LMFDB - Embedded newform 6014.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.29039 q^{3} +1.00000 q^{4} -1.87953 q^{5} +2.29039 q^{6} +0.391521 q^{7} -1.00000 q^{8} +2.24587 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.29039 q^{3} +1.00000 q^{4} -1.87953 q^{5} +2.29039 q^{6} +0.391521 q^{7} -1.00000 q^{8} +2.24587 q^{9} +1.87953 q^{10} -5.81381 q^{11} -2.29039 q^{12} -1.94880 q^{13} -0.391521 q^{14} +4.30484 q^{15} +1.00000 q^{16} +5.39325 q^{17} -2.24587 q^{18} -2.96756 q^{19} -1.87953 q^{20} -0.896733 q^{21} +5.81381 q^{22} +2.44693 q^{23} +2.29039 q^{24} -1.46738 q^{25} +1.94880 q^{26} +1.72726 q^{27} +0.391521 q^{28} -6.93955 q^{29} -4.30484 q^{30} -1.00000 q^{31} -1.00000 q^{32} +13.3159 q^{33} -5.39325 q^{34} -0.735873 q^{35} +2.24587 q^{36} -4.52625 q^{37} +2.96756 q^{38} +4.46351 q^{39} +1.87953 q^{40} +0.408195 q^{41} +0.896733 q^{42} -7.35218 q^{43} -5.81381 q^{44} -4.22117 q^{45} -2.44693 q^{46} -2.43763 q^{47} -2.29039 q^{48} -6.84671 q^{49} +1.46738 q^{50} -12.3526 q^{51} -1.94880 q^{52} +0.587180 q^{53} -1.72726 q^{54} +10.9272 q^{55} -0.391521 q^{56} +6.79686 q^{57} +6.93955 q^{58} -12.2393 q^{59} +4.30484 q^{60} +2.97822 q^{61} +1.00000 q^{62} +0.879303 q^{63} +1.00000 q^{64} +3.66283 q^{65} -13.3159 q^{66} +4.71552 q^{67} +5.39325 q^{68} -5.60441 q^{69} +0.735873 q^{70} -5.44385 q^{71} -2.24587 q^{72} -1.46949 q^{73} +4.52625 q^{74} +3.36087 q^{75} -2.96756 q^{76} -2.27623 q^{77} -4.46351 q^{78} +6.54992 q^{79} -1.87953 q^{80} -10.6937 q^{81} -0.408195 q^{82} -4.77339 q^{83} -0.896733 q^{84} -10.1367 q^{85} +7.35218 q^{86} +15.8943 q^{87} +5.81381 q^{88} -15.5444 q^{89} +4.22117 q^{90} -0.762997 q^{91} +2.44693 q^{92} +2.29039 q^{93} +2.43763 q^{94} +5.57761 q^{95} +2.29039 q^{96} +1.00000 q^{97} +6.84671 q^{98} -13.0570 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.29039	−1.32235	−0.661177	−	0.750230i	$-0.729943\pi$
$3$	−2.29039	−1.32235	−0.661177	+	0.750230i	$0.729943\pi$
$4$	1.00000	0.500000
$5$	−1.87953	−0.840550	−0.420275	−	0.907397i	$-0.638066\pi$
$5$	−1.87953	−0.840550	−0.420275	+	0.907397i	$0.638066\pi$
$6$	2.29039	0.935046
$7$	0.391521	0.147981	0.0739904	−	0.997259i	$-0.476427\pi$
$7$	0.391521	0.147981	0.0739904	+	0.997259i	$0.476427\pi$
$8$	−1.00000	−0.353553
$9$	2.24587	0.748622
$10$	1.87953	0.594358
$11$	−5.81381	−1.75293	−0.876464	−	0.481467i	$-0.840104\pi$
$11$	−5.81381	−1.75293	−0.876464	+	0.481467i	$0.840104\pi$
$12$	−2.29039	−0.661177
$13$	−1.94880	−0.540501	−0.270251	−	0.962790i	$-0.587107\pi$
$13$	−1.94880	−0.540501	−0.270251	+	0.962790i	$0.587107\pi$
$14$	−0.391521	−0.104638
$15$	4.30484	1.11151
$16$	1.00000	0.250000
$17$	5.39325	1.30805	0.654027	−	0.756471i	$-0.273078\pi$
$17$	5.39325	1.30805	0.654027	+	0.756471i	$0.273078\pi$
$18$	−2.24587	−0.529356
$19$	−2.96756	−0.680805	−0.340403	−	0.940280i	$-0.610563\pi$
$19$	−2.96756	−0.680805	−0.340403	+	0.940280i	$0.610563\pi$
$20$	−1.87953	−0.420275
$21$	−0.896733	−0.195683
$22$	5.81381	1.23951
$23$	2.44693	0.510220	0.255110	−	0.966912i	$-0.417888\pi$
$23$	2.44693	0.510220	0.255110	+	0.966912i	$0.417888\pi$
$24$	2.29039	0.467523
$25$	−1.46738	−0.293476
$26$	1.94880	0.382192
$27$	1.72726	0.332411
$28$	0.391521	0.0739904
$29$	−6.93955	−1.28864	−0.644321	−	0.764755i	$-0.722860\pi$
$29$	−6.93955	−1.28864	−0.644321	+	0.764755i	$0.722860\pi$
$30$	−4.30484	−0.785953
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	13.3159	2.31799
$34$	−5.39325	−0.924934
$35$	−0.735873	−0.124385
$36$	2.24587	0.374311
$37$	−4.52625	−0.744110	−0.372055	−	0.928211i	$-0.621347\pi$
$37$	−4.52625	−0.744110	−0.372055	+	0.928211i	$0.621347\pi$
$38$	2.96756	0.481402
$39$	4.46351	0.714734
$40$	1.87953	0.297179
$41$	0.408195	0.0637493	0.0318747	−	0.999492i	$-0.489852\pi$
$41$	0.408195	0.0637493	0.0318747	+	0.999492i	$0.489852\pi$
$42$	0.896733	0.138369
$43$	−7.35218	−1.12120	−0.560598	−	0.828088i	$-0.689429\pi$
$43$	−7.35218	−1.12120	−0.560598	+	0.828088i	$0.689429\pi$
$44$	−5.81381	−0.876464
$45$	−4.22117	−0.629254
$46$	−2.44693	−0.360780
$47$	−2.43763	−0.355565	−0.177782	−	0.984070i	$-0.556892\pi$
$47$	−2.43763	−0.355565	−0.177782	+	0.984070i	$0.556892\pi$
$48$	−2.29039	−0.330589
$49$	−6.84671	−0.978102
$50$	1.46738	0.207519
$51$	−12.3526	−1.72971
$52$	−1.94880	−0.270251
$53$	0.587180	0.0806554	0.0403277	−	0.999187i	$-0.487160\pi$
$53$	0.587180	0.0806554	0.0403277	+	0.999187i	$0.487160\pi$
$54$	−1.72726	−0.235050
$55$	10.9272	1.47342
$56$	−0.391521	−0.0523191
$57$	6.79686	0.900266
$58$	6.93955	0.911208
$59$	−12.2393	−1.59342	−0.796711	−	0.604360i	$-0.793429\pi$
$59$	−12.2393	−1.59342	−0.796711	+	0.604360i	$0.793429\pi$
$60$	4.30484	0.555753
$61$	2.97822	0.381321	0.190661	−	0.981656i	$-0.438937\pi$
$61$	2.97822	0.381321	0.190661	+	0.981656i	$0.438937\pi$
$62$	1.00000	0.127000
$63$	0.879303	0.110782
$64$	1.00000	0.125000
$65$	3.66283	0.454318
$66$	−13.3159	−1.63907
$67$	4.71552	0.576093	0.288046	−	0.957616i	$-0.406994\pi$
$67$	4.71552	0.576093	0.288046	+	0.957616i	$0.406994\pi$
$68$	5.39325	0.654027
$69$	−5.60441	−0.674691
$70$	0.735873	0.0879537
$71$	−5.44385	−0.646066	−0.323033	−	0.946388i	$-0.604703\pi$
$71$	−5.44385	−0.646066	−0.323033	+	0.946388i	$0.604703\pi$
$72$	−2.24587	−0.264678
$73$	−1.46949	−0.171990	−0.0859951	−	0.996296i	$-0.527407\pi$
$73$	−1.46949	−0.171990	−0.0859951	+	0.996296i	$0.527407\pi$
$74$	4.52625	0.526165
$75$	3.36087	0.388079
$76$	−2.96756	−0.340403
$77$	−2.27623	−0.259400
$78$	−4.46351	−0.505393
$79$	6.54992	0.736923	0.368462	−	0.929643i	$-0.379885\pi$
$79$	6.54992	0.736923	0.368462	+	0.929643i	$0.379885\pi$
$80$	−1.87953	−0.210137
$81$	−10.6937	−1.18819
$82$	−0.408195	−0.0450776
$83$	−4.77339	−0.523947	−0.261974	−	0.965075i	$-0.584373\pi$
$83$	−4.77339	−0.523947	−0.261974	+	0.965075i	$0.584373\pi$
$84$	−0.896733	−0.0978416
$85$	−10.1367	−1.09948
$86$	7.35218	0.792806
$87$	15.8943	1.70404
$88$	5.81381	0.619754
$89$	−15.5444	−1.64770	−0.823850	−	0.566808i	$-0.808178\pi$
$89$	−15.5444	−1.64770	−0.823850	+	0.566808i	$0.808178\pi$
$90$	4.22117	0.444950
$91$	−0.762997	−0.0799838
$92$	2.44693	0.255110
$93$	2.29039	0.237502
$94$	2.43763	0.251422
$95$	5.57761	0.572251
$96$	2.29039	0.233762
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	6.84671	0.691622
$99$	−13.0570	−1.31228
$100$	−1.46738	−0.146738
$101$	−12.6733	−1.26104	−0.630520	−	0.776173i	$-0.717158\pi$
$101$	−12.6733	−1.26104	−0.630520	+	0.776173i	$0.717158\pi$
$102$	12.3526	1.22309
$103$	−15.0889	−1.48675	−0.743377	−	0.668873i	$-0.766777\pi$
$103$	−15.0889	−1.48675	−0.743377	+	0.668873i	$0.766777\pi$
$104$	1.94880	0.191096
$105$	1.68543	0.164482
$106$	−0.587180	−0.0570320
$107$	−8.62159	−0.833481	−0.416740	−	0.909026i	$-0.636828\pi$
$107$	−8.62159	−0.833481	−0.416740	+	0.909026i	$0.636828\pi$
$108$	1.72726	0.166205
$109$	14.4326	1.38239	0.691195	−	0.722668i	$-0.257084\pi$
$109$	14.4326	1.38239	0.691195	+	0.722668i	$0.257084\pi$
$110$	−10.9272	−1.04187
$111$	10.3669	0.983978
$112$	0.391521	0.0369952
$113$	2.50120	0.235293	0.117647	−	0.993056i	$-0.462465\pi$
$113$	2.50120	0.235293	0.117647	+	0.993056i	$0.462465\pi$
$114$	−6.79686	−0.636584
$115$	−4.59906	−0.428865
$116$	−6.93955	−0.644321
$117$	−4.37675	−0.404631
$118$	12.2393	1.12672
$119$	2.11157	0.193567
$120$	−4.30484	−0.392976
$121$	22.8003	2.07276
$122$	−2.97822	−0.269635
$123$	−0.934923	−0.0842992
$124$	−1.00000	−0.0898027
$125$	12.1556	1.08723
$126$	−0.879303	−0.0783345
$127$	−3.34952	−0.297222	−0.148611	−	0.988896i	$-0.547480\pi$
$127$	−3.34952	−0.297222	−0.148611	+	0.988896i	$0.547480\pi$
$128$	−1.00000	−0.0883883
$129$	16.8393	1.48262
$130$	−3.66283	−0.321251
$131$	1.38374	0.120898	0.0604489	−	0.998171i	$-0.480747\pi$
$131$	1.38374	0.120898	0.0604489	+	0.998171i	$0.480747\pi$
$132$	13.3159	1.15900
$133$	−1.16186	−0.100746
$134$	−4.71552	−0.407359
$135$	−3.24642	−0.279408
$136$	−5.39325	−0.462467
$137$	−8.51209	−0.727237	−0.363618	−	0.931548i	$-0.618459\pi$
$137$	−8.51209	−0.727237	−0.363618	+	0.931548i	$0.618459\pi$
$138$	5.60441	0.477079
$139$	−17.8605	−1.51491	−0.757456	−	0.652887i	$-0.773558\pi$
$139$	−17.8605	−1.51491	−0.757456	+	0.652887i	$0.773558\pi$
$140$	−0.735873	−0.0621927
$141$	5.58311	0.470183
$142$	5.44385	0.456838
$143$	11.3300	0.947460
$144$	2.24587	0.187156
$145$	13.0431	1.08317
$146$	1.46949	0.121615
$147$	15.6816	1.29340
$148$	−4.52625	−0.372055
$149$	2.01997	0.165483	0.0827413	−	0.996571i	$-0.473632\pi$
$149$	2.01997	0.165483	0.0827413	+	0.996571i	$0.473632\pi$
$150$	−3.36087	−0.274414
$151$	3.69109	0.300377	0.150188	−	0.988657i	$-0.452012\pi$
$151$	3.69109	0.300377	0.150188	+	0.988657i	$0.452012\pi$
$152$	2.96756	0.240701
$153$	12.1125	0.979238
$154$	2.27623	0.183423
$155$	1.87953	0.150967
$156$	4.46351	0.357367
$157$	−1.04292	−0.0832342	−0.0416171	−	0.999134i	$-0.513251\pi$
$157$	−1.04292	−0.0832342	−0.0416171	+	0.999134i	$0.513251\pi$
$158$	−6.54992	−0.521083
$159$	−1.34487	−0.106655
$160$	1.87953	0.148590
$161$	0.958022	0.0755027
$162$	10.6937	0.840175
$163$	−21.9112	−1.71622	−0.858111	−	0.513465i	$-0.828362\pi$
$163$	−21.9112	−1.71622	−0.858111	+	0.513465i	$0.828362\pi$
$164$	0.408195	0.0318747
$165$	−25.0275	−1.94839
$166$	4.77339	0.370487
$167$	−20.1448	−1.55885	−0.779426	−	0.626495i	$-0.784489\pi$
$167$	−20.1448	−1.55885	−0.779426	+	0.626495i	$0.784489\pi$
$168$	0.896733	0.0691845
$169$	−9.20216	−0.707859
$170$	10.1367	0.777453
$171$	−6.66475	−0.509666
$172$	−7.35218	−0.560598
$173$	5.77371	0.438967	0.219483	−	0.975616i	$-0.429563\pi$
$173$	5.77371	0.438967	0.219483	+	0.975616i	$0.429563\pi$
$174$	−15.8943	−1.20494
$175$	−0.574510	−0.0434289
$176$	−5.81381	−0.438232
$177$	28.0327	2.10707
$178$	15.5444	1.16510
$179$	−11.8783	−0.887824	−0.443912	−	0.896070i	$-0.646410\pi$
$179$	−11.8783	−0.887824	−0.443912	+	0.896070i	$0.646410\pi$
$180$	−4.22117	−0.314627
$181$	−3.39693	−0.252492	−0.126246	−	0.991999i	$-0.540293\pi$
$181$	−3.39693	−0.252492	−0.126246	+	0.991999i	$0.540293\pi$
$182$	0.762997	0.0565571
$183$	−6.82126	−0.504242
$184$	−2.44693	−0.180390
$185$	8.50720	0.625462
$186$	−2.29039	−0.167939
$187$	−31.3553	−2.29293
$188$	−2.43763	−0.177782
$189$	0.676257	0.0491904
$190$	−5.57761	−0.404642
$191$	−1.42482	−0.103096	−0.0515482	−	0.998671i	$-0.516416\pi$
$191$	−1.42482	−0.103096	−0.0515482	+	0.998671i	$0.516416\pi$
$192$	−2.29039	−0.165294
$193$	17.1041	1.23118	0.615591	−	0.788066i	$-0.288917\pi$
$193$	17.1041	1.23118	0.615591	+	0.788066i	$0.288917\pi$
$194$	−1.00000	−0.0717958
$195$	−8.38929	−0.600770
$196$	−6.84671	−0.489051
$197$	8.74533	0.623079	0.311540	−	0.950233i	$-0.399155\pi$
$197$	8.74533	0.623079	0.311540	+	0.950233i	$0.399155\pi$
$198$	13.0570	0.927923
$199$	−8.18082	−0.579923	−0.289961	−	0.957038i	$-0.593642\pi$
$199$	−8.18082	−0.579923	−0.289961	+	0.957038i	$0.593642\pi$
$200$	1.46738	0.103759
$201$	−10.8004	−0.761799
$202$	12.6733	0.891690
$203$	−2.71698	−0.190695
$204$	−12.3526	−0.864856
$205$	−0.767213	−0.0535845
$206$	15.0889	1.05129
$207$	5.49547	0.381962
$208$	−1.94880	−0.135125
$209$	17.2528	1.19340
$210$	−1.68543	−0.116306
$211$	19.5966	1.34909	0.674544	−	0.738234i	$-0.264340\pi$
$211$	19.5966	1.34909	0.674544	+	0.738234i	$0.264340\pi$
$212$	0.587180	0.0403277
$213$	12.4685	0.854329
$214$	8.62159	0.589360
$215$	13.8186	0.942421
$216$	−1.72726	−0.117525
$217$	−0.391521	−0.0265782
$218$	−14.4326	−0.977498
$219$	3.36569	0.227432
$220$	10.9272	0.736712
$221$	−10.5104	−0.707005
$222$	−10.3669	−0.695777
$223$	2.48685	0.166532	0.0832658	−	0.996527i	$-0.473465\pi$
$223$	2.48685	0.166532	0.0832658	+	0.996527i	$0.473465\pi$
$224$	−0.391521	−0.0261596
$225$	−3.29554	−0.219703
$226$	−2.50120	−0.166377
$227$	−24.7875	−1.64520	−0.822601	−	0.568619i	$-0.807478\pi$
$227$	−24.7875	−1.64520	−0.822601	+	0.568619i	$0.807478\pi$
$228$	6.79686	0.450133
$229$	0.688331	0.0454862	0.0227431	−	0.999741i	$-0.492760\pi$
$229$	0.688331	0.0454862	0.0227431	+	0.999741i	$0.492760\pi$
$230$	4.59906	0.303253
$231$	5.21343	0.343019
$232$	6.93955	0.455604
$233$	−27.3158	−1.78952	−0.894759	−	0.446549i	$-0.852653\pi$
$233$	−27.3158	−1.78952	−0.894759	+	0.446549i	$0.852653\pi$
$234$	4.37675	0.286117
$235$	4.58159	0.298870
$236$	−12.2393	−0.796711
$237$	−15.0018	−0.974474
$238$	−2.11157	−0.136873
$239$	6.16810	0.398981	0.199491	−	0.979900i	$-0.436071\pi$
$239$	6.16810	0.398981	0.199491	+	0.979900i	$0.436071\pi$
$240$	4.30484	0.277876
$241$	6.01180	0.387254	0.193627	−	0.981075i	$-0.437975\pi$
$241$	6.01180	0.387254	0.193627	+	0.981075i	$0.437975\pi$
$242$	−22.8003	−1.46566
$243$	19.3109	1.23879
$244$	2.97822	0.190661
$245$	12.8686	0.822143
$246$	0.934923	0.0596085
$247$	5.78320	0.367976
$248$	1.00000	0.0635001
$249$	10.9329	0.692844
$250$	−12.1556	−0.768788
$251$	−20.9988	−1.32543	−0.662717	−	0.748870i	$-0.730597\pi$
$251$	−20.9988	−1.32543	−0.662717	+	0.748870i	$0.730597\pi$
$252$	0.879303	0.0553909
$253$	−14.2260	−0.894378
$254$	3.34952	0.210168
$255$	23.2171	1.45391
$256$	1.00000	0.0625000
$257$	−18.1764	−1.13381	−0.566907	−	0.823782i	$-0.691860\pi$
$257$	−18.1764	−1.13381	−0.566907	+	0.823782i	$0.691860\pi$
$258$	−16.8393	−1.04837
$259$	−1.77212	−0.110114
$260$	3.66283	0.227159
$261$	−15.5853	−0.964707
$262$	−1.38374	−0.0854877
$263$	−14.4187	−0.889097	−0.444549	−	0.895755i	$-0.646636\pi$
$263$	−14.4187	−0.889097	−0.444549	+	0.895755i	$0.646636\pi$
$264$	−13.3159	−0.819534
$265$	−1.10362	−0.0677949
$266$	1.16186	0.0712383
$267$	35.6026	2.17884
$268$	4.71552	0.288046
$269$	−19.4064	−1.18323	−0.591614	−	0.806222i	$-0.701509\pi$
$269$	−19.4064	−1.18323	−0.591614	+	0.806222i	$0.701509\pi$
$270$	3.24642	0.197571
$271$	29.8540	1.81350	0.906751	−	0.421666i	$-0.138555\pi$
$271$	29.8540	1.81350	0.906751	+	0.421666i	$0.138555\pi$
$272$	5.39325	0.327014
$273$	1.74756	0.105767
$274$	8.51209	0.514234
$275$	8.53107	0.514443
$276$	−5.60441	−0.337346
$277$	17.0591	1.02498	0.512492	−	0.858692i	$-0.328723\pi$
$277$	17.0591	1.02498	0.512492	+	0.858692i	$0.328723\pi$
$278$	17.8605	1.07120
$279$	−2.24587	−0.134457
$280$	0.735873	0.0439768
$281$	30.4596	1.81707	0.908534	−	0.417811i	$-0.137202\pi$
$281$	30.4596	1.81707	0.908534	+	0.417811i	$0.137202\pi$
$282$	−5.58311	−0.332470
$283$	26.5308	1.57709	0.788545	−	0.614976i	$-0.210834\pi$
$283$	26.5308	1.57709	0.788545	+	0.614976i	$0.210834\pi$
$284$	−5.44385	−0.323033
$285$	−12.7749	−0.756719
$286$	−11.3300	−0.669955
$287$	0.159817	0.00943368
$288$	−2.24587	−0.132339
$289$	12.0871	0.711006
$290$	−13.0431	−0.765916
$291$	−2.29039	−0.134265
$292$	−1.46949	−0.0859951
$293$	−26.2125	−1.53135	−0.765676	−	0.643226i	$-0.777595\pi$
$293$	−26.2125	−1.53135	−0.765676	+	0.643226i	$0.777595\pi$
$294$	−15.6816	−0.914570
$295$	23.0041	1.33935
$296$	4.52625	0.263083
$297$	−10.0419	−0.582692
$298$	−2.01997	−0.117014
$299$	−4.76858	−0.275774
$300$	3.36087	0.194040
$301$	−2.87853	−0.165916
$302$	−3.69109	−0.212399
$303$	29.0267	1.66754
$304$	−2.96756	−0.170201
$305$	−5.59764	−0.320520
$306$	−12.1125	−0.692426
$307$	18.7531	1.07029	0.535147	−	0.844759i	$-0.320256\pi$
$307$	18.7531	1.07029	0.535147	+	0.844759i	$0.320256\pi$
$308$	−2.27623	−0.129700
$309$	34.5594	1.96602
$310$	−1.87953	−0.106750
$311$	−5.42245	−0.307479	−0.153740	−	0.988111i	$-0.549132\pi$
$311$	−5.42245	−0.307479	−0.153740	+	0.988111i	$0.549132\pi$
$312$	−4.46351	−0.252697
$313$	15.1672	0.857302	0.428651	−	0.903470i	$-0.358989\pi$
$313$	15.1672	0.857302	0.428651	+	0.903470i	$0.358989\pi$
$314$	1.04292	0.0588555
$315$	−1.65267	−0.0931176
$316$	6.54992	0.368462
$317$	0.282897	0.0158891	0.00794453	−	0.999968i	$-0.497471\pi$
$317$	0.282897	0.0158891	0.00794453	+	0.999968i	$0.497471\pi$
$318$	1.34487	0.0754165
$319$	40.3452	2.25890
$320$	−1.87953	−0.105069
$321$	19.7468	1.10216
$322$	−0.958022	−0.0533885
$323$	−16.0048	−0.890530
$324$	−10.6937	−0.594094
$325$	2.85964	0.158624
$326$	21.9112	1.21355
$327$	−33.0562	−1.82801
$328$	−0.408195	−0.0225388
$329$	−0.954383	−0.0526168
$330$	25.0275	1.37772
$331$	−5.93789	−0.326376	−0.163188	−	0.986595i	$-0.552178\pi$
$331$	−5.93789	−0.326376	−0.163188	+	0.986595i	$0.552178\pi$
$332$	−4.77339	−0.261974
$333$	−10.1653	−0.557058
$334$	20.1448	1.10227
$335$	−8.86295	−0.484235
$336$	−0.896733	−0.0489208
$337$	−0.476027	−0.0259308	−0.0129654	−	0.999916i	$-0.504127\pi$
$337$	−0.476027	−0.0259308	−0.0129654	+	0.999916i	$0.504127\pi$
$338$	9.20216	0.500532
$339$	−5.72872	−0.311141
$340$	−10.1367	−0.549742
$341$	5.81381	0.314835
$342$	6.66475	0.360388
$343$	−5.42127	−0.292721
$344$	7.35218	0.396403
$345$	10.5336	0.567112
$346$	−5.77371	−0.310396
$347$	−12.7048	−0.682027	−0.341013	−	0.940058i	$-0.610770\pi$
$347$	−12.7048	−0.682027	−0.341013	+	0.940058i	$0.610770\pi$
$348$	15.8943	0.852022
$349$	23.2176	1.24281	0.621405	−	0.783490i	$-0.286562\pi$
$349$	23.2176	1.24281	0.621405	+	0.783490i	$0.286562\pi$
$350$	0.574510	0.0307088
$351$	−3.36609	−0.179668
$352$	5.81381	0.309877
$353$	−14.7537	−0.785259	−0.392630	−	0.919697i	$-0.628435\pi$
$353$	−14.7537	−0.785259	−0.392630	+	0.919697i	$0.628435\pi$
$354$	−28.0327	−1.48992
$355$	10.2319	0.543051
$356$	−15.5444	−0.823850
$357$	−4.83630	−0.255964
$358$	11.8783	0.627786
$359$	−11.7064	−0.617839	−0.308920	−	0.951088i	$-0.599967\pi$
$359$	−11.7064	−0.617839	−0.308920	+	0.951088i	$0.599967\pi$
$360$	4.22117	0.222475
$361$	−10.1936	−0.536504
$362$	3.39693	0.178538
$363$	−52.2216	−2.74092
$364$	−0.762997	−0.0399919
$365$	2.76194	0.144566
$366$	6.82126	0.356553
$367$	−12.6572	−0.660702	−0.330351	−	0.943858i	$-0.607167\pi$
$367$	−12.6572	−0.660702	−0.330351	+	0.943858i	$0.607167\pi$
$368$	2.44693	0.127555
$369$	0.916751	0.0477241
$370$	−8.50720	−0.442268
$371$	0.229893	0.0119355
$372$	2.29039	0.118751
$373$	−11.5396	−0.597495	−0.298748	−	0.954332i	$-0.596569\pi$
$373$	−11.5396	−0.597495	−0.298748	+	0.954332i	$0.596569\pi$
$374$	31.3553	1.62134
$375$	−27.8410	−1.43771
$376$	2.43763	0.125711
$377$	13.5238	0.696513
$378$	−0.676257	−0.0347829
$379$	−6.46194	−0.331928	−0.165964	−	0.986132i	$-0.553073\pi$
$379$	−6.46194	−0.331928	−0.165964	+	0.986132i	$0.553073\pi$
$380$	5.57761	0.286125
$381$	7.67170	0.393033
$382$	1.42482	0.0729002
$383$	35.1916	1.79821	0.899105	−	0.437734i	$-0.144219\pi$
$383$	35.1916	1.79821	0.899105	+	0.437734i	$0.144219\pi$
$384$	2.29039	0.116881
$385$	4.27823	0.218039
$386$	−17.1041	−0.870578
$387$	−16.5120	−0.839353
$388$	1.00000	0.0507673
$389$	−22.7611	−1.15403	−0.577016	−	0.816733i	$-0.695783\pi$
$389$	−22.7611	−1.15403	−0.577016	+	0.816733i	$0.695783\pi$
$390$	8.38929	0.424808
$391$	13.1969	0.667395
$392$	6.84671	0.345811
$393$	−3.16930	−0.159870
$394$	−8.74533	−0.440584
$395$	−12.3107	−0.619421
$396$	−13.0570	−0.656141
$397$	18.9523	0.951188	0.475594	−	0.879665i	$-0.342233\pi$
$397$	18.9523	0.951188	0.475594	+	0.879665i	$0.342233\pi$
$398$	8.18082	0.410067
$399$	2.66111	0.133222
$400$	−1.46738	−0.0733690
$401$	39.6354	1.97930	0.989650	−	0.143506i	$-0.0458375\pi$
$401$	39.6354	1.97930	0.989650	+	0.143506i	$0.0458375\pi$
$402$	10.8004	0.538673
$403$	1.94880	0.0970769
$404$	−12.6733	−0.630520
$405$	20.0991	0.998730
$406$	2.71698	0.134841
$407$	26.3147	1.30437
$408$	12.3526	0.611545
$409$	36.8124	1.82026	0.910128	−	0.414327i	$-0.135983\pi$
$409$	36.8124	1.82026	0.910128	+	0.414327i	$0.135983\pi$
$410$	0.767213	0.0378899
$411$	19.4960	0.961665
$412$	−15.0889	−0.743377
$413$	−4.79194	−0.235796
$414$	−5.49547	−0.270088
$415$	8.97170	0.440404
$416$	1.94880	0.0955480
$417$	40.9075	2.00325
$418$	−17.2528	−0.843864
$419$	11.5587	0.564682	0.282341	−	0.959314i	$-0.408889\pi$
$419$	11.5587	0.564682	0.282341	+	0.959314i	$0.408889\pi$
$420$	1.68543	0.0822408
$421$	36.2368	1.76608	0.883038	−	0.469302i	$-0.155494\pi$
$421$	36.2368	1.76608	0.883038	+	0.469302i	$0.155494\pi$
$422$	−19.5966	−0.953950
$423$	−5.47459	−0.266184
$424$	−0.587180	−0.0285160
$425$	−7.91394	−0.383883
$426$	−12.4685	−0.604102
$427$	1.16603	0.0564283
$428$	−8.62159	−0.416740
$429$	−25.9500	−1.25288
$430$	−13.8186	−0.666393
$431$	1.42685	0.0687288	0.0343644	−	0.999409i	$-0.489059\pi$
$431$	1.42685	0.0687288	0.0343644	+	0.999409i	$0.489059\pi$
$432$	1.72726	0.0831027
$433$	23.0250	1.10651	0.553257	−	0.833011i	$-0.313385\pi$
$433$	23.0250	1.10651	0.553257	+	0.833011i	$0.313385\pi$
$434$	0.391521	0.0187936
$435$	−29.8737	−1.43233
$436$	14.4326	0.691195
$437$	−7.26141	−0.347360
$438$	−3.36569	−0.160819
$439$	1.21161	0.0578269	0.0289135	−	0.999582i	$-0.490795\pi$
$439$	1.21161	0.0578269	0.0289135	+	0.999582i	$0.490795\pi$
$440$	−10.9272	−0.520934
$441$	−15.3768	−0.732229
$442$	10.5104	0.499928
$443$	−9.28258	−0.441029	−0.220514	−	0.975384i	$-0.570774\pi$
$443$	−9.28258	−0.441029	−0.220514	+	0.975384i	$0.570774\pi$
$444$	10.3669	0.491989
$445$	29.2161	1.38497
$446$	−2.48685	−0.117756
$447$	−4.62652	−0.218827
$448$	0.391521	0.0184976
$449$	−6.21146	−0.293137	−0.146568	−	0.989201i	$-0.546823\pi$
$449$	−6.21146	−0.293137	−0.146568	+	0.989201i	$0.546823\pi$
$450$	3.29554	0.155353
$451$	−2.37317	−0.111748
$452$	2.50120	0.117647
$453$	−8.45403	−0.397205
$454$	24.7875	1.16333
$455$	1.43407	0.0672304
$456$	−6.79686	−0.318292
$457$	20.4086	0.954673	0.477336	−	0.878721i	$-0.341602\pi$
$457$	20.4086	0.954673	0.477336	+	0.878721i	$0.341602\pi$
$458$	−0.688331	−0.0321636
$459$	9.31552	0.434811
$460$	−4.59906	−0.214432
$461$	22.4769	1.04686	0.523428	−	0.852070i	$-0.324653\pi$
$461$	22.4769	1.04686	0.523428	+	0.852070i	$0.324653\pi$
$462$	−5.21343	−0.242551
$463$	14.8437	0.689844	0.344922	−	0.938631i	$-0.387905\pi$
$463$	14.8437	0.689844	0.344922	+	0.938631i	$0.387905\pi$
$464$	−6.93955	−0.322161
$465$	−4.30484	−0.199632
$466$	27.3158	1.26538
$467$	31.1016	1.43921	0.719605	−	0.694383i	$-0.244323\pi$
$467$	31.1016	1.43921	0.719605	+	0.694383i	$0.244323\pi$
$468$	−4.37675	−0.202316
$469$	1.84622	0.0852507
$470$	−4.58159	−0.211333
$471$	2.38869	0.110065
$472$	12.2393	0.563360
$473$	42.7441	1.96538
$474$	15.0018	0.689057
$475$	4.35454	0.199800
$476$	2.11157	0.0967835
$477$	1.31873	0.0603804
$478$	−6.16810	−0.282122
$479$	3.69589	0.168869	0.0844347	−	0.996429i	$-0.473092\pi$
$479$	3.69589	0.168869	0.0844347	+	0.996429i	$0.473092\pi$
$480$	−4.30484	−0.196488
$481$	8.82077	0.402193
$482$	−6.01180	−0.273830
$483$	−2.19424	−0.0998414
$484$	22.8003	1.03638
$485$	−1.87953	−0.0853449
$486$	−19.3109	−0.875960
$487$	−27.8939	−1.26399	−0.631996	−	0.774972i	$-0.717764\pi$
$487$	−27.8939	−1.26399	−0.631996	+	0.774972i	$0.717764\pi$
$488$	−2.97822	−0.134817
$489$	50.1852	2.26945
$490$	−12.8686	−0.581343
$491$	24.2926	1.09631	0.548155	−	0.836377i	$-0.315330\pi$
$491$	24.2926	1.09631	0.548155	+	0.836377i	$0.315330\pi$
$492$	−0.934923	−0.0421496
$493$	−37.4267	−1.68561
$494$	−5.78320	−0.260198
$495$	24.5410	1.10304
$496$	−1.00000	−0.0449013
$497$	−2.13138	−0.0956055
$498$	−10.9329	−0.489915
$499$	1.21566	0.0544204	0.0272102	−	0.999630i	$-0.491338\pi$
$499$	1.21566	0.0544204	0.0272102	+	0.999630i	$0.491338\pi$
$500$	12.1556	0.543616
$501$	46.1394	2.06135
$502$	20.9988	0.937224
$503$	27.3602	1.21993	0.609966	−	0.792428i	$-0.291183\pi$
$503$	27.3602	1.21993	0.609966	+	0.792428i	$0.291183\pi$
$504$	−0.879303	−0.0391673
$505$	23.8198	1.05997
$506$	14.2260	0.632421
$507$	21.0765	0.936040
$508$	−3.34952	−0.148611
$509$	−11.1646	−0.494863	−0.247431	−	0.968905i	$-0.579586\pi$
$509$	−11.1646	−0.494863	−0.247431	+	0.968905i	$0.579586\pi$
$510$	−23.2171	−1.02807
$511$	−0.575334	−0.0254513
$512$	−1.00000	−0.0441942
$513$	−5.12574	−0.226307
$514$	18.1764	0.801727
$515$	28.3600	1.24969
$516$	16.8393	0.741310
$517$	14.1719	0.623280
$518$	1.77212	0.0778624
$519$	−13.2240	−0.580470
$520$	−3.66283	−0.160626
$521$	33.1036	1.45030	0.725148	−	0.688593i	$-0.241771\pi$
$521$	33.1036	1.45030	0.725148	+	0.688593i	$0.241771\pi$
$522$	15.5853	0.682151
$523$	22.1050	0.966584	0.483292	−	0.875459i	$-0.339441\pi$
$523$	22.1050	0.966584	0.483292	+	0.875459i	$0.339441\pi$
$524$	1.38374	0.0604489
$525$	1.31585	0.0574283
$526$	14.4187	0.628687
$527$	−5.39325	−0.234933
$528$	13.3159	0.579498
$529$	−17.0125	−0.739676
$530$	1.10362	0.0479382
$531$	−27.4879	−1.19287
$532$	−1.16186	−0.0503731
$533$	−0.795492	−0.0344566
$534$	−35.6026	−1.54068
$535$	16.2045	0.700582
$536$	−4.71552	−0.203680
$537$	27.2058	1.17402
$538$	19.4064	0.836668
$539$	39.8055	1.71454
$540$	−3.24642	−0.139704
$541$	−31.1847	−1.34074	−0.670368	−	0.742029i	$-0.733864\pi$
$541$	−31.1847	−1.34074	−0.670368	+	0.742029i	$0.733864\pi$
$542$	−29.8540	−1.28234
$543$	7.78027	0.333883
$544$	−5.39325	−0.231233
$545$	−27.1264	−1.16197
$546$	−1.74756	−0.0747886
$547$	−41.8217	−1.78817	−0.894083	−	0.447902i	$-0.852171\pi$
$547$	−41.8217	−1.78817	−0.894083	+	0.447902i	$0.852171\pi$
$548$	−8.51209	−0.363618
$549$	6.68868	0.285466
$550$	−8.53107	−0.363766
$551$	20.5936	0.877315
$552$	5.60441	0.238539
$553$	2.56443	0.109051
$554$	−17.0591	−0.724773
$555$	−19.4848	−0.827082
$556$	−17.8605	−0.757456
$557$	−17.0506	−0.722457	−0.361228	−	0.932477i	$-0.617643\pi$
$557$	−17.0506	−0.722457	−0.361228	+	0.932477i	$0.617643\pi$
$558$	2.24587	0.0950751
$559$	14.3280	0.606008
$560$	−0.735873	−0.0310963
$561$	71.8157	3.03206
$562$	−30.4596	−1.28486
$563$	16.3994	0.691150	0.345575	−	0.938391i	$-0.387684\pi$
$563$	16.3994	0.691150	0.345575	+	0.938391i	$0.387684\pi$
$564$	5.58311	0.235091
$565$	−4.70108	−0.197776
$566$	−26.5308	−1.11517
$567$	−4.18680	−0.175829
$568$	5.44385	0.228419
$569$	−18.6123	−0.780266	−0.390133	−	0.920758i	$-0.627571\pi$
$569$	−18.6123	−0.780266	−0.390133	+	0.920758i	$0.627571\pi$
$570$	12.7749	0.535081
$571$	43.5946	1.82438	0.912189	−	0.409770i	$-0.134391\pi$
$571$	43.5946	1.82438	0.912189	+	0.409770i	$0.134391\pi$
$572$	11.3300	0.473730
$573$	3.26339	0.136330
$574$	−0.159817	−0.00667062
$575$	−3.59057	−0.149737
$576$	2.24587	0.0935778
$577$	−6.42177	−0.267342	−0.133671	−	0.991026i	$-0.542677\pi$
$577$	−6.42177	−0.267342	−0.133671	+	0.991026i	$0.542677\pi$
$578$	−12.0871	−0.502757
$579$	−39.1751	−1.62806
$580$	13.0431	0.541584
$581$	−1.86888	−0.0775342
$582$	2.29039	0.0949395
$583$	−3.41375	−0.141383
$584$	1.46949	0.0608077
$585$	8.22623	0.340113
$586$	26.2125	1.08283
$587$	−29.0626	−1.19954	−0.599770	−	0.800172i	$-0.704741\pi$
$587$	−29.0626	−1.19954	−0.599770	+	0.800172i	$0.704741\pi$
$588$	15.6816	0.646699
$589$	2.96756	0.122276
$590$	−23.0041	−0.947064
$591$	−20.0302	−0.823932
$592$	−4.52625	−0.186028
$593$	20.0362	0.822790	0.411395	−	0.911457i	$-0.365042\pi$
$593$	20.0362	0.822790	0.411395	+	0.911457i	$0.365042\pi$
$594$	10.0419	0.412026
$595$	−3.96875	−0.162703
$596$	2.01997	0.0827413
$597$	18.7372	0.766864
$598$	4.76858	0.195002
$599$	−28.7836	−1.17607	−0.588033	−	0.808837i	$-0.700098\pi$
$599$	−28.7836	−1.17607	−0.588033	+	0.808837i	$0.700098\pi$
$600$	−3.36087	−0.137207
$601$	0.116265	0.00474254	0.00237127	−	0.999997i	$-0.499245\pi$
$601$	0.116265	0.00474254	0.00237127	+	0.999997i	$0.499245\pi$
$602$	2.87853	0.117320
$603$	10.5904	0.431276
$604$	3.69109	0.150188
$605$	−42.8539	−1.74226
$606$	−29.0267	−1.17913
$607$	−28.4921	−1.15646	−0.578229	−	0.815875i	$-0.696256\pi$
$607$	−28.4921	−1.15646	−0.578229	+	0.815875i	$0.696256\pi$
$608$	2.96756	0.120351
$609$	6.22293	0.252166
$610$	5.59764	0.226642
$611$	4.75047	0.192183
$612$	12.1125	0.489619
$613$	13.6971	0.553223	0.276611	−	0.960982i	$-0.410789\pi$
$613$	13.6971	0.553223	0.276611	+	0.960982i	$0.410789\pi$
$614$	−18.7531	−0.756813
$615$	1.75721	0.0708577
$616$	2.27623	0.0917117
$617$	26.6809	1.07413	0.537066	−	0.843540i	$-0.319533\pi$
$617$	26.6809	1.07413	0.537066	+	0.843540i	$0.319533\pi$
$618$	−34.5594	−1.39018
$619$	−5.07645	−0.204040	−0.102020	−	0.994782i	$-0.532531\pi$
$619$	−5.07645	−0.204040	−0.102020	+	0.994782i	$0.532531\pi$
$620$	1.87953	0.0754836
$621$	4.22647	0.169602
$622$	5.42245	0.217420
$623$	−6.08594	−0.243828
$624$	4.46351	0.178684
$625$	−15.5099	−0.620396
$626$	−15.1672	−0.606204
$627$	−39.5156	−1.57810
$628$	−1.04292	−0.0416171
$629$	−24.4112	−0.973337
$630$	1.65267	0.0658441
$631$	41.3090	1.64448	0.822242	−	0.569138i	$-0.192723\pi$
$631$	41.3090	1.64448	0.822242	+	0.569138i	$0.192723\pi$
$632$	−6.54992	−0.260542
$633$	−44.8839	−1.78397
$634$	−0.282897	−0.0112353
$635$	6.29551	0.249830
$636$	−1.34487	−0.0533275
$637$	13.3429	0.528665
$638$	−40.3452	−1.59728
$639$	−12.2262	−0.483660
$640$	1.87953	0.0742948
$641$	−1.43691	−0.0567546	−0.0283773	−	0.999597i	$-0.509034\pi$
$641$	−1.43691	−0.0567546	−0.0283773	+	0.999597i	$0.509034\pi$
$642$	−19.7468	−0.779343
$643$	11.0988	0.437694	0.218847	−	0.975759i	$-0.429770\pi$
$643$	11.0988	0.437694	0.218847	+	0.975759i	$0.429770\pi$
$644$	0.958022	0.0377514
$645$	−31.6499	−1.24622
$646$	16.0048	0.629700
$647$	−35.3776	−1.39084	−0.695418	−	0.718606i	$-0.744781\pi$
$647$	−35.3776	−1.39084	−0.695418	+	0.718606i	$0.744781\pi$
$648$	10.6937	0.420088
$649$	71.1570	2.79316
$650$	−2.85964	−0.112164
$651$	0.896733	0.0351457
$652$	−21.9112	−0.858111
$653$	2.14504	0.0839419	0.0419709	−	0.999119i	$-0.486636\pi$
$653$	2.14504	0.0839419	0.0419709	+	0.999119i	$0.486636\pi$
$654$	33.0562	1.29260
$655$	−2.60077	−0.101621
$656$	0.408195	0.0159373
$657$	−3.30027	−0.128756
$658$	0.954383	0.0372057
$659$	−7.22637	−0.281499	−0.140750	−	0.990045i	$-0.544951\pi$
$659$	−7.22637	−0.281499	−0.140750	+	0.990045i	$0.544951\pi$
$660$	−25.0275	−0.974194
$661$	6.62964	0.257863	0.128932	−	0.991653i	$-0.458845\pi$
$661$	6.62964	0.257863	0.128932	+	0.991653i	$0.458845\pi$
$662$	5.93789	0.230783
$663$	24.0728	0.934911
$664$	4.77339	0.185243
$665$	2.18375	0.0846822
$666$	10.1653	0.393899
$667$	−16.9806	−0.657491
$668$	−20.1448	−0.779426
$669$	−5.69584	−0.220214
$670$	8.86295	0.342406
$671$	−17.3148	−0.668429
$672$	0.896733	0.0345922
$673$	−43.9962	−1.69593	−0.847965	−	0.530052i	$-0.822173\pi$
$673$	−43.9962	−1.69593	−0.847965	+	0.530052i	$0.822173\pi$
$674$	0.476027	0.0183359
$675$	−2.53454	−0.0975546
$676$	−9.20216	−0.353929
$677$	−3.47446	−0.133534	−0.0667672	−	0.997769i	$-0.521268\pi$
$677$	−3.47446	−0.133534	−0.0667672	+	0.997769i	$0.521268\pi$
$678$	5.72872	0.220010
$679$	0.391521	0.0150252
$680$	10.1367	0.388727
$681$	56.7728	2.17554
$682$	−5.81381	−0.222622
$683$	−20.6048	−0.788420	−0.394210	−	0.919020i	$-0.628982\pi$
$683$	−20.6048	−0.788420	−0.394210	+	0.919020i	$0.628982\pi$
$684$	−6.66475	−0.254833
$685$	15.9987	0.611279
$686$	5.42127	0.206985
$687$	−1.57654	−0.0601489
$688$	−7.35218	−0.280299
$689$	−1.14430	−0.0435943
$690$	−10.5336	−0.401008
$691$	−31.2591	−1.18915	−0.594576	−	0.804039i	$-0.702680\pi$
$691$	−31.2591	−1.18915	−0.594576	+	0.804039i	$0.702680\pi$
$692$	5.77371	0.219483
$693$	−5.11210	−0.194193
$694$	12.7048	0.482266
$695$	33.5694	1.27336
$696$	−15.8943	−0.602470
$697$	2.20149	0.0833875
$698$	−23.2176	−0.878799
$699$	62.5637	2.36638
$700$	−0.574510	−0.0217144
$701$	41.8076	1.57905	0.789525	−	0.613719i	$-0.210327\pi$
$701$	41.8076	1.57905	0.789525	+	0.613719i	$0.210327\pi$
$702$	3.36609	0.127045
$703$	13.4319	0.506594
$704$	−5.81381	−0.219116
$705$	−10.4936	−0.395212
$706$	14.7537	0.555262
$707$	−4.96186	−0.186610
$708$	28.0327	1.05354
$709$	−9.48020	−0.356036	−0.178018	−	0.984027i	$-0.556969\pi$
$709$	−9.48020	−0.356036	−0.178018	+	0.984027i	$0.556969\pi$
$710$	−10.2319	−0.383995
$711$	14.7102	0.551677
$712$	15.5444	0.582550
$713$	−2.44693	−0.0916381
$714$	4.83630	0.180994
$715$	−21.2950	−0.796387
$716$	−11.8783	−0.443912
$717$	−14.1273	−0.527595
$718$	11.7064	0.436878
$719$	27.6392	1.03077	0.515384	−	0.856959i	$-0.327649\pi$
$719$	27.6392	1.03077	0.515384	+	0.856959i	$0.327649\pi$
$720$	−4.22117	−0.157314
$721$	−5.90761	−0.220011
$722$	10.1936	0.379366
$723$	−13.7693	−0.512088
$724$	−3.39693	−0.126246
$725$	10.1830	0.378186
$726$	52.2216	1.93812
$727$	−36.3705	−1.34891	−0.674454	−	0.738317i	$-0.735621\pi$
$727$	−36.3705	−1.34891	−0.674454	+	0.738317i	$0.735621\pi$
$728$	0.762997	0.0282786
$729$	−12.1483	−0.449938
$730$	−2.76194	−0.102224
$731$	−39.6521	−1.46659
$732$	−6.82126	−0.252121
$733$	28.9188	1.06814	0.534070	−	0.845440i	$-0.320662\pi$
$733$	28.9188	1.06814	0.534070	+	0.845440i	$0.320662\pi$
$734$	12.6572	0.467187
$735$	−29.4740	−1.08716
$736$	−2.44693	−0.0901949
$737$	−27.4151	−1.00985
$738$	−0.916751	−0.0337461
$739$	−7.88896	−0.290200	−0.145100	−	0.989417i	$-0.546350\pi$
$739$	−7.88896	−0.290200	−0.145100	+	0.989417i	$0.546350\pi$
$740$	8.50720	0.312731
$741$	−13.2458	−0.486595
$742$	−0.229893	−0.00843964
$743$	19.1051	0.700897	0.350449	−	0.936582i	$-0.386029\pi$
$743$	19.1051	0.700897	0.350449	+	0.936582i	$0.386029\pi$
$744$	−2.29039	−0.0839696
$745$	−3.79659	−0.139096
$746$	11.5396	0.422493
$747$	−10.7204	−0.392238
$748$	−31.3553	−1.14646
$749$	−3.37553	−0.123339
$750$	27.8410	1.01661
$751$	−27.2192	−0.993244	−0.496622	−	0.867967i	$-0.665427\pi$
$751$	−27.2192	−0.993244	−0.496622	+	0.867967i	$0.665427\pi$
$752$	−2.43763	−0.0888912
$753$	48.0954	1.75269
$754$	−13.5238	−0.492509
$755$	−6.93751	−0.252482
$756$	0.676257	0.0245952
$757$	−36.8673	−1.33996	−0.669982	−	0.742377i	$-0.733698\pi$
$757$	−36.8673	−1.33996	−0.669982	+	0.742377i	$0.733698\pi$
$758$	6.46194	0.234708
$759$	32.5829	1.18269
$760$	−5.57761	−0.202321
$761$	16.9963	0.616117	0.308059	−	0.951367i	$-0.400321\pi$
$761$	16.9963	0.616117	0.308059	+	0.951367i	$0.400321\pi$
$762$	−7.67170	−0.277916
$763$	5.65065	0.204567
$764$	−1.42482	−0.0515482
$765$	−22.7658	−0.823099
$766$	−35.1916	−1.27153
$767$	23.8520	0.861247
$768$	−2.29039	−0.0826472
$769$	−13.1793	−0.475258	−0.237629	−	0.971356i	$-0.576370\pi$
$769$	−13.1793	−0.475258	−0.237629	+	0.971356i	$0.576370\pi$
$770$	−4.27823	−0.154177
$771$	41.6310	1.49930
$772$	17.1041	0.615591
$773$	−12.5879	−0.452754	−0.226377	−	0.974040i	$-0.572688\pi$
$773$	−12.5879	−0.452754	−0.226377	+	0.974040i	$0.572688\pi$
$774$	16.5120	0.593512
$775$	1.46738	0.0527099
$776$	−1.00000	−0.0358979
$777$	4.05884	0.145610
$778$	22.7611	0.816023
$779$	−1.21134	−0.0434009
$780$	−8.38929	−0.300385
$781$	31.6495	1.13251
$782$	−13.1969	−0.471919
$783$	−11.9864	−0.428359
$784$	−6.84671	−0.244525
$785$	1.96020	0.0699625
$786$	3.16930	0.113045
$787$	−24.9707	−0.890108	−0.445054	−	0.895504i	$-0.646816\pi$
$787$	−24.9707	−0.890108	−0.445054	+	0.895504i	$0.646816\pi$
$788$	8.74533	0.311540
$789$	33.0245	1.17570
$790$	12.3107	0.437996
$791$	0.979272	0.0348189
$792$	13.0570	0.463961
$793$	−5.80396	−0.206105
$794$	−18.9523	−0.672591
$795$	2.52772	0.0896489
$796$	−8.18082	−0.289961
$797$	−30.0117	−1.06307	−0.531534	−	0.847037i	$-0.678384\pi$
$797$	−30.0117	−1.06307	−0.531534	+	0.847037i	$0.678384\pi$
$798$	−2.66111	−0.0942023
$799$	−13.1467	−0.465098
$800$	1.46738	0.0518797
$801$	−34.9106	−1.23350
$802$	−39.6354	−1.39958
$803$	8.54330	0.301487
$804$	−10.8004	−0.380900
$805$	−1.80063	−0.0634638
$806$	−1.94880	−0.0686437
$807$	44.4481	1.56465
$808$	12.6733	0.445845
$809$	42.2056	1.48387	0.741935	−	0.670472i	$-0.233908\pi$
$809$	42.2056	1.48387	0.741935	+	0.670472i	$0.233908\pi$
$810$	−20.0991	−0.706209
$811$	−19.6399	−0.689651	−0.344825	−	0.938667i	$-0.612062\pi$
$811$	−19.6399	−0.689651	−0.344825	+	0.938667i	$0.612062\pi$
$812$	−2.71698	−0.0953473
$813$	−68.3772	−2.39809
$814$	−26.3147	−0.922331
$815$	41.1828	1.44257
$816$	−12.3526	−0.432428
$817$	21.8180	0.763317
$818$	−36.8124	−1.28712
$819$	−1.71359	−0.0598777
$820$	−0.767213	−0.0267922
$821$	28.6523	0.999972	0.499986	−	0.866034i	$-0.333339\pi$
$821$	28.6523	0.999972	0.499986	+	0.866034i	$0.333339\pi$
$822$	−19.4960	−0.680000
$823$	0.392255	0.0136732	0.00683658	−	0.999977i	$-0.497824\pi$
$823$	0.392255	0.0136732	0.00683658	+	0.999977i	$0.497824\pi$
$824$	15.0889	0.525647
$825$	−19.5394	−0.680276
$826$	4.79194	0.166733
$827$	26.0724	0.906628	0.453314	−	0.891351i	$-0.350242\pi$
$827$	26.0724	0.906628	0.453314	+	0.891351i	$0.350242\pi$
$828$	5.49547	0.190981
$829$	26.9238	0.935103	0.467552	−	0.883966i	$-0.345136\pi$
$829$	26.9238	0.935103	0.467552	+	0.883966i	$0.345136\pi$
$830$	−8.97170	−0.311412
$831$	−39.0720	−1.35539
$832$	−1.94880	−0.0675626
$833$	−36.9260	−1.27941
$834$	−40.9075	−1.41651
$835$	37.8627	1.31029
$836$	17.2528	0.596702
$837$	−1.72726	−0.0597027
$838$	−11.5587	−0.399290
$839$	−26.6096	−0.918665	−0.459332	−	0.888264i	$-0.651911\pi$
$839$	−26.6096	−0.918665	−0.459332	+	0.888264i	$0.651911\pi$
$840$	−1.68543	−0.0581530
$841$	19.1574	0.660600
$842$	−36.2368	−1.24880
$843$	−69.7643	−2.40281
$844$	19.5966	0.674544
$845$	17.2957	0.594990
$846$	5.47459	0.188220
$847$	8.92681	0.306729
$848$	0.587180	0.0201638
$849$	−60.7657	−2.08547
$850$	7.91394	0.271446
$851$	−11.0754	−0.379660
$852$	12.4685	0.427165
$853$	26.6551	0.912652	0.456326	−	0.889813i	$-0.349165\pi$
$853$	26.6551	0.912652	0.456326	+	0.889813i	$0.349165\pi$
$854$	−1.16603	−0.0399008
$855$	12.5266	0.428400
$856$	8.62159	0.294680
$857$	−52.0290	−1.77728	−0.888639	−	0.458607i	$-0.848348\pi$
$857$	−52.0290	−1.77728	−0.888639	+	0.458607i	$0.848348\pi$
$858$	25.9500	0.885919
$859$	−5.77401	−0.197007	−0.0985034	−	0.995137i	$-0.531406\pi$
$859$	−5.77401	−0.197007	−0.0985034	+	0.995137i	$0.531406\pi$
$860$	13.8186	0.471211
$861$	−0.366042	−0.0124747
$862$	−1.42685	−0.0485986
$863$	50.8018	1.72931	0.864656	−	0.502364i	$-0.167536\pi$
$863$	50.8018	1.72931	0.864656	+	0.502364i	$0.167536\pi$
$864$	−1.72726	−0.0587625
$865$	−10.8518	−0.368973
$866$	−23.0250	−0.782423
$867$	−27.6841	−0.940202
$868$	−0.391521	−0.0132891
$869$	−38.0799	−1.29177
$870$	29.8737	1.01281
$871$	−9.18963	−0.311379
$872$	−14.4326	−0.488749
$873$	2.24587	0.0760111
$874$	7.26141	0.245621
$875$	4.75917	0.160889
$876$	3.36569	0.113716
$877$	14.4629	0.488377	0.244188	−	0.969728i	$-0.421478\pi$
$877$	14.4629	0.488377	0.244188	+	0.969728i	$0.421478\pi$
$878$	−1.21161	−0.0408898
$879$	60.0368	2.02499
$880$	10.9272	0.368356
$881$	20.2252	0.681404	0.340702	−	0.940171i	$-0.389335\pi$
$881$	20.2252	0.681404	0.340702	+	0.940171i	$0.389335\pi$
$882$	15.3768	0.517764
$883$	−25.3269	−0.852320	−0.426160	−	0.904648i	$-0.640134\pi$
$883$	−25.3269	−0.852320	−0.426160	+	0.904648i	$0.640134\pi$
$884$	−10.5104	−0.353502
$885$	−52.6883	−1.77110
$886$	9.28258	0.311855
$887$	10.1918	0.342207	0.171104	−	0.985253i	$-0.445267\pi$
$887$	10.1918	0.342207	0.171104	+	0.985253i	$0.445267\pi$
$888$	−10.3669	−0.347889
$889$	−1.31141	−0.0439832
$890$	−29.2161	−0.979324
$891$	62.1710	2.08281
$892$	2.48685	0.0832658
$893$	7.23382	0.242071
$894$	4.62652	0.154734
$895$	22.3255	0.746260
$896$	−0.391521	−0.0130798
$897$	10.9219	0.364671
$898$	6.21146	0.207279
$899$	6.93955	0.231447
$900$	−3.29554	−0.109851
$901$	3.16681	0.105502
$902$	2.37317	0.0790178
$903$	6.59294	0.219399
$904$	−2.50120	−0.0831887
$905$	6.38461	0.212232
$906$	8.45403	0.280866
$907$	−33.1134	−1.09951	−0.549756	−	0.835325i	$-0.685279\pi$
$907$	−33.1134	−1.09951	−0.549756	+	0.835325i	$0.685279\pi$
$908$	−24.7875	−0.822601
$909$	−28.4625	−0.944043
$910$	−1.43407	−0.0475391
$911$	−52.3241	−1.73357	−0.866787	−	0.498678i	$-0.833819\pi$
$911$	−52.3241	−1.73357	−0.866787	+	0.498678i	$0.833819\pi$
$912$	6.79686	0.225067
$913$	27.7515	0.918442
$914$	−20.4086	−0.675056
$915$	12.8207	0.423841
$916$	0.688331	0.0227431
$917$	0.541762	0.0178906
$918$	−9.31552	−0.307458
$919$	−42.9257	−1.41599	−0.707993	−	0.706219i	$-0.750399\pi$
$919$	−42.9257	−1.41599	−0.707993	+	0.706219i	$0.750399\pi$
$920$	4.59906	0.151627
$921$	−42.9518	−1.41531
$922$	−22.4769	−0.740238
$923$	10.6090	0.349200
$924$	5.21343	0.171509
$925$	6.64173	0.218379
$926$	−14.8437	−0.487794
$927$	−33.8876	−1.11302
$928$	6.93955	0.227802
$929$	−29.1638	−0.956835	−0.478417	−	0.878133i	$-0.658789\pi$
$929$	−29.1638	−0.956835	−0.478417	+	0.878133i	$0.658789\pi$
$930$	4.30484	0.141161
$931$	20.3180	0.665897
$932$	−27.3158	−0.894759
$933$	12.4195	0.406596
$934$	−31.1016	−1.01768
$935$	58.9331	1.92732
$936$	4.37675	0.143059
$937$	−22.8941	−0.747918	−0.373959	−	0.927445i	$-0.622000\pi$
$937$	−22.8941	−0.747918	−0.373959	+	0.927445i	$0.622000\pi$
$938$	−1.84622	−0.0602814
$939$	−34.7388	−1.13366
$940$	4.58159	0.149435
$941$	−24.8326	−0.809521	−0.404760	−	0.914423i	$-0.632645\pi$
$941$	−24.8326	−0.809521	−0.404760	+	0.914423i	$0.632645\pi$
$942$	−2.38869	−0.0778278
$943$	0.998823	0.0325261
$944$	−12.2393	−0.398356
$945$	−1.27104	−0.0413470
$946$	−42.7441	−1.38973
$947$	42.2551	1.37311	0.686553	−	0.727080i	$-0.259123\pi$
$947$	42.2551	1.37311	0.686553	+	0.727080i	$0.259123\pi$
$948$	−15.0018	−0.487237
$949$	2.86374	0.0929609
$950$	−4.35454	−0.141280
$951$	−0.647943	−0.0210110
$952$	−2.11157	−0.0684363
$953$	14.2255	0.460809	0.230405	−	0.973095i	$-0.425995\pi$
$953$	14.2255	0.460809	0.230405	+	0.973095i	$0.425995\pi$
$954$	−1.31873	−0.0426954
$955$	2.67799	0.0866577
$956$	6.16810	0.199491
$957$	−92.4061	−2.98707
$958$	−3.69589	−0.119409
$959$	−3.33266	−0.107617
$960$	4.30484	0.138938
$961$	1.00000	0.0322581
$962$	−8.82077	−0.284393
$963$	−19.3629	−0.623962
$964$	6.01180	0.193627
$965$	−32.1477	−1.03487
$966$	2.19424	0.0705985
$967$	6.15335	0.197878	0.0989392	−	0.995093i	$-0.468455\pi$
$967$	6.15335	0.197878	0.0989392	+	0.995093i	$0.468455\pi$
$968$	−22.8003	−0.732831
$969$	36.6571	1.17760
$970$	1.87953	0.0603480
$971$	8.43139	0.270576	0.135288	−	0.990806i	$-0.456804\pi$
$971$	8.43139	0.270576	0.135288	+	0.990806i	$0.456804\pi$
$972$	19.3109	0.619397
$973$	−6.99277	−0.224178
$974$	27.8939	0.893777
$975$	−6.54967	−0.209757
$976$	2.97822	0.0953304
$977$	−29.8491	−0.954956	−0.477478	−	0.878644i	$-0.658449\pi$
$977$	−29.8491	−0.954956	−0.477478	+	0.878644i	$0.658449\pi$
$978$	−50.1852	−1.60475
$979$	90.3720	2.88830
$980$	12.8686	0.411072
$981$	32.4137	1.03489
$982$	−24.2926	−0.775208
$983$	36.3831	1.16044	0.580220	−	0.814460i	$-0.302967\pi$
$983$	36.3831	1.16044	0.580220	+	0.814460i	$0.302967\pi$
$984$	0.934923	0.0298043
$985$	−16.4371	−0.523729
$986$	37.4267	1.19191
$987$	2.18590	0.0695781
$988$	5.78320	0.183988
$989$	−17.9902	−0.572056
$990$	−24.5410	−0.779965
$991$	−3.53429	−0.112270	−0.0561352	−	0.998423i	$-0.517878\pi$
$991$	−3.53429	−0.112270	−0.0561352	+	0.998423i	$0.517878\pi$
$992$	1.00000	0.0317500
$993$	13.6001	0.431585
$994$	2.13138	0.0676033
$995$	15.3761	0.487454
$996$	10.9329	0.346422
$997$	−52.1701	−1.65224	−0.826121	−	0.563492i	$-0.809458\pi$
$997$	−52.1701	−1.65224	−0.826121	+	0.563492i	$0.809458\pi$
$998$	−1.21566	−0.0384810
$999$	−7.81799	−0.247350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.6	✓	32	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.29039 q^{3} +1.00000 q^{4} -1.87953 q^{5} +2.29039 q^{6} +0.391521 q^{7} -1.00000 q^{8} +2.24587 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.29039 q^{3} +1.00000 q^{4} -1.87953 q^{5} +2.29039 q^{6} +0.391521 q^{7} -1.00000 q^{8} +2.24587 q^{9} +1.87953 q^{10} -5.81381 q^{11} -2.29039 q^{12} -1.94880 q^{13} -0.391521 q^{14} +4.30484 q^{15} +1.00000 q^{16} +5.39325 q^{17} -2.24587 q^{18} -2.96756 q^{19} -1.87953 q^{20} -0.896733 q^{21} +5.81381 q^{22} +2.44693 q^{23} +2.29039 q^{24} -1.46738 q^{25} +1.94880 q^{26} +1.72726 q^{27} +0.391521 q^{28} -6.93955 q^{29} -4.30484 q^{30} -1.00000 q^{31} -1.00000 q^{32} +13.3159 q^{33} -5.39325 q^{34} -0.735873 q^{35} +2.24587 q^{36} -4.52625 q^{37} +2.96756 q^{38} +4.46351 q^{39} +1.87953 q^{40} +0.408195 q^{41} +0.896733 q^{42} -7.35218 q^{43} -5.81381 q^{44} -4.22117 q^{45} -2.44693 q^{46} -2.43763 q^{47} -2.29039 q^{48} -6.84671 q^{49} +1.46738 q^{50} -12.3526 q^{51} -1.94880 q^{52} +0.587180 q^{53} -1.72726 q^{54} +10.9272 q^{55} -0.391521 q^{56} +6.79686 q^{57} +6.93955 q^{58} -12.2393 q^{59} +4.30484 q^{60} +2.97822 q^{61} +1.00000 q^{62} +0.879303 q^{63} +1.00000 q^{64} +3.66283 q^{65} -13.3159 q^{66} +4.71552 q^{67} +5.39325 q^{68} -5.60441 q^{69} +0.735873 q^{70} -5.44385 q^{71} -2.24587 q^{72} -1.46949 q^{73} +4.52625 q^{74} +3.36087 q^{75} -2.96756 q^{76} -2.27623 q^{77} -4.46351 q^{78} +6.54992 q^{79} -1.87953 q^{80} -10.6937 q^{81} -0.408195 q^{82} -4.77339 q^{83} -0.896733 q^{84} -10.1367 q^{85} +7.35218 q^{86} +15.8943 q^{87} +5.81381 q^{88} -15.5444 q^{89} +4.22117 q^{90} -0.762997 q^{91} +2.44693 q^{92} +2.29039 q^{93} +2.43763 q^{94} +5.57761 q^{95} +2.29039 q^{96} +1.00000 q^{97} +6.84671 q^{98} -13.0570 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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