LMFDB - Embedded newform 8023.2.a.e.1.100

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.100
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.582518 q^{2} -0.386642 q^{3} -1.66067 q^{4} -0.219930 q^{5} -0.225226 q^{6} +4.05323 q^{7} -2.13241 q^{8} -2.85051 q^{9} +O(q^{10})$	\(q+0.582518 q^{2} -0.386642 q^{3} -1.66067 q^{4} -0.219930 q^{5} -0.225226 q^{6} +4.05323 q^{7} -2.13241 q^{8} -2.85051 q^{9} -0.128113 q^{10} -4.20508 q^{11} +0.642086 q^{12} +1.21600 q^{13} +2.36108 q^{14} +0.0850341 q^{15} +2.07918 q^{16} -5.69797 q^{17} -1.66047 q^{18} +0.904368 q^{19} +0.365231 q^{20} -1.56715 q^{21} -2.44953 q^{22} -6.58292 q^{23} +0.824479 q^{24} -4.95163 q^{25} +0.708341 q^{26} +2.26205 q^{27} -6.73108 q^{28} +7.37473 q^{29} +0.0495339 q^{30} -6.26219 q^{31} +5.47598 q^{32} +1.62586 q^{33} -3.31917 q^{34} -0.891425 q^{35} +4.73376 q^{36} -5.60221 q^{37} +0.526811 q^{38} -0.470156 q^{39} +0.468980 q^{40} +4.37191 q^{41} -0.912893 q^{42} -3.69129 q^{43} +6.98326 q^{44} +0.626911 q^{45} -3.83467 q^{46} -3.70331 q^{47} -0.803898 q^{48} +9.42865 q^{49} -2.88442 q^{50} +2.20308 q^{51} -2.01937 q^{52} +10.6652 q^{53} +1.31769 q^{54} +0.924821 q^{55} -8.64314 q^{56} -0.349667 q^{57} +4.29591 q^{58} +7.56565 q^{59} -0.141214 q^{60} +12.5279 q^{61} -3.64784 q^{62} -11.5538 q^{63} -0.968500 q^{64} -0.267434 q^{65} +0.947093 q^{66} -1.65987 q^{67} +9.46247 q^{68} +2.54523 q^{69} -0.519271 q^{70} -1.00000 q^{71} +6.07845 q^{72} +0.00926832 q^{73} -3.26339 q^{74} +1.91451 q^{75} -1.50186 q^{76} -17.0441 q^{77} -0.273874 q^{78} -9.99096 q^{79} -0.457273 q^{80} +7.67692 q^{81} +2.54672 q^{82} +6.98022 q^{83} +2.60252 q^{84} +1.25315 q^{85} -2.15024 q^{86} -2.85138 q^{87} +8.96694 q^{88} -8.43358 q^{89} +0.365187 q^{90} +4.92871 q^{91} +10.9321 q^{92} +2.42123 q^{93} -2.15725 q^{94} -0.198897 q^{95} -2.11724 q^{96} -0.400591 q^{97} +5.49236 q^{98} +11.9866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) $ 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * 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 $

$2$	0.582518	0.411903	0.205951	−	0.978562i	$-0.433971\pi$
$2$	0.582518	0.411903	0.205951	+	0.978562i	$0.433971\pi$
$3$	−0.386642	−0.223228	−0.111614	−	0.993752i	$-0.535602\pi$
$3$	−0.386642	−0.223228	−0.111614	+	0.993752i	$0.535602\pi$
$4$	−1.66067	−0.830336
$5$	−0.219930	−0.0983555	−0.0491778	−	0.998790i	$-0.515660\pi$
$5$	−0.219930	−0.0983555	−0.0491778	+	0.998790i	$0.515660\pi$
$6$	−0.225226	−0.0919482
$7$	4.05323	1.53198	0.765988	−	0.642855i	$-0.222250\pi$
$7$	4.05323	1.53198	0.765988	+	0.642855i	$0.222250\pi$
$8$	−2.13241	−0.753920
$9$	−2.85051	−0.950169
$10$	−0.128113	−0.0405129
$11$	−4.20508	−1.26788	−0.633939	−	0.773383i	$-0.718563\pi$
$11$	−4.20508	−1.26788	−0.633939	+	0.773383i	$0.718563\pi$
$12$	0.642086	0.185354
$13$	1.21600	0.337257	0.168629	−	0.985680i	$-0.446066\pi$
$13$	1.21600	0.337257	0.168629	+	0.985680i	$0.446066\pi$
$14$	2.36108	0.631025
$15$	0.0850341	0.0219557
$16$	2.07918	0.519795
$17$	−5.69797	−1.38196	−0.690981	−	0.722873i	$-0.742821\pi$
$17$	−5.69797	−1.38196	−0.690981	+	0.722873i	$0.742821\pi$
$18$	−1.66047	−0.391377
$19$	0.904368	0.207476	0.103738	−	0.994605i	$-0.466920\pi$
$19$	0.904368	0.207476	0.103738	+	0.994605i	$0.466920\pi$
$20$	0.365231	0.0816682
$21$	−1.56715	−0.341980
$22$	−2.44953	−0.522242
$23$	−6.58292	−1.37263	−0.686317	−	0.727302i	$-0.740774\pi$
$23$	−6.58292	−1.37263	−0.686317	+	0.727302i	$0.740774\pi$
$24$	0.824479	0.168296
$25$	−4.95163	−0.990326
$26$	0.708341	0.138917
$27$	2.26205	0.435332
$28$	−6.73108	−1.27206
$29$	7.37473	1.36945	0.684726	−	0.728800i	$-0.259922\pi$
$29$	7.37473	1.36945	0.684726	+	0.728800i	$0.259922\pi$
$30$	0.0495339	0.00904361
$31$	−6.26219	−1.12472	−0.562361	−	0.826892i	$-0.690107\pi$
$31$	−6.26219	−1.12472	−0.562361	+	0.826892i	$0.690107\pi$
$32$	5.47598	0.968025
$33$	1.62586	0.283026
$34$	−3.31917	−0.569234
$35$	−0.891425	−0.150678
$36$	4.73376	0.788960
$37$	−5.60221	−0.920998	−0.460499	−	0.887660i	$-0.652330\pi$
$37$	−5.60221	−0.920998	−0.460499	+	0.887660i	$0.652330\pi$
$38$	0.526811	0.0854600
$39$	−0.470156	−0.0752852
$40$	0.468980	0.0741522
$41$	4.37191	0.682778	0.341389	−	0.939922i	$-0.389103\pi$
$41$	4.37191	0.682778	0.341389	+	0.939922i	$0.389103\pi$
$42$	−0.912893	−0.140862
$43$	−3.69129	−0.562917	−0.281458	−	0.959573i	$-0.590818\pi$
$43$	−3.69129	−0.562917	−0.281458	+	0.959573i	$0.590818\pi$
$44$	6.98326	1.05277
$45$	0.626911	0.0934544
$46$	−3.83467	−0.565392
$47$	−3.70331	−0.540184	−0.270092	−	0.962835i	$-0.587054\pi$
$47$	−3.70331	−0.540184	−0.270092	+	0.962835i	$0.587054\pi$
$48$	−0.803898	−0.116033
$49$	9.42865	1.34695
$50$	−2.88442	−0.407918
$51$	2.20308	0.308492
$52$	−2.01937	−0.280037
$53$	10.6652	1.46497	0.732487	−	0.680781i	$-0.238359\pi$
$53$	10.6652	1.46497	0.732487	+	0.680781i	$0.238359\pi$
$54$	1.31769	0.179314
$55$	0.924821	0.124703
$56$	−8.64314	−1.15499
$57$	−0.349667	−0.0463145
$58$	4.29591	0.564081
$59$	7.56565	0.984964	0.492482	−	0.870323i	$-0.336090\pi$
$59$	7.56565	0.984964	0.492482	+	0.870323i	$0.336090\pi$
$60$	−0.141214	−0.0182306
$61$	12.5279	1.60403	0.802015	−	0.597303i	$-0.203761\pi$
$61$	12.5279	1.60403	0.802015	+	0.597303i	$0.203761\pi$
$62$	−3.64784	−0.463276
$63$	−11.5538	−1.45564
$64$	−0.968500	−0.121062
$65$	−0.267434	−0.0331711
$66$	0.947093	0.116579
$67$	−1.65987	−0.202785	−0.101393	−	0.994846i	$-0.532330\pi$
$67$	−1.65987	−0.202785	−0.101393	+	0.994846i	$0.532330\pi$
$68$	9.46247	1.14749
$69$	2.54523	0.306410
$70$	−0.519271	−0.0620648
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	6.07845	0.716352
$73$	0.00926832	0.00108478	0.000542388	−	1.00000i	$-0.499827\pi$
$73$	0.00926832	0.00108478	0.000542388		1.00000i	$0.499827\pi$
$74$	−3.26339	−0.379362
$75$	1.91451	0.221068
$76$	−1.50186	−0.172275
$77$	−17.0441	−1.94236
$78$	−0.273874	−0.0310102
$79$	−9.99096	−1.12407	−0.562036	−	0.827113i	$-0.689982\pi$
$79$	−9.99096	−1.12407	−0.562036	+	0.827113i	$0.689982\pi$
$80$	−0.457273	−0.0511247
$81$	7.67692	0.852991
$82$	2.54672	0.281238
$83$	6.98022	0.766179	0.383089	−	0.923711i	$-0.374860\pi$
$83$	6.98022	0.766179	0.383089	+	0.923711i	$0.374860\pi$
$84$	2.60252	0.283958
$85$	1.25315	0.135924
$86$	−2.15024	−0.231867
$87$	−2.85138	−0.305700
$88$	8.96694	0.955879
$89$	−8.43358	−0.893957	−0.446979	−	0.894545i	$-0.647500\pi$
$89$	−8.43358	−0.893957	−0.446979	+	0.894545i	$0.647500\pi$
$90$	0.365187	0.0384941
$91$	4.92871	0.516670
$92$	10.9321	1.13975
$93$	2.42123	0.251069
$94$	−2.15725	−0.222503
$95$	−0.198897	−0.0204064
$96$	−2.11724	−0.216090
$97$	−0.400591	−0.0406738	−0.0203369	−	0.999793i	$-0.506474\pi$
$97$	−0.400591	−0.0406738	−0.0203369	+	0.999793i	$0.506474\pi$
$98$	5.49236	0.554812
$99$	11.9866	1.20470
$100$	8.22304	0.822304
$101$	6.31431	0.628297	0.314149	−	0.949374i	$-0.398281\pi$
$101$	6.31431	0.628297	0.314149	+	0.949374i	$0.398281\pi$
$102$	1.28333	0.127069
$103$	−10.1050	−0.995677	−0.497839	−	0.867270i	$-0.665873\pi$
$103$	−10.1050	−0.995677	−0.497839	+	0.867270i	$0.665873\pi$
$104$	−2.59300	−0.254265
$105$	0.344662	0.0336356
$106$	6.21266	0.603427
$107$	3.13370	0.302946	0.151473	−	0.988461i	$-0.451598\pi$
$107$	3.13370	0.302946	0.151473	+	0.988461i	$0.451598\pi$
$108$	−3.75653	−0.361472
$109$	6.05677	0.580133	0.290067	−	0.957006i	$-0.406322\pi$
$109$	6.05677	0.580133	0.290067	+	0.957006i	$0.406322\pi$
$110$	0.538725	0.0513654
$111$	2.16605	0.205592
$112$	8.42738	0.796313
$113$	1.00000	0.0940721
$113$	1.00000	0.0940721
$114$	−0.203687	−0.0190771
$115$	1.44778	0.135006
$116$	−12.2470	−1.13711
$117$	−3.46621	−0.320451
$118$	4.40713	0.405709
$119$	−23.0952	−2.11713
$120$	−0.181327	−0.0165528
$121$	6.68267	0.607515
$122$	7.29772	0.660704
$123$	−1.69036	−0.152415
$124$	10.3994	0.933898
$125$	2.18866	0.195760
$126$	−6.73027	−0.599580
$127$	9.64203	0.855592	0.427796	−	0.903875i	$-0.359290\pi$
$127$	9.64203	0.855592	0.427796	+	0.903875i	$0.359290\pi$
$128$	−11.5161	−1.01789
$129$	1.42721	0.125659
$130$	−0.155785	−0.0136633
$131$	13.0438	1.13964	0.569822	−	0.821768i	$-0.307012\pi$
$131$	13.0438	1.13964	0.569822	+	0.821768i	$0.307012\pi$
$132$	−2.70002	−0.235007
$133$	3.66561	0.317849
$134$	−0.966903	−0.0835277
$135$	−0.497492	−0.0428173
$136$	12.1504	1.04189
$137$	7.05534	0.602779	0.301389	−	0.953501i	$-0.402550\pi$
$137$	7.05534	0.602779	0.301389	+	0.953501i	$0.402550\pi$
$138$	1.48265	0.126211
$139$	−6.92085	−0.587019	−0.293509	−	0.955956i	$-0.594823\pi$
$139$	−6.92085	−0.587019	−0.293509	+	0.955956i	$0.594823\pi$
$140$	1.48036	0.125114
$141$	1.43186	0.120584
$142$	−0.582518	−0.0488838
$143$	−5.11336	−0.427601
$144$	−5.92671	−0.493893
$145$	−1.62192	−0.134693
$146$	0.00539897	0.000446822 0
$147$	−3.64551	−0.300677
$148$	9.30344	0.764738
$149$	−21.7549	−1.78223	−0.891113	−	0.453781i	$-0.850075\pi$
$149$	−21.7549	−1.78223	−0.891113	+	0.453781i	$0.850075\pi$
$150$	1.11524	0.0910587
$151$	1.98802	0.161782	0.0808912	−	0.996723i	$-0.474223\pi$
$151$	1.98802	0.161782	0.0808912	+	0.996723i	$0.474223\pi$
$152$	−1.92848	−0.156421
$153$	16.2421	1.31310
$154$	−9.92852	−0.800063
$155$	1.37724	0.110623
$156$	0.780775	0.0625120
$157$	4.15613	0.331695	0.165848	−	0.986151i	$-0.446964\pi$
$157$	4.15613	0.331695	0.165848	+	0.986151i	$0.446964\pi$
$158$	−5.81992	−0.463008
$159$	−4.12361	−0.327023
$160$	−1.20433	−0.0952106
$161$	−26.6821	−2.10284
$162$	4.47195	0.351349
$163$	−0.0740288	−0.00579838	−0.00289919	−	0.999996i	$-0.500923\pi$
$163$	−0.0740288	−0.00579838	−0.00289919	+	0.999996i	$0.500923\pi$
$164$	−7.26031	−0.566935
$165$	−0.357575	−0.0278372
$166$	4.06611	0.315591
$167$	−8.57618	−0.663645	−0.331822	−	0.943342i	$-0.607663\pi$
$167$	−8.57618	−0.663645	−0.331822	+	0.943342i	$0.607663\pi$
$168$	3.34180	0.257826
$169$	−11.5214	−0.886258
$170$	0.729985	0.0559873
$171$	−2.57791	−0.197138
$172$	6.13003	0.467410
$173$	11.4979	0.874167	0.437084	−	0.899421i	$-0.356011\pi$
$173$	11.4979	0.874167	0.437084	+	0.899421i	$0.356011\pi$
$174$	−1.66098	−0.125919
$175$	−20.0701	−1.51716
$176$	−8.74310	−0.659036
$177$	−2.92520	−0.219872
$178$	−4.91271	−0.368223
$179$	3.74351	0.279803	0.139901	−	0.990165i	$-0.455321\pi$
$179$	3.74351	0.279803	0.139901	+	0.990165i	$0.455321\pi$
$180$	−1.04109	−0.0775986
$181$	0.0260002	0.00193258	0.000966288	−	1.00000i	$-0.499692\pi$
$181$	0.0260002	0.00193258	0.000966288		1.00000i	$0.499692\pi$
$182$	2.87107	0.212818
$183$	−4.84381	−0.358064
$184$	14.0375	1.03486
$185$	1.23209	0.0905852
$186$	1.41041	0.103416
$187$	23.9604	1.75216
$188$	6.14999	0.448534
$189$	9.16861	0.666919
$190$	−0.115861	−0.00840547
$191$	−2.12848	−0.154012	−0.0770059	−	0.997031i	$-0.524536\pi$
$191$	−2.12848	−0.154012	−0.0770059	+	0.997031i	$0.524536\pi$
$192$	0.374463	0.0270245
$193$	2.64183	0.190163	0.0950817	−	0.995469i	$-0.469689\pi$
$193$	2.64183	0.190163	0.0950817	+	0.995469i	$0.469689\pi$
$194$	−0.233351	−0.0167537
$195$	0.103401	0.00740471
$196$	−15.6579	−1.11842
$197$	23.6235	1.68310	0.841552	−	0.540176i	$-0.181642\pi$
$197$	23.6235	1.68310	0.841552	+	0.540176i	$0.181642\pi$
$198$	6.98242	0.496219
$199$	3.51077	0.248872	0.124436	−	0.992228i	$-0.460288\pi$
$199$	3.51077	0.248872	0.124436	+	0.992228i	$0.460288\pi$
$200$	10.5589	0.746627
$201$	0.641775	0.0452673
$202$	3.67820	0.258797
$203$	29.8914	2.09797
$204$	−3.65859	−0.256152
$205$	−0.961513	−0.0671550
$206$	−5.88636	−0.410122
$207$	18.7647	1.30423
$208$	2.52828	0.175304
$209$	−3.80294	−0.263055
$210$	0.200772	0.0138546
$211$	7.39822	0.509314	0.254657	−	0.967031i	$-0.418037\pi$
$211$	7.39822	0.509314	0.254657	+	0.967031i	$0.418037\pi$
$212$	−17.7114	−1.21642
$213$	0.386642	0.0264923
$214$	1.82544	0.124784
$215$	0.811824	0.0553660
$216$	−4.82362	−0.328206
$217$	−25.3821	−1.72305
$218$	3.52818	0.238958
$219$	−0.00358352	−0.000242152 0
$220$	−1.53582	−0.103545
$221$	−6.92872	−0.466076
$222$	1.26176	0.0846841
$223$	−20.4343	−1.36838	−0.684192	−	0.729302i	$-0.739845\pi$
$223$	−20.4343	−1.36838	−0.684192	+	0.729302i	$0.739845\pi$
$224$	22.1954	1.48299
$225$	14.1147	0.940978
$226$	0.582518	0.0387485
$227$	22.1478	1.47000	0.735001	−	0.678066i	$-0.237182\pi$
$227$	22.1478	1.47000	0.735001	+	0.678066i	$0.237182\pi$
$228$	0.580682	0.0384566
$229$	−13.3204	−0.880237	−0.440119	−	0.897940i	$-0.645064\pi$
$229$	−13.3204	−0.880237	−0.440119	+	0.897940i	$0.645064\pi$
$230$	0.843358	0.0556094
$231$	6.58998	0.433589
$232$	−15.7259	−1.03246
$233$	26.8885	1.76152	0.880761	−	0.473562i	$-0.157032\pi$
$233$	26.8885	1.76152	0.880761	+	0.473562i	$0.157032\pi$
$234$	−2.01913	−0.131995
$235$	0.814468	0.0531300
$236$	−12.5641	−0.817851
$237$	3.86293	0.250924
$238$	−13.4534	−0.872052
$239$	2.40770	0.155741	0.0778706	−	0.996963i	$-0.475188\pi$
$239$	2.40770	0.155741	0.0778706	+	0.996963i	$0.475188\pi$
$240$	0.176801	0.0114125
$241$	5.28457	0.340409	0.170204	−	0.985409i	$-0.445557\pi$
$241$	5.28457	0.340409	0.170204	+	0.985409i	$0.445557\pi$
$242$	3.89278	0.250237
$243$	−9.75438	−0.625744
$244$	−20.8047	−1.33188
$245$	−2.07364	−0.132480
$246$	−0.984668	−0.0627802
$247$	1.09971	0.0699729
$248$	13.3535	0.847951
$249$	−2.69885	−0.171033
$250$	1.27493	0.0806339
$251$	−4.16767	−0.263061	−0.131530	−	0.991312i	$-0.541989\pi$
$251$	−4.16767	−0.263061	−0.131530	+	0.991312i	$0.541989\pi$
$252$	19.1870	1.20867
$253$	27.6817	1.74033
$254$	5.61666	0.352421
$255$	−0.484522	−0.0303419
$256$	−4.77135	−0.298209
$257$	18.6392	1.16268	0.581339	−	0.813661i	$-0.302529\pi$
$257$	18.6392	1.16268	0.581339	+	0.813661i	$0.302529\pi$
$258$	0.831375	0.0517592
$259$	−22.7070	−1.41095
$260$	0.444120	0.0275432
$261$	−21.0217	−1.30121
$262$	7.59826	0.469422
$263$	−5.63535	−0.347491	−0.173745	−	0.984791i	$-0.555587\pi$
$263$	−5.63535	−0.347491	−0.173745	+	0.984791i	$0.555587\pi$
$264$	−3.46700	−0.213379
$265$	−2.34559	−0.144088
$266$	2.13529	0.130923
$267$	3.26078	0.199556
$268$	2.75650	0.168380
$269$	21.5704	1.31517	0.657584	−	0.753381i	$-0.271578\pi$
$269$	21.5704	1.31517	0.657584	+	0.753381i	$0.271578\pi$
$270$	−0.289798	−0.0176366
$271$	−16.2690	−0.988274	−0.494137	−	0.869384i	$-0.664516\pi$
$271$	−16.2690	−0.988274	−0.494137	+	0.869384i	$0.664516\pi$
$272$	−11.8471	−0.718336
$273$	−1.90565	−0.115335
$274$	4.10987	0.248286
$275$	20.8220	1.25561
$276$	−4.22680	−0.254424
$277$	−12.8363	−0.771261	−0.385630	−	0.922653i	$-0.626016\pi$
$277$	−12.8363	−0.771261	−0.385630	+	0.922653i	$0.626016\pi$
$278$	−4.03152	−0.241795
$279$	17.8504	1.06868
$280$	1.90088	0.113599
$281$	21.8965	1.30624	0.653119	−	0.757255i	$-0.273460\pi$
$281$	21.8965	1.30624	0.653119	+	0.757255i	$0.273460\pi$
$282$	0.834083	0.0496689
$283$	16.3954	0.974605	0.487302	−	0.873233i	$-0.337981\pi$
$283$	16.3954	0.974605	0.487302	+	0.873233i	$0.337981\pi$
$284$	1.66067	0.0985428
$285$	0.0769021	0.00455529
$286$	−2.97863	−0.176130
$287$	17.7203	1.04600
$288$	−15.6093	−0.919788
$289$	15.4669	0.909819
$290$	−0.944799	−0.0554805
$291$	0.154885	0.00907953
$292$	−0.0153916	−0.000900728 0
$293$	5.01082	0.292735	0.146368	−	0.989230i	$-0.453242\pi$
$293$	5.01082	0.292735	0.146368	+	0.989230i	$0.453242\pi$
$294$	−2.12358	−0.123850
$295$	−1.66391	−0.0968767
$296$	11.9462	0.694359
$297$	−9.51211	−0.551948
$298$	−12.6726	−0.734104
$299$	−8.00482	−0.462931
$300$	−3.17937	−0.183561
$301$	−14.9616	−0.862375
$302$	1.15806	0.0666386
$303$	−2.44138	−0.140253
$304$	1.88034	0.107845
$305$	−2.75525	−0.157765
$306$	9.46133	0.540868
$307$	27.8775	1.59105	0.795525	−	0.605920i	$-0.207195\pi$
$307$	27.8775	1.59105	0.795525	+	0.605920i	$0.207195\pi$
$308$	28.3047	1.61281
$309$	3.90703	0.222263
$310$	0.802268	0.0455658
$311$	23.3331	1.32310	0.661550	−	0.749901i	$-0.269899\pi$
$311$	23.3331	1.32310	0.661550	+	0.749901i	$0.269899\pi$
$312$	1.00256	0.0567590
$313$	−4.75659	−0.268858	−0.134429	−	0.990923i	$-0.542920\pi$
$313$	−4.75659	−0.268858	−0.134429	+	0.990923i	$0.542920\pi$
$314$	2.42102	0.136626
$315$	2.54101	0.143170
$316$	16.5917	0.933357
$317$	29.3882	1.65060	0.825302	−	0.564691i	$-0.191005\pi$
$317$	29.3882	1.65060	0.825302	+	0.564691i	$0.191005\pi$
$318$	−2.40208	−0.134702
$319$	−31.0113	−1.73630
$320$	0.213002	0.0119072
$321$	−1.21162	−0.0676261
$322$	−15.5428	−0.866166
$323$	−5.15307	−0.286724
$324$	−12.7488	−0.708269
$325$	−6.02117	−0.333994
$326$	−0.0431231	−0.00238837
$327$	−2.34180	−0.129502
$328$	−9.32270	−0.514760
$329$	−15.0104	−0.827548
$330$	−0.208294	−0.0114662
$331$	−0.627937	−0.0345145	−0.0172573	−	0.999851i	$-0.505493\pi$
$331$	−0.627937	−0.0345145	−0.0172573	+	0.999851i	$0.505493\pi$
$332$	−11.5919	−0.636186
$333$	15.9692	0.875104
$334$	−4.99578	−0.273357
$335$	0.365054	0.0199450
$336$	−3.25838	−0.177759
$337$	−9.81105	−0.534442	−0.267221	−	0.963635i	$-0.586105\pi$
$337$	−9.81105	−0.534442	−0.267221	+	0.963635i	$0.586105\pi$
$338$	−6.71140	−0.365052
$339$	−0.386642	−0.0209995
$340$	−2.08108	−0.112862
$341$	26.3330	1.42601
$342$	−1.50168	−0.0812015
$343$	9.84388	0.531519
$344$	7.87134	0.424394
$345$	−0.559773	−0.0301371
$346$	6.69772	0.360072
$347$	11.1873	0.600567	0.300284	−	0.953850i	$-0.402919\pi$
$347$	11.1873	0.600567	0.300284	+	0.953850i	$0.402919\pi$
$348$	4.73521	0.253834
$349$	−0.729724	−0.0390612	−0.0195306	−	0.999809i	$-0.506217\pi$
$349$	−0.729724	−0.0390612	−0.0195306	+	0.999809i	$0.506217\pi$
$350$	−11.6912	−0.624920
$351$	2.75065	0.146819
$352$	−23.0269	−1.22734
$353$	12.2140	0.650087	0.325043	−	0.945699i	$-0.394621\pi$
$353$	12.2140	0.650087	0.325043	+	0.945699i	$0.394621\pi$
$354$	−1.70398	−0.0905657
$355$	0.219930	0.0116727
$356$	14.0054	0.742285
$357$	8.92957	0.472603
$358$	2.18066	0.115252
$359$	−12.4536	−0.657275	−0.328637	−	0.944456i	$-0.606589\pi$
$359$	−12.4536	−0.657275	−0.328637	+	0.944456i	$0.606589\pi$
$360$	−1.33683	−0.0704572
$361$	−18.1821	−0.956954
$362$	0.0151456	0.000796033 0
$363$	−2.58380	−0.135614
$364$	−8.18498	−0.429010
$365$	−0.00203838	−0.000106694 0
$366$	−2.82161	−0.147488
$367$	0.926147	0.0483445	0.0241722	−	0.999708i	$-0.492305\pi$
$367$	0.926147	0.0483445	0.0241722	+	0.999708i	$0.492305\pi$
$368$	−13.6871	−0.713488
$369$	−12.4622	−0.648754
$370$	0.717716	0.0373123
$371$	43.2284	2.24431
$372$	−4.02086	−0.208472
$373$	8.98371	0.465159	0.232580	−	0.972577i	$-0.425283\pi$
$373$	8.98371	0.465159	0.232580	+	0.972577i	$0.425283\pi$
$374$	13.9574	0.721719
$375$	−0.846228	−0.0436990
$376$	7.89698	0.407255
$377$	8.96765	0.461858
$378$	5.34088	0.274705
$379$	−4.48086	−0.230166	−0.115083	−	0.993356i	$-0.536713\pi$
$379$	−4.48086	−0.230166	−0.115083	+	0.993356i	$0.536713\pi$
$380$	0.330303	0.0169442
$381$	−3.72801	−0.190992
$382$	−1.23988	−0.0634378
$383$	2.10826	0.107727	0.0538636	−	0.998548i	$-0.482846\pi$
$383$	2.10826	0.107727	0.0538636	+	0.998548i	$0.482846\pi$
$384$	4.45262	0.227222
$385$	3.74851	0.191042
$386$	1.53892	0.0783288
$387$	10.5221	0.534866
$388$	0.665250	0.0337730
$389$	−35.9481	−1.82264	−0.911320	−	0.411699i	$-0.864935\pi$
$389$	−35.9481	−1.82264	−0.911320	+	0.411699i	$0.864935\pi$
$390$	0.0602331	0.00305002
$391$	37.5093	1.89693
$392$	−20.1057	−1.01549
$393$	−5.04329	−0.254400
$394$	13.7611	0.693275
$395$	2.19731	0.110559
$396$	−19.9058	−1.00031
$397$	−27.3846	−1.37439	−0.687197	−	0.726471i	$-0.741159\pi$
$397$	−27.3846	−1.37439	−0.687197	+	0.726471i	$0.741159\pi$
$398$	2.04509	0.102511
$399$	−1.41728	−0.0709527
$400$	−10.2953	−0.514766
$401$	−3.95340	−0.197424	−0.0987118	−	0.995116i	$-0.531472\pi$
$401$	−3.95340	−0.197424	−0.0987118	+	0.995116i	$0.531472\pi$
$402$	0.373845	0.0186457
$403$	−7.61481	−0.379321
$404$	−10.4860	−0.521698
$405$	−1.68838	−0.0838964
$406$	17.4123	0.864159
$407$	23.5577	1.16771
$408$	−4.69786	−0.232579
$409$	18.1366	0.896796	0.448398	−	0.893834i	$-0.351995\pi$
$409$	18.1366	0.896796	0.448398	+	0.893834i	$0.351995\pi$
$410$	−0.560099	−0.0276613
$411$	−2.72789	−0.134557
$412$	16.7811	0.826747
$413$	30.6653	1.50894
$414$	10.9308	0.537218
$415$	−1.53516	−0.0753579
$416$	6.65877	0.326473
$417$	2.67589	0.131039
$418$	−2.21528	−0.108353
$419$	7.56619	0.369632	0.184816	−	0.982773i	$-0.440831\pi$
$419$	7.56619	0.369632	0.184816	+	0.982773i	$0.440831\pi$
$420$	−0.572371	−0.0279289
$421$	26.7502	1.30372	0.651862	−	0.758338i	$-0.273988\pi$
$421$	26.7502	1.30372	0.651862	+	0.758338i	$0.273988\pi$
$422$	4.30960	0.209788
$423$	10.5563	0.513266
$424$	−22.7425	−1.10447
$425$	28.2143	1.36859
$426$	0.225226	0.0109122
$427$	50.7783	2.45734
$428$	−5.20405	−0.251547
$429$	1.97704	0.0954525
$430$	0.472903	0.0228054
$431$	29.0866	1.40105	0.700526	−	0.713627i	$-0.252949\pi$
$431$	29.0866	1.40105	0.700526	+	0.713627i	$0.252949\pi$
$432$	4.70321	0.226283
$433$	−2.78065	−0.133629	−0.0668147	−	0.997765i	$-0.521284\pi$
$433$	−2.78065	−0.133629	−0.0668147	+	0.997765i	$0.521284\pi$
$434$	−14.7855	−0.709728
$435$	0.627103	0.0300673
$436$	−10.0583	−0.481706
$437$	−5.95339	−0.284789
$438$	−0.00208747	−9.97431e−5 0
$439$	31.4792	1.50242	0.751209	−	0.660064i	$-0.229471\pi$
$439$	31.4792	1.50242	0.751209	+	0.660064i	$0.229471\pi$
$440$	−1.97210	−0.0940160
$441$	−26.8764	−1.27983
$442$	−4.03611	−0.191978
$443$	5.88974	0.279830	0.139915	−	0.990164i	$-0.455317\pi$
$443$	5.88974	0.279830	0.139915	+	0.990164i	$0.455317\pi$
$444$	−3.59710	−0.170711
$445$	1.85479	0.0879257
$446$	−11.9034	−0.563641
$447$	8.41134	0.397843
$448$	−3.92555	−0.185465
$449$	19.5987	0.924919	0.462459	−	0.886640i	$-0.346967\pi$
$449$	19.5987	0.924919	0.462459	+	0.886640i	$0.346967\pi$
$450$	8.22205	0.387591
$451$	−18.3842	−0.865679
$452$	−1.66067	−0.0781115
$453$	−0.768651	−0.0361144
$454$	12.9015	0.605498
$455$	−1.08397	−0.0508173
$456$	0.745633	0.0349175
$457$	−36.7462	−1.71892	−0.859458	−	0.511206i	$-0.829199\pi$
$457$	−36.7462	−1.71892	−0.859458	+	0.511206i	$0.829199\pi$
$458$	−7.75938	−0.362572
$459$	−12.8891	−0.601613
$460$	−2.40429	−0.112100
$461$	17.2699	0.804340	0.402170	−	0.915565i	$-0.368256\pi$
$461$	17.2699	0.804340	0.402170	+	0.915565i	$0.368256\pi$
$462$	3.83878	0.178596
$463$	−6.14823	−0.285732	−0.142866	−	0.989742i	$-0.545632\pi$
$463$	−6.14823	−0.285732	−0.142866	+	0.989742i	$0.545632\pi$
$464$	15.3334	0.711834
$465$	−0.532499	−0.0246941
$466$	15.6630	0.725575
$467$	−38.8199	−1.79637	−0.898184	−	0.439619i	$-0.855114\pi$
$467$	−38.8199	−1.79637	−0.898184	+	0.439619i	$0.855114\pi$
$468$	5.75624	0.266082
$469$	−6.72782	−0.310662
$470$	0.474443	0.0218844
$471$	−1.60694	−0.0740437
$472$	−16.1331	−0.742585
$473$	15.5222	0.713710
$474$	2.25023	0.103356
$475$	−4.47810	−0.205469
$476$	38.3535	1.75793
$477$	−30.4012	−1.39197
$478$	1.40253	0.0641502
$479$	−37.9110	−1.73220	−0.866099	−	0.499872i	$-0.833380\pi$
$479$	−37.9110	−1.73220	−0.866099	+	0.499872i	$0.833380\pi$
$480$	0.465644	0.0212537
$481$	−6.81228	−0.310613
$482$	3.07836	0.140215
$483$	10.3164	0.469413
$484$	−11.0977	−0.504442
$485$	0.0881018	0.00400050
$486$	−5.68210	−0.257745
$487$	−6.85880	−0.310802	−0.155401	−	0.987851i	$-0.549667\pi$
$487$	−6.85880	−0.310802	−0.155401	+	0.987851i	$0.549667\pi$
$488$	−26.7146	−1.20931
$489$	0.0286226	0.00129436
$490$	−1.20793	−0.0545689
$491$	12.8454	0.579706	0.289853	−	0.957071i	$-0.406394\pi$
$491$	12.8454	0.579706	0.289853	+	0.957071i	$0.406394\pi$
$492$	2.80714	0.126556
$493$	−42.0210	−1.89253
$494$	0.640601	0.0288220
$495$	−2.63621	−0.118489
$496$	−13.0202	−0.584625
$497$	−4.05323	−0.181812
$498$	−1.57213	−0.0704487
$499$	28.3173	1.26766	0.633828	−	0.773474i	$-0.281483\pi$
$499$	28.3173	1.26766	0.633828	+	0.773474i	$0.281483\pi$
$500$	−3.63464	−0.162546
$501$	3.31591	0.148144
$502$	−2.42774	−0.108355
$503$	10.1700	0.453459	0.226730	−	0.973958i	$-0.427197\pi$
$503$	10.1700	0.453459	0.226730	+	0.973958i	$0.427197\pi$
$504$	24.6373	1.09743
$505$	−1.38870	−0.0617965
$506$	16.1251	0.716848
$507$	4.45464	0.197837
$508$	−16.0123	−0.710429
$509$	−18.6906	−0.828445	−0.414223	−	0.910176i	$-0.635947\pi$
$509$	−18.6906	−0.828445	−0.414223	+	0.910176i	$0.635947\pi$
$510$	−0.282243	−0.0124979
$511$	0.0375666	0.00166185
$512$	20.2528	0.895058
$513$	2.04573	0.0903211
$514$	10.8577	0.478910
$515$	2.22239	0.0979304
$516$	−2.37013	−0.104339
$517$	15.5727	0.684887
$518$	−13.2273	−0.581173
$519$	−4.44556	−0.195139
$520$	0.570278	0.0250084
$521$	−19.9522	−0.874121	−0.437060	−	0.899432i	$-0.643980\pi$
$521$	−19.9522	−0.874121	−0.437060	+	0.899432i	$0.643980\pi$
$522$	−12.2455	−0.535973
$523$	−37.7838	−1.65217	−0.826084	−	0.563547i	$-0.809436\pi$
$523$	−37.7838	−1.65217	−0.826084	+	0.563547i	$0.809436\pi$
$524$	−21.6615	−0.946287
$525$	7.75994	0.338672
$526$	−3.28270	−0.143132
$527$	35.6818	1.55432
$528$	3.38045	0.147115
$529$	20.3349	0.884125
$530$	−1.36635	−0.0593504
$531$	−21.5660	−0.935883
$532$	−6.08738	−0.263921
$533$	5.31623	0.230272
$534$	1.89946	0.0821977
$535$	−0.689194	−0.0297964
$536$	3.53952	0.152884
$537$	−1.44740	−0.0624598
$538$	12.5651	0.541721
$539$	−39.6482	−1.70777
$540$	0.826172	0.0355528
$541$	−12.7430	−0.547866	−0.273933	−	0.961749i	$-0.588325\pi$
$541$	−12.7430	−0.547866	−0.273933	+	0.961749i	$0.588325\pi$
$542$	−9.47702	−0.407073
$543$	−0.0100528	−0.000431405 0
$544$	−31.2020	−1.33777
$545$	−1.33206	−0.0570593
$546$	−1.11008	−0.0475068
$547$	24.5699	1.05053	0.525266	−	0.850938i	$-0.323966\pi$
$547$	24.5699	1.05053	0.525266	+	0.850938i	$0.323966\pi$
$548$	−11.7166	−0.500509
$549$	−35.7108	−1.52410
$550$	12.1292	0.517190
$551$	6.66947	0.284129
$552$	−5.42748	−0.231009
$553$	−40.4956	−1.72205
$554$	−7.47740	−0.317684
$555$	−0.476379	−0.0202212
$556$	11.4933	0.487423
$557$	31.0287	1.31473	0.657363	−	0.753574i	$-0.271672\pi$
$557$	31.0287	1.31473	0.657363	+	0.753574i	$0.271672\pi$
$558$	10.3982	0.440191
$559$	−4.48860	−0.189848
$560$	−1.85343	−0.0783217
$561$	−9.26411	−0.391131
$562$	12.7551	0.538043
$563$	0.554883	0.0233855	0.0116928	−	0.999932i	$-0.496278\pi$
$563$	0.554883	0.0233855	0.0116928	+	0.999932i	$0.496278\pi$
$564$	−2.37784	−0.100125
$565$	−0.219930	−0.00925251
$566$	9.55061	0.401442
$567$	31.1163	1.30676
$568$	2.13241	0.0894739
$569$	−5.33548	−0.223675	−0.111837	−	0.993727i	$-0.535674\pi$
$569$	−5.33548	−0.223675	−0.111837	+	0.993727i	$0.535674\pi$
$570$	0.0447969	0.00187634
$571$	11.0740	0.463434	0.231717	−	0.972783i	$-0.425566\pi$
$571$	11.0740	0.463434	0.231717	+	0.972783i	$0.425566\pi$
$572$	8.49162	0.355053
$573$	0.822962	0.0343797
$574$	10.3224	0.430850
$575$	32.5962	1.35936
$576$	2.76072	0.115030
$577$	−7.22582	−0.300815	−0.150407	−	0.988624i	$-0.548059\pi$
$577$	−7.22582	−0.300815	−0.150407	+	0.988624i	$0.548059\pi$
$578$	9.00976	0.374757
$579$	−1.02144	−0.0424498
$580$	2.69348	0.111841
$581$	28.2924	1.17377
$582$	0.0902235	0.00373988
$583$	−44.8479	−1.85741
$584$	−0.0197639	−0.000817834 0
$585$	0.762322	0.0315182
$586$	2.91890	0.120578
$587$	24.5652	1.01391	0.506957	−	0.861971i	$-0.330770\pi$
$587$	24.5652	1.01391	0.506957	+	0.861971i	$0.330770\pi$
$588$	6.05400	0.249663
$589$	−5.66333	−0.233353
$590$	−0.969259	−0.0399038
$591$	−9.13384	−0.375716
$592$	−11.6480	−0.478730
$593$	−9.87971	−0.405711	−0.202855	−	0.979209i	$-0.565022\pi$
$593$	−9.87971	−0.405711	−0.202855	+	0.979209i	$0.565022\pi$
$594$	−5.54097	−0.227349
$595$	5.07932	0.208232
$596$	36.1277	1.47985
$597$	−1.35741	−0.0555552
$598$	−4.66295	−0.190682
$599$	18.0105	0.735889	0.367945	−	0.929848i	$-0.380062\pi$
$599$	18.0105	0.735889	0.367945	+	0.929848i	$0.380062\pi$
$600$	−4.08252	−0.166668
$601$	16.0843	0.656093	0.328046	−	0.944662i	$-0.393610\pi$
$601$	16.0843	0.656093	0.328046	+	0.944662i	$0.393610\pi$
$602$	−8.71543	−0.355214
$603$	4.73147	0.192680
$604$	−3.30144	−0.134334
$605$	−1.46972	−0.0597525
$606$	−1.42215	−0.0577708
$607$	8.03638	0.326187	0.163093	−	0.986611i	$-0.447853\pi$
$607$	8.03638	0.326187	0.163093	+	0.986611i	$0.447853\pi$
$608$	4.95230	0.200842
$609$	−11.5573	−0.468325
$610$	−1.60498	−0.0649839
$611$	−4.50322	−0.182181
$612$	−26.9728	−1.09031
$613$	24.9737	1.00868	0.504339	−	0.863506i	$-0.331736\pi$
$613$	24.9737	1.00868	0.504339	+	0.863506i	$0.331736\pi$
$614$	16.2391	0.655358
$615$	0.371761	0.0149909
$616$	36.3451	1.46438
$617$	−17.5251	−0.705533	−0.352767	−	0.935711i	$-0.614759\pi$
$617$	−17.5251	−0.705533	−0.352767	+	0.935711i	$0.614759\pi$
$618$	2.27591	0.0915507
$619$	30.6642	1.23250	0.616250	−	0.787551i	$-0.288651\pi$
$619$	30.6642	1.23250	0.616250	+	0.787551i	$0.288651\pi$
$620$	−2.28715	−0.0918540
$621$	−14.8909	−0.597552
$622$	13.5920	0.544988
$623$	−34.1832	−1.36952
$624$	−0.977538	−0.0391328
$625$	24.2768	0.971072
$626$	−2.77080	−0.110743
$627$	1.47038	0.0587212
$628$	−6.90197	−0.275419
$629$	31.9213	1.27278
$630$	1.48019	0.0589720
$631$	23.6822	0.942775	0.471387	−	0.881926i	$-0.343753\pi$
$631$	23.6822	0.942775	0.471387	+	0.881926i	$0.343753\pi$
$632$	21.3048	0.847460
$633$	−2.86046	−0.113693
$634$	17.1191	0.679888
$635$	−2.12057	−0.0841522
$636$	6.84796	0.271539
$637$	11.4652	0.454268
$638$	−18.0646	−0.715186
$639$	2.85051	0.112764
$640$	2.53274	0.100115
$641$	35.8740	1.41694	0.708469	−	0.705742i	$-0.249386\pi$
$641$	35.8740	1.41694	0.708469	+	0.705742i	$0.249386\pi$
$642$	−0.705791	−0.0278554
$643$	−13.1289	−0.517755	−0.258877	−	0.965910i	$-0.583353\pi$
$643$	−13.1289	−0.517755	−0.258877	+	0.965910i	$0.583353\pi$
$644$	44.3102	1.74607
$645$	−0.313885	−0.0123592
$646$	−3.00176	−0.118103
$647$	−34.7553	−1.36637	−0.683185	−	0.730245i	$-0.739406\pi$
$647$	−34.7553	−1.36637	−0.683185	+	0.730245i	$0.739406\pi$
$648$	−16.3703	−0.643087
$649$	−31.8142	−1.24881
$650$	−3.50744	−0.137573
$651$	9.81378	0.384632
$652$	0.122938	0.00481461
$653$	−16.4593	−0.644102	−0.322051	−	0.946722i	$-0.604372\pi$
$653$	−16.4593	−0.644102	−0.322051	+	0.946722i	$0.604372\pi$
$654$	−1.36414	−0.0533422
$655$	−2.86872	−0.112090
$656$	9.08998	0.354904
$657$	−0.0264194	−0.00103072
$658$	−8.74381	−0.340869
$659$	4.88905	0.190450	0.0952252	−	0.995456i	$-0.469643\pi$
$659$	4.88905	0.190450	0.0952252	+	0.995456i	$0.469643\pi$
$660$	0.593815	0.0231142
$661$	−38.8007	−1.50917	−0.754587	−	0.656200i	$-0.772163\pi$
$661$	−38.8007	−1.50917	−0.754587	+	0.656200i	$0.772163\pi$
$662$	−0.365785	−0.0142166
$663$	2.67894	0.104041
$664$	−14.8847	−0.577638
$665$	−0.806176	−0.0312622
$666$	9.30232	0.360458
$667$	−48.5473	−1.87976
$668$	14.2422	0.551048
$669$	7.90077	0.305462
$670$	0.212651	0.00821541
$671$	−52.6807	−2.03372
$672$	−8.58167	−0.331045
$673$	−25.0068	−0.963940	−0.481970	−	0.876188i	$-0.660079\pi$
$673$	−25.0068	−0.963940	−0.481970	+	0.876188i	$0.660079\pi$
$674$	−5.71512	−0.220138
$675$	−11.2009	−0.431121
$676$	19.1332	0.735892
$677$	38.8188	1.49193	0.745964	−	0.665986i	$-0.231989\pi$
$677$	38.8188	1.49193	0.745964	+	0.665986i	$0.231989\pi$
$678$	−0.225226	−0.00864976
$679$	−1.62369	−0.0623113
$680$	−2.67224	−0.102476
$681$	−8.56328	−0.328145
$682$	15.3394	0.587378
$683$	−19.8900	−0.761070	−0.380535	−	0.924766i	$-0.624260\pi$
$683$	−19.8900	−0.761070	−0.380535	+	0.924766i	$0.624260\pi$
$684$	4.28106	0.163691
$685$	−1.55168	−0.0592866
$686$	5.73424	0.218934
$687$	5.15023	0.196493
$688$	−7.67485	−0.292601
$689$	12.9688	0.494073
$690$	−0.326078	−0.0124136
$691$	11.3804	0.432930	0.216465	−	0.976290i	$-0.430547\pi$
$691$	11.3804	0.432930	0.216465	+	0.976290i	$0.430547\pi$
$692$	−19.0942	−0.725853
$693$	48.5844	1.84557
$694$	6.51682	0.247375
$695$	1.52210	0.0577365
$696$	6.08031	0.230473
$697$	−24.9110	−0.943573
$698$	−0.425078	−0.0160894
$699$	−10.3962	−0.393221
$700$	33.3298	1.25975
$701$	0.845121	0.0319198	0.0159599	−	0.999873i	$-0.494920\pi$
$701$	0.845121	0.0319198	0.0159599	+	0.999873i	$0.494920\pi$
$702$	1.60230	0.0604751
$703$	−5.06646	−0.191085
$704$	4.07262	0.153492
$705$	−0.314908	−0.0118601
$706$	7.11489	0.267772
$707$	25.5933	0.962536
$708$	4.85780	0.182567
$709$	12.5283	0.470509	0.235255	−	0.971934i	$-0.424408\pi$
$709$	12.5283	0.470509	0.235255	+	0.971934i	$0.424408\pi$
$710$	0.128113	0.00480800
$711$	28.4793	1.06806
$712$	17.9838	0.673973
$713$	41.2235	1.54383
$714$	5.20164	0.194666
$715$	1.12458	0.0420569
$716$	−6.21674	−0.232330
$717$	−0.930918	−0.0347658
$718$	−7.25444	−0.270733
$719$	45.1581	1.68411	0.842056	−	0.539390i	$-0.181345\pi$
$719$	45.1581	1.68411	0.842056	+	0.539390i	$0.181345\pi$
$720$	1.30346	0.0485771
$721$	−40.9579	−1.52535
$722$	−10.5914	−0.394172
$723$	−2.04324	−0.0759887
$724$	−0.0431777	−0.00160469
$725$	−36.5169	−1.35620
$726$	−1.50511	−0.0558599
$727$	36.8673	1.36733	0.683667	−	0.729794i	$-0.260384\pi$
$727$	36.8673	1.36733	0.683667	+	0.729794i	$0.260384\pi$
$728$	−10.5100	−0.389528
$729$	−19.2593	−0.713308
$730$	−0.00118739	−4.39474e−5 0
$731$	21.0329	0.777929
$732$	8.04398	0.297314
$733$	−14.4256	−0.532821	−0.266411	−	0.963860i	$-0.585838\pi$
$733$	−14.4256	−0.532821	−0.266411	+	0.963860i	$0.585838\pi$
$734$	0.539497	0.0199132
$735$	0.801756	0.0295732
$736$	−36.0479	−1.32874
$737$	6.97987	0.257107
$738$	−7.25944	−0.267224
$739$	42.5446	1.56503	0.782514	−	0.622633i	$-0.213937\pi$
$739$	42.5446	1.56503	0.782514	+	0.622633i	$0.213937\pi$
$740$	−2.04610	−0.0752162
$741$	−0.425194	−0.0156199
$742$	25.1813	0.924435
$743$	41.5054	1.52269	0.761343	−	0.648349i	$-0.224540\pi$
$743$	41.5054	1.52269	0.761343	+	0.648349i	$0.224540\pi$
$744$	−5.16304	−0.189286
$745$	4.78454	0.175292
$746$	5.23318	0.191600
$747$	−19.8972	−0.728000
$748$	−39.7904	−1.45488
$749$	12.7016	0.464106
$750$	−0.492943	−0.0179997
$751$	−33.2412	−1.21299	−0.606495	−	0.795087i	$-0.707425\pi$
$751$	−33.2412	−1.21299	−0.606495	+	0.795087i	$0.707425\pi$
$752$	−7.69985	−0.280785
$753$	1.61140	0.0587226
$754$	5.22382	0.190240
$755$	−0.437224	−0.0159122
$756$	−15.2261	−0.553767
$757$	24.1336	0.877150	0.438575	−	0.898694i	$-0.355483\pi$
$757$	24.1336	0.877150	0.438575	+	0.898694i	$0.355483\pi$
$758$	−2.61018	−0.0948061
$759$	−10.7029	−0.388491
$760$	0.424131	0.0153848
$761$	23.8521	0.864640	0.432320	−	0.901720i	$-0.357695\pi$
$761$	23.8521	0.864640	0.432320	+	0.901720i	$0.357695\pi$
$762$	−2.17164	−0.0786701
$763$	24.5495	0.888750
$764$	3.53472	0.127882
$765$	−3.57212	−0.129150
$766$	1.22810	0.0443731
$767$	9.19982	0.332186
$768$	1.84481	0.0665687
$769$	0.409827	0.0147787	0.00738937	−	0.999973i	$-0.497648\pi$
$769$	0.409827	0.0147787	0.00738937	+	0.999973i	$0.497648\pi$
$770$	2.18358	0.0786906
$771$	−7.20668	−0.259542
$772$	−4.38722	−0.157900
$773$	−23.8297	−0.857094	−0.428547	−	0.903520i	$-0.640974\pi$
$773$	−23.8297	−0.857094	−0.428547	+	0.903520i	$0.640974\pi$
$774$	6.12929	0.220313
$775$	31.0081	1.11384
$776$	0.854223	0.0306648
$777$	8.77950	0.314963
$778$	−20.9404	−0.750750
$779$	3.95382	0.141660
$780$	−0.171716	−0.00614840
$781$	4.20508	0.150469
$782$	21.8499	0.781350
$783$	16.6820	0.596167
$784$	19.6038	0.700137
$785$	−0.914056	−0.0326241
$786$	−2.93781	−0.104788
$787$	40.2936	1.43631	0.718156	−	0.695883i	$-0.244987\pi$
$787$	40.2936	1.43631	0.718156	+	0.695883i	$0.244987\pi$
$788$	−39.2309	−1.39754
$789$	2.17886	0.0775696
$790$	1.27997	0.0455394
$791$	4.05323	0.144116
$792$	−25.5603	−0.908247
$793$	15.2339	0.540971
$794$	−15.9520	−0.566116
$795$	0.906903	0.0321645
$796$	−5.83024	−0.206647
$797$	−19.1603	−0.678692	−0.339346	−	0.940662i	$-0.610206\pi$
$797$	−19.1603	−0.678692	−0.339346	+	0.940662i	$0.610206\pi$
$798$	−0.825591	−0.0292256
$799$	21.1014	0.746513
$800$	−27.1150	−0.958661
$801$	24.0400	0.849411
$802$	−2.30293	−0.0813193
$803$	−0.0389740	−0.00137536
$804$	−1.06578	−0.0375871
$805$	5.86818	0.206826
$806$	−4.43576	−0.156243
$807$	−8.34001	−0.293582
$808$	−13.4647	−0.473686
$809$	24.8622	0.874108	0.437054	−	0.899435i	$-0.356022\pi$
$809$	24.8622	0.874108	0.437054	+	0.899435i	$0.356022\pi$
$810$	−0.983513	−0.0345571
$811$	−45.3518	−1.59252	−0.796258	−	0.604957i	$-0.793190\pi$
$811$	−45.3518	−1.59252	−0.796258	+	0.604957i	$0.793190\pi$
$812$	−49.6399	−1.74202
$813$	6.29030	0.220610
$814$	13.7228	0.480984
$815$	0.0162811	0.000570303 0
$816$	4.58059	0.160353
$817$	−3.33829	−0.116792
$818$	10.5649	0.369393
$819$	−14.0493	−0.490924
$820$	1.59676	0.0557612
$821$	−31.0727	−1.08444	−0.542222	−	0.840236i	$-0.682417\pi$
$821$	−31.0727	−1.08444	−0.542222	+	0.840236i	$0.682417\pi$
$822$	−1.58905	−0.0554244
$823$	−3.83025	−0.133514	−0.0667571	−	0.997769i	$-0.521265\pi$
$823$	−3.83025	−0.133514	−0.0667571	+	0.997769i	$0.521265\pi$
$824$	21.5480	0.750661
$825$	−8.05066	−0.280288
$826$	17.8631	0.621537
$827$	21.7926	0.757801	0.378901	−	0.925437i	$-0.376302\pi$
$827$	21.7926	0.757801	0.378901	+	0.925437i	$0.376302\pi$
$828$	−31.1620	−1.08295
$829$	34.5983	1.20165	0.600825	−	0.799381i	$-0.294839\pi$
$829$	34.5983	1.20165	0.600825	+	0.799381i	$0.294839\pi$
$830$	−0.894257	−0.0310401
$831$	4.96307	0.172167
$832$	−1.17769	−0.0408292
$833$	−53.7242	−1.86143
$834$	1.55876	0.0539753
$835$	1.88616	0.0652731
$836$	6.31544	0.218424
$837$	−14.1654	−0.489628
$838$	4.40744	0.152253
$839$	−17.8596	−0.616582	−0.308291	−	0.951292i	$-0.599757\pi$
$839$	−17.8596	−0.616582	−0.308291	+	0.951292i	$0.599757\pi$
$840$	−0.734961	−0.0253586
$841$	25.3866	0.875400
$842$	15.5825	0.537007
$843$	−8.46612	−0.291589
$844$	−12.2860	−0.422902
$845$	2.53389	0.0871683
$846$	6.14925	0.211416
$847$	27.0864	0.930699
$848$	22.1748	0.761486
$849$	−6.33915	−0.217559
$850$	16.4353	0.563727
$851$	36.8789	1.26419
$852$	−0.642086	−0.0219975
$853$	−28.6937	−0.982455	−0.491227	−	0.871031i	$-0.663452\pi$
$853$	−28.6937	−0.982455	−0.491227	+	0.871031i	$0.663452\pi$
$854$	29.5793	1.01218
$855$	0.566959	0.0193896
$856$	−6.68233	−0.228397
$857$	13.8009	0.471431	0.235715	−	0.971822i	$-0.424257\pi$
$857$	13.8009	0.471431	0.235715	+	0.971822i	$0.424257\pi$
$858$	1.15166	0.0393171
$859$	−24.1456	−0.823837	−0.411918	−	0.911221i	$-0.635141\pi$
$859$	−24.1456	−0.823837	−0.411918	+	0.911221i	$0.635141\pi$
$860$	−1.34817	−0.0459724
$861$	−6.85143	−0.233496
$862$	16.9435	0.577097
$863$	29.4811	1.00355	0.501774	−	0.864998i	$-0.332681\pi$
$863$	29.4811	1.00355	0.501774	+	0.864998i	$0.332681\pi$
$864$	12.3869	0.421412
$865$	−2.52872	−0.0859792
$866$	−1.61978	−0.0550423
$867$	−5.98016	−0.203097
$868$	42.1513	1.43071
$869$	42.0128	1.42519
$870$	0.365299	0.0123848
$871$	−2.01839	−0.0683907
$872$	−12.9155	−0.437374
$873$	1.14189	0.0386470
$874$	−3.46796	−0.117305
$875$	8.87113	0.299899
$876$	0.00595106	0.000201068 0
$877$	36.5603	1.23455	0.617277	−	0.786746i	$-0.288236\pi$
$877$	36.5603	1.23455	0.617277	+	0.786746i	$0.288236\pi$
$878$	18.3372	0.618850
$879$	−1.93739	−0.0653467
$880$	1.92287	0.0648198
$881$	5.16594	0.174045	0.0870224	−	0.996206i	$-0.472265\pi$
$881$	5.16594	0.174045	0.0870224	+	0.996206i	$0.472265\pi$
$882$	−15.6560	−0.527166
$883$	−55.1185	−1.85488	−0.927442	−	0.373966i	$-0.877998\pi$
$883$	−55.1185	−1.85488	−0.927442	+	0.373966i	$0.877998\pi$
$884$	11.5063	0.387000
$885$	0.643338	0.0216256
$886$	3.43088	0.115263
$887$	−6.82181	−0.229054	−0.114527	−	0.993420i	$-0.536535\pi$
$887$	−6.82181	−0.229054	−0.114527	+	0.993420i	$0.536535\pi$
$888$	−4.61891	−0.155000
$889$	39.0813	1.31075
$890$	1.08045	0.0362168
$891$	−32.2820	−1.08149
$892$	33.9347	1.13622
$893$	−3.34916	−0.112075
$894$	4.89976	0.163873
$895$	−0.823308	−0.0275202
$896$	−46.6775	−1.55938
$897$	3.09500	0.103339
$898$	11.4166	0.380976
$899$	−46.1819	−1.54025
$900$	−23.4398	−0.781328
$901$	−60.7699	−2.02454
$902$	−10.7091	−0.356575
$903$	5.78480	0.192506
$904$	−2.13241	−0.0709229
$905$	−0.00571820	−0.000190080 0
$906$	−0.447753	−0.0148756
$907$	−10.5681	−0.350908	−0.175454	−	0.984488i	$-0.556139\pi$
$907$	−10.5681	−0.350908	−0.175454	+	0.984488i	$0.556139\pi$
$908$	−36.7803	−1.22060
$909$	−17.9990	−0.596989
$910$	−0.631432	−0.0209318
$911$	37.7700	1.25138	0.625688	−	0.780073i	$-0.284818\pi$
$911$	37.7700	1.25138	0.625688	+	0.780073i	$0.284818\pi$
$912$	−0.727020	−0.0240740
$913$	−29.3524	−0.971421
$914$	−21.4053	−0.708026
$915$	1.06530	0.0352176
$916$	22.1208	0.730893
$917$	52.8695	1.74591
$918$	−7.50815	−0.247806
$919$	−18.3660	−0.605838	−0.302919	−	0.953016i	$-0.597961\pi$
$919$	−18.3660	−0.605838	−0.302919	+	0.953016i	$0.597961\pi$
$920$	−3.08726	−0.101784
$921$	−10.7786	−0.355167
$922$	10.0600	0.331310
$923$	−1.21600	−0.0400250
$924$	−10.9438	−0.360024
$925$	27.7401	0.912088
$926$	−3.58146	−0.117694
$927$	28.8044	0.946062
$928$	40.3838	1.32566
$929$	−51.0959	−1.67640	−0.838202	−	0.545360i	$-0.816393\pi$
$929$	−51.0959	−1.67640	−0.838202	+	0.545360i	$0.816393\pi$
$930$	−0.310191	−0.0101716
$931$	8.52697	0.279460
$932$	−44.6529	−1.46265
$933$	−9.02157	−0.295353
$934$	−22.6133	−0.739929
$935$	−5.26961	−0.172335
$936$	7.39138	0.241595
$937$	−14.5804	−0.476321	−0.238160	−	0.971226i	$-0.576544\pi$
$937$	−14.5804	−0.476321	−0.238160	+	0.971226i	$0.576544\pi$
$938$	−3.91908	−0.127962
$939$	1.83910	0.0600167
$940$	−1.35256	−0.0441158
$941$	−35.2770	−1.15000	−0.574999	−	0.818154i	$-0.694997\pi$
$941$	−35.2770	−1.15000	−0.574999	+	0.818154i	$0.694997\pi$
$942$	−0.936069	−0.0304988
$943$	−28.7799	−0.937204
$944$	15.7303	0.511979
$945$	−2.01645	−0.0655951
$946$	9.04194	0.293979
$947$	52.8392	1.71704	0.858522	−	0.512777i	$-0.171383\pi$
$947$	52.8392	1.71704	0.858522	+	0.512777i	$0.171383\pi$
$948$	−6.41506	−0.208351
$949$	0.0112703	0.000365848 0
$950$	−2.60857	−0.0846333
$951$	−11.3627	−0.368461
$952$	49.2484	1.59615
$953$	−20.9073	−0.677254	−0.338627	−	0.940921i	$-0.609963\pi$
$953$	−20.9073	−0.677254	−0.338627	+	0.940921i	$0.609963\pi$
$954$	−17.7092	−0.573358
$955$	0.468117	0.0151479
$956$	−3.99840	−0.129318
$957$	11.9903	0.387590
$958$	−22.0839	−0.713497
$959$	28.5969	0.923443
$960$	−0.0823555	−0.00265801
$961$	8.21502	0.265001
$962$	−3.96828	−0.127942
$963$	−8.93264	−0.287850
$964$	−8.77593	−0.282654
$965$	−0.581018	−0.0187036
$966$	6.00950	0.193353
$967$	43.4500	1.39726	0.698628	−	0.715485i	$-0.253794\pi$
$967$	43.4500	1.39726	0.698628	+	0.715485i	$0.253794\pi$
$968$	−14.2502	−0.458018
$969$	1.99239	0.0640049
$970$	0.0513209	0.00164781
$971$	−39.2461	−1.25947	−0.629734	−	0.776811i	$-0.716836\pi$
$971$	−39.2461	−1.25947	−0.629734	+	0.776811i	$0.716836\pi$
$972$	16.1988	0.519578
$973$	−28.0518	−0.899299
$974$	−3.99537	−0.128020
$975$	2.32804	0.0745569
$976$	26.0477	0.833766
$977$	−19.3645	−0.619524	−0.309762	−	0.950814i	$-0.600249\pi$
$977$	−19.3645	−0.619524	−0.309762	+	0.950814i	$0.600249\pi$
$978$	0.0166732	0.000533151 0
$979$	35.4638	1.13343
$980$	3.44364	0.110003
$981$	−17.2649	−0.551225
$982$	7.48269	0.238782
$983$	42.1334	1.34385	0.671924	−	0.740620i	$-0.265468\pi$
$983$	42.1334	1.34385	0.671924	+	0.740620i	$0.265468\pi$
$984$	3.60455	0.114909
$985$	−5.19551	−0.165543
$986$	−24.4780	−0.779539
$987$	5.80364	0.184732
$988$	−1.82626	−0.0581010
$989$	24.2995	0.772679
$990$	−1.53564	−0.0488058
$991$	−45.3200	−1.43964	−0.719819	−	0.694162i	$-0.755775\pi$
$991$	−45.3200	−1.43964	−0.719819	+	0.694162i	$0.755775\pi$
$992$	−34.2916	−1.08876
$993$	0.242787	0.00770460
$994$	−2.36108	−0.0748889
$995$	−0.772122	−0.0244779
$996$	4.48190	0.142014
$997$	−28.8687	−0.914282	−0.457141	−	0.889394i	$-0.651127\pi$
$997$	−28.8687	−0.914282	−0.457141	+	0.889394i	$0.651127\pi$
$998$	16.4953	0.522151
$999$	−12.6725	−0.400940

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.e.1.100	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.e.1.100	✓	172	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q+0.582518 q^{2} -0.386642 q^{3} -1.66067 q^{4} -0.219930 q^{5} -0.225226 q^{6} +4.05323 q^{7} -2.13241 q^{8} -2.85051 q^{9} +O(q^{10})\)	\(q+0.582518 q^{2} -0.386642 q^{3} -1.66067 q^{4} -0.219930 q^{5} -0.225226 q^{6} +4.05323 q^{7} -2.13241 q^{8} -2.85051 q^{9} -0.128113 q^{10} -4.20508 q^{11} +0.642086 q^{12} +1.21600 q^{13} +2.36108 q^{14} +0.0850341 q^{15} +2.07918 q^{16} -5.69797 q^{17} -1.66047 q^{18} +0.904368 q^{19} +0.365231 q^{20} -1.56715 q^{21} -2.44953 q^{22} -6.58292 q^{23} +0.824479 q^{24} -4.95163 q^{25} +0.708341 q^{26} +2.26205 q^{27} -6.73108 q^{28} +7.37473 q^{29} +0.0495339 q^{30} -6.26219 q^{31} +5.47598 q^{32} +1.62586 q^{33} -3.31917 q^{34} -0.891425 q^{35} +4.73376 q^{36} -5.60221 q^{37} +0.526811 q^{38} -0.470156 q^{39} +0.468980 q^{40} +4.37191 q^{41} -0.912893 q^{42} -3.69129 q^{43} +6.98326 q^{44} +0.626911 q^{45} -3.83467 q^{46} -3.70331 q^{47} -0.803898 q^{48} +9.42865 q^{49} -2.88442 q^{50} +2.20308 q^{51} -2.01937 q^{52} +10.6652 q^{53} +1.31769 q^{54} +0.924821 q^{55} -8.64314 q^{56} -0.349667 q^{57} +4.29591 q^{58} +7.56565 q^{59} -0.141214 q^{60} +12.5279 q^{61} -3.64784 q^{62} -11.5538 q^{63} -0.968500 q^{64} -0.267434 q^{65} +0.947093 q^{66} -1.65987 q^{67} +9.46247 q^{68} +2.54523 q^{69} -0.519271 q^{70} -1.00000 q^{71} +6.07845 q^{72} +0.00926832 q^{73} -3.26339 q^{74} +1.91451 q^{75} -1.50186 q^{76} -17.0441 q^{77} -0.273874 q^{78} -9.99096 q^{79} -0.457273 q^{80} +7.67692 q^{81} +2.54672 q^{82} +6.98022 q^{83} +2.60252 q^{84} +1.25315 q^{85} -2.15024 q^{86} -2.85138 q^{87} +8.96694 q^{88} -8.43358 q^{89} +0.365187 q^{90} +4.92871 q^{91} +10.9321 q^{92} +2.42123 q^{93} -2.15725 q^{94} -0.198897 q^{95} -2.11724 q^{96} -0.400591 q^{97} +5.49236 q^{98} +11.9866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9	\( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) 172 * q + 24 * q^2 + 18 * q^3 + 180 * q^4 + 28 * q^5 + 16 * q^6 + 4 * q^7 + 72 * q^8 + 198 * q^9 + 14 * q^10 + 20 * q^11 + 54 * q^12 + 36 * q^13 + 26 * q^14 + 32 * q^15 + 196 * q^16 + 123 * q^17 + 74 * q^18 + 20 * q^19 + 70 * q^20 + 37 * q^21 + 11 * q^22 + 22 * q^23 + 62 * q^24 + 210 * q^25 + 50 * q^26 + 69 * q^27 + 42 * q^28 + 58 * q^29 + 36 * q^30 + 10 * q^31 + 168 * q^32 + 124 * q^33 + 5 * q^34 + 59 * q^35 + 192 * q^36 + 40 * q^37 + 58 * q^38 + 15 * q^39 + 7 * q^40 + 155 * q^41 - 6 * q^42 + 19 * q^43 + 22 * q^44 + 76 * q^45 + q^46 + 71 * q^47 + 144 * q^48 + 206 * q^49 + 126 * q^50 + 33 * q^51 + 71 * q^52 + 101 * q^53 + 92 * q^54 - 2 * q^55 + 57 * q^56 + 114 * q^57 + 4 * q^58 + 71 * q^59 + 38 * q^60 + 50 * q^61 + 86 * q^62 + 14 * q^63 + 240 * q^64 + 143 * q^65 + 21 * q^66 + 8 * q^67 + 192 * q^68 + 41 * q^69 - 12 * q^70 - 172 * q^71 + 156 * q^72 + 128 * q^73 + 30 * q^74 + 72 * q^75 + 74 * q^76 + 127 * q^77 + 107 * q^78 + 2 * q^79 + 50 * q^80 + 236 * q^81 + 42 * q^82 + 140 * q^83 + 71 * q^84 + 55 * q^85 + 46 * q^86 + 100 * q^87 - 31 * q^88 + 215 * q^89 - 7 * q^90 + 22 * q^91 - 15 * q^92 + 60 * q^93 + 5 * q^94 + 74 * q^95 + 182 * q^96 + 120 * q^97 + 164 * q^98 + 60 * q^99

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