LMFDB - Embedded newform 4011.2.a.k.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.74433 q^{2} +1.00000 q^{3} +1.04268 q^{4} -1.87140 q^{5} +1.74433 q^{6} +1.00000 q^{7} -1.66989 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.74433 q^{2} +1.00000 q^{3} +1.04268 q^{4} -1.87140 q^{5} +1.74433 q^{6} +1.00000 q^{7} -1.66989 q^{8} +1.00000 q^{9} -3.26434 q^{10} -1.19331 q^{11} +1.04268 q^{12} -2.11385 q^{13} +1.74433 q^{14} -1.87140 q^{15} -4.99818 q^{16} +2.89464 q^{17} +1.74433 q^{18} +4.97899 q^{19} -1.95127 q^{20} +1.00000 q^{21} -2.08152 q^{22} +9.10126 q^{23} -1.66989 q^{24} -1.49785 q^{25} -3.68724 q^{26} +1.00000 q^{27} +1.04268 q^{28} -0.663516 q^{29} -3.26434 q^{30} -2.67099 q^{31} -5.37868 q^{32} -1.19331 q^{33} +5.04921 q^{34} -1.87140 q^{35} +1.04268 q^{36} +10.3910 q^{37} +8.68499 q^{38} -2.11385 q^{39} +3.12503 q^{40} +8.03278 q^{41} +1.74433 q^{42} +8.48602 q^{43} -1.24423 q^{44} -1.87140 q^{45} +15.8756 q^{46} +10.9554 q^{47} -4.99818 q^{48} +1.00000 q^{49} -2.61274 q^{50} +2.89464 q^{51} -2.20406 q^{52} -5.09321 q^{53} +1.74433 q^{54} +2.23316 q^{55} -1.66989 q^{56} +4.97899 q^{57} -1.15739 q^{58} -2.67136 q^{59} -1.95127 q^{60} +1.17563 q^{61} -4.65909 q^{62} +1.00000 q^{63} +0.614175 q^{64} +3.95586 q^{65} -2.08152 q^{66} -1.69768 q^{67} +3.01818 q^{68} +9.10126 q^{69} -3.26434 q^{70} +2.80656 q^{71} -1.66989 q^{72} +5.86075 q^{73} +18.1253 q^{74} -1.49785 q^{75} +5.19147 q^{76} -1.19331 q^{77} -3.68724 q^{78} -3.80396 q^{79} +9.35361 q^{80} +1.00000 q^{81} +14.0118 q^{82} -0.958929 q^{83} +1.04268 q^{84} -5.41705 q^{85} +14.8024 q^{86} -0.663516 q^{87} +1.99269 q^{88} -15.9305 q^{89} -3.26434 q^{90} -2.11385 q^{91} +9.48966 q^{92} -2.67099 q^{93} +19.1097 q^{94} -9.31770 q^{95} -5.37868 q^{96} -2.11325 q^{97} +1.74433 q^{98} -1.19331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.74433	1.23343	0.616713	−	0.787188i	$-0.288464\pi$
$2$	1.74433	1.23343	0.616713	+	0.787188i	$0.288464\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.04268	0.521338
$5$	−1.87140	−0.836917	−0.418459	−	0.908236i	$-0.637429\pi$
$5$	−1.87140	−0.836917	−0.418459	+	0.908236i	$0.637429\pi$
$6$	1.74433	0.712118
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.66989	−0.590394
$9$	1.00000	0.333333
$10$	−3.26434	−1.03227
$11$	−1.19331	−0.359796	−0.179898	−	0.983685i	$-0.557577\pi$
$11$	−1.19331	−0.359796	−0.179898	+	0.983685i	$0.557577\pi$
$12$	1.04268	0.300995
$13$	−2.11385	−0.586276	−0.293138	−	0.956070i	$-0.594699\pi$
$13$	−2.11385	−0.586276	−0.293138	+	0.956070i	$0.594699\pi$
$14$	1.74433	0.466191
$15$	−1.87140	−0.483194
$16$	−4.99818	−1.24954
$17$	2.89464	0.702054	0.351027	−	0.936365i	$-0.385832\pi$
$17$	2.89464	0.702054	0.351027	+	0.936365i	$0.385832\pi$
$18$	1.74433	0.411142
$19$	4.97899	1.14226	0.571130	−	0.820860i	$-0.306505\pi$
$19$	4.97899	1.14226	0.571130	+	0.820860i	$0.306505\pi$
$20$	−1.95127	−0.436317
$21$	1.00000	0.218218
$22$	−2.08152	−0.443781
$23$	9.10126	1.89774	0.948872	−	0.315662i	$-0.102227\pi$
$23$	9.10126	1.89774	0.948872	+	0.315662i	$0.102227\pi$
$24$	−1.66989	−0.340864
$25$	−1.49785	−0.299570
$26$	−3.68724	−0.723127
$27$	1.00000	0.192450
$28$	1.04268	0.197047
$29$	−0.663516	−0.123212	−0.0616059	−	0.998101i	$-0.519622\pi$
$29$	−0.663516	−0.123212	−0.0616059	+	0.998101i	$0.519622\pi$
$30$	−3.26434	−0.595984
$31$	−2.67099	−0.479725	−0.239862	−	0.970807i	$-0.577102\pi$
$31$	−2.67099	−0.479725	−0.239862	+	0.970807i	$0.577102\pi$
$32$	−5.37868	−0.950826
$33$	−1.19331	−0.207728
$34$	5.04921	0.865932
$35$	−1.87140	−0.316325
$36$	1.04268	0.173779
$37$	10.3910	1.70827	0.854133	−	0.520055i	$-0.174089\pi$
$37$	10.3910	1.70827	0.854133	+	0.520055i	$0.174089\pi$
$38$	8.68499	1.40889
$39$	−2.11385	−0.338486
$40$	3.12503	0.494111
$41$	8.03278	1.25451	0.627255	−	0.778814i	$-0.284178\pi$
$41$	8.03278	1.25451	0.627255	+	0.778814i	$0.284178\pi$
$42$	1.74433	0.269155
$43$	8.48602	1.29411	0.647053	−	0.762445i	$-0.276001\pi$
$43$	8.48602	1.29411	0.647053	+	0.762445i	$0.276001\pi$
$44$	−1.24423	−0.187575
$45$	−1.87140	−0.278972
$46$	15.8756	2.34072
$47$	10.9554	1.59800	0.799002	−	0.601328i	$-0.205362\pi$
$47$	10.9554	1.59800	0.799002	+	0.601328i	$0.205362\pi$
$48$	−4.99818	−0.721425
$49$	1.00000	0.142857
$50$	−2.61274	−0.369497
$51$	2.89464	0.405331
$52$	−2.20406	−0.305648
$53$	−5.09321	−0.699606	−0.349803	−	0.936823i	$-0.613751\pi$
$53$	−5.09321	−0.699606	−0.349803	+	0.936823i	$0.613751\pi$
$54$	1.74433	0.237373
$55$	2.23316	0.301119
$56$	−1.66989	−0.223148
$57$	4.97899	0.659484
$58$	−1.15739	−0.151973
$59$	−2.67136	−0.347781	−0.173891	−	0.984765i	$-0.555634\pi$
$59$	−2.67136	−0.347781	−0.173891	+	0.984765i	$0.555634\pi$
$60$	−1.95127	−0.251908
$61$	1.17563	0.150525	0.0752623	−	0.997164i	$-0.476021\pi$
$61$	1.17563	0.150525	0.0752623	+	0.997164i	$0.476021\pi$
$62$	−4.65909	−0.591705
$63$	1.00000	0.125988
$64$	0.614175	0.0767719
$65$	3.95586	0.490664
$66$	−2.08152	−0.256217
$67$	−1.69768	−0.207404	−0.103702	−	0.994608i	$-0.533069\pi$
$67$	−1.69768	−0.207404	−0.103702	+	0.994608i	$0.533069\pi$
$68$	3.01818	0.366007
$69$	9.10126	1.09566
$70$	−3.26434	−0.390163
$71$	2.80656	0.333077	0.166538	−	0.986035i	$-0.446741\pi$
$71$	2.80656	0.333077	0.166538	+	0.986035i	$0.446741\pi$
$72$	−1.66989	−0.196798
$73$	5.86075	0.685949	0.342974	−	0.939345i	$-0.388566\pi$
$73$	5.86075	0.685949	0.342974	+	0.939345i	$0.388566\pi$
$74$	18.1253	2.10702
$75$	−1.49785	−0.172957
$76$	5.19147	0.595503
$77$	−1.19331	−0.135990
$78$	−3.68724	−0.417498
$79$	−3.80396	−0.427979	−0.213989	−	0.976836i	$-0.568646\pi$
$79$	−3.80396	−0.427979	−0.213989	+	0.976836i	$0.568646\pi$
$80$	9.35361	1.04577
$81$	1.00000	0.111111
$82$	14.0118	1.54734
$83$	−0.958929	−0.105256	−0.0526281	−	0.998614i	$-0.516760\pi$
$83$	−0.958929	−0.105256	−0.0526281	+	0.998614i	$0.516760\pi$
$84$	1.04268	0.113765
$85$	−5.41705	−0.587561
$86$	14.8024	1.59618
$87$	−0.663516	−0.0711364
$88$	1.99269	0.212421
$89$	−15.9305	−1.68863	−0.844317	−	0.535843i	$-0.819994\pi$
$89$	−15.9305	−1.68863	−0.844317	+	0.535843i	$0.819994\pi$
$90$	−3.26434	−0.344092
$91$	−2.11385	−0.221591
$92$	9.48966	0.989365
$93$	−2.67099	−0.276969
$94$	19.1097	1.97102
$95$	−9.31770	−0.955976
$96$	−5.37868	−0.548960
$97$	−2.11325	−0.214568	−0.107284	−	0.994228i	$-0.534215\pi$
$97$	−2.11325	−0.214568	−0.107284	+	0.994228i	$0.534215\pi$
$98$	1.74433	0.176204
$99$	−1.19331	−0.119932
$100$	−1.56177	−0.156177
$101$	−4.15733	−0.413670	−0.206835	−	0.978376i	$-0.566316\pi$
$101$	−4.15733	−0.413670	−0.206835	+	0.978376i	$0.566316\pi$
$102$	5.04921	0.499946
$103$	1.26695	0.124837	0.0624184	−	0.998050i	$-0.480119\pi$
$103$	1.26695	0.124837	0.0624184	+	0.998050i	$0.480119\pi$
$104$	3.52988	0.346134
$105$	−1.87140	−0.182630
$106$	−8.88422	−0.862912
$107$	12.9122	1.24827	0.624134	−	0.781317i	$-0.285452\pi$
$107$	12.9122	1.24827	0.624134	+	0.781317i	$0.285452\pi$
$108$	1.04268	0.100332
$109$	−3.62522	−0.347234	−0.173617	−	0.984813i	$-0.555545\pi$
$109$	−3.62522	−0.347234	−0.173617	+	0.984813i	$0.555545\pi$
$110$	3.89536	0.371408
$111$	10.3910	0.986268
$112$	−4.99818	−0.472284
$113$	−10.2145	−0.960900	−0.480450	−	0.877022i	$-0.659527\pi$
$113$	−10.2145	−0.960900	−0.480450	+	0.877022i	$0.659527\pi$
$114$	8.68499	0.813424
$115$	−17.0321	−1.58825
$116$	−0.691832	−0.0642350
$117$	−2.11385	−0.195425
$118$	−4.65972	−0.428962
$119$	2.89464	0.265352
$120$	3.12503	0.285275
$121$	−9.57602	−0.870547
$122$	2.05069	0.185661
$123$	8.03278	0.724291
$124$	−2.78498	−0.250099
$125$	12.1601	1.08763
$126$	1.74433	0.155397
$127$	1.42098	0.126092	0.0630458	−	0.998011i	$-0.479919\pi$
$127$	1.42098	0.126092	0.0630458	+	0.998011i	$0.479919\pi$
$128$	11.8287	1.04552
$129$	8.48602	0.747152
$130$	6.90031	0.605197
$131$	13.5004	1.17953	0.589766	−	0.807574i	$-0.299220\pi$
$131$	13.5004	1.17953	0.589766	+	0.807574i	$0.299220\pi$
$132$	−1.24423	−0.108297
$133$	4.97899	0.431733
$134$	−2.96130	−0.255817
$135$	−1.87140	−0.161065
$136$	−4.83373	−0.414489
$137$	8.34007	0.712540	0.356270	−	0.934383i	$-0.384048\pi$
$137$	8.34007	0.712540	0.356270	+	0.934383i	$0.384048\pi$
$138$	15.8756	1.35142
$139$	9.97805	0.846327	0.423164	−	0.906053i	$-0.360920\pi$
$139$	9.97805	0.846327	0.423164	+	0.906053i	$0.360920\pi$
$140$	−1.95127	−0.164912
$141$	10.9554	0.922608
$142$	4.89555	0.410825
$143$	2.52247	0.210939
$144$	−4.99818	−0.416515
$145$	1.24171	0.103118
$146$	10.2231	0.846066
$147$	1.00000	0.0824786
$148$	10.8344	0.890584
$149$	6.09003	0.498915	0.249457	−	0.968386i	$-0.419748\pi$
$149$	6.09003	0.498915	0.249457	+	0.968386i	$0.419748\pi$
$150$	−2.61274	−0.213329
$151$	−8.01799	−0.652495	−0.326247	−	0.945284i	$-0.605784\pi$
$151$	−8.01799	−0.652495	−0.326247	+	0.945284i	$0.605784\pi$
$152$	−8.31435	−0.674383
$153$	2.89464	0.234018
$154$	−2.08152	−0.167733
$155$	4.99851	0.401490
$156$	−2.20406	−0.176466
$157$	4.97201	0.396810	0.198405	−	0.980120i	$-0.436424\pi$
$157$	4.97201	0.396810	0.198405	+	0.980120i	$0.436424\pi$
$158$	−6.63535	−0.527880
$159$	−5.09321	−0.403918
$160$	10.0657	0.795763
$161$	9.10126	0.717280
$162$	1.74433	0.137047
$163$	−8.88541	−0.695959	−0.347980	−	0.937502i	$-0.613132\pi$
$163$	−8.88541	−0.695959	−0.347980	+	0.937502i	$0.613132\pi$
$164$	8.37558	0.654023
$165$	2.23316	0.173851
$166$	−1.67269	−0.129826
$167$	12.1209	0.937944	0.468972	−	0.883213i	$-0.344624\pi$
$167$	12.1209	0.937944	0.468972	+	0.883213i	$0.344624\pi$
$168$	−1.66989	−0.128835
$169$	−8.53165	−0.656281
$170$	−9.44910	−0.724713
$171$	4.97899	0.380753
$172$	8.84816	0.674666
$173$	−3.49909	−0.266031	−0.133016	−	0.991114i	$-0.542466\pi$
$173$	−3.49909	−0.266031	−0.133016	+	0.991114i	$0.542466\pi$
$174$	−1.15739	−0.0877414
$175$	−1.49785	−0.113227
$176$	5.96436	0.449581
$177$	−2.67136	−0.200792
$178$	−27.7881	−2.08280
$179$	−22.3558	−1.67095	−0.835476	−	0.549527i	$-0.814808\pi$
$179$	−22.3558	−1.67095	−0.835476	+	0.549527i	$0.814808\pi$
$180$	−1.95127	−0.145439
$181$	−3.53843	−0.263010	−0.131505	−	0.991316i	$-0.541981\pi$
$181$	−3.53843	−0.263010	−0.131505	+	0.991316i	$0.541981\pi$
$182$	−3.68724	−0.273316
$183$	1.17563	0.0869054
$184$	−15.1981	−1.12042
$185$	−19.4457	−1.42968
$186$	−4.65909	−0.341621
$187$	−3.45420	−0.252596
$188$	11.4229	0.833100
$189$	1.00000	0.0727393
$190$	−16.2531	−1.17913
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	0.614175	0.0443243
$193$	−11.4616	−0.825021	−0.412511	−	0.910953i	$-0.635348\pi$
$193$	−11.4616	−0.825021	−0.412511	+	0.910953i	$0.635348\pi$
$194$	−3.68620	−0.264654
$195$	3.95586	0.283285
$196$	1.04268	0.0744768
$197$	1.31757	0.0938732	0.0469366	−	0.998898i	$-0.485054\pi$
$197$	1.31757	0.0938732	0.0469366	+	0.998898i	$0.485054\pi$
$198$	−2.08152	−0.147927
$199$	−0.890668	−0.0631378	−0.0315689	−	0.999502i	$-0.510050\pi$
$199$	−0.890668	−0.0631378	−0.0315689	+	0.999502i	$0.510050\pi$
$200$	2.50124	0.176864
$201$	−1.69768	−0.119745
$202$	−7.25175	−0.510231
$203$	−0.663516	−0.0465697
$204$	3.01818	0.211315
$205$	−15.0326	−1.04992
$206$	2.20998	0.153977
$207$	9.10126	0.632581
$208$	10.5654	0.732577
$209$	−5.94147	−0.410980
$210$	−3.26434	−0.225261
$211$	−5.16839	−0.355807	−0.177903	−	0.984048i	$-0.556931\pi$
$211$	−5.16839	−0.355807	−0.177903	+	0.984048i	$0.556931\pi$
$212$	−5.31056	−0.364731
$213$	2.80656	0.192302
$214$	22.5231	1.53964
$215$	−15.8808	−1.08306
$216$	−1.66989	−0.113621
$217$	−2.67099	−0.181319
$218$	−6.32358	−0.428287
$219$	5.86075	0.396033
$220$	2.32846	0.156985
$221$	−6.11883	−0.411597
$222$	18.1253	1.21649
$223$	−2.49900	−0.167346	−0.0836728	−	0.996493i	$-0.526665\pi$
$223$	−2.49900	−0.167346	−0.0836728	+	0.996493i	$0.526665\pi$
$224$	−5.37868	−0.359378
$225$	−1.49785	−0.0998565
$226$	−17.8174	−1.18520
$227$	25.9976	1.72552	0.862762	−	0.505611i	$-0.168733\pi$
$227$	25.9976	1.72552	0.862762	+	0.505611i	$0.168733\pi$
$228$	5.19147	0.343814
$229$	−27.7577	−1.83428	−0.917141	−	0.398563i	$-0.869509\pi$
$229$	−27.7577	−1.83428	−0.917141	+	0.398563i	$0.869509\pi$
$230$	−29.7096	−1.95899
$231$	−1.19331	−0.0785138
$232$	1.10800	0.0727435
$233$	16.5811	1.08626	0.543131	−	0.839648i	$-0.317239\pi$
$233$	16.5811	1.08626	0.543131	+	0.839648i	$0.317239\pi$
$234$	−3.68724	−0.241042
$235$	−20.5019	−1.33740
$236$	−2.78536	−0.181312
$237$	−3.80396	−0.247094
$238$	5.04921	0.327291
$239$	−6.39071	−0.413381	−0.206690	−	0.978406i	$-0.566269\pi$
$239$	−6.39071	−0.413381	−0.206690	+	0.978406i	$0.566269\pi$
$240$	9.35361	0.603773
$241$	4.04283	0.260422	0.130211	−	0.991486i	$-0.458435\pi$
$241$	4.04283	0.260422	0.130211	+	0.991486i	$0.458435\pi$
$242$	−16.7037	−1.07375
$243$	1.00000	0.0641500
$244$	1.22581	0.0784742
$245$	−1.87140	−0.119560
$246$	14.0118	0.893359
$247$	−10.5248	−0.669679
$248$	4.46026	0.283227
$249$	−0.958929	−0.0607696
$250$	21.2112	1.34151
$251$	4.27687	0.269953	0.134977	−	0.990849i	$-0.456904\pi$
$251$	4.27687	0.269953	0.134977	+	0.990849i	$0.456904\pi$
$252$	1.04268	0.0656824
$253$	−10.8606	−0.682800
$254$	2.47865	0.155525
$255$	−5.41705	−0.339229
$256$	19.4048	1.21280
$257$	−13.2499	−0.826509	−0.413254	−	0.910616i	$-0.635608\pi$
$257$	−13.2499	−0.826509	−0.413254	+	0.910616i	$0.635608\pi$
$258$	14.8024	0.921556
$259$	10.3910	0.645664
$260$	4.12468	0.255802
$261$	−0.663516	−0.0410706
$262$	23.5490	1.45486
$263$	10.8844	0.671158	0.335579	−	0.942012i	$-0.391068\pi$
$263$	10.8844	0.671158	0.335579	+	0.942012i	$0.391068\pi$
$264$	1.99269	0.122641
$265$	9.53145	0.585512
$266$	8.68499	0.532511
$267$	−15.9305	−0.974934
$268$	−1.77013	−0.108128
$269$	30.0174	1.83019	0.915096	−	0.403236i	$-0.132114\pi$
$269$	30.0174	1.83019	0.915096	+	0.403236i	$0.132114\pi$
$270$	−3.26434	−0.198661
$271$	15.5158	0.942519	0.471260	−	0.881995i	$-0.343800\pi$
$271$	15.5158	0.942519	0.471260	+	0.881995i	$0.343800\pi$
$272$	−14.4679	−0.877248
$273$	−2.11385	−0.127936
$274$	14.5478	0.878865
$275$	1.78739	0.107784
$276$	9.48966	0.571210
$277$	7.69366	0.462267	0.231134	−	0.972922i	$-0.425757\pi$
$277$	7.69366	0.462267	0.231134	+	0.972922i	$0.425757\pi$
$278$	17.4050	1.04388
$279$	−2.67099	−0.159908
$280$	3.12503	0.186756
$281$	−19.9318	−1.18903	−0.594516	−	0.804084i	$-0.702656\pi$
$281$	−19.9318	−1.18903	−0.594516	+	0.804084i	$0.702656\pi$
$282$	19.1097	1.13797
$283$	19.7645	1.17488	0.587438	−	0.809269i	$-0.300136\pi$
$283$	19.7645	1.17488	0.587438	+	0.809269i	$0.300136\pi$
$284$	2.92633	0.173646
$285$	−9.31770	−0.551933
$286$	4.40001	0.260178
$287$	8.03278	0.474160
$288$	−5.37868	−0.316942
$289$	−8.62104	−0.507120
$290$	2.16594	0.127188
$291$	−2.11325	−0.123881
$292$	6.11086	0.357611
$293$	2.77679	0.162222	0.0811110	−	0.996705i	$-0.474153\pi$
$293$	2.77679	0.162222	0.0811110	+	0.996705i	$0.474153\pi$
$294$	1.74433	0.101731
$295$	4.99919	0.291064
$296$	−17.3517	−1.00855
$297$	−1.19331	−0.0692427
$298$	10.6230	0.615374
$299$	−19.2387	−1.11260
$300$	−1.56177	−0.0901688
$301$	8.48602	0.489126
$302$	−13.9860	−0.804804
$303$	−4.15733	−0.238833
$304$	−24.8859	−1.42730
$305$	−2.20009	−0.125977
$306$	5.04921	0.288644
$307$	4.37277	0.249567	0.124784	−	0.992184i	$-0.460176\pi$
$307$	4.37277	0.249567	0.124784	+	0.992184i	$0.460176\pi$
$308$	−1.24423	−0.0708967
$309$	1.26695	0.0720745
$310$	8.71903	0.495208
$311$	−15.7813	−0.894874	−0.447437	−	0.894315i	$-0.647663\pi$
$311$	−15.7813	−0.894874	−0.447437	+	0.894315i	$0.647663\pi$
$312$	3.52988	0.199840
$313$	−1.93348	−0.109287	−0.0546433	−	0.998506i	$-0.517402\pi$
$313$	−1.93348	−0.109287	−0.0546433	+	0.998506i	$0.517402\pi$
$314$	8.67282	0.489435
$315$	−1.87140	−0.105442
$316$	−3.96630	−0.223122
$317$	13.1928	0.740983	0.370492	−	0.928836i	$-0.379189\pi$
$317$	13.1928	0.740983	0.370492	+	0.928836i	$0.379189\pi$
$318$	−8.88422	−0.498202
$319$	0.791778	0.0443311
$320$	−1.14937	−0.0642517
$321$	12.9122	0.720688
$322$	15.8756	0.884711
$323$	14.4124	0.801928
$324$	1.04268	0.0579264
$325$	3.16622	0.175630
$326$	−15.4991	−0.858414
$327$	−3.62522	−0.200475
$328$	−13.4138	−0.740655
$329$	10.9554	0.603989
$330$	3.89536	0.214432
$331$	−1.05675	−0.0580844	−0.0290422	−	0.999578i	$-0.509246\pi$
$331$	−1.05675	−0.0580844	−0.0290422	+	0.999578i	$0.509246\pi$
$332$	−0.999852	−0.0548740
$333$	10.3910	0.569422
$334$	21.1428	1.15688
$335$	3.17704	0.173580
$336$	−4.99818	−0.272673
$337$	−11.6724	−0.635833	−0.317917	−	0.948119i	$-0.602983\pi$
$337$	−11.6724	−0.635833	−0.317917	+	0.948119i	$0.602983\pi$
$338$	−14.8820	−0.809474
$339$	−10.2145	−0.554776
$340$	−5.64822	−0.306318
$341$	3.18732	0.172603
$342$	8.68499	0.469630
$343$	1.00000	0.0539949
$344$	−14.1707	−0.764032
$345$	−17.0321	−0.916979
$346$	−6.10356	−0.328130
$347$	33.7606	1.81236	0.906182	−	0.422887i	$-0.138983\pi$
$347$	33.7606	1.81236	0.906182	+	0.422887i	$0.138983\pi$
$348$	−0.691832	−0.0370861
$349$	25.0202	1.33930	0.669650	−	0.742677i	$-0.266444\pi$
$349$	25.0202	1.33930	0.669650	+	0.742677i	$0.266444\pi$
$350$	−2.61274	−0.139657
$351$	−2.11385	−0.112829
$352$	6.41842	0.342103
$353$	1.44275	0.0767899	0.0383950	−	0.999263i	$-0.487775\pi$
$353$	1.44275	0.0767899	0.0383950	+	0.999263i	$0.487775\pi$
$354$	−4.65972	−0.247661
$355$	−5.25220	−0.278758
$356$	−16.6104	−0.880349
$357$	2.89464	0.153201
$358$	−38.9958	−2.06099
$359$	−10.0965	−0.532875	−0.266437	−	0.963852i	$-0.585847\pi$
$359$	−10.0965	−0.532875	−0.266437	+	0.963852i	$0.585847\pi$
$360$	3.12503	0.164704
$361$	5.79036	0.304756
$362$	−6.17219	−0.324403
$363$	−9.57602	−0.502611
$364$	−2.20406	−0.115524
$365$	−10.9678	−0.574082
$366$	2.05069	0.107191
$367$	−13.3640	−0.697594	−0.348797	−	0.937198i	$-0.613410\pi$
$367$	−13.3640	−0.697594	−0.348797	+	0.937198i	$0.613410\pi$
$368$	−45.4897	−2.37132
$369$	8.03278	0.418170
$370$	−33.9197	−1.76340
$371$	−5.09321	−0.264426
$372$	−2.78498	−0.144395
$373$	−15.2020	−0.787128	−0.393564	−	0.919297i	$-0.628758\pi$
$373$	−15.2020	−0.787128	−0.393564	+	0.919297i	$0.628758\pi$
$374$	−6.02525	−0.311558
$375$	12.1601	0.627945
$376$	−18.2942	−0.943452
$377$	1.40257	0.0722361
$378$	1.74433	0.0897185
$379$	−22.3389	−1.14747	−0.573736	−	0.819041i	$-0.694506\pi$
$379$	−22.3389	−1.14747	−0.573736	+	0.819041i	$0.694506\pi$
$380$	−9.71534	−0.498387
$381$	1.42098	0.0727991
$382$	1.74433	0.0892475
$383$	20.9179	1.06885	0.534427	−	0.845215i	$-0.320527\pi$
$383$	20.9179	1.06885	0.534427	+	0.845215i	$0.320527\pi$
$384$	11.8287	0.603630
$385$	2.23316	0.113812
$386$	−19.9927	−1.01760
$387$	8.48602	0.431368
$388$	−2.20343	−0.111862
$389$	−11.8457	−0.600599	−0.300300	−	0.953845i	$-0.597087\pi$
$389$	−11.8457	−0.600599	−0.300300	+	0.953845i	$0.597087\pi$
$390$	6.90031	0.349411
$391$	26.3449	1.33232
$392$	−1.66989	−0.0843420
$393$	13.5004	0.681003
$394$	2.29828	0.115786
$395$	7.11875	0.358183
$396$	−1.24423	−0.0625250
$397$	−4.73582	−0.237684	−0.118842	−	0.992913i	$-0.537918\pi$
$397$	−4.73582	−0.237684	−0.118842	+	0.992913i	$0.537918\pi$
$398$	−1.55362	−0.0778757
$399$	4.97899	0.249261
$400$	7.48651	0.374326
$401$	0.0642921	0.00321059	0.00160530	−	0.999999i	$-0.499489\pi$
$401$	0.0642921	0.00321059	0.00160530	+	0.999999i	$0.499489\pi$
$402$	−2.96130	−0.147696
$403$	5.64607	0.281251
$404$	−4.33475	−0.215662
$405$	−1.87140	−0.0929908
$406$	−1.15739	−0.0574402
$407$	−12.3996	−0.614626
$408$	−4.83373	−0.239305
$409$	−28.4542	−1.40697	−0.703484	−	0.710711i	$-0.748373\pi$
$409$	−28.4542	−1.40697	−0.703484	+	0.710711i	$0.748373\pi$
$410$	−26.2217	−1.29500
$411$	8.34007	0.411385
$412$	1.32102	0.0650821
$413$	−2.67136	−0.131449
$414$	15.8756	0.780242
$415$	1.79454	0.0880906
$416$	11.3697	0.557446
$417$	9.97805	0.488627
$418$	−10.3639	−0.506913
$419$	23.2025	1.13352	0.566759	−	0.823884i	$-0.308197\pi$
$419$	23.2025	1.13352	0.566759	+	0.823884i	$0.308197\pi$
$420$	−1.95127	−0.0952121
$421$	−29.0806	−1.41730	−0.708650	−	0.705560i	$-0.750696\pi$
$421$	−29.0806	−1.41730	−0.708650	+	0.705560i	$0.750696\pi$
$422$	−9.01536	−0.438861
$423$	10.9554	0.532668
$424$	8.50508	0.413043
$425$	−4.33574	−0.210314
$426$	4.89555	0.237190
$427$	1.17563	0.0568929
$428$	13.4632	0.650769
$429$	2.52247	0.121786
$430$	−27.7012	−1.33587
$431$	3.01578	0.145265	0.0726325	−	0.997359i	$-0.476860\pi$
$431$	3.01578	0.145265	0.0726325	+	0.997359i	$0.476860\pi$
$432$	−4.99818	−0.240475
$433$	−12.1615	−0.584443	−0.292222	−	0.956351i	$-0.594394\pi$
$433$	−12.1615	−0.584443	−0.292222	+	0.956351i	$0.594394\pi$
$434$	−4.65909	−0.223643
$435$	1.24171	0.0595352
$436$	−3.77993	−0.181026
$437$	45.3151	2.16771
$438$	10.2231	0.488477
$439$	−3.12241	−0.149024	−0.0745122	−	0.997220i	$-0.523740\pi$
$439$	−3.12241	−0.149024	−0.0745122	+	0.997220i	$0.523740\pi$
$440$	−3.72912	−0.177779
$441$	1.00000	0.0476190
$442$	−10.6732	−0.507674
$443$	−29.8597	−1.41868	−0.709340	−	0.704867i	$-0.751007\pi$
$443$	−29.8597	−1.41868	−0.709340	+	0.704867i	$0.751007\pi$
$444$	10.8344	0.514179
$445$	29.8125	1.41325
$446$	−4.35908	−0.206408
$447$	6.09003	0.288049
$448$	0.614175	0.0290171
$449$	−36.1871	−1.70778	−0.853888	−	0.520457i	$-0.825762\pi$
$449$	−36.1871	−1.70778	−0.853888	+	0.520457i	$0.825762\pi$
$450$	−2.61274	−0.123166
$451$	−9.58557	−0.451367
$452$	−10.6504	−0.500954
$453$	−8.01799	−0.376718
$454$	45.3484	2.12830
$455$	3.95586	0.185454
$456$	−8.31435	−0.389355
$457$	−9.14910	−0.427977	−0.213988	−	0.976836i	$-0.568646\pi$
$457$	−9.14910	−0.427977	−0.213988	+	0.976836i	$0.568646\pi$
$458$	−48.4185	−2.26245
$459$	2.89464	0.135110
$460$	−17.7590	−0.828017
$461$	10.3470	0.481907	0.240954	−	0.970537i	$-0.422540\pi$
$461$	10.3470	0.481907	0.240954	+	0.970537i	$0.422540\pi$
$462$	−2.08152	−0.0968409
$463$	1.51973	0.0706280	0.0353140	−	0.999376i	$-0.488757\pi$
$463$	1.51973	0.0706280	0.0353140	+	0.999376i	$0.488757\pi$
$464$	3.31637	0.153959
$465$	4.99851	0.231800
$466$	28.9228	1.33982
$467$	25.1510	1.16385	0.581925	−	0.813243i	$-0.302300\pi$
$467$	25.1510	1.16385	0.581925	+	0.813243i	$0.302300\pi$
$468$	−2.20406	−0.101883
$469$	−1.69768	−0.0783914
$470$	−35.7620	−1.64958
$471$	4.97201	0.229098
$472$	4.46087	0.205328
$473$	−10.1264	−0.465613
$474$	−6.63535	−0.304772
$475$	−7.45777	−0.342186
$476$	3.01818	0.138338
$477$	−5.09321	−0.233202
$478$	−11.1475	−0.509874
$479$	−18.3268	−0.837374	−0.418687	−	0.908131i	$-0.637510\pi$
$479$	−18.3268	−0.837374	−0.418687	+	0.908131i	$0.637510\pi$
$480$	10.0657	0.459434
$481$	−21.9649	−1.00151
$482$	7.05202	0.321211
$483$	9.10126	0.414122
$484$	−9.98468	−0.453849
$485$	3.95474	0.179576
$486$	1.74433	0.0791243
$487$	11.6153	0.526338	0.263169	−	0.964750i	$-0.415232\pi$
$487$	11.6153	0.526338	0.263169	+	0.964750i	$0.415232\pi$
$488$	−1.96318	−0.0888688
$489$	−8.88541	−0.401812
$490$	−3.26434	−0.147468
$491$	−16.3636	−0.738481	−0.369241	−	0.929334i	$-0.620382\pi$
$491$	−16.3636	−0.738481	−0.369241	+	0.929334i	$0.620382\pi$
$492$	8.37558	0.377601
$493$	−1.92064	−0.0865014
$494$	−18.3587	−0.825998
$495$	2.23316	0.100373
$496$	13.3501	0.599438
$497$	2.80656	0.125891
$498$	−1.67269	−0.0749548
$499$	10.4577	0.468150	0.234075	−	0.972219i	$-0.424794\pi$
$499$	10.4577	0.468150	0.234075	+	0.972219i	$0.424794\pi$
$500$	12.6790	0.567024
$501$	12.1209	0.541522
$502$	7.46025	0.332967
$503$	−32.9249	−1.46805	−0.734025	−	0.679123i	$-0.762360\pi$
$503$	−32.9249	−1.46805	−0.734025	+	0.679123i	$0.762360\pi$
$504$	−1.66989	−0.0743827
$505$	7.78005	0.346208
$506$	−18.9444	−0.842182
$507$	−8.53165	−0.378904
$508$	1.48162	0.0657364
$509$	−8.83675	−0.391682	−0.195841	−	0.980636i	$-0.562744\pi$
$509$	−8.83675	−0.391682	−0.195841	+	0.980636i	$0.562744\pi$
$510$	−9.44910	−0.418413
$511$	5.86075	0.259264
$512$	10.1908	0.450376
$513$	4.97899	0.219828
$514$	−23.1122	−1.01944
$515$	−2.37098	−0.104478
$516$	8.84816	0.389519
$517$	−13.0731	−0.574955
$518$	18.1253	0.796378
$519$	−3.49909	−0.153593
$520$	−6.60584	−0.289685
$521$	5.14641	0.225468	0.112734	−	0.993625i	$-0.464039\pi$
$521$	5.14641	0.225468	0.112734	+	0.993625i	$0.464039\pi$
$522$	−1.15739	−0.0506575
$523$	28.0016	1.22443	0.612213	−	0.790693i	$-0.290280\pi$
$523$	28.0016	1.22443	0.612213	+	0.790693i	$0.290280\pi$
$524$	14.0765	0.614935
$525$	−1.49785	−0.0653715
$526$	18.9859	0.827823
$527$	−7.73158	−0.336793
$528$	5.96436	0.259566
$529$	59.8329	2.60143
$530$	16.6260	0.722186
$531$	−2.67136	−0.115927
$532$	5.19147	0.225079
$533$	−16.9801	−0.735488
$534$	−27.7881	−1.20251
$535$	−24.1639	−1.04470
$536$	2.83493	0.122450
$537$	−22.3558	−0.964725
$538$	52.3601	2.25741
$539$	−1.19331	−0.0513994
$540$	−1.95127	−0.0839692
$541$	−0.570971	−0.0245479	−0.0122740	−	0.999925i	$-0.503907\pi$
$541$	−0.570971	−0.0245479	−0.0122740	+	0.999925i	$0.503907\pi$
$542$	27.0647	1.16253
$543$	−3.53843	−0.151849
$544$	−15.5694	−0.667531
$545$	6.78426	0.290606
$546$	−3.68724	−0.157799
$547$	21.0063	0.898165	0.449083	−	0.893490i	$-0.351751\pi$
$547$	21.0063	0.898165	0.449083	+	0.893490i	$0.351751\pi$
$548$	8.69599	0.371474
$549$	1.17563	0.0501749
$550$	3.11780	0.132943
$551$	−3.30364	−0.140740
$552$	−15.1981	−0.646873
$553$	−3.80396	−0.161761
$554$	13.4203	0.570172
$555$	−19.4457	−0.825424
$556$	10.4039	0.441222
$557$	36.5376	1.54815	0.774074	−	0.633095i	$-0.218216\pi$
$557$	36.5376	1.54815	0.774074	+	0.633095i	$0.218216\pi$
$558$	−4.65909	−0.197235
$559$	−17.9381	−0.758702
$560$	9.35361	0.395262
$561$	−3.45420	−0.145836
$562$	−34.7676	−1.46658
$563$	−41.6454	−1.75514	−0.877572	−	0.479445i	$-0.840838\pi$
$563$	−41.6454	−1.75514	−0.877572	+	0.479445i	$0.840838\pi$
$564$	11.4229	0.480991
$565$	19.1155	0.804194
$566$	34.4757	1.44912
$567$	1.00000	0.0419961
$568$	−4.68663	−0.196647
$569$	−9.06089	−0.379852	−0.189926	−	0.981798i	$-0.560825\pi$
$569$	−9.06089	−0.379852	−0.189926	+	0.981798i	$0.560825\pi$
$570$	−16.2531	−0.680768
$571$	−37.9576	−1.58848	−0.794238	−	0.607607i	$-0.792130\pi$
$571$	−37.9576	−1.58848	−0.794238	+	0.607607i	$0.792130\pi$
$572$	2.63012	0.109971
$573$	1.00000	0.0417756
$574$	14.0118	0.584841
$575$	−13.6323	−0.568506
$576$	0.614175	0.0255906
$577$	−3.14027	−0.130731	−0.0653656	−	0.997861i	$-0.520821\pi$
$577$	−3.14027	−0.130731	−0.0653656	+	0.997861i	$0.520821\pi$
$578$	−15.0379	−0.625494
$579$	−11.4616	−0.476326
$580$	1.29470	0.0537593
$581$	−0.958929	−0.0397831
$582$	−3.68620	−0.152798
$583$	6.07776	0.251715
$584$	−9.78678	−0.404980
$585$	3.95586	0.163555
$586$	4.84363	0.200089
$587$	−3.44905	−0.142357	−0.0711787	−	0.997464i	$-0.522676\pi$
$587$	−3.44905	−0.142357	−0.0711787	+	0.997464i	$0.522676\pi$
$588$	1.04268	0.0429992
$589$	−13.2989	−0.547970
$590$	8.72022	0.359006
$591$	1.31757	0.0541977
$592$	−51.9359	−2.13455
$593$	24.8186	1.01918	0.509590	−	0.860417i	$-0.329797\pi$
$593$	24.8186	1.01918	0.509590	+	0.860417i	$0.329797\pi$
$594$	−2.08152	−0.0854057
$595$	−5.41705	−0.222077
$596$	6.34993	0.260103
$597$	−0.890668	−0.0364526
$598$	−33.5585	−1.37231
$599$	21.6010	0.882594	0.441297	−	0.897361i	$-0.354519\pi$
$599$	21.6010	0.882594	0.441297	+	0.897361i	$0.354519\pi$
$600$	2.50124	0.102113
$601$	11.9822	0.488763	0.244381	−	0.969679i	$-0.421415\pi$
$601$	11.9822	0.488763	0.244381	+	0.969679i	$0.421415\pi$
$602$	14.8024	0.603300
$603$	−1.69768	−0.0691347
$604$	−8.36016	−0.340170
$605$	17.9206	0.728576
$606$	−7.25175	−0.294582
$607$	10.0436	0.407659	0.203829	−	0.979006i	$-0.434661\pi$
$607$	10.0436	0.407659	0.203829	+	0.979006i	$0.434661\pi$
$608$	−26.7804	−1.08609
$609$	−0.663516	−0.0268870
$610$	−3.83767	−0.155383
$611$	−23.1580	−0.936871
$612$	3.01818	0.122002
$613$	−28.3627	−1.14556	−0.572780	−	0.819709i	$-0.694135\pi$
$613$	−28.3627	−1.14556	−0.572780	+	0.819709i	$0.694135\pi$
$614$	7.62755	0.307823
$615$	−15.0326	−0.606172
$616$	1.99269	0.0802876
$617$	−22.7217	−0.914742	−0.457371	−	0.889276i	$-0.651209\pi$
$617$	−22.7217	−0.914742	−0.457371	+	0.889276i	$0.651209\pi$
$618$	2.20998	0.0888985
$619$	12.3376	0.495888	0.247944	−	0.968774i	$-0.420245\pi$
$619$	12.3376	0.495888	0.247944	+	0.968774i	$0.420245\pi$
$620$	5.21182	0.209312
$621$	9.10126	0.365221
$622$	−27.5277	−1.10376
$623$	−15.9305	−0.638244
$624$	10.5654	0.422954
$625$	−15.2672	−0.610688
$626$	−3.37262	−0.134797
$627$	−5.94147	−0.237279
$628$	5.18420	0.206872
$629$	30.0782	1.19930
$630$	−3.26434	−0.130054
$631$	−12.6695	−0.504366	−0.252183	−	0.967680i	$-0.581149\pi$
$631$	−12.6695	−0.504366	−0.252183	+	0.967680i	$0.581149\pi$
$632$	6.35218	0.252676
$633$	−5.16839	−0.205425
$634$	23.0126	0.913947
$635$	−2.65923	−0.105528
$636$	−5.31056	−0.210578
$637$	−2.11385	−0.0837536
$638$	1.38112	0.0546790
$639$	2.80656	0.111026
$640$	−22.1363	−0.875012
$641$	−41.5428	−1.64084	−0.820421	−	0.571760i	$-0.806261\pi$
$641$	−41.5428	−1.64084	−0.820421	+	0.571760i	$0.806261\pi$
$642$	22.5231	0.888914
$643$	3.70465	0.146097	0.0730485	−	0.997328i	$-0.476727\pi$
$643$	3.70465	0.146097	0.0730485	+	0.997328i	$0.476727\pi$
$644$	9.48966	0.373945
$645$	−15.8808	−0.625304
$646$	25.1400	0.989118
$647$	32.5100	1.27810	0.639049	−	0.769166i	$-0.279328\pi$
$647$	32.5100	1.27810	0.639049	+	0.769166i	$0.279328\pi$
$648$	−1.66989	−0.0655993
$649$	3.18775	0.125130
$650$	5.52292	0.216627
$651$	−2.67099	−0.104685
$652$	−9.26460	−0.362830
$653$	44.6626	1.74778	0.873891	−	0.486123i	$-0.161589\pi$
$653$	44.6626	1.74778	0.873891	+	0.486123i	$0.161589\pi$
$654$	−6.32358	−0.247271
$655$	−25.2646	−0.987170
$656$	−40.1493	−1.56757
$657$	5.86075	0.228650
$658$	19.1097	0.744975
$659$	14.1852	0.552578	0.276289	−	0.961075i	$-0.410895\pi$
$659$	14.1852	0.552578	0.276289	+	0.961075i	$0.410895\pi$
$660$	2.32846	0.0906352
$661$	8.42642	0.327750	0.163875	−	0.986481i	$-0.447601\pi$
$661$	8.42642	0.327750	0.163875	+	0.986481i	$0.447601\pi$
$662$	−1.84332	−0.0716428
$663$	−6.11883	−0.237636
$664$	1.60130	0.0621426
$665$	−9.31770	−0.361325
$666$	18.1253	0.702339
$667$	−6.03883	−0.233824
$668$	12.6382	0.488986
$669$	−2.49900	−0.0966170
$670$	5.54179	0.214098
$671$	−1.40289	−0.0541581
$672$	−5.37868	−0.207487
$673$	−26.5093	−1.02186	−0.510929	−	0.859623i	$-0.670699\pi$
$673$	−26.5093	−1.02186	−0.510929	+	0.859623i	$0.670699\pi$
$674$	−20.3604	−0.784253
$675$	−1.49785	−0.0576522
$676$	−8.89575	−0.342144
$677$	12.5731	0.483225	0.241612	−	0.970373i	$-0.422324\pi$
$677$	12.5731	0.483225	0.241612	+	0.970373i	$0.422324\pi$
$678$	−17.8174	−0.684275
$679$	−2.11325	−0.0810991
$680$	9.04585	0.346893
$681$	25.9976	0.996231
$682$	5.55972	0.212893
$683$	11.4779	0.439191	0.219596	−	0.975591i	$-0.429526\pi$
$683$	11.4779	0.439191	0.219596	+	0.975591i	$0.429526\pi$
$684$	5.19147	0.198501
$685$	−15.6076	−0.596337
$686$	1.74433	0.0665987
$687$	−27.7577	−1.05902
$688$	−42.4146	−1.61704
$689$	10.7663	0.410162
$690$	−29.7096	−1.13102
$691$	−11.8473	−0.450693	−0.225347	−	0.974279i	$-0.572351\pi$
$691$	−11.8473	−0.450693	−0.225347	+	0.974279i	$0.572351\pi$
$692$	−3.64842	−0.138692
$693$	−1.19331	−0.0453300
$694$	58.8895	2.23542
$695$	−18.6730	−0.708306
$696$	1.10800	0.0419985
$697$	23.2520	0.880734
$698$	43.6434	1.65193
$699$	16.5811	0.627153
$700$	−1.56177	−0.0590294
$701$	8.20019	0.309717	0.154858	−	0.987937i	$-0.450508\pi$
$701$	8.20019	0.309717	0.154858	+	0.987937i	$0.450508\pi$
$702$	−3.68724	−0.139166
$703$	51.7366	1.95128
$704$	−0.732900	−0.0276222
$705$	−20.5019	−0.772147
$706$	2.51663	0.0947147
$707$	−4.15733	−0.156353
$708$	−2.78536	−0.104680
$709$	14.3879	0.540347	0.270174	−	0.962812i	$-0.412919\pi$
$709$	14.3879	0.540347	0.270174	+	0.962812i	$0.412919\pi$
$710$	−9.16155	−0.343827
$711$	−3.80396	−0.142660
$712$	26.6022	0.996960
$713$	−24.3094	−0.910395
$714$	5.04921	0.188962
$715$	−4.72056	−0.176539
$716$	−23.3099	−0.871130
$717$	−6.39071	−0.238666
$718$	−17.6117	−0.657261
$719$	31.5914	1.17816	0.589080	−	0.808075i	$-0.299490\pi$
$719$	31.5914	1.17816	0.589080	+	0.808075i	$0.299490\pi$
$720$	9.35361	0.348588
$721$	1.26695	0.0471838
$722$	10.1003	0.375894
$723$	4.04283	0.150355
$724$	−3.68944	−0.137117
$725$	0.993846	0.0369105
$726$	−16.7037	−0.619933
$727$	−19.8546	−0.736367	−0.368183	−	0.929753i	$-0.620020\pi$
$727$	−19.8546	−0.736367	−0.368183	+	0.929753i	$0.620020\pi$
$728$	3.52988	0.130826
$729$	1.00000	0.0370370
$730$	−19.1315	−0.708088
$731$	24.5640	0.908532
$732$	1.22581	0.0453071
$733$	−8.62949	−0.318737	−0.159369	−	0.987219i	$-0.550946\pi$
$733$	−8.62949	−0.318737	−0.159369	+	0.987219i	$0.550946\pi$
$734$	−23.3111	−0.860430
$735$	−1.87140	−0.0690278
$736$	−48.9528	−1.80442
$737$	2.02585	0.0746231
$738$	14.0118	0.515781
$739$	−14.0396	−0.516455	−0.258227	−	0.966084i	$-0.583138\pi$
$739$	−14.0396	−0.516455	−0.258227	+	0.966084i	$0.583138\pi$
$740$	−20.2756	−0.745345
$741$	−10.5248	−0.386639
$742$	−8.88422	−0.326150
$743$	25.8650	0.948894	0.474447	−	0.880284i	$-0.342648\pi$
$743$	25.8650	0.948894	0.474447	+	0.880284i	$0.342648\pi$
$744$	4.46026	0.163521
$745$	−11.3969	−0.417550
$746$	−26.5172	−0.970864
$747$	−0.958929	−0.0350854
$748$	−3.60161	−0.131688
$749$	12.9122	0.471801
$750$	21.2112	0.774523
$751$	27.8804	1.01737	0.508686	−	0.860952i	$-0.330131\pi$
$751$	27.8804	1.01737	0.508686	+	0.860952i	$0.330131\pi$
$752$	−54.7569	−1.99678
$753$	4.27687	0.155858
$754$	2.44654	0.0890978
$755$	15.0049	0.546084
$756$	1.04268	0.0379217
$757$	10.2067	0.370970	0.185485	−	0.982647i	$-0.440614\pi$
$757$	10.2067	0.370970	0.185485	+	0.982647i	$0.440614\pi$
$758$	−38.9663	−1.41532
$759$	−10.8606	−0.394215
$760$	15.5595	0.564403
$761$	21.5048	0.779548	0.389774	−	0.920911i	$-0.372553\pi$
$761$	21.5048	0.779548	0.389774	+	0.920911i	$0.372553\pi$
$762$	2.47865	0.0897922
$763$	−3.62522	−0.131242
$764$	1.04268	0.0377227
$765$	−5.41705	−0.195854
$766$	36.4876	1.31835
$767$	5.64684	0.203896
$768$	19.4048	0.700209
$769$	28.7488	1.03671	0.518353	−	0.855167i	$-0.326545\pi$
$769$	28.7488	1.03671	0.518353	+	0.855167i	$0.326545\pi$
$770$	3.89536	0.140379
$771$	−13.2499	−0.477185
$772$	−11.9507	−0.430115
$773$	−45.9669	−1.65332	−0.826658	−	0.562705i	$-0.809761\pi$
$773$	−45.9669	−1.65332	−0.826658	+	0.562705i	$0.809761\pi$
$774$	14.8024	0.532061
$775$	4.00075	0.143711
$776$	3.52889	0.126680
$777$	10.3910	0.372774
$778$	−20.6627	−0.740795
$779$	39.9952	1.43297
$780$	4.12468	0.147687
$781$	−3.34908	−0.119840
$782$	45.9541	1.64332
$783$	−0.663516	−0.0237121
$784$	−4.99818	−0.178506
$785$	−9.30465	−0.332097
$786$	23.5490	0.839966
$787$	−29.1275	−1.03828	−0.519142	−	0.854688i	$-0.673749\pi$
$787$	−29.1275	−1.03828	−0.519142	+	0.854688i	$0.673749\pi$
$788$	1.37380	0.0489396
$789$	10.8844	0.387493
$790$	12.4174	0.441792
$791$	−10.2145	−0.363186
$792$	1.99269	0.0708071
$793$	−2.48511	−0.0882489
$794$	−8.26081	−0.293165
$795$	9.53145	0.338046
$796$	−0.928678	−0.0329161
$797$	−16.2211	−0.574582	−0.287291	−	0.957843i	$-0.592755\pi$
$797$	−16.2211	−0.574582	−0.287291	+	0.957843i	$0.592755\pi$
$798$	8.68499	0.307445
$799$	31.7119	1.12189
$800$	8.05645	0.284839
$801$	−15.9305	−0.562878
$802$	0.112146	0.00396003
$803$	−6.99367	−0.246801
$804$	−1.77013	−0.0624275
$805$	−17.0321	−0.600304
$806$	9.84860	0.346902
$807$	30.0174	1.05666
$808$	6.94227	0.244228
$809$	−25.6243	−0.900901	−0.450451	−	0.892801i	$-0.648737\pi$
$809$	−25.6243	−0.900901	−0.450451	+	0.892801i	$0.648737\pi$
$810$	−3.26434	−0.114697
$811$	−10.8034	−0.379357	−0.189679	−	0.981846i	$-0.560745\pi$
$811$	−10.8034	−0.379357	−0.189679	+	0.981846i	$0.560745\pi$
$812$	−0.691832	−0.0242785
$813$	15.5158	0.544164
$814$	−21.6290	−0.758096
$815$	16.6282	0.582460
$816$	−14.4679	−0.506480
$817$	42.2518	1.47820
$818$	−49.6334	−1.73539
$819$	−2.11385	−0.0738638
$820$	−15.6741	−0.547363
$821$	17.4363	0.608531	0.304265	−	0.952587i	$-0.401589\pi$
$821$	17.4363	0.608531	0.304265	+	0.952587i	$0.401589\pi$
$822$	14.5478	0.507413
$823$	−52.2204	−1.82029	−0.910144	−	0.414293i	$-0.864029\pi$
$823$	−52.2204	−1.82029	−0.910144	+	0.414293i	$0.864029\pi$
$824$	−2.11567	−0.0737028
$825$	1.78739	0.0622290
$826$	−4.65972	−0.162133
$827$	2.95955	0.102914	0.0514568	−	0.998675i	$-0.483614\pi$
$827$	2.95955	0.102914	0.0514568	+	0.998675i	$0.483614\pi$
$828$	9.48966	0.329788
$829$	19.2721	0.669349	0.334675	−	0.942334i	$-0.391374\pi$
$829$	19.2721	0.669349	0.334675	+	0.942334i	$0.391374\pi$
$830$	3.13027	0.108653
$831$	7.69366	0.266890
$832$	−1.29827	−0.0450095
$833$	2.89464	0.100293
$834$	17.4050	0.602685
$835$	−22.6831	−0.784982
$836$	−6.19502	−0.214259
$837$	−2.67099	−0.0923231
$838$	40.4728	1.39811
$839$	7.51821	0.259557	0.129779	−	0.991543i	$-0.458573\pi$
$839$	7.51821	0.259557	0.129779	+	0.991543i	$0.458573\pi$
$840$	3.12503	0.107824
$841$	−28.5597	−0.984819
$842$	−50.7260	−1.74813
$843$	−19.9318	−0.686488
$844$	−5.38895	−0.185495
$845$	15.9662	0.549253
$846$	19.1097	0.657006
$847$	−9.57602	−0.329036
$848$	25.4568	0.874189
$849$	19.7645	0.678315
$850$	−7.56294	−0.259407
$851$	94.5709	3.24185
$852$	2.92633	0.100254
$853$	−5.08900	−0.174244	−0.0871220	−	0.996198i	$-0.527767\pi$
$853$	−5.08900	−0.174244	−0.0871220	+	0.996198i	$0.527767\pi$
$854$	2.05069	0.0701732
$855$	−9.31770	−0.318659
$856$	−21.5619	−0.736970
$857$	13.7352	0.469186	0.234593	−	0.972094i	$-0.424624\pi$
$857$	13.7352	0.469186	0.234593	+	0.972094i	$0.424624\pi$
$858$	4.40001	0.150214
$859$	−22.6856	−0.774024	−0.387012	−	0.922075i	$-0.626493\pi$
$859$	−22.6856	−0.774024	−0.387012	+	0.922075i	$0.626493\pi$
$860$	−16.5585	−0.564640
$861$	8.03278	0.273756
$862$	5.26050	0.179174
$863$	14.3486	0.488433	0.244217	−	0.969721i	$-0.421469\pi$
$863$	14.3486	0.488433	0.244217	+	0.969721i	$0.421469\pi$
$864$	−5.37868	−0.182987
$865$	6.54822	0.222646
$866$	−21.2136	−0.720867
$867$	−8.62104	−0.292786
$868$	−2.78498	−0.0945284
$869$	4.53929	0.153985
$870$	2.16594	0.0734323
$871$	3.58863	0.121596
$872$	6.05371	0.205005
$873$	−2.11325	−0.0715227
$874$	79.0443	2.67371
$875$	12.1601	0.411086
$876$	6.11086	0.206467
$877$	−33.1203	−1.11839	−0.559197	−	0.829035i	$-0.688891\pi$
$877$	−33.1203	−1.11839	−0.559197	+	0.829035i	$0.688891\pi$
$878$	−5.44650	−0.183810
$879$	2.77679	0.0936589
$880$	−11.1617	−0.376262
$881$	−51.1113	−1.72198	−0.860992	−	0.508618i	$-0.830156\pi$
$881$	−51.1113	−1.72198	−0.860992	+	0.508618i	$0.830156\pi$
$882$	1.74433	0.0587345
$883$	36.6046	1.23184	0.615922	−	0.787807i	$-0.288784\pi$
$883$	36.6046	1.23184	0.615922	+	0.787807i	$0.288784\pi$
$884$	−6.37996	−0.214581
$885$	4.99919	0.168046
$886$	−52.0852	−1.74984
$887$	−33.5638	−1.12696	−0.563482	−	0.826129i	$-0.690538\pi$
$887$	−33.5638	−1.12696	−0.563482	+	0.826129i	$0.690538\pi$
$888$	−17.3517	−0.582287
$889$	1.42098	0.0476582
$890$	52.0027	1.74314
$891$	−1.19331	−0.0399773
$892$	−2.60565	−0.0872436
$893$	54.5467	1.82533
$894$	10.6230	0.355286
$895$	41.8367	1.39845
$896$	11.8287	0.395169
$897$	−19.2387	−0.642360
$898$	−63.1222	−2.10641
$899$	1.77225	0.0591078
$900$	−1.56177	−0.0520590
$901$	−14.7430	−0.491161
$902$	−16.7204	−0.556727
$903$	8.48602	0.282397
$904$	17.0571	0.567310
$905$	6.62184	0.220117
$906$	−13.9860	−0.464654
$907$	−8.96103	−0.297546	−0.148773	−	0.988871i	$-0.547532\pi$
$907$	−8.96103	−0.297546	−0.148773	+	0.988871i	$0.547532\pi$
$908$	27.1071	0.899580
$909$	−4.15733	−0.137890
$910$	6.90031	0.228743
$911$	−48.9566	−1.62200	−0.811002	−	0.585044i	$-0.801077\pi$
$911$	−48.9566	−1.62200	−0.811002	+	0.585044i	$0.801077\pi$
$912$	−24.8859	−0.824054
$913$	1.14430	0.0378707
$914$	−15.9590	−0.527878
$915$	−2.20009	−0.0727326
$916$	−28.9423	−0.956280
$917$	13.5004	0.445821
$918$	5.04921	0.166649
$919$	−24.1408	−0.796332	−0.398166	−	0.917313i	$-0.630353\pi$
$919$	−24.1408	−0.796332	−0.398166	+	0.917313i	$0.630353\pi$
$920$	28.4417	0.937696
$921$	4.37277	0.144088
$922$	18.0485	0.594397
$923$	−5.93263	−0.195275
$924$	−1.24423	−0.0409322
$925$	−15.5641	−0.511745
$926$	2.65091	0.0871143
$927$	1.26695	0.0416122
$928$	3.56884	0.117153
$929$	50.7288	1.66436	0.832179	−	0.554507i	$-0.187093\pi$
$929$	50.7288	1.66436	0.832179	+	0.554507i	$0.187093\pi$
$930$	8.71903	0.285908
$931$	4.97899	0.163180
$932$	17.2887	0.566309
$933$	−15.7813	−0.516656
$934$	43.8716	1.43552
$935$	6.46420	0.211402
$936$	3.52988	0.115378
$937$	−14.4717	−0.472768	−0.236384	−	0.971660i	$-0.575962\pi$
$937$	−14.4717	−0.472768	−0.236384	+	0.971660i	$0.575962\pi$
$938$	−2.96130	−0.0966899
$939$	−1.93348	−0.0630967
$940$	−21.3768	−0.697236
$941$	−48.1384	−1.56927	−0.784633	−	0.619961i	$-0.787149\pi$
$941$	−48.1384	−1.56927	−0.784633	+	0.619961i	$0.787149\pi$
$942$	8.67282	0.282576
$943$	73.1084	2.38074
$944$	13.3519	0.434568
$945$	−1.87140	−0.0608768
$946$	−17.6638	−0.574299
$947$	−7.02153	−0.228169	−0.114084	−	0.993471i	$-0.536393\pi$
$947$	−7.02153	−0.228169	−0.114084	+	0.993471i	$0.536393\pi$
$948$	−3.96630	−0.128819
$949$	−12.3887	−0.402155
$950$	−13.0088	−0.422061
$951$	13.1928	0.427807
$952$	−4.83373	−0.156662
$953$	40.9881	1.32774	0.663868	−	0.747850i	$-0.268914\pi$
$953$	40.9881	1.32774	0.663868	+	0.747850i	$0.268914\pi$
$954$	−8.88422	−0.287637
$955$	−1.87140	−0.0605572
$956$	−6.66344	−0.215511
$957$	0.791778	0.0255945
$958$	−31.9680	−1.03284
$959$	8.34007	0.269315
$960$	−1.14937	−0.0370958
$961$	−23.8658	−0.769864
$962$	−38.3140	−1.23529
$963$	12.9122	0.416089
$964$	4.21536	0.135768
$965$	21.4492	0.690474
$966$	15.8756	0.510788
$967$	−4.78789	−0.153968	−0.0769840	−	0.997032i	$-0.524529\pi$
$967$	−4.78789	−0.153968	−0.0769840	+	0.997032i	$0.524529\pi$
$968$	15.9909	0.513966
$969$	14.4124	0.462993
$970$	6.89836	0.221493
$971$	31.5156	1.01138	0.505692	−	0.862714i	$-0.331237\pi$
$971$	31.5156	1.01138	0.505692	+	0.862714i	$0.331237\pi$
$972$	1.04268	0.0334438
$973$	9.97805	0.319882
$974$	20.2608	0.649199
$975$	3.16622	0.101400
$976$	−5.87603	−0.188087
$977$	−57.6499	−1.84438	−0.922192	−	0.386733i	$-0.873604\pi$
$977$	−57.6499	−1.84438	−0.922192	+	0.386733i	$0.873604\pi$
$978$	−15.4991	−0.495605
$979$	19.0100	0.607563
$980$	−1.95127	−0.0623309
$981$	−3.62522	−0.115745
$982$	−28.5435	−0.910861
$983$	23.0117	0.733958	0.366979	−	0.930229i	$-0.380392\pi$
$983$	23.0117	0.733958	0.366979	+	0.930229i	$0.380392\pi$
$984$	−13.4138	−0.427617
$985$	−2.46571	−0.0785641
$986$	−3.35023	−0.106693
$987$	10.9554	0.348713
$988$	−10.9740	−0.349129
$989$	77.2334	2.45588
$990$	3.89536	0.123803
$991$	−1.75027	−0.0555991	−0.0277995	−	0.999614i	$-0.508850\pi$
$991$	−1.75027	−0.0555991	−0.0277995	+	0.999614i	$0.508850\pi$
$992$	14.3664	0.456135
$993$	−1.05675	−0.0335351
$994$	4.89555	0.155277
$995$	1.66680	0.0528411
$996$	−0.999852	−0.0316815
$997$	−25.8661	−0.819189	−0.409594	−	0.912268i	$-0.634330\pi$
$997$	−25.8661	−0.819189	−0.409594	+	0.912268i	$0.634330\pi$
$998$	18.2416	0.577428
$999$	10.3910	0.328756

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.20	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.20	✓	27	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.74433 q^{2} +1.00000 q^{3} +1.04268 q^{4} -1.87140 q^{5} +1.74433 q^{6} +1.00000 q^{7} -1.66989 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.74433 q^{2} +1.00000 q^{3} +1.04268 q^{4} -1.87140 q^{5} +1.74433 q^{6} +1.00000 q^{7} -1.66989 q^{8} +1.00000 q^{9} -3.26434 q^{10} -1.19331 q^{11} +1.04268 q^{12} -2.11385 q^{13} +1.74433 q^{14} -1.87140 q^{15} -4.99818 q^{16} +2.89464 q^{17} +1.74433 q^{18} +4.97899 q^{19} -1.95127 q^{20} +1.00000 q^{21} -2.08152 q^{22} +9.10126 q^{23} -1.66989 q^{24} -1.49785 q^{25} -3.68724 q^{26} +1.00000 q^{27} +1.04268 q^{28} -0.663516 q^{29} -3.26434 q^{30} -2.67099 q^{31} -5.37868 q^{32} -1.19331 q^{33} +5.04921 q^{34} -1.87140 q^{35} +1.04268 q^{36} +10.3910 q^{37} +8.68499 q^{38} -2.11385 q^{39} +3.12503 q^{40} +8.03278 q^{41} +1.74433 q^{42} +8.48602 q^{43} -1.24423 q^{44} -1.87140 q^{45} +15.8756 q^{46} +10.9554 q^{47} -4.99818 q^{48} +1.00000 q^{49} -2.61274 q^{50} +2.89464 q^{51} -2.20406 q^{52} -5.09321 q^{53} +1.74433 q^{54} +2.23316 q^{55} -1.66989 q^{56} +4.97899 q^{57} -1.15739 q^{58} -2.67136 q^{59} -1.95127 q^{60} +1.17563 q^{61} -4.65909 q^{62} +1.00000 q^{63} +0.614175 q^{64} +3.95586 q^{65} -2.08152 q^{66} -1.69768 q^{67} +3.01818 q^{68} +9.10126 q^{69} -3.26434 q^{70} +2.80656 q^{71} -1.66989 q^{72} +5.86075 q^{73} +18.1253 q^{74} -1.49785 q^{75} +5.19147 q^{76} -1.19331 q^{77} -3.68724 q^{78} -3.80396 q^{79} +9.35361 q^{80} +1.00000 q^{81} +14.0118 q^{82} -0.958929 q^{83} +1.04268 q^{84} -5.41705 q^{85} +14.8024 q^{86} -0.663516 q^{87} +1.99269 q^{88} -15.9305 q^{89} -3.26434 q^{90} -2.11385 q^{91} +9.48966 q^{92} -2.67099 q^{93} +19.1097 q^{94} -9.31770 q^{95} -5.37868 q^{96} -2.11325 q^{97} +1.74433 q^{98} -1.19331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 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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