LMFDB - Embedded newform 8003.2.a.b.1.20

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:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-2.32654 q^{2} -0.105675 q^{3} +3.41278 q^{4} -1.05522 q^{5} +0.245856 q^{6} +0.945293 q^{7} -3.28688 q^{8} -2.98883 q^{9} +O(q^{10})$	\(q-2.32654 q^{2} -0.105675 q^{3} +3.41278 q^{4} -1.05522 q^{5} +0.245856 q^{6} +0.945293 q^{7} -3.28688 q^{8} -2.98883 q^{9} +2.45502 q^{10} +2.00424 q^{11} -0.360644 q^{12} +4.81051 q^{13} -2.19926 q^{14} +0.111511 q^{15} +0.821491 q^{16} +5.66382 q^{17} +6.95363 q^{18} +0.270587 q^{19} -3.60125 q^{20} -0.0998935 q^{21} -4.66293 q^{22} +2.04703 q^{23} +0.347340 q^{24} -3.88650 q^{25} -11.1918 q^{26} +0.632868 q^{27} +3.22608 q^{28} -5.94578 q^{29} -0.259433 q^{30} +3.29742 q^{31} +4.66253 q^{32} -0.211797 q^{33} -13.1771 q^{34} -0.997497 q^{35} -10.2002 q^{36} -5.04927 q^{37} -0.629531 q^{38} -0.508349 q^{39} +3.46840 q^{40} -5.06296 q^{41} +0.232406 q^{42} +1.81524 q^{43} +6.84001 q^{44} +3.15389 q^{45} -4.76249 q^{46} +12.2205 q^{47} -0.0868108 q^{48} -6.10642 q^{49} +9.04209 q^{50} -0.598522 q^{51} +16.4172 q^{52} -1.00000 q^{53} -1.47239 q^{54} -2.11492 q^{55} -3.10706 q^{56} -0.0285942 q^{57} +13.8331 q^{58} -11.0180 q^{59} +0.380560 q^{60} -7.84960 q^{61} -7.67157 q^{62} -2.82532 q^{63} -12.4905 q^{64} -5.07617 q^{65} +0.492754 q^{66} -11.3588 q^{67} +19.3293 q^{68} -0.216319 q^{69} +2.32071 q^{70} -6.29987 q^{71} +9.82393 q^{72} -1.26449 q^{73} +11.7473 q^{74} +0.410705 q^{75} +0.923454 q^{76} +1.89459 q^{77} +1.18269 q^{78} -9.25154 q^{79} -0.866858 q^{80} +8.89962 q^{81} +11.7792 q^{82} -15.9049 q^{83} -0.340914 q^{84} -5.97660 q^{85} -4.22323 q^{86} +0.628318 q^{87} -6.58768 q^{88} -9.97305 q^{89} -7.33765 q^{90} +4.54735 q^{91} +6.98606 q^{92} -0.348453 q^{93} -28.4314 q^{94} -0.285530 q^{95} -0.492711 q^{96} +13.8158 q^{97} +14.2068 q^{98} -5.99033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.32654	−1.64511	−0.822555	−	0.568685i	$-0.807452\pi$
$2$	−2.32654	−1.64511	−0.822555	+	0.568685i	$0.807452\pi$
$3$	−0.105675	−0.0610113	−0.0305056	−	0.999535i	$-0.509712\pi$
$3$	−0.105675	−0.0610113	−0.0305056	+	0.999535i	$0.509712\pi$
$4$	3.41278	1.70639
$5$	−1.05522	−0.471911	−0.235955	−	0.971764i	$-0.575822\pi$
$5$	−1.05522	−0.471911	−0.235955	+	0.971764i	$0.575822\pi$
$6$	0.245856	0.100370
$7$	0.945293	0.357287	0.178644	−	0.983914i	$-0.442829\pi$
$7$	0.945293	0.357287	0.178644	+	0.983914i	$0.442829\pi$
$8$	−3.28688	−1.16209
$9$	−2.98883	−0.996278
$10$	2.45502	0.776346
$11$	2.00424	0.604300	0.302150	−	0.953260i	$-0.402296\pi$
$11$	2.00424	0.604300	0.302150	+	0.953260i	$0.402296\pi$
$12$	−0.360644	−0.104109
$13$	4.81051	1.33420	0.667098	−	0.744970i	$-0.267536\pi$
$13$	4.81051	1.33420	0.667098	+	0.744970i	$0.267536\pi$
$14$	−2.19926	−0.587777
$15$	0.111511	0.0287919
$16$	0.821491	0.205373
$17$	5.66382	1.37368	0.686839	−	0.726810i	$-0.258998\pi$
$17$	5.66382	1.37368	0.686839	+	0.726810i	$0.258998\pi$
$18$	6.95363	1.63899
$19$	0.270587	0.0620770	0.0310385	−	0.999518i	$-0.490119\pi$
$19$	0.270587	0.0620770	0.0310385	+	0.999518i	$0.490119\pi$
$20$	−3.60125	−0.805263
$21$	−0.0998935	−0.0217986
$22$	−4.66293	−0.994140
$23$	2.04703	0.426835	0.213418	−	0.976961i	$-0.431540\pi$
$23$	2.04703	0.426835	0.213418	+	0.976961i	$0.431540\pi$
$24$	0.347340	0.0709004
$25$	−3.88650	−0.777300
$26$	−11.1918	−2.19490
$27$	0.632868	0.121795
$28$	3.22608	0.609671
$29$	−5.94578	−1.10410	−0.552052	−	0.833810i	$-0.686155\pi$
$29$	−5.94578	−1.10410	−0.552052	+	0.833810i	$0.686155\pi$
$30$	−0.259433	−0.0473658
$31$	3.29742	0.592234	0.296117	−	0.955152i	$-0.404308\pi$
$31$	3.29742	0.592234	0.296117	+	0.955152i	$0.404308\pi$
$32$	4.66253	0.824226
$33$	−0.211797	−0.0368691
$34$	−13.1771	−2.25985
$35$	−0.997497	−0.168608
$36$	−10.2002	−1.70004
$37$	−5.04927	−0.830095	−0.415047	−	0.909800i	$-0.636235\pi$
$37$	−5.04927	−0.830095	−0.415047	+	0.909800i	$0.636235\pi$
$38$	−0.629531	−0.102123
$39$	−0.508349	−0.0814010
$40$	3.46840	0.548401
$41$	−5.06296	−0.790701	−0.395350	−	0.918530i	$-0.629377\pi$
$41$	−5.06296	−0.790701	−0.395350	+	0.918530i	$0.629377\pi$
$42$	0.232406	0.0358610
$43$	1.81524	0.276822	0.138411	−	0.990375i	$-0.455801\pi$
$43$	1.81524	0.276822	0.138411	+	0.990375i	$0.455801\pi$
$44$	6.84001	1.03117
$45$	3.15389	0.470154
$46$	−4.76249	−0.702191
$47$	12.2205	1.78254	0.891269	−	0.453474i	$-0.149816\pi$
$47$	12.2205	1.78254	0.891269	+	0.453474i	$0.149816\pi$
$48$	−0.0868108	−0.0125301
$49$	−6.10642	−0.872346
$50$	9.04209	1.27874
$51$	−0.598522	−0.0838098
$52$	16.4172	2.27666
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.47239	−0.200367
$55$	−2.11492	−0.285176
$56$	−3.10706	−0.415199
$57$	−0.0285942	−0.00378739
$58$	13.8331	1.81637
$59$	−11.0180	−1.43442	−0.717211	−	0.696856i	$-0.754581\pi$
$59$	−11.0180	−1.43442	−0.717211	+	0.696856i	$0.754581\pi$
$60$	0.380560	0.0491301
$61$	−7.84960	−1.00504	−0.502519	−	0.864566i	$-0.667593\pi$
$61$	−7.84960	−1.00504	−0.502519	+	0.864566i	$0.667593\pi$
$62$	−7.67157	−0.974290
$63$	−2.82532	−0.355957
$64$	−12.4905	−1.56132
$65$	−5.07617	−0.629622
$66$	0.492754	0.0606538
$67$	−11.3588	−1.38769	−0.693847	−	0.720122i	$-0.744086\pi$
$67$	−11.3588	−1.38769	−0.693847	+	0.720122i	$0.744086\pi$
$68$	19.3293	2.34403
$69$	−0.216319	−0.0260418
$70$	2.32071	0.277378
$71$	−6.29987	−0.747657	−0.373829	−	0.927498i	$-0.621955\pi$
$71$	−6.29987	−0.747657	−0.373829	+	0.927498i	$0.621955\pi$
$72$	9.82393	1.15776
$73$	−1.26449	−0.147997	−0.0739985	−	0.997258i	$-0.523576\pi$
$73$	−1.26449	−0.147997	−0.0739985	+	0.997258i	$0.523576\pi$
$74$	11.7473	1.36560
$75$	0.410705	0.0474241
$76$	0.923454	0.105927
$77$	1.89459	0.215909
$78$	1.18269	0.133914
$79$	−9.25154	−1.04088	−0.520440	−	0.853899i	$-0.674232\pi$
$79$	−9.25154	−1.04088	−0.520440	+	0.853899i	$0.674232\pi$
$80$	−0.866858	−0.0969177
$81$	8.89962	0.988847
$82$	11.7792	1.30079
$83$	−15.9049	−1.74579	−0.872893	−	0.487912i	$-0.837759\pi$
$83$	−15.9049	−1.74579	−0.872893	+	0.487912i	$0.837759\pi$
$84$	−0.340914	−0.0371968
$85$	−5.97660	−0.648253
$86$	−4.22323	−0.455402
$87$	0.628318	0.0673628
$88$	−6.58768	−0.702249
$89$	−9.97305	−1.05714	−0.528570	−	0.848889i	$-0.677272\pi$
$89$	−9.97305	−1.05714	−0.528570	+	0.848889i	$0.677272\pi$
$90$	−7.33765	−0.773456
$91$	4.54735	0.476691
$92$	6.98606	0.728347
$93$	−0.348453	−0.0361329
$94$	−28.4314	−2.93247
$95$	−0.285530	−0.0292948
$96$	−0.492711	−0.0502871
$97$	13.8158	1.40278	0.701389	−	0.712779i	$-0.252564\pi$
$97$	13.8158	1.40278	0.701389	+	0.712779i	$0.252564\pi$
$98$	14.2068	1.43511
$99$	−5.99033	−0.602051
$100$	−13.2638	−1.32638
$101$	11.6367	1.15790	0.578949	−	0.815364i	$-0.303463\pi$
$101$	11.6367	1.15790	0.578949	+	0.815364i	$0.303463\pi$
$102$	1.39248	0.137876
$103$	−1.85596	−0.182873	−0.0914365	−	0.995811i	$-0.529146\pi$
$103$	−1.85596	−0.182873	−0.0914365	+	0.995811i	$0.529146\pi$
$104$	−15.8116	−1.55045
$105$	0.105410	0.0102870
$106$	2.32654	0.225973
$107$	14.4919	1.40099	0.700493	−	0.713660i	$-0.252964\pi$
$107$	14.4919	1.40099	0.700493	+	0.713660i	$0.252964\pi$
$108$	2.15984	0.207830
$109$	11.5306	1.10443	0.552215	−	0.833702i	$-0.313783\pi$
$109$	11.5306	1.10443	0.552215	+	0.833702i	$0.313783\pi$
$110$	4.92044	0.469146
$111$	0.533580	0.0506451
$112$	0.776550	0.0733771
$113$	10.6900	1.00563	0.502814	−	0.864395i	$-0.332298\pi$
$113$	10.6900	1.00563	0.502814	+	0.864395i	$0.332298\pi$
$114$	0.0665255	0.00623068
$115$	−2.16008	−0.201428
$116$	−20.2916	−1.88403
$117$	−14.3778	−1.32923
$118$	25.6338	2.35978
$119$	5.35397	0.490798
$120$	−0.366521	−0.0334587
$121$	−6.98304	−0.634821
$122$	18.2624	1.65340
$123$	0.535026	0.0482417
$124$	11.2534	1.01058
$125$	9.37726	0.838727
$126$	6.57322	0.585589
$127$	8.78273	0.779341	0.389671	−	0.920954i	$-0.372589\pi$
$127$	8.78273	0.779341	0.389671	+	0.920954i	$0.372589\pi$
$128$	19.7346	1.74431
$129$	−0.191825	−0.0168892
$130$	11.8099	1.03580
$131$	−0.515780	−0.0450639	−0.0225320	−	0.999746i	$-0.507173\pi$
$131$	−0.515780	−0.0450639	−0.0225320	+	0.999746i	$0.507173\pi$
$132$	−0.722816	−0.0629130
$133$	0.255784	0.0221793
$134$	26.4266	2.28291
$135$	−0.667818	−0.0574766
$136$	−18.6163	−1.59633
$137$	6.81055	0.581865	0.290932	−	0.956744i	$-0.406035\pi$
$137$	6.81055	0.581865	0.290932	+	0.956744i	$0.406035\pi$
$138$	0.503275	0.0428416
$139$	−17.8245	−1.51186	−0.755928	−	0.654655i	$-0.772814\pi$
$139$	−17.8245	−1.51186	−0.755928	+	0.654655i	$0.772814\pi$
$140$	−3.40424	−0.287710
$141$	−1.29139	−0.108755
$142$	14.6569	1.22998
$143$	9.64140	0.806255
$144$	−2.45530	−0.204608
$145$	6.27413	0.521039
$146$	2.94188	0.243471
$147$	0.645294	0.0532229
$148$	−17.2320	−1.41646
$149$	24.2110	1.98345	0.991723	−	0.128394i	$-0.0409823\pi$
$149$	24.2110	1.98345	0.991723	+	0.128394i	$0.0409823\pi$
$150$	−0.955520	−0.0780178
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	−0.889387	−0.0721388
$153$	−16.9282	−1.36856
$154$	−4.40784	−0.355194
$155$	−3.47952	−0.279482
$156$	−1.73488	−0.138902
$157$	−13.5873	−1.08439	−0.542194	−	0.840254i	$-0.682406\pi$
$157$	−13.5873	−1.08439	−0.542194	+	0.840254i	$0.682406\pi$
$158$	21.5240	1.71236
$159$	0.105675	0.00838054
$160$	−4.92001	−0.388961
$161$	1.93504	0.152503
$162$	−20.7053	−1.62676
$163$	−11.0521	−0.865671	−0.432835	−	0.901473i	$-0.642487\pi$
$163$	−11.0521	−0.865671	−0.432835	+	0.901473i	$0.642487\pi$
$164$	−17.2787	−1.34924
$165$	0.223493	0.0173989
$166$	37.0033	2.87201
$167$	13.3755	1.03503	0.517515	−	0.855674i	$-0.326857\pi$
$167$	13.3755	1.03503	0.517515	+	0.855674i	$0.326857\pi$
$168$	0.328338	0.0253318
$169$	10.1410	0.780079
$170$	13.9048	1.06645
$171$	−0.808740	−0.0618459
$172$	6.19501	0.472365
$173$	−11.2195	−0.853004	−0.426502	−	0.904487i	$-0.640254\pi$
$173$	−11.2195	−0.853004	−0.426502	+	0.904487i	$0.640254\pi$
$174$	−1.46181	−0.110819
$175$	−3.67388	−0.277719
$176$	1.64646	0.124107
$177$	1.16432	0.0875159
$178$	23.2027	1.73911
$179$	−18.7923	−1.40460	−0.702302	−	0.711879i	$-0.747844\pi$
$179$	−18.7923	−1.40460	−0.702302	+	0.711879i	$0.747844\pi$
$180$	10.7635	0.802266
$181$	9.04545	0.672343	0.336172	−	0.941801i	$-0.390868\pi$
$181$	9.04545	0.672343	0.336172	+	0.941801i	$0.390868\pi$
$182$	−10.5796	−0.784210
$183$	0.829503	0.0613187
$184$	−6.72834	−0.496020
$185$	5.32811	0.391731
$186$	0.810690	0.0594427
$187$	11.3516	0.830113
$188$	41.7057	3.04170
$189$	0.598246	0.0435160
$190$	0.664297	0.0481932
$191$	−27.2592	−1.97240	−0.986202	−	0.165547i	$-0.947061\pi$
$191$	−27.2592	−1.97240	−0.986202	+	0.165547i	$0.947061\pi$
$192$	1.31993	0.0952579
$193$	−25.5753	−1.84095	−0.920476	−	0.390798i	$-0.872199\pi$
$193$	−25.5753	−1.84095	−0.920476	+	0.390798i	$0.872199\pi$
$194$	−32.1429	−2.30772
$195$	0.536423	0.0384140
$196$	−20.8398	−1.48856
$197$	−25.1873	−1.79452	−0.897259	−	0.441504i	$-0.854445\pi$
$197$	−25.1873	−1.79452	−0.897259	+	0.441504i	$0.854445\pi$
$198$	13.9367	0.990440
$199$	−12.9728	−0.919620	−0.459810	−	0.888017i	$-0.652082\pi$
$199$	−12.9728	−0.919620	−0.459810	+	0.888017i	$0.652082\pi$
$200$	12.7745	0.903290
$201$	1.20033	0.0846650
$202$	−27.0733	−1.90487
$203$	−5.62051	−0.394482
$204$	−2.04262	−0.143012
$205$	5.34256	0.373140
$206$	4.31795	0.300846
$207$	−6.11823	−0.425246
$208$	3.95179	0.274008
$209$	0.542321	0.0375131
$210$	−0.245241	−0.0169232
$211$	−19.2950	−1.32832	−0.664161	−	0.747589i	$-0.731211\pi$
$211$	−19.2950	−1.32832	−0.664161	+	0.747589i	$0.731211\pi$
$212$	−3.41278	−0.234390
$213$	0.665737	0.0456155
$214$	−33.7160	−2.30478
$215$	−1.91549	−0.130635
$216$	−2.08016	−0.141537
$217$	3.11703	0.211598
$218$	−26.8264	−1.81691
$219$	0.133624	0.00902949
$220$	−7.21775	−0.486621
$221$	27.2459	1.83275
$222$	−1.24139	−0.0833168
$223$	4.64432	0.311007	0.155503	−	0.987835i	$-0.450300\pi$
$223$	4.64432	0.311007	0.155503	+	0.987835i	$0.450300\pi$
$224$	4.40745	0.294485
$225$	11.6161	0.774407
$226$	−24.8706	−1.65437
$227$	18.5004	1.22791	0.613957	−	0.789340i	$-0.289577\pi$
$227$	18.5004	1.22791	0.613957	+	0.789340i	$0.289577\pi$
$228$	−0.0975856	−0.00646277
$229$	12.9241	0.854047	0.427023	−	0.904241i	$-0.359562\pi$
$229$	12.9241	0.854047	0.427023	+	0.904241i	$0.359562\pi$
$230$	5.02550	0.331372
$231$	−0.200210	−0.0131729
$232$	19.5431	1.28306
$233$	4.88210	0.319837	0.159919	−	0.987130i	$-0.448877\pi$
$233$	4.88210	0.319837	0.159919	+	0.987130i	$0.448877\pi$
$234$	33.4505	2.18673
$235$	−12.8953	−0.841199
$236$	−37.6020	−2.44768
$237$	0.977653	0.0635054
$238$	−12.4562	−0.807416
$239$	13.1707	0.851943	0.425971	−	0.904737i	$-0.359932\pi$
$239$	13.1707	0.851943	0.425971	+	0.904737i	$0.359932\pi$
$240$	0.0916049	0.00591307
$241$	2.09034	0.134651	0.0673253	−	0.997731i	$-0.478553\pi$
$241$	2.09034	0.134651	0.0673253	+	0.997731i	$0.478553\pi$
$242$	16.2463	1.04435
$243$	−2.83907	−0.182126
$244$	−26.7889	−1.71499
$245$	6.44365	0.411669
$246$	−1.24476	−0.0793629
$247$	1.30166	0.0828228
$248$	−10.8382	−0.688227
$249$	1.68074	0.106513
$250$	−21.8165	−1.37980
$251$	−6.82059	−0.430512	−0.215256	−	0.976558i	$-0.569059\pi$
$251$	−6.82059	−0.430512	−0.215256	+	0.976558i	$0.569059\pi$
$252$	−9.64220	−0.607402
$253$	4.10273	0.257937
$254$	−20.4333	−1.28210
$255$	0.631575	0.0395508
$256$	−20.9323	−1.30827
$257$	9.96701	0.621725	0.310862	−	0.950455i	$-0.399382\pi$
$257$	9.96701	0.621725	0.310862	+	0.950455i	$0.399382\pi$
$258$	0.446288	0.0277847
$259$	−4.77304	−0.296582
$260$	−17.3238	−1.07438
$261$	17.7709	1.09999
$262$	1.19998	0.0741351
$263$	17.4636	1.07685	0.538426	−	0.842673i	$-0.319019\pi$
$263$	17.4636	1.07685	0.538426	+	0.842673i	$0.319019\pi$
$264$	0.696151	0.0428451
$265$	1.05522	0.0648219
$266$	−0.595092	−0.0364874
$267$	1.05390	0.0644975
$268$	−38.7649	−2.36794
$269$	−3.40003	−0.207303	−0.103652	−	0.994614i	$-0.533053\pi$
$269$	−3.40003	−0.207303	−0.103652	+	0.994614i	$0.533053\pi$
$270$	1.55370	0.0945554
$271$	9.85897	0.598890	0.299445	−	0.954114i	$-0.403199\pi$
$271$	9.85897	0.598890	0.299445	+	0.954114i	$0.403199\pi$
$272$	4.65278	0.282116
$273$	−0.480539	−0.0290835
$274$	−15.8450	−0.957232
$275$	−7.78947	−0.469723
$276$	−0.738249	−0.0444374
$277$	27.4781	1.65100	0.825500	−	0.564401i	$-0.190893\pi$
$277$	27.4781	1.65100	0.825500	+	0.564401i	$0.190893\pi$
$278$	41.4694	2.48717
$279$	−9.85543	−0.590029
$280$	3.27865	0.195937
$281$	−22.4075	−1.33672	−0.668360	−	0.743838i	$-0.733004\pi$
$281$	−22.4075	−1.33672	−0.668360	+	0.743838i	$0.733004\pi$
$282$	3.00448	0.178914
$283$	4.32478	0.257081	0.128541	−	0.991704i	$-0.458971\pi$
$283$	4.32478	0.257081	0.128541	+	0.991704i	$0.458971\pi$
$284$	−21.5001	−1.27579
$285$	0.0301733	0.00178731
$286$	−22.4311	−1.32638
$287$	−4.78598	−0.282507
$288$	−13.9355	−0.821158
$289$	15.0788	0.886990
$290$	−14.5970	−0.857166
$291$	−1.45998	−0.0855853
$292$	−4.31541	−0.252540
$293$	−10.7815	−0.629862	−0.314931	−	0.949115i	$-0.601981\pi$
$293$	−10.7815	−0.629862	−0.314931	+	0.949115i	$0.601981\pi$
$294$	−1.50130	−0.0875576
$295$	11.6265	0.676919
$296$	16.5963	0.964642
$297$	1.26842	0.0736010
$298$	−56.3279	−3.26299
$299$	9.84726	0.569482
$300$	1.40164	0.0809239
$301$	1.71594	0.0989049
$302$	2.32654	0.133877
$303$	−1.22971	−0.0706448
$304$	0.222285	0.0127489
$305$	8.28309	0.474288
$306$	39.3841	2.25144
$307$	−16.9354	−0.966556	−0.483278	−	0.875467i	$-0.660554\pi$
$307$	−16.9354	−0.966556	−0.483278	+	0.875467i	$0.660554\pi$
$308$	6.46582	0.368424
$309$	0.196128	0.0111573
$310$	8.09523	0.459778
$311$	17.4501	0.989505	0.494753	−	0.869034i	$-0.335259\pi$
$311$	17.4501	0.989505	0.494753	+	0.869034i	$0.335259\pi$
$312$	1.67088	0.0945950
$313$	4.11461	0.232571	0.116286	−	0.993216i	$-0.462901\pi$
$313$	4.11461	0.232571	0.116286	+	0.993216i	$0.462901\pi$
$314$	31.6114	1.78394
$315$	2.98135	0.167980
$316$	−31.5734	−1.77614
$317$	−6.94553	−0.390100	−0.195050	−	0.980793i	$-0.562487\pi$
$317$	−6.94553	−0.390100	−0.195050	+	0.980793i	$0.562487\pi$
$318$	−0.245856	−0.0137869
$319$	−11.9168	−0.667210
$320$	13.1803	0.736802
$321$	−1.53143	−0.0854759
$322$	−4.50195	−0.250884
$323$	1.53256	0.0852737
$324$	30.3724	1.68736
$325$	−18.6961	−1.03707
$326$	25.7132	1.42412
$327$	−1.21849	−0.0673827
$328$	16.6413	0.918863
$329$	11.5519	0.636878
$330$	−0.519966	−0.0286232
$331$	−2.27204	−0.124883	−0.0624414	−	0.998049i	$-0.519889\pi$
$331$	−2.27204	−0.124883	−0.0624414	+	0.998049i	$0.519889\pi$
$332$	−54.2798	−2.97899
$333$	15.0914	0.827005
$334$	−31.1187	−1.70274
$335$	11.9861	0.654868
$336$	−0.0820617	−0.00447683
$337$	−8.13127	−0.442939	−0.221469	−	0.975167i	$-0.571085\pi$
$337$	−8.13127	−0.442939	−0.221469	+	0.975167i	$0.571085\pi$
$338$	−23.5935	−1.28332
$339$	−1.12966	−0.0613547
$340$	−20.3968	−1.10617
$341$	6.60881	0.357887
$342$	1.88156	0.101743
$343$	−12.3894	−0.668965
$344$	−5.96648	−0.321691
$345$	0.228265	0.0122894
$346$	26.1026	1.40329
$347$	1.24494	0.0668321	0.0334161	−	0.999442i	$-0.489361\pi$
$347$	1.24494	0.0668321	0.0334161	+	0.999442i	$0.489361\pi$
$348$	2.14431	0.114947
$349$	−31.3306	−1.67709	−0.838544	−	0.544833i	$-0.816593\pi$
$349$	−31.3306	−1.67709	−0.838544	+	0.544833i	$0.816593\pi$
$350$	8.54743	0.456879
$351$	3.04442	0.162499
$352$	9.34480	0.498080
$353$	−7.46509	−0.397327	−0.198663	−	0.980068i	$-0.563660\pi$
$353$	−7.46509	−0.397327	−0.198663	+	0.980068i	$0.563660\pi$
$354$	−2.70884	−0.143973
$355$	6.64778	0.352828
$356$	−34.0358	−1.80389
$357$	−0.565779	−0.0299442
$358$	43.7210	2.31073
$359$	18.2435	0.962854	0.481427	−	0.876486i	$-0.340119\pi$
$359$	18.2435	0.962854	0.481427	+	0.876486i	$0.340119\pi$
$360$	−10.3665	−0.546360
$361$	−18.9268	−0.996146
$362$	−21.0446	−1.10608
$363$	0.737930	0.0387313
$364$	15.5191	0.813421
$365$	1.33432	0.0698414
$366$	−1.92987	−0.100876
$367$	33.6861	1.75840	0.879199	−	0.476455i	$-0.158078\pi$
$367$	33.6861	1.75840	0.879199	+	0.476455i	$0.158078\pi$
$368$	1.68162	0.0876604
$369$	15.1323	0.787758
$370$	−12.3961	−0.644440
$371$	−0.945293	−0.0490772
$372$	−1.18919	−0.0616568
$373$	−31.5618	−1.63421	−0.817104	−	0.576490i	$-0.804422\pi$
$373$	−31.5618	−1.63421	−0.817104	+	0.576490i	$0.804422\pi$
$374$	−26.4100	−1.36563
$375$	−0.990938	−0.0511718
$376$	−40.1672	−2.07146
$377$	−28.6022	−1.47309
$378$	−1.39184	−0.0715886
$379$	10.3087	0.529523	0.264761	−	0.964314i	$-0.414707\pi$
$379$	10.3087	0.529523	0.264761	+	0.964314i	$0.414707\pi$
$380$	−0.974451	−0.0499883
$381$	−0.928112	−0.0475486
$382$	63.4195	3.24482
$383$	1.01110	0.0516647	0.0258323	−	0.999666i	$-0.491776\pi$
$383$	1.01110	0.0516647	0.0258323	+	0.999666i	$0.491776\pi$
$384$	−2.08545	−0.106423
$385$	−1.99922	−0.101890
$386$	59.5020	3.02857
$387$	−5.42545	−0.275791
$388$	47.1501	2.39368
$389$	22.5036	1.14098	0.570488	−	0.821306i	$-0.306754\pi$
$389$	22.5036	1.14098	0.570488	+	0.821306i	$0.306754\pi$
$390$	−1.24801	−0.0631953
$391$	11.5940	0.586334
$392$	20.0711	1.01374
$393$	0.0545049	0.00274941
$394$	58.5991	2.95218
$395$	9.76245	0.491202
$396$	−20.4437	−1.02733
$397$	23.3877	1.17379	0.586896	−	0.809662i	$-0.300350\pi$
$397$	23.3877	1.17379	0.586896	+	0.809662i	$0.300350\pi$
$398$	30.1818	1.51288
$399$	−0.0270299	−0.00135319
$400$	−3.19273	−0.159636
$401$	36.5891	1.82717	0.913587	−	0.406644i	$-0.133301\pi$
$401$	36.5891	1.82717	0.913587	+	0.406644i	$0.133301\pi$
$402$	−2.79262	−0.139283
$403$	15.8623	0.790156
$404$	39.7135	1.97582
$405$	−9.39110	−0.466648
$406$	13.0763	0.648967
$407$	−10.1199	−0.501626
$408$	1.96727	0.0973943
$409$	18.8697	0.933047	0.466524	−	0.884509i	$-0.345506\pi$
$409$	18.8697	0.933047	0.466524	+	0.884509i	$0.345506\pi$
$410$	−12.4297	−0.613857
$411$	−0.719703	−0.0355003
$412$	−6.33397	−0.312052
$413$	−10.4152	−0.512501
$414$	14.2343	0.699577
$415$	16.7832	0.823855
$416$	22.4291	1.09968
$417$	1.88360	0.0922403
$418$	−1.26173	−0.0617132
$419$	13.1710	0.643447	0.321724	−	0.946834i	$-0.395738\pi$
$419$	13.1710	0.643447	0.321724	+	0.946834i	$0.395738\pi$
$420$	0.359741	0.0175536
$421$	−33.5068	−1.63302	−0.816510	−	0.577331i	$-0.804094\pi$
$421$	−33.5068	−1.63302	−0.816510	+	0.577331i	$0.804094\pi$
$422$	44.8905	2.18524
$423$	−36.5249	−1.77590
$424$	3.28688	0.159625
$425$	−22.0124	−1.06776
$426$	−1.54886	−0.0750426
$427$	−7.42017	−0.359087
$428$	49.4576	2.39063
$429$	−1.01885	−0.0491906
$430$	4.45645	0.214909
$431$	−12.4916	−0.601700	−0.300850	−	0.953671i	$-0.597270\pi$
$431$	−12.4916	−0.601700	−0.300850	+	0.953671i	$0.597270\pi$
$432$	0.519895	0.0250135
$433$	−29.8047	−1.43232	−0.716162	−	0.697935i	$-0.754103\pi$
$433$	−29.8047	−1.43232	−0.716162	+	0.697935i	$0.754103\pi$
$434$	−7.25188	−0.348101
$435$	−0.663017	−0.0317892
$436$	39.3513	1.88459
$437$	0.553900	0.0264966
$438$	−0.310882	−0.0148545
$439$	−25.7071	−1.22693	−0.613467	−	0.789721i	$-0.710225\pi$
$439$	−25.7071	−1.22693	−0.613467	+	0.789721i	$0.710225\pi$
$440$	6.95149	0.331399
$441$	18.2511	0.869099
$442$	−63.3885	−3.01508
$443$	−1.37364	−0.0652636	−0.0326318	−	0.999467i	$-0.510389\pi$
$443$	−1.37364	−0.0652636	−0.0326318	+	0.999467i	$0.510389\pi$
$444$	1.82099	0.0864203
$445$	10.5238	0.498876
$446$	−10.8052	−0.511641
$447$	−2.55849	−0.121013
$448$	−11.8072	−0.557838
$449$	−3.08402	−0.145544	−0.0727719	−	0.997349i	$-0.523185\pi$
$449$	−3.08402	−0.145544	−0.0727719	+	0.997349i	$0.523185\pi$
$450$	−27.0253	−1.27398
$451$	−10.1474	−0.477821
$452$	36.4825	1.71599
$453$	0.105675	0.00496503
$454$	−43.0418	−2.02005
$455$	−4.79847	−0.224956
$456$	0.0939857	0.00440128
$457$	27.5201	1.28734	0.643669	−	0.765304i	$-0.277411\pi$
$457$	27.5201	1.28734	0.643669	+	0.765304i	$0.277411\pi$
$458$	−30.0683	−1.40500
$459$	3.58445	0.167308
$460$	−7.37186	−0.343715
$461$	21.4450	0.998792	0.499396	−	0.866374i	$-0.333555\pi$
$461$	21.4450	0.998792	0.499396	+	0.866374i	$0.333555\pi$
$462$	0.465797	0.0216708
$463$	5.50370	0.255779	0.127889	−	0.991788i	$-0.459180\pi$
$463$	5.50370	0.255779	0.127889	+	0.991788i	$0.459180\pi$
$464$	−4.88441	−0.226753
$465$	0.367697	0.0170515
$466$	−11.3584	−0.526168
$467$	−13.3843	−0.619351	−0.309676	−	0.950842i	$-0.600220\pi$
$467$	−13.3843	−0.619351	−0.309676	+	0.950842i	$0.600220\pi$
$468$	−49.0683	−2.26818
$469$	−10.7374	−0.495806
$470$	30.0015	1.38387
$471$	1.43584	0.0661598
$472$	36.2148	1.66692
$473$	3.63817	0.167283
$474$	−2.27455	−0.104473
$475$	−1.05164	−0.0482524
$476$	18.2719	0.837491
$477$	2.98883	0.136849
$478$	−30.6422	−1.40154
$479$	−25.0429	−1.14424	−0.572119	−	0.820171i	$-0.693878\pi$
$479$	−25.0429	−1.14424	−0.572119	+	0.820171i	$0.693878\pi$
$480$	0.519921	0.0237310
$481$	−24.2896	−1.10751
$482$	−4.86326	−0.221515
$483$	−0.204485	−0.00930439
$484$	−23.8315	−1.08325
$485$	−14.5787	−0.661986
$486$	6.60520	0.299618
$487$	−14.1657	−0.641911	−0.320956	−	0.947094i	$-0.604004\pi$
$487$	−14.1657	−0.641911	−0.320956	+	0.947094i	$0.604004\pi$
$488$	25.8007	1.16794
$489$	1.16793	0.0528157
$490$	−14.9914	−0.677242
$491$	−20.4328	−0.922121	−0.461061	−	0.887369i	$-0.652531\pi$
$491$	−20.4328	−0.922121	−0.461061	+	0.887369i	$0.652531\pi$
$492$	1.82592	0.0823190
$493$	−33.6758	−1.51668
$494$	−3.02837	−0.136253
$495$	6.32114	0.284114
$496$	2.70880	0.121629
$497$	−5.95523	−0.267129
$498$	−3.91031	−0.175225
$499$	−24.5326	−1.09823	−0.549114	−	0.835747i	$-0.685035\pi$
$499$	−24.5326	−1.09823	−0.549114	+	0.835747i	$0.685035\pi$
$500$	32.0025	1.43119
$501$	−1.41346	−0.0631485
$502$	15.8684	0.708239
$503$	−27.2903	−1.21681	−0.608406	−	0.793626i	$-0.708191\pi$
$503$	−27.2903	−1.21681	−0.608406	+	0.793626i	$0.708191\pi$
$504$	9.28650	0.413653
$505$	−12.2794	−0.546424
$506$	−9.54516	−0.424334
$507$	−1.07165	−0.0475936
$508$	29.9735	1.32986
$509$	37.3185	1.65411	0.827057	−	0.562117i	$-0.190013\pi$
$509$	37.3185	1.65411	0.827057	+	0.562117i	$0.190013\pi$
$510$	−1.46938	−0.0650654
$511$	−1.19531	−0.0528775
$512$	9.23051	0.407935
$513$	0.171246	0.00756069
$514$	−23.1886	−1.02281
$515$	1.95845	0.0862997
$516$	−0.654656	−0.0288196
$517$	24.4927	1.07719
$518$	11.1047	0.487911
$519$	1.18562	0.0520429
$520$	16.6848	0.731675
$521$	29.2842	1.28296	0.641482	−	0.767138i	$-0.278320\pi$
$521$	29.2842	1.28296	0.641482	+	0.767138i	$0.278320\pi$
$522$	−41.3448	−1.80961
$523$	31.4200	1.37390	0.686950	−	0.726705i	$-0.258949\pi$
$523$	31.4200	1.37390	0.686950	+	0.726705i	$0.258949\pi$
$524$	−1.76024	−0.0768965
$525$	0.388236	0.0169440
$526$	−40.6297	−1.77154
$527$	18.6760	0.813538
$528$	−0.173989	−0.00757192
$529$	−18.8097	−0.817812
$530$	−2.45502	−0.106639
$531$	32.9310	1.42908
$532$	0.872935	0.0378465
$533$	−24.3554	−1.05495
$534$	−2.45193	−0.106106
$535$	−15.2922	−0.661140
$536$	37.3349	1.61262
$537$	1.98587	0.0856966
$538$	7.91029	0.341037
$539$	−12.2387	−0.527159
$540$	−2.27911	−0.0980774
$541$	−18.8032	−0.808415	−0.404207	−	0.914667i	$-0.632453\pi$
$541$	−18.8032	−0.808415	−0.404207	+	0.914667i	$0.632453\pi$
$542$	−22.9373	−0.985240
$543$	−0.955875	−0.0410205
$544$	26.4077	1.13222
$545$	−12.1674	−0.521193
$546$	1.11799	0.0478456
$547$	−44.2854	−1.89351	−0.946754	−	0.321958i	$-0.895659\pi$
$547$	−44.2854	−1.89351	−0.946754	+	0.321958i	$0.895659\pi$
$548$	23.2429	0.992887
$549$	23.4611	1.00130
$550$	18.1225	0.772745
$551$	−1.60885	−0.0685394
$552$	0.711015	0.0302628
$553$	−8.74542	−0.371893
$554$	−63.9289	−2.71608
$555$	−0.563046	−0.0239000
$556$	−60.8311	−2.57981
$557$	24.4583	1.03633	0.518166	−	0.855280i	$-0.326615\pi$
$557$	24.4583	1.03633	0.518166	+	0.855280i	$0.326615\pi$
$558$	22.9290	0.970663
$559$	8.73224	0.369334
$560$	−0.819435	−0.0346275
$561$	−1.19958	−0.0506463
$562$	52.1319	2.19905
$563$	−23.3970	−0.986067	−0.493033	−	0.870010i	$-0.664112\pi$
$563$	−23.3970	−0.986067	−0.493033	+	0.870010i	$0.664112\pi$
$564$	−4.40724	−0.185578
$565$	−11.2803	−0.474567
$566$	−10.0618	−0.422927
$567$	8.41275	0.353302
$568$	20.7069	0.868843
$569$	32.9512	1.38138	0.690692	−	0.723149i	$-0.257306\pi$
$569$	32.9512	1.38138	0.690692	+	0.723149i	$0.257306\pi$
$570$	−0.0701993	−0.00294033
$571$	−35.6656	−1.49256	−0.746280	−	0.665632i	$-0.768162\pi$
$571$	−35.6656	−1.49256	−0.746280	+	0.665632i	$0.768162\pi$
$572$	32.9040	1.37578
$573$	2.88060	0.120339
$574$	11.1348	0.464756
$575$	−7.95578	−0.331779
$576$	37.3321	1.55550
$577$	12.4895	0.519944	0.259972	−	0.965616i	$-0.416287\pi$
$577$	12.4895	0.519944	0.259972	+	0.965616i	$0.416287\pi$
$578$	−35.0814	−1.45920
$579$	2.70266	0.112319
$580$	21.4122	0.889094
$581$	−15.0348	−0.623747
$582$	3.39669	0.140797
$583$	−2.00424	−0.0830070
$584$	4.15621	0.171985
$585$	15.1718	0.627278
$586$	25.0835	1.03619
$587$	11.3770	0.469581	0.234790	−	0.972046i	$-0.424560\pi$
$587$	11.3770	0.469581	0.234790	+	0.972046i	$0.424560\pi$
$588$	2.20224	0.0908190
$589$	0.892239	0.0367641
$590$	−27.0494	−1.11361
$591$	2.66166	0.109486
$592$	−4.14793	−0.170479
$593$	−5.62730	−0.231086	−0.115543	−	0.993302i	$-0.536861\pi$
$593$	−5.62730	−0.231086	−0.115543	+	0.993302i	$0.536861\pi$
$594$	−2.95102	−0.121082
$595$	−5.64964	−0.231613
$596$	82.6269	3.38453
$597$	1.37090	0.0561072
$598$	−22.9100	−0.936861
$599$	−22.0472	−0.900823	−0.450412	−	0.892821i	$-0.648723\pi$
$599$	−22.0472	−0.900823	−0.450412	+	0.892821i	$0.648723\pi$
$600$	−1.34994	−0.0551109
$601$	5.80486	0.236785	0.118393	−	0.992967i	$-0.462226\pi$
$601$	5.80486	0.236785	0.118393	+	0.992967i	$0.462226\pi$
$602$	−3.99219	−0.162709
$603$	33.9495	1.38253
$604$	−3.41278	−0.138864
$605$	7.36867	0.299579
$606$	2.86096	0.116219
$607$	17.0397	0.691621	0.345810	−	0.938304i	$-0.387604\pi$
$607$	17.0397	0.691621	0.345810	+	0.938304i	$0.387604\pi$
$608$	1.26162	0.0511654
$609$	0.593945	0.0240679
$610$	−19.2709	−0.780257
$611$	58.7867	2.37826
$612$	−57.7722	−2.33530
$613$	−25.1182	−1.01451	−0.507256	−	0.861795i	$-0.669340\pi$
$613$	−25.1182	−1.01451	−0.507256	+	0.861795i	$0.669340\pi$
$614$	39.4009	1.59009
$615$	−0.564573	−0.0227658
$616$	−6.22729	−0.250905
$617$	−35.5411	−1.43083	−0.715414	−	0.698700i	$-0.753762\pi$
$617$	−35.5411	−1.43083	−0.715414	+	0.698700i	$0.753762\pi$
$618$	−0.456298	−0.0183550
$619$	9.59120	0.385503	0.192751	−	0.981248i	$-0.438259\pi$
$619$	9.59120	0.385503	0.192751	+	0.981248i	$0.438259\pi$
$620$	−11.8748	−0.476904
$621$	1.29550	0.0519866
$622$	−40.5983	−1.62785
$623$	−9.42746	−0.377703
$624$	−0.417604	−0.0167176
$625$	9.53739	0.381496
$626$	−9.57279	−0.382606
$627$	−0.0573096	−0.00228872
$628$	−46.3705	−1.85039
$629$	−28.5981	−1.14028
$630$	−6.93623	−0.276346
$631$	−17.1033	−0.680871	−0.340436	−	0.940268i	$-0.610575\pi$
$631$	−17.1033	−0.680871	−0.340436	+	0.940268i	$0.610575\pi$
$632$	30.4087	1.20959
$633$	2.03899	0.0810426
$634$	16.1590	0.641757
$635$	−9.26775	−0.367780
$636$	0.360644	0.0143005
$637$	−29.3750	−1.16388
$638$	27.7248	1.09763
$639$	18.8293	0.744874
$640$	−20.8245	−0.823159
$641$	8.39218	0.331471	0.165736	−	0.986170i	$-0.447000\pi$
$641$	8.39218	0.331471	0.165736	+	0.986170i	$0.447000\pi$
$642$	3.56292	0.140617
$643$	4.57793	0.180536	0.0902680	−	0.995918i	$-0.471228\pi$
$643$	4.57793	0.180536	0.0902680	+	0.995918i	$0.471228\pi$
$644$	6.60387	0.260229
$645$	0.202418	0.00797022
$646$	−3.56555	−0.140285
$647$	37.0464	1.45644	0.728221	−	0.685342i	$-0.240347\pi$
$647$	37.0464	1.45644	0.728221	+	0.685342i	$0.240347\pi$
$648$	−29.2520	−1.14913
$649$	−22.0827	−0.866821
$650$	43.4971	1.70610
$651$	−0.329391	−0.0129098
$652$	−37.7185	−1.47717
$653$	11.6546	0.456079	0.228039	−	0.973652i	$-0.426768\pi$
$653$	11.6546	0.456079	0.228039	+	0.973652i	$0.426768\pi$
$654$	2.83487	0.110852
$655$	0.544264	0.0212661
$656$	−4.15917	−0.162388
$657$	3.77934	0.147446
$658$	−26.8760	−1.04774
$659$	0.398028	0.0155050	0.00775248	−	0.999970i	$-0.497532\pi$
$659$	0.398028	0.0155050	0.00775248	+	0.999970i	$0.497532\pi$
$660$	0.762733	0.0296894
$661$	1.51832	0.0590559	0.0295279	−	0.999564i	$-0.490600\pi$
$661$	1.51832	0.0590559	0.0295279	+	0.999564i	$0.490600\pi$
$662$	5.28600	0.205446
$663$	−2.87920	−0.111819
$664$	52.2774	2.02875
$665$	−0.269910	−0.0104667
$666$	−35.1107	−1.36051
$667$	−12.1712	−0.471270
$668$	45.6477	1.76616
$669$	−0.490787	−0.0189749
$670$	−27.8860	−1.07733
$671$	−15.7325	−0.607345
$672$	−0.465756	−0.0179669
$673$	24.7578	0.954343	0.477171	−	0.878810i	$-0.341662\pi$
$673$	24.7578	0.954343	0.477171	+	0.878810i	$0.341662\pi$
$674$	18.9177	0.728683
$675$	−2.45964	−0.0946716
$676$	34.6091	1.33112
$677$	−9.46609	−0.363812	−0.181906	−	0.983316i	$-0.558227\pi$
$677$	−9.46609	−0.363812	−0.181906	+	0.983316i	$0.558227\pi$
$678$	2.62819	0.100935
$679$	13.0599	0.501195
$680$	19.6444	0.753327
$681$	−1.95502	−0.0749166
$682$	−15.3756	−0.588764
$683$	−29.9564	−1.14625	−0.573124	−	0.819469i	$-0.694269\pi$
$683$	−29.9564	−1.14625	−0.573124	+	0.819469i	$0.694269\pi$
$684$	−2.76005	−0.105533
$685$	−7.18666	−0.274588
$686$	28.8244	1.10052
$687$	−1.36575	−0.0521065
$688$	1.49121	0.0568517
$689$	−4.81051	−0.183266
$690$	−0.531068	−0.0202174
$691$	13.8166	0.525609	0.262804	−	0.964849i	$-0.415353\pi$
$691$	13.8166	0.525609	0.262804	+	0.964849i	$0.415353\pi$
$692$	−38.2897	−1.45556
$693$	−5.66262	−0.215105
$694$	−2.89641	−0.109946
$695$	18.8089	0.713461
$696$	−2.06521	−0.0782814
$697$	−28.6757	−1.08617
$698$	72.8918	2.75900
$699$	−0.515915	−0.0195137
$700$	−12.5381	−0.473897
$701$	−25.0831	−0.947377	−0.473688	−	0.880692i	$-0.657078\pi$
$701$	−25.0831	−0.947377	−0.473688	+	0.880692i	$0.657078\pi$
$702$	−7.08295	−0.267329
$703$	−1.36627	−0.0515297
$704$	−25.0340	−0.943503
$705$	1.36271	0.0513227
$706$	17.3678	0.653646
$707$	11.0001	0.413702
$708$	3.97357	0.149336
$709$	−39.9093	−1.49882	−0.749412	−	0.662104i	$-0.769664\pi$
$709$	−39.9093	−1.49882	−0.749412	+	0.662104i	$0.769664\pi$
$710$	−15.4663	−0.580441
$711$	27.6513	1.03700
$712$	32.7802	1.22849
$713$	6.74992	0.252786
$714$	1.31631	0.0492615
$715$	−10.1739	−0.380480
$716$	−64.1340	−2.39680
$717$	−1.39181	−0.0519781
$718$	−42.4441	−1.58400
$719$	11.7807	0.439348	0.219674	−	0.975573i	$-0.429501\pi$
$719$	11.7807	0.439348	0.219674	+	0.975573i	$0.429501\pi$
$720$	2.59089	0.0965569
$721$	−1.75442	−0.0653382
$722$	44.0339	1.63877
$723$	−0.220896	−0.00821521
$724$	30.8701	1.14728
$725$	23.1083	0.858220
$726$	−1.71682	−0.0637172
$727$	48.5814	1.80178	0.900892	−	0.434043i	$-0.142914\pi$
$727$	48.5814	1.80178	0.900892	+	0.434043i	$0.142914\pi$
$728$	−14.9466	−0.553957
$729$	−26.3988	−0.977735
$730$	−3.10434	−0.114897
$731$	10.2812	0.380264
$732$	2.83091	0.104633
$733$	−45.4763	−1.67970	−0.839852	−	0.542815i	$-0.817358\pi$
$733$	−45.4763	−1.67970	−0.839852	+	0.542815i	$0.817358\pi$
$734$	−78.3719	−2.89276
$735$	−0.680930	−0.0251165
$736$	9.54433	0.351809
$737$	−22.7657	−0.838584
$738$	−35.2059	−1.29595
$739$	0.141290	0.00519742	0.00259871	−	0.999997i	$-0.499173\pi$
$739$	0.141290	0.00519742	0.00259871	+	0.999997i	$0.499173\pi$
$740$	18.1837	0.668445
$741$	−0.137553	−0.00505313
$742$	2.19926	0.0807374
$743$	−18.1142	−0.664545	−0.332272	−	0.943183i	$-0.607815\pi$
$743$	−18.1142	−0.664545	−0.332272	+	0.943183i	$0.607815\pi$
$744$	1.14532	0.0419896
$745$	−25.5481	−0.936010
$746$	73.4297	2.68845
$747$	47.5370	1.73929
$748$	38.7406	1.41650
$749$	13.6991	0.500554
$750$	2.30545	0.0841833
$751$	−44.4699	−1.62273	−0.811364	−	0.584541i	$-0.801275\pi$
$751$	−44.4699	−1.62273	−0.811364	+	0.584541i	$0.801275\pi$
$752$	10.0390	0.366085
$753$	0.720763	0.0262661
$754$	66.5442	2.42340
$755$	1.05522	0.0384036
$756$	2.04168	0.0742552
$757$	16.5346	0.600959	0.300480	−	0.953788i	$-0.402853\pi$
$757$	16.5346	0.600959	0.300480	+	0.953788i	$0.402853\pi$
$758$	−23.9836	−0.871123
$759$	−0.433555	−0.0157370
$760$	0.938503	0.0340431
$761$	−47.3243	−1.71551	−0.857753	−	0.514063i	$-0.828140\pi$
$761$	−47.3243	−1.71551	−0.857753	+	0.514063i	$0.828140\pi$
$762$	2.15929	0.0782227
$763$	10.8998	0.394599
$764$	−93.0294	−3.36569
$765$	17.8631	0.645840
$766$	−2.35236	−0.0849941
$767$	−53.0022	−1.91380
$768$	2.21201	0.0798191
$769$	19.6585	0.708903	0.354452	−	0.935074i	$-0.384668\pi$
$769$	19.6585	0.708903	0.354452	+	0.935074i	$0.384668\pi$
$770$	4.65126	0.167620
$771$	−1.05326	−0.0379322
$772$	−87.2829	−3.14138
$773$	−41.1572	−1.48032	−0.740160	−	0.672431i	$-0.765250\pi$
$773$	−41.1572	−1.48032	−0.740160	+	0.672431i	$0.765250\pi$
$774$	12.6225	0.453707
$775$	−12.8154	−0.460343
$776$	−45.4107	−1.63015
$777$	0.504389	0.0180949
$778$	−52.3554	−1.87703
$779$	−1.36997	−0.0490843
$780$	1.83069	0.0655492
$781$	−12.6264	−0.451809
$782$	−26.9739	−0.964584
$783$	−3.76289	−0.134475
$784$	−5.01637	−0.179156
$785$	14.3377	0.511734
$786$	−0.126808	−0.00452308
$787$	−9.52652	−0.339584	−0.169792	−	0.985480i	$-0.554310\pi$
$787$	−9.52652	−0.339584	−0.169792	+	0.985480i	$0.554310\pi$
$788$	−85.9585	−3.06215
$789$	−1.84546	−0.0657001
$790$	−22.7127	−0.808082
$791$	10.1052	0.359298
$792$	19.6895	0.699635
$793$	−37.7606	−1.34092
$794$	−54.4123	−1.93102
$795$	−0.111511	−0.00395487
$796$	−44.2734	−1.56923
$797$	6.28050	0.222467	0.111233	−	0.993794i	$-0.464520\pi$
$797$	6.28050	0.222467	0.111233	+	0.993794i	$0.464520\pi$
$798$	0.0628861	0.00222614
$799$	69.2145	2.44863
$800$	−18.1209	−0.640671
$801$	29.8078	1.05321
$802$	−85.1260	−3.00590
$803$	−2.53433	−0.0894346
$804$	4.09647	0.144471
$805$	−2.04191	−0.0719678
$806$	−36.9042	−1.29989
$807$	0.359297	0.0126478
$808$	−38.2485	−1.34558
$809$	−40.6225	−1.42821	−0.714105	−	0.700038i	$-0.753166\pi$
$809$	−40.6225	−1.42821	−0.714105	+	0.700038i	$0.753166\pi$
$810$	21.8487	0.767687
$811$	3.23697	0.113665	0.0568327	−	0.998384i	$-0.481900\pi$
$811$	3.23697	0.113665	0.0568327	+	0.998384i	$0.481900\pi$
$812$	−19.1815	−0.673140
$813$	−1.04184	−0.0365390
$814$	23.5444	0.825231
$815$	11.6625	0.408520
$816$	−0.491680	−0.0172123
$817$	0.491181	0.0171843
$818$	−43.9011	−1.53497
$819$	−13.5913	−0.474917
$820$	18.2330	0.636722
$821$	−4.72802	−0.165009	−0.0825046	−	0.996591i	$-0.526292\pi$
$821$	−4.72802	−0.165009	−0.0825046	+	0.996591i	$0.526292\pi$
$822$	1.67442	0.0584019
$823$	−33.8363	−1.17946	−0.589729	−	0.807601i	$-0.700765\pi$
$823$	−33.8363	−1.17946	−0.589729	+	0.807601i	$0.700765\pi$
$824$	6.10031	0.212514
$825$	0.823149	0.0286584
$826$	24.2315	0.843120
$827$	−51.8419	−1.80272	−0.901360	−	0.433070i	$-0.857430\pi$
$827$	−51.8419	−1.80272	−0.901360	+	0.433070i	$0.857430\pi$
$828$	−20.8802	−0.725636
$829$	6.74425	0.234238	0.117119	−	0.993118i	$-0.462634\pi$
$829$	6.74425	0.234238	0.117119	+	0.993118i	$0.462634\pi$
$830$	−39.0468	−1.35533
$831$	−2.90374	−0.100730
$832$	−60.0858	−2.08310
$833$	−34.5856	−1.19832
$834$	−4.38226	−0.151745
$835$	−14.1142	−0.488442
$836$	1.85082	0.0640119
$837$	2.08683	0.0721314
$838$	−30.6429	−1.05854
$839$	6.13693	0.211870	0.105935	−	0.994373i	$-0.466216\pi$
$839$	6.13693	0.211870	0.105935	+	0.994373i	$0.466216\pi$
$840$	−0.346470	−0.0119544
$841$	6.35230	0.219045
$842$	77.9548	2.68650
$843$	2.36791	0.0815551
$844$	−65.8495	−2.26663
$845$	−10.7011	−0.368128
$846$	84.9766	2.92156
$847$	−6.60102	−0.226814
$848$	−0.821491	−0.0282101
$849$	−0.457019	−0.0156849
$850$	51.2127	1.75658
$851$	−10.3360	−0.354314
$852$	2.27201	0.0778378
$853$	−30.3243	−1.03828	−0.519142	−	0.854688i	$-0.673748\pi$
$853$	−30.3243	−1.03828	−0.519142	+	0.854688i	$0.673748\pi$
$854$	17.2633	0.590738
$855$	0.853402	0.0291857
$856$	−47.6331	−1.62807
$857$	−49.2665	−1.68291	−0.841456	−	0.540325i	$-0.818301\pi$
$857$	−49.2665	−1.68291	−0.841456	+	0.540325i	$0.818301\pi$
$858$	2.37040	0.0809240
$859$	52.8682	1.80384	0.901920	−	0.431904i	$-0.142158\pi$
$859$	52.8682	1.80384	0.901920	+	0.431904i	$0.142158\pi$
$860$	−6.53713	−0.222914
$861$	0.505757	0.0172361
$862$	29.0622	0.989863
$863$	52.0226	1.77087	0.885434	−	0.464765i	$-0.153861\pi$
$863$	52.0226	1.77087	0.885434	+	0.464765i	$0.153861\pi$
$864$	2.95076	0.100387
$865$	11.8391	0.402542
$866$	69.3418	2.35633
$867$	−1.59345	−0.0541164
$868$	10.6377	0.361068
$869$	−18.5423	−0.629003
$870$	1.54253	0.0522968
$871$	−54.6415	−1.85146
$872$	−37.8997	−1.28344
$873$	−41.2930	−1.39756
$874$	−1.28867	−0.0435899
$875$	8.86426	0.299667
$876$	0.456030	0.0154078
$877$	9.80581	0.331119	0.165559	−	0.986200i	$-0.447057\pi$
$877$	9.80581	0.331119	0.165559	+	0.986200i	$0.447057\pi$
$878$	59.8085	2.01844
$879$	1.13933	0.0384287
$880$	−1.73739	−0.0585674
$881$	−43.3366	−1.46005	−0.730024	−	0.683421i	$-0.760491\pi$
$881$	−43.3366	−1.46005	−0.730024	+	0.683421i	$0.760491\pi$
$882$	−42.4618	−1.42976
$883$	2.69451	0.0906774	0.0453387	−	0.998972i	$-0.485563\pi$
$883$	2.69451	0.0906774	0.0453387	+	0.998972i	$0.485563\pi$
$884$	92.9840	3.12739
$885$	−1.22862	−0.0412997
$886$	3.19582	0.107366
$887$	12.1789	0.408927	0.204463	−	0.978874i	$-0.434455\pi$
$887$	12.1789	0.408927	0.204463	+	0.978874i	$0.434455\pi$
$888$	−1.75381	−0.0588540
$889$	8.30226	0.278449
$890$	−24.4840	−0.820707
$891$	17.8369	0.597560
$892$	15.8500	0.530699
$893$	3.30670	0.110655
$894$	5.95243	0.199079
$895$	19.8301	0.662848
$896$	18.6550	0.623220
$897$	−1.04061	−0.0347448
$898$	7.17508	0.239436
$899$	−19.6057	−0.653887
$900$	39.6432	1.32144
$901$	−5.66382	−0.188689
$902$	23.6082	0.786068
$903$	−0.181331	−0.00603431
$904$	−35.1366	−1.16863
$905$	−9.54499	−0.317286
$906$	−0.245856	−0.00816802
$907$	−21.4756	−0.713084	−0.356542	−	0.934279i	$-0.616044\pi$
$907$	−21.4756	−0.713084	−0.356542	+	0.934279i	$0.616044\pi$
$908$	63.1377	2.09530
$909$	−34.7802	−1.15359
$910$	11.1638	0.370077
$911$	−3.06655	−0.101599	−0.0507997	−	0.998709i	$-0.516177\pi$
$911$	−3.06655	−0.101599	−0.0507997	+	0.998709i	$0.516177\pi$
$912$	−0.0234899	−0.000777828 0
$913$	−31.8771	−1.05498
$914$	−64.0266	−2.11781
$915$	−0.875313	−0.0289369
$916$	44.1070	1.45734
$917$	−0.487563	−0.0161008
$918$	−8.33935	−0.275240
$919$	−31.8045	−1.04913	−0.524567	−	0.851369i	$-0.675773\pi$
$919$	−31.8045	−1.04913	−0.524567	+	0.851369i	$0.675773\pi$
$920$	7.09991	0.234077
$921$	1.78965	0.0589708
$922$	−49.8926	−1.64312
$923$	−30.3056	−0.997522
$924$	−0.683273	−0.0224780
$925$	19.6240	0.645233
$926$	−12.8046	−0.420784
$927$	5.54715	0.182192
$928$	−27.7224	−0.910031
$929$	35.0498	1.14995	0.574973	−	0.818172i	$-0.305012\pi$
$929$	35.0498	1.14995	0.574973	+	0.818172i	$0.305012\pi$
$930$	−0.855460	−0.0280517
$931$	−1.65232	−0.0541526
$932$	16.6615	0.545767
$933$	−1.84403	−0.0603710
$934$	31.1391	1.01890
$935$	−11.9785	−0.391740
$936$	47.2581	1.54468
$937$	16.7390	0.546839	0.273419	−	0.961895i	$-0.411845\pi$
$937$	16.7390	0.546839	0.273419	+	0.961895i	$0.411845\pi$
$938$	24.9809	0.815655
$939$	−0.434810	−0.0141895
$940$	−44.0089	−1.43541
$941$	21.0001	0.684583	0.342291	−	0.939594i	$-0.388797\pi$
$941$	21.0001	0.684583	0.342291	+	0.939594i	$0.388797\pi$
$942$	−3.34053	−0.108840
$943$	−10.3640	−0.337499
$944$	−9.05119	−0.294591
$945$	−0.631284	−0.0205357
$946$	−8.46435	−0.275200
$947$	27.2102	0.884214	0.442107	−	0.896962i	$-0.354231\pi$
$947$	27.2102	0.884214	0.442107	+	0.896962i	$0.354231\pi$
$948$	3.33651	0.108365
$949$	−6.08283	−0.197457
$950$	2.44667	0.0793806
$951$	0.733966	0.0238005
$952$	−17.5978	−0.570349
$953$	−58.4981	−1.89494	−0.947470	−	0.319846i	$-0.896369\pi$
$953$	−58.4981	−1.89494	−0.947470	+	0.319846i	$0.896369\pi$
$954$	−6.95363	−0.225132
$955$	28.7645	0.930799
$956$	44.9487	1.45375
$957$	1.25930	0.0407073
$958$	58.2632	1.88240
$959$	6.43797	0.207893
$960$	−1.39282	−0.0449532
$961$	−20.1270	−0.649259
$962$	56.5106	1.82197
$963$	−43.3139	−1.39577
$964$	7.13387	0.229766
$965$	26.9877	0.868766
$966$	0.475742	0.0153068
$967$	−24.8688	−0.799726	−0.399863	−	0.916575i	$-0.630942\pi$
$967$	−24.8688	−0.799726	−0.399863	+	0.916575i	$0.630942\pi$
$968$	22.9524	0.737718
$969$	−0.161952	−0.00520266
$970$	33.9180	1.08904
$971$	−42.4789	−1.36321	−0.681606	−	0.731719i	$-0.738718\pi$
$971$	−42.4789	−1.36321	−0.681606	+	0.731719i	$0.738718\pi$
$972$	−9.68910	−0.310778
$973$	−16.8494	−0.540167
$974$	32.9571	1.05601
$975$	1.97570	0.0632730
$976$	−6.44838	−0.206407
$977$	−26.2243	−0.838990	−0.419495	−	0.907758i	$-0.637793\pi$
$977$	−26.2243	−0.838990	−0.419495	+	0.907758i	$0.637793\pi$
$978$	−2.71724	−0.0868876
$979$	−19.9883	−0.638830
$980$	21.9907	0.702468
$981$	−34.4630	−1.10032
$982$	47.5378	1.51699
$983$	52.1294	1.66267	0.831335	−	0.555772i	$-0.187577\pi$
$983$	52.1294	1.66267	0.831335	+	0.555772i	$0.187577\pi$
$984$	−1.75857	−0.0560610
$985$	26.5782	0.846853
$986$	78.3480	2.49511
$987$	−1.22075	−0.0388568
$988$	4.44228	0.141328
$989$	3.71585	0.118157
$990$	−14.7064	−0.467399
$991$	−21.5566	−0.684768	−0.342384	−	0.939560i	$-0.611234\pi$
$991$	−21.5566	−0.684768	−0.342384	+	0.939560i	$0.611234\pi$
$992$	15.3743	0.488134
$993$	0.240097	0.00761926
$994$	13.8551	0.439456
$995$	13.6893	0.433978
$996$	5.73599	0.181752
$997$	−9.97917	−0.316043	−0.158022	−	0.987436i	$-0.550512\pi$
$997$	−9.97917	−0.316043	−0.158022	+	0.987436i	$0.550512\pi$
$998$	57.0759	1.80671
$999$	−3.19552	−0.101102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.20	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.20	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.32654 q^{2} -0.105675 q^{3} +3.41278 q^{4} -1.05522 q^{5} +0.245856 q^{6} +0.945293 q^{7} -3.28688 q^{8} -2.98883 q^{9} +O(q^{10})\)	\(q-2.32654 q^{2} -0.105675 q^{3} +3.41278 q^{4} -1.05522 q^{5} +0.245856 q^{6} +0.945293 q^{7} -3.28688 q^{8} -2.98883 q^{9} +2.45502 q^{10} +2.00424 q^{11} -0.360644 q^{12} +4.81051 q^{13} -2.19926 q^{14} +0.111511 q^{15} +0.821491 q^{16} +5.66382 q^{17} +6.95363 q^{18} +0.270587 q^{19} -3.60125 q^{20} -0.0998935 q^{21} -4.66293 q^{22} +2.04703 q^{23} +0.347340 q^{24} -3.88650 q^{25} -11.1918 q^{26} +0.632868 q^{27} +3.22608 q^{28} -5.94578 q^{29} -0.259433 q^{30} +3.29742 q^{31} +4.66253 q^{32} -0.211797 q^{33} -13.1771 q^{34} -0.997497 q^{35} -10.2002 q^{36} -5.04927 q^{37} -0.629531 q^{38} -0.508349 q^{39} +3.46840 q^{40} -5.06296 q^{41} +0.232406 q^{42} +1.81524 q^{43} +6.84001 q^{44} +3.15389 q^{45} -4.76249 q^{46} +12.2205 q^{47} -0.0868108 q^{48} -6.10642 q^{49} +9.04209 q^{50} -0.598522 q^{51} +16.4172 q^{52} -1.00000 q^{53} -1.47239 q^{54} -2.11492 q^{55} -3.10706 q^{56} -0.0285942 q^{57} +13.8331 q^{58} -11.0180 q^{59} +0.380560 q^{60} -7.84960 q^{61} -7.67157 q^{62} -2.82532 q^{63} -12.4905 q^{64} -5.07617 q^{65} +0.492754 q^{66} -11.3588 q^{67} +19.3293 q^{68} -0.216319 q^{69} +2.32071 q^{70} -6.29987 q^{71} +9.82393 q^{72} -1.26449 q^{73} +11.7473 q^{74} +0.410705 q^{75} +0.923454 q^{76} +1.89459 q^{77} +1.18269 q^{78} -9.25154 q^{79} -0.866858 q^{80} +8.89962 q^{81} +11.7792 q^{82} -15.9049 q^{83} -0.340914 q^{84} -5.97660 q^{85} -4.22323 q^{86} +0.628318 q^{87} -6.58768 q^{88} -9.97305 q^{89} -7.33765 q^{90} +4.54735 q^{91} +6.98606 q^{92} -0.348453 q^{93} -28.4314 q^{94} -0.285530 q^{95} -0.492711 q^{96} +13.8158 q^{97} +14.2068 q^{98} -5.99033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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