LMFDB - Embedded newform 4022.2.a.c.1.15

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:	$1$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.691780 q^{3} +1.00000 q^{4} -1.18527 q^{5} -0.691780 q^{6} +3.22162 q^{7} +1.00000 q^{8} -2.52144 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.691780 q^{3} +1.00000 q^{4} -1.18527 q^{5} -0.691780 q^{6} +3.22162 q^{7} +1.00000 q^{8} -2.52144 q^{9} -1.18527 q^{10} +2.03875 q^{11} -0.691780 q^{12} -0.549185 q^{13} +3.22162 q^{14} +0.819944 q^{15} +1.00000 q^{16} -3.75802 q^{17} -2.52144 q^{18} -6.51476 q^{19} -1.18527 q^{20} -2.22865 q^{21} +2.03875 q^{22} +2.82417 q^{23} -0.691780 q^{24} -3.59514 q^{25} -0.549185 q^{26} +3.81962 q^{27} +3.22162 q^{28} -4.77818 q^{29} +0.819944 q^{30} -3.95835 q^{31} +1.00000 q^{32} -1.41036 q^{33} -3.75802 q^{34} -3.81848 q^{35} -2.52144 q^{36} -0.749445 q^{37} -6.51476 q^{38} +0.379915 q^{39} -1.18527 q^{40} -4.07854 q^{41} -2.22865 q^{42} +3.41347 q^{43} +2.03875 q^{44} +2.98858 q^{45} +2.82417 q^{46} +3.84594 q^{47} -0.691780 q^{48} +3.37883 q^{49} -3.59514 q^{50} +2.59972 q^{51} -0.549185 q^{52} -6.86282 q^{53} +3.81962 q^{54} -2.41646 q^{55} +3.22162 q^{56} +4.50678 q^{57} -4.77818 q^{58} -7.54198 q^{59} +0.819944 q^{60} -2.31162 q^{61} -3.95835 q^{62} -8.12312 q^{63} +1.00000 q^{64} +0.650931 q^{65} -1.41036 q^{66} +8.04511 q^{67} -3.75802 q^{68} -1.95371 q^{69} -3.81848 q^{70} +12.2630 q^{71} -2.52144 q^{72} -8.56483 q^{73} -0.749445 q^{74} +2.48705 q^{75} -6.51476 q^{76} +6.56807 q^{77} +0.379915 q^{78} -6.15390 q^{79} -1.18527 q^{80} +4.92199 q^{81} -4.07854 q^{82} -2.80668 q^{83} -2.22865 q^{84} +4.45426 q^{85} +3.41347 q^{86} +3.30545 q^{87} +2.03875 q^{88} +2.10752 q^{89} +2.98858 q^{90} -1.76926 q^{91} +2.82417 q^{92} +2.73831 q^{93} +3.84594 q^{94} +7.72173 q^{95} -0.691780 q^{96} -12.3878 q^{97} +3.37883 q^{98} -5.14058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - 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
$3$	−0.691780	−0.399399	−0.199700	−	0.979857i	$-0.563997\pi$
$3$	−0.691780	−0.399399	−0.199700	+	0.979857i	$0.563997\pi$
$4$	1.00000	0.500000
$5$	−1.18527	−0.530068	−0.265034	−	0.964239i	$-0.585383\pi$
$5$	−1.18527	−0.530068	−0.265034	+	0.964239i	$0.585383\pi$
$6$	−0.691780	−0.282418
$7$	3.22162	1.21766	0.608829	−	0.793302i	$-0.291640\pi$
$7$	3.22162	1.21766	0.608829	+	0.793302i	$0.291640\pi$
$8$	1.00000	0.353553
$9$	−2.52144	−0.840480
$10$	−1.18527	−0.374815
$11$	2.03875	0.614706	0.307353	−	0.951596i	$-0.400557\pi$
$11$	2.03875	0.614706	0.307353	+	0.951596i	$0.400557\pi$
$12$	−0.691780	−0.199700
$13$	−0.549185	−0.152316	−0.0761582	−	0.997096i	$-0.524265\pi$
$13$	−0.549185	−0.152316	−0.0761582	+	0.997096i	$0.524265\pi$
$14$	3.22162	0.861014
$15$	0.819944	0.211709
$16$	1.00000	0.250000
$17$	−3.75802	−0.911454	−0.455727	−	0.890120i	$-0.650621\pi$
$17$	−3.75802	−0.911454	−0.455727	+	0.890120i	$0.650621\pi$
$18$	−2.52144	−0.594309
$19$	−6.51476	−1.49459	−0.747294	−	0.664494i	$-0.768647\pi$
$19$	−6.51476	−1.49459	−0.747294	+	0.664494i	$0.768647\pi$
$20$	−1.18527	−0.265034
$21$	−2.22865	−0.486332
$22$	2.03875	0.434663
$23$	2.82417	0.588881	0.294440	−	0.955670i	$-0.404867\pi$
$23$	2.82417	0.588881	0.294440	+	0.955670i	$0.404867\pi$
$24$	−0.691780	−0.141209
$25$	−3.59514	−0.719028
$26$	−0.549185	−0.107704
$27$	3.81962	0.735086
$28$	3.22162	0.608829
$29$	−4.77818	−0.887286	−0.443643	−	0.896204i	$-0.646314\pi$
$29$	−4.77818	−0.887286	−0.443643	+	0.896204i	$0.646314\pi$
$30$	0.819944	0.149701
$31$	−3.95835	−0.710941	−0.355471	−	0.934687i	$-0.615679\pi$
$31$	−3.95835	−0.710941	−0.355471	+	0.934687i	$0.615679\pi$
$32$	1.00000	0.176777
$33$	−1.41036	−0.245513
$34$	−3.75802	−0.644495
$35$	−3.81848	−0.645441
$36$	−2.52144	−0.420240
$37$	−0.749445	−0.123208	−0.0616040	−	0.998101i	$-0.519622\pi$
$37$	−0.749445	−0.123208	−0.0616040	+	0.998101i	$0.519622\pi$
$38$	−6.51476	−1.05683
$39$	0.379915	0.0608351
$40$	−1.18527	−0.187407
$41$	−4.07854	−0.636961	−0.318480	−	0.947929i	$-0.603172\pi$
$41$	−4.07854	−0.636961	−0.318480	+	0.947929i	$0.603172\pi$
$42$	−2.22865	−0.343888
$43$	3.41347	0.520550	0.260275	−	0.965535i	$-0.416187\pi$
$43$	3.41347	0.520550	0.260275	+	0.965535i	$0.416187\pi$
$44$	2.03875	0.307353
$45$	2.98858	0.445512
$46$	2.82417	0.416402
$47$	3.84594	0.560988	0.280494	−	0.959856i	$-0.409502\pi$
$47$	3.84594	0.560988	0.280494	+	0.959856i	$0.409502\pi$
$48$	−0.691780	−0.0998498
$49$	3.37883	0.482691
$50$	−3.59514	−0.508430
$51$	2.59972	0.364034
$52$	−0.549185	−0.0761582
$53$	−6.86282	−0.942681	−0.471341	−	0.881951i	$-0.656230\pi$
$53$	−6.86282	−0.942681	−0.471341	+	0.881951i	$0.656230\pi$
$54$	3.81962	0.519785
$55$	−2.41646	−0.325836
$56$	3.22162	0.430507
$57$	4.50678	0.596937
$58$	−4.77818	−0.627406
$59$	−7.54198	−0.981883	−0.490941	−	0.871193i	$-0.663347\pi$
$59$	−7.54198	−0.981883	−0.490941	+	0.871193i	$0.663347\pi$
$60$	0.819944	0.105854
$61$	−2.31162	−0.295972	−0.147986	−	0.988989i	$-0.547279\pi$
$61$	−2.31162	−0.295972	−0.147986	+	0.988989i	$0.547279\pi$
$62$	−3.95835	−0.502712
$63$	−8.12312	−1.02342
$64$	1.00000	0.125000
$65$	0.650931	0.0807380
$66$	−1.41036	−0.173604
$67$	8.04511	0.982867	0.491434	−	0.870915i	$-0.336473\pi$
$67$	8.04511	0.982867	0.491434	+	0.870915i	$0.336473\pi$
$68$	−3.75802	−0.455727
$69$	−1.95371	−0.235199
$70$	−3.81848	−0.456396
$71$	12.2630	1.45535	0.727676	−	0.685921i	$-0.240601\pi$
$71$	12.2630	1.45535	0.727676	+	0.685921i	$0.240601\pi$
$72$	−2.52144	−0.297155
$73$	−8.56483	−1.00244	−0.501219	−	0.865321i	$-0.667115\pi$
$73$	−8.56483	−1.00244	−0.501219	+	0.865321i	$0.667115\pi$
$74$	−0.749445	−0.0871212
$75$	2.48705	0.287179
$76$	−6.51476	−0.747294
$77$	6.56807	0.748501
$78$	0.379915	0.0430169
$79$	−6.15390	−0.692368	−0.346184	−	0.938167i	$-0.612523\pi$
$79$	−6.15390	−0.692368	−0.346184	+	0.938167i	$0.612523\pi$
$80$	−1.18527	−0.132517
$81$	4.92199	0.546887
$82$	−4.07854	−0.450399
$83$	−2.80668	−0.308073	−0.154037	−	0.988065i	$-0.549227\pi$
$83$	−2.80668	−0.308073	−0.154037	+	0.988065i	$0.549227\pi$
$84$	−2.22865	−0.243166
$85$	4.45426	0.483132
$86$	3.41347	0.368084
$87$	3.30545	0.354381
$88$	2.03875	0.217331
$89$	2.10752	0.223397	0.111699	−	0.993742i	$-0.464371\pi$
$89$	2.10752	0.223397	0.111699	+	0.993742i	$0.464371\pi$
$90$	2.98858	0.315024
$91$	−1.76926	−0.185469
$92$	2.82417	0.294440
$93$	2.73831	0.283949
$94$	3.84594	0.396678
$95$	7.72173	0.792233
$96$	−0.691780	−0.0706045
$97$	−12.3878	−1.25779	−0.628897	−	0.777489i	$-0.716493\pi$
$97$	−12.3878	−1.25779	−0.628897	+	0.777489i	$0.716493\pi$
$98$	3.37883	0.341314
$99$	−5.14058	−0.516648
$100$	−3.59514	−0.359514
$101$	−10.9075	−1.08534	−0.542670	−	0.839946i	$-0.682587\pi$
$101$	−10.9075	−1.08534	−0.542670	+	0.839946i	$0.682587\pi$
$102$	2.59972	0.257411
$103$	1.77225	0.174625	0.0873127	−	0.996181i	$-0.472172\pi$
$103$	1.77225	0.174625	0.0873127	+	0.996181i	$0.472172\pi$
$104$	−0.549185	−0.0538520
$105$	2.64155	0.257789
$106$	−6.86282	−0.666576
$107$	12.7944	1.23688	0.618441	−	0.785832i	$-0.287765\pi$
$107$	12.7944	1.23688	0.618441	+	0.785832i	$0.287765\pi$
$108$	3.81962	0.367543
$109$	−7.47432	−0.715910	−0.357955	−	0.933739i	$-0.616526\pi$
$109$	−7.47432	−0.715910	−0.357955	+	0.933739i	$0.616526\pi$
$110$	−2.41646	−0.230401
$111$	0.518451	0.0492092
$112$	3.22162	0.304414
$113$	−6.83873	−0.643333	−0.321667	−	0.946853i	$-0.604243\pi$
$113$	−6.83873	−0.643333	−0.321667	+	0.946853i	$0.604243\pi$
$114$	4.50678	0.422098
$115$	−3.34740	−0.312147
$116$	−4.77818	−0.443643
$117$	1.38474	0.128019
$118$	−7.54198	−0.694296
$119$	−12.1069	−1.10984
$120$	0.819944	0.0748503
$121$	−6.84351	−0.622137
$122$	−2.31162	−0.209284
$123$	2.82145	0.254402
$124$	−3.95835	−0.355471
$125$	10.1875	0.911201
$126$	−8.12312	−0.723665
$127$	10.9795	0.974275	0.487137	−	0.873325i	$-0.338041\pi$
$127$	10.9795	0.974275	0.487137	+	0.873325i	$0.338041\pi$
$128$	1.00000	0.0883883
$129$	−2.36137	−0.207907
$130$	0.650931	0.0570904
$131$	−3.34168	−0.291964	−0.145982	−	0.989287i	$-0.546634\pi$
$131$	−3.34168	−0.291964	−0.145982	+	0.989287i	$0.546634\pi$
$132$	−1.41036	−0.122757
$133$	−20.9881	−1.81990
$134$	8.04511	0.694992
$135$	−4.52727	−0.389646
$136$	−3.75802	−0.322248
$137$	−11.3259	−0.967638	−0.483819	−	0.875168i	$-0.660751\pi$
$137$	−11.3259	−0.967638	−0.483819	+	0.875168i	$0.660751\pi$
$138$	−1.95371	−0.166310
$139$	20.7388	1.75904	0.879520	−	0.475862i	$-0.157864\pi$
$139$	20.7388	1.75904	0.879520	+	0.475862i	$0.157864\pi$
$140$	−3.81848	−0.322721
$141$	−2.66054	−0.224058
$142$	12.2630	1.02909
$143$	−1.11965	−0.0936298
$144$	−2.52144	−0.210120
$145$	5.66342	0.470322
$146$	−8.56483	−0.708830
$147$	−2.33741	−0.192786
$148$	−0.749445	−0.0616040
$149$	−7.37871	−0.604487	−0.302244	−	0.953231i	$-0.597736\pi$
$149$	−7.37871	−0.604487	−0.302244	+	0.953231i	$0.597736\pi$
$150$	2.48705	0.203066
$151$	−23.0325	−1.87436	−0.937180	−	0.348847i	$-0.886573\pi$
$151$	−23.0325	−1.87436	−0.937180	+	0.348847i	$0.886573\pi$
$152$	−6.51476	−0.528417
$153$	9.47563	0.766059
$154$	6.56807	0.529270
$155$	4.69171	0.376847
$156$	0.379915	0.0304175
$157$	−0.0955862	−0.00762861	−0.00381430	−	0.999993i	$-0.501214\pi$
$157$	−0.0955862	−0.00762861	−0.00381430	+	0.999993i	$0.501214\pi$
$158$	−6.15390	−0.489578
$159$	4.74756	0.376506
$160$	−1.18527	−0.0937036
$161$	9.09841	0.717055
$162$	4.92199	0.386708
$163$	24.2027	1.89570	0.947850	−	0.318717i	$-0.103252\pi$
$163$	24.2027	1.89570	0.947850	+	0.318717i	$0.103252\pi$
$164$	−4.07854	−0.318480
$165$	1.67166	0.130139
$166$	−2.80668	−0.217841
$167$	−11.3897	−0.881364	−0.440682	−	0.897663i	$-0.645263\pi$
$167$	−11.3897	−0.881364	−0.440682	+	0.897663i	$0.645263\pi$
$168$	−2.22865	−0.171944
$169$	−12.6984	−0.976800
$170$	4.45426	0.341626
$171$	16.4266	1.25617
$172$	3.41347	0.260275
$173$	−13.3485	−1.01487	−0.507433	−	0.861691i	$-0.669405\pi$
$173$	−13.3485	−1.01487	−0.507433	+	0.861691i	$0.669405\pi$
$174$	3.30545	0.250585
$175$	−11.5822	−0.875530
$176$	2.03875	0.153676
$177$	5.21739	0.392163
$178$	2.10752	0.157966
$179$	−16.2953	−1.21797	−0.608984	−	0.793183i	$-0.708423\pi$
$179$	−16.2953	−1.21797	−0.608984	+	0.793183i	$0.708423\pi$
$180$	2.98858	0.222756
$181$	−11.4019	−0.847498	−0.423749	−	0.905780i	$-0.639286\pi$
$181$	−11.4019	−0.847498	−0.423749	+	0.905780i	$0.639286\pi$
$182$	−1.76926	−0.131147
$183$	1.59913	0.118211
$184$	2.82417	0.208201
$185$	0.888293	0.0653086
$186$	2.73831	0.200783
$187$	−7.66166	−0.560276
$188$	3.84594	0.280494
$189$	12.3054	0.895084
$190$	7.72173	0.560193
$191$	−1.72888	−0.125097	−0.0625486	−	0.998042i	$-0.519923\pi$
$191$	−1.72888	−0.125097	−0.0625486	+	0.998042i	$0.519923\pi$
$192$	−0.691780	−0.0499249
$193$	9.43158	0.678900	0.339450	−	0.940624i	$-0.389759\pi$
$193$	9.43158	0.678900	0.339450	+	0.940624i	$0.389759\pi$
$194$	−12.3878	−0.889394
$195$	−0.450301	−0.0322467
$196$	3.37883	0.241345
$197$	10.6116	0.756049	0.378024	−	0.925796i	$-0.376604\pi$
$197$	10.6116	0.756049	0.378024	+	0.925796i	$0.376604\pi$
$198$	−5.14058	−0.365325
$199$	2.50208	0.177368	0.0886839	−	0.996060i	$-0.471734\pi$
$199$	2.50208	0.177368	0.0886839	+	0.996060i	$0.471734\pi$
$200$	−3.59514	−0.254215
$201$	−5.56545	−0.392556
$202$	−10.9075	−0.767452
$203$	−15.3935	−1.08041
$204$	2.59972	0.182017
$205$	4.83416	0.337632
$206$	1.77225	0.123479
$207$	−7.12098	−0.494943
$208$	−0.549185	−0.0380791
$209$	−13.2820	−0.918732
$210$	2.64155	0.182284
$211$	−0.862112	−0.0593502	−0.0296751	−	0.999560i	$-0.509447\pi$
$211$	−0.862112	−0.0593502	−0.0296751	+	0.999560i	$0.509447\pi$
$212$	−6.86282	−0.471341
$213$	−8.48330	−0.581266
$214$	12.7944	0.874607
$215$	−4.04588	−0.275927
$216$	3.81962	0.259892
$217$	−12.7523	−0.865683
$218$	−7.47432	−0.506225
$219$	5.92497	0.400373
$220$	−2.41646	−0.162918
$221$	2.06385	0.138829
$222$	0.518451	0.0347962
$223$	−5.73208	−0.383848	−0.191924	−	0.981410i	$-0.561473\pi$
$223$	−5.73208	−0.383848	−0.191924	+	0.981410i	$0.561473\pi$
$224$	3.22162	0.215254
$225$	9.06493	0.604329
$226$	−6.83873	−0.454905
$227$	−2.50078	−0.165982	−0.0829912	−	0.996550i	$-0.526447\pi$
$227$	−2.50078	−0.165982	−0.0829912	+	0.996550i	$0.526447\pi$
$228$	4.50678	0.298469
$229$	−10.5996	−0.700443	−0.350221	−	0.936667i	$-0.613894\pi$
$229$	−10.5996	−0.700443	−0.350221	+	0.936667i	$0.613894\pi$
$230$	−3.34740	−0.220721
$231$	−4.54366	−0.298951
$232$	−4.77818	−0.313703
$233$	−15.7407	−1.03121	−0.515605	−	0.856827i	$-0.672433\pi$
$233$	−15.7407	−1.03121	−0.515605	+	0.856827i	$0.672433\pi$
$234$	1.38474	0.0905231
$235$	−4.55847	−0.297361
$236$	−7.54198	−0.490941
$237$	4.25714	0.276531
$238$	−12.1069	−0.784775
$239$	−2.27828	−0.147369	−0.0736847	−	0.997282i	$-0.523476\pi$
$239$	−2.27828	−0.147369	−0.0736847	+	0.997282i	$0.523476\pi$
$240$	0.819944	0.0529272
$241$	−10.1993	−0.656993	−0.328497	−	0.944505i	$-0.606542\pi$
$241$	−10.1993	−0.656993	−0.328497	+	0.944505i	$0.606542\pi$
$242$	−6.84351	−0.439917
$243$	−14.8638	−0.953513
$244$	−2.31162	−0.147986
$245$	−4.00482	−0.255859
$246$	2.82145	0.179889
$247$	3.57781	0.227650
$248$	−3.95835	−0.251356
$249$	1.94160	0.123044
$250$	10.1875	0.644317
$251$	12.3284	0.778160	0.389080	−	0.921204i	$-0.372793\pi$
$251$	12.3284	0.778160	0.389080	+	0.921204i	$0.372793\pi$
$252$	−8.12312	−0.511709
$253$	5.75778	0.361988
$254$	10.9795	0.688916
$255$	−3.08137	−0.192963
$256$	1.00000	0.0625000
$257$	11.8095	0.736655	0.368328	−	0.929696i	$-0.379930\pi$
$257$	11.8095	0.736655	0.368328	+	0.929696i	$0.379930\pi$
$258$	−2.36137	−0.147013
$259$	−2.41443	−0.150025
$260$	0.650931	0.0403690
$261$	12.0479	0.745746
$262$	−3.34168	−0.206450
$263$	15.8142	0.975147	0.487574	−	0.873082i	$-0.337882\pi$
$263$	15.8142	0.975147	0.487574	+	0.873082i	$0.337882\pi$
$264$	−1.41036	−0.0868020
$265$	8.13428	0.499685
$266$	−20.9881	−1.28686
$267$	−1.45794	−0.0892246
$268$	8.04511	0.491434
$269$	−3.26390	−0.199003	−0.0995017	−	0.995037i	$-0.531725\pi$
$269$	−3.26390	−0.199003	−0.0995017	+	0.995037i	$0.531725\pi$
$270$	−4.52727	−0.275521
$271$	−23.3208	−1.41664	−0.708318	−	0.705893i	$-0.750546\pi$
$271$	−23.3208	−1.41664	−0.708318	+	0.705893i	$0.750546\pi$
$272$	−3.75802	−0.227863
$273$	1.22394	0.0740763
$274$	−11.3259	−0.684223
$275$	−7.32959	−0.441991
$276$	−1.95371	−0.117599
$277$	0.488585	0.0293562	0.0146781	−	0.999892i	$-0.495328\pi$
$277$	0.488585	0.0293562	0.0146781	+	0.999892i	$0.495328\pi$
$278$	20.7388	1.24383
$279$	9.98076	0.597532
$280$	−3.81848	−0.228198
$281$	−0.954589	−0.0569460	−0.0284730	−	0.999595i	$-0.509064\pi$
$281$	−0.954589	−0.0569460	−0.0284730	+	0.999595i	$0.509064\pi$
$282$	−2.66054	−0.158433
$283$	−10.0730	−0.598776	−0.299388	−	0.954131i	$-0.596783\pi$
$283$	−10.0730	−0.598776	−0.299388	+	0.954131i	$0.596783\pi$
$284$	12.2630	0.727676
$285$	−5.34174	−0.316417
$286$	−1.11965	−0.0662063
$287$	−13.1395	−0.775600
$288$	−2.52144	−0.148577
$289$	−2.87728	−0.169252
$290$	5.66342	0.332568
$291$	8.56965	0.502362
$292$	−8.56483	−0.501219
$293$	14.0568	0.821206	0.410603	−	0.911814i	$-0.365318\pi$
$293$	14.0568	0.821206	0.410603	+	0.911814i	$0.365318\pi$
$294$	−2.33741	−0.136320
$295$	8.93927	0.520464
$296$	−0.749445	−0.0435606
$297$	7.78725	0.451862
$298$	−7.37871	−0.427437
$299$	−1.55099	−0.0896962
$300$	2.48705	0.143590
$301$	10.9969	0.633852
$302$	−23.0325	−1.32537
$303$	7.54561	0.433484
$304$	−6.51476	−0.373647
$305$	2.73988	0.156885
$306$	9.47563	0.541686
$307$	23.7820	1.35731	0.678657	−	0.734456i	$-0.262563\pi$
$307$	23.7820	1.35731	0.678657	+	0.734456i	$0.262563\pi$
$308$	6.56807	0.374251
$309$	−1.22601	−0.0697452
$310$	4.69171	0.266471
$311$	2.63202	0.149248	0.0746241	−	0.997212i	$-0.476224\pi$
$311$	2.63202	0.149248	0.0746241	+	0.997212i	$0.476224\pi$
$312$	0.379915	0.0215084
$313$	17.2755	0.976467	0.488234	−	0.872713i	$-0.337641\pi$
$313$	17.2755	0.976467	0.488234	+	0.872713i	$0.337641\pi$
$314$	−0.0955862	−0.00539424
$315$	9.62808	0.542481
$316$	−6.15390	−0.346184
$317$	28.8858	1.62239	0.811193	−	0.584779i	$-0.198819\pi$
$317$	28.8858	1.62239	0.811193	+	0.584779i	$0.198819\pi$
$318$	4.74756	0.266230
$319$	−9.74150	−0.545420
$320$	−1.18527	−0.0662585
$321$	−8.85091	−0.494009
$322$	9.09841	0.507035
$323$	24.4826	1.36225
$324$	4.92199	0.273444
$325$	1.97440	0.109520
$326$	24.2027	1.34046
$327$	5.17058	0.285934
$328$	−4.07854	−0.225200
$329$	12.3901	0.683091
$330$	1.67166	0.0920218
$331$	−6.84326	−0.376140	−0.188070	−	0.982156i	$-0.560223\pi$
$331$	−6.84326	−0.376140	−0.188070	+	0.982156i	$0.560223\pi$
$332$	−2.80668	−0.154037
$333$	1.88968	0.103554
$334$	−11.3897	−0.623218
$335$	−9.53561	−0.520986
$336$	−2.22865	−0.121583
$337$	−10.8405	−0.590521	−0.295260	−	0.955417i	$-0.595406\pi$
$337$	−10.8405	−0.590521	−0.295260	+	0.955417i	$0.595406\pi$
$338$	−12.6984	−0.690702
$339$	4.73089	0.256947
$340$	4.45426	0.241566
$341$	−8.07009	−0.437020
$342$	16.4266	0.888247
$343$	−11.6660	−0.629906
$344$	3.41347	0.184042
$345$	2.31566	0.124671
$346$	−13.3485	−0.717618
$347$	17.4291	0.935643	0.467821	−	0.883823i	$-0.345039\pi$
$347$	17.4291	0.935643	0.467821	+	0.883823i	$0.345039\pi$
$348$	3.30545	0.177191
$349$	−28.5136	−1.52630	−0.763150	−	0.646221i	$-0.776348\pi$
$349$	−28.5136	−1.52630	−0.763150	+	0.646221i	$0.776348\pi$
$350$	−11.5822	−0.619093
$351$	−2.09768	−0.111966
$352$	2.03875	0.108666
$353$	26.3955	1.40489	0.702445	−	0.711738i	$-0.252092\pi$
$353$	26.3955	1.40489	0.702445	+	0.711738i	$0.252092\pi$
$354$	5.21739	0.277301
$355$	−14.5349	−0.771435
$356$	2.10752	0.111699
$357$	8.37532	0.443269
$358$	−16.2953	−0.861233
$359$	−6.94938	−0.366774	−0.183387	−	0.983041i	$-0.558706\pi$
$359$	−6.94938	−0.366774	−0.183387	+	0.983041i	$0.558706\pi$
$360$	2.98858	0.157512
$361$	23.4421	1.23379
$362$	−11.4019	−0.599271
$363$	4.73420	0.248481
$364$	−1.76926	−0.0927347
$365$	10.1516	0.531360
$366$	1.59913	0.0835879
$367$	26.4782	1.38215	0.691076	−	0.722782i	$-0.257137\pi$
$367$	26.4782	1.38215	0.691076	+	0.722782i	$0.257137\pi$
$368$	2.82417	0.147220
$369$	10.2838	0.535353
$370$	0.888293	0.0461802
$371$	−22.1094	−1.14786
$372$	2.73831	0.141975
$373$	−12.2564	−0.634614	−0.317307	−	0.948323i	$-0.602779\pi$
$373$	−12.2564	−0.634614	−0.317307	+	0.948323i	$0.602779\pi$
$374$	−7.66166	−0.396175
$375$	−7.04754	−0.363933
$376$	3.84594	0.198339
$377$	2.62410	0.135148
$378$	12.3054	0.632920
$379$	10.0891	0.518241	0.259121	−	0.965845i	$-0.416567\pi$
$379$	10.0891	0.518241	0.259121	+	0.965845i	$0.416567\pi$
$380$	7.72173	0.396116
$381$	−7.59541	−0.389125
$382$	−1.72888	−0.0884571
$383$	17.2218	0.879994	0.439997	−	0.897999i	$-0.354980\pi$
$383$	17.2218	0.879994	0.439997	+	0.897999i	$0.354980\pi$
$384$	−0.691780	−0.0353022
$385$	−7.78492	−0.396756
$386$	9.43158	0.480055
$387$	−8.60687	−0.437512
$388$	−12.3878	−0.628897
$389$	6.43252	0.326142	0.163071	−	0.986614i	$-0.447860\pi$
$389$	6.43252	0.326142	0.163071	+	0.986614i	$0.447860\pi$
$390$	−0.450301	−0.0228019
$391$	−10.6133	−0.536738
$392$	3.37883	0.170657
$393$	2.31171	0.116610
$394$	10.6116	0.534607
$395$	7.29402	0.367002
$396$	−5.14058	−0.258324
$397$	−11.7841	−0.591429	−0.295715	−	0.955276i	$-0.595558\pi$
$397$	−11.7841	−0.591429	−0.295715	+	0.955276i	$0.595558\pi$
$398$	2.50208	0.125418
$399$	14.5191	0.726865
$400$	−3.59514	−0.179757
$401$	31.9062	1.59332	0.796659	−	0.604429i	$-0.206599\pi$
$401$	31.9062	1.59332	0.796659	+	0.604429i	$0.206599\pi$
$402$	−5.56545	−0.277579
$403$	2.17387	0.108288
$404$	−10.9075	−0.542670
$405$	−5.83387	−0.289887
$406$	−15.3935	−0.763965
$407$	−1.52793	−0.0757367
$408$	2.59972	0.128705
$409$	−30.5474	−1.51047	−0.755235	−	0.655454i	$-0.772477\pi$
$409$	−30.5474	−1.51047	−0.755235	+	0.655454i	$0.772477\pi$
$410$	4.83416	0.238742
$411$	7.83503	0.386474
$412$	1.77225	0.0873127
$413$	−24.2974	−1.19560
$414$	−7.12098	−0.349977
$415$	3.32667	0.163300
$416$	−0.549185	−0.0269260
$417$	−14.3467	−0.702559
$418$	−13.2820	−0.649641
$419$	−21.5518	−1.05288	−0.526438	−	0.850214i	$-0.676473\pi$
$419$	−21.5518	−1.05288	−0.526438	+	0.850214i	$0.676473\pi$
$420$	2.64155	0.128894
$421$	−9.04665	−0.440907	−0.220453	−	0.975398i	$-0.570754\pi$
$421$	−9.04665	−0.440907	−0.220453	+	0.975398i	$0.570754\pi$
$422$	−0.862112	−0.0419669
$423$	−9.69730	−0.471499
$424$	−6.86282	−0.333288
$425$	13.5106	0.655361
$426$	−8.48330	−0.411017
$427$	−7.44715	−0.360393
$428$	12.7944	0.618441
$429$	0.774551	0.0373957
$430$	−4.04588	−0.195110
$431$	1.72924	0.0832947	0.0416473	−	0.999132i	$-0.486739\pi$
$431$	1.72924	0.0832947	0.0416473	+	0.999132i	$0.486739\pi$
$432$	3.81962	0.183772
$433$	−19.7569	−0.949455	−0.474727	−	0.880133i	$-0.657453\pi$
$433$	−19.7569	−0.949455	−0.474727	+	0.880133i	$0.657453\pi$
$434$	−12.7523	−0.612131
$435$	−3.91784	−0.187846
$436$	−7.47432	−0.357955
$437$	−18.3988	−0.880134
$438$	5.92497	0.283106
$439$	13.2783	0.633738	0.316869	−	0.948469i	$-0.397368\pi$
$439$	13.2783	0.633738	0.316869	+	0.948469i	$0.397368\pi$
$440$	−2.41646	−0.115200
$441$	−8.51953	−0.405692
$442$	2.06385	0.0981672
$443$	37.8786	1.79967	0.899834	−	0.436233i	$-0.143688\pi$
$443$	37.8786	1.79967	0.899834	+	0.436233i	$0.143688\pi$
$444$	0.518451	0.0246046
$445$	−2.49798	−0.118416
$446$	−5.73208	−0.271422
$447$	5.10444	0.241432
$448$	3.22162	0.152207
$449$	−6.38645	−0.301395	−0.150697	−	0.988580i	$-0.548152\pi$
$449$	−6.38645	−0.301395	−0.150697	+	0.988580i	$0.548152\pi$
$450$	9.06493	0.427325
$451$	−8.31511	−0.391543
$452$	−6.83873	−0.321667
$453$	15.9334	0.748618
$454$	−2.50078	−0.117367
$455$	2.09705	0.0983113
$456$	4.50678	0.211049
$457$	13.9145	0.650892	0.325446	−	0.945561i	$-0.394486\pi$
$457$	13.9145	0.650892	0.325446	+	0.945561i	$0.394486\pi$
$458$	−10.5996	−0.495288
$459$	−14.3542	−0.669997
$460$	−3.34740	−0.156073
$461$	33.7746	1.57304	0.786520	−	0.617565i	$-0.211881\pi$
$461$	33.7746	1.57304	0.786520	+	0.617565i	$0.211881\pi$
$462$	−4.54366	−0.211390
$463$	−31.8339	−1.47945	−0.739723	−	0.672912i	$-0.765043\pi$
$463$	−31.8339	−1.47945	−0.739723	+	0.672912i	$0.765043\pi$
$464$	−4.77818	−0.221821
$465$	−3.24563	−0.150512
$466$	−15.7407	−0.729175
$467$	−25.7410	−1.19115	−0.595576	−	0.803299i	$-0.703076\pi$
$467$	−25.7410	−1.19115	−0.595576	+	0.803299i	$0.703076\pi$
$468$	1.38474	0.0640095
$469$	25.9183	1.19680
$470$	−4.55847	−0.210266
$471$	0.0661246	0.00304686
$472$	−7.54198	−0.347148
$473$	6.95922	0.319985
$474$	4.25714	0.195537
$475$	23.4215	1.07465
$476$	−12.1069	−0.554920
$477$	17.3042	0.792305
$478$	−2.27828	−0.104206
$479$	4.73168	0.216196	0.108098	−	0.994140i	$-0.465524\pi$
$479$	4.73168	0.216196	0.108098	+	0.994140i	$0.465524\pi$
$480$	0.819944	0.0374252
$481$	0.411584	0.0187666
$482$	−10.1993	−0.464564
$483$	−6.29410	−0.286391
$484$	−6.84351	−0.311068
$485$	14.6829	0.666716
$486$	−14.8638	−0.674235
$487$	7.94211	0.359891	0.179946	−	0.983677i	$-0.442408\pi$
$487$	7.94211	0.359891	0.179946	+	0.983677i	$0.442408\pi$
$488$	−2.31162	−0.104642
$489$	−16.7429	−0.757141
$490$	−4.00482	−0.180919
$491$	−38.9296	−1.75687	−0.878435	−	0.477863i	$-0.841412\pi$
$491$	−38.9296	−1.75687	−0.878435	+	0.477863i	$0.841412\pi$
$492$	2.82145	0.127201
$493$	17.9565	0.808720
$494$	3.57781	0.160973
$495$	6.09297	0.273858
$496$	−3.95835	−0.177735
$497$	39.5067	1.77212
$498$	1.94160	0.0870054
$499$	0.646610	0.0289463	0.0144731	−	0.999895i	$-0.495393\pi$
$499$	0.646610	0.0289463	0.0144731	+	0.999895i	$0.495393\pi$
$500$	10.1875	0.455601
$501$	7.87918	0.352016
$502$	12.3284	0.550242
$503$	−11.8917	−0.530226	−0.265113	−	0.964217i	$-0.585409\pi$
$503$	−11.8917	−0.530226	−0.265113	+	0.964217i	$0.585409\pi$
$504$	−8.12312	−0.361833
$505$	12.9284	0.575304
$506$	5.75778	0.255964
$507$	8.78449	0.390133
$508$	10.9795	0.487137
$509$	36.3409	1.61078	0.805391	−	0.592744i	$-0.201955\pi$
$509$	36.3409	1.61078	0.805391	+	0.592744i	$0.201955\pi$
$510$	−3.08137	−0.136445
$511$	−27.5926	−1.22063
$512$	1.00000	0.0441942
$513$	−24.8839	−1.09865
$514$	11.8095	0.520894
$515$	−2.10060	−0.0925633
$516$	−2.36137	−0.103954
$517$	7.84090	0.344842
$518$	−2.41443	−0.106084
$519$	9.23420	0.405336
$520$	0.650931	0.0285452
$521$	3.43033	0.150285	0.0751427	−	0.997173i	$-0.476059\pi$
$521$	3.43033	0.150285	0.0751427	+	0.997173i	$0.476059\pi$
$522$	12.0479	0.527322
$523$	33.8364	1.47956	0.739781	−	0.672848i	$-0.234929\pi$
$523$	33.8364	1.47956	0.739781	+	0.672848i	$0.234929\pi$
$524$	−3.34168	−0.145982
$525$	8.01232	0.349686
$526$	15.8142	0.689533
$527$	14.8756	0.647990
$528$	−1.41036	−0.0613783
$529$	−15.0240	−0.653219
$530$	8.13428	0.353331
$531$	19.0167	0.825253
$532$	−20.9881	−0.909948
$533$	2.23987	0.0970196
$534$	−1.45794	−0.0630913
$535$	−15.1648	−0.655631
$536$	8.04511	0.347496
$537$	11.2728	0.486455
$538$	−3.26390	−0.140717
$539$	6.88859	0.296713
$540$	−4.52727	−0.194823
$541$	−2.95361	−0.126985	−0.0634927	−	0.997982i	$-0.520224\pi$
$541$	−2.95361	−0.126985	−0.0634927	+	0.997982i	$0.520224\pi$
$542$	−23.3208	−1.00171
$543$	7.88761	0.338490
$544$	−3.75802	−0.161124
$545$	8.85907	0.379481
$546$	1.22394	0.0523799
$547$	29.5493	1.26344	0.631719	−	0.775198i	$-0.282350\pi$
$547$	29.5493	1.26344	0.631719	+	0.775198i	$0.282350\pi$
$548$	−11.3259	−0.483819
$549$	5.82860	0.248759
$550$	−7.32959	−0.312535
$551$	31.1287	1.32613
$552$	−1.95371	−0.0831552
$553$	−19.8255	−0.843067
$554$	0.488585	0.0207580
$555$	−0.614503	−0.0260842
$556$	20.7388	0.879520
$557$	42.8469	1.81548	0.907740	−	0.419532i	$-0.137806\pi$
$557$	42.8469	1.81548	0.907740	+	0.419532i	$0.137806\pi$
$558$	9.98076	0.422519
$559$	−1.87463	−0.0792883
$560$	−3.81848	−0.161360
$561$	5.30018	0.223774
$562$	−0.954589	−0.0402669
$563$	40.1312	1.69133	0.845664	−	0.533716i	$-0.179205\pi$
$563$	40.1312	1.69133	0.845664	+	0.533716i	$0.179205\pi$
$564$	−2.66054	−0.112029
$565$	8.10572	0.341010
$566$	−10.0730	−0.423399
$567$	15.8568	0.665922
$568$	12.2630	0.514544
$569$	29.0580	1.21818	0.609088	−	0.793103i	$-0.291536\pi$
$569$	29.0580	1.21818	0.609088	+	0.793103i	$0.291536\pi$
$570$	−5.34174	−0.223741
$571$	−7.31014	−0.305920	−0.152960	−	0.988232i	$-0.548881\pi$
$571$	−7.31014	−0.305920	−0.152960	+	0.988232i	$0.548881\pi$
$572$	−1.11965	−0.0468149
$573$	1.19600	0.0499637
$574$	−13.1395	−0.548432
$575$	−10.1533	−0.423422
$576$	−2.52144	−0.105060
$577$	−1.15629	−0.0481370	−0.0240685	−	0.999710i	$-0.507662\pi$
$577$	−1.15629	−0.0481370	−0.0240685	+	0.999710i	$0.507662\pi$
$578$	−2.87728	−0.119679
$579$	−6.52457	−0.271152
$580$	5.66342	0.235161
$581$	−9.04206	−0.375128
$582$	8.56965	0.355223
$583$	−13.9916	−0.579471
$584$	−8.56483	−0.354415
$585$	−1.64128	−0.0678587
$586$	14.0568	0.580680
$587$	−24.2413	−1.00055	−0.500273	−	0.865868i	$-0.666767\pi$
$587$	−24.2413	−1.00055	−0.500273	+	0.865868i	$0.666767\pi$
$588$	−2.33741	−0.0963931
$589$	25.7877	1.06256
$590$	8.93927	0.368024
$591$	−7.34092	−0.301965
$592$	−0.749445	−0.0308020
$593$	5.12248	0.210355	0.105178	−	0.994453i	$-0.466459\pi$
$593$	5.12248	0.210355	0.105178	+	0.994453i	$0.466459\pi$
$594$	7.78725	0.319515
$595$	14.3499	0.588290
$596$	−7.37871	−0.302244
$597$	−1.73089	−0.0708405
$598$	−1.55099	−0.0634248
$599$	1.41900	0.0579787	0.0289893	−	0.999580i	$-0.490771\pi$
$599$	1.41900	0.0579787	0.0289893	+	0.999580i	$0.490771\pi$
$600$	2.48705	0.101533
$601$	37.9287	1.54715	0.773573	−	0.633708i	$-0.218468\pi$
$601$	37.9287	1.54715	0.773573	+	0.633708i	$0.218468\pi$
$602$	10.9969	0.448201
$603$	−20.2853	−0.826080
$604$	−23.0325	−0.937180
$605$	8.11139	0.329775
$606$	7.54561	0.306520
$607$	14.8166	0.601387	0.300693	−	0.953721i	$-0.402782\pi$
$607$	14.8166	0.601387	0.300693	+	0.953721i	$0.402782\pi$
$608$	−6.51476	−0.264208
$609$	10.6489	0.431515
$610$	2.73988	0.110935
$611$	−2.11213	−0.0854476
$612$	9.47563	0.383030
$613$	−36.4606	−1.47263	−0.736315	−	0.676639i	$-0.763436\pi$
$613$	−36.4606	−1.47263	−0.736315	+	0.676639i	$0.763436\pi$
$614$	23.7820	0.959765
$615$	−3.34417	−0.134850
$616$	6.56807	0.264635
$617$	−28.6470	−1.15328	−0.576641	−	0.816997i	$-0.695637\pi$
$617$	−28.6470	−1.15328	−0.576641	+	0.816997i	$0.695637\pi$
$618$	−1.22601	−0.0493173
$619$	−5.35725	−0.215326	−0.107663	−	0.994187i	$-0.534337\pi$
$619$	−5.35725	−0.215326	−0.107663	+	0.994187i	$0.534337\pi$
$620$	4.69171	0.188424
$621$	10.7873	0.432878
$622$	2.63202	0.105534
$623$	6.78964	0.272021
$624$	0.379915	0.0152088
$625$	5.90074	0.236030
$626$	17.2755	0.690467
$627$	9.18818	0.366941
$628$	−0.0955862	−0.00381430
$629$	2.81643	0.112298
$630$	9.62808	0.383592
$631$	6.03057	0.240073	0.120037	−	0.992769i	$-0.461699\pi$
$631$	6.03057	0.240073	0.120037	+	0.992769i	$0.461699\pi$
$632$	−6.15390	−0.244789
$633$	0.596391	0.0237044
$634$	28.8858	1.14720
$635$	−13.0137	−0.516432
$636$	4.74756	0.188253
$637$	−1.85560	−0.0735217
$638$	−9.74150	−0.385670
$639$	−30.9204	−1.22319
$640$	−1.18527	−0.0468518
$641$	28.9779	1.14456	0.572278	−	0.820059i	$-0.306060\pi$
$641$	28.9779	1.14456	0.572278	+	0.820059i	$0.306060\pi$
$642$	−8.85091	−0.349317
$643$	17.1528	0.676442	0.338221	−	0.941067i	$-0.390175\pi$
$643$	17.1528	0.676442	0.338221	+	0.941067i	$0.390175\pi$
$644$	9.09841	0.358528
$645$	2.79886	0.110205
$646$	24.4826	0.963255
$647$	−17.8419	−0.701436	−0.350718	−	0.936481i	$-0.614063\pi$
$647$	−17.8419	−0.701436	−0.350718	+	0.936481i	$0.614063\pi$
$648$	4.92199	0.193354
$649$	−15.3762	−0.603569
$650$	1.97440	0.0774422
$651$	8.82179	0.345753
$652$	24.2027	0.947850
$653$	−27.0554	−1.05876	−0.529380	−	0.848385i	$-0.677576\pi$
$653$	−27.0554	−1.05876	−0.529380	+	0.848385i	$0.677576\pi$
$654$	5.17058	0.202186
$655$	3.96078	0.154761
$656$	−4.07854	−0.159240
$657$	21.5957	0.842529
$658$	12.3901	0.483018
$659$	47.9041	1.86608	0.933040	−	0.359773i	$-0.117146\pi$
$659$	47.9041	1.86608	0.933040	+	0.359773i	$0.117146\pi$
$660$	1.67166	0.0650693
$661$	−45.8136	−1.78194	−0.890971	−	0.454061i	$-0.849975\pi$
$661$	−45.8136	−1.78194	−0.890971	+	0.454061i	$0.849975\pi$
$662$	−6.84326	−0.265971
$663$	−1.42773	−0.0554484
$664$	−2.80668	−0.108920
$665$	24.8765	0.964669
$666$	1.88968	0.0732237
$667$	−13.4944	−0.522505
$668$	−11.3897	−0.440682
$669$	3.96534	0.153309
$670$	−9.53561	−0.368393
$671$	−4.71280	−0.181936
$672$	−2.22865	−0.0859721
$673$	21.4103	0.825306	0.412653	−	0.910888i	$-0.364602\pi$
$673$	21.4103	0.825306	0.412653	+	0.910888i	$0.364602\pi$
$674$	−10.8405	−0.417561
$675$	−13.7321	−0.528548
$676$	−12.6984	−0.488400
$677$	24.1722	0.929015	0.464507	−	0.885569i	$-0.346231\pi$
$677$	24.1722	0.929015	0.464507	+	0.885569i	$0.346231\pi$
$678$	4.73089	0.181689
$679$	−39.9089	−1.53156
$680$	4.45426	0.170813
$681$	1.72999	0.0662933
$682$	−8.07009	−0.309020
$683$	−16.3129	−0.624194	−0.312097	−	0.950050i	$-0.601031\pi$
$683$	−16.3129	−0.624194	−0.312097	+	0.950050i	$0.601031\pi$
$684$	16.4266	0.628086
$685$	13.4242	0.512913
$686$	−11.6660	−0.445411
$687$	7.33260	0.279756
$688$	3.41347	0.130138
$689$	3.76896	0.143586
$690$	2.31566	0.0881558
$691$	−0.737456	−0.0280541	−0.0140271	−	0.999902i	$-0.504465\pi$
$691$	−0.737456	−0.0280541	−0.0140271	+	0.999902i	$0.504465\pi$
$692$	−13.3485	−0.507433
$693$	−16.5610	−0.629101
$694$	17.4291	0.661599
$695$	−24.5810	−0.932411
$696$	3.30545	0.125293
$697$	15.3272	0.580560
$698$	−28.5136	−1.07926
$699$	10.8891	0.411864
$700$	−11.5822	−0.437765
$701$	17.9889	0.679430	0.339715	−	0.940528i	$-0.389669\pi$
$701$	17.9889	0.679430	0.339715	+	0.940528i	$0.389669\pi$
$702$	−2.09768	−0.0791717
$703$	4.88245	0.184145
$704$	2.03875	0.0768382
$705$	3.15345	0.118766
$706$	26.3955	0.993407
$707$	−35.1399	−1.32157
$708$	5.21739	0.196082
$709$	48.7720	1.83167	0.915835	−	0.401555i	$-0.131530\pi$
$709$	48.7720	1.83167	0.915835	+	0.401555i	$0.131530\pi$
$710$	−14.5349	−0.545487
$711$	15.5167	0.581921
$712$	2.10752	0.0789828
$713$	−11.1791	−0.418660
$714$	8.37532	0.313438
$715$	1.32708	0.0496301
$716$	−16.2953	−0.608984
$717$	1.57607	0.0588593
$718$	−6.94938	−0.259348
$719$	24.8948	0.928421	0.464210	−	0.885725i	$-0.346338\pi$
$719$	24.8948	0.928421	0.464210	+	0.885725i	$0.346338\pi$
$720$	2.98858	0.111378
$721$	5.70953	0.212634
$722$	23.4421	0.872423
$723$	7.05565	0.262403
$724$	−11.4019	−0.423749
$725$	17.1782	0.637983
$726$	4.73420	0.175703
$727$	−7.41425	−0.274979	−0.137490	−	0.990503i	$-0.543903\pi$
$727$	−7.41425	−0.274979	−0.137490	+	0.990503i	$0.543903\pi$
$728$	−1.76926	−0.0655733
$729$	−4.48348	−0.166055
$730$	10.1516	0.375728
$731$	−12.8279	−0.474457
$732$	1.59913	0.0591055
$733$	−34.6594	−1.28018	−0.640088	−	0.768302i	$-0.721102\pi$
$733$	−34.6594	−1.28018	−0.640088	+	0.768302i	$0.721102\pi$
$734$	26.4782	0.977330
$735$	2.77046	0.102190
$736$	2.82417	0.104100
$737$	16.4020	0.604174
$738$	10.2838	0.378552
$739$	16.5928	0.610375	0.305188	−	0.952292i	$-0.401281\pi$
$739$	16.5928	0.610375	0.305188	+	0.952292i	$0.401281\pi$
$740$	0.888293	0.0326543
$741$	−2.47505	−0.0909234
$742$	−22.1094	−0.811662
$743$	−9.39706	−0.344745	−0.172372	−	0.985032i	$-0.555143\pi$
$743$	−9.39706	−0.344745	−0.172372	+	0.985032i	$0.555143\pi$
$744$	2.73831	0.100391
$745$	8.74574	0.320419
$746$	−12.2564	−0.448740
$747$	7.07688	0.258929
$748$	−7.66166	−0.280138
$749$	41.2187	1.50610
$750$	−7.04754	−0.257340
$751$	−6.21663	−0.226848	−0.113424	−	0.993547i	$-0.536182\pi$
$751$	−6.21663	−0.226848	−0.113424	+	0.993547i	$0.536182\pi$
$752$	3.84594	0.140247
$753$	−8.52851	−0.310796
$754$	2.62410	0.0955642
$755$	27.2997	0.993538
$756$	12.3054	0.447542
$757$	−49.5197	−1.79982	−0.899911	−	0.436073i	$-0.856369\pi$
$757$	−49.5197	−1.79982	−0.899911	+	0.436073i	$0.856369\pi$
$758$	10.0891	0.366452
$759$	−3.98311	−0.144578
$760$	7.72173	0.280097
$761$	25.8700	0.937786	0.468893	−	0.883255i	$-0.344653\pi$
$761$	25.8700	0.937786	0.468893	+	0.883255i	$0.344653\pi$
$762$	−7.59541	−0.275153
$763$	−24.0794	−0.871733
$764$	−1.72888	−0.0625486
$765$	−11.2312	−0.406063
$766$	17.2218	0.622250
$767$	4.14194	0.149557
$768$	−0.691780	−0.0249625
$769$	1.60308	0.0578084	0.0289042	−	0.999582i	$-0.490798\pi$
$769$	1.60308	0.0578084	0.0289042	+	0.999582i	$0.490798\pi$
$770$	−7.78492	−0.280549
$771$	−8.16956	−0.294220
$772$	9.43158	0.339450
$773$	−42.8656	−1.54177	−0.770885	−	0.636975i	$-0.780186\pi$
$773$	−42.8656	−1.54177	−0.770885	+	0.636975i	$0.780186\pi$
$774$	−8.60687	−0.309368
$775$	14.2308	0.511187
$776$	−12.3878	−0.444697
$777$	1.67025	0.0599200
$778$	6.43252	0.230617
$779$	26.5707	0.951994
$780$	−0.450301	−0.0161234
$781$	25.0012	0.894613
$782$	−10.6133	−0.379531
$783$	−18.2508	−0.652232
$784$	3.37883	0.120673
$785$	0.113295	0.00404368
$786$	2.31171	0.0824558
$787$	−2.95264	−0.105250	−0.0526250	−	0.998614i	$-0.516759\pi$
$787$	−2.95264	−0.105250	−0.0526250	+	0.998614i	$0.516759\pi$
$788$	10.6116	0.378024
$789$	−10.9400	−0.389473
$790$	7.29402	0.259509
$791$	−22.0318	−0.783360
$792$	−5.14058	−0.182663
$793$	1.26950	0.0450814
$794$	−11.7841	−0.418204
$795$	−5.62713	−0.199574
$796$	2.50208	0.0886839
$797$	−3.95491	−0.140090	−0.0700450	−	0.997544i	$-0.522314\pi$
$797$	−3.95491	−0.140090	−0.0700450	+	0.997544i	$0.522314\pi$
$798$	14.5191	0.513971
$799$	−14.4531	−0.511314
$800$	−3.59514	−0.127107
$801$	−5.31400	−0.187761
$802$	31.9062	1.12665
$803$	−17.4615	−0.616204
$804$	−5.56545	−0.196278
$805$	−10.7841	−0.380088
$806$	2.17387	0.0765712
$807$	2.25790	0.0794818
$808$	−10.9075	−0.383726
$809$	−13.0590	−0.459130	−0.229565	−	0.973293i	$-0.573730\pi$
$809$	−13.0590	−0.459130	−0.229565	+	0.973293i	$0.573730\pi$
$810$	−5.83387	−0.204981
$811$	−42.4782	−1.49161	−0.745805	−	0.666164i	$-0.767935\pi$
$811$	−42.4782	−1.49161	−0.745805	+	0.666164i	$0.767935\pi$
$812$	−15.3935	−0.540205
$813$	16.1328	0.565804
$814$	−1.52793	−0.0535539
$815$	−28.6866	−1.00485
$816$	2.59972	0.0910085
$817$	−22.2380	−0.778008
$818$	−30.5474	−1.06806
$819$	4.46110	0.155883
$820$	4.83416	0.168816
$821$	22.4550	0.783684	0.391842	−	0.920032i	$-0.371838\pi$
$821$	22.4550	0.783684	0.391842	+	0.920032i	$0.371838\pi$
$822$	7.83503	0.273278
$823$	−24.2842	−0.846493	−0.423247	−	0.906014i	$-0.639110\pi$
$823$	−24.2842	−0.846493	−0.423247	+	0.906014i	$0.639110\pi$
$824$	1.77225	0.0617394
$825$	5.07046	0.176531
$826$	−24.2974	−0.845415
$827$	46.8980	1.63080	0.815402	−	0.578894i	$-0.196516\pi$
$827$	46.8980	1.63080	0.815402	+	0.578894i	$0.196516\pi$
$828$	−7.12098	−0.247471
$829$	−22.1716	−0.770051	−0.385026	−	0.922906i	$-0.625807\pi$
$829$	−22.1716	−0.770051	−0.385026	+	0.922906i	$0.625807\pi$
$830$	3.32667	0.115470
$831$	−0.337993	−0.0117249
$832$	−0.549185	−0.0190396
$833$	−12.6977	−0.439950
$834$	−14.3467	−0.496784
$835$	13.4999	0.467183
$836$	−13.2820	−0.459366
$837$	−15.1194	−0.522603
$838$	−21.5518	−0.744495
$839$	−37.3400	−1.28912	−0.644560	−	0.764553i	$-0.722960\pi$
$839$	−37.3400	−1.28912	−0.644560	+	0.764553i	$0.722960\pi$
$840$	2.64155	0.0911421
$841$	−6.16900	−0.212724
$842$	−9.04665	−0.311768
$843$	0.660366	0.0227442
$844$	−0.862112	−0.0296751
$845$	15.0510	0.517770
$846$	−9.69730	−0.333400
$847$	−22.0472	−0.757550
$848$	−6.86282	−0.235670
$849$	6.96828	0.239151
$850$	13.5106	0.463410
$851$	−2.11656	−0.0725548
$852$	−8.48330	−0.290633
$853$	−26.5401	−0.908717	−0.454358	−	0.890819i	$-0.650131\pi$
$853$	−26.5401	−0.908717	−0.454358	+	0.890819i	$0.650131\pi$
$854$	−7.44715	−0.254836
$855$	−19.4699	−0.665856
$856$	12.7944	0.437304
$857$	46.3022	1.58165	0.790826	−	0.612041i	$-0.209651\pi$
$857$	46.3022	1.58165	0.790826	+	0.612041i	$0.209651\pi$
$858$	0.774551	0.0264427
$859$	7.60912	0.259620	0.129810	−	0.991539i	$-0.458563\pi$
$859$	7.60912	0.259620	0.129810	+	0.991539i	$0.458563\pi$
$860$	−4.04588	−0.137963
$861$	9.08964	0.309774
$862$	1.72924	0.0588982
$863$	−5.71036	−0.194383	−0.0971915	−	0.995266i	$-0.530986\pi$
$863$	−5.71036	−0.194383	−0.0971915	+	0.995266i	$0.530986\pi$
$864$	3.81962	0.129946
$865$	15.8215	0.537947
$866$	−19.7569	−0.671366
$867$	1.99044	0.0675990
$868$	−12.7523	−0.432842
$869$	−12.5463	−0.425602
$870$	−3.91784	−0.132827
$871$	−4.41825	−0.149707
$872$	−7.47432	−0.253112
$873$	31.2352	1.05715
$874$	−18.3988	−0.622349
$875$	32.8204	1.10953
$876$	5.92497	0.200186
$877$	44.2488	1.49417	0.747087	−	0.664726i	$-0.231452\pi$
$877$	44.2488	1.49417	0.747087	+	0.664726i	$0.231452\pi$
$878$	13.2783	0.448121
$879$	−9.72420	−0.327989
$880$	−2.41646	−0.0814589
$881$	11.5460	0.388995	0.194498	−	0.980903i	$-0.437692\pi$
$881$	11.5460	0.388995	0.194498	+	0.980903i	$0.437692\pi$
$882$	−8.51953	−0.286867
$883$	−16.4691	−0.554229	−0.277115	−	0.960837i	$-0.589378\pi$
$883$	−16.4691	−0.554229	−0.277115	+	0.960837i	$0.589378\pi$
$884$	2.06385	0.0694147
$885$	−6.18401	−0.207873
$886$	37.8786	1.27256
$887$	24.7065	0.829563	0.414781	−	0.909921i	$-0.363858\pi$
$887$	24.7065	0.829563	0.414781	+	0.909921i	$0.363858\pi$
$888$	0.518451	0.0173981
$889$	35.3718	1.18633
$890$	−2.49798	−0.0837325
$891$	10.0347	0.336175
$892$	−5.73208	−0.191924
$893$	−25.0553	−0.838445
$894$	5.10444	0.170718
$895$	19.3143	0.645605
$896$	3.22162	0.107627
$897$	1.07295	0.0358246
$898$	−6.38645	−0.213118
$899$	18.9137	0.630808
$900$	9.06493	0.302164
$901$	25.7906	0.859210
$902$	−8.31511	−0.276863
$903$	−7.60745	−0.253160
$904$	−6.83873	−0.227453
$905$	13.5143	0.449231
$906$	15.9334	0.529353
$907$	−3.68263	−0.122280	−0.0611399	−	0.998129i	$-0.519474\pi$
$907$	−3.68263	−0.122280	−0.0611399	+	0.998129i	$0.519474\pi$
$908$	−2.50078	−0.0829912
$909$	27.5027	0.912207
$910$	2.09705	0.0695166
$911$	−53.2512	−1.76429	−0.882146	−	0.470977i	$-0.843902\pi$
$911$	−53.2512	−1.76429	−0.882146	+	0.470977i	$0.843902\pi$
$912$	4.50678	0.149234
$913$	−5.72211	−0.189374
$914$	13.9145	0.460250
$915$	−1.89540	−0.0626599
$916$	−10.5996	−0.350221
$917$	−10.7656	−0.355512
$918$	−14.3542	−0.473760
$919$	−13.3652	−0.440877	−0.220439	−	0.975401i	$-0.570749\pi$
$919$	−13.3652	−0.440877	−0.220439	+	0.975401i	$0.570749\pi$
$920$	−3.34740	−0.110361
$921$	−16.4519	−0.542110
$922$	33.7746	1.11231
$923$	−6.73466	−0.221674
$924$	−4.54366	−0.149475
$925$	2.69436	0.0885900
$926$	−31.8339	−1.04613
$927$	−4.46863	−0.146769
$928$	−4.77818	−0.156851
$929$	−6.40561	−0.210161	−0.105081	−	0.994464i	$-0.533510\pi$
$929$	−6.40561	−0.210161	−0.105081	+	0.994464i	$0.533510\pi$
$930$	−3.24563	−0.106428
$931$	−22.0123	−0.721423
$932$	−15.7407	−0.515605
$933$	−1.82078	−0.0596096
$934$	−25.7410	−0.842271
$935$	9.08112	0.296984
$936$	1.38474	0.0452615
$937$	13.2838	0.433964	0.216982	−	0.976176i	$-0.430379\pi$
$937$	13.2838	0.433964	0.216982	+	0.976176i	$0.430379\pi$
$938$	25.9183	0.846262
$939$	−11.9508	−0.390000
$940$	−4.55847	−0.148681
$941$	46.2785	1.50863	0.754317	−	0.656510i	$-0.227968\pi$
$941$	46.2785	1.50863	0.754317	+	0.656510i	$0.227968\pi$
$942$	0.0661246	0.00215445
$943$	−11.5185	−0.375094
$944$	−7.54198	−0.245471
$945$	−14.5852	−0.474455
$946$	6.95922	0.226264
$947$	23.7559	0.771962	0.385981	−	0.922507i	$-0.373863\pi$
$947$	23.7559	0.771962	0.385981	+	0.922507i	$0.373863\pi$
$948$	4.25714	0.138266
$949$	4.70367	0.152688
$950$	23.4215	0.759893
$951$	−19.9826	−0.647980
$952$	−12.1069	−0.392387
$953$	−32.3768	−1.04879	−0.524394	−	0.851476i	$-0.675708\pi$
$953$	−32.3768	−1.04879	−0.524394	+	0.851476i	$0.675708\pi$
$954$	17.3042	0.560244
$955$	2.04918	0.0663100
$956$	−2.27828	−0.0736847
$957$	6.73898	0.217840
$958$	4.73168	0.152874
$959$	−36.4878	−1.17825
$960$	0.819944	0.0264636
$961$	−15.3314	−0.494562
$962$	0.411584	0.0132700
$963$	−32.2603	−1.03957
$964$	−10.1993	−0.328497
$965$	−11.1789	−0.359863
$966$	−6.29410	−0.202509
$967$	−45.7316	−1.47063	−0.735315	−	0.677726i	$-0.762966\pi$
$967$	−45.7316	−1.47063	−0.735315	+	0.677726i	$0.762966\pi$
$968$	−6.84351	−0.219959
$969$	−16.9366	−0.544081
$970$	14.6829	0.471439
$971$	20.9237	0.671475	0.335737	−	0.941956i	$-0.391015\pi$
$971$	20.9237	0.671475	0.335737	+	0.941956i	$0.391015\pi$
$972$	−14.8638	−0.476756
$973$	66.8125	2.14191
$974$	7.94211	0.254482
$975$	−1.36585	−0.0437421
$976$	−2.31162	−0.0739931
$977$	−2.85650	−0.0913875	−0.0456937	−	0.998955i	$-0.514550\pi$
$977$	−2.85650	−0.0913875	−0.0456937	+	0.998955i	$0.514550\pi$
$978$	−16.7429	−0.535380
$979$	4.29671	0.137323
$980$	−4.00482	−0.127929
$981$	18.8461	0.601708
$982$	−38.9296	−1.24229
$983$	−18.6860	−0.595990	−0.297995	−	0.954567i	$-0.596318\pi$
$983$	−18.6860	−0.595990	−0.297995	+	0.954567i	$0.596318\pi$
$984$	2.82145	0.0899445
$985$	−12.5776	−0.400757
$986$	17.9565	0.571851
$987$	−8.57125	−0.272826
$988$	3.57781	0.113825
$989$	9.64024	0.306542
$990$	6.09297	0.193647
$991$	0.437077	0.0138842	0.00694210	−	0.999976i	$-0.497790\pi$
$991$	0.437077	0.0138842	0.00694210	+	0.999976i	$0.497790\pi$
$992$	−3.95835	−0.125678
$993$	4.73403	0.150230
$994$	39.5067	1.25308
$995$	−2.96563	−0.0940169
$996$	1.94160	0.0615221
$997$	6.40786	0.202939	0.101469	−	0.994839i	$-0.467646\pi$
$997$	6.40786	0.202939	0.101469	+	0.994839i	$0.467646\pi$
$998$	0.646610	0.0204681
$999$	−2.86260	−0.0905685

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.c.1.15	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.c.1.15	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.691780 q^{3} +1.00000 q^{4} -1.18527 q^{5} -0.691780 q^{6} +3.22162 q^{7} +1.00000 q^{8} -2.52144 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.691780 q^{3} +1.00000 q^{4} -1.18527 q^{5} -0.691780 q^{6} +3.22162 q^{7} +1.00000 q^{8} -2.52144 q^{9} -1.18527 q^{10} +2.03875 q^{11} -0.691780 q^{12} -0.549185 q^{13} +3.22162 q^{14} +0.819944 q^{15} +1.00000 q^{16} -3.75802 q^{17} -2.52144 q^{18} -6.51476 q^{19} -1.18527 q^{20} -2.22865 q^{21} +2.03875 q^{22} +2.82417 q^{23} -0.691780 q^{24} -3.59514 q^{25} -0.549185 q^{26} +3.81962 q^{27} +3.22162 q^{28} -4.77818 q^{29} +0.819944 q^{30} -3.95835 q^{31} +1.00000 q^{32} -1.41036 q^{33} -3.75802 q^{34} -3.81848 q^{35} -2.52144 q^{36} -0.749445 q^{37} -6.51476 q^{38} +0.379915 q^{39} -1.18527 q^{40} -4.07854 q^{41} -2.22865 q^{42} +3.41347 q^{43} +2.03875 q^{44} +2.98858 q^{45} +2.82417 q^{46} +3.84594 q^{47} -0.691780 q^{48} +3.37883 q^{49} -3.59514 q^{50} +2.59972 q^{51} -0.549185 q^{52} -6.86282 q^{53} +3.81962 q^{54} -2.41646 q^{55} +3.22162 q^{56} +4.50678 q^{57} -4.77818 q^{58} -7.54198 q^{59} +0.819944 q^{60} -2.31162 q^{61} -3.95835 q^{62} -8.12312 q^{63} +1.00000 q^{64} +0.650931 q^{65} -1.41036 q^{66} +8.04511 q^{67} -3.75802 q^{68} -1.95371 q^{69} -3.81848 q^{70} +12.2630 q^{71} -2.52144 q^{72} -8.56483 q^{73} -0.749445 q^{74} +2.48705 q^{75} -6.51476 q^{76} +6.56807 q^{77} +0.379915 q^{78} -6.15390 q^{79} -1.18527 q^{80} +4.92199 q^{81} -4.07854 q^{82} -2.80668 q^{83} -2.22865 q^{84} +4.45426 q^{85} +3.41347 q^{86} +3.30545 q^{87} +2.03875 q^{88} +2.10752 q^{89} +2.98858 q^{90} -1.76926 q^{91} +2.82417 q^{92} +2.73831 q^{93} +3.84594 q^{94} +7.72173 q^{95} -0.691780 q^{96} -12.3878 q^{97} +3.37883 q^{98} -5.14058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9	\( 31 q + 31 q^{2} - 14 q^{3} + 31 q^{4} - 13 q^{5} - 14 q^{6} - 29 q^{7} + 31 q^{8} + 27 q^{9} - 13 q^{10} - 29 q^{11} - 14 q^{12} - 23 q^{13} - 29 q^{14} - 14 q^{15} + 31 q^{16} - 19 q^{17} + 27 q^{18} - 36 q^{19} - 13 q^{20} - 29 q^{22} - 24 q^{23} - 14 q^{24} + 4 q^{25} - 23 q^{26} - 65 q^{27} - 29 q^{28} + 18 q^{29} - 14 q^{30} - 41 q^{31} + 31 q^{32} - 18 q^{33} - 19 q^{34} - 28 q^{35} + 27 q^{36} - 31 q^{37} - 36 q^{38} - 31 q^{39} - 13 q^{40} - 51 q^{41} - 14 q^{43} - 29 q^{44} - 34 q^{45} - 24 q^{46} - 64 q^{47} - 14 q^{48} + 8 q^{49} + 4 q^{50} - 17 q^{51} - 23 q^{52} + 3 q^{53} - 65 q^{54} - 50 q^{55} - 29 q^{56} - 19 q^{57} + 18 q^{58} - 58 q^{59} - 14 q^{60} - 14 q^{61} - 41 q^{62} - 66 q^{63} + 31 q^{64} + 6 q^{65} - 18 q^{66} - 55 q^{67} - 19 q^{68} + q^{69} - 28 q^{70} - 42 q^{71} + 27 q^{72} - 83 q^{73} - 31 q^{74} - 49 q^{75} - 36 q^{76} + 18 q^{77} - 31 q^{78} - 56 q^{79} - 13 q^{80} + 3 q^{81} - 51 q^{82} - 43 q^{83} + 4 q^{85} - 14 q^{86} - 76 q^{87} - 29 q^{88} + 17 q^{89} - 34 q^{90} - 49 q^{91} - 24 q^{92} - 24 q^{93} - 64 q^{94} - 43 q^{95} - 14 q^{96} - 98 q^{97} + 8 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 - 14 * q^3 + 31 * q^4 - 13 * q^5 - 14 * q^6 - 29 * q^7 + 31 * q^8 + 27 * q^9 - 13 * q^10 - 29 * q^11 - 14 * q^12 - 23 * q^13 - 29 * q^14 - 14 * q^15 + 31 * q^16 - 19 * q^17 + 27 * q^18 - 36 * q^19 - 13 * q^20 - 29 * q^22 - 24 * q^23 - 14 * q^24 + 4 * q^25 - 23 * q^26 - 65 * q^27 - 29 * q^28 + 18 * q^29 - 14 * q^30 - 41 * q^31 + 31 * q^32 - 18 * q^33 - 19 * q^34 - 28 * q^35 + 27 * q^36 - 31 * q^37 - 36 * q^38 - 31 * q^39 - 13 * q^40 - 51 * q^41 - 14 * q^43 - 29 * q^44 - 34 * q^45 - 24 * q^46 - 64 * q^47 - 14 * q^48 + 8 * q^49 + 4 * q^50 - 17 * q^51 - 23 * q^52 + 3 * q^53 - 65 * q^54 - 50 * q^55 - 29 * q^56 - 19 * q^57 + 18 * q^58 - 58 * q^59 - 14 * q^60 - 14 * q^61 - 41 * q^62 - 66 * q^63 + 31 * q^64 + 6 * q^65 - 18 * q^66 - 55 * q^67 - 19 * q^68 + q^69 - 28 * q^70 - 42 * q^71 + 27 * q^72 - 83 * q^73 - 31 * q^74 - 49 * q^75 - 36 * q^76 + 18 * q^77 - 31 * q^78 - 56 * q^79 - 13 * q^80 + 3 * q^81 - 51 * q^82 - 43 * q^83 + 4 * q^85 - 14 * q^86 - 76 * q^87 - 29 * q^88 + 17 * q^89 - 34 * q^90 - 49 * q^91 - 24 * q^92 - 24 * q^93 - 64 * q^94 - 43 * q^95 - 14 * q^96 - 98 * q^97 + 8 * q^98 - q^99

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