LMFDB - Embedded newform 4017.2.a.l.1.20

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			1.20
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)

$f(q)$	$=$	$q+1.11274 q^{2} +1.00000 q^{3} -0.761813 q^{4} -3.97825 q^{5} +1.11274 q^{6} -2.83032 q^{7} -3.07318 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.11274 q^{2} +1.00000 q^{3} -0.761813 q^{4} -3.97825 q^{5} +1.11274 q^{6} -2.83032 q^{7} -3.07318 q^{8} +1.00000 q^{9} -4.42675 q^{10} -6.16163 q^{11} -0.761813 q^{12} -1.00000 q^{13} -3.14940 q^{14} -3.97825 q^{15} -1.89601 q^{16} -4.78248 q^{17} +1.11274 q^{18} -2.58467 q^{19} +3.03068 q^{20} -2.83032 q^{21} -6.85628 q^{22} +2.04954 q^{23} -3.07318 q^{24} +10.8264 q^{25} -1.11274 q^{26} +1.00000 q^{27} +2.15617 q^{28} +8.49865 q^{29} -4.42675 q^{30} -7.24099 q^{31} +4.03658 q^{32} -6.16163 q^{33} -5.32165 q^{34} +11.2597 q^{35} -0.761813 q^{36} -0.839686 q^{37} -2.87607 q^{38} -1.00000 q^{39} +12.2259 q^{40} +11.2411 q^{41} -3.14940 q^{42} -0.205293 q^{43} +4.69401 q^{44} -3.97825 q^{45} +2.28060 q^{46} -5.44420 q^{47} -1.89601 q^{48} +1.01070 q^{49} +12.0470 q^{50} -4.78248 q^{51} +0.761813 q^{52} -9.08575 q^{53} +1.11274 q^{54} +24.5125 q^{55} +8.69806 q^{56} -2.58467 q^{57} +9.45677 q^{58} -9.01200 q^{59} +3.03068 q^{60} -2.48191 q^{61} -8.05733 q^{62} -2.83032 q^{63} +8.28369 q^{64} +3.97825 q^{65} -6.85628 q^{66} +5.27819 q^{67} +3.64336 q^{68} +2.04954 q^{69} +12.5291 q^{70} -0.585183 q^{71} -3.07318 q^{72} -2.33591 q^{73} -0.934351 q^{74} +10.8264 q^{75} +1.96904 q^{76} +17.4394 q^{77} -1.11274 q^{78} +15.3026 q^{79} +7.54281 q^{80} +1.00000 q^{81} +12.5085 q^{82} +0.848656 q^{83} +2.15617 q^{84} +19.0259 q^{85} -0.228437 q^{86} +8.49865 q^{87} +18.9358 q^{88} -14.1259 q^{89} -4.42675 q^{90} +2.83032 q^{91} -1.56137 q^{92} -7.24099 q^{93} -6.05797 q^{94} +10.2825 q^{95} +4.03658 q^{96} -6.93579 q^{97} +1.12464 q^{98} -6.16163 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	1.11274	0.786825	0.393412	−	0.919362i	$-0.371294\pi$
$2$	1.11274	0.786825	0.393412	+	0.919362i	$0.371294\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.761813	−0.380907
$5$	−3.97825	−1.77913	−0.889563	−	0.456813i	$-0.848991\pi$
$5$	−3.97825	−1.77913	−0.889563	+	0.456813i	$0.848991\pi$
$6$	1.11274	0.454274
$7$	−2.83032	−1.06976	−0.534880	−	0.844928i	$-0.679643\pi$
$7$	−2.83032	−1.06976	−0.534880	+	0.844928i	$0.679643\pi$
$8$	−3.07318	−1.08653
$9$	1.00000	0.333333
$10$	−4.42675	−1.39986
$11$	−6.16163	−1.85780	−0.928900	−	0.370330i	$-0.879245\pi$
$11$	−6.16163	−1.85780	−0.928900	+	0.370330i	$0.879245\pi$
$12$	−0.761813	−0.219917
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.14940	−0.841713
$15$	−3.97825	−1.02718
$16$	−1.89601	−0.474004
$17$	−4.78248	−1.15992	−0.579961	−	0.814644i	$-0.696932\pi$
$17$	−4.78248	−1.15992	−0.579961	+	0.814644i	$0.696932\pi$
$18$	1.11274	0.262275
$19$	−2.58467	−0.592965	−0.296483	−	0.955038i	$-0.595814\pi$
$19$	−2.58467	−0.592965	−0.296483	+	0.955038i	$0.595814\pi$
$20$	3.03068	0.677681
$21$	−2.83032	−0.617626
$22$	−6.85628	−1.46176
$23$	2.04954	0.427359	0.213679	−	0.976904i	$-0.431455\pi$
$23$	2.04954	0.427359	0.213679	+	0.976904i	$0.431455\pi$
$24$	−3.07318	−0.627309
$25$	10.8264	2.16529
$26$	−1.11274	−0.218226
$27$	1.00000	0.192450
$28$	2.15617	0.407478
$29$	8.49865	1.57816	0.789080	−	0.614291i	$-0.210558\pi$
$29$	8.49865	1.57816	0.789080	+	0.614291i	$0.210558\pi$
$30$	−4.42675	−0.808210
$31$	−7.24099	−1.30052	−0.650260	−	0.759712i	$-0.725340\pi$
$31$	−7.24099	−1.30052	−0.650260	+	0.759712i	$0.725340\pi$
$32$	4.03658	0.713574
$33$	−6.16163	−1.07260
$34$	−5.32165	−0.912656
$35$	11.2597	1.90324
$36$	−0.761813	−0.126969
$37$	−0.839686	−0.138044	−0.0690218	−	0.997615i	$-0.521988\pi$
$37$	−0.839686	−0.138044	−0.0690218	+	0.997615i	$0.521988\pi$
$38$	−2.87607	−0.466560
$39$	−1.00000	−0.160128
$40$	12.2259	1.93308
$41$	11.2411	1.75557	0.877786	−	0.479052i	$-0.159020\pi$
$41$	11.2411	1.75557	0.877786	+	0.479052i	$0.159020\pi$
$42$	−3.14940	−0.485963
$43$	−0.205293	−0.0313069	−0.0156534	−	0.999877i	$-0.504983\pi$
$43$	−0.205293	−0.0313069	−0.0156534	+	0.999877i	$0.504983\pi$
$44$	4.69401	0.707649
$45$	−3.97825	−0.593042
$46$	2.28060	0.336256
$47$	−5.44420	−0.794118	−0.397059	−	0.917793i	$-0.629969\pi$
$47$	−5.44420	−0.794118	−0.397059	+	0.917793i	$0.629969\pi$
$48$	−1.89601	−0.273666
$49$	1.01070	0.144385
$50$	12.0470	1.70370
$51$	−4.78248	−0.669682
$52$	0.761813	0.105644
$53$	−9.08575	−1.24802	−0.624012	−	0.781415i	$-0.714498\pi$
$53$	−9.08575	−1.24802	−0.624012	+	0.781415i	$0.714498\pi$
$54$	1.11274	0.151425
$55$	24.5125	3.30526
$56$	8.69806	1.16233
$57$	−2.58467	−0.342349
$58$	9.45677	1.24173
$59$	−9.01200	−1.17326	−0.586631	−	0.809854i	$-0.699546\pi$
$59$	−9.01200	−1.17326	−0.586631	+	0.809854i	$0.699546\pi$
$60$	3.03068	0.391259
$61$	−2.48191	−0.317776	−0.158888	−	0.987297i	$-0.550791\pi$
$61$	−2.48191	−0.317776	−0.158888	+	0.987297i	$0.550791\pi$
$62$	−8.05733	−1.02328
$63$	−2.83032	−0.356586
$64$	8.28369	1.03546
$65$	3.97825	0.493441
$66$	−6.85628	−0.843950
$67$	5.27819	0.644834	0.322417	−	0.946598i	$-0.395505\pi$
$67$	5.27819	0.644834	0.322417	+	0.946598i	$0.395505\pi$
$68$	3.64336	0.441822
$69$	2.04954	0.246736
$70$	12.5291	1.49751
$71$	−0.585183	−0.0694484	−0.0347242	−	0.999397i	$-0.511055\pi$
$71$	−0.585183	−0.0694484	−0.0347242	+	0.999397i	$0.511055\pi$
$72$	−3.07318	−0.362177
$73$	−2.33591	−0.273397	−0.136699	−	0.990613i	$-0.543649\pi$
$73$	−2.33591	−0.273397	−0.136699	+	0.990613i	$0.543649\pi$
$74$	−0.934351	−0.108616
$75$	10.8264	1.25013
$76$	1.96904	0.225864
$77$	17.4394	1.98740
$78$	−1.11274	−0.125993
$79$	15.3026	1.72168	0.860840	−	0.508876i	$-0.169939\pi$
$79$	15.3026	1.72168	0.860840	+	0.508876i	$0.169939\pi$
$80$	7.54281	0.843312
$81$	1.00000	0.111111
$82$	12.5085	1.38133
$83$	0.848656	0.0931521	0.0465761	−	0.998915i	$-0.485169\pi$
$83$	0.848656	0.0931521	0.0465761	+	0.998915i	$0.485169\pi$
$84$	2.15617	0.235258
$85$	19.0259	2.06365
$86$	−0.228437	−0.0246330
$87$	8.49865	0.911151
$88$	18.9358	2.01856
$89$	−14.1259	−1.49734	−0.748670	−	0.662943i	$-0.769307\pi$
$89$	−14.1259	−1.49734	−0.748670	+	0.662943i	$0.769307\pi$
$90$	−4.42675	−0.466620
$91$	2.83032	0.296698
$92$	−1.56137	−0.162784
$93$	−7.24099	−0.750856
$94$	−6.05797	−0.624832
$95$	10.2825	1.05496
$96$	4.03658	0.411982
$97$	−6.93579	−0.704223	−0.352111	−	0.935958i	$-0.614536\pi$
$97$	−6.93579	−0.704223	−0.352111	+	0.935958i	$0.614536\pi$
$98$	1.12464	0.113606
$99$	−6.16163	−0.619267
$100$	−8.24773	−0.824773
$101$	−13.0832	−1.30183	−0.650914	−	0.759151i	$-0.725614\pi$
$101$	−13.0832	−1.30183	−0.650914	+	0.759151i	$0.725614\pi$
$102$	−5.32165	−0.526922
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	3.07318	0.301350
$105$	11.2597	1.09883
$106$	−10.1101	−0.981976
$107$	−1.64194	−0.158733	−0.0793663	−	0.996846i	$-0.525290\pi$
$107$	−1.64194	−0.158733	−0.0793663	+	0.996846i	$0.525290\pi$
$108$	−0.761813	−0.0733055
$109$	0.230240	0.0220530	0.0110265	−	0.999939i	$-0.496490\pi$
$109$	0.230240	0.0220530	0.0110265	+	0.999939i	$0.496490\pi$
$110$	27.2760	2.60066
$111$	−0.839686	−0.0796995
$112$	5.36632	0.507070
$113$	−17.7321	−1.66810	−0.834050	−	0.551690i	$-0.813983\pi$
$113$	−17.7321	−1.66810	−0.834050	+	0.551690i	$0.813983\pi$
$114$	−2.87607	−0.269368
$115$	−8.15358	−0.760325
$116$	−6.47438	−0.601131
$117$	−1.00000	−0.0924500
$118$	−10.0280	−0.923152
$119$	13.5359	1.24084
$120$	12.2259	1.11606
$121$	26.9657	2.45142
$122$	−2.76172	−0.250034
$123$	11.2411	1.01358
$124$	5.51628	0.495377
$125$	−23.1790	−2.07320
$126$	−3.14940	−0.280571
$127$	19.1327	1.69775	0.848875	−	0.528594i	$-0.177281\pi$
$127$	19.1327	1.69775	0.848875	+	0.528594i	$0.177281\pi$
$128$	1.14441	0.101153
$129$	−0.205293	−0.0180750
$130$	4.42675	0.388251
$131$	−4.92786	−0.430549	−0.215274	−	0.976554i	$-0.569065\pi$
$131$	−4.92786	−0.430549	−0.215274	+	0.976554i	$0.569065\pi$
$132$	4.69401	0.408561
$133$	7.31545	0.634330
$134$	5.87325	0.507371
$135$	−3.97825	−0.342393
$136$	14.6974	1.26029
$137$	5.39936	0.461298	0.230649	−	0.973037i	$-0.425915\pi$
$137$	5.39936	0.461298	0.230649	+	0.973037i	$0.425915\pi$
$138$	2.28060	0.194138
$139$	−20.3514	−1.72619	−0.863093	−	0.505044i	$-0.831476\pi$
$139$	−20.3514	−1.72619	−0.863093	+	0.505044i	$0.831476\pi$
$140$	−8.57779	−0.724955
$141$	−5.44420	−0.458484
$142$	−0.651155	−0.0546437
$143$	6.16163	0.515261
$144$	−1.89601	−0.158001
$145$	−33.8097	−2.80774
$146$	−2.59925	−0.215116
$147$	1.01070	0.0833609
$148$	0.639684	0.0525817
$149$	−8.06947	−0.661077	−0.330538	−	0.943793i	$-0.607230\pi$
$149$	−8.06947	−0.661077	−0.330538	+	0.943793i	$0.607230\pi$
$150$	12.0470	0.983634
$151$	2.12606	0.173017	0.0865083	−	0.996251i	$-0.472429\pi$
$151$	2.12606	0.173017	0.0865083	+	0.996251i	$0.472429\pi$
$152$	7.94316	0.644275
$153$	−4.78248	−0.386641
$154$	19.4054	1.56374
$155$	28.8065	2.31379
$156$	0.761813	0.0609939
$157$	4.18541	0.334032	0.167016	−	0.985954i	$-0.446587\pi$
$157$	4.18541	0.334032	0.167016	+	0.985954i	$0.446587\pi$
$158$	17.0278	1.35466
$159$	−9.08575	−0.720547
$160$	−16.0585	−1.26954
$161$	−5.80085	−0.457171
$162$	1.11274	0.0874250
$163$	−12.4697	−0.976702	−0.488351	−	0.872647i	$-0.662401\pi$
$163$	−12.4697	−0.976702	−0.488351	+	0.872647i	$0.662401\pi$
$164$	−8.56366	−0.668709
$165$	24.5125	1.90829
$166$	0.944333	0.0732944
$167$	15.6671	1.21236	0.606178	−	0.795329i	$-0.292702\pi$
$167$	15.6671	1.21236	0.606178	+	0.795329i	$0.292702\pi$
$168$	8.69806	0.671070
$169$	1.00000	0.0769231
$170$	21.1709	1.62373
$171$	−2.58467	−0.197655
$172$	0.156395	0.0119250
$173$	−17.3731	−1.32085	−0.660425	−	0.750892i	$-0.729624\pi$
$173$	−17.3731	−1.32085	−0.660425	+	0.750892i	$0.729624\pi$
$174$	9.45677	0.716916
$175$	−30.6423	−2.31634
$176$	11.6825	0.880604
$177$	−9.01200	−0.677384
$178$	−15.7184	−1.17814
$179$	10.7415	0.802858	0.401429	−	0.915890i	$-0.368514\pi$
$179$	10.7415	0.802858	0.401429	+	0.915890i	$0.368514\pi$
$180$	3.03068	0.225894
$181$	7.21728	0.536456	0.268228	−	0.963355i	$-0.413562\pi$
$181$	7.21728	0.536456	0.268228	+	0.963355i	$0.413562\pi$
$182$	3.14940	0.233449
$183$	−2.48191	−0.183468
$184$	−6.29860	−0.464339
$185$	3.34048	0.245597
$186$	−8.05733	−0.590792
$187$	29.4679	2.15491
$188$	4.14746	0.302485
$189$	−2.83032	−0.205875
$190$	11.4417	0.830068
$191$	−18.5783	−1.34428	−0.672138	−	0.740426i	$-0.734624\pi$
$191$	−18.5783	−1.34428	−0.672138	+	0.740426i	$0.734624\pi$
$192$	8.28369	0.597824
$193$	−4.44352	−0.319851	−0.159926	−	0.987129i	$-0.551125\pi$
$193$	−4.44352	−0.319851	−0.159926	+	0.987129i	$0.551125\pi$
$194$	−7.71772	−0.554100
$195$	3.97825	0.284888
$196$	−0.769962	−0.0549973
$197$	−1.88356	−0.134198	−0.0670991	−	0.997746i	$-0.521374\pi$
$197$	−1.88356	−0.134198	−0.0670991	+	0.997746i	$0.521374\pi$
$198$	−6.85628	−0.487255
$199$	−22.6695	−1.60700	−0.803498	−	0.595307i	$-0.797030\pi$
$199$	−22.6695	−1.60700	−0.803498	+	0.595307i	$0.797030\pi$
$200$	−33.2716	−2.35266
$201$	5.27819	0.372295
$202$	−14.5582	−1.02431
$203$	−24.0539	−1.68825
$204$	3.64336	0.255086
$205$	−44.7201	−3.12338
$206$	−1.11274	−0.0775282
$207$	2.04954	0.142453
$208$	1.89601	0.131465
$209$	15.9258	1.10161
$210$	12.5291	0.864590
$211$	20.3609	1.40170	0.700850	−	0.713308i	$-0.252804\pi$
$211$	20.3609	1.40170	0.700850	+	0.713308i	$0.252804\pi$
$212$	6.92164	0.475380
$213$	−0.585183	−0.0400961
$214$	−1.82705	−0.124895
$215$	0.816706	0.0556989
$216$	−3.07318	−0.209103
$217$	20.4943	1.39124
$218$	0.256197	0.0173518
$219$	−2.33591	−0.157846
$220$	−18.6739	−1.25900
$221$	4.78248	0.321705
$222$	−0.934351	−0.0627095
$223$	21.5007	1.43979	0.719897	−	0.694081i	$-0.244189\pi$
$223$	21.5007	1.43979	0.719897	+	0.694081i	$0.244189\pi$
$224$	−11.4248	−0.763352
$225$	10.8264	0.721763
$226$	−19.7312	−1.31250
$227$	9.96605	0.661470	0.330735	−	0.943724i	$-0.392703\pi$
$227$	9.96605	0.661470	0.330735	+	0.943724i	$0.392703\pi$
$228$	1.96904	0.130403
$229$	9.99399	0.660421	0.330211	−	0.943907i	$-0.392880\pi$
$229$	9.99399	0.660421	0.330211	+	0.943907i	$0.392880\pi$
$230$	−9.07280	−0.598243
$231$	17.4394	1.14743
$232$	−26.1178	−1.71472
$233$	24.7768	1.62318	0.811592	−	0.584224i	$-0.198601\pi$
$233$	24.7768	1.62318	0.811592	+	0.584224i	$0.198601\pi$
$234$	−1.11274	−0.0727420
$235$	21.6584	1.41284
$236$	6.86546	0.446904
$237$	15.3026	0.994012
$238$	15.0620	0.976322
$239$	13.5169	0.874333	0.437167	−	0.899381i	$-0.355982\pi$
$239$	13.5169	0.874333	0.437167	+	0.899381i	$0.355982\pi$
$240$	7.54281	0.486886
$241$	−8.77390	−0.565177	−0.282588	−	0.959241i	$-0.591193\pi$
$241$	−8.77390	−0.565177	−0.282588	+	0.959241i	$0.591193\pi$
$242$	30.0057	1.92884
$243$	1.00000	0.0641500
$244$	1.89075	0.121043
$245$	−4.02080	−0.256880
$246$	12.5085	0.797510
$247$	2.58467	0.164459
$248$	22.2528	1.41306
$249$	0.848656	0.0537814
$250$	−25.7922	−1.63124
$251$	3.31695	0.209364	0.104682	−	0.994506i	$-0.466618\pi$
$251$	3.31695	0.209364	0.104682	+	0.994506i	$0.466618\pi$
$252$	2.15617	0.135826
$253$	−12.6285	−0.793947
$254$	21.2896	1.33583
$255$	19.0259	1.19145
$256$	−15.2939	−0.955872
$257$	−26.4332	−1.64886	−0.824428	−	0.565967i	$-0.808503\pi$
$257$	−26.4332	−1.64886	−0.824428	+	0.565967i	$0.808503\pi$
$258$	−0.228437	−0.0142219
$259$	2.37658	0.147673
$260$	−3.03068	−0.187955
$261$	8.49865	0.526053
$262$	−5.48341	−0.338766
$263$	2.15061	0.132612	0.0663060	−	0.997799i	$-0.478879\pi$
$263$	2.15061	0.132612	0.0663060	+	0.997799i	$0.478879\pi$
$264$	18.9358	1.16542
$265$	36.1453	2.22039
$266$	8.14018	0.499107
$267$	−14.1259	−0.864489
$268$	−4.02100	−0.245621
$269$	−10.1132	−0.616613	−0.308306	−	0.951287i	$-0.599762\pi$
$269$	−10.1132	−0.616613	−0.308306	+	0.951287i	$0.599762\pi$
$270$	−4.42675	−0.269403
$271$	24.4405	1.48466	0.742328	−	0.670037i	$-0.233722\pi$
$271$	24.4405	1.48466	0.742328	+	0.670037i	$0.233722\pi$
$272$	9.06766	0.549808
$273$	2.83032	0.171299
$274$	6.00807	0.362961
$275$	−66.7085	−4.02268
$276$	−1.56137	−0.0939832
$277$	−9.80306	−0.589009	−0.294504	−	0.955650i	$-0.595155\pi$
$277$	−9.80306	−0.589009	−0.294504	+	0.955650i	$0.595155\pi$
$278$	−22.6458	−1.35821
$279$	−7.24099	−0.433507
$280$	−34.6030	−2.06793
$281$	−7.59624	−0.453154	−0.226577	−	0.973993i	$-0.572753\pi$
$281$	−7.59624	−0.453154	−0.226577	+	0.973993i	$0.572753\pi$
$282$	−6.05797	−0.360747
$283$	6.16940	0.366733	0.183366	−	0.983045i	$-0.441300\pi$
$283$	6.16940	0.366733	0.183366	+	0.983045i	$0.441300\pi$
$284$	0.445800	0.0264534
$285$	10.2825	0.609081
$286$	6.85628	0.405420
$287$	−31.8160	−1.87804
$288$	4.03658	0.237858
$289$	5.87216	0.345421
$290$	−37.6214	−2.20920
$291$	−6.93579	−0.406583
$292$	1.77953	0.104139
$293$	5.49331	0.320922	0.160461	−	0.987042i	$-0.448702\pi$
$293$	5.49331	0.320922	0.160461	+	0.987042i	$0.448702\pi$
$294$	1.12464	0.0655904
$295$	35.8520	2.08738
$296$	2.58050	0.149989
$297$	−6.16163	−0.357534
$298$	−8.97921	−0.520152
$299$	−2.04954	−0.118528
$300$	−8.24773	−0.476183
$301$	0.581044	0.0334908
$302$	2.36575	0.136134
$303$	−13.0832	−0.751611
$304$	4.90058	0.281068
$305$	9.87366	0.565364
$306$	−5.32165	−0.304219
$307$	25.3825	1.44866	0.724328	−	0.689456i	$-0.242150\pi$
$307$	25.3825	1.44866	0.724328	+	0.689456i	$0.242150\pi$
$308$	−13.2855	−0.757014
$309$	−1.00000	−0.0568880
$310$	32.0540	1.82055
$311$	−0.0593296	−0.00336427	−0.00168214	−	0.999999i	$-0.500535\pi$
$311$	−0.0593296	−0.00336427	−0.00168214	+	0.999999i	$0.500535\pi$
$312$	3.07318	0.173984
$313$	30.6846	1.73440	0.867199	−	0.497962i	$-0.165918\pi$
$313$	30.6846	1.73440	0.867199	+	0.497962i	$0.165918\pi$
$314$	4.65727	0.262825
$315$	11.2597	0.634412
$316$	−11.6577	−0.655799
$317$	−26.2387	−1.47371	−0.736857	−	0.676048i	$-0.763691\pi$
$317$	−26.2387	−1.47371	−0.736857	+	0.676048i	$0.763691\pi$
$318$	−10.1101	−0.566944
$319$	−52.3655	−2.93190
$320$	−32.9546	−1.84222
$321$	−1.64194	−0.0916443
$322$	−6.45483	−0.359714
$323$	12.3612	0.687794
$324$	−0.761813	−0.0423230
$325$	−10.8264	−0.600543
$326$	−13.8755	−0.768493
$327$	0.230240	0.0127323
$328$	−34.5460	−1.90749
$329$	15.4088	0.849515
$330$	27.2760	1.50149
$331$	5.48573	0.301523	0.150761	−	0.988570i	$-0.451827\pi$
$331$	5.48573	0.301523	0.150761	+	0.988570i	$0.451827\pi$
$332$	−0.646518	−0.0354823
$333$	−0.839686	−0.0460145
$334$	17.4334	0.953912
$335$	−20.9980	−1.14724
$336$	5.36632	0.292757
$337$	19.2443	1.04830	0.524152	−	0.851625i	$-0.324382\pi$
$337$	19.2443	1.04830	0.524152	+	0.851625i	$0.324382\pi$
$338$	1.11274	0.0605250
$339$	−17.7321	−0.963077
$340$	−14.4942	−0.786057
$341$	44.6163	2.41611
$342$	−2.87607	−0.155520
$343$	16.9516	0.915302
$344$	0.630901	0.0340159
$345$	−8.15358	−0.438974
$346$	−19.3317	−1.03928
$347$	25.2224	1.35401	0.677006	−	0.735978i	$-0.263277\pi$
$347$	25.2224	1.35401	0.677006	+	0.735978i	$0.263277\pi$
$348$	−6.47438	−0.347063
$349$	−19.7007	−1.05456	−0.527278	−	0.849693i	$-0.676787\pi$
$349$	−19.7007	−1.05456	−0.527278	+	0.849693i	$0.676787\pi$
$350$	−34.0968	−1.82255
$351$	−1.00000	−0.0533761
$352$	−24.8719	−1.32568
$353$	−4.97523	−0.264805	−0.132402	−	0.991196i	$-0.542269\pi$
$353$	−4.97523	−0.264805	−0.132402	+	0.991196i	$0.542269\pi$
$354$	−10.0280	−0.532982
$355$	2.32800	0.123557
$356$	10.7613	0.570347
$357$	13.5359	0.716398
$358$	11.9525	0.631709
$359$	30.7288	1.62181	0.810903	−	0.585181i	$-0.198976\pi$
$359$	30.7288	1.62181	0.810903	+	0.585181i	$0.198976\pi$
$360$	12.2259	0.644359
$361$	−12.3195	−0.648392
$362$	8.03095	0.422097
$363$	26.9657	1.41533
$364$	−2.15617	−0.113014
$365$	9.29282	0.486408
$366$	−2.76172	−0.144357
$367$	9.35401	0.488275	0.244138	−	0.969741i	$-0.421495\pi$
$367$	9.35401	0.488275	0.244138	+	0.969741i	$0.421495\pi$
$368$	−3.88596	−0.202570
$369$	11.2411	0.585191
$370$	3.71708	0.193242
$371$	25.7155	1.33508
$372$	5.51628	0.286006
$373$	−7.51207	−0.388960	−0.194480	−	0.980906i	$-0.562302\pi$
$373$	−7.51207	−0.388960	−0.194480	+	0.980906i	$0.562302\pi$
$374$	32.7900	1.69553
$375$	−23.1790	−1.19696
$376$	16.7310	0.862834
$377$	−8.49865	−0.437703
$378$	−3.14940	−0.161988
$379$	−4.49719	−0.231005	−0.115502	−	0.993307i	$-0.536848\pi$
$379$	−4.49719	−0.231005	−0.115502	+	0.993307i	$0.536848\pi$
$380$	−7.83332	−0.401841
$381$	19.1327	0.980196
$382$	−20.6727	−1.05771
$383$	1.65349	0.0844894	0.0422447	−	0.999107i	$-0.486549\pi$
$383$	1.65349	0.0844894	0.0422447	+	0.999107i	$0.486549\pi$
$384$	1.14441	0.0584006
$385$	−69.3781	−3.53583
$386$	−4.94447	−0.251667
$387$	−0.205293	−0.0104356
$388$	5.28378	0.268243
$389$	−24.6665	−1.25064	−0.625320	−	0.780368i	$-0.715032\pi$
$389$	−24.6665	−1.25064	−0.625320	+	0.780368i	$0.715032\pi$
$390$	4.42675	0.224157
$391$	−9.80189	−0.495703
$392$	−3.10605	−0.156879
$393$	−4.92786	−0.248577
$394$	−2.09591	−0.105591
$395$	−60.8776	−3.06308
$396$	4.69401	0.235883
$397$	11.6355	0.583969	0.291984	−	0.956423i	$-0.405684\pi$
$397$	11.6355	0.583969	0.291984	+	0.956423i	$0.405684\pi$
$398$	−25.2252	−1.26442
$399$	7.31545	0.366231
$400$	−20.5271	−1.02635
$401$	−30.2509	−1.51066	−0.755329	−	0.655345i	$-0.772523\pi$
$401$	−30.2509	−1.51066	−0.755329	+	0.655345i	$0.772523\pi$
$402$	5.87325	0.292931
$403$	7.24099	0.360699
$404$	9.96696	0.495875
$405$	−3.97825	−0.197681
$406$	−26.7657	−1.32836
$407$	5.17383	0.256457
$408$	14.6974	0.727630
$409$	13.3155	0.658410	0.329205	−	0.944259i	$-0.393219\pi$
$409$	13.3155	0.658410	0.329205	+	0.944259i	$0.393219\pi$
$410$	−49.7617	−2.45756
$411$	5.39936	0.266331
$412$	0.761813	0.0375318
$413$	25.5068	1.25511
$414$	2.28060	0.112085
$415$	−3.37616	−0.165729
$416$	−4.03658	−0.197910
$417$	−20.3514	−0.996614
$418$	17.7213	0.866775
$419$	34.6114	1.69088	0.845440	−	0.534071i	$-0.179339\pi$
$419$	34.6114	1.69088	0.845440	+	0.534071i	$0.179339\pi$
$420$	−8.57779	−0.418553
$421$	36.8223	1.79461	0.897306	−	0.441410i	$-0.145521\pi$
$421$	36.8223	1.79461	0.897306	+	0.441410i	$0.145521\pi$
$422$	22.6563	1.10289
$423$	−5.44420	−0.264706
$424$	27.9221	1.35602
$425$	−51.7773	−2.51157
$426$	−0.651155	−0.0315486
$427$	7.02460	0.339944
$428$	1.25085	0.0604623
$429$	6.16163	0.297486
$430$	0.908780	0.0438253
$431$	13.8580	0.667517	0.333759	−	0.942659i	$-0.391683\pi$
$431$	13.8580	0.667517	0.333759	+	0.942659i	$0.391683\pi$
$432$	−1.89601	−0.0912220
$433$	−9.22748	−0.443444	−0.221722	−	0.975110i	$-0.571168\pi$
$433$	−9.22748	−0.443444	−0.221722	+	0.975110i	$0.571168\pi$
$434$	22.8048	1.09467
$435$	−33.8097	−1.62105
$436$	−0.175400	−0.00840013
$437$	−5.29740	−0.253409
$438$	−2.59925	−0.124197
$439$	1.90054	0.0907077	0.0453538	−	0.998971i	$-0.485558\pi$
$439$	1.90054	0.0907077	0.0453538	+	0.998971i	$0.485558\pi$
$440$	−75.3311	−3.59127
$441$	1.01070	0.0481284
$442$	5.32165	0.253125
$443$	−32.6631	−1.55187	−0.775935	−	0.630812i	$-0.782722\pi$
$443$	−32.6631	−1.55187	−0.775935	+	0.630812i	$0.782722\pi$
$444$	0.639684	0.0303580
$445$	56.1962	2.66396
$446$	23.9247	1.13287
$447$	−8.06947	−0.381673
$448$	−23.4455	−1.10769
$449$	1.33397	0.0629541	0.0314770	−	0.999504i	$-0.489979\pi$
$449$	1.33397	0.0629541	0.0314770	+	0.999504i	$0.489979\pi$
$450$	12.0470	0.567901
$451$	−69.2638	−3.26150
$452$	13.5086	0.635390
$453$	2.12606	0.0998912
$454$	11.0896	0.520461
$455$	−11.2597	−0.527863
$456$	7.94316	0.371973
$457$	−32.3921	−1.51524	−0.757620	−	0.652695i	$-0.773638\pi$
$457$	−32.3921	−1.51524	−0.757620	+	0.652695i	$0.773638\pi$
$458$	11.1207	0.519636
$459$	−4.78248	−0.223227
$460$	6.21150	0.289613
$461$	−12.7694	−0.594731	−0.297365	−	0.954764i	$-0.596108\pi$
$461$	−12.7694	−0.594731	−0.297365	+	0.954764i	$0.596108\pi$
$462$	19.4054	0.902823
$463$	14.2444	0.661995	0.330997	−	0.943632i	$-0.392615\pi$
$463$	14.2444	0.661995	0.330997	+	0.943632i	$0.392615\pi$
$464$	−16.1136	−0.748053
$465$	28.8065	1.33587
$466$	27.5701	1.27716
$467$	−21.0479	−0.973983	−0.486991	−	0.873407i	$-0.661906\pi$
$467$	−21.0479	−0.973983	−0.486991	+	0.873407i	$0.661906\pi$
$468$	0.761813	0.0352148
$469$	−14.9390	−0.689817
$470$	24.1001	1.11165
$471$	4.18541	0.192854
$472$	27.6955	1.27479
$473$	1.26494	0.0581619
$474$	17.0278	0.782113
$475$	−27.9828	−1.28394
$476$	−10.3119	−0.472644
$477$	−9.08575	−0.416008
$478$	15.0407	0.687947
$479$	−16.9313	−0.773609	−0.386805	−	0.922162i	$-0.626421\pi$
$479$	−16.9313	−0.773609	−0.386805	+	0.922162i	$0.626421\pi$
$480$	−16.0585	−0.732968
$481$	0.839686	0.0382864
$482$	−9.76306	−0.444695
$483$	−5.80085	−0.263948
$484$	−20.5428	−0.933763
$485$	27.5923	1.25290
$486$	1.11274	0.0504748
$487$	14.4004	0.652542	0.326271	−	0.945276i	$-0.394208\pi$
$487$	14.4004	0.652542	0.326271	+	0.945276i	$0.394208\pi$
$488$	7.62735	0.345274
$489$	−12.4697	−0.563899
$490$	−4.47410	−0.202119
$491$	14.6508	0.661182	0.330591	−	0.943774i	$-0.392752\pi$
$491$	14.6508	0.661182	0.330591	+	0.943774i	$0.392752\pi$
$492$	−8.56366	−0.386079
$493$	−40.6446	−1.83054
$494$	2.87607	0.129400
$495$	24.5125	1.10175
$496$	13.7290	0.616451
$497$	1.65625	0.0742931
$498$	0.944333	0.0423166
$499$	−23.5051	−1.05223	−0.526117	−	0.850412i	$-0.676353\pi$
$499$	−23.5051	−1.05223	−0.526117	+	0.850412i	$0.676353\pi$
$500$	17.6581	0.789694
$501$	15.6671	0.699954
$502$	3.69090	0.164733
$503$	16.1968	0.722181	0.361090	−	0.932531i	$-0.382405\pi$
$503$	16.1968	0.722181	0.361090	+	0.932531i	$0.382405\pi$
$504$	8.69806	0.387443
$505$	52.0482	2.31612
$506$	−14.0522	−0.624697
$507$	1.00000	0.0444116
$508$	−14.5755	−0.646684
$509$	32.9962	1.46253	0.731266	−	0.682092i	$-0.238930\pi$
$509$	32.9962	1.46253	0.731266	+	0.682092i	$0.238930\pi$
$510$	21.1709	0.937461
$511$	6.61136	0.292469
$512$	−19.3070	−0.853256
$513$	−2.58467	−0.114116
$514$	−29.4132	−1.29736
$515$	3.97825	0.175302
$516$	0.156395	0.00688490
$517$	33.5451	1.47531
$518$	2.64451	0.116193
$519$	−17.3731	−0.762593
$520$	−12.2259	−0.536139
$521$	−14.6427	−0.641510	−0.320755	−	0.947162i	$-0.603937\pi$
$521$	−14.6427	−0.641510	−0.320755	+	0.947162i	$0.603937\pi$
$522$	9.45677	0.413912
$523$	−12.7082	−0.555691	−0.277846	−	0.960626i	$-0.589620\pi$
$523$	−12.7082	−0.555691	−0.277846	+	0.960626i	$0.589620\pi$
$524$	3.75411	0.163999
$525$	−30.6423	−1.33734
$526$	2.39306	0.104342
$527$	34.6299	1.50850
$528$	11.6825	0.508417
$529$	−18.7994	−0.817365
$530$	40.2203	1.74706
$531$	−9.01200	−0.391088
$532$	−5.57301	−0.241620
$533$	−11.2411	−0.486908
$534$	−15.7184	−0.680202
$535$	6.53205	0.282405
$536$	−16.2208	−0.700632
$537$	10.7415	0.463530
$538$	−11.2534	−0.485166
$539$	−6.22754	−0.268239
$540$	3.03068	0.130420
$541$	15.1014	0.649260	0.324630	−	0.945841i	$-0.394760\pi$
$541$	15.1014	0.649260	0.324630	+	0.945841i	$0.394760\pi$
$542$	27.1959	1.16816
$543$	7.21728	0.309723
$544$	−19.3049	−0.827691
$545$	−0.915951	−0.0392350
$546$	3.14940	0.134782
$547$	−32.8850	−1.40606	−0.703030	−	0.711160i	$-0.748170\pi$
$547$	−32.8850	−1.40606	−0.703030	+	0.711160i	$0.748170\pi$
$548$	−4.11330	−0.175712
$549$	−2.48191	−0.105925
$550$	−74.2291	−3.16514
$551$	−21.9662	−0.935793
$552$	−6.29860	−0.268086
$553$	−43.3113	−1.84178
$554$	−10.9082	−0.463447
$555$	3.34048	0.141795
$556$	15.5040	0.657516
$557$	−2.56464	−0.108667	−0.0543336	−	0.998523i	$-0.517303\pi$
$557$	−2.56464	−0.108667	−0.0543336	+	0.998523i	$0.517303\pi$
$558$	−8.05733	−0.341094
$559$	0.205293	0.00868297
$560$	−21.3486	−0.902141
$561$	29.4679	1.24414
$562$	−8.45263	−0.356553
$563$	3.40803	0.143631	0.0718157	−	0.997418i	$-0.477121\pi$
$563$	3.40803	0.143631	0.0718157	+	0.997418i	$0.477121\pi$
$564$	4.14746	0.174640
$565$	70.5428	2.96776
$566$	6.86493	0.288555
$567$	−2.83032	−0.118862
$568$	1.79837	0.0754579
$569$	−11.1676	−0.468170	−0.234085	−	0.972216i	$-0.575209\pi$
$569$	−11.1676	−0.468170	−0.234085	+	0.972216i	$0.575209\pi$
$570$	11.4417	0.479240
$571$	30.7319	1.28609	0.643046	−	0.765828i	$-0.277670\pi$
$571$	30.7319	1.28609	0.643046	+	0.765828i	$0.277670\pi$
$572$	−4.69401	−0.196266
$573$	−18.5783	−0.776118
$574$	−35.4029	−1.47769
$575$	22.1892	0.925355
$576$	8.28369	0.345154
$577$	−27.6270	−1.15013	−0.575065	−	0.818108i	$-0.695023\pi$
$577$	−27.6270	−1.15013	−0.575065	+	0.818108i	$0.695023\pi$
$578$	6.53417	0.271786
$579$	−4.44352	−0.184666
$580$	25.7567	1.06949
$581$	−2.40197	−0.0996504
$582$	−7.71772	−0.319910
$583$	55.9830	2.31858
$584$	7.17866	0.297055
$585$	3.97825	0.164480
$586$	6.11261	0.252510
$587$	−29.6814	−1.22508	−0.612540	−	0.790439i	$-0.709852\pi$
$587$	−29.6814	−1.22508	−0.612540	+	0.790439i	$0.709852\pi$
$588$	−0.769962	−0.0317527
$589$	18.7156	0.771163
$590$	39.8939	1.64240
$591$	−1.88356	−0.0774794
$592$	1.59206	0.0654331
$593$	−13.5166	−0.555062	−0.277531	−	0.960717i	$-0.589516\pi$
$593$	−13.5166	−0.555062	−0.277531	+	0.960717i	$0.589516\pi$
$594$	−6.85628	−0.281317
$595$	−53.8493	−2.20761
$596$	6.14743	0.251809
$597$	−22.6695	−0.927800
$598$	−2.28060	−0.0932608
$599$	15.7555	0.643752	0.321876	−	0.946782i	$-0.395687\pi$
$599$	15.7555	0.643752	0.321876	+	0.946782i	$0.395687\pi$
$600$	−33.2716	−1.35831
$601$	11.8160	0.481984	0.240992	−	0.970527i	$-0.422527\pi$
$601$	11.8160	0.481984	0.240992	+	0.970527i	$0.422527\pi$
$602$	0.646550	0.0263514
$603$	5.27819	0.214945
$604$	−1.61966	−0.0659032
$605$	−107.276	−4.36139
$606$	−14.5582	−0.591386
$607$	−26.4353	−1.07298	−0.536489	−	0.843908i	$-0.680250\pi$
$607$	−26.4353	−1.07298	−0.536489	+	0.843908i	$0.680250\pi$
$608$	−10.4333	−0.423124
$609$	−24.0539	−0.974712
$610$	10.9868	0.444842
$611$	5.44420	0.220249
$612$	3.64336	0.147274
$613$	10.7672	0.434885	0.217442	−	0.976073i	$-0.430229\pi$
$613$	10.7672	0.434885	0.217442	+	0.976073i	$0.430229\pi$
$614$	28.2441	1.13984
$615$	−44.7201	−1.80329
$616$	−53.5942	−2.15937
$617$	22.5104	0.906234	0.453117	−	0.891451i	$-0.350312\pi$
$617$	22.5104	0.906234	0.453117	+	0.891451i	$0.350312\pi$
$618$	−1.11274	−0.0447609
$619$	10.9080	0.438430	0.219215	−	0.975677i	$-0.429650\pi$
$619$	10.9080	0.438430	0.219215	+	0.975677i	$0.429650\pi$
$620$	−21.9451	−0.881338
$621$	2.04954	0.0822452
$622$	−0.0660183	−0.00264709
$623$	39.9807	1.60179
$624$	1.89601	0.0759013
$625$	38.0797	1.52319
$626$	34.1440	1.36467
$627$	15.9258	0.636015
$628$	−3.18850	−0.127235
$629$	4.01578	0.160120
$630$	12.5291	0.499171
$631$	−49.9180	−1.98720	−0.993602	−	0.112936i	$-0.963975\pi$
$631$	−49.9180	−1.98720	−0.993602	+	0.112936i	$0.963975\pi$
$632$	−47.0276	−1.87066
$633$	20.3609	0.809272
$634$	−29.1969	−1.15956
$635$	−76.1144	−3.02051
$636$	6.92164	0.274461
$637$	−1.01070	−0.0400453
$638$	−58.2691	−2.30690
$639$	−0.585183	−0.0231495
$640$	−4.55276	−0.179964
$641$	−20.7155	−0.818213	−0.409106	−	0.912487i	$-0.634159\pi$
$641$	−20.7155	−0.818213	−0.409106	+	0.912487i	$0.634159\pi$
$642$	−1.82705	−0.0721080
$643$	−30.9695	−1.22132	−0.610660	−	0.791893i	$-0.709096\pi$
$643$	−30.9695	−1.22132	−0.610660	+	0.791893i	$0.709096\pi$
$644$	4.41916	0.174139
$645$	0.816706	0.0321578
$646$	13.7547	0.541173
$647$	22.8939	0.900050	0.450025	−	0.893016i	$-0.351415\pi$
$647$	22.8939	0.900050	0.450025	+	0.893016i	$0.351415\pi$
$648$	−3.07318	−0.120726
$649$	55.5286	2.17969
$650$	−12.0470	−0.472522
$651$	20.4943	0.803235
$652$	9.49958	0.372032
$653$	−23.4346	−0.917069	−0.458534	−	0.888677i	$-0.651625\pi$
$653$	−23.4346	−0.917069	−0.458534	+	0.888677i	$0.651625\pi$
$654$	0.256197	0.0100181
$655$	19.6042	0.766000
$656$	−21.3134	−0.832148
$657$	−2.33591	−0.0911325
$658$	17.1460	0.668420
$659$	−0.737910	−0.0287449	−0.0143724	−	0.999897i	$-0.504575\pi$
$659$	−0.737910	−0.0287449	−0.0143724	+	0.999897i	$0.504575\pi$
$660$	−18.6739	−0.726882
$661$	14.8674	0.578274	0.289137	−	0.957288i	$-0.406632\pi$
$661$	14.8674	0.578274	0.289137	+	0.957288i	$0.406632\pi$
$662$	6.10418	0.237246
$663$	4.78248	0.185736
$664$	−2.60807	−0.101213
$665$	−29.1027	−1.12855
$666$	−0.934351	−0.0362054
$667$	17.4183	0.674440
$668$	−11.9354	−0.461794
$669$	21.5007	0.831266
$670$	−23.3652	−0.902678
$671$	15.2926	0.590365
$672$	−11.4248	−0.440722
$673$	43.4225	1.67381	0.836907	−	0.547346i	$-0.184362\pi$
$673$	43.4225	1.67381	0.836907	+	0.547346i	$0.184362\pi$
$674$	21.4139	0.824832
$675$	10.8264	0.416710
$676$	−0.761813	−0.0293005
$677$	−1.14115	−0.0438579	−0.0219290	−	0.999760i	$-0.506981\pi$
$677$	−1.14115	−0.0438579	−0.0219290	+	0.999760i	$0.506981\pi$
$678$	−19.7312	−0.757773
$679$	19.6305	0.753349
$680$	−58.4699	−2.24222
$681$	9.96605	0.381900
$682$	49.6463	1.90105
$683$	36.6012	1.40051	0.700253	−	0.713895i	$-0.253070\pi$
$683$	36.6012	1.40051	0.700253	+	0.713895i	$0.253070\pi$
$684$	1.96904	0.0752881
$685$	−21.4800	−0.820708
$686$	18.8627	0.720182
$687$	9.99399	0.381295
$688$	0.389238	0.0148396
$689$	9.08575	0.346139
$690$	−9.07280	−0.345396
$691$	−17.7673	−0.675901	−0.337951	−	0.941164i	$-0.609734\pi$
$691$	−17.7673	−0.675901	−0.337951	+	0.941164i	$0.609734\pi$
$692$	13.2350	0.503120
$693$	17.4394	0.662467
$694$	28.0660	1.06537
$695$	80.9631	3.07110
$696$	−26.1178	−0.989994
$697$	−53.7606	−2.03633
$698$	−21.9217	−0.829750
$699$	24.7768	0.937146
$700$	23.3437	0.882309
$701$	−18.9036	−0.713979	−0.356989	−	0.934108i	$-0.616197\pi$
$701$	−18.9036	−0.713979	−0.356989	+	0.934108i	$0.616197\pi$
$702$	−1.11274	−0.0419976
$703$	2.17031	0.0818550
$704$	−51.0410	−1.92368
$705$	21.6584	0.815701
$706$	−5.53613	−0.208355
$707$	37.0296	1.39264
$708$	6.86546	0.258020
$709$	8.76787	0.329284	0.164642	−	0.986353i	$-0.447353\pi$
$709$	8.76787	0.329284	0.164642	+	0.986353i	$0.447353\pi$
$710$	2.59046	0.0972181
$711$	15.3026	0.573893
$712$	43.4113	1.62691
$713$	−14.8407	−0.555789
$714$	15.0620	0.563680
$715$	−24.5125	−0.916715
$716$	−8.18302	−0.305814
$717$	13.5169	0.504796
$718$	34.1932	1.27608
$719$	−44.3375	−1.65351	−0.826756	−	0.562561i	$-0.809816\pi$
$719$	−44.3375	−1.65351	−0.826756	+	0.562561i	$0.809816\pi$
$720$	7.54281	0.281104
$721$	2.83032	0.105407
$722$	−13.7083	−0.510171
$723$	−8.77390	−0.326305
$724$	−5.49822	−0.204340
$725$	92.0101	3.41717
$726$	30.0057	1.11362
$727$	−27.5975	−1.02354	−0.511768	−	0.859124i	$-0.671009\pi$
$727$	−27.5975	−1.02354	−0.511768	+	0.859124i	$0.671009\pi$
$728$	−8.69806	−0.322372
$729$	1.00000	0.0370370
$730$	10.3405	0.382718
$731$	0.981810	0.0363136
$732$	1.89075	0.0698842
$733$	49.8613	1.84167	0.920835	−	0.389953i	$-0.127509\pi$
$733$	49.8613	1.84167	0.920835	+	0.389953i	$0.127509\pi$
$734$	10.4086	0.384187
$735$	−4.02080	−0.148309
$736$	8.27314	0.304952
$737$	−32.5223	−1.19797
$738$	12.5085	0.460443
$739$	38.9566	1.43304	0.716521	−	0.697565i	$-0.245733\pi$
$739$	38.9566	1.43304	0.716521	+	0.697565i	$0.245733\pi$
$740$	−2.54482	−0.0935494
$741$	2.58467	0.0949504
$742$	28.6147	1.05048
$743$	13.1520	0.482502	0.241251	−	0.970463i	$-0.422442\pi$
$743$	13.1520	0.482502	0.241251	+	0.970463i	$0.422442\pi$
$744$	22.2528	0.815829
$745$	32.1023	1.17614
$746$	−8.35896	−0.306043
$747$	0.848656	0.0310507
$748$	−22.4490	−0.820818
$749$	4.64722	0.169806
$750$	−25.7922	−0.941798
$751$	0.0588072	0.00214591	0.00107295	−	0.999999i	$-0.499658\pi$
$751$	0.0588072	0.00214591	0.00107295	+	0.999999i	$0.499658\pi$
$752$	10.3223	0.376415
$753$	3.31695	0.120876
$754$	−9.45677	−0.344395
$755$	−8.45800	−0.307818
$756$	2.15617	0.0784193
$757$	−1.51470	−0.0550528	−0.0275264	−	0.999621i	$-0.508763\pi$
$757$	−1.51470	−0.0550528	−0.0275264	+	0.999621i	$0.508763\pi$
$758$	−5.00419	−0.181760
$759$	−12.6285	−0.458386
$760$	−31.5998	−1.14625
$761$	−50.2298	−1.82083	−0.910415	−	0.413696i	$-0.864238\pi$
$761$	−50.2298	−1.82083	−0.910415	+	0.413696i	$0.864238\pi$
$762$	21.2896	0.771243
$763$	−0.651652	−0.0235914
$764$	14.1532	0.512043
$765$	19.0259	0.687883
$766$	1.83990	0.0664783
$767$	9.01200	0.325405
$768$	−15.2939	−0.551873
$769$	17.8921	0.645207	0.322603	−	0.946534i	$-0.395442\pi$
$769$	17.8921	0.645207	0.322603	+	0.946534i	$0.395442\pi$
$770$	−77.1997	−2.78208
$771$	−26.4332	−0.951967
$772$	3.38513	0.121834
$773$	23.1718	0.833432	0.416716	−	0.909037i	$-0.363181\pi$
$773$	23.1718	0.833432	0.416716	+	0.909037i	$0.363181\pi$
$774$	−0.228437	−0.00821101
$775$	−78.3942	−2.81600
$776$	21.3149	0.765160
$777$	2.37658	0.0852592
$778$	−27.4473	−0.984035
$779$	−29.0547	−1.04099
$780$	−3.03068	−0.108516
$781$	3.60568	0.129021
$782$	−10.9069	−0.390032
$783$	8.49865	0.303717
$784$	−1.91630	−0.0684391
$785$	−16.6506	−0.594285
$786$	−5.48341	−0.195587
$787$	−24.7625	−0.882689	−0.441344	−	0.897338i	$-0.645498\pi$
$787$	−24.7625	−0.882689	−0.441344	+	0.897338i	$0.645498\pi$
$788$	1.43492	0.0511170
$789$	2.15061	0.0765636
$790$	−67.7408	−2.41011
$791$	50.1876	1.78446
$792$	18.9358	0.672853
$793$	2.48191	0.0881353
$794$	12.9473	0.459481
$795$	36.1453	1.28194
$796$	17.2699	0.612116
$797$	31.5635	1.11803	0.559017	−	0.829156i	$-0.311178\pi$
$797$	31.5635	1.11803	0.559017	+	0.829156i	$0.311178\pi$
$798$	8.14018	0.288159
$799$	26.0368	0.921116
$800$	43.7018	1.54509
$801$	−14.1259	−0.499113
$802$	−33.6614	−1.18862
$803$	14.3930	0.507918
$804$	−4.02100	−0.141810
$805$	23.0772	0.813365
$806$	8.05733	0.283807
$807$	−10.1132	−0.356002
$808$	40.2070	1.41448
$809$	18.3368	0.644689	0.322345	−	0.946622i	$-0.395529\pi$
$809$	18.3368	0.644689	0.322345	+	0.946622i	$0.395529\pi$
$810$	−4.42675	−0.155540
$811$	30.0554	1.05539	0.527693	−	0.849435i	$-0.323057\pi$
$811$	30.0554	1.05539	0.527693	+	0.849435i	$0.323057\pi$
$812$	18.3246	0.643066
$813$	24.4405	0.857166
$814$	5.75712	0.201787
$815$	49.6075	1.73768
$816$	9.06766	0.317432
$817$	0.530616	0.0185639
$818$	14.8167	0.518053
$819$	2.83032	0.0988993
$820$	34.0683	1.18972
$821$	−15.6476	−0.546106	−0.273053	−	0.961999i	$-0.588033\pi$
$821$	−15.6476	−0.546106	−0.273053	+	0.961999i	$0.588033\pi$
$822$	6.00807	0.209556
$823$	30.7698	1.07257	0.536284	−	0.844038i	$-0.319828\pi$
$823$	30.7698	1.07257	0.536284	+	0.844038i	$0.319828\pi$
$824$	3.07318	0.107059
$825$	−66.7085	−2.32249
$826$	28.3824	0.987551
$827$	−48.2946	−1.67937	−0.839685	−	0.543074i	$-0.817260\pi$
$827$	−48.2946	−1.67937	−0.839685	+	0.543074i	$0.817260\pi$
$828$	−1.56137	−0.0542612
$829$	53.8744	1.87114	0.935568	−	0.353146i	$-0.114888\pi$
$829$	53.8744	1.87114	0.935568	+	0.353146i	$0.114888\pi$
$830$	−3.75679	−0.130400
$831$	−9.80306	−0.340064
$832$	−8.28369	−0.287185
$833$	−4.83364	−0.167476
$834$	−22.6458	−0.784161
$835$	−62.3275	−2.15693
$836$	−12.1325	−0.419611
$837$	−7.24099	−0.250285
$838$	38.5135	1.33043
$839$	−2.36320	−0.0815869	−0.0407934	−	0.999168i	$-0.512989\pi$
$839$	−2.36320	−0.0815869	−0.0407934	+	0.999168i	$0.512989\pi$
$840$	−34.6030	−1.19392
$841$	43.2270	1.49059
$842$	40.9736	1.41204
$843$	−7.59624	−0.261629
$844$	−15.5112	−0.533917
$845$	−3.97825	−0.136856
$846$	−6.05797	−0.208277
$847$	−76.3214	−2.62243
$848$	17.2267	0.591567
$849$	6.16940	0.211733
$850$	−57.6146	−1.97616
$851$	−1.72097	−0.0589941
$852$	0.445800	0.0152729
$853$	−31.0296	−1.06243	−0.531216	−	0.847236i	$-0.678265\pi$
$853$	−31.0296	−1.06243	−0.531216	+	0.847236i	$0.678265\pi$
$854$	7.81654	0.267477
$855$	10.2825	0.351653
$856$	5.04598	0.172468
$857$	55.3842	1.89189	0.945945	−	0.324327i	$-0.105138\pi$
$857$	55.3842	1.89189	0.945945	+	0.324327i	$0.105138\pi$
$858$	6.85628	0.234070
$859$	−34.6307	−1.18158	−0.590792	−	0.806824i	$-0.701184\pi$
$859$	−34.6307	−1.18158	−0.590792	+	0.806824i	$0.701184\pi$
$860$	−0.622177	−0.0212161
$861$	−31.8160	−1.08429
$862$	15.4203	0.525219
$863$	18.7190	0.637202	0.318601	−	0.947889i	$-0.396787\pi$
$863$	18.7190	0.637202	0.318601	+	0.947889i	$0.396787\pi$
$864$	4.03658	0.137327
$865$	69.1143	2.34996
$866$	−10.2678	−0.348913
$867$	5.87216	0.199429
$868$	−15.6128	−0.529934
$869$	−94.2890	−3.19854
$870$	−37.6214	−1.27548
$871$	−5.27819	−0.178845
$872$	−0.707568	−0.0239613
$873$	−6.93579	−0.234741
$874$	−5.89461	−0.199388
$875$	65.6040	2.21782
$876$	1.77953	0.0601246
$877$	11.6770	0.394304	0.197152	−	0.980373i	$-0.436831\pi$
$877$	11.6770	0.394304	0.197152	+	0.980373i	$0.436831\pi$
$878$	2.11480	0.0713710
$879$	5.49331	0.185285
$880$	−46.4760	−1.56671
$881$	33.4358	1.12648	0.563241	−	0.826293i	$-0.309554\pi$
$881$	33.4358	1.12648	0.563241	+	0.826293i	$0.309554\pi$
$882$	1.12464	0.0378686
$883$	14.0778	0.473756	0.236878	−	0.971539i	$-0.423876\pi$
$883$	14.0778	0.473756	0.236878	+	0.971539i	$0.423876\pi$
$884$	−3.64336	−0.122539
$885$	35.8520	1.20515
$886$	−36.3455	−1.22105
$887$	23.2329	0.780086	0.390043	−	0.920797i	$-0.372460\pi$
$887$	23.2329	0.780086	0.390043	+	0.920797i	$0.372460\pi$
$888$	2.58050	0.0865960
$889$	−54.1515	−1.81618
$890$	62.5317	2.09607
$891$	−6.16163	−0.206422
$892$	−16.3795	−0.548427
$893$	14.0715	0.470884
$894$	−8.97921	−0.300310
$895$	−42.7324	−1.42839
$896$	−3.23905	−0.108209
$897$	−2.04954	−0.0684322
$898$	1.48436	0.0495338
$899$	−61.5386	−2.05243
$900$	−8.24773	−0.274924
$901$	43.4524	1.44761
$902$	−77.0725	−2.56623
$903$	0.581044	0.0193359
$904$	54.4940	1.81244
$905$	−28.7121	−0.954424
$906$	2.36575	0.0785969
$907$	−35.3063	−1.17233	−0.586164	−	0.810193i	$-0.699362\pi$
$907$	−35.3063	−1.17233	−0.586164	+	0.810193i	$0.699362\pi$
$908$	−7.59227	−0.251958
$909$	−13.0832	−0.433943
$910$	−12.5291	−0.415336
$911$	32.9483	1.09163	0.545813	−	0.837907i	$-0.316221\pi$
$911$	32.9483	1.09163	0.545813	+	0.837907i	$0.316221\pi$
$912$	4.90058	0.162274
$913$	−5.22911	−0.173058
$914$	−36.0440	−1.19223
$915$	9.87366	0.326413
$916$	−7.61355	−0.251559
$917$	13.9474	0.460584
$918$	−5.32165	−0.175641
$919$	−20.0943	−0.662849	−0.331424	−	0.943482i	$-0.607529\pi$
$919$	−20.0943	−0.662849	−0.331424	+	0.943482i	$0.607529\pi$
$920$	25.0574	0.826117
$921$	25.3825	0.836381
$922$	−14.2090	−0.467949
$923$	0.585183	0.0192615
$924$	−13.2855	−0.437062
$925$	−9.09081	−0.298904
$926$	15.8503	0.520874
$927$	−1.00000	−0.0328443
$928$	34.3055	1.12613
$929$	−44.8518	−1.47154	−0.735770	−	0.677232i	$-0.763180\pi$
$929$	−44.8518	−1.47154	−0.735770	+	0.677232i	$0.763180\pi$
$930$	32.0540	1.05109
$931$	−2.61232	−0.0856154
$932$	−18.8753	−0.618282
$933$	−0.0593296	−0.00194236
$934$	−23.4209	−0.766354
$935$	−117.231	−3.83385
$936$	3.07318	0.100450
$937$	−31.0267	−1.01360	−0.506799	−	0.862065i	$-0.669171\pi$
$937$	−31.0267	−1.01360	−0.506799	+	0.862065i	$0.669171\pi$
$938$	−16.6232	−0.542765
$939$	30.6846	1.00135
$940$	−16.4996	−0.538158
$941$	12.9642	0.422622	0.211311	−	0.977419i	$-0.432227\pi$
$941$	12.9642	0.422622	0.211311	+	0.977419i	$0.432227\pi$
$942$	4.65727	0.151742
$943$	23.0392	0.750259
$944$	17.0869	0.556131
$945$	11.2597	0.366278
$946$	1.40755	0.0457633
$947$	23.8432	0.774798	0.387399	−	0.921912i	$-0.373374\pi$
$947$	23.8432	0.774798	0.387399	+	0.921912i	$0.373374\pi$
$948$	−11.6577	−0.378626
$949$	2.33591	0.0758268
$950$	−31.1376	−1.01024
$951$	−26.2387	−0.850849
$952$	−41.5983	−1.34821
$953$	0.368238	0.0119284	0.00596421	−	0.999982i	$-0.498102\pi$
$953$	0.368238	0.0119284	0.00596421	+	0.999982i	$0.498102\pi$
$954$	−10.1101	−0.327325
$955$	73.9089	2.39163
$956$	−10.2973	−0.333039
$957$	−52.3655	−1.69274
$958$	−18.8401	−0.608695
$959$	−15.2819	−0.493478
$960$	−32.9546	−1.06360
$961$	21.4320	0.691354
$962$	0.934351	0.0301247
$963$	−1.64194	−0.0529108
$964$	6.68407	0.215280
$965$	17.6774	0.569056
$966$	−6.45483	−0.207681
$967$	−13.2794	−0.427037	−0.213519	−	0.976939i	$-0.568492\pi$
$967$	−13.2794	−0.427037	−0.213519	+	0.976939i	$0.568492\pi$
$968$	−82.8702	−2.66355
$969$	12.3612	0.397098
$970$	30.7030	0.985813
$971$	28.2186	0.905579	0.452790	−	0.891617i	$-0.350429\pi$
$971$	28.2186	0.905579	0.452790	+	0.891617i	$0.350429\pi$
$972$	−0.761813	−0.0244352
$973$	57.6010	1.84660
$974$	16.0238	0.513437
$975$	−10.8264	−0.346724
$976$	4.70574	0.150627
$977$	−1.33979	−0.0428637	−0.0214318	−	0.999770i	$-0.506822\pi$
$977$	−1.33979	−0.0428637	−0.0214318	+	0.999770i	$0.506822\pi$
$978$	−13.8755	−0.443690
$979$	87.0384	2.78176
$980$	3.06310	0.0978471
$981$	0.230240	0.00735100
$982$	16.3025	0.520235
$983$	6.56242	0.209309	0.104654	−	0.994509i	$-0.466626\pi$
$983$	6.56242	0.209309	0.104654	+	0.994509i	$0.466626\pi$
$984$	−34.5460	−1.10129
$985$	7.49328	0.238756
$986$	−45.2269	−1.44032
$987$	15.4088	0.490468
$988$	−1.96904	−0.0626435
$989$	−0.420756	−0.0133793
$990$	27.2760	0.866887
$991$	−30.3574	−0.964334	−0.482167	−	0.876079i	$-0.660150\pi$
$991$	−30.3574	−0.964334	−0.482167	+	0.876079i	$0.660150\pi$
$992$	−29.2289	−0.928017
$993$	5.48573	0.174084
$994$	1.84298	0.0584557
$995$	90.1848	2.85905
$996$	−0.646518	−0.0204857
$997$	1.74607	0.0552985	0.0276493	−	0.999618i	$-0.491198\pi$
$997$	1.74607	0.0552985	0.0276493	+	0.999618i	$0.491198\pi$
$998$	−26.1550	−0.827923
$999$	−0.839686	−0.0265665

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.20	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+1.11274 q^{2} +1.00000 q^{3} -0.761813 q^{4} -3.97825 q^{5} +1.11274 q^{6} -2.83032 q^{7} -3.07318 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.11274 q^{2} +1.00000 q^{3} -0.761813 q^{4} -3.97825 q^{5} +1.11274 q^{6} -2.83032 q^{7} -3.07318 q^{8} +1.00000 q^{9} -4.42675 q^{10} -6.16163 q^{11} -0.761813 q^{12} -1.00000 q^{13} -3.14940 q^{14} -3.97825 q^{15} -1.89601 q^{16} -4.78248 q^{17} +1.11274 q^{18} -2.58467 q^{19} +3.03068 q^{20} -2.83032 q^{21} -6.85628 q^{22} +2.04954 q^{23} -3.07318 q^{24} +10.8264 q^{25} -1.11274 q^{26} +1.00000 q^{27} +2.15617 q^{28} +8.49865 q^{29} -4.42675 q^{30} -7.24099 q^{31} +4.03658 q^{32} -6.16163 q^{33} -5.32165 q^{34} +11.2597 q^{35} -0.761813 q^{36} -0.839686 q^{37} -2.87607 q^{38} -1.00000 q^{39} +12.2259 q^{40} +11.2411 q^{41} -3.14940 q^{42} -0.205293 q^{43} +4.69401 q^{44} -3.97825 q^{45} +2.28060 q^{46} -5.44420 q^{47} -1.89601 q^{48} +1.01070 q^{49} +12.0470 q^{50} -4.78248 q^{51} +0.761813 q^{52} -9.08575 q^{53} +1.11274 q^{54} +24.5125 q^{55} +8.69806 q^{56} -2.58467 q^{57} +9.45677 q^{58} -9.01200 q^{59} +3.03068 q^{60} -2.48191 q^{61} -8.05733 q^{62} -2.83032 q^{63} +8.28369 q^{64} +3.97825 q^{65} -6.85628 q^{66} +5.27819 q^{67} +3.64336 q^{68} +2.04954 q^{69} +12.5291 q^{70} -0.585183 q^{71} -3.07318 q^{72} -2.33591 q^{73} -0.934351 q^{74} +10.8264 q^{75} +1.96904 q^{76} +17.4394 q^{77} -1.11274 q^{78} +15.3026 q^{79} +7.54281 q^{80} +1.00000 q^{81} +12.5085 q^{82} +0.848656 q^{83} +2.15617 q^{84} +19.0259 q^{85} -0.228437 q^{86} +8.49865 q^{87} +18.9358 q^{88} -14.1259 q^{89} -4.42675 q^{90} +2.83032 q^{91} -1.56137 q^{92} -7.24099 q^{93} -6.05797 q^{94} +10.2825 q^{95} +4.03658 q^{96} -6.93579 q^{97} +1.12464 q^{98} -6.16163 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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