LMFDB - Embedded newform 8041.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.65992 q^{2} +0.748300 q^{3} +0.755318 q^{4} -4.19197 q^{5} -1.24211 q^{6} -4.84394 q^{7} +2.06607 q^{8} -2.44005 q^{9} +O(q^{10})$	\(q-1.65992 q^{2} +0.748300 q^{3} +0.755318 q^{4} -4.19197 q^{5} -1.24211 q^{6} -4.84394 q^{7} +2.06607 q^{8} -2.44005 q^{9} +6.95831 q^{10} -1.00000 q^{11} +0.565204 q^{12} -6.28082 q^{13} +8.04053 q^{14} -3.13685 q^{15} -4.94013 q^{16} -1.00000 q^{17} +4.05027 q^{18} -2.93145 q^{19} -3.16627 q^{20} -3.62472 q^{21} +1.65992 q^{22} +1.05441 q^{23} +1.54604 q^{24} +12.5726 q^{25} +10.4256 q^{26} -4.07079 q^{27} -3.65871 q^{28} -3.95333 q^{29} +5.20690 q^{30} +8.30927 q^{31} +4.06806 q^{32} -0.748300 q^{33} +1.65992 q^{34} +20.3056 q^{35} -1.84301 q^{36} -6.24581 q^{37} +4.86596 q^{38} -4.69994 q^{39} -8.66088 q^{40} -1.26183 q^{41} +6.01673 q^{42} -1.00000 q^{43} -0.755318 q^{44} +10.2286 q^{45} -1.75022 q^{46} +0.558074 q^{47} -3.69670 q^{48} +16.4638 q^{49} -20.8694 q^{50} -0.748300 q^{51} -4.74402 q^{52} +14.0460 q^{53} +6.75716 q^{54} +4.19197 q^{55} -10.0079 q^{56} -2.19360 q^{57} +6.56219 q^{58} +15.2740 q^{59} -2.36932 q^{60} -5.01667 q^{61} -13.7927 q^{62} +11.8194 q^{63} +3.12762 q^{64} +26.3290 q^{65} +1.24211 q^{66} +1.59494 q^{67} -0.755318 q^{68} +0.789011 q^{69} -33.7056 q^{70} -15.0010 q^{71} -5.04130 q^{72} -6.68215 q^{73} +10.3675 q^{74} +9.40805 q^{75} -2.21418 q^{76} +4.84394 q^{77} +7.80150 q^{78} -0.622145 q^{79} +20.7089 q^{80} +4.27397 q^{81} +2.09454 q^{82} +4.32948 q^{83} -2.73782 q^{84} +4.19197 q^{85} +1.65992 q^{86} -2.95828 q^{87} -2.06607 q^{88} -9.83661 q^{89} -16.9786 q^{90} +30.4239 q^{91} +0.796411 q^{92} +6.21783 q^{93} -0.926355 q^{94} +12.2885 q^{95} +3.04413 q^{96} -6.90135 q^{97} -27.3284 q^{98} +2.44005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) $ 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.65992	−1.17374	−0.586869	−	0.809682i	$-0.699639\pi$
$2$	−1.65992	−1.17374	−0.586869	+	0.809682i	$0.699639\pi$
$3$	0.748300	0.432031	0.216016	−	0.976390i	$-0.430694\pi$
$3$	0.748300	0.432031	0.216016	+	0.976390i	$0.430694\pi$
$4$	0.755318	0.377659
$5$	−4.19197	−1.87470	−0.937352	−	0.348384i	$-0.886731\pi$
$5$	−4.19197	−1.87470	−0.937352	+	0.348384i	$0.886731\pi$
$6$	−1.24211	−0.507091
$7$	−4.84394	−1.83084	−0.915419	−	0.402503i	$-0.868140\pi$
$7$	−4.84394	−1.83084	−0.915419	+	0.402503i	$0.868140\pi$
$8$	2.06607	0.730465
$9$	−2.44005	−0.813349
$10$	6.95831	2.20041
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.565204	0.163160
$13$	−6.28082	−1.74199	−0.870994	−	0.491294i	$-0.836524\pi$
$13$	−6.28082	−1.74199	−0.870994	+	0.491294i	$0.836524\pi$
$14$	8.04053	2.14892
$15$	−3.13685	−0.809930
$16$	−4.94013	−1.23503
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	4.05027	0.954658
$19$	−2.93145	−0.672521	−0.336261	−	0.941769i	$-0.609162\pi$
$19$	−2.93145	−0.672521	−0.336261	+	0.941769i	$0.609162\pi$
$20$	−3.16627	−0.707999
$21$	−3.62472	−0.790979
$22$	1.65992	0.353895
$23$	1.05441	0.219859	0.109929	−	0.993939i	$-0.464938\pi$
$23$	1.05441	0.219859	0.109929	+	0.993939i	$0.464938\pi$
$24$	1.54604	0.315583
$25$	12.5726	2.51451
$26$	10.4256	2.04464
$27$	−4.07079	−0.783423
$28$	−3.65871	−0.691432
$29$	−3.95333	−0.734115	−0.367057	−	0.930198i	$-0.619635\pi$
$29$	−3.95333	−0.734115	−0.367057	+	0.930198i	$0.619635\pi$
$30$	5.20690	0.950645
$31$	8.30927	1.49239	0.746194	−	0.665728i	$-0.231879\pi$
$31$	8.30927	1.49239	0.746194	+	0.665728i	$0.231879\pi$
$32$	4.06806	0.719139
$33$	−0.748300	−0.130262
$34$	1.65992	0.284673
$35$	20.3056	3.43228
$36$	−1.84301	−0.307169
$37$	−6.24581	−1.02680	−0.513402	−	0.858148i	$-0.671615\pi$
$37$	−6.24581	−1.02680	−0.513402	+	0.858148i	$0.671615\pi$
$38$	4.86596	0.789363
$39$	−4.69994	−0.752593
$40$	−8.66088	−1.36941
$41$	−1.26183	−0.197065	−0.0985326	−	0.995134i	$-0.531415\pi$
$41$	−1.26183	−0.197065	−0.0985326	+	0.995134i	$0.531415\pi$
$42$	6.01673	0.928401
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−0.755318	−0.113868
$45$	10.2286	1.52479
$46$	−1.75022	−0.258056
$47$	0.558074	0.0814035	0.0407017	−	0.999171i	$-0.487041\pi$
$47$	0.558074	0.0814035	0.0407017	+	0.999171i	$0.487041\pi$
$48$	−3.69670	−0.533573
$49$	16.4638	2.35196
$50$	−20.8694	−2.95138
$51$	−0.748300	−0.104783
$52$	−4.74402	−0.657877
$53$	14.0460	1.92937	0.964683	−	0.263413i	$-0.0848483\pi$
$53$	14.0460	1.92937	0.964683	+	0.263413i	$0.0848483\pi$
$54$	6.75716	0.919533
$55$	4.19197	0.565244
$56$	−10.0079	−1.33736
$57$	−2.19360	−0.290550
$58$	6.56219	0.861658
$59$	15.2740	1.98851	0.994255	−	0.107040i	$-0.0341374\pi$
$59$	15.2740	1.98851	0.994255	+	0.107040i	$0.0341374\pi$
$60$	−2.36932	−0.305877
$61$	−5.01667	−0.642319	−0.321159	−	0.947025i	$-0.604073\pi$
$61$	−5.01667	−0.642319	−0.321159	+	0.947025i	$0.604073\pi$
$62$	−13.7927	−1.75167
$63$	11.8194	1.48911
$64$	3.12762	0.390952
$65$	26.3290	3.26571
$66$	1.24211	0.152894
$67$	1.59494	0.194853	0.0974267	−	0.995243i	$-0.468939\pi$
$67$	1.59494	0.194853	0.0974267	+	0.995243i	$0.468939\pi$
$68$	−0.755318	−0.0915958
$69$	0.789011	0.0949858
$70$	−33.7056	−4.02859
$71$	−15.0010	−1.78029	−0.890147	−	0.455674i	$-0.849398\pi$
$71$	−15.0010	−1.78029	−0.890147	+	0.455674i	$0.849398\pi$
$72$	−5.04130	−0.594123
$73$	−6.68215	−0.782087	−0.391044	−	0.920372i	$-0.627886\pi$
$73$	−6.68215	−0.782087	−0.391044	+	0.920372i	$0.627886\pi$
$74$	10.3675	1.20520
$75$	9.40805	1.08635
$76$	−2.21418	−0.253984
$77$	4.84394	0.552018
$78$	7.80150	0.883346
$79$	−0.622145	−0.0699967	−0.0349984	−	0.999387i	$-0.511143\pi$
$79$	−0.622145	−0.0699967	−0.0349984	+	0.999387i	$0.511143\pi$
$80$	20.7089	2.31532
$81$	4.27397	0.474886
$82$	2.09454	0.231303
$83$	4.32948	0.475222	0.237611	−	0.971360i	$-0.423636\pi$
$83$	4.32948	0.475222	0.237611	+	0.971360i	$0.423636\pi$
$84$	−2.73782	−0.298720
$85$	4.19197	0.454682
$86$	1.65992	0.178993
$87$	−2.95828	−0.317160
$88$	−2.06607	−0.220243
$89$	−9.83661	−1.04268	−0.521339	−	0.853349i	$-0.674567\pi$
$89$	−9.83661	−1.04268	−0.521339	+	0.853349i	$0.674567\pi$
$90$	−16.9786	−1.78970
$91$	30.4239	3.18930
$92$	0.796411	0.0830316
$93$	6.21783	0.644758
$94$	−0.926355	−0.0955463
$95$	12.2885	1.26078
$96$	3.04413	0.310690
$97$	−6.90135	−0.700726	−0.350363	−	0.936614i	$-0.613942\pi$
$97$	−6.90135	−0.700726	−0.350363	+	0.936614i	$0.613942\pi$
$98$	−27.3284	−2.76059
$99$	2.44005	0.245234
$100$	9.49629	0.949629
$101$	2.85983	0.284563	0.142282	−	0.989826i	$-0.454556\pi$
$101$	2.85983	0.284563	0.142282	+	0.989826i	$0.454556\pi$
$102$	1.24211	0.122988
$103$	7.49956	0.738954	0.369477	−	0.929240i	$-0.379537\pi$
$103$	7.49956	0.738954	0.369477	+	0.929240i	$0.379537\pi$
$104$	−12.9766	−1.27246
$105$	15.1947	1.48285
$106$	−23.3152	−2.26457
$107$	3.64837	0.352702	0.176351	−	0.984327i	$-0.443571\pi$
$107$	3.64837	0.352702	0.176351	+	0.984327i	$0.443571\pi$
$108$	−3.07474	−0.295867
$109$	−10.4995	−1.00567	−0.502834	−	0.864383i	$-0.667709\pi$
$109$	−10.4995	−1.00567	−0.502834	+	0.864383i	$0.667709\pi$
$110$	−6.95831	−0.663448
$111$	−4.67374	−0.443611
$112$	23.9297	2.26114
$113$	7.60601	0.715513	0.357757	−	0.933815i	$-0.383542\pi$
$113$	7.60601	0.715513	0.357757	+	0.933815i	$0.383542\pi$
$114$	3.64120	0.341029
$115$	−4.42003	−0.412170
$116$	−2.98602	−0.277245
$117$	15.3255	1.41684
$118$	−25.3536	−2.33399
$119$	4.84394	0.444043
$120$	−6.48093	−0.591626
$121$	1.00000	0.0909091
$122$	8.32725	0.753913
$123$	−0.944229	−0.0851383
$124$	6.27614	0.563614
$125$	−31.7440	−2.83927
$126$	−19.6193	−1.74782
$127$	10.9743	0.973811	0.486905	−	0.873455i	$-0.338126\pi$
$127$	10.9743	0.973811	0.486905	+	0.873455i	$0.338126\pi$
$128$	−13.3277	−1.17801
$129$	−0.748300	−0.0658841
$130$	−43.7039	−3.83309
$131$	−1.24622	−0.108883	−0.0544413	−	0.998517i	$-0.517338\pi$
$131$	−1.24622	−0.108883	−0.0544413	+	0.998517i	$0.517338\pi$
$132$	−0.565204	−0.0491947
$133$	14.1998	1.23128
$134$	−2.64747	−0.228707
$135$	17.0646	1.46869
$136$	−2.06607	−0.177164
$137$	−4.42236	−0.377827	−0.188914	−	0.981994i	$-0.560497\pi$
$137$	−4.42236	−0.377827	−0.188914	+	0.981994i	$0.560497\pi$
$138$	−1.30969	−0.111488
$139$	−20.1310	−1.70749	−0.853745	−	0.520691i	$-0.825674\pi$
$139$	−20.1310	−1.70749	−0.853745	+	0.520691i	$0.825674\pi$
$140$	15.3372	1.29623
$141$	0.417607	0.0351688
$142$	24.9004	2.08960
$143$	6.28082	0.525229
$144$	12.0542	1.00451
$145$	16.5722	1.37625
$146$	11.0918	0.917965
$147$	12.3198	1.01612
$148$	−4.71757	−0.387782
$149$	14.0325	1.14959	0.574795	−	0.818297i	$-0.305082\pi$
$149$	14.0325	1.14959	0.574795	+	0.818297i	$0.305082\pi$
$150$	−15.6166	−1.27509
$151$	−16.8362	−1.37011	−0.685054	−	0.728492i	$-0.740222\pi$
$151$	−16.8362	−1.37011	−0.685054	+	0.728492i	$0.740222\pi$
$152$	−6.05657	−0.491253
$153$	2.44005	0.197266
$154$	−8.04053	−0.647924
$155$	−34.8322	−2.79779
$156$	−3.54995	−0.284223
$157$	−11.4215	−0.911538	−0.455769	−	0.890098i	$-0.650636\pi$
$157$	−11.4215	−0.911538	−0.455769	+	0.890098i	$0.650636\pi$
$158$	1.03271	0.0821578
$159$	10.5106	0.833546
$160$	−17.0532	−1.34817
$161$	−5.10748	−0.402526
$162$	−7.09443	−0.557391
$163$	14.3182	1.12149	0.560744	−	0.827989i	$-0.310515\pi$
$163$	14.3182	1.12149	0.560744	+	0.827989i	$0.310515\pi$
$164$	−0.953085	−0.0744234
$165$	3.13685	0.244203
$166$	−7.18657	−0.557786
$167$	−1.32051	−0.102184	−0.0510920	−	0.998694i	$-0.516270\pi$
$167$	−1.32051	−0.102184	−0.0510920	+	0.998694i	$0.516270\pi$
$168$	−7.48891	−0.577782
$169$	26.4488	2.03452
$170$	−6.95831	−0.533678
$171$	7.15288	0.546994
$172$	−0.755318	−0.0575925
$173$	2.99821	0.227950	0.113975	−	0.993484i	$-0.463642\pi$
$173$	2.99821	0.227950	0.113975	+	0.993484i	$0.463642\pi$
$174$	4.91049	0.372263
$175$	−60.9008	−4.60367
$176$	4.94013	0.372376
$177$	11.4296	0.859098
$178$	16.3279	1.22383
$179$	−4.35032	−0.325158	−0.162579	−	0.986696i	$-0.551981\pi$
$179$	−4.35032	−0.325158	−0.162579	+	0.986696i	$0.551981\pi$
$180$	7.72584	0.575850
$181$	−8.25994	−0.613956	−0.306978	−	0.951717i	$-0.599318\pi$
$181$	−8.25994	−0.613956	−0.306978	+	0.951717i	$0.599318\pi$
$182$	−50.5011	−3.74339
$183$	−3.75397	−0.277502
$184$	2.17847	0.160599
$185$	26.1822	1.92495
$186$	−10.3211	−0.756777
$187$	1.00000	0.0731272
$188$	0.421523	0.0307428
$189$	19.7186	1.43432
$190$	−20.3979	−1.47982
$191$	4.95836	0.358775	0.179387	−	0.983779i	$-0.442588\pi$
$191$	4.95836	0.358775	0.179387	+	0.983779i	$0.442588\pi$
$192$	2.34040	0.168904
$193$	12.4907	0.899100	0.449550	−	0.893255i	$-0.351584\pi$
$193$	12.4907	0.899100	0.449550	+	0.893255i	$0.351584\pi$
$194$	11.4557	0.822468
$195$	19.7020	1.41089
$196$	12.4354	0.888241
$197$	−16.1404	−1.14995	−0.574977	−	0.818169i	$-0.694989\pi$
$197$	−16.1404	−1.14995	−0.574977	+	0.818169i	$0.694989\pi$
$198$	−4.05027	−0.287840
$199$	11.8332	0.838831	0.419415	−	0.907794i	$-0.362235\pi$
$199$	11.8332	0.838831	0.419415	+	0.907794i	$0.362235\pi$
$200$	25.9758	1.83676
$201$	1.19350	0.0841827
$202$	−4.74707	−0.334003
$203$	19.1497	1.34404
$204$	−0.565204	−0.0395722
$205$	5.28956	0.369439
$206$	−12.4486	−0.867337
$207$	−2.57280	−0.178822
$208$	31.0281	2.15141
$209$	2.93145	0.202773
$210$	−25.2219	−1.74048
$211$	11.7935	0.811901	0.405950	−	0.913895i	$-0.366941\pi$
$211$	11.7935	0.811901	0.405950	+	0.913895i	$0.366941\pi$
$212$	10.6092	0.728642
$213$	−11.2253	−0.769142
$214$	−6.05599	−0.413979
$215$	4.19197	0.285890
$216$	−8.41052	−0.572263
$217$	−40.2496	−2.73232
$218$	17.4282	1.18039
$219$	−5.00026	−0.337886
$220$	3.16627	0.213470
$221$	6.28082	0.422494
$222$	7.75801	0.520683
$223$	18.5900	1.24488	0.622441	−	0.782667i	$-0.286141\pi$
$223$	18.5900	1.24488	0.622441	+	0.782667i	$0.286141\pi$
$224$	−19.7055	−1.31663
$225$	−30.6777	−2.04518
$226$	−12.6253	−0.839825
$227$	23.1495	1.53649	0.768244	−	0.640157i	$-0.221131\pi$
$227$	23.1495	1.53649	0.768244	+	0.640157i	$0.221131\pi$
$228$	−1.65687	−0.109729
$229$	−13.9404	−0.921207	−0.460603	−	0.887606i	$-0.652367\pi$
$229$	−13.9404	−0.921207	−0.460603	+	0.887606i	$0.652367\pi$
$230$	7.33688	0.483779
$231$	3.62472	0.238489
$232$	−8.16784	−0.536245
$233$	−18.7536	−1.22859	−0.614295	−	0.789076i	$-0.710560\pi$
$233$	−18.7536	−1.22859	−0.614295	+	0.789076i	$0.710560\pi$
$234$	−25.4390	−1.66300
$235$	−2.33943	−0.152607
$236$	11.5367	0.750978
$237$	−0.465551	−0.0302408
$238$	−8.04053	−0.521190
$239$	−16.0295	−1.03686	−0.518430	−	0.855120i	$-0.673483\pi$
$239$	−16.0295	−1.03686	−0.518430	+	0.855120i	$0.673483\pi$
$240$	15.4964	1.00029
$241$	29.2477	1.88401	0.942004	−	0.335601i	$-0.108939\pi$
$241$	29.2477	1.88401	0.942004	+	0.335601i	$0.108939\pi$
$242$	−1.65992	−0.106703
$243$	15.4106	0.988589
$244$	−3.78918	−0.242577
$245$	−69.0155	−4.40924
$246$	1.56734	0.0999300
$247$	18.4119	1.17152
$248$	17.1675	1.09014
$249$	3.23975	0.205311
$250$	52.6923	3.33255
$251$	4.61912	0.291556	0.145778	−	0.989317i	$-0.453431\pi$
$251$	4.61912	0.291556	0.145778	+	0.989317i	$0.453431\pi$
$252$	8.92744	0.562376
$253$	−1.05441	−0.0662899
$254$	−18.2164	−1.14300
$255$	3.13685	0.196437
$256$	15.8676	0.991727
$257$	−9.98817	−0.623045	−0.311522	−	0.950239i	$-0.600839\pi$
$257$	−9.98817	−0.623045	−0.311522	+	0.950239i	$0.600839\pi$
$258$	1.24211	0.0773306
$259$	30.2543	1.87991
$260$	19.8868	1.23332
$261$	9.64631	0.597092
$262$	2.06862	0.127799
$263$	16.3803	1.01005	0.505026	−	0.863104i	$-0.331483\pi$
$263$	16.3803	1.01005	0.505026	+	0.863104i	$0.331483\pi$
$264$	−1.54604	−0.0951520
$265$	−58.8803	−3.61699
$266$	−23.5704	−1.44520
$267$	−7.36073	−0.450470
$268$	1.20469	0.0735881
$269$	3.69553	0.225321	0.112660	−	0.993634i	$-0.464063\pi$
$269$	3.69553	0.225321	0.112660	+	0.993634i	$0.464063\pi$
$270$	−28.3258	−1.72385
$271$	−1.96926	−0.119624	−0.0598121	−	0.998210i	$-0.519050\pi$
$271$	−1.96926	−0.119624	−0.0598121	+	0.998210i	$0.519050\pi$
$272$	4.94013	0.299539
$273$	22.7662	1.37787
$274$	7.34074	0.443470
$275$	−12.5726	−0.758155
$276$	0.595955	0.0358722
$277$	−12.2466	−0.735825	−0.367912	−	0.929860i	$-0.619927\pi$
$277$	−12.2466	−0.735825	−0.367912	+	0.929860i	$0.619927\pi$
$278$	33.4158	2.00415
$279$	−20.2750	−1.21383
$280$	41.9528	2.50716
$281$	−16.1496	−0.963406	−0.481703	−	0.876334i	$-0.659982\pi$
$281$	−16.1496	−0.963406	−0.481703	+	0.876334i	$0.659982\pi$
$282$	−0.693192	−0.0412790
$283$	−11.3884	−0.676973	−0.338486	−	0.940971i	$-0.609915\pi$
$283$	−11.3884	−0.676973	−0.338486	+	0.940971i	$0.609915\pi$
$284$	−11.3305	−0.672344
$285$	9.19551	0.544695
$286$	−10.4256	−0.616481
$287$	6.11224	0.360794
$288$	−9.92627	−0.584911
$289$	1.00000	0.0588235
$290$	−27.5085	−1.61535
$291$	−5.16428	−0.302735
$292$	−5.04715	−0.295362
$293$	21.4206	1.25140	0.625701	−	0.780063i	$-0.284813\pi$
$293$	21.4206	1.25140	0.625701	+	0.780063i	$0.284813\pi$
$294$	−20.4499	−1.19266
$295$	−64.0282	−3.72787
$296$	−12.9043	−0.750044
$297$	4.07079	0.236211
$298$	−23.2928	−1.34932
$299$	−6.62254	−0.382991
$300$	7.10607	0.410269
$301$	4.84394	0.279200
$302$	27.9466	1.60815
$303$	2.14001	0.122940
$304$	14.4818	0.830586
$305$	21.0297	1.20416
$306$	−4.05027	−0.231539
$307$	13.5387	0.772692	0.386346	−	0.922354i	$-0.373737\pi$
$307$	13.5387	0.772692	0.386346	+	0.922354i	$0.373737\pi$
$308$	3.65871	0.208475
$309$	5.61192	0.319251
$310$	57.8184	3.28387
$311$	−14.3700	−0.814846	−0.407423	−	0.913240i	$-0.633573\pi$
$311$	−14.3700	−0.814846	−0.407423	+	0.913240i	$0.633573\pi$
$312$	−9.71039	−0.549742
$313$	26.5219	1.49911	0.749553	−	0.661944i	$-0.230268\pi$
$313$	26.5219	1.49911	0.749553	+	0.661944i	$0.230268\pi$
$314$	18.9588	1.06991
$315$	−49.5467	−2.79164
$316$	−0.469917	−0.0264349
$317$	−6.68822	−0.375648	−0.187824	−	0.982203i	$-0.560143\pi$
$317$	−6.68822	−0.375648	−0.187824	+	0.982203i	$0.560143\pi$
$318$	−17.4467	−0.978364
$319$	3.95333	0.221344
$320$	−13.1109	−0.732920
$321$	2.73008	0.152378
$322$	8.47798	0.472459
$323$	2.93145	0.163110
$324$	3.22821	0.179345
$325$	−78.9661	−4.38025
$326$	−23.7670	−1.31633
$327$	−7.85676	−0.434480
$328$	−2.60703	−0.143949
$329$	−2.70328	−0.149036
$330$	−5.20690	−0.286630
$331$	5.75600	0.316379	0.158189	−	0.987409i	$-0.449434\pi$
$331$	5.75600	0.316379	0.158189	+	0.987409i	$0.449434\pi$
$332$	3.27013	0.179472
$333$	15.2401	0.835150
$334$	2.19193	0.119937
$335$	−6.68595	−0.365292
$336$	17.9066	0.976884
$337$	5.51727	0.300545	0.150273	−	0.988645i	$-0.451985\pi$
$337$	5.51727	0.300545	0.150273	+	0.988645i	$0.451985\pi$
$338$	−43.9027	−2.38799
$339$	5.69158	0.309124
$340$	3.16627	0.171715
$341$	−8.30927	−0.449972
$342$	−11.8732	−0.642028
$343$	−45.8419	−2.47523
$344$	−2.06607	−0.111395
$345$	−3.30751	−0.178070
$346$	−4.97677	−0.267553
$347$	5.45601	0.292894	0.146447	−	0.989219i	$-0.453216\pi$
$347$	5.45601	0.292894	0.146447	+	0.989219i	$0.453216\pi$
$348$	−2.23444	−0.119778
$349$	28.9211	1.54811	0.774054	−	0.633119i	$-0.218226\pi$
$349$	28.9211	1.54811	0.774054	+	0.633119i	$0.218226\pi$
$350$	101.090	5.40349
$351$	25.5679	1.36471
$352$	−4.06806	−0.216829
$353$	−25.1437	−1.33826	−0.669132	−	0.743143i	$-0.733334\pi$
$353$	−25.1437	−1.33826	−0.669132	+	0.743143i	$0.733334\pi$
$354$	−18.9721	−1.00836
$355$	62.8837	3.33752
$356$	−7.42977	−0.393777
$357$	3.62472	0.191840
$358$	7.22116	0.381650
$359$	−30.6370	−1.61696	−0.808479	−	0.588525i	$-0.799709\pi$
$359$	−30.6370	−1.61696	−0.808479	+	0.588525i	$0.799709\pi$
$360$	21.1330	1.11380
$361$	−10.4066	−0.547715
$362$	13.7108	0.720623
$363$	0.748300	0.0392756
$364$	22.9797	1.20447
$365$	28.0114	1.46618
$366$	6.23128	0.325714
$367$	−0.270533	−0.0141217	−0.00706084	−	0.999975i	$-0.502248\pi$
$367$	−0.270533	−0.0141217	−0.00706084	+	0.999975i	$0.502248\pi$
$368$	−5.20890	−0.271533
$369$	3.07893	0.160283
$370$	−43.4602	−2.25939
$371$	−68.0380	−3.53236
$372$	4.69644	0.243499
$373$	16.5054	0.854619	0.427309	−	0.904105i	$-0.359462\pi$
$373$	16.5054	0.854619	0.427309	+	0.904105i	$0.359462\pi$
$374$	−1.65992	−0.0858322
$375$	−23.7540	−1.22665
$376$	1.15302	0.0594624
$377$	24.8302	1.27882
$378$	−32.7313	−1.68352
$379$	31.9969	1.64357	0.821785	−	0.569797i	$-0.192978\pi$
$379$	31.9969	1.64357	0.821785	+	0.569797i	$0.192978\pi$
$380$	9.28176	0.476144
$381$	8.21206	0.420717
$382$	−8.23046	−0.421107
$383$	15.6854	0.801487	0.400744	−	0.916190i	$-0.368752\pi$
$383$	15.6854	0.801487	0.400744	+	0.916190i	$0.368752\pi$
$384$	−9.97312	−0.508939
$385$	−20.3056	−1.03487
$386$	−20.7335	−1.05531
$387$	2.44005	0.124035
$388$	−5.21272	−0.264636
$389$	−33.7230	−1.70982	−0.854912	−	0.518773i	$-0.826389\pi$
$389$	−33.7230	−1.70982	−0.854912	+	0.518773i	$0.826389\pi$
$390$	−32.7036	−1.65601
$391$	−1.05441	−0.0533236
$392$	34.0152	1.71803
$393$	−0.932544	−0.0470406
$394$	26.7917	1.34974
$395$	2.60801	0.131223
$396$	1.84301	0.0926148
$397$	−3.36733	−0.169002	−0.0845008	−	0.996423i	$-0.526930\pi$
$397$	−3.36733	−0.169002	−0.0845008	+	0.996423i	$0.526930\pi$
$398$	−19.6421	−0.984567
$399$	10.6257	0.531950
$400$	−62.1102	−3.10551
$401$	−24.3690	−1.21693	−0.608466	−	0.793580i	$-0.708215\pi$
$401$	−24.3690	−1.21693	−0.608466	+	0.793580i	$0.708215\pi$
$402$	−1.98110	−0.0988084
$403$	−52.1891	−2.59972
$404$	2.16008	0.107468
$405$	−17.9163	−0.890271
$406$	−31.7869	−1.57756
$407$	6.24581	0.309593
$408$	−1.54604	−0.0765402
$409$	−13.9069	−0.687653	−0.343827	−	0.939033i	$-0.611723\pi$
$409$	−13.9069	−0.687653	−0.343827	+	0.939033i	$0.611723\pi$
$410$	−8.78022	−0.433624
$411$	−3.30925	−0.163233
$412$	5.66455	0.279072
$413$	−73.9865	−3.64064
$414$	4.27063	0.209890
$415$	−18.1490	−0.890900
$416$	−25.5508	−1.25273
$417$	−15.0640	−0.737689
$418$	−4.86596	−0.238002
$419$	−14.3978	−0.703378	−0.351689	−	0.936117i	$-0.614393\pi$
$419$	−14.3978	−0.703378	−0.351689	+	0.936117i	$0.614393\pi$
$420$	11.4768	0.560012
$421$	10.9606	0.534188	0.267094	−	0.963671i	$-0.413937\pi$
$421$	10.9606	0.534188	0.267094	+	0.963671i	$0.413937\pi$
$422$	−19.5763	−0.952958
$423$	−1.36173	−0.0662094
$424$	29.0200	1.40933
$425$	−12.5726	−0.609859
$426$	18.6330	0.902771
$427$	24.3004	1.17598
$428$	2.75568	0.133201
$429$	4.69994	0.226915
$430$	−6.95831	−0.335559
$431$	−29.3010	−1.41138	−0.705689	−	0.708522i	$-0.749362\pi$
$431$	−29.3010	−1.41138	−0.705689	+	0.708522i	$0.749362\pi$
$432$	20.1102	0.967553
$433$	−29.3956	−1.41266	−0.706332	−	0.707881i	$-0.749651\pi$
$433$	−29.3956	−1.41266	−0.706332	+	0.707881i	$0.749651\pi$
$434$	66.8109	3.20703
$435$	12.4010	0.594582
$436$	−7.93044	−0.379799
$437$	−3.09094	−0.147860
$438$	8.30000	0.396589
$439$	−3.26017	−0.155599	−0.0777997	−	0.996969i	$-0.524789\pi$
$439$	−3.26017	−0.155599	−0.0777997	+	0.996969i	$0.524789\pi$
$440$	8.66088	0.412891
$441$	−40.1723	−1.91297
$442$	−10.4256	−0.495897
$443$	0.721239	0.0342671	0.0171336	−	0.999853i	$-0.494546\pi$
$443$	0.721239	0.0342671	0.0171336	+	0.999853i	$0.494546\pi$
$444$	−3.53016	−0.167534
$445$	41.2347	1.95471
$446$	−30.8579	−1.46116
$447$	10.5005	0.496659
$448$	−15.1500	−0.715770
$449$	−36.3085	−1.71350	−0.856752	−	0.515729i	$-0.827521\pi$
$449$	−36.3085	−1.71350	−0.856752	+	0.515729i	$0.827521\pi$
$450$	50.9223	2.40050
$451$	1.26183	0.0594174
$452$	5.74496	0.270220
$453$	−12.5985	−0.591930
$454$	−38.4263	−1.80343
$455$	−127.536	−5.97898
$456$	−4.53213	−0.212237
$457$	−8.69797	−0.406874	−0.203437	−	0.979088i	$-0.565211\pi$
$457$	−8.69797	−0.406874	−0.203437	+	0.979088i	$0.565211\pi$
$458$	23.1399	1.08125
$459$	4.07079	0.190008
$460$	−3.33853	−0.155660
$461$	22.3554	1.04119	0.520597	−	0.853803i	$-0.325709\pi$
$461$	22.3554	1.04119	0.520597	+	0.853803i	$0.325709\pi$
$462$	−6.01673	−0.279923
$463$	20.6109	0.957869	0.478935	−	0.877851i	$-0.341023\pi$
$463$	20.6109	0.957869	0.478935	+	0.877851i	$0.341023\pi$
$464$	19.5300	0.906656
$465$	−26.0649	−1.20873
$466$	31.1294	1.44204
$467$	15.9024	0.735875	0.367937	−	0.929851i	$-0.380064\pi$
$467$	15.9024	0.735875	0.367937	+	0.929851i	$0.380064\pi$
$468$	11.5756	0.535084
$469$	−7.72581	−0.356745
$470$	3.88325	0.179121
$471$	−8.54673	−0.393813
$472$	31.5572	1.45254
$473$	1.00000	0.0459800
$474$	0.772775	0.0354947
$475$	−36.8559	−1.69106
$476$	3.65871	0.167697
$477$	−34.2729	−1.56925
$478$	26.6075	1.21700
$479$	32.9750	1.50667	0.753334	−	0.657638i	$-0.228444\pi$
$479$	32.9750	1.50667	0.753334	+	0.657638i	$0.228444\pi$
$480$	−12.7609	−0.582453
$481$	39.2288	1.78868
$482$	−48.5487	−2.21133
$483$	−3.82192	−0.173904
$484$	0.755318	0.0343326
$485$	28.9302	1.31365
$486$	−25.5802	−1.16034
$487$	0.659605	0.0298895	0.0149448	−	0.999888i	$-0.495243\pi$
$487$	0.659605	0.0298895	0.0149448	+	0.999888i	$0.495243\pi$
$488$	−10.3648	−0.469191
$489$	10.7143	0.484517
$490$	114.560	5.17529
$491$	9.54344	0.430689	0.215345	−	0.976538i	$-0.430912\pi$
$491$	9.54344	0.430689	0.215345	+	0.976538i	$0.430912\pi$
$492$	−0.713193	−0.0321532
$493$	3.95333	0.178049
$494$	−30.5622	−1.37506
$495$	−10.2286	−0.459741
$496$	−41.0489	−1.84315
$497$	72.6640	3.25943
$498$	−5.37771	−0.240981
$499$	−40.7447	−1.82398	−0.911991	−	0.410210i	$-0.865455\pi$
$499$	−40.7447	−1.82398	−0.911991	+	0.410210i	$0.865455\pi$
$500$	−23.9768	−1.07227
$501$	−0.988136	−0.0441467
$502$	−7.66735	−0.342211
$503$	−11.5257	−0.513904	−0.256952	−	0.966424i	$-0.582718\pi$
$503$	−11.5257	−0.513904	−0.256952	+	0.966424i	$0.582718\pi$
$504$	24.4198	1.08774
$505$	−11.9883	−0.533472
$506$	1.75022	0.0778069
$507$	19.7916	0.878976
$508$	8.28908	0.367768
$509$	35.9366	1.59286	0.796432	−	0.604729i	$-0.206718\pi$
$509$	35.9366	1.59286	0.796432	+	0.604729i	$0.206718\pi$
$510$	−5.20690	−0.230565
$511$	32.3680	1.43187
$512$	0.316506	0.0139877
$513$	11.9333	0.526869
$514$	16.5795	0.731291
$515$	−31.4379	−1.38532
$516$	−0.565204	−0.0248817
$517$	−0.558074	−0.0245441
$518$	−50.2196	−2.20652
$519$	2.24356	0.0984813
$520$	54.3975	2.38549
$521$	24.1351	1.05738	0.528689	−	0.848815i	$-0.322684\pi$
$521$	24.1351	1.05738	0.528689	+	0.848815i	$0.322684\pi$
$522$	−16.0121	−0.700829
$523$	24.2416	1.06001	0.530006	−	0.847994i	$-0.322190\pi$
$523$	24.2416	1.06001	0.530006	+	0.847994i	$0.322190\pi$
$524$	−0.941291	−0.0411205
$525$	−45.5720	−1.98893
$526$	−27.1899	−1.18554
$527$	−8.30927	−0.361957
$528$	3.69670	0.160878
$529$	−21.8882	−0.951662
$530$	97.7364	4.24540
$531$	−37.2694	−1.61735
$532$	10.7253	0.465003
$533$	7.92535	0.343285
$534$	12.2182	0.528733
$535$	−15.2939	−0.661211
$536$	3.29526	0.142334
$537$	−3.25534	−0.140478
$538$	−6.13427	−0.264467
$539$	−16.4638	−0.709144
$540$	12.8892	0.554663
$541$	12.5408	0.539169	0.269585	−	0.962977i	$-0.413114\pi$
$541$	12.5408	0.539169	0.269585	+	0.962977i	$0.413114\pi$
$542$	3.26881	0.140407
$543$	−6.18091	−0.265248
$544$	−4.06806	−0.174417
$545$	44.0134	1.88533
$546$	−37.7900	−1.61726
$547$	23.2311	0.993291	0.496646	−	0.867953i	$-0.334565\pi$
$547$	23.2311	0.993291	0.496646	+	0.867953i	$0.334565\pi$
$548$	−3.34029	−0.142690
$549$	12.2409	0.522429
$550$	20.8694	0.889874
$551$	11.5890	0.493708
$552$	1.63015	0.0693838
$553$	3.01363	0.128153
$554$	20.3283	0.863665
$555$	19.5921	0.831640
$556$	−15.2053	−0.644849
$557$	−14.2236	−0.602673	−0.301336	−	0.953518i	$-0.597433\pi$
$557$	−14.2236	−0.602673	−0.301336	+	0.953518i	$0.597433\pi$
$558$	33.6548	1.42472
$559$	6.28082	0.265651
$560$	−100.312	−4.23897
$561$	0.748300	0.0315932
$562$	26.8070	1.13079
$563$	32.8224	1.38330	0.691650	−	0.722233i	$-0.256884\pi$
$563$	32.8224	1.38330	0.691650	+	0.722233i	$0.256884\pi$
$564$	0.315426	0.0132818
$565$	−31.8841	−1.34138
$566$	18.9039	0.794588
$567$	−20.7029	−0.869439
$568$	−30.9931	−1.30044
$569$	31.7758	1.33211	0.666056	−	0.745902i	$-0.267981\pi$
$569$	31.7758	1.33211	0.666056	+	0.745902i	$0.267981\pi$
$570$	−15.2638	−0.639329
$571$	31.3723	1.31289	0.656445	−	0.754374i	$-0.272059\pi$
$571$	31.3723	1.31289	0.656445	+	0.754374i	$0.272059\pi$
$572$	4.74402	0.198357
$573$	3.71034	0.155002
$574$	−10.1458	−0.423478
$575$	13.2566	0.552838
$576$	−7.63154	−0.317981
$577$	−31.3695	−1.30593	−0.652966	−	0.757388i	$-0.726475\pi$
$577$	−31.3695	−1.30593	−0.652966	+	0.757388i	$0.726475\pi$
$578$	−1.65992	−0.0690434
$579$	9.34678	0.388439
$580$	12.5173	0.519752
$581$	−20.9717	−0.870054
$582$	8.57227	0.355332
$583$	−14.0460	−0.581726
$584$	−13.8058	−0.571287
$585$	−64.2440	−2.65616
$586$	−35.5563	−1.46882
$587$	18.2496	0.753243	0.376622	−	0.926367i	$-0.377086\pi$
$587$	18.2496	0.753243	0.376622	+	0.926367i	$0.377086\pi$
$588$	9.30538	0.383748
$589$	−24.3582	−1.00366
$590$	106.281	4.37554
$591$	−12.0778	−0.496816
$592$	30.8551	1.26814
$593$	−7.34187	−0.301494	−0.150747	−	0.988572i	$-0.548168\pi$
$593$	−7.34187	−0.301494	−0.150747	+	0.988572i	$0.548168\pi$
$594$	−6.75716	−0.277250
$595$	−20.3056	−0.832450
$596$	10.5990	0.434153
$597$	8.85476	0.362401
$598$	10.9928	0.449531
$599$	−48.7027	−1.98994	−0.994969	−	0.100188i	$-0.968056\pi$
$599$	−48.7027	−1.98994	−0.994969	+	0.100188i	$0.968056\pi$
$600$	19.4377	0.793539
$601$	39.5910	1.61495	0.807476	−	0.589900i	$-0.200833\pi$
$601$	39.5910	1.61495	0.807476	+	0.589900i	$0.200833\pi$
$602$	−8.04053	−0.327707
$603$	−3.89174	−0.158484
$604$	−12.7167	−0.517434
$605$	−4.19197	−0.170428
$606$	−3.55223	−0.144299
$607$	−4.78672	−0.194287	−0.0971434	−	0.995270i	$-0.530971\pi$
$607$	−4.78672	−0.194287	−0.0971434	+	0.995270i	$0.530971\pi$
$608$	−11.9253	−0.483636
$609$	14.3297	0.580669
$610$	−34.9075	−1.41336
$611$	−3.50516	−0.141804
$612$	1.84301	0.0744993
$613$	15.6460	0.631937	0.315969	−	0.948770i	$-0.397671\pi$
$613$	15.6460	0.631937	0.315969	+	0.948770i	$0.397671\pi$
$614$	−22.4730	−0.906938
$615$	3.95818	0.159609
$616$	10.0079	0.403230
$617$	42.6394	1.71660	0.858298	−	0.513152i	$-0.171522\pi$
$617$	42.6394	1.71660	0.858298	+	0.513152i	$0.171522\pi$
$618$	−9.31531	−0.374717
$619$	47.2806	1.90037	0.950184	−	0.311689i	$-0.100895\pi$
$619$	47.2806	1.90037	0.950184	+	0.311689i	$0.100895\pi$
$620$	−26.3094	−1.05661
$621$	−4.29226	−0.172242
$622$	23.8529	0.956415
$623$	47.6479	1.90897
$624$	23.2183	0.929477
$625$	70.2067	2.80827
$626$	−44.0241	−1.75956
$627$	2.19360	0.0876041
$628$	−8.62689	−0.344250
$629$	6.24581	0.249037
$630$	82.2433	3.27665
$631$	−45.5649	−1.81391	−0.906955	−	0.421227i	$-0.861600\pi$
$631$	−45.5649	−1.81391	−0.906955	+	0.421227i	$0.861600\pi$
$632$	−1.28539	−0.0511301
$633$	8.82510	0.350766
$634$	11.1019	0.440912
$635$	−46.0038	−1.82561
$636$	7.93886	0.314796
$637$	−103.406	−4.09709
$638$	−6.56219	−0.259800
$639$	36.6032	1.44800
$640$	55.8693	2.20843
$641$	40.3077	1.59206	0.796029	−	0.605259i	$-0.206930\pi$
$641$	40.3077	1.59206	0.796029	+	0.605259i	$0.206930\pi$
$642$	−4.53170	−0.178852
$643$	47.0140	1.85405	0.927026	−	0.374998i	$-0.122357\pi$
$643$	47.0140	1.85405	0.927026	+	0.374998i	$0.122357\pi$
$644$	−3.85777	−0.152017
$645$	3.13685	0.123513
$646$	−4.86596	−0.191449
$647$	19.0359	0.748377	0.374189	−	0.927353i	$-0.377921\pi$
$647$	19.0359	0.748377	0.374189	+	0.927353i	$0.377921\pi$
$648$	8.83031	0.346887
$649$	−15.2740	−0.599558
$650$	131.077	5.14126
$651$	−30.1188	−1.18045
$652$	10.8148	0.423540
$653$	−9.36412	−0.366447	−0.183223	−	0.983071i	$-0.558653\pi$
$653$	−9.36412	−0.366447	−0.183223	+	0.983071i	$0.558653\pi$
$654$	13.0415	0.509965
$655$	5.22410	0.204123
$656$	6.23362	0.243382
$657$	16.3048	0.636110
$658$	4.48721	0.174930
$659$	10.5023	0.409111	0.204555	−	0.978855i	$-0.434425\pi$
$659$	10.5023	0.409111	0.204555	+	0.978855i	$0.434425\pi$
$660$	2.36932	0.0922255
$661$	26.0634	1.01375	0.506874	−	0.862020i	$-0.330801\pi$
$661$	26.0634	1.01375	0.506874	+	0.862020i	$0.330801\pi$
$662$	−9.55448	−0.371345
$663$	4.69994	0.182531
$664$	8.94499	0.347133
$665$	−59.5250	−2.30828
$666$	−25.2972	−0.980247
$667$	−4.16841	−0.161402
$668$	−0.997404	−0.0385907
$669$	13.9109	0.537828
$670$	11.0981	0.428757
$671$	5.01667	0.193666
$672$	−14.7456	−0.568824
$673$	0.460715	0.0177593	0.00887963	−	0.999961i	$-0.497173\pi$
$673$	0.460715	0.0177593	0.00887963	+	0.999961i	$0.497173\pi$
$674$	−9.15821	−0.352761
$675$	−51.1803	−1.96993
$676$	19.9772	0.768355
$677$	−8.44152	−0.324434	−0.162217	−	0.986755i	$-0.551864\pi$
$677$	−8.44152	−0.324434	−0.162217	+	0.986755i	$0.551864\pi$
$678$	−9.44753	−0.362830
$679$	33.4297	1.28292
$680$	8.66088	0.332130
$681$	17.3228	0.663811
$682$	13.7927	0.528149
$683$	17.3761	0.664876	0.332438	−	0.943125i	$-0.392129\pi$
$683$	17.3761	0.664876	0.332438	+	0.943125i	$0.392129\pi$
$684$	5.40270	0.206577
$685$	18.5384	0.708315
$686$	76.0936	2.90527
$687$	−10.4316	−0.397990
$688$	4.94013	0.188341
$689$	−88.2204	−3.36093
$690$	5.49018	0.209008
$691$	23.9542	0.911259	0.455630	−	0.890169i	$-0.349414\pi$
$691$	23.9542	0.911259	0.455630	+	0.890169i	$0.349414\pi$
$692$	2.26460	0.0860872
$693$	−11.8194	−0.448984
$694$	−9.05651	−0.343781
$695$	84.3885	3.20104
$696$	−6.11199	−0.231675
$697$	1.26183	0.0477953
$698$	−48.0065	−1.81707
$699$	−14.0333	−0.530789
$700$	−45.9995	−1.73862
$701$	21.7328	0.820837	0.410419	−	0.911897i	$-0.365383\pi$
$701$	21.7328	0.820837	0.410419	+	0.911897i	$0.365383\pi$
$702$	−42.4405	−1.60181
$703$	18.3093	0.690548
$704$	−3.12762	−0.117877
$705$	−1.75059	−0.0659311
$706$	41.7364	1.57077
$707$	−13.8528	−0.520989
$708$	8.63295	0.324446
$709$	−15.0549	−0.565399	−0.282700	−	0.959208i	$-0.591230\pi$
$709$	−15.0549	−0.565399	−0.282700	+	0.959208i	$0.591230\pi$
$710$	−104.382	−3.91737
$711$	1.51806	0.0569318
$712$	−20.3231	−0.761640
$713$	8.76134	0.328115
$714$	−6.01673	−0.225170
$715$	−26.3290	−0.984649
$716$	−3.28588	−0.122799
$717$	−11.9948	−0.447956
$718$	50.8548	1.89788
$719$	−2.97089	−0.110795	−0.0553977	−	0.998464i	$-0.517643\pi$
$719$	−2.97089	−0.110795	−0.0553977	+	0.998464i	$0.517643\pi$
$720$	−50.5306	−1.88316
$721$	−36.3274	−1.35290
$722$	17.2741	0.642874
$723$	21.8860	0.813950
$724$	−6.23888	−0.231866
$725$	−49.7035	−1.84594
$726$	−1.24211	−0.0460992
$727$	−10.1691	−0.377151	−0.188576	−	0.982059i	$-0.560387\pi$
$727$	−10.1691	−0.377151	−0.188576	+	0.982059i	$0.560387\pi$
$728$	62.8579	2.32967
$729$	−1.29019	−0.0477849
$730$	−46.4965	−1.72091
$731$	1.00000	0.0369863
$732$	−2.83544	−0.104801
$733$	−36.8645	−1.36162	−0.680810	−	0.732460i	$-0.738372\pi$
$733$	−36.8645	−1.36162	−0.680810	+	0.732460i	$0.738372\pi$
$734$	0.449061	0.0165752
$735$	−51.6443	−1.90493
$736$	4.28939	0.158109
$737$	−1.59494	−0.0587505
$738$	−5.11076	−0.188130
$739$	−21.5423	−0.792448	−0.396224	−	0.918154i	$-0.629680\pi$
$739$	−21.5423	−0.792448	−0.396224	+	0.918154i	$0.629680\pi$
$740$	19.7759	0.726976
$741$	13.7776	0.506134
$742$	112.937	4.14606
$743$	−13.9268	−0.510924	−0.255462	−	0.966819i	$-0.582228\pi$
$743$	−13.9268	−0.510924	−0.255462	+	0.966819i	$0.582228\pi$
$744$	12.8464	0.470973
$745$	−58.8239	−2.15514
$746$	−27.3976	−1.00310
$747$	−10.5641	−0.386521
$748$	0.755318	0.0276172
$749$	−17.6725	−0.645739
$750$	39.4296	1.43977
$751$	14.8201	0.540791	0.270396	−	0.962749i	$-0.412845\pi$
$751$	14.8201	0.540791	0.270396	+	0.962749i	$0.412845\pi$
$752$	−2.75696	−0.100536
$753$	3.45649	0.125961
$754$	−41.2160	−1.50100
$755$	70.5767	2.56855
$756$	14.8938	0.541684
$757$	2.76362	0.100445	0.0502227	−	0.998738i	$-0.484007\pi$
$757$	2.76362	0.100445	0.0502227	+	0.998738i	$0.484007\pi$
$758$	−53.1121	−1.92912
$759$	−0.789011	−0.0286393
$760$	25.3889	0.920954
$761$	−42.9345	−1.55637	−0.778187	−	0.628033i	$-0.783860\pi$
$761$	−42.9345	−1.55637	−0.778187	+	0.628033i	$0.783860\pi$
$762$	−13.6313	−0.493811
$763$	50.8588	1.84121
$764$	3.74514	0.135494
$765$	−10.2286	−0.369816
$766$	−26.0365	−0.940736
$767$	−95.9335	−3.46396
$768$	11.8737	0.428457
$769$	−9.49894	−0.342540	−0.171270	−	0.985224i	$-0.554787\pi$
$769$	−9.49894	−0.342540	−0.171270	+	0.985224i	$0.554787\pi$
$770$	33.7056	1.21467
$771$	−7.47415	−0.269175
$772$	9.43444	0.339553
$773$	−17.9773	−0.646600	−0.323300	−	0.946297i	$-0.604792\pi$
$773$	−17.9773	−0.646600	−0.323300	+	0.946297i	$0.604792\pi$
$774$	−4.05027	−0.145584
$775$	104.469	3.75263
$776$	−14.2587	−0.511856
$777$	22.6393	0.812180
$778$	55.9773	2.00688
$779$	3.69900	0.132530
$780$	14.8813	0.532835
$781$	15.0010	0.536779
$782$	1.75022	0.0625879
$783$	16.0932	0.575123
$784$	−81.3331	−2.90475
$785$	47.8787	1.70886
$786$	1.54794	0.0552134
$787$	−17.5727	−0.626400	−0.313200	−	0.949687i	$-0.601401\pi$
$787$	−17.5727	−0.626400	−0.313200	+	0.949687i	$0.601401\pi$
$788$	−12.1911	−0.434291
$789$	12.2574	0.436374
$790$	−4.32907	−0.154021
$791$	−36.8431	−1.30999
$792$	5.04130	0.179135
$793$	31.5088	1.11891
$794$	5.58949	0.198364
$795$	−44.0601	−1.56265
$796$	8.93780	0.316792
$797$	−2.74406	−0.0971995	−0.0485997	−	0.998818i	$-0.515476\pi$
$797$	−2.74406	−0.0971995	−0.0485997	+	0.998818i	$0.515476\pi$
$798$	−17.6377	−0.624369
$799$	−0.558074	−0.0197432
$800$	51.1460	1.80829
$801$	24.0018	0.848062
$802$	40.4506	1.42836
$803$	6.68215	0.235808
$804$	0.901469	0.0317924
$805$	21.4104	0.754616
$806$	86.6294	3.05139
$807$	2.76537	0.0973455
$808$	5.90859	0.207863
$809$	30.6731	1.07841	0.539204	−	0.842175i	$-0.318725\pi$
$809$	30.6731	1.07841	0.539204	+	0.842175i	$0.318725\pi$
$810$	29.7396	1.04494
$811$	−4.37804	−0.153734	−0.0768668	−	0.997041i	$-0.524492\pi$
$811$	−4.37804	−0.153734	−0.0768668	+	0.997041i	$0.524492\pi$
$812$	14.4641	0.507591
$813$	−1.47360	−0.0516814
$814$	−10.3675	−0.363381
$815$	−60.0214	−2.10246
$816$	3.69670	0.129410
$817$	2.93145	0.102559
$818$	23.0843	0.807124
$819$	−74.2358	−2.59401
$820$	3.99530	0.139522
$821$	−21.4480	−0.748540	−0.374270	−	0.927320i	$-0.622107\pi$
$821$	−21.4480	−0.748540	−0.374270	+	0.927320i	$0.622107\pi$
$822$	5.49307	0.191593
$823$	48.2740	1.68273	0.841364	−	0.540469i	$-0.181753\pi$
$823$	48.2740	1.68273	0.841364	+	0.540469i	$0.181753\pi$
$824$	15.4946	0.539780
$825$	−9.40805	−0.327546
$826$	122.811	4.27315
$827$	−29.6162	−1.02986	−0.514928	−	0.857234i	$-0.672181\pi$
$827$	−29.6162	−1.02986	−0.514928	+	0.857234i	$0.672181\pi$
$828$	−1.94328	−0.0675337
$829$	20.9282	0.726865	0.363433	−	0.931620i	$-0.381605\pi$
$829$	20.9282	0.726865	0.363433	+	0.931620i	$0.381605\pi$
$830$	30.1258	1.04568
$831$	−9.16410	−0.317899
$832$	−19.6440	−0.681034
$833$	−16.4638	−0.570435
$834$	25.0050	0.865853
$835$	5.53553	0.191565
$836$	2.21418	0.0765790
$837$	−33.8253	−1.16917
$838$	23.8991	0.825581
$839$	24.2176	0.836083	0.418041	−	0.908428i	$-0.362717\pi$
$839$	24.2176	0.836083	0.418041	+	0.908428i	$0.362717\pi$
$840$	31.3933	1.08317
$841$	−13.3712	−0.461075
$842$	−18.1937	−0.626996
$843$	−12.0848	−0.416222
$844$	8.90787	0.306622
$845$	−110.872	−3.81412
$846$	2.26035	0.0777125
$847$	−4.84394	−0.166440
$848$	−69.3891	−2.38283
$849$	−8.52197	−0.292473
$850$	20.8694	0.715815
$851$	−6.58561	−0.225752
$852$	−8.47864	−0.290473
$853$	−35.4526	−1.21387	−0.606937	−	0.794750i	$-0.707602\pi$
$853$	−35.4526	−1.21387	−0.606937	+	0.794750i	$0.707602\pi$
$854$	−40.3367	−1.38029
$855$	−29.9846	−1.02545
$856$	7.53778	0.257636
$857$	−25.2119	−0.861221	−0.430611	−	0.902538i	$-0.641702\pi$
$857$	−25.2119	−0.861221	−0.430611	+	0.902538i	$0.641702\pi$
$858$	−7.80150	−0.266339
$859$	11.3017	0.385608	0.192804	−	0.981237i	$-0.438242\pi$
$859$	11.3017	0.385608	0.192804	+	0.981237i	$0.438242\pi$
$860$	3.16627	0.107969
$861$	4.57379	0.155874
$862$	48.6371	1.65659
$863$	−19.7984	−0.673946	−0.336973	−	0.941514i	$-0.609403\pi$
$863$	−19.7984	−0.673946	−0.336973	+	0.941514i	$0.609403\pi$
$864$	−16.5602	−0.563390
$865$	−12.5684	−0.427338
$866$	48.7942	1.65810
$867$	0.748300	0.0254136
$868$	−30.4013	−1.03189
$869$	0.622145	0.0211048
$870$	−20.5846	−0.697883
$871$	−10.0176	−0.339432
$872$	−21.6926	−0.734605
$873$	16.8396	0.569935
$874$	5.13070	0.173548
$875$	153.766	5.19823
$876$	−3.77678	−0.127606
$877$	8.44053	0.285016	0.142508	−	0.989794i	$-0.454483\pi$
$877$	8.44053	0.285016	0.142508	+	0.989794i	$0.454483\pi$
$878$	5.41161	0.182633
$879$	16.0290	0.540645
$880$	−20.7089	−0.698095
$881$	−25.3386	−0.853679	−0.426839	−	0.904327i	$-0.640373\pi$
$881$	−25.3386	−0.853679	−0.426839	+	0.904327i	$0.640373\pi$
$882$	66.6827	2.24532
$883$	−11.2129	−0.377345	−0.188673	−	0.982040i	$-0.560419\pi$
$883$	−11.2129	−0.377345	−0.188673	+	0.982040i	$0.560419\pi$
$884$	4.74402	0.159559
$885$	−47.9123	−1.61055
$886$	−1.19720	−0.0402206
$887$	−43.6585	−1.46591	−0.732954	−	0.680278i	$-0.761859\pi$
$887$	−43.6585	−1.46591	−0.732954	+	0.680278i	$0.761859\pi$
$888$	−9.65625	−0.324043
$889$	−53.1588	−1.78289
$890$	−68.4461	−2.29432
$891$	−4.27397	−0.143184
$892$	14.0414	0.470141
$893$	−1.63597	−0.0547456
$894$	−17.4300	−0.582947
$895$	18.2364	0.609575
$896$	64.5586	2.15675
$897$	−4.95564	−0.165464
$898$	60.2690	2.01120
$899$	−32.8493	−1.09558
$900$	−23.1714	−0.772380
$901$	−14.0460	−0.467940
$902$	−2.09454	−0.0697404
$903$	3.62472	0.120623
$904$	15.7145	0.522657
$905$	34.6254	1.15099
$906$	20.9125	0.694770
$907$	−8.24484	−0.273765	−0.136883	−	0.990587i	$-0.543708\pi$
$907$	−8.24484	−0.273765	−0.136883	+	0.990587i	$0.543708\pi$
$908$	17.4853	0.580269
$909$	−6.97811	−0.231449
$910$	211.699	7.01776
$911$	5.28115	0.174972	0.0874861	−	0.996166i	$-0.472117\pi$
$911$	5.28115	0.174972	0.0874861	+	0.996166i	$0.472117\pi$
$912$	10.8367	0.358839
$913$	−4.32948	−0.143285
$914$	14.4379	0.477563
$915$	15.7365	0.520233
$916$	−10.5294	−0.347902
$917$	6.03660	0.199346
$918$	−6.75716	−0.223020
$919$	9.39302	0.309847	0.154924	−	0.987926i	$-0.450487\pi$
$919$	9.39302	0.309847	0.154924	+	0.987926i	$0.450487\pi$
$920$	−9.13208	−0.301076
$921$	10.1310	0.333827
$922$	−37.1080	−1.22209
$923$	94.2188	3.10125
$924$	2.73782	0.0900675
$925$	−78.5259	−2.58191
$926$	−34.2123	−1.12429
$927$	−18.2993	−0.601027
$928$	−16.0824	−0.527931
$929$	2.44089	0.0800830	0.0400415	−	0.999198i	$-0.487251\pi$
$929$	2.44089	0.0800830	0.0400415	+	0.999198i	$0.487251\pi$
$930$	43.2655	1.41873
$931$	−48.2627	−1.58175
$932$	−14.1650	−0.463988
$933$	−10.7530	−0.352039
$934$	−26.3966	−0.863723
$935$	−4.19197	−0.137092
$936$	31.6635	1.03495
$937$	−31.7626	−1.03764	−0.518819	−	0.854884i	$-0.673628\pi$
$937$	−31.7626	−1.03764	−0.518819	+	0.854884i	$0.673628\pi$
$938$	12.8242	0.418725
$939$	19.8463	0.647661
$940$	−1.76701	−0.0576336
$941$	−44.8123	−1.46084	−0.730420	−	0.682998i	$-0.760676\pi$
$941$	−44.8123	−1.46084	−0.730420	+	0.682998i	$0.760676\pi$
$942$	14.1869	0.462233
$943$	−1.33048	−0.0433265
$944$	−75.4557	−2.45587
$945$	−82.6599	−2.68893
$946$	−1.65992	−0.0539685
$947$	43.3275	1.40795	0.703977	−	0.710223i	$-0.251406\pi$
$947$	43.3275	1.40795	0.703977	+	0.710223i	$0.251406\pi$
$948$	−0.351639	−0.0114207
$949$	41.9694	1.36239
$950$	61.1776	1.98486
$951$	−5.00479	−0.162292
$952$	10.0079	0.324358
$953$	−30.6277	−0.992129	−0.496064	−	0.868286i	$-0.665222\pi$
$953$	−30.6277	−0.992129	−0.496064	+	0.868286i	$0.665222\pi$
$954$	56.8901	1.84189
$955$	−20.7853	−0.672596
$956$	−12.1073	−0.391579
$957$	2.95828	0.0956275
$958$	−54.7357	−1.76843
$959$	21.4216	0.691741
$960$	−9.81086	−0.316644
$961$	38.0440	1.22722
$962$	−65.1165	−2.09944
$963$	−8.90220	−0.286870
$964$	22.0913	0.711513
$965$	−52.3605	−1.68555
$966$	6.34407	0.204117
$967$	4.84734	0.155880	0.0779400	−	0.996958i	$-0.475166\pi$
$967$	4.84734	0.155880	0.0779400	+	0.996958i	$0.475166\pi$
$968$	2.06607	0.0664059
$969$	2.19360	0.0704687
$970$	−48.0217	−1.54188
$971$	5.16076	0.165617	0.0828083	−	0.996565i	$-0.473611\pi$
$971$	5.16076	0.165617	0.0828083	+	0.996565i	$0.473611\pi$
$972$	11.6399	0.373349
$973$	97.5134	3.12614
$974$	−1.09489	−0.0350825
$975$	−59.0903	−1.89241
$976$	24.7830	0.793285
$977$	−52.1470	−1.66833	−0.834166	−	0.551514i	$-0.814050\pi$
$977$	−52.1470	−1.66833	−0.834166	+	0.551514i	$0.814050\pi$
$978$	−17.7848	−0.568696
$979$	9.83661	0.314379
$980$	−52.1286	−1.66519
$981$	25.6192	0.817959
$982$	−15.8413	−0.505516
$983$	−47.8234	−1.52533	−0.762665	−	0.646794i	$-0.776109\pi$
$983$	−47.8234	−1.52533	−0.762665	+	0.646794i	$0.776109\pi$
$984$	−1.95084	−0.0621905
$985$	67.6599	2.15582
$986$	−6.56219	−0.208983
$987$	−2.02286	−0.0643884
$988$	13.9069	0.442436
$989$	−1.05441	−0.0335281
$990$	16.9786	0.539615
$991$	−7.60793	−0.241674	−0.120837	−	0.992672i	$-0.538558\pi$
$991$	−7.60793	−0.241674	−0.120837	+	0.992672i	$0.538558\pi$
$992$	33.8026	1.07324
$993$	4.30722	0.136685
$994$	−120.616	−3.82571
$995$	−49.6042	−1.57256
$996$	2.44704	0.0775374
$997$	27.8752	0.882818	0.441409	−	0.897306i	$-0.354479\pi$
$997$	27.8752	0.882818	0.441409	+	0.897306i	$0.354479\pi$
$998$	67.6327	2.14088
$999$	25.4253	0.804422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.h.1.20	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.h.1.20	✓	74	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.65992 q^{2} +0.748300 q^{3} +0.755318 q^{4} -4.19197 q^{5} -1.24211 q^{6} -4.84394 q^{7} +2.06607 q^{8} -2.44005 q^{9} +O(q^{10})\)	\(q-1.65992 q^{2} +0.748300 q^{3} +0.755318 q^{4} -4.19197 q^{5} -1.24211 q^{6} -4.84394 q^{7} +2.06607 q^{8} -2.44005 q^{9} +6.95831 q^{10} -1.00000 q^{11} +0.565204 q^{12} -6.28082 q^{13} +8.04053 q^{14} -3.13685 q^{15} -4.94013 q^{16} -1.00000 q^{17} +4.05027 q^{18} -2.93145 q^{19} -3.16627 q^{20} -3.62472 q^{21} +1.65992 q^{22} +1.05441 q^{23} +1.54604 q^{24} +12.5726 q^{25} +10.4256 q^{26} -4.07079 q^{27} -3.65871 q^{28} -3.95333 q^{29} +5.20690 q^{30} +8.30927 q^{31} +4.06806 q^{32} -0.748300 q^{33} +1.65992 q^{34} +20.3056 q^{35} -1.84301 q^{36} -6.24581 q^{37} +4.86596 q^{38} -4.69994 q^{39} -8.66088 q^{40} -1.26183 q^{41} +6.01673 q^{42} -1.00000 q^{43} -0.755318 q^{44} +10.2286 q^{45} -1.75022 q^{46} +0.558074 q^{47} -3.69670 q^{48} +16.4638 q^{49} -20.8694 q^{50} -0.748300 q^{51} -4.74402 q^{52} +14.0460 q^{53} +6.75716 q^{54} +4.19197 q^{55} -10.0079 q^{56} -2.19360 q^{57} +6.56219 q^{58} +15.2740 q^{59} -2.36932 q^{60} -5.01667 q^{61} -13.7927 q^{62} +11.8194 q^{63} +3.12762 q^{64} +26.3290 q^{65} +1.24211 q^{66} +1.59494 q^{67} -0.755318 q^{68} +0.789011 q^{69} -33.7056 q^{70} -15.0010 q^{71} -5.04130 q^{72} -6.68215 q^{73} +10.3675 q^{74} +9.40805 q^{75} -2.21418 q^{76} +4.84394 q^{77} +7.80150 q^{78} -0.622145 q^{79} +20.7089 q^{80} +4.27397 q^{81} +2.09454 q^{82} +4.32948 q^{83} -2.73782 q^{84} +4.19197 q^{85} +1.65992 q^{86} -2.95828 q^{87} -2.06607 q^{88} -9.83661 q^{89} -16.9786 q^{90} +30.4239 q^{91} +0.796411 q^{92} +6.21783 q^{93} -0.926355 q^{94} +12.2885 q^{95} +3.04413 q^{96} -6.90135 q^{97} -27.3284 q^{98} +2.44005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9}+O(q^{10}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9	\( 74 q - 7 q^{2} - 3 q^{3} + 79 q^{4} - 6 q^{5} - 12 q^{6} - 16 q^{7} - 21 q^{8} + 75 q^{9} - 9 q^{10} - 74 q^{11} - 3 q^{12} + 4 q^{13} - 5 q^{14} - 17 q^{15} + 85 q^{16} - 74 q^{17} - 23 q^{18} - 21 q^{20} - 22 q^{21} + 7 q^{22} - 23 q^{23} - 51 q^{24} + 90 q^{25} - 46 q^{26} - 27 q^{27} - 61 q^{28} - 63 q^{29} - 22 q^{30} - 31 q^{31} - 69 q^{32} + 3 q^{33} + 7 q^{34} - 20 q^{35} + 51 q^{36} + 8 q^{37} - 2 q^{38} - 77 q^{39} - 37 q^{40} - 64 q^{41} + 13 q^{42} - 74 q^{43} - 79 q^{44} - 12 q^{45} - 53 q^{46} - 32 q^{47} + 2 q^{48} + 78 q^{49} - 104 q^{50} + 3 q^{51} + 13 q^{52} + 25 q^{53} - 110 q^{54} + 6 q^{55} - 29 q^{56} - 29 q^{57} - 14 q^{58} - 61 q^{59} - 82 q^{60} - 36 q^{61} - 63 q^{62} - 104 q^{63} + 107 q^{64} - 65 q^{65} + 12 q^{66} + 33 q^{67} - 79 q^{68} - 34 q^{69} - 3 q^{70} - 168 q^{71} - 67 q^{72} - 47 q^{73} - 54 q^{74} - 53 q^{75} - 4 q^{76} + 16 q^{77} - 3 q^{78} - 79 q^{79} - 59 q^{80} + 70 q^{81} - 18 q^{82} - 36 q^{83} - 118 q^{84} + 6 q^{85} + 7 q^{86} - 24 q^{87} + 21 q^{88} - 24 q^{89} + 25 q^{90} - 14 q^{91} - 18 q^{92} - 13 q^{93} + 9 q^{94} - 155 q^{95} - 50 q^{96} + q^{97} - 60 q^{98} - 75 q^{99}+O(q^{100}) \) 74 * q - 7 * q^2 - 3 * q^3 + 79 * q^4 - 6 * q^5 - 12 * q^6 - 16 * q^7 - 21 * q^8 + 75 * q^9 - 9 * q^10 - 74 * q^11 - 3 * q^12 + 4 * q^13 - 5 * q^14 - 17 * q^15 + 85 * q^16 - 74 * q^17 - 23 * q^18 - 21 * q^20 - 22 * q^21 + 7 * q^22 - 23 * q^23 - 51 * q^24 + 90 * q^25 - 46 * q^26 - 27 * q^27 - 61 * q^28 - 63 * q^29 - 22 * q^30 - 31 * q^31 - 69 * q^32 + 3 * q^33 + 7 * q^34 - 20 * q^35 + 51 * q^36 + 8 * q^37 - 2 * q^38 - 77 * q^39 - 37 * q^40 - 64 * q^41 + 13 * q^42 - 74 * q^43 - 79 * q^44 - 12 * q^45 - 53 * q^46 - 32 * q^47 + 2 * q^48 + 78 * q^49 - 104 * q^50 + 3 * q^51 + 13 * q^52 + 25 * q^53 - 110 * q^54 + 6 * q^55 - 29 * q^56 - 29 * q^57 - 14 * q^58 - 61 * q^59 - 82 * q^60 - 36 * q^61 - 63 * q^62 - 104 * q^63 + 107 * q^64 - 65 * q^65 + 12 * q^66 + 33 * q^67 - 79 * q^68 - 34 * q^69 - 3 * q^70 - 168 * q^71 - 67 * q^72 - 47 * q^73 - 54 * q^74 - 53 * q^75 - 4 * q^76 + 16 * q^77 - 3 * q^78 - 79 * q^79 - 59 * q^80 + 70 * q^81 - 18 * q^82 - 36 * q^83 - 118 * q^84 + 6 * q^85 + 7 * q^86 - 24 * q^87 + 21 * q^88 - 24 * q^89 + 25 * q^90 - 14 * q^91 - 18 * q^92 - 13 * q^93 + 9 * q^94 - 155 * q^95 - 50 * q^96 + q^97 - 60 * q^98 - 75 * q^99

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