281$	−2.21382	−0.132065	−0.0660326	−	0.997817i	$-0.521034\pi$
$281$	−2.21382	−0.132065	−0.0660326	+	0.997817i	$0.521034\pi$
$282$	−61.8942	−3.68575
$283$	5.00337	0.297419	0.148710	−	0.988881i	$-0.452488\pi$
$283$	5.00337	0.297419	0.148710	+	0.988881i	$0.452488\pi$
$284$	−65.3226	−3.87618
$285$	33.4800	1.98318
$286$	−14.2686	−0.843721
$287$	48.9053	2.88679
$288$	−22.4266	−1.32150
$289$	−16.4070	−0.965121
$290$	47.0373	2.76213
$291$	34.6688	2.03232
$292$	−15.6749	−0.917306
$293$	−1.88780	−0.110286	−0.0551431	−	0.998478i	$-0.517562\pi$
$293$	−1.88780	−0.110286	−0.0551431	+	0.998478i	$0.517562\pi$
$294$	66.1909	3.86033
$295$	−27.2455	−1.58630
$296$	54.5364	3.16986
$297$	−11.6045	−0.673360
$298$	−5.18706	−0.300478
$299$	1.87353	0.108349
$300$	−34.5706	−1.99594
$301$	30.5855	1.76292
$302$	−34.9134	−2.00904
$303$	−33.0077	−1.89624
$304$	30.2449	1.73466
$305$	−39.0820	−2.23783
$306$	8.64423	0.494158
$307$	8.06209	0.460128	0.230064	−	0.973176i	$-0.426106\pi$
$307$	8.06209	0.460128	0.230064	+	0.973176i	$0.426106\pi$
$308$	−54.3097	−3.09458
$309$	−48.8792	−2.78064
$310$	−17.9727	−1.02078
$311$	34.6192	1.96308	0.981538	−	0.191266i	$-0.0612594\pi$
$311$	34.6192	1.96308	0.981538	+	0.191266i	$0.0612594\pi$
$312$	31.7409	1.79698
$313$	12.2967	0.695051	0.347526	−	0.937671i	$-0.387022\pi$
$313$	12.2967	0.695051	0.347526	+	0.937671i	$0.387022\pi$
$314$	0.325485	0.0183682
$315$	50.4211	2.84091
$316$	−60.0896	−3.38030
$317$	25.9615	1.45815	0.729073	−	0.684436i	$-0.239952\pi$
$317$	25.9615	1.45815	0.729073	+	0.684436i	$0.239952\pi$
$318$	16.7441	0.938961
$319$	19.8228	1.10986
$320$	2.54440	0.142236
$321$	−44.7217	−2.49612
$322$	10.3368	0.576048
$323$	−3.37734	−0.187920
$324$	−12.1048	−0.672489
$325$	5.34425	0.296446
$326$	−52.8530	−2.92725
$327$	31.2416	1.72766
$328$	74.7239	4.12594
$329$	36.4188	2.00783
$330$	−58.1354	−3.20025
$331$	20.2555	1.11334	0.556671	−	0.830733i	$-0.312078\pi$
$331$	20.2555	1.11334	0.556671	+	0.830733i	$0.312078\pi$
$332$	39.8150	2.18513
$333$	−38.7627	−2.12418
$334$	50.7138	2.77493
$335$	5.34733	0.292156
$336$	76.4614	4.17131
$337$	6.46456	0.352147	0.176073	−	0.984377i	$-0.443660\pi$
$337$	6.46456	0.352147	0.176073	+	0.984377i	$0.443660\pi$
$338$	24.0995	1.31084
$339$	−11.8190	−0.641921
$340$	9.60017	0.520642
$341$	−7.57416	−0.410164
$342$	−49.2360	−2.66238
$343$	−10.4540	−0.564465
$344$	46.7325	2.51965
$345$	7.63344	0.410970
$346$	33.8339	1.81892
$347$	−17.4739	−0.938049	−0.469024	−	0.883185i	$-0.655394\pi$
$347$	−17.4739	−0.938049	−0.469024	+	0.883185i	$0.655394\pi$
$348$	−80.1075	−4.29421
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	29.4857	1.57608
$351$	−7.24960	−0.386955
$352$	−15.2148	−0.810951
$353$	18.3675	0.977602	0.488801	−	0.872395i	$-0.337434\pi$
$353$	18.3675	0.977602	0.488801	+	0.872395i	$0.337434\pi$
$354$	67.2597	3.57481
$355$	41.1436	2.18367
$356$	−14.7980	−0.784291
$357$	−8.53816	−0.451887
$358$	15.7613	0.833011
$359$	−5.93103	−0.313028	−0.156514	−	0.987676i	$-0.550026\pi$
$359$	−5.93103	−0.313028	−0.156514	+	0.987676i	$0.550026\pi$
$360$	77.0400	4.06036
$361$	0.236697	0.0124577
$362$	−16.4903	−0.866712
$363$	5.46484	0.286830
$364$	−33.9286	−1.77834
$365$	9.87288	0.516770
$366$	96.4797	5.04308
$367$	−13.5077	−0.705095	−0.352548	−	0.935794i	$-0.614685\pi$
$367$	−13.5077	−0.705095	−0.352548	+	0.935794i	$0.614685\pi$
$368$	6.89584	0.359470
$369$	−53.1113	−2.76487
$370$	−62.4015	−3.24410
$371$	−9.85228	−0.511505
$372$	30.6086	1.58698
$373$	−25.4032	−1.31533	−0.657664	−	0.753311i	$-0.728456\pi$
$373$	−25.4032	−1.31533	−0.657664	+	0.753311i	$0.728456\pi$
$374$	5.86448	0.303245
$375$	−16.3928	−0.846521
$376$	55.6453	2.86969
$377$	12.3838	0.637796
$378$	−39.9981	−2.05728
$379$	−10.1251	−0.520091	−0.260046	−	0.965596i	$-0.583738\pi$
$379$	−10.1251	−0.520091	−0.260046	+	0.965596i	$0.583738\pi$
$380$	−54.6808	−2.80507
$381$	−11.8513	−0.607160
$382$	−29.3019	−1.49921
$383$	24.4048	1.24703	0.623515	−	0.781812i	$-0.285704\pi$
$383$	24.4048	1.24703	0.623515	+	0.781812i	$0.285704\pi$
$384$	−33.9213	−1.73104
$385$	34.2071	1.74335
$386$	61.1398	3.11194
$387$	−33.2159	−1.68846
$388$	−56.6224	−2.87457
$389$	−35.0658	−1.77791	−0.888953	−	0.457998i	$-0.848567\pi$
$389$	−35.0658	−1.77791	−0.888953	+	0.457998i	$0.848567\pi$
$390$	−36.3186	−1.83906
$391$	−0.770033	−0.0389422
$392$	−59.5082	−3.00562
$393$	−32.6489	−1.64692
$394$	−32.8026	−1.65257
$395$	37.8475	1.90431
$396$	58.9805	2.96388
$397$	−24.4213	−1.22567	−0.612834	−	0.790211i	$-0.709971\pi$
$397$	−24.4213	−1.22567	−0.612834	+	0.790211i	$0.709971\pi$
$398$	56.4914	2.83166
$399$	48.6318	2.43463
$400$	19.6704	0.983519
$401$	18.0227	0.900013	0.450006	−	0.893025i	$-0.351422\pi$
$401$	18.0227	0.900013	0.450006	+	0.893025i	$0.351422\pi$
$402$	−13.2007	−0.658390
$403$	−4.73176	−0.235706
$404$	53.9094	2.68209
$405$	7.62423	0.378851
$406$	68.3247	3.39090
$407$	−26.2976	−1.30353
$408$	−13.0457	−0.645859
$409$	−5.29026	−0.261587	−0.130793	−	0.991410i	$-0.541752\pi$
$409$	−5.29026	−0.261587	−0.130793	+	0.991410i	$0.541752\pi$
$410$	−85.5005	−4.22257
$411$	−37.8891	−1.86893
$412$	79.8315	3.93301
$413$	−39.5758	−1.94740
$414$	−11.2258	−0.551718
$415$	−25.0776	−1.23101
$416$	−9.50505	−0.466023
$417$	20.8539	1.02122
$418$	−33.4030	−1.63379
$419$	15.1364	0.739461	0.369731	−	0.929139i	$-0.379450\pi$
$419$	15.1364	0.739461	0.369731	+	0.929139i	$0.379450\pi$
$420$	−138.237	−6.74528
$421$	−2.96861	−0.144681	−0.0723406	−	0.997380i	$-0.523047\pi$
$421$	−2.96861	−0.144681	−0.0723406	+	0.997380i	$0.523047\pi$
$422$	−44.7879	−2.18024
$423$	−39.5509	−1.92303
$424$	−15.0536	−0.731067
$425$	−2.19652	−0.106547
$426$	−101.569	−4.92104
$427$	−56.7690	−2.74725
$428$	73.0412	3.53058
$429$	−15.3056	−0.738962
$430$	−53.4722	−2.57866
$431$	−4.88165	−0.235141	−0.117570	−	0.993065i	$-0.537511\pi$
$431$	−4.88165	−0.235141	−0.117570	+	0.993065i	$0.537511\pi$
$432$	−26.6833	−1.28380
$433$	25.0593	1.20427	0.602136	−	0.798393i	$-0.294316\pi$
$433$	25.0593	1.20427	0.602136	+	0.798393i	$0.294316\pi$
$434$	−26.1065	−1.25315
$435$	50.4558	2.41917
$436$	−51.0250	−2.44365
$437$	4.38597	0.209809
$438$	−24.3727	−1.16457
$439$	7.58537	0.362030	0.181015	−	0.983480i	$-0.442062\pi$
$439$	7.58537	0.362030	0.181015	+	0.983480i	$0.442062\pi$
$440$	52.2660	2.49168
$441$	42.2965	2.01412
$442$	3.66368	0.174264
$443$	−12.7314	−0.604887	−0.302443	−	0.953167i	$-0.597802\pi$
$443$	−12.7314	−0.604887	−0.302443	+	0.953167i	$0.597802\pi$
$444$	106.274	5.04353
$445$	9.32052	0.441835
$446$	−37.5216	−1.77670
$447$	−5.56404	−0.263170
$448$	3.69590	0.174615
$449$	26.0762	1.23061	0.615307	−	0.788287i	$-0.289032\pi$
$449$	26.0762	1.23061	0.615307	+	0.788287i	$0.289032\pi$
$450$	−32.0216	−1.50951
$451$	−36.0322	−1.69669
$452$	19.3033	0.907950
$453$	−37.4508	−1.75959
$454$	67.3735	3.16200
$455$	21.3700	1.00184
$456$	74.3060	3.47970
$457$	22.4018	1.04791	0.523957	−	0.851745i	$-0.324455\pi$
$457$	22.4018	1.04791	0.523957	+	0.851745i	$0.324455\pi$
$458$	68.8011	3.21487
$459$	2.97963	0.139077
$460$	−12.4672	−0.581287
$461$	21.1534	0.985210	0.492605	−	0.870253i	$-0.336045\pi$
$461$	21.1534	0.985210	0.492605	+	0.870253i	$0.336045\pi$
$462$	−84.4453	−3.92875
$463$	23.6278	1.09808	0.549039	−	0.835797i	$-0.314994\pi$
$463$	23.6278	1.09808	0.549039	+	0.835797i	$0.314994\pi$
$464$	45.5804	2.11602
$465$	−19.2789	−0.894036
$466$	19.4649	0.901696
$467$	22.8968	1.05954	0.529768	−	0.848142i	$-0.322279\pi$
$467$	22.8968	1.05954	0.529768	+	0.848142i	$0.322279\pi$
$468$	36.8466	1.70323
$469$	7.76733	0.358662
$470$	−63.6704	−2.93690
$471$	0.349140	0.0160875
$472$	−60.4691	−2.78332
$473$	−22.5346	−1.03614
$474$	−93.4322	−4.29149
$475$	12.5110	0.574042
$476$	13.9449	0.639161
$477$	10.6996	0.489901
$478$	22.4666	1.02760
$479$	−19.8722	−0.907982	−0.453991	−	0.891006i	$-0.650000\pi$
$479$	−19.8722	−0.907982	−0.453991	+	0.891006i	$0.650000\pi$
$480$	−38.7269	−1.76763
$481$	−16.4288	−0.749088
$482$	−21.6414	−0.985741
$483$	11.0880	0.504524
$484$	−8.92539	−0.405699
$485$	35.6637	1.61940
$486$	−48.3011	−2.19098
$487$	16.3997	0.743141	0.371570	−	0.928405i	$-0.378819\pi$
$487$	16.3997	0.743141	0.371570	+	0.928405i	$0.378819\pi$
$488$	−86.7391	−3.92649
$489$	−56.6941	−2.56380
$490$	68.0904	3.07601
$491$	5.89805	0.266175	0.133088	−	0.991104i	$-0.457511\pi$
$491$	5.89805	0.266175	0.133088	+	0.991104i	$0.457511\pi$
$492$	145.613	6.56473
$493$	−5.08980	−0.229233
$494$	−20.8677	−0.938881
$495$	−37.1490	−1.66972
$496$	−17.4160	−0.782002
$497$	59.7636	2.68076
$498$	61.9077	2.77415
$499$	−4.15628	−0.186061	−0.0930304	−	0.995663i	$-0.529655\pi$
$499$	−4.15628	−0.186061	−0.0930304	+	0.995663i	$0.529655\pi$
$500$	26.7734	1.19734
$501$	54.3995	2.43039
$502$	−37.4636	−1.67208
$503$	18.6477	0.831459	0.415730	−	0.909488i	$-0.363526\pi$
$503$	18.6477	0.831459	0.415730	+	0.909488i	$0.363526\pi$
$504$	111.905	4.98466
$505$	−33.9549	−1.51097
$506$	−7.61589	−0.338567
$507$	25.8510	1.14808
$508$	19.3560	0.858784
$509$	−13.6520	−0.605114	−0.302557	−	0.953131i	$-0.597840\pi$
$509$	−13.6520	−0.605114	−0.302557	+	0.953131i	$0.597840\pi$
$510$	14.9271	0.660985
$511$	14.3410	0.634407
$512$	50.7899	2.24462
$513$	−16.9714	−0.749306
$514$	−36.9070	−1.62790
$515$	−50.2820	−2.21569
$516$	91.0665	4.00898
$517$	−26.8324	−1.18009
$518$	−90.6421	−3.98259
$519$	36.2928	1.59308
$520$	32.6518	1.43188
$521$	35.3950	1.55068	0.775341	−	0.631542i	$-0.217578\pi$
$521$	35.3950	1.55068	0.775341	+	0.631542i	$0.217578\pi$
$522$	−74.2008	−3.24768
$523$	19.0348	0.832333	0.416167	−	0.909288i	$-0.363373\pi$
$523$	19.0348	0.832333	0.416167	+	0.909288i	$0.363373\pi$
$524$	53.3235	2.32945
$525$	31.6286	1.38039
$526$	10.3951	0.453246
$527$	1.94478	0.0847160
$528$	−56.3347	−2.45165
$529$	1.00000	0.0434783
$530$	17.2246	0.748189
$531$	42.9795	1.86515
$532$	−79.4273	−3.44361
$533$	−22.5102	−0.975024
$534$	−23.0091	−0.995701
$535$	−46.0051	−1.98897
$536$	11.8679	0.512617
$537$	16.9068	0.729581
$538$	−23.0773	−0.994932
$539$	28.6951	1.23599
$540$	48.2417	2.07599
$541$	−10.0063	−0.430204	−0.215102	−	0.976592i	$-0.569008\pi$
$541$	−10.0063	−0.430204	−0.215102	+	0.976592i	$0.569008\pi$
$542$	36.3166	1.55993
$543$	−17.6888	−0.759099
$544$	3.90663	0.167495
$545$	32.1382	1.37665
$546$	−52.7550	−2.25771
$547$	−12.5880	−0.538223	−0.269111	−	0.963109i	$-0.586730\pi$
$547$	−12.5880	−0.538223	−0.269111	+	0.963109i	$0.586730\pi$
$548$	61.8820	2.64347
$549$	61.6513	2.63121
$550$	−21.7243	−0.926327
$551$	28.9906	1.23504
$552$	16.9418	0.721089
$553$	54.9759	2.33781
$554$	−57.6405	−2.44891
$555$	−66.9366	−2.84130
$556$	−34.0595	−1.44444
$557$	22.1712	0.939426	0.469713	−	0.882819i	$-0.344357\pi$
$557$	22.1712	0.939426	0.469713	+	0.882819i	$0.344357\pi$
$558$	28.3517	1.20022
$559$	−14.0779	−0.595432
$560$	78.6557	3.32381
$561$	6.29069	0.265593
$562$	5.62198	0.237149
$563$	39.4458	1.66244	0.831221	−	0.555943i	$-0.187643\pi$
$563$	39.4458	1.66244	0.831221	+	0.555943i	$0.187643\pi$
$564$	108.435	4.56593
$565$	−12.1582	−0.511500
$566$	−12.7060	−0.534074
$567$	11.0747	0.465092
$568$	91.3146	3.83147
$569$	−24.8707	−1.04263	−0.521316	−	0.853364i	$-0.674559\pi$
$569$	−24.8707	−1.04263	−0.521316	+	0.853364i	$0.674559\pi$
$570$	−85.0223	−3.56119
$571$	−33.0639	−1.38368	−0.691840	−	0.722051i	$-0.743200\pi$
$571$	−33.0639	−1.38368	−0.691840	+	0.722051i	$0.743200\pi$
$572$	24.9977	1.04521
$573$	−31.4314	−1.31307
$574$	−124.195	−5.18379
$575$	2.85250	0.118957
$576$	−4.01375	−0.167240
$577$	−6.99339	−0.291138	−0.145569	−	0.989348i	$-0.546501\pi$
$577$	−6.99339	−0.291138	−0.145569	+	0.989348i	$0.546501\pi$
$578$	41.6656	1.73306
$579$	65.5833	2.72555
$580$	−82.4064	−3.42174
$581$	−36.4267	−1.51124
$582$	−88.0412	−3.64942
$583$	7.25890	0.300633
$584$	21.9120	0.906725
$585$	−23.2079	−0.959527
$586$	4.79405	0.198040
$587$	−12.8123	−0.528822	−0.264411	−	0.964410i	$-0.585178\pi$
$587$	−12.8123	−0.528822	−0.264411	+	0.964410i	$0.585178\pi$
$588$	−115.962	−4.78220
$589$	−11.0771	−0.456425
$590$	69.1899	2.84850
$591$	−35.1866	−1.44738
$592$	−60.4687	−2.48525
$593$	29.2806	1.20241	0.601204	−	0.799095i	$-0.294688\pi$
$593$	29.2806	1.20241	0.601204	+	0.799095i	$0.294688\pi$
$594$	29.4695	1.20915
$595$	−8.78319	−0.360076
$596$	9.08740	0.372234
$597$	60.5970	2.48007
$598$	−4.75783	−0.194562
$599$	−4.44189	−0.181491	−0.0907454	−	0.995874i	$-0.528925\pi$
$599$	−4.44189	−0.181491	−0.0907454	+	0.995874i	$0.528925\pi$
$600$	48.3263	1.97291
$601$	−31.9112	−1.30168	−0.650842	−	0.759213i	$-0.725584\pi$
$601$	−31.9112	−1.30168	−0.650842	+	0.759213i	$0.725584\pi$
$602$	−77.6717	−3.16566
$603$	−8.43534	−0.343514
$604$	61.1661	2.48881
$605$	5.62167	0.228553
$606$	83.8228	3.40507
$607$	−16.3177	−0.662315	−0.331157	−	0.943576i	$-0.607439\pi$
$607$	−16.3177	−0.662315	−0.331157	+	0.943576i	$0.607439\pi$
$608$	−22.2514	−0.902415
$609$	73.2903	2.96987
$610$	99.2485	4.01845
$611$	−16.7629	−0.678152
$612$	−15.1442	−0.612166
$613$	16.4243	0.663372	0.331686	−	0.943390i	$-0.392383\pi$
$613$	16.4243	0.663372	0.331686	+	0.943390i	$0.392383\pi$
$614$	−20.4736	−0.826249
$615$	−91.7144	−3.69828
$616$	75.9197	3.05889
$617$	14.5905	0.587391	0.293695	−	0.955899i	$-0.405115\pi$
$617$	14.5905	0.587391	0.293695	+	0.955899i	$0.405115\pi$
$618$	124.129	4.99318
$619$	−7.41471	−0.298023	−0.149011	−	0.988835i	$-0.547609\pi$
$619$	−7.41471	−0.298023	−0.149011	+	0.988835i	$0.547609\pi$
$620$	31.4870	1.26455
$621$	−3.86948	−0.155277
$622$	−87.9154	−3.52508
$623$	13.5386	0.542414
$624$	−35.1937	−1.40887
$625$	−31.1257	−1.24503
$626$	−31.2274	−1.24810
$627$	−35.8306	−1.43094
$628$	−0.570230	−0.0227546
$629$	6.75232	0.269233
$630$	−128.044	−5.10140
$631$	35.0112	1.39377	0.696886	−	0.717182i	$-0.254568\pi$
$631$	35.0112	1.39377	0.696886	+	0.717182i	$0.254568\pi$
$632$	83.9993	3.34131
$633$	−48.0429	−1.90953
$634$	−65.9292	−2.61838
$635$	−12.1914	−0.483801
$636$	−29.3346	−1.16319
$637$	17.9265	0.710274
$638$	−50.3398	−1.99297
$639$	−64.9034	−2.56754
$640$	−34.8948	−1.37934
$641$	4.68263	0.184953	0.0924764	−	0.995715i	$-0.470522\pi$
$641$	4.68263	0.184953	0.0924764	+	0.995715i	$0.470522\pi$
$642$	113.571	4.48227
$643$	−14.7759	−0.582704	−0.291352	−	0.956616i	$-0.594105\pi$
$643$	−14.7759	−0.582704	−0.291352	+	0.956616i	$0.594105\pi$
$644$	−18.1094	−0.713611
$645$	−57.3584	−2.25848
$646$	8.57673	0.337447
$647$	−30.8021	−1.21096	−0.605478	−	0.795862i	$-0.707018\pi$
$647$	−30.8021	−1.21096	−0.605478	+	0.795862i	$0.707018\pi$
$648$	16.9213	0.664732
$649$	29.1584	1.14457
$650$	−13.5717	−0.532326
$651$	−28.0038	−1.09755
$652$	92.5950	3.62630
$653$	0.773755	0.0302794	0.0151397	−	0.999885i	$-0.495181\pi$
$653$	0.773755	0.0302794	0.0151397	+	0.999885i	$0.495181\pi$
$654$	−79.3379	−3.10236
$655$	−33.5859	−1.31231
$656$	−82.8523	−3.23484
$657$	−15.5743	−0.607613
$658$	−92.4853	−3.60545
$659$	12.3570	0.481359	0.240679	−	0.970605i	$-0.422630\pi$
$659$	12.3570	0.481359	0.240679	+	0.970605i	$0.422630\pi$
$660$	101.849	3.96449
$661$	−5.13865	−0.199871	−0.0999353	−	0.994994i	$-0.531864\pi$
$661$	−5.13865	−0.199871	−0.0999353	+	0.994994i	$0.531864\pi$
$662$	−51.4387	−1.99922
$663$	3.92995	0.152627
$664$	−55.6575	−2.15993
$665$	50.0274	1.93998
$666$	98.4376	3.81438
$667$	6.60985	0.255934
$668$	−88.8473	−3.43761
$669$	−40.2486	−1.55610
$670$	−13.5795	−0.524622
$671$	41.8259	1.61467
$672$	−56.2533	−2.17002
$673$	−17.3313	−0.668074	−0.334037	−	0.942560i	$-0.608411\pi$
$673$	−17.3313	−0.668074	−0.334037	+	0.942560i	$0.608411\pi$
$674$	−16.4167	−0.632348
$675$	−11.0377	−0.424841
$676$	−42.2208	−1.62388
$677$	−46.4108	−1.78371	−0.891855	−	0.452321i	$-0.850596\pi$
$677$	−46.4108	−1.78371	−0.891855	+	0.452321i	$0.850596\pi$
$678$	30.0144	1.15269
$679$	51.8038	1.98805
$680$	−13.4201	−0.514637
$681$	72.2700	2.76939
$682$	19.2345	0.736529
$683$	−48.3405	−1.84970	−0.924848	−	0.380337i	$-0.875808\pi$
$683$	−48.3405	−1.84970	−0.924848	+	0.380337i	$0.875808\pi$
$684$	86.2583	3.29817
$685$	−38.9764	−1.48921
$686$	26.5480	1.01361
$687$	73.8014	2.81570
$688$	−51.8160	−1.97547
$689$	4.53481	0.172763
$690$	−19.3851	−0.737977
$691$	25.0059	0.951271	0.475635	−	0.879643i	$-0.342218\pi$
$691$	25.0059	0.951271	0.475635	+	0.879643i	$0.342218\pi$
$692$	−59.2748	−2.25329
$693$	−53.9612	−2.04982
$694$	44.3749	1.68445
$695$	21.4524	0.813736
$696$	111.982	4.24468
$697$	9.25181	0.350437
$698$	−2.53949	−0.0961213
$699$	20.8796	0.789739
$700$	−51.6571	−1.95246
$701$	−27.6303	−1.04358	−0.521790	−	0.853074i	$-0.674736\pi$
$701$	−27.6303	−1.04358	−0.521790	+	0.853074i	$0.674736\pi$
$702$	18.4103	0.694853
$703$	−38.4600	−1.45055
$704$	−2.72304	−0.102628
$705$	−68.2978	−2.57224
$706$	−46.6441	−1.75547
$707$	−49.3216	−1.85493
$708$	−117.835	−4.42850
$709$	14.8630	0.558192	0.279096	−	0.960263i	$-0.409965\pi$
$709$	14.8630	0.558192	0.279096	+	0.960263i	$0.409965\pi$
$710$	−104.484	−3.92121
$711$	−59.7040	−2.23907
$712$	20.6861	0.775244
$713$	−2.52558	−0.0945838
$714$	21.6826	0.811452
$715$	−15.7448	−0.588824
$716$	−27.6128	−1.03194
$717$	24.0994	0.900009
$718$	15.0618	0.562102
$719$	23.0476	0.859529	0.429765	−	0.902941i	$-0.358597\pi$
$719$	23.0476	0.859529	0.429765	+	0.902941i	$0.358597\pi$
$720$	−85.4203	−3.18343
$721$	−73.0377	−2.72007
$722$	−0.601090	−0.0223703
$723$	−23.2143	−0.863348
$724$	28.8900	1.07369
$725$	18.8546	0.700241
$726$	−13.8779	−0.515058
$727$	−35.5594	−1.31882	−0.659412	−	0.751782i	$-0.729195\pi$
$727$	−35.5594	−1.31882	−0.659412	+	0.751782i	$0.729195\pi$
$728$	47.4288	1.75783
$729$	−43.6492	−1.61664
$730$	−25.0721	−0.927961
$731$	5.78610	0.214007
$732$	−169.026	−6.24739
$733$	−14.3265	−0.529160	−0.264580	−	0.964364i	$-0.585233\pi$
$733$	−14.3265	−0.529160	−0.264580	+	0.964364i	$0.585233\pi$
$734$	34.3027	1.26614
$735$	73.0390	2.69408
$736$	−5.07333	−0.187005
$737$	−5.72277	−0.210801
$738$	134.876	4.96485
$739$	22.8639	0.841062	0.420531	−	0.907278i	$-0.361844\pi$
$739$	22.8639	0.841062	0.420531	+	0.907278i	$0.361844\pi$
$740$	109.324	4.01881
$741$	−22.3843	−0.822306
$742$	25.0198	0.918506
$743$	15.9832	0.586369	0.293184	−	0.956056i	$-0.405285\pi$
$743$	15.9832	0.586369	0.293184	+	0.956056i	$0.405285\pi$
$744$	−42.7878	−1.56868
$745$	−5.72371	−0.209701
$746$	64.5114	2.36193
$747$	39.5595	1.44741
$748$	−10.2742	−0.375662
$749$	−66.8253	−2.44174
$750$	41.6295	1.52009
$751$	26.0418	0.950280	0.475140	−	0.879910i	$-0.342397\pi$
$751$	26.0418	0.950280	0.475140	+	0.879910i	$0.342397\pi$
$752$	−61.6984	−2.24991
$753$	−40.1863	−1.46447
$754$	−31.4485	−1.14529
$755$	−38.5256	−1.40209
$756$	70.0741	2.54857
$757$	−38.4565	−1.39773	−0.698863	−	0.715255i	$-0.746310\pi$
$757$	−38.4565	−1.39773	−0.698863	+	0.715255i	$0.746310\pi$
$758$	25.7126	0.933925
$759$	−8.16938	−0.296530
$760$	76.4384	2.77271
$761$	18.1282	0.657147	0.328573	−	0.944478i	$-0.393432\pi$
$761$	18.1282	0.657147	0.328573	+	0.944478i	$0.393432\pi$
$762$	30.0963	1.09027
$763$	46.6827	1.69003
$764$	51.3350	1.85724
$765$	9.53857	0.344868
$766$	−61.9760	−2.23928
$767$	18.2160	0.657741
$768$	81.1961	2.92991
$769$	−9.07516	−0.327259	−0.163629	−	0.986522i	$-0.552320\pi$
$769$	−9.07516	−0.327259	−0.163629	+	0.986522i	$0.552320\pi$
$770$	−86.8687	−3.13053
$771$	−39.5893	−1.42577
$772$	−107.113	−3.85509
$773$	−28.9973	−1.04296	−0.521480	−	0.853264i	$-0.674620\pi$
$773$	−28.9973	−1.04296	−0.521480	+	0.853264i	$0.674620\pi$
$774$	84.3517	3.03196
$775$	−7.20422	−0.258783
$776$	79.1525	2.84141
$777$	−97.2297	−3.48810
$778$	89.0494	3.19258
$779$	−52.6966	−1.88805
$780$	63.6278	2.27824
$781$	−44.0323	−1.57560
$782$	1.95549	0.0699283
$783$	−25.5767	−0.914036
$784$	65.9814	2.35648
$785$	0.359160	0.0128190
$786$	82.9117	2.95736
$787$	−44.6520	−1.59167	−0.795836	−	0.605512i	$-0.792968\pi$
$787$	−44.6520	−1.59167	−0.795836	+	0.605512i	$0.792968\pi$
$788$	57.4681	2.04722
$789$	11.1505	0.396969
$790$	−96.1135	−3.41957
$791$	−17.6606	−0.627937
$792$	−82.4490	−2.92970
$793$	26.1297	0.927892
$794$	62.0177	2.20093
$795$	18.4764	0.655291
$796$	−98.9694	−3.50788
$797$	−14.6003	−0.517169	−0.258585	−	0.965989i	$-0.583256\pi$
$797$	−14.6003	−0.517169	−0.258585	+	0.965989i	$0.583256\pi$
$798$	−123.500	−4.37186
$799$	6.88963	0.243738
$800$	−14.4717	−0.511650
$801$	−14.7030	−0.519505
$802$	−45.7687	−1.61615
$803$	−10.5661	−0.372868
$804$	23.1268	0.815618
$805$	11.4062	0.402017
$806$	12.0163	0.423256
$807$	−24.7544	−0.871398
$808$	−75.3600	−2.65116
$809$	39.8137	1.39978	0.699888	−	0.714253i	$-0.253233\pi$
$809$	39.8137	1.39978	0.699888	+	0.714253i	$0.253233\pi$
$810$	−19.3617	−0.680300
$811$	0.943553	0.0331326	0.0165663	−	0.999863i	$-0.494727\pi$
$811$	0.943553	0.0331326	0.0165663	+	0.999863i	$0.494727\pi$
$812$	−119.701	−4.20066
$813$	38.9560	1.36625
$814$	66.7827	2.34073
$815$	−58.3211	−2.04290
$816$	14.4648	0.506369
$817$	−32.9566	−1.15300
$818$	13.4346	0.469729
$819$	−33.7109	−1.17795
$820$	149.791	5.23095
$821$	−5.59859	−0.195392	−0.0976960	−	0.995216i	$-0.531147\pi$
$821$	−5.59859	−0.195392	−0.0976960	+	0.995216i	$0.531147\pi$
$822$	96.2192	3.35603
$823$	3.99956	0.139416	0.0697080	−	0.997567i	$-0.477793\pi$
$823$	3.99956	0.139416	0.0697080	+	0.997567i	$0.477793\pi$
$824$	−111.597	−3.88765
$825$	−23.3031	−0.811311
$826$	100.503	3.49693
$827$	33.1897	1.15412	0.577060	−	0.816702i	$-0.304200\pi$
$827$	33.1897	1.15412	0.577060	+	0.816702i	$0.304200\pi$
$828$	19.6669	0.683472
$829$	51.6579	1.79415	0.897076	−	0.441876i	$-0.145687\pi$
$829$	51.6579	1.79415	0.897076	+	0.441876i	$0.145687\pi$
$830$	63.6844	2.21052
$831$	−61.8297	−2.14485
$832$	−1.70115	−0.0589767
$833$	−7.36790	−0.255283
$834$	−52.9585	−1.83380
$835$	55.9606	1.93660
$836$	58.5200	2.02396
$837$	9.77269	0.337794
$838$	−38.4388	−1.32785
$839$	−13.0973	−0.452170	−0.226085	−	0.974108i	$-0.572593\pi$
$839$	−13.0973	−0.452170	−0.226085	+	0.974108i	$0.572593\pi$
$840$	193.242	6.66748
$841$	14.6901	0.506554
$842$	7.53877	0.259803
$843$	6.03056	0.207704
$844$	78.4655	2.70089
$845$	26.5928	0.914821
$846$	100.439	3.45317
$847$	8.16583	0.280581
$848$	16.6911	0.573175
$849$	−13.6295	−0.467762
$850$	5.57805	0.191325
$851$	−8.76887	−0.300593
$852$	177.943	6.09621
$853$	−11.5771	−0.396393	−0.198196	−	0.980162i	$-0.563508\pi$
$853$	−11.5771	−0.396393	−0.198196	+	0.980162i	$0.563508\pi$
$854$	144.165	4.93321
$855$	−54.3299	−1.85804
$856$	−102.104	−3.48986
$857$	−8.21262	−0.280538	−0.140269	−	0.990113i	$-0.544797\pi$
$857$	−8.21262	−0.280538	−0.140269	+	0.990113i	$0.544797\pi$
$858$	38.8685	1.32695
$859$	33.7980	1.15317	0.576587	−	0.817036i	$-0.304384\pi$
$859$	33.7980	1.15317	0.576587	+	0.817036i	$0.304384\pi$
$860$	93.6799	3.19446
$861$	−133.221	−4.54016
$862$	12.3969	0.422241
$863$	−39.0876	−1.33056	−0.665279	−	0.746595i	$-0.731688\pi$
$863$	−39.0876	−1.33056	−0.665279	+	0.746595i	$0.731688\pi$
$864$	19.6311	0.667865
$865$	37.3343	1.26941
$866$	−63.6379	−2.16250
$867$	44.6937	1.51788
$868$	45.7369	1.55241
$869$	−40.5048	−1.37403
$870$	−128.132	−4.34409
$871$	−3.57515	−0.121139
$872$	71.3279	2.41547
$873$	−56.2590	−1.90408
$874$	−11.1381	−0.376753
$875$	−24.4949	−0.828080
$876$	42.6994	1.44268
$877$	−19.3687	−0.654034	−0.327017	−	0.945019i	$-0.606043\pi$
$877$	−19.3687	−0.654034	−0.327017	+	0.945019i	$0.606043\pi$
$878$	−19.2630	−0.650095
$879$	5.14246	0.173451
$880$	−57.9514	−1.95354
$881$	14.5312	0.489569	0.244784	−	0.969578i	$-0.421283\pi$
$881$	14.5312	0.489569	0.244784	+	0.969578i	$0.421283\pi$
$882$	−107.412	−3.61674
$883$	8.66726	0.291677	0.145838	−	0.989308i	$-0.453412\pi$
$883$	8.66726	0.291677	0.145838	+	0.989308i	$0.453412\pi$
$884$	−6.41854	−0.215879
$885$	74.2184	2.49482
$886$	32.3313	1.08619
$887$	48.8886	1.64152	0.820760	−	0.571273i	$-0.193550\pi$
$887$	48.8886	1.64152	0.820760	+	0.571273i	$0.193550\pi$
$888$	−148.560	−4.98535
$889$	−17.7088	−0.593933
$890$	−23.6694	−0.793401
$891$	−8.15953	−0.273354
$892$	65.7355	2.20099
$893$	−39.2421	−1.31319
$894$	14.1298	0.472573
$895$	17.3920	0.581349
$896$	−50.6868	−1.69333
$897$	−5.10361	−0.170405
$898$	−66.2205	−2.20981
$899$	−16.6937	−0.556767
$900$	56.0998	1.86999
$901$	−1.86383	−0.0620933
$902$	91.5035	3.04673
$903$	−83.3166	−2.77260
$904$	−26.9841	−0.897478
$905$	−18.1964	−0.604869
$906$	95.1062	3.15969
$907$	36.3492	1.20696	0.603478	−	0.797380i	$-0.293781\pi$
$907$	36.3492	1.20696	0.603478	+	0.797380i	$0.293781\pi$
$908$	−118.034	−3.91710
$909$	53.5634	1.77659
$910$	−54.2690	−1.79900
$911$	−13.6011	−0.450623	−0.225312	−	0.974287i	$-0.572340\pi$
$911$	−13.6011	−0.450623	−0.225312	+	0.974287i	$0.572340\pi$
$912$	−82.3889	−2.72817
$913$	26.8383	0.888217
$914$	−56.8893	−1.88173
$915$	106.462	3.51951
$916$	−120.535	−3.98260
$917$	−48.7856	−1.61104
$918$	−7.56675	−0.249740
$919$	14.5074	0.478555	0.239277	−	0.970951i	$-0.423089\pi$
$919$	14.5074	0.478555	0.239277	+	0.970951i	$0.423089\pi$
$920$	17.4279	0.574582
$921$	−21.9616	−0.723659
$922$	−53.7189	−1.76914
$923$	−27.5080	−0.905437
$924$	147.943	4.86696
$925$	−25.0132	−0.822429
$926$	−60.0027	−1.97181
$927$	79.3192	2.60518
$928$	−33.5339	−1.10080
$929$	−16.1160	−0.528748	−0.264374	−	0.964420i	$-0.585165\pi$
$929$	−16.1160	−0.528748	−0.264374	+	0.964420i	$0.585165\pi$
$930$	48.9586	1.60542
$931$	41.9662	1.37539
$932$	−34.1014	−1.11703
$933$	−94.3047	−3.08740
$934$	−58.1462	−1.90260
$935$	6.47122	0.211632
$936$	−51.5079	−1.68359
$937$	−17.5183	−0.572299	−0.286149	−	0.958185i	$-0.592375\pi$
$937$	−17.5183	−0.572299	−0.286149	+	0.958185i	$0.592375\pi$
$938$	−19.7251	−0.644047
$939$	−33.4969	−1.09313
$940$	111.547	3.63825
$941$	−33.5411	−1.09341	−0.546704	−	0.837326i	$-0.684118\pi$
$941$	−33.5411	−1.09341	−0.546704	+	0.837326i	$0.684118\pi$
$942$	−0.886640	−0.0288883
$943$	−12.0148	−0.391256
$944$	67.0469	2.18219
$945$	−44.1363	−1.43575
$946$	57.2265	1.86059
$947$	−4.44539	−0.144456	−0.0722279	−	0.997388i	$-0.523011\pi$
$947$	−4.44539	−0.144456	−0.0722279	+	0.997388i	$0.523011\pi$
$948$	163.687	5.31632
$949$	−6.60087	−0.214273
$950$	−31.7715	−1.03080
$951$	−70.7207	−2.29328
$952$	−19.4935	−0.631789
$953$	1.55382	0.0503331	0.0251665	−	0.999683i	$-0.491988\pi$
$953$	1.55382	0.0503331	0.0251665	+	0.999683i	$0.491988\pi$
$954$	−27.1716	−0.879713
$955$	−32.3335	−1.04629
$956$	−39.3601	−1.27300
$957$	−53.9984	−1.74552
$958$	50.4652	1.63046
$959$	−56.6157	−1.82822
$960$	−6.93108	−0.223700
$961$	−24.6214	−0.794240
$962$	41.7208	1.34513
$963$	72.5725	2.33862
$964$	37.9144	1.22114
$965$	67.4654	2.17179
$966$	−28.1580	−0.905970
$967$	−32.9989	−1.06117	−0.530587	−	0.847630i	$-0.678029\pi$
$967$	−32.9989	−1.06117	−0.530587	+	0.847630i	$0.678029\pi$
$968$	12.4768	0.401020
$969$	9.20006	0.295549
$970$	−90.5677	−2.90796
$971$	61.0290	1.95852	0.979258	−	0.202619i	$-0.0649452\pi$
$971$	61.0290	1.95852	0.979258	+	0.202619i	$0.0649452\pi$
$972$	84.6205	2.71420
$973$	31.1610	0.998975
$974$	−41.6469	−1.33445
$975$	−14.5580	−0.466230
$976$	96.1744	3.07847
$977$	−44.9672	−1.43863	−0.719314	−	0.694686i	$-0.755544\pi$
$977$	−44.9672	−1.43863	−0.719314	+	0.694686i	$0.755544\pi$
$978$	143.974	4.60379
$979$	−9.97492	−0.318800
$980$	−119.290	−3.81058
$981$	−50.6975	−1.61865
$982$	−14.9781	−0.477969
$983$	17.5984	0.561302	0.280651	−	0.959810i	$-0.409450\pi$
$983$	17.5984	0.561302	0.280651	+	0.959810i	$0.409450\pi$
$984$	−203.552	−6.48901
$985$	−36.1964	−1.15331
$986$	12.9255	0.411632
$987$	−99.2068	−3.15779
$988$	36.5588	1.16309
$989$	−7.51409	−0.238934
$990$	94.3396	2.99831
$991$	−10.2478	−0.325534	−0.162767	−	0.986665i	$-0.552042\pi$
$991$	−10.2478	−0.325534	−0.162767	+	0.986665i	$0.552042\pi$
$992$	12.8131	0.406817
$993$	−55.1771	−1.75099
$994$	−151.769	−4.81383
$995$	62.3360	1.97618
$996$	−108.458	−3.43664
$997$	13.5762	0.429961	0.214981	−	0.976618i	$-0.431031\pi$
$997$	13.5762	0.429961	0.214981	+	0.976618i	$0.431031\pi$
$998$	10.5549	0.334108
$999$	33.9310	1.07353

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.11	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.11	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53949 q^{2} -2.72406 q^{3} +4.44903 q^{4} -2.80223 q^{5} +6.91773 q^{6} -4.07042 q^{7} -6.21931 q^{8} +4.42048 q^{9} +O(q^{10})\)	\(q-2.53949 q^{2} -2.72406 q^{3} +4.44903 q^{4} -2.80223 q^{5} +6.91773 q^{6} -4.07042 q^{7} -6.21931 q^{8} +4.42048 q^{9} +7.11625 q^{10} +2.99898 q^{11} -12.1194 q^{12} +1.87353 q^{13} +10.3368 q^{14} +7.63344 q^{15} +6.89584 q^{16} -0.770033 q^{17} -11.2258 q^{18} +4.38597 q^{19} -12.4672 q^{20} +11.0880 q^{21} -7.61589 q^{22} +1.00000 q^{23} +16.9418 q^{24} +2.85250 q^{25} -4.75783 q^{26} -3.86948 q^{27} -18.1094 q^{28} +6.60985 q^{29} -19.3851 q^{30} -2.52558 q^{31} -5.07333 q^{32} -8.16938 q^{33} +1.95549 q^{34} +11.4062 q^{35} +19.6669 q^{36} -8.76887 q^{37} -11.1381 q^{38} -5.10361 q^{39} +17.4279 q^{40} -12.0148 q^{41} -28.1580 q^{42} -7.51409 q^{43} +13.3425 q^{44} -12.3872 q^{45} -2.53949 q^{46} -8.94719 q^{47} -18.7847 q^{48} +9.56830 q^{49} -7.24391 q^{50} +2.09761 q^{51} +8.33541 q^{52} +2.42046 q^{53} +9.82652 q^{54} -8.40382 q^{55} +25.3152 q^{56} -11.9476 q^{57} -16.7857 q^{58} +9.72280 q^{59} +33.9614 q^{60} +13.9467 q^{61} +6.41370 q^{62} -17.9932 q^{63} -0.907990 q^{64} -5.25007 q^{65} +20.7461 q^{66} -1.90824 q^{67} -3.42590 q^{68} -2.72406 q^{69} -28.9661 q^{70} -14.6824 q^{71} -27.4924 q^{72} -3.52322 q^{73} +22.2685 q^{74} -7.77037 q^{75} +19.5133 q^{76} -12.2071 q^{77} +12.9606 q^{78} -13.5062 q^{79} -19.3237 q^{80} -2.72077 q^{81} +30.5116 q^{82} +8.94914 q^{83} +49.3311 q^{84} +2.15781 q^{85} +19.0820 q^{86} -18.0056 q^{87} -18.6516 q^{88} -3.32611 q^{89} +31.4573 q^{90} -7.62606 q^{91} +4.44903 q^{92} +6.87983 q^{93} +22.7213 q^{94} -12.2905 q^{95} +13.8200 q^{96} -12.7269 q^{97} -24.2986 q^{98} +13.2569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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