LMFDB - Embedded newform 6015.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.274127 q^{2} -1.00000 q^{3} -1.92485 q^{4} +1.00000 q^{5} -0.274127 q^{6} +0.857432 q^{7} -1.07591 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.274127 q^{2} -1.00000 q^{3} -1.92485 q^{4} +1.00000 q^{5} -0.274127 q^{6} +0.857432 q^{7} -1.07591 q^{8} +1.00000 q^{9} +0.274127 q^{10} +2.26386 q^{11} +1.92485 q^{12} +6.47474 q^{13} +0.235045 q^{14} -1.00000 q^{15} +3.55477 q^{16} +5.15672 q^{17} +0.274127 q^{18} +4.82735 q^{19} -1.92485 q^{20} -0.857432 q^{21} +0.620585 q^{22} +6.01099 q^{23} +1.07591 q^{24} +1.00000 q^{25} +1.77490 q^{26} -1.00000 q^{27} -1.65043 q^{28} +1.38889 q^{29} -0.274127 q^{30} +10.7063 q^{31} +3.12628 q^{32} -2.26386 q^{33} +1.41360 q^{34} +0.857432 q^{35} -1.92485 q^{36} -7.65209 q^{37} +1.32331 q^{38} -6.47474 q^{39} -1.07591 q^{40} +6.50630 q^{41} -0.235045 q^{42} -4.45571 q^{43} -4.35760 q^{44} +1.00000 q^{45} +1.64777 q^{46} -11.5085 q^{47} -3.55477 q^{48} -6.26481 q^{49} +0.274127 q^{50} -5.15672 q^{51} -12.4629 q^{52} -2.91882 q^{53} -0.274127 q^{54} +2.26386 q^{55} -0.922518 q^{56} -4.82735 q^{57} +0.380732 q^{58} +8.94468 q^{59} +1.92485 q^{60} -1.05037 q^{61} +2.93488 q^{62} +0.857432 q^{63} -6.25255 q^{64} +6.47474 q^{65} -0.620585 q^{66} +7.50642 q^{67} -9.92594 q^{68} -6.01099 q^{69} +0.235045 q^{70} -7.37833 q^{71} -1.07591 q^{72} +7.86300 q^{73} -2.09764 q^{74} -1.00000 q^{75} -9.29194 q^{76} +1.94110 q^{77} -1.77490 q^{78} -12.8766 q^{79} +3.55477 q^{80} +1.00000 q^{81} +1.78355 q^{82} -5.76282 q^{83} +1.65043 q^{84} +5.15672 q^{85} -1.22143 q^{86} -1.38889 q^{87} -2.43570 q^{88} +2.61732 q^{89} +0.274127 q^{90} +5.55165 q^{91} -11.5703 q^{92} -10.7063 q^{93} -3.15480 q^{94} +4.82735 q^{95} -3.12628 q^{96} -12.8391 q^{97} -1.71735 q^{98} +2.26386 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * 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 $

$2$	0.274127	0.193837	0.0969185	−	0.995292i	$-0.469101\pi$
$2$	0.274127	0.193837	0.0969185	+	0.995292i	$0.469101\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.92485	−0.962427
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.274127	−0.111912
$7$	0.857432	0.324079	0.162039	−	0.986784i	$-0.448193\pi$
$7$	0.857432	0.324079	0.162039	+	0.986784i	$0.448193\pi$
$8$	−1.07591	−0.380391
$9$	1.00000	0.333333
$10$	0.274127	0.0866865
$11$	2.26386	0.682579	0.341290	−	0.939958i	$-0.389136\pi$
$11$	2.26386	0.682579	0.341290	+	0.939958i	$0.389136\pi$
$12$	1.92485	0.555658
$13$	6.47474	1.79577	0.897885	−	0.440230i	$-0.145103\pi$
$13$	6.47474	1.79577	0.897885	+	0.440230i	$0.145103\pi$
$14$	0.235045	0.0628184
$15$	−1.00000	−0.258199
$16$	3.55477	0.888693
$17$	5.15672	1.25069	0.625345	−	0.780349i	$-0.284958\pi$
$17$	5.15672	1.25069	0.625345	+	0.780349i	$0.284958\pi$
$18$	0.274127	0.0646123
$19$	4.82735	1.10747	0.553734	−	0.832693i	$-0.313202\pi$
$19$	4.82735	1.10747	0.553734	+	0.832693i	$0.313202\pi$
$20$	−1.92485	−0.430411
$21$	−0.857432	−0.187107
$22$	0.620585	0.132309
$23$	6.01099	1.25338	0.626689	−	0.779269i	$-0.284409\pi$
$23$	6.01099	1.25338	0.626689	+	0.779269i	$0.284409\pi$
$24$	1.07591	0.219619
$25$	1.00000	0.200000
$26$	1.77490	0.348087
$27$	−1.00000	−0.192450
$28$	−1.65043	−0.311902
$29$	1.38889	0.257910	0.128955	−	0.991650i	$-0.458838\pi$
$29$	1.38889	0.257910	0.128955	+	0.991650i	$0.458838\pi$
$30$	−0.274127	−0.0500485
$31$	10.7063	1.92291	0.961453	−	0.274970i	$-0.0886680\pi$
$31$	10.7063	1.92291	0.961453	+	0.274970i	$0.0886680\pi$
$32$	3.12628	0.552653
$33$	−2.26386	−0.394087
$34$	1.41360	0.242430
$35$	0.857432	0.144932
$36$	−1.92485	−0.320809
$37$	−7.65209	−1.25800	−0.628998	−	0.777407i	$-0.716534\pi$
$37$	−7.65209	−1.25800	−0.628998	+	0.777407i	$0.716534\pi$
$38$	1.32331	0.214668
$39$	−6.47474	−1.03679
$40$	−1.07591	−0.170116
$41$	6.50630	1.01611	0.508056	−	0.861324i	$-0.330364\pi$
$41$	6.50630	1.01611	0.508056	+	0.861324i	$0.330364\pi$
$42$	−0.235045	−0.0362682
$43$	−4.45571	−0.679489	−0.339744	−	0.940518i	$-0.610341\pi$
$43$	−4.45571	−0.679489	−0.339744	+	0.940518i	$0.610341\pi$
$44$	−4.35760	−0.656933
$45$	1.00000	0.149071
$46$	1.64777	0.242951
$47$	−11.5085	−1.67869	−0.839347	−	0.543597i	$-0.817062\pi$
$47$	−11.5085	−1.67869	−0.839347	+	0.543597i	$0.817062\pi$
$48$	−3.55477	−0.513087
$49$	−6.26481	−0.894973
$50$	0.274127	0.0387674
$51$	−5.15672	−0.722086
$52$	−12.4629	−1.72830
$53$	−2.91882	−0.400931	−0.200465	−	0.979701i	$-0.564245\pi$
$53$	−2.91882	−0.400931	−0.200465	+	0.979701i	$0.564245\pi$
$54$	−0.274127	−0.0373039
$55$	2.26386	0.305259
$56$	−0.922518	−0.123277
$57$	−4.82735	−0.639398
$58$	0.380732	0.0499926
$59$	8.94468	1.16450	0.582249	−	0.813011i	$-0.302173\pi$
$59$	8.94468	1.16450	0.582249	+	0.813011i	$0.302173\pi$
$60$	1.92485	0.248498
$61$	−1.05037	−0.134486	−0.0672428	−	0.997737i	$-0.521420\pi$
$61$	−1.05037	−0.134486	−0.0672428	+	0.997737i	$0.521420\pi$
$62$	2.93488	0.372730
$63$	0.857432	0.108026
$64$	−6.25255	−0.781569
$65$	6.47474	0.803093
$66$	−0.620585	−0.0763887
$67$	7.50642	0.917056	0.458528	−	0.888680i	$-0.348377\pi$
$67$	7.50642	0.917056	0.458528	+	0.888680i	$0.348377\pi$
$68$	−9.92594	−1.20370
$69$	−6.01099	−0.723639
$70$	0.235045	0.0280933
$71$	−7.37833	−0.875647	−0.437823	−	0.899061i	$-0.644250\pi$
$71$	−7.37833	−0.875647	−0.437823	+	0.899061i	$0.644250\pi$
$72$	−1.07591	−0.126797
$73$	7.86300	0.920295	0.460147	−	0.887843i	$-0.347797\pi$
$73$	7.86300	0.920295	0.460147	+	0.887843i	$0.347797\pi$
$74$	−2.09764	−0.243846
$75$	−1.00000	−0.115470
$76$	−9.29194	−1.06586
$77$	1.94110	0.221209
$78$	−1.77490	−0.200968
$79$	−12.8766	−1.44873	−0.724367	−	0.689415i	$-0.757868\pi$
$79$	−12.8766	−1.44873	−0.724367	+	0.689415i	$0.757868\pi$
$80$	3.55477	0.397436
$81$	1.00000	0.111111
$82$	1.78355	0.196960
$83$	−5.76282	−0.632551	−0.316276	−	0.948667i	$-0.602432\pi$
$83$	−5.76282	−0.632551	−0.316276	+	0.948667i	$0.602432\pi$
$84$	1.65043	0.180077
$85$	5.15672	0.559325
$86$	−1.22143	−0.131710
$87$	−1.38889	−0.148905
$88$	−2.43570	−0.259647
$89$	2.61732	0.277435	0.138717	−	0.990332i	$-0.455702\pi$
$89$	2.61732	0.277435	0.138717	+	0.990332i	$0.455702\pi$
$90$	0.274127	0.0288955
$91$	5.55165	0.581971
$92$	−11.5703	−1.20629
$93$	−10.7063	−1.11019
$94$	−3.15480	−0.325393
$95$	4.82735	0.495275
$96$	−3.12628	−0.319074
$97$	−12.8391	−1.30361	−0.651805	−	0.758387i	$-0.725988\pi$
$97$	−12.8391	−1.30361	−0.651805	+	0.758387i	$0.725988\pi$
$98$	−1.71735	−0.173479
$99$	2.26386	0.227526
$100$	−1.92485	−0.192485
$101$	−5.15539	−0.512980	−0.256490	−	0.966547i	$-0.582566\pi$
$101$	−5.15539	−0.512980	−0.256490	+	0.966547i	$0.582566\pi$
$102$	−1.41360	−0.139967
$103$	15.4628	1.52360	0.761799	−	0.647813i	$-0.224316\pi$
$103$	15.4628	1.52360	0.761799	+	0.647813i	$0.224316\pi$
$104$	−6.96623	−0.683095
$105$	−0.857432	−0.0836768
$106$	−0.800127	−0.0777152
$107$	15.7810	1.52561	0.762804	−	0.646630i	$-0.223822\pi$
$107$	15.7810	1.52561	0.762804	+	0.646630i	$0.223822\pi$
$108$	1.92485	0.185219
$109$	4.87176	0.466630	0.233315	−	0.972401i	$-0.425043\pi$
$109$	4.87176	0.466630	0.233315	+	0.972401i	$0.425043\pi$
$110$	0.620585	0.0591704
$111$	7.65209	0.726304
$112$	3.04798	0.288007
$113$	15.9951	1.50469	0.752346	−	0.658769i	$-0.228922\pi$
$113$	15.9951	1.50469	0.752346	+	0.658769i	$0.228922\pi$
$114$	−1.32331	−0.123939
$115$	6.01099	0.560528
$116$	−2.67341	−0.248220
$117$	6.47474	0.598590
$118$	2.45198	0.225723
$119$	4.42154	0.405322
$120$	1.07591	0.0982165
$121$	−5.87494	−0.534086
$122$	−0.287934	−0.0260683
$123$	−6.50630	−0.586653
$124$	−20.6080	−1.85066
$125$	1.00000	0.0894427
$126$	0.235045	0.0209395
$127$	−3.87805	−0.344121	−0.172061	−	0.985086i	$-0.555042\pi$
$127$	−3.87805	−0.344121	−0.172061	+	0.985086i	$0.555042\pi$
$128$	−7.96654	−0.704150
$129$	4.45571	0.392303
$130$	1.77490	0.155669
$131$	−4.33321	−0.378595	−0.189297	−	0.981920i	$-0.560621\pi$
$131$	−4.33321	−0.378595	−0.189297	+	0.981920i	$0.560621\pi$
$132$	4.35760	0.379280
$133$	4.13912	0.358907
$134$	2.05771	0.177759
$135$	−1.00000	−0.0860663
$136$	−5.54816	−0.475751
$137$	18.0029	1.53809	0.769046	−	0.639193i	$-0.220732\pi$
$137$	18.0029	1.53809	0.769046	+	0.639193i	$0.220732\pi$
$138$	−1.64777	−0.140268
$139$	15.7841	1.33879	0.669396	−	0.742905i	$-0.266553\pi$
$139$	15.7841	1.33879	0.669396	+	0.742905i	$0.266553\pi$
$140$	−1.65043	−0.139487
$141$	11.5085	0.969194
$142$	−2.02260	−0.169733
$143$	14.6579	1.22576
$144$	3.55477	0.296231
$145$	1.38889	0.115341
$146$	2.15546	0.178387
$147$	6.26481	0.516713
$148$	14.7292	1.21073
$149$	0.201283	0.0164897	0.00824486	−	0.999966i	$-0.497376\pi$
$149$	0.201283	0.0164897	0.00824486	+	0.999966i	$0.497376\pi$
$150$	−0.274127	−0.0223824
$151$	−22.2885	−1.81381	−0.906906	−	0.421333i	$-0.861562\pi$
$151$	−22.2885	−1.81381	−0.906906	+	0.421333i	$0.861562\pi$
$152$	−5.19378	−0.421271
$153$	5.15672	0.416896
$154$	0.532109	0.0428786
$155$	10.7063	0.859949
$156$	12.4629	0.997833
$157$	−12.8419	−1.02489	−0.512446	−	0.858719i	$-0.671261\pi$
$157$	−12.8419	−1.02489	−0.512446	+	0.858719i	$0.671261\pi$
$158$	−3.52983	−0.280818
$159$	2.91882	0.231478
$160$	3.12628	0.247154
$161$	5.15402	0.406193
$162$	0.274127	0.0215374
$163$	12.9873	1.01724	0.508622	−	0.860990i	$-0.330155\pi$
$163$	12.9873	1.01724	0.508622	+	0.860990i	$0.330155\pi$
$164$	−12.5237	−0.977934
$165$	−2.26386	−0.176241
$166$	−1.57974	−0.122612
$167$	−21.9179	−1.69606	−0.848029	−	0.529950i	$-0.822211\pi$
$167$	−21.9179	−1.69606	−0.848029	+	0.529950i	$0.822211\pi$
$168$	0.922518	0.0711738
$169$	28.9223	2.22479
$170$	1.41360	0.108418
$171$	4.82735	0.369156
$172$	8.57659	0.653959
$173$	−12.9252	−0.982681	−0.491341	−	0.870967i	$-0.663493\pi$
$173$	−12.9252	−0.982681	−0.491341	+	0.870967i	$0.663493\pi$
$174$	−0.380732	−0.0288632
$175$	0.857432	0.0648157
$176$	8.04751	0.606604
$177$	−8.94468	−0.672323
$178$	0.717476	0.0537771
$179$	−12.0344	−0.899492	−0.449746	−	0.893157i	$-0.648485\pi$
$179$	−12.0344	−0.899492	−0.449746	+	0.893157i	$0.648485\pi$
$180$	−1.92485	−0.143470
$181$	−21.2872	−1.58227	−0.791133	−	0.611644i	$-0.790508\pi$
$181$	−21.2872	−1.58227	−0.791133	+	0.611644i	$0.790508\pi$
$182$	1.52186	0.112807
$183$	1.05037	0.0776454
$184$	−6.46728	−0.476774
$185$	−7.65209	−0.562592
$186$	−2.93488	−0.215196
$187$	11.6741	0.853694
$188$	22.1523	1.61562
$189$	−0.857432	−0.0623690
$190$	1.32331	0.0960026
$191$	−15.1362	−1.09522	−0.547608	−	0.836735i	$-0.684461\pi$
$191$	−15.1362	−1.09522	−0.547608	+	0.836735i	$0.684461\pi$
$192$	6.25255	0.451239
$193$	8.65991	0.623354	0.311677	−	0.950188i	$-0.399109\pi$
$193$	8.65991	0.623354	0.311677	+	0.950188i	$0.399109\pi$
$194$	−3.51953	−0.252688
$195$	−6.47474	−0.463666
$196$	12.0588	0.861346
$197$	−17.9059	−1.27574	−0.637872	−	0.770143i	$-0.720185\pi$
$197$	−17.9059	−1.27574	−0.637872	+	0.770143i	$0.720185\pi$
$198$	0.620585	0.0441030
$199$	−11.0430	−0.782815	−0.391407	−	0.920218i	$-0.628012\pi$
$199$	−11.0430	−0.782815	−0.391407	+	0.920218i	$0.628012\pi$
$200$	−1.07591	−0.0760782
$201$	−7.50642	−0.529462
$202$	−1.41323	−0.0994346
$203$	1.19088	0.0835833
$204$	9.92594	0.694955
$205$	6.50630	0.454419
$206$	4.23878	0.295330
$207$	6.01099	0.417793
$208$	23.0162	1.59589
$209$	10.9284	0.755935
$210$	−0.235045	−0.0162196
$211$	−2.88855	−0.198856	−0.0994280	−	0.995045i	$-0.531701\pi$
$211$	−2.88855	−0.198856	−0.0994280	+	0.995045i	$0.531701\pi$
$212$	5.61830	0.385867
$213$	7.37833	0.505555
$214$	4.32600	0.295719
$215$	−4.45571	−0.303877
$216$	1.07591	0.0732063
$217$	9.17991	0.623173
$218$	1.33548	0.0904502
$219$	−7.86300	−0.531332
$220$	−4.35760	−0.293789
$221$	33.3884	2.24595
$222$	2.09764	0.140785
$223$	−18.9209	−1.26704	−0.633518	−	0.773728i	$-0.718390\pi$
$223$	−18.9209	−1.26704	−0.633518	+	0.773728i	$0.718390\pi$
$224$	2.68057	0.179103
$225$	1.00000	0.0666667
$226$	4.38468	0.291665
$227$	−21.7660	−1.44466	−0.722331	−	0.691548i	$-0.756929\pi$
$227$	−21.7660	−1.44466	−0.722331	+	0.691548i	$0.756929\pi$
$228$	9.29194	0.615374
$229$	−15.3938	−1.01725	−0.508626	−	0.860987i	$-0.669847\pi$
$229$	−15.3938	−1.01725	−0.508626	+	0.860987i	$0.669847\pi$
$230$	1.64777	0.108651
$231$	−1.94110	−0.127715
$232$	−1.49432	−0.0981068
$233$	5.60255	0.367035	0.183518	−	0.983016i	$-0.441252\pi$
$233$	5.60255	0.367035	0.183518	+	0.983016i	$0.441252\pi$
$234$	1.77490	0.116029
$235$	−11.5085	−0.750734
$236$	−17.2172	−1.12074
$237$	12.8766	0.836427
$238$	1.21206	0.0785663
$239$	8.08105	0.522720	0.261360	−	0.965241i	$-0.415829\pi$
$239$	8.08105	0.522720	0.261360	+	0.965241i	$0.415829\pi$
$240$	−3.55477	−0.229460
$241$	30.0164	1.93352	0.966762	−	0.255678i	$-0.0822986\pi$
$241$	30.0164	1.93352	0.966762	+	0.255678i	$0.0822986\pi$
$242$	−1.61048	−0.103526
$243$	−1.00000	−0.0641500
$244$	2.02180	0.129433
$245$	−6.26481	−0.400244
$246$	−1.78355	−0.113715
$247$	31.2558	1.98876
$248$	−11.5190	−0.731456
$249$	5.76282	0.365204
$250$	0.274127	0.0173373
$251$	−11.4760	−0.724359	−0.362180	−	0.932108i	$-0.617967\pi$
$251$	−11.4760	−0.724359	−0.362180	+	0.932108i	$0.617967\pi$
$252$	−1.65043	−0.103967
$253$	13.6080	0.855530
$254$	−1.06308	−0.0667034
$255$	−5.15672	−0.322927
$256$	10.3213	0.645079
$257$	13.0542	0.814299	0.407150	−	0.913361i	$-0.366523\pi$
$257$	13.0542	0.814299	0.407150	+	0.913361i	$0.366523\pi$
$258$	1.22143	0.0760429
$259$	−6.56114	−0.407689
$260$	−12.4629	−0.772918
$261$	1.38889	0.0859702
$262$	−1.18785	−0.0733856
$263$	9.15134	0.564296	0.282148	−	0.959371i	$-0.408953\pi$
$263$	9.15134	0.564296	0.282148	+	0.959371i	$0.408953\pi$
$264$	2.43570	0.149907
$265$	−2.91882	−0.179302
$266$	1.13464	0.0695695
$267$	−2.61732	−0.160177
$268$	−14.4488	−0.882599
$269$	6.55715	0.399797	0.199898	−	0.979817i	$-0.435939\pi$
$269$	6.55715	0.399797	0.199898	+	0.979817i	$0.435939\pi$
$270$	−0.274127	−0.0166828
$271$	24.4863	1.48744	0.743719	−	0.668492i	$-0.233060\pi$
$271$	24.4863	1.48744	0.743719	+	0.668492i	$0.233060\pi$
$272$	18.3310	1.11148
$273$	−5.55165	−0.336001
$274$	4.93508	0.298139
$275$	2.26386	0.136516
$276$	11.5703	0.696450
$277$	15.9259	0.956897	0.478448	−	0.878116i	$-0.341199\pi$
$277$	15.9259	0.956897	0.478448	+	0.878116i	$0.341199\pi$
$278$	4.32685	0.259508
$279$	10.7063	0.640969
$280$	−0.922518	−0.0551310
$281$	7.98010	0.476053	0.238026	−	0.971259i	$-0.423500\pi$
$281$	7.98010	0.476053	0.238026	+	0.971259i	$0.423500\pi$
$282$	3.15480	0.187866
$283$	11.6029	0.689719	0.344859	−	0.938654i	$-0.387927\pi$
$283$	11.6029	0.689719	0.344859	+	0.938654i	$0.387927\pi$
$284$	14.2022	0.842746
$285$	−4.82735	−0.285947
$286$	4.01812	0.237597
$287$	5.57870	0.329300
$288$	3.12628	0.184218
$289$	9.59179	0.564223
$290$	0.380732	0.0223574
$291$	12.8391	0.752639
$292$	−15.1351	−0.885717
$293$	23.9320	1.39812	0.699061	−	0.715062i	$-0.253601\pi$
$293$	23.9320	1.39812	0.699061	+	0.715062i	$0.253601\pi$
$294$	1.71735	0.100158
$295$	8.94468	0.520779
$296$	8.23294	0.478530
$297$	−2.26386	−0.131362
$298$	0.0551770	0.00319632
$299$	38.9196	2.25078
$300$	1.92485	0.111132
$301$	−3.82046	−0.220208
$302$	−6.10988	−0.351584
$303$	5.15539	0.296169
$304$	17.1601	0.984200
$305$	−1.05037	−0.0601438
$306$	1.41360	0.0808099
$307$	−32.1516	−1.83499	−0.917495	−	0.397748i	$-0.869792\pi$
$307$	−32.1516	−1.83499	−0.917495	+	0.397748i	$0.869792\pi$
$308$	−3.73634	−0.212898
$309$	−15.4628	−0.879650
$310$	2.93488	0.166690
$311$	−9.55657	−0.541904	−0.270952	−	0.962593i	$-0.587338\pi$
$311$	−9.55657	−0.541904	−0.270952	+	0.962593i	$0.587338\pi$
$312$	6.96623	0.394385
$313$	−9.03248	−0.510546	−0.255273	−	0.966869i	$-0.582165\pi$
$313$	−9.03248	−0.510546	−0.255273	+	0.966869i	$0.582165\pi$
$314$	−3.52030	−0.198662
$315$	0.857432	0.0483108
$316$	24.7856	1.39430
$317$	−18.4666	−1.03719	−0.518593	−	0.855021i	$-0.673544\pi$
$317$	−18.4666	−1.03719	−0.518593	+	0.855021i	$0.673544\pi$
$318$	0.800127	0.0448689
$319$	3.14425	0.176044
$320$	−6.25255	−0.349528
$321$	−15.7810	−0.880810
$322$	1.41285	0.0787353
$323$	24.8933	1.38510
$324$	−1.92485	−0.106936
$325$	6.47474	0.359154
$326$	3.56017	0.197179
$327$	−4.87176	−0.269409
$328$	−7.00018	−0.386520
$329$	−9.86779	−0.544029
$330$	−0.620585	−0.0341621
$331$	11.9642	0.657614	0.328807	−	0.944397i	$-0.393353\pi$
$331$	11.9642	0.657614	0.328807	+	0.944397i	$0.393353\pi$
$332$	11.0926	0.608785
$333$	−7.65209	−0.419332
$334$	−6.00829	−0.328759
$335$	7.50642	0.410120
$336$	−3.04798	−0.166281
$337$	3.46003	0.188480	0.0942399	−	0.995550i	$-0.469958\pi$
$337$	3.46003	0.188480	0.0942399	+	0.995550i	$0.469958\pi$
$338$	7.92837	0.431247
$339$	−15.9951	−0.868734
$340$	−9.92594	−0.538310
$341$	24.2375	1.31254
$342$	1.32331	0.0715561
$343$	−11.3737	−0.614120
$344$	4.79393	0.258471
$345$	−6.01099	−0.323621
$346$	−3.54313	−0.190480
$347$	−29.9141	−1.60587	−0.802935	−	0.596066i	$-0.796730\pi$
$347$	−29.9141	−1.60587	−0.802935	+	0.596066i	$0.796730\pi$
$348$	2.67341	0.143310
$349$	−11.4581	−0.613337	−0.306668	−	0.951816i	$-0.599214\pi$
$349$	−11.4581	−0.613337	−0.306668	+	0.951816i	$0.599214\pi$
$350$	0.235045	0.0125637
$351$	−6.47474	−0.345596
$352$	7.07745	0.377229
$353$	−19.4175	−1.03349	−0.516746	−	0.856139i	$-0.672857\pi$
$353$	−19.4175	−1.03349	−0.516746	+	0.856139i	$0.672857\pi$
$354$	−2.45198	−0.130321
$355$	−7.37833	−0.391601
$356$	−5.03795	−0.267011
$357$	−4.42154	−0.234013
$358$	−3.29895	−0.174355
$359$	−14.4322	−0.761700	−0.380850	−	0.924637i	$-0.624369\pi$
$359$	−14.4322	−0.761700	−0.380850	+	0.924637i	$0.624369\pi$
$360$	−1.07591	−0.0567053
$361$	4.30326	0.226487
$362$	−5.83539	−0.306702
$363$	5.87494	0.308355
$364$	−10.6861	−0.560105
$365$	7.86300	0.411568
$366$	0.287934	0.0150505
$367$	−29.2161	−1.52507	−0.762533	−	0.646949i	$-0.776045\pi$
$367$	−29.2161	−1.52507	−0.762533	+	0.646949i	$0.776045\pi$
$368$	21.3677	1.11387
$369$	6.50630	0.338704
$370$	−2.09764	−0.109051
$371$	−2.50269	−0.129933
$372$	20.6080	1.06848
$373$	−27.0446	−1.40031	−0.700157	−	0.713989i	$-0.746887\pi$
$373$	−27.0446	−1.40031	−0.700157	+	0.713989i	$0.746887\pi$
$374$	3.20018	0.165478
$375$	−1.00000	−0.0516398
$376$	12.3821	0.638560
$377$	8.99271	0.463148
$378$	−0.235045	−0.0120894
$379$	2.20256	0.113138	0.0565690	−	0.998399i	$-0.481984\pi$
$379$	2.20256	0.113138	0.0565690	+	0.998399i	$0.481984\pi$
$380$	−9.29194	−0.476666
$381$	3.87805	0.198678
$382$	−4.14923	−0.212293
$383$	−27.2953	−1.39472	−0.697362	−	0.716719i	$-0.745643\pi$
$383$	−27.2953	−1.39472	−0.697362	+	0.716719i	$0.745643\pi$
$384$	7.96654	0.406541
$385$	1.94110	0.0989278
$386$	2.37391	0.120829
$387$	−4.45571	−0.226496
$388$	24.7133	1.25463
$389$	−3.36895	−0.170812	−0.0854062	−	0.996346i	$-0.527219\pi$
$389$	−3.36895	−0.170812	−0.0854062	+	0.996346i	$0.527219\pi$
$390$	−1.77490	−0.0898756
$391$	30.9970	1.56759
$392$	6.74036	0.340440
$393$	4.33321	0.218582
$394$	−4.90849	−0.247286
$395$	−12.8766	−0.647894
$396$	−4.35760	−0.218978
$397$	3.62113	0.181739	0.0908697	−	0.995863i	$-0.471035\pi$
$397$	3.62113	0.181739	0.0908697	+	0.995863i	$0.471035\pi$
$398$	−3.02717	−0.151738
$399$	−4.13912	−0.207215
$400$	3.55477	0.177739
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−2.05771	−0.102629
$403$	69.3204	3.45310
$404$	9.92337	0.493706
$405$	1.00000	0.0496904
$406$	0.326452	0.0162015
$407$	−17.3232	−0.858681
$408$	5.54816	0.274675
$409$	−16.4598	−0.813884	−0.406942	−	0.913454i	$-0.633405\pi$
$409$	−16.4598	−0.813884	−0.406942	+	0.913454i	$0.633405\pi$
$410$	1.78355	0.0880833
$411$	−18.0029	−0.888018
$412$	−29.7637	−1.46635
$413$	7.66945	0.377389
$414$	1.64777	0.0809837
$415$	−5.76282	−0.282886
$416$	20.2418	0.992437
$417$	−15.7841	−0.772952
$418$	2.99578	0.146528
$419$	0.112976	0.00551922	0.00275961	−	0.999996i	$-0.499122\pi$
$419$	0.112976	0.00551922	0.00275961	+	0.999996i	$0.499122\pi$
$420$	1.65043	0.0805328
$421$	19.7506	0.962587	0.481293	−	0.876560i	$-0.340167\pi$
$421$	19.7506	0.962587	0.481293	+	0.876560i	$0.340167\pi$
$422$	−0.791829	−0.0385456
$423$	−11.5085	−0.559564
$424$	3.14038	0.152510
$425$	5.15672	0.250138
$426$	2.02260	0.0979952
$427$	−0.900618	−0.0435840
$428$	−30.3761	−1.46829
$429$	−14.6579	−0.707690
$430$	−1.22143	−0.0589025
$431$	30.6598	1.47683	0.738415	−	0.674347i	$-0.235575\pi$
$431$	30.6598	1.47683	0.738415	+	0.674347i	$0.235575\pi$
$432$	−3.55477	−0.171029
$433$	5.13299	0.246676	0.123338	−	0.992365i	$-0.460640\pi$
$433$	5.13299	0.246676	0.123338	+	0.992365i	$0.460640\pi$
$434$	2.51646	0.120794
$435$	−1.38889	−0.0665922
$436$	−9.37744	−0.449098
$437$	29.0171	1.38808
$438$	−2.15546	−0.102992
$439$	−0.0738069	−0.00352261	−0.00176130	−	0.999998i	$-0.500561\pi$
$439$	−0.0738069	−0.00352261	−0.00176130	+	0.999998i	$0.500561\pi$
$440$	−2.43570	−0.116118
$441$	−6.26481	−0.298324
$442$	9.15267	0.435348
$443$	0.733120	0.0348316	0.0174158	−	0.999848i	$-0.494456\pi$
$443$	0.733120	0.0348316	0.0174158	+	0.999848i	$0.494456\pi$
$444$	−14.7292	−0.699015
$445$	2.61732	0.124073
$446$	−5.18672	−0.245598
$447$	−0.201283	−0.00952034
$448$	−5.36114	−0.253290
$449$	13.0839	0.617469	0.308734	−	0.951148i	$-0.400095\pi$
$449$	13.0839	0.617469	0.308734	+	0.951148i	$0.400095\pi$
$450$	0.274127	0.0129225
$451$	14.7293	0.693577
$452$	−30.7882	−1.44816
$453$	22.2885	1.04720
$454$	−5.96665	−0.280029
$455$	5.55165	0.260265
$456$	5.19378	0.243221
$457$	26.6762	1.24786	0.623930	−	0.781480i	$-0.285535\pi$
$457$	26.6762	1.24786	0.623930	+	0.781480i	$0.285535\pi$
$458$	−4.21986	−0.197181
$459$	−5.15672	−0.240695
$460$	−11.5703	−0.539468
$461$	26.5557	1.23682	0.618412	−	0.785854i	$-0.287776\pi$
$461$	26.5557	1.23682	0.618412	+	0.785854i	$0.287776\pi$
$462$	−0.532109	−0.0247559
$463$	−9.00431	−0.418466	−0.209233	−	0.977866i	$-0.567097\pi$
$463$	−9.00431	−0.418466	−0.209233	+	0.977866i	$0.567097\pi$
$464$	4.93719	0.229203
$465$	−10.7063	−0.496492
$466$	1.53581	0.0711450
$467$	4.30428	0.199178	0.0995891	−	0.995029i	$-0.468247\pi$
$467$	4.30428	0.199178	0.0995891	+	0.995029i	$0.468247\pi$
$468$	−12.4629	−0.576099
$469$	6.43625	0.297198
$470$	−3.15480	−0.145520
$471$	12.8419	0.591722
$472$	−9.62365	−0.442964
$473$	−10.0871	−0.463805
$474$	3.52983	0.162130
$475$	4.82735	0.221494
$476$	−8.51082	−0.390093
$477$	−2.91882	−0.133644
$478$	2.21523	0.101322
$479$	−0.768987	−0.0351359	−0.0175680	−	0.999846i	$-0.505592\pi$
$479$	−0.768987	−0.0351359	−0.0175680	+	0.999846i	$0.505592\pi$
$480$	−3.12628	−0.142694
$481$	−49.5453	−2.25907
$482$	8.22829	0.374788
$483$	−5.15402	−0.234516
$484$	11.3084	0.514019
$485$	−12.8391	−0.582992
$486$	−0.274127	−0.0124346
$487$	−35.3544	−1.60206	−0.801030	−	0.598624i	$-0.795715\pi$
$487$	−35.3544	−1.60206	−0.801030	+	0.598624i	$0.795715\pi$
$488$	1.13010	0.0511571
$489$	−12.9873	−0.587306
$490$	−1.71735	−0.0775821
$491$	26.6452	1.20248	0.601241	−	0.799068i	$-0.294673\pi$
$491$	26.6452	1.20248	0.601241	+	0.799068i	$0.294673\pi$
$492$	12.5237	0.564611
$493$	7.16212	0.322566
$494$	8.56806	0.385495
$495$	2.26386	0.101753
$496$	38.0584	1.70887
$497$	−6.32642	−0.283779
$498$	1.57974	0.0707900
$499$	3.55648	0.159210	0.0796051	−	0.996826i	$-0.474634\pi$
$499$	3.55648	0.159210	0.0796051	+	0.996826i	$0.474634\pi$
$500$	−1.92485	−0.0860821
$501$	21.9179	0.979220
$502$	−3.14588	−0.140408
$503$	−9.58408	−0.427333	−0.213667	−	0.976907i	$-0.568541\pi$
$503$	−9.58408	−0.427333	−0.213667	+	0.976907i	$0.568541\pi$
$504$	−0.922518	−0.0410922
$505$	−5.15539	−0.229412
$506$	3.73033	0.165833
$507$	−28.9223	−1.28448
$508$	7.46468	0.331191
$509$	0.344010	0.0152480	0.00762398	−	0.999971i	$-0.497573\pi$
$509$	0.344010	0.0152480	0.00762398	+	0.999971i	$0.497573\pi$
$510$	−1.41360	−0.0625951
$511$	6.74199	0.298248
$512$	18.7624	0.829190
$513$	−4.82735	−0.213133
$514$	3.57851	0.157841
$515$	15.4628	0.681374
$516$	−8.57659	−0.377563
$517$	−26.0537	−1.14584
$518$	−1.79858	−0.0790253
$519$	12.9252	0.567351
$520$	−6.96623	−0.305489
$521$	−3.83410	−0.167975	−0.0839875	−	0.996467i	$-0.526766\pi$
$521$	−3.83410	−0.167975	−0.0839875	+	0.996467i	$0.526766\pi$
$522$	0.380732	0.0166642
$523$	−22.6597	−0.990840	−0.495420	−	0.868654i	$-0.664986\pi$
$523$	−22.6597	−0.990840	−0.495420	+	0.868654i	$0.664986\pi$
$524$	8.34080	0.364370
$525$	−0.857432	−0.0374214
$526$	2.50863	0.109381
$527$	55.2093	2.40496
$528$	−8.04751	−0.350223
$529$	13.1321	0.570959
$530$	−0.800127	−0.0347553
$531$	8.94468	0.388166
$532$	−7.96720	−0.345422
$533$	42.1266	1.82470
$534$	−0.717476	−0.0310482
$535$	15.7810	0.682272
$536$	−8.07622	−0.348840
$537$	12.0344	0.519322
$538$	1.79749	0.0774954
$539$	−14.1826	−0.610890
$540$	1.92485	0.0828325
$541$	−2.63291	−0.113198	−0.0565988	−	0.998397i	$-0.518026\pi$
$541$	−2.63291	−0.113198	−0.0565988	+	0.998397i	$0.518026\pi$
$542$	6.71236	0.288320
$543$	21.2872	0.913521
$544$	16.1213	0.691197
$545$	4.87176	0.208683
$546$	−1.52186	−0.0651294
$547$	−27.5846	−1.17943	−0.589716	−	0.807611i	$-0.700760\pi$
$547$	−27.5846	−1.17943	−0.589716	+	0.807611i	$0.700760\pi$
$548$	−34.6530	−1.48030
$549$	−1.05037	−0.0448286
$550$	0.620585	0.0264618
$551$	6.70465	0.285628
$552$	6.46728	0.275266
$553$	−11.0408	−0.469504
$554$	4.36573	0.185482
$555$	7.65209	0.324813
$556$	−30.3822	−1.28849
$557$	12.4586	0.527887	0.263944	−	0.964538i	$-0.414977\pi$
$557$	12.4586	0.527887	0.263944	+	0.964538i	$0.414977\pi$
$558$	2.93488	0.124243
$559$	−28.8496	−1.22021
$560$	3.04798	0.128800
$561$	−11.6741	−0.492881
$562$	2.18756	0.0922766
$563$	3.42291	0.144258	0.0721291	−	0.997395i	$-0.477021\pi$
$563$	3.42291	0.144258	0.0721291	+	0.997395i	$0.477021\pi$
$564$	−22.1523	−0.932779
$565$	15.9951	0.672918
$566$	3.18066	0.133693
$567$	0.857432	0.0360087
$568$	7.93841	0.333088
$569$	−3.62288	−0.151879	−0.0759395	−	0.997112i	$-0.524196\pi$
$569$	−3.62288	−0.151879	−0.0759395	+	0.997112i	$0.524196\pi$
$570$	−1.32331	−0.0554271
$571$	19.2731	0.806554	0.403277	−	0.915078i	$-0.367871\pi$
$571$	19.2731	0.806554	0.403277	+	0.915078i	$0.367871\pi$
$572$	−28.2143	−1.17970
$573$	15.1362	0.632323
$574$	1.52927	0.0638306
$575$	6.01099	0.250676
$576$	−6.25255	−0.260523
$577$	−36.7255	−1.52890	−0.764452	−	0.644681i	$-0.776990\pi$
$577$	−36.7255	−1.52890	−0.764452	+	0.644681i	$0.776990\pi$
$578$	2.62937	0.109367
$579$	−8.65991	−0.359893
$580$	−2.67341	−0.111007
$581$	−4.94122	−0.204996
$582$	3.51953	0.145889
$583$	−6.60780	−0.273667
$584$	−8.45987	−0.350072
$585$	6.47474	0.267698
$586$	6.56040	0.271008
$587$	38.1420	1.57429	0.787145	−	0.616768i	$-0.211558\pi$
$587$	38.1420	1.57429	0.787145	+	0.616768i	$0.211558\pi$
$588$	−12.0588	−0.497299
$589$	51.6829	2.12956
$590$	2.45198	0.100946
$591$	17.9059	0.736551
$592$	−27.2014	−1.11797
$593$	43.0242	1.76679	0.883396	−	0.468626i	$-0.155251\pi$
$593$	43.0242	1.76679	0.883396	+	0.468626i	$0.155251\pi$
$594$	−0.620585	−0.0254629
$595$	4.42154	0.181265
$596$	−0.387440	−0.0158701
$597$	11.0430	0.451958
$598$	10.6689	0.436284
$599$	42.3110	1.72878	0.864391	−	0.502821i	$-0.167704\pi$
$599$	42.3110	1.72878	0.864391	+	0.502821i	$0.167704\pi$
$600$	1.07591	0.0439238
$601$	24.2804	0.990419	0.495209	−	0.868774i	$-0.335091\pi$
$601$	24.2804	0.990419	0.495209	+	0.868774i	$0.335091\pi$
$602$	−1.04729	−0.0426844
$603$	7.50642	0.305685
$604$	42.9021	1.74566
$605$	−5.87494	−0.238850
$606$	1.41323	0.0574086
$607$	−37.6134	−1.52668	−0.763340	−	0.645997i	$-0.776442\pi$
$607$	−37.6134	−1.52668	−0.763340	+	0.645997i	$0.776442\pi$
$608$	15.0916	0.612046
$609$	−1.19088	−0.0482568
$610$	−0.287934	−0.0116581
$611$	−74.5148	−3.01455
$612$	−9.92594	−0.401232
$613$	2.57315	0.103929	0.0519643	−	0.998649i	$-0.483452\pi$
$613$	2.57315	0.103929	0.0519643	+	0.998649i	$0.483452\pi$
$614$	−8.81362	−0.355689
$615$	−6.50630	−0.262359
$616$	−2.08845	−0.0841460
$617$	−3.26623	−0.131493	−0.0657466	−	0.997836i	$-0.520943\pi$
$617$	−3.26623	−0.131493	−0.0657466	+	0.997836i	$0.520943\pi$
$618$	−4.23878	−0.170509
$619$	−7.42711	−0.298521	−0.149260	−	0.988798i	$-0.547689\pi$
$619$	−7.42711	−0.298521	−0.149260	+	0.988798i	$0.547689\pi$
$620$	−20.6080	−0.827639
$621$	−6.01099	−0.241213
$622$	−2.61971	−0.105041
$623$	2.24417	0.0899107
$624$	−23.0162	−0.921387
$625$	1.00000	0.0400000
$626$	−2.47605	−0.0989627
$627$	−10.9284	−0.436439
$628$	24.7187	0.986384
$629$	−39.4597	−1.57336
$630$	0.235045	0.00936442
$631$	6.11330	0.243367	0.121683	−	0.992569i	$-0.461171\pi$
$631$	6.11330	0.243367	0.121683	+	0.992569i	$0.461171\pi$
$632$	13.8541	0.551085
$633$	2.88855	0.114810
$634$	−5.06218	−0.201045
$635$	−3.87805	−0.153896
$636$	−5.61830	−0.222780
$637$	−40.5630	−1.60717
$638$	0.861924	0.0341239
$639$	−7.37833	−0.291882
$640$	−7.96654	−0.314905
$641$	−3.68024	−0.145361	−0.0726803	−	0.997355i	$-0.523155\pi$
$641$	−3.68024	−0.145361	−0.0726803	+	0.997355i	$0.523155\pi$
$642$	−4.32600	−0.170734
$643$	−37.7716	−1.48957	−0.744784	−	0.667306i	$-0.767447\pi$
$643$	−37.7716	−1.48957	−0.744784	+	0.667306i	$0.767447\pi$
$644$	−9.92073	−0.390932
$645$	4.45571	0.175443
$646$	6.82392	0.268483
$647$	−12.6669	−0.497988	−0.248994	−	0.968505i	$-0.580100\pi$
$647$	−12.6669	−0.497988	−0.248994	+	0.968505i	$0.580100\pi$
$648$	−1.07591	−0.0422657
$649$	20.2495	0.794862
$650$	1.77490	0.0696173
$651$	−9.17991	−0.359789
$652$	−24.9987	−0.979023
$653$	18.7794	0.734896	0.367448	−	0.930044i	$-0.380232\pi$
$653$	18.7794	0.734896	0.367448	+	0.930044i	$0.380232\pi$
$654$	−1.33548	−0.0522215
$655$	−4.33321	−0.169313
$656$	23.1284	0.903013
$657$	7.86300	0.306765
$658$	−2.70503	−0.105453
$659$	−21.6258	−0.842423	−0.421211	−	0.906963i	$-0.638395\pi$
$659$	−21.6258	−0.842423	−0.421211	+	0.906963i	$0.638395\pi$
$660$	4.35760	0.169619
$661$	−22.0763	−0.858668	−0.429334	−	0.903146i	$-0.641252\pi$
$661$	−22.0763	−0.858668	−0.429334	+	0.903146i	$0.641252\pi$
$662$	3.27972	0.127470
$663$	−33.3884	−1.29670
$664$	6.20026	0.240617
$665$	4.13912	0.160508
$666$	−2.09764	−0.0812820
$667$	8.34861	0.323260
$668$	42.1888	1.63233
$669$	18.9209	0.731523
$670$	2.05771	0.0794964
$671$	−2.37788	−0.0917971
$672$	−2.68057	−0.103405
$673$	24.6752	0.951160	0.475580	−	0.879673i	$-0.342238\pi$
$673$	24.6752	0.951160	0.475580	+	0.879673i	$0.342238\pi$
$674$	0.948487	0.0365343
$675$	−1.00000	−0.0384900
$676$	−55.6712	−2.14120
$677$	19.6760	0.756212	0.378106	−	0.925762i	$-0.376576\pi$
$677$	19.6760	0.756212	0.378106	+	0.925762i	$0.376576\pi$
$678$	−4.38468	−0.168393
$679$	−11.0086	−0.422472
$680$	−5.54816	−0.212762
$681$	21.7660	0.834076
$682$	6.64415	0.254418
$683$	−19.9741	−0.764288	−0.382144	−	0.924103i	$-0.624814\pi$
$683$	−19.9741	−0.764288	−0.382144	+	0.924103i	$0.624814\pi$
$684$	−9.29194	−0.355286
$685$	18.0029	0.687856
$686$	−3.11783	−0.119039
$687$	15.3938	0.587311
$688$	−15.8390	−0.603857
$689$	−18.8986	−0.719980
$690$	−1.64777	−0.0627297
$691$	8.78362	0.334145	0.167072	−	0.985945i	$-0.446569\pi$
$691$	8.78362	0.334145	0.167072	+	0.985945i	$0.446569\pi$
$692$	24.8790	0.945759
$693$	1.94110	0.0737365
$694$	−8.20025	−0.311277
$695$	15.7841	0.598726
$696$	1.49432	0.0566420
$697$	33.5512	1.27084
$698$	−3.14097	−0.118887
$699$	−5.60255	−0.211908
$700$	−1.65043	−0.0623804
$701$	−23.5039	−0.887732	−0.443866	−	0.896093i	$-0.646393\pi$
$701$	−23.5039	−0.887732	−0.443866	+	0.896093i	$0.646393\pi$
$702$	−1.77490	−0.0669893
$703$	−36.9393	−1.39319
$704$	−14.1549	−0.533483
$705$	11.5085	0.433437
$706$	−5.32287	−0.200329
$707$	−4.42039	−0.166246
$708$	17.2172	0.647062
$709$	−18.1770	−0.682652	−0.341326	−	0.939945i	$-0.610876\pi$
$709$	−18.1770	−0.682652	−0.341326	+	0.939945i	$0.610876\pi$
$710$	−2.02260	−0.0759068
$711$	−12.8766	−0.482911
$712$	−2.81599	−0.105534
$713$	64.3554	2.41013
$714$	−1.21206	−0.0453603
$715$	14.6579	0.548174
$716$	23.1644	0.865696
$717$	−8.08105	−0.301792
$718$	−3.95624	−0.147646
$719$	47.8812	1.78567	0.892834	−	0.450385i	$-0.148713\pi$
$719$	47.8812	1.78567	0.892834	+	0.450385i	$0.148713\pi$
$720$	3.55477	0.132479
$721$	13.2583	0.493766
$722$	1.17964	0.0439016
$723$	−30.0164	−1.11632
$724$	40.9748	1.52282
$725$	1.38889	0.0515821
$726$	1.61048	0.0597705
$727$	−32.5980	−1.20899	−0.604497	−	0.796608i	$-0.706626\pi$
$727$	−32.5980	−1.20899	−0.604497	+	0.796608i	$0.706626\pi$
$728$	−5.97306	−0.221376
$729$	1.00000	0.0370370
$730$	2.15546	0.0797772
$731$	−22.9768	−0.849829
$732$	−2.02180	−0.0747280
$733$	18.6432	0.688603	0.344302	−	0.938859i	$-0.388116\pi$
$733$	18.6432	0.688603	0.344302	+	0.938859i	$0.388116\pi$
$734$	−8.00891	−0.295614
$735$	6.26481	0.231081
$736$	18.7920	0.692683
$737$	16.9935	0.625963
$738$	1.78355	0.0656534
$739$	−19.2498	−0.708116	−0.354058	−	0.935224i	$-0.615198\pi$
$739$	−19.2498	−0.708116	−0.354058	+	0.935224i	$0.615198\pi$
$740$	14.7292	0.541454
$741$	−31.2558	−1.14821
$742$	−0.686054	−0.0251858
$743$	−31.1742	−1.14367	−0.571835	−	0.820369i	$-0.693768\pi$
$743$	−31.1742	−1.14367	−0.571835	+	0.820369i	$0.693768\pi$
$744$	11.5190	0.422306
$745$	0.201283	0.00737442
$746$	−7.41364	−0.271433
$747$	−5.76282	−0.210850
$748$	−22.4709	−0.821619
$749$	13.5311	0.494417
$750$	−0.274127	−0.0100097
$751$	10.0805	0.367841	0.183920	−	0.982941i	$-0.441121\pi$
$751$	10.0805	0.367841	0.183920	+	0.982941i	$0.441121\pi$
$752$	−40.9103	−1.49184
$753$	11.4760	0.418209
$754$	2.46514	0.0897752
$755$	−22.2885	−0.811161
$756$	1.65043	0.0600256
$757$	17.8080	0.647244	0.323622	−	0.946186i	$-0.395099\pi$
$757$	17.8080	0.647244	0.323622	+	0.946186i	$0.395099\pi$
$758$	0.603781	0.0219303
$759$	−13.6080	−0.493941
$760$	−5.19378	−0.188398
$761$	29.1084	1.05518	0.527590	−	0.849499i	$-0.323096\pi$
$761$	29.1084	1.05518	0.527590	+	0.849499i	$0.323096\pi$
$762$	1.06308	0.0385112
$763$	4.17720	0.151225
$764$	29.1349	1.05406
$765$	5.15672	0.186442
$766$	−7.48238	−0.270349
$767$	57.9145	2.09117
$768$	−10.3213	−0.372436
$769$	−11.3219	−0.408277	−0.204138	−	0.978942i	$-0.565439\pi$
$769$	−11.3219	−0.408277	−0.204138	+	0.978942i	$0.565439\pi$
$770$	0.532109	0.0191759
$771$	−13.0542	−0.470136
$772$	−16.6691	−0.599933
$773$	6.52374	0.234643	0.117321	−	0.993094i	$-0.462569\pi$
$773$	6.52374	0.234643	0.117321	+	0.993094i	$0.462569\pi$
$774$	−1.22143	−0.0439034
$775$	10.7063	0.384581
$776$	13.8136	0.495881
$777$	6.56114	0.235380
$778$	−0.923519	−0.0331098
$779$	31.4081	1.12531
$780$	12.4629	0.446245
$781$	−16.7035	−0.597698
$782$	8.49712	0.303856
$783$	−1.38889	−0.0496349
$784$	−22.2700	−0.795357
$785$	−12.8419	−0.458346
$786$	1.18785	0.0423692
$787$	44.8533	1.59885	0.799423	−	0.600768i	$-0.205138\pi$
$787$	44.8533	1.59885	0.799423	+	0.600768i	$0.205138\pi$
$788$	34.4663	1.22781
$789$	−9.15134	−0.325796
$790$	−3.52983	−0.125586
$791$	13.7147	0.487638
$792$	−2.43570	−0.0865490
$793$	−6.80085	−0.241505
$794$	0.992649	0.0352278
$795$	2.91882	0.103520
$796$	21.2561	0.753402
$797$	36.4891	1.29251	0.646256	−	0.763121i	$-0.276334\pi$
$797$	36.4891	1.29251	0.646256	+	0.763121i	$0.276334\pi$
$798$	−1.13464	−0.0401659
$799$	−59.3464	−2.09952
$800$	3.12628	0.110531
$801$	2.61732	0.0924783
$802$	−0.274127	−0.00967976
$803$	17.8007	0.628174
$804$	14.4488	0.509569
$805$	5.15402	0.181655
$806$	19.0026	0.669338
$807$	−6.55715	−0.230823
$808$	5.54672	0.195133
$809$	−19.7917	−0.695838	−0.347919	−	0.937525i	$-0.613112\pi$
$809$	−19.7917	−0.695838	−0.347919	+	0.937525i	$0.613112\pi$
$810$	0.274127	0.00963184
$811$	−28.4953	−1.00060	−0.500302	−	0.865851i	$-0.666778\pi$
$811$	−28.4953	−1.00060	−0.500302	+	0.865851i	$0.666778\pi$
$812$	−2.29227	−0.0804428
$813$	−24.4863	−0.858773
$814$	−4.74877	−0.166444
$815$	12.9873	0.454925
$816$	−18.3310	−0.641713
$817$	−21.5092	−0.752513
$818$	−4.51207	−0.157761
$819$	5.55165	0.193990
$820$	−12.5237	−0.437346
$821$	1.67805	0.0585645	0.0292823	−	0.999571i	$-0.490678\pi$
$821$	1.67805	0.0585645	0.0292823	+	0.999571i	$0.490678\pi$
$822$	−4.93508	−0.172131
$823$	−17.6641	−0.615732	−0.307866	−	0.951430i	$-0.599615\pi$
$823$	−17.6641	−0.615732	−0.307866	+	0.951430i	$0.599615\pi$
$824$	−16.6366	−0.579563
$825$	−2.26386	−0.0788175
$826$	2.10240	0.0731519
$827$	−17.7404	−0.616896	−0.308448	−	0.951241i	$-0.599810\pi$
$827$	−17.7404	−0.616896	−0.308448	+	0.951241i	$0.599810\pi$
$828$	−11.5703	−0.402095
$829$	22.2406	0.772448	0.386224	−	0.922405i	$-0.373779\pi$
$829$	22.2406	0.772448	0.386224	+	0.922405i	$0.373779\pi$
$830$	−1.57974	−0.0548337
$831$	−15.9259	−0.552465
$832$	−40.4837	−1.40352
$833$	−32.3059	−1.11933
$834$	−4.32685	−0.149827
$835$	−21.9179	−0.758500
$836$	−21.0356	−0.727533
$837$	−10.7063	−0.370063
$838$	0.0309696	0.00106983
$839$	−26.7343	−0.922971	−0.461485	−	0.887148i	$-0.652683\pi$
$839$	−26.7343	−0.922971	−0.461485	+	0.887148i	$0.652683\pi$
$840$	0.922518	0.0318299
$841$	−27.0710	−0.933482
$842$	5.41418	0.186585
$843$	−7.98010	−0.274849
$844$	5.56004	0.191384
$845$	28.9223	0.994957
$846$	−3.15480	−0.108464
$847$	−5.03736	−0.173086
$848$	−10.3757	−0.356305
$849$	−11.6029	−0.398209
$850$	1.41360	0.0484860
$851$	−45.9966	−1.57674
$852$	−14.2022	−0.486560
$853$	−41.7388	−1.42911	−0.714554	−	0.699580i	$-0.753370\pi$
$853$	−41.7388	−1.42911	−0.714554	+	0.699580i	$0.753370\pi$
$854$	−0.246884	−0.00844818
$855$	4.82735	0.165092
$856$	−16.9789	−0.580327
$857$	−39.0255	−1.33309	−0.666543	−	0.745466i	$-0.732227\pi$
$857$	−39.0255	−1.33309	−0.666543	+	0.745466i	$0.732227\pi$
$858$	−4.01812	−0.137177
$859$	35.3381	1.20572	0.602859	−	0.797847i	$-0.294028\pi$
$859$	35.3381	1.20572	0.602859	+	0.797847i	$0.294028\pi$
$860$	8.57659	0.292459
$861$	−5.57870	−0.190122
$862$	8.40467	0.286264
$863$	6.54341	0.222740	0.111370	−	0.993779i	$-0.464476\pi$
$863$	6.54341	0.222740	0.111370	+	0.993779i	$0.464476\pi$
$864$	−3.12628	−0.106358
$865$	−12.9252	−0.439468
$866$	1.40709	0.0478148
$867$	−9.59179	−0.325754
$868$	−17.6700	−0.599758
$869$	−29.1509	−0.988876
$870$	−0.380732	−0.0129080
$871$	48.6022	1.64682
$872$	−5.24157	−0.177502
$873$	−12.8391	−0.434536
$874$	7.95438	0.269061
$875$	0.857432	0.0289865
$876$	15.1351	0.511369
$877$	2.86282	0.0966706	0.0483353	−	0.998831i	$-0.484608\pi$
$877$	2.86282	0.0966706	0.0483353	+	0.998831i	$0.484608\pi$
$878$	−0.0202324	−0.000682812 0
$879$	−23.9320	−0.807206
$880$	8.04751	0.271281
$881$	3.90148	0.131444	0.0657221	−	0.997838i	$-0.479065\pi$
$881$	3.90148	0.131444	0.0657221	+	0.997838i	$0.479065\pi$
$882$	−1.71735	−0.0578263
$883$	−36.9227	−1.24255	−0.621273	−	0.783594i	$-0.713384\pi$
$883$	−36.9227	−1.24255	−0.621273	+	0.783594i	$0.713384\pi$
$884$	−64.2679	−2.16156
$885$	−8.94468	−0.300672
$886$	0.200968	0.00675165
$887$	−38.7229	−1.30019	−0.650094	−	0.759853i	$-0.725271\pi$
$887$	−38.7229	−1.30019	−0.650094	+	0.759853i	$0.725271\pi$
$888$	−8.23294	−0.276279
$889$	−3.32516	−0.111522
$890$	0.717476	0.0240499
$891$	2.26386	0.0758421
$892$	36.4199	1.21943
$893$	−55.5557	−1.85910
$894$	−0.0551770	−0.00184539
$895$	−12.0344	−0.402265
$896$	−6.83077	−0.228200
$897$	−38.9196	−1.29949
$898$	3.58666	0.119688
$899$	14.8699	0.495937
$900$	−1.92485	−0.0641618
$901$	−15.0515	−0.501440
$902$	4.03771	0.134441
$903$	3.82046	0.127137
$904$	−17.2092	−0.572371
$905$	−21.2872	−0.707611
$906$	6.10988	0.202987
$907$	−56.6001	−1.87938	−0.939688	−	0.342034i	$-0.888884\pi$
$907$	−56.6001	−1.87938	−0.939688	+	0.342034i	$0.888884\pi$
$908$	41.8964	1.39038
$909$	−5.15539	−0.170993
$910$	1.52186	0.0504490
$911$	42.8668	1.42024	0.710120	−	0.704080i	$-0.248641\pi$
$911$	42.8668	1.42024	0.710120	+	0.704080i	$0.248641\pi$
$912$	−17.1601	−0.568228
$913$	−13.0462	−0.431766
$914$	7.31267	0.241882
$915$	1.05037	0.0347241
$916$	29.6309	0.979032
$917$	−3.71543	−0.122694
$918$	−1.41360	−0.0466556
$919$	−33.4046	−1.10191	−0.550957	−	0.834533i	$-0.685737\pi$
$919$	−33.4046	−1.10191	−0.550957	+	0.834533i	$0.685737\pi$
$920$	−6.46728	−0.213220
$921$	32.1516	1.05943
$922$	7.27964	0.239742
$923$	−47.7728	−1.57246
$924$	3.73634	0.122917
$925$	−7.65209	−0.251599
$926$	−2.46832	−0.0811141
$927$	15.4628	0.507866
$928$	4.34205	0.142535
$929$	48.7679	1.60002	0.800011	−	0.599986i	$-0.204827\pi$
$929$	48.7679	1.60002	0.800011	+	0.599986i	$0.204827\pi$
$930$	−2.93488	−0.0962385
$931$	−30.2424	−0.991155
$932$	−10.7841	−0.353245
$933$	9.55657	0.312868
$934$	1.17992	0.0386081
$935$	11.6741	0.381784
$936$	−6.96623	−0.227698
$937$	24.8140	0.810638	0.405319	−	0.914175i	$-0.367161\pi$
$937$	24.8140	0.810638	0.405319	+	0.914175i	$0.367161\pi$
$938$	1.76435	0.0576080
$939$	9.03248	0.294764
$940$	22.1523	0.722527
$941$	33.7752	1.10104	0.550521	−	0.834821i	$-0.314429\pi$
$941$	33.7752	1.10104	0.550521	+	0.834821i	$0.314429\pi$
$942$	3.52030	0.114698
$943$	39.1093	1.27357
$944$	31.7963	1.03488
$945$	−0.857432	−0.0278923
$946$	−2.76514	−0.0899026
$947$	35.6628	1.15888	0.579442	−	0.815014i	$-0.303271\pi$
$947$	35.6628	1.15888	0.579442	+	0.815014i	$0.303271\pi$
$948$	−24.7856	−0.805000
$949$	50.9109	1.65264
$950$	1.32331	0.0429337
$951$	18.4666	0.598820
$952$	−4.75717	−0.154181
$953$	21.8359	0.707333	0.353667	−	0.935371i	$-0.384935\pi$
$953$	21.8359	0.707333	0.353667	+	0.935371i	$0.384935\pi$
$954$	−0.800127	−0.0259051
$955$	−15.1362	−0.489795
$956$	−15.5548	−0.503080
$957$	−3.14425	−0.101639
$958$	−0.210800	−0.00681064
$959$	15.4363	0.498463
$960$	6.25255	0.201800
$961$	83.6245	2.69757
$962$	−13.5817	−0.437891
$963$	15.7810	0.508536
$964$	−57.7771	−1.86088
$965$	8.65991	0.278772
$966$	−1.41285	−0.0454578
$967$	36.1599	1.16282	0.581412	−	0.813610i	$-0.302501\pi$
$967$	36.1599	1.16282	0.581412	+	0.813610i	$0.302501\pi$
$968$	6.32090	0.203161
$969$	−24.8933	−0.799687
$970$	−3.51953	−0.113005
$971$	22.2925	0.715400	0.357700	−	0.933837i	$-0.383561\pi$
$971$	22.2925	0.715400	0.357700	+	0.933837i	$0.383561\pi$
$972$	1.92485	0.0617397
$973$	13.5338	0.433874
$974$	−9.69159	−0.310539
$975$	−6.47474	−0.207358
$976$	−3.73382	−0.119517
$977$	50.3911	1.61215	0.806077	−	0.591811i	$-0.201587\pi$
$977$	50.3911	1.61215	0.806077	+	0.591811i	$0.201587\pi$
$978$	−3.56017	−0.113842
$979$	5.92523	0.189371
$980$	12.0588	0.385206
$981$	4.87176	0.155543
$982$	7.30417	0.233086
$983$	−16.7085	−0.532918	−0.266459	−	0.963846i	$-0.585854\pi$
$983$	−16.7085	−0.532918	−0.266459	+	0.963846i	$0.585854\pi$
$984$	7.00018	0.223157
$985$	−17.9059	−0.570530
$986$	1.96333	0.0625252
$987$	9.86779	0.314095
$988$	−60.1629	−1.91404
$989$	−26.7832	−0.851657
$990$	0.620585	0.0197235
$991$	−12.8684	−0.408777	−0.204388	−	0.978890i	$-0.565521\pi$
$991$	−12.8684	−0.408777	−0.204388	+	0.978890i	$0.565521\pi$
$992$	33.4708	1.06270
$993$	−11.9642	−0.379674
$994$	−1.73424	−0.0550068
$995$	−11.0430	−0.350085
$996$	−11.0926	−0.351482
$997$	−53.3420	−1.68936	−0.844679	−	0.535274i	$-0.820208\pi$
$997$	−53.3420	−1.68936	−0.844679	+	0.535274i	$0.820208\pi$
$998$	0.974928	0.0308608
$999$	7.65209	0.242101

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.19	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.19	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.274127 q^{2} -1.00000 q^{3} -1.92485 q^{4} +1.00000 q^{5} -0.274127 q^{6} +0.857432 q^{7} -1.07591 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.274127 q^{2} -1.00000 q^{3} -1.92485 q^{4} +1.00000 q^{5} -0.274127 q^{6} +0.857432 q^{7} -1.07591 q^{8} +1.00000 q^{9} +0.274127 q^{10} +2.26386 q^{11} +1.92485 q^{12} +6.47474 q^{13} +0.235045 q^{14} -1.00000 q^{15} +3.55477 q^{16} +5.15672 q^{17} +0.274127 q^{18} +4.82735 q^{19} -1.92485 q^{20} -0.857432 q^{21} +0.620585 q^{22} +6.01099 q^{23} +1.07591 q^{24} +1.00000 q^{25} +1.77490 q^{26} -1.00000 q^{27} -1.65043 q^{28} +1.38889 q^{29} -0.274127 q^{30} +10.7063 q^{31} +3.12628 q^{32} -2.26386 q^{33} +1.41360 q^{34} +0.857432 q^{35} -1.92485 q^{36} -7.65209 q^{37} +1.32331 q^{38} -6.47474 q^{39} -1.07591 q^{40} +6.50630 q^{41} -0.235045 q^{42} -4.45571 q^{43} -4.35760 q^{44} +1.00000 q^{45} +1.64777 q^{46} -11.5085 q^{47} -3.55477 q^{48} -6.26481 q^{49} +0.274127 q^{50} -5.15672 q^{51} -12.4629 q^{52} -2.91882 q^{53} -0.274127 q^{54} +2.26386 q^{55} -0.922518 q^{56} -4.82735 q^{57} +0.380732 q^{58} +8.94468 q^{59} +1.92485 q^{60} -1.05037 q^{61} +2.93488 q^{62} +0.857432 q^{63} -6.25255 q^{64} +6.47474 q^{65} -0.620585 q^{66} +7.50642 q^{67} -9.92594 q^{68} -6.01099 q^{69} +0.235045 q^{70} -7.37833 q^{71} -1.07591 q^{72} +7.86300 q^{73} -2.09764 q^{74} -1.00000 q^{75} -9.29194 q^{76} +1.94110 q^{77} -1.77490 q^{78} -12.8766 q^{79} +3.55477 q^{80} +1.00000 q^{81} +1.78355 q^{82} -5.76282 q^{83} +1.65043 q^{84} +5.15672 q^{85} -1.22143 q^{86} -1.38889 q^{87} -2.43570 q^{88} +2.61732 q^{89} +0.274127 q^{90} +5.55165 q^{91} -11.5703 q^{92} -10.7063 q^{93} -3.15480 q^{94} +4.82735 q^{95} -3.12628 q^{96} -12.8391 q^{97} -1.71735 q^{98} +2.26386 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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