LMFDB - Embedded newform 983.2.a.b.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.01514 q^{2} -3.15226 q^{3} -0.969484 q^{4} -2.87277 q^{5} -3.19999 q^{6} -2.07820 q^{7} -3.01445 q^{8} +6.93672 q^{9} +O(q^{10})$	\(q+1.01514 q^{2} -3.15226 q^{3} -0.969484 q^{4} -2.87277 q^{5} -3.19999 q^{6} -2.07820 q^{7} -3.01445 q^{8} +6.93672 q^{9} -2.91628 q^{10} -5.58027 q^{11} +3.05606 q^{12} -2.86298 q^{13} -2.10967 q^{14} +9.05571 q^{15} -1.12113 q^{16} -6.40019 q^{17} +7.04177 q^{18} -4.17807 q^{19} +2.78510 q^{20} +6.55101 q^{21} -5.66478 q^{22} +9.05143 q^{23} +9.50233 q^{24} +3.25282 q^{25} -2.90634 q^{26} -12.4096 q^{27} +2.01478 q^{28} +1.31188 q^{29} +9.19285 q^{30} -4.51884 q^{31} +4.89079 q^{32} +17.5904 q^{33} -6.49711 q^{34} +5.97018 q^{35} -6.72504 q^{36} +4.87674 q^{37} -4.24134 q^{38} +9.02485 q^{39} +8.65983 q^{40} -5.42883 q^{41} +6.65021 q^{42} -3.82487 q^{43} +5.40998 q^{44} -19.9276 q^{45} +9.18850 q^{46} +0.0396045 q^{47} +3.53410 q^{48} -2.68110 q^{49} +3.30207 q^{50} +20.1750 q^{51} +2.77561 q^{52} -6.55004 q^{53} -12.5975 q^{54} +16.0308 q^{55} +6.26462 q^{56} +13.1703 q^{57} +1.33174 q^{58} -7.60141 q^{59} -8.77937 q^{60} +8.37770 q^{61} -4.58727 q^{62} -14.4159 q^{63} +7.20712 q^{64} +8.22469 q^{65} +17.8568 q^{66} -2.97364 q^{67} +6.20488 q^{68} -28.5324 q^{69} +6.06059 q^{70} -5.05049 q^{71} -20.9104 q^{72} +15.5871 q^{73} +4.95059 q^{74} -10.2537 q^{75} +4.05057 q^{76} +11.5969 q^{77} +9.16152 q^{78} -14.5560 q^{79} +3.22076 q^{80} +18.3080 q^{81} -5.51104 q^{82} -11.7419 q^{83} -6.35110 q^{84} +18.3863 q^{85} -3.88279 q^{86} -4.13537 q^{87} +16.8215 q^{88} -7.02298 q^{89} -20.2294 q^{90} +5.94984 q^{91} -8.77521 q^{92} +14.2445 q^{93} +0.0402042 q^{94} +12.0026 q^{95} -15.4170 q^{96} +9.64562 q^{97} -2.72170 q^{98} -38.7088 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	1.01514	0.717815	0.358907	−	0.933373i	$-0.383149\pi$
$2$	1.01514	0.717815	0.358907	+	0.933373i	$0.383149\pi$
$3$	−3.15226	−1.81996	−0.909978	−	0.414656i	$-0.863902\pi$
$3$	−3.15226	−1.81996	−0.909978	+	0.414656i	$0.863902\pi$
$4$	−0.969484	−0.484742
$5$	−2.87277	−1.28474	−0.642371	−	0.766394i	$-0.722049\pi$
$5$	−2.87277	−1.28474	−0.642371	+	0.766394i	$0.722049\pi$
$6$	−3.19999	−1.30639
$7$	−2.07820	−0.785484	−0.392742	−	0.919649i	$-0.628474\pi$
$7$	−2.07820	−0.785484	−0.392742	+	0.919649i	$0.628474\pi$
$8$	−3.01445	−1.06577
$9$	6.93672	2.31224
$10$	−2.91628	−0.922207
$11$	−5.58027	−1.68252	−0.841258	−	0.540635i	$-0.818184\pi$
$11$	−5.58027	−1.68252	−0.841258	+	0.540635i	$0.818184\pi$
$12$	3.05606	0.882209
$13$	−2.86298	−0.794048	−0.397024	−	0.917808i	$-0.629957\pi$
$13$	−2.86298	−0.794048	−0.397024	+	0.917808i	$0.629957\pi$
$14$	−2.10967	−0.563832
$15$	9.05571	2.33818
$16$	−1.12113	−0.280284
$17$	−6.40019	−1.55227	−0.776137	−	0.630564i	$-0.782824\pi$
$17$	−6.40019	−1.55227	−0.776137	+	0.630564i	$0.782824\pi$
$18$	7.04177	1.65976
$19$	−4.17807	−0.958515	−0.479257	−	0.877674i	$-0.659094\pi$
$19$	−4.17807	−0.958515	−0.479257	+	0.877674i	$0.659094\pi$
$20$	2.78510	0.622768
$21$	6.55101	1.42955
$22$	−5.66478	−1.20773
$23$	9.05143	1.88735	0.943677	−	0.330868i	$-0.107342\pi$
$23$	9.05143	1.88735	0.943677	+	0.330868i	$0.107342\pi$
$24$	9.50233	1.93965
$25$	3.25282	0.650563
$26$	−2.90634	−0.569979
$27$	−12.4096	−2.38822
$28$	2.01478	0.380757
$29$	1.31188	0.243609	0.121805	−	0.992554i	$-0.461132\pi$
$29$	1.31188	0.243609	0.121805	+	0.992554i	$0.461132\pi$
$30$	9.19285	1.67838
$31$	−4.51884	−0.811607	−0.405804	−	0.913960i	$-0.633008\pi$
$31$	−4.51884	−0.811607	−0.405804	+	0.913960i	$0.633008\pi$
$32$	4.89079	0.864578
$33$	17.5904	3.06210
$34$	−6.49711	−1.11425
$35$	5.97018	1.00915
$36$	−6.72504	−1.12084
$37$	4.87674	0.801731	0.400865	−	0.916137i	$-0.368710\pi$
$37$	4.87674	0.801731	0.400865	+	0.916137i	$0.368710\pi$
$38$	−4.24134	−0.688036
$39$	9.02485	1.44513
$40$	8.65983	1.36924
$41$	−5.42883	−0.847841	−0.423920	−	0.905699i	$-0.639346\pi$
$41$	−5.42883	−0.847841	−0.423920	+	0.905699i	$0.639346\pi$
$42$	6.65021	1.02615
$43$	−3.82487	−0.583287	−0.291644	−	0.956527i	$-0.594202\pi$
$43$	−3.82487	−0.583287	−0.291644	+	0.956527i	$0.594202\pi$
$44$	5.40998	0.815585
$45$	−19.9276	−2.97063
$46$	9.18850	1.35477
$47$	0.0396045	0.00577691	0.00288845	−	0.999996i	$-0.499081\pi$
$47$	0.0396045	0.00577691	0.00288845	+	0.999996i	$0.499081\pi$
$48$	3.53410	0.510104
$49$	−2.68110	−0.383014
$50$	3.30207	0.466984
$51$	20.1750	2.82507
$52$	2.77561	0.384908
$53$	−6.55004	−0.899718	−0.449859	−	0.893100i	$-0.648526\pi$
$53$	−6.55004	−0.899718	−0.449859	+	0.893100i	$0.648526\pi$
$54$	−12.5975	−1.71430
$55$	16.0308	2.16160
$56$	6.26462	0.837146
$57$	13.1703	1.74446
$58$	1.33174	0.174867
$59$	−7.60141	−0.989619	−0.494809	−	0.869002i	$-0.664762\pi$
$59$	−7.60141	−0.989619	−0.494809	+	0.869002i	$0.664762\pi$
$60$	−8.77937	−1.13341
$61$	8.37770	1.07265	0.536327	−	0.844010i	$-0.319811\pi$
$61$	8.37770	1.07265	0.536327	+	0.844010i	$0.319811\pi$
$62$	−4.58727	−0.582584
$63$	−14.4159	−1.81623
$64$	7.20712	0.900891
$65$	8.22469	1.02015
$66$	17.8568	2.19802
$67$	−2.97364	−0.363288	−0.181644	−	0.983364i	$-0.558142\pi$
$67$	−2.97364	−0.363288	−0.181644	+	0.983364i	$0.558142\pi$
$68$	6.20488	0.752452
$69$	−28.5324	−3.43490
$70$	6.06059	0.724379
$71$	−5.05049	−0.599383	−0.299692	−	0.954036i	$-0.596884\pi$
$71$	−5.05049	−0.599383	−0.299692	+	0.954036i	$0.596884\pi$
$72$	−20.9104	−2.46432
$73$	15.5871	1.82433	0.912165	−	0.409824i	$-0.134410\pi$
$73$	15.5871	1.82433	0.912165	+	0.409824i	$0.134410\pi$
$74$	4.95059	0.575494
$75$	−10.2537	−1.18400
$76$	4.05057	0.464632
$77$	11.5969	1.32159
$78$	9.16152	1.03734
$79$	−14.5560	−1.63768	−0.818841	−	0.574020i	$-0.805383\pi$
$79$	−14.5560	−1.63768	−0.818841	+	0.574020i	$0.805383\pi$
$80$	3.22076	0.360092
$81$	18.3080	2.03422
$82$	−5.51104	−0.608593
$83$	−11.7419	−1.28884	−0.644420	−	0.764671i	$-0.722901\pi$
$83$	−11.7419	−1.28884	−0.644420	+	0.764671i	$0.722901\pi$
$84$	−6.35110	−0.692961
$85$	18.3863	1.99427
$86$	−3.88279	−0.418692
$87$	−4.13537	−0.443359
$88$	16.8215	1.79317
$89$	−7.02298	−0.744434	−0.372217	−	0.928146i	$-0.621402\pi$
$89$	−7.02298	−0.744434	−0.372217	+	0.928146i	$0.621402\pi$
$90$	−20.2294	−2.13237
$91$	5.94984	0.623712
$92$	−8.77521	−0.914879
$93$	14.2445	1.47709
$94$	0.0402042	0.00414675
$95$	12.0026	1.23144
$96$	−15.4170	−1.57349
$97$	9.64562	0.979364	0.489682	−	0.871901i	$-0.337113\pi$
$97$	9.64562	0.979364	0.489682	+	0.871901i	$0.337113\pi$
$98$	−2.72170	−0.274933
$99$	−38.7088	−3.89038
$100$	−3.15355	−0.315355
$101$	−7.23987	−0.720394	−0.360197	−	0.932876i	$-0.617291\pi$
$101$	−7.23987	−0.720394	−0.360197	+	0.932876i	$0.617291\pi$
$102$	20.4806	2.02788
$103$	−10.7086	−1.05515	−0.527576	−	0.849508i	$-0.676899\pi$
$103$	−10.7086	−1.05515	−0.527576	+	0.849508i	$0.676899\pi$
$104$	8.63032	0.846272
$105$	−18.8196	−1.83660
$106$	−6.64924	−0.645831
$107$	−15.2935	−1.47848	−0.739238	−	0.673444i	$-0.764814\pi$
$107$	−15.2935	−1.47848	−0.739238	+	0.673444i	$0.764814\pi$
$108$	12.0309	1.15767
$109$	−8.14463	−0.780114	−0.390057	−	0.920791i	$-0.627545\pi$
$109$	−8.14463	−0.780114	−0.390057	+	0.920791i	$0.627545\pi$
$110$	16.2736	1.55163
$111$	−15.3727	−1.45911
$112$	2.32994	0.220158
$113$	1.04158	0.0979834	0.0489917	−	0.998799i	$-0.484399\pi$
$113$	1.04158	0.0979834	0.0489917	+	0.998799i	$0.484399\pi$
$114$	13.3698	1.25220
$115$	−26.0027	−2.42476
$116$	−1.27184	−0.118088
$117$	−19.8597	−1.83603
$118$	−7.71652	−0.710363
$119$	13.3009	1.21929
$120$	−27.2980	−2.49196
$121$	20.1394	1.83086
$122$	8.50457	0.769968
$123$	17.1131	1.54303
$124$	4.38094	0.393420
$125$	5.01926	0.448936
$126$	−14.6342	−1.30372
$127$	−16.5602	−1.46948	−0.734740	−	0.678349i	$-0.762696\pi$
$127$	−16.5602	−1.46948	−0.734740	+	0.678349i	$0.762696\pi$
$128$	−2.46532	−0.217905
$129$	12.0570	1.06156
$130$	8.34924	0.732277
$131$	−3.55081	−0.310236	−0.155118	−	0.987896i	$-0.549576\pi$
$131$	−3.55081	−0.310236	−0.155118	+	0.987896i	$0.549576\pi$
$132$	−17.0537	−1.48433
$133$	8.68285	0.752899
$134$	−3.01867	−0.260774
$135$	35.6498	3.06825
$136$	19.2931	1.65437
$137$	−3.38248	−0.288985	−0.144492	−	0.989506i	$-0.546155\pi$
$137$	−3.38248	−0.288985	−0.144492	+	0.989506i	$0.546155\pi$
$138$	−28.9645	−2.46562
$139$	−11.5750	−0.981782	−0.490891	−	0.871221i	$-0.663329\pi$
$139$	−11.5750	−0.981782	−0.490891	+	0.871221i	$0.663329\pi$
$140$	−5.78799	−0.489175
$141$	−0.124844	−0.0105137
$142$	−5.12698	−0.430246
$143$	15.9762	1.33600
$144$	−7.77700	−0.648083
$145$	−3.76872	−0.312975
$146$	15.8231	1.30953
$147$	8.45151	0.697069
$148$	−4.72792	−0.388632
$149$	−13.0140	−1.06615	−0.533074	−	0.846069i	$-0.678963\pi$
$149$	−13.0140	−1.06615	−0.533074	+	0.846069i	$0.678963\pi$
$150$	−10.4090	−0.849890
$151$	15.1820	1.23549	0.617746	−	0.786378i	$-0.288046\pi$
$151$	15.1820	1.23549	0.617746	+	0.786378i	$0.288046\pi$
$152$	12.5946	1.02156
$153$	−44.3964	−3.58923
$154$	11.7725	0.948657
$155$	12.9816	1.04271
$156$	−8.74944	−0.700516
$157$	14.5690	1.16273	0.581366	−	0.813642i	$-0.302518\pi$
$157$	14.5690	1.16273	0.581366	+	0.813642i	$0.302518\pi$
$158$	−14.7765	−1.17555
$159$	20.6474	1.63745
$160$	−14.0501	−1.11076
$161$	−18.8107	−1.48249
$162$	18.5852	1.46019
$163$	13.2220	1.03563	0.517813	−	0.855494i	$-0.326746\pi$
$163$	13.2220	1.03563	0.517813	+	0.855494i	$0.326746\pi$
$164$	5.26316	0.410984
$165$	−50.5333	−3.93401
$166$	−11.9197	−0.925149
$167$	17.8743	1.38315	0.691577	−	0.722302i	$-0.256916\pi$
$167$	17.8743	1.38315	0.691577	+	0.722302i	$0.256916\pi$
$168$	−19.7477	−1.52357
$169$	−4.80334	−0.369488
$170$	18.6647	1.43152
$171$	−28.9821	−2.21632
$172$	3.70815	0.282744
$173$	14.9253	1.13475	0.567373	−	0.823461i	$-0.307960\pi$
$173$	14.9253	1.13475	0.567373	+	0.823461i	$0.307960\pi$
$174$	−4.19800	−0.318249
$175$	−6.75999	−0.511007
$176$	6.25623	0.471581
$177$	23.9616	1.80106
$178$	−7.12933	−0.534366
$179$	−2.79830	−0.209155	−0.104577	−	0.994517i	$-0.533349\pi$
$179$	−2.79830	−0.209155	−0.104577	+	0.994517i	$0.533349\pi$
$180$	19.3195	1.43999
$181$	−16.9744	−1.26170	−0.630848	−	0.775906i	$-0.717293\pi$
$181$	−16.9744	−1.26170	−0.630848	+	0.775906i	$0.717293\pi$
$182$	6.03994	0.447710
$183$	−26.4087	−1.95218
$184$	−27.2851	−2.01148
$185$	−14.0098	−1.03002
$186$	14.4603	1.06028
$187$	35.7148	2.61173
$188$	−0.0383959	−0.00280031
$189$	25.7895	1.87591
$190$	12.1844	0.883949
$191$	−8.54799	−0.618511	−0.309256	−	0.950979i	$-0.600080\pi$
$191$	−8.54799	−0.618511	−0.309256	+	0.950979i	$0.600080\pi$
$192$	−22.7187	−1.63958
$193$	5.62743	0.405072	0.202536	−	0.979275i	$-0.435082\pi$
$193$	5.62743	0.405072	0.202536	+	0.979275i	$0.435082\pi$
$194$	9.79169	0.703002
$195$	−25.9263	−1.85662
$196$	2.59928	0.185663
$197$	19.3009	1.37513	0.687567	−	0.726121i	$-0.258679\pi$
$197$	19.3009	1.37513	0.687567	+	0.726121i	$0.258679\pi$
$198$	−39.2950	−2.79257
$199$	−2.31923	−0.164406	−0.0822029	−	0.996616i	$-0.526196\pi$
$199$	−2.31923	−0.164406	−0.0822029	+	0.996616i	$0.526196\pi$
$200$	−9.80546	−0.693350
$201$	9.37368	0.661168
$202$	−7.34951	−0.517110
$203$	−2.72634	−0.191351
$204$	−19.5594	−1.36943
$205$	15.5958	1.08926
$206$	−10.8708	−0.757403
$207$	62.7873	4.36402
$208$	3.20979	0.222559
$209$	23.3148	1.61272
$210$	−19.1045	−1.31834
$211$	6.36829	0.438411	0.219206	−	0.975679i	$-0.429653\pi$
$211$	6.36829	0.438411	0.219206	+	0.975679i	$0.429653\pi$
$212$	6.35016	0.436131
$213$	15.9205	1.09085
$214$	−15.5251	−1.06127
$215$	10.9880	0.749374
$216$	37.4080	2.54529
$217$	9.39104	0.637505
$218$	−8.26797	−0.559978
$219$	−49.1345	−3.32020
$220$	−15.5416	−1.04782
$221$	18.3236	1.23258
$222$	−15.6055	−1.04737
$223$	−1.63337	−0.109379	−0.0546893	−	0.998503i	$-0.517417\pi$
$223$	−1.63337	−0.109379	−0.0546893	+	0.998503i	$0.517417\pi$
$224$	−10.1640	−0.679113
$225$	22.5639	1.50426
$226$	1.05735	0.0703339
$227$	−19.6346	−1.30320	−0.651598	−	0.758565i	$-0.725901\pi$
$227$	−19.6346	−1.30320	−0.651598	+	0.758565i	$0.725901\pi$
$228$	−12.7684	−0.845610
$229$	15.2350	1.00676	0.503379	−	0.864066i	$-0.332090\pi$
$229$	15.2350	1.00676	0.503379	+	0.864066i	$0.332090\pi$
$230$	−26.3965	−1.74053
$231$	−36.5564	−2.40524
$232$	−3.95459	−0.259632
$233$	−8.78125	−0.575279	−0.287639	−	0.957739i	$-0.592870\pi$
$233$	−8.78125	−0.575279	−0.287639	+	0.957739i	$0.592870\pi$
$234$	−20.1604	−1.31793
$235$	−0.113775	−0.00742184
$236$	7.36944	0.479710
$237$	45.8844	2.98051
$238$	13.5023	0.875223
$239$	19.7820	1.27959	0.639794	−	0.768546i	$-0.279020\pi$
$239$	19.7820	1.27959	0.639794	+	0.768546i	$0.279020\pi$
$240$	−10.1527	−0.655352
$241$	−27.5849	−1.77690	−0.888451	−	0.458972i	$-0.848218\pi$
$241$	−27.5849	−1.77690	−0.888451	+	0.458972i	$0.848218\pi$
$242$	20.4444	1.31422
$243$	−20.4827	−1.31397
$244$	−8.12204	−0.519961
$245$	7.70218	0.492075
$246$	17.3722	1.10761
$247$	11.9617	0.761107
$248$	13.6218	0.864987
$249$	37.0135	2.34563
$250$	5.09527	0.322253
$251$	−12.3609	−0.780214	−0.390107	−	0.920770i	$-0.627562\pi$
$251$	−12.3609	−0.780214	−0.390107	+	0.920770i	$0.627562\pi$
$252$	13.9760	0.880402
$253$	−50.5094	−3.17550
$254$	−16.8110	−1.05481
$255$	−57.9583	−3.62949
$256$	−16.9169	−1.05731
$257$	−24.6823	−1.53964	−0.769820	−	0.638261i	$-0.779654\pi$
$257$	−24.6823	−1.53964	−0.769820	+	0.638261i	$0.779654\pi$
$258$	12.2396	0.762002
$259$	−10.1348	−0.629747
$260$	−7.97370	−0.494508
$261$	9.10013	0.563284
$262$	−3.60458	−0.222692
$263$	1.77319	0.109340	0.0546698	−	0.998504i	$-0.482589\pi$
$263$	1.77319	0.109340	0.0546698	+	0.998504i	$0.482589\pi$
$264$	−53.0256	−3.26350
$265$	18.8168	1.15591
$266$	8.81434	0.540442
$267$	22.1382	1.35484
$268$	2.88290	0.176101
$269$	−9.13297	−0.556847	−0.278424	−	0.960458i	$-0.589812\pi$
$269$	−9.13297	−0.556847	−0.278424	+	0.960458i	$0.589812\pi$
$270$	36.1897	2.20244
$271$	31.4457	1.91019	0.955096	−	0.296296i	$-0.0957514\pi$
$271$	31.4457	1.91019	0.955096	+	0.296296i	$0.0957514\pi$
$272$	7.17548	0.435077
$273$	−18.7554	−1.13513
$274$	−3.43371	−0.207438
$275$	−18.1516	−1.09458
$276$	27.6617	1.66504
$277$	19.5363	1.17382	0.586911	−	0.809651i	$-0.300344\pi$
$277$	19.5363	1.17382	0.586911	+	0.809651i	$0.300344\pi$
$278$	−11.7503	−0.704738
$279$	−31.3459	−1.87663
$280$	−17.9968	−1.07552
$281$	12.4293	0.741472	0.370736	−	0.928738i	$-0.379105\pi$
$281$	12.4293	0.741472	0.370736	+	0.928738i	$0.379105\pi$
$282$	−0.126734	−0.00754691
$283$	−9.07291	−0.539328	−0.269664	−	0.962954i	$-0.586913\pi$
$283$	−9.07291	−0.539328	−0.269664	+	0.962954i	$0.586913\pi$
$284$	4.89637	0.290546
$285$	−37.8354	−2.24118
$286$	16.2181	0.958999
$287$	11.2822	0.665966
$288$	33.9261	1.99911
$289$	23.9625	1.40956
$290$	−3.82580	−0.224658
$291$	−30.4055	−1.78240
$292$	−15.1114	−0.884329
$293$	−28.0638	−1.63951	−0.819753	−	0.572718i	$-0.805889\pi$
$293$	−28.0638	−1.63951	−0.819753	+	0.572718i	$0.805889\pi$
$294$	8.57950	0.500367
$295$	21.8371	1.27141
$296$	−14.7007	−0.854460
$297$	69.2487	4.01822
$298$	−13.2111	−0.765296
$299$	−25.9141	−1.49865
$300$	9.94080	0.573932
$301$	7.94883	0.458163
$302$	15.4119	0.886854
$303$	22.8219	1.31109
$304$	4.68418	0.268656
$305$	−24.0672	−1.37809
$306$	−45.0687	−2.57640
$307$	22.9815	1.31162	0.655811	−	0.754925i	$-0.272327\pi$
$307$	22.9815	1.31162	0.655811	+	0.754925i	$0.272327\pi$
$308$	−11.2430	−0.640630
$309$	33.7563	1.92033
$310$	13.1782	0.748470
$311$	−5.89990	−0.334552	−0.167276	−	0.985910i	$-0.553497\pi$
$311$	−5.89990	−0.334552	−0.167276	+	0.985910i	$0.553497\pi$
$312$	−27.2050	−1.54018
$313$	21.0751	1.19123	0.595617	−	0.803269i	$-0.296908\pi$
$313$	21.0751	1.19123	0.595617	+	0.803269i	$0.296908\pi$
$314$	14.7896	0.834627
$315$	41.4135	2.33339
$316$	14.1118	0.793853
$317$	21.1674	1.18888	0.594440	−	0.804140i	$-0.297374\pi$
$317$	21.1674	1.18888	0.594440	+	0.804140i	$0.297374\pi$
$318$	20.9601	1.17538
$319$	−7.32063	−0.409877
$320$	−20.7044	−1.15741
$321$	48.2090	2.69076
$322$	−19.0955	−1.06415
$323$	26.7404	1.48788
$324$	−17.7493	−0.986070
$325$	−9.31275	−0.516578
$326$	13.4222	0.743388
$327$	25.6740	1.41977
$328$	16.3649	0.903603
$329$	−0.0823059	−0.00453767
$330$	−51.2986	−2.82389
$331$	−0.265422	−0.0145889	−0.00729445	−	0.999973i	$-0.502322\pi$
$331$	−0.265422	−0.0145889	−0.00729445	+	0.999973i	$0.502322\pi$
$332$	11.3836	0.624755
$333$	33.8286	1.85379
$334$	18.1450	0.992849
$335$	8.54259	0.466732
$336$	−7.34456	−0.400679
$337$	5.24785	0.285869	0.142934	−	0.989732i	$-0.454346\pi$
$337$	5.24785	0.285869	0.142934	+	0.989732i	$0.454346\pi$
$338$	−4.87608	−0.265224
$339$	−3.28332	−0.178325
$340$	−17.8252	−0.966707
$341$	25.2163	1.36554
$342$	−29.4210	−1.59091
$343$	20.1192	1.08634
$344$	11.5299	0.621650
$345$	81.9672	4.41296
$346$	15.1513	0.814538
$347$	−10.1665	−0.545764	−0.272882	−	0.962048i	$-0.587977\pi$
$347$	−10.1665	−0.545764	−0.272882	+	0.962048i	$0.587977\pi$
$348$	4.00918	0.214914
$349$	22.8317	1.22215	0.611077	−	0.791571i	$-0.290736\pi$
$349$	22.8317	1.22215	0.611077	+	0.791571i	$0.290736\pi$
$350$	−6.86236	−0.366809
$351$	35.5283	1.89636
$352$	−27.2919	−1.45467
$353$	−3.47434	−0.184921	−0.0924603	−	0.995716i	$-0.529473\pi$
$353$	−3.47434	−0.184921	−0.0924603	+	0.995716i	$0.529473\pi$
$354$	24.3245	1.29283
$355$	14.5089	0.770053
$356$	6.80866	0.360858
$357$	−41.9277	−2.21905
$358$	−2.84068	−0.150134
$359$	−5.95548	−0.314318	−0.157159	−	0.987573i	$-0.550234\pi$
$359$	−5.95548	−0.314318	−0.157159	+	0.987573i	$0.550234\pi$
$360$	60.0709	3.16601
$361$	−1.54374	−0.0812493
$362$	−17.2314	−0.905664
$363$	−63.4846	−3.33208
$364$	−5.76827	−0.302339
$365$	−44.7781	−2.34379
$366$	−26.8086	−1.40131
$367$	−2.39635	−0.125088	−0.0625441	−	0.998042i	$-0.519921\pi$
$367$	−2.39635	−0.125088	−0.0625441	+	0.998042i	$0.519921\pi$
$368$	−10.1479	−0.528994
$369$	−37.6583	−1.96041
$370$	−14.2219	−0.739362
$371$	13.6123	0.706714
$372$	−13.8098	−0.716007
$373$	−21.8360	−1.13062	−0.565312	−	0.824877i	$-0.691244\pi$
$373$	−21.8360	−1.13062	−0.565312	+	0.824877i	$0.691244\pi$
$374$	36.2557	1.87474
$375$	−15.8220	−0.817045
$376$	−0.119386	−0.00615686
$377$	−3.75588	−0.193438
$378$	26.1801	1.34656
$379$	−25.3397	−1.30161	−0.650807	−	0.759243i	$-0.725569\pi$
$379$	−25.3397	−1.30161	−0.650807	+	0.759243i	$0.725569\pi$
$380$	−11.6364	−0.596933
$381$	52.2020	2.67439
$382$	−8.67744	−0.443977
$383$	−0.418752	−0.0213973	−0.0106986	−	0.999943i	$-0.503406\pi$
$383$	−0.418752	−0.0213973	−0.0106986	+	0.999943i	$0.503406\pi$
$384$	7.77131	0.396578
$385$	−33.3152	−1.69790
$386$	5.71265	0.290766
$387$	−26.5321	−1.34870
$388$	−9.35127	−0.474739
$389$	−9.89192	−0.501540	−0.250770	−	0.968047i	$-0.580684\pi$
$389$	−9.89192	−0.501540	−0.250770	+	0.968047i	$0.580684\pi$
$390$	−26.3189	−1.33271
$391$	−57.9309	−2.92969
$392$	8.08204	0.408205
$393$	11.1931	0.564616
$394$	19.5932	0.987091
$395$	41.8162	2.10400
$396$	37.5275	1.88583
$397$	15.1414	0.759925	0.379962	−	0.925002i	$-0.375937\pi$
$397$	15.1414	0.759925	0.379962	+	0.925002i	$0.375937\pi$
$398$	−2.35435	−0.118013
$399$	−27.3706	−1.37024
$400$	−3.64684	−0.182342
$401$	−19.0595	−0.951785	−0.475892	−	0.879503i	$-0.657875\pi$
$401$	−19.0595	−0.951785	−0.475892	+	0.879503i	$0.657875\pi$
$402$	9.51563	0.474597
$403$	12.9373	0.644455
$404$	7.01894	0.349205
$405$	−52.5946	−2.61345
$406$	−2.76763	−0.137355
$407$	−27.2135	−1.34892
$408$	−60.8167	−3.01088
$409$	−31.9365	−1.57916	−0.789580	−	0.613647i	$-0.789702\pi$
$409$	−31.9365	−1.57916	−0.789580	+	0.613647i	$0.789702\pi$
$410$	15.8320	0.781885
$411$	10.6625	0.525940
$412$	10.3818	0.511476
$413$	15.7972	0.777330
$414$	63.7381	3.13256
$415$	33.7318	1.65583
$416$	−14.0022	−0.686516
$417$	36.4875	1.78680
$418$	23.6678	1.15763
$419$	−15.8505	−0.774349	−0.387174	−	0.922007i	$-0.626549\pi$
$419$	−15.8505	−0.774349	−0.387174	+	0.922007i	$0.626549\pi$
$420$	18.2452	0.890277
$421$	2.88582	0.140646	0.0703231	−	0.997524i	$-0.477597\pi$
$421$	2.88582	0.140646	0.0703231	+	0.997524i	$0.477597\pi$
$422$	6.46473	0.314698
$423$	0.274725	0.0133576
$424$	19.7448	0.958892
$425$	−20.8186	−1.00985
$426$	16.1615	0.783029
$427$	−17.4105	−0.842554
$428$	14.8268	0.716679
$429$	−50.3611	−2.43146
$430$	11.1544	0.537912
$431$	21.3834	1.03000	0.515000	−	0.857190i	$-0.327792\pi$
$431$	21.3834	1.03000	0.515000	+	0.857190i	$0.327792\pi$
$432$	13.9128	0.669379
$433$	−2.78809	−0.133987	−0.0669935	−	0.997753i	$-0.521341\pi$
$433$	−2.78809	−0.133987	−0.0669935	+	0.997753i	$0.521341\pi$
$434$	9.53325	0.457611
$435$	11.8800	0.569602
$436$	7.89609	0.378154
$437$	−37.8175	−1.80906
$438$	−49.8785	−2.38329
$439$	8.00030	0.381833	0.190917	−	0.981606i	$-0.438854\pi$
$439$	8.00030	0.381833	0.190917	+	0.981606i	$0.438854\pi$
$440$	−48.3242	−2.30377
$441$	−18.5980	−0.885621
$442$	18.6011	0.884764
$443$	−37.4854	−1.78099	−0.890493	−	0.454996i	$-0.849641\pi$
$443$	−37.4854	−1.78099	−0.890493	+	0.454996i	$0.849641\pi$
$444$	14.9036	0.707294
$445$	20.1754	0.956406
$446$	−1.65811	−0.0785136
$447$	41.0234	1.94034
$448$	−14.9778	−0.707636
$449$	3.77533	0.178169	0.0890844	−	0.996024i	$-0.471606\pi$
$449$	3.77533	0.178169	0.0890844	+	0.996024i	$0.471606\pi$
$450$	22.9056	1.07978
$451$	30.2943	1.42650
$452$	−1.00979	−0.0474966
$453$	−47.8575	−2.24854
$454$	−19.9320	−0.935453
$455$	−17.0925	−0.801310
$456$	−39.7014	−1.85919
$457$	−15.3430	−0.717714	−0.358857	−	0.933393i	$-0.616833\pi$
$457$	−15.3430	−0.717714	−0.358857	+	0.933393i	$0.616833\pi$
$458$	15.4657	0.722665
$459$	79.4236	3.70718
$460$	25.2092	1.17538
$461$	−4.05597	−0.188905	−0.0944526	−	0.995529i	$-0.530110\pi$
$461$	−4.05597	−0.188905	−0.0944526	+	0.995529i	$0.530110\pi$
$462$	−37.1100	−1.72651
$463$	−21.6447	−1.00591	−0.502956	−	0.864312i	$-0.667754\pi$
$463$	−21.6447	−1.00591	−0.502956	+	0.864312i	$0.667754\pi$
$464$	−1.47079	−0.0682797
$465$	−40.9213	−1.89768
$466$	−8.91423	−0.412944
$467$	12.2481	0.566772	0.283386	−	0.959006i	$-0.408542\pi$
$467$	12.2481	0.566772	0.283386	+	0.959006i	$0.408542\pi$
$468$	19.2537	0.890001
$469$	6.17981	0.285357
$470$	−0.115498	−0.00532751
$471$	−45.9252	−2.11612
$472$	22.9141	1.05471
$473$	21.3438	0.981390
$474$	46.5792	2.13945
$475$	−13.5905	−0.623574
$476$	−12.8950	−0.591040
$477$	−45.4359	−2.08036
$478$	20.0815	0.918508
$479$	−3.08635	−0.141019	−0.0705094	−	0.997511i	$-0.522462\pi$
$479$	−3.08635	−0.141019	−0.0705094	+	0.997511i	$0.522462\pi$
$480$	44.2896	2.02153
$481$	−13.9620	−0.636613
$482$	−28.0027	−1.27549
$483$	59.2960	2.69806
$484$	−19.5248	−0.887493
$485$	−27.7097	−1.25823
$486$	−20.7929	−0.943185
$487$	−25.6503	−1.16233	−0.581164	−	0.813786i	$-0.697403\pi$
$487$	−25.6503	−1.16233	−0.581164	+	0.813786i	$0.697403\pi$
$488$	−25.2542	−1.14320
$489$	−41.6791	−1.88479
$490$	7.81882	0.353218
$491$	5.97490	0.269643	0.134822	−	0.990870i	$-0.456954\pi$
$491$	5.97490	0.269643	0.134822	+	0.990870i	$0.456954\pi$
$492$	−16.5908	−0.747973
$493$	−8.39627	−0.378149
$494$	12.1429	0.546334
$495$	111.202	4.99814
$496$	5.06623	0.227480
$497$	10.4959	0.470806
$498$	37.5740	1.68373
$499$	3.55609	0.159192	0.0795962	−	0.996827i	$-0.474637\pi$
$499$	3.55609	0.159192	0.0795962	+	0.996827i	$0.474637\pi$
$500$	−4.86609	−0.217618
$501$	−56.3444	−2.51728
$502$	−12.5481	−0.560049
$503$	−12.5708	−0.560503	−0.280252	−	0.959927i	$-0.590418\pi$
$503$	−12.5708	−0.560503	−0.280252	+	0.959927i	$0.590418\pi$
$504$	43.4560	1.93568
$505$	20.7985	0.925521
$506$	−51.2743	−2.27942
$507$	15.1414	0.672452
$508$	16.0548	0.712318
$509$	−21.7242	−0.962909	−0.481455	−	0.876471i	$-0.659891\pi$
$509$	−21.7242	−0.962909	−0.481455	+	0.876471i	$0.659891\pi$
$510$	−58.8360	−2.60530
$511$	−32.3930	−1.43298
$512$	−12.2424	−0.541045
$513$	51.8480	2.28915
$514$	−25.0561	−1.10518
$515$	30.7634	1.35560
$516$	−11.6890	−0.514581
$517$	−0.221004	−0.00971974
$518$	−10.2883	−0.452042
$519$	−47.0483	−2.06519
$520$	−24.7929	−1.08724
$521$	−22.2898	−0.976534	−0.488267	−	0.872694i	$-0.662371\pi$
$521$	−22.2898	−0.976534	−0.488267	+	0.872694i	$0.662371\pi$
$522$	9.23794	0.404334
$523$	−5.05925	−0.221225	−0.110613	−	0.993864i	$-0.535281\pi$
$523$	−5.05925	−0.221225	−0.110613	+	0.993864i	$0.535281\pi$
$524$	3.44245	0.150384
$525$	21.3092	0.930011
$526$	1.80004	0.0784856
$527$	28.9214	1.25984
$528$	−19.7213	−0.858258
$529$	58.9284	2.56210
$530$	19.1017	0.829726
$531$	−52.7289	−2.28824
$532$	−8.41788	−0.364961
$533$	15.5426	0.673226
$534$	22.4735	0.972523
$535$	43.9347	1.89946
$536$	8.96390	0.387181
$537$	8.82096	0.380653
$538$	−9.27128	−0.399713
$539$	14.9613	0.644427
$540$	−34.5619	−1.48731
$541$	−26.4269	−1.13618	−0.568092	−	0.822965i	$-0.692318\pi$
$541$	−26.4269	−1.13618	−0.568092	+	0.822965i	$0.692318\pi$
$542$	31.9219	1.37116
$543$	53.5076	2.29623
$544$	−31.3020	−1.34206
$545$	23.3977	1.00225
$546$	−19.0394	−0.814813
$547$	27.6389	1.18175	0.590877	−	0.806761i	$-0.298782\pi$
$547$	27.6389	1.18175	0.590877	+	0.806761i	$0.298782\pi$
$548$	3.27926	0.140083
$549$	58.1138	2.48024
$550$	−18.4265	−0.785707
$551$	−5.48111	−0.233503
$552$	86.0097	3.66081
$553$	30.2503	1.28637
$554$	19.8321	0.842587
$555$	44.1623	1.87459
$556$	11.2218	0.475911
$557$	−32.0815	−1.35934	−0.679669	−	0.733519i	$-0.737877\pi$
$557$	−32.0815	−1.35934	−0.679669	+	0.733519i	$0.737877\pi$
$558$	−31.8206	−1.34707
$559$	10.9505	0.463158
$560$	−6.69338	−0.282847
$561$	−112.582	−4.75323
$562$	12.6176	0.532240
$563$	5.72024	0.241079	0.120540	−	0.992709i	$-0.461537\pi$
$563$	5.72024	0.241079	0.120540	+	0.992709i	$0.461537\pi$
$564$	0.121034	0.00509644
$565$	−2.99221	−0.125883
$566$	−9.21030	−0.387138
$567$	−38.0475	−1.59785
$568$	15.2245	0.638805
$569$	44.1954	1.85277	0.926383	−	0.376583i	$-0.122901\pi$
$569$	44.1954	1.85277	0.926383	+	0.376583i	$0.122901\pi$
$570$	−38.4084	−1.60875
$571$	18.2289	0.762854	0.381427	−	0.924399i	$-0.375433\pi$
$571$	18.2289	0.762854	0.381427	+	0.924399i	$0.375433\pi$
$572$	−15.4887	−0.647614
$573$	26.9455	1.12566
$574$	11.4530	0.478040
$575$	29.4426	1.22784
$576$	49.9938	2.08308
$577$	−4.82692	−0.200947	−0.100474	−	0.994940i	$-0.532036\pi$
$577$	−4.82692	−0.200947	−0.100474	+	0.994940i	$0.532036\pi$
$578$	24.3253	1.01180
$579$	−17.7391	−0.737212
$580$	3.65372	0.151712
$581$	24.4020	1.01236
$582$	−30.8659	−1.27943
$583$	36.5510	1.51379
$584$	−46.9865	−1.94432
$585$	57.0524	2.35883
$586$	−28.4888	−1.17686
$587$	23.6991	0.978165	0.489083	−	0.872238i	$-0.337332\pi$
$587$	23.6991	0.978165	0.489083	+	0.872238i	$0.337332\pi$
$588$	−8.19360	−0.337898
$589$	18.8800	0.777938
$590$	22.1678	0.912634
$591$	−60.8415	−2.50268
$592$	−5.46748	−0.224712
$593$	−19.6707	−0.807777	−0.403889	−	0.914808i	$-0.632342\pi$
$593$	−19.6707	−0.807777	−0.403889	+	0.914808i	$0.632342\pi$
$594$	70.2974	2.88434
$595$	−38.2103	−1.56647
$596$	12.6168	0.516806
$597$	7.31080	0.299211
$598$	−26.3065	−1.07575
$599$	−11.6864	−0.477495	−0.238748	−	0.971082i	$-0.576737\pi$
$599$	−11.6864	−0.477495	−0.238748	+	0.971082i	$0.576737\pi$
$600$	30.9093	1.26187
$601$	39.6567	1.61763	0.808816	−	0.588062i	$-0.200109\pi$
$601$	39.6567	1.61763	0.808816	+	0.588062i	$0.200109\pi$
$602$	8.06921	0.328876
$603$	−20.6273	−0.840010
$604$	−14.7187	−0.598894
$605$	−57.8560	−2.35218
$606$	23.1675	0.941117
$607$	−23.3900	−0.949373	−0.474686	−	0.880155i	$-0.657438\pi$
$607$	−23.3900	−0.949373	−0.474686	+	0.880155i	$0.657438\pi$
$608$	−20.4341	−0.828711
$609$	8.59412	0.348251
$610$	−24.4317	−0.989210
$611$	−0.113387	−0.00458714
$612$	43.0415	1.73985
$613$	27.2133	1.09914	0.549568	−	0.835449i	$-0.314792\pi$
$613$	27.2133	1.09914	0.549568	+	0.835449i	$0.314792\pi$
$614$	23.3295	0.941502
$615$	−49.1619	−1.98240
$616$	−34.9583	−1.40851
$617$	20.5284	0.826442	0.413221	−	0.910631i	$-0.364404\pi$
$617$	20.5284	0.826442	0.413221	+	0.910631i	$0.364404\pi$
$618$	34.2675	1.37844
$619$	−25.4894	−1.02451	−0.512253	−	0.858835i	$-0.671189\pi$
$619$	−25.4894	−1.02451	−0.512253	+	0.858835i	$0.671189\pi$
$620$	−12.5854	−0.505443
$621$	−112.324	−4.50742
$622$	−5.98924	−0.240147
$623$	14.5951	0.584742
$624$	−10.1181	−0.405047
$625$	−30.6833	−1.22733
$626$	21.3942	0.855085
$627$	−73.4941	−2.93507
$628$	−14.1244	−0.563625
$629$	−31.2121	−1.24451
$630$	42.0407	1.67494
$631$	−26.8763	−1.06993	−0.534963	−	0.844875i	$-0.679675\pi$
$631$	−26.8763	−1.06993	−0.534963	+	0.844875i	$0.679675\pi$
$632$	43.8785	1.74539
$633$	−20.0745	−0.797889
$634$	21.4879	0.853395
$635$	47.5736	1.88790
$636$	−20.0173	−0.793739
$637$	7.67593	0.304132
$638$	−7.43149	−0.294216
$639$	−35.0339	−1.38592
$640$	7.08229	0.279952
$641$	21.8470	0.862905	0.431452	−	0.902136i	$-0.358001\pi$
$641$	21.8470	0.862905	0.431452	+	0.902136i	$0.358001\pi$
$642$	48.9390	1.93147
$643$	12.2305	0.482323	0.241161	−	0.970485i	$-0.422472\pi$
$643$	12.2305	0.482323	0.241161	+	0.970485i	$0.422472\pi$
$644$	18.2366	0.718623
$645$	−34.6369	−1.36383
$646$	27.1454	1.06802
$647$	−4.17312	−0.164062	−0.0820310	−	0.996630i	$-0.526141\pi$
$647$	−4.17312	−0.164062	−0.0820310	+	0.996630i	$0.526141\pi$
$648$	−55.1885	−2.16801
$649$	42.4179	1.66505
$650$	−9.45377	−0.370807
$651$	−29.6030	−1.16023
$652$	−12.8185	−0.502011
$653$	−31.3638	−1.22736	−0.613680	−	0.789555i	$-0.710311\pi$
$653$	−31.3638	−1.22736	−0.613680	+	0.789555i	$0.710311\pi$
$654$	26.0628	1.01913
$655$	10.2007	0.398573
$656$	6.08645	0.237636
$657$	108.123	4.21829
$658$	−0.0835523	−0.00325721
$659$	−13.2588	−0.516489	−0.258244	−	0.966080i	$-0.583144\pi$
$659$	−13.2588	−0.516489	−0.258244	+	0.966080i	$0.583144\pi$
$660$	48.9912	1.90698
$661$	3.66170	0.142424	0.0712118	−	0.997461i	$-0.477313\pi$
$661$	3.66170	0.142424	0.0712118	+	0.997461i	$0.477313\pi$
$662$	−0.269441	−0.0104721
$663$	−57.7608	−2.24324
$664$	35.3954	1.37361
$665$	−24.9438	−0.967281
$666$	34.3409	1.33068
$667$	11.8744	0.459777
$668$	−17.3288	−0.670473
$669$	5.14881	0.199064
$670$	8.67196	0.335027
$671$	−46.7498	−1.80476
$672$	32.0396	1.23596
$673$	−18.4025	−0.709365	−0.354683	−	0.934987i	$-0.615411\pi$
$673$	−18.4025	−0.709365	−0.354683	+	0.934987i	$0.615411\pi$
$674$	5.32732	0.205201
$675$	−40.3660	−1.55369
$676$	4.65676	0.179106
$677$	−24.0105	−0.922800	−0.461400	−	0.887192i	$-0.652653\pi$
$677$	−24.0105	−0.922800	−0.461400	+	0.887192i	$0.652653\pi$
$678$	−3.33304	−0.128005
$679$	−20.0455	−0.769275
$680$	−55.4246	−2.12544
$681$	61.8934	2.37176
$682$	25.5982	0.980206
$683$	−21.5362	−0.824060	−0.412030	−	0.911170i	$-0.635180\pi$
$683$	−21.5362	−0.824060	−0.412030	+	0.911170i	$0.635180\pi$
$684$	28.0977	1.07434
$685$	9.71710	0.371271
$686$	20.4239	0.779788
$687$	−48.0246	−1.83225
$688$	4.28820	0.163486
$689$	18.7526	0.714419
$690$	83.2084	3.16769
$691$	48.7727	1.85540	0.927701	−	0.373325i	$-0.121782\pi$
$691$	48.7727	1.85540	0.927701	+	0.373325i	$0.121782\pi$
$692$	−14.4698	−0.550059
$693$	80.4445	3.05583
$694$	−10.3204	−0.391757
$695$	33.2524	1.26134
$696$	12.4659	0.472518
$697$	34.7456	1.31608
$698$	23.1775	0.877281
$699$	27.6808	1.04698
$700$	6.55370	0.247707
$701$	4.00494	0.151265	0.0756323	−	0.997136i	$-0.475902\pi$
$701$	4.00494	0.151265	0.0756323	+	0.997136i	$0.475902\pi$
$702$	36.0664	1.36124
$703$	−20.3753	−0.768471
$704$	−40.2177	−1.51576
$705$	0.358647	0.0135074
$706$	−3.52696	−0.132739
$707$	15.0459	0.565858
$708$	−23.2304	−0.873051
$709$	−12.6878	−0.476501	−0.238250	−	0.971204i	$-0.576574\pi$
$709$	−12.6878	−0.476501	−0.238250	+	0.971204i	$0.576574\pi$
$710$	14.7286	0.552756
$711$	−100.971	−3.78672
$712$	21.1704	0.793396
$713$	−40.9020	−1.53179
$714$	−42.5627	−1.59287
$715$	−45.8960	−1.71641
$716$	2.71291	0.101386
$717$	−62.3578	−2.32880
$718$	−6.04567	−0.225622
$719$	13.7523	0.512874	0.256437	−	0.966561i	$-0.417451\pi$
$719$	13.7523	0.512874	0.256437	+	0.966561i	$0.417451\pi$
$720$	22.3415	0.832620
$721$	22.2546	0.828805
$722$	−1.56711	−0.0583220
$723$	86.9548	3.23388
$724$	16.4564	0.611597
$725$	4.26729	0.158483
$726$	−64.4460	−2.39182
$727$	41.4959	1.53900	0.769499	−	0.638648i	$-0.220506\pi$
$727$	41.4959	1.53900	0.769499	+	0.638648i	$0.220506\pi$
$728$	−17.9355	−0.664734
$729$	9.64287	0.357143
$730$	−45.4562	−1.68241
$731$	24.4799	0.905422
$732$	25.6028	0.946306
$733$	1.68503	0.0622382	0.0311191	−	0.999516i	$-0.490093\pi$
$733$	1.68503	0.0622382	0.0311191	+	0.999516i	$0.490093\pi$
$734$	−2.43264	−0.0897902
$735$	−24.2793	−0.895554
$736$	44.2687	1.63176
$737$	16.5937	0.611238
$738$	−38.2286	−1.40721
$739$	−23.1960	−0.853279	−0.426639	−	0.904422i	$-0.640303\pi$
$739$	−23.1960	−0.853279	−0.426639	+	0.904422i	$0.640303\pi$
$740$	13.5822	0.499293
$741$	−37.7064	−1.38518
$742$	13.8184	0.507290
$743$	−6.44294	−0.236369	−0.118184	−	0.992992i	$-0.537707\pi$
$743$	−6.44294	−0.236369	−0.118184	+	0.992992i	$0.537707\pi$
$744$	−42.9395	−1.57424
$745$	37.3862	1.36972
$746$	−22.1666	−0.811579
$747$	−81.4503	−2.98011
$748$	−34.6249	−1.26601
$749$	31.7828	1.16132
$750$	−16.0616	−0.586487
$751$	0.673139	0.0245632	0.0122816	−	0.999925i	$-0.496091\pi$
$751$	0.673139	0.0245632	0.0122816	+	0.999925i	$0.496091\pi$
$752$	−0.0444020	−0.00161917
$753$	38.9648	1.41996
$754$	−3.81276	−0.138852
$755$	−43.6143	−1.58729
$756$	−25.0025	−0.909332
$757$	−5.51029	−0.200275	−0.100138	−	0.994974i	$-0.531928\pi$
$757$	−5.51029	−0.200275	−0.100138	+	0.994974i	$0.531928\pi$
$758$	−25.7235	−0.934318
$759$	159.219	5.77927
$760$	−36.1814	−1.31244
$761$	48.0700	1.74254	0.871269	−	0.490807i	$-0.163298\pi$
$761$	48.0700	1.74254	0.871269	+	0.490807i	$0.163298\pi$
$762$	52.9925	1.91972
$763$	16.9261	0.612768
$764$	8.28714	0.299818
$765$	127.541	4.61124
$766$	−0.425094	−0.0153593
$767$	21.7627	0.785805
$768$	53.3264	1.92425
$769$	−27.9428	−1.00764	−0.503822	−	0.863808i	$-0.668073\pi$
$769$	−27.9428	−1.00764	−0.503822	+	0.863808i	$0.668073\pi$
$770$	−33.8198	−1.21878
$771$	77.8049	2.80208
$772$	−5.45570	−0.196355
$773$	40.9837	1.47408	0.737041	−	0.675849i	$-0.236223\pi$
$773$	40.9837	1.47408	0.737041	+	0.675849i	$0.236223\pi$
$774$	−26.9339	−0.968118
$775$	−14.6989	−0.528002
$776$	−29.0763	−1.04378
$777$	31.9476	1.14611
$778$	−10.0417	−0.360013
$779$	22.6820	0.812668
$780$	25.1351	0.899983
$781$	28.1831	1.00847
$782$	−58.8082	−2.10298
$783$	−16.2798	−0.581793
$784$	3.00587	0.107353
$785$	−41.8534	−1.49381
$786$	11.3626	0.405290
$787$	−12.5399	−0.446999	−0.223500	−	0.974704i	$-0.571748\pi$
$787$	−12.5399	−0.446999	−0.223500	+	0.974704i	$0.571748\pi$
$788$	−18.7119	−0.666585
$789$	−5.58955	−0.198993
$790$	42.4494	1.51028
$791$	−2.16460	−0.0769644
$792$	116.686	4.14625
$793$	−23.9852	−0.851739
$794$	15.3707	0.545485
$795$	−59.3153	−2.10370
$796$	2.24845	0.0796943
$797$	12.6498	0.448081	0.224040	−	0.974580i	$-0.428075\pi$
$797$	12.6498	0.448081	0.224040	+	0.974580i	$0.428075\pi$
$798$	−27.7851	−0.983580
$799$	−0.253476	−0.00896735
$800$	15.9088	0.562462
$801$	−48.7165	−1.72131
$802$	−19.3481	−0.683205
$803$	−86.9801	−3.06946
$804$	−9.08763	−0.320496
$805$	54.0387	1.90461
$806$	13.1333	0.462600
$807$	28.7895	1.01344
$808$	21.8242	0.767774
$809$	−40.8367	−1.43574	−0.717871	−	0.696177i	$-0.754883\pi$
$809$	−40.8367	−1.43574	−0.717871	+	0.696177i	$0.754883\pi$
$810$	−53.3911	−1.87597
$811$	29.0788	1.02109	0.510547	−	0.859850i	$-0.329443\pi$
$811$	29.0788	1.02109	0.510547	+	0.859850i	$0.329443\pi$
$812$	2.64314	0.0927561
$813$	−99.1250	−3.47647
$814$	−27.6256	−0.968278
$815$	−37.9837	−1.33051
$816$	−22.6189	−0.791821
$817$	15.9806	0.559090
$818$	−32.4202	−1.13354
$819$	41.2724	1.44217
$820$	−15.1199	−0.528008
$821$	35.2648	1.23075	0.615374	−	0.788235i	$-0.289005\pi$
$821$	35.2648	1.23075	0.615374	+	0.788235i	$0.289005\pi$
$822$	10.8239	0.377528
$823$	35.8997	1.25138	0.625692	−	0.780070i	$-0.284817\pi$
$823$	35.8997	1.25138	0.625692	+	0.780070i	$0.284817\pi$
$824$	32.2806	1.12455
$825$	57.2185	1.99209
$826$	16.0364	0.557979
$827$	−9.83029	−0.341833	−0.170916	−	0.985286i	$-0.554673\pi$
$827$	−9.83029	−0.341833	−0.170916	+	0.985286i	$0.554673\pi$
$828$	−60.8712	−2.11542
$829$	−49.8088	−1.72993	−0.864966	−	0.501830i	$-0.832660\pi$
$829$	−49.8088	−1.72993	−0.864966	+	0.501830i	$0.832660\pi$
$830$	34.2426	1.18858
$831$	−61.5834	−2.13630
$832$	−20.6339	−0.715350
$833$	17.1595	0.594543
$834$	37.0401	1.28259
$835$	−51.3488	−1.77700
$836$	−22.6033	−0.781751
$837$	56.0768	1.93830
$838$	−16.0906	−0.555839
$839$	−29.1266	−1.00556	−0.502781	−	0.864414i	$-0.667690\pi$
$839$	−29.1266	−1.00556	−0.502781	+	0.864414i	$0.667690\pi$
$840$	56.7306	1.95739
$841$	−27.2790	−0.940654
$842$	2.92952	0.100958
$843$	−39.1805	−1.34945
$844$	−6.17395	−0.212516
$845$	13.7989	0.474697
$846$	0.278886	0.00958829
$847$	−41.8537	−1.43811
$848$	7.34348	0.252176
$849$	28.6001	0.981554
$850$	−21.1339	−0.724887
$851$	44.1415	1.51315
$852$	−15.4346	−0.528781
$853$	16.4719	0.563987	0.281993	−	0.959416i	$-0.409004\pi$
$853$	16.4719	0.563987	0.281993	+	0.959416i	$0.409004\pi$
$854$	−17.6742	−0.604798
$855$	83.2590	2.84740
$856$	46.1014	1.57572
$857$	−23.6855	−0.809080	−0.404540	−	0.914520i	$-0.632568\pi$
$857$	−23.6855	−0.809080	−0.404540	+	0.914520i	$0.632568\pi$
$858$	−51.1238	−1.74534
$859$	14.6827	0.500967	0.250483	−	0.968121i	$-0.419410\pi$
$859$	14.6827	0.500967	0.250483	+	0.968121i	$0.419410\pi$
$860$	−10.6527	−0.363253
$861$	−35.5643	−1.21203
$862$	21.7072	0.739350
$863$	−48.5866	−1.65391	−0.826953	−	0.562270i	$-0.809928\pi$
$863$	−48.5866	−1.65391	−0.826953	+	0.562270i	$0.809928\pi$
$864$	−60.6926	−2.06480
$865$	−42.8769	−1.45786
$866$	−2.83031	−0.0961778
$867$	−75.5358	−2.56533
$868$	−9.10446	−0.309025
$869$	81.2266	2.75543
$870$	12.0599	0.408869
$871$	8.51347	0.288468
$872$	24.5516	0.831422
$873$	66.9090	2.26453
$874$	−38.3902	−1.29857
$875$	−10.4310	−0.352633
$876$	47.6351	1.60944
$877$	−3.56546	−0.120397	−0.0601985	−	0.998186i	$-0.519173\pi$
$877$	−3.56546	−0.120397	−0.0601985	+	0.998186i	$0.519173\pi$
$878$	8.12145	0.274086
$879$	88.4643	2.98383
$880$	−17.9727	−0.605861
$881$	−13.0566	−0.439888	−0.219944	−	0.975512i	$-0.570587\pi$
$881$	−13.0566	−0.439888	−0.219944	+	0.975512i	$0.570587\pi$
$882$	−18.8797	−0.635712
$883$	−47.0441	−1.58316	−0.791580	−	0.611065i	$-0.790741\pi$
$883$	−47.0441	−1.58316	−0.791580	+	0.611065i	$0.790741\pi$
$884$	−17.7645	−0.597483
$885$	−68.8362	−2.31390
$886$	−38.0531	−1.27842
$887$	−29.0903	−0.976758	−0.488379	−	0.872632i	$-0.662412\pi$
$887$	−29.0903	−0.976758	−0.488379	+	0.872632i	$0.662412\pi$
$888$	46.3404	1.55508
$889$	34.4153	1.15425
$890$	20.4809	0.686523
$891$	−102.163	−3.42260
$892$	1.58353	0.0530204
$893$	−0.165470	−0.00553725
$894$	41.6447	1.39281
$895$	8.03888	0.268710
$896$	5.12341	0.171161
$897$	81.6878	2.72748
$898$	3.83250	0.127892
$899$	−5.92816	−0.197715
$900$	−21.8753	−0.729177
$901$	41.9215	1.39661
$902$	30.7531	1.02397
$903$	−25.0568	−0.833837
$904$	−3.13979	−0.104428
$905$	48.7635	1.62095
$906$	−48.5822	−1.61404
$907$	45.7097	1.51777	0.758883	−	0.651226i	$-0.225745\pi$
$907$	45.7097	1.51777	0.758883	+	0.651226i	$0.225745\pi$
$908$	19.0354	0.631713
$909$	−50.2210	−1.66573
$910$	−17.3514	−0.575192
$911$	−26.3798	−0.874001	−0.437001	−	0.899461i	$-0.643959\pi$
$911$	−26.3798	−0.874001	−0.437001	+	0.899461i	$0.643959\pi$
$912$	−14.7657	−0.488942
$913$	65.5230	2.16849
$914$	−15.5753	−0.515186
$915$	75.8661	2.50805
$916$	−14.7701	−0.488017
$917$	7.37929	0.243685
$918$	80.6263	2.66107
$919$	37.1370	1.22504	0.612518	−	0.790457i	$-0.290157\pi$
$919$	37.1370	1.22504	0.612518	+	0.790457i	$0.290157\pi$
$920$	78.3839	2.58424
$921$	−72.4435	−2.38709
$922$	−4.11739	−0.135599
$923$	14.4595	0.475939
$924$	35.4408	1.16592
$925$	15.8631	0.521576
$926$	−21.9724	−0.722059
$927$	−74.2827	−2.43976
$928$	6.41612	0.210619
$929$	−51.4145	−1.68685	−0.843427	−	0.537244i	$-0.819465\pi$
$929$	−51.4145	−1.68685	−0.843427	+	0.537244i	$0.819465\pi$
$930$	−41.5410	−1.36218
$931$	11.2018	0.367125
$932$	8.51328	0.278862
$933$	18.5980	0.608871
$934$	12.4335	0.406838
$935$	−102.600	−3.35539
$936$	59.8661	1.95679
$937$	−38.9446	−1.27226	−0.636132	−	0.771580i	$-0.719467\pi$
$937$	−38.9446	−1.27226	−0.636132	+	0.771580i	$0.719467\pi$
$938$	6.27339	0.204834
$939$	−66.4340	−2.16799
$940$	0.110303	0.00359768
$941$	−4.88470	−0.159237	−0.0796183	−	0.996825i	$-0.525370\pi$
$941$	−4.88470	−0.159237	−0.0796183	+	0.996825i	$0.525370\pi$
$942$	−46.6207	−1.51898
$943$	−49.1387	−1.60018
$944$	8.52220	0.277374
$945$	−74.0874	−2.41006
$946$	21.6670	0.704456
$947$	−50.1548	−1.62981	−0.814906	−	0.579593i	$-0.803211\pi$
$947$	−50.1548	−1.62981	−0.814906	+	0.579593i	$0.803211\pi$
$948$	−44.4841	−1.44478
$949$	−44.6255	−1.44860
$950$	−13.7963	−0.447611
$951$	−66.7251	−2.16371
$952$	−40.0948	−1.29948
$953$	46.9191	1.51986	0.759929	−	0.650006i	$-0.225234\pi$
$953$	46.9191	1.51986	0.759929	+	0.650006i	$0.225234\pi$
$954$	−46.1239	−1.49332
$955$	24.5564	0.794628
$956$	−19.1783	−0.620270
$957$	23.0765	0.745958
$958$	−3.13308	−0.101225
$959$	7.02946	0.226993
$960$	65.2657	2.10644
$961$	−10.5801	−0.341293
$962$	−14.1734	−0.456970
$963$	−106.087	−3.41859
$964$	26.7431	0.861339
$965$	−16.1663	−0.520413
$966$	60.1940	1.93671
$967$	36.4391	1.17180	0.585900	−	0.810383i	$-0.300741\pi$
$967$	36.4391	1.17180	0.585900	+	0.810383i	$0.300741\pi$
$968$	−60.7093	−1.95127
$969$	−84.2928	−2.70787
$970$	−28.1293	−0.903177
$971$	−3.87617	−0.124392	−0.0621961	−	0.998064i	$-0.519810\pi$
$971$	−3.87617	−0.124392	−0.0621961	+	0.998064i	$0.519810\pi$
$972$	19.8576	0.636934
$973$	24.0552	0.771175
$974$	−26.0388	−0.834336
$975$	29.3562	0.940150
$976$	−9.39253	−0.300648
$977$	9.93270	0.317775	0.158888	−	0.987297i	$-0.449209\pi$
$977$	9.93270	0.317775	0.158888	+	0.987297i	$0.449209\pi$
$978$	−42.3103	−1.35293
$979$	39.1901	1.25252
$980$	−7.46714	−0.238529
$981$	−56.4971	−1.80381
$982$	6.06538	0.193554
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−51.5865	−1.64452
$985$	−55.4471	−1.76669
$986$	−8.52342	−0.271441
$987$	0.259449	0.00825837
$988$	−11.5967	−0.368940
$989$	−34.6206	−1.10087
$990$	112.886	3.58774
$991$	−35.8697	−1.13944	−0.569720	−	0.821839i	$-0.692948\pi$
$991$	−35.8697	−1.13944	−0.569720	+	0.821839i	$0.692948\pi$
$992$	−22.1007	−0.701698
$993$	0.836677	0.0265511
$994$	10.6549	0.337952
$995$	6.66261	0.211219
$996$	−35.8840	−1.13703
$997$	14.4216	0.456738	0.228369	−	0.973575i	$-0.426661\pi$
$997$	14.4216	0.456738	0.228369	+	0.973575i	$0.426661\pi$
$998$	3.60994	0.114271
$999$	−60.5182	−1.91471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.33	✓	54
3.2	odd	2		8847.2.a.g.1.22		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.33	✓	54	1.1	even	1	trivial
8847.2.a.g.1.22		54	3.2	odd	2

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q+1.01514 q^{2} -3.15226 q^{3} -0.969484 q^{4} -2.87277 q^{5} -3.19999 q^{6} -2.07820 q^{7} -3.01445 q^{8} +6.93672 q^{9} +O(q^{10})\)	\(q+1.01514 q^{2} -3.15226 q^{3} -0.969484 q^{4} -2.87277 q^{5} -3.19999 q^{6} -2.07820 q^{7} -3.01445 q^{8} +6.93672 q^{9} -2.91628 q^{10} -5.58027 q^{11} +3.05606 q^{12} -2.86298 q^{13} -2.10967 q^{14} +9.05571 q^{15} -1.12113 q^{16} -6.40019 q^{17} +7.04177 q^{18} -4.17807 q^{19} +2.78510 q^{20} +6.55101 q^{21} -5.66478 q^{22} +9.05143 q^{23} +9.50233 q^{24} +3.25282 q^{25} -2.90634 q^{26} -12.4096 q^{27} +2.01478 q^{28} +1.31188 q^{29} +9.19285 q^{30} -4.51884 q^{31} +4.89079 q^{32} +17.5904 q^{33} -6.49711 q^{34} +5.97018 q^{35} -6.72504 q^{36} +4.87674 q^{37} -4.24134 q^{38} +9.02485 q^{39} +8.65983 q^{40} -5.42883 q^{41} +6.65021 q^{42} -3.82487 q^{43} +5.40998 q^{44} -19.9276 q^{45} +9.18850 q^{46} +0.0396045 q^{47} +3.53410 q^{48} -2.68110 q^{49} +3.30207 q^{50} +20.1750 q^{51} +2.77561 q^{52} -6.55004 q^{53} -12.5975 q^{54} +16.0308 q^{55} +6.26462 q^{56} +13.1703 q^{57} +1.33174 q^{58} -7.60141 q^{59} -8.77937 q^{60} +8.37770 q^{61} -4.58727 q^{62} -14.4159 q^{63} +7.20712 q^{64} +8.22469 q^{65} +17.8568 q^{66} -2.97364 q^{67} +6.20488 q^{68} -28.5324 q^{69} +6.06059 q^{70} -5.05049 q^{71} -20.9104 q^{72} +15.5871 q^{73} +4.95059 q^{74} -10.2537 q^{75} +4.05057 q^{76} +11.5969 q^{77} +9.16152 q^{78} -14.5560 q^{79} +3.22076 q^{80} +18.3080 q^{81} -5.51104 q^{82} -11.7419 q^{83} -6.35110 q^{84} +18.3863 q^{85} -3.88279 q^{86} -4.13537 q^{87} +16.8215 q^{88} -7.02298 q^{89} -20.2294 q^{90} +5.94984 q^{91} -8.77521 q^{92} +14.2445 q^{93} +0.0402042 q^{94} +12.0026 q^{95} -15.4170 q^{96} +9.64562 q^{97} -2.72170 q^{98} -38.7088 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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