LMFDB - Embedded newform 8003.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.68534 q^{2} -1.17289 q^{3} +5.21107 q^{4} +0.884422 q^{5} +3.14961 q^{6} -0.361098 q^{7} -8.62282 q^{8} -1.62433 q^{9} +O(q^{10})$	\(q-2.68534 q^{2} -1.17289 q^{3} +5.21107 q^{4} +0.884422 q^{5} +3.14961 q^{6} -0.361098 q^{7} -8.62282 q^{8} -1.62433 q^{9} -2.37498 q^{10} -0.487997 q^{11} -6.11201 q^{12} +3.81664 q^{13} +0.969672 q^{14} -1.03733 q^{15} +12.7331 q^{16} +1.24710 q^{17} +4.36188 q^{18} +2.14182 q^{19} +4.60878 q^{20} +0.423529 q^{21} +1.31044 q^{22} -8.74394 q^{23} +10.1136 q^{24} -4.21780 q^{25} -10.2490 q^{26} +5.42383 q^{27} -1.88171 q^{28} -1.05174 q^{29} +2.78559 q^{30} +1.50367 q^{31} -16.9471 q^{32} +0.572367 q^{33} -3.34889 q^{34} -0.319363 q^{35} -8.46448 q^{36} +8.49233 q^{37} -5.75152 q^{38} -4.47650 q^{39} -7.62621 q^{40} +9.25630 q^{41} -1.13732 q^{42} +7.47251 q^{43} -2.54298 q^{44} -1.43659 q^{45} +23.4805 q^{46} -1.75620 q^{47} -14.9345 q^{48} -6.86961 q^{49} +11.3262 q^{50} -1.46271 q^{51} +19.8887 q^{52} -1.00000 q^{53} -14.5648 q^{54} -0.431595 q^{55} +3.11368 q^{56} -2.51212 q^{57} +2.82428 q^{58} -4.21030 q^{59} -5.40559 q^{60} +6.49096 q^{61} -4.03787 q^{62} +0.586542 q^{63} +20.0425 q^{64} +3.37552 q^{65} -1.53700 q^{66} -15.1703 q^{67} +6.49872 q^{68} +10.2557 q^{69} +0.857599 q^{70} -11.2902 q^{71} +14.0063 q^{72} +15.6610 q^{73} -22.8048 q^{74} +4.94701 q^{75} +11.1612 q^{76} +0.176215 q^{77} +12.0209 q^{78} -7.81059 q^{79} +11.2614 q^{80} -1.48857 q^{81} -24.8564 q^{82} +12.9474 q^{83} +2.20704 q^{84} +1.10296 q^{85} -20.0663 q^{86} +1.23358 q^{87} +4.20791 q^{88} -7.41778 q^{89} +3.85774 q^{90} -1.37818 q^{91} -45.5653 q^{92} -1.76364 q^{93} +4.71600 q^{94} +1.89427 q^{95} +19.8771 q^{96} -12.2137 q^{97} +18.4473 q^{98} +0.792667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * 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 $

$2$	−2.68534	−1.89882	−0.949412	−	0.314033i	$-0.898320\pi$
$2$	−2.68534	−1.89882	−0.949412	+	0.314033i	$0.898320\pi$
$3$	−1.17289	−0.677169	−0.338584	−	0.940936i	$-0.609948\pi$
$3$	−1.17289	−0.677169	−0.338584	+	0.940936i	$0.609948\pi$
$4$	5.21107	2.60553
$5$	0.884422	0.395525	0.197763	−	0.980250i	$-0.436632\pi$
$5$	0.884422	0.395525	0.197763	+	0.980250i	$0.436632\pi$
$6$	3.14961	1.28582
$7$	−0.361098	−0.136482	−0.0682411	−	0.997669i	$-0.521739\pi$
$7$	−0.361098	−0.136482	−0.0682411	+	0.997669i	$0.521739\pi$
$8$	−8.62282	−3.04863
$9$	−1.62433	−0.541443
$10$	−2.37498	−0.751033
$11$	−0.487997	−0.147137	−0.0735683	−	0.997290i	$-0.523439\pi$
$11$	−0.487997	−0.147137	−0.0735683	+	0.997290i	$0.523439\pi$
$12$	−6.11201	−1.76439
$13$	3.81664	1.05854	0.529272	−	0.848452i	$-0.322465\pi$
$13$	3.81664	1.05854	0.529272	+	0.848452i	$0.322465\pi$
$14$	0.969672	0.259156
$15$	−1.03733	−0.267837
$16$	12.7331	3.18327
$17$	1.24710	0.302466	0.151233	−	0.988498i	$-0.451676\pi$
$17$	1.24710	0.302466	0.151233	+	0.988498i	$0.451676\pi$
$18$	4.36188	1.02810
$19$	2.14182	0.491367	0.245684	−	0.969350i	$-0.420988\pi$
$19$	2.14182	0.491367	0.245684	+	0.969350i	$0.420988\pi$
$20$	4.60878	1.03055
$21$	0.423529	0.0924215
$22$	1.31044	0.279386
$23$	−8.74394	−1.82324	−0.911619	−	0.411036i	$-0.865167\pi$
$23$	−8.74394	−1.82324	−0.911619	+	0.411036i	$0.865167\pi$
$24$	10.1136	2.06443
$25$	−4.21780	−0.843560
$26$	−10.2490	−2.00999
$27$	5.42383	1.04382
$28$	−1.88171	−0.355609
$29$	−1.05174	−0.195303	−0.0976517	−	0.995221i	$-0.531133\pi$
$29$	−1.05174	−0.195303	−0.0976517	+	0.995221i	$0.531133\pi$
$30$	2.78559	0.508576
$31$	1.50367	0.270067	0.135034	−	0.990841i	$-0.456886\pi$
$31$	1.50367	0.270067	0.135034	+	0.990841i	$0.456886\pi$
$32$	−16.9471	−2.99585
$33$	0.572367	0.0996362
$34$	−3.34889	−0.574330
$35$	−0.319363	−0.0539822
$36$	−8.46448	−1.41075
$37$	8.49233	1.39613	0.698065	−	0.716034i	$-0.254045\pi$
$37$	8.49233	1.39613	0.698065	+	0.716034i	$0.254045\pi$
$38$	−5.75152	−0.933020
$39$	−4.47650	−0.716813
$40$	−7.62621	−1.20581
$41$	9.25630	1.44559	0.722796	−	0.691062i	$-0.242857\pi$
$41$	9.25630	1.44559	0.722796	+	0.691062i	$0.242857\pi$
$42$	−1.13732	−0.175492
$43$	7.47251	1.13955	0.569774	−	0.821802i	$-0.307031\pi$
$43$	7.47251	1.13955	0.569774	+	0.821802i	$0.307031\pi$
$44$	−2.54298	−0.383369
$45$	−1.43659	−0.214154
$46$	23.4805	3.46201
$47$	−1.75620	−0.256168	−0.128084	−	0.991763i	$-0.540883\pi$
$47$	−1.75620	−0.256168	−0.128084	+	0.991763i	$0.540883\pi$
$48$	−14.9345	−2.15561
$49$	−6.86961	−0.981373
$50$	11.3262	1.60177
$51$	−1.46271	−0.204820
$52$	19.8887	2.75807
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−14.5648	−1.98202
$55$	−0.431595	−0.0581962
$56$	3.11368	0.416084
$57$	−2.51212	−0.332738
$58$	2.82428	0.370847
$59$	−4.21030	−0.548134	−0.274067	−	0.961711i	$-0.588369\pi$
$59$	−4.21030	−0.548134	−0.274067	+	0.961711i	$0.588369\pi$
$60$	−5.40559	−0.697859
$61$	6.49096	0.831083	0.415541	−	0.909574i	$-0.363592\pi$
$61$	6.49096	0.831083	0.415541	+	0.909574i	$0.363592\pi$
$62$	−4.03787	−0.512811
$63$	0.586542	0.0738973
$64$	20.0425	2.50532
$65$	3.37552	0.418681
$66$	−1.53700	−0.189192
$67$	−15.1703	−1.85334	−0.926671	−	0.375874i	$-0.877342\pi$
$67$	−15.1703	−1.85334	−0.926671	+	0.375874i	$0.877342\pi$
$68$	6.49872	0.788086
$69$	10.2557	1.23464
$70$	0.857599	0.102503
$71$	−11.2902	−1.33990	−0.669949	−	0.742407i	$-0.733684\pi$
$71$	−11.2902	−1.33990	−0.669949	+	0.742407i	$0.733684\pi$
$72$	14.0063	1.65066
$73$	15.6610	1.83298	0.916492	−	0.400052i	$-0.131008\pi$
$73$	15.6610	1.83298	0.916492	+	0.400052i	$0.131008\pi$
$74$	−22.8048	−2.65101
$75$	4.94701	0.571232
$76$	11.1612	1.28027
$77$	0.176215	0.0200815
$78$	12.0209	1.36110
$79$	−7.81059	−0.878760	−0.439380	−	0.898301i	$-0.644802\pi$
$79$	−7.81059	−0.878760	−0.439380	+	0.898301i	$0.644802\pi$
$80$	11.2614	1.25907
$81$	−1.48857	−0.165397
$82$	−24.8564	−2.74492
$83$	12.9474	1.42117	0.710583	−	0.703613i	$-0.248431\pi$
$83$	12.9474	1.42117	0.710583	+	0.703613i	$0.248431\pi$
$84$	2.20704	0.240807
$85$	1.10296	0.119633
$86$	−20.0663	−2.16380
$87$	1.23358	0.132253
$88$	4.20791	0.448564
$89$	−7.41778	−0.786284	−0.393142	−	0.919478i	$-0.628612\pi$
$89$	−7.41778	−0.786284	−0.393142	+	0.919478i	$0.628612\pi$
$90$	3.85774	0.406642
$91$	−1.37818	−0.144473
$92$	−45.5653	−4.75051
$93$	−1.76364	−0.182881
$94$	4.71600	0.486418
$95$	1.89427	0.194348
$96$	19.8771	2.02869
$97$	−12.2137	−1.24011	−0.620055	−	0.784558i	$-0.712890\pi$
$97$	−12.2137	−1.24011	−0.620055	+	0.784558i	$0.712890\pi$
$98$	18.4473	1.86345
$99$	0.792667	0.0796660
$100$	−21.9792	−2.19792
$101$	−10.0030	−0.995334	−0.497667	−	0.867368i	$-0.665810\pi$
$101$	−10.0030	−0.995334	−0.497667	+	0.867368i	$0.665810\pi$
$102$	3.92788	0.388918
$103$	10.0840	0.993608	0.496804	−	0.867863i	$-0.334507\pi$
$103$	10.0840	0.993608	0.496804	+	0.867863i	$0.334507\pi$
$104$	−32.9102	−3.22711
$105$	0.374578	0.0365551
$106$	2.68534	0.260824
$107$	−2.87826	−0.278252	−0.139126	−	0.990275i	$-0.544429\pi$
$107$	−2.87826	−0.278252	−0.139126	+	0.990275i	$0.544429\pi$
$108$	28.2639	2.71970
$109$	3.78290	0.362337	0.181168	−	0.983452i	$-0.442012\pi$
$109$	3.78290	0.362337	0.181168	+	0.983452i	$0.442012\pi$
$110$	1.15898	0.110504
$111$	−9.96057	−0.945416
$112$	−4.59790	−0.434460
$113$	−0.945287	−0.0889251	−0.0444626	−	0.999011i	$-0.514158\pi$
$113$	−0.945287	−0.0889251	−0.0444626	+	0.999011i	$0.514158\pi$
$114$	6.74590	0.631812
$115$	−7.73333	−0.721137
$116$	−5.48069	−0.508870
$117$	−6.19947	−0.573141
$118$	11.3061	1.04081
$119$	−0.450325	−0.0412813
$120$	8.94471	0.816536
$121$	−10.7619	−0.978351
$122$	−17.4305	−1.57808
$123$	−10.8566	−0.978909
$124$	7.83573	0.703670
$125$	−8.15242	−0.729175
$126$	−1.57507	−0.140318
$127$	14.4738	1.28434	0.642171	−	0.766562i	$-0.278034\pi$
$127$	14.4738	1.28434	0.642171	+	0.766562i	$0.278034\pi$
$128$	−19.9269	−1.76131
$129$	−8.76443	−0.771665
$130$	−9.06442	−0.795002
$131$	1.81293	0.158396	0.0791980	−	0.996859i	$-0.474764\pi$
$131$	1.81293	0.158396	0.0791980	+	0.996859i	$0.474764\pi$
$132$	2.98264	0.259606
$133$	−0.773407	−0.0670629
$134$	40.7373	3.51917
$135$	4.79695	0.412856
$136$	−10.7535	−0.922106
$137$	20.2414	1.72934	0.864671	−	0.502339i	$-0.167527\pi$
$137$	20.2414	1.72934	0.864671	+	0.502339i	$0.167527\pi$
$138$	−27.5400	−2.34436
$139$	5.02638	0.426332	0.213166	−	0.977016i	$-0.431622\pi$
$139$	5.02638	0.426332	0.213166	+	0.977016i	$0.431622\pi$
$140$	−1.66422	−0.140652
$141$	2.05983	0.173469
$142$	30.3180	2.54423
$143$	−1.86251	−0.155751
$144$	−20.6827	−1.72356
$145$	−0.930182	−0.0772474
$146$	−42.0552	−3.48052
$147$	8.05730	0.664555
$148$	44.2541	3.63767
$149$	11.8723	0.972618	0.486309	−	0.873787i	$-0.338343\pi$
$149$	11.8723	0.972618	0.486309	+	0.873787i	$0.338343\pi$
$150$	−13.2844	−1.08467
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−18.4685	−1.49800
$153$	−2.02570	−0.163768
$154$	−0.473197	−0.0381313
$155$	1.32988	0.106819
$156$	−23.3273	−1.86768
$157$	−1.16809	−0.0932236	−0.0466118	−	0.998913i	$-0.514842\pi$
$157$	−1.16809	−0.0932236	−0.0466118	+	0.998913i	$0.514842\pi$
$158$	20.9741	1.66861
$159$	1.17289	0.0930163
$160$	−14.9884	−1.18493
$161$	3.15742	0.248840
$162$	3.99733	0.314060
$163$	−6.12530	−0.479770	−0.239885	−	0.970801i	$-0.577110\pi$
$163$	−6.12530	−0.479770	−0.239885	+	0.970801i	$0.577110\pi$
$164$	48.2352	3.76654
$165$	0.506213	0.0394087
$166$	−34.7683	−2.69855
$167$	−5.90499	−0.456942	−0.228471	−	0.973551i	$-0.573373\pi$
$167$	−5.90499	−0.456942	−0.228471	+	0.973551i	$0.573373\pi$
$168$	−3.65201	−0.281759
$169$	1.56671	0.120516
$170$	−2.96183	−0.227162
$171$	−3.47902	−0.266047
$172$	38.9398	2.96913
$173$	16.5708	1.25985	0.629926	−	0.776655i	$-0.283085\pi$
$173$	16.5708	1.25985	0.629926	+	0.776655i	$0.283085\pi$
$174$	−3.31258	−0.251126
$175$	1.52304	0.115131
$176$	−6.21371	−0.468376
$177$	4.93822	0.371179
$178$	19.9193	1.49301
$179$	−4.28985	−0.320639	−0.160319	−	0.987065i	$-0.551252\pi$
$179$	−4.28985	−0.320639	−0.160319	+	0.987065i	$0.551252\pi$
$180$	−7.48617	−0.557986
$181$	−7.42026	−0.551543	−0.275772	−	0.961223i	$-0.588933\pi$
$181$	−7.42026	−0.551543	−0.275772	+	0.961223i	$0.588933\pi$
$182$	3.70089	0.274328
$183$	−7.61319	−0.562783
$184$	75.3974	5.55837
$185$	7.51080	0.552205
$186$	4.73598	0.347259
$187$	−0.608580	−0.0445038
$188$	−9.15168	−0.667455
$189$	−1.95853	−0.142462
$190$	−5.08677	−0.369033
$191$	13.2090	0.955766	0.477883	−	0.878423i	$-0.341404\pi$
$191$	13.2090	0.955766	0.477883	+	0.878423i	$0.341404\pi$
$192$	−23.5077	−1.69652
$193$	12.0278	0.865778	0.432889	−	0.901447i	$-0.357494\pi$
$193$	12.0278	0.865778	0.432889	+	0.901447i	$0.357494\pi$
$194$	32.7979	2.35475
$195$	−3.95911	−0.283518
$196$	−35.7980	−2.55700
$197$	−22.8987	−1.63146	−0.815732	−	0.578430i	$-0.803666\pi$
$197$	−22.8987	−1.63146	−0.815732	+	0.578430i	$0.803666\pi$
$198$	−2.12858	−0.151272
$199$	8.38940	0.594709	0.297355	−	0.954767i	$-0.403896\pi$
$199$	8.38940	0.594709	0.297355	+	0.954767i	$0.403896\pi$
$200$	36.3693	2.57170
$201$	17.7930	1.25502
$202$	26.8614	1.88996
$203$	0.379782	0.0266554
$204$	−7.62229	−0.533667
$205$	8.18648	0.571768
$206$	−27.0790	−1.88669
$207$	14.2030	0.987179
$208$	48.5976	3.36964
$209$	−1.04520	−0.0722981
$210$	−1.00587	−0.0694116
$211$	8.92553	0.614459	0.307229	−	0.951636i	$-0.400598\pi$
$211$	8.92553	0.614459	0.307229	+	0.951636i	$0.400598\pi$
$212$	−5.21107	−0.357898
$213$	13.2422	0.907337
$214$	7.72911	0.528351
$215$	6.60885	0.450720
$216$	−46.7687	−3.18221
$217$	−0.542973	−0.0368594
$218$	−10.1584	−0.688013
$219$	−18.3687	−1.24124
$220$	−2.24907	−0.151632
$221$	4.75972	0.320174
$222$	26.7476	1.79518
$223$	−15.7402	−1.05404	−0.527022	−	0.849852i	$-0.676691\pi$
$223$	−15.7402	−1.05404	−0.527022	+	0.849852i	$0.676691\pi$
$224$	6.11956	0.408880
$225$	6.85109	0.456739
$226$	2.53842	0.168853
$227$	−14.5190	−0.963659	−0.481829	−	0.876265i	$-0.660028\pi$
$227$	−14.5190	−0.963659	−0.481829	+	0.876265i	$0.660028\pi$
$228$	−13.0908	−0.866961
$229$	10.6816	0.705858	0.352929	−	0.935650i	$-0.385186\pi$
$229$	10.6816	0.705858	0.352929	+	0.935650i	$0.385186\pi$
$230$	20.7667	1.36931
$231$	−0.206681	−0.0135986
$232$	9.06897	0.595407
$233$	9.25329	0.606203	0.303101	−	0.952958i	$-0.401978\pi$
$233$	9.25329	0.606203	0.303101	+	0.952958i	$0.401978\pi$
$234$	16.6477	1.08829
$235$	−1.55322	−0.101321
$236$	−21.9402	−1.42818
$237$	9.16096	0.595069
$238$	1.20928	0.0783858
$239$	−14.2837	−0.923939	−0.461969	−	0.886896i	$-0.652857\pi$
$239$	−14.2837	−0.923939	−0.461969	+	0.886896i	$0.652857\pi$
$240$	−13.2084	−0.852599
$241$	13.1156	0.844851	0.422426	−	0.906398i	$-0.361179\pi$
$241$	13.1156	0.844851	0.422426	+	0.906398i	$0.361179\pi$
$242$	28.8993	1.85772
$243$	−14.5256	−0.931815
$244$	33.8248	2.16541
$245$	−6.07563	−0.388158
$246$	29.1538	1.85878
$247$	8.17455	0.520134
$248$	−12.9659	−0.823335
$249$	−15.1859	−0.962369
$250$	21.8920	1.38457
$251$	−22.1267	−1.39662	−0.698312	−	0.715794i	$-0.746065\pi$
$251$	−22.1267	−1.39662	−0.698312	+	0.715794i	$0.746065\pi$
$252$	3.05651	0.192542
$253$	4.26702	0.268265
$254$	−38.8671	−2.43874
$255$	−1.29365	−0.0810117
$256$	13.4256	0.839100
$257$	20.1509	1.25698	0.628490	−	0.777818i	$-0.283673\pi$
$257$	20.1509	1.25698	0.628490	+	0.777818i	$0.283673\pi$
$258$	23.5355	1.46526
$259$	−3.06657	−0.190547
$260$	17.5900	1.09089
$261$	1.70837	0.105746
$262$	−4.86833	−0.300766
$263$	16.1841	0.997957	0.498978	−	0.866614i	$-0.333709\pi$
$263$	16.1841	0.997957	0.498978	+	0.866614i	$0.333709\pi$
$264$	−4.93541	−0.303754
$265$	−0.884422	−0.0543296
$266$	2.07686	0.127341
$267$	8.70025	0.532446
$268$	−79.0532	−4.82894
$269$	22.3131	1.36045	0.680227	−	0.733001i	$-0.261881\pi$
$269$	22.3131	1.36045	0.680227	+	0.733001i	$0.261881\pi$
$270$	−12.8815	−0.783941
$271$	−7.62998	−0.463488	−0.231744	−	0.972777i	$-0.574443\pi$
$271$	−7.62998	−0.463488	−0.231744	+	0.972777i	$0.574443\pi$
$272$	15.8794	0.962832
$273$	1.61645	0.0978323
$274$	−54.3552	−3.28372
$275$	2.05827	0.124118
$276$	53.4431	3.21689
$277$	−8.61319	−0.517516	−0.258758	−	0.965942i	$-0.583313\pi$
$277$	−8.61319	−0.517516	−0.258758	+	0.965942i	$0.583313\pi$
$278$	−13.4976	−0.809530
$279$	−2.44246	−0.146226
$280$	2.75381	0.164572
$281$	13.4241	0.800815	0.400408	−	0.916337i	$-0.368869\pi$
$281$	13.4241	0.800815	0.400408	+	0.916337i	$0.368869\pi$
$282$	−5.53135	−0.329387
$283$	24.0622	1.43035	0.715176	−	0.698945i	$-0.246347\pi$
$283$	24.0622	1.43035	0.715176	+	0.698945i	$0.246347\pi$
$284$	−58.8339	−3.49115
$285$	−2.22177	−0.131606
$286$	5.00147	0.295743
$287$	−3.34243	−0.197298
$288$	27.5276	1.62208
$289$	−15.4447	−0.908514
$290$	2.49786	0.146679
$291$	14.3253	0.839764
$292$	81.6107	4.77590
$293$	−30.3761	−1.77459	−0.887294	−	0.461204i	$-0.847418\pi$
$293$	−30.3761	−1.77459	−0.887294	+	0.461204i	$0.847418\pi$
$294$	−21.6366	−1.26187
$295$	−3.72368	−0.216801
$296$	−73.2278	−4.25628
$297$	−2.64681	−0.153584
$298$	−31.8812	−1.84683
$299$	−33.3724	−1.92998
$300$	25.7792	1.48836
$301$	−2.69831	−0.155528
$302$	−2.68534	−0.154524
$303$	11.7324	0.674009
$304$	27.2720	1.56416
$305$	5.74075	0.328714
$306$	5.43970	0.310967
$307$	2.56443	0.146360	0.0731800	−	0.997319i	$-0.476685\pi$
$307$	2.56443	0.146360	0.0731800	+	0.997319i	$0.476685\pi$
$308$	0.918267	0.0523231
$309$	−11.8274	−0.672840
$310$	−3.57118	−0.202830
$311$	9.57297	0.542833	0.271417	−	0.962462i	$-0.412508\pi$
$311$	9.57297	0.542833	0.271417	+	0.962462i	$0.412508\pi$
$312$	38.6000	2.18530
$313$	33.9493	1.91893	0.959465	−	0.281829i	$-0.0909411\pi$
$313$	33.9493	1.91893	0.959465	+	0.281829i	$0.0909411\pi$
$314$	3.13672	0.177015
$315$	0.518750	0.0292283
$316$	−40.7015	−2.28964
$317$	16.7272	0.939492	0.469746	−	0.882802i	$-0.344346\pi$
$317$	16.7272	0.939492	0.469746	+	0.882802i	$0.344346\pi$
$318$	−3.14961	−0.176622
$319$	0.513246	0.0287363
$320$	17.7261	0.990917
$321$	3.37588	0.188423
$322$	−8.47876	−0.472503
$323$	2.67106	0.148622
$324$	−7.75705	−0.430947
$325$	−16.0978	−0.892945
$326$	16.4485	0.910999
$327$	−4.43693	−0.245363
$328$	−79.8154	−4.40707
$329$	0.634161	0.0349624
$330$	−1.35936	−0.0748301
$331$	−29.1574	−1.60264	−0.801319	−	0.598238i	$-0.795868\pi$
$331$	−29.1574	−1.60264	−0.801319	+	0.598238i	$0.795868\pi$
$332$	67.4700	3.70290
$333$	−13.7943	−0.755925
$334$	15.8569	0.867652
$335$	−13.4169	−0.733044
$336$	5.39283	0.294203
$337$	27.6815	1.50791	0.753955	−	0.656926i	$-0.228144\pi$
$337$	27.6815	1.50791	0.753955	+	0.656926i	$0.228144\pi$
$338$	−4.20716	−0.228839
$339$	1.10872	0.0602173
$340$	5.74761	0.311708
$341$	−0.733787	−0.0397368
$342$	9.34236	0.505177
$343$	5.00829	0.270422
$344$	−64.4341	−3.47405
$345$	9.07035	0.488331
$346$	−44.4982	−2.39224
$347$	−6.39575	−0.343342	−0.171671	−	0.985154i	$-0.554917\pi$
$347$	−6.39575	−0.343342	−0.171671	+	0.985154i	$0.554917\pi$
$348$	6.42825	0.344590
$349$	−17.7946	−0.952521	−0.476261	−	0.879304i	$-0.658008\pi$
$349$	−17.7946	−0.952521	−0.476261	+	0.879304i	$0.658008\pi$
$350$	−4.08988	−0.218613
$351$	20.7008	1.10493
$352$	8.27012	0.440799
$353$	2.17367	0.115693	0.0578465	−	0.998325i	$-0.481577\pi$
$353$	2.17367	0.115693	0.0578465	+	0.998325i	$0.481577\pi$
$354$	−13.2608	−0.704804
$355$	−9.98529	−0.529964
$356$	−38.6546	−2.04869
$357$	0.528182	0.0279544
$358$	11.5197	0.608837
$359$	−31.3541	−1.65481	−0.827404	−	0.561607i	$-0.810183\pi$
$359$	−31.3541	−1.65481	−0.827404	+	0.561607i	$0.810183\pi$
$360$	12.3875	0.652877
$361$	−14.4126	−0.758558
$362$	19.9259	1.04728
$363$	12.6225	0.662508
$364$	−7.18179	−0.376428
$365$	13.8510	0.724992
$366$	20.4440	1.06863
$367$	20.1479	1.05171	0.525856	−	0.850574i	$-0.323745\pi$
$367$	20.1479	1.05171	0.525856	+	0.850574i	$0.323745\pi$
$368$	−111.337	−5.80386
$369$	−15.0353	−0.782705
$370$	−20.1691	−1.04854
$371$	0.361098	0.0187473
$372$	−9.19046	−0.476503
$373$	−23.9812	−1.24170	−0.620849	−	0.783930i	$-0.713212\pi$
$373$	−23.9812	−1.24170	−0.620849	+	0.783930i	$0.713212\pi$
$374$	1.63425	0.0845049
$375$	9.56190	0.493774
$376$	15.1434	0.780961
$377$	−4.01411	−0.206737
$378$	5.25934	0.270511
$379$	16.6262	0.854030	0.427015	−	0.904244i	$-0.359565\pi$
$379$	16.6262	0.854030	0.427015	+	0.904244i	$0.359565\pi$
$380$	9.87118	0.506381
$381$	−16.9762	−0.869716
$382$	−35.4706	−1.81483
$383$	−26.8236	−1.37062	−0.685310	−	0.728251i	$-0.740333\pi$
$383$	−26.8236	−1.37062	−0.685310	+	0.728251i	$0.740333\pi$
$384$	23.3721	1.19270
$385$	0.155848	0.00794276
$386$	−32.2987	−1.64396
$387$	−12.1378	−0.617000
$388$	−63.6463	−3.23115
$389$	34.1360	1.73077	0.865383	−	0.501111i	$-0.167075\pi$
$389$	34.1360	1.73077	0.865383	+	0.501111i	$0.167075\pi$
$390$	10.6316	0.538350
$391$	−10.9046	−0.551468
$392$	59.2354	2.99184
$393$	−2.12636	−0.107261
$394$	61.4908	3.09786
$395$	−6.90785	−0.347572
$396$	4.13064	0.207573
$397$	−25.8571	−1.29773	−0.648867	−	0.760902i	$-0.724757\pi$
$397$	−25.8571	−1.29773	−0.648867	+	0.760902i	$0.724757\pi$
$398$	−22.5284	−1.12925
$399$	0.907122	0.0454129
$400$	−53.7056	−2.68528
$401$	−29.5208	−1.47420	−0.737100	−	0.675784i	$-0.763805\pi$
$401$	−29.5208	−1.47420	−0.737100	+	0.675784i	$0.763805\pi$
$402$	−47.7804	−2.38307
$403$	5.73897	0.285878
$404$	−52.1262	−2.59338
$405$	−1.31653	−0.0654187
$406$	−1.01984	−0.0506140
$407$	−4.14423	−0.205422
$408$	12.6127	0.624421
$409$	−8.24400	−0.407640	−0.203820	−	0.979008i	$-0.565336\pi$
$409$	−8.24400	−0.407640	−0.203820	+	0.979008i	$0.565336\pi$
$410$	−21.9835	−1.08569
$411$	−23.7410	−1.17106
$412$	52.5485	2.58888
$413$	1.52033	0.0748106
$414$	−38.1400	−1.87448
$415$	11.4510	0.562108
$416$	−64.6808	−3.17124
$417$	−5.89540	−0.288699
$418$	2.80672	0.137281
$419$	−3.03519	−0.148279	−0.0741393	−	0.997248i	$-0.523621\pi$
$419$	−3.03519	−0.148279	−0.0741393	+	0.997248i	$0.523621\pi$
$420$	1.95195	0.0952454
$421$	1.82390	0.0888913	0.0444457	−	0.999012i	$-0.485848\pi$
$421$	1.82390	0.0888913	0.0444457	+	0.999012i	$0.485848\pi$
$422$	−23.9681	−1.16675
$423$	2.85265	0.138700
$424$	8.62282	0.418761
$425$	−5.26001	−0.255148
$426$	−35.5597	−1.72287
$427$	−2.34387	−0.113428
$428$	−14.9988	−0.724995
$429$	2.18452	0.105469
$430$	−17.7470	−0.855838
$431$	12.1740	0.586401	0.293201	−	0.956051i	$-0.405280\pi$
$431$	12.1740	0.586401	0.293201	+	0.956051i	$0.405280\pi$
$432$	69.0621	3.32275
$433$	−16.4391	−0.790015	−0.395008	−	0.918678i	$-0.629258\pi$
$433$	−16.4391	−0.790015	−0.395008	+	0.918678i	$0.629258\pi$
$434$	1.45807	0.0699896
$435$	1.09100	0.0523095
$436$	19.7130	0.944080
$437$	−18.7280	−0.895879
$438$	49.3262	2.35690
$439$	12.2301	0.583709	0.291854	−	0.956463i	$-0.405728\pi$
$439$	12.2301	0.583709	0.291854	+	0.956463i	$0.405728\pi$
$440$	3.72156	0.177419
$441$	11.1585	0.531357
$442$	−12.7815	−0.607954
$443$	−37.1334	−1.76426	−0.882130	−	0.471007i	$-0.843891\pi$
$443$	−37.1334	−1.76426	−0.882130	+	0.471007i	$0.843891\pi$
$444$	−51.9052	−2.46331
$445$	−6.56045	−0.310995
$446$	42.2679	2.00144
$447$	−13.9249	−0.658626
$448$	−7.23733	−0.341932
$449$	3.29013	0.155271	0.0776354	−	0.996982i	$-0.475263\pi$
$449$	3.29013	0.155271	0.0776354	+	0.996982i	$0.475263\pi$
$450$	−18.3975	−0.867268
$451$	−4.51705	−0.212699
$452$	−4.92596	−0.231697
$453$	−1.17289	−0.0551072
$454$	38.9885	1.82982
$455$	−1.21889	−0.0571426
$456$	21.6616	1.01440
$457$	−6.13031	−0.286764	−0.143382	−	0.989667i	$-0.545798\pi$
$457$	−6.13031	−0.286764	−0.143382	+	0.989667i	$0.545798\pi$
$458$	−28.6837	−1.34030
$459$	6.76406	0.315719
$460$	−40.2989	−1.87895
$461$	1.04742	0.0487831	0.0243915	−	0.999702i	$-0.492235\pi$
$461$	1.04742	0.0487831	0.0243915	+	0.999702i	$0.492235\pi$
$462$	0.555008	0.0258213
$463$	20.6117	0.957906	0.478953	−	0.877841i	$-0.341016\pi$
$463$	20.6117	0.957906	0.478953	+	0.877841i	$0.341016\pi$
$464$	−13.3919	−0.621704
$465$	−1.55980	−0.0723341
$466$	−24.8482	−1.15107
$467$	2.59284	0.119982	0.0599911	−	0.998199i	$-0.480893\pi$
$467$	2.59284	0.119982	0.0599911	+	0.998199i	$0.480893\pi$
$468$	−32.3059	−1.49334
$469$	5.47795	0.252948
$470$	4.17093	0.192391
$471$	1.37004	0.0631281
$472$	36.3047	1.67106
$473$	−3.64656	−0.167669
$474$	−24.6003	−1.12993
$475$	−9.03376	−0.414498
$476$	−2.34668	−0.107560
$477$	1.62433	0.0743729
$478$	38.3568	1.75440
$479$	31.3486	1.43236	0.716178	−	0.697918i	$-0.245890\pi$
$479$	31.3486	1.43236	0.716178	+	0.697918i	$0.245890\pi$
$480$	17.5797	0.802400
$481$	32.4121	1.47787
$482$	−35.2199	−1.60422
$483$	−3.70331	−0.168506
$484$	−56.0808	−2.54913
$485$	−10.8020	−0.490495
$486$	39.0061	1.76935
$487$	−18.2798	−0.828336	−0.414168	−	0.910201i	$-0.635927\pi$
$487$	−18.2798	−0.828336	−0.414168	+	0.910201i	$0.635927\pi$
$488$	−55.9704	−2.53366
$489$	7.18430	0.324885
$490$	16.3152	0.737043
$491$	4.95438	0.223588	0.111794	−	0.993731i	$-0.464340\pi$
$491$	4.95438	0.223588	0.111794	+	0.993731i	$0.464340\pi$
$492$	−56.5746	−2.55058
$493$	−1.31163	−0.0590726
$494$	−21.9515	−0.987643
$495$	0.701052	0.0315099
$496$	19.1464	0.859698
$497$	4.07687	0.182872
$498$	40.7794	1.82737
$499$	1.73032	0.0774596	0.0387298	−	0.999250i	$-0.487669\pi$
$499$	1.73032	0.0774596	0.0387298	+	0.999250i	$0.487669\pi$
$500$	−42.4828	−1.89989
$501$	6.92591	0.309427
$502$	59.4177	2.65194
$503$	26.5135	1.18218	0.591088	−	0.806607i	$-0.298698\pi$
$503$	26.5135	1.18218	0.591088	+	0.806607i	$0.298698\pi$
$504$	−5.05764	−0.225285
$505$	−8.84685	−0.393680
$506$	−11.4584	−0.509388
$507$	−1.83758	−0.0816098
$508$	75.4239	3.34640
$509$	−22.0325	−0.976573	−0.488286	−	0.872684i	$-0.662378\pi$
$509$	−22.0325	−0.976573	−0.488286	+	0.872684i	$0.662378\pi$
$510$	3.47390	0.153827
$511$	−5.65517	−0.250170
$512$	3.80154	0.168006
$513$	11.6169	0.512897
$514$	−54.1121	−2.38678
$515$	8.91852	0.392997
$516$	−45.6721	−2.01060
$517$	0.857020	0.0376917
$518$	8.23478	0.361815
$519$	−19.4357	−0.853133
$520$	−29.1065	−1.27640
$521$	−24.3157	−1.06529	−0.532646	−	0.846338i	$-0.678802\pi$
$521$	−24.3157	−1.06529	−0.532646	+	0.846338i	$0.678802\pi$
$522$	−4.58757	−0.200792
$523$	−18.7224	−0.818674	−0.409337	−	0.912383i	$-0.634240\pi$
$523$	−18.7224	−0.818674	−0.409337	+	0.912383i	$0.634240\pi$
$524$	9.44728	0.412706
$525$	−1.78636	−0.0779630
$526$	−43.4600	−1.89494
$527$	1.87523	0.0816862
$528$	7.28800	0.317169
$529$	53.4565	2.32420
$530$	2.37498	0.103162
$531$	6.83891	0.296783
$532$	−4.03028	−0.174735
$533$	35.3279	1.53022
$534$	−23.3631	−1.01102
$535$	−2.54560	−0.110056
$536$	130.810	5.65015
$537$	5.03153	0.217126
$538$	−59.9184	−2.58326
$539$	3.35235	0.144396
$540$	24.9972	1.07571
$541$	30.8987	1.32844	0.664219	−	0.747538i	$-0.268764\pi$
$541$	30.8987	1.32844	0.664219	+	0.747538i	$0.268764\pi$
$542$	20.4891	0.880083
$543$	8.70315	0.373488
$544$	−21.1347	−0.906143
$545$	3.34568	0.143313
$546$	−4.34073	−0.185766
$547$	18.2914	0.782082	0.391041	−	0.920373i	$-0.372115\pi$
$547$	18.2914	0.782082	0.391041	+	0.920373i	$0.372115\pi$
$548$	105.479	4.50586
$549$	−10.5435	−0.449984
$550$	−5.52717	−0.235679
$551$	−2.25264	−0.0959657
$552$	−88.4329	−3.76395
$553$	2.82039	0.119935
$554$	23.1294	0.982673
$555$	−8.80935	−0.373936
$556$	26.1928	1.11082
$557$	−34.9434	−1.48060	−0.740299	−	0.672278i	$-0.765316\pi$
$557$	−34.9434	−1.48060	−0.740299	+	0.672278i	$0.765316\pi$
$558$	6.55883	0.277658
$559$	28.5199	1.20626
$560$	−4.06648	−0.171840
$561$	0.713798	0.0301366
$562$	−36.0483	−1.52061
$563$	9.92320	0.418213	0.209107	−	0.977893i	$-0.432944\pi$
$563$	9.92320	0.418213	0.209107	+	0.977893i	$0.432944\pi$
$564$	10.7339	0.451980
$565$	−0.836032	−0.0351721
$566$	−64.6154	−2.71599
$567$	0.537521	0.0225737
$568$	97.3532	4.08485
$569$	−0.327086	−0.0137121	−0.00685607	−	0.999976i	$-0.502182\pi$
$569$	−0.327086	−0.0137121	−0.00685607	+	0.999976i	$0.502182\pi$
$570$	5.96622	0.249898
$571$	27.0523	1.13211	0.566053	−	0.824369i	$-0.308470\pi$
$571$	27.0523	1.13211	0.566053	+	0.824369i	$0.308470\pi$
$572$	−9.70564	−0.405813
$573$	−15.4927	−0.647215
$574$	8.97558	0.374634
$575$	36.8802	1.53801
$576$	−32.5557	−1.35649
$577$	31.8857	1.32742	0.663709	−	0.747991i	$-0.268981\pi$
$577$	31.8857	1.32742	0.663709	+	0.747991i	$0.268981\pi$
$578$	41.4744	1.72511
$579$	−14.1072	−0.586277
$580$	−4.84724	−0.201271
$581$	−4.67530	−0.193964
$582$	−38.4683	−1.59456
$583$	0.487997	0.0202108
$584$	−135.042	−5.58809
$585$	−5.48295	−0.226692
$586$	81.5702	3.36963
$587$	42.6627	1.76088	0.880439	−	0.474160i	$-0.157248\pi$
$587$	42.6627	1.76088	0.880439	+	0.474160i	$0.157248\pi$
$588$	41.9871	1.73152
$589$	3.22059	0.132702
$590$	9.99936	0.411667
$591$	26.8576	1.10478
$592$	108.134	4.44426
$593$	−17.0411	−0.699792	−0.349896	−	0.936788i	$-0.613783\pi$
$593$	−17.0411	−0.699792	−0.349896	+	0.936788i	$0.613783\pi$
$594$	7.10760	0.291628
$595$	−0.398277	−0.0163278
$596$	61.8674	2.53419
$597$	−9.83985	−0.402718
$598$	89.6165	3.66469
$599$	30.2852	1.23742	0.618710	−	0.785620i	$-0.287656\pi$
$599$	30.2852	1.23742	0.618710	+	0.785620i	$0.287656\pi$
$600$	−42.6572	−1.74147
$601$	−14.5319	−0.592770	−0.296385	−	0.955069i	$-0.595781\pi$
$601$	−14.5319	−0.592770	−0.296385	+	0.955069i	$0.595781\pi$
$602$	7.24589	0.295320
$603$	24.6415	1.00348
$604$	5.21107	0.212035
$605$	−9.51802	−0.386963
$606$	−31.5055	−1.27982
$607$	36.4525	1.47956	0.739781	−	0.672848i	$-0.234929\pi$
$607$	36.4525	1.47956	0.739781	+	0.672848i	$0.234929\pi$
$608$	−36.2976	−1.47206
$609$	−0.445442	−0.0180502
$610$	−15.4159	−0.624171
$611$	−6.70278	−0.271165
$612$	−10.5561	−0.426703
$613$	41.6822	1.68353	0.841765	−	0.539844i	$-0.181517\pi$
$613$	41.6822	1.68353	0.841765	+	0.539844i	$0.181517\pi$
$614$	−6.88638	−0.277912
$615$	−9.60184	−0.387184
$616$	−1.51947	−0.0612211
$617$	36.0920	1.45301	0.726504	−	0.687162i	$-0.241144\pi$
$617$	36.0920	1.45301	0.726504	+	0.687162i	$0.241144\pi$
$618$	31.7608	1.27760
$619$	−10.3980	−0.417930	−0.208965	−	0.977923i	$-0.567009\pi$
$619$	−10.3980	−0.417930	−0.208965	+	0.977923i	$0.567009\pi$
$620$	6.93009	0.278319
$621$	−47.4257	−1.90313
$622$	−25.7067	−1.03074
$623$	2.67855	0.107314
$624$	−56.9996	−2.28181
$625$	13.8788	0.555153
$626$	−91.1656	−3.64371
$627$	1.22591	0.0489580
$628$	−6.08698	−0.242897
$629$	10.5908	0.422282
$630$	−1.39302	−0.0554994
$631$	37.3536	1.48702	0.743511	−	0.668723i	$-0.233159\pi$
$631$	37.3536	1.48702	0.743511	+	0.668723i	$0.233159\pi$
$632$	67.3493	2.67901
$633$	−10.4687	−0.416092
$634$	−44.9182	−1.78393
$635$	12.8009	0.507990
$636$	6.11201	0.242357
$637$	−26.2188	−1.03883
$638$	−1.37824	−0.0545651
$639$	18.3390	0.725479
$640$	−17.6238	−0.696643
$641$	−4.30166	−0.169905	−0.0849527	−	0.996385i	$-0.527074\pi$
$641$	−4.30166	−0.169905	−0.0849527	+	0.996385i	$0.527074\pi$
$642$	−9.06540	−0.357783
$643$	2.21238	0.0872476	0.0436238	−	0.999048i	$-0.486110\pi$
$643$	2.21238	0.0872476	0.0436238	+	0.999048i	$0.486110\pi$
$644$	16.4535	0.648360
$645$	−7.75146	−0.305213
$646$	−7.17272	−0.282207
$647$	−30.0019	−1.17950	−0.589749	−	0.807587i	$-0.700773\pi$
$647$	−30.0019	−1.17950	−0.589749	+	0.807587i	$0.700773\pi$
$648$	12.8357	0.504233
$649$	2.05461	0.0806506
$650$	43.2281	1.69555
$651$	0.636848	0.0249600
$652$	−31.9193	−1.25006
$653$	30.8115	1.20575	0.602874	−	0.797836i	$-0.294022\pi$
$653$	30.8115	1.20575	0.602874	+	0.797836i	$0.294022\pi$
$654$	11.9147	0.465901
$655$	1.60339	0.0626497
$656$	117.861	4.60171
$657$	−25.4386	−0.992456
$658$	−1.70294	−0.0663875
$659$	−28.4467	−1.10813	−0.554063	−	0.832475i	$-0.686923\pi$
$659$	−28.4467	−1.10813	−0.554063	+	0.832475i	$0.686923\pi$
$660$	2.63791	0.102681
$661$	2.48366	0.0966033	0.0483017	−	0.998833i	$-0.484619\pi$
$661$	2.48366	0.0966033	0.0483017	+	0.998833i	$0.484619\pi$
$662$	78.2977	3.04313
$663$	−5.58263	−0.216812
$664$	−111.643	−4.33261
$665$	−0.684018	−0.0265251
$666$	37.0425	1.43537
$667$	9.19636	0.356085
$668$	−30.7713	−1.19058
$669$	18.4616	0.713765
$670$	36.0290	1.39192
$671$	−3.16757	−0.122283
$672$	−7.17757	−0.276881
$673$	12.8091	0.493756	0.246878	−	0.969047i	$-0.420595\pi$
$673$	12.8091	0.493756	0.246878	+	0.969047i	$0.420595\pi$
$674$	−74.3345	−2.86326
$675$	−22.8766	−0.880522
$676$	8.16423	0.314009
$677$	39.2090	1.50692	0.753462	−	0.657492i	$-0.228383\pi$
$677$	39.2090	1.50692	0.753462	+	0.657492i	$0.228383\pi$
$678$	−2.97729	−0.114342
$679$	4.41033	0.169253
$680$	−9.51064	−0.364716
$681$	17.0292	0.652559
$682$	1.97047	0.0754532
$683$	−22.1384	−0.847101	−0.423550	−	0.905873i	$-0.639216\pi$
$683$	−22.1384	−0.847101	−0.423550	+	0.905873i	$0.639216\pi$
$684$	−18.1294	−0.693195
$685$	17.9020	0.683999
$686$	−13.4490	−0.513484
$687$	−12.5283	−0.477985
$688$	95.1482	3.62749
$689$	−3.81664	−0.145402
$690$	−24.3570	−0.927255
$691$	−16.9735	−0.645704	−0.322852	−	0.946449i	$-0.604642\pi$
$691$	−16.9735	−0.645704	−0.322852	+	0.946449i	$0.604642\pi$
$692$	86.3514	3.28259
$693$	−0.286231	−0.0108730
$694$	17.1748	0.651946
$695$	4.44544	0.168625
$696$	−10.6369	−0.403191
$697$	11.5435	0.437242
$698$	47.7845	1.80867
$699$	−10.8531	−0.410501
$700$	7.93666	0.299978
$701$	1.86972	0.0706183	0.0353092	−	0.999376i	$-0.488758\pi$
$701$	1.86972	0.0706183	0.0353092	+	0.999376i	$0.488758\pi$
$702$	−55.5887	−2.09806
$703$	18.1890	0.686013
$704$	−9.78070	−0.368624
$705$	1.82176	0.0686114
$706$	−5.83706	−0.219681
$707$	3.61206	0.135845
$708$	25.7334	0.967120
$709$	−41.4439	−1.55646	−0.778230	−	0.627980i	$-0.783882\pi$
$709$	−41.4439	−1.55646	−0.778230	+	0.627980i	$0.783882\pi$
$710$	26.8139	1.00631
$711$	12.6870	0.475798
$712$	63.9622	2.39708
$713$	−13.1480	−0.492397
$714$	−1.41835	−0.0530804
$715$	−1.64724	−0.0616033
$716$	−22.3547	−0.835435
$717$	16.7533	0.625662
$718$	84.1966	3.14219
$719$	−5.41599	−0.201982	−0.100991	−	0.994887i	$-0.532201\pi$
$719$	−5.41599	−0.201982	−0.100991	+	0.994887i	$0.532201\pi$
$720$	−18.2922	−0.681712
$721$	−3.64132	−0.135610
$722$	38.7028	1.44037
$723$	−15.3832	−0.572107
$724$	−38.6675	−1.43706
$725$	4.43603	0.164750
$726$	−33.8957	−1.25799
$727$	−22.7235	−0.842770	−0.421385	−	0.906882i	$-0.638456\pi$
$727$	−22.7235	−0.842770	−0.421385	+	0.906882i	$0.638456\pi$
$728$	11.8838	0.440443
$729$	21.5026	0.796393
$730$	−37.1946	−1.37663
$731$	9.31896	0.344674
$732$	−39.6728	−1.46635
$733$	34.8033	1.28549	0.642744	−	0.766081i	$-0.277796\pi$
$733$	34.8033	1.28549	0.642744	+	0.766081i	$0.277796\pi$
$734$	−54.1040	−1.99702
$735$	7.12605	0.262848
$736$	148.184	5.46215
$737$	7.40303	0.272694
$738$	40.3749	1.48622
$739$	1.86685	0.0686732	0.0343366	−	0.999410i	$-0.489068\pi$
$739$	1.86685	0.0686732	0.0343366	+	0.999410i	$0.489068\pi$
$740$	39.1393	1.43879
$741$	−9.58785	−0.352218
$742$	−0.969672	−0.0355978
$743$	42.3785	1.55472	0.777359	−	0.629057i	$-0.216559\pi$
$743$	42.3785	1.55472	0.777359	+	0.629057i	$0.216559\pi$
$744$	15.2076	0.557536
$745$	10.5001	0.384695
$746$	64.3977	2.35777
$747$	−21.0309	−0.769481
$748$	−3.17135	−0.115956
$749$	1.03933	0.0379764
$750$	−25.6770	−0.937590
$751$	−19.2375	−0.701985	−0.350993	−	0.936378i	$-0.614156\pi$
$751$	−19.2375	−0.701985	−0.350993	+	0.936378i	$0.614156\pi$
$752$	−22.3619	−0.815453
$753$	25.9522	0.945749
$754$	10.7793	0.392558
$755$	0.884422	0.0321874
$756$	−10.2061	−0.371191
$757$	13.1138	0.476631	0.238315	−	0.971188i	$-0.423405\pi$
$757$	13.1138	0.476631	0.238315	+	0.971188i	$0.423405\pi$
$758$	−44.6470	−1.62165
$759$	−5.00474	−0.181661
$760$	−16.3340	−0.592495
$761$	−35.9168	−1.30198	−0.650992	−	0.759085i	$-0.725647\pi$
$761$	−35.9168	−1.30198	−0.650992	+	0.759085i	$0.725647\pi$
$762$	45.5868	1.65144
$763$	−1.36600	−0.0494525
$764$	68.8328	2.49028
$765$	−1.79157	−0.0647744
$766$	72.0305	2.60257
$767$	−16.0692	−0.580225
$768$	−15.7468	−0.568212
$769$	−9.59014	−0.345829	−0.172915	−	0.984937i	$-0.555318\pi$
$769$	−9.59014	−0.345829	−0.172915	+	0.984937i	$0.555318\pi$
$770$	−0.418506	−0.0150819
$771$	−23.6348	−0.851187
$772$	62.6775	2.25581
$773$	40.3150	1.45003	0.725015	−	0.688733i	$-0.241833\pi$
$773$	40.3150	1.45003	0.725015	+	0.688733i	$0.241833\pi$
$774$	32.5942	1.17157
$775$	−6.34218	−0.227818
$776$	105.316	3.78063
$777$	3.59674	0.129032
$778$	−91.6670	−3.28642
$779$	19.8253	0.710316
$780$	−20.6312	−0.738715
$781$	5.50958	0.197148
$782$	29.2825	1.04714
$783$	−5.70446	−0.203861
$784$	−87.4713	−3.12398
$785$	−1.03308	−0.0368723
$786$	5.71001	0.203669
$787$	4.79720	0.171002	0.0855009	−	0.996338i	$-0.472751\pi$
$787$	4.79720	0.171002	0.0855009	+	0.996338i	$0.472751\pi$
$788$	−119.327	−4.25083
$789$	−18.9822	−0.675785
$790$	18.5500	0.659978
$791$	0.341341	0.0121367
$792$	−6.83502	−0.242872
$793$	24.7736	0.879738
$794$	69.4353	2.46417
$795$	1.03733	0.0367903
$796$	43.7178	1.54953
$797$	−47.4236	−1.67983	−0.839915	−	0.542719i	$-0.817395\pi$
$797$	−47.4236	−1.67983	−0.839915	+	0.542719i	$0.817395\pi$
$798$	−2.43593	−0.0862311
$799$	−2.19016	−0.0774822
$800$	71.4794	2.52718
$801$	12.0489	0.425728
$802$	79.2736	2.79925
$803$	−7.64253	−0.269699
$804$	92.7207	3.27001
$805$	2.79249	0.0984224
$806$	−15.4111	−0.542833
$807$	−26.1708	−0.921257
$808$	86.2539	3.03440
$809$	28.1963	0.991329	0.495665	−	0.868514i	$-0.334925\pi$
$809$	28.1963	0.991329	0.495665	+	0.868514i	$0.334925\pi$
$810$	3.53532	0.124219
$811$	42.8750	1.50554	0.752772	−	0.658281i	$-0.228716\pi$
$811$	42.8750	1.50554	0.752772	+	0.658281i	$0.228716\pi$
$812$	1.97907	0.0694517
$813$	8.94913	0.313860
$814$	11.1287	0.390060
$815$	−5.41734	−0.189761
$816$	−18.6248	−0.651999
$817$	16.0048	0.559936
$818$	22.1380	0.774036
$819$	2.23862	0.0782236
$820$	42.6603	1.48976
$821$	7.52722	0.262702	0.131351	−	0.991336i	$-0.458069\pi$
$821$	7.52722	0.262702	0.131351	+	0.991336i	$0.458069\pi$
$822$	63.7526	2.22363
$823$	−14.1945	−0.494788	−0.247394	−	0.968915i	$-0.579574\pi$
$823$	−14.1945	−0.494788	−0.247394	+	0.968915i	$0.579574\pi$
$824$	−86.9527	−3.02914
$825$	−2.41413	−0.0840491
$826$	−4.08261	−0.142052
$827$	29.4427	1.02382	0.511911	−	0.859039i	$-0.328938\pi$
$827$	29.4427	1.02382	0.511911	+	0.859039i	$0.328938\pi$
$828$	74.0130	2.57213
$829$	30.6806	1.06558	0.532791	−	0.846247i	$-0.321143\pi$
$829$	30.6806	1.06558	0.532791	+	0.846247i	$0.321143\pi$
$830$	−30.7499	−1.06734
$831$	10.1023	0.350446
$832$	76.4951	2.65199
$833$	−8.56708	−0.296832
$834$	15.8312	0.548188
$835$	−5.22250	−0.180732
$836$	−5.44661	−0.188375
$837$	8.15566	0.281901
$838$	8.15052	0.281555
$839$	11.2298	0.387694	0.193847	−	0.981032i	$-0.437903\pi$
$839$	11.2298	0.387694	0.193847	+	0.981032i	$0.437903\pi$
$840$	−3.22992	−0.111443
$841$	−27.8938	−0.961857
$842$	−4.89779	−0.168789
$843$	−15.7450	−0.542287
$844$	46.5115	1.60099
$845$	1.38563	0.0476672
$846$	−7.66034	−0.263368
$847$	3.88609	0.133528
$848$	−12.7331	−0.437256
$849$	−28.2224	−0.968589
$850$	14.1249	0.484482
$851$	−74.2565	−2.54548
$852$	69.0058	2.36410
$853$	27.2043	0.931458	0.465729	−	0.884927i	$-0.345792\pi$
$853$	27.2043	0.931458	0.465729	+	0.884927i	$0.345792\pi$
$854$	6.29411	0.215380
$855$	−3.07692	−0.105228
$856$	24.8187	0.848286
$857$	−3.25762	−0.111278	−0.0556391	−	0.998451i	$-0.517720\pi$
$857$	−3.25762	−0.111278	−0.0556391	+	0.998451i	$0.517720\pi$
$858$	−5.86617	−0.200268
$859$	−44.2838	−1.51094	−0.755472	−	0.655181i	$-0.772592\pi$
$859$	−44.2838	−1.51094	−0.755472	+	0.655181i	$0.772592\pi$
$860$	34.4392	1.17437
$861$	3.92031	0.133604
$862$	−32.6914	−1.11347
$863$	54.8601	1.86746	0.933731	−	0.357977i	$-0.116533\pi$
$863$	54.8601	1.86746	0.933731	+	0.357977i	$0.116533\pi$
$864$	−91.9181	−3.12712
$865$	14.6556	0.498304
$866$	44.1448	1.50010
$867$	18.1150	0.615217
$868$	−2.82947	−0.0960385
$869$	3.81154	0.129298
$870$	−2.92971	−0.0993266
$871$	−57.8993	−1.96184
$872$	−32.6193	−1.10463
$873$	19.8390	0.671449
$874$	50.2910	1.70112
$875$	2.94382	0.0995194
$876$	−95.7204	−3.23409
$877$	14.0994	0.476104	0.238052	−	0.971252i	$-0.423491\pi$
$877$	14.0994	0.476104	0.238052	+	0.971252i	$0.423491\pi$
$878$	−32.8419	−1.10836
$879$	35.6278	1.20170
$880$	−5.49554	−0.185255
$881$	−0.786599	−0.0265012	−0.0132506	−	0.999912i	$-0.504218\pi$
$881$	−0.786599	−0.0265012	−0.0132506	+	0.999912i	$0.504218\pi$
$882$	−29.9644	−1.00895
$883$	25.1514	0.846413	0.423207	−	0.906033i	$-0.360904\pi$
$883$	25.1514	0.846413	0.423207	+	0.906033i	$0.360904\pi$
$884$	24.8032	0.834223
$885$	4.36747	0.146811
$886$	99.7158	3.35002
$887$	−30.0873	−1.01023	−0.505117	−	0.863051i	$-0.668551\pi$
$887$	−30.0873	−1.01023	−0.505117	+	0.863051i	$0.668551\pi$
$888$	85.8882	2.88222
$889$	−5.22646	−0.175290
$890$	17.6171	0.590525
$891$	0.726418	0.0243359
$892$	−82.0234	−2.74635
$893$	−3.76147	−0.125873
$894$	37.3932	1.25062
$895$	−3.79404	−0.126821
$896$	7.19558	0.240388
$897$	39.1422	1.30692
$898$	−8.83512	−0.294832
$899$	−1.58147	−0.0527451
$900$	35.7015	1.19005
$901$	−1.24710	−0.0415469
$902$	12.1298	0.403879
$903$	3.16482	0.105319
$904$	8.15104	0.271100
$905$	−6.56264	−0.218149
$906$	3.14961	0.104639
$907$	−24.1132	−0.800666	−0.400333	−	0.916370i	$-0.631106\pi$
$907$	−24.1132	−0.800666	−0.400333	+	0.916370i	$0.631106\pi$
$908$	−75.6594	−2.51085
$909$	16.2481	0.538916
$910$	3.27314	0.108504
$911$	10.7343	0.355645	0.177822	−	0.984063i	$-0.443095\pi$
$911$	10.7343	0.355645	0.177822	+	0.984063i	$0.443095\pi$
$912$	−31.9870	−1.05920
$913$	−6.31831	−0.209106
$914$	16.4620	0.544514
$915$	−6.73327	−0.222595
$916$	55.6624	1.83914
$917$	−0.654644	−0.0216182
$918$	−18.1638	−0.599495
$919$	31.9719	1.05466	0.527328	−	0.849662i	$-0.323194\pi$
$919$	31.9719	1.05466	0.527328	+	0.849662i	$0.323194\pi$
$920$	66.6831	2.19848
$921$	−3.00780	−0.0991103
$922$	−2.81267	−0.0926305
$923$	−43.0905	−1.41834
$924$	−1.07703	−0.0354316
$925$	−35.8189	−1.17772
$926$	−55.3494	−1.81889
$927$	−16.3798	−0.537982
$928$	17.8239	0.585099
$929$	−21.2448	−0.697018	−0.348509	−	0.937305i	$-0.613312\pi$
$929$	−21.2448	−0.697018	−0.348509	+	0.937305i	$0.613312\pi$
$930$	4.18861	0.137350
$931$	−14.7135	−0.482214
$932$	48.2195	1.57948
$933$	−11.2280	−0.367589
$934$	−6.96266	−0.227825
$935$	−0.538242	−0.0176024
$936$	53.4569	1.74729
$937$	48.1485	1.57294	0.786471	−	0.617627i	$-0.211906\pi$
$937$	48.1485	1.57294	0.786471	+	0.617627i	$0.211906\pi$
$938$	−14.7102	−0.480304
$939$	−39.8188	−1.29944
$940$	−8.09395	−0.263995
$941$	24.2579	0.790785	0.395393	−	0.918512i	$-0.370608\pi$
$941$	24.2579	0.790785	0.395393	+	0.918512i	$0.370608\pi$
$942$	−3.67902	−0.119869
$943$	−80.9366	−2.63566
$944$	−53.6101	−1.74486
$945$	−1.73217	−0.0563475
$946$	9.79227	0.318374
$947$	30.4608	0.989841	0.494921	−	0.868938i	$-0.335197\pi$
$947$	30.4608	0.989841	0.494921	+	0.868938i	$0.335197\pi$
$948$	47.7384	1.55047
$949$	59.7724	1.94030
$950$	24.2588	0.787058
$951$	−19.6191	−0.636194
$952$	3.88307	0.125851
$953$	46.5873	1.50911	0.754555	−	0.656236i	$-0.227853\pi$
$953$	46.5873	1.50911	0.754555	+	0.656236i	$0.227853\pi$
$954$	−4.36188	−0.141221
$955$	11.6823	0.378030
$956$	−74.4336	−2.40735
$957$	−0.601981	−0.0194593
$958$	−84.1819	−2.71979
$959$	−7.30914	−0.236024
$960$	−20.7907	−0.671018
$961$	−28.7390	−0.927064
$962$	−87.0377	−2.80621
$963$	4.67524	0.150657
$964$	68.3464	2.20129
$965$	10.6376	0.342437
$966$	9.94466	0.319964
$967$	−13.5693	−0.436360	−0.218180	−	0.975909i	$-0.570012\pi$
$967$	−13.5693	−0.436360	−0.218180	+	0.975909i	$0.570012\pi$
$968$	92.7976	2.98263
$969$	−3.13286	−0.100642
$970$	29.0072	0.931364
$971$	−4.24439	−0.136209	−0.0681045	−	0.997678i	$-0.521695\pi$
$971$	−4.24439	−0.136209	−0.0681045	+	0.997678i	$0.521695\pi$
$972$	−75.6937	−2.42788
$973$	−1.81502	−0.0581868
$974$	49.0875	1.57286
$975$	18.8810	0.604674
$976$	82.6500	2.64556
$977$	37.1885	1.18976	0.594882	−	0.803813i	$-0.297199\pi$
$977$	37.1885	1.18976	0.594882	+	0.803813i	$0.297199\pi$
$978$	−19.2923	−0.616900
$979$	3.61985	0.115691
$980$	−31.6605	−1.01136
$981$	−6.14468	−0.196185
$982$	−13.3042	−0.424555
$983$	−37.3592	−1.19157	−0.595786	−	0.803143i	$-0.703160\pi$
$983$	−37.3592	−1.19157	−0.595786	+	0.803143i	$0.703160\pi$
$984$	93.6147	2.98433
$985$	−20.2521	−0.645285
$986$	3.52216	0.112169
$987$	−0.743801	−0.0236755
$988$	42.5981	1.35523
$989$	−65.3392	−2.07767
$990$	−1.88256	−0.0598318
$991$	41.3444	1.31335	0.656674	−	0.754175i	$-0.271963\pi$
$991$	41.3444	1.31335	0.656674	+	0.754175i	$0.271963\pi$
$992$	−25.4828	−0.809081
$993$	34.1985	1.08526
$994$	−10.9478	−0.347243
$995$	7.41977	0.235223
$996$	−79.1349	−2.50749
$997$	−48.2596	−1.52840	−0.764199	−	0.644981i	$-0.776865\pi$
$997$	−48.2596	−1.52840	−0.764199	+	0.644981i	$0.776865\pi$
$998$	−4.64649	−0.147082
$999$	46.0610	1.45730

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.5	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.5	✓	172	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.68534 q^{2} -1.17289 q^{3} +5.21107 q^{4} +0.884422 q^{5} +3.14961 q^{6} -0.361098 q^{7} -8.62282 q^{8} -1.62433 q^{9} +O(q^{10})\)	\(q-2.68534 q^{2} -1.17289 q^{3} +5.21107 q^{4} +0.884422 q^{5} +3.14961 q^{6} -0.361098 q^{7} -8.62282 q^{8} -1.62433 q^{9} -2.37498 q^{10} -0.487997 q^{11} -6.11201 q^{12} +3.81664 q^{13} +0.969672 q^{14} -1.03733 q^{15} +12.7331 q^{16} +1.24710 q^{17} +4.36188 q^{18} +2.14182 q^{19} +4.60878 q^{20} +0.423529 q^{21} +1.31044 q^{22} -8.74394 q^{23} +10.1136 q^{24} -4.21780 q^{25} -10.2490 q^{26} +5.42383 q^{27} -1.88171 q^{28} -1.05174 q^{29} +2.78559 q^{30} +1.50367 q^{31} -16.9471 q^{32} +0.572367 q^{33} -3.34889 q^{34} -0.319363 q^{35} -8.46448 q^{36} +8.49233 q^{37} -5.75152 q^{38} -4.47650 q^{39} -7.62621 q^{40} +9.25630 q^{41} -1.13732 q^{42} +7.47251 q^{43} -2.54298 q^{44} -1.43659 q^{45} +23.4805 q^{46} -1.75620 q^{47} -14.9345 q^{48} -6.86961 q^{49} +11.3262 q^{50} -1.46271 q^{51} +19.8887 q^{52} -1.00000 q^{53} -14.5648 q^{54} -0.431595 q^{55} +3.11368 q^{56} -2.51212 q^{57} +2.82428 q^{58} -4.21030 q^{59} -5.40559 q^{60} +6.49096 q^{61} -4.03787 q^{62} +0.586542 q^{63} +20.0425 q^{64} +3.37552 q^{65} -1.53700 q^{66} -15.1703 q^{67} +6.49872 q^{68} +10.2557 q^{69} +0.857599 q^{70} -11.2902 q^{71} +14.0063 q^{72} +15.6610 q^{73} -22.8048 q^{74} +4.94701 q^{75} +11.1612 q^{76} +0.176215 q^{77} +12.0209 q^{78} -7.81059 q^{79} +11.2614 q^{80} -1.48857 q^{81} -24.8564 q^{82} +12.9474 q^{83} +2.20704 q^{84} +1.10296 q^{85} -20.0663 q^{86} +1.23358 q^{87} +4.20791 q^{88} -7.41778 q^{89} +3.85774 q^{90} -1.37818 q^{91} -45.5653 q^{92} -1.76364 q^{93} +4.71600 q^{94} +1.89427 q^{95} +19.8771 q^{96} -12.2137 q^{97} +18.4473 q^{98} +0.792667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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