LMFDB - Embedded newform 6023.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22566 q^{2} -1.96365 q^{3} +2.95355 q^{4} +3.43373 q^{5} +4.37041 q^{6} -3.81546 q^{7} -2.12228 q^{8} +0.855918 q^{9} +O(q^{10})$	\(q-2.22566 q^{2} -1.96365 q^{3} +2.95355 q^{4} +3.43373 q^{5} +4.37041 q^{6} -3.81546 q^{7} -2.12228 q^{8} +0.855918 q^{9} -7.64232 q^{10} +0.846149 q^{11} -5.79974 q^{12} +2.93913 q^{13} +8.49190 q^{14} -6.74265 q^{15} -1.18363 q^{16} +6.22689 q^{17} -1.90498 q^{18} +1.00000 q^{19} +10.1417 q^{20} +7.49222 q^{21} -1.88324 q^{22} +1.18735 q^{23} +4.16742 q^{24} +6.79052 q^{25} -6.54149 q^{26} +4.21022 q^{27} -11.2692 q^{28} +9.56253 q^{29} +15.0068 q^{30} +2.78927 q^{31} +6.87892 q^{32} -1.66154 q^{33} -13.8589 q^{34} -13.1013 q^{35} +2.52800 q^{36} +2.48059 q^{37} -2.22566 q^{38} -5.77142 q^{39} -7.28736 q^{40} +4.02711 q^{41} -16.6751 q^{42} +1.33853 q^{43} +2.49915 q^{44} +2.93899 q^{45} -2.64263 q^{46} +8.35870 q^{47} +2.32423 q^{48} +7.55771 q^{49} -15.1134 q^{50} -12.2274 q^{51} +8.68087 q^{52} -1.08897 q^{53} -9.37052 q^{54} +2.90545 q^{55} +8.09748 q^{56} -1.96365 q^{57} -21.2829 q^{58} -7.84574 q^{59} -19.9148 q^{60} -11.4882 q^{61} -6.20795 q^{62} -3.26572 q^{63} -12.9429 q^{64} +10.0922 q^{65} +3.69802 q^{66} -9.66088 q^{67} +18.3915 q^{68} -2.33153 q^{69} +29.1589 q^{70} +14.7494 q^{71} -1.81650 q^{72} +9.35560 q^{73} -5.52094 q^{74} -13.3342 q^{75} +2.95355 q^{76} -3.22844 q^{77} +12.8452 q^{78} -8.27961 q^{79} -4.06427 q^{80} -10.8352 q^{81} -8.96298 q^{82} +5.94745 q^{83} +22.1287 q^{84} +21.3815 q^{85} -2.97910 q^{86} -18.7775 q^{87} -1.79577 q^{88} +12.8072 q^{89} -6.54120 q^{90} -11.2141 q^{91} +3.50689 q^{92} -5.47714 q^{93} -18.6036 q^{94} +3.43373 q^{95} -13.5078 q^{96} +17.2779 q^{97} -16.8209 q^{98} +0.724234 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.22566	−1.57378	−0.786889	−	0.617095i	$-0.788310\pi$
$2$	−2.22566	−1.57378	−0.786889	+	0.617095i	$0.788310\pi$
$3$	−1.96365	−1.13371	−0.566857	−	0.823816i	$-0.691841\pi$
$3$	−1.96365	−1.13371	−0.566857	+	0.823816i	$0.691841\pi$
$4$	2.95355	1.47678
$5$	3.43373	1.53561	0.767806	−	0.640682i	$-0.221348\pi$
$5$	3.43373	1.53561	0.767806	+	0.640682i	$0.221348\pi$
$6$	4.37041	1.78421
$7$	−3.81546	−1.44211	−0.721053	−	0.692879i	$-0.756342\pi$
$7$	−3.81546	−1.44211	−0.721053	+	0.692879i	$0.756342\pi$
$8$	−2.12228	−0.750341
$9$	0.855918	0.285306
$10$	−7.64232	−2.41671
$11$	0.846149	0.255124	0.127562	−	0.991831i	$-0.459285\pi$
$11$	0.846149	0.255124	0.127562	+	0.991831i	$0.459285\pi$
$12$	−5.79974	−1.67424
$13$	2.93913	0.815167	0.407584	−	0.913168i	$-0.366371\pi$
$13$	2.93913	0.815167	0.407584	+	0.913168i	$0.366371\pi$
$14$	8.49190	2.26956
$15$	−6.74265	−1.74094
$16$	−1.18363	−0.295907
$17$	6.22689	1.51024	0.755122	−	0.655585i	$-0.227578\pi$
$17$	6.22689	1.51024	0.755122	+	0.655585i	$0.227578\pi$
$18$	−1.90498	−0.449008
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	10.1417	2.26776
$21$	7.49222	1.63494
$22$	−1.88324	−0.401508
$23$	1.18735	0.247579	0.123789	−	0.992309i	$-0.460495\pi$
$23$	1.18735	0.247579	0.123789	+	0.992309i	$0.460495\pi$
$24$	4.16742	0.850671
$25$	6.79052	1.35810
$26$	−6.54149	−1.28289
$27$	4.21022	0.810258
$28$	−11.2692	−2.12967
$29$	9.56253	1.77572	0.887859	−	0.460116i	$-0.152192\pi$
$29$	9.56253	1.77572	0.887859	+	0.460116i	$0.152192\pi$
$30$	15.0068	2.73986
$31$	2.78927	0.500967	0.250483	−	0.968121i	$-0.419410\pi$
$31$	2.78927	0.500967	0.250483	+	0.968121i	$0.419410\pi$
$32$	6.87892	1.21603
$33$	−1.66154	−0.289237
$34$	−13.8589	−2.37679
$35$	−13.1013	−2.21452
$36$	2.52800	0.421333
$37$	2.48059	0.407806	0.203903	−	0.978991i	$-0.434637\pi$
$37$	2.48059	0.407806	0.203903	+	0.978991i	$0.434637\pi$
$38$	−2.22566	−0.361049
$39$	−5.77142	−0.924166
$40$	−7.28736	−1.15223
$41$	4.02711	0.628929	0.314465	−	0.949269i	$-0.398175\pi$
$41$	4.02711	0.628929	0.314465	+	0.949269i	$0.398175\pi$
$42$	−16.6751	−2.57303
$43$	1.33853	0.204123	0.102062	−	0.994778i	$-0.467456\pi$
$43$	1.33853	0.204123	0.102062	+	0.994778i	$0.467456\pi$
$44$	2.49915	0.376760
$45$	2.93899	0.438119
$46$	−2.64263	−0.389634
$47$	8.35870	1.21924	0.609621	−	0.792693i	$-0.291322\pi$
$47$	8.35870	1.21924	0.609621	+	0.792693i	$0.291322\pi$
$48$	2.32423	0.335474
$49$	7.55771	1.07967
$50$	−15.1134	−2.13736
$51$	−12.2274	−1.71218
$52$	8.68087	1.20382
$53$	−1.08897	−0.149582	−0.0747909	−	0.997199i	$-0.523829\pi$
$53$	−1.08897	−0.149582	−0.0747909	+	0.997199i	$0.523829\pi$
$54$	−9.37052	−1.27517
$55$	2.90545	0.391771
$56$	8.09748	1.08207
$57$	−1.96365	−0.260092
$58$	−21.2829	−2.79458
$59$	−7.84574	−1.02143	−0.510714	−	0.859751i	$-0.670619\pi$
$59$	−7.84574	−1.02143	−0.510714	+	0.859751i	$0.670619\pi$
$60$	−19.9148	−2.57099
$61$	−11.4882	−1.47091	−0.735455	−	0.677573i	$-0.763032\pi$
$61$	−11.4882	−1.47091	−0.735455	+	0.677573i	$0.763032\pi$
$62$	−6.20795	−0.788411
$63$	−3.26572	−0.411442
$64$	−12.9429	−1.61786
$65$	10.0922	1.25178
$66$	3.69802	0.455195
$67$	−9.66088	−1.18026	−0.590132	−	0.807307i	$-0.700924\pi$
$67$	−9.66088	−1.18026	−0.590132	+	0.807307i	$0.700924\pi$
$68$	18.3915	2.23029
$69$	−2.33153	−0.280683
$70$	29.1589	3.48516
$71$	14.7494	1.75043	0.875213	−	0.483738i	$-0.160721\pi$
$71$	14.7494	1.75043	0.875213	+	0.483738i	$0.160721\pi$
$72$	−1.81650	−0.214077
$73$	9.35560	1.09499	0.547495	−	0.836809i	$-0.315581\pi$
$73$	9.35560	1.09499	0.547495	+	0.836809i	$0.315581\pi$
$74$	−5.52094	−0.641796
$75$	−13.3342	−1.53970
$76$	2.95355	0.338796
$77$	−3.22844	−0.367915
$78$	12.8452	1.45443
$79$	−8.27961	−0.931529	−0.465764	−	0.884909i	$-0.654221\pi$
$79$	−8.27961	−0.931529	−0.465764	+	0.884909i	$0.654221\pi$
$80$	−4.06427	−0.454399
$81$	−10.8352	−1.20391
$82$	−8.96298	−0.989795
$83$	5.94745	0.652817	0.326409	−	0.945229i	$-0.394161\pi$
$83$	5.94745	0.652817	0.326409	+	0.945229i	$0.394161\pi$
$84$	22.1287	2.41444
$85$	21.3815	2.31915
$86$	−2.97910	−0.321245
$87$	−18.7775	−2.01315
$88$	−1.79577	−0.191430
$89$	12.8072	1.35756	0.678778	−	0.734343i	$-0.262510\pi$
$89$	12.8072	1.35756	0.678778	+	0.734343i	$0.262510\pi$
$90$	−6.54120	−0.689503
$91$	−11.2141	−1.17556
$92$	3.50689	0.365619
$93$	−5.47714	−0.567953
$94$	−18.6036	−1.91882
$95$	3.43373	0.352294
$96$	−13.5078	−1.37863
$97$	17.2779	1.75430	0.877152	−	0.480212i	$-0.159440\pi$
$97$	17.2779	1.75430	0.877152	+	0.480212i	$0.159440\pi$
$98$	−16.8209	−1.69916
$99$	0.724234	0.0727883
$100$	20.0562	2.00562
$101$	7.22941	0.719354	0.359677	−	0.933077i	$-0.382887\pi$
$101$	7.22941	0.719354	0.359677	+	0.933077i	$0.382887\pi$
$102$	27.2141	2.69460
$103$	−15.7891	−1.55575	−0.777876	−	0.628418i	$-0.783703\pi$
$103$	−15.7891	−1.55575	−0.777876	+	0.628418i	$0.783703\pi$
$104$	−6.23766	−0.611653
$105$	25.7263	2.51063
$106$	2.42368	0.235408
$107$	3.43902	0.332462	0.166231	−	0.986087i	$-0.446840\pi$
$107$	3.43902	0.332462	0.166231	+	0.986087i	$0.446840\pi$
$108$	12.4351	1.19657
$109$	−16.7948	−1.60865	−0.804324	−	0.594191i	$-0.797472\pi$
$109$	−16.7948	−1.60865	−0.804324	+	0.594191i	$0.797472\pi$
$110$	−6.46654	−0.616560
$111$	−4.87100	−0.462335
$112$	4.51608	0.426730
$113$	11.8491	1.11467	0.557336	−	0.830287i	$-0.311824\pi$
$113$	11.8491	1.11467	0.557336	+	0.830287i	$0.311824\pi$
$114$	4.37041	0.409327
$115$	4.07703	0.380185
$116$	28.2434	2.62234
$117$	2.51565	0.232572
$118$	17.4619	1.60750
$119$	−23.7584	−2.17793
$120$	14.3098	1.30630
$121$	−10.2840	−0.934912
$122$	25.5688	2.31489
$123$	−7.90784	−0.713026
$124$	8.23825	0.739816
$125$	6.14818	0.549910
$126$	7.26837	0.647518
$127$	−0.111357	−0.00988138	−0.00494069	−	0.999988i	$-0.501573\pi$
$127$	−0.111357	−0.00988138	−0.00494069	+	0.999988i	$0.501573\pi$
$128$	15.0486	1.33012
$129$	−2.62839	−0.231417
$130$	−22.4617	−1.97003
$131$	−0.554995	−0.0484902	−0.0242451	−	0.999706i	$-0.507718\pi$
$131$	−0.554995	−0.0484902	−0.0242451	+	0.999706i	$0.507718\pi$
$132$	−4.90745	−0.427138
$133$	−3.81546	−0.330842
$134$	21.5018	1.85747
$135$	14.4568	1.24424
$136$	−13.2152	−1.13320
$137$	20.7111	1.76947	0.884734	−	0.466095i	$-0.154340\pi$
$137$	20.7111	1.76947	0.884734	+	0.466095i	$0.154340\pi$
$138$	5.18919	0.441733
$139$	19.5404	1.65740	0.828698	−	0.559697i	$-0.189082\pi$
$139$	19.5404	1.65740	0.828698	+	0.559697i	$0.189082\pi$
$140$	−38.6953	−3.27035
$141$	−16.4136	−1.38227
$142$	−32.8270	−2.75478
$143$	2.48694	0.207968
$144$	−1.01309	−0.0844241
$145$	32.8352	2.72681
$146$	−20.8224	−1.72327
$147$	−14.8407	−1.22404
$148$	7.32654	0.602238
$149$	5.26718	0.431504	0.215752	−	0.976448i	$-0.430780\pi$
$149$	5.26718	0.431504	0.215752	+	0.976448i	$0.430780\pi$
$150$	29.6774	2.42315
$151$	7.70701	0.627188	0.313594	−	0.949557i	$-0.398467\pi$
$151$	7.70701	0.627188	0.313594	+	0.949557i	$0.398467\pi$
$152$	−2.12228	−0.172140
$153$	5.32971	0.430882
$154$	7.18541	0.579017
$155$	9.57759	0.769291
$156$	−17.0462	−1.36479
$157$	−21.7059	−1.73232	−0.866159	−	0.499769i	$-0.833418\pi$
$157$	−21.7059	−1.73232	−0.866159	+	0.499769i	$0.833418\pi$
$158$	18.4276	1.46602
$159$	2.13836	0.169583
$160$	23.6204	1.86735
$161$	−4.53027	−0.357035
$162$	24.1154	1.89468
$163$	−5.66236	−0.443510	−0.221755	−	0.975102i	$-0.571179\pi$
$163$	−5.66236	−0.443510	−0.221755	+	0.975102i	$0.571179\pi$
$164$	11.8943	0.928788
$165$	−5.70528	−0.444156
$166$	−13.2370	−1.02739
$167$	−12.8183	−0.991914	−0.495957	−	0.868347i	$-0.665183\pi$
$167$	−12.8183	−0.991914	−0.495957	+	0.868347i	$0.665183\pi$
$168$	−15.9006	−1.22676
$169$	−4.36153	−0.335502
$170$	−47.5879	−3.64982
$171$	0.855918	0.0654537
$172$	3.95341	0.301444
$173$	5.27547	0.401087	0.200543	−	0.979685i	$-0.435729\pi$
$173$	5.27547	0.401087	0.200543	+	0.979685i	$0.435729\pi$
$174$	41.7922	3.16826
$175$	−25.9089	−1.95853
$176$	−1.00153	−0.0754929
$177$	15.4063	1.15801
$178$	−28.5044	−2.13649
$179$	15.8122	1.18186	0.590930	−	0.806723i	$-0.298761\pi$
$179$	15.8122	1.18186	0.590930	+	0.806723i	$0.298761\pi$
$180$	8.68048	0.647005
$181$	−22.2882	−1.65667	−0.828336	−	0.560232i	$-0.810712\pi$
$181$	−22.2882	−1.65667	−0.828336	+	0.560232i	$0.810712\pi$
$182$	24.9588	1.85007
$183$	22.5588	1.66759
$184$	−2.51989	−0.185768
$185$	8.51767	0.626232
$186$	12.1902	0.893832
$187$	5.26888	0.385299
$188$	24.6879	1.80055
$189$	−16.0639	−1.16848
$190$	−7.64232	−0.554432
$191$	−23.5291	−1.70250	−0.851252	−	0.524757i	$-0.824156\pi$
$191$	−23.5291	−1.70250	−0.851252	+	0.524757i	$0.824156\pi$
$192$	25.4153	1.83419
$193$	18.2846	1.31615	0.658076	−	0.752952i	$-0.271371\pi$
$193$	18.2846	1.31615	0.658076	+	0.752952i	$0.271371\pi$
$194$	−38.4547	−2.76089
$195$	−19.8175	−1.41916
$196$	22.3221	1.59443
$197$	−22.5236	−1.60474	−0.802370	−	0.596826i	$-0.796428\pi$
$197$	−22.5236	−1.60474	−0.802370	+	0.596826i	$0.796428\pi$
$198$	−1.61190	−0.114553
$199$	−15.5961	−1.10558	−0.552789	−	0.833322i	$-0.686436\pi$
$199$	−15.5961	−1.10558	−0.552789	+	0.833322i	$0.686436\pi$
$200$	−14.4114	−1.01904
$201$	18.9706	1.33808
$202$	−16.0902	−1.13210
$203$	−36.4854	−2.56077
$204$	−36.1144	−2.52851
$205$	13.8280	0.965792
$206$	35.1412	2.44841
$207$	1.01627	0.0706357
$208$	−3.47884	−0.241214
$209$	0.846149	0.0585294
$210$	−57.2579	−3.95117
$211$	−10.4763	−0.721217	−0.360608	−	0.932717i	$-0.617431\pi$
$211$	−10.4763	−0.721217	−0.360608	+	0.932717i	$0.617431\pi$
$212$	−3.21634	−0.220899
$213$	−28.9626	−1.98448
$214$	−7.65407	−0.523222
$215$	4.59614	0.313454
$216$	−8.93529	−0.607970
$217$	−10.6423	−0.722448
$218$	37.3794	2.53166
$219$	−18.3711	−1.24141
$220$	8.58140	0.578558
$221$	18.3016	1.23110
$222$	10.8412	0.727613
$223$	24.6187	1.64859	0.824296	−	0.566159i	$-0.191571\pi$
$223$	24.6187	1.64859	0.824296	+	0.566159i	$0.191571\pi$
$224$	−26.2462	−1.75365
$225$	5.81213	0.387475
$226$	−26.3721	−1.75425
$227$	13.3568	0.886522	0.443261	−	0.896393i	$-0.353822\pi$
$227$	13.3568	0.886522	0.443261	+	0.896393i	$0.353822\pi$
$228$	−5.79974	−0.384097
$229$	−21.8022	−1.44073	−0.720366	−	0.693594i	$-0.756026\pi$
$229$	−21.8022	−1.44073	−0.720366	+	0.693594i	$0.756026\pi$
$230$	−9.07408	−0.598327
$231$	6.33953	0.417111
$232$	−20.2944	−1.33239
$233$	−27.7299	−1.81665	−0.908324	−	0.418266i	$-0.862638\pi$
$233$	−27.7299	−1.81665	−0.908324	+	0.418266i	$0.862638\pi$
$234$	−5.59898	−0.366017
$235$	28.7016	1.87228
$236$	−23.1728	−1.50842
$237$	16.2582	1.05609
$238$	52.8782	3.42758
$239$	−15.8153	−1.02300	−0.511502	−	0.859282i	$-0.670911\pi$
$239$	−15.8153	−1.02300	−0.511502	+	0.859282i	$0.670911\pi$
$240$	7.98079	0.515158
$241$	18.8242	1.21258	0.606288	−	0.795245i	$-0.292658\pi$
$241$	18.8242	1.21258	0.606288	+	0.795245i	$0.292658\pi$
$242$	22.8887	1.47134
$243$	8.64578	0.554627
$244$	−33.9310	−2.17221
$245$	25.9511	1.65796
$246$	17.6001	1.12214
$247$	2.93913	0.187012
$248$	−5.91961	−0.375896
$249$	−11.6787	−0.740108
$250$	−13.6837	−0.865436
$251$	−0.00570469	−0.000360077 0	−0.000180038	−	1.00000i	$-0.500057\pi$
$251$	−0.00570469	−0.000360077 0	−0.000180038		1.00000i	$0.500057\pi$
$252$	−9.64547	−0.607608
$253$	1.00467	0.0631632
$254$	0.247844	0.0155511
$255$	−41.9857	−2.62925
$256$	−7.60720	−0.475450
$257$	25.5644	1.59466	0.797330	−	0.603543i	$-0.206245\pi$
$257$	25.5644	1.59466	0.797330	+	0.603543i	$0.206245\pi$
$258$	5.84991	0.364199
$259$	−9.46457	−0.588100
$260$	29.8078	1.84860
$261$	8.18474	0.506623
$262$	1.23523	0.0763127
$263$	23.2059	1.43094	0.715469	−	0.698645i	$-0.246213\pi$
$263$	23.2059	1.43094	0.715469	+	0.698645i	$0.246213\pi$
$264$	3.52626	0.217026
$265$	−3.73924	−0.229700
$266$	8.49190	0.520672
$267$	−25.1488	−1.53908
$268$	−28.5339	−1.74299
$269$	−7.96298	−0.485512	−0.242756	−	0.970087i	$-0.578051\pi$
$269$	−7.96298	−0.485512	−0.242756	+	0.970087i	$0.578051\pi$
$270$	−32.1759	−1.95816
$271$	27.9160	1.69578	0.847889	−	0.530174i	$-0.177874\pi$
$271$	27.9160	1.69578	0.847889	+	0.530174i	$0.177874\pi$
$272$	−7.37033	−0.446892
$273$	22.0206	1.33275
$274$	−46.0958	−2.78475
$275$	5.74579	0.346484
$276$	−6.88630	−0.414507
$277$	−12.6594	−0.760628	−0.380314	−	0.924857i	$-0.624184\pi$
$277$	−12.6594	−0.760628	−0.380314	+	0.924857i	$0.624184\pi$
$278$	−43.4902	−2.60837
$279$	2.38738	0.142929
$280$	27.8046	1.66164
$281$	−16.6697	−0.994432	−0.497216	−	0.867627i	$-0.665644\pi$
$281$	−16.6697	−0.994432	−0.497216	+	0.867627i	$0.665644\pi$
$282$	36.5310	2.17539
$283$	−30.5659	−1.81695	−0.908476	−	0.417937i	$-0.862753\pi$
$283$	−30.5659	−1.81695	−0.908476	+	0.417937i	$0.862753\pi$
$284$	43.5630	2.58499
$285$	−6.74265	−0.399400
$286$	−5.53508	−0.327296
$287$	−15.3653	−0.906984
$288$	5.88779	0.346942
$289$	21.7742	1.28083
$290$	−73.0799	−4.29140
$291$	−33.9277	−1.98888
$292$	27.6323	1.61706
$293$	1.36488	0.0797370	0.0398685	−	0.999205i	$-0.487306\pi$
$293$	1.36488	0.0797370	0.0398685	+	0.999205i	$0.487306\pi$
$294$	33.0303	1.92637
$295$	−26.9402	−1.56852
$296$	−5.26451	−0.305993
$297$	3.56248	0.206716
$298$	−11.7229	−0.679092
$299$	3.48976	0.201818
$300$	−39.3833	−2.27380
$301$	−5.10709	−0.294368
$302$	−17.1532	−0.987054
$303$	−14.1960	−0.815541
$304$	−1.18363	−0.0678858
$305$	−39.4473	−2.25875
$306$	−11.8621	−0.678112
$307$	22.2208	1.26821	0.634104	−	0.773248i	$-0.281369\pi$
$307$	22.2208	1.26821	0.634104	+	0.773248i	$0.281369\pi$
$308$	−9.53538	−0.543329
$309$	31.0043	1.76378
$310$	−21.3164	−1.21069
$311$	−23.3345	−1.32318	−0.661590	−	0.749866i	$-0.730118\pi$
$311$	−23.3345	−1.32318	−0.661590	+	0.749866i	$0.730118\pi$
$312$	12.2486	0.693440
$313$	−21.2546	−1.20138	−0.600691	−	0.799481i	$-0.705108\pi$
$313$	−21.2546	−1.20138	−0.600691	+	0.799481i	$0.705108\pi$
$314$	48.3099	2.72628
$315$	−11.2136	−0.631815
$316$	−24.4543	−1.37566
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−4.75925	−0.266886
$319$	8.09133	0.453027
$320$	−44.4424	−2.48440
$321$	−6.75302	−0.376917
$322$	10.0828	0.561894
$323$	6.22689	0.346474
$324$	−32.0022	−1.77790
$325$	19.9582	1.10708
$326$	12.6025	0.697987
$327$	32.9791	1.82375
$328$	−8.54668	−0.471911
$329$	−31.8923	−1.75828
$330$	12.6980	0.699003
$331$	−20.6291	−1.13388	−0.566938	−	0.823760i	$-0.691872\pi$
$331$	−20.6291	−1.13388	−0.566938	+	0.823760i	$0.691872\pi$
$332$	17.5661	0.964066
$333$	2.12318	0.116349
$334$	28.5293	1.56105
$335$	−33.1729	−1.81243
$336$	−8.86800	−0.483789
$337$	24.3873	1.32846	0.664229	−	0.747529i	$-0.268760\pi$
$337$	24.3873	1.32846	0.664229	+	0.747529i	$0.268760\pi$
$338$	9.70727	0.528006
$339$	−23.2675	−1.26372
$340$	63.1514	3.42486
$341$	2.36013	0.127808
$342$	−1.90498	−0.103010
$343$	−2.12790	−0.114896
$344$	−2.84073	−0.153162
$345$	−8.00586	−0.431021
$346$	−11.7414	−0.631222
$347$	−9.47080	−0.508419	−0.254210	−	0.967149i	$-0.581815\pi$
$347$	−9.47080	−0.508419	−0.254210	+	0.967149i	$0.581815\pi$
$348$	−55.4602	−2.97298
$349$	−7.26228	−0.388741	−0.194370	−	0.980928i	$-0.562266\pi$
$349$	−7.26228	−0.388741	−0.194370	+	0.980928i	$0.562266\pi$
$350$	57.6644	3.08229
$351$	12.3744	0.660496
$352$	5.82059	0.310239
$353$	−6.37863	−0.339500	−0.169750	−	0.985487i	$-0.554296\pi$
$353$	−6.37863	−0.339500	−0.169750	+	0.985487i	$0.554296\pi$
$354$	−34.2891	−1.82244
$355$	50.6453	2.68798
$356$	37.8266	2.00481
$357$	46.6532	2.46915
$358$	−35.1926	−1.85999
$359$	−0.447357	−0.0236106	−0.0118053	−	0.999930i	$-0.503758\pi$
$359$	−0.447357	−0.0236106	−0.0118053	+	0.999930i	$0.503758\pi$
$360$	−6.23738	−0.328739
$361$	1.00000	0.0526316
$362$	49.6060	2.60723
$363$	20.1942	1.05992
$364$	−33.1215	−1.73604
$365$	32.1246	1.68148
$366$	−50.2081	−2.62442
$367$	−0.0559573	−0.00292095	−0.00146047	−	0.999999i	$-0.500465\pi$
$367$	−0.0559573	−0.00292095	−0.00146047	+	0.999999i	$0.500465\pi$
$368$	−1.40538	−0.0732604
$369$	3.44688	0.179437
$370$	−18.9574	−0.985550
$371$	4.15492	0.215713
$372$	−16.1770	−0.838740
$373$	−14.8470	−0.768750	−0.384375	−	0.923177i	$-0.625583\pi$
$373$	−14.8470	−0.768750	−0.384375	+	0.923177i	$0.625583\pi$
$374$	−11.7267	−0.606374
$375$	−12.0729	−0.623440
$376$	−17.7395	−0.914847
$377$	28.1055	1.44751
$378$	35.7528	1.83893
$379$	23.8901	1.22715	0.613577	−	0.789635i	$-0.289730\pi$
$379$	23.8901	1.22715	0.613577	+	0.789635i	$0.289730\pi$
$380$	10.1417	0.520259
$381$	0.218667	0.0112027
$382$	52.3677	2.67936
$383$	18.7143	0.956256	0.478128	−	0.878290i	$-0.341316\pi$
$383$	18.7143	0.956256	0.478128	+	0.878290i	$0.341316\pi$
$384$	−29.5501	−1.50797
$385$	−11.0856	−0.564975
$386$	−40.6952	−2.07133
$387$	1.14567	0.0582376
$388$	51.0312	2.59072
$389$	7.61726	0.386210	0.193105	−	0.981178i	$-0.438144\pi$
$389$	7.61726	0.386210	0.193105	+	0.981178i	$0.438144\pi$
$390$	44.1070	2.23344
$391$	7.39348	0.373904
$392$	−16.0396	−0.810122
$393$	1.08982	0.0549740
$394$	50.1298	2.52551
$395$	−28.4300	−1.43047
$396$	2.13906	0.107492
$397$	25.8750	1.29863	0.649314	−	0.760520i	$-0.275056\pi$
$397$	25.8750	1.29863	0.649314	+	0.760520i	$0.275056\pi$
$398$	34.7115	1.73993
$399$	7.49222	0.375080
$400$	−8.03746	−0.401873
$401$	0.703485	0.0351303	0.0175652	−	0.999846i	$-0.494409\pi$
$401$	0.703485	0.0351303	0.0175652	+	0.999846i	$0.494409\pi$
$402$	−42.2220	−2.10584
$403$	8.19801	0.408372
$404$	21.3525	1.06232
$405$	−37.2050	−1.84873
$406$	81.2041	4.03009
$407$	2.09895	0.104041
$408$	25.9501	1.28472
$409$	−11.7890	−0.582931	−0.291465	−	0.956581i	$-0.594143\pi$
$409$	−11.7890	−0.582931	−0.291465	+	0.956581i	$0.594143\pi$
$410$	−30.7765	−1.51994
$411$	−40.6693	−2.00607
$412$	−46.6341	−2.29750
$413$	29.9351	1.47301
$414$	−2.26187	−0.111165
$415$	20.4220	1.00247
$416$	20.2180	0.991270
$417$	−38.3705	−1.87901
$418$	−1.88324	−0.0921122
$419$	−35.6234	−1.74031	−0.870157	−	0.492774i	$-0.835983\pi$
$419$	−35.6234	−1.74031	−0.870157	+	0.492774i	$0.835983\pi$
$420$	75.9839	3.70764
$421$	−9.45126	−0.460626	−0.230313	−	0.973117i	$-0.573975\pi$
$421$	−9.45126	−0.460626	−0.230313	+	0.973117i	$0.573975\pi$
$422$	23.3166	1.13503
$423$	7.15436	0.347857
$424$	2.31111	0.112237
$425$	42.2839	2.05107
$426$	64.4607	3.12313
$427$	43.8326	2.12121
$428$	10.1573	0.490972
$429$	−4.88348	−0.235777
$430$	−10.2294	−0.493307
$431$	−11.2096	−0.539948	−0.269974	−	0.962868i	$-0.587015\pi$
$431$	−11.2096	−0.539948	−0.269974	+	0.962868i	$0.587015\pi$
$432$	−4.98334	−0.239761
$433$	−3.81287	−0.183235	−0.0916175	−	0.995794i	$-0.529204\pi$
$433$	−3.81287	−0.183235	−0.0916175	+	0.995794i	$0.529204\pi$
$434$	23.6862	1.13697
$435$	−64.4768	−3.09142
$436$	−49.6043	−2.37561
$437$	1.18735	0.0567985
$438$	40.8878	1.95370
$439$	−1.64571	−0.0785453	−0.0392727	−	0.999229i	$-0.512504\pi$
$439$	−1.64571	−0.0785453	−0.0392727	+	0.999229i	$0.512504\pi$
$440$	−6.16619	−0.293962
$441$	6.46878	0.308037
$442$	−40.7332	−1.93748
$443$	26.9553	1.28068	0.640342	−	0.768090i	$-0.278793\pi$
$443$	26.9553	1.28068	0.640342	+	0.768090i	$0.278793\pi$
$444$	−14.3868	−0.682766
$445$	43.9764	2.08468
$446$	−54.7929	−2.59452
$447$	−10.3429	−0.489202
$448$	49.3829	2.33312
$449$	−4.15347	−0.196014	−0.0980071	−	0.995186i	$-0.531247\pi$
$449$	−4.15347	−0.196014	−0.0980071	+	0.995186i	$0.531247\pi$
$450$	−12.9358	−0.609800
$451$	3.40754	0.160455
$452$	34.9970	1.64612
$453$	−15.1339	−0.711051
$454$	−29.7277	−1.39519
$455$	−38.5063	−1.80520
$456$	4.16742	0.195157
$457$	5.71015	0.267109	0.133555	−	0.991041i	$-0.457361\pi$
$457$	5.71015	0.267109	0.133555	+	0.991041i	$0.457361\pi$
$458$	48.5243	2.26739
$459$	26.2166	1.22369
$460$	12.0417	0.561448
$461$	13.5013	0.628819	0.314409	−	0.949287i	$-0.398194\pi$
$461$	13.5013	0.628819	0.314409	+	0.949287i	$0.398194\pi$
$462$	−14.1096	−0.656439
$463$	16.3634	0.760473	0.380236	−	0.924889i	$-0.375843\pi$
$463$	16.3634	0.760473	0.380236	+	0.924889i	$0.375843\pi$
$464$	−11.3185	−0.525448
$465$	−18.8070	−0.872155
$466$	61.7174	2.85900
$467$	−18.1664	−0.840642	−0.420321	−	0.907375i	$-0.638083\pi$
$467$	−18.1664	−0.840642	−0.420321	+	0.907375i	$0.638083\pi$
$468$	7.43012	0.343457
$469$	36.8607	1.70207
$470$	−63.8798	−2.94656
$471$	42.6227	1.96395
$472$	16.6509	0.766419
$473$	1.13259	0.0520766
$474$	−36.1853	−1.66205
$475$	6.79052	0.311571
$476$	−70.1718	−3.21632
$477$	−0.932070	−0.0426766
$478$	35.1993	1.60998
$479$	10.4666	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$479$	10.4666	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$480$	−46.3821	−2.11705
$481$	7.29076	0.332430
$482$	−41.8963	−1.90833
$483$	8.89586	0.404776
$484$	−30.3744	−1.38066
$485$	59.3277	2.69393
$486$	−19.2425	−0.872859
$487$	−11.5867	−0.525044	−0.262522	−	0.964926i	$-0.584554\pi$
$487$	−11.5867	−0.525044	−0.262522	+	0.964926i	$0.584554\pi$
$488$	24.3812	1.10368
$489$	11.1189	0.502814
$490$	−57.7584	−2.60926
$491$	−19.6733	−0.887846	−0.443923	−	0.896065i	$-0.646414\pi$
$491$	−19.6733	−0.887846	−0.443923	+	0.896065i	$0.646414\pi$
$492$	−23.3562	−1.05298
$493$	59.5448	2.68177
$494$	−6.54149	−0.294316
$495$	2.48683	0.111775
$496$	−3.30146	−0.148240
$497$	−56.2755	−2.52430
$498$	25.9928	1.16477
$499$	−10.2622	−0.459399	−0.229700	−	0.973262i	$-0.573774\pi$
$499$	−10.2622	−0.459399	−0.229700	+	0.973262i	$0.573774\pi$
$500$	18.1590	0.812094
$501$	25.1707	1.12455
$502$	0.0126967	0.000566681 0
$503$	−12.8369	−0.572369	−0.286185	−	0.958174i	$-0.592387\pi$
$503$	−12.8369	−0.572369	−0.286185	+	0.958174i	$0.592387\pi$
$504$	6.93078	0.308721
$505$	24.8239	1.10465
$506$	−2.23606	−0.0994048
$507$	8.56451	0.380363
$508$	−0.328900	−0.0145926
$509$	8.96986	0.397582	0.198791	−	0.980042i	$-0.436298\pi$
$509$	8.96986	0.397582	0.198791	+	0.980042i	$0.436298\pi$
$510$	93.4459	4.13785
$511$	−35.6959	−1.57909
$512$	−13.1661	−0.581864
$513$	4.21022	0.185886
$514$	−56.8975	−2.50964
$515$	−54.2157	−2.38903
$516$	−7.76310	−0.341752
$517$	7.07271	0.311057
$518$	21.0649	0.925538
$519$	−10.3592	−0.454718
$520$	−21.4185	−0.939262
$521$	38.8305	1.70120	0.850598	−	0.525817i	$-0.176240\pi$
$521$	38.8305	1.70120	0.850598	+	0.525817i	$0.176240\pi$
$522$	−18.2164	−0.797312
$523$	−11.8280	−0.517202	−0.258601	−	0.965984i	$-0.583261\pi$
$523$	−11.8280	−0.517202	−0.258601	+	0.965984i	$0.583261\pi$
$524$	−1.63921	−0.0716091
$525$	50.8761	2.22041
$526$	−51.6484	−2.25198
$527$	17.3685	0.756582
$528$	1.96665	0.0855873
$529$	−21.5902	−0.938705
$530$	8.32226	0.361496
$531$	−6.71531	−0.291419
$532$	−11.2692	−0.488580
$533$	11.8362	0.512683
$534$	55.9726	2.42217
$535$	11.8087	0.510533
$536$	20.5031	0.885601
$537$	−31.0496	−1.33989
$538$	17.7229	0.764088
$539$	6.39495	0.275450
$540$	42.6989	1.83747
$541$	44.3171	1.90534	0.952671	−	0.304003i	$-0.0983233\pi$
$541$	44.3171	1.90534	0.952671	+	0.304003i	$0.0983233\pi$
$542$	−62.1315	−2.66878
$543$	43.7663	1.87819
$544$	42.8343	1.83651
$545$	−57.6688	−2.47026
$546$	−49.0103	−2.09745
$547$	−25.9714	−1.11046	−0.555229	−	0.831697i	$-0.687369\pi$
$547$	−25.9714	−1.11046	−0.555229	+	0.831697i	$0.687369\pi$
$548$	61.1713	2.61311
$549$	−9.83294	−0.419660
$550$	−12.7882	−0.545290
$551$	9.56253	0.407377
$552$	4.94817	0.210608
$553$	31.5905	1.34336
$554$	28.1754	1.19706
$555$	−16.7257	−0.709967
$556$	57.7136	2.44760
$557$	−17.1737	−0.727674	−0.363837	−	0.931463i	$-0.618533\pi$
$557$	−17.1737	−0.727674	−0.363837	+	0.931463i	$0.618533\pi$
$558$	−5.31350	−0.224938
$559$	3.93410	0.166395
$560$	15.5070	0.655291
$561$	−10.3462	−0.436818
$562$	37.1011	1.56501
$563$	26.1213	1.10088	0.550440	−	0.834875i	$-0.314460\pi$
$563$	26.1213	1.10088	0.550440	+	0.834875i	$0.314460\pi$
$564$	−48.4783	−2.04131
$565$	40.6867	1.71170
$566$	68.0292	2.85948
$567$	41.3411	1.73616
$568$	−31.3023	−1.31342
$569$	−24.0366	−1.00767	−0.503833	−	0.863801i	$-0.668077\pi$
$569$	−24.0366	−1.00767	−0.503833	+	0.863801i	$0.668077\pi$
$570$	15.0068	0.628567
$571$	−2.28972	−0.0958219	−0.0479110	−	0.998852i	$-0.515256\pi$
$571$	−2.28972	−0.0958219	−0.0479110	+	0.998852i	$0.515256\pi$
$572$	7.34531	0.307123
$573$	46.2029	1.93015
$574$	34.1978	1.42739
$575$	8.06270	0.336238
$576$	−11.0780	−0.461585
$577$	30.0497	1.25098	0.625492	−	0.780230i	$-0.284898\pi$
$577$	30.0497	1.25098	0.625492	+	0.780230i	$0.284898\pi$
$578$	−48.4619	−2.01575
$579$	−35.9045	−1.49214
$580$	96.9805	4.02689
$581$	−22.6922	−0.941433
$582$	75.5115	3.13005
$583$	−0.921432	−0.0381618
$584$	−19.8552	−0.821616
$585$	8.63808	0.357141
$586$	−3.03775	−0.125488
$587$	41.0985	1.69632	0.848158	−	0.529744i	$-0.177712\pi$
$587$	41.0985	1.69632	0.848158	+	0.529744i	$0.177712\pi$
$588$	−43.8327	−1.80763
$589$	2.78927	0.114930
$590$	59.9596	2.46850
$591$	44.2285	1.81932
$592$	−2.93609	−0.120673
$593$	−7.48137	−0.307223	−0.153612	−	0.988131i	$-0.549090\pi$
$593$	−7.48137	−0.307223	−0.153612	+	0.988131i	$0.549090\pi$
$594$	−7.92886	−0.325325
$595$	−81.5801	−3.34446
$596$	15.5569	0.637236
$597$	30.6252	1.25341
$598$	−7.76702	−0.317617
$599$	34.1413	1.39497	0.697487	−	0.716598i	$-0.254302\pi$
$599$	34.1413	1.39497	0.697487	+	0.716598i	$0.254302\pi$
$600$	28.2990	1.15530
$601$	36.7779	1.50020	0.750100	−	0.661324i	$-0.230005\pi$
$601$	36.7779	1.50020	0.750100	+	0.661324i	$0.230005\pi$
$602$	11.3666	0.463269
$603$	−8.26892	−0.336737
$604$	22.7631	0.926216
$605$	−35.3126	−1.43566
$606$	31.5955	1.28348
$607$	−13.2285	−0.536930	−0.268465	−	0.963289i	$-0.586516\pi$
$607$	−13.2285	−0.536930	−0.268465	+	0.963289i	$0.586516\pi$
$608$	6.87892	0.278977
$609$	71.6446	2.90318
$610$	87.7963	3.55477
$611$	24.5673	0.993886
$612$	15.7416	0.636316
$613$	0.397749	0.0160649	0.00803247	−	0.999968i	$-0.497443\pi$
$613$	0.397749	0.0160649	0.00803247	+	0.999968i	$0.497443\pi$
$614$	−49.4559	−1.99588
$615$	−27.1534	−1.09493
$616$	6.85168	0.276062
$617$	−14.1456	−0.569481	−0.284740	−	0.958605i	$-0.591907\pi$
$617$	−14.1456	−0.569481	−0.284740	+	0.958605i	$0.591907\pi$
$618$	−69.0051	−2.77579
$619$	23.2391	0.934058	0.467029	−	0.884242i	$-0.345324\pi$
$619$	23.2391	0.934058	0.467029	+	0.884242i	$0.345324\pi$
$620$	28.2879	1.13607
$621$	4.99900	0.200603
$622$	51.9347	2.08239
$623$	−48.8652	−1.95774
$624$	6.83122	0.273467
$625$	−12.8414	−0.513656
$626$	47.3055	1.89071
$627$	−1.66154	−0.0663555
$628$	−64.1095	−2.55825
$629$	15.4463	0.615886
$630$	24.9576	0.994336
$631$	−8.69216	−0.346029	−0.173015	−	0.984919i	$-0.555351\pi$
$631$	−8.69216	−0.346029	−0.173015	+	0.984919i	$0.555351\pi$
$632$	17.5717	0.698964
$633$	20.5717	0.817653
$634$	2.22566	0.0883922
$635$	−0.382372	−0.0151740
$636$	6.31575	0.250436
$637$	22.2131	0.880114
$638$	−18.0085	−0.712964
$639$	12.6242	0.499407
$640$	51.6727	2.04254
$641$	−17.1669	−0.678053	−0.339027	−	0.940777i	$-0.610098\pi$
$641$	−17.1669	−0.678053	−0.339027	+	0.940777i	$0.610098\pi$
$642$	15.0299	0.593183
$643$	12.6361	0.498318	0.249159	−	0.968463i	$-0.419846\pi$
$643$	12.6361	0.498318	0.249159	+	0.968463i	$0.419846\pi$
$644$	−13.3804	−0.527261
$645$	−9.02521	−0.355367
$646$	−13.8589	−0.545272
$647$	−1.21173	−0.0476379	−0.0238190	−	0.999716i	$-0.507583\pi$
$647$	−1.21173	−0.0476379	−0.0238190	+	0.999716i	$0.507583\pi$
$648$	22.9953	0.903340
$649$	−6.63866	−0.260590
$650$	−44.4202	−1.74230
$651$	20.8978	0.819049
$652$	−16.7241	−0.654966
$653$	35.2234	1.37840	0.689200	−	0.724571i	$-0.257962\pi$
$653$	35.2234	1.37840	0.689200	+	0.724571i	$0.257962\pi$
$654$	−73.4001	−2.87017
$655$	−1.90571	−0.0744621
$656$	−4.76661	−0.186105
$657$	8.00763	0.312407
$658$	70.9813	2.76714
$659$	36.8261	1.43454	0.717270	−	0.696795i	$-0.245391\pi$
$659$	36.8261	1.43454	0.717270	+	0.696795i	$0.245391\pi$
$660$	−16.8509	−0.655919
$661$	−26.4657	−1.02940	−0.514698	−	0.857371i	$-0.672096\pi$
$661$	−26.4657	−1.02940	−0.514698	+	0.857371i	$0.672096\pi$
$662$	45.9133	1.78447
$663$	−35.9380	−1.39572
$664$	−12.6222	−0.489835
$665$	−13.1013	−0.508045
$666$	−4.72547	−0.183108
$667$	11.3540	0.439630
$668$	−37.8597	−1.46483
$669$	−48.3425	−1.86903
$670$	73.8315	2.85236
$671$	−9.72071	−0.375264
$672$	51.5384	1.98814
$673$	47.6831	1.83805	0.919024	−	0.394200i	$-0.128978\pi$
$673$	47.6831	1.83805	0.919024	+	0.394200i	$0.128978\pi$
$674$	−54.2777	−2.09070
$675$	28.5896	1.10042
$676$	−12.8820	−0.495462
$677$	41.5577	1.59719	0.798595	−	0.601868i	$-0.205577\pi$
$677$	41.5577	1.59719	0.798595	+	0.601868i	$0.205577\pi$
$678$	51.7855	1.98881
$679$	−65.9231	−2.52989
$680$	−45.3776	−1.74015
$681$	−26.2281	−1.00506
$682$	−5.25285	−0.201142
$683$	33.1945	1.27015	0.635076	−	0.772449i	$-0.280969\pi$
$683$	33.1945	1.27015	0.635076	+	0.772449i	$0.280969\pi$
$684$	2.52800	0.0966605
$685$	71.1164	2.71722
$686$	4.73598	0.180820
$687$	42.8120	1.63338
$688$	−1.58432	−0.0604015
$689$	−3.20063	−0.121934
$690$	17.8183	0.678331
$691$	45.2846	1.72271	0.861353	−	0.508007i	$-0.169618\pi$
$691$	45.2846	1.72271	0.861353	+	0.508007i	$0.169618\pi$
$692$	15.5814	0.592316
$693$	−2.76328	−0.104968
$694$	21.0788	0.800139
$695$	67.0965	2.54512
$696$	39.8511	1.51055
$697$	25.0764	0.949837
$698$	16.1633	0.611792
$699$	54.4519	2.05956
$700$	−76.5235	−2.89231
$701$	−25.2849	−0.954998	−0.477499	−	0.878632i	$-0.658457\pi$
$701$	−25.2849	−0.954998	−0.477499	+	0.878632i	$0.658457\pi$
$702$	−27.5412	−1.03947
$703$	2.48059	0.0935571
$704$	−10.9516	−0.412754
$705$	−56.3598	−2.12263
$706$	14.1966	0.534298
$707$	−27.5835	−1.03738
$708$	45.5032	1.71012
$709$	0.828034	0.0310975	0.0155487	−	0.999879i	$-0.495050\pi$
$709$	0.828034	0.0310975	0.0155487	+	0.999879i	$0.495050\pi$
$710$	−112.719	−4.23028
$711$	−7.08667	−0.265771
$712$	−27.1804	−1.01863
$713$	3.31182	0.124029
$714$	−103.834	−3.88589
$715$	8.53949	0.319359
$716$	46.7022	1.74534
$717$	31.0556	1.15979
$718$	0.995665	0.0371579
$719$	1.35057	0.0503679	0.0251839	−	0.999683i	$-0.491983\pi$
$719$	1.35057	0.0503679	0.0251839	+	0.999683i	$0.491983\pi$
$720$	−3.47868	−0.129643
$721$	60.2428	2.24356
$722$	−2.22566	−0.0828304
$723$	−36.9642	−1.37471
$724$	−65.8295	−2.44653
$725$	64.9346	2.41161
$726$	−44.9455	−1.66808
$727$	−34.2099	−1.26877	−0.634387	−	0.773016i	$-0.718747\pi$
$727$	−34.2099	−1.26877	−0.634387	+	0.773016i	$0.718747\pi$
$728$	23.7995	0.882069
$729$	15.5282	0.575119
$730$	−71.4985	−2.64628
$731$	8.33486	0.308276
$732$	66.6285	2.46266
$733$	−19.2079	−0.709458	−0.354729	−	0.934969i	$-0.615427\pi$
$733$	−19.2079	−0.709458	−0.354729	+	0.934969i	$0.615427\pi$
$734$	0.124542	0.00459692
$735$	−50.9589	−1.87965
$736$	8.16766	0.301064
$737$	−8.17455	−0.301113
$738$	−7.67157	−0.282395
$739$	8.22127	0.302424	0.151212	−	0.988501i	$-0.451682\pi$
$739$	8.22127	0.302424	0.151212	+	0.988501i	$0.451682\pi$
$740$	25.1574	0.924804
$741$	−5.77142	−0.212018
$742$	−9.24744	−0.339484
$743$	6.44156	0.236318	0.118159	−	0.992995i	$-0.462301\pi$
$743$	6.44156	0.236318	0.118159	+	0.992995i	$0.462301\pi$
$744$	11.6240	0.426158
$745$	18.0861	0.662624
$746$	33.0444	1.20984
$747$	5.09053	0.186253
$748$	15.5619	0.569000
$749$	−13.1214	−0.479446
$750$	26.8701	0.981156
$751$	−7.51493	−0.274224	−0.137112	−	0.990556i	$-0.543782\pi$
$751$	−7.51493	−0.274224	−0.137112	+	0.990556i	$0.543782\pi$
$752$	−9.89360	−0.360783
$753$	0.0112020	0.000408224 0
$754$	−62.5532	−2.27805
$755$	26.4638	0.963117
$756$	−47.4457	−1.72558
$757$	−21.9317	−0.797120	−0.398560	−	0.917142i	$-0.630490\pi$
$757$	−21.9317	−0.797120	−0.398560	+	0.917142i	$0.630490\pi$
$758$	−53.1713	−1.93127
$759$	−1.97282	−0.0716089
$760$	−7.28736	−0.264340
$761$	15.7529	0.571041	0.285521	−	0.958373i	$-0.407834\pi$
$761$	15.7529	0.571041	0.285521	+	0.958373i	$0.407834\pi$
$762$	−0.486678	−0.0176305
$763$	64.0798	2.31984
$764$	−69.4944	−2.51422
$765$	18.3008	0.661667
$766$	−41.6516	−1.50493
$767$	−23.0596	−0.832635
$768$	14.9379	0.539024
$769$	−12.2778	−0.442749	−0.221375	−	0.975189i	$-0.571054\pi$
$769$	−12.2778	−0.442749	−0.221375	+	0.975189i	$0.571054\pi$
$770$	24.6728	0.889146
$771$	−50.1994	−1.80789
$772$	54.0044	1.94366
$773$	−12.0060	−0.431824	−0.215912	−	0.976413i	$-0.569272\pi$
$773$	−12.0060	−0.431824	−0.215912	+	0.976413i	$0.569272\pi$
$774$	−2.54987	−0.0916530
$775$	18.9406	0.680365
$776$	−36.6686	−1.31633
$777$	18.5851	0.666736
$778$	−16.9534	−0.607809
$779$	4.02711	0.144286
$780$	−58.5321	−2.09578
$781$	12.4801	0.446575
$782$	−16.4554	−0.588442
$783$	40.2604	1.43879
$784$	−8.94552	−0.319483
$785$	−74.5322	−2.66017
$786$	−2.42556	−0.0865168
$787$	1.44308	0.0514402	0.0257201	−	0.999669i	$-0.491812\pi$
$787$	1.44308	0.0514402	0.0257201	+	0.999669i	$0.491812\pi$
$788$	−66.5247	−2.36984
$789$	−45.5683	−1.62227
$790$	63.2754	2.25124
$791$	−45.2098	−1.60748
$792$	−1.53703	−0.0546160
$793$	−33.7652	−1.19904
$794$	−57.5889	−2.04375
$795$	7.34255	0.260413
$796$	−46.0639	−1.63269
$797$	−24.5606	−0.869981	−0.434991	−	0.900435i	$-0.643248\pi$
$797$	−24.5606	−0.869981	−0.434991	+	0.900435i	$0.643248\pi$
$798$	−16.6751	−0.590293
$799$	52.0487	1.84135
$800$	46.7115	1.65150
$801$	10.9619	0.387319
$802$	−1.56572	−0.0552874
$803$	7.91623	0.279358
$804$	56.0306	1.97605
$805$	−15.5557	−0.548267
$806$	−18.2460	−0.642687
$807$	15.6365	0.550431
$808$	−15.3429	−0.539760
$809$	−13.7637	−0.483907	−0.241954	−	0.970288i	$-0.577788\pi$
$809$	−13.7637	−0.483907	−0.241954	+	0.970288i	$0.577788\pi$
$810$	82.8057	2.90950
$811$	10.6754	0.374865	0.187433	−	0.982277i	$-0.439983\pi$
$811$	10.6754	0.374865	0.187433	+	0.982277i	$0.439983\pi$
$812$	−107.762	−3.78169
$813$	−54.8173	−1.92253
$814$	−4.67154	−0.163737
$815$	−19.4430	−0.681060
$816$	14.4727	0.506647
$817$	1.33853	0.0468291
$818$	26.2384	0.917403
$819$	−9.59836	−0.335394
$820$	40.8418	1.42626
$821$	−32.9497	−1.14995	−0.574977	−	0.818170i	$-0.694989\pi$
$821$	−32.9497	−1.14995	−0.574977	+	0.818170i	$0.694989\pi$
$822$	90.5160	3.15711
$823$	12.2154	0.425801	0.212901	−	0.977074i	$-0.431709\pi$
$823$	12.2154	0.425801	0.212901	+	0.977074i	$0.431709\pi$
$824$	33.5091	1.16734
$825$	−11.2827	−0.392814
$826$	−66.6252	−2.31819
$827$	−26.0685	−0.906491	−0.453245	−	0.891386i	$-0.649734\pi$
$827$	−26.0685	−0.906491	−0.453245	+	0.891386i	$0.649734\pi$
$828$	3.00161	0.104313
$829$	25.8157	0.896618	0.448309	−	0.893879i	$-0.352026\pi$
$829$	25.8157	0.896618	0.448309	+	0.893879i	$0.352026\pi$
$830$	−45.4523	−1.57767
$831$	24.8586	0.862335
$832$	−38.0407	−1.31883
$833$	47.0610	1.63057
$834$	85.3996	2.95715
$835$	−44.0148	−1.52319
$836$	2.49915	0.0864348
$837$	11.7434	0.405913
$838$	79.2854	2.73887
$839$	−23.0634	−0.796237	−0.398119	−	0.917334i	$-0.630337\pi$
$839$	−23.0634	−0.796237	−0.398119	+	0.917334i	$0.630337\pi$
$840$	−54.5985	−1.88383
$841$	62.4420	2.15317
$842$	21.0353	0.724923
$843$	32.7335	1.12740
$844$	−30.9422	−1.06508
$845$	−14.9763	−0.515201
$846$	−15.9232	−0.547450
$847$	39.2383	1.34824
$848$	1.28894	0.0442623
$849$	60.0206	2.05990
$850$	−94.1094	−3.22793
$851$	2.94532	0.100964
$852$	−85.5424	−2.93064
$853$	22.3961	0.766826	0.383413	−	0.923577i	$-0.374749\pi$
$853$	22.3961	0.766826	0.383413	+	0.923577i	$0.374749\pi$
$854$	−97.5565	−3.33831
$855$	2.93899	0.100511
$856$	−7.29857	−0.249460
$857$	19.2624	0.657990	0.328995	−	0.944332i	$-0.393290\pi$
$857$	19.2624	0.657990	0.328995	+	0.944332i	$0.393290\pi$
$858$	10.8690	0.371060
$859$	17.7115	0.604309	0.302154	−	0.953259i	$-0.402294\pi$
$859$	17.7115	0.604309	0.302154	+	0.953259i	$0.402294\pi$
$860$	13.5749	0.462902
$861$	30.1720	1.02826
$862$	24.9488	0.849758
$863$	6.69033	0.227741	0.113871	−	0.993496i	$-0.463675\pi$
$863$	6.69033	0.227741	0.113871	+	0.993496i	$0.463675\pi$
$864$	28.9618	0.985301
$865$	18.1146	0.615914
$866$	8.48615	0.288371
$867$	−42.7569	−1.45210
$868$	−31.4327	−1.06689
$869$	−7.00578	−0.237655
$870$	143.503	4.86522
$871$	−28.3946	−0.962113
$872$	35.6433	1.20703
$873$	14.7885	0.500514
$874$	−2.64263	−0.0893882
$875$	−23.4581	−0.793029
$876$	−54.2601	−1.83328
$877$	−43.0632	−1.45414	−0.727070	−	0.686564i	$-0.759118\pi$
$877$	−43.0632	−1.45414	−0.727070	+	0.686564i	$0.759118\pi$
$878$	3.66278	0.123613
$879$	−2.68014	−0.0903989
$880$	−3.43897	−0.115928
$881$	28.7465	0.968495	0.484248	−	0.874931i	$-0.339093\pi$
$881$	28.7465	0.968495	0.484248	+	0.874931i	$0.339093\pi$
$882$	−14.3973	−0.484782
$883$	49.8616	1.67798	0.838989	−	0.544149i	$-0.183147\pi$
$883$	49.8616	1.67798	0.838989	+	0.544149i	$0.183147\pi$
$884$	54.0549	1.81806
$885$	52.9010	1.77825
$886$	−59.9932	−2.01551
$887$	0.194166	0.00651947	0.00325974	−	0.999995i	$-0.498962\pi$
$887$	0.194166	0.00651947	0.00325974	+	0.999995i	$0.498962\pi$
$888$	10.3376	0.346909
$889$	0.424880	0.0142500
$890$	−97.8764	−3.28082
$891$	−9.16816	−0.307145
$892$	72.7127	2.43460
$893$	8.35870	0.279713
$894$	23.0198	0.769896
$895$	54.2949	1.81488
$896$	−57.4171	−1.91817
$897$	−6.85267	−0.228804
$898$	9.24419	0.308483
$899$	26.6724	0.889576
$900$	17.1664	0.572215
$901$	−6.78091	−0.225905
$902$	−7.58401	−0.252520
$903$	10.0285	0.333728
$904$	−25.1472	−0.836383
$905$	−76.5318	−2.54400
$906$	33.6828	1.11904
$907$	18.7117	0.621310	0.310655	−	0.950523i	$-0.399452\pi$
$907$	18.7117	0.621310	0.310655	+	0.950523i	$0.399452\pi$
$908$	39.4500	1.30919
$909$	6.18779	0.205236
$910$	85.7018	2.84099
$911$	23.5268	0.779476	0.389738	−	0.920926i	$-0.372565\pi$
$911$	23.5268	0.779476	0.389738	+	0.920926i	$0.372565\pi$
$912$	2.32423	0.0769630
$913$	5.03243	0.166549
$914$	−12.7088	−0.420371
$915$	77.4607	2.56077
$916$	−64.3941	−2.12764
$917$	2.11756	0.0699280
$918$	−58.3492	−1.92581
$919$	−1.52702	−0.0503716	−0.0251858	−	0.999683i	$-0.508018\pi$
$919$	−1.52702	−0.0503716	−0.0251858	+	0.999683i	$0.508018\pi$
$920$	−8.65262	−0.285268
$921$	−43.6338	−1.43778
$922$	−30.0493	−0.989621
$923$	43.3502	1.42689
$924$	18.7241	0.615979
$925$	16.8445	0.553843
$926$	−36.4194	−1.19682
$927$	−13.5142	−0.443865
$928$	65.7799	2.15933
$929$	40.6171	1.33260	0.666301	−	0.745683i	$-0.267877\pi$
$929$	40.6171	1.33260	0.666301	+	0.745683i	$0.267877\pi$
$930$	41.8580	1.37258
$931$	7.55771	0.247694
$932$	−81.9019	−2.68278
$933$	45.8208	1.50011
$934$	40.4323	1.32298
$935$	18.0919	0.591669
$936$	−5.33893	−0.174508
$937$	−21.4823	−0.701795	−0.350897	−	0.936414i	$-0.614123\pi$
$937$	−21.4823	−0.701795	−0.350897	+	0.936414i	$0.614123\pi$
$938$	−82.0393	−2.67868
$939$	41.7366	1.36202
$940$	84.7716	2.76494
$941$	−50.4900	−1.64593	−0.822964	−	0.568093i	$-0.807681\pi$
$941$	−50.4900	−1.64593	−0.822964	+	0.568093i	$0.807681\pi$
$942$	−94.8636	−3.09082
$943$	4.78158	0.155710
$944$	9.28644	0.302248
$945$	−55.1592	−1.79433
$946$	−2.52076	−0.0819571
$947$	−31.9609	−1.03859	−0.519295	−	0.854595i	$-0.673805\pi$
$947$	−31.9609	−1.03859	−0.519295	+	0.854595i	$0.673805\pi$
$948$	48.0196	1.55960
$949$	27.4973	0.892600
$950$	−15.1134	−0.490343
$951$	1.96365	0.0636757
$952$	50.4221	1.63419
$953$	−38.4471	−1.24542	−0.622711	−	0.782452i	$-0.713969\pi$
$953$	−38.4471	−1.24542	−0.622711	+	0.782452i	$0.713969\pi$
$954$	2.07447	0.0671634
$955$	−80.7926	−2.61439
$956$	−46.7112	−1.51075
$957$	−15.8885	−0.513603
$958$	−23.2951	−0.752629
$959$	−79.0223	−2.55176
$960$	87.2692	2.81660
$961$	−23.2200	−0.749032
$962$	−16.2267	−0.523171
$963$	2.94352	0.0948535
$964$	55.5984	1.79070
$965$	62.7843	2.02110
$966$	−19.7991	−0.637027
$967$	−52.9018	−1.70121	−0.850604	−	0.525807i	$-0.823763\pi$
$967$	−52.9018	−1.70121	−0.850604	+	0.525807i	$0.823763\pi$
$968$	21.8256	0.701502
$969$	−12.2274	−0.392802
$970$	−132.043	−4.23965
$971$	−34.5622	−1.10915	−0.554576	−	0.832133i	$-0.687120\pi$
$971$	−34.5622	−1.10915	−0.554576	+	0.832133i	$0.687120\pi$
$972$	25.5358	0.819060
$973$	−74.5555	−2.39014
$974$	25.7881	0.826303
$975$	−39.1909	−1.25511
$976$	13.5977	0.435253
$977$	−1.11500	−0.0356721	−0.0178361	−	0.999841i	$-0.505678\pi$
$977$	−1.11500	−0.0356721	−0.0178361	+	0.999841i	$0.505678\pi$
$978$	−24.7468	−0.791317
$979$	10.8368	0.346345
$980$	76.6481	2.44843
$981$	−14.3750	−0.458957
$982$	43.7861	1.39727
$983$	−25.6952	−0.819550	−0.409775	−	0.912187i	$-0.634393\pi$
$983$	−25.6952	−0.819550	−0.409775	+	0.912187i	$0.634393\pi$
$984$	16.7827	0.535012
$985$	−77.3401	−2.46426
$986$	−132.526	−4.22050
$987$	62.6252	1.99338
$988$	8.68087	0.276175
$989$	1.58929	0.0505366
$990$	−5.53483	−0.175908
$991$	8.92778	0.283600	0.141800	−	0.989895i	$-0.454711\pi$
$991$	8.92778	0.283600	0.141800	+	0.989895i	$0.454711\pi$
$992$	19.1871	0.609192
$993$	40.5083	1.28549
$994$	125.250	3.97269
$995$	−53.5528	−1.69774
$996$	−34.4937	−1.09297
$997$	−47.7886	−1.51348	−0.756740	−	0.653716i	$-0.773209\pi$
$997$	−47.7886	−1.51348	−0.756740	+	0.653716i	$0.773209\pi$
$998$	22.8401	0.722992
$999$	10.4438	0.330428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.18	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.18	✓	138	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22566 q^{2} -1.96365 q^{3} +2.95355 q^{4} +3.43373 q^{5} +4.37041 q^{6} -3.81546 q^{7} -2.12228 q^{8} +0.855918 q^{9} +O(q^{10})\)	\(q-2.22566 q^{2} -1.96365 q^{3} +2.95355 q^{4} +3.43373 q^{5} +4.37041 q^{6} -3.81546 q^{7} -2.12228 q^{8} +0.855918 q^{9} -7.64232 q^{10} +0.846149 q^{11} -5.79974 q^{12} +2.93913 q^{13} +8.49190 q^{14} -6.74265 q^{15} -1.18363 q^{16} +6.22689 q^{17} -1.90498 q^{18} +1.00000 q^{19} +10.1417 q^{20} +7.49222 q^{21} -1.88324 q^{22} +1.18735 q^{23} +4.16742 q^{24} +6.79052 q^{25} -6.54149 q^{26} +4.21022 q^{27} -11.2692 q^{28} +9.56253 q^{29} +15.0068 q^{30} +2.78927 q^{31} +6.87892 q^{32} -1.66154 q^{33} -13.8589 q^{34} -13.1013 q^{35} +2.52800 q^{36} +2.48059 q^{37} -2.22566 q^{38} -5.77142 q^{39} -7.28736 q^{40} +4.02711 q^{41} -16.6751 q^{42} +1.33853 q^{43} +2.49915 q^{44} +2.93899 q^{45} -2.64263 q^{46} +8.35870 q^{47} +2.32423 q^{48} +7.55771 q^{49} -15.1134 q^{50} -12.2274 q^{51} +8.68087 q^{52} -1.08897 q^{53} -9.37052 q^{54} +2.90545 q^{55} +8.09748 q^{56} -1.96365 q^{57} -21.2829 q^{58} -7.84574 q^{59} -19.9148 q^{60} -11.4882 q^{61} -6.20795 q^{62} -3.26572 q^{63} -12.9429 q^{64} +10.0922 q^{65} +3.69802 q^{66} -9.66088 q^{67} +18.3915 q^{68} -2.33153 q^{69} +29.1589 q^{70} +14.7494 q^{71} -1.81650 q^{72} +9.35560 q^{73} -5.52094 q^{74} -13.3342 q^{75} +2.95355 q^{76} -3.22844 q^{77} +12.8452 q^{78} -8.27961 q^{79} -4.06427 q^{80} -10.8352 q^{81} -8.96298 q^{82} +5.94745 q^{83} +22.1287 q^{84} +21.3815 q^{85} -2.97910 q^{86} -18.7775 q^{87} -1.79577 q^{88} +12.8072 q^{89} -6.54120 q^{90} -11.2141 q^{91} +3.50689 q^{92} -5.47714 q^{93} -18.6036 q^{94} +3.43373 q^{95} -13.5078 q^{96} +17.2779 q^{97} -16.8209 q^{98} +0.724234 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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