LMFDB - Embedded newform 401.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [401,2,Mod(1,401)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(401, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("401.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	401.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:	$3.20200112105$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.84210 q^{2} +0.198794 q^{3} +1.39332 q^{4} -4.07083 q^{5} -0.366198 q^{6} +3.95639 q^{7} +1.11757 q^{8} -2.96048 q^{9} +O(q^{10})$	\(q-1.84210 q^{2} +0.198794 q^{3} +1.39332 q^{4} -4.07083 q^{5} -0.366198 q^{6} +3.95639 q^{7} +1.11757 q^{8} -2.96048 q^{9} +7.49886 q^{10} -3.96010 q^{11} +0.276984 q^{12} +0.680321 q^{13} -7.28805 q^{14} -0.809258 q^{15} -4.84530 q^{16} +3.44122 q^{17} +5.45349 q^{18} +2.72511 q^{19} -5.67196 q^{20} +0.786508 q^{21} +7.29488 q^{22} +5.35353 q^{23} +0.222166 q^{24} +11.5717 q^{25} -1.25322 q^{26} -1.18491 q^{27} +5.51251 q^{28} +1.43913 q^{29} +1.49073 q^{30} -0.796980 q^{31} +6.69038 q^{32} -0.787246 q^{33} -6.33906 q^{34} -16.1058 q^{35} -4.12489 q^{36} +5.72186 q^{37} -5.01991 q^{38} +0.135244 q^{39} -4.54942 q^{40} +12.6571 q^{41} -1.44882 q^{42} +4.82186 q^{43} -5.51768 q^{44} +12.0516 q^{45} -9.86171 q^{46} -4.33648 q^{47} -0.963219 q^{48} +8.65302 q^{49} -21.3161 q^{50} +0.684095 q^{51} +0.947904 q^{52} +3.29057 q^{53} +2.18272 q^{54} +16.1209 q^{55} +4.42152 q^{56} +0.541736 q^{57} -2.65101 q^{58} +8.70175 q^{59} -1.12755 q^{60} -10.6565 q^{61} +1.46811 q^{62} -11.7128 q^{63} -2.63372 q^{64} -2.76947 q^{65} +1.45018 q^{66} -10.3155 q^{67} +4.79472 q^{68} +1.06425 q^{69} +29.6684 q^{70} +13.4640 q^{71} -3.30853 q^{72} +8.56762 q^{73} -10.5402 q^{74} +2.30038 q^{75} +3.79694 q^{76} -15.6677 q^{77} -0.249133 q^{78} -15.9684 q^{79} +19.7244 q^{80} +8.64589 q^{81} -23.3157 q^{82} -6.51924 q^{83} +1.09586 q^{84} -14.0086 q^{85} -8.88233 q^{86} +0.286091 q^{87} -4.42567 q^{88} -5.63795 q^{89} -22.2002 q^{90} +2.69162 q^{91} +7.45917 q^{92} -0.158435 q^{93} +7.98821 q^{94} -11.0934 q^{95} +1.33001 q^{96} -1.98430 q^{97} -15.9397 q^{98} +11.7238 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} + 9 q^{13} - 11 q^{14} + q^{15} + 30 q^{16} - q^{17} - 10 q^{18} + 38 q^{19} + q^{20} + q^{21} - q^{22} + 3 q^{23} + 21 q^{24} + 26 q^{25} - 2 q^{26} + 6 q^{27} + 25 q^{28} - 4 q^{29} - 21 q^{30} + 70 q^{31} - 10 q^{32} - 8 q^{33} + 13 q^{34} + 12 q^{35} + 15 q^{36} + 3 q^{37} - 13 q^{38} + 36 q^{39} - 7 q^{40} - 2 q^{41} - 21 q^{42} + 10 q^{43} - 26 q^{44} - 21 q^{45} - 4 q^{46} + 9 q^{47} - 34 q^{48} + 39 q^{49} - 24 q^{50} - 16 q^{51} - q^{52} - 17 q^{53} + 5 q^{54} + 45 q^{55} - 65 q^{56} - 21 q^{57} - 27 q^{58} + 7 q^{59} - 66 q^{60} + 32 q^{61} - 9 q^{62} + 41 q^{63} + 22 q^{64} - 39 q^{65} - 66 q^{66} + 6 q^{67} - 46 q^{68} - 7 q^{69} - 33 q^{70} + 15 q^{71} - 73 q^{72} + 18 q^{73} - 39 q^{74} - 9 q^{75} + 48 q^{76} - 26 q^{77} - 76 q^{78} + 49 q^{79} - 51 q^{80} - 39 q^{81} - 26 q^{82} - 3 q^{83} - 81 q^{84} - q^{85} - 64 q^{86} + 15 q^{87} - 46 q^{88} - 35 q^{89} - 68 q^{90} + 34 q^{91} - 54 q^{92} - 40 q^{93} - 4 q^{94} - 6 q^{95} - 14 q^{96} - 6 q^{97} - 90 q^{98} - 36 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9 + 7 * q^10 + q^11 - 7 * q^12 + 9 * q^13 - 11 * q^14 + q^15 + 30 * q^16 - q^17 - 10 * q^18 + 38 * q^19 + q^20 + q^21 - q^22 + 3 * q^23 + 21 * q^24 + 26 * q^25 - 2 * q^26 + 6 * q^27 + 25 * q^28 - 4 * q^29 - 21 * q^30 + 70 * q^31 - 10 * q^32 - 8 * q^33 + 13 * q^34 + 12 * q^35 + 15 * q^36 + 3 * q^37 - 13 * q^38 + 36 * q^39 - 7 * q^40 - 2 * q^41 - 21 * q^42 + 10 * q^43 - 26 * q^44 - 21 * q^45 - 4 * q^46 + 9 * q^47 - 34 * q^48 + 39 * q^49 - 24 * q^50 - 16 * q^51 - q^52 - 17 * q^53 + 5 * q^54 + 45 * q^55 - 65 * q^56 - 21 * q^57 - 27 * q^58 + 7 * q^59 - 66 * q^60 + 32 * q^61 - 9 * q^62 + 41 * q^63 + 22 * q^64 - 39 * q^65 - 66 * q^66 + 6 * q^67 - 46 * q^68 - 7 * q^69 - 33 * q^70 + 15 * q^71 - 73 * q^72 + 18 * q^73 - 39 * q^74 - 9 * q^75 + 48 * q^76 - 26 * q^77 - 76 * q^78 + 49 * q^79 - 51 * q^80 - 39 * q^81 - 26 * q^82 - 3 * q^83 - 81 * q^84 - q^85 - 64 * q^86 + 15 * q^87 - 46 * q^88 - 35 * q^89 - 68 * q^90 + 34 * q^91 - 54 * q^92 - 40 * q^93 - 4 * q^94 - 6 * q^95 - 14 * q^96 - 6 * q^97 - 90 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.84210	−1.30256	−0.651279	−	0.758838i	$-0.725767\pi$
$2$	−1.84210	−1.30256	−0.651279	+	0.758838i	$0.725767\pi$
$3$	0.198794	0.114774	0.0573870	−	0.998352i	$-0.481723\pi$
$3$	0.198794	0.114774	0.0573870	+	0.998352i	$0.481723\pi$
$4$	1.39332	0.696659
$5$	−4.07083	−1.82053	−0.910265	−	0.414026i	$-0.864122\pi$
$5$	−4.07083	−1.82053	−0.910265	+	0.414026i	$0.864122\pi$
$6$	−0.366198	−0.149500
$7$	3.95639	1.49537	0.747687	−	0.664051i	$-0.231164\pi$
$7$	3.95639	1.49537	0.747687	+	0.664051i	$0.231164\pi$
$8$	1.11757	0.395119
$9$	−2.96048	−0.986827
$10$	7.49886	2.37135
$11$	−3.96010	−1.19401	−0.597007	−	0.802236i	$-0.703644\pi$
$11$	−3.96010	−1.19401	−0.597007	+	0.802236i	$0.703644\pi$
$12$	0.276984	0.0799584
$13$	0.680321	0.188687	0.0943436	−	0.995540i	$-0.469925\pi$
$13$	0.680321	0.188687	0.0943436	+	0.995540i	$0.469925\pi$
$14$	−7.28805	−1.94781
$15$	−0.809258	−0.208950
$16$	−4.84530	−1.21133
$17$	3.44122	0.834618	0.417309	−	0.908765i	$-0.362973\pi$
$17$	3.44122	0.834618	0.417309	+	0.908765i	$0.362973\pi$
$18$	5.45349	1.28540
$19$	2.72511	0.625183	0.312591	−	0.949888i	$-0.398803\pi$
$19$	2.72511	0.625183	0.312591	+	0.949888i	$0.398803\pi$
$20$	−5.67196	−1.26829
$21$	0.786508	0.171630
$22$	7.29488	1.55527
$23$	5.35353	1.11629	0.558144	−	0.829744i	$-0.311514\pi$
$23$	5.35353	1.11629	0.558144	+	0.829744i	$0.311514\pi$
$24$	0.222166	0.0453494
$25$	11.5717	2.31433
$26$	−1.25322	−0.245776
$27$	−1.18491	−0.228036
$28$	5.51251	1.04177
$29$	1.43913	0.267239	0.133620	−	0.991033i	$-0.457340\pi$
$29$	1.43913	0.267239	0.133620	+	0.991033i	$0.457340\pi$
$30$	1.49073	0.272169
$31$	−0.796980	−0.143142	−0.0715710	−	0.997436i	$-0.522801\pi$
$31$	−0.796980	−0.143142	−0.0715710	+	0.997436i	$0.522801\pi$
$32$	6.69038	1.18270
$33$	−0.787246	−0.137042
$34$	−6.33906	−1.08714
$35$	−16.1058	−2.72237
$36$	−4.12489	−0.687482
$37$	5.72186	0.940667	0.470334	−	0.882489i	$-0.344134\pi$
$37$	5.72186	0.940667	0.470334	+	0.882489i	$0.344134\pi$
$38$	−5.01991	−0.814337
$39$	0.135244	0.0216564
$40$	−4.54942	−0.719326
$41$	12.6571	1.97671	0.988356	−	0.152161i	$-0.0486231\pi$
$41$	12.6571	1.97671	0.988356	+	0.152161i	$0.0486231\pi$
$42$	−1.44882	−0.223558
$43$	4.82186	0.735326	0.367663	−	0.929959i	$-0.380158\pi$
$43$	4.82186	0.735326	0.367663	+	0.929959i	$0.380158\pi$
$44$	−5.51768	−0.831822
$45$	12.0516	1.79655
$46$	−9.86171	−1.45403
$47$	−4.33648	−0.632540	−0.316270	−	0.948669i	$-0.602431\pi$
$47$	−4.33648	−0.632540	−0.316270	+	0.948669i	$0.602431\pi$
$48$	−0.963219	−0.139029
$49$	8.65302	1.23615
$50$	−21.3161	−3.01455
$51$	0.684095	0.0957925
$52$	0.947904	0.131451
$53$	3.29057	0.451994	0.225997	−	0.974128i	$-0.427436\pi$
$53$	3.29057	0.451994	0.225997	+	0.974128i	$0.427436\pi$
$54$	2.18272	0.297030
$55$	16.1209	2.17374
$56$	4.42152	0.590851
$57$	0.541736	0.0717547
$58$	−2.65101	−0.348095
$59$	8.70175	1.13287	0.566436	−	0.824106i	$-0.308322\pi$
$59$	8.70175	1.13287	0.566436	+	0.824106i	$0.308322\pi$
$60$	−1.12755	−0.145567
$61$	−10.6565	−1.36443	−0.682213	−	0.731154i	$-0.738982\pi$
$61$	−10.6565	−1.36443	−0.682213	+	0.731154i	$0.738982\pi$
$62$	1.46811	0.186451
$63$	−11.7128	−1.47568
$64$	−2.63372	−0.329215
$65$	−2.76947	−0.343511
$66$	1.45018	0.178505
$67$	−10.3155	−1.26024	−0.630121	−	0.776497i	$-0.716995\pi$
$67$	−10.3155	−1.26024	−0.630121	+	0.776497i	$0.716995\pi$
$68$	4.79472	0.581445
$69$	1.06425	0.128121
$70$	29.6684	3.54605
$71$	13.4640	1.59789	0.798944	−	0.601405i	$-0.205392\pi$
$71$	13.4640	1.59789	0.798944	+	0.601405i	$0.205392\pi$
$72$	−3.30853	−0.389914
$73$	8.56762	1.00276	0.501382	−	0.865226i	$-0.332825\pi$
$73$	8.56762	1.00276	0.501382	+	0.865226i	$0.332825\pi$
$74$	−10.5402	−1.22527
$75$	2.30038	0.265625
$76$	3.79694	0.435539
$77$	−15.6677	−1.78550
$78$	−0.249133	−0.0282087
$79$	−15.9684	−1.79658	−0.898291	−	0.439401i	$-0.855191\pi$
$79$	−15.9684	−1.79658	−0.898291	+	0.439401i	$0.855191\pi$
$80$	19.7244	2.20525
$81$	8.64589	0.960654
$82$	−23.3157	−2.57478
$83$	−6.51924	−0.715579	−0.357790	−	0.933802i	$-0.616469\pi$
$83$	−6.51924	−0.715579	−0.357790	+	0.933802i	$0.616469\pi$
$84$	1.09586	0.119568
$85$	−14.0086	−1.51945
$86$	−8.88233	−0.957806
$87$	0.286091	0.0306721
$88$	−4.42567	−0.471778
$89$	−5.63795	−0.597622	−0.298811	−	0.954312i	$-0.596590\pi$
$89$	−5.63795	−0.597622	−0.298811	+	0.954312i	$0.596590\pi$
$90$	−22.2002	−2.34011
$91$	2.69162	0.282158
$92$	7.45917	0.777672
$93$	−0.158435	−0.0164290
$94$	7.98821	0.823921
$95$	−11.0934	−1.13816
$96$	1.33001	0.135744
$97$	−1.98430	−0.201475	−0.100737	−	0.994913i	$-0.532120\pi$
$97$	−1.98430	−0.201475	−0.100737	+	0.994913i	$0.532120\pi$
$98$	−15.9397	−1.61015
$99$	11.7238	1.17829
$100$	16.1230	1.61230
$101$	−0.0419970	−0.00417886	−0.00208943	−	0.999998i	$-0.500665\pi$
$101$	−0.0419970	−0.00417886	−0.00208943	+	0.999998i	$0.500665\pi$
$102$	−1.26017	−0.124775
$103$	9.40858	0.927055	0.463527	−	0.886083i	$-0.346584\pi$
$103$	9.40858	0.927055	0.463527	+	0.886083i	$0.346584\pi$
$104$	0.760304	0.0745539
$105$	−3.20174	−0.312458
$106$	−6.06154	−0.588749
$107$	10.1537	0.981591	0.490795	−	0.871275i	$-0.336706\pi$
$107$	10.1537	0.981591	0.490795	+	0.871275i	$0.336706\pi$
$108$	−1.65096	−0.158863
$109$	3.75993	0.360136	0.180068	−	0.983654i	$-0.442368\pi$
$109$	3.75993	0.360136	0.180068	+	0.983654i	$0.442368\pi$
$110$	−29.6962	−2.83142
$111$	1.13747	0.107964
$112$	−19.1699	−1.81138
$113$	−16.7872	−1.57921	−0.789605	−	0.613615i	$-0.789715\pi$
$113$	−16.7872	−1.57921	−0.789605	+	0.613615i	$0.789715\pi$
$114$	−0.997930	−0.0934647
$115$	−21.7933	−2.03224
$116$	2.00516	0.186175
$117$	−2.01408	−0.186202
$118$	−16.0295	−1.47563
$119$	13.6148	1.24807
$120$	−0.904399	−0.0825600
$121$	4.68239	0.425672
$122$	19.6303	1.77724
$123$	2.51617	0.226875
$124$	−1.11045	−0.0997212
$125$	−26.7521	−2.39278
$126$	21.5761	1.92215
$127$	−3.60172	−0.319601	−0.159800	−	0.987149i	$-0.551085\pi$
$127$	−3.60172	−0.319601	−0.159800	+	0.987149i	$0.551085\pi$
$128$	−8.52919	−0.753881
$129$	0.958558	0.0843963
$130$	5.10163	0.447443
$131$	1.46323	0.127843	0.0639214	−	0.997955i	$-0.479639\pi$
$131$	1.46323	0.127843	0.0639214	+	0.997955i	$0.479639\pi$
$132$	−1.09688	−0.0954715
$133$	10.7816	0.934882
$134$	19.0022	1.64154
$135$	4.82357	0.415147
$136$	3.84579	0.329774
$137$	2.85646	0.244044	0.122022	−	0.992527i	$-0.461062\pi$
$137$	2.85646	0.244044	0.122022	+	0.992527i	$0.461062\pi$
$138$	−1.96045	−0.166885
$139$	−18.8542	−1.59919	−0.799597	−	0.600537i	$-0.794953\pi$
$139$	−18.8542	−1.59919	−0.799597	+	0.600537i	$0.794953\pi$
$140$	−22.4405	−1.89657
$141$	−0.862067	−0.0725992
$142$	−24.8021	−2.08134
$143$	−2.69414	−0.225295
$144$	14.3444	1.19537
$145$	−5.85845	−0.486517
$146$	−15.7824	−1.30616
$147$	1.72017	0.141877
$148$	7.97237	0.655325
$149$	5.84790	0.479078	0.239539	−	0.970887i	$-0.423004\pi$
$149$	5.84790	0.479078	0.239539	+	0.970887i	$0.423004\pi$
$150$	−4.23752	−0.345992
$151$	11.1884	0.910499	0.455250	−	0.890364i	$-0.349550\pi$
$151$	11.1884	0.910499	0.455250	+	0.890364i	$0.349550\pi$
$152$	3.04549	0.247022
$153$	−10.1877	−0.823624
$154$	28.8614	2.32572
$155$	3.24437	0.260594
$156$	0.188438	0.0150871
$157$	18.5037	1.47675	0.738376	−	0.674389i	$-0.235593\pi$
$157$	18.5037	1.47675	0.738376	+	0.674389i	$0.235593\pi$
$158$	29.4153	2.34015
$159$	0.654146	0.0518772
$160$	−27.2354	−2.15315
$161$	21.1806	1.66927
$162$	−15.9266	−1.25131
$163$	15.6931	1.22918	0.614588	−	0.788848i	$-0.289322\pi$
$163$	15.6931	1.22918	0.614588	+	0.788848i	$0.289322\pi$
$164$	17.6354	1.37709
$165$	3.20474	0.249489
$166$	12.0091	0.932084
$167$	0.113251	0.00876365	0.00438183	−	0.999990i	$-0.498605\pi$
$167$	0.113251	0.00876365	0.00438183	+	0.999990i	$0.498605\pi$
$168$	0.878974	0.0678143
$169$	−12.5372	−0.964397
$170$	25.8052	1.97917
$171$	−8.06763	−0.616947
$172$	6.71838	0.512272
$173$	2.52649	0.192085	0.0960427	−	0.995377i	$-0.469381\pi$
$173$	2.52649	0.192085	0.0960427	+	0.995377i	$0.469381\pi$
$174$	−0.527006	−0.0399523
$175$	45.7820	3.46079
$176$	19.1879	1.44634
$177$	1.72986	0.130024
$178$	10.3857	0.778438
$179$	−6.61205	−0.494208	−0.247104	−	0.968989i	$-0.579479\pi$
$179$	−6.61205	−0.494208	−0.247104	+	0.968989i	$0.579479\pi$
$180$	16.7917	1.25158
$181$	22.9239	1.70392	0.851958	−	0.523610i	$-0.175415\pi$
$181$	22.9239	1.70392	0.851958	+	0.523610i	$0.175415\pi$
$182$	−4.95822	−0.367527
$183$	−2.11845	−0.156601
$184$	5.98292	0.441066
$185$	−23.2927	−1.71251
$186$	0.291853	0.0213997
$187$	−13.6276	−0.996547
$188$	−6.04209	−0.440665
$189$	−4.68797	−0.340999
$190$	20.4352	1.48253
$191$	16.2598	1.17652	0.588261	−	0.808671i	$-0.299813\pi$
$191$	16.2598	1.17652	0.588261	+	0.808671i	$0.299813\pi$
$192$	−0.523569	−0.0377853
$193$	25.1490	1.81026	0.905131	−	0.425133i	$-0.139773\pi$
$193$	25.1490	1.81026	0.905131	+	0.425133i	$0.139773\pi$
$194$	3.65526	0.262433
$195$	−0.550556	−0.0394261
$196$	12.0564	0.861172
$197$	−16.2134	−1.15516	−0.577578	−	0.816336i	$-0.696002\pi$
$197$	−16.2134	−1.15516	−0.577578	+	0.816336i	$0.696002\pi$
$198$	−21.5964	−1.53479
$199$	8.07868	0.572683	0.286341	−	0.958128i	$-0.407561\pi$
$199$	8.07868	0.572683	0.286341	+	0.958128i	$0.407561\pi$
$200$	12.9321	0.914436
$201$	−2.05067	−0.144643
$202$	0.0773625	0.00544321
$203$	5.69375	0.399623
$204$	0.953162	0.0667347
$205$	−51.5250	−3.59866
$206$	−17.3315	−1.20754
$207$	−15.8490	−1.10158
$208$	−3.29636	−0.228562
$209$	−10.7917	−0.746477
$210$	5.89791	0.406995
$211$	15.7224	1.08237	0.541187	−	0.840903i	$-0.317975\pi$
$211$	15.7224	1.08237	0.541187	+	0.840903i	$0.317975\pi$
$212$	4.58481	0.314886
$213$	2.67658	0.183396
$214$	−18.7040	−1.27858
$215$	−19.6290	−1.33868
$216$	−1.32421	−0.0901014
$217$	−3.15317	−0.214051
$218$	−6.92615	−0.469098
$219$	1.70320	0.115091
$220$	22.4615	1.51436
$221$	2.34113	0.157482
$222$	−2.09533	−0.140630
$223$	18.8968	1.26543	0.632713	−	0.774387i	$-0.281941\pi$
$223$	18.8968	1.26543	0.632713	+	0.774387i	$0.281941\pi$
$224$	26.4697	1.76858
$225$	−34.2577	−2.28384
$226$	30.9237	2.05701
$227$	−7.02355	−0.466169	−0.233085	−	0.972456i	$-0.574882\pi$
$227$	−7.02355	−0.466169	−0.233085	+	0.972456i	$0.574882\pi$
$228$	0.754811	0.0499886
$229$	−25.6379	−1.69420	−0.847099	−	0.531436i	$-0.821653\pi$
$229$	−25.6379	−1.69420	−0.847099	+	0.531436i	$0.821653\pi$
$230$	40.1453	2.64711
$231$	−3.11465	−0.204929
$232$	1.60832	0.105591
$233$	−9.40938	−0.616429	−0.308214	−	0.951317i	$-0.599731\pi$
$233$	−9.40938	−0.616429	−0.308214	+	0.951317i	$0.599731\pi$
$234$	3.71013	0.242539
$235$	17.6531	1.15156
$236$	12.1243	0.789226
$237$	−3.17442	−0.206201
$238$	−25.0798	−1.62568
$239$	2.66097	0.172124	0.0860620	−	0.996290i	$-0.472572\pi$
$239$	2.66097	0.172124	0.0860620	+	0.996290i	$0.472572\pi$
$240$	3.92110	0.253106
$241$	−20.4445	−1.31694	−0.658472	−	0.752605i	$-0.728797\pi$
$241$	−20.4445	−1.31694	−0.658472	+	0.752605i	$0.728797\pi$
$242$	−8.62541	−0.554462
$243$	5.27348	0.338294
$244$	−14.8479	−0.950540
$245$	−35.2250	−2.25044
$246$	−4.63502	−0.295518
$247$	1.85395	0.117964
$248$	−0.890678	−0.0565581
$249$	−1.29599	−0.0821299
$250$	49.2799	3.11674
$251$	−2.00039	−0.126264	−0.0631318	−	0.998005i	$-0.520109\pi$
$251$	−2.00039	−0.126264	−0.0631318	+	0.998005i	$0.520109\pi$
$252$	−16.3197	−1.02804
$253$	−21.2005	−1.33286
$254$	6.63471	0.416299
$255$	−2.78483	−0.174393
$256$	20.9790	1.31119
$257$	5.03182	0.313876	0.156938	−	0.987608i	$-0.449838\pi$
$257$	5.03182	0.313876	0.156938	+	0.987608i	$0.449838\pi$
$258$	−1.76576	−0.109931
$259$	22.6379	1.40665
$260$	−3.85876	−0.239310
$261$	−4.26051	−0.263719
$262$	−2.69541	−0.166523
$263$	−8.22432	−0.507133	−0.253567	−	0.967318i	$-0.581604\pi$
$263$	−8.22432	−0.507133	−0.253567	+	0.967318i	$0.581604\pi$
$264$	−0.879799	−0.0541479
$265$	−13.3953	−0.822869
$266$	−19.8607	−1.21774
$267$	−1.12079	−0.0685914
$268$	−14.3728	−0.877959
$269$	−0.0388419	−0.00236823	−0.00118412	−	0.999999i	$-0.500377\pi$
$269$	−0.0388419	−0.00236823	−0.00118412	+	0.999999i	$0.500377\pi$
$270$	−8.88548	−0.540753
$271$	16.8977	1.02646	0.513230	−	0.858251i	$-0.328449\pi$
$271$	16.8977	1.02646	0.513230	+	0.858251i	$0.328449\pi$
$272$	−16.6737	−1.01099
$273$	0.535078	0.0323844
$274$	−5.26187	−0.317881
$275$	−45.8249	−2.76335
$276$	1.48284	0.0892565
$277$	−14.1836	−0.852209	−0.426104	−	0.904674i	$-0.640114\pi$
$277$	−14.1836	−0.852209	−0.426104	+	0.904674i	$0.640114\pi$
$278$	34.7313	2.08304
$279$	2.35945	0.141256
$280$	−17.9993	−1.07566
$281$	22.9612	1.36975	0.684875	−	0.728661i	$-0.259857\pi$
$281$	22.9612	1.36975	0.684875	+	0.728661i	$0.259857\pi$
$282$	1.58801	0.0945647
$283$	19.9509	1.18596	0.592979	−	0.805218i	$-0.297952\pi$
$283$	19.9509	1.18596	0.592979	+	0.805218i	$0.297952\pi$
$284$	18.7597	1.11318
$285$	−2.20532	−0.130632
$286$	4.96287	0.293460
$287$	50.0765	2.95592
$288$	−19.8067	−1.16712
$289$	−5.15801	−0.303412
$290$	10.7918	0.633718
$291$	−0.394467	−0.0231241
$292$	11.9374	0.698585
$293$	14.9143	0.871301	0.435651	−	0.900116i	$-0.356518\pi$
$293$	14.9143	0.871301	0.435651	+	0.900116i	$0.356518\pi$
$294$	−3.16872	−0.184804
$295$	−35.4234	−2.06243
$296$	6.39455	0.371676
$297$	4.69236	0.272278
$298$	−10.7724	−0.624028
$299$	3.64212	0.210629
$300$	3.20516	0.185050
$301$	19.0771	1.09959
$302$	−20.6101	−1.18598
$303$	−0.00834877	−0.000479624 0
$304$	−13.2040	−0.757299
$305$	43.3808	2.48398
$306$	18.7667	1.07282
$307$	12.6229	0.720429	0.360214	−	0.932870i	$-0.382704\pi$
$307$	12.6229	0.720429	0.360214	+	0.932870i	$0.382704\pi$
$308$	−21.8301	−1.24388
$309$	1.87037	0.106402
$310$	−5.97645	−0.339439
$311$	20.3973	1.15662	0.578311	−	0.815816i	$-0.303712\pi$
$311$	20.3973	1.15662	0.578311	+	0.815816i	$0.303712\pi$
$312$	0.151144	0.00855685
$313$	−30.0516	−1.69862	−0.849308	−	0.527898i	$-0.822980\pi$
$313$	−30.0516	−1.69862	−0.849308	+	0.527898i	$0.822980\pi$
$314$	−34.0855	−1.92356
$315$	47.6809	2.68651
$316$	−22.2490	−1.25161
$317$	13.2139	0.742167	0.371084	−	0.928599i	$-0.378986\pi$
$317$	13.2139	0.742167	0.371084	+	0.928599i	$0.378986\pi$
$318$	−1.20500	−0.0675731
$319$	−5.69909	−0.319088
$320$	10.7214	0.599346
$321$	2.01849	0.112661
$322$	−39.0168	−2.17432
$323$	9.37769	0.521789
$324$	12.0465	0.669249
$325$	7.87244	0.436685
$326$	−28.9081	−1.60107
$327$	0.747452	0.0413342
$328$	14.1452	0.781036
$329$	−17.1568	−0.945884
$330$	−5.90344	−0.324974
$331$	−11.2953	−0.620848	−0.310424	−	0.950598i	$-0.600471\pi$
$331$	−11.2953	−0.620848	−0.310424	+	0.950598i	$0.600471\pi$
$332$	−9.08337	−0.498515
$333$	−16.9394	−0.928276
$334$	−0.208620	−0.0114152
$335$	41.9928	2.29431
$336$	−3.81087	−0.207900
$337$	−8.97755	−0.489038	−0.244519	−	0.969644i	$-0.578630\pi$
$337$	−8.97755	−0.489038	−0.244519	+	0.969644i	$0.578630\pi$
$338$	23.0947	1.25618
$339$	−3.33721	−0.181252
$340$	−19.5185	−1.05854
$341$	3.15612	0.170914
$342$	14.8613	0.803610
$343$	6.53998	0.353126
$344$	5.38874	0.290541
$345$	−4.33238	−0.233248
$346$	−4.65403	−0.250202
$347$	−33.2713	−1.78610	−0.893050	−	0.449958i	$-0.851439\pi$
$347$	−33.2713	−1.78610	−0.893050	+	0.449958i	$0.851439\pi$
$348$	0.398615	0.0213680
$349$	32.6815	1.74940	0.874699	−	0.484666i	$-0.161059\pi$
$349$	32.6815	1.74940	0.874699	+	0.484666i	$0.161059\pi$
$350$	−84.3348	−4.50788
$351$	−0.806120	−0.0430275
$352$	−26.4946	−1.41217
$353$	31.8064	1.69288	0.846442	−	0.532480i	$-0.178740\pi$
$353$	31.8064	1.69288	0.846442	+	0.532480i	$0.178740\pi$
$354$	−3.18657	−0.169364
$355$	−54.8098	−2.90900
$356$	−7.85547	−0.416339
$357$	2.70655	0.143246
$358$	12.1800	0.643734
$359$	−25.1732	−1.32859	−0.664296	−	0.747469i	$-0.731269\pi$
$359$	−25.1732	−1.32859	−0.664296	+	0.747469i	$0.731269\pi$
$360$	13.4685	0.709851
$361$	−11.5738	−0.609147
$362$	−42.2279	−2.21945
$363$	0.930833	0.0488560
$364$	3.75028	0.196568
$365$	−34.8773	−1.82556
$366$	3.90240	0.203981
$367$	−20.4637	−1.06820	−0.534098	−	0.845422i	$-0.679349\pi$
$367$	−20.4637	−1.06820	−0.534098	+	0.845422i	$0.679349\pi$
$368$	−25.9394	−1.35219
$369$	−37.4712	−1.95067
$370$	42.9074	2.23065
$371$	13.0188	0.675900
$372$	−0.220751	−0.0114454
$373$	13.2641	0.686791	0.343396	−	0.939191i	$-0.388423\pi$
$373$	13.2641	0.686791	0.343396	+	0.939191i	$0.388423\pi$
$374$	25.1033	1.29806
$375$	−5.31816	−0.274629
$376$	−4.84630	−0.249929
$377$	0.979070	0.0504247
$378$	8.63568	0.444172
$379$	−2.04743	−0.105169	−0.0525846	−	0.998616i	$-0.516746\pi$
$379$	−2.04743	−0.105169	−0.0525846	+	0.998616i	$0.516746\pi$
$380$	−15.4567	−0.792912
$381$	−0.716002	−0.0366819
$382$	−29.9522	−1.53249
$383$	12.4712	0.637249	0.318625	−	0.947881i	$-0.396779\pi$
$383$	12.4712	0.637249	0.318625	+	0.947881i	$0.396779\pi$
$384$	−1.69556	−0.0865259
$385$	63.7805	3.25056
$386$	−46.3268	−2.35797
$387$	−14.2750	−0.725640
$388$	−2.76476	−0.140359
$389$	−16.4099	−0.832016	−0.416008	−	0.909361i	$-0.636571\pi$
$389$	−16.4099	−0.832016	−0.416008	+	0.909361i	$0.636571\pi$
$390$	1.01418	0.0513548
$391$	18.4227	0.931674
$392$	9.67031	0.488425
$393$	0.290882	0.0146730
$394$	29.8666	1.50466
$395$	65.0045	3.27073
$396$	16.3350	0.820864
$397$	−9.40318	−0.471932	−0.235966	−	0.971761i	$-0.575825\pi$
$397$	−9.40318	−0.471932	−0.235966	+	0.971761i	$0.575825\pi$
$398$	−14.8817	−0.745953
$399$	2.14332	0.107300
$400$	−56.0681	−2.80341
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	3.77753	0.188406
$403$	−0.542203	−0.0270090
$404$	−0.0585152	−0.00291124
$405$	−35.1959	−1.74890
$406$	−10.4884	−0.520532
$407$	−22.6591	−1.12317
$408$	0.764521	0.0378494
$409$	−36.7287	−1.81612	−0.908058	−	0.418845i	$-0.862435\pi$
$409$	−36.7287	−1.81612	−0.908058	+	0.418845i	$0.862435\pi$
$410$	94.9140	4.68747
$411$	0.567847	0.0280098
$412$	13.1091	0.645841
$413$	34.4275	1.69407
$414$	29.1954	1.43488
$415$	26.5387	1.30273
$416$	4.55161	0.223161
$417$	−3.74811	−0.183546
$418$	19.8793	0.972331
$419$	−8.38110	−0.409444	−0.204722	−	0.978820i	$-0.565629\pi$
$419$	−8.38110	−0.409444	−0.204722	+	0.978820i	$0.565629\pi$
$420$	−4.46104	−0.217677
$421$	15.9025	0.775041	0.387521	−	0.921861i	$-0.373332\pi$
$421$	15.9025	0.775041	0.387521	+	0.921861i	$0.373332\pi$
$422$	−28.9621	−1.40985
$423$	12.8381	0.624208
$424$	3.67742	0.178591
$425$	39.8206	1.93158
$426$	−4.93051	−0.238884
$427$	−42.1613	−2.04033
$428$	14.1473	0.683834
$429$	−0.535580	−0.0258580
$430$	36.1584	1.74371
$431$	−23.9555	−1.15390	−0.576949	−	0.816780i	$-0.695757\pi$
$431$	−23.9555	−1.15390	−0.576949	+	0.816780i	$0.695757\pi$
$432$	5.74125	0.276226
$433$	−23.8117	−1.14432	−0.572158	−	0.820144i	$-0.693894\pi$
$433$	−23.8117	−1.14432	−0.572158	+	0.820144i	$0.693894\pi$
$434$	5.80843	0.278814
$435$	−1.16463	−0.0558396
$436$	5.23878	0.250892
$437$	14.5889	0.697883
$438$	−3.13745	−0.149913
$439$	38.6728	1.84575	0.922877	−	0.385095i	$-0.125831\pi$
$439$	38.6728	1.84575	0.922877	+	0.385095i	$0.125831\pi$
$440$	18.0162	0.858886
$441$	−25.6171	−1.21986
$442$	−4.31260	−0.205129
$443$	−18.7558	−0.891114	−0.445557	−	0.895254i	$-0.646994\pi$
$443$	−18.7558	−0.891114	−0.445557	+	0.895254i	$0.646994\pi$
$444$	1.58486	0.0752142
$445$	22.9511	1.08799
$446$	−34.8098	−1.64829
$447$	1.16253	0.0549857
$448$	−10.4200	−0.492300
$449$	0.278669	0.0131512	0.00657560	−	0.999978i	$-0.497907\pi$
$449$	0.278669	0.0131512	0.00657560	+	0.999978i	$0.497907\pi$
$450$	63.1059	2.97484
$451$	−50.1235	−2.36022
$452$	−23.3900	−1.10017
$453$	2.22419	0.104502
$454$	12.9380	0.607213
$455$	−10.9571	−0.513677
$456$	0.605426	0.0283516
$457$	1.13698	0.0531858	0.0265929	−	0.999646i	$-0.491534\pi$
$457$	1.13698	0.0531858	0.0265929	+	0.999646i	$0.491534\pi$
$458$	47.2274	2.20679
$459$	−4.07754	−0.190323
$460$	−30.3650	−1.41578
$461$	−1.20395	−0.0560734	−0.0280367	−	0.999607i	$-0.508926\pi$
$461$	−1.20395	−0.0560734	−0.0280367	+	0.999607i	$0.508926\pi$
$462$	5.73749	0.266932
$463$	−13.6266	−0.633283	−0.316642	−	0.948545i	$-0.602555\pi$
$463$	−13.6266	−0.633283	−0.316642	+	0.948545i	$0.602555\pi$
$464$	−6.97301	−0.323714
$465$	0.644963	0.0299094
$466$	17.3330	0.802935
$467$	−4.68285	−0.216696	−0.108348	−	0.994113i	$-0.534556\pi$
$467$	−4.68285	−0.216696	−0.108348	+	0.994113i	$0.534556\pi$
$468$	−2.80625	−0.129719
$469$	−40.8122	−1.88453
$470$	−32.5186	−1.49997
$471$	3.67842	0.169493
$472$	9.72478	0.447619
$473$	−19.0950	−0.877991
$474$	5.84759	0.268589
$475$	31.5340	1.44688
$476$	18.9698	0.869478
$477$	−9.74166	−0.446040
$478$	−4.90177	−0.224202
$479$	31.9417	1.45945	0.729727	−	0.683738i	$-0.239647\pi$
$479$	31.9417	1.45945	0.729727	+	0.683738i	$0.239647\pi$
$480$	−5.41424	−0.247125
$481$	3.89270	0.177492
$482$	37.6607	1.71540
$483$	4.21059	0.191589
$484$	6.52406	0.296548
$485$	8.07773	0.366791
$486$	−9.71427	−0.440648
$487$	19.1501	0.867774	0.433887	−	0.900967i	$-0.357142\pi$
$487$	19.1501	0.867774	0.433887	+	0.900967i	$0.357142\pi$
$488$	−11.9093	−0.539111
$489$	3.11969	0.141077
$490$	64.8878	2.93133
$491$	−38.2497	−1.72619	−0.863093	−	0.505045i	$-0.831476\pi$
$491$	−38.2497	−1.72619	−0.863093	+	0.505045i	$0.831476\pi$
$492$	3.50582	0.158055
$493$	4.95236	0.223043
$494$	−3.41515	−0.153655
$495$	−47.7256	−2.14511
$496$	3.86161	0.173391
$497$	53.2690	2.38944
$498$	2.38733	0.106979
$499$	4.98355	0.223094	0.111547	−	0.993759i	$-0.464419\pi$
$499$	4.98355	0.223094	0.111547	+	0.993759i	$0.464419\pi$
$500$	−37.2742	−1.66695
$501$	0.0225137	0.00100584
$502$	3.68491	0.164466
$503$	7.29755	0.325382	0.162691	−	0.986677i	$-0.447983\pi$
$503$	7.29755	0.325382	0.162691	+	0.986677i	$0.447983\pi$
$504$	−13.0898	−0.583068
$505$	0.170963	0.00760774
$506$	39.0534	1.73613
$507$	−2.49232	−0.110688
$508$	−5.01834	−0.222653
$509$	−34.5320	−1.53060	−0.765301	−	0.643672i	$-0.777410\pi$
$509$	−34.5320	−1.53060	−0.765301	+	0.643672i	$0.777410\pi$
$510$	5.12993	0.227157
$511$	33.8969	1.49951
$512$	−21.5870	−0.954020
$513$	−3.22901	−0.142564
$514$	−9.26910	−0.408842
$515$	−38.3007	−1.68773
$516$	1.33558	0.0587955
$517$	17.1729	0.755262
$518$	−41.7012	−1.83224
$519$	0.502252	0.0220464
$520$	−3.09507	−0.135728
$521$	0.466475	0.0204367	0.0102183	−	0.999948i	$-0.496747\pi$
$521$	0.466475	0.0204367	0.0102183	+	0.999948i	$0.496747\pi$
$522$	7.84827	0.343510
$523$	15.1258	0.661406	0.330703	−	0.943735i	$-0.392714\pi$
$523$	15.1258	0.661406	0.330703	+	0.943735i	$0.392714\pi$
$524$	2.03874	0.0890629
$525$	9.10120	0.397209
$526$	15.1500	0.660571
$527$	−2.74258	−0.119469
$528$	3.81444	0.166002
$529$	5.66024	0.246098
$530$	24.6755	1.07184
$531$	−25.7614	−1.11795
$532$	15.0222	0.651294
$533$	8.61092	0.372980
$534$	2.06461	0.0893444
$535$	−41.3338	−1.78702
$536$	−11.5283	−0.497946
$537$	−1.31444	−0.0567222
$538$	0.0715505	0.00308476
$539$	−34.2668	−1.47598
$540$	6.72077	0.289216
$541$	37.4508	1.61013	0.805067	−	0.593184i	$-0.202129\pi$
$541$	37.4508	1.61013	0.805067	+	0.593184i	$0.202129\pi$
$542$	−31.1271	−1.33703
$543$	4.55713	0.195565
$544$	23.0231	0.987106
$545$	−15.3060	−0.655638
$546$	−0.985665	−0.0421826
$547$	−22.5690	−0.964980	−0.482490	−	0.875901i	$-0.660268\pi$
$547$	−22.5690	−0.964980	−0.482490	+	0.875901i	$0.660268\pi$
$548$	3.97995	0.170015
$549$	31.5484	1.34645
$550$	84.4139	3.59942
$551$	3.92178	0.167073
$552$	1.18937	0.0506230
$553$	−63.1771	−2.68656
$554$	26.1275	1.11005
$555$	−4.63046	−0.196552
$556$	−26.2699	−1.11409
$557$	9.39377	0.398027	0.199013	−	0.979997i	$-0.436226\pi$
$557$	9.39377	0.398027	0.199013	+	0.979997i	$0.436226\pi$
$558$	−4.34633	−0.183995
$559$	3.28041	0.138747
$560$	78.0374	3.29768
$561$	−2.70908	−0.114378
$562$	−42.2967	−1.78418
$563$	2.35606	0.0992961	0.0496480	−	0.998767i	$-0.484190\pi$
$563$	2.35606	0.0992961	0.0496480	+	0.998767i	$0.484190\pi$
$564$	−1.20113	−0.0505769
$565$	68.3380	2.87500
$566$	−36.7515	−1.54478
$567$	34.2065	1.43654
$568$	15.0470	0.631356
$569$	21.9749	0.921236	0.460618	−	0.887599i	$-0.347628\pi$
$569$	21.9749	0.921236	0.460618	+	0.887599i	$0.347628\pi$
$570$	4.06240	0.170155
$571$	−41.6258	−1.74199	−0.870993	−	0.491296i	$-0.836523\pi$
$571$	−41.6258	−1.74199	−0.870993	+	0.491296i	$0.836523\pi$
$572$	−3.75380	−0.156954
$573$	3.23237	0.135034
$574$	−92.2458	−3.85027
$575$	61.9492	2.58346
$576$	7.79708	0.324878
$577$	−13.7981	−0.574421	−0.287211	−	0.957867i	$-0.592728\pi$
$577$	−13.7981	−0.574421	−0.287211	+	0.957867i	$0.592728\pi$
$578$	9.50155	0.395212
$579$	4.99947	0.207771
$580$	−8.16268	−0.338937
$581$	−25.7926	−1.07006
$582$	0.726646	0.0301204
$583$	−13.0310	−0.539688
$584$	9.57488	0.396211
$585$	8.19897	0.338986
$586$	−27.4735	−1.13492
$587$	17.9259	0.739881	0.369940	−	0.929055i	$-0.379378\pi$
$587$	17.9259	0.739881	0.369940	+	0.929055i	$0.379378\pi$
$588$	2.39675	0.0988402
$589$	−2.17186	−0.0894898
$590$	65.2532	2.68643
$591$	−3.22313	−0.132582
$592$	−27.7241	−1.13945
$593$	28.1377	1.15548	0.577739	−	0.816222i	$-0.303935\pi$
$593$	28.1377	1.15548	0.577739	+	0.816222i	$0.303935\pi$
$594$	−8.64378	−0.354659
$595$	−55.4235	−2.27214
$596$	8.14798	0.333754
$597$	1.60600	0.0657291
$598$	−6.70913	−0.274357
$599$	44.2924	1.80974	0.904870	−	0.425688i	$-0.139968\pi$
$599$	44.2924	1.80974	0.904870	+	0.425688i	$0.139968\pi$
$600$	2.57083	0.104954
$601$	10.4912	0.427946	0.213973	−	0.976840i	$-0.431360\pi$
$601$	10.4912	0.427946	0.213973	+	0.976840i	$0.431360\pi$
$602$	−35.1419	−1.43228
$603$	30.5389	1.24364
$604$	15.5890	0.634308
$605$	−19.0612	−0.774948
$606$	0.0153792	0.000624739 0
$607$	−25.6555	−1.04132	−0.520662	−	0.853763i	$-0.674315\pi$
$607$	−25.6555	−1.04132	−0.520662	+	0.853763i	$0.674315\pi$
$608$	18.2320	0.739405
$609$	1.13189	0.0458663
$610$	−79.9117	−3.23553
$611$	−2.95020	−0.119352
$612$	−14.1947	−0.573785
$613$	−42.6336	−1.72195	−0.860977	−	0.508644i	$-0.830147\pi$
$613$	−42.6336	−1.72195	−0.860977	+	0.508644i	$0.830147\pi$
$614$	−23.2527	−0.938401
$615$	−10.2429	−0.413033
$616$	−17.5097	−0.705485
$617$	0.322948	0.0130014	0.00650071	−	0.999979i	$-0.497931\pi$
$617$	0.322948	0.0130014	0.00650071	+	0.999979i	$0.497931\pi$
$618$	−3.44541	−0.138595
$619$	1.61498	0.0649116	0.0324558	−	0.999473i	$-0.489667\pi$
$619$	1.61498	0.0649116	0.0324558	+	0.999473i	$0.489667\pi$
$620$	4.52044	0.181545
$621$	−6.34345	−0.254554
$622$	−37.5737	−1.50657
$623$	−22.3059	−0.893669
$624$	−0.655298	−0.0262329
$625$	51.0449	2.04180
$626$	55.3579	2.21255
$627$	−2.14533	−0.0856762
$628$	25.7815	1.02879
$629$	19.6902	0.785098
$630$	−87.8328	−3.49934
$631$	29.0198	1.15526	0.577630	−	0.816299i	$-0.303978\pi$
$631$	29.0198	1.15526	0.577630	+	0.816299i	$0.303978\pi$
$632$	−17.8457	−0.709864
$633$	3.12552	0.124228
$634$	−24.3413	−0.966716
$635$	14.6620	0.581843
$636$	0.911434	0.0361407
$637$	5.88683	0.233245
$638$	10.4983	0.415631
$639$	−39.8600	−1.57684
$640$	34.7209	1.37246
$641$	6.70707	0.264913	0.132457	−	0.991189i	$-0.457713\pi$
$641$	6.70707	0.264913	0.132457	+	0.991189i	$0.457713\pi$
$642$	−3.71825	−0.146748
$643$	20.1639	0.795186	0.397593	−	0.917562i	$-0.369846\pi$
$643$	20.1639	0.795186	0.397593	+	0.917562i	$0.369846\pi$
$644$	29.5114	1.16291
$645$	−3.90213	−0.153646
$646$	−17.2746	−0.679661
$647$	−16.7001	−0.656550	−0.328275	−	0.944582i	$-0.606467\pi$
$647$	−16.7001	−0.656550	−0.328275	+	0.944582i	$0.606467\pi$
$648$	9.66235	0.379573
$649$	−34.4598	−1.35267
$650$	−14.5018	−0.568807
$651$	−0.626832	−0.0245675
$652$	21.8654	0.856317
$653$	25.6077	1.00211	0.501053	−	0.865416i	$-0.332946\pi$
$653$	25.6077	1.00211	0.501053	+	0.865416i	$0.332946\pi$
$654$	−1.37688	−0.0538402
$655$	−5.95655	−0.232742
$656$	−61.3276	−2.39444
$657$	−25.3643	−0.989555
$658$	31.6045	1.23207
$659$	−9.77403	−0.380742	−0.190371	−	0.981712i	$-0.560969\pi$
$659$	−9.77403	−0.380742	−0.190371	+	0.981712i	$0.560969\pi$
$660$	4.46523	0.173809
$661$	−18.2878	−0.711314	−0.355657	−	0.934616i	$-0.615743\pi$
$661$	−18.2878	−0.711314	−0.355657	+	0.934616i	$0.615743\pi$
$662$	20.8071	0.808691
$663$	0.465405	0.0180748
$664$	−7.28567	−0.282739
$665$	−43.8900	−1.70198
$666$	31.2041	1.20913
$667$	7.70441	0.298316
$668$	0.157795	0.00610528
$669$	3.75658	0.145238
$670$	−77.3547	−2.98847
$671$	42.2008	1.62914
$672$	5.26204	0.202987
$673$	−23.5550	−0.907979	−0.453989	−	0.891007i	$-0.650000\pi$
$673$	−23.5550	−0.907979	−0.453989	+	0.891007i	$0.650000\pi$
$674$	16.5375	0.637001
$675$	−13.7114	−0.527751
$676$	−17.4683	−0.671856
$677$	30.5849	1.17547	0.587737	−	0.809052i	$-0.300019\pi$
$677$	30.5849	1.17547	0.587737	+	0.809052i	$0.300019\pi$
$678$	6.14746	0.236092
$679$	−7.85065	−0.301280
$680$	−15.6555	−0.600363
$681$	−1.39624	−0.0535041
$682$	−5.81388	−0.222625
$683$	−20.2542	−0.775005	−0.387503	−	0.921869i	$-0.626662\pi$
$683$	−20.2542	−0.775005	−0.387503	+	0.921869i	$0.626662\pi$
$684$	−11.2408	−0.429802
$685$	−11.6281	−0.444289
$686$	−12.0473	−0.459967
$687$	−5.09666	−0.194450
$688$	−23.3633	−0.890719
$689$	2.23864	0.0852855
$690$	7.98067	0.303819
$691$	39.0331	1.48489	0.742444	−	0.669909i	$-0.233667\pi$
$691$	39.0331	1.48489	0.742444	+	0.669909i	$0.233667\pi$
$692$	3.52020	0.133818
$693$	46.3839	1.76198
$694$	61.2890	2.32650
$695$	76.7523	2.91138
$696$	0.319725	0.0121191
$697$	43.5560	1.64980
$698$	−60.2024	−2.27869
$699$	−1.87053	−0.0707500
$700$	63.7889	2.41099
$701$	−5.57812	−0.210683	−0.105341	−	0.994436i	$-0.533593\pi$
$701$	−5.57812	−0.210683	−0.105341	+	0.994436i	$0.533593\pi$
$702$	1.48495	0.0560458
$703$	15.5927	0.588089
$704$	10.4298	0.393088
$705$	3.50933	0.132169
$706$	−58.5905	−2.20508
$707$	−0.166157	−0.00624896
$708$	2.41025	0.0905826
$709$	3.75346	0.140964	0.0704821	−	0.997513i	$-0.477546\pi$
$709$	3.75346	0.140964	0.0704821	+	0.997513i	$0.477546\pi$
$710$	100.965	3.78915
$711$	47.2740	1.77292
$712$	−6.30078	−0.236132
$713$	−4.26666	−0.159788
$714$	−4.98572	−0.186586
$715$	10.9674	0.410157
$716$	−9.21269	−0.344294
$717$	0.528987	0.0197554
$718$	46.3715	1.73057
$719$	23.2964	0.868808	0.434404	−	0.900718i	$-0.356959\pi$
$719$	23.2964	0.868808	0.434404	+	0.900718i	$0.356959\pi$
$720$	−58.3937	−2.17620
$721$	37.2240	1.38629
$722$	21.3200	0.793449
$723$	−4.06425	−0.151151
$724$	31.9402	1.18705
$725$	16.6531	0.618480
$726$	−1.71468	−0.0636379
$727$	−7.56053	−0.280405	−0.140202	−	0.990123i	$-0.544775\pi$
$727$	−7.56053	−0.280405	−0.140202	+	0.990123i	$0.544775\pi$
$728$	3.00806	0.111486
$729$	−24.8893	−0.921827
$730$	64.2474	2.37790
$731$	16.5931	0.613717
$732$	−2.95168	−0.109097
$733$	6.21614	0.229598	0.114799	−	0.993389i	$-0.463378\pi$
$733$	6.21614	0.229598	0.114799	+	0.993389i	$0.463378\pi$
$734$	37.6961	1.39139
$735$	−7.00252	−0.258292
$736$	35.8171	1.32024
$737$	40.8505	1.50475
$738$	69.0255	2.54087
$739$	22.0387	0.810707	0.405354	−	0.914160i	$-0.367148\pi$
$739$	22.0387	0.810707	0.405354	+	0.914160i	$0.367148\pi$
$740$	−32.4542	−1.19304
$741$	0.368555	0.0135392
$742$	−23.9818	−0.880400
$743$	−21.8772	−0.802598	−0.401299	−	0.915947i	$-0.631441\pi$
$743$	−21.8772	−0.802598	−0.401299	+	0.915947i	$0.631441\pi$
$744$	−0.177062	−0.00649140
$745$	−23.8058	−0.872177
$746$	−24.4338	−0.894586
$747$	19.3001	0.706153
$748$	−18.9875	−0.694254
$749$	40.1718	1.46785
$750$	9.79657	0.357720
$751$	−11.7154	−0.427502	−0.213751	−	0.976888i	$-0.568568\pi$
$751$	−11.7154	−0.427502	−0.213751	+	0.976888i	$0.568568\pi$
$752$	21.0115	0.766212
$753$	−0.397667	−0.0144918
$754$	−1.80354	−0.0656811
$755$	−45.5461	−1.65759
$756$	−6.53183	−0.237560
$757$	−9.14063	−0.332222	−0.166111	−	0.986107i	$-0.553121\pi$
$757$	−9.14063	−0.332222	−0.166111	+	0.986107i	$0.553121\pi$
$758$	3.77156	0.136989
$759$	−4.21454	−0.152978
$760$	−12.3977	−0.449710
$761$	−43.1277	−1.56338	−0.781690	−	0.623667i	$-0.785642\pi$
$761$	−43.1277	−1.56338	−0.781690	+	0.623667i	$0.785642\pi$
$762$	1.31894	0.0477803
$763$	14.8757	0.538538
$764$	22.6551	0.819634
$765$	41.4722	1.49943
$766$	−22.9732	−0.830054
$767$	5.91999	0.213758
$768$	4.17051	0.150490
$769$	−0.950822	−0.0342875	−0.0171438	−	0.999853i	$-0.505457\pi$
$769$	−0.950822	−0.0342875	−0.0171438	+	0.999853i	$0.505457\pi$
$770$	−117.490	−4.23404
$771$	1.00030	0.0360248
$772$	35.0405	1.26114
$773$	−24.0485	−0.864966	−0.432483	−	0.901642i	$-0.642362\pi$
$773$	−24.0485	−0.864966	−0.432483	+	0.901642i	$0.642362\pi$
$774$	26.2960	0.945189
$775$	−9.22238	−0.331278
$776$	−2.21758	−0.0796065
$777$	4.50029	0.161447
$778$	30.2286	1.08375
$779$	34.4920	1.23581
$780$	−0.767099	−0.0274666
$781$	−53.3190	−1.90790
$782$	−33.9363	−1.21356
$783$	−1.70524	−0.0609402
$784$	−41.9265	−1.49737
$785$	−75.3252	−2.68847
$786$	−0.535832	−0.0191125
$787$	−7.70953	−0.274815	−0.137408	−	0.990515i	$-0.543877\pi$
$787$	−7.70953	−0.274815	−0.137408	+	0.990515i	$0.543877\pi$
$788$	−22.5904	−0.804750
$789$	−1.63495	−0.0582057
$790$	−119.745	−4.26032
$791$	−66.4169	−2.36151
$792$	13.1021	0.465563
$793$	−7.24985	−0.257450
$794$	17.3216	0.614719
$795$	−2.66292	−0.0944440
$796$	11.2562	0.398965
$797$	46.6648	1.65295	0.826477	−	0.562971i	$-0.190342\pi$
$797$	46.6648	1.65295	0.826477	+	0.562971i	$0.190342\pi$
$798$	−3.94820	−0.139765
$799$	−14.9228	−0.527930
$800$	77.4188	2.73717
$801$	16.6911	0.589749
$802$	−1.84210	−0.0650467
$803$	−33.9286	−1.19732
$804$	−2.85724	−0.100767
$805$	−86.2228	−3.03895
$806$	0.998790	0.0351809
$807$	−0.00772155	−0.000271812 0
$808$	−0.0469344	−0.00165115
$809$	−52.8312	−1.85744	−0.928722	−	0.370776i	$-0.879092\pi$
$809$	−52.8312	−1.85744	−0.928722	+	0.370776i	$0.879092\pi$
$810$	64.8343	2.27805
$811$	41.8214	1.46855	0.734274	−	0.678853i	$-0.237523\pi$
$811$	41.8214	1.46855	0.734274	+	0.678853i	$0.237523\pi$
$812$	7.93321	0.278401
$813$	3.35916	0.117811
$814$	41.7403	1.46300
$815$	−63.8838	−2.23775
$816$	−3.31465	−0.116036
$817$	13.1401	0.459713
$818$	67.6577	2.36560
$819$	−7.96848	−0.278441
$820$	−71.7908	−2.50704
$821$	6.45685	0.225345	0.112673	−	0.993632i	$-0.464059\pi$
$821$	6.45685	0.225345	0.112673	+	0.993632i	$0.464059\pi$
$822$	−1.04603	−0.0364845
$823$	−11.4021	−0.397452	−0.198726	−	0.980055i	$-0.563680\pi$
$823$	−11.4021	−0.397452	−0.198726	+	0.980055i	$0.563680\pi$
$824$	10.5147	0.366297
$825$	−9.10973	−0.317160
$826$	−63.4188	−2.20662
$827$	54.4266	1.89260	0.946300	−	0.323291i	$-0.104789\pi$
$827$	54.4266	1.89260	0.946300	+	0.323291i	$0.104789\pi$
$828$	−22.0827	−0.767428
$829$	35.2670	1.22487	0.612437	−	0.790520i	$-0.290189\pi$
$829$	35.2670	1.22487	0.612437	+	0.790520i	$0.290189\pi$
$830$	−48.8868	−1.69689
$831$	−2.81962	−0.0978114
$832$	−1.79178	−0.0621187
$833$	29.7769	1.03171
$834$	6.90438	0.239079
$835$	−0.461027	−0.0159545
$836$	−15.0363	−0.520040
$837$	0.944350	0.0326415
$838$	15.4388	0.533325
$839$	−11.1177	−0.383826	−0.191913	−	0.981412i	$-0.561469\pi$
$839$	−11.1177	−0.383826	−0.191913	+	0.981412i	$0.561469\pi$
$840$	−3.57815	−0.123458
$841$	−26.9289	−0.928583
$842$	−29.2940	−1.00954
$843$	4.56455	0.157212
$844$	21.9063	0.754045
$845$	51.0367	1.75571
$846$	−23.6489	−0.813067
$847$	18.5254	0.636539
$848$	−15.9438	−0.547512
$849$	3.96613	0.136117
$850$	−73.3534	−2.51600
$851$	30.6321	1.05006
$852$	3.72932	0.127765
$853$	5.66936	0.194115	0.0970576	−	0.995279i	$-0.469057\pi$
$853$	5.66936	0.194115	0.0970576	+	0.995279i	$0.469057\pi$
$854$	77.6652	2.65765
$855$	32.8419	1.12317
$856$	11.3474	0.387845
$857$	−2.16104	−0.0738196	−0.0369098	−	0.999319i	$-0.511751\pi$
$857$	−2.16104	−0.0738196	−0.0369098	+	0.999319i	$0.511751\pi$
$858$	0.986590	0.0336816
$859$	35.8451	1.22302	0.611509	−	0.791237i	$-0.290563\pi$
$859$	35.8451	1.22302	0.611509	+	0.791237i	$0.290563\pi$
$860$	−27.3494	−0.932607
$861$	9.95493	0.339263
$862$	44.1284	1.50302
$863$	−27.6011	−0.939553	−0.469777	−	0.882785i	$-0.655666\pi$
$863$	−27.6011	−0.939553	−0.469777	+	0.882785i	$0.655666\pi$
$864$	−7.92750	−0.269699
$865$	−10.2849	−0.349697
$866$	43.8634	1.49054
$867$	−1.02538	−0.0348238
$868$	−4.39336	−0.149120
$869$	63.2363	2.14515
$870$	2.14535	0.0727343
$871$	−7.01787	−0.237792
$872$	4.20196	0.142296
$873$	5.87447	0.198821
$874$	−26.8742	−0.909034
$875$	−105.842	−3.57810
$876$	2.37309	0.0801794
$877$	16.5557	0.559045	0.279523	−	0.960139i	$-0.409824\pi$
$877$	16.5557	0.559045	0.279523	+	0.960139i	$0.409824\pi$
$878$	−71.2391	−2.40420
$879$	2.96487	0.100003
$880$	−78.1106	−2.63311
$881$	−39.7796	−1.34021	−0.670105	−	0.742266i	$-0.733751\pi$
$881$	−39.7796	−1.34021	−0.670105	+	0.742266i	$0.733751\pi$
$882$	47.1891	1.58894
$883$	−1.86504	−0.0627636	−0.0313818	−	0.999507i	$-0.509991\pi$
$883$	−1.86504	−0.0627636	−0.0313818	+	0.999507i	$0.509991\pi$
$884$	3.26195	0.109711
$885$	−7.04196	−0.236713
$886$	34.5500	1.16073
$887$	−23.8871	−0.802051	−0.401025	−	0.916067i	$-0.631346\pi$
$887$	−23.8871	−0.802051	−0.401025	+	0.916067i	$0.631346\pi$
$888$	1.27120	0.0426587
$889$	−14.2498	−0.477923
$890$	−42.2782	−1.41717
$891$	−34.2386	−1.14704
$892$	26.3293	0.881570
$893$	−11.8174	−0.395453
$894$	−2.14149	−0.0716222
$895$	26.9165	0.899720
$896$	−33.7448	−1.12733
$897$	0.724033	0.0241747
$898$	−0.513335	−0.0171302
$899$	−1.14696	−0.0382532
$900$	−47.7318	−1.59106
$901$	11.3236	0.377243
$902$	92.3323	3.07433
$903$	3.79243	0.126204
$904$	−18.7608	−0.623976
$905$	−93.3191	−3.10203
$906$	−4.09718	−0.136120
$907$	−47.9725	−1.59290	−0.796450	−	0.604704i	$-0.793291\pi$
$907$	−47.9725	−1.59290	−0.796450	+	0.604704i	$0.793291\pi$
$908$	−9.78604	−0.324761
$909$	0.124331	0.00412381
$910$	20.1841	0.669095
$911$	14.3449	0.475268	0.237634	−	0.971355i	$-0.423628\pi$
$911$	14.3449	0.475268	0.237634	+	0.971355i	$0.423628\pi$
$912$	−2.62487	−0.0869183
$913$	25.8168	0.854412
$914$	−2.09443	−0.0692776
$915$	8.62386	0.285096
$916$	−35.7217	−1.18028
$917$	5.78910	0.191173
$918$	7.51121	0.247907
$919$	1.86254	0.0614396	0.0307198	−	0.999528i	$-0.490220\pi$
$919$	1.86254	0.0614396	0.0307198	+	0.999528i	$0.490220\pi$
$920$	−24.3554	−0.802975
$921$	2.50937	0.0826865
$922$	2.21779	0.0730389
$923$	9.15988	0.301501
$924$	−4.33970	−0.142766
$925$	66.2114	2.17702
$926$	25.1016	0.824889
$927$	−27.8539	−0.914843
$928$	9.62831	0.316065
$929$	12.8200	0.420610	0.210305	−	0.977636i	$-0.432554\pi$
$929$	12.8200	0.420610	0.210305	+	0.977636i	$0.432554\pi$
$930$	−1.18808	−0.0389588
$931$	23.5804	0.772816
$932$	−13.1103	−0.429441
$933$	4.05486	0.132750
$934$	8.62626	0.282260
$935$	55.4755	1.81424
$936$	−2.25086	−0.0735718
$937$	7.48523	0.244532	0.122266	−	0.992497i	$-0.460984\pi$
$937$	7.48523	0.244532	0.122266	+	0.992497i	$0.460984\pi$
$938$	75.1801	2.45472
$939$	−5.97408	−0.194957
$940$	24.5963	0.802244
$941$	1.67946	0.0547490	0.0273745	−	0.999625i	$-0.491285\pi$
$941$	1.67946	0.0547490	0.0273745	+	0.999625i	$0.491285\pi$
$942$	−6.77601	−0.220774
$943$	67.7603	2.20658
$944$	−42.1626	−1.37228
$945$	19.0839	0.620800
$946$	35.1749	1.14363
$947$	−23.3128	−0.757564	−0.378782	−	0.925486i	$-0.623657\pi$
$947$	−23.3128	−0.757564	−0.378782	+	0.925486i	$0.623657\pi$
$948$	−4.42298	−0.143652
$949$	5.82874	0.189209
$950$	−58.0887	−1.88465
$951$	2.62685	0.0851815
$952$	15.2154	0.493135
$953$	−31.8359	−1.03127	−0.515633	−	0.856809i	$-0.672443\pi$
$953$	−31.8359	−1.03127	−0.515633	+	0.856809i	$0.672443\pi$
$954$	17.9451	0.580993
$955$	−66.1911	−2.14189
$956$	3.70758	0.119912
$957$	−1.13295	−0.0366230
$958$	−58.8397	−1.90103
$959$	11.3013	0.364936
$960$	2.13136	0.0687893
$961$	−30.3648	−0.979510
$962$	−7.17073	−0.231194
$963$	−30.0597	−0.968660
$964$	−28.4857	−0.917462
$965$	−102.377	−3.29564
$966$	−7.75631	−0.249555
$967$	−45.7159	−1.47013	−0.735063	−	0.677999i	$-0.762847\pi$
$967$	−45.7159	−1.47013	−0.735063	+	0.677999i	$0.762847\pi$
$968$	5.23288	0.168191
$969$	1.86423	0.0598878
$970$	−14.8800	−0.477767
$971$	−4.43553	−0.142343	−0.0711715	−	0.997464i	$-0.522674\pi$
$971$	−4.43553	−0.142343	−0.0711715	+	0.997464i	$0.522674\pi$
$972$	7.34764	0.235676
$973$	−74.5946	−2.39139
$974$	−35.2764	−1.13033
$975$	1.56500	0.0501200
$976$	51.6340	1.65276
$977$	16.5389	0.529125	0.264563	−	0.964369i	$-0.414772\pi$
$977$	16.5389	0.529125	0.264563	+	0.964369i	$0.414772\pi$
$978$	−5.74678	−0.183762
$979$	22.3269	0.713569
$980$	−49.0796	−1.56779
$981$	−11.1312	−0.355392
$982$	70.4597	2.24846
$983$	50.6641	1.61593	0.807966	−	0.589229i	$-0.200568\pi$
$983$	50.6641	1.61593	0.807966	+	0.589229i	$0.200568\pi$
$984$	2.81198	0.0896427
$985$	66.0019	2.10300
$986$	−9.12272	−0.290526
$987$	−3.41067	−0.108563
$988$	2.58314	0.0821807
$989$	25.8139	0.820836
$990$	87.9151	2.79413
$991$	0.412462	0.0131023	0.00655114	−	0.999979i	$-0.497915\pi$
$991$	0.412462	0.0131023	0.00655114	+	0.999979i	$0.497915\pi$
$992$	−5.33210	−0.169294
$993$	−2.24545	−0.0712572
$994$	−98.1266	−3.11239
$995$	−32.8869	−1.04259
$996$	−1.80572	−0.0572165
$997$	−45.5851	−1.44370	−0.721848	−	0.692052i	$-0.756707\pi$
$997$	−45.5851	−1.44370	−0.721848	+	0.692052i	$0.756707\pi$
$998$	−9.18017	−0.290593
$999$	−6.77989	−0.214506

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	401.2.a.b.1.5	✓	21
3.2	odd	2		3609.2.a.g.1.17		21
4.3	odd	2		6416.2.a.m.1.12		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
401.2.a.b.1.5	✓	21	1.1	even	1	trivial
3609.2.a.g.1.17		21	3.2	odd	2
6416.2.a.m.1.12		21	4.3	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:	\( N \)	\(=\)	\( 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	401.a (trivial)

\(f(q)\)	\(=\)	\(q-1.84210 q^{2} +0.198794 q^{3} +1.39332 q^{4} -4.07083 q^{5} -0.366198 q^{6} +3.95639 q^{7} +1.11757 q^{8} -2.96048 q^{9} +O(q^{10})\)	\(q-1.84210 q^{2} +0.198794 q^{3} +1.39332 q^{4} -4.07083 q^{5} -0.366198 q^{6} +3.95639 q^{7} +1.11757 q^{8} -2.96048 q^{9} +7.49886 q^{10} -3.96010 q^{11} +0.276984 q^{12} +0.680321 q^{13} -7.28805 q^{14} -0.809258 q^{15} -4.84530 q^{16} +3.44122 q^{17} +5.45349 q^{18} +2.72511 q^{19} -5.67196 q^{20} +0.786508 q^{21} +7.29488 q^{22} +5.35353 q^{23} +0.222166 q^{24} +11.5717 q^{25} -1.25322 q^{26} -1.18491 q^{27} +5.51251 q^{28} +1.43913 q^{29} +1.49073 q^{30} -0.796980 q^{31} +6.69038 q^{32} -0.787246 q^{33} -6.33906 q^{34} -16.1058 q^{35} -4.12489 q^{36} +5.72186 q^{37} -5.01991 q^{38} +0.135244 q^{39} -4.54942 q^{40} +12.6571 q^{41} -1.44882 q^{42} +4.82186 q^{43} -5.51768 q^{44} +12.0516 q^{45} -9.86171 q^{46} -4.33648 q^{47} -0.963219 q^{48} +8.65302 q^{49} -21.3161 q^{50} +0.684095 q^{51} +0.947904 q^{52} +3.29057 q^{53} +2.18272 q^{54} +16.1209 q^{55} +4.42152 q^{56} +0.541736 q^{57} -2.65101 q^{58} +8.70175 q^{59} -1.12755 q^{60} -10.6565 q^{61} +1.46811 q^{62} -11.7128 q^{63} -2.63372 q^{64} -2.76947 q^{65} +1.45018 q^{66} -10.3155 q^{67} +4.79472 q^{68} +1.06425 q^{69} +29.6684 q^{70} +13.4640 q^{71} -3.30853 q^{72} +8.56762 q^{73} -10.5402 q^{74} +2.30038 q^{75} +3.79694 q^{76} -15.6677 q^{77} -0.249133 q^{78} -15.9684 q^{79} +19.7244 q^{80} +8.64589 q^{81} -23.3157 q^{82} -6.51924 q^{83} +1.09586 q^{84} -14.0086 q^{85} -8.88233 q^{86} +0.286091 q^{87} -4.42567 q^{88} -5.63795 q^{89} -22.2002 q^{90} +2.69162 q^{91} +7.45917 q^{92} -0.158435 q^{93} +7.98821 q^{94} -11.0934 q^{95} +1.33001 q^{96} -1.98430 q^{97} -15.9397 q^{98} +11.7238 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9	\( 21 q + 3 q^{3} + 28 q^{4} + 3 q^{5} + 9 q^{6} + 24 q^{7} + 20 q^{9} + 7 q^{10} + q^{11} - 7 q^{12} + 9 q^{13} - 11 q^{14} + q^{15} + 30 q^{16} - q^{17} - 10 q^{18} + 38 q^{19} + q^{20} + q^{21} - q^{22} + 3 q^{23} + 21 q^{24} + 26 q^{25} - 2 q^{26} + 6 q^{27} + 25 q^{28} - 4 q^{29} - 21 q^{30} + 70 q^{31} - 10 q^{32} - 8 q^{33} + 13 q^{34} + 12 q^{35} + 15 q^{36} + 3 q^{37} - 13 q^{38} + 36 q^{39} - 7 q^{40} - 2 q^{41} - 21 q^{42} + 10 q^{43} - 26 q^{44} - 21 q^{45} - 4 q^{46} + 9 q^{47} - 34 q^{48} + 39 q^{49} - 24 q^{50} - 16 q^{51} - q^{52} - 17 q^{53} + 5 q^{54} + 45 q^{55} - 65 q^{56} - 21 q^{57} - 27 q^{58} + 7 q^{59} - 66 q^{60} + 32 q^{61} - 9 q^{62} + 41 q^{63} + 22 q^{64} - 39 q^{65} - 66 q^{66} + 6 q^{67} - 46 q^{68} - 7 q^{69} - 33 q^{70} + 15 q^{71} - 73 q^{72} + 18 q^{73} - 39 q^{74} - 9 q^{75} + 48 q^{76} - 26 q^{77} - 76 q^{78} + 49 q^{79} - 51 q^{80} - 39 q^{81} - 26 q^{82} - 3 q^{83} - 81 q^{84} - q^{85} - 64 q^{86} + 15 q^{87} - 46 q^{88} - 35 q^{89} - 68 q^{90} + 34 q^{91} - 54 q^{92} - 40 q^{93} - 4 q^{94} - 6 q^{95} - 14 q^{96} - 6 q^{97} - 90 q^{98} - 36 q^{99}+O(q^{100}) \) 21 * q + 3 * q^3 + 28 * q^4 + 3 * q^5 + 9 * q^6 + 24 * q^7 + 20 * q^9 + 7 * q^10 + q^11 - 7 * q^12 + 9 * q^13 - 11 * q^14 + q^15 + 30 * q^16 - q^17 - 10 * q^18 + 38 * q^19 + q^20 + q^21 - q^22 + 3 * q^23 + 21 * q^24 + 26 * q^25 - 2 * q^26 + 6 * q^27 + 25 * q^28 - 4 * q^29 - 21 * q^30 + 70 * q^31 - 10 * q^32 - 8 * q^33 + 13 * q^34 + 12 * q^35 + 15 * q^36 + 3 * q^37 - 13 * q^38 + 36 * q^39 - 7 * q^40 - 2 * q^41 - 21 * q^42 + 10 * q^43 - 26 * q^44 - 21 * q^45 - 4 * q^46 + 9 * q^47 - 34 * q^48 + 39 * q^49 - 24 * q^50 - 16 * q^51 - q^52 - 17 * q^53 + 5 * q^54 + 45 * q^55 - 65 * q^56 - 21 * q^57 - 27 * q^58 + 7 * q^59 - 66 * q^60 + 32 * q^61 - 9 * q^62 + 41 * q^63 + 22 * q^64 - 39 * q^65 - 66 * q^66 + 6 * q^67 - 46 * q^68 - 7 * q^69 - 33 * q^70 + 15 * q^71 - 73 * q^72 + 18 * q^73 - 39 * q^74 - 9 * q^75 + 48 * q^76 - 26 * q^77 - 76 * q^78 + 49 * q^79 - 51 * q^80 - 39 * q^81 - 26 * q^82 - 3 * q^83 - 81 * q^84 - q^85 - 64 * q^86 + 15 * q^87 - 46 * q^88 - 35 * q^89 - 68 * q^90 + 34 * q^91 - 54 * q^92 - 40 * q^93 - 4 * q^94 - 6 * q^95 - 14 * q^96 - 6 * q^97 - 90 * q^98 - 36 * q^99

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