LMFDB - Embedded newform 8023.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, 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("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37665 q^{2} -1.52236 q^{3} +3.64846 q^{4} +1.09798 q^{5} +3.61812 q^{6} +2.78247 q^{7} -3.91780 q^{8} -0.682408 q^{9} +O(q^{10})$	\(q-2.37665 q^{2} -1.52236 q^{3} +3.64846 q^{4} +1.09798 q^{5} +3.61812 q^{6} +2.78247 q^{7} -3.91780 q^{8} -0.682408 q^{9} -2.60952 q^{10} +5.59204 q^{11} -5.55428 q^{12} +4.16972 q^{13} -6.61295 q^{14} -1.67153 q^{15} +2.01433 q^{16} +6.68310 q^{17} +1.62184 q^{18} +4.71717 q^{19} +4.00594 q^{20} -4.23593 q^{21} -13.2903 q^{22} -7.66895 q^{23} +5.96432 q^{24} -3.79444 q^{25} -9.90997 q^{26} +5.60597 q^{27} +10.1517 q^{28} -6.66964 q^{29} +3.97263 q^{30} +0.700609 q^{31} +3.04826 q^{32} -8.51312 q^{33} -15.8834 q^{34} +3.05510 q^{35} -2.48974 q^{36} -6.03390 q^{37} -11.2111 q^{38} -6.34784 q^{39} -4.30168 q^{40} +8.91122 q^{41} +10.0673 q^{42} +10.7110 q^{43} +20.4023 q^{44} -0.749271 q^{45} +18.2264 q^{46} +5.25225 q^{47} -3.06654 q^{48} +0.742131 q^{49} +9.01804 q^{50} -10.1741 q^{51} +15.2131 q^{52} -8.25659 q^{53} -13.3234 q^{54} +6.13996 q^{55} -10.9012 q^{56} -7.18125 q^{57} +15.8514 q^{58} +12.8576 q^{59} -6.09850 q^{60} -6.39999 q^{61} -1.66510 q^{62} -1.89878 q^{63} -11.2733 q^{64} +4.57828 q^{65} +20.2327 q^{66} +2.59424 q^{67} +24.3830 q^{68} +11.6749 q^{69} -7.26089 q^{70} -1.00000 q^{71} +2.67354 q^{72} -10.1531 q^{73} +14.3404 q^{74} +5.77651 q^{75} +17.2104 q^{76} +15.5597 q^{77} +15.0866 q^{78} +2.03904 q^{79} +2.21169 q^{80} -6.48710 q^{81} -21.1788 q^{82} +10.9359 q^{83} -15.4546 q^{84} +7.33791 q^{85} -25.4563 q^{86} +10.1536 q^{87} -21.9085 q^{88} +6.86098 q^{89} +1.78075 q^{90} +11.6021 q^{91} -27.9798 q^{92} -1.06658 q^{93} -12.4828 q^{94} +5.17936 q^{95} -4.64056 q^{96} -4.78188 q^{97} -1.76378 q^{98} -3.81605 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	−2.37665	−1.68054	−0.840272	−	0.542165i	$-0.817605\pi$
$2$	−2.37665	−1.68054	−0.840272	+	0.542165i	$0.817605\pi$
$3$	−1.52236	−0.878937	−0.439469	−	0.898258i	$-0.644833\pi$
$3$	−1.52236	−0.878937	−0.439469	+	0.898258i	$0.644833\pi$
$4$	3.64846	1.82423
$5$	1.09798	0.491032	0.245516	−	0.969393i	$-0.421043\pi$
$5$	1.09798	0.491032	0.245516	+	0.969393i	$0.421043\pi$
$6$	3.61812	1.47709
$7$	2.78247	1.05167	0.525837	−	0.850585i	$-0.323752\pi$
$7$	2.78247	1.05167	0.525837	+	0.850585i	$0.323752\pi$
$8$	−3.91780	−1.38515
$9$	−0.682408	−0.227469
$10$	−2.60952	−0.825201
$11$	5.59204	1.68606	0.843032	−	0.537863i	$-0.180768\pi$
$11$	5.59204	1.68606	0.843032	+	0.537863i	$0.180768\pi$
$12$	−5.55428	−1.60338
$13$	4.16972	1.15647	0.578237	−	0.815869i	$-0.303741\pi$
$13$	4.16972	1.15647	0.578237	+	0.815869i	$0.303741\pi$
$14$	−6.61295	−1.76739
$15$	−1.67153	−0.431586
$16$	2.01433	0.503582
$17$	6.68310	1.62089	0.810445	−	0.585815i	$-0.199226\pi$
$17$	6.68310	1.62089	0.810445	+	0.585815i	$0.199226\pi$
$18$	1.62184	0.382272
$19$	4.71717	1.08219	0.541096	−	0.840961i	$-0.318009\pi$
$19$	4.71717	1.08219	0.541096	+	0.840961i	$0.318009\pi$
$20$	4.00594	0.895755
$21$	−4.23593	−0.924356
$22$	−13.2903	−2.83351
$23$	−7.66895	−1.59909	−0.799543	−	0.600608i	$-0.794925\pi$
$23$	−7.66895	−1.59909	−0.799543	+	0.600608i	$0.794925\pi$
$24$	5.96432	1.21746
$25$	−3.79444	−0.758887
$26$	−9.90997	−1.94351
$27$	5.60597	1.07887
$28$	10.1517	1.91849
$29$	−6.66964	−1.23852	−0.619261	−	0.785185i	$-0.712568\pi$
$29$	−6.66964	−1.23852	−0.619261	+	0.785185i	$0.712568\pi$
$30$	3.97263	0.725300
$31$	0.700609	0.125833	0.0629166	−	0.998019i	$-0.479960\pi$
$31$	0.700609	0.125833	0.0629166	+	0.998019i	$0.479960\pi$
$32$	3.04826	0.538861
$33$	−8.51312	−1.48194
$34$	−15.8834	−2.72398
$35$	3.05510	0.516406
$36$	−2.48974	−0.414956
$37$	−6.03390	−0.991966	−0.495983	−	0.868332i	$-0.665192\pi$
$37$	−6.03390	−0.991966	−0.495983	+	0.868332i	$0.665192\pi$
$38$	−11.2111	−1.81867
$39$	−6.34784	−1.01647
$40$	−4.30168	−0.680155
$41$	8.91122	1.39170	0.695849	−	0.718188i	$-0.255028\pi$
$41$	8.91122	1.39170	0.695849	+	0.718188i	$0.255028\pi$
$42$	10.0673	1.55342
$43$	10.7110	1.63341	0.816705	−	0.577055i	$-0.195798\pi$
$43$	10.7110	1.63341	0.816705	+	0.577055i	$0.195798\pi$
$44$	20.4023	3.07577
$45$	−0.749271	−0.111695
$46$	18.2264	2.68734
$47$	5.25225	0.766119	0.383060	−	0.923724i	$-0.374870\pi$
$47$	5.25225	0.766119	0.383060	+	0.923724i	$0.374870\pi$
$48$	−3.06654	−0.442617
$49$	0.742131	0.106019
$50$	9.01804	1.27534
$51$	−10.1741	−1.42466
$52$	15.2131	2.10967
$53$	−8.25659	−1.13413	−0.567065	−	0.823673i	$-0.691921\pi$
$53$	−8.25659	−1.13413	−0.567065	+	0.823673i	$0.691921\pi$
$54$	−13.3234	−1.81309
$55$	6.13996	0.827912
$56$	−10.9012	−1.45673
$57$	−7.18125	−0.951180
$58$	15.8514	2.08139
$59$	12.8576	1.67391	0.836957	−	0.547268i	$-0.184332\pi$
$59$	12.8576	1.67391	0.836957	+	0.547268i	$0.184332\pi$
$60$	−6.09850	−0.787312
$61$	−6.39999	−0.819435	−0.409717	−	0.912213i	$-0.634373\pi$
$61$	−6.39999	−0.819435	−0.409717	+	0.912213i	$0.634373\pi$
$62$	−1.66510	−0.211468
$63$	−1.89878	−0.239224
$64$	−11.2733	−1.40916
$65$	4.57828	0.567866
$66$	20.2327	2.49047
$67$	2.59424	0.316936	0.158468	−	0.987364i	$-0.449344\pi$
$67$	2.59424	0.316936	0.158468	+	0.987364i	$0.449344\pi$
$68$	24.3830	2.95687
$69$	11.6749	1.40550
$70$	−7.26089	−0.867843
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	2.67354	0.315080
$73$	−10.1531	−1.18833	−0.594165	−	0.804343i	$-0.702518\pi$
$73$	−10.1531	−1.18833	−0.594165	+	0.804343i	$0.702518\pi$
$74$	14.3404	1.66704
$75$	5.77651	0.667014
$76$	17.2104	1.97417
$77$	15.5597	1.77319
$78$	15.0866	1.70822
$79$	2.03904	0.229410	0.114705	−	0.993400i	$-0.463408\pi$
$79$	2.03904	0.229410	0.114705	+	0.993400i	$0.463408\pi$
$80$	2.21169	0.247275
$81$	−6.48710	−0.720788
$82$	−21.1788	−2.33881
$83$	10.9359	1.20037	0.600185	−	0.799861i	$-0.295094\pi$
$83$	10.9359	1.20037	0.600185	+	0.799861i	$0.295094\pi$
$84$	−15.4546	−1.68624
$85$	7.33791	0.795909
$86$	−25.4563	−2.74502
$87$	10.1536	1.08858
$88$	−21.9085	−2.33546
$89$	6.86098	0.727263	0.363631	−	0.931543i	$-0.381537\pi$
$89$	6.86098	0.727263	0.363631	+	0.931543i	$0.381537\pi$
$90$	1.78075	0.187708
$91$	11.6021	1.21623
$92$	−27.9798	−2.91710
$93$	−1.06658	−0.110599
$94$	−12.4828	−1.28750
$95$	5.17936	0.531391
$96$	−4.64056	−0.473625
$97$	−4.78188	−0.485527	−0.242763	−	0.970086i	$-0.578054\pi$
$97$	−4.78188	−0.485527	−0.242763	+	0.970086i	$0.578054\pi$
$98$	−1.76378	−0.178169
$99$	−3.81605	−0.383528
$100$	−13.8438	−1.38438
$101$	−5.79349	−0.576474	−0.288237	−	0.957559i	$-0.593069\pi$
$101$	−5.79349	−0.576474	−0.288237	+	0.957559i	$0.593069\pi$
$102$	24.1803	2.39420
$103$	16.6185	1.63747	0.818735	−	0.574172i	$-0.194676\pi$
$103$	16.6185	1.63747	0.818735	+	0.574172i	$0.194676\pi$
$104$	−16.3362	−1.60189
$105$	−4.65097	−0.453888
$106$	19.6230	1.90596
$107$	−5.16947	−0.499751	−0.249876	−	0.968278i	$-0.580390\pi$
$107$	−5.16947	−0.499751	−0.249876	+	0.968278i	$0.580390\pi$
$108$	20.4531	1.96810
$109$	14.8662	1.42393	0.711964	−	0.702216i	$-0.247806\pi$
$109$	14.8662	1.42393	0.711964	+	0.702216i	$0.247806\pi$
$110$	−14.5925	−1.39134
$111$	9.18579	0.871876
$112$	5.60480	0.529604
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	17.0673	1.59850
$115$	−8.42036	−0.785203
$116$	−24.3339	−2.25935
$117$	−2.84545	−0.263062
$118$	−30.5580	−2.81309
$119$	18.5955	1.70465
$120$	6.54872	0.597813
$121$	20.2709	1.84281
$122$	15.2105	1.37710
$123$	−13.5661	−1.22322
$124$	2.55614	0.229548
$125$	−9.65613	−0.863670
$126$	4.51273	0.402026
$127$	−16.2530	−1.44222	−0.721111	−	0.692819i	$-0.756368\pi$
$127$	−16.2530	−1.44222	−0.721111	+	0.692819i	$0.756368\pi$
$128$	20.6961	1.82930
$129$	−16.3060	−1.43567
$130$	−10.8810	−0.954323
$131$	11.2955	0.986891	0.493445	−	0.869777i	$-0.335737\pi$
$131$	11.2955	0.986891	0.493445	+	0.869777i	$0.335737\pi$
$132$	−31.0598	−2.70341
$133$	13.1254	1.13811
$134$	−6.16559	−0.532626
$135$	6.15524	0.529759
$136$	−26.1831	−2.24518
$137$	3.16221	0.270166	0.135083	−	0.990834i	$-0.456870\pi$
$137$	3.16221	0.270166	0.135083	+	0.990834i	$0.456870\pi$
$138$	−27.7472	−2.36200
$139$	−7.60597	−0.645130	−0.322565	−	0.946547i	$-0.604545\pi$
$139$	−7.60597	−0.645130	−0.322565	+	0.946547i	$0.604545\pi$
$140$	11.1464	0.942042
$141$	−7.99584	−0.673371
$142$	2.37665	0.199444
$143$	23.3173	1.94989
$144$	−1.37459	−0.114549
$145$	−7.32314	−0.608154
$146$	24.1304	1.99704
$147$	−1.12979	−0.0931838
$148$	−22.0144	−1.80957
$149$	18.7734	1.53798	0.768988	−	0.639264i	$-0.220761\pi$
$149$	18.7734	1.53798	0.768988	+	0.639264i	$0.220761\pi$
$150$	−13.7287	−1.12095
$151$	16.3118	1.32744	0.663718	−	0.747983i	$-0.268977\pi$
$151$	16.3118	1.32744	0.663718	+	0.747983i	$0.268977\pi$
$152$	−18.4809	−1.49900
$153$	−4.56060	−0.368703
$154$	−36.9799	−2.97992
$155$	0.769256	0.0617881
$156$	−23.1598	−1.85427
$157$	−15.0358	−1.19999	−0.599994	−	0.800004i	$-0.704830\pi$
$157$	−15.0358	−1.19999	−0.599994	+	0.800004i	$0.704830\pi$
$158$	−4.84608	−0.385534
$159$	12.5695	0.996829
$160$	3.34693	0.264598
$161$	−21.3386	−1.68172
$162$	15.4175	1.21132
$163$	3.49374	0.273651	0.136825	−	0.990595i	$-0.456310\pi$
$163$	3.49374	0.273651	0.136825	+	0.990595i	$0.456310\pi$
$164$	32.5122	2.53878
$165$	−9.34725	−0.727682
$166$	−25.9908	−2.01727
$167$	−8.61957	−0.667003	−0.333501	−	0.942750i	$-0.608230\pi$
$167$	−8.61957	−0.667003	−0.333501	+	0.942750i	$0.608230\pi$
$168$	16.5955	1.28037
$169$	4.38661	0.337431
$170$	−17.4396	−1.33756
$171$	−3.21903	−0.246166
$172$	39.0786	2.97972
$173$	6.79172	0.516365	0.258182	−	0.966096i	$-0.416876\pi$
$173$	6.79172	0.516365	0.258182	+	0.966096i	$0.416876\pi$
$174$	−24.1316	−1.82941
$175$	−10.5579	−0.798102
$176$	11.2642	0.849071
$177$	−19.5739	−1.47127
$178$	−16.3061	−1.22220
$179$	12.8637	0.961481	0.480740	−	0.876863i	$-0.340368\pi$
$179$	12.8637	0.961481	0.480740	+	0.876863i	$0.340368\pi$
$180$	−2.73368	−0.203757
$181$	2.37797	0.176753	0.0883767	−	0.996087i	$-0.471832\pi$
$181$	2.37797	0.176753	0.0883767	+	0.996087i	$0.471832\pi$
$182$	−27.5742	−2.04393
$183$	9.74311	0.720232
$184$	30.0454	2.21498
$185$	−6.62510	−0.487087
$186$	2.53489	0.185867
$187$	37.3722	2.73292
$188$	19.1626	1.39758
$189$	15.5984	1.13462
$190$	−12.3095	−0.893027
$191$	−15.5055	−1.12194	−0.560971	−	0.827836i	$-0.689572\pi$
$191$	−15.5055	−1.12194	−0.560971	+	0.827836i	$0.689572\pi$
$192$	17.1621	1.23857
$193$	21.1889	1.52521	0.762604	−	0.646866i	$-0.223921\pi$
$193$	21.1889	1.52521	0.762604	+	0.646866i	$0.223921\pi$
$194$	11.3649	0.815949
$195$	−6.96981	−0.499118
$196$	2.70763	0.193402
$197$	16.4026	1.16864	0.584320	−	0.811524i	$-0.301361\pi$
$197$	16.4026	1.16864	0.584320	+	0.811524i	$0.301361\pi$
$198$	9.06942	0.644535
$199$	−16.2326	−1.15070	−0.575348	−	0.817909i	$-0.695133\pi$
$199$	−16.2326	−1.15070	−0.575348	+	0.817909i	$0.695133\pi$
$200$	14.8659	1.05118
$201$	−3.94937	−0.278567
$202$	13.7691	0.968790
$203$	−18.5581	−1.30252
$204$	−37.1198	−2.59891
$205$	9.78435	0.683369
$206$	−39.4963	−2.75184
$207$	5.23335	0.363743
$208$	8.39919	0.582379
$209$	26.3786	1.82465
$210$	11.0537	0.762779
$211$	−8.25815	−0.568514	−0.284257	−	0.958748i	$-0.591747\pi$
$211$	−8.25815	−0.568514	−0.284257	+	0.958748i	$0.591747\pi$
$212$	−30.1238	−2.06891
$213$	1.52236	0.104311
$214$	12.2860	0.839854
$215$	11.7605	0.802057
$216$	−21.9631	−1.49440
$217$	1.94942	0.132336
$218$	−35.3318	−2.39297
$219$	15.4567	1.04447
$220$	22.4014	1.51030
$221$	27.8667	1.87452
$222$	−21.8314	−1.46523
$223$	−1.32173	−0.0885096	−0.0442548	−	0.999020i	$-0.514091\pi$
$223$	−1.32173	−0.0885096	−0.0442548	+	0.999020i	$0.514091\pi$
$224$	8.48169	0.566707
$225$	2.58935	0.172624
$226$	−2.37665	−0.158092
$227$	22.2080	1.47400	0.736999	−	0.675893i	$-0.236242\pi$
$227$	22.2080	1.47400	0.736999	+	0.675893i	$0.236242\pi$
$228$	−26.2005	−1.73517
$229$	13.5080	0.892634	0.446317	−	0.894875i	$-0.352735\pi$
$229$	13.5080	0.892634	0.446317	+	0.894875i	$0.352735\pi$
$230$	20.0122	1.31957
$231$	−23.6875	−1.55852
$232$	26.1303	1.71554
$233$	13.7462	0.900540	0.450270	−	0.892892i	$-0.351328\pi$
$233$	13.7462	0.900540	0.450270	+	0.892892i	$0.351328\pi$
$234$	6.76264	0.442088
$235$	5.76687	0.376189
$236$	46.9103	3.05360
$237$	−3.10416	−0.201637
$238$	−44.1950	−2.86474
$239$	−17.3698	−1.12356	−0.561780	−	0.827287i	$-0.689883\pi$
$239$	−17.3698	−1.12356	−0.561780	+	0.827287i	$0.689883\pi$
$240$	−3.36700	−0.217339
$241$	−26.8169	−1.72743	−0.863713	−	0.503985i	$-0.831867\pi$
$241$	−26.8169	−1.72743	−0.863713	+	0.503985i	$0.831867\pi$
$242$	−48.1769	−3.09693
$243$	−6.94217	−0.445341
$244$	−23.3501	−1.49484
$245$	0.814846	0.0520586
$246$	32.2419	2.05567
$247$	19.6693	1.25153
$248$	−2.74485	−0.174298
$249$	−16.6484	−1.05505
$250$	22.9492	1.45144
$251$	4.81704	0.304049	0.152024	−	0.988377i	$-0.451421\pi$
$251$	4.81704	0.304049	0.152024	+	0.988377i	$0.451421\pi$
$252$	−6.92761	−0.436399
$253$	−42.8851	−2.69616
$254$	38.6277	2.42372
$255$	−11.1710	−0.699554
$256$	−26.6409	−1.66505
$257$	20.0633	1.25152	0.625759	−	0.780017i	$-0.284790\pi$
$257$	20.0633	1.25152	0.625759	+	0.780017i	$0.284790\pi$
$258$	38.7537	2.41270
$259$	−16.7891	−1.04323
$260$	16.7037	1.03592
$261$	4.55142	0.281726
$262$	−26.8454	−1.65851
$263$	11.0217	0.679628	0.339814	−	0.940493i	$-0.389636\pi$
$263$	11.0217	0.679628	0.339814	+	0.940493i	$0.389636\pi$
$264$	33.3527	2.05272
$265$	−9.06558	−0.556894
$266$	−31.1944	−1.91265
$267$	−10.4449	−0.639218
$268$	9.46496	0.578164
$269$	−28.2508	−1.72248	−0.861240	−	0.508199i	$-0.830311\pi$
$269$	−28.2508	−1.72248	−0.861240	+	0.508199i	$0.830311\pi$
$270$	−14.6289	−0.890284
$271$	−19.6956	−1.19642	−0.598210	−	0.801339i	$-0.704121\pi$
$271$	−19.6956	−1.19642	−0.598210	+	0.801339i	$0.704121\pi$
$272$	13.4619	0.816250
$273$	−17.6627	−1.06899
$274$	−7.51547	−0.454026
$275$	−21.2187	−1.27953
$276$	42.5955	2.56395
$277$	28.7396	1.72679	0.863396	−	0.504526i	$-0.168333\pi$
$277$	28.7396	1.72679	0.863396	+	0.504526i	$0.168333\pi$
$278$	18.0767	1.08417
$279$	−0.478101	−0.0286232
$280$	−11.9693	−0.715301
$281$	−26.3874	−1.57414	−0.787069	−	0.616865i	$-0.788402\pi$
$281$	−26.3874	−1.57414	−0.787069	+	0.616865i	$0.788402\pi$
$282$	19.0033	1.13163
$283$	−22.8496	−1.35827	−0.679134	−	0.734014i	$-0.737644\pi$
$283$	−22.8496	−1.35827	−0.679134	+	0.734014i	$0.737644\pi$
$284$	−3.64846	−0.216496
$285$	−7.88488	−0.467060
$286$	−55.4170	−3.27687
$287$	24.7952	1.46361
$288$	−2.08016	−0.122574
$289$	27.6638	1.62728
$290$	17.4045	1.02203
$291$	7.27977	0.426747
$292$	−37.0432	−2.16779
$293$	−6.91335	−0.403882	−0.201941	−	0.979398i	$-0.564725\pi$
$293$	−6.91335	−0.403882	−0.201941	+	0.979398i	$0.564725\pi$
$294$	2.68512	0.156600
$295$	14.1174	0.821946
$296$	23.6396	1.37403
$297$	31.3488	1.81904
$298$	−44.6177	−2.58464
$299$	−31.9774	−1.84930
$300$	21.0754	1.21679
$301$	29.8030	1.71782
$302$	−38.7674	−2.23082
$303$	8.81981	0.506685
$304$	9.50192	0.544973
$305$	−7.02707	−0.402369
$306$	10.8389	0.619621
$307$	−7.85770	−0.448463	−0.224231	−	0.974536i	$-0.571987\pi$
$307$	−7.85770	−0.448463	−0.224231	+	0.974536i	$0.571987\pi$
$308$	56.7688	3.23470
$309$	−25.2994	−1.43923
$310$	−1.82825	−0.103838
$311$	−29.2261	−1.65726	−0.828630	−	0.559796i	$-0.810879\pi$
$311$	−29.2261	−1.65726	−0.828630	+	0.559796i	$0.810879\pi$
$312$	24.8696	1.40796
$313$	6.26393	0.354058	0.177029	−	0.984206i	$-0.443351\pi$
$313$	6.26393	0.354058	0.177029	+	0.984206i	$0.443351\pi$
$314$	35.7348	2.01663
$315$	−2.08482	−0.117466
$316$	7.43935	0.418496
$317$	7.65786	0.430108	0.215054	−	0.976602i	$-0.431007\pi$
$317$	7.65786	0.430108	0.215054	+	0.976602i	$0.431007\pi$
$318$	−29.8734	−1.67522
$319$	−37.2969	−2.08823
$320$	−12.3779	−0.691944
$321$	7.86981	0.439250
$322$	50.7144	2.82620
$323$	31.5253	1.75411
$324$	−23.6679	−1.31488
$325$	−15.8218	−0.877633
$326$	−8.30339	−0.459882
$327$	−22.6318	−1.25154
$328$	−34.9124	−1.92772
$329$	14.6142	0.805708
$330$	22.2151	1.22290
$331$	−12.6846	−0.697208	−0.348604	−	0.937270i	$-0.613344\pi$
$331$	−12.6846	−0.697208	−0.348604	+	0.937270i	$0.613344\pi$
$332$	39.8991	2.18975
$333$	4.11758	0.225642
$334$	20.4857	1.12093
$335$	2.84842	0.155626
$336$	−8.53255	−0.465489
$337$	−15.0359	−0.819059	−0.409529	−	0.912297i	$-0.634307\pi$
$337$	−15.0359	−0.819059	−0.409529	+	0.912297i	$0.634307\pi$
$338$	−10.4254	−0.567068
$339$	−1.52236	−0.0826835
$340$	26.7721	1.45192
$341$	3.91784	0.212163
$342$	7.65051	0.413692
$343$	−17.4123	−0.940177
$344$	−41.9636	−2.26252
$345$	12.8189	0.690144
$346$	−16.1415	−0.867774
$347$	−13.7185	−0.736446	−0.368223	−	0.929738i	$-0.620034\pi$
$347$	−13.7185	−0.736446	−0.368223	+	0.929738i	$0.620034\pi$
$348$	37.0451	1.98582
$349$	−0.507825	−0.0271832	−0.0135916	−	0.999908i	$-0.504326\pi$
$349$	−0.507825	−0.0271832	−0.0135916	+	0.999908i	$0.504326\pi$
$350$	25.0924	1.34125
$351$	23.3753	1.24768
$352$	17.0460	0.908555
$353$	14.0488	0.747743	0.373872	−	0.927480i	$-0.378030\pi$
$353$	14.0488	0.747743	0.373872	+	0.927480i	$0.378030\pi$
$354$	46.5203	2.47253
$355$	−1.09798	−0.0582748
$356$	25.0320	1.32669
$357$	−28.3091	−1.49828
$358$	−30.5726	−1.61581
$359$	−17.3275	−0.914512	−0.457256	−	0.889335i	$-0.651168\pi$
$359$	−17.3275	−0.914512	−0.457256	+	0.889335i	$0.651168\pi$
$360$	2.93550	0.154714
$361$	3.25169	0.171141
$362$	−5.65161	−0.297042
$363$	−30.8597	−1.61972
$364$	42.3299	2.21869
$365$	−11.1479	−0.583509
$366$	−23.1560	−1.21038
$367$	12.1464	0.634036	0.317018	−	0.948420i	$-0.397318\pi$
$367$	12.1464	0.634036	0.317018	+	0.948420i	$0.397318\pi$
$368$	−15.4478	−0.805271
$369$	−6.08109	−0.316569
$370$	15.7455	0.818572
$371$	−22.9737	−1.19274
$372$	−3.89138	−0.201759
$373$	−4.07319	−0.210902	−0.105451	−	0.994425i	$-0.533629\pi$
$373$	−4.07319	−0.210902	−0.105451	+	0.994425i	$0.533629\pi$
$374$	−88.8205	−4.59280
$375$	14.7001	0.759112
$376$	−20.5773	−1.06119
$377$	−27.8106	−1.43232
$378$	−37.0720	−1.90678
$379$	17.0444	0.875509	0.437755	−	0.899094i	$-0.355774\pi$
$379$	17.0444	0.875509	0.437755	+	0.899094i	$0.355774\pi$
$380$	18.8967	0.969380
$381$	24.7430	1.26762
$382$	36.8512	1.88547
$383$	11.3282	0.578845	0.289422	−	0.957201i	$-0.406537\pi$
$383$	11.3282	0.578845	0.289422	+	0.957201i	$0.406537\pi$
$384$	−31.5071	−1.60784
$385$	17.0842	0.870693
$386$	−50.3585	−2.56318
$387$	−7.30927	−0.371551
$388$	−17.4465	−0.885712
$389$	−29.8942	−1.51569	−0.757847	−	0.652432i	$-0.773749\pi$
$389$	−29.8942	−1.51569	−0.757847	+	0.652432i	$0.773749\pi$
$390$	16.5648	0.838790
$391$	−51.2523	−2.59194
$392$	−2.90752	−0.146852
$393$	−17.1958	−0.867415
$394$	−38.9833	−1.96395
$395$	2.23883	0.112648
$396$	−13.9227	−0.699642
$397$	−24.7101	−1.24017	−0.620083	−	0.784536i	$-0.712901\pi$
$397$	−24.7101	−1.24017	−0.620083	+	0.784536i	$0.712901\pi$
$398$	38.5791	1.93379
$399$	−19.9816	−1.00033
$400$	−7.64324	−0.382162
$401$	−4.42311	−0.220879	−0.110440	−	0.993883i	$-0.535226\pi$
$401$	−4.42311	−0.220879	−0.110440	+	0.993883i	$0.535226\pi$
$402$	9.38627	0.468144
$403$	2.92135	0.145523
$404$	−21.1373	−1.05162
$405$	−7.12271	−0.353930
$406$	44.1060	2.18894
$407$	−33.7418	−1.67252
$408$	39.8602	1.97337
$409$	−27.8472	−1.37695	−0.688477	−	0.725258i	$-0.741720\pi$
$409$	−27.8472	−1.37695	−0.688477	+	0.725258i	$0.741720\pi$
$410$	−23.2540	−1.14843
$411$	−4.81404	−0.237459
$412$	60.6319	2.98712
$413$	35.7758	1.76041
$414$	−12.4378	−0.611286
$415$	12.0074	0.589420
$416$	12.7104	0.623179
$417$	11.5791	0.567029
$418$	−62.6927	−3.06640
$419$	35.0204	1.71086	0.855430	−	0.517918i	$-0.173293\pi$
$419$	35.0204	1.71086	0.855430	+	0.517918i	$0.173293\pi$
$420$	−16.9689	−0.827996
$421$	−3.39517	−0.165471	−0.0827353	−	0.996572i	$-0.526366\pi$
$421$	−3.39517	−0.165471	−0.0827353	+	0.996572i	$0.526366\pi$
$422$	19.6267	0.955414
$423$	−3.58418	−0.174269
$424$	32.3477	1.57094
$425$	−25.3586	−1.23007
$426$	−3.61812	−0.175299
$427$	−17.8078	−0.861778
$428$	−18.8606	−0.911660
$429$	−35.4974	−1.71383
$430$	−27.9505	−1.34789
$431$	−12.7675	−0.614988	−0.307494	−	0.951550i	$-0.599490\pi$
$431$	−12.7675	−0.614988	−0.307494	+	0.951550i	$0.599490\pi$
$432$	11.2923	0.543299
$433$	−18.4819	−0.888181	−0.444091	−	0.895982i	$-0.646473\pi$
$433$	−18.4819	−0.888181	−0.444091	+	0.895982i	$0.646473\pi$
$434$	−4.63309	−0.222396
$435$	11.1485	0.534529
$436$	54.2388	2.59757
$437$	−36.1757	−1.73052
$438$	−36.7352	−1.75527
$439$	34.7871	1.66030	0.830150	−	0.557540i	$-0.188255\pi$
$439$	34.7871	1.66030	0.830150	+	0.557540i	$0.188255\pi$
$440$	−24.0551	−1.14678
$441$	−0.506436	−0.0241160
$442$	−66.2293	−3.15021
$443$	−5.89630	−0.280142	−0.140071	−	0.990141i	$-0.544733\pi$
$443$	−5.89630	−0.280142	−0.140071	+	0.990141i	$0.544733\pi$
$444$	33.5139	1.59050
$445$	7.53323	0.357109
$446$	3.14129	0.148744
$447$	−28.5799	−1.35178
$448$	−31.3676	−1.48198
$449$	−1.06936	−0.0504663	−0.0252331	−	0.999682i	$-0.508033\pi$
$449$	−1.06936	−0.0504663	−0.0252331	+	0.999682i	$0.508033\pi$
$450$	−6.15398	−0.290102
$451$	49.8319	2.34649
$452$	3.64846	0.171609
$453$	−24.8325	−1.16673
$454$	−52.7807	−2.47712
$455$	12.7389	0.597210
$456$	28.1347	1.31753
$457$	−26.8495	−1.25597	−0.627984	−	0.778226i	$-0.716120\pi$
$457$	−26.8495	−1.25597	−0.627984	+	0.778226i	$0.716120\pi$
$458$	−32.1038	−1.50011
$459$	37.4652	1.74873
$460$	−30.7213	−1.43239
$461$	−28.3813	−1.32185	−0.660925	−	0.750452i	$-0.729836\pi$
$461$	−28.3813	−1.32185	−0.660925	+	0.750452i	$0.729836\pi$
$462$	56.2968	2.61917
$463$	−3.40681	−0.158328	−0.0791640	−	0.996862i	$-0.525225\pi$
$463$	−3.40681	−0.158328	−0.0791640	+	0.996862i	$0.525225\pi$
$464$	−13.4348	−0.623697
$465$	−1.17109	−0.0543079
$466$	−32.6698	−1.51340
$467$	32.6134	1.50917	0.754584	−	0.656204i	$-0.227839\pi$
$467$	32.6134	1.50917	0.754584	+	0.656204i	$0.227839\pi$
$468$	−10.3815	−0.479886
$469$	7.21838	0.333314
$470$	−13.7058	−0.632203
$471$	22.8900	1.05471
$472$	−50.3735	−2.31863
$473$	59.8963	2.75404
$474$	7.37750	0.338860
$475$	−17.8990	−0.821263
$476$	67.8449	3.10967
$477$	5.63436	0.257980
$478$	41.2819	1.88819
$479$	14.1783	0.647822	0.323911	−	0.946088i	$-0.395002\pi$
$479$	14.1783	0.647822	0.323911	+	0.946088i	$0.395002\pi$
$480$	−5.09525	−0.232565
$481$	−25.1597	−1.14718
$482$	63.7342	2.90301
$483$	32.4851	1.47812
$484$	73.9576	3.36171
$485$	−5.25042	−0.238409
$486$	16.4991	0.748415
$487$	−20.2941	−0.919614	−0.459807	−	0.888019i	$-0.652081\pi$
$487$	−20.2941	−0.919614	−0.459807	+	0.888019i	$0.652081\pi$
$488$	25.0739	1.13504
$489$	−5.31874	−0.240522
$490$	−1.93660	−0.0874868
$491$	0.0975320	0.00440156	0.00220078	−	0.999998i	$-0.499299\pi$
$491$	0.0975320	0.00440156	0.00220078	+	0.999998i	$0.499299\pi$
$492$	−49.4954	−2.23143
$493$	−44.5739	−2.00751
$494$	−46.7470	−2.10325
$495$	−4.18996	−0.188324
$496$	1.41126	0.0633673
$497$	−2.78247	−0.124811
$498$	39.5674	1.77306
$499$	16.1844	0.724515	0.362258	−	0.932078i	$-0.382006\pi$
$499$	16.1844	0.724515	0.362258	+	0.932078i	$0.382006\pi$
$500$	−35.2300	−1.57553
$501$	13.1221	0.586253
$502$	−11.4484	−0.510968
$503$	−9.36858	−0.417724	−0.208862	−	0.977945i	$-0.566976\pi$
$503$	−9.36858	−0.417724	−0.208862	+	0.977945i	$0.566976\pi$
$504$	7.43904	0.331361
$505$	−6.36115	−0.283067
$506$	101.923	4.53102
$507$	−6.67801	−0.296581
$508$	−59.2984	−2.63094
$509$	29.5500	1.30978	0.654890	−	0.755724i	$-0.272715\pi$
$509$	29.5500	1.30978	0.654890	+	0.755724i	$0.272715\pi$
$510$	26.5495	1.17563
$511$	−28.2507	−1.24974
$512$	21.9237	0.968899
$513$	26.4443	1.16754
$514$	−47.6835	−2.10323
$515$	18.2468	0.804050
$516$	−59.4918	−2.61898
$517$	29.3708	1.29173
$518$	39.9018	1.75319
$519$	−10.3395	−0.453852
$520$	−17.9368	−0.786581
$521$	7.36895	0.322839	0.161420	−	0.986886i	$-0.448393\pi$
$521$	7.36895	0.322839	0.161420	+	0.986886i	$0.448393\pi$
$522$	−10.8171	−0.473452
$523$	35.9618	1.57250	0.786251	−	0.617908i	$-0.212020\pi$
$523$	35.9618	1.57250	0.786251	+	0.617908i	$0.212020\pi$
$524$	41.2111	1.80031
$525$	16.0730	0.701482
$526$	−26.1947	−1.14214
$527$	4.68224	0.203962
$528$	−17.1482	−0.746280
$529$	35.8128	1.55708
$530$	21.5457	0.935886
$531$	−8.77412	−0.380764
$532$	47.8874	2.07618
$533$	37.1573	1.60946
$534$	24.8239	1.07423
$535$	−5.67598	−0.245394
$536$	−10.1637	−0.439005
$537$	−19.5833	−0.845081
$538$	67.1421	2.89470
$539$	4.15003	0.178754
$540$	22.4571	0.966402
$541$	20.5404	0.883101	0.441551	−	0.897236i	$-0.354429\pi$
$541$	20.5404	0.883101	0.441551	+	0.897236i	$0.354429\pi$
$542$	46.8094	2.01064
$543$	−3.62014	−0.155355
$544$	20.3718	0.873434
$545$	16.3229	0.699194
$546$	41.9779	1.79649
$547$	−15.9733	−0.682970	−0.341485	−	0.939887i	$-0.610930\pi$
$547$	−15.9733	−0.682970	−0.341485	+	0.939887i	$0.610930\pi$
$548$	11.5372	0.492845
$549$	4.36740	0.186396
$550$	50.4293	2.15031
$551$	−31.4618	−1.34032
$552$	−45.7401	−1.94683
$553$	5.67356	0.241265
$554$	−68.3038	−2.90195
$555$	10.0858	0.428119
$556$	−27.7501	−1.17687
$557$	28.3052	1.19933	0.599664	−	0.800252i	$-0.295301\pi$
$557$	28.3052	1.19933	0.599664	+	0.800252i	$0.295301\pi$
$558$	1.13628	0.0481025
$559$	44.6619	1.88900
$560$	6.15397	0.260053
$561$	−56.8940	−2.40207
$562$	62.7135	2.64541
$563$	39.4935	1.66445	0.832226	−	0.554436i	$-0.187066\pi$
$563$	39.4935	1.66445	0.832226	+	0.554436i	$0.187066\pi$
$564$	−29.1725	−1.22838
$565$	1.09798	0.0461924
$566$	54.3055	2.28263
$567$	−18.0501	−0.758035
$568$	3.91780	0.164387
$569$	5.31495	0.222814	0.111407	−	0.993775i	$-0.464464\pi$
$569$	5.31495	0.222814	0.111407	+	0.993775i	$0.464464\pi$
$570$	18.7396	0.784915
$571$	23.1867	0.970334	0.485167	−	0.874422i	$-0.338759\pi$
$571$	23.1867	0.970334	0.485167	+	0.874422i	$0.338759\pi$
$572$	85.0721	3.55704
$573$	23.6051	0.986116
$574$	−58.9294	−2.45967
$575$	29.0994	1.21353
$576$	7.69299	0.320541
$577$	46.2192	1.92413	0.962066	−	0.272818i	$-0.0879556\pi$
$577$	46.2192	1.92413	0.962066	+	0.272818i	$0.0879556\pi$
$578$	−65.7471	−2.73472
$579$	−32.2572	−1.34056
$580$	−26.7182	−1.10941
$581$	30.4288	1.26240
$582$	−17.3014	−0.717168
$583$	−46.1712	−1.91222
$584$	39.7779	1.64602
$585$	−3.12425	−0.129172
$586$	16.4306	0.678742
$587$	7.18139	0.296408	0.148204	−	0.988957i	$-0.452651\pi$
$587$	7.18139	0.296408	0.148204	+	0.988957i	$0.452651\pi$
$588$	−4.12200	−0.169989
$589$	3.30489	0.136176
$590$	−33.5521	−1.38132
$591$	−24.9708	−1.02716
$592$	−12.1542	−0.499536
$593$	10.3618	0.425509	0.212755	−	0.977106i	$-0.431757\pi$
$593$	10.3618	0.425509	0.212755	+	0.977106i	$0.431757\pi$
$594$	−74.5051	−3.05698
$595$	20.4175	0.837037
$596$	68.4939	2.80562
$597$	24.7119	1.01139
$598$	75.9991	3.10783
$599$	−4.99501	−0.204091	−0.102045	−	0.994780i	$-0.532539\pi$
$599$	−4.99501	−0.204091	−0.102045	+	0.994780i	$0.532539\pi$
$600$	−22.6313	−0.923917
$601$	−30.3046	−1.23615	−0.618074	−	0.786120i	$-0.712087\pi$
$601$	−30.3046	−1.23615	−0.618074	+	0.786120i	$0.712087\pi$
$602$	−70.8312	−2.88687
$603$	−1.77033	−0.0720933
$604$	59.5129	2.42155
$605$	22.2571	0.904880
$606$	−20.9616	−0.851506
$607$	−20.4950	−0.831868	−0.415934	−	0.909395i	$-0.636545\pi$
$607$	−20.4950	−0.831868	−0.415934	+	0.909395i	$0.636545\pi$
$608$	14.3792	0.583152
$609$	28.2521	1.14483
$610$	16.7009	0.676198
$611$	21.9004	0.885997
$612$	−16.6391	−0.672598
$613$	37.4503	1.51260	0.756301	−	0.654223i	$-0.227004\pi$
$613$	37.4503	1.51260	0.756301	+	0.654223i	$0.227004\pi$
$614$	18.6750	0.753661
$615$	−14.8953	−0.600638
$616$	−60.9598	−2.45614
$617$	33.2337	1.33794	0.668969	−	0.743290i	$-0.266736\pi$
$617$	33.2337	1.33794	0.668969	+	0.743290i	$0.266736\pi$
$618$	60.1278	2.41869
$619$	−27.0979	−1.08916	−0.544579	−	0.838710i	$-0.683310\pi$
$619$	−27.0979	−1.08916	−0.544579	+	0.838710i	$0.683310\pi$
$620$	2.80660	0.112716
$621$	−42.9919	−1.72520
$622$	69.4602	2.78510
$623$	19.0905	0.764843
$624$	−12.7866	−0.511875
$625$	8.36994	0.334798
$626$	−14.8872	−0.595010
$627$	−40.1578	−1.60375
$628$	−54.8575	−2.18905
$629$	−40.3251	−1.60787
$630$	4.95489	0.197408
$631$	−43.4383	−1.72925	−0.864626	−	0.502416i	$-0.832445\pi$
$631$	−43.4383	−1.72925	−0.864626	+	0.502416i	$0.832445\pi$
$632$	−7.98856	−0.317768
$633$	12.5719	0.499688
$634$	−18.2000	−0.722816
$635$	−17.8455	−0.708177
$636$	45.8594	1.81844
$637$	3.09448	0.122608
$638$	88.6416	3.50936
$639$	0.682408	0.0269956
$640$	22.7240	0.898244
$641$	−4.00121	−0.158038	−0.0790191	−	0.996873i	$-0.525179\pi$
$641$	−4.00121	−0.158038	−0.0790191	+	0.996873i	$0.525179\pi$
$642$	−18.7038	−0.738179
$643$	−24.4689	−0.964960	−0.482480	−	0.875907i	$-0.660264\pi$
$643$	−24.4689	−0.964960	−0.482480	+	0.875907i	$0.660264\pi$
$644$	−77.8530	−3.06784
$645$	−17.9037	−0.704958
$646$	−74.9246	−2.94787
$647$	−15.6489	−0.615222	−0.307611	−	0.951512i	$-0.599529\pi$
$647$	−15.6489	−0.615222	−0.307611	+	0.951512i	$0.599529\pi$
$648$	25.4152	0.998402
$649$	71.9001	2.82233
$650$	37.6028	1.47490
$651$	−2.96773	−0.116315
$652$	12.7468	0.499201
$653$	−10.7075	−0.419016	−0.209508	−	0.977807i	$-0.567186\pi$
$653$	−10.7075	−0.419016	−0.209508	+	0.977807i	$0.567186\pi$
$654$	53.7879	2.10327
$655$	12.4022	0.484595
$656$	17.9501	0.700834
$657$	6.92856	0.270309
$658$	−34.7329	−1.35403
$659$	5.10028	0.198679	0.0993394	−	0.995054i	$-0.468327\pi$
$659$	5.10028	0.198679	0.0993394	+	0.995054i	$0.468327\pi$
$660$	−34.1030	−1.32746
$661$	−29.2559	−1.13792	−0.568962	−	0.822364i	$-0.692655\pi$
$661$	−29.2559	−1.13792	−0.568962	+	0.822364i	$0.692655\pi$
$662$	30.1468	1.17169
$663$	−42.4232	−1.64758
$664$	−42.8447	−1.66270
$665$	14.4114	0.558851
$666$	−9.78604	−0.379201
$667$	51.1492	1.98050
$668$	−31.4481	−1.21677
$669$	2.01215	0.0777944
$670$	−6.76970	−0.261536
$671$	−35.7890	−1.38162
$672$	−12.9122	−0.498099
$673$	29.2904	1.12906	0.564531	−	0.825412i	$-0.309057\pi$
$673$	29.2904	1.12906	0.564531	+	0.825412i	$0.309057\pi$
$674$	35.7351	1.37646
$675$	−21.2715	−0.818740
$676$	16.0043	0.615552
$677$	−7.11543	−0.273468	−0.136734	−	0.990608i	$-0.543661\pi$
$677$	−7.11543	−0.273468	−0.136734	+	0.990608i	$0.543661\pi$
$678$	3.61812	0.138953
$679$	−13.3054	−0.510616
$680$	−28.7485	−1.10246
$681$	−33.8087	−1.29555
$682$	−9.31132	−0.356549
$683$	13.2627	0.507483	0.253742	−	0.967272i	$-0.418339\pi$
$683$	13.2627	0.507483	0.253742	+	0.967272i	$0.418339\pi$
$684$	−11.7445	−0.449062
$685$	3.47205	0.132660
$686$	41.3830	1.58001
$687$	−20.5641	−0.784569
$688$	21.5754	0.822556
$689$	−34.4277	−1.31159
$690$	−30.4659	−1.15982
$691$	−43.7133	−1.66293	−0.831465	−	0.555576i	$-0.812498\pi$
$691$	−43.7133	−1.66293	−0.831465	+	0.555576i	$0.812498\pi$
$692$	24.7793	0.941967
$693$	−10.6180	−0.403346
$694$	32.6040	1.23763
$695$	−8.35121	−0.316780
$696$	−39.7799	−1.50785
$697$	59.5545	2.25579
$698$	1.20692	0.0456827
$699$	−20.9266	−0.791518
$700$	−38.5201	−1.45592
$701$	−39.2244	−1.48149	−0.740743	−	0.671788i	$-0.765527\pi$
$701$	−39.2244	−1.48149	−0.740743	+	0.671788i	$0.765527\pi$
$702$	−55.5549	−2.09679
$703$	−28.4629	−1.07350
$704$	−63.0407	−2.37594
$705$	−8.77928	−0.330647
$706$	−33.3891	−1.25662
$707$	−16.1202	−0.606263
$708$	−71.4146	−2.68393
$709$	−1.95057	−0.0732553	−0.0366276	−	0.999329i	$-0.511662\pi$
$709$	−1.95057	−0.0732553	−0.0366276	+	0.999329i	$0.511662\pi$
$710$	2.60952	0.0979334
$711$	−1.39146	−0.0521837
$712$	−26.8800	−1.00737
$713$	−5.37294	−0.201218
$714$	67.2808	2.51792
$715$	25.6019	0.957458
$716$	46.9328	1.75396
$717$	26.4432	0.987538
$718$	41.1814	1.53688
$719$	−38.1165	−1.42150	−0.710752	−	0.703442i	$-0.751645\pi$
$719$	−38.1165	−1.42150	−0.710752	+	0.703442i	$0.751645\pi$
$720$	−1.50928	−0.0562474
$721$	46.2405	1.72208
$722$	−7.72811	−0.287611
$723$	40.8250	1.51830
$724$	8.67594	0.322439
$725$	25.3075	0.939898
$726$	73.3427	2.72200
$727$	−19.3988	−0.719461	−0.359730	−	0.933056i	$-0.617131\pi$
$727$	−19.3988	−0.719461	−0.359730	+	0.933056i	$0.617131\pi$
$728$	−45.4549	−1.68467
$729$	30.0298	1.11221
$730$	26.4947	0.980612
$731$	71.5826	2.64758
$732$	35.5473	1.31387
$733$	23.9892	0.886060	0.443030	−	0.896507i	$-0.353904\pi$
$733$	23.9892	0.886060	0.443030	+	0.896507i	$0.353904\pi$
$734$	−28.8677	−1.06553
$735$	−1.24049	−0.0457562
$736$	−23.3770	−0.861686
$737$	14.5071	0.534375
$738$	14.4526	0.532008
$739$	23.4003	0.860793	0.430397	−	0.902640i	$-0.358374\pi$
$739$	23.4003	0.860793	0.430397	+	0.902640i	$0.358374\pi$
$740$	−24.1714	−0.888559
$741$	−29.9438	−1.10001
$742$	54.6004	2.00444
$743$	25.9478	0.951931	0.475966	−	0.879464i	$-0.342099\pi$
$743$	25.9478	0.951931	0.475966	+	0.879464i	$0.342099\pi$
$744$	4.17866	0.153197
$745$	20.6128	0.755195
$746$	9.68055	0.354430
$747$	−7.46274	−0.273047
$748$	136.351	4.98548
$749$	−14.3839	−0.525575
$750$	−34.9371	−1.27572
$751$	29.7033	1.08389	0.541944	−	0.840415i	$-0.317688\pi$
$751$	29.7033	1.08389	0.541944	+	0.840415i	$0.317688\pi$
$752$	10.5798	0.385804
$753$	−7.33329	−0.267240
$754$	66.0959	2.40707
$755$	17.9101	0.651814
$756$	56.9102	2.06980
$757$	−22.4908	−0.817443	−0.408721	−	0.912659i	$-0.634025\pi$
$757$	−22.4908	−0.817443	−0.408721	+	0.912659i	$0.634025\pi$
$758$	−40.5084	−1.47133
$759$	65.2867	2.36976
$760$	−20.2917	−0.736058
$761$	−10.2445	−0.371364	−0.185682	−	0.982610i	$-0.559449\pi$
$761$	−10.2445	−0.371364	−0.185682	+	0.982610i	$0.559449\pi$
$762$	−58.8054	−2.13030
$763$	41.3648	1.49751
$764$	−56.5713	−2.04668
$765$	−5.00745	−0.181045
$766$	−26.9232	−0.972774
$767$	53.6126	1.93584
$768$	40.5571	1.46348
$769$	−23.6522	−0.852921	−0.426460	−	0.904506i	$-0.640240\pi$
$769$	−23.6522	−0.852921	−0.426460	+	0.904506i	$0.640240\pi$
$770$	−40.6032	−1.46324
$771$	−30.5437	−1.10001
$772$	77.3067	2.78233
$773$	25.3533	0.911894	0.455947	−	0.890007i	$-0.349301\pi$
$773$	25.3533	0.911894	0.455947	+	0.890007i	$0.349301\pi$
$774$	17.3716	0.624408
$775$	−2.65842	−0.0954932
$776$	18.7345	0.672529
$777$	25.5592	0.916930
$778$	71.0479	2.54719
$779$	42.0357	1.50609
$780$	−25.4290	−0.910506
$781$	−5.59204	−0.200099
$782$	121.809	4.35587
$783$	−37.3898	−1.33620
$784$	1.49490	0.0533891
$785$	−16.5090	−0.589233
$786$	40.8685	1.45773
$787$	34.8881	1.24363	0.621814	−	0.783165i	$-0.286396\pi$
$787$	34.8881	1.24363	0.621814	+	0.783165i	$0.286396\pi$
$788$	59.8443	2.13186
$789$	−16.7791	−0.597350
$790$	−5.32091	−0.189309
$791$	2.78247	0.0989332
$792$	14.9506	0.531245
$793$	−26.6862	−0.947654
$794$	58.7273	2.08415
$795$	13.8011	0.489475
$796$	−59.2238	−2.09913
$797$	41.7991	1.48060	0.740300	−	0.672277i	$-0.234683\pi$
$797$	41.7991	1.48060	0.740300	+	0.672277i	$0.234683\pi$
$798$	47.4892	1.68110
$799$	35.1013	1.24179
$800$	−11.5664	−0.408935
$801$	−4.68199	−0.165430
$802$	10.5122	0.371197
$803$	−56.7766	−2.00360
$804$	−14.4091	−0.508170
$805$	−23.4294	−0.825778
$806$	−6.94302	−0.244557
$807$	43.0079	1.51395
$808$	22.6978	0.798505
$809$	−38.8525	−1.36598	−0.682991	−	0.730426i	$-0.739321\pi$
$809$	−38.8525	−1.36598	−0.682991	+	0.730426i	$0.739321\pi$
$810$	16.9282	0.594795
$811$	−49.8097	−1.74906	−0.874528	−	0.484975i	$-0.838829\pi$
$811$	−49.8097	−1.74906	−0.874528	+	0.484975i	$0.838829\pi$
$812$	−67.7083	−2.37610
$813$	29.9838	1.05158
$814$	80.1924	2.81074
$815$	3.83606	0.134371
$816$	−20.4940	−0.717433
$817$	50.5256	1.76767
$818$	66.1829	2.31403
$819$	−7.91738	−0.276656
$820$	35.6978	1.24662
$821$	0.455216	0.0158871	0.00794357	−	0.999968i	$-0.497471\pi$
$821$	0.455216	0.0158871	0.00794357	+	0.999968i	$0.497471\pi$
$822$	11.4413	0.399061
$823$	25.5977	0.892278	0.446139	−	0.894964i	$-0.352799\pi$
$823$	25.5977	0.892278	0.446139	+	0.894964i	$0.352799\pi$
$824$	−65.1080	−2.26815
$825$	32.3025	1.12463
$826$	−85.0265	−2.95845
$827$	40.6492	1.41351	0.706756	−	0.707457i	$-0.250158\pi$
$827$	40.6492	1.41351	0.706756	+	0.707457i	$0.250158\pi$
$828$	19.0937	0.663551
$829$	26.2225	0.910744	0.455372	−	0.890301i	$-0.349506\pi$
$829$	26.2225	0.910744	0.455372	+	0.890301i	$0.349506\pi$
$830$	−28.5374	−0.990546
$831$	−43.7521	−1.51774
$832$	−47.0065	−1.62966
$833$	4.95973	0.171845
$834$	−27.5194	−0.952917
$835$	−9.46413	−0.327520
$836$	96.2412	3.32857
$837$	3.92759	0.135757
$838$	−83.2313	−2.87518
$839$	26.9231	0.929490	0.464745	−	0.885445i	$-0.346146\pi$
$839$	26.9231	0.929490	0.464745	+	0.885445i	$0.346146\pi$
$840$	18.2216	0.628705
$841$	15.4841	0.533935
$842$	8.06913	0.278081
$843$	40.1712	1.38357
$844$	−30.1295	−1.03710
$845$	4.81641	0.165690
$846$	8.51833	0.292866
$847$	56.4032	1.93804
$848$	−16.6315	−0.571127
$849$	34.7854	1.19383
$850$	60.2685	2.06719
$851$	46.2736	1.58624
$852$	5.55428	0.190287
$853$	−24.1883	−0.828190	−0.414095	−	0.910234i	$-0.635902\pi$
$853$	−24.1883	−0.828190	−0.414095	+	0.910234i	$0.635902\pi$
$854$	42.3228	1.44826
$855$	−3.53444	−0.120875
$856$	20.2530	0.692232
$857$	−46.2335	−1.57931	−0.789654	−	0.613553i	$-0.789740\pi$
$857$	−46.2335	−1.57931	−0.789654	+	0.613553i	$0.789740\pi$
$858$	84.3648	2.88017
$859$	2.72746	0.0930599	0.0465299	−	0.998917i	$-0.485184\pi$
$859$	2.72746	0.0930599	0.0465299	+	0.998917i	$0.485184\pi$
$860$	42.9076	1.46314
$861$	−37.7473	−1.28642
$862$	30.3438	1.03352
$863$	12.1490	0.413556	0.206778	−	0.978388i	$-0.433702\pi$
$863$	12.1490	0.413556	0.206778	+	0.978388i	$0.433702\pi$
$864$	17.0884	0.581360
$865$	7.45718	0.253552
$866$	43.9249	1.49263
$867$	−42.1143	−1.43028
$868$	7.11239	0.241410
$869$	11.4024	0.386800
$870$	−26.4960	−0.898300
$871$	10.8172	0.366529
$872$	−58.2430	−1.97236
$873$	3.26319	0.110442
$874$	85.9770	2.90822
$875$	−26.8679	−0.908300
$876$	56.3932	1.90535
$877$	−37.6696	−1.27201	−0.636005	−	0.771685i	$-0.719414\pi$
$877$	−37.6696	−1.27201	−0.636005	+	0.771685i	$0.719414\pi$
$878$	−82.6768	−2.79021
$879$	10.5246	0.354987
$880$	12.3679	0.416921
$881$	44.2506	1.49084	0.745420	−	0.666595i	$-0.232249\pi$
$881$	44.2506	1.49084	0.745420	+	0.666595i	$0.232249\pi$
$882$	1.20362	0.0405280
$883$	−55.2651	−1.85982	−0.929909	−	0.367790i	$-0.880115\pi$
$883$	−55.2651	−1.85982	−0.929909	+	0.367790i	$0.880115\pi$
$884$	101.670	3.41955
$885$	−21.4918	−0.722439
$886$	14.0134	0.470790
$887$	−40.2229	−1.35055	−0.675277	−	0.737564i	$-0.735976\pi$
$887$	−40.2229	−1.35055	−0.675277	+	0.737564i	$0.735976\pi$
$888$	−35.9881	−1.20768
$889$	−45.2235	−1.51675
$890$	−17.9038	−0.600138
$891$	−36.2761	−1.21530
$892$	−4.82228	−0.161462
$893$	24.7758	0.829089
$894$	67.9244	2.27173
$895$	14.1241	0.472118
$896$	57.5864	1.92383
$897$	48.6813	1.62542
$898$	2.54149	0.0848108
$899$	−4.67281	−0.155847
$900$	9.44715	0.314905
$901$	−55.1796	−1.83830
$902$	−118.433	−3.94339
$903$	−45.3710	−1.50985
$904$	−3.91780	−0.130304
$905$	2.61097	0.0867916
$906$	59.0181	1.96075
$907$	−26.2708	−0.872307	−0.436153	−	0.899872i	$-0.643660\pi$
$907$	−26.2708	−0.872307	−0.436153	+	0.899872i	$0.643660\pi$
$908$	81.0251	2.68891
$909$	3.95353	0.131130
$910$	−30.2759	−1.00364
$911$	23.6606	0.783911	0.391955	−	0.919984i	$-0.371799\pi$
$911$	23.6606	0.783911	0.391955	+	0.919984i	$0.371799\pi$
$912$	−14.4654	−0.478997
$913$	61.1539	2.02390
$914$	63.8119	2.11071
$915$	10.6978	0.353657
$916$	49.2834	1.62837
$917$	31.4293	1.03789
$918$	−89.0416	−2.93881
$919$	28.6081	0.943693	0.471847	−	0.881681i	$-0.343588\pi$
$919$	28.6081	0.943693	0.471847	+	0.881681i	$0.343588\pi$
$920$	32.9893	1.08763
$921$	11.9623	0.394171
$922$	67.4525	2.22143
$923$	−4.16972	−0.137248
$924$	−86.4228	−2.84310
$925$	22.8952	0.752791
$926$	8.09679	0.266077
$927$	−11.3406	−0.372474
$928$	−20.3308	−0.667391
$929$	32.9207	1.08009	0.540046	−	0.841636i	$-0.318407\pi$
$929$	32.9207	1.08009	0.540046	+	0.841636i	$0.318407\pi$
$930$	2.78326	0.0912668
$931$	3.50076	0.114733
$932$	50.1523	1.64279
$933$	44.4928	1.45663
$934$	−77.5106	−2.53622
$935$	41.0339	1.34195
$936$	11.1479	0.364381
$937$	−46.7072	−1.52586	−0.762929	−	0.646483i	$-0.776239\pi$
$937$	−46.7072	−1.52586	−0.762929	+	0.646483i	$0.776239\pi$
$938$	−17.1556	−0.560149
$939$	−9.53598	−0.311195
$940$	21.0402	0.686255
$941$	−38.8294	−1.26580	−0.632901	−	0.774233i	$-0.718136\pi$
$941$	−38.8294	−1.26580	−0.632901	+	0.774233i	$0.718136\pi$
$942$	−54.4014	−1.77249
$943$	−68.3397	−2.22545
$944$	25.8994	0.842953
$945$	17.1268	0.557134
$946$	−142.352	−4.62828
$947$	34.2049	1.11151	0.555754	−	0.831347i	$-0.312430\pi$
$947$	34.2049	1.11151	0.555754	+	0.831347i	$0.312430\pi$
$948$	−11.3254	−0.367832
$949$	−42.3356	−1.37427
$950$	42.5396	1.38017
$951$	−11.6580	−0.378038
$952$	−72.8536	−2.36120
$953$	1.31948	0.0427422	0.0213711	−	0.999772i	$-0.493197\pi$
$953$	1.31948	0.0427422	0.0213711	+	0.999772i	$0.493197\pi$
$954$	−13.3909	−0.433547
$955$	−17.0248	−0.550909
$956$	−63.3730	−2.04963
$957$	56.7795	1.83542
$958$	−33.6968	−1.08869
$959$	8.79876	0.284127
$960$	18.8436	0.608175
$961$	−30.5091	−0.984166
$962$	59.7957	1.92789
$963$	3.52768	0.113678
$964$	−97.8401	−3.15122
$965$	23.2650	0.748926
$966$	−77.2057	−2.48405
$967$	12.8234	0.412372	0.206186	−	0.978513i	$-0.433895\pi$
$967$	12.8234	0.412372	0.206186	+	0.978513i	$0.433895\pi$
$968$	−79.4175	−2.55258
$969$	−47.9930	−1.54176
$970$	12.4784	0.400657
$971$	20.6287	0.662007	0.331003	−	0.943630i	$-0.392613\pi$
$971$	20.6287	0.662007	0.331003	+	0.943630i	$0.392613\pi$
$972$	−25.3282	−0.812403
$973$	−21.1634	−0.678467
$974$	48.2320	1.54545
$975$	24.0865	0.771385
$976$	−12.8917	−0.412652
$977$	50.8790	1.62776	0.813881	−	0.581031i	$-0.197350\pi$
$977$	50.8790	1.62776	0.813881	+	0.581031i	$0.197350\pi$
$978$	12.6408	0.404207
$979$	38.3669	1.22621
$980$	2.97293	0.0949668
$981$	−10.1448	−0.323900
$982$	−0.231799	−0.00739702
$983$	12.4044	0.395640	0.197820	−	0.980238i	$-0.436614\pi$
$983$	12.4044	0.395640	0.197820	+	0.980238i	$0.436614\pi$
$984$	53.1494	1.69434
$985$	18.0098	0.573839
$986$	105.936	3.37370
$987$	−22.2482	−0.708167
$988$	71.7626	2.28307
$989$	−82.1421	−2.61197
$990$	9.95805	0.316488
$991$	−39.7649	−1.26317	−0.631586	−	0.775305i	$-0.717596\pi$
$991$	−39.7649	−1.26317	−0.631586	+	0.775305i	$0.717596\pi$
$992$	2.13564	0.0678066
$993$	19.3106	0.612802
$994$	6.61295	0.209750
$995$	−17.8230	−0.565028
$996$	−60.7410	−1.92465
$997$	26.5404	0.840541	0.420271	−	0.907399i	$-0.361935\pi$
$997$	26.5404	0.840541	0.420271	+	0.907399i	$0.361935\pi$
$998$	−38.4647	−1.21758
$999$	−33.8258	−1.07020

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.16	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.16	✓	172	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37665 q^{2} -1.52236 q^{3} +3.64846 q^{4} +1.09798 q^{5} +3.61812 q^{6} +2.78247 q^{7} -3.91780 q^{8} -0.682408 q^{9} +O(q^{10})\)	\(q-2.37665 q^{2} -1.52236 q^{3} +3.64846 q^{4} +1.09798 q^{5} +3.61812 q^{6} +2.78247 q^{7} -3.91780 q^{8} -0.682408 q^{9} -2.60952 q^{10} +5.59204 q^{11} -5.55428 q^{12} +4.16972 q^{13} -6.61295 q^{14} -1.67153 q^{15} +2.01433 q^{16} +6.68310 q^{17} +1.62184 q^{18} +4.71717 q^{19} +4.00594 q^{20} -4.23593 q^{21} -13.2903 q^{22} -7.66895 q^{23} +5.96432 q^{24} -3.79444 q^{25} -9.90997 q^{26} +5.60597 q^{27} +10.1517 q^{28} -6.66964 q^{29} +3.97263 q^{30} +0.700609 q^{31} +3.04826 q^{32} -8.51312 q^{33} -15.8834 q^{34} +3.05510 q^{35} -2.48974 q^{36} -6.03390 q^{37} -11.2111 q^{38} -6.34784 q^{39} -4.30168 q^{40} +8.91122 q^{41} +10.0673 q^{42} +10.7110 q^{43} +20.4023 q^{44} -0.749271 q^{45} +18.2264 q^{46} +5.25225 q^{47} -3.06654 q^{48} +0.742131 q^{49} +9.01804 q^{50} -10.1741 q^{51} +15.2131 q^{52} -8.25659 q^{53} -13.3234 q^{54} +6.13996 q^{55} -10.9012 q^{56} -7.18125 q^{57} +15.8514 q^{58} +12.8576 q^{59} -6.09850 q^{60} -6.39999 q^{61} -1.66510 q^{62} -1.89878 q^{63} -11.2733 q^{64} +4.57828 q^{65} +20.2327 q^{66} +2.59424 q^{67} +24.3830 q^{68} +11.6749 q^{69} -7.26089 q^{70} -1.00000 q^{71} +2.67354 q^{72} -10.1531 q^{73} +14.3404 q^{74} +5.77651 q^{75} +17.2104 q^{76} +15.5597 q^{77} +15.0866 q^{78} +2.03904 q^{79} +2.21169 q^{80} -6.48710 q^{81} -21.1788 q^{82} +10.9359 q^{83} -15.4546 q^{84} +7.33791 q^{85} -25.4563 q^{86} +10.1536 q^{87} -21.9085 q^{88} +6.86098 q^{89} +1.78075 q^{90} +11.6021 q^{91} -27.9798 q^{92} -1.06658 q^{93} -12.4828 q^{94} +5.17936 q^{95} -4.64056 q^{96} -4.78188 q^{97} -1.76378 q^{98} -3.81605 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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