LMFDB - Embedded newform 6043.2.a.c.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6043,2,Mod(1,6043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6043, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6043 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6043.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:	$48.2535979415$
Analytic rank:	$0$
Dimension:	$259$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.50362 q^{2} +3.44242 q^{3} +4.26813 q^{4} +0.601384 q^{5} -8.61852 q^{6} +3.68483 q^{7} -5.67855 q^{8} +8.85024 q^{9} +O(q^{10})$	\(q-2.50362 q^{2} +3.44242 q^{3} +4.26813 q^{4} +0.601384 q^{5} -8.61852 q^{6} +3.68483 q^{7} -5.67855 q^{8} +8.85024 q^{9} -1.50564 q^{10} +4.70224 q^{11} +14.6927 q^{12} +0.222646 q^{13} -9.22542 q^{14} +2.07021 q^{15} +5.68069 q^{16} -0.630946 q^{17} -22.1577 q^{18} +0.280486 q^{19} +2.56678 q^{20} +12.6847 q^{21} -11.7726 q^{22} -0.670251 q^{23} -19.5479 q^{24} -4.63834 q^{25} -0.557422 q^{26} +20.1390 q^{27} +15.7273 q^{28} -1.78989 q^{29} -5.18304 q^{30} -3.49144 q^{31} -2.86521 q^{32} +16.1871 q^{33} +1.57965 q^{34} +2.21599 q^{35} +37.7740 q^{36} -11.7023 q^{37} -0.702231 q^{38} +0.766441 q^{39} -3.41499 q^{40} -0.712242 q^{41} -31.7577 q^{42} -8.67514 q^{43} +20.0698 q^{44} +5.32239 q^{45} +1.67806 q^{46} -3.29971 q^{47} +19.5553 q^{48} +6.57794 q^{49} +11.6127 q^{50} -2.17198 q^{51} +0.950283 q^{52} +11.3177 q^{53} -50.4204 q^{54} +2.82785 q^{55} -20.9245 q^{56} +0.965550 q^{57} +4.48121 q^{58} -7.57734 q^{59} +8.83595 q^{60} +13.2622 q^{61} +8.74126 q^{62} +32.6116 q^{63} -4.18797 q^{64} +0.133896 q^{65} -40.5264 q^{66} +8.11519 q^{67} -2.69296 q^{68} -2.30728 q^{69} -5.54801 q^{70} +4.49705 q^{71} -50.2566 q^{72} +4.62607 q^{73} +29.2981 q^{74} -15.9671 q^{75} +1.19715 q^{76} +17.3269 q^{77} -1.91888 q^{78} +2.34215 q^{79} +3.41627 q^{80} +42.7761 q^{81} +1.78319 q^{82} +11.9405 q^{83} +54.1400 q^{84} -0.379441 q^{85} +21.7193 q^{86} -6.16155 q^{87} -26.7019 q^{88} -4.52740 q^{89} -13.3253 q^{90} +0.820412 q^{91} -2.86072 q^{92} -12.0190 q^{93} +8.26123 q^{94} +0.168680 q^{95} -9.86325 q^{96} +2.77688 q^{97} -16.4687 q^{98} +41.6160 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) $ 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * 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 $

$2$	−2.50362	−1.77033	−0.885165	−	0.465278i	$-0.845954\pi$
$2$	−2.50362	−1.77033	−0.885165	+	0.465278i	$0.845954\pi$
$3$	3.44242	1.98748	0.993741	−	0.111713i	$-0.0356336\pi$
$3$	3.44242	1.98748	0.993741	+	0.111713i	$0.0356336\pi$
$4$	4.26813	2.13407
$5$	0.601384	0.268947	0.134473	−	0.990917i	$-0.457066\pi$
$5$	0.601384	0.268947	0.134473	+	0.990917i	$0.457066\pi$
$6$	−8.61852	−3.51850
$7$	3.68483	1.39273	0.696367	−	0.717686i	$-0.254799\pi$
$7$	3.68483	1.39273	0.696367	+	0.717686i	$0.254799\pi$
$8$	−5.67855	−2.00767
$9$	8.85024	2.95008
$10$	−1.50564	−0.476125
$11$	4.70224	1.41778	0.708890	−	0.705319i	$-0.249196\pi$
$11$	4.70224	1.41778	0.708890	+	0.705319i	$0.249196\pi$
$12$	14.6927	4.24142
$13$	0.222646	0.0617509	0.0308755	−	0.999523i	$-0.490170\pi$
$13$	0.222646	0.0617509	0.0308755	+	0.999523i	$0.490170\pi$
$14$	−9.22542	−2.46560
$15$	2.07021	0.534527
$16$	5.68069	1.42017
$17$	−0.630946	−0.153027	−0.0765134	−	0.997069i	$-0.524379\pi$
$17$	−0.630946	−0.153027	−0.0765134	+	0.997069i	$0.524379\pi$
$18$	−22.1577	−5.22262
$19$	0.280486	0.0643479	0.0321739	−	0.999482i	$-0.489757\pi$
$19$	0.280486	0.0643479	0.0321739	+	0.999482i	$0.489757\pi$
$20$	2.56678	0.573951
$21$	12.6847	2.76803
$22$	−11.7726	−2.50994
$23$	−0.670251	−0.139757	−0.0698784	−	0.997556i	$-0.522261\pi$
$23$	−0.670251	−0.139757	−0.0698784	+	0.997556i	$0.522261\pi$
$24$	−19.5479	−3.99021
$25$	−4.63834	−0.927668
$26$	−0.557422	−0.109320
$27$	20.1390	3.87575
$28$	15.7273	2.97218
$29$	−1.78989	−0.332374	−0.166187	−	0.986094i	$-0.553146\pi$
$29$	−1.78989	−0.332374	−0.166187	+	0.986094i	$0.553146\pi$
$30$	−5.18304	−0.946289
$31$	−3.49144	−0.627082	−0.313541	−	0.949575i	$-0.601515\pi$
$31$	−3.49144	−0.627082	−0.313541	+	0.949575i	$0.601515\pi$
$32$	−2.86521	−0.506502
$33$	16.1871	2.81781
$34$	1.57965	0.270908
$35$	2.21599	0.374571
$36$	37.7740	6.29567
$37$	−11.7023	−1.92384	−0.961922	−	0.273323i	$-0.911877\pi$
$37$	−11.7023	−1.92384	−0.961922	+	0.273323i	$0.911877\pi$
$38$	−0.702231	−0.113917
$39$	0.766441	0.122729
$40$	−3.41499	−0.539957
$41$	−0.712242	−0.111234	−0.0556168	−	0.998452i	$-0.517713\pi$
$41$	−0.712242	−0.111234	−0.0556168	+	0.998452i	$0.517713\pi$
$42$	−31.7577	−4.90033
$43$	−8.67514	−1.32295	−0.661473	−	0.749969i	$-0.730068\pi$
$43$	−8.67514	−1.32295	−0.661473	+	0.749969i	$0.730068\pi$
$44$	20.0698	3.02563
$45$	5.32239	0.793415
$46$	1.67806	0.247416
$47$	−3.29971	−0.481312	−0.240656	−	0.970610i	$-0.577363\pi$
$47$	−3.29971	−0.481312	−0.240656	+	0.970610i	$0.577363\pi$
$48$	19.5553	2.82257
$49$	6.57794	0.939706
$50$	11.6127	1.64228
$51$	−2.17198	−0.304138
$52$	0.950283	0.131781
$53$	11.3177	1.55461	0.777305	−	0.629124i	$-0.216586\pi$
$53$	11.3177	1.55461	0.777305	+	0.629124i	$0.216586\pi$
$54$	−50.4204	−6.86135
$55$	2.82785	0.381307
$56$	−20.9245	−2.79615
$57$	0.965550	0.127890
$58$	4.48121	0.588412
$59$	−7.57734	−0.986486	−0.493243	−	0.869892i	$-0.664189\pi$
$59$	−7.57734	−0.986486	−0.493243	+	0.869892i	$0.664189\pi$
$60$	8.83595	1.14072
$61$	13.2622	1.69805	0.849024	−	0.528355i	$-0.177191\pi$
$61$	13.2622	1.69805	0.849024	+	0.528355i	$0.177191\pi$
$62$	8.74126	1.11014
$63$	32.6116	4.10868
$64$	−4.18797	−0.523497
$65$	0.133896	0.0166077
$66$	−40.5264	−4.98845
$67$	8.11519	0.991429	0.495714	−	0.868486i	$-0.334906\pi$
$67$	8.11519	0.991429	0.495714	+	0.868486i	$0.334906\pi$
$68$	−2.69296	−0.326570
$69$	−2.30728	−0.277764
$70$	−5.54801	−0.663115
$71$	4.49705	0.533701	0.266851	−	0.963738i	$-0.414017\pi$
$71$	4.49705	0.533701	0.266851	+	0.963738i	$0.414017\pi$
$72$	−50.2566	−5.92279
$73$	4.62607	0.541441	0.270720	−	0.962658i	$-0.412738\pi$
$73$	4.62607	0.541441	0.270720	+	0.962658i	$0.412738\pi$
$74$	29.2981	3.40584
$75$	−15.9671	−1.84372
$76$	1.19715	0.137323
$77$	17.3269	1.97459
$78$	−1.91888	−0.217270
$79$	2.34215	0.263512	0.131756	−	0.991282i	$-0.457938\pi$
$79$	2.34215	0.263512	0.131756	+	0.991282i	$0.457938\pi$
$80$	3.41627	0.381951
$81$	42.7761	4.75290
$82$	1.78319	0.196920
$83$	11.9405	1.31064	0.655322	−	0.755350i	$-0.272533\pi$
$83$	11.9405	1.31064	0.655322	+	0.755350i	$0.272533\pi$
$84$	54.1400	5.90716
$85$	−0.379441	−0.0411561
$86$	21.7193	2.34205
$87$	−6.16155	−0.660587
$88$	−26.7019	−2.84643
$89$	−4.52740	−0.479903	−0.239952	−	0.970785i	$-0.577132\pi$
$89$	−4.52740	−0.479903	−0.239952	+	0.970785i	$0.577132\pi$
$90$	−13.3253	−1.40461
$91$	0.820412	0.0860026
$92$	−2.86072	−0.298250
$93$	−12.0190	−1.24631
$94$	8.26123	0.852081
$95$	0.168680	0.0173062
$96$	−9.86325	−1.00666
$97$	2.77688	0.281949	0.140975	−	0.990013i	$-0.454976\pi$
$97$	2.77688	0.281949	0.140975	+	0.990013i	$0.454976\pi$
$98$	−16.4687	−1.66359
$99$	41.6160	4.18256
$100$	−19.7970	−1.97970
$101$	−3.85989	−0.384074	−0.192037	−	0.981388i	$-0.561509\pi$
$101$	−3.85989	−0.384074	−0.192037	+	0.981388i	$0.561509\pi$
$102$	5.43782	0.538425
$103$	−1.73880	−0.171329	−0.0856647	−	0.996324i	$-0.527301\pi$
$103$	−1.73880	−0.171329	−0.0856647	+	0.996324i	$0.527301\pi$
$104$	−1.26431	−0.123976
$105$	7.62838	0.744453
$106$	−28.3354	−2.75217
$107$	−9.52902	−0.921205	−0.460602	−	0.887607i	$-0.652367\pi$
$107$	−9.52902	−0.921205	−0.460602	+	0.887607i	$0.652367\pi$
$108$	85.9559	8.27111
$109$	8.68117	0.831505	0.415753	−	0.909478i	$-0.363518\pi$
$109$	8.68117	0.831505	0.415753	+	0.909478i	$0.363518\pi$
$110$	−7.07988	−0.675040
$111$	−40.2842	−3.82360
$112$	20.9324	1.97792
$113$	4.50679	0.423963	0.211982	−	0.977274i	$-0.432008\pi$
$113$	4.50679	0.423963	0.211982	+	0.977274i	$0.432008\pi$
$114$	−2.41737	−0.226408
$115$	−0.403078	−0.0375872
$116$	−7.63948	−0.709308
$117$	1.97047	0.182170
$118$	18.9708	1.74640
$119$	−2.32493	−0.213126
$120$	−11.7558	−1.07315
$121$	11.1111	1.01010
$122$	−33.2035	−3.00610
$123$	−2.45183	−0.221074
$124$	−14.9019	−1.33823
$125$	−5.79634	−0.518440
$126$	−81.6472	−7.27371
$127$	1.06489	0.0944941	0.0472470	−	0.998883i	$-0.484955\pi$
$127$	1.06489	0.0944941	0.0472470	+	0.998883i	$0.484955\pi$
$128$	16.2155	1.43326
$129$	−29.8635	−2.62933
$130$	−0.335225	−0.0294011
$131$	−6.57721	−0.574654	−0.287327	−	0.957833i	$-0.592767\pi$
$131$	−6.57721	−0.574654	−0.287327	+	0.957833i	$0.592767\pi$
$132$	69.0886	6.01339
$133$	1.03354	0.0896195
$134$	−20.3174	−1.75516
$135$	12.1113	1.04237
$136$	3.58286	0.307228
$137$	4.35021	0.371664	0.185832	−	0.982582i	$-0.440502\pi$
$137$	4.35021	0.371664	0.185832	+	0.982582i	$0.440502\pi$
$138$	5.77657	0.491734
$139$	−20.2251	−1.71547	−0.857734	−	0.514093i	$-0.828129\pi$
$139$	−20.2251	−1.71547	−0.857734	+	0.514093i	$0.828129\pi$
$140$	9.45816	0.799360
$141$	−11.3590	−0.956598
$142$	−11.2589	−0.944827
$143$	1.04694	0.0875492
$144$	50.2755	4.18962
$145$	−1.07641	−0.0893910
$146$	−11.5819	−0.958529
$147$	22.6440	1.86765
$148$	−49.9469	−4.10561
$149$	11.9647	0.980189	0.490095	−	0.871669i	$-0.336962\pi$
$149$	11.9647	0.980189	0.490095	+	0.871669i	$0.336962\pi$
$150$	39.9756	3.26399
$151$	3.05767	0.248829	0.124415	−	0.992230i	$-0.460295\pi$
$151$	3.05767	0.248829	0.124415	+	0.992230i	$0.460295\pi$
$152$	−1.59275	−0.129189
$153$	−5.58403	−0.451442
$154$	−43.3801	−3.49567
$155$	−2.09970	−0.168652
$156$	3.27127	0.261911
$157$	−9.30810	−0.742868	−0.371434	−	0.928459i	$-0.621134\pi$
$157$	−9.30810	−0.742868	−0.371434	+	0.928459i	$0.621134\pi$
$158$	−5.86386	−0.466504
$159$	38.9604	3.08976
$160$	−1.72309	−0.136222
$161$	−2.46976	−0.194644
$162$	−107.095	−8.41419
$163$	−15.0675	−1.18018	−0.590090	−	0.807337i	$-0.700908\pi$
$163$	−15.0675	−1.18018	−0.590090	+	0.807337i	$0.700908\pi$
$164$	−3.03994	−0.237380
$165$	9.73465	0.757841
$166$	−29.8946	−2.32027
$167$	2.98185	0.230742	0.115371	−	0.993322i	$-0.463194\pi$
$167$	2.98185	0.230742	0.115371	+	0.993322i	$0.463194\pi$
$168$	−72.0308	−5.55729
$169$	−12.9504	−0.996187
$170$	0.949977	0.0728599
$171$	2.48237	0.189832
$172$	−37.0266	−2.82326
$173$	6.77389	0.515010	0.257505	−	0.966277i	$-0.417100\pi$
$173$	6.77389	0.515010	0.257505	+	0.966277i	$0.417100\pi$
$174$	15.4262	1.16946
$175$	−17.0915	−1.29199
$176$	26.7120	2.01349
$177$	−26.0844	−1.96062
$178$	11.3349	0.849587
$179$	11.7355	0.877156	0.438578	−	0.898693i	$-0.355482\pi$
$179$	11.7355	0.877156	0.438578	+	0.898693i	$0.355482\pi$
$180$	22.7167	1.69320
$181$	−0.701212	−0.0521207	−0.0260603	−	0.999660i	$-0.508296\pi$
$181$	−0.701212	−0.0521207	−0.0260603	+	0.999660i	$0.508296\pi$
$182$	−2.05400	−0.152253
$183$	45.6539	3.37484
$184$	3.80605	0.280586
$185$	−7.03757	−0.517412
$186$	30.0911	2.20638
$187$	−2.96686	−0.216958
$188$	−14.0836	−1.02715
$189$	74.2087	5.39789
$190$	−0.422310	−0.0306376
$191$	25.8966	1.87381	0.936907	−	0.349580i	$-0.113676\pi$
$191$	25.8966	1.87381	0.936907	+	0.349580i	$0.113676\pi$
$192$	−14.4168	−1.04044
$193$	1.96641	0.141545	0.0707725	−	0.997492i	$-0.477454\pi$
$193$	1.96641	0.141545	0.0707725	+	0.997492i	$0.477454\pi$
$194$	−6.95226	−0.499143
$195$	0.460925	0.0330075
$196$	28.0755	2.00539
$197$	22.4247	1.59769	0.798846	−	0.601535i	$-0.205444\pi$
$197$	22.4247	1.59769	0.798846	+	0.601535i	$0.205444\pi$
$198$	−104.191	−7.40452
$199$	20.0352	1.42025	0.710127	−	0.704073i	$-0.248637\pi$
$199$	20.0352	1.42025	0.710127	+	0.704073i	$0.248637\pi$
$200$	26.3390	1.86245
$201$	27.9359	1.97045
$202$	9.66372	0.679937
$203$	−6.59543	−0.462908
$204$	−9.27030	−0.649051
$205$	−0.428331	−0.0299159
$206$	4.35331	0.303309
$207$	−5.93188	−0.412294
$208$	1.26478	0.0876970
$209$	1.31891	0.0912311
$210$	−19.0986	−1.31793
$211$	−7.11010	−0.489479	−0.244740	−	0.969589i	$-0.578703\pi$
$211$	−7.11010	−0.489479	−0.244740	+	0.969589i	$0.578703\pi$
$212$	48.3056	3.31764
$213$	15.4807	1.06072
$214$	23.8571	1.63084
$215$	−5.21709	−0.355802
$216$	−114.360	−7.78123
$217$	−12.8654	−0.873358
$218$	−21.7344	−1.47204
$219$	15.9249	1.07610
$220$	12.0696	0.813735
$221$	−0.140478	−0.00944955
$222$	100.856	6.76904
$223$	−24.5638	−1.64492	−0.822458	−	0.568825i	$-0.807398\pi$
$223$	−24.5638	−1.64492	−0.822458	+	0.568825i	$0.807398\pi$
$224$	−10.5578	−0.705422
$225$	−41.0504	−2.73669
$226$	−11.2833	−0.750555
$227$	23.7922	1.57914	0.789571	−	0.613659i	$-0.210303\pi$
$227$	23.7922	1.57914	0.789571	+	0.613659i	$0.210303\pi$
$228$	4.12110	0.272926
$229$	−12.2917	−0.812260	−0.406130	−	0.913815i	$-0.633122\pi$
$229$	−12.2917	−0.812260	−0.406130	+	0.913815i	$0.633122\pi$
$230$	1.00915	0.0665417
$231$	59.6466	3.92446
$232$	10.1640	0.667298
$233$	7.21429	0.472624	0.236312	−	0.971677i	$-0.424061\pi$
$233$	7.21429	0.472624	0.236312	+	0.971677i	$0.424061\pi$
$234$	−4.93332	−0.322501
$235$	−1.98439	−0.129447
$236$	−32.3411	−2.10523
$237$	8.06266	0.523726
$238$	5.82074	0.377303
$239$	1.80031	0.116453	0.0582263	−	0.998303i	$-0.481455\pi$
$239$	1.80031	0.116453	0.0582263	+	0.998303i	$0.481455\pi$
$240$	11.7602	0.759120
$241$	−29.1252	−1.87612	−0.938059	−	0.346475i	$-0.887379\pi$
$241$	−29.1252	−1.87612	−0.938059	+	0.346475i	$0.887379\pi$
$242$	−27.8180	−1.78821
$243$	86.8362	5.57054
$244$	56.6047	3.62375
$245$	3.95587	0.252731
$246$	6.13847	0.391375
$247$	0.0624491	0.00397354
$248$	19.8263	1.25897
$249$	41.1043	2.60488
$250$	14.5119	0.917810
$251$	−16.3707	−1.03331	−0.516654	−	0.856194i	$-0.672823\pi$
$251$	−16.3707	−1.03331	−0.516654	+	0.856194i	$0.672823\pi$
$252$	139.191	8.76819
$253$	−3.15168	−0.198144
$254$	−2.66609	−0.167286
$255$	−1.30619	−0.0817970
$256$	−32.2216	−2.01385
$257$	8.53691	0.532518	0.266259	−	0.963902i	$-0.414212\pi$
$257$	8.53691	0.532518	0.266259	+	0.963902i	$0.414212\pi$
$258$	74.7669	4.65478
$259$	−43.1209	−2.67940
$260$	0.571485	0.0354420
$261$	−15.8410	−0.980530
$262$	16.4669	1.01733
$263$	−29.3936	−1.81249	−0.906243	−	0.422757i	$-0.861062\pi$
$263$	−29.3936	−1.81249	−0.906243	+	0.422757i	$0.861062\pi$
$264$	−91.9192	−5.65723
$265$	6.80630	0.418108
$266$	−2.58760	−0.158656
$267$	−15.5852	−0.953798
$268$	34.6367	2.11577
$269$	−23.1922	−1.41405	−0.707026	−	0.707187i	$-0.749964\pi$
$269$	−23.1922	−1.41405	−0.707026	+	0.707187i	$0.749964\pi$
$270$	−30.3220	−1.84534
$271$	9.44314	0.573630	0.286815	−	0.957986i	$-0.407404\pi$
$271$	9.44314	0.573630	0.286815	+	0.957986i	$0.407404\pi$
$272$	−3.58421	−0.217325
$273$	2.82420	0.170929
$274$	−10.8913	−0.657967
$275$	−21.8106	−1.31523
$276$	−9.84779	−0.592767
$277$	−14.7075	−0.883689	−0.441844	−	0.897092i	$-0.645676\pi$
$277$	−14.7075	−0.883689	−0.441844	+	0.897092i	$0.645676\pi$
$278$	50.6360	3.03695
$279$	−30.9001	−1.84994
$280$	−12.5836	−0.752016
$281$	−15.6721	−0.934920	−0.467460	−	0.884014i	$-0.654831\pi$
$281$	−15.6721	−0.934920	−0.467460	+	0.884014i	$0.654831\pi$
$282$	28.4386	1.69349
$283$	−4.89546	−0.291005	−0.145502	−	0.989358i	$-0.546480\pi$
$283$	−4.89546	−0.291005	−0.145502	+	0.989358i	$0.546480\pi$
$284$	19.1940	1.13895
$285$	0.580666	0.0343957
$286$	−2.62113	−0.154991
$287$	−2.62449	−0.154919
$288$	−25.3578	−1.49422
$289$	−16.6019	−0.976583
$290$	2.69493	0.158251
$291$	9.55917	0.560369
$292$	19.7447	1.15547
$293$	7.89324	0.461128	0.230564	−	0.973057i	$-0.425943\pi$
$293$	7.89324	0.461128	0.230564	+	0.973057i	$0.425943\pi$
$294$	−56.6921	−3.30635
$295$	−4.55689	−0.265312
$296$	66.4520	3.86245
$297$	94.6984	5.49496
$298$	−29.9552	−1.73526
$299$	−0.149229	−0.00863012
$300$	−68.1497	−3.93462
$301$	−31.9664	−1.84251
$302$	−7.65525	−0.440510
$303$	−13.2874	−0.763339
$304$	1.59335	0.0913851
$305$	7.97565	0.456685
$306$	13.9803	0.799201
$307$	21.8685	1.24810	0.624050	−	0.781384i	$-0.285486\pi$
$307$	21.8685	1.24810	0.624050	+	0.781384i	$0.285486\pi$
$308$	73.9537	4.21390
$309$	−5.98569	−0.340514
$310$	5.25685	0.298569
$311$	8.92946	0.506343	0.253172	−	0.967421i	$-0.418526\pi$
$311$	8.92946	0.506343	0.253172	+	0.967421i	$0.418526\pi$
$312$	−4.35228	−0.246399
$313$	−1.95613	−0.110567	−0.0552834	−	0.998471i	$-0.517606\pi$
$313$	−1.95613	−0.110567	−0.0552834	+	0.998471i	$0.517606\pi$
$314$	23.3040	1.31512
$315$	19.6121	1.10502
$316$	9.99661	0.562353
$317$	33.2474	1.86736	0.933680	−	0.358108i	$-0.116578\pi$
$317$	33.2474	1.86736	0.933680	+	0.358108i	$0.116578\pi$
$318$	−97.5421	−5.46989
$319$	−8.41649	−0.471233
$320$	−2.51858	−0.140793
$321$	−32.8029	−1.83088
$322$	6.18334	0.344584
$323$	−0.176972	−0.00984696
$324$	182.574	10.1430
$325$	−1.03271	−0.0572843
$326$	37.7235	2.08931
$327$	29.8842	1.65260
$328$	4.04450	0.223320
$329$	−12.1589	−0.670339
$330$	−24.3719	−1.34163
$331$	−29.1375	−1.60154	−0.800771	−	0.598971i	$-0.795576\pi$
$331$	−29.1375	−1.60154	−0.800771	+	0.598971i	$0.795576\pi$
$332$	50.9638	2.79700
$333$	−103.568	−5.67550
$334$	−7.46542	−0.408490
$335$	4.88034	0.266642
$336$	72.0579	3.93108
$337$	−4.71386	−0.256780	−0.128390	−	0.991724i	$-0.540981\pi$
$337$	−4.71386	−0.256780	−0.128390	+	0.991724i	$0.540981\pi$
$338$	32.4230	1.76358
$339$	15.5143	0.842619
$340$	−1.61950	−0.0878299
$341$	−16.4176	−0.889064
$342$	−6.21492	−0.336064
$343$	−1.55521	−0.0839735
$344$	49.2622	2.65604
$345$	−1.38756	−0.0747038
$346$	−16.9593	−0.911737
$347$	−7.86851	−0.422404	−0.211202	−	0.977442i	$-0.567738\pi$
$347$	−7.86851	−0.422404	−0.211202	+	0.977442i	$0.567738\pi$
$348$	−26.2983	−1.40974
$349$	−17.5031	−0.936920	−0.468460	−	0.883485i	$-0.655191\pi$
$349$	−17.5031	−0.936920	−0.468460	+	0.883485i	$0.655191\pi$
$350$	42.7906	2.28725
$351$	4.48387	0.239331
$352$	−13.4729	−0.718108
$353$	−0.930894	−0.0495465	−0.0247732	−	0.999693i	$-0.507886\pi$
$353$	−0.930894	−0.0495465	−0.0247732	+	0.999693i	$0.507886\pi$
$354$	65.3055	3.47095
$355$	2.70445	0.143537
$356$	−19.3235	−1.02415
$357$	−8.00337	−0.423583
$358$	−29.3814	−1.55286
$359$	22.5848	1.19198	0.595989	−	0.802992i	$-0.296760\pi$
$359$	22.5848	1.19198	0.595989	+	0.802992i	$0.296760\pi$
$360$	−30.2235	−1.59292
$361$	−18.9213	−0.995859
$362$	1.75557	0.0922707
$363$	38.2490	2.00755
$364$	3.50163	0.183535
$365$	2.78204	0.145619
$366$	−114.300	−5.97457
$367$	−2.41337	−0.125977	−0.0629883	−	0.998014i	$-0.520063\pi$
$367$	−2.41337	−0.125977	−0.0629883	+	0.998014i	$0.520063\pi$
$368$	−3.80748	−0.198479
$369$	−6.30351	−0.328148
$370$	17.6194	0.915990
$371$	41.7039	2.16516
$372$	−51.2987	−2.65971
$373$	22.8099	1.18105	0.590525	−	0.807019i	$-0.298921\pi$
$373$	22.8099	1.18105	0.590525	+	0.807019i	$0.298921\pi$
$374$	7.42790	0.384088
$375$	−19.9534	−1.03039
$376$	18.7376	0.966316
$377$	−0.398512	−0.0205244
$378$	−185.791	−9.55603
$379$	−8.05802	−0.413913	−0.206956	−	0.978350i	$-0.566356\pi$
$379$	−8.05802	−0.413913	−0.206956	+	0.978350i	$0.566356\pi$
$380$	0.719947	0.0369325
$381$	3.66581	0.187805
$382$	−64.8354	−3.31727
$383$	−28.0909	−1.43538	−0.717690	−	0.696363i	$-0.754800\pi$
$383$	−28.0909	−1.43538	−0.717690	+	0.696363i	$0.754800\pi$
$384$	55.8206	2.84858
$385$	10.4201	0.531059
$386$	−4.92314	−0.250581
$387$	−76.7771	−3.90280
$388$	11.8521	0.601698
$389$	−5.47366	−0.277526	−0.138763	−	0.990326i	$-0.544313\pi$
$389$	−5.47366	−0.277526	−0.138763	+	0.990326i	$0.544313\pi$
$390$	−1.15398	−0.0584342
$391$	0.422892	0.0213866
$392$	−37.3532	−1.88662
$393$	−22.6415	−1.14211
$394$	−56.1430	−2.82844
$395$	1.40853	0.0708709
$396$	177.623	8.92587
$397$	17.8580	0.896268	0.448134	−	0.893966i	$-0.352089\pi$
$397$	17.8580	0.896268	0.448134	+	0.893966i	$0.352089\pi$
$398$	−50.1605	−2.51432
$399$	3.55788	0.178117
$400$	−26.3490	−1.31745
$401$	−25.0854	−1.25270	−0.626352	−	0.779540i	$-0.715453\pi$
$401$	−25.0854	−1.25270	−0.626352	+	0.779540i	$0.715453\pi$
$402$	−69.9410	−3.48834
$403$	−0.777357	−0.0387229
$404$	−16.4745	−0.819639
$405$	25.7248	1.27828
$406$	16.5125	0.819500
$407$	−55.0270	−2.72759
$408$	12.3337	0.610609
$409$	33.7500	1.66883	0.834414	−	0.551138i	$-0.185806\pi$
$409$	33.7500	1.66883	0.834414	+	0.551138i	$0.185806\pi$
$410$	1.07238	0.0529610
$411$	14.9752	0.738675
$412$	−7.42144	−0.365628
$413$	−27.9212	−1.37391
$414$	14.8512	0.729897
$415$	7.18084	0.352494
$416$	−0.637928	−0.0312770
$417$	−69.6232	−3.40946
$418$	−3.30206	−0.161509
$419$	−10.0414	−0.490554	−0.245277	−	0.969453i	$-0.578879\pi$
$419$	−10.0414	−0.490554	−0.245277	+	0.969453i	$0.578879\pi$
$420$	32.5589	1.58871
$421$	18.5453	0.903844	0.451922	−	0.892058i	$-0.350739\pi$
$421$	18.5453	0.903844	0.451922	+	0.892058i	$0.350739\pi$
$422$	17.8010	0.866540
$423$	−29.2032	−1.41991
$424$	−64.2683	−3.12115
$425$	2.92654	0.141958
$426$	−38.7579	−1.87783
$427$	48.8688	2.36493
$428$	−40.6711	−1.96591
$429$	3.60399	0.174002
$430$	13.0616	0.629887
$431$	25.2706	1.21724	0.608620	−	0.793462i	$-0.291723\pi$
$431$	25.2706	1.21724	0.608620	+	0.793462i	$0.291723\pi$
$432$	114.403	5.50423
$433$	−7.54925	−0.362794	−0.181397	−	0.983410i	$-0.558062\pi$
$433$	−7.54925	−0.362794	−0.181397	+	0.983410i	$0.558062\pi$
$434$	32.2100	1.54613
$435$	−3.70545	−0.177663
$436$	37.0524	1.77449
$437$	−0.187996	−0.00899306
$438$	−39.8699	−1.90506
$439$	13.6089	0.649519	0.324759	−	0.945797i	$-0.394717\pi$
$439$	13.6089	0.649519	0.324759	+	0.945797i	$0.394717\pi$
$440$	−16.0581	−0.765540
$441$	58.2164	2.77221
$442$	0.351703	0.0167288
$443$	−10.8631	−0.516120	−0.258060	−	0.966129i	$-0.583083\pi$
$443$	−10.8631	−0.516120	−0.258060	+	0.966129i	$0.583083\pi$
$444$	−171.938	−8.15983
$445$	−2.72270	−0.129068
$446$	61.4986	2.91204
$447$	41.1876	1.94811
$448$	−15.4320	−0.729091
$449$	−33.3503	−1.57390	−0.786950	−	0.617017i	$-0.788341\pi$
$449$	−33.3503	−1.57390	−0.786950	+	0.617017i	$0.788341\pi$
$450$	102.775	4.84485
$451$	−3.34913	−0.157705
$452$	19.2356	0.904766
$453$	10.5258	0.494544
$454$	−59.5667	−2.79560
$455$	0.493383	0.0231301
$456$	−5.48292	−0.256761
$457$	−2.80387	−0.131159	−0.0655797	−	0.997847i	$-0.520890\pi$
$457$	−2.80387	−0.131159	−0.0655797	+	0.997847i	$0.520890\pi$
$458$	30.7739	1.43797
$459$	−12.7066	−0.593094
$460$	−1.72039	−0.0802135
$461$	−28.0547	−1.30664	−0.653319	−	0.757083i	$-0.726624\pi$
$461$	−28.0547	−1.30664	−0.653319	+	0.757083i	$0.726624\pi$
$462$	−149.333	−6.94758
$463$	−25.5562	−1.18770	−0.593848	−	0.804577i	$-0.702392\pi$
$463$	−25.5562	−1.18770	−0.593848	+	0.804577i	$0.702392\pi$
$464$	−10.1678	−0.472028
$465$	−7.22803	−0.335192
$466$	−18.0619	−0.836700
$467$	−6.56749	−0.303907	−0.151954	−	0.988388i	$-0.548556\pi$
$467$	−6.56749	−0.303907	−0.151954	+	0.988388i	$0.548556\pi$
$468$	8.41024	0.388763
$469$	29.9031	1.38080
$470$	4.96817	0.229164
$471$	−32.0424	−1.47644
$472$	43.0283	1.98054
$473$	−40.7926	−1.87565
$474$	−20.1859	−0.927168
$475$	−1.30099	−0.0596935
$476$	−9.92309	−0.454824
$477$	100.165	4.58623
$478$	−4.50731	−0.206160
$479$	−23.7754	−1.08632	−0.543162	−	0.839628i	$-0.682773\pi$
$479$	−23.7754	−1.08632	−0.543162	+	0.839628i	$0.682773\pi$
$480$	−5.93159	−0.270739
$481$	−2.60547	−0.118799
$482$	72.9185	3.32135
$483$	−8.50193	−0.386851
$484$	47.4235	2.15562
$485$	1.66997	0.0758294
$486$	−217.405	−9.86170
$487$	−9.30339	−0.421577	−0.210788	−	0.977532i	$-0.567603\pi$
$487$	−9.30339	−0.421577	−0.210788	+	0.977532i	$0.567603\pi$
$488$	−75.3099	−3.40912
$489$	−51.8688	−2.34559
$490$	−9.90400	−0.447417
$491$	−13.8522	−0.625141	−0.312571	−	0.949895i	$-0.601190\pi$
$491$	−13.8522	−0.625141	−0.312571	+	0.949895i	$0.601190\pi$
$492$	−10.4648	−0.471788
$493$	1.12932	0.0508622
$494$	−0.156349	−0.00703448
$495$	25.0272	1.12489
$496$	−19.8338	−0.890564
$497$	16.5708	0.743303
$498$	−102.910	−4.61150
$499$	−18.6065	−0.832943	−0.416471	−	0.909149i	$-0.636733\pi$
$499$	−18.6065	−0.832943	−0.416471	+	0.909149i	$0.636733\pi$
$500$	−24.7395	−1.10639
$501$	10.2648	0.458596
$502$	40.9860	1.82929
$503$	28.1599	1.25559	0.627793	−	0.778380i	$-0.283958\pi$
$503$	28.1599	1.25559	0.627793	+	0.778380i	$0.283958\pi$
$504$	−185.187	−8.24887
$505$	−2.32128	−0.103295
$506$	7.89062	0.350781
$507$	−44.5808	−1.97990
$508$	4.54511	0.201657
$509$	−17.2458	−0.764407	−0.382203	−	0.924078i	$-0.624835\pi$
$509$	−17.2458	−0.764407	−0.382203	+	0.924078i	$0.624835\pi$
$510$	3.27022	0.144808
$511$	17.0463	0.754083
$512$	48.2398	2.13192
$513$	5.64870	0.249396
$514$	−21.3732	−0.942732
$515$	−1.04569	−0.0460785
$516$	−127.461	−5.61117
$517$	−15.5160	−0.682394
$518$	107.959	4.74343
$519$	23.3186	1.02357
$520$	−0.760334	−0.0333428
$521$	−0.358320	−0.0156983	−0.00784913	−	0.999969i	$-0.502498\pi$
$521$	−0.358320	−0.0156983	−0.00784913	+	0.999969i	$0.502498\pi$
$522$	39.6598	1.73586
$523$	6.73239	0.294387	0.147193	−	0.989108i	$-0.452976\pi$
$523$	6.73239	0.294387	0.147193	+	0.989108i	$0.452976\pi$
$524$	−28.0724	−1.22635
$525$	−58.8360	−2.56781
$526$	73.5905	3.20870
$527$	2.20291	0.0959604
$528$	91.9538	4.00177
$529$	−22.5508	−0.980468
$530$	−17.0404	−0.740188
$531$	−67.0613	−2.91021
$532$	4.41129	0.191254
$533$	−0.158578	−0.00686877
$534$	39.0195	1.68854
$535$	−5.73059	−0.247755
$536$	−46.0825	−1.99046
$537$	40.3987	1.74333
$538$	58.0645	2.50334
$539$	30.9311	1.33230
$540$	51.6924	2.22449
$541$	3.65606	0.157186	0.0785931	−	0.996907i	$-0.474957\pi$
$541$	3.65606	0.157186	0.0785931	+	0.996907i	$0.474957\pi$
$542$	−23.6421	−1.01551
$543$	−2.41386	−0.103589
$544$	1.80779	0.0775084
$545$	5.22071	0.223631
$546$	−7.07074	−0.302600
$547$	−10.7426	−0.459319	−0.229659	−	0.973271i	$-0.573761\pi$
$547$	−10.7426	−0.459319	−0.229659	+	0.973271i	$0.573761\pi$
$548$	18.5673	0.793155
$549$	117.373	5.00938
$550$	54.6055	2.32839
$551$	−0.502039	−0.0213876
$552$	13.1020	0.557659
$553$	8.63042	0.367003
$554$	36.8221	1.56442
$555$	−24.2262	−1.02835
$556$	−86.3233	−3.66092
$557$	−40.8555	−1.73110	−0.865551	−	0.500821i	$-0.833031\pi$
$557$	−40.8555	−1.73110	−0.865551	+	0.500821i	$0.833031\pi$
$558$	77.3623	3.27501
$559$	−1.93149	−0.0816932
$560$	12.5884	0.531956
$561$	−10.2132	−0.431201
$562$	39.2371	1.65512
$563$	16.9720	0.715285	0.357642	−	0.933859i	$-0.383581\pi$
$563$	16.9720	0.715285	0.357642	+	0.933859i	$0.383581\pi$
$564$	−48.4816	−2.04144
$565$	2.71031	0.114024
$566$	12.2564	0.515174
$567$	157.622	6.61952
$568$	−25.5367	−1.07150
$569$	−5.20012	−0.218000	−0.109000	−	0.994042i	$-0.534765\pi$
$569$	−5.20012	−0.218000	−0.109000	+	0.994042i	$0.534765\pi$
$570$	−1.45377	−0.0608917
$571$	40.8048	1.70763	0.853814	−	0.520578i	$-0.174284\pi$
$571$	40.8048	1.70763	0.853814	+	0.520578i	$0.174284\pi$
$572$	4.46846	0.186836
$573$	89.1470	3.72417
$574$	6.57073	0.274257
$575$	3.10885	0.129648
$576$	−37.0646	−1.54436
$577$	9.26836	0.385847	0.192923	−	0.981214i	$-0.438203\pi$
$577$	9.26836	0.385847	0.192923	+	0.981214i	$0.438203\pi$
$578$	41.5649	1.72887
$579$	6.76919	0.281318
$580$	−4.59426	−0.190766
$581$	43.9988	1.82538
$582$	−23.9326	−0.992037
$583$	53.2187	2.20409
$584$	−26.2694	−1.08704
$585$	1.18501	0.0489941
$586$	−19.7617	−0.816348
$587$	−41.3822	−1.70803	−0.854013	−	0.520252i	$-0.825838\pi$
$587$	−41.3822	−1.70803	−0.854013	+	0.520252i	$0.825838\pi$
$588$	96.6477	3.98568
$589$	−0.979301	−0.0403514
$590$	11.4087	0.469690
$591$	77.1951	3.17538
$592$	−66.4771	−2.73219
$593$	−30.2442	−1.24198	−0.620991	−	0.783818i	$-0.713270\pi$
$593$	−30.2442	−1.24198	−0.620991	+	0.783818i	$0.713270\pi$
$594$	−237.089	−9.72788
$595$	−1.39817	−0.0573195
$596$	51.0671	2.09179
$597$	68.9694	2.82273
$598$	0.373613	0.0152782
$599$	−5.89565	−0.240890	−0.120445	−	0.992720i	$-0.538432\pi$
$599$	−5.89565	−0.240890	−0.120445	+	0.992720i	$0.538432\pi$
$600$	90.6700	3.70159
$601$	35.1474	1.43369	0.716845	−	0.697232i	$-0.245585\pi$
$601$	35.1474	1.43369	0.716845	+	0.697232i	$0.245585\pi$
$602$	80.0318	3.26185
$603$	71.8214	2.92479
$604$	13.0505	0.531019
$605$	6.68202	0.271663
$606$	33.2666	1.35136
$607$	−16.5194	−0.670500	−0.335250	−	0.942129i	$-0.608821\pi$
$607$	−16.5194	−0.670500	−0.335250	+	0.942129i	$0.608821\pi$
$608$	−0.803651	−0.0325923
$609$	−22.7042	−0.920022
$610$	−19.9680	−0.808482
$611$	−0.734668	−0.0297215
$612$	−23.8334	−0.963407
$613$	−41.3493	−1.67008	−0.835042	−	0.550186i	$-0.814557\pi$
$613$	−41.3493	−1.67008	−0.835042	+	0.550186i	$0.814557\pi$
$614$	−54.7505	−2.20955
$615$	−1.47449	−0.0594573
$616$	−98.3919	−3.96432
$617$	13.4557	0.541707	0.270853	−	0.962621i	$-0.412694\pi$
$617$	13.4557	0.541707	0.270853	+	0.962621i	$0.412694\pi$
$618$	14.9859	0.602822
$619$	6.61032	0.265691	0.132846	−	0.991137i	$-0.457589\pi$
$619$	6.61032	0.265691	0.132846	+	0.991137i	$0.457589\pi$
$620$	−8.96178	−0.359914
$621$	−13.4982	−0.541663
$622$	−22.3560	−0.896394
$623$	−16.6827	−0.668377
$624$	4.35391	0.174296
$625$	19.7059	0.788235
$626$	4.89740	0.195740
$627$	4.54025	0.181320
$628$	−39.7282	−1.58533
$629$	7.38351	0.294400
$630$	−49.1013	−1.95624
$631$	−47.6946	−1.89869	−0.949347	−	0.314231i	$-0.898253\pi$
$631$	−47.6946	−1.89869	−0.949347	+	0.314231i	$0.898253\pi$
$632$	−13.3000	−0.529046
$633$	−24.4759	−0.972831
$634$	−83.2390	−3.30584
$635$	0.640410	0.0254139
$636$	166.288	6.59375
$637$	1.46455	0.0580277
$638$	21.0717	0.834238
$639$	39.8000	1.57446
$640$	9.75175	0.385472
$641$	−36.1972	−1.42970	−0.714851	−	0.699277i	$-0.753505\pi$
$641$	−36.1972	−1.42970	−0.714851	+	0.699277i	$0.753505\pi$
$642$	82.1260	3.24126
$643$	−23.2964	−0.918721	−0.459361	−	0.888250i	$-0.651921\pi$
$643$	−23.2964	−0.918721	−0.459361	+	0.888250i	$0.651921\pi$
$644$	−10.5412	−0.415383
$645$	−17.9594	−0.707151
$646$	0.443070	0.0174324
$647$	−26.0118	−1.02263	−0.511316	−	0.859393i	$-0.670842\pi$
$647$	−26.0118	−1.02263	−0.511316	+	0.859393i	$0.670842\pi$
$648$	−242.906	−9.54225
$649$	−35.6305	−1.39862
$650$	2.58551	0.101412
$651$	−44.2880	−1.73578
$652$	−64.3103	−2.51858
$653$	5.00308	0.195786	0.0978928	−	0.995197i	$-0.468790\pi$
$653$	5.00308	0.195786	0.0978928	+	0.995197i	$0.468790\pi$
$654$	−74.8188	−2.92565
$655$	−3.95543	−0.154551
$656$	−4.04603	−0.157971
$657$	40.9419	1.59729
$658$	30.4412	1.18672
$659$	−32.3420	−1.25987	−0.629933	−	0.776649i	$-0.716918\pi$
$659$	−32.3420	−1.25987	−0.629933	+	0.776649i	$0.716918\pi$
$660$	41.5488	1.61728
$661$	7.86640	0.305967	0.152984	−	0.988229i	$-0.451112\pi$
$661$	7.86640	0.305967	0.152984	+	0.988229i	$0.451112\pi$
$662$	72.9493	2.83526
$663$	−0.483583	−0.0187808
$664$	−67.8049	−2.63134
$665$	0.621555	0.0241029
$666$	259.296	10.0475
$667$	1.19967	0.0464516
$668$	12.7269	0.492419
$669$	−84.5590	−3.26924
$670$	−12.2185	−0.472044
$671$	62.3619	2.40746
$672$	−36.3443	−1.40201
$673$	−17.3324	−0.668114	−0.334057	−	0.942553i	$-0.608418\pi$
$673$	−17.3324	−0.668114	−0.334057	+	0.942553i	$0.608418\pi$
$674$	11.8017	0.454586
$675$	−93.4114	−3.59541
$676$	−55.2741	−2.12593
$677$	33.5117	1.28796	0.643980	−	0.765042i	$-0.277282\pi$
$677$	33.5117	1.28796	0.643980	+	0.765042i	$0.277282\pi$
$678$	−38.8419	−1.49171
$679$	10.2323	0.392680
$680$	2.15467	0.0826279
$681$	81.9026	3.13852
$682$	41.1035	1.57394
$683$	17.6339	0.674742	0.337371	−	0.941372i	$-0.390462\pi$
$683$	17.6339	0.674742	0.337371	+	0.941372i	$0.390462\pi$
$684$	10.5951	0.405113
$685$	2.61615	0.0999578
$686$	3.89366	0.148661
$687$	−42.3133	−1.61435
$688$	−49.2808	−1.87881
$689$	2.51985	0.0959987
$690$	3.47393	0.132250
$691$	35.1060	1.33549	0.667747	−	0.744388i	$-0.267259\pi$
$691$	35.1060	1.33549	0.667747	+	0.744388i	$0.267259\pi$
$692$	28.9119	1.09906
$693$	153.348	5.82520
$694$	19.6998	0.747794
$695$	−12.1630	−0.461370
$696$	34.9887	1.32624
$697$	0.449386	0.0170217
$698$	43.8212	1.65866
$699$	24.8346	0.939332
$700$	−72.9486	−2.75720
$701$	36.6566	1.38450	0.692251	−	0.721657i	$-0.256619\pi$
$701$	36.6566	1.38450	0.692251	+	0.721657i	$0.256619\pi$
$702$	−11.2259	−0.423695
$703$	−3.28233	−0.123795
$704$	−19.6929	−0.742203
$705$	−6.83110	−0.257274
$706$	2.33061	0.0877136
$707$	−14.2230	−0.534912
$708$	−111.332	−4.18410
$709$	−19.3743	−0.727618	−0.363809	−	0.931474i	$-0.618524\pi$
$709$	−19.3743	−0.727618	−0.363809	+	0.931474i	$0.618524\pi$
$710$	−6.77092	−0.254108
$711$	20.7286	0.777383
$712$	25.7091	0.963487
$713$	2.34014	0.0876390
$714$	20.0374	0.749882
$715$	0.629610	0.0235461
$716$	50.0889	1.87191
$717$	6.19743	0.231447
$718$	−56.5438	−2.11020
$719$	−20.9674	−0.781952	−0.390976	−	0.920401i	$-0.627862\pi$
$719$	−20.9674	−0.781952	−0.390976	+	0.920401i	$0.627862\pi$
$720$	30.2349	1.12679
$721$	−6.40719	−0.238616
$722$	47.3719	1.76300
$723$	−100.261	−3.72875
$724$	−2.99286	−0.111229
$725$	8.30211	0.308333
$726$	−95.7610	−3.55403
$727$	34.8020	1.29073	0.645367	−	0.763873i	$-0.276705\pi$
$727$	34.8020	1.29073	0.645367	+	0.763873i	$0.276705\pi$
$728$	−4.65875	−0.172665
$729$	170.598	6.31845
$730$	−6.96519	−0.257793
$731$	5.47355	0.202446
$732$	194.857	7.20213
$733$	−26.6790	−0.985412	−0.492706	−	0.870196i	$-0.663992\pi$
$733$	−26.6790	−0.985412	−0.492706	+	0.870196i	$0.663992\pi$
$734$	6.04216	0.223020
$735$	13.6177	0.502298
$736$	1.92041	0.0707872
$737$	38.1596	1.40563
$738$	15.7816	0.580930
$739$	−41.0238	−1.50908	−0.754542	−	0.656252i	$-0.772141\pi$
$739$	−41.0238	−1.50908	−0.754542	+	0.656252i	$0.772141\pi$
$740$	−30.0373	−1.10419
$741$	0.214976	0.00789734
$742$	−104.411	−3.83304
$743$	39.5759	1.45190	0.725950	−	0.687748i	$-0.241400\pi$
$743$	39.5759	1.45190	0.725950	+	0.687748i	$0.241400\pi$
$744$	68.2505	2.50219
$745$	7.19539	0.263619
$746$	−57.1073	−2.09085
$747$	105.677	3.86651
$748$	−12.6630	−0.463003
$749$	−35.1128	−1.28299
$750$	49.9559	1.82413
$751$	28.5162	1.04057	0.520285	−	0.853992i	$-0.325826\pi$
$751$	28.5162	1.04057	0.520285	+	0.853992i	$0.325826\pi$
$752$	−18.7446	−0.683546
$753$	−56.3547	−2.05368
$754$	0.997724	0.0363350
$755$	1.83883	0.0669219
$756$	316.732	11.5194
$757$	−27.4823	−0.998862	−0.499431	−	0.866354i	$-0.666458\pi$
$757$	−27.4823	−0.998862	−0.499431	+	0.866354i	$0.666458\pi$
$758$	20.1742	0.732762
$759$	−10.8494	−0.393808
$760$	−0.957856	−0.0347451
$761$	40.6798	1.47464	0.737320	−	0.675543i	$-0.236091\pi$
$761$	40.6798	1.47464	0.737320	+	0.675543i	$0.236091\pi$
$762$	−9.17781	−0.332477
$763$	31.9886	1.15807
$764$	110.530	3.99884
$765$	−3.35814	−0.121414
$766$	70.3291	2.54109
$767$	−1.68707	−0.0609164
$768$	−110.920	−4.00249
$769$	48.1795	1.73740	0.868698	−	0.495342i	$-0.164957\pi$
$769$	48.1795	1.73740	0.868698	+	0.495342i	$0.164957\pi$
$770$	−26.0881	−0.940150
$771$	29.3876	1.05837
$772$	8.39288	0.302066
$773$	44.1041	1.58632	0.793158	−	0.609016i	$-0.208435\pi$
$773$	44.1041	1.58632	0.793158	+	0.609016i	$0.208435\pi$
$774$	192.221	6.90924
$775$	16.1945	0.581723
$776$	−15.7686	−0.566061
$777$	−148.440	−5.32526
$778$	13.7040	0.491312
$779$	−0.199774	−0.00715764
$780$	1.96729	0.0704403
$781$	21.1462	0.756670
$782$	−1.05876	−0.0378613
$783$	−36.0465	−1.28820
$784$	37.3672	1.33454
$785$	−5.59774	−0.199792
$786$	56.6858	2.02192
$787$	5.08160	0.181140	0.0905698	−	0.995890i	$-0.471131\pi$
$787$	5.08160	0.181140	0.0905698	+	0.995890i	$0.471131\pi$
$788$	95.7115	3.40958
$789$	−101.185	−3.60228
$790$	−3.52643	−0.125465
$791$	16.6067	0.590468
$792$	−236.318	−8.39721
$793$	2.95277	0.104856
$794$	−44.7097	−1.58669
$795$	23.4301	0.830981
$796$	85.5127	3.03092
$797$	16.8492	0.596830	0.298415	−	0.954436i	$-0.403542\pi$
$797$	16.8492	0.596830	0.298415	+	0.954436i	$0.403542\pi$
$798$	−8.90760	−0.315326
$799$	2.08194	0.0736537
$800$	13.2898	0.469866
$801$	−40.0686	−1.41575
$802$	62.8044	2.21770
$803$	21.7529	0.767644
$804$	119.234	4.20506
$805$	−1.48527	−0.0523489
$806$	1.94621	0.0685523
$807$	−79.8372	−2.81040
$808$	21.9186	0.771093
$809$	−33.9145	−1.19237	−0.596185	−	0.802847i	$-0.703318\pi$
$809$	−33.9145	−1.19237	−0.596185	+	0.802847i	$0.703318\pi$
$810$	−64.4053	−2.26297
$811$	14.3143	0.502645	0.251322	−	0.967903i	$-0.419135\pi$
$811$	14.3143	0.502645	0.251322	+	0.967903i	$0.419135\pi$
$812$	−28.1502	−0.987877
$813$	32.5072	1.14008
$814$	137.767	4.82873
$815$	−9.06137	−0.317406
$816$	−12.3383	−0.431928
$817$	−2.43326	−0.0851288
$818$	−84.4972	−2.95438
$819$	7.26085	0.253715
$820$	−1.82817	−0.0638425
$821$	−9.15271	−0.319432	−0.159716	−	0.987163i	$-0.551058\pi$
$821$	−9.15271	−0.319432	−0.159716	+	0.987163i	$0.551058\pi$
$822$	−37.4924	−1.30770
$823$	11.1850	0.389885	0.194943	−	0.980815i	$-0.437548\pi$
$823$	11.1850	0.389885	0.194943	+	0.980815i	$0.437548\pi$
$824$	9.87388	0.343973
$825$	−75.0812	−2.61399
$826$	69.9041	2.43228
$827$	41.2221	1.43343	0.716716	−	0.697365i	$-0.245644\pi$
$827$	41.2221	1.43343	0.716716	+	0.697365i	$0.245644\pi$
$828$	−25.3181	−0.879863
$829$	17.7050	0.614920	0.307460	−	0.951561i	$-0.400521\pi$
$829$	17.7050	0.614920	0.307460	+	0.951561i	$0.400521\pi$
$830$	−17.9781	−0.624030
$831$	−50.6294	−1.75631
$832$	−0.932436	−0.0323264
$833$	−4.15033	−0.143800
$834$	174.310	6.03587
$835$	1.79323	0.0620574
$836$	5.62929	0.194693
$837$	−70.3141	−2.43041
$838$	25.1398	0.868442
$839$	52.2861	1.80512	0.902559	−	0.430566i	$-0.141686\pi$
$839$	52.2861	1.80512	0.902559	+	0.430566i	$0.141686\pi$
$840$	−43.3181	−1.49462
$841$	−25.7963	−0.889527
$842$	−46.4305	−1.60010
$843$	−53.9500	−1.85814
$844$	−30.3468	−1.04458
$845$	−7.78818	−0.267921
$846$	73.1139	2.51371
$847$	40.9424	1.40680
$848$	64.2925	2.20782
$849$	−16.8522	−0.578367
$850$	−7.32696	−0.251313
$851$	7.84347	0.268871
$852$	66.0737	2.26365
$853$	−27.2945	−0.934547	−0.467274	−	0.884113i	$-0.654764\pi$
$853$	−27.2945	−0.934547	−0.467274	+	0.884113i	$0.654764\pi$
$854$	−122.349	−4.18670
$855$	1.49286	0.0510546
$856$	54.1110	1.84948
$857$	−46.4193	−1.58565	−0.792827	−	0.609446i	$-0.791392\pi$
$857$	−46.4193	−1.58565	−0.792827	+	0.609446i	$0.791392\pi$
$858$	−9.02304	−0.308042
$859$	12.6235	0.430710	0.215355	−	0.976536i	$-0.430909\pi$
$859$	12.6235	0.430710	0.215355	+	0.976536i	$0.430909\pi$
$860$	−22.2672	−0.759306
$861$	−9.03458	−0.307898
$862$	−63.2680	−2.15492
$863$	28.5085	0.970441	0.485220	−	0.874392i	$-0.338739\pi$
$863$	28.5085	0.970441	0.485220	+	0.874392i	$0.338739\pi$
$864$	−57.7024	−1.96308
$865$	4.07371	0.138510
$866$	18.9005	0.642264
$867$	−57.1507	−1.94094
$868$	−54.9111	−1.86380
$869$	11.0134	0.373602
$870$	9.27706	0.314522
$871$	1.80682	0.0612216
$872$	−49.2965	−1.66939
$873$	24.5760	0.831773
$874$	0.470671	0.0159207
$875$	−21.3585	−0.722049
$876$	67.9695	2.29648
$877$	46.7758	1.57951	0.789754	−	0.613424i	$-0.210208\pi$
$877$	46.7758	1.57951	0.789754	+	0.613424i	$0.210208\pi$
$878$	−34.0716	−1.14986
$879$	27.1718	0.916483
$880$	16.0641	0.541522
$881$	−8.23413	−0.277415	−0.138707	−	0.990333i	$-0.544295\pi$
$881$	−8.23413	−0.277415	−0.138707	+	0.990333i	$0.544295\pi$
$882$	−145.752	−4.90772
$883$	−8.62295	−0.290185	−0.145093	−	0.989418i	$-0.546348\pi$
$883$	−8.62295	−0.290185	−0.145093	+	0.989418i	$0.546348\pi$
$884$	−0.599578	−0.0201660
$885$	−15.6867	−0.527303
$886$	27.1970	0.913702
$887$	−15.4218	−0.517814	−0.258907	−	0.965902i	$-0.583362\pi$
$887$	−15.4218	−0.517814	−0.258907	+	0.965902i	$0.583362\pi$
$888$	228.756	7.67654
$889$	3.92395	0.131605
$890$	6.81662	0.228494
$891$	201.143	6.73856
$892$	−104.842	−3.51036
$893$	−0.925522	−0.0309714
$894$	−103.118	−3.44879
$895$	7.05757	0.235908
$896$	59.7514	1.99615
$897$	−0.513708	−0.0171522
$898$	83.4967	2.78632
$899$	6.24930	0.208426
$900$	−175.209	−5.84029
$901$	−7.14088	−0.237897
$902$	8.38497	0.279189
$903$	−110.042	−3.66196
$904$	−25.5920	−0.851179
$905$	−0.421697	−0.0140177
$906$	−26.3526	−0.875506
$907$	−52.9641	−1.75864	−0.879322	−	0.476228i	$-0.842004\pi$
$907$	−52.9641	−1.75864	−0.879322	+	0.476228i	$0.842004\pi$
$908$	101.548	3.37000
$909$	−34.1610	−1.13305
$910$	−1.23524	−0.0409480
$911$	14.2320	0.471527	0.235763	−	0.971811i	$-0.424241\pi$
$911$	14.2320	0.471527	0.235763	+	0.971811i	$0.424241\pi$
$912$	5.48499	0.181626
$913$	56.1473	1.85820
$914$	7.01983	0.232195
$915$	27.4555	0.907652
$916$	−52.4627	−1.73342
$917$	−24.2359	−0.800339
$918$	31.8126	1.04997
$919$	21.4214	0.706625	0.353313	−	0.935505i	$-0.385055\pi$
$919$	21.4214	0.706625	0.353313	+	0.935505i	$0.385055\pi$
$920$	2.28890	0.0754627
$921$	75.2805	2.48058
$922$	70.2384	2.31318
$923$	1.00125	0.0329565
$924$	254.579	8.37505
$925$	54.2792	1.78469
$926$	63.9831	2.10261
$927$	−15.3888	−0.505436
$928$	5.12841	0.168348
$929$	3.31419	0.108735	0.0543675	−	0.998521i	$-0.482686\pi$
$929$	3.31419	0.108735	0.0543675	+	0.998521i	$0.482686\pi$
$930$	18.0963	0.593400
$931$	1.84502	0.0604681
$932$	30.7916	1.00861
$933$	30.7389	1.00635
$934$	16.4425	0.538016
$935$	−1.78422	−0.0583503
$936$	−11.1894	−0.365738
$937$	−29.7721	−0.972613	−0.486307	−	0.873788i	$-0.661656\pi$
$937$	−29.7721	−0.972613	−0.486307	+	0.873788i	$0.661656\pi$
$938$	−74.8660	−2.44446
$939$	−6.73380	−0.219749
$940$	−8.46964	−0.276249
$941$	−24.8970	−0.811620	−0.405810	−	0.913958i	$-0.633010\pi$
$941$	−24.8970	−0.811620	−0.405810	+	0.913958i	$0.633010\pi$
$942$	80.2221	2.61378
$943$	0.477381	0.0155456
$944$	−43.0445	−1.40098
$945$	44.6279	1.45174
$946$	102.129	3.32051
$947$	18.6210	0.605101	0.302550	−	0.953133i	$-0.402162\pi$
$947$	18.6210	0.605101	0.302550	+	0.953133i	$0.402162\pi$
$948$	34.4125	1.11767
$949$	1.02998	0.0334345
$950$	3.25719	0.105677
$951$	114.451	3.71134
$952$	13.2022	0.427886
$953$	−13.4341	−0.435173	−0.217586	−	0.976041i	$-0.569818\pi$
$953$	−13.4341	−0.435173	−0.217586	+	0.976041i	$0.569818\pi$
$954$	−250.775	−8.11913
$955$	15.5738	0.503956
$956$	7.68398	0.248518
$957$	−28.9731	−0.936567
$958$	59.5246	1.92315
$959$	16.0298	0.517628
$960$	−8.67000	−0.279823
$961$	−18.8098	−0.606768
$962$	6.52312	0.210314
$963$	−84.3341	−2.71763
$964$	−124.310	−4.00376
$965$	1.18256	0.0380681
$966$	21.2856	0.684854
$967$	21.8545	0.702792	0.351396	−	0.936227i	$-0.385707\pi$
$967$	21.8545	0.702792	0.351396	+	0.936227i	$0.385707\pi$
$968$	−63.0948	−2.02794
$969$	−0.609210	−0.0195706
$970$	−4.18097	−0.134243
$971$	−23.1515	−0.742966	−0.371483	−	0.928440i	$-0.621151\pi$
$971$	−23.1515	−0.742966	−0.371483	+	0.928440i	$0.621151\pi$
$972$	370.628	11.8879
$973$	−74.5259	−2.38919
$974$	23.2922	0.746330
$975$	−3.55501	−0.113852
$976$	75.3383	2.41152
$977$	53.7478	1.71955	0.859773	−	0.510677i	$-0.170605\pi$
$977$	53.7478	1.71955	0.859773	+	0.510677i	$0.170605\pi$
$978$	129.860	4.15246
$979$	−21.2889	−0.680397
$980$	16.8842	0.539345
$981$	76.8305	2.45301
$982$	34.6807	1.10671
$983$	−3.46260	−0.110440	−0.0552198	−	0.998474i	$-0.517586\pi$
$983$	−3.46260	−0.110440	−0.0552198	+	0.998474i	$0.517586\pi$
$984$	13.9229	0.443845
$985$	13.4858	0.429694
$986$	−2.82740	−0.0900428
$987$	−41.8559	−1.33229
$988$	0.266541	0.00847980
$989$	5.81452	0.184891
$990$	−62.6586	−1.99142
$991$	42.7999	1.35958	0.679792	−	0.733405i	$-0.262070\pi$
$991$	42.7999	1.35958	0.679792	+	0.733405i	$0.262070\pi$
$992$	10.0037	0.317618
$993$	−100.303	−3.18303
$994$	−41.4871	−1.31589
$995$	12.0488	0.381973
$996$	175.439	5.55899
$997$	−51.6729	−1.63650	−0.818248	−	0.574865i	$-0.805054\pi$
$997$	−51.6729	−1.63650	−0.818248	+	0.574865i	$0.805054\pi$
$998$	46.5838	1.47458
$999$	−235.672	−7.45634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6043.2.a.c.1.16	✓	259

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6043.2.a.c.1.16	✓	259	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:	\( N \)	\(=\)	\( 6043 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.50362 q^{2} +3.44242 q^{3} +4.26813 q^{4} +0.601384 q^{5} -8.61852 q^{6} +3.68483 q^{7} -5.67855 q^{8} +8.85024 q^{9} +O(q^{10})\)	\(q-2.50362 q^{2} +3.44242 q^{3} +4.26813 q^{4} +0.601384 q^{5} -8.61852 q^{6} +3.68483 q^{7} -5.67855 q^{8} +8.85024 q^{9} -1.50564 q^{10} +4.70224 q^{11} +14.6927 q^{12} +0.222646 q^{13} -9.22542 q^{14} +2.07021 q^{15} +5.68069 q^{16} -0.630946 q^{17} -22.1577 q^{18} +0.280486 q^{19} +2.56678 q^{20} +12.6847 q^{21} -11.7726 q^{22} -0.670251 q^{23} -19.5479 q^{24} -4.63834 q^{25} -0.557422 q^{26} +20.1390 q^{27} +15.7273 q^{28} -1.78989 q^{29} -5.18304 q^{30} -3.49144 q^{31} -2.86521 q^{32} +16.1871 q^{33} +1.57965 q^{34} +2.21599 q^{35} +37.7740 q^{36} -11.7023 q^{37} -0.702231 q^{38} +0.766441 q^{39} -3.41499 q^{40} -0.712242 q^{41} -31.7577 q^{42} -8.67514 q^{43} +20.0698 q^{44} +5.32239 q^{45} +1.67806 q^{46} -3.29971 q^{47} +19.5553 q^{48} +6.57794 q^{49} +11.6127 q^{50} -2.17198 q^{51} +0.950283 q^{52} +11.3177 q^{53} -50.4204 q^{54} +2.82785 q^{55} -20.9245 q^{56} +0.965550 q^{57} +4.48121 q^{58} -7.57734 q^{59} +8.83595 q^{60} +13.2622 q^{61} +8.74126 q^{62} +32.6116 q^{63} -4.18797 q^{64} +0.133896 q^{65} -40.5264 q^{66} +8.11519 q^{67} -2.69296 q^{68} -2.30728 q^{69} -5.54801 q^{70} +4.49705 q^{71} -50.2566 q^{72} +4.62607 q^{73} +29.2981 q^{74} -15.9671 q^{75} +1.19715 q^{76} +17.3269 q^{77} -1.91888 q^{78} +2.34215 q^{79} +3.41627 q^{80} +42.7761 q^{81} +1.78319 q^{82} +11.9405 q^{83} +54.1400 q^{84} -0.379441 q^{85} +21.7193 q^{86} -6.16155 q^{87} -26.7019 q^{88} -4.52740 q^{89} -13.3253 q^{90} +0.820412 q^{91} -2.86072 q^{92} -12.0190 q^{93} +8.26123 q^{94} +0.168680 q^{95} -9.86325 q^{96} +2.77688 q^{97} -16.4687 q^{98} +41.6160 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9}+O(q^{10}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9	\( 259 q + 39 q^{2} + 25 q^{3} + 271 q^{4} + 83 q^{5} + 18 q^{6} + 26 q^{7} + 111 q^{8} + 286 q^{9} + 36 q^{10} + 35 q^{11} + 58 q^{12} + 109 q^{13} + 31 q^{14} + 30 q^{15} + 287 q^{16} + 124 q^{17} + 97 q^{18} + 42 q^{19} + 149 q^{20} + 99 q^{21} + 22 q^{22} + 63 q^{23} + 53 q^{24} + 308 q^{25} + 86 q^{26} + 82 q^{27} + 52 q^{28} + 131 q^{29} + 6 q^{30} + 29 q^{31} + 251 q^{32} + 147 q^{33} + 24 q^{34} + 79 q^{35} + 315 q^{36} + 108 q^{37} + 124 q^{38} + 48 q^{39} + 87 q^{40} + 190 q^{41} + 28 q^{42} + 36 q^{43} + 70 q^{44} + 211 q^{45} + 19 q^{46} + 186 q^{47} + 103 q^{48} + 297 q^{49} + 161 q^{50} + 20 q^{51} + 173 q^{52} + 213 q^{53} + 56 q^{54} + 35 q^{55} + 99 q^{56} + 80 q^{57} + 32 q^{58} + 135 q^{59} + 23 q^{60} + 83 q^{61} + 172 q^{62} + 85 q^{63} + 297 q^{64} + 177 q^{65} + 41 q^{66} + 30 q^{67} + 271 q^{68} + 168 q^{69} + 24 q^{70} + 63 q^{71} + 241 q^{72} + 152 q^{73} + 32 q^{74} + 36 q^{75} + 92 q^{76} + 396 q^{77} + 21 q^{78} - 2 q^{79} + 242 q^{80} + 343 q^{81} + 40 q^{82} + 236 q^{83} + 92 q^{84} + 124 q^{85} + 55 q^{86} + 113 q^{87} + 7 q^{88} + 214 q^{89} + 100 q^{90} + 2 q^{91} + 176 q^{92} + 228 q^{93} + 51 q^{94} + 96 q^{95} + 48 q^{96} + 135 q^{97} + 261 q^{98} + 26 q^{99}+O(q^{100}) \) 259 * q + 39 * q^2 + 25 * q^3 + 271 * q^4 + 83 * q^5 + 18 * q^6 + 26 * q^7 + 111 * q^8 + 286 * q^9 + 36 * q^10 + 35 * q^11 + 58 * q^12 + 109 * q^13 + 31 * q^14 + 30 * q^15 + 287 * q^16 + 124 * q^17 + 97 * q^18 + 42 * q^19 + 149 * q^20 + 99 * q^21 + 22 * q^22 + 63 * q^23 + 53 * q^24 + 308 * q^25 + 86 * q^26 + 82 * q^27 + 52 * q^28 + 131 * q^29 + 6 * q^30 + 29 * q^31 + 251 * q^32 + 147 * q^33 + 24 * q^34 + 79 * q^35 + 315 * q^36 + 108 * q^37 + 124 * q^38 + 48 * q^39 + 87 * q^40 + 190 * q^41 + 28 * q^42 + 36 * q^43 + 70 * q^44 + 211 * q^45 + 19 * q^46 + 186 * q^47 + 103 * q^48 + 297 * q^49 + 161 * q^50 + 20 * q^51 + 173 * q^52 + 213 * q^53 + 56 * q^54 + 35 * q^55 + 99 * q^56 + 80 * q^57 + 32 * q^58 + 135 * q^59 + 23 * q^60 + 83 * q^61 + 172 * q^62 + 85 * q^63 + 297 * q^64 + 177 * q^65 + 41 * q^66 + 30 * q^67 + 271 * q^68 + 168 * q^69 + 24 * q^70 + 63 * q^71 + 241 * q^72 + 152 * q^73 + 32 * q^74 + 36 * q^75 + 92 * q^76 + 396 * q^77 + 21 * q^78 - 2 * q^79 + 242 * q^80 + 343 * q^81 + 40 * q^82 + 236 * q^83 + 92 * q^84 + 124 * q^85 + 55 * q^86 + 113 * q^87 + 7 * q^88 + 214 * q^89 + 100 * q^90 + 2 * q^91 + 176 * q^92 + 228 * q^93 + 51 * q^94 + 96 * q^95 + 48 * q^96 + 135 * q^97 + 261 * q^98 + 26 * q^99

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