LMFDB - Embedded newform 8003.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.52938 q^{2} -2.71474 q^{3} +4.39775 q^{4} -1.01620 q^{5} +6.86661 q^{6} +3.17147 q^{7} -6.06482 q^{8} +4.36984 q^{9} +O(q^{10})$	\(q-2.52938 q^{2} -2.71474 q^{3} +4.39775 q^{4} -1.01620 q^{5} +6.86661 q^{6} +3.17147 q^{7} -6.06482 q^{8} +4.36984 q^{9} +2.57036 q^{10} -1.72198 q^{11} -11.9388 q^{12} -2.04995 q^{13} -8.02184 q^{14} +2.75873 q^{15} +6.54472 q^{16} +2.02987 q^{17} -11.0530 q^{18} +7.44930 q^{19} -4.46901 q^{20} -8.60972 q^{21} +4.35555 q^{22} +1.64276 q^{23} +16.4644 q^{24} -3.96733 q^{25} +5.18511 q^{26} -3.71876 q^{27} +13.9473 q^{28} -6.77724 q^{29} -6.97788 q^{30} +1.15418 q^{31} -4.42443 q^{32} +4.67474 q^{33} -5.13430 q^{34} -3.22286 q^{35} +19.2175 q^{36} +6.28134 q^{37} -18.8421 q^{38} +5.56510 q^{39} +6.16310 q^{40} -7.21808 q^{41} +21.7772 q^{42} -0.235456 q^{43} -7.57285 q^{44} -4.44065 q^{45} -4.15517 q^{46} -2.65341 q^{47} -17.7672 q^{48} +3.05821 q^{49} +10.0349 q^{50} -5.51057 q^{51} -9.01519 q^{52} -1.00000 q^{53} +9.40614 q^{54} +1.74989 q^{55} -19.2344 q^{56} -20.2229 q^{57} +17.1422 q^{58} -5.75196 q^{59} +12.1322 q^{60} +11.7353 q^{61} -2.91937 q^{62} +13.8588 q^{63} -1.89839 q^{64} +2.08317 q^{65} -11.8242 q^{66} +6.26921 q^{67} +8.92686 q^{68} -4.45968 q^{69} +8.15183 q^{70} +4.36727 q^{71} -26.5023 q^{72} -8.97038 q^{73} -15.8879 q^{74} +10.7703 q^{75} +32.7602 q^{76} -5.46121 q^{77} -14.0762 q^{78} -1.76049 q^{79} -6.65077 q^{80} -3.01404 q^{81} +18.2573 q^{82} +2.45457 q^{83} -37.8634 q^{84} -2.06276 q^{85} +0.595557 q^{86} +18.3985 q^{87} +10.4435 q^{88} +5.38980 q^{89} +11.2321 q^{90} -6.50136 q^{91} +7.22446 q^{92} -3.13331 q^{93} +6.71149 q^{94} -7.57001 q^{95} +12.0112 q^{96} +4.45042 q^{97} -7.73536 q^{98} -7.52478 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.52938	−1.78854	−0.894270	−	0.447528i	$-0.852305\pi$
$2$	−2.52938	−1.78854	−0.894270	+	0.447528i	$0.852305\pi$
$3$	−2.71474	−1.56736	−0.783679	−	0.621166i	$-0.786659\pi$
$3$	−2.71474	−1.56736	−0.783679	+	0.621166i	$0.786659\pi$
$4$	4.39775	2.19888
$5$	−1.01620	−0.454460	−0.227230	−	0.973841i	$-0.572967\pi$
$5$	−1.01620	−0.454460	−0.227230	+	0.973841i	$0.572967\pi$
$6$	6.86661	2.80328
$7$	3.17147	1.19870	0.599351	−	0.800486i	$-0.295425\pi$
$7$	3.17147	1.19870	0.599351	+	0.800486i	$0.295425\pi$
$8$	−6.06482	−2.14424
$9$	4.36984	1.45661
$10$	2.57036	0.812821
$11$	−1.72198	−0.519197	−0.259599	−	0.965717i	$-0.583590\pi$
$11$	−1.72198	−0.519197	−0.259599	+	0.965717i	$0.583590\pi$
$12$	−11.9388	−3.44643
$13$	−2.04995	−0.568555	−0.284278	−	0.958742i	$-0.591754\pi$
$13$	−2.04995	−0.568555	−0.284278	+	0.958742i	$0.591754\pi$
$14$	−8.02184	−2.14393
$15$	2.75873	0.712302
$16$	6.54472	1.63618
$17$	2.02987	0.492315	0.246158	−	0.969230i	$-0.420832\pi$
$17$	2.02987	0.492315	0.246158	+	0.969230i	$0.420832\pi$
$18$	−11.0530	−2.60521
$19$	7.44930	1.70899	0.854493	−	0.519463i	$-0.173868\pi$
$19$	7.44930	1.70899	0.854493	+	0.519463i	$0.173868\pi$
$20$	−4.46901	−0.999302
$21$	−8.60972	−1.87880
$22$	4.35555	0.928605
$23$	1.64276	0.342540	0.171270	−	0.985224i	$-0.445213\pi$
$23$	1.64276	0.342540	0.171270	+	0.985224i	$0.445213\pi$
$24$	16.4644	3.36079
$25$	−3.96733	−0.793466
$26$	5.18511	1.01688
$27$	−3.71876	−0.715675
$28$	13.9473	2.63580
$29$	−6.77724	−1.25850	−0.629251	−	0.777202i	$-0.716638\pi$
$29$	−6.77724	−1.25850	−0.629251	+	0.777202i	$0.716638\pi$
$30$	−6.97788	−1.27398
$31$	1.15418	0.207298	0.103649	−	0.994614i	$-0.466948\pi$
$31$	1.15418	0.207298	0.103649	+	0.994614i	$0.466948\pi$
$32$	−4.42443	−0.782136
$33$	4.67474	0.813768
$34$	−5.13430	−0.880526
$35$	−3.22286	−0.544763
$36$	19.2175	3.20291
$37$	6.28134	1.03265	0.516323	−	0.856394i	$-0.327300\pi$
$37$	6.28134	1.03265	0.516323	+	0.856394i	$0.327300\pi$
$38$	−18.8421	−3.05659
$39$	5.56510	0.891129
$40$	6.16310	0.974471
$41$	−7.21808	−1.12727	−0.563637	−	0.826022i	$-0.690598\pi$
$41$	−7.21808	−1.12727	−0.563637	+	0.826022i	$0.690598\pi$
$42$	21.7772	3.36030
$43$	−0.235456	−0.0359067	−0.0179534	−	0.999839i	$-0.505715\pi$
$43$	−0.235456	−0.0359067	−0.0179534	+	0.999839i	$0.505715\pi$
$44$	−7.57285	−1.14165
$45$	−4.44065	−0.661973
$46$	−4.15517	−0.612646
$47$	−2.65341	−0.387040	−0.193520	−	0.981096i	$-0.561990\pi$
$47$	−2.65341	−0.387040	−0.193520	+	0.981096i	$0.561990\pi$
$48$	−17.7672	−2.56448
$49$	3.05821	0.436886
$50$	10.0349	1.41915
$51$	−5.51057	−0.771635
$52$	−9.01519	−1.25018
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	9.40614	1.28001
$55$	1.74989	0.235955
$56$	−19.2344	−2.57030
$57$	−20.2229	−2.67859
$58$	17.1422	2.25088
$59$	−5.75196	−0.748841	−0.374421	−	0.927259i	$-0.622158\pi$
$59$	−5.75196	−0.748841	−0.374421	+	0.927259i	$0.622158\pi$
$60$	12.1322	1.56626
$61$	11.7353	1.50255	0.751277	−	0.659987i	$-0.229438\pi$
$61$	11.7353	1.50255	0.751277	+	0.659987i	$0.229438\pi$
$62$	−2.91937	−0.370760
$63$	13.8588	1.74604
$64$	−1.89839	−0.237299
$65$	2.08317	0.258386
$66$	−11.8242	−1.45546
$67$	6.26921	0.765906	0.382953	−	0.923768i	$-0.374907\pi$
$67$	6.26921	0.765906	0.382953	+	0.923768i	$0.374907\pi$
$68$	8.92686	1.08254
$69$	−4.45968	−0.536882
$70$	8.15183	0.974330
$71$	4.36727	0.518300	0.259150	−	0.965837i	$-0.416558\pi$
$71$	4.36727	0.518300	0.259150	+	0.965837i	$0.416558\pi$
$72$	−26.5023	−3.12332
$73$	−8.97038	−1.04990	−0.524952	−	0.851132i	$-0.675917\pi$
$73$	−8.97038	−1.04990	−0.524952	+	0.851132i	$0.675917\pi$
$74$	−15.8879	−1.84693
$75$	10.7703	1.24365
$76$	32.7602	3.75785
$77$	−5.46121	−0.622363
$78$	−14.0762	−1.59382
$79$	−1.76049	−0.198070	−0.0990351	−	0.995084i	$-0.531576\pi$
$79$	−1.76049	−0.198070	−0.0990351	+	0.995084i	$0.531576\pi$
$80$	−6.65077	−0.743579
$81$	−3.01404	−0.334893
$82$	18.2573	2.01618
$83$	2.45457	0.269424	0.134712	−	0.990885i	$-0.456989\pi$
$83$	2.45457	0.269424	0.134712	+	0.990885i	$0.456989\pi$
$84$	−37.8634	−4.13124
$85$	−2.06276	−0.223738
$86$	0.595557	0.0642206
$87$	18.3985	1.97252
$88$	10.4435	1.11328
$89$	5.38980	0.571318	0.285659	−	0.958331i	$-0.407788\pi$
$89$	5.38980	0.571318	0.285659	+	0.958331i	$0.407788\pi$
$90$	11.2321	1.18396
$91$	−6.50136	−0.681528
$92$	7.22446	0.753202
$93$	−3.13331	−0.324910
$94$	6.71149	0.692237
$95$	−7.57001	−0.776666
$96$	12.0112	1.22589
$97$	4.45042	0.451871	0.225936	−	0.974142i	$-0.427456\pi$
$97$	4.45042	0.451871	0.225936	+	0.974142i	$0.427456\pi$
$98$	−7.73536	−0.781389
$99$	−7.52478	−0.756269
$100$	−17.4473	−1.74473
$101$	3.09905	0.308367	0.154184	−	0.988042i	$-0.450725\pi$
$101$	3.09905	0.308367	0.154184	+	0.988042i	$0.450725\pi$
$102$	13.9383	1.38010
$103$	15.9941	1.57595	0.787974	−	0.615708i	$-0.211130\pi$
$103$	15.9941	1.57595	0.787974	+	0.615708i	$0.211130\pi$
$104$	12.4326	1.21912
$105$	8.74924	0.853838
$106$	2.52938	0.245675
$107$	6.28801	0.607885	0.303942	−	0.952690i	$-0.401697\pi$
$107$	6.28801	0.607885	0.303942	+	0.952690i	$0.401697\pi$
$108$	−16.3542	−1.57368
$109$	3.12327	0.299155	0.149577	−	0.988750i	$-0.452209\pi$
$109$	3.12327	0.299155	0.149577	+	0.988750i	$0.452209\pi$
$110$	−4.42612	−0.422014
$111$	−17.0522	−1.61853
$112$	20.7564	1.96129
$113$	2.35174	0.221233	0.110616	−	0.993863i	$-0.464718\pi$
$113$	2.35174	0.221233	0.110616	+	0.993863i	$0.464718\pi$
$114$	51.1515	4.79077
$115$	−1.66938	−0.155671
$116$	−29.8046	−2.76729
$117$	−8.95797	−0.828164
$118$	14.5489	1.33933
$119$	6.43766	0.590139
$120$	−16.7312	−1.52735
$121$	−8.03477	−0.730434
$122$	−29.6831	−2.68738
$123$	19.5952	1.76684
$124$	5.07582	0.455822
$125$	9.11264	0.815059
$126$	−35.0541	−3.12287
$127$	6.48154	0.575143	0.287572	−	0.957759i	$-0.407152\pi$
$127$	6.48154	0.575143	0.287572	+	0.957759i	$0.407152\pi$
$128$	13.6506	1.20655
$129$	0.639203	0.0562787
$130$	−5.26913	−0.462133
$131$	−1.50294	−0.131312	−0.0656562	−	0.997842i	$-0.520914\pi$
$131$	−1.50294	−0.131312	−0.0656562	+	0.997842i	$0.520914\pi$
$132$	20.5584	1.78938
$133$	23.6252	2.04856
$134$	−15.8572	−1.36985
$135$	3.77902	0.325246
$136$	−12.3108	−1.05564
$137$	4.03923	0.345094	0.172547	−	0.985001i	$-0.444800\pi$
$137$	4.03923	0.345094	0.172547	+	0.985001i	$0.444800\pi$
$138$	11.2802	0.960236
$139$	−7.51618	−0.637514	−0.318757	−	0.947836i	$-0.603265\pi$
$139$	−7.51618	−0.637514	−0.318757	+	0.947836i	$0.603265\pi$
$140$	−14.1733	−1.19787
$141$	7.20334	0.606631
$142$	−11.0465	−0.927000
$143$	3.52999	0.295192
$144$	28.5994	2.38328
$145$	6.88706	0.571939
$146$	22.6895	1.87779
$147$	−8.30225	−0.684758
$148$	27.6238	2.27066
$149$	7.81344	0.640102	0.320051	−	0.947400i	$-0.396300\pi$
$149$	7.81344	0.640102	0.320051	+	0.947400i	$0.396300\pi$
$150$	−27.2421	−2.22431
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−45.1787	−3.66447
$153$	8.87019	0.717113
$154$	13.8135	1.11312
$155$	−1.17289	−0.0942085
$156$	24.4739	1.95948
$157$	−2.02541	−0.161646	−0.0808228	−	0.996728i	$-0.525755\pi$
$157$	−2.02541	−0.161646	−0.0808228	+	0.996728i	$0.525755\pi$
$158$	4.45293	0.354256
$159$	2.71474	0.215293
$160$	4.49612	0.355450
$161$	5.20997	0.410603
$162$	7.62364	0.598970
$163$	11.5818	0.907158	0.453579	−	0.891216i	$-0.350147\pi$
$163$	11.5818	0.907158	0.453579	+	0.891216i	$0.350147\pi$
$164$	−31.7433	−2.47874
$165$	−4.75049	−0.369825
$166$	−6.20853	−0.481876
$167$	3.16302	0.244762	0.122381	−	0.992483i	$-0.460947\pi$
$167$	3.16302	0.244762	0.122381	+	0.992483i	$0.460947\pi$
$168$	52.2164	4.02859
$169$	−8.79769	−0.676745
$170$	5.21750	0.400164
$171$	32.5522	2.48933
$172$	−1.03548	−0.0789544
$173$	−10.8951	−0.828336	−0.414168	−	0.910200i	$-0.635927\pi$
$173$	−10.8951	−0.828336	−0.414168	+	0.910200i	$0.635927\pi$
$174$	−46.5367	−3.52794
$175$	−12.5823	−0.951129
$176$	−11.2699	−0.849500
$177$	15.6151	1.17370
$178$	−13.6328	−1.02182
$179$	13.6802	1.02250	0.511252	−	0.859431i	$-0.329182\pi$
$179$	13.6802	1.02250	0.511252	+	0.859431i	$0.329182\pi$
$180$	−19.5289	−1.45560
$181$	6.15797	0.457719	0.228859	−	0.973460i	$-0.426500\pi$
$181$	6.15797	0.457719	0.228859	+	0.973460i	$0.426500\pi$
$182$	16.4444	1.21894
$183$	−31.8584	−2.35504
$184$	−9.96306	−0.734487
$185$	−6.38312	−0.469297
$186$	7.92534	0.581114
$187$	−3.49540	−0.255609
$188$	−11.6691	−0.851054
$189$	−11.7939	−0.857881
$190$	19.1474	1.38910
$191$	17.3418	1.25481	0.627403	−	0.778695i	$-0.284118\pi$
$191$	17.3418	1.25481	0.627403	+	0.778695i	$0.284118\pi$
$192$	5.15364	0.371932
$193$	−6.26252	−0.450786	−0.225393	−	0.974268i	$-0.572367\pi$
$193$	−6.26252	−0.450786	−0.225393	+	0.974268i	$0.572367\pi$
$194$	−11.2568	−0.808190
$195$	−5.65528	−0.404983
$196$	13.4492	0.960659
$197$	9.08386	0.647198	0.323599	−	0.946194i	$-0.395107\pi$
$197$	9.08386	0.647198	0.323599	+	0.946194i	$0.395107\pi$
$198$	19.0330	1.35262
$199$	−22.8262	−1.61811	−0.809055	−	0.587733i	$-0.800020\pi$
$199$	−22.8262	−1.61811	−0.809055	+	0.587733i	$0.800020\pi$
$200$	24.0611	1.70138
$201$	−17.0193	−1.20045
$202$	−7.83867	−0.551527
$203$	−21.4938	−1.50857
$204$	−24.2341	−1.69673
$205$	7.33504	0.512302
$206$	−40.4552	−2.81865
$207$	7.17860	0.498947
$208$	−13.4164	−0.930258
$209$	−12.8276	−0.887301
$210$	−22.1301	−1.52712
$211$	22.4759	1.54730	0.773651	−	0.633612i	$-0.218428\pi$
$211$	22.4759	1.54730	0.773651	+	0.633612i	$0.218428\pi$
$212$	−4.39775	−0.302039
$213$	−11.8560	−0.812362
$214$	−15.9047	−1.08723
$215$	0.239271	0.0163182
$216$	22.5536	1.53458
$217$	3.66046	0.248488
$218$	−7.89993	−0.535051
$219$	24.3523	1.64557
$220$	7.69557	0.518835
$221$	−4.16114	−0.279908
$222$	43.1315	2.89480
$223$	−2.25917	−0.151286	−0.0756428	−	0.997135i	$-0.524101\pi$
$223$	−2.25917	−0.151286	−0.0756428	+	0.997135i	$0.524101\pi$
$224$	−14.0319	−0.937548
$225$	−17.3366	−1.15577
$226$	−5.94843	−0.395684
$227$	14.8801	0.987626	0.493813	−	0.869568i	$-0.335603\pi$
$227$	14.8801	0.987626	0.493813	+	0.869568i	$0.335603\pi$
$228$	−88.9355	−5.88990
$229$	−15.1342	−1.00009	−0.500047	−	0.865998i	$-0.666684\pi$
$229$	−15.1342	−1.00009	−0.500047	+	0.865998i	$0.666684\pi$
$230$	4.22250	0.278423
$231$	14.8258	0.975466
$232$	41.1027	2.69853
$233$	−14.5354	−0.952248	−0.476124	−	0.879378i	$-0.657959\pi$
$233$	−14.5354	−0.952248	−0.476124	+	0.879378i	$0.657959\pi$
$234$	22.6581	1.48121
$235$	2.69641	0.175894
$236$	−25.2957	−1.64661
$237$	4.77927	0.310447
$238$	−16.2833	−1.05549
$239$	−14.3070	−0.925445	−0.462723	−	0.886503i	$-0.653127\pi$
$239$	−14.3070	−0.925445	−0.462723	+	0.886503i	$0.653127\pi$
$240$	18.0551	1.16545
$241$	−17.5599	−1.13113	−0.565567	−	0.824703i	$-0.691343\pi$
$241$	−17.5599	−1.13113	−0.565567	+	0.824703i	$0.691343\pi$
$242$	20.3230	1.30641
$243$	19.3386	1.24057
$244$	51.6091	3.30393
$245$	−3.10776	−0.198548
$246$	−49.5638	−3.16007
$247$	−15.2707	−0.971653
$248$	−6.99992	−0.444495
$249$	−6.66353	−0.422284
$250$	−23.0493	−1.45777
$251$	−14.3877	−0.908147	−0.454073	−	0.890964i	$-0.650030\pi$
$251$	−14.3877	−0.908147	−0.454073	+	0.890964i	$0.650030\pi$
$252$	60.9475	3.83933
$253$	−2.82881	−0.177846
$254$	−16.3943	−1.02867
$255$	5.59987	0.350677
$256$	−30.7308	−1.92067
$257$	26.4230	1.64822	0.824112	−	0.566427i	$-0.191675\pi$
$257$	26.4230	1.64822	0.824112	+	0.566427i	$0.191675\pi$
$258$	−1.61679	−0.100657
$259$	19.9211	1.23783
$260$	9.16128	0.568158
$261$	−29.6154	−1.83315
$262$	3.80150	0.234857
$263$	−31.3019	−1.93016	−0.965078	−	0.261961i	$-0.915631\pi$
$263$	−31.3019	−1.93016	−0.965078	+	0.261961i	$0.915631\pi$
$264$	−28.3515	−1.74491
$265$	1.01620	0.0624249
$266$	−59.7571	−3.66394
$267$	−14.6319	−0.895459
$268$	27.5704	1.68413
$269$	10.2698	0.626164	0.313082	−	0.949726i	$-0.398639\pi$
$269$	10.2698	0.626164	0.313082	+	0.949726i	$0.398639\pi$
$270$	−9.55856	−0.581715
$271$	−11.2224	−0.681715	−0.340858	−	0.940115i	$-0.610717\pi$
$271$	−11.2224	−0.681715	−0.340858	+	0.940115i	$0.610717\pi$
$272$	13.2849	0.805517
$273$	17.6495	1.06820
$274$	−10.2167	−0.617215
$275$	6.83167	0.411965
$276$	−19.6126	−1.18054
$277$	1.47933	0.0888846	0.0444423	−	0.999012i	$-0.485849\pi$
$277$	1.47933	0.0888846	0.0444423	+	0.999012i	$0.485849\pi$
$278$	19.0113	1.14022
$279$	5.04360	0.301952
$280$	19.5461	1.16810
$281$	−24.5959	−1.46727	−0.733635	−	0.679544i	$-0.762178\pi$
$281$	−24.5959	−1.46727	−0.733635	+	0.679544i	$0.762178\pi$
$282$	−18.2200	−1.08498
$283$	−15.4686	−0.919515	−0.459757	−	0.888045i	$-0.652064\pi$
$283$	−15.4686	−0.919515	−0.459757	+	0.888045i	$0.652064\pi$
$284$	19.2062	1.13968
$285$	20.5506	1.21731
$286$	−8.92867	−0.527963
$287$	−22.8919	−1.35127
$288$	−19.3340	−1.13927
$289$	−12.8796	−0.757626
$290$	−17.4200	−1.02294
$291$	−12.0817	−0.708244
$292$	−39.4495	−2.30861
$293$	−8.77489	−0.512634	−0.256317	−	0.966593i	$-0.582509\pi$
$293$	−8.77489	−0.512634	−0.256317	+	0.966593i	$0.582509\pi$
$294$	20.9995	1.22472
$295$	5.84517	0.340319
$296$	−38.0952	−2.21424
$297$	6.40364	0.371577
$298$	−19.7631	−1.14485
$299$	−3.36759	−0.194753
$300$	47.3650	2.73462
$301$	−0.746741	−0.0430414
$302$	−2.52938	−0.145549
$303$	−8.41313	−0.483322
$304$	48.7536	2.79621
$305$	−11.9255	−0.682852
$306$	−22.4361	−1.28258
$307$	12.5464	0.716058	0.358029	−	0.933710i	$-0.383449\pi$
$307$	12.5464	0.716058	0.358029	+	0.933710i	$0.383449\pi$
$308$	−24.0171	−1.36850
$309$	−43.4200	−2.47008
$310$	2.96667	0.168496
$311$	7.12651	0.404107	0.202054	−	0.979374i	$-0.435238\pi$
$311$	7.12651	0.404107	0.202054	+	0.979374i	$0.435238\pi$
$312$	−33.7513	−1.91079
$313$	13.1008	0.740499	0.370249	−	0.928932i	$-0.379272\pi$
$313$	13.1008	0.740499	0.370249	+	0.928932i	$0.379272\pi$
$314$	5.12304	0.289110
$315$	−14.0834	−0.793508
$316$	−7.74218	−0.435532
$317$	−11.5990	−0.651464	−0.325732	−	0.945462i	$-0.605611\pi$
$317$	−11.5990	−0.651464	−0.325732	+	0.945462i	$0.605611\pi$
$318$	−6.86661	−0.385061
$319$	11.6703	0.653410
$320$	1.92915	0.107843
$321$	−17.0703	−0.952773
$322$	−13.1780	−0.734380
$323$	15.1211	0.841360
$324$	−13.2550	−0.736388
$325$	8.13284	0.451129
$326$	−29.2948	−1.62249
$327$	−8.47888	−0.468883
$328$	43.7764	2.41715
$329$	−8.41522	−0.463946
$330$	12.0158	0.661448
$331$	−12.7462	−0.700594	−0.350297	−	0.936639i	$-0.613919\pi$
$331$	−12.7462	−0.700594	−0.350297	+	0.936639i	$0.613919\pi$
$332$	10.7946	0.592430
$333$	27.4484	1.50416
$334$	−8.00046	−0.437766
$335$	−6.37080	−0.348074
$336$	−56.3482	−3.07405
$337$	9.06122	0.493596	0.246798	−	0.969067i	$-0.420622\pi$
$337$	9.06122	0.493596	0.246798	+	0.969067i	$0.420622\pi$
$338$	22.2527	1.21039
$339$	−6.38436	−0.346751
$340$	−9.07151	−0.491972
$341$	−1.98749	−0.107628
$342$	−82.3369	−4.45227
$343$	−12.5013	−0.675005
$344$	1.42800	0.0769925
$345$	4.53195	0.243992
$346$	27.5577	1.48151
$347$	17.6582	0.947944	0.473972	−	0.880540i	$-0.342820\pi$
$347$	17.6582	0.947944	0.473972	+	0.880540i	$0.342820\pi$
$348$	80.9119	4.33733
$349$	−24.4833	−1.31056	−0.655279	−	0.755387i	$-0.727449\pi$
$349$	−24.4833	−1.31056	−0.655279	+	0.755387i	$0.727449\pi$
$350$	31.8253	1.70113
$351$	7.62328	0.406901
$352$	7.61879	0.406083
$353$	−25.2002	−1.34127	−0.670635	−	0.741787i	$-0.733978\pi$
$353$	−25.2002	−1.34127	−0.670635	+	0.741787i	$0.733978\pi$
$354$	−39.4965	−2.09921
$355$	−4.43804	−0.235547
$356$	23.7030	1.25626
$357$	−17.4766	−0.924960
$358$	−34.6023	−1.82879
$359$	2.44838	0.129220	0.0646102	−	0.997911i	$-0.479420\pi$
$359$	2.44838	0.129220	0.0646102	+	0.997911i	$0.479420\pi$
$360$	26.9317	1.41943
$361$	36.4920	1.92063
$362$	−15.5758	−0.818648
$363$	21.8124	1.14485
$364$	−28.5914	−1.49860
$365$	9.11573	0.477139
$366$	80.5820	4.21209
$367$	13.6426	0.712140	0.356070	−	0.934459i	$-0.384116\pi$
$367$	13.6426	0.712140	0.356070	+	0.934459i	$0.384116\pi$
$368$	10.7514	0.560457
$369$	−31.5418	−1.64200
$370$	16.1453	0.839356
$371$	−3.17147	−0.164654
$372$	−13.7795	−0.714436
$373$	21.4117	1.10866	0.554328	−	0.832298i	$-0.312975\pi$
$373$	21.4117	1.10866	0.554328	+	0.832298i	$0.312975\pi$
$374$	8.84118	0.457167
$375$	−24.7385	−1.27749
$376$	16.0925	0.829907
$377$	13.8930	0.715527
$378$	29.8313	1.53435
$379$	−10.2618	−0.527113	−0.263556	−	0.964644i	$-0.584896\pi$
$379$	−10.2618	−0.527113	−0.263556	+	0.964644i	$0.584896\pi$
$380$	−33.2910	−1.70779
$381$	−17.5957	−0.901456
$382$	−43.8639	−2.24427
$383$	3.78554	0.193432	0.0967160	−	0.995312i	$-0.469166\pi$
$383$	3.78554	0.193432	0.0967160	+	0.995312i	$0.469166\pi$
$384$	−37.0579	−1.89110
$385$	5.54971	0.282839
$386$	15.8403	0.806249
$387$	−1.02890	−0.0523022
$388$	19.5718	0.993609
$389$	−20.0779	−1.01799	−0.508995	−	0.860769i	$-0.669983\pi$
$389$	−20.0779	−1.01799	−0.508995	+	0.860769i	$0.669983\pi$
$390$	14.3043	0.724328
$391$	3.33459	0.168638
$392$	−18.5475	−0.936789
$393$	4.08009	0.205814
$394$	−22.9765	−1.15754
$395$	1.78901	0.0900150
$396$	−33.0921	−1.66294
$397$	4.93872	0.247867	0.123934	−	0.992291i	$-0.460449\pi$
$397$	4.93872	0.247867	0.123934	+	0.992291i	$0.460449\pi$
$398$	57.7362	2.89405
$399$	−64.1364	−3.21084
$400$	−25.9651	−1.29825
$401$	−0.931897	−0.0465367	−0.0232684	−	0.999729i	$-0.507407\pi$
$401$	−0.931897	−0.0465367	−0.0232684	+	0.999729i	$0.507407\pi$
$402$	43.0482	2.14705
$403$	−2.36602	−0.117860
$404$	13.6289	0.678061
$405$	3.06288	0.152196
$406$	54.3659	2.69813
$407$	−10.8164	−0.536147
$408$	33.4206	1.65457
$409$	22.9404	1.13433	0.567165	−	0.823604i	$-0.308040\pi$
$409$	22.9404	1.13433	0.567165	+	0.823604i	$0.308040\pi$
$410$	−18.5531	−0.916272
$411$	−10.9655	−0.540887
$412$	70.3382	3.46532
$413$	−18.2422	−0.897638
$414$	−18.1574	−0.892388
$415$	−2.49434	−0.122443
$416$	9.06988	0.444687
$417$	20.4045	0.999213
$418$	32.4458	1.58697
$419$	−18.6195	−0.909624	−0.454812	−	0.890587i	$-0.650294\pi$
$419$	−18.6195	−0.909624	−0.454812	+	0.890587i	$0.650294\pi$
$420$	38.4770	1.87748
$421$	22.7000	1.10633	0.553164	−	0.833072i	$-0.313420\pi$
$421$	22.7000	1.10633	0.553164	+	0.833072i	$0.313420\pi$
$422$	−56.8500	−2.76741
$423$	−11.5950	−0.563768
$424$	6.06482	0.294534
$425$	−8.05316	−0.390635
$426$	29.9884	1.45294
$427$	37.2182	1.80112
$428$	27.6531	1.33666
$429$	−9.58301	−0.462672
$430$	−0.605208	−0.0291857
$431$	−14.4004	−0.693644	−0.346822	−	0.937931i	$-0.612739\pi$
$431$	−14.4004	−0.693644	−0.346822	+	0.937931i	$0.612739\pi$
$432$	−24.3382	−1.17097
$433$	−24.4765	−1.17627	−0.588133	−	0.808764i	$-0.700137\pi$
$433$	−24.4765	−1.17627	−0.588133	+	0.808764i	$0.700137\pi$
$434$	−9.25868	−0.444431
$435$	−18.6966	−0.896433
$436$	13.7354	0.657805
$437$	12.2374	0.585395
$438$	−61.5961	−2.94318
$439$	3.45083	0.164699	0.0823497	−	0.996603i	$-0.473758\pi$
$439$	3.45083	0.164699	0.0823497	+	0.996603i	$0.473758\pi$
$440$	−10.6127	−0.505943
$441$	13.3639	0.636374
$442$	10.5251	0.500627
$443$	−26.9828	−1.28199	−0.640995	−	0.767545i	$-0.721478\pi$
$443$	−26.9828	−1.28199	−0.640995	+	0.767545i	$0.721478\pi$
$444$	−74.9915	−3.55894
$445$	−5.47714	−0.259641
$446$	5.71431	0.270580
$447$	−21.2115	−1.00327
$448$	−6.02068	−0.284450
$449$	29.3930	1.38714	0.693571	−	0.720389i	$-0.256036\pi$
$449$	29.3930	1.38714	0.693571	+	0.720389i	$0.256036\pi$
$450$	43.8508	2.06714
$451$	12.4294	0.585278
$452$	10.3424	0.486464
$453$	−2.71474	−0.127550
$454$	−37.6374	−1.76641
$455$	6.60671	0.309727
$456$	122.649	5.74354
$457$	33.8081	1.58148	0.790739	−	0.612154i	$-0.209697\pi$
$457$	33.8081	1.58148	0.790739	+	0.612154i	$0.209697\pi$
$458$	38.2801	1.78871
$459$	−7.54859	−0.352338
$460$	−7.34153	−0.342301
$461$	−40.2491	−1.87459	−0.937294	−	0.348539i	$-0.886678\pi$
$461$	−40.2491	−1.87459	−0.937294	+	0.348539i	$0.886678\pi$
$462$	−37.5000	−1.74466
$463$	1.78696	0.0830470	0.0415235	−	0.999138i	$-0.486779\pi$
$463$	1.78696	0.0830470	0.0415235	+	0.999138i	$0.486779\pi$
$464$	−44.3551	−2.05913
$465$	3.18409	0.147659
$466$	36.7656	1.70313
$467$	−21.1120	−0.976946	−0.488473	−	0.872579i	$-0.662446\pi$
$467$	−21.1120	−0.976946	−0.488473	+	0.872579i	$0.662446\pi$
$468$	−39.3949	−1.82103
$469$	19.8826	0.918093
$470$	−6.82024	−0.314594
$471$	5.49848	0.253357
$472$	34.8846	1.60569
$473$	0.405451	0.0186427
$474$	−12.0886	−0.555247
$475$	−29.5538	−1.35602
$476$	28.3112	1.29764
$477$	−4.36984	−0.200081
$478$	36.1879	1.65520
$479$	−26.6458	−1.21748	−0.608739	−	0.793371i	$-0.708324\pi$
$479$	−26.6458	−1.21748	−0.608739	+	0.793371i	$0.708324\pi$
$480$	−12.2058	−0.557117
$481$	−12.8765	−0.587116
$482$	44.4157	2.02308
$483$	−14.1437	−0.643562
$484$	−35.3350	−1.60613
$485$	−4.52253	−0.205358
$486$	−48.9147	−2.21881
$487$	−2.04352	−0.0926008	−0.0463004	−	0.998928i	$-0.514743\pi$
$487$	−2.04352	−0.0926008	−0.0463004	+	0.998928i	$0.514743\pi$
$488$	−71.1727	−3.22184
$489$	−31.4417	−1.42184
$490$	7.86070	0.355110
$491$	21.0945	0.951980	0.475990	−	0.879451i	$-0.342090\pi$
$491$	21.0945	0.951980	0.475990	+	0.879451i	$0.342090\pi$
$492$	86.1750	3.88507
$493$	−13.7569	−0.619579
$494$	38.6254	1.73784
$495$	7.64672	0.343694
$496$	7.55381	0.339176
$497$	13.8507	0.621287
$498$	16.8546	0.755272
$499$	29.4438	1.31809	0.659043	−	0.752106i	$-0.270962\pi$
$499$	29.4438	1.31809	0.659043	+	0.752106i	$0.270962\pi$
$500$	40.0751	1.79221
$501$	−8.58678	−0.383629
$502$	36.3921	1.62426
$503$	6.91994	0.308545	0.154272	−	0.988028i	$-0.450697\pi$
$503$	6.91994	0.308545	0.154272	+	0.988028i	$0.450697\pi$
$504$	−84.0511	−3.74393
$505$	−3.14927	−0.140141
$506$	7.15513	0.318084
$507$	23.8835	1.06070
$508$	28.5042	1.26467
$509$	27.4112	1.21498	0.607490	−	0.794327i	$-0.292176\pi$
$509$	27.4112	1.21498	0.607490	+	0.794327i	$0.292176\pi$
$510$	−14.1642	−0.627201
$511$	−28.4493	−1.25852
$512$	50.4285	2.22864
$513$	−27.7021	−1.22308
$514$	−66.8338	−2.94791
$515$	−16.2533	−0.716206
$516$	2.81106	0.123750
$517$	4.56913	0.200950
$518$	−50.3879	−2.21392
$519$	29.5773	1.29830
$520$	−12.6341	−0.554041
$521$	45.3683	1.98762	0.993811	−	0.111080i	$-0.0354311\pi$
$521$	45.3683	1.98762	0.993811	+	0.111080i	$0.0354311\pi$
$522$	74.9086	3.27866
$523$	−18.1937	−0.795556	−0.397778	−	0.917482i	$-0.630219\pi$
$523$	−18.1937	−0.795556	−0.397778	+	0.917482i	$0.630219\pi$
$524$	−6.60955	−0.288740
$525$	34.1576	1.49076
$526$	79.1743	3.45216
$527$	2.34284	0.102056
$528$	30.5949	1.33147
$529$	−20.3013	−0.882667
$530$	−2.57036	−0.111650
$531$	−25.1351	−1.09077
$532$	103.898	4.50454
$533$	14.7967	0.640918
$534$	37.0097	1.60157
$535$	−6.38990	−0.276259
$536$	−38.0216	−1.64228
$537$	−37.1382	−1.60263
$538$	−25.9763	−1.11992
$539$	−5.26618	−0.226830
$540$	16.6192	0.715176
$541$	−15.2149	−0.654140	−0.327070	−	0.945000i	$-0.606061\pi$
$541$	−15.2149	−0.654140	−0.327070	+	0.945000i	$0.606061\pi$
$542$	28.3858	1.21928
$543$	−16.7173	−0.717409
$544$	−8.98101	−0.385058
$545$	−3.17388	−0.135954
$546$	−44.6424	−1.91052
$547$	26.3853	1.12815	0.564076	−	0.825723i	$-0.309233\pi$
$547$	26.3853	1.12815	0.564076	+	0.825723i	$0.309233\pi$
$548$	17.7635	0.758820
$549$	51.2815	2.18864
$550$	−17.2799	−0.736817
$551$	−50.4856	−2.15076
$552$	27.0472	1.15120
$553$	−5.58332	−0.237427
$554$	−3.74180	−0.158974
$555$	17.3285	0.735556
$556$	−33.0543	−1.40181
$557$	30.1573	1.27781	0.638904	−	0.769287i	$-0.279388\pi$
$557$	30.1573	1.27781	0.638904	+	0.769287i	$0.279388\pi$
$558$	−12.7572	−0.540054
$559$	0.482674	0.0204149
$560$	−21.0927	−0.891330
$561$	9.48911	0.400631
$562$	62.2124	2.62427
$563$	22.1569	0.933801	0.466901	−	0.884310i	$-0.345371\pi$
$563$	22.1569	0.933801	0.466901	+	0.884310i	$0.345371\pi$
$564$	31.6785	1.33391
$565$	−2.38985	−0.100542
$566$	39.1260	1.64459
$567$	−9.55892	−0.401437
$568$	−26.4867	−1.11136
$569$	−21.0799	−0.883715	−0.441858	−	0.897085i	$-0.645680\pi$
$569$	−21.0799	−0.883715	−0.441858	+	0.897085i	$0.645680\pi$
$570$	−51.9803	−2.17722
$571$	28.6673	1.19969	0.599845	−	0.800116i	$-0.295229\pi$
$571$	28.6673	1.19969	0.599845	+	0.800116i	$0.295229\pi$
$572$	15.5240	0.649091
$573$	−47.0785	−1.96673
$574$	57.9023	2.41679
$575$	−6.51738	−0.271793
$576$	−8.29565	−0.345652
$577$	12.7371	0.530252	0.265126	−	0.964214i	$-0.414586\pi$
$577$	12.7371	0.530252	0.265126	+	0.964214i	$0.414586\pi$
$578$	32.5775	1.35504
$579$	17.0011	0.706543
$580$	30.2876	1.25762
$581$	7.78459	0.322959
$582$	30.5593	1.26672
$583$	1.72198	0.0713172
$584$	54.4037	2.25124
$585$	9.10312	0.376368
$586$	22.1950	0.916867
$587$	29.2069	1.20550	0.602749	−	0.797931i	$-0.294072\pi$
$587$	29.2069	1.20550	0.602749	+	0.797931i	$0.294072\pi$
$588$	−36.5112	−1.50570
$589$	8.59786	0.354269
$590$	−14.7846	−0.608674
$591$	−24.6604	−1.01439
$592$	41.1096	1.68959
$593$	−2.97743	−0.122269	−0.0611343	−	0.998130i	$-0.519472\pi$
$593$	−2.97743	−0.122269	−0.0611343	+	0.998130i	$0.519472\pi$
$594$	−16.1972	−0.664580
$595$	−6.54198	−0.268195
$596$	34.3616	1.40750
$597$	61.9674	2.53616
$598$	8.51790	0.348323
$599$	−13.6794	−0.558924	−0.279462	−	0.960157i	$-0.590156\pi$
$599$	−13.6794	−0.558924	−0.279462	+	0.960157i	$0.590156\pi$
$600$	−65.3198	−2.66667
$601$	16.9758	0.692457	0.346229	−	0.938150i	$-0.387462\pi$
$601$	16.9758	0.692457	0.346229	+	0.938150i	$0.387462\pi$
$602$	1.88879	0.0769814
$603$	27.3954	1.11563
$604$	4.39775	0.178942
$605$	8.16497	0.331953
$606$	21.2800	0.864441
$607$	−6.88128	−0.279303	−0.139651	−	0.990201i	$-0.544598\pi$
$607$	−6.88128	−0.279303	−0.139651	+	0.990201i	$0.544598\pi$
$608$	−32.9589	−1.33666
$609$	58.3501	2.36447
$610$	30.1641	1.22131
$611$	5.43938	0.220054
$612$	39.0089	1.57684
$613$	37.1082	1.49879	0.749393	−	0.662126i	$-0.230346\pi$
$613$	37.1082	1.49879	0.749393	+	0.662126i	$0.230346\pi$
$614$	−31.7345	−1.28070
$615$	−19.9128	−0.802960
$616$	33.1213	1.33449
$617$	12.9883	0.522889	0.261445	−	0.965219i	$-0.415801\pi$
$617$	12.9883	0.522889	0.261445	+	0.965219i	$0.415801\pi$
$618$	109.826	4.41783
$619$	−1.98564	−0.0798097	−0.0399048	−	0.999203i	$-0.512705\pi$
$619$	−1.98564	−0.0798097	−0.0399048	+	0.999203i	$0.512705\pi$
$620$	−5.15807	−0.207153
$621$	−6.10903	−0.245147
$622$	−18.0256	−0.722762
$623$	17.0936	0.684840
$624$	36.4220	1.45805
$625$	10.5763	0.423054
$626$	−33.1368	−1.32441
$627$	34.8236	1.39072
$628$	−8.90727	−0.355439
$629$	12.7503	0.508387
$630$	35.6222	1.41922
$631$	−24.8408	−0.988898	−0.494449	−	0.869207i	$-0.664630\pi$
$631$	−24.8408	−0.988898	−0.494449	+	0.869207i	$0.664630\pi$
$632$	10.6770	0.424710
$633$	−61.0162	−2.42518
$634$	29.3382	1.16517
$635$	−6.58656	−0.261380
$636$	11.9388	0.473403
$637$	−6.26918	−0.248394
$638$	−29.5186	−1.16865
$639$	19.0843	0.754962
$640$	−13.8718	−0.548331
$641$	−26.4597	−1.04510	−0.522548	−	0.852610i	$-0.675018\pi$
$641$	−26.4597	−1.04510	−0.522548	+	0.852610i	$0.675018\pi$
$642$	43.1773	1.70407
$643$	15.6491	0.617142	0.308571	−	0.951201i	$-0.400149\pi$
$643$	15.6491	0.617142	0.308571	+	0.951201i	$0.400149\pi$
$644$	22.9121	0.902865
$645$	−0.649561	−0.0255764
$646$	−38.2470	−1.50481
$647$	10.7335	0.421979	0.210989	−	0.977488i	$-0.432331\pi$
$647$	10.7335	0.421979	0.210989	+	0.977488i	$0.432331\pi$
$648$	18.2796	0.718090
$649$	9.90478	0.388796
$650$	−20.5710	−0.806862
$651$	−9.93720	−0.389470
$652$	50.9340	1.99473
$653$	32.8211	1.28439	0.642194	−	0.766542i	$-0.278024\pi$
$653$	32.8211	1.28439	0.642194	+	0.766542i	$0.278024\pi$
$654$	21.4463	0.838616
$655$	1.52729	0.0596763
$656$	−47.2403	−1.84442
$657$	−39.1991	−1.52930
$658$	21.2853	0.829786
$659$	22.8968	0.891934	0.445967	−	0.895049i	$-0.352860\pi$
$659$	22.8968	0.891934	0.445967	+	0.895049i	$0.352860\pi$
$660$	−20.8915	−0.813200
$661$	7.94221	0.308916	0.154458	−	0.987999i	$-0.450637\pi$
$661$	7.94221	0.308916	0.154458	+	0.987999i	$0.450637\pi$
$662$	32.2399	1.25304
$663$	11.2964	0.438717
$664$	−14.8865	−0.577709
$665$	−24.0080	−0.930992
$666$	−69.4274	−2.69026
$667$	−11.1334	−0.431087
$668$	13.9102	0.538200
$669$	6.13308	0.237119
$670$	16.1141	0.622544
$671$	−20.2080	−0.780122
$672$	38.0931	1.46947
$673$	17.3319	0.668097	0.334049	−	0.942556i	$-0.391585\pi$
$673$	17.3319	0.668097	0.334049	+	0.942556i	$0.391585\pi$
$674$	−22.9192	−0.882817
$675$	14.7535	0.567864
$676$	−38.6901	−1.48808
$677$	−5.31753	−0.204369	−0.102185	−	0.994765i	$-0.532583\pi$
$677$	−5.31753	−0.204369	−0.102185	+	0.994765i	$0.532583\pi$
$678$	16.1485	0.620178
$679$	14.1144	0.541659
$680$	12.5103	0.479747
$681$	−40.3956	−1.54796
$682$	5.02710	0.192498
$683$	−27.3281	−1.04568	−0.522840	−	0.852431i	$-0.675128\pi$
$683$	−27.3281	−1.04568	−0.522840	+	0.852431i	$0.675128\pi$
$684$	143.157	5.47373
$685$	−4.10468	−0.156832
$686$	31.6204	1.20727
$687$	41.0854	1.56751
$688$	−1.54099	−0.0587498
$689$	2.04995	0.0780970
$690$	−11.4630	−0.436389
$691$	−11.5393	−0.438974	−0.219487	−	0.975615i	$-0.570438\pi$
$691$	−11.5393	−0.438974	−0.219487	+	0.975615i	$0.570438\pi$
$692$	−47.9138	−1.82141
$693$	−23.8646	−0.906541
$694$	−44.6644	−1.69544
$695$	7.63798	0.289725
$696$	−111.583	−4.22956
$697$	−14.6518	−0.554975
$698$	61.9274	2.34399
$699$	39.4600	1.49251
$700$	−55.3336	−2.09141
$701$	16.5174	0.623855	0.311928	−	0.950106i	$-0.399025\pi$
$701$	16.5174	0.623855	0.311928	+	0.950106i	$0.399025\pi$
$702$	−19.2822	−0.727758
$703$	46.7916	1.76478
$704$	3.26899	0.123205
$705$	−7.32007	−0.275690
$706$	63.7408	2.39892
$707$	9.82854	0.369640
$708$	68.6713	2.58083
$709$	32.5822	1.22365	0.611825	−	0.790993i	$-0.290436\pi$
$709$	32.5822	1.22365	0.611825	+	0.790993i	$0.290436\pi$
$710$	11.2255	0.421285
$711$	−7.69304	−0.288511
$712$	−32.6882	−1.22504
$713$	1.89605	0.0710076
$714$	44.2049	1.65433
$715$	−3.58719	−0.134153
$716$	60.1620	2.24836
$717$	38.8400	1.45050
$718$	−6.19287	−0.231116
$719$	−23.0005	−0.857773	−0.428887	−	0.903358i	$-0.641094\pi$
$719$	−23.0005	−0.857773	−0.428887	+	0.903358i	$0.641094\pi$
$720$	−29.0628	−1.08311
$721$	50.7249	1.88909
$722$	−92.3021	−3.43513
$723$	47.6707	1.77289
$724$	27.0812	1.00647
$725$	26.8875	0.998578
$726$	−55.1717	−2.04761
$727$	9.33453	0.346199	0.173099	−	0.984904i	$-0.444622\pi$
$727$	9.33453	0.346199	0.173099	+	0.984904i	$0.444622\pi$
$728$	39.4296	1.46136
$729$	−43.4573	−1.60953
$730$	−23.0571	−0.853383
$731$	−0.477945	−0.0176774
$732$	−140.105	−5.17844
$733$	−6.28618	−0.232185	−0.116093	−	0.993238i	$-0.537037\pi$
$733$	−6.28618	−0.232185	−0.116093	+	0.993238i	$0.537037\pi$
$734$	−34.5074	−1.27369
$735$	8.43678	0.311195
$736$	−7.26829	−0.267913
$737$	−10.7955	−0.397656
$738$	79.7812	2.93679
$739$	−4.21019	−0.154874	−0.0774371	−	0.996997i	$-0.524674\pi$
$739$	−4.21019	−0.154874	−0.0774371	+	0.996997i	$0.524674\pi$
$740$	−28.0714	−1.03192
$741$	41.4561	1.52293
$742$	8.02184	0.294491
$743$	−27.0743	−0.993259	−0.496630	−	0.867963i	$-0.665429\pi$
$743$	−27.0743	−0.993259	−0.496630	+	0.867963i	$0.665429\pi$
$744$	19.0030	0.696684
$745$	−7.94005	−0.290901
$746$	−54.1583	−1.98288
$747$	10.7261	0.392446
$748$	−15.3719	−0.562052
$749$	19.9422	0.728672
$750$	62.5730	2.28484
$751$	−24.8042	−0.905116	−0.452558	−	0.891735i	$-0.649489\pi$
$751$	−24.8042	−0.905116	−0.452558	+	0.891735i	$0.649489\pi$
$752$	−17.3659	−0.633268
$753$	39.0591	1.42339
$754$	−35.1407	−1.27975
$755$	−1.01620	−0.0369835
$756$	−51.8667	−1.88637
$757$	−18.3549	−0.667120	−0.333560	−	0.942729i	$-0.608250\pi$
$757$	−18.3549	−0.667120	−0.333560	+	0.942729i	$0.608250\pi$
$758$	25.9560	0.942763
$759$	7.67949	0.278748
$760$	45.9107	1.66536
$761$	14.4782	0.524834	0.262417	−	0.964955i	$-0.415480\pi$
$761$	14.4782	0.524834	0.262417	+	0.964955i	$0.415480\pi$
$762$	44.5062	1.61229
$763$	9.90535	0.358598
$764$	76.2648	2.75916
$765$	−9.01393	−0.325899
$766$	−9.57506	−0.345961
$767$	11.7913	0.425758
$768$	83.4261	3.01038
$769$	−23.3086	−0.840529	−0.420265	−	0.907402i	$-0.638063\pi$
$769$	−23.3086	−0.840529	−0.420265	+	0.907402i	$0.638063\pi$
$770$	−14.0373	−0.505869
$771$	−71.7318	−2.58336
$772$	−27.5410	−0.991222
$773$	−35.4208	−1.27400	−0.636999	−	0.770865i	$-0.719824\pi$
$773$	−35.4208	−1.27400	−0.636999	+	0.770865i	$0.719824\pi$
$774$	2.60249	0.0935445
$775$	−4.57903	−0.164484
$776$	−26.9910	−0.968920
$777$	−54.0806	−1.94013
$778$	50.7846	1.82072
$779$	−53.7696	−1.92650
$780$	−24.8705	−0.890508
$781$	−7.52037	−0.269100
$782$	−8.43444	−0.301615
$783$	25.2029	0.900678
$784$	20.0151	0.714825
$785$	2.05824	0.0734616
$786$	−10.3201	−0.368106
$787$	34.9955	1.24745	0.623727	−	0.781642i	$-0.285618\pi$
$787$	34.9955	1.24745	0.623727	+	0.781642i	$0.285618\pi$
$788$	39.9486	1.42311
$789$	84.9766	3.02525
$790$	−4.52509	−0.160995
$791$	7.45846	0.265192
$792$	45.6365	1.62162
$793$	−24.0569	−0.854285
$794$	−12.4919	−0.443320
$795$	−2.75873	−0.0978422
$796$	−100.384	−3.55802
$797$	17.1187	0.606374	0.303187	−	0.952931i	$-0.401949\pi$
$797$	17.1187	0.606374	0.303187	+	0.952931i	$0.401949\pi$
$798$	162.225	5.74271
$799$	−5.38608	−0.190546
$800$	17.5532	0.620598
$801$	23.5525	0.832188
$802$	2.35712	0.0832328
$803$	15.4468	0.545107
$804$	−74.8466	−2.63964
$805$	−5.29439	−0.186603
$806$	5.98457	0.210797
$807$	−27.8800	−0.981423
$808$	−18.7952	−0.661213
$809$	−13.0541	−0.458957	−0.229478	−	0.973314i	$-0.573702\pi$
$809$	−13.0541	−0.458957	−0.229478	+	0.973314i	$0.573702\pi$
$810$	−7.74717	−0.272208
$811$	−19.0442	−0.668731	−0.334366	−	0.942443i	$-0.608522\pi$
$811$	−19.0442	−0.668731	−0.334366	+	0.942443i	$0.608522\pi$
$812$	−94.5243	−3.31715
$813$	30.4661	1.06849
$814$	27.3587	0.958920
$815$	−11.7695	−0.412267
$816$	−36.0652	−1.26253
$817$	−1.75398	−0.0613641
$818$	−58.0249	−2.02879
$819$	−28.4099	−0.992722
$820$	32.2577	1.12649
$821$	−31.1681	−1.08778	−0.543888	−	0.839158i	$-0.683048\pi$
$821$	−31.1681	−1.08778	−0.543888	+	0.839158i	$0.683048\pi$
$822$	27.7358	0.967397
$823$	12.0162	0.418858	0.209429	−	0.977824i	$-0.432840\pi$
$823$	12.0162	0.418858	0.209429	+	0.977824i	$0.432840\pi$
$824$	−97.0016	−3.37921
$825$	−18.5462	−0.645697
$826$	46.1413	1.60546
$827$	−4.69508	−0.163264	−0.0816319	−	0.996663i	$-0.526013\pi$
$827$	−4.69508	−0.163264	−0.0816319	+	0.996663i	$0.526013\pi$
$828$	31.5697	1.09712
$829$	27.0897	0.940865	0.470432	−	0.882436i	$-0.344098\pi$
$829$	27.0897	0.940865	0.470432	+	0.882436i	$0.344098\pi$
$830$	6.30914	0.218993
$831$	−4.01601	−0.139314
$832$	3.89161	0.134917
$833$	6.20775	0.215086
$834$	−51.6107	−1.78713
$835$	−3.21427	−0.111234
$836$	−56.4124	−1.95107
$837$	−4.29213	−0.148358
$838$	47.0959	1.62690
$839$	1.37006	0.0472997	0.0236499	−	0.999720i	$-0.492471\pi$
$839$	1.37006	0.0472997	0.0236499	+	0.999720i	$0.492471\pi$
$840$	−53.0626	−1.83083
$841$	16.9309	0.583825
$842$	−57.4168	−1.97871
$843$	66.7716	2.29974
$844$	98.8433	3.40233
$845$	8.94025	0.307554
$846$	29.3281	1.00832
$847$	−25.4820	−0.875573
$848$	−6.54472	−0.224747
$849$	41.9934	1.44121
$850$	20.3695	0.698667
$851$	10.3187	0.353722
$852$	−52.1399	−1.78628
$853$	−31.1102	−1.06519	−0.532597	−	0.846369i	$-0.678784\pi$
$853$	−31.1102	−1.06519	−0.532597	+	0.846369i	$0.678784\pi$
$854$	−94.1389	−3.22137
$855$	−33.0797	−1.13130
$856$	−38.1356	−1.30345
$857$	−18.3794	−0.627830	−0.313915	−	0.949451i	$-0.601641\pi$
$857$	−18.3794	−0.627830	−0.313915	+	0.949451i	$0.601641\pi$
$858$	24.2391	0.827508
$859$	−20.7343	−0.707446	−0.353723	−	0.935350i	$-0.615084\pi$
$859$	−20.7343	−0.707446	−0.353723	+	0.935350i	$0.615084\pi$
$860$	1.05226	0.0358817
$861$	62.1457	2.11792
$862$	36.4241	1.24061
$863$	−23.7444	−0.808270	−0.404135	−	0.914699i	$-0.632427\pi$
$863$	−23.7444	−0.808270	−0.404135	+	0.914699i	$0.632427\pi$
$864$	16.4534	0.559755
$865$	11.0716	0.376446
$866$	61.9103	2.10380
$867$	34.9649	1.18747
$868$	16.0978	0.546394
$869$	3.03153	0.102837
$870$	47.2908	1.60331
$871$	−12.8516	−0.435459
$872$	−18.9421	−0.641459
$873$	19.4476	0.658201
$874$	−30.9531	−1.04700
$875$	28.9004	0.977013
$876$	107.095	3.61841
$877$	−27.4326	−0.926333	−0.463166	−	0.886271i	$-0.653287\pi$
$877$	−27.4326	−0.926333	−0.463166	+	0.886271i	$0.653287\pi$
$878$	−8.72846	−0.294571
$879$	23.8216	0.803482
$880$	11.4525	0.386064
$881$	0.962467	0.0324263	0.0162132	−	0.999869i	$-0.494839\pi$
$881$	0.962467	0.0324263	0.0162132	+	0.999869i	$0.494839\pi$
$882$	−33.8022	−1.13818
$883$	20.2621	0.681875	0.340938	−	0.940086i	$-0.389256\pi$
$883$	20.2621	0.681875	0.340938	+	0.940086i	$0.389256\pi$
$884$	−18.2997	−0.615484
$885$	−15.8681	−0.533401
$886$	68.2496	2.29289
$887$	34.3812	1.15441	0.577204	−	0.816600i	$-0.304144\pi$
$887$	34.3812	1.15441	0.577204	+	0.816600i	$0.304144\pi$
$888$	103.419	3.47050
$889$	20.5560	0.689425
$890$	13.8538	0.464379
$891$	5.19012	0.173876
$892$	−9.93529	−0.332658
$893$	−19.7661	−0.661446
$894$	53.6519	1.79439
$895$	−13.9019	−0.464688
$896$	43.2924	1.44630
$897$	9.14214	0.305247
$898$	−74.3460	−2.48096
$899$	−7.82218	−0.260884
$900$	−76.2420	−2.54140
$901$	−2.02987	−0.0676247
$902$	−31.4387	−1.04679
$903$	2.02721	0.0674614
$904$	−14.2629	−0.474376
$905$	−6.25776	−0.208015
$906$	6.86661	0.228128
$907$	−33.9325	−1.12671	−0.563355	−	0.826215i	$-0.690490\pi$
$907$	−33.9325	−1.12671	−0.563355	+	0.826215i	$0.690490\pi$
$908$	65.4389	2.17167
$909$	13.5424	0.449171
$910$	−16.7109	−0.553960
$911$	1.32998	0.0440642	0.0220321	−	0.999757i	$-0.492986\pi$
$911$	1.32998	0.0440642	0.0220321	+	0.999757i	$0.492986\pi$
$912$	−132.353	−4.38266
$913$	−4.22673	−0.139884
$914$	−85.5135	−2.82854
$915$	32.3747	1.07027
$916$	−66.5564	−2.19908
$917$	−4.76652	−0.157404
$918$	19.0932	0.630170
$919$	5.26297	0.173609	0.0868047	−	0.996225i	$-0.472334\pi$
$919$	5.26297	0.173609	0.0868047	+	0.996225i	$0.472334\pi$
$920$	10.1245	0.333795
$921$	−34.0602	−1.12232
$922$	101.805	3.35278
$923$	−8.95271	−0.294682
$924$	65.2002	2.14493
$925$	−24.9201	−0.819369
$926$	−4.51990	−0.148533
$927$	69.8918	2.29555
$928$	29.9854	0.984319
$929$	−3.65409	−0.119887	−0.0599434	−	0.998202i	$-0.519092\pi$
$929$	−3.65409	−0.119887	−0.0599434	+	0.998202i	$0.519092\pi$
$930$	−8.05376	−0.264093
$931$	22.7815	0.746633
$932$	−63.9232	−2.09387
$933$	−19.3467	−0.633381
$934$	53.4002	1.74731
$935$	3.55204	0.116164
$936$	54.3285	1.77578
$937$	26.3386	0.860445	0.430222	−	0.902723i	$-0.358435\pi$
$937$	26.3386	0.860445	0.430222	+	0.902723i	$0.358435\pi$
$938$	−50.2906	−1.64205
$939$	−35.5652	−1.16063
$940$	11.8581	0.386770
$941$	10.2228	0.333255	0.166627	−	0.986020i	$-0.446712\pi$
$941$	10.2228	0.333255	0.166627	+	0.986020i	$0.446712\pi$
$942$	−13.9077	−0.453139
$943$	−11.8576	−0.386136
$944$	−37.6450	−1.22524
$945$	11.9850	0.389873
$946$	−1.02554	−0.0333432
$947$	37.2758	1.21130	0.605650	−	0.795731i	$-0.292913\pi$
$947$	37.2758	1.21130	0.605650	+	0.795731i	$0.292913\pi$
$948$	21.0180	0.682634
$949$	18.3889	0.596928
$950$	74.7528	2.42530
$951$	31.4883	1.02108
$952$	−39.0433	−1.26540
$953$	−9.20020	−0.298024	−0.149012	−	0.988835i	$-0.547609\pi$
$953$	−9.20020	−0.298024	−0.149012	+	0.988835i	$0.547609\pi$
$954$	11.0530	0.357853
$955$	−17.6228	−0.570260
$956$	−62.9188	−2.03494
$957$	−31.6818	−1.02413
$958$	67.3973	2.17751
$959$	12.8103	0.413665
$960$	−5.23715	−0.169028
$961$	−29.6679	−0.957028
$962$	32.5694	1.05008
$963$	27.4776	0.885452
$964$	−77.2241	−2.48722
$965$	6.36400	0.204864
$966$	35.7748	1.15104
$967$	25.9819	0.835521	0.417761	−	0.908557i	$-0.362815\pi$
$967$	25.9819	0.835521	0.417761	+	0.908557i	$0.362815\pi$
$968$	48.7295	1.56622
$969$	−41.0499	−1.31871
$970$	11.4392	0.367290
$971$	51.3733	1.64865	0.824324	−	0.566118i	$-0.191555\pi$
$971$	51.3733	1.64865	0.824324	+	0.566118i	$0.191555\pi$
$972$	85.0464	2.72787
$973$	−23.8373	−0.764190
$974$	5.16884	0.165620
$975$	−22.0786	−0.707081
$976$	76.8044	2.45845
$977$	52.3252	1.67403	0.837016	−	0.547179i	$-0.184298\pi$
$977$	52.3252	1.67403	0.837016	+	0.547179i	$0.184298\pi$
$978$	79.5279	2.54302
$979$	−9.28114	−0.296627
$980$	−13.6672	−0.436582
$981$	13.6482	0.435753
$982$	−53.3559	−1.70265
$983$	−18.3941	−0.586682	−0.293341	−	0.956008i	$-0.594767\pi$
$983$	−18.3941	−0.586682	−0.293341	+	0.956008i	$0.594767\pi$
$984$	−118.842	−3.78853
$985$	−9.23106	−0.294126
$986$	34.7964	1.10814
$987$	22.8452	0.727170
$988$	−67.1568	−2.13654
$989$	−0.386798	−0.0122995
$990$	−19.3414	−0.614711
$991$	35.1814	1.11757	0.558787	−	0.829311i	$-0.311267\pi$
$991$	35.1814	1.11757	0.558787	+	0.829311i	$0.311267\pi$
$992$	−5.10660	−0.162135
$993$	34.6026	1.09808
$994$	−35.0336	−1.11120
$995$	23.1961	0.735367
$996$	−29.3046	−0.928550
$997$	−0.242728	−0.00768728	−0.00384364	−	0.999993i	$-0.501223\pi$
$997$	−0.242728	−0.00768728	−0.00384364	+	0.999993i	$0.501223\pi$
$998$	−74.4745	−2.35745
$999$	−23.3588	−0.739039

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.13	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.13	✓	172	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.52938 q^{2} -2.71474 q^{3} +4.39775 q^{4} -1.01620 q^{5} +6.86661 q^{6} +3.17147 q^{7} -6.06482 q^{8} +4.36984 q^{9} +O(q^{10})\)	\(q-2.52938 q^{2} -2.71474 q^{3} +4.39775 q^{4} -1.01620 q^{5} +6.86661 q^{6} +3.17147 q^{7} -6.06482 q^{8} +4.36984 q^{9} +2.57036 q^{10} -1.72198 q^{11} -11.9388 q^{12} -2.04995 q^{13} -8.02184 q^{14} +2.75873 q^{15} +6.54472 q^{16} +2.02987 q^{17} -11.0530 q^{18} +7.44930 q^{19} -4.46901 q^{20} -8.60972 q^{21} +4.35555 q^{22} +1.64276 q^{23} +16.4644 q^{24} -3.96733 q^{25} +5.18511 q^{26} -3.71876 q^{27} +13.9473 q^{28} -6.77724 q^{29} -6.97788 q^{30} +1.15418 q^{31} -4.42443 q^{32} +4.67474 q^{33} -5.13430 q^{34} -3.22286 q^{35} +19.2175 q^{36} +6.28134 q^{37} -18.8421 q^{38} +5.56510 q^{39} +6.16310 q^{40} -7.21808 q^{41} +21.7772 q^{42} -0.235456 q^{43} -7.57285 q^{44} -4.44065 q^{45} -4.15517 q^{46} -2.65341 q^{47} -17.7672 q^{48} +3.05821 q^{49} +10.0349 q^{50} -5.51057 q^{51} -9.01519 q^{52} -1.00000 q^{53} +9.40614 q^{54} +1.74989 q^{55} -19.2344 q^{56} -20.2229 q^{57} +17.1422 q^{58} -5.75196 q^{59} +12.1322 q^{60} +11.7353 q^{61} -2.91937 q^{62} +13.8588 q^{63} -1.89839 q^{64} +2.08317 q^{65} -11.8242 q^{66} +6.26921 q^{67} +8.92686 q^{68} -4.45968 q^{69} +8.15183 q^{70} +4.36727 q^{71} -26.5023 q^{72} -8.97038 q^{73} -15.8879 q^{74} +10.7703 q^{75} +32.7602 q^{76} -5.46121 q^{77} -14.0762 q^{78} -1.76049 q^{79} -6.65077 q^{80} -3.01404 q^{81} +18.2573 q^{82} +2.45457 q^{83} -37.8634 q^{84} -2.06276 q^{85} +0.595557 q^{86} +18.3985 q^{87} +10.4435 q^{88} +5.38980 q^{89} +11.2321 q^{90} -6.50136 q^{91} +7.22446 q^{92} -3.13331 q^{93} +6.71149 q^{94} -7.57001 q^{95} +12.0112 q^{96} +4.45042 q^{97} -7.73536 q^{98} -7.52478 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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