LMFDB - Embedded newform 6034.2.a.p.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.94651 q^{3} +1.00000 q^{4} +3.30450 q^{5} -1.94651 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.788913 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.94651 q^{3} +1.00000 q^{4} +3.30450 q^{5} -1.94651 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.788913 q^{9} -3.30450 q^{10} +5.79059 q^{11} +1.94651 q^{12} +4.91914 q^{13} -1.00000 q^{14} +6.43226 q^{15} +1.00000 q^{16} -7.24062 q^{17} -0.788913 q^{18} +4.79894 q^{19} +3.30450 q^{20} +1.94651 q^{21} -5.79059 q^{22} -3.99081 q^{23} -1.94651 q^{24} +5.91975 q^{25} -4.91914 q^{26} -4.30391 q^{27} +1.00000 q^{28} -1.92453 q^{29} -6.43226 q^{30} -1.90386 q^{31} -1.00000 q^{32} +11.2715 q^{33} +7.24062 q^{34} +3.30450 q^{35} +0.788913 q^{36} -4.37764 q^{37} -4.79894 q^{38} +9.57517 q^{39} -3.30450 q^{40} +8.68104 q^{41} -1.94651 q^{42} -7.23289 q^{43} +5.79059 q^{44} +2.60697 q^{45} +3.99081 q^{46} +10.5218 q^{47} +1.94651 q^{48} +1.00000 q^{49} -5.91975 q^{50} -14.0940 q^{51} +4.91914 q^{52} -1.16951 q^{53} +4.30391 q^{54} +19.1350 q^{55} -1.00000 q^{56} +9.34120 q^{57} +1.92453 q^{58} +8.64226 q^{59} +6.43226 q^{60} +7.35293 q^{61} +1.90386 q^{62} +0.788913 q^{63} +1.00000 q^{64} +16.2553 q^{65} -11.2715 q^{66} +3.06173 q^{67} -7.24062 q^{68} -7.76817 q^{69} -3.30450 q^{70} +0.887326 q^{71} -0.788913 q^{72} +2.87421 q^{73} +4.37764 q^{74} +11.5229 q^{75} +4.79894 q^{76} +5.79059 q^{77} -9.57517 q^{78} -15.1757 q^{79} +3.30450 q^{80} -10.7444 q^{81} -8.68104 q^{82} -1.96604 q^{83} +1.94651 q^{84} -23.9267 q^{85} +7.23289 q^{86} -3.74612 q^{87} -5.79059 q^{88} +16.3774 q^{89} -2.60697 q^{90} +4.91914 q^{91} -3.99081 q^{92} -3.70588 q^{93} -10.5218 q^{94} +15.8581 q^{95} -1.94651 q^{96} -14.9147 q^{97} -1.00000 q^{98} +4.56828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.94651	1.12382	0.561910	−	0.827198i	$-0.310067\pi$
$3$	1.94651	1.12382	0.561910	+	0.827198i	$0.310067\pi$
$4$	1.00000	0.500000
$5$	3.30450	1.47782	0.738910	−	0.673805i	$-0.235341\pi$
$5$	3.30450	1.47782	0.738910	+	0.673805i	$0.235341\pi$
$6$	−1.94651	−0.794661
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	0.788913	0.262971
$10$	−3.30450	−1.04498
$11$	5.79059	1.74593	0.872965	−	0.487784i	$-0.162195\pi$
$11$	5.79059	1.74593	0.872965	+	0.487784i	$0.162195\pi$
$12$	1.94651	0.561910
$13$	4.91914	1.36432	0.682162	−	0.731201i	$-0.261040\pi$
$13$	4.91914	1.36432	0.682162	+	0.731201i	$0.261040\pi$
$14$	−1.00000	−0.267261
$15$	6.43226	1.66080
$16$	1.00000	0.250000
$17$	−7.24062	−1.75611	−0.878054	−	0.478561i	$-0.841158\pi$
$17$	−7.24062	−1.75611	−0.878054	+	0.478561i	$0.841158\pi$
$18$	−0.788913	−0.185949
$19$	4.79894	1.10095	0.550476	−	0.834851i	$-0.314446\pi$
$19$	4.79894	1.10095	0.550476	+	0.834851i	$0.314446\pi$
$20$	3.30450	0.738910
$21$	1.94651	0.424764
$22$	−5.79059	−1.23456
$23$	−3.99081	−0.832142	−0.416071	−	0.909332i	$-0.636593\pi$
$23$	−3.99081	−0.832142	−0.416071	+	0.909332i	$0.636593\pi$
$24$	−1.94651	−0.397330
$25$	5.91975	1.18395
$26$	−4.91914	−0.964723
$27$	−4.30391	−0.828288
$28$	1.00000	0.188982
$29$	−1.92453	−0.357376	−0.178688	−	0.983906i	$-0.557185\pi$
$29$	−1.92453	−0.357376	−0.178688	+	0.983906i	$0.557185\pi$
$30$	−6.43226	−1.17436
$31$	−1.90386	−0.341943	−0.170971	−	0.985276i	$-0.554691\pi$
$31$	−1.90386	−0.341943	−0.170971	+	0.985276i	$0.554691\pi$
$32$	−1.00000	−0.176777
$33$	11.2715	1.96211
$34$	7.24062	1.24176
$35$	3.30450	0.558563
$36$	0.788913	0.131486
$37$	−4.37764	−0.719680	−0.359840	−	0.933014i	$-0.617169\pi$
$37$	−4.37764	−0.719680	−0.359840	+	0.933014i	$0.617169\pi$
$38$	−4.79894	−0.778491
$39$	9.57517	1.53325
$40$	−3.30450	−0.522488
$41$	8.68104	1.35575	0.677875	−	0.735177i	$-0.262901\pi$
$41$	8.68104	1.35575	0.677875	+	0.735177i	$0.262901\pi$
$42$	−1.94651	−0.300353
$43$	−7.23289	−1.10300	−0.551502	−	0.834173i	$-0.685945\pi$
$43$	−7.23289	−1.10300	−0.551502	+	0.834173i	$0.685945\pi$
$44$	5.79059	0.872965
$45$	2.60697	0.388624
$46$	3.99081	0.588413
$47$	10.5218	1.53476	0.767381	−	0.641192i	$-0.221560\pi$
$47$	10.5218	1.53476	0.767381	+	0.641192i	$0.221560\pi$
$48$	1.94651	0.280955
$49$	1.00000	0.142857
$50$	−5.91975	−0.837178
$51$	−14.0940	−1.97355
$52$	4.91914	0.682162
$53$	−1.16951	−0.160644	−0.0803220	−	0.996769i	$-0.525595\pi$
$53$	−1.16951	−0.160644	−0.0803220	+	0.996769i	$0.525595\pi$
$54$	4.30391	0.585688
$55$	19.1350	2.58017
$56$	−1.00000	−0.133631
$57$	9.34120	1.23727
$58$	1.92453	0.252703
$59$	8.64226	1.12513	0.562563	−	0.826754i	$-0.309815\pi$
$59$	8.64226	1.12513	0.562563	+	0.826754i	$0.309815\pi$
$60$	6.43226	0.830401
$61$	7.35293	0.941446	0.470723	−	0.882281i	$-0.343993\pi$
$61$	7.35293	0.941446	0.470723	+	0.882281i	$0.343993\pi$
$62$	1.90386	0.241790
$63$	0.788913	0.0993937
$64$	1.00000	0.125000
$65$	16.2553	2.01622
$66$	−11.2715	−1.38742
$67$	3.06173	0.374050	0.187025	−	0.982355i	$-0.440115\pi$
$67$	3.06173	0.374050	0.187025	+	0.982355i	$0.440115\pi$
$68$	−7.24062	−0.878054
$69$	−7.76817	−0.935178
$70$	−3.30450	−0.394964
$71$	0.887326	0.105306	0.0526531	−	0.998613i	$-0.483232\pi$
$71$	0.887326	0.105306	0.0526531	+	0.998613i	$0.483232\pi$
$72$	−0.788913	−0.0929743
$73$	2.87421	0.336401	0.168200	−	0.985753i	$-0.446204\pi$
$73$	2.87421	0.336401	0.168200	+	0.985753i	$0.446204\pi$
$74$	4.37764	0.508891
$75$	11.5229	1.33055
$76$	4.79894	0.550476
$77$	5.79059	0.659899
$78$	−9.57517	−1.08417
$79$	−15.1757	−1.70740	−0.853701	−	0.520764i	$-0.825647\pi$
$79$	−15.1757	−1.70740	−0.853701	+	0.520764i	$0.825647\pi$
$80$	3.30450	0.369455
$81$	−10.7444	−1.19382
$82$	−8.68104	−0.958661
$83$	−1.96604	−0.215801	−0.107901	−	0.994162i	$-0.534413\pi$
$83$	−1.96604	−0.215801	−0.107901	+	0.994162i	$0.534413\pi$
$84$	1.94651	0.212382
$85$	−23.9267	−2.59521
$86$	7.23289	0.779942
$87$	−3.74612	−0.401627
$88$	−5.79059	−0.617279
$89$	16.3774	1.73600	0.868001	−	0.496562i	$-0.165405\pi$
$89$	16.3774	1.73600	0.868001	+	0.496562i	$0.165405\pi$
$90$	−2.60697	−0.274798
$91$	4.91914	0.515666
$92$	−3.99081	−0.416071
$93$	−3.70588	−0.384282
$94$	−10.5218	−1.08524
$95$	15.8581	1.62701
$96$	−1.94651	−0.198665
$97$	−14.9147	−1.51436	−0.757179	−	0.653208i	$-0.773423\pi$
$97$	−14.9147	−1.51436	−0.757179	+	0.653208i	$0.773423\pi$
$98$	−1.00000	−0.101015
$99$	4.56828	0.459129
$100$	5.91975	0.591975
$101$	6.99617	0.696145	0.348073	−	0.937468i	$-0.386836\pi$
$101$	6.99617	0.696145	0.348073	+	0.937468i	$0.386836\pi$
$102$	14.0940	1.39551
$103$	2.53656	0.249934	0.124967	−	0.992161i	$-0.460117\pi$
$103$	2.53656	0.249934	0.124967	+	0.992161i	$0.460117\pi$
$104$	−4.91914	−0.482361
$105$	6.43226	0.627724
$106$	1.16951	0.113592
$107$	−9.17146	−0.886638	−0.443319	−	0.896364i	$-0.646199\pi$
$107$	−9.17146	−0.886638	−0.443319	+	0.896364i	$0.646199\pi$
$108$	−4.30391	−0.414144
$109$	10.7961	1.03408	0.517039	−	0.855962i	$-0.327034\pi$
$109$	10.7961	1.03408	0.517039	+	0.855962i	$0.327034\pi$
$110$	−19.1350	−1.82445
$111$	−8.52114	−0.808791
$112$	1.00000	0.0944911
$113$	−5.33453	−0.501830	−0.250915	−	0.968009i	$-0.580732\pi$
$113$	−5.33453	−0.501830	−0.250915	+	0.968009i	$0.580732\pi$
$114$	−9.34120	−0.874884
$115$	−13.1877	−1.22976
$116$	−1.92453	−0.178688
$117$	3.88078	0.358778
$118$	−8.64226	−0.795585
$119$	−7.24062	−0.663746
$120$	−6.43226	−0.587182
$121$	22.5310	2.04827
$122$	−7.35293	−0.665703
$123$	16.8978	1.52362
$124$	−1.90386	−0.170971
$125$	3.03930	0.271843
$126$	−0.788913	−0.0702820
$127$	8.20497	0.728073	0.364037	−	0.931385i	$-0.381398\pi$
$127$	8.20497	0.728073	0.364037	+	0.931385i	$0.381398\pi$
$128$	−1.00000	−0.0883883
$129$	−14.0789	−1.23958
$130$	−16.2553	−1.42569
$131$	−15.2021	−1.32821	−0.664107	−	0.747638i	$-0.731188\pi$
$131$	−15.2021	−1.32821	−0.664107	+	0.747638i	$0.731188\pi$
$132$	11.2715	0.981055
$133$	4.79894	0.416121
$134$	−3.06173	−0.264493
$135$	−14.2223	−1.22406
$136$	7.24062	0.620878
$137$	−8.04937	−0.687704	−0.343852	−	0.939024i	$-0.611732\pi$
$137$	−8.04937	−0.687704	−0.343852	+	0.939024i	$0.611732\pi$
$138$	7.76817	0.661270
$139$	15.8971	1.34838	0.674188	−	0.738560i	$-0.264494\pi$
$139$	15.8971	1.34838	0.674188	+	0.738560i	$0.264494\pi$
$140$	3.30450	0.279282
$141$	20.4808	1.72480
$142$	−0.887326	−0.0744628
$143$	28.4847	2.38201
$144$	0.788913	0.0657428
$145$	−6.35962	−0.528138
$146$	−2.87421	−0.237871
$147$	1.94651	0.160546
$148$	−4.37764	−0.359840
$149$	−6.49607	−0.532179	−0.266089	−	0.963948i	$-0.585732\pi$
$149$	−6.49607	−0.532179	−0.266089	+	0.963948i	$0.585732\pi$
$150$	−11.5229	−0.940838
$151$	−8.96605	−0.729647	−0.364823	−	0.931077i	$-0.618871\pi$
$151$	−8.96605	−0.729647	−0.364823	+	0.931077i	$0.618871\pi$
$152$	−4.79894	−0.389246
$153$	−5.71222	−0.461806
$154$	−5.79059	−0.466619
$155$	−6.29130	−0.505329
$156$	9.57517	0.766627
$157$	−9.52799	−0.760417	−0.380208	−	0.924901i	$-0.624148\pi$
$157$	−9.52799	−0.760417	−0.380208	+	0.924901i	$0.624148\pi$
$158$	15.1757	1.20732
$159$	−2.27646	−0.180535
$160$	−3.30450	−0.261244
$161$	−3.99081	−0.314520
$162$	10.7444	0.844156
$163$	−10.5890	−0.829395	−0.414697	−	0.909959i	$-0.636113\pi$
$163$	−10.5890	−0.829395	−0.414697	+	0.909959i	$0.636113\pi$
$164$	8.68104	0.677875
$165$	37.2466	2.89964
$166$	1.96604	0.152595
$167$	−1.05797	−0.0818685	−0.0409342	−	0.999162i	$-0.513033\pi$
$167$	−1.05797	−0.0818685	−0.0409342	+	0.999162i	$0.513033\pi$
$168$	−1.94651	−0.150177
$169$	11.1980	0.861381
$170$	23.9267	1.83509
$171$	3.78595	0.289519
$172$	−7.23289	−0.551502
$173$	5.54014	0.421209	0.210604	−	0.977571i	$-0.432457\pi$
$173$	5.54014	0.421209	0.210604	+	0.977571i	$0.432457\pi$
$174$	3.74612	0.283993
$175$	5.91975	0.447491
$176$	5.79059	0.436482
$177$	16.8223	1.26444
$178$	−16.3774	−1.22754
$179$	12.1374	0.907188	0.453594	−	0.891208i	$-0.350142\pi$
$179$	12.1374	0.907188	0.453594	+	0.891208i	$0.350142\pi$
$180$	2.60697	0.194312
$181$	−16.1967	−1.20389	−0.601944	−	0.798538i	$-0.705607\pi$
$181$	−16.1967	−1.20389	−0.601944	+	0.798538i	$0.705607\pi$
$182$	−4.91914	−0.364631
$183$	14.3126	1.05802
$184$	3.99081	0.294207
$185$	−14.4659	−1.06356
$186$	3.70588	0.271728
$187$	−41.9275	−3.06604
$188$	10.5218	0.767381
$189$	−4.30391	−0.313063
$190$	−15.8581	−1.15047
$191$	13.7431	0.994413	0.497207	−	0.867632i	$-0.334359\pi$
$191$	13.7431	0.994413	0.497207	+	0.867632i	$0.334359\pi$
$192$	1.94651	0.140477
$193$	−7.63753	−0.549762	−0.274881	−	0.961478i	$-0.588638\pi$
$193$	−7.63753	−0.549762	−0.274881	+	0.961478i	$0.588638\pi$
$194$	14.9147	1.07081
$195$	31.6412	2.26587
$196$	1.00000	0.0714286
$197$	1.35528	0.0965597	0.0482799	−	0.998834i	$-0.484626\pi$
$197$	1.35528	0.0965597	0.0482799	+	0.998834i	$0.484626\pi$
$198$	−4.56828	−0.324653
$199$	−0.825587	−0.0585243	−0.0292622	−	0.999572i	$-0.509316\pi$
$199$	−0.825587	−0.0585243	−0.0292622	+	0.999572i	$0.509316\pi$
$200$	−5.91975	−0.418589
$201$	5.95970	0.420365
$202$	−6.99617	−0.492249
$203$	−1.92453	−0.135076
$204$	−14.0940	−0.986775
$205$	28.6865	2.00355
$206$	−2.53656	−0.176730
$207$	−3.14840	−0.218829
$208$	4.91914	0.341081
$209$	27.7887	1.92219
$210$	−6.43226	−0.443868
$211$	−16.4980	−1.13577	−0.567885	−	0.823108i	$-0.692238\pi$
$211$	−16.4980	−1.13577	−0.567885	+	0.823108i	$0.692238\pi$
$212$	−1.16951	−0.0803220
$213$	1.72719	0.118345
$214$	9.17146	0.626948
$215$	−23.9011	−1.63004
$216$	4.30391	0.292844
$217$	−1.90386	−0.129242
$218$	−10.7961	−0.731204
$219$	5.59469	0.378054
$220$	19.1350	1.29008
$221$	−35.6176	−2.39590
$222$	8.52114	0.571901
$223$	12.1082	0.810824	0.405412	−	0.914134i	$-0.367128\pi$
$223$	12.1082	0.810824	0.405412	+	0.914134i	$0.367128\pi$
$224$	−1.00000	−0.0668153
$225$	4.67017	0.311344
$226$	5.33453	0.354848
$227$	−16.1588	−1.07250	−0.536248	−	0.844060i	$-0.680159\pi$
$227$	−16.1588	−1.07250	−0.536248	+	0.844060i	$0.680159\pi$
$228$	9.34120	0.618636
$229$	7.77831	0.514005	0.257003	−	0.966411i	$-0.417265\pi$
$229$	7.77831	0.514005	0.257003	+	0.966411i	$0.417265\pi$
$230$	13.1877	0.869568
$231$	11.2715	0.741608
$232$	1.92453	0.126352
$233$	−18.8463	−1.23467	−0.617333	−	0.786702i	$-0.711787\pi$
$233$	−18.8463	−1.23467	−0.617333	+	0.786702i	$0.711787\pi$
$234$	−3.88078	−0.253694
$235$	34.7693	2.26810
$236$	8.64226	0.562563
$237$	−29.5397	−1.91881
$238$	7.24062	0.469340
$239$	2.34508	0.151691	0.0758455	−	0.997120i	$-0.475834\pi$
$239$	2.34508	0.151691	0.0758455	+	0.997120i	$0.475834\pi$
$240$	6.43226	0.415201
$241$	2.23211	0.143783	0.0718915	−	0.997412i	$-0.477096\pi$
$241$	2.23211	0.143783	0.0718915	+	0.997412i	$0.477096\pi$
$242$	−22.5310	−1.44834
$243$	−8.00230	−0.513348
$244$	7.35293	0.470723
$245$	3.30450	0.211117
$246$	−16.8978	−1.07736
$247$	23.6067	1.50206
$248$	1.90386	0.120895
$249$	−3.82693	−0.242522
$250$	−3.03930	−0.192222
$251$	−0.711638	−0.0449182	−0.0224591	−	0.999748i	$-0.507150\pi$
$251$	−0.711638	−0.0449182	−0.0224591	+	0.999748i	$0.507150\pi$
$252$	0.788913	0.0496969
$253$	−23.1092	−1.45286
$254$	−8.20497	−0.514825
$255$	−46.5735	−2.91655
$256$	1.00000	0.0625000
$257$	18.8165	1.17374	0.586871	−	0.809680i	$-0.300359\pi$
$257$	18.8165	1.17374	0.586871	+	0.809680i	$0.300359\pi$
$258$	14.0789	0.876515
$259$	−4.37764	−0.272014
$260$	16.2553	1.00811
$261$	−1.51829	−0.0939797
$262$	15.2021	0.939189
$263$	−26.7984	−1.65246	−0.826230	−	0.563333i	$-0.809519\pi$
$263$	−26.7984	−1.65246	−0.826230	+	0.563333i	$0.809519\pi$
$264$	−11.2715	−0.693711
$265$	−3.86464	−0.237403
$266$	−4.79894	−0.294242
$267$	31.8788	1.95095
$268$	3.06173	0.187025
$269$	23.1056	1.40878	0.704388	−	0.709815i	$-0.251221\pi$
$269$	23.1056	1.40878	0.704388	+	0.709815i	$0.251221\pi$
$270$	14.2223	0.865541
$271$	4.68990	0.284891	0.142445	−	0.989803i	$-0.454503\pi$
$271$	4.68990	0.284891	0.142445	+	0.989803i	$0.454503\pi$
$272$	−7.24062	−0.439027
$273$	9.57517	0.579516
$274$	8.04937	0.486280
$275$	34.2788	2.06709
$276$	−7.76817	−0.467589
$277$	−3.95025	−0.237348	−0.118674	−	0.992933i	$-0.537864\pi$
$277$	−3.95025	−0.237348	−0.118674	+	0.992933i	$0.537864\pi$
$278$	−15.8971	−0.953446
$279$	−1.50198	−0.0899210
$280$	−3.30450	−0.197482
$281$	26.1730	1.56135	0.780676	−	0.624936i	$-0.214875\pi$
$281$	26.1730	1.56135	0.780676	+	0.624936i	$0.214875\pi$
$282$	−20.4808	−1.21961
$283$	−16.4159	−0.975824	−0.487912	−	0.872893i	$-0.662241\pi$
$283$	−16.4159	−0.975824	−0.487912	+	0.872893i	$0.662241\pi$
$284$	0.887326	0.0526531
$285$	30.8680	1.82846
$286$	−28.4847	−1.68434
$287$	8.68104	0.512426
$288$	−0.788913	−0.0464872
$289$	35.4266	2.08392
$290$	6.35962	0.373450
$291$	−29.0316	−1.70187
$292$	2.87421	0.168200
$293$	2.47441	0.144556	0.0722781	−	0.997385i	$-0.476973\pi$
$293$	2.47441	0.144556	0.0722781	+	0.997385i	$0.476973\pi$
$294$	−1.94651	−0.113523
$295$	28.5584	1.66273
$296$	4.37764	0.254445
$297$	−24.9222	−1.44613
$298$	6.49607	0.376307
$299$	−19.6314	−1.13531
$300$	11.5229	0.665273
$301$	−7.23289	−0.416897
$302$	8.96605	0.515938
$303$	13.6181	0.782342
$304$	4.79894	0.275238
$305$	24.2978	1.39129
$306$	5.71222	0.326546
$307$	−12.4782	−0.712168	−0.356084	−	0.934454i	$-0.615888\pi$
$307$	−12.4782	−0.712168	−0.356084	+	0.934454i	$0.615888\pi$
$308$	5.79059	0.329950
$309$	4.93744	0.280881
$310$	6.29130	0.357322
$311$	11.7510	0.666338	0.333169	−	0.942867i	$-0.391882\pi$
$311$	11.7510	0.666338	0.333169	+	0.942867i	$0.391882\pi$
$312$	−9.57517	−0.542087
$313$	−5.93439	−0.335432	−0.167716	−	0.985835i	$-0.553639\pi$
$313$	−5.93439	−0.335432	−0.167716	+	0.985835i	$0.553639\pi$
$314$	9.52799	0.537696
$315$	2.60697	0.146886
$316$	−15.1757	−0.853701
$317$	−13.3989	−0.752558	−0.376279	−	0.926506i	$-0.622797\pi$
$317$	−13.3989	−0.752558	−0.376279	+	0.926506i	$0.622797\pi$
$318$	2.27646	0.127657
$319$	−11.1442	−0.623954
$320$	3.30450	0.184727
$321$	−17.8524	−0.996422
$322$	3.99081	0.222399
$323$	−34.7473	−1.93339
$324$	−10.7444	−0.596909
$325$	29.1201	1.61529
$326$	10.5890	0.586471
$327$	21.0147	1.16212
$328$	−8.68104	−0.479330
$329$	10.5218	0.580085
$330$	−37.2466	−2.05036
$331$	−22.8387	−1.25533	−0.627665	−	0.778483i	$-0.715989\pi$
$331$	−22.8387	−1.25533	−0.627665	+	0.778483i	$0.715989\pi$
$332$	−1.96604	−0.107901
$333$	−3.45358	−0.189255
$334$	1.05797	0.0578898
$335$	10.1175	0.552778
$336$	1.94651	0.106191
$337$	11.6107	0.632478	0.316239	−	0.948680i	$-0.397580\pi$
$337$	11.6107	0.632478	0.316239	+	0.948680i	$0.397580\pi$
$338$	−11.1980	−0.609088
$339$	−10.3837	−0.563967
$340$	−23.9267	−1.29761
$341$	−11.0245	−0.597008
$342$	−3.78595	−0.204721
$343$	1.00000	0.0539949
$344$	7.23289	0.389971
$345$	−25.6699	−1.38202
$346$	−5.54014	−0.297840
$347$	−29.1286	−1.56370	−0.781852	−	0.623464i	$-0.785725\pi$
$347$	−29.1286	−1.56370	−0.781852	+	0.623464i	$0.785725\pi$
$348$	−3.74612	−0.200813
$349$	−0.484513	−0.0259354	−0.0129677	−	0.999916i	$-0.504128\pi$
$349$	−0.484513	−0.0259354	−0.0129677	+	0.999916i	$0.504128\pi$
$350$	−5.91975	−0.316424
$351$	−21.1715	−1.13005
$352$	−5.79059	−0.308640
$353$	17.9682	0.956351	0.478176	−	0.878264i	$-0.341298\pi$
$353$	17.9682	0.956351	0.478176	+	0.878264i	$0.341298\pi$
$354$	−16.8223	−0.894094
$355$	2.93217	0.155624
$356$	16.3774	0.868001
$357$	−14.0940	−0.745931
$358$	−12.1374	−0.641479
$359$	−35.9179	−1.89567	−0.947837	−	0.318756i	$-0.896735\pi$
$359$	−35.9179	−1.89567	−0.947837	+	0.318756i	$0.896735\pi$
$360$	−2.60697	−0.137399
$361$	4.02984	0.212097
$362$	16.1967	0.851278
$363$	43.8568	2.30188
$364$	4.91914	0.257833
$365$	9.49784	0.497140
$366$	−14.3126	−0.748130
$367$	1.45502	0.0759514	0.0379757	−	0.999279i	$-0.487909\pi$
$367$	1.45502	0.0759514	0.0379757	+	0.999279i	$0.487909\pi$
$368$	−3.99081	−0.208035
$369$	6.84859	0.356523
$370$	14.4659	0.752048
$371$	−1.16951	−0.0607177
$372$	−3.70588	−0.192141
$373$	−9.71319	−0.502930	−0.251465	−	0.967866i	$-0.580912\pi$
$373$	−9.71319	−0.502930	−0.251465	+	0.967866i	$0.580912\pi$
$374$	41.9275	2.16802
$375$	5.91604	0.305503
$376$	−10.5218	−0.542620
$377$	−9.46704	−0.487577
$378$	4.30391	0.221369
$379$	−3.93631	−0.202195	−0.101097	−	0.994877i	$-0.532235\pi$
$379$	−3.93631	−0.202195	−0.101097	+	0.994877i	$0.532235\pi$
$380$	15.8581	0.813504
$381$	15.9711	0.818223
$382$	−13.7431	−0.703156
$383$	−14.7525	−0.753816	−0.376908	−	0.926251i	$-0.623013\pi$
$383$	−14.7525	−0.753816	−0.376908	+	0.926251i	$0.623013\pi$
$384$	−1.94651	−0.0993326
$385$	19.1350	0.975212
$386$	7.63753	0.388740
$387$	−5.70612	−0.290058
$388$	−14.9147	−0.757179
$389$	−36.4596	−1.84857	−0.924287	−	0.381699i	$-0.875339\pi$
$389$	−36.4596	−1.84857	−0.924287	+	0.381699i	$0.875339\pi$
$390$	−31.6412	−1.60221
$391$	28.8960	1.46133
$392$	−1.00000	−0.0505076
$393$	−29.5911	−1.49267
$394$	−1.35528	−0.0682781
$395$	−50.1482	−2.52323
$396$	4.56828	0.229564
$397$	−28.0849	−1.40954	−0.704770	−	0.709435i	$-0.748950\pi$
$397$	−28.0849	−1.40954	−0.704770	+	0.709435i	$0.748950\pi$
$398$	0.825587	0.0413830
$399$	9.34120	0.467645
$400$	5.91975	0.295987
$401$	−33.2160	−1.65873	−0.829365	−	0.558707i	$-0.811298\pi$
$401$	−33.2160	−1.65873	−0.829365	+	0.558707i	$0.811298\pi$
$402$	−5.95970	−0.297243
$403$	−9.36534	−0.466521
$404$	6.99617	0.348073
$405$	−35.5048	−1.76425
$406$	1.92453	0.0955128
$407$	−25.3491	−1.25651
$408$	14.0940	0.697755
$409$	−4.55881	−0.225419	−0.112709	−	0.993628i	$-0.535953\pi$
$409$	−4.55881	−0.225419	−0.112709	+	0.993628i	$0.535953\pi$
$410$	−28.6865	−1.41673
$411$	−15.6682	−0.772855
$412$	2.53656	0.124967
$413$	8.64226	0.425258
$414$	3.14840	0.154736
$415$	−6.49680	−0.318915
$416$	−4.91914	−0.241181
$417$	30.9440	1.51533
$418$	−27.7887	−1.35919
$419$	1.56411	0.0764118	0.0382059	−	0.999270i	$-0.487836\pi$
$419$	1.56411	0.0764118	0.0382059	+	0.999270i	$0.487836\pi$
$420$	6.43226	0.313862
$421$	−33.5235	−1.63384	−0.816919	−	0.576753i	$-0.804320\pi$
$421$	−33.5235	−1.63384	−0.816919	+	0.576753i	$0.804320\pi$
$422$	16.4980	0.803111
$423$	8.30078	0.403598
$424$	1.16951	0.0567962
$425$	−42.8626	−2.07914
$426$	−1.72719	−0.0836827
$427$	7.35293	0.355833
$428$	−9.17146	−0.443319
$429$	55.4459	2.67695
$430$	23.9011	1.15261
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−4.30391	−0.207072
$433$	−9.47100	−0.455147	−0.227574	−	0.973761i	$-0.573079\pi$
$433$	−9.47100	−0.455147	−0.227574	+	0.973761i	$0.573079\pi$
$434$	1.90386	0.0913880
$435$	−12.3791	−0.593532
$436$	10.7961	0.517039
$437$	−19.1517	−0.916149
$438$	−5.59469	−0.267325
$439$	3.02553	0.144401	0.0722004	−	0.997390i	$-0.476998\pi$
$439$	3.02553	0.144401	0.0722004	+	0.997390i	$0.476998\pi$
$440$	−19.1350	−0.912227
$441$	0.788913	0.0375673
$442$	35.6176	1.69416
$443$	37.2187	1.76832	0.884158	−	0.467188i	$-0.154733\pi$
$443$	37.2187	1.76832	0.884158	+	0.467188i	$0.154733\pi$
$444$	−8.52114	−0.404395
$445$	54.1192	2.56550
$446$	−12.1082	−0.573339
$447$	−12.6447	−0.598073
$448$	1.00000	0.0472456
$449$	38.4914	1.81652	0.908261	−	0.418404i	$-0.137411\pi$
$449$	38.4914	1.81652	0.908261	+	0.418404i	$0.137411\pi$
$450$	−4.67017	−0.220154
$451$	50.2684	2.36704
$452$	−5.33453	−0.250915
$453$	−17.4525	−0.819991
$454$	16.1588	0.758370
$455$	16.2553	0.762061
$456$	−9.34120	−0.437442
$457$	29.8100	1.39446	0.697228	−	0.716850i	$-0.254417\pi$
$457$	29.8100	1.39446	0.697228	+	0.716850i	$0.254417\pi$
$458$	−7.77831	−0.363457
$459$	31.1630	1.45456
$460$	−13.1877	−0.614878
$461$	26.4183	1.23042	0.615211	−	0.788362i	$-0.289071\pi$
$461$	26.4183	1.23042	0.615211	+	0.788362i	$0.289071\pi$
$462$	−11.2715	−0.524396
$463$	1.01551	0.0471948	0.0235974	−	0.999722i	$-0.492488\pi$
$463$	1.01551	0.0471948	0.0235974	+	0.999722i	$0.492488\pi$
$464$	−1.92453	−0.0893441
$465$	−12.2461	−0.567899
$466$	18.8463	0.873040
$467$	25.4456	1.17748	0.588741	−	0.808322i	$-0.299624\pi$
$467$	25.4456	1.17748	0.588741	+	0.808322i	$0.299624\pi$
$468$	3.88078	0.179389
$469$	3.06173	0.141378
$470$	−34.7693	−1.60379
$471$	−18.5464	−0.854571
$472$	−8.64226	−0.397792
$473$	−41.8827	−1.92577
$474$	29.5397	1.35681
$475$	28.4085	1.30347
$476$	−7.24062	−0.331873
$477$	−0.922639	−0.0422447
$478$	−2.34508	−0.107262
$479$	38.6546	1.76617	0.883087	−	0.469209i	$-0.155461\pi$
$479$	38.6546	1.76617	0.883087	+	0.469209i	$0.155461\pi$
$480$	−6.43226	−0.293591
$481$	−21.5342	−0.981877
$482$	−2.23211	−0.101670
$483$	−7.76817	−0.353464
$484$	22.5310	1.02413
$485$	−49.2857	−2.23795
$486$	8.00230	0.362992
$487$	−10.3747	−0.470121	−0.235061	−	0.971981i	$-0.575529\pi$
$487$	−10.3747	−0.470121	−0.235061	+	0.971981i	$0.575529\pi$
$488$	−7.35293	−0.332852
$489$	−20.6116	−0.932090
$490$	−3.30450	−0.149282
$491$	−10.5438	−0.475834	−0.237917	−	0.971285i	$-0.576465\pi$
$491$	−10.5438	−0.475834	−0.237917	+	0.971285i	$0.576465\pi$
$492$	16.8978	0.761810
$493$	13.9348	0.627592
$494$	−23.6067	−1.06211
$495$	15.0959	0.678509
$496$	−1.90386	−0.0854857
$497$	0.887326	0.0398020
$498$	3.82693	0.171489
$499$	15.7907	0.706888	0.353444	−	0.935456i	$-0.385011\pi$
$499$	15.7907	0.706888	0.353444	+	0.935456i	$0.385011\pi$
$500$	3.03930	0.135922
$501$	−2.05936	−0.0920054
$502$	0.711638	0.0317620
$503$	−20.8692	−0.930510	−0.465255	−	0.885177i	$-0.654037\pi$
$503$	−20.8692	−0.930510	−0.465255	+	0.885177i	$0.654037\pi$
$504$	−0.788913	−0.0351410
$505$	23.1189	1.02878
$506$	23.1092	1.02733
$507$	21.7970	0.968037
$508$	8.20497	0.364037
$509$	−1.23366	−0.0546808	−0.0273404	−	0.999626i	$-0.508704\pi$
$509$	−1.23366	−0.0546808	−0.0273404	+	0.999626i	$0.508704\pi$
$510$	46.5735	2.06231
$511$	2.87421	0.127148
$512$	−1.00000	−0.0441942
$513$	−20.6542	−0.911906
$514$	−18.8165	−0.829962
$515$	8.38206	0.369358
$516$	−14.0789	−0.619789
$517$	60.9274	2.67958
$518$	4.37764	0.192343
$519$	10.7839	0.473363
$520$	−16.2553	−0.712843
$521$	−23.6849	−1.03766	−0.518828	−	0.854879i	$-0.673632\pi$
$521$	−23.6849	−1.03766	−0.518828	+	0.854879i	$0.673632\pi$
$522$	1.51829	0.0664537
$523$	27.9656	1.22285	0.611426	−	0.791302i	$-0.290596\pi$
$523$	27.9656	1.22285	0.611426	+	0.791302i	$0.290596\pi$
$524$	−15.2021	−0.664107
$525$	11.5229	0.502899
$526$	26.7984	1.16847
$527$	13.7851	0.600488
$528$	11.2715	0.490527
$529$	−7.07342	−0.307540
$530$	3.86464	0.167869
$531$	6.81800	0.295876
$532$	4.79894	0.208061
$533$	42.7033	1.84968
$534$	−31.8788	−1.37953
$535$	−30.3071	−1.31029
$536$	−3.06173	−0.132247
$537$	23.6255	1.01952
$538$	−23.1056	−0.996155
$539$	5.79059	0.249418
$540$	−14.2223	−0.612030
$541$	−31.1865	−1.34081	−0.670406	−	0.741995i	$-0.733880\pi$
$541$	−31.1865	−1.34081	−0.670406	+	0.741995i	$0.733880\pi$
$542$	−4.68990	−0.201448
$543$	−31.5270	−1.35295
$544$	7.24062	0.310439
$545$	35.6757	1.52818
$546$	−9.57517	−0.409780
$547$	10.0267	0.428710	0.214355	−	0.976756i	$-0.431235\pi$
$547$	10.0267	0.428710	0.214355	+	0.976756i	$0.431235\pi$
$548$	−8.04937	−0.343852
$549$	5.80083	0.247573
$550$	−34.2788	−1.46165
$551$	−9.23571	−0.393454
$552$	7.76817	0.330635
$553$	−15.1757	−0.645337
$554$	3.95025	0.167830
$555$	−28.1581	−1.19525
$556$	15.8971	0.674188
$557$	30.3839	1.28741	0.643704	−	0.765275i	$-0.277397\pi$
$557$	30.3839	1.28741	0.643704	+	0.765275i	$0.277397\pi$
$558$	1.50198	0.0635838
$559$	−35.5796	−1.50486
$560$	3.30450	0.139641
$561$	−81.6124	−3.44568
$562$	−26.1730	−1.10404
$563$	23.4593	0.988693	0.494347	−	0.869265i	$-0.335407\pi$
$563$	23.4593	0.988693	0.494347	+	0.869265i	$0.335407\pi$
$564$	20.4808	0.862398
$565$	−17.6280	−0.741615
$566$	16.4159	0.690012
$567$	−10.7444	−0.451221
$568$	−0.887326	−0.0372314
$569$	14.5552	0.610184	0.305092	−	0.952323i	$-0.401313\pi$
$569$	14.5552	0.610184	0.305092	+	0.952323i	$0.401313\pi$
$570$	−30.8680	−1.29292
$571$	41.1163	1.72066	0.860332	−	0.509734i	$-0.170256\pi$
$571$	41.1163	1.72066	0.860332	+	0.509734i	$0.170256\pi$
$572$	28.4847	1.19101
$573$	26.7511	1.11754
$574$	−8.68104	−0.362340
$575$	−23.6246	−0.985214
$576$	0.788913	0.0328714
$577$	15.5752	0.648402	0.324201	−	0.945988i	$-0.394905\pi$
$577$	15.5752	0.648402	0.324201	+	0.945988i	$0.394905\pi$
$578$	−35.4266	−1.47355
$579$	−14.8666	−0.617833
$580$	−6.35962	−0.264069
$581$	−1.96604	−0.0815652
$582$	29.0316	1.20340
$583$	−6.77213	−0.280473
$584$	−2.87421	−0.118936
$585$	12.8240	0.530209
$586$	−2.47441	−0.102217
$587$	32.5857	1.34495	0.672477	−	0.740118i	$-0.265230\pi$
$587$	32.5857	1.34495	0.672477	+	0.740118i	$0.265230\pi$
$588$	1.94651	0.0802728
$589$	−9.13650	−0.376463
$590$	−28.5584	−1.17573
$591$	2.63807	0.108516
$592$	−4.37764	−0.179920
$593$	−27.5224	−1.13021	−0.565104	−	0.825020i	$-0.691164\pi$
$593$	−27.5224	−1.13021	−0.565104	+	0.825020i	$0.691164\pi$
$594$	24.9222	1.02257
$595$	−23.9267	−0.980897
$596$	−6.49607	−0.266089
$597$	−1.60702	−0.0657708
$598$	19.6314	0.802786
$599$	11.9529	0.488382	0.244191	−	0.969727i	$-0.421478\pi$
$599$	11.9529	0.488382	0.244191	+	0.969727i	$0.421478\pi$
$600$	−11.5229	−0.470419
$601$	17.6157	0.718560	0.359280	−	0.933230i	$-0.383022\pi$
$601$	17.6157	0.718560	0.359280	+	0.933230i	$0.383022\pi$
$602$	7.23289	0.294790
$603$	2.41544	0.0983643
$604$	−8.96605	−0.364823
$605$	74.4536	3.02697
$606$	−13.6181	−0.553199
$607$	−0.171431	−0.00695815	−0.00347908	−	0.999994i	$-0.501107\pi$
$607$	−0.171431	−0.00695815	−0.00347908	+	0.999994i	$0.501107\pi$
$608$	−4.79894	−0.194623
$609$	−3.74612	−0.151801
$610$	−24.2978	−0.983789
$611$	51.7582	2.09391
$612$	−5.71222	−0.230903
$613$	−43.2760	−1.74790	−0.873950	−	0.486016i	$-0.838450\pi$
$613$	−43.2760	−1.74790	−0.873950	+	0.486016i	$0.838450\pi$
$614$	12.4782	0.503579
$615$	55.8387	2.25163
$616$	−5.79059	−0.233310
$617$	14.1501	0.569662	0.284831	−	0.958578i	$-0.408063\pi$
$617$	14.1501	0.569662	0.284831	+	0.958578i	$0.408063\pi$
$618$	−4.93744	−0.198613
$619$	26.0654	1.04766	0.523828	−	0.851824i	$-0.324503\pi$
$619$	26.0654	1.04766	0.523828	+	0.851824i	$0.324503\pi$
$620$	−6.29130	−0.252665
$621$	17.1761	0.689253
$622$	−11.7510	−0.471172
$623$	16.3774	0.656147
$624$	9.57517	0.383314
$625$	−19.5553	−0.782214
$626$	5.93439	0.237186
$627$	54.0911	2.16019
$628$	−9.52799	−0.380208
$629$	31.6968	1.26384
$630$	−2.60697	−0.103864
$631$	26.2825	1.04629	0.523146	−	0.852243i	$-0.324758\pi$
$631$	26.2825	1.04629	0.523146	+	0.852243i	$0.324758\pi$
$632$	15.1757	0.603658
$633$	−32.1136	−1.27640
$634$	13.3989	0.532139
$635$	27.1133	1.07596
$636$	−2.27646	−0.0902675
$637$	4.91914	0.194903
$638$	11.1442	0.441202
$639$	0.700023	0.0276925
$640$	−3.30450	−0.130622
$641$	−38.7979	−1.53243	−0.766213	−	0.642587i	$-0.777861\pi$
$641$	−38.7979	−1.53243	−0.766213	+	0.642587i	$0.777861\pi$
$642$	17.8524	0.704577
$643$	47.3690	1.86805	0.934025	−	0.357208i	$-0.116271\pi$
$643$	47.3690	1.86805	0.934025	+	0.357208i	$0.116271\pi$
$644$	−3.99081	−0.157260
$645$	−46.5238	−1.83187
$646$	34.7473	1.36711
$647$	−42.5240	−1.67179	−0.835895	−	0.548889i	$-0.815051\pi$
$647$	−42.5240	−1.67179	−0.835895	+	0.548889i	$0.815051\pi$
$648$	10.7444	0.422078
$649$	50.0438	1.96439
$650$	−29.1201	−1.14218
$651$	−3.70588	−0.145245
$652$	−10.5890	−0.414697
$653$	15.9595	0.624545	0.312273	−	0.949993i	$-0.398910\pi$
$653$	15.9595	0.624545	0.312273	+	0.949993i	$0.398910\pi$
$654$	−21.0147	−0.821741
$655$	−50.2354	−1.96286
$656$	8.68104	0.338938
$657$	2.26750	0.0884637
$658$	−10.5218	−0.410182
$659$	42.2695	1.64658	0.823292	−	0.567618i	$-0.192135\pi$
$659$	42.2695	1.64658	0.823292	+	0.567618i	$0.192135\pi$
$660$	37.2466	1.44982
$661$	−38.1126	−1.48241	−0.741205	−	0.671279i	$-0.765745\pi$
$661$	−38.1126	−1.48241	−0.741205	+	0.671279i	$0.765745\pi$
$662$	22.8387	0.887653
$663$	−69.3302	−2.69256
$664$	1.96604	0.0762973
$665$	15.8581	0.614952
$666$	3.45358	0.133824
$667$	7.68044	0.297388
$668$	−1.05797	−0.0409342
$669$	23.5688	0.911221
$670$	−10.1175	−0.390873
$671$	42.5778	1.64370
$672$	−1.94651	−0.0750884
$673$	−46.8159	−1.80462	−0.902311	−	0.431087i	$-0.858130\pi$
$673$	−46.8159	−1.80462	−0.902311	+	0.431087i	$0.858130\pi$
$674$	−11.6107	−0.447229
$675$	−25.4780	−0.980650
$676$	11.1980	0.430690
$677$	−13.9785	−0.537238	−0.268619	−	0.963247i	$-0.586567\pi$
$677$	−13.9785	−0.537238	−0.268619	+	0.963247i	$0.586567\pi$
$678$	10.3837	0.398785
$679$	−14.9147	−0.572373
$680$	23.9267	0.917545
$681$	−31.4533	−1.20529
$682$	11.0245	0.422148
$683$	−33.7165	−1.29013	−0.645064	−	0.764129i	$-0.723169\pi$
$683$	−33.7165	−1.29013	−0.645064	+	0.764129i	$0.723169\pi$
$684$	3.78595	0.144759
$685$	−26.5992	−1.01630
$686$	−1.00000	−0.0381802
$687$	15.1406	0.577650
$688$	−7.23289	−0.275751
$689$	−5.75297	−0.219171
$690$	25.6699	0.977238
$691$	−35.1779	−1.33823	−0.669115	−	0.743159i	$-0.733327\pi$
$691$	−35.1779	−1.33823	−0.669115	+	0.743159i	$0.733327\pi$
$692$	5.54014	0.210604
$693$	4.56828	0.173534
$694$	29.1286	1.10571
$695$	52.5321	1.99266
$696$	3.74612	0.141996
$697$	−62.8561	−2.38085
$698$	0.484513	0.0183391
$699$	−36.6847	−1.38754
$700$	5.91975	0.223745
$701$	−20.9063	−0.789620	−0.394810	−	0.918763i	$-0.629190\pi$
$701$	−20.9063	−0.789620	−0.394810	+	0.918763i	$0.629190\pi$
$702$	21.1715	0.799068
$703$	−21.0081	−0.792334
$704$	5.79059	0.218241
$705$	67.6789	2.54893
$706$	−17.9682	−0.676242
$707$	6.99617	0.263118
$708$	16.8223	0.632220
$709$	−30.3583	−1.14013	−0.570065	−	0.821600i	$-0.693082\pi$
$709$	−30.3583	−1.14013	−0.570065	+	0.821600i	$0.693082\pi$
$710$	−2.93217	−0.110042
$711$	−11.9723	−0.448997
$712$	−16.3774	−0.613769
$713$	7.59793	0.284545
$714$	14.0940	0.527453
$715$	94.1279	3.52018
$716$	12.1374	0.453594
$717$	4.56474	0.170473
$718$	35.9179	1.34044
$719$	−13.5953	−0.507018	−0.253509	−	0.967333i	$-0.581585\pi$
$719$	−13.5953	−0.507018	−0.253509	+	0.967333i	$0.581585\pi$
$720$	2.60697	0.0971559
$721$	2.53656	0.0944663
$722$	−4.02984	−0.149975
$723$	4.34483	0.161586
$724$	−16.1967	−0.601944
$725$	−11.3927	−0.423115
$726$	−43.8568	−1.62768
$727$	17.3383	0.643042	0.321521	−	0.946903i	$-0.395806\pi$
$727$	17.3383	0.643042	0.321521	+	0.946903i	$0.395806\pi$
$728$	−4.91914	−0.182316
$729$	16.6565	0.616907
$730$	−9.49784	−0.351531
$731$	52.3706	1.93700
$732$	14.3126	0.529008
$733$	29.6209	1.09407	0.547037	−	0.837109i	$-0.315756\pi$
$733$	29.6209	1.09407	0.547037	+	0.837109i	$0.315756\pi$
$734$	−1.45502	−0.0537057
$735$	6.43226	0.237257
$736$	3.99081	0.147103
$737$	17.7292	0.653065
$738$	−6.84859	−0.252100
$739$	−51.1699	−1.88231	−0.941157	−	0.337970i	$-0.890260\pi$
$739$	−51.1699	−1.88231	−0.941157	+	0.337970i	$0.890260\pi$
$740$	−14.4659	−0.531778
$741$	45.9507	1.68804
$742$	1.16951	0.0429339
$743$	10.5802	0.388150	0.194075	−	0.980987i	$-0.437829\pi$
$743$	10.5802	0.388150	0.194075	+	0.980987i	$0.437829\pi$
$744$	3.70588	0.135864
$745$	−21.4663	−0.786464
$746$	9.71319	0.355625
$747$	−1.55104	−0.0567495
$748$	−41.9275	−1.53302
$749$	−9.17146	−0.335118
$750$	−5.91604	−0.216023
$751$	13.9300	0.508312	0.254156	−	0.967163i	$-0.418202\pi$
$751$	13.9300	0.508312	0.254156	+	0.967163i	$0.418202\pi$
$752$	10.5218	0.383690
$753$	−1.38521	−0.0504800
$754$	9.46704	0.344769
$755$	−29.6283	−1.07829
$756$	−4.30391	−0.156532
$757$	−13.5784	−0.493516	−0.246758	−	0.969077i	$-0.579365\pi$
$757$	−13.5784	−0.493516	−0.246758	+	0.969077i	$0.579365\pi$
$758$	3.93631	0.142973
$759$	−44.9823	−1.63275
$760$	−15.8581	−0.575235
$761$	−26.9766	−0.977901	−0.488950	−	0.872312i	$-0.662620\pi$
$761$	−26.9766	−0.977901	−0.488950	+	0.872312i	$0.662620\pi$
$762$	−15.9711	−0.578571
$763$	10.7961	0.390845
$764$	13.7431	0.497207
$765$	−18.8761	−0.682465
$766$	14.7525	0.533029
$767$	42.5125	1.53504
$768$	1.94651	0.0702387
$769$	43.2757	1.56056	0.780281	−	0.625429i	$-0.215076\pi$
$769$	43.2757	1.56056	0.780281	+	0.625429i	$0.215076\pi$
$770$	−19.1350	−0.689579
$771$	36.6266	1.31908
$772$	−7.63753	−0.274881
$773$	3.55266	0.127780	0.0638901	−	0.997957i	$-0.479649\pi$
$773$	3.55266	0.127780	0.0638901	+	0.997957i	$0.479649\pi$
$774$	5.70612	0.205102
$775$	−11.2703	−0.404843
$776$	14.9147	0.535406
$777$	−8.52114	−0.305694
$778$	36.4596	1.30714
$779$	41.6598	1.49262
$780$	31.6412	1.13294
$781$	5.13814	0.183857
$782$	−28.8960	−1.03332
$783$	8.28300	0.296010
$784$	1.00000	0.0357143
$785$	−31.4853	−1.12376
$786$	29.5911	1.05548
$787$	40.9508	1.45974	0.729869	−	0.683587i	$-0.239581\pi$
$787$	40.9508	1.45974	0.729869	+	0.683587i	$0.239581\pi$
$788$	1.35528	0.0482799
$789$	−52.1634	−1.85707
$790$	50.1482	1.78419
$791$	−5.33453	−0.189674
$792$	−4.56828	−0.162327
$793$	36.1701	1.28444
$794$	28.0849	0.996696
$795$	−7.52257	−0.266798
$796$	−0.825587	−0.0292622
$797$	21.5897	0.764746	0.382373	−	0.924008i	$-0.375107\pi$
$797$	21.5897	0.764746	0.382373	+	0.924008i	$0.375107\pi$
$798$	−9.34120	−0.330675
$799$	−76.1843	−2.69521
$800$	−5.91975	−0.209295
$801$	12.9204	0.456518
$802$	33.2160	1.17290
$803$	16.6434	0.587332
$804$	5.95970	0.210182
$805$	−13.1877	−0.464804
$806$	9.36534	0.329880
$807$	44.9755	1.58321
$808$	−6.99617	−0.246125
$809$	6.46201	0.227192	0.113596	−	0.993527i	$-0.463763\pi$
$809$	6.46201	0.227192	0.113596	+	0.993527i	$0.463763\pi$
$810$	35.5048	1.24751
$811$	−7.58990	−0.266518	−0.133259	−	0.991081i	$-0.542544\pi$
$811$	−7.58990	−0.266518	−0.133259	+	0.991081i	$0.542544\pi$
$812$	−1.92453	−0.0675378
$813$	9.12895	0.320166
$814$	25.3491	0.888487
$815$	−34.9914	−1.22570
$816$	−14.0940	−0.493387
$817$	−34.7102	−1.21436
$818$	4.55881	0.159395
$819$	3.88078	0.135605
$820$	28.6865	1.00178
$821$	−15.3937	−0.537244	−0.268622	−	0.963246i	$-0.586568\pi$
$821$	−15.3937	−0.537244	−0.268622	+	0.963246i	$0.586568\pi$
$822$	15.6682	0.546491
$823$	47.5482	1.65742	0.828712	−	0.559675i	$-0.189074\pi$
$823$	47.5482	1.65742	0.828712	+	0.559675i	$0.189074\pi$
$824$	−2.53656	−0.0883651
$825$	66.7242	2.32304
$826$	−8.64226	−0.300703
$827$	−41.0585	−1.42775	−0.713873	−	0.700275i	$-0.753061\pi$
$827$	−41.0585	−1.42775	−0.713873	+	0.700275i	$0.753061\pi$
$828$	−3.14840	−0.109415
$829$	24.9342	0.866001	0.433001	−	0.901394i	$-0.357455\pi$
$829$	24.9342	0.866001	0.433001	+	0.901394i	$0.357455\pi$
$830$	6.49680	0.225507
$831$	−7.68922	−0.266736
$832$	4.91914	0.170541
$833$	−7.24062	−0.250873
$834$	−30.9440	−1.07150
$835$	−3.49608	−0.120987
$836$	27.7887	0.961093
$837$	8.19402	0.283227
$838$	−1.56411	−0.0540313
$839$	−31.5094	−1.08783	−0.543913	−	0.839142i	$-0.683058\pi$
$839$	−31.5094	−1.08783	−0.543913	+	0.839142i	$0.683058\pi$
$840$	−6.43226	−0.221934
$841$	−25.2962	−0.872282
$842$	33.5235	1.15530
$843$	50.9461	1.75468
$844$	−16.4980	−0.567885
$845$	37.0037	1.27296
$846$	−8.30078	−0.285387
$847$	22.5310	0.774173
$848$	−1.16951	−0.0401610
$849$	−31.9538	−1.09665
$850$	42.8626	1.47018
$851$	17.4704	0.598876
$852$	1.72719	0.0591726
$853$	−1.04226	−0.0356864	−0.0178432	−	0.999841i	$-0.505680\pi$
$853$	−1.04226	−0.0356864	−0.0178432	+	0.999841i	$0.505680\pi$
$854$	−7.35293	−0.251612
$855$	12.5107	0.427856
$856$	9.17146	0.313474
$857$	−19.7076	−0.673198	−0.336599	−	0.941648i	$-0.609277\pi$
$857$	−19.7076	−0.673198	−0.336599	+	0.941648i	$0.609277\pi$
$858$	−55.4459	−1.89289
$859$	−25.8329	−0.881406	−0.440703	−	0.897653i	$-0.645271\pi$
$859$	−25.8329	−0.881406	−0.440703	+	0.897653i	$0.645271\pi$
$860$	−23.9011	−0.815021
$861$	16.8978	0.575874
$862$	1.00000	0.0340601
$863$	−3.80136	−0.129400	−0.0646999	−	0.997905i	$-0.520609\pi$
$863$	−3.80136	−0.129400	−0.0646999	+	0.997905i	$0.520609\pi$
$864$	4.30391	0.146422
$865$	18.3074	0.622470
$866$	9.47100	0.321838
$867$	68.9583	2.34195
$868$	−1.90386	−0.0646211
$869$	−87.8764	−2.98100
$870$	12.3791	0.419690
$871$	15.0611	0.510325
$872$	−10.7961	−0.365602
$873$	−11.7664	−0.398232
$874$	19.1517	0.647815
$875$	3.03930	0.102747
$876$	5.59469	0.189027
$877$	−1.73611	−0.0586241	−0.0293121	−	0.999570i	$-0.509332\pi$
$877$	−1.73611	−0.0586241	−0.0293121	+	0.999570i	$0.509332\pi$
$878$	−3.02553	−0.102107
$879$	4.81646	0.162455
$880$	19.1350	0.645042
$881$	−2.81508	−0.0948426	−0.0474213	−	0.998875i	$-0.515100\pi$
$881$	−2.81508	−0.0948426	−0.0474213	+	0.998875i	$0.515100\pi$
$882$	−0.788913	−0.0265641
$883$	23.2210	0.781447	0.390724	−	0.920508i	$-0.372225\pi$
$883$	23.2210	0.781447	0.390724	+	0.920508i	$0.372225\pi$
$884$	−35.6176	−1.19795
$885$	55.5893	1.86861
$886$	−37.2187	−1.25039
$887$	−10.8433	−0.364081	−0.182041	−	0.983291i	$-0.558270\pi$
$887$	−10.8433	−0.364081	−0.182041	+	0.983291i	$0.558270\pi$
$888$	8.52114	0.285951
$889$	8.20497	0.275186
$890$	−54.1192	−1.81408
$891$	−62.2162	−2.08432
$892$	12.1082	0.405412
$893$	50.4935	1.68970
$894$	12.6447	0.422902
$895$	40.1079	1.34066
$896$	−1.00000	−0.0334077
$897$	−38.2127	−1.27589
$898$	−38.4914	−1.28447
$899$	3.66403	0.122202
$900$	4.67017	0.155672
$901$	8.46795	0.282108
$902$	−50.2684	−1.67375
$903$	−14.0789	−0.468517
$904$	5.33453	0.177424
$905$	−53.5219	−1.77913
$906$	17.4525	0.579822
$907$	−4.41267	−0.146520	−0.0732601	−	0.997313i	$-0.523340\pi$
$907$	−4.41267	−0.146520	−0.0732601	+	0.997313i	$0.523340\pi$
$908$	−16.1588	−0.536248
$909$	5.51937	0.183066
$910$	−16.2553	−0.538859
$911$	58.0730	1.92404	0.962022	−	0.272972i	$-0.0880065\pi$
$911$	58.0730	1.92404	0.962022	+	0.272972i	$0.0880065\pi$
$912$	9.34120	0.309318
$913$	−11.3846	−0.376774
$914$	−29.8100	−0.986029
$915$	47.2960	1.56356
$916$	7.77831	0.257003
$917$	−15.2021	−0.502018
$918$	−31.1630	−1.02853
$919$	−31.2417	−1.03057	−0.515285	−	0.857019i	$-0.672314\pi$
$919$	−31.2417	−1.03057	−0.515285	+	0.857019i	$0.672314\pi$
$920$	13.1877	0.434784
$921$	−24.2890	−0.800348
$922$	−26.4183	−0.870040
$923$	4.36488	0.143672
$924$	11.2715	0.370804
$925$	−25.9145	−0.852065
$926$	−1.01551	−0.0333718
$927$	2.00112	0.0657255
$928$	1.92453	0.0631758
$929$	33.6362	1.10357	0.551784	−	0.833987i	$-0.313947\pi$
$929$	33.6362	1.10357	0.551784	+	0.833987i	$0.313947\pi$
$930$	12.2461	0.401565
$931$	4.79894	0.157279
$932$	−18.8463	−0.617333
$933$	22.8735	0.748844
$934$	−25.4456	−0.832605
$935$	−138.549	−4.53105
$936$	−3.88078	−0.126847
$937$	−37.0260	−1.20959	−0.604793	−	0.796383i	$-0.706744\pi$
$937$	−37.0260	−1.20959	−0.604793	+	0.796383i	$0.706744\pi$
$938$	−3.06173	−0.0999690
$939$	−11.5514	−0.376965
$940$	34.7693	1.13405
$941$	27.7898	0.905920	0.452960	−	0.891531i	$-0.350368\pi$
$941$	27.7898	0.905920	0.452960	+	0.891531i	$0.350368\pi$
$942$	18.5464	0.604273
$943$	−34.6444	−1.12818
$944$	8.64226	0.281282
$945$	−14.2223	−0.462651
$946$	41.8827	1.36172
$947$	−15.0295	−0.488393	−0.244196	−	0.969726i	$-0.578524\pi$
$947$	−15.0295	−0.488393	−0.244196	+	0.969726i	$0.578524\pi$
$948$	−29.5397	−0.959406
$949$	14.1386	0.458960
$950$	−28.4085	−0.921694
$951$	−26.0812	−0.845740
$952$	7.24062	0.234670
$953$	43.2437	1.40080	0.700400	−	0.713750i	$-0.253005\pi$
$953$	43.2437	1.40080	0.700400	+	0.713750i	$0.253005\pi$
$954$	0.922639	0.0298715
$955$	45.4140	1.46956
$956$	2.34508	0.0758455
$957$	−21.6923	−0.701212
$958$	−38.6546	−1.24887
$959$	−8.04937	−0.259928
$960$	6.43226	0.207600
$961$	−27.3753	−0.883075
$962$	21.5342	0.694292
$963$	−7.23549	−0.233160
$964$	2.23211	0.0718915
$965$	−25.2382	−0.812448
$966$	7.76817	0.249937
$967$	9.16862	0.294843	0.147422	−	0.989074i	$-0.452903\pi$
$967$	9.16862	0.294843	0.147422	+	0.989074i	$0.452903\pi$
$968$	−22.5310	−0.724172
$969$	−67.6361	−2.17278
$970$	49.2857	1.58247
$971$	−30.1057	−0.966137	−0.483068	−	0.875583i	$-0.660478\pi$
$971$	−30.1057	−0.966137	−0.483068	+	0.875583i	$0.660478\pi$
$972$	−8.00230	−0.256674
$973$	15.8971	0.509638
$974$	10.3747	0.332426
$975$	56.6826	1.81530
$976$	7.35293	0.235362
$977$	18.1427	0.580436	0.290218	−	0.956961i	$-0.406272\pi$
$977$	18.1427	0.580436	0.290218	+	0.956961i	$0.406272\pi$
$978$	20.6116	0.659087
$979$	94.8349	3.03094
$980$	3.30450	0.105559
$981$	8.51718	0.271933
$982$	10.5438	0.336465
$983$	8.55253	0.272783	0.136392	−	0.990655i	$-0.456449\pi$
$983$	8.55253	0.272783	0.136392	+	0.990655i	$0.456449\pi$
$984$	−16.8978	−0.538681
$985$	4.47853	0.142698
$986$	−13.9348	−0.443774
$987$	20.4808	0.651911
$988$	23.6067	0.751028
$989$	28.8651	0.917857
$990$	−15.0959	−0.479779
$991$	−54.9415	−1.74527	−0.872637	−	0.488369i	$-0.837592\pi$
$991$	−54.9415	−1.74527	−0.872637	+	0.488369i	$0.837592\pi$
$992$	1.90386	0.0604475
$993$	−44.4559	−1.41077
$994$	−0.887326	−0.0281443
$995$	−2.72816	−0.0864884
$996$	−3.82693	−0.121261
$997$	59.8700	1.89610	0.948051	−	0.318118i	$-0.103051\pi$
$997$	59.8700	1.89610	0.948051	+	0.318118i	$0.103051\pi$
$998$	−15.7907	−0.499845
$999$	18.8410	0.596102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.20	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.20	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.94651 q^{3} +1.00000 q^{4} +3.30450 q^{5} -1.94651 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.788913 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.94651 q^{3} +1.00000 q^{4} +3.30450 q^{5} -1.94651 q^{6} +1.00000 q^{7} -1.00000 q^{8} +0.788913 q^{9} -3.30450 q^{10} +5.79059 q^{11} +1.94651 q^{12} +4.91914 q^{13} -1.00000 q^{14} +6.43226 q^{15} +1.00000 q^{16} -7.24062 q^{17} -0.788913 q^{18} +4.79894 q^{19} +3.30450 q^{20} +1.94651 q^{21} -5.79059 q^{22} -3.99081 q^{23} -1.94651 q^{24} +5.91975 q^{25} -4.91914 q^{26} -4.30391 q^{27} +1.00000 q^{28} -1.92453 q^{29} -6.43226 q^{30} -1.90386 q^{31} -1.00000 q^{32} +11.2715 q^{33} +7.24062 q^{34} +3.30450 q^{35} +0.788913 q^{36} -4.37764 q^{37} -4.79894 q^{38} +9.57517 q^{39} -3.30450 q^{40} +8.68104 q^{41} -1.94651 q^{42} -7.23289 q^{43} +5.79059 q^{44} +2.60697 q^{45} +3.99081 q^{46} +10.5218 q^{47} +1.94651 q^{48} +1.00000 q^{49} -5.91975 q^{50} -14.0940 q^{51} +4.91914 q^{52} -1.16951 q^{53} +4.30391 q^{54} +19.1350 q^{55} -1.00000 q^{56} +9.34120 q^{57} +1.92453 q^{58} +8.64226 q^{59} +6.43226 q^{60} +7.35293 q^{61} +1.90386 q^{62} +0.788913 q^{63} +1.00000 q^{64} +16.2553 q^{65} -11.2715 q^{66} +3.06173 q^{67} -7.24062 q^{68} -7.76817 q^{69} -3.30450 q^{70} +0.887326 q^{71} -0.788913 q^{72} +2.87421 q^{73} +4.37764 q^{74} +11.5229 q^{75} +4.79894 q^{76} +5.79059 q^{77} -9.57517 q^{78} -15.1757 q^{79} +3.30450 q^{80} -10.7444 q^{81} -8.68104 q^{82} -1.96604 q^{83} +1.94651 q^{84} -23.9267 q^{85} +7.23289 q^{86} -3.74612 q^{87} -5.79059 q^{88} +16.3774 q^{89} -2.60697 q^{90} +4.91914 q^{91} -3.99081 q^{92} -3.70588 q^{93} -10.5218 q^{94} +15.8581 q^{95} -1.94651 q^{96} -14.9147 q^{97} -1.00000 q^{98} +4.56828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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