LMFDB - Embedded newform 4021.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1078466528$
Analytic rank:	$1$
Dimension:	$151$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69273 q^{2} +1.85515 q^{3} +5.25082 q^{4} +1.44838 q^{5} -4.99542 q^{6} +4.11859 q^{7} -8.75359 q^{8} +0.441579 q^{9} +O(q^{10})$	\(q-2.69273 q^{2} +1.85515 q^{3} +5.25082 q^{4} +1.44838 q^{5} -4.99542 q^{6} +4.11859 q^{7} -8.75359 q^{8} +0.441579 q^{9} -3.90011 q^{10} -4.00658 q^{11} +9.74105 q^{12} -0.291050 q^{13} -11.0903 q^{14} +2.68697 q^{15} +13.0695 q^{16} -5.21222 q^{17} -1.18906 q^{18} -1.94144 q^{19} +7.60520 q^{20} +7.64060 q^{21} +10.7887 q^{22} -4.43715 q^{23} -16.2392 q^{24} -2.90219 q^{25} +0.783720 q^{26} -4.74625 q^{27} +21.6260 q^{28} -2.59272 q^{29} -7.23529 q^{30} -1.29908 q^{31} -17.6854 q^{32} -7.43281 q^{33} +14.0351 q^{34} +5.96530 q^{35} +2.31865 q^{36} -6.89791 q^{37} +5.22777 q^{38} -0.539941 q^{39} -12.6786 q^{40} -1.89251 q^{41} -20.5741 q^{42} +4.64323 q^{43} -21.0378 q^{44} +0.639576 q^{45} +11.9481 q^{46} +11.2511 q^{47} +24.2458 q^{48} +9.96281 q^{49} +7.81482 q^{50} -9.66944 q^{51} -1.52825 q^{52} +0.362232 q^{53} +12.7804 q^{54} -5.80307 q^{55} -36.0525 q^{56} -3.60165 q^{57} +6.98150 q^{58} +5.58855 q^{59} +14.1088 q^{60} +1.70945 q^{61} +3.49807 q^{62} +1.81868 q^{63} +21.4832 q^{64} -0.421552 q^{65} +20.0146 q^{66} -2.27753 q^{67} -27.3684 q^{68} -8.23157 q^{69} -16.0630 q^{70} -10.6241 q^{71} -3.86540 q^{72} +4.85967 q^{73} +18.5742 q^{74} -5.38399 q^{75} -10.1941 q^{76} -16.5015 q^{77} +1.45392 q^{78} -6.21736 q^{79} +18.9296 q^{80} -10.1297 q^{81} +5.09602 q^{82} -16.6630 q^{83} +40.1194 q^{84} -7.54929 q^{85} -12.5030 q^{86} -4.80988 q^{87} +35.0720 q^{88} -4.73527 q^{89} -1.72221 q^{90} -1.19872 q^{91} -23.2987 q^{92} -2.40998 q^{93} -30.2963 q^{94} -2.81194 q^{95} -32.8091 q^{96} -9.29060 q^{97} -26.8272 q^{98} -1.76922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) $ 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * 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 $

$2$	−2.69273	−1.90405	−0.952025	−	0.306019i	$-0.901003\pi$
$2$	−2.69273	−1.90405	−0.952025	+	0.306019i	$0.901003\pi$
$3$	1.85515	1.07107	0.535535	−	0.844513i	$-0.320110\pi$
$3$	1.85515	1.07107	0.535535	+	0.844513i	$0.320110\pi$
$4$	5.25082	2.62541
$5$	1.44838	0.647737	0.323868	−	0.946102i	$-0.395017\pi$
$5$	1.44838	0.647737	0.323868	+	0.946102i	$0.395017\pi$
$6$	−4.99542	−2.03937
$7$	4.11859	1.55668	0.778341	−	0.627842i	$-0.216062\pi$
$7$	4.11859	1.55668	0.778341	+	0.627842i	$0.216062\pi$
$8$	−8.75359	−3.09486
$9$	0.441579	0.147193
$10$	−3.90011	−1.23332
$11$	−4.00658	−1.20803	−0.604015	−	0.796973i	$-0.706433\pi$
$11$	−4.00658	−1.20803	−0.604015	+	0.796973i	$0.706433\pi$
$12$	9.74105	2.81200
$13$	−0.291050	−0.0807227	−0.0403613	−	0.999185i	$-0.512851\pi$
$13$	−0.291050	−0.0807227	−0.0403613	+	0.999185i	$0.512851\pi$
$14$	−11.0903	−2.96400
$15$	2.68697	0.693772
$16$	13.0695	3.26736
$17$	−5.21222	−1.26415	−0.632074	−	0.774908i	$-0.717796\pi$
$17$	−5.21222	−1.26415	−0.632074	+	0.774908i	$0.717796\pi$
$18$	−1.18906	−0.280263
$19$	−1.94144	−0.445396	−0.222698	−	0.974887i	$-0.571486\pi$
$19$	−1.94144	−0.445396	−0.222698	+	0.974887i	$0.571486\pi$
$20$	7.60520	1.70057
$21$	7.64060	1.66732
$22$	10.7887	2.30015
$23$	−4.43715	−0.925209	−0.462605	−	0.886565i	$-0.653085\pi$
$23$	−4.43715	−0.925209	−0.462605	+	0.886565i	$0.653085\pi$
$24$	−16.2392	−3.31482
$25$	−2.90219	−0.580437
$26$	0.783720	0.153700
$27$	−4.74625	−0.913417
$28$	21.6260	4.08693
$29$	−2.59272	−0.481456	−0.240728	−	0.970593i	$-0.577386\pi$
$29$	−2.59272	−0.481456	−0.240728	+	0.970593i	$0.577386\pi$
$30$	−7.23529	−1.32098
$31$	−1.29908	−0.233321	−0.116660	−	0.993172i	$-0.537219\pi$
$31$	−1.29908	−0.233321	−0.116660	+	0.993172i	$0.537219\pi$
$32$	−17.6854	−3.12637
$33$	−7.43281	−1.29389
$34$	14.0351	2.40700
$35$	5.96530	1.00832
$36$	2.31865	0.386442
$37$	−6.89791	−1.13401	−0.567005	−	0.823714i	$-0.691898\pi$
$37$	−6.89791	−1.13401	−0.567005	+	0.823714i	$0.691898\pi$
$38$	5.22777	0.848057
$39$	−0.539941	−0.0864597
$40$	−12.6786	−2.00466
$41$	−1.89251	−0.295560	−0.147780	−	0.989020i	$-0.547213\pi$
$41$	−1.89251	−0.295560	−0.147780	+	0.989020i	$0.547213\pi$
$42$	−20.5741	−3.17466
$43$	4.64323	0.708087	0.354043	−	0.935229i	$-0.384807\pi$
$43$	4.64323	0.708087	0.354043	+	0.935229i	$0.384807\pi$
$44$	−21.0378	−3.17157
$45$	0.639576	0.0953423
$46$	11.9481	1.76165
$47$	11.2511	1.64115	0.820573	−	0.571542i	$-0.193654\pi$
$47$	11.2511	1.64115	0.820573	+	0.571542i	$0.193654\pi$
$48$	24.2458	3.49958
$49$	9.96281	1.42326
$50$	7.81482	1.10518
$51$	−9.66944	−1.35399
$52$	−1.52825	−0.211930
$53$	0.362232	0.0497564	0.0248782	−	0.999690i	$-0.492080\pi$
$53$	0.362232	0.0497564	0.0248782	+	0.999690i	$0.492080\pi$
$54$	12.7804	1.73919
$55$	−5.80307	−0.782486
$56$	−36.0525	−4.81772
$57$	−3.60165	−0.477051
$58$	6.98150	0.916716
$59$	5.58855	0.727567	0.363784	−	0.931483i	$-0.381485\pi$
$59$	5.58855	0.727567	0.363784	+	0.931483i	$0.381485\pi$
$60$	14.1088	1.82144
$61$	1.70945	0.218872	0.109436	−	0.993994i	$-0.465095\pi$
$61$	1.70945	0.218872	0.109436	+	0.993994i	$0.465095\pi$
$62$	3.49807	0.444255
$63$	1.81868	0.229133
$64$	21.4832	2.68540
$65$	−0.421552	−0.0522870
$66$	20.0146	2.46363
$67$	−2.27753	−0.278245	−0.139122	−	0.990275i	$-0.544428\pi$
$67$	−2.27753	−0.278245	−0.139122	+	0.990275i	$0.544428\pi$
$68$	−27.3684	−3.31891
$69$	−8.23157	−0.990965
$70$	−16.0630	−1.91989
$71$	−10.6241	−1.26085	−0.630426	−	0.776249i	$-0.717120\pi$
$71$	−10.6241	−1.26085	−0.630426	+	0.776249i	$0.717120\pi$
$72$	−3.86540	−0.455542
$73$	4.85967	0.568781	0.284391	−	0.958709i	$-0.408209\pi$
$73$	4.85967	0.568781	0.284391	+	0.958709i	$0.408209\pi$
$74$	18.5742	2.15921
$75$	−5.38399	−0.621689
$76$	−10.1941	−1.16935
$77$	−16.5015	−1.88052
$78$	1.45392	0.164624
$79$	−6.21736	−0.699508	−0.349754	−	0.936842i	$-0.613735\pi$
$79$	−6.21736	−0.699508	−0.349754	+	0.936842i	$0.613735\pi$
$80$	18.9296	2.11639
$81$	−10.1297	−1.12553
$82$	5.09602	0.562761
$83$	−16.6630	−1.82900	−0.914502	−	0.404580i	$-0.867418\pi$
$83$	−16.6630	−1.82900	−0.914502	+	0.404580i	$0.867418\pi$
$84$	40.1194	4.37739
$85$	−7.54929	−0.818835
$86$	−12.5030	−1.34823
$87$	−4.80988	−0.515673
$88$	35.0720	3.73869
$89$	−4.73527	−0.501938	−0.250969	−	0.967995i	$-0.580749\pi$
$89$	−4.73527	−0.501938	−0.250969	+	0.967995i	$0.580749\pi$
$90$	−1.72221	−0.181537
$91$	−1.19872	−0.125660
$92$	−23.2987	−2.42905
$93$	−2.40998	−0.249903
$94$	−30.2963	−3.12483
$95$	−2.81194	−0.288499
$96$	−32.8091	−3.34856
$97$	−9.29060	−0.943318	−0.471659	−	0.881781i	$-0.656345\pi$
$97$	−9.29060	−0.943318	−0.471659	+	0.881781i	$0.656345\pi$
$98$	−26.8272	−2.70996
$99$	−1.76922	−0.177814
$100$	−15.2389	−1.52389
$101$	7.79023	0.775156	0.387578	−	0.921837i	$-0.373312\pi$
$101$	7.79023	0.775156	0.387578	+	0.921837i	$0.373312\pi$
$102$	26.0372	2.57807
$103$	15.5440	1.53160	0.765800	−	0.643079i	$-0.222343\pi$
$103$	15.5440	1.53160	0.765800	+	0.643079i	$0.222343\pi$
$104$	2.54773	0.249826
$105$	11.0665	1.07998
$106$	−0.975395	−0.0947388
$107$	2.05405	0.198573	0.0992863	−	0.995059i	$-0.468344\pi$
$107$	2.05405	0.198573	0.0992863	+	0.995059i	$0.468344\pi$
$108$	−24.9217	−2.39809
$109$	1.36766	0.130998	0.0654992	−	0.997853i	$-0.479136\pi$
$109$	1.36766	0.130998	0.0654992	+	0.997853i	$0.479136\pi$
$110$	15.6261	1.48989
$111$	−12.7967	−1.21460
$112$	53.8278	5.08625
$113$	−9.84946	−0.926559	−0.463280	−	0.886212i	$-0.653327\pi$
$113$	−9.84946	−0.926559	−0.463280	+	0.886212i	$0.653327\pi$
$114$	9.69830	0.908329
$115$	−6.42669	−0.599292
$116$	−13.6139	−1.26402
$117$	−0.128521	−0.0118818
$118$	−15.0485	−1.38533
$119$	−21.4670	−1.96788
$120$	−23.5206	−2.14713
$121$	5.05272	0.459338
$122$	−4.60309	−0.416744
$123$	−3.51088	−0.316566
$124$	−6.82121	−0.612563
$125$	−11.4454	−1.02371
$126$	−4.89723	−0.436280
$127$	1.06258	0.0942892	0.0471446	−	0.998888i	$-0.484988\pi$
$127$	1.06258	0.0942892	0.0471446	+	0.998888i	$0.484988\pi$
$128$	−22.4777	−1.98676
$129$	8.61389	0.758411
$130$	1.13513	0.0995572
$131$	−6.72683	−0.587726	−0.293863	−	0.955848i	$-0.594941\pi$
$131$	−6.72683	−0.587726	−0.293863	+	0.955848i	$0.594941\pi$
$132$	−39.0283	−3.39698
$133$	−7.99599	−0.693340
$134$	6.13279	0.529792
$135$	−6.87439	−0.591654
$136$	45.6256	3.91236
$137$	−16.0483	−1.37110	−0.685548	−	0.728028i	$-0.740437\pi$
$137$	−16.0483	−1.37110	−0.685548	+	0.728028i	$0.740437\pi$
$138$	22.1654	1.88685
$139$	2.46046	0.208693	0.104347	−	0.994541i	$-0.466725\pi$
$139$	2.46046	0.208693	0.104347	+	0.994541i	$0.466725\pi$
$140$	31.3227	2.64725
$141$	20.8725	1.75778
$142$	28.6080	2.40073
$143$	1.16612	0.0975155
$144$	5.77120	0.480933
$145$	−3.75525	−0.311856
$146$	−13.0858	−1.08299
$147$	18.4825	1.52441
$148$	−36.2197	−2.97724
$149$	8.39841	0.688024	0.344012	−	0.938965i	$-0.388214\pi$
$149$	8.39841	0.688024	0.344012	+	0.938965i	$0.388214\pi$
$150$	14.4977	1.18373
$151$	−3.65452	−0.297401	−0.148700	−	0.988882i	$-0.547509\pi$
$151$	−3.65452	−0.297401	−0.148700	+	0.988882i	$0.547509\pi$
$152$	16.9945	1.37844
$153$	−2.30161	−0.186074
$154$	44.4341	3.58060
$155$	−1.88156	−0.151131
$156$	−2.83513	−0.226992
$157$	−13.4257	−1.07149	−0.535743	−	0.844381i	$-0.679968\pi$
$157$	−13.4257	−1.07149	−0.535743	+	0.844381i	$0.679968\pi$
$158$	16.7417	1.33190
$159$	0.671995	0.0532927
$160$	−25.6152	−2.02506
$161$	−18.2748	−1.44026
$162$	27.2767	2.14306
$163$	−15.9473	−1.24909	−0.624545	−	0.780989i	$-0.714716\pi$
$163$	−15.9473	−1.24909	−0.624545	+	0.780989i	$0.714716\pi$
$164$	−9.93721	−0.775965
$165$	−10.7656	−0.838098
$166$	44.8691	3.48252
$167$	20.2301	1.56545	0.782727	−	0.622365i	$-0.213828\pi$
$167$	20.2301	1.56545	0.782727	+	0.622365i	$0.213828\pi$
$168$	−66.8827	−5.16011
$169$	−12.9153	−0.993484
$170$	20.3282	1.55910
$171$	−0.857298	−0.0655592
$172$	24.3808	1.85902
$173$	−18.8124	−1.43028	−0.715142	−	0.698979i	$-0.753638\pi$
$173$	−18.8124	−1.43028	−0.715142	+	0.698979i	$0.753638\pi$
$174$	12.9517	0.981868
$175$	−11.9529	−0.903556
$176$	−52.3639	−3.94708
$177$	10.3676	0.779276
$178$	12.7508	0.955715
$179$	12.5741	0.939829	0.469915	−	0.882712i	$-0.344285\pi$
$179$	12.5741	0.939829	0.469915	+	0.882712i	$0.344285\pi$
$180$	3.35830	0.250313
$181$	13.5254	1.00533	0.502667	−	0.864480i	$-0.332352\pi$
$181$	13.5254	1.00533	0.502667	+	0.864480i	$0.332352\pi$
$182$	3.22782	0.239262
$183$	3.17128	0.234428
$184$	38.8410	2.86339
$185$	−9.99082	−0.734540
$186$	6.48944	0.475829
$187$	20.8832	1.52713
$188$	59.0777	4.30868
$189$	−19.5479	−1.42190
$190$	7.57182	0.549317
$191$	−10.7266	−0.776149	−0.388075	−	0.921628i	$-0.626860\pi$
$191$	−10.7266	−0.776149	−0.388075	+	0.921628i	$0.626860\pi$
$192$	39.8545	2.87625
$193$	0.970850	0.0698833	0.0349416	−	0.999389i	$-0.488875\pi$
$193$	0.970850	0.0698833	0.0349416	+	0.999389i	$0.488875\pi$
$194$	25.0171	1.79613
$195$	−0.782041	−0.0560031
$196$	52.3129	3.73664
$197$	6.84255	0.487511	0.243756	−	0.969837i	$-0.421621\pi$
$197$	6.84255	0.487511	0.243756	+	0.969837i	$0.421621\pi$
$198$	4.76405	0.338566
$199$	4.95588	0.351313	0.175657	−	0.984452i	$-0.443795\pi$
$199$	4.95588	0.351313	0.175657	+	0.984452i	$0.443795\pi$
$200$	25.4046	1.79637
$201$	−4.22516	−0.298020
$202$	−20.9770	−1.47594
$203$	−10.6783	−0.749473
$204$	−50.7725	−3.55478
$205$	−2.74107	−0.191445
$206$	−41.8560	−2.91624
$207$	−1.95935	−0.136184
$208$	−3.80386	−0.263750
$209$	7.77853	0.538052
$210$	−29.7992	−2.05634
$211$	17.2302	1.18617	0.593087	−	0.805139i	$-0.297909\pi$
$211$	17.2302	1.18617	0.593087	+	0.805139i	$0.297909\pi$
$212$	1.90202	0.130631
$213$	−19.7094	−1.35046
$214$	−5.53101	−0.378092
$215$	6.72518	0.458654
$216$	41.5468	2.82690
$217$	−5.35037	−0.363206
$218$	−3.68276	−0.249428
$219$	9.01541	0.609205
$220$	−30.4709	−2.05435
$221$	1.51701	0.102045
$222$	34.4580	2.31267
$223$	−25.4953	−1.70729	−0.853647	−	0.520853i	$-0.825614\pi$
$223$	−25.4953	−1.70729	−0.853647	+	0.520853i	$0.825614\pi$
$224$	−72.8390	−4.86676
$225$	−1.28154	−0.0854363
$226$	26.5220	1.76422
$227$	7.96401	0.528590	0.264295	−	0.964442i	$-0.414861\pi$
$227$	7.96401	0.528590	0.264295	+	0.964442i	$0.414861\pi$
$228$	−18.9116	−1.25245
$229$	−28.4411	−1.87944	−0.939722	−	0.341941i	$-0.888916\pi$
$229$	−28.4411	−1.87944	−0.939722	+	0.341941i	$0.888916\pi$
$230$	17.3054	1.14108
$231$	−30.6127	−2.01417
$232$	22.6956	1.49004
$233$	19.9242	1.30528	0.652640	−	0.757668i	$-0.273661\pi$
$233$	19.9242	1.30528	0.652640	+	0.757668i	$0.273661\pi$
$234$	0.346074	0.0226236
$235$	16.2959	1.06303
$236$	29.3445	1.91016
$237$	−11.5341	−0.749222
$238$	57.8049	3.74694
$239$	2.57413	0.166507	0.0832535	−	0.996528i	$-0.473469\pi$
$239$	2.57413	0.166507	0.0832535	+	0.996528i	$0.473469\pi$
$240$	35.1172	2.26681
$241$	4.89013	0.315001	0.157501	−	0.987519i	$-0.449656\pi$
$241$	4.89013	0.315001	0.157501	+	0.987519i	$0.449656\pi$
$242$	−13.6056	−0.874603
$243$	−4.55343	−0.292103
$244$	8.97600	0.574629
$245$	14.4300	0.921897
$246$	9.45387	0.602757
$247$	0.565055	0.0359536
$248$	11.3716	0.722096
$249$	−30.9124	−1.95899
$250$	30.8194	1.94919
$251$	7.05903	0.445562	0.222781	−	0.974869i	$-0.428487\pi$
$251$	7.05903	0.445562	0.222781	+	0.974869i	$0.428487\pi$
$252$	9.54958	0.601567
$253$	17.7778	1.11768
$254$	−2.86126	−0.179531
$255$	−14.0051	−0.877030
$256$	17.5600	1.09750
$257$	19.7304	1.23075	0.615373	−	0.788236i	$-0.289005\pi$
$257$	19.7304	1.23075	0.615373	+	0.788236i	$0.289005\pi$
$258$	−23.1949	−1.44405
$259$	−28.4097	−1.76529
$260$	−2.21349	−0.137275
$261$	−1.14489	−0.0708669
$262$	18.1136	1.11906
$263$	7.18865	0.443271	0.221636	−	0.975130i	$-0.428860\pi$
$263$	7.18865	0.443271	0.221636	+	0.975130i	$0.428860\pi$
$264$	65.0638	4.00440
$265$	0.524651	0.0322291
$266$	21.5311	1.32015
$267$	−8.78463	−0.537611
$268$	−11.9589	−0.730506
$269$	7.55507	0.460641	0.230320	−	0.973115i	$-0.426023\pi$
$269$	7.55507	0.460641	0.230320	+	0.973115i	$0.426023\pi$
$270$	18.5109	1.12654
$271$	9.93222	0.603340	0.301670	−	0.953412i	$-0.402456\pi$
$271$	9.93222	0.603340	0.301670	+	0.953412i	$0.402456\pi$
$272$	−68.1209	−4.13043
$273$	−2.22380	−0.134590
$274$	43.2137	2.61063
$275$	11.6279	0.701186
$276$	−43.2225	−2.60169
$277$	−12.4600	−0.748650	−0.374325	−	0.927298i	$-0.622125\pi$
$277$	−12.4600	−0.748650	−0.374325	+	0.927298i	$0.622125\pi$
$278$	−6.62536	−0.397363
$279$	−0.573645	−0.0343432
$280$	−52.2178	−3.12061
$281$	19.8684	1.18525	0.592625	−	0.805478i	$-0.298092\pi$
$281$	19.8684	1.18525	0.592625	+	0.805478i	$0.298092\pi$
$282$	−56.2042	−3.34691
$283$	−20.1957	−1.20051	−0.600256	−	0.799808i	$-0.704935\pi$
$283$	−20.1957	−1.20051	−0.600256	+	0.799808i	$0.704935\pi$
$284$	−55.7854	−3.31026
$285$	−5.21658	−0.309003
$286$	−3.14004	−0.185674
$287$	−7.79446	−0.460093
$288$	−7.80950	−0.460179
$289$	10.1672	0.598071
$290$	10.1119	0.593790
$291$	−17.2355	−1.01036
$292$	25.5172	1.49328
$293$	26.5761	1.55259	0.776297	−	0.630367i	$-0.217096\pi$
$293$	26.5761	1.55259	0.776297	+	0.630367i	$0.217096\pi$
$294$	−49.7685	−2.90256
$295$	8.09436	0.471272
$296$	60.3815	3.50960
$297$	19.0163	1.10344
$298$	−22.6147	−1.31003
$299$	1.29143	0.0746854
$300$	−28.2703	−1.63219
$301$	19.1236	1.10227
$302$	9.84066	0.566266
$303$	14.4520	0.830248
$304$	−25.3735	−1.45527
$305$	2.47593	0.141772
$306$	6.19761	0.354294
$307$	11.4137	0.651413	0.325707	−	0.945471i	$-0.394398\pi$
$307$	11.4137	0.651413	0.325707	+	0.945471i	$0.394398\pi$
$308$	−86.6463	−4.93713
$309$	28.8365	1.64045
$310$	5.06654	0.287760
$311$	9.52722	0.540239	0.270120	−	0.962827i	$-0.412937\pi$
$311$	9.52722	0.540239	0.270120	+	0.962827i	$0.412937\pi$
$312$	4.72642	0.267581
$313$	34.0275	1.92335	0.961673	−	0.274198i	$-0.0884122\pi$
$313$	34.0275	1.92335	0.961673	+	0.274198i	$0.0884122\pi$
$314$	36.1518	2.04016
$315$	2.63415	0.148418
$316$	−32.6462	−1.83649
$317$	−18.9222	−1.06278	−0.531389	−	0.847128i	$-0.678330\pi$
$317$	−18.9222	−1.06278	−0.531389	+	0.847128i	$0.678330\pi$
$318$	−1.80950	−0.101472
$319$	10.3879	0.581613
$320$	31.1159	1.73943
$321$	3.81057	0.212685
$322$	49.2092	2.74232
$323$	10.1192	0.563047
$324$	−53.1895	−2.95497
$325$	0.844681	0.0468544
$326$	42.9419	2.37833
$327$	2.53722	0.140309
$328$	16.5662	0.914717
$329$	46.3388	2.55474
$330$	28.9888	1.59578
$331$	22.2550	1.22325	0.611623	−	0.791149i	$-0.290517\pi$
$331$	22.2550	1.22325	0.611623	+	0.791149i	$0.290517\pi$
$332$	−87.4945	−4.80189
$333$	−3.04597	−0.166918
$334$	−54.4744	−2.98071
$335$	−3.29874	−0.180229
$336$	99.8586	5.44773
$337$	15.3644	0.836954	0.418477	−	0.908227i	$-0.362564\pi$
$337$	15.3644	0.836954	0.418477	+	0.908227i	$0.362564\pi$
$338$	34.7774	1.89164
$339$	−18.2722	−0.992411
$340$	−39.6399	−2.14978
$341$	5.20486	0.281859
$342$	2.30847	0.124828
$343$	12.2026	0.658878
$344$	−40.6450	−2.19143
$345$	−11.9225	−0.641884
$346$	50.6569	2.72333
$347$	−19.6473	−1.05472	−0.527361	−	0.849641i	$-0.676819\pi$
$347$	−19.6473	−1.05472	−0.527361	+	0.849641i	$0.676819\pi$
$348$	−25.2558	−1.35385
$349$	−18.4852	−0.989488	−0.494744	−	0.869039i	$-0.664738\pi$
$349$	−18.4852	−0.989488	−0.494744	+	0.869039i	$0.664738\pi$
$350$	32.1861	1.72042
$351$	1.38140	0.0737334
$352$	70.8580	3.77675
$353$	13.5615	0.721805	0.360903	−	0.932604i	$-0.382469\pi$
$353$	13.5615	0.721805	0.360903	+	0.932604i	$0.382469\pi$
$354$	−27.9172	−1.48378
$355$	−15.3878	−0.816701
$356$	−24.8640	−1.31779
$357$	−39.8245	−2.10774
$358$	−33.8586	−1.78948
$359$	−12.0800	−0.637558	−0.318779	−	0.947829i	$-0.603273\pi$
$359$	−12.0800	−0.637558	−0.318779	+	0.947829i	$0.603273\pi$
$360$	−5.59858	−0.295071
$361$	−15.2308	−0.801622
$362$	−36.4203	−1.91421
$363$	9.37354	0.491984
$364$	−6.29424	−0.329908
$365$	7.03866	0.368420
$366$	−8.53941	−0.446362
$367$	−35.9594	−1.87706	−0.938532	−	0.345193i	$-0.887813\pi$
$367$	−35.9594	−1.87706	−0.938532	+	0.345193i	$0.887813\pi$
$368$	−57.9911	−3.02300
$369$	−0.835691	−0.0435043
$370$	26.9026	1.39860
$371$	1.49189	0.0774549
$372$	−12.6544	−0.656098
$373$	−9.49818	−0.491797	−0.245898	−	0.969296i	$-0.579083\pi$
$373$	−9.49818	−0.491797	−0.245898	+	0.969296i	$0.579083\pi$
$374$	−56.2329	−2.90773
$375$	−21.2329	−1.09646
$376$	−98.4878	−5.07912
$377$	0.754610	0.0388644
$378$	52.6373	2.70737
$379$	14.8655	0.763588	0.381794	−	0.924248i	$-0.375306\pi$
$379$	14.8655	0.763588	0.381794	+	0.924248i	$0.375306\pi$
$380$	−14.7650	−0.757429
$381$	1.97125	0.100990
$382$	28.8839	1.47783
$383$	14.9982	0.766374	0.383187	−	0.923671i	$-0.374826\pi$
$383$	14.9982	0.766374	0.383187	+	0.923671i	$0.374826\pi$
$384$	−41.6994	−2.12796
$385$	−23.9005	−1.21808
$386$	−2.61424	−0.133061
$387$	2.05035	0.104225
$388$	−48.7833	−2.47660
$389$	−8.32650	−0.422170	−0.211085	−	0.977468i	$-0.567700\pi$
$389$	−8.32650	−0.422170	−0.211085	+	0.977468i	$0.567700\pi$
$390$	2.10583	0.106633
$391$	23.1274	1.16960
$392$	−87.2103	−4.40479
$393$	−12.4793	−0.629496
$394$	−18.4252	−0.928246
$395$	−9.00512	−0.453097
$396$	−9.28987	−0.466834
$397$	−25.9463	−1.30221	−0.651103	−	0.758989i	$-0.725694\pi$
$397$	−25.9463	−1.30221	−0.651103	+	0.758989i	$0.725694\pi$
$398$	−13.3449	−0.668918
$399$	−14.8337	−0.742616
$400$	−37.9300	−1.89650
$401$	−10.7477	−0.536717	−0.268358	−	0.963319i	$-0.586481\pi$
$401$	−10.7477	−0.536717	−0.268358	+	0.963319i	$0.586481\pi$
$402$	11.3772	0.567445
$403$	0.378096	0.0188343
$404$	40.9051	2.03510
$405$	−14.6718	−0.729045
$406$	28.7540	1.42703
$407$	27.6371	1.36992
$408$	84.6423	4.19042
$409$	7.84090	0.387707	0.193854	−	0.981030i	$-0.437901\pi$
$409$	7.84090	0.387707	0.193854	+	0.981030i	$0.437901\pi$
$410$	7.38098	0.364521
$411$	−29.7719	−1.46854
$412$	81.6189	4.02108
$413$	23.0170	1.13259
$414$	5.27601	0.259302
$415$	−24.1344	−1.18471
$416$	5.14733	0.252369
$417$	4.56452	0.223526
$418$	−20.9455	−1.02448
$419$	−26.2943	−1.28456	−0.642281	−	0.766469i	$-0.722012\pi$
$419$	−26.2943	−1.28456	−0.642281	+	0.766469i	$0.722012\pi$
$420$	58.1083	2.83540
$421$	16.4424	0.801354	0.400677	−	0.916219i	$-0.368775\pi$
$421$	16.4424	0.801354	0.400677	+	0.916219i	$0.368775\pi$
$422$	−46.3963	−2.25853
$423$	4.96826	0.241565
$424$	−3.17083	−0.153989
$425$	15.1268	0.733759
$426$	53.0721	2.57135
$427$	7.04052	0.340715
$428$	10.7854	0.521334
$429$	2.16332	0.104446
$430$	−18.1091	−0.873300
$431$	−8.62155	−0.415286	−0.207643	−	0.978205i	$-0.566579\pi$
$431$	−8.62155	−0.415286	−0.207643	+	0.978205i	$0.566579\pi$
$432$	−62.0310	−2.98447
$433$	−27.3644	−1.31505	−0.657524	−	0.753434i	$-0.728396\pi$
$433$	−27.3644	−1.31505	−0.657524	+	0.753434i	$0.728396\pi$
$434$	14.4071	0.691564
$435$	−6.96655	−0.334020
$436$	7.18135	0.343924
$437$	8.61444	0.412084
$438$	−24.2761	−1.15996
$439$	−23.4365	−1.11856	−0.559282	−	0.828978i	$-0.688923\pi$
$439$	−23.4365	−1.11856	−0.559282	+	0.828978i	$0.688923\pi$
$440$	50.7977	2.42169
$441$	4.39937	0.209494
$442$	−4.08492	−0.194300
$443$	−21.6584	−1.02902	−0.514512	−	0.857483i	$-0.672027\pi$
$443$	−21.6584	−1.02902	−0.514512	+	0.857483i	$0.672027\pi$
$444$	−67.1929	−3.18883
$445$	−6.85849	−0.325123
$446$	68.6521	3.25077
$447$	15.5803	0.736923
$448$	88.4804	4.18031
$449$	7.02790	0.331667	0.165834	−	0.986154i	$-0.446969\pi$
$449$	7.02790	0.331667	0.165834	+	0.986154i	$0.446969\pi$
$450$	3.45086	0.162675
$451$	7.58248	0.357045
$452$	−51.7177	−2.43260
$453$	−6.77969	−0.318537
$454$	−21.4450	−1.00646
$455$	−1.73620	−0.0813943
$456$	31.5274	1.47641
$457$	26.2926	1.22992	0.614958	−	0.788560i	$-0.289173\pi$
$457$	26.2926	1.22992	0.614958	+	0.788560i	$0.289173\pi$
$458$	76.5844	3.57856
$459$	24.7385	1.15469
$460$	−33.7454	−1.57339
$461$	−17.4776	−0.814013	−0.407007	−	0.913425i	$-0.633427\pi$
$461$	−17.4776	−0.814013	−0.407007	+	0.913425i	$0.633427\pi$
$462$	82.4319	3.83508
$463$	−10.0854	−0.468710	−0.234355	−	0.972151i	$-0.575298\pi$
$463$	−10.0854	−0.468710	−0.234355	+	0.972151i	$0.575298\pi$
$464$	−33.8854	−1.57309
$465$	−3.49057	−0.161872
$466$	−53.6507	−2.48532
$467$	34.1317	1.57943	0.789714	−	0.613475i	$-0.210229\pi$
$467$	34.1317	1.57943	0.789714	+	0.613475i	$0.210229\pi$
$468$	−0.674843	−0.0311946
$469$	−9.38022	−0.433138
$470$	−43.8807	−2.02406
$471$	−24.9066	−1.14764
$472$	−48.9199	−2.25172
$473$	−18.6035	−0.855390
$474$	31.0584	1.42656
$475$	5.63441	0.258524
$476$	−112.719	−5.16648
$477$	0.159954	0.00732380
$478$	−6.93146	−0.317038
$479$	−30.2233	−1.38094	−0.690468	−	0.723363i	$-0.742595\pi$
$479$	−30.2233	−1.38094	−0.690468	+	0.723363i	$0.742595\pi$
$480$	−47.5201	−2.16899
$481$	2.00764	0.0915403
$482$	−13.1678	−0.599778
$483$	−33.9025	−1.54262
$484$	26.5309	1.20595
$485$	−13.4564	−0.611022
$486$	12.2612	0.556178
$487$	34.5694	1.56649	0.783244	−	0.621715i	$-0.213564\pi$
$487$	34.5694	1.56649	0.783244	+	0.621715i	$0.213564\pi$
$488$	−14.9638	−0.677380
$489$	−29.5846	−1.33786
$490$	−38.8561	−1.75534
$491$	16.8473	0.760310	0.380155	−	0.924923i	$-0.375871\pi$
$491$	16.8473	0.760310	0.380155	+	0.924923i	$0.375871\pi$
$492$	−18.4350	−0.831114
$493$	13.5138	0.608631
$494$	−1.52154	−0.0684574
$495$	−2.56251	−0.115176
$496$	−16.9782	−0.762345
$497$	−43.7565	−1.96275
$498$	83.2389	3.73002
$499$	25.4793	1.14061	0.570306	−	0.821432i	$-0.306825\pi$
$499$	25.4793	1.14061	0.570306	+	0.821432i	$0.306825\pi$
$500$	−60.0977	−2.68765
$501$	37.5299	1.67671
$502$	−19.0081	−0.848373
$503$	−6.62516	−0.295401	−0.147701	−	0.989032i	$-0.547187\pi$
$503$	−6.62516	−0.295401	−0.147701	+	0.989032i	$0.547187\pi$
$504$	−15.9200	−0.709134
$505$	11.2832	0.502097
$506$	−47.8709	−2.12812
$507$	−23.9598	−1.06409
$508$	5.57944	0.247548
$509$	−43.2746	−1.91811	−0.959056	−	0.283215i	$-0.908599\pi$
$509$	−43.2746	−1.91811	−0.959056	+	0.283215i	$0.908599\pi$
$510$	37.7119	1.66991
$511$	20.0150	0.885411
$512$	−2.32921	−0.102938
$513$	9.21455	0.406832
$514$	−53.1286	−2.34340
$515$	22.5137	0.992073
$516$	45.2300	1.99114
$517$	−45.0786	−1.98255
$518$	76.4997	3.36121
$519$	−34.8999	−1.53194
$520$	3.69009	0.161821
$521$	−6.60354	−0.289307	−0.144653	−	0.989482i	$-0.546207\pi$
$521$	−6.60354	−0.289307	−0.144653	+	0.989482i	$0.546207\pi$
$522$	3.08288	0.134934
$523$	41.1611	1.79985	0.899924	−	0.436047i	$-0.143622\pi$
$523$	41.1611	1.79985	0.899924	+	0.436047i	$0.143622\pi$
$524$	−35.3214	−1.54302
$525$	−22.1745	−0.967773
$526$	−19.3571	−0.844011
$527$	6.77107	0.294952
$528$	−97.1428	−4.22760
$529$	−3.31173	−0.143988
$530$	−1.41275	−0.0613658
$531$	2.46779	0.107093
$532$	−41.9855	−1.82030
$533$	0.550813	0.0238584
$534$	23.6547	1.02364
$535$	2.97505	0.128623
$536$	19.9366	0.861129
$537$	23.3268	1.00662
$538$	−20.3438	−0.877084
$539$	−39.9168	−1.71934
$540$	−36.0962	−1.55333
$541$	4.90304	0.210798	0.105399	−	0.994430i	$-0.466388\pi$
$541$	4.90304	0.210798	0.105399	+	0.994430i	$0.466388\pi$
$542$	−26.7448	−1.14879
$543$	25.0916	1.07678
$544$	92.1801	3.95219
$545$	1.98090	0.0848525
$546$	5.98809	0.256267
$547$	34.8737	1.49109	0.745545	−	0.666455i	$-0.232189\pi$
$547$	34.8737	1.49109	0.745545	+	0.666455i	$0.232189\pi$
$548$	−84.2665	−3.59969
$549$	0.754856	0.0322165
$550$	−31.3107	−1.33509
$551$	5.03360	0.214438
$552$	72.0558	3.06690
$553$	−25.6068	−1.08891
$554$	33.5515	1.42547
$555$	−18.5345	−0.786744
$556$	12.9194	0.547906
$557$	5.49095	0.232659	0.116330	−	0.993211i	$-0.462887\pi$
$557$	5.49095	0.232659	0.116330	+	0.993211i	$0.462887\pi$
$558$	1.54467	0.0653912
$559$	−1.35141	−0.0571586
$560$	77.9633	3.29455
$561$	38.7414	1.63566
$562$	−53.5004	−2.25678
$563$	−11.8912	−0.501153	−0.250576	−	0.968097i	$-0.580620\pi$
$563$	−11.8912	−0.501153	−0.250576	+	0.968097i	$0.580620\pi$
$564$	109.598	4.61490
$565$	−14.2658	−0.600167
$566$	54.3818	2.28584
$567$	−41.7203	−1.75209
$568$	92.9993	3.90217
$569$	−45.9119	−1.92473	−0.962364	−	0.271763i	$-0.912393\pi$
$569$	−45.9119	−1.92473	−0.962364	+	0.271763i	$0.912393\pi$
$570$	14.0469	0.588358
$571$	−33.7933	−1.41420	−0.707102	−	0.707111i	$-0.749998\pi$
$571$	−33.7933	−1.41420	−0.707102	+	0.707111i	$0.749998\pi$
$572$	6.12306	0.256018
$573$	−19.8994	−0.831311
$574$	20.9884	0.876040
$575$	12.8774	0.537026
$576$	9.48652	0.395272
$577$	−17.7770	−0.740065	−0.370033	−	0.929019i	$-0.620654\pi$
$577$	−17.7770	−0.740065	−0.370033	+	0.929019i	$0.620654\pi$
$578$	−27.3776	−1.13876
$579$	1.80107	0.0748500
$580$	−19.7181	−0.818751
$581$	−68.6282	−2.84718
$582$	46.4105	1.92378
$583$	−1.45131	−0.0601073
$584$	−42.5395	−1.76030
$585$	−0.186148	−0.00769629
$586$	−71.5625	−2.95622
$587$	28.3874	1.17167	0.585836	−	0.810429i	$-0.300766\pi$
$587$	28.3874	1.17167	0.585836	+	0.810429i	$0.300766\pi$
$588$	97.0482	4.00220
$589$	2.52207	0.103920
$590$	−21.7960	−0.897326
$591$	12.6939	0.522159
$592$	−90.1520	−3.70522
$593$	−3.91890	−0.160930	−0.0804651	−	0.996757i	$-0.525641\pi$
$593$	−3.91890	−0.160930	−0.0804651	+	0.996757i	$0.525641\pi$
$594$	−51.2057	−2.10100
$595$	−31.0924	−1.27467
$596$	44.0985	1.80635
$597$	9.19390	0.376281
$598$	−3.47748	−0.142205
$599$	28.1525	1.15028	0.575141	−	0.818055i	$-0.304947\pi$
$599$	28.1525	1.15028	0.575141	+	0.818055i	$0.304947\pi$
$600$	47.1292	1.92404
$601$	−42.6373	−1.73921	−0.869605	−	0.493748i	$-0.835626\pi$
$601$	−42.6373	−1.73921	−0.869605	+	0.493748i	$0.835626\pi$
$602$	−51.4948	−2.09877
$603$	−1.00571	−0.0409557
$604$	−19.1892	−0.780799
$605$	7.31827	0.297530
$606$	−38.9155	−1.58083
$607$	−17.9025	−0.726641	−0.363321	−	0.931664i	$-0.618357\pi$
$607$	−17.9025	−0.726641	−0.363321	+	0.931664i	$0.618357\pi$
$608$	34.3351	1.39247
$609$	−19.8099	−0.802739
$610$	−6.66703	−0.269940
$611$	−3.27464	−0.132478
$612$	−12.0853	−0.488520
$613$	23.4262	0.946177	0.473089	−	0.881015i	$-0.343139\pi$
$613$	23.4262	0.946177	0.473089	+	0.881015i	$0.343139\pi$
$614$	−30.7340	−1.24032
$615$	−5.08510	−0.205051
$616$	144.447	5.81995
$617$	21.0179	0.846148	0.423074	−	0.906095i	$-0.360951\pi$
$617$	21.0179	0.846148	0.423074	+	0.906095i	$0.360951\pi$
$618$	−77.6491	−3.12350
$619$	21.2638	0.854666	0.427333	−	0.904094i	$-0.359453\pi$
$619$	21.2638	0.854666	0.427333	+	0.904094i	$0.359453\pi$
$620$	−9.87973	−0.396780
$621$	21.0598	0.845102
$622$	−25.6543	−1.02864
$623$	−19.5027	−0.781357
$624$	−7.05673	−0.282495
$625$	−2.06638	−0.0826553
$626$	−91.6270	−3.66215
$627$	14.4303	0.576292
$628$	−70.4958	−2.81309
$629$	35.9534	1.43356
$630$	−7.09307	−0.282595
$631$	−6.55919	−0.261117	−0.130559	−	0.991441i	$-0.541677\pi$
$631$	−6.55919	−0.261117	−0.130559	+	0.991441i	$0.541677\pi$
$632$	54.4242	2.16488
$633$	31.9645	1.27048
$634$	50.9526	2.02358
$635$	1.53903	0.0610745
$636$	3.52852	0.139915
$637$	−2.89967	−0.114889
$638$	−27.9720	−1.10742
$639$	−4.69140	−0.185589
$640$	−32.5563	−1.28690
$641$	−13.1384	−0.518936	−0.259468	−	0.965752i	$-0.583547\pi$
$641$	−13.1384	−0.518936	−0.259468	+	0.965752i	$0.583547\pi$
$642$	−10.2609	−0.404964
$643$	14.6799	0.578920	0.289460	−	0.957190i	$-0.406524\pi$
$643$	14.6799	0.578920	0.289460	+	0.957190i	$0.406524\pi$
$644$	−95.9577	−3.78126
$645$	12.4762	0.491251
$646$	−27.2483	−1.07207
$647$	35.6548	1.40174	0.700868	−	0.713291i	$-0.252796\pi$
$647$	35.6548	1.40174	0.700868	+	0.713291i	$0.252796\pi$
$648$	88.6716	3.48335
$649$	−22.3910	−0.878924
$650$	−2.27450	−0.0892132
$651$	−9.92573	−0.389020
$652$	−83.7364	−3.27937
$653$	25.9825	1.01677	0.508387	−	0.861129i	$-0.330242\pi$
$653$	25.9825	1.01677	0.508387	+	0.861129i	$0.330242\pi$
$654$	−6.83206	−0.267155
$655$	−9.74302	−0.380691
$656$	−24.7340	−0.965702
$657$	2.14593	0.0837206
$658$	−124.778	−4.86436
$659$	−10.3347	−0.402581	−0.201291	−	0.979532i	$-0.564514\pi$
$659$	−10.3347	−0.402581	−0.201291	+	0.979532i	$0.564514\pi$
$660$	−56.5280	−2.20035
$661$	35.4978	1.38071	0.690353	−	0.723473i	$-0.257455\pi$
$661$	35.4978	1.38071	0.690353	+	0.723473i	$0.257455\pi$
$662$	−59.9268	−2.32912
$663$	2.81429	0.109298
$664$	145.861	5.66052
$665$	−11.5813	−0.449102
$666$	8.20200	0.317821
$667$	11.5043	0.445447
$668$	106.225	4.10996
$669$	−47.2976	−1.82863
$670$	8.88262	0.343166
$671$	−6.84904	−0.264404
$672$	−135.127	−5.21264
$673$	−20.4647	−0.788856	−0.394428	−	0.918927i	$-0.629057\pi$
$673$	−20.4647	−0.788856	−0.394428	+	0.918927i	$0.629057\pi$
$674$	−41.3723	−1.59360
$675$	13.7745	0.530181
$676$	−67.8158	−2.60830
$677$	−12.7878	−0.491475	−0.245737	−	0.969336i	$-0.579030\pi$
$677$	−12.7878	−0.491475	−0.245737	+	0.969336i	$0.579030\pi$
$678$	49.2022	1.88960
$679$	−38.2642	−1.46845
$680$	66.0834	2.53418
$681$	14.7744	0.566158
$682$	−14.0153	−0.536674
$683$	−5.39169	−0.206307	−0.103154	−	0.994665i	$-0.532893\pi$
$683$	−5.39169	−0.206307	−0.103154	+	0.994665i	$0.532893\pi$
$684$	−4.50151	−0.172120
$685$	−23.2440	−0.888109
$686$	−32.8584	−1.25454
$687$	−52.7626	−2.01302
$688$	60.6846	2.31358
$689$	−0.105428	−0.00401647
$690$	32.1040	1.22218
$691$	−9.38062	−0.356855	−0.178428	−	0.983953i	$-0.557101\pi$
$691$	−9.38062	−0.356855	−0.178428	+	0.983953i	$0.557101\pi$
$692$	−98.7807	−3.75508
$693$	−7.28671	−0.276799
$694$	52.9050	2.00825
$695$	3.56369	0.135178
$696$	42.1037	1.59594
$697$	9.86415	0.373631
$698$	49.7756	1.88404
$699$	36.9625	1.39805
$700$	−62.7626	−2.37220
$701$	8.44813	0.319081	0.159541	−	0.987191i	$-0.448999\pi$
$701$	8.44813	0.319081	0.159541	+	0.987191i	$0.448999\pi$
$702$	−3.71973	−0.140392
$703$	13.3919	0.505083
$704$	−86.0741	−3.24404
$705$	30.2314	1.13858
$706$	−36.5175	−1.37435
$707$	32.0848	1.20667
$708$	54.4384	2.04592
$709$	42.2746	1.58766	0.793829	−	0.608141i	$-0.208085\pi$
$709$	42.2746	1.58766	0.793829	+	0.608141i	$0.208085\pi$
$710$	41.4353	1.55504
$711$	−2.74546	−0.102963
$712$	41.4506	1.55343
$713$	5.76419	0.215871
$714$	107.237	4.01324
$715$	1.68898	0.0631643
$716$	66.0241	2.46744
$717$	4.77540	0.178341
$718$	32.5282	1.21394
$719$	−13.8917	−0.518072	−0.259036	−	0.965868i	$-0.583405\pi$
$719$	−13.8917	−0.518072	−0.259036	+	0.965868i	$0.583405\pi$
$720$	8.35891	0.311518
$721$	64.0196	2.38421
$722$	41.0126	1.52633
$723$	9.07193	0.337389
$724$	71.0193	2.63941
$725$	7.52455	0.279455
$726$	−25.2405	−0.936762
$727$	−5.42583	−0.201233	−0.100616	−	0.994925i	$-0.532082\pi$
$727$	−5.42583	−0.201233	−0.100616	+	0.994925i	$0.532082\pi$
$728$	10.4931	0.388899
$729$	21.9419	0.812664
$730$	−18.9532	−0.701491
$731$	−24.2015	−0.895126
$732$	16.6518	0.615469
$733$	−16.6603	−0.615364	−0.307682	−	0.951489i	$-0.599553\pi$
$733$	−16.6603	−0.615364	−0.307682	+	0.951489i	$0.599553\pi$
$734$	96.8290	3.57402
$735$	26.7697	0.987417
$736$	78.4727	2.89254
$737$	9.12512	0.336128
$738$	2.25029	0.0828345
$739$	16.3653	0.602008	0.301004	−	0.953623i	$-0.402678\pi$
$739$	16.3653	0.602008	0.301004	+	0.953623i	$0.402678\pi$
$740$	−52.4600	−1.92847
$741$	1.04826	0.0385088
$742$	−4.01726	−0.147478
$743$	−5.31132	−0.194853	−0.0974267	−	0.995243i	$-0.531061\pi$
$743$	−5.31132	−0.194853	−0.0974267	+	0.995243i	$0.531061\pi$
$744$	21.0960	0.773416
$745$	12.1641	0.445658
$746$	25.5761	0.936406
$747$	−7.35804	−0.269217
$748$	109.654	4.00934
$749$	8.45980	0.309114
$750$	57.1746	2.08772
$751$	−19.8573	−0.724604	−0.362302	−	0.932061i	$-0.618009\pi$
$751$	−19.8573	−0.724604	−0.362302	+	0.932061i	$0.618009\pi$
$752$	147.046	5.36222
$753$	13.0956	0.477228
$754$	−2.03196	−0.0739998
$755$	−5.29315	−0.192637
$756$	−102.642	−3.73307
$757$	−16.4515	−0.597939	−0.298969	−	0.954263i	$-0.596643\pi$
$757$	−16.4515	−0.597939	−0.298969	+	0.954263i	$0.596643\pi$
$758$	−40.0287	−1.45391
$759$	32.9805	1.19712
$760$	24.6146	0.892866
$761$	39.2344	1.42225	0.711123	−	0.703067i	$-0.248187\pi$
$761$	39.2344	1.42225	0.711123	+	0.703067i	$0.248187\pi$
$762$	−5.30806	−0.192291
$763$	5.63285	0.203923
$764$	−56.3234	−2.03771
$765$	−3.33361	−0.120527
$766$	−40.3863	−1.45922
$767$	−1.62655	−0.0587312
$768$	32.5765	1.17550
$769$	35.1735	1.26839	0.634195	−	0.773173i	$-0.281332\pi$
$769$	35.1735	1.26839	0.634195	+	0.773173i	$0.281332\pi$
$770$	64.3576	2.31929
$771$	36.6028	1.31822
$772$	5.09776	0.183472
$773$	−6.15087	−0.221231	−0.110616	−	0.993863i	$-0.535282\pi$
$773$	−6.15087	−0.221231	−0.110616	+	0.993863i	$0.535282\pi$
$774$	−5.52106	−0.198450
$775$	3.77016	0.135428
$776$	81.3262	2.91944
$777$	−52.7042	−1.89075
$778$	22.4211	0.803834
$779$	3.67418	0.131641
$780$	−4.10636	−0.147031
$781$	42.5665	1.52315
$782$	−62.2759	−2.22698
$783$	12.3057	0.439770
$784$	130.209	4.65030
$785$	−19.4455	−0.694040
$786$	33.6034	1.19859
$787$	51.3312	1.82976	0.914880	−	0.403726i	$-0.132285\pi$
$787$	51.3312	1.82976	0.914880	+	0.403726i	$0.132285\pi$
$788$	35.9290	1.27992
$789$	13.3360	0.474775
$790$	24.2484	0.862719
$791$	−40.5659	−1.44236
$792$	15.4871	0.550309
$793$	−0.497534	−0.0176680
$794$	69.8664	2.47947
$795$	0.973306	0.0345196
$796$	26.0224	0.922341
$797$	−49.4219	−1.75061	−0.875307	−	0.483567i	$-0.839341\pi$
$797$	−49.4219	−1.75061	−0.875307	+	0.483567i	$0.839341\pi$
$798$	39.9433	1.41398
$799$	−58.6433	−2.07465
$800$	51.3263	1.81466
$801$	−2.09100	−0.0738817
$802$	28.9408	1.02194
$803$	−19.4707	−0.687105
$804$	−22.1855	−0.782424
$805$	−26.4689	−0.932907
$806$	−1.01811	−0.0358614
$807$	14.0158	0.493379
$808$	−68.1925	−2.39900
$809$	−10.8039	−0.379844	−0.189922	−	0.981799i	$-0.560824\pi$
$809$	−10.8039	−0.379844	−0.189922	+	0.981799i	$0.560824\pi$
$810$	39.5071	1.38814
$811$	−41.2201	−1.44743	−0.723717	−	0.690097i	$-0.757568\pi$
$811$	−41.2201	−1.44743	−0.723717	+	0.690097i	$0.757568\pi$
$812$	−56.0701	−1.96767
$813$	18.4258	0.646220
$814$	−74.4193	−2.60839
$815$	−23.0978	−0.809081
$816$	−126.374	−4.42399
$817$	−9.01454	−0.315379
$818$	−21.1135	−0.738215
$819$	−0.529328	−0.0184962
$820$	−14.3929	−0.502621
$821$	−25.6426	−0.894931	−0.447466	−	0.894301i	$-0.647673\pi$
$821$	−25.6426	−0.894931	−0.447466	+	0.894301i	$0.647673\pi$
$822$	80.1679	2.79618
$823$	15.9995	0.557706	0.278853	−	0.960334i	$-0.410046\pi$
$823$	15.9995	0.557706	0.278853	+	0.960334i	$0.410046\pi$
$824$	−136.066	−4.74009
$825$	21.5714	0.751020
$826$	−61.9786	−2.15651
$827$	−29.4409	−1.02376	−0.511880	−	0.859057i	$-0.671051\pi$
$827$	−29.4409	−1.02376	−0.511880	+	0.859057i	$0.671051\pi$
$828$	−10.2882	−0.357540
$829$	14.8610	0.516143	0.258072	−	0.966126i	$-0.416913\pi$
$829$	14.8610	0.516143	0.258072	+	0.966126i	$0.416913\pi$
$830$	64.9877	2.25575
$831$	−23.1152	−0.801857
$832$	−6.25267	−0.216772
$833$	−51.9283	−1.79921
$834$	−12.2910	−0.425604
$835$	29.3010	1.01400
$836$	40.8436	1.41261
$837$	6.16574	0.213119
$838$	70.8037	2.44587
$839$	−11.4541	−0.395438	−0.197719	−	0.980259i	$-0.563353\pi$
$839$	−11.4541	−0.395438	−0.197719	+	0.980259i	$0.563353\pi$
$840$	−96.8718	−3.34240
$841$	−22.2778	−0.768201
$842$	−44.2750	−1.52582
$843$	36.8589	1.26949
$844$	90.4725	3.11419
$845$	−18.7063	−0.643516
$846$	−13.3782	−0.459953
$847$	20.8101	0.715043
$848$	4.73418	0.162572
$849$	−37.4661	−1.28583
$850$	−40.7325	−1.39711
$851$	30.6070	1.04920
$852$	−103.490	−3.54552
$853$	39.7638	1.36149	0.680743	−	0.732522i	$-0.261657\pi$
$853$	39.7638	1.36149	0.680743	+	0.732522i	$0.261657\pi$
$854$	−18.9582	−0.648738
$855$	−1.24170	−0.0424651
$856$	−17.9803	−0.614555
$857$	−51.5780	−1.76187	−0.880936	−	0.473236i	$-0.843086\pi$
$857$	−51.5780	−1.76187	−0.880936	+	0.473236i	$0.843086\pi$
$858$	−5.82524	−0.198870
$859$	−16.1248	−0.550173	−0.275086	−	0.961420i	$-0.588706\pi$
$859$	−16.1248	−0.550173	−0.275086	+	0.961420i	$0.588706\pi$
$860$	35.3127	1.20415
$861$	−14.4599	−0.492792
$862$	23.2155	0.790725
$863$	47.8800	1.62986	0.814928	−	0.579563i	$-0.196777\pi$
$863$	47.8800	1.62986	0.814928	+	0.579563i	$0.196777\pi$
$864$	83.9394	2.85568
$865$	−27.2476	−0.926447
$866$	73.6849	2.50392
$867$	18.8617	0.640576
$868$	−28.0938	−0.953566
$869$	24.9104	0.845027
$870$	18.7591	0.635992
$871$	0.662875	0.0224607
$872$	−11.9720	−0.405422
$873$	−4.10254	−0.138850
$874$	−23.1964	−0.784630
$875$	−47.1389	−1.59359
$876$	47.3383	1.59941
$877$	−18.5360	−0.625915	−0.312958	−	0.949767i	$-0.601320\pi$
$877$	−18.5360	−0.625915	−0.312958	+	0.949767i	$0.601320\pi$
$878$	63.1083	2.12980
$879$	49.3027	1.66294
$880$	−75.8430	−2.55667
$881$	−13.5908	−0.457887	−0.228944	−	0.973440i	$-0.573527\pi$
$881$	−13.5908	−0.457887	−0.228944	+	0.973440i	$0.573527\pi$
$882$	−11.8463	−0.398887
$883$	42.8843	1.44317	0.721587	−	0.692324i	$-0.243413\pi$
$883$	42.8843	1.44317	0.721587	+	0.692324i	$0.243413\pi$
$884$	7.96557	0.267911
$885$	15.0163	0.504766
$886$	58.3204	1.95931
$887$	30.2081	1.01429	0.507145	−	0.861861i	$-0.330701\pi$
$887$	30.2081	1.01429	0.507145	+	0.861861i	$0.330701\pi$
$888$	112.017	3.75903
$889$	4.37635	0.146778
$890$	18.4681	0.619051
$891$	40.5857	1.35967
$892$	−133.871	−4.48234
$893$	−21.8434	−0.730960
$894$	−41.9536	−1.40314
$895$	18.2121	0.608762
$896$	−92.5764	−3.09276
$897$	2.39580	0.0799933
$898$	−18.9243	−0.631511
$899$	3.36814	0.112334
$900$	−6.72916	−0.224305
$901$	−1.88803	−0.0628995
$902$	−20.4176	−0.679832
$903$	35.4771	1.18060
$904$	86.2182	2.86757
$905$	19.5899	0.651191
$906$	18.2559	0.606511
$907$	7.06946	0.234738	0.117369	−	0.993088i	$-0.462554\pi$
$907$	7.06946	0.234738	0.117369	+	0.993088i	$0.462554\pi$
$908$	41.8176	1.38777
$909$	3.44000	0.114098
$910$	4.67512	0.154979
$911$	−54.8635	−1.81771	−0.908854	−	0.417115i	$-0.863041\pi$
$911$	−54.8635	−1.81771	−0.908854	+	0.417115i	$0.863041\pi$
$912$	−47.0717	−1.55870
$913$	66.7618	2.20949
$914$	−70.7990	−2.34182
$915$	4.59323	0.151847
$916$	−149.339	−4.93431
$917$	−27.7051	−0.914902
$918$	−66.6142	−2.19860
$919$	−45.7050	−1.50767	−0.753834	−	0.657065i	$-0.771798\pi$
$919$	−45.7050	−1.50767	−0.753834	+	0.657065i	$0.771798\pi$
$920$	56.2566	1.85473
$921$	21.1741	0.697710
$922$	47.0625	1.54992
$923$	3.09215	0.101779
$924$	−160.742	−5.28802
$925$	20.0190	0.658221
$926$	27.1574	0.892448
$927$	6.86392	0.225441
$928$	45.8532	1.50521
$929$	32.8167	1.07668	0.538341	−	0.842727i	$-0.319051\pi$
$929$	32.8167	1.07668	0.538341	+	0.842727i	$0.319051\pi$
$930$	9.39919	0.308212
$931$	−19.3422	−0.633914
$932$	104.619	3.42690
$933$	17.6744	0.578635
$934$	−91.9077	−3.00731
$935$	30.2469	0.989178
$936$	1.12502	0.0367726
$937$	20.2996	0.663158	0.331579	−	0.943427i	$-0.392419\pi$
$937$	20.2996	0.663158	0.331579	+	0.943427i	$0.392419\pi$
$938$	25.2584	0.824718
$939$	63.1261	2.06004
$940$	85.5671	2.79089
$941$	42.6377	1.38995	0.694974	−	0.719035i	$-0.255416\pi$
$941$	42.6377	1.38995	0.694974	+	0.719035i	$0.255416\pi$
$942$	67.0669	2.18516
$943$	8.39733	0.273455
$944$	73.0393	2.37723
$945$	−28.3128	−0.921016
$946$	50.0943	1.62871
$947$	−53.9965	−1.75465	−0.877325	−	0.479898i	$-0.840674\pi$
$947$	−53.9965	−1.75465	−0.877325	+	0.479898i	$0.840674\pi$
$948$	−60.5636	−1.96702
$949$	−1.41440	−0.0459135
$950$	−15.1720	−0.492244
$951$	−35.1036	−1.13831
$952$	187.913	6.09031
$953$	6.19350	0.200627	0.100314	−	0.994956i	$-0.468015\pi$
$953$	6.19350	0.200627	0.100314	+	0.994956i	$0.468015\pi$
$954$	−0.430714	−0.0139449
$955$	−15.5362	−0.502740
$956$	13.5163	0.437149
$957$	19.2712	0.622949
$958$	81.3832	2.62937
$959$	−66.0962	−2.13436
$960$	57.7246	1.86305
$961$	−29.3124	−0.945561
$962$	−5.40603	−0.174297
$963$	0.907026	0.0292285
$964$	25.6772	0.827007
$965$	1.40616	0.0452660
$966$	91.2904	2.93722
$967$	13.3775	0.430192	0.215096	−	0.976593i	$-0.430994\pi$
$967$	13.3775	0.430192	0.215096	+	0.976593i	$0.430994\pi$
$968$	−44.2294	−1.42159
$969$	18.7726	0.603063
$970$	36.2344	1.16342
$971$	−18.5926	−0.596665	−0.298332	−	0.954462i	$-0.596430\pi$
$971$	−18.5926	−0.596665	−0.298332	+	0.954462i	$0.596430\pi$
$972$	−23.9092	−0.766889
$973$	10.1336	0.324869
$974$	−93.0861	−2.98267
$975$	1.56701	0.0501844
$976$	22.3416	0.715136
$977$	2.81760	0.0901431	0.0450716	−	0.998984i	$-0.485648\pi$
$977$	2.81760	0.0901431	0.0450716	+	0.998984i	$0.485648\pi$
$978$	79.6636	2.54736
$979$	18.9723	0.606356
$980$	75.7691	2.42036
$981$	0.603932	0.0192821
$982$	−45.3654	−1.44767
$983$	42.6993	1.36190	0.680948	−	0.732331i	$-0.261568\pi$
$983$	42.6993	1.36190	0.680948	+	0.732331i	$0.261568\pi$
$984$	30.7328	0.979727
$985$	9.91063	0.315779
$986$	−36.3891	−1.15886
$987$	85.9655	2.73631
$988$	2.96700	0.0943928
$989$	−20.6027	−0.655128
$990$	6.90017	0.219302
$991$	−23.4742	−0.745682	−0.372841	−	0.927895i	$-0.621616\pi$
$991$	−23.4742	−0.745682	−0.372841	+	0.927895i	$0.621616\pi$
$992$	22.9747	0.729447
$993$	41.2864	1.31018
$994$	117.825	3.73717
$995$	7.17802	0.227558
$996$	−162.315	−5.14316
$997$	−41.0365	−1.29964	−0.649819	−	0.760089i	$-0.725155\pi$
$997$	−41.0365	−1.29964	−0.649819	+	0.760089i	$0.725155\pi$
$998$	−68.6091	−2.17178
$999$	32.7392	1.03582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.b.1.4	✓	151

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.b.1.4	✓	151	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69273 q^{2} +1.85515 q^{3} +5.25082 q^{4} +1.44838 q^{5} -4.99542 q^{6} +4.11859 q^{7} -8.75359 q^{8} +0.441579 q^{9} +O(q^{10})\)	\(q-2.69273 q^{2} +1.85515 q^{3} +5.25082 q^{4} +1.44838 q^{5} -4.99542 q^{6} +4.11859 q^{7} -8.75359 q^{8} +0.441579 q^{9} -3.90011 q^{10} -4.00658 q^{11} +9.74105 q^{12} -0.291050 q^{13} -11.0903 q^{14} +2.68697 q^{15} +13.0695 q^{16} -5.21222 q^{17} -1.18906 q^{18} -1.94144 q^{19} +7.60520 q^{20} +7.64060 q^{21} +10.7887 q^{22} -4.43715 q^{23} -16.2392 q^{24} -2.90219 q^{25} +0.783720 q^{26} -4.74625 q^{27} +21.6260 q^{28} -2.59272 q^{29} -7.23529 q^{30} -1.29908 q^{31} -17.6854 q^{32} -7.43281 q^{33} +14.0351 q^{34} +5.96530 q^{35} +2.31865 q^{36} -6.89791 q^{37} +5.22777 q^{38} -0.539941 q^{39} -12.6786 q^{40} -1.89251 q^{41} -20.5741 q^{42} +4.64323 q^{43} -21.0378 q^{44} +0.639576 q^{45} +11.9481 q^{46} +11.2511 q^{47} +24.2458 q^{48} +9.96281 q^{49} +7.81482 q^{50} -9.66944 q^{51} -1.52825 q^{52} +0.362232 q^{53} +12.7804 q^{54} -5.80307 q^{55} -36.0525 q^{56} -3.60165 q^{57} +6.98150 q^{58} +5.58855 q^{59} +14.1088 q^{60} +1.70945 q^{61} +3.49807 q^{62} +1.81868 q^{63} +21.4832 q^{64} -0.421552 q^{65} +20.0146 q^{66} -2.27753 q^{67} -27.3684 q^{68} -8.23157 q^{69} -16.0630 q^{70} -10.6241 q^{71} -3.86540 q^{72} +4.85967 q^{73} +18.5742 q^{74} -5.38399 q^{75} -10.1941 q^{76} -16.5015 q^{77} +1.45392 q^{78} -6.21736 q^{79} +18.9296 q^{80} -10.1297 q^{81} +5.09602 q^{82} -16.6630 q^{83} +40.1194 q^{84} -7.54929 q^{85} -12.5030 q^{86} -4.80988 q^{87} +35.0720 q^{88} -4.73527 q^{89} -1.72221 q^{90} -1.19872 q^{91} -23.2987 q^{92} -2.40998 q^{93} -30.2963 q^{94} -2.81194 q^{95} -32.8091 q^{96} -9.29060 q^{97} -26.8272 q^{98} -1.76922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9}+O(q^{10}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9	\( 151 q - 16 q^{2} - 29 q^{3} + 120 q^{4} - 27 q^{5} - 18 q^{6} - 18 q^{7} - 48 q^{8} + 98 q^{9} - 7 q^{10} - 126 q^{11} - 47 q^{12} - 10 q^{13} - 58 q^{14} - 50 q^{15} + 74 q^{16} - 39 q^{17} - 47 q^{18} - 48 q^{19} - 64 q^{20} - 50 q^{21} - 7 q^{22} - 91 q^{23} - 44 q^{24} + 102 q^{25} - 94 q^{26} - 92 q^{27} - 27 q^{28} - 79 q^{29} - 12 q^{30} - 33 q^{31} - 102 q^{32} - 7 q^{33} - 17 q^{34} - 183 q^{35} - 6 q^{36} - 24 q^{37} - 77 q^{38} - 81 q^{39} - 37 q^{40} - 62 q^{41} + 4 q^{42} - 74 q^{43} - 209 q^{44} - 35 q^{45} - 37 q^{46} - 127 q^{47} - 59 q^{48} + 75 q^{49} - 79 q^{50} - 138 q^{51} - 12 q^{52} - 104 q^{53} - 43 q^{54} - 49 q^{55} - 167 q^{56} - 19 q^{57} - 32 q^{58} - 207 q^{59} - 94 q^{60} - 57 q^{61} - 69 q^{62} - 49 q^{63} - 4 q^{64} - 78 q^{65} - 51 q^{66} - 92 q^{67} - 80 q^{68} - 84 q^{69} + 5 q^{70} - 217 q^{71} - 79 q^{72} + 2 q^{73} - 113 q^{74} - 173 q^{75} - 70 q^{76} - 85 q^{77} - 46 q^{78} - 70 q^{79} - 95 q^{80} - 49 q^{81} - 12 q^{82} - 109 q^{83} - 114 q^{84} - 25 q^{85} - 136 q^{86} - 60 q^{87} - 2 q^{88} - 144 q^{89} - 55 q^{90} - 62 q^{91} - 175 q^{92} - 42 q^{93} - 15 q^{94} - 189 q^{95} - 64 q^{96} - 24 q^{97} - 37 q^{98} - 293 q^{99}+O(q^{100}) \) 151 * q - 16 * q^2 - 29 * q^3 + 120 * q^4 - 27 * q^5 - 18 * q^6 - 18 * q^7 - 48 * q^8 + 98 * q^9 - 7 * q^10 - 126 * q^11 - 47 * q^12 - 10 * q^13 - 58 * q^14 - 50 * q^15 + 74 * q^16 - 39 * q^17 - 47 * q^18 - 48 * q^19 - 64 * q^20 - 50 * q^21 - 7 * q^22 - 91 * q^23 - 44 * q^24 + 102 * q^25 - 94 * q^26 - 92 * q^27 - 27 * q^28 - 79 * q^29 - 12 * q^30 - 33 * q^31 - 102 * q^32 - 7 * q^33 - 17 * q^34 - 183 * q^35 - 6 * q^36 - 24 * q^37 - 77 * q^38 - 81 * q^39 - 37 * q^40 - 62 * q^41 + 4 * q^42 - 74 * q^43 - 209 * q^44 - 35 * q^45 - 37 * q^46 - 127 * q^47 - 59 * q^48 + 75 * q^49 - 79 * q^50 - 138 * q^51 - 12 * q^52 - 104 * q^53 - 43 * q^54 - 49 * q^55 - 167 * q^56 - 19 * q^57 - 32 * q^58 - 207 * q^59 - 94 * q^60 - 57 * q^61 - 69 * q^62 - 49 * q^63 - 4 * q^64 - 78 * q^65 - 51 * q^66 - 92 * q^67 - 80 * q^68 - 84 * q^69 + 5 * q^70 - 217 * q^71 - 79 * q^72 + 2 * q^73 - 113 * q^74 - 173 * q^75 - 70 * q^76 - 85 * q^77 - 46 * q^78 - 70 * q^79 - 95 * q^80 - 49 * q^81 - 12 * q^82 - 109 * q^83 - 114 * q^84 - 25 * q^85 - 136 * q^86 - 60 * q^87 - 2 * q^88 - 144 * q^89 - 55 * q^90 - 62 * q^91 - 175 * q^92 - 42 * q^93 - 15 * q^94 - 189 * q^95 - 64 * q^96 - 24 * q^97 - 37 * q^98 - 293 * q^99

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