LMFDB - Embedded newform 6034.2.a.p.1.19

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			1.19
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.64919 q^{3} +1.00000 q^{4} +0.930561 q^{5} -1.64919 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.280182 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.64919 q^{3} +1.00000 q^{4} +0.930561 q^{5} -1.64919 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.280182 q^{9} -0.930561 q^{10} -4.41648 q^{11} +1.64919 q^{12} +3.34131 q^{13} -1.00000 q^{14} +1.53467 q^{15} +1.00000 q^{16} +1.14383 q^{17} +0.280182 q^{18} -6.72758 q^{19} +0.930561 q^{20} +1.64919 q^{21} +4.41648 q^{22} +8.59758 q^{23} -1.64919 q^{24} -4.13406 q^{25} -3.34131 q^{26} -5.40963 q^{27} +1.00000 q^{28} +5.75279 q^{29} -1.53467 q^{30} +9.27992 q^{31} -1.00000 q^{32} -7.28361 q^{33} -1.14383 q^{34} +0.930561 q^{35} -0.280182 q^{36} -5.57428 q^{37} +6.72758 q^{38} +5.51045 q^{39} -0.930561 q^{40} +7.96610 q^{41} -1.64919 q^{42} +3.96609 q^{43} -4.41648 q^{44} -0.260727 q^{45} -8.59758 q^{46} -2.15547 q^{47} +1.64919 q^{48} +1.00000 q^{49} +4.13406 q^{50} +1.88639 q^{51} +3.34131 q^{52} -3.87657 q^{53} +5.40963 q^{54} -4.10981 q^{55} -1.00000 q^{56} -11.0950 q^{57} -5.75279 q^{58} -0.164364 q^{59} +1.53467 q^{60} +4.35568 q^{61} -9.27992 q^{62} -0.280182 q^{63} +1.00000 q^{64} +3.10929 q^{65} +7.28361 q^{66} +8.90523 q^{67} +1.14383 q^{68} +14.1790 q^{69} -0.930561 q^{70} -11.1896 q^{71} +0.280182 q^{72} +12.6052 q^{73} +5.57428 q^{74} -6.81783 q^{75} -6.72758 q^{76} -4.41648 q^{77} -5.51045 q^{78} -1.79502 q^{79} +0.930561 q^{80} -8.08095 q^{81} -7.96610 q^{82} +15.8232 q^{83} +1.64919 q^{84} +1.06440 q^{85} -3.96609 q^{86} +9.48743 q^{87} +4.41648 q^{88} +6.24260 q^{89} +0.260727 q^{90} +3.34131 q^{91} +8.59758 q^{92} +15.3043 q^{93} +2.15547 q^{94} -6.26042 q^{95} -1.64919 q^{96} -3.39096 q^{97} -1.00000 q^{98} +1.23742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.64919	0.952159	0.476079	−	0.879402i	$-0.342058\pi$
$3$	1.64919	0.952159	0.476079	+	0.879402i	$0.342058\pi$
$4$	1.00000	0.500000
$5$	0.930561	0.416160	0.208080	−	0.978112i	$-0.433279\pi$
$5$	0.930561	0.416160	0.208080	+	0.978112i	$0.433279\pi$
$6$	−1.64919	−0.673278
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−0.280182	−0.0933941
$10$	−0.930561	−0.294269
$11$	−4.41648	−1.33162	−0.665810	−	0.746121i	$-0.731914\pi$
$11$	−4.41648	−1.33162	−0.665810	+	0.746121i	$0.731914\pi$
$12$	1.64919	0.476079
$13$	3.34131	0.926713	0.463356	−	0.886172i	$-0.346645\pi$
$13$	3.34131	0.926713	0.463356	+	0.886172i	$0.346645\pi$
$14$	−1.00000	−0.267261
$15$	1.53467	0.396250
$16$	1.00000	0.250000
$17$	1.14383	0.277419	0.138710	−	0.990333i	$-0.455705\pi$
$17$	1.14383	0.277419	0.138710	+	0.990333i	$0.455705\pi$
$18$	0.280182	0.0660396
$19$	−6.72758	−1.54341	−0.771706	−	0.635979i	$-0.780596\pi$
$19$	−6.72758	−1.54341	−0.771706	+	0.635979i	$0.780596\pi$
$20$	0.930561	0.208080
$21$	1.64919	0.359882
$22$	4.41648	0.941597
$23$	8.59758	1.79272	0.896360	−	0.443328i	$-0.146202\pi$
$23$	8.59758	1.79272	0.896360	+	0.443328i	$0.146202\pi$
$24$	−1.64919	−0.336639
$25$	−4.13406	−0.826811
$26$	−3.34131	−0.655285
$27$	−5.40963	−1.04108
$28$	1.00000	0.188982
$29$	5.75279	1.06827	0.534133	−	0.845400i	$-0.320638\pi$
$29$	5.75279	1.06827	0.534133	+	0.845400i	$0.320638\pi$
$30$	−1.53467	−0.280191
$31$	9.27992	1.66672	0.833362	−	0.552728i	$-0.186413\pi$
$31$	9.27992	1.66672	0.833362	+	0.552728i	$0.186413\pi$
$32$	−1.00000	−0.176777
$33$	−7.28361	−1.26791
$34$	−1.14383	−0.196165
$35$	0.930561	0.157294
$36$	−0.280182	−0.0466970
$37$	−5.57428	−0.916406	−0.458203	−	0.888848i	$-0.651507\pi$
$37$	−5.57428	−0.916406	−0.458203	+	0.888848i	$0.651507\pi$
$38$	6.72758	1.09136
$39$	5.51045	0.882377
$40$	−0.930561	−0.147135
$41$	7.96610	1.24410	0.622048	−	0.782979i	$-0.286301\pi$
$41$	7.96610	1.24410	0.622048	+	0.782979i	$0.286301\pi$
$42$	−1.64919	−0.254475
$43$	3.96609	0.604823	0.302412	−	0.953177i	$-0.402208\pi$
$43$	3.96609	0.604823	0.302412	+	0.953177i	$0.402208\pi$
$44$	−4.41648	−0.665810
$45$	−0.260727	−0.0388668
$46$	−8.59758	−1.26764
$47$	−2.15547	−0.314408	−0.157204	−	0.987566i	$-0.550248\pi$
$47$	−2.15547	−0.314408	−0.157204	+	0.987566i	$0.550248\pi$
$48$	1.64919	0.238040
$49$	1.00000	0.142857
$50$	4.13406	0.584644
$51$	1.88639	0.264147
$52$	3.34131	0.463356
$53$	−3.87657	−0.532488	−0.266244	−	0.963906i	$-0.585783\pi$
$53$	−3.87657	−0.532488	−0.266244	+	0.963906i	$0.585783\pi$
$54$	5.40963	0.736158
$55$	−4.10981	−0.554166
$56$	−1.00000	−0.133631
$57$	−11.0950	−1.46957
$58$	−5.75279	−0.755379
$59$	−0.164364	−0.0213984	−0.0106992	−	0.999943i	$-0.503406\pi$
$59$	−0.164364	−0.0213984	−0.0106992	+	0.999943i	$0.503406\pi$
$60$	1.53467	0.198125
$61$	4.35568	0.557688	0.278844	−	0.960336i	$-0.410049\pi$
$61$	4.35568	0.557688	0.278844	+	0.960336i	$0.410049\pi$
$62$	−9.27992	−1.17855
$63$	−0.280182	−0.0352996
$64$	1.00000	0.125000
$65$	3.10929	0.385660
$66$	7.28361	0.896550
$67$	8.90523	1.08795	0.543974	−	0.839102i	$-0.316919\pi$
$67$	8.90523	1.08795	0.543974	+	0.839102i	$0.316919\pi$
$68$	1.14383	0.138710
$69$	14.1790	1.70695
$70$	−0.930561	−0.111223
$71$	−11.1896	−1.32796	−0.663980	−	0.747750i	$-0.731134\pi$
$71$	−11.1896	−1.32796	−0.663980	+	0.747750i	$0.731134\pi$
$72$	0.280182	0.0330198
$73$	12.6052	1.47533	0.737666	−	0.675166i	$-0.235928\pi$
$73$	12.6052	1.47533	0.737666	+	0.675166i	$0.235928\pi$
$74$	5.57428	0.647997
$75$	−6.81783	−0.787255
$76$	−6.72758	−0.771706
$77$	−4.41648	−0.503305
$78$	−5.51045	−0.623935
$79$	−1.79502	−0.201955	−0.100978	−	0.994889i	$-0.532197\pi$
$79$	−1.79502	−0.201955	−0.100978	+	0.994889i	$0.532197\pi$
$80$	0.930561	0.104040
$81$	−8.08095	−0.897883
$82$	−7.96610	−0.879709
$83$	15.8232	1.73683	0.868413	−	0.495842i	$-0.165140\pi$
$83$	15.8232	1.73683	0.868413	+	0.495842i	$0.165140\pi$
$84$	1.64919	0.179941
$85$	1.06440	0.115451
$86$	−3.96609	−0.427674
$87$	9.48743	1.01716
$88$	4.41648	0.470799
$89$	6.24260	0.661715	0.330857	−	0.943681i	$-0.392662\pi$
$89$	6.24260	0.661715	0.330857	+	0.943681i	$0.392662\pi$
$90$	0.260727	0.0274830
$91$	3.34131	0.350264
$92$	8.59758	0.896360
$93$	15.3043	1.58698
$94$	2.15547	0.222320
$95$	−6.26042	−0.642306
$96$	−1.64919	−0.168319
$97$	−3.39096	−0.344300	−0.172150	−	0.985071i	$-0.555071\pi$
$97$	−3.39096	−0.344300	−0.172150	+	0.985071i	$0.555071\pi$
$98$	−1.00000	−0.101015
$99$	1.23742	0.124365
$100$	−4.13406	−0.413406
$101$	−5.14556	−0.512003	−0.256001	−	0.966676i	$-0.582405\pi$
$101$	−5.14556	−0.512003	−0.256001	+	0.966676i	$0.582405\pi$
$102$	−1.88639	−0.186780
$103$	−2.45821	−0.242215	−0.121108	−	0.992639i	$-0.538645\pi$
$103$	−2.45821	−0.242215	−0.121108	+	0.992639i	$0.538645\pi$
$104$	−3.34131	−0.327642
$105$	1.53467	0.149768
$106$	3.87657	0.376526
$107$	6.83841	0.661094	0.330547	−	0.943790i	$-0.392767\pi$
$107$	6.83841	0.661094	0.330547	+	0.943790i	$0.392767\pi$
$108$	−5.40963	−0.520542
$109$	5.28935	0.506628	0.253314	−	0.967384i	$-0.418479\pi$
$109$	5.28935	0.506628	0.253314	+	0.967384i	$0.418479\pi$
$110$	4.10981	0.391855
$111$	−9.19303	−0.872564
$112$	1.00000	0.0944911
$113$	−1.53580	−0.144476	−0.0722379	−	0.997387i	$-0.523014\pi$
$113$	−1.53580	−0.144476	−0.0722379	+	0.997387i	$0.523014\pi$
$114$	11.0950	1.03915
$115$	8.00057	0.746057
$116$	5.75279	0.534133
$117$	−0.936175	−0.0865495
$118$	0.164364	0.0151310
$119$	1.14383	0.104855
$120$	−1.53467	−0.140096
$121$	8.50533	0.773211
$122$	−4.35568	−0.394345
$123$	13.1376	1.18458
$124$	9.27992	0.833362
$125$	−8.49980	−0.760245
$126$	0.280182	0.0249606
$127$	15.7443	1.39708	0.698542	−	0.715569i	$-0.253833\pi$
$127$	15.7443	1.39708	0.698542	+	0.715569i	$0.253833\pi$
$128$	−1.00000	−0.0883883
$129$	6.54082	0.575887
$130$	−3.10929	−0.272703
$131$	−9.17398	−0.801534	−0.400767	−	0.916180i	$-0.631256\pi$
$131$	−9.17398	−0.801534	−0.400767	+	0.916180i	$0.631256\pi$
$132$	−7.28361	−0.633957
$133$	−6.72758	−0.583355
$134$	−8.90523	−0.769295
$135$	−5.03400	−0.433257
$136$	−1.14383	−0.0980826
$137$	17.5257	1.49732	0.748662	−	0.662952i	$-0.230697\pi$
$137$	17.5257	1.49732	0.748662	+	0.662952i	$0.230697\pi$
$138$	−14.1790	−1.20700
$139$	5.01160	0.425079	0.212539	−	0.977153i	$-0.431827\pi$
$139$	5.01160	0.425079	0.212539	+	0.977153i	$0.431827\pi$
$140$	0.930561	0.0786468
$141$	−3.55478	−0.299366
$142$	11.1896	0.939010
$143$	−14.7568	−1.23403
$144$	−0.280182	−0.0233485
$145$	5.35333	0.444570
$146$	−12.6052	−1.04322
$147$	1.64919	0.136023
$148$	−5.57428	−0.458203
$149$	8.60580	0.705015	0.352507	−	0.935809i	$-0.385329\pi$
$149$	8.60580	0.705015	0.352507	+	0.935809i	$0.385329\pi$
$150$	6.81783	0.556674
$151$	−9.02941	−0.734803	−0.367401	−	0.930062i	$-0.619752\pi$
$151$	−9.02941	−0.734803	−0.367401	+	0.930062i	$0.619752\pi$
$152$	6.72758	0.545679
$153$	−0.320481	−0.0259093
$154$	4.41648	0.355890
$155$	8.63554	0.693623
$156$	5.51045	0.441189
$157$	10.8643	0.867067	0.433534	−	0.901137i	$-0.357267\pi$
$157$	10.8643	0.867067	0.433534	+	0.901137i	$0.357267\pi$
$158$	1.79502	0.142804
$159$	−6.39320	−0.507013
$160$	−0.930561	−0.0735673
$161$	8.59758	0.677584
$162$	8.08095	0.634900
$163$	8.68325	0.680125	0.340062	−	0.940403i	$-0.389552\pi$
$163$	8.68325	0.680125	0.340062	+	0.940403i	$0.389552\pi$
$164$	7.96610	0.622048
$165$	−6.77784	−0.527654
$166$	−15.8232	−1.22812
$167$	23.8971	1.84921	0.924605	−	0.380927i	$-0.124395\pi$
$167$	23.8971	1.84921	0.924605	+	0.380927i	$0.124395\pi$
$168$	−1.64919	−0.127238
$169$	−1.83565	−0.141204
$170$	−1.06440	−0.0816360
$171$	1.88495	0.144146
$172$	3.96609	0.302412
$173$	7.93714	0.603450	0.301725	−	0.953395i	$-0.402438\pi$
$173$	7.93714	0.603450	0.301725	+	0.953395i	$0.402438\pi$
$174$	−9.48743	−0.719240
$175$	−4.13406	−0.312505
$176$	−4.41648	−0.332905
$177$	−0.271067	−0.0203747
$178$	−6.24260	−0.467903
$179$	14.0291	1.04858	0.524292	−	0.851538i	$-0.324330\pi$
$179$	14.0291	1.04858	0.524292	+	0.851538i	$0.324330\pi$
$180$	−0.260727	−0.0194334
$181$	−22.3384	−1.66040	−0.830198	−	0.557468i	$-0.811773\pi$
$181$	−22.3384	−1.66040	−0.830198	+	0.557468i	$0.811773\pi$
$182$	−3.34131	−0.247674
$183$	7.18333	0.531007
$184$	−8.59758	−0.633822
$185$	−5.18721	−0.381371
$186$	−15.3043	−1.12217
$187$	−5.05170	−0.369417
$188$	−2.15547	−0.157204
$189$	−5.40963	−0.393493
$190$	6.26042	0.454179
$191$	15.4332	1.11670	0.558352	−	0.829604i	$-0.311434\pi$
$191$	15.4332	1.11670	0.558352	+	0.829604i	$0.311434\pi$
$192$	1.64919	0.119020
$193$	−8.23611	−0.592848	−0.296424	−	0.955056i	$-0.595794\pi$
$193$	−8.23611	−0.592848	−0.296424	+	0.955056i	$0.595794\pi$
$194$	3.39096	0.243457
$195$	5.12781	0.367210
$196$	1.00000	0.0714286
$197$	−10.1682	−0.724456	−0.362228	−	0.932090i	$-0.617984\pi$
$197$	−10.1682	−0.724456	−0.362228	+	0.932090i	$0.617984\pi$
$198$	−1.23742	−0.0879396
$199$	−5.76669	−0.408790	−0.204395	−	0.978889i	$-0.565523\pi$
$199$	−5.76669	−0.408790	−0.204395	+	0.978889i	$0.565523\pi$
$200$	4.13406	0.292322
$201$	14.6864	1.03590
$202$	5.14556	0.362041
$203$	5.75279	0.403767
$204$	1.88639	0.132074
$205$	7.41295	0.517743
$206$	2.45821	0.171272
$207$	−2.40889	−0.167429
$208$	3.34131	0.231678
$209$	29.7122	2.05524
$210$	−1.53467	−0.105902
$211$	13.0518	0.898525	0.449263	−	0.893400i	$-0.351687\pi$
$211$	13.0518	0.898525	0.449263	+	0.893400i	$0.351687\pi$
$212$	−3.87657	−0.266244
$213$	−18.4537	−1.26443
$214$	−6.83841	−0.467464
$215$	3.69069	0.251703
$216$	5.40963	0.368079
$217$	9.27992	0.629962
$218$	−5.28935	−0.358240
$219$	20.7884	1.40475
$220$	−4.10981	−0.277083
$221$	3.82189	0.257088
$222$	9.19303	0.616996
$223$	6.55218	0.438767	0.219383	−	0.975639i	$-0.429595\pi$
$223$	6.55218	0.438767	0.219383	+	0.975639i	$0.429595\pi$
$224$	−1.00000	−0.0668153
$225$	1.15829	0.0772192
$226$	1.53580	0.102160
$227$	0.101466	0.00673452	0.00336726	−	0.999994i	$-0.498928\pi$
$227$	0.101466	0.00673452	0.00336726	+	0.999994i	$0.498928\pi$
$228$	−11.0950	−0.734787
$229$	−4.87298	−0.322015	−0.161008	−	0.986953i	$-0.551474\pi$
$229$	−4.87298	−0.322015	−0.161008	+	0.986953i	$0.551474\pi$
$230$	−8.00057	−0.527542
$231$	−7.28361	−0.479226
$232$	−5.75279	−0.377689
$233$	−27.4717	−1.79973	−0.899866	−	0.436167i	$-0.856336\pi$
$233$	−27.4717	−1.79973	−0.899866	+	0.436167i	$0.856336\pi$
$234$	0.936175	0.0611997
$235$	−2.00580	−0.130844
$236$	−0.164364	−0.0106992
$237$	−2.96032	−0.192293
$238$	−1.14383	−0.0741435
$239$	23.9533	1.54941	0.774705	−	0.632322i	$-0.217898\pi$
$239$	23.9533	1.54941	0.774705	+	0.632322i	$0.217898\pi$
$240$	1.53467	0.0990625
$241$	3.50470	0.225757	0.112879	−	0.993609i	$-0.463993\pi$
$241$	3.50470	0.225757	0.112879	+	0.993609i	$0.463993\pi$
$242$	−8.50533	−0.546743
$243$	2.90190	0.186157
$244$	4.35568	0.278844
$245$	0.930561	0.0594514
$246$	−13.1376	−0.837622
$247$	−22.4789	−1.43030
$248$	−9.27992	−0.589276
$249$	26.0955	1.65373
$250$	8.49980	0.537574
$251$	12.3581	0.780034	0.390017	−	0.920808i	$-0.372469\pi$
$251$	12.3581	0.780034	0.390017	+	0.920808i	$0.372469\pi$
$252$	−0.280182	−0.0176498
$253$	−37.9711	−2.38722
$254$	−15.7443	−0.987887
$255$	1.75540	0.109927
$256$	1.00000	0.0625000
$257$	20.9473	1.30666	0.653328	−	0.757075i	$-0.273372\pi$
$257$	20.9473	1.30666	0.653328	+	0.757075i	$0.273372\pi$
$258$	−6.54082	−0.407214
$259$	−5.57428	−0.346369
$260$	3.10929	0.192830
$261$	−1.61183	−0.0997698
$262$	9.17398	0.566770
$263$	26.3883	1.62717	0.813586	−	0.581445i	$-0.197512\pi$
$263$	26.3883	1.62717	0.813586	+	0.581445i	$0.197512\pi$
$264$	7.28361	0.448275
$265$	−3.60739	−0.221600
$266$	6.72758	0.412494
$267$	10.2952	0.630057
$268$	8.90523	0.543974
$269$	−20.4308	−1.24569	−0.622845	−	0.782346i	$-0.714023\pi$
$269$	−20.4308	−1.24569	−0.622845	+	0.782346i	$0.714023\pi$
$270$	5.03400	0.306359
$271$	−17.2645	−1.04874	−0.524372	−	0.851489i	$-0.675700\pi$
$271$	−17.2645	−1.04874	−0.524372	+	0.851489i	$0.675700\pi$
$272$	1.14383	0.0693549
$273$	5.51045	0.333507
$274$	−17.5257	−1.05877
$275$	18.2580	1.10100
$276$	14.1790	0.853477
$277$	−4.18231	−0.251291	−0.125645	−	0.992075i	$-0.540100\pi$
$277$	−4.18231	−0.251291	−0.125645	+	0.992075i	$0.540100\pi$
$278$	−5.01160	−0.300576
$279$	−2.60007	−0.155662
$280$	−0.930561	−0.0556117
$281$	−23.2379	−1.38625	−0.693127	−	0.720815i	$-0.743768\pi$
$281$	−23.2379	−1.38625	−0.693127	+	0.720815i	$0.743768\pi$
$282$	3.55478	0.211684
$283$	−12.1476	−0.722099	−0.361049	−	0.932547i	$-0.617581\pi$
$283$	−12.1476	−0.722099	−0.361049	+	0.932547i	$0.617581\pi$
$284$	−11.1896	−0.663980
$285$	−10.3246	−0.611577
$286$	14.7568	0.872590
$287$	7.96610	0.470224
$288$	0.280182	0.0165099
$289$	−15.6917	−0.923038
$290$	−5.35333	−0.314358
$291$	−5.59233	−0.327828
$292$	12.6052	0.737666
$293$	22.1442	1.29368	0.646839	−	0.762627i	$-0.276091\pi$
$293$	22.1442	1.29368	0.646839	+	0.762627i	$0.276091\pi$
$294$	−1.64919	−0.0961825
$295$	−0.152951	−0.00890515
$296$	5.57428	0.323998
$297$	23.8916	1.38633
$298$	−8.60580	−0.498521
$299$	28.7272	1.66134
$300$	−6.81783	−0.393628
$301$	3.96609	0.228602
$302$	9.02941	0.519584
$303$	−8.48600	−0.487508
$304$	−6.72758	−0.385853
$305$	4.05323	0.232087
$306$	0.320481	0.0183207
$307$	12.4806	0.712303	0.356152	−	0.934428i	$-0.384089\pi$
$307$	12.4806	0.712303	0.356152	+	0.934428i	$0.384089\pi$
$308$	−4.41648	−0.251652
$309$	−4.05406	−0.230627
$310$	−8.63554	−0.490465
$311$	−18.5507	−1.05191	−0.525957	−	0.850511i	$-0.676293\pi$
$311$	−18.5507	−1.05191	−0.525957	+	0.850511i	$0.676293\pi$
$312$	−5.51045	−0.311968
$313$	8.23120	0.465255	0.232627	−	0.972566i	$-0.425268\pi$
$313$	8.23120	0.465255	0.232627	+	0.972566i	$0.425268\pi$
$314$	−10.8643	−0.613109
$315$	−0.260727	−0.0146903
$316$	−1.79502	−0.100978
$317$	−14.1190	−0.793000	−0.396500	−	0.918035i	$-0.629775\pi$
$317$	−14.1190	−0.793000	−0.396500	+	0.918035i	$0.629775\pi$
$318$	6.39320	0.358513
$319$	−25.4071	−1.42253
$320$	0.930561	0.0520200
$321$	11.2778	0.629466
$322$	−8.59758	−0.479124
$323$	−7.69520	−0.428173
$324$	−8.08095	−0.448942
$325$	−13.8132	−0.766216
$326$	−8.68325	−0.480921
$327$	8.72314	0.482390
$328$	−7.96610	−0.439854
$329$	−2.15547	−0.118835
$330$	6.77784	0.373108
$331$	−16.8198	−0.924502	−0.462251	−	0.886749i	$-0.652958\pi$
$331$	−16.8198	−0.924502	−0.462251	+	0.886749i	$0.652958\pi$
$332$	15.8232	0.868413
$333$	1.56181	0.0855869
$334$	−23.8971	−1.30759
$335$	8.28686	0.452760
$336$	1.64919	0.0899705
$337$	−18.5309	−1.00944	−0.504720	−	0.863283i	$-0.668404\pi$
$337$	−18.5309	−1.00944	−0.504720	+	0.863283i	$0.668404\pi$
$338$	1.83565	0.0998461
$339$	−2.53282	−0.137564
$340$	1.06440	0.0577254
$341$	−40.9846	−2.21944
$342$	−1.88495	−0.101926
$343$	1.00000	0.0539949
$344$	−3.96609	−0.213837
$345$	13.1944	0.710365
$346$	−7.93714	−0.426703
$347$	−26.7662	−1.43688	−0.718441	−	0.695587i	$-0.755144\pi$
$347$	−26.7662	−1.43688	−0.718441	+	0.695587i	$0.755144\pi$
$348$	9.48743	0.508580
$349$	3.24445	0.173671	0.0868356	−	0.996223i	$-0.472325\pi$
$349$	3.24445	0.173671	0.0868356	+	0.996223i	$0.472325\pi$
$350$	4.13406	0.220975
$351$	−18.0753	−0.964786
$352$	4.41648	0.235399
$353$	9.27221	0.493510	0.246755	−	0.969078i	$-0.420636\pi$
$353$	9.27221	0.493510	0.246755	+	0.969078i	$0.420636\pi$
$354$	0.271067	0.0144071
$355$	−10.4126	−0.552644
$356$	6.24260	0.330857
$357$	1.88639	0.0998383
$358$	−14.0291	−0.741461
$359$	−6.91995	−0.365221	−0.182610	−	0.983185i	$-0.558455\pi$
$359$	−6.91995	−0.365221	−0.182610	+	0.983185i	$0.558455\pi$
$360$	0.260727	0.0137415
$361$	26.2603	1.38212
$362$	22.3384	1.17408
$363$	14.0269	0.736220
$364$	3.34131	0.175132
$365$	11.7300	0.613974
$366$	−7.18333	−0.375479
$367$	−2.40745	−0.125668	−0.0628340	−	0.998024i	$-0.520014\pi$
$367$	−2.40745	−0.125668	−0.0628340	+	0.998024i	$0.520014\pi$
$368$	8.59758	0.448180
$369$	−2.23196	−0.116191
$370$	5.18721	0.269670
$371$	−3.87657	−0.201262
$372$	15.3043	0.793492
$373$	−10.1462	−0.525351	−0.262675	−	0.964884i	$-0.584605\pi$
$373$	−10.1462	−0.525351	−0.262675	+	0.964884i	$0.584605\pi$
$374$	5.05170	0.261217
$375$	−14.0178	−0.723874
$376$	2.15547	0.111160
$377$	19.2219	0.989977
$378$	5.40963	0.278242
$379$	−32.2965	−1.65896	−0.829480	−	0.558536i	$-0.811363\pi$
$379$	−32.2965	−1.65896	−0.829480	+	0.558536i	$0.811363\pi$
$380$	−6.26042	−0.321153
$381$	25.9653	1.33024
$382$	−15.4332	−0.789630
$383$	32.4325	1.65722	0.828612	−	0.559823i	$-0.189131\pi$
$383$	32.4325	1.65722	0.828612	+	0.559823i	$0.189131\pi$
$384$	−1.64919	−0.0841597
$385$	−4.10981	−0.209455
$386$	8.23611	0.419207
$387$	−1.11123	−0.0564869
$388$	−3.39096	−0.172150
$389$	−26.7262	−1.35507	−0.677537	−	0.735489i	$-0.736952\pi$
$389$	−26.7262	−1.35507	−0.677537	+	0.735489i	$0.736952\pi$
$390$	−5.12781	−0.259657
$391$	9.83417	0.497335
$392$	−1.00000	−0.0505076
$393$	−15.1296	−0.763188
$394$	10.1682	0.512267
$395$	−1.67037	−0.0840456
$396$	1.23742	0.0621827
$397$	−1.22114	−0.0612873	−0.0306437	−	0.999530i	$-0.509756\pi$
$397$	−1.22114	−0.0612873	−0.0306437	+	0.999530i	$0.509756\pi$
$398$	5.76669	0.289058
$399$	−11.0950	−0.555447
$400$	−4.13406	−0.206703
$401$	8.11646	0.405317	0.202658	−	0.979249i	$-0.435042\pi$
$401$	8.11646	0.405317	0.202658	+	0.979249i	$0.435042\pi$
$402$	−14.6864	−0.732491
$403$	31.0071	1.54457
$404$	−5.14556	−0.256001
$405$	−7.51982	−0.373663
$406$	−5.75279	−0.285506
$407$	24.6187	1.22030
$408$	−1.88639	−0.0933902
$409$	22.2576	1.10057	0.550283	−	0.834978i	$-0.314520\pi$
$409$	22.2576	1.10057	0.550283	+	0.834978i	$0.314520\pi$
$410$	−7.41295	−0.366099
$411$	28.9032	1.42569
$412$	−2.45821	−0.121108
$413$	−0.164364	−0.00808784
$414$	2.40889	0.118390
$415$	14.7245	0.722797
$416$	−3.34131	−0.163821
$417$	8.26507	0.404742
$418$	−29.7122	−1.45327
$419$	32.3057	1.57824	0.789119	−	0.614240i	$-0.210537\pi$
$419$	32.3057	1.57824	0.789119	+	0.614240i	$0.210537\pi$
$420$	1.53467	0.0748842
$421$	2.61466	0.127431	0.0637154	−	0.997968i	$-0.479705\pi$
$421$	2.61466	0.127431	0.0637154	+	0.997968i	$0.479705\pi$
$422$	−13.0518	−0.635353
$423$	0.603925	0.0293638
$424$	3.87657	0.188263
$425$	−4.72866	−0.229373
$426$	18.4537	0.894086
$427$	4.35568	0.210786
$428$	6.83841	0.330547
$429$	−24.3368	−1.17499
$430$	−3.69069	−0.177981
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−5.40963	−0.260271
$433$	17.1126	0.822378	0.411189	−	0.911550i	$-0.365114\pi$
$433$	17.1126	0.822378	0.411189	+	0.911550i	$0.365114\pi$
$434$	−9.27992	−0.445450
$435$	8.82864	0.423301
$436$	5.28935	0.253314
$437$	−57.8409	−2.76691
$438$	−20.7884	−0.993308
$439$	−12.7514	−0.608593	−0.304296	−	0.952577i	$-0.598421\pi$
$439$	−12.7514	−0.608593	−0.304296	+	0.952577i	$0.598421\pi$
$440$	4.10981	0.195927
$441$	−0.280182	−0.0133420
$442$	−3.82189	−0.181789
$443$	22.3862	1.06360	0.531801	−	0.846869i	$-0.321515\pi$
$443$	22.3862	1.06360	0.531801	+	0.846869i	$0.321515\pi$
$444$	−9.19303	−0.436282
$445$	5.80912	0.275379
$446$	−6.55218	−0.310255
$447$	14.1926	0.671286
$448$	1.00000	0.0472456
$449$	−0.814941	−0.0384595	−0.0192297	−	0.999815i	$-0.506121\pi$
$449$	−0.814941	−0.0384595	−0.0192297	+	0.999815i	$0.506121\pi$
$450$	−1.15829	−0.0546023
$451$	−35.1822	−1.65666
$452$	−1.53580	−0.0722379
$453$	−14.8912	−0.699649
$454$	−0.101466	−0.00476202
$455$	3.10929	0.145766
$456$	11.0950	0.519573
$457$	−33.2927	−1.55737	−0.778684	−	0.627416i	$-0.784113\pi$
$457$	−33.2927	−1.55737	−0.778684	+	0.627416i	$0.784113\pi$
$458$	4.87298	0.227699
$459$	−6.18770	−0.288817
$460$	8.00057	0.373029
$461$	−1.99185	−0.0927699	−0.0463850	−	0.998924i	$-0.514770\pi$
$461$	−1.99185	−0.0927699	−0.0463850	+	0.998924i	$0.514770\pi$
$462$	7.28361	0.338864
$463$	6.28185	0.291942	0.145971	−	0.989289i	$-0.453369\pi$
$463$	6.28185	0.291942	0.145971	+	0.989289i	$0.453369\pi$
$464$	5.75279	0.267067
$465$	14.2416	0.660439
$466$	27.4717	1.27260
$467$	−7.19566	−0.332975	−0.166488	−	0.986044i	$-0.553243\pi$
$467$	−7.19566	−0.332975	−0.166488	+	0.986044i	$0.553243\pi$
$468$	−0.936175	−0.0432747
$469$	8.90523	0.411205
$470$	2.00580	0.0925206
$471$	17.9173	0.825586
$472$	0.164364	0.00756548
$473$	−17.5162	−0.805394
$474$	2.96032	0.135972
$475$	27.8122	1.27611
$476$	1.14383	0.0524273
$477$	1.08615	0.0497313
$478$	−23.9533	−1.09560
$479$	13.0364	0.595650	0.297825	−	0.954621i	$-0.403739\pi$
$479$	13.0364	0.595650	0.297825	+	0.954621i	$0.403739\pi$
$480$	−1.53467	−0.0700478
$481$	−18.6254	−0.849245
$482$	−3.50470	−0.159634
$483$	14.1790	0.645168
$484$	8.50533	0.386606
$485$	−3.15550	−0.143284
$486$	−2.90190	−0.131633
$487$	−8.39568	−0.380445	−0.190222	−	0.981741i	$-0.560921\pi$
$487$	−8.39568	−0.380445	−0.190222	+	0.981741i	$0.560921\pi$
$488$	−4.35568	−0.197172
$489$	14.3203	0.647586
$490$	−0.930561	−0.0420385
$491$	−38.6407	−1.74383	−0.871914	−	0.489659i	$-0.837121\pi$
$491$	−38.6407	−1.74383	−0.871914	+	0.489659i	$0.837121\pi$
$492$	13.1376	0.592288
$493$	6.58022	0.296358
$494$	22.4789	1.01137
$495$	1.15150	0.0517559
$496$	9.27992	0.416681
$497$	−11.1896	−0.501922
$498$	−26.0955	−1.16937
$499$	−14.7496	−0.660283	−0.330142	−	0.943931i	$-0.607097\pi$
$499$	−14.7496	−0.660283	−0.330142	+	0.943931i	$0.607097\pi$
$500$	−8.49980	−0.380123
$501$	39.4107	1.76074
$502$	−12.3581	−0.551567
$503$	7.97068	0.355395	0.177697	−	0.984085i	$-0.443135\pi$
$503$	7.97068	0.355395	0.177697	+	0.984085i	$0.443135\pi$
$504$	0.280182	0.0124803
$505$	−4.78826	−0.213075
$506$	37.9711	1.68802
$507$	−3.02733	−0.134448
$508$	15.7443	0.698542
$509$	14.1632	0.627773	0.313886	−	0.949461i	$-0.398369\pi$
$509$	14.1632	0.627773	0.313886	+	0.949461i	$0.398369\pi$
$510$	−1.75540	−0.0777304
$511$	12.6052	0.557623
$512$	−1.00000	−0.0441942
$513$	36.3937	1.60682
$514$	−20.9473	−0.923946
$515$	−2.28752	−0.100800
$516$	6.54082	0.287944
$517$	9.51961	0.418672
$518$	5.57428	0.244920
$519$	13.0898	0.574580
$520$	−3.10929	−0.136352
$521$	35.4653	1.55376	0.776882	−	0.629647i	$-0.216800\pi$
$521$	35.4653	1.55376	0.776882	+	0.629647i	$0.216800\pi$
$522$	1.61183	0.0705479
$523$	−27.2023	−1.18947	−0.594737	−	0.803920i	$-0.702744\pi$
$523$	−27.2023	−1.18947	−0.594737	+	0.803920i	$0.702744\pi$
$524$	−9.17398	−0.400767
$525$	−6.81783	−0.297555
$526$	−26.3883	−1.15058
$527$	10.6146	0.462381
$528$	−7.28361	−0.316978
$529$	50.9184	2.21384
$530$	3.60739	0.156695
$531$	0.0460519	0.00199848
$532$	−6.72758	−0.291678
$533$	26.6172	1.15292
$534$	−10.2952	−0.445518
$535$	6.36356	0.275121
$536$	−8.90523	−0.384647
$537$	23.1366	0.998419
$538$	20.4308	0.880835
$539$	−4.41648	−0.190231
$540$	−5.03400	−0.216629
$541$	−38.4867	−1.65467	−0.827335	−	0.561708i	$-0.810144\pi$
$541$	−38.4867	−1.65467	−0.827335	+	0.561708i	$0.810144\pi$
$542$	17.2645	0.741575
$543$	−36.8401	−1.58096
$544$	−1.14383	−0.0490413
$545$	4.92207	0.210838
$546$	−5.51045	−0.235825
$547$	25.8457	1.10508	0.552542	−	0.833485i	$-0.313658\pi$
$547$	25.8457	1.10508	0.552542	+	0.833485i	$0.313658\pi$
$548$	17.5257	0.748662
$549$	−1.22038	−0.0520847
$550$	−18.2580	−0.778523
$551$	−38.7024	−1.64878
$552$	−14.1790	−0.603499
$553$	−1.79502	−0.0763319
$554$	4.18231	0.177689
$555$	−8.55468	−0.363126
$556$	5.01160	0.212539
$557$	30.4953	1.29213	0.646064	−	0.763283i	$-0.276414\pi$
$557$	30.4953	1.29213	0.646064	+	0.763283i	$0.276414\pi$
$558$	2.60007	0.110070
$559$	13.2519	0.560497
$560$	0.930561	0.0393234
$561$	−8.33121	−0.351744
$562$	23.2379	0.980230
$563$	−19.7672	−0.833088	−0.416544	−	0.909115i	$-0.636759\pi$
$563$	−19.7672	−0.833088	−0.416544	+	0.909115i	$0.636759\pi$
$564$	−3.55478	−0.149683
$565$	−1.42915	−0.0601250
$566$	12.1476	0.510601
$567$	−8.08095	−0.339368
$568$	11.1896	0.469505
$569$	−16.3907	−0.687134	−0.343567	−	0.939128i	$-0.611635\pi$
$569$	−16.3907	−0.687134	−0.343567	+	0.939128i	$0.611635\pi$
$570$	10.3246	0.432450
$571$	−37.1456	−1.55449	−0.777247	−	0.629195i	$-0.783385\pi$
$571$	−37.1456	−1.55449	−0.777247	+	0.629195i	$0.783385\pi$
$572$	−14.7568	−0.617014
$573$	25.4522	1.06328
$574$	−7.96610	−0.332499
$575$	−35.5429	−1.48224
$576$	−0.280182	−0.0116743
$577$	22.5586	0.939128	0.469564	−	0.882898i	$-0.344411\pi$
$577$	22.5586	0.939128	0.469564	+	0.882898i	$0.344411\pi$
$578$	15.6917	0.652687
$579$	−13.5829	−0.564485
$580$	5.35333	0.222285
$581$	15.8232	0.656459
$582$	5.59233	0.231809
$583$	17.1208	0.709072
$584$	−12.6052	−0.521609
$585$	−0.871169	−0.0360184
$586$	−22.1442	−0.914768
$587$	−13.8548	−0.571849	−0.285925	−	0.958252i	$-0.592301\pi$
$587$	−13.8548	−0.571849	−0.285925	+	0.958252i	$0.592301\pi$
$588$	1.64919	0.0680113
$589$	−62.4314	−2.57244
$590$	0.152951	0.00629689
$591$	−16.7693	−0.689797
$592$	−5.57428	−0.229101
$593$	17.0613	0.700622	0.350311	−	0.936633i	$-0.386076\pi$
$593$	17.0613	0.700622	0.350311	+	0.936633i	$0.386076\pi$
$594$	−23.8916	−0.980283
$595$	1.06440	0.0436363
$596$	8.60580	0.352507
$597$	−9.51035	−0.389233
$598$	−28.7272	−1.17474
$599$	−22.9938	−0.939501	−0.469751	−	0.882799i	$-0.655656\pi$
$599$	−22.9938	−0.939501	−0.469751	+	0.882799i	$0.655656\pi$
$600$	6.81783	0.278337
$601$	−11.2700	−0.459714	−0.229857	−	0.973224i	$-0.573826\pi$
$601$	−11.2700	−0.459714	−0.229857	+	0.973224i	$0.573826\pi$
$602$	−3.96609	−0.161646
$603$	−2.49509	−0.101608
$604$	−9.02941	−0.367401
$605$	7.91473	0.321779
$606$	8.48600	0.344720
$607$	−37.3492	−1.51596	−0.757978	−	0.652280i	$-0.773813\pi$
$607$	−37.3492	−1.51596	−0.757978	+	0.652280i	$0.773813\pi$
$608$	6.72758	0.272839
$609$	9.48743	0.384450
$610$	−4.05323	−0.164110
$611$	−7.20210	−0.291366
$612$	−0.320481	−0.0129547
$613$	−46.5833	−1.88148	−0.940741	−	0.339125i	$-0.889869\pi$
$613$	−46.5833	−1.88148	−0.940741	+	0.339125i	$0.889869\pi$
$614$	−12.4806	−0.503674
$615$	12.2253	0.492973
$616$	4.41648	0.177945
$617$	35.3391	1.42270	0.711348	−	0.702840i	$-0.248085\pi$
$617$	35.3391	1.42270	0.711348	+	0.702840i	$0.248085\pi$
$618$	4.05406	0.163078
$619$	1.21851	0.0489760	0.0244880	−	0.999700i	$-0.492204\pi$
$619$	1.21851	0.0489760	0.0244880	+	0.999700i	$0.492204\pi$
$620$	8.63554	0.346811
$621$	−46.5098	−1.86637
$622$	18.5507	0.743816
$623$	6.24260	0.250105
$624$	5.51045	0.220594
$625$	12.7607	0.510428
$626$	−8.23120	−0.328985
$627$	49.0010	1.95691
$628$	10.8643	0.433534
$629$	−6.37603	−0.254229
$630$	0.260727	0.0103876
$631$	−6.45220	−0.256858	−0.128429	−	0.991719i	$-0.540993\pi$
$631$	−6.45220	−0.256858	−0.128429	+	0.991719i	$0.540993\pi$
$632$	1.79502	0.0714019
$633$	21.5249	0.855538
$634$	14.1190	0.560735
$635$	14.6511	0.581410
$636$	−6.39320	−0.253507
$637$	3.34131	0.132388
$638$	25.4071	1.00588
$639$	3.13513	0.124024
$640$	−0.930561	−0.0367837
$641$	29.4452	1.16301	0.581507	−	0.813541i	$-0.302463\pi$
$641$	29.4452	1.16301	0.581507	+	0.813541i	$0.302463\pi$
$642$	−11.2778	−0.445100
$643$	12.5628	0.495428	0.247714	−	0.968833i	$-0.420321\pi$
$643$	12.5628	0.495428	0.247714	+	0.968833i	$0.420321\pi$
$644$	8.59758	0.338792
$645$	6.08664	0.239661
$646$	7.69520	0.302764
$647$	49.1117	1.93078	0.965390	−	0.260809i	$-0.0839893\pi$
$647$	49.1117	1.93078	0.965390	+	0.260809i	$0.0839893\pi$
$648$	8.08095	0.317450
$649$	0.725912	0.0284945
$650$	13.8132	0.541797
$651$	15.3043	0.599824
$652$	8.68325	0.340062
$653$	−3.39394	−0.132815	−0.0664075	−	0.997793i	$-0.521154\pi$
$653$	−3.39394	−0.132815	−0.0664075	+	0.997793i	$0.521154\pi$
$654$	−8.72314	−0.341102
$655$	−8.53695	−0.333566
$656$	7.96610	0.311024
$657$	−3.53176	−0.137787
$658$	2.15547	0.0840290
$659$	21.0664	0.820631	0.410316	−	0.911944i	$-0.365419\pi$
$659$	21.0664	0.820631	0.410316	+	0.911944i	$0.365419\pi$
$660$	−6.77784	−0.263827
$661$	17.5117	0.681125	0.340563	−	0.940222i	$-0.389382\pi$
$661$	17.5117	0.681125	0.340563	+	0.940222i	$0.389382\pi$
$662$	16.8198	0.653721
$663$	6.30301	0.244789
$664$	−15.8232	−0.614061
$665$	−6.26042	−0.242769
$666$	−1.56181	−0.0605191
$667$	49.4601	1.91510
$668$	23.8971	0.924605
$669$	10.8058	0.417775
$670$	−8.28686	−0.320149
$671$	−19.2368	−0.742628
$672$	−1.64919	−0.0636188
$673$	−3.51396	−0.135453	−0.0677266	−	0.997704i	$-0.521575\pi$
$673$	−3.51396	−0.135453	−0.0677266	+	0.997704i	$0.521575\pi$
$674$	18.5309	0.713782
$675$	22.3637	0.860780
$676$	−1.83565	−0.0706018
$677$	−10.7361	−0.412620	−0.206310	−	0.978487i	$-0.566146\pi$
$677$	−10.7361	−0.412620	−0.206310	+	0.978487i	$0.566146\pi$
$678$	2.53282	0.0972723
$679$	−3.39096	−0.130133
$680$	−1.06440	−0.0408180
$681$	0.167336	0.00641233
$682$	40.9846	1.56938
$683$	0.751768	0.0287656	0.0143828	−	0.999897i	$-0.495422\pi$
$683$	0.751768	0.0287656	0.0143828	+	0.999897i	$0.495422\pi$
$684$	1.88495	0.0720728
$685$	16.3088	0.623126
$686$	−1.00000	−0.0381802
$687$	−8.03645	−0.306610
$688$	3.96609	0.151206
$689$	−12.9528	−0.493464
$690$	−13.1944	−0.502304
$691$	−14.0773	−0.535526	−0.267763	−	0.963485i	$-0.586284\pi$
$691$	−14.0773	−0.535526	−0.267763	+	0.963485i	$0.586284\pi$
$692$	7.93714	0.301725
$693$	1.23742	0.0470057
$694$	26.7662	1.01603
$695$	4.66360	0.176901
$696$	−9.48743	−0.359620
$697$	9.11186	0.345136
$698$	−3.24445	−0.122804
$699$	−45.3060	−1.71363
$700$	−4.13406	−0.156253
$701$	−14.7077	−0.555501	−0.277751	−	0.960653i	$-0.589589\pi$
$701$	−14.7077	−0.555501	−0.277751	+	0.960653i	$0.589589\pi$
$702$	18.0753	0.682207
$703$	37.5014	1.41439
$704$	−4.41648	−0.166452
$705$	−3.30794	−0.124584
$706$	−9.27221	−0.348964
$707$	−5.14556	−0.193519
$708$	−0.271067	−0.0101873
$709$	−20.1214	−0.755676	−0.377838	−	0.925872i	$-0.623332\pi$
$709$	−20.1214	−0.755676	−0.377838	+	0.925872i	$0.623332\pi$
$710$	10.4126	0.390778
$711$	0.502932	0.0188614
$712$	−6.24260	−0.233951
$713$	79.7849	2.98797
$714$	−1.88639	−0.0705963
$715$	−13.7321	−0.513553
$716$	14.0291	0.524292
$717$	39.5035	1.47528
$718$	6.91995	0.258250
$719$	−44.2409	−1.64991	−0.824953	−	0.565202i	$-0.808798\pi$
$719$	−44.2409	−1.64991	−0.824953	+	0.565202i	$0.808798\pi$
$720$	−0.260727	−0.00971671
$721$	−2.45821	−0.0915487
$722$	−26.2603	−0.977308
$723$	5.77990	0.214957
$724$	−22.3384	−0.830198
$725$	−23.7824	−0.883255
$726$	−14.0269	−0.520586
$727$	35.1523	1.30373	0.651864	−	0.758336i	$-0.273987\pi$
$727$	35.1523	1.30373	0.651864	+	0.758336i	$0.273987\pi$
$728$	−3.34131	−0.123837
$729$	29.0286	1.07513
$730$	−11.7300	−0.434145
$731$	4.53653	0.167790
$732$	7.18333	0.265504
$733$	37.2288	1.37508	0.687538	−	0.726148i	$-0.258691\pi$
$733$	37.2288	1.37508	0.687538	+	0.726148i	$0.258691\pi$
$734$	2.40745	0.0888607
$735$	1.53467	0.0566071
$736$	−8.59758	−0.316911
$737$	−39.3298	−1.44873
$738$	2.23196	0.0821596
$739$	−14.9795	−0.551028	−0.275514	−	0.961297i	$-0.588848\pi$
$739$	−14.9795	−0.551028	−0.275514	+	0.961297i	$0.588848\pi$
$740$	−5.18721	−0.190686
$741$	−37.0720	−1.36187
$742$	3.87657	0.142314
$743$	45.4861	1.66872	0.834362	−	0.551217i	$-0.185836\pi$
$743$	45.4861	1.66872	0.834362	+	0.551217i	$0.185836\pi$
$744$	−15.3043	−0.561084
$745$	8.00822	0.293399
$746$	10.1462	0.371479
$747$	−4.43339	−0.162209
$748$	−5.05170	−0.184709
$749$	6.83841	0.249870
$750$	14.0178	0.511856
$751$	−4.86432	−0.177502	−0.0887508	−	0.996054i	$-0.528287\pi$
$751$	−4.86432	−0.177502	−0.0887508	+	0.996054i	$0.528287\pi$
$752$	−2.15547	−0.0786020
$753$	20.3807	0.742716
$754$	−19.2219	−0.700019
$755$	−8.40242	−0.305795
$756$	−5.40963	−0.196746
$757$	−2.28465	−0.0830370	−0.0415185	−	0.999138i	$-0.513220\pi$
$757$	−2.28465	−0.0830370	−0.0415185	+	0.999138i	$0.513220\pi$
$758$	32.2965	1.17306
$759$	−62.6214	−2.27301
$760$	6.26042	0.227089
$761$	−10.1724	−0.368749	−0.184374	−	0.982856i	$-0.559026\pi$
$761$	−10.1724	−0.368749	−0.184374	+	0.982856i	$0.559026\pi$
$762$	−25.9653	−0.940625
$763$	5.28935	0.191487
$764$	15.4332	0.558352
$765$	−0.298227	−0.0107824
$766$	−32.4325	−1.17183
$767$	−0.549192	−0.0198302
$768$	1.64919	0.0595099
$769$	19.1352	0.690032	0.345016	−	0.938597i	$-0.387874\pi$
$769$	19.1352	0.690032	0.345016	+	0.938597i	$0.387874\pi$
$770$	4.10981	0.148107
$771$	34.5460	1.24414
$772$	−8.23611	−0.296424
$773$	28.7644	1.03458	0.517292	−	0.855809i	$-0.326940\pi$
$773$	28.7644	1.03458	0.517292	+	0.855809i	$0.326940\pi$
$774$	1.11123	0.0399423
$775$	−38.3637	−1.37807
$776$	3.39096	0.121728
$777$	−9.19303	−0.329798
$778$	26.7262	0.958182
$779$	−53.5926	−1.92015
$780$	5.12781	0.183605
$781$	49.4187	1.76834
$782$	−9.83417	−0.351669
$783$	−31.1205	−1.11216
$784$	1.00000	0.0357143
$785$	10.1099	0.360838
$786$	15.1296	0.539655
$787$	4.89415	0.174458	0.0872289	−	0.996188i	$-0.472199\pi$
$787$	4.89415	0.174458	0.0872289	+	0.996188i	$0.472199\pi$
$788$	−10.1682	−0.362228
$789$	43.5192	1.54933
$790$	1.67037	0.0594292
$791$	−1.53580	−0.0546067
$792$	−1.23742	−0.0439698
$793$	14.5537	0.516816
$794$	1.22114	0.0433367
$795$	−5.94926	−0.210999
$796$	−5.76669	−0.204395
$797$	30.2882	1.07286	0.536432	−	0.843944i	$-0.319772\pi$
$797$	30.2882	1.07286	0.536432	+	0.843944i	$0.319772\pi$
$798$	11.0950	0.392760
$799$	−2.46549	−0.0872229
$800$	4.13406	0.146161
$801$	−1.74907	−0.0618002
$802$	−8.11646	−0.286602
$803$	−55.6709	−1.96458
$804$	14.6864	0.517949
$805$	8.00057	0.281983
$806$	−31.0071	−1.09218
$807$	−33.6942	−1.18609
$808$	5.14556	0.181020
$809$	−36.4894	−1.28290	−0.641449	−	0.767166i	$-0.721666\pi$
$809$	−36.4894	−1.28290	−0.641449	+	0.767166i	$0.721666\pi$
$810$	7.51982	0.264220
$811$	−46.6657	−1.63865	−0.819327	−	0.573326i	$-0.805653\pi$
$811$	−46.6657	−1.63865	−0.819327	+	0.573326i	$0.805653\pi$
$812$	5.75279	0.201883
$813$	−28.4724	−0.998571
$814$	−24.6187	−0.862886
$815$	8.08029	0.283040
$816$	1.88639	0.0660368
$817$	−26.6822	−0.933491
$818$	−22.2576	−0.778217
$819$	−0.936175	−0.0327126
$820$	7.41295	0.258871
$821$	40.8258	1.42483	0.712415	−	0.701758i	$-0.247601\pi$
$821$	40.8258	1.42483	0.712415	+	0.701758i	$0.247601\pi$
$822$	−28.9032	−1.00812
$823$	−31.8605	−1.11059	−0.555294	−	0.831654i	$-0.687394\pi$
$823$	−31.8605	−1.11059	−0.555294	+	0.831654i	$0.687394\pi$
$824$	2.45821	0.0856360
$825$	30.1108	1.04832
$826$	0.164364	0.00571896
$827$	37.9660	1.32021	0.660103	−	0.751175i	$-0.270513\pi$
$827$	37.9660	1.32021	0.660103	+	0.751175i	$0.270513\pi$
$828$	−2.40889	−0.0837147
$829$	17.4800	0.607105	0.303552	−	0.952815i	$-0.401827\pi$
$829$	17.4800	0.607105	0.303552	+	0.952815i	$0.401827\pi$
$830$	−14.7245	−0.511095
$831$	−6.89741	−0.239268
$832$	3.34131	0.115839
$833$	1.14383	0.0396313
$834$	−8.26507	−0.286196
$835$	22.2377	0.769567
$836$	29.7122	1.02762
$837$	−50.2010	−1.73520
$838$	−32.3057	−1.11598
$839$	40.2210	1.38858	0.694291	−	0.719694i	$-0.255718\pi$
$839$	40.2210	1.38858	0.694291	+	0.719694i	$0.255718\pi$
$840$	−1.53467	−0.0529511
$841$	4.09463	0.141194
$842$	−2.61466	−0.0901072
$843$	−38.3236	−1.31993
$844$	13.0518	0.449263
$845$	−1.70818	−0.0587633
$846$	−0.603925	−0.0207634
$847$	8.50533	0.292246
$848$	−3.87657	−0.133122
$849$	−20.0336	−0.687553
$850$	4.72866	0.162192
$851$	−47.9253	−1.64286
$852$	−18.4537	−0.632215
$853$	35.9998	1.23261	0.616305	−	0.787507i	$-0.288629\pi$
$853$	35.9998	1.23261	0.616305	+	0.787507i	$0.288629\pi$
$854$	−4.35568	−0.149048
$855$	1.75406	0.0599876
$856$	−6.83841	−0.233732
$857$	−53.6710	−1.83337	−0.916683	−	0.399614i	$-0.869144\pi$
$857$	−53.6710	−1.83337	−0.916683	+	0.399614i	$0.869144\pi$
$858$	24.3368	0.830844
$859$	46.7381	1.59468	0.797342	−	0.603528i	$-0.206239\pi$
$859$	46.7381	1.59468	0.797342	+	0.603528i	$0.206239\pi$
$860$	3.69069	0.125851
$861$	13.1376	0.447728
$862$	1.00000	0.0340601
$863$	0.893302	0.0304084	0.0152042	−	0.999884i	$-0.495160\pi$
$863$	0.893302	0.0304084	0.0152042	+	0.999884i	$0.495160\pi$
$864$	5.40963	0.184039
$865$	7.38600	0.251131
$866$	−17.1126	−0.581509
$867$	−25.8785	−0.878879
$868$	9.27992	0.314981
$869$	7.92766	0.268927
$870$	−8.82864	−0.299319
$871$	29.7551	1.00821
$872$	−5.28935	−0.179120
$873$	0.950087	0.0321556
$874$	57.8409	1.95650
$875$	−8.49980	−0.287346
$876$	20.7884	0.702375
$877$	−32.1463	−1.08550	−0.542751	−	0.839894i	$-0.682617\pi$
$877$	−32.1463	−1.08550	−0.542751	+	0.839894i	$0.682617\pi$
$878$	12.7514	0.430340
$879$	36.5199	1.23179
$880$	−4.10981	−0.138542
$881$	−17.7452	−0.597853	−0.298926	−	0.954276i	$-0.596628\pi$
$881$	−17.7452	−0.597853	−0.298926	+	0.954276i	$0.596628\pi$
$882$	0.280182	0.00943422
$883$	54.1451	1.82213	0.911063	−	0.412266i	$-0.135263\pi$
$883$	54.1451	1.82213	0.911063	+	0.412266i	$0.135263\pi$
$884$	3.82189	0.128544
$885$	−0.252245	−0.00847912
$886$	−22.3862	−0.752081
$887$	−30.9163	−1.03807	−0.519035	−	0.854753i	$-0.673708\pi$
$887$	−30.9163	−1.03807	−0.519035	+	0.854753i	$0.673708\pi$
$888$	9.19303	0.308498
$889$	15.7443	0.528048
$890$	−5.80912	−0.194722
$891$	35.6894	1.19564
$892$	6.55218	0.219383
$893$	14.5011	0.485261
$894$	−14.1926	−0.474671
$895$	13.0549	0.436379
$896$	−1.00000	−0.0334077
$897$	47.3765	1.58186
$898$	0.814941	0.0271949
$899$	53.3855	1.78051
$900$	1.15829	0.0386096
$901$	−4.43414	−0.147723
$902$	35.1822	1.17144
$903$	6.54082	0.217665
$904$	1.53580	0.0510799
$905$	−20.7872	−0.690990
$906$	14.8912	0.494726
$907$	−9.04523	−0.300342	−0.150171	−	0.988660i	$-0.547982\pi$
$907$	−9.04523	−0.300342	−0.150171	+	0.988660i	$0.547982\pi$
$908$	0.101466	0.00336726
$909$	1.44169	0.0478180
$910$	−3.10929	−0.103072
$911$	7.80935	0.258735	0.129368	−	0.991597i	$-0.458705\pi$
$911$	7.80935	0.258735	0.129368	+	0.991597i	$0.458705\pi$
$912$	−11.0950	−0.367393
$913$	−69.8831	−2.31279
$914$	33.2927	1.10123
$915$	6.68453	0.220984
$916$	−4.87298	−0.161008
$917$	−9.17398	−0.302952
$918$	6.18770	0.204225
$919$	−5.35707	−0.176713	−0.0883566	−	0.996089i	$-0.528162\pi$
$919$	−5.35707	−0.176713	−0.0883566	+	0.996089i	$0.528162\pi$
$920$	−8.00057	−0.263771
$921$	20.5828	0.678226
$922$	1.99185	0.0655982
$923$	−37.3879	−1.23064
$924$	−7.28361	−0.239613
$925$	23.0444	0.757695
$926$	−6.28185	−0.206434
$927$	0.688748	0.0226214
$928$	−5.75279	−0.188845
$929$	40.3285	1.32314	0.661568	−	0.749885i	$-0.269891\pi$
$929$	40.3285	1.32314	0.661568	+	0.749885i	$0.269891\pi$
$930$	−14.2416	−0.467001
$931$	−6.72758	−0.220488
$932$	−27.4717	−0.899866
$933$	−30.5936	−1.00159
$934$	7.19566	0.235449
$935$	−4.70092	−0.153737
$936$	0.936175	0.0305999
$937$	−26.1738	−0.855062	−0.427531	−	0.904001i	$-0.640616\pi$
$937$	−26.1738	−0.855062	−0.427531	+	0.904001i	$0.640616\pi$
$938$	−8.90523	−0.290766
$939$	13.5748	0.442997
$940$	−2.00580	−0.0654219
$941$	−59.7538	−1.94792	−0.973959	−	0.226726i	$-0.927198\pi$
$941$	−59.7538	−1.94792	−0.973959	+	0.226726i	$0.927198\pi$
$942$	−17.9173	−0.583777
$943$	68.4892	2.23032
$944$	−0.164364	−0.00534960
$945$	−5.03400	−0.163756
$946$	17.5162	0.569500
$947$	35.5387	1.15485	0.577426	−	0.816443i	$-0.304057\pi$
$947$	35.5387	1.15485	0.577426	+	0.816443i	$0.304057\pi$
$948$	−2.96032	−0.0961466
$949$	42.1180	1.36721
$950$	−27.8122	−0.902347
$951$	−23.2848	−0.755061
$952$	−1.14383	−0.0370717
$953$	−15.3238	−0.496387	−0.248193	−	0.968711i	$-0.579837\pi$
$953$	−15.3238	−0.496387	−0.248193	+	0.968711i	$0.579837\pi$
$954$	−1.08615	−0.0351653
$955$	14.3615	0.464728
$956$	23.9533	0.774705
$957$	−41.9011	−1.35447
$958$	−13.0364	−0.421188
$959$	17.5257	0.565935
$960$	1.53467	0.0495312
$961$	55.1169	1.77797
$962$	18.6254	0.600507
$963$	−1.91600	−0.0617422
$964$	3.50470	0.112879
$965$	−7.66421	−0.246719
$966$	−14.1790	−0.456202
$967$	16.9701	0.545722	0.272861	−	0.962054i	$-0.412030\pi$
$967$	16.9701	0.545722	0.272861	+	0.962054i	$0.412030\pi$
$968$	−8.50533	−0.273372
$969$	−12.6908	−0.407688
$970$	3.15550	0.101317
$971$	−52.7460	−1.69270	−0.846350	−	0.532627i	$-0.821205\pi$
$971$	−52.7460	−1.69270	−0.846350	+	0.532627i	$0.821205\pi$
$972$	2.90190	0.0930785
$973$	5.01160	0.160665
$974$	8.39568	0.269015
$975$	−22.7805	−0.729559
$976$	4.35568	0.139422
$977$	9.26925	0.296550	0.148275	−	0.988946i	$-0.452628\pi$
$977$	9.26925	0.296550	0.148275	+	0.988946i	$0.452628\pi$
$978$	−14.3203	−0.457913
$979$	−27.5703	−0.881152
$980$	0.930561	0.0297257
$981$	−1.48198	−0.0473161
$982$	38.6407	1.23307
$983$	−9.32103	−0.297295	−0.148647	−	0.988890i	$-0.547492\pi$
$983$	−9.32103	−0.297295	−0.148647	+	0.988890i	$0.547492\pi$
$984$	−13.1376	−0.418811
$985$	−9.46215	−0.301489
$986$	−6.58022	−0.209557
$987$	−3.55478	−0.113150
$988$	−22.4789	−0.715150
$989$	34.0988	1.08428
$990$	−1.15150	−0.0365969
$991$	24.9726	0.793282	0.396641	−	0.917974i	$-0.370176\pi$
$991$	24.9726	0.793282	0.396641	+	0.917974i	$0.370176\pi$
$992$	−9.27992	−0.294638
$993$	−27.7390	−0.880272
$994$	11.1896	0.354912
$995$	−5.36626	−0.170122
$996$	26.0955	0.826867
$997$	48.1336	1.52441	0.762204	−	0.647337i	$-0.224118\pi$
$997$	48.1336	1.52441	0.762204	+	0.647337i	$0.224118\pi$
$998$	14.7496	0.466891
$999$	30.1548	0.954056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.19	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.64919 q^{3} +1.00000 q^{4} +0.930561 q^{5} -1.64919 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.280182 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.64919 q^{3} +1.00000 q^{4} +0.930561 q^{5} -1.64919 q^{6} +1.00000 q^{7} -1.00000 q^{8} -0.280182 q^{9} -0.930561 q^{10} -4.41648 q^{11} +1.64919 q^{12} +3.34131 q^{13} -1.00000 q^{14} +1.53467 q^{15} +1.00000 q^{16} +1.14383 q^{17} +0.280182 q^{18} -6.72758 q^{19} +0.930561 q^{20} +1.64919 q^{21} +4.41648 q^{22} +8.59758 q^{23} -1.64919 q^{24} -4.13406 q^{25} -3.34131 q^{26} -5.40963 q^{27} +1.00000 q^{28} +5.75279 q^{29} -1.53467 q^{30} +9.27992 q^{31} -1.00000 q^{32} -7.28361 q^{33} -1.14383 q^{34} +0.930561 q^{35} -0.280182 q^{36} -5.57428 q^{37} +6.72758 q^{38} +5.51045 q^{39} -0.930561 q^{40} +7.96610 q^{41} -1.64919 q^{42} +3.96609 q^{43} -4.41648 q^{44} -0.260727 q^{45} -8.59758 q^{46} -2.15547 q^{47} +1.64919 q^{48} +1.00000 q^{49} +4.13406 q^{50} +1.88639 q^{51} +3.34131 q^{52} -3.87657 q^{53} +5.40963 q^{54} -4.10981 q^{55} -1.00000 q^{56} -11.0950 q^{57} -5.75279 q^{58} -0.164364 q^{59} +1.53467 q^{60} +4.35568 q^{61} -9.27992 q^{62} -0.280182 q^{63} +1.00000 q^{64} +3.10929 q^{65} +7.28361 q^{66} +8.90523 q^{67} +1.14383 q^{68} +14.1790 q^{69} -0.930561 q^{70} -11.1896 q^{71} +0.280182 q^{72} +12.6052 q^{73} +5.57428 q^{74} -6.81783 q^{75} -6.72758 q^{76} -4.41648 q^{77} -5.51045 q^{78} -1.79502 q^{79} +0.930561 q^{80} -8.08095 q^{81} -7.96610 q^{82} +15.8232 q^{83} +1.64919 q^{84} +1.06440 q^{85} -3.96609 q^{86} +9.48743 q^{87} +4.41648 q^{88} +6.24260 q^{89} +0.260727 q^{90} +3.34131 q^{91} +8.59758 q^{92} +15.3043 q^{93} +2.15547 q^{94} -6.26042 q^{95} -1.64919 q^{96} -3.39096 q^{97} -1.00000 q^{98} +1.23742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 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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