LMFDB - Embedded newform 4011.2.a.k.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.44666 q^{2} +1.00000 q^{3} +0.0928390 q^{4} +2.29705 q^{5} +1.44666 q^{6} +1.00000 q^{7} -2.75902 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.44666 q^{2} +1.00000 q^{3} +0.0928390 q^{4} +2.29705 q^{5} +1.44666 q^{6} +1.00000 q^{7} -2.75902 q^{8} +1.00000 q^{9} +3.32306 q^{10} -1.55059 q^{11} +0.0928390 q^{12} +6.79355 q^{13} +1.44666 q^{14} +2.29705 q^{15} -4.17706 q^{16} +0.345531 q^{17} +1.44666 q^{18} -2.91373 q^{19} +0.213255 q^{20} +1.00000 q^{21} -2.24319 q^{22} +1.63076 q^{23} -2.75902 q^{24} +0.276426 q^{25} +9.82798 q^{26} +1.00000 q^{27} +0.0928390 q^{28} -0.433560 q^{29} +3.32306 q^{30} +4.80690 q^{31} -0.524759 q^{32} -1.55059 q^{33} +0.499867 q^{34} +2.29705 q^{35} +0.0928390 q^{36} +10.0381 q^{37} -4.21520 q^{38} +6.79355 q^{39} -6.33761 q^{40} +3.90936 q^{41} +1.44666 q^{42} +1.20993 q^{43} -0.143955 q^{44} +2.29705 q^{45} +2.35916 q^{46} -0.954438 q^{47} -4.17706 q^{48} +1.00000 q^{49} +0.399895 q^{50} +0.345531 q^{51} +0.630706 q^{52} +8.65047 q^{53} +1.44666 q^{54} -3.56178 q^{55} -2.75902 q^{56} -2.91373 q^{57} -0.627216 q^{58} +8.57590 q^{59} +0.213255 q^{60} -11.7313 q^{61} +6.95397 q^{62} +1.00000 q^{63} +7.59497 q^{64} +15.6051 q^{65} -2.24319 q^{66} -4.10150 q^{67} +0.0320787 q^{68} +1.63076 q^{69} +3.32306 q^{70} +1.62313 q^{71} -2.75902 q^{72} -12.2835 q^{73} +14.5218 q^{74} +0.276426 q^{75} -0.270508 q^{76} -1.55059 q^{77} +9.82798 q^{78} +12.3790 q^{79} -9.59490 q^{80} +1.00000 q^{81} +5.65554 q^{82} -6.27329 q^{83} +0.0928390 q^{84} +0.793701 q^{85} +1.75036 q^{86} -0.433560 q^{87} +4.27812 q^{88} -8.34020 q^{89} +3.32306 q^{90} +6.79355 q^{91} +0.151398 q^{92} +4.80690 q^{93} -1.38075 q^{94} -6.69298 q^{95} -0.524759 q^{96} -2.81227 q^{97} +1.44666 q^{98} -1.55059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.44666	1.02295	0.511473	−	0.859299i	$-0.329100\pi$
$2$	1.44666	1.02295	0.511473	+	0.859299i	$0.329100\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0928390	0.0464195
$5$	2.29705	1.02727	0.513635	−	0.858009i	$-0.328298\pi$
$5$	2.29705	1.02727	0.513635	+	0.858009i	$0.328298\pi$
$6$	1.44666	0.590598
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.75902	−0.975462
$9$	1.00000	0.333333
$10$	3.32306	1.05084
$11$	−1.55059	−0.467521	−0.233761	−	0.972294i	$-0.575103\pi$
$11$	−1.55059	−0.467521	−0.233761	+	0.972294i	$0.575103\pi$
$12$	0.0928390	0.0268003
$13$	6.79355	1.88419	0.942095	−	0.335346i	$-0.108853\pi$
$13$	6.79355	1.88419	0.942095	+	0.335346i	$0.108853\pi$
$14$	1.44666	0.386637
$15$	2.29705	0.593095
$16$	−4.17706	−1.04426
$17$	0.345531	0.0838036	0.0419018	−	0.999122i	$-0.486658\pi$
$17$	0.345531	0.0838036	0.0419018	+	0.999122i	$0.486658\pi$
$18$	1.44666	0.340982
$19$	−2.91373	−0.668456	−0.334228	−	0.942492i	$-0.608476\pi$
$19$	−2.91373	−0.668456	−0.334228	+	0.942492i	$0.608476\pi$
$20$	0.213255	0.0476854
$21$	1.00000	0.218218
$22$	−2.24319	−0.478249
$23$	1.63076	0.340036	0.170018	−	0.985441i	$-0.445617\pi$
$23$	1.63076	0.340036	0.170018	+	0.985441i	$0.445617\pi$
$24$	−2.75902	−0.563183
$25$	0.276426	0.0552851
$26$	9.82798	1.92743
$27$	1.00000	0.192450
$28$	0.0928390	0.0175449
$29$	−0.433560	−0.0805101	−0.0402551	−	0.999189i	$-0.512817\pi$
$29$	−0.433560	−0.0805101	−0.0402551	+	0.999189i	$0.512817\pi$
$30$	3.32306	0.606704
$31$	4.80690	0.863344	0.431672	−	0.902031i	$-0.357924\pi$
$31$	4.80690	0.863344	0.431672	+	0.902031i	$0.357924\pi$
$32$	−0.524759	−0.0927651
$33$	−1.55059	−0.269924
$34$	0.499867	0.0857265
$35$	2.29705	0.388272
$36$	0.0928390	0.0154732
$37$	10.0381	1.65026	0.825130	−	0.564943i	$-0.191102\pi$
$37$	10.0381	1.65026	0.825130	+	0.564943i	$0.191102\pi$
$38$	−4.21520	−0.683795
$39$	6.79355	1.08784
$40$	−6.33761	−1.00206
$41$	3.90936	0.610540	0.305270	−	0.952266i	$-0.401253\pi$
$41$	3.90936	0.610540	0.305270	+	0.952266i	$0.401253\pi$
$42$	1.44666	0.223225
$43$	1.20993	0.184512	0.0922560	−	0.995735i	$-0.470592\pi$
$43$	1.20993	0.184512	0.0922560	+	0.995735i	$0.470592\pi$
$44$	−0.143955	−0.0217021
$45$	2.29705	0.342424
$46$	2.35916	0.347839
$47$	−0.954438	−0.139219	−0.0696095	−	0.997574i	$-0.522175\pi$
$47$	−0.954438	−0.139219	−0.0696095	+	0.997574i	$0.522175\pi$
$48$	−4.17706	−0.602907
$49$	1.00000	0.142857
$50$	0.399895	0.0565537
$51$	0.345531	0.0483840
$52$	0.630706	0.0874631
$53$	8.65047	1.18823	0.594117	−	0.804379i	$-0.297502\pi$
$53$	8.65047	1.18823	0.594117	+	0.804379i	$0.297502\pi$
$54$	1.44666	0.196866
$55$	−3.56178	−0.480271
$56$	−2.75902	−0.368690
$57$	−2.91373	−0.385933
$58$	−0.627216	−0.0823575
$59$	8.57590	1.11649	0.558244	−	0.829677i	$-0.311475\pi$
$59$	8.57590	1.11649	0.558244	+	0.829677i	$0.311475\pi$
$60$	0.213255	0.0275312
$61$	−11.7313	−1.50204	−0.751018	−	0.660282i	$-0.770437\pi$
$61$	−11.7313	−1.50204	−0.751018	+	0.660282i	$0.770437\pi$
$62$	6.95397	0.883155
$63$	1.00000	0.125988
$64$	7.59497	0.949371
$65$	15.6051	1.93557
$66$	−2.24319	−0.276117
$67$	−4.10150	−0.501078	−0.250539	−	0.968106i	$-0.580608\pi$
$67$	−4.10150	−0.501078	−0.250539	+	0.968106i	$0.580608\pi$
$68$	0.0320787	0.00389012
$69$	1.63076	0.196320
$70$	3.32306	0.397181
$71$	1.62313	0.192630	0.0963150	−	0.995351i	$-0.469294\pi$
$71$	1.62313	0.192630	0.0963150	+	0.995351i	$0.469294\pi$
$72$	−2.75902	−0.325154
$73$	−12.2835	−1.43767	−0.718836	−	0.695180i	$-0.755325\pi$
$73$	−12.2835	−1.43767	−0.718836	+	0.695180i	$0.755325\pi$
$74$	14.5218	1.68813
$75$	0.276426	0.0319189
$76$	−0.270508	−0.0310294
$77$	−1.55059	−0.176706
$78$	9.82798	1.11280
$79$	12.3790	1.39275	0.696374	−	0.717679i	$-0.254796\pi$
$79$	12.3790	1.39275	0.696374	+	0.717679i	$0.254796\pi$
$80$	−9.59490	−1.07274
$81$	1.00000	0.111111
$82$	5.65554	0.624550
$83$	−6.27329	−0.688583	−0.344292	−	0.938863i	$-0.611881\pi$
$83$	−6.27329	−0.688583	−0.344292	+	0.938863i	$0.611881\pi$
$84$	0.0928390	0.0101296
$85$	0.793701	0.0860889
$86$	1.75036	0.188746
$87$	−0.433560	−0.0464825
$88$	4.27812	0.456049
$89$	−8.34020	−0.884059	−0.442029	−	0.897001i	$-0.645741\pi$
$89$	−8.34020	−0.884059	−0.442029	+	0.897001i	$0.645741\pi$
$90$	3.32306	0.350281
$91$	6.79355	0.712157
$92$	0.151398	0.0157843
$93$	4.80690	0.498452
$94$	−1.38075	−0.142414
$95$	−6.69298	−0.686686
$96$	−0.524759	−0.0535579
$97$	−2.81227	−0.285543	−0.142771	−	0.989756i	$-0.545601\pi$
$97$	−2.81227	−0.285543	−0.142771	+	0.989756i	$0.545601\pi$
$98$	1.44666	0.146135
$99$	−1.55059	−0.155840
$100$	0.0256631	0.00256631
$101$	14.8150	1.47415	0.737075	−	0.675811i	$-0.236207\pi$
$101$	14.8150	1.47415	0.737075	+	0.675811i	$0.236207\pi$
$102$	0.499867	0.0494942
$103$	0.0282793	0.00278644	0.00139322	−	0.999999i	$-0.499557\pi$
$103$	0.0282793	0.00278644	0.00139322	+	0.999999i	$0.499557\pi$
$104$	−18.7435	−1.83796
$105$	2.29705	0.224169
$106$	12.5143	1.21550
$107$	−11.4334	−1.10531	−0.552654	−	0.833411i	$-0.686385\pi$
$107$	−11.4334	−1.10531	−0.552654	+	0.833411i	$0.686385\pi$
$108$	0.0928390	0.00893343
$109$	−16.5721	−1.58732	−0.793661	−	0.608360i	$-0.791828\pi$
$109$	−16.5721	−1.58732	−0.793661	+	0.608360i	$0.791828\pi$
$110$	−5.15271	−0.491291
$111$	10.0381	0.952778
$112$	−4.17706	−0.394695
$113$	10.2026	0.959779	0.479889	−	0.877329i	$-0.340677\pi$
$113$	10.2026	0.959779	0.479889	+	0.877329i	$0.340677\pi$
$114$	−4.21520	−0.394789
$115$	3.74593	0.349309
$116$	−0.0402513	−0.00373724
$117$	6.79355	0.628063
$118$	12.4065	1.14211
$119$	0.345531	0.0316748
$120$	−6.33761	−0.578542
$121$	−8.59566	−0.781424
$122$	−16.9712	−1.53650
$123$	3.90936	0.352495
$124$	0.446267	0.0400760
$125$	−10.8503	−0.970478
$126$	1.44666	0.128879
$127$	−14.8559	−1.31825	−0.659124	−	0.752034i	$-0.729073\pi$
$127$	−14.8559	−1.31825	−0.659124	+	0.752034i	$0.729073\pi$
$128$	12.0369	1.06392
$129$	1.20993	0.106528
$130$	22.5753	1.97999
$131$	12.2275	1.06832	0.534160	−	0.845383i	$-0.320628\pi$
$131$	12.2275	1.06832	0.534160	+	0.845383i	$0.320628\pi$
$132$	−0.143955	−0.0125297
$133$	−2.91373	−0.252653
$134$	−5.93350	−0.512576
$135$	2.29705	0.197698
$136$	−0.953328	−0.0817472
$137$	21.9927	1.87896	0.939481	−	0.342602i	$-0.111308\pi$
$137$	21.9927	1.87896	0.939481	+	0.342602i	$0.111308\pi$
$138$	2.35916	0.200825
$139$	−2.56524	−0.217581	−0.108791	−	0.994065i	$-0.534698\pi$
$139$	−2.56524	−0.217581	−0.108791	+	0.994065i	$0.534698\pi$
$140$	0.213255	0.0180234
$141$	−0.954438	−0.0803782
$142$	2.34812	0.197050
$143$	−10.5340	−0.880899
$144$	−4.17706	−0.348088
$145$	−0.995908	−0.0827057
$146$	−17.7701	−1.47066
$147$	1.00000	0.0824786
$148$	0.931931	0.0766042
$149$	14.7479	1.20820	0.604099	−	0.796909i	$-0.293533\pi$
$149$	14.7479	1.20820	0.604099	+	0.796909i	$0.293533\pi$
$150$	0.399895	0.0326513
$151$	−16.7912	−1.36644	−0.683222	−	0.730210i	$-0.739422\pi$
$151$	−16.7912	−1.36644	−0.683222	+	0.730210i	$0.739422\pi$
$152$	8.03906	0.652054
$153$	0.345531	0.0279345
$154$	−2.24319	−0.180761
$155$	11.0417	0.886888
$156$	0.630706	0.0504969
$157$	15.4938	1.23654	0.618271	−	0.785965i	$-0.287833\pi$
$157$	15.4938	1.23654	0.618271	+	0.785965i	$0.287833\pi$
$158$	17.9083	1.42471
$159$	8.65047	0.686027
$160$	−1.20540	−0.0952949
$161$	1.63076	0.128522
$162$	1.44666	0.113661
$163$	−1.44414	−0.113114	−0.0565570	−	0.998399i	$-0.518012\pi$
$163$	−1.44414	−0.113114	−0.0565570	+	0.998399i	$0.518012\pi$
$164$	0.362941	0.0283410
$165$	−3.56178	−0.277285
$166$	−9.07535	−0.704384
$167$	−15.5979	−1.20700	−0.603500	−	0.797363i	$-0.706228\pi$
$167$	−15.5979	−1.20700	−0.603500	+	0.797363i	$0.706228\pi$
$168$	−2.75902	−0.212863
$169$	33.1523	2.55017
$170$	1.14822	0.0880644
$171$	−2.91373	−0.222819
$172$	0.112328	0.00856495
$173$	−11.7616	−0.894217	−0.447108	−	0.894480i	$-0.647546\pi$
$173$	−11.7616	−0.894217	−0.447108	+	0.894480i	$0.647546\pi$
$174$	−0.627216	−0.0475491
$175$	0.276426	0.0208958
$176$	6.47692	0.488216
$177$	8.57590	0.644604
$178$	−12.0655	−0.904345
$179$	14.0088	1.04706	0.523532	−	0.852006i	$-0.324614\pi$
$179$	14.0088	1.04706	0.523532	+	0.852006i	$0.324614\pi$
$180$	0.213255	0.0158951
$181$	−8.23660	−0.612222	−0.306111	−	0.951996i	$-0.599028\pi$
$181$	−8.23660	−0.612222	−0.306111	+	0.951996i	$0.599028\pi$
$182$	9.82798	0.728499
$183$	−11.7313	−0.867201
$184$	−4.49930	−0.331693
$185$	23.0581	1.69526
$186$	6.95397	0.509890
$187$	−0.535778	−0.0391799
$188$	−0.0886090	−0.00646248
$189$	1.00000	0.0727393
$190$	−9.68250	−0.702443
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	7.59497	0.548120
$193$	18.7391	1.34887	0.674434	−	0.738335i	$-0.264388\pi$
$193$	18.7391	1.34887	0.674434	+	0.738335i	$0.264388\pi$
$194$	−4.06841	−0.292095
$195$	15.6051	1.11750
$196$	0.0928390	0.00663136
$197$	−23.9515	−1.70648	−0.853238	−	0.521521i	$-0.825365\pi$
$197$	−23.9515	−1.70648	−0.853238	+	0.521521i	$0.825365\pi$
$198$	−2.24319	−0.159416
$199$	−11.1584	−0.790995	−0.395498	−	0.918467i	$-0.629428\pi$
$199$	−11.1584	−0.790995	−0.395498	+	0.918467i	$0.629428\pi$
$200$	−0.762665	−0.0539285
$201$	−4.10150	−0.289298
$202$	21.4324	1.50798
$203$	−0.433560	−0.0304300
$204$	0.0320787	0.00224596
$205$	8.97999	0.627190
$206$	0.0409106	0.00285038
$207$	1.63076	0.113345
$208$	−28.3770	−1.96759
$209$	4.51801	0.312518
$210$	3.32306	0.229313
$211$	−0.915953	−0.0630568	−0.0315284	−	0.999503i	$-0.510037\pi$
$211$	−0.915953	−0.0630568	−0.0315284	+	0.999503i	$0.510037\pi$
$212$	0.803101	0.0551572
$213$	1.62313	0.111215
$214$	−16.5403	−1.13067
$215$	2.77926	0.189544
$216$	−2.75902	−0.187728
$217$	4.80690	0.326313
$218$	−23.9743	−1.62375
$219$	−12.2835	−0.830040
$220$	−0.330672	−0.0222939
$221$	2.34738	0.157902
$222$	14.5218	0.974641
$223$	22.8614	1.53091	0.765457	−	0.643487i	$-0.222513\pi$
$223$	22.8614	1.53091	0.765457	+	0.643487i	$0.222513\pi$
$224$	−0.524759	−0.0350619
$225$	0.276426	0.0184284
$226$	14.7597	0.981802
$227$	−8.68001	−0.576113	−0.288056	−	0.957613i	$-0.593009\pi$
$227$	−8.68001	−0.576113	−0.288056	+	0.957613i	$0.593009\pi$
$228$	−0.270508	−0.0179148
$229$	24.6444	1.62855	0.814273	−	0.580482i	$-0.197136\pi$
$229$	24.6444	1.62855	0.814273	+	0.580482i	$0.197136\pi$
$230$	5.41910	0.357325
$231$	−1.55059	−0.102022
$232$	1.19620	0.0785345
$233$	−1.46332	−0.0958651	−0.0479325	−	0.998851i	$-0.515263\pi$
$233$	−1.46332	−0.0958651	−0.0479325	+	0.998851i	$0.515263\pi$
$234$	9.82798	0.642475
$235$	−2.19239	−0.143016
$236$	0.796178	0.0518268
$237$	12.3790	0.804103
$238$	0.499867	0.0324016
$239$	−10.9192	−0.706306	−0.353153	−	0.935566i	$-0.614890\pi$
$239$	−10.9192	−0.706306	−0.353153	+	0.935566i	$0.614890\pi$
$240$	−9.59490	−0.619348
$241$	−12.4088	−0.799323	−0.399662	−	0.916663i	$-0.630872\pi$
$241$	−12.4088	−0.799323	−0.399662	+	0.916663i	$0.630872\pi$
$242$	−12.4350	−0.799355
$243$	1.00000	0.0641500
$244$	−1.08912	−0.0697237
$245$	2.29705	0.146753
$246$	5.65554	0.360584
$247$	−19.7946	−1.25950
$248$	−13.2623	−0.842159
$249$	−6.27329	−0.397554
$250$	−15.6967	−0.992747
$251$	−14.7948	−0.933837	−0.466919	−	0.884300i	$-0.654636\pi$
$251$	−14.7948	−0.933837	−0.466919	+	0.884300i	$0.654636\pi$
$252$	0.0928390	0.00584831
$253$	−2.52864	−0.158974
$254$	−21.4915	−1.34850
$255$	0.793701	0.0497035
$256$	2.22341	0.138963
$257$	25.5928	1.59643	0.798216	−	0.602371i	$-0.205777\pi$
$257$	25.5928	1.59643	0.798216	+	0.602371i	$0.205777\pi$
$258$	1.75036	0.108973
$259$	10.0381	0.623740
$260$	1.44876	0.0898483
$261$	−0.433560	−0.0268367
$262$	17.6891	1.09283
$263$	−20.4041	−1.25817	−0.629085	−	0.777337i	$-0.716570\pi$
$263$	−20.4041	−1.25817	−0.629085	+	0.777337i	$0.716570\pi$
$264$	4.27812	0.263300
$265$	19.8705	1.22064
$266$	−4.21520	−0.258450
$267$	−8.34020	−0.510412
$268$	−0.380779	−0.0232598
$269$	−29.4425	−1.79514	−0.897571	−	0.440870i	$-0.854670\pi$
$269$	−29.4425	−1.79514	−0.897571	+	0.440870i	$0.854670\pi$
$270$	3.32306	0.202235
$271$	18.8066	1.14242	0.571208	−	0.820805i	$-0.306475\pi$
$271$	18.8066	1.14242	0.571208	+	0.820805i	$0.306475\pi$
$272$	−1.44330	−0.0875131
$273$	6.79355	0.411164
$274$	31.8160	1.92208
$275$	−0.428624	−0.0258470
$276$	0.151398	0.00911308
$277$	−6.94256	−0.417138	−0.208569	−	0.978008i	$-0.566881\pi$
$277$	−6.94256	−0.417138	−0.208569	+	0.978008i	$0.566881\pi$
$278$	−3.71105	−0.222574
$279$	4.80690	0.287781
$280$	−6.33761	−0.378744
$281$	−26.0632	−1.55480	−0.777400	−	0.629006i	$-0.783462\pi$
$281$	−26.0632	−1.55480	−0.777400	+	0.629006i	$0.783462\pi$
$282$	−1.38075	−0.0822225
$283$	−15.3703	−0.913672	−0.456836	−	0.889551i	$-0.651017\pi$
$283$	−15.3703	−0.913672	−0.456836	+	0.889551i	$0.651017\pi$
$284$	0.150690	0.00894179
$285$	−6.69298	−0.396458
$286$	−15.2392	−0.901113
$287$	3.90936	0.230762
$288$	−0.524759	−0.0309217
$289$	−16.8806	−0.992977
$290$	−1.44075	−0.0846035
$291$	−2.81227	−0.164858
$292$	−1.14039	−0.0667360
$293$	−7.52281	−0.439487	−0.219744	−	0.975558i	$-0.570522\pi$
$293$	−7.52281	−0.439487	−0.219744	+	0.975558i	$0.570522\pi$
$294$	1.44666	0.0843712
$295$	19.6993	1.14693
$296$	−27.6955	−1.60977
$297$	−1.55059	−0.0899745
$298$	21.3353	1.23592
$299$	11.0786	0.640693
$300$	0.0256631	0.00148166
$301$	1.20993	0.0697390
$302$	−24.2912	−1.39780
$303$	14.8150	0.851100
$304$	12.1708	0.698045
$305$	−26.9473	−1.54300
$306$	0.499867	0.0285755
$307$	−4.95308	−0.282687	−0.141344	−	0.989961i	$-0.545142\pi$
$307$	−4.95308	−0.282687	−0.141344	+	0.989961i	$0.545142\pi$
$308$	−0.143955	−0.00820262
$309$	0.0282793	0.00160875
$310$	15.9736	0.907239
$311$	−21.1289	−1.19811	−0.599056	−	0.800707i	$-0.704457\pi$
$311$	−21.1289	−1.19811	−0.599056	+	0.800707i	$0.704457\pi$
$312$	−18.7435	−1.06114
$313$	−1.72079	−0.0972647	−0.0486324	−	0.998817i	$-0.515486\pi$
$313$	−1.72079	−0.0972647	−0.0486324	+	0.998817i	$0.515486\pi$
$314$	22.4144	1.26492
$315$	2.29705	0.129424
$316$	1.14925	0.0646506
$317$	8.02561	0.450763	0.225382	−	0.974271i	$-0.427637\pi$
$317$	8.02561	0.450763	0.225382	+	0.974271i	$0.427637\pi$
$318$	12.5143	0.701769
$319$	0.672275	0.0376402
$320$	17.4460	0.975261
$321$	−11.4334	−0.638150
$322$	2.35916	0.131471
$323$	−1.00679	−0.0560190
$324$	0.0928390	0.00515772
$325$	1.87791	0.104168
$326$	−2.08919	−0.115710
$327$	−16.5721	−0.916441
$328$	−10.7860	−0.595559
$329$	−0.954438	−0.0526199
$330$	−5.15271	−0.283647
$331$	−0.781302	−0.0429442	−0.0214721	−	0.999769i	$-0.506835\pi$
$331$	−0.781302	−0.0429442	−0.0214721	+	0.999769i	$0.506835\pi$
$332$	−0.582406	−0.0319637
$333$	10.0381	0.550087
$334$	−22.5649	−1.23470
$335$	−9.42135	−0.514743
$336$	−4.17706	−0.227877
$337$	20.0272	1.09095	0.545474	−	0.838128i	$-0.316350\pi$
$337$	20.0272	1.09095	0.545474	+	0.838128i	$0.316350\pi$
$338$	47.9602	2.60869
$339$	10.2026	0.554129
$340$	0.0736864	0.00399620
$341$	−7.45354	−0.403632
$342$	−4.21520	−0.227932
$343$	1.00000	0.0539949
$344$	−3.33821	−0.179984
$345$	3.74593	0.201674
$346$	−17.0151	−0.914736
$347$	−8.94164	−0.480013	−0.240006	−	0.970771i	$-0.577150\pi$
$347$	−8.94164	−0.480013	−0.240006	+	0.970771i	$0.577150\pi$
$348$	−0.0402513	−0.00215770
$349$	−22.3913	−1.19858	−0.599290	−	0.800532i	$-0.704550\pi$
$349$	−22.3913	−1.19858	−0.599290	+	0.800532i	$0.704550\pi$
$350$	0.399895	0.0213753
$351$	6.79355	0.362613
$352$	0.813687	0.0433696
$353$	14.7335	0.784186	0.392093	−	0.919926i	$-0.371751\pi$
$353$	14.7335	0.784186	0.392093	+	0.919926i	$0.371751\pi$
$354$	12.4065	0.659396
$355$	3.72841	0.197883
$356$	−0.774295	−0.0410376
$357$	0.345531	0.0182874
$358$	20.2660	1.07109
$359$	−17.5946	−0.928608	−0.464304	−	0.885676i	$-0.653695\pi$
$359$	−17.5946	−0.928608	−0.464304	+	0.885676i	$0.653695\pi$
$360$	−6.33761	−0.334021
$361$	−10.5102	−0.553166
$362$	−11.9156	−0.626270
$363$	−8.59566	−0.451155
$364$	0.630706	0.0330580
$365$	−28.2157	−1.47688
$366$	−16.9712	−0.887100
$367$	−36.9088	−1.92662	−0.963312	−	0.268385i	$-0.913510\pi$
$367$	−36.9088	−1.92662	−0.963312	+	0.268385i	$0.913510\pi$
$368$	−6.81177	−0.355088
$369$	3.90936	0.203513
$370$	33.3573	1.73416
$371$	8.65047	0.449110
$372$	0.446267	0.0231379
$373$	20.1858	1.04518	0.522590	−	0.852584i	$-0.324966\pi$
$373$	20.1858	1.04518	0.522590	+	0.852584i	$0.324966\pi$
$374$	−0.775091	−0.0400790
$375$	−10.8503	−0.560306
$376$	2.63332	0.135803
$377$	−2.94541	−0.151696
$378$	1.44666	0.0744084
$379$	−24.8599	−1.27697	−0.638484	−	0.769635i	$-0.720438\pi$
$379$	−24.8599	−1.27697	−0.638484	+	0.769635i	$0.720438\pi$
$380$	−0.621370	−0.0318756
$381$	−14.8559	−0.761091
$382$	1.44666	0.0740178
$383$	8.95363	0.457509	0.228755	−	0.973484i	$-0.426535\pi$
$383$	8.95363	0.457509	0.228755	+	0.973484i	$0.426535\pi$
$384$	12.0369	0.614255
$385$	−3.56178	−0.181525
$386$	27.1092	1.37982
$387$	1.20993	0.0615040
$388$	−0.261088	−0.0132547
$389$	10.8380	0.549509	0.274754	−	0.961514i	$-0.411403\pi$
$389$	10.8380	0.549509	0.274754	+	0.961514i	$0.411403\pi$
$390$	22.5753	1.14315
$391$	0.563477	0.0284963
$392$	−2.75902	−0.139352
$393$	12.2275	0.616795
$394$	−34.6498	−1.74563
$395$	28.4352	1.43073
$396$	−0.143955	−0.00723403
$397$	20.1990	1.01376	0.506879	−	0.862017i	$-0.330799\pi$
$397$	20.1990	1.01376	0.506879	+	0.862017i	$0.330799\pi$
$398$	−16.1424	−0.809146
$399$	−2.91373	−0.145869
$400$	−1.15465	−0.0577323
$401$	27.3260	1.36459	0.682297	−	0.731075i	$-0.260981\pi$
$401$	27.3260	1.36459	0.682297	+	0.731075i	$0.260981\pi$
$402$	−5.93350	−0.295936
$403$	32.6559	1.62671
$404$	1.37541	0.0684292
$405$	2.29705	0.114141
$406$	−0.627216	−0.0311282
$407$	−15.5651	−0.771532
$408$	−0.953328	−0.0471967
$409$	−22.6663	−1.12077	−0.560387	−	0.828231i	$-0.689348\pi$
$409$	−22.6663	−1.12077	−0.560387	+	0.828231i	$0.689348\pi$
$410$	12.9910	0.641582
$411$	21.9927	1.08482
$412$	0.00262542	0.000129345 0
$413$	8.57590	0.421993
$414$	2.35916	0.115946
$415$	−14.4100	−0.707361
$416$	−3.56497	−0.174787
$417$	−2.56524	−0.125621
$418$	6.53605	0.319689
$419$	15.9350	0.778473	0.389237	−	0.921138i	$-0.372739\pi$
$419$	15.9350	0.778473	0.389237	+	0.921138i	$0.372739\pi$
$420$	0.213255	0.0104058
$421$	−31.8626	−1.55289	−0.776444	−	0.630186i	$-0.782979\pi$
$421$	−31.8626	−1.55289	−0.776444	+	0.630186i	$0.782979\pi$
$422$	−1.32508	−0.0645038
$423$	−0.954438	−0.0464063
$424$	−23.8668	−1.15908
$425$	0.0955136	0.00463309
$426$	2.34812	0.113767
$427$	−11.7313	−0.567716
$428$	−1.06146	−0.0513078
$429$	−10.5340	−0.508587
$430$	4.02065	0.193893
$431$	32.6221	1.57135	0.785676	−	0.618639i	$-0.212316\pi$
$431$	32.6221	1.57135	0.785676	+	0.618639i	$0.212316\pi$
$432$	−4.17706	−0.200969
$433$	32.6827	1.57063	0.785315	−	0.619097i	$-0.212501\pi$
$433$	32.6827	1.57063	0.785315	+	0.619097i	$0.212501\pi$
$434$	6.95397	0.333801
$435$	−0.995908	−0.0477501
$436$	−1.53854	−0.0736827
$437$	−4.75159	−0.227300
$438$	−17.7701	−0.849087
$439$	−34.1065	−1.62782	−0.813908	−	0.580994i	$-0.802664\pi$
$439$	−34.1065	−1.62782	−0.813908	+	0.580994i	$0.802664\pi$
$440$	9.82704	0.468486
$441$	1.00000	0.0476190
$442$	3.39587	0.161525
$443$	2.91445	0.138470	0.0692349	−	0.997600i	$-0.477944\pi$
$443$	2.91445	0.138470	0.0692349	+	0.997600i	$0.477944\pi$
$444$	0.931931	0.0442275
$445$	−19.1578	−0.908168
$446$	33.0728	1.56604
$447$	14.7479	0.697553
$448$	7.59497	0.358829
$449$	2.79471	0.131890	0.0659452	−	0.997823i	$-0.478994\pi$
$449$	2.79471	0.131890	0.0659452	+	0.997823i	$0.478994\pi$
$450$	0.399895	0.0188512
$451$	−6.06183	−0.285440
$452$	0.947198	0.0445524
$453$	−16.7912	−0.788917
$454$	−12.5571	−0.589332
$455$	15.6051	0.731578
$456$	8.03906	0.376463
$457$	20.3304	0.951017	0.475509	−	0.879711i	$-0.342264\pi$
$457$	20.3304	0.951017	0.475509	+	0.879711i	$0.342264\pi$
$458$	35.6522	1.66592
$459$	0.345531	0.0161280
$460$	0.347768	0.0162148
$461$	1.26859	0.0590840	0.0295420	−	0.999564i	$-0.490595\pi$
$461$	1.26859	0.0590840	0.0295420	+	0.999564i	$0.490595\pi$
$462$	−2.24319	−0.104363
$463$	−32.9303	−1.53040	−0.765201	−	0.643791i	$-0.777361\pi$
$463$	−32.9303	−1.53040	−0.765201	+	0.643791i	$0.777361\pi$
$464$	1.81101	0.0840739
$465$	11.0417	0.512045
$466$	−2.11693	−0.0980648
$467$	15.1577	0.701413	0.350707	−	0.936485i	$-0.385941\pi$
$467$	15.1577	0.701413	0.350707	+	0.936485i	$0.385941\pi$
$468$	0.630706	0.0291544
$469$	−4.10150	−0.189390
$470$	−3.17165	−0.146297
$471$	15.4938	0.713918
$472$	−23.6611	−1.08909
$473$	−1.87610	−0.0862633
$474$	17.9083	0.822555
$475$	−0.805431	−0.0369557
$476$	0.0320787	0.00147033
$477$	8.65047	0.396078
$478$	−15.7965	−0.722513
$479$	−16.4409	−0.751202	−0.375601	−	0.926782i	$-0.622564\pi$
$479$	−16.4409	−0.751202	−0.375601	+	0.926782i	$0.622564\pi$
$480$	−1.20540	−0.0550185
$481$	68.1946	3.10940
$482$	−17.9514	−0.817665
$483$	1.63076	0.0742020
$484$	−0.798012	−0.0362733
$485$	−6.45991	−0.293330
$486$	1.44666	0.0656220
$487$	33.8971	1.53603	0.768013	−	0.640435i	$-0.221246\pi$
$487$	33.8971	1.53603	0.768013	+	0.640435i	$0.221246\pi$
$488$	32.3668	1.46518
$489$	−1.44414	−0.0653065
$490$	3.32306	0.150120
$491$	−3.72768	−0.168228	−0.0841138	−	0.996456i	$-0.526806\pi$
$491$	−3.72768	−0.168228	−0.0841138	+	0.996456i	$0.526806\pi$
$492$	0.362941	0.0163627
$493$	−0.149808	−0.00674703
$494$	−28.6361	−1.28840
$495$	−3.56178	−0.160090
$496$	−20.0787	−0.901560
$497$	1.62313	0.0728073
$498$	−9.07535	−0.406676
$499$	−36.3993	−1.62946	−0.814728	−	0.579843i	$-0.803114\pi$
$499$	−36.3993	−1.62946	−0.814728	+	0.579843i	$0.803114\pi$
$500$	−1.00733	−0.0450491
$501$	−15.5979	−0.696862
$502$	−21.4031	−0.955266
$503$	1.33472	0.0595123	0.0297561	−	0.999557i	$-0.490527\pi$
$503$	1.33472	0.0595123	0.0297561	+	0.999557i	$0.490527\pi$
$504$	−2.75902	−0.122897
$505$	34.0308	1.51435
$506$	−3.65810	−0.162622
$507$	33.1523	1.47234
$508$	−1.37921	−0.0611924
$509$	19.9491	0.884229	0.442114	−	0.896959i	$-0.354229\pi$
$509$	19.9491	0.884229	0.442114	+	0.896959i	$0.354229\pi$
$510$	1.14822	0.0508440
$511$	−12.2835	−0.543389
$512$	−20.8573	−0.921769
$513$	−2.91373	−0.128644
$514$	37.0241	1.63306
$515$	0.0649588	0.00286243
$516$	0.112328	0.00494498
$517$	1.47994	0.0650879
$518$	14.5218	0.638052
$519$	−11.7616	−0.516276
$520$	−43.0548	−1.88808
$521$	−28.7820	−1.26096	−0.630481	−	0.776205i	$-0.717142\pi$
$521$	−28.7820	−1.26096	−0.630481	+	0.776205i	$0.717142\pi$
$522$	−0.627216	−0.0274525
$523$	−5.22368	−0.228416	−0.114208	−	0.993457i	$-0.536433\pi$
$523$	−5.22368	−0.228416	−0.114208	+	0.993457i	$0.536433\pi$
$524$	1.13519	0.0495909
$525$	0.276426	0.0120642
$526$	−29.5179	−1.28704
$527$	1.66093	0.0723513
$528$	6.47692	0.281872
$529$	−20.3406	−0.884375
$530$	28.7460	1.24865
$531$	8.57590	0.372162
$532$	−0.270508	−0.0117280
$533$	26.5584	1.15037
$534$	−12.0655	−0.522124
$535$	−26.2630	−1.13545
$536$	11.3161	0.488783
$537$	14.0088	0.604522
$538$	−42.5935	−1.83633
$539$	−1.55059	−0.0667888
$540$	0.213255	0.00917706
$541$	28.3102	1.21715	0.608576	−	0.793496i	$-0.291741\pi$
$541$	28.3102	1.21715	0.608576	+	0.793496i	$0.291741\pi$
$542$	27.2068	1.16863
$543$	−8.23660	−0.353466
$544$	−0.181320	−0.00777404
$545$	−38.0670	−1.63061
$546$	9.82798	0.420599
$547$	−11.7332	−0.501675	−0.250837	−	0.968029i	$-0.580706\pi$
$547$	−11.7332	−0.501675	−0.250837	+	0.968029i	$0.580706\pi$
$548$	2.04178	0.0872204
$549$	−11.7313	−0.500678
$550$	−0.620075	−0.0264401
$551$	1.26328	0.0538175
$552$	−4.49930	−0.191503
$553$	12.3790	0.526409
$554$	−10.0435	−0.426710
$555$	23.0581	0.978761
$556$	−0.238155	−0.0101000
$557$	−35.8122	−1.51741	−0.758706	−	0.651433i	$-0.774168\pi$
$557$	−35.8122	−1.51741	−0.758706	+	0.651433i	$0.774168\pi$
$558$	6.95397	0.294385
$559$	8.21969	0.347656
$560$	−9.59490	−0.405459
$561$	−0.535778	−0.0226205
$562$	−37.7047	−1.59048
$563$	−0.104672	−0.00441140	−0.00220570	−	0.999998i	$-0.500702\pi$
$563$	−0.104672	−0.00441140	−0.00220570	+	0.999998i	$0.500702\pi$
$564$	−0.0886090	−0.00373111
$565$	23.4358	0.985953
$566$	−22.2357	−0.934638
$567$	1.00000	0.0419961
$568$	−4.47825	−0.187903
$569$	42.9015	1.79853	0.899263	−	0.437408i	$-0.144103\pi$
$569$	42.9015	1.79853	0.899263	+	0.437408i	$0.144103\pi$
$570$	−9.68250	−0.405555
$571$	−16.0428	−0.671370	−0.335685	−	0.941974i	$-0.608968\pi$
$571$	−16.0428	−0.671370	−0.335685	+	0.941974i	$0.608968\pi$
$572$	−0.977968	−0.0408909
$573$	1.00000	0.0417756
$574$	5.65554	0.236058
$575$	0.450783	0.0187990
$576$	7.59497	0.316457
$577$	18.7902	0.782245	0.391122	−	0.920339i	$-0.372087\pi$
$577$	18.7902	0.782245	0.391122	+	0.920339i	$0.372087\pi$
$578$	−24.4206	−1.01576
$579$	18.7391	0.778770
$580$	−0.0924591	−0.00383916
$581$	−6.27329	−0.260260
$582$	−4.06841	−0.168641
$583$	−13.4134	−0.555524
$584$	33.8904	1.40239
$585$	15.6051	0.645191
$586$	−10.8830	−0.449572
$587$	32.2245	1.33005	0.665025	−	0.746821i	$-0.268421\pi$
$587$	32.2245	1.33005	0.665025	+	0.746821i	$0.268421\pi$
$588$	0.0928390	0.00382861
$589$	−14.0060	−0.577108
$590$	28.4982	1.17325
$591$	−23.9515	−0.985235
$592$	−41.9299	−1.72331
$593$	15.0250	0.617002	0.308501	−	0.951224i	$-0.400173\pi$
$593$	15.0250	0.617002	0.308501	+	0.951224i	$0.400173\pi$
$594$	−2.24319	−0.0920391
$595$	0.793701	0.0325386
$596$	1.36918	0.0560839
$597$	−11.1584	−0.456681
$598$	16.0271	0.655395
$599$	−34.1886	−1.39691	−0.698455	−	0.715654i	$-0.746129\pi$
$599$	−34.1886	−1.39691	−0.698455	+	0.715654i	$0.746129\pi$
$600$	−0.762665	−0.0311357
$601$	−30.8885	−1.25997	−0.629984	−	0.776608i	$-0.716939\pi$
$601$	−30.8885	−1.25997	−0.629984	+	0.776608i	$0.716939\pi$
$602$	1.75036	0.0713393
$603$	−4.10150	−0.167026
$604$	−1.55887	−0.0634297
$605$	−19.7446	−0.802734
$606$	21.4324	0.870630
$607$	6.23697	0.253151	0.126575	−	0.991957i	$-0.459601\pi$
$607$	6.23697	0.253151	0.126575	+	0.991957i	$0.459601\pi$
$608$	1.52901	0.0620094
$609$	−0.433560	−0.0175687
$610$	−38.9837	−1.57840
$611$	−6.48402	−0.262315
$612$	0.0320787	0.00129671
$613$	4.15130	0.167669	0.0838347	−	0.996480i	$-0.473283\pi$
$613$	4.15130	0.167669	0.0838347	+	0.996480i	$0.473283\pi$
$614$	−7.16545	−0.289174
$615$	8.97999	0.362108
$616$	4.27812	0.172370
$617$	−9.63513	−0.387896	−0.193948	−	0.981012i	$-0.562129\pi$
$617$	−9.63513	−0.387896	−0.193948	+	0.981012i	$0.562129\pi$
$618$	0.0409106	0.00164567
$619$	1.53316	0.0616231	0.0308115	−	0.999525i	$-0.490191\pi$
$619$	1.53316	0.0616231	0.0308115	+	0.999525i	$0.490191\pi$
$620$	1.02510	0.0411689
$621$	1.63076	0.0654400
$622$	−30.5665	−1.22560
$623$	−8.34020	−0.334143
$624$	−28.3770	−1.13599
$625$	−26.3057	−1.05223
$626$	−2.48940	−0.0994966
$627$	4.51801	0.180432
$628$	1.43843	0.0573997
$629$	3.46849	0.138298
$630$	3.32306	0.132394
$631$	−17.4677	−0.695378	−0.347689	−	0.937610i	$-0.613033\pi$
$631$	−17.4677	−0.695378	−0.347689	+	0.937610i	$0.613033\pi$
$632$	−34.1540	−1.35857
$633$	−0.915953	−0.0364059
$634$	11.6104	0.461107
$635$	−34.1247	−1.35420
$636$	0.803101	0.0318450
$637$	6.79355	0.269170
$638$	0.972557	0.0385039
$639$	1.62313	0.0642100
$640$	27.6493	1.09293
$641$	−39.1903	−1.54792	−0.773961	−	0.633233i	$-0.781728\pi$
$641$	−39.1903	−1.54792	−0.773961	+	0.633233i	$0.781728\pi$
$642$	−16.5403	−0.652793
$643$	−21.4359	−0.845350	−0.422675	−	0.906281i	$-0.638909\pi$
$643$	−21.4359	−0.845350	−0.422675	+	0.906281i	$0.638909\pi$
$644$	0.151398	0.00596591
$645$	2.77926	0.109433
$646$	−1.45648	−0.0573045
$647$	−13.1862	−0.518402	−0.259201	−	0.965823i	$-0.583459\pi$
$647$	−13.1862	−0.518402	−0.259201	+	0.965823i	$0.583459\pi$
$648$	−2.75902	−0.108385
$649$	−13.2977	−0.521982
$650$	2.71671	0.106558
$651$	4.80690	0.188397
$652$	−0.134073	−0.00525070
$653$	19.9558	0.780929	0.390465	−	0.920618i	$-0.372314\pi$
$653$	19.9558	0.780929	0.390465	+	0.920618i	$0.372314\pi$
$654$	−23.9743	−0.937470
$655$	28.0871	1.09745
$656$	−16.3296	−0.637565
$657$	−12.2835	−0.479224
$658$	−1.38075	−0.0538273
$659$	43.2563	1.68503	0.842514	−	0.538675i	$-0.181075\pi$
$659$	43.2563	1.68503	0.842514	+	0.538675i	$0.181075\pi$
$660$	−0.330672	−0.0128714
$661$	−35.3725	−1.37583	−0.687915	−	0.725791i	$-0.741474\pi$
$661$	−35.3725	−1.37583	−0.687915	+	0.725791i	$0.741474\pi$
$662$	−1.13028	−0.0439296
$663$	2.34738	0.0911647
$664$	17.3082	0.671687
$665$	−6.69298	−0.259543
$666$	14.5218	0.562709
$667$	−0.707032	−0.0273764
$668$	−1.44809	−0.0560283
$669$	22.8614	0.883874
$670$	−13.6295	−0.526555
$671$	18.1904	0.702234
$672$	−0.524759	−0.0202430
$673$	−38.9001	−1.49949	−0.749745	−	0.661727i	$-0.769824\pi$
$673$	−38.9001	−1.49949	−0.749745	+	0.661727i	$0.769824\pi$
$674$	28.9726	1.11598
$675$	0.276426	0.0106396
$676$	3.07782	0.118378
$677$	30.8945	1.18737	0.593687	−	0.804696i	$-0.297672\pi$
$677$	30.8945	1.18737	0.593687	+	0.804696i	$0.297672\pi$
$678$	14.7597	0.566844
$679$	−2.81227	−0.107925
$680$	−2.18984	−0.0839765
$681$	−8.68001	−0.332619
$682$	−10.7828	−0.412894
$683$	−16.6009	−0.635216	−0.317608	−	0.948222i	$-0.602880\pi$
$683$	−16.6009	−0.635216	−0.317608	+	0.948222i	$0.602880\pi$
$684$	−0.270508	−0.0103431
$685$	50.5182	1.93020
$686$	1.44666	0.0552339
$687$	24.6444	0.940242
$688$	−5.05393	−0.192679
$689$	58.7674	2.23886
$690$	5.41910	0.206302
$691$	−34.0092	−1.29377	−0.646886	−	0.762587i	$-0.723929\pi$
$691$	−34.0092	−1.29377	−0.646886	+	0.762587i	$0.723929\pi$
$692$	−1.09193	−0.0415091
$693$	−1.55059	−0.0589021
$694$	−12.9356	−0.491027
$695$	−5.89248	−0.223515
$696$	1.19620	0.0453419
$697$	1.35081	0.0511654
$698$	−32.3927	−1.22608
$699$	−1.46332	−0.0553477
$700$	0.0256631	0.000969973 0
$701$	−3.64060	−0.137504	−0.0687518	−	0.997634i	$-0.521902\pi$
$701$	−3.64060	−0.137504	−0.0687518	+	0.997634i	$0.521902\pi$
$702$	9.82798	0.370933
$703$	−29.2485	−1.10313
$704$	−11.7767	−0.443851
$705$	−2.19239	−0.0825701
$706$	21.3145	0.802180
$707$	14.8150	0.557176
$708$	0.796178	0.0299222
$709$	2.80080	0.105186	0.0525931	−	0.998616i	$-0.483251\pi$
$709$	2.80080	0.105186	0.0525931	+	0.998616i	$0.483251\pi$
$710$	5.39375	0.202424
$711$	12.3790	0.464249
$712$	23.0108	0.862366
$713$	7.83888	0.293569
$714$	0.499867	0.0187071
$715$	−24.1971	−0.904922
$716$	1.30056	0.0486042
$717$	−10.9192	−0.407786
$718$	−25.4535	−0.949916
$719$	33.2293	1.23924	0.619621	−	0.784901i	$-0.287286\pi$
$719$	33.2293	1.23924	0.619621	+	0.784901i	$0.287286\pi$
$720$	−9.59490	−0.357581
$721$	0.0282793	0.00105318
$722$	−15.2047	−0.565859
$723$	−12.4088	−0.461489
$724$	−0.764678	−0.0284190
$725$	−0.119847	−0.00445101
$726$	−12.4350	−0.461508
$727$	−39.2885	−1.45713	−0.728564	−	0.684978i	$-0.759812\pi$
$727$	−39.2885	−1.45713	−0.728564	+	0.684978i	$0.759812\pi$
$728$	−18.7435	−0.694682
$729$	1.00000	0.0370370
$730$	−40.8187	−1.51077
$731$	0.418067	0.0154628
$732$	−1.08912	−0.0402550
$733$	−27.9732	−1.03321	−0.516607	−	0.856222i	$-0.672805\pi$
$733$	−27.9732	−1.03321	−0.516607	+	0.856222i	$0.672805\pi$
$734$	−53.3947	−1.97083
$735$	2.29705	0.0847279
$736$	−0.855754	−0.0315435
$737$	6.35976	0.234265
$738$	5.65554	0.208183
$739$	−22.9280	−0.843420	−0.421710	−	0.906731i	$-0.638570\pi$
$739$	−22.9280	−0.843420	−0.421710	+	0.906731i	$0.638570\pi$
$740$	2.14069	0.0786933
$741$	−19.7946	−0.727172
$742$	12.5143	0.459416
$743$	41.4110	1.51922	0.759612	−	0.650376i	$-0.225389\pi$
$743$	41.4110	1.51922	0.759612	+	0.650376i	$0.225389\pi$
$744$	−13.2623	−0.486221
$745$	33.8767	1.24115
$746$	29.2021	1.06916
$747$	−6.27329	−0.229528
$748$	−0.0497410	−0.00181871
$749$	−11.4334	−0.417767
$750$	−15.6967	−0.573163
$751$	−39.3929	−1.43747	−0.718734	−	0.695285i	$-0.755278\pi$
$751$	−39.3929	−1.43747	−0.718734	+	0.695285i	$0.755278\pi$
$752$	3.98674	0.145382
$753$	−14.7948	−0.539151
$754$	−4.26102	−0.155177
$755$	−38.5701	−1.40371
$756$	0.0928390	0.00337652
$757$	−0.122445	−0.00445033	−0.00222516	−	0.999998i	$-0.500708\pi$
$757$	−0.122445	−0.00445033	−0.00222516	+	0.999998i	$0.500708\pi$
$758$	−35.9640	−1.30627
$759$	−2.52864	−0.0917838
$760$	18.4661	0.669836
$761$	−15.7519	−0.571005	−0.285502	−	0.958378i	$-0.592160\pi$
$761$	−15.7519	−0.571005	−0.285502	+	0.958378i	$0.592160\pi$
$762$	−21.4915	−0.778556
$763$	−16.5721	−0.599951
$764$	0.0928390	0.00335880
$765$	0.793701	0.0286963
$766$	12.9529	0.468007
$767$	58.2608	2.10367
$768$	2.22341	0.0802303
$769$	15.8435	0.571330	0.285665	−	0.958330i	$-0.407786\pi$
$769$	15.8435	0.571330	0.285665	+	0.958330i	$0.407786\pi$
$770$	−5.15271	−0.185691
$771$	25.5928	0.921701
$772$	1.73972	0.0626138
$773$	18.2105	0.654986	0.327493	−	0.944854i	$-0.393796\pi$
$773$	18.2105	0.654986	0.327493	+	0.944854i	$0.393796\pi$
$774$	1.75036	0.0629153
$775$	1.32875	0.0477301
$776$	7.75911	0.278536
$777$	10.0381	0.360116
$778$	15.6790	0.562118
$779$	−11.3908	−0.408119
$780$	1.44876	0.0518740
$781$	−2.51681	−0.0900586
$782$	0.815162	0.0291502
$783$	−0.433560	−0.0154942
$784$	−4.17706	−0.149181
$785$	35.5901	1.27026
$786$	17.6891	0.630948
$787$	16.5945	0.591530	0.295765	−	0.955261i	$-0.404426\pi$
$787$	16.5945	0.591530	0.295765	+	0.955261i	$0.404426\pi$
$788$	−2.22364	−0.0792138
$789$	−20.4041	−0.726404
$790$	41.1362	1.46356
$791$	10.2026	0.362762
$792$	4.27812	0.152016
$793$	−79.6969	−2.83012
$794$	29.2211	1.03702
$795$	19.8705	0.704735
$796$	−1.03593	−0.0367176
$797$	−10.6790	−0.378270	−0.189135	−	0.981951i	$-0.560568\pi$
$797$	−10.6790	−0.378270	−0.189135	+	0.981951i	$0.560568\pi$
$798$	−4.21520	−0.149216
$799$	−0.329788	−0.0116671
$800$	−0.145057	−0.00512853
$801$	−8.34020	−0.294686
$802$	39.5315	1.39591
$803$	19.0467	0.672142
$804$	−0.380779	−0.0134291
$805$	3.74593	0.132027
$806$	47.2421	1.66403
$807$	−29.4425	−1.03643
$808$	−40.8750	−1.43798
$809$	0.561890	0.0197550	0.00987750	−	0.999951i	$-0.496856\pi$
$809$	0.561890	0.0197550	0.00987750	+	0.999951i	$0.496856\pi$
$810$	3.32306	0.116760
$811$	32.4780	1.14046	0.570228	−	0.821486i	$-0.306855\pi$
$811$	32.4780	1.14046	0.570228	+	0.821486i	$0.306855\pi$
$812$	−0.0402513	−0.00141254
$813$	18.8066	0.659575
$814$	−22.5174	−0.789236
$815$	−3.31727	−0.116199
$816$	−1.44330	−0.0505257
$817$	−3.52540	−0.123338
$818$	−32.7905	−1.14649
$819$	6.79355	0.237386
$820$	0.833693	0.0291138
$821$	−51.9444	−1.81287	−0.906436	−	0.422343i	$-0.861208\pi$
$821$	−51.9444	−1.81287	−0.906436	+	0.422343i	$0.861208\pi$
$822$	31.8160	1.10971
$823$	52.9289	1.84499	0.922493	−	0.386013i	$-0.126148\pi$
$823$	52.9289	1.84499	0.922493	+	0.386013i	$0.126148\pi$
$824$	−0.0780232	−0.00271807
$825$	−0.428624	−0.0149228
$826$	12.4065	0.431676
$827$	−31.5022	−1.09544	−0.547719	−	0.836663i	$-0.684504\pi$
$827$	−31.5022	−1.09544	−0.547719	+	0.836663i	$0.684504\pi$
$828$	0.151398	0.00526144
$829$	12.3261	0.428102	0.214051	−	0.976822i	$-0.431334\pi$
$829$	12.3261	0.428102	0.214051	+	0.976822i	$0.431334\pi$
$830$	−20.8465	−0.723593
$831$	−6.94256	−0.240835
$832$	51.5968	1.78880
$833$	0.345531	0.0119719
$834$	−3.71105	−0.128503
$835$	−35.8291	−1.23992
$836$	0.419448	0.0145069
$837$	4.80690	0.166151
$838$	23.0525	0.796337
$839$	−2.55151	−0.0880880	−0.0440440	−	0.999030i	$-0.514024\pi$
$839$	−2.55151	−0.0880880	−0.0440440	+	0.999030i	$0.514024\pi$
$840$	−6.33761	−0.218668
$841$	−28.8120	−0.993518
$842$	−46.0945	−1.58852
$843$	−26.0632	−0.897664
$844$	−0.0850362	−0.00292707
$845$	76.1523	2.61972
$846$	−1.38075	−0.0474712
$847$	−8.59566	−0.295350
$848$	−36.1335	−1.24083
$849$	−15.3703	−0.527509
$850$	0.138176	0.00473940
$851$	16.3698	0.561149
$852$	0.150690	0.00516254
$853$	−23.2866	−0.797319	−0.398660	−	0.917099i	$-0.630525\pi$
$853$	−23.2866	−0.797319	−0.398660	+	0.917099i	$0.630525\pi$
$854$	−16.9712	−0.580743
$855$	−6.69298	−0.228895
$856$	31.5450	1.07819
$857$	25.9856	0.887652	0.443826	−	0.896113i	$-0.353621\pi$
$857$	25.9856	0.887652	0.443826	+	0.896113i	$0.353621\pi$
$858$	−15.2392	−0.520258
$859$	2.11075	0.0720179	0.0360090	−	0.999351i	$-0.488536\pi$
$859$	2.11075	0.0720179	0.0360090	+	0.999351i	$0.488536\pi$
$860$	0.258023	0.00879853
$861$	3.90936	0.133231
$862$	47.1932	1.60741
$863$	−5.03257	−0.171311	−0.0856553	−	0.996325i	$-0.527298\pi$
$863$	−5.03257	−0.171311	−0.0856553	+	0.996325i	$0.527298\pi$
$864$	−0.524759	−0.0178526
$865$	−27.0169	−0.918602
$866$	47.2809	1.60667
$867$	−16.8806	−0.573296
$868$	0.446267	0.0151473
$869$	−19.1948	−0.651139
$870$	−1.44075	−0.0488458
$871$	−27.8637	−0.944127
$872$	45.7229	1.54837
$873$	−2.81227	−0.0951809
$874$	−6.87396	−0.232515
$875$	−10.8503	−0.366806
$876$	−1.14039	−0.0385300
$877$	47.7494	1.61238	0.806191	−	0.591655i	$-0.201525\pi$
$877$	47.7494	1.61238	0.806191	+	0.591655i	$0.201525\pi$
$878$	−49.3407	−1.66517
$879$	−7.52281	−0.253738
$880$	14.8778	0.501530
$881$	10.1638	0.342426	0.171213	−	0.985234i	$-0.445231\pi$
$881$	10.1638	0.342426	0.171213	+	0.985234i	$0.445231\pi$
$882$	1.44666	0.0487117
$883$	−27.1497	−0.913659	−0.456830	−	0.889554i	$-0.651015\pi$
$883$	−27.1497	−0.913659	−0.456830	+	0.889554i	$0.651015\pi$
$884$	0.217928	0.00732972
$885$	19.6993	0.662183
$886$	4.21623	0.141647
$887$	−2.75485	−0.0924989	−0.0462495	−	0.998930i	$-0.514727\pi$
$887$	−2.75485	−0.0924989	−0.0462495	+	0.998930i	$0.514727\pi$
$888$	−27.6955	−0.929399
$889$	−14.8559	−0.498251
$890$	−27.7149	−0.929007
$891$	−1.55059	−0.0519468
$892$	2.12243	0.0710643
$893$	2.78098	0.0930619
$894$	21.3353	0.713560
$895$	32.1788	1.07562
$896$	12.0369	0.402124
$897$	11.0786	0.369905
$898$	4.04300	0.134917
$899$	−2.08408	−0.0695079
$900$	0.0256631	0.000855436 0
$901$	2.98900	0.0995782
$902$	−8.76944	−0.291990
$903$	1.20993	0.0402638
$904$	−28.1492	−0.936228
$905$	−18.9199	−0.628917
$906$	−24.2912	−0.807020
$907$	46.8374	1.55521	0.777606	−	0.628752i	$-0.216434\pi$
$907$	46.8374	1.55521	0.777606	+	0.628752i	$0.216434\pi$
$908$	−0.805843	−0.0267428
$909$	14.8150	0.491383
$910$	22.5753	0.748365
$911$	−16.5906	−0.549671	−0.274836	−	0.961491i	$-0.588623\pi$
$911$	−16.5906	−0.549671	−0.274836	+	0.961491i	$0.588623\pi$
$912$	12.1708	0.403017
$913$	9.72732	0.321927
$914$	29.4113	0.972840
$915$	−26.9473	−0.890850
$916$	2.28796	0.0755963
$917$	12.2275	0.403787
$918$	0.499867	0.0164981
$919$	10.6275	0.350570	0.175285	−	0.984518i	$-0.443915\pi$
$919$	10.6275	0.350570	0.175285	+	0.984518i	$0.443915\pi$
$920$	−10.3351	−0.340738
$921$	−4.95308	−0.163210
$922$	1.83522	0.0604397
$923$	11.0268	0.362952
$924$	−0.143955	−0.00473579
$925$	2.77480	0.0912349
$926$	−47.6392	−1.56552
$927$	0.0282793	0.000928813 0
$928$	0.227514	0.00746853
$929$	−18.3532	−0.602150	−0.301075	−	0.953600i	$-0.597345\pi$
$929$	−18.3532	−0.602150	−0.301075	+	0.953600i	$0.597345\pi$
$930$	15.9736	0.523795
$931$	−2.91373	−0.0954938
$932$	−0.135853	−0.00445001
$933$	−21.1289	−0.691730
$934$	21.9281	0.717508
$935$	−1.23071	−0.0402484
$936$	−18.7435	−0.612652
$937$	32.2660	1.05408	0.527042	−	0.849839i	$-0.323301\pi$
$937$	32.2660	1.05408	0.527042	+	0.849839i	$0.323301\pi$
$938$	−5.93350	−0.193736
$939$	−1.72079	−0.0561558
$940$	−0.203539	−0.00663871
$941$	30.3908	0.990712	0.495356	−	0.868690i	$-0.335038\pi$
$941$	30.3908	0.990712	0.495356	+	0.868690i	$0.335038\pi$
$942$	22.4144	0.730300
$943$	6.37522	0.207606
$944$	−35.8220	−1.16591
$945$	2.29705	0.0747229
$946$	−2.71409	−0.0882427
$947$	−45.1373	−1.46677	−0.733383	−	0.679816i	$-0.762060\pi$
$947$	−45.1373	−1.46677	−0.733383	+	0.679816i	$0.762060\pi$
$948$	1.14925	0.0373261
$949$	−83.4484	−2.70885
$950$	−1.16519	−0.0378037
$951$	8.02561	0.260248
$952$	−0.953328	−0.0308975
$953$	−19.0928	−0.618477	−0.309239	−	0.950984i	$-0.600074\pi$
$953$	−19.0928	−0.618477	−0.309239	+	0.950984i	$0.600074\pi$
$954$	12.5143	0.405166
$955$	2.29705	0.0743307
$956$	−1.01373	−0.0327863
$957$	0.672275	0.0217316
$958$	−23.7844	−0.768439
$959$	21.9927	0.710181
$960$	17.4460	0.563067
$961$	−7.89374	−0.254637
$962$	98.6547	3.18075
$963$	−11.4334	−0.368436
$964$	−1.15202	−0.0371042
$965$	43.0445	1.38565
$966$	2.35916	0.0759047
$967$	9.69015	0.311614	0.155807	−	0.987787i	$-0.450202\pi$
$967$	9.69015	0.311614	0.155807	+	0.987787i	$0.450202\pi$
$968$	23.7156	0.762249
$969$	−1.00679	−0.0323426
$970$	−9.34533	−0.300060
$971$	−32.1505	−1.03176	−0.515880	−	0.856661i	$-0.672535\pi$
$971$	−32.1505	−1.03176	−0.515880	+	0.856661i	$0.672535\pi$
$972$	0.0928390	0.00297781
$973$	−2.56524	−0.0822379
$974$	49.0378	1.57127
$975$	1.87791	0.0601413
$976$	49.0022	1.56852
$977$	43.1957	1.38195	0.690976	−	0.722878i	$-0.257181\pi$
$977$	43.1957	1.38195	0.690976	+	0.722878i	$0.257181\pi$
$978$	−2.08919	−0.0668050
$979$	12.9322	0.413316
$980$	0.213255	0.00681220
$981$	−16.5721	−0.529107
$982$	−5.39270	−0.172088
$983$	−18.2231	−0.581228	−0.290614	−	0.956840i	$-0.593860\pi$
$983$	−18.2231	−0.581228	−0.290614	+	0.956840i	$0.593860\pi$
$984$	−10.7860	−0.343846
$985$	−55.0178	−1.75301
$986$	−0.216723	−0.00690185
$987$	−0.954438	−0.0303801
$988$	−1.83771	−0.0584653
$989$	1.97310	0.0627408
$990$	−5.15271	−0.163764
$991$	16.2382	0.515825	0.257912	−	0.966168i	$-0.416965\pi$
$991$	16.2382	0.515825	0.257912	+	0.966168i	$0.416965\pi$
$992$	−2.52246	−0.0800882
$993$	−0.781302	−0.0247939
$994$	2.34812	0.0744780
$995$	−25.6313	−0.812566
$996$	−0.582406	−0.0184542
$997$	−50.4409	−1.59748	−0.798740	−	0.601676i	$-0.794500\pi$
$997$	−50.4409	−1.59748	−0.798740	+	0.601676i	$0.794500\pi$
$998$	−52.6576	−1.66685
$999$	10.0381	0.317593

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.19	✓	27

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

\(f(q)\)	\(=\)	\(q+1.44666 q^{2} +1.00000 q^{3} +0.0928390 q^{4} +2.29705 q^{5} +1.44666 q^{6} +1.00000 q^{7} -2.75902 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.44666 q^{2} +1.00000 q^{3} +0.0928390 q^{4} +2.29705 q^{5} +1.44666 q^{6} +1.00000 q^{7} -2.75902 q^{8} +1.00000 q^{9} +3.32306 q^{10} -1.55059 q^{11} +0.0928390 q^{12} +6.79355 q^{13} +1.44666 q^{14} +2.29705 q^{15} -4.17706 q^{16} +0.345531 q^{17} +1.44666 q^{18} -2.91373 q^{19} +0.213255 q^{20} +1.00000 q^{21} -2.24319 q^{22} +1.63076 q^{23} -2.75902 q^{24} +0.276426 q^{25} +9.82798 q^{26} +1.00000 q^{27} +0.0928390 q^{28} -0.433560 q^{29} +3.32306 q^{30} +4.80690 q^{31} -0.524759 q^{32} -1.55059 q^{33} +0.499867 q^{34} +2.29705 q^{35} +0.0928390 q^{36} +10.0381 q^{37} -4.21520 q^{38} +6.79355 q^{39} -6.33761 q^{40} +3.90936 q^{41} +1.44666 q^{42} +1.20993 q^{43} -0.143955 q^{44} +2.29705 q^{45} +2.35916 q^{46} -0.954438 q^{47} -4.17706 q^{48} +1.00000 q^{49} +0.399895 q^{50} +0.345531 q^{51} +0.630706 q^{52} +8.65047 q^{53} +1.44666 q^{54} -3.56178 q^{55} -2.75902 q^{56} -2.91373 q^{57} -0.627216 q^{58} +8.57590 q^{59} +0.213255 q^{60} -11.7313 q^{61} +6.95397 q^{62} +1.00000 q^{63} +7.59497 q^{64} +15.6051 q^{65} -2.24319 q^{66} -4.10150 q^{67} +0.0320787 q^{68} +1.63076 q^{69} +3.32306 q^{70} +1.62313 q^{71} -2.75902 q^{72} -12.2835 q^{73} +14.5218 q^{74} +0.276426 q^{75} -0.270508 q^{76} -1.55059 q^{77} +9.82798 q^{78} +12.3790 q^{79} -9.59490 q^{80} +1.00000 q^{81} +5.65554 q^{82} -6.27329 q^{83} +0.0928390 q^{84} +0.793701 q^{85} +1.75036 q^{86} -0.433560 q^{87} +4.27812 q^{88} -8.34020 q^{89} +3.32306 q^{90} +6.79355 q^{91} +0.151398 q^{92} +4.80690 q^{93} -1.38075 q^{94} -6.69298 q^{95} -0.524759 q^{96} -2.81227 q^{97} +1.44666 q^{98} -1.55059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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