LMFDB - Embedded newform 4031.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$0$
Dimension:	$98$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08450 q^{2} +0.675318 q^{3} +2.34516 q^{4} -1.05546 q^{5} -1.40770 q^{6} -4.46025 q^{7} -0.719483 q^{8} -2.54395 q^{9} +O(q^{10})$	\(q-2.08450 q^{2} +0.675318 q^{3} +2.34516 q^{4} -1.05546 q^{5} -1.40770 q^{6} -4.46025 q^{7} -0.719483 q^{8} -2.54395 q^{9} +2.20012 q^{10} +3.41671 q^{11} +1.58373 q^{12} -1.13635 q^{13} +9.29741 q^{14} -0.712772 q^{15} -3.19055 q^{16} -5.08799 q^{17} +5.30287 q^{18} +0.618161 q^{19} -2.47523 q^{20} -3.01208 q^{21} -7.12214 q^{22} -7.25585 q^{23} -0.485880 q^{24} -3.88600 q^{25} +2.36872 q^{26} -3.74392 q^{27} -10.4600 q^{28} +1.00000 q^{29} +1.48578 q^{30} +3.87154 q^{31} +8.08968 q^{32} +2.30736 q^{33} +10.6059 q^{34} +4.70762 q^{35} -5.96596 q^{36} -0.331880 q^{37} -1.28856 q^{38} -0.767396 q^{39} +0.759387 q^{40} -2.73464 q^{41} +6.27870 q^{42} -10.7254 q^{43} +8.01272 q^{44} +2.68504 q^{45} +15.1249 q^{46} +5.64222 q^{47} -2.15463 q^{48} +12.8938 q^{49} +8.10038 q^{50} -3.43601 q^{51} -2.66492 q^{52} -12.9130 q^{53} +7.80423 q^{54} -3.60620 q^{55} +3.20908 q^{56} +0.417455 q^{57} -2.08450 q^{58} +8.45719 q^{59} -1.67156 q^{60} +0.103400 q^{61} -8.07024 q^{62} +11.3466 q^{63} -10.4819 q^{64} +1.19937 q^{65} -4.80971 q^{66} -13.7768 q^{67} -11.9321 q^{68} -4.90000 q^{69} -9.81306 q^{70} +1.82915 q^{71} +1.83033 q^{72} -2.52886 q^{73} +0.691804 q^{74} -2.62428 q^{75} +1.44968 q^{76} -15.2394 q^{77} +1.59964 q^{78} -11.4027 q^{79} +3.36750 q^{80} +5.10350 q^{81} +5.70037 q^{82} +11.5415 q^{83} -7.06381 q^{84} +5.37018 q^{85} +22.3571 q^{86} +0.675318 q^{87} -2.45826 q^{88} -3.58564 q^{89} -5.59697 q^{90} +5.06840 q^{91} -17.0161 q^{92} +2.61452 q^{93} -11.7612 q^{94} -0.652445 q^{95} +5.46310 q^{96} +9.56316 q^{97} -26.8772 q^{98} -8.69192 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) $ 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.08450	−1.47397	−0.736984	−	0.675911i	$-0.763751\pi$
$2$	−2.08450	−1.47397	−0.736984	+	0.675911i	$0.763751\pi$
$3$	0.675318	0.389895	0.194947	−	0.980814i	$-0.437546\pi$
$3$	0.675318	0.389895	0.194947	+	0.980814i	$0.437546\pi$
$4$	2.34516	1.17258
$5$	−1.05546	−0.472017	−0.236008	−	0.971751i	$-0.575839\pi$
$5$	−1.05546	−0.472017	−0.236008	+	0.971751i	$0.575839\pi$
$6$	−1.40770	−0.574692
$7$	−4.46025	−1.68582	−0.842908	−	0.538058i	$-0.819158\pi$
$7$	−4.46025	−1.68582	−0.842908	+	0.538058i	$0.819158\pi$
$8$	−0.719483	−0.254376
$9$	−2.54395	−0.847982
$10$	2.20012	0.695738
$11$	3.41671	1.03018	0.515088	−	0.857137i	$-0.327759\pi$
$11$	3.41671	1.03018	0.515088	+	0.857137i	$0.327759\pi$
$12$	1.58373	0.457182
$13$	−1.13635	−0.315166	−0.157583	−	0.987506i	$-0.550370\pi$
$13$	−1.13635	−0.315166	−0.157583	+	0.987506i	$0.550370\pi$
$14$	9.29741	2.48484
$15$	−0.712772	−0.184037
$16$	−3.19055	−0.797637
$17$	−5.08799	−1.23402	−0.617010	−	0.786955i	$-0.711656\pi$
$17$	−5.08799	−1.23402	−0.617010	+	0.786955i	$0.711656\pi$
$18$	5.30287	1.24990
$19$	0.618161	0.141816	0.0709079	−	0.997483i	$-0.477410\pi$
$19$	0.618161	0.141816	0.0709079	+	0.997483i	$0.477410\pi$
$20$	−2.47523	−0.553477
$21$	−3.01208	−0.657291
$22$	−7.12214	−1.51845
$23$	−7.25585	−1.51295	−0.756475	−	0.654023i	$-0.773080\pi$
$23$	−7.25585	−1.51295	−0.756475	+	0.654023i	$0.773080\pi$
$24$	−0.485880	−0.0991798
$25$	−3.88600	−0.777200
$26$	2.36872	0.464545
$27$	−3.74392	−0.720519
$28$	−10.4600	−1.97675
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.48578	0.271264
$31$	3.87154	0.695349	0.347674	−	0.937615i	$-0.386971\pi$
$31$	3.87154	0.695349	0.347674	+	0.937615i	$0.386971\pi$
$32$	8.08968	1.43007
$33$	2.30736	0.401660
$34$	10.6059	1.81890
$35$	4.70762	0.795734
$36$	−5.96596	−0.994326
$37$	−0.331880	−0.0545607	−0.0272803	−	0.999628i	$-0.508685\pi$
$37$	−0.331880	−0.0545607	−0.0272803	+	0.999628i	$0.508685\pi$
$38$	−1.28856	−0.209032
$39$	−0.767396	−0.122882
$40$	0.759387	0.120070
$41$	−2.73464	−0.427079	−0.213539	−	0.976934i	$-0.568499\pi$
$41$	−2.73464	−0.427079	−0.213539	+	0.976934i	$0.568499\pi$
$42$	6.27870	0.968825
$43$	−10.7254	−1.63561	−0.817804	−	0.575496i	$-0.804809\pi$
$43$	−10.7254	−1.63561	−0.817804	+	0.575496i	$0.804809\pi$
$44$	8.01272	1.20796
$45$	2.68504	0.400262
$46$	15.1249	2.23004
$47$	5.64222	0.823002	0.411501	−	0.911409i	$-0.365005\pi$
$47$	5.64222	0.823002	0.411501	+	0.911409i	$0.365005\pi$
$48$	−2.15463	−0.310995
$49$	12.8938	1.84198
$50$	8.10038	1.14557
$51$	−3.43601	−0.481138
$52$	−2.66492	−0.369558
$53$	−12.9130	−1.77373	−0.886867	−	0.462025i	$-0.847123\pi$
$53$	−12.9130	−1.77373	−0.886867	+	0.462025i	$0.847123\pi$
$54$	7.80423	1.06202
$55$	−3.60620	−0.486260
$56$	3.20908	0.428831
$57$	0.417455	0.0552932
$58$	−2.08450	−0.273709
$59$	8.45719	1.10103	0.550516	−	0.834825i	$-0.314431\pi$
$59$	8.45719	1.10103	0.550516	+	0.834825i	$0.314431\pi$
$60$	−1.67156	−0.215798
$61$	0.103400	0.0132390	0.00661951	−	0.999978i	$-0.497893\pi$
$61$	0.103400	0.0132390	0.00661951	+	0.999978i	$0.497893\pi$
$62$	−8.07024	−1.02492
$63$	11.3466	1.42954
$64$	−10.4819	−1.31023
$65$	1.19937	0.148764
$66$	−4.80971	−0.592034
$67$	−13.7768	−1.68311	−0.841553	−	0.540175i	$-0.818358\pi$
$67$	−13.7768	−1.68311	−0.841553	+	0.540175i	$0.818358\pi$
$68$	−11.9321	−1.44699
$69$	−4.90000	−0.589891
$70$	−9.81306	−1.17289
$71$	1.82915	0.217081	0.108540	−	0.994092i	$-0.465382\pi$
$71$	1.82915	0.217081	0.108540	+	0.994092i	$0.465382\pi$
$72$	1.83033	0.215706
$73$	−2.52886	−0.295980	−0.147990	−	0.988989i	$-0.547280\pi$
$73$	−2.52886	−0.295980	−0.147990	+	0.988989i	$0.547280\pi$
$74$	0.691804	0.0804206
$75$	−2.62428	−0.303026
$76$	1.44968	0.166290
$77$	−15.2394	−1.73669
$78$	1.59964	0.181124
$79$	−11.4027	−1.28290	−0.641450	−	0.767164i	$-0.721667\pi$
$79$	−11.4027	−1.28290	−0.641450	+	0.767164i	$0.721667\pi$
$80$	3.36750	0.376498
$81$	5.10350	0.567056
$82$	5.70037	0.629500
$83$	11.5415	1.26684	0.633420	−	0.773808i	$-0.281650\pi$
$83$	11.5415	1.26684	0.633420	+	0.773808i	$0.281650\pi$
$84$	−7.06381	−0.770725
$85$	5.37018	0.582478
$86$	22.3571	2.41083
$87$	0.675318	0.0724016
$88$	−2.45826	−0.262052
$89$	−3.58564	−0.380077	−0.190039	−	0.981777i	$-0.560861\pi$
$89$	−3.58564	−0.380077	−0.190039	+	0.981777i	$0.560861\pi$
$90$	−5.59697	−0.589973
$91$	5.06840	0.531313
$92$	−17.0161	−1.77405
$93$	2.61452	0.271113
$94$	−11.7612	−1.21308
$95$	−0.652445	−0.0669395
$96$	5.46310	0.557576
$97$	9.56316	0.970992	0.485496	−	0.874239i	$-0.338639\pi$
$97$	9.56316	0.970992	0.485496	+	0.874239i	$0.338639\pi$
$98$	−26.8772	−2.71501
$99$	−8.69192	−0.873570
$100$	−9.11328	−0.911328
$101$	−13.2182	−1.31526	−0.657629	−	0.753342i	$-0.728440\pi$
$101$	−13.2182	−1.31526	−0.657629	+	0.753342i	$0.728440\pi$
$102$	7.16238	0.709181
$103$	−8.12406	−0.800488	−0.400244	−	0.916409i	$-0.631075\pi$
$103$	−8.12406	−0.800488	−0.400244	+	0.916409i	$0.631075\pi$
$104$	0.817584	0.0801707
$105$	3.17914	0.310252
$106$	26.9171	2.61442
$107$	1.42653	0.137908	0.0689538	−	0.997620i	$-0.478034\pi$
$107$	1.42653	0.137908	0.0689538	+	0.997620i	$0.478034\pi$
$108$	−8.78009	−0.844865
$109$	−0.772312	−0.0739741	−0.0369870	−	0.999316i	$-0.511776\pi$
$109$	−0.772312	−0.0739741	−0.0369870	+	0.999316i	$0.511776\pi$
$110$	7.51715	0.716732
$111$	−0.224124	−0.0212729
$112$	14.2306	1.34467
$113$	−18.3009	−1.72160	−0.860802	−	0.508939i	$-0.830038\pi$
$113$	−18.3009	−1.72160	−0.860802	+	0.508939i	$0.830038\pi$
$114$	−0.870186	−0.0815004
$115$	7.65828	0.714138
$116$	2.34516	0.217742
$117$	2.89081	0.267255
$118$	−17.6290	−1.62289
$119$	22.6937	2.08033
$120$	0.512828	0.0468145
$121$	0.673881	0.0612619
$122$	−0.215538	−0.0195139
$123$	−1.84675	−0.166516
$124$	9.07937	0.815352
$125$	9.37884	0.838869
$126$	−23.6521	−2.10710
$127$	17.1679	1.52340	0.761701	−	0.647929i	$-0.224365\pi$
$127$	17.1679	1.52340	0.761701	+	0.647929i	$0.224365\pi$
$128$	5.67015	0.501175
$129$	−7.24305	−0.637715
$130$	−2.50010	−0.219273
$131$	4.81415	0.420614	0.210307	−	0.977635i	$-0.432554\pi$
$131$	4.81415	0.420614	0.210307	+	0.977635i	$0.432554\pi$
$132$	5.41113	0.470978
$133$	−2.75715	−0.239075
$134$	28.7178	2.48084
$135$	3.95157	0.340097
$136$	3.66073	0.313905
$137$	16.0639	1.37243	0.686216	−	0.727398i	$-0.259271\pi$
$137$	16.0639	1.37243	0.686216	+	0.727398i	$0.259271\pi$
$138$	10.2141	0.869480
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	11.0401	0.933061
$141$	3.81029	0.320884
$142$	−3.81288	−0.319970
$143$	−3.88257	−0.324677
$144$	8.11659	0.676382
$145$	−1.05546	−0.0876514
$146$	5.27141	0.436265
$147$	8.70743	0.718177
$148$	−0.778310	−0.0639767
$149$	13.6804	1.12074	0.560372	−	0.828241i	$-0.310658\pi$
$149$	13.6804	1.12074	0.560372	+	0.828241i	$0.310658\pi$
$150$	5.47033	0.446651
$151$	18.3090	1.48997	0.744984	−	0.667082i	$-0.232457\pi$
$151$	18.3090	1.48997	0.744984	+	0.667082i	$0.232457\pi$
$152$	−0.444756	−0.0360745
$153$	12.9436	1.04643
$154$	31.7665	2.55982
$155$	−4.08626	−0.328217
$156$	−1.79967	−0.144089
$157$	16.7761	1.33888	0.669440	−	0.742867i	$-0.266534\pi$
$157$	16.7761	1.33888	0.669440	+	0.742867i	$0.266534\pi$
$158$	23.7689	1.89095
$159$	−8.72036	−0.691569
$160$	−8.53835	−0.675016
$161$	32.3629	2.55055
$162$	−10.6383	−0.835821
$163$	−5.18510	−0.406128	−0.203064	−	0.979165i	$-0.565090\pi$
$163$	−5.18510	−0.406128	−0.203064	+	0.979165i	$0.565090\pi$
$164$	−6.41316	−0.500784
$165$	−2.43533	−0.189590
$166$	−24.0582	−1.86728
$167$	−25.7882	−1.99555	−0.997777	−	0.0666421i	$-0.978771\pi$
$167$	−25.7882	−1.99555	−0.997777	+	0.0666421i	$0.978771\pi$
$168$	2.16714	0.167199
$169$	−11.7087	−0.900670
$170$	−11.1942	−0.858554
$171$	−1.57257	−0.120257
$172$	−25.1528	−1.91788
$173$	−13.2397	−1.00660	−0.503298	−	0.864113i	$-0.667880\pi$
$173$	−13.2397	−1.00660	−0.503298	+	0.864113i	$0.667880\pi$
$174$	−1.40770	−0.106718
$175$	17.3325	1.31022
$176$	−10.9012	−0.821707
$177$	5.71129	0.429287
$178$	7.47428	0.560221
$179$	20.1004	1.50237	0.751186	−	0.660091i	$-0.229482\pi$
$179$	20.1004	1.50237	0.751186	+	0.660091i	$0.229482\pi$
$180$	6.29684	0.469339
$181$	9.71878	0.722391	0.361196	−	0.932490i	$-0.382369\pi$
$181$	9.71878	0.722391	0.361196	+	0.932490i	$0.382369\pi$
$182$	−10.5651	−0.783137
$183$	0.0698278	0.00516182
$184$	5.22046	0.384858
$185$	0.350286	0.0257536
$186$	−5.44997	−0.399612
$187$	−17.3842	−1.27126
$188$	13.2319	0.965035
$189$	16.6988	1.21466
$190$	1.36002	0.0986666
$191$	−23.7788	−1.72057	−0.860286	−	0.509812i	$-0.829715\pi$
$191$	−23.7788	−1.72057	−0.860286	+	0.509812i	$0.829715\pi$
$192$	−7.07859	−0.510854
$193$	−0.936601	−0.0674180	−0.0337090	−	0.999432i	$-0.510732\pi$
$193$	−0.936601	−0.0674180	−0.0337090	+	0.999432i	$0.510732\pi$
$194$	−19.9344	−1.43121
$195$	0.809958	0.0580023
$196$	30.2381	2.15986
$197$	−8.56192	−0.610011	−0.305006	−	0.952351i	$-0.598658\pi$
$197$	−8.56192	−0.610011	−0.305006	+	0.952351i	$0.598658\pi$
$198$	18.1183	1.28761
$199$	−0.452650	−0.0320875	−0.0160437	−	0.999871i	$-0.505107\pi$
$199$	−0.452650	−0.0320875	−0.0160437	+	0.999871i	$0.505107\pi$
$200$	2.79591	0.197701
$201$	−9.30372	−0.656234
$202$	27.5533	1.93865
$203$	−4.46025	−0.313048
$204$	−8.05799	−0.564172
$205$	2.88631	0.201588
$206$	16.9346	1.17989
$207$	18.4585	1.28295
$208$	3.62558	0.251389
$209$	2.11207	0.146095
$210$	−6.62693	−0.457302
$211$	17.3468	1.19420	0.597100	−	0.802167i	$-0.296320\pi$
$211$	17.3468	1.19420	0.597100	+	0.802167i	$0.296320\pi$
$212$	−30.2830	−2.07984
$213$	1.23526	0.0846386
$214$	−2.97360	−0.203271
$215$	11.3203	0.772035
$216$	2.69369	0.183282
$217$	−17.2680	−1.17223
$218$	1.60989	0.109035
$219$	−1.70778	−0.115401
$220$	−8.45712	−0.570179
$221$	5.78173	0.388922
$222$	0.467188	0.0313556
$223$	5.96131	0.399199	0.199599	−	0.979878i	$-0.436036\pi$
$223$	5.96131	0.399199	0.199599	+	0.979878i	$0.436036\pi$
$224$	−36.0820	−2.41083
$225$	9.88577	0.659052
$226$	38.1483	2.53759
$227$	17.1263	1.13671	0.568356	−	0.822782i	$-0.307579\pi$
$227$	17.1263	1.13671	0.568356	+	0.822782i	$0.307579\pi$
$228$	0.978997	0.0648357
$229$	−1.92122	−0.126958	−0.0634789	−	0.997983i	$-0.520220\pi$
$229$	−1.92122	−0.126958	−0.0634789	+	0.997983i	$0.520220\pi$
$230$	−15.9637	−1.05262
$231$	−10.2914	−0.677125
$232$	−0.719483	−0.0472364
$233$	−24.4304	−1.60049	−0.800245	−	0.599673i	$-0.795297\pi$
$233$	−24.4304	−1.60049	−0.800245	+	0.599673i	$0.795297\pi$
$234$	−6.02591	−0.393926
$235$	−5.95514	−0.388471
$236$	19.8334	1.29105
$237$	−7.70042	−0.500196
$238$	−47.3052	−3.06634
$239$	0.0183458	0.00118669	0.000593345	−	1.00000i	$-0.499811\pi$
$239$	0.0183458	0.00118669	0.000593345		1.00000i	$0.499811\pi$
$240$	2.27413	0.146795
$241$	6.72380	0.433118	0.216559	−	0.976270i	$-0.430517\pi$
$241$	6.72380	0.433118	0.216559	+	0.976270i	$0.430517\pi$
$242$	−1.40471	−0.0902980
$243$	14.6783	0.941611
$244$	0.242489	0.0155238
$245$	−13.6089	−0.869444
$246$	3.84956	0.245439
$247$	−0.702446	−0.0446956
$248$	−2.78551	−0.176880
$249$	7.79416	0.493935
$250$	−19.5502	−1.23646
$251$	−24.7796	−1.56408	−0.782038	−	0.623231i	$-0.785820\pi$
$251$	−24.7796	−1.56408	−0.782038	+	0.623231i	$0.785820\pi$
$252$	26.6097	1.67625
$253$	−24.7911	−1.55860
$254$	−35.7865	−2.24544
$255$	3.62658	0.227105
$256$	9.14430	0.571519
$257$	28.8583	1.80013	0.900066	−	0.435754i	$-0.143518\pi$
$257$	28.8583	1.80013	0.900066	+	0.435754i	$0.143518\pi$
$258$	15.0982	0.939971
$259$	1.48027	0.0919792
$260$	2.81272	0.174437
$261$	−2.54395	−0.157466
$262$	−10.0351	−0.619972
$263$	−10.3087	−0.635663	−0.317831	−	0.948147i	$-0.602955\pi$
$263$	−10.3087	−0.635663	−0.317831	+	0.948147i	$0.602955\pi$
$264$	−1.66011	−0.102173
$265$	13.6292	0.837232
$266$	5.74729	0.352389
$267$	−2.42145	−0.148190
$268$	−32.3088	−1.97357
$269$	−30.4910	−1.85907	−0.929534	−	0.368736i	$-0.879791\pi$
$269$	−30.4910	−1.85907	−0.929534	+	0.368736i	$0.879791\pi$
$270$	−8.23706	−0.501292
$271$	24.1764	1.46861	0.734306	−	0.678819i	$-0.237508\pi$
$271$	24.1764	1.46861	0.734306	+	0.678819i	$0.237508\pi$
$272$	16.2335	0.984300
$273$	3.42278	0.207156
$274$	−33.4853	−2.02292
$275$	−13.2773	−0.800652
$276$	−11.4913	−0.691694
$277$	9.78687	0.588036	0.294018	−	0.955800i	$-0.405007\pi$
$277$	9.78687	0.588036	0.294018	+	0.955800i	$0.405007\pi$
$278$	2.08450	0.125020
$279$	−9.84899	−0.589643
$280$	−3.38706	−0.202415
$281$	−15.3456	−0.915441	−0.457721	−	0.889096i	$-0.651334\pi$
$281$	−15.3456	−0.915441	−0.457721	+	0.889096i	$0.651334\pi$
$282$	−7.94256	−0.472973
$283$	29.7960	1.77119	0.885593	−	0.464462i	$-0.153752\pi$
$283$	29.7960	1.77119	0.885593	+	0.464462i	$0.153752\pi$
$284$	4.28965	0.254544
$285$	−0.440608	−0.0260993
$286$	8.09323	0.478563
$287$	12.1972	0.719976
$288$	−20.5797	−1.21267
$289$	8.88768	0.522805
$290$	2.20012	0.129195
$291$	6.45817	0.378585
$292$	−5.93057	−0.347060
$293$	−3.03022	−0.177027	−0.0885136	−	0.996075i	$-0.528212\pi$
$293$	−3.03022	−0.177027	−0.0885136	+	0.996075i	$0.528212\pi$
$294$	−18.1507	−1.05857
$295$	−8.92624	−0.519706
$296$	0.238782	0.0138789
$297$	−12.7919	−0.742261
$298$	−28.5169	−1.65194
$299$	8.24518	0.476831
$300$	−6.15436	−0.355322
$301$	47.8380	2.75733
$302$	−38.1653	−2.19616
$303$	−8.92646	−0.512812
$304$	−1.97227	−0.113118
$305$	−0.109135	−0.00624904
$306$	−26.9810	−1.54240
$307$	−6.49343	−0.370599	−0.185300	−	0.982682i	$-0.559326\pi$
$307$	−6.49343	−0.370599	−0.185300	+	0.982682i	$0.559326\pi$
$308$	−35.7387	−2.03640
$309$	−5.48632	−0.312106
$310$	8.51783	0.483780
$311$	−12.2569	−0.695024	−0.347512	−	0.937676i	$-0.612973\pi$
$311$	−12.2569	−0.695024	−0.347512	+	0.937676i	$0.612973\pi$
$312$	0.552129	0.0312581
$313$	18.9791	1.07276	0.536381	−	0.843976i	$-0.319791\pi$
$313$	18.9791	1.07276	0.536381	+	0.843976i	$0.319791\pi$
$314$	−34.9699	−1.97346
$315$	−11.9759	−0.674768
$316$	−26.7411	−1.50430
$317$	−13.8489	−0.777829	−0.388915	−	0.921274i	$-0.627150\pi$
$317$	−13.8489	−0.777829	−0.388915	+	0.921274i	$0.627150\pi$
$318$	18.1776	1.01935
$319$	3.41671	0.191299
$320$	11.0632	0.618453
$321$	0.963360	0.0537695
$322$	−67.4606	−3.75943
$323$	−3.14520	−0.175003
$324$	11.9685	0.664918
$325$	4.41585	0.244947
$326$	10.8084	0.598619
$327$	−0.521556	−0.0288421
$328$	1.96753	0.108639
$329$	−25.1657	−1.38743
$330$	5.07646	0.279450
$331$	20.2594	1.11355	0.556777	−	0.830662i	$-0.312038\pi$
$331$	20.2594	1.11355	0.556777	+	0.830662i	$0.312038\pi$
$332$	27.0666	1.48547
$333$	0.844284	0.0462665
$334$	53.7557	2.94138
$335$	14.5409	0.794454
$336$	9.61021	0.524280
$337$	−7.48842	−0.407920	−0.203960	−	0.978979i	$-0.565381\pi$
$337$	−7.48842	−0.407920	−0.203960	+	0.978979i	$0.565381\pi$
$338$	24.4069	1.32756
$339$	−12.3589	−0.671245
$340$	12.5939	0.683002
$341$	13.2279	0.716332
$342$	3.27802	0.177255
$343$	−26.2879	−1.41942
$344$	7.71675	0.416059
$345$	5.17177	0.278439
$346$	27.5982	1.48369
$347$	34.9403	1.87569	0.937846	−	0.347053i	$-0.112817\pi$
$347$	34.9403	1.87569	0.937846	+	0.347053i	$0.112817\pi$
$348$	1.58373	0.0848966
$349$	−13.7041	−0.733565	−0.366782	−	0.930307i	$-0.619541\pi$
$349$	−13.7041	−0.733565	−0.366782	+	0.930307i	$0.619541\pi$
$350$	−36.1297	−1.93122
$351$	4.25440	0.227083
$352$	27.6401	1.47322
$353$	29.1644	1.55227	0.776133	−	0.630569i	$-0.217179\pi$
$353$	29.1644	1.55227	0.776133	+	0.630569i	$0.217179\pi$
$354$	−11.9052	−0.632754
$355$	−1.93060	−0.102466
$356$	−8.40889	−0.445670
$357$	15.3255	0.811110
$358$	−41.8993	−2.21445
$359$	0.873559	0.0461047	0.0230523	−	0.999734i	$-0.492662\pi$
$359$	0.873559	0.0461047	0.0230523	+	0.999734i	$0.492662\pi$
$360$	−1.93184	−0.101817
$361$	−18.6179	−0.979888
$362$	−20.2588	−1.06478
$363$	0.455084	0.0238857
$364$	11.8862	0.623006
$365$	2.66911	0.139708
$366$	−0.145556	−0.00760835
$367$	10.9683	0.572541	0.286270	−	0.958149i	$-0.407584\pi$
$367$	10.9683	0.572541	0.286270	+	0.958149i	$0.407584\pi$
$368$	23.1502	1.20679
$369$	6.95677	0.362155
$370$	−0.730173	−0.0379599
$371$	57.5951	2.99019
$372$	6.13146	0.317901
$373$	16.9007	0.875087	0.437544	−	0.899197i	$-0.355849\pi$
$373$	16.9007	0.875087	0.437544	+	0.899197i	$0.355849\pi$
$374$	36.2374	1.87379
$375$	6.33369	0.327070
$376$	−4.05948	−0.209352
$377$	−1.13635	−0.0585249
$378$	−34.8088	−1.79037
$379$	−7.36209	−0.378165	−0.189083	−	0.981961i	$-0.560551\pi$
$379$	−7.36209	−0.378165	−0.189083	+	0.981961i	$0.560551\pi$
$380$	−1.53009	−0.0784918
$381$	11.5938	0.593966
$382$	49.5670	2.53607
$383$	18.4873	0.944654	0.472327	−	0.881423i	$-0.343414\pi$
$383$	18.4873	0.944654	0.472327	+	0.881423i	$0.343414\pi$
$384$	3.82915	0.195406
$385$	16.0846	0.819746
$386$	1.95235	0.0993720
$387$	27.2848	1.38697
$388$	22.4271	1.13856
$389$	7.53765	0.382174	0.191087	−	0.981573i	$-0.438799\pi$
$389$	7.53765	0.382174	0.191087	+	0.981573i	$0.438799\pi$
$390$	−1.68836	−0.0854934
$391$	36.9177	1.86701
$392$	−9.27689	−0.468554
$393$	3.25108	0.163995
$394$	17.8474	0.899137
$395$	12.0351	0.605551
$396$	−20.3839	−1.02433
$397$	−0.585866	−0.0294038	−0.0147019	−	0.999892i	$-0.504680\pi$
$397$	−0.585866	−0.0294038	−0.0147019	+	0.999892i	$0.504680\pi$
$398$	0.943550	0.0472959
$399$	−1.86195	−0.0932142
$400$	12.3985	0.619924
$401$	−8.79080	−0.438992	−0.219496	−	0.975613i	$-0.570441\pi$
$401$	−8.79080	−0.438992	−0.219496	+	0.975613i	$0.570441\pi$
$402$	19.3936	0.967267
$403$	−4.39942	−0.219151
$404$	−30.9987	−1.54224
$405$	−5.38655	−0.267660
$406$	9.29741	0.461423
$407$	−1.13393	−0.0562071
$408$	2.47215	0.122390
$409$	23.5170	1.16284	0.581421	−	0.813603i	$-0.302497\pi$
$409$	23.5170	1.16284	0.581421	+	0.813603i	$0.302497\pi$
$410$	−6.01652	−0.297135
$411$	10.8482	0.535104
$412$	−19.0522	−0.938635
$413$	−37.7212	−1.85614
$414$	−38.4768	−1.89103
$415$	−12.1816	−0.597970
$416$	−9.19270	−0.450709
$417$	−0.675318	−0.0330704
$418$	−4.40263	−0.215339
$419$	20.1236	0.983100	0.491550	−	0.870849i	$-0.336430\pi$
$419$	20.1236	0.983100	0.491550	+	0.870849i	$0.336430\pi$
$420$	7.45559	0.363795
$421$	6.37619	0.310756	0.155378	−	0.987855i	$-0.450340\pi$
$421$	6.37619	0.310756	0.155378	+	0.987855i	$0.450340\pi$
$422$	−36.1594	−1.76021
$423$	−14.3535	−0.697891
$424$	9.29067	0.451195
$425$	19.7719	0.959080
$426$	−2.57490	−0.124754
$427$	−0.461190	−0.0223185
$428$	3.34543	0.161708
$429$	−2.62197	−0.126590
$430$	−23.5971	−1.13795
$431$	−0.0942294	−0.00453887	−0.00226944	−	0.999997i	$-0.500722\pi$
$431$	−0.0942294	−0.00453887	−0.00226944	+	0.999997i	$0.500722\pi$
$432$	11.9452	0.574713
$433$	11.3307	0.544519	0.272260	−	0.962224i	$-0.412229\pi$
$433$	11.3307	0.544519	0.272260	+	0.962224i	$0.412229\pi$
$434$	35.9953	1.72783
$435$	−0.712772	−0.0341748
$436$	−1.81119	−0.0867404
$437$	−4.48528	−0.214560
$438$	3.55988	0.170098
$439$	13.7418	0.655860	0.327930	−	0.944702i	$-0.393649\pi$
$439$	13.7418	0.655860	0.327930	+	0.944702i	$0.393649\pi$
$440$	2.59460	0.123693
$441$	−32.8012	−1.56196
$442$	−12.0521	−0.573258
$443$	−8.26354	−0.392613	−0.196306	−	0.980543i	$-0.562895\pi$
$443$	−8.26354	−0.392613	−0.196306	+	0.980543i	$0.562895\pi$
$444$	−0.525606	−0.0249442
$445$	3.78451	0.179403
$446$	−12.4264	−0.588406
$447$	9.23864	0.436973
$448$	46.7518	2.20881
$449$	−26.3231	−1.24226	−0.621132	−	0.783706i	$-0.713327\pi$
$449$	−26.3231	−1.24226	−0.621132	+	0.783706i	$0.713327\pi$
$450$	−20.6069	−0.971420
$451$	−9.34346	−0.439966
$452$	−42.9185	−2.01872
$453$	12.3644	0.580931
$454$	−35.6999	−1.67548
$455$	−5.34950	−0.250789
$456$	−0.300352	−0.0140653
$457$	20.5645	0.961968	0.480984	−	0.876729i	$-0.340280\pi$
$457$	20.5645	0.961968	0.480984	+	0.876729i	$0.340280\pi$
$458$	4.00479	0.187132
$459$	19.0491	0.889134
$460$	17.9599	0.837383
$461$	18.5076	0.861987	0.430994	−	0.902355i	$-0.358163\pi$
$461$	18.5076	0.861987	0.430994	+	0.902355i	$0.358163\pi$
$462$	21.4525	0.998060
$463$	−8.50393	−0.395211	−0.197606	−	0.980282i	$-0.563317\pi$
$463$	−8.50393	−0.395211	−0.197606	+	0.980282i	$0.563317\pi$
$464$	−3.19055	−0.148118
$465$	−2.75952	−0.127970
$466$	50.9253	2.35907
$467$	3.71225	0.171782	0.0858911	−	0.996305i	$-0.472626\pi$
$467$	3.71225	0.171782	0.0858911	+	0.996305i	$0.472626\pi$
$468$	6.77941	0.313378
$469$	61.4480	2.83741
$470$	12.4135	0.572593
$471$	11.3292	0.522022
$472$	−6.08481	−0.280076
$473$	−36.6455	−1.68496
$474$	16.0516	0.737273
$475$	−2.40217	−0.110219
$476$	53.2204	2.43935
$477$	32.8499	1.50409
$478$	−0.0382419	−0.00174914
$479$	−22.3175	−1.01971	−0.509856	−	0.860260i	$-0.670301\pi$
$479$	−22.3175	−1.01971	−0.509856	+	0.860260i	$0.670301\pi$
$480$	−5.76610	−0.263185
$481$	0.377131	0.0171957
$482$	−14.0158	−0.638402
$483$	21.8552	0.994448
$484$	1.58036	0.0718344
$485$	−10.0936	−0.458325
$486$	−30.5969	−1.38790
$487$	−8.58459	−0.389005	−0.194502	−	0.980902i	$-0.562309\pi$
$487$	−8.58459	−0.389005	−0.194502	+	0.980902i	$0.562309\pi$
$488$	−0.0743946	−0.00336768
$489$	−3.50159	−0.158347
$490$	28.3679	1.28153
$491$	11.7907	0.532109	0.266054	−	0.963958i	$-0.414280\pi$
$491$	11.7907	0.532109	0.266054	+	0.963958i	$0.414280\pi$
$492$	−4.33092	−0.195253
$493$	−5.08799	−0.229152
$494$	1.46425	0.0658798
$495$	9.17399	0.412340
$496$	−12.3523	−0.554636
$497$	−8.15848	−0.365958
$498$	−16.2470	−0.728043
$499$	−27.6417	−1.23741	−0.618706	−	0.785623i	$-0.712343\pi$
$499$	−27.6417	−1.23741	−0.618706	+	0.785623i	$0.712343\pi$
$500$	21.9949	0.983640
$501$	−17.4153	−0.778056
$502$	51.6532	2.30540
$503$	5.36667	0.239288	0.119644	−	0.992817i	$-0.461825\pi$
$503$	5.36667	0.239288	0.119644	+	0.992817i	$0.461825\pi$
$504$	−8.16372	−0.363641
$505$	13.9513	0.620824
$506$	51.6772	2.29733
$507$	−7.90710	−0.351167
$508$	40.2613	1.78631
$509$	2.61691	0.115993	0.0579964	−	0.998317i	$-0.481529\pi$
$509$	2.61691	0.115993	0.0579964	+	0.998317i	$0.481529\pi$
$510$	−7.55962	−0.334746
$511$	11.2793	0.498968
$512$	−30.4016	−1.34357
$513$	−2.31435	−0.102181
$514$	−60.1553	−2.65334
$515$	8.57464	0.377844
$516$	−16.9861	−0.747771
$517$	19.2778	0.847836
$518$	−3.08562	−0.135574
$519$	−8.94100	−0.392466
$520$	−0.862929	−0.0378419
$521$	−40.4559	−1.77241	−0.886203	−	0.463298i	$-0.846666\pi$
$521$	−40.4559	−1.77241	−0.886203	+	0.463298i	$0.846666\pi$
$522$	5.30287	0.232100
$523$	15.2392	0.666365	0.333182	−	0.942862i	$-0.391878\pi$
$523$	15.2392	0.666365	0.333182	+	0.942862i	$0.391878\pi$
$524$	11.2899	0.493203
$525$	11.7050	0.510846
$526$	21.4886	0.936946
$527$	−19.6984	−0.858074
$528$	−7.36175	−0.320379
$529$	29.6474	1.28902
$530$	−28.4100	−1.23405
$531$	−21.5146	−0.933656
$532$	−6.46596	−0.280335
$533$	3.10750	0.134601
$534$	5.04751	0.218427
$535$	−1.50565	−0.0650948
$536$	9.91219	0.428141
$537$	13.5741	0.585767
$538$	63.5586	2.74021
$539$	44.0544	1.89756
$540$	9.26706	0.398791
$541$	14.2505	0.612679	0.306339	−	0.951922i	$-0.400896\pi$
$541$	14.2505	0.612679	0.306339	+	0.951922i	$0.400896\pi$
$542$	−50.3958	−2.16469
$543$	6.56326	0.281657
$544$	−41.1603	−1.76473
$545$	0.815146	0.0349170
$546$	−7.13480	−0.305341
$547$	−38.2495	−1.63543	−0.817716	−	0.575621i	$-0.804760\pi$
$547$	−38.2495	−1.63543	−0.817716	+	0.575621i	$0.804760\pi$
$548$	37.6724	1.60928
$549$	−0.263044	−0.0112264
$550$	27.6766	1.18014
$551$	0.618161	0.0263345
$552$	3.52547	0.150054
$553$	50.8588	2.16273
$554$	−20.4008	−0.866746
$555$	0.236554	0.0100412
$556$	−2.34516	−0.0994569
$557$	−11.0649	−0.468835	−0.234418	−	0.972136i	$-0.575318\pi$
$557$	−11.0649	−0.468835	−0.234418	+	0.972136i	$0.575318\pi$
$558$	20.5303	0.869115
$559$	12.1878	0.515489
$560$	−15.0199	−0.634707
$561$	−11.7398	−0.495656
$562$	31.9880	1.34933
$563$	−35.9931	−1.51693	−0.758463	−	0.651716i	$-0.774050\pi$
$563$	−35.9931	−1.51693	−0.758463	+	0.651716i	$0.774050\pi$
$564$	8.93573	0.376262
$565$	19.3159	0.812627
$566$	−62.1098	−2.61067
$567$	−22.7629	−0.955952
$568$	−1.31605	−0.0552200
$569$	32.8236	1.37604	0.688018	−	0.725693i	$-0.258481\pi$
$569$	32.8236	1.37604	0.688018	+	0.725693i	$0.258481\pi$
$570$	0.918449	0.0384696
$571$	27.7249	1.16025	0.580125	−	0.814527i	$-0.303004\pi$
$571$	27.7249	1.16025	0.580125	+	0.814527i	$0.303004\pi$
$572$	−9.10524	−0.380709
$573$	−16.0582	−0.670842
$574$	−25.4251	−1.06122
$575$	28.1962	1.17586
$576$	26.6653	1.11106
$577$	8.10036	0.337223	0.168611	−	0.985683i	$-0.446072\pi$
$577$	8.10036	0.337223	0.168611	+	0.985683i	$0.446072\pi$
$578$	−18.5264	−0.770597
$579$	−0.632503	−0.0262859
$580$	−2.47523	−0.102778
$581$	−51.4778	−2.13566
$582$	−13.4621	−0.558021
$583$	−44.1198	−1.82726
$584$	1.81947	0.0752902
$585$	−3.05114	−0.126149
$586$	6.31650	0.260932
$587$	−8.07451	−0.333270	−0.166635	−	0.986019i	$-0.553290\pi$
$587$	−8.07451	−0.333270	−0.166635	+	0.986019i	$0.553290\pi$
$588$	20.4203	0.842119
$589$	2.39323	0.0986115
$590$	18.6068	0.766029
$591$	−5.78201	−0.237840
$592$	1.05888	0.0435196
$593$	26.5293	1.08943	0.544713	−	0.838622i	$-0.316639\pi$
$593$	26.5293	1.08943	0.544713	+	0.838622i	$0.316639\pi$
$594$	26.6647	1.09407
$595$	−23.9524	−0.981951
$596$	32.0828	1.31416
$597$	−0.305682	−0.0125107
$598$	−17.1871	−0.702833
$599$	−10.1086	−0.413026	−0.206513	−	0.978444i	$-0.566212\pi$
$599$	−10.1086	−0.413026	−0.206513	+	0.978444i	$0.566212\pi$
$600$	1.88813	0.0770825
$601$	7.44814	0.303816	0.151908	−	0.988395i	$-0.451458\pi$
$601$	7.44814	0.303816	0.151908	+	0.988395i	$0.451458\pi$
$602$	−99.7185	−4.06422
$603$	35.0475	1.42724
$604$	42.9376	1.74711
$605$	−0.711256	−0.0289167
$606$	18.6073	0.755868
$607$	28.7249	1.16591	0.582954	−	0.812505i	$-0.301897\pi$
$607$	28.7249	1.16591	0.582954	+	0.812505i	$0.301897\pi$
$608$	5.00072	0.202806
$609$	−3.01208	−0.122056
$610$	0.227492	0.00921088
$611$	−6.41152	−0.259382
$612$	30.3547	1.22702
$613$	8.55372	0.345482	0.172741	−	0.984967i	$-0.444738\pi$
$613$	8.55372	0.345482	0.172741	+	0.984967i	$0.444738\pi$
$614$	13.5356	0.546251
$615$	1.94917	0.0785983
$616$	10.9645	0.441771
$617$	16.6510	0.670344	0.335172	−	0.942157i	$-0.391206\pi$
$617$	16.6510	0.670344	0.335172	+	0.942157i	$0.391206\pi$
$618$	11.4363	0.460034
$619$	2.74701	0.110412	0.0552058	−	0.998475i	$-0.482419\pi$
$619$	2.74701	0.110412	0.0552058	+	0.998475i	$0.482419\pi$
$620$	−9.58293	−0.384860
$621$	27.1654	1.09011
$622$	25.5495	1.02444
$623$	15.9928	0.640740
$624$	2.44842	0.0980151
$625$	9.53099	0.381240
$626$	−39.5620	−1.58122
$627$	1.42632	0.0569617
$628$	39.3426	1.56994
$629$	1.68860	0.0673289
$630$	24.9639	0.994586
$631$	−48.8148	−1.94329	−0.971644	−	0.236449i	$-0.924017\pi$
$631$	−48.8148	−1.94329	−0.971644	+	0.236449i	$0.924017\pi$
$632$	8.20403	0.326339
$633$	11.7146	0.465612
$634$	28.8680	1.14649
$635$	−18.1200	−0.719071
$636$	−20.4506	−0.810920
$637$	−14.6519	−0.580529
$638$	−7.12214	−0.281968
$639$	−4.65327	−0.184080
$640$	−5.98463	−0.236563
$641$	20.4597	0.808109	0.404055	−	0.914735i	$-0.367601\pi$
$641$	20.4597	0.808109	0.404055	+	0.914735i	$0.367601\pi$
$642$	−2.00813	−0.0792545
$643$	42.4320	1.67335	0.836677	−	0.547697i	$-0.184495\pi$
$643$	42.4320	1.67335	0.836677	+	0.547697i	$0.184495\pi$
$644$	75.8961	2.99073
$645$	7.64477	0.301012
$646$	6.55618	0.257949
$647$	−42.3907	−1.66655	−0.833276	−	0.552858i	$-0.813537\pi$
$647$	−42.3907	−1.66655	−0.833276	+	0.552858i	$0.813537\pi$
$648$	−3.67188	−0.144245
$649$	28.8957	1.13426
$650$	−9.20486	−0.361044
$651$	−11.6614	−0.457046
$652$	−12.1599	−0.476217
$653$	0.0404139	0.00158152	0.000790758	−	1.00000i	$-0.499748\pi$
$653$	0.0404139	0.00158152	0.000790758		1.00000i	$0.499748\pi$
$654$	1.08719	0.0425123
$655$	−5.08115	−0.198537
$656$	8.72500	0.340654
$657$	6.43328	0.250986
$658$	52.4580	2.04503
$659$	5.10664	0.198927	0.0994633	−	0.995041i	$-0.468287\pi$
$659$	5.10664	0.198927	0.0994633	+	0.995041i	$0.468287\pi$
$660$	−5.71124	−0.222310
$661$	30.2222	1.17551	0.587754	−	0.809039i	$-0.300012\pi$
$661$	30.2222	1.17551	0.587754	+	0.809039i	$0.300012\pi$
$662$	−42.2307	−1.64134
$663$	3.90451	0.151638
$664$	−8.30390	−0.322254
$665$	2.91007	0.112848
$666$	−1.75991	−0.0681952
$667$	−7.25585	−0.280948
$668$	−60.4775	−2.33994
$669$	4.02578	0.155646
$670$	−30.3106	−1.17100
$671$	0.353287	0.0136385
$672$	−24.3668	−0.939970
$673$	−34.8039	−1.34159	−0.670796	−	0.741642i	$-0.734047\pi$
$673$	−34.8039	−1.34159	−0.670796	+	0.741642i	$0.734047\pi$
$674$	15.6096	0.601261
$675$	14.5489	0.559987
$676$	−27.4588	−1.05611
$677$	−38.5040	−1.47983	−0.739914	−	0.672702i	$-0.765134\pi$
$677$	−38.5040	−1.47983	−0.739914	+	0.672702i	$0.765134\pi$
$678$	25.7622	0.989393
$679$	−42.6541	−1.63691
$680$	−3.86376	−0.148168
$681$	11.5657	0.443198
$682$	−27.5736	−1.05585
$683$	41.7040	1.59576	0.797880	−	0.602817i	$-0.205955\pi$
$683$	41.7040	1.59576	0.797880	+	0.602817i	$0.205955\pi$
$684$	−3.68792	−0.141011
$685$	−16.9548	−0.647811
$686$	54.7973	2.09217
$687$	−1.29743	−0.0495002
$688$	34.2199	1.30462
$689$	14.6736	0.559021
$690$	−10.7806	−0.410409
$691$	−16.5973	−0.631393	−0.315696	−	0.948860i	$-0.602238\pi$
$691$	−16.5973	−0.631393	−0.315696	+	0.948860i	$0.602238\pi$
$692$	−31.0492	−1.18031
$693$	38.7681	1.47268
$694$	−72.8331	−2.76471
$695$	1.05546	0.0400360
$696$	−0.485880	−0.0184172
$697$	13.9138	0.527024
$698$	28.5663	1.08125
$699$	−16.4983	−0.624023
$700$	40.6475	1.53633
$701$	14.7383	0.556659	0.278330	−	0.960486i	$-0.410219\pi$
$701$	14.7383	0.556659	0.278330	+	0.960486i	$0.410219\pi$
$702$	−8.86832	−0.334713
$703$	−0.205155	−0.00773756
$704$	−35.8135	−1.34977
$705$	−4.02161	−0.151463
$706$	−60.7934	−2.28799
$707$	58.9564	2.21728
$708$	13.3939	0.503373
$709$	6.19457	0.232642	0.116321	−	0.993212i	$-0.462890\pi$
$709$	6.19457	0.232642	0.116321	+	0.993212i	$0.462890\pi$
$710$	4.02435	0.151031
$711$	29.0078	1.08788
$712$	2.57981	0.0966824
$713$	−28.0913	−1.05203
$714$	−31.9460	−1.19555
$715$	4.09790	0.153253
$716$	47.1385	1.76165
$717$	0.0123892	0.000462684 0
$718$	−1.82094	−0.0679568
$719$	−32.4660	−1.21078	−0.605388	−	0.795930i	$-0.706982\pi$
$719$	−32.4660	−1.21078	−0.605388	+	0.795930i	$0.706982\pi$
$720$	−8.56675	−0.319264
$721$	36.2354	1.34948
$722$	38.8090	1.44432
$723$	4.54070	0.168870
$724$	22.7921	0.847061
$725$	−3.88600	−0.144322
$726$	−0.948624	−0.0352067
$727$	28.3178	1.05025	0.525125	−	0.851025i	$-0.324019\pi$
$727$	28.3178	1.05025	0.525125	+	0.851025i	$0.324019\pi$
$728$	−3.64663	−0.135153
$729$	−5.39802	−0.199927
$730$	−5.56378	−0.205925
$731$	54.5708	2.01837
$732$	0.163757	0.00605264
$733$	19.1050	0.705659	0.352829	−	0.935688i	$-0.385220\pi$
$733$	19.1050	0.705659	0.352829	+	0.935688i	$0.385220\pi$
$734$	−22.8635	−0.843906
$735$	−9.19036	−0.338992
$736$	−58.6975	−2.16362
$737$	−47.0713	−1.73389
$738$	−14.5014	−0.533805
$739$	−44.5396	−1.63842	−0.819208	−	0.573497i	$-0.805586\pi$
$739$	−44.5396	−1.63842	−0.819208	+	0.573497i	$0.805586\pi$
$740$	0.821477	0.0301981
$741$	−0.474374	−0.0174266
$742$	−120.057	−4.40744
$743$	−50.2070	−1.84192	−0.920959	−	0.389661i	$-0.872592\pi$
$743$	−50.2070	−1.84192	−0.920959	+	0.389661i	$0.872592\pi$
$744$	−1.88110	−0.0689646
$745$	−14.4392	−0.529011
$746$	−35.2297	−1.28985
$747$	−29.3609	−1.07426
$748$	−40.7686	−1.49065
$749$	−6.36267	−0.232487
$750$	−13.2026	−0.482091
$751$	2.22914	0.0813424	0.0406712	−	0.999173i	$-0.487050\pi$
$751$	2.22914	0.0813424	0.0406712	+	0.999173i	$0.487050\pi$
$752$	−18.0018	−0.656457
$753$	−16.7341	−0.609825
$754$	2.36872	0.0862638
$755$	−19.3245	−0.703291
$756$	39.1614	1.42429
$757$	3.59224	0.130562	0.0652811	−	0.997867i	$-0.479206\pi$
$757$	3.59224	0.130562	0.0652811	+	0.997867i	$0.479206\pi$
$758$	15.3463	0.557403
$759$	−16.7419	−0.607691
$760$	0.469423	0.0170278
$761$	−6.68938	−0.242490	−0.121245	−	0.992623i	$-0.538689\pi$
$761$	−6.68938	−0.242490	−0.121245	+	0.992623i	$0.538689\pi$
$762$	−24.1672	−0.875487
$763$	3.44470	0.124707
$764$	−55.7650	−2.01751
$765$	−13.6615	−0.493931
$766$	−38.5368	−1.39239
$767$	−9.61032	−0.347008
$768$	6.17530	0.222832
$769$	−45.0135	−1.62323	−0.811615	−	0.584193i	$-0.801411\pi$
$769$	−45.0135	−1.62323	−0.811615	+	0.584193i	$0.801411\pi$
$770$	−33.5284	−1.20828
$771$	19.4885	0.701862
$772$	−2.19648	−0.0790530
$773$	30.0578	1.08110	0.540551	−	0.841311i	$-0.318216\pi$
$773$	30.0578	1.08110	0.540551	+	0.841311i	$0.318216\pi$
$774$	−56.8754	−2.04434
$775$	−15.0448	−0.540425
$776$	−6.88053	−0.246997
$777$	0.999649	0.0358622
$778$	−15.7123	−0.563312
$779$	−1.69045	−0.0605665
$780$	1.89948	0.0680122
$781$	6.24968	0.223631
$782$	−76.9552	−2.75191
$783$	−3.74392	−0.133797
$784$	−41.1384	−1.46923
$785$	−17.7065	−0.631974
$786$	−6.77689	−0.241724
$787$	18.0745	0.644288	0.322144	−	0.946691i	$-0.395597\pi$
$787$	18.0745	0.644288	0.322144	+	0.946691i	$0.395597\pi$
$788$	−20.0791	−0.715287
$789$	−6.96166	−0.247842
$790$	−25.0872	−0.892562
$791$	81.6266	2.90231
$792$	6.25369	0.222215
$793$	−0.117498	−0.00417249
$794$	1.22124	0.0433402
$795$	9.20401	0.326432
$796$	−1.06153	−0.0376251
$797$	36.3251	1.28670	0.643351	−	0.765572i	$-0.277544\pi$
$797$	36.3251	1.28670	0.643351	+	0.765572i	$0.277544\pi$
$798$	3.88125	0.137395
$799$	−28.7076	−1.01560
$800$	−31.4365	−1.11145
$801$	9.12167	0.322298
$802$	18.3245	0.647059
$803$	−8.64036	−0.304912
$804$	−21.8187	−0.769486
$805$	−34.1578	−1.20390
$806$	9.17061	0.323021
$807$	−20.5911	−0.724841
$808$	9.51026	0.334570
$809$	−9.35333	−0.328846	−0.164423	−	0.986390i	$-0.552576\pi$
$809$	−9.35333	−0.328846	−0.164423	+	0.986390i	$0.552576\pi$
$810$	11.2283	0.394522
$811$	−46.2580	−1.62434	−0.812169	−	0.583422i	$-0.801714\pi$
$811$	−46.2580	−1.62434	−0.812169	+	0.583422i	$0.801714\pi$
$812$	−10.4600	−0.367074
$813$	16.3267	0.572604
$814$	2.36369	0.0828474
$815$	5.47267	0.191699
$816$	10.9628	0.383774
$817$	−6.63002	−0.231955
$818$	−49.0213	−1.71399
$819$	−12.8937	−0.450544
$820$	6.76885	0.236378
$821$	−16.6686	−0.581738	−0.290869	−	0.956763i	$-0.593944\pi$
$821$	−16.6686	−0.581738	−0.290869	+	0.956763i	$0.593944\pi$
$822$	−22.6132	−0.788726
$823$	−8.49071	−0.295968	−0.147984	−	0.988990i	$-0.547278\pi$
$823$	−8.49071	−0.295968	−0.147984	+	0.988990i	$0.547278\pi$
$824$	5.84513	0.203625
$825$	−8.96641	−0.312170
$826$	78.6300	2.73589
$827$	1.72886	0.0601185	0.0300592	−	0.999548i	$-0.490430\pi$
$827$	1.72886	0.0601185	0.0300592	+	0.999548i	$0.490430\pi$
$828$	43.2881	1.50436
$829$	41.8634	1.45398	0.726988	−	0.686650i	$-0.240920\pi$
$829$	41.8634	1.45398	0.726988	+	0.686650i	$0.240920\pi$
$830$	25.3926	0.881389
$831$	6.60925	0.229272
$832$	11.9111	0.412942
$833$	−65.6037	−2.27303
$834$	1.40770	0.0487447
$835$	27.2185	0.941935
$836$	4.95315	0.171308
$837$	−14.4947	−0.501012
$838$	−41.9476	−1.44906
$839$	41.0285	1.41646	0.708231	−	0.705981i	$-0.249493\pi$
$839$	41.0285	1.41646	0.708231	+	0.705981i	$0.249493\pi$
$840$	−2.28734	−0.0789207
$841$	1.00000	0.0344828
$842$	−13.2912	−0.458045
$843$	−10.3631	−0.356926
$844$	40.6809	1.40029
$845$	12.3581	0.425132
$846$	29.9199	1.02867
$847$	−3.00568	−0.103276
$848$	41.1995	1.41480
$849$	20.1217	0.690576
$850$	−41.2147	−1.41365
$851$	2.40807	0.0825475
$852$	2.89688	0.0992454
$853$	−3.44729	−0.118033	−0.0590164	−	0.998257i	$-0.518796\pi$
$853$	−3.44729	−0.118033	−0.0590164	+	0.998257i	$0.518796\pi$
$854$	0.961352	0.0328968
$855$	1.65979	0.0567635
$856$	−1.02636	−0.0350804
$857$	−49.9311	−1.70562	−0.852808	−	0.522225i	$-0.825102\pi$
$857$	−49.9311	−1.70562	−0.852808	+	0.522225i	$0.825102\pi$
$858$	5.46550	0.186589
$859$	47.2252	1.61130	0.805651	−	0.592391i	$-0.201816\pi$
$859$	47.2252	1.61130	0.805651	+	0.592391i	$0.201816\pi$
$860$	26.5478	0.905272
$861$	8.23696	0.280715
$862$	0.196422	0.00669015
$863$	−46.2033	−1.57278	−0.786389	−	0.617732i	$-0.788052\pi$
$863$	−46.2033	−1.57278	−0.786389	+	0.617732i	$0.788052\pi$
$864$	−30.2872	−1.03039
$865$	13.9740	0.475130
$866$	−23.6189	−0.802603
$867$	6.00201	0.203839
$868$	−40.4963	−1.37453
$869$	−38.9596	−1.32161
$870$	1.48578	0.0503725
$871$	15.6553	0.530458
$872$	0.555666	0.0188172
$873$	−24.3282	−0.823384
$874$	9.34959	0.316255
$875$	−41.8319	−1.41418
$876$	−4.00502	−0.135317
$877$	26.6466	0.899792	0.449896	−	0.893081i	$-0.351461\pi$
$877$	26.6466	0.899792	0.449896	+	0.893081i	$0.351461\pi$
$878$	−28.6448	−0.966716
$879$	−2.04636	−0.0690220
$880$	11.5058	0.387860
$881$	27.7842	0.936074	0.468037	−	0.883709i	$-0.344961\pi$
$881$	27.7842	0.936074	0.468037	+	0.883709i	$0.344961\pi$
$882$	68.3743	2.30228
$883$	−53.8452	−1.81203	−0.906017	−	0.423241i	$-0.860892\pi$
$883$	−53.8452	−1.81203	−0.906017	+	0.423241i	$0.860892\pi$
$884$	13.5591	0.456041
$885$	−6.02805	−0.202631
$886$	17.2254	0.578698
$887$	0.536307	0.0180074	0.00900372	−	0.999959i	$-0.497134\pi$
$887$	0.536307	0.0180074	0.00900372	+	0.999959i	$0.497134\pi$
$888$	0.161254	0.00541131
$889$	−76.5729	−2.56817
$890$	−7.88882	−0.264434
$891$	17.4372	0.584167
$892$	13.9802	0.468092
$893$	3.48780	0.116715
$894$	−19.2580	−0.644083
$895$	−21.2152	−0.709145
$896$	−25.2903	−0.844889
$897$	5.56811	0.185914
$898$	54.8706	1.83106
$899$	3.87154	0.129123
$900$	23.1837	0.772790
$901$	65.7011	2.18882
$902$	19.4765	0.648496
$903$	32.3058	1.07507
$904$	13.1672	0.437935
$905$	−10.2578	−0.340981
$906$	−25.7737	−0.856273
$907$	37.8000	1.25513	0.627564	−	0.778565i	$-0.284052\pi$
$907$	37.8000	1.25513	0.627564	+	0.778565i	$0.284052\pi$
$908$	40.1639	1.33289
$909$	33.6263	1.11531
$910$	11.1511	0.369654
$911$	0.641496	0.0212537	0.0106269	−	0.999944i	$-0.496617\pi$
$911$	0.641496	0.0212537	0.0106269	+	0.999944i	$0.496617\pi$
$912$	−1.33191	−0.0441040
$913$	39.4338	1.30507
$914$	−42.8668	−1.41791
$915$	−0.0737006	−0.00243647
$916$	−4.50557	−0.148868
$917$	−21.4723	−0.709078
$918$	−39.7079	−1.31055
$919$	−30.5688	−1.00837	−0.504185	−	0.863596i	$-0.668207\pi$
$919$	−30.5688	−1.00837	−0.504185	+	0.863596i	$0.668207\pi$
$920$	−5.51000	−0.181659
$921$	−4.38513	−0.144495
$922$	−38.5793	−1.27054
$923$	−2.07856	−0.0684165
$924$	−24.1350	−0.793983
$925$	1.28968	0.0424045
$926$	17.7265	0.582529
$927$	20.6672	0.678799
$928$	8.08968	0.265557
$929$	−57.4583	−1.88515	−0.942573	−	0.334001i	$-0.891601\pi$
$929$	−57.4583	−1.88515	−0.942573	+	0.334001i	$0.891601\pi$
$930$	5.75224	0.188623
$931$	7.97046	0.261221
$932$	−57.2932	−1.87670
$933$	−8.27729	−0.270986
$934$	−7.73819	−0.253201
$935$	18.3483	0.600055
$936$	−2.07989	−0.0679833
$937$	−28.1473	−0.919532	−0.459766	−	0.888040i	$-0.652067\pi$
$937$	−28.1473	−0.919532	−0.459766	+	0.888040i	$0.652067\pi$
$938$	−128.089	−4.18224
$939$	12.8169	0.418265
$940$	−13.9658	−0.455513
$941$	49.8996	1.62668	0.813340	−	0.581789i	$-0.197647\pi$
$941$	49.8996	1.62668	0.813340	+	0.581789i	$0.197647\pi$
$942$	−23.6158	−0.769443
$943$	19.8421	0.646149
$944$	−26.9831	−0.878225
$945$	−17.6250	−0.573341
$946$	76.3878	2.48358
$947$	−32.9118	−1.06949	−0.534744	−	0.845014i	$-0.679592\pi$
$947$	−32.9118	−1.06949	−0.534744	+	0.845014i	$0.679592\pi$
$948$	−18.0587	−0.586520
$949$	2.87366	0.0932831
$950$	5.00734	0.162460
$951$	−9.35238	−0.303272
$952$	−16.3278	−0.529186
$953$	40.8707	1.32393	0.661966	−	0.749534i	$-0.269722\pi$
$953$	40.8707	1.32393	0.661966	+	0.749534i	$0.269722\pi$
$954$	−68.4758	−2.21699
$955$	25.0976	0.812139
$956$	0.0430238	0.00139149
$957$	2.30736	0.0745864
$958$	46.5209	1.50302
$959$	−71.6490	−2.31367
$960$	7.47119	0.241132
$961$	−16.0112	−0.516490
$962$	−0.786131	−0.0253459
$963$	−3.62901	−0.116943
$964$	15.7684	0.507865
$965$	0.988547	0.0318225
$966$	−45.5573	−1.46578
$967$	−38.3688	−1.23386	−0.616928	−	0.787019i	$-0.711623\pi$
$967$	−38.3688	−1.23386	−0.616928	+	0.787019i	$0.711623\pi$
$968$	−0.484846	−0.0155835
$969$	−2.12401	−0.0682329
$970$	21.0401	0.675555
$971$	−11.6950	−0.375309	−0.187655	−	0.982235i	$-0.560089\pi$
$971$	−11.6950	−0.375309	−0.187655	+	0.982235i	$0.560089\pi$
$972$	34.4228	1.10411
$973$	4.46025	0.142989
$974$	17.8946	0.573380
$975$	2.98210	0.0955037
$976$	−0.329903	−0.0105599
$977$	3.95004	0.126373	0.0631865	−	0.998002i	$-0.479874\pi$
$977$	3.95004	0.126373	0.0631865	+	0.998002i	$0.479874\pi$
$978$	7.29907	0.233399
$979$	−12.2511	−0.391546
$980$	−31.9151	−1.01949
$981$	1.96472	0.0627287
$982$	−24.5779	−0.784311
$983$	−14.0025	−0.446611	−0.223305	−	0.974749i	$-0.571685\pi$
$983$	−14.0025	−0.446611	−0.223305	+	0.974749i	$0.571685\pi$
$984$	1.32871	0.0423576
$985$	9.03678	0.287936
$986$	10.6059	0.337762
$987$	−16.9948	−0.540951
$988$	−1.64735	−0.0524091
$989$	77.8219	2.47459
$990$	−19.1232	−0.607776
$991$	22.8076	0.724506	0.362253	−	0.932080i	$-0.382008\pi$
$991$	22.8076	0.724506	0.362253	+	0.932080i	$0.382008\pi$
$992$	31.3195	0.994396
$993$	13.6815	0.434169
$994$	17.0064	0.539410
$995$	0.477754	0.0151458
$996$	18.2785	0.579177
$997$	5.71050	0.180853	0.0904266	−	0.995903i	$-0.471177\pi$
$997$	5.71050	0.180853	0.0904266	+	0.995903i	$0.471177\pi$
$998$	57.6192	1.82390
$999$	1.24253	0.0393120

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.d.1.14	✓	98

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.d.1.14	✓	98	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08450 q^{2} +0.675318 q^{3} +2.34516 q^{4} -1.05546 q^{5} -1.40770 q^{6} -4.46025 q^{7} -0.719483 q^{8} -2.54395 q^{9} +O(q^{10})\)	\(q-2.08450 q^{2} +0.675318 q^{3} +2.34516 q^{4} -1.05546 q^{5} -1.40770 q^{6} -4.46025 q^{7} -0.719483 q^{8} -2.54395 q^{9} +2.20012 q^{10} +3.41671 q^{11} +1.58373 q^{12} -1.13635 q^{13} +9.29741 q^{14} -0.712772 q^{15} -3.19055 q^{16} -5.08799 q^{17} +5.30287 q^{18} +0.618161 q^{19} -2.47523 q^{20} -3.01208 q^{21} -7.12214 q^{22} -7.25585 q^{23} -0.485880 q^{24} -3.88600 q^{25} +2.36872 q^{26} -3.74392 q^{27} -10.4600 q^{28} +1.00000 q^{29} +1.48578 q^{30} +3.87154 q^{31} +8.08968 q^{32} +2.30736 q^{33} +10.6059 q^{34} +4.70762 q^{35} -5.96596 q^{36} -0.331880 q^{37} -1.28856 q^{38} -0.767396 q^{39} +0.759387 q^{40} -2.73464 q^{41} +6.27870 q^{42} -10.7254 q^{43} +8.01272 q^{44} +2.68504 q^{45} +15.1249 q^{46} +5.64222 q^{47} -2.15463 q^{48} +12.8938 q^{49} +8.10038 q^{50} -3.43601 q^{51} -2.66492 q^{52} -12.9130 q^{53} +7.80423 q^{54} -3.60620 q^{55} +3.20908 q^{56} +0.417455 q^{57} -2.08450 q^{58} +8.45719 q^{59} -1.67156 q^{60} +0.103400 q^{61} -8.07024 q^{62} +11.3466 q^{63} -10.4819 q^{64} +1.19937 q^{65} -4.80971 q^{66} -13.7768 q^{67} -11.9321 q^{68} -4.90000 q^{69} -9.81306 q^{70} +1.82915 q^{71} +1.83033 q^{72} -2.52886 q^{73} +0.691804 q^{74} -2.62428 q^{75} +1.44968 q^{76} -15.2394 q^{77} +1.59964 q^{78} -11.4027 q^{79} +3.36750 q^{80} +5.10350 q^{81} +5.70037 q^{82} +11.5415 q^{83} -7.06381 q^{84} +5.37018 q^{85} +22.3571 q^{86} +0.675318 q^{87} -2.45826 q^{88} -3.58564 q^{89} -5.59697 q^{90} +5.06840 q^{91} -17.0161 q^{92} +2.61452 q^{93} -11.7612 q^{94} -0.652445 q^{95} +5.46310 q^{96} +9.56316 q^{97} -26.8772 q^{98} -8.69192 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9}+O(q^{10}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9	\( 98 q + 6 q^{2} + 6 q^{3} + 116 q^{4} + q^{5} + 7 q^{6} + 12 q^{7} + 15 q^{8} + 136 q^{9} + 16 q^{10} + 25 q^{11} + 8 q^{12} + 18 q^{13} + 34 q^{14} + 14 q^{15} + 136 q^{16} + 35 q^{17} + 20 q^{18} + 48 q^{19} - 20 q^{20} + 62 q^{21} + 32 q^{22} + q^{23} + 8 q^{24} + 173 q^{25} + 15 q^{26} + 18 q^{27} + 37 q^{28} + 98 q^{29} - 6 q^{30} + 20 q^{31} + 16 q^{32} + 24 q^{33} - 6 q^{34} + 11 q^{35} + 155 q^{36} + 62 q^{37} - 5 q^{38} + 45 q^{39} + 38 q^{40} + 50 q^{41} + 7 q^{42} + 72 q^{43} + 92 q^{44} - 13 q^{45} + 32 q^{46} - 16 q^{47} - 13 q^{48} + 194 q^{49} + 50 q^{50} + 2 q^{51} + 83 q^{52} - 11 q^{53} + 58 q^{54} + 32 q^{55} + 106 q^{56} + 84 q^{57} + 6 q^{58} + 20 q^{59} + 62 q^{60} + 142 q^{61} - 27 q^{62} + 26 q^{63} + 213 q^{64} + 13 q^{65} - 35 q^{66} + 5 q^{67} + 69 q^{68} + 68 q^{69} - 2 q^{70} - 10 q^{71} - 9 q^{72} + 74 q^{73} + 21 q^{74} + 19 q^{75} + 116 q^{76} + 41 q^{77} - 162 q^{78} + 104 q^{79} - 86 q^{80} + 230 q^{81} + 53 q^{82} - 19 q^{83} + 76 q^{84} + 125 q^{85} + 9 q^{86} + 6 q^{87} + 68 q^{88} + 120 q^{89} + 122 q^{90} + 30 q^{91} + 3 q^{92} - 56 q^{93} + 22 q^{94} + 32 q^{95} - 55 q^{96} + 98 q^{97} - 15 q^{98} + 69 q^{99}+O(q^{100}) \) 98 * q + 6 * q^2 + 6 * q^3 + 116 * q^4 + q^5 + 7 * q^6 + 12 * q^7 + 15 * q^8 + 136 * q^9 + 16 * q^10 + 25 * q^11 + 8 * q^12 + 18 * q^13 + 34 * q^14 + 14 * q^15 + 136 * q^16 + 35 * q^17 + 20 * q^18 + 48 * q^19 - 20 * q^20 + 62 * q^21 + 32 * q^22 + q^23 + 8 * q^24 + 173 * q^25 + 15 * q^26 + 18 * q^27 + 37 * q^28 + 98 * q^29 - 6 * q^30 + 20 * q^31 + 16 * q^32 + 24 * q^33 - 6 * q^34 + 11 * q^35 + 155 * q^36 + 62 * q^37 - 5 * q^38 + 45 * q^39 + 38 * q^40 + 50 * q^41 + 7 * q^42 + 72 * q^43 + 92 * q^44 - 13 * q^45 + 32 * q^46 - 16 * q^47 - 13 * q^48 + 194 * q^49 + 50 * q^50 + 2 * q^51 + 83 * q^52 - 11 * q^53 + 58 * q^54 + 32 * q^55 + 106 * q^56 + 84 * q^57 + 6 * q^58 + 20 * q^59 + 62 * q^60 + 142 * q^61 - 27 * q^62 + 26 * q^63 + 213 * q^64 + 13 * q^65 - 35 * q^66 + 5 * q^67 + 69 * q^68 + 68 * q^69 - 2 * q^70 - 10 * q^71 - 9 * q^72 + 74 * q^73 + 21 * q^74 + 19 * q^75 + 116 * q^76 + 41 * q^77 - 162 * q^78 + 104 * q^79 - 86 * q^80 + 230 * q^81 + 53 * q^82 - 19 * q^83 + 76 * q^84 + 125 * q^85 + 9 * q^86 + 6 * q^87 + 68 * q^88 + 120 * q^89 + 122 * q^90 + 30 * q^91 + 3 * q^92 - 56 * q^93 + 22 * q^94 + 32 * q^95 - 55 * q^96 + 98 * q^97 - 15 * q^98 + 69 * q^99

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