LMFDB - Embedded newform 4017.2.a.k.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.397144 q^{2} +1.00000 q^{3} -1.84228 q^{4} -2.35712 q^{5} +0.397144 q^{6} -3.48052 q^{7} -1.52594 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.397144 q^{2} +1.00000 q^{3} -1.84228 q^{4} -2.35712 q^{5} +0.397144 q^{6} -3.48052 q^{7} -1.52594 q^{8} +1.00000 q^{9} -0.936118 q^{10} -2.40080 q^{11} -1.84228 q^{12} +1.00000 q^{13} -1.38227 q^{14} -2.35712 q^{15} +3.07854 q^{16} -3.14162 q^{17} +0.397144 q^{18} -4.44194 q^{19} +4.34247 q^{20} -3.48052 q^{21} -0.953462 q^{22} -4.93504 q^{23} -1.52594 q^{24} +0.556030 q^{25} +0.397144 q^{26} +1.00000 q^{27} +6.41207 q^{28} -5.92403 q^{29} -0.936118 q^{30} -0.388959 q^{31} +4.27450 q^{32} -2.40080 q^{33} -1.24767 q^{34} +8.20400 q^{35} -1.84228 q^{36} +6.82411 q^{37} -1.76409 q^{38} +1.00000 q^{39} +3.59682 q^{40} -7.16201 q^{41} -1.38227 q^{42} -1.48525 q^{43} +4.42293 q^{44} -2.35712 q^{45} -1.95992 q^{46} +5.27915 q^{47} +3.07854 q^{48} +5.11399 q^{49} +0.220824 q^{50} -3.14162 q^{51} -1.84228 q^{52} -4.17847 q^{53} +0.397144 q^{54} +5.65897 q^{55} +5.31105 q^{56} -4.44194 q^{57} -2.35269 q^{58} +8.22759 q^{59} +4.34247 q^{60} +5.23185 q^{61} -0.154473 q^{62} -3.48052 q^{63} -4.45948 q^{64} -2.35712 q^{65} -0.953462 q^{66} -1.95588 q^{67} +5.78772 q^{68} -4.93504 q^{69} +3.25817 q^{70} +7.92857 q^{71} -1.52594 q^{72} +13.3362 q^{73} +2.71016 q^{74} +0.556030 q^{75} +8.18329 q^{76} +8.35601 q^{77} +0.397144 q^{78} -8.23551 q^{79} -7.25649 q^{80} +1.00000 q^{81} -2.84435 q^{82} -5.00152 q^{83} +6.41207 q^{84} +7.40517 q^{85} -0.589857 q^{86} -5.92403 q^{87} +3.66347 q^{88} +5.34007 q^{89} -0.936118 q^{90} -3.48052 q^{91} +9.09170 q^{92} -0.388959 q^{93} +2.09659 q^{94} +10.4702 q^{95} +4.27450 q^{96} +3.62112 q^{97} +2.03099 q^{98} -2.40080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	0.397144	0.280823	0.140412	−	0.990093i	$-0.455157\pi$
$2$	0.397144	0.280823	0.140412	+	0.990093i	$0.455157\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.84228	−0.921138
$5$	−2.35712	−1.05414	−0.527069	−	0.849823i	$-0.676709\pi$
$5$	−2.35712	−1.05414	−0.527069	+	0.849823i	$0.676709\pi$
$6$	0.397144	0.162133
$7$	−3.48052	−1.31551	−0.657756	−	0.753231i	$-0.728494\pi$
$7$	−3.48052	−1.31551	−0.657756	+	0.753231i	$0.728494\pi$
$8$	−1.52594	−0.539501
$9$	1.00000	0.333333
$10$	−0.936118	−0.296027
$11$	−2.40080	−0.723867	−0.361934	−	0.932204i	$-0.617883\pi$
$11$	−2.40080	−0.723867	−0.361934	+	0.932204i	$0.617883\pi$
$12$	−1.84228	−0.531819
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.38227	−0.369426
$15$	−2.35712	−0.608607
$16$	3.07854	0.769634
$17$	−3.14162	−0.761954	−0.380977	−	0.924585i	$-0.624412\pi$
$17$	−3.14162	−0.761954	−0.380977	+	0.924585i	$0.624412\pi$
$18$	0.397144	0.0936078
$19$	−4.44194	−1.01905	−0.509526	−	0.860455i	$-0.670179\pi$
$19$	−4.44194	−1.01905	−0.509526	+	0.860455i	$0.670179\pi$
$20$	4.34247	0.971006
$21$	−3.48052	−0.759511
$22$	−0.953462	−0.203279
$23$	−4.93504	−1.02903	−0.514513	−	0.857482i	$-0.672027\pi$
$23$	−4.93504	−1.02903	−0.514513	+	0.857482i	$0.672027\pi$
$24$	−1.52594	−0.311481
$25$	0.556030	0.111206
$26$	0.397144	0.0778864
$27$	1.00000	0.192450
$28$	6.41207	1.21177
$29$	−5.92403	−1.10006	−0.550032	−	0.835143i	$-0.685385\pi$
$29$	−5.92403	−1.10006	−0.550032	+	0.835143i	$0.685385\pi$
$30$	−0.936118	−0.170911
$31$	−0.388959	−0.0698590	−0.0349295	−	0.999390i	$-0.511121\pi$
$31$	−0.388959	−0.0698590	−0.0349295	+	0.999390i	$0.511121\pi$
$32$	4.27450	0.755632
$33$	−2.40080	−0.417925
$34$	−1.24767	−0.213974
$35$	8.20400	1.38673
$36$	−1.84228	−0.307046
$37$	6.82411	1.12188	0.560939	−	0.827857i	$-0.310440\pi$
$37$	6.82411	1.12188	0.560939	+	0.827857i	$0.310440\pi$
$38$	−1.76409	−0.286174
$39$	1.00000	0.160128
$40$	3.59682	0.568708
$41$	−7.16201	−1.11852	−0.559259	−	0.828993i	$-0.688914\pi$
$41$	−7.16201	−1.11852	−0.559259	+	0.828993i	$0.688914\pi$
$42$	−1.38227	−0.213288
$43$	−1.48525	−0.226498	−0.113249	−	0.993567i	$-0.536126\pi$
$43$	−1.48525	−0.226498	−0.113249	+	0.993567i	$0.536126\pi$
$44$	4.42293	0.666782
$45$	−2.35712	−0.351379
$46$	−1.95992	−0.288975
$47$	5.27915	0.770044	0.385022	−	0.922907i	$-0.374194\pi$
$47$	5.27915	0.770044	0.385022	+	0.922907i	$0.374194\pi$
$48$	3.07854	0.444348
$49$	5.11399	0.730570
$50$	0.220824	0.0312293
$51$	−3.14162	−0.439914
$52$	−1.84228	−0.255478
$53$	−4.17847	−0.573957	−0.286979	−	0.957937i	$-0.592651\pi$
$53$	−4.17847	−0.573957	−0.286979	+	0.957937i	$0.592651\pi$
$54$	0.397144	0.0540445
$55$	5.65897	0.763056
$56$	5.31105	0.709719
$57$	−4.44194	−0.588350
$58$	−2.35269	−0.308924
$59$	8.22759	1.07114	0.535570	−	0.844491i	$-0.320097\pi$
$59$	8.22759	1.07114	0.535570	+	0.844491i	$0.320097\pi$
$60$	4.34247	0.560611
$61$	5.23185	0.669870	0.334935	−	0.942241i	$-0.391286\pi$
$61$	5.23185	0.669870	0.334935	+	0.942241i	$0.391286\pi$
$62$	−0.154473	−0.0196181
$63$	−3.48052	−0.438504
$64$	−4.45948	−0.557435
$65$	−2.35712	−0.292365
$66$	−0.953462	−0.117363
$67$	−1.95588	−0.238949	−0.119475	−	0.992837i	$-0.538121\pi$
$67$	−1.95588	−0.238949	−0.119475	+	0.992837i	$0.538121\pi$
$68$	5.78772	0.701865
$69$	−4.93504	−0.594109
$70$	3.25817	0.389426
$71$	7.92857	0.940948	0.470474	−	0.882414i	$-0.344083\pi$
$71$	7.92857	0.940948	0.470474	+	0.882414i	$0.344083\pi$
$72$	−1.52594	−0.179834
$73$	13.3362	1.56088	0.780441	−	0.625230i	$-0.214995\pi$
$73$	13.3362	1.56088	0.780441	+	0.625230i	$0.214995\pi$
$74$	2.71016	0.315049
$75$	0.556030	0.0642048
$76$	8.18329	0.938688
$77$	8.35601	0.952255
$78$	0.397144	0.0449677
$79$	−8.23551	−0.926567	−0.463284	−	0.886210i	$-0.653329\pi$
$79$	−8.23551	−0.926567	−0.463284	+	0.886210i	$0.653329\pi$
$80$	−7.25649	−0.811300
$81$	1.00000	0.111111
$82$	−2.84435	−0.314106
$83$	−5.00152	−0.548989	−0.274494	−	0.961589i	$-0.588510\pi$
$83$	−5.00152	−0.548989	−0.274494	+	0.961589i	$0.588510\pi$
$84$	6.41207	0.699614
$85$	7.40517	0.803204
$86$	−0.589857	−0.0636059
$87$	−5.92403	−0.635123
$88$	3.66347	0.390527
$89$	5.34007	0.566046	0.283023	−	0.959113i	$-0.408663\pi$
$89$	5.34007	0.566046	0.283023	+	0.959113i	$0.408663\pi$
$90$	−0.936118	−0.0986755
$91$	−3.48052	−0.364857
$92$	9.09170	0.947876
$93$	−0.388959	−0.0403331
$94$	2.09659	0.216246
$95$	10.4702	1.07422
$96$	4.27450	0.436264
$97$	3.62112	0.367669	0.183835	−	0.982957i	$-0.441149\pi$
$97$	3.62112	0.367669	0.183835	+	0.982957i	$0.441149\pi$
$98$	2.03099	0.205161
$99$	−2.40080	−0.241289
$100$	−1.02436	−0.102436
$101$	−5.18787	−0.516213	−0.258106	−	0.966117i	$-0.583098\pi$
$101$	−5.18787	−0.516213	−0.258106	+	0.966117i	$0.583098\pi$
$102$	−1.24767	−0.123538
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.52594	−0.149631
$105$	8.20400	0.800629
$106$	−1.65946	−0.161181
$107$	−12.4808	−1.20656	−0.603282	−	0.797528i	$-0.706141\pi$
$107$	−12.4808	−1.20656	−0.603282	+	0.797528i	$0.706141\pi$
$108$	−1.84228	−0.177273
$109$	−9.30985	−0.891722	−0.445861	−	0.895102i	$-0.647102\pi$
$109$	−9.30985	−0.891722	−0.445861	+	0.895102i	$0.647102\pi$
$110$	2.24743	0.214284
$111$	6.82411	0.647716
$112$	−10.7149	−1.01246
$113$	1.86339	0.175293	0.0876465	−	0.996152i	$-0.472065\pi$
$113$	1.86339	0.175293	0.0876465	+	0.996152i	$0.472065\pi$
$114$	−1.76409	−0.165222
$115$	11.6325	1.08474
$116$	10.9137	1.01331
$117$	1.00000	0.0924500
$118$	3.26754	0.300801
$119$	10.9344	1.00236
$120$	3.59682	0.328344
$121$	−5.23618	−0.476016
$122$	2.07780	0.188115
$123$	−7.16201	−0.645777
$124$	0.716569	0.0643498
$125$	10.4750	0.936911
$126$	−1.38227	−0.123142
$127$	3.22601	0.286262	0.143131	−	0.989704i	$-0.454283\pi$
$127$	3.22601	0.286262	0.143131	+	0.989704i	$0.454283\pi$
$128$	−10.3201	−0.912173
$129$	−1.48525	−0.130769
$130$	−0.936118	−0.0821030
$131$	12.7909	1.11755	0.558774	−	0.829320i	$-0.311272\pi$
$131$	12.7909	1.11755	0.558774	+	0.829320i	$0.311272\pi$
$132$	4.42293	0.384967
$133$	15.4603	1.34057
$134$	−0.776768	−0.0671025
$135$	−2.35712	−0.202869
$136$	4.79391	0.411074
$137$	−3.90797	−0.333880	−0.166940	−	0.985967i	$-0.553389\pi$
$137$	−3.90797	−0.333880	−0.166940	+	0.985967i	$0.553389\pi$
$138$	−1.95992	−0.166840
$139$	4.51689	0.383118	0.191559	−	0.981481i	$-0.438646\pi$
$139$	4.51689	0.383118	0.191559	+	0.981481i	$0.438646\pi$
$140$	−15.1140	−1.27737
$141$	5.27915	0.444585
$142$	3.14879	0.264240
$143$	−2.40080	−0.200765
$144$	3.07854	0.256545
$145$	13.9637	1.15962
$146$	5.29639	0.438332
$147$	5.11399	0.421795
$148$	−12.5719	−1.03340
$149$	−6.91038	−0.566121	−0.283060	−	0.959102i	$-0.591350\pi$
$149$	−6.91038	−0.566121	−0.283060	+	0.959102i	$0.591350\pi$
$150$	0.220824	0.0180302
$151$	19.5386	1.59003	0.795013	−	0.606592i	$-0.207464\pi$
$151$	19.5386	1.59003	0.795013	+	0.606592i	$0.207464\pi$
$152$	6.77813	0.549779
$153$	−3.14162	−0.253985
$154$	3.31854	0.267416
$155$	0.916824	0.0736410
$156$	−1.84228	−0.147500
$157$	−3.39708	−0.271116	−0.135558	−	0.990769i	$-0.543283\pi$
$157$	−3.39708	−0.271116	−0.135558	+	0.990769i	$0.543283\pi$
$158$	−3.27069	−0.260202
$159$	−4.17847	−0.331374
$160$	−10.0755	−0.796540
$161$	17.1765	1.35370
$162$	0.397144	0.0312026
$163$	6.54289	0.512479	0.256239	−	0.966613i	$-0.417516\pi$
$163$	6.54289	0.512479	0.256239	+	0.966613i	$0.417516\pi$
$164$	13.1944	1.03031
$165$	5.65897	0.440550
$166$	−1.98633	−0.154169
$167$	16.7843	1.29881	0.649404	−	0.760444i	$-0.275019\pi$
$167$	16.7843	1.29881	0.649404	+	0.760444i	$0.275019\pi$
$168$	5.31105	0.409756
$169$	1.00000	0.0769231
$170$	2.94092	0.225558
$171$	−4.44194	−0.339684
$172$	2.73623	0.208636
$173$	0.0317184	0.00241150	0.00120575	−	0.999999i	$-0.499616\pi$
$173$	0.0317184	0.00241150	0.00120575	+	0.999999i	$0.499616\pi$
$174$	−2.35269	−0.178357
$175$	−1.93527	−0.146293
$176$	−7.39093	−0.557113
$177$	8.22759	0.618423
$178$	2.12078	0.158959
$179$	15.4218	1.15268	0.576341	−	0.817210i	$-0.304480\pi$
$179$	15.4218	1.15268	0.576341	+	0.817210i	$0.304480\pi$
$180$	4.34247	0.323669
$181$	−5.32824	−0.396045	−0.198022	−	0.980198i	$-0.563452\pi$
$181$	−5.32824	−0.396045	−0.198022	+	0.980198i	$0.563452\pi$
$182$	−1.38227	−0.102460
$183$	5.23185	0.386750
$184$	7.53056	0.555160
$185$	−16.0853	−1.18261
$186$	−0.154473	−0.0113265
$187$	7.54238	0.551553
$188$	−9.72566	−0.709317
$189$	−3.48052	−0.253170
$190$	4.15818	0.301666
$191$	0.325735	0.0235694	0.0117847	−	0.999931i	$-0.496249\pi$
$191$	0.325735	0.0235694	0.0117847	+	0.999931i	$0.496249\pi$
$192$	−4.45948	−0.321835
$193$	−2.29090	−0.164902	−0.0824512	−	0.996595i	$-0.526275\pi$
$193$	−2.29090	−0.164902	−0.0824512	+	0.996595i	$0.526275\pi$
$194$	1.43811	0.103250
$195$	−2.35712	−0.168797
$196$	−9.42138	−0.672956
$197$	−2.42916	−0.173070	−0.0865352	−	0.996249i	$-0.527580\pi$
$197$	−2.42916	−0.173070	−0.0865352	+	0.996249i	$0.527580\pi$
$198$	−0.953462	−0.0677596
$199$	−1.02712	−0.0728106	−0.0364053	−	0.999337i	$-0.511591\pi$
$199$	−1.02712	−0.0728106	−0.0364053	+	0.999337i	$0.511591\pi$
$200$	−0.848468	−0.0599957
$201$	−1.95588	−0.137957
$202$	−2.06033	−0.144965
$203$	20.6187	1.44715
$204$	5.78772	0.405222
$205$	16.8818	1.17907
$206$	0.397144	0.0276704
$207$	−4.93504	−0.343009
$208$	3.07854	0.213458
$209$	10.6642	0.737658
$210$	3.25817	0.224835
$211$	−7.74145	−0.532944	−0.266472	−	0.963843i	$-0.585858\pi$
$211$	−7.74145	−0.532944	−0.266472	+	0.963843i	$0.585858\pi$
$212$	7.69790	0.528694
$213$	7.92857	0.543257
$214$	−4.95668	−0.338831
$215$	3.50091	0.238760
$216$	−1.52594	−0.103827
$217$	1.35378	0.0919004
$218$	−3.69736	−0.250417
$219$	13.3362	0.901175
$220$	−10.4254	−0.702880
$221$	−3.14162	−0.211328
$222$	2.71016	0.181894
$223$	−6.83742	−0.457867	−0.228934	−	0.973442i	$-0.573524\pi$
$223$	−6.83742	−0.457867	−0.228934	+	0.973442i	$0.573524\pi$
$224$	−14.8775	−0.994042
$225$	0.556030	0.0370687
$226$	0.740035	0.0492264
$227$	−21.0247	−1.39546	−0.697730	−	0.716361i	$-0.745806\pi$
$227$	−21.0247	−1.39546	−0.697730	+	0.716361i	$0.745806\pi$
$228$	8.18329	0.541952
$229$	13.1123	0.866486	0.433243	−	0.901277i	$-0.357369\pi$
$229$	13.1123	0.866486	0.433243	+	0.901277i	$0.357369\pi$
$230$	4.61978	0.304619
$231$	8.35601	0.549785
$232$	9.03970	0.593485
$233$	−11.2307	−0.735749	−0.367875	−	0.929875i	$-0.619914\pi$
$233$	−11.2307	−0.735749	−0.367875	+	0.929875i	$0.619914\pi$
$234$	0.397144	0.0259621
$235$	−12.4436	−0.811732
$236$	−15.1575	−0.986668
$237$	−8.23551	−0.534954
$238$	4.34255	0.281486
$239$	13.8874	0.898298	0.449149	−	0.893457i	$-0.351727\pi$
$239$	13.8874	0.898298	0.449149	+	0.893457i	$0.351727\pi$
$240$	−7.25649	−0.468404
$241$	20.7251	1.33502	0.667512	−	0.744599i	$-0.267359\pi$
$241$	20.7251	1.33502	0.667512	+	0.744599i	$0.267359\pi$
$242$	−2.07952	−0.133677
$243$	1.00000	0.0641500
$244$	−9.63852	−0.617043
$245$	−12.0543	−0.770121
$246$	−2.84435	−0.181349
$247$	−4.44194	−0.282634
$248$	0.593527	0.0376890
$249$	−5.00152	−0.316959
$250$	4.16008	0.263107
$251$	2.94913	0.186147	0.0930737	−	0.995659i	$-0.470331\pi$
$251$	2.94913	0.186147	0.0930737	+	0.995659i	$0.470331\pi$
$252$	6.41207	0.403923
$253$	11.8480	0.744878
$254$	1.28119	0.0803892
$255$	7.40517	0.463730
$256$	4.82040	0.301275
$257$	−16.8302	−1.04984	−0.524921	−	0.851151i	$-0.675905\pi$
$257$	−16.8302	−1.04984	−0.524921	+	0.851151i	$0.675905\pi$
$258$	−0.589857	−0.0367229
$259$	−23.7514	−1.47584
$260$	4.34247	0.269309
$261$	−5.92403	−0.366688
$262$	5.07984	0.313834
$263$	−14.1113	−0.870143	−0.435071	−	0.900396i	$-0.643277\pi$
$263$	−14.1113	−0.870143	−0.435071	+	0.900396i	$0.643277\pi$
$264$	3.66347	0.225471
$265$	9.84918	0.605030
$266$	6.13995	0.376465
$267$	5.34007	0.326807
$268$	3.60328	0.220105
$269$	13.0066	0.793027	0.396514	−	0.918029i	$-0.370220\pi$
$269$	13.0066	0.793027	0.396514	+	0.918029i	$0.370220\pi$
$270$	−0.936118	−0.0569703
$271$	8.88481	0.539714	0.269857	−	0.962900i	$-0.413024\pi$
$271$	8.88481	0.539714	0.269857	+	0.962900i	$0.413024\pi$
$272$	−9.67157	−0.586425
$273$	−3.48052	−0.210650
$274$	−1.55203	−0.0937614
$275$	−1.33491	−0.0804984
$276$	9.09170	0.547256
$277$	−7.14661	−0.429398	−0.214699	−	0.976680i	$-0.568877\pi$
$277$	−7.14661	−0.429398	−0.214699	+	0.976680i	$0.568877\pi$
$278$	1.79386	0.107588
$279$	−0.388959	−0.0232863
$280$	−12.5188	−0.748142
$281$	−8.74367	−0.521604	−0.260802	−	0.965392i	$-0.583987\pi$
$281$	−8.74367	−0.521604	−0.260802	+	0.965392i	$0.583987\pi$
$282$	2.09659	0.124850
$283$	3.43102	0.203953	0.101976	−	0.994787i	$-0.467483\pi$
$283$	3.43102	0.203953	0.101976	+	0.994787i	$0.467483\pi$
$284$	−14.6066	−0.866743
$285$	10.4702	0.620202
$286$	−0.953462	−0.0563794
$287$	24.9275	1.47142
$288$	4.27450	0.251877
$289$	−7.13025	−0.419427
$290$	5.54559	0.325648
$291$	3.62112	0.212274
$292$	−24.5689	−1.43779
$293$	−25.6328	−1.49748	−0.748741	−	0.662863i	$-0.769341\pi$
$293$	−25.6328	−1.49748	−0.748741	+	0.662863i	$0.769341\pi$
$294$	2.03099	0.118450
$295$	−19.3934	−1.12913
$296$	−10.4132	−0.605253
$297$	−2.40080	−0.139308
$298$	−2.74442	−0.158980
$299$	−4.93504	−0.285401
$300$	−1.02436	−0.0591415
$301$	5.16942	0.297960
$302$	7.75963	0.446517
$303$	−5.18787	−0.298036
$304$	−13.6747	−0.784297
$305$	−12.3321	−0.706135
$306$	−1.24767	−0.0713248
$307$	0.124655	0.00711445	0.00355722	−	0.999994i	$-0.498868\pi$
$307$	0.124655	0.00711445	0.00355722	+	0.999994i	$0.498868\pi$
$308$	−15.3941	−0.877159
$309$	1.00000	0.0568880
$310$	0.364111	0.0206801
$311$	7.65997	0.434357	0.217179	−	0.976132i	$-0.430315\pi$
$311$	7.65997	0.434357	0.217179	+	0.976132i	$0.430315\pi$
$312$	−1.52594	−0.0863892
$313$	−25.2691	−1.42829	−0.714146	−	0.699997i	$-0.753185\pi$
$313$	−25.2691	−1.42829	−0.714146	+	0.699997i	$0.753185\pi$
$314$	−1.34913	−0.0761359
$315$	8.20400	0.462243
$316$	15.1721	0.853496
$317$	18.7718	1.05433	0.527164	−	0.849763i	$-0.323255\pi$
$317$	18.7718	1.05433	0.527164	+	0.849763i	$0.323255\pi$
$318$	−1.65946	−0.0930577
$319$	14.2224	0.796301
$320$	10.5115	0.587613
$321$	−12.4808	−0.696610
$322$	6.82154	0.380149
$323$	13.9549	0.776470
$324$	−1.84228	−0.102349
$325$	0.556030	0.0308430
$326$	2.59847	0.143916
$327$	−9.30985	−0.514836
$328$	10.9288	0.603442
$329$	−18.3742	−1.01300
$330$	2.24743	0.123717
$331$	12.9031	0.709218	0.354609	−	0.935015i	$-0.384614\pi$
$331$	12.9031	0.709218	0.354609	+	0.935015i	$0.384614\pi$
$332$	9.21419	0.505694
$333$	6.82411	0.373959
$334$	6.66578	0.364735
$335$	4.61026	0.251885
$336$	−10.7149	−0.584545
$337$	17.4183	0.948833	0.474417	−	0.880300i	$-0.342659\pi$
$337$	17.4183	0.948833	0.474417	+	0.880300i	$0.342659\pi$
$338$	0.397144	0.0216018
$339$	1.86339	0.101205
$340$	−13.6424	−0.739862
$341$	0.933810	0.0505687
$342$	−1.76409	−0.0953912
$343$	6.56430	0.354439
$344$	2.26639	0.122196
$345$	11.6325	0.626272
$346$	0.0125968	0.000677207 0
$347$	17.4696	0.937820	0.468910	−	0.883246i	$-0.344647\pi$
$347$	17.4696	0.937820	0.468910	+	0.883246i	$0.344647\pi$
$348$	10.9137	0.585036
$349$	−24.8670	−1.33110	−0.665549	−	0.746354i	$-0.731803\pi$
$349$	−24.8670	−1.33110	−0.665549	+	0.746354i	$0.731803\pi$
$350$	−0.768582	−0.0410824
$351$	1.00000	0.0533761
$352$	−10.2622	−0.546977
$353$	0.0965503	0.00513885	0.00256943	−	0.999997i	$-0.499182\pi$
$353$	0.0965503	0.00513885	0.00256943	+	0.999997i	$0.499182\pi$
$354$	3.26754	0.173668
$355$	−18.6886	−0.991889
$356$	−9.83788	−0.521406
$357$	10.9344	0.578712
$358$	6.12469	0.323700
$359$	−21.3388	−1.12622	−0.563109	−	0.826382i	$-0.690395\pi$
$359$	−21.3388	−1.12622	−0.563109	+	0.826382i	$0.690395\pi$
$360$	3.59682	0.189569
$361$	0.730866	0.0384666
$362$	−2.11608	−0.111219
$363$	−5.23618	−0.274828
$364$	6.41207	0.336084
$365$	−31.4350	−1.64538
$366$	2.07780	0.108608
$367$	2.40738	0.125664	0.0628320	−	0.998024i	$-0.479987\pi$
$367$	2.40738	0.125664	0.0628320	+	0.998024i	$0.479987\pi$
$368$	−15.1927	−0.791974
$369$	−7.16201	−0.372840
$370$	−6.38818	−0.332105
$371$	14.5432	0.755047
$372$	0.716569	0.0371524
$373$	−9.79067	−0.506942	−0.253471	−	0.967343i	$-0.581572\pi$
$373$	−9.79067	−0.506942	−0.253471	+	0.967343i	$0.581572\pi$
$374$	2.99541	0.154889
$375$	10.4750	0.540926
$376$	−8.05566	−0.415439
$377$	−5.92403	−0.305103
$378$	−1.38227	−0.0710961
$379$	23.0944	1.18628	0.593140	−	0.805099i	$-0.297888\pi$
$379$	23.0944	1.18628	0.593140	+	0.805099i	$0.297888\pi$
$380$	−19.2890	−0.989506
$381$	3.22601	0.165274
$382$	0.129364	0.00661883
$383$	14.7851	0.755485	0.377742	−	0.925911i	$-0.376700\pi$
$383$	14.7851	0.755485	0.377742	+	0.925911i	$0.376700\pi$
$384$	−10.3201	−0.526643
$385$	−19.6961	−1.00381
$386$	−0.909817	−0.0463085
$387$	−1.48525	−0.0754993
$388$	−6.67111	−0.338674
$389$	−21.8573	−1.10821	−0.554106	−	0.832446i	$-0.686940\pi$
$389$	−21.8573	−1.10821	−0.554106	+	0.832446i	$0.686940\pi$
$390$	−0.936118	−0.0474022
$391$	15.5040	0.784070
$392$	−7.80363	−0.394143
$393$	12.7909	0.645216
$394$	−0.964727	−0.0486022
$395$	19.4121	0.976729
$396$	4.42293	0.222261
$397$	13.2181	0.663399	0.331700	−	0.943385i	$-0.392378\pi$
$397$	13.2181	0.663399	0.331700	+	0.943385i	$0.392378\pi$
$398$	−0.407915	−0.0204469
$399$	15.4603	0.773981
$400$	1.71176	0.0855879
$401$	−27.0651	−1.35157	−0.675783	−	0.737100i	$-0.736195\pi$
$401$	−27.0651	−1.35157	−0.675783	+	0.737100i	$0.736195\pi$
$402$	−0.776768	−0.0387417
$403$	−0.388959	−0.0193754
$404$	9.55750	0.475503
$405$	−2.35712	−0.117126
$406$	8.18859	0.406393
$407$	−16.3833	−0.812090
$408$	4.79391	0.237334
$409$	−16.4451	−0.813160	−0.406580	−	0.913615i	$-0.633279\pi$
$409$	−16.4451	−0.813160	−0.406580	+	0.913615i	$0.633279\pi$
$410$	6.70449	0.331111
$411$	−3.90797	−0.192766
$412$	−1.84228	−0.0907624
$413$	−28.6362	−1.40910
$414$	−1.95992	−0.0963249
$415$	11.7892	0.578709
$416$	4.27450	0.209575
$417$	4.51689	0.221193
$418$	4.23523	0.207152
$419$	−6.69477	−0.327061	−0.163531	−	0.986538i	$-0.552288\pi$
$419$	−6.69477	−0.327061	−0.163531	+	0.986538i	$0.552288\pi$
$420$	−15.1140	−0.737490
$421$	32.8074	1.59893	0.799467	−	0.600710i	$-0.205115\pi$
$421$	32.8074	1.59893	0.799467	+	0.600710i	$0.205115\pi$
$422$	−3.07447	−0.149663
$423$	5.27915	0.256681
$424$	6.37609	0.309650
$425$	−1.74683	−0.0847338
$426$	3.14879	0.152559
$427$	−18.2095	−0.881222
$428$	22.9931	1.11141
$429$	−2.40080	−0.115912
$430$	1.39037	0.0670494
$431$	−8.91059	−0.429208	−0.214604	−	0.976701i	$-0.568846\pi$
$431$	−8.91059	−0.429208	−0.214604	+	0.976701i	$0.568846\pi$
$432$	3.07854	0.148116
$433$	−15.9392	−0.765988	−0.382994	−	0.923751i	$-0.625107\pi$
$433$	−15.9392	−0.765988	−0.382994	+	0.923751i	$0.625107\pi$
$434$	0.537645	0.0258078
$435$	13.9637	0.669506
$436$	17.1513	0.821399
$437$	21.9212	1.04863
$438$	5.29639	0.253071
$439$	−12.4877	−0.596007	−0.298003	−	0.954565i	$-0.596321\pi$
$439$	−12.4877	−0.596007	−0.298003	+	0.954565i	$0.596321\pi$
$440$	−8.63524	−0.411669
$441$	5.11399	0.243523
$442$	−1.24767	−0.0593458
$443$	−25.6300	−1.21772	−0.608859	−	0.793279i	$-0.708372\pi$
$443$	−25.6300	−1.21772	−0.608859	+	0.793279i	$0.708372\pi$
$444$	−12.5719	−0.596636
$445$	−12.5872	−0.596690
$446$	−2.71544	−0.128580
$447$	−6.91038	−0.326850
$448$	15.5213	0.733312
$449$	−15.6993	−0.740895	−0.370448	−	0.928853i	$-0.620796\pi$
$449$	−15.6993	−0.740895	−0.370448	+	0.928853i	$0.620796\pi$
$450$	0.220824	0.0104098
$451$	17.1945	0.809659
$452$	−3.43288	−0.161469
$453$	19.5386	0.918002
$454$	−8.34985	−0.391878
$455$	8.20400	0.384610
$456$	6.77813	0.317415
$457$	−18.4016	−0.860790	−0.430395	−	0.902641i	$-0.641626\pi$
$457$	−18.4016	−0.860790	−0.430395	+	0.902641i	$0.641626\pi$
$458$	5.20748	0.243330
$459$	−3.14162	−0.146638
$460$	−21.4303	−0.999191
$461$	−31.2633	−1.45608	−0.728038	−	0.685536i	$-0.759568\pi$
$461$	−31.2633	−1.45608	−0.728038	+	0.685536i	$0.759568\pi$
$462$	3.31854	0.154392
$463$	28.9557	1.34569	0.672843	−	0.739785i	$-0.265073\pi$
$463$	28.9557	1.34569	0.672843	+	0.739785i	$0.265073\pi$
$464$	−18.2373	−0.846647
$465$	0.916824	0.0425167
$466$	−4.46022	−0.206616
$467$	6.73411	0.311617	0.155809	−	0.987787i	$-0.450202\pi$
$467$	6.73411	0.311617	0.155809	+	0.987787i	$0.450202\pi$
$468$	−1.84228	−0.0851593
$469$	6.80748	0.314340
$470$	−4.94191	−0.227953
$471$	−3.39708	−0.156529
$472$	−12.5548	−0.577881
$473$	3.56577	0.163954
$474$	−3.27069	−0.150228
$475$	−2.46985	−0.113325
$476$	−20.1443	−0.923311
$477$	−4.17847	−0.191319
$478$	5.51528	0.252263
$479$	−33.3492	−1.52377	−0.761883	−	0.647715i	$-0.775725\pi$
$479$	−33.3492	−1.52377	−0.761883	+	0.647715i	$0.775725\pi$
$480$	−10.0755	−0.459883
$481$	6.82411	0.311153
$482$	8.23087	0.374906
$483$	17.1765	0.781557
$484$	9.64649	0.438477
$485$	−8.53544	−0.387574
$486$	0.397144	0.0180148
$487$	−19.8951	−0.901533	−0.450766	−	0.892642i	$-0.648849\pi$
$487$	−19.8951	−0.901533	−0.450766	+	0.892642i	$0.648849\pi$
$488$	−7.98349	−0.361395
$489$	6.54289	0.295880
$490$	−4.78730	−0.216268
$491$	21.2170	0.957509	0.478755	−	0.877949i	$-0.341088\pi$
$491$	21.2170	0.957509	0.478755	+	0.877949i	$0.341088\pi$
$492$	13.1944	0.594850
$493$	18.6110	0.838198
$494$	−1.76409	−0.0793703
$495$	5.65897	0.254352
$496$	−1.19742	−0.0537659
$497$	−27.5955	−1.23783
$498$	−1.98633	−0.0890094
$499$	−14.8073	−0.662865	−0.331432	−	0.943479i	$-0.607532\pi$
$499$	−14.8073	−0.662865	−0.331432	+	0.943479i	$0.607532\pi$
$500$	−19.2978	−0.863025
$501$	16.7843	0.749867
$502$	1.17123	0.0522746
$503$	−3.97517	−0.177244	−0.0886220	−	0.996065i	$-0.528246\pi$
$503$	−3.97517	−0.177244	−0.0886220	+	0.996065i	$0.528246\pi$
$504$	5.31105	0.236573
$505$	12.2285	0.544159
$506$	4.70537	0.209179
$507$	1.00000	0.0444116
$508$	−5.94321	−0.263687
$509$	−10.9613	−0.485849	−0.242925	−	0.970045i	$-0.578107\pi$
$509$	−10.9613	−0.485849	−0.242925	+	0.970045i	$0.578107\pi$
$510$	2.94092	0.130226
$511$	−46.4168	−2.05336
$512$	22.5545	0.996778
$513$	−4.44194	−0.196117
$514$	−6.68403	−0.294820
$515$	−2.35712	−0.103867
$516$	2.73623	0.120456
$517$	−12.6742	−0.557409
$518$	−9.43274	−0.414451
$519$	0.0317184	0.00139228
$520$	3.59682	0.157731
$521$	−12.0409	−0.527523	−0.263761	−	0.964588i	$-0.584963\pi$
$521$	−12.0409	−0.527523	−0.263761	+	0.964588i	$0.584963\pi$
$522$	−2.35269	−0.102975
$523$	−24.9546	−1.09119	−0.545593	−	0.838050i	$-0.683696\pi$
$523$	−24.9546	−1.09119	−0.545593	+	0.838050i	$0.683696\pi$
$524$	−23.5644	−1.02942
$525$	−1.93527	−0.0844622
$526$	−5.60424	−0.244356
$527$	1.22196	0.0532294
$528$	−7.39093	−0.321649
$529$	1.35459	0.0588954
$530$	3.91154	0.169907
$531$	8.22759	0.357047
$532$	−28.4821	−1.23485
$533$	−7.16201	−0.310221
$534$	2.12078	0.0917750
$535$	29.4188	1.27188
$536$	2.98456	0.128913
$537$	15.4218	0.665501
$538$	5.16550	0.222701
$539$	−12.2776	−0.528835
$540$	4.34247	0.186870
$541$	37.3584	1.60616	0.803081	−	0.595870i	$-0.203193\pi$
$541$	37.3584	1.60616	0.803081	+	0.595870i	$0.203193\pi$
$542$	3.52855	0.151564
$543$	−5.32824	−0.228657
$544$	−13.4288	−0.575756
$545$	21.9445	0.939998
$546$	−1.38227	−0.0591556
$547$	17.2512	0.737609	0.368805	−	0.929507i	$-0.379767\pi$
$547$	17.2512	0.737609	0.368805	+	0.929507i	$0.379767\pi$
$548$	7.19956	0.307550
$549$	5.23185	0.223290
$550$	−0.530154	−0.0226058
$551$	26.3142	1.12102
$552$	7.53056	0.320522
$553$	28.6638	1.21891
$554$	−2.83824	−0.120585
$555$	−16.0853	−0.682782
$556$	−8.32136	−0.352904
$557$	5.79022	0.245339	0.122670	−	0.992448i	$-0.460854\pi$
$557$	5.79022	0.245339	0.122670	+	0.992448i	$0.460854\pi$
$558$	−0.154473	−0.00653935
$559$	−1.48525	−0.0628192
$560$	25.2563	1.06727
$561$	7.54238	0.318439
$562$	−3.47250	−0.146479
$563$	−39.7533	−1.67540	−0.837700	−	0.546131i	$-0.816100\pi$
$563$	−39.7533	−1.67540	−0.837700	+	0.546131i	$0.816100\pi$
$564$	−9.72566	−0.409524
$565$	−4.39224	−0.184783
$566$	1.36261	0.0572747
$567$	−3.48052	−0.146168
$568$	−12.0985	−0.507642
$569$	−22.8090	−0.956203	−0.478102	−	0.878305i	$-0.658675\pi$
$569$	−22.8090	−0.956203	−0.478102	+	0.878305i	$0.658675\pi$
$570$	4.15818	0.174167
$571$	5.62181	0.235265	0.117633	−	0.993057i	$-0.462469\pi$
$571$	5.62181	0.235265	0.117633	+	0.993057i	$0.462469\pi$
$572$	4.42293	0.184932
$573$	0.325735	0.0136078
$574$	9.89981	0.413210
$575$	−2.74403	−0.114434
$576$	−4.45948	−0.185812
$577$	31.9368	1.32955	0.664773	−	0.747045i	$-0.268528\pi$
$577$	31.9368	1.32955	0.664773	+	0.747045i	$0.268528\pi$
$578$	−2.83174	−0.117785
$579$	−2.29090	−0.0952065
$580$	−25.7249	−1.06817
$581$	17.4079	0.722201
$582$	1.43811	0.0596115
$583$	10.0317	0.415469
$584$	−20.3502	−0.842096
$585$	−2.35712	−0.0974551
$586$	−10.1799	−0.420528
$587$	12.9537	0.534658	0.267329	−	0.963605i	$-0.413859\pi$
$587$	12.9537	0.534658	0.267329	+	0.963605i	$0.413859\pi$
$588$	−9.42138	−0.388531
$589$	1.72773	0.0711900
$590$	−7.70199	−0.317086
$591$	−2.42916	−0.0999223
$592$	21.0083	0.863435
$593$	2.34052	0.0961136	0.0480568	−	0.998845i	$-0.484697\pi$
$593$	2.34052	0.0961136	0.0480568	+	0.998845i	$0.484697\pi$
$594$	−0.953462	−0.0391210
$595$	−25.7738	−1.05662
$596$	12.7308	0.521475
$597$	−1.02712	−0.0420372
$598$	−1.95992	−0.0801472
$599$	−1.30918	−0.0534915	−0.0267458	−	0.999642i	$-0.508514\pi$
$599$	−1.30918	−0.0534915	−0.0267458	+	0.999642i	$0.508514\pi$
$600$	−0.848468	−0.0346385
$601$	−7.83622	−0.319646	−0.159823	−	0.987146i	$-0.551092\pi$
$601$	−7.83622	−0.319646	−0.159823	+	0.987146i	$0.551092\pi$
$602$	2.05301	0.0836743
$603$	−1.95588	−0.0796497
$604$	−35.9954	−1.46463
$605$	12.3423	0.501787
$606$	−2.06033	−0.0836954
$607$	45.6358	1.85230	0.926150	−	0.377155i	$-0.123097\pi$
$607$	45.6358	1.85230	0.926150	+	0.377155i	$0.123097\pi$
$608$	−18.9871	−0.770028
$609$	20.6187	0.835511
$610$	−4.89763	−0.198299
$611$	5.27915	0.213572
$612$	5.78772	0.233955
$613$	14.3427	0.579298	0.289649	−	0.957133i	$-0.406461\pi$
$613$	14.3427	0.579298	0.289649	+	0.957133i	$0.406461\pi$
$614$	0.0495061	0.00199790
$615$	16.8818	0.680738
$616$	−12.7507	−0.513742
$617$	7.16435	0.288426	0.144213	−	0.989547i	$-0.453935\pi$
$617$	7.16435	0.288426	0.144213	+	0.989547i	$0.453935\pi$
$618$	0.397144	0.0159755
$619$	22.4773	0.903439	0.451719	−	0.892160i	$-0.350811\pi$
$619$	22.4773	0.903439	0.451719	+	0.892160i	$0.350811\pi$
$620$	−1.68904	−0.0678336
$621$	−4.93504	−0.198036
$622$	3.04211	0.121978
$623$	−18.5862	−0.744640
$624$	3.07854	0.123240
$625$	−27.4710	−1.09884
$626$	−10.0355	−0.401098
$627$	10.6642	0.425887
$628$	6.25836	0.249736
$629$	−21.4387	−0.854818
$630$	3.25817	0.129809
$631$	29.0139	1.15502	0.577512	−	0.816382i	$-0.304024\pi$
$631$	29.0139	1.15502	0.577512	+	0.816382i	$0.304024\pi$
$632$	12.5669	0.499884
$633$	−7.74145	−0.307695
$634$	7.45511	0.296080
$635$	−7.60411	−0.301760
$636$	7.69790	0.305242
$637$	5.11399	0.202624
$638$	5.64834	0.223620
$639$	7.92857	0.313649
$640$	24.3256	0.961555
$641$	37.8495	1.49496	0.747482	−	0.664282i	$-0.231263\pi$
$641$	37.8495	1.49496	0.747482	+	0.664282i	$0.231263\pi$
$642$	−4.95668	−0.195624
$643$	−2.28985	−0.0903031	−0.0451515	−	0.998980i	$-0.514377\pi$
$643$	−2.28985	−0.0903031	−0.0451515	+	0.998980i	$0.514377\pi$
$644$	−31.6438	−1.24694
$645$	3.50091	0.137848
$646$	5.54210	0.218051
$647$	−34.6411	−1.36188	−0.680940	−	0.732339i	$-0.738429\pi$
$647$	−34.6411	−1.36188	−0.680940	+	0.732339i	$0.738429\pi$
$648$	−1.52594	−0.0599445
$649$	−19.7528	−0.775363
$650$	0.220824	0.00866144
$651$	1.35378	0.0530587
$652$	−12.0538	−0.472064
$653$	21.6499	0.847228	0.423614	−	0.905843i	$-0.360761\pi$
$653$	21.6499	0.847228	0.423614	+	0.905843i	$0.360761\pi$
$654$	−3.69736	−0.144578
$655$	−30.1498	−1.17805
$656$	−22.0485	−0.860850
$657$	13.3362	0.520294
$658$	−7.29720	−0.284474
$659$	4.53043	0.176480	0.0882402	−	0.996099i	$-0.471876\pi$
$659$	4.53043	0.176480	0.0882402	+	0.996099i	$0.471876\pi$
$660$	−10.4254	−0.405808
$661$	9.80453	0.381352	0.190676	−	0.981653i	$-0.438932\pi$
$661$	9.80453	0.381352	0.190676	+	0.981653i	$0.438932\pi$
$662$	5.12439	0.199165
$663$	−3.14162	−0.122010
$664$	7.63202	0.296180
$665$	−36.4417	−1.41315
$666$	2.71016	0.105016
$667$	29.2353	1.13200
$668$	−30.9213	−1.19638
$669$	−6.83742	−0.264350
$670$	1.83094	0.0707353
$671$	−12.5606	−0.484897
$672$	−14.8775	−0.573910
$673$	−3.49659	−0.134784	−0.0673919	−	0.997727i	$-0.521468\pi$
$673$	−3.49659	−0.134784	−0.0673919	+	0.997727i	$0.521468\pi$
$674$	6.91756	0.266455
$675$	0.556030	0.0214016
$676$	−1.84228	−0.0708568
$677$	15.8835	0.610452	0.305226	−	0.952280i	$-0.401268\pi$
$677$	15.8835	0.610452	0.305226	+	0.952280i	$0.401268\pi$
$678$	0.740035	0.0284209
$679$	−12.6034	−0.483673
$680$	−11.2998	−0.433329
$681$	−21.0247	−0.805669
$682$	0.370857	0.0142009
$683$	−48.1726	−1.84327	−0.921636	−	0.388055i	$-0.873147\pi$
$683$	−48.1726	−1.84327	−0.921636	+	0.388055i	$0.873147\pi$
$684$	8.18329	0.312896
$685$	9.21156	0.351956
$686$	2.60697	0.0995347
$687$	13.1123	0.500266
$688$	−4.57238	−0.174320
$689$	−4.17847	−0.159187
$690$	4.61978	0.175872
$691$	21.0433	0.800523	0.400262	−	0.916401i	$-0.368919\pi$
$691$	21.0433	0.800523	0.400262	+	0.916401i	$0.368919\pi$
$692$	−0.0584340	−0.00222133
$693$	8.35601	0.317418
$694$	6.93797	0.263362
$695$	−10.6469	−0.403859
$696$	9.03970	0.342649
$697$	22.5003	0.852259
$698$	−9.87578	−0.373804
$699$	−11.2307	−0.424785
$700$	3.56530	0.134756
$701$	16.5936	0.626732	0.313366	−	0.949632i	$-0.398543\pi$
$701$	16.5936	0.626732	0.313366	+	0.949632i	$0.398543\pi$
$702$	0.397144	0.0149892
$703$	−30.3123	−1.14325
$704$	10.7063	0.403509
$705$	−12.4436	−0.468654
$706$	0.0383444	0.00144311
$707$	18.0565	0.679084
$708$	−15.1575	−0.569653
$709$	−13.0948	−0.491784	−0.245892	−	0.969297i	$-0.579081\pi$
$709$	−13.0948	−0.491784	−0.245892	+	0.969297i	$0.579081\pi$
$710$	−7.42208	−0.278546
$711$	−8.23551	−0.308856
$712$	−8.14861	−0.305382
$713$	1.91953	0.0718868
$714$	4.34255	0.162516
$715$	5.65897	0.211634
$716$	−28.4113	−1.06178
$717$	13.8874	0.518633
$718$	−8.47458	−0.316269
$719$	20.7748	0.774770	0.387385	−	0.921918i	$-0.373378\pi$
$719$	20.7748	0.774770	0.387385	+	0.921918i	$0.373378\pi$
$720$	−7.25649	−0.270433
$721$	−3.48052	−0.129621
$722$	0.290259	0.0108023
$723$	20.7251	0.770777
$724$	9.81609	0.364812
$725$	−3.29394	−0.122334
$726$	−2.07952	−0.0771782
$727$	30.3858	1.12695	0.563473	−	0.826135i	$-0.309465\pi$
$727$	30.3858	1.12695	0.563473	+	0.826135i	$0.309465\pi$
$728$	5.31105	0.196841
$729$	1.00000	0.0370370
$730$	−12.4842	−0.462062
$731$	4.66607	0.172581
$732$	−9.63852	−0.356250
$733$	39.5921	1.46237	0.731184	−	0.682180i	$-0.238968\pi$
$733$	39.5921	1.46237	0.731184	+	0.682180i	$0.238968\pi$
$734$	0.956076	0.0352894
$735$	−12.0543	−0.444629
$736$	−21.0948	−0.777565
$737$	4.69568	0.172967
$738$	−2.84435	−0.104702
$739$	−32.2639	−1.18685	−0.593423	−	0.804891i	$-0.702224\pi$
$739$	−32.2639	−1.18685	−0.593423	+	0.804891i	$0.702224\pi$
$740$	29.6335	1.08935
$741$	−4.44194	−0.163179
$742$	5.77576	0.212035
$743$	32.7064	1.19988	0.599940	−	0.800045i	$-0.295191\pi$
$743$	32.7064	1.19988	0.599940	+	0.800045i	$0.295191\pi$
$744$	0.593527	0.0217598
$745$	16.2886	0.596769
$746$	−3.88831	−0.142361
$747$	−5.00152	−0.182996
$748$	−13.8951	−0.508057
$749$	43.4396	1.58725
$750$	4.16008	0.151905
$751$	2.74468	0.100155	0.0500773	−	0.998745i	$-0.484053\pi$
$751$	2.74468	0.100155	0.0500773	+	0.998745i	$0.484053\pi$
$752$	16.2521	0.592652
$753$	2.94913	0.107472
$754$	−2.35269	−0.0856801
$755$	−46.0548	−1.67611
$756$	6.41207	0.233205
$757$	38.2344	1.38965	0.694826	−	0.719178i	$-0.255481\pi$
$757$	38.2344	1.38965	0.694826	+	0.719178i	$0.255481\pi$
$758$	9.17181	0.333135
$759$	11.8480	0.430056
$760$	−15.9769	−0.579543
$761$	43.6650	1.58285	0.791427	−	0.611263i	$-0.209338\pi$
$761$	43.6650	1.58285	0.791427	+	0.611263i	$0.209338\pi$
$762$	1.28119	0.0464127
$763$	32.4031	1.17307
$764$	−0.600094	−0.0217106
$765$	7.40517	0.267735
$766$	5.87183	0.212158
$767$	8.22759	0.297081
$768$	4.82040	0.173941
$769$	8.85788	0.319423	0.159712	−	0.987164i	$-0.448944\pi$
$769$	8.85788	0.319423	0.159712	+	0.987164i	$0.448944\pi$
$770$	−7.82221	−0.281893
$771$	−16.8302	−0.606126
$772$	4.22047	0.151898
$773$	31.0381	1.11636	0.558181	−	0.829719i	$-0.311500\pi$
$773$	31.0381	1.11636	0.558181	+	0.829719i	$0.311500\pi$
$774$	−0.589857	−0.0212020
$775$	−0.216273	−0.00776875
$776$	−5.52561	−0.198358
$777$	−23.7514	−0.852078
$778$	−8.68052	−0.311212
$779$	31.8133	1.13983
$780$	4.34247	0.155485
$781$	−19.0349	−0.681121
$782$	6.15732	0.220185
$783$	−5.92403	−0.211708
$784$	15.7436	0.562271
$785$	8.00734	0.285794
$786$	5.07984	0.181192
$787$	−47.2558	−1.68449	−0.842243	−	0.539098i	$-0.818765\pi$
$787$	−47.2558	−1.68449	−0.842243	+	0.539098i	$0.818765\pi$
$788$	4.47518	0.159422
$789$	−14.1113	−0.502377
$790$	7.70941	0.274288
$791$	−6.48556	−0.230600
$792$	3.66347	0.130176
$793$	5.23185	0.185789
$794$	5.24951	0.186298
$795$	9.84918	0.349314
$796$	1.89224	0.0670686
$797$	25.8105	0.914256	0.457128	−	0.889401i	$-0.348878\pi$
$797$	25.8105	0.914256	0.457128	+	0.889401i	$0.348878\pi$
$798$	6.13995	0.217352
$799$	−16.5851	−0.586738
$800$	2.37675	0.0840308
$801$	5.34007	0.188682
$802$	−10.7488	−0.379552
$803$	−32.0174	−1.12987
$804$	3.60328	0.127078
$805$	−40.4871	−1.42698
$806$	−0.154473	−0.00544107
$807$	13.0066	0.457855
$808$	7.91637	0.278497
$809$	−13.7138	−0.482152	−0.241076	−	0.970506i	$-0.577500\pi$
$809$	−13.7138	−0.482152	−0.241076	+	0.970506i	$0.577500\pi$
$810$	−0.936118	−0.0328918
$811$	51.5793	1.81119	0.905597	−	0.424139i	$-0.139423\pi$
$811$	51.5793	1.81119	0.905597	+	0.424139i	$0.139423\pi$
$812$	−37.9853	−1.33302
$813$	8.88481	0.311604
$814$	−6.50653	−0.228054
$815$	−15.4224	−0.540223
$816$	−9.67157	−0.338573
$817$	6.59738	0.230813
$818$	−6.53109	−0.228354
$819$	−3.48052	−0.121619
$820$	−31.1009	−1.08609
$821$	20.7263	0.723353	0.361677	−	0.932304i	$-0.382204\pi$
$821$	20.7263	0.723353	0.361677	+	0.932304i	$0.382204\pi$
$822$	−1.55203	−0.0541332
$823$	7.09347	0.247263	0.123631	−	0.992328i	$-0.460546\pi$
$823$	7.09347	0.247263	0.123631	+	0.992328i	$0.460546\pi$
$824$	−1.52594	−0.0531586
$825$	−1.33491	−0.0464758
$826$	−11.3727	−0.395708
$827$	−27.4532	−0.954641	−0.477320	−	0.878729i	$-0.658392\pi$
$827$	−27.4532	−0.954641	−0.477320	+	0.878729i	$0.658392\pi$
$828$	9.09170	0.315959
$829$	−12.8835	−0.447462	−0.223731	−	0.974651i	$-0.571824\pi$
$829$	−12.8835	−0.447462	−0.223731	+	0.974651i	$0.571824\pi$
$830$	4.68202	0.162515
$831$	−7.14661	−0.247913
$832$	−4.45948	−0.154605
$833$	−16.0662	−0.556660
$834$	1.79386	0.0621162
$835$	−39.5626	−1.36912
$836$	−19.6464	−0.679485
$837$	−0.388959	−0.0134444
$838$	−2.65879	−0.0918464
$839$	−3.41681	−0.117961	−0.0589807	−	0.998259i	$-0.518785\pi$
$839$	−3.41681	−0.117961	−0.0589807	+	0.998259i	$0.518785\pi$
$840$	−12.5188	−0.431940
$841$	6.09411	0.210142
$842$	13.0293	0.449018
$843$	−8.74367	−0.301148
$844$	14.2619	0.490915
$845$	−2.35712	−0.0810875
$846$	2.09659	0.0720821
$847$	18.2246	0.626205
$848$	−12.8636	−0.441737
$849$	3.43102	0.117752
$850$	−0.693745	−0.0237952
$851$	−33.6773	−1.15444
$852$	−14.6066	−0.500414
$853$	8.81682	0.301882	0.150941	−	0.988543i	$-0.451770\pi$
$853$	8.81682	0.301882	0.150941	+	0.988543i	$0.451770\pi$
$854$	−7.23182	−0.247468
$855$	10.4702	0.358074
$856$	19.0449	0.650942
$857$	−10.8195	−0.369586	−0.184793	−	0.982777i	$-0.559162\pi$
$857$	−10.8195	−0.369586	−0.184793	+	0.982777i	$0.559162\pi$
$858$	−0.953462	−0.0325507
$859$	41.9314	1.43068	0.715340	−	0.698777i	$-0.246272\pi$
$859$	41.9314	1.43068	0.715340	+	0.698777i	$0.246272\pi$
$860$	−6.44964	−0.219931
$861$	24.9275	0.849527
$862$	−3.53879	−0.120532
$863$	39.3104	1.33814	0.669071	−	0.743199i	$-0.266692\pi$
$863$	39.3104	1.33814	0.669071	+	0.743199i	$0.266692\pi$
$864$	4.27450	0.145421
$865$	−0.0747641	−0.00254206
$866$	−6.33016	−0.215107
$867$	−7.13025	−0.242156
$868$	−2.49403	−0.0846529
$869$	19.7718	0.670712
$870$	5.54559	0.188013
$871$	−1.95588	−0.0662726
$872$	14.2063	0.481085
$873$	3.62112	0.122556
$874$	8.70586	0.294480
$875$	−36.4583	−1.23252
$876$	−24.5689	−0.830107
$877$	−54.6299	−1.84472	−0.922361	−	0.386330i	$-0.873743\pi$
$877$	−54.6299	−1.84472	−0.922361	+	0.386330i	$0.873743\pi$
$878$	−4.95943	−0.167373
$879$	−25.6328	−0.864572
$880$	17.4213	0.587273
$881$	−31.7061	−1.06821	−0.534103	−	0.845420i	$-0.679350\pi$
$881$	−31.7061	−1.06821	−0.534103	+	0.845420i	$0.679350\pi$
$882$	2.03099	0.0683870
$883$	13.3853	0.450453	0.225226	−	0.974306i	$-0.427688\pi$
$883$	13.3853	0.450453	0.225226	+	0.974306i	$0.427688\pi$
$884$	5.78772	0.194662
$885$	−19.3934	−0.651903
$886$	−10.1788	−0.341964
$887$	19.9669	0.670424	0.335212	−	0.942143i	$-0.391192\pi$
$887$	19.9669	0.670424	0.335212	+	0.942143i	$0.391192\pi$
$888$	−10.4132	−0.349443
$889$	−11.2282	−0.376581
$890$	−4.99893	−0.167565
$891$	−2.40080	−0.0804297
$892$	12.5964	0.421759
$893$	−23.4497	−0.784715
$894$	−2.74442	−0.0917871
$895$	−36.3511	−1.21508
$896$	35.9191	1.19997
$897$	−4.93504	−0.164776
$898$	−6.23488	−0.208061
$899$	2.30420	0.0768495
$900$	−1.02436	−0.0341454
$901$	13.1272	0.437329
$902$	6.82871	0.227371
$903$	5.16942	0.172028
$904$	−2.84342	−0.0945707
$905$	12.5593	0.417486
$906$	7.75963	0.257796
$907$	39.7196	1.31887	0.659433	−	0.751763i	$-0.270796\pi$
$907$	39.7196	1.31887	0.659433	+	0.751763i	$0.270796\pi$
$908$	38.7333	1.28541
$909$	−5.18787	−0.172071
$910$	3.25817	0.108007
$911$	5.23724	0.173518	0.0867588	−	0.996229i	$-0.472349\pi$
$911$	5.23724	0.173518	0.0867588	+	0.996229i	$0.472349\pi$
$912$	−13.6747	−0.452814
$913$	12.0076	0.397395
$914$	−7.30809	−0.241730
$915$	−12.3321	−0.407687
$916$	−24.1565	−0.798153
$917$	−44.5190	−1.47015
$918$	−1.24767	−0.0411794
$919$	41.8696	1.38115	0.690575	−	0.723261i	$-0.257358\pi$
$919$	41.8696	1.38115	0.690575	+	0.723261i	$0.257358\pi$
$920$	−17.7505	−0.585215
$921$	0.124655	0.00410753
$922$	−12.4160	−0.408900
$923$	7.92857	0.260972
$924$	−15.3941	−0.506428
$925$	3.79441	0.124760
$926$	11.4996	0.377900
$927$	1.00000	0.0328443
$928$	−25.3223	−0.831244
$929$	−28.6129	−0.938758	−0.469379	−	0.882997i	$-0.655522\pi$
$929$	−28.6129	−0.938758	−0.469379	+	0.882997i	$0.655522\pi$
$930$	0.364111	0.0119397
$931$	−22.7160	−0.744488
$932$	20.6901	0.677727
$933$	7.65997	0.250776
$934$	2.67441	0.0875095
$935$	−17.7783	−0.581413
$936$	−1.52594	−0.0498768
$937$	28.2078	0.921508	0.460754	−	0.887528i	$-0.347579\pi$
$937$	28.2078	0.921508	0.460754	+	0.887528i	$0.347579\pi$
$938$	2.70355	0.0882741
$939$	−25.2691	−0.824625
$940$	22.9246	0.747717
$941$	−18.2388	−0.594569	−0.297285	−	0.954789i	$-0.596081\pi$
$941$	−18.2388	−0.594569	−0.297285	+	0.954789i	$0.596081\pi$
$942$	−1.34913	−0.0439571
$943$	35.3448	1.15099
$944$	25.3289	0.824386
$945$	8.20400	0.266876
$946$	1.41613	0.0460422
$947$	28.8789	0.938439	0.469220	−	0.883081i	$-0.344535\pi$
$947$	28.8789	0.938439	0.469220	+	0.883081i	$0.344535\pi$
$948$	15.1721	0.492766
$949$	13.3362	0.432911
$950$	−0.980889	−0.0318242
$951$	18.7718	0.608717
$952$	−16.6853	−0.540773
$953$	57.4480	1.86092	0.930461	−	0.366390i	$-0.119406\pi$
$953$	57.4480	1.86092	0.930461	+	0.366390i	$0.119406\pi$
$954$	−1.65946	−0.0537269
$955$	−0.767798	−0.0248454
$956$	−25.5843	−0.827457
$957$	14.2224	0.459744
$958$	−13.2445	−0.427909
$959$	13.6017	0.439223
$960$	10.5115	0.339258
$961$	−30.8487	−0.995120
$962$	2.71016	0.0873790
$963$	−12.4808	−0.402188
$964$	−38.1815	−1.22974
$965$	5.39993	0.173830
$966$	6.82154	0.219479
$967$	−40.7520	−1.31050	−0.655248	−	0.755414i	$-0.727436\pi$
$967$	−40.7520	−1.31050	−0.655248	+	0.755414i	$0.727436\pi$
$968$	7.99009	0.256811
$969$	13.9549	0.448295
$970$	−3.38980	−0.108840
$971$	−36.7267	−1.17862	−0.589308	−	0.807909i	$-0.700599\pi$
$971$	−36.7267	−1.17862	−0.589308	+	0.807909i	$0.700599\pi$
$972$	−1.84228	−0.0590910
$973$	−15.7211	−0.503995
$974$	−7.90122	−0.253172
$975$	0.556030	0.0178072
$976$	16.1064	0.515555
$977$	−12.3534	−0.395220	−0.197610	−	0.980281i	$-0.563318\pi$
$977$	−12.3534	−0.395220	−0.197610	+	0.980281i	$0.563318\pi$
$978$	2.59847	0.0830900
$979$	−12.8204	−0.409742
$980$	22.2073	0.709388
$981$	−9.30985	−0.297241
$982$	8.42621	0.268891
$983$	−33.9289	−1.08216	−0.541082	−	0.840970i	$-0.681985\pi$
$983$	−33.9289	−1.08216	−0.541082	+	0.840970i	$0.681985\pi$
$984$	10.9288	0.348397
$985$	5.72583	0.182440
$986$	7.39126	0.235386
$987$	−18.3742	−0.584857
$988$	8.18329	0.260345
$989$	7.32974	0.233072
$990$	2.24743	0.0714280
$991$	8.99524	0.285743	0.142872	−	0.989741i	$-0.454366\pi$
$991$	8.99524	0.285743	0.142872	+	0.989741i	$0.454366\pi$
$992$	−1.66260	−0.0527877
$993$	12.9031	0.409467
$994$	−10.9594	−0.347611
$995$	2.42105	0.0767524
$996$	9.21419	0.291963
$997$	49.6759	1.57325	0.786626	−	0.617429i	$-0.211826\pi$
$997$	49.6759	1.57325	0.786626	+	0.617429i	$0.211826\pi$
$998$	−5.88063	−0.186148
$999$	6.82411	0.215905

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.18	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.18	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.397144 q^{2} +1.00000 q^{3} -1.84228 q^{4} -2.35712 q^{5} +0.397144 q^{6} -3.48052 q^{7} -1.52594 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.397144 q^{2} +1.00000 q^{3} -1.84228 q^{4} -2.35712 q^{5} +0.397144 q^{6} -3.48052 q^{7} -1.52594 q^{8} +1.00000 q^{9} -0.936118 q^{10} -2.40080 q^{11} -1.84228 q^{12} +1.00000 q^{13} -1.38227 q^{14} -2.35712 q^{15} +3.07854 q^{16} -3.14162 q^{17} +0.397144 q^{18} -4.44194 q^{19} +4.34247 q^{20} -3.48052 q^{21} -0.953462 q^{22} -4.93504 q^{23} -1.52594 q^{24} +0.556030 q^{25} +0.397144 q^{26} +1.00000 q^{27} +6.41207 q^{28} -5.92403 q^{29} -0.936118 q^{30} -0.388959 q^{31} +4.27450 q^{32} -2.40080 q^{33} -1.24767 q^{34} +8.20400 q^{35} -1.84228 q^{36} +6.82411 q^{37} -1.76409 q^{38} +1.00000 q^{39} +3.59682 q^{40} -7.16201 q^{41} -1.38227 q^{42} -1.48525 q^{43} +4.42293 q^{44} -2.35712 q^{45} -1.95992 q^{46} +5.27915 q^{47} +3.07854 q^{48} +5.11399 q^{49} +0.220824 q^{50} -3.14162 q^{51} -1.84228 q^{52} -4.17847 q^{53} +0.397144 q^{54} +5.65897 q^{55} +5.31105 q^{56} -4.44194 q^{57} -2.35269 q^{58} +8.22759 q^{59} +4.34247 q^{60} +5.23185 q^{61} -0.154473 q^{62} -3.48052 q^{63} -4.45948 q^{64} -2.35712 q^{65} -0.953462 q^{66} -1.95588 q^{67} +5.78772 q^{68} -4.93504 q^{69} +3.25817 q^{70} +7.92857 q^{71} -1.52594 q^{72} +13.3362 q^{73} +2.71016 q^{74} +0.556030 q^{75} +8.18329 q^{76} +8.35601 q^{77} +0.397144 q^{78} -8.23551 q^{79} -7.25649 q^{80} +1.00000 q^{81} -2.84435 q^{82} -5.00152 q^{83} +6.41207 q^{84} +7.40517 q^{85} -0.589857 q^{86} -5.92403 q^{87} +3.66347 q^{88} +5.34007 q^{89} -0.936118 q^{90} -3.48052 q^{91} +9.09170 q^{92} -0.388959 q^{93} +2.09659 q^{94} +10.4702 q^{95} +4.27450 q^{96} +3.62112 q^{97} +2.03099 q^{98} -2.40080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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