LMFDB - Embedded newform 8043.2.a.o.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07017 q^{2} -1.00000 q^{3} +2.28561 q^{4} +2.60848 q^{5} +2.07017 q^{6} +1.00000 q^{7} -0.591253 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.07017 q^{2} -1.00000 q^{3} +2.28561 q^{4} +2.60848 q^{5} +2.07017 q^{6} +1.00000 q^{7} -0.591253 q^{8} +1.00000 q^{9} -5.40001 q^{10} -3.64355 q^{11} -2.28561 q^{12} +5.83645 q^{13} -2.07017 q^{14} -2.60848 q^{15} -3.34722 q^{16} -5.59112 q^{17} -2.07017 q^{18} -4.09194 q^{19} +5.96197 q^{20} -1.00000 q^{21} +7.54277 q^{22} +9.10416 q^{23} +0.591253 q^{24} +1.80419 q^{25} -12.0824 q^{26} -1.00000 q^{27} +2.28561 q^{28} -2.10969 q^{29} +5.40001 q^{30} -8.26629 q^{31} +8.11182 q^{32} +3.64355 q^{33} +11.5746 q^{34} +2.60848 q^{35} +2.28561 q^{36} -3.27225 q^{37} +8.47102 q^{38} -5.83645 q^{39} -1.54228 q^{40} +0.0750955 q^{41} +2.07017 q^{42} +2.15544 q^{43} -8.32772 q^{44} +2.60848 q^{45} -18.8472 q^{46} +6.51153 q^{47} +3.34722 q^{48} +1.00000 q^{49} -3.73499 q^{50} +5.59112 q^{51} +13.3398 q^{52} +0.620829 q^{53} +2.07017 q^{54} -9.50414 q^{55} -0.591253 q^{56} +4.09194 q^{57} +4.36742 q^{58} -4.96605 q^{59} -5.96197 q^{60} +4.16515 q^{61} +17.1126 q^{62} +1.00000 q^{63} -10.0984 q^{64} +15.2243 q^{65} -7.54277 q^{66} +6.27465 q^{67} -12.7791 q^{68} -9.10416 q^{69} -5.40001 q^{70} +1.99897 q^{71} -0.591253 q^{72} -9.21256 q^{73} +6.77411 q^{74} -1.80419 q^{75} -9.35257 q^{76} -3.64355 q^{77} +12.0824 q^{78} -14.2317 q^{79} -8.73117 q^{80} +1.00000 q^{81} -0.155460 q^{82} +14.0763 q^{83} -2.28561 q^{84} -14.5844 q^{85} -4.46213 q^{86} +2.10969 q^{87} +2.15426 q^{88} -9.13783 q^{89} -5.40001 q^{90} +5.83645 q^{91} +20.8085 q^{92} +8.26629 q^{93} -13.4800 q^{94} -10.6738 q^{95} -8.11182 q^{96} +6.91714 q^{97} -2.07017 q^{98} -3.64355 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.07017	−1.46383	−0.731916	−	0.681395i	$-0.761374\pi$
$2$	−2.07017	−1.46383	−0.731916	+	0.681395i	$0.761374\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.28561	1.14280
$5$	2.60848	1.16655	0.583275	−	0.812275i	$-0.301771\pi$
$5$	2.60848	1.16655	0.583275	+	0.812275i	$0.301771\pi$
$6$	2.07017	0.845144
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.591253	−0.209040
$9$	1.00000	0.333333
$10$	−5.40001	−1.70763
$11$	−3.64355	−1.09857	−0.549286	−	0.835635i	$-0.685100\pi$
$11$	−3.64355	−1.09857	−0.549286	+	0.835635i	$0.685100\pi$
$12$	−2.28561	−0.659798
$13$	5.83645	1.61874	0.809369	−	0.587300i	$-0.199809\pi$
$13$	5.83645	1.61874	0.809369	+	0.587300i	$0.199809\pi$
$14$	−2.07017	−0.553276
$15$	−2.60848	−0.673508
$16$	−3.34722	−0.836804
$17$	−5.59112	−1.35605	−0.678023	−	0.735041i	$-0.737163\pi$
$17$	−5.59112	−1.35605	−0.678023	+	0.735041i	$0.737163\pi$
$18$	−2.07017	−0.487944
$19$	−4.09194	−0.938756	−0.469378	−	0.882997i	$-0.655522\pi$
$19$	−4.09194	−0.938756	−0.469378	+	0.882997i	$0.655522\pi$
$20$	5.96197	1.33314
$21$	−1.00000	−0.218218
$22$	7.54277	1.60812
$23$	9.10416	1.89835	0.949174	−	0.314752i	$-0.101921\pi$
$23$	9.10416	1.89835	0.949174	+	0.314752i	$0.101921\pi$
$24$	0.591253	0.120689
$25$	1.80419	0.360839
$26$	−12.0824	−2.36956
$27$	−1.00000	−0.192450
$28$	2.28561	0.431939
$29$	−2.10969	−0.391760	−0.195880	−	0.980628i	$-0.562756\pi$
$29$	−2.10969	−0.391760	−0.195880	+	0.980628i	$0.562756\pi$
$30$	5.40001	0.985902
$31$	−8.26629	−1.48467	−0.742335	−	0.670029i	$-0.766282\pi$
$31$	−8.26629	−1.48467	−0.742335	+	0.670029i	$0.766282\pi$
$32$	8.11182	1.43398
$33$	3.64355	0.634261
$34$	11.5746	1.98502
$35$	2.60848	0.440914
$36$	2.28561	0.380934
$37$	−3.27225	−0.537954	−0.268977	−	0.963147i	$-0.586686\pi$
$37$	−3.27225	−0.537954	−0.268977	+	0.963147i	$0.586686\pi$
$38$	8.47102	1.37418
$39$	−5.83645	−0.934579
$40$	−1.54228	−0.243855
$41$	0.0750955	0.0117279	0.00586397	−	0.999983i	$-0.498133\pi$
$41$	0.0750955	0.0117279	0.00586397	+	0.999983i	$0.498133\pi$
$42$	2.07017	0.319434
$43$	2.15544	0.328702	0.164351	−	0.986402i	$-0.447447\pi$
$43$	2.15544	0.328702	0.164351	+	0.986402i	$0.447447\pi$
$44$	−8.32772	−1.25545
$45$	2.60848	0.388850
$46$	−18.8472	−2.77886
$47$	6.51153	0.949804	0.474902	−	0.880039i	$-0.342483\pi$
$47$	6.51153	0.949804	0.474902	+	0.880039i	$0.342483\pi$
$48$	3.34722	0.483129
$49$	1.00000	0.142857
$50$	−3.73499	−0.528207
$51$	5.59112	0.782913
$52$	13.3398	1.84990
$53$	0.620829	0.0852774	0.0426387	−	0.999091i	$-0.486424\pi$
$53$	0.620829	0.0852774	0.0426387	+	0.999091i	$0.486424\pi$
$54$	2.07017	0.281715
$55$	−9.50414	−1.28154
$56$	−0.591253	−0.0790095
$57$	4.09194	0.541991
$58$	4.36742	0.573470
$59$	−4.96605	−0.646524	−0.323262	−	0.946309i	$-0.604780\pi$
$59$	−4.96605	−0.646524	−0.323262	+	0.946309i	$0.604780\pi$
$60$	−5.96197	−0.769687
$61$	4.16515	0.533293	0.266646	−	0.963794i	$-0.414084\pi$
$61$	4.16515	0.533293	0.266646	+	0.963794i	$0.414084\pi$
$62$	17.1126	2.17331
$63$	1.00000	0.125988
$64$	−10.0984	−1.26230
$65$	15.2243	1.88834
$66$	−7.54277	−0.928451
$67$	6.27465	0.766571	0.383285	−	0.923630i	$-0.374793\pi$
$67$	6.27465	0.766571	0.383285	+	0.923630i	$0.374793\pi$
$68$	−12.7791	−1.54969
$69$	−9.10416	−1.09601
$70$	−5.40001	−0.645424
$71$	1.99897	0.237234	0.118617	−	0.992940i	$-0.462154\pi$
$71$	1.99897	0.237234	0.118617	+	0.992940i	$0.462154\pi$
$72$	−0.591253	−0.0696799
$73$	−9.21256	−1.07825	−0.539124	−	0.842226i	$-0.681245\pi$
$73$	−9.21256	−1.07825	−0.539124	+	0.842226i	$0.681245\pi$
$74$	6.77411	0.787474
$75$	−1.80419	−0.208330
$76$	−9.35257	−1.07281
$77$	−3.64355	−0.415221
$78$	12.0824	1.36807
$79$	−14.2317	−1.60119	−0.800597	−	0.599204i	$-0.795484\pi$
$79$	−14.2317	−1.60119	−0.800597	+	0.599204i	$0.795484\pi$
$80$	−8.73117	−0.976174
$81$	1.00000	0.111111
$82$	−0.155460	−0.0171677
$83$	14.0763	1.54507	0.772536	−	0.634970i	$-0.218988\pi$
$83$	14.0763	1.54507	0.772536	+	0.634970i	$0.218988\pi$
$84$	−2.28561	−0.249380
$85$	−14.5844	−1.58190
$86$	−4.46213	−0.481164
$87$	2.10969	0.226183
$88$	2.15426	0.229645
$89$	−9.13783	−0.968608	−0.484304	−	0.874900i	$-0.660927\pi$
$89$	−9.13783	−0.968608	−0.484304	+	0.874900i	$0.660927\pi$
$90$	−5.40001	−0.569211
$91$	5.83645	0.611826
$92$	20.8085	2.16944
$93$	8.26629	0.857174
$94$	−13.4800	−1.39035
$95$	−10.6738	−1.09511
$96$	−8.11182	−0.827909
$97$	6.91714	0.702329	0.351165	−	0.936314i	$-0.385786\pi$
$97$	6.91714	0.702329	0.351165	+	0.936314i	$0.385786\pi$
$98$	−2.07017	−0.209119
$99$	−3.64355	−0.366190
$100$	4.12368	0.412368
$101$	1.44421	0.143704	0.0718521	−	0.997415i	$-0.477109\pi$
$101$	1.44421	0.143704	0.0718521	+	0.997415i	$0.477109\pi$
$102$	−11.5746	−1.14605
$103$	3.48038	0.342932	0.171466	−	0.985190i	$-0.445150\pi$
$103$	3.48038	0.342932	0.171466	+	0.985190i	$0.445150\pi$
$104$	−3.45082	−0.338381
$105$	−2.60848	−0.254562
$106$	−1.28522	−0.124832
$107$	10.7478	1.03902	0.519512	−	0.854463i	$-0.326114\pi$
$107$	10.7478	1.03902	0.519512	+	0.854463i	$0.326114\pi$
$108$	−2.28561	−0.219933
$109$	−18.4356	−1.76581	−0.882903	−	0.469556i	$-0.844414\pi$
$109$	−18.4356	−1.76581	−0.882903	+	0.469556i	$0.844414\pi$
$110$	19.6752	1.87596
$111$	3.27225	0.310588
$112$	−3.34722	−0.316282
$113$	−14.7654	−1.38901	−0.694504	−	0.719489i	$-0.744376\pi$
$113$	−14.7654	−1.38901	−0.694504	+	0.719489i	$0.744376\pi$
$114$	−8.47102	−0.793384
$115$	23.7481	2.21452
$116$	−4.82192	−0.447704
$117$	5.83645	0.539580
$118$	10.2806	0.946403
$119$	−5.59112	−0.512537
$120$	1.54228	0.140790
$121$	2.27545	0.206859
$122$	−8.62257	−0.780651
$123$	−0.0750955	−0.00677113
$124$	−18.8935	−1.69668
$125$	−8.33621	−0.745614
$126$	−2.07017	−0.184425
$127$	−1.91048	−0.169528	−0.0847639	−	0.996401i	$-0.527014\pi$
$127$	−1.91048	−0.169528	−0.0847639	+	0.996401i	$0.527014\pi$
$128$	4.68180	0.413816
$129$	−2.15544	−0.189776
$130$	−31.5169	−2.76421
$131$	0.416522	0.0363917	0.0181959	−	0.999834i	$-0.494208\pi$
$131$	0.416522	0.0363917	0.0181959	+	0.999834i	$0.494208\pi$
$132$	8.32772	0.724835
$133$	−4.09194	−0.354817
$134$	−12.9896	−1.12213
$135$	−2.60848	−0.224503
$136$	3.30577	0.283467
$137$	−15.3600	−1.31229	−0.656146	−	0.754634i	$-0.727815\pi$
$137$	−15.3600	−1.31229	−0.656146	+	0.754634i	$0.727815\pi$
$138$	18.8472	1.60438
$139$	−5.57342	−0.472732	−0.236366	−	0.971664i	$-0.575956\pi$
$139$	−5.57342	−0.472732	−0.236366	+	0.971664i	$0.575956\pi$
$140$	5.96197	0.503878
$141$	−6.51153	−0.548370
$142$	−4.13820	−0.347270
$143$	−21.2654	−1.77830
$144$	−3.34722	−0.278935
$145$	−5.50310	−0.457007
$146$	19.0716	1.57837
$147$	−1.00000	−0.0824786
$148$	−7.47906	−0.614775
$149$	−7.33184	−0.600648	−0.300324	−	0.953837i	$-0.597095\pi$
$149$	−7.33184	−0.600648	−0.300324	+	0.953837i	$0.597095\pi$
$150$	3.73499	0.304961
$151$	−9.22621	−0.750818	−0.375409	−	0.926859i	$-0.622498\pi$
$151$	−9.22621	−0.750818	−0.375409	+	0.926859i	$0.622498\pi$
$152$	2.41938	0.196237
$153$	−5.59112	−0.452015
$154$	7.54277	0.607814
$155$	−21.5625	−1.73194
$156$	−13.3398	−1.06804
$157$	−10.4473	−0.833785	−0.416892	−	0.908956i	$-0.636881\pi$
$157$	−10.4473	−0.833785	−0.416892	+	0.908956i	$0.636881\pi$
$158$	29.4621	2.34388
$159$	−0.620829	−0.0492349
$160$	21.1596	1.67281
$161$	9.10416	0.717508
$162$	−2.07017	−0.162648
$163$	12.0003	0.939934	0.469967	−	0.882684i	$-0.344266\pi$
$163$	12.0003	0.939934	0.469967	+	0.882684i	$0.344266\pi$
$164$	0.171639	0.0134027
$165$	9.50414	0.739897
$166$	−29.1403	−2.26173
$167$	14.2824	1.10520	0.552601	−	0.833446i	$-0.313635\pi$
$167$	14.2824	1.10520	0.552601	+	0.833446i	$0.313635\pi$
$168$	0.591253	0.0456162
$169$	21.0641	1.62032
$170$	30.1921	2.31563
$171$	−4.09194	−0.312919
$172$	4.92649	0.375641
$173$	−1.18692	−0.0902399	−0.0451199	−	0.998982i	$-0.514367\pi$
$173$	−1.18692	−0.0902399	−0.0451199	+	0.998982i	$0.514367\pi$
$174$	−4.36742	−0.331093
$175$	1.80419	0.136384
$176$	12.1958	0.919289
$177$	4.96605	0.373271
$178$	18.9169	1.41788
$179$	−5.97540	−0.446622	−0.223311	−	0.974747i	$-0.571687\pi$
$179$	−5.97540	−0.446622	−0.223311	+	0.974747i	$0.571687\pi$
$180$	5.96197	0.444379
$181$	−18.3120	−1.36112	−0.680561	−	0.732691i	$-0.738264\pi$
$181$	−18.3120	−1.36112	−0.680561	+	0.732691i	$0.738264\pi$
$182$	−12.0824	−0.895610
$183$	−4.16515	−0.307897
$184$	−5.38286	−0.396830
$185$	−8.53560	−0.627550
$186$	−17.1126	−1.25476
$187$	20.3715	1.48971
$188$	14.8828	1.08544
$189$	−1.00000	−0.0727393
$190$	22.0965	1.60305
$191$	−13.7749	−0.996718	−0.498359	−	0.866971i	$-0.666064\pi$
$191$	−13.7749	−0.996718	−0.498359	+	0.866971i	$0.666064\pi$
$192$	10.0984	0.728790
$193$	−11.2959	−0.813093	−0.406547	−	0.913630i	$-0.633267\pi$
$193$	−11.2959	−0.813093	−0.406547	+	0.913630i	$0.633267\pi$
$194$	−14.3197	−1.02809
$195$	−15.2243	−1.09023
$196$	2.28561	0.163258
$197$	−9.33425	−0.665038	−0.332519	−	0.943097i	$-0.607899\pi$
$197$	−9.33425	−0.665038	−0.332519	+	0.943097i	$0.607899\pi$
$198$	7.54277	0.536041
$199$	10.0990	0.715897	0.357949	−	0.933741i	$-0.383476\pi$
$199$	10.0990	0.715897	0.357949	+	0.933741i	$0.383476\pi$
$200$	−1.06674	−0.0754296
$201$	−6.27465	−0.442580
$202$	−2.98976	−0.210359
$203$	−2.10969	−0.148071
$204$	12.7791	0.894716
$205$	0.195885	0.0136812
$206$	−7.20498	−0.501995
$207$	9.10416	0.632783
$208$	−19.5359	−1.35457
$209$	14.9092	1.03129
$210$	5.40001	0.372636
$211$	9.48283	0.652825	0.326413	−	0.945227i	$-0.394160\pi$
$211$	9.48283	0.652825	0.326413	+	0.945227i	$0.394160\pi$
$212$	1.41897	0.0974552
$213$	−1.99897	−0.136967
$214$	−22.2497	−1.52096
$215$	5.62243	0.383447
$216$	0.591253	0.0402297
$217$	−8.26629	−0.561152
$218$	38.1647	2.58484
$219$	9.21256	0.622527
$220$	−21.7227	−1.46455
$221$	−32.6323	−2.19508
$222$	−6.77411	−0.454648
$223$	−8.82137	−0.590723	−0.295361	−	0.955386i	$-0.595440\pi$
$223$	−8.82137	−0.590723	−0.295361	+	0.955386i	$0.595440\pi$
$224$	8.11182	0.541994
$225$	1.80419	0.120280
$226$	30.5668	2.03327
$227$	16.2825	1.08071	0.540355	−	0.841437i	$-0.318290\pi$
$227$	16.2825	1.08071	0.540355	+	0.841437i	$0.318290\pi$
$228$	9.35257	0.619389
$229$	−21.4643	−1.41840	−0.709201	−	0.705006i	$-0.750944\pi$
$229$	−21.4643	−1.41840	−0.709201	+	0.705006i	$0.750944\pi$
$230$	−49.1625	−3.24168
$231$	3.64355	0.239728
$232$	1.24736	0.0818933
$233$	9.70502	0.635797	0.317899	−	0.948125i	$-0.397023\pi$
$233$	9.70502	0.635797	0.317899	+	0.948125i	$0.397023\pi$
$234$	−12.0824	−0.789854
$235$	16.9852	1.10799
$236$	−11.3504	−0.738850
$237$	14.2317	0.924449
$238$	11.5746	0.750268
$239$	17.6448	1.14135	0.570673	−	0.821177i	$-0.306682\pi$
$239$	17.6448	1.14135	0.570673	+	0.821177i	$0.306682\pi$
$240$	8.73117	0.563594
$241$	6.99870	0.450826	0.225413	−	0.974263i	$-0.427627\pi$
$241$	6.99870	0.450826	0.225413	+	0.974263i	$0.427627\pi$
$242$	−4.71057	−0.302807
$243$	−1.00000	−0.0641500
$244$	9.51989	0.609449
$245$	2.60848	0.166650
$246$	0.155460	0.00991179
$247$	−23.8824	−1.51960
$248$	4.88747	0.310355
$249$	−14.0763	−0.892048
$250$	17.2574	1.09145
$251$	6.76208	0.426819	0.213409	−	0.976963i	$-0.431543\pi$
$251$	6.76208	0.426819	0.213409	+	0.976963i	$0.431543\pi$
$252$	2.28561	0.143980
$253$	−33.1714	−2.08547
$254$	3.95502	0.248160
$255$	14.5844	0.913308
$256$	10.5047	0.656544
$257$	−12.6259	−0.787579	−0.393790	−	0.919201i	$-0.628836\pi$
$257$	−12.6259	−0.787579	−0.393790	+	0.919201i	$0.628836\pi$
$258$	4.46213	0.277800
$259$	−3.27225	−0.203327
$260$	34.7967	2.15800
$261$	−2.10969	−0.130587
$262$	−0.862272	−0.0532714
$263$	−4.58564	−0.282763	−0.141381	−	0.989955i	$-0.545154\pi$
$263$	−4.58564	−0.282763	−0.141381	+	0.989955i	$0.545154\pi$
$264$	−2.15426	−0.132586
$265$	1.61942	0.0994803
$266$	8.47102	0.519392
$267$	9.13783	0.559226
$268$	14.3414	0.876040
$269$	26.1688	1.59554	0.797769	−	0.602963i	$-0.206013\pi$
$269$	26.1688	1.59554	0.797769	+	0.602963i	$0.206013\pi$
$270$	5.40001	0.328634
$271$	−25.4057	−1.54329	−0.771643	−	0.636056i	$-0.780565\pi$
$271$	−25.4057	−1.54329	−0.771643	+	0.636056i	$0.780565\pi$
$272$	18.7147	1.13474
$273$	−5.83645	−0.353238
$274$	31.7978	1.92097
$275$	−6.57367	−0.396407
$276$	−20.8085	−1.25253
$277$	8.03045	0.482503	0.241252	−	0.970463i	$-0.422442\pi$
$277$	8.03045	0.482503	0.241252	+	0.970463i	$0.422442\pi$
$278$	11.5379	0.692000
$279$	−8.26629	−0.494890
$280$	−1.54228	−0.0921686
$281$	−24.2004	−1.44367	−0.721836	−	0.692064i	$-0.756702\pi$
$281$	−24.2004	−1.44367	−0.721836	+	0.692064i	$0.756702\pi$
$282$	13.4800	0.802721
$283$	0.974359	0.0579196	0.0289598	−	0.999581i	$-0.490781\pi$
$283$	0.974359	0.0579196	0.0289598	+	0.999581i	$0.490781\pi$
$284$	4.56885	0.271111
$285$	10.6738	0.632260
$286$	44.0230	2.60313
$287$	0.0750955	0.00443274
$288$	8.11182	0.477993
$289$	14.2606	0.838860
$290$	11.3923	0.668982
$291$	−6.91714	−0.405490
$292$	−21.0563	−1.23223
$293$	−14.8931	−0.870064	−0.435032	−	0.900415i	$-0.643263\pi$
$293$	−14.8931	−0.870064	−0.435032	+	0.900415i	$0.643263\pi$
$294$	2.07017	0.120735
$295$	−12.9539	−0.754203
$296$	1.93473	0.112454
$297$	3.64355	0.211420
$298$	15.1782	0.879247
$299$	53.1359	3.07293
$300$	−4.12368	−0.238081
$301$	2.15544	0.124238
$302$	19.0998	1.09907
$303$	−1.44421	−0.0829677
$304$	13.6966	0.785555
$305$	10.8647	0.622113
$306$	11.5746	0.661674
$307$	5.11256	0.291789	0.145895	−	0.989300i	$-0.453394\pi$
$307$	5.11256	0.291789	0.145895	+	0.989300i	$0.453394\pi$
$308$	−8.32772	−0.474516
$309$	−3.48038	−0.197992
$310$	44.6380	2.53527
$311$	10.5229	0.596698	0.298349	−	0.954457i	$-0.403564\pi$
$311$	10.5229	0.596698	0.298349	+	0.954457i	$0.403564\pi$
$312$	3.45082	0.195364
$313$	−11.0486	−0.624502	−0.312251	−	0.950000i	$-0.601083\pi$
$313$	−11.0486	−0.624502	−0.312251	+	0.950000i	$0.601083\pi$
$314$	21.6277	1.22052
$315$	2.60848	0.146971
$316$	−32.5281	−1.82985
$317$	30.4551	1.71053	0.855263	−	0.518194i	$-0.173395\pi$
$317$	30.4551	1.71053	0.855263	+	0.518194i	$0.173395\pi$
$318$	1.28522	0.0720716
$319$	7.68676	0.430376
$320$	−26.3415	−1.47254
$321$	−10.7478	−0.599881
$322$	−18.8472	−1.05031
$323$	22.8786	1.27300
$324$	2.28561	0.126978
$325$	10.5301	0.584104
$326$	−24.8426	−1.37591
$327$	18.4356	1.01949
$328$	−0.0444004	−0.00245160
$329$	6.51153	0.358992
$330$	−19.6752	−1.08308
$331$	−14.1598	−0.778293	−0.389146	−	0.921176i	$-0.627230\pi$
$331$	−14.1598	−0.778293	−0.389146	+	0.921176i	$0.627230\pi$
$332$	32.1728	1.76571
$333$	−3.27225	−0.179318
$334$	−29.5669	−1.61783
$335$	16.3673	0.894243
$336$	3.34722	0.182606
$337$	23.8320	1.29821	0.649107	−	0.760697i	$-0.275143\pi$
$337$	23.8320	1.29821	0.649107	+	0.760697i	$0.275143\pi$
$338$	−43.6063	−2.37187
$339$	14.7654	0.801944
$340$	−33.3341	−1.80779
$341$	30.1186	1.63102
$342$	8.47102	0.458060
$343$	1.00000	0.0539949
$344$	−1.27441	−0.0687116
$345$	−23.7481	−1.27855
$346$	2.45713	0.132096
$347$	−17.2741	−0.927322	−0.463661	−	0.886013i	$-0.653464\pi$
$347$	−17.2741	−0.927322	−0.463661	+	0.886013i	$0.653464\pi$
$348$	4.82192	0.258482
$349$	1.43950	0.0770544	0.0385272	−	0.999258i	$-0.487733\pi$
$349$	1.43950	0.0770544	0.0385272	+	0.999258i	$0.487733\pi$
$350$	−3.73499	−0.199644
$351$	−5.83645	−0.311526
$352$	−29.5558	−1.57533
$353$	18.3747	0.977989	0.488994	−	0.872287i	$-0.337364\pi$
$353$	18.3747	0.977989	0.488994	+	0.872287i	$0.337364\pi$
$354$	−10.2806	−0.546406
$355$	5.21427	0.276745
$356$	−20.8855	−1.10693
$357$	5.59112	0.295913
$358$	12.3701	0.653780
$359$	36.2572	1.91358	0.956792	−	0.290774i	$-0.0939129\pi$
$359$	36.2572	1.91358	0.956792	+	0.290774i	$0.0939129\pi$
$360$	−1.54228	−0.0812850
$361$	−2.25599	−0.118736
$362$	37.9090	1.99245
$363$	−2.27545	−0.119430
$364$	13.3398	0.699196
$365$	−24.0308	−1.25783
$366$	8.62257	0.450709
$367$	−19.2144	−1.00299	−0.501493	−	0.865162i	$-0.667216\pi$
$367$	−19.2144	−1.00299	−0.501493	+	0.865162i	$0.667216\pi$
$368$	−30.4736	−1.58855
$369$	0.0750955	0.00390931
$370$	17.6702	0.918628
$371$	0.620829	0.0322318
$372$	18.8935	0.979581
$373$	−34.1861	−1.77009	−0.885045	−	0.465505i	$-0.845873\pi$
$373$	−34.1861	−1.77009	−0.885045	+	0.465505i	$0.845873\pi$
$374$	−42.1725	−2.18069
$375$	8.33621	0.430480
$376$	−3.84996	−0.198547
$377$	−12.3131	−0.634157
$378$	2.07017	0.106478
$379$	−1.54947	−0.0795908	−0.0397954	−	0.999208i	$-0.512671\pi$
$379$	−1.54947	−0.0795908	−0.0397954	+	0.999208i	$0.512671\pi$
$380$	−24.3960	−1.25149
$381$	1.91048	0.0978769
$382$	28.5164	1.45903
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−4.68180	−0.238917
$385$	−9.50414	−0.484376
$386$	23.3843	1.19023
$387$	2.15544	0.109567
$388$	15.8099	0.802624
$389$	17.6974	0.897295	0.448648	−	0.893709i	$-0.351906\pi$
$389$	17.6974	0.897295	0.448648	+	0.893709i	$0.351906\pi$
$390$	31.5169	1.59592
$391$	−50.9024	−2.57425
$392$	−0.591253	−0.0298628
$393$	−0.416522	−0.0210108
$394$	19.3235	0.973504
$395$	−37.1232	−1.86787
$396$	−8.32772	−0.418484
$397$	−3.15327	−0.158258	−0.0791289	−	0.996864i	$-0.525214\pi$
$397$	−3.15327	−0.158258	−0.0791289	+	0.996864i	$0.525214\pi$
$398$	−20.9066	−1.04795
$399$	4.09194	0.204853
$400$	−6.03903	−0.301951
$401$	−28.5281	−1.42463	−0.712313	−	0.701862i	$-0.752352\pi$
$401$	−28.5281	−1.42463	−0.712313	+	0.701862i	$0.752352\pi$
$402$	12.9896	0.647863
$403$	−48.2458	−2.40329
$404$	3.30090	0.164226
$405$	2.60848	0.129617
$406$	4.36742	0.216751
$407$	11.9226	0.590981
$408$	−3.30577	−0.163660
$409$	19.6337	0.970823	0.485411	−	0.874286i	$-0.338670\pi$
$409$	19.6337	0.970823	0.485411	+	0.874286i	$0.338670\pi$
$410$	−0.405516	−0.0200270
$411$	15.3600	0.757652
$412$	7.95478	0.391904
$413$	−4.96605	−0.244363
$414$	−18.8472	−0.926287
$415$	36.7178	1.80240
$416$	47.3442	2.32124
$417$	5.57342	0.272932
$418$	−30.8646	−1.50964
$419$	30.4870	1.48939	0.744693	−	0.667408i	$-0.232596\pi$
$419$	30.4870	1.48939	0.744693	+	0.667408i	$0.232596\pi$
$420$	−5.96197	−0.290914
$421$	30.8288	1.50251	0.751253	−	0.660015i	$-0.229450\pi$
$421$	30.8288	1.50251	0.751253	+	0.660015i	$0.229450\pi$
$422$	−19.6311	−0.955626
$423$	6.51153	0.316601
$424$	−0.367067	−0.0178263
$425$	−10.0875	−0.489314
$426$	4.13820	0.200497
$427$	4.16515	0.201566
$428$	24.5651	1.18740
$429$	21.2654	1.02670
$430$	−11.6394	−0.561302
$431$	7.50603	0.361553	0.180776	−	0.983524i	$-0.442139\pi$
$431$	7.50603	0.361553	0.180776	+	0.983524i	$0.442139\pi$
$432$	3.34722	0.161043
$433$	−21.9024	−1.05256	−0.526281	−	0.850311i	$-0.676414\pi$
$433$	−21.9024	−1.05256	−0.526281	+	0.850311i	$0.676414\pi$
$434$	17.1126	0.821432
$435$	5.50310	0.263853
$436$	−42.1364	−2.01797
$437$	−37.2537	−1.78209
$438$	−19.0716	−0.911275
$439$	−26.7012	−1.27438	−0.637190	−	0.770707i	$-0.719903\pi$
$439$	−26.7012	−1.27438	−0.637190	+	0.770707i	$0.719903\pi$
$440$	5.61936	0.267892
$441$	1.00000	0.0476190
$442$	67.5544	3.21323
$443$	−16.5273	−0.785236	−0.392618	−	0.919702i	$-0.628431\pi$
$443$	−16.5273	−0.785236	−0.392618	+	0.919702i	$0.628431\pi$
$444$	7.47906	0.354941
$445$	−23.8359	−1.12993
$446$	18.2617	0.864719
$447$	7.33184	0.346784
$448$	−10.0984	−0.477105
$449$	−6.58527	−0.310778	−0.155389	−	0.987853i	$-0.549663\pi$
$449$	−6.58527	−0.310778	−0.155389	+	0.987853i	$0.549663\pi$
$450$	−3.73499	−0.176069
$451$	−0.273614	−0.0128840
$452$	−33.7478	−1.58736
$453$	9.22621	0.433485
$454$	−33.7076	−1.58198
$455$	15.2243	0.713725
$456$	−2.41938	−0.113298
$457$	5.31583	0.248664	0.124332	−	0.992241i	$-0.460321\pi$
$457$	5.31583	0.248664	0.124332	+	0.992241i	$0.460321\pi$
$458$	44.4348	2.07630
$459$	5.59112	0.260971
$460$	54.2787	2.53076
$461$	−33.2887	−1.55041	−0.775205	−	0.631710i	$-0.782354\pi$
$461$	−33.2887	−1.55041	−0.775205	+	0.631710i	$0.782354\pi$
$462$	−7.54277	−0.350921
$463$	−14.3040	−0.664762	−0.332381	−	0.943145i	$-0.607852\pi$
$463$	−14.3040	−0.664762	−0.332381	+	0.943145i	$0.607852\pi$
$464$	7.06159	0.327826
$465$	21.5625	0.999937
$466$	−20.0910	−0.930700
$467$	31.3087	1.44880	0.724398	−	0.689382i	$-0.242118\pi$
$467$	31.3087	1.44880	0.724398	+	0.689382i	$0.242118\pi$
$468$	13.3398	0.616633
$469$	6.27465	0.289737
$470$	−35.1623	−1.62192
$471$	10.4473	0.481386
$472$	2.93619	0.135149
$473$	−7.85345	−0.361102
$474$	−29.4621	−1.35324
$475$	−7.38266	−0.338740
$476$	−12.7791	−0.585729
$477$	0.620829	0.0284258
$478$	−36.5277	−1.67074
$479$	−24.3957	−1.11467	−0.557334	−	0.830288i	$-0.688176\pi$
$479$	−24.3957	−1.11467	−0.557334	+	0.830288i	$0.688176\pi$
$480$	−21.1596	−0.965797
$481$	−19.0983	−0.870807
$482$	−14.4885	−0.659933
$483$	−9.10416	−0.414254
$484$	5.20079	0.236399
$485$	18.0433	0.819302
$486$	2.07017	0.0939048
$487$	24.8345	1.12536	0.562680	−	0.826675i	$-0.309770\pi$
$487$	24.8345	1.12536	0.562680	+	0.826675i	$0.309770\pi$
$488$	−2.46266	−0.111479
$489$	−12.0003	−0.542671
$490$	−5.40001	−0.243948
$491$	−5.27816	−0.238200	−0.119100	−	0.992882i	$-0.538001\pi$
$491$	−5.27816	−0.238200	−0.119100	+	0.992882i	$0.538001\pi$
$492$	−0.171639	−0.00773807
$493$	11.7955	0.531244
$494$	49.4407	2.22444
$495$	−9.50414	−0.427180
$496$	27.6691	1.24238
$497$	1.99897	0.0896659
$498$	29.1403	1.30581
$499$	−8.74243	−0.391365	−0.195682	−	0.980667i	$-0.562692\pi$
$499$	−8.74243	−0.391365	−0.195682	+	0.980667i	$0.562692\pi$
$500$	−19.0533	−0.852089
$501$	−14.2824	−0.638089
$502$	−13.9987	−0.624791
$503$	−11.8479	−0.528270	−0.264135	−	0.964486i	$-0.585086\pi$
$503$	−11.8479	−0.528270	−0.264135	+	0.964486i	$0.585086\pi$
$504$	−0.591253	−0.0263365
$505$	3.76720	0.167638
$506$	68.6706	3.05278
$507$	−21.0641	−0.935490
$508$	−4.36661	−0.193737
$509$	−31.2788	−1.38641	−0.693204	−	0.720741i	$-0.743802\pi$
$509$	−31.2788	−1.38641	−0.693204	+	0.720741i	$0.743802\pi$
$510$	−30.1921	−1.33693
$511$	−9.21256	−0.407540
$512$	−31.1101	−1.37489
$513$	4.09194	0.180664
$514$	26.1377	1.15288
$515$	9.07852	0.400048
$516$	−4.92649	−0.216877
$517$	−23.7251	−1.04343
$518$	6.77411	0.297637
$519$	1.18692	0.0521000
$520$	−9.00141	−0.394738
$521$	−29.2272	−1.28047	−0.640234	−	0.768180i	$-0.721162\pi$
$521$	−29.2272	−1.28047	−0.640234	+	0.768180i	$0.721162\pi$
$522$	4.36742	0.191157
$523$	−23.8853	−1.04443	−0.522216	−	0.852813i	$-0.674895\pi$
$523$	−23.8853	−1.04443	−0.522216	+	0.852813i	$0.674895\pi$
$524$	0.952006	0.0415886
$525$	−1.80419	−0.0787415
$526$	9.49306	0.413917
$527$	46.2178	2.01328
$528$	−12.1958	−0.530752
$529$	59.8857	2.60373
$530$	−3.35248	−0.145622
$531$	−4.96605	−0.215508
$532$	−9.35257	−0.405485
$533$	0.438291	0.0189845
$534$	−18.9169	−0.818613
$535$	28.0354	1.21207
$536$	−3.70991	−0.160244
$537$	5.97540	0.257858
$538$	−54.1738	−2.33560
$539$	−3.64355	−0.156939
$540$	−5.96197	−0.256562
$541$	−11.9935	−0.515640	−0.257820	−	0.966193i	$-0.583004\pi$
$541$	−11.9935	−0.515640	−0.257820	+	0.966193i	$0.583004\pi$
$542$	52.5941	2.25911
$543$	18.3120	0.785844
$544$	−45.3541	−1.94454
$545$	−48.0889	−2.05990
$546$	12.0824	0.517081
$547$	−4.78729	−0.204690	−0.102345	−	0.994749i	$-0.532635\pi$
$547$	−4.78729	−0.204690	−0.102345	+	0.994749i	$0.532635\pi$
$548$	−35.1069	−1.49969
$549$	4.16515	0.177764
$550$	13.6086	0.580273
$551$	8.63274	0.367767
$552$	5.38286	0.229110
$553$	−14.2317	−0.605194
$554$	−16.6244	−0.706303
$555$	8.53560	0.362316
$556$	−12.7387	−0.540239
$557$	6.86511	0.290884	0.145442	−	0.989367i	$-0.453540\pi$
$557$	6.86511	0.290884	0.145442	+	0.989367i	$0.453540\pi$
$558$	17.1126	0.724435
$559$	12.5801	0.532082
$560$	−8.73117	−0.368959
$561$	−20.3715	−0.860086
$562$	50.0989	2.11329
$563$	41.9957	1.76991	0.884953	−	0.465679i	$-0.154190\pi$
$563$	41.9957	1.76991	0.884953	+	0.465679i	$0.154190\pi$
$564$	−14.8828	−0.626679
$565$	−38.5152	−1.62035
$566$	−2.01709	−0.0847846
$567$	1.00000	0.0419961
$568$	−1.18190	−0.0495912
$569$	−1.27408	−0.0534121	−0.0267060	−	0.999643i	$-0.508502\pi$
$569$	−1.27408	−0.0534121	−0.0267060	+	0.999643i	$0.508502\pi$
$570$	−22.0965	−0.925522
$571$	9.67330	0.404815	0.202408	−	0.979301i	$-0.435123\pi$
$571$	9.67330	0.404815	0.202408	+	0.979301i	$0.435123\pi$
$572$	−48.6043	−2.03225
$573$	13.7749	0.575455
$574$	−0.155460	−0.00648879
$575$	16.4257	0.684998
$576$	−10.0984	−0.420767
$577$	27.8939	1.16124	0.580619	−	0.814176i	$-0.302811\pi$
$577$	27.8939	1.16124	0.580619	+	0.814176i	$0.302811\pi$
$578$	−29.5219	−1.22795
$579$	11.2959	0.469440
$580$	−12.5779	−0.522269
$581$	14.0763	0.583983
$582$	14.3197	0.593569
$583$	−2.26202	−0.0936833
$584$	5.44696	0.225397
$585$	15.2243	0.629447
$586$	30.8313	1.27363
$587$	−3.00604	−0.124072	−0.0620362	−	0.998074i	$-0.519759\pi$
$587$	−3.00604	−0.124072	−0.0620362	+	0.998074i	$0.519759\pi$
$588$	−2.28561	−0.0942568
$589$	33.8252	1.39374
$590$	26.8167	1.10403
$591$	9.33425	0.383960
$592$	10.9529	0.450162
$593$	28.0502	1.15189	0.575943	−	0.817490i	$-0.304635\pi$
$593$	28.0502	1.15189	0.575943	+	0.817490i	$0.304635\pi$
$594$	−7.54277	−0.309484
$595$	−14.5844	−0.597900
$596$	−16.7577	−0.686422
$597$	−10.0990	−0.413323
$598$	−110.000	−4.49825
$599$	36.1685	1.47780	0.738902	−	0.673813i	$-0.235345\pi$
$599$	36.1685	1.47780	0.738902	+	0.673813i	$0.235345\pi$
$600$	1.06674	0.0435493
$601$	−5.01250	−0.204464	−0.102232	−	0.994761i	$-0.532598\pi$
$601$	−5.01250	−0.204464	−0.102232	+	0.994761i	$0.532598\pi$
$602$	−4.46213	−0.181863
$603$	6.27465	0.255524
$604$	−21.0875	−0.858037
$605$	5.93548	0.241312
$606$	2.98976	0.121451
$607$	−40.7335	−1.65332	−0.826662	−	0.562699i	$-0.809763\pi$
$607$	−40.7335	−1.65332	−0.826662	+	0.562699i	$0.809763\pi$
$608$	−33.1931	−1.34616
$609$	2.10969	0.0854890
$610$	−22.4918	−0.910668
$611$	38.0042	1.53749
$612$	−12.7791	−0.516564
$613$	−11.8946	−0.480417	−0.240209	−	0.970721i	$-0.577216\pi$
$613$	−11.8946	−0.480417	−0.240209	+	0.970721i	$0.577216\pi$
$614$	−10.5839	−0.427130
$615$	−0.195885	−0.00789886
$616$	2.15426	0.0867976
$617$	44.5224	1.79240	0.896202	−	0.443646i	$-0.146315\pi$
$617$	44.5224	1.79240	0.896202	+	0.443646i	$0.146315\pi$
$618$	7.20498	0.289827
$619$	−27.3815	−1.10056	−0.550278	−	0.834982i	$-0.685478\pi$
$619$	−27.3815	−1.10056	−0.550278	+	0.834982i	$0.685478\pi$
$620$	−49.2834	−1.97927
$621$	−9.10416	−0.365337
$622$	−21.7842	−0.873466
$623$	−9.13783	−0.366099
$624$	19.5359	0.782060
$625$	−30.7659	−1.23063
$626$	22.8724	0.914166
$627$	−14.9092	−0.595416
$628$	−23.8784	−0.952852
$629$	18.2955	0.729490
$630$	−5.40001	−0.215141
$631$	0.779157	0.0310177	0.0155089	−	0.999880i	$-0.495063\pi$
$631$	0.779157	0.0310177	0.0155089	+	0.999880i	$0.495063\pi$
$632$	8.41455	0.334713
$633$	−9.48283	−0.376909
$634$	−63.0472	−2.50392
$635$	−4.98346	−0.197763
$636$	−1.41897	−0.0562658
$637$	5.83645	0.231248
$638$	−15.9129	−0.629998
$639$	1.99897	0.0790779
$640$	12.2124	0.482737
$641$	−24.7985	−0.979483	−0.489742	−	0.871868i	$-0.662909\pi$
$641$	−24.7985	−0.979483	−0.489742	+	0.871868i	$0.662909\pi$
$642$	22.2497	0.878125
$643$	−26.2424	−1.03490	−0.517450	−	0.855714i	$-0.673119\pi$
$643$	−26.2424	−1.03490	−0.517450	+	0.855714i	$0.673119\pi$
$644$	20.8085	0.819970
$645$	−5.62243	−0.221383
$646$	−47.3625	−1.86345
$647$	−21.0273	−0.826669	−0.413335	−	0.910579i	$-0.635636\pi$
$647$	−21.0273	−0.826669	−0.413335	+	0.910579i	$0.635636\pi$
$648$	−0.591253	−0.0232266
$649$	18.0940	0.710253
$650$	−21.7991	−0.855030
$651$	8.26629	0.323981
$652$	27.4279	1.07416
$653$	−10.1284	−0.396353	−0.198177	−	0.980166i	$-0.563502\pi$
$653$	−10.1284	−0.396353	−0.198177	+	0.980166i	$0.563502\pi$
$654$	−38.1647	−1.49236
$655$	1.08649	0.0424528
$656$	−0.251361	−0.00981399
$657$	−9.21256	−0.359416
$658$	−13.4800	−0.525504
$659$	−17.3054	−0.674124	−0.337062	−	0.941482i	$-0.609433\pi$
$659$	−17.3054	−0.674124	−0.337062	+	0.941482i	$0.609433\pi$
$660$	21.7227	0.845556
$661$	0.148749	0.00578566	0.00289283	−	0.999996i	$-0.499079\pi$
$661$	0.148749	0.00578566	0.00289283	+	0.999996i	$0.499079\pi$
$662$	29.3132	1.13929
$663$	32.6323	1.26733
$664$	−8.32265	−0.322981
$665$	−10.6738	−0.413911
$666$	6.77411	0.262491
$667$	−19.2070	−0.743696
$668$	32.6438	1.26303
$669$	8.82137	0.341054
$670$	−33.8832	−1.30902
$671$	−15.1759	−0.585860
$672$	−8.11182	−0.312920
$673$	25.8403	0.996072	0.498036	−	0.867156i	$-0.334055\pi$
$673$	25.8403	0.996072	0.498036	+	0.867156i	$0.334055\pi$
$674$	−49.3364	−1.90037
$675$	−1.80419	−0.0694435
$676$	48.1442	1.85170
$677$	24.9306	0.958161	0.479081	−	0.877771i	$-0.340970\pi$
$677$	24.9306	0.958161	0.479081	+	0.877771i	$0.340970\pi$
$678$	−30.5668	−1.17391
$679$	6.91714	0.265455
$680$	8.62305	0.330679
$681$	−16.2825	−0.623948
$682$	−62.3507	−2.38753
$683$	−8.92335	−0.341443	−0.170721	−	0.985319i	$-0.554610\pi$
$683$	−8.92335	−0.341443	−0.170721	+	0.985319i	$0.554610\pi$
$684$	−9.35257	−0.357605
$685$	−40.0663	−1.53085
$686$	−2.07017	−0.0790395
$687$	21.4643	0.818915
$688$	−7.21473	−0.275059
$689$	3.62343	0.138042
$690$	49.1625	1.87159
$691$	−49.7345	−1.89199	−0.945995	−	0.324181i	$-0.894911\pi$
$691$	−49.7345	−1.89199	−0.945995	+	0.324181i	$0.894911\pi$
$692$	−2.71283	−0.103126
$693$	−3.64355	−0.138407
$694$	35.7603	1.35744
$695$	−14.5382	−0.551465
$696$	−1.24736	−0.0472811
$697$	−0.419868	−0.0159036
$698$	−2.98000	−0.112795
$699$	−9.70502	−0.367078
$700$	4.12368	0.155860
$701$	−11.3202	−0.427558	−0.213779	−	0.976882i	$-0.568577\pi$
$701$	−11.3202	−0.427558	−0.213779	+	0.976882i	$0.568577\pi$
$702$	12.0824	0.456022
$703$	13.3898	0.505008
$704$	36.7941	1.38673
$705$	−16.9852	−0.639701
$706$	−38.0388	−1.43161
$707$	1.44421	0.0543151
$708$	11.3504	0.426575
$709$	−51.5586	−1.93633	−0.968163	−	0.250322i	$-0.919463\pi$
$709$	−51.5586	−1.93633	−0.968163	+	0.250322i	$0.919463\pi$
$710$	−10.7944	−0.405108
$711$	−14.2317	−0.533731
$712$	5.40277	0.202477
$713$	−75.2576	−2.81842
$714$	−11.5746	−0.433167
$715$	−55.4704	−2.07448
$716$	−13.6574	−0.510402
$717$	−17.6448	−0.658957
$718$	−75.0586	−2.80116
$719$	−33.5520	−1.25128	−0.625640	−	0.780112i	$-0.715162\pi$
$719$	−33.5520	−1.25128	−0.625640	+	0.780112i	$0.715162\pi$
$720$	−8.73117	−0.325391
$721$	3.48038	0.129616
$722$	4.67029	0.173810
$723$	−6.99870	−0.260284
$724$	−41.8541	−1.55549
$725$	−3.80629	−0.141362
$726$	4.71057	0.174826
$727$	−40.6196	−1.50650	−0.753250	−	0.657735i	$-0.771515\pi$
$727$	−40.6196	−1.50650	−0.753250	+	0.657735i	$0.771515\pi$
$728$	−3.45082	−0.127896
$729$	1.00000	0.0370370
$730$	49.7479	1.84125
$731$	−12.0513	−0.445734
$732$	−9.51989	−0.351865
$733$	26.9870	0.996789	0.498395	−	0.866950i	$-0.333923\pi$
$733$	26.9870	0.996789	0.498395	+	0.866950i	$0.333923\pi$
$734$	39.7772	1.46820
$735$	−2.60848	−0.0962154
$736$	73.8513	2.72219
$737$	−22.8620	−0.842133
$738$	−0.155460	−0.00572258
$739$	22.5897	0.830976	0.415488	−	0.909599i	$-0.363611\pi$
$739$	22.5897	0.830976	0.415488	+	0.909599i	$0.363611\pi$
$740$	−19.5090	−0.717166
$741$	23.8824	0.877342
$742$	−1.28522	−0.0471820
$743$	2.85989	0.104919	0.0524595	−	0.998623i	$-0.483294\pi$
$743$	2.85989	0.104919	0.0524595	+	0.998623i	$0.483294\pi$
$744$	−4.88747	−0.179183
$745$	−19.1250	−0.700685
$746$	70.7711	2.59111
$747$	14.0763	0.515024
$748$	46.5613	1.70245
$749$	10.7478	0.392715
$750$	−17.2574	−0.630150
$751$	−1.17677	−0.0429411	−0.0214705	−	0.999769i	$-0.506835\pi$
$751$	−1.17677	−0.0429411	−0.0214705	+	0.999769i	$0.506835\pi$
$752$	−21.7955	−0.794800
$753$	−6.76208	−0.246424
$754$	25.4902	0.928299
$755$	−24.0664	−0.875867
$756$	−2.28561	−0.0831267
$757$	−0.512513	−0.0186276	−0.00931381	−	0.999957i	$-0.502965\pi$
$757$	−0.512513	−0.0186276	−0.00931381	+	0.999957i	$0.502965\pi$
$758$	3.20766	0.116508
$759$	33.1714	1.20405
$760$	6.31090	0.228921
$761$	−8.80756	−0.319274	−0.159637	−	0.987176i	$-0.551032\pi$
$761$	−8.80756	−0.319274	−0.159637	+	0.987176i	$0.551032\pi$
$762$	−3.95502	−0.143275
$763$	−18.4356	−0.667412
$764$	−31.4840	−1.13905
$765$	−14.5844	−0.527298
$766$	−2.07017	−0.0747983
$767$	−28.9841	−1.04655
$768$	−10.5047	−0.379056
$769$	−9.45598	−0.340991	−0.170496	−	0.985358i	$-0.554537\pi$
$769$	−9.45598	−0.340991	−0.170496	+	0.985358i	$0.554537\pi$
$770$	19.6752	0.709045
$771$	12.6259	0.454709
$772$	−25.8179	−0.929205
$773$	3.96202	0.142504	0.0712520	−	0.997458i	$-0.477301\pi$
$773$	3.96202	0.142504	0.0712520	+	0.997458i	$0.477301\pi$
$774$	−4.46213	−0.160388
$775$	−14.9140	−0.535726
$776$	−4.08978	−0.146815
$777$	3.27225	0.117391
$778$	−36.6367	−1.31349
$779$	−0.307286	−0.0110097
$780$	−34.7967	−1.24592
$781$	−7.28333	−0.260618
$782$	105.377	3.76826
$783$	2.10969	0.0753942
$784$	−3.34722	−0.119543
$785$	−27.2516	−0.972652
$786$	0.862272	0.0307562
$787$	10.5250	0.375175	0.187587	−	0.982248i	$-0.439933\pi$
$787$	10.5250	0.375175	0.187587	+	0.982248i	$0.439933\pi$
$788$	−21.3344	−0.760007
$789$	4.58564	0.163253
$790$	76.8514	2.73425
$791$	−14.7654	−0.524996
$792$	2.15426	0.0765483
$793$	24.3097	0.863262
$794$	6.52780	0.231663
$795$	−1.61942	−0.0574350
$796$	23.0823	0.818130
$797$	−34.1301	−1.20895	−0.604475	−	0.796624i	$-0.706617\pi$
$797$	−34.1301	−1.20895	−0.604475	+	0.796624i	$0.706617\pi$
$798$	−8.47102	−0.299871
$799$	−36.4067	−1.28798
$800$	14.6353	0.517436
$801$	−9.13783	−0.322869
$802$	59.0580	2.08541
$803$	33.5664	1.18453
$804$	−14.3414	−0.505782
$805$	23.7481	0.837009
$806$	99.8769	3.51801
$807$	−26.1688	−0.921185
$808$	−0.853894	−0.0300399
$809$	−4.01297	−0.141088	−0.0705442	−	0.997509i	$-0.522474\pi$
$809$	−4.01297	−0.141088	−0.0705442	+	0.997509i	$0.522474\pi$
$810$	−5.40001	−0.189737
$811$	12.1358	0.426145	0.213073	−	0.977036i	$-0.431653\pi$
$811$	12.1358	0.426145	0.213073	+	0.977036i	$0.431653\pi$
$812$	−4.82192	−0.169216
$813$	25.4057	0.891016
$814$	−24.6818	−0.865096
$815$	31.3025	1.09648
$816$	−18.7147	−0.655145
$817$	−8.81994	−0.308571
$818$	−40.6451	−1.42112
$819$	5.83645	0.203942
$820$	0.447717	0.0156349
$821$	51.0611	1.78205	0.891023	−	0.453958i	$-0.149989\pi$
$821$	51.0611	1.78205	0.891023	+	0.453958i	$0.149989\pi$
$822$	−31.7978	−1.10908
$823$	5.31541	0.185284	0.0926418	−	0.995700i	$-0.470469\pi$
$823$	5.31541	0.185284	0.0926418	+	0.995700i	$0.470469\pi$
$824$	−2.05779	−0.0716864
$825$	6.57367	0.228866
$826$	10.2806	0.357707
$827$	−20.4651	−0.711642	−0.355821	−	0.934554i	$-0.615799\pi$
$827$	−20.4651	−0.711642	−0.355821	+	0.934554i	$0.615799\pi$
$828$	20.8085	0.723146
$829$	−20.6394	−0.716835	−0.358418	−	0.933561i	$-0.616684\pi$
$829$	−20.6394	−0.716835	−0.358418	+	0.933561i	$0.616684\pi$
$830$	−76.0121	−2.63842
$831$	−8.03045	−0.278573
$832$	−58.9388	−2.04334
$833$	−5.59112	−0.193721
$834$	−11.5379	−0.399526
$835$	37.2553	1.28927
$836$	34.0766	1.17856
$837$	8.26629	0.285725
$838$	−63.1132	−2.18021
$839$	−16.9881	−0.586493	−0.293246	−	0.956037i	$-0.594736\pi$
$839$	−16.9881	−0.586493	−0.293246	+	0.956037i	$0.594736\pi$
$840$	1.54228	0.0532135
$841$	−24.5492	−0.846524
$842$	−63.8209	−2.19942
$843$	24.2004	0.833504
$844$	21.6740	0.746050
$845$	54.9454	1.89018
$846$	−13.4800	−0.463451
$847$	2.27545	0.0781855
$848$	−2.07805	−0.0713605
$849$	−0.974359	−0.0334399
$850$	20.8828	0.716273
$851$	−29.7910	−1.02122
$852$	−4.56885	−0.156526
$853$	−9.45208	−0.323633	−0.161817	−	0.986821i	$-0.551735\pi$
$853$	−9.45208	−0.323633	−0.161817	+	0.986821i	$0.551735\pi$
$854$	−8.62257	−0.295058
$855$	−10.6738	−0.365035
$856$	−6.35465	−0.217197
$857$	−3.95598	−0.135134	−0.0675669	−	0.997715i	$-0.521524\pi$
$857$	−3.95598	−0.135134	−0.0675669	+	0.997715i	$0.521524\pi$
$858$	−44.0230	−1.50292
$859$	6.38712	0.217926	0.108963	−	0.994046i	$-0.465247\pi$
$859$	6.38712	0.217926	0.108963	+	0.994046i	$0.465247\pi$
$860$	12.8507	0.438204
$861$	−0.0750955	−0.00255925
$862$	−15.5388	−0.529253
$863$	14.5465	0.495169	0.247584	−	0.968866i	$-0.420363\pi$
$863$	14.5465	0.495169	0.247584	+	0.968866i	$0.420363\pi$
$864$	−8.11182	−0.275970
$865$	−3.09606	−0.105269
$866$	45.3417	1.54077
$867$	−14.2606	−0.484316
$868$	−18.8935	−0.641287
$869$	51.8540	1.75903
$870$	−11.3923	−0.386237
$871$	36.6217	1.24088
$872$	10.9001	0.369123
$873$	6.91714	0.234110
$874$	77.1215	2.60867
$875$	−8.33621	−0.281815
$876$	21.0563	0.711426
$877$	2.27004	0.0766540	0.0383270	−	0.999265i	$-0.487797\pi$
$877$	2.27004	0.0766540	0.0383270	+	0.999265i	$0.487797\pi$
$878$	55.2761	1.86548
$879$	14.8931	0.502332
$880$	31.8124	1.07240
$881$	−31.2363	−1.05238	−0.526188	−	0.850368i	$-0.676379\pi$
$881$	−31.2363	−1.05238	−0.526188	+	0.850368i	$0.676379\pi$
$882$	−2.07017	−0.0697063
$883$	−28.4967	−0.958992	−0.479496	−	0.877544i	$-0.659180\pi$
$883$	−28.4967	−0.958992	−0.479496	+	0.877544i	$0.659180\pi$
$884$	−74.5845	−2.50855
$885$	12.9539	0.435439
$886$	34.2143	1.14945
$887$	8.89114	0.298535	0.149268	−	0.988797i	$-0.452308\pi$
$887$	8.89114	0.298535	0.149268	+	0.988797i	$0.452308\pi$
$888$	−1.93473	−0.0649251
$889$	−1.91048	−0.0640755
$890$	49.3444	1.65403
$891$	−3.64355	−0.122063
$892$	−20.1622	−0.675080
$893$	−26.6448	−0.891635
$894$	−15.1782	−0.507634
$895$	−15.5867	−0.521007
$896$	4.68180	0.156408
$897$	−53.1359	−1.77416
$898$	13.6326	0.454927
$899$	17.4393	0.581634
$900$	4.12368	0.137456
$901$	−3.47113	−0.115640
$902$	0.566428	0.0188600
$903$	−2.15544	−0.0717286
$904$	8.73007	0.290358
$905$	−47.7667	−1.58782
$906$	−19.0998	−0.634549
$907$	−4.39936	−0.146078	−0.0730391	−	0.997329i	$-0.523270\pi$
$907$	−4.39936	−0.146078	−0.0730391	+	0.997329i	$0.523270\pi$
$908$	37.2154	1.23504
$909$	1.44421	0.0479014
$910$	−31.5169	−1.04477
$911$	−4.63245	−0.153480	−0.0767399	−	0.997051i	$-0.524451\pi$
$911$	−4.63245	−0.153480	−0.0767399	+	0.997051i	$0.524451\pi$
$912$	−13.6966	−0.453541
$913$	−51.2876	−1.69737
$914$	−11.0047	−0.364002
$915$	−10.8647	−0.359177
$916$	−49.0590	−1.62096
$917$	0.416522	0.0137548
$918$	−11.5746	−0.382018
$919$	48.5034	1.59998	0.799989	−	0.600014i	$-0.204839\pi$
$919$	48.5034	1.59998	0.799989	+	0.600014i	$0.204839\pi$
$920$	−14.0411	−0.462922
$921$	−5.11256	−0.168465
$922$	68.9133	2.26954
$923$	11.6669	0.384019
$924$	8.32772	0.273962
$925$	−5.90376	−0.194115
$926$	29.6117	0.973100
$927$	3.48038	0.114311
$928$	−17.1134	−0.561776
$929$	50.9618	1.67200	0.836001	−	0.548728i	$-0.184888\pi$
$929$	50.9618	1.67200	0.836001	+	0.548728i	$0.184888\pi$
$930$	−44.6380	−1.46374
$931$	−4.09194	−0.134108
$932$	22.1819	0.726591
$933$	−10.5229	−0.344504
$934$	−64.8144	−2.12079
$935$	53.1388	1.73782
$936$	−3.45082	−0.112794
$937$	15.8544	0.517940	0.258970	−	0.965885i	$-0.416617\pi$
$937$	15.8544	0.517940	0.258970	+	0.965885i	$0.416617\pi$
$938$	−12.9896	−0.424126
$939$	11.0486	0.360557
$940$	38.8215	1.26622
$941$	8.99331	0.293174	0.146587	−	0.989198i	$-0.453171\pi$
$941$	8.99331	0.293174	0.146587	+	0.989198i	$0.453171\pi$
$942$	−21.6277	−0.704668
$943$	0.683681	0.0222637
$944$	16.6224	0.541014
$945$	−2.60848	−0.0848540
$946$	16.2580	0.528593
$947$	23.9865	0.779457	0.389729	−	0.920930i	$-0.372569\pi$
$947$	23.9865	0.779457	0.389729	+	0.920930i	$0.372569\pi$
$948$	32.5281	1.05646
$949$	−53.7686	−1.74540
$950$	15.2834	0.495858
$951$	−30.4551	−0.987573
$952$	3.30577	0.107141
$953$	−29.2811	−0.948509	−0.474255	−	0.880388i	$-0.657282\pi$
$953$	−29.2811	−0.948509	−0.474255	+	0.880388i	$0.657282\pi$
$954$	−1.28522	−0.0416106
$955$	−35.9317	−1.16272
$956$	40.3290	1.30433
$957$	−7.68676	−0.248478
$958$	50.5033	1.63169
$959$	−15.3600	−0.496000
$960$	26.3415	0.850170
$961$	37.3315	1.20424
$962$	39.5367	1.27471
$963$	10.7478	0.346342
$964$	15.9963	0.515205
$965$	−29.4651	−0.948514
$966$	18.8472	0.606397
$967$	9.83189	0.316172	0.158086	−	0.987425i	$-0.449468\pi$
$967$	9.83189	0.316172	0.158086	+	0.987425i	$0.449468\pi$
$968$	−1.34537	−0.0432418
$969$	−22.8786	−0.734965
$970$	−37.3526	−1.19932
$971$	−32.3737	−1.03892	−0.519461	−	0.854494i	$-0.673867\pi$
$971$	−32.3737	−1.03892	−0.519461	+	0.854494i	$0.673867\pi$
$972$	−2.28561	−0.0733108
$973$	−5.57342	−0.178676
$974$	−51.4117	−1.64734
$975$	−10.5301	−0.337232
$976$	−13.9417	−0.446262
$977$	−35.2636	−1.12818	−0.564091	−	0.825712i	$-0.690773\pi$
$977$	−35.2636	−1.12818	−0.564091	+	0.825712i	$0.690773\pi$
$978$	24.8426	0.794380
$979$	33.2941	1.06409
$980$	5.96197	0.190448
$981$	−18.4356	−0.588602
$982$	10.9267	0.348685
$983$	37.8998	1.20881	0.604407	−	0.796675i	$-0.293410\pi$
$983$	37.8998	1.20881	0.604407	+	0.796675i	$0.293410\pi$
$984$	0.0444004	0.00141543
$985$	−24.3483	−0.775800
$986$	−24.4188	−0.777652
$987$	−6.51153	−0.207264
$988$	−54.5858	−1.73661
$989$	19.6235	0.623990
$990$	19.6752	0.625319
$991$	−57.6083	−1.82999	−0.914994	−	0.403467i	$-0.867805\pi$
$991$	−57.6083	−1.82999	−0.914994	+	0.403467i	$0.867805\pi$
$992$	−67.0546	−2.12899
$993$	14.1598	0.449348
$994$	−4.13820	−0.131256
$995$	26.3430	0.835130
$996$	−32.1728	−1.01944
$997$	−1.78395	−0.0564984	−0.0282492	−	0.999601i	$-0.508993\pi$
$997$	−1.78395	−0.0564984	−0.0282492	+	0.999601i	$0.508993\pi$
$998$	18.0983	0.572892
$999$	3.27225	0.103529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.7	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.7	✓	41	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07017 q^{2} -1.00000 q^{3} +2.28561 q^{4} +2.60848 q^{5} +2.07017 q^{6} +1.00000 q^{7} -0.591253 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.07017 q^{2} -1.00000 q^{3} +2.28561 q^{4} +2.60848 q^{5} +2.07017 q^{6} +1.00000 q^{7} -0.591253 q^{8} +1.00000 q^{9} -5.40001 q^{10} -3.64355 q^{11} -2.28561 q^{12} +5.83645 q^{13} -2.07017 q^{14} -2.60848 q^{15} -3.34722 q^{16} -5.59112 q^{17} -2.07017 q^{18} -4.09194 q^{19} +5.96197 q^{20} -1.00000 q^{21} +7.54277 q^{22} +9.10416 q^{23} +0.591253 q^{24} +1.80419 q^{25} -12.0824 q^{26} -1.00000 q^{27} +2.28561 q^{28} -2.10969 q^{29} +5.40001 q^{30} -8.26629 q^{31} +8.11182 q^{32} +3.64355 q^{33} +11.5746 q^{34} +2.60848 q^{35} +2.28561 q^{36} -3.27225 q^{37} +8.47102 q^{38} -5.83645 q^{39} -1.54228 q^{40} +0.0750955 q^{41} +2.07017 q^{42} +2.15544 q^{43} -8.32772 q^{44} +2.60848 q^{45} -18.8472 q^{46} +6.51153 q^{47} +3.34722 q^{48} +1.00000 q^{49} -3.73499 q^{50} +5.59112 q^{51} +13.3398 q^{52} +0.620829 q^{53} +2.07017 q^{54} -9.50414 q^{55} -0.591253 q^{56} +4.09194 q^{57} +4.36742 q^{58} -4.96605 q^{59} -5.96197 q^{60} +4.16515 q^{61} +17.1126 q^{62} +1.00000 q^{63} -10.0984 q^{64} +15.2243 q^{65} -7.54277 q^{66} +6.27465 q^{67} -12.7791 q^{68} -9.10416 q^{69} -5.40001 q^{70} +1.99897 q^{71} -0.591253 q^{72} -9.21256 q^{73} +6.77411 q^{74} -1.80419 q^{75} -9.35257 q^{76} -3.64355 q^{77} +12.0824 q^{78} -14.2317 q^{79} -8.73117 q^{80} +1.00000 q^{81} -0.155460 q^{82} +14.0763 q^{83} -2.28561 q^{84} -14.5844 q^{85} -4.46213 q^{86} +2.10969 q^{87} +2.15426 q^{88} -9.13783 q^{89} -5.40001 q^{90} +5.83645 q^{91} +20.8085 q^{92} +8.26629 q^{93} -13.4800 q^{94} -10.6738 q^{95} -8.11182 q^{96} +6.91714 q^{97} -2.07017 q^{98} -3.64355 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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