LMFDB - Embedded newform 6019.2.a.e.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.39514 q^{2} +1.83196 q^{3} +3.73671 q^{4} +3.10935 q^{5} -4.38781 q^{6} +4.25584 q^{7} -4.15967 q^{8} +0.356083 q^{9} +O(q^{10})$	\(q-2.39514 q^{2} +1.83196 q^{3} +3.73671 q^{4} +3.10935 q^{5} -4.38781 q^{6} +4.25584 q^{7} -4.15967 q^{8} +0.356083 q^{9} -7.44733 q^{10} +0.789001 q^{11} +6.84551 q^{12} +1.00000 q^{13} -10.1934 q^{14} +5.69620 q^{15} +2.48959 q^{16} +4.81547 q^{17} -0.852869 q^{18} +3.04616 q^{19} +11.6187 q^{20} +7.79654 q^{21} -1.88977 q^{22} -2.25355 q^{23} -7.62036 q^{24} +4.66804 q^{25} -2.39514 q^{26} -4.84355 q^{27} +15.9029 q^{28} +1.42383 q^{29} -13.6432 q^{30} -10.1287 q^{31} +2.35642 q^{32} +1.44542 q^{33} -11.5338 q^{34} +13.2329 q^{35} +1.33058 q^{36} +9.32565 q^{37} -7.29599 q^{38} +1.83196 q^{39} -12.9339 q^{40} +5.54964 q^{41} -18.6738 q^{42} -3.36399 q^{43} +2.94827 q^{44} +1.10718 q^{45} +5.39756 q^{46} +12.5644 q^{47} +4.56083 q^{48} +11.1122 q^{49} -11.1806 q^{50} +8.82176 q^{51} +3.73671 q^{52} -11.7348 q^{53} +11.6010 q^{54} +2.45328 q^{55} -17.7029 q^{56} +5.58045 q^{57} -3.41028 q^{58} -6.06915 q^{59} +21.2851 q^{60} +4.21305 q^{61} +24.2597 q^{62} +1.51543 q^{63} -10.6231 q^{64} +3.10935 q^{65} -3.46198 q^{66} -8.92148 q^{67} +17.9940 q^{68} -4.12841 q^{69} -31.6947 q^{70} -4.64957 q^{71} -1.48119 q^{72} +10.5462 q^{73} -22.3363 q^{74} +8.55166 q^{75} +11.3826 q^{76} +3.35786 q^{77} -4.38781 q^{78} -5.35512 q^{79} +7.74099 q^{80} -9.94145 q^{81} -13.2922 q^{82} -12.2806 q^{83} +29.1334 q^{84} +14.9730 q^{85} +8.05724 q^{86} +2.60840 q^{87} -3.28198 q^{88} +2.58525 q^{89} -2.65186 q^{90} +4.25584 q^{91} -8.42085 q^{92} -18.5554 q^{93} -30.0936 q^{94} +9.47156 q^{95} +4.31688 q^{96} +0.0227200 q^{97} -26.6153 q^{98} +0.280949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.39514	−1.69362	−0.846811	−	0.531894i	$-0.821481\pi$
$2$	−2.39514	−1.69362	−0.846811	+	0.531894i	$0.821481\pi$
$3$	1.83196	1.05768	0.528842	−	0.848720i	$-0.322627\pi$
$3$	1.83196	1.05768	0.528842	+	0.848720i	$0.322627\pi$
$4$	3.73671	1.86836
$5$	3.10935	1.39054	0.695271	−	0.718748i	$-0.255284\pi$
$5$	3.10935	1.39054	0.695271	+	0.718748i	$0.255284\pi$
$6$	−4.38781	−1.79132
$7$	4.25584	1.60856	0.804279	−	0.594252i	$-0.202552\pi$
$7$	4.25584	1.60856	0.804279	+	0.594252i	$0.202552\pi$
$8$	−4.15967	−1.47067
$9$	0.356083	0.118694
$10$	−7.44733	−2.35505
$11$	0.789001	0.237893	0.118946	−	0.992901i	$-0.462048\pi$
$11$	0.789001	0.237893	0.118946	+	0.992901i	$0.462048\pi$
$12$	6.84551	1.97613
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−10.1934	−2.72429
$15$	5.69620	1.47075
$16$	2.48959	0.622397
$17$	4.81547	1.16792	0.583962	−	0.811781i	$-0.301502\pi$
$17$	4.81547	1.16792	0.583962	+	0.811781i	$0.301502\pi$
$18$	−0.852869	−0.201023
$19$	3.04616	0.698837	0.349418	−	0.936967i	$-0.386379\pi$
$19$	3.04616	0.698837	0.349418	+	0.936967i	$0.386379\pi$
$20$	11.6187	2.59803
$21$	7.79654	1.70134
$22$	−1.88977	−0.402900
$23$	−2.25355	−0.469897	−0.234948	−	0.972008i	$-0.575492\pi$
$23$	−2.25355	−0.469897	−0.234948	+	0.972008i	$0.575492\pi$
$24$	−7.62036	−1.55550
$25$	4.66804	0.933607
$26$	−2.39514	−0.469726
$27$	−4.84355	−0.932143
$28$	15.9029	3.00536
$29$	1.42383	0.264398	0.132199	−	0.991223i	$-0.457796\pi$
$29$	1.42383	0.264398	0.132199	+	0.991223i	$0.457796\pi$
$30$	−13.6432	−2.49090
$31$	−10.1287	−1.81917	−0.909584	−	0.415520i	$-0.863600\pi$
$31$	−10.1287	−1.81917	−0.909584	+	0.415520i	$0.863600\pi$
$32$	2.35642	0.416561
$33$	1.44542	0.251615
$34$	−11.5338	−1.97802
$35$	13.2329	2.23677
$36$	1.33058	0.221763
$37$	9.32565	1.53313	0.766563	−	0.642169i	$-0.221965\pi$
$37$	9.32565	1.53313	0.766563	+	0.642169i	$0.221965\pi$
$38$	−7.29599	−1.18357
$39$	1.83196	0.293349
$40$	−12.9339	−2.04502
$41$	5.54964	0.866708	0.433354	−	0.901224i	$-0.357330\pi$
$41$	5.54964	0.866708	0.433354	+	0.901224i	$0.357330\pi$
$42$	−18.6738	−2.88143
$43$	−3.36399	−0.513004	−0.256502	−	0.966544i	$-0.582570\pi$
$43$	−3.36399	−0.513004	−0.256502	+	0.966544i	$0.582570\pi$
$44$	2.94827	0.444468
$45$	1.10718	0.165049
$46$	5.39756	0.795827
$47$	12.5644	1.83271	0.916354	−	0.400370i	$-0.131118\pi$
$47$	12.5644	1.83271	0.916354	+	0.400370i	$0.131118\pi$
$48$	4.56083	0.658299
$49$	11.1122	1.58746
$50$	−11.1806	−1.58118
$51$	8.82176	1.23529
$52$	3.73671	0.518189
$53$	−11.7348	−1.61189	−0.805946	−	0.591989i	$-0.798343\pi$
$53$	−11.7348	−1.61189	−0.805946	+	0.591989i	$0.798343\pi$
$54$	11.6010	1.57870
$55$	2.45328	0.330800
$56$	−17.7029	−2.36565
$57$	5.58045	0.739148
$58$	−3.41028	−0.447791
$59$	−6.06915	−0.790135	−0.395068	−	0.918652i	$-0.629279\pi$
$59$	−6.06915	−0.790135	−0.395068	+	0.918652i	$0.629279\pi$
$60$	21.2851	2.74789
$61$	4.21305	0.539426	0.269713	−	0.962941i	$-0.413071\pi$
$61$	4.21305	0.539426	0.269713	+	0.962941i	$0.413071\pi$
$62$	24.2597	3.08098
$63$	1.51543	0.190926
$64$	−10.6231	−1.32789
$65$	3.10935	0.385667
$66$	−3.46198	−0.426141
$67$	−8.92148	−1.08993	−0.544966	−	0.838458i	$-0.683457\pi$
$67$	−8.92148	−1.08993	−0.544966	+	0.838458i	$0.683457\pi$
$68$	17.9940	2.18210
$69$	−4.12841	−0.497002
$70$	−31.6947	−3.78824
$71$	−4.64957	−0.551803	−0.275901	−	0.961186i	$-0.588976\pi$
$71$	−4.64957	−0.551803	−0.275901	+	0.961186i	$0.588976\pi$
$72$	−1.48119	−0.174560
$73$	10.5462	1.23434	0.617170	−	0.786830i	$-0.288279\pi$
$73$	10.5462	1.23434	0.617170	+	0.786830i	$0.288279\pi$
$74$	−22.3363	−2.59654
$75$	8.55166	0.987461
$76$	11.3826	1.30568
$77$	3.35786	0.382664
$78$	−4.38781	−0.496822
$79$	−5.35512	−0.602498	−0.301249	−	0.953546i	$-0.597404\pi$
$79$	−5.35512	−0.602498	−0.301249	+	0.953546i	$0.597404\pi$
$80$	7.74099	0.865469
$81$	−9.94145	−1.10461
$82$	−13.2922	−1.46788
$83$	−12.2806	−1.34797	−0.673983	−	0.738747i	$-0.735418\pi$
$83$	−12.2806	−1.34797	−0.673983	+	0.738747i	$0.735418\pi$
$84$	29.1334	3.17872
$85$	14.9730	1.62405
$86$	8.05724	0.868834
$87$	2.60840	0.279650
$88$	−3.28198	−0.349861
$89$	2.58525	0.274036	0.137018	−	0.990569i	$-0.456248\pi$
$89$	2.58525	0.274036	0.137018	+	0.990569i	$0.456248\pi$
$90$	−2.65186	−0.279531
$91$	4.25584	0.446134
$92$	−8.42085	−0.877934
$93$	−18.5554	−1.92410
$94$	−30.0936	−3.10391
$95$	9.47156	0.971762
$96$	4.31688	0.440590
$97$	0.0227200	0.00230686	0.00115343	−	0.999999i	$-0.499633\pi$
$97$	0.0227200	0.00230686	0.00115343	+	0.999999i	$0.499633\pi$
$98$	−26.6153	−2.68855
$99$	0.280949	0.0282365
$100$	17.4431	1.74431
$101$	−8.71126	−0.866803	−0.433401	−	0.901201i	$-0.642687\pi$
$101$	−8.71126	−0.866803	−0.433401	+	0.901201i	$0.642687\pi$
$102$	−21.1294	−2.09212
$103$	−7.55117	−0.744039	−0.372020	−	0.928225i	$-0.621335\pi$
$103$	−7.55117	−0.744039	−0.372020	+	0.928225i	$0.621335\pi$
$104$	−4.15967	−0.407889
$105$	24.2421	2.36579
$106$	28.1064	2.72994
$107$	13.3418	1.28980	0.644900	−	0.764267i	$-0.276899\pi$
$107$	13.3418	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$108$	−18.0990	−1.74157
$109$	2.92553	0.280215	0.140108	−	0.990136i	$-0.455255\pi$
$109$	2.92553	0.280215	0.140108	+	0.990136i	$0.455255\pi$
$110$	−5.87595	−0.560250
$111$	17.0842	1.62156
$112$	10.5953	1.00116
$113$	14.7666	1.38912	0.694562	−	0.719433i	$-0.255598\pi$
$113$	14.7666	1.38912	0.694562	+	0.719433i	$0.255598\pi$
$114$	−13.3660	−1.25184
$115$	−7.00705	−0.653411
$116$	5.32044	0.493990
$117$	0.356083	0.0329198
$118$	14.5365	1.33819
$119$	20.4939	1.87867
$120$	−23.6943	−2.16299
$121$	−10.3775	−0.943407
$122$	−10.0909	−0.913584
$123$	10.1667	0.916702
$124$	−37.8480	−3.39885
$125$	−1.03219	−0.0923221
$126$	−3.62968	−0.323357
$127$	8.30675	0.737105	0.368552	−	0.929607i	$-0.379854\pi$
$127$	8.30675	0.737105	0.368552	+	0.929607i	$0.379854\pi$
$128$	20.7311	1.83239
$129$	−6.16270	−0.542595
$130$	−7.44733	−0.653174
$131$	4.42658	0.386752	0.193376	−	0.981125i	$-0.438056\pi$
$131$	4.42658	0.386752	0.193376	+	0.981125i	$0.438056\pi$
$132$	5.40111	0.470106
$133$	12.9640	1.12412
$134$	21.3682	1.84593
$135$	−15.0603	−1.29618
$136$	−20.0308	−1.71763
$137$	22.5489	1.92649	0.963243	−	0.268631i	$-0.0865712\pi$
$137$	22.5489	1.92649	0.963243	+	0.268631i	$0.0865712\pi$
$138$	9.88813	0.841733
$139$	1.03075	0.0874272	0.0437136	−	0.999044i	$-0.486081\pi$
$139$	1.03075	0.0874272	0.0437136	+	0.999044i	$0.486081\pi$
$140$	49.4475	4.17908
$141$	23.0175	1.93842
$142$	11.1364	0.934545
$143$	0.789001	0.0659795
$144$	0.886499	0.0738749
$145$	4.42718	0.367657
$146$	−25.2597	−2.09051
$147$	20.3571	1.67903
$148$	34.8472	2.86443
$149$	3.46250	0.283659	0.141830	−	0.989891i	$-0.454701\pi$
$149$	3.46250	0.283659	0.141830	+	0.989891i	$0.454701\pi$
$150$	−20.4825	−1.67239
$151$	−1.68323	−0.136979	−0.0684896	−	0.997652i	$-0.521818\pi$
$151$	−1.68323	−0.136979	−0.0684896	+	0.997652i	$0.521818\pi$
$152$	−12.6710	−1.02776
$153$	1.71471	0.138626
$154$	−8.04256	−0.648088
$155$	−31.4936	−2.52963
$156$	6.84551	0.548079
$157$	21.2534	1.69620	0.848101	−	0.529834i	$-0.177746\pi$
$157$	21.2534	1.69620	0.848101	+	0.529834i	$0.177746\pi$
$158$	12.8263	1.02040
$159$	−21.4976	−1.70487
$160$	7.32694	0.579245
$161$	−9.59074	−0.755856
$162$	23.8112	1.87078
$163$	−15.7832	−1.23624	−0.618118	−	0.786085i	$-0.712105\pi$
$163$	−15.7832	−1.23624	−0.618118	+	0.786085i	$0.712105\pi$
$164$	20.7374	1.61932
$165$	4.49431	0.349881
$166$	29.4137	2.28294
$167$	16.2360	1.25638	0.628191	−	0.778059i	$-0.283796\pi$
$167$	16.2360	1.25638	0.628191	+	0.778059i	$0.283796\pi$
$168$	−32.4311	−2.50211
$169$	1.00000	0.0769231
$170$	−35.8624	−2.75052
$171$	1.08468	0.0829479
$172$	−12.5703	−0.958473
$173$	7.72855	0.587590	0.293795	−	0.955868i	$-0.405082\pi$
$173$	7.72855	0.587590	0.293795	+	0.955868i	$0.405082\pi$
$174$	−6.24749	−0.473621
$175$	19.8664	1.50176
$176$	1.96429	0.148064
$177$	−11.1184	−0.835713
$178$	−6.19205	−0.464114
$179$	4.86638	0.363730	0.181865	−	0.983323i	$-0.441787\pi$
$179$	4.86638	0.363730	0.181865	+	0.983323i	$0.441787\pi$
$180$	4.13723	0.308371
$181$	8.57011	0.637011	0.318506	−	0.947921i	$-0.396819\pi$
$181$	8.57011	0.637011	0.318506	+	0.947921i	$0.396819\pi$
$182$	−10.1934	−0.755582
$183$	7.71815	0.570542
$184$	9.37401	0.691061
$185$	28.9967	2.13188
$186$	44.4428	3.25871
$187$	3.79941	0.277841
$188$	46.9496	3.42415
$189$	−20.6134	−1.49941
$190$	−22.6858	−1.64580
$191$	−5.58524	−0.404133	−0.202067	−	0.979372i	$-0.564766\pi$
$191$	−5.58524	−0.404133	−0.202067	+	0.979372i	$0.564766\pi$
$192$	−19.4612	−1.40449
$193$	−19.9700	−1.43747	−0.718734	−	0.695285i	$-0.755278\pi$
$193$	−19.9700	−1.43747	−0.718734	+	0.695285i	$0.755278\pi$
$194$	−0.0544176	−0.00390695
$195$	5.69620	0.407914
$196$	41.5231	2.96594
$197$	20.0038	1.42521	0.712606	−	0.701565i	$-0.247515\pi$
$197$	20.0038	1.42521	0.712606	+	0.701565i	$0.247515\pi$
$198$	−0.672914	−0.0478219
$199$	−19.9576	−1.41476	−0.707380	−	0.706834i	$-0.750123\pi$
$199$	−19.9576	−1.41476	−0.707380	+	0.706834i	$0.750123\pi$
$200$	−19.4175	−1.37302
$201$	−16.3438	−1.15280
$202$	20.8647	1.46804
$203$	6.05960	0.425300
$204$	32.9644	2.30797
$205$	17.2557	1.20519
$206$	18.0861	1.26012
$207$	−0.802448	−0.0557740
$208$	2.48959	0.172622
$209$	2.40342	0.166248
$210$	−58.0634	−4.00676
$211$	−10.2474	−0.705462	−0.352731	−	0.935725i	$-0.614747\pi$
$211$	−10.2474	−0.705462	−0.352731	+	0.935725i	$0.614747\pi$
$212$	−43.8494	−3.01159
$213$	−8.51784	−0.583633
$214$	−31.9555	−2.18443
$215$	−10.4598	−0.713353
$216$	20.1476	1.37087
$217$	−43.1062	−2.92624
$218$	−7.00707	−0.474579
$219$	19.3202	1.30554
$220$	9.16718	0.618051
$221$	4.81547	0.323924
$222$	−40.9192	−2.74631
$223$	−19.7064	−1.31964	−0.659819	−	0.751424i	$-0.729367\pi$
$223$	−19.7064	−1.31964	−0.659819	+	0.751424i	$0.729367\pi$
$224$	10.0286	0.670062
$225$	1.66221	0.110814
$226$	−35.3681	−2.35265
$227$	−15.3374	−1.01798	−0.508989	−	0.860773i	$-0.669981\pi$
$227$	−15.3374	−1.01798	−0.508989	+	0.860773i	$0.669981\pi$
$228$	20.8525	1.38099
$229$	23.6710	1.56423	0.782113	−	0.623137i	$-0.214142\pi$
$229$	23.6710	1.56423	0.782113	+	0.623137i	$0.214142\pi$
$230$	16.7829	1.10663
$231$	6.15148	0.404737
$232$	−5.92266	−0.388842
$233$	3.89836	0.255390	0.127695	−	0.991813i	$-0.459242\pi$
$233$	3.89836	0.255390	0.127695	+	0.991813i	$0.459242\pi$
$234$	−0.852869	−0.0557538
$235$	39.0671	2.54846
$236$	−22.6786	−1.47625
$237$	−9.81037	−0.637252
$238$	−49.0858	−3.18176
$239$	8.01124	0.518204	0.259102	−	0.965850i	$-0.416573\pi$
$239$	8.01124	0.518204	0.259102	+	0.965850i	$0.416573\pi$
$240$	14.1812	0.915392
$241$	−30.2758	−1.95023	−0.975116	−	0.221694i	$-0.928841\pi$
$241$	−30.2758	−1.95023	−0.975116	+	0.221694i	$0.928841\pi$
$242$	24.8555	1.59778
$243$	−3.68169	−0.236181
$244$	15.7430	1.00784
$245$	34.5517	2.20743
$246$	−24.3508	−1.55255
$247$	3.04616	0.193822
$248$	42.1321	2.67539
$249$	−22.4975	−1.42572
$250$	2.47225	0.156359
$251$	−11.6412	−0.734788	−0.367394	−	0.930065i	$-0.619750\pi$
$251$	−11.6412	−0.734788	−0.367394	+	0.930065i	$0.619750\pi$
$252$	5.66273	0.356719
$253$	−1.77805	−0.111785
$254$	−19.8958	−1.24838
$255$	27.4299	1.71773
$256$	−28.4077	−1.77548
$257$	20.2505	1.26319	0.631596	−	0.775298i	$-0.282400\pi$
$257$	20.2505	1.26319	0.631596	+	0.775298i	$0.282400\pi$
$258$	14.7605	0.918951
$259$	39.6885	2.46612
$260$	11.6187	0.720563
$261$	0.507001	0.0313826
$262$	−10.6023	−0.655012
$263$	−7.84735	−0.483889	−0.241944	−	0.970290i	$-0.577785\pi$
$263$	−7.84735	−0.483889	−0.241944	+	0.970290i	$0.577785\pi$
$264$	−6.01247	−0.370042
$265$	−36.4874	−2.24140
$266$	−31.0506	−1.90383
$267$	4.73608	0.289844
$268$	−33.3370	−2.03638
$269$	−19.9560	−1.21674	−0.608370	−	0.793653i	$-0.708176\pi$
$269$	−19.9560	−1.21674	−0.608370	+	0.793653i	$0.708176\pi$
$270$	36.0716	2.19524
$271$	−17.3787	−1.05568	−0.527842	−	0.849343i	$-0.676999\pi$
$271$	−17.3787	−1.05568	−0.527842	+	0.849343i	$0.676999\pi$
$272$	11.9885	0.726912
$273$	7.79654	0.471868
$274$	−54.0080	−3.26274
$275$	3.68308	0.222098
$276$	−15.4267	−0.928576
$277$	−5.99386	−0.360136	−0.180068	−	0.983654i	$-0.557632\pi$
$277$	−5.99386	−0.360136	−0.180068	+	0.983654i	$0.557632\pi$
$278$	−2.46880	−0.148069
$279$	−3.60665	−0.215925
$280$	−55.0445	−3.28954
$281$	−16.6902	−0.995657	−0.497828	−	0.867276i	$-0.665869\pi$
$281$	−16.6902	−0.995657	−0.497828	+	0.867276i	$0.665869\pi$
$282$	−55.1302	−3.28296
$283$	−15.1165	−0.898580	−0.449290	−	0.893386i	$-0.648323\pi$
$283$	−15.1165	−0.898580	−0.449290	+	0.893386i	$0.648323\pi$
$284$	−17.3741	−1.03096
$285$	17.3515	1.02782
$286$	−1.88977	−0.111744
$287$	23.6184	1.39415
$288$	0.839082	0.0494434
$289$	6.18879	0.364047
$290$	−10.6037	−0.622672
$291$	0.0416221	0.00243993
$292$	39.4081	2.30619
$293$	−5.86971	−0.342912	−0.171456	−	0.985192i	$-0.554847\pi$
$293$	−5.86971	−0.342912	−0.171456	+	0.985192i	$0.554847\pi$
$294$	−48.7582	−2.84364
$295$	−18.8711	−1.09872
$296$	−38.7916	−2.25472
$297$	−3.82157	−0.221750
$298$	−8.29319	−0.480412
$299$	−2.25355	−0.130326
$300$	31.9551	1.84493
$301$	−14.3166	−0.825196
$302$	4.03158	0.231991
$303$	−15.9587	−0.916803
$304$	7.58368	0.434954
$305$	13.0998	0.750095
$306$	−4.10697	−0.234780
$307$	9.19323	0.524686	0.262343	−	0.964975i	$-0.415505\pi$
$307$	9.19323	0.524686	0.262343	+	0.964975i	$0.415505\pi$
$308$	12.5474	0.714952
$309$	−13.8335	−0.786958
$310$	75.4318	4.28424
$311$	1.57747	0.0894503	0.0447251	−	0.998999i	$-0.485759\pi$
$311$	1.57747	0.0894503	0.0447251	+	0.998999i	$0.485759\pi$
$312$	−7.62036	−0.431418
$313$	11.8525	0.669944	0.334972	−	0.942228i	$-0.391273\pi$
$313$	11.8525	0.669944	0.334972	+	0.942228i	$0.391273\pi$
$314$	−50.9048	−2.87273
$315$	4.71200	0.265491
$316$	−20.0105	−1.12568
$317$	−19.7883	−1.11142	−0.555710	−	0.831376i	$-0.687553\pi$
$317$	−19.7883	−1.11142	−0.555710	+	0.831376i	$0.687553\pi$
$318$	51.4899	2.88741
$319$	1.12340	0.0628985
$320$	−33.0311	−1.84649
$321$	24.4417	1.36420
$322$	22.9712	1.28013
$323$	14.6687	0.816188
$324$	−37.1483	−2.06380
$325$	4.66804	0.258936
$326$	37.8030	2.09372
$327$	5.35946	0.296379
$328$	−23.0847	−1.27464
$329$	53.4722	2.94802
$330$	−10.7645	−0.592567
$331$	17.7347	0.974789	0.487395	−	0.873182i	$-0.337947\pi$
$331$	17.7347	0.974789	0.487395	+	0.873182i	$0.337947\pi$
$332$	−45.8889	−2.51848
$333$	3.32070	0.181973
$334$	−38.8876	−2.12784
$335$	−27.7400	−1.51560
$336$	19.4102	1.05891
$337$	10.8786	0.592593	0.296297	−	0.955096i	$-0.404248\pi$
$337$	10.8786	0.592593	0.296297	+	0.955096i	$0.404248\pi$
$338$	−2.39514	−0.130279
$339$	27.0518	1.46925
$340$	55.9497	3.03430
$341$	−7.99155	−0.432767
$342$	−2.59797	−0.140482
$343$	17.5009	0.944960
$344$	13.9931	0.754457
$345$	−12.8367	−0.691102
$346$	−18.5110	−0.995156
$347$	−4.84089	−0.259873	−0.129936	−	0.991522i	$-0.541477\pi$
$347$	−4.84089	−0.259873	−0.129936	+	0.991522i	$0.541477\pi$
$348$	9.74684	0.522485
$349$	7.13011	0.381666	0.190833	−	0.981623i	$-0.438881\pi$
$349$	7.13011	0.381666	0.190833	+	0.981623i	$0.438881\pi$
$350$	−47.5829	−2.54342
$351$	−4.84355	−0.258530
$352$	1.85922	0.0990968
$353$	26.8850	1.43094	0.715471	−	0.698642i	$-0.246212\pi$
$353$	26.8850	1.43094	0.715471	+	0.698642i	$0.246212\pi$
$354$	26.6303	1.41538
$355$	−14.4571	−0.767305
$356$	9.66034	0.511997
$357$	37.5440	1.98704
$358$	−11.6557	−0.616022
$359$	−13.4861	−0.711767	−0.355883	−	0.934530i	$-0.615820\pi$
$359$	−13.4861	−0.711767	−0.355883	+	0.934530i	$0.615820\pi$
$360$	−4.60552	−0.242732
$361$	−9.72092	−0.511627
$362$	−20.5266	−1.07886
$363$	−19.0111	−0.997826
$364$	15.9029	0.833536
$365$	32.7918	1.71640
$366$	−18.4861	−0.966283
$367$	−0.990467	−0.0517020	−0.0258510	−	0.999666i	$-0.508230\pi$
$367$	−0.990467	−0.0517020	−0.0258510	+	0.999666i	$0.508230\pi$
$368$	−5.61040	−0.292462
$369$	1.97613	0.102873
$370$	−69.4512	−3.61059
$371$	−49.9413	−2.59282
$372$	−69.3361	−3.59491
$373$	−13.7095	−0.709851	−0.354926	−	0.934895i	$-0.615494\pi$
$373$	−13.7095	−0.709851	−0.354926	+	0.934895i	$0.615494\pi$
$374$	−9.10014	−0.470557
$375$	−1.89094	−0.0976476
$376$	−52.2638	−2.69530
$377$	1.42383	0.0733309
$378$	49.3721	2.53943
$379$	−25.4657	−1.30808	−0.654042	−	0.756459i	$-0.726928\pi$
$379$	−25.4657	−1.30808	−0.654042	+	0.756459i	$0.726928\pi$
$380$	35.3925	1.81560
$381$	15.2176	0.779623
$382$	13.3774	0.684449
$383$	−26.8031	−1.36957	−0.684786	−	0.728744i	$-0.740104\pi$
$383$	−26.8031	−1.36957	−0.684786	+	0.728744i	$0.740104\pi$
$384$	37.9786	1.93809
$385$	10.4408	0.532110
$386$	47.8309	2.43453
$387$	−1.19786	−0.0608905
$388$	0.0848979	0.00431004
$389$	25.8315	1.30971	0.654854	−	0.755756i	$-0.272730\pi$
$389$	25.8315	1.30971	0.654854	+	0.755756i	$0.272730\pi$
$390$	−13.6432	−0.690851
$391$	−10.8519	−0.548804
$392$	−46.2231	−2.33462
$393$	8.10933	0.409061
$394$	−47.9119	−2.41377
$395$	−16.6509	−0.837799
$396$	1.04983	0.0527558
$397$	18.8202	0.944561	0.472281	−	0.881448i	$-0.343431\pi$
$397$	18.8202	0.944561	0.472281	+	0.881448i	$0.343431\pi$
$398$	47.8014	2.39607
$399$	23.7495	1.18896
$400$	11.6215	0.581074
$401$	−13.1263	−0.655497	−0.327749	−	0.944765i	$-0.606290\pi$
$401$	−13.1263	−0.655497	−0.327749	+	0.944765i	$0.606290\pi$
$402$	39.1457	1.95241
$403$	−10.1287	−0.504547
$404$	−32.5515	−1.61950
$405$	−30.9114	−1.53600
$406$	−14.5136	−0.720298
$407$	7.35794	0.364720
$408$	−36.6956	−1.81670
$409$	−9.45965	−0.467750	−0.233875	−	0.972267i	$-0.575141\pi$
$409$	−9.45965	−0.467750	−0.233875	+	0.972267i	$0.575141\pi$
$410$	−41.3300	−2.04114
$411$	41.3088	2.03761
$412$	−28.2166	−1.39013
$413$	−25.8293	−1.27098
$414$	1.92198	0.0944601
$415$	−38.1845	−1.87440
$416$	2.35642	0.115533
$417$	1.88830	0.0924703
$418$	−5.75654	−0.281561
$419$	−30.3210	−1.48128	−0.740638	−	0.671904i	$-0.765477\pi$
$419$	−30.3210	−1.48128	−0.740638	+	0.671904i	$0.765477\pi$
$420$	90.5859	4.42014
$421$	−31.3813	−1.52943	−0.764714	−	0.644369i	$-0.777120\pi$
$421$	−31.3813	−1.52943	−0.764714	+	0.644369i	$0.777120\pi$
$422$	24.5441	1.19479
$423$	4.47397	0.217532
$424$	48.8127	2.37056
$425$	22.4788	1.09038
$426$	20.4014	0.988453
$427$	17.9301	0.867698
$428$	49.8545	2.40981
$429$	1.44542	0.0697855
$430$	25.0527	1.20815
$431$	−2.41024	−0.116097	−0.0580485	−	0.998314i	$-0.518488\pi$
$431$	−2.41024	−0.116097	−0.0580485	+	0.998314i	$0.518488\pi$
$432$	−12.0585	−0.580163
$433$	−2.69945	−0.129727	−0.0648635	−	0.997894i	$-0.520661\pi$
$433$	−2.69945	−0.129727	−0.0648635	+	0.997894i	$0.520661\pi$
$434$	103.245	4.95594
$435$	8.11042	0.388865
$436$	10.9319	0.523542
$437$	−6.86466	−0.328381
$438$	−46.2747	−2.21109
$439$	7.90175	0.377130	0.188565	−	0.982061i	$-0.439616\pi$
$439$	7.90175	0.377130	0.188565	+	0.982061i	$0.439616\pi$
$440$	−10.2048	−0.486496
$441$	3.95686	0.188422
$442$	−11.5338	−0.548605
$443$	40.3660	1.91785	0.958924	−	0.283662i	$-0.0915493\pi$
$443$	40.3660	1.91785	0.958924	+	0.283662i	$0.0915493\pi$
$444$	63.8388	3.02966
$445$	8.03845	0.381059
$446$	47.1997	2.23497
$447$	6.34317	0.300022
$448$	−45.2105	−2.13599
$449$	−31.4459	−1.48403	−0.742013	−	0.670385i	$-0.766129\pi$
$449$	−31.4459	−1.48403	−0.742013	+	0.670385i	$0.766129\pi$
$450$	−3.98122	−0.187677
$451$	4.37867	0.206183
$452$	55.1785	2.59538
$453$	−3.08361	−0.144881
$454$	36.7353	1.72407
$455$	13.2329	0.620368
$456$	−23.2128	−1.08704
$457$	−1.90434	−0.0890811	−0.0445406	−	0.999008i	$-0.514182\pi$
$457$	−1.90434	−0.0890811	−0.0445406	+	0.999008i	$0.514182\pi$
$458$	−56.6955	−2.64921
$459$	−23.3240	−1.08867
$460$	−26.1833	−1.22080
$461$	4.82908	0.224913	0.112456	−	0.993657i	$-0.464128\pi$
$461$	4.82908	0.224913	0.112456	+	0.993657i	$0.464128\pi$
$462$	−14.7337	−0.685472
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	3.54475	0.164561
$465$	−57.6951	−2.67555
$466$	−9.33714	−0.432535
$467$	−1.05116	−0.0486417	−0.0243208	−	0.999704i	$-0.507742\pi$
$467$	−1.05116	−0.0486417	−0.0243208	+	0.999704i	$0.507742\pi$
$468$	1.33058	0.0615060
$469$	−37.9684	−1.75322
$470$	−93.5713	−4.31612
$471$	38.9353	1.79405
$472$	25.2457	1.16203
$473$	−2.65419	−0.122040
$474$	23.4972	1.07926
$475$	14.2196	0.652439
$476$	76.5798	3.51003
$477$	−4.17854	−0.191322
$478$	−19.1881	−0.877641
$479$	−16.1451	−0.737687	−0.368843	−	0.929492i	$-0.620246\pi$
$479$	−16.1451	−0.737687	−0.368843	+	0.929492i	$0.620246\pi$
$480$	13.4227	0.612658
$481$	9.32565	0.425213
$482$	72.5148	3.30296
$483$	−17.5699	−0.799456
$484$	−38.7776	−1.76262
$485$	0.0706442	0.00320779
$486$	8.81818	0.400001
$487$	16.9445	0.767830	0.383915	−	0.923369i	$-0.374576\pi$
$487$	16.9445	0.767830	0.383915	+	0.923369i	$0.374576\pi$
$488$	−17.5249	−0.793316
$489$	−28.9142	−1.30755
$490$	−82.7563	−3.73855
$491$	28.2384	1.27438	0.637190	−	0.770707i	$-0.280097\pi$
$491$	28.2384	1.27438	0.637190	+	0.770707i	$0.280097\pi$
$492$	37.9901	1.71273
$493$	6.85641	0.308797
$494$	−7.29599	−0.328262
$495$	0.873569	0.0392640
$496$	−25.2163	−1.13224
$497$	−19.7879	−0.887607
$498$	53.8847	2.41463
$499$	−18.8783	−0.845110	−0.422555	−	0.906337i	$-0.638867\pi$
$499$	−18.8783	−0.845110	−0.422555	+	0.906337i	$0.638867\pi$
$500$	−3.85701	−0.172491
$501$	29.7438	1.32885
$502$	27.8824	1.24445
$503$	12.0566	0.537579	0.268789	−	0.963199i	$-0.413376\pi$
$503$	12.0566	0.537579	0.268789	+	0.963199i	$0.413376\pi$
$504$	−6.30370	−0.280789
$505$	−27.0863	−1.20533
$506$	4.25868	0.189321
$507$	1.83196	0.0813603
$508$	31.0399	1.37717
$509$	42.9169	1.90226	0.951129	−	0.308795i	$-0.0999257\pi$
$509$	42.9169	1.90226	0.951129	+	0.308795i	$0.0999257\pi$
$510$	−65.6986	−2.90918
$511$	44.8830	1.98551
$512$	26.5783	1.17460
$513$	−14.7542	−0.651415
$514$	−48.5028	−2.13937
$515$	−23.4792	−1.03462
$516$	−23.0282	−1.01376
$517$	9.91333	0.435988
$518$	−95.0596	−4.17668
$519$	14.1584	0.621485
$520$	−12.9339	−0.567187
$521$	−6.10541	−0.267483	−0.133741	−	0.991016i	$-0.542699\pi$
$521$	−6.10541	−0.267483	−0.133741	+	0.991016i	$0.542699\pi$
$522$	−1.21434	−0.0531502
$523$	4.07869	0.178349	0.0891743	−	0.996016i	$-0.471577\pi$
$523$	4.07869	0.178349	0.0891743	+	0.996016i	$0.471577\pi$
$524$	16.5409	0.722591
$525$	36.3945	1.58839
$526$	18.7955	0.819524
$527$	−48.7745	−2.12465
$528$	3.59850	0.156604
$529$	−17.9215	−0.779197
$530$	87.3926	3.79609
$531$	−2.16112	−0.0937845
$532$	48.4426	2.10025
$533$	5.54964	0.240381
$534$	−11.3436	−0.490885
$535$	41.4843	1.79352
$536$	37.1104	1.60293
$537$	8.91502	0.384712
$538$	47.7975	2.06070
$539$	8.76754	0.377645
$540$	−56.2760	−2.42173
$541$	7.38075	0.317323	0.158662	−	0.987333i	$-0.449282\pi$
$541$	7.38075	0.317323	0.158662	+	0.987333i	$0.449282\pi$
$542$	41.6246	1.78793
$543$	15.7001	0.673756
$544$	11.3473	0.486512
$545$	9.09649	0.389651
$546$	−18.6738	−0.799166
$547$	−39.0389	−1.66918	−0.834591	−	0.550870i	$-0.814296\pi$
$547$	−39.0389	−1.66918	−0.834591	+	0.550870i	$0.814296\pi$
$548$	84.2589	3.59936
$549$	1.50020	0.0640268
$550$	−8.82151	−0.376151
$551$	4.33721	0.184771
$552$	17.1728	0.730924
$553$	−22.7905	−0.969153
$554$	14.3561	0.609934
$555$	53.1208	2.25485
$556$	3.85162	0.163345
$557$	−29.2070	−1.23754	−0.618771	−	0.785571i	$-0.712369\pi$
$557$	−29.2070	−1.23754	−0.618771	+	0.785571i	$0.712369\pi$
$558$	8.63845	0.365695
$559$	−3.36399	−0.142282
$560$	32.9444	1.39216
$561$	6.96038	0.293867
$562$	39.9755	1.68627
$563$	35.7496	1.50667	0.753334	−	0.657638i	$-0.228445\pi$
$563$	35.7496	1.50667	0.753334	+	0.657638i	$0.228445\pi$
$564$	86.0098	3.62167
$565$	45.9144	1.93163
$566$	36.2061	1.52185
$567$	−42.3093	−1.77682
$568$	19.3407	0.811518
$569$	39.9786	1.67599	0.837994	−	0.545679i	$-0.183728\pi$
$569$	39.9786	1.67599	0.837994	+	0.545679i	$0.183728\pi$
$570$	−41.5594	−1.74073
$571$	41.1700	1.72291	0.861456	−	0.507832i	$-0.169553\pi$
$571$	41.1700	1.72291	0.861456	+	0.507832i	$0.169553\pi$
$572$	2.94827	0.123273
$573$	−10.2319	−0.427445
$574$	−56.5694	−2.36116
$575$	−10.5196	−0.438699
$576$	−3.78272	−0.157613
$577$	−34.0551	−1.41773	−0.708865	−	0.705344i	$-0.750793\pi$
$577$	−34.0551	−1.41773	−0.708865	+	0.705344i	$0.750793\pi$
$578$	−14.8231	−0.616558
$579$	−36.5842	−1.52039
$580$	16.5431	0.686914
$581$	−52.2641	−2.16828
$582$	−0.0996909	−0.00413232
$583$	−9.25873	−0.383457
$584$	−43.8688	−1.81530
$585$	1.10718	0.0457764
$586$	14.0588	0.580764
$587$	−16.2536	−0.670860	−0.335430	−	0.942065i	$-0.608882\pi$
$587$	−16.2536	−0.670860	−0.335430	+	0.942065i	$0.608882\pi$
$588$	76.0687	3.13702
$589$	−30.8536	−1.27130
$590$	45.1989	1.86081
$591$	36.6462	1.50742
$592$	23.2170	0.954213
$593$	−38.1596	−1.56703	−0.783513	−	0.621376i	$-0.786574\pi$
$593$	−38.1596	−1.56703	−0.783513	+	0.621376i	$0.786574\pi$
$594$	9.15320	0.375560
$595$	63.7227	2.61237
$596$	12.9384	0.529976
$597$	−36.5616	−1.49637
$598$	5.39756	0.220723
$599$	−10.4790	−0.428160	−0.214080	−	0.976816i	$-0.568675\pi$
$599$	−10.4790	−0.428160	−0.214080	+	0.976816i	$0.568675\pi$
$600$	−35.5721	−1.45223
$601$	−33.5987	−1.37052	−0.685260	−	0.728298i	$-0.740312\pi$
$601$	−33.5987	−1.37052	−0.685260	+	0.728298i	$0.740312\pi$
$602$	34.2903	1.39757
$603$	−3.17678	−0.129369
$604$	−6.28974	−0.255926
$605$	−32.2672	−1.31185
$606$	38.2234	1.55272
$607$	14.7698	0.599489	0.299745	−	0.954020i	$-0.403099\pi$
$607$	14.7698	0.599489	0.299745	+	0.954020i	$0.403099\pi$
$608$	7.17804	0.291108
$609$	11.1009	0.449833
$610$	−31.3760	−1.27038
$611$	12.5644	0.508302
$612$	6.40736	0.259002
$613$	−6.33400	−0.255828	−0.127914	−	0.991785i	$-0.540828\pi$
$613$	−6.33400	−0.255828	−0.127914	+	0.991785i	$0.540828\pi$
$614$	−22.0191	−0.888619
$615$	31.6119	1.27471
$616$	−13.9676	−0.562771
$617$	−24.2257	−0.975291	−0.487645	−	0.873042i	$-0.662144\pi$
$617$	−24.2257	−0.975291	−0.487645	+	0.873042i	$0.662144\pi$
$618$	33.1331	1.33281
$619$	−10.6512	−0.428108	−0.214054	−	0.976822i	$-0.568667\pi$
$619$	−10.6512	−0.428108	−0.214054	+	0.976822i	$0.568667\pi$
$620$	−117.683	−4.72625
$621$	10.9152	0.438011
$622$	−3.77827	−0.151495
$623$	11.0024	0.440803
$624$	4.56083	0.182579
$625$	−26.5496	−1.06198
$626$	−28.3885	−1.13463
$627$	4.40297	0.175838
$628$	79.4177	3.16911
$629$	44.9074	1.79058
$630$	−11.2859	−0.449642
$631$	7.31001	0.291007	0.145503	−	0.989358i	$-0.453520\pi$
$631$	7.31001	0.291007	0.145503	+	0.989358i	$0.453520\pi$
$632$	22.2755	0.886073
$633$	−18.7729	−0.746156
$634$	47.3957	1.88232
$635$	25.8286	1.02497
$636$	−80.3304	−3.18531
$637$	11.1122	0.440282
$638$	−2.69071	−0.106526
$639$	−1.65563	−0.0654958
$640$	64.4602	2.54801
$641$	32.4720	1.28257	0.641283	−	0.767305i	$-0.278403\pi$
$641$	32.4720	1.28257	0.641283	+	0.767305i	$0.278403\pi$
$642$	−58.5413	−2.31044
$643$	43.7358	1.72477	0.862386	−	0.506252i	$-0.168969\pi$
$643$	43.7358	1.72477	0.862386	+	0.506252i	$0.168969\pi$
$644$	−35.8378	−1.41221
$645$	−19.1620	−0.754502
$646$	−35.1336	−1.38231
$647$	−14.9589	−0.588094	−0.294047	−	0.955791i	$-0.595002\pi$
$647$	−14.9589	−0.588094	−0.294047	+	0.955791i	$0.595002\pi$
$648$	41.3532	1.62451
$649$	−4.78856	−0.187967
$650$	−11.1806	−0.438540
$651$	−78.9688	−3.09503
$652$	−58.9773	−2.30973
$653$	29.5956	1.15817	0.579083	−	0.815269i	$-0.303411\pi$
$653$	29.5956	1.15817	0.579083	+	0.815269i	$0.303411\pi$
$654$	−12.8367	−0.501954
$655$	13.7638	0.537795
$656$	13.8163	0.539436
$657$	3.75532	0.146509
$658$	−128.073	−4.99282
$659$	28.9854	1.12911	0.564556	−	0.825395i	$-0.309047\pi$
$659$	28.9854	1.12911	0.564556	+	0.825395i	$0.309047\pi$
$660$	16.7939	0.653703
$661$	−5.76665	−0.224297	−0.112148	−	0.993691i	$-0.535773\pi$
$661$	−5.76665	−0.224297	−0.112148	+	0.993691i	$0.535773\pi$
$662$	−42.4772	−1.65092
$663$	8.82176	0.342609
$664$	51.0831	1.98241
$665$	40.3095	1.56314
$666$	−7.95355	−0.308194
$667$	−3.20866	−0.124240
$668$	60.6694	2.34737
$669$	−36.1014	−1.39576
$670$	66.4412	2.56685
$671$	3.32410	0.128326
$672$	18.3720	0.708714
$673$	−27.3060	−1.05257	−0.526285	−	0.850308i	$-0.676416\pi$
$673$	−27.3060	−1.05257	−0.526285	+	0.850308i	$0.676416\pi$
$674$	−26.0557	−1.00363
$675$	−22.6099	−0.870255
$676$	3.73671	0.143720
$677$	−33.6971	−1.29509	−0.647543	−	0.762029i	$-0.724203\pi$
$677$	−33.6971	−1.29509	−0.647543	+	0.762029i	$0.724203\pi$
$678$	−64.7930	−2.48836
$679$	0.0966926	0.00371072
$680$	−62.2827	−2.38843
$681$	−28.0975	−1.07670
$682$	19.1409	0.732943
$683$	40.0370	1.53197	0.765987	−	0.642856i	$-0.222251\pi$
$683$	40.0370	1.53197	0.765987	+	0.642856i	$0.222251\pi$
$684$	4.05315	0.154976
$685$	70.1125	2.67886
$686$	−41.9172	−1.60040
$687$	43.3644	1.65446
$688$	−8.37495	−0.319292
$689$	−11.7348	−0.447058
$690$	30.7456	1.17047
$691$	−23.3396	−0.887881	−0.443941	−	0.896056i	$-0.646420\pi$
$691$	−23.3396	−0.887881	−0.443941	+	0.896056i	$0.646420\pi$
$692$	28.8793	1.09783
$693$	1.19568	0.0454200
$694$	11.5946	0.440126
$695$	3.20496	0.121571
$696$	−10.8501	−0.411272
$697$	26.7241	1.01225
$698$	−17.0776	−0.646398
$699$	7.14165	0.270122
$700$	74.2351	2.80582
$701$	16.0328	0.605550	0.302775	−	0.953062i	$-0.402087\pi$
$701$	16.0328	0.605550	0.302775	+	0.953062i	$0.402087\pi$
$702$	11.6010	0.437852
$703$	28.4074	1.07141
$704$	−8.38167	−0.315896
$705$	71.5694	2.69546
$706$	−64.3934	−2.42348
$707$	−37.0738	−1.39430
$708$	−41.5464	−1.56141
$709$	−43.9713	−1.65138	−0.825689	−	0.564126i	$-0.809213\pi$
$709$	−43.9713	−1.65138	−0.825689	+	0.564126i	$0.809213\pi$
$710$	34.6269	1.29952
$711$	−1.90686	−0.0715130
$712$	−10.7538	−0.403016
$713$	22.8255	0.854821
$714$	−89.9234	−3.36530
$715$	2.45328	0.0917473
$716$	18.1843	0.679578
$717$	14.6763	0.548096
$718$	32.3010	1.20546
$719$	−28.9432	−1.07940	−0.539700	−	0.841858i	$-0.681462\pi$
$719$	−28.9432	−1.07940	−0.539700	+	0.841858i	$0.681462\pi$
$720$	2.75643	0.102726
$721$	−32.1366	−1.19683
$722$	23.2830	0.866503
$723$	−55.4640	−2.06273
$724$	32.0240	1.19016
$725$	6.64649	0.246844
$726$	45.5344	1.68994
$727$	46.8709	1.73835	0.869173	−	0.494508i	$-0.164652\pi$
$727$	46.8709	1.73835	0.869173	+	0.494508i	$0.164652\pi$
$728$	−17.7029	−0.656114
$729$	23.0796	0.854801
$730$	−78.5411	−2.90694
$731$	−16.1992	−0.599149
$732$	28.8405	1.06598
$733$	19.7331	0.728859	0.364430	−	0.931231i	$-0.381264\pi$
$733$	19.7331	0.728859	0.364430	+	0.931231i	$0.381264\pi$
$734$	2.37231	0.0875636
$735$	63.2974	2.33476
$736$	−5.31031	−0.195741
$737$	−7.03905	−0.259287
$738$	−4.73311	−0.174228
$739$	−52.0077	−1.91313	−0.956567	−	0.291511i	$-0.905842\pi$
$739$	−52.0077	−1.91313	−0.956567	+	0.291511i	$0.905842\pi$
$740$	108.352	3.98310
$741$	5.58045	0.205003
$742$	119.617	4.39126
$743$	5.14746	0.188842	0.0944210	−	0.995532i	$-0.469900\pi$
$743$	5.14746	0.188842	0.0944210	+	0.995532i	$0.469900\pi$
$744$	77.1843	2.82971
$745$	10.7661	0.394440
$746$	32.8362	1.20222
$747$	−4.37289	−0.159996
$748$	14.1973	0.519105
$749$	56.7806	2.07472
$750$	4.52906	0.165378
$751$	−26.0548	−0.950752	−0.475376	−	0.879783i	$-0.657688\pi$
$751$	−26.0548	−0.950752	−0.475376	+	0.879783i	$0.657688\pi$
$752$	31.2802	1.14067
$753$	−21.3263	−0.777173
$754$	−3.41028	−0.124195
$755$	−5.23374	−0.190475
$756$	−77.0264	−2.80142
$757$	10.6884	0.388478	0.194239	−	0.980954i	$-0.437776\pi$
$757$	10.6884	0.388478	0.194239	+	0.980954i	$0.437776\pi$
$758$	60.9939	2.21540
$759$	−3.25732	−0.118233
$760$	−39.3986	−1.42914
$761$	10.2903	0.373024	0.186512	−	0.982453i	$-0.440282\pi$
$761$	10.2903	0.373024	0.186512	+	0.982453i	$0.440282\pi$
$762$	−36.4484	−1.32039
$763$	12.4506	0.450742
$764$	−20.8704	−0.755065
$765$	5.33162	0.192765
$766$	64.1972	2.31954
$767$	−6.06915	−0.219144
$768$	−52.0418	−1.87790
$769$	38.2764	1.38028	0.690142	−	0.723674i	$-0.257548\pi$
$769$	38.2764	1.38028	0.690142	+	0.723674i	$0.257548\pi$
$770$	−25.0071	−0.901194
$771$	37.0981	1.33606
$772$	−74.6219	−2.68570
$773$	−14.3165	−0.514930	−0.257465	−	0.966288i	$-0.582887\pi$
$773$	−14.3165	−0.514930	−0.257465	+	0.966288i	$0.582887\pi$
$774$	2.86904	0.103126
$775$	−47.2811	−1.69839
$776$	−0.0945076	−0.00339262
$777$	72.7078	2.60838
$778$	−61.8701	−2.21815
$779$	16.9051	0.605687
$780$	21.2851	0.762128
$781$	−3.66852	−0.131270
$782$	25.9918	0.929466
$783$	−6.89640	−0.246457
$784$	27.6648	0.988029
$785$	66.0841	2.35864
$786$	−19.4230	−0.692796
$787$	38.8496	1.38484	0.692419	−	0.721496i	$-0.256545\pi$
$787$	38.8496	1.38484	0.692419	+	0.721496i	$0.256545\pi$
$788$	74.7484	2.66280
$789$	−14.3760	−0.511801
$790$	39.8813	1.41891
$791$	62.8443	2.23449
$792$	−1.16866	−0.0415264
$793$	4.21305	0.149610
$794$	−45.0772	−1.59973
$795$	−66.8435	−2.37070
$796$	−74.5759	−2.64327
$797$	−41.2954	−1.46276	−0.731379	−	0.681971i	$-0.761123\pi$
$797$	−41.2954	−1.46276	−0.731379	+	0.681971i	$0.761123\pi$
$798$	−56.8835	−2.01365
$799$	60.5036	2.14046
$800$	10.9999	0.388904
$801$	0.920563	0.0325265
$802$	31.4394	1.11016
$803$	8.32096	0.293640
$804$	−61.0721	−2.15385
$805$	−29.8209	−1.05105
$806$	24.2597	0.854511
$807$	−36.5587	−1.28693
$808$	36.2360	1.27478
$809$	−21.1867	−0.744885	−0.372442	−	0.928055i	$-0.621480\pi$
$809$	−21.1867	−0.744885	−0.372442	+	0.928055i	$0.621480\pi$
$810$	74.0373	2.60140
$811$	28.7013	1.00784	0.503919	−	0.863751i	$-0.331891\pi$
$811$	28.7013	1.00784	0.503919	+	0.863751i	$0.331891\pi$
$812$	22.6430	0.794612
$813$	−31.8372	−1.11658
$814$	−17.6233	−0.617697
$815$	−49.0755	−1.71904
$816$	21.9626	0.768843
$817$	−10.2472	−0.358506
$818$	22.6572	0.792191
$819$	1.51543	0.0529535
$820$	64.4797	2.25173
$821$	−8.37211	−0.292189	−0.146094	−	0.989271i	$-0.546670\pi$
$821$	−8.37211	−0.292189	−0.146094	+	0.989271i	$0.546670\pi$
$822$	−98.9405	−3.45095
$823$	23.2709	0.811173	0.405587	−	0.914057i	$-0.367067\pi$
$823$	23.2709	0.811173	0.405587	+	0.914057i	$0.367067\pi$
$824$	31.4104	1.09423
$825$	6.74727	0.234910
$826$	61.8650	2.15256
$827$	−7.43873	−0.258670	−0.129335	−	0.991601i	$-0.541284\pi$
$827$	−7.43873	−0.258670	−0.129335	+	0.991601i	$0.541284\pi$
$828$	−2.99852	−0.104206
$829$	12.7997	0.444553	0.222276	−	0.974984i	$-0.428651\pi$
$829$	12.7997	0.444553	0.222276	+	0.974984i	$0.428651\pi$
$830$	91.4573	3.17453
$831$	−10.9805	−0.380910
$832$	−10.6231	−0.368291
$833$	53.5105	1.85403
$834$	−4.52274	−0.156610
$835$	50.4834	1.74705
$836$	8.98089	0.310611
$837$	49.0589	1.69572
$838$	72.6231	2.50872
$839$	27.1097	0.935931	0.467966	−	0.883747i	$-0.344987\pi$
$839$	27.1097	0.935931	0.467966	+	0.883747i	$0.344987\pi$
$840$	−100.839	−3.47929
$841$	−26.9727	−0.930093
$842$	75.1626	2.59027
$843$	−30.5759	−1.05309
$844$	−38.2917	−1.31805
$845$	3.10935	0.106965
$846$	−10.7158	−0.368417
$847$	−44.1649	−1.51752
$848$	−29.2147	−1.00324
$849$	−27.6928	−0.950413
$850$	−53.8400	−1.84670
$851$	−21.0158	−0.720411
$852$	−31.8287	−1.09043
$853$	−12.6281	−0.432378	−0.216189	−	0.976352i	$-0.569363\pi$
$853$	−12.6281	−0.432378	−0.216189	+	0.976352i	$0.569363\pi$
$854$	−42.9452	−1.46955
$855$	3.37266	0.115342
$856$	−55.4975	−1.89687
$857$	0.928238	0.0317080	0.0158540	−	0.999874i	$-0.494953\pi$
$857$	0.928238	0.0317080	0.0158540	+	0.999874i	$0.494953\pi$
$858$	−3.46198	−0.118190
$859$	−14.8785	−0.507648	−0.253824	−	0.967250i	$-0.581688\pi$
$859$	−14.8785	−0.507648	−0.253824	+	0.967250i	$0.581688\pi$
$860$	−39.0853	−1.33280
$861$	43.2680	1.47457
$862$	5.77286	0.196624
$863$	17.4765	0.594908	0.297454	−	0.954736i	$-0.403863\pi$
$863$	17.4765	0.594908	0.297454	+	0.954736i	$0.403863\pi$
$864$	−11.4135	−0.388294
$865$	24.0307	0.817069
$866$	6.46556	0.219709
$867$	11.3376	0.385046
$868$	−161.075	−5.46725
$869$	−4.22519	−0.143330
$870$	−19.4256	−0.658590
$871$	−8.92148	−0.302293
$872$	−12.1693	−0.412103
$873$	0.00809018	0.000273811 0
$874$	16.4418	0.556153
$875$	−4.39285	−0.148505
$876$	72.1942	2.43921
$877$	−48.3870	−1.63391	−0.816956	−	0.576699i	$-0.804340\pi$
$877$	−48.3870	−1.63391	−0.816956	+	0.576699i	$0.804340\pi$
$878$	−18.9258	−0.638716
$879$	−10.7531	−0.362692
$880$	6.10765	0.205889
$881$	51.0043	1.71838	0.859189	−	0.511658i	$-0.170968\pi$
$881$	51.0043	1.71838	0.859189	+	0.511658i	$0.170968\pi$
$882$	−9.47725	−0.319116
$883$	25.9385	0.872900	0.436450	−	0.899728i	$-0.356236\pi$
$883$	25.9385	0.872900	0.436450	+	0.899728i	$0.356236\pi$
$884$	17.9940	0.605205
$885$	−34.5711	−1.16209
$886$	−96.6825	−3.24811
$887$	−23.7991	−0.799095	−0.399548	−	0.916712i	$-0.630833\pi$
$887$	−23.7991	−0.799095	−0.399548	+	0.916712i	$0.630833\pi$
$888$	−71.0648	−2.38478
$889$	35.3522	1.18568
$890$	−19.2532	−0.645370
$891$	−7.84381	−0.262778
$892$	−73.6371	−2.46555
$893$	38.2732	1.28076
$894$	−15.1928	−0.508123
$895$	15.1313	0.505783
$896$	88.2284	2.94750
$897$	−4.12841	−0.137844
$898$	75.3176	2.51338
$899$	−14.4215	−0.480985
$900$	6.21118	0.207039
$901$	−56.5084	−1.88257
$902$	−10.4875	−0.349197
$903$	−26.2275	−0.872796
$904$	−61.4242	−2.04294
$905$	26.6474	0.885791
$906$	7.38569	0.245373
$907$	44.0697	1.46331	0.731656	−	0.681675i	$-0.238748\pi$
$907$	44.0697	1.46331	0.731656	+	0.681675i	$0.238748\pi$
$908$	−57.3114	−1.90195
$909$	−3.10193	−0.102884
$910$	−31.6947	−1.05067
$911$	34.0894	1.12943	0.564716	−	0.825285i	$-0.308986\pi$
$911$	34.0894	1.12943	0.564716	+	0.825285i	$0.308986\pi$
$912$	13.8930	0.460044
$913$	−9.68936	−0.320671
$914$	4.56116	0.150870
$915$	23.9984	0.793363
$916$	88.4518	2.92253
$917$	18.8388	0.622113
$918$	55.8644	1.84380
$919$	35.3249	1.16526	0.582630	−	0.812737i	$-0.302024\pi$
$919$	35.3249	1.16526	0.582630	+	0.812737i	$0.302024\pi$
$920$	29.1470	0.960950
$921$	16.8417	0.554951
$922$	−11.5663	−0.380917
$923$	−4.64957	−0.153043
$924$	22.9863	0.756193
$925$	43.5324	1.43134
$926$	2.39514	0.0787093
$927$	−2.68884	−0.0883131
$928$	3.35515	0.110138
$929$	25.1128	0.823924	0.411962	−	0.911201i	$-0.364844\pi$
$929$	25.1128	0.823924	0.411962	+	0.911201i	$0.364844\pi$
$930$	138.188	4.53137
$931$	33.8495	1.10937
$932$	14.5671	0.477160
$933$	2.88987	0.0946101
$934$	2.51767	0.0823806
$935$	11.8137	0.386349
$936$	−1.48119	−0.0484141
$937$	−8.44686	−0.275947	−0.137973	−	0.990436i	$-0.544059\pi$
$937$	−8.44686	−0.275947	−0.137973	+	0.990436i	$0.544059\pi$
$938$	90.9398	2.96929
$939$	21.7133	0.708588
$940$	145.982	4.76142
$941$	−13.6606	−0.445322	−0.222661	−	0.974896i	$-0.571474\pi$
$941$	−13.6606	−0.445322	−0.222661	+	0.974896i	$0.571474\pi$
$942$	−93.2557	−3.03843
$943$	−12.5064	−0.407263
$944$	−15.1097	−0.491778
$945$	−64.0942	−2.08499
$946$	6.35716	0.206689
$947$	−36.4662	−1.18499	−0.592496	−	0.805573i	$-0.701858\pi$
$947$	−36.4662	−1.18499	−0.592496	+	0.805573i	$0.701858\pi$
$948$	−36.6585	−1.19061
$949$	10.5462	0.342344
$950$	−34.0579	−1.10499
$951$	−36.2513	−1.17553
$952$	−85.2479	−2.76290
$953$	−17.0183	−0.551275	−0.275638	−	0.961262i	$-0.588889\pi$
$953$	−17.0183	−0.551275	−0.275638	+	0.961262i	$0.588889\pi$
$954$	10.0082	0.324028
$955$	−17.3664	−0.561965
$956$	29.9357	0.968189
$957$	2.05803	0.0665267
$958$	38.6697	1.24936
$959$	95.9648	3.09886
$960$	−60.5116	−1.95300
$961$	71.5906	2.30937
$962$	−22.3363	−0.720150
$963$	4.75078	0.153092
$964$	−113.132	−3.64373
$965$	−62.0935	−1.99886
$966$	42.0823	1.35398
$967$	−14.7182	−0.473306	−0.236653	−	0.971594i	$-0.576050\pi$
$967$	−14.7182	−0.473306	−0.236653	+	0.971594i	$0.576050\pi$
$968$	43.1669	1.38744
$969$	26.8725	0.863269
$970$	−0.169203	−0.00543278
$971$	41.6307	1.33599	0.667996	−	0.744164i	$-0.267152\pi$
$971$	41.6307	1.33599	0.667996	+	0.744164i	$0.267152\pi$
$972$	−13.7574	−0.441270
$973$	4.38672	0.140632
$974$	−40.5846	−1.30041
$975$	8.55166	0.273872
$976$	10.4888	0.335737
$977$	54.1006	1.73083	0.865416	−	0.501054i	$-0.167054\pi$
$977$	54.1006	1.73083	0.865416	+	0.501054i	$0.167054\pi$
$978$	69.2537	2.21449
$979$	2.03977	0.0651912
$980$	129.110	4.12426
$981$	1.04173	0.0332599
$982$	−67.6349	−2.15832
$983$	−42.8598	−1.36701	−0.683507	−	0.729944i	$-0.739546\pi$
$983$	−42.8598	−1.36701	−0.683507	+	0.729944i	$0.739546\pi$
$984$	−42.2902	−1.34816
$985$	62.1987	1.98182
$986$	−16.4221	−0.522986
$987$	97.9589	3.11807
$988$	11.3826	0.362129
$989$	7.58090	0.241059
$990$	−2.09232	−0.0664984
$991$	19.2067	0.610120	0.305060	−	0.952333i	$-0.401324\pi$
$991$	19.2067	0.610120	0.305060	+	0.952333i	$0.401324\pi$
$992$	−23.8675	−0.757794
$993$	32.4894	1.03102
$994$	47.3948	1.50327
$995$	−62.0552	−1.96728
$996$	−84.0667	−2.66375
$997$	27.9567	0.885396	0.442698	−	0.896671i	$-0.354021\pi$
$997$	27.9567	0.885396	0.442698	+	0.896671i	$0.354021\pi$
$998$	45.2163	1.43130
$999$	−45.1693	−1.42909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.15	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.15	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.39514 q^{2} +1.83196 q^{3} +3.73671 q^{4} +3.10935 q^{5} -4.38781 q^{6} +4.25584 q^{7} -4.15967 q^{8} +0.356083 q^{9} +O(q^{10})\)	\(q-2.39514 q^{2} +1.83196 q^{3} +3.73671 q^{4} +3.10935 q^{5} -4.38781 q^{6} +4.25584 q^{7} -4.15967 q^{8} +0.356083 q^{9} -7.44733 q^{10} +0.789001 q^{11} +6.84551 q^{12} +1.00000 q^{13} -10.1934 q^{14} +5.69620 q^{15} +2.48959 q^{16} +4.81547 q^{17} -0.852869 q^{18} +3.04616 q^{19} +11.6187 q^{20} +7.79654 q^{21} -1.88977 q^{22} -2.25355 q^{23} -7.62036 q^{24} +4.66804 q^{25} -2.39514 q^{26} -4.84355 q^{27} +15.9029 q^{28} +1.42383 q^{29} -13.6432 q^{30} -10.1287 q^{31} +2.35642 q^{32} +1.44542 q^{33} -11.5338 q^{34} +13.2329 q^{35} +1.33058 q^{36} +9.32565 q^{37} -7.29599 q^{38} +1.83196 q^{39} -12.9339 q^{40} +5.54964 q^{41} -18.6738 q^{42} -3.36399 q^{43} +2.94827 q^{44} +1.10718 q^{45} +5.39756 q^{46} +12.5644 q^{47} +4.56083 q^{48} +11.1122 q^{49} -11.1806 q^{50} +8.82176 q^{51} +3.73671 q^{52} -11.7348 q^{53} +11.6010 q^{54} +2.45328 q^{55} -17.7029 q^{56} +5.58045 q^{57} -3.41028 q^{58} -6.06915 q^{59} +21.2851 q^{60} +4.21305 q^{61} +24.2597 q^{62} +1.51543 q^{63} -10.6231 q^{64} +3.10935 q^{65} -3.46198 q^{66} -8.92148 q^{67} +17.9940 q^{68} -4.12841 q^{69} -31.6947 q^{70} -4.64957 q^{71} -1.48119 q^{72} +10.5462 q^{73} -22.3363 q^{74} +8.55166 q^{75} +11.3826 q^{76} +3.35786 q^{77} -4.38781 q^{78} -5.35512 q^{79} +7.74099 q^{80} -9.94145 q^{81} -13.2922 q^{82} -12.2806 q^{83} +29.1334 q^{84} +14.9730 q^{85} +8.05724 q^{86} +2.60840 q^{87} -3.28198 q^{88} +2.58525 q^{89} -2.65186 q^{90} +4.25584 q^{91} -8.42085 q^{92} -18.5554 q^{93} -30.0936 q^{94} +9.47156 q^{95} +4.31688 q^{96} +0.0227200 q^{97} -26.6153 q^{98} +0.280949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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