LMFDB - Embedded newform 983.2.a.b.1.11

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			1.11
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)

$f(q)$	$=$	$q-1.70929 q^{2} -2.85036 q^{3} +0.921666 q^{4} +3.70678 q^{5} +4.87208 q^{6} -1.37276 q^{7} +1.84318 q^{8} +5.12455 q^{9} +O(q^{10})$	\(q-1.70929 q^{2} -2.85036 q^{3} +0.921666 q^{4} +3.70678 q^{5} +4.87208 q^{6} -1.37276 q^{7} +1.84318 q^{8} +5.12455 q^{9} -6.33595 q^{10} +3.92956 q^{11} -2.62708 q^{12} +3.78935 q^{13} +2.34645 q^{14} -10.5656 q^{15} -4.99386 q^{16} +5.66731 q^{17} -8.75933 q^{18} +0.487265 q^{19} +3.41641 q^{20} +3.91287 q^{21} -6.71674 q^{22} +4.17726 q^{23} -5.25374 q^{24} +8.74019 q^{25} -6.47709 q^{26} -6.05572 q^{27} -1.26523 q^{28} -2.50248 q^{29} +18.0597 q^{30} -9.32238 q^{31} +4.84958 q^{32} -11.2006 q^{33} -9.68707 q^{34} -5.08853 q^{35} +4.72312 q^{36} -11.1496 q^{37} -0.832876 q^{38} -10.8010 q^{39} +6.83227 q^{40} -5.91513 q^{41} -6.68822 q^{42} +3.90809 q^{43} +3.62174 q^{44} +18.9956 q^{45} -7.14015 q^{46} +12.2128 q^{47} +14.2343 q^{48} -5.11552 q^{49} -14.9395 q^{50} -16.1539 q^{51} +3.49251 q^{52} +13.4922 q^{53} +10.3510 q^{54} +14.5660 q^{55} -2.53026 q^{56} -1.38888 q^{57} +4.27746 q^{58} -3.83380 q^{59} -9.73799 q^{60} +7.79226 q^{61} +15.9346 q^{62} -7.03479 q^{63} +1.69839 q^{64} +14.0463 q^{65} +19.1451 q^{66} +11.9922 q^{67} +5.22337 q^{68} -11.9067 q^{69} +8.69776 q^{70} -10.0466 q^{71} +9.44548 q^{72} +6.60333 q^{73} +19.0579 q^{74} -24.9127 q^{75} +0.449095 q^{76} -5.39435 q^{77} +18.4620 q^{78} -1.49724 q^{79} -18.5111 q^{80} +1.88734 q^{81} +10.1107 q^{82} -14.3759 q^{83} +3.60636 q^{84} +21.0075 q^{85} -6.68005 q^{86} +7.13297 q^{87} +7.24289 q^{88} +14.3563 q^{89} -32.4689 q^{90} -5.20188 q^{91} +3.85004 q^{92} +26.5721 q^{93} -20.8752 q^{94} +1.80618 q^{95} -13.8231 q^{96} +7.29792 q^{97} +8.74390 q^{98} +20.1372 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.70929	−1.20865	−0.604325	−	0.796738i	$-0.706557\pi$
$2$	−1.70929	−1.20865	−0.604325	+	0.796738i	$0.706557\pi$
$3$	−2.85036	−1.64566	−0.822828	−	0.568291i	$-0.807605\pi$
$3$	−2.85036	−1.64566	−0.822828	+	0.568291i	$0.807605\pi$
$4$	0.921666	0.460833
$5$	3.70678	1.65772	0.828860	−	0.559455i	$-0.188990\pi$
$5$	3.70678	1.65772	0.828860	+	0.559455i	$0.188990\pi$
$6$	4.87208	1.98902
$7$	−1.37276	−0.518856	−0.259428	−	0.965762i	$-0.583534\pi$
$7$	−1.37276	−0.518856	−0.259428	+	0.965762i	$0.583534\pi$
$8$	1.84318	0.651664
$9$	5.12455	1.70818
$10$	−6.33595	−2.00360
$11$	3.92956	1.18481	0.592403	−	0.805642i	$-0.298179\pi$
$11$	3.92956	1.18481	0.592403	+	0.805642i	$0.298179\pi$
$12$	−2.62708	−0.758372
$13$	3.78935	1.05098	0.525488	−	0.850801i	$-0.323883\pi$
$13$	3.78935	1.05098	0.525488	+	0.850801i	$0.323883\pi$
$14$	2.34645	0.627115
$15$	−10.5656	−2.72804
$16$	−4.99386	−1.24847
$17$	5.66731	1.37453	0.687263	−	0.726409i	$-0.258812\pi$
$17$	5.66731	1.37453	0.687263	+	0.726409i	$0.258812\pi$
$18$	−8.75933	−2.06459
$19$	0.487265	0.111786	0.0558931	−	0.998437i	$-0.482199\pi$
$19$	0.487265	0.111786	0.0558931	+	0.998437i	$0.482199\pi$
$20$	3.41641	0.763932
$21$	3.91287	0.853858
$22$	−6.71674	−1.43201
$23$	4.17726	0.871020	0.435510	−	0.900184i	$-0.356568\pi$
$23$	4.17726	0.871020	0.435510	+	0.900184i	$0.356568\pi$
$24$	−5.25374	−1.07241
$25$	8.74019	1.74804
$26$	−6.47709	−1.27026
$27$	−6.05572	−1.16542
$28$	−1.26523	−0.239106
$29$	−2.50248	−0.464699	−0.232349	−	0.972632i	$-0.574641\pi$
$29$	−2.50248	−0.464699	−0.232349	+	0.972632i	$0.574641\pi$
$30$	18.0597	3.29724
$31$	−9.32238	−1.67435	−0.837174	−	0.546937i	$-0.815794\pi$
$31$	−9.32238	−1.67435	−0.837174	+	0.546937i	$0.815794\pi$
$32$	4.84958	0.857293
$33$	−11.2006	−1.94978
$34$	−9.68707	−1.66132
$35$	−5.08853	−0.860118
$36$	4.72312	0.787187
$37$	−11.1496	−1.83298	−0.916491	−	0.400054i	$-0.868991\pi$
$37$	−11.1496	−1.83298	−0.916491	+	0.400054i	$0.868991\pi$
$38$	−0.832876	−0.135110
$39$	−10.8010	−1.72955
$40$	6.83227	1.08028
$41$	−5.91513	−0.923788	−0.461894	−	0.886935i	$-0.652830\pi$
$41$	−5.91513	−0.923788	−0.461894	+	0.886935i	$0.652830\pi$
$42$	−6.68822	−1.03201
$43$	3.90809	0.595978	0.297989	−	0.954569i	$-0.403684\pi$
$43$	3.90809	0.595978	0.297989	+	0.954569i	$0.403684\pi$
$44$	3.62174	0.545997
$45$	18.9956	2.83169
$46$	−7.14015	−1.05276
$47$	12.2128	1.78142	0.890709	−	0.454575i	$-0.150209\pi$
$47$	12.2128	1.78142	0.890709	+	0.454575i	$0.150209\pi$
$48$	14.2343	2.05454
$49$	−5.11552	−0.730789
$50$	−14.9395	−2.11277
$51$	−16.1539	−2.26200
$52$	3.49251	0.484325
$53$	13.4922	1.85329	0.926646	−	0.375935i	$-0.122678\pi$
$53$	13.4922	1.85329	0.926646	+	0.375935i	$0.122678\pi$
$54$	10.3510	1.40859
$55$	14.5660	1.96408
$56$	−2.53026	−0.338120
$57$	−1.38888	−0.183962
$58$	4.27746	0.561658
$59$	−3.83380	−0.499118	−0.249559	−	0.968360i	$-0.580286\pi$
$59$	−3.83380	−0.499118	−0.249559	+	0.968360i	$0.580286\pi$
$60$	−9.73799	−1.25717
$61$	7.79226	0.997697	0.498849	−	0.866689i	$-0.333756\pi$
$61$	7.79226	0.997697	0.498849	+	0.866689i	$0.333756\pi$
$62$	15.9346	2.02370
$63$	−7.03479	−0.886300
$64$	1.69839	0.212299
$65$	14.0463	1.74223
$66$	19.1451	2.35660
$67$	11.9922	1.46508	0.732540	−	0.680724i	$-0.238335\pi$
$67$	11.9922	1.46508	0.732540	+	0.680724i	$0.238335\pi$
$68$	5.22337	0.633427
$69$	−11.9067	−1.43340
$70$	8.69776	1.03958
$71$	−10.0466	−1.19231	−0.596153	−	0.802871i	$-0.703305\pi$
$71$	−10.0466	−1.19231	−0.596153	+	0.802871i	$0.703305\pi$
$72$	9.44548	1.11316
$73$	6.60333	0.772861	0.386431	−	0.922318i	$-0.373708\pi$
$73$	6.60333	0.772861	0.386431	+	0.922318i	$0.373708\pi$
$74$	19.0579	2.21543
$75$	−24.9127	−2.87667
$76$	0.449095	0.0515148
$77$	−5.39435	−0.614743
$78$	18.4620	2.09041
$79$	−1.49724	−0.168453	−0.0842264	−	0.996447i	$-0.526842\pi$
$79$	−1.49724	−0.168453	−0.0842264	+	0.996447i	$0.526842\pi$
$80$	−18.5111	−2.06961
$81$	1.88734	0.209704
$82$	10.1107	1.11654
$83$	−14.3759	−1.57795	−0.788977	−	0.614422i	$-0.789389\pi$
$83$	−14.3759	−1.57795	−0.788977	+	0.614422i	$0.789389\pi$
$84$	3.60636	0.393486
$85$	21.0075	2.27858
$86$	−6.68005	−0.720328
$87$	7.13297	0.764734
$88$	7.24289	0.772095
$89$	14.3563	1.52177	0.760885	−	0.648887i	$-0.224765\pi$
$89$	14.3563	1.52177	0.760885	+	0.648887i	$0.224765\pi$
$90$	−32.4689	−3.42252
$91$	−5.20188	−0.545305
$92$	3.85004	0.401395
$93$	26.5721	2.75540
$94$	−20.8752	−2.15311
$95$	1.80618	0.185310
$96$	−13.8231	−1.41081
$97$	7.29792	0.740991	0.370496	−	0.928834i	$-0.379188\pi$
$97$	7.29792	0.740991	0.370496	+	0.928834i	$0.379188\pi$
$98$	8.74390	0.883267
$99$	20.1372	2.02386
$100$	8.05554	0.805554
$101$	−1.41990	−0.141285	−0.0706426	−	0.997502i	$-0.522505\pi$
$101$	−1.41990	−0.141285	−0.0706426	+	0.997502i	$0.522505\pi$
$102$	27.6116	2.73396
$103$	−15.5571	−1.53289	−0.766445	−	0.642309i	$-0.777976\pi$
$103$	−15.5571	−1.53289	−0.766445	+	0.642309i	$0.777976\pi$
$104$	6.98447	0.684884
$105$	14.5041	1.41546
$106$	−23.0620	−2.23998
$107$	−8.89355	−0.859772	−0.429886	−	0.902883i	$-0.641446\pi$
$107$	−8.89355	−0.859772	−0.429886	+	0.902883i	$0.641446\pi$
$108$	−5.58135	−0.537066
$109$	3.94790	0.378140	0.189070	−	0.981964i	$-0.439453\pi$
$109$	3.94790	0.378140	0.189070	+	0.981964i	$0.439453\pi$
$110$	−24.8975	−2.37388
$111$	31.7804	3.01646
$112$	6.85539	0.647774
$113$	8.53708	0.803100	0.401550	−	0.915837i	$-0.368472\pi$
$113$	8.53708	0.803100	0.401550	+	0.915837i	$0.368472\pi$
$114$	2.37400	0.222345
$115$	15.4842	1.44391
$116$	−2.30645	−0.214149
$117$	19.4187	1.79526
$118$	6.55307	0.603259
$119$	−7.77988	−0.713180
$120$	−19.4744	−1.77776
$121$	4.44140	0.403764
$122$	−13.3192	−1.20587
$123$	16.8602	1.52024
$124$	−8.59211	−0.771595
$125$	13.8641	1.24004
$126$	12.0245	1.07123
$127$	−13.6883	−1.21464	−0.607320	−	0.794457i	$-0.707755\pi$
$127$	−13.6883	−1.21464	−0.607320	+	0.794457i	$0.707755\pi$
$128$	−12.6022	−1.11389
$129$	−11.1395	−0.980775
$130$	−24.0091	−2.10574
$131$	1.32001	0.115330	0.0576648	−	0.998336i	$-0.481635\pi$
$131$	1.32001	0.115330	0.0576648	+	0.998336i	$0.481635\pi$
$132$	−10.3232	−0.898523
$133$	−0.668899	−0.0580009
$134$	−20.4981	−1.77077
$135$	−22.4472	−1.93195
$136$	10.4459	0.895729
$137$	2.17852	0.186124	0.0930619	−	0.995660i	$-0.470335\pi$
$137$	2.17852	0.186124	0.0930619	+	0.995660i	$0.470335\pi$
$138$	20.3520	1.73248
$139$	9.83262	0.833992	0.416996	−	0.908908i	$-0.363083\pi$
$139$	9.83262	0.833992	0.416996	+	0.908908i	$0.363083\pi$
$140$	−4.68992	−0.396371
$141$	−34.8108	−2.93160
$142$	17.1725	1.44108
$143$	14.8905	1.24520
$144$	−25.5913	−2.13261
$145$	−9.27613	−0.770341
$146$	−11.2870	−0.934118
$147$	14.5811	1.20263
$148$	−10.2762	−0.844699
$149$	6.07614	0.497777	0.248888	−	0.968532i	$-0.419935\pi$
$149$	6.07614	0.497777	0.248888	+	0.968532i	$0.419935\pi$
$150$	42.5830	3.47688
$151$	−3.09439	−0.251818	−0.125909	−	0.992042i	$-0.540185\pi$
$151$	−3.09439	−0.251818	−0.125909	+	0.992042i	$0.540185\pi$
$152$	0.898119	0.0728470
$153$	29.0424	2.34794
$154$	9.22050	0.743009
$155$	−34.5560	−2.77560
$156$	−9.95492	−0.797031
$157$	−6.84594	−0.546365	−0.273183	−	0.961962i	$-0.588076\pi$
$157$	−6.84594	−0.546365	−0.273183	+	0.961962i	$0.588076\pi$
$158$	2.55922	0.203600
$159$	−38.4575	−3.04988
$160$	17.9763	1.42115
$161$	−5.73439	−0.451934
$162$	−3.22601	−0.253459
$163$	11.1899	0.876462	0.438231	−	0.898862i	$-0.355605\pi$
$163$	11.1899	0.876462	0.438231	+	0.898862i	$0.355605\pi$
$164$	−5.45177	−0.425712
$165$	−41.5183	−3.23219
$166$	24.5725	1.90719
$167$	−1.79137	−0.138621	−0.0693103	−	0.997595i	$-0.522080\pi$
$167$	−1.79137	−0.138621	−0.0693103	+	0.997595i	$0.522080\pi$
$168$	7.21214	0.556428
$169$	1.35917	0.104552
$170$	−35.9078	−2.75400
$171$	2.49701	0.190951
$172$	3.60195	0.274646
$173$	−14.1982	−1.07947	−0.539735	−	0.841835i	$-0.681475\pi$
$173$	−14.1982	−1.07947	−0.539735	+	0.841835i	$0.681475\pi$
$174$	−12.1923	−0.924295
$175$	−11.9982	−0.906980
$176$	−19.6237	−1.47919
$177$	10.9277	0.821377
$178$	−24.5391	−1.83929
$179$	14.7410	1.10179	0.550896	−	0.834574i	$-0.314286\pi$
$179$	14.7410	1.10179	0.550896	+	0.834574i	$0.314286\pi$
$180$	17.5075	1.30494
$181$	20.3915	1.51569	0.757844	−	0.652436i	$-0.226253\pi$
$181$	20.3915	1.51569	0.757844	+	0.652436i	$0.226253\pi$
$182$	8.89151	0.659083
$183$	−22.2107	−1.64187
$184$	7.69947	0.567612
$185$	−41.3291	−3.03857
$186$	−45.4194	−3.33031
$187$	22.2700	1.62855
$188$	11.2561	0.820936
$189$	8.31307	0.604687
$190$	−3.08728	−0.223975
$191$	−10.9013	−0.788791	−0.394395	−	0.918941i	$-0.629046\pi$
$191$	−10.9013	−0.788791	−0.394395	+	0.918941i	$0.629046\pi$
$192$	−4.84103	−0.349371
$193$	7.37714	0.531018	0.265509	−	0.964108i	$-0.414460\pi$
$193$	7.37714	0.531018	0.265509	+	0.964108i	$0.414460\pi$
$194$	−12.4742	−0.895599
$195$	−40.0369	−2.86710
$196$	−4.71480	−0.336771
$197$	−11.2392	−0.800757	−0.400379	−	0.916350i	$-0.631121\pi$
$197$	−11.2392	−0.800757	−0.400379	+	0.916350i	$0.631121\pi$
$198$	−34.4203	−2.44614
$199$	1.94105	0.137597	0.0687986	−	0.997631i	$-0.478083\pi$
$199$	1.94105	0.137597	0.0687986	+	0.997631i	$0.478083\pi$
$200$	16.1098	1.13913
$201$	−34.1821	−2.41102
$202$	2.42701	0.170764
$203$	3.43531	0.241112
$204$	−14.8885	−1.04240
$205$	−21.9261	−1.53138
$206$	26.5916	1.85273
$207$	21.4066	1.48786
$208$	−18.9235	−1.31211
$209$	1.91473	0.132445
$210$	−24.7917	−1.71079
$211$	19.4120	1.33638	0.668190	−	0.743991i	$-0.267069\pi$
$211$	19.4120	1.33638	0.668190	+	0.743991i	$0.267069\pi$
$212$	12.4353	0.854058
$213$	28.6363	1.96213
$214$	15.2016	1.03916
$215$	14.4864	0.987965
$216$	−11.1618	−0.759465
$217$	12.7974	0.868745
$218$	−6.74809	−0.457038
$219$	−18.8219	−1.27186
$220$	13.4250	0.905111
$221$	21.4754	1.44459
$222$	−54.3218	−3.64584
$223$	−1.36355	−0.0913101	−0.0456551	−	0.998957i	$-0.514538\pi$
$223$	−1.36355	−0.0913101	−0.0456551	+	0.998957i	$0.514538\pi$
$224$	−6.65733	−0.444812
$225$	44.7895	2.98597
$226$	−14.5923	−0.970667
$227$	15.2114	1.00961	0.504807	−	0.863232i	$-0.331564\pi$
$227$	15.2114	1.00961	0.504807	+	0.863232i	$0.331564\pi$
$228$	−1.28008	−0.0847755
$229$	−5.70094	−0.376729	−0.188364	−	0.982099i	$-0.560319\pi$
$229$	−5.70094	−0.376729	−0.188364	+	0.982099i	$0.560319\pi$
$230$	−26.4669	−1.74518
$231$	15.3758	1.01166
$232$	−4.61253	−0.302827
$233$	−17.6797	−1.15823	−0.579117	−	0.815245i	$-0.696602\pi$
$233$	−17.6797	−1.15823	−0.579117	+	0.815245i	$0.696602\pi$
$234$	−33.1922	−2.16984
$235$	45.2701	2.95309
$236$	−3.53348	−0.230010
$237$	4.26767	0.277215
$238$	13.2981	0.861985
$239$	26.4330	1.70981	0.854903	−	0.518788i	$-0.173616\pi$
$239$	26.4330	1.70981	0.854903	+	0.518788i	$0.173616\pi$
$240$	52.7634	3.40586
$241$	1.64901	0.106222	0.0531110	−	0.998589i	$-0.483086\pi$
$241$	1.64901	0.106222	0.0531110	+	0.998589i	$0.483086\pi$
$242$	−7.59164	−0.488009
$243$	12.7876	0.820323
$244$	7.18186	0.459772
$245$	−18.9621	−1.21144
$246$	−28.8190	−1.83743
$247$	1.84642	0.117485
$248$	−17.1829	−1.09111
$249$	40.9763	2.59677
$250$	−23.6977	−1.49877
$251$	−5.47630	−0.345661	−0.172830	−	0.984952i	$-0.555291\pi$
$251$	−5.47630	−0.345661	−0.172830	+	0.984952i	$0.555291\pi$
$252$	−6.48372	−0.408436
$253$	16.4148	1.03199
$254$	23.3972	1.46807
$255$	−59.8788	−3.74976
$256$	18.1440	1.13400
$257$	−22.0860	−1.37769	−0.688843	−	0.724910i	$-0.741881\pi$
$257$	−22.0860	−1.37769	−0.688843	+	0.724910i	$0.741881\pi$
$258$	19.0405	1.18541
$259$	15.3058	0.951054
$260$	12.9460	0.802875
$261$	−12.8241	−0.793790
$262$	−2.25628	−0.139393
$263$	−2.48737	−0.153378	−0.0766888	−	0.997055i	$-0.524435\pi$
$263$	−2.48737	−0.153378	−0.0766888	+	0.997055i	$0.524435\pi$
$264$	−20.6448	−1.27060
$265$	50.0125	3.07224
$266$	1.14334	0.0701028
$267$	−40.9207	−2.50431
$268$	11.0528	0.675157
$269$	16.2105	0.988370	0.494185	−	0.869357i	$-0.335467\pi$
$269$	16.2105	0.988370	0.494185	+	0.869357i	$0.335467\pi$
$270$	38.3687	2.33505
$271$	−16.7399	−1.01688	−0.508439	−	0.861098i	$-0.669777\pi$
$271$	−16.7399	−1.01688	−0.508439	+	0.861098i	$0.669777\pi$
$272$	−28.3018	−1.71605
$273$	14.8272	0.897385
$274$	−3.72372	−0.224958
$275$	34.3451	2.07109
$276$	−10.9740	−0.660557
$277$	−14.4003	−0.865228	−0.432614	−	0.901579i	$-0.642409\pi$
$277$	−14.4003	−0.865228	−0.432614	+	0.901579i	$0.642409\pi$
$278$	−16.8068	−1.00800
$279$	−47.7730	−2.86009
$280$	−9.37909	−0.560508
$281$	−13.1333	−0.783465	−0.391732	−	0.920079i	$-0.628124\pi$
$281$	−13.1333	−0.783465	−0.391732	+	0.920079i	$0.628124\pi$
$282$	59.5017	3.54328
$283$	−4.53693	−0.269692	−0.134846	−	0.990867i	$-0.543054\pi$
$283$	−4.53693	−0.269692	−0.134846	+	0.990867i	$0.543054\pi$
$284$	−9.25956	−0.549454
$285$	−5.14827	−0.304957
$286$	−25.4521	−1.50501
$287$	8.12007	0.479312
$288$	24.8519	1.46441
$289$	15.1184	0.889320
$290$	15.8556	0.931072
$291$	−20.8017	−1.21942
$292$	6.08606	0.356160
$293$	−16.3672	−0.956179	−0.478090	−	0.878311i	$-0.658671\pi$
$293$	−16.3672	−0.956179	−0.478090	+	0.878311i	$0.658671\pi$
$294$	−24.9233	−1.45355
$295$	−14.2110	−0.827399
$296$	−20.5508	−1.19449
$297$	−23.7963	−1.38080
$298$	−10.3859	−0.601637
$299$	15.8291	0.915421
$300$	−22.9612	−1.32566
$301$	−5.36488	−0.309227
$302$	5.28921	0.304360
$303$	4.04722	0.232507
$304$	−2.43333	−0.139561
$305$	28.8842	1.65390
$306$	−49.6419	−2.83784
$307$	21.9829	1.25463	0.627316	−	0.778765i	$-0.284153\pi$
$307$	21.9829	1.25463	0.627316	+	0.778765i	$0.284153\pi$
$308$	−4.97179	−0.283294
$309$	44.3434	2.52261
$310$	59.0661	3.35473
$311$	22.8936	1.29817	0.649087	−	0.760714i	$-0.275151\pi$
$311$	22.8936	1.29817	0.649087	+	0.760714i	$0.275151\pi$
$312$	−19.9082	−1.12708
$313$	−15.1606	−0.856926	−0.428463	−	0.903559i	$-0.640945\pi$
$313$	−15.1606	−0.856926	−0.428463	+	0.903559i	$0.640945\pi$
$314$	11.7017	0.660364
$315$	−26.0764	−1.46924
$316$	−1.37996	−0.0776286
$317$	9.44499	0.530483	0.265242	−	0.964182i	$-0.414548\pi$
$317$	9.44499	0.530483	0.265242	+	0.964182i	$0.414548\pi$
$318$	65.7350	3.68624
$319$	−9.83363	−0.550578
$320$	6.29556	0.351932
$321$	25.3498	1.41489
$322$	9.80173	0.546229
$323$	2.76148	0.153653
$324$	1.73950	0.0966386
$325$	33.1197	1.83715
$326$	−19.1268	−1.05934
$327$	−11.2529	−0.622288
$328$	−10.9027	−0.601999
$329$	−16.7653	−0.924299
$330$	70.9667	3.90659
$331$	−13.2835	−0.730125	−0.365062	−	0.930983i	$-0.618952\pi$
$331$	−13.2835	−0.730125	−0.365062	+	0.930983i	$0.618952\pi$
$332$	−13.2497	−0.727173
$333$	−57.1366	−3.13107
$334$	3.06197	0.167544
$335$	44.4524	2.42869
$336$	−19.5403	−1.06601
$337$	32.9629	1.79560	0.897801	−	0.440401i	$-0.145164\pi$
$337$	32.9629	1.79560	0.897801	+	0.440401i	$0.145164\pi$
$338$	−2.32322	−0.126366
$339$	−24.3337	−1.32163
$340$	19.3619	1.05004
$341$	−36.6328	−1.98378
$342$	−4.26811	−0.230793
$343$	16.6317	0.898030
$344$	7.20333	0.388377
$345$	−44.1355	−2.37617
$346$	24.2688	1.30470
$347$	23.4187	1.25718	0.628592	−	0.777735i	$-0.283632\pi$
$347$	23.4187	1.25718	0.628592	+	0.777735i	$0.283632\pi$
$348$	6.57421	0.352415
$349$	−20.5932	−1.10233	−0.551165	−	0.834396i	$-0.685817\pi$
$349$	−20.5932	−1.10233	−0.551165	+	0.834396i	$0.685817\pi$
$350$	20.5084	1.09622
$351$	−22.9472	−1.22483
$352$	19.0567	1.01573
$353$	29.6694	1.57914	0.789571	−	0.613660i	$-0.210303\pi$
$353$	29.6694	1.57914	0.789571	+	0.613660i	$0.210303\pi$
$354$	−18.6786	−0.992756
$355$	−37.2403	−1.97651
$356$	13.2318	0.701281
$357$	22.1755	1.17365
$358$	−25.1965	−1.33168
$359$	−2.12059	−0.111920	−0.0559602	−	0.998433i	$-0.517822\pi$
$359$	−2.12059	−0.111920	−0.0559602	+	0.998433i	$0.517822\pi$
$360$	35.0123	1.84531
$361$	−18.7626	−0.987504
$362$	−34.8549	−1.83194
$363$	−12.6596	−0.664456
$364$	−4.79439	−0.251295
$365$	24.4771	1.28119
$366$	37.9646	1.98444
$367$	8.86718	0.462863	0.231431	−	0.972851i	$-0.425659\pi$
$367$	8.86718	0.462863	0.231431	+	0.972851i	$0.425659\pi$
$368$	−20.8607	−1.08744
$369$	−30.3123	−1.57800
$370$	70.6433	3.67257
$371$	−18.5216	−0.961591
$372$	24.4906	1.26978
$373$	−13.7651	−0.712732	−0.356366	−	0.934346i	$-0.615984\pi$
$373$	−13.7651	−0.712732	−0.356366	+	0.934346i	$0.615984\pi$
$374$	−38.0659	−1.96834
$375$	−39.5176	−2.04068
$376$	22.5104	1.16089
$377$	−9.48277	−0.488388
$378$	−14.2094	−0.730854
$379$	14.0160	0.719951	0.359976	−	0.932962i	$-0.382785\pi$
$379$	14.0160	0.719951	0.359976	+	0.932962i	$0.382785\pi$
$380$	1.66470	0.0853971
$381$	39.0166	1.99888
$382$	18.6335	0.953371
$383$	9.39766	0.480198	0.240099	−	0.970748i	$-0.422820\pi$
$383$	9.39766	0.480198	0.240099	+	0.970748i	$0.422820\pi$
$384$	35.9208	1.83308
$385$	−19.9956	−1.01907
$386$	−12.6096	−0.641814
$387$	20.0272	1.01804
$388$	6.72624	0.341473
$389$	−17.6426	−0.894514	−0.447257	−	0.894406i	$-0.647599\pi$
$389$	−17.6426	−0.894514	−0.447257	+	0.894406i	$0.647599\pi$
$390$	68.4346	3.46532
$391$	23.6739	1.19724
$392$	−9.42885	−0.476229
$393$	−3.76250	−0.189793
$394$	19.2110	0.967834
$395$	−5.54994	−0.279248
$396$	18.5598	0.932663
$397$	0.987848	0.0495787	0.0247893	−	0.999693i	$-0.492108\pi$
$397$	0.987848	0.0495787	0.0247893	+	0.999693i	$0.492108\pi$
$398$	−3.31781	−0.166307
$399$	1.90660	0.0954495
$400$	−43.6473	−2.18237
$401$	2.48597	0.124143	0.0620717	−	0.998072i	$-0.480229\pi$
$401$	2.48597	0.124143	0.0620717	+	0.998072i	$0.480229\pi$
$402$	58.4270	2.91407
$403$	−35.3257	−1.75970
$404$	−1.30867	−0.0651088
$405$	6.99594	0.347631
$406$	−5.87194	−0.291419
$407$	−43.8130	−2.17173
$408$	−29.7746	−1.47406
$409$	11.5467	0.570948	0.285474	−	0.958386i	$-0.407849\pi$
$409$	11.5467	0.570948	0.285474	+	0.958386i	$0.407849\pi$
$410$	37.4779	1.85090
$411$	−6.20957	−0.306296
$412$	−14.3385	−0.706406
$413$	5.26290	0.258970
$414$	−36.5900	−1.79830
$415$	−53.2881	−2.61581
$416$	18.3768	0.900995
$417$	−28.0265	−1.37246
$418$	−3.27283	−0.160079
$419$	−1.54476	−0.0754665	−0.0377333	−	0.999288i	$-0.512014\pi$
$419$	−1.54476	−0.0754665	−0.0377333	+	0.999288i	$0.512014\pi$
$420$	13.3680	0.652290
$421$	−30.0535	−1.46472	−0.732360	−	0.680918i	$-0.761581\pi$
$421$	−30.0535	−1.46472	−0.732360	+	0.680918i	$0.761581\pi$
$422$	−33.1808	−1.61521
$423$	62.5850	3.04299
$424$	24.8686	1.20772
$425$	49.5334	2.40272
$426$	−48.9476	−2.37152
$427$	−10.6969	−0.517661
$428$	−8.19688	−0.396211
$429$	−42.4432	−2.04917
$430$	−24.7615	−1.19410
$431$	11.1976	0.539368	0.269684	−	0.962949i	$-0.413081\pi$
$431$	11.1976	0.539368	0.269684	+	0.962949i	$0.413081\pi$
$432$	30.2414	1.45499
$433$	1.44474	0.0694297	0.0347149	−	0.999397i	$-0.488948\pi$
$433$	1.44474	0.0694297	0.0347149	+	0.999397i	$0.488948\pi$
$434$	−21.8745	−1.05001
$435$	26.4403	1.26772
$436$	3.63864	0.174259
$437$	2.03543	0.0973680
$438$	32.1720	1.53724
$439$	7.16954	0.342183	0.171092	−	0.985255i	$-0.445271\pi$
$439$	7.16954	0.342183	0.171092	+	0.985255i	$0.445271\pi$
$440$	26.8478	1.27992
$441$	−26.2147	−1.24832
$442$	−36.7077	−1.74601
$443$	−28.6728	−1.36229	−0.681144	−	0.732149i	$-0.738517\pi$
$443$	−28.6728	−1.36229	−0.681144	+	0.732149i	$0.738517\pi$
$444$	29.2909	1.39008
$445$	53.2158	2.52267
$446$	2.33070	0.110362
$447$	−17.3192	−0.819169
$448$	−2.33149	−0.110153
$449$	37.8371	1.78564	0.892822	−	0.450410i	$-0.148722\pi$
$449$	37.8371	1.78564	0.892822	+	0.450410i	$0.148722\pi$
$450$	−76.5582	−3.60899
$451$	−23.2438	−1.09451
$452$	7.86833	0.370095
$453$	8.82014	0.414406
$454$	−26.0006	−1.22027
$455$	−19.2822	−0.903964
$456$	−2.55996	−0.119881
$457$	3.12581	0.146219	0.0731097	−	0.997324i	$-0.476708\pi$
$457$	3.12581	0.146219	0.0731097	+	0.997324i	$0.476708\pi$
$458$	9.74454	0.455333
$459$	−34.3197	−1.60191
$460$	14.2712	0.665400
$461$	−42.3885	−1.97423	−0.987115	−	0.160015i	$-0.948846\pi$
$461$	−42.3885	−1.97423	−0.987115	+	0.160015i	$0.948846\pi$
$462$	−26.2817	−1.22274
$463$	11.3494	0.527450	0.263725	−	0.964598i	$-0.415049\pi$
$463$	11.3494	0.527450	0.263725	+	0.964598i	$0.415049\pi$
$464$	12.4970	0.580161
$465$	98.4969	4.56768
$466$	30.2196	1.39990
$467$	23.2648	1.07657	0.538283	−	0.842764i	$-0.319073\pi$
$467$	23.2648	1.07657	0.538283	+	0.842764i	$0.319073\pi$
$468$	17.8976	0.827315
$469$	−16.4624	−0.760165
$470$	−77.3796	−3.56925
$471$	19.5134	0.899129
$472$	−7.06640	−0.325257
$473$	15.3571	0.706118
$474$	−7.29468	−0.335056
$475$	4.25879	0.195407
$476$	−7.17045	−0.328657
$477$	69.1413	3.16576
$478$	−45.1816	−2.06656
$479$	22.1611	1.01257	0.506283	−	0.862368i	$-0.331019\pi$
$479$	22.1611	1.01257	0.506283	+	0.862368i	$0.331019\pi$
$480$	−51.2390	−2.33873
$481$	−42.2497	−1.92642
$482$	−2.81863	−0.128385
$483$	16.3451	0.743727
$484$	4.09349	0.186068
$485$	27.0518	1.22836
$486$	−21.8576	−0.991483
$487$	17.6147	0.798199	0.399099	−	0.916908i	$-0.369323\pi$
$487$	17.6147	0.798199	0.399099	+	0.916908i	$0.369323\pi$
$488$	14.3626	0.650163
$489$	−31.8953	−1.44235
$490$	32.4117	1.46421
$491$	−4.11098	−0.185526	−0.0927629	−	0.995688i	$-0.529570\pi$
$491$	−4.11098	−0.185526	−0.0927629	+	0.995688i	$0.529570\pi$
$492$	15.5395	0.700575
$493$	−14.1823	−0.638740
$494$	−3.15606	−0.141998
$495$	74.6441	3.35500
$496$	46.5547	2.09037
$497$	13.7915	0.618635
$498$	−70.0404	−3.13858
$499$	−4.64245	−0.207825	−0.103912	−	0.994586i	$-0.533136\pi$
$499$	−4.64245	−0.207825	−0.103912	+	0.994586i	$0.533136\pi$
$500$	12.7780	0.571451
$501$	5.10606	0.228122
$502$	9.36057	0.417783
$503$	34.8611	1.55438	0.777189	−	0.629267i	$-0.216645\pi$
$503$	34.8611	1.55438	0.777189	+	0.629267i	$0.216645\pi$
$504$	−12.9664	−0.577570
$505$	−5.26325	−0.234211
$506$	−28.0576	−1.24731
$507$	−3.87413	−0.172056
$508$	−12.6160	−0.559746
$509$	−30.3573	−1.34556	−0.672782	−	0.739841i	$-0.734901\pi$
$509$	−30.3573	−1.34556	−0.672782	+	0.739841i	$0.734901\pi$
$510$	102.350	4.53214
$511$	−9.06481	−0.401003
$512$	−5.80894	−0.256721
$513$	−2.95074	−0.130278
$514$	37.7513	1.66514
$515$	−57.6669	−2.54111
$516$	−10.2669	−0.451973
$517$	47.9908	2.11063
$518$	−26.1620	−1.14949
$519$	40.4700	1.77643
$520$	25.8899	1.13535
$521$	−23.0698	−1.01071	−0.505354	−	0.862912i	$-0.668638\pi$
$521$	−23.0698	−1.01071	−0.505354	+	0.862912i	$0.668638\pi$
$522$	21.9200	0.959414
$523$	−30.0184	−1.31261	−0.656306	−	0.754495i	$-0.727882\pi$
$523$	−30.0184	−1.31261	−0.656306	+	0.754495i	$0.727882\pi$
$524$	1.21661	0.0531477
$525$	34.1992	1.49258
$526$	4.25163	0.185380
$527$	−52.8328	−2.30143
$528$	55.9345	2.43424
$529$	−5.55047	−0.241325
$530$	−85.4857	−3.71326
$531$	−19.6465	−0.852585
$532$	−0.616501	−0.0267287
$533$	−22.4145	−0.970879
$534$	69.9453	3.02683
$535$	−32.9664	−1.42526
$536$	22.1038	0.954740
$537$	−42.0170	−1.81317
$538$	−27.7084	−1.19459
$539$	−20.1017	−0.865842
$540$	−20.6888	−0.890305
$541$	−2.90004	−0.124682	−0.0623411	−	0.998055i	$-0.519857\pi$
$541$	−2.90004	−0.124682	−0.0623411	+	0.998055i	$0.519857\pi$
$542$	28.6134	1.22905
$543$	−58.1231	−2.49430
$544$	27.4841	1.17837
$545$	14.6340	0.626850
$546$	−25.3440	−1.08462
$547$	12.5043	0.534644	0.267322	−	0.963607i	$-0.413861\pi$
$547$	12.5043	0.534644	0.267322	+	0.963607i	$0.413861\pi$
$548$	2.00787	0.0857720
$549$	39.9318	1.70425
$550$	−58.7056	−2.50322
$551$	−1.21937	−0.0519469
$552$	−21.9462	−0.934094
$553$	2.05536	0.0874027
$554$	24.6142	1.04576
$555$	117.803	5.00045
$556$	9.06238	0.384331
$557$	−5.25214	−0.222541	−0.111270	−	0.993790i	$-0.535492\pi$
$557$	−5.25214	−0.222541	−0.111270	+	0.993790i	$0.535492\pi$
$558$	81.6577	3.45685
$559$	14.8091	0.626359
$560$	25.4114	1.07383
$561$	−63.4776	−2.68002
$562$	22.4485	0.946934
$563$	−4.85703	−0.204699	−0.102350	−	0.994748i	$-0.532636\pi$
$563$	−4.85703	−0.204699	−0.102350	+	0.994748i	$0.532636\pi$
$564$	−32.0839	−1.35098
$565$	31.6450	1.33132
$566$	7.75492	0.325963
$567$	−2.59087	−0.108806
$568$	−18.5176	−0.776983
$569$	1.08456	0.0454673	0.0227336	−	0.999742i	$-0.492763\pi$
$569$	1.08456	0.0454673	0.0227336	+	0.999742i	$0.492763\pi$
$570$	8.79987	0.368586
$571$	−13.4905	−0.564562	−0.282281	−	0.959332i	$-0.591091\pi$
$571$	−13.4905	−0.564562	−0.282281	+	0.959332i	$0.591091\pi$
$572$	13.7240	0.573830
$573$	31.0726	1.29808
$574$	−13.8795	−0.579321
$575$	36.5101	1.52258
$576$	8.70349	0.362645
$577$	28.2200	1.17481	0.587407	−	0.809292i	$-0.300149\pi$
$577$	28.2200	1.17481	0.587407	+	0.809292i	$0.300149\pi$
$578$	−25.8418	−1.07488
$579$	−21.0275	−0.873872
$580$	−8.54950	−0.354998
$581$	19.7346	0.818731
$582$	35.5561	1.47385
$583$	53.0182	2.19579
$584$	12.1711	0.503646
$585$	71.9808	2.97604
$586$	27.9762	1.15569
$587$	1.10958	0.0457974	0.0228987	−	0.999738i	$-0.492710\pi$
$587$	1.10958	0.0457974	0.0228987	+	0.999738i	$0.492710\pi$
$588$	13.4389	0.554210
$589$	−4.54247	−0.187169
$590$	24.2908	1.00003
$591$	32.0356	1.31777
$592$	55.6796	2.28842
$593$	9.45332	0.388201	0.194101	−	0.980982i	$-0.437821\pi$
$593$	9.45332	0.388201	0.194101	+	0.980982i	$0.437821\pi$
$594$	40.6747	1.66890
$595$	−28.8383	−1.18225
$596$	5.60017	0.229392
$597$	−5.53268	−0.226438
$598$	−27.0565	−1.10642
$599$	0.475038	0.0194095	0.00970477	−	0.999953i	$-0.496911\pi$
$599$	0.475038	0.0194095	0.00970477	+	0.999953i	$0.496911\pi$
$600$	−45.9187	−1.87462
$601$	−8.90191	−0.363116	−0.181558	−	0.983380i	$-0.558114\pi$
$601$	−8.90191	−0.363116	−0.181558	+	0.983380i	$0.558114\pi$
$602$	9.17013	0.373747
$603$	61.4546	2.50262
$604$	−2.85200	−0.116046
$605$	16.4633	0.669328
$606$	−6.91786	−0.281019
$607$	11.4979	0.466683	0.233342	−	0.972395i	$-0.425034\pi$
$607$	11.4979	0.466683	0.233342	+	0.972395i	$0.425034\pi$
$608$	2.36303	0.0958336
$609$	−9.79187	−0.396787
$610$	−49.3714	−1.99899
$611$	46.2785	1.87223
$612$	26.7674	1.08201
$613$	29.4969	1.19137	0.595685	−	0.803218i	$-0.296881\pi$
$613$	29.4969	1.19137	0.595685	+	0.803218i	$0.296881\pi$
$614$	−37.5752	−1.51641
$615$	62.4971	2.52013
$616$	−9.94278	−0.400606
$617$	−16.9236	−0.681319	−0.340659	−	0.940187i	$-0.610650\pi$
$617$	−16.9236	−0.681319	−0.340659	+	0.940187i	$0.610650\pi$
$618$	−75.7957	−3.04895
$619$	−34.2933	−1.37836	−0.689181	−	0.724589i	$-0.742030\pi$
$619$	−34.2933	−1.37836	−0.689181	+	0.724589i	$0.742030\pi$
$620$	−31.8491	−1.27909
$621$	−25.2963	−1.01511
$622$	−39.1317	−1.56904
$623$	−19.7079	−0.789579
$624$	53.9388	2.15928
$625$	7.69002	0.307601
$626$	25.9138	1.03572
$627$	−5.45768	−0.217959
$628$	−6.30967	−0.251783
$629$	−63.1883	−2.51948
$630$	44.5721	1.77579
$631$	−22.5000	−0.895712	−0.447856	−	0.894106i	$-0.647812\pi$
$631$	−22.5000	−0.895712	−0.447856	+	0.894106i	$0.647812\pi$
$632$	−2.75969	−0.109775
$633$	−55.3313	−2.19922
$634$	−16.1442	−0.641168
$635$	−50.7395	−2.01353
$636$	−35.4450	−1.40549
$637$	−19.3845	−0.768042
$638$	16.8085	0.665455
$639$	−51.4840	−2.03668
$640$	−46.7136	−1.84652
$641$	37.4614	1.47964	0.739818	−	0.672807i	$-0.234912\pi$
$641$	37.4614	1.47964	0.739818	+	0.672807i	$0.234912\pi$
$642$	−43.3301	−1.71010
$643$	−19.3163	−0.761760	−0.380880	−	0.924624i	$-0.624379\pi$
$643$	−19.3163	−0.761760	−0.380880	+	0.924624i	$0.624379\pi$
$644$	−5.28519	−0.208266
$645$	−41.2915	−1.62585
$646$	−4.72017	−0.185713
$647$	−15.5248	−0.610342	−0.305171	−	0.952298i	$-0.598714\pi$
$647$	−15.5248	−0.610342	−0.305171	+	0.952298i	$0.598714\pi$
$648$	3.47871	0.136657
$649$	−15.0651	−0.591358
$650$	−56.6110	−2.22047
$651$	−36.4772	−1.42966
$652$	10.3134	0.403903
$653$	−7.90601	−0.309386	−0.154693	−	0.987963i	$-0.549439\pi$
$653$	−7.90601	−0.309386	−0.154693	+	0.987963i	$0.549439\pi$
$654$	19.2345	0.752128
$655$	4.89298	0.191184
$656$	29.5393	1.15332
$657$	33.8391	1.32019
$658$	28.6567	1.11715
$659$	43.8802	1.70933	0.854665	−	0.519180i	$-0.173763\pi$
$659$	43.8802	1.70933	0.854665	+	0.519180i	$0.173763\pi$
$660$	−38.2660	−1.48950
$661$	−8.04164	−0.312784	−0.156392	−	0.987695i	$-0.549986\pi$
$661$	−8.04164	−0.312784	−0.156392	+	0.987695i	$0.549986\pi$
$662$	22.7053	0.882465
$663$	−61.2127	−2.37730
$664$	−26.4973	−1.02830
$665$	−2.47946	−0.0961493
$666$	97.6630	3.78436
$667$	−10.4535	−0.404762
$668$	−1.65105	−0.0638810
$669$	3.88661	0.150265
$670$	−75.9819	−2.93544
$671$	30.6201	1.18208
$672$	18.9758	0.732007
$673$	24.9990	0.963639	0.481820	−	0.876270i	$-0.339976\pi$
$673$	24.9990	0.963639	0.481820	+	0.876270i	$0.339976\pi$
$674$	−56.3430	−2.17025
$675$	−52.9282	−2.03721
$676$	1.25270	0.0481809
$677$	19.6439	0.754977	0.377488	−	0.926014i	$-0.376788\pi$
$677$	19.6439	0.754977	0.377488	+	0.926014i	$0.376788\pi$
$678$	41.5934	1.59738
$679$	−10.0183	−0.384468
$680$	38.7206	1.48487
$681$	−43.3579	−1.66148
$682$	62.6160	2.39769
$683$	−6.58391	−0.251926	−0.125963	−	0.992035i	$-0.540202\pi$
$683$	−6.58391	−0.251926	−0.125963	+	0.992035i	$0.540202\pi$
$684$	2.30141	0.0879966
$685$	8.07530	0.308541
$686$	−28.4284	−1.08540
$687$	16.2497	0.619965
$688$	−19.5165	−0.744058
$689$	51.1266	1.94777
$690$	75.4403	2.87196
$691$	−16.3328	−0.621329	−0.310664	−	0.950520i	$-0.600551\pi$
$691$	−16.3328	−0.621329	−0.310664	+	0.950520i	$0.600551\pi$
$692$	−13.0860	−0.497455
$693$	−27.6436	−1.05009
$694$	−40.0294	−1.51949
$695$	36.4473	1.38253
$696$	13.1474	0.498350
$697$	−33.5229	−1.26977
$698$	35.1997	1.33233
$699$	50.3934	1.90605
$700$	−11.0583	−0.417966
$701$	10.9190	0.412406	0.206203	−	0.978509i	$-0.433889\pi$
$701$	10.9190	0.412406	0.206203	+	0.978509i	$0.433889\pi$
$702$	39.2235	1.48039
$703$	−5.43281	−0.204902
$704$	6.67392	0.251533
$705$	−129.036	−4.85977
$706$	−50.7135	−1.90863
$707$	1.94918	0.0733066
$708$	10.0717	0.378517
$709$	−36.5473	−1.37256	−0.686281	−	0.727336i	$-0.740758\pi$
$709$	−36.5473	−1.37256	−0.686281	+	0.727336i	$0.740758\pi$
$710$	63.6544	2.38891
$711$	−7.67268	−0.287748
$712$	26.4614	0.991682
$713$	−38.9420	−1.45839
$714$	−37.9042	−1.41853
$715$	55.1956	2.06420
$716$	13.5862	0.507742
$717$	−75.3434	−2.81375
$718$	3.62470	0.135272
$719$	53.4221	1.99231	0.996154	−	0.0876162i	$-0.0279249\pi$
$719$	53.4221	1.99231	0.996154	+	0.0876162i	$0.0279249\pi$
$720$	−94.8612	−3.53527
$721$	21.3563	0.795349
$722$	32.0706	1.19355
$723$	−4.70027	−0.174805
$724$	18.7941	0.698479
$725$	−21.8722	−0.812312
$726$	21.6389	0.803095
$727$	−46.7335	−1.73325	−0.866625	−	0.498960i	$-0.833716\pi$
$727$	−46.7335	−1.73325	−0.866625	+	0.498960i	$0.833716\pi$
$728$	−9.58802	−0.355356
$729$	−42.1112	−1.55967
$730$	−41.8384	−1.54851
$731$	22.1484	0.819187
$732$	−20.4709	−0.756626
$733$	30.7535	1.13591	0.567954	−	0.823061i	$-0.307735\pi$
$733$	30.7535	1.13591	0.567954	+	0.823061i	$0.307735\pi$
$734$	−15.1566	−0.559439
$735$	54.0488	1.99362
$736$	20.2580	0.746720
$737$	47.1240	1.73583
$738$	51.8125	1.90725
$739$	5.51728	0.202956	0.101478	−	0.994838i	$-0.467643\pi$
$739$	5.51728	0.202956	0.101478	+	0.994838i	$0.467643\pi$
$740$	−38.0916	−1.40027
$741$	−5.26295	−0.193339
$742$	31.6587	1.16223
$743$	−28.5642	−1.04792	−0.523959	−	0.851743i	$-0.675545\pi$
$743$	−28.5642	−1.04792	−0.523959	+	0.851743i	$0.675545\pi$
$744$	48.9773	1.79560
$745$	22.5229	0.825175
$746$	23.5286	0.861443
$747$	−73.6697	−2.69543
$748$	20.5255	0.750487
$749$	12.2087	0.446098
$750$	67.5469	2.46646
$751$	1.08551	0.0396108	0.0198054	−	0.999804i	$-0.493695\pi$
$751$	1.08551	0.0396108	0.0198054	+	0.999804i	$0.493695\pi$
$752$	−60.9890	−2.22404
$753$	15.6094	0.568839
$754$	16.2088	0.590289
$755$	−11.4702	−0.417444
$756$	7.66187	0.278660
$757$	−18.5905	−0.675681	−0.337841	−	0.941203i	$-0.609697\pi$
$757$	−18.5905	−0.675681	−0.337841	+	0.941203i	$0.609697\pi$
$758$	−23.9573	−0.870168
$759$	−46.7880	−1.69830
$760$	3.32913	0.120760
$761$	−40.9308	−1.48374	−0.741870	−	0.670544i	$-0.766061\pi$
$761$	−40.9308	−1.48374	−0.741870	+	0.670544i	$0.766061\pi$
$762$	−66.6905	−2.41594
$763$	−5.41953	−0.196200
$764$	−10.0474	−0.363501
$765$	107.654	3.89223
$766$	−16.0633	−0.580391
$767$	−14.5276	−0.524562
$768$	−51.7170	−1.86618
$769$	−9.56459	−0.344908	−0.172454	−	0.985018i	$-0.555170\pi$
$769$	−9.56459	−0.344908	−0.172454	+	0.985018i	$0.555170\pi$
$770$	34.1783	1.23170
$771$	62.9530	2.26720
$772$	6.79925	0.244710
$773$	4.97708	0.179013	0.0895066	−	0.995986i	$-0.471471\pi$
$773$	4.97708	0.179013	0.0895066	+	0.995986i	$0.471471\pi$
$774$	−34.2322	−1.23045
$775$	−81.4794	−2.92683
$776$	13.4514	0.482877
$777$	−43.6269	−1.56511
$778$	30.1562	1.08115
$779$	−2.88223	−0.103267
$780$	−36.9007	−1.32126
$781$	−39.4785	−1.41265
$782$	−40.4655	−1.44704
$783$	15.1543	0.541571
$784$	25.5462	0.912365
$785$	−25.3764	−0.905722
$786$	6.43119	0.229393
$787$	−8.93006	−0.318322	−0.159161	−	0.987253i	$-0.550879\pi$
$787$	−8.93006	−0.318322	−0.159161	+	0.987253i	$0.550879\pi$
$788$	−10.3587	−0.369015
$789$	7.08989	0.252407
$790$	9.48644	0.337512
$791$	−11.7194	−0.416693
$792$	37.1165	1.31888
$793$	29.5276	1.04856
$794$	−1.68852	−0.0599232
$795$	−142.553	−5.05585
$796$	1.78900	0.0634093
$797$	−34.9799	−1.23905	−0.619527	−	0.784976i	$-0.712675\pi$
$797$	−34.9799	−1.23905	−0.619527	+	0.784976i	$0.712675\pi$
$798$	−3.25893	−0.115365
$799$	69.2137	2.44860
$800$	42.3863	1.49858
$801$	73.5698	2.59946
$802$	−4.24924	−0.150046
$803$	25.9481	0.915690
$804$	−31.5044	−1.11108
$805$	−21.2561	−0.749180
$806$	60.3819	2.12686
$807$	−46.2056	−1.62652
$808$	−2.61713	−0.0920704
$809$	−18.4489	−0.648630	−0.324315	−	0.945949i	$-0.605134\pi$
$809$	−18.4489	−0.648630	−0.324315	+	0.945949i	$0.605134\pi$
$810$	−11.9581	−0.420164
$811$	−4.36453	−0.153260	−0.0766298	−	0.997060i	$-0.524416\pi$
$811$	−4.36453	−0.153260	−0.0766298	+	0.997060i	$0.524416\pi$
$812$	3.16621	0.111112
$813$	47.7148	1.67343
$814$	74.8890	2.62486
$815$	41.4785	1.45293
$816$	80.6703	2.82402
$817$	1.90427	0.0666221
$818$	−19.7367	−0.690076
$819$	−26.6573	−0.931481
$820$	−20.2085	−0.705711
$821$	33.6516	1.17445	0.587225	−	0.809424i	$-0.300221\pi$
$821$	33.6516	1.17445	0.587225	+	0.809424i	$0.300221\pi$
$822$	10.6140	0.370204
$823$	41.2554	1.43807	0.719036	−	0.694973i	$-0.244584\pi$
$823$	41.2554	1.43807	0.719036	+	0.694973i	$0.244584\pi$
$824$	−28.6747	−0.998930
$825$	−97.8958	−3.40829
$826$	−8.99581	−0.313004
$827$	46.7797	1.62669	0.813344	−	0.581783i	$-0.197645\pi$
$827$	46.7797	1.62669	0.813344	+	0.581783i	$0.197645\pi$
$828$	19.7297	0.685655
$829$	−32.0343	−1.11260	−0.556299	−	0.830982i	$-0.687779\pi$
$829$	−32.0343	−1.11260	−0.556299	+	0.830982i	$0.687779\pi$
$830$	91.0847	3.16160
$831$	41.0459	1.42387
$832$	6.43580	0.223121
$833$	−28.9913	−1.00449
$834$	47.9053	1.65883
$835$	−6.64022	−0.229794
$836$	1.76474	0.0610350
$837$	56.4537	1.95133
$838$	2.64044	0.0912125
$839$	−25.5429	−0.881838	−0.440919	−	0.897547i	$-0.645347\pi$
$839$	−25.5429	−0.881838	−0.440919	+	0.897547i	$0.645347\pi$
$840$	26.7338	0.922403
$841$	−22.7376	−0.784055
$842$	51.3702	1.77033
$843$	37.4345	1.28931
$844$	17.8914	0.615848
$845$	5.03815	0.173318
$846$	−106.976	−3.67790
$847$	−6.09700	−0.209495
$848$	−67.3781	−2.31377
$849$	12.9319	0.443821
$850$	−84.6669	−2.90405
$851$	−46.5748	−1.59656
$852$	26.3931	0.904212
$853$	−25.5660	−0.875363	−0.437681	−	0.899130i	$-0.644200\pi$
$853$	−25.5660	−0.875363	−0.437681	+	0.899130i	$0.644200\pi$
$854$	18.2841	0.625670
$855$	9.25586	0.316544
$856$	−16.3925	−0.560283
$857$	−55.9615	−1.91161	−0.955803	−	0.294006i	$-0.905011\pi$
$857$	−55.9615	−1.91161	−0.955803	+	0.294006i	$0.905011\pi$
$858$	72.5476	2.47673
$859$	1.66344	0.0567558	0.0283779	−	0.999597i	$-0.490966\pi$
$859$	1.66344	0.0567558	0.0283779	+	0.999597i	$0.490966\pi$
$860$	13.3516	0.455287
$861$	−23.1451	−0.788783
$862$	−19.1399	−0.651907
$863$	−27.1278	−0.923441	−0.461721	−	0.887025i	$-0.652768\pi$
$863$	−27.1278	−0.923441	−0.461721	+	0.887025i	$0.652768\pi$
$864$	−29.3677	−0.999110
$865$	−52.6296	−1.78946
$866$	−2.46947	−0.0839162
$867$	−43.0930	−1.46352
$868$	11.7949	0.400346
$869$	−5.88349	−0.199584
$870$	−45.1941	−1.53222
$871$	45.4426	1.53976
$872$	7.27670	0.246420
$873$	37.3985	1.26575
$874$	−3.47914	−0.117684
$875$	−19.0321	−0.643402
$876$	−17.3475	−0.586116
$877$	53.6676	1.81223	0.906113	−	0.423035i	$-0.139035\pi$
$877$	53.6676	1.81223	0.906113	+	0.423035i	$0.139035\pi$
$878$	−12.2548	−0.413580
$879$	46.6523	1.57354
$880$	−72.7405	−2.45208
$881$	−44.0900	−1.48543	−0.742715	−	0.669607i	$-0.766462\pi$
$881$	−44.0900	−1.48543	−0.742715	+	0.669607i	$0.766462\pi$
$882$	44.8085	1.50878
$883$	−35.3425	−1.18937	−0.594685	−	0.803959i	$-0.702723\pi$
$883$	−35.3425	−1.18937	−0.594685	+	0.803959i	$0.702723\pi$
$884$	19.7932	0.665716
$885$	40.5066	1.36161
$886$	49.0102	1.64653
$887$	−6.47452	−0.217393	−0.108697	−	0.994075i	$-0.534668\pi$
$887$	−6.47452	−0.217393	−0.108697	+	0.994075i	$0.534668\pi$
$888$	58.5770	1.96572
$889$	18.7908	0.630223
$890$	−90.9611	−3.04902
$891$	7.41640	0.248459
$892$	−1.25674	−0.0420787
$893$	5.95086	0.199138
$894$	29.6035	0.990088
$895$	54.6415	1.82646
$896$	17.2998	0.577947
$897$	−45.1187	−1.50647
$898$	−64.6745	−2.15822
$899$	23.3291	0.778068
$900$	41.2810	1.37603
$901$	76.4644	2.54740
$902$	39.7304	1.32288
$903$	15.2918	0.508881
$904$	15.7354	0.523352
$905$	75.5867	2.51259
$906$	−15.0762	−0.500872
$907$	−27.3232	−0.907252	−0.453626	−	0.891192i	$-0.649870\pi$
$907$	−27.3232	−0.907252	−0.453626	+	0.891192i	$0.649870\pi$
$908$	14.0198	0.465264
$909$	−7.27633	−0.241341
$910$	32.9589	1.09258
$911$	−36.7156	−1.21644	−0.608221	−	0.793768i	$-0.708117\pi$
$911$	−36.7156	−1.21644	−0.608221	+	0.793768i	$0.708117\pi$
$912$	6.93588	0.229670
$913$	−56.4907	−1.86957
$914$	−5.34292	−0.176728
$915$	−82.3303	−2.72176
$916$	−5.25436	−0.173609
$917$	−1.81206	−0.0598395
$918$	58.6622	1.93614
$919$	31.8755	1.05148	0.525738	−	0.850647i	$-0.323789\pi$
$919$	31.8755	1.05148	0.525738	+	0.850647i	$0.323789\pi$
$920$	28.5402	0.940943
$921$	−62.6593	−2.06469
$922$	72.4542	2.38615
$923$	−38.0699	−1.25309
$924$	14.1714	0.466204
$925$	−97.4497	−3.20412
$926$	−19.3993	−0.637502
$927$	−79.7233	−2.61846
$928$	−12.1360	−0.398383
$929$	−44.6882	−1.46617	−0.733087	−	0.680135i	$-0.761921\pi$
$929$	−44.6882	−1.46617	−0.733087	+	0.680135i	$0.761921\pi$
$930$	−168.360	−5.52073
$931$	−2.49261	−0.0816921
$932$	−16.2947	−0.533752
$933$	−65.2549	−2.13635
$934$	−39.7662	−1.30119
$935$	82.5500	2.69967
$936$	35.7922	1.16991
$937$	−17.5936	−0.574757	−0.287378	−	0.957817i	$-0.592784\pi$
$937$	−17.5936	−0.574757	−0.287378	+	0.957817i	$0.592784\pi$
$938$	28.1391	0.918773
$939$	43.2131	1.41021
$940$	41.7239	1.36088
$941$	55.3302	1.80371	0.901857	−	0.432034i	$-0.142204\pi$
$941$	55.3302	1.80371	0.901857	+	0.432034i	$0.142204\pi$
$942$	−33.3540	−1.08673
$943$	−24.7090	−0.804637
$944$	19.1455	0.623132
$945$	30.8147	1.00240
$946$	−26.2496	−0.853449
$947$	22.3932	0.727681	0.363840	−	0.931461i	$-0.381465\pi$
$947$	22.3932	0.727681	0.363840	+	0.931461i	$0.381465\pi$
$948$	3.93337	0.127750
$949$	25.0223	0.812259
$950$	−7.27950	−0.236178
$951$	−26.9216	−0.872993
$952$	−14.3398	−0.464754
$953$	56.9432	1.84457	0.922286	−	0.386508i	$-0.126319\pi$
$953$	56.9432	1.84457	0.922286	+	0.386508i	$0.126319\pi$
$954$	−118.182	−3.82629
$955$	−40.4087	−1.30759
$956$	24.3624	0.787935
$957$	28.0294	0.906061
$958$	−37.8797	−1.22384
$959$	−2.99060	−0.0965714
$960$	−17.9446	−0.579160
$961$	55.9067	1.80344
$962$	72.2170	2.32837
$963$	−45.5754	−1.46865
$964$	1.51983	0.0489506
$965$	27.3454	0.880279
$966$	−27.9385	−0.898905
$967$	−5.80233	−0.186590	−0.0932951	−	0.995639i	$-0.529740\pi$
$967$	−5.80233	−0.186590	−0.0932951	+	0.995639i	$0.529740\pi$
$968$	8.18632	0.263118
$969$	−7.87122	−0.252860
$970$	−46.2392	−1.48465
$971$	−49.7261	−1.59579	−0.797894	−	0.602798i	$-0.794052\pi$
$971$	−49.7261	−1.59579	−0.797894	+	0.602798i	$0.794052\pi$
$972$	11.7859	0.378032
$973$	−13.4979	−0.432721
$974$	−30.1086	−0.964742
$975$	−94.4029	−3.02331
$976$	−38.9135	−1.24559
$977$	−49.0743	−1.57002	−0.785012	−	0.619480i	$-0.787343\pi$
$977$	−49.0743	−1.57002	−0.785012	+	0.619480i	$0.787343\pi$
$978$	54.5182	1.74330
$979$	56.4141	1.80300
$980$	−17.4767	−0.558273
$981$	20.2312	0.645932
$982$	7.02685	0.224236
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	31.0765	0.990683
$985$	−41.6611	−1.32743
$986$	24.2417	0.772013
$987$	47.7870	1.52108
$988$	1.70178	0.0541408
$989$	16.3251	0.519109
$990$	−127.588	−4.05502
$991$	26.3584	0.837302	0.418651	−	0.908147i	$-0.362503\pi$
$991$	26.3584	0.837302	0.418651	+	0.908147i	$0.362503\pi$
$992$	−45.2096	−1.43541
$993$	37.8626	1.20153
$994$	−23.5737	−0.747713
$995$	7.19503	0.228098
$996$	37.7665	1.19668
$997$	−23.0702	−0.730640	−0.365320	−	0.930882i	$-0.619040\pi$
$997$	−23.0702	−0.730640	−0.365320	+	0.930882i	$0.619040\pi$
$998$	7.93528	0.251187
$999$	67.5189	2.13620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.11	✓	54
3.2	odd	2		8847.2.a.g.1.44		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.11	✓	54	1.1	even	1	trivial
8847.2.a.g.1.44		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)

\(f(q)\)	\(=\)	\(q-1.70929 q^{2} -2.85036 q^{3} +0.921666 q^{4} +3.70678 q^{5} +4.87208 q^{6} -1.37276 q^{7} +1.84318 q^{8} +5.12455 q^{9} +O(q^{10})\)	\(q-1.70929 q^{2} -2.85036 q^{3} +0.921666 q^{4} +3.70678 q^{5} +4.87208 q^{6} -1.37276 q^{7} +1.84318 q^{8} +5.12455 q^{9} -6.33595 q^{10} +3.92956 q^{11} -2.62708 q^{12} +3.78935 q^{13} +2.34645 q^{14} -10.5656 q^{15} -4.99386 q^{16} +5.66731 q^{17} -8.75933 q^{18} +0.487265 q^{19} +3.41641 q^{20} +3.91287 q^{21} -6.71674 q^{22} +4.17726 q^{23} -5.25374 q^{24} +8.74019 q^{25} -6.47709 q^{26} -6.05572 q^{27} -1.26523 q^{28} -2.50248 q^{29} +18.0597 q^{30} -9.32238 q^{31} +4.84958 q^{32} -11.2006 q^{33} -9.68707 q^{34} -5.08853 q^{35} +4.72312 q^{36} -11.1496 q^{37} -0.832876 q^{38} -10.8010 q^{39} +6.83227 q^{40} -5.91513 q^{41} -6.68822 q^{42} +3.90809 q^{43} +3.62174 q^{44} +18.9956 q^{45} -7.14015 q^{46} +12.2128 q^{47} +14.2343 q^{48} -5.11552 q^{49} -14.9395 q^{50} -16.1539 q^{51} +3.49251 q^{52} +13.4922 q^{53} +10.3510 q^{54} +14.5660 q^{55} -2.53026 q^{56} -1.38888 q^{57} +4.27746 q^{58} -3.83380 q^{59} -9.73799 q^{60} +7.79226 q^{61} +15.9346 q^{62} -7.03479 q^{63} +1.69839 q^{64} +14.0463 q^{65} +19.1451 q^{66} +11.9922 q^{67} +5.22337 q^{68} -11.9067 q^{69} +8.69776 q^{70} -10.0466 q^{71} +9.44548 q^{72} +6.60333 q^{73} +19.0579 q^{74} -24.9127 q^{75} +0.449095 q^{76} -5.39435 q^{77} +18.4620 q^{78} -1.49724 q^{79} -18.5111 q^{80} +1.88734 q^{81} +10.1107 q^{82} -14.3759 q^{83} +3.60636 q^{84} +21.0075 q^{85} -6.68005 q^{86} +7.13297 q^{87} +7.24289 q^{88} +14.3563 q^{89} -32.4689 q^{90} -5.20188 q^{91} +3.85004 q^{92} +26.5721 q^{93} -20.8752 q^{94} +1.80618 q^{95} -13.8231 q^{96} +7.29792 q^{97} +8.74390 q^{98} +20.1372 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 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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