LMFDB - Embedded newform 4022.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.20305 q^{3} +1.00000 q^{4} +2.72503 q^{5} -2.20305 q^{6} +3.76461 q^{7} +1.00000 q^{8} +1.85345 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.20305 q^{3} +1.00000 q^{4} +2.72503 q^{5} -2.20305 q^{6} +3.76461 q^{7} +1.00000 q^{8} +1.85345 q^{9} +2.72503 q^{10} -6.14059 q^{11} -2.20305 q^{12} +5.77413 q^{13} +3.76461 q^{14} -6.00338 q^{15} +1.00000 q^{16} -8.03614 q^{17} +1.85345 q^{18} +0.163009 q^{19} +2.72503 q^{20} -8.29363 q^{21} -6.14059 q^{22} +8.68402 q^{23} -2.20305 q^{24} +2.42576 q^{25} +5.77413 q^{26} +2.52592 q^{27} +3.76461 q^{28} -8.02437 q^{29} -6.00338 q^{30} +9.30563 q^{31} +1.00000 q^{32} +13.5280 q^{33} -8.03614 q^{34} +10.2586 q^{35} +1.85345 q^{36} -2.01729 q^{37} +0.163009 q^{38} -12.7207 q^{39} +2.72503 q^{40} +10.4485 q^{41} -8.29363 q^{42} +8.21980 q^{43} -6.14059 q^{44} +5.05069 q^{45} +8.68402 q^{46} -6.75229 q^{47} -2.20305 q^{48} +7.17226 q^{49} +2.42576 q^{50} +17.7041 q^{51} +5.77413 q^{52} +13.2443 q^{53} +2.52592 q^{54} -16.7333 q^{55} +3.76461 q^{56} -0.359118 q^{57} -8.02437 q^{58} +2.35824 q^{59} -6.00338 q^{60} -3.06896 q^{61} +9.30563 q^{62} +6.97750 q^{63} +1.00000 q^{64} +15.7346 q^{65} +13.5280 q^{66} -1.00141 q^{67} -8.03614 q^{68} -19.1314 q^{69} +10.2586 q^{70} +3.15229 q^{71} +1.85345 q^{72} -3.71808 q^{73} -2.01729 q^{74} -5.34409 q^{75} +0.163009 q^{76} -23.1169 q^{77} -12.7207 q^{78} +1.57240 q^{79} +2.72503 q^{80} -11.1251 q^{81} +10.4485 q^{82} -14.6946 q^{83} -8.29363 q^{84} -21.8987 q^{85} +8.21980 q^{86} +17.6781 q^{87} -6.14059 q^{88} +12.8725 q^{89} +5.05069 q^{90} +21.7373 q^{91} +8.68402 q^{92} -20.5008 q^{93} -6.75229 q^{94} +0.444204 q^{95} -2.20305 q^{96} -1.09215 q^{97} +7.17226 q^{98} -11.3813 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.20305	−1.27193	−0.635967	−	0.771716i	$-0.719399\pi$
$3$	−2.20305	−1.27193	−0.635967	+	0.771716i	$0.719399\pi$
$4$	1.00000	0.500000
$5$	2.72503	1.21867	0.609334	−	0.792913i	$-0.291437\pi$
$5$	2.72503	1.21867	0.609334	+	0.792913i	$0.291437\pi$
$6$	−2.20305	−0.899393
$7$	3.76461	1.42289	0.711444	−	0.702743i	$-0.248042\pi$
$7$	3.76461	1.42289	0.711444	+	0.702743i	$0.248042\pi$
$8$	1.00000	0.353553
$9$	1.85345	0.617816
$10$	2.72503	0.861729
$11$	−6.14059	−1.85146	−0.925729	−	0.378188i	$-0.876547\pi$
$11$	−6.14059	−1.85146	−0.925729	+	0.378188i	$0.876547\pi$
$12$	−2.20305	−0.635967
$13$	5.77413	1.60145	0.800727	−	0.599029i	$-0.204447\pi$
$13$	5.77413	1.60145	0.800727	+	0.599029i	$0.204447\pi$
$14$	3.76461	1.00613
$15$	−6.00338	−1.55007
$16$	1.00000	0.250000
$17$	−8.03614	−1.94905	−0.974525	−	0.224278i	$-0.927998\pi$
$17$	−8.03614	−1.94905	−0.974525	+	0.224278i	$0.927998\pi$
$18$	1.85345	0.436862
$19$	0.163009	0.0373968	0.0186984	−	0.999825i	$-0.494048\pi$
$19$	0.163009	0.0373968	0.0186984	+	0.999825i	$0.494048\pi$
$20$	2.72503	0.609334
$21$	−8.29363	−1.80982
$22$	−6.14059	−1.30918
$23$	8.68402	1.81074	0.905372	−	0.424620i	$-0.139592\pi$
$23$	8.68402	1.81074	0.905372	+	0.424620i	$0.139592\pi$
$24$	−2.20305	−0.449696
$25$	2.42576	0.485153
$26$	5.77413	1.13240
$27$	2.52592	0.486113
$28$	3.76461	0.711444
$29$	−8.02437	−1.49009	−0.745044	−	0.667016i	$-0.767571\pi$
$29$	−8.02437	−1.49009	−0.745044	+	0.667016i	$0.767571\pi$
$30$	−6.00338	−1.09606
$31$	9.30563	1.67134	0.835671	−	0.549231i	$-0.185079\pi$
$31$	9.30563	1.67134	0.835671	+	0.549231i	$0.185079\pi$
$32$	1.00000	0.176777
$33$	13.5280	2.35493
$34$	−8.03614	−1.37819
$35$	10.2586	1.73403
$36$	1.85345	0.308908
$37$	−2.01729	−0.331640	−0.165820	−	0.986156i	$-0.553027\pi$
$37$	−2.01729	−0.331640	−0.165820	+	0.986156i	$0.553027\pi$
$38$	0.163009	0.0264435
$39$	−12.7207	−2.03694
$40$	2.72503	0.430864
$41$	10.4485	1.63179	0.815893	−	0.578202i	$-0.196246\pi$
$41$	10.4485	1.63179	0.815893	+	0.578202i	$0.196246\pi$
$42$	−8.29363	−1.27973
$43$	8.21980	1.25351	0.626754	−	0.779217i	$-0.284383\pi$
$43$	8.21980	1.25351	0.626754	+	0.779217i	$0.284383\pi$
$44$	−6.14059	−0.925729
$45$	5.05069	0.752912
$46$	8.68402	1.28039
$47$	−6.75229	−0.984922	−0.492461	−	0.870334i	$-0.663903\pi$
$47$	−6.75229	−0.984922	−0.492461	+	0.870334i	$0.663903\pi$
$48$	−2.20305	−0.317983
$49$	7.17226	1.02461
$50$	2.42576	0.343055
$51$	17.7041	2.47906
$52$	5.77413	0.800727
$53$	13.2443	1.81925	0.909625	−	0.415430i	$-0.136369\pi$
$53$	13.2443	1.81925	0.909625	+	0.415430i	$0.136369\pi$
$54$	2.52592	0.343734
$55$	−16.7333	−2.25631
$56$	3.76461	0.503067
$57$	−0.359118	−0.0475663
$58$	−8.02437	−1.05365
$59$	2.35824	0.307017	0.153508	−	0.988147i	$-0.450943\pi$
$59$	2.35824	0.307017	0.153508	+	0.988147i	$0.450943\pi$
$60$	−6.00338	−0.775033
$61$	−3.06896	−0.392940	−0.196470	−	0.980510i	$-0.562948\pi$
$61$	−3.06896	−0.392940	−0.196470	+	0.980510i	$0.562948\pi$
$62$	9.30563	1.18182
$63$	6.97750	0.879082
$64$	1.00000	0.125000
$65$	15.7346	1.95164
$66$	13.5280	1.66519
$67$	−1.00141	−0.122341	−0.0611706	−	0.998127i	$-0.519483\pi$
$67$	−1.00141	−0.122341	−0.0611706	+	0.998127i	$0.519483\pi$
$68$	−8.03614	−0.974525
$69$	−19.1314	−2.30315
$70$	10.2586	1.22614
$71$	3.15229	0.374108	0.187054	−	0.982350i	$-0.440106\pi$
$71$	3.15229	0.374108	0.187054	+	0.982350i	$0.440106\pi$
$72$	1.85345	0.218431
$73$	−3.71808	−0.435169	−0.217584	−	0.976042i	$-0.569818\pi$
$73$	−3.71808	−0.435169	−0.217584	+	0.976042i	$0.569818\pi$
$74$	−2.01729	−0.234505
$75$	−5.34409	−0.617082
$76$	0.163009	0.0186984
$77$	−23.1169	−2.63442
$78$	−12.7207	−1.44034
$79$	1.57240	0.176909	0.0884544	−	0.996080i	$-0.471807\pi$
$79$	1.57240	0.176909	0.0884544	+	0.996080i	$0.471807\pi$
$80$	2.72503	0.304667
$81$	−11.1251	−1.23612
$82$	10.4485	1.15385
$83$	−14.6946	−1.61294	−0.806472	−	0.591272i	$-0.798626\pi$
$83$	−14.6946	−1.61294	−0.806472	+	0.591272i	$0.798626\pi$
$84$	−8.29363	−0.904909
$85$	−21.8987	−2.37525
$86$	8.21980	0.886364
$87$	17.6781	1.89529
$88$	−6.14059	−0.654589
$89$	12.8725	1.36448	0.682240	−	0.731128i	$-0.261006\pi$
$89$	12.8725	1.36448	0.682240	+	0.731128i	$0.261006\pi$
$90$	5.05069	0.532389
$91$	21.7373	2.27869
$92$	8.68402	0.905372
$93$	−20.5008	−2.12584
$94$	−6.75229	−0.696445
$95$	0.444204	0.0455743
$96$	−2.20305	−0.224848
$97$	−1.09215	−0.110891	−0.0554455	−	0.998462i	$-0.517658\pi$
$97$	−1.09215	−0.110891	−0.0554455	+	0.998462i	$0.517658\pi$
$98$	7.17226	0.724508
$99$	−11.3813	−1.14386
$100$	2.42576	0.242576
$101$	−4.43590	−0.441389	−0.220695	−	0.975343i	$-0.570832\pi$
$101$	−4.43590	−0.441389	−0.220695	+	0.975343i	$0.570832\pi$
$102$	17.7041	1.75296
$103$	4.55834	0.449147	0.224573	−	0.974457i	$-0.427901\pi$
$103$	4.55834	0.449147	0.224573	+	0.974457i	$0.427901\pi$
$104$	5.77413	0.566200
$105$	−22.6004	−2.20557
$106$	13.2443	1.28640
$107$	9.34901	0.903803	0.451901	−	0.892068i	$-0.350746\pi$
$107$	9.34901	0.903803	0.451901	+	0.892068i	$0.350746\pi$
$108$	2.52592	0.243057
$109$	0.832238	0.0797140	0.0398570	−	0.999205i	$-0.487310\pi$
$109$	0.832238	0.0797140	0.0398570	+	0.999205i	$0.487310\pi$
$110$	−16.7333	−1.59545
$111$	4.44419	0.421824
$112$	3.76461	0.355722
$113$	1.17435	0.110473	0.0552366	−	0.998473i	$-0.482409\pi$
$113$	1.17435	0.110473	0.0552366	+	0.998473i	$0.482409\pi$
$114$	−0.359118	−0.0336344
$115$	23.6642	2.20670
$116$	−8.02437	−0.745044
$117$	10.7020	0.989403
$118$	2.35824	0.217094
$119$	−30.2529	−2.77328
$120$	−6.00338	−0.548031
$121$	26.7068	2.42789
$122$	−3.06896	−0.277851
$123$	−23.0187	−2.07552
$124$	9.30563	0.835671
$125$	−7.01486	−0.627428
$126$	6.97750	0.621605
$127$	5.35882	0.475518	0.237759	−	0.971324i	$-0.423587\pi$
$127$	5.35882	0.475518	0.237759	+	0.971324i	$0.423587\pi$
$128$	1.00000	0.0883883
$129$	−18.1087	−1.59438
$130$	15.7346	1.38002
$131$	−4.50630	−0.393718	−0.196859	−	0.980432i	$-0.563074\pi$
$131$	−4.50630	−0.393718	−0.196859	+	0.980432i	$0.563074\pi$
$132$	13.5280	1.17747
$133$	0.613664	0.0532115
$134$	−1.00141	−0.0865083
$135$	6.88319	0.592411
$136$	−8.03614	−0.689093
$137$	−22.5635	−1.92773	−0.963863	−	0.266398i	$-0.914167\pi$
$137$	−22.5635	−1.92773	−0.963863	+	0.266398i	$0.914167\pi$
$138$	−19.1314	−1.62857
$139$	9.95987	0.844785	0.422392	−	0.906413i	$-0.361190\pi$
$139$	9.95987	0.844785	0.422392	+	0.906413i	$0.361190\pi$
$140$	10.2586	0.867014
$141$	14.8757	1.25276
$142$	3.15229	0.264534
$143$	−35.4565	−2.96502
$144$	1.85345	0.154454
$145$	−21.8666	−1.81592
$146$	−3.71808	−0.307711
$147$	−15.8009	−1.30323
$148$	−2.01729	−0.165820
$149$	8.22599	0.673899	0.336950	−	0.941523i	$-0.390605\pi$
$149$	8.22599	0.673899	0.336950	+	0.941523i	$0.390605\pi$
$150$	−5.34409	−0.436343
$151$	16.5404	1.34604	0.673020	−	0.739625i	$-0.264997\pi$
$151$	16.5404	1.34604	0.673020	+	0.739625i	$0.264997\pi$
$152$	0.163009	0.0132218
$153$	−14.8946	−1.20415
$154$	−23.1169	−1.86281
$155$	25.3581	2.03681
$156$	−12.7207	−1.01847
$157$	−12.5434	−1.00107	−0.500537	−	0.865715i	$-0.666864\pi$
$157$	−12.5434	−1.00107	−0.500537	+	0.865715i	$0.666864\pi$
$158$	1.57240	0.125093
$159$	−29.1780	−2.31397
$160$	2.72503	0.215432
$161$	32.6919	2.57648
$162$	−11.1251	−0.874068
$163$	13.3990	1.04949	0.524744	−	0.851260i	$-0.324161\pi$
$163$	13.3990	1.04949	0.524744	+	0.851260i	$0.324161\pi$
$164$	10.4485	0.815893
$165$	36.8643	2.86988
$166$	−14.6946	−1.14052
$167$	−6.17103	−0.477528	−0.238764	−	0.971078i	$-0.576742\pi$
$167$	−6.17103	−0.477528	−0.238764	+	0.971078i	$0.576742\pi$
$168$	−8.29363	−0.639867
$169$	20.3405	1.56466
$170$	−21.8987	−1.67955
$171$	0.302128	0.0231043
$172$	8.21980	0.626754
$173$	8.39281	0.638093	0.319047	−	0.947739i	$-0.396637\pi$
$173$	8.39281	0.638093	0.319047	+	0.947739i	$0.396637\pi$
$174$	17.6781	1.34017
$175$	9.13205	0.690318
$176$	−6.14059	−0.462864
$177$	−5.19533	−0.390505
$178$	12.8725	0.964834
$179$	4.93199	0.368634	0.184317	−	0.982867i	$-0.440993\pi$
$179$	4.93199	0.368634	0.184317	+	0.982867i	$0.440993\pi$
$180$	5.05069	0.376456
$181$	−8.52019	−0.633301	−0.316650	−	0.948542i	$-0.602558\pi$
$181$	−8.52019	−0.633301	−0.316650	+	0.948542i	$0.602558\pi$
$182$	21.7373	1.61128
$183$	6.76108	0.499794
$184$	8.68402	0.640194
$185$	−5.49716	−0.404159
$186$	−20.5008	−1.50319
$187$	49.3466	3.60858
$188$	−6.75229	−0.492461
$189$	9.50909	0.691685
$190$	0.444204	0.0322259
$191$	3.66785	0.265396	0.132698	−	0.991157i	$-0.457636\pi$
$191$	3.66785	0.265396	0.132698	+	0.991157i	$0.457636\pi$
$192$	−2.20305	−0.158992
$193$	−7.40495	−0.533020	−0.266510	−	0.963832i	$-0.585871\pi$
$193$	−7.40495	−0.533020	−0.266510	+	0.963832i	$0.585871\pi$
$194$	−1.09215	−0.0784118
$195$	−34.6643	−2.48236
$196$	7.17226	0.512304
$197$	5.96096	0.424701	0.212350	−	0.977194i	$-0.431888\pi$
$197$	5.96096	0.424701	0.212350	+	0.977194i	$0.431888\pi$
$198$	−11.3813	−0.808830
$199$	10.0796	0.714526	0.357263	−	0.934004i	$-0.383710\pi$
$199$	10.0796	0.714526	0.357263	+	0.934004i	$0.383710\pi$
$200$	2.42576	0.171527
$201$	2.20615	0.155610
$202$	−4.43590	−0.312109
$203$	−30.2086	−2.12023
$204$	17.7041	1.23953
$205$	28.4725	1.98861
$206$	4.55834	0.317595
$207$	16.0954	1.11871
$208$	5.77413	0.400364
$209$	−1.00097	−0.0692386
$210$	−22.6004	−1.55957
$211$	5.92529	0.407914	0.203957	−	0.978980i	$-0.434620\pi$
$211$	5.92529	0.407914	0.203957	+	0.978980i	$0.434620\pi$
$212$	13.2443	0.909625
$213$	−6.94466	−0.475840
$214$	9.34901	0.639085
$215$	22.3992	1.52761
$216$	2.52592	0.171867
$217$	35.0320	2.37813
$218$	0.832238	0.0563663
$219$	8.19114	0.553506
$220$	−16.7333	−1.12816
$221$	−46.4017	−3.12132
$222$	4.44419	0.298275
$223$	13.9838	0.936425	0.468213	−	0.883616i	$-0.344898\pi$
$223$	13.9838	0.936425	0.468213	+	0.883616i	$0.344898\pi$
$224$	3.76461	0.251533
$225$	4.49602	0.299735
$226$	1.17435	0.0781164
$227$	−7.66821	−0.508957	−0.254478	−	0.967078i	$-0.581904\pi$
$227$	−7.66821	−0.508957	−0.254478	+	0.967078i	$0.581904\pi$
$228$	−0.359118	−0.0237831
$229$	−14.9556	−0.988294	−0.494147	−	0.869378i	$-0.664520\pi$
$229$	−14.9556	−0.988294	−0.494147	+	0.869378i	$0.664520\pi$
$230$	23.6642	1.56037
$231$	50.9278	3.35080
$232$	−8.02437	−0.526825
$233$	5.14194	0.336860	0.168430	−	0.985714i	$-0.446130\pi$
$233$	5.14194	0.336860	0.168430	+	0.985714i	$0.446130\pi$
$234$	10.7020	0.699614
$235$	−18.4002	−1.20029
$236$	2.35824	0.153508
$237$	−3.46408	−0.225016
$238$	−30.2529	−1.96100
$239$	−6.59092	−0.426331	−0.213166	−	0.977016i	$-0.568377\pi$
$239$	−6.59092	−0.426331	−0.213166	+	0.977016i	$0.568377\pi$
$240$	−6.00338	−0.387516
$241$	4.65097	0.299595	0.149798	−	0.988717i	$-0.452138\pi$
$241$	4.65097	0.299595	0.149798	+	0.988717i	$0.452138\pi$
$242$	26.7068	1.71678
$243$	16.9314	1.08615
$244$	−3.06896	−0.196470
$245$	19.5446	1.24866
$246$	−23.0187	−1.46762
$247$	0.941234	0.0598893
$248$	9.30563	0.590908
$249$	32.3731	2.05156
$250$	−7.01486	−0.443659
$251$	18.9912	1.19871	0.599356	−	0.800482i	$-0.295423\pi$
$251$	18.9912	1.19871	0.599356	+	0.800482i	$0.295423\pi$
$252$	6.97750	0.439541
$253$	−53.3250	−3.35251
$254$	5.35882	0.336242
$255$	48.2440	3.02116
$256$	1.00000	0.0625000
$257$	10.0178	0.624895	0.312448	−	0.949935i	$-0.398851\pi$
$257$	10.0178	0.624895	0.312448	+	0.949935i	$0.398851\pi$
$258$	−18.1087	−1.12740
$259$	−7.59429	−0.471886
$260$	15.7346	0.975821
$261$	−14.8727	−0.920599
$262$	−4.50630	−0.278400
$263$	−13.4125	−0.827051	−0.413526	−	0.910492i	$-0.635703\pi$
$263$	−13.4125	−0.827051	−0.413526	+	0.910492i	$0.635703\pi$
$264$	13.5280	0.832594
$265$	36.0912	2.21706
$266$	0.613664	0.0376262
$267$	−28.3588	−1.73553
$268$	−1.00141	−0.0611706
$269$	−29.6521	−1.80792	−0.903959	−	0.427618i	$-0.859353\pi$
$269$	−29.6521	−1.80792	−0.903959	+	0.427618i	$0.859353\pi$
$270$	6.88319	0.418898
$271$	1.46321	0.0888838	0.0444419	−	0.999012i	$-0.485849\pi$
$271$	1.46321	0.0888838	0.0444419	+	0.999012i	$0.485849\pi$
$272$	−8.03614	−0.487263
$273$	−47.8885	−2.89834
$274$	−22.5635	−1.36311
$275$	−14.8956	−0.898240
$276$	−19.1314	−1.15157
$277$	−28.9576	−1.73989	−0.869947	−	0.493145i	$-0.835847\pi$
$277$	−28.9576	−1.73989	−0.869947	+	0.493145i	$0.835847\pi$
$278$	9.95987	0.597353
$279$	17.2475	1.03258
$280$	10.2586	0.613071
$281$	−16.0950	−0.960149	−0.480074	−	0.877228i	$-0.659390\pi$
$281$	−16.0950	−0.960149	−0.480074	+	0.877228i	$0.659390\pi$
$282$	14.8757	0.885832
$283$	6.41954	0.381602	0.190801	−	0.981629i	$-0.438892\pi$
$283$	6.41954	0.381602	0.190801	+	0.981629i	$0.438892\pi$
$284$	3.15229	0.187054
$285$	−0.978604	−0.0579675
$286$	−35.4565	−2.09659
$287$	39.3346	2.32185
$288$	1.85345	0.109215
$289$	47.5796	2.79880
$290$	−21.8666	−1.28405
$291$	2.40606	0.141046
$292$	−3.71808	−0.217584
$293$	18.5082	1.08126	0.540630	−	0.841260i	$-0.318186\pi$
$293$	18.5082	1.08126	0.540630	+	0.841260i	$0.318186\pi$
$294$	−15.8009	−0.921526
$295$	6.42626	0.374151
$296$	−2.01729	−0.117252
$297$	−15.5106	−0.900018
$298$	8.22599	0.476519
$299$	50.1426	2.89982
$300$	−5.34409	−0.308541
$301$	30.9443	1.78360
$302$	16.5404	0.951794
$303$	9.77254	0.561418
$304$	0.163009	0.00934920
$305$	−8.36299	−0.478864
$306$	−14.8946	−0.851465
$307$	−15.1239	−0.863168	−0.431584	−	0.902073i	$-0.642045\pi$
$307$	−15.1239	−0.863168	−0.431584	+	0.902073i	$0.642045\pi$
$308$	−23.1169	−1.31721
$309$	−10.0423	−0.571285
$310$	25.3581	1.44024
$311$	26.8651	1.52338	0.761691	−	0.647941i	$-0.224370\pi$
$311$	26.8651	1.52338	0.761691	+	0.647941i	$0.224370\pi$
$312$	−12.7207	−0.720169
$313$	−29.4601	−1.66518	−0.832591	−	0.553888i	$-0.813144\pi$
$313$	−29.4601	−1.66518	−0.832591	+	0.553888i	$0.813144\pi$
$314$	−12.5434	−0.707866
$315$	19.0139	1.07131
$316$	1.57240	0.0884544
$317$	0.461533	0.0259223	0.0129611	−	0.999916i	$-0.495874\pi$
$317$	0.461533	0.0259223	0.0129611	+	0.999916i	$0.495874\pi$
$318$	−29.1780	−1.63622
$319$	49.2743	2.75883
$320$	2.72503	0.152334
$321$	−20.5964	−1.14958
$322$	32.6919	1.82185
$323$	−1.30996	−0.0728883
$324$	−11.1251	−0.618060
$325$	14.0067	0.776950
$326$	13.3990	0.742100
$327$	−1.83347	−0.101391
$328$	10.4485	0.576924
$329$	−25.4197	−1.40143
$330$	36.8643	2.02931
$331$	12.0316	0.661319	0.330659	−	0.943750i	$-0.392729\pi$
$331$	12.0316	0.661319	0.330659	+	0.943750i	$0.392729\pi$
$332$	−14.6946	−0.806472
$333$	−3.73893	−0.204892
$334$	−6.17103	−0.337664
$335$	−2.72886	−0.149093
$336$	−8.29363	−0.452455
$337$	1.50816	0.0821548	0.0410774	−	0.999156i	$-0.486921\pi$
$337$	1.50816	0.0821548	0.0410774	+	0.999156i	$0.486921\pi$
$338$	20.3405	1.10638
$339$	−2.58715	−0.140515
$340$	−21.8987	−1.18762
$341$	−57.1421	−3.09442
$342$	0.302128	0.0163372
$343$	0.648489	0.0350151
$344$	8.21980	0.443182
$345$	−52.1334	−2.80677
$346$	8.39281	0.451200
$347$	−12.2609	−0.658200	−0.329100	−	0.944295i	$-0.606745\pi$
$347$	−12.2609	−0.658200	−0.329100	+	0.944295i	$0.606745\pi$
$348$	17.6781	0.947646
$349$	−12.0392	−0.644443	−0.322221	−	0.946664i	$-0.604430\pi$
$349$	−12.0392	−0.644443	−0.322221	+	0.946664i	$0.604430\pi$
$350$	9.13205	0.488128
$351$	14.5850	0.778488
$352$	−6.14059	−0.327294
$353$	8.94094	0.475878	0.237939	−	0.971280i	$-0.423528\pi$
$353$	8.94094	0.475878	0.237939	+	0.971280i	$0.423528\pi$
$354$	−5.19533	−0.276129
$355$	8.59006	0.455913
$356$	12.8725	0.682240
$357$	66.6488	3.52743
$358$	4.93199	0.260664
$359$	−2.81302	−0.148465	−0.0742326	−	0.997241i	$-0.523651\pi$
$359$	−2.81302	−0.148465	−0.0742326	+	0.997241i	$0.523651\pi$
$360$	5.05069	0.266195
$361$	−18.9734	−0.998601
$362$	−8.52019	−0.447811
$363$	−58.8366	−3.08812
$364$	21.7373	1.13934
$365$	−10.1319	−0.530326
$366$	6.76108	0.353408
$367$	14.5154	0.757697	0.378848	−	0.925459i	$-0.376320\pi$
$367$	14.5154	0.757697	0.378848	+	0.925459i	$0.376320\pi$
$368$	8.68402	0.452686
$369$	19.3658	1.00814
$370$	−5.49716	−0.285784
$371$	49.8597	2.58859
$372$	−20.5008	−1.06292
$373$	23.3194	1.20743	0.603716	−	0.797199i	$-0.293686\pi$
$373$	23.3194	1.20743	0.603716	+	0.797199i	$0.293686\pi$
$374$	49.3466	2.55165
$375$	15.4541	0.798047
$376$	−6.75229	−0.348223
$377$	−46.3337	−2.38631
$378$	9.50909	0.489095
$379$	−24.2526	−1.24577	−0.622887	−	0.782312i	$-0.714040\pi$
$379$	−24.2526	−1.24577	−0.622887	+	0.782312i	$0.714040\pi$
$380$	0.444204	0.0227872
$381$	−11.8058	−0.604827
$382$	3.66785	0.187663
$383$	−14.6932	−0.750788	−0.375394	−	0.926865i	$-0.622493\pi$
$383$	−14.6932	−0.750788	−0.375394	+	0.926865i	$0.622493\pi$
$384$	−2.20305	−0.112424
$385$	−62.9941	−3.21048
$386$	−7.40495	−0.376902
$387$	15.2350	0.774437
$388$	−1.09215	−0.0554455
$389$	−32.4603	−1.64580	−0.822902	−	0.568183i	$-0.807646\pi$
$389$	−32.4603	−1.64580	−0.822902	+	0.568183i	$0.807646\pi$
$390$	−34.6643	−1.75529
$391$	−69.7860	−3.52923
$392$	7.17226	0.362254
$393$	9.92763	0.500783
$394$	5.96096	0.300309
$395$	4.28483	0.215593
$396$	−11.3813	−0.571930
$397$	37.9889	1.90661	0.953304	−	0.302011i	$-0.0976579\pi$
$397$	37.9889	1.90661	0.953304	+	0.302011i	$0.0976579\pi$
$398$	10.0796	0.505246
$399$	−1.35194	−0.0676815
$400$	2.42576	0.121288
$401$	−2.61530	−0.130602	−0.0653008	−	0.997866i	$-0.520801\pi$
$401$	−2.61530	−0.130602	−0.0653008	+	0.997866i	$0.520801\pi$
$402$	2.20615	0.110033
$403$	53.7319	2.67658
$404$	−4.43590	−0.220695
$405$	−30.3161	−1.50642
$406$	−30.2086	−1.49923
$407$	12.3873	0.614017
$408$	17.7041	0.876481
$409$	2.63391	0.130239	0.0651193	−	0.997877i	$-0.479257\pi$
$409$	2.63391	0.130239	0.0651193	+	0.997877i	$0.479257\pi$
$410$	28.4725	1.40616
$411$	49.7085	2.45194
$412$	4.55834	0.224573
$413$	8.87784	0.436850
$414$	16.0954	0.791044
$415$	−40.0432	−1.96564
$416$	5.77413	0.283100
$417$	−21.9421	−1.07451
$418$	−1.00097	−0.0489591
$419$	−5.77310	−0.282034	−0.141017	−	0.990007i	$-0.545037\pi$
$419$	−5.77310	−0.282034	−0.141017	+	0.990007i	$0.545037\pi$
$420$	−22.6004	−1.10278
$421$	20.6728	1.00753	0.503766	−	0.863840i	$-0.331947\pi$
$421$	20.6728	1.00753	0.503766	+	0.863840i	$0.331947\pi$
$422$	5.92529	0.288439
$423$	−12.5150	−0.608500
$424$	13.2443	0.643202
$425$	−19.4938	−0.945587
$426$	−6.94466	−0.336470
$427$	−11.5534	−0.559109
$428$	9.34901	0.451901
$429$	78.1127	3.77132
$430$	22.3992	1.08018
$431$	19.0374	0.916997	0.458498	−	0.888695i	$-0.348387\pi$
$431$	19.0374	0.916997	0.458498	+	0.888695i	$0.348387\pi$
$432$	2.52592	0.121528
$433$	−3.46686	−0.166607	−0.0833034	−	0.996524i	$-0.526547\pi$
$433$	−3.46686	−0.166607	−0.0833034	+	0.996524i	$0.526547\pi$
$434$	35.0320	1.68159
$435$	48.1733	2.30973
$436$	0.832238	0.0398570
$437$	1.41557	0.0677160
$438$	8.19114	0.391388
$439$	13.2589	0.632815	0.316407	−	0.948623i	$-0.397523\pi$
$439$	13.2589	0.632815	0.316407	+	0.948623i	$0.397523\pi$
$440$	−16.7333	−0.797727
$441$	13.2934	0.633019
$442$	−46.4017	−2.20710
$443$	−13.3697	−0.635214	−0.317607	−	0.948222i	$-0.602879\pi$
$443$	−13.3697	−0.635214	−0.317607	+	0.948222i	$0.602879\pi$
$444$	4.44419	0.210912
$445$	35.0779	1.66285
$446$	13.9838	0.662153
$447$	−18.1223	−0.857155
$448$	3.76461	0.177861
$449$	6.78506	0.320207	0.160103	−	0.987100i	$-0.448817\pi$
$449$	6.78506	0.320207	0.160103	+	0.987100i	$0.448817\pi$
$450$	4.49602	0.211945
$451$	−64.1601	−3.02118
$452$	1.17435	0.0552366
$453$	−36.4394	−1.71207
$454$	−7.66821	−0.359887
$455$	59.2347	2.77697
$456$	−0.359118	−0.0168172
$457$	−34.5478	−1.61608	−0.808040	−	0.589128i	$-0.799471\pi$
$457$	−34.5478	−1.61608	−0.808040	+	0.589128i	$0.799471\pi$
$458$	−14.9556	−0.698830
$459$	−20.2986	−0.947459
$460$	23.6642	1.10335
$461$	−13.2062	−0.615073	−0.307536	−	0.951536i	$-0.599505\pi$
$461$	−13.2062	−0.615073	−0.307536	+	0.951536i	$0.599505\pi$
$462$	50.9278	2.36937
$463$	15.9853	0.742898	0.371449	−	0.928453i	$-0.378861\pi$
$463$	15.9853	0.742898	0.371449	+	0.928453i	$0.378861\pi$
$464$	−8.02437	−0.372522
$465$	−55.8652	−2.59069
$466$	5.14194	0.238196
$467$	−10.7310	−0.496571	−0.248285	−	0.968687i	$-0.579867\pi$
$467$	−10.7310	−0.496571	−0.248285	+	0.968687i	$0.579867\pi$
$468$	10.7020	0.494702
$469$	−3.76990	−0.174078
$470$	−18.4002	−0.848736
$471$	27.6338	1.27330
$472$	2.35824	0.108547
$473$	−50.4744	−2.32082
$474$	−3.46408	−0.159110
$475$	0.395421	0.0181432
$476$	−30.2529	−1.38664
$477$	24.5477	1.12396
$478$	−6.59092	−0.301462
$479$	11.3778	0.519865	0.259933	−	0.965627i	$-0.416300\pi$
$479$	11.3778	0.519865	0.259933	+	0.965627i	$0.416300\pi$
$480$	−6.00338	−0.274015
$481$	−11.6481	−0.531106
$482$	4.65097	0.211846
$483$	−72.0220	−3.27712
$484$	26.7068	1.21395
$485$	−2.97614	−0.135139
$486$	16.9314	0.768023
$487$	−15.5016	−0.702443	−0.351222	−	0.936292i	$-0.614234\pi$
$487$	−15.5016	−0.702443	−0.351222	+	0.936292i	$0.614234\pi$
$488$	−3.06896	−0.138925
$489$	−29.5186	−1.33488
$490$	19.5446	0.882935
$491$	−0.433207	−0.0195504	−0.00977518	−	0.999952i	$-0.503112\pi$
$491$	−0.433207	−0.0195504	−0.00977518	+	0.999952i	$0.503112\pi$
$492$	−23.0187	−1.03776
$493$	64.4849	2.90426
$494$	0.941234	0.0423481
$495$	−31.0142	−1.39398
$496$	9.30563	0.417835
$497$	11.8671	0.532313
$498$	32.3731	1.45067
$499$	−34.0835	−1.52579	−0.762893	−	0.646525i	$-0.776222\pi$
$499$	−34.0835	−1.52579	−0.762893	+	0.646525i	$0.776222\pi$
$500$	−7.01486	−0.313714
$501$	13.5951	0.607385
$502$	18.9912	0.847618
$503$	−20.2486	−0.902838	−0.451419	−	0.892312i	$-0.649082\pi$
$503$	−20.2486	−0.902838	−0.451419	+	0.892312i	$0.649082\pi$
$504$	6.97750	0.310802
$505$	−12.0880	−0.537907
$506$	−53.3250	−2.37058
$507$	−44.8113	−1.99014
$508$	5.35882	0.237759
$509$	24.0699	1.06688	0.533439	−	0.845839i	$-0.320899\pi$
$509$	24.0699	1.06688	0.533439	+	0.845839i	$0.320899\pi$
$510$	48.2440	2.13628
$511$	−13.9971	−0.619196
$512$	1.00000	0.0441942
$513$	0.411747	0.0181791
$514$	10.0178	0.441868
$515$	12.4216	0.547361
$516$	−18.1087	−0.797190
$517$	41.4630	1.82354
$518$	−7.59429	−0.333674
$519$	−18.4898	−0.811612
$520$	15.7346	0.690010
$521$	−37.9885	−1.66431	−0.832154	−	0.554545i	$-0.812892\pi$
$521$	−37.9885	−1.66431	−0.832154	+	0.554545i	$0.812892\pi$
$522$	−14.8727	−0.650962
$523$	−38.4732	−1.68232	−0.841158	−	0.540789i	$-0.818126\pi$
$523$	−38.4732	−1.68232	−0.841158	+	0.540789i	$0.818126\pi$
$524$	−4.50630	−0.196859
$525$	−20.1184	−0.878038
$526$	−13.4125	−0.584814
$527$	−74.7814	−3.25753
$528$	13.5280	0.588733
$529$	52.4122	2.27879
$530$	36.0912	1.56770
$531$	4.37087	0.189680
$532$	0.613664	0.0266057
$533$	60.3312	2.61323
$534$	−28.3588	−1.22720
$535$	25.4763	1.10144
$536$	−1.00141	−0.0432541
$537$	−10.8654	−0.468878
$538$	−29.6521	−1.27839
$539$	−44.0419	−1.89702
$540$	6.88319	0.296206
$541$	−15.1608	−0.651813	−0.325906	−	0.945402i	$-0.605669\pi$
$541$	−15.1608	−0.651813	−0.325906	+	0.945402i	$0.605669\pi$
$542$	1.46321	0.0628503
$543$	18.7704	0.805517
$544$	−8.03614	−0.344547
$545$	2.26787	0.0971449
$546$	−47.8885	−2.04944
$547$	9.22432	0.394403	0.197202	−	0.980363i	$-0.436815\pi$
$547$	9.22432	0.394403	0.197202	+	0.980363i	$0.436815\pi$
$548$	−22.5635	−0.963863
$549$	−5.68815	−0.242764
$550$	−14.8956	−0.635151
$551$	−1.30804	−0.0557245
$552$	−19.1314	−0.814285
$553$	5.91946	0.251721
$554$	−28.9576	−1.23029
$555$	12.1105	0.514064
$556$	9.95987	0.422392
$557$	−19.0038	−0.805216	−0.402608	−	0.915373i	$-0.631896\pi$
$557$	−19.0038	−0.805216	−0.402608	+	0.915373i	$0.631896\pi$
$558$	17.2475	0.730145
$559$	47.4622	2.00744
$560$	10.2586	0.433507
$561$	−108.713	−4.58988
$562$	−16.0950	−0.678928
$563$	34.7433	1.46426	0.732128	−	0.681167i	$-0.238527\pi$
$563$	34.7433	1.46426	0.732128	+	0.681167i	$0.238527\pi$
$564$	14.8757	0.626378
$565$	3.20012	0.134630
$566$	6.41954	0.269833
$567$	−41.8815	−1.75886
$568$	3.15229	0.132267
$569$	40.6198	1.70287	0.851435	−	0.524461i	$-0.175733\pi$
$569$	40.6198	1.70287	0.851435	+	0.524461i	$0.175733\pi$
$570$	−0.978604	−0.0409892
$571$	10.4289	0.436435	0.218218	−	0.975900i	$-0.429976\pi$
$571$	10.4289	0.436435	0.218218	+	0.975900i	$0.429976\pi$
$572$	−35.4565	−1.48251
$573$	−8.08047	−0.337566
$574$	39.3346	1.64179
$575$	21.0654	0.878487
$576$	1.85345	0.0772269
$577$	−1.76772	−0.0735911	−0.0367956	−	0.999323i	$-0.511715\pi$
$577$	−1.76772	−0.0735911	−0.0367956	+	0.999323i	$0.511715\pi$
$578$	47.5796	1.97905
$579$	16.3135	0.677966
$580$	−21.8666	−0.907961
$581$	−55.3195	−2.29504
$582$	2.40606	0.0997346
$583$	−81.3281	−3.36826
$584$	−3.71808	−0.153855
$585$	29.1633	1.20575
$586$	18.5082	0.764567
$587$	−26.1871	−1.08086	−0.540430	−	0.841389i	$-0.681738\pi$
$587$	−26.1871	−1.08086	−0.540430	+	0.841389i	$0.681738\pi$
$588$	−15.8009	−0.651617
$589$	1.51690	0.0625028
$590$	6.42626	0.264565
$591$	−13.1323	−0.540191
$592$	−2.01729	−0.0829100
$593$	30.1901	1.23976	0.619880	−	0.784697i	$-0.287181\pi$
$593$	30.1901	1.23976	0.619880	+	0.784697i	$0.287181\pi$
$594$	−15.5106	−0.636409
$595$	−82.4399	−3.37971
$596$	8.22599	0.336950
$597$	−22.2060	−0.908830
$598$	50.1426	2.05048
$599$	14.1427	0.577854	0.288927	−	0.957351i	$-0.406701\pi$
$599$	14.1427	0.577854	0.288927	+	0.957351i	$0.406701\pi$
$600$	−5.34409	−0.218171
$601$	−11.0104	−0.449125	−0.224563	−	0.974460i	$-0.572095\pi$
$601$	−11.0104	−0.449125	−0.224563	+	0.974460i	$0.572095\pi$
$602$	30.9443	1.26120
$603$	−1.85605	−0.0755843
$604$	16.5404	0.673020
$605$	72.7768	2.95880
$606$	9.77254	0.396982
$607$	39.7705	1.61423	0.807117	−	0.590391i	$-0.201027\pi$
$607$	39.7705	1.61423	0.807117	+	0.590391i	$0.201027\pi$
$608$	0.163009	0.00661089
$609$	66.5511	2.69679
$610$	−8.36299	−0.338608
$611$	−38.9886	−1.57731
$612$	−14.8946	−0.602077
$613$	0.482662	0.0194945	0.00974727	−	0.999952i	$-0.496897\pi$
$613$	0.482662	0.0194945	0.00974727	+	0.999952i	$0.496897\pi$
$614$	−15.1239	−0.610352
$615$	−62.7265	−2.52938
$616$	−23.1169	−0.931406
$617$	19.7699	0.795906	0.397953	−	0.917406i	$-0.369721\pi$
$617$	19.7699	0.795906	0.397953	+	0.917406i	$0.369721\pi$
$618$	−10.0423	−0.403960
$619$	0.328244	0.0131933	0.00659663	−	0.999978i	$-0.497900\pi$
$619$	0.328244	0.0131933	0.00659663	+	0.999978i	$0.497900\pi$
$620$	25.3581	1.01841
$621$	21.9351	0.880226
$622$	26.8651	1.07719
$623$	48.4598	1.94150
$624$	−12.7207	−0.509236
$625$	−31.2445	−1.24978
$626$	−29.4601	−1.17746
$627$	2.20519	0.0880669
$628$	−12.5434	−0.500537
$629$	16.2112	0.646383
$630$	19.0139	0.757530
$631$	−10.8369	−0.431411	−0.215706	−	0.976458i	$-0.569205\pi$
$631$	−10.8369	−0.431411	−0.215706	+	0.976458i	$0.569205\pi$
$632$	1.57240	0.0625467
$633$	−13.0537	−0.518839
$634$	0.461533	0.0183298
$635$	14.6029	0.579499
$636$	−29.1780	−1.15698
$637$	41.4135	1.64086
$638$	49.2743	1.95079
$639$	5.84260	0.231130
$640$	2.72503	0.107716
$641$	26.9331	1.06379	0.531896	−	0.846810i	$-0.321480\pi$
$641$	26.9331	1.06379	0.531896	+	0.846810i	$0.321480\pi$
$642$	−20.5964	−0.812874
$643$	35.7849	1.41122	0.705610	−	0.708600i	$-0.250673\pi$
$643$	35.7849	1.41122	0.705610	+	0.708600i	$0.250673\pi$
$644$	32.6919	1.28824
$645$	−49.3466	−1.94302
$646$	−1.30996	−0.0515398
$647$	−24.4926	−0.962905	−0.481452	−	0.876472i	$-0.659891\pi$
$647$	−24.4926	−0.962905	−0.481452	+	0.876472i	$0.659891\pi$
$648$	−11.1251	−0.437034
$649$	−14.4810	−0.568428
$650$	14.0067	0.549387
$651$	−77.1775	−3.02482
$652$	13.3990	0.524744
$653$	2.23095	0.0873039	0.0436520	−	0.999047i	$-0.486101\pi$
$653$	2.23095	0.0873039	0.0436520	+	0.999047i	$0.486101\pi$
$654$	−1.83347	−0.0716942
$655$	−12.2798	−0.479811
$656$	10.4485	0.407947
$657$	−6.89127	−0.268854
$658$	−25.4197	−0.990963
$659$	−13.2208	−0.515009	−0.257504	−	0.966277i	$-0.582900\pi$
$659$	−13.2208	−0.515009	−0.257504	+	0.966277i	$0.582900\pi$
$660$	36.8643	1.43494
$661$	−6.59305	−0.256440	−0.128220	−	0.991746i	$-0.540926\pi$
$661$	−6.59305	−0.256440	−0.128220	+	0.991746i	$0.540926\pi$
$662$	12.0316	0.467623
$663$	102.225	3.97011
$664$	−14.6946	−0.570262
$665$	1.67225	0.0648471
$666$	−3.73893	−0.144881
$667$	−69.6837	−2.69817
$668$	−6.17103	−0.238764
$669$	−30.8071	−1.19107
$670$	−2.72886	−0.105425
$671$	18.8452	0.727512
$672$	−8.29363	−0.319934
$673$	−27.9116	−1.07591	−0.537956	−	0.842973i	$-0.680803\pi$
$673$	−27.9116	−1.07591	−0.537956	+	0.842973i	$0.680803\pi$
$674$	1.50816	0.0580922
$675$	6.12728	0.235839
$676$	20.3405	0.782328
$677$	−40.6441	−1.56208	−0.781040	−	0.624481i	$-0.785310\pi$
$677$	−40.6441	−1.56208	−0.781040	+	0.624481i	$0.785310\pi$
$678$	−2.58715	−0.0993589
$679$	−4.11151	−0.157785
$680$	−21.8987	−0.839776
$681$	16.8935	0.647359
$682$	−57.1421	−2.18808
$683$	−19.4564	−0.744480	−0.372240	−	0.928136i	$-0.621410\pi$
$683$	−19.4564	−0.744480	−0.372240	+	0.928136i	$0.621410\pi$
$684$	0.302128	0.0115522
$685$	−61.4860	−2.34926
$686$	0.648489	0.0247594
$687$	32.9480	1.25704
$688$	8.21980	0.313377
$689$	76.4745	2.91345
$690$	−52.1334	−1.98469
$691$	−45.6056	−1.73492	−0.867460	−	0.497507i	$-0.834249\pi$
$691$	−45.6056	−1.73492	−0.867460	+	0.497507i	$0.834249\pi$
$692$	8.39281	0.319047
$693$	−42.8459	−1.62758
$694$	−12.2609	−0.465418
$695$	27.1409	1.02951
$696$	17.6781	0.670087
$697$	−83.9659	−3.18043
$698$	−12.0392	−0.455690
$699$	−11.3280	−0.428463
$700$	9.13205	0.345159
$701$	−38.3771	−1.44948	−0.724741	−	0.689022i	$-0.758040\pi$
$701$	−38.3771	−1.44948	−0.724741	+	0.689022i	$0.758040\pi$
$702$	14.5850	0.550474
$703$	−0.328836	−0.0124023
$704$	−6.14059	−0.231432
$705$	40.5365	1.52669
$706$	8.94094	0.336497
$707$	−16.6994	−0.628047
$708$	−5.19533	−0.195252
$709$	−36.2722	−1.36223	−0.681116	−	0.732175i	$-0.738505\pi$
$709$	−36.2722	−1.36223	−0.681116	+	0.732175i	$0.738505\pi$
$710$	8.59006	0.322379
$711$	2.91436	0.109297
$712$	12.8725	0.482417
$713$	80.8103	3.02637
$714$	66.6488	2.49427
$715$	−96.6200	−3.61338
$716$	4.93199	0.184317
$717$	14.5202	0.542265
$718$	−2.81302	−0.104981
$719$	−41.7817	−1.55820	−0.779098	−	0.626902i	$-0.784323\pi$
$719$	−41.7817	−1.55820	−0.779098	+	0.626902i	$0.784323\pi$
$720$	5.05069	0.188228
$721$	17.1604	0.639085
$722$	−18.9734	−0.706118
$723$	−10.2463	−0.381065
$724$	−8.52019	−0.316650
$725$	−19.4652	−0.722920
$726$	−58.8366	−2.18363
$727$	−18.1411	−0.672815	−0.336407	−	0.941717i	$-0.609212\pi$
$727$	−18.1411	−0.672815	−0.336407	+	0.941717i	$0.609212\pi$
$728$	21.7373	0.805638
$729$	−3.92552	−0.145390
$730$	−10.1319	−0.374997
$731$	−66.0555	−2.44315
$732$	6.76108	0.249897
$733$	−7.96459	−0.294179	−0.147089	−	0.989123i	$-0.546991\pi$
$733$	−7.96459	−0.294179	−0.147089	+	0.989123i	$0.546991\pi$
$734$	14.5154	0.535773
$735$	−43.0578	−1.58821
$736$	8.68402	0.320097
$737$	6.14922	0.226510
$738$	19.3658	0.712865
$739$	6.29759	0.231661	0.115830	−	0.993269i	$-0.463047\pi$
$739$	6.29759	0.231661	0.115830	+	0.993269i	$0.463047\pi$
$740$	−5.49716	−0.202080
$741$	−2.07359	−0.0761752
$742$	49.8597	1.83041
$743$	3.77882	0.138632	0.0693158	−	0.997595i	$-0.477918\pi$
$743$	3.77882	0.138632	0.0693158	+	0.997595i	$0.477918\pi$
$744$	−20.5008	−0.751596
$745$	22.4160	0.821260
$746$	23.3194	0.853783
$747$	−27.2357	−0.996502
$748$	49.3466	1.80429
$749$	35.1953	1.28601
$750$	15.4541	0.564304
$751$	−41.1796	−1.50266	−0.751332	−	0.659924i	$-0.770588\pi$
$751$	−41.1796	−1.50266	−0.751332	+	0.659924i	$0.770588\pi$
$752$	−6.75229	−0.246231
$753$	−41.8386	−1.52468
$754$	−46.3337	−1.68737
$755$	45.0730	1.64038
$756$	9.50909	0.345842
$757$	13.3600	0.485576	0.242788	−	0.970079i	$-0.421938\pi$
$757$	13.3600	0.485576	0.242788	+	0.970079i	$0.421938\pi$
$758$	−24.2526	−0.880895
$759$	117.478	4.26417
$760$	0.444204	0.0161130
$761$	−34.9631	−1.26741	−0.633705	−	0.773574i	$-0.718467\pi$
$761$	−34.9631	−1.26741	−0.633705	+	0.773574i	$0.718467\pi$
$762$	−11.8058	−0.427678
$763$	3.13305	0.113424
$764$	3.66785	0.132698
$765$	−40.5880	−1.46746
$766$	−14.6932	−0.530887
$767$	13.6168	0.491673
$768$	−2.20305	−0.0794959
$769$	−43.8693	−1.58197	−0.790983	−	0.611838i	$-0.790430\pi$
$769$	−43.8693	−1.58197	−0.790983	+	0.611838i	$0.790430\pi$
$770$	−62.9941	−2.27015
$771$	−22.0698	−0.794825
$772$	−7.40495	−0.266510
$773$	37.0178	1.33144	0.665720	−	0.746202i	$-0.268125\pi$
$773$	37.0178	1.33144	0.665720	+	0.746202i	$0.268125\pi$
$774$	15.2350	0.547610
$775$	22.5733	0.810856
$776$	−1.09215	−0.0392059
$777$	16.7306	0.600208
$778$	−32.4603	−1.16376
$779$	1.70320	0.0610236
$780$	−34.6643	−1.24118
$781$	−19.3569	−0.692644
$782$	−69.7860	−2.49554
$783$	−20.2689	−0.724351
$784$	7.17226	0.256152
$785$	−34.1811	−1.21998
$786$	9.92763	0.354107
$787$	8.88185	0.316604	0.158302	−	0.987391i	$-0.449398\pi$
$787$	8.88185	0.316604	0.158302	+	0.987391i	$0.449398\pi$
$788$	5.96096	0.212350
$789$	29.5485	1.05195
$790$	4.28483	0.152447
$791$	4.42095	0.157191
$792$	−11.3813	−0.404415
$793$	−17.7206	−0.629276
$794$	37.9889	1.34818
$795$	−79.5108	−2.81996
$796$	10.0796	0.357263
$797$	23.4149	0.829398	0.414699	−	0.909959i	$-0.363887\pi$
$797$	23.4149	0.829398	0.414699	+	0.909959i	$0.363887\pi$
$798$	−1.35194	−0.0478580
$799$	54.2623	1.91966
$800$	2.42576	0.0857637
$801$	23.8585	0.842997
$802$	−2.61530	−0.0923493
$803$	22.8312	0.805696
$804$	2.20615	0.0778050
$805$	89.0863	3.13988
$806$	53.7319	1.89263
$807$	65.3251	2.29955
$808$	−4.43590	−0.156055
$809$	−19.8475	−0.697802	−0.348901	−	0.937160i	$-0.613445\pi$
$809$	−19.8475	−0.697802	−0.348901	+	0.937160i	$0.613445\pi$
$810$	−30.3161	−1.06520
$811$	−28.0381	−0.984551	−0.492275	−	0.870440i	$-0.663835\pi$
$811$	−28.0381	−0.984551	−0.492275	+	0.870440i	$0.663835\pi$
$812$	−30.2086	−1.06011
$813$	−3.22353	−0.113054
$814$	12.3873	0.434176
$815$	36.5125	1.27898
$816$	17.7041	0.619766
$817$	1.33990	0.0468772
$818$	2.63391	0.0920926
$819$	40.2889	1.40781
$820$	28.4725	0.994303
$821$	−2.58290	−0.0901438	−0.0450719	−	0.998984i	$-0.514352\pi$
$821$	−2.58290	−0.0901438	−0.0450719	+	0.998984i	$0.514352\pi$
$822$	49.7085	1.73378
$823$	−16.2220	−0.565464	−0.282732	−	0.959199i	$-0.591241\pi$
$823$	−16.2220	−0.565464	−0.282732	+	0.959199i	$0.591241\pi$
$824$	4.55834	0.158797
$825$	32.8159	1.14250
$826$	8.87784	0.308900
$827$	13.2507	0.460773	0.230386	−	0.973099i	$-0.426001\pi$
$827$	13.2507	0.460773	0.230386	+	0.973099i	$0.426001\pi$
$828$	16.0954	0.559353
$829$	3.47039	0.120532	0.0602658	−	0.998182i	$-0.480805\pi$
$829$	3.47039	0.120532	0.0602658	+	0.998182i	$0.480805\pi$
$830$	−40.0432	−1.38992
$831$	63.7952	2.21303
$832$	5.77413	0.200182
$833$	−57.6373	−1.99701
$834$	−21.9421	−0.759794
$835$	−16.8162	−0.581949
$836$	−1.00097	−0.0346193
$837$	23.5053	0.812461
$838$	−5.77310	−0.199428
$839$	13.5971	0.469423	0.234712	−	0.972065i	$-0.424585\pi$
$839$	13.5971	0.469423	0.234712	+	0.972065i	$0.424585\pi$
$840$	−22.6004	−0.779786
$841$	35.3904	1.22036
$842$	20.6728	0.712433
$843$	35.4582	1.22125
$844$	5.92529	0.203957
$845$	55.4285	1.90680
$846$	−12.5150	−0.430275
$847$	100.541	3.45462
$848$	13.2443	0.454813
$849$	−14.1426	−0.485372
$850$	−19.4938	−0.668631
$851$	−17.5182	−0.600515
$852$	−6.94466	−0.237920
$853$	−33.8743	−1.15984	−0.579918	−	0.814675i	$-0.696915\pi$
$853$	−33.8743	−1.15984	−0.579918	+	0.814675i	$0.696915\pi$
$854$	−11.5534	−0.395350
$855$	0.823307	0.0281565
$856$	9.34901	0.319543
$857$	14.8521	0.507337	0.253669	−	0.967291i	$-0.418363\pi$
$857$	14.8521	0.507337	0.253669	+	0.967291i	$0.418363\pi$
$858$	78.1127	2.66672
$859$	38.0271	1.29747	0.648734	−	0.761015i	$-0.275299\pi$
$859$	38.0271	1.29747	0.648734	+	0.761015i	$0.275299\pi$
$860$	22.3992	0.763806
$861$	−86.6563	−2.95324
$862$	19.0374	0.648415
$863$	−11.2269	−0.382169	−0.191084	−	0.981574i	$-0.561200\pi$
$863$	−11.2269	−0.382169	−0.191084	+	0.981574i	$0.561200\pi$
$864$	2.52592	0.0859335
$865$	22.8706	0.777624
$866$	−3.46686	−0.117809
$867$	−104.820	−3.55988
$868$	35.0320	1.18907
$869$	−9.65546	−0.327539
$870$	48.1733	1.63323
$871$	−5.78224	−0.195924
$872$	0.832238	0.0281831
$873$	−2.02424	−0.0685102
$874$	1.41557	0.0478825
$875$	−26.4082	−0.892760
$876$	8.19114	0.276753
$877$	−19.7463	−0.666784	−0.333392	−	0.942788i	$-0.608193\pi$
$877$	−19.7463	−0.666784	−0.333392	+	0.942788i	$0.608193\pi$
$878$	13.2589	0.447468
$879$	−40.7746	−1.37529
$880$	−16.7333	−0.564078
$881$	−5.97119	−0.201175	−0.100587	−	0.994928i	$-0.532072\pi$
$881$	−5.97119	−0.201175	−0.100587	+	0.994928i	$0.532072\pi$
$882$	13.2934	0.447612
$883$	−35.7805	−1.20411	−0.602055	−	0.798454i	$-0.705651\pi$
$883$	−35.7805	−1.20411	−0.602055	+	0.798454i	$0.705651\pi$
$884$	−46.4017	−1.56066
$885$	−14.1574	−0.475896
$886$	−13.3697	−0.449164
$887$	47.9737	1.61080	0.805400	−	0.592731i	$-0.201950\pi$
$887$	47.9737	1.61080	0.805400	+	0.592731i	$0.201950\pi$
$888$	4.44419	0.149137
$889$	20.1738	0.676609
$890$	35.0779	1.17581
$891$	68.3145	2.28862
$892$	13.9838	0.468213
$893$	−1.10068	−0.0368330
$894$	−18.1223	−0.606100
$895$	13.4398	0.449243
$896$	3.76461	0.125767
$897$	−110.467	−3.68838
$898$	6.78506	0.226420
$899$	−74.6718	−2.49044
$900$	4.49602	0.149867
$901$	−106.433	−3.54581
$902$	−64.1601	−2.13630
$903$	−68.1720	−2.26862
$904$	1.17435	0.0390582
$905$	−23.2177	−0.771784
$906$	−36.4394	−1.21062
$907$	44.5313	1.47864	0.739319	−	0.673355i	$-0.235148\pi$
$907$	44.5313	1.47864	0.739319	+	0.673355i	$0.235148\pi$
$908$	−7.66821	−0.254478
$909$	−8.22171	−0.272697
$910$	59.2347	1.96361
$911$	−35.9688	−1.19170	−0.595849	−	0.803096i	$-0.703184\pi$
$911$	−35.9688	−1.19170	−0.595849	+	0.803096i	$0.703184\pi$
$912$	−0.359118	−0.0118916
$913$	90.2337	2.98630
$914$	−34.5478	−1.14274
$915$	18.4241	0.609083
$916$	−14.9556	−0.494147
$917$	−16.9645	−0.560216
$918$	−20.2986	−0.669955
$919$	−37.7332	−1.24470	−0.622351	−	0.782738i	$-0.713822\pi$
$919$	−37.7332	−1.24470	−0.622351	+	0.782738i	$0.713822\pi$
$920$	23.6642	0.780185
$921$	33.3188	1.09789
$922$	−13.2062	−0.434922
$923$	18.2017	0.599117
$924$	50.9278	1.67540
$925$	−4.89346	−0.160896
$926$	15.9853	0.525308
$927$	8.44864	0.277490
$928$	−8.02437	−0.263413
$929$	−4.06157	−0.133256	−0.0666280	−	0.997778i	$-0.521224\pi$
$929$	−4.06157	−0.133256	−0.0666280	+	0.997778i	$0.521224\pi$
$930$	−55.8652	−1.83189
$931$	1.16914	0.0383171
$932$	5.14194	0.168430
$933$	−59.1853	−1.93764
$934$	−10.7310	−0.351129
$935$	134.471	4.39767
$936$	10.7020	0.349807
$937$	−19.0541	−0.622469	−0.311234	−	0.950333i	$-0.600742\pi$
$937$	−19.0541	−0.622469	−0.311234	+	0.950333i	$0.600742\pi$
$938$	−3.76990	−0.123092
$939$	64.9021	2.11800
$940$	−18.4002	−0.600147
$941$	8.55584	0.278912	0.139456	−	0.990228i	$-0.455465\pi$
$941$	8.55584	0.278912	0.139456	+	0.990228i	$0.455465\pi$
$942$	27.6338	0.900358
$943$	90.7353	2.95475
$944$	2.35824	0.0767542
$945$	25.9125	0.842934
$946$	−50.4744	−1.64107
$947$	−30.2956	−0.984474	−0.492237	−	0.870461i	$-0.663821\pi$
$947$	−30.2956	−0.984474	−0.492237	+	0.870461i	$0.663821\pi$
$948$	−3.46408	−0.112508
$949$	−21.4687	−0.696903
$950$	0.395421	0.0128292
$951$	−1.01678	−0.0329714
$952$	−30.2529	−0.980502
$953$	−12.3052	−0.398606	−0.199303	−	0.979938i	$-0.563868\pi$
$953$	−12.3052	−0.398606	−0.199303	+	0.979938i	$0.563868\pi$
$954$	24.5477	0.794760
$955$	9.99498	0.323430
$956$	−6.59092	−0.213166
$957$	−108.554	−3.50905
$958$	11.3778	0.367600
$959$	−84.9425	−2.74294
$960$	−6.00338	−0.193758
$961$	55.5948	1.79338
$962$	−11.6481	−0.375549
$963$	17.3279	0.558383
$964$	4.65097	0.149798
$965$	−20.1787	−0.649575
$966$	−72.0220	−2.31727
$967$	−23.5679	−0.757894	−0.378947	−	0.925418i	$-0.623714\pi$
$967$	−23.5679	−0.757894	−0.378947	+	0.925418i	$0.623714\pi$
$968$	26.7068	0.858390
$969$	2.88592	0.0927091
$970$	−2.97614	−0.0955580
$971$	−15.5342	−0.498516	−0.249258	−	0.968437i	$-0.580187\pi$
$971$	−15.5342	−0.498516	−0.249258	+	0.968437i	$0.580187\pi$
$972$	16.9314	0.543074
$973$	37.4950	1.20203
$974$	−15.5016	−0.496702
$975$	−30.8574	−0.988229
$976$	−3.06896	−0.0982350
$977$	0.655691	0.0209774	0.0104887	−	0.999945i	$-0.496661\pi$
$977$	0.655691	0.0209774	0.0104887	+	0.999945i	$0.496661\pi$
$978$	−29.5186	−0.943902
$979$	−79.0446	−2.52628
$980$	19.5446	0.624329
$981$	1.54251	0.0492485
$982$	−0.433207	−0.0138242
$983$	−17.5727	−0.560483	−0.280241	−	0.959930i	$-0.590415\pi$
$983$	−17.5727	−0.560483	−0.280241	+	0.959930i	$0.590415\pi$
$984$	−23.0187	−0.733809
$985$	16.2438	0.517570
$986$	64.4849	2.05362
$987$	56.0010	1.78253
$988$	0.941234	0.0299447
$989$	71.3809	2.26978
$990$	−31.0142	−0.985696
$991$	−15.4397	−0.490459	−0.245230	−	0.969465i	$-0.578863\pi$
$991$	−15.4397	−0.490459	−0.245230	+	0.969465i	$0.578863\pi$
$992$	9.30563	0.295454
$993$	−26.5064	−0.841154
$994$	11.8671	0.376402
$995$	27.4673	0.870771
$996$	32.3731	1.02578
$997$	6.94694	0.220012	0.110006	−	0.993931i	$-0.464913\pi$
$997$	6.94694	0.220012	0.110006	+	0.993931i	$0.464913\pi$
$998$	−34.0835	−1.07889
$999$	−5.09550	−0.161215

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.9	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.9	✓	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.20305 q^{3} +1.00000 q^{4} +2.72503 q^{5} -2.20305 q^{6} +3.76461 q^{7} +1.00000 q^{8} +1.85345 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.20305 q^{3} +1.00000 q^{4} +2.72503 q^{5} -2.20305 q^{6} +3.76461 q^{7} +1.00000 q^{8} +1.85345 q^{9} +2.72503 q^{10} -6.14059 q^{11} -2.20305 q^{12} +5.77413 q^{13} +3.76461 q^{14} -6.00338 q^{15} +1.00000 q^{16} -8.03614 q^{17} +1.85345 q^{18} +0.163009 q^{19} +2.72503 q^{20} -8.29363 q^{21} -6.14059 q^{22} +8.68402 q^{23} -2.20305 q^{24} +2.42576 q^{25} +5.77413 q^{26} +2.52592 q^{27} +3.76461 q^{28} -8.02437 q^{29} -6.00338 q^{30} +9.30563 q^{31} +1.00000 q^{32} +13.5280 q^{33} -8.03614 q^{34} +10.2586 q^{35} +1.85345 q^{36} -2.01729 q^{37} +0.163009 q^{38} -12.7207 q^{39} +2.72503 q^{40} +10.4485 q^{41} -8.29363 q^{42} +8.21980 q^{43} -6.14059 q^{44} +5.05069 q^{45} +8.68402 q^{46} -6.75229 q^{47} -2.20305 q^{48} +7.17226 q^{49} +2.42576 q^{50} +17.7041 q^{51} +5.77413 q^{52} +13.2443 q^{53} +2.52592 q^{54} -16.7333 q^{55} +3.76461 q^{56} -0.359118 q^{57} -8.02437 q^{58} +2.35824 q^{59} -6.00338 q^{60} -3.06896 q^{61} +9.30563 q^{62} +6.97750 q^{63} +1.00000 q^{64} +15.7346 q^{65} +13.5280 q^{66} -1.00141 q^{67} -8.03614 q^{68} -19.1314 q^{69} +10.2586 q^{70} +3.15229 q^{71} +1.85345 q^{72} -3.71808 q^{73} -2.01729 q^{74} -5.34409 q^{75} +0.163009 q^{76} -23.1169 q^{77} -12.7207 q^{78} +1.57240 q^{79} +2.72503 q^{80} -11.1251 q^{81} +10.4485 q^{82} -14.6946 q^{83} -8.29363 q^{84} -21.8987 q^{85} +8.21980 q^{86} +17.6781 q^{87} -6.14059 q^{88} +12.8725 q^{89} +5.05069 q^{90} +21.7373 q^{91} +8.68402 q^{92} -20.5008 q^{93} -6.75229 q^{94} +0.444204 q^{95} -2.20305 q^{96} -1.09215 q^{97} +7.17226 q^{98} -11.3813 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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