LMFDB - Embedded newform 6005.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6005,2,Mod(1,6005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6005, 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("6005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6005 = 5 \cdot 1201 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6005.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:	$47.9501664138$
Analytic rank:	$0$
Dimension:	$111$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65700 q^{2} -0.218117 q^{3} +5.05966 q^{4} +1.00000 q^{5} +0.579538 q^{6} +4.50653 q^{7} -8.12951 q^{8} -2.95242 q^{9} +O(q^{10})$	\(q-2.65700 q^{2} -0.218117 q^{3} +5.05966 q^{4} +1.00000 q^{5} +0.579538 q^{6} +4.50653 q^{7} -8.12951 q^{8} -2.95242 q^{9} -2.65700 q^{10} +2.26992 q^{11} -1.10360 q^{12} +2.05571 q^{13} -11.9739 q^{14} -0.218117 q^{15} +11.4808 q^{16} -3.82604 q^{17} +7.84460 q^{18} +5.02854 q^{19} +5.05966 q^{20} -0.982952 q^{21} -6.03117 q^{22} +9.03090 q^{23} +1.77319 q^{24} +1.00000 q^{25} -5.46203 q^{26} +1.29833 q^{27} +22.8015 q^{28} +0.875732 q^{29} +0.579538 q^{30} +5.68852 q^{31} -14.2455 q^{32} -0.495108 q^{33} +10.1658 q^{34} +4.50653 q^{35} -14.9383 q^{36} +4.99557 q^{37} -13.3608 q^{38} -0.448387 q^{39} -8.12951 q^{40} -4.93104 q^{41} +2.61171 q^{42} +3.34050 q^{43} +11.4850 q^{44} -2.95242 q^{45} -23.9951 q^{46} -8.00055 q^{47} -2.50416 q^{48} +13.3088 q^{49} -2.65700 q^{50} +0.834524 q^{51} +10.4012 q^{52} +3.38945 q^{53} -3.44966 q^{54} +2.26992 q^{55} -36.6359 q^{56} -1.09681 q^{57} -2.32682 q^{58} +3.44998 q^{59} -1.10360 q^{60} -6.06078 q^{61} -15.1144 q^{62} -13.3052 q^{63} +14.8887 q^{64} +2.05571 q^{65} +1.31550 q^{66} -0.809823 q^{67} -19.3584 q^{68} -1.96979 q^{69} -11.9739 q^{70} -2.67686 q^{71} +24.0018 q^{72} +6.92294 q^{73} -13.2732 q^{74} -0.218117 q^{75} +25.4427 q^{76} +10.2295 q^{77} +1.19136 q^{78} -6.60172 q^{79} +11.4808 q^{80} +8.57409 q^{81} +13.1018 q^{82} -10.2601 q^{83} -4.97340 q^{84} -3.82604 q^{85} -8.87570 q^{86} -0.191012 q^{87} -18.4533 q^{88} +13.8563 q^{89} +7.84460 q^{90} +9.26414 q^{91} +45.6932 q^{92} -1.24076 q^{93} +21.2575 q^{94} +5.02854 q^{95} +3.10719 q^{96} +13.6768 q^{97} -35.3616 q^{98} -6.70176 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) $ 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * 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 $

$2$	−2.65700	−1.87878	−0.939392	−	0.342846i	$-0.888609\pi$
$2$	−2.65700	−1.87878	−0.939392	+	0.342846i	$0.888609\pi$
$3$	−0.218117	−0.125930	−0.0629650	−	0.998016i	$-0.520056\pi$
$3$	−0.218117	−0.125930	−0.0629650	+	0.998016i	$0.520056\pi$
$4$	5.05966	2.52983
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.579538	0.236595
$7$	4.50653	1.70331	0.851654	−	0.524104i	$-0.175600\pi$
$7$	4.50653	1.70331	0.851654	+	0.524104i	$0.175600\pi$
$8$	−8.12951	−2.87422
$9$	−2.95242	−0.984142
$10$	−2.65700	−0.840218
$11$	2.26992	0.684406	0.342203	−	0.939626i	$-0.388827\pi$
$11$	2.26992	0.684406	0.342203	+	0.939626i	$0.388827\pi$
$12$	−1.10360	−0.318581
$13$	2.05571	0.570152	0.285076	−	0.958505i	$-0.407981\pi$
$13$	2.05571	0.570152	0.285076	+	0.958505i	$0.407981\pi$
$14$	−11.9739	−3.20015
$15$	−0.218117	−0.0563176
$16$	11.4808	2.87020
$17$	−3.82604	−0.927950	−0.463975	−	0.885848i	$-0.653577\pi$
$17$	−3.82604	−0.927950	−0.463975	+	0.885848i	$0.653577\pi$
$18$	7.84460	1.84899
$19$	5.02854	1.15363	0.576813	−	0.816876i	$-0.304296\pi$
$19$	5.02854	1.15363	0.576813	+	0.816876i	$0.304296\pi$
$20$	5.05966	1.13137
$21$	−0.982952	−0.214498
$22$	−6.03117	−1.28585
$23$	9.03090	1.88307	0.941536	−	0.336912i	$-0.109382\pi$
$23$	9.03090	1.88307	0.941536	+	0.336912i	$0.109382\pi$
$24$	1.77319	0.361950
$25$	1.00000	0.200000
$26$	−5.46203	−1.07119
$27$	1.29833	0.249863
$28$	22.8015	4.30908
$29$	0.875732	0.162619	0.0813096	−	0.996689i	$-0.474090\pi$
$29$	0.875732	0.162619	0.0813096	+	0.996689i	$0.474090\pi$
$30$	0.579538	0.105809
$31$	5.68852	1.02169	0.510844	−	0.859673i	$-0.329333\pi$
$31$	5.68852	1.02169	0.510844	+	0.859673i	$0.329333\pi$
$32$	−14.2455	−2.51827
$33$	−0.495108	−0.0861873
$34$	10.1658	1.74342
$35$	4.50653	0.761743
$36$	−14.9383	−2.48971
$37$	4.99557	0.821266	0.410633	−	0.911801i	$-0.365308\pi$
$37$	4.99557	0.821266	0.410633	+	0.911801i	$0.365308\pi$
$38$	−13.3608	−2.16741
$39$	−0.448387	−0.0717993
$40$	−8.12951	−1.28539
$41$	−4.93104	−0.770098	−0.385049	−	0.922896i	$-0.625816\pi$
$41$	−4.93104	−0.770098	−0.385049	+	0.922896i	$0.625816\pi$
$42$	2.61171	0.402995
$43$	3.34050	0.509421	0.254710	−	0.967017i	$-0.418020\pi$
$43$	3.34050	0.509421	0.254710	+	0.967017i	$0.418020\pi$
$44$	11.4850	1.73143
$45$	−2.95242	−0.440122
$46$	−23.9951	−3.53789
$47$	−8.00055	−1.16700	−0.583500	−	0.812113i	$-0.698317\pi$
$47$	−8.00055	−1.16700	−0.583500	+	0.812113i	$0.698317\pi$
$48$	−2.50416	−0.361445
$49$	13.3088	1.90126
$50$	−2.65700	−0.375757
$51$	0.834524	0.116857
$52$	10.4012	1.44239
$53$	3.38945	0.465577	0.232789	−	0.972527i	$-0.425215\pi$
$53$	3.38945	0.465577	0.232789	+	0.972527i	$0.425215\pi$
$54$	−3.44966	−0.469439
$55$	2.26992	0.306076
$56$	−36.6359	−4.89568
$57$	−1.09681	−0.145276
$58$	−2.32682	−0.305526
$59$	3.44998	0.449150	0.224575	−	0.974457i	$-0.427901\pi$
$59$	3.44998	0.449150	0.224575	+	0.974457i	$0.427901\pi$
$60$	−1.10360	−0.142474
$61$	−6.06078	−0.776003	−0.388001	−	0.921659i	$-0.626834\pi$
$61$	−6.06078	−0.776003	−0.388001	+	0.921659i	$0.626834\pi$
$62$	−15.1144	−1.91953
$63$	−13.3052	−1.67630
$64$	14.8887	1.86109
$65$	2.05571	0.254980
$66$	1.31550	0.161927
$67$	−0.809823	−0.0989357	−0.0494678	−	0.998776i	$-0.515753\pi$
$67$	−0.809823	−0.0989357	−0.0494678	+	0.998776i	$0.515753\pi$
$68$	−19.3584	−2.34755
$69$	−1.96979	−0.237135
$70$	−11.9739	−1.43115
$71$	−2.67686	−0.317684	−0.158842	−	0.987304i	$-0.550776\pi$
$71$	−2.67686	−0.317684	−0.158842	+	0.987304i	$0.550776\pi$
$72$	24.0018	2.82863
$73$	6.92294	0.810269	0.405134	−	0.914257i	$-0.367225\pi$
$73$	6.92294	0.810269	0.405134	+	0.914257i	$0.367225\pi$
$74$	−13.2732	−1.54298
$75$	−0.218117	−0.0251860
$76$	25.4427	2.91847
$77$	10.2295	1.16575
$78$	1.19136	0.134895
$79$	−6.60172	−0.742751	−0.371376	−	0.928483i	$-0.621114\pi$
$79$	−6.60172	−0.742751	−0.371376	+	0.928483i	$0.621114\pi$
$80$	11.4808	1.28359
$81$	8.57409	0.952676
$82$	13.1018	1.44685
$83$	−10.2601	−1.12619	−0.563097	−	0.826391i	$-0.690390\pi$
$83$	−10.2601	−1.12619	−0.563097	+	0.826391i	$0.690390\pi$
$84$	−4.97340	−0.542642
$85$	−3.82604	−0.414992
$86$	−8.87570	−0.957092
$87$	−0.191012	−0.0204787
$88$	−18.4533	−1.96713
$89$	13.8563	1.46877	0.734385	−	0.678733i	$-0.237471\pi$
$89$	13.8563	1.46877	0.734385	+	0.678733i	$0.237471\pi$
$90$	7.84460	0.826893
$91$	9.26414	0.971146
$92$	45.6932	4.76385
$93$	−1.24076	−0.128661
$94$	21.2575	2.19254
$95$	5.02854	0.515917
$96$	3.10719	0.317126
$97$	13.6768	1.38867	0.694336	−	0.719651i	$-0.255698\pi$
$97$	13.6768	1.38867	0.694336	+	0.719651i	$0.255698\pi$
$98$	−35.3616	−3.57206
$99$	−6.70176	−0.673552
$100$	5.05966	0.505966
$101$	−7.46912	−0.743205	−0.371603	−	0.928392i	$-0.621192\pi$
$101$	−7.46912	−0.743205	−0.371603	+	0.928392i	$0.621192\pi$
$102$	−2.21733	−0.219549
$103$	−7.41374	−0.730498	−0.365249	−	0.930910i	$-0.619016\pi$
$103$	−7.41374	−0.730498	−0.365249	+	0.930910i	$0.619016\pi$
$104$	−16.7119	−1.63874
$105$	−0.982952	−0.0959263
$106$	−9.00579	−0.874719
$107$	2.31789	0.224079	0.112040	−	0.993704i	$-0.464262\pi$
$107$	2.31789	0.224079	0.112040	+	0.993704i	$0.464262\pi$
$108$	6.56909	0.632111
$109$	−13.8853	−1.32997	−0.664984	−	0.746857i	$-0.731562\pi$
$109$	−13.8853	−1.32997	−0.664984	+	0.746857i	$0.731562\pi$
$110$	−6.03117	−0.575050
$111$	−1.08962	−0.103422
$112$	51.7386	4.88884
$113$	15.1367	1.42395	0.711973	−	0.702207i	$-0.247802\pi$
$113$	15.1367	1.42395	0.711973	+	0.702207i	$0.247802\pi$
$114$	2.91423	0.272942
$115$	9.03090	0.842136
$116$	4.43090	0.411399
$117$	−6.06934	−0.561111
$118$	−9.16661	−0.843855
$119$	−17.2422	−1.58059
$120$	1.77319	0.161869
$121$	−5.84748	−0.531589
$122$	16.1035	1.45794
$123$	1.07554	0.0969785
$124$	28.7819	2.58469
$125$	1.00000	0.0894427
$126$	35.3519	3.14940
$127$	19.9413	1.76950	0.884750	−	0.466066i	$-0.154329\pi$
$127$	19.9413	1.76950	0.884750	+	0.466066i	$0.154329\pi$
$128$	−11.0683	−0.978305
$129$	−0.728620	−0.0641514
$130$	−5.46203	−0.479052
$131$	−0.809994	−0.0707695	−0.0353848	−	0.999374i	$-0.511266\pi$
$131$	−0.809994	−0.0707695	−0.0353848	+	0.999374i	$0.511266\pi$
$132$	−2.50508	−0.218039
$133$	22.6613	1.96498
$134$	2.15170	0.185879
$135$	1.29833	0.111742
$136$	31.1038	2.66713
$137$	−1.03467	−0.0883982	−0.0441991	−	0.999023i	$-0.514074\pi$
$137$	−1.03467	−0.0883982	−0.0441991	+	0.999023i	$0.514074\pi$
$138$	5.23375	0.445526
$139$	−5.98675	−0.507790	−0.253895	−	0.967232i	$-0.581712\pi$
$139$	−5.98675	−0.507790	−0.253895	+	0.967232i	$0.581712\pi$
$140$	22.8015	1.92708
$141$	1.74506	0.146960
$142$	7.11241	0.596860
$143$	4.66630	0.390216
$144$	−33.8962	−2.82468
$145$	0.875732	0.0727256
$146$	−18.3943	−1.52232
$147$	−2.90289	−0.239426
$148$	25.2758	2.07766
$149$	1.68605	0.138126	0.0690632	−	0.997612i	$-0.477999\pi$
$149$	1.68605	0.138126	0.0690632	+	0.997612i	$0.477999\pi$
$150$	0.579538	0.0473191
$151$	−17.1346	−1.39439	−0.697197	−	0.716879i	$-0.745570\pi$
$151$	−17.1346	−1.39439	−0.697197	+	0.716879i	$0.745570\pi$
$152$	−40.8795	−3.31577
$153$	11.2961	0.913234
$154$	−27.1797	−2.19020
$155$	5.68852	0.456913
$156$	−2.26868	−0.181640
$157$	3.84592	0.306938	0.153469	−	0.988153i	$-0.450955\pi$
$157$	3.84592	0.306938	0.153469	+	0.988153i	$0.450955\pi$
$158$	17.5408	1.39547
$159$	−0.739299	−0.0586302
$160$	−14.2455	−1.12620
$161$	40.6980	3.20745
$162$	−22.7814	−1.78987
$163$	13.7125	1.07405	0.537023	−	0.843568i	$-0.319549\pi$
$163$	13.7125	1.07405	0.537023	+	0.843568i	$0.319549\pi$
$164$	−24.9493	−1.94822
$165$	−0.495108	−0.0385441
$166$	27.2612	2.11588
$167$	−15.6138	−1.20823	−0.604115	−	0.796897i	$-0.706473\pi$
$167$	−15.6138	−1.20823	−0.604115	+	0.796897i	$0.706473\pi$
$168$	7.99092	0.616513
$169$	−8.77404	−0.674926
$170$	10.1658	0.779680
$171$	−14.8464	−1.13533
$172$	16.9018	1.28875
$173$	−15.6591	−1.19054	−0.595268	−	0.803527i	$-0.702954\pi$
$173$	−15.6591	−1.19054	−0.595268	+	0.803527i	$0.702954\pi$
$174$	0.507520	0.0384750
$175$	4.50653	0.340662
$176$	26.0605	1.96438
$177$	−0.752501	−0.0565614
$178$	−36.8163	−2.75950
$179$	19.5716	1.46285	0.731424	−	0.681923i	$-0.238856\pi$
$179$	19.5716	1.46285	0.731424	+	0.681923i	$0.238856\pi$
$180$	−14.9383	−1.11343
$181$	−0.465232	−0.0345805	−0.0172902	−	0.999851i	$-0.505504\pi$
$181$	−0.465232	−0.0345805	−0.0172902	+	0.999851i	$0.505504\pi$
$182$	−24.6148	−1.82457
$183$	1.32196	0.0977221
$184$	−73.4168	−5.41236
$185$	4.99557	0.367281
$186$	3.29671	0.241727
$187$	−8.68479	−0.635094
$188$	−40.4800	−2.95231
$189$	5.85095	0.425594
$190$	−13.3608	−0.969296
$191$	1.64326	0.118902	0.0594510	−	0.998231i	$-0.481065\pi$
$191$	1.64326	0.118902	0.0594510	+	0.998231i	$0.481065\pi$
$192$	−3.24748	−0.234367
$193$	13.6472	0.982344	0.491172	−	0.871062i	$-0.336569\pi$
$193$	13.6472	0.982344	0.491172	+	0.871062i	$0.336569\pi$
$194$	−36.3394	−2.60901
$195$	−0.448387	−0.0321096
$196$	67.3381	4.80986
$197$	22.7415	1.62026	0.810131	−	0.586249i	$-0.199396\pi$
$197$	22.7415	1.62026	0.810131	+	0.586249i	$0.199396\pi$
$198$	17.8066	1.26546
$199$	−14.9995	−1.06329	−0.531644	−	0.846968i	$-0.678426\pi$
$199$	−14.9995	−1.06329	−0.531644	+	0.846968i	$0.678426\pi$
$200$	−8.12951	−0.574843
$201$	0.176636	0.0124590
$202$	19.8455	1.39632
$203$	3.94651	0.276991
$204$	4.22241	0.295628
$205$	−4.93104	−0.344398
$206$	19.6983	1.37245
$207$	−26.6631	−1.85321
$208$	23.6012	1.63645
$209$	11.4144	0.789548
$210$	2.61171	0.180225
$211$	−18.0727	−1.24418	−0.622088	−	0.782947i	$-0.713715\pi$
$211$	−18.0727	−1.24418	−0.622088	+	0.782947i	$0.713715\pi$
$212$	17.1495	1.17783
$213$	0.583869	0.0400060
$214$	−6.15864	−0.420996
$215$	3.34050	0.227820
$216$	−10.5548	−0.718160
$217$	25.6355	1.74025
$218$	36.8932	2.49872
$219$	−1.51001	−0.102037
$220$	11.4850	0.774319
$221$	−7.86523	−0.529073
$222$	2.89512	0.194308
$223$	−5.61605	−0.376078	−0.188039	−	0.982162i	$-0.560213\pi$
$223$	−5.61605	−0.376078	−0.188039	+	0.982162i	$0.560213\pi$
$224$	−64.1978	−4.28939
$225$	−2.95242	−0.196828
$226$	−40.2183	−2.67528
$227$	25.5212	1.69390	0.846950	−	0.531673i	$-0.178436\pi$
$227$	25.5212	1.69390	0.846950	+	0.531673i	$0.178436\pi$
$228$	−5.54948	−0.367523
$229$	−1.87464	−0.123880	−0.0619400	−	0.998080i	$-0.519729\pi$
$229$	−1.87464	−0.123880	−0.0619400	+	0.998080i	$0.519729\pi$
$230$	−23.9951	−1.58219
$231$	−2.23122	−0.146804
$232$	−7.11927	−0.467403
$233$	−6.87432	−0.450351	−0.225176	−	0.974318i	$-0.572296\pi$
$233$	−6.87432	−0.450351	−0.225176	+	0.974318i	$0.572296\pi$
$234$	16.1262	1.05421
$235$	−8.00055	−0.521898
$236$	17.4557	1.13627
$237$	1.43995	0.0935347
$238$	45.8124	2.96958
$239$	−0.0832547	−0.00538530	−0.00269265	−	0.999996i	$-0.500857\pi$
$239$	−0.0832547	−0.00538530	−0.00269265	+	0.999996i	$0.500857\pi$
$240$	−2.50416	−0.161643
$241$	9.13707	0.588571	0.294285	−	0.955718i	$-0.404918\pi$
$241$	9.13707	0.588571	0.294285	+	0.955718i	$0.404918\pi$
$242$	15.5367	0.998740
$243$	−5.76514	−0.369834
$244$	−30.6654	−1.96315
$245$	13.3088	0.850270
$246$	−2.85772	−0.182202
$247$	10.3372	0.657742
$248$	−46.2449	−2.93655
$249$	2.23791	0.141822
$250$	−2.65700	−0.168044
$251$	−12.5027	−0.789164	−0.394582	−	0.918861i	$-0.629111\pi$
$251$	−12.5027	−0.789164	−0.394582	+	0.918861i	$0.629111\pi$
$252$	−67.3197	−4.24074
$253$	20.4994	1.28879
$254$	−52.9839	−3.32451
$255$	0.834524	0.0522600
$256$	−0.368975	−0.0230610
$257$	−11.2580	−0.702252	−0.351126	−	0.936328i	$-0.614201\pi$
$257$	−11.2580	−0.702252	−0.351126	+	0.936328i	$0.614201\pi$
$258$	1.93594	0.120527
$259$	22.5127	1.39887
$260$	10.4012	0.645055
$261$	−2.58553	−0.160040
$262$	2.15216	0.132961
$263$	−3.15148	−0.194329	−0.0971643	−	0.995268i	$-0.530977\pi$
$263$	−3.15148	−0.194329	−0.0971643	+	0.995268i	$0.530977\pi$
$264$	4.02499	0.247721
$265$	3.38945	0.208213
$266$	−60.2110	−3.69177
$267$	−3.02231	−0.184962
$268$	−4.09743	−0.250290
$269$	−21.9404	−1.33773	−0.668866	−	0.743383i	$-0.733220\pi$
$269$	−21.9404	−1.33773	−0.668866	+	0.743383i	$0.733220\pi$
$270$	−3.44966	−0.209939
$271$	−11.0418	−0.670739	−0.335369	−	0.942087i	$-0.608861\pi$
$271$	−11.0418	−0.670739	−0.335369	+	0.942087i	$0.608861\pi$
$272$	−43.9260	−2.66340
$273$	−2.02067	−0.122296
$274$	2.74913	0.166081
$275$	2.26992	0.136881
$276$	−9.96648	−0.599912
$277$	14.2043	0.853452	0.426726	−	0.904381i	$-0.359667\pi$
$277$	14.2043	0.853452	0.426726	+	0.904381i	$0.359667\pi$
$278$	15.9068	0.954027
$279$	−16.7949	−1.00549
$280$	−36.6359	−2.18941
$281$	−18.7392	−1.11788	−0.558942	−	0.829206i	$-0.688793\pi$
$281$	−18.7392	−1.11788	−0.558942	+	0.829206i	$0.688793\pi$
$282$	−4.63662	−0.276107
$283$	18.2672	1.08587	0.542937	−	0.839774i	$-0.317312\pi$
$283$	18.2672	1.08587	0.542937	+	0.839774i	$0.317312\pi$
$284$	−13.5440	−0.803687
$285$	−1.09681	−0.0649694
$286$	−12.3984	−0.733131
$287$	−22.2219	−1.31172
$288$	42.0587	2.47834
$289$	−2.36145	−0.138909
$290$	−2.32682	−0.136636
$291$	−2.98315	−0.174876
$292$	35.0277	2.04984
$293$	5.63454	0.329173	0.164587	−	0.986363i	$-0.447371\pi$
$293$	5.63454	0.329173	0.164587	+	0.986363i	$0.447371\pi$
$294$	7.71297	0.449830
$295$	3.44998	0.200866
$296$	−40.6115	−2.36050
$297$	2.94709	0.171008
$298$	−4.47983	−0.259510
$299$	18.5649	1.07364
$300$	−1.10360	−0.0637163
$301$	15.0541	0.867701
$302$	45.5267	2.61977
$303$	1.62914	0.0935919
$304$	57.7316	3.31114
$305$	−6.06078	−0.347039
$306$	−30.0137	−1.71577
$307$	−26.3493	−1.50383	−0.751917	−	0.659257i	$-0.770871\pi$
$307$	−26.3493	−1.50383	−0.751917	+	0.659257i	$0.770871\pi$
$308$	51.7575	2.94916
$309$	1.61706	0.0919916
$310$	−15.1144	−0.858440
$311$	−31.7804	−1.80210	−0.901049	−	0.433716i	$-0.857202\pi$
$311$	−31.7804	−1.80210	−0.901049	+	0.433716i	$0.857202\pi$
$312$	3.64516	0.206367
$313$	−14.4884	−0.818932	−0.409466	−	0.912325i	$-0.634285\pi$
$313$	−14.4884	−0.818932	−0.409466	+	0.912325i	$0.634285\pi$
$314$	−10.2186	−0.576670
$315$	−13.3052	−0.749663
$316$	−33.4024	−1.87903
$317$	−3.51197	−0.197252	−0.0986260	−	0.995125i	$-0.531445\pi$
$317$	−3.51197	−0.197252	−0.0986260	+	0.995125i	$0.531445\pi$
$318$	1.96432	0.110153
$319$	1.98784	0.111298
$320$	14.8887	0.832303
$321$	−0.505572	−0.0282183
$322$	−108.135	−6.02611
$323$	−19.2394	−1.07051
$324$	43.3819	2.41011
$325$	2.05571	0.114030
$326$	−36.4341	−2.01790
$327$	3.02862	0.167483
$328$	40.0869	2.21343
$329$	−36.0547	−1.98776
$330$	1.31550	0.0724161
$331$	−5.64091	−0.310052	−0.155026	−	0.987910i	$-0.549546\pi$
$331$	−5.64091	−0.310052	−0.155026	+	0.987910i	$0.549546\pi$
$332$	−51.9127	−2.84908
$333$	−14.7490	−0.808242
$334$	41.4858	2.27000
$335$	−0.809823	−0.0442454
$336$	−11.2851	−0.615652
$337$	22.4718	1.22411	0.612057	−	0.790813i	$-0.290342\pi$
$337$	22.4718	1.22411	0.612057	+	0.790813i	$0.290342\pi$
$338$	23.3126	1.26804
$339$	−3.30159	−0.179317
$340$	−19.3584	−1.04986
$341$	12.9125	0.699249
$342$	39.4468	2.13304
$343$	28.4309	1.53513
$344$	−27.1566	−1.46419
$345$	−1.96979	−0.106050
$346$	41.6062	2.23676
$347$	−6.01793	−0.323060	−0.161530	−	0.986868i	$-0.551643\pi$
$347$	−6.01793	−0.323060	−0.161530	+	0.986868i	$0.551643\pi$
$348$	−0.966456	−0.0518075
$349$	31.0791	1.66363	0.831813	−	0.555056i	$-0.187303\pi$
$349$	31.0791	1.66363	0.831813	+	0.555056i	$0.187303\pi$
$350$	−11.9739	−0.640030
$351$	2.66899	0.142460
$352$	−32.3361	−1.72352
$353$	−10.8698	−0.578538	−0.289269	−	0.957248i	$-0.593412\pi$
$353$	−10.8698	−0.578538	−0.289269	+	0.957248i	$0.593412\pi$
$354$	1.99940	0.106267
$355$	−2.67686	−0.142073
$356$	70.1083	3.71573
$357$	3.76081	0.199043
$358$	−52.0017	−2.74837
$359$	−2.90164	−0.153143	−0.0765714	−	0.997064i	$-0.524397\pi$
$359$	−2.90164	−0.153143	−0.0765714	+	0.997064i	$0.524397\pi$
$360$	24.0018	1.26500
$361$	6.28617	0.330851
$362$	1.23612	0.0649692
$363$	1.27544	0.0669430
$364$	46.8734	2.45683
$365$	6.92294	0.362363
$366$	−3.51245	−0.183599
$367$	−3.16853	−0.165396	−0.0826979	−	0.996575i	$-0.526354\pi$
$367$	−3.16853	−0.165396	−0.0826979	+	0.996575i	$0.526354\pi$
$368$	103.682	5.40480
$369$	14.5585	0.757886
$370$	−13.2732	−0.690042
$371$	15.2747	0.793022
$372$	−6.27784	−0.325491
$373$	−3.00904	−0.155802	−0.0779010	−	0.996961i	$-0.524822\pi$
$373$	−3.00904	−0.155802	−0.0779010	+	0.996961i	$0.524822\pi$
$374$	23.0755	1.19321
$375$	−0.218117	−0.0112635
$376$	65.0405	3.35421
$377$	1.80025	0.0927178
$378$	−15.5460	−0.799599
$379$	29.7622	1.52878	0.764391	−	0.644753i	$-0.223040\pi$
$379$	29.7622	1.52878	0.764391	+	0.644753i	$0.223040\pi$
$380$	25.4427	1.30518
$381$	−4.34953	−0.222833
$382$	−4.36614	−0.223391
$383$	−10.9492	−0.559476	−0.279738	−	0.960076i	$-0.590248\pi$
$383$	−10.9492	−0.559476	−0.279738	+	0.960076i	$0.590248\pi$
$384$	2.41418	0.123198
$385$	10.2295	0.521341
$386$	−36.2605	−1.84561
$387$	−9.86256	−0.501342
$388$	69.2001	3.51310
$389$	−12.1690	−0.616994	−0.308497	−	0.951225i	$-0.599826\pi$
$389$	−12.1690	−0.616994	−0.308497	+	0.951225i	$0.599826\pi$
$390$	1.19136	0.0603271
$391$	−34.5525	−1.74740
$392$	−108.194	−5.46463
$393$	0.176674	0.00891201
$394$	−60.4241	−3.04412
$395$	−6.60172	−0.332169
$396$	−33.9086	−1.70397
$397$	7.06535	0.354600	0.177300	−	0.984157i	$-0.443264\pi$
$397$	7.06535	0.354600	0.177300	+	0.984157i	$0.443264\pi$
$398$	39.8538	1.99769
$399$	−4.94281	−0.247450
$400$	11.4808	0.574040
$401$	0.827748	0.0413358	0.0206679	−	0.999786i	$-0.493421\pi$
$401$	0.827748	0.0413358	0.0206679	+	0.999786i	$0.493421\pi$
$402$	−0.469323	−0.0234077
$403$	11.6940	0.582518
$404$	−37.7912	−1.88018
$405$	8.57409	0.426050
$406$	−10.4859	−0.520406
$407$	11.3395	0.562079
$408$	−6.78427	−0.335872
$409$	−25.4615	−1.25899	−0.629494	−	0.777005i	$-0.716738\pi$
$409$	−25.4615	−1.25899	−0.629494	+	0.777005i	$0.716738\pi$
$410$	13.1018	0.647050
$411$	0.225680	0.0111320
$412$	−37.5110	−1.84803
$413$	15.5475	0.765041
$414$	70.8438	3.48178
$415$	−10.2601	−0.503650
$416$	−29.2847	−1.43580
$417$	1.30581	0.0639460
$418$	−30.3280	−1.48339
$419$	−14.5252	−0.709601	−0.354801	−	0.934942i	$-0.615451\pi$
$419$	−14.5252	−0.709601	−0.354801	+	0.934942i	$0.615451\pi$
$420$	−4.97340	−0.242677
$421$	12.8413	0.625848	0.312924	−	0.949778i	$-0.398691\pi$
$421$	12.8413	0.625848	0.312924	+	0.949778i	$0.398691\pi$
$422$	48.0192	2.33754
$423$	23.6210	1.14849
$424$	−27.5546	−1.33817
$425$	−3.82604	−0.185590
$426$	−1.55134	−0.0751626
$427$	−27.3131	−1.32177
$428$	11.7277	0.566881
$429$	−1.01780	−0.0491399
$430$	−8.87570	−0.428024
$431$	6.46706	0.311507	0.155754	−	0.987796i	$-0.450219\pi$
$431$	6.46706	0.311507	0.155754	+	0.987796i	$0.450219\pi$
$432$	14.9058	0.717157
$433$	6.24277	0.300008	0.150004	−	0.988685i	$-0.452071\pi$
$433$	6.24277	0.300008	0.150004	+	0.988685i	$0.452071\pi$
$434$	−68.1135	−3.26955
$435$	−0.191012	−0.00915833
$436$	−70.2547	−3.36459
$437$	45.4122	2.17236
$438$	4.01210	0.191706
$439$	35.0984	1.67516	0.837579	−	0.546317i	$-0.183971\pi$
$439$	35.0984	1.67516	0.837579	+	0.546317i	$0.183971\pi$
$440$	−18.4533	−0.879727
$441$	−39.2933	−1.87111
$442$	20.8979	0.994014
$443$	−39.4940	−1.87642	−0.938208	−	0.346072i	$-0.887515\pi$
$443$	−39.4940	−1.87642	−0.938208	+	0.346072i	$0.887515\pi$
$444$	−5.51310	−0.261640
$445$	13.8563	0.656854
$446$	14.9218	0.706570
$447$	−0.367756	−0.0173943
$448$	67.0963	3.17000
$449$	33.6791	1.58942	0.794708	−	0.606992i	$-0.207624\pi$
$449$	33.6791	1.58942	0.794708	+	0.606992i	$0.207624\pi$
$450$	7.84460	0.369798
$451$	−11.1930	−0.527060
$452$	76.5867	3.60234
$453$	3.73735	0.175596
$454$	−67.8098	−3.18247
$455$	9.26414	0.434310
$456$	8.91653	0.417555
$457$	−28.5057	−1.33344	−0.666721	−	0.745307i	$-0.732303\pi$
$457$	−28.5057	−1.33344	−0.666721	+	0.745307i	$0.732303\pi$
$458$	4.98093	0.232744
$459$	−4.96744	−0.231860
$460$	45.6932	2.13046
$461$	28.5306	1.32880	0.664401	−	0.747376i	$-0.268687\pi$
$461$	28.5306	1.32880	0.664401	+	0.747376i	$0.268687\pi$
$462$	5.92836	0.275812
$463$	10.4803	0.487062	0.243531	−	0.969893i	$-0.421694\pi$
$463$	10.4803	0.487062	0.243531	+	0.969893i	$0.421694\pi$
$464$	10.0541	0.466750
$465$	−1.24076	−0.0575390
$466$	18.2651	0.846113
$467$	−15.8415	−0.733058	−0.366529	−	0.930407i	$-0.619454\pi$
$467$	−15.8415	−0.733058	−0.366529	+	0.930407i	$0.619454\pi$
$468$	−30.7088	−1.41951
$469$	−3.64949	−0.168518
$470$	21.2575	0.980534
$471$	−0.838862	−0.0386527
$472$	−28.0467	−1.29095
$473$	7.58265	0.348651
$474$	−3.82595	−0.175732
$475$	5.02854	0.230725
$476$	−87.2394	−3.99861
$477$	−10.0071	−0.458194
$478$	0.221208	0.0101178
$479$	29.2761	1.33766	0.668829	−	0.743417i	$-0.266796\pi$
$479$	29.2761	1.33766	0.668829	+	0.743417i	$0.266796\pi$
$480$	3.10719	0.141823
$481$	10.2695	0.468247
$482$	−24.2772	−1.10580
$483$	−8.87694	−0.403915
$484$	−29.5862	−1.34483
$485$	13.6768	0.621033
$486$	15.3180	0.694837
$487$	−8.05748	−0.365119	−0.182560	−	0.983195i	$-0.558438\pi$
$487$	−8.05748	−0.365119	−0.182560	+	0.983195i	$0.558438\pi$
$488$	49.2711	2.23040
$489$	−2.99093	−0.135255
$490$	−35.3616	−1.59747
$491$	26.6711	1.20365	0.601825	−	0.798628i	$-0.294441\pi$
$491$	26.6711	1.20365	0.601825	+	0.798628i	$0.294441\pi$
$492$	5.44188	0.245339
$493$	−3.35058	−0.150903
$494$	−27.4660	−1.23576
$495$	−6.70176	−0.301222
$496$	65.3087	2.93245
$497$	−12.0633	−0.541115
$498$	−5.94613	−0.266452
$499$	3.65035	0.163412	0.0817060	−	0.996656i	$-0.473963\pi$
$499$	3.65035	0.163412	0.0817060	+	0.996656i	$0.473963\pi$
$500$	5.05966	0.226275
$501$	3.40563	0.152152
$502$	33.2197	1.48267
$503$	−19.2795	−0.859632	−0.429816	−	0.902916i	$-0.641422\pi$
$503$	−19.2795	−0.859632	−0.429816	+	0.902916i	$0.641422\pi$
$504$	108.165	4.81804
$505$	−7.46912	−0.332371
$506$	−54.4669	−2.42135
$507$	1.91377	0.0849935
$508$	100.896	4.47653
$509$	−39.2342	−1.73902	−0.869512	−	0.493911i	$-0.835567\pi$
$509$	−39.2342	−1.73902	−0.869512	+	0.493911i	$0.835567\pi$
$510$	−2.21733	−0.0981851
$511$	31.1984	1.38014
$512$	23.1169	1.02163
$513$	6.52868	0.288248
$514$	29.9124	1.31938
$515$	−7.41374	−0.326688
$516$	−3.68657	−0.162292
$517$	−18.1606	−0.798701
$518$	−59.8162	−2.62817
$519$	3.41551	0.149924
$520$	−16.7119	−0.732867
$521$	32.9880	1.44523	0.722616	−	0.691249i	$-0.242939\pi$
$521$	32.9880	1.44523	0.722616	+	0.691249i	$0.242939\pi$
$522$	6.86976	0.300681
$523$	−17.0939	−0.747466	−0.373733	−	0.927536i	$-0.621922\pi$
$523$	−17.0939	−0.747466	−0.373733	+	0.927536i	$0.621922\pi$
$524$	−4.09829	−0.179035
$525$	−0.982952	−0.0428996
$526$	8.37349	0.365101
$527$	−21.7645	−0.948075
$528$	−5.68424	−0.247375
$529$	58.5571	2.54596
$530$	−9.00579	−0.391186
$531$	−10.1858	−0.442027
$532$	114.658	4.97106
$533$	−10.1368	−0.439073
$534$	8.03028	0.347504
$535$	2.31789	0.100211
$536$	6.58347	0.284362
$537$	−4.26890	−0.184216
$538$	58.2958	2.51331
$539$	30.2099	1.30123
$540$	6.56909	0.282688
$541$	−28.8057	−1.23845	−0.619227	−	0.785212i	$-0.712554\pi$
$541$	−28.8057	−1.23845	−0.619227	+	0.785212i	$0.712554\pi$
$542$	29.3380	1.26017
$543$	0.101475	0.00435472
$544$	54.5038	2.33683
$545$	−13.8853	−0.594780
$546$	5.36892	0.229769
$547$	−23.0441	−0.985295	−0.492647	−	0.870229i	$-0.663971\pi$
$547$	−23.0441	−0.985295	−0.492647	+	0.870229i	$0.663971\pi$
$548$	−5.23510	−0.223632
$549$	17.8940	0.763697
$550$	−6.03117	−0.257170
$551$	4.40365	0.187602
$552$	16.0135	0.681578
$553$	−29.7509	−1.26514
$554$	−37.7408	−1.60345
$555$	−1.08962	−0.0462518
$556$	−30.2909	−1.28462
$557$	−3.73402	−0.158216	−0.0791078	−	0.996866i	$-0.525207\pi$
$557$	−3.73402	−0.158216	−0.0791078	+	0.996866i	$0.525207\pi$
$558$	44.6241	1.88909
$559$	6.86710	0.290448
$560$	51.7386	2.18636
$561$	1.89430	0.0799775
$562$	49.7900	2.10026
$563$	−35.3679	−1.49058	−0.745289	−	0.666742i	$-0.767688\pi$
$563$	−35.3679	−1.49058	−0.745289	+	0.666742i	$0.767688\pi$
$564$	8.82939	0.371784
$565$	15.1367	0.636808
$566$	−48.5360	−2.04012
$567$	38.6394	1.62270
$568$	21.7615	0.913093
$569$	23.5084	0.985522	0.492761	−	0.870165i	$-0.335988\pi$
$569$	23.5084	0.985522	0.492761	+	0.870165i	$0.335988\pi$
$570$	2.91423	0.122064
$571$	−17.9777	−0.752343	−0.376172	−	0.926550i	$-0.622760\pi$
$571$	−17.9777	−0.752343	−0.376172	+	0.926550i	$0.622760\pi$
$572$	23.6099	0.987178
$573$	−0.358423	−0.0149733
$574$	59.0435	2.46443
$575$	9.03090	0.376615
$576$	−43.9577	−1.83157
$577$	−11.5974	−0.482805	−0.241402	−	0.970425i	$-0.577607\pi$
$577$	−11.5974	−0.482805	−0.241402	+	0.970425i	$0.577607\pi$
$578$	6.27437	0.260979
$579$	−2.97668	−0.123707
$580$	4.43090	0.183983
$581$	−46.2376	−1.91826
$582$	7.92624	0.328553
$583$	7.69378	0.318644
$584$	−56.2801	−2.32889
$585$	−6.06934	−0.250936
$586$	−14.9710	−0.618445
$587$	34.1992	1.41155	0.705776	−	0.708435i	$-0.250598\pi$
$587$	34.1992	1.41155	0.705776	+	0.708435i	$0.250598\pi$
$588$	−14.6876	−0.605706
$589$	28.6049	1.17864
$590$	−9.16661	−0.377383
$591$	−4.96031	−0.204040
$592$	57.3531	2.35720
$593$	23.7879	0.976851	0.488425	−	0.872606i	$-0.337571\pi$
$593$	23.7879	0.976851	0.488425	+	0.872606i	$0.337571\pi$
$594$	−7.83043	−0.321287
$595$	−17.2422	−0.706859
$596$	8.53083	0.349436
$597$	3.27166	0.133900
$598$	−49.3271	−2.01713
$599$	42.7674	1.74743	0.873715	−	0.486438i	$-0.161704\pi$
$599$	42.7674	1.74743	0.873715	+	0.486438i	$0.161704\pi$
$600$	1.77319	0.0723900
$601$	−15.9245	−0.649575	−0.324787	−	0.945787i	$-0.605293\pi$
$601$	−15.9245	−0.649575	−0.324787	+	0.945787i	$0.605293\pi$
$602$	−39.9986	−1.63022
$603$	2.39094	0.0973667
$604$	−86.6952	−3.52758
$605$	−5.84748	−0.237734
$606$	−4.32864	−0.175839
$607$	28.8189	1.16972	0.584862	−	0.811133i	$-0.301149\pi$
$607$	28.8189	1.16972	0.584862	+	0.811133i	$0.301149\pi$
$608$	−71.6340	−2.90514
$609$	−0.860803	−0.0348815
$610$	16.1035	0.652011
$611$	−16.4468	−0.665368
$612$	57.1543	2.31033
$613$	−19.7331	−0.797012	−0.398506	−	0.917166i	$-0.630471\pi$
$613$	−19.7331	−0.797012	−0.398506	+	0.917166i	$0.630471\pi$
$614$	70.0101	2.82538
$615$	1.07554	0.0433701
$616$	−83.1604	−3.35063
$617$	6.93616	0.279239	0.139620	−	0.990205i	$-0.455412\pi$
$617$	6.93616	0.279239	0.139620	+	0.990205i	$0.455412\pi$
$618$	−4.29654	−0.172832
$619$	−6.45768	−0.259556	−0.129778	−	0.991543i	$-0.541426\pi$
$619$	−6.45768	−0.259556	−0.129778	+	0.991543i	$0.541426\pi$
$620$	28.7819	1.15591
$621$	11.7251	0.470510
$622$	84.4405	3.38575
$623$	62.4441	2.50177
$624$	−5.14784	−0.206078
$625$	1.00000	0.0400000
$626$	38.4957	1.53860
$627$	−2.48967	−0.0994278
$628$	19.4590	0.776500
$629$	−19.1132	−0.762094
$630$	35.3519	1.40845
$631$	−20.8497	−0.830014	−0.415007	−	0.909818i	$-0.636221\pi$
$631$	−20.8497	−0.830014	−0.415007	+	0.909818i	$0.636221\pi$
$632$	53.6687	2.13483
$633$	3.94197	0.156679
$634$	9.33131	0.370594
$635$	19.9413	0.791345
$636$	−3.74060	−0.148324
$637$	27.3591	1.08401
$638$	−5.28169	−0.209104
$639$	7.90322	0.312646
$640$	−11.0683	−0.437512
$641$	37.9347	1.49833	0.749165	−	0.662383i	$-0.230455\pi$
$641$	37.9347	1.49833	0.749165	+	0.662383i	$0.230455\pi$
$642$	1.34331	0.0530161
$643$	−2.95410	−0.116498	−0.0582491	−	0.998302i	$-0.518552\pi$
$643$	−2.95410	−0.116498	−0.0582491	+	0.998302i	$0.518552\pi$
$644$	205.918	8.11431
$645$	−0.728620	−0.0286894
$646$	51.1190	2.01125
$647$	29.8189	1.17230	0.586151	−	0.810202i	$-0.300643\pi$
$647$	29.8189	1.17230	0.586151	+	0.810202i	$0.300643\pi$
$648$	−69.7031	−2.73820
$649$	7.83118	0.307401
$650$	−5.46203	−0.214239
$651$	−5.59154	−0.219150
$652$	69.3805	2.71715
$653$	−14.9107	−0.583502	−0.291751	−	0.956494i	$-0.594238\pi$
$653$	−14.9107	−0.583502	−0.291751	+	0.956494i	$0.594238\pi$
$654$	−8.04705	−0.314664
$655$	−0.809994	−0.0316491
$656$	−56.6123	−2.21034
$657$	−20.4395	−0.797419
$658$	95.7974	3.73457
$659$	−0.322866	−0.0125771	−0.00628853	−	0.999980i	$-0.502002\pi$
$659$	−0.322866	−0.0125771	−0.00628853	+	0.999980i	$0.502002\pi$
$660$	−2.50508	−0.0975100
$661$	−18.9232	−0.736027	−0.368014	−	0.929820i	$-0.619962\pi$
$661$	−18.9232	−0.736027	−0.368014	+	0.929820i	$0.619962\pi$
$662$	14.9879	0.582521
$663$	1.71554	0.0666262
$664$	83.4097	3.23693
$665$	22.6613	0.878766
$666$	39.1882	1.51851
$667$	7.90864	0.306224
$668$	−79.0003	−3.05661
$669$	1.22496	0.0473596
$670$	2.15170	0.0831275
$671$	−13.7575	−0.531101
$672$	14.0026	0.540164
$673$	8.44975	0.325714	0.162857	−	0.986650i	$-0.447929\pi$
$673$	8.44975	0.325714	0.162857	+	0.986650i	$0.447929\pi$
$674$	−59.7075	−2.29985
$675$	1.29833	0.0499726
$676$	−44.3936	−1.70745
$677$	2.87812	0.110615	0.0553076	−	0.998469i	$-0.482386\pi$
$677$	2.87812	0.110615	0.0553076	+	0.998469i	$0.482386\pi$
$678$	8.77232	0.336899
$679$	61.6351	2.36534
$680$	31.1038	1.19278
$681$	−5.56661	−0.213313
$682$	−34.3084	−1.31374
$683$	48.4016	1.85204	0.926018	−	0.377480i	$-0.123209\pi$
$683$	48.4016	1.85204	0.926018	+	0.377480i	$0.123209\pi$
$684$	−75.1175	−2.87219
$685$	−1.03467	−0.0395329
$686$	−75.5410	−2.88417
$687$	0.408892	0.0156002
$688$	38.3516	1.46214
$689$	6.96775	0.265450
$690$	5.23375	0.199245
$691$	27.9128	1.06185	0.530927	−	0.847418i	$-0.321844\pi$
$691$	27.9128	1.06185	0.530927	+	0.847418i	$0.321844\pi$
$692$	−79.2295	−3.01185
$693$	−30.2017	−1.14727
$694$	15.9897	0.606959
$695$	−5.98675	−0.227091
$696$	1.55284	0.0588601
$697$	18.8663	0.714613
$698$	−82.5772	−3.12559
$699$	1.49941	0.0567128
$700$	22.8015	0.861816
$701$	−6.08346	−0.229769	−0.114885	−	0.993379i	$-0.536650\pi$
$701$	−6.08346	−0.229769	−0.114885	+	0.993379i	$0.536650\pi$
$702$	−7.09150	−0.267652
$703$	25.1204	0.947433
$704$	33.7961	1.27374
$705$	1.74506	0.0657227
$706$	28.8809	1.08695
$707$	−33.6598	−1.26591
$708$	−3.80740	−0.143091
$709$	8.39805	0.315395	0.157698	−	0.987487i	$-0.449593\pi$
$709$	8.39805	0.315395	0.157698	+	0.987487i	$0.449593\pi$
$710$	7.11241	0.266924
$711$	19.4911	0.730973
$712$	−112.645	−4.22156
$713$	51.3724	1.92391
$714$	−9.99248	−0.373959
$715$	4.66630	0.174510
$716$	99.0254	3.70075
$717$	0.0181593	0.000678171 0
$718$	7.70966	0.287722
$719$	5.25611	0.196020	0.0980100	−	0.995185i	$-0.468752\pi$
$719$	5.25611	0.196020	0.0980100	+	0.995185i	$0.468752\pi$
$720$	−33.8962	−1.26324
$721$	−33.4103	−1.24426
$722$	−16.7024	−0.621598
$723$	−1.99295	−0.0741187
$724$	−2.35392	−0.0874826
$725$	0.875732	0.0325239
$726$	−3.38883	−0.125771
$727$	35.7640	1.32641	0.663207	−	0.748436i	$-0.269195\pi$
$727$	35.7640	1.32641	0.663207	+	0.748436i	$0.269195\pi$
$728$	−75.3129	−2.79128
$729$	−24.4648	−0.906103
$730$	−18.3943	−0.680802
$731$	−12.7809	−0.472717
$732$	6.68866	0.247220
$733$	33.6066	1.24129	0.620644	−	0.784092i	$-0.286871\pi$
$733$	33.6066	1.24129	0.620644	+	0.784092i	$0.286871\pi$
$734$	8.41878	0.310743
$735$	−2.90289	−0.107075
$736$	−128.650	−4.74209
$737$	−1.83823	−0.0677121
$738$	−38.6820	−1.42390
$739$	30.1307	1.10838	0.554188	−	0.832392i	$-0.313029\pi$
$739$	30.1307	1.10838	0.554188	+	0.832392i	$0.313029\pi$
$740$	25.2758	0.929159
$741$	−2.25473	−0.0828295
$742$	−40.5849	−1.48992
$743$	14.8723	0.545613	0.272806	−	0.962069i	$-0.412048\pi$
$743$	14.8723	0.545613	0.272806	+	0.962069i	$0.412048\pi$
$744$	10.0868	0.369800
$745$	1.68605	0.0617720
$746$	7.99502	0.292718
$747$	30.2922	1.10834
$748$	−43.9420	−1.60668
$749$	10.4457	0.381676
$750$	0.579538	0.0211617
$751$	11.4621	0.418259	0.209129	−	0.977888i	$-0.432937\pi$
$751$	11.4621	0.418259	0.209129	+	0.977888i	$0.432937\pi$
$752$	−91.8527	−3.34952
$753$	2.72706	0.0993794
$754$	−4.78328	−0.174197
$755$	−17.1346	−0.623592
$756$	29.6038	1.07668
$757$	12.7018	0.461654	0.230827	−	0.972995i	$-0.425857\pi$
$757$	12.7018	0.461654	0.230827	+	0.972995i	$0.425857\pi$
$758$	−79.0783	−2.87225
$759$	−4.47127	−0.162297
$760$	−40.8795	−1.48286
$761$	−36.8644	−1.33633	−0.668166	−	0.744012i	$-0.732920\pi$
$761$	−36.8644	−1.33633	−0.668166	+	0.744012i	$0.732920\pi$
$762$	11.5567	0.418656
$763$	−62.5745	−2.26535
$764$	8.31433	0.300802
$765$	11.2961	0.408411
$766$	29.0920	1.05113
$767$	7.09218	0.256084
$768$	0.0804799	0.00290407
$769$	−39.8533	−1.43715	−0.718573	−	0.695451i	$-0.755204\pi$
$769$	−39.8533	−1.43715	−0.718573	+	0.695451i	$0.755204\pi$
$770$	−27.1797	−0.979487
$771$	2.45556	0.0884347
$772$	69.0500	2.48516
$773$	−41.8401	−1.50488	−0.752442	−	0.658658i	$-0.771124\pi$
$773$	−41.8401	−1.50488	−0.752442	+	0.658658i	$0.771124\pi$
$774$	26.2048	0.941914
$775$	5.68852	0.204338
$776$	−111.186	−3.99134
$777$	−4.91040	−0.176160
$778$	32.3331	1.15920
$779$	−24.7959	−0.888405
$780$	−2.26868	−0.0812318
$781$	−6.07624	−0.217425
$782$	91.8062	3.28298
$783$	1.13699	0.0406326
$784$	152.796	5.45700
$785$	3.84592	0.137267
$786$	−0.469422	−0.0167437
$787$	35.3023	1.25839	0.629196	−	0.777247i	$-0.283384\pi$
$787$	35.3023	1.25839	0.629196	+	0.777247i	$0.283384\pi$
$788$	115.064	4.09899
$789$	0.687392	0.0244718
$790$	17.5408	0.624073
$791$	68.2142	2.42542
$792$	54.4820	1.93593
$793$	−12.4592	−0.442440
$794$	−18.7727	−0.666216
$795$	−0.739299	−0.0262202
$796$	−75.8925	−2.68994
$797$	7.46363	0.264375	0.132188	−	0.991225i	$-0.457800\pi$
$797$	7.46363	0.264375	0.132188	+	0.991225i	$0.457800\pi$
$798$	13.1331	0.464905
$799$	30.6104	1.08292
$800$	−14.2455	−0.503654
$801$	−40.9098	−1.44548
$802$	−2.19933	−0.0776610
$803$	15.7145	0.554553
$804$	0.893720	0.0315191
$805$	40.6980	1.43442
$806$	−31.0709	−1.09442
$807$	4.78559	0.168461
$808$	60.7203	2.13613
$809$	24.4137	0.858339	0.429169	−	0.903224i	$-0.358806\pi$
$809$	24.4137	0.858339	0.429169	+	0.903224i	$0.358806\pi$
$810$	−22.7814	−0.800455
$811$	6.98083	0.245130	0.122565	−	0.992460i	$-0.460888\pi$
$811$	6.98083	0.245130	0.122565	+	0.992460i	$0.460888\pi$
$812$	19.9680	0.700739
$813$	2.40840	0.0844662
$814$	−30.1291	−1.05603
$815$	13.7125	0.480328
$816$	9.58101	0.335402
$817$	16.7978	0.587681
$818$	67.6511	2.36537
$819$	−27.3517	−0.955745
$820$	−24.9493	−0.871269
$821$	15.2569	0.532470	0.266235	−	0.963908i	$-0.414220\pi$
$821$	15.2569	0.532470	0.266235	+	0.963908i	$0.414220\pi$
$822$	−0.599633	−0.0209146
$823$	−37.2883	−1.29979	−0.649894	−	0.760025i	$-0.725187\pi$
$823$	−37.2883	−1.29979	−0.649894	+	0.760025i	$0.725187\pi$
$824$	60.2701	2.09961
$825$	−0.495108	−0.0172375
$826$	−41.3096	−1.43735
$827$	−46.5878	−1.62002	−0.810009	−	0.586418i	$-0.800538\pi$
$827$	−46.5878	−1.62002	−0.810009	+	0.586418i	$0.800538\pi$
$828$	−134.906	−4.68830
$829$	5.32462	0.184932	0.0924659	−	0.995716i	$-0.470525\pi$
$829$	5.32462	0.184932	0.0924659	+	0.995716i	$0.470525\pi$
$830$	27.2612	0.946249
$831$	−3.09820	−0.107475
$832$	30.6069	1.06110
$833$	−50.9201	−1.76428
$834$	−3.46955	−0.120141
$835$	−15.6138	−0.540337
$836$	57.7527	1.99742
$837$	7.38555	0.255282
$838$	38.5934	1.33319
$839$	−36.1353	−1.24753	−0.623764	−	0.781612i	$-0.714397\pi$
$839$	−36.1353	−1.24753	−0.623764	+	0.781612i	$0.714397\pi$
$840$	7.99092	0.275713
$841$	−28.2331	−0.973555
$842$	−34.1194	−1.17583
$843$	4.08734	0.140775
$844$	−91.4416	−3.14755
$845$	−8.77404	−0.301836
$846$	−62.7611	−2.15777
$847$	−26.3518	−0.905460
$848$	38.9137	1.33630
$849$	−3.98439	−0.136744
$850$	10.1658	0.348683
$851$	45.1145	1.54650
$852$	2.95417	0.101208
$853$	−15.0585	−0.515594	−0.257797	−	0.966199i	$-0.582997\pi$
$853$	−15.0585	−0.515594	−0.257797	+	0.966199i	$0.582997\pi$
$854$	72.5709	2.48332
$855$	−14.8464	−0.507735
$856$	−18.8433	−0.644052
$857$	−34.4950	−1.17833	−0.589163	−	0.808014i	$-0.700542\pi$
$857$	−34.4950	−1.17833	−0.589163	+	0.808014i	$0.700542\pi$
$858$	2.70430	0.0923232
$859$	17.1406	0.584829	0.292414	−	0.956292i	$-0.405541\pi$
$859$	17.1406	0.584829	0.292414	+	0.956292i	$0.405541\pi$
$860$	16.9018	0.576345
$861$	4.84697	0.165184
$862$	−17.1830	−0.585255
$863$	49.9756	1.70119	0.850595	−	0.525821i	$-0.176242\pi$
$863$	49.9756	1.70119	0.850595	+	0.525821i	$0.176242\pi$
$864$	−18.4953	−0.629223
$865$	−15.6591	−0.532424
$866$	−16.5870	−0.563651
$867$	0.515072	0.0174928
$868$	129.707	4.40253
$869$	−14.9854	−0.508343
$870$	0.507520	0.0172065
$871$	−1.66476	−0.0564084
$872$	112.881	3.82262
$873$	−40.3798	−1.36665
$874$	−120.660	−4.08139
$875$	4.50653	0.152349
$876$	−7.64014	−0.258136
$877$	26.7417	0.903005	0.451502	−	0.892270i	$-0.350888\pi$
$877$	26.7417	0.903005	0.451502	+	0.892270i	$0.350888\pi$
$878$	−93.2566	−3.14726
$879$	−1.22899	−0.0414528
$880$	26.0605	0.878498
$881$	−17.8429	−0.601141	−0.300571	−	0.953760i	$-0.597177\pi$
$881$	−17.8429	−0.601141	−0.300571	+	0.953760i	$0.597177\pi$
$882$	104.402	3.51541
$883$	3.37442	0.113558	0.0567792	−	0.998387i	$-0.481917\pi$
$883$	3.37442	0.113558	0.0567792	+	0.998387i	$0.481917\pi$
$884$	−39.7954	−1.33846
$885$	−0.752501	−0.0252950
$886$	104.936	3.52538
$887$	9.58248	0.321748	0.160874	−	0.986975i	$-0.448569\pi$
$887$	9.58248	0.321748	0.160874	+	0.986975i	$0.448569\pi$
$888$	8.85807	0.297257
$889$	89.8659	3.01401
$890$	−36.8163	−1.23409
$891$	19.4625	0.652017
$892$	−28.4153	−0.951413
$893$	−40.2310	−1.34628
$894$	0.977129	0.0326801
$895$	19.5716	0.654205
$896$	−49.8795	−1.66636
$897$	−4.04933	−0.135203
$898$	−89.4855	−2.98617
$899$	4.98161	0.166146
$900$	−14.9383	−0.497942
$901$	−12.9682	−0.432033
$902$	29.7399	0.990231
$903$	−3.28355	−0.109270
$904$	−123.054	−4.09272
$905$	−0.465232	−0.0154649
$906$	−9.93015	−0.329907
$907$	−6.38557	−0.212030	−0.106015	−	0.994365i	$-0.533809\pi$
$907$	−6.38557	−0.212030	−0.106015	+	0.994365i	$0.533809\pi$
$908$	129.128	4.28527
$909$	22.0520	0.731419
$910$	−24.6148	−0.815974
$911$	7.56978	0.250798	0.125399	−	0.992106i	$-0.459979\pi$
$911$	7.56978	0.250798	0.125399	+	0.992106i	$0.459979\pi$
$912$	−12.5923	−0.416972
$913$	−23.2896	−0.770774
$914$	75.7398	2.50525
$915$	1.32196	0.0437026
$916$	−9.48505	−0.313395
$917$	−3.65027	−0.120542
$918$	13.1985	0.435616
$919$	10.3207	0.340449	0.170225	−	0.985405i	$-0.445551\pi$
$919$	10.3207	0.340449	0.170225	+	0.985405i	$0.445551\pi$
$920$	−73.4168	−2.42048
$921$	5.74724	0.189378
$922$	−75.8058	−2.49653
$923$	−5.50285	−0.181129
$924$	−11.2892	−0.371388
$925$	4.99557	0.164253
$926$	−27.8462	−0.915084
$927$	21.8885	0.718913
$928$	−12.4752	−0.409519
$929$	18.2692	0.599395	0.299697	−	0.954034i	$-0.403114\pi$
$929$	18.2692	0.599395	0.299697	+	0.954034i	$0.403114\pi$
$930$	3.29671	0.108103
$931$	66.9239	2.19334
$932$	−34.7817	−1.13931
$933$	6.93184	0.226938
$934$	42.0909	1.37726
$935$	−8.68479	−0.284023
$936$	49.3408	1.61275
$937$	49.4662	1.61599	0.807996	−	0.589189i	$-0.200552\pi$
$937$	49.4662	1.61599	0.807996	+	0.589189i	$0.200552\pi$
$938$	9.69671	0.316609
$939$	3.16017	0.103128
$940$	−40.4800	−1.32031
$941$	−31.7611	−1.03538	−0.517691	−	0.855568i	$-0.673208\pi$
$941$	−31.7611	−1.03538	−0.517691	+	0.855568i	$0.673208\pi$
$942$	2.22886	0.0726201
$943$	−44.5317	−1.45015
$944$	39.6086	1.28915
$945$	5.85095	0.190331
$946$	−20.1471	−0.655039
$947$	55.8585	1.81516	0.907578	−	0.419883i	$-0.137929\pi$
$947$	55.8585	1.81516	0.907578	+	0.419883i	$0.137929\pi$
$948$	7.28565	0.236627
$949$	14.2316	0.461977
$950$	−13.3608	−0.433482
$951$	0.766022	0.0248400
$952$	140.170	4.54294
$953$	11.0534	0.358054	0.179027	−	0.983844i	$-0.442705\pi$
$953$	11.0534	0.358054	0.179027	+	0.983844i	$0.442705\pi$
$954$	26.5889	0.860848
$955$	1.64326	0.0531746
$956$	−0.421240	−0.0136239
$957$	−0.433582	−0.0140157
$958$	−77.7865	−2.51317
$959$	−4.66279	−0.150569
$960$	−3.24748	−0.104812
$961$	1.35923	0.0438461
$962$	−27.2860	−0.879735
$963$	−6.84340	−0.220526
$964$	46.2305	1.48898
$965$	13.6472	0.439318
$966$	23.5860	0.758869
$967$	−37.9663	−1.22091	−0.610457	−	0.792049i	$-0.709014\pi$
$967$	−37.9663	−1.22091	−0.610457	+	0.792049i	$0.709014\pi$
$968$	47.5371	1.52790
$969$	4.19644	0.134809
$970$	−36.3394	−1.16679
$971$	−13.9127	−0.446481	−0.223240	−	0.974763i	$-0.571664\pi$
$971$	−13.9127	−0.446481	−0.223240	+	0.974763i	$0.571664\pi$
$972$	−29.1696	−0.935615
$973$	−26.9795	−0.864923
$974$	21.4087	0.685980
$975$	−0.448387	−0.0143599
$976$	−69.5826	−2.22728
$977$	44.9387	1.43772	0.718858	−	0.695157i	$-0.244665\pi$
$977$	44.9387	1.43772	0.718858	+	0.695157i	$0.244665\pi$
$978$	7.94691	0.254114
$979$	31.4528	1.00523
$980$	67.3381	2.15104
$981$	40.9952	1.30888
$982$	−70.8651	−2.26140
$983$	34.3121	1.09438	0.547192	−	0.837007i	$-0.315697\pi$
$983$	34.3121	1.09438	0.547192	+	0.837007i	$0.315697\pi$
$984$	−8.74364	−0.278737
$985$	22.7415	0.724603
$986$	8.90250	0.283513
$987$	7.86416	0.250319
$988$	52.3028	1.66397
$989$	30.1677	0.959276
$990$	17.8066	0.565930
$991$	−49.8633	−1.58396	−0.791980	−	0.610547i	$-0.790950\pi$
$991$	−49.8633	−1.58396	−0.791980	+	0.610547i	$0.790950\pi$
$992$	−81.0357	−2.57289
$993$	1.23038	0.0390449
$994$	32.0523	1.01664
$995$	−14.9995	−0.475517
$996$	11.3231	0.358785
$997$	−5.68330	−0.179992	−0.0899959	−	0.995942i	$-0.528685\pi$
$997$	−5.68330	−0.179992	−0.0899959	+	0.995942i	$0.528685\pi$
$998$	−9.69898	−0.307016
$999$	6.48588	0.205204

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6005.2.a.f.1.4	✓	111

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6005.2.a.f.1.4	✓	111	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:	\( N \)	\(=\)	\( 6005 = 5 \cdot 1201 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65700 q^{2} -0.218117 q^{3} +5.05966 q^{4} +1.00000 q^{5} +0.579538 q^{6} +4.50653 q^{7} -8.12951 q^{8} -2.95242 q^{9} +O(q^{10})\)	\(q-2.65700 q^{2} -0.218117 q^{3} +5.05966 q^{4} +1.00000 q^{5} +0.579538 q^{6} +4.50653 q^{7} -8.12951 q^{8} -2.95242 q^{9} -2.65700 q^{10} +2.26992 q^{11} -1.10360 q^{12} +2.05571 q^{13} -11.9739 q^{14} -0.218117 q^{15} +11.4808 q^{16} -3.82604 q^{17} +7.84460 q^{18} +5.02854 q^{19} +5.05966 q^{20} -0.982952 q^{21} -6.03117 q^{22} +9.03090 q^{23} +1.77319 q^{24} +1.00000 q^{25} -5.46203 q^{26} +1.29833 q^{27} +22.8015 q^{28} +0.875732 q^{29} +0.579538 q^{30} +5.68852 q^{31} -14.2455 q^{32} -0.495108 q^{33} +10.1658 q^{34} +4.50653 q^{35} -14.9383 q^{36} +4.99557 q^{37} -13.3608 q^{38} -0.448387 q^{39} -8.12951 q^{40} -4.93104 q^{41} +2.61171 q^{42} +3.34050 q^{43} +11.4850 q^{44} -2.95242 q^{45} -23.9951 q^{46} -8.00055 q^{47} -2.50416 q^{48} +13.3088 q^{49} -2.65700 q^{50} +0.834524 q^{51} +10.4012 q^{52} +3.38945 q^{53} -3.44966 q^{54} +2.26992 q^{55} -36.6359 q^{56} -1.09681 q^{57} -2.32682 q^{58} +3.44998 q^{59} -1.10360 q^{60} -6.06078 q^{61} -15.1144 q^{62} -13.3052 q^{63} +14.8887 q^{64} +2.05571 q^{65} +1.31550 q^{66} -0.809823 q^{67} -19.3584 q^{68} -1.96979 q^{69} -11.9739 q^{70} -2.67686 q^{71} +24.0018 q^{72} +6.92294 q^{73} -13.2732 q^{74} -0.218117 q^{75} +25.4427 q^{76} +10.2295 q^{77} +1.19136 q^{78} -6.60172 q^{79} +11.4808 q^{80} +8.57409 q^{81} +13.1018 q^{82} -10.2601 q^{83} -4.97340 q^{84} -3.82604 q^{85} -8.87570 q^{86} -0.191012 q^{87} -18.4533 q^{88} +13.8563 q^{89} +7.84460 q^{90} +9.26414 q^{91} +45.6932 q^{92} -1.24076 q^{93} +21.2575 q^{94} +5.02854 q^{95} +3.10719 q^{96} +13.6768 q^{97} -35.3616 q^{98} -6.70176 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9}+O(q^{10}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9	\( 111 q + 20 q^{2} + 40 q^{3} + 136 q^{4} + 111 q^{5} + 3 q^{6} + 39 q^{7} + 45 q^{8} + 139 q^{9} + 20 q^{10} + 36 q^{11} + 80 q^{12} + 36 q^{13} + 7 q^{14} + 40 q^{15} + 190 q^{16} + 38 q^{17} + 48 q^{18} + 77 q^{19} + 136 q^{20} + 11 q^{21} + 39 q^{22} + 82 q^{23} - 3 q^{24} + 111 q^{25} - 3 q^{26} + 130 q^{27} + 87 q^{28} + 20 q^{29} + 3 q^{30} + 41 q^{31} + 85 q^{32} + 33 q^{33} + 7 q^{34} + 39 q^{35} + 191 q^{36} + 80 q^{37} + 42 q^{38} + 21 q^{39} + 45 q^{40} + 16 q^{41} + 33 q^{42} + 164 q^{43} + 37 q^{44} + 139 q^{45} + 32 q^{46} + 148 q^{47} + 149 q^{48} + 160 q^{49} + 20 q^{50} + 51 q^{51} + 87 q^{52} + 83 q^{53} - 6 q^{54} + 36 q^{55} - 10 q^{56} + 28 q^{57} + 47 q^{58} + 14 q^{59} + 80 q^{60} + 20 q^{61} + 14 q^{62} + 120 q^{63} + 231 q^{64} + 36 q^{65} - 4 q^{66} + 253 q^{67} + 80 q^{68} + 6 q^{69} + 7 q^{70} + 5 q^{71} + 124 q^{72} + 64 q^{73} - 37 q^{74} + 40 q^{75} + 92 q^{76} + 63 q^{77} + 29 q^{78} + 91 q^{79} + 190 q^{80} + 187 q^{81} - 7 q^{82} + 63 q^{83} - 69 q^{84} + 38 q^{85} - 22 q^{86} + 57 q^{87} + 121 q^{88} - 6 q^{89} + 48 q^{90} + 119 q^{91} + 104 q^{92} + 14 q^{93} - q^{94} + 77 q^{95} - 38 q^{96} + 96 q^{97} + 81 q^{98} + 106 q^{99}+O(q^{100}) \) 111 * q + 20 * q^2 + 40 * q^3 + 136 * q^4 + 111 * q^5 + 3 * q^6 + 39 * q^7 + 45 * q^8 + 139 * q^9 + 20 * q^10 + 36 * q^11 + 80 * q^12 + 36 * q^13 + 7 * q^14 + 40 * q^15 + 190 * q^16 + 38 * q^17 + 48 * q^18 + 77 * q^19 + 136 * q^20 + 11 * q^21 + 39 * q^22 + 82 * q^23 - 3 * q^24 + 111 * q^25 - 3 * q^26 + 130 * q^27 + 87 * q^28 + 20 * q^29 + 3 * q^30 + 41 * q^31 + 85 * q^32 + 33 * q^33 + 7 * q^34 + 39 * q^35 + 191 * q^36 + 80 * q^37 + 42 * q^38 + 21 * q^39 + 45 * q^40 + 16 * q^41 + 33 * q^42 + 164 * q^43 + 37 * q^44 + 139 * q^45 + 32 * q^46 + 148 * q^47 + 149 * q^48 + 160 * q^49 + 20 * q^50 + 51 * q^51 + 87 * q^52 + 83 * q^53 - 6 * q^54 + 36 * q^55 - 10 * q^56 + 28 * q^57 + 47 * q^58 + 14 * q^59 + 80 * q^60 + 20 * q^61 + 14 * q^62 + 120 * q^63 + 231 * q^64 + 36 * q^65 - 4 * q^66 + 253 * q^67 + 80 * q^68 + 6 * q^69 + 7 * q^70 + 5 * q^71 + 124 * q^72 + 64 * q^73 - 37 * q^74 + 40 * q^75 + 92 * q^76 + 63 * q^77 + 29 * q^78 + 91 * q^79 + 190 * q^80 + 187 * q^81 - 7 * q^82 + 63 * q^83 - 69 * q^84 + 38 * q^85 - 22 * q^86 + 57 * q^87 + 121 * q^88 - 6 * q^89 + 48 * q^90 + 119 * q^91 + 104 * q^92 + 14 * q^93 - q^94 + 77 * q^95 - 38 * q^96 + 96 * q^97 + 81 * q^98 + 106 * q^99

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