LMFDB - Embedded newform 4011.2.a.j.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.71993 q^{2} -1.00000 q^{3} +0.958143 q^{4} +2.53174 q^{5} +1.71993 q^{6} -1.00000 q^{7} +1.79192 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.71993 q^{2} -1.00000 q^{3} +0.958143 q^{4} +2.53174 q^{5} +1.71993 q^{6} -1.00000 q^{7} +1.79192 q^{8} +1.00000 q^{9} -4.35441 q^{10} -3.56514 q^{11} -0.958143 q^{12} +4.94300 q^{13} +1.71993 q^{14} -2.53174 q^{15} -4.99825 q^{16} -1.94233 q^{17} -1.71993 q^{18} -7.00809 q^{19} +2.42577 q^{20} +1.00000 q^{21} +6.13178 q^{22} +3.07611 q^{23} -1.79192 q^{24} +1.40972 q^{25} -8.50158 q^{26} -1.00000 q^{27} -0.958143 q^{28} +2.82983 q^{29} +4.35441 q^{30} -5.03077 q^{31} +5.01278 q^{32} +3.56514 q^{33} +3.34067 q^{34} -2.53174 q^{35} +0.958143 q^{36} +6.63671 q^{37} +12.0534 q^{38} -4.94300 q^{39} +4.53667 q^{40} -6.03500 q^{41} -1.71993 q^{42} +1.53412 q^{43} -3.41592 q^{44} +2.53174 q^{45} -5.29069 q^{46} +3.04024 q^{47} +4.99825 q^{48} +1.00000 q^{49} -2.42461 q^{50} +1.94233 q^{51} +4.73610 q^{52} +2.78025 q^{53} +1.71993 q^{54} -9.02602 q^{55} -1.79192 q^{56} +7.00809 q^{57} -4.86709 q^{58} -8.61302 q^{59} -2.42577 q^{60} +11.9097 q^{61} +8.65255 q^{62} -1.00000 q^{63} +1.37488 q^{64} +12.5144 q^{65} -6.13178 q^{66} +11.8454 q^{67} -1.86103 q^{68} -3.07611 q^{69} +4.35441 q^{70} +12.8514 q^{71} +1.79192 q^{72} -11.0014 q^{73} -11.4146 q^{74} -1.40972 q^{75} -6.71475 q^{76} +3.56514 q^{77} +8.50158 q^{78} -5.04357 q^{79} -12.6543 q^{80} +1.00000 q^{81} +10.3797 q^{82} +3.26819 q^{83} +0.958143 q^{84} -4.91748 q^{85} -2.63857 q^{86} -2.82983 q^{87} -6.38843 q^{88} +7.77848 q^{89} -4.35441 q^{90} -4.94300 q^{91} +2.94736 q^{92} +5.03077 q^{93} -5.22899 q^{94} -17.7427 q^{95} -5.01278 q^{96} +2.70849 q^{97} -1.71993 q^{98} -3.56514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	−1.71993	−1.21617	−0.608085	−	0.793872i	$-0.708062\pi$
$2$	−1.71993	−1.21617	−0.608085	+	0.793872i	$0.708062\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.958143	0.479072
$5$	2.53174	1.13223	0.566115	−	0.824326i	$-0.308446\pi$
$5$	2.53174	1.13223	0.566115	+	0.824326i	$0.308446\pi$
$6$	1.71993	0.702157
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.79192	0.633538
$9$	1.00000	0.333333
$10$	−4.35441	−1.37698
$11$	−3.56514	−1.07493	−0.537465	−	0.843286i	$-0.680618\pi$
$11$	−3.56514	−1.07493	−0.537465	+	0.843286i	$0.680618\pi$
$12$	−0.958143	−0.276592
$13$	4.94300	1.37094	0.685470	−	0.728101i	$-0.259597\pi$
$13$	4.94300	1.37094	0.685470	+	0.728101i	$0.259597\pi$
$14$	1.71993	0.459669
$15$	−2.53174	−0.653693
$16$	−4.99825	−1.24956
$17$	−1.94233	−0.471085	−0.235542	−	0.971864i	$-0.575687\pi$
$17$	−1.94233	−0.471085	−0.235542	+	0.971864i	$0.575687\pi$
$18$	−1.71993	−0.405390
$19$	−7.00809	−1.60777	−0.803883	−	0.594788i	$-0.797236\pi$
$19$	−7.00809	−1.60777	−0.803883	+	0.594788i	$0.797236\pi$
$20$	2.42577	0.542419
$21$	1.00000	0.218218
$22$	6.13178	1.30730
$23$	3.07611	0.641414	0.320707	−	0.947178i	$-0.396080\pi$
$23$	3.07611	0.641414	0.320707	+	0.947178i	$0.396080\pi$
$24$	−1.79192	−0.365773
$25$	1.40972	0.281943
$26$	−8.50158	−1.66730
$27$	−1.00000	−0.192450
$28$	−0.958143	−0.181072
$29$	2.82983	0.525485	0.262743	−	0.964866i	$-0.415373\pi$
$29$	2.82983	0.525485	0.262743	+	0.964866i	$0.415373\pi$
$30$	4.35441	0.795002
$31$	−5.03077	−0.903553	−0.451777	−	0.892131i	$-0.649210\pi$
$31$	−5.03077	−0.903553	−0.451777	+	0.892131i	$0.649210\pi$
$32$	5.01278	0.886143
$33$	3.56514	0.620611
$34$	3.34067	0.572920
$35$	−2.53174	−0.427942
$36$	0.958143	0.159691
$37$	6.63671	1.09107	0.545534	−	0.838089i	$-0.316327\pi$
$37$	6.63671	1.09107	0.545534	+	0.838089i	$0.316327\pi$
$38$	12.0534	1.95532
$39$	−4.94300	−0.791513
$40$	4.53667	0.717310
$41$	−6.03500	−0.942508	−0.471254	−	0.881998i	$-0.656198\pi$
$41$	−6.03500	−0.942508	−0.471254	+	0.881998i	$0.656198\pi$
$42$	−1.71993	−0.265390
$43$	1.53412	0.233951	0.116975	−	0.993135i	$-0.462680\pi$
$43$	1.53412	0.233951	0.116975	+	0.993135i	$0.462680\pi$
$44$	−3.41592	−0.514969
$45$	2.53174	0.377410
$46$	−5.29069	−0.780069
$47$	3.04024	0.443465	0.221732	−	0.975108i	$-0.428829\pi$
$47$	3.04024	0.443465	0.221732	+	0.975108i	$0.428829\pi$
$48$	4.99825	0.721435
$49$	1.00000	0.142857
$50$	−2.42461	−0.342891
$51$	1.94233	0.271981
$52$	4.73610	0.656779
$53$	2.78025	0.381897	0.190949	−	0.981600i	$-0.438844\pi$
$53$	2.78025	0.381897	0.190949	+	0.981600i	$0.438844\pi$
$54$	1.71993	0.234052
$55$	−9.02602	−1.21707
$56$	−1.79192	−0.239455
$57$	7.00809	0.928244
$58$	−4.86709	−0.639080
$59$	−8.61302	−1.12132	−0.560660	−	0.828046i	$-0.689452\pi$
$59$	−8.61302	−1.12132	−0.560660	+	0.828046i	$0.689452\pi$
$60$	−2.42577	−0.313166
$61$	11.9097	1.52488	0.762440	−	0.647059i	$-0.224001\pi$
$61$	11.9097	1.52488	0.762440	+	0.647059i	$0.224001\pi$
$62$	8.65255	1.09888
$63$	−1.00000	−0.125988
$64$	1.37488	0.171860
$65$	12.5144	1.55222
$66$	−6.13178	−0.754770
$67$	11.8454	1.44714	0.723571	−	0.690250i	$-0.242499\pi$
$67$	11.8454	1.44714	0.723571	+	0.690250i	$0.242499\pi$
$68$	−1.86103	−0.225683
$69$	−3.07611	−0.370320
$70$	4.35441	0.520451
$71$	12.8514	1.52518	0.762588	−	0.646884i	$-0.223928\pi$
$71$	12.8514	1.52518	0.762588	+	0.646884i	$0.223928\pi$
$72$	1.79192	0.211179
$73$	−11.0014	−1.28762	−0.643811	−	0.765185i	$-0.722648\pi$
$73$	−11.0014	−1.28762	−0.643811	+	0.765185i	$0.722648\pi$
$74$	−11.4146	−1.32693
$75$	−1.40972	−0.162780
$76$	−6.71475	−0.770235
$77$	3.56514	0.406286
$78$	8.50158	0.962615
$79$	−5.04357	−0.567446	−0.283723	−	0.958906i	$-0.591570\pi$
$79$	−5.04357	−0.567446	−0.283723	+	0.958906i	$0.591570\pi$
$80$	−12.6543	−1.41479
$81$	1.00000	0.111111
$82$	10.3797	1.14625
$83$	3.26819	0.358730	0.179365	−	0.983783i	$-0.442596\pi$
$83$	3.26819	0.358730	0.179365	+	0.983783i	$0.442596\pi$
$84$	0.958143	0.104542
$85$	−4.91748	−0.533376
$86$	−2.63857	−0.284524
$87$	−2.82983	−0.303389
$88$	−6.38843	−0.681009
$89$	7.77848	0.824518	0.412259	−	0.911067i	$-0.364740\pi$
$89$	7.77848	0.824518	0.412259	+	0.911067i	$0.364740\pi$
$90$	−4.35441	−0.458995
$91$	−4.94300	−0.518167
$92$	2.94736	0.307283
$93$	5.03077	0.521667
$94$	−5.22899	−0.539329
$95$	−17.7427	−1.82036
$96$	−5.01278	−0.511615
$97$	2.70849	0.275006	0.137503	−	0.990501i	$-0.456092\pi$
$97$	2.70849	0.275006	0.137503	+	0.990501i	$0.456092\pi$
$98$	−1.71993	−0.173739
$99$	−3.56514	−0.358310
$100$	1.35071	0.135071
$101$	−1.24152	−0.123536	−0.0617678	−	0.998091i	$-0.519674\pi$
$101$	−1.24152	−0.123536	−0.0617678	+	0.998091i	$0.519674\pi$
$102$	−3.34067	−0.330775
$103$	8.61732	0.849090	0.424545	−	0.905407i	$-0.360434\pi$
$103$	8.61732	0.849090	0.424545	+	0.905407i	$0.360434\pi$
$104$	8.85743	0.868542
$105$	2.53174	0.247073
$106$	−4.78183	−0.464452
$107$	1.12925	0.109169	0.0545843	−	0.998509i	$-0.482617\pi$
$107$	1.12925	0.109169	0.0545843	+	0.998509i	$0.482617\pi$
$108$	−0.958143	−0.0921974
$109$	−1.10385	−0.105730	−0.0528648	−	0.998602i	$-0.516835\pi$
$109$	−1.10385	−0.105730	−0.0528648	+	0.998602i	$0.516835\pi$
$110$	15.5241	1.48016
$111$	−6.63671	−0.629929
$112$	4.99825	0.472290
$113$	−2.61008	−0.245536	−0.122768	−	0.992435i	$-0.539177\pi$
$113$	−2.61008	−0.245536	−0.122768	+	0.992435i	$0.539177\pi$
$114$	−12.0534	−1.12890
$115$	7.78792	0.726228
$116$	2.71138	0.251745
$117$	4.94300	0.456980
$118$	14.8137	1.36372
$119$	1.94233	0.178053
$120$	−4.53667	−0.414139
$121$	1.71023	0.155476
$122$	−20.4838	−1.85451
$123$	6.03500	0.544157
$124$	−4.82020	−0.432867
$125$	−9.08967	−0.813005
$126$	1.71993	0.153223
$127$	0.181946	0.0161451	0.00807255	−	0.999967i	$-0.497430\pi$
$127$	0.181946	0.0161451	0.00807255	+	0.999967i	$0.497430\pi$
$128$	−12.3903	−1.09515
$129$	−1.53412	−0.135071
$130$	−21.5238	−1.88776
$131$	−17.3131	−1.51265	−0.756325	−	0.654196i	$-0.773007\pi$
$131$	−17.3131	−1.51265	−0.756325	+	0.654196i	$0.773007\pi$
$132$	3.41592	0.297317
$133$	7.00809	0.607678
$134$	−20.3732	−1.75997
$135$	−2.53174	−0.217898
$136$	−3.48050	−0.298450
$137$	13.4782	1.15152	0.575760	−	0.817619i	$-0.304706\pi$
$137$	13.4782	1.15152	0.575760	+	0.817619i	$0.304706\pi$
$138$	5.29069	0.450373
$139$	2.71107	0.229950	0.114975	−	0.993368i	$-0.463321\pi$
$139$	2.71107	0.229950	0.114975	+	0.993368i	$0.463321\pi$
$140$	−2.42577	−0.205015
$141$	−3.04024	−0.256035
$142$	−22.1034	−1.85488
$143$	−17.6225	−1.47367
$144$	−4.99825	−0.416521
$145$	7.16439	0.594970
$146$	18.9217	1.56597
$147$	−1.00000	−0.0824786
$148$	6.35892	0.522700
$149$	−3.83501	−0.314177	−0.157088	−	0.987585i	$-0.550211\pi$
$149$	−3.83501	−0.314177	−0.157088	+	0.987585i	$0.550211\pi$
$150$	2.42461	0.197968
$151$	15.0103	1.22152	0.610761	−	0.791815i	$-0.290864\pi$
$151$	15.0103	1.22152	0.610761	+	0.791815i	$0.290864\pi$
$152$	−12.5579	−1.01858
$153$	−1.94233	−0.157028
$154$	−6.13178	−0.494113
$155$	−12.7366	−1.02303
$156$	−4.73610	−0.379191
$157$	12.6144	1.00674	0.503371	−	0.864071i	$-0.332093\pi$
$157$	12.6144	1.00674	0.503371	+	0.864071i	$0.332093\pi$
$158$	8.67457	0.690112
$159$	−2.78025	−0.220488
$160$	12.6911	1.00332
$161$	−3.07611	−0.242432
$162$	−1.71993	−0.135130
$163$	−11.8661	−0.929427	−0.464714	−	0.885461i	$-0.653843\pi$
$163$	−11.8661	−0.929427	−0.464714	+	0.885461i	$0.653843\pi$
$164$	−5.78239	−0.451529
$165$	9.02602	0.702674
$166$	−5.62104	−0.436278
$167$	6.98938	0.540854	0.270427	−	0.962740i	$-0.412835\pi$
$167$	6.98938	0.540854	0.270427	+	0.962740i	$0.412835\pi$
$168$	1.79192	0.138249
$169$	11.4332	0.879477
$170$	8.45771	0.648677
$171$	−7.00809	−0.535922
$172$	1.46990	0.112079
$173$	1.12178	0.0852873	0.0426436	−	0.999090i	$-0.486422\pi$
$173$	1.12178	0.0852873	0.0426436	+	0.999090i	$0.486422\pi$
$174$	4.86709	0.368973
$175$	−1.40972	−0.106565
$176$	17.8195	1.34319
$177$	8.61302	0.647394
$178$	−13.3784	−1.00275
$179$	−16.6227	−1.24244	−0.621218	−	0.783638i	$-0.713362\pi$
$179$	−16.6227	−1.24244	−0.621218	+	0.783638i	$0.713362\pi$
$180$	2.42577	0.180806
$181$	22.5546	1.67647	0.838234	−	0.545310i	$-0.183588\pi$
$181$	22.5546	1.67647	0.838234	+	0.545310i	$0.183588\pi$
$182$	8.50158	0.630179
$183$	−11.9097	−0.880389
$184$	5.51213	0.406360
$185$	16.8024	1.23534
$186$	−8.65255	−0.634436
$187$	6.92469	0.506384
$188$	2.91299	0.212452
$189$	1.00000	0.0727393
$190$	30.5161	2.21387
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−1.37488	−0.0992237
$193$	8.39234	0.604094	0.302047	−	0.953293i	$-0.402330\pi$
$193$	8.39234	0.604094	0.302047	+	0.953293i	$0.402330\pi$
$194$	−4.65841	−0.334454
$195$	−12.5144	−0.896174
$196$	0.958143	0.0684388
$197$	−11.5347	−0.821810	−0.410905	−	0.911678i	$-0.634787\pi$
$197$	−11.5347	−0.821810	−0.410905	+	0.911678i	$0.634787\pi$
$198$	6.13178	0.435766
$199$	−6.94702	−0.492462	−0.246231	−	0.969211i	$-0.579192\pi$
$199$	−6.94702	−0.492462	−0.246231	+	0.969211i	$0.579192\pi$
$200$	2.52609	0.178622
$201$	−11.8454	−0.835508
$202$	2.13532	0.150240
$203$	−2.82983	−0.198615
$204$	1.86103	0.130298
$205$	−15.2791	−1.06714
$206$	−14.8212	−1.03264
$207$	3.07611	0.213805
$208$	−24.7063	−1.71307
$209$	24.9848	1.72824
$210$	−4.35441	−0.300483
$211$	12.8124	0.882044	0.441022	−	0.897496i	$-0.354616\pi$
$211$	12.8124	0.882044	0.441022	+	0.897496i	$0.354616\pi$
$212$	2.66388	0.182956
$213$	−12.8514	−0.880561
$214$	−1.94222	−0.132768
$215$	3.88399	0.264886
$216$	−1.79192	−0.121924
$217$	5.03077	0.341511
$218$	1.89854	0.128585
$219$	11.0014	0.743408
$220$	−8.64822	−0.583063
$221$	−9.60094	−0.645829
$222$	11.4146	0.766101
$223$	25.0177	1.67531	0.837654	−	0.546202i	$-0.183927\pi$
$223$	25.0177	1.67531	0.837654	+	0.546202i	$0.183927\pi$
$224$	−5.01278	−0.334931
$225$	1.40972	0.0939811
$226$	4.48915	0.298614
$227$	−22.2807	−1.47882	−0.739411	−	0.673255i	$-0.764896\pi$
$227$	−22.2807	−1.47882	−0.739411	+	0.673255i	$0.764896\pi$
$228$	6.71475	0.444695
$229$	−23.3965	−1.54609	−0.773044	−	0.634353i	$-0.781267\pi$
$229$	−23.3965	−1.54609	−0.773044	+	0.634353i	$0.781267\pi$
$230$	−13.3946	−0.883217
$231$	−3.56514	−0.234569
$232$	5.07081	0.332915
$233$	24.2188	1.58663	0.793314	−	0.608813i	$-0.208354\pi$
$233$	24.2188	1.58663	0.793314	+	0.608813i	$0.208354\pi$
$234$	−8.50158	−0.555766
$235$	7.69711	0.502104
$236$	−8.25250	−0.537192
$237$	5.04357	0.327615
$238$	−3.34067	−0.216543
$239$	−30.5191	−1.97411	−0.987057	−	0.160372i	$-0.948731\pi$
$239$	−30.5191	−1.97411	−0.987057	+	0.160372i	$0.948731\pi$
$240$	12.6543	0.816830
$241$	17.7488	1.14330	0.571650	−	0.820498i	$-0.306304\pi$
$241$	17.7488	1.14330	0.571650	+	0.820498i	$0.306304\pi$
$242$	−2.94147	−0.189085
$243$	−1.00000	−0.0641500
$244$	11.4112	0.730526
$245$	2.53174	0.161747
$246$	−10.3797	−0.661788
$247$	−34.6409	−2.20415
$248$	−9.01472	−0.572435
$249$	−3.26819	−0.207113
$250$	15.6336	0.988753
$251$	8.87731	0.560331	0.280165	−	0.959952i	$-0.409611\pi$
$251$	8.87731	0.560331	0.280165	+	0.959952i	$0.409611\pi$
$252$	−0.958143	−0.0603574
$253$	−10.9668	−0.689475
$254$	−0.312933	−0.0196352
$255$	4.91748	0.307945
$256$	18.5606	1.16004
$257$	7.60188	0.474192	0.237096	−	0.971486i	$-0.423804\pi$
$257$	7.60188	0.474192	0.237096	+	0.971486i	$0.423804\pi$
$258$	2.63857	0.164270
$259$	−6.63671	−0.412385
$260$	11.9906	0.743624
$261$	2.82983	0.175162
$262$	29.7772	1.83964
$263$	0.782694	0.0482630	0.0241315	−	0.999709i	$-0.492318\pi$
$263$	0.782694	0.0482630	0.0241315	+	0.999709i	$0.492318\pi$
$264$	6.38843	0.393181
$265$	7.03888	0.432395
$266$	−12.0534	−0.739041
$267$	−7.77848	−0.476036
$268$	11.3496	0.693285
$269$	5.88827	0.359014	0.179507	−	0.983757i	$-0.442550\pi$
$269$	5.88827	0.359014	0.179507	+	0.983757i	$0.442550\pi$
$270$	4.35441	0.265001
$271$	22.7901	1.38440	0.692199	−	0.721707i	$-0.256642\pi$
$271$	22.7901	1.38440	0.692199	+	0.721707i	$0.256642\pi$
$272$	9.70826	0.588650
$273$	4.94300	0.299164
$274$	−23.1815	−1.40045
$275$	−5.02584	−0.303069
$276$	−2.94736	−0.177410
$277$	17.1516	1.03054	0.515271	−	0.857027i	$-0.327691\pi$
$277$	17.1516	1.03054	0.515271	+	0.857027i	$0.327691\pi$
$278$	−4.66283	−0.279658
$279$	−5.03077	−0.301184
$280$	−4.53667	−0.271118
$281$	4.26125	0.254205	0.127102	−	0.991890i	$-0.459432\pi$
$281$	4.26125	0.254205	0.127102	+	0.991890i	$0.459432\pi$
$282$	5.22899	0.311382
$283$	9.67564	0.575157	0.287578	−	0.957757i	$-0.407150\pi$
$283$	9.67564	0.575157	0.287578	+	0.957757i	$0.407150\pi$
$284$	12.3135	0.730669
$285$	17.7427	1.05098
$286$	30.3093	1.79223
$287$	6.03500	0.356235
$288$	5.01278	0.295381
$289$	−13.2273	−0.778079
$290$	−12.3222	−0.723585
$291$	−2.70849	−0.158775
$292$	−10.5410	−0.616863
$293$	−27.7794	−1.62289	−0.811445	−	0.584429i	$-0.801319\pi$
$293$	−27.7794	−1.62289	−0.811445	+	0.584429i	$0.801319\pi$
$294$	1.71993	0.100308
$295$	−21.8059	−1.26959
$296$	11.8924	0.691233
$297$	3.56514	0.206870
$298$	6.59594	0.382092
$299$	15.2052	0.879340
$300$	−1.35071	−0.0779833
$301$	−1.53412	−0.0884250
$302$	−25.8166	−1.48558
$303$	1.24152	0.0713233
$304$	35.0282	2.00900
$305$	30.1523	1.72651
$306$	3.34067	0.190973
$307$	27.3874	1.56308	0.781540	−	0.623855i	$-0.214434\pi$
$307$	27.3874	1.56308	0.781540	+	0.623855i	$0.214434\pi$
$308$	3.41592	0.194640
$309$	−8.61732	−0.490222
$310$	21.9060	1.24418
$311$	0.228713	0.0129691	0.00648457	−	0.999979i	$-0.497936\pi$
$311$	0.228713	0.0129691	0.00648457	+	0.999979i	$0.497936\pi$
$312$	−8.85743	−0.501453
$313$	3.46198	0.195683	0.0978413	−	0.995202i	$-0.468806\pi$
$313$	3.46198	0.195683	0.0978413	+	0.995202i	$0.468806\pi$
$314$	−21.6959	−1.22437
$315$	−2.53174	−0.142647
$316$	−4.83247	−0.271848
$317$	−7.20773	−0.404826	−0.202413	−	0.979300i	$-0.564878\pi$
$317$	−7.20773	−0.404826	−0.202413	+	0.979300i	$0.564878\pi$
$318$	4.78183	0.268152
$319$	−10.0887	−0.564860
$320$	3.48085	0.194585
$321$	−1.12925	−0.0630285
$322$	5.29069	0.294838
$323$	13.6120	0.757394
$324$	0.958143	0.0532302
$325$	6.96822	0.386527
$326$	20.4089	1.13034
$327$	1.10385	0.0610431
$328$	−10.8142	−0.597114
$329$	−3.04024	−0.167614
$330$	−15.5241	−0.854572
$331$	30.9446	1.70087	0.850434	−	0.526082i	$-0.176340\pi$
$331$	30.9446	1.70087	0.850434	+	0.526082i	$0.176340\pi$
$332$	3.13139	0.171858
$333$	6.63671	0.363689
$334$	−12.0212	−0.657771
$335$	29.9894	1.63850
$336$	−4.99825	−0.272677
$337$	−9.16543	−0.499273	−0.249637	−	0.968340i	$-0.580311\pi$
$337$	−9.16543	−0.499273	−0.249637	+	0.968340i	$0.580311\pi$
$338$	−19.6643	−1.06959
$339$	2.61008	0.141760
$340$	−4.71166	−0.255525
$341$	17.9354	0.971257
$342$	12.0534	0.651773
$343$	−1.00000	−0.0539949
$344$	2.74901	0.148217
$345$	−7.78792	−0.419288
$346$	−1.92938	−0.103724
$347$	−6.58528	−0.353516	−0.176758	−	0.984254i	$-0.556561\pi$
$347$	−6.58528	−0.353516	−0.176758	+	0.984254i	$0.556561\pi$
$348$	−2.71138	−0.145345
$349$	28.6003	1.53094	0.765469	−	0.643472i	$-0.222507\pi$
$349$	28.6003	1.53094	0.765469	+	0.643472i	$0.222507\pi$
$350$	2.42461	0.129601
$351$	−4.94300	−0.263838
$352$	−17.8713	−0.952542
$353$	16.3670	0.871129	0.435564	−	0.900158i	$-0.356549\pi$
$353$	16.3670	0.871129	0.435564	+	0.900158i	$0.356549\pi$
$354$	−14.8137	−0.787342
$355$	32.5363	1.72685
$356$	7.45290	0.395003
$357$	−1.94233	−0.102799
$358$	28.5897	1.51101
$359$	12.1632	0.641947	0.320973	−	0.947088i	$-0.395990\pi$
$359$	12.1632	0.641947	0.320973	+	0.947088i	$0.395990\pi$
$360$	4.53667	0.239103
$361$	30.1133	1.58491
$362$	−38.7922	−2.03887
$363$	−1.71023	−0.0897639
$364$	−4.73610	−0.248239
$365$	−27.8528	−1.45788
$366$	20.4838	1.07070
$367$	24.1494	1.26059	0.630294	−	0.776357i	$-0.282935\pi$
$367$	24.1494	1.26059	0.630294	+	0.776357i	$0.282935\pi$
$368$	−15.3752	−0.801486
$369$	−6.03500	−0.314169
$370$	−28.8989	−1.50238
$371$	−2.78025	−0.144344
$372$	4.82020	0.249916
$373$	−12.1490	−0.629049	−0.314525	−	0.949249i	$-0.601845\pi$
$373$	−12.1490	−0.629049	−0.314525	+	0.949249i	$0.601845\pi$
$374$	−11.9100	−0.615849
$375$	9.08967	0.469389
$376$	5.44786	0.280952
$377$	13.9878	0.720409
$378$	−1.71993	−0.0884634
$379$	28.3172	1.45456	0.727278	−	0.686343i	$-0.240785\pi$
$379$	28.3172	1.45456	0.727278	+	0.686343i	$0.240785\pi$
$380$	−17.0000	−0.872083
$381$	−0.181946	−0.00932137
$382$	−1.71993	−0.0879990
$383$	5.23839	0.267669	0.133835	−	0.991004i	$-0.457271\pi$
$383$	5.23839	0.267669	0.133835	+	0.991004i	$0.457271\pi$
$384$	12.3903	0.632288
$385$	9.02602	0.460008
$386$	−14.4342	−0.734681
$387$	1.53412	0.0779835
$388$	2.59513	0.131748
$389$	22.2345	1.12733	0.563666	−	0.826003i	$-0.309391\pi$
$389$	22.2345	1.12733	0.563666	+	0.826003i	$0.309391\pi$
$390$	21.5238	1.08990
$391$	−5.97483	−0.302160
$392$	1.79192	0.0905054
$393$	17.3131	0.873329
$394$	19.8387	0.999461
$395$	−12.7690	−0.642479
$396$	−3.41592	−0.171656
$397$	0.0874785	0.00439042	0.00219521	−	0.999998i	$-0.499301\pi$
$397$	0.0874785	0.00439042	0.00219521	+	0.999998i	$0.499301\pi$
$398$	11.9484	0.598917
$399$	−7.00809	−0.350843
$400$	−7.04611	−0.352306
$401$	38.9098	1.94306	0.971532	−	0.236908i	$-0.0761341\pi$
$401$	38.9098	1.94306	0.971532	+	0.236908i	$0.0761341\pi$
$402$	20.3732	1.01612
$403$	−24.8671	−1.23872
$404$	−1.18955	−0.0591824
$405$	2.53174	0.125803
$406$	4.86709	0.241550
$407$	−23.6608	−1.17282
$408$	3.48050	0.172310
$409$	−19.2694	−0.952813	−0.476406	−	0.879225i	$-0.658061\pi$
$409$	−19.2694	−0.952813	−0.476406	+	0.879225i	$0.658061\pi$
$410$	26.2788	1.29782
$411$	−13.4782	−0.664830
$412$	8.25663	0.406775
$413$	8.61302	0.423819
$414$	−5.29069	−0.260023
$415$	8.27421	0.406165
$416$	24.7782	1.21485
$417$	−2.71107	−0.132761
$418$	−42.9720	−2.10183
$419$	−23.2009	−1.13344	−0.566720	−	0.823910i	$-0.691788\pi$
$419$	−23.2009	−1.13344	−0.566720	+	0.823910i	$0.691788\pi$
$420$	2.42577	0.118366
$421$	15.4622	0.753584	0.376792	−	0.926298i	$-0.377027\pi$
$421$	15.4622	0.753584	0.376792	+	0.926298i	$0.377027\pi$
$422$	−22.0364	−1.07272
$423$	3.04024	0.147822
$424$	4.98198	0.241946
$425$	−2.73814	−0.132819
$426$	22.1034	1.07091
$427$	−11.9097	−0.576350
$428$	1.08198	0.0522996
$429$	17.6225	0.850821
$430$	−6.68017	−0.322146
$431$	1.88541	0.0908171	0.0454085	−	0.998969i	$-0.485541\pi$
$431$	1.88541	0.0908171	0.0454085	+	0.998969i	$0.485541\pi$
$432$	4.99825	0.240478
$433$	−24.9328	−1.19819	−0.599096	−	0.800677i	$-0.704473\pi$
$433$	−24.9328	−1.19819	−0.599096	+	0.800677i	$0.704473\pi$
$434$	−8.65255	−0.415336
$435$	−7.16439	−0.343506
$436$	−1.05765	−0.0506521
$437$	−21.5577	−1.03124
$438$	−18.9217	−0.904112
$439$	15.5609	0.742681	0.371341	−	0.928497i	$-0.378898\pi$
$439$	15.5609	0.742681	0.371341	+	0.928497i	$0.378898\pi$
$440$	−16.1739	−0.771059
$441$	1.00000	0.0476190
$442$	16.5129	0.785439
$443$	−1.92827	−0.0916149	−0.0458074	−	0.998950i	$-0.514586\pi$
$443$	−1.92827	−0.0916149	−0.0458074	+	0.998950i	$0.514586\pi$
$444$	−6.35892	−0.301781
$445$	19.6931	0.933543
$446$	−43.0285	−2.03746
$447$	3.83501	0.181390
$448$	−1.37488	−0.0649571
$449$	−20.1552	−0.951184	−0.475592	−	0.879666i	$-0.657766\pi$
$449$	−20.1552	−0.951184	−0.475592	+	0.879666i	$0.657766\pi$
$450$	−2.42461	−0.114297
$451$	21.5156	1.01313
$452$	−2.50084	−0.117629
$453$	−15.0103	−0.705246
$454$	38.3211	1.79850
$455$	−12.5144	−0.586684
$456$	12.5579	0.588078
$457$	35.6685	1.66850	0.834250	−	0.551386i	$-0.185901\pi$
$457$	35.6685	1.66850	0.834250	+	0.551386i	$0.185901\pi$
$458$	40.2403	1.88031
$459$	1.94233	0.0906603
$460$	7.46195	0.347915
$461$	35.9061	1.67231	0.836157	−	0.548490i	$-0.184797\pi$
$461$	35.9061	1.67231	0.836157	+	0.548490i	$0.184797\pi$
$462$	6.13178	0.285276
$463$	22.3079	1.03674	0.518369	−	0.855157i	$-0.326539\pi$
$463$	22.3079	1.03674	0.518369	+	0.855157i	$0.326539\pi$
$464$	−14.1442	−0.656627
$465$	12.7366	0.590646
$466$	−41.6546	−1.92961
$467$	−6.15226	−0.284692	−0.142346	−	0.989817i	$-0.545465\pi$
$467$	−6.15226	−0.284692	−0.142346	+	0.989817i	$0.545465\pi$
$468$	4.73610	0.218926
$469$	−11.8454	−0.546968
$470$	−13.2385	−0.610644
$471$	−12.6144	−0.581242
$472$	−15.4338	−0.710398
$473$	−5.46934	−0.251481
$474$	−8.67457	−0.398436
$475$	−9.87942	−0.453299
$476$	1.86103	0.0853003
$477$	2.78025	0.127299
$478$	52.4905	2.40086
$479$	−12.9205	−0.590355	−0.295177	−	0.955442i	$-0.595379\pi$
$479$	−12.9205	−0.590355	−0.295177	+	0.955442i	$0.595379\pi$
$480$	−12.6911	−0.579266
$481$	32.8052	1.49579
$482$	−30.5266	−1.39045
$483$	3.07611	0.139968
$484$	1.63865	0.0744840
$485$	6.85721	0.311370
$486$	1.71993	0.0780174
$487$	23.2547	1.05377	0.526887	−	0.849936i	$-0.323359\pi$
$487$	23.2547	1.05377	0.526887	+	0.849936i	$0.323359\pi$
$488$	21.3412	0.966069
$489$	11.8661	0.536605
$490$	−4.35441	−0.196712
$491$	24.4922	1.10532	0.552658	−	0.833408i	$-0.313614\pi$
$491$	24.4922	1.10532	0.552658	+	0.833408i	$0.313614\pi$
$492$	5.78239	0.260690
$493$	−5.49646	−0.247548
$494$	59.5798	2.68062
$495$	−9.02602	−0.405689
$496$	25.1450	1.12905
$497$	−12.8514	−0.576462
$498$	5.62104	0.251885
$499$	−6.64319	−0.297390	−0.148695	−	0.988883i	$-0.547507\pi$
$499$	−6.64319	−0.297390	−0.148695	+	0.988883i	$0.547507\pi$
$500$	−8.70921	−0.389488
$501$	−6.98938	−0.312262
$502$	−15.2683	−0.681458
$503$	−6.19316	−0.276139	−0.138070	−	0.990423i	$-0.544090\pi$
$503$	−6.19316	−0.276139	−0.138070	+	0.990423i	$0.544090\pi$
$504$	−1.79192	−0.0798183
$505$	−3.14320	−0.139871
$506$	18.8620	0.838520
$507$	−11.4332	−0.507766
$508$	0.174330	0.00773466
$509$	21.7765	0.965225	0.482612	−	0.875834i	$-0.339688\pi$
$509$	21.7765	0.965225	0.482612	+	0.875834i	$0.339688\pi$
$510$	−8.45771	−0.374514
$511$	11.0014	0.486675
$512$	−7.14226	−0.315646
$513$	7.00809	0.309415
$514$	−13.0747	−0.576699
$515$	21.8168	0.961365
$516$	−1.46990	−0.0647089
$517$	−10.8389	−0.476694
$518$	11.4146	0.501531
$519$	−1.12178	−0.0492406
$520$	22.4247	0.983389
$521$	−1.80101	−0.0789037	−0.0394519	−	0.999221i	$-0.512561\pi$
$521$	−1.80101	−0.0789037	−0.0394519	+	0.999221i	$0.512561\pi$
$522$	−4.86709	−0.213027
$523$	21.5196	0.940988	0.470494	−	0.882403i	$-0.344076\pi$
$523$	21.5196	0.940988	0.470494	+	0.882403i	$0.344076\pi$
$524$	−16.5884	−0.724668
$525$	1.40972	0.0615251
$526$	−1.34617	−0.0586960
$527$	9.77143	0.425650
$528$	−17.8195	−0.775492
$529$	−13.5375	−0.588588
$530$	−12.1064	−0.525866
$531$	−8.61302	−0.373773
$532$	6.71475	0.291121
$533$	−29.8310	−1.29212
$534$	13.3784	0.578941
$535$	2.85897	0.123604
$536$	21.2259	0.916820
$537$	16.6227	0.717321
$538$	−10.1274	−0.436623
$539$	−3.56514	−0.153562
$540$	−2.42577	−0.104389
$541$	−11.9818	−0.515140	−0.257570	−	0.966260i	$-0.582922\pi$
$541$	−11.9818	−0.515140	−0.257570	+	0.966260i	$0.582922\pi$
$542$	−39.1972	−1.68366
$543$	−22.5546	−0.967910
$544$	−9.73649	−0.417449
$545$	−2.79466	−0.119710
$546$	−8.50158	−0.363834
$547$	−6.77312	−0.289597	−0.144799	−	0.989461i	$-0.546253\pi$
$547$	−6.77312	−0.289597	−0.144799	+	0.989461i	$0.546253\pi$
$548$	12.9140	0.551661
$549$	11.9097	0.508293
$550$	8.64407	0.368584
$551$	−19.8317	−0.844857
$552$	−5.51213	−0.234612
$553$	5.04357	0.214475
$554$	−29.4996	−1.25332
$555$	−16.8024	−0.713224
$556$	2.59759	0.110162
$557$	22.3685	0.947784	0.473892	−	0.880583i	$-0.342849\pi$
$557$	22.3685	0.947784	0.473892	+	0.880583i	$0.342849\pi$
$558$	8.65255	0.366292
$559$	7.58313	0.320732
$560$	12.6543	0.534741
$561$	−6.92469	−0.292361
$562$	−7.32904	−0.309157
$563$	−35.9665	−1.51581	−0.757904	−	0.652367i	$-0.773776\pi$
$563$	−35.9665	−1.51581	−0.757904	+	0.652367i	$0.773776\pi$
$564$	−2.91299	−0.122659
$565$	−6.60806	−0.278003
$566$	−16.6414	−0.699489
$567$	−1.00000	−0.0419961
$568$	23.0286	0.966257
$569$	14.5948	0.611847	0.305923	−	0.952056i	$-0.401035\pi$
$569$	14.5948	0.611847	0.305923	+	0.952056i	$0.401035\pi$
$570$	−30.5161	−1.27818
$571$	−3.25769	−0.136330	−0.0681650	−	0.997674i	$-0.521714\pi$
$571$	−3.25769	−0.136330	−0.0681650	+	0.997674i	$0.521714\pi$
$572$	−16.8849	−0.705991
$573$	−1.00000	−0.0417756
$574$	−10.3797	−0.433242
$575$	4.33645	0.180842
$576$	1.37488	0.0572868
$577$	−18.2700	−0.760590	−0.380295	−	0.924865i	$-0.624178\pi$
$577$	−18.2700	−0.760590	−0.380295	+	0.924865i	$0.624178\pi$
$578$	22.7500	0.946277
$579$	−8.39234	−0.348774
$580$	6.86451	0.285033
$581$	−3.26819	−0.135587
$582$	4.65841	0.193097
$583$	−9.91199	−0.410513
$584$	−19.7137	−0.815757
$585$	12.5144	0.517406
$586$	47.7785	1.97371
$587$	21.3531	0.881336	0.440668	−	0.897670i	$-0.354742\pi$
$587$	21.3531	0.881336	0.440668	+	0.897670i	$0.354742\pi$
$588$	−0.958143	−0.0395132
$589$	35.2561	1.45270
$590$	37.5046	1.54404
$591$	11.5347	0.474472
$592$	−33.1719	−1.36336
$593$	−23.8803	−0.980645	−0.490323	−	0.871541i	$-0.663121\pi$
$593$	−23.8803	−0.980645	−0.490323	+	0.871541i	$0.663121\pi$
$594$	−6.13178	−0.251590
$595$	4.91748	0.201597
$596$	−3.67449	−0.150513
$597$	6.94702	0.284323
$598$	−26.1518	−1.06943
$599$	8.86823	0.362346	0.181173	−	0.983451i	$-0.442011\pi$
$599$	8.86823	0.362346	0.181173	+	0.983451i	$0.442011\pi$
$600$	−2.52609	−0.103127
$601$	14.0543	0.573288	0.286644	−	0.958037i	$-0.407460\pi$
$601$	14.0543	0.573288	0.286644	+	0.958037i	$0.407460\pi$
$602$	2.63857	0.107540
$603$	11.8454	0.482381
$604$	14.3820	0.585196
$605$	4.32987	0.176034
$606$	−2.13532	−0.0867413
$607$	35.7569	1.45133	0.725663	−	0.688050i	$-0.241533\pi$
$607$	35.7569	1.45133	0.725663	+	0.688050i	$0.241533\pi$
$608$	−35.1300	−1.42471
$609$	2.82983	0.114670
$610$	−51.8596	−2.09973
$611$	15.0279	0.607964
$612$	−1.86103	−0.0752278
$613$	32.0679	1.29521	0.647605	−	0.761976i	$-0.275771\pi$
$613$	32.0679	1.29521	0.647605	+	0.761976i	$0.275771\pi$
$614$	−47.1043	−1.90097
$615$	15.2791	0.616111
$616$	6.38843	0.257397
$617$	26.5685	1.06961	0.534804	−	0.844976i	$-0.320385\pi$
$617$	26.5685	1.06961	0.534804	+	0.844976i	$0.320385\pi$
$618$	14.8212	0.596194
$619$	−19.7460	−0.793661	−0.396830	−	0.917892i	$-0.629890\pi$
$619$	−19.7460	−0.793661	−0.396830	+	0.917892i	$0.629890\pi$
$620$	−12.2035	−0.490104
$621$	−3.07611	−0.123440
$622$	−0.393370	−0.0157727
$623$	−7.77848	−0.311638
$624$	24.7063	0.989044
$625$	−30.0613	−1.20245
$626$	−5.95434	−0.237983
$627$	−24.9848	−0.997798
$628$	12.0864	0.482301
$629$	−12.8907	−0.513986
$630$	4.35441	0.173484
$631$	−21.0750	−0.838984	−0.419492	−	0.907759i	$-0.637792\pi$
$631$	−21.0750	−0.838984	−0.419492	+	0.907759i	$0.637792\pi$
$632$	−9.03766	−0.359499
$633$	−12.8124	−0.509248
$634$	12.3968	0.492338
$635$	0.460640	0.0182799
$636$	−2.66388	−0.105630
$637$	4.94300	0.195849
$638$	17.3519	0.686967
$639$	12.8514	0.508392
$640$	−31.3689	−1.23997
$641$	−17.5977	−0.695066	−0.347533	−	0.937668i	$-0.612981\pi$
$641$	−17.5977	−0.695066	−0.347533	+	0.937668i	$0.612981\pi$
$642$	1.94222	0.0766534
$643$	−20.2848	−0.799954	−0.399977	−	0.916525i	$-0.630982\pi$
$643$	−20.2848	−0.799954	−0.399977	+	0.916525i	$0.630982\pi$
$644$	−2.94736	−0.116142
$645$	−3.88399	−0.152932
$646$	−23.4117	−0.921121
$647$	−45.4345	−1.78621	−0.893107	−	0.449845i	$-0.851479\pi$
$647$	−45.4345	−1.78621	−0.893107	+	0.449845i	$0.851479\pi$
$648$	1.79192	0.0703931
$649$	30.7066	1.20534
$650$	−11.9848	−0.470083
$651$	−5.03077	−0.197171
$652$	−11.3695	−0.445262
$653$	13.2686	0.519240	0.259620	−	0.965711i	$-0.416403\pi$
$653$	13.2686	0.519240	0.259620	+	0.965711i	$0.416403\pi$
$654$	−1.89854	−0.0742388
$655$	−43.8322	−1.71267
$656$	30.1644	1.17772
$657$	−11.0014	−0.429207
$658$	5.22899	0.203847
$659$	26.1795	1.01981	0.509904	−	0.860231i	$-0.329681\pi$
$659$	26.1795	1.01981	0.509904	+	0.860231i	$0.329681\pi$
$660$	8.64822	0.336631
$661$	−28.0120	−1.08954	−0.544770	−	0.838585i	$-0.683383\pi$
$661$	−28.0120	−1.08954	−0.544770	+	0.838585i	$0.683383\pi$
$662$	−53.2224	−2.06855
$663$	9.60094	0.372870
$664$	5.85632	0.227269
$665$	17.7427	0.688031
$666$	−11.4146	−0.442309
$667$	8.70486	0.337054
$668$	6.69683	0.259108
$669$	−25.0177	−0.967239
$670$	−51.5796	−1.99269
$671$	−42.4597	−1.63914
$672$	5.01278	0.193372
$673$	−39.7583	−1.53257	−0.766286	−	0.642500i	$-0.777897\pi$
$673$	−39.7583	−1.53257	−0.766286	+	0.642500i	$0.777897\pi$
$674$	15.7639	0.607201
$675$	−1.40972	−0.0542600
$676$	10.9546	0.421333
$677$	−31.1435	−1.19694	−0.598472	−	0.801144i	$-0.704225\pi$
$677$	−31.1435	−1.19694	−0.598472	+	0.801144i	$0.704225\pi$
$678$	−4.48915	−0.172405
$679$	−2.70849	−0.103942
$680$	−8.81172	−0.337914
$681$	22.2807	0.853798
$682$	−30.8476	−1.18121
$683$	23.8223	0.911533	0.455767	−	0.890099i	$-0.349365\pi$
$683$	23.8223	0.911533	0.455767	+	0.890099i	$0.349365\pi$
$684$	−6.71475	−0.256745
$685$	34.1233	1.30378
$686$	1.71993	0.0656671
$687$	23.3965	0.892634
$688$	−7.66790	−0.292336
$689$	13.7428	0.523558
$690$	13.3946	0.509926
$691$	32.2479	1.22677	0.613384	−	0.789785i	$-0.289808\pi$
$691$	32.2479	1.22677	0.613384	+	0.789785i	$0.289808\pi$
$692$	1.07483	0.0408587
$693$	3.56514	0.135429
$694$	11.3262	0.429936
$695$	6.86372	0.260356
$696$	−5.07081	−0.192209
$697$	11.7220	0.444001
$698$	−49.1904	−1.86188
$699$	−24.2188	−0.916040
$700$	−1.35071	−0.0510521
$701$	−48.2680	−1.82306	−0.911529	−	0.411237i	$-0.865097\pi$
$701$	−48.2680	−1.82306	−0.911529	+	0.411237i	$0.865097\pi$
$702$	8.50158	0.320872
$703$	−46.5106	−1.75418
$704$	−4.90165	−0.184738
$705$	−7.69711	−0.289890
$706$	−28.1501	−1.05944
$707$	1.24152	0.0466920
$708$	8.25250	0.310148
$709$	−3.20939	−0.120531	−0.0602656	−	0.998182i	$-0.519195\pi$
$709$	−3.20939	−0.120531	−0.0602656	+	0.998182i	$0.519195\pi$
$710$	−55.9601	−2.10014
$711$	−5.04357	−0.189149
$712$	13.9384	0.522363
$713$	−15.4752	−0.579552
$714$	3.34067	0.125021
$715$	−44.6156	−1.66853
$716$	−15.9269	−0.595216
$717$	30.5191	1.13975
$718$	−20.9197	−0.780717
$719$	−33.8428	−1.26212	−0.631062	−	0.775733i	$-0.717381\pi$
$719$	−33.8428	−1.26212	−0.631062	+	0.775733i	$0.717381\pi$
$720$	−12.6543	−0.471597
$721$	−8.61732	−0.320926
$722$	−51.7926	−1.92752
$723$	−17.7488	−0.660085
$724$	21.6105	0.803149
$725$	3.98925	0.148157
$726$	2.94147	0.109168
$727$	−53.0217	−1.96647	−0.983233	−	0.182353i	$-0.941629\pi$
$727$	−53.0217	−1.96647	−0.983233	+	0.182353i	$0.941629\pi$
$728$	−8.85743	−0.328278
$729$	1.00000	0.0370370
$730$	47.9048	1.77303
$731$	−2.97977	−0.110211
$732$	−11.4112	−0.421770
$733$	−35.2459	−1.30184	−0.650918	−	0.759148i	$-0.725616\pi$
$733$	−35.2459	−1.30184	−0.650918	+	0.759148i	$0.725616\pi$
$734$	−41.5351	−1.53309
$735$	−2.53174	−0.0933847
$736$	15.4199	0.568385
$737$	−42.2304	−1.55558
$738$	10.3797	0.382084
$739$	48.7537	1.79343	0.896717	−	0.442604i	$-0.145945\pi$
$739$	48.7537	1.79343	0.896717	+	0.442604i	$0.145945\pi$
$740$	16.0991	0.591816
$741$	34.6409	1.27257
$742$	4.78183	0.175546
$743$	−15.8597	−0.581835	−0.290918	−	0.956748i	$-0.593961\pi$
$743$	−15.8597	−0.581835	−0.290918	+	0.956748i	$0.593961\pi$
$744$	9.01472	0.330496
$745$	−9.70927	−0.355720
$746$	20.8953	0.765032
$747$	3.26819	0.119577
$748$	6.63485	0.242594
$749$	−1.12925	−0.0412618
$750$	−15.6336	−0.570857
$751$	−47.7015	−1.74065	−0.870325	−	0.492477i	$-0.836092\pi$
$751$	−47.7015	−1.74065	−0.870325	+	0.492477i	$0.836092\pi$
$752$	−15.1959	−0.554137
$753$	−8.87731	−0.323507
$754$	−24.0580	−0.876141
$755$	38.0022	1.38304
$756$	0.958143	0.0348473
$757$	−10.8781	−0.395370	−0.197685	−	0.980266i	$-0.563342\pi$
$757$	−10.8781	−0.395370	−0.197685	+	0.980266i	$0.563342\pi$
$758$	−48.7035	−1.76899
$759$	10.9668	0.398069
$760$	−31.7934	−1.15327
$761$	45.1338	1.63610	0.818049	−	0.575148i	$-0.195056\pi$
$761$	45.1338	1.63610	0.818049	+	0.575148i	$0.195056\pi$
$762$	0.312933	0.0113364
$763$	1.10385	0.0399621
$764$	0.958143	0.0346644
$765$	−4.91748	−0.177792
$766$	−9.00965	−0.325532
$767$	−42.5741	−1.53726
$768$	−18.5606	−0.669747
$769$	13.2372	0.477344	0.238672	−	0.971100i	$-0.423288\pi$
$769$	13.2372	0.477344	0.238672	+	0.971100i	$0.423288\pi$
$770$	−15.5241	−0.559449
$771$	−7.60188	−0.273775
$772$	8.04106	0.289404
$773$	1.85384	0.0666781	0.0333390	−	0.999444i	$-0.489386\pi$
$773$	1.85384	0.0666781	0.0333390	+	0.999444i	$0.489386\pi$
$774$	−2.63857	−0.0948413
$775$	−7.09196	−0.254751
$776$	4.85339	0.174227
$777$	6.63671	0.238091
$778$	−38.2416	−1.37103
$779$	42.2938	1.51533
$780$	−11.9906	−0.429332
$781$	−45.8169	−1.63946
$782$	10.2763	0.367479
$783$	−2.82983	−0.101130
$784$	−4.99825	−0.178509
$785$	31.9365	1.13986
$786$	−29.7772	−1.06212
$787$	54.7023	1.94993	0.974964	−	0.222363i	$-0.0713770\pi$
$787$	54.7023	1.94993	0.974964	+	0.222363i	$0.0713770\pi$
$788$	−11.0519	−0.393706
$789$	−0.782694	−0.0278646
$790$	21.9618	0.781365
$791$	2.61008	0.0928039
$792$	−6.38843	−0.227003
$793$	58.8695	2.09052
$794$	−0.150457	−0.00533950
$795$	−7.03888	−0.249643
$796$	−6.65625	−0.235924
$797$	43.0479	1.52483	0.762417	−	0.647086i	$-0.224012\pi$
$797$	43.0479	1.52483	0.762417	+	0.647086i	$0.224012\pi$
$798$	12.0534	0.426685
$799$	−5.90516	−0.208910
$800$	7.06660	0.249842
$801$	7.77848	0.274839
$802$	−66.9220	−2.36310
$803$	39.2217	1.38410
$804$	−11.3496	−0.400268
$805$	−7.78792	−0.274488
$806$	42.7695	1.50649
$807$	−5.88827	−0.207277
$808$	−2.22469	−0.0782644
$809$	4.29390	0.150965	0.0754827	−	0.997147i	$-0.475950\pi$
$809$	4.29390	0.150965	0.0754827	+	0.997147i	$0.475950\pi$
$810$	−4.35441	−0.152998
$811$	−7.26267	−0.255027	−0.127513	−	0.991837i	$-0.540700\pi$
$811$	−7.26267	−0.255027	−0.127513	+	0.991837i	$0.540700\pi$
$812$	−2.71138	−0.0951508
$813$	−22.7901	−0.799282
$814$	40.6948	1.42635
$815$	−30.0420	−1.05232
$816$	−9.70826	−0.339857
$817$	−10.7512	−0.376138
$818$	33.1420	1.15878
$819$	−4.94300	−0.172722
$820$	−14.6395	−0.511234
$821$	34.2532	1.19545	0.597723	−	0.801703i	$-0.296072\pi$
$821$	34.2532	1.19545	0.597723	+	0.801703i	$0.296072\pi$
$822$	23.1815	0.808547
$823$	1.98705	0.0692644	0.0346322	−	0.999400i	$-0.488974\pi$
$823$	1.98705	0.0692644	0.0346322	+	0.999400i	$0.488974\pi$
$824$	15.4415	0.537931
$825$	5.02584	0.174977
$826$	−14.8137	−0.515436
$827$	−11.2115	−0.389861	−0.194931	−	0.980817i	$-0.562448\pi$
$827$	−11.2115	−0.389861	−0.194931	+	0.980817i	$0.562448\pi$
$828$	2.94736	0.102428
$829$	8.68888	0.301777	0.150889	−	0.988551i	$-0.451787\pi$
$829$	8.68888	0.301777	0.150889	+	0.988551i	$0.451787\pi$
$830$	−14.2310	−0.493966
$831$	−17.1516	−0.594984
$832$	6.79604	0.235610
$833$	−1.94233	−0.0672978
$834$	4.66283	0.161461
$835$	17.6953	0.612371
$836$	23.9390	0.827949
$837$	5.03077	0.173889
$838$	39.9039	1.37846
$839$	34.6975	1.19789	0.598945	−	0.800790i	$-0.295587\pi$
$839$	34.6975	1.19789	0.598945	+	0.800790i	$0.295587\pi$
$840$	4.53667	0.156530
$841$	−20.9921	−0.723865
$842$	−26.5939	−0.916487
$843$	−4.26125	−0.146765
$844$	12.2761	0.422562
$845$	28.9459	0.995770
$846$	−5.22899	−0.179776
$847$	−1.71023	−0.0587643
$848$	−13.8964	−0.477204
$849$	−9.67564	−0.332067
$850$	4.70939	0.161531
$851$	20.4153	0.699826
$852$	−12.3135	−0.421852
$853$	−4.41843	−0.151284	−0.0756421	−	0.997135i	$-0.524101\pi$
$853$	−4.41843	−0.151284	−0.0756421	+	0.997135i	$0.524101\pi$
$854$	20.4838	0.700940
$855$	−17.7427	−0.606786
$856$	2.02352	0.0691624
$857$	−4.47000	−0.152692	−0.0763461	−	0.997081i	$-0.524325\pi$
$857$	−4.47000	−0.152692	−0.0763461	+	0.997081i	$0.524325\pi$
$858$	−30.3093	−1.03474
$859$	36.3499	1.24024	0.620121	−	0.784506i	$-0.287083\pi$
$859$	36.3499	1.24024	0.620121	+	0.784506i	$0.287083\pi$
$860$	3.72142	0.126899
$861$	−6.03500	−0.205672
$862$	−3.24277	−0.110449
$863$	0.912919	0.0310761	0.0155381	−	0.999879i	$-0.495054\pi$
$863$	0.912919	0.0310761	0.0155381	+	0.999879i	$0.495054\pi$
$864$	−5.01278	−0.170538
$865$	2.84005	0.0965648
$866$	42.8825	1.45721
$867$	13.2273	0.449224
$868$	4.82020	0.163608
$869$	17.9811	0.609965
$870$	12.3222	0.417762
$871$	58.5516	1.98395
$872$	−1.97801	−0.0669838
$873$	2.70849	0.0916686
$874$	37.0776	1.25417
$875$	9.08967	0.307287
$876$	10.5410	0.356146
$877$	−30.0693	−1.01537	−0.507684	−	0.861543i	$-0.669498\pi$
$877$	−30.0693	−1.01537	−0.507684	+	0.861543i	$0.669498\pi$
$878$	−26.7636	−0.903228
$879$	27.7794	0.936976
$880$	45.1143	1.52080
$881$	−43.3324	−1.45991	−0.729953	−	0.683498i	$-0.760458\pi$
$881$	−43.3324	−1.45991	−0.729953	+	0.683498i	$0.760458\pi$
$882$	−1.71993	−0.0579129
$883$	−22.8142	−0.767757	−0.383879	−	0.923384i	$-0.625412\pi$
$883$	−22.8142	−0.767757	−0.383879	+	0.923384i	$0.625412\pi$
$884$	−9.19908	−0.309399
$885$	21.8059	0.732998
$886$	3.31648	0.111419
$887$	15.7393	0.528473	0.264237	−	0.964458i	$-0.414880\pi$
$887$	15.7393	0.528473	0.264237	+	0.964458i	$0.414880\pi$
$888$	−11.8924	−0.399084
$889$	−0.181946	−0.00610227
$890$	−33.8707	−1.13535
$891$	−3.56514	−0.119437
$892$	23.9705	0.802592
$893$	−21.3063	−0.712988
$894$	−6.59594	−0.220601
$895$	−42.0843	−1.40672
$896$	12.3903	0.413930
$897$	−15.2052	−0.507687
$898$	34.6655	1.15680
$899$	−14.2362	−0.474804
$900$	1.35071	0.0450237
$901$	−5.40017	−0.179906
$902$	−37.0053	−1.23214
$903$	1.53412	0.0510522
$904$	−4.67705	−0.155556
$905$	57.1024	1.89815
$906$	25.8166	0.857699
$907$	−16.0960	−0.534460	−0.267230	−	0.963633i	$-0.586108\pi$
$907$	−16.0960	−0.534460	−0.267230	+	0.963633i	$0.586108\pi$
$908$	−21.3481	−0.708461
$909$	−1.24152	−0.0411785
$910$	21.5238	0.713507
$911$	51.5443	1.70774	0.853869	−	0.520488i	$-0.174250\pi$
$911$	51.5443	1.70774	0.853869	+	0.520488i	$0.174250\pi$
$912$	−35.0282	−1.15990
$913$	−11.6516	−0.385610
$914$	−61.3471	−2.02918
$915$	−30.1523	−0.996803
$916$	−22.4173	−0.740687
$917$	17.3131	0.571728
$918$	−3.34067	−0.110258
$919$	13.9361	0.459711	0.229855	−	0.973225i	$-0.426175\pi$
$919$	13.9361	0.459711	0.229855	+	0.973225i	$0.426175\pi$
$920$	13.9553	0.460093
$921$	−27.3874	−0.902445
$922$	−61.7558	−2.03382
$923$	63.5242	2.09093
$924$	−3.41592	−0.112375
$925$	9.35588	0.307619
$926$	−38.3680	−1.26085
$927$	8.61732	0.283030
$928$	14.1853	0.465655
$929$	56.5708	1.85603	0.928014	−	0.372547i	$-0.121515\pi$
$929$	56.5708	1.85603	0.928014	+	0.372547i	$0.121515\pi$
$930$	−21.9060	−0.718327
$931$	−7.00809	−0.229681
$932$	23.2051	0.760109
$933$	−0.228713	−0.00748773
$934$	10.5814	0.346235
$935$	17.5315	0.573342
$936$	8.85743	0.289514
$937$	−23.5150	−0.768202	−0.384101	−	0.923291i	$-0.625489\pi$
$937$	−23.5150	−0.768202	−0.384101	+	0.923291i	$0.625489\pi$
$938$	20.3732	0.665207
$939$	−3.46198	−0.112977
$940$	7.37494	0.240544
$941$	−38.0025	−1.23885	−0.619423	−	0.785057i	$-0.712633\pi$
$941$	−38.0025	−1.23885	−0.619423	+	0.785057i	$0.712633\pi$
$942$	21.6959	0.706890
$943$	−18.5643	−0.604538
$944$	43.0500	1.40116
$945$	2.53174	0.0823576
$946$	9.40686	0.305843
$947$	−2.79992	−0.0909852	−0.0454926	−	0.998965i	$-0.514486\pi$
$947$	−2.79992	−0.0909852	−0.0454926	+	0.998965i	$0.514486\pi$
$948$	4.83247	0.156951
$949$	−54.3801	−1.76525
$950$	16.9919	0.551289
$951$	7.20773	0.233727
$952$	3.48050	0.112804
$953$	13.9272	0.451145	0.225573	−	0.974226i	$-0.427575\pi$
$953$	13.9272	0.451145	0.225573	+	0.974226i	$0.427575\pi$
$954$	−4.78183	−0.154817
$955$	2.53174	0.0819252
$956$	−29.2416	−0.945742
$957$	10.0887	0.326122
$958$	22.2224	0.717973
$959$	−13.4782	−0.435234
$960$	−3.48085	−0.112344
$961$	−5.69134	−0.183592
$962$	−56.4225	−1.81914
$963$	1.12925	0.0363895
$964$	17.0059	0.547723
$965$	21.2472	0.683972
$966$	−5.29069	−0.170225
$967$	−46.4663	−1.49426	−0.747128	−	0.664680i	$-0.768568\pi$
$967$	−46.4663	−1.49426	−0.747128	+	0.664680i	$0.768568\pi$
$968$	3.06459	0.0984997
$969$	−13.6120	−0.437282
$970$	−11.7939	−0.378679
$971$	4.12051	0.132233	0.0661167	−	0.997812i	$-0.478939\pi$
$971$	4.12051	0.132233	0.0661167	+	0.997812i	$0.478939\pi$
$972$	−0.958143	−0.0307325
$973$	−2.71107	−0.0869128
$974$	−39.9964	−1.28157
$975$	−6.96822	−0.223162
$976$	−59.5276	−1.90543
$977$	38.7291	1.23905	0.619527	−	0.784976i	$-0.287325\pi$
$977$	38.7291	1.23905	0.619527	+	0.784976i	$0.287325\pi$
$978$	−20.4089	−0.652603
$979$	−27.7314	−0.886299
$980$	2.42577	0.0774884
$981$	−1.10385	−0.0352432
$982$	−42.1247	−1.34425
$983$	60.1755	1.91930	0.959651	−	0.281195i	$-0.0907309\pi$
$983$	60.1755	1.91930	0.959651	+	0.281195i	$0.0907309\pi$
$984$	10.8142	0.344744
$985$	−29.2028	−0.930477
$986$	9.45351	0.301061
$987$	3.04024	0.0967720
$988$	−33.1910	−1.05595
$989$	4.71912	0.150059
$990$	15.5241	0.493388
$991$	8.44422	0.268240	0.134120	−	0.990965i	$-0.457179\pi$
$991$	8.44422	0.268240	0.134120	+	0.990965i	$0.457179\pi$
$992$	−25.2182	−0.800677
$993$	−30.9446	−0.981996
$994$	22.1034	0.701077
$995$	−17.5881	−0.557579
$996$	−3.13139	−0.0992220
$997$	−12.9301	−0.409501	−0.204750	−	0.978814i	$-0.565638\pi$
$997$	−12.9301	−0.409501	−0.204750	+	0.978814i	$0.565638\pi$
$998$	11.4258	0.361677
$999$	−6.63671	−0.209976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.7	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.7	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-1.71993 q^{2} -1.00000 q^{3} +0.958143 q^{4} +2.53174 q^{5} +1.71993 q^{6} -1.00000 q^{7} +1.79192 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.71993 q^{2} -1.00000 q^{3} +0.958143 q^{4} +2.53174 q^{5} +1.71993 q^{6} -1.00000 q^{7} +1.79192 q^{8} +1.00000 q^{9} -4.35441 q^{10} -3.56514 q^{11} -0.958143 q^{12} +4.94300 q^{13} +1.71993 q^{14} -2.53174 q^{15} -4.99825 q^{16} -1.94233 q^{17} -1.71993 q^{18} -7.00809 q^{19} +2.42577 q^{20} +1.00000 q^{21} +6.13178 q^{22} +3.07611 q^{23} -1.79192 q^{24} +1.40972 q^{25} -8.50158 q^{26} -1.00000 q^{27} -0.958143 q^{28} +2.82983 q^{29} +4.35441 q^{30} -5.03077 q^{31} +5.01278 q^{32} +3.56514 q^{33} +3.34067 q^{34} -2.53174 q^{35} +0.958143 q^{36} +6.63671 q^{37} +12.0534 q^{38} -4.94300 q^{39} +4.53667 q^{40} -6.03500 q^{41} -1.71993 q^{42} +1.53412 q^{43} -3.41592 q^{44} +2.53174 q^{45} -5.29069 q^{46} +3.04024 q^{47} +4.99825 q^{48} +1.00000 q^{49} -2.42461 q^{50} +1.94233 q^{51} +4.73610 q^{52} +2.78025 q^{53} +1.71993 q^{54} -9.02602 q^{55} -1.79192 q^{56} +7.00809 q^{57} -4.86709 q^{58} -8.61302 q^{59} -2.42577 q^{60} +11.9097 q^{61} +8.65255 q^{62} -1.00000 q^{63} +1.37488 q^{64} +12.5144 q^{65} -6.13178 q^{66} +11.8454 q^{67} -1.86103 q^{68} -3.07611 q^{69} +4.35441 q^{70} +12.8514 q^{71} +1.79192 q^{72} -11.0014 q^{73} -11.4146 q^{74} -1.40972 q^{75} -6.71475 q^{76} +3.56514 q^{77} +8.50158 q^{78} -5.04357 q^{79} -12.6543 q^{80} +1.00000 q^{81} +10.3797 q^{82} +3.26819 q^{83} +0.958143 q^{84} -4.91748 q^{85} -2.63857 q^{86} -2.82983 q^{87} -6.38843 q^{88} +7.77848 q^{89} -4.35441 q^{90} -4.94300 q^{91} +2.94736 q^{92} +5.03077 q^{93} -5.22899 q^{94} -17.7427 q^{95} -5.01278 q^{96} +2.70849 q^{97} -1.71993 q^{98} -3.56514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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