LMFDB - Embedded newform 6001.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26295 q^{2} -1.98147 q^{3} +3.12095 q^{4} +3.45141 q^{5} +4.48397 q^{6} -1.45595 q^{7} -2.53665 q^{8} +0.926221 q^{9} +O(q^{10})$	\(q-2.26295 q^{2} -1.98147 q^{3} +3.12095 q^{4} +3.45141 q^{5} +4.48397 q^{6} -1.45595 q^{7} -2.53665 q^{8} +0.926221 q^{9} -7.81036 q^{10} +0.211853 q^{11} -6.18406 q^{12} +2.14991 q^{13} +3.29474 q^{14} -6.83886 q^{15} -0.501583 q^{16} -1.00000 q^{17} -2.09599 q^{18} -1.31437 q^{19} +10.7717 q^{20} +2.88492 q^{21} -0.479412 q^{22} -3.84476 q^{23} +5.02629 q^{24} +6.91221 q^{25} -4.86513 q^{26} +4.10913 q^{27} -4.54394 q^{28} -2.11733 q^{29} +15.4760 q^{30} -3.67903 q^{31} +6.20835 q^{32} -0.419780 q^{33} +2.26295 q^{34} -5.02507 q^{35} +2.89069 q^{36} +2.91876 q^{37} +2.97435 q^{38} -4.25997 q^{39} -8.75501 q^{40} +10.3772 q^{41} -6.52843 q^{42} -4.92082 q^{43} +0.661181 q^{44} +3.19677 q^{45} +8.70050 q^{46} -6.81275 q^{47} +0.993871 q^{48} -4.88021 q^{49} -15.6420 q^{50} +1.98147 q^{51} +6.70974 q^{52} +11.4172 q^{53} -9.29876 q^{54} +0.731190 q^{55} +3.69323 q^{56} +2.60438 q^{57} +4.79141 q^{58} -5.01988 q^{59} -21.3437 q^{60} +8.78869 q^{61} +8.32546 q^{62} -1.34853 q^{63} -13.0460 q^{64} +7.42020 q^{65} +0.949941 q^{66} +9.91625 q^{67} -3.12095 q^{68} +7.61828 q^{69} +11.3715 q^{70} +0.870025 q^{71} -2.34950 q^{72} -6.76624 q^{73} -6.60502 q^{74} -13.6963 q^{75} -4.10208 q^{76} -0.308447 q^{77} +9.64011 q^{78} +4.24139 q^{79} -1.73117 q^{80} -10.9208 q^{81} -23.4830 q^{82} -3.03092 q^{83} +9.00368 q^{84} -3.45141 q^{85} +11.1356 q^{86} +4.19543 q^{87} -0.537396 q^{88} +4.91055 q^{89} -7.23412 q^{90} -3.13016 q^{91} -11.9993 q^{92} +7.28988 q^{93} +15.4169 q^{94} -4.53642 q^{95} -12.3017 q^{96} -2.07370 q^{97} +11.0437 q^{98} +0.196222 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.26295	−1.60015	−0.800074	−	0.599901i	$-0.795206\pi$
$2$	−2.26295	−1.60015	−0.800074	+	0.599901i	$0.795206\pi$
$3$	−1.98147	−1.14400	−0.572001	−	0.820253i	$-0.693833\pi$
$3$	−1.98147	−1.14400	−0.572001	+	0.820253i	$0.693833\pi$
$4$	3.12095	1.56047
$5$	3.45141	1.54352	0.771758	−	0.635916i	$-0.219378\pi$
$5$	3.45141	1.54352	0.771758	+	0.635916i	$0.219378\pi$
$6$	4.48397	1.83057
$7$	−1.45595	−0.550297	−0.275149	−	0.961402i	$-0.588727\pi$
$7$	−1.45595	−0.550297	−0.275149	+	0.961402i	$0.588727\pi$
$8$	−2.53665	−0.896841
$9$	0.926221	0.308740
$10$	−7.81036	−2.46985
$11$	0.211853	0.0638760	0.0319380	−	0.999490i	$-0.489832\pi$
$11$	0.211853	0.0638760	0.0319380	+	0.999490i	$0.489832\pi$
$12$	−6.18406	−1.78518
$13$	2.14991	0.596277	0.298138	−	0.954523i	$-0.403634\pi$
$13$	2.14991	0.596277	0.298138	+	0.954523i	$0.403634\pi$
$14$	3.29474	0.880557
$15$	−6.83886	−1.76579
$16$	−0.501583	−0.125396
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.09599	−0.494030
$19$	−1.31437	−0.301537	−0.150769	−	0.988569i	$-0.548175\pi$
$19$	−1.31437	−0.301537	−0.150769	+	0.988569i	$0.548175\pi$
$20$	10.7717	2.40862
$21$	2.88492	0.629541
$22$	−0.479412	−0.102211
$23$	−3.84476	−0.801688	−0.400844	−	0.916146i	$-0.631283\pi$
$23$	−3.84476	−0.801688	−0.400844	+	0.916146i	$0.631283\pi$
$24$	5.02629	1.02599
$25$	6.91221	1.38244
$26$	−4.86513	−0.954131
$27$	4.10913	0.790802
$28$	−4.54394	−0.858725
$29$	−2.11733	−0.393178	−0.196589	−	0.980486i	$-0.562987\pi$
$29$	−2.11733	−0.393178	−0.196589	+	0.980486i	$0.562987\pi$
$30$	15.4760	2.82552
$31$	−3.67903	−0.660773	−0.330386	−	0.943846i	$-0.607179\pi$
$31$	−3.67903	−0.660773	−0.330386	+	0.943846i	$0.607179\pi$
$32$	6.20835	1.09749
$33$	−0.419780	−0.0730743
$34$	2.26295	0.388093
$35$	−5.02507	−0.849393
$36$	2.89069	0.481781
$37$	2.91876	0.479842	0.239921	−	0.970792i	$-0.422878\pi$
$37$	2.91876	0.479842	0.239921	+	0.970792i	$0.422878\pi$
$38$	2.97435	0.482504
$39$	−4.25997	−0.682142
$40$	−8.75501	−1.38429
$41$	10.3772	1.62064	0.810321	−	0.585986i	$-0.199293\pi$
$41$	10.3772	1.62064	0.810321	+	0.585986i	$0.199293\pi$
$42$	−6.52843	−1.00736
$43$	−4.92082	−0.750418	−0.375209	−	0.926940i	$-0.622429\pi$
$43$	−4.92082	−0.750418	−0.375209	+	0.926940i	$0.622429\pi$
$44$	0.661181	0.0996768
$45$	3.19677	0.476546
$46$	8.70050	1.28282
$47$	−6.81275	−0.993741	−0.496871	−	0.867825i	$-0.665518\pi$
$47$	−6.81275	−0.993741	−0.496871	+	0.867825i	$0.665518\pi$
$48$	0.993871	0.143453
$49$	−4.88021	−0.697173
$50$	−15.6420	−2.21211
$51$	1.98147	0.277461
$52$	6.70974	0.930474
$53$	11.4172	1.56827	0.784135	−	0.620590i	$-0.213107\pi$
$53$	11.4172	1.56827	0.784135	+	0.620590i	$0.213107\pi$
$54$	−9.29876	−1.26540
$55$	0.731190	0.0985936
$56$	3.69323	0.493529
$57$	2.60438	0.344959
$58$	4.79141	0.629144
$59$	−5.01988	−0.653532	−0.326766	−	0.945105i	$-0.605959\pi$
$59$	−5.01988	−0.653532	−0.326766	+	0.945105i	$0.605959\pi$
$60$	−21.3437	−2.75546
$61$	8.78869	1.12528	0.562638	−	0.826703i	$-0.309786\pi$
$61$	8.78869	1.12528	0.562638	+	0.826703i	$0.309786\pi$
$62$	8.32546	1.05733
$63$	−1.34853	−0.169899
$64$	−13.0460	−1.63075
$65$	7.42020	0.920363
$66$	0.949941	0.116930
$67$	9.91625	1.21146	0.605731	−	0.795669i	$-0.292881\pi$
$67$	9.91625	1.21146	0.605731	+	0.795669i	$0.292881\pi$
$68$	−3.12095	−0.378470
$69$	7.61828	0.917133
$70$	11.3715	1.35915
$71$	0.870025	0.103253	0.0516265	−	0.998666i	$-0.483559\pi$
$71$	0.870025	0.103253	0.0516265	+	0.998666i	$0.483559\pi$
$72$	−2.34950	−0.276891
$73$	−6.76624	−0.791929	−0.395964	−	0.918266i	$-0.629590\pi$
$73$	−6.76624	−0.791929	−0.395964	+	0.918266i	$0.629590\pi$
$74$	−6.60502	−0.767818
$75$	−13.6963	−1.58152
$76$	−4.10208	−0.470541
$77$	−0.308447	−0.0351508
$78$	9.64011	1.09153
$79$	4.24139	0.477194	0.238597	−	0.971119i	$-0.423313\pi$
$79$	4.24139	0.477194	0.238597	+	0.971119i	$0.423313\pi$
$80$	−1.73117	−0.193550
$81$	−10.9208	−1.21342
$82$	−23.4830	−2.59327
$83$	−3.03092	−0.332686	−0.166343	−	0.986068i	$-0.553196\pi$
$83$	−3.03092	−0.332686	−0.166343	+	0.986068i	$0.553196\pi$
$84$	9.00368	0.982383
$85$	−3.45141	−0.374358
$86$	11.1356	1.20078
$87$	4.19543	0.449797
$88$	−0.537396	−0.0572866
$89$	4.91055	0.520518	0.260259	−	0.965539i	$-0.416192\pi$
$89$	4.91055	0.520518	0.260259	+	0.965539i	$0.416192\pi$
$90$	−7.23412	−0.762544
$91$	−3.13016	−0.328130
$92$	−11.9993	−1.25101
$93$	7.28988	0.755925
$94$	15.4169	1.59013
$95$	−4.53642	−0.465427
$96$	−12.3017	−1.25553
$97$	−2.07370	−0.210552	−0.105276	−	0.994443i	$-0.533573\pi$
$97$	−2.07370	−0.210552	−0.105276	+	0.994443i	$0.533573\pi$
$98$	11.0437	1.11558
$99$	0.196222	0.0197211
$100$	21.5726	2.15726
$101$	−16.0807	−1.60009	−0.800045	−	0.599940i	$-0.795191\pi$
$101$	−16.0807	−1.60009	−0.800045	+	0.599940i	$0.795191\pi$
$102$	−4.48397	−0.443979
$103$	−11.3049	−1.11390	−0.556952	−	0.830545i	$-0.688029\pi$
$103$	−11.3049	−1.11390	−0.556952	+	0.830545i	$0.688029\pi$
$104$	−5.45356	−0.534765
$105$	9.95703	0.971707
$106$	−25.8365	−2.50946
$107$	−1.03668	−0.100220	−0.0501098	−	0.998744i	$-0.515957\pi$
$107$	−1.03668	−0.100220	−0.0501098	+	0.998744i	$0.515957\pi$
$108$	12.8244	1.23403
$109$	−15.3033	−1.46579	−0.732894	−	0.680343i	$-0.761831\pi$
$109$	−15.3033	−1.46579	−0.732894	+	0.680343i	$0.761831\pi$
$110$	−1.65465	−0.157764
$111$	−5.78344	−0.548940
$112$	0.730279	0.0690049
$113$	−8.13274	−0.765064	−0.382532	−	0.923942i	$-0.624948\pi$
$113$	−8.13274	−0.765064	−0.382532	+	0.923942i	$0.624948\pi$
$114$	−5.89359	−0.551985
$115$	−13.2698	−1.23742
$116$	−6.60808	−0.613544
$117$	1.99129	0.184095
$118$	11.3597	1.04575
$119$	1.45595	0.133467
$120$	17.3478	1.58363
$121$	−10.9551	−0.995920
$122$	−19.8884	−1.80061
$123$	−20.5621	−1.85402
$124$	−11.4820	−1.03112
$125$	6.59980	0.590304
$126$	3.05166	0.271864
$127$	4.87026	0.432165	0.216083	−	0.976375i	$-0.430672\pi$
$127$	4.87026	0.432165	0.216083	+	0.976375i	$0.430672\pi$
$128$	17.1058	1.51196
$129$	9.75045	0.858480
$130$	−16.7916	−1.47272
$131$	−21.3523	−1.86556	−0.932780	−	0.360445i	$-0.882625\pi$
$131$	−21.3523	−1.86556	−0.932780	+	0.360445i	$0.882625\pi$
$132$	−1.31011	−0.114030
$133$	1.91366	0.165935
$134$	−22.4400	−1.93852
$135$	14.1823	1.22062
$136$	2.53665	0.217516
$137$	16.8349	1.43830	0.719152	−	0.694853i	$-0.244530\pi$
$137$	16.8349	1.43830	0.719152	+	0.694853i	$0.244530\pi$
$138$	−17.2398	−1.46755
$139$	−16.2838	−1.38117	−0.690587	−	0.723249i	$-0.742648\pi$
$139$	−16.2838	−1.38117	−0.690587	+	0.723249i	$0.742648\pi$
$140$	−15.6830	−1.32545
$141$	13.4993	1.13684
$142$	−1.96882	−0.165220
$143$	0.455463	0.0380878
$144$	−0.464577	−0.0387147
$145$	−7.30777	−0.606877
$146$	15.3117	1.26720
$147$	9.66999	0.797567
$148$	9.10931	0.748781
$149$	23.2807	1.90723	0.953616	−	0.301025i	$-0.0973287\pi$
$149$	23.2807	1.90723	0.953616	+	0.301025i	$0.0973287\pi$
$150$	30.9941	2.53066
$151$	−0.207074	−0.0168514	−0.00842571	−	0.999965i	$-0.502682\pi$
$151$	−0.207074	−0.0168514	−0.00842571	+	0.999965i	$0.502682\pi$
$152$	3.33409	0.270431
$153$	−0.926221	−0.0748805
$154$	0.698000	0.0562465
$155$	−12.6978	−1.01991
$156$	−13.2952	−1.06446
$157$	2.45525	0.195950	0.0979750	−	0.995189i	$-0.468763\pi$
$157$	2.45525	0.195950	0.0979750	+	0.995189i	$0.468763\pi$
$158$	−9.59806	−0.763580
$159$	−22.6228	−1.79410
$160$	21.4276	1.69400
$161$	5.59778	0.441167
$162$	24.7132	1.94165
$163$	24.6602	1.93153	0.965767	−	0.259411i	$-0.0835283\pi$
$163$	24.6602	1.93153	0.965767	+	0.259411i	$0.0835283\pi$
$164$	32.3866	2.52897
$165$	−1.44883	−0.112791
$166$	6.85882	0.532348
$167$	12.5485	0.971031	0.485516	−	0.874228i	$-0.338632\pi$
$167$	12.5485	0.971031	0.485516	+	0.874228i	$0.338632\pi$
$168$	−7.31803	−0.564598
$169$	−8.37790	−0.644454
$170$	7.81036	0.599028
$171$	−1.21740	−0.0930967
$172$	−15.3576	−1.17101
$173$	−25.9573	−1.97350	−0.986750	−	0.162246i	$-0.948126\pi$
$173$	−25.9573	−1.97350	−0.986750	+	0.162246i	$0.948126\pi$
$174$	−9.49404	−0.719741
$175$	−10.0638	−0.760754
$176$	−0.106262	−0.00800977
$177$	9.94674	0.747642
$178$	−11.1123	−0.832905
$179$	8.66269	0.647480	0.323740	−	0.946146i	$-0.395060\pi$
$179$	8.66269	0.647480	0.323740	+	0.946146i	$0.395060\pi$
$180$	9.97694	0.743637
$181$	−10.4907	−0.779765	−0.389883	−	0.920865i	$-0.627484\pi$
$181$	−10.4907	−0.779765	−0.389883	+	0.920865i	$0.627484\pi$
$182$	7.08339	0.525056
$183$	−17.4145	−1.28732
$184$	9.75281	0.718986
$185$	10.0738	0.740644
$186$	−16.4966	−1.20959
$187$	−0.211853	−0.0154922
$188$	−21.2622	−1.55071
$189$	−5.98269	−0.435176
$190$	10.2657	0.744753
$191$	−0.789726	−0.0571426	−0.0285713	−	0.999592i	$-0.509096\pi$
$191$	−0.789726	−0.0571426	−0.0285713	+	0.999592i	$0.509096\pi$
$192$	25.8503	1.86559
$193$	17.6346	1.26936	0.634681	−	0.772774i	$-0.281131\pi$
$193$	17.6346	1.26936	0.634681	+	0.772774i	$0.281131\pi$
$194$	4.69268	0.336915
$195$	−14.7029	−1.05290
$196$	−15.2309	−1.08792
$197$	26.4155	1.88203	0.941014	−	0.338367i	$-0.109874\pi$
$197$	26.4155	1.88203	0.941014	+	0.338367i	$0.109874\pi$
$198$	−0.444042	−0.0315567
$199$	−14.8470	−1.05247	−0.526237	−	0.850338i	$-0.676398\pi$
$199$	−14.8470	−1.05247	−0.526237	+	0.850338i	$0.676398\pi$
$200$	−17.5338	−1.23983
$201$	−19.6487	−1.38592
$202$	36.3898	2.56038
$203$	3.08273	0.216365
$204$	6.18406	0.432971
$205$	35.8158	2.50149
$206$	25.5824	1.78241
$207$	−3.56110	−0.247513
$208$	−1.07836	−0.0747705
$209$	−0.278453	−0.0192610
$210$	−22.5323	−1.55487
$211$	21.1264	1.45440	0.727201	−	0.686425i	$-0.240821\pi$
$211$	21.1264	1.45440	0.727201	+	0.686425i	$0.240821\pi$
$212$	35.6324	2.44724
$213$	−1.72393	−0.118122
$214$	2.34595	0.160366
$215$	−16.9837	−1.15828
$216$	−10.4234	−0.709224
$217$	5.35648	0.363622
$218$	34.6306	2.34548
$219$	13.4071	0.905968
$220$	2.28200	0.153853
$221$	−2.14991	−0.144618
$222$	13.0876	0.878385
$223$	−11.1019	−0.743441	−0.371720	−	0.928345i	$-0.621232\pi$
$223$	−11.1019	−0.743441	−0.371720	+	0.928345i	$0.621232\pi$
$224$	−9.03905	−0.603947
$225$	6.40223	0.426815
$226$	18.4040	1.22422
$227$	−11.6746	−0.774867	−0.387434	−	0.921898i	$-0.626638\pi$
$227$	−11.6746	−0.774867	−0.387434	+	0.921898i	$0.626638\pi$
$228$	8.12814	0.538299
$229$	12.6286	0.834521	0.417260	−	0.908787i	$-0.362990\pi$
$229$	12.6286	0.834521	0.417260	+	0.908787i	$0.362990\pi$
$230$	30.0290	1.98005
$231$	0.611178	0.0402126
$232$	5.37092	0.352618
$233$	−8.42637	−0.552030	−0.276015	−	0.961153i	$-0.589014\pi$
$233$	−8.42637	−0.552030	−0.276015	+	0.961153i	$0.589014\pi$
$234$	−4.50619	−0.294579
$235$	−23.5136	−1.53386
$236$	−15.6668	−1.01982
$237$	−8.40418	−0.545910
$238$	−3.29474	−0.213566
$239$	7.35130	0.475516	0.237758	−	0.971324i	$-0.423587\pi$
$239$	7.35130	0.475516	0.237758	+	0.971324i	$0.423587\pi$
$240$	3.43025	0.221422
$241$	−14.5127	−0.934847	−0.467423	−	0.884034i	$-0.654818\pi$
$241$	−14.5127	−0.934847	−0.467423	+	0.884034i	$0.654818\pi$
$242$	24.7909	1.59362
$243$	9.31180	0.597352
$244$	27.4290	1.75596
$245$	−16.8436	−1.07610
$246$	46.5309	2.96670
$247$	−2.82577	−0.179800
$248$	9.33240	0.592608
$249$	6.00567	0.380594
$250$	−14.9350	−0.944574
$251$	−9.24034	−0.583245	−0.291622	−	0.956533i	$-0.594195\pi$
$251$	−9.24034	−0.583245	−0.291622	+	0.956533i	$0.594195\pi$
$252$	−4.20870	−0.265123
$253$	−0.814523	−0.0512086
$254$	−11.0212	−0.691529
$255$	6.83886	0.428266
$256$	−12.6176	−0.788599
$257$	28.5094	1.77837	0.889183	−	0.457552i	$-0.151274\pi$
$257$	28.5094	1.77837	0.889183	+	0.457552i	$0.151274\pi$
$258$	−22.0648	−1.37369
$259$	−4.24957	−0.264056
$260$	23.1581	1.43620
$261$	−1.96112	−0.121390
$262$	48.3192	2.98517
$263$	25.2023	1.55404	0.777021	−	0.629475i	$-0.216730\pi$
$263$	25.2023	1.55404	0.777021	+	0.629475i	$0.216730\pi$
$264$	1.06483	0.0655360
$265$	39.4053	2.42065
$266$	−4.33051	−0.265521
$267$	−9.73011	−0.595473
$268$	30.9481	1.89046
$269$	−20.9044	−1.27456	−0.637281	−	0.770632i	$-0.719941\pi$
$269$	−20.9044	−1.27456	−0.637281	+	0.770632i	$0.719941\pi$
$270$	−32.0938	−1.95317
$271$	19.4333	1.18049	0.590244	−	0.807225i	$-0.299031\pi$
$271$	19.4333	1.18049	0.590244	+	0.807225i	$0.299031\pi$
$272$	0.501583	0.0304129
$273$	6.20231	0.375381
$274$	−38.0966	−2.30150
$275$	1.46437	0.0883048
$276$	23.7762	1.43116
$277$	16.3870	0.984600	0.492300	−	0.870425i	$-0.336156\pi$
$277$	16.3870	0.984600	0.492300	+	0.870425i	$0.336156\pi$
$278$	36.8495	2.21008
$279$	−3.40759	−0.204007
$280$	12.7468	0.761770
$281$	−24.2979	−1.44949	−0.724747	−	0.689015i	$-0.758043\pi$
$281$	−24.2979	−1.44949	−0.724747	+	0.689015i	$0.758043\pi$
$282$	−30.5481	−1.81912
$283$	−23.2519	−1.38218	−0.691090	−	0.722769i	$-0.742869\pi$
$283$	−23.2519	−1.38218	−0.691090	+	0.722769i	$0.742869\pi$
$284$	2.71530	0.161124
$285$	8.98879	0.532450
$286$	−1.03069	−0.0609461
$287$	−15.1086	−0.891835
$288$	5.75031	0.338840
$289$	1.00000	0.0588235
$290$	16.5371	0.971093
$291$	4.10897	0.240872
$292$	−21.1171	−1.23578
$293$	−17.1032	−0.999177	−0.499589	−	0.866263i	$-0.666516\pi$
$293$	−17.1032	−0.999177	−0.499589	+	0.866263i	$0.666516\pi$
$294$	−21.8827	−1.27623
$295$	−17.3256	−1.00874
$296$	−7.40388	−0.430342
$297$	0.870530	0.0505133
$298$	−52.6832	−3.05185
$299$	−8.26588	−0.478028
$300$	−42.7455	−2.46791
$301$	7.16447	0.412953
$302$	0.468598	0.0269648
$303$	31.8634	1.83051
$304$	0.659265	0.0378115
$305$	30.3333	1.73688
$306$	2.09599	0.119820
$307$	−22.2222	−1.26829	−0.634144	−	0.773215i	$-0.718648\pi$
$307$	−22.2222	−1.26829	−0.634144	+	0.773215i	$0.718648\pi$
$308$	−0.962647	−0.0548519
$309$	22.4003	1.27431
$310$	28.7345	1.63201
$311$	10.5296	0.597076	0.298538	−	0.954398i	$-0.403501\pi$
$311$	10.5296	0.597076	0.298538	+	0.954398i	$0.403501\pi$
$312$	10.8061	0.611773
$313$	11.8150	0.667825	0.333913	−	0.942604i	$-0.391631\pi$
$313$	11.8150	0.667825	0.333913	+	0.942604i	$0.391631\pi$
$314$	−5.55610	−0.313549
$315$	−4.65433	−0.262242
$316$	13.2372	0.744648
$317$	−26.7416	−1.50196	−0.750980	−	0.660325i	$-0.770418\pi$
$317$	−26.7416	−1.50196	−0.750980	+	0.660325i	$0.770418\pi$
$318$	51.1943	2.87083
$319$	−0.448562	−0.0251147
$320$	−45.0272	−2.51710
$321$	2.05415	0.114651
$322$	−12.6675	−0.705932
$323$	1.31437	0.0731335
$324$	−34.0832	−1.89351
$325$	14.8606	0.824318
$326$	−55.8048	−3.09074
$327$	30.3230	1.67686
$328$	−26.3232	−1.45346
$329$	9.91902	0.546853
$330$	3.27863	0.180483
$331$	−8.42878	−0.463288	−0.231644	−	0.972801i	$-0.574410\pi$
$331$	−8.42878	−0.463288	−0.231644	+	0.972801i	$0.574410\pi$
$332$	−9.45934	−0.519148
$333$	2.70342	0.148147
$334$	−28.3966	−1.55379
$335$	34.2250	1.86991
$336$	−1.44703	−0.0789418
$337$	7.39977	0.403091	0.201545	−	0.979479i	$-0.435404\pi$
$337$	7.39977	0.403091	0.201545	+	0.979479i	$0.435404\pi$
$338$	18.9588	1.03122
$339$	16.1148	0.875234
$340$	−10.7717	−0.584175
$341$	−0.779412	−0.0422075
$342$	2.75491	0.148968
$343$	17.2970	0.933950
$344$	12.4824	0.673005
$345$	26.2938	1.41561
$346$	58.7402	3.15789
$347$	−31.3615	−1.68357	−0.841787	−	0.539809i	$-0.818496\pi$
$347$	−31.3615	−1.68357	−0.841787	+	0.539809i	$0.818496\pi$
$348$	13.0937	0.701896
$349$	32.2682	1.72728	0.863638	−	0.504112i	$-0.168180\pi$
$349$	32.2682	1.72728	0.863638	+	0.504112i	$0.168180\pi$
$350$	22.7739	1.21732
$351$	8.83424	0.471537
$352$	1.31526	0.0701034
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−22.5090	−1.19634
$355$	3.00281	0.159373
$356$	15.3256	0.812254
$357$	−2.88492	−0.152686
$358$	−19.6032	−1.03606
$359$	−25.8177	−1.36261	−0.681303	−	0.732002i	$-0.738586\pi$
$359$	−25.8177	−1.36261	−0.681303	+	0.732002i	$0.738586\pi$
$360$	−8.10907	−0.427386
$361$	−17.2724	−0.909075
$362$	23.7399	1.24774
$363$	21.7072	1.13933
$364$	−9.76905	−0.512037
$365$	−23.3530	−1.22235
$366$	39.4082	2.05990
$367$	−32.0436	−1.67266	−0.836331	−	0.548225i	$-0.815304\pi$
$367$	−32.0436	−1.67266	−0.836331	+	0.548225i	$0.815304\pi$
$368$	1.92847	0.100528
$369$	9.61156	0.500358
$370$	−22.7966	−1.18514
$371$	−16.6228	−0.863015
$372$	22.7513	1.17960
$373$	11.4582	0.593284	0.296642	−	0.954989i	$-0.404133\pi$
$373$	11.4582	0.593284	0.296642	+	0.954989i	$0.404133\pi$
$374$	0.479412	0.0247898
$375$	−13.0773	−0.675309
$376$	17.2815	0.891228
$377$	−4.55206	−0.234443
$378$	13.5385	0.696347
$379$	10.4791	0.538275	0.269138	−	0.963102i	$-0.413261\pi$
$379$	10.4791	0.538275	0.269138	+	0.963102i	$0.413261\pi$
$380$	−14.1579	−0.726287
$381$	−9.65027	−0.494398
$382$	1.78711	0.0914366
$383$	−5.00780	−0.255887	−0.127943	−	0.991781i	$-0.540838\pi$
$383$	−5.00780	−0.255887	−0.127943	+	0.991781i	$0.540838\pi$
$384$	−33.8947	−1.72968
$385$	−1.06458	−0.0542558
$386$	−39.9061	−2.03117
$387$	−4.55777	−0.231684
$388$	−6.47190	−0.328561
$389$	−36.7639	−1.86400	−0.932001	−	0.362456i	$-0.881938\pi$
$389$	−36.7639	−1.86400	−0.932001	+	0.362456i	$0.881938\pi$
$390$	33.2719	1.68479
$391$	3.84476	0.194438
$392$	12.3794	0.625253
$393$	42.3090	2.13420
$394$	−59.7771	−3.01152
$395$	14.6388	0.736556
$396$	0.612400	0.0307743
$397$	21.5865	1.08339	0.541697	−	0.840574i	$-0.317782\pi$
$397$	21.5865	1.08339	0.541697	+	0.840574i	$0.317782\pi$
$398$	33.5980	1.68412
$399$	−3.79185	−0.189830
$400$	−3.46704	−0.173352
$401$	−27.6606	−1.38130	−0.690652	−	0.723187i	$-0.742677\pi$
$401$	−27.6606	−1.38130	−0.690652	+	0.723187i	$0.742677\pi$
$402$	44.4641	2.21767
$403$	−7.90956	−0.394003
$404$	−50.1870	−2.49690
$405$	−37.6920	−1.87293
$406$	−6.97606	−0.346216
$407$	0.618348	0.0306504
$408$	−5.02629	−0.248839
$409$	−1.09068	−0.0539308	−0.0269654	−	0.999636i	$-0.508584\pi$
$409$	−1.09068	−0.0539308	−0.0269654	+	0.999636i	$0.508584\pi$
$410$	−81.0495	−4.00275
$411$	−33.3579	−1.64542
$412$	−35.2820	−1.73822
$413$	7.30869	0.359637
$414$	8.05859	0.396058
$415$	−10.4609	−0.513507
$416$	13.3474	0.654409
$417$	32.2659	1.58007
$418$	0.630125	0.0308204
$419$	26.5368	1.29641	0.648203	−	0.761468i	$-0.275521\pi$
$419$	26.5368	1.29641	0.648203	+	0.761468i	$0.275521\pi$
$420$	31.0754	1.51632
$421$	−3.88363	−0.189276	−0.0946382	−	0.995512i	$-0.530169\pi$
$421$	−3.88363	−0.189276	−0.0946382	+	0.995512i	$0.530169\pi$
$422$	−47.8080	−2.32726
$423$	−6.31011	−0.306808
$424$	−28.9614	−1.40649
$425$	−6.91221	−0.335291
$426$	3.90116	0.189012
$427$	−12.7959	−0.619237
$428$	−3.23542	−0.156390
$429$	−0.902487	−0.0435725
$430$	38.4334	1.85342
$431$	18.6620	0.898917	0.449458	−	0.893301i	$-0.351617\pi$
$431$	18.6620	0.898917	0.449458	+	0.893301i	$0.351617\pi$
$432$	−2.06107	−0.0991632
$433$	19.0158	0.913843	0.456922	−	0.889507i	$-0.348952\pi$
$433$	19.0158	0.913843	0.456922	+	0.889507i	$0.348952\pi$
$434$	−12.1215	−0.581848
$435$	14.4801	0.694268
$436$	−47.7607	−2.28732
$437$	5.05344	0.241739
$438$	−30.3396	−1.44968
$439$	37.1105	1.77119	0.885593	−	0.464462i	$-0.153752\pi$
$439$	37.1105	1.77119	0.885593	+	0.464462i	$0.153752\pi$
$440$	−1.85477	−0.0884228
$441$	−4.52015	−0.215245
$442$	4.86513	0.231411
$443$	14.9892	0.712158	0.356079	−	0.934456i	$-0.384113\pi$
$443$	14.9892	0.712158	0.356079	+	0.934456i	$0.384113\pi$
$444$	−18.0498	−0.856606
$445$	16.9483	0.803427
$446$	25.1231	1.18962
$447$	−46.1301	−2.18188
$448$	18.9944	0.897400
$449$	2.06202	0.0973126	0.0486563	−	0.998816i	$-0.484506\pi$
$449$	2.06202	0.0973126	0.0486563	+	0.998816i	$0.484506\pi$
$450$	−14.4879	−0.682968
$451$	2.19843	0.103520
$452$	−25.3818	−1.19386
$453$	0.410310	0.0192781
$454$	26.4189	1.23990
$455$	−10.8034	−0.506473
$456$	−6.60641	−0.309373
$457$	10.0544	0.470326	0.235163	−	0.971956i	$-0.424438\pi$
$457$	10.0544	0.470326	0.235163	+	0.971956i	$0.424438\pi$
$458$	−28.5779	−1.33536
$459$	−4.10913	−0.191798
$460$	−41.4144	−1.93096
$461$	−15.0217	−0.699631	−0.349816	−	0.936819i	$-0.613756\pi$
$461$	−15.0217	−0.699631	−0.349816	+	0.936819i	$0.613756\pi$
$462$	−1.38307	−0.0643461
$463$	−17.3713	−0.807312	−0.403656	−	0.914911i	$-0.632261\pi$
$463$	−17.3713	−0.807312	−0.403656	+	0.914911i	$0.632261\pi$
$464$	1.06202	0.0493029
$465$	25.1603	1.16678
$466$	19.0685	0.883330
$467$	−31.4642	−1.45599	−0.727995	−	0.685583i	$-0.759548\pi$
$467$	−31.4642	−1.45599	−0.727995	+	0.685583i	$0.759548\pi$
$468$	6.21471	0.287275
$469$	−14.4376	−0.666665
$470$	53.2100	2.45440
$471$	−4.86500	−0.224167
$472$	12.7337	0.586115
$473$	−1.04249	−0.0479337
$474$	19.0183	0.873538
$475$	−9.08519	−0.416857
$476$	4.54394	0.208271
$477$	10.5748	0.484188
$478$	−16.6356	−0.760897
$479$	−22.5655	−1.03104	−0.515522	−	0.856876i	$-0.672402\pi$
$479$	−22.5655	−1.03104	−0.515522	+	0.856876i	$0.672402\pi$
$480$	−42.4580	−1.93794
$481$	6.27507	0.286119
$482$	32.8416	1.49589
$483$	−11.0918	−0.504696
$484$	−34.1903	−1.55411
$485$	−7.15717	−0.324990
$486$	−21.0721	−0.955852
$487$	−33.1880	−1.50389	−0.751947	−	0.659224i	$-0.770885\pi$
$487$	−33.1880	−1.50389	−0.751947	+	0.659224i	$0.770885\pi$
$488$	−22.2938	−1.00919
$489$	−48.8634	−2.20968
$490$	38.1162	1.72191
$491$	−32.6835	−1.47499	−0.737493	−	0.675354i	$-0.763991\pi$
$491$	−32.6835	−1.47499	−0.737493	+	0.675354i	$0.763991\pi$
$492$	−64.1731	−2.89315
$493$	2.11733	0.0953598
$494$	6.39458	0.287706
$495$	0.677243	0.0304398
$496$	1.84534	0.0828581
$497$	−1.26671	−0.0568198
$498$	−13.5905	−0.609007
$499$	37.3482	1.67194	0.835968	−	0.548778i	$-0.184907\pi$
$499$	37.3482	1.67194	0.835968	+	0.548778i	$0.184907\pi$
$500$	20.5976	0.921154
$501$	−24.8645	−1.11086
$502$	20.9104	0.933278
$503$	21.1029	0.940932	0.470466	−	0.882418i	$-0.344086\pi$
$503$	21.1029	0.940932	0.470466	+	0.882418i	$0.344086\pi$
$504$	3.42075	0.152372
$505$	−55.5010	−2.46976
$506$	1.84323	0.0819414
$507$	16.6006	0.737257
$508$	15.1998	0.674383
$509$	−0.169028	−0.00749205	−0.00374603	−	0.999993i	$-0.501192\pi$
$509$	−0.169028	−0.00749205	−0.00374603	+	0.999993i	$0.501192\pi$
$510$	−15.4760	−0.685289
$511$	9.85131	0.435796
$512$	−5.65868	−0.250081
$513$	−5.40092	−0.238456
$514$	−64.5153	−2.84565
$515$	−39.0178	−1.71933
$516$	30.4307	1.33963
$517$	−1.44330	−0.0634762
$518$	9.61658	0.422528
$519$	51.4337	2.25769
$520$	−18.8224	−0.825419
$521$	−11.3618	−0.497772	−0.248886	−	0.968533i	$-0.580064\pi$
$521$	−11.3618	−0.497772	−0.248886	+	0.968533i	$0.580064\pi$
$522$	4.43791	0.194242
$523$	−14.4223	−0.630644	−0.315322	−	0.948985i	$-0.602113\pi$
$523$	−14.4223	−0.630644	−0.315322	+	0.948985i	$0.602113\pi$
$524$	−66.6395	−2.91116
$525$	19.9412	0.870304
$526$	−57.0316	−2.48670
$527$	3.67903	0.160261
$528$	0.210554	0.00916320
$529$	−8.21782	−0.357296
$530$	−89.1723	−3.87340
$531$	−4.64952	−0.201772
$532$	5.97242	0.258937
$533$	22.3100	0.966351
$534$	22.0188	0.952845
$535$	−3.57800	−0.154691
$536$	−25.1540	−1.08649
$537$	−17.1648	−0.740718
$538$	47.3056	2.03949
$539$	−1.03389	−0.0445326
$540$	44.2621	1.90474
$541$	−2.75855	−0.118599	−0.0592997	−	0.998240i	$-0.518887\pi$
$541$	−2.75855	−0.118599	−0.0592997	+	0.998240i	$0.518887\pi$
$542$	−43.9766	−1.88896
$543$	20.7869	0.892053
$544$	−6.20835	−0.266181
$545$	−52.8178	−2.26247
$546$	−14.0355	−0.600665
$547$	0.756753	0.0323564	0.0161782	−	0.999869i	$-0.494850\pi$
$547$	0.756753	0.0323564	0.0161782	+	0.999869i	$0.494850\pi$
$548$	52.5409	2.24444
$549$	8.14027	0.347418
$550$	−3.31380	−0.141301
$551$	2.78295	0.118558
$552$	−19.3249	−0.822522
$553$	−6.17525	−0.262598
$554$	−37.0830	−1.57551
$555$	−19.9610	−0.847298
$556$	−50.8209	−2.15529
$557$	−5.93820	−0.251610	−0.125805	−	0.992055i	$-0.540151\pi$
$557$	−5.93820	−0.251610	−0.125805	+	0.992055i	$0.540151\pi$
$558$	7.71122	0.326442
$559$	−10.5793	−0.447457
$560$	2.52049	0.106510
$561$	0.419780	0.0177231
$562$	54.9851	2.31940
$563$	−27.7644	−1.17013	−0.585066	−	0.810986i	$-0.698931\pi$
$563$	−27.7644	−1.17013	−0.585066	+	0.810986i	$0.698931\pi$
$564$	42.1305	1.77401
$565$	−28.0694	−1.18089
$566$	52.6178	2.21169
$567$	15.9001	0.667742
$568$	−2.20695	−0.0926015
$569$	−26.1875	−1.09784	−0.548919	−	0.835876i	$-0.684960\pi$
$569$	−26.1875	−1.09784	−0.548919	+	0.835876i	$0.684960\pi$
$570$	−20.3412	−0.851998
$571$	18.9621	0.793539	0.396770	−	0.917918i	$-0.370131\pi$
$571$	18.9621	0.793539	0.396770	+	0.917918i	$0.370131\pi$
$572$	1.42148	0.0594350
$573$	1.56482	0.0653712
$574$	34.1901	1.42707
$575$	−26.5758	−1.10829
$576$	−12.0835	−0.503480
$577$	19.9237	0.829433	0.414716	−	0.909951i	$-0.363881\pi$
$577$	19.9237	0.829433	0.414716	+	0.909951i	$0.363881\pi$
$578$	−2.26295	−0.0941264
$579$	−34.9423	−1.45215
$580$	−22.8072	−0.947016
$581$	4.41286	0.183076
$582$	−9.29839	−0.385431
$583$	2.41876	0.100175
$584$	17.1636	0.710234
$585$	6.87275	0.284153
$586$	38.7036	1.59883
$587$	19.4781	0.803947	0.401974	−	0.915651i	$-0.368324\pi$
$587$	19.4781	0.803947	0.401974	+	0.915651i	$0.368324\pi$
$588$	30.1795	1.24458
$589$	4.83560	0.199248
$590$	39.2071	1.61413
$591$	−52.3416	−2.15304
$592$	−1.46400	−0.0601701
$593$	−12.0290	−0.493972	−0.246986	−	0.969019i	$-0.579440\pi$
$593$	−12.0290	−0.493972	−0.246986	+	0.969019i	$0.579440\pi$
$594$	−1.96997	−0.0808287
$595$	5.02507	0.206008
$596$	72.6580	2.97619
$597$	29.4188	1.20403
$598$	18.7053	0.764915
$599$	−3.11898	−0.127438	−0.0637189	−	0.997968i	$-0.520296\pi$
$599$	−3.11898	−0.127438	−0.0637189	+	0.997968i	$0.520296\pi$
$600$	34.7428	1.41837
$601$	−13.8694	−0.565745	−0.282873	−	0.959157i	$-0.591287\pi$
$601$	−13.8694	−0.565745	−0.282873	+	0.959157i	$0.591287\pi$
$602$	−16.2128	−0.660786
$603$	9.18464	0.374027
$604$	−0.646266	−0.0262962
$605$	−37.8106	−1.53722
$606$	−72.1053	−2.92908
$607$	15.2030	0.617071	0.308536	−	0.951213i	$-0.400161\pi$
$607$	15.2030	0.617071	0.308536	+	0.951213i	$0.400161\pi$
$608$	−8.16007	−0.330935
$609$	−6.10833	−0.247522
$610$	−68.6429	−2.77927
$611$	−14.6468	−0.592545
$612$	−2.89069	−0.116849
$613$	−28.2229	−1.13991	−0.569956	−	0.821675i	$-0.693040\pi$
$613$	−28.2229	−1.13991	−0.569956	+	0.821675i	$0.693040\pi$
$614$	50.2878	2.02945
$615$	−70.9680	−2.86171
$616$	0.782421	0.0315247
$617$	−7.66646	−0.308640	−0.154320	−	0.988021i	$-0.549319\pi$
$617$	−7.66646	−0.308640	−0.154320	+	0.988021i	$0.549319\pi$
$618$	−50.6908	−2.03908
$619$	10.7214	0.430930	0.215465	−	0.976512i	$-0.430873\pi$
$619$	10.7214	0.430930	0.215465	+	0.976512i	$0.430873\pi$
$620$	−39.6292	−1.59155
$621$	−15.7986	−0.633977
$622$	−23.8279	−0.955411
$623$	−7.14952	−0.286439
$624$	2.13673	0.0855376
$625$	−11.7824	−0.471298
$626$	−26.7368	−1.06862
$627$	0.551746	0.0220346
$628$	7.66270	0.305775
$629$	−2.91876	−0.116379
$630$	10.5325	0.419626
$631$	−30.8076	−1.22643	−0.613215	−	0.789916i	$-0.710124\pi$
$631$	−30.8076	−1.22643	−0.613215	+	0.789916i	$0.710124\pi$
$632$	−10.7589	−0.427967
$633$	−41.8613	−1.66384
$634$	60.5150	2.40336
$635$	16.8092	0.667054
$636$	−70.6045	−2.79965
$637$	−10.4920	−0.415708
$638$	1.01507	0.0401872
$639$	0.805836	0.0318784
$640$	59.0392	2.33373
$641$	−4.93510	−0.194925	−0.0974624	−	0.995239i	$-0.531073\pi$
$641$	−4.93510	−0.194925	−0.0974624	+	0.995239i	$0.531073\pi$
$642$	−4.64844	−0.183459
$643$	11.0893	0.437318	0.218659	−	0.975801i	$-0.429832\pi$
$643$	11.0893	0.437318	0.218659	+	0.975801i	$0.429832\pi$
$644$	17.4704	0.688429
$645$	33.6528	1.32508
$646$	−2.97435	−0.117024
$647$	36.4971	1.43485	0.717425	−	0.696636i	$-0.245321\pi$
$647$	36.4971	1.43485	0.717425	+	0.696636i	$0.245321\pi$
$648$	27.7022	1.08824
$649$	−1.06347	−0.0417450
$650$	−33.6288	−1.31903
$651$	−10.6137	−0.415984
$652$	76.9631	3.01411
$653$	−48.7767	−1.90878	−0.954391	−	0.298561i	$-0.903493\pi$
$653$	−48.7767	−1.90878	−0.954391	+	0.298561i	$0.903493\pi$
$654$	−68.6194	−2.68323
$655$	−73.6955	−2.87952
$656$	−5.20501	−0.203222
$657$	−6.26704	−0.244500
$658$	−22.4463	−0.875046
$659$	9.86268	0.384196	0.192098	−	0.981376i	$-0.438471\pi$
$659$	9.86268	0.384196	0.192098	+	0.981376i	$0.438471\pi$
$660$	−4.52172	−0.176008
$661$	10.5618	0.410806	0.205403	−	0.978677i	$-0.434149\pi$
$661$	10.5618	0.410806	0.205403	+	0.978677i	$0.434149\pi$
$662$	19.0739	0.741329
$663$	4.25997	0.165444
$664$	7.68837	0.298367
$665$	6.60481	0.256123
$666$	−6.11771	−0.237056
$667$	8.14063	0.315206
$668$	39.1632	1.51527
$669$	21.9982	0.850498
$670$	−77.4495	−2.99214
$671$	1.86191	0.0718781
$672$	17.9106	0.690917
$673$	44.1316	1.70115	0.850574	−	0.525856i	$-0.176255\pi$
$673$	44.1316	1.70115	0.850574	+	0.525856i	$0.176255\pi$
$674$	−16.7453	−0.645005
$675$	28.4031	1.09324
$676$	−26.1470	−1.00565
$677$	−16.4559	−0.632450	−0.316225	−	0.948684i	$-0.602415\pi$
$677$	−16.4559	−0.632450	−0.316225	+	0.948684i	$0.602415\pi$
$678$	−36.4669	−1.40050
$679$	3.01920	0.115866
$680$	8.75501	0.335739
$681$	23.1328	0.886450
$682$	1.76377	0.0675383
$683$	−21.9596	−0.840261	−0.420130	−	0.907464i	$-0.638016\pi$
$683$	−21.9596	−0.840261	−0.420130	+	0.907464i	$0.638016\pi$
$684$	−3.79943	−0.145275
$685$	58.1042	2.22005
$686$	−39.1422	−1.49446
$687$	−25.0232	−0.954693
$688$	2.46820	0.0940992
$689$	24.5459	0.935123
$690$	−59.5015	−2.26518
$691$	−7.92521	−0.301489	−0.150745	−	0.988573i	$-0.548167\pi$
$691$	−7.92521	−0.301489	−0.150745	+	0.988573i	$0.548167\pi$
$692$	−81.0115	−3.07960
$693$	−0.285690	−0.0108525
$694$	70.9696	2.69397
$695$	−56.2021	−2.13187
$696$	−10.6423	−0.403396
$697$	−10.3772	−0.393063
$698$	−73.0213	−2.76390
$699$	16.6966	0.631523
$700$	−31.4087	−1.18714
$701$	−18.6592	−0.704747	−0.352374	−	0.935859i	$-0.614625\pi$
$701$	−18.6592	−0.704747	−0.352374	+	0.935859i	$0.614625\pi$
$702$	−19.9915	−0.754529
$703$	−3.83634	−0.144690
$704$	−2.76384	−0.104166
$705$	46.5914	1.75473
$706$	2.26295	0.0851673
$707$	23.4127	0.880525
$708$	31.0432	1.16668
$709$	−30.2968	−1.13782	−0.568911	−	0.822399i	$-0.692635\pi$
$709$	−30.2968	−1.13782	−0.568911	+	0.822399i	$0.692635\pi$
$710$	−6.79521	−0.255020
$711$	3.92847	0.147329
$712$	−12.4563	−0.466821
$713$	14.1450	0.529734
$714$	6.52843	0.244320
$715$	1.57199	0.0587891
$716$	27.0358	1.01037
$717$	−14.5664	−0.543992
$718$	58.4242	2.18037
$719$	3.34874	0.124887	0.0624434	−	0.998049i	$-0.480111\pi$
$719$	3.34874	0.124887	0.0624434	+	0.998049i	$0.480111\pi$
$720$	−1.60344	−0.0597568
$721$	16.4594	0.612978
$722$	39.0867	1.45466
$723$	28.7565	1.06947
$724$	−32.7408	−1.21680
$725$	−14.6354	−0.543546
$726$	−49.1224	−1.82310
$727$	−46.2993	−1.71715	−0.858573	−	0.512691i	$-0.828649\pi$
$727$	−46.2993	−1.71715	−0.858573	+	0.512691i	$0.828649\pi$
$728$	7.94011	0.294280
$729$	14.3113	0.530048
$730$	52.8468	1.95595
$731$	4.92082	0.182003
$732$	−54.3498	−2.00883
$733$	7.49635	0.276884	0.138442	−	0.990371i	$-0.455791\pi$
$733$	7.49635	0.276884	0.138442	+	0.990371i	$0.455791\pi$
$734$	72.5131	2.67651
$735$	33.3751	1.23106
$736$	−23.8696	−0.879846
$737$	2.10078	0.0773834
$738$	−21.7505	−0.800646
$739$	−28.9311	−1.06425	−0.532123	−	0.846667i	$-0.678606\pi$
$739$	−28.9311	−1.06425	−0.532123	+	0.846667i	$0.678606\pi$
$740$	31.4399	1.15575
$741$	5.59918	0.205691
$742$	37.6167	1.38095
$743$	−7.01866	−0.257490	−0.128745	−	0.991678i	$-0.541095\pi$
$743$	−7.01866	−0.257490	−0.128745	+	0.991678i	$0.541095\pi$
$744$	−18.4919	−0.677945
$745$	80.3513	2.94384
$746$	−25.9294	−0.949342
$747$	−2.80730	−0.102714
$748$	−0.661181	−0.0241752
$749$	1.50935	0.0551506
$750$	29.5933	1.08059
$751$	−49.1567	−1.79375	−0.896877	−	0.442279i	$-0.854170\pi$
$751$	−49.1567	−1.79375	−0.896877	+	0.442279i	$0.854170\pi$
$752$	3.41716	0.124611
$753$	18.3094	0.667233
$754$	10.3011	0.375144
$755$	−0.714696	−0.0260104
$756$	−18.6716	−0.679081
$757$	−26.3063	−0.956120	−0.478060	−	0.878327i	$-0.658660\pi$
$757$	−26.3063	−0.956120	−0.478060	+	0.878327i	$0.658660\pi$
$758$	−23.7137	−0.861320
$759$	1.61395	0.0585828
$760$	11.5073	0.417414
$761$	−21.6883	−0.786200	−0.393100	−	0.919496i	$-0.628597\pi$
$761$	−21.6883	−0.786200	−0.393100	+	0.919496i	$0.628597\pi$
$762$	21.8381	0.791110
$763$	22.2808	0.806619
$764$	−2.46469	−0.0891695
$765$	−3.19677	−0.115579
$766$	11.3324	0.409456
$767$	−10.7923	−0.389686
$768$	25.0014	0.902159
$769$	10.9987	0.396624	0.198312	−	0.980139i	$-0.436454\pi$
$769$	10.9987	0.396624	0.198312	+	0.980139i	$0.436454\pi$
$770$	2.40908	0.0868173
$771$	−56.4904	−2.03445
$772$	55.0365	1.98081
$773$	−31.0721	−1.11758	−0.558792	−	0.829308i	$-0.688735\pi$
$773$	−31.0721	−1.11758	−0.558792	+	0.829308i	$0.688735\pi$
$774$	10.3140	0.370729
$775$	−25.4302	−0.913479
$776$	5.26024	0.188832
$777$	8.42040	0.302080
$778$	83.1948	2.98268
$779$	−13.6394	−0.488684
$780$	−45.8870	−1.64302
$781$	0.184317	0.00659539
$782$	−8.70050	−0.311129
$783$	−8.70038	−0.310926
$784$	2.44783	0.0874225
$785$	8.47406	0.302452
$786$	−95.7431	−3.41504
$787$	45.9628	1.63840	0.819198	−	0.573510i	$-0.194419\pi$
$787$	45.9628	1.63840	0.819198	+	0.573510i	$0.194419\pi$
$788$	82.4415	2.93686
$789$	−49.9376	−1.77783
$790$	−33.1268	−1.17860
$791$	11.8409	0.421013
$792$	−0.497747	−0.0176867
$793$	18.8949	0.670976
$794$	−48.8491	−1.73359
$795$	−78.0804	−2.76923
$796$	−46.3367	−1.64236
$797$	30.0384	1.06402	0.532008	−	0.846739i	$-0.321438\pi$
$797$	30.0384	1.06402	0.532008	+	0.846739i	$0.321438\pi$
$798$	8.58078	0.303756
$799$	6.81275	0.241018
$800$	42.9134	1.51722
$801$	4.54826	0.160705
$802$	62.5946	2.21029
$803$	−1.43345	−0.0505852
$804$	−61.3227	−2.16268
$805$	19.3202	0.680948
$806$	17.8990	0.630464
$807$	41.4214	1.45810
$808$	40.7911	1.43503
$809$	−43.4943	−1.52918	−0.764589	−	0.644518i	$-0.777058\pi$
$809$	−43.4943	−1.52918	−0.764589	+	0.644518i	$0.777058\pi$
$810$	85.2952	2.99697
$811$	−41.0824	−1.44260	−0.721298	−	0.692625i	$-0.756454\pi$
$811$	−41.0824	−1.44260	−0.721298	+	0.692625i	$0.756454\pi$
$812$	9.62103	0.337632
$813$	−38.5065	−1.35048
$814$	−1.39929	−0.0490451
$815$	85.1123	2.98135
$816$	−0.993871	−0.0347924
$817$	6.46778	0.226279
$818$	2.46816	0.0862972
$819$	−2.89922	−0.101307
$820$	111.779	3.90350
$821$	−5.24446	−0.183033	−0.0915165	−	0.995804i	$-0.529171\pi$
$821$	−5.24446	−0.183033	−0.0915165	+	0.995804i	$0.529171\pi$
$822$	75.4873	2.63292
$823$	7.89937	0.275355	0.137677	−	0.990477i	$-0.456036\pi$
$823$	7.89937	0.275355	0.137677	+	0.990477i	$0.456036\pi$
$824$	28.6765	0.998994
$825$	−2.90160	−0.101021
$826$	−16.5392	−0.575473
$827$	−12.5545	−0.436561	−0.218281	−	0.975886i	$-0.570045\pi$
$827$	−12.5545	−0.436561	−0.218281	+	0.975886i	$0.570045\pi$
$828$	−11.1140	−0.386238
$829$	−23.2133	−0.806230	−0.403115	−	0.915149i	$-0.632073\pi$
$829$	−23.2133	−0.806230	−0.403115	+	0.915149i	$0.632073\pi$
$830$	23.6726	0.821687
$831$	−32.4704	−1.12638
$832$	−28.0478	−0.972381
$833$	4.88021	0.169089
$834$	−73.0161	−2.52834
$835$	43.3099	1.49880
$836$	−0.869036	−0.0300563
$837$	−15.1176	−0.522541
$838$	−60.0514	−2.07444
$839$	−5.86226	−0.202388	−0.101194	−	0.994867i	$-0.532266\pi$
$839$	−5.86226	−0.202388	−0.101194	+	0.994867i	$0.532266\pi$
$840$	−25.2575	−0.871466
$841$	−24.5169	−0.845411
$842$	8.78846	0.302870
$843$	48.1456	1.65822
$844$	65.9344	2.26955
$845$	−28.9155	−0.994725
$846$	14.2795	0.490938
$847$	15.9501	0.548052
$848$	−5.72666	−0.196654
$849$	46.0729	1.58122
$850$	15.6420	0.536516
$851$	−11.2219	−0.384683
$852$	−5.38029	−0.184326
$853$	−6.56941	−0.224932	−0.112466	−	0.993656i	$-0.535875\pi$
$853$	−6.56941	−0.224932	−0.112466	+	0.993656i	$0.535875\pi$
$854$	28.9565	0.990870
$855$	−4.20173	−0.143696
$856$	2.62969	0.0898810
$857$	−41.8906	−1.43096	−0.715478	−	0.698635i	$-0.753791\pi$
$857$	−41.8906	−1.43096	−0.715478	+	0.698635i	$0.753791\pi$
$858$	2.04228	0.0697224
$859$	−34.4381	−1.17501	−0.587506	−	0.809220i	$-0.699890\pi$
$859$	−34.4381	−1.17501	−0.587506	+	0.809220i	$0.699890\pi$
$860$	−53.0054	−1.80747
$861$	29.9373	1.02026
$862$	−42.2312	−1.43840
$863$	−23.6287	−0.804330	−0.402165	−	0.915567i	$-0.631742\pi$
$863$	−23.6287	−0.804330	−0.402165	+	0.915567i	$0.631742\pi$
$864$	25.5109	0.867900
$865$	−89.5894	−3.04613
$866$	−43.0319	−1.46228
$867$	−1.98147	−0.0672942
$868$	16.7173	0.567422
$869$	0.898550	0.0304812
$870$	−32.7678	−1.11093
$871$	21.3190	0.722367
$872$	38.8190	1.31458
$873$	−1.92070	−0.0650059
$874$	−11.4357	−0.386818
$875$	−9.60898	−0.324843
$876$	41.8429	1.41374
$877$	1.71058	0.0577620	0.0288810	−	0.999583i	$-0.490806\pi$
$877$	1.71058	0.0577620	0.0288810	+	0.999583i	$0.490806\pi$
$878$	−83.9792	−2.83416
$879$	33.8894	1.14306
$880$	−0.366752	−0.0123632
$881$	1.22716	0.0413439	0.0206720	−	0.999786i	$-0.493419\pi$
$881$	1.22716	0.0413439	0.0206720	+	0.999786i	$0.493419\pi$
$882$	10.2289	0.344425
$883$	39.1025	1.31590	0.657952	−	0.753060i	$-0.271423\pi$
$883$	39.1025	1.31590	0.657952	+	0.753060i	$0.271423\pi$
$884$	−6.70974	−0.225673
$885$	34.3302	1.15400
$886$	−33.9198	−1.13956
$887$	−21.5995	−0.725240	−0.362620	−	0.931937i	$-0.618118\pi$
$887$	−21.5995	−0.725240	−0.362620	+	0.931937i	$0.618118\pi$
$888$	14.6706	0.492312
$889$	−7.09085	−0.237820
$890$	−38.3532	−1.28560
$891$	−2.31360	−0.0775084
$892$	−34.6486	−1.16012
$893$	8.95447	0.299650
$894$	104.390	3.49133
$895$	29.8984	0.999395
$896$	−24.9052	−0.832026
$897$	16.3786	0.546865
$898$	−4.66624	−0.155715
$899$	7.78971	0.259802
$900$	19.9810	0.666034
$901$	−11.4172	−0.380361
$902$	−4.97494	−0.165648
$903$	−14.1962	−0.472419
$904$	20.6299	0.686140
$905$	−36.2076	−1.20358
$906$	−0.928512	−0.0308478
$907$	−25.7395	−0.854667	−0.427334	−	0.904094i	$-0.640547\pi$
$907$	−25.7395	−0.854667	−0.427334	+	0.904094i	$0.640547\pi$
$908$	−36.4357	−1.20916
$909$	−14.8943	−0.494012
$910$	24.4477	0.810432
$911$	18.4368	0.610838	0.305419	−	0.952218i	$-0.401203\pi$
$911$	18.4368	0.610838	0.305419	+	0.952218i	$0.401203\pi$
$912$	−1.30631	−0.0432564
$913$	−0.642108	−0.0212507
$914$	−22.7527	−0.752592
$915$	−60.1046	−1.98700
$916$	39.4132	1.30225
$917$	31.0879	1.02661
$918$	9.29876	0.306905
$919$	−14.0476	−0.463387	−0.231694	−	0.972789i	$-0.574427\pi$
$919$	−14.0476	−0.463387	−0.231694	+	0.972789i	$0.574427\pi$
$920$	33.6609	1.10977
$921$	44.0326	1.45093
$922$	33.9934	1.11951
$923$	1.87047	0.0615674
$924$	1.90745	0.0627507
$925$	20.1751	0.663353
$926$	39.3104	1.29182
$927$	−10.4708	−0.343907
$928$	−13.1451	−0.431510
$929$	52.7785	1.73161	0.865804	−	0.500383i	$-0.166808\pi$
$929$	52.7785	1.73161	0.865804	+	0.500383i	$0.166808\pi$
$930$	−56.9366	−1.86702
$931$	6.41440	0.210223
$932$	−26.2983	−0.861428
$933$	−20.8640	−0.683057
$934$	71.2020	2.32980
$935$	−0.731190	−0.0239125
$936$	−5.05120	−0.165104
$937$	45.1361	1.47453	0.737266	−	0.675603i	$-0.236117\pi$
$937$	45.1361	1.47453	0.737266	+	0.675603i	$0.236117\pi$
$938$	32.6715	1.06676
$939$	−23.4111	−0.763993
$940$	−73.3846	−2.39354
$941$	−30.9374	−1.00853	−0.504264	−	0.863549i	$-0.668236\pi$
$941$	−30.9374	−1.00853	−0.504264	+	0.863549i	$0.668236\pi$
$942$	11.0093	0.358701
$943$	−39.8977	−1.29925
$944$	2.51788	0.0819502
$945$	−20.6487	−0.671702
$946$	2.35910	0.0767010
$947$	6.11462	0.198698	0.0993492	−	0.995053i	$-0.468324\pi$
$947$	6.11462	0.198698	0.0993492	+	0.995053i	$0.468324\pi$
$948$	−26.2290	−0.851879
$949$	−14.5468	−0.472209
$950$	20.5593	0.667033
$951$	52.9877	1.71824
$952$	−3.69323	−0.119698
$953$	50.6097	1.63941	0.819704	−	0.572787i	$-0.194138\pi$
$953$	50.6097	1.63941	0.819704	+	0.572787i	$0.194138\pi$
$954$	−23.9303	−0.774773
$955$	−2.72567	−0.0882005
$956$	22.9430	0.742031
$957$	0.888812	0.0287312
$958$	51.0646	1.64982
$959$	−24.5108	−0.791495
$960$	89.2200	2.87956
$961$	−17.4648	−0.563379
$962$	−14.2002	−0.457832
$963$	−0.960195	−0.0309418
$964$	−45.2934	−1.45880
$965$	60.8640	1.95928
$966$	25.1003	0.807588
$967$	22.5409	0.724866	0.362433	−	0.932010i	$-0.381946\pi$
$967$	22.5409	0.724866	0.362433	+	0.932010i	$0.381946\pi$
$968$	27.7893	0.893182
$969$	−2.60438	−0.0836649
$970$	16.1963	0.520033
$971$	−46.0528	−1.47790	−0.738952	−	0.673758i	$-0.764679\pi$
$971$	−46.0528	−1.47790	−0.738952	+	0.673758i	$0.764679\pi$
$972$	29.0616	0.932152
$973$	23.7084	0.760057
$974$	75.1029	2.40645
$975$	−29.4458	−0.943021
$976$	−4.40826	−0.141105
$977$	33.7648	1.08023	0.540116	−	0.841590i	$-0.318380\pi$
$977$	33.7648	1.08023	0.540116	+	0.841590i	$0.318380\pi$
$978$	110.575	3.53581
$979$	1.04031	0.0332486
$980$	−52.5679	−1.67922
$981$	−14.1742	−0.452548
$982$	73.9612	2.36020
$983$	−46.5634	−1.48514	−0.742571	−	0.669767i	$-0.766394\pi$
$983$	−46.5634	−1.48514	−0.742571	+	0.669767i	$0.766394\pi$
$984$	52.1587	1.66276
$985$	91.1707	2.90494
$986$	−4.79141	−0.152590
$987$	−19.6542	−0.625601
$988$	−8.81909	−0.280572
$989$	18.9194	0.601601
$990$	−1.53257	−0.0487082
$991$	−29.6582	−0.942122	−0.471061	−	0.882101i	$-0.656129\pi$
$991$	−29.6582	−0.942122	−0.471061	+	0.882101i	$0.656129\pi$
$992$	−22.8407	−0.725193
$993$	16.7014	0.530002
$994$	2.86651	0.0909201
$995$	−51.2430	−1.62451
$996$	18.7434	0.593907
$997$	−40.0257	−1.26763	−0.633814	−	0.773486i	$-0.718511\pi$
$997$	−40.0257	−1.26763	−0.633814	+	0.773486i	$0.718511\pi$
$998$	−84.5172	−2.67535
$999$	11.9936	0.379460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.14	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.14	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26295 q^{2} -1.98147 q^{3} +3.12095 q^{4} +3.45141 q^{5} +4.48397 q^{6} -1.45595 q^{7} -2.53665 q^{8} +0.926221 q^{9} +O(q^{10})\)	\(q-2.26295 q^{2} -1.98147 q^{3} +3.12095 q^{4} +3.45141 q^{5} +4.48397 q^{6} -1.45595 q^{7} -2.53665 q^{8} +0.926221 q^{9} -7.81036 q^{10} +0.211853 q^{11} -6.18406 q^{12} +2.14991 q^{13} +3.29474 q^{14} -6.83886 q^{15} -0.501583 q^{16} -1.00000 q^{17} -2.09599 q^{18} -1.31437 q^{19} +10.7717 q^{20} +2.88492 q^{21} -0.479412 q^{22} -3.84476 q^{23} +5.02629 q^{24} +6.91221 q^{25} -4.86513 q^{26} +4.10913 q^{27} -4.54394 q^{28} -2.11733 q^{29} +15.4760 q^{30} -3.67903 q^{31} +6.20835 q^{32} -0.419780 q^{33} +2.26295 q^{34} -5.02507 q^{35} +2.89069 q^{36} +2.91876 q^{37} +2.97435 q^{38} -4.25997 q^{39} -8.75501 q^{40} +10.3772 q^{41} -6.52843 q^{42} -4.92082 q^{43} +0.661181 q^{44} +3.19677 q^{45} +8.70050 q^{46} -6.81275 q^{47} +0.993871 q^{48} -4.88021 q^{49} -15.6420 q^{50} +1.98147 q^{51} +6.70974 q^{52} +11.4172 q^{53} -9.29876 q^{54} +0.731190 q^{55} +3.69323 q^{56} +2.60438 q^{57} +4.79141 q^{58} -5.01988 q^{59} -21.3437 q^{60} +8.78869 q^{61} +8.32546 q^{62} -1.34853 q^{63} -13.0460 q^{64} +7.42020 q^{65} +0.949941 q^{66} +9.91625 q^{67} -3.12095 q^{68} +7.61828 q^{69} +11.3715 q^{70} +0.870025 q^{71} -2.34950 q^{72} -6.76624 q^{73} -6.60502 q^{74} -13.6963 q^{75} -4.10208 q^{76} -0.308447 q^{77} +9.64011 q^{78} +4.24139 q^{79} -1.73117 q^{80} -10.9208 q^{81} -23.4830 q^{82} -3.03092 q^{83} +9.00368 q^{84} -3.45141 q^{85} +11.1356 q^{86} +4.19543 q^{87} -0.537396 q^{88} +4.91055 q^{89} -7.23412 q^{90} -3.13016 q^{91} -11.9993 q^{92} +7.28988 q^{93} +15.4169 q^{94} -4.53642 q^{95} -12.3017 q^{96} -2.07370 q^{97} +11.0437 q^{98} +0.196222 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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