LMFDB - Embedded newform 8041.2.a.e.1.7

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:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.39048 q^{2} +1.48105 q^{3} +3.71439 q^{4} +1.30814 q^{5} -3.54043 q^{6} -2.95859 q^{7} -4.09821 q^{8} -0.806479 q^{9} +O(q^{10})$	\(q-2.39048 q^{2} +1.48105 q^{3} +3.71439 q^{4} +1.30814 q^{5} -3.54043 q^{6} -2.95859 q^{7} -4.09821 q^{8} -0.806479 q^{9} -3.12708 q^{10} -1.00000 q^{11} +5.50121 q^{12} +5.91169 q^{13} +7.07245 q^{14} +1.93742 q^{15} +2.36790 q^{16} -1.00000 q^{17} +1.92787 q^{18} +1.78243 q^{19} +4.85894 q^{20} -4.38183 q^{21} +2.39048 q^{22} +1.31611 q^{23} -6.06967 q^{24} -3.28877 q^{25} -14.1318 q^{26} -5.63760 q^{27} -10.9894 q^{28} +0.143512 q^{29} -4.63137 q^{30} -7.04670 q^{31} +2.53599 q^{32} -1.48105 q^{33} +2.39048 q^{34} -3.87025 q^{35} -2.99558 q^{36} +4.01891 q^{37} -4.26087 q^{38} +8.75553 q^{39} -5.36103 q^{40} -6.56089 q^{41} +10.4747 q^{42} +1.00000 q^{43} -3.71439 q^{44} -1.05499 q^{45} -3.14613 q^{46} +0.301895 q^{47} +3.50699 q^{48} +1.75326 q^{49} +7.86174 q^{50} -1.48105 q^{51} +21.9583 q^{52} +7.19015 q^{53} +13.4766 q^{54} -1.30814 q^{55} +12.1249 q^{56} +2.63988 q^{57} -0.343063 q^{58} +2.41098 q^{59} +7.19635 q^{60} -4.70530 q^{61} +16.8450 q^{62} +2.38604 q^{63} -10.7980 q^{64} +7.73331 q^{65} +3.54043 q^{66} +1.57926 q^{67} -3.71439 q^{68} +1.94923 q^{69} +9.25174 q^{70} -3.07793 q^{71} +3.30512 q^{72} +14.9031 q^{73} -9.60711 q^{74} -4.87085 q^{75} +6.62065 q^{76} +2.95859 q^{77} -20.9299 q^{78} +13.8474 q^{79} +3.09755 q^{80} -5.93015 q^{81} +15.6837 q^{82} +15.8617 q^{83} -16.2758 q^{84} -1.30814 q^{85} -2.39048 q^{86} +0.212549 q^{87} +4.09821 q^{88} +1.26840 q^{89} +2.52192 q^{90} -17.4903 q^{91} +4.88853 q^{92} -10.4365 q^{93} -0.721673 q^{94} +2.33167 q^{95} +3.75594 q^{96} -6.02576 q^{97} -4.19113 q^{98} +0.806479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−2.39048	−1.69032	−0.845162	−	0.534510i	$-0.820496\pi$
$2$	−2.39048	−1.69032	−0.845162	+	0.534510i	$0.820496\pi$
$3$	1.48105	0.855087	0.427543	−	0.903995i	$-0.359379\pi$
$3$	1.48105	0.855087	0.427543	+	0.903995i	$0.359379\pi$
$4$	3.71439	1.85719
$5$	1.30814	0.585017	0.292509	−	0.956263i	$-0.405510\pi$
$5$	1.30814	0.585017	0.292509	+	0.956263i	$0.405510\pi$
$6$	−3.54043	−1.44537
$7$	−2.95859	−1.11824	−0.559121	−	0.829086i	$-0.688861\pi$
$7$	−2.95859	−1.11824	−0.559121	+	0.829086i	$0.688861\pi$
$8$	−4.09821	−1.44894
$9$	−0.806479	−0.268826
$10$	−3.12708	−0.988869
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.50121	1.58806
$13$	5.91169	1.63961	0.819803	−	0.572645i	$-0.194083\pi$
$13$	5.91169	1.63961	0.819803	+	0.572645i	$0.194083\pi$
$14$	7.07245	1.89019
$15$	1.93742	0.500241
$16$	2.36790	0.591976
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.92787	0.454404
$19$	1.78243	0.408918	0.204459	−	0.978875i	$-0.434456\pi$
$19$	1.78243	0.408918	0.204459	+	0.978875i	$0.434456\pi$
$20$	4.85894	1.08649
$21$	−4.38183	−0.956194
$22$	2.39048	0.509652
$23$	1.31611	0.274427	0.137214	−	0.990541i	$-0.456185\pi$
$23$	1.31611	0.274427	0.137214	+	0.990541i	$0.456185\pi$
$24$	−6.06967	−1.23897
$25$	−3.28877	−0.657755
$26$	−14.1318	−2.77147
$27$	−5.63760	−1.08496
$28$	−10.9894	−2.07679
$29$	0.143512	0.0266496	0.0133248	−	0.999911i	$-0.495758\pi$
$29$	0.143512	0.0266496	0.0133248	+	0.999911i	$0.495758\pi$
$30$	−4.63137	−0.845569
$31$	−7.04670	−1.26563	−0.632813	−	0.774305i	$-0.718100\pi$
$31$	−7.04670	−1.26563	−0.632813	+	0.774305i	$0.718100\pi$
$32$	2.53599	0.448305
$33$	−1.48105	−0.257818
$34$	2.39048	0.409964
$35$	−3.87025	−0.654191
$36$	−2.99558	−0.499263
$37$	4.01891	0.660704	0.330352	−	0.943858i	$-0.392833\pi$
$37$	4.01891	0.660704	0.330352	+	0.943858i	$0.392833\pi$
$38$	−4.26087	−0.691204
$39$	8.75553	1.40201
$40$	−5.36103	−0.847653
$41$	−6.56089	−1.02464	−0.512320	−	0.858795i	$-0.671214\pi$
$41$	−6.56089	−1.02464	−0.512320	+	0.858795i	$0.671214\pi$
$42$	10.4747	1.61628
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−3.71439	−0.559965
$45$	−1.05499	−0.157268
$46$	−3.14613	−0.463871
$47$	0.301895	0.0440359	0.0220179	−	0.999758i	$-0.492991\pi$
$47$	0.301895	0.0440359	0.0220179	+	0.999758i	$0.492991\pi$
$48$	3.50699	0.506191
$49$	1.75326	0.250466
$50$	7.86174	1.11182
$51$	−1.48105	−0.207389
$52$	21.9583	3.04507
$53$	7.19015	0.987643	0.493822	−	0.869563i	$-0.335600\pi$
$53$	7.19015	0.987643	0.493822	+	0.869563i	$0.335600\pi$
$54$	13.4766	1.83393
$55$	−1.30814	−0.176389
$56$	12.1249	1.62026
$57$	2.63988	0.349660
$58$	−0.343063	−0.0450464
$59$	2.41098	0.313883	0.156941	−	0.987608i	$-0.449837\pi$
$59$	2.41098	0.313883	0.156941	+	0.987608i	$0.449837\pi$
$60$	7.19635	0.929044
$61$	−4.70530	−0.602451	−0.301226	−	0.953553i	$-0.597396\pi$
$61$	−4.70530	−0.602451	−0.301226	+	0.953553i	$0.597396\pi$
$62$	16.8450	2.13932
$63$	2.38604	0.300613
$64$	−10.7980	−1.34976
$65$	7.73331	0.959199
$66$	3.54043	0.435797
$67$	1.57926	0.192937	0.0964684	−	0.995336i	$-0.469245\pi$
$67$	1.57926	0.192937	0.0964684	+	0.995336i	$0.469245\pi$
$68$	−3.71439	−0.450436
$69$	1.94923	0.234659
$70$	9.25174	1.10579
$71$	−3.07793	−0.365283	−0.182641	−	0.983180i	$-0.558465\pi$
$71$	−3.07793	−0.365283	−0.182641	+	0.983180i	$0.558465\pi$
$72$	3.30512	0.389512
$73$	14.9031	1.74428	0.872139	−	0.489259i	$-0.162733\pi$
$73$	14.9031	1.74428	0.872139	+	0.489259i	$0.162733\pi$
$74$	−9.60711	−1.11680
$75$	−4.87085	−0.562437
$76$	6.62065	0.759440
$77$	2.95859	0.337163
$78$	−20.9299	−2.36984
$79$	13.8474	1.55795	0.778976	−	0.627053i	$-0.215739\pi$
$79$	13.8474	1.55795	0.778976	+	0.627053i	$0.215739\pi$
$80$	3.09755	0.346316
$81$	−5.93015	−0.658906
$82$	15.6837	1.73197
$83$	15.8617	1.74104	0.870522	−	0.492129i	$-0.163781\pi$
$83$	15.8617	1.74104	0.870522	+	0.492129i	$0.163781\pi$
$84$	−16.2758	−1.77584
$85$	−1.30814	−0.141888
$86$	−2.39048	−0.257772
$87$	0.212549	0.0227877
$88$	4.09821	0.436870
$89$	1.26840	0.134450	0.0672250	−	0.997738i	$-0.478585\pi$
$89$	1.26840	0.134450	0.0672250	+	0.997738i	$0.478585\pi$
$90$	2.52192	0.265834
$91$	−17.4903	−1.83348
$92$	4.88853	0.509665
$93$	−10.4365	−1.08222
$94$	−0.721673	−0.0744349
$95$	2.33167	0.239224
$96$	3.75594	0.383339
$97$	−6.02576	−0.611823	−0.305912	−	0.952060i	$-0.598961\pi$
$97$	−6.02576	−0.611823	−0.305912	+	0.952060i	$0.598961\pi$
$98$	−4.19113	−0.423368
$99$	0.806479	0.0810542
$100$	−12.2158	−1.22158
$101$	−1.17304	−0.116722	−0.0583610	−	0.998296i	$-0.518587\pi$
$101$	−1.17304	−0.116722	−0.0583610	+	0.998296i	$0.518587\pi$
$102$	3.54043	0.350555
$103$	1.33626	0.131666	0.0658329	−	0.997831i	$-0.479030\pi$
$103$	1.33626	0.131666	0.0658329	+	0.997831i	$0.479030\pi$
$104$	−24.2273	−2.37568
$105$	−5.73205	−0.559390
$106$	−17.1879	−1.66944
$107$	3.83587	0.370827	0.185414	−	0.982661i	$-0.440637\pi$
$107$	3.83587	0.370827	0.185414	+	0.982661i	$0.440637\pi$
$108$	−20.9402	−2.01498
$109$	−3.05264	−0.292390	−0.146195	−	0.989256i	$-0.546703\pi$
$109$	−3.05264	−0.292390	−0.146195	+	0.989256i	$0.546703\pi$
$110$	3.12708	0.298155
$111$	5.95222	0.564960
$112$	−7.00566	−0.661972
$113$	9.85854	0.927414	0.463707	−	0.885989i	$-0.346519\pi$
$113$	9.85854	0.927414	0.463707	+	0.885989i	$0.346519\pi$
$114$	−6.31057	−0.591039
$115$	1.72165	0.160545
$116$	0.533060	0.0494934
$117$	−4.76765	−0.440770
$118$	−5.76339	−0.530563
$119$	2.95859	0.271214
$120$	−7.93997	−0.724817
$121$	1.00000	0.0909091
$122$	11.2479	1.01834
$123$	−9.71704	−0.876156
$124$	−26.1742	−2.35051
$125$	−10.8429	−0.969815
$126$	−5.70378	−0.508133
$127$	−2.08983	−0.185442	−0.0927212	−	0.995692i	$-0.529557\pi$
$127$	−2.08983	−0.185442	−0.0927212	+	0.995692i	$0.529557\pi$
$128$	20.7405	1.83322
$129$	1.48105	0.130400
$130$	−18.4863	−1.62136
$131$	6.63126	0.579375	0.289688	−	0.957121i	$-0.406449\pi$
$131$	6.63126	0.579375	0.289688	+	0.957121i	$0.406449\pi$
$132$	−5.50121	−0.478819
$133$	−5.27349	−0.457269
$134$	−3.77518	−0.326126
$135$	−7.37476	−0.634719
$136$	4.09821	0.351418
$137$	0.946371	0.0808540	0.0404270	−	0.999182i	$-0.487128\pi$
$137$	0.946371	0.0808540	0.0404270	+	0.999182i	$0.487128\pi$
$138$	−4.65958	−0.396650
$139$	3.03396	0.257337	0.128668	−	0.991688i	$-0.458930\pi$
$139$	3.03396	0.257337	0.128668	+	0.991688i	$0.458930\pi$
$140$	−14.3756	−1.21496
$141$	0.447122	0.0376545
$142$	7.35771	0.617446
$143$	−5.91169	−0.494360
$144$	−1.90966	−0.159139
$145$	0.187734	0.0155905
$146$	−35.6256	−2.94839
$147$	2.59667	0.214170
$148$	14.9278	1.22706
$149$	−3.25957	−0.267035	−0.133517	−	0.991046i	$-0.542627\pi$
$149$	−3.25957	−0.267035	−0.133517	+	0.991046i	$0.542627\pi$
$150$	11.6437	0.950701
$151$	−1.91171	−0.155573	−0.0777864	−	0.996970i	$-0.524785\pi$
$151$	−1.91171	−0.155573	−0.0777864	+	0.996970i	$0.524785\pi$
$152$	−7.30478	−0.592496
$153$	0.806479	0.0652000
$154$	−7.07245	−0.569914
$155$	−9.21806	−0.740413
$156$	32.5214	2.60380
$157$	−7.39557	−0.590231	−0.295116	−	0.955462i	$-0.595358\pi$
$157$	−7.39557	−0.590231	−0.295116	+	0.955462i	$0.595358\pi$
$158$	−33.1019	−2.63344
$159$	10.6490	0.844521
$160$	3.31743	0.262266
$161$	−3.89382	−0.306876
$162$	14.1759	1.11376
$163$	−22.4707	−1.76004	−0.880021	−	0.474934i	$-0.842472\pi$
$163$	−22.4707	−1.76004	−0.880021	+	0.474934i	$0.842472\pi$
$164$	−24.3697	−1.90295
$165$	−1.93742	−0.150828
$166$	−37.9170	−2.94293
$167$	20.4494	1.58242	0.791211	−	0.611544i	$-0.209451\pi$
$167$	20.4494	1.58242	0.791211	+	0.611544i	$0.209451\pi$
$168$	17.9577	1.38546
$169$	21.9480	1.68831
$170$	3.12708	0.239836
$171$	−1.43749	−0.109928
$172$	3.71439	0.283219
$173$	−12.5913	−0.957296	−0.478648	−	0.878007i	$-0.658873\pi$
$173$	−12.5913	−0.957296	−0.478648	+	0.878007i	$0.658873\pi$
$174$	−0.508095	−0.0385186
$175$	9.73013	0.735529
$176$	−2.36790	−0.178487
$177$	3.57079	0.268397
$178$	−3.03208	−0.227264
$179$	0.103395	0.00772808	0.00386404	−	0.999993i	$-0.498770\pi$
$179$	0.103395	0.00772808	0.00386404	+	0.999993i	$0.498770\pi$
$180$	−3.91863	−0.292077
$181$	−2.77883	−0.206549	−0.103275	−	0.994653i	$-0.532932\pi$
$181$	−2.77883	−0.206549	−0.103275	+	0.994653i	$0.532932\pi$
$182$	41.8101	3.09917
$183$	−6.96880	−0.515148
$184$	−5.39368	−0.397628
$185$	5.25729	0.386524
$186$	24.9483	1.82930
$187$	1.00000	0.0731272
$188$	1.12135	0.0817832
$189$	16.6794	1.21324
$190$	−5.57381	−0.404366
$191$	16.8686	1.22057	0.610285	−	0.792182i	$-0.291055\pi$
$191$	16.8686	1.22057	0.610285	+	0.792182i	$0.291055\pi$
$192$	−15.9925	−1.15416
$193$	13.0893	0.942189	0.471094	−	0.882083i	$-0.343859\pi$
$193$	13.0893	0.942189	0.471094	+	0.882083i	$0.343859\pi$
$194$	14.4044	1.03418
$195$	11.4534	0.820198
$196$	6.51229	0.465163
$197$	−1.79736	−0.128057	−0.0640285	−	0.997948i	$-0.520395\pi$
$197$	−1.79736	−0.128057	−0.0640285	+	0.997948i	$0.520395\pi$
$198$	−1.92787	−0.137008
$199$	9.90024	0.701809	0.350905	−	0.936411i	$-0.385874\pi$
$199$	9.90024	0.701809	0.350905	+	0.936411i	$0.385874\pi$
$200$	13.4781	0.953044
$201$	2.33896	0.164978
$202$	2.80413	0.197298
$203$	−0.424594	−0.0298007
$204$	−5.50121	−0.385162
$205$	−8.58256	−0.599432
$206$	−3.19431	−0.222558
$207$	−1.06141	−0.0737733
$208$	13.9983	0.970608
$209$	−1.78243	−0.123293
$210$	13.7023	0.945551
$211$	13.5605	0.933543	0.466772	−	0.884378i	$-0.345417\pi$
$211$	13.5605	0.933543	0.466772	+	0.884378i	$0.345417\pi$
$212$	26.7070	1.83425
$213$	−4.55857	−0.312348
$214$	−9.16956	−0.626818
$215$	1.30814	0.0892143
$216$	23.1041	1.57203
$217$	20.8483	1.41528
$218$	7.29727	0.494233
$219$	22.0723	1.49151
$220$	−4.85894	−0.327589
$221$	−5.91169	−0.397663
$222$	−14.2287	−0.954965
$223$	5.71051	0.382404	0.191202	−	0.981551i	$-0.438761\pi$
$223$	5.71051	0.382404	0.191202	+	0.981551i	$0.438761\pi$
$224$	−7.50297	−0.501313
$225$	2.65233	0.176822
$226$	−23.5666	−1.56763
$227$	10.8242	0.718428	0.359214	−	0.933255i	$-0.383045\pi$
$227$	10.8242	0.718428	0.359214	+	0.933255i	$0.383045\pi$
$228$	9.80553	0.649387
$229$	−0.576245	−0.0380794	−0.0190397	−	0.999819i	$-0.506061\pi$
$229$	−0.576245	−0.0380794	−0.0190397	+	0.999819i	$0.506061\pi$
$230$	−4.11557	−0.271373
$231$	4.38183	0.288303
$232$	−0.588143	−0.0386135
$233$	−9.72156	−0.636880	−0.318440	−	0.947943i	$-0.603159\pi$
$233$	−9.72156	−0.636880	−0.318440	+	0.947943i	$0.603159\pi$
$234$	11.3970	0.745043
$235$	0.394920	0.0257618
$236$	8.95531	0.582941
$237$	20.5087	1.33219
$238$	−7.07245	−0.458439
$239$	9.36450	0.605739	0.302869	−	0.953032i	$-0.402055\pi$
$239$	9.36450	0.605739	0.302869	+	0.953032i	$0.402055\pi$
$240$	4.58763	0.296130
$241$	16.4880	1.06209	0.531043	−	0.847345i	$-0.321800\pi$
$241$	16.4880	1.06209	0.531043	+	0.847345i	$0.321800\pi$
$242$	−2.39048	−0.153666
$243$	8.12992	0.521535
$244$	−17.4773	−1.11887
$245$	2.29351	0.146527
$246$	23.2284	1.48099
$247$	10.5372	0.670465
$248$	28.8789	1.83381
$249$	23.4920	1.48874
$250$	25.9196	1.63930
$251$	−12.0934	−0.763331	−0.381665	−	0.924301i	$-0.624649\pi$
$251$	−12.0934	−0.763331	−0.381665	+	0.924301i	$0.624649\pi$
$252$	8.86268	0.558297
$253$	−1.31611	−0.0827430
$254$	4.99569	0.313458
$255$	−1.93742	−0.121326
$256$	−27.9837	−1.74898
$257$	6.84154	0.426764	0.213382	−	0.976969i	$-0.431552\pi$
$257$	6.84154	0.426764	0.213382	+	0.976969i	$0.431552\pi$
$258$	−3.54043	−0.220417
$259$	−11.8903	−0.738827
$260$	28.7245	1.78142
$261$	−0.115740	−0.00716410
$262$	−15.8519	−0.979332
$263$	20.5194	1.26528	0.632639	−	0.774447i	$-0.281972\pi$
$263$	20.5194	1.26528	0.632639	+	0.774447i	$0.281972\pi$
$264$	6.06967	0.373562
$265$	9.40572	0.577789
$266$	12.6062	0.772933
$267$	1.87857	0.114966
$268$	5.86597	0.358321
$269$	19.5219	1.19027	0.595137	−	0.803624i	$-0.297098\pi$
$269$	19.5219	1.19027	0.595137	+	0.803624i	$0.297098\pi$
$270$	17.6292	1.07288
$271$	−20.0830	−1.21996	−0.609978	−	0.792418i	$-0.708822\pi$
$271$	−20.0830	−1.21996	−0.609978	+	0.792418i	$0.708822\pi$
$272$	−2.36790	−0.143575
$273$	−25.9040	−1.56778
$274$	−2.26228	−0.136669
$275$	3.28877	0.198320
$276$	7.24018	0.435808
$277$	3.08508	0.185365	0.0926823	−	0.995696i	$-0.470456\pi$
$277$	3.08508	0.185365	0.0926823	+	0.995696i	$0.470456\pi$
$278$	−7.25261	−0.434982
$279$	5.68302	0.340233
$280$	15.8611	0.947881
$281$	−7.14069	−0.425978	−0.212989	−	0.977055i	$-0.568320\pi$
$281$	−7.14069	−0.425978	−0.212989	+	0.977055i	$0.568320\pi$
$282$	−1.06884	−0.0636483
$283$	19.3897	1.15260	0.576299	−	0.817239i	$-0.304496\pi$
$283$	19.3897	1.15260	0.576299	+	0.817239i	$0.304496\pi$
$284$	−11.4326	−0.678401
$285$	3.45333	0.204557
$286$	14.1318	0.835629
$287$	19.4110	1.14579
$288$	−2.04523	−0.120516
$289$	1.00000	0.0588235
$290$	−0.448774	−0.0263529
$291$	−8.92447	−0.523162
$292$	55.3559	3.23946
$293$	−6.74274	−0.393915	−0.196957	−	0.980412i	$-0.563106\pi$
$293$	−6.74274	−0.393915	−0.196957	+	0.980412i	$0.563106\pi$
$294$	−6.20729	−0.362016
$295$	3.15389	0.183627
$296$	−16.4703	−0.957318
$297$	5.63760	0.327127
$298$	7.79194	0.451375
$299$	7.78041	0.449953
$300$	−18.0922	−1.04456
$301$	−2.95859	−0.170530
$302$	4.56991	0.262969
$303$	−1.73734	−0.0998074
$304$	4.22063	0.242070
$305$	−6.15518	−0.352445
$306$	−1.92787	−0.110209
$307$	−24.5396	−1.40055	−0.700275	−	0.713873i	$-0.746939\pi$
$307$	−24.5396	−1.40055	−0.700275	+	0.713873i	$0.746939\pi$
$308$	10.9894	0.626177
$309$	1.97908	0.112586
$310$	22.0356	1.25154
$311$	18.1736	1.03053	0.515266	−	0.857031i	$-0.327693\pi$
$311$	18.1736	1.03053	0.515266	+	0.857031i	$0.327693\pi$
$312$	−35.8820	−2.03142
$313$	−20.1345	−1.13807	−0.569034	−	0.822314i	$-0.692683\pi$
$313$	−20.1345	−1.13807	−0.569034	+	0.822314i	$0.692683\pi$
$314$	17.6790	0.997681
$315$	3.12127	0.175864
$316$	51.4346	2.89342
$317$	−14.3507	−0.806016	−0.403008	−	0.915196i	$-0.632035\pi$
$317$	−14.3507	−0.806016	−0.403008	+	0.915196i	$0.632035\pi$
$318$	−25.4562	−1.42751
$319$	−0.143512	−0.00803514
$320$	−14.1253	−0.789631
$321$	5.68113	0.317090
$322$	9.30810	0.518720
$323$	−1.78243	−0.0991772
$324$	−22.0269	−1.22372
$325$	−19.4422	−1.07846
$326$	53.7158	2.97504
$327$	−4.52112	−0.250019
$328$	26.8879	1.48464
$329$	−0.893183	−0.0492428
$330$	4.63137	0.254949
$331$	15.3291	0.842563	0.421281	−	0.906930i	$-0.361580\pi$
$331$	15.3291	0.842563	0.421281	+	0.906930i	$0.361580\pi$
$332$	58.9164	3.23346
$333$	−3.24116	−0.177615
$334$	−48.8838	−2.67480
$335$	2.06589	0.112871
$336$	−10.3758	−0.566044
$337$	25.8174	1.40636	0.703181	−	0.711011i	$-0.251762\pi$
$337$	25.8174	1.40636	0.703181	+	0.711011i	$0.251762\pi$
$338$	−52.4663	−2.85379
$339$	14.6010	0.793019
$340$	−4.85894	−0.263513
$341$	7.04670	0.381600
$342$	3.43630	0.185814
$343$	15.5230	0.838161
$344$	−4.09821	−0.220961
$345$	2.54986	0.137280
$346$	30.0992	1.61814
$347$	−1.89731	−0.101853	−0.0509266	−	0.998702i	$-0.516217\pi$
$347$	−1.89731	−0.101853	−0.0509266	+	0.998702i	$0.516217\pi$
$348$	0.789491	0.0423212
$349$	4.04700	0.216631	0.108316	−	0.994117i	$-0.465454\pi$
$349$	4.04700	0.216631	0.108316	+	0.994117i	$0.465454\pi$
$350$	−23.2597	−1.24328
$351$	−33.3277	−1.77890
$352$	−2.53599	−0.135169
$353$	−10.6493	−0.566804	−0.283402	−	0.959001i	$-0.591463\pi$
$353$	−10.6493	−0.566804	−0.283402	+	0.959001i	$0.591463\pi$
$354$	−8.53590	−0.453678
$355$	−4.02635	−0.213697
$356$	4.71132	0.249700
$357$	4.38183	0.231911
$358$	−0.247163	−0.0130630
$359$	16.4985	0.870757	0.435379	−	0.900247i	$-0.356614\pi$
$359$	16.4985	0.870757	0.435379	+	0.900247i	$0.356614\pi$
$360$	4.32355	0.227871
$361$	−15.8229	−0.832786
$362$	6.64274	0.349135
$363$	1.48105	0.0777352
$364$	−64.9656	−3.40512
$365$	19.4953	1.02043
$366$	16.6588	0.870767
$367$	−19.2069	−1.00259	−0.501295	−	0.865276i	$-0.667143\pi$
$367$	−19.2069	−1.00259	−0.501295	+	0.865276i	$0.667143\pi$
$368$	3.11642	0.162454
$369$	5.29122	0.275450
$370$	−12.5674	−0.653350
$371$	−21.2727	−1.10442
$372$	−38.7654	−2.00989
$373$	−17.9700	−0.930451	−0.465225	−	0.885192i	$-0.654027\pi$
$373$	−17.9700	−0.930451	−0.465225	+	0.885192i	$0.654027\pi$
$374$	−2.39048	−0.123609
$375$	−16.0589	−0.829276
$376$	−1.23723	−0.0638051
$377$	0.848399	0.0436948
$378$	−39.8716	−2.05078
$379$	20.5495	1.05556	0.527778	−	0.849383i	$-0.323025\pi$
$379$	20.5495	1.05556	0.527778	+	0.849383i	$0.323025\pi$
$380$	8.66072	0.444286
$381$	−3.09515	−0.158569
$382$	−40.3241	−2.06316
$383$	−4.80164	−0.245353	−0.122676	−	0.992447i	$-0.539148\pi$
$383$	−4.80164	−0.245353	−0.122676	+	0.992447i	$0.539148\pi$
$384$	30.7178	1.56756
$385$	3.87025	0.197246
$386$	−31.2897	−1.59260
$387$	−0.806479	−0.0409956
$388$	−22.3820	−1.13627
$389$	−13.7925	−0.699309	−0.349654	−	0.936879i	$-0.613701\pi$
$389$	−13.7925	−0.699309	−0.349654	+	0.936879i	$0.613701\pi$
$390$	−27.3792	−1.38640
$391$	−1.31611	−0.0665584
$392$	−7.18522	−0.362909
$393$	9.82125	0.495416
$394$	4.29656	0.216458
$395$	18.1143	0.911430
$396$	2.99558	0.150533
$397$	22.3402	1.12122	0.560612	−	0.828079i	$-0.310566\pi$
$397$	22.3402	1.12122	0.560612	+	0.828079i	$0.310566\pi$
$398$	−23.6663	−1.18629
$399$	−7.81032	−0.391005
$400$	−7.78750	−0.389375
$401$	−6.09529	−0.304384	−0.152192	−	0.988351i	$-0.548633\pi$
$401$	−6.09529	−0.304384	−0.152192	+	0.988351i	$0.548633\pi$
$402$	−5.59124	−0.278866
$403$	−41.6579	−2.07513
$404$	−4.35713	−0.216775
$405$	−7.75747	−0.385472
$406$	1.01498	0.0503728
$407$	−4.01891	−0.199210
$408$	6.06967	0.300493
$409$	−5.42480	−0.268239	−0.134120	−	0.990965i	$-0.542821\pi$
$409$	−5.42480	−0.268239	−0.134120	+	0.990965i	$0.542821\pi$
$410$	20.5164	1.01323
$411$	1.40163	0.0691372
$412$	4.96340	0.244529
$413$	−7.13310	−0.350997
$414$	2.53728	0.124701
$415$	20.7493	1.01854
$416$	14.9920	0.735043
$417$	4.49345	0.220045
$418$	4.26087	0.208406
$419$	31.2023	1.52433	0.762165	−	0.647383i	$-0.224137\pi$
$419$	31.2023	1.52433	0.762165	+	0.647383i	$0.224137\pi$
$420$	−21.2910	−1.03890
$421$	33.5197	1.63365	0.816825	−	0.576886i	$-0.195732\pi$
$421$	33.5197	1.63365	0.816825	+	0.576886i	$0.195732\pi$
$422$	−32.4161	−1.57799
$423$	−0.243472	−0.0118380
$424$	−29.4667	−1.43103
$425$	3.28877	0.159529
$426$	10.8972	0.527970
$427$	13.9210	0.673687
$428$	14.2479	0.688698
$429$	−8.75553	−0.422721
$430$	−3.12708	−0.150801
$431$	27.4000	1.31981	0.659907	−	0.751347i	$-0.270596\pi$
$431$	27.4000	1.31981	0.659907	+	0.751347i	$0.270596\pi$
$432$	−13.3493	−0.642268
$433$	−2.45261	−0.117865	−0.0589325	−	0.998262i	$-0.518770\pi$
$433$	−2.45261	−0.117865	−0.0589325	+	0.998262i	$0.518770\pi$
$434$	−49.8374	−2.39227
$435$	0.278044	0.0133312
$436$	−11.3387	−0.543024
$437$	2.34587	0.112218
$438$	−52.7634	−2.52113
$439$	−24.8871	−1.18780	−0.593899	−	0.804540i	$-0.702412\pi$
$439$	−24.8871	−1.18780	−0.593899	+	0.804540i	$0.702412\pi$
$440$	5.36103	0.255577
$441$	−1.41397	−0.0673318
$442$	14.1318	0.672179
$443$	−0.583115	−0.0277046	−0.0138523	−	0.999904i	$-0.504409\pi$
$443$	−0.583115	−0.0277046	−0.0138523	+	0.999904i	$0.504409\pi$
$444$	22.1089	1.04924
$445$	1.65924	0.0786556
$446$	−13.6508	−0.646386
$447$	−4.82760	−0.228338
$448$	31.9470	1.50935
$449$	−15.6560	−0.738854	−0.369427	−	0.929260i	$-0.620446\pi$
$449$	−15.6560	−0.738854	−0.369427	+	0.929260i	$0.620446\pi$
$450$	−6.34033	−0.298886
$451$	6.56089	0.308940
$452$	36.6185	1.72239
$453$	−2.83135	−0.133028
$454$	−25.8750	−1.21438
$455$	−22.8797	−1.07262
$456$	−10.8188	−0.506635
$457$	−7.30518	−0.341722	−0.170861	−	0.985295i	$-0.554655\pi$
$457$	−7.30518	−0.341722	−0.170861	+	0.985295i	$0.554655\pi$
$458$	1.37750	0.0643664
$459$	5.63760	0.263141
$460$	6.39488	0.298163
$461$	−1.86595	−0.0869057	−0.0434529	−	0.999055i	$-0.513836\pi$
$461$	−1.86595	−0.0869057	−0.0434529	+	0.999055i	$0.513836\pi$
$462$	−10.4747	−0.487326
$463$	−1.72332	−0.0800896	−0.0400448	−	0.999198i	$-0.512750\pi$
$463$	−1.72332	−0.0800896	−0.0400448	+	0.999198i	$0.512750\pi$
$464$	0.339823	0.0157759
$465$	−13.6525	−0.633117
$466$	23.2392	1.07653
$467$	−3.66041	−0.169384	−0.0846918	−	0.996407i	$-0.526991\pi$
$467$	−3.66041	−0.169384	−0.0846918	+	0.996407i	$0.526991\pi$
$468$	−17.7089	−0.818595
$469$	−4.67237	−0.215750
$470$	−0.944048	−0.0435457
$471$	−10.9532	−0.504699
$472$	−9.88069	−0.454796
$473$	−1.00000	−0.0459800
$474$	−49.0257	−2.25182
$475$	−5.86201	−0.268968
$476$	10.9894	0.503696
$477$	−5.79871	−0.265504
$478$	−22.3856	−1.02389
$479$	2.99994	0.137071	0.0685354	−	0.997649i	$-0.478167\pi$
$479$	2.99994	0.137071	0.0685354	+	0.997649i	$0.478167\pi$
$480$	4.91330	0.224260
$481$	23.7585	1.08330
$482$	−39.4142	−1.79527
$483$	−5.76696	−0.262406
$484$	3.71439	0.168836
$485$	−7.88253	−0.357927
$486$	−19.4344	−0.881563
$487$	−4.88253	−0.221249	−0.110624	−	0.993862i	$-0.535285\pi$
$487$	−4.88253	−0.221249	−0.110624	+	0.993862i	$0.535285\pi$
$488$	19.2833	0.872913
$489$	−33.2803	−1.50499
$490$	−5.48258	−0.247678
$491$	23.6185	1.06589	0.532944	−	0.846151i	$-0.321086\pi$
$491$	23.6185	1.06589	0.532944	+	0.846151i	$0.321086\pi$
$492$	−36.0928	−1.62719
$493$	−0.143512	−0.00646347
$494$	−25.1889	−1.13330
$495$	1.05499	0.0474181
$496$	−16.6859	−0.749219
$497$	9.10632	0.408474
$498$	−56.1571	−2.51646
$499$	37.5935	1.68292	0.841459	−	0.540322i	$-0.181697\pi$
$499$	37.5935	1.68292	0.841459	+	0.540322i	$0.181697\pi$
$500$	−40.2746	−1.80114
$501$	30.2867	1.35311
$502$	28.9091	1.29028
$503$	−15.9605	−0.711642	−0.355821	−	0.934554i	$-0.615799\pi$
$503$	−15.9605	−0.711642	−0.355821	+	0.934554i	$0.615799\pi$
$504$	−9.77849	−0.435569
$505$	−1.53450	−0.0682844
$506$	3.14613	0.139862
$507$	32.5062	1.44365
$508$	−7.76244	−0.344403
$509$	25.7665	1.14208	0.571040	−	0.820922i	$-0.306540\pi$
$509$	25.7665	1.14208	0.571040	+	0.820922i	$0.306540\pi$
$510$	4.63137	0.205081
$511$	−44.0922	−1.95052
$512$	25.4133	1.12312
$513$	−10.0486	−0.443658
$514$	−16.3546	−0.721369
$515$	1.74802	0.0770268
$516$	5.50121	0.242177
$517$	−0.301895	−0.0132773
$518$	28.4235	1.24886
$519$	−18.6483	−0.818571
$520$	−31.6927	−1.38982
$521$	−23.1276	−1.01324	−0.506620	−	0.862170i	$-0.669105\pi$
$521$	−23.1276	−1.01324	−0.506620	+	0.862170i	$0.669105\pi$
$522$	0.276673	0.0121097
$523$	−6.99688	−0.305952	−0.152976	−	0.988230i	$-0.548886\pi$
$523$	−6.99688	−0.305952	−0.152976	+	0.988230i	$0.548886\pi$
$524$	24.6311	1.07601
$525$	14.4109	0.628941
$526$	−49.0511	−2.13873
$527$	7.04670	0.306959
$528$	−3.50699	−0.152622
$529$	−21.2679	−0.924690
$530$	−22.4842	−0.976650
$531$	−1.94440	−0.0843799
$532$	−19.5878	−0.849238
$533$	−38.7859	−1.68001
$534$	−4.49067	−0.194330
$535$	5.01785	0.216940
$536$	−6.47212	−0.279553
$537$	0.153133	0.00660818
$538$	−46.6668	−2.01195
$539$	−1.75326	−0.0755182
$540$	−27.3927	−1.17880
$541$	9.11296	0.391797	0.195898	−	0.980624i	$-0.437238\pi$
$541$	9.11296	0.391797	0.195898	+	0.980624i	$0.437238\pi$
$542$	48.0080	2.06212
$543$	−4.11560	−0.176617
$544$	−2.53599	−0.108730
$545$	−3.99327	−0.171053
$546$	61.9230	2.65006
$547$	23.0799	0.986827	0.493414	−	0.869795i	$-0.335749\pi$
$547$	23.0799	0.986827	0.493414	+	0.869795i	$0.335749\pi$
$548$	3.51519	0.150162
$549$	3.79472	0.161955
$550$	−7.86174	−0.335226
$551$	0.255801	0.0108975
$552$	−7.98833	−0.340006
$553$	−40.9688	−1.74217
$554$	−7.37482	−0.313326
$555$	7.78633	0.330511
$556$	11.2693	0.477924
$557$	6.94714	0.294360	0.147180	−	0.989110i	$-0.452980\pi$
$557$	6.94714	0.294360	0.147180	+	0.989110i	$0.452980\pi$
$558$	−13.5851	−0.575104
$559$	5.91169	0.250038
$560$	−9.16437	−0.387265
$561$	1.48105	0.0625301
$562$	17.0697	0.720040
$563$	4.01894	0.169378	0.0846890	−	0.996407i	$-0.473010\pi$
$563$	4.01894	0.169378	0.0846890	+	0.996407i	$0.473010\pi$
$564$	1.66079	0.0699317
$565$	12.8963	0.542553
$566$	−46.3506	−1.94826
$567$	17.5449	0.736817
$568$	12.6140	0.529271
$569$	17.2066	0.721337	0.360669	−	0.932694i	$-0.382549\pi$
$569$	17.2066	0.721337	0.360669	+	0.932694i	$0.382549\pi$
$570$	−8.25511	−0.345768
$571$	−30.3805	−1.27138	−0.635692	−	0.771943i	$-0.719285\pi$
$571$	−30.3805	−1.27138	−0.635692	+	0.771943i	$0.719285\pi$
$572$	−21.9583	−0.918123
$573$	24.9833	1.04369
$574$	−46.4016	−1.93676
$575$	−4.32838	−0.180506
$576$	8.70840	0.362850
$577$	−24.4635	−1.01843	−0.509214	−	0.860640i	$-0.670064\pi$
$577$	−24.4635	−1.01843	−0.509214	+	0.860640i	$0.670064\pi$
$578$	−2.39048	−0.0994308
$579$	19.3860	0.805653
$580$	0.697317	0.0289545
$581$	−46.9282	−1.94691
$582$	21.3338	0.884313
$583$	−7.19015	−0.297786
$584$	−61.0761	−2.52735
$585$	−6.23675	−0.257858
$586$	16.1184	0.665844
$587$	−4.02132	−0.165978	−0.0829888	−	0.996550i	$-0.526447\pi$
$587$	−4.02132	−0.165978	−0.0829888	+	0.996550i	$0.526447\pi$
$588$	9.64505	0.397755
$589$	−12.5603	−0.517537
$590$	−7.53932	−0.310389
$591$	−2.66199	−0.109500
$592$	9.51638	0.391121
$593$	25.1415	1.03244	0.516219	−	0.856456i	$-0.327339\pi$
$593$	25.1415	1.03244	0.516219	+	0.856456i	$0.327339\pi$
$594$	−13.4766	−0.552950
$595$	3.87025	0.158665
$596$	−12.1073	−0.495935
$597$	14.6628	0.600108
$598$	−18.5989	−0.760566
$599$	13.0250	0.532189	0.266094	−	0.963947i	$-0.414267\pi$
$599$	13.0250	0.532189	0.266094	+	0.963947i	$0.414267\pi$
$600$	19.9618	0.814935
$601$	17.9415	0.731848	0.365924	−	0.930645i	$-0.380753\pi$
$601$	17.9415	0.731848	0.365924	+	0.930645i	$0.380753\pi$
$602$	7.07245	0.288251
$603$	−1.27364	−0.0518665
$604$	−7.10084	−0.288929
$605$	1.30814	0.0531834
$606$	4.15307	0.168707
$607$	−30.3161	−1.23049	−0.615246	−	0.788335i	$-0.710943\pi$
$607$	−30.3161	−1.23049	−0.615246	+	0.788335i	$0.710943\pi$
$608$	4.52024	0.183320
$609$	−0.628847	−0.0254822
$610$	14.7138	0.595745
$611$	1.78471	0.0722015
$612$	2.99558	0.121089
$613$	−7.84796	−0.316976	−0.158488	−	0.987361i	$-0.550662\pi$
$613$	−7.84796	−0.316976	−0.158488	+	0.987361i	$0.550662\pi$
$614$	58.6614	2.36738
$615$	−12.7112	−0.512566
$616$	−12.1249	−0.488527
$617$	22.9499	0.923930	0.461965	−	0.886898i	$-0.347145\pi$
$617$	22.9499	0.923930	0.461965	+	0.886898i	$0.347145\pi$
$618$	−4.73094	−0.190306
$619$	−7.64588	−0.307314	−0.153657	−	0.988124i	$-0.549105\pi$
$619$	−7.64588	−0.307314	−0.153657	+	0.988124i	$0.549105\pi$
$620$	−34.2395	−1.37509
$621$	−7.41969	−0.297742
$622$	−43.4436	−1.74193
$623$	−3.75267	−0.150348
$624$	20.7322	0.829954
$625$	2.25989	0.0903956
$626$	48.1310	1.92370
$627$	−2.63988	−0.105427
$628$	−27.4700	−1.09617
$629$	−4.01891	−0.160244
$630$	−7.46134	−0.297267
$631$	−6.66769	−0.265437	−0.132718	−	0.991154i	$-0.542371\pi$
$631$	−6.66769	−0.265437	−0.132718	+	0.991154i	$0.542371\pi$
$632$	−56.7495	−2.25737
$633$	20.0838	0.798261
$634$	34.3051	1.36243
$635$	−2.73379	−0.108487
$636$	39.5545	1.56844
$637$	10.3647	0.410665
$638$	0.343063	0.0135820
$639$	2.48228	0.0981976
$640$	27.1315	1.07247
$641$	45.3799	1.79240	0.896199	−	0.443653i	$-0.146318\pi$
$641$	45.3799	1.79240	0.896199	+	0.443653i	$0.146318\pi$
$642$	−13.5806	−0.535984
$643$	19.9699	0.787537	0.393768	−	0.919210i	$-0.371171\pi$
$643$	19.9699	0.787537	0.393768	+	0.919210i	$0.371171\pi$
$644$	−14.4632	−0.569929
$645$	1.93742	0.0762860
$646$	4.26087	0.167642
$647$	5.68069	0.223331	0.111665	−	0.993746i	$-0.464381\pi$
$647$	5.68069	0.223331	0.111665	+	0.993746i	$0.464381\pi$
$648$	24.3030	0.954712
$649$	−2.41098	−0.0946392
$650$	46.4762	1.82294
$651$	30.8775	1.21018
$652$	−83.4650	−3.26874
$653$	47.8696	1.87328	0.936640	−	0.350293i	$-0.113918\pi$
$653$	47.8696	1.87328	0.936640	+	0.350293i	$0.113918\pi$
$654$	10.8076	0.422612
$655$	8.67460	0.338945
$656$	−15.5356	−0.606562
$657$	−12.0190	−0.468908
$658$	2.13513	0.0832362
$659$	43.8185	1.70692	0.853462	−	0.521154i	$-0.174498\pi$
$659$	43.8185	1.70692	0.853462	+	0.521154i	$0.174498\pi$
$660$	−7.19635	−0.280117
$661$	−3.88374	−0.151060	−0.0755300	−	0.997144i	$-0.524065\pi$
$661$	−3.88374	−0.151060	−0.0755300	+	0.997144i	$0.524065\pi$
$662$	−36.6438	−1.42420
$663$	−8.75553	−0.340037
$664$	−65.0044	−2.52266
$665$	−6.89845	−0.267511
$666$	7.74793	0.300226
$667$	0.188878	0.00731337
$668$	75.9570	2.93886
$669$	8.45757	0.326988
$670$	−4.93846	−0.190789
$671$	4.70530	0.181646
$672$	−11.1123	−0.428666
$673$	−34.8661	−1.34399	−0.671995	−	0.740556i	$-0.734562\pi$
$673$	−34.8661	−1.34399	−0.671995	+	0.740556i	$0.734562\pi$
$674$	−61.7159	−2.37721
$675$	18.5408	0.713635
$676$	81.5236	3.13552
$677$	50.1079	1.92580	0.962902	−	0.269852i	$-0.0869749\pi$
$677$	50.1079	1.92580	0.962902	+	0.269852i	$0.0869749\pi$
$678$	−34.9035	−1.34046
$679$	17.8278	0.684166
$680$	5.36103	0.205586
$681$	16.0312	0.614318
$682$	−16.8450	−0.645028
$683$	39.4573	1.50979	0.754896	−	0.655844i	$-0.227687\pi$
$683$	39.4573	1.50979	0.754896	+	0.655844i	$0.227687\pi$
$684$	−5.33941	−0.204158
$685$	1.23799	0.0473010
$686$	−37.1073	−1.41676
$687$	−0.853450	−0.0325612
$688$	2.36790	0.0902755
$689$	42.5059	1.61935
$690$	−6.09538	−0.232047
$691$	14.2812	0.543282	0.271641	−	0.962399i	$-0.412434\pi$
$691$	14.2812	0.543282	0.271641	+	0.962399i	$0.412434\pi$
$692$	−46.7688	−1.77788
$693$	−2.38604	−0.0906382
$694$	4.53549	0.172165
$695$	3.96884	0.150547
$696$	−0.871072	−0.0330179
$697$	6.56089	0.248511
$698$	−9.67428	−0.366177
$699$	−14.3982	−0.544588
$700$	36.1415	1.36602
$701$	2.64327	0.0998351	0.0499176	−	0.998753i	$-0.484104\pi$
$701$	2.64327	0.0998351	0.0499176	+	0.998753i	$0.484104\pi$
$702$	79.6692	3.00692
$703$	7.16343	0.270174
$704$	10.7980	0.406967
$705$	0.584898	0.0220285
$706$	25.4569	0.958082
$707$	3.47055	0.130523
$708$	13.2633	0.498465
$709$	0.557197	0.0209260	0.0104630	−	0.999945i	$-0.496669\pi$
$709$	0.557197	0.0209260	0.0104630	+	0.999945i	$0.496669\pi$
$710$	9.62491	0.361217
$711$	−11.1676	−0.418819
$712$	−5.19816	−0.194809
$713$	−9.27422	−0.347322
$714$	−10.4747	−0.392005
$715$	−7.73331	−0.289209
$716$	0.384048	0.0143525
$717$	13.8693	0.517959
$718$	−39.4393	−1.47186
$719$	26.6345	0.993299	0.496649	−	0.867951i	$-0.334564\pi$
$719$	26.6345	0.993299	0.496649	+	0.867951i	$0.334564\pi$
$720$	−2.49811	−0.0930989
$721$	−3.95345	−0.147234
$722$	37.8244	1.40768
$723$	24.4196	0.908175
$724$	−10.3217	−0.383602
$725$	−0.471979	−0.0175289
$726$	−3.54043	−0.131398
$727$	35.7925	1.32747	0.663736	−	0.747967i	$-0.268970\pi$
$727$	35.7925	1.32747	0.663736	+	0.747967i	$0.268970\pi$
$728$	71.6787	2.65659
$729$	29.8313	1.10486
$730$	−46.6032	−1.72486
$731$	−1.00000	−0.0369863
$732$	−25.8848	−0.956730
$733$	−7.74714	−0.286147	−0.143074	−	0.989712i	$-0.545699\pi$
$733$	−7.74714	−0.286147	−0.143074	+	0.989712i	$0.545699\pi$
$734$	45.9136	1.69470
$735$	3.39681	0.125293
$736$	3.33764	0.123027
$737$	−1.57926	−0.0581727
$738$	−12.6486	−0.465600
$739$	−28.4870	−1.04791	−0.523955	−	0.851746i	$-0.675544\pi$
$739$	−28.4870	−1.04791	−0.523955	+	0.851746i	$0.675544\pi$
$740$	19.5276	0.717849
$741$	15.6061	0.573306
$742$	50.8520	1.86683
$743$	−32.1364	−1.17897	−0.589485	−	0.807779i	$-0.700669\pi$
$743$	−32.1364	−1.17897	−0.589485	+	0.807779i	$0.700669\pi$
$744$	42.7711	1.56807
$745$	−4.26397	−0.156220
$746$	42.9569	1.57276
$747$	−12.7921	−0.468039
$748$	3.71439	0.135811
$749$	−11.3488	−0.414675
$750$	38.3884	1.40175
$751$	−16.2604	−0.593349	−0.296674	−	0.954979i	$-0.595878\pi$
$751$	−16.2604	−0.593349	−0.296674	+	0.954979i	$0.595878\pi$
$752$	0.714858	0.0260682
$753$	−17.9110	−0.652714
$754$	−2.02808	−0.0738583
$755$	−2.50078	−0.0910129
$756$	61.9536	2.25323
$757$	−25.1742	−0.914970	−0.457485	−	0.889217i	$-0.651250\pi$
$757$	−25.1742	−0.914970	−0.457485	+	0.889217i	$0.651250\pi$
$758$	−49.1231	−1.78423
$759$	−1.94923	−0.0707524
$760$	−9.55567	−0.346620
$761$	20.7416	0.751883	0.375941	−	0.926643i	$-0.377319\pi$
$761$	20.7416	0.751883	0.375941	+	0.926643i	$0.377319\pi$
$762$	7.39889	0.268034
$763$	9.03151	0.326962
$764$	62.6566	2.26684
$765$	1.05499	0.0381431
$766$	11.4782	0.414725
$767$	14.2529	0.514644
$768$	−41.4453	−1.49553
$769$	2.93078	0.105687	0.0528433	−	0.998603i	$-0.483172\pi$
$769$	2.93078	0.105687	0.0528433	+	0.998603i	$0.483172\pi$
$770$	−9.25174	−0.333410
$771$	10.1327	0.364920
$772$	48.6188	1.74983
$773$	15.9060	0.572099	0.286049	−	0.958215i	$-0.407658\pi$
$773$	15.9060	0.572099	0.286049	+	0.958215i	$0.407658\pi$
$774$	1.92787	0.0692959
$775$	23.1750	0.832471
$776$	24.6948	0.886492
$777$	−17.6102	−0.631762
$778$	32.9707	1.18206
$779$	−11.6943	−0.418993
$780$	42.5425	1.52327
$781$	3.07793	0.110137
$782$	3.14613	0.112505
$783$	−0.809065	−0.0289136
$784$	4.15155	0.148270
$785$	−9.67444	−0.345295
$786$	−23.4775	−0.837414
$787$	43.7884	1.56089	0.780444	−	0.625226i	$-0.214993\pi$
$787$	43.7884	1.56089	0.780444	+	0.625226i	$0.214993\pi$
$788$	−6.67611	−0.237827
$789$	30.3903	1.08192
$790$	−43.3019	−1.54061
$791$	−29.1674	−1.03707
$792$	−3.30512	−0.117442
$793$	−27.8162	−0.987784
$794$	−53.4039	−1.89523
$795$	13.9304	0.494059
$796$	36.7733	1.30340
$797$	−37.1147	−1.31467	−0.657335	−	0.753598i	$-0.728316\pi$
$797$	−37.1147	−1.31467	−0.657335	+	0.753598i	$0.728316\pi$
$798$	18.6704	0.660925
$799$	−0.301895	−0.0106803
$800$	−8.34031	−0.294874
$801$	−1.02294	−0.0361437
$802$	14.5707	0.514508
$803$	−14.9031	−0.525919
$804$	8.68782	0.306396
$805$	−5.09366	−0.179528
$806$	99.5823	3.50764
$807$	28.9131	1.01779
$808$	4.80737	0.169123
$809$	25.5543	0.898443	0.449221	−	0.893420i	$-0.351701\pi$
$809$	25.5543	0.898443	0.449221	+	0.893420i	$0.351701\pi$
$810$	18.5441	0.651572
$811$	−38.0834	−1.33729	−0.668645	−	0.743582i	$-0.733125\pi$
$811$	−38.0834	−1.33729	−0.668645	+	0.743582i	$0.733125\pi$
$812$	−1.57711	−0.0553456
$813$	−29.7440	−1.04317
$814$	9.60711	0.336729
$815$	−29.3948	−1.02966
$816$	−3.50699	−0.122769
$817$	1.78243	0.0623594
$818$	12.9679	0.453411
$819$	14.1055	0.492887
$820$	−31.8790	−1.11326
$821$	7.50008	0.261755	0.130877	−	0.991399i	$-0.458221\pi$
$821$	7.50008	0.261755	0.130877	+	0.991399i	$0.458221\pi$
$822$	−3.35056	−0.116864
$823$	−2.72360	−0.0949386	−0.0474693	−	0.998873i	$-0.515116\pi$
$823$	−2.72360	−0.0949386	−0.0474693	+	0.998873i	$0.515116\pi$
$824$	−5.47628	−0.190775
$825$	4.87085	0.169581
$826$	17.0515	0.593298
$827$	32.1113	1.11662	0.558310	−	0.829632i	$-0.311450\pi$
$827$	32.1113	1.11662	0.558310	+	0.829632i	$0.311450\pi$
$828$	−3.94250	−0.137011
$829$	−44.2921	−1.53833	−0.769164	−	0.639051i	$-0.779327\pi$
$829$	−44.2921	−1.53833	−0.769164	+	0.639051i	$0.779327\pi$
$830$	−49.6007	−1.72166
$831$	4.56917	0.158503
$832$	−63.8347	−2.21307
$833$	−1.75326	−0.0607468
$834$	−10.7415	−0.371948
$835$	26.7506	0.925744
$836$	−6.62065	−0.228980
$837$	39.7265	1.37315
$838$	−74.5883	−2.57661
$839$	24.1225	0.832803	0.416401	−	0.909181i	$-0.363291\pi$
$839$	24.1225	0.832803	0.416401	+	0.909181i	$0.363291\pi$
$840$	23.4911	0.810521
$841$	−28.9794	−0.999290
$842$	−80.1281	−2.76140
$843$	−10.5757	−0.364248
$844$	50.3690	1.73377
$845$	28.7111	0.987692
$846$	0.582014	0.0200101
$847$	−2.95859	−0.101658
$848$	17.0256	0.584661
$849$	28.7172	0.985571
$850$	−7.86174	−0.269655
$851$	5.28931	0.181315
$852$	−16.9323	−0.580091
$853$	−2.43978	−0.0835366	−0.0417683	−	0.999127i	$-0.513299\pi$
$853$	−2.43978	−0.0835366	−0.0417683	+	0.999127i	$0.513299\pi$
$854$	−33.2780	−1.13875
$855$	−1.88044	−0.0643098
$856$	−15.7202	−0.537305
$857$	23.6984	0.809522	0.404761	−	0.914423i	$-0.367355\pi$
$857$	23.6984	0.809522	0.404761	+	0.914423i	$0.367355\pi$
$858$	20.9299	0.714535
$859$	2.43851	0.0832007	0.0416004	−	0.999134i	$-0.486754\pi$
$859$	2.43851	0.0832007	0.0416004	+	0.999134i	$0.486754\pi$
$860$	4.85894	0.165688
$861$	28.7487	0.979754
$862$	−65.4992	−2.23091
$863$	−7.19579	−0.244947	−0.122474	−	0.992472i	$-0.539083\pi$
$863$	−7.19579	−0.244947	−0.122474	+	0.992472i	$0.539083\pi$
$864$	−14.2969	−0.486391
$865$	−16.4711	−0.560035
$866$	5.86291	0.199230
$867$	1.48105	0.0502992
$868$	77.4387	2.62844
$869$	−13.8474	−0.469740
$870$	−0.664658	−0.0225340
$871$	9.33607	0.316341
$872$	12.5103	0.423654
$873$	4.85965	0.164474
$874$	−5.60776	−0.189685
$875$	32.0796	1.08449
$876$	81.9851	2.77002
$877$	−11.7051	−0.395254	−0.197627	−	0.980277i	$-0.563324\pi$
$877$	−11.7051	−0.395254	−0.197627	+	0.980277i	$0.563324\pi$
$878$	59.4921	2.00776
$879$	−9.98636	−0.336831
$880$	−3.09755	−0.104418
$881$	15.6443	0.527070	0.263535	−	0.964650i	$-0.415111\pi$
$881$	15.6443	0.527070	0.263535	+	0.964650i	$0.415111\pi$
$882$	3.38006	0.113812
$883$	53.1564	1.78886	0.894428	−	0.447213i	$-0.147583\pi$
$883$	53.1564	1.78886	0.894428	+	0.447213i	$0.147583\pi$
$884$	−21.9583	−0.738538
$885$	4.67109	0.157017
$886$	1.39392	0.0468298
$887$	−19.6626	−0.660206	−0.330103	−	0.943945i	$-0.607083\pi$
$887$	−19.6626	−0.660206	−0.330103	+	0.943945i	$0.607083\pi$
$888$	−24.3934	−0.818590
$889$	6.18295	0.207370
$890$	−3.96638	−0.132953
$891$	5.93015	0.198668
$892$	21.2110	0.710198
$893$	0.538107	0.0180071
$894$	11.5403	0.385965
$895$	0.135255	0.00452106
$896$	−61.3627	−2.04998
$897$	11.5232	0.384749
$898$	37.4254	1.24890
$899$	−1.01129	−0.0337283
$900$	9.85177	0.328392
$901$	−7.19015	−0.239539
$902$	−15.6837	−0.522209
$903$	−4.38183	−0.145818
$904$	−40.4024	−1.34376
$905$	−3.63510	−0.120835
$906$	6.76828	0.224861
$907$	−27.9115	−0.926785	−0.463392	−	0.886153i	$-0.653368\pi$
$907$	−27.9115	−0.926785	−0.463392	+	0.886153i	$0.653368\pi$
$908$	40.2053	1.33426
$909$	0.946033	0.0313779
$910$	54.6934	1.81307
$911$	−5.92361	−0.196258	−0.0981290	−	0.995174i	$-0.531286\pi$
$911$	−5.92361	−0.196258	−0.0981290	+	0.995174i	$0.531286\pi$
$912$	6.25098	0.206991
$913$	−15.8617	−0.524945
$914$	17.4629	0.577620
$915$	−9.11615	−0.301371
$916$	−2.14040	−0.0707207
$917$	−19.6192	−0.647882
$918$	−13.4766	−0.444793
$919$	−8.21661	−0.271041	−0.135521	−	0.990775i	$-0.543271\pi$
$919$	−8.21661	−0.271041	−0.135521	+	0.990775i	$0.543271\pi$
$920$	−7.05569	−0.232619
$921$	−36.3445	−1.19759
$922$	4.46050	0.146899
$923$	−18.1957	−0.598920
$924$	16.2758	0.535435
$925$	−13.2173	−0.434581
$926$	4.11957	0.135377
$927$	−1.07767	−0.0353952
$928$	0.363946	0.0119471
$929$	−21.3948	−0.701940	−0.350970	−	0.936387i	$-0.614148\pi$
$929$	−21.3948	−0.701940	−0.350970	+	0.936387i	$0.614148\pi$
$930$	32.6359	1.07017
$931$	3.12507	0.102420
$932$	−36.1096	−1.18281
$933$	26.9161	0.881194
$934$	8.75013	0.286313
$935$	1.30814	0.0427807
$936$	19.5388	0.638647
$937$	−38.8332	−1.26863	−0.634313	−	0.773077i	$-0.718717\pi$
$937$	−38.8332	−1.26863	−0.634313	+	0.773077i	$0.718717\pi$
$938$	11.1692	0.364688
$939$	−29.8203	−0.973147
$940$	1.46689	0.0478446
$941$	−43.2458	−1.40977	−0.704887	−	0.709320i	$-0.749002\pi$
$941$	−43.2458	−1.40977	−0.704887	+	0.709320i	$0.749002\pi$
$942$	26.1835	0.853104
$943$	−8.63484	−0.281189
$944$	5.70896	0.185811
$945$	21.8189	0.709769
$946$	2.39048	0.0777212
$947$	16.7111	0.543039	0.271520	−	0.962433i	$-0.412474\pi$
$947$	16.7111	0.543039	0.271520	+	0.962433i	$0.412474\pi$
$948$	76.1774	2.47413
$949$	88.1025	2.85993
$950$	14.0130	0.454642
$951$	−21.2542	−0.689214
$952$	−12.1249	−0.392971
$953$	47.9548	1.55341	0.776704	−	0.629866i	$-0.216890\pi$
$953$	47.9548	1.55341	0.776704	+	0.629866i	$0.216890\pi$
$954$	13.8617	0.448789
$955$	22.0665	0.714055
$956$	34.7834	1.12497
$957$	−0.212549	−0.00687075
$958$	−7.17129	−0.231694
$959$	−2.79993	−0.0904143
$960$	−20.9204	−0.675203
$961$	18.6560	0.601807
$962$	−56.7942	−1.83112
$963$	−3.09355	−0.0996882
$964$	61.2428	1.97250
$965$	17.1226	0.551197
$966$	13.7858	0.443551
$967$	54.3014	1.74621	0.873107	−	0.487528i	$-0.162101\pi$
$967$	54.3014	1.74621	0.873107	+	0.487528i	$0.162101\pi$
$968$	−4.09821	−0.131721
$969$	−2.63988	−0.0848051
$970$	18.8430	0.605013
$971$	−26.5979	−0.853567	−0.426783	−	0.904354i	$-0.640353\pi$
$971$	−26.5979	−0.853567	−0.426783	+	0.904354i	$0.640353\pi$
$972$	30.1977	0.968591
$973$	−8.97623	−0.287765
$974$	11.6716	0.373982
$975$	−28.7949	−0.922176
$976$	−11.1417	−0.356637
$977$	−49.2974	−1.57716	−0.788582	−	0.614930i	$-0.789184\pi$
$977$	−49.2974	−1.57716	−0.788582	+	0.614930i	$0.789184\pi$
$978$	79.5560	2.54392
$979$	−1.26840	−0.0405382
$980$	8.51897	0.272129
$981$	2.46189	0.0786021
$982$	−56.4595	−1.80170
$983$	21.2767	0.678623	0.339311	−	0.940674i	$-0.389806\pi$
$983$	21.2767	0.678623	0.339311	+	0.940674i	$0.389806\pi$
$984$	39.8224	1.26949
$985$	−2.35120	−0.0749156
$986$	0.343063	0.0109253
$987$	−1.32285	−0.0421069
$988$	39.1392	1.24518
$989$	1.31611	0.0418498
$990$	−2.52192	−0.0801520
$991$	12.4638	0.395925	0.197962	−	0.980210i	$-0.436568\pi$
$991$	12.4638	0.395925	0.197962	+	0.980210i	$0.436568\pi$
$992$	−17.8704	−0.567386
$993$	22.7032	0.720464
$994$	−21.7685	−0.690454
$995$	12.9509	0.410571
$996$	87.2584	2.76489
$997$	−53.5735	−1.69669	−0.848345	−	0.529444i	$-0.822401\pi$
$997$	−53.5735	−1.69669	−0.848345	+	0.529444i	$0.822401\pi$
$998$	−89.8665	−2.84467
$999$	−22.6570	−0.716836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.7	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.7	✓	66	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)

\(f(q)\)	\(=\)	\(q-2.39048 q^{2} +1.48105 q^{3} +3.71439 q^{4} +1.30814 q^{5} -3.54043 q^{6} -2.95859 q^{7} -4.09821 q^{8} -0.806479 q^{9} +O(q^{10})\)	\(q-2.39048 q^{2} +1.48105 q^{3} +3.71439 q^{4} +1.30814 q^{5} -3.54043 q^{6} -2.95859 q^{7} -4.09821 q^{8} -0.806479 q^{9} -3.12708 q^{10} -1.00000 q^{11} +5.50121 q^{12} +5.91169 q^{13} +7.07245 q^{14} +1.93742 q^{15} +2.36790 q^{16} -1.00000 q^{17} +1.92787 q^{18} +1.78243 q^{19} +4.85894 q^{20} -4.38183 q^{21} +2.39048 q^{22} +1.31611 q^{23} -6.06967 q^{24} -3.28877 q^{25} -14.1318 q^{26} -5.63760 q^{27} -10.9894 q^{28} +0.143512 q^{29} -4.63137 q^{30} -7.04670 q^{31} +2.53599 q^{32} -1.48105 q^{33} +2.39048 q^{34} -3.87025 q^{35} -2.99558 q^{36} +4.01891 q^{37} -4.26087 q^{38} +8.75553 q^{39} -5.36103 q^{40} -6.56089 q^{41} +10.4747 q^{42} +1.00000 q^{43} -3.71439 q^{44} -1.05499 q^{45} -3.14613 q^{46} +0.301895 q^{47} +3.50699 q^{48} +1.75326 q^{49} +7.86174 q^{50} -1.48105 q^{51} +21.9583 q^{52} +7.19015 q^{53} +13.4766 q^{54} -1.30814 q^{55} +12.1249 q^{56} +2.63988 q^{57} -0.343063 q^{58} +2.41098 q^{59} +7.19635 q^{60} -4.70530 q^{61} +16.8450 q^{62} +2.38604 q^{63} -10.7980 q^{64} +7.73331 q^{65} +3.54043 q^{66} +1.57926 q^{67} -3.71439 q^{68} +1.94923 q^{69} +9.25174 q^{70} -3.07793 q^{71} +3.30512 q^{72} +14.9031 q^{73} -9.60711 q^{74} -4.87085 q^{75} +6.62065 q^{76} +2.95859 q^{77} -20.9299 q^{78} +13.8474 q^{79} +3.09755 q^{80} -5.93015 q^{81} +15.6837 q^{82} +15.8617 q^{83} -16.2758 q^{84} -1.30814 q^{85} -2.39048 q^{86} +0.212549 q^{87} +4.09821 q^{88} +1.26840 q^{89} +2.52192 q^{90} -17.4903 q^{91} +4.88853 q^{92} -10.4365 q^{93} -0.721673 q^{94} +2.33167 q^{95} +3.75594 q^{96} -6.02576 q^{97} -4.19113 q^{98} +0.806479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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