LMFDB - Embedded newform 6031.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6031,2,Mod(1,6031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6031, 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("6031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6031 = 37 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6031.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:	$48.1577774590$
Analytic rank:	$1$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12748 q^{2} -2.55539 q^{3} +2.52618 q^{4} +2.02951 q^{5} +5.43655 q^{6} -1.20737 q^{7} -1.11945 q^{8} +3.53003 q^{9} +O(q^{10})$	\(q-2.12748 q^{2} -2.55539 q^{3} +2.52618 q^{4} +2.02951 q^{5} +5.43655 q^{6} -1.20737 q^{7} -1.11945 q^{8} +3.53003 q^{9} -4.31775 q^{10} +3.59738 q^{11} -6.45539 q^{12} +1.63977 q^{13} +2.56867 q^{14} -5.18620 q^{15} -2.67076 q^{16} +4.23345 q^{17} -7.51008 q^{18} +6.43146 q^{19} +5.12692 q^{20} +3.08531 q^{21} -7.65338 q^{22} +0.914574 q^{23} +2.86063 q^{24} -0.881079 q^{25} -3.48857 q^{26} -1.35443 q^{27} -3.05005 q^{28} -0.385766 q^{29} +11.0336 q^{30} -7.25065 q^{31} +7.92090 q^{32} -9.19273 q^{33} -9.00660 q^{34} -2.45038 q^{35} +8.91751 q^{36} -1.00000 q^{37} -13.6828 q^{38} -4.19025 q^{39} -2.27194 q^{40} -9.72067 q^{41} -6.56395 q^{42} +5.48532 q^{43} +9.08766 q^{44} +7.16424 q^{45} -1.94574 q^{46} +2.22957 q^{47} +6.82484 q^{48} -5.54225 q^{49} +1.87448 q^{50} -10.8181 q^{51} +4.14235 q^{52} +8.07990 q^{53} +2.88154 q^{54} +7.30094 q^{55} +1.35159 q^{56} -16.4349 q^{57} +0.820710 q^{58} -7.78535 q^{59} -13.1013 q^{60} -5.24097 q^{61} +15.4256 q^{62} -4.26206 q^{63} -11.5101 q^{64} +3.32793 q^{65} +19.5574 q^{66} -13.6429 q^{67} +10.6945 q^{68} -2.33710 q^{69} +5.21314 q^{70} +7.92960 q^{71} -3.95169 q^{72} -3.48999 q^{73} +2.12748 q^{74} +2.25150 q^{75} +16.2471 q^{76} -4.34339 q^{77} +8.91468 q^{78} -5.02885 q^{79} -5.42034 q^{80} -7.12898 q^{81} +20.6806 q^{82} -13.5839 q^{83} +7.79407 q^{84} +8.59184 q^{85} -11.6699 q^{86} +0.985783 q^{87} -4.02709 q^{88} -1.73565 q^{89} -15.2418 q^{90} -1.97981 q^{91} +2.31038 q^{92} +18.5283 q^{93} -4.74338 q^{94} +13.0527 q^{95} -20.2410 q^{96} -16.4103 q^{97} +11.7910 q^{98} +12.6989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) $ 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * 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 $

$2$	−2.12748	−1.50436	−0.752179	−	0.658959i	$-0.770997\pi$
$2$	−2.12748	−1.50436	−0.752179	+	0.658959i	$0.770997\pi$
$3$	−2.55539	−1.47536	−0.737678	−	0.675152i	$-0.764078\pi$
$3$	−2.55539	−1.47536	−0.737678	+	0.675152i	$0.764078\pi$
$4$	2.52618	1.26309
$5$	2.02951	0.907626	0.453813	−	0.891097i	$-0.350063\pi$
$5$	2.02951	0.907626	0.453813	+	0.891097i	$0.350063\pi$
$6$	5.43655	2.21946
$7$	−1.20737	−0.456344	−0.228172	−	0.973621i	$-0.573275\pi$
$7$	−1.20737	−0.456344	−0.228172	+	0.973621i	$0.573275\pi$
$8$	−1.11945	−0.395785
$9$	3.53003	1.17668
$10$	−4.31775	−1.36539
$11$	3.59738	1.08465	0.542326	−	0.840168i	$-0.317544\pi$
$11$	3.59738	1.08465	0.542326	+	0.840168i	$0.317544\pi$
$12$	−6.45539	−1.86351
$13$	1.63977	0.454789	0.227395	−	0.973803i	$-0.426979\pi$
$13$	1.63977	0.454789	0.227395	+	0.973803i	$0.426979\pi$
$14$	2.56867	0.686505
$15$	−5.18620	−1.33907
$16$	−2.67076	−0.667690
$17$	4.23345	1.02676	0.513381	−	0.858161i	$-0.328393\pi$
$17$	4.23345	1.02676	0.513381	+	0.858161i	$0.328393\pi$
$18$	−7.51008	−1.77014
$19$	6.43146	1.47548	0.737739	−	0.675086i	$-0.235893\pi$
$19$	6.43146	1.47548	0.737739	+	0.675086i	$0.235893\pi$
$20$	5.12692	1.14642
$21$	3.08531	0.673270
$22$	−7.65338	−1.63171
$23$	0.914574	0.190702	0.0953509	−	0.995444i	$-0.469603\pi$
$23$	0.914574	0.190702	0.0953509	+	0.995444i	$0.469603\pi$
$24$	2.86063	0.583924
$25$	−0.881079	−0.176216
$26$	−3.48857	−0.684166
$27$	−1.35443	−0.260661
$28$	−3.05005	−0.576405
$29$	−0.385766	−0.0716349	−0.0358175	−	0.999358i	$-0.511403\pi$
$29$	−0.385766	−0.0716349	−0.0358175	+	0.999358i	$0.511403\pi$
$30$	11.0336	2.01444
$31$	−7.25065	−1.30226	−0.651128	−	0.758968i	$-0.725704\pi$
$31$	−7.25065	−1.30226	−0.651128	+	0.758968i	$0.725704\pi$
$32$	7.92090	1.40023
$33$	−9.19273	−1.60025
$34$	−9.00660	−1.54462
$35$	−2.45038	−0.414190
$36$	8.91751	1.48625
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−13.6828	−2.21965
$39$	−4.19025	−0.670976
$40$	−2.27194	−0.359225
$41$	−9.72067	−1.51811	−0.759057	−	0.651024i	$-0.774340\pi$
$41$	−9.72067	−1.51811	−0.759057	+	0.651024i	$0.774340\pi$
$42$	−6.56395	−1.01284
$43$	5.48532	0.836503	0.418251	−	0.908331i	$-0.362643\pi$
$43$	5.48532	0.836503	0.418251	+	0.908331i	$0.362643\pi$
$44$	9.08766	1.37002
$45$	7.16424	1.06798
$46$	−1.94574	−0.286884
$47$	2.22957	0.325216	0.162608	−	0.986691i	$-0.448009\pi$
$47$	2.22957	0.325216	0.162608	+	0.986691i	$0.448009\pi$
$48$	6.82484	0.985081
$49$	−5.54225	−0.791750
$50$	1.87448	0.265091
$51$	−10.8181	−1.51484
$52$	4.14235	0.574441
$53$	8.07990	1.10986	0.554930	−	0.831897i	$-0.312745\pi$
$53$	8.07990	1.10986	0.554930	+	0.831897i	$0.312745\pi$
$54$	2.88154	0.392128
$55$	7.30094	0.984458
$56$	1.35159	0.180614
$57$	−16.4349	−2.17686
$58$	0.820710	0.107765
$59$	−7.78535	−1.01357	−0.506783	−	0.862074i	$-0.669165\pi$
$59$	−7.78535	−1.01357	−0.506783	+	0.862074i	$0.669165\pi$
$60$	−13.1013	−1.69137
$61$	−5.24097	−0.671038	−0.335519	−	0.942033i	$-0.608912\pi$
$61$	−5.24097	−0.671038	−0.335519	+	0.942033i	$0.608912\pi$
$62$	15.4256	1.95906
$63$	−4.26206	−0.536970
$64$	−11.5101	−1.43876
$65$	3.32793	0.412778
$66$	19.5574	2.40735
$67$	−13.6429	−1.66675	−0.833375	−	0.552708i	$-0.813594\pi$
$67$	−13.6429	−1.66675	−0.833375	+	0.552708i	$0.813594\pi$
$68$	10.6945	1.29690
$69$	−2.33710	−0.281353
$70$	5.21314	0.623089
$71$	7.92960	0.941070	0.470535	−	0.882381i	$-0.344061\pi$
$71$	7.92960	0.941070	0.470535	+	0.882381i	$0.344061\pi$
$72$	−3.95169	−0.465711
$73$	−3.48999	−0.408472	−0.204236	−	0.978922i	$-0.565471\pi$
$73$	−3.48999	−0.408472	−0.204236	+	0.978922i	$0.565471\pi$
$74$	2.12748	0.247315
$75$	2.25150	0.259981
$76$	16.2471	1.86367
$77$	−4.34339	−0.494975
$78$	8.91468	1.00939
$79$	−5.02885	−0.565790	−0.282895	−	0.959151i	$-0.591295\pi$
$79$	−5.02885	−0.565790	−0.282895	+	0.959151i	$0.591295\pi$
$80$	−5.42034	−0.606012
$81$	−7.12898	−0.792109
$82$	20.6806	2.28379
$83$	−13.5839	−1.49103	−0.745514	−	0.666490i	$-0.767796\pi$
$83$	−13.5839	−1.49103	−0.745514	+	0.666490i	$0.767796\pi$
$84$	7.79407	0.850403
$85$	8.59184	0.931916
$86$	−11.6699	−1.25840
$87$	0.985783	0.105687
$88$	−4.02709	−0.429289
$89$	−1.73565	−0.183978	−0.0919891	−	0.995760i	$-0.529322\pi$
$89$	−1.73565	−0.183978	−0.0919891	+	0.995760i	$0.529322\pi$
$90$	−15.2418	−1.60663
$91$	−1.97981	−0.207540
$92$	2.31038	0.240874
$93$	18.5283	1.92129
$94$	−4.74338	−0.489242
$95$	13.0527	1.33918
$96$	−20.2410	−2.06584
$97$	−16.4103	−1.66621	−0.833106	−	0.553113i	$-0.813440\pi$
$97$	−16.4103	−1.66621	−0.833106	+	0.553113i	$0.813440\pi$
$98$	11.7910	1.19108
$99$	12.6989	1.27629
$100$	−2.22577	−0.222577
$101$	−13.3137	−1.32476	−0.662379	−	0.749169i	$-0.730453\pi$
$101$	−13.3137	−1.32476	−0.662379	+	0.749169i	$0.730453\pi$
$102$	23.0154	2.27886
$103$	−18.1001	−1.78345	−0.891727	−	0.452573i	$-0.850506\pi$
$103$	−18.1001	−1.78345	−0.891727	+	0.452573i	$0.850506\pi$
$104$	−1.83564	−0.179999
$105$	6.26168	0.611077
$106$	−17.1899	−1.66963
$107$	0.0479059	0.00463124	0.00231562	−	0.999997i	$-0.499263\pi$
$107$	0.0479059	0.00463124	0.00231562	+	0.999997i	$0.499263\pi$
$108$	−3.42155	−0.329239
$109$	−2.20470	−0.211172	−0.105586	−	0.994410i	$-0.533672\pi$
$109$	−2.20470	−0.211172	−0.105586	+	0.994410i	$0.533672\pi$
$110$	−15.5326	−1.48098
$111$	2.55539	0.242547
$112$	3.22460	0.304696
$113$	3.76739	0.354406	0.177203	−	0.984174i	$-0.443295\pi$
$113$	3.76739	0.354406	0.177203	+	0.984174i	$0.443295\pi$
$114$	34.9650	3.27477
$115$	1.85614	0.173086
$116$	−0.974516	−0.0904815
$117$	5.78842	0.535140
$118$	16.5632	1.52477
$119$	−5.11136	−0.468557
$120$	5.80569	0.529985
$121$	1.94118	0.176470
$122$	11.1501	1.00948
$123$	24.8401	2.23976
$124$	−18.3165	−1.64487
$125$	−11.9357	−1.06756
$126$	9.06747	0.807794
$127$	16.8158	1.49216	0.746079	−	0.665857i	$-0.231934\pi$
$127$	16.8158	1.49216	0.746079	+	0.665857i	$0.231934\pi$
$128$	8.64565	0.764175
$129$	−14.0171	−1.23414
$130$	−7.08011	−0.620966
$131$	−2.88949	−0.252456	−0.126228	−	0.992001i	$-0.540287\pi$
$131$	−2.88949	−0.252456	−0.126228	+	0.992001i	$0.540287\pi$
$132$	−23.2225	−2.02126
$133$	−7.76518	−0.673326
$134$	29.0251	2.50739
$135$	−2.74884	−0.236583
$136$	−4.73913	−0.406377
$137$	−17.8473	−1.52479	−0.762397	−	0.647110i	$-0.775978\pi$
$137$	−17.8473	−1.52479	−0.762397	+	0.647110i	$0.775978\pi$
$138$	4.97213	0.423256
$139$	−4.84059	−0.410573	−0.205287	−	0.978702i	$-0.565813\pi$
$139$	−4.84059	−0.410573	−0.205287	+	0.978702i	$0.565813\pi$
$140$	−6.19011	−0.523160
$141$	−5.69743	−0.479810
$142$	−16.8701	−1.41571
$143$	5.89887	0.493288
$144$	−9.42786	−0.785655
$145$	−0.782917	−0.0650177
$146$	7.42490	0.614489
$147$	14.1626	1.16811
$148$	−2.52618	−0.207651
$149$	−9.13221	−0.748140	−0.374070	−	0.927401i	$-0.622038\pi$
$149$	−9.13221	−0.748140	−0.374070	+	0.927401i	$0.622038\pi$
$150$	−4.79003	−0.391104
$151$	12.9546	1.05423	0.527116	−	0.849793i	$-0.323273\pi$
$151$	12.9546	1.05423	0.527116	+	0.849793i	$0.323273\pi$
$152$	−7.19970	−0.583973
$153$	14.9442	1.20817
$154$	9.24048	0.744619
$155$	−14.7153	−1.18196
$156$	−10.5853	−0.847505
$157$	−23.5931	−1.88294	−0.941469	−	0.337100i	$-0.890554\pi$
$157$	−23.5931	−1.88294	−0.941469	+	0.337100i	$0.890554\pi$
$158$	10.6988	0.851151
$159$	−20.6473	−1.63744
$160$	16.0756	1.27088
$161$	−1.10423	−0.0870257
$162$	15.1668	1.19161
$163$	−1.00000	−0.0783260
$163$	−1.00000	−0.0783260
$164$	−24.5562	−1.91752
$165$	−18.6568	−1.45243
$166$	28.8995	2.24304
$167$	16.8538	1.30418	0.652092	−	0.758140i	$-0.273892\pi$
$167$	16.8538	1.30418	0.652092	+	0.758140i	$0.273892\pi$
$168$	−3.45385	−0.266470
$169$	−10.3112	−0.793167
$170$	−18.2790	−1.40194
$171$	22.7033	1.73616
$172$	13.8569	1.05658
$173$	20.5274	1.56067	0.780336	−	0.625361i	$-0.215048\pi$
$173$	20.5274	1.56067	0.780336	+	0.625361i	$0.215048\pi$
$174$	−2.09724	−0.158991
$175$	1.06379	0.0804150
$176$	−9.60775	−0.724211
$177$	19.8946	1.49537
$178$	3.69256	0.276769
$179$	6.70961	0.501500	0.250750	−	0.968052i	$-0.419323\pi$
$179$	6.70961	0.501500	0.250750	+	0.968052i	$0.419323\pi$
$180$	18.0982	1.34896
$181$	−21.3046	−1.58356	−0.791779	−	0.610807i	$-0.790845\pi$
$181$	−21.3046	−1.58356	−0.791779	+	0.610807i	$0.790845\pi$
$182$	4.21201	0.312215
$183$	13.3927	0.990020
$184$	−1.02382	−0.0754770
$185$	−2.02951	−0.149213
$186$	−39.4186	−2.89031
$187$	15.2294	1.11368
$188$	5.63231	0.410778
$189$	1.63531	0.118951
$190$	−27.7695	−2.01461
$191$	19.8973	1.43972	0.719860	−	0.694119i	$-0.244206\pi$
$191$	19.8973	1.43972	0.719860	+	0.694119i	$0.244206\pi$
$192$	29.4127	2.12268
$193$	16.4505	1.18413	0.592066	−	0.805890i	$-0.298313\pi$
$193$	16.4505	1.18413	0.592066	+	0.805890i	$0.298313\pi$
$194$	34.9126	2.50658
$195$	−8.50416	−0.608995
$196$	−14.0007	−1.00005
$197$	−13.0503	−0.929797	−0.464898	−	0.885364i	$-0.653909\pi$
$197$	−13.0503	−0.929797	−0.464898	+	0.885364i	$0.653909\pi$
$198$	−27.0166	−1.91999
$199$	8.79559	0.623503	0.311751	−	0.950164i	$-0.399084\pi$
$199$	8.79559	0.623503	0.311751	+	0.950164i	$0.399084\pi$
$200$	0.986323	0.0697436
$201$	34.8631	2.45905
$202$	28.3246	1.99291
$203$	0.465763	0.0326902
$204$	−27.3286	−1.91338
$205$	−19.7282	−1.37788
$206$	38.5076	2.68295
$207$	3.22847	0.224394
$208$	−4.37942	−0.303658
$209$	23.1364	1.60038
$210$	−13.3216	−0.919279
$211$	−10.8291	−0.745507	−0.372754	−	0.927930i	$-0.621586\pi$
$211$	−10.8291	−0.745507	−0.372754	+	0.927930i	$0.621586\pi$
$212$	20.4113	1.40186
$213$	−20.2632	−1.38841
$214$	−0.101919	−0.00696704
$215$	11.1325	0.759231
$216$	1.51622	0.103166
$217$	8.75425	0.594277
$218$	4.69047	0.317678
$219$	8.91830	0.602643
$220$	18.4435	1.24346
$221$	6.94187	0.466961
$222$	−5.43655	−0.364878
$223$	15.5312	1.04005	0.520024	−	0.854152i	$-0.325923\pi$
$223$	15.5312	1.04005	0.520024	+	0.854152i	$0.325923\pi$
$224$	−9.56348	−0.638987
$225$	−3.11023	−0.207349
$226$	−8.01506	−0.533154
$227$	−2.22057	−0.147384	−0.0736921	−	0.997281i	$-0.523478\pi$
$227$	−2.22057	−0.147384	−0.0736921	+	0.997281i	$0.523478\pi$
$228$	−41.5176	−2.74957
$229$	−3.61512	−0.238894	−0.119447	−	0.992841i	$-0.538112\pi$
$229$	−3.61512	−0.238894	−0.119447	+	0.992841i	$0.538112\pi$
$230$	−3.94891	−0.260383
$231$	11.0991	0.730264
$232$	0.431845	0.0283520
$233$	−5.21506	−0.341650	−0.170825	−	0.985301i	$-0.554643\pi$
$233$	−5.21506	−0.341650	−0.170825	+	0.985301i	$0.554643\pi$
$234$	−12.3148	−0.805042
$235$	4.52494	0.295175
$236$	−19.6672	−1.28023
$237$	12.8507	0.834742
$238$	10.8743	0.704878
$239$	1.98319	0.128282	0.0641409	−	0.997941i	$-0.479569\pi$
$239$	1.98319	0.128282	0.0641409	+	0.997941i	$0.479569\pi$
$240$	13.8511	0.894084
$241$	23.4140	1.50823	0.754113	−	0.656744i	$-0.228067\pi$
$241$	23.4140	1.50823	0.754113	+	0.656744i	$0.228067\pi$
$242$	−4.12982	−0.265475
$243$	22.2806	1.42930
$244$	−13.2397	−0.847583
$245$	−11.2481	−0.718613
$246$	−52.8470	−3.36940
$247$	10.5461	0.671032
$248$	8.11674	0.515414
$249$	34.7122	2.19980
$250$	25.3931	1.60600
$251$	−19.2864	−1.21735	−0.608674	−	0.793421i	$-0.708298\pi$
$251$	−19.2864	−1.21735	−0.608674	+	0.793421i	$0.708298\pi$
$252$	−10.7668	−0.678242
$253$	3.29007	0.206845
$254$	−35.7753	−2.24474
$255$	−21.9555	−1.37491
$256$	4.62662	0.289164
$257$	20.5457	1.28161	0.640803	−	0.767705i	$-0.278601\pi$
$257$	20.5457	1.28161	0.640803	+	0.767705i	$0.278601\pi$
$258$	29.8212	1.85659
$259$	1.20737	0.0750225
$260$	8.40696	0.521377
$261$	−1.36176	−0.0842911
$262$	6.14733	0.379783
$263$	−7.31079	−0.450802	−0.225401	−	0.974266i	$-0.572369\pi$
$263$	−7.31079	−0.450802	−0.225401	+	0.974266i	$0.572369\pi$
$264$	10.2908	0.633355
$265$	16.3983	1.00734
$266$	16.5203	1.01292
$267$	4.43526	0.271433
$268$	−34.4646	−2.10526
$269$	−18.6020	−1.13418	−0.567092	−	0.823655i	$-0.691931\pi$
$269$	−18.6020	−1.13418	−0.567092	+	0.823655i	$0.691931\pi$
$270$	5.84812	0.355905
$271$	−15.2035	−0.923547	−0.461774	−	0.886998i	$-0.652787\pi$
$271$	−15.2035	−0.923547	−0.461774	+	0.886998i	$0.652787\pi$
$272$	−11.3065	−0.685559
$273$	5.05919	0.306196
$274$	37.9697	2.29384
$275$	−3.16958	−0.191133
$276$	−5.90394	−0.355375
$277$	10.6240	0.638332	0.319166	−	0.947699i	$-0.396597\pi$
$277$	10.6240	0.638332	0.319166	+	0.947699i	$0.396597\pi$
$278$	10.2983	0.617649
$279$	−25.5950	−1.53233
$280$	2.74308	0.163930
$281$	9.57227	0.571034	0.285517	−	0.958374i	$-0.407835\pi$
$281$	9.57227	0.571034	0.285517	+	0.958374i	$0.407835\pi$
$282$	12.1212	0.721806
$283$	28.8821	1.71686	0.858432	−	0.512927i	$-0.171439\pi$
$283$	28.8821	1.71686	0.858432	+	0.512927i	$0.171439\pi$
$284$	20.0316	1.18866
$285$	−33.3549	−1.97577
$286$	−12.5497	−0.742082
$287$	11.7365	0.692782
$288$	27.9610	1.64762
$289$	0.922107	0.0542416
$290$	1.66564	0.0978099
$291$	41.9347	2.45826
$292$	−8.81636	−0.515939
$293$	4.13637	0.241650	0.120825	−	0.992674i	$-0.461446\pi$
$293$	4.13637	0.241650	0.120825	+	0.992674i	$0.461446\pi$
$294$	−30.1307	−1.75726
$295$	−15.8005	−0.919938
$296$	1.11945	0.0650667
$297$	−4.87242	−0.282727
$298$	19.4286	1.12547
$299$	1.49969	0.0867292
$300$	5.68771	0.328380
$301$	−6.62282	−0.381733
$302$	−27.5608	−1.58594
$303$	34.0216	1.95449
$304$	−17.1769	−0.985162
$305$	−10.6366	−0.609051
$306$	−31.7936	−1.81752
$307$	25.6786	1.46555	0.732777	−	0.680469i	$-0.238224\pi$
$307$	25.6786	1.46555	0.732777	+	0.680469i	$0.238224\pi$
$308$	−10.9722	−0.625199
$309$	46.2528	2.63123
$310$	31.3065	1.77809
$311$	−25.2023	−1.42909	−0.714545	−	0.699589i	$-0.753366\pi$
$311$	−25.2023	−1.42909	−0.714545	+	0.699589i	$0.753366\pi$
$312$	4.69077	0.265562
$313$	−14.6425	−0.827645	−0.413823	−	0.910358i	$-0.635807\pi$
$313$	−14.6425	−0.827645	−0.413823	+	0.910358i	$0.635807\pi$
$314$	50.1940	2.83261
$315$	−8.64991	−0.487367
$316$	−12.7038	−0.714645
$317$	−12.6919	−0.712850	−0.356425	−	0.934324i	$-0.616005\pi$
$317$	−12.6919	−0.712850	−0.356425	+	0.934324i	$0.616005\pi$
$318$	43.9268	2.46329
$319$	−1.38775	−0.0776990
$320$	−23.3598	−1.30585
$321$	−0.122418	−0.00683273
$322$	2.34924	0.130918
$323$	27.2273	1.51497
$324$	−18.0091	−1.00051
$325$	−1.44476	−0.0801410
$326$	2.12748	0.117830
$327$	5.63388	0.311554
$328$	10.8818	0.600847
$329$	−2.69192	−0.148411
$330$	39.6919	2.18497
$331$	10.3761	0.570322	0.285161	−	0.958480i	$-0.407953\pi$
$331$	10.3761	0.570322	0.285161	+	0.958480i	$0.407953\pi$
$332$	−34.3155	−1.88331
$333$	−3.53003	−0.193444
$334$	−35.8561	−1.96196
$335$	−27.6885	−1.51278
$336$	−8.24013	−0.449536
$337$	15.4928	0.843945	0.421972	−	0.906609i	$-0.361338\pi$
$337$	15.4928	0.843945	0.421972	+	0.906609i	$0.361338\pi$
$338$	21.9368	1.19321
$339$	−9.62716	−0.522876
$340$	21.7046	1.17710
$341$	−26.0834	−1.41249
$342$	−48.3008	−2.61181
$343$	15.1432	0.817655
$344$	−6.14053	−0.331075
$345$	−4.74316	−0.255363
$346$	−43.6718	−2.34781
$347$	−31.7895	−1.70655	−0.853274	−	0.521462i	$-0.825387\pi$
$347$	−31.7895	−1.70655	−0.853274	+	0.521462i	$0.825387\pi$
$348$	2.49027	0.133492
$349$	−4.85217	−0.259731	−0.129865	−	0.991532i	$-0.541455\pi$
$349$	−4.85217	−0.259731	−0.129865	+	0.991532i	$0.541455\pi$
$350$	−2.26320	−0.120973
$351$	−2.22096	−0.118546
$352$	28.4945	1.51876
$353$	8.95166	0.476449	0.238224	−	0.971210i	$-0.423435\pi$
$353$	8.95166	0.476449	0.238224	+	0.971210i	$0.423435\pi$
$354$	−42.3255	−2.24957
$355$	16.0932	0.854139
$356$	−4.38456	−0.232381
$357$	13.0615	0.691289
$358$	−14.2746	−0.754435
$359$	−25.0779	−1.32356	−0.661782	−	0.749697i	$-0.730199\pi$
$359$	−25.0779	−1.32356	−0.661782	+	0.749697i	$0.730199\pi$
$360$	−8.02001	−0.422691
$361$	22.3637	1.17704
$362$	45.3252	2.38224
$363$	−4.96046	−0.260357
$364$	−5.00137	−0.262143
$365$	−7.08298	−0.370740
$366$	−28.4928	−1.48934
$367$	−29.0114	−1.51439	−0.757193	−	0.653192i	$-0.773430\pi$
$367$	−29.0114	−1.51439	−0.757193	+	0.653192i	$0.773430\pi$
$368$	−2.44261	−0.127330
$369$	−34.3143	−1.78633
$370$	4.31775	0.224469
$371$	−9.75546	−0.506478
$372$	46.8058	2.42677
$373$	19.3503	1.00192	0.500960	−	0.865470i	$-0.332980\pi$
$373$	19.3503	1.00192	0.500960	+	0.865470i	$0.332980\pi$
$374$	−32.4002	−1.67537
$375$	30.5005	1.57504
$376$	−2.49589	−0.128716
$377$	−0.632566	−0.0325788
$378$	−3.47909	−0.178945
$379$	−37.2922	−1.91557	−0.957785	−	0.287487i	$-0.907180\pi$
$379$	−37.2922	−1.91557	−0.957785	+	0.287487i	$0.907180\pi$
$380$	32.9736	1.69151
$381$	−42.9709	−2.20147
$382$	−42.3313	−2.16586
$383$	−11.5619	−0.590787	−0.295394	−	0.955376i	$-0.595451\pi$
$383$	−11.5619	−0.590787	−0.295394	+	0.955376i	$0.595451\pi$
$384$	−22.0930	−1.12743
$385$	−8.81496	−0.449252
$386$	−34.9981	−1.78136
$387$	19.3633	0.984293
$388$	−41.4554	−2.10458
$389$	−28.0320	−1.42128	−0.710638	−	0.703558i	$-0.751594\pi$
$389$	−28.0320	−1.42128	−0.710638	+	0.703558i	$0.751594\pi$
$390$	18.0925	0.916147
$391$	3.87180	0.195806
$392$	6.20427	0.313363
$393$	7.38377	0.372462
$394$	27.7643	1.39875
$395$	−10.2061	−0.513526
$396$	32.0797	1.61207
$397$	−26.1695	−1.31341	−0.656705	−	0.754147i	$-0.728051\pi$
$397$	−26.1695	−1.31341	−0.656705	+	0.754147i	$0.728051\pi$
$398$	−18.7125	−0.937971
$399$	19.8431	0.993396
$400$	2.35315	0.117657
$401$	−17.8610	−0.891935	−0.445967	−	0.895049i	$-0.647140\pi$
$401$	−17.8610	−0.891935	−0.445967	+	0.895049i	$0.647140\pi$
$402$	−74.1706	−3.69929
$403$	−11.8894	−0.592252
$404$	−33.6328	−1.67329
$405$	−14.4683	−0.718938
$406$	−0.990904	−0.0491777
$407$	−3.59738	−0.178316
$408$	12.1103	0.599552
$409$	−17.8085	−0.880574	−0.440287	−	0.897857i	$-0.645123\pi$
$409$	−17.8085	−0.880574	−0.440287	+	0.897857i	$0.645123\pi$
$410$	41.9715	2.07282
$411$	45.6067	2.24961
$412$	−45.7242	−2.25267
$413$	9.39982	0.462535
$414$	−6.86852	−0.337570
$415$	−27.5687	−1.35329
$416$	12.9884	0.636809
$417$	12.3696	0.605742
$418$	−49.2224	−2.40755
$419$	−7.13490	−0.348563	−0.174281	−	0.984696i	$-0.555760\pi$
$419$	−7.13490	−0.348563	−0.174281	+	0.984696i	$0.555760\pi$
$420$	15.8182	0.771847
$421$	27.5771	1.34403	0.672013	−	0.740540i	$-0.265430\pi$
$421$	27.5771	1.34403	0.672013	+	0.740540i	$0.265430\pi$
$422$	23.0388	1.12151
$423$	7.87045	0.382675
$424$	−9.04504	−0.439266
$425$	−3.73000	−0.180932
$426$	43.1097	2.08867
$427$	6.32781	0.306224
$428$	0.121019	0.00584968
$429$	−15.0739	−0.727776
$430$	−23.6842	−1.14216
$431$	40.9302	1.97154	0.985769	−	0.168104i	$-0.0537645\pi$
$431$	40.9302	1.97154	0.985769	+	0.168104i	$0.0537645\pi$
$432$	3.61737	0.174041
$433$	18.3828	0.883420	0.441710	−	0.897158i	$-0.354372\pi$
$433$	18.3828	0.883420	0.441710	+	0.897158i	$0.354372\pi$
$434$	−18.6245	−0.894005
$435$	2.00066	0.0959243
$436$	−5.56948	−0.266730
$437$	5.88205	0.281377
$438$	−18.9735	−0.906590
$439$	−30.6326	−1.46202	−0.731008	−	0.682369i	$-0.760950\pi$
$439$	−30.6326	−1.46202	−0.731008	+	0.682369i	$0.760950\pi$
$440$	−8.17303	−0.389634
$441$	−19.5643	−0.931634
$442$	−14.7687	−0.702476
$443$	−31.0017	−1.47294	−0.736469	−	0.676472i	$-0.763508\pi$
$443$	−31.0017	−1.47294	−0.736469	+	0.676472i	$0.763508\pi$
$444$	6.45539	0.306359
$445$	−3.52252	−0.166983
$446$	−33.0424	−1.56460
$447$	23.3364	1.10377
$448$	13.8969	0.656568
$449$	26.8368	1.26650	0.633252	−	0.773945i	$-0.281720\pi$
$449$	26.8368	1.26650	0.633252	+	0.773945i	$0.281720\pi$
$450$	6.61697	0.311927
$451$	−34.9690	−1.64663
$452$	9.51712	0.447648
$453$	−33.1042	−1.55537
$454$	4.72422	0.221719
$455$	−4.01805	−0.188369
$456$	18.3981	0.861568
$457$	27.2064	1.27266	0.636331	−	0.771416i	$-0.280451\pi$
$457$	27.2064	1.27266	0.636331	+	0.771416i	$0.280451\pi$
$458$	7.69110	0.359382
$459$	−5.73393	−0.267637
$460$	4.68895	0.218623
$461$	−31.8945	−1.48548	−0.742738	−	0.669582i	$-0.766473\pi$
$461$	−31.8945	−1.48548	−0.742738	+	0.669582i	$0.766473\pi$
$462$	−23.6131	−1.09858
$463$	−10.2907	−0.478250	−0.239125	−	0.970989i	$-0.576861\pi$
$463$	−10.2907	−0.478250	−0.239125	+	0.970989i	$0.576861\pi$
$464$	1.03029	0.0478299
$465$	37.6034	1.74381
$466$	11.0950	0.513964
$467$	35.6825	1.65119	0.825594	−	0.564264i	$-0.190840\pi$
$467$	35.6825	1.65119	0.825594	+	0.564264i	$0.190840\pi$
$468$	14.6226	0.675931
$469$	16.4721	0.760612
$470$	−9.62674	−0.444048
$471$	60.2897	2.77800
$472$	8.71530	0.401154
$473$	19.7328	0.907315
$474$	−27.3396	−1.25575
$475$	−5.66662	−0.260003
$476$	−12.9122	−0.591831
$477$	28.5223	1.30595
$478$	−4.21920	−0.192982
$479$	−7.96141	−0.363766	−0.181883	−	0.983320i	$-0.558219\pi$
$479$	−7.96141	−0.363766	−0.181883	+	0.983320i	$0.558219\pi$
$480$	−41.0794	−1.87501
$481$	−1.63977	−0.0747669
$482$	−49.8128	−2.26891
$483$	2.82175	0.128394
$484$	4.90377	0.222899
$485$	−33.3049	−1.51230
$486$	−47.4017	−2.15018
$487$	−4.06253	−0.184091	−0.0920454	−	0.995755i	$-0.529340\pi$
$487$	−4.06253	−0.184091	−0.0920454	+	0.995755i	$0.529340\pi$
$488$	5.86701	0.265587
$489$	2.55539	0.115559
$490$	23.9301	1.08105
$491$	−13.9210	−0.628247	−0.314123	−	0.949382i	$-0.601711\pi$
$491$	−13.9210	−0.628247	−0.314123	+	0.949382i	$0.601711\pi$
$492$	62.7508	2.82902
$493$	−1.63312	−0.0735521
$494$	−22.4366	−1.00947
$495$	25.7725	1.15839
$496$	19.3648	0.869503
$497$	−9.57398	−0.429452
$498$	−73.8496	−3.30928
$499$	35.6265	1.59486	0.797431	−	0.603410i	$-0.206192\pi$
$499$	35.6265	1.59486	0.797431	+	0.603410i	$0.206192\pi$
$500$	−30.1518	−1.34843
$501$	−43.0680	−1.92414
$502$	41.0315	1.83133
$503$	23.6500	1.05450	0.527251	−	0.849710i	$-0.323223\pi$
$503$	23.6500	1.05450	0.527251	+	0.849710i	$0.323223\pi$
$504$	4.77117	0.212525
$505$	−27.0202	−1.20238
$506$	−6.99958	−0.311169
$507$	26.3491	1.17020
$508$	42.4798	1.88473
$509$	12.4216	0.550579	0.275290	−	0.961361i	$-0.411226\pi$
$509$	12.4216	0.550579	0.275290	+	0.961361i	$0.411226\pi$
$510$	46.7100	2.06835
$511$	4.21372	0.186404
$512$	−27.1344	−1.19918
$513$	−8.71100	−0.384600
$514$	−43.7107	−1.92799
$515$	−36.7344	−1.61871
$516$	−35.4099	−1.55883
$517$	8.02062	0.352747
$518$	−2.56867	−0.112861
$519$	−52.4556	−2.30255
$520$	−3.72545	−0.163372
$521$	−25.0381	−1.09694	−0.548470	−	0.836170i	$-0.684790\pi$
$521$	−25.0381	−1.09694	−0.548470	+	0.836170i	$0.684790\pi$
$522$	2.89713	0.126804
$523$	10.8865	0.476032	0.238016	−	0.971261i	$-0.423503\pi$
$523$	10.8865	0.476032	0.238016	+	0.971261i	$0.423503\pi$
$524$	−7.29937	−0.318875
$525$	−2.71840	−0.118641
$526$	15.5536	0.678168
$527$	−30.6953	−1.33711
$528$	24.5516	1.06847
$529$	−22.1636	−0.963633
$530$	−34.8870	−1.51540
$531$	−27.4825	−1.19264
$532$	−19.6163	−0.850473
$533$	−15.9396	−0.690422
$534$	−9.43593	−0.408333
$535$	0.0972257	0.00420343
$536$	15.2726	0.659675
$537$	−17.1457	−0.739891
$538$	39.5754	1.70622
$539$	−19.9376	−0.858773
$540$	−6.94409	−0.298826
$541$	−7.41014	−0.318587	−0.159293	−	0.987231i	$-0.550922\pi$
$541$	−7.41014	−0.318587	−0.159293	+	0.987231i	$0.550922\pi$
$542$	32.3452	1.38935
$543$	54.4416	2.33631
$544$	33.5327	1.43770
$545$	−4.47447	−0.191665
$546$	−10.7633	−0.460629
$547$	26.3799	1.12792	0.563961	−	0.825802i	$-0.309277\pi$
$547$	26.3799	1.12792	0.563961	+	0.825802i	$0.309277\pi$
$548$	−45.0855	−1.92596
$549$	−18.5008	−0.789595
$550$	6.74322	0.287532
$551$	−2.48104	−0.105696
$552$	2.61626	0.111355
$553$	6.07170	0.258195
$554$	−22.6023	−0.960280
$555$	5.18620	0.220142
$556$	−12.2282	−0.518592
$557$	−0.456735	−0.0193525	−0.00967625	−	0.999953i	$-0.503080\pi$
$557$	−0.456735	−0.0193525	−0.00967625	+	0.999953i	$0.503080\pi$
$558$	54.4530	2.30518
$559$	8.99463	0.380432
$560$	6.54437	0.276550
$561$	−38.9170	−1.64308
$562$	−20.3648	−0.859039
$563$	−33.2269	−1.40035	−0.700174	−	0.713973i	$-0.746894\pi$
$563$	−33.2269	−1.40035	−0.700174	+	0.713973i	$0.746894\pi$
$564$	−14.3928	−0.606044
$565$	7.64597	0.321668
$566$	−61.4463	−2.58278
$567$	8.60734	0.361474
$568$	−8.87679	−0.372462
$569$	−19.3048	−0.809298	−0.404649	−	0.914472i	$-0.632606\pi$
$569$	−19.3048	−0.809298	−0.404649	+	0.914472i	$0.632606\pi$
$570$	70.9619	2.97227
$571$	−8.23138	−0.344473	−0.172236	−	0.985056i	$-0.555099\pi$
$571$	−8.23138	−0.344473	−0.172236	+	0.985056i	$0.555099\pi$
$572$	14.9016	0.623069
$573$	−50.8455	−2.12410
$574$	−24.9692	−1.04219
$575$	−0.805812	−0.0336047
$576$	−40.6308	−1.69295
$577$	32.1359	1.33783	0.668917	−	0.743337i	$-0.266758\pi$
$577$	32.1359	1.33783	0.668917	+	0.743337i	$0.266758\pi$
$578$	−1.96177	−0.0815987
$579$	−42.0374	−1.74702
$580$	−1.97779	−0.0821233
$581$	16.4008	0.680422
$582$	−89.2154	−3.69810
$583$	29.0665	1.20381
$584$	3.90687	0.161667
$585$	11.7477	0.485707
$586$	−8.80007	−0.363527
$587$	29.9957	1.23805	0.619027	−	0.785370i	$-0.287527\pi$
$587$	29.9957	1.23805	0.619027	+	0.785370i	$0.287527\pi$
$588$	35.7774	1.47544
$589$	−46.6323	−1.92145
$590$	33.6152	1.38392
$591$	33.3487	1.37178
$592$	2.67076	0.109768
$593$	9.39563	0.385832	0.192916	−	0.981215i	$-0.438205\pi$
$593$	9.39563	0.385832	0.192916	+	0.981215i	$0.438205\pi$
$594$	10.3660	0.425322
$595$	−10.3736	−0.425274
$596$	−23.0696	−0.944969
$597$	−22.4762	−0.919889
$598$	−3.19056	−0.130472
$599$	35.6838	1.45800	0.729001	−	0.684513i	$-0.239985\pi$
$599$	35.6838	1.45800	0.729001	+	0.684513i	$0.239985\pi$
$600$	−2.52044	−0.102897
$601$	−21.2053	−0.864984	−0.432492	−	0.901638i	$-0.642366\pi$
$601$	−21.2053	−0.864984	−0.432492	+	0.901638i	$0.642366\pi$
$602$	14.0899	0.574263
$603$	−48.1600	−1.96123
$604$	32.7258	1.33159
$605$	3.93964	0.160169
$606$	−72.3804	−2.94025
$607$	−6.55163	−0.265922	−0.132961	−	0.991121i	$-0.542449\pi$
$607$	−6.55163	−0.265922	−0.132961	+	0.991121i	$0.542449\pi$
$608$	50.9429	2.06601
$609$	−1.19021	−0.0482297
$610$	22.6292	0.916231
$611$	3.65597	0.147905
$612$	37.7518	1.52603
$613$	−38.0125	−1.53531	−0.767655	−	0.640864i	$-0.778576\pi$
$613$	−38.0125	−1.53531	−0.767655	+	0.640864i	$0.778576\pi$
$614$	−54.6308	−2.20472
$615$	50.4134	2.03286
$616$	4.86220	0.195904
$617$	−23.9301	−0.963391	−0.481696	−	0.876339i	$-0.659979\pi$
$617$	−23.9301	−0.963391	−0.481696	+	0.876339i	$0.659979\pi$
$618$	−98.4021	−3.95831
$619$	23.5430	0.946271	0.473136	−	0.880990i	$-0.343122\pi$
$619$	23.5430	0.946271	0.473136	+	0.880990i	$0.343122\pi$
$620$	−37.1736	−1.49293
$621$	−1.23873	−0.0497086
$622$	53.6174	2.14986
$623$	2.09557	0.0839573
$624$	11.1911	0.448004
$625$	−19.8183	−0.792732
$626$	31.1518	1.24507
$627$	−59.1227	−2.36113
$628$	−59.6006	−2.37832
$629$	−4.23345	−0.168799
$630$	18.4025	0.733175
$631$	9.41330	0.374737	0.187369	−	0.982290i	$-0.440004\pi$
$631$	9.41330	0.374737	0.187369	+	0.982290i	$0.440004\pi$
$632$	5.62955	0.223931
$633$	27.6726	1.09989
$634$	27.0019	1.07238
$635$	34.1278	1.35432
$636$	−52.1590	−2.06824
$637$	−9.08799	−0.360079
$638$	2.95241	0.116887
$639$	27.9917	1.10734
$640$	17.5465	0.693585
$641$	7.42968	0.293455	0.146727	−	0.989177i	$-0.453126\pi$
$641$	7.42968	0.293455	0.146727	+	0.989177i	$0.453126\pi$
$642$	0.260443	0.0102789
$643$	−16.0046	−0.631160	−0.315580	−	0.948899i	$-0.602199\pi$
$643$	−16.0046	−0.631160	−0.315580	+	0.948899i	$0.602199\pi$
$644$	−2.78949	−0.109921
$645$	−28.4479	−1.12014
$646$	−57.9256	−2.27905
$647$	−27.7973	−1.09282	−0.546412	−	0.837516i	$-0.684007\pi$
$647$	−27.7973	−1.09282	−0.546412	+	0.837516i	$0.684007\pi$
$648$	7.98053	0.313505
$649$	−28.0069	−1.09937
$650$	3.07371	0.120561
$651$	−22.3705	−0.876770
$652$	−2.52618	−0.0989330
$653$	−2.73580	−0.107060	−0.0535301	−	0.998566i	$-0.517047\pi$
$653$	−2.73580	−0.107060	−0.0535301	+	0.998566i	$0.517047\pi$
$654$	−11.9860	−0.468689
$655$	−5.86425	−0.229135
$656$	25.9616	1.01363
$657$	−12.3198	−0.480640
$658$	5.72702	0.223263
$659$	6.32957	0.246565	0.123282	−	0.992372i	$-0.460658\pi$
$659$	6.32957	0.246565	0.123282	+	0.992372i	$0.460658\pi$
$660$	−47.1304	−1.83455
$661$	−43.7524	−1.70177	−0.850885	−	0.525352i	$-0.823934\pi$
$661$	−43.7524	−1.70177	−0.850885	+	0.525352i	$0.823934\pi$
$662$	−22.0750	−0.857969
$663$	−17.7392	−0.688933
$664$	15.2065	0.590127
$665$	−15.7595	−0.611128
$666$	7.51008	0.291010
$667$	−0.352811	−0.0136609
$668$	42.5757	1.64730
$669$	−39.6884	−1.53444
$670$	58.9068	2.27577
$671$	−18.8538	−0.727843
$672$	24.4384	0.942733
$673$	−9.26209	−0.357027	−0.178514	−	0.983937i	$-0.557129\pi$
$673$	−9.26209	−0.357027	−0.178514	+	0.983937i	$0.557129\pi$
$674$	−32.9606	−1.26960
$675$	1.19336	0.0459326
$676$	−26.0479	−1.00184
$677$	−0.168130	−0.00646174	−0.00323087	−	0.999995i	$-0.501028\pi$
$677$	−0.168130	−0.00646174	−0.00323087	+	0.999995i	$0.501028\pi$
$678$	20.4816	0.786592
$679$	19.8133	0.760366
$680$	−9.61813	−0.368839
$681$	5.67442	0.217444
$682$	55.4920	2.12490
$683$	−32.7364	−1.25262	−0.626311	−	0.779573i	$-0.715436\pi$
$683$	−32.7364	−1.25262	−0.626311	+	0.779573i	$0.715436\pi$
$684$	57.3526	2.19293
$685$	−36.2212	−1.38394
$686$	−32.2169	−1.23005
$687$	9.23804	0.352453
$688$	−14.6500	−0.558524
$689$	13.2492	0.504752
$690$	10.0910	0.384158
$691$	36.2760	1.38000	0.690001	−	0.723808i	$-0.257610\pi$
$691$	36.2760	1.38000	0.690001	+	0.723808i	$0.257610\pi$
$692$	51.8561	1.97127
$693$	−15.3323	−0.582425
$694$	67.6316	2.56726
$695$	−9.82404	−0.372647
$696$	−1.10353	−0.0418294
$697$	−41.1520	−1.55874
$698$	10.3229	0.390728
$699$	13.3265	0.504055
$700$	2.68733	0.101572
$701$	5.05086	0.190768	0.0953841	−	0.995441i	$-0.469592\pi$
$701$	5.05086	0.190768	0.0953841	+	0.995441i	$0.469592\pi$
$702$	4.72505	0.178335
$703$	−6.43146	−0.242567
$704$	−41.4061	−1.56055
$705$	−11.5630	−0.435488
$706$	−19.0445	−0.716750
$707$	16.0746	0.604546
$708$	50.2575	1.88879
$709$	33.9233	1.27402	0.637008	−	0.770857i	$-0.280172\pi$
$709$	33.9233	1.27402	0.637008	+	0.770857i	$0.280172\pi$
$710$	−34.2381	−1.28493
$711$	−17.7520	−0.665752
$712$	1.94297	0.0728158
$713$	−6.63126	−0.248343
$714$	−27.7882	−1.03995
$715$	11.9718	0.447721
$716$	16.9497	0.633440
$717$	−5.06783	−0.189262
$718$	53.3529	1.99111
$719$	43.4384	1.61998	0.809990	−	0.586444i	$-0.199473\pi$
$719$	43.4384	1.61998	0.809990	+	0.586444i	$0.199473\pi$
$720$	−19.1340	−0.713081
$721$	21.8536	0.813869
$722$	−47.5784	−1.77069
$723$	−59.8319	−2.22517
$724$	−53.8194	−2.00018
$725$	0.339890	0.0126232
$726$	10.5533	0.391670
$727$	−13.6796	−0.507349	−0.253674	−	0.967290i	$-0.581639\pi$
$727$	−13.6796	−0.507349	−0.253674	+	0.967290i	$0.581639\pi$
$728$	2.21630	0.0821414
$729$	−35.5488	−1.31662
$730$	15.0689	0.557726
$731$	23.2218	0.858890
$732$	33.8326	1.25049
$733$	0.0405830	0.00149897	0.000749484	−	1.00000i	$-0.499761\pi$
$733$	0.0405830	0.00149897	0.000749484		1.00000i	$0.499761\pi$
$734$	61.7214	2.27818
$735$	28.7432	1.06021
$736$	7.24424	0.267026
$737$	−49.0789	−1.80784
$738$	73.0030	2.68728
$739$	27.3318	1.00542	0.502708	−	0.864456i	$-0.332337\pi$
$739$	27.3318	1.00542	0.502708	+	0.864456i	$0.332337\pi$
$740$	−5.12692	−0.188469
$741$	−26.9494	−0.990011
$742$	20.7546	0.761924
$743$	−36.5204	−1.33980	−0.669902	−	0.742449i	$-0.733664\pi$
$743$	−36.5204	−1.33980	−0.669902	+	0.742449i	$0.733664\pi$
$744$	−20.7415	−0.760419
$745$	−18.5339	−0.679031
$746$	−41.1674	−1.50725
$747$	−47.9516	−1.75446
$748$	38.4722	1.40668
$749$	−0.0578403	−0.00211344
$750$	−64.8892	−2.36942
$751$	−17.3935	−0.634697	−0.317348	−	0.948309i	$-0.602792\pi$
$751$	−17.3935	−0.634697	−0.317348	+	0.948309i	$0.602792\pi$
$752$	−5.95465	−0.217144
$753$	49.2843	1.79602
$754$	1.34577	0.0490102
$755$	26.2916	0.956849
$756$	4.13109	0.150246
$757$	−22.1405	−0.804710	−0.402355	−	0.915484i	$-0.631808\pi$
$757$	−22.1405	−0.804710	−0.402355	+	0.915484i	$0.631808\pi$
$758$	79.3384	2.88170
$759$	−8.40743	−0.305170
$760$	−14.6119	−0.530029
$761$	−51.2246	−1.85689	−0.928445	−	0.371470i	$-0.878854\pi$
$761$	−51.2246	−1.85689	−0.928445	+	0.371470i	$0.878854\pi$
$762$	91.4199	3.31179
$763$	2.66190	0.0963672
$764$	50.2644	1.81850
$765$	30.3295	1.09656
$766$	24.5978	0.888755
$767$	−12.7661	−0.460959
$768$	−11.8228	−0.426620
$769$	43.2257	1.55876	0.779380	−	0.626551i	$-0.215534\pi$
$769$	43.2257	1.55876	0.779380	+	0.626551i	$0.215534\pi$
$770$	18.7537	0.675835
$771$	−52.5024	−1.89083
$772$	41.5569	1.49567
$773$	−17.6966	−0.636504	−0.318252	−	0.948006i	$-0.603096\pi$
$773$	−17.6966	−0.636504	−0.318252	+	0.948006i	$0.603096\pi$
$774$	−41.1952	−1.48073
$775$	6.38840	0.229478
$776$	18.3705	0.659462
$777$	−3.08531	−0.110685
$778$	59.6375	2.13811
$779$	−62.5181	−2.23994
$780$	−21.4831	−0.769217
$781$	28.5258	1.02073
$782$	−8.23720	−0.294562
$783$	0.522495	0.0186724
$784$	14.8020	0.528643
$785$	−47.8826	−1.70900
$786$	−15.7088	−0.560316
$787$	34.9190	1.24473	0.622364	−	0.782728i	$-0.286172\pi$
$787$	34.9190	1.24473	0.622364	+	0.782728i	$0.286172\pi$
$788$	−32.9675	−1.17442
$789$	18.6819	0.665094
$790$	21.7134	0.772527
$791$	−4.54865	−0.161731
$792$	−14.2158	−0.505135
$793$	−8.59397	−0.305181
$794$	55.6752	1.97584
$795$	−41.9040	−1.48618
$796$	22.2193	0.787542
$797$	9.07453	0.321436	0.160718	−	0.987000i	$-0.448619\pi$
$797$	9.07453	0.321436	0.160718	+	0.987000i	$0.448619\pi$
$798$	−42.2158	−1.49442
$799$	9.43878	0.333920
$800$	−6.97893	−0.246742
$801$	−6.12688	−0.216483
$802$	37.9989	1.34179
$803$	−12.5548	−0.443051
$804$	88.0705	3.10601
$805$	−2.24105	−0.0789867
$806$	25.2945	0.890959
$807$	47.5354	1.67332
$808$	14.9040	0.524320
$809$	40.6461	1.42904	0.714520	−	0.699615i	$-0.246645\pi$
$809$	40.6461	1.42904	0.714520	+	0.699615i	$0.246645\pi$
$810$	30.7812	1.08154
$811$	−15.1165	−0.530812	−0.265406	−	0.964137i	$-0.585506\pi$
$811$	−15.1165	−0.530812	−0.265406	+	0.964137i	$0.585506\pi$
$812$	1.17660	0.0412907
$813$	38.8509	1.36256
$814$	7.65338	0.268251
$815$	−2.02951	−0.0710907
$816$	28.8926	1.01144
$817$	35.2786	1.23424
$818$	37.8873	1.32470
$819$	−6.98879	−0.244208
$820$	−49.8371	−1.74039
$821$	−10.3870	−0.362508	−0.181254	−	0.983436i	$-0.558016\pi$
$821$	−10.3870	−0.362508	−0.181254	+	0.983436i	$0.558016\pi$
$822$	−97.0276	−3.38423
$823$	15.4072	0.537060	0.268530	−	0.963271i	$-0.413462\pi$
$823$	15.4072	0.537060	0.268530	+	0.963271i	$0.413462\pi$
$824$	20.2621	0.705865
$825$	8.09952	0.281989
$826$	−19.9980	−0.695818
$827$	−8.83970	−0.307386	−0.153693	−	0.988119i	$-0.549117\pi$
$827$	−8.83970	−0.307386	−0.153693	+	0.988119i	$0.549117\pi$
$828$	8.15572	0.283431
$829$	34.7518	1.20698	0.603490	−	0.797371i	$-0.293776\pi$
$829$	34.7518	1.20698	0.603490	+	0.797371i	$0.293776\pi$
$830$	58.6520	2.03584
$831$	−27.1484	−0.941768
$832$	−18.8738	−0.654331
$833$	−23.4628	−0.812939
$834$	−26.3161	−0.911253
$835$	34.2049	1.18371
$836$	58.4469	2.02143
$837$	9.82054	0.339448
$838$	15.1794	0.524363
$839$	−0.445118	−0.0153672	−0.00768359	−	0.999970i	$-0.502446\pi$
$839$	−0.445118	−0.0153672	−0.00768359	+	0.999970i	$0.502446\pi$
$840$	−7.00964	−0.241855
$841$	−28.8512	−0.994868
$842$	−58.6698	−2.02189
$843$	−24.4609	−0.842478
$844$	−27.3564	−0.941645
$845$	−20.9266	−0.719898
$846$	−16.7443	−0.575679
$847$	−2.34372	−0.0805313
$848$	−21.5795	−0.741042
$849$	−73.8052	−2.53299
$850$	7.93552	0.272186
$851$	−0.914574	−0.0313512
$852$	−51.1887	−1.75370
$853$	40.4178	1.38388	0.691940	−	0.721955i	$-0.256756\pi$
$853$	40.4178	1.38388	0.691940	+	0.721955i	$0.256756\pi$
$854$	−13.4623	−0.460671
$855$	46.0765	1.57578
$856$	−0.0536283	−0.00183298
$857$	37.5639	1.28316	0.641580	−	0.767056i	$-0.278279\pi$
$857$	37.5639	1.28316	0.641580	+	0.767056i	$0.278279\pi$
$858$	32.0695	1.09484
$859$	−19.7656	−0.674395	−0.337197	−	0.941434i	$-0.609479\pi$
$859$	−19.7656	−0.674395	−0.337197	+	0.941434i	$0.609479\pi$
$860$	28.1228	0.958979
$861$	−29.9913	−1.02210
$862$	−87.0783	−2.96590
$863$	−33.6601	−1.14580	−0.572901	−	0.819624i	$-0.694182\pi$
$863$	−33.6601	−1.14580	−0.572901	+	0.819624i	$0.694182\pi$
$864$	−10.7283	−0.364985
$865$	41.6607	1.41651
$866$	−39.1091	−1.32898
$867$	−2.35634	−0.0800257
$868$	22.1148	0.750627
$869$	−18.0907	−0.613686
$870$	−4.25637	−0.144304
$871$	−22.3712	−0.758020
$872$	2.46805	0.0835788
$873$	−57.9288	−1.96059
$874$	−12.5140	−0.423291
$875$	14.4109	0.487176
$876$	22.5293	0.761193
$877$	31.2352	1.05474	0.527370	−	0.849636i	$-0.323178\pi$
$877$	31.2352	1.05474	0.527370	+	0.849636i	$0.323178\pi$
$878$	65.1704	2.19939
$879$	−10.5701	−0.356519
$880$	−19.4990	−0.657313
$881$	−52.6303	−1.77316	−0.886580	−	0.462574i	$-0.846926\pi$
$881$	−52.6303	−1.77316	−0.886580	+	0.462574i	$0.846926\pi$
$882$	41.6227	1.40151
$883$	−1.18485	−0.0398734	−0.0199367	−	0.999801i	$-0.506346\pi$
$883$	−1.18485	−0.0398734	−0.0199367	+	0.999801i	$0.506346\pi$
$884$	17.5364	0.589814
$885$	40.3764	1.35724
$886$	65.9557	2.21582
$887$	−18.3779	−0.617071	−0.308536	−	0.951213i	$-0.599839\pi$
$887$	−18.3779	−0.617071	−0.308536	+	0.951213i	$0.599839\pi$
$888$	−2.86063	−0.0959966
$889$	−20.3029	−0.680938
$890$	7.49409	0.251203
$891$	−25.6457	−0.859162
$892$	39.2348	1.31368
$893$	14.3394	0.479850
$894$	−49.6477	−1.66047
$895$	13.6172	0.455174
$896$	−10.4385	−0.348727
$897$	−3.83229	−0.127956
$898$	−57.0947	−1.90528
$899$	2.79705	0.0932870
$900$	−7.85703	−0.261901
$901$	34.2059	1.13956
$902$	74.3959	2.47711
$903$	16.9239	0.563192
$904$	−4.21740	−0.140269
$905$	−43.2380	−1.43728
$906$	70.4285	2.33983
$907$	33.4999	1.11235	0.556173	−	0.831067i	$-0.312269\pi$
$907$	33.4999	1.11235	0.556173	+	0.831067i	$0.312269\pi$
$908$	−5.60956	−0.186160
$909$	−46.9976	−1.55881
$910$	8.54833	0.283374
$911$	−34.1429	−1.13120	−0.565602	−	0.824679i	$-0.691356\pi$
$911$	−34.1429	−1.13120	−0.565602	+	0.824679i	$0.691356\pi$
$912$	43.8937	1.45347
$913$	−48.8665	−1.61725
$914$	−57.8811	−1.91454
$915$	27.1807	0.898568
$916$	−9.13245	−0.301745
$917$	3.48869	0.115207
$918$	12.1988	0.402622
$919$	10.6976	0.352882	0.176441	−	0.984311i	$-0.443542\pi$
$919$	10.6976	0.352882	0.176441	+	0.984311i	$0.443542\pi$
$920$	−2.07785	−0.0685048
$921$	−65.6189	−2.16222
$922$	67.8551	2.23469
$923$	13.0027	0.427989
$924$	28.0383	0.922391
$925$	0.881079	0.0289697
$926$	21.8933	0.719460
$927$	−63.8939	−2.09855
$928$	−3.05561	−0.100305
$929$	−0.422490	−0.0138614	−0.00693072	−	0.999976i	$-0.502206\pi$
$929$	−0.422490	−0.0138614	−0.00693072	+	0.999976i	$0.502206\pi$
$930$	−80.0005	−2.62332
$931$	−35.6448	−1.16821
$932$	−13.1742	−0.431535
$933$	64.4017	2.10842
$934$	−75.9139	−2.48398
$935$	30.9082	1.01080
$936$	−6.47985	−0.211800
$937$	−9.07265	−0.296391	−0.148195	−	0.988958i	$-0.547346\pi$
$937$	−9.07265	−0.296391	−0.148195	+	0.988958i	$0.547346\pi$
$938$	−35.0441	−1.14423
$939$	37.4174	1.22107
$940$	11.4308	0.372833
$941$	−54.5867	−1.77947	−0.889737	−	0.456473i	$-0.849112\pi$
$941$	−54.5867	−1.77947	−0.889737	+	0.456473i	$0.849112\pi$
$942$	−128.265	−4.17911
$943$	−8.89027	−0.289507
$944$	20.7928	0.676748
$945$	3.31888	0.107963
$946$	−41.9812	−1.36493
$947$	−27.5639	−0.895707	−0.447853	−	0.894107i	$-0.647811\pi$
$947$	−27.5639	−0.895707	−0.447853	+	0.894107i	$0.647811\pi$
$948$	32.4632	1.05436
$949$	−5.72277	−0.185769
$950$	12.0556	0.391137
$951$	32.4329	1.05171
$952$	5.72190	0.185448
$953$	−1.64675	−0.0533434	−0.0266717	−	0.999644i	$-0.508491\pi$
$953$	−1.64675	−0.0533434	−0.0266717	+	0.999644i	$0.508491\pi$
$954$	−60.6807	−1.96461
$955$	40.3819	1.30673
$956$	5.00990	0.162032
$957$	3.54624	0.114634
$958$	16.9378	0.547234
$959$	21.5483	0.695831
$960$	59.6934	1.92660
$961$	21.5720	0.695871
$962$	3.48857	0.112476
$963$	0.169109	0.00544947
$964$	59.1480	1.90503
$965$	33.3865	1.07475
$966$	−6.00322	−0.193150
$967$	−2.58506	−0.0831299	−0.0415649	−	0.999136i	$-0.513234\pi$
$967$	−2.58506	−0.0831299	−0.0415649	+	0.999136i	$0.513234\pi$
$968$	−2.17305	−0.0698444
$969$	−69.5764	−2.23512
$970$	70.8556	2.27504
$971$	49.2280	1.57980	0.789901	−	0.613235i	$-0.210132\pi$
$971$	49.2280	1.57980	0.789901	+	0.613235i	$0.210132\pi$
$972$	56.2850	1.80534
$973$	5.84440	0.187363
$974$	8.64297	0.276938
$975$	3.69194	0.118237
$976$	13.9974	0.448045
$977$	39.5500	1.26532	0.632658	−	0.774431i	$-0.281964\pi$
$977$	39.5500	1.26532	0.632658	+	0.774431i	$0.281964\pi$
$978$	−5.43655	−0.173842
$979$	−6.24379	−0.199552
$980$	−28.4147	−0.907674
$981$	−7.78266	−0.248481
$982$	29.6167	0.945108
$983$	−9.45013	−0.301412	−0.150706	−	0.988579i	$-0.548155\pi$
$983$	−9.45013	−0.301412	−0.150706	+	0.988579i	$0.548155\pi$
$984$	−27.8073	−0.886463
$985$	−26.4858	−0.843907
$986$	3.47444	0.110649
$987$	6.87892	0.218959
$988$	26.6414	0.847575
$989$	5.01673	0.159523
$990$	−54.8306	−1.74263
$991$	−22.2034	−0.705315	−0.352658	−	0.935752i	$-0.614722\pi$
$991$	−22.2034	−0.705315	−0.352658	+	0.935752i	$0.614722\pi$
$992$	−57.4317	−1.82346
$993$	−26.5150	−0.841429
$994$	20.3685	0.646049
$995$	17.8508	0.565907
$996$	87.6895	2.77855
$997$	3.26287	0.103336	0.0516681	−	0.998664i	$-0.483546\pi$
$997$	3.26287	0.103336	0.0516681	+	0.998664i	$0.483546\pi$
$998$	−75.7948	−2.39924
$999$	1.35443	0.0428524

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6031.2.a.c.1.18	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6031.2.a.c.1.18	✓	110	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:	\( N \)	\(=\)	\( 6031 = 37 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12748 q^{2} -2.55539 q^{3} +2.52618 q^{4} +2.02951 q^{5} +5.43655 q^{6} -1.20737 q^{7} -1.11945 q^{8} +3.53003 q^{9} +O(q^{10})\)	\(q-2.12748 q^{2} -2.55539 q^{3} +2.52618 q^{4} +2.02951 q^{5} +5.43655 q^{6} -1.20737 q^{7} -1.11945 q^{8} +3.53003 q^{9} -4.31775 q^{10} +3.59738 q^{11} -6.45539 q^{12} +1.63977 q^{13} +2.56867 q^{14} -5.18620 q^{15} -2.67076 q^{16} +4.23345 q^{17} -7.51008 q^{18} +6.43146 q^{19} +5.12692 q^{20} +3.08531 q^{21} -7.65338 q^{22} +0.914574 q^{23} +2.86063 q^{24} -0.881079 q^{25} -3.48857 q^{26} -1.35443 q^{27} -3.05005 q^{28} -0.385766 q^{29} +11.0336 q^{30} -7.25065 q^{31} +7.92090 q^{32} -9.19273 q^{33} -9.00660 q^{34} -2.45038 q^{35} +8.91751 q^{36} -1.00000 q^{37} -13.6828 q^{38} -4.19025 q^{39} -2.27194 q^{40} -9.72067 q^{41} -6.56395 q^{42} +5.48532 q^{43} +9.08766 q^{44} +7.16424 q^{45} -1.94574 q^{46} +2.22957 q^{47} +6.82484 q^{48} -5.54225 q^{49} +1.87448 q^{50} -10.8181 q^{51} +4.14235 q^{52} +8.07990 q^{53} +2.88154 q^{54} +7.30094 q^{55} +1.35159 q^{56} -16.4349 q^{57} +0.820710 q^{58} -7.78535 q^{59} -13.1013 q^{60} -5.24097 q^{61} +15.4256 q^{62} -4.26206 q^{63} -11.5101 q^{64} +3.32793 q^{65} +19.5574 q^{66} -13.6429 q^{67} +10.6945 q^{68} -2.33710 q^{69} +5.21314 q^{70} +7.92960 q^{71} -3.95169 q^{72} -3.48999 q^{73} +2.12748 q^{74} +2.25150 q^{75} +16.2471 q^{76} -4.34339 q^{77} +8.91468 q^{78} -5.02885 q^{79} -5.42034 q^{80} -7.12898 q^{81} +20.6806 q^{82} -13.5839 q^{83} +7.79407 q^{84} +8.59184 q^{85} -11.6699 q^{86} +0.985783 q^{87} -4.02709 q^{88} -1.73565 q^{89} -15.2418 q^{90} -1.97981 q^{91} +2.31038 q^{92} +18.5283 q^{93} -4.74338 q^{94} +13.0527 q^{95} -20.2410 q^{96} -16.4103 q^{97} +11.7910 q^{98} +12.6989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9}+O(q^{10}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9	\( 110 q - 9 q^{2} + 97 q^{4} - 26 q^{5} - 26 q^{6} - 4 q^{7} - 27 q^{8} + 62 q^{9} - 17 q^{10} - 9 q^{11} - 21 q^{13} - 29 q^{14} - 23 q^{15} + 79 q^{16} - 76 q^{17} - 31 q^{18} - 27 q^{19} - 67 q^{20} - 30 q^{21} - 28 q^{22} - 32 q^{23} - 63 q^{24} + 66 q^{25} - 55 q^{26} - 4 q^{28} - 81 q^{29} - 48 q^{30} - 30 q^{31} - 73 q^{32} - 53 q^{33} - 23 q^{34} - 78 q^{35} + 7 q^{36} - 110 q^{37} - 50 q^{38} - 64 q^{39} - 37 q^{40} - 123 q^{41} - 63 q^{42} - 40 q^{43} - 31 q^{44} - 73 q^{45} + 16 q^{46} - 37 q^{47} - 29 q^{48} + 46 q^{49} - 58 q^{50} - 73 q^{51} - 39 q^{52} - 16 q^{53} - 53 q^{54} - 59 q^{55} - 113 q^{56} - 39 q^{57} + 11 q^{58} - 93 q^{59} - 18 q^{60} - 66 q^{61} - 40 q^{62} - 21 q^{63} + 23 q^{64} - 92 q^{65} - 31 q^{66} + q^{67} - 121 q^{68} - 80 q^{69} - 3 q^{70} - 75 q^{71} - 114 q^{72} - 39 q^{73} + 9 q^{74} - 25 q^{75} - 58 q^{76} - 31 q^{77} + 68 q^{78} - 36 q^{79} - 82 q^{80} - 50 q^{81} - 18 q^{82} - 57 q^{83} - 9 q^{84} - 14 q^{85} - 58 q^{86} - 58 q^{87} - 15 q^{88} - 181 q^{89} + 8 q^{90} - 55 q^{91} - 116 q^{92} - 86 q^{93} - 39 q^{94} - 70 q^{95} - 127 q^{96} - 91 q^{97} - 19 q^{98} - 21 q^{99}+O(q^{100}) \) 110 * q - 9 * q^2 + 97 * q^4 - 26 * q^5 - 26 * q^6 - 4 * q^7 - 27 * q^8 + 62 * q^9 - 17 * q^10 - 9 * q^11 - 21 * q^13 - 29 * q^14 - 23 * q^15 + 79 * q^16 - 76 * q^17 - 31 * q^18 - 27 * q^19 - 67 * q^20 - 30 * q^21 - 28 * q^22 - 32 * q^23 - 63 * q^24 + 66 * q^25 - 55 * q^26 - 4 * q^28 - 81 * q^29 - 48 * q^30 - 30 * q^31 - 73 * q^32 - 53 * q^33 - 23 * q^34 - 78 * q^35 + 7 * q^36 - 110 * q^37 - 50 * q^38 - 64 * q^39 - 37 * q^40 - 123 * q^41 - 63 * q^42 - 40 * q^43 - 31 * q^44 - 73 * q^45 + 16 * q^46 - 37 * q^47 - 29 * q^48 + 46 * q^49 - 58 * q^50 - 73 * q^51 - 39 * q^52 - 16 * q^53 - 53 * q^54 - 59 * q^55 - 113 * q^56 - 39 * q^57 + 11 * q^58 - 93 * q^59 - 18 * q^60 - 66 * q^61 - 40 * q^62 - 21 * q^63 + 23 * q^64 - 92 * q^65 - 31 * q^66 + q^67 - 121 * q^68 - 80 * q^69 - 3 * q^70 - 75 * q^71 - 114 * q^72 - 39 * q^73 + 9 * q^74 - 25 * q^75 - 58 * q^76 - 31 * q^77 + 68 * q^78 - 36 * q^79 - 82 * q^80 - 50 * q^81 - 18 * q^82 - 57 * q^83 - 9 * q^84 - 14 * q^85 - 58 * q^86 - 58 * q^87 - 15 * q^88 - 181 * q^89 + 8 * q^90 - 55 * q^91 - 116 * q^92 - 86 * q^93 - 39 * q^94 - 70 * q^95 - 127 * q^96 - 91 * q^97 - 19 * q^98 - 21 * q^99

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