LMFDB - Embedded newform 4017.2.a.g.1.10

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:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-0.574597 q^{2} -1.00000 q^{3} -1.66984 q^{4} -2.72483 q^{5} +0.574597 q^{6} +0.829930 q^{7} +2.10868 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.574597 q^{2} -1.00000 q^{3} -1.66984 q^{4} -2.72483 q^{5} +0.574597 q^{6} +0.829930 q^{7} +2.10868 q^{8} +1.00000 q^{9} +1.56568 q^{10} +4.58531 q^{11} +1.66984 q^{12} -1.00000 q^{13} -0.476875 q^{14} +2.72483 q^{15} +2.12804 q^{16} -2.51006 q^{17} -0.574597 q^{18} +3.53359 q^{19} +4.55002 q^{20} -0.829930 q^{21} -2.63470 q^{22} +0.402139 q^{23} -2.10868 q^{24} +2.42468 q^{25} +0.574597 q^{26} -1.00000 q^{27} -1.38585 q^{28} +6.35746 q^{29} -1.56568 q^{30} -2.35016 q^{31} -5.44012 q^{32} -4.58531 q^{33} +1.44227 q^{34} -2.26142 q^{35} -1.66984 q^{36} +1.47697 q^{37} -2.03039 q^{38} +1.00000 q^{39} -5.74578 q^{40} +0.900084 q^{41} +0.476875 q^{42} +5.57724 q^{43} -7.65672 q^{44} -2.72483 q^{45} -0.231068 q^{46} -5.90709 q^{47} -2.12804 q^{48} -6.31122 q^{49} -1.39321 q^{50} +2.51006 q^{51} +1.66984 q^{52} +5.35669 q^{53} +0.574597 q^{54} -12.4942 q^{55} +1.75006 q^{56} -3.53359 q^{57} -3.65298 q^{58} -2.99418 q^{59} -4.55002 q^{60} +0.725723 q^{61} +1.35040 q^{62} +0.829930 q^{63} -1.13020 q^{64} +2.72483 q^{65} +2.63470 q^{66} -5.01665 q^{67} +4.19140 q^{68} -0.402139 q^{69} +1.29940 q^{70} -1.44069 q^{71} +2.10868 q^{72} -7.03940 q^{73} -0.848661 q^{74} -2.42468 q^{75} -5.90053 q^{76} +3.80548 q^{77} -0.574597 q^{78} -8.55905 q^{79} -5.79853 q^{80} +1.00000 q^{81} -0.517186 q^{82} +1.90485 q^{83} +1.38585 q^{84} +6.83949 q^{85} -3.20466 q^{86} -6.35746 q^{87} +9.66893 q^{88} -0.222073 q^{89} +1.56568 q^{90} -0.829930 q^{91} -0.671507 q^{92} +2.35016 q^{93} +3.39419 q^{94} -9.62843 q^{95} +5.44012 q^{96} +10.4953 q^{97} +3.62641 q^{98} +4.58531 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * 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 $

$2$	−0.574597	−0.406301	−0.203151	−	0.979147i	$-0.565118\pi$
$2$	−0.574597	−0.406301	−0.203151	+	0.979147i	$0.565118\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.66984	−0.834919
$5$	−2.72483	−1.21858	−0.609290	−	0.792948i	$-0.708545\pi$
$5$	−2.72483	−1.21858	−0.609290	+	0.792948i	$0.708545\pi$
$6$	0.574597	0.234578
$7$	0.829930	0.313684	0.156842	−	0.987624i	$-0.449869\pi$
$7$	0.829930	0.313684	0.156842	+	0.987624i	$0.449869\pi$
$8$	2.10868	0.745530
$9$	1.00000	0.333333
$10$	1.56568	0.495111
$11$	4.58531	1.38252	0.691261	−	0.722605i	$-0.257056\pi$
$11$	4.58531	1.38252	0.691261	+	0.722605i	$0.257056\pi$
$12$	1.66984	0.482041
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.476875	−0.127450
$15$	2.72483	0.703547
$16$	2.12804	0.532009
$17$	−2.51006	−0.608780	−0.304390	−	0.952548i	$-0.598453\pi$
$17$	−2.51006	−0.608780	−0.304390	+	0.952548i	$0.598453\pi$
$18$	−0.574597	−0.135434
$19$	3.53359	0.810662	0.405331	−	0.914170i	$-0.367156\pi$
$19$	3.53359	0.810662	0.405331	+	0.914170i	$0.367156\pi$
$20$	4.55002	1.01742
$21$	−0.829930	−0.181106
$22$	−2.63470	−0.561721
$23$	0.402139	0.0838518	0.0419259	−	0.999121i	$-0.486651\pi$
$23$	0.402139	0.0838518	0.0419259	+	0.999121i	$0.486651\pi$
$24$	−2.10868	−0.430432
$25$	2.42468	0.484936
$26$	0.574597	0.112688
$27$	−1.00000	−0.192450
$28$	−1.38585	−0.261901
$29$	6.35746	1.18055	0.590276	−	0.807202i	$-0.299019\pi$
$29$	6.35746	1.18055	0.590276	+	0.807202i	$0.299019\pi$
$30$	−1.56568	−0.285852
$31$	−2.35016	−0.422102	−0.211051	−	0.977475i	$-0.567689\pi$
$31$	−2.35016	−0.422102	−0.211051	+	0.977475i	$0.567689\pi$
$32$	−5.44012	−0.961686
$33$	−4.58531	−0.798199
$34$	1.44227	0.247348
$35$	−2.26142	−0.382249
$36$	−1.66984	−0.278306
$37$	1.47697	0.242812	0.121406	−	0.992603i	$-0.461260\pi$
$37$	1.47697	0.242812	0.121406	+	0.992603i	$0.461260\pi$
$38$	−2.03039	−0.329373
$39$	1.00000	0.160128
$40$	−5.74578	−0.908488
$41$	0.900084	0.140570	0.0702848	−	0.997527i	$-0.477609\pi$
$41$	0.900084	0.140570	0.0702848	+	0.997527i	$0.477609\pi$
$42$	0.476875	0.0735835
$43$	5.57724	0.850520	0.425260	−	0.905071i	$-0.360183\pi$
$43$	5.57724	0.850520	0.425260	+	0.905071i	$0.360183\pi$
$44$	−7.65672	−1.15429
$45$	−2.72483	−0.406193
$46$	−0.231068	−0.0340691
$47$	−5.90709	−0.861637	−0.430818	−	0.902439i	$-0.641775\pi$
$47$	−5.90709	−0.861637	−0.430818	+	0.902439i	$0.641775\pi$
$48$	−2.12804	−0.307156
$49$	−6.31122	−0.901602
$50$	−1.39321	−0.197030
$51$	2.51006	0.351479
$52$	1.66984	0.231565
$53$	5.35669	0.735798	0.367899	−	0.929866i	$-0.380077\pi$
$53$	5.35669	0.735798	0.367899	+	0.929866i	$0.380077\pi$
$54$	0.574597	0.0781927
$55$	−12.4942	−1.68471
$56$	1.75006	0.233861
$57$	−3.53359	−0.468036
$58$	−3.65298	−0.479660
$59$	−2.99418	−0.389809	−0.194904	−	0.980822i	$-0.562440\pi$
$59$	−2.99418	−0.389809	−0.194904	+	0.980822i	$0.562440\pi$
$60$	−4.55002	−0.587405
$61$	0.725723	0.0929193	0.0464597	−	0.998920i	$-0.485206\pi$
$61$	0.725723	0.0929193	0.0464597	+	0.998920i	$0.485206\pi$
$62$	1.35040	0.171500
$63$	0.829930	0.104561
$64$	−1.13020	−0.141275
$65$	2.72483	0.337973
$66$	2.63470	0.324310
$67$	−5.01665	−0.612882	−0.306441	−	0.951890i	$-0.599138\pi$
$67$	−5.01665	−0.612882	−0.306441	+	0.951890i	$0.599138\pi$
$68$	4.19140	0.508282
$69$	−0.402139	−0.0484118
$70$	1.29940	0.155308
$71$	−1.44069	−0.170978	−0.0854892	−	0.996339i	$-0.527245\pi$
$71$	−1.44069	−0.170978	−0.0854892	+	0.996339i	$0.527245\pi$
$72$	2.10868	0.248510
$73$	−7.03940	−0.823899	−0.411949	−	0.911207i	$-0.635152\pi$
$73$	−7.03940	−0.823899	−0.411949	+	0.911207i	$0.635152\pi$
$74$	−0.848661	−0.0986548
$75$	−2.42468	−0.279978
$76$	−5.90053	−0.676837
$77$	3.80548	0.433675
$78$	−0.574597	−0.0650603
$79$	−8.55905	−0.962968	−0.481484	−	0.876455i	$-0.659902\pi$
$79$	−8.55905	−0.962968	−0.481484	+	0.876455i	$0.659902\pi$
$80$	−5.79853	−0.648295
$81$	1.00000	0.111111
$82$	−0.517186	−0.0571136
$83$	1.90485	0.209084	0.104542	−	0.994520i	$-0.466662\pi$
$83$	1.90485	0.209084	0.104542	+	0.994520i	$0.466662\pi$
$84$	1.38585	0.151209
$85$	6.83949	0.741847
$86$	−3.20466	−0.345568
$87$	−6.35746	−0.681592
$88$	9.66893	1.03071
$89$	−0.222073	−0.0235397	−0.0117699	−	0.999931i	$-0.503747\pi$
$89$	−0.222073	−0.0235397	−0.0117699	+	0.999931i	$0.503747\pi$
$90$	1.56568	0.165037
$91$	−0.829930	−0.0870003
$92$	−0.671507	−0.0700094
$93$	2.35016	0.243700
$94$	3.39419	0.350084
$95$	−9.62843	−0.987856
$96$	5.44012	0.555230
$97$	10.4953	1.06563	0.532816	−	0.846231i	$-0.321134\pi$
$97$	10.4953	1.06563	0.532816	+	0.846231i	$0.321134\pi$
$98$	3.62641	0.366322
$99$	4.58531	0.460841
$100$	−4.04882	−0.404882
$101$	−8.22317	−0.818236	−0.409118	−	0.912481i	$-0.634164\pi$
$101$	−8.22317	−0.818236	−0.409118	+	0.912481i	$0.634164\pi$
$102$	−1.44227	−0.142807
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−2.10868	−0.206773
$105$	2.26142	0.220692
$106$	−3.07794	−0.298956
$107$	10.6330	1.02794	0.513968	−	0.857809i	$-0.328175\pi$
$107$	10.6330	1.02794	0.513968	+	0.857809i	$0.328175\pi$
$108$	1.66984	0.160680
$109$	−8.31780	−0.796701	−0.398350	−	0.917233i	$-0.630417\pi$
$109$	−8.31780	−0.796701	−0.398350	+	0.917233i	$0.630417\pi$
$110$	7.17911	0.684501
$111$	−1.47697	−0.140187
$112$	1.76612	0.166883
$113$	−16.5489	−1.55679	−0.778397	−	0.627773i	$-0.783967\pi$
$113$	−16.5489	−1.55679	−0.778397	+	0.627773i	$0.783967\pi$
$114$	2.03039	0.190164
$115$	−1.09576	−0.102180
$116$	−10.6159	−0.985665
$117$	−1.00000	−0.0924500
$118$	1.72045	0.158380
$119$	−2.08318	−0.190965
$120$	5.74578	0.524516
$121$	10.0250	0.911366
$122$	−0.416998	−0.0377533
$123$	−0.900084	−0.0811578
$124$	3.92439	0.352421
$125$	7.01730	0.627646
$126$	−0.476875	−0.0424834
$127$	19.4057	1.72197	0.860987	−	0.508628i	$-0.169847\pi$
$127$	19.4057	1.72197	0.860987	+	0.508628i	$0.169847\pi$
$128$	11.5296	1.01909
$129$	−5.57724	−0.491048
$130$	−1.56568	−0.137319
$131$	−1.61764	−0.141334	−0.0706671	−	0.997500i	$-0.522513\pi$
$131$	−1.61764	−0.141334	−0.0706671	+	0.997500i	$0.522513\pi$
$132$	7.65672	0.666432
$133$	2.93264	0.254292
$134$	2.88255	0.249015
$135$	2.72483	0.234516
$136$	−5.29292	−0.453864
$137$	14.9719	1.27913	0.639566	−	0.768736i	$-0.279114\pi$
$137$	14.9719	1.27913	0.639566	+	0.768736i	$0.279114\pi$
$138$	0.231068	0.0196698
$139$	−22.1699	−1.88043	−0.940215	−	0.340581i	$-0.889376\pi$
$139$	−22.1699	−1.88043	−0.940215	+	0.340581i	$0.889376\pi$
$140$	3.77620	0.319147
$141$	5.90709	0.497466
$142$	0.827816	0.0694688
$143$	−4.58531	−0.383443
$144$	2.12804	0.177336
$145$	−17.3230	−1.43860
$146$	4.04482	0.334751
$147$	6.31122	0.520540
$148$	−2.46630	−0.202728
$149$	9.69817	0.794505	0.397253	−	0.917709i	$-0.369964\pi$
$149$	9.69817	0.794505	0.397253	+	0.917709i	$0.369964\pi$
$150$	1.39321	0.113755
$151$	5.28800	0.430331	0.215166	−	0.976578i	$-0.430971\pi$
$151$	5.28800	0.430331	0.215166	+	0.976578i	$0.430971\pi$
$152$	7.45121	0.604373
$153$	−2.51006	−0.202927
$154$	−2.18662	−0.176203
$155$	6.40378	0.514364
$156$	−1.66984	−0.133694
$157$	−3.04262	−0.242827	−0.121414	−	0.992602i	$-0.538743\pi$
$157$	−3.04262	−0.242827	−0.121414	+	0.992602i	$0.538743\pi$
$158$	4.91800	0.391255
$159$	−5.35669	−0.424813
$160$	14.8234	1.17189
$161$	0.333747	0.0263030
$162$	−0.574597	−0.0451446
$163$	−7.02881	−0.550539	−0.275270	−	0.961367i	$-0.588767\pi$
$163$	−7.02881	−0.550539	−0.275270	+	0.961367i	$0.588767\pi$
$164$	−1.50299	−0.117364
$165$	12.4942	0.972669
$166$	−1.09452	−0.0849512
$167$	21.4736	1.66168	0.830839	−	0.556514i	$-0.187861\pi$
$167$	21.4736	1.66168	0.830839	+	0.556514i	$0.187861\pi$
$168$	−1.75006	−0.135020
$169$	1.00000	0.0769231
$170$	−3.92995	−0.301413
$171$	3.53359	0.270221
$172$	−9.31308	−0.710116
$173$	12.0542	0.916467	0.458233	−	0.888832i	$-0.348482\pi$
$173$	12.0542	0.916467	0.458233	+	0.888832i	$0.348482\pi$
$174$	3.65298	0.276932
$175$	2.01232	0.152117
$176$	9.75770	0.735514
$177$	2.99418	0.225056
$178$	0.127603	0.00956422
$179$	8.23249	0.615325	0.307663	−	0.951496i	$-0.400453\pi$
$179$	8.23249	0.615325	0.307663	+	0.951496i	$0.400453\pi$
$180$	4.55002	0.339138
$181$	−4.50639	−0.334957	−0.167479	−	0.985876i	$-0.553563\pi$
$181$	−4.50639	−0.334957	−0.167479	+	0.985876i	$0.553563\pi$
$182$	0.476875	0.0353484
$183$	−0.725723	−0.0536470
$184$	0.847982	0.0625140
$185$	−4.02448	−0.295885
$186$	−1.35040	−0.0990158
$187$	−11.5094	−0.841651
$188$	9.86388	0.719397
$189$	−0.829930	−0.0603685
$190$	5.53247	0.401367
$191$	3.88899	0.281398	0.140699	−	0.990052i	$-0.455065\pi$
$191$	3.88899	0.281398	0.140699	+	0.990052i	$0.455065\pi$
$192$	1.13020	0.0815649
$193$	19.3683	1.39416	0.697082	−	0.716992i	$-0.254481\pi$
$193$	19.3683	1.39416	0.697082	+	0.716992i	$0.254481\pi$
$194$	−6.03054	−0.432968
$195$	−2.72483	−0.195129
$196$	10.5387	0.752765
$197$	25.1399	1.79115	0.895573	−	0.444915i	$-0.146766\pi$
$197$	25.1399	1.79115	0.895573	+	0.444915i	$0.146766\pi$
$198$	−2.63470	−0.187240
$199$	−4.46177	−0.316287	−0.158143	−	0.987416i	$-0.550551\pi$
$199$	−4.46177	−0.316287	−0.158143	+	0.987416i	$0.550551\pi$
$200$	5.11287	0.361535
$201$	5.01665	0.353847
$202$	4.72501	0.332451
$203$	5.27625	0.370320
$204$	−4.19140	−0.293457
$205$	−2.45257	−0.171295
$206$	−0.574597	−0.0400341
$207$	0.402139	0.0279506
$208$	−2.12804	−0.147553
$209$	16.2026	1.12076
$210$	−1.29940	−0.0896673
$211$	−10.2956	−0.708776	−0.354388	−	0.935099i	$-0.615311\pi$
$211$	−10.2956	−0.708776	−0.354388	+	0.935099i	$0.615311\pi$
$212$	−8.94481	−0.614332
$213$	1.44069	0.0987144
$214$	−6.10972	−0.417652
$215$	−15.1970	−1.03643
$216$	−2.10868	−0.143477
$217$	−1.95047	−0.132407
$218$	4.77938	0.323701
$219$	7.03940	0.475678
$220$	20.8632	1.40660
$221$	2.51006	0.168845
$222$	0.848661	0.0569584
$223$	3.93511	0.263515	0.131757	−	0.991282i	$-0.457938\pi$
$223$	3.93511	0.263515	0.131757	+	0.991282i	$0.457938\pi$
$224$	−4.51492	−0.301666
$225$	2.42468	0.161645
$226$	9.50897	0.632527
$227$	14.9727	0.993771	0.496886	−	0.867816i	$-0.334477\pi$
$227$	14.9727	0.993771	0.496886	+	0.867816i	$0.334477\pi$
$228$	5.90053	0.390772
$229$	3.78131	0.249876	0.124938	−	0.992165i	$-0.460127\pi$
$229$	3.78131	0.249876	0.124938	+	0.992165i	$0.460127\pi$
$230$	0.629620	0.0415159
$231$	−3.80548	−0.250382
$232$	13.4058	0.880137
$233$	19.7372	1.29303	0.646514	−	0.762902i	$-0.276226\pi$
$233$	19.7372	1.29303	0.646514	+	0.762902i	$0.276226\pi$
$234$	0.574597	0.0375626
$235$	16.0958	1.04997
$236$	4.99979	0.325459
$237$	8.55905	0.555970
$238$	1.19699	0.0775892
$239$	−19.0926	−1.23500	−0.617499	−	0.786572i	$-0.711854\pi$
$239$	−19.0926	−1.23500	−0.617499	+	0.786572i	$0.711854\pi$
$240$	5.79853	0.374294
$241$	25.6640	1.65316	0.826582	−	0.562817i	$-0.190282\pi$
$241$	25.6640	1.65316	0.826582	+	0.562817i	$0.190282\pi$
$242$	−5.76035	−0.370289
$243$	−1.00000	−0.0641500
$244$	−1.21184	−0.0775801
$245$	17.1970	1.09867
$246$	0.517186	0.0329745
$247$	−3.53359	−0.224837
$248$	−4.95573	−0.314689
$249$	−1.90485	−0.120715
$250$	−4.03212	−0.255014
$251$	8.26499	0.521681	0.260841	−	0.965382i	$-0.416000\pi$
$251$	8.26499	0.521681	0.260841	+	0.965382i	$0.416000\pi$
$252$	−1.38585	−0.0873003
$253$	1.84393	0.115927
$254$	−11.1504	−0.699640
$255$	−6.83949	−0.428305
$256$	−4.36451	−0.272782
$257$	−3.87605	−0.241782	−0.120891	−	0.992666i	$-0.538575\pi$
$257$	−3.87605	−0.241782	−0.120891	+	0.992666i	$0.538575\pi$
$258$	3.20466	0.199514
$259$	1.22578	0.0761662
$260$	−4.55002	−0.282180
$261$	6.35746	0.393517
$262$	0.929493	0.0574243
$263$	3.83375	0.236399	0.118200	−	0.992990i	$-0.462288\pi$
$263$	3.83375	0.236399	0.118200	+	0.992990i	$0.462288\pi$
$264$	−9.66893	−0.595082
$265$	−14.5961	−0.896629
$266$	−1.68508	−0.103319
$267$	0.222073	0.0135907
$268$	8.37700	0.511707
$269$	−2.44988	−0.149372	−0.0746860	−	0.997207i	$-0.523795\pi$
$269$	−2.44988	−0.149372	−0.0746860	+	0.997207i	$0.523795\pi$
$270$	−1.56568	−0.0952841
$271$	−0.135006	−0.00820101	−0.00410050	−	0.999992i	$-0.501305\pi$
$271$	−0.135006	−0.00820101	−0.00410050	+	0.999992i	$0.501305\pi$
$272$	−5.34151	−0.323876
$273$	0.829930	0.0502297
$274$	−8.60278	−0.519713
$275$	11.1179	0.670435
$276$	0.671507	0.0404200
$277$	7.08218	0.425527	0.212763	−	0.977104i	$-0.431754\pi$
$277$	7.08218	0.425527	0.212763	+	0.977104i	$0.431754\pi$
$278$	12.7388	0.764022
$279$	−2.35016	−0.140701
$280$	−4.76860	−0.284978
$281$	3.64732	0.217581	0.108790	−	0.994065i	$-0.465302\pi$
$281$	3.64732	0.217581	0.108790	+	0.994065i	$0.465302\pi$
$282$	−3.39419	−0.202121
$283$	1.88115	0.111823	0.0559113	−	0.998436i	$-0.482194\pi$
$283$	1.88115	0.111823	0.0559113	+	0.998436i	$0.482194\pi$
$284$	2.40572	0.142753
$285$	9.62843	0.570339
$286$	2.63470	0.155793
$287$	0.747007	0.0440944
$288$	−5.44012	−0.320562
$289$	−10.6996	−0.629387
$290$	9.95374	0.584504
$291$	−10.4953	−0.615243
$292$	11.7547	0.687889
$293$	22.3259	1.30429	0.652146	−	0.758093i	$-0.273869\pi$
$293$	22.3259	1.30429	0.652146	+	0.758093i	$0.273869\pi$
$294$	−3.62641	−0.211496
$295$	8.15862	0.475013
$296$	3.11445	0.181024
$297$	−4.58531	−0.266066
$298$	−5.57254	−0.322809
$299$	−0.402139	−0.0232563
$300$	4.04882	0.233759
$301$	4.62872	0.266795
$302$	−3.03847	−0.174844
$303$	8.22317	0.472409
$304$	7.51962	0.431280
$305$	−1.97747	−0.113230
$306$	1.44227	0.0824494
$307$	−26.5286	−1.51407	−0.757033	−	0.653376i	$-0.773352\pi$
$307$	−26.5286	−1.51407	−0.757033	+	0.653376i	$0.773352\pi$
$308$	−6.35454	−0.362084
$309$	−1.00000	−0.0568880
$310$	−3.67959	−0.208987
$311$	−5.86964	−0.332837	−0.166418	−	0.986055i	$-0.553220\pi$
$311$	−5.86964	−0.332837	−0.166418	+	0.986055i	$0.553220\pi$
$312$	2.10868	0.119380
$313$	18.7349	1.05896	0.529479	−	0.848323i	$-0.322387\pi$
$313$	18.7349	1.05896	0.529479	+	0.848323i	$0.322387\pi$
$314$	1.74828	0.0986611
$315$	−2.26142	−0.127416
$316$	14.2922	0.804000
$317$	26.0561	1.46345	0.731727	−	0.681598i	$-0.238715\pi$
$317$	26.0561	1.46345	0.731727	+	0.681598i	$0.238715\pi$
$318$	3.07794	0.172602
$319$	29.1509	1.63214
$320$	3.07959	0.172154
$321$	−10.6330	−0.593479
$322$	−0.191770	−0.0106869
$323$	−8.86954	−0.493515
$324$	−1.66984	−0.0927688
$325$	−2.42468	−0.134497
$326$	4.03873	0.223685
$327$	8.31780	0.459975
$328$	1.89799	0.104799
$329$	−4.90247	−0.270282
$330$	−7.17911	−0.395197
$331$	−1.27592	−0.0701308	−0.0350654	−	0.999385i	$-0.511164\pi$
$331$	−1.27592	−0.0701308	−0.0350654	+	0.999385i	$0.511164\pi$
$332$	−3.18079	−0.174568
$333$	1.47697	0.0809373
$334$	−12.3387	−0.675142
$335$	13.6695	0.746845
$336$	−1.76612	−0.0963498
$337$	2.78326	0.151614	0.0758069	−	0.997123i	$-0.475847\pi$
$337$	2.78326	0.151614	0.0758069	+	0.997123i	$0.475847\pi$
$338$	−0.574597	−0.0312540
$339$	16.5489	0.898815
$340$	−11.4208	−0.619382
$341$	−10.7762	−0.583564
$342$	−2.03039	−0.109791
$343$	−11.0474	−0.596502
$344$	11.7606	0.634089
$345$	1.09576	0.0589937
$346$	−6.92633	−0.372362
$347$	−29.0431	−1.55911	−0.779557	−	0.626332i	$-0.784556\pi$
$347$	−29.0431	−1.55911	−0.779557	+	0.626332i	$0.784556\pi$
$348$	10.6159	0.569074
$349$	5.38209	0.288097	0.144048	−	0.989571i	$-0.453988\pi$
$349$	5.38209	0.288097	0.144048	+	0.989571i	$0.453988\pi$
$350$	−1.15627	−0.0618053
$351$	1.00000	0.0533761
$352$	−24.9446	−1.32955
$353$	−28.3605	−1.50948	−0.754739	−	0.656025i	$-0.772237\pi$
$353$	−28.3605	−1.50948	−0.754739	+	0.656025i	$0.772237\pi$
$354$	−1.72045	−0.0914407
$355$	3.92563	0.208351
$356$	0.370827	0.0196538
$357$	2.08318	0.110253
$358$	−4.73036	−0.250008
$359$	12.7814	0.674578	0.337289	−	0.941401i	$-0.390490\pi$
$359$	12.7814	0.674578	0.337289	+	0.941401i	$0.390490\pi$
$360$	−5.74578	−0.302829
$361$	−6.51372	−0.342827
$362$	2.58936	0.136094
$363$	−10.0250	−0.526177
$364$	1.38585	0.0726382
$365$	19.1811	1.00399
$366$	0.416998	0.0217969
$367$	−24.9423	−1.30197	−0.650987	−	0.759088i	$-0.725645\pi$
$367$	−24.9423	−1.30197	−0.650987	+	0.759088i	$0.725645\pi$
$368$	0.855766	0.0446099
$369$	0.900084	0.0468565
$370$	2.31245	0.120219
$371$	4.44568	0.230808
$372$	−3.92439	−0.203470
$373$	4.30705	0.223010	0.111505	−	0.993764i	$-0.464433\pi$
$373$	4.30705	0.223010	0.111505	+	0.993764i	$0.464433\pi$
$374$	6.61327	0.341964
$375$	−7.01730	−0.362372
$376$	−12.4561	−0.642376
$377$	−6.35746	−0.327426
$378$	0.476875	0.0245278
$379$	−20.1551	−1.03530	−0.517649	−	0.855593i	$-0.673193\pi$
$379$	−20.1551	−1.03530	−0.517649	+	0.855593i	$0.673193\pi$
$380$	16.0779	0.824780
$381$	−19.4057	−0.994182
$382$	−2.23460	−0.114332
$383$	16.3053	0.833162	0.416581	−	0.909099i	$-0.363228\pi$
$383$	16.3053	0.833162	0.416581	+	0.909099i	$0.363228\pi$
$384$	−11.5296	−0.588370
$385$	−10.3693	−0.528468
$386$	−11.1290	−0.566451
$387$	5.57724	0.283507
$388$	−17.5254	−0.889717
$389$	7.84668	0.397842	0.198921	−	0.980016i	$-0.436256\pi$
$389$	7.84668	0.397842	0.198921	+	0.980016i	$0.436256\pi$
$390$	1.56568	0.0792811
$391$	−1.00939	−0.0510473
$392$	−13.3083	−0.672172
$393$	1.61764	0.0815993
$394$	−14.4453	−0.727745
$395$	23.3219	1.17345
$396$	−7.65672	−0.384765
$397$	−13.0111	−0.653008	−0.326504	−	0.945196i	$-0.605871\pi$
$397$	−13.0111	−0.653008	−0.326504	+	0.945196i	$0.605871\pi$
$398$	2.56372	0.128508
$399$	−2.93264	−0.146815
$400$	5.15981	0.257990
$401$	−9.66724	−0.482759	−0.241379	−	0.970431i	$-0.577600\pi$
$401$	−9.66724	−0.482759	−0.241379	+	0.970431i	$0.577600\pi$
$402$	−2.88255	−0.143769
$403$	2.35016	0.117070
$404$	13.7314	0.683161
$405$	−2.72483	−0.135398
$406$	−3.03172	−0.150462
$407$	6.77234	0.335693
$408$	5.29292	0.262038
$409$	−14.9407	−0.738771	−0.369386	−	0.929276i	$-0.620432\pi$
$409$	−14.9407	−0.738771	−0.369386	+	0.929276i	$0.620432\pi$
$410$	1.40924	0.0695975
$411$	−14.9719	−0.738507
$412$	−1.66984	−0.0822670
$413$	−2.48496	−0.122277
$414$	−0.231068	−0.0113564
$415$	−5.19038	−0.254786
$416$	5.44012	0.266724
$417$	22.1699	1.08567
$418$	−9.30997	−0.455365
$419$	−20.8330	−1.01776	−0.508880	−	0.860837i	$-0.669940\pi$
$419$	−20.8330	−1.01776	−0.508880	+	0.860837i	$0.669940\pi$
$420$	−3.77620	−0.184260
$421$	−10.3969	−0.506715	−0.253357	−	0.967373i	$-0.581535\pi$
$421$	−10.3969	−0.506715	−0.253357	+	0.967373i	$0.581535\pi$
$422$	5.91580	0.287977
$423$	−5.90709	−0.287212
$424$	11.2955	0.548560
$425$	−6.08610	−0.295219
$426$	−0.827816	−0.0401078
$427$	0.602300	0.0291473
$428$	−17.7555	−0.858243
$429$	4.58531	0.221381
$430$	8.73215	0.421102
$431$	−21.1083	−1.01675	−0.508377	−	0.861135i	$-0.669754\pi$
$431$	−21.1083	−1.01675	−0.508377	+	0.861135i	$0.669754\pi$
$432$	−2.12804	−0.102385
$433$	24.7691	1.19033	0.595164	−	0.803604i	$-0.297087\pi$
$433$	24.7691	1.19033	0.595164	+	0.803604i	$0.297087\pi$
$434$	1.12073	0.0537970
$435$	17.3230	0.830574
$436$	13.8894	0.665181
$437$	1.42100	0.0679754
$438$	−4.04482	−0.193269
$439$	12.0603	0.575605	0.287802	−	0.957690i	$-0.407075\pi$
$439$	12.0603	0.575605	0.287802	+	0.957690i	$0.407075\pi$
$440$	−26.3462	−1.25600
$441$	−6.31122	−0.300534
$442$	−1.44227	−0.0686020
$443$	14.0773	0.668832	0.334416	−	0.942426i	$-0.391461\pi$
$443$	14.0773	0.668832	0.334416	+	0.942426i	$0.391461\pi$
$444$	2.46630	0.117045
$445$	0.605111	0.0286850
$446$	−2.26110	−0.107066
$447$	−9.69817	−0.458708
$448$	−0.937984	−0.0443156
$449$	−0.676095	−0.0319069	−0.0159535	−	0.999873i	$-0.505078\pi$
$449$	−0.676095	−0.0319069	−0.0159535	+	0.999873i	$0.505078\pi$
$450$	−1.39321	−0.0656767
$451$	4.12716	0.194340
$452$	27.6340	1.29980
$453$	−5.28800	−0.248452
$454$	−8.60325	−0.403771
$455$	2.26142	0.106017
$456$	−7.45121	−0.348935
$457$	−16.5712	−0.775166	−0.387583	−	0.921835i	$-0.626690\pi$
$457$	−16.5712	−0.775166	−0.387583	+	0.921835i	$0.626690\pi$
$458$	−2.17273	−0.101525
$459$	2.51006	0.117160
$460$	1.82974	0.0853121
$461$	2.28915	0.106617	0.0533083	−	0.998578i	$-0.483023\pi$
$461$	2.28915	0.106617	0.0533083	+	0.998578i	$0.483023\pi$
$462$	2.18662	0.101731
$463$	26.0859	1.21231	0.606157	−	0.795345i	$-0.292710\pi$
$463$	26.0859	1.21231	0.606157	+	0.795345i	$0.292710\pi$
$464$	13.5289	0.628064
$465$	−6.40378	−0.296968
$466$	−11.3409	−0.525359
$467$	28.1638	1.30326	0.651632	−	0.758535i	$-0.274085\pi$
$467$	28.1638	1.30326	0.651632	+	0.758535i	$0.274085\pi$
$468$	1.66984	0.0771883
$469$	−4.16347	−0.192251
$470$	−9.24859	−0.426606
$471$	3.04262	0.140196
$472$	−6.31376	−0.290614
$473$	25.5733	1.17586
$474$	−4.91800	−0.225891
$475$	8.56784	0.393119
$476$	3.47857	0.159440
$477$	5.35669	0.245266
$478$	10.9706	0.501781
$479$	8.38893	0.383300	0.191650	−	0.981463i	$-0.438616\pi$
$479$	8.38893	0.383300	0.191650	+	0.981463i	$0.438616\pi$
$480$	−14.8234	−0.676592
$481$	−1.47697	−0.0673439
$482$	−14.7465	−0.671683
$483$	−0.333747	−0.0151860
$484$	−16.7402	−0.760917
$485$	−28.5978	−1.29856
$486$	0.574597	0.0260642
$487$	−30.5617	−1.38488	−0.692442	−	0.721474i	$-0.743465\pi$
$487$	−30.5617	−1.38488	−0.692442	+	0.721474i	$0.743465\pi$
$488$	1.53032	0.0692742
$489$	7.02881	0.317854
$490$	−9.88133	−0.446393
$491$	26.6803	1.20406	0.602032	−	0.798472i	$-0.294358\pi$
$491$	26.6803	1.20406	0.602032	+	0.798472i	$0.294358\pi$
$492$	1.50299	0.0677602
$493$	−15.9576	−0.718696
$494$	2.03039	0.0913517
$495$	−12.4942	−0.561571
$496$	−5.00123	−0.224562
$497$	−1.19567	−0.0536332
$498$	1.09452	0.0490466
$499$	5.56443	0.249098	0.124549	−	0.992213i	$-0.460252\pi$
$499$	5.56443	0.249098	0.124549	+	0.992213i	$0.460252\pi$
$500$	−11.7178	−0.524034
$501$	−21.4736	−0.959370
$502$	−4.74904	−0.211960
$503$	−6.13960	−0.273751	−0.136876	−	0.990588i	$-0.543706\pi$
$503$	−6.13960	−0.273751	−0.136876	+	0.990588i	$0.543706\pi$
$504$	1.75006	0.0779537
$505$	22.4067	0.997086
$506$	−1.05952	−0.0471013
$507$	−1.00000	−0.0444116
$508$	−32.4043	−1.43771
$509$	−31.9328	−1.41540	−0.707698	−	0.706515i	$-0.750266\pi$
$509$	−31.9328	−1.41540	−0.707698	+	0.706515i	$0.750266\pi$
$510$	3.92995	0.174021
$511$	−5.84221	−0.258444
$512$	−20.5515	−0.908255
$513$	−3.53359	−0.156012
$514$	2.22717	0.0982362
$515$	−2.72483	−0.120070
$516$	9.31308	0.409986
$517$	−27.0858	−1.19123
$518$	−0.704329	−0.0309464
$519$	−12.0542	−0.529122
$520$	5.74578	0.251969
$521$	34.7631	1.52300	0.761499	−	0.648166i	$-0.224464\pi$
$521$	34.7631	1.52300	0.761499	+	0.648166i	$0.224464\pi$
$522$	−3.65298	−0.159887
$523$	22.9485	1.00347	0.501734	−	0.865022i	$-0.332696\pi$
$523$	22.9485	1.00347	0.501734	+	0.865022i	$0.332696\pi$
$524$	2.70120	0.118003
$525$	−2.01232	−0.0878247
$526$	−2.20286	−0.0960494
$527$	5.89906	0.256967
$528$	−9.75770	−0.424649
$529$	−22.8383	−0.992969
$530$	8.38685	0.364302
$531$	−2.99418	−0.129936
$532$	−4.89703	−0.212313
$533$	−0.900084	−0.0389870
$534$	−0.127603	−0.00552191
$535$	−28.9732	−1.25262
$536$	−10.5785	−0.456922
$537$	−8.23249	−0.355258
$538$	1.40770	0.0606901
$539$	−28.9389	−1.24648
$540$	−4.55002	−0.195802
$541$	30.7537	1.32220	0.661102	−	0.750296i	$-0.270089\pi$
$541$	30.7537	1.32220	0.661102	+	0.750296i	$0.270089\pi$
$542$	0.0775738	0.00333208
$543$	4.50639	0.193388
$544$	13.6550	0.585455
$545$	22.6646	0.970843
$546$	−0.476875	−0.0204084
$547$	4.65814	0.199168	0.0995838	−	0.995029i	$-0.468249\pi$
$547$	4.65814	0.199168	0.0995838	+	0.995029i	$0.468249\pi$
$548$	−25.0006	−1.06797
$549$	0.725723	0.0309731
$550$	−6.38831	−0.272399
$551$	22.4647	0.957028
$552$	−0.847982	−0.0360925
$553$	−7.10341	−0.302068
$554$	−4.06940	−0.172892
$555$	4.02448	0.170830
$556$	37.0202	1.57001
$557$	−5.98748	−0.253698	−0.126849	−	0.991922i	$-0.540486\pi$
$557$	−5.98748	−0.253698	−0.126849	+	0.991922i	$0.540486\pi$
$558$	1.35040	0.0571668
$559$	−5.57724	−0.235892
$560$	−4.81238	−0.203360
$561$	11.5094	0.485928
$562$	−2.09574	−0.0884033
$563$	7.32033	0.308515	0.154258	−	0.988031i	$-0.450701\pi$
$563$	7.32033	0.308515	0.154258	+	0.988031i	$0.450701\pi$
$564$	−9.86388	−0.415344
$565$	45.0930	1.89708
$566$	−1.08090	−0.0454337
$567$	0.829930	0.0348538
$568$	−3.03795	−0.127470
$569$	6.05158	0.253695	0.126848	−	0.991922i	$-0.459514\pi$
$569$	6.05158	0.253695	0.126848	+	0.991922i	$0.459514\pi$
$570$	−5.53247	−0.231730
$571$	41.8731	1.75233	0.876167	−	0.482008i	$-0.160092\pi$
$571$	41.8731	1.75233	0.876167	+	0.482008i	$0.160092\pi$
$572$	7.65672	0.320144
$573$	−3.88899	−0.162465
$574$	−0.429228	−0.0179156
$575$	0.975059	0.0406628
$576$	−1.13020	−0.0470915
$577$	−33.5241	−1.39563	−0.697813	−	0.716280i	$-0.745843\pi$
$577$	−33.5241	−1.39563	−0.697813	+	0.716280i	$0.745843\pi$
$578$	6.14795	0.255721
$579$	−19.3683	−0.804921
$580$	28.9266	1.20111
$581$	1.58089	0.0655864
$582$	6.03054	0.249974
$583$	24.5621	1.01726
$584$	−14.8438	−0.614242
$585$	2.72483	0.112658
$586$	−12.8284	−0.529936
$587$	−15.3890	−0.635172	−0.317586	−	0.948230i	$-0.602872\pi$
$587$	−15.3890	−0.635172	−0.317586	+	0.948230i	$0.602872\pi$
$588$	−10.5387	−0.434609
$589$	−8.30452	−0.342182
$590$	−4.68792	−0.192999
$591$	−25.1399	−1.03412
$592$	3.14304	0.129178
$593$	−5.79712	−0.238059	−0.119030	−	0.992891i	$-0.537978\pi$
$593$	−5.79712	−0.238059	−0.119030	+	0.992891i	$0.537978\pi$
$594$	2.63470	0.108103
$595$	5.67630	0.232706
$596$	−16.1944	−0.663348
$597$	4.46177	0.182608
$598$	0.231068	0.00944907
$599$	27.2002	1.11137	0.555684	−	0.831393i	$-0.312456\pi$
$599$	27.2002	1.11137	0.555684	+	0.831393i	$0.312456\pi$
$600$	−5.11287	−0.208732
$601$	−5.74528	−0.234355	−0.117177	−	0.993111i	$-0.537385\pi$
$601$	−5.74528	−0.234355	−0.117177	+	0.993111i	$0.537385\pi$
$602$	−2.65965	−0.108399
$603$	−5.01665	−0.204294
$604$	−8.83011	−0.359292
$605$	−27.3165	−1.11057
$606$	−4.72501	−0.191940
$607$	18.6330	0.756291	0.378146	−	0.925746i	$-0.376562\pi$
$607$	18.6330	0.756291	0.378146	+	0.925746i	$0.376562\pi$
$608$	−19.2232	−0.779603
$609$	−5.27625	−0.213805
$610$	1.13625	0.0460054
$611$	5.90709	0.238975
$612$	4.19140	0.169427
$613$	−9.84374	−0.397585	−0.198792	−	0.980042i	$-0.563702\pi$
$613$	−9.84374	−0.397585	−0.198792	+	0.980042i	$0.563702\pi$
$614$	15.2432	0.615167
$615$	2.45257	0.0988973
$616$	8.02454	0.323318
$617$	16.3635	0.658771	0.329386	−	0.944195i	$-0.393158\pi$
$617$	16.3635	0.658771	0.329386	+	0.944195i	$0.393158\pi$
$618$	0.574597	0.0231137
$619$	−21.6463	−0.870040	−0.435020	−	0.900421i	$-0.643259\pi$
$619$	−21.6463	−0.870040	−0.435020	+	0.900421i	$0.643259\pi$
$620$	−10.6933	−0.429453
$621$	−0.402139	−0.0161373
$622$	3.37268	0.135232
$623$	−0.184305	−0.00738404
$624$	2.12804	0.0851896
$625$	−31.2443	−1.24977
$626$	−10.7650	−0.430256
$627$	−16.2026	−0.647070
$628$	5.08068	0.202741
$629$	−3.70728	−0.147819
$630$	1.29940	0.0517695
$631$	12.9153	0.514149	0.257075	−	0.966392i	$-0.417241\pi$
$631$	12.9153	0.514149	0.257075	+	0.966392i	$0.417241\pi$
$632$	−18.0483	−0.717922
$633$	10.2956	0.409212
$634$	−14.9717	−0.594603
$635$	−52.8770	−2.09836
$636$	8.94481	0.354685
$637$	6.31122	0.250059
$638$	−16.7500	−0.663140
$639$	−1.44069	−0.0569928
$640$	−31.4163	−1.24184
$641$	32.3193	1.27653	0.638267	−	0.769815i	$-0.279651\pi$
$641$	32.3193	1.27653	0.638267	+	0.769815i	$0.279651\pi$
$642$	6.10972	0.241131
$643$	31.0350	1.22390	0.611951	−	0.790896i	$-0.290385\pi$
$643$	31.0350	1.22390	0.611951	+	0.790896i	$0.290385\pi$
$644$	−0.557304	−0.0219609
$645$	15.1970	0.598381
$646$	5.09641	0.200516
$647$	22.3814	0.879902	0.439951	−	0.898022i	$-0.354996\pi$
$647$	22.3814	0.879902	0.439951	+	0.898022i	$0.354996\pi$
$648$	2.10868	0.0828367
$649$	−13.7292	−0.538919
$650$	1.39321	0.0546464
$651$	1.95047	0.0764450
$652$	11.7370	0.459656
$653$	49.0933	1.92117	0.960585	−	0.277986i	$-0.0896670\pi$
$653$	49.0933	1.92117	0.960585	+	0.277986i	$0.0896670\pi$
$654$	−4.77938	−0.186889
$655$	4.40780	0.172227
$656$	1.91541	0.0747843
$657$	−7.03940	−0.274633
$658$	2.81694	0.109816
$659$	14.6139	0.569277	0.284639	−	0.958635i	$-0.408126\pi$
$659$	14.6139	0.569277	0.284639	+	0.958635i	$0.408126\pi$
$660$	−20.8632	−0.812100
$661$	46.4992	1.80861	0.904305	−	0.426888i	$-0.140390\pi$
$661$	46.4992	1.80861	0.904305	+	0.426888i	$0.140390\pi$
$662$	0.733139	0.0284942
$663$	−2.51006	−0.0974828
$664$	4.01671	0.155879
$665$	−7.99093	−0.309875
$666$	−0.848661	−0.0328849
$667$	2.55658	0.0989913
$668$	−35.8574	−1.38737
$669$	−3.93511	−0.152140
$670$	−7.85446	−0.303444
$671$	3.32766	0.128463
$672$	4.51492	0.174167
$673$	18.4198	0.710029	0.355015	−	0.934861i	$-0.384476\pi$
$673$	18.4198	0.710029	0.355015	+	0.934861i	$0.384476\pi$
$674$	−1.59925	−0.0616009
$675$	−2.42468	−0.0933260
$676$	−1.66984	−0.0642245
$677$	15.6815	0.602690	0.301345	−	0.953515i	$-0.402564\pi$
$677$	15.6815	0.602690	0.301345	+	0.953515i	$0.402564\pi$
$678$	−9.50897	−0.365190
$679$	8.71033	0.334272
$680$	14.4223	0.553069
$681$	−14.9727	−0.573754
$682$	6.19198	0.237103
$683$	6.56603	0.251242	0.125621	−	0.992078i	$-0.459908\pi$
$683$	6.56603	0.251242	0.125621	+	0.992078i	$0.459908\pi$
$684$	−5.90053	−0.225612
$685$	−40.7957	−1.55872
$686$	6.34779	0.242360
$687$	−3.78131	−0.144266
$688$	11.8686	0.452485
$689$	−5.35669	−0.204074
$690$	−0.629620	−0.0239692
$691$	−33.3295	−1.26792	−0.633958	−	0.773368i	$-0.718571\pi$
$691$	−33.3295	−1.26792	−0.633958	+	0.773368i	$0.718571\pi$
$692$	−20.1286	−0.765175
$693$	3.80548	0.144558
$694$	16.6881	0.633470
$695$	60.4093	2.29145
$696$	−13.4058	−0.508147
$697$	−2.25927	−0.0855759
$698$	−3.09254	−0.117054
$699$	−19.7372	−0.746530
$700$	−3.36024	−0.127005
$701$	3.23259	0.122093	0.0610467	−	0.998135i	$-0.480556\pi$
$701$	3.23259	0.122093	0.0610467	+	0.998135i	$0.480556\pi$
$702$	−0.574597	−0.0216868
$703$	5.21900	0.196838
$704$	−5.18230	−0.195315
$705$	−16.0958	−0.606202
$706$	16.2959	0.613303
$707$	−6.82466	−0.256668
$708$	−4.99979	−0.187904
$709$	6.97790	0.262061	0.131030	−	0.991378i	$-0.458171\pi$
$709$	6.97790	0.262061	0.131030	+	0.991378i	$0.458171\pi$
$710$	−2.25565	−0.0846532
$711$	−8.55905	−0.320989
$712$	−0.468281	−0.0175496
$713$	−0.945092	−0.0353940
$714$	−1.19699	−0.0447961
$715$	12.4942	0.467255
$716$	−13.7469	−0.513747
$717$	19.0926	0.713026
$718$	−7.34417	−0.274082
$719$	−5.69966	−0.212561	−0.106281	−	0.994336i	$-0.533894\pi$
$719$	−5.69966	−0.212561	−0.106281	+	0.994336i	$0.533894\pi$
$720$	−5.79853	−0.216098
$721$	0.829930	0.0309082
$722$	3.74276	0.139291
$723$	−25.6640	−0.954454
$724$	7.52494	0.279662
$725$	15.4148	0.572492
$726$	5.76035	0.213787
$727$	14.4979	0.537698	0.268849	−	0.963182i	$-0.413357\pi$
$727$	14.4979	0.537698	0.268849	+	0.963182i	$0.413357\pi$
$728$	−1.75006	−0.0648614
$729$	1.00000	0.0370370
$730$	−11.0214	−0.407921
$731$	−13.9992	−0.517780
$732$	1.21184	0.0447909
$733$	−35.5181	−1.31189	−0.655945	−	0.754809i	$-0.727730\pi$
$733$	−35.5181	−1.31189	−0.655945	+	0.754809i	$0.727730\pi$
$734$	14.3317	0.528994
$735$	−17.1970	−0.634320
$736$	−2.18768	−0.0806391
$737$	−23.0029	−0.847322
$738$	−0.517186	−0.0190379
$739$	34.0917	1.25408	0.627041	−	0.778986i	$-0.284266\pi$
$739$	34.0917	1.25408	0.627041	+	0.778986i	$0.284266\pi$
$740$	6.72023	0.247040
$741$	3.53359	0.129810
$742$	−2.55448	−0.0937777
$743$	9.35395	0.343163	0.171582	−	0.985170i	$-0.445112\pi$
$743$	9.35395	0.343163	0.171582	+	0.985170i	$0.445112\pi$
$744$	4.95573	0.181686
$745$	−26.4258	−0.968168
$746$	−2.47482	−0.0906095
$747$	1.90485	0.0696947
$748$	19.2189	0.702711
$749$	8.82469	0.322447
$750$	4.03212	0.147232
$751$	22.1397	0.807888	0.403944	−	0.914784i	$-0.367639\pi$
$751$	22.1397	0.807888	0.403944	+	0.914784i	$0.367639\pi$
$752$	−12.5705	−0.458399
$753$	−8.26499	−0.301193
$754$	3.65298	0.133034
$755$	−14.4089	−0.524393
$756$	1.38585	0.0504029
$757$	−24.6390	−0.895520	−0.447760	−	0.894154i	$-0.647778\pi$
$757$	−24.6390	−0.895520	−0.447760	+	0.894154i	$0.647778\pi$
$758$	11.5811	0.420643
$759$	−1.84393	−0.0669304
$760$	−20.3033	−0.736477
$761$	38.3864	1.39150	0.695752	−	0.718282i	$-0.255071\pi$
$761$	38.3864	1.39150	0.695752	+	0.718282i	$0.255071\pi$
$762$	11.1504	0.403937
$763$	−6.90319	−0.249912
$764$	−6.49399	−0.234944
$765$	6.83949	0.247282
$766$	−9.36898	−0.338515
$767$	2.99418	0.108114
$768$	4.36451	0.157491
$769$	8.26083	0.297893	0.148947	−	0.988845i	$-0.452412\pi$
$769$	8.26083	0.297893	0.148947	+	0.988845i	$0.452412\pi$
$770$	5.95816	0.214717
$771$	3.87605	0.139593
$772$	−32.3420	−1.16401
$773$	21.3605	0.768285	0.384142	−	0.923274i	$-0.374497\pi$
$773$	21.3605	0.768285	0.384142	+	0.923274i	$0.374497\pi$
$774$	−3.20466	−0.115189
$775$	−5.69839	−0.204692
$776$	22.1311	0.794461
$777$	−1.22578	−0.0439746
$778$	−4.50868	−0.161644
$779$	3.18053	0.113954
$780$	4.55002	0.162917
$781$	−6.60600	−0.236381
$782$	0.579995	0.0207406
$783$	−6.35746	−0.227197
$784$	−13.4305	−0.479661
$785$	8.29061	0.295905
$786$	−0.929493	−0.0331539
$787$	−8.27948	−0.295132	−0.147566	−	0.989052i	$-0.547144\pi$
$787$	−8.27948	−0.295132	−0.147566	+	0.989052i	$0.547144\pi$
$788$	−41.9796	−1.49546
$789$	−3.83375	−0.136485
$790$	−13.4007	−0.476776
$791$	−13.7345	−0.488341
$792$	9.66893	0.343571
$793$	−0.725723	−0.0257712
$794$	7.47614	0.265318
$795$	14.5961	0.517669
$796$	7.45044	0.264074
$797$	4.36531	0.154627	0.0773137	−	0.997007i	$-0.475366\pi$
$797$	4.36531	0.154627	0.0773137	+	0.997007i	$0.475366\pi$
$798$	1.68508	0.0596513
$799$	14.8272	0.524547
$800$	−13.1906	−0.466356
$801$	−0.222073	−0.00784658
$802$	5.55477	0.196146
$803$	−32.2778	−1.13906
$804$	−8.37700	−0.295434
$805$	−0.909404	−0.0320523
$806$	−1.35040	−0.0475657
$807$	2.44988	0.0862400
$808$	−17.3400	−0.610020
$809$	−12.8649	−0.452305	−0.226152	−	0.974092i	$-0.572615\pi$
$809$	−12.8649	−0.452305	−0.226152	+	0.974092i	$0.572615\pi$
$810$	1.56568	0.0550123
$811$	45.7255	1.60564	0.802819	−	0.596222i	$-0.203332\pi$
$811$	45.7255	1.60564	0.802819	+	0.596222i	$0.203332\pi$
$812$	−8.81049	−0.309188
$813$	0.135006	0.00473485
$814$	−3.89137	−0.136392
$815$	19.1523	0.670876
$816$	5.34151	0.186990
$817$	19.7077	0.689485
$818$	8.58490	0.300164
$819$	−0.829930	−0.0290001
$820$	4.09540	0.143018
$821$	−5.52788	−0.192924	−0.0964622	−	0.995337i	$-0.530753\pi$
$821$	−5.52788	−0.192924	−0.0964622	+	0.995337i	$0.530753\pi$
$822$	8.60278	0.300057
$823$	36.7096	1.27962	0.639808	−	0.768535i	$-0.279014\pi$
$823$	36.7096	1.27962	0.639808	+	0.768535i	$0.279014\pi$
$824$	2.10868	0.0734593
$825$	−11.1179	−0.387076
$826$	1.42785	0.0496813
$827$	13.5634	0.471645	0.235823	−	0.971796i	$-0.424222\pi$
$827$	13.5634	0.471645	0.235823	+	0.971796i	$0.424222\pi$
$828$	−0.671507	−0.0233365
$829$	−42.3917	−1.47232	−0.736162	−	0.676805i	$-0.763364\pi$
$829$	−42.3917	−1.47232	−0.736162	+	0.676805i	$0.763364\pi$
$830$	2.98237	0.103520
$831$	−7.08218	−0.245678
$832$	1.13020	0.0391825
$833$	15.8416	0.548877
$834$	−12.7388	−0.441108
$835$	−58.5118	−2.02489
$836$	−27.0557	−0.935742
$837$	2.35016	0.0812335
$838$	11.9706	0.413517
$839$	−31.8208	−1.09857	−0.549287	−	0.835633i	$-0.685101\pi$
$839$	−31.8208	−1.09857	−0.549287	+	0.835633i	$0.685101\pi$
$840$	4.76860	0.164532
$841$	11.4174	0.393702
$842$	5.97404	0.205879
$843$	−3.64732	−0.125620
$844$	17.1919	0.591770
$845$	−2.72483	−0.0937369
$846$	3.39419	0.116695
$847$	8.32007	0.285881
$848$	11.3992	0.391451
$849$	−1.88115	−0.0645608
$850$	3.49706	0.119948
$851$	0.593946	0.0203602
$852$	−2.40572	−0.0824185
$853$	1.81093	0.0620052	0.0310026	−	0.999519i	$-0.490130\pi$
$853$	1.81093	0.0620052	0.0310026	+	0.999519i	$0.490130\pi$
$854$	−0.346080	−0.0118426
$855$	−9.62843	−0.329285
$856$	22.4217	0.766357
$857$	−28.1829	−0.962709	−0.481354	−	0.876526i	$-0.659855\pi$
$857$	−28.1829	−0.962709	−0.481354	+	0.876526i	$0.659855\pi$
$858$	−2.63470	−0.0899473
$859$	−28.1259	−0.959643	−0.479822	−	0.877366i	$-0.659299\pi$
$859$	−28.1259	−0.959643	−0.479822	+	0.877366i	$0.659299\pi$
$860$	25.3765	0.865333
$861$	−0.747007	−0.0254579
$862$	12.1288	0.413108
$863$	53.6170	1.82514	0.912572	−	0.408916i	$-0.134093\pi$
$863$	53.6170	1.82514	0.912572	+	0.408916i	$0.134093\pi$
$864$	5.44012	0.185077
$865$	−32.8457	−1.11679
$866$	−14.2323	−0.483632
$867$	10.6996	0.363377
$868$	3.25697	0.110549
$869$	−39.2458	−1.33132
$870$	−9.95374	−0.337463
$871$	5.01665	0.169983
$872$	−17.5396	−0.593964
$873$	10.4953	0.355211
$874$	−0.816500	−0.0276185
$875$	5.82387	0.196883
$876$	−11.7547	−0.397153
$877$	−42.3837	−1.43120	−0.715598	−	0.698513i	$-0.753846\pi$
$877$	−42.3837	−1.43120	−0.715598	+	0.698513i	$0.753846\pi$
$878$	−6.92979	−0.233869
$879$	−22.3259	−0.753034
$880$	−26.5880	−0.896282
$881$	25.7088	0.866152	0.433076	−	0.901357i	$-0.357428\pi$
$881$	25.7088	0.866152	0.433076	+	0.901357i	$0.357428\pi$
$882$	3.62641	0.122107
$883$	44.6853	1.50378	0.751890	−	0.659288i	$-0.229142\pi$
$883$	44.6853	1.50378	0.751890	+	0.659288i	$0.229142\pi$
$884$	−4.19140	−0.140972
$885$	−8.15862	−0.274249
$886$	−8.08876	−0.271747
$887$	39.9892	1.34270	0.671352	−	0.741138i	$-0.265714\pi$
$887$	39.9892	1.34270	0.671352	+	0.741138i	$0.265714\pi$
$888$	−3.11445	−0.104514
$889$	16.1053	0.540156
$890$	−0.347695	−0.0116548
$891$	4.58531	0.153614
$892$	−6.57100	−0.220013
$893$	−20.8732	−0.698496
$894$	5.57254	0.186374
$895$	−22.4321	−0.749823
$896$	9.56880	0.319671
$897$	0.402139	0.0134270
$898$	0.388482	0.0129638
$899$	−14.9411	−0.498313
$900$	−4.04882	−0.134961
$901$	−13.4456	−0.447939
$902$	−2.37145	−0.0789608
$903$	−4.62872	−0.154034
$904$	−34.8964	−1.16064
$905$	12.2791	0.408172
$906$	3.03847	0.100946
$907$	−5.86245	−0.194659	−0.0973297	−	0.995252i	$-0.531030\pi$
$907$	−5.86245	−0.194659	−0.0973297	+	0.995252i	$0.531030\pi$
$908$	−25.0019	−0.829719
$909$	−8.22317	−0.272745
$910$	−1.29940	−0.0430748
$911$	28.0218	0.928404	0.464202	−	0.885729i	$-0.346341\pi$
$911$	28.0218	0.928404	0.464202	+	0.885729i	$0.346341\pi$
$912$	−7.51962	−0.248999
$913$	8.73430	0.289063
$914$	9.52174	0.314951
$915$	1.97747	0.0653731
$916$	−6.31417	−0.208626
$917$	−1.34253	−0.0443343
$918$	−1.44227	−0.0476022
$919$	22.6987	0.748761	0.374380	−	0.927275i	$-0.377855\pi$
$919$	22.6987	0.748761	0.374380	+	0.927275i	$0.377855\pi$
$920$	−2.31060	−0.0761783
$921$	26.5286	0.874147
$922$	−1.31534	−0.0433185
$923$	1.44069	0.0474209
$924$	6.35454	0.209049
$925$	3.58117	0.117748
$926$	−14.9889	−0.492565
$927$	1.00000	0.0328443
$928$	−34.5854	−1.13532
$929$	−16.9739	−0.556896	−0.278448	−	0.960451i	$-0.589820\pi$
$929$	−16.9739	−0.556896	−0.278448	+	0.960451i	$0.589820\pi$
$930$	3.67959	0.120659
$931$	−22.3013	−0.730895
$932$	−32.9579	−1.07957
$933$	5.86964	0.192163
$934$	−16.1828	−0.529518
$935$	31.3611	1.02562
$936$	−2.10868	−0.0689243
$937$	30.9721	1.01181	0.505906	−	0.862588i	$-0.331158\pi$
$937$	30.9721	1.01181	0.505906	+	0.862588i	$0.331158\pi$
$938$	2.39232	0.0781120
$939$	−18.7349	−0.611390
$940$	−26.8774	−0.876643
$941$	15.2846	0.498264	0.249132	−	0.968470i	$-0.419855\pi$
$941$	15.2846	0.498264	0.249132	+	0.968470i	$0.419855\pi$
$942$	−1.74828	−0.0569620
$943$	0.361959	0.0117870
$944$	−6.37172	−0.207382
$945$	2.26142	0.0735639
$946$	−14.6944	−0.477755
$947$	−36.8368	−1.19703	−0.598517	−	0.801110i	$-0.704243\pi$
$947$	−36.8368	−1.19703	−0.598517	+	0.801110i	$0.704243\pi$
$948$	−14.2922	−0.464190
$949$	7.03940	0.228508
$950$	−4.92305	−0.159725
$951$	−26.0561	−0.844925
$952$	−4.39275	−0.142370
$953$	37.5095	1.21505	0.607526	−	0.794300i	$-0.292162\pi$
$953$	37.5095	1.21505	0.607526	+	0.794300i	$0.292162\pi$
$954$	−3.07794	−0.0996520
$955$	−10.5968	−0.342905
$956$	31.8816	1.03112
$957$	−29.1509	−0.942315
$958$	−4.82025	−0.155735
$959$	12.4256	0.401243
$960$	−3.07959	−0.0993933
$961$	−25.4767	−0.821830
$962$	0.848661	0.0273619
$963$	10.6330	0.342645
$964$	−42.8547	−1.38026
$965$	−52.7754	−1.69890
$966$	0.191770	0.00617010
$967$	13.2210	0.425160	0.212580	−	0.977144i	$-0.431813\pi$
$967$	13.2210	0.425160	0.212580	+	0.977144i	$0.431813\pi$
$968$	21.1396	0.679451
$969$	8.86954	0.284931
$970$	16.4322	0.527606
$971$	−24.2831	−0.779281	−0.389640	−	0.920967i	$-0.627401\pi$
$971$	−24.2831	−0.779281	−0.389640	+	0.920967i	$0.627401\pi$
$972$	1.66984	0.0535601
$973$	−18.3995	−0.589861
$974$	17.5607	0.562680
$975$	2.42468	0.0776519
$976$	1.54437	0.0494339
$977$	26.2657	0.840316	0.420158	−	0.907451i	$-0.361975\pi$
$977$	26.2657	0.840316	0.420158	+	0.907451i	$0.361975\pi$
$978$	−4.03873	−0.129144
$979$	−1.01827	−0.0325442
$980$	−28.7162	−0.917304
$981$	−8.31780	−0.265567
$982$	−15.3304	−0.489213
$983$	31.6277	1.00877	0.504384	−	0.863480i	$-0.331720\pi$
$983$	31.6277	1.00877	0.504384	+	0.863480i	$0.331720\pi$
$984$	−1.89799	−0.0605056
$985$	−68.5019	−2.18265
$986$	9.16921	0.292007
$987$	4.90247	0.156047
$988$	5.90053	0.187721
$989$	2.24282	0.0713176
$990$	7.17911	0.228167
$991$	20.5775	0.653666	0.326833	−	0.945082i	$-0.394019\pi$
$991$	20.5775	0.653666	0.326833	+	0.945082i	$0.394019\pi$
$992$	12.7852	0.405929
$993$	1.27592	0.0404900
$994$	0.687029	0.0217912
$995$	12.1576	0.385420
$996$	3.18079	0.100787
$997$	40.2520	1.27479	0.637397	−	0.770536i	$-0.280011\pi$
$997$	40.2520	1.27479	0.637397	+	0.770536i	$0.280011\pi$
$998$	−3.19730	−0.101209
$999$	−1.47697	−0.0467292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.10	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.10	✓	24	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)

\(f(q)\)	\(=\)	\(q-0.574597 q^{2} -1.00000 q^{3} -1.66984 q^{4} -2.72483 q^{5} +0.574597 q^{6} +0.829930 q^{7} +2.10868 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.574597 q^{2} -1.00000 q^{3} -1.66984 q^{4} -2.72483 q^{5} +0.574597 q^{6} +0.829930 q^{7} +2.10868 q^{8} +1.00000 q^{9} +1.56568 q^{10} +4.58531 q^{11} +1.66984 q^{12} -1.00000 q^{13} -0.476875 q^{14} +2.72483 q^{15} +2.12804 q^{16} -2.51006 q^{17} -0.574597 q^{18} +3.53359 q^{19} +4.55002 q^{20} -0.829930 q^{21} -2.63470 q^{22} +0.402139 q^{23} -2.10868 q^{24} +2.42468 q^{25} +0.574597 q^{26} -1.00000 q^{27} -1.38585 q^{28} +6.35746 q^{29} -1.56568 q^{30} -2.35016 q^{31} -5.44012 q^{32} -4.58531 q^{33} +1.44227 q^{34} -2.26142 q^{35} -1.66984 q^{36} +1.47697 q^{37} -2.03039 q^{38} +1.00000 q^{39} -5.74578 q^{40} +0.900084 q^{41} +0.476875 q^{42} +5.57724 q^{43} -7.65672 q^{44} -2.72483 q^{45} -0.231068 q^{46} -5.90709 q^{47} -2.12804 q^{48} -6.31122 q^{49} -1.39321 q^{50} +2.51006 q^{51} +1.66984 q^{52} +5.35669 q^{53} +0.574597 q^{54} -12.4942 q^{55} +1.75006 q^{56} -3.53359 q^{57} -3.65298 q^{58} -2.99418 q^{59} -4.55002 q^{60} +0.725723 q^{61} +1.35040 q^{62} +0.829930 q^{63} -1.13020 q^{64} +2.72483 q^{65} +2.63470 q^{66} -5.01665 q^{67} +4.19140 q^{68} -0.402139 q^{69} +1.29940 q^{70} -1.44069 q^{71} +2.10868 q^{72} -7.03940 q^{73} -0.848661 q^{74} -2.42468 q^{75} -5.90053 q^{76} +3.80548 q^{77} -0.574597 q^{78} -8.55905 q^{79} -5.79853 q^{80} +1.00000 q^{81} -0.517186 q^{82} +1.90485 q^{83} +1.38585 q^{84} +6.83949 q^{85} -3.20466 q^{86} -6.35746 q^{87} +9.66893 q^{88} -0.222073 q^{89} +1.56568 q^{90} -0.829930 q^{91} -0.671507 q^{92} +2.35016 q^{93} +3.39419 q^{94} -9.62843 q^{95} +5.44012 q^{96} +10.4953 q^{97} +3.62641 q^{98} +4.58531 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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