LMFDB - Embedded newform 6019.2.a.e.1.20

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			1.20
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)

$f(q)$	$=$	$q-2.07170 q^{2} +0.913939 q^{3} +2.29195 q^{4} -0.284252 q^{5} -1.89341 q^{6} -4.46498 q^{7} -0.604826 q^{8} -2.16472 q^{9} +O(q^{10})$	\(q-2.07170 q^{2} +0.913939 q^{3} +2.29195 q^{4} -0.284252 q^{5} -1.89341 q^{6} -4.46498 q^{7} -0.604826 q^{8} -2.16472 q^{9} +0.588884 q^{10} +3.53098 q^{11} +2.09470 q^{12} +1.00000 q^{13} +9.25011 q^{14} -0.259789 q^{15} -3.33087 q^{16} +1.07403 q^{17} +4.48464 q^{18} +6.73810 q^{19} -0.651489 q^{20} -4.08072 q^{21} -7.31514 q^{22} -6.43947 q^{23} -0.552774 q^{24} -4.91920 q^{25} -2.07170 q^{26} -4.72023 q^{27} -10.2335 q^{28} +0.777240 q^{29} +0.538204 q^{30} +5.84561 q^{31} +8.11023 q^{32} +3.22710 q^{33} -2.22507 q^{34} +1.26918 q^{35} -4.96141 q^{36} -6.17332 q^{37} -13.9593 q^{38} +0.913939 q^{39} +0.171923 q^{40} +3.52418 q^{41} +8.45403 q^{42} +1.84769 q^{43} +8.09282 q^{44} +0.615324 q^{45} +13.3407 q^{46} -10.4841 q^{47} -3.04422 q^{48} +12.9360 q^{49} +10.1911 q^{50} +0.981599 q^{51} +2.29195 q^{52} +2.94644 q^{53} +9.77892 q^{54} -1.00369 q^{55} +2.70054 q^{56} +6.15821 q^{57} -1.61021 q^{58} -7.39568 q^{59} -0.595421 q^{60} +10.1787 q^{61} -12.1104 q^{62} +9.66541 q^{63} -10.1402 q^{64} -0.284252 q^{65} -6.68559 q^{66} -8.69623 q^{67} +2.46162 q^{68} -5.88528 q^{69} -2.62936 q^{70} +6.44132 q^{71} +1.30928 q^{72} -3.42553 q^{73} +12.7893 q^{74} -4.49585 q^{75} +15.4434 q^{76} -15.7658 q^{77} -1.89341 q^{78} +10.7379 q^{79} +0.946806 q^{80} +2.18014 q^{81} -7.30105 q^{82} -1.12261 q^{83} -9.35279 q^{84} -0.305295 q^{85} -3.82787 q^{86} +0.710350 q^{87} -2.13563 q^{88} -14.1946 q^{89} -1.27477 q^{90} -4.46498 q^{91} -14.7589 q^{92} +5.34253 q^{93} +21.7200 q^{94} -1.91532 q^{95} +7.41225 q^{96} -12.6939 q^{97} -26.7996 q^{98} -7.64357 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.07170	−1.46491	−0.732457	−	0.680813i	$-0.761627\pi$
$2$	−2.07170	−1.46491	−0.732457	+	0.680813i	$0.761627\pi$
$3$	0.913939	0.527663	0.263831	−	0.964569i	$-0.415014\pi$
$3$	0.913939	0.527663	0.263831	+	0.964569i	$0.415014\pi$
$4$	2.29195	1.14597
$5$	−0.284252	−0.127121	−0.0635606	−	0.997978i	$-0.520246\pi$
$5$	−0.284252	−0.127121	−0.0635606	+	0.997978i	$0.520246\pi$
$6$	−1.89341	−0.772981
$7$	−4.46498	−1.68760	−0.843802	−	0.536655i	$-0.819688\pi$
$7$	−4.46498	−1.68760	−0.843802	+	0.536655i	$0.819688\pi$
$8$	−0.604826	−0.213838
$9$	−2.16472	−0.721572
$10$	0.588884	0.186222
$11$	3.53098	1.06463	0.532316	−	0.846546i	$-0.321322\pi$
$11$	3.53098	1.06463	0.532316	+	0.846546i	$0.321322\pi$
$12$	2.09470	0.604687
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	9.25011	2.47219
$15$	−0.259789	−0.0670771
$16$	−3.33087	−0.832719
$17$	1.07403	0.260491	0.130245	−	0.991482i	$-0.458423\pi$
$17$	1.07403	0.260491	0.130245	+	0.991482i	$0.458423\pi$
$18$	4.48464	1.05704
$19$	6.73810	1.54583	0.772913	−	0.634512i	$-0.218799\pi$
$19$	6.73810	1.54583	0.772913	+	0.634512i	$0.218799\pi$
$20$	−0.651489	−0.145677
$21$	−4.08072	−0.890486
$22$	−7.31514	−1.55959
$23$	−6.43947	−1.34272	−0.671361	−	0.741131i	$-0.734290\pi$
$23$	−6.43947	−1.34272	−0.671361	+	0.741131i	$0.734290\pi$
$24$	−0.552774	−0.112834
$25$	−4.91920	−0.983840
$26$	−2.07170	−0.406294
$27$	−4.72023	−0.908410
$28$	−10.2335	−1.93395
$29$	0.777240	0.144330	0.0721649	−	0.997393i	$-0.477009\pi$
$29$	0.777240	0.144330	0.0721649	+	0.997393i	$0.477009\pi$
$30$	0.538204	0.0982622
$31$	5.84561	1.04990	0.524951	−	0.851132i	$-0.324084\pi$
$31$	5.84561	1.04990	0.524951	+	0.851132i	$0.324084\pi$
$32$	8.11023	1.43370
$33$	3.22710	0.561766
$34$	−2.22507	−0.381597
$35$	1.26918	0.214530
$36$	−4.96141	−0.826902
$37$	−6.17332	−1.01489	−0.507444	−	0.861685i	$-0.669410\pi$
$37$	−6.17332	−1.01489	−0.507444	+	0.861685i	$0.669410\pi$
$38$	−13.9593	−2.26450
$39$	0.913939	0.146347
$40$	0.171923	0.0271834
$41$	3.52418	0.550385	0.275192	−	0.961389i	$-0.411258\pi$
$41$	3.52418	0.550385	0.275192	+	0.961389i	$0.411258\pi$
$42$	8.45403	1.30449
$43$	1.84769	0.281770	0.140885	−	0.990026i	$-0.455005\pi$
$43$	1.84769	0.281770	0.140885	+	0.990026i	$0.455005\pi$
$44$	8.09282	1.22004
$45$	0.615324	0.0917271
$46$	13.3407	1.96697
$47$	−10.4841	−1.52927	−0.764634	−	0.644464i	$-0.777080\pi$
$47$	−10.4841	−1.52927	−0.764634	+	0.644464i	$0.777080\pi$
$48$	−3.04422	−0.439395
$49$	12.9360	1.84801
$50$	10.1911	1.44124
$51$	0.981599	0.137451
$52$	2.29195	0.317836
$53$	2.94644	0.404724	0.202362	−	0.979311i	$-0.435138\pi$
$53$	2.94644	0.404724	0.202362	+	0.979311i	$0.435138\pi$
$54$	9.77892	1.33074
$55$	−1.00369	−0.135337
$56$	2.70054	0.360874
$57$	6.15821	0.815675
$58$	−1.61021	−0.211431
$59$	−7.39568	−0.962836	−0.481418	−	0.876491i	$-0.659878\pi$
$59$	−7.39568	−0.962836	−0.481418	+	0.876491i	$0.659878\pi$
$60$	−0.595421	−0.0768686
$61$	10.1787	1.30325	0.651625	−	0.758541i	$-0.274088\pi$
$61$	10.1787	1.30325	0.651625	+	0.758541i	$0.274088\pi$
$62$	−12.1104	−1.53802
$63$	9.66541	1.21773
$64$	−10.1402	−1.26753
$65$	−0.284252	−0.0352571
$66$	−6.68559	−0.822939
$67$	−8.69623	−1.06241	−0.531207	−	0.847242i	$-0.678261\pi$
$67$	−8.69623	−1.06241	−0.531207	+	0.847242i	$0.678261\pi$
$68$	2.46162	0.298516
$69$	−5.88528	−0.708504
$70$	−2.62936	−0.314268
$71$	6.44132	0.764444	0.382222	−	0.924071i	$-0.375159\pi$
$71$	6.44132	0.764444	0.382222	+	0.924071i	$0.375159\pi$
$72$	1.30928	0.154300
$73$	−3.42553	−0.400928	−0.200464	−	0.979701i	$-0.564245\pi$
$73$	−3.42553	−0.400928	−0.200464	+	0.979701i	$0.564245\pi$
$74$	12.7893	1.48672
$75$	−4.49585	−0.519136
$76$	15.4434	1.77148
$77$	−15.7658	−1.79668
$78$	−1.89341	−0.214386
$79$	10.7379	1.20811	0.604054	−	0.796943i	$-0.293551\pi$
$79$	10.7379	1.20811	0.604054	+	0.796943i	$0.293551\pi$
$80$	0.946806	0.105856
$81$	2.18014	0.242238
$82$	−7.30105	−0.806267
$83$	−1.12261	−0.123223	−0.0616114	−	0.998100i	$-0.519624\pi$
$83$	−1.12261	−0.123223	−0.0616114	+	0.998100i	$0.519624\pi$
$84$	−9.35279	−1.02047
$85$	−0.305295	−0.0331139
$86$	−3.82787	−0.412769
$87$	0.710350	0.0761575
$88$	−2.13563	−0.227659
$89$	−14.1946	−1.50462	−0.752310	−	0.658809i	$-0.771061\pi$
$89$	−14.1946	−1.50462	−0.752310	+	0.658809i	$0.771061\pi$
$90$	−1.27477	−0.134372
$91$	−4.46498	−0.468057
$92$	−14.7589	−1.53872
$93$	5.34253	0.553994
$94$	21.7200	2.24025
$95$	−1.91532	−0.196507
$96$	7.41225	0.756510
$97$	−12.6939	−1.28887	−0.644437	−	0.764657i	$-0.722908\pi$
$97$	−12.6939	−1.28887	−0.644437	+	0.764657i	$0.722908\pi$
$98$	−26.7996	−2.70717
$99$	−7.64357	−0.768208
$100$	−11.2745	−1.12745
$101$	17.6419	1.75544	0.877718	−	0.479177i	$-0.159065\pi$
$101$	17.6419	1.75544	0.877718	+	0.479177i	$0.159065\pi$
$102$	−2.03358	−0.201354
$103$	−9.53014	−0.939032	−0.469516	−	0.882924i	$-0.655572\pi$
$103$	−9.53014	−0.939032	−0.469516	+	0.882924i	$0.655572\pi$
$104$	−0.604826	−0.0593081
$105$	1.15995	0.113200
$106$	−6.10414	−0.592887
$107$	6.38500	0.617261	0.308630	−	0.951182i	$-0.400129\pi$
$107$	6.38500	0.617261	0.308630	+	0.951182i	$0.400129\pi$
$108$	−10.8185	−1.04101
$109$	10.2108	0.978017	0.489008	−	0.872279i	$-0.337359\pi$
$109$	10.2108	0.978017	0.489008	+	0.872279i	$0.337359\pi$
$110$	2.07934	0.198257
$111$	−5.64204	−0.535519
$112$	14.8723	1.40530
$113$	−16.2676	−1.53033	−0.765164	−	0.643836i	$-0.777342\pi$
$113$	−16.2676	−1.53033	−0.765164	+	0.643836i	$0.777342\pi$
$114$	−12.7580	−1.19489
$115$	1.83043	0.170688
$116$	1.78139	0.165398
$117$	−2.16472	−0.200128
$118$	15.3216	1.41047
$119$	−4.79553	−0.439605
$120$	0.157127	0.0143437
$121$	1.46784	0.133440
$122$	−21.0872	−1.90915
$123$	3.22089	0.290418
$124$	13.3978	1.20316
$125$	2.81955	0.252188
$126$	−20.0238	−1.78387
$127$	−13.2716	−1.17766	−0.588831	−	0.808256i	$-0.700412\pi$
$127$	−13.2716	−1.17766	−0.588831	+	0.808256i	$0.700412\pi$
$128$	4.78706	0.423120
$129$	1.68868	0.148680
$130$	0.588884	0.0516486
$131$	−3.76458	−0.328913	−0.164456	−	0.986384i	$-0.552587\pi$
$131$	−3.76458	−0.328913	−0.164456	+	0.986384i	$0.552587\pi$
$132$	7.39635	0.643769
$133$	−30.0855	−2.60874
$134$	18.0160	1.55634
$135$	1.34173	0.115478
$136$	−0.649602	−0.0557029
$137$	2.46956	0.210989	0.105494	−	0.994420i	$-0.466357\pi$
$137$	2.46956	0.210989	0.105494	+	0.994420i	$0.466357\pi$
$138$	12.1925	1.03790
$139$	−6.18157	−0.524314	−0.262157	−	0.965025i	$-0.584434\pi$
$139$	−6.18157	−0.524314	−0.262157	+	0.965025i	$0.584434\pi$
$140$	2.90889	0.245846
$141$	−9.58186	−0.806938
$142$	−13.3445	−1.11984
$143$	3.53098	0.295276
$144$	7.21040	0.600866
$145$	−0.220932	−0.0183474
$146$	7.09668	0.587326
$147$	11.8228	0.975125
$148$	−14.1489	−1.16303
$149$	−21.1806	−1.73518	−0.867590	−	0.497280i	$-0.834332\pi$
$149$	−21.1806	−1.73518	−0.867590	+	0.497280i	$0.834332\pi$
$150$	9.31406	0.760490
$151$	−8.24458	−0.670934	−0.335467	−	0.942052i	$-0.608894\pi$
$151$	−8.24458	−0.670934	−0.335467	+	0.942052i	$0.608894\pi$
$152$	−4.07538	−0.330557
$153$	−2.32497	−0.187963
$154$	32.6620	2.63198
$155$	−1.66162	−0.133465
$156$	2.09470	0.167710
$157$	23.7193	1.89301	0.946503	−	0.322695i	$-0.104589\pi$
$157$	23.7193	1.89301	0.946503	+	0.322695i	$0.104589\pi$
$158$	−22.2457	−1.76978
$159$	2.69286	0.213558
$160$	−2.30535	−0.182254
$161$	28.7521	2.26598
$162$	−4.51660	−0.354858
$163$	11.4632	0.897867	0.448933	−	0.893565i	$-0.351804\pi$
$163$	11.4632	0.897867	0.448933	+	0.893565i	$0.351804\pi$
$164$	8.07724	0.630726
$165$	−0.917309	−0.0714124
$166$	2.32572	0.180511
$167$	6.11199	0.472960	0.236480	−	0.971636i	$-0.424006\pi$
$167$	6.11199	0.472960	0.236480	+	0.971636i	$0.424006\pi$
$168$	2.46812	0.190420
$169$	1.00000	0.0769231
$170$	0.632480	0.0485090
$171$	−14.5861	−1.11543
$172$	4.23481	0.322901
$173$	21.9508	1.66889	0.834443	−	0.551094i	$-0.185789\pi$
$173$	21.9508	1.66889	0.834443	+	0.551094i	$0.185789\pi$
$174$	−1.47163	−0.111564
$175$	21.9641	1.66033
$176$	−11.7613	−0.886538
$177$	−6.75920	−0.508053
$178$	29.4069	2.20414
$179$	10.8462	0.810680	0.405340	−	0.914166i	$-0.367153\pi$
$179$	10.8462	0.810680	0.405340	+	0.914166i	$0.367153\pi$
$180$	1.41029	0.105117
$181$	22.3437	1.66080	0.830398	−	0.557170i	$-0.188113\pi$
$181$	22.3437	1.66080	0.830398	+	0.557170i	$0.188113\pi$
$182$	9.25011	0.685663
$183$	9.30272	0.687677
$184$	3.89476	0.287125
$185$	1.75478	0.129014
$186$	−11.0681	−0.811554
$187$	3.79239	0.277327
$188$	−24.0291	−1.75250
$189$	21.0758	1.53304
$190$	3.96796	0.287866
$191$	−1.40549	−0.101698	−0.0508488	−	0.998706i	$-0.516193\pi$
$191$	−1.40549	−0.101698	−0.0508488	+	0.998706i	$0.516193\pi$
$192$	−9.26754	−0.668827
$193$	12.5243	0.901516	0.450758	−	0.892646i	$-0.351154\pi$
$193$	12.5243	0.901516	0.450758	+	0.892646i	$0.351154\pi$
$194$	26.2981	1.88809
$195$	−0.259789	−0.0186038
$196$	29.6487	2.11777
$197$	−2.55738	−0.182206	−0.0911029	−	0.995841i	$-0.529039\pi$
$197$	−2.55738	−0.182206	−0.0911029	+	0.995841i	$0.529039\pi$
$198$	15.8352	1.12536
$199$	−1.45499	−0.103142	−0.0515708	−	0.998669i	$-0.516423\pi$
$199$	−1.45499	−0.103142	−0.0515708	+	0.998669i	$0.516423\pi$
$200$	2.97526	0.210383
$201$	−7.94782	−0.560596
$202$	−36.5488	−2.57156
$203$	−3.47036	−0.243571
$204$	2.24977	0.157516
$205$	−1.00175	−0.0699656
$206$	19.7436	1.37560
$207$	13.9396	0.968870
$208$	−3.33087	−0.230955
$209$	23.7921	1.64574
$210$	−2.40307	−0.165828
$211$	0.256121	0.0176321	0.00881605	−	0.999961i	$-0.497194\pi$
$211$	0.256121	0.0176321	0.00881605	+	0.999961i	$0.497194\pi$
$212$	6.75308	0.463803
$213$	5.88697	0.403369
$214$	−13.2278	−0.904234
$215$	−0.525209	−0.0358190
$216$	2.85492	0.194253
$217$	−26.1005	−1.77182
$218$	−21.1537	−1.43271
$219$	−3.13073	−0.211555
$220$	−2.30040	−0.155093
$221$	1.07403	0.0722472
$222$	11.6886	0.784489
$223$	17.0429	1.14128	0.570639	−	0.821201i	$-0.306696\pi$
$223$	17.0429	1.14128	0.570639	+	0.821201i	$0.306696\pi$
$224$	−36.2120	−2.41952
$225$	10.6487	0.709911
$226$	33.7016	2.24180
$227$	17.8552	1.18509	0.592546	−	0.805536i	$-0.298123\pi$
$227$	17.8552	1.18509	0.592546	+	0.805536i	$0.298123\pi$
$228$	14.1143	0.934742
$229$	12.8072	0.846323	0.423161	−	0.906054i	$-0.360920\pi$
$229$	12.8072	0.846323	0.423161	+	0.906054i	$0.360920\pi$
$230$	−3.79210	−0.250044
$231$	−14.4089	−0.948039
$232$	−0.470095	−0.0308632
$233$	6.08901	0.398904	0.199452	−	0.979908i	$-0.436084\pi$
$233$	6.08901	0.398904	0.199452	+	0.979908i	$0.436084\pi$
$234$	4.48464	0.293170
$235$	2.98013	0.194402
$236$	−16.9505	−1.10338
$237$	9.81379	0.637474
$238$	9.93491	0.643984
$239$	16.0036	1.03519	0.517593	−	0.855627i	$-0.326828\pi$
$239$	16.0036	1.03519	0.517593	+	0.855627i	$0.326828\pi$
$240$	0.865323	0.0558564
$241$	−24.5657	−1.58242	−0.791208	−	0.611547i	$-0.790548\pi$
$241$	−24.5657	−1.58242	−0.791208	+	0.611547i	$0.790548\pi$
$242$	−3.04092	−0.195478
$243$	16.1532	1.03623
$244$	23.3291	1.49349
$245$	−3.67709	−0.234921
$246$	−6.67272	−0.425437
$247$	6.73810	0.428735
$248$	−3.53557	−0.224509
$249$	−1.02600	−0.0650201
$250$	−5.84126	−0.369434
$251$	17.3392	1.09444	0.547221	−	0.836988i	$-0.315686\pi$
$251$	17.3392	1.09444	0.547221	+	0.836988i	$0.315686\pi$
$252$	22.1526	1.39548
$253$	−22.7376	−1.42950
$254$	27.4947	1.72517
$255$	−0.279021	−0.0174730
$256$	10.3631	0.647693
$257$	−17.0072	−1.06088	−0.530439	−	0.847723i	$-0.677973\pi$
$257$	−17.0072	−1.06088	−0.530439	+	0.847723i	$0.677973\pi$
$258$	−3.49844	−0.217803
$259$	27.5638	1.71273
$260$	−0.651489	−0.0404037
$261$	−1.68250	−0.104144
$262$	7.79908	0.481829
$263$	24.5858	1.51602	0.758012	−	0.652241i	$-0.226171\pi$
$263$	24.5858	1.51602	0.758012	+	0.652241i	$0.226171\pi$
$264$	−1.95183	−0.120127
$265$	−0.837530	−0.0514490
$266$	62.3282	3.82158
$267$	−12.9730	−0.793932
$268$	−19.9313	−1.21750
$269$	−30.9865	−1.88928	−0.944641	−	0.328105i	$-0.893590\pi$
$269$	−30.9865	−1.88928	−0.944641	+	0.328105i	$0.893590\pi$
$270$	−2.77967	−0.169165
$271$	−26.5313	−1.61166	−0.805831	−	0.592146i	$-0.798281\pi$
$271$	−26.5313	−1.61166	−0.805831	+	0.592146i	$0.798281\pi$
$272$	−3.57746	−0.216916
$273$	−4.08072	−0.246976
$274$	−5.11620	−0.309081
$275$	−17.3696	−1.04743
$276$	−13.4887	−0.811927
$277$	−0.191560	−0.0115097	−0.00575485	−	0.999983i	$-0.501832\pi$
$277$	−0.191560	−0.0115097	−0.00575485	+	0.999983i	$0.501832\pi$
$278$	12.8064	0.768075
$279$	−12.6541	−0.757580
$280$	−0.767631	−0.0458748
$281$	−1.00425	−0.0599087	−0.0299544	−	0.999551i	$-0.509536\pi$
$281$	−1.00425	−0.0599087	−0.0299544	+	0.999551i	$0.509536\pi$
$282$	19.8508	1.18210
$283$	−12.7607	−0.758542	−0.379271	−	0.925286i	$-0.623825\pi$
$283$	−12.7607	−0.758542	−0.379271	+	0.925286i	$0.623825\pi$
$284$	14.7632	0.876032
$285$	−1.75048	−0.103690
$286$	−7.31514	−0.432553
$287$	−15.7354	−0.928832
$288$	−17.5563	−1.03452
$289$	−15.8465	−0.932144
$290$	0.457704	0.0268773
$291$	−11.6015	−0.680091
$292$	−7.85114	−0.459453
$293$	−5.75967	−0.336484	−0.168242	−	0.985746i	$-0.553809\pi$
$293$	−5.75967	−0.336484	−0.168242	+	0.985746i	$0.553809\pi$
$294$	−24.4932	−1.42847
$295$	2.10223	0.122397
$296$	3.73379	0.217022
$297$	−16.6671	−0.967121
$298$	43.8798	2.54189
$299$	−6.43947	−0.372404
$300$	−10.3042	−0.594916
$301$	−8.24991	−0.475517
$302$	17.0803	0.982861
$303$	16.1236	0.926279
$304$	−22.4438	−1.28724
$305$	−2.89331	−0.165671
$306$	4.81665	0.275350
$307$	32.7858	1.87118	0.935591	−	0.353086i	$-0.114868\pi$
$307$	32.7858	1.87118	0.935591	+	0.353086i	$0.114868\pi$
$308$	−36.1343	−2.05894
$309$	−8.70996	−0.495493
$310$	3.44239	0.195514
$311$	27.4035	1.55391	0.776954	−	0.629557i	$-0.216764\pi$
$311$	27.4035	1.55391	0.776954	+	0.629557i	$0.216764\pi$
$312$	−0.552774	−0.0312947
$313$	8.43636	0.476851	0.238426	−	0.971161i	$-0.423369\pi$
$313$	8.43636	0.476851	0.238426	+	0.971161i	$0.423369\pi$
$314$	−49.1393	−2.77309
$315$	−2.74741	−0.154799
$316$	24.6107	1.38446
$317$	−22.6648	−1.27298	−0.636490	−	0.771285i	$-0.719614\pi$
$317$	−22.6648	−1.27298	−0.636490	+	0.771285i	$0.719614\pi$
$318$	−5.57881	−0.312844
$319$	2.74442	0.153658
$320$	2.88237	0.161130
$321$	5.83550	0.325706
$322$	−59.5657	−3.31947
$323$	7.23693	0.402674
$324$	4.99677	0.277598
$325$	−4.91920	−0.272868
$326$	−23.7483	−1.31530
$327$	9.33204	0.516063
$328$	−2.13152	−0.117693
$329$	46.8115	2.58080
$330$	1.90039	0.104613
$331$	−26.1936	−1.43973	−0.719866	−	0.694113i	$-0.755797\pi$
$331$	−26.1936	−1.43973	−0.719866	+	0.694113i	$0.755797\pi$
$332$	−2.57297	−0.141210
$333$	13.3635	0.732315
$334$	−12.6622	−0.692846
$335$	2.47192	0.135055
$336$	13.5924	0.741524
$337$	22.6978	1.23643	0.618214	−	0.786010i	$-0.287857\pi$
$337$	22.6978	1.23643	0.618214	+	0.786010i	$0.287857\pi$
$338$	−2.07170	−0.112686
$339$	−14.8676	−0.807497
$340$	−0.699720	−0.0379477
$341$	20.6407	1.11776
$342$	30.2180	1.63400
$343$	−26.5043	−1.43110
$344$	−1.11753	−0.0602533
$345$	1.67290	0.0900659
$346$	−45.4754	−2.44477
$347$	16.5838	0.890267	0.445133	−	0.895464i	$-0.353156\pi$
$347$	16.5838	0.890267	0.445133	+	0.895464i	$0.353156\pi$
$348$	1.62808	0.0872744
$349$	29.9755	1.60455	0.802276	−	0.596954i	$-0.203622\pi$
$349$	29.9755	1.60455	0.802276	+	0.596954i	$0.203622\pi$
$350$	−45.5031	−2.43224
$351$	−4.72023	−0.251947
$352$	28.6371	1.52636
$353$	32.7084	1.74089	0.870446	−	0.492264i	$-0.163830\pi$
$353$	32.7084	1.74089	0.870446	+	0.492264i	$0.163830\pi$
$354$	14.0030	0.744253
$355$	−1.83096	−0.0971770
$356$	−32.5332	−1.72426
$357$	−4.38282	−0.231963
$358$	−22.4700	−1.18758
$359$	22.9101	1.20915	0.604574	−	0.796549i	$-0.293344\pi$
$359$	22.9101	1.20915	0.604574	+	0.796549i	$0.293344\pi$
$360$	−0.372164	−0.0196148
$361$	26.4020	1.38958
$362$	−46.2895	−2.43292
$363$	1.34151	0.0704112
$364$	−10.2335	−0.536381
$365$	0.973713	0.0509665
$366$	−19.2725	−1.00739
$367$	−27.9698	−1.46001	−0.730007	−	0.683440i	$-0.760483\pi$
$367$	−27.9698	−1.46001	−0.730007	+	0.683440i	$0.760483\pi$
$368$	21.4491	1.11811
$369$	−7.62885	−0.397142
$370$	−3.63537	−0.188994
$371$	−13.1558	−0.683015
$372$	12.2448	0.634863
$373$	17.8407	0.923756	0.461878	−	0.886943i	$-0.347176\pi$
$373$	17.8407	0.923756	0.461878	+	0.886943i	$0.347176\pi$
$374$	−7.85669	−0.406260
$375$	2.57689	0.133070
$376$	6.34108	0.327016
$377$	0.777240	0.0400299
$378$	−43.6627	−2.24577
$379$	4.76806	0.244919	0.122460	−	0.992474i	$-0.460922\pi$
$379$	4.76806	0.244919	0.122460	+	0.992474i	$0.460922\pi$
$380$	−4.38980	−0.225192
$381$	−12.1294	−0.621408
$382$	2.91175	0.148978
$383$	27.7751	1.41924	0.709621	−	0.704584i	$-0.248866\pi$
$383$	27.7751	1.41924	0.709621	+	0.704584i	$0.248866\pi$
$384$	4.37508	0.223265
$385$	4.48144	0.228396
$386$	−25.9465	−1.32064
$387$	−3.99973	−0.203318
$388$	−29.0938	−1.47702
$389$	26.1885	1.32781	0.663904	−	0.747818i	$-0.268898\pi$
$389$	26.1885	1.32781	0.663904	+	0.747818i	$0.268898\pi$
$390$	0.538204	0.0272530
$391$	−6.91619	−0.349767
$392$	−7.82406	−0.395175
$393$	−3.44059	−0.173555
$394$	5.29813	0.266916
$395$	−3.05227	−0.153576
$396$	−17.5187	−0.880346
$397$	−11.9920	−0.601862	−0.300931	−	0.953646i	$-0.597297\pi$
$397$	−11.9920	−0.601862	−0.300931	+	0.953646i	$0.597297\pi$
$398$	3.01431	0.151094
$399$	−27.4963	−1.37654
$400$	16.3852	0.819262
$401$	4.14102	0.206793	0.103396	−	0.994640i	$-0.467029\pi$
$401$	4.14102	0.206793	0.103396	+	0.994640i	$0.467029\pi$
$402$	16.4655	0.821225
$403$	5.84561	0.291190
$404$	40.4343	2.01168
$405$	−0.619709	−0.0307936
$406$	7.18955	0.356811
$407$	−21.7979	−1.08048
$408$	−0.593697	−0.0293924
$409$	−7.56418	−0.374025	−0.187012	−	0.982358i	$-0.559880\pi$
$409$	−7.56418	−0.374025	−0.187012	+	0.982358i	$0.559880\pi$
$410$	2.07534	0.102494
$411$	2.25703	0.111331
$412$	−21.8426	−1.07611
$413$	33.0216	1.62489
$414$	−28.8787	−1.41931
$415$	0.319104	0.0156642
$416$	8.11023	0.397637
$417$	−5.64958	−0.276661
$418$	−49.2902	−2.41086
$419$	5.39650	0.263636	0.131818	−	0.991274i	$-0.457918\pi$
$419$	5.39650	0.263636	0.131818	+	0.991274i	$0.457918\pi$
$420$	2.65855	0.129724
$421$	−39.6383	−1.93185	−0.965927	−	0.258813i	$-0.916669\pi$
$421$	−39.6383	−1.93185	−0.965927	+	0.258813i	$0.916669\pi$
$422$	−0.530606	−0.0258295
$423$	22.6952	1.10348
$424$	−1.78208	−0.0865456
$425$	−5.28338	−0.256281
$426$	−12.1960	−0.590900
$427$	−45.4477	−2.19937
$428$	14.6341	0.707364
$429$	3.22710	0.155806
$430$	1.08808	0.0524717
$431$	14.9352	0.719404	0.359702	−	0.933067i	$-0.382878\pi$
$431$	14.9352	0.719404	0.359702	+	0.933067i	$0.382878\pi$
$432$	15.7225	0.756450
$433$	−3.05234	−0.146686	−0.0733430	−	0.997307i	$-0.523367\pi$
$433$	−3.05234	−0.146686	−0.0733430	+	0.997307i	$0.523367\pi$
$434$	54.0725	2.59556
$435$	−0.201918	−0.00968123
$436$	23.4026	1.12078
$437$	−43.3898	−2.07561
$438$	6.48593	0.309910
$439$	−9.44736	−0.450898	−0.225449	−	0.974255i	$-0.572385\pi$
$439$	−9.44736	−0.450898	−0.225449	+	0.974255i	$0.572385\pi$
$440$	0.607056	0.0289403
$441$	−28.0029	−1.33347
$442$	−2.22507	−0.105836
$443$	4.38569	0.208370	0.104185	−	0.994558i	$-0.466777\pi$
$443$	4.38569	0.208370	0.104185	+	0.994558i	$0.466777\pi$
$444$	−12.9313	−0.613690
$445$	4.03483	0.191269
$446$	−35.3078	−1.67187
$447$	−19.3578	−0.915590
$448$	45.2759	2.13908
$449$	2.55709	0.120677	0.0603384	−	0.998178i	$-0.480782\pi$
$449$	2.55709	0.120677	0.0603384	+	0.998178i	$0.480782\pi$
$450$	−22.0609	−1.03996
$451$	12.4438	0.585957
$452$	−37.2845	−1.75371
$453$	−7.53504	−0.354027
$454$	−36.9907	−1.73606
$455$	1.26918	0.0595000
$456$	−3.72465	−0.174423
$457$	−39.5496	−1.85005	−0.925026	−	0.379904i	$-0.875957\pi$
$457$	−39.5496	−1.85005	−0.925026	+	0.379904i	$0.875957\pi$
$458$	−26.5327	−1.23979
$459$	−5.06968	−0.236632
$460$	4.19524	0.195604
$461$	6.39386	0.297792	0.148896	−	0.988853i	$-0.452428\pi$
$461$	6.39386	0.297792	0.148896	+	0.988853i	$0.452428\pi$
$462$	29.8510	1.38880
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−2.58889	−0.120186
$465$	−1.51862	−0.0704244
$466$	−12.6146	−0.584360
$467$	−0.612171	−0.0283279	−0.0141639	−	0.999900i	$-0.504509\pi$
$467$	−0.612171	−0.0283279	−0.0141639	+	0.999900i	$0.504509\pi$
$468$	−4.96141	−0.229341
$469$	38.8285	1.79293
$470$	−6.17394	−0.284783
$471$	21.6780	0.998869
$472$	4.47310	0.205891
$473$	6.52417	0.299982
$474$	−20.3312	−0.933845
$475$	−33.1461	−1.52085
$476$	−10.9911	−0.503776
$477$	−6.37820	−0.292038
$478$	−33.1546	−1.51646
$479$	−6.98968	−0.319367	−0.159683	−	0.987168i	$-0.551047\pi$
$479$	−6.98968	−0.319367	−0.159683	+	0.987168i	$0.551047\pi$
$480$	−2.10694	−0.0961684
$481$	−6.17332	−0.281479
$482$	50.8928	2.31810
$483$	26.2777	1.19567
$484$	3.36420	0.152918
$485$	3.60827	0.163843
$486$	−33.4646	−1.51799
$487$	21.4104	0.970197	0.485099	−	0.874459i	$-0.338784\pi$
$487$	21.4104	0.970197	0.485099	+	0.874459i	$0.338784\pi$
$488$	−6.15635	−0.278685
$489$	10.4767	0.473771
$490$	7.61784	0.344139
$491$	1.34495	0.0606967	0.0303483	−	0.999539i	$-0.490338\pi$
$491$	1.34495	0.0606967	0.0303483	+	0.999539i	$0.490338\pi$
$492$	7.38210	0.332811
$493$	0.834780	0.0375966
$494$	−13.9593	−0.628060
$495$	2.17270	0.0976555
$496$	−19.4710	−0.874273
$497$	−28.7604	−1.29008
$498$	2.12556	0.0952488
$499$	17.9454	0.803346	0.401673	−	0.915783i	$-0.368429\pi$
$499$	17.9454	0.803346	0.401673	+	0.915783i	$0.368429\pi$
$500$	6.46225	0.289001
$501$	5.58598	0.249563
$502$	−35.9217	−1.60326
$503$	26.0991	1.16370	0.581851	−	0.813296i	$-0.302329\pi$
$503$	26.0991	1.16370	0.581851	+	0.813296i	$0.302329\pi$
$504$	−5.84589	−0.260397
$505$	−5.01474	−0.223153
$506$	47.1056	2.09410
$507$	0.913939	0.0405894
$508$	−30.4177	−1.34957
$509$	32.0592	1.42100	0.710499	−	0.703698i	$-0.248469\pi$
$509$	32.0592	1.42100	0.710499	+	0.703698i	$0.248469\pi$
$510$	0.578048	0.0255964
$511$	15.2949	0.676608
$512$	−31.0434	−1.37194
$513$	−31.8054	−1.40424
$514$	35.2338	1.55409
$515$	2.70896	0.119371
$516$	3.87036	0.170383
$517$	−37.0193	−1.62811
$518$	−57.1039	−2.50900
$519$	20.0617	0.880609
$520$	0.171923	0.00753931
$521$	28.5139	1.24922	0.624609	−	0.780938i	$-0.285258\pi$
$521$	28.5139	1.24922	0.624609	+	0.780938i	$0.285258\pi$
$522$	3.48564	0.152562
$523$	42.7656	1.87001	0.935006	−	0.354633i	$-0.115394\pi$
$523$	42.7656	1.87001	0.935006	+	0.354633i	$0.115394\pi$
$524$	−8.62821	−0.376925
$525$	20.0739	0.876096
$526$	−50.9344	−2.22084
$527$	6.27837	0.273490
$528$	−10.7491	−0.467793
$529$	18.4667	0.802901
$530$	1.73511	0.0753684
$531$	16.0095	0.694755
$532$	−68.9543	−2.98955
$533$	3.52418	0.152649
$534$	26.8761	1.16304
$535$	−1.81494	−0.0784669
$536$	5.25970	0.227185
$537$	9.91272	0.427765
$538$	64.1948	2.76764
$539$	45.6770	1.96745
$540$	3.07518	0.132335
$541$	17.2529	0.741759	0.370880	−	0.928681i	$-0.379056\pi$
$541$	17.2529	0.741759	0.370880	+	0.928681i	$0.379056\pi$
$542$	54.9649	2.36095
$543$	20.4208	0.876341
$544$	8.71064	0.373466
$545$	−2.90243	−0.124327
$546$	8.45403	0.361799
$547$	20.1376	0.861021	0.430511	−	0.902585i	$-0.358333\pi$
$547$	20.1376	0.861021	0.430511	+	0.902585i	$0.358333\pi$
$548$	5.66010	0.241788
$549$	−22.0340	−0.940389
$550$	35.9847	1.53439
$551$	5.23712	0.223109
$552$	3.55957	0.151505
$553$	−47.9445	−2.03881
$554$	0.396854	0.0168607
$555$	1.60376	0.0680758
$556$	−14.1678	−0.600850
$557$	25.2118	1.06826	0.534128	−	0.845403i	$-0.320640\pi$
$557$	25.2118	1.06826	0.534128	+	0.845403i	$0.320640\pi$
$558$	26.2155	1.10979
$559$	1.84769	0.0781491
$560$	−4.22747	−0.178643
$561$	3.46601	0.146335
$562$	2.08051	0.0877612
$563$	−20.0038	−0.843060	−0.421530	−	0.906815i	$-0.638507\pi$
$563$	−20.0038	−0.843060	−0.421530	+	0.906815i	$0.638507\pi$
$564$	−21.9611	−0.924730
$565$	4.62409	0.194537
$566$	26.4363	1.11120
$567$	−9.73429	−0.408802
$568$	−3.89588	−0.163467
$569$	11.0189	0.461938	0.230969	−	0.972961i	$-0.425810\pi$
$569$	11.0189	0.461938	0.230969	+	0.972961i	$0.425810\pi$
$570$	3.62648	0.151896
$571$	18.1839	0.760971	0.380486	−	0.924787i	$-0.375757\pi$
$571$	18.1839	0.760971	0.380486	+	0.924787i	$0.375757\pi$
$572$	8.09282	0.338378
$573$	−1.28453	−0.0536620
$574$	32.5991	1.36066
$575$	31.6770	1.32102
$576$	21.9507	0.914612
$577$	−29.1552	−1.21375	−0.606873	−	0.794798i	$-0.707577\pi$
$577$	−29.1552	−1.21375	−0.606873	+	0.794798i	$0.707577\pi$
$578$	32.8291	1.36551
$579$	11.4464	0.475697
$580$	−0.506363	−0.0210256
$581$	5.01244	0.207951
$582$	24.0348	0.996275
$583$	10.4038	0.430882
$584$	2.07185	0.0857338
$585$	0.615324	0.0254405
$586$	11.9323	0.492920
$587$	−38.2379	−1.57825	−0.789123	−	0.614235i	$-0.789465\pi$
$587$	−38.2379	−1.57825	−0.789123	+	0.614235i	$0.789465\pi$
$588$	27.0971	1.11747
$589$	39.3883	1.62297
$590$	−4.35520	−0.179301
$591$	−2.33729	−0.0961432
$592$	20.5626	0.845116
$593$	18.4462	0.757495	0.378747	−	0.925500i	$-0.376355\pi$
$593$	18.4462	0.757495	0.378747	+	0.925500i	$0.376355\pi$
$594$	34.5292	1.41675
$595$	1.36314	0.0558832
$596$	−48.5447	−1.98847
$597$	−1.32977	−0.0544240
$598$	13.3407	0.545540
$599$	4.72596	0.193097	0.0965486	−	0.995328i	$-0.469220\pi$
$599$	4.72596	0.193097	0.0965486	+	0.995328i	$0.469220\pi$
$600$	2.71921	0.111011
$601$	−29.4941	−1.20309	−0.601544	−	0.798840i	$-0.705448\pi$
$601$	−29.4941	−1.20309	−0.601544	+	0.798840i	$0.705448\pi$
$602$	17.0913	0.696591
$603$	18.8249	0.766608
$604$	−18.8961	−0.768872
$605$	−0.417235	−0.0169630
$606$	−33.4034	−1.35692
$607$	30.3048	1.23003	0.615017	−	0.788514i	$-0.289149\pi$
$607$	30.3048	1.23003	0.615017	+	0.788514i	$0.289149\pi$
$608$	54.6476	2.21625
$609$	−3.17170	−0.128524
$610$	5.99408	0.242693
$611$	−10.4841	−0.424143
$612$	−5.32871	−0.215400
$613$	−2.03596	−0.0822317	−0.0411158	−	0.999154i	$-0.513091\pi$
$613$	−2.03596	−0.0822317	−0.0411158	+	0.999154i	$0.513091\pi$
$614$	−67.9223	−2.74112
$615$	−0.915542	−0.0369182
$616$	9.53554	0.384198
$617$	21.5305	0.866786	0.433393	−	0.901205i	$-0.357316\pi$
$617$	21.5305	0.866786	0.433393	+	0.901205i	$0.357316\pi$
$618$	18.0444	0.725854
$619$	−41.4229	−1.66493	−0.832464	−	0.554080i	$-0.813070\pi$
$619$	−41.4229	−1.66493	−0.832464	+	0.554080i	$0.813070\pi$
$620$	−3.80835	−0.152947
$621$	30.3958	1.21974
$622$	−56.7718	−2.27634
$623$	63.3784	2.53920
$624$	−3.04422	−0.121866
$625$	23.7945	0.951782
$626$	−17.4776	−0.698546
$627$	21.7445	0.868393
$628$	54.3634	2.16933
$629$	−6.63034	−0.264369
$630$	5.69181	0.226767
$631$	0.448217	0.0178432	0.00892162	−	0.999960i	$-0.497160\pi$
$631$	0.448217	0.0178432	0.00892162	+	0.999960i	$0.497160\pi$
$632$	−6.49456	−0.258340
$633$	0.234079	0.00930380
$634$	46.9546	1.86481
$635$	3.77247	0.149706
$636$	6.17190	0.244732
$637$	12.9360	0.512545
$638$	−5.68562	−0.225096
$639$	−13.9436	−0.551601
$640$	−1.36073	−0.0537875
$641$	−21.5600	−0.851569	−0.425785	−	0.904825i	$-0.640002\pi$
$641$	−21.5600	−0.851569	−0.425785	+	0.904825i	$0.640002\pi$
$642$	−12.0894	−0.477131
$643$	27.8757	1.09931	0.549655	−	0.835391i	$-0.314759\pi$
$643$	27.8757	1.09931	0.549655	+	0.835391i	$0.314759\pi$
$644$	65.8983	2.59675
$645$	−0.480009	−0.0189003
$646$	−14.9928	−0.589883
$647$	13.6112	0.535113	0.267556	−	0.963542i	$-0.413784\pi$
$647$	13.6112	0.535113	0.267556	+	0.963542i	$0.413784\pi$
$648$	−1.31861	−0.0517997
$649$	−26.1140	−1.02506
$650$	10.1911	0.399728
$651$	−23.8543	−0.934923
$652$	26.2730	1.02893
$653$	21.0009	0.821828	0.410914	−	0.911674i	$-0.365210\pi$
$653$	21.0009	0.821828	0.410914	+	0.911674i	$0.365210\pi$
$654$	−19.3332	−0.755988
$655$	1.07009	0.0418117
$656$	−11.7386	−0.458316
$657$	7.41531	0.289299
$658$	−96.9794	−3.78065
$659$	−35.7159	−1.39129	−0.695646	−	0.718384i	$-0.744882\pi$
$659$	−35.7159	−1.39129	−0.695646	+	0.718384i	$0.744882\pi$
$660$	−2.10242	−0.0818367
$661$	36.8874	1.43475	0.717377	−	0.696685i	$-0.245343\pi$
$661$	36.8874	1.43475	0.717377	+	0.696685i	$0.245343\pi$
$662$	54.2654	2.10908
$663$	0.981599	0.0381222
$664$	0.678985	0.0263497
$665$	8.55185	0.331626
$666$	−27.6852	−1.07278
$667$	−5.00501	−0.193795
$668$	14.0084	0.541999
$669$	15.5762	0.602210
$670$	−5.12107	−0.197844
$671$	35.9408	1.38748
$672$	−33.0956	−1.27669
$673$	−11.2994	−0.435558	−0.217779	−	0.975998i	$-0.569881\pi$
$673$	−11.2994	−0.435558	−0.217779	+	0.975998i	$0.569881\pi$
$674$	−47.0231	−1.81126
$675$	23.2198	0.893730
$676$	2.29195	0.0881518
$677$	22.6318	0.869811	0.434906	−	0.900476i	$-0.356782\pi$
$677$	22.6318	0.869811	0.434906	+	0.900476i	$0.356782\pi$
$678$	30.8012	1.18291
$679$	56.6782	2.17511
$680$	0.184650	0.00708102
$681$	16.3186	0.625330
$682$	−42.7614	−1.63742
$683$	−12.0621	−0.461542	−0.230771	−	0.973008i	$-0.574125\pi$
$683$	−12.0621	−0.461542	−0.230771	+	0.973008i	$0.574125\pi$
$684$	−33.4305	−1.27825
$685$	−0.701977	−0.0268212
$686$	54.9091	2.09644
$687$	11.7050	0.446573
$688$	−6.15443	−0.234635
$689$	2.94644	0.112250
$690$	−3.46575	−0.131939
$691$	−11.0777	−0.421417	−0.210708	−	0.977549i	$-0.567577\pi$
$691$	−11.0777	−0.421417	−0.210708	+	0.977549i	$0.567577\pi$
$692$	50.3100	1.91250
$693$	34.1284	1.29643
$694$	−34.3568	−1.30416
$695$	1.75712	0.0666514
$696$	−0.429638	−0.0162854
$697$	3.78508	0.143370
$698$	−62.1003	−2.35053
$699$	5.56498	0.210487
$700$	50.3406	1.90270
$701$	26.5638	1.00330	0.501650	−	0.865071i	$-0.332727\pi$
$701$	26.5638	1.00330	0.501650	+	0.865071i	$0.332727\pi$
$702$	9.77892	0.369081
$703$	−41.5965	−1.56884
$704$	−35.8049	−1.34945
$705$	2.72366	0.102579
$706$	−67.7620	−2.55026
$707$	−78.7708	−2.96248
$708$	−15.4917	−0.582215
$709$	−24.7476	−0.929415	−0.464708	−	0.885464i	$-0.653841\pi$
$709$	−24.7476	−0.929415	−0.464708	+	0.885464i	$0.653841\pi$
$710$	3.79319	0.142356
$711$	−23.2445	−0.871737
$712$	8.58524	0.321745
$713$	−37.6426	−1.40973
$714$	9.07990	0.339807
$715$	−1.00369	−0.0375358
$716$	24.8588	0.929017
$717$	14.6263	0.546229
$718$	−47.4628	−1.77130
$719$	49.4613	1.84460	0.922298	−	0.386479i	$-0.126309\pi$
$719$	49.4613	1.84460	0.922298	+	0.386479i	$0.126309\pi$
$720$	−2.04957	−0.0763828
$721$	42.5519	1.58471
$722$	−54.6971	−2.03562
$723$	−22.4516	−0.834983
$724$	51.2106	1.90323
$725$	−3.82340	−0.141997
$726$	−2.77922	−0.103146
$727$	3.24233	0.120251	0.0601257	−	0.998191i	$-0.480850\pi$
$727$	3.24233	0.120251	0.0601257	+	0.998191i	$0.480850\pi$
$728$	2.70054	0.100089
$729$	8.22263	0.304542
$730$	−2.01724	−0.0746615
$731$	1.98448	0.0733986
$732$	21.3213	0.788059
$733$	29.7861	1.10018	0.550088	−	0.835107i	$-0.314594\pi$
$733$	29.7861	1.10018	0.550088	+	0.835107i	$0.314594\pi$
$734$	57.9451	2.13879
$735$	−3.36064	−0.123959
$736$	−52.2255	−1.92506
$737$	−30.7062	−1.13108
$738$	15.8047	0.581779
$739$	−10.6060	−0.390149	−0.195074	−	0.980788i	$-0.562495\pi$
$739$	−10.6060	−0.390149	−0.195074	+	0.980788i	$0.562495\pi$
$740$	4.02185	0.147846
$741$	6.15821	0.226228
$742$	27.2549	1.00056
$743$	−0.299308	−0.0109806	−0.00549028	−	0.999985i	$-0.501748\pi$
$743$	−0.299308	−0.0109806	−0.00549028	+	0.999985i	$0.501748\pi$
$744$	−3.23130	−0.118465
$745$	6.02061	0.220578
$746$	−36.9606	−1.35322
$747$	2.43014	0.0889141
$748$	8.69195	0.317809
$749$	−28.5089	−1.04169
$750$	−5.33856	−0.194937
$751$	−29.5152	−1.07703	−0.538513	−	0.842617i	$-0.681014\pi$
$751$	−29.5152	−1.07703	−0.538513	+	0.842617i	$0.681014\pi$
$752$	34.9213	1.27345
$753$	15.8470	0.577497
$754$	−1.61021	−0.0586403
$755$	2.34353	0.0852899
$756$	48.3045	1.75682
$757$	26.3529	0.957813	0.478907	−	0.877866i	$-0.341033\pi$
$757$	26.3529	0.957813	0.478907	+	0.877866i	$0.341033\pi$
$758$	−9.87801	−0.358785
$759$	−20.7808	−0.754296
$760$	1.15843	0.0420208
$761$	46.5705	1.68818	0.844090	−	0.536202i	$-0.180141\pi$
$761$	46.5705	1.68818	0.844090	+	0.536202i	$0.180141\pi$
$762$	25.1285	0.910310
$763$	−45.5910	−1.65050
$764$	−3.22130	−0.116543
$765$	0.660877	0.0238941
$766$	−57.5417	−2.07907
$767$	−7.39568	−0.267043
$768$	9.47124	0.341764
$769$	2.99990	0.108179	0.0540895	−	0.998536i	$-0.482774\pi$
$769$	2.99990	0.108179	0.0540895	+	0.998536i	$0.482774\pi$
$770$	−9.28421	−0.334580
$771$	−15.5435	−0.559786
$772$	28.7049	1.03311
$773$	0.0498684	0.00179364	0.000896821	−	1.00000i	$-0.499715\pi$
$773$	0.0498684	0.00179364	0.000896821		1.00000i	$0.499715\pi$
$774$	8.28624	0.297843
$775$	−28.7557	−1.03294
$776$	7.67762	0.275611
$777$	25.1916	0.903744
$778$	−54.2547	−1.94512
$779$	23.7463	0.850800
$780$	−0.595421	−0.0213195
$781$	22.7442	0.813851
$782$	14.3283	0.512378
$783$	−3.66875	−0.131111
$784$	−43.0884	−1.53887
$785$	−6.74225	−0.240641
$786$	7.12788	0.254243
$787$	−32.0371	−1.14200	−0.571000	−	0.820950i	$-0.693445\pi$
$787$	−32.0371	−1.14200	−0.571000	+	0.820950i	$0.693445\pi$
$788$	−5.86138	−0.208803
$789$	22.4699	0.799949
$790$	6.32338	0.224976
$791$	72.6345	2.58259
$792$	4.62303	0.164272
$793$	10.1787	0.361457
$794$	24.8439	0.881676
$795$	−0.765451	−0.0271477
$796$	−3.33476	−0.118198
$797$	39.6042	1.40285	0.701427	−	0.712742i	$-0.252547\pi$
$797$	39.6042	1.40285	0.701427	+	0.712742i	$0.252547\pi$
$798$	56.9641	2.01651
$799$	−11.2603	−0.398361
$800$	−39.8958	−1.41053
$801$	30.7272	1.08569
$802$	−8.57895	−0.302933
$803$	−12.0955	−0.426841
$804$	−18.2160	−0.642428
$805$	−8.17283	−0.288054
$806$	−12.1104	−0.426569
$807$	−28.3198	−0.996904
$808$	−10.6703	−0.375379
$809$	−4.00578	−0.140836	−0.0704179	−	0.997518i	$-0.522433\pi$
$809$	−4.00578	−0.140836	−0.0704179	+	0.997518i	$0.522433\pi$
$810$	1.28385	0.0451099
$811$	20.5576	0.721877	0.360938	−	0.932590i	$-0.382456\pi$
$811$	20.5576	0.721877	0.360938	+	0.932590i	$0.382456\pi$
$812$	−7.95388	−0.279126
$813$	−24.2480	−0.850414
$814$	45.1587	1.58281
$815$	−3.25843	−0.114138
$816$	−3.26958	−0.114458
$817$	12.4499	0.435568
$818$	15.6707	0.547914
$819$	9.66541	0.337737
$820$	−2.29597	−0.0801787
$821$	−26.8103	−0.935687	−0.467843	−	0.883811i	$-0.654969\pi$
$821$	−26.8103	−0.935687	−0.467843	+	0.883811i	$0.654969\pi$
$822$	−4.67589	−0.163090
$823$	27.2800	0.950921	0.475460	−	0.879737i	$-0.342281\pi$
$823$	27.2800	0.950921	0.475460	+	0.879737i	$0.342281\pi$
$824$	5.76407	0.200801
$825$	−15.8748	−0.552688
$826$	−68.4108	−2.38032
$827$	5.30470	0.184463	0.0922313	−	0.995738i	$-0.470600\pi$
$827$	5.30470	0.184463	0.0922313	+	0.995738i	$0.470600\pi$
$828$	31.9488	1.11030
$829$	29.9944	1.04175	0.520873	−	0.853634i	$-0.325606\pi$
$829$	29.9944	1.04175	0.520873	+	0.853634i	$0.325606\pi$
$830$	−0.661089	−0.0229467
$831$	−0.175074	−0.00607324
$832$	−10.1402	−0.351549
$833$	13.8937	0.481389
$834$	11.7042	0.405285
$835$	−1.73734	−0.0601232
$836$	54.5303	1.88597
$837$	−27.5926	−0.953741
$838$	−11.1799	−0.386205
$839$	−16.3282	−0.563712	−0.281856	−	0.959457i	$-0.590950\pi$
$839$	−16.3282	−0.563712	−0.281856	+	0.959457i	$0.590950\pi$
$840$	−0.701568	−0.0242064
$841$	−28.3959	−0.979169
$842$	82.1188	2.83000
$843$	−0.917826	−0.0316116
$844$	0.587016	0.0202059
$845$	−0.284252	−0.00977855
$846$	−47.0176	−1.61650
$847$	−6.55387	−0.225193
$848$	−9.81422	−0.337022
$849$	−11.6625	−0.400255
$850$	10.9456	0.375430
$851$	39.7529	1.36271
$852$	13.4926	0.462250
$853$	−2.27025	−0.0777320	−0.0388660	−	0.999244i	$-0.512375\pi$
$853$	−2.27025	−0.0777320	−0.0388660	+	0.999244i	$0.512375\pi$
$854$	94.1541	3.22189
$855$	4.14612	0.141794
$856$	−3.86181	−0.131994
$857$	48.1102	1.64341	0.821706	−	0.569911i	$-0.193022\pi$
$857$	48.1102	1.64341	0.821706	+	0.569911i	$0.193022\pi$
$858$	−6.68559	−0.228242
$859$	−35.7597	−1.22011	−0.610053	−	0.792361i	$-0.708852\pi$
$859$	−35.7597	−1.22011	−0.610053	+	0.792361i	$0.708852\pi$
$860$	−1.20375	−0.0410476
$861$	−14.3812	−0.490110
$862$	−30.9413	−1.05387
$863$	37.6709	1.28233	0.641166	−	0.767402i	$-0.278451\pi$
$863$	37.6709	1.28233	0.641166	+	0.767402i	$0.278451\pi$
$864$	−38.2822	−1.30239
$865$	−6.23954	−0.212151
$866$	6.32353	0.214882
$867$	−14.4827	−0.491858
$868$	−59.8210	−2.03046
$869$	37.9153	1.28619
$870$	0.418314	0.0141822
$871$	−8.69623	−0.294661
$872$	−6.17575	−0.209137
$873$	27.4788	0.930015
$874$	89.8907	3.04060
$875$	−12.5892	−0.425594
$876$	−7.17546	−0.242436
$877$	−2.35918	−0.0796638	−0.0398319	−	0.999206i	$-0.512682\pi$
$877$	−2.35918	−0.0796638	−0.0398319	+	0.999206i	$0.512682\pi$
$878$	19.5721	0.660527
$879$	−5.26399	−0.177550
$880$	3.34316	0.112698
$881$	33.9861	1.14502	0.572510	−	0.819898i	$-0.305970\pi$
$881$	33.9861	1.14502	0.572510	+	0.819898i	$0.305970\pi$
$882$	58.0136	1.95342
$883$	−38.1226	−1.28293	−0.641463	−	0.767154i	$-0.721672\pi$
$883$	−38.1226	−1.28293	−0.641463	+	0.767154i	$0.721672\pi$
$884$	2.46162	0.0827933
$885$	1.92131	0.0645842
$886$	−9.08584	−0.305245
$887$	−45.2649	−1.51985	−0.759923	−	0.650013i	$-0.774763\pi$
$887$	−45.2649	−1.51985	−0.759923	+	0.650013i	$0.774763\pi$
$888$	3.41245	0.114514
$889$	59.2573	1.98743
$890$	−8.35896	−0.280193
$891$	7.69804	0.257894
$892$	39.0614	1.30787
$893$	−70.6432	−2.36398
$894$	40.1035	1.34126
$895$	−3.08304	−0.103055
$896$	−21.3741	−0.714059
$897$	−5.88528	−0.196504
$898$	−5.29753	−0.176781
$899$	4.54344	0.151532
$900$	24.4062	0.813540
$901$	3.16457	0.105427
$902$	−25.7799	−0.858377
$903$	−7.53991	−0.250913
$904$	9.83907	0.327243
$905$	−6.35124	−0.211122
$906$	15.6103	0.518619
$907$	−11.4057	−0.378721	−0.189361	−	0.981908i	$-0.560642\pi$
$907$	−11.4057	−0.378721	−0.189361	+	0.981908i	$0.560642\pi$
$908$	40.9232	1.35808
$909$	−38.1897	−1.26667
$910$	−2.62936	−0.0871623
$911$	−50.9018	−1.68645	−0.843226	−	0.537559i	$-0.819347\pi$
$911$	−50.9018	−1.68645	−0.843226	+	0.537559i	$0.819347\pi$
$912$	−20.5122	−0.679228
$913$	−3.96393	−0.131187
$914$	81.9349	2.71017
$915$	−2.64431	−0.0874183
$916$	29.3534	0.969863
$917$	16.8088	0.555074
$918$	10.5029	0.346646
$919$	−11.6700	−0.384959	−0.192479	−	0.981301i	$-0.561653\pi$
$919$	−11.6700	−0.384959	−0.192479	+	0.981301i	$0.561653\pi$
$920$	−1.10709	−0.0364997
$921$	29.9642	0.987353
$922$	−13.2462	−0.436239
$923$	6.44132	0.212019
$924$	−33.0245	−1.08643
$925$	30.3678	0.998488
$926$	2.07170	0.0680803
$927$	20.6300	0.677579
$928$	6.30359	0.206926
$929$	−18.7769	−0.616049	−0.308025	−	0.951378i	$-0.599668\pi$
$929$	−18.7769	−0.616049	−0.308025	+	0.951378i	$0.599668\pi$
$930$	3.14613	0.103166
$931$	87.1644	2.85670
$932$	13.9557	0.457133
$933$	25.0451	0.819939
$934$	1.26823	0.0414979
$935$	−1.07799	−0.0352541
$936$	1.30928	0.0427950
$937$	12.3936	0.404881	0.202441	−	0.979295i	$-0.435113\pi$
$937$	12.3936	0.404881	0.202441	+	0.979295i	$0.435113\pi$
$938$	−80.4410	−2.62649
$939$	7.71032	0.251617
$940$	6.83030	0.222780
$941$	44.0020	1.43442	0.717212	−	0.696855i	$-0.245418\pi$
$941$	44.0020	1.43442	0.717212	+	0.696855i	$0.245418\pi$
$942$	−44.9103	−1.46326
$943$	−22.6939	−0.739014
$944$	24.6341	0.801771
$945$	−5.99082	−0.194881
$946$	−13.5161	−0.439447
$947$	−24.8471	−0.807421	−0.403711	−	0.914887i	$-0.632280\pi$
$947$	−24.8471	−0.807421	−0.403711	+	0.914887i	$0.632280\pi$
$948$	22.4927	0.730528
$949$	−3.42553	−0.111198
$950$	68.6688	2.22791
$951$	−20.7142	−0.671704
$952$	2.90046	0.0940045
$953$	−10.8293	−0.350795	−0.175397	−	0.984498i	$-0.556121\pi$
$953$	−10.8293	−0.350795	−0.175397	+	0.984498i	$0.556121\pi$
$954$	13.2137	0.427810
$955$	0.399512	0.0129279
$956$	36.6794	1.18630
$957$	2.50823	0.0810796
$958$	14.4805	0.467845
$959$	−11.0265	−0.356066
$960$	2.63431	0.0850221
$961$	3.17113	0.102295
$962$	12.7893	0.412343
$963$	−13.8217	−0.445398
$964$	−56.3033	−1.81341
$965$	−3.56004	−0.114602
$966$	−54.4394	−1.75156
$967$	23.7159	0.762653	0.381327	−	0.924440i	$-0.375467\pi$
$967$	23.7159	0.762653	0.381327	+	0.924440i	$0.375467\pi$
$968$	−0.887786	−0.0285345
$969$	6.61412	0.212476
$970$	−7.47526	−0.240016
$971$	−2.41317	−0.0774422	−0.0387211	−	0.999250i	$-0.512328\pi$
$971$	−2.41317	−0.0774422	−0.0387211	+	0.999250i	$0.512328\pi$
$972$	37.0223	1.18749
$973$	27.6006	0.884835
$974$	−44.3559	−1.42126
$975$	−4.49585	−0.143982
$976$	−33.9040	−1.08524
$977$	−8.20092	−0.262371	−0.131185	−	0.991358i	$-0.541878\pi$
$977$	−8.20092	−0.262371	−0.131185	+	0.991358i	$0.541878\pi$
$978$	−21.7045	−0.694034
$979$	−50.1208	−1.60187
$980$	−8.42770	−0.269213
$981$	−22.1035	−0.705709
$982$	−2.78633	−0.0889154
$983$	34.2260	1.09164	0.545820	−	0.837903i	$-0.316218\pi$
$983$	34.2260	1.09164	0.545820	+	0.837903i	$0.316218\pi$
$984$	−1.94808	−0.0621024
$985$	0.726939	0.0231622
$986$	−1.72941	−0.0550758
$987$	42.7828	1.36179
$988$	15.4434	0.491319
$989$	−11.8982	−0.378339
$990$	−4.50118	−0.143057
$991$	−3.58465	−0.113870	−0.0569351	−	0.998378i	$-0.518133\pi$
$991$	−3.58465	−0.113870	−0.0569351	+	0.998378i	$0.518133\pi$
$992$	47.4092	1.50524
$993$	−23.9394	−0.759693
$994$	59.5829	1.88985
$995$	0.413584	0.0131115
$996$	−2.35154	−0.0745113
$997$	24.6876	0.781865	0.390933	−	0.920419i	$-0.372153\pi$
$997$	24.6876	0.781865	0.390933	+	0.920419i	$0.372153\pi$
$998$	−37.1775	−1.17683
$999$	29.1395	0.921934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.20	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-2.07170 q^{2} +0.913939 q^{3} +2.29195 q^{4} -0.284252 q^{5} -1.89341 q^{6} -4.46498 q^{7} -0.604826 q^{8} -2.16472 q^{9} +O(q^{10})\)	\(q-2.07170 q^{2} +0.913939 q^{3} +2.29195 q^{4} -0.284252 q^{5} -1.89341 q^{6} -4.46498 q^{7} -0.604826 q^{8} -2.16472 q^{9} +0.588884 q^{10} +3.53098 q^{11} +2.09470 q^{12} +1.00000 q^{13} +9.25011 q^{14} -0.259789 q^{15} -3.33087 q^{16} +1.07403 q^{17} +4.48464 q^{18} +6.73810 q^{19} -0.651489 q^{20} -4.08072 q^{21} -7.31514 q^{22} -6.43947 q^{23} -0.552774 q^{24} -4.91920 q^{25} -2.07170 q^{26} -4.72023 q^{27} -10.2335 q^{28} +0.777240 q^{29} +0.538204 q^{30} +5.84561 q^{31} +8.11023 q^{32} +3.22710 q^{33} -2.22507 q^{34} +1.26918 q^{35} -4.96141 q^{36} -6.17332 q^{37} -13.9593 q^{38} +0.913939 q^{39} +0.171923 q^{40} +3.52418 q^{41} +8.45403 q^{42} +1.84769 q^{43} +8.09282 q^{44} +0.615324 q^{45} +13.3407 q^{46} -10.4841 q^{47} -3.04422 q^{48} +12.9360 q^{49} +10.1911 q^{50} +0.981599 q^{51} +2.29195 q^{52} +2.94644 q^{53} +9.77892 q^{54} -1.00369 q^{55} +2.70054 q^{56} +6.15821 q^{57} -1.61021 q^{58} -7.39568 q^{59} -0.595421 q^{60} +10.1787 q^{61} -12.1104 q^{62} +9.66541 q^{63} -10.1402 q^{64} -0.284252 q^{65} -6.68559 q^{66} -8.69623 q^{67} +2.46162 q^{68} -5.88528 q^{69} -2.62936 q^{70} +6.44132 q^{71} +1.30928 q^{72} -3.42553 q^{73} +12.7893 q^{74} -4.49585 q^{75} +15.4434 q^{76} -15.7658 q^{77} -1.89341 q^{78} +10.7379 q^{79} +0.946806 q^{80} +2.18014 q^{81} -7.30105 q^{82} -1.12261 q^{83} -9.35279 q^{84} -0.305295 q^{85} -3.82787 q^{86} +0.710350 q^{87} -2.13563 q^{88} -14.1946 q^{89} -1.27477 q^{90} -4.46498 q^{91} -14.7589 q^{92} +5.34253 q^{93} +21.7200 q^{94} -1.91532 q^{95} +7.41225 q^{96} -12.6939 q^{97} -26.7996 q^{98} -7.64357 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 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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