LMFDB - Embedded newform 6015.2.a.c.1.10

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:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-0.932405 q^{2} +1.00000 q^{3} -1.13062 q^{4} -1.00000 q^{5} -0.932405 q^{6} +3.48092 q^{7} +2.91901 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.932405 q^{2} +1.00000 q^{3} -1.13062 q^{4} -1.00000 q^{5} -0.932405 q^{6} +3.48092 q^{7} +2.91901 q^{8} +1.00000 q^{9} +0.932405 q^{10} +0.767572 q^{11} -1.13062 q^{12} -1.54484 q^{13} -3.24563 q^{14} -1.00000 q^{15} -0.460452 q^{16} +3.24341 q^{17} -0.932405 q^{18} -5.95438 q^{19} +1.13062 q^{20} +3.48092 q^{21} -0.715688 q^{22} -6.09124 q^{23} +2.91901 q^{24} +1.00000 q^{25} +1.44042 q^{26} +1.00000 q^{27} -3.93560 q^{28} +2.55858 q^{29} +0.932405 q^{30} +3.78917 q^{31} -5.40868 q^{32} +0.767572 q^{33} -3.02417 q^{34} -3.48092 q^{35} -1.13062 q^{36} -5.61966 q^{37} +5.55189 q^{38} -1.54484 q^{39} -2.91901 q^{40} -5.26170 q^{41} -3.24563 q^{42} -4.05335 q^{43} -0.867833 q^{44} -1.00000 q^{45} +5.67950 q^{46} -4.27135 q^{47} -0.460452 q^{48} +5.11680 q^{49} -0.932405 q^{50} +3.24341 q^{51} +1.74663 q^{52} +4.47286 q^{53} -0.932405 q^{54} -0.767572 q^{55} +10.1608 q^{56} -5.95438 q^{57} -2.38563 q^{58} -11.6648 q^{59} +1.13062 q^{60} +3.90798 q^{61} -3.53304 q^{62} +3.48092 q^{63} +5.96399 q^{64} +1.54484 q^{65} -0.715688 q^{66} -12.6114 q^{67} -3.66707 q^{68} -6.09124 q^{69} +3.24563 q^{70} -10.3873 q^{71} +2.91901 q^{72} -1.65061 q^{73} +5.23980 q^{74} +1.00000 q^{75} +6.73215 q^{76} +2.67186 q^{77} +1.44042 q^{78} -7.21553 q^{79} +0.460452 q^{80} +1.00000 q^{81} +4.90604 q^{82} +17.7902 q^{83} -3.93560 q^{84} -3.24341 q^{85} +3.77937 q^{86} +2.55858 q^{87} +2.24055 q^{88} -8.21578 q^{89} +0.932405 q^{90} -5.37746 q^{91} +6.88689 q^{92} +3.78917 q^{93} +3.98263 q^{94} +5.95438 q^{95} -5.40868 q^{96} -3.48666 q^{97} -4.77093 q^{98} +0.767572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * 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 $

$2$	−0.932405	−0.659310	−0.329655	−	0.944102i	$-0.606932\pi$
$2$	−0.932405	−0.659310	−0.329655	+	0.944102i	$0.606932\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.13062	−0.565311
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.932405	−0.380653
$7$	3.48092	1.31566	0.657832	−	0.753165i	$-0.271474\pi$
$7$	3.48092	1.31566	0.657832	+	0.753165i	$0.271474\pi$
$8$	2.91901	1.03202
$9$	1.00000	0.333333
$10$	0.932405	0.294852
$11$	0.767572	0.231432	0.115716	−	0.993282i	$-0.463084\pi$
$11$	0.767572	0.231432	0.115716	+	0.993282i	$0.463084\pi$
$12$	−1.13062	−0.326382
$13$	−1.54484	−0.428462	−0.214231	−	0.976783i	$-0.568724\pi$
$13$	−1.54484	−0.428462	−0.214231	+	0.976783i	$0.568724\pi$
$14$	−3.24563	−0.867430
$15$	−1.00000	−0.258199
$16$	−0.460452	−0.115113
$17$	3.24341	0.786642	0.393321	−	0.919401i	$-0.371326\pi$
$17$	3.24341	0.786642	0.393321	+	0.919401i	$0.371326\pi$
$18$	−0.932405	−0.219770
$19$	−5.95438	−1.36603	−0.683014	−	0.730405i	$-0.739331\pi$
$19$	−5.95438	−1.36603	−0.683014	+	0.730405i	$0.739331\pi$
$20$	1.13062	0.252815
$21$	3.48092	0.759599
$22$	−0.715688	−0.152585
$23$	−6.09124	−1.27011	−0.635056	−	0.772466i	$-0.719023\pi$
$23$	−6.09124	−1.27011	−0.635056	+	0.772466i	$0.719023\pi$
$24$	2.91901	0.595840
$25$	1.00000	0.200000
$26$	1.44042	0.282489
$27$	1.00000	0.192450
$28$	−3.93560	−0.743759
$29$	2.55858	0.475117	0.237558	−	0.971373i	$-0.423653\pi$
$29$	2.55858	0.475117	0.237558	+	0.971373i	$0.423653\pi$
$30$	0.932405	0.170233
$31$	3.78917	0.680555	0.340278	−	0.940325i	$-0.389479\pi$
$31$	3.78917	0.680555	0.340278	+	0.940325i	$0.389479\pi$
$32$	−5.40868	−0.956129
$33$	0.767572	0.133617
$34$	−3.02417	−0.518641
$35$	−3.48092	−0.588383
$36$	−1.13062	−0.188437
$37$	−5.61966	−0.923867	−0.461933	−	0.886915i	$-0.652844\pi$
$37$	−5.61966	−0.923867	−0.461933	+	0.886915i	$0.652844\pi$
$38$	5.55189	0.900636
$39$	−1.54484	−0.247372
$40$	−2.91901	−0.461535
$41$	−5.26170	−0.821740	−0.410870	−	0.911694i	$-0.634775\pi$
$41$	−5.26170	−0.821740	−0.410870	+	0.911694i	$0.634775\pi$
$42$	−3.24563	−0.500811
$43$	−4.05335	−0.618131	−0.309065	−	0.951041i	$-0.600016\pi$
$43$	−4.05335	−0.618131	−0.309065	+	0.951041i	$0.600016\pi$
$44$	−0.867833	−0.130831
$45$	−1.00000	−0.149071
$46$	5.67950	0.837397
$47$	−4.27135	−0.623041	−0.311520	−	0.950239i	$-0.600838\pi$
$47$	−4.27135	−0.623041	−0.311520	+	0.950239i	$0.600838\pi$
$48$	−0.460452	−0.0664605
$49$	5.11680	0.730971
$50$	−0.932405	−0.131862
$51$	3.24341	0.454168
$52$	1.74663	0.242214
$53$	4.47286	0.614394	0.307197	−	0.951646i	$-0.400609\pi$
$53$	4.47286	0.614394	0.307197	+	0.951646i	$0.400609\pi$
$54$	−0.932405	−0.126884
$55$	−0.767572	−0.103499
$56$	10.1608	1.35780
$57$	−5.95438	−0.788677
$58$	−2.38563	−0.313249
$59$	−11.6648	−1.51863	−0.759315	−	0.650724i	$-0.774466\pi$
$59$	−11.6648	−1.51863	−0.759315	+	0.650724i	$0.774466\pi$
$60$	1.13062	0.145963
$61$	3.90798	0.500365	0.250183	−	0.968199i	$-0.419509\pi$
$61$	3.90798	0.500365	0.250183	+	0.968199i	$0.419509\pi$
$62$	−3.53304	−0.448697
$63$	3.48092	0.438555
$64$	5.96399	0.745498
$65$	1.54484	0.191614
$66$	−0.715688	−0.0880951
$67$	−12.6114	−1.54072	−0.770362	−	0.637607i	$-0.779924\pi$
$67$	−12.6114	−1.54072	−0.770362	+	0.637607i	$0.779924\pi$
$68$	−3.66707	−0.444697
$69$	−6.09124	−0.733299
$70$	3.24563	0.387926
$71$	−10.3873	−1.23274	−0.616372	−	0.787455i	$-0.711398\pi$
$71$	−10.3873	−1.23274	−0.616372	+	0.787455i	$0.711398\pi$
$72$	2.91901	0.344008
$73$	−1.65061	−0.193189	−0.0965946	−	0.995324i	$-0.530795\pi$
$73$	−1.65061	−0.193189	−0.0965946	+	0.995324i	$0.530795\pi$
$74$	5.23980	0.609114
$75$	1.00000	0.115470
$76$	6.73215	0.772230
$77$	2.67186	0.304486
$78$	1.44042	0.163095
$79$	−7.21553	−0.811810	−0.405905	−	0.913915i	$-0.633044\pi$
$79$	−7.21553	−0.811810	−0.405905	+	0.913915i	$0.633044\pi$
$80$	0.460452	0.0514801
$81$	1.00000	0.111111
$82$	4.90604	0.541781
$83$	17.7902	1.95273	0.976366	−	0.216124i	$-0.0693416\pi$
$83$	17.7902	1.95273	0.976366	+	0.216124i	$0.0693416\pi$
$84$	−3.93560	−0.429409
$85$	−3.24341	−0.351797
$86$	3.77937	0.407539
$87$	2.55858	0.274309
$88$	2.24055	0.238843
$89$	−8.21578	−0.870871	−0.435435	−	0.900220i	$-0.643406\pi$
$89$	−8.21578	−0.870871	−0.435435	+	0.900220i	$0.643406\pi$
$90$	0.932405	0.0982841
$91$	−5.37746	−0.563711
$92$	6.88689	0.718008
$93$	3.78917	0.392919
$94$	3.98263	0.410777
$95$	5.95438	0.610906
$96$	−5.40868	−0.552022
$97$	−3.48666	−0.354017	−0.177008	−	0.984209i	$-0.556642\pi$
$97$	−3.48666	−0.354017	−0.177008	+	0.984209i	$0.556642\pi$
$98$	−4.77093	−0.481937
$99$	0.767572	0.0771439
$100$	−1.13062	−0.113062
$101$	−13.2760	−1.32101	−0.660507	−	0.750820i	$-0.729659\pi$
$101$	−13.2760	−1.32101	−0.660507	+	0.750820i	$0.729659\pi$
$102$	−3.02417	−0.299437
$103$	11.6934	1.15219	0.576093	−	0.817384i	$-0.304577\pi$
$103$	11.6934	1.15219	0.576093	+	0.817384i	$0.304577\pi$
$104$	−4.50940	−0.442183
$105$	−3.48092	−0.339703
$106$	−4.17051	−0.405076
$107$	19.6228	1.89701	0.948505	−	0.316762i	$-0.102596\pi$
$107$	19.6228	1.89701	0.948505	+	0.316762i	$0.102596\pi$
$108$	−1.13062	−0.108794
$109$	−6.17925	−0.591865	−0.295932	−	0.955209i	$-0.595630\pi$
$109$	−6.17925	−0.591865	−0.295932	+	0.955209i	$0.595630\pi$
$110$	0.715688	0.0682381
$111$	−5.61966	−0.533395
$112$	−1.60280	−0.151450
$113$	−14.7217	−1.38490	−0.692448	−	0.721467i	$-0.743468\pi$
$113$	−14.7217	−1.38490	−0.692448	+	0.721467i	$0.743468\pi$
$114$	5.55189	0.519982
$115$	6.09124	0.568011
$116$	−2.89279	−0.268589
$117$	−1.54484	−0.142821
$118$	10.8763	1.00125
$119$	11.2900	1.03496
$120$	−2.91901	−0.266468
$121$	−10.4108	−0.946439
$122$	−3.64382	−0.329896
$123$	−5.26170	−0.474432
$124$	−4.28412	−0.384725
$125$	−1.00000	−0.0894427
$126$	−3.24563	−0.289143
$127$	−6.18545	−0.548869	−0.274435	−	0.961606i	$-0.588491\pi$
$127$	−6.18545	−0.548869	−0.274435	+	0.961606i	$0.588491\pi$
$128$	5.25652	0.464615
$129$	−4.05335	−0.356878
$130$	−1.44042	−0.126333
$131$	8.27270	0.722789	0.361394	−	0.932413i	$-0.382301\pi$
$131$	8.27270	0.722789	0.361394	+	0.932413i	$0.382301\pi$
$132$	−0.867833	−0.0755352
$133$	−20.7267	−1.79723
$134$	11.7589	1.01581
$135$	−1.00000	−0.0860663
$136$	9.46753	0.811834
$137$	9.67615	0.826690	0.413345	−	0.910575i	$-0.364360\pi$
$137$	9.67615	0.826690	0.413345	+	0.910575i	$0.364360\pi$
$138$	5.67950	0.483471
$139$	−0.294544	−0.0249829	−0.0124914	−	0.999922i	$-0.503976\pi$
$139$	−0.294544	−0.0249829	−0.0124914	+	0.999922i	$0.503976\pi$
$140$	3.93560	0.332619
$141$	−4.27135	−0.359713
$142$	9.68515	0.812760
$143$	−1.18578	−0.0991596
$144$	−0.460452	−0.0383710
$145$	−2.55858	−0.212479
$146$	1.53904	0.127372
$147$	5.11680	0.422027
$148$	6.35371	0.522272
$149$	15.1437	1.24062	0.620308	−	0.784358i	$-0.287007\pi$
$149$	15.1437	1.24062	0.620308	+	0.784358i	$0.287007\pi$
$150$	−0.932405	−0.0761305
$151$	8.45716	0.688234	0.344117	−	0.938927i	$-0.388178\pi$
$151$	8.45716	0.688234	0.344117	+	0.938927i	$0.388178\pi$
$152$	−17.3809	−1.40977
$153$	3.24341	0.262214
$154$	−2.49125	−0.200751
$155$	−3.78917	−0.304354
$156$	1.74663	0.139842
$157$	−13.6424	−1.08878	−0.544390	−	0.838832i	$-0.683239\pi$
$157$	−13.6424	−1.08878	−0.544390	+	0.838832i	$0.683239\pi$
$158$	6.72779	0.535234
$159$	4.47286	0.354721
$160$	5.40868	0.427594
$161$	−21.2031	−1.67104
$162$	−0.932405	−0.0732566
$163$	9.19927	0.720542	0.360271	−	0.932848i	$-0.382684\pi$
$163$	9.19927	0.720542	0.360271	+	0.932848i	$0.382684\pi$
$164$	5.94900	0.464539
$165$	−0.767572	−0.0597554
$166$	−16.5877	−1.28745
$167$	14.9562	1.15735	0.578673	−	0.815560i	$-0.303571\pi$
$167$	14.9562	1.15735	0.578673	+	0.815560i	$0.303571\pi$
$168$	10.1608	0.783925
$169$	−10.6135	−0.816421
$170$	3.02417	0.231943
$171$	−5.95438	−0.455343
$172$	4.58281	0.349436
$173$	12.6538	0.962050	0.481025	−	0.876707i	$-0.340265\pi$
$173$	12.6538	0.962050	0.481025	+	0.876707i	$0.340265\pi$
$174$	−2.38563	−0.180855
$175$	3.48092	0.263133
$176$	−0.353430	−0.0266408
$177$	−11.6648	−0.876781
$178$	7.66043	0.574174
$179$	−14.0896	−1.05310	−0.526552	−	0.850143i	$-0.676515\pi$
$179$	−14.0896	−1.05310	−0.526552	+	0.850143i	$0.676515\pi$
$180$	1.13062	0.0842716
$181$	−1.09103	−0.0810956	−0.0405478	−	0.999178i	$-0.512910\pi$
$181$	−1.09103	−0.0810956	−0.0405478	+	0.999178i	$0.512910\pi$
$182$	5.01397	0.371660
$183$	3.90798	0.288886
$184$	−17.7804	−1.31079
$185$	5.61966	0.413166
$186$	−3.53304	−0.259055
$187$	2.48955	0.182054
$188$	4.82928	0.352212
$189$	3.48092	0.253200
$190$	−5.55189	−0.402776
$191$	23.7190	1.71625	0.858123	−	0.513443i	$-0.171630\pi$
$191$	23.7190	1.71625	0.858123	+	0.513443i	$0.171630\pi$
$192$	5.96399	0.430414
$193$	−3.07101	−0.221056	−0.110528	−	0.993873i	$-0.535254\pi$
$193$	−3.07101	−0.221056	−0.110528	+	0.993873i	$0.535254\pi$
$194$	3.25098	0.233407
$195$	1.54484	0.110628
$196$	−5.78516	−0.413226
$197$	−6.63464	−0.472698	−0.236349	−	0.971668i	$-0.575951\pi$
$197$	−6.63464	−0.472698	−0.236349	+	0.971668i	$0.575951\pi$
$198$	−0.715688	−0.0508617
$199$	−22.2667	−1.57844	−0.789221	−	0.614109i	$-0.789516\pi$
$199$	−22.2667	−1.57844	−0.789221	+	0.614109i	$0.789516\pi$
$200$	2.91901	0.206405
$201$	−12.6114	−0.889537
$202$	12.3786	0.870958
$203$	8.90622	0.625094
$204$	−3.66707	−0.256746
$205$	5.26170	0.367493
$206$	−10.9030	−0.759647
$207$	−6.09124	−0.423370
$208$	0.711325	0.0493215
$209$	−4.57041	−0.316142
$210$	3.24563	0.223969
$211$	23.9353	1.64777	0.823886	−	0.566756i	$-0.191802\pi$
$211$	23.9353	1.64777	0.823886	+	0.566756i	$0.191802\pi$
$212$	−5.05711	−0.347324
$213$	−10.3873	−0.711725
$214$	−18.2964	−1.25072
$215$	4.05335	0.276436
$216$	2.91901	0.198613
$217$	13.1898	0.895382
$218$	5.76156	0.390222
$219$	−1.65061	−0.111538
$220$	0.867833	0.0585093
$221$	−5.01055	−0.337046
$222$	5.23980	0.351672
$223$	−8.57606	−0.574296	−0.287148	−	0.957886i	$-0.592707\pi$
$223$	−8.57606	−0.574296	−0.287148	+	0.957886i	$0.592707\pi$
$224$	−18.8272	−1.25794
$225$	1.00000	0.0666667
$226$	13.7265	0.913076
$227$	21.7125	1.44111	0.720555	−	0.693398i	$-0.243887\pi$
$227$	21.7125	1.44111	0.720555	+	0.693398i	$0.243887\pi$
$228$	6.73215	0.445847
$229$	−15.8129	−1.04494	−0.522472	−	0.852657i	$-0.674990\pi$
$229$	−15.8129	−1.04494	−0.522472	+	0.852657i	$0.674990\pi$
$230$	−5.67950	−0.374495
$231$	2.67186	0.175795
$232$	7.46852	0.490332
$233$	−4.55198	−0.298210	−0.149105	−	0.988821i	$-0.547639\pi$
$233$	−4.55198	−0.298210	−0.149105	+	0.988821i	$0.547639\pi$
$234$	1.44042	0.0941630
$235$	4.27135	0.278632
$236$	13.1885	0.858498
$237$	−7.21553	−0.468699
$238$	−10.5269	−0.682357
$239$	−15.1732	−0.981476	−0.490738	−	0.871307i	$-0.663273\pi$
$239$	−15.1732	−0.981476	−0.490738	+	0.871307i	$0.663273\pi$
$240$	0.460452	0.0297220
$241$	4.39769	0.283280	0.141640	−	0.989918i	$-0.454762\pi$
$241$	4.39769	0.283280	0.141640	+	0.989918i	$0.454762\pi$
$242$	9.70711	0.623997
$243$	1.00000	0.0641500
$244$	−4.41844	−0.282862
$245$	−5.11680	−0.326900
$246$	4.90604	0.312798
$247$	9.19856	0.585291
$248$	11.0606	0.702350
$249$	17.7902	1.12741
$250$	0.932405	0.0589704
$251$	−9.33566	−0.589262	−0.294631	−	0.955611i	$-0.595197\pi$
$251$	−9.33566	−0.589262	−0.294631	+	0.955611i	$0.595197\pi$
$252$	−3.93560	−0.247920
$253$	−4.67546	−0.293944
$254$	5.76734	0.361875
$255$	−3.24341	−0.203110
$256$	−16.8292	−1.05182
$257$	30.9366	1.92977	0.964886	−	0.262670i	$-0.0846031\pi$
$257$	30.9366	1.92977	0.964886	+	0.262670i	$0.0846031\pi$
$258$	3.77937	0.235293
$259$	−19.5616	−1.21550
$260$	−1.74663	−0.108321
$261$	2.55858	0.158372
$262$	−7.71350	−0.476542
$263$	−29.1595	−1.79805	−0.899024	−	0.437899i	$-0.855723\pi$
$263$	−29.1595	−1.79805	−0.899024	+	0.437899i	$0.855723\pi$
$264$	2.24055	0.137896
$265$	−4.47286	−0.274766
$266$	19.3257	1.18493
$267$	−8.21578	−0.502797
$268$	14.2587	0.870988
$269$	19.4065	1.18323	0.591617	−	0.806219i	$-0.298490\pi$
$269$	19.4065	1.18323	0.591617	+	0.806219i	$0.298490\pi$
$270$	0.932405	0.0567443
$271$	6.44200	0.391324	0.195662	−	0.980671i	$-0.437315\pi$
$271$	6.44200	0.391324	0.195662	+	0.980671i	$0.437315\pi$
$272$	−1.49343	−0.0905527
$273$	−5.37746	−0.325459
$274$	−9.02209	−0.545044
$275$	0.767572	0.0462863
$276$	6.88689	0.414542
$277$	8.33640	0.500886	0.250443	−	0.968131i	$-0.419424\pi$
$277$	8.33640	0.500886	0.250443	+	0.968131i	$0.419424\pi$
$278$	0.274634	0.0164714
$279$	3.78917	0.226852
$280$	−10.1608	−0.607225
$281$	30.5557	1.82280	0.911399	−	0.411524i	$-0.135003\pi$
$281$	30.5557	1.82280	0.911399	+	0.411524i	$0.135003\pi$
$282$	3.98263	0.237162
$283$	−20.5590	−1.22210	−0.611052	−	0.791590i	$-0.709253\pi$
$283$	−20.5590	−1.22210	−0.611052	+	0.791590i	$0.709253\pi$
$284$	11.7441	0.696883
$285$	5.95438	0.352707
$286$	1.10562	0.0653769
$287$	−18.3156	−1.08113
$288$	−5.40868	−0.318710
$289$	−6.48030	−0.381194
$290$	2.38563	0.140089
$291$	−3.48666	−0.204392
$292$	1.86622	0.109212
$293$	−31.6837	−1.85098	−0.925490	−	0.378771i	$-0.876347\pi$
$293$	−31.6837	−1.85098	−0.925490	+	0.378771i	$0.876347\pi$
$294$	−4.77093	−0.278246
$295$	11.6648	0.679152
$296$	−16.4038	−0.953453
$297$	0.767572	0.0445390
$298$	−14.1200	−0.817950
$299$	9.40999	0.544194
$300$	−1.13062	−0.0652765
$301$	−14.1094	−0.813252
$302$	−7.88549	−0.453759
$303$	−13.2760	−0.762688
$304$	2.74170	0.157248
$305$	−3.90798	−0.223770
$306$	−3.02417	−0.172880
$307$	−2.29329	−0.130885	−0.0654425	−	0.997856i	$-0.520846\pi$
$307$	−2.29329	−0.130885	−0.0654425	+	0.997856i	$0.520846\pi$
$308$	−3.02086	−0.172129
$309$	11.6934	0.665215
$310$	3.53304	0.200663
$311$	−31.9147	−1.80972	−0.904859	−	0.425712i	$-0.860024\pi$
$311$	−31.9147	−1.80972	−0.904859	+	0.425712i	$0.860024\pi$
$312$	−4.50940	−0.255294
$313$	−19.2628	−1.08880	−0.544400	−	0.838826i	$-0.683243\pi$
$313$	−19.2628	−1.08880	−0.544400	+	0.838826i	$0.683243\pi$
$314$	12.7202	0.717844
$315$	−3.48092	−0.196128
$316$	8.15803	0.458925
$317$	−6.55887	−0.368383	−0.184191	−	0.982890i	$-0.558967\pi$
$317$	−6.55887	−0.368383	−0.184191	+	0.982890i	$0.558967\pi$
$318$	−4.17051	−0.233871
$319$	1.96390	0.109957
$320$	−5.96399	−0.333397
$321$	19.6228	1.09524
$322$	19.7699	1.10173
$323$	−19.3125	−1.07458
$324$	−1.13062	−0.0628123
$325$	−1.54484	−0.0856923
$326$	−8.57744	−0.475061
$327$	−6.17925	−0.341713
$328$	−15.3589	−0.848056
$329$	−14.8682	−0.819712
$330$	0.715688	0.0393973
$331$	−21.8873	−1.20303	−0.601517	−	0.798860i	$-0.705437\pi$
$331$	−21.8873	−1.20303	−0.601517	+	0.798860i	$0.705437\pi$
$332$	−20.1140	−1.10390
$333$	−5.61966	−0.307956
$334$	−13.9452	−0.763049
$335$	12.6114	0.689033
$336$	−1.60280	−0.0874397
$337$	−16.6969	−0.909537	−0.454769	−	0.890610i	$-0.650278\pi$
$337$	−16.6969	−0.909537	−0.454769	+	0.890610i	$0.650278\pi$
$338$	9.89605	0.538274
$339$	−14.7217	−0.799570
$340$	3.66707	0.198875
$341$	2.90846	0.157502
$342$	5.55189	0.300212
$343$	−6.55527	−0.353951
$344$	−11.8318	−0.637926
$345$	6.09124	0.327941
$346$	−11.7985	−0.634289
$347$	−35.2510	−1.89237	−0.946186	−	0.323622i	$-0.895099\pi$
$347$	−35.2510	−1.89237	−0.946186	+	0.323622i	$0.895099\pi$
$348$	−2.89279	−0.155070
$349$	−0.490158	−0.0262376	−0.0131188	−	0.999914i	$-0.504176\pi$
$349$	−0.490158	−0.0262376	−0.0131188	+	0.999914i	$0.504176\pi$
$350$	−3.24563	−0.173486
$351$	−1.54484	−0.0824575
$352$	−4.15155	−0.221279
$353$	−21.6382	−1.15168	−0.575842	−	0.817561i	$-0.695326\pi$
$353$	−21.6382	−1.15168	−0.575842	+	0.817561i	$0.695326\pi$
$354$	10.8763	0.578070
$355$	10.3873	0.551300
$356$	9.28894	0.492313
$357$	11.2900	0.597533
$358$	13.1372	0.694322
$359$	−5.98624	−0.315942	−0.157971	−	0.987444i	$-0.550495\pi$
$359$	−5.98624	−0.315942	−0.157971	+	0.987444i	$0.550495\pi$
$360$	−2.91901	−0.153845
$361$	16.4546	0.866033
$362$	1.01728	0.0534671
$363$	−10.4108	−0.546427
$364$	6.07988	0.318672
$365$	1.65061	0.0863969
$366$	−3.64382	−0.190465
$367$	−34.0060	−1.77510	−0.887550	−	0.460711i	$-0.847595\pi$
$367$	−34.0060	−1.77510	−0.887550	+	0.460711i	$0.847595\pi$
$368$	2.80472	0.146206
$369$	−5.26170	−0.273913
$370$	−5.23980	−0.272404
$371$	15.5697	0.808336
$372$	−4.28412	−0.222121
$373$	−17.1490	−0.887939	−0.443970	−	0.896042i	$-0.646430\pi$
$373$	−17.1490	−0.887939	−0.443970	+	0.896042i	$0.646430\pi$
$374$	−2.32127	−0.120030
$375$	−1.00000	−0.0516398
$376$	−12.4681	−0.642993
$377$	−3.95260	−0.203569
$378$	−3.24563	−0.166937
$379$	−30.0297	−1.54252	−0.771260	−	0.636520i	$-0.780373\pi$
$379$	−30.0297	−1.54252	−0.771260	+	0.636520i	$0.780373\pi$
$380$	−6.73215	−0.345352
$381$	−6.18545	−0.316890
$382$	−22.1157	−1.13154
$383$	14.5236	0.742124	0.371062	−	0.928608i	$-0.378994\pi$
$383$	14.5236	0.742124	0.371062	+	0.928608i	$0.378994\pi$
$384$	5.25652	0.268246
$385$	−2.67186	−0.136170
$386$	2.86342	0.145744
$387$	−4.05335	−0.206044
$388$	3.94209	0.200129
$389$	−28.9378	−1.46720	−0.733601	−	0.679580i	$-0.762162\pi$
$389$	−28.9378	−1.46720	−0.733601	+	0.679580i	$0.762162\pi$
$390$	−1.44042	−0.0729383
$391$	−19.7564	−0.999123
$392$	14.9360	0.754380
$393$	8.27270	0.417302
$394$	6.18617	0.311655
$395$	7.21553	0.363053
$396$	−0.867833	−0.0436103
$397$	34.7385	1.74347	0.871737	−	0.489973i	$-0.162993\pi$
$397$	34.7385	1.74347	0.871737	+	0.489973i	$0.162993\pi$
$398$	20.7616	1.04068
$399$	−20.7267	−1.03763
$400$	−0.460452	−0.0230226
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	11.7589	0.586481
$403$	−5.85367	−0.291592
$404$	15.0102	0.746784
$405$	−1.00000	−0.0496904
$406$	−8.30420	−0.412131
$407$	−4.31349	−0.213812
$408$	9.46753	0.468713
$409$	1.58769	0.0785064	0.0392532	−	0.999229i	$-0.487502\pi$
$409$	1.58769	0.0785064	0.0392532	+	0.999229i	$0.487502\pi$
$410$	−4.90604	−0.242292
$411$	9.67615	0.477290
$412$	−13.2208	−0.651343
$413$	−40.6043	−1.99801
$414$	5.67950	0.279132
$415$	−17.7902	−0.873288
$416$	8.35555	0.409665
$417$	−0.294544	−0.0144239
$418$	4.26147	0.208436
$419$	23.6009	1.15298	0.576489	−	0.817105i	$-0.304422\pi$
$419$	23.6009	1.15298	0.576489	+	0.817105i	$0.304422\pi$
$420$	3.93560	0.192038
$421$	−9.25994	−0.451302	−0.225651	−	0.974208i	$-0.572451\pi$
$421$	−9.25994	−0.451302	−0.225651	+	0.974208i	$0.572451\pi$
$422$	−22.3173	−1.08639
$423$	−4.27135	−0.207680
$424$	13.0563	0.634070
$425$	3.24341	0.157328
$426$	9.68515	0.469247
$427$	13.6034	0.658313
$428$	−22.1860	−1.07240
$429$	−1.18578	−0.0572498
$430$	−3.77937	−0.182257
$431$	−14.2979	−0.688708	−0.344354	−	0.938840i	$-0.611902\pi$
$431$	−14.2979	−0.688708	−0.344354	+	0.938840i	$0.611902\pi$
$432$	−0.460452	−0.0221535
$433$	−6.66179	−0.320145	−0.160073	−	0.987105i	$-0.551173\pi$
$433$	−6.66179	−0.320145	−0.160073	+	0.987105i	$0.551173\pi$
$434$	−12.2982	−0.590334
$435$	−2.55858	−0.122675
$436$	6.98639	0.334588
$437$	36.2695	1.73501
$438$	1.53904	0.0735380
$439$	−2.03968	−0.0973485	−0.0486743	−	0.998815i	$-0.515500\pi$
$439$	−2.03968	−0.0973485	−0.0486743	+	0.998815i	$0.515500\pi$
$440$	−2.24055	−0.106814
$441$	5.11680	0.243657
$442$	4.67186	0.222218
$443$	−10.5315	−0.500367	−0.250184	−	0.968198i	$-0.580491\pi$
$443$	−10.5315	−0.500367	−0.250184	+	0.968198i	$0.580491\pi$
$444$	6.35371	0.301534
$445$	8.21578	0.389465
$446$	7.99636	0.378639
$447$	15.1437	0.716270
$448$	20.7602	0.980825
$449$	5.78305	0.272919	0.136460	−	0.990646i	$-0.456428\pi$
$449$	5.78305	0.272919	0.136460	+	0.990646i	$0.456428\pi$
$450$	−0.932405	−0.0439540
$451$	−4.03874	−0.190177
$452$	16.6446	0.782897
$453$	8.45716	0.397352
$454$	−20.2448	−0.950138
$455$	5.37746	0.252099
$456$	−17.3809	−0.813934
$457$	15.5565	0.727701	0.363851	−	0.931457i	$-0.381462\pi$
$457$	15.5565	0.727701	0.363851	+	0.931457i	$0.381462\pi$
$458$	14.7440	0.688941
$459$	3.24341	0.151389
$460$	−6.88689	−0.321103
$461$	36.7181	1.71013	0.855067	−	0.518517i	$-0.173516\pi$
$461$	36.7181	1.71013	0.855067	+	0.518517i	$0.173516\pi$
$462$	−2.49125	−0.115903
$463$	−24.9177	−1.15802	−0.579011	−	0.815319i	$-0.696561\pi$
$463$	−24.9177	−1.15802	−0.579011	+	0.815319i	$0.696561\pi$
$464$	−1.17810	−0.0546921
$465$	−3.78917	−0.175719
$466$	4.24429	0.196613
$467$	12.1387	0.561714	0.280857	−	0.959750i	$-0.409381\pi$
$467$	12.1387	0.561714	0.280857	+	0.959750i	$0.409381\pi$
$468$	1.74663	0.0807380
$469$	−43.8992	−2.02707
$470$	−3.98263	−0.183705
$471$	−13.6424	−0.628608
$472$	−34.0497	−1.56726
$473$	−3.11124	−0.143055
$474$	6.72779	0.309018
$475$	−5.95438	−0.273206
$476$	−12.7648	−0.585072
$477$	4.47286	0.204798
$478$	14.1476	0.647096
$479$	−26.1746	−1.19595	−0.597973	−	0.801516i	$-0.704027\pi$
$479$	−26.1746	−1.19595	−0.597973	+	0.801516i	$0.704027\pi$
$480$	5.40868	0.246872
$481$	8.68148	0.395841
$482$	−4.10043	−0.186769
$483$	−21.2031	−0.964775
$484$	11.7707	0.535032
$485$	3.48666	0.158321
$486$	−0.932405	−0.0422947
$487$	38.7795	1.75727	0.878633	−	0.477497i	$-0.158456\pi$
$487$	38.7795	1.75727	0.878633	+	0.477497i	$0.158456\pi$
$488$	11.4074	0.516389
$489$	9.19927	0.416005
$490$	4.77093	0.215529
$491$	5.92077	0.267200	0.133600	−	0.991035i	$-0.457346\pi$
$491$	5.92077	0.267200	0.133600	+	0.991035i	$0.457346\pi$
$492$	5.94900	0.268201
$493$	8.29853	0.373747
$494$	−8.57678	−0.385888
$495$	−0.767572	−0.0344998
$496$	−1.74473	−0.0783407
$497$	−36.1573	−1.62188
$498$	−16.5877	−0.743312
$499$	21.8909	0.979972	0.489986	−	0.871730i	$-0.337002\pi$
$499$	21.8909	0.979972	0.489986	+	0.871730i	$0.337002\pi$
$500$	1.13062	0.0505629
$501$	14.9562	0.668194
$502$	8.70461	0.388506
$503$	27.2536	1.21518	0.607589	−	0.794252i	$-0.292137\pi$
$503$	27.2536	1.21518	0.607589	+	0.794252i	$0.292137\pi$
$504$	10.1608	0.452599
$505$	13.2760	0.590776
$506$	4.35942	0.193800
$507$	−10.6135	−0.471361
$508$	6.99340	0.310282
$509$	18.5057	0.820251	0.410126	−	0.912029i	$-0.365485\pi$
$509$	18.5057	0.820251	0.410126	+	0.912029i	$0.365485\pi$
$510$	3.02417	0.133912
$511$	−5.74564	−0.254172
$512$	5.17856	0.228862
$513$	−5.95438	−0.262892
$514$	−28.8454	−1.27232
$515$	−11.6934	−0.515273
$516$	4.58281	0.201747
$517$	−3.27857	−0.144191
$518$	18.2393	0.801390
$519$	12.6538	0.555440
$520$	4.50940	0.197750
$521$	−27.7420	−1.21540	−0.607699	−	0.794168i	$-0.707907\pi$
$521$	−27.7420	−1.21540	−0.607699	+	0.794168i	$0.707907\pi$
$522$	−2.38563	−0.104416
$523$	0.0498103	0.00217805	0.00108903	−	0.999999i	$-0.499653\pi$
$523$	0.0498103	0.00217805	0.00108903	+	0.999999i	$0.499653\pi$
$524$	−9.35329	−0.408600
$525$	3.48092	0.151920
$526$	27.1884	1.18547
$527$	12.2898	0.535354
$528$	−0.353430	−0.0153811
$529$	14.1032	0.613183
$530$	4.17051	0.181156
$531$	−11.6648	−0.506210
$532$	23.4341	1.01600
$533$	8.12849	0.352084
$534$	7.66043	0.331499
$535$	−19.6228	−0.848369
$536$	−36.8127	−1.59006
$537$	−14.0896	−0.608010
$538$	−18.0947	−0.780117
$539$	3.92751	0.169170
$540$	1.13062	0.0486542
$541$	−21.9004	−0.941570	−0.470785	−	0.882248i	$-0.656029\pi$
$541$	−21.9004	−0.941570	−0.470785	+	0.882248i	$0.656029\pi$
$542$	−6.00655	−0.258003
$543$	−1.09103	−0.0468206
$544$	−17.5426	−0.752132
$545$	6.17925	0.264690
$546$	5.01397	0.214578
$547$	−20.3920	−0.871898	−0.435949	−	0.899971i	$-0.643587\pi$
$547$	−20.3920	−0.871898	−0.435949	+	0.899971i	$0.643587\pi$
$548$	−10.9401	−0.467337
$549$	3.90798	0.166788
$550$	−0.715688	−0.0305170
$551$	−15.2348	−0.649023
$552$	−17.7804	−0.756783
$553$	−25.1167	−1.06807
$554$	−7.77290	−0.330239
$555$	5.61966	0.238541
$556$	0.333017	0.0141231
$557$	37.2518	1.57841	0.789205	−	0.614130i	$-0.210493\pi$
$557$	37.2518	1.57841	0.789205	+	0.614130i	$0.210493\pi$
$558$	−3.53304	−0.149566
$559$	6.26178	0.264845
$560$	1.60280	0.0677305
$561$	2.48955	0.105109
$562$	−28.4902	−1.20179
$563$	−27.1848	−1.14570	−0.572850	−	0.819660i	$-0.694162\pi$
$563$	−27.1848	−1.14570	−0.572850	+	0.819660i	$0.694162\pi$
$564$	4.82928	0.203349
$565$	14.7217	0.619345
$566$	19.1693	0.805745
$567$	3.48092	0.146185
$568$	−30.3205	−1.27222
$569$	27.2564	1.14265	0.571324	−	0.820725i	$-0.306430\pi$
$569$	27.2564	1.14265	0.571324	+	0.820725i	$0.306430\pi$
$570$	−5.55189	−0.232543
$571$	40.9605	1.71415	0.857073	−	0.515196i	$-0.172281\pi$
$571$	40.9605	1.71415	0.857073	+	0.515196i	$0.172281\pi$
$572$	1.34066	0.0560560
$573$	23.7190	0.990876
$574$	17.0775	0.712802
$575$	−6.09124	−0.254022
$576$	5.96399	0.248499
$577$	−43.7750	−1.82238	−0.911188	−	0.411991i	$-0.864834\pi$
$577$	−43.7750	−1.82238	−0.911188	+	0.411991i	$0.864834\pi$
$578$	6.04226	0.251325
$579$	−3.07101	−0.127627
$580$	2.89279	0.120117
$581$	61.9264	2.56914
$582$	3.25098	0.134757
$583$	3.43324	0.142190
$584$	−4.81814	−0.199376
$585$	1.54484	0.0638713
$586$	29.5420	1.22037
$587$	18.2442	0.753018	0.376509	−	0.926413i	$-0.377124\pi$
$587$	18.2442	0.753018	0.376509	+	0.926413i	$0.377124\pi$
$588$	−5.78516	−0.238576
$589$	−22.5622	−0.929658
$590$	−10.8763	−0.447771
$591$	−6.63464	−0.272913
$592$	2.58758	0.106349
$593$	−30.4053	−1.24860	−0.624298	−	0.781186i	$-0.714615\pi$
$593$	−30.4053	−1.24860	−0.624298	+	0.781186i	$0.714615\pi$
$594$	−0.715688	−0.0293650
$595$	−11.2900	−0.462847
$596$	−17.1217	−0.701334
$597$	−22.2667	−0.911314
$598$	−8.77392	−0.358792
$599$	−26.8864	−1.09855	−0.549275	−	0.835642i	$-0.685096\pi$
$599$	−26.8864	−1.09855	−0.549275	+	0.835642i	$0.685096\pi$
$600$	2.91901	0.119168
$601$	−40.2584	−1.64217	−0.821087	−	0.570803i	$-0.806632\pi$
$601$	−40.2584	−1.64217	−0.821087	+	0.570803i	$0.806632\pi$
$602$	13.1557	0.536185
$603$	−12.6114	−0.513575
$604$	−9.56184	−0.389066
$605$	10.4108	0.423261
$606$	12.3786	0.502848
$607$	20.7647	0.842815	0.421408	−	0.906871i	$-0.361536\pi$
$607$	20.7647	0.842815	0.421408	+	0.906871i	$0.361536\pi$
$608$	32.2054	1.30610
$609$	8.90622	0.360898
$610$	3.64382	0.147534
$611$	6.59856	0.266949
$612$	−3.66707	−0.148232
$613$	−21.9936	−0.888315	−0.444158	−	0.895949i	$-0.646497\pi$
$613$	−21.9936	−0.888315	−0.444158	+	0.895949i	$0.646497\pi$
$614$	2.13827	0.0862937
$615$	5.26170	0.212172
$616$	7.79916	0.314237
$617$	−9.11318	−0.366883	−0.183441	−	0.983031i	$-0.558724\pi$
$617$	−9.11318	−0.366883	−0.183441	+	0.983031i	$0.558724\pi$
$618$	−10.9030	−0.438583
$619$	−19.2089	−0.772072	−0.386036	−	0.922484i	$-0.626156\pi$
$619$	−19.2089	−0.772072	−0.386036	+	0.922484i	$0.626156\pi$
$620$	4.28412	0.172054
$621$	−6.09124	−0.244433
$622$	29.7574	1.19316
$623$	−28.5985	−1.14577
$624$	0.711325	0.0284758
$625$	1.00000	0.0400000
$626$	17.9608	0.717856
$627$	−4.57041	−0.182525
$628$	15.4244	0.615499
$629$	−18.2269	−0.726753
$630$	3.24563	0.129309
$631$	41.2380	1.64166	0.820829	−	0.571173i	$-0.193512\pi$
$631$	41.2380	1.64166	0.820829	+	0.571173i	$0.193512\pi$
$632$	−21.0622	−0.837808
$633$	23.9353	0.951341
$634$	6.11552	0.242878
$635$	6.18545	0.245462
$636$	−5.05711	−0.200527
$637$	−7.90464	−0.313193
$638$	−1.83115	−0.0724958
$639$	−10.3873	−0.410915
$640$	−5.25652	−0.207782
$641$	22.2895	0.880384	0.440192	−	0.897904i	$-0.354910\pi$
$641$	22.2895	0.880384	0.440192	+	0.897904i	$0.354910\pi$
$642$	−18.2964	−0.722102
$643$	46.1272	1.81908	0.909540	−	0.415617i	$-0.136434\pi$
$643$	46.1272	1.81908	0.909540	+	0.415617i	$0.136434\pi$
$644$	23.9727	0.944657
$645$	4.05335	0.159601
$646$	18.0071	0.708478
$647$	10.4813	0.412063	0.206031	−	0.978545i	$-0.433945\pi$
$647$	10.4813	0.412063	0.206031	+	0.978545i	$0.433945\pi$
$648$	2.91901	0.114669
$649$	−8.95358	−0.351459
$650$	1.44042	0.0564978
$651$	13.1898	0.516949
$652$	−10.4009	−0.407330
$653$	24.1973	0.946913	0.473456	−	0.880817i	$-0.343006\pi$
$653$	24.1973	0.946913	0.473456	+	0.880817i	$0.343006\pi$
$654$	5.76156	0.225295
$655$	−8.27270	−0.323241
$656$	2.42276	0.0945929
$657$	−1.65061	−0.0643964
$658$	13.8632	0.540444
$659$	8.34760	0.325176	0.162588	−	0.986694i	$-0.448016\pi$
$659$	8.34760	0.325176	0.162588	+	0.986694i	$0.448016\pi$
$660$	0.867833	0.0337804
$661$	20.6582	0.803509	0.401755	−	0.915747i	$-0.368401\pi$
$661$	20.6582	0.803509	0.401755	+	0.915747i	$0.368401\pi$
$662$	20.4078	0.793171
$663$	−5.01055	−0.194594
$664$	51.9298	2.01527
$665$	20.7267	0.803747
$666$	5.23980	0.203038
$667$	−15.5849	−0.603451
$668$	−16.9098	−0.654260
$669$	−8.57606	−0.331570
$670$	−11.7589	−0.454286
$671$	2.99965	0.115800
$672$	−18.8272	−0.726275
$673$	37.8680	1.45970	0.729852	−	0.683606i	$-0.239589\pi$
$673$	37.8680	1.45970	0.729852	+	0.683606i	$0.239589\pi$
$674$	15.5683	0.599667
$675$	1.00000	0.0384900
$676$	11.9998	0.461531
$677$	19.1519	0.736066	0.368033	−	0.929813i	$-0.380031\pi$
$677$	19.1519	0.736066	0.368033	+	0.929813i	$0.380031\pi$
$678$	13.7265	0.527165
$679$	−12.1368	−0.465767
$680$	−9.46753	−0.363063
$681$	21.7125	0.832025
$682$	−2.71186	−0.103843
$683$	−2.59789	−0.0994056	−0.0497028	−	0.998764i	$-0.515827\pi$
$683$	−2.59789	−0.0994056	−0.0497028	+	0.998764i	$0.515827\pi$
$684$	6.73215	0.257410
$685$	−9.67615	−0.369707
$686$	6.11216	0.233363
$687$	−15.8129	−0.603298
$688$	1.86637	0.0711548
$689$	−6.90985	−0.263244
$690$	−5.67950	−0.216215
$691$	12.5417	0.477110	0.238555	−	0.971129i	$-0.423326\pi$
$691$	12.5417	0.477110	0.238555	+	0.971129i	$0.423326\pi$
$692$	−14.3066	−0.543857
$693$	2.67186	0.101495
$694$	32.8682	1.24766
$695$	0.294544	0.0111727
$696$	7.46852	0.283093
$697$	−17.0659	−0.646415
$698$	0.457026	0.0172987
$699$	−4.55198	−0.172172
$700$	−3.93560	−0.148752
$701$	−24.2122	−0.914481	−0.457240	−	0.889343i	$-0.651162\pi$
$701$	−24.2122	−0.914481	−0.457240	+	0.889343i	$0.651162\pi$
$702$	1.44042	0.0543650
$703$	33.4616	1.26203
$704$	4.57779	0.172532
$705$	4.27135	0.160868
$706$	20.1755	0.759316
$707$	−46.2128	−1.73801
$708$	13.1885	0.495654
$709$	24.9460	0.936865	0.468432	−	0.883499i	$-0.344819\pi$
$709$	24.9460	0.936865	0.468432	+	0.883499i	$0.344819\pi$
$710$	−9.68515	−0.363477
$711$	−7.21553	−0.270603
$712$	−23.9819	−0.898760
$713$	−23.0808	−0.864381
$714$	−10.5269	−0.393959
$715$	1.18578	0.0443455
$716$	15.9300	0.595331
$717$	−15.1732	−0.566655
$718$	5.58160	0.208303
$719$	−8.07833	−0.301271	−0.150635	−	0.988589i	$-0.548132\pi$
$719$	−8.07833	−0.301271	−0.150635	+	0.988589i	$0.548132\pi$
$720$	0.460452	0.0171600
$721$	40.7038	1.51589
$722$	−15.3424	−0.570984
$723$	4.39769	0.163552
$724$	1.23354	0.0458442
$725$	2.55858	0.0950234
$726$	9.70711	0.360265
$727$	8.91632	0.330688	0.165344	−	0.986236i	$-0.447127\pi$
$727$	8.91632	0.330688	0.165344	+	0.986236i	$0.447127\pi$
$728$	−15.6969	−0.581764
$729$	1.00000	0.0370370
$730$	−1.53904	−0.0569623
$731$	−13.1467	−0.486248
$732$	−4.41844	−0.163310
$733$	−25.9511	−0.958524	−0.479262	−	0.877672i	$-0.659096\pi$
$733$	−25.9511	−0.958524	−0.479262	+	0.877672i	$0.659096\pi$
$734$	31.7074	1.17034
$735$	−5.11680	−0.188736
$736$	32.9456	1.21439
$737$	−9.68013	−0.356572
$738$	4.90604	0.180594
$739$	−7.11505	−0.261732	−0.130866	−	0.991400i	$-0.541776\pi$
$739$	−7.11505	−0.261732	−0.130866	+	0.991400i	$0.541776\pi$
$740$	−6.35371	−0.233567
$741$	9.19856	0.337918
$742$	−14.5172	−0.532944
$743$	0.766108	0.0281058	0.0140529	−	0.999901i	$-0.495527\pi$
$743$	0.766108	0.0281058	0.0140529	+	0.999901i	$0.495527\pi$
$744$	11.0606	0.405502
$745$	−15.1437	−0.554821
$746$	15.9898	0.585427
$747$	17.7902	0.650911
$748$	−2.81474	−0.102917
$749$	68.3055	2.49583
$750$	0.932405	0.0340466
$751$	7.77382	0.283671	0.141835	−	0.989890i	$-0.454700\pi$
$751$	7.77382	0.283671	0.141835	+	0.989890i	$0.454700\pi$
$752$	1.96675	0.0717201
$753$	−9.33566	−0.340210
$754$	3.68542	0.134215
$755$	−8.45716	−0.307787
$756$	−3.93560	−0.143136
$757$	−41.5451	−1.50998	−0.754992	−	0.655734i	$-0.772359\pi$
$757$	−41.5451	−1.50998	−0.754992	+	0.655734i	$0.772359\pi$
$758$	27.9998	1.01700
$759$	−4.67546	−0.169709
$760$	17.3809	0.630470
$761$	23.8435	0.864328	0.432164	−	0.901795i	$-0.357750\pi$
$761$	23.8435	0.864328	0.432164	+	0.901795i	$0.357750\pi$
$762$	5.76734	0.208929
$763$	−21.5095	−0.778695
$764$	−26.8172	−0.970213
$765$	−3.24341	−0.117266
$766$	−13.5419	−0.489289
$767$	18.0203	0.650674
$768$	−16.8292	−0.607271
$769$	−22.2966	−0.804035	−0.402017	−	0.915632i	$-0.631691\pi$
$769$	−22.2966	−0.804035	−0.402017	+	0.915632i	$0.631691\pi$
$770$	2.49125	0.0897784
$771$	30.9366	1.11415
$772$	3.47215	0.124965
$773$	10.0352	0.360943	0.180471	−	0.983580i	$-0.442238\pi$
$773$	10.0352	0.360943	0.180471	+	0.983580i	$0.442238\pi$
$774$	3.77937	0.135846
$775$	3.78917	0.136111
$776$	−10.1776	−0.365354
$777$	−19.5616	−0.701768
$778$	26.9817	0.967341
$779$	31.3302	1.12252
$780$	−1.74663	−0.0625394
$781$	−7.97299	−0.285296
$782$	18.4209	0.658732
$783$	2.55858	0.0914363
$784$	−2.35604	−0.0841443
$785$	13.6424	0.486918
$786$	−7.71350	−0.275132
$787$	−36.1593	−1.28894	−0.644469	−	0.764630i	$-0.722922\pi$
$787$	−36.1593	−1.28894	−0.644469	+	0.764630i	$0.722922\pi$
$788$	7.50127	0.267222
$789$	−29.1595	−1.03810
$790$	−6.72779	−0.239364
$791$	−51.2449	−1.82206
$792$	2.24055	0.0796144
$793$	−6.03720	−0.214387
$794$	−32.3903	−1.14949
$795$	−4.47286	−0.158636
$796$	25.1752	0.892311
$797$	37.6116	1.33227	0.666136	−	0.745831i	$-0.267947\pi$
$797$	37.6116	1.33227	0.666136	+	0.745831i	$0.267947\pi$
$798$	19.3257	0.684122
$799$	−13.8537	−0.490110
$800$	−5.40868	−0.191226
$801$	−8.21578	−0.290290
$802$	−0.932405	−0.0329244
$803$	−1.26696	−0.0447101
$804$	14.2587	0.502865
$805$	21.2031	0.747312
$806$	5.45798	0.192249
$807$	19.4065	0.683140
$808$	−38.7528	−1.36332
$809$	13.1901	0.463738	0.231869	−	0.972747i	$-0.425516\pi$
$809$	13.1901	0.463738	0.231869	+	0.972747i	$0.425516\pi$
$810$	0.932405	0.0327614
$811$	−9.48778	−0.333161	−0.166580	−	0.986028i	$-0.553273\pi$
$811$	−9.48778	−0.333161	−0.166580	+	0.986028i	$0.553273\pi$
$812$	−10.0696	−0.353372
$813$	6.44200	0.225931
$814$	4.02192	0.140968
$815$	−9.19927	−0.322236
$816$	−1.49343	−0.0522806
$817$	24.1352	0.844384
$818$	−1.48037	−0.0517600
$819$	−5.37746	−0.187904
$820$	−5.94900	−0.207748
$821$	2.80300	0.0978253	0.0489127	−	0.998803i	$-0.484424\pi$
$821$	2.80300	0.0978253	0.0489127	+	0.998803i	$0.484424\pi$
$822$	−9.02209	−0.314682
$823$	−40.6620	−1.41739	−0.708693	−	0.705517i	$-0.750715\pi$
$823$	−40.6620	−1.41739	−0.708693	+	0.705517i	$0.750715\pi$
$824$	34.1331	1.18908
$825$	0.767572	0.0267234
$826$	37.8596	1.31730
$827$	48.6131	1.69044	0.845222	−	0.534415i	$-0.179468\pi$
$827$	48.6131	1.69044	0.845222	+	0.534415i	$0.179468\pi$
$828$	6.88689	0.239336
$829$	−33.7888	−1.17353	−0.586766	−	0.809756i	$-0.699599\pi$
$829$	−33.7888	−1.17353	−0.586766	+	0.809756i	$0.699599\pi$
$830$	16.5877	0.575767
$831$	8.33640	0.289186
$832$	−9.21341	−0.319417
$833$	16.5959	0.575013
$834$	0.274634	0.00950979
$835$	−14.9562	−0.517581
$836$	5.16741	0.178719
$837$	3.78917	0.130973
$838$	−22.0056	−0.760170
$839$	52.2179	1.80276	0.901382	−	0.433025i	$-0.142554\pi$
$839$	52.2179	1.80276	0.901382	+	0.433025i	$0.142554\pi$
$840$	−10.1608	−0.350582
$841$	−22.4537	−0.774264
$842$	8.63401	0.297548
$843$	30.5557	1.05239
$844$	−27.0617	−0.931503
$845$	10.6135	0.365114
$846$	3.98263	0.136926
$847$	−36.2393	−1.24520
$848$	−2.05954	−0.0707248
$849$	−20.5590	−0.705582
$850$	−3.02417	−0.103728
$851$	34.2307	1.17341
$852$	11.7441	0.402346
$853$	39.0889	1.33838	0.669189	−	0.743093i	$-0.266642\pi$
$853$	39.0889	1.33838	0.669189	+	0.743093i	$0.266642\pi$
$854$	−12.6838	−0.434032
$855$	5.95438	0.203635
$856$	57.2791	1.95776
$857$	−7.95579	−0.271764	−0.135882	−	0.990725i	$-0.543387\pi$
$857$	−7.95579	−0.271764	−0.135882	+	0.990725i	$0.543387\pi$
$858$	1.10562	0.0377453
$859$	21.0683	0.718842	0.359421	−	0.933176i	$-0.382974\pi$
$859$	21.0683	0.718842	0.359421	+	0.933176i	$0.382974\pi$
$860$	−4.58281	−0.156272
$861$	−18.3156	−0.624193
$862$	13.3315	0.454072
$863$	−8.25221	−0.280908	−0.140454	−	0.990087i	$-0.544856\pi$
$863$	−8.25221	−0.280908	−0.140454	+	0.990087i	$0.544856\pi$
$864$	−5.40868	−0.184007
$865$	−12.6538	−0.430242
$866$	6.21148	0.211075
$867$	−6.48030	−0.220082
$868$	−14.9127	−0.506169
$869$	−5.53844	−0.187879
$870$	2.38563	0.0808806
$871$	19.4825	0.660141
$872$	−18.0373	−0.610819
$873$	−3.48666	−0.118006
$874$	−33.8179	−1.14391
$875$	−3.48092	−0.117677
$876$	1.86622	0.0630536
$877$	25.9927	0.877712	0.438856	−	0.898557i	$-0.355384\pi$
$877$	25.9927	0.877712	0.438856	+	0.898557i	$0.355384\pi$
$878$	1.90181	0.0641828
$879$	−31.6837	−1.06866
$880$	0.353430	0.0119141
$881$	−45.4840	−1.53239	−0.766197	−	0.642605i	$-0.777854\pi$
$881$	−45.4840	−1.53239	−0.766197	+	0.642605i	$0.777854\pi$
$882$	−4.77093	−0.160646
$883$	15.1522	0.509912	0.254956	−	0.966953i	$-0.417939\pi$
$883$	15.1522	0.509912	0.254956	+	0.966953i	$0.417939\pi$
$884$	5.66503	0.190536
$885$	11.6648	0.392108
$886$	9.81963	0.329897
$887$	−6.27365	−0.210649	−0.105324	−	0.994438i	$-0.533588\pi$
$887$	−6.27365	−0.210649	−0.105324	+	0.994438i	$0.533588\pi$
$888$	−16.4038	−0.550476
$889$	−21.5310	−0.722128
$890$	−7.66043	−0.256778
$891$	0.767572	0.0257146
$892$	9.69628	0.324656
$893$	25.4332	0.851091
$894$	−14.1200	−0.472244
$895$	14.0896	0.470963
$896$	18.2975	0.611277
$897$	9.40999	0.314191
$898$	−5.39214	−0.179938
$899$	9.69491	0.323343
$900$	−1.13062	−0.0376874
$901$	14.5073	0.483309
$902$	3.76574	0.125385
$903$	−14.1094	−0.469531
$904$	−42.9726	−1.42925
$905$	1.09103	0.0362670
$906$	−7.88549	−0.261978
$907$	−30.5388	−1.01402	−0.507012	−	0.861939i	$-0.669250\pi$
$907$	−30.5388	−1.01402	−0.507012	+	0.861939i	$0.669250\pi$
$908$	−24.5486	−0.814675
$909$	−13.2760	−0.440338
$910$	−5.01397	−0.166212
$911$	−34.2462	−1.13463	−0.567313	−	0.823502i	$-0.692017\pi$
$911$	−34.2462	−1.13463	−0.567313	+	0.823502i	$0.692017\pi$
$912$	2.74170	0.0907869
$913$	13.6553	0.451924
$914$	−14.5049	−0.479780
$915$	−3.90798	−0.129194
$916$	17.8784	0.590718
$917$	28.7966	0.950947
$918$	−3.02417	−0.0998125
$919$	18.2544	0.602158	0.301079	−	0.953599i	$-0.402653\pi$
$919$	18.2544	0.602158	0.301079	+	0.953599i	$0.402653\pi$
$920$	17.7804	0.586201
$921$	−2.29329	−0.0755665
$922$	−34.2362	−1.12751
$923$	16.0467	0.528183
$924$	−3.02086	−0.0993789
$925$	−5.61966	−0.184773
$926$	23.2334	0.763496
$927$	11.6934	0.384062
$928$	−13.8386	−0.454273
$929$	27.0465	0.887368	0.443684	−	0.896183i	$-0.353671\pi$
$929$	27.0465	0.887368	0.443684	+	0.896183i	$0.353671\pi$
$930$	3.53304	0.115853
$931$	−30.4674	−0.998527
$932$	5.14657	0.168581
$933$	−31.9147	−1.04484
$934$	−11.3182	−0.370343
$935$	−2.48955	−0.0814170
$936$	−4.50940	−0.147394
$937$	−2.49486	−0.0815034	−0.0407517	−	0.999169i	$-0.512975\pi$
$937$	−2.49486	−0.0815034	−0.0407517	+	0.999169i	$0.512975\pi$
$938$	40.9318	1.33647
$939$	−19.2628	−0.628619
$940$	−4.82928	−0.157514
$941$	8.63965	0.281645	0.140822	−	0.990035i	$-0.455025\pi$
$941$	8.63965	0.281645	0.140822	+	0.990035i	$0.455025\pi$
$942$	12.7202	0.414447
$943$	32.0503	1.04370
$944$	5.37109	0.174814
$945$	−3.48092	−0.113234
$946$	2.90093	0.0943175
$947$	−36.8031	−1.19594	−0.597970	−	0.801518i	$-0.704026\pi$
$947$	−36.8031	−1.19594	−0.597970	+	0.801518i	$0.704026\pi$
$948$	8.15803	0.264961
$949$	2.54993	0.0827742
$950$	5.55189	0.180127
$951$	−6.55887	−0.212686
$952$	32.9557	1.06810
$953$	−13.8884	−0.449888	−0.224944	−	0.974372i	$-0.572220\pi$
$953$	−13.8884	−0.449888	−0.224944	+	0.974372i	$0.572220\pi$
$954$	−4.17051	−0.135025
$955$	−23.7190	−0.767529
$956$	17.1552	0.554839
$957$	1.96390	0.0634838
$958$	24.4053	0.788499
$959$	33.6819	1.08765
$960$	−5.96399	−0.192487
$961$	−16.6422	−0.536844
$962$	−8.09465	−0.260982
$963$	19.6228	0.632337
$964$	−4.97212	−0.160141
$965$	3.07101	0.0988593
$966$	19.7699	0.636086
$967$	−8.89573	−0.286067	−0.143034	−	0.989718i	$-0.545686\pi$
$967$	−8.89573	−0.286067	−0.143034	+	0.989718i	$0.545686\pi$
$968$	−30.3893	−0.976749
$969$	−19.3125	−0.620406
$970$	−3.25098	−0.104383
$971$	33.6245	1.07906	0.539531	−	0.841965i	$-0.318601\pi$
$971$	33.6245	1.07906	0.539531	+	0.841965i	$0.318601\pi$
$972$	−1.13062	−0.0362647
$973$	−1.02528	−0.0328691
$974$	−36.1582	−1.15858
$975$	−1.54484	−0.0494745
$976$	−1.79944	−0.0575985
$977$	−46.5737	−1.49002	−0.745012	−	0.667051i	$-0.767557\pi$
$977$	−46.5737	−1.49002	−0.745012	+	0.667051i	$0.767557\pi$
$978$	−8.57744	−0.274276
$979$	−6.30620	−0.201547
$980$	5.78516	0.184800
$981$	−6.17925	−0.197288
$982$	−5.52055	−0.176168
$983$	11.8623	0.378349	0.189175	−	0.981943i	$-0.439419\pi$
$983$	11.8623	0.378349	0.189175	+	0.981943i	$0.439419\pi$
$984$	−15.3589	−0.489625
$985$	6.63464	0.211397
$986$	−7.73759	−0.246415
$987$	−14.8682	−0.473261
$988$	−10.4001	−0.330871
$989$	24.6899	0.785095
$990$	0.715688	0.0227460
$991$	−4.31237	−0.136987	−0.0684934	−	0.997652i	$-0.521819\pi$
$991$	−4.31237	−0.136987	−0.0684934	+	0.997652i	$0.521819\pi$
$992$	−20.4944	−0.650699
$993$	−21.8873	−0.694572
$994$	33.7132	1.06932
$995$	22.2667	0.705901
$996$	−20.1140	−0.637337
$997$	8.66682	0.274481	0.137241	−	0.990538i	$-0.456177\pi$
$997$	8.66682	0.274481	0.137241	+	0.990538i	$0.456177\pi$
$998$	−20.4112	−0.646105
$999$	−5.61966	−0.177798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.10	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.10	✓	28	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)

\(f(q)\)	\(=\)	\(q-0.932405 q^{2} +1.00000 q^{3} -1.13062 q^{4} -1.00000 q^{5} -0.932405 q^{6} +3.48092 q^{7} +2.91901 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.932405 q^{2} +1.00000 q^{3} -1.13062 q^{4} -1.00000 q^{5} -0.932405 q^{6} +3.48092 q^{7} +2.91901 q^{8} +1.00000 q^{9} +0.932405 q^{10} +0.767572 q^{11} -1.13062 q^{12} -1.54484 q^{13} -3.24563 q^{14} -1.00000 q^{15} -0.460452 q^{16} +3.24341 q^{17} -0.932405 q^{18} -5.95438 q^{19} +1.13062 q^{20} +3.48092 q^{21} -0.715688 q^{22} -6.09124 q^{23} +2.91901 q^{24} +1.00000 q^{25} +1.44042 q^{26} +1.00000 q^{27} -3.93560 q^{28} +2.55858 q^{29} +0.932405 q^{30} +3.78917 q^{31} -5.40868 q^{32} +0.767572 q^{33} -3.02417 q^{34} -3.48092 q^{35} -1.13062 q^{36} -5.61966 q^{37} +5.55189 q^{38} -1.54484 q^{39} -2.91901 q^{40} -5.26170 q^{41} -3.24563 q^{42} -4.05335 q^{43} -0.867833 q^{44} -1.00000 q^{45} +5.67950 q^{46} -4.27135 q^{47} -0.460452 q^{48} +5.11680 q^{49} -0.932405 q^{50} +3.24341 q^{51} +1.74663 q^{52} +4.47286 q^{53} -0.932405 q^{54} -0.767572 q^{55} +10.1608 q^{56} -5.95438 q^{57} -2.38563 q^{58} -11.6648 q^{59} +1.13062 q^{60} +3.90798 q^{61} -3.53304 q^{62} +3.48092 q^{63} +5.96399 q^{64} +1.54484 q^{65} -0.715688 q^{66} -12.6114 q^{67} -3.66707 q^{68} -6.09124 q^{69} +3.24563 q^{70} -10.3873 q^{71} +2.91901 q^{72} -1.65061 q^{73} +5.23980 q^{74} +1.00000 q^{75} +6.73215 q^{76} +2.67186 q^{77} +1.44042 q^{78} -7.21553 q^{79} +0.460452 q^{80} +1.00000 q^{81} +4.90604 q^{82} +17.7902 q^{83} -3.93560 q^{84} -3.24341 q^{85} +3.77937 q^{86} +2.55858 q^{87} +2.24055 q^{88} -8.21578 q^{89} +0.932405 q^{90} -5.37746 q^{91} +6.88689 q^{92} +3.78917 q^{93} +3.98263 q^{94} +5.95438 q^{95} -5.40868 q^{96} -3.48666 q^{97} -4.77093 q^{98} +0.767572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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