LMFDB - Embedded newform 4011.2.a.k.1.18

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:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q+1.40876 q^{2} +1.00000 q^{3} -0.0154013 q^{4} -2.50452 q^{5} +1.40876 q^{6} +1.00000 q^{7} -2.83921 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.40876 q^{2} +1.00000 q^{3} -0.0154013 q^{4} -2.50452 q^{5} +1.40876 q^{6} +1.00000 q^{7} -2.83921 q^{8} +1.00000 q^{9} -3.52826 q^{10} +1.33563 q^{11} -0.0154013 q^{12} +0.606834 q^{13} +1.40876 q^{14} -2.50452 q^{15} -3.96896 q^{16} +4.81564 q^{17} +1.40876 q^{18} -4.64209 q^{19} +0.0385729 q^{20} +1.00000 q^{21} +1.88157 q^{22} +0.157797 q^{23} -2.83921 q^{24} +1.27260 q^{25} +0.854882 q^{26} +1.00000 q^{27} -0.0154013 q^{28} +4.63189 q^{29} -3.52826 q^{30} +10.5578 q^{31} +0.0871212 q^{32} +1.33563 q^{33} +6.78407 q^{34} -2.50452 q^{35} -0.0154013 q^{36} -7.47175 q^{37} -6.53958 q^{38} +0.606834 q^{39} +7.11085 q^{40} -0.698457 q^{41} +1.40876 q^{42} +5.44433 q^{43} -0.0205704 q^{44} -2.50452 q^{45} +0.222298 q^{46} -6.83270 q^{47} -3.96896 q^{48} +1.00000 q^{49} +1.79279 q^{50} +4.81564 q^{51} -0.00934605 q^{52} +3.77705 q^{53} +1.40876 q^{54} -3.34510 q^{55} -2.83921 q^{56} -4.64209 q^{57} +6.52521 q^{58} +5.87222 q^{59} +0.0385729 q^{60} -2.73142 q^{61} +14.8733 q^{62} +1.00000 q^{63} +8.06065 q^{64} -1.51983 q^{65} +1.88157 q^{66} +10.9589 q^{67} -0.0741673 q^{68} +0.157797 q^{69} -3.52826 q^{70} +5.87488 q^{71} -2.83921 q^{72} +9.58657 q^{73} -10.5259 q^{74} +1.27260 q^{75} +0.0714943 q^{76} +1.33563 q^{77} +0.854882 q^{78} +14.0028 q^{79} +9.94033 q^{80} +1.00000 q^{81} -0.983957 q^{82} -1.26515 q^{83} -0.0154013 q^{84} -12.0608 q^{85} +7.66974 q^{86} +4.63189 q^{87} -3.79213 q^{88} +4.03365 q^{89} -3.52826 q^{90} +0.606834 q^{91} -0.00243029 q^{92} +10.5578 q^{93} -9.62562 q^{94} +11.6262 q^{95} +0.0871212 q^{96} +14.8344 q^{97} +1.40876 q^{98} +1.33563 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	1.40876	0.996142	0.498071	−	0.867136i	$-0.334042\pi$
$2$	1.40876	0.996142	0.498071	+	0.867136i	$0.334042\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.0154013	−0.00770067
$5$	−2.50452	−1.12005	−0.560027	−	0.828474i	$-0.689209\pi$
$5$	−2.50452	−1.12005	−0.560027	+	0.828474i	$0.689209\pi$
$6$	1.40876	0.575123
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.83921	−1.00381
$9$	1.00000	0.333333
$10$	−3.52826	−1.11573
$11$	1.33563	0.402706	0.201353	−	0.979519i	$-0.435466\pi$
$11$	1.33563	0.402706	0.201353	+	0.979519i	$0.435466\pi$
$12$	−0.0154013	−0.00444598
$13$	0.606834	0.168305	0.0841527	−	0.996453i	$-0.473182\pi$
$13$	0.606834	0.168305	0.0841527	+	0.996453i	$0.473182\pi$
$14$	1.40876	0.376506
$15$	−2.50452	−0.646663
$16$	−3.96896	−0.992240
$17$	4.81564	1.16796	0.583982	−	0.811767i	$-0.301494\pi$
$17$	4.81564	1.16796	0.583982	+	0.811767i	$0.301494\pi$
$18$	1.40876	0.332047
$19$	−4.64209	−1.06497	−0.532484	−	0.846440i	$-0.678741\pi$
$19$	−4.64209	−1.06497	−0.532484	+	0.846440i	$0.678741\pi$
$20$	0.0385729	0.00862516
$21$	1.00000	0.218218
$22$	1.88157	0.401153
$23$	0.157797	0.0329030	0.0164515	−	0.999865i	$-0.494763\pi$
$23$	0.157797	0.0329030	0.0164515	+	0.999865i	$0.494763\pi$
$24$	−2.83921	−0.579552
$25$	1.27260	0.254521
$26$	0.854882	0.167656
$27$	1.00000	0.192450
$28$	−0.0154013	−0.00291058
$29$	4.63189	0.860121	0.430060	−	0.902800i	$-0.358492\pi$
$29$	4.63189	0.860121	0.430060	+	0.902800i	$0.358492\pi$
$30$	−3.52826	−0.644169
$31$	10.5578	1.89623	0.948115	−	0.317927i	$-0.102987\pi$
$31$	10.5578	1.89623	0.948115	+	0.317927i	$0.102987\pi$
$32$	0.0871212	0.0154010
$33$	1.33563	0.232503
$34$	6.78407	1.16346
$35$	−2.50452	−0.423341
$36$	−0.0154013	−0.00256689
$37$	−7.47175	−1.22835	−0.614174	−	0.789171i	$-0.710511\pi$
$37$	−7.47175	−1.22835	−0.614174	+	0.789171i	$0.710511\pi$
$38$	−6.53958	−1.06086
$39$	0.606834	0.0971712
$40$	7.11085	1.12432
$41$	−0.698457	−0.109081	−0.0545403	−	0.998512i	$-0.517369\pi$
$41$	−0.698457	−0.109081	−0.0545403	+	0.998512i	$0.517369\pi$
$42$	1.40876	0.217376
$43$	5.44433	0.830253	0.415126	−	0.909764i	$-0.363737\pi$
$43$	5.44433	0.830253	0.415126	+	0.909764i	$0.363737\pi$
$44$	−0.0205704	−0.00310111
$45$	−2.50452	−0.373351
$46$	0.222298	0.0327760
$47$	−6.83270	−0.996652	−0.498326	−	0.866990i	$-0.666052\pi$
$47$	−6.83270	−0.996652	−0.498326	+	0.866990i	$0.666052\pi$
$48$	−3.96896	−0.572870
$49$	1.00000	0.142857
$50$	1.79279	0.253539
$51$	4.81564	0.674324
$52$	−0.00934605	−0.00129606
$53$	3.77705	0.518817	0.259409	−	0.965768i	$-0.416472\pi$
$53$	3.77705	0.518817	0.259409	+	0.965768i	$0.416472\pi$
$54$	1.40876	0.191708
$55$	−3.34510	−0.451053
$56$	−2.83921	−0.379406
$57$	−4.64209	−0.614860
$58$	6.52521	0.856803
$59$	5.87222	0.764498	0.382249	−	0.924059i	$-0.375150\pi$
$59$	5.87222	0.764498	0.382249	+	0.924059i	$0.375150\pi$
$60$	0.0385729	0.00497974
$61$	−2.73142	−0.349722	−0.174861	−	0.984593i	$-0.555948\pi$
$61$	−2.73142	−0.349722	−0.174861	+	0.984593i	$0.555948\pi$
$62$	14.8733	1.88892
$63$	1.00000	0.125988
$64$	8.06065	1.00758
$65$	−1.51983	−0.188511
$66$	1.88157	0.231606
$67$	10.9589	1.33884	0.669420	−	0.742884i	$-0.266543\pi$
$67$	10.9589	1.33884	0.669420	+	0.742884i	$0.266543\pi$
$68$	−0.0741673	−0.00899410
$69$	0.157797	0.0189965
$70$	−3.52826	−0.421707
$71$	5.87488	0.697220	0.348610	−	0.937268i	$-0.386654\pi$
$71$	5.87488	0.697220	0.348610	+	0.937268i	$0.386654\pi$
$72$	−2.83921	−0.334604
$73$	9.58657	1.12202	0.561011	−	0.827808i	$-0.310412\pi$
$73$	9.58657	1.12202	0.561011	+	0.827808i	$0.310412\pi$
$74$	−10.5259	−1.22361
$75$	1.27260	0.146948
$76$	0.0714943	0.00820096
$77$	1.33563	0.152209
$78$	0.854882	0.0967963
$79$	14.0028	1.57543	0.787717	−	0.616037i	$-0.211263\pi$
$79$	14.0028	1.57543	0.787717	+	0.616037i	$0.211263\pi$
$80$	9.94033	1.11136
$81$	1.00000	0.111111
$82$	−0.983957	−0.108660
$83$	−1.26515	−0.138868	−0.0694339	−	0.997587i	$-0.522119\pi$
$83$	−1.26515	−0.138868	−0.0694339	+	0.997587i	$0.522119\pi$
$84$	−0.0154013	−0.00168042
$85$	−12.0608	−1.30818
$86$	7.66974	0.827050
$87$	4.63189	0.496591
$88$	−3.79213	−0.404242
$89$	4.03365	0.427566	0.213783	−	0.976881i	$-0.431421\pi$
$89$	4.03365	0.427566	0.213783	+	0.976881i	$0.431421\pi$
$90$	−3.52826	−0.371911
$91$	0.606834	0.0636135
$92$	−0.00243029	−0.000253375 0
$93$	10.5578	1.09479
$94$	−9.62562	−0.992807
$95$	11.6262	1.19282
$96$	0.0871212	0.00889177
$97$	14.8344	1.50621	0.753104	−	0.657902i	$-0.228556\pi$
$97$	14.8344	1.50621	0.753104	+	0.657902i	$0.228556\pi$
$98$	1.40876	0.142306
$99$	1.33563	0.134235
$100$	−0.0195998	−0.00195998
$101$	11.7652	1.17068	0.585342	−	0.810786i	$-0.300960\pi$
$101$	11.7652	1.17068	0.585342	+	0.810786i	$0.300960\pi$
$102$	6.78407	0.671723
$103$	−9.41346	−0.927535	−0.463768	−	0.885957i	$-0.653503\pi$
$103$	−9.41346	−0.927535	−0.463768	+	0.885957i	$0.653503\pi$
$104$	−1.72293	−0.168947
$105$	−2.50452	−0.244416
$106$	5.32094	0.516816
$107$	−2.46959	−0.238744	−0.119372	−	0.992850i	$-0.538088\pi$
$107$	−2.46959	−0.238744	−0.119372	+	0.992850i	$0.538088\pi$
$108$	−0.0154013	−0.00148199
$109$	10.0768	0.965181	0.482591	−	0.875846i	$-0.339696\pi$
$109$	10.0768	0.965181	0.482591	+	0.875846i	$0.339696\pi$
$110$	−4.71243	−0.449313
$111$	−7.47175	−0.709187
$112$	−3.96896	−0.375031
$113$	−1.21750	−0.114532	−0.0572662	−	0.998359i	$-0.518238\pi$
$113$	−1.21750	−0.114532	−0.0572662	+	0.998359i	$0.518238\pi$
$114$	−6.53958	−0.612488
$115$	−0.395206	−0.0368531
$116$	−0.0713373	−0.00662350
$117$	0.606834	0.0561018
$118$	8.27254	0.761549
$119$	4.81564	0.441449
$120$	7.11085	0.649129
$121$	−9.21610	−0.837828
$122$	−3.84790	−0.348373
$123$	−0.698457	−0.0629778
$124$	−0.162604	−0.0146022
$125$	9.33533	0.834977
$126$	1.40876	0.125502
$127$	−12.4552	−1.10522	−0.552609	−	0.833440i	$-0.686368\pi$
$127$	−12.4552	−1.10522	−0.552609	+	0.833440i	$0.686368\pi$
$128$	11.1813	0.988294
$129$	5.44433	0.479347
$130$	−2.14107	−0.187784
$131$	−2.72601	−0.238173	−0.119086	−	0.992884i	$-0.537997\pi$
$131$	−2.72601	−0.238173	−0.119086	+	0.992884i	$0.537997\pi$
$132$	−0.0205704	−0.00179043
$133$	−4.64209	−0.402520
$134$	15.4384	1.33367
$135$	−2.50452	−0.215554
$136$	−13.6726	−1.17242
$137$	−19.1709	−1.63788	−0.818942	−	0.573876i	$-0.805439\pi$
$137$	−19.1709	−1.63788	−0.818942	+	0.573876i	$0.805439\pi$
$138$	0.222298	0.0189233
$139$	16.1412	1.36908	0.684538	−	0.728977i	$-0.260004\pi$
$139$	16.1412	1.36908	0.684538	+	0.728977i	$0.260004\pi$
$140$	0.0385729	0.00326000
$141$	−6.83270	−0.575417
$142$	8.27628	0.694530
$143$	0.810503	0.0677777
$144$	−3.96896	−0.330747
$145$	−11.6007	−0.963382
$146$	13.5052	1.11769
$147$	1.00000	0.0824786
$148$	0.115075	0.00945910
$149$	23.7434	1.94513	0.972567	−	0.232622i	$-0.0747307\pi$
$149$	23.7434	1.94513	0.972567	+	0.232622i	$0.0747307\pi$
$150$	1.79279	0.146381
$151$	5.45192	0.443671	0.221835	−	0.975084i	$-0.428795\pi$
$151$	5.45192	0.443671	0.221835	+	0.975084i	$0.428795\pi$
$152$	13.1799	1.06903
$153$	4.81564	0.389321
$154$	1.88157	0.151622
$155$	−26.4421	−2.12388
$156$	−0.00934605	−0.000748283 0
$157$	−16.9158	−1.35003	−0.675014	−	0.737805i	$-0.735862\pi$
$157$	−16.9158	−1.35003	−0.675014	+	0.737805i	$0.735862\pi$
$158$	19.7265	1.56936
$159$	3.77705	0.299539
$160$	−0.218196	−0.0172499
$161$	0.157797	0.0124362
$162$	1.40876	0.110682
$163$	−18.7950	−1.47214	−0.736070	−	0.676906i	$-0.763321\pi$
$163$	−18.7950	−1.47214	−0.736070	+	0.676906i	$0.763321\pi$
$164$	0.0107572	0.000839994 0
$165$	−3.34510	−0.260415
$166$	−1.78228	−0.138332
$167$	20.9783	1.62335	0.811673	−	0.584112i	$-0.198557\pi$
$167$	20.9783	1.62335	0.811673	+	0.584112i	$0.198557\pi$
$168$	−2.83921	−0.219050
$169$	−12.6318	−0.971673
$170$	−16.9908	−1.30314
$171$	−4.64209	−0.354989
$172$	−0.0838500	−0.00639350
$173$	18.8832	1.43566	0.717832	−	0.696217i	$-0.245135\pi$
$173$	18.8832	1.43566	0.717832	+	0.696217i	$0.245135\pi$
$174$	6.52521	0.494675
$175$	1.27260	0.0961998
$176$	−5.30105	−0.399581
$177$	5.87222	0.441383
$178$	5.68243	0.425916
$179$	−0.816698	−0.0610429	−0.0305214	−	0.999534i	$-0.509717\pi$
$179$	−0.816698	−0.0610429	−0.0305214	+	0.999534i	$0.509717\pi$
$180$	0.0385729	0.00287505
$181$	9.73072	0.723279	0.361640	−	0.932318i	$-0.382217\pi$
$181$	9.73072	0.723279	0.361640	+	0.932318i	$0.382217\pi$
$182$	0.854882	0.0633681
$183$	−2.73142	−0.201912
$184$	−0.448020	−0.0330284
$185$	18.7131	1.37582
$186$	14.8733	1.09057
$187$	6.43189	0.470347
$188$	0.105233	0.00767489
$189$	1.00000	0.0727393
$190$	16.3785	1.18822
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	8.06065	0.581728
$193$	−9.82523	−0.707236	−0.353618	−	0.935390i	$-0.615049\pi$
$193$	−9.82523	−0.707236	−0.353618	+	0.935390i	$0.615049\pi$
$194$	20.8981	1.50040
$195$	−1.51983	−0.108837
$196$	−0.0154013	−0.00110010
$197$	−14.8918	−1.06100	−0.530498	−	0.847686i	$-0.677995\pi$
$197$	−14.8918	−1.06100	−0.530498	+	0.847686i	$0.677995\pi$
$198$	1.88157	0.133718
$199$	−14.1267	−1.00142	−0.500708	−	0.865616i	$-0.666927\pi$
$199$	−14.1267	−1.00142	−0.500708	+	0.865616i	$0.666927\pi$
$200$	−3.61319	−0.255491
$201$	10.9589	0.772979
$202$	16.5744	1.16617
$203$	4.63189	0.325095
$204$	−0.0741673	−0.00519275
$205$	1.74930	0.122176
$206$	−13.2613	−0.923957
$207$	0.157797	0.0109677
$208$	−2.40850	−0.166999
$209$	−6.20009	−0.428869
$210$	−3.52826	−0.243473
$211$	−10.4808	−0.721526	−0.360763	−	0.932657i	$-0.617484\pi$
$211$	−10.4808	−0.721526	−0.360763	+	0.932657i	$0.617484\pi$
$212$	−0.0581716	−0.00399524
$213$	5.87488	0.402540
$214$	−3.47905	−0.237823
$215$	−13.6354	−0.929928
$216$	−2.83921	−0.193184
$217$	10.5578	0.716708
$218$	14.1958	0.961458
$219$	9.58657	0.647800
$220$	0.0515190	0.00347341
$221$	2.92229	0.196575
$222$	−10.5259	−0.706451
$223$	−23.5729	−1.57855	−0.789277	−	0.614037i	$-0.789545\pi$
$223$	−23.5729	−1.57855	−0.789277	+	0.614037i	$0.789545\pi$
$224$	0.0871212	0.00582103
$225$	1.27260	0.0848402
$226$	−1.71516	−0.114090
$227$	4.47506	0.297020	0.148510	−	0.988911i	$-0.452552\pi$
$227$	4.47506	0.297020	0.148510	+	0.988911i	$0.452552\pi$
$228$	0.0714943	0.00473483
$229$	2.37664	0.157053	0.0785263	−	0.996912i	$-0.474979\pi$
$229$	2.37664	0.157053	0.0785263	+	0.996912i	$0.474979\pi$
$230$	−0.556749	−0.0367109
$231$	1.33563	0.0878777
$232$	−13.1509	−0.863401
$233$	21.2710	1.39351	0.696754	−	0.717310i	$-0.254627\pi$
$233$	21.2710	1.39351	0.696754	+	0.717310i	$0.254627\pi$
$234$	0.854882	0.0558854
$235$	17.1126	1.11630
$236$	−0.0904400	−0.00588715
$237$	14.0028	0.909577
$238$	6.78407	0.439746
$239$	14.6490	0.947565	0.473782	−	0.880642i	$-0.342888\pi$
$239$	14.6490	0.947565	0.473782	+	0.880642i	$0.342888\pi$
$240$	9.94033	0.641645
$241$	−1.97524	−0.127236	−0.0636181	−	0.997974i	$-0.520264\pi$
$241$	−1.97524	−0.127236	−0.0636181	+	0.997974i	$0.520264\pi$
$242$	−12.9833	−0.834595
$243$	1.00000	0.0641500
$244$	0.0420675	0.00269309
$245$	−2.50452	−0.160008
$246$	−0.983957	−0.0627348
$247$	−2.81698	−0.179240
$248$	−29.9757	−1.90346
$249$	−1.26515	−0.0801753
$250$	13.1512	0.831756
$251$	−1.58706	−0.100174	−0.0500872	−	0.998745i	$-0.515950\pi$
$251$	−1.58706	−0.100174	−0.0500872	+	0.998745i	$0.515950\pi$
$252$	−0.0154013	−0.000970193 0
$253$	0.210758	0.0132502
$254$	−17.5463	−1.10095
$255$	−12.0608	−0.755280
$256$	−0.369610	−0.0231006
$257$	−20.2185	−1.26120	−0.630599	−	0.776109i	$-0.717191\pi$
$257$	−20.2185	−1.26120	−0.630599	+	0.776109i	$0.717191\pi$
$258$	7.66974	0.477497
$259$	−7.47175	−0.464272
$260$	0.0234073	0.00145166
$261$	4.63189	0.286707
$262$	−3.84029	−0.237254
$263$	−22.0854	−1.36185	−0.680923	−	0.732355i	$-0.738421\pi$
$263$	−22.0854	−1.36185	−0.680923	+	0.732355i	$0.738421\pi$
$264$	−3.79213	−0.233389
$265$	−9.45968	−0.581103
$266$	−6.53958	−0.400967
$267$	4.03365	0.246855
$268$	−0.168781	−0.0103100
$269$	8.88629	0.541807	0.270903	−	0.962607i	$-0.412678\pi$
$269$	8.88629	0.541807	0.270903	+	0.962607i	$0.412678\pi$
$270$	−3.52826	−0.214723
$271$	−21.8846	−1.32939	−0.664697	−	0.747113i	$-0.731439\pi$
$271$	−21.8846	−1.32939	−0.664697	+	0.747113i	$0.731439\pi$
$272$	−19.1131	−1.15890
$273$	0.606834	0.0367272
$274$	−27.0072	−1.63157
$275$	1.69972	0.102497
$276$	−0.00243029	−0.000146286 0
$277$	−0.339138	−0.0203768	−0.0101884	−	0.999948i	$-0.503243\pi$
$277$	−0.339138	−0.0203768	−0.0101884	+	0.999948i	$0.503243\pi$
$278$	22.7390	1.36379
$279$	10.5578	0.632077
$280$	7.11085	0.424955
$281$	−31.1185	−1.85638	−0.928188	−	0.372112i	$-0.878634\pi$
$281$	−31.1185	−1.85638	−0.928188	+	0.372112i	$0.878634\pi$
$282$	−9.62562	−0.573197
$283$	14.1337	0.840162	0.420081	−	0.907487i	$-0.362002\pi$
$283$	14.1337	0.840162	0.420081	+	0.907487i	$0.362002\pi$
$284$	−0.0904810	−0.00536906
$285$	11.6262	0.688676
$286$	1.14180	0.0675162
$287$	−0.698457	−0.0412286
$288$	0.0871212	0.00513366
$289$	6.19038	0.364140
$290$	−16.3425	−0.959665
$291$	14.8344	0.869609
$292$	−0.147646	−0.00864032
$293$	16.7333	0.977572	0.488786	−	0.872404i	$-0.337440\pi$
$293$	16.7333	0.977572	0.488786	+	0.872404i	$0.337440\pi$
$294$	1.40876	0.0821604
$295$	−14.7071	−0.856279
$296$	21.2139	1.23303
$297$	1.33563	0.0775009
$298$	33.4487	1.93763
$299$	0.0957566	0.00553775
$300$	−0.0195998	−0.00113159
$301$	5.44433	0.313806
$302$	7.68043	0.441959
$303$	11.7652	0.675895
$304$	18.4243	1.05670
$305$	6.84088	0.391707
$306$	6.78407	0.387819
$307$	26.8861	1.53447	0.767237	−	0.641364i	$-0.221631\pi$
$307$	26.8861	1.53447	0.767237	+	0.641364i	$0.221631\pi$
$308$	−0.0205704	−0.00117211
$309$	−9.41346	−0.535513
$310$	−37.2505	−2.11569
$311$	26.0197	1.47544	0.737721	−	0.675106i	$-0.235902\pi$
$311$	26.0197	1.47544	0.737721	+	0.675106i	$0.235902\pi$
$312$	−1.72293	−0.0975417
$313$	−23.2560	−1.31451	−0.657253	−	0.753670i	$-0.728282\pi$
$313$	−23.2560	−1.31451	−0.657253	+	0.753670i	$0.728282\pi$
$314$	−23.8303	−1.34482
$315$	−2.50452	−0.141114
$316$	−0.215661	−0.0121319
$317$	8.91958	0.500974	0.250487	−	0.968120i	$-0.419409\pi$
$317$	8.91958	0.500974	0.250487	+	0.968120i	$0.419409\pi$
$318$	5.32094	0.298384
$319$	6.18648	0.346376
$320$	−20.1880	−1.12855
$321$	−2.46959	−0.137839
$322$	0.222298	0.0123882
$323$	−22.3546	−1.24384
$324$	−0.0154013	−0.000855630 0
$325$	0.772259	0.0428372
$326$	−26.4776	−1.46646
$327$	10.0768	0.557248
$328$	1.98307	0.109497
$329$	−6.83270	−0.376699
$330$	−4.71243	−0.259411
$331$	−31.1990	−1.71485	−0.857426	−	0.514608i	$-0.827938\pi$
$331$	−31.1990	−1.71485	−0.857426	+	0.514608i	$0.827938\pi$
$332$	0.0194849	0.00106937
$333$	−7.47175	−0.409449
$334$	29.5533	1.61708
$335$	−27.4467	−1.49957
$336$	−3.96896	−0.216525
$337$	13.9396	0.759337	0.379668	−	0.925123i	$-0.376038\pi$
$337$	13.9396	0.759337	0.379668	+	0.925123i	$0.376038\pi$
$338$	−17.7951	−0.967925
$339$	−1.21750	−0.0661253
$340$	0.185753	0.0100739
$341$	14.1012	0.763624
$342$	−6.53958	−0.353620
$343$	1.00000	0.0539949
$344$	−15.4576	−0.833419
$345$	−0.395206	−0.0212772
$346$	26.6019	1.43012
$347$	−18.4270	−0.989216	−0.494608	−	0.869116i	$-0.664688\pi$
$347$	−18.4270	−0.989216	−0.494608	+	0.869116i	$0.664688\pi$
$348$	−0.0713373	−0.00382408
$349$	−20.5231	−1.09858	−0.549289	−	0.835633i	$-0.685101\pi$
$349$	−20.5231	−1.09858	−0.549289	+	0.835633i	$0.685101\pi$
$350$	1.79279	0.0958287
$351$	0.606834	0.0323904
$352$	0.116361	0.00620208
$353$	−9.58900	−0.510371	−0.255186	−	0.966892i	$-0.582137\pi$
$353$	−9.58900	−0.510371	−0.255186	+	0.966892i	$0.582137\pi$
$354$	8.27254	0.439680
$355$	−14.7137	−0.780924
$356$	−0.0621236	−0.00329254
$357$	4.81564	0.254871
$358$	−1.15053	−0.0608074
$359$	31.0064	1.63646	0.818228	−	0.574894i	$-0.194957\pi$
$359$	31.0064	1.63646	0.818228	+	0.574894i	$0.194957\pi$
$360$	7.11085	0.374775
$361$	2.54898	0.134157
$362$	13.7082	0.720489
$363$	−9.21610	−0.483720
$364$	−0.00934605	−0.000489866 0
$365$	−24.0097	−1.25673
$366$	−3.84790	−0.201133
$367$	−2.36393	−0.123396	−0.0616979	−	0.998095i	$-0.519652\pi$
$367$	−2.36393	−0.123396	−0.0616979	+	0.998095i	$0.519652\pi$
$368$	−0.626291	−0.0326476
$369$	−0.698457	−0.0363602
$370$	26.3622	1.37051
$371$	3.77705	0.196095
$372$	−0.162604	−0.00843061
$373$	−30.3777	−1.57290	−0.786449	−	0.617655i	$-0.788083\pi$
$373$	−30.3777	−1.57290	−0.786449	+	0.617655i	$0.788083\pi$
$374$	9.06098	0.468532
$375$	9.33533	0.482074
$376$	19.3995	1.00045
$377$	2.81079	0.144763
$378$	1.40876	0.0724587
$379$	35.4153	1.81916	0.909581	−	0.415526i	$-0.136403\pi$
$379$	35.4153	1.81916	0.909581	+	0.415526i	$0.136403\pi$
$380$	−0.179059	−0.00918552
$381$	−12.4552	−0.638098
$382$	1.40876	0.0720783
$383$	13.1486	0.671861	0.335931	−	0.941887i	$-0.390949\pi$
$383$	13.1486	0.671861	0.335931	+	0.941887i	$0.390949\pi$
$384$	11.1813	0.570592
$385$	−3.34510	−0.170482
$386$	−13.8414	−0.704507
$387$	5.44433	0.276751
$388$	−0.228470	−0.0115988
$389$	8.12819	0.412116	0.206058	−	0.978540i	$-0.433936\pi$
$389$	8.12819	0.412116	0.206058	+	0.978540i	$0.433936\pi$
$390$	−2.14107	−0.108417
$391$	0.759894	0.0384295
$392$	−2.83921	−0.143402
$393$	−2.72601	−0.137509
$394$	−20.9789	−1.05690
$395$	−35.0702	−1.76457
$396$	−0.0205704	−0.00103370
$397$	36.3493	1.82432	0.912159	−	0.409837i	$-0.134414\pi$
$397$	36.3493	1.82432	0.912159	+	0.409837i	$0.134414\pi$
$398$	−19.9011	−0.997553
$399$	−4.64209	−0.232395
$400$	−5.05091	−0.252546
$401$	−29.9455	−1.49541	−0.747704	−	0.664032i	$-0.768844\pi$
$401$	−29.9455	−1.49541	−0.747704	+	0.664032i	$0.768844\pi$
$402$	15.4384	0.769997
$403$	6.40681	0.319146
$404$	−0.181200	−0.00901505
$405$	−2.50452	−0.124450
$406$	6.52521	0.323841
$407$	−9.97946	−0.494663
$408$	−13.6726	−0.676896
$409$	6.04071	0.298694	0.149347	−	0.988785i	$-0.452283\pi$
$409$	6.04071	0.298694	0.149347	+	0.988785i	$0.452283\pi$
$410$	2.46434	0.121705
$411$	−19.1709	−0.945633
$412$	0.144980	0.00714264
$413$	5.87222	0.288953
$414$	0.222298	0.0109253
$415$	3.16858	0.155539
$416$	0.0528681	0.00259207
$417$	16.1412	0.790437
$418$	−8.73443	−0.427215
$419$	−1.35671	−0.0662794	−0.0331397	−	0.999451i	$-0.510551\pi$
$419$	−1.35671	−0.0662794	−0.0331397	+	0.999451i	$0.510551\pi$
$420$	0.0385729	0.00188216
$421$	23.7838	1.15915	0.579575	−	0.814919i	$-0.303219\pi$
$421$	23.7838	1.15915	0.579575	+	0.814919i	$0.303219\pi$
$422$	−14.7649	−0.718743
$423$	−6.83270	−0.332217
$424$	−10.7238	−0.520796
$425$	6.12840	0.297271
$426$	8.27628	0.400987
$427$	−2.73142	−0.132182
$428$	0.0380349	0.00183849
$429$	0.810503	0.0391314
$430$	−19.2090	−0.926340
$431$	−33.2855	−1.60331	−0.801653	−	0.597790i	$-0.796046\pi$
$431$	−33.2855	−1.60331	−0.801653	+	0.597790i	$0.796046\pi$
$432$	−3.96896	−0.190957
$433$	−40.1074	−1.92744	−0.963720	−	0.266916i	$-0.913995\pi$
$433$	−40.1074	−1.92744	−0.963720	+	0.266916i	$0.913995\pi$
$434$	14.8733	0.713943
$435$	−11.6007	−0.556209
$436$	−0.155196	−0.00743254
$437$	−0.732508	−0.0350406
$438$	13.5052	0.645301
$439$	1.56885	0.0748773	0.0374387	−	0.999299i	$-0.488080\pi$
$439$	1.56885	0.0748773	0.0374387	+	0.999299i	$0.488080\pi$
$440$	9.49744	0.452773
$441$	1.00000	0.0476190
$442$	4.11680	0.195816
$443$	36.0924	1.71480	0.857400	−	0.514650i	$-0.172078\pi$
$443$	36.0924	1.71480	0.857400	+	0.514650i	$0.172078\pi$
$444$	0.115075	0.00546121
$445$	−10.1023	−0.478897
$446$	−33.2084	−1.57247
$447$	23.7434	1.12302
$448$	8.06065	0.380830
$449$	38.3723	1.81090	0.905450	−	0.424453i	$-0.139533\pi$
$449$	38.3723	1.81090	0.905450	+	0.424453i	$0.139533\pi$
$450$	1.79279	0.0845129
$451$	−0.932877	−0.0439275
$452$	0.0187511	0.000881975 0
$453$	5.45192	0.256153
$454$	6.30428	0.295875
$455$	−1.51983	−0.0712505
$456$	13.1799	0.617204
$457$	−2.58535	−0.120938	−0.0604688	−	0.998170i	$-0.519260\pi$
$457$	−2.58535	−0.120938	−0.0604688	+	0.998170i	$0.519260\pi$
$458$	3.34811	0.156447
$459$	4.81564	0.224775
$460$	0.00608669	0.000283793 0
$461$	2.26117	0.105313	0.0526565	−	0.998613i	$-0.483231\pi$
$461$	2.26117	0.105313	0.0526565	+	0.998613i	$0.483231\pi$
$462$	1.88157	0.0875387
$463$	−27.7160	−1.28807	−0.644037	−	0.764994i	$-0.722742\pi$
$463$	−27.7160	−1.28807	−0.644037	+	0.764994i	$0.722742\pi$
$464$	−18.3838	−0.853446
$465$	−26.4421	−1.22622
$466$	29.9657	1.38813
$467$	−12.2615	−0.567396	−0.283698	−	0.958914i	$-0.591561\pi$
$467$	−12.2615	−0.567396	−0.283698	+	0.958914i	$0.591561\pi$
$468$	−0.00934605	−0.000432021 0
$469$	10.9589	0.506034
$470$	24.1075	1.11200
$471$	−16.9158	−0.779439
$472$	−16.6725	−0.767413
$473$	7.27159	0.334348
$474$	19.7265	0.906068
$475$	−5.90754	−0.271056
$476$	−0.0741673	−0.00339945
$477$	3.77705	0.172939
$478$	20.6369	0.943909
$479$	17.0769	0.780265	0.390132	−	0.920759i	$-0.372429\pi$
$479$	17.0769	0.780265	0.390132	+	0.920759i	$0.372429\pi$
$480$	−0.218196	−0.00995926
$481$	−4.53411	−0.206738
$482$	−2.78263	−0.126745
$483$	0.157797	0.00718002
$484$	0.141940	0.00645183
$485$	−37.1531	−1.68703
$486$	1.40876	0.0639026
$487$	−24.4549	−1.10816	−0.554079	−	0.832464i	$-0.686930\pi$
$487$	−24.4549	−1.10816	−0.554079	+	0.832464i	$0.686930\pi$
$488$	7.75507	0.351056
$489$	−18.7950	−0.849940
$490$	−3.52826	−0.159390
$491$	−3.48317	−0.157193	−0.0785966	−	0.996906i	$-0.525044\pi$
$491$	−3.48317	−0.157193	−0.0785966	+	0.996906i	$0.525044\pi$
$492$	0.0107572	0.000484971 0
$493$	22.3055	1.00459
$494$	−3.96844	−0.178548
$495$	−3.34510	−0.150351
$496$	−41.9033	−1.88152
$497$	5.87488	0.263524
$498$	−1.78228	−0.0798660
$499$	−18.9256	−0.847227	−0.423614	−	0.905843i	$-0.639239\pi$
$499$	−18.9256	−0.847227	−0.423614	+	0.905843i	$0.639239\pi$
$500$	−0.143776	−0.00642988
$501$	20.9783	0.937240
$502$	−2.23578	−0.0997879
$503$	37.0593	1.65239	0.826196	−	0.563383i	$-0.190500\pi$
$503$	37.0593	1.65239	0.826196	+	0.563383i	$0.190500\pi$
$504$	−2.83921	−0.126469
$505$	−29.4662	−1.31123
$506$	0.296907	0.0131991
$507$	−12.6318	−0.560996
$508$	0.191826	0.00851092
$509$	−13.3654	−0.592411	−0.296206	−	0.955124i	$-0.595721\pi$
$509$	−13.3654	−0.592411	−0.296206	+	0.955124i	$0.595721\pi$
$510$	−16.9908	−0.752366
$511$	9.58657	0.424085
$512$	−22.8832	−1.01131
$513$	−4.64209	−0.204953
$514$	−28.4830	−1.25633
$515$	23.5762	1.03889
$516$	−0.0838500	−0.00369129
$517$	−9.12593	−0.401358
$518$	−10.5259	−0.462481
$519$	18.8832	0.828881
$520$	4.31511	0.189230
$521$	−11.5140	−0.504437	−0.252218	−	0.967670i	$-0.581160\pi$
$521$	−11.5140	−0.504437	−0.252218	+	0.967670i	$0.581160\pi$
$522$	6.52521	0.285601
$523$	14.1766	0.619901	0.309951	−	0.950753i	$-0.399687\pi$
$523$	14.1766	0.619901	0.309951	+	0.950753i	$0.399687\pi$
$524$	0.0419842	0.00183409
$525$	1.27260	0.0555410
$526$	−31.1130	−1.35659
$527$	50.8424	2.21473
$528$	−5.30105	−0.230698
$529$	−22.9751	−0.998917
$530$	−13.3264	−0.578862
$531$	5.87222	0.254833
$532$	0.0714943	0.00309967
$533$	−0.423847	−0.0183589
$534$	5.68243	0.245903
$535$	6.18512	0.267406
$536$	−31.1146	−1.34394
$537$	−0.816698	−0.0352431
$538$	12.5186	0.539716
$539$	1.33563	0.0575295
$540$	0.0385729	0.00165991
$541$	−19.2545	−0.827814	−0.413907	−	0.910319i	$-0.635836\pi$
$541$	−19.2545	−0.827814	−0.413907	+	0.910319i	$0.635836\pi$
$542$	−30.8301	−1.32427
$543$	9.73072	0.417585
$544$	0.419544	0.0179878
$545$	−25.2375	−1.08106
$546$	0.854882	0.0365856
$547$	−22.9244	−0.980177	−0.490089	−	0.871673i	$-0.663036\pi$
$547$	−22.9244	−0.980177	−0.490089	+	0.871673i	$0.663036\pi$
$548$	0.295258	0.0126128
$549$	−2.73142	−0.116574
$550$	2.39450	0.102102
$551$	−21.5017	−0.916001
$552$	−0.448020	−0.0190690
$553$	14.0028	0.595458
$554$	−0.477764	−0.0202982
$555$	18.7131	0.794327
$556$	−0.248596	−0.0105428
$557$	−4.29060	−0.181798	−0.0908992	−	0.995860i	$-0.528974\pi$
$557$	−4.29060	−0.181798	−0.0908992	+	0.995860i	$0.528974\pi$
$558$	14.8733	0.629638
$559$	3.30380	0.139736
$560$	9.94033	0.420055
$561$	6.43189	0.271555
$562$	−43.8385	−1.84921
$563$	−1.86793	−0.0787237	−0.0393619	−	0.999225i	$-0.512533\pi$
$563$	−1.86793	−0.0787237	−0.0393619	+	0.999225i	$0.512533\pi$
$564$	0.105233	0.00443110
$565$	3.04924	0.128282
$566$	19.9110	0.836920
$567$	1.00000	0.0419961
$568$	−16.6800	−0.699879
$569$	−18.4824	−0.774823	−0.387412	−	0.921907i	$-0.626631\pi$
$569$	−18.4824	−0.774823	−0.387412	+	0.921907i	$0.626631\pi$
$570$	16.3785	0.686019
$571$	25.7761	1.07870	0.539348	−	0.842083i	$-0.318671\pi$
$571$	25.7761	1.07870	0.539348	+	0.842083i	$0.318671\pi$
$572$	−0.0124828	−0.000521933 0
$573$	1.00000	0.0417756
$574$	−0.983957	−0.0410696
$575$	0.200813	0.00837449
$576$	8.06065	0.335861
$577$	22.3817	0.931762	0.465881	−	0.884847i	$-0.345738\pi$
$577$	22.3817	0.931762	0.465881	+	0.884847i	$0.345738\pi$
$578$	8.72075	0.362735
$579$	−9.82523	−0.408323
$580$	0.178666	0.00741868
$581$	−1.26515	−0.0524871
$582$	20.8981	0.866254
$583$	5.04472	0.208931
$584$	−27.2183	−1.12630
$585$	−1.51983	−0.0628370
$586$	23.5732	0.973801
$587$	−0.651776	−0.0269017	−0.0134508	−	0.999910i	$-0.504282\pi$
$587$	−0.651776	−0.0269017	−0.0134508	+	0.999910i	$0.504282\pi$
$588$	−0.0154013	−0.000635140 0
$589$	−49.0101	−2.01942
$590$	−20.7187	−0.852976
$591$	−14.8918	−0.612567
$592$	29.6551	1.21882
$593$	−5.82053	−0.239020	−0.119510	−	0.992833i	$-0.538132\pi$
$593$	−5.82053	−0.239020	−0.119510	+	0.992833i	$0.538132\pi$
$594$	1.88157	0.0772019
$595$	−12.0608	−0.494447
$596$	−0.365680	−0.0149788
$597$	−14.1267	−0.578168
$598$	0.134898	0.00551639
$599$	15.6950	0.641280	0.320640	−	0.947201i	$-0.396102\pi$
$599$	15.6950	0.641280	0.320640	+	0.947201i	$0.396102\pi$
$600$	−3.61319	−0.147508
$601$	−30.8747	−1.25940	−0.629702	−	0.776837i	$-0.716823\pi$
$601$	−30.8747	−1.25940	−0.629702	+	0.776837i	$0.716823\pi$
$602$	7.66974	0.312595
$603$	10.9589	0.446280
$604$	−0.0839668	−0.00341656
$605$	23.0819	0.938412
$606$	16.5744	0.673287
$607$	37.9874	1.54186	0.770930	−	0.636920i	$-0.219792\pi$
$607$	37.9874	1.54186	0.770930	+	0.636920i	$0.219792\pi$
$608$	−0.404424	−0.0164016
$609$	4.63189	0.187694
$610$	9.63714	0.390196
$611$	−4.14631	−0.167742
$612$	−0.0741673	−0.00299803
$613$	14.4667	0.584305	0.292153	−	0.956372i	$-0.405628\pi$
$613$	14.4667	0.584305	0.292153	+	0.956372i	$0.405628\pi$
$614$	37.8761	1.52855
$615$	1.74930	0.0705385
$616$	−3.79213	−0.152789
$617$	−26.4788	−1.06600	−0.532998	−	0.846116i	$-0.678935\pi$
$617$	−26.4788	−1.06600	−0.532998	+	0.846116i	$0.678935\pi$
$618$	−13.2613	−0.533447
$619$	−4.38435	−0.176222	−0.0881110	−	0.996111i	$-0.528083\pi$
$619$	−4.38435	−0.176222	−0.0881110	+	0.996111i	$0.528083\pi$
$620$	0.407244	0.0163553
$621$	0.157797	0.00633218
$622$	36.6554	1.46975
$623$	4.03365	0.161605
$624$	−2.40850	−0.0964171
$625$	−29.7435	−1.18974
$626$	−32.7620	−1.30943
$627$	−6.20009	−0.247608
$628$	0.260526	0.0103961
$629$	−35.9812	−1.43467
$630$	−3.52826	−0.140569
$631$	−28.4608	−1.13300	−0.566502	−	0.824060i	$-0.691704\pi$
$631$	−28.4608	−1.13300	−0.566502	+	0.824060i	$0.691704\pi$
$632$	−39.7568	−1.58144
$633$	−10.4808	−0.416573
$634$	12.5655	0.499041
$635$	31.1942	1.23790
$636$	−0.0581716	−0.00230665
$637$	0.606834	0.0240436
$638$	8.71525	0.345040
$639$	5.87488	0.232407
$640$	−28.0037	−1.10694
$641$	42.2641	1.66933	0.834667	−	0.550755i	$-0.185660\pi$
$641$	42.2641	1.66933	0.834667	+	0.550755i	$0.185660\pi$
$642$	−3.47905	−0.137307
$643$	0.716033	0.0282376	0.0141188	−	0.999900i	$-0.495506\pi$
$643$	0.716033	0.0282376	0.0141188	+	0.999900i	$0.495506\pi$
$644$	−0.00243029	−9.57667e−5 0
$645$	−13.6354	−0.536894
$646$	−31.4922	−1.23905
$647$	7.98731	0.314014	0.157007	−	0.987598i	$-0.449816\pi$
$647$	7.98731	0.314014	0.157007	+	0.987598i	$0.449816\pi$
$648$	−2.83921	−0.111535
$649$	7.84309	0.307868
$650$	1.08793	0.0426719
$651$	10.5578	0.413791
$652$	0.289468	0.0113365
$653$	−19.1681	−0.750104	−0.375052	−	0.927004i	$-0.622375\pi$
$653$	−19.1681	−0.750104	−0.375052	+	0.927004i	$0.622375\pi$
$654$	14.1958	0.555098
$655$	6.82734	0.266766
$656$	2.77215	0.108234
$657$	9.58657	0.374008
$658$	−9.62562	−0.375246
$659$	40.2543	1.56808	0.784042	−	0.620708i	$-0.213155\pi$
$659$	40.2543	1.56808	0.784042	+	0.620708i	$0.213155\pi$
$660$	0.0515190	0.00200537
$661$	−0.148448	−0.00577396	−0.00288698	−	0.999996i	$-0.500919\pi$
$661$	−0.148448	−0.00577396	−0.00288698	+	0.999996i	$0.500919\pi$
$662$	−43.9518	−1.70824
$663$	2.92229	0.113492
$664$	3.59202	0.139397
$665$	11.6262	0.450844
$666$	−10.5259	−0.407870
$667$	0.730899	0.0283005
$668$	−0.323093	−0.0125009
$669$	−23.5729	−0.911379
$670$	−38.6657	−1.49379
$671$	−3.64815	−0.140835
$672$	0.0871212	0.00336077
$673$	−11.2061	−0.431963	−0.215981	−	0.976397i	$-0.569295\pi$
$673$	−11.2061	−0.431963	−0.215981	+	0.976397i	$0.569295\pi$
$674$	19.6375	0.756408
$675$	1.27260	0.0489825
$676$	0.194546	0.00748253
$677$	15.2156	0.584782	0.292391	−	0.956299i	$-0.405549\pi$
$677$	15.2156	0.584782	0.292391	+	0.956299i	$0.405549\pi$
$678$	−1.71516	−0.0658702
$679$	14.8344	0.569293
$680$	34.2433	1.31317
$681$	4.47506	0.171485
$682$	19.8652	0.760678
$683$	−2.39544	−0.0916589	−0.0458294	−	0.998949i	$-0.514593\pi$
$683$	−2.39544	−0.0916589	−0.0458294	+	0.998949i	$0.514593\pi$
$684$	0.0714943	0.00273365
$685$	48.0139	1.83452
$686$	1.40876	0.0537866
$687$	2.37664	0.0906744
$688$	−21.6083	−0.823810
$689$	2.29204	0.0873198
$690$	−0.556749	−0.0211951
$691$	−17.8978	−0.680866	−0.340433	−	0.940269i	$-0.610574\pi$
$691$	−17.8978	−0.680866	−0.340433	+	0.940269i	$0.610574\pi$
$692$	−0.290827	−0.0110556
$693$	1.33563	0.0507362
$694$	−25.9592	−0.985400
$695$	−40.4258	−1.53344
$696$	−13.1509	−0.498485
$697$	−3.36352	−0.127402
$698$	−28.9121	−1.09434
$699$	21.2710	0.804543
$700$	−0.0195998	−0.000740802 0
$701$	23.7574	0.897303	0.448651	−	0.893707i	$-0.351904\pi$
$701$	23.7574	0.897303	0.448651	+	0.893707i	$0.351904\pi$
$702$	0.854882	0.0322654
$703$	34.6845	1.30815
$704$	10.7660	0.405759
$705$	17.1126	0.644498
$706$	−13.5086	−0.508402
$707$	11.7652	0.442477
$708$	−0.0904400	−0.00339894
$709$	21.5795	0.810435	0.405218	−	0.914220i	$-0.367196\pi$
$709$	21.5795	0.810435	0.405218	+	0.914220i	$0.367196\pi$
$710$	−20.7281	−0.777911
$711$	14.0028	0.525145
$712$	−11.4524	−0.429196
$713$	1.66599	0.0623916
$714$	6.78407	0.253887
$715$	−2.02992	−0.0759146
$716$	0.0125782	0.000470071 0
$717$	14.6490	0.547077
$718$	43.6805	1.63014
$719$	9.42530	0.351504	0.175752	−	0.984434i	$-0.443764\pi$
$719$	9.42530	0.351504	0.175752	+	0.984434i	$0.443764\pi$
$720$	9.94033	0.370454
$721$	−9.41346	−0.350575
$722$	3.59089	0.133639
$723$	−1.97524	−0.0734598
$724$	−0.149866	−0.00556973
$725$	5.89456	0.218919
$726$	−12.9833	−0.481854
$727$	32.8143	1.21702	0.608508	−	0.793547i	$-0.291768\pi$
$727$	32.8143	1.21702	0.608508	+	0.793547i	$0.291768\pi$
$728$	−1.72293	−0.0638560
$729$	1.00000	0.0370370
$730$	−33.8239	−1.25188
$731$	26.2179	0.969705
$732$	0.0420675	0.00155486
$733$	23.3840	0.863710	0.431855	−	0.901943i	$-0.357859\pi$
$733$	23.3840	0.863710	0.431855	+	0.901943i	$0.357859\pi$
$734$	−3.33020	−0.122920
$735$	−2.50452	−0.0923805
$736$	0.0137475	0.000506738 0
$737$	14.6370	0.539159
$738$	−0.983957	−0.0362200
$739$	34.7038	1.27660	0.638301	−	0.769787i	$-0.279638\pi$
$739$	34.7038	1.27660	0.638301	+	0.769787i	$0.279638\pi$
$740$	−0.288207	−0.0105947
$741$	−2.81698	−0.103484
$742$	5.32094	0.195338
$743$	−38.3062	−1.40532	−0.702659	−	0.711526i	$-0.748004\pi$
$743$	−38.3062	−1.40532	−0.702659	+	0.711526i	$0.748004\pi$
$744$	−29.9757	−1.09896
$745$	−59.4657	−2.17866
$746$	−42.7948	−1.56683
$747$	−1.26515	−0.0462892
$748$	−0.0990597	−0.00362198
$749$	−2.46959	−0.0902368
$750$	13.1512	0.480214
$751$	−43.6815	−1.59396	−0.796980	−	0.604006i	$-0.793570\pi$
$751$	−43.6815	−1.59396	−0.796980	+	0.604006i	$0.793570\pi$
$752$	27.1187	0.988918
$753$	−1.58706	−0.0578357
$754$	3.95972	0.144205
$755$	−13.6544	−0.496935
$756$	−0.0154013	−0.000560141 0
$757$	32.6369	1.18621	0.593105	−	0.805125i	$-0.297902\pi$
$757$	32.6369	1.18621	0.593105	+	0.805125i	$0.297902\pi$
$758$	49.8916	1.81214
$759$	0.210758	0.00765003
$760$	−33.0092	−1.19737
$761$	4.08464	0.148068	0.0740340	−	0.997256i	$-0.476413\pi$
$761$	4.08464	0.148068	0.0740340	+	0.997256i	$0.476413\pi$
$762$	−17.5463	−0.635637
$763$	10.0768	0.364804
$764$	−0.0154013	−0.000557201 0
$765$	−12.0608	−0.436061
$766$	18.5232	0.669269
$767$	3.56346	0.128669
$768$	−0.369610	−0.0133372
$769$	−0.0842302	−0.00303742	−0.00151871	−	0.999999i	$-0.500483\pi$
$769$	−0.0842302	−0.00303742	−0.00151871	+	0.999999i	$0.500483\pi$
$770$	−4.71243	−0.169824
$771$	−20.2185	−0.728153
$772$	0.151322	0.00544619
$773$	−8.94364	−0.321680	−0.160840	−	0.986980i	$-0.551420\pi$
$773$	−8.94364	−0.321680	−0.160840	+	0.986980i	$0.551420\pi$
$774$	7.66974	0.275683
$775$	13.4358	0.482630
$776$	−42.1181	−1.51195
$777$	−7.47175	−0.268047
$778$	11.4507	0.410526
$779$	3.24230	0.116167
$780$	0.0234073	0.000838117 0
$781$	7.84664	0.280775
$782$	1.07051	0.0382812
$783$	4.63189	0.165530
$784$	−3.96896	−0.141749
$785$	42.3659	1.51210
$786$	−3.84029	−0.136978
$787$	−36.7574	−1.31026	−0.655130	−	0.755516i	$-0.727386\pi$
$787$	−36.7574	−1.31026	−0.655130	+	0.755516i	$0.727386\pi$
$788$	0.229354	0.00817038
$789$	−22.0854	−0.786262
$790$	−49.4054	−1.75776
$791$	−1.21750	−0.0432891
$792$	−3.79213	−0.134747
$793$	−1.65752	−0.0588601
$794$	51.2073	1.81728
$795$	−9.45968	−0.335500
$796$	0.217570	0.00771157
$797$	−16.9630	−0.600861	−0.300431	−	0.953804i	$-0.597130\pi$
$797$	−16.9630	−0.600861	−0.300431	+	0.953804i	$0.597130\pi$
$798$	−6.53958	−0.231499
$799$	−32.9038	−1.16405
$800$	0.110871	0.00391987
$801$	4.03365	0.142522
$802$	−42.1860	−1.48964
$803$	12.8041	0.451846
$804$	−0.168781	−0.00595246
$805$	−0.395206	−0.0139292
$806$	9.02564	0.317915
$807$	8.88629	0.312812
$808$	−33.4040	−1.17515
$809$	−41.2801	−1.45133	−0.725666	−	0.688047i	$-0.758468\pi$
$809$	−41.2801	−1.45133	−0.725666	+	0.688047i	$0.758468\pi$
$810$	−3.52826	−0.123970
$811$	41.4441	1.45530	0.727650	−	0.685949i	$-0.240613\pi$
$811$	41.4441	1.45530	0.727650	+	0.685949i	$0.240613\pi$
$812$	−0.0713373	−0.00250345
$813$	−21.8846	−0.767526
$814$	−14.0586	−0.492755
$815$	47.0724	1.64888
$816$	−19.1131	−0.669092
$817$	−25.2731	−0.884193
$818$	8.50989	0.297541
$819$	0.606834	0.0212045
$820$	−0.0269415	−0.000940839 0
$821$	−25.0814	−0.875347	−0.437673	−	0.899134i	$-0.644197\pi$
$821$	−25.0814	−0.875347	−0.437673	+	0.899134i	$0.644197\pi$
$822$	−27.0072	−0.941985
$823$	−36.5506	−1.27407	−0.637036	−	0.770834i	$-0.719840\pi$
$823$	−36.5506	−1.27407	−0.637036	+	0.770834i	$0.719840\pi$
$824$	26.7268	0.931072
$825$	1.69972	0.0591767
$826$	8.27254	0.287838
$827$	47.1633	1.64003	0.820015	−	0.572343i	$-0.193965\pi$
$827$	47.1633	1.64003	0.820015	+	0.572343i	$0.193965\pi$
$828$	−0.00243029	−8.44583e−5 0
$829$	13.2745	0.461043	0.230521	−	0.973067i	$-0.425957\pi$
$829$	13.2745	0.461043	0.230521	+	0.973067i	$0.425957\pi$
$830$	4.46376	0.154939
$831$	−0.339138	−0.0117646
$832$	4.89148	0.169581
$833$	4.81564	0.166852
$834$	22.7390	0.787387
$835$	−52.5404	−1.81824
$836$	0.0954897	0.00330258
$837$	10.5578	0.364930
$838$	−1.91127	−0.0660237
$839$	49.9714	1.72520	0.862602	−	0.505884i	$-0.168834\pi$
$839$	49.9714	1.72520	0.862602	+	0.505884i	$0.168834\pi$
$840$	7.11085	0.245348
$841$	−7.54557	−0.260192
$842$	33.5055	1.15468
$843$	−31.1185	−1.07178
$844$	0.161418	0.00555623
$845$	31.6364	1.08833
$846$	−9.62562	−0.330936
$847$	−9.21610	−0.316669
$848$	−14.9909	−0.514791
$849$	14.1337	0.485068
$850$	8.63343	0.296124
$851$	−1.17902	−0.0404163
$852$	−0.0904810	−0.00309983
$853$	−12.7998	−0.438256	−0.219128	−	0.975696i	$-0.570321\pi$
$853$	−12.7998	−0.438256	−0.219128	+	0.975696i	$0.570321\pi$
$854$	−3.84790	−0.131673
$855$	11.6262	0.397607
$856$	7.01168	0.239654
$857$	38.3349	1.30950	0.654748	−	0.755847i	$-0.272775\pi$
$857$	38.3349	1.30950	0.654748	+	0.755847i	$0.272775\pi$
$858$	1.14180	0.0389805
$859$	28.2601	0.964222	0.482111	−	0.876110i	$-0.339870\pi$
$859$	28.2601	0.964222	0.482111	+	0.876110i	$0.339870\pi$
$860$	0.210004	0.00716106
$861$	−0.698457	−0.0238034
$862$	−46.8912	−1.59712
$863$	−16.4564	−0.560184	−0.280092	−	0.959973i	$-0.590365\pi$
$863$	−16.4564	−0.560184	−0.280092	+	0.959973i	$0.590365\pi$
$864$	0.0871212	0.00296392
$865$	−47.2933	−1.60802
$866$	−56.5016	−1.92000
$867$	6.19038	0.210236
$868$	−0.162604	−0.00551913
$869$	18.7025	0.634437
$870$	−16.3425	−0.554063
$871$	6.65021	0.225334
$872$	−28.6101	−0.968862
$873$	14.8344	0.502069
$874$	−1.03193	−0.0349054
$875$	9.33533	0.315592
$876$	−0.147646	−0.00498849
$877$	11.4727	0.387405	0.193702	−	0.981060i	$-0.437950\pi$
$877$	11.4727	0.387405	0.193702	+	0.981060i	$0.437950\pi$
$878$	2.21014	0.0745885
$879$	16.7333	0.564401
$880$	13.2766	0.447553
$881$	40.8380	1.37587	0.687934	−	0.725773i	$-0.258518\pi$
$881$	40.8380	1.37587	0.687934	+	0.725773i	$0.258518\pi$
$882$	1.40876	0.0474353
$883$	−4.67346	−0.157275	−0.0786373	−	0.996903i	$-0.525057\pi$
$883$	−4.67346	−0.157275	−0.0786373	+	0.996903i	$0.525057\pi$
$884$	−0.0450072	−0.00151376
$885$	−14.7071	−0.494373
$886$	50.8454	1.70819
$887$	39.8420	1.33776	0.668882	−	0.743369i	$-0.266773\pi$
$887$	39.8420	1.33776	0.668882	+	0.743369i	$0.266773\pi$
$888$	21.2139	0.711891
$889$	−12.4552	−0.417733
$890$	−14.2317	−0.477049
$891$	1.33563	0.0447451
$892$	0.363053	0.0121559
$893$	31.7180	1.06140
$894$	33.4487	1.11869
$895$	2.04543	0.0683713
$896$	11.1813	0.373540
$897$	0.0957566	0.00319722
$898$	54.0573	1.80391
$899$	48.9024	1.63099
$900$	−0.0195998	−0.000653326 0
$901$	18.1889	0.605960
$902$	−1.31420	−0.0437580
$903$	5.44433	0.181176
$904$	3.45673	0.114969
$905$	−24.3708	−0.810112
$906$	7.68043	0.255165
$907$	48.9848	1.62651	0.813257	−	0.581905i	$-0.197693\pi$
$907$	48.9848	1.62651	0.813257	+	0.581905i	$0.197693\pi$
$908$	−0.0689219	−0.00228725
$909$	11.7652	0.390228
$910$	−2.14107	−0.0709756
$911$	−8.27357	−0.274115	−0.137058	−	0.990563i	$-0.543765\pi$
$911$	−8.27357	−0.274115	−0.137058	+	0.990563i	$0.543765\pi$
$912$	18.4243	0.610088
$913$	−1.68976	−0.0559229
$914$	−3.64214	−0.120471
$915$	6.84088	0.226152
$916$	−0.0366034	−0.00120941
$917$	−2.72601	−0.0900208
$918$	6.78407	0.223908
$919$	−41.7283	−1.37649	−0.688245	−	0.725478i	$-0.741619\pi$
$919$	−41.7283	−1.37649	−0.688245	+	0.725478i	$0.741619\pi$
$920$	1.12207	0.0369936
$921$	26.8861	0.885928
$922$	3.18543	0.104907
$923$	3.56508	0.117346
$924$	−0.0205704	−0.000676717 0
$925$	−9.50857	−0.312640
$926$	−39.0452	−1.28310
$927$	−9.41346	−0.309178
$928$	0.403536	0.0132467
$929$	42.8571	1.40610	0.703049	−	0.711142i	$-0.251822\pi$
$929$	42.8571	1.40610	0.703049	+	0.711142i	$0.251822\pi$
$930$	−37.2505	−1.22149
$931$	−4.64209	−0.152138
$932$	−0.327602	−0.0107309
$933$	26.0197	0.851846
$934$	−17.2735	−0.565207
$935$	−16.1088	−0.526813
$936$	−1.72293	−0.0563157
$937$	19.3535	0.632253	0.316126	−	0.948717i	$-0.397618\pi$
$937$	19.3535	0.632253	0.316126	+	0.948717i	$0.397618\pi$
$938$	15.4384	0.504082
$939$	−23.2560	−0.758930
$940$	−0.263557	−0.00859629
$941$	−17.4650	−0.569343	−0.284671	−	0.958625i	$-0.591884\pi$
$941$	−17.4650	−0.569343	−0.284671	+	0.958625i	$0.591884\pi$
$942$	−23.8303	−0.776432
$943$	−0.110215	−0.00358908
$944$	−23.3066	−0.758566
$945$	−2.50452	−0.0814719
$946$	10.2439	0.333058
$947$	7.05319	0.229198	0.114599	−	0.993412i	$-0.463442\pi$
$947$	7.05319	0.229198	0.114599	+	0.993412i	$0.463442\pi$
$948$	−0.215661	−0.00700435
$949$	5.81745	0.188843
$950$	−8.32229	−0.270011
$951$	8.91958	0.289237
$952$	−13.6726	−0.443132
$953$	−38.4114	−1.24427	−0.622133	−	0.782912i	$-0.713734\pi$
$953$	−38.4114	−1.24427	−0.622133	+	0.782912i	$0.713734\pi$
$954$	5.32094	0.172272
$955$	−2.50452	−0.0810443
$956$	−0.225614	−0.00729688
$957$	6.18648	0.199980
$958$	24.0573	0.777254
$959$	−19.1709	−0.619062
$960$	−20.1880	−0.651566
$961$	80.4664	2.59569
$962$	−6.38746	−0.205940
$963$	−2.46959	−0.0795814
$964$	0.0304213	0.000979803 0
$965$	24.6075	0.792142
$966$	0.222298	0.00715232
$967$	−24.7766	−0.796762	−0.398381	−	0.917220i	$-0.630428\pi$
$967$	−24.7766	−0.796762	−0.398381	+	0.917220i	$0.630428\pi$
$968$	26.1665	0.841022
$969$	−22.3546	−0.718134
$970$	−52.3397	−1.68053
$971$	19.3460	0.620844	0.310422	−	0.950599i	$-0.399530\pi$
$971$	19.3460	0.620844	0.310422	+	0.950599i	$0.399530\pi$
$972$	−0.0154013	−0.000493998 0
$973$	16.1412	0.517462
$974$	−34.4511	−1.10388
$975$	0.772259	0.0247321
$976$	10.8409	0.347008
$977$	33.7845	1.08086	0.540432	−	0.841388i	$-0.318261\pi$
$977$	33.7845	1.08086	0.540432	+	0.841388i	$0.318261\pi$
$978$	−26.4776	−0.846661
$979$	5.38744	0.172183
$980$	0.0385729	0.00123217
$981$	10.0768	0.321727
$982$	−4.90694	−0.156587
$983$	36.9390	1.17817	0.589086	−	0.808071i	$-0.299488\pi$
$983$	36.9390	1.17817	0.589086	+	0.808071i	$0.299488\pi$
$984$	1.98307	0.0632179
$985$	37.2968	1.18837
$986$	31.4231	1.00071
$987$	−6.83270	−0.217487
$988$	0.0433852	0.00138027
$989$	0.859100	0.0273178
$990$	−4.71243	−0.149771
$991$	−36.2741	−1.15228	−0.576142	−	0.817350i	$-0.695442\pi$
$991$	−36.2741	−1.15228	−0.576142	+	0.817350i	$0.695442\pi$
$992$	0.919805	0.0292038
$993$	−31.1990	−0.990070
$994$	8.27628	0.262508
$995$	35.3806	1.12164
$996$	0.0194849	0.000617403 0
$997$	−19.2814	−0.610648	−0.305324	−	0.952249i	$-0.598765\pi$
$997$	−19.2814	−0.610648	−0.305324	+	0.952249i	$0.598765\pi$
$998$	−26.6616	−0.843959
$999$	−7.47175	−0.236396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.18	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.18	✓	27	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)

\(f(q)\)	\(=\)	\(q+1.40876 q^{2} +1.00000 q^{3} -0.0154013 q^{4} -2.50452 q^{5} +1.40876 q^{6} +1.00000 q^{7} -2.83921 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.40876 q^{2} +1.00000 q^{3} -0.0154013 q^{4} -2.50452 q^{5} +1.40876 q^{6} +1.00000 q^{7} -2.83921 q^{8} +1.00000 q^{9} -3.52826 q^{10} +1.33563 q^{11} -0.0154013 q^{12} +0.606834 q^{13} +1.40876 q^{14} -2.50452 q^{15} -3.96896 q^{16} +4.81564 q^{17} +1.40876 q^{18} -4.64209 q^{19} +0.0385729 q^{20} +1.00000 q^{21} +1.88157 q^{22} +0.157797 q^{23} -2.83921 q^{24} +1.27260 q^{25} +0.854882 q^{26} +1.00000 q^{27} -0.0154013 q^{28} +4.63189 q^{29} -3.52826 q^{30} +10.5578 q^{31} +0.0871212 q^{32} +1.33563 q^{33} +6.78407 q^{34} -2.50452 q^{35} -0.0154013 q^{36} -7.47175 q^{37} -6.53958 q^{38} +0.606834 q^{39} +7.11085 q^{40} -0.698457 q^{41} +1.40876 q^{42} +5.44433 q^{43} -0.0205704 q^{44} -2.50452 q^{45} +0.222298 q^{46} -6.83270 q^{47} -3.96896 q^{48} +1.00000 q^{49} +1.79279 q^{50} +4.81564 q^{51} -0.00934605 q^{52} +3.77705 q^{53} +1.40876 q^{54} -3.34510 q^{55} -2.83921 q^{56} -4.64209 q^{57} +6.52521 q^{58} +5.87222 q^{59} +0.0385729 q^{60} -2.73142 q^{61} +14.8733 q^{62} +1.00000 q^{63} +8.06065 q^{64} -1.51983 q^{65} +1.88157 q^{66} +10.9589 q^{67} -0.0741673 q^{68} +0.157797 q^{69} -3.52826 q^{70} +5.87488 q^{71} -2.83921 q^{72} +9.58657 q^{73} -10.5259 q^{74} +1.27260 q^{75} +0.0714943 q^{76} +1.33563 q^{77} +0.854882 q^{78} +14.0028 q^{79} +9.94033 q^{80} +1.00000 q^{81} -0.983957 q^{82} -1.26515 q^{83} -0.0154013 q^{84} -12.0608 q^{85} +7.66974 q^{86} +4.63189 q^{87} -3.79213 q^{88} +4.03365 q^{89} -3.52826 q^{90} +0.606834 q^{91} -0.00243029 q^{92} +10.5578 q^{93} -9.62562 q^{94} +11.6262 q^{95} +0.0871212 q^{96} +14.8344 q^{97} +1.40876 q^{98} +1.33563 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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