LMFDB - Embedded newform 671.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.472572 q^{2} -1.64615 q^{3} -1.77668 q^{4} -3.20957 q^{5} -0.777925 q^{6} +4.06194 q^{7} -1.78475 q^{8} -0.290187 q^{9} +O(q^{10})$	\(q+0.472572 q^{2} -1.64615 q^{3} -1.77668 q^{4} -3.20957 q^{5} -0.777925 q^{6} +4.06194 q^{7} -1.78475 q^{8} -0.290187 q^{9} -1.51675 q^{10} -1.00000 q^{11} +2.92468 q^{12} -6.29425 q^{13} +1.91956 q^{14} +5.28343 q^{15} +2.70993 q^{16} +2.28683 q^{17} -0.137134 q^{18} +4.41630 q^{19} +5.70236 q^{20} -6.68657 q^{21} -0.472572 q^{22} +4.18874 q^{23} +2.93797 q^{24} +5.30131 q^{25} -2.97449 q^{26} +5.41614 q^{27} -7.21675 q^{28} +2.32215 q^{29} +2.49680 q^{30} +4.52296 q^{31} +4.85014 q^{32} +1.64615 q^{33} +1.08069 q^{34} -13.0371 q^{35} +0.515568 q^{36} -8.64218 q^{37} +2.08702 q^{38} +10.3613 q^{39} +5.72828 q^{40} +4.05541 q^{41} -3.15989 q^{42} +11.3037 q^{43} +1.77668 q^{44} +0.931374 q^{45} +1.97948 q^{46} -0.746581 q^{47} -4.46095 q^{48} +9.49937 q^{49} +2.50525 q^{50} -3.76447 q^{51} +11.1828 q^{52} -9.63873 q^{53} +2.55952 q^{54} +3.20957 q^{55} -7.24956 q^{56} -7.26990 q^{57} +1.09738 q^{58} +2.52363 q^{59} -9.38694 q^{60} +1.00000 q^{61} +2.13743 q^{62} -1.17872 q^{63} -3.12782 q^{64} +20.2018 q^{65} +0.777925 q^{66} +10.5600 q^{67} -4.06296 q^{68} -6.89530 q^{69} -6.16095 q^{70} -14.4115 q^{71} +0.517912 q^{72} +5.36468 q^{73} -4.08405 q^{74} -8.72675 q^{75} -7.84634 q^{76} -4.06194 q^{77} +4.89646 q^{78} +10.4811 q^{79} -8.69769 q^{80} -8.04523 q^{81} +1.91647 q^{82} -1.73345 q^{83} +11.8799 q^{84} -7.33974 q^{85} +5.34181 q^{86} -3.82261 q^{87} +1.78475 q^{88} -13.7096 q^{89} +0.440141 q^{90} -25.5669 q^{91} -7.44203 q^{92} -7.44548 q^{93} -0.352813 q^{94} -14.1744 q^{95} -7.98406 q^{96} +0.00104411 q^{97} +4.48914 q^{98} +0.290187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * 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 $

$2$	0.472572	0.334159	0.167079	−	0.985943i	$-0.446566\pi$
$2$	0.472572	0.334159	0.167079	+	0.985943i	$0.446566\pi$
$3$	−1.64615	−0.950406	−0.475203	−	0.879876i	$-0.657625\pi$
$3$	−1.64615	−0.950406	−0.475203	+	0.879876i	$0.657625\pi$
$4$	−1.77668	−0.888338
$5$	−3.20957	−1.43536	−0.717681	−	0.696372i	$-0.754796\pi$
$5$	−3.20957	−1.43536	−0.717681	+	0.696372i	$0.754796\pi$
$6$	−0.777925	−0.317587
$7$	4.06194	1.53527	0.767635	−	0.640888i	$-0.221434\pi$
$7$	4.06194	1.53527	0.767635	+	0.640888i	$0.221434\pi$
$8$	−1.78475	−0.631005
$9$	−0.290187	−0.0967290
$10$	−1.51675	−0.479639
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.92468	0.844281
$13$	−6.29425	−1.74571	−0.872856	−	0.487978i	$-0.837734\pi$
$13$	−6.29425	−1.74571	−0.872856	+	0.487978i	$0.837734\pi$
$14$	1.91956	0.513024
$15$	5.28343	1.36418
$16$	2.70993	0.677482
$17$	2.28683	0.554638	0.277319	−	0.960778i	$-0.410554\pi$
$17$	2.28683	0.554638	0.277319	+	0.960778i	$0.410554\pi$
$18$	−0.137134	−0.0323229
$19$	4.41630	1.01317	0.506585	−	0.862190i	$-0.330908\pi$
$19$	4.41630	1.01317	0.506585	+	0.862190i	$0.330908\pi$
$20$	5.70236	1.27509
$21$	−6.68657	−1.45913
$22$	−0.472572	−0.100753
$23$	4.18874	0.873413	0.436706	−	0.899604i	$-0.356145\pi$
$23$	4.18874	0.873413	0.436706	+	0.899604i	$0.356145\pi$
$24$	2.93797	0.599711
$25$	5.30131	1.06026
$26$	−2.97449	−0.583345
$27$	5.41614	1.04234
$28$	−7.21675	−1.36384
$29$	2.32215	0.431213	0.215606	−	0.976480i	$-0.430827\pi$
$29$	2.32215	0.431213	0.215606	+	0.976480i	$0.430827\pi$
$30$	2.49680	0.455851
$31$	4.52296	0.812348	0.406174	−	0.913796i	$-0.366863\pi$
$31$	4.52296	0.812348	0.406174	+	0.913796i	$0.366863\pi$
$32$	4.85014	0.857392
$33$	1.64615	0.286558
$34$	1.08069	0.185337
$35$	−13.0371	−2.20367
$36$	0.515568	0.0859280
$37$	−8.64218	−1.42077	−0.710383	−	0.703816i	$-0.751478\pi$
$37$	−8.64218	−1.42077	−0.710383	+	0.703816i	$0.751478\pi$
$38$	2.08702	0.338560
$39$	10.3613	1.65913
$40$	5.72828	0.905720
$41$	4.05541	0.633349	0.316674	−	0.948534i	$-0.397434\pi$
$41$	4.05541	0.633349	0.316674	+	0.948534i	$0.397434\pi$
$42$	−3.15989	−0.487581
$43$	11.3037	1.72380	0.861898	−	0.507081i	$-0.169276\pi$
$43$	11.3037	1.72380	0.861898	+	0.507081i	$0.169276\pi$
$44$	1.77668	0.267844
$45$	0.931374	0.138841
$46$	1.97948	0.291859
$47$	−0.746581	−0.108900	−0.0544500	−	0.998516i	$-0.517341\pi$
$47$	−0.746581	−0.108900	−0.0544500	+	0.998516i	$0.517341\pi$
$48$	−4.46095	−0.643883
$49$	9.49937	1.35705
$50$	2.50525	0.354296
$51$	−3.76447	−0.527131
$52$	11.1828	1.55078
$53$	−9.63873	−1.32398	−0.661991	−	0.749512i	$-0.730288\pi$
$53$	−9.63873	−1.32398	−0.661991	+	0.749512i	$0.730288\pi$
$54$	2.55952	0.348306
$55$	3.20957	0.432778
$56$	−7.24956	−0.968763
$57$	−7.26990	−0.962922
$58$	1.09738	0.144094
$59$	2.52363	0.328549	0.164275	−	0.986415i	$-0.447472\pi$
$59$	2.52363	0.328549	0.164275	+	0.986415i	$0.447472\pi$
$60$	−9.38694	−1.21185
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	2.13743	0.271453
$63$	−1.17872	−0.148505
$64$	−3.12782	−0.390977
$65$	20.2018	2.50573
$66$	0.777925	0.0957559
$67$	10.5600	1.29011	0.645056	−	0.764135i	$-0.276834\pi$
$67$	10.5600	1.29011	0.645056	+	0.764135i	$0.276834\pi$
$68$	−4.06296	−0.492706
$69$	−6.89530	−0.830096
$70$	−6.16095	−0.736375
$71$	−14.4115	−1.71033	−0.855167	−	0.518353i	$-0.826545\pi$
$71$	−14.4115	−1.71033	−0.855167	+	0.518353i	$0.826545\pi$
$72$	0.517912	0.0610365
$73$	5.36468	0.627888	0.313944	−	0.949442i	$-0.398350\pi$
$73$	5.36468	0.627888	0.313944	+	0.949442i	$0.398350\pi$
$74$	−4.08405	−0.474761
$75$	−8.72675	−1.00768
$76$	−7.84634	−0.900037
$77$	−4.06194	−0.462901
$78$	4.89646	0.554414
$79$	10.4811	1.17921	0.589606	−	0.807691i	$-0.299283\pi$
$79$	10.4811	1.17921	0.589606	+	0.807691i	$0.299283\pi$
$80$	−8.69769	−0.972431
$81$	−8.04523	−0.893914
$82$	1.91647	0.211639
$83$	−1.73345	−0.190271	−0.0951355	−	0.995464i	$-0.530328\pi$
$83$	−1.73345	−0.190271	−0.0951355	+	0.995464i	$0.530328\pi$
$84$	11.8799	1.29620
$85$	−7.33974	−0.796106
$86$	5.34181	0.576022
$87$	−3.82261	−0.409827
$88$	1.78475	0.190255
$89$	−13.7096	−1.45321	−0.726607	−	0.687053i	$-0.758904\pi$
$89$	−13.7096	−1.45321	−0.726607	+	0.687053i	$0.758904\pi$
$90$	0.440141	0.0463950
$91$	−25.5669	−2.68014
$92$	−7.44203	−0.775886
$93$	−7.44548	−0.772060
$94$	−0.352813	−0.0363899
$95$	−14.1744	−1.45426
$96$	−7.98406	−0.814870
$97$	0.00104411	0.000106013 0	5.30065e−5	−	1.00000i	$-0.499983\pi$
$97$	0.00104411	0.000106013 0	5.30065e−5		1.00000i	$0.499983\pi$
$98$	4.48914	0.453471
$99$	0.290187	0.0291649
$100$	−9.41870	−0.941870
$101$	−15.3172	−1.52412	−0.762059	−	0.647508i	$-0.775811\pi$
$101$	−15.3172	−1.52412	−0.762059	+	0.647508i	$0.775811\pi$
$102$	−1.77898	−0.176146
$103$	−6.50221	−0.640682	−0.320341	−	0.947302i	$-0.603797\pi$
$103$	−6.50221	−0.640682	−0.320341	+	0.947302i	$0.603797\pi$
$104$	11.2337	1.10155
$105$	21.4610	2.09438
$106$	−4.55499	−0.442420
$107$	8.21543	0.794216	0.397108	−	0.917772i	$-0.370014\pi$
$107$	8.21543	0.794216	0.397108	+	0.917772i	$0.370014\pi$
$108$	−9.62273	−0.925948
$109$	12.7951	1.22555	0.612775	−	0.790258i	$-0.290053\pi$
$109$	12.7951	1.22555	0.612775	+	0.790258i	$0.290053\pi$
$110$	1.51675	0.144617
$111$	14.2263	1.35030
$112$	11.0076	1.04012
$113$	13.0118	1.22405	0.612023	−	0.790840i	$-0.290356\pi$
$113$	13.0118	1.22405	0.612023	+	0.790840i	$0.290356\pi$
$114$	−3.43555	−0.321769
$115$	−13.4440	−1.25366
$116$	−4.12571	−0.383063
$117$	1.82651	0.168861
$118$	1.19260	0.109788
$119$	9.28898	0.851519
$120$	−9.42961	−0.860801
$121$	1.00000	0.0909091
$122$	0.472572	0.0427847
$123$	−6.67582	−0.601938
$124$	−8.03584	−0.721640
$125$	−0.967067	−0.0864971
$126$	−0.557031	−0.0496243
$127$	20.7171	1.83834	0.919172	−	0.393857i	$-0.128859\pi$
$127$	20.7171	1.83834	0.919172	+	0.393857i	$0.128859\pi$
$128$	−11.1784	−0.988040
$129$	−18.6076	−1.63831
$130$	9.54681	0.837311
$131$	−1.48312	−0.129581	−0.0647905	−	0.997899i	$-0.520638\pi$
$131$	−1.48312	−0.129581	−0.0647905	+	0.997899i	$0.520638\pi$
$132$	−2.92468	−0.254560
$133$	17.9388	1.55549
$134$	4.99037	0.431103
$135$	−17.3835	−1.49613
$136$	−4.08143	−0.349979
$137$	13.6041	1.16227	0.581136	−	0.813806i	$-0.302608\pi$
$137$	13.6041	1.16227	0.581136	+	0.813806i	$0.302608\pi$
$138$	−3.25853	−0.277384
$139$	−1.83421	−0.155575	−0.0777877	−	0.996970i	$-0.524786\pi$
$139$	−1.83421	−0.155575	−0.0777877	+	0.996970i	$0.524786\pi$
$140$	23.1626	1.95760
$141$	1.22898	0.103499
$142$	−6.81049	−0.571523
$143$	6.29425	0.526352
$144$	−0.786386	−0.0655322
$145$	−7.45310	−0.618946
$146$	2.53520	0.209814
$147$	−15.6374	−1.28975
$148$	15.3543	1.26212
$149$	20.6171	1.68902	0.844509	−	0.535542i	$-0.179893\pi$
$149$	20.6171	1.68902	0.844509	+	0.535542i	$0.179893\pi$
$150$	−4.12402	−0.336725
$151$	13.2251	1.07624	0.538121	−	0.842867i	$-0.319134\pi$
$151$	13.2251	1.07624	0.538121	+	0.842867i	$0.319134\pi$
$152$	−7.88200	−0.639315
$153$	−0.663609	−0.0536496
$154$	−1.91956	−0.154683
$155$	−14.5167	−1.16601
$156$	−18.4087	−1.47387
$157$	−23.4605	−1.87235	−0.936175	−	0.351534i	$-0.885660\pi$
$157$	−23.4605	−1.87235	−0.936175	+	0.351534i	$0.885660\pi$
$158$	4.95306	0.394044
$159$	15.8668	1.25832
$160$	−15.5668	−1.23067
$161$	17.0144	1.34092
$162$	−3.80195	−0.298709
$163$	5.47984	0.429214	0.214607	−	0.976700i	$-0.431153\pi$
$163$	5.47984	0.429214	0.214607	+	0.976700i	$0.431153\pi$
$164$	−7.20515	−0.562628
$165$	−5.28343	−0.411314
$166$	−0.819181	−0.0635808
$167$	−7.23804	−0.560096	−0.280048	−	0.959986i	$-0.590350\pi$
$167$	−7.23804	−0.560096	−0.280048	+	0.959986i	$0.590350\pi$
$168$	11.9339	0.920717
$169$	26.6176	2.04751
$170$	−3.46855	−0.266026
$171$	−1.28155	−0.0980029
$172$	−20.0830	−1.53131
$173$	5.48190	0.416781	0.208390	−	0.978046i	$-0.433178\pi$
$173$	5.48190	0.416781	0.208390	+	0.978046i	$0.433178\pi$
$174$	−1.80646	−0.136947
$175$	21.5336	1.62779
$176$	−2.70993	−0.204268
$177$	−4.15428	−0.312255
$178$	−6.47877	−0.485605
$179$	−13.5770	−1.01479	−0.507395	−	0.861713i	$-0.669392\pi$
$179$	−13.5770	−1.01479	−0.507395	+	0.861713i	$0.669392\pi$
$180$	−1.65475	−0.123338
$181$	21.3974	1.59046	0.795230	−	0.606308i	$-0.207350\pi$
$181$	21.3974	1.59046	0.795230	+	0.606308i	$0.207350\pi$
$182$	−12.0822	−0.895592
$183$	−1.64615	−0.121687
$184$	−7.47586	−0.551128
$185$	27.7376	2.03931
$186$	−3.51853	−0.257991
$187$	−2.28683	−0.167230
$188$	1.32643	0.0967400
$189$	22.0001	1.60027
$190$	−6.69843	−0.485955
$191$	−6.13364	−0.443815	−0.221907	−	0.975068i	$-0.571228\pi$
$191$	−6.13364	−0.443815	−0.221907	+	0.975068i	$0.571228\pi$
$192$	5.14886	0.371587
$193$	−15.0531	−1.08355	−0.541774	−	0.840524i	$-0.682247\pi$
$193$	−15.0531	−1.08355	−0.541774	+	0.840524i	$0.682247\pi$
$194$	0.000493416 0	3.54252e−5 0
$195$	−33.2552	−2.38146
$196$	−16.8773	−1.20552
$197$	8.07480	0.575306	0.287653	−	0.957735i	$-0.407125\pi$
$197$	8.07480	0.575306	0.287653	+	0.957735i	$0.407125\pi$
$198$	0.137134	0.00974571
$199$	7.43252	0.526877	0.263439	−	0.964676i	$-0.415143\pi$
$199$	7.43252	0.526877	0.263439	+	0.964676i	$0.415143\pi$
$200$	−9.46152	−0.669030
$201$	−17.3834	−1.22613
$202$	−7.23848	−0.509298
$203$	9.43245	0.662028
$204$	6.68824	0.468271
$205$	−13.0161	−0.909084
$206$	−3.07276	−0.214089
$207$	−1.21552	−0.0844844
$208$	−17.0570	−1.18269
$209$	−4.41630	−0.305482
$210$	10.1419	0.699855
$211$	26.4730	1.82247	0.911237	−	0.411883i	$-0.135129\pi$
$211$	26.4730	1.82247	0.911237	+	0.411883i	$0.135129\pi$
$212$	17.1249	1.17614
$213$	23.7236	1.62551
$214$	3.88238	0.265394
$215$	−36.2799	−2.47427
$216$	−9.66647	−0.657720
$217$	18.3720	1.24717
$218$	6.04661	0.409528
$219$	−8.83107	−0.596748
$220$	−5.70236	−0.384453
$221$	−14.3939	−0.968238
$222$	6.72297	0.451216
$223$	−2.84013	−0.190189	−0.0950946	−	0.995468i	$-0.530315\pi$
$223$	−2.84013	−0.190189	−0.0950946	+	0.995468i	$0.530315\pi$
$224$	19.7010	1.31633
$225$	−1.53837	−0.102558
$226$	6.14901	0.409026
$227$	12.8755	0.854576	0.427288	−	0.904115i	$-0.359469\pi$
$227$	12.8755	0.854576	0.427288	+	0.904115i	$0.359469\pi$
$228$	12.9163	0.855400
$229$	−11.1339	−0.735749	−0.367874	−	0.929876i	$-0.619914\pi$
$229$	−11.1339	−0.735749	−0.367874	+	0.929876i	$0.619914\pi$
$230$	−6.35327	−0.418923
$231$	6.68657	0.439944
$232$	−4.14446	−0.272097
$233$	17.1736	1.12508	0.562539	−	0.826771i	$-0.309825\pi$
$233$	17.1736	1.12508	0.562539	+	0.826771i	$0.309825\pi$
$234$	0.863158	0.0564264
$235$	2.39620	0.156311
$236$	−4.48368	−0.291863
$237$	−17.2534	−1.12073
$238$	4.38971	0.284543
$239$	10.9538	0.708545	0.354273	−	0.935142i	$-0.384728\pi$
$239$	10.9538	0.708545	0.354273	+	0.935142i	$0.384728\pi$
$240$	14.3177	0.924204
$241$	7.88182	0.507713	0.253856	−	0.967242i	$-0.418301\pi$
$241$	7.88182	0.507713	0.253856	+	0.967242i	$0.418301\pi$
$242$	0.472572	0.0303781
$243$	−3.00477	−0.192756
$244$	−1.77668	−0.113740
$245$	−30.4888	−1.94786
$246$	−3.15480	−0.201143
$247$	−27.7973	−1.76870
$248$	−8.07237	−0.512596
$249$	2.85352	0.180835
$250$	−0.457009	−0.0289038
$251$	1.64472	0.103814	0.0519068	−	0.998652i	$-0.483470\pi$
$251$	1.64472	0.103814	0.0519068	+	0.998652i	$0.483470\pi$
$252$	2.09421	0.131923
$253$	−4.18874	−0.263344
$254$	9.79031	0.614299
$255$	12.0823	0.756624
$256$	0.973033	0.0608146
$257$	−14.2756	−0.890486	−0.445243	−	0.895410i	$-0.646883\pi$
$257$	−14.2756	−0.890486	−0.445243	+	0.895410i	$0.646883\pi$
$258$	−8.79342	−0.547455
$259$	−35.1040	−2.18126
$260$	−35.8921	−2.22593
$261$	−0.673858	−0.0417108
$262$	−0.700882	−0.0433007
$263$	−12.4281	−0.766352	−0.383176	−	0.923675i	$-0.625170\pi$
$263$	−12.4281	−0.766352	−0.383176	+	0.923675i	$0.625170\pi$
$264$	−2.93797	−0.180820
$265$	30.9361	1.90039
$266$	8.47736	0.519780
$267$	22.5681	1.38114
$268$	−18.7617	−1.14606
$269$	22.2727	1.35799	0.678996	−	0.734142i	$-0.262415\pi$
$269$	22.2727	1.35799	0.678996	+	0.734142i	$0.262415\pi$
$270$	−8.21494	−0.499945
$271$	3.83646	0.233048	0.116524	−	0.993188i	$-0.462825\pi$
$271$	3.83646	0.233048	0.116524	+	0.993188i	$0.462825\pi$
$272$	6.19715	0.375757
$273$	42.0869	2.54722
$274$	6.42889	0.388384
$275$	−5.30131	−0.319681
$276$	12.2507	0.737406
$277$	−16.9872	−1.02066	−0.510331	−	0.859978i	$-0.670477\pi$
$277$	−16.9872	−1.02066	−0.510331	+	0.859978i	$0.670477\pi$
$278$	−0.866794	−0.0519869
$279$	−1.31251	−0.0785777
$280$	23.2679	1.39052
$281$	17.7829	1.06084	0.530418	−	0.847736i	$-0.322035\pi$
$281$	17.7829	1.06084	0.530418	+	0.847736i	$0.322035\pi$
$282$	0.580784	0.0345852
$283$	−10.1655	−0.604277	−0.302138	−	0.953264i	$-0.597700\pi$
$283$	−10.1655	−0.604277	−0.302138	+	0.953264i	$0.597700\pi$
$284$	25.6046	1.51935
$285$	23.3332	1.38214
$286$	2.97449	0.175885
$287$	16.4728	0.972361
$288$	−1.40745	−0.0829346
$289$	−11.7704	−0.692376
$290$	−3.52213	−0.206826
$291$	−0.00171876	−0.000100755 0
$292$	−9.53129	−0.557776
$293$	16.0638	0.938458	0.469229	−	0.883077i	$-0.344532\pi$
$293$	16.0638	0.938458	0.469229	+	0.883077i	$0.344532\pi$
$294$	−7.38980	−0.430982
$295$	−8.09976	−0.471586
$296$	15.4241	0.896510
$297$	−5.41614	−0.314277
$298$	9.74306	0.564400
$299$	−26.3650	−1.52473
$300$	15.5046	0.895159
$301$	45.9149	2.64649
$302$	6.24981	0.359636
$303$	25.2144	1.44853
$304$	11.9679	0.686404
$305$	−3.20957	−0.183779
$306$	−0.313603	−0.0179275
$307$	20.5144	1.17082	0.585409	−	0.810738i	$-0.300934\pi$
$307$	20.5144	1.17082	0.585409	+	0.810738i	$0.300934\pi$
$308$	7.21675	0.411213
$309$	10.7036	0.608908
$310$	−6.86021	−0.389634
$311$	7.38695	0.418876	0.209438	−	0.977822i	$-0.432837\pi$
$311$	7.38695	0.418876	0.209438	+	0.977822i	$0.432837\pi$
$312$	−18.4923	−1.04692
$313$	−18.4731	−1.04416	−0.522081	−	0.852896i	$-0.674844\pi$
$313$	−18.4731	−1.04416	−0.522081	+	0.852896i	$0.674844\pi$
$314$	−11.0868	−0.625662
$315$	3.78319	0.213158
$316$	−18.6214	−1.04754
$317$	−27.1083	−1.52256	−0.761278	−	0.648426i	$-0.775428\pi$
$317$	−27.1083	−1.52256	−0.761278	+	0.648426i	$0.775428\pi$
$318$	7.49821	0.420479
$319$	−2.32215	−0.130016
$320$	10.0389	0.561193
$321$	−13.5238	−0.754827
$322$	8.04054	0.448082
$323$	10.0993	0.561943
$324$	14.2938	0.794098
$325$	−33.3678	−1.85091
$326$	2.58962	0.143426
$327$	−21.0627	−1.16477
$328$	−7.23790	−0.399646
$329$	−3.03257	−0.167191
$330$	−2.49680	−0.137444
$331$	23.6583	1.30038	0.650188	−	0.759773i	$-0.274690\pi$
$331$	23.6583	1.30038	0.650188	+	0.759773i	$0.274690\pi$
$332$	3.07978	0.169025
$333$	2.50785	0.137429
$334$	−3.42049	−0.187161
$335$	−33.8931	−1.85178
$336$	−18.1201	−0.988533
$337$	28.0015	1.52534	0.762670	−	0.646788i	$-0.223888\pi$
$337$	28.0015	1.52534	0.762670	+	0.646788i	$0.223888\pi$
$338$	12.5787	0.684193
$339$	−21.4194	−1.16334
$340$	13.0403	0.707211
$341$	−4.52296	−0.244932
$342$	−0.605627	−0.0327485
$343$	10.1523	0.548172
$344$	−20.1743	−1.08772
$345$	22.1309	1.19149
$346$	2.59059	0.139271
$347$	−16.4975	−0.885634	−0.442817	−	0.896612i	$-0.646021\pi$
$347$	−16.4975	−0.885634	−0.442817	+	0.896612i	$0.646021\pi$
$348$	6.79154	0.364065
$349$	−1.46317	−0.0783219	−0.0391610	−	0.999233i	$-0.512469\pi$
$349$	−1.46317	−0.0783219	−0.0391610	+	0.999233i	$0.512469\pi$
$350$	10.1762	0.543940
$351$	−34.0906	−1.81962
$352$	−4.85014	−0.258513
$353$	−34.4299	−1.83252	−0.916259	−	0.400587i	$-0.868806\pi$
$353$	−34.4299	−1.83252	−0.916259	+	0.400587i	$0.868806\pi$
$354$	−1.96320	−0.104343
$355$	46.2547	2.45495
$356$	24.3575	1.29095
$357$	−15.2911	−0.809289
$358$	−6.41610	−0.339101
$359$	−19.9722	−1.05409	−0.527045	−	0.849837i	$-0.676700\pi$
$359$	−19.9722	−1.05409	−0.527045	+	0.849837i	$0.676700\pi$
$360$	−1.66227	−0.0876094
$361$	0.503742	0.0265127
$362$	10.1118	0.531466
$363$	−1.64615	−0.0864005
$364$	45.4241	2.38087
$365$	−17.2183	−0.901246
$366$	−0.777925	−0.0406628
$367$	9.55281	0.498653	0.249326	−	0.968420i	$-0.419791\pi$
$367$	9.55281	0.498653	0.249326	+	0.968420i	$0.419791\pi$
$368$	11.3512	0.591721
$369$	−1.17683	−0.0612632
$370$	13.1080	0.681454
$371$	−39.1520	−2.03267
$372$	13.2282	0.685851
$373$	−6.77266	−0.350675	−0.175337	−	0.984508i	$-0.556102\pi$
$373$	−6.77266	−0.350675	−0.175337	+	0.984508i	$0.556102\pi$
$374$	−1.08069	−0.0558813
$375$	1.59194	0.0822073
$376$	1.33246	0.0687164
$377$	−14.6162	−0.752773
$378$	10.3966	0.534744
$379$	0.317739	0.0163212	0.00816058	−	0.999967i	$-0.497402\pi$
$379$	0.317739	0.0163212	0.00816058	+	0.999967i	$0.497402\pi$
$380$	25.1833	1.29188
$381$	−34.1034	−1.74717
$382$	−2.89859	−0.148305
$383$	24.0805	1.23045	0.615227	−	0.788350i	$-0.289064\pi$
$383$	24.0805	1.23045	0.615227	+	0.788350i	$0.289064\pi$
$384$	18.4013	0.939039
$385$	13.0371	0.664430
$386$	−7.11369	−0.362078
$387$	−3.28018	−0.166741
$388$	−0.00185504	−9.41754e−5 0
$389$	−2.26775	−0.114980	−0.0574898	−	0.998346i	$-0.518310\pi$
$389$	−2.26775	−0.114980	−0.0574898	+	0.998346i	$0.518310\pi$
$390$	−15.7155	−0.795785
$391$	9.57895	0.484428
$392$	−16.9540	−0.856307
$393$	2.44144	0.123155
$394$	3.81593	0.192244
$395$	−33.6396	−1.69259
$396$	−0.515568	−0.0259083
$397$	8.47515	0.425355	0.212678	−	0.977122i	$-0.431782\pi$
$397$	8.47515	0.425355	0.212678	+	0.977122i	$0.431782\pi$
$398$	3.51240	0.176061
$399$	−29.5299	−1.47835
$400$	14.3662	0.718308
$401$	−1.69131	−0.0844600	−0.0422300	−	0.999108i	$-0.513446\pi$
$401$	−1.69131	−0.0844600	−0.0422300	+	0.999108i	$0.513446\pi$
$402$	−8.21491	−0.409722
$403$	−28.4687	−1.41813
$404$	27.2137	1.35393
$405$	25.8217	1.28309
$406$	4.45751	0.221223
$407$	8.64218	0.428377
$408$	6.71864	0.332622
$409$	2.03412	0.100581	0.0502903	−	0.998735i	$-0.483985\pi$
$409$	2.03412	0.100581	0.0502903	+	0.998735i	$0.483985\pi$
$410$	−6.15105	−0.303779
$411$	−22.3943	−1.10463
$412$	11.5523	0.569142
$413$	10.2508	0.504411
$414$	−0.574420	−0.0282312
$415$	5.56362	0.273108
$416$	−30.5280	−1.49676
$417$	3.01938	0.147860
$418$	−2.08702	−0.102080
$419$	−17.6278	−0.861174	−0.430587	−	0.902549i	$-0.641693\pi$
$419$	−17.6278	−0.861174	−0.430587	+	0.902549i	$0.641693\pi$
$420$	−38.1292	−1.86051
$421$	2.65032	0.129169	0.0645844	−	0.997912i	$-0.479428\pi$
$421$	2.65032	0.129169	0.0645844	+	0.997912i	$0.479428\pi$
$422$	12.5104	0.608996
$423$	0.216648	0.0105338
$424$	17.2027	0.835439
$425$	12.1232	0.588062
$426$	11.2111	0.543179
$427$	4.06194	0.196571
$428$	−14.5962	−0.705532
$429$	−10.3613	−0.500248
$430$	−17.1449	−0.826800
$431$	−27.8920	−1.34351	−0.671756	−	0.740773i	$-0.734459\pi$
$431$	−27.8920	−1.34351	−0.671756	+	0.740773i	$0.734459\pi$
$432$	14.6774	0.706165
$433$	−24.3263	−1.16905	−0.584523	−	0.811377i	$-0.698718\pi$
$433$	−24.3263	−1.16905	−0.584523	+	0.811377i	$0.698718\pi$
$434$	8.68210	0.416754
$435$	12.2689	0.588250
$436$	−22.7328	−1.08870
$437$	18.4988	0.884915
$438$	−4.17331	−0.199409
$439$	20.9152	0.998226	0.499113	−	0.866537i	$-0.333659\pi$
$439$	20.9152	0.998226	0.499113	+	0.866537i	$0.333659\pi$
$440$	−5.72828	−0.273085
$441$	−2.75659	−0.131266
$442$	−6.80215	−0.323545
$443$	28.9601	1.37593	0.687967	−	0.725742i	$-0.258503\pi$
$443$	28.9601	1.37593	0.687967	+	0.725742i	$0.258503\pi$
$444$	−25.2756	−1.19953
$445$	44.0018	2.08589
$446$	−1.34217	−0.0635534
$447$	−33.9388	−1.60525
$448$	−12.7050	−0.600255
$449$	23.4527	1.10680	0.553401	−	0.832915i	$-0.313330\pi$
$449$	23.4527	1.10680	0.553401	+	0.832915i	$0.313330\pi$
$450$	−0.726991	−0.0342707
$451$	−4.05541	−0.190962
$452$	−23.1177	−1.08737
$453$	−21.7705	−1.02287
$454$	6.08460	0.285564
$455$	82.0586	3.84697
$456$	12.9750	0.607609
$457$	21.3664	0.999476	0.499738	−	0.866177i	$-0.333430\pi$
$457$	21.3664	0.999476	0.499738	+	0.866177i	$0.333430\pi$
$458$	−5.26157	−0.245857
$459$	12.3858	0.578120
$460$	23.8857	1.11368
$461$	28.7391	1.33851	0.669257	−	0.743031i	$-0.266612\pi$
$461$	28.7391	1.33851	0.669257	+	0.743031i	$0.266612\pi$
$462$	3.15989	0.147011
$463$	4.67274	0.217161	0.108580	−	0.994088i	$-0.465370\pi$
$463$	4.67274	0.217161	0.108580	+	0.994088i	$0.465370\pi$
$464$	6.29286	0.292139
$465$	23.8968	1.10819
$466$	8.11575	0.375955
$467$	−31.9660	−1.47921	−0.739605	−	0.673041i	$-0.764988\pi$
$467$	−31.9660	−1.47921	−0.739605	+	0.673041i	$0.764988\pi$
$468$	−3.24512	−0.150006
$469$	42.8942	1.98067
$470$	1.13238	0.0522327
$471$	38.6195	1.77949
$472$	−4.50406	−0.207316
$473$	−11.3037	−0.519744
$474$	−8.15348	−0.374502
$475$	23.4122	1.07422
$476$	−16.5035	−0.756437
$477$	2.79703	0.128067
$478$	5.17648	0.236767
$479$	28.9406	1.32233	0.661165	−	0.750241i	$-0.270062\pi$
$479$	28.9406	1.32233	0.661165	+	0.750241i	$0.270062\pi$
$480$	25.6254	1.16963
$481$	54.3960	2.48025
$482$	3.72473	0.169657
$483$	−28.0083	−1.27442
$484$	−1.77668	−0.0807580
$485$	−0.00335113	−0.000152167 0
$486$	−1.41997	−0.0644112
$487$	−16.6396	−0.754014	−0.377007	−	0.926210i	$-0.623047\pi$
$487$	−16.6396	−0.754014	−0.377007	+	0.926210i	$0.623047\pi$
$488$	−1.78475	−0.0807919
$489$	−9.02064	−0.407927
$490$	−14.4082	−0.650895
$491$	−0.638708	−0.0288245	−0.0144122	−	0.999896i	$-0.504588\pi$
$491$	−0.638708	−0.0288245	−0.0144122	+	0.999896i	$0.504588\pi$
$492$	11.8608	0.534724
$493$	5.31037	0.239167
$494$	−13.1362	−0.591027
$495$	−0.931374	−0.0418622
$496$	12.2569	0.550351
$497$	−58.5388	−2.62582
$498$	1.34850	0.0604275
$499$	−15.9228	−0.712803	−0.356401	−	0.934333i	$-0.615996\pi$
$499$	−15.9228	−0.712803	−0.356401	+	0.934333i	$0.615996\pi$
$500$	1.71816	0.0768386
$501$	11.9149	0.532319
$502$	0.777248	0.0346903
$503$	−10.8102	−0.482001	−0.241001	−	0.970525i	$-0.577476\pi$
$503$	−10.8102	−0.482001	−0.241001	+	0.970525i	$0.577476\pi$
$504$	2.10373	0.0937075
$505$	49.1615	2.18766
$506$	−1.97948	−0.0879987
$507$	−43.8166	−1.94596
$508$	−36.8075	−1.63307
$509$	−26.4197	−1.17103	−0.585516	−	0.810661i	$-0.699108\pi$
$509$	−26.4197	−1.17103	−0.585516	+	0.810661i	$0.699108\pi$
$510$	5.70976	0.252833
$511$	21.7910	0.963977
$512$	22.8166	1.00836
$513$	23.9193	1.05606
$514$	−6.74624	−0.297564
$515$	20.8693	0.919610
$516$	33.0596	1.45537
$517$	0.746581	0.0328346
$518$	−16.5892	−0.728887
$519$	−9.02403	−0.396111
$520$	−36.0552	−1.58113
$521$	−4.91123	−0.215165	−0.107583	−	0.994196i	$-0.534311\pi$
$521$	−4.91123	−0.215165	−0.107583	+	0.994196i	$0.534311\pi$
$522$	−0.318447	−0.0139380
$523$	−0.691542	−0.0302390	−0.0151195	−	0.999886i	$-0.504813\pi$
$523$	−0.691542	−0.0302390	−0.0151195	+	0.999886i	$0.504813\pi$
$524$	2.63503	0.115112
$525$	−35.4476	−1.54706
$526$	−5.87319	−0.256083
$527$	10.3433	0.450559
$528$	4.46095	0.194138
$529$	−5.45445	−0.237150
$530$	14.6195	0.635033
$531$	−0.732326	−0.0317802
$532$	−31.8714	−1.38180
$533$	−25.5258	−1.10564
$534$	10.6650	0.461521
$535$	−26.3680	−1.13999
$536$	−18.8470	−0.814067
$537$	22.3497	0.964463
$538$	10.5255	0.453785
$539$	−9.49937	−0.409167
$540$	30.8848	1.32907
$541$	29.4372	1.26560	0.632801	−	0.774314i	$-0.281905\pi$
$541$	29.4372	1.26560	0.632801	+	0.774314i	$0.281905\pi$
$542$	1.81300	0.0778751
$543$	−35.2234	−1.51158
$544$	11.0915	0.475542
$545$	−41.0668	−1.75911
$546$	19.8891	0.851176
$547$	−12.2980	−0.525826	−0.262913	−	0.964820i	$-0.584683\pi$
$547$	−12.2980	−0.525826	−0.262913	+	0.964820i	$0.584683\pi$
$548$	−24.1700	−1.03249
$549$	−0.290187	−0.0123849
$550$	−2.50525	−0.106824
$551$	10.2553	0.436892
$552$	12.3064	0.523795
$553$	42.5735	1.81041
$554$	−8.02767	−0.341063
$555$	−45.6603	−1.93817
$556$	3.25879	0.138203
$557$	−0.790508	−0.0334949	−0.0167474	−	0.999860i	$-0.505331\pi$
$557$	−0.790508	−0.0334949	−0.0167474	+	0.999860i	$0.505331\pi$
$558$	−0.620253	−0.0262574
$559$	−71.1483	−3.00925
$560$	−35.3295	−1.49294
$561$	3.76447	0.158936
$562$	8.40369	0.354488
$563$	13.6547	0.575479	0.287739	−	0.957709i	$-0.407096\pi$
$563$	13.6547	0.575479	0.287739	+	0.957709i	$0.407096\pi$
$564$	−2.18351	−0.0919423
$565$	−41.7622	−1.75695
$566$	−4.80393	−0.201924
$567$	−32.6793	−1.37240
$568$	25.7210	1.07923
$569$	4.57231	0.191681	0.0958406	−	0.995397i	$-0.469446\pi$
$569$	4.57231	0.191681	0.0958406	+	0.995397i	$0.469446\pi$
$570$	11.0266	0.461855
$571$	0.856002	0.0358226	0.0179113	−	0.999840i	$-0.494298\pi$
$571$	0.856002	0.0358226	0.0179113	+	0.999840i	$0.494298\pi$
$572$	−11.1828	−0.467578
$573$	10.0969	0.421804
$574$	7.78460	0.324923
$575$	22.2058	0.926046
$576$	0.907651	0.0378188
$577$	−5.43867	−0.226415	−0.113207	−	0.993571i	$-0.536112\pi$
$577$	−5.43867	−0.226415	−0.113207	+	0.993571i	$0.536112\pi$
$578$	−5.56236	−0.231364
$579$	24.7797	1.02981
$580$	13.2417	0.549833
$581$	−7.04118	−0.292117
$582$	−0.000812237 0	−3.36683e−5 0
$583$	9.63873	0.399195
$584$	−9.57461	−0.396200
$585$	−5.86230	−0.242376
$586$	7.59131	0.313594
$587$	8.73008	0.360329	0.180165	−	0.983636i	$-0.442337\pi$
$587$	8.73008	0.360329	0.180165	+	0.983636i	$0.442337\pi$
$588$	27.7826	1.14573
$589$	19.9748	0.823047
$590$	−3.82772	−0.157585
$591$	−13.2923	−0.546774
$592$	−23.4197	−0.962543
$593$	−17.6920	−0.726522	−0.363261	−	0.931687i	$-0.618337\pi$
$593$	−17.6920	−0.726522	−0.363261	+	0.931687i	$0.618337\pi$
$594$	−2.55952	−0.105018
$595$	−29.8136	−1.22224
$596$	−36.6299	−1.50042
$597$	−12.2350	−0.500747
$598$	−12.4594	−0.509501
$599$	41.7205	1.70465	0.852327	−	0.523009i	$-0.175190\pi$
$599$	41.7205	1.70465	0.852327	+	0.523009i	$0.175190\pi$
$600$	15.5751	0.635850
$601$	29.0422	1.18466	0.592328	−	0.805697i	$-0.298209\pi$
$601$	29.0422	1.18466	0.592328	+	0.805697i	$0.298209\pi$
$602$	21.6981	0.884349
$603$	−3.06438	−0.124791
$604$	−23.4967	−0.956067
$605$	−3.20957	−0.130487
$606$	11.9156	0.484039
$607$	−10.3868	−0.421589	−0.210795	−	0.977530i	$-0.567605\pi$
$607$	−10.3868	−0.421589	−0.210795	+	0.977530i	$0.567605\pi$
$608$	21.4197	0.868683
$609$	−15.5272	−0.629195
$610$	−1.51675	−0.0614114
$611$	4.69917	0.190108
$612$	1.17902	0.0476590
$613$	−13.7211	−0.554191	−0.277095	−	0.960842i	$-0.589372\pi$
$613$	−13.7211	−0.554191	−0.277095	+	0.960842i	$0.589372\pi$
$614$	9.69452	0.391239
$615$	21.4265	0.863999
$616$	7.24956	0.292093
$617$	−27.1311	−1.09226	−0.546129	−	0.837701i	$-0.683899\pi$
$617$	−27.1311	−1.09226	−0.546129	+	0.837701i	$0.683899\pi$
$618$	5.05823	0.203472
$619$	17.0390	0.684854	0.342427	−	0.939544i	$-0.388751\pi$
$619$	17.0390	0.684854	0.342427	+	0.939544i	$0.388751\pi$
$620$	25.7916	1.03581
$621$	22.6868	0.910391
$622$	3.49087	0.139971
$623$	−55.6876	−2.23108
$624$	28.0783	1.12403
$625$	−23.4027	−0.936107
$626$	−8.72988	−0.348916
$627$	7.26990	0.290332
$628$	41.6817	1.66328
$629$	−19.7632	−0.788011
$630$	1.78783	0.0712288
$631$	−4.70714	−0.187388	−0.0936942	−	0.995601i	$-0.529868\pi$
$631$	−4.70714	−0.187388	−0.0936942	+	0.995601i	$0.529868\pi$
$632$	−18.7061	−0.744088
$633$	−43.5785	−1.73209
$634$	−12.8106	−0.508776
$635$	−66.4928	−2.63869
$636$	−28.1902	−1.11781
$637$	−59.7914	−2.36902
$638$	−1.09738	−0.0434459
$639$	4.18204	0.165439
$640$	35.8778	1.41819
$641$	29.1072	1.14967	0.574833	−	0.818270i	$-0.305067\pi$
$641$	29.1072	1.14967	0.574833	+	0.818270i	$0.305067\pi$
$642$	−6.39099	−0.252232
$643$	6.29208	0.248135	0.124068	−	0.992274i	$-0.460406\pi$
$643$	6.29208	0.248135	0.124068	+	0.992274i	$0.460406\pi$
$644$	−30.2291	−1.19119
$645$	59.7222	2.35156
$646$	4.77267	0.187778
$647$	−1.36523	−0.0536729	−0.0268365	−	0.999640i	$-0.508543\pi$
$647$	−1.36523	−0.0536729	−0.0268365	+	0.999640i	$0.508543\pi$
$648$	14.3587	0.564064
$649$	−2.52363	−0.0990613
$650$	−15.7687	−0.618498
$651$	−30.2431	−1.18532
$652$	−9.73589	−0.381287
$653$	−28.7882	−1.12657	−0.563285	−	0.826263i	$-0.690463\pi$
$653$	−28.7882	−1.12657	−0.563285	+	0.826263i	$0.690463\pi$
$654$	−9.95364	−0.389218
$655$	4.76018	0.185996
$656$	10.9899	0.429082
$657$	−1.55676	−0.0607350
$658$	−1.43311	−0.0558683
$659$	37.0741	1.44420	0.722101	−	0.691788i	$-0.243177\pi$
$659$	37.0741	1.44420	0.722101	+	0.691788i	$0.243177\pi$
$660$	9.38694	0.365386
$661$	−14.6348	−0.569227	−0.284614	−	0.958642i	$-0.591865\pi$
$661$	−14.6348	−0.569227	−0.284614	+	0.958642i	$0.591865\pi$
$662$	11.1802	0.434532
$663$	23.6945	0.920219
$664$	3.09378	0.120062
$665$	−57.5756	−2.23269
$666$	1.18514	0.0459232
$667$	9.72689	0.376627
$668$	12.8596	0.497555
$669$	4.67529	0.180757
$670$	−16.0169	−0.618788
$671$	−1.00000	−0.0386046
$672$	−32.4308	−1.25104
$673$	−32.0014	−1.23356	−0.616782	−	0.787134i	$-0.711564\pi$
$673$	−32.0014	−1.23356	−0.616782	+	0.787134i	$0.711564\pi$
$674$	13.2327	0.509706
$675$	28.7126	1.10515
$676$	−47.2909	−1.81888
$677$	11.1250	0.427569	0.213785	−	0.976881i	$-0.431421\pi$
$677$	11.1250	0.427569	0.213785	+	0.976881i	$0.431421\pi$
$678$	−10.1222	−0.388740
$679$	0.00424110	0.000162759 0
$680$	13.0996	0.502347
$681$	−21.1950	−0.812194
$682$	−2.13743	−0.0818463
$683$	10.0372	0.384063	0.192031	−	0.981389i	$-0.438492\pi$
$683$	10.0372	0.384063	0.192031	+	0.981389i	$0.438492\pi$
$684$	2.27691	0.0870597
$685$	−43.6631	−1.66828
$686$	4.79769	0.183177
$687$	18.3281	0.699260
$688$	30.6322	1.16784
$689$	60.6686	2.31129
$690$	10.4584	0.398146
$691$	−47.0727	−1.79073	−0.895365	−	0.445332i	$-0.853086\pi$
$691$	−47.0727	−1.79073	−0.895365	+	0.445332i	$0.853086\pi$
$692$	−9.73955	−0.370242
$693$	1.17872	0.0447760
$694$	−7.79627	−0.295942
$695$	5.88700	0.223307
$696$	6.82241	0.258603
$697$	9.27404	0.351279
$698$	−0.691455	−0.0261720
$699$	−28.2703	−1.06928
$700$	−38.2582	−1.44602
$701$	3.00915	0.113654	0.0568271	−	0.998384i	$-0.481902\pi$
$701$	3.00915	0.113654	0.0568271	+	0.998384i	$0.481902\pi$
$702$	−16.1103	−0.608042
$703$	−38.1665	−1.43948
$704$	3.12782	0.117884
$705$	−3.94451	−0.148559
$706$	−16.2706	−0.612352
$707$	−62.2176	−2.33993
$708$	7.38081	0.277388
$709$	−5.46583	−0.205274	−0.102637	−	0.994719i	$-0.532728\pi$
$709$	−5.46583	−0.205274	−0.102637	+	0.994719i	$0.532728\pi$
$710$	21.8587	0.820342
$711$	−3.04147	−0.114064
$712$	24.4682	0.916986
$713$	18.9455	0.709515
$714$	−7.22613	−0.270431
$715$	−20.2018	−0.755505
$716$	24.1219	0.901477
$717$	−18.0317	−0.673406
$718$	−9.43829	−0.352234
$719$	8.76833	0.327003	0.163502	−	0.986543i	$-0.447721\pi$
$719$	8.76833	0.327003	0.163502	+	0.986543i	$0.447721\pi$
$720$	2.52396	0.0940623
$721$	−26.4116	−0.983619
$722$	0.238054	0.00885946
$723$	−12.9747	−0.482533
$724$	−38.0163	−1.41286
$725$	12.3104	0.457198
$726$	−0.777925	−0.0288715
$727$	−42.9839	−1.59418	−0.797092	−	0.603858i	$-0.793629\pi$
$727$	−42.9839	−1.59418	−0.797092	+	0.603858i	$0.793629\pi$
$728$	45.6305	1.69118
$729$	29.0820	1.07711
$730$	−8.13688	−0.301159
$731$	25.8496	0.956084
$732$	2.92468	0.108099
$733$	−20.6856	−0.764042	−0.382021	−	0.924154i	$-0.624772\pi$
$733$	−20.6856	−0.764042	−0.382021	+	0.924154i	$0.624772\pi$
$734$	4.51439	0.166629
$735$	50.1892	1.85126
$736$	20.3160	0.748857
$737$	−10.5600	−0.388984
$738$	−0.556136	−0.0204716
$739$	31.1414	1.14555	0.572777	−	0.819711i	$-0.305866\pi$
$739$	31.1414	1.14555	0.572777	+	0.819711i	$0.305866\pi$
$740$	−49.2808	−1.81160
$741$	45.7586	1.68098
$742$	−18.5021	−0.679234
$743$	0.409099	0.0150084	0.00750420	−	0.999972i	$-0.497611\pi$
$743$	0.409099	0.0150084	0.00750420	+	0.999972i	$0.497611\pi$
$744$	13.2883	0.487174
$745$	−66.1719	−2.42435
$746$	−3.20057	−0.117181
$747$	0.503025	0.0184047
$748$	4.06296	0.148556
$749$	33.3706	1.21933
$750$	0.752305	0.0274703
$751$	47.1958	1.72220	0.861100	−	0.508436i	$-0.169776\pi$
$751$	47.1958	1.72220	0.861100	+	0.508436i	$0.169776\pi$
$752$	−2.02318	−0.0737778
$753$	−2.70745	−0.0986651
$754$	−6.90721	−0.251546
$755$	−42.4468	−1.54480
$756$	−39.0870	−1.42158
$757$	−21.2920	−0.773871	−0.386935	−	0.922107i	$-0.626466\pi$
$757$	−21.2920	−0.773871	−0.386935	+	0.922107i	$0.626466\pi$
$758$	0.150155	0.00545386
$759$	6.89530	0.250283
$760$	25.2978	0.917648
$761$	−40.4700	−1.46703	−0.733517	−	0.679671i	$-0.762123\pi$
$761$	−40.4700	−1.46703	−0.733517	+	0.679671i	$0.762123\pi$
$762$	−16.1163	−0.583833
$763$	51.9730	1.88155
$764$	10.8975	0.394257
$765$	2.12990	0.0770066
$766$	11.3798	0.411167
$767$	−15.8844	−0.573552
$768$	−1.60176	−0.0577985
$769$	−28.0251	−1.01061	−0.505306	−	0.862940i	$-0.668620\pi$
$769$	−28.0251	−1.01061	−0.505306	+	0.862940i	$0.668620\pi$
$770$	6.16095	0.222025
$771$	23.4998	0.846323
$772$	26.7446	0.962557
$773$	10.8737	0.391100	0.195550	−	0.980694i	$-0.437351\pi$
$773$	10.8737	0.391100	0.195550	+	0.980694i	$0.437351\pi$
$774$	−1.55012	−0.0557180
$775$	23.9776	0.861302
$776$	−0.00186347	−6.68948e−5 0
$777$	57.7865	2.07308
$778$	−1.07168	−0.0384215
$779$	17.9099	0.641690
$780$	59.0838	2.11554
$781$	14.4115	0.515685
$782$	4.52674	0.161876
$783$	12.5771	0.449469
$784$	25.7426	0.919379
$785$	75.2979	2.68750
$786$	1.15376	0.0411532
$787$	13.1203	0.467690	0.233845	−	0.972274i	$-0.424869\pi$
$787$	13.1203	0.467690	0.233845	+	0.972274i	$0.424869\pi$
$788$	−14.3463	−0.511066
$789$	20.4586	0.728345
$790$	−15.8972	−0.565596
$791$	52.8531	1.87924
$792$	−0.517912	−0.0184032
$793$	−6.29425	−0.223515
$794$	4.00512	0.142136
$795$	−50.9255	−1.80614
$796$	−13.2052	−0.468045
$797$	15.1688	0.537307	0.268653	−	0.963237i	$-0.413421\pi$
$797$	15.1688	0.537307	0.268653	+	0.963237i	$0.413421\pi$
$798$	−13.9550	−0.494002
$799$	−1.70731	−0.0604001
$800$	25.7121	0.909059
$801$	3.97835	0.140568
$802$	−0.799266	−0.0282231
$803$	−5.36468	−0.189315
$804$	30.8847	1.08922
$805$	−54.6089	−1.92471
$806$	−13.4535	−0.473879
$807$	−36.6643	−1.29064
$808$	27.3374	0.961726
$809$	−34.4544	−1.21135	−0.605676	−	0.795712i	$-0.707097\pi$
$809$	−34.4544	−1.21135	−0.605676	+	0.795712i	$0.707097\pi$
$810$	12.2026	0.428756
$811$	−21.5549	−0.756896	−0.378448	−	0.925623i	$-0.623542\pi$
$811$	−21.5549	−0.756896	−0.378448	+	0.925623i	$0.623542\pi$
$812$	−16.7584	−0.588104
$813$	−6.31539	−0.221490
$814$	4.08405	0.143146
$815$	−17.5879	−0.616077
$816$	−10.2014	−0.357122
$817$	49.9205	1.74650
$818$	0.961267	0.0336099
$819$	7.41918	0.259247
$820$	23.1254	0.807574
$821$	−16.6186	−0.579994	−0.289997	−	0.957027i	$-0.593654\pi$
$821$	−16.6186	−0.579994	−0.289997	+	0.957027i	$0.593654\pi$
$822$	−10.5829	−0.369122
$823$	−18.1054	−0.631113	−0.315557	−	0.948907i	$-0.602191\pi$
$823$	−18.1054	−0.631113	−0.315557	+	0.948907i	$0.602191\pi$
$824$	11.6048	0.404273
$825$	8.72675	0.303827
$826$	4.84426	0.168554
$827$	16.4273	0.571234	0.285617	−	0.958344i	$-0.407802\pi$
$827$	16.4273	0.571234	0.285617	+	0.958344i	$0.407802\pi$
$828$	2.15958	0.0750506
$829$	−31.9926	−1.11115	−0.555575	−	0.831467i	$-0.687502\pi$
$829$	−31.9926	−1.11115	−0.555575	+	0.831467i	$0.687502\pi$
$830$	2.62921	0.0912613
$831$	27.9635	0.970042
$832$	19.6873	0.682533
$833$	21.7235	0.752673
$834$	1.42687	0.0494086
$835$	23.2310	0.803940
$836$	7.84634	0.271371
$837$	24.4970	0.846741
$838$	−8.33041	−0.287769
$839$	33.0036	1.13941	0.569706	−	0.821849i	$-0.307057\pi$
$839$	33.0036	1.13941	0.569706	+	0.821849i	$0.307057\pi$
$840$	−38.3025	−1.32156
$841$	−23.6076	−0.814056
$842$	1.25247	0.0431629
$843$	−29.2733	−1.00823
$844$	−47.0339	−1.61897
$845$	−85.4310	−2.93891
$846$	0.102382	0.00351996
$847$	4.06194	0.139570
$848$	−26.1203	−0.896973
$849$	16.7340	0.574308
$850$	5.72909	0.196506
$851$	−36.1998	−1.24091
$852$	−42.1491	−1.44400
$853$	10.9871	0.376190	0.188095	−	0.982151i	$-0.439769\pi$
$853$	10.9871	0.376190	0.188095	+	0.982151i	$0.439769\pi$
$854$	1.91956	0.0656860
$855$	4.11323	0.140670
$856$	−14.6625	−0.501154
$857$	15.7703	0.538705	0.269352	−	0.963042i	$-0.413190\pi$
$857$	15.7703	0.538705	0.269352	+	0.963042i	$0.413190\pi$
$858$	−4.89646	−0.167162
$859$	27.0638	0.923403	0.461702	−	0.887035i	$-0.347239\pi$
$859$	27.0638	0.923403	0.461702	+	0.887035i	$0.347239\pi$
$860$	64.4577	2.19799
$861$	−27.1168	−0.924137
$862$	−13.1810	−0.448946
$863$	−6.40423	−0.218002	−0.109001	−	0.994042i	$-0.534765\pi$
$863$	−6.40423	−0.218002	−0.109001	+	0.994042i	$0.534765\pi$
$864$	26.2691	0.893691
$865$	−17.5945	−0.598231
$866$	−11.4959	−0.390647
$867$	19.3759	0.658039
$868$	−32.6411	−1.10791
$869$	−10.4811	−0.355546
$870$	5.79795	0.196569
$871$	−66.4675	−2.25216
$872$	−22.8361	−0.773328
$873$	−0.000302986 0	−1.02545e−5 0
$874$	8.74199	0.295702
$875$	−3.92817	−0.132796
$876$	15.6899	0.530114
$877$	−18.4953	−0.624543	−0.312272	−	0.949993i	$-0.601090\pi$
$877$	−18.4953	−0.624543	−0.312272	+	0.949993i	$0.601090\pi$
$878$	9.88392	0.333566
$879$	−26.4435	−0.891916
$880$	8.69769	0.293199
$881$	17.1991	0.579454	0.289727	−	0.957109i	$-0.406436\pi$
$881$	17.1991	0.579454	0.289727	+	0.957109i	$0.406436\pi$
$882$	−1.30269	−0.0438638
$883$	21.1699	0.712422	0.356211	−	0.934406i	$-0.384068\pi$
$883$	21.1699	0.712422	0.356211	+	0.934406i	$0.384068\pi$
$884$	25.5733	0.860123
$885$	13.3334	0.448198
$886$	13.6857	0.459780
$887$	41.1741	1.38249	0.691245	−	0.722620i	$-0.257063\pi$
$887$	41.1741	1.38249	0.691245	+	0.722620i	$0.257063\pi$
$888$	−25.3905	−0.852048
$889$	84.1516	2.82235
$890$	20.7940	0.697018
$891$	8.04523	0.269525
$892$	5.04599	0.168952
$893$	−3.29713	−0.110334
$894$	−16.0385	−0.536409
$895$	43.5762	1.45659
$896$	−45.4060	−1.51691
$897$	43.4007	1.44911
$898$	11.0831	0.369847
$899$	10.5030	0.350295
$900$	2.73319	0.0911062
$901$	−22.0422	−0.734331
$902$	−1.91647	−0.0638116
$903$	−75.5829	−2.51524
$904$	−23.2228	−0.772379
$905$	−68.6765	−2.28288
$906$	−10.2881	−0.341800
$907$	35.5805	1.18143	0.590715	−	0.806880i	$-0.298846\pi$
$907$	35.5805	1.18143	0.590715	+	0.806880i	$0.298846\pi$
$908$	−22.8756	−0.759152
$909$	4.44485	0.147426
$910$	38.7786	1.28550
$911$	8.92521	0.295705	0.147853	−	0.989009i	$-0.452764\pi$
$911$	8.92521	0.295705	0.147853	+	0.989009i	$0.452764\pi$
$912$	−19.7009	−0.652362
$913$	1.73345	0.0573689
$914$	10.0971	0.333984
$915$	5.28343	0.174665
$916$	19.7813	0.653593
$917$	−6.02436	−0.198942
$918$	5.85319	0.193184
$919$	−43.8505	−1.44649	−0.723247	−	0.690590i	$-0.757351\pi$
$919$	−43.8505	−1.44649	−0.723247	+	0.690590i	$0.757351\pi$
$920$	23.9943	0.791067
$921$	−33.7698	−1.11275
$922$	13.5813	0.447276
$923$	90.7098	2.98575
$924$	−11.8799	−0.390819
$925$	−45.8148	−1.50638
$926$	2.20821	0.0725662
$927$	1.88686	0.0619725
$928$	11.2628	0.369718
$929$	16.9397	0.555772	0.277886	−	0.960614i	$-0.410366\pi$
$929$	16.9397	0.555772	0.277886	+	0.960614i	$0.410366\pi$
$930$	11.2929	0.370310
$931$	41.9521	1.37492
$932$	−30.5119	−0.999450
$933$	−12.1600	−0.398102
$934$	−15.1062	−0.494291
$935$	7.33974	0.240035
$936$	−3.25987	−0.106552
$937$	−14.7259	−0.481076	−0.240538	−	0.970640i	$-0.577324\pi$
$937$	−14.7259	−0.481076	−0.240538	+	0.970640i	$0.577324\pi$
$938$	20.2706	0.661859
$939$	30.4095	0.992378
$940$	−4.25727	−0.138857
$941$	21.5676	0.703083	0.351542	−	0.936172i	$-0.385658\pi$
$941$	21.5676	0.703083	0.351542	+	0.936172i	$0.385658\pi$
$942$	18.2505	0.594633
$943$	16.9871	0.553175
$944$	6.83886	0.222586
$945$	−70.6106	−2.29696
$946$	−5.34181	−0.173677
$947$	−0.356161	−0.0115737	−0.00578685	−	0.999983i	$-0.501842\pi$
$947$	−0.356161	−0.0115737	−0.00578685	+	0.999983i	$0.501842\pi$
$948$	30.6537	0.995586
$949$	−33.7666	−1.09611
$950$	11.0639	0.358962
$951$	44.6244	1.44705
$952$	−16.5785	−0.537313
$953$	0.771616	0.0249951	0.0124975	−	0.999922i	$-0.496022\pi$
$953$	0.771616	0.0249951	0.0124975	+	0.999922i	$0.496022\pi$
$954$	1.32180	0.0427949
$955$	19.6863	0.637034
$956$	−19.4614	−0.629428
$957$	3.82261	0.123568
$958$	13.6765	0.441868
$959$	55.2589	1.78440
$960$	−16.5256	−0.533361
$961$	−10.5428	−0.340090
$962$	25.7061	0.828796
$963$	−2.38401	−0.0768237
$964$	−14.0034	−0.451020
$965$	48.3140	1.55528
$966$	−13.2359	−0.425859
$967$	39.1087	1.25765	0.628826	−	0.777546i	$-0.283536\pi$
$967$	39.1087	1.25765	0.628826	+	0.777546i	$0.283536\pi$
$968$	−1.78475	−0.0573641
$969$	−16.6250	−0.534073
$970$	−0.00158365	−5.08480e−5 0
$971$	62.2015	1.99614	0.998071	−	0.0620867i	$-0.0197755\pi$
$971$	62.2015	1.99614	0.998071	+	0.0620867i	$0.0197755\pi$
$972$	5.33850	0.171233
$973$	−7.45044	−0.238850
$974$	−7.86343	−0.251960
$975$	54.9284	1.75912
$976$	2.70993	0.0867427
$977$	33.6565	1.07677	0.538383	−	0.842700i	$-0.319036\pi$
$977$	33.6565	1.07677	0.538383	+	0.842700i	$0.319036\pi$
$978$	−4.26290	−0.136313
$979$	13.7096	0.438161
$980$	54.1688	1.73036
$981$	−3.71298	−0.118546
$982$	−0.301836	−0.00963196
$983$	−31.7228	−1.01180	−0.505901	−	0.862592i	$-0.668840\pi$
$983$	−31.7228	−1.01180	−0.505901	+	0.862592i	$0.668840\pi$
$984$	11.9147	0.379826
$985$	−25.9166	−0.825772
$986$	2.50953	0.0799198
$987$	4.99206	0.158899
$988$	49.3868	1.57120
$989$	47.3482	1.50559
$990$	−0.440141	−0.0139886
$991$	−14.2004	−0.451089	−0.225545	−	0.974233i	$-0.572416\pi$
$991$	−14.2004	−0.451089	−0.225545	+	0.974233i	$0.572416\pi$
$992$	21.9370	0.696501
$993$	−38.9451	−1.23589
$994$	−27.6638	−0.877442
$995$	−23.8551	−0.756259
$996$	−5.06978	−0.160642
$997$	−15.9252	−0.504357	−0.252179	−	0.967681i	$-0.581147\pi$
$997$	−15.9252	−0.504357	−0.252179	+	0.967681i	$0.581147\pi$
$998$	−7.52468	−0.238189
$999$	−46.8073	−1.48092

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.d.1.11	✓	21
3.2	odd	2		6039.2.a.l.1.11		21
11.10	odd	2		7381.2.a.j.1.11		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.11	✓	21	1.1	even	1	trivial
6039.2.a.l.1.11		21	3.2	odd	2
7381.2.a.j.1.11		21	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.472572 q^{2} -1.64615 q^{3} -1.77668 q^{4} -3.20957 q^{5} -0.777925 q^{6} +4.06194 q^{7} -1.78475 q^{8} -0.290187 q^{9} +O(q^{10})\)	\(q+0.472572 q^{2} -1.64615 q^{3} -1.77668 q^{4} -3.20957 q^{5} -0.777925 q^{6} +4.06194 q^{7} -1.78475 q^{8} -0.290187 q^{9} -1.51675 q^{10} -1.00000 q^{11} +2.92468 q^{12} -6.29425 q^{13} +1.91956 q^{14} +5.28343 q^{15} +2.70993 q^{16} +2.28683 q^{17} -0.137134 q^{18} +4.41630 q^{19} +5.70236 q^{20} -6.68657 q^{21} -0.472572 q^{22} +4.18874 q^{23} +2.93797 q^{24} +5.30131 q^{25} -2.97449 q^{26} +5.41614 q^{27} -7.21675 q^{28} +2.32215 q^{29} +2.49680 q^{30} +4.52296 q^{31} +4.85014 q^{32} +1.64615 q^{33} +1.08069 q^{34} -13.0371 q^{35} +0.515568 q^{36} -8.64218 q^{37} +2.08702 q^{38} +10.3613 q^{39} +5.72828 q^{40} +4.05541 q^{41} -3.15989 q^{42} +11.3037 q^{43} +1.77668 q^{44} +0.931374 q^{45} +1.97948 q^{46} -0.746581 q^{47} -4.46095 q^{48} +9.49937 q^{49} +2.50525 q^{50} -3.76447 q^{51} +11.1828 q^{52} -9.63873 q^{53} +2.55952 q^{54} +3.20957 q^{55} -7.24956 q^{56} -7.26990 q^{57} +1.09738 q^{58} +2.52363 q^{59} -9.38694 q^{60} +1.00000 q^{61} +2.13743 q^{62} -1.17872 q^{63} -3.12782 q^{64} +20.2018 q^{65} +0.777925 q^{66} +10.5600 q^{67} -4.06296 q^{68} -6.89530 q^{69} -6.16095 q^{70} -14.4115 q^{71} +0.517912 q^{72} +5.36468 q^{73} -4.08405 q^{74} -8.72675 q^{75} -7.84634 q^{76} -4.06194 q^{77} +4.89646 q^{78} +10.4811 q^{79} -8.69769 q^{80} -8.04523 q^{81} +1.91647 q^{82} -1.73345 q^{83} +11.8799 q^{84} -7.33974 q^{85} +5.34181 q^{86} -3.82261 q^{87} +1.78475 q^{88} -13.7096 q^{89} +0.440141 q^{90} -25.5669 q^{91} -7.44203 q^{92} -7.44548 q^{93} -0.352813 q^{94} -14.1744 q^{95} -7.98406 q^{96} +0.00104411 q^{97} +4.48914 q^{98} +0.290187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} + 5 q^{6} + 5 q^{7} - 6 q^{8} + 40 q^{9} + q^{10} - 21 q^{11} + 6 q^{12} + 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} + q^{17} - 5 q^{18} + 15 q^{19} - 2 q^{20} + 16 q^{21} + 11 q^{23} - 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} - 16 q^{28} - 9 q^{29} + 16 q^{30} + 22 q^{31} + 3 q^{32} - 3 q^{33} + 33 q^{34} - 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} - 28 q^{39} - 16 q^{40} + 7 q^{41} - 55 q^{42} + 16 q^{43} - 32 q^{44} + 44 q^{45} - 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} - 33 q^{50} - 19 q^{51} + 60 q^{52} + 9 q^{53} + 13 q^{54} - 7 q^{55} + 44 q^{56} + 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} + 21 q^{61} - 23 q^{62} + 24 q^{63} + 66 q^{64} + 25 q^{65} - 5 q^{66} + 38 q^{67} - 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} - 75 q^{72} + 20 q^{73} - 12 q^{74} - 10 q^{75} + 59 q^{76} - 5 q^{77} - 14 q^{78} + q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} - 19 q^{83} - 14 q^{84} + 38 q^{85} - 3 q^{86} + 4 q^{87} + 6 q^{88} + 37 q^{89} - 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} - 64 q^{94} - 43 q^{95} - 38 q^{96} + 68 q^{97} - 2 q^{98} - 40 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 + 5 * q^6 + 5 * q^7 - 6 * q^8 + 40 * q^9 + q^10 - 21 * q^11 + 6 * q^12 + 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 + q^17 - 5 * q^18 + 15 * q^19 - 2 * q^20 + 16 * q^21 + 11 * q^23 - 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 - 16 * q^28 - 9 * q^29 + 16 * q^30 + 22 * q^31 + 3 * q^32 - 3 * q^33 + 33 * q^34 - 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 - 28 * q^39 - 16 * q^40 + 7 * q^41 - 55 * q^42 + 16 * q^43 - 32 * q^44 + 44 * q^45 - 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 - 33 * q^50 - 19 * q^51 + 60 * q^52 + 9 * q^53 + 13 * q^54 - 7 * q^55 + 44 * q^56 + 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 + 21 * q^61 - 23 * q^62 + 24 * q^63 + 66 * q^64 + 25 * q^65 - 5 * q^66 + 38 * q^67 - 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 - 75 * q^72 + 20 * q^73 - 12 * q^74 - 10 * q^75 + 59 * q^76 - 5 * q^77 - 14 * q^78 + q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 - 19 * q^83 - 14 * q^84 + 38 * q^85 - 3 * q^86 + 4 * q^87 + 6 * q^88 + 37 * q^89 - 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 - 64 * q^94 - 43 * q^95 - 38 * q^96 + 68 * q^97 - 2 * q^98 - 40 * q^99

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