LMFDB - Embedded newform 6015.2.a.h.1.7

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:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-2.17202 q^{2} +1.00000 q^{3} +2.71767 q^{4} -1.00000 q^{5} -2.17202 q^{6} -0.722026 q^{7} -1.55879 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.17202 q^{2} +1.00000 q^{3} +2.71767 q^{4} -1.00000 q^{5} -2.17202 q^{6} -0.722026 q^{7} -1.55879 q^{8} +1.00000 q^{9} +2.17202 q^{10} +3.51451 q^{11} +2.71767 q^{12} +5.21945 q^{13} +1.56825 q^{14} -1.00000 q^{15} -2.04961 q^{16} +2.33888 q^{17} -2.17202 q^{18} +7.25112 q^{19} -2.71767 q^{20} -0.722026 q^{21} -7.63359 q^{22} +1.16716 q^{23} -1.55879 q^{24} +1.00000 q^{25} -11.3367 q^{26} +1.00000 q^{27} -1.96223 q^{28} -10.5614 q^{29} +2.17202 q^{30} +6.42467 q^{31} +7.56938 q^{32} +3.51451 q^{33} -5.08008 q^{34} +0.722026 q^{35} +2.71767 q^{36} -0.191811 q^{37} -15.7496 q^{38} +5.21945 q^{39} +1.55879 q^{40} +8.24409 q^{41} +1.56825 q^{42} +6.00834 q^{43} +9.55128 q^{44} -1.00000 q^{45} -2.53510 q^{46} +10.6156 q^{47} -2.04961 q^{48} -6.47868 q^{49} -2.17202 q^{50} +2.33888 q^{51} +14.1847 q^{52} -7.42761 q^{53} -2.17202 q^{54} -3.51451 q^{55} +1.12549 q^{56} +7.25112 q^{57} +22.9395 q^{58} +3.93902 q^{59} -2.71767 q^{60} +8.42212 q^{61} -13.9545 q^{62} -0.722026 q^{63} -12.3416 q^{64} -5.21945 q^{65} -7.63359 q^{66} +0.356294 q^{67} +6.35629 q^{68} +1.16716 q^{69} -1.56825 q^{70} +12.4798 q^{71} -1.55879 q^{72} +1.19724 q^{73} +0.416616 q^{74} +1.00000 q^{75} +19.7061 q^{76} -2.53757 q^{77} -11.3367 q^{78} +9.01975 q^{79} +2.04961 q^{80} +1.00000 q^{81} -17.9063 q^{82} +0.233260 q^{83} -1.96223 q^{84} -2.33888 q^{85} -13.0502 q^{86} -10.5614 q^{87} -5.47840 q^{88} -6.48999 q^{89} +2.17202 q^{90} -3.76858 q^{91} +3.17197 q^{92} +6.42467 q^{93} -23.0574 q^{94} -7.25112 q^{95} +7.56938 q^{96} -1.29315 q^{97} +14.0718 q^{98} +3.51451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - 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 $

$2$	−2.17202	−1.53585	−0.767925	−	0.640540i	$-0.778711\pi$
$2$	−2.17202	−1.53585	−0.767925	+	0.640540i	$0.778711\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.71767	1.35884
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.17202	−0.886723
$7$	−0.722026	−0.272900	−0.136450	−	0.990647i	$-0.543569\pi$
$7$	−0.722026	−0.272900	−0.136450	+	0.990647i	$0.543569\pi$
$8$	−1.55879	−0.551117
$9$	1.00000	0.333333
$10$	2.17202	0.686853
$11$	3.51451	1.05966	0.529832	−	0.848102i	$-0.322255\pi$
$11$	3.51451	1.05966	0.529832	+	0.848102i	$0.322255\pi$
$12$	2.71767	0.784524
$13$	5.21945	1.44761	0.723807	−	0.690002i	$-0.242390\pi$
$13$	5.21945	1.44761	0.723807	+	0.690002i	$0.242390\pi$
$14$	1.56825	0.419134
$15$	−1.00000	−0.258199
$16$	−2.04961	−0.512402
$17$	2.33888	0.567261	0.283630	−	0.958934i	$-0.408461\pi$
$17$	2.33888	0.567261	0.283630	+	0.958934i	$0.408461\pi$
$18$	−2.17202	−0.511950
$19$	7.25112	1.66352	0.831760	−	0.555135i	$-0.187334\pi$
$19$	7.25112	1.66352	0.831760	+	0.555135i	$0.187334\pi$
$20$	−2.71767	−0.607690
$21$	−0.722026	−0.157559
$22$	−7.63359	−1.62749
$23$	1.16716	0.243371	0.121685	−	0.992569i	$-0.461170\pi$
$23$	1.16716	0.243371	0.121685	+	0.992569i	$0.461170\pi$
$24$	−1.55879	−0.318188
$25$	1.00000	0.200000
$26$	−11.3367	−2.22332
$27$	1.00000	0.192450
$28$	−1.96223	−0.370826
$29$	−10.5614	−1.96120	−0.980600	−	0.196022i	$-0.937198\pi$
$29$	−10.5614	−1.96120	−0.980600	+	0.196022i	$0.937198\pi$
$30$	2.17202	0.396555
$31$	6.42467	1.15391	0.576953	−	0.816778i	$-0.304242\pi$
$31$	6.42467	1.15391	0.576953	+	0.816778i	$0.304242\pi$
$32$	7.56938	1.33809
$33$	3.51451	0.611798
$34$	−5.08008	−0.871227
$35$	0.722026	0.122045
$36$	2.71767	0.452945
$37$	−0.191811	−0.0315335	−0.0157667	−	0.999876i	$-0.505019\pi$
$37$	−0.191811	−0.0315335	−0.0157667	+	0.999876i	$0.505019\pi$
$38$	−15.7496	−2.55492
$39$	5.21945	0.835781
$40$	1.55879	0.246467
$41$	8.24409	1.28751	0.643756	−	0.765231i	$-0.277375\pi$
$41$	8.24409	1.28751	0.643756	+	0.765231i	$0.277375\pi$
$42$	1.56825	0.241987
$43$	6.00834	0.916263	0.458132	−	0.888884i	$-0.348519\pi$
$43$	6.00834	0.916263	0.458132	+	0.888884i	$0.348519\pi$
$44$	9.55128	1.43991
$45$	−1.00000	−0.149071
$46$	−2.53510	−0.373781
$47$	10.6156	1.54845	0.774225	−	0.632910i	$-0.218140\pi$
$47$	10.6156	1.54845	0.774225	+	0.632910i	$0.218140\pi$
$48$	−2.04961	−0.295835
$49$	−6.47868	−0.925526
$50$	−2.17202	−0.307170
$51$	2.33888	0.327508
$52$	14.1847	1.96707
$53$	−7.42761	−1.02026	−0.510131	−	0.860097i	$-0.670403\pi$
$53$	−7.42761	−1.02026	−0.510131	+	0.860097i	$0.670403\pi$
$54$	−2.17202	−0.295574
$55$	−3.51451	−0.473896
$56$	1.12549	0.150400
$57$	7.25112	0.960434
$58$	22.9395	3.01211
$59$	3.93902	0.512816	0.256408	−	0.966569i	$-0.417461\pi$
$59$	3.93902	0.512816	0.256408	+	0.966569i	$0.417461\pi$
$60$	−2.71767	−0.350850
$61$	8.42212	1.07834	0.539171	−	0.842197i	$-0.318738\pi$
$61$	8.42212	1.07834	0.539171	+	0.842197i	$0.318738\pi$
$62$	−13.9545	−1.77223
$63$	−0.722026	−0.0909667
$64$	−12.3416	−1.54270
$65$	−5.21945	−0.647393
$66$	−7.63359	−0.939629
$67$	0.356294	0.0435283	0.0217641	−	0.999763i	$-0.493072\pi$
$67$	0.356294	0.0435283	0.0217641	+	0.999763i	$0.493072\pi$
$68$	6.35629	0.770814
$69$	1.16716	0.140510
$70$	−1.56825	−0.187442
$71$	12.4798	1.48107	0.740537	−	0.672015i	$-0.234571\pi$
$71$	12.4798	1.48107	0.740537	+	0.672015i	$0.234571\pi$
$72$	−1.55879	−0.183706
$73$	1.19724	0.140126	0.0700630	−	0.997543i	$-0.477680\pi$
$73$	1.19724	0.140126	0.0700630	+	0.997543i	$0.477680\pi$
$74$	0.416616	0.0484307
$75$	1.00000	0.115470
$76$	19.7061	2.26045
$77$	−2.53757	−0.289183
$78$	−11.3367	−1.28363
$79$	9.01975	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$79$	9.01975	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$80$	2.04961	0.229153
$81$	1.00000	0.111111
$82$	−17.9063	−1.97742
$83$	0.233260	0.0256036	0.0128018	−	0.999918i	$-0.495925\pi$
$83$	0.233260	0.0256036	0.0128018	+	0.999918i	$0.495925\pi$
$84$	−1.96223	−0.214097
$85$	−2.33888	−0.253687
$86$	−13.0502	−1.40724
$87$	−10.5614	−1.13230
$88$	−5.47840	−0.583999
$89$	−6.48999	−0.687938	−0.343969	−	0.938981i	$-0.611771\pi$
$89$	−6.48999	−0.687938	−0.343969	+	0.938981i	$0.611771\pi$
$90$	2.17202	0.228951
$91$	−3.76858	−0.395054
$92$	3.17197	0.330700
$93$	6.42467	0.666208
$94$	−23.0574	−2.37819
$95$	−7.25112	−0.743949
$96$	7.56938	0.772547
$97$	−1.29315	−0.131300	−0.0656500	−	0.997843i	$-0.520912\pi$
$97$	−1.29315	−0.131300	−0.0656500	+	0.997843i	$0.520912\pi$
$98$	14.0718	1.42147
$99$	3.51451	0.353222
$100$	2.71767	0.271767
$101$	−18.0463	−1.79567	−0.897836	−	0.440329i	$-0.854862\pi$
$101$	−18.0463	−1.79567	−0.897836	+	0.440329i	$0.854862\pi$
$102$	−5.08008	−0.503003
$103$	18.6362	1.83627	0.918137	−	0.396262i	$-0.129693\pi$
$103$	18.6362	1.83627	0.918137	+	0.396262i	$0.129693\pi$
$104$	−8.13605	−0.797805
$105$	0.722026	0.0704625
$106$	16.1329	1.56697
$107$	−7.26136	−0.701982	−0.350991	−	0.936379i	$-0.614155\pi$
$107$	−7.26136	−0.701982	−0.350991	+	0.936379i	$0.614155\pi$
$108$	2.71767	0.261508
$109$	−19.9690	−1.91268	−0.956341	−	0.292252i	$-0.905595\pi$
$109$	−19.9690	−1.91268	−0.956341	+	0.292252i	$0.905595\pi$
$110$	7.63359	0.727834
$111$	−0.191811	−0.0182059
$112$	1.47987	0.139835
$113$	−14.9558	−1.40692	−0.703462	−	0.710732i	$-0.748364\pi$
$113$	−14.9558	−1.40692	−0.703462	+	0.710732i	$0.748364\pi$
$114$	−15.7496	−1.47508
$115$	−1.16716	−0.108839
$116$	−28.7023	−2.66495
$117$	5.21945	0.482538
$118$	−8.55562	−0.787609
$119$	−1.68873	−0.154805
$120$	1.55879	0.142298
$121$	1.35178	0.122889
$122$	−18.2930	−1.65617
$123$	8.24409	0.743345
$124$	17.4601	1.56797
$125$	−1.00000	−0.0894427
$126$	1.56825	0.139711
$127$	−5.64314	−0.500748	−0.250374	−	0.968149i	$-0.580554\pi$
$127$	−5.64314	−0.500748	−0.250374	+	0.968149i	$0.580554\pi$
$128$	11.6675	1.03127
$129$	6.00834	0.529005
$130$	11.3367	0.994299
$131$	−19.3517	−1.69077	−0.845384	−	0.534159i	$-0.820628\pi$
$131$	−19.3517	−1.69077	−0.845384	+	0.534159i	$0.820628\pi$
$132$	9.55128	0.831332
$133$	−5.23549	−0.453975
$134$	−0.773878	−0.0668529
$135$	−1.00000	−0.0860663
$136$	−3.64583	−0.312627
$137$	15.6380	1.33604	0.668021	−	0.744142i	$-0.267142\pi$
$137$	15.6380	1.33604	0.668021	+	0.744142i	$0.267142\pi$
$138$	−2.53510	−0.215802
$139$	−8.60340	−0.729731	−0.364865	−	0.931060i	$-0.618885\pi$
$139$	−8.60340	−0.729731	−0.364865	+	0.931060i	$0.618885\pi$
$140$	1.96223	0.165839
$141$	10.6156	0.893998
$142$	−27.1063	−2.27471
$143$	18.3438	1.53399
$144$	−2.04961	−0.170801
$145$	10.5614	0.877075
$146$	−2.60042	−0.215213
$147$	−6.47868	−0.534352
$148$	−0.521278	−0.0428488
$149$	−7.84552	−0.642730	−0.321365	−	0.946955i	$-0.604142\pi$
$149$	−7.84552	−0.642730	−0.321365	+	0.946955i	$0.604142\pi$
$150$	−2.17202	−0.177345
$151$	4.43824	0.361179	0.180589	−	0.983559i	$-0.442199\pi$
$151$	4.43824	0.361179	0.180589	+	0.983559i	$0.442199\pi$
$152$	−11.3030	−0.916794
$153$	2.33888	0.189087
$154$	5.51164	0.444141
$155$	−6.42467	−0.516042
$156$	14.1847	1.13569
$157$	−18.1790	−1.45084	−0.725421	−	0.688306i	$-0.758355\pi$
$157$	−18.1790	−1.45084	−0.725421	+	0.688306i	$0.758355\pi$
$158$	−19.5911	−1.55858
$159$	−7.42761	−0.589048
$160$	−7.56938	−0.598412
$161$	−0.842722	−0.0664158
$162$	−2.17202	−0.170650
$163$	18.8798	1.47878	0.739389	−	0.673279i	$-0.235115\pi$
$163$	18.8798	1.47878	0.739389	+	0.673279i	$0.235115\pi$
$164$	22.4047	1.74952
$165$	−3.51451	−0.273604
$166$	−0.506646	−0.0393234
$167$	3.82014	0.295611	0.147806	−	0.989016i	$-0.452779\pi$
$167$	3.82014	0.295611	0.147806	+	0.989016i	$0.452779\pi$
$168$	1.12549	0.0868334
$169$	14.2427	1.09559
$170$	5.08008	0.389625
$171$	7.25112	0.554507
$172$	16.3287	1.24505
$173$	−0.147794	−0.0112366	−0.00561829	−	0.999984i	$-0.501788\pi$
$173$	−0.147794	−0.0112366	−0.00561829	+	0.999984i	$0.501788\pi$
$174$	22.9395	1.73904
$175$	−0.722026	−0.0545800
$176$	−7.20337	−0.542974
$177$	3.93902	0.296075
$178$	14.0964	1.05657
$179$	−25.0399	−1.87157	−0.935785	−	0.352572i	$-0.885307\pi$
$179$	−25.0399	−1.87157	−0.935785	+	0.352572i	$0.885307\pi$
$180$	−2.71767	−0.202563
$181$	−18.7119	−1.39085	−0.695423	−	0.718601i	$-0.744783\pi$
$181$	−18.7119	−1.39085	−0.695423	+	0.718601i	$0.744783\pi$
$182$	8.18542	0.606744
$183$	8.42212	0.622581
$184$	−1.81937	−0.134126
$185$	0.191811	0.0141022
$186$	−13.9545	−1.02319
$187$	8.22000	0.601106
$188$	28.8498	2.10409
$189$	−0.722026	−0.0525196
$190$	15.7496	1.14259
$191$	18.8448	1.36356	0.681781	−	0.731556i	$-0.261206\pi$
$191$	18.8448	1.36356	0.681781	+	0.731556i	$0.261206\pi$
$192$	−12.3416	−0.890680
$193$	5.55334	0.399738	0.199869	−	0.979823i	$-0.435948\pi$
$193$	5.55334	0.399738	0.199869	+	0.979823i	$0.435948\pi$
$194$	2.80876	0.201657
$195$	−5.21945	−0.373773
$196$	−17.6069	−1.25764
$197$	−5.45935	−0.388963	−0.194481	−	0.980906i	$-0.562302\pi$
$197$	−5.45935	−0.388963	−0.194481	+	0.980906i	$0.562302\pi$
$198$	−7.63359	−0.542495
$199$	0.256761	0.0182013	0.00910066	−	0.999959i	$-0.497103\pi$
$199$	0.256761	0.0182013	0.00910066	+	0.999959i	$0.497103\pi$
$200$	−1.55879	−0.110223
$201$	0.356294	0.0251310
$202$	39.1969	2.75788
$203$	7.62559	0.535211
$204$	6.35629	0.445029
$205$	−8.24409	−0.575793
$206$	−40.4781	−2.82024
$207$	1.16716	0.0811235
$208$	−10.6978	−0.741761
$209$	25.4841	1.76277
$210$	−1.56825	−0.108220
$211$	19.5219	1.34395	0.671973	−	0.740576i	$-0.265447\pi$
$211$	19.5219	1.34395	0.671973	+	0.740576i	$0.265447\pi$
$212$	−20.1858	−1.38637
$213$	12.4798	0.855099
$214$	15.7718	1.07814
$215$	−6.00834	−0.409765
$216$	−1.55879	−0.106063
$217$	−4.63878	−0.314901
$218$	43.3730	2.93759
$219$	1.19724	0.0809018
$220$	−9.55128	−0.643947
$221$	12.2076	0.821175
$222$	0.416616	0.0279615
$223$	15.8677	1.06258	0.531291	−	0.847190i	$-0.321707\pi$
$223$	15.8677	1.06258	0.531291	+	0.847190i	$0.321707\pi$
$224$	−5.46529	−0.365165
$225$	1.00000	0.0666667
$226$	32.4843	2.16083
$227$	−24.2538	−1.60978	−0.804890	−	0.593424i	$-0.797776\pi$
$227$	−24.2538	−1.60978	−0.804890	+	0.593424i	$0.797776\pi$
$228$	19.7061	1.30507
$229$	−10.4032	−0.687464	−0.343732	−	0.939068i	$-0.611691\pi$
$229$	−10.4032	−0.687464	−0.343732	+	0.939068i	$0.611691\pi$
$230$	2.53510	0.167160
$231$	−2.53757	−0.166960
$232$	16.4630	1.08085
$233$	−11.0431	−0.723456	−0.361728	−	0.932284i	$-0.617813\pi$
$233$	−11.0431	−0.723456	−0.361728	+	0.932284i	$0.617813\pi$
$234$	−11.3367	−0.741106
$235$	−10.6156	−0.692488
$236$	10.7050	0.696833
$237$	9.01975	0.585896
$238$	3.66795	0.237758
$239$	−22.4165	−1.45000	−0.725002	−	0.688747i	$-0.758161\pi$
$239$	−22.4165	−1.45000	−0.725002	+	0.688747i	$0.758161\pi$
$240$	2.04961	0.132302
$241$	19.6497	1.26575	0.632874	−	0.774255i	$-0.281875\pi$
$241$	19.6497	1.26575	0.632874	+	0.774255i	$0.281875\pi$
$242$	−2.93609	−0.188739
$243$	1.00000	0.0641500
$244$	22.8885	1.46529
$245$	6.47868	0.413908
$246$	−17.9063	−1.14167
$247$	37.8468	2.40814
$248$	−10.0147	−0.635937
$249$	0.233260	0.0147823
$250$	2.17202	0.137371
$251$	−3.21617	−0.203003	−0.101501	−	0.994835i	$-0.532365\pi$
$251$	−3.21617	−0.203003	−0.101501	+	0.994835i	$0.532365\pi$
$252$	−1.96223	−0.123609
$253$	4.10201	0.257891
$254$	12.2570	0.769073
$255$	−2.33888	−0.146466
$256$	−0.658785	−0.0411741
$257$	5.25537	0.327821	0.163910	−	0.986475i	$-0.447589\pi$
$257$	5.25537	0.327821	0.163910	+	0.986475i	$0.447589\pi$
$258$	−13.0502	−0.812472
$259$	0.138492	0.00860548
$260$	−14.1847	−0.879701
$261$	−10.5614	−0.653733
$262$	42.0323	2.59677
$263$	15.9986	0.986517	0.493259	−	0.869883i	$-0.335806\pi$
$263$	15.9986	0.986517	0.493259	+	0.869883i	$0.335806\pi$
$264$	−5.47840	−0.337172
$265$	7.42761	0.456275
$266$	11.3716	0.697237
$267$	−6.48999	−0.397181
$268$	0.968290	0.0591477
$269$	−21.2447	−1.29531	−0.647656	−	0.761933i	$-0.724250\pi$
$269$	−21.2447	−1.29531	−0.647656	+	0.761933i	$0.724250\pi$
$270$	2.17202	0.132185
$271$	7.31997	0.444656	0.222328	−	0.974972i	$-0.428634\pi$
$271$	7.31997	0.444656	0.222328	+	0.974972i	$0.428634\pi$
$272$	−4.79378	−0.290666
$273$	−3.76858	−0.228085
$274$	−33.9660	−2.05196
$275$	3.51451	0.211933
$276$	3.17197	0.190930
$277$	23.3805	1.40480	0.702399	−	0.711784i	$-0.252112\pi$
$277$	23.3805	1.40480	0.702399	+	0.711784i	$0.252112\pi$
$278$	18.6867	1.12076
$279$	6.42467	0.384635
$280$	−1.12549	−0.0672609
$281$	22.1189	1.31951	0.659753	−	0.751483i	$-0.270661\pi$
$281$	22.1189	1.31951	0.659753	+	0.751483i	$0.270661\pi$
$282$	−23.0574	−1.37305
$283$	10.3373	0.614488	0.307244	−	0.951631i	$-0.400593\pi$
$283$	10.3373	0.614488	0.307244	+	0.951631i	$0.400593\pi$
$284$	33.9159	2.01254
$285$	−7.25112	−0.429519
$286$	−39.8431	−2.35597
$287$	−5.95245	−0.351362
$288$	7.56938	0.446030
$289$	−11.5297	−0.678215
$290$	−22.9395	−1.34706
$291$	−1.29315	−0.0758060
$292$	3.25370	0.190408
$293$	−9.28607	−0.542498	−0.271249	−	0.962509i	$-0.587437\pi$
$293$	−9.28607	−0.542498	−0.271249	+	0.962509i	$0.587437\pi$
$294$	14.0718	0.820685
$295$	−3.93902	−0.229338
$296$	0.298993	0.0173786
$297$	3.51451	0.203933
$298$	17.0406	0.987137
$299$	6.09195	0.352307
$300$	2.71767	0.156905
$301$	−4.33817	−0.250048
$302$	−9.63995	−0.554717
$303$	−18.0463	−1.03673
$304$	−14.8619	−0.852391
$305$	−8.42212	−0.482249
$306$	−5.08008	−0.290409
$307$	−8.15718	−0.465555	−0.232778	−	0.972530i	$-0.574781\pi$
$307$	−8.15718	−0.465555	−0.232778	+	0.972530i	$0.574781\pi$
$308$	−6.89627	−0.392951
$309$	18.6362	1.06017
$310$	13.9545	0.792563
$311$	−23.8355	−1.35158	−0.675792	−	0.737092i	$-0.736198\pi$
$311$	−23.8355	−1.35158	−0.675792	+	0.737092i	$0.736198\pi$
$312$	−8.13605	−0.460613
$313$	2.03645	0.115107	0.0575535	−	0.998342i	$-0.481670\pi$
$313$	2.03645	0.115107	0.0575535	+	0.998342i	$0.481670\pi$
$314$	39.4851	2.22827
$315$	0.722026	0.0406815
$316$	24.5127	1.37895
$317$	8.85082	0.497111	0.248556	−	0.968618i	$-0.420044\pi$
$317$	8.85082	0.497111	0.248556	+	0.968618i	$0.420044\pi$
$318$	16.1329	0.904690
$319$	−37.1181	−2.07821
$320$	12.3416	0.689918
$321$	−7.26136	−0.405290
$322$	1.83041	0.102005
$323$	16.9595	0.943649
$324$	2.71767	0.150982
$325$	5.21945	0.289523
$326$	−41.0072	−2.27118
$327$	−19.9690	−1.10429
$328$	−12.8508	−0.709569
$329$	−7.66477	−0.422572
$330$	7.63359	0.420215
$331$	3.21020	0.176449	0.0882244	−	0.996101i	$-0.471881\pi$
$331$	3.21020	0.176449	0.0882244	+	0.996101i	$0.471881\pi$
$332$	0.633925	0.0347911
$333$	−0.191811	−0.0105112
$334$	−8.29742	−0.454014
$335$	−0.356294	−0.0194664
$336$	1.47987	0.0807335
$337$	5.44134	0.296409	0.148204	−	0.988957i	$-0.452651\pi$
$337$	5.44134	0.296409	0.148204	+	0.988957i	$0.452651\pi$
$338$	−30.9353	−1.68266
$339$	−14.9558	−0.812289
$340$	−6.35629	−0.344718
$341$	22.5796	1.22275
$342$	−15.7496	−0.851639
$343$	9.73195	0.525476
$344$	−9.36576	−0.504968
$345$	−1.16716	−0.0628380
$346$	0.321012	0.0172577
$347$	25.5060	1.36923	0.684617	−	0.728903i	$-0.259969\pi$
$347$	25.5060	1.36923	0.684617	+	0.728903i	$0.259969\pi$
$348$	−28.7023	−1.53861
$349$	7.62761	0.408297	0.204148	−	0.978940i	$-0.434557\pi$
$349$	7.62761	0.408297	0.204148	+	0.978940i	$0.434557\pi$
$350$	1.56825	0.0838267
$351$	5.21945	0.278594
$352$	26.6027	1.41793
$353$	−19.7452	−1.05093	−0.525467	−	0.850814i	$-0.676109\pi$
$353$	−19.7452	−1.05093	−0.525467	+	0.850814i	$0.676109\pi$
$354$	−8.55562	−0.454726
$355$	−12.4798	−0.662357
$356$	−17.6377	−0.934794
$357$	−1.68873	−0.0893770
$358$	54.3871	2.87445
$359$	−25.1554	−1.32765	−0.663825	−	0.747888i	$-0.731068\pi$
$359$	−25.1554	−1.32765	−0.663825	+	0.747888i	$0.731068\pi$
$360$	1.55879	0.0821557
$361$	33.5787	1.76730
$362$	40.6426	2.13613
$363$	1.35178	0.0709500
$364$	−10.2417	−0.536814
$365$	−1.19724	−0.0626663
$366$	−18.2930	−0.956191
$367$	26.5211	1.38439	0.692196	−	0.721709i	$-0.256643\pi$
$367$	26.5211	1.38439	0.692196	+	0.721709i	$0.256643\pi$
$368$	−2.39223	−0.124704
$369$	8.24409	0.429170
$370$	−0.416616	−0.0216589
$371$	5.36293	0.278429
$372$	17.4601	0.905266
$373$	−21.1068	−1.09287	−0.546436	−	0.837501i	$-0.684016\pi$
$373$	−21.1068	−1.09287	−0.546436	+	0.837501i	$0.684016\pi$
$374$	−17.8540	−0.923209
$375$	−1.00000	−0.0516398
$376$	−16.5476	−0.853377
$377$	−55.1246	−2.83906
$378$	1.56825	0.0806623
$379$	2.55660	0.131324	0.0656619	−	0.997842i	$-0.479084\pi$
$379$	2.55660	0.131324	0.0656619	+	0.997842i	$0.479084\pi$
$380$	−19.7061	−1.01090
$381$	−5.64314	−0.289107
$382$	−40.9313	−2.09423
$383$	−28.1678	−1.43931	−0.719654	−	0.694333i	$-0.755699\pi$
$383$	−28.1678	−1.43931	−0.719654	+	0.694333i	$0.755699\pi$
$384$	11.6675	0.595404
$385$	2.53757	0.129326
$386$	−12.0620	−0.613938
$387$	6.00834	0.305421
$388$	−3.51437	−0.178415
$389$	14.4020	0.730212	0.365106	−	0.930966i	$-0.381033\pi$
$389$	14.4020	0.730212	0.365106	+	0.930966i	$0.381033\pi$
$390$	11.3367	0.574059
$391$	2.72985	0.138055
$392$	10.0989	0.510073
$393$	−19.3517	−0.976165
$394$	11.8578	0.597389
$395$	−9.01975	−0.453833
$396$	9.55128	0.479970
$397$	−3.75089	−0.188252	−0.0941258	−	0.995560i	$-0.530006\pi$
$397$	−3.75089	−0.188252	−0.0941258	+	0.995560i	$0.530006\pi$
$398$	−0.557690	−0.0279545
$399$	−5.23549	−0.262102
$400$	−2.04961	−0.102480
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−0.773878	−0.0385975
$403$	33.5333	1.67041
$404$	−49.0439	−2.44002
$405$	−1.00000	−0.0496904
$406$	−16.5629	−0.822004
$407$	−0.674120	−0.0334149
$408$	−3.64583	−0.180495
$409$	19.7524	0.976694	0.488347	−	0.872649i	$-0.337600\pi$
$409$	19.7524	0.976694	0.488347	+	0.872649i	$0.337600\pi$
$410$	17.9063	0.884331
$411$	15.6380	0.771364
$412$	50.6469	2.49520
$413$	−2.84407	−0.139948
$414$	−2.53510	−0.124594
$415$	−0.233260	−0.0114503
$416$	39.5080	1.93704
$417$	−8.60340	−0.421310
$418$	−55.3520	−2.70736
$419$	20.4807	1.00055	0.500273	−	0.865868i	$-0.333233\pi$
$419$	20.4807	1.00055	0.500273	+	0.865868i	$0.333233\pi$
$420$	1.96223	0.0957469
$421$	−15.6326	−0.761888	−0.380944	−	0.924598i	$-0.624401\pi$
$421$	−15.6326	−0.761888	−0.380944	+	0.924598i	$0.624401\pi$
$422$	−42.4021	−2.06410
$423$	10.6156	0.516150
$424$	11.5781	0.562283
$425$	2.33888	0.113452
$426$	−27.1063	−1.31330
$427$	−6.08098	−0.294279
$428$	−19.7340	−0.953878
$429$	18.3438	0.885647
$430$	13.0502	0.629338
$431$	−4.24956	−0.204694	−0.102347	−	0.994749i	$-0.532635\pi$
$431$	−4.24956	−0.204694	−0.102347	+	0.994749i	$0.532635\pi$
$432$	−2.04961	−0.0986118
$433$	11.5596	0.555520	0.277760	−	0.960650i	$-0.410408\pi$
$433$	11.5596	0.555520	0.277760	+	0.960650i	$0.410408\pi$
$434$	10.0755	0.483640
$435$	10.5614	0.506379
$436$	−54.2691	−2.59902
$437$	8.46324	0.404852
$438$	−2.60042	−0.124253
$439$	−23.9398	−1.14259	−0.571293	−	0.820746i	$-0.693558\pi$
$439$	−23.9398	−1.14259	−0.571293	+	0.820746i	$0.693558\pi$
$440$	5.47840	0.261172
$441$	−6.47868	−0.308509
$442$	−26.5152	−1.26120
$443$	−40.6637	−1.93199	−0.965996	−	0.258558i	$-0.916753\pi$
$443$	−40.6637	−1.93199	−0.965996	+	0.258558i	$0.916753\pi$
$444$	−0.521278	−0.0247388
$445$	6.48999	0.307655
$446$	−34.4650	−1.63197
$447$	−7.84552	−0.371080
$448$	8.91097	0.421004
$449$	24.4439	1.15358	0.576788	−	0.816894i	$-0.304306\pi$
$449$	24.4439	1.15358	0.576788	+	0.816894i	$0.304306\pi$
$450$	−2.17202	−0.102390
$451$	28.9740	1.36433
$452$	−40.6450	−1.91178
$453$	4.43824	0.208527
$454$	52.6797	2.47238
$455$	3.76858	0.176674
$456$	−11.3030	−0.529311
$457$	−6.94927	−0.325073	−0.162536	−	0.986703i	$-0.551968\pi$
$457$	−6.94927	−0.325073	−0.162536	+	0.986703i	$0.551968\pi$
$458$	22.5960	1.05584
$459$	2.33888	0.109169
$460$	−3.17197	−0.147894
$461$	22.7309	1.05868	0.529342	−	0.848408i	$-0.322439\pi$
$461$	22.7309	1.05868	0.529342	+	0.848408i	$0.322439\pi$
$462$	5.51164	0.256425
$463$	15.7905	0.733847	0.366923	−	0.930251i	$-0.380411\pi$
$463$	15.7905	0.733847	0.366923	+	0.930251i	$0.380411\pi$
$464$	21.6467	1.00492
$465$	−6.42467	−0.297937
$466$	23.9858	1.11112
$467$	16.2694	0.752859	0.376429	−	0.926445i	$-0.377152\pi$
$467$	16.2694	0.752859	0.376429	+	0.926445i	$0.377152\pi$
$468$	14.1847	0.655690
$469$	−0.257253	−0.0118789
$470$	23.0574	1.06356
$471$	−18.1790	−0.837644
$472$	−6.14012	−0.282622
$473$	21.1164	0.970931
$474$	−19.5911	−0.899848
$475$	7.25112	0.332704
$476$	−4.58941	−0.210355
$477$	−7.42761	−0.340087
$478$	48.6891	2.22699
$479$	−15.9673	−0.729564	−0.364782	−	0.931093i	$-0.618857\pi$
$479$	−15.9673	−0.729564	−0.364782	+	0.931093i	$0.618857\pi$
$480$	−7.56938	−0.345493
$481$	−1.00115	−0.0456483
$482$	−42.6795	−1.94400
$483$	−0.842722	−0.0383452
$484$	3.67369	0.166986
$485$	1.29315	0.0587191
$486$	−2.17202	−0.0985248
$487$	23.1357	1.04838	0.524188	−	0.851602i	$-0.324369\pi$
$487$	23.1357	1.04838	0.524188	+	0.851602i	$0.324369\pi$
$488$	−13.1283	−0.594292
$489$	18.8798	0.853773
$490$	−14.0718	−0.635700
$491$	17.8683	0.806384	0.403192	−	0.915115i	$-0.367901\pi$
$491$	17.8683	0.806384	0.403192	+	0.915115i	$0.367901\pi$
$492$	22.4047	1.01008
$493$	−24.7018	−1.11251
$494$	−82.2041	−3.69854
$495$	−3.51451	−0.157965
$496$	−13.1681	−0.591264
$497$	−9.01071	−0.404185
$498$	−0.506646	−0.0227034
$499$	−37.5643	−1.68161	−0.840805	−	0.541338i	$-0.817918\pi$
$499$	−37.5643	−1.68161	−0.840805	+	0.541338i	$0.817918\pi$
$500$	−2.71767	−0.121538
$501$	3.82014	0.170671
$502$	6.98558	0.311782
$503$	6.05063	0.269784	0.134892	−	0.990860i	$-0.456931\pi$
$503$	6.05063	0.269784	0.134892	+	0.990860i	$0.456931\pi$
$504$	1.12549	0.0501333
$505$	18.0463	0.803049
$506$	−8.90965	−0.396082
$507$	14.2427	0.632539
$508$	−15.3362	−0.680433
$509$	16.0628	0.711972	0.355986	−	0.934491i	$-0.384145\pi$
$509$	16.0628	0.711972	0.355986	+	0.934491i	$0.384145\pi$
$510$	5.08008	0.224950
$511$	−0.864437	−0.0382404
$512$	−21.9041	−0.968034
$513$	7.25112	0.320145
$514$	−11.4148	−0.503484
$515$	−18.6362	−0.821207
$516$	16.3287	0.718830
$517$	37.3088	1.64084
$518$	−0.300808	−0.0132167
$519$	−0.147794	−0.00648745
$520$	8.13605	0.356789
$521$	15.0359	0.658736	0.329368	−	0.944202i	$-0.393164\pi$
$521$	15.0359	0.658736	0.329368	+	0.944202i	$0.393164\pi$
$522$	22.9395	1.00404
$523$	41.7342	1.82491	0.912454	−	0.409178i	$-0.134185\pi$
$523$	41.7342	1.82491	0.912454	+	0.409178i	$0.134185\pi$
$524$	−52.5916	−2.29747
$525$	−0.722026	−0.0315118
$526$	−34.7493	−1.51514
$527$	15.0265	0.654565
$528$	−7.20337	−0.313486
$529$	−21.6377	−0.940771
$530$	−16.1329	−0.700769
$531$	3.93902	0.170939
$532$	−14.2283	−0.616877
$533$	43.0296	1.86382
$534$	14.0964	0.610010
$535$	7.26136	0.313936
$536$	−0.555389	−0.0239892
$537$	−25.0399	−1.08055
$538$	46.1439	1.98940
$539$	−22.7694	−0.980747
$540$	−2.71767	−0.116950
$541$	−42.8386	−1.84178	−0.920888	−	0.389828i	$-0.872535\pi$
$541$	−42.8386	−1.84178	−0.920888	+	0.389828i	$0.872535\pi$
$542$	−15.8991	−0.682925
$543$	−18.7119	−0.803005
$544$	17.7038	0.759046
$545$	19.9690	0.855378
$546$	8.18542	0.350304
$547$	−27.5055	−1.17605	−0.588024	−	0.808843i	$-0.700094\pi$
$547$	−27.5055	−1.17605	−0.588024	+	0.808843i	$0.700094\pi$
$548$	42.4989	1.81546
$549$	8.42212	0.359447
$550$	−7.63359	−0.325497
$551$	−76.5818	−3.26249
$552$	−1.81937	−0.0774375
$553$	−6.51249	−0.276939
$554$	−50.7829	−2.15756
$555$	0.191811	0.00814190
$556$	−23.3812	−0.991584
$557$	30.1333	1.27679	0.638394	−	0.769709i	$-0.279599\pi$
$557$	30.1333	1.27679	0.638394	+	0.769709i	$0.279599\pi$
$558$	−13.9545	−0.590742
$559$	31.3602	1.32640
$560$	−1.47987	−0.0625359
$561$	8.22000	0.347049
$562$	−48.0428	−2.02656
$563$	−8.65025	−0.364565	−0.182282	−	0.983246i	$-0.558348\pi$
$563$	−8.65025	−0.364565	−0.182282	+	0.983246i	$0.558348\pi$
$564$	28.8498	1.21480
$565$	14.9558	0.629196
$566$	−22.4528	−0.943761
$567$	−0.722026	−0.0303222
$568$	−19.4534	−0.816246
$569$	26.2282	1.09954	0.549772	−	0.835315i	$-0.314715\pi$
$569$	26.2282	1.09954	0.549772	+	0.835315i	$0.314715\pi$
$570$	15.7496	0.659677
$571$	−1.50787	−0.0631025	−0.0315512	−	0.999502i	$-0.510045\pi$
$571$	−1.50787	−0.0631025	−0.0315512	+	0.999502i	$0.510045\pi$
$572$	49.8524	2.08443
$573$	18.8448	0.787253
$574$	12.9288	0.539639
$575$	1.16716	0.0486741
$576$	−12.3416	−0.514234
$577$	9.85368	0.410214	0.205107	−	0.978740i	$-0.434246\pi$
$577$	9.85368	0.410214	0.205107	+	0.978740i	$0.434246\pi$
$578$	25.0427	1.04164
$579$	5.55334	0.230789
$580$	28.7023	1.19180
$581$	−0.168420	−0.00698724
$582$	2.80876	0.116427
$583$	−26.1044	−1.08113
$584$	−1.86625	−0.0772259
$585$	−5.21945	−0.215798
$586$	20.1695	0.833195
$587$	25.1616	1.03853	0.519265	−	0.854613i	$-0.326206\pi$
$587$	25.1616	1.03853	0.519265	+	0.854613i	$0.326206\pi$
$588$	−17.6069	−0.726097
$589$	46.5860	1.91954
$590$	8.55562	0.352229
$591$	−5.45935	−0.224568
$592$	0.393137	0.0161578
$593$	30.2239	1.24115	0.620574	−	0.784148i	$-0.286900\pi$
$593$	30.2239	1.24115	0.620574	+	0.784148i	$0.286900\pi$
$594$	−7.63359	−0.313210
$595$	1.68873	0.0692311
$596$	−21.3215	−0.873364
$597$	0.256761	0.0105085
$598$	−13.2318	−0.541090
$599$	16.4438	0.671875	0.335937	−	0.941884i	$-0.390947\pi$
$599$	16.4438	0.671875	0.335937	+	0.941884i	$0.390947\pi$
$600$	−1.55879	−0.0636375
$601$	−36.4102	−1.48520	−0.742602	−	0.669733i	$-0.766408\pi$
$601$	−36.4102	−1.48520	−0.742602	+	0.669733i	$0.766408\pi$
$602$	9.42260	0.384037
$603$	0.356294	0.0145094
$604$	12.0617	0.490783
$605$	−1.35178	−0.0549577
$606$	39.1969	1.59227
$607$	−20.8364	−0.845725	−0.422862	−	0.906194i	$-0.638975\pi$
$607$	−20.8364	−0.845725	−0.422862	+	0.906194i	$0.638975\pi$
$608$	54.8864	2.22594
$609$	7.62559	0.309004
$610$	18.2930	0.740662
$611$	55.4078	2.24156
$612$	6.35629	0.256938
$613$	12.6732	0.511867	0.255933	−	0.966694i	$-0.417617\pi$
$613$	12.6732	0.511867	0.255933	+	0.966694i	$0.417617\pi$
$614$	17.7176	0.715023
$615$	−8.24409	−0.332434
$616$	3.95554	0.159373
$617$	7.11050	0.286258	0.143129	−	0.989704i	$-0.454284\pi$
$617$	7.11050	0.286258	0.143129	+	0.989704i	$0.454284\pi$
$618$	−40.4781	−1.62827
$619$	22.6606	0.910808	0.455404	−	0.890285i	$-0.349495\pi$
$619$	22.6606	0.910808	0.455404	+	0.890285i	$0.349495\pi$
$620$	−17.4601	−0.701216
$621$	1.16716	0.0468367
$622$	51.7711	2.07583
$623$	4.68594	0.187738
$624$	−10.6978	−0.428256
$625$	1.00000	0.0400000
$626$	−4.42321	−0.176787
$627$	25.4841	1.01774
$628$	−49.4045	−1.97145
$629$	−0.448621	−0.0178877
$630$	−1.56825	−0.0624807
$631$	−18.4454	−0.734300	−0.367150	−	0.930162i	$-0.619666\pi$
$631$	−18.4454	−0.734300	−0.367150	+	0.930162i	$0.619666\pi$
$632$	−14.0599	−0.559274
$633$	19.5219	0.775928
$634$	−19.2241	−0.763488
$635$	5.64314	0.223941
$636$	−20.1858	−0.800419
$637$	−33.8151	−1.33980
$638$	80.6212	3.19182
$639$	12.4798	0.493692
$640$	−11.6675	−0.461198
$641$	10.9976	0.434378	0.217189	−	0.976130i	$-0.430311\pi$
$641$	10.9976	0.434378	0.217189	+	0.976130i	$0.430311\pi$
$642$	15.7718	0.622464
$643$	6.83077	0.269379	0.134690	−	0.990888i	$-0.456996\pi$
$643$	6.83077	0.269379	0.134690	+	0.990888i	$0.456996\pi$
$644$	−2.29024	−0.0902482
$645$	−6.00834	−0.236578
$646$	−36.8363	−1.44930
$647$	1.61068	0.0633222	0.0316611	−	0.999499i	$-0.489920\pi$
$647$	1.61068	0.0633222	0.0316611	+	0.999499i	$0.489920\pi$
$648$	−1.55879	−0.0612352
$649$	13.8437	0.543413
$650$	−11.3367	−0.444664
$651$	−4.63878	−0.181808
$652$	51.3090	2.00941
$653$	41.6120	1.62840	0.814202	−	0.580581i	$-0.197175\pi$
$653$	41.6120	1.62840	0.814202	+	0.580581i	$0.197175\pi$
$654$	43.3730	1.69602
$655$	19.3517	0.756134
$656$	−16.8972	−0.659723
$657$	1.19724	0.0467087
$658$	16.6480	0.649007
$659$	19.5281	0.760708	0.380354	−	0.924841i	$-0.375802\pi$
$659$	19.5281	0.760708	0.380354	+	0.924841i	$0.375802\pi$
$660$	−9.55128	−0.371783
$661$	−49.4617	−1.92384	−0.961919	−	0.273335i	$-0.911873\pi$
$661$	−49.4617	−1.92384	−0.961919	+	0.273335i	$0.911873\pi$
$662$	−6.97262	−0.270999
$663$	12.2076	0.474106
$664$	−0.363605	−0.0141106
$665$	5.23549	0.203024
$666$	0.416616	0.0161436
$667$	−12.3269	−0.477298
$668$	10.3819	0.401687
$669$	15.8677	0.613482
$670$	0.773878	0.0298975
$671$	29.5996	1.14268
$672$	−5.46529	−0.210828
$673$	−13.8834	−0.535166	−0.267583	−	0.963535i	$-0.586225\pi$
$673$	−13.8834	−0.535166	−0.267583	+	0.963535i	$0.586225\pi$
$674$	−11.8187	−0.455240
$675$	1.00000	0.0384900
$676$	38.7068	1.48872
$677$	−43.7910	−1.68303	−0.841513	−	0.540237i	$-0.818335\pi$
$677$	−43.7910	−1.68303	−0.841513	+	0.540237i	$0.818335\pi$
$678$	32.4843	1.24755
$679$	0.933690	0.0358318
$680$	3.64583	0.139811
$681$	−24.2538	−0.929407
$682$	−49.0433	−1.87796
$683$	44.6719	1.70932	0.854662	−	0.519186i	$-0.173765\pi$
$683$	44.6719	1.70932	0.854662	+	0.519186i	$0.173765\pi$
$684$	19.7061	0.753483
$685$	−15.6380	−0.597496
$686$	−21.1380	−0.807052
$687$	−10.4032	−0.396907
$688$	−12.3147	−0.469495
$689$	−38.7681	−1.47695
$690$	2.53510	0.0965097
$691$	−12.0169	−0.457145	−0.228573	−	0.973527i	$-0.573406\pi$
$691$	−12.0169	−0.457145	−0.228573	+	0.973527i	$0.573406\pi$
$692$	−0.401656	−0.0152687
$693$	−2.53757	−0.0963942
$694$	−55.3996	−2.10294
$695$	8.60340	0.326345
$696$	16.4630	0.624029
$697$	19.2819	0.730354
$698$	−16.5673	−0.627083
$699$	−11.0431	−0.417688
$700$	−1.96223	−0.0741652
$701$	−17.3718	−0.656124	−0.328062	−	0.944656i	$-0.606396\pi$
$701$	−17.3718	−0.656124	−0.328062	+	0.944656i	$0.606396\pi$
$702$	−11.3367	−0.427878
$703$	−1.39084	−0.0524565
$704$	−43.3748	−1.63475
$705$	−10.6156	−0.399808
$706$	42.8871	1.61408
$707$	13.0299	0.490039
$708$	10.7050	0.402317
$709$	10.1634	0.381696	0.190848	−	0.981620i	$-0.438876\pi$
$709$	10.1634	0.381696	0.190848	+	0.981620i	$0.438876\pi$
$710$	27.1063	1.01728
$711$	9.01975	0.338267
$712$	10.1166	0.379134
$713$	7.49865	0.280827
$714$	3.66795	0.137270
$715$	−18.3438	−0.686020
$716$	−68.0502	−2.54315
$717$	−22.4165	−0.837160
$718$	54.6380	2.03907
$719$	1.00051	0.0373126	0.0186563	−	0.999826i	$-0.494061\pi$
$719$	1.00051	0.0373126	0.0186563	+	0.999826i	$0.494061\pi$
$720$	2.04961	0.0763844
$721$	−13.4558	−0.501120
$722$	−72.9335	−2.71431
$723$	19.6497	0.730779
$724$	−50.8528	−1.88993
$725$	−10.5614	−0.392240
$726$	−2.93609	−0.108969
$727$	−39.5004	−1.46499	−0.732495	−	0.680772i	$-0.761644\pi$
$727$	−39.5004	−1.46499	−0.732495	+	0.680772i	$0.761644\pi$
$728$	5.87444	0.217721
$729$	1.00000	0.0370370
$730$	2.60042	0.0962460
$731$	14.0528	0.519760
$732$	22.8885	0.845985
$733$	−26.3517	−0.973321	−0.486661	−	0.873591i	$-0.661785\pi$
$733$	−26.3517	−0.973321	−0.486661	+	0.873591i	$0.661785\pi$
$734$	−57.6045	−2.12622
$735$	6.47868	0.238970
$736$	8.83471	0.325652
$737$	1.25220	0.0461253
$738$	−17.9063	−0.659141
$739$	−51.1032	−1.87986	−0.939931	−	0.341365i	$-0.889111\pi$
$739$	−51.1032	−1.87986	−0.939931	+	0.341365i	$0.889111\pi$
$740$	0.521278	0.0191626
$741$	37.8468	1.39034
$742$	−11.6484	−0.427626
$743$	30.4132	1.11575	0.557876	−	0.829924i	$-0.311616\pi$
$743$	30.4132	1.11575	0.557876	+	0.829924i	$0.311616\pi$
$744$	−10.0147	−0.367158
$745$	7.84552	0.287438
$746$	45.8445	1.67849
$747$	0.233260	0.00853455
$748$	22.3393	0.816804
$749$	5.24289	0.191571
$750$	2.17202	0.0793110
$751$	−5.35980	−0.195582	−0.0977910	−	0.995207i	$-0.531178\pi$
$751$	−5.35980	−0.195582	−0.0977910	+	0.995207i	$0.531178\pi$
$752$	−21.7579	−0.793429
$753$	−3.21617	−0.117204
$754$	119.732	4.36037
$755$	−4.43824	−0.161524
$756$	−1.96223	−0.0713655
$757$	1.34520	0.0488923	0.0244461	−	0.999701i	$-0.492218\pi$
$757$	1.34520	0.0488923	0.0244461	+	0.999701i	$0.492218\pi$
$758$	−5.55299	−0.201694
$759$	4.10201	0.148894
$760$	11.3030	0.410003
$761$	7.75272	0.281036	0.140518	−	0.990078i	$-0.455123\pi$
$761$	7.75272	0.281036	0.140518	+	0.990078i	$0.455123\pi$
$762$	12.2570	0.444025
$763$	14.4181	0.521971
$764$	51.2140	1.85286
$765$	−2.33888	−0.0845622
$766$	61.1810	2.21056
$767$	20.5595	0.742361
$768$	−0.658785	−0.0237719
$769$	12.9556	0.467190	0.233595	−	0.972334i	$-0.424951\pi$
$769$	12.9556	0.467190	0.233595	+	0.972334i	$0.424951\pi$
$770$	−5.51164	−0.198626
$771$	5.25537	0.189267
$772$	15.0922	0.543179
$773$	4.89841	0.176184	0.0880918	−	0.996112i	$-0.471923\pi$
$773$	4.89841	0.176184	0.0880918	+	0.996112i	$0.471923\pi$
$774$	−13.0502	−0.469081
$775$	6.42467	0.230781
$776$	2.01576	0.0723616
$777$	0.138492	0.00496838
$778$	−31.2815	−1.12150
$779$	59.7789	2.14180
$780$	−14.1847	−0.507895
$781$	43.8602	1.56944
$782$	−5.92929	−0.212031
$783$	−10.5614	−0.377433
$784$	13.2788	0.474241
$785$	18.1790	0.648836
$786$	42.0323	1.49924
$787$	−35.2759	−1.25745	−0.628725	−	0.777628i	$-0.716423\pi$
$787$	−35.2759	−1.25745	−0.628725	+	0.777628i	$0.716423\pi$
$788$	−14.8367	−0.528536
$789$	15.9986	0.569566
$790$	19.5911	0.697019
$791$	10.7985	0.383950
$792$	−5.47840	−0.194666
$793$	43.9588	1.56102
$794$	8.14700	0.289126
$795$	7.42761	0.263430
$796$	0.697792	0.0247326
$797$	−3.55618	−0.125966	−0.0629832	−	0.998015i	$-0.520061\pi$
$797$	−3.55618	−0.125966	−0.0629832	+	0.998015i	$0.520061\pi$
$798$	11.3716	0.402550
$799$	24.8287	0.878375
$800$	7.56938	0.267618
$801$	−6.48999	−0.229313
$802$	2.17202	0.0766967
$803$	4.20770	0.148487
$804$	0.968290	0.0341490
$805$	0.842722	0.0297021
$806$	−72.8349	−2.56550
$807$	−21.2447	−0.747848
$808$	28.1305	0.989626
$809$	14.7947	0.520153	0.260076	−	0.965588i	$-0.416252\pi$
$809$	14.7947	0.520153	0.260076	+	0.965588i	$0.416252\pi$
$810$	2.17202	0.0763170
$811$	13.0169	0.457084	0.228542	−	0.973534i	$-0.426604\pi$
$811$	13.0169	0.457084	0.228542	+	0.973534i	$0.426604\pi$
$812$	20.7238	0.727264
$813$	7.31997	0.256722
$814$	1.46420	0.0513203
$815$	−18.8798	−0.661329
$816$	−4.79378	−0.167816
$817$	43.5672	1.52422
$818$	−42.9027	−1.50006
$819$	−3.76858	−0.131685
$820$	−22.4047	−0.782407
$821$	−51.4546	−1.79578	−0.897889	−	0.440223i	$-0.854899\pi$
$821$	−51.4546	−1.79578	−0.897889	+	0.440223i	$0.854899\pi$
$822$	−33.9660	−1.18470
$823$	25.9205	0.903532	0.451766	−	0.892137i	$-0.350794\pi$
$823$	25.9205	0.903532	0.451766	+	0.892137i	$0.350794\pi$
$824$	−29.0499	−1.01200
$825$	3.51451	0.122360
$826$	6.17738	0.214939
$827$	30.2104	1.05052	0.525259	−	0.850942i	$-0.323968\pi$
$827$	30.2104	1.05052	0.525259	+	0.850942i	$0.323968\pi$
$828$	3.17197	0.110233
$829$	52.4610	1.82205	0.911023	−	0.412355i	$-0.135294\pi$
$829$	52.4610	1.82205	0.911023	+	0.412355i	$0.135294\pi$
$830$	0.506646	0.0175859
$831$	23.3805	0.811060
$832$	−64.4165	−2.23324
$833$	−15.1528	−0.525014
$834$	18.6867	0.647069
$835$	−3.82014	−0.132201
$836$	69.2574	2.39532
$837$	6.42467	0.222069
$838$	−44.4844	−1.53669
$839$	−5.14899	−0.177763	−0.0888815	−	0.996042i	$-0.528329\pi$
$839$	−5.14899	−0.177763	−0.0888815	+	0.996042i	$0.528329\pi$
$840$	−1.12549	−0.0388331
$841$	82.5427	2.84630
$842$	33.9544	1.17015
$843$	22.1189	0.761817
$844$	53.0542	1.82620
$845$	−14.2427	−0.489962
$846$	−23.0574	−0.792729
$847$	−0.976020	−0.0335364
$848$	15.2237	0.522784
$849$	10.3373	0.354775
$850$	−5.08008	−0.174245
$851$	−0.223874	−0.00767431
$852$	33.9159	1.16194
$853$	37.3951	1.28038	0.640192	−	0.768215i	$-0.278855\pi$
$853$	37.3951	1.28038	0.640192	+	0.768215i	$0.278855\pi$
$854$	13.2080	0.451969
$855$	−7.25112	−0.247983
$856$	11.3190	0.386874
$857$	49.7681	1.70004	0.850022	−	0.526746i	$-0.176588\pi$
$857$	49.7681	1.70004	0.850022	+	0.526746i	$0.176588\pi$
$858$	−39.8431	−1.36022
$859$	−18.9741	−0.647388	−0.323694	−	0.946162i	$-0.604925\pi$
$859$	−18.9741	−0.647388	−0.323694	+	0.946162i	$0.604925\pi$
$860$	−16.3287	−0.556803
$861$	−5.95245	−0.202859
$862$	9.23014	0.314380
$863$	−44.4758	−1.51397	−0.756986	−	0.653431i	$-0.773329\pi$
$863$	−44.4758	−1.51397	−0.756986	+	0.653431i	$0.773329\pi$
$864$	7.56938	0.257516
$865$	0.147794	0.00502515
$866$	−25.1077	−0.853196
$867$	−11.5297	−0.391568
$868$	−12.6067	−0.427898
$869$	31.7000	1.07535
$870$	−22.9395	−0.777723
$871$	1.85966	0.0630121
$872$	31.1276	1.05411
$873$	−1.29315	−0.0437666
$874$	−18.3823	−0.621791
$875$	0.722026	0.0244089
$876$	3.25370	0.109932
$877$	8.25483	0.278746	0.139373	−	0.990240i	$-0.455491\pi$
$877$	8.25483	0.278746	0.139373	+	0.990240i	$0.455491\pi$
$878$	51.9978	1.75484
$879$	−9.28607	−0.313211
$880$	7.20337	0.242826
$881$	30.8699	1.04003	0.520017	−	0.854156i	$-0.325925\pi$
$881$	30.8699	1.04003	0.520017	+	0.854156i	$0.325925\pi$
$882$	14.0718	0.473823
$883$	11.9203	0.401149	0.200575	−	0.979678i	$-0.435719\pi$
$883$	11.9203	0.401149	0.200575	+	0.979678i	$0.435719\pi$
$884$	33.1764	1.11584
$885$	−3.93902	−0.132409
$886$	88.3224	2.96725
$887$	34.4944	1.15821	0.579105	−	0.815253i	$-0.303402\pi$
$887$	34.4944	1.15821	0.579105	+	0.815253i	$0.303402\pi$
$888$	0.298993	0.0100336
$889$	4.07449	0.136654
$890$	−14.0964	−0.472512
$891$	3.51451	0.117741
$892$	43.1232	1.44387
$893$	76.9752	2.57588
$894$	17.0406	0.569924
$895$	25.0399	0.836991
$896$	−8.42423	−0.281434
$897$	6.09195	0.203404
$898$	−53.0925	−1.77172
$899$	−67.8534	−2.26304
$900$	2.71767	0.0905890
$901$	−17.3723	−0.578754
$902$	−62.9320	−2.09541
$903$	−4.33817	−0.144365
$904$	23.3130	0.775380
$905$	18.7119	0.622005
$906$	−9.63995	−0.320266
$907$	16.8500	0.559496	0.279748	−	0.960073i	$-0.409749\pi$
$907$	16.8500	0.559496	0.279748	+	0.960073i	$0.409749\pi$
$908$	−65.9138	−2.18743
$909$	−18.0463	−0.598558
$910$	−8.18542	−0.271344
$911$	−50.7377	−1.68102	−0.840508	−	0.541799i	$-0.817743\pi$
$911$	−50.7377	−1.68102	−0.840508	+	0.541799i	$0.817743\pi$
$912$	−14.8619	−0.492128
$913$	0.819796	0.0271313
$914$	15.0939	0.499263
$915$	−8.42212	−0.278427
$916$	−28.2725	−0.934150
$917$	13.9724	0.461411
$918$	−5.08008	−0.167668
$919$	6.38035	0.210468	0.105234	−	0.994447i	$-0.466441\pi$
$919$	6.38035	0.210468	0.105234	+	0.994447i	$0.466441\pi$
$920$	1.81937	0.0599828
$921$	−8.15718	−0.268788
$922$	−49.3720	−1.62598
$923$	65.1375	2.14403
$924$	−6.89627	−0.226871
$925$	−0.191811	−0.00630669
$926$	−34.2973	−1.12708
$927$	18.6362	0.612092
$928$	−79.9431	−2.62426
$929$	−17.4190	−0.571500	−0.285750	−	0.958304i	$-0.592243\pi$
$929$	−17.4190	−0.571500	−0.285750	+	0.958304i	$0.592243\pi$
$930$	13.9545	0.457587
$931$	−46.9776	−1.53963
$932$	−30.0114	−0.983057
$933$	−23.8355	−0.780338
$934$	−35.3375	−1.15628
$935$	−8.22000	−0.268823
$936$	−8.13605	−0.265935
$937$	−9.10341	−0.297395	−0.148698	−	0.988883i	$-0.547508\pi$
$937$	−9.10341	−0.297395	−0.148698	+	0.988883i	$0.547508\pi$
$938$	0.558760	0.0182442
$939$	2.03645	0.0664571
$940$	−28.8498	−0.940977
$941$	−25.7667	−0.839971	−0.419985	−	0.907531i	$-0.637965\pi$
$941$	−25.7667	−0.839971	−0.419985	+	0.907531i	$0.637965\pi$
$942$	39.4851	1.28649
$943$	9.62221	0.313342
$944$	−8.07344	−0.262768
$945$	0.722026	0.0234875
$946$	−45.8652	−1.49121
$947$	54.4199	1.76841	0.884205	−	0.467100i	$-0.154701\pi$
$947$	54.4199	1.76841	0.884205	+	0.467100i	$0.154701\pi$
$948$	24.5127	0.796136
$949$	6.24892	0.202849
$950$	−15.7496	−0.510983
$951$	8.85082	0.287007
$952$	2.63238	0.0853159
$953$	8.99170	0.291270	0.145635	−	0.989338i	$-0.453478\pi$
$953$	8.99170	0.291270	0.145635	+	0.989338i	$0.453478\pi$
$954$	16.1329	0.522323
$955$	−18.8448	−0.609804
$956$	−60.9207	−1.97032
$957$	−37.1181	−1.19986
$958$	34.6813	1.12050
$959$	−11.2910	−0.364606
$960$	12.3416	0.398324
$961$	10.2764	0.331498
$962$	2.17451	0.0701090
$963$	−7.26136	−0.233994
$964$	53.4014	1.71994
$965$	−5.55334	−0.178768
$966$	1.83041	0.0588925
$967$	0.437339	0.0140639	0.00703193	−	0.999975i	$-0.497762\pi$
$967$	0.437339	0.0140639	0.00703193	+	0.999975i	$0.497762\pi$
$968$	−2.10715	−0.0677263
$969$	16.9595	0.544816
$970$	−2.80876	−0.0901837
$971$	27.0620	0.868460	0.434230	−	0.900802i	$-0.357021\pi$
$971$	27.0620	0.868460	0.434230	+	0.900802i	$0.357021\pi$
$972$	2.71767	0.0871693
$973$	6.21187	0.199144
$974$	−50.2511	−1.61015
$975$	5.21945	0.167156
$976$	−17.2620	−0.552544
$977$	22.9883	0.735459	0.367730	−	0.929933i	$-0.380135\pi$
$977$	22.9883	0.735459	0.367730	+	0.929933i	$0.380135\pi$
$978$	−41.0072	−1.31127
$979$	−22.8091	−0.728983
$980$	17.6069	0.562432
$981$	−19.9690	−0.637561
$982$	−38.8103	−1.23849
$983$	59.2130	1.88860	0.944300	−	0.329085i	$-0.106740\pi$
$983$	59.2130	1.88860	0.944300	+	0.329085i	$0.106740\pi$
$984$	−12.8508	−0.409670
$985$	5.45935	0.173949
$986$	53.6527	1.70865
$987$	−7.66477	−0.243972
$988$	102.855	3.27226
$989$	7.01272	0.222991
$990$	7.63359	0.242611
$991$	1.43875	0.0457035	0.0228518	−	0.999739i	$-0.492725\pi$
$991$	1.43875	0.0457035	0.0228518	+	0.999739i	$0.492725\pi$
$992$	48.6308	1.54403
$993$	3.21020	0.101873
$994$	19.5714	0.620768
$995$	−0.256761	−0.00813988
$996$	0.633925	0.0200867
$997$	13.6594	0.432596	0.216298	−	0.976327i	$-0.430602\pi$
$997$	13.6594	0.432596	0.216298	+	0.976327i	$0.430602\pi$
$998$	81.5905	2.58270
$999$	−0.191811	−0.00606862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.h.1.7	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.h.1.7	✓	39	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)

\(f(q)\)	\(=\)	\(q-2.17202 q^{2} +1.00000 q^{3} +2.71767 q^{4} -1.00000 q^{5} -2.17202 q^{6} -0.722026 q^{7} -1.55879 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.17202 q^{2} +1.00000 q^{3} +2.71767 q^{4} -1.00000 q^{5} -2.17202 q^{6} -0.722026 q^{7} -1.55879 q^{8} +1.00000 q^{9} +2.17202 q^{10} +3.51451 q^{11} +2.71767 q^{12} +5.21945 q^{13} +1.56825 q^{14} -1.00000 q^{15} -2.04961 q^{16} +2.33888 q^{17} -2.17202 q^{18} +7.25112 q^{19} -2.71767 q^{20} -0.722026 q^{21} -7.63359 q^{22} +1.16716 q^{23} -1.55879 q^{24} +1.00000 q^{25} -11.3367 q^{26} +1.00000 q^{27} -1.96223 q^{28} -10.5614 q^{29} +2.17202 q^{30} +6.42467 q^{31} +7.56938 q^{32} +3.51451 q^{33} -5.08008 q^{34} +0.722026 q^{35} +2.71767 q^{36} -0.191811 q^{37} -15.7496 q^{38} +5.21945 q^{39} +1.55879 q^{40} +8.24409 q^{41} +1.56825 q^{42} +6.00834 q^{43} +9.55128 q^{44} -1.00000 q^{45} -2.53510 q^{46} +10.6156 q^{47} -2.04961 q^{48} -6.47868 q^{49} -2.17202 q^{50} +2.33888 q^{51} +14.1847 q^{52} -7.42761 q^{53} -2.17202 q^{54} -3.51451 q^{55} +1.12549 q^{56} +7.25112 q^{57} +22.9395 q^{58} +3.93902 q^{59} -2.71767 q^{60} +8.42212 q^{61} -13.9545 q^{62} -0.722026 q^{63} -12.3416 q^{64} -5.21945 q^{65} -7.63359 q^{66} +0.356294 q^{67} +6.35629 q^{68} +1.16716 q^{69} -1.56825 q^{70} +12.4798 q^{71} -1.55879 q^{72} +1.19724 q^{73} +0.416616 q^{74} +1.00000 q^{75} +19.7061 q^{76} -2.53757 q^{77} -11.3367 q^{78} +9.01975 q^{79} +2.04961 q^{80} +1.00000 q^{81} -17.9063 q^{82} +0.233260 q^{83} -1.96223 q^{84} -2.33888 q^{85} -13.0502 q^{86} -10.5614 q^{87} -5.47840 q^{88} -6.48999 q^{89} +2.17202 q^{90} -3.76858 q^{91} +3.17197 q^{92} +6.42467 q^{93} -23.0574 q^{94} -7.25112 q^{95} +7.56938 q^{96} -1.29315 q^{97} +14.0718 q^{98} +3.51451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9	\( 39 q + 39 q^{3} + 48 q^{4} - 39 q^{5} + 22 q^{7} + 3 q^{8} + 39 q^{9} - q^{11} + 48 q^{12} + 30 q^{13} + 8 q^{14} - 39 q^{15} + 58 q^{16} + 32 q^{17} + 27 q^{19} - 48 q^{20} + 22 q^{21} + 23 q^{22} - 8 q^{23} + 3 q^{24} + 39 q^{25} - 4 q^{26} + 39 q^{27} + 60 q^{28} - 9 q^{29} + 19 q^{31} + q^{32} - q^{33} + 26 q^{34} - 22 q^{35} + 48 q^{36} + 44 q^{37} + 14 q^{38} + 30 q^{39} - 3 q^{40} + 31 q^{41} + 8 q^{42} + 75 q^{43} + q^{44} - 39 q^{45} + 19 q^{46} - 16 q^{47} + 58 q^{48} + 91 q^{49} + 32 q^{51} + 94 q^{52} + 17 q^{53} + q^{55} + 27 q^{56} + 27 q^{57} + 26 q^{58} - q^{59} - 48 q^{60} + 55 q^{61} + 11 q^{62} + 22 q^{63} + 77 q^{64} - 30 q^{65} + 23 q^{66} + 84 q^{67} + 36 q^{68} - 8 q^{69} - 8 q^{70} - 2 q^{71} + 3 q^{72} + 79 q^{73} + 20 q^{74} + 39 q^{75} + 58 q^{76} + 32 q^{77} - 4 q^{78} + 29 q^{79} - 58 q^{80} + 39 q^{81} + 53 q^{82} + 9 q^{83} + 60 q^{84} - 32 q^{85} - 17 q^{86} - 9 q^{87} + 57 q^{88} + 37 q^{89} + 71 q^{91} + 7 q^{92} + 19 q^{93} + 32 q^{94} - 27 q^{95} + q^{96} + 91 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 39 * q + 39 * q^3 + 48 * q^4 - 39 * q^5 + 22 * q^7 + 3 * q^8 + 39 * q^9 - q^11 + 48 * q^12 + 30 * q^13 + 8 * q^14 - 39 * q^15 + 58 * q^16 + 32 * q^17 + 27 * q^19 - 48 * q^20 + 22 * q^21 + 23 * q^22 - 8 * q^23 + 3 * q^24 + 39 * q^25 - 4 * q^26 + 39 * q^27 + 60 * q^28 - 9 * q^29 + 19 * q^31 + q^32 - q^33 + 26 * q^34 - 22 * q^35 + 48 * q^36 + 44 * q^37 + 14 * q^38 + 30 * q^39 - 3 * q^40 + 31 * q^41 + 8 * q^42 + 75 * q^43 + q^44 - 39 * q^45 + 19 * q^46 - 16 * q^47 + 58 * q^48 + 91 * q^49 + 32 * q^51 + 94 * q^52 + 17 * q^53 + q^55 + 27 * q^56 + 27 * q^57 + 26 * q^58 - q^59 - 48 * q^60 + 55 * q^61 + 11 * q^62 + 22 * q^63 + 77 * q^64 - 30 * q^65 + 23 * q^66 + 84 * q^67 + 36 * q^68 - 8 * q^69 - 8 * q^70 - 2 * q^71 + 3 * q^72 + 79 * q^73 + 20 * q^74 + 39 * q^75 + 58 * q^76 + 32 * q^77 - 4 * q^78 + 29 * q^79 - 58 * q^80 + 39 * q^81 + 53 * q^82 + 9 * q^83 + 60 * q^84 - 32 * q^85 - 17 * q^86 - 9 * q^87 + 57 * q^88 + 37 * q^89 + 71 * q^91 + 7 * q^92 + 19 * q^93 + 32 * q^94 - 27 * q^95 + q^96 + 91 * q^97 - 9 * q^98 - q^99

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