LMFDB - Embedded newform 4017.2.a.f.1.6

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:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 16 x^{17} + 77 x^{16} + 88 x^{15} - 594 x^{14} - 154 x^{13} + 2388 x^{12} - 278 x^{11} + \cdots + 4 $ x^19 - 4x^18 - 16x^17 + 77x^16 + 88x^15 - 594x^14 - 154x^13 + 2388x^12 - 278x^11 - 5460x^10 + 1491x^9 + 7285x^8 - 2223x^7 - 5579x^6 + 1430x^5 + 2261x^4 - 352x^3 - 378x^2 + 11x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.44458$ of defining polynomial
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)

$f(q)$	$=$	$q-1.44458 q^{2} +1.00000 q^{3} +0.0867978 q^{4} -1.93878 q^{5} -1.44458 q^{6} +1.10404 q^{7} +2.76376 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.44458 q^{2} +1.00000 q^{3} +0.0867978 q^{4} -1.93878 q^{5} -1.44458 q^{6} +1.10404 q^{7} +2.76376 q^{8} +1.00000 q^{9} +2.80071 q^{10} +6.28272 q^{11} +0.0867978 q^{12} +1.00000 q^{13} -1.59487 q^{14} -1.93878 q^{15} -4.16606 q^{16} -6.18912 q^{17} -1.44458 q^{18} -0.632632 q^{19} -0.168282 q^{20} +1.10404 q^{21} -9.07587 q^{22} -8.14192 q^{23} +2.76376 q^{24} -1.24114 q^{25} -1.44458 q^{26} +1.00000 q^{27} +0.0958286 q^{28} +6.18300 q^{29} +2.80071 q^{30} -6.33107 q^{31} +0.490661 q^{32} +6.28272 q^{33} +8.94065 q^{34} -2.14050 q^{35} +0.0867978 q^{36} +2.32050 q^{37} +0.913884 q^{38} +1.00000 q^{39} -5.35833 q^{40} +8.88389 q^{41} -1.59487 q^{42} -2.49165 q^{43} +0.545327 q^{44} -1.93878 q^{45} +11.7616 q^{46} -11.8048 q^{47} -4.16606 q^{48} -5.78109 q^{49} +1.79292 q^{50} -6.18912 q^{51} +0.0867978 q^{52} -7.40229 q^{53} -1.44458 q^{54} -12.1808 q^{55} +3.05132 q^{56} -0.632632 q^{57} -8.93181 q^{58} +6.06616 q^{59} -0.168282 q^{60} -6.83400 q^{61} +9.14570 q^{62} +1.10404 q^{63} +7.62333 q^{64} -1.93878 q^{65} -9.07587 q^{66} -5.89201 q^{67} -0.537202 q^{68} -8.14192 q^{69} +3.09211 q^{70} +10.8934 q^{71} +2.76376 q^{72} -4.31744 q^{73} -3.35213 q^{74} -1.24114 q^{75} -0.0549111 q^{76} +6.93640 q^{77} -1.44458 q^{78} +9.64471 q^{79} +8.07707 q^{80} +1.00000 q^{81} -12.8334 q^{82} -7.21777 q^{83} +0.0958286 q^{84} +11.9993 q^{85} +3.59938 q^{86} +6.18300 q^{87} +17.3640 q^{88} +7.80116 q^{89} +2.80071 q^{90} +1.10404 q^{91} -0.706701 q^{92} -6.33107 q^{93} +17.0529 q^{94} +1.22653 q^{95} +0.490661 q^{96} +0.781021 q^{97} +8.35122 q^{98} +6.28272 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * 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 $

$2$	−1.44458	−1.02147	−0.510734	−	0.859738i	$-0.670626\pi$
$2$	−1.44458	−1.02147	−0.510734	+	0.859738i	$0.670626\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0867978	0.0433989
$5$	−1.93878	−0.867048	−0.433524	−	0.901142i	$-0.642730\pi$
$5$	−1.93878	−0.867048	−0.433524	+	0.901142i	$0.642730\pi$
$6$	−1.44458	−0.589745
$7$	1.10404	0.417289	0.208645	−	0.977992i	$-0.433095\pi$
$7$	1.10404	0.417289	0.208645	+	0.977992i	$0.433095\pi$
$8$	2.76376	0.977138
$9$	1.00000	0.333333
$10$	2.80071	0.885663
$11$	6.28272	1.89431	0.947156	−	0.320772i	$-0.103942\pi$
$11$	6.28272	1.89431	0.947156	+	0.320772i	$0.103942\pi$
$12$	0.0867978	0.0250564
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.59487	−0.426248
$15$	−1.93878	−0.500590
$16$	−4.16606	−1.04152
$17$	−6.18912	−1.50108	−0.750541	−	0.660824i	$-0.770207\pi$
$17$	−6.18912	−1.50108	−0.750541	+	0.660824i	$0.770207\pi$
$18$	−1.44458	−0.340490
$19$	−0.632632	−0.145136	−0.0725679	−	0.997363i	$-0.523119\pi$
$19$	−0.632632	−0.145136	−0.0725679	+	0.997363i	$0.523119\pi$
$20$	−0.168282	−0.0376289
$21$	1.10404	0.240922
$22$	−9.07587	−1.93498
$23$	−8.14192	−1.69771	−0.848854	−	0.528627i	$-0.822707\pi$
$23$	−8.14192	−1.69771	−0.848854	+	0.528627i	$0.822707\pi$
$24$	2.76376	0.564151
$25$	−1.24114	−0.248228
$26$	−1.44458	−0.283305
$27$	1.00000	0.192450
$28$	0.0958286	0.0181099
$29$	6.18300	1.14815	0.574077	−	0.818801i	$-0.305361\pi$
$29$	6.18300	1.14815	0.574077	+	0.818801i	$0.305361\pi$
$30$	2.80071	0.511338
$31$	−6.33107	−1.13709	−0.568546	−	0.822651i	$-0.692494\pi$
$31$	−6.33107	−1.13709	−0.568546	+	0.822651i	$0.692494\pi$
$32$	0.490661	0.0867374
$33$	6.28272	1.09368
$34$	8.94065	1.53331
$35$	−2.14050	−0.361810
$36$	0.0867978	0.0144663
$37$	2.32050	0.381487	0.190744	−	0.981640i	$-0.438910\pi$
$37$	2.32050	0.381487	0.190744	+	0.981640i	$0.438910\pi$
$38$	0.913884	0.148252
$39$	1.00000	0.160128
$40$	−5.35833	−0.847226
$41$	8.88389	1.38743	0.693715	−	0.720250i	$-0.255973\pi$
$41$	8.88389	1.38743	0.693715	+	0.720250i	$0.255973\pi$
$42$	−1.59487	−0.246094
$43$	−2.49165	−0.379974	−0.189987	−	0.981787i	$-0.560845\pi$
$43$	−2.49165	−0.379974	−0.189987	+	0.981787i	$0.560845\pi$
$44$	0.545327	0.0822111
$45$	−1.93878	−0.289016
$46$	11.7616	1.73416
$47$	−11.8048	−1.72190	−0.860950	−	0.508689i	$-0.830130\pi$
$47$	−11.8048	−1.72190	−0.860950	+	0.508689i	$0.830130\pi$
$48$	−4.16606	−0.601319
$49$	−5.78109	−0.825870
$50$	1.79292	0.253557
$51$	−6.18912	−0.866650
$52$	0.0867978	0.0120367
$53$	−7.40229	−1.01678	−0.508392	−	0.861126i	$-0.669760\pi$
$53$	−7.40229	−1.01678	−0.508392	+	0.861126i	$0.669760\pi$
$54$	−1.44458	−0.196582
$55$	−12.1808	−1.64246
$56$	3.05132	0.407749
$57$	−0.632632	−0.0837941
$58$	−8.93181	−1.17280
$59$	6.06616	0.789747	0.394874	−	0.918735i	$-0.370788\pi$
$59$	6.06616	0.789747	0.394874	+	0.918735i	$0.370788\pi$
$60$	−0.168282	−0.0217251
$61$	−6.83400	−0.875004	−0.437502	−	0.899217i	$-0.644137\pi$
$61$	−6.83400	−0.875004	−0.437502	+	0.899217i	$0.644137\pi$
$62$	9.14570	1.16151
$63$	1.10404	0.139096
$64$	7.62333	0.952916
$65$	−1.93878	−0.240476
$66$	−9.07587	−1.11716
$67$	−5.89201	−0.719823	−0.359912	−	0.932986i	$-0.617193\pi$
$67$	−5.89201	−0.719823	−0.359912	+	0.932986i	$0.617193\pi$
$68$	−0.537202	−0.0651453
$69$	−8.14192	−0.980172
$70$	3.09211	0.369578
$71$	10.8934	1.29281	0.646407	−	0.762993i	$-0.276271\pi$
$71$	10.8934	1.29281	0.646407	+	0.762993i	$0.276271\pi$
$72$	2.76376	0.325713
$73$	−4.31744	−0.505318	−0.252659	−	0.967555i	$-0.581305\pi$
$73$	−4.31744	−0.505318	−0.252659	+	0.967555i	$0.581305\pi$
$74$	−3.35213	−0.389677
$75$	−1.24114	−0.143314
$76$	−0.0549111	−0.00629873
$77$	6.93640	0.790476
$78$	−1.44458	−0.163566
$79$	9.64471	1.08511	0.542557	−	0.840019i	$-0.317456\pi$
$79$	9.64471	1.08511	0.542557	+	0.840019i	$0.317456\pi$
$80$	8.07707	0.903044
$81$	1.00000	0.111111
$82$	−12.8334	−1.41722
$83$	−7.21777	−0.792253	−0.396126	−	0.918196i	$-0.629646\pi$
$83$	−7.21777	−0.792253	−0.396126	+	0.918196i	$0.629646\pi$
$84$	0.0958286	0.0104558
$85$	11.9993	1.30151
$86$	3.59938	0.388131
$87$	6.18300	0.662887
$88$	17.3640	1.85101
$89$	7.80116	0.826922	0.413461	−	0.910522i	$-0.364320\pi$
$89$	7.80116	0.826922	0.413461	+	0.910522i	$0.364320\pi$
$90$	2.80071	0.295221
$91$	1.10404	0.115735
$92$	−0.706701	−0.0736787
$93$	−6.33107	−0.656501
$94$	17.0529	1.75887
$95$	1.22653	0.125840
$96$	0.490661	0.0500778
$97$	0.781021	0.0793006	0.0396503	−	0.999214i	$-0.487376\pi$
$97$	0.781021	0.0793006	0.0396503	+	0.999214i	$0.487376\pi$
$98$	8.35122	0.843600
$99$	6.28272	0.631438
$100$	−0.107728	−0.0107728
$101$	6.90252	0.686826	0.343413	−	0.939184i	$-0.388417\pi$
$101$	6.90252	0.686826	0.343413	+	0.939184i	$0.388417\pi$
$102$	8.94065	0.885256
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.76376	0.271009
$105$	−2.14050	−0.208891
$106$	10.6932	1.03861
$107$	−13.9916	−1.35262	−0.676310	−	0.736617i	$-0.736422\pi$
$107$	−13.9916	−1.35262	−0.676310	+	0.736617i	$0.736422\pi$
$108$	0.0867978	0.00835212
$109$	−14.5300	−1.39172	−0.695862	−	0.718176i	$-0.744977\pi$
$109$	−14.5300	−1.39172	−0.695862	+	0.718176i	$0.744977\pi$
$110$	17.5961	1.67772
$111$	2.32050	0.220252
$112$	−4.59951	−0.434613
$113$	9.66432	0.909143	0.454571	−	0.890710i	$-0.349792\pi$
$113$	9.66432	0.909143	0.454571	+	0.890710i	$0.349792\pi$
$114$	0.913884	0.0855931
$115$	15.7854	1.47199
$116$	0.536671	0.0498286
$117$	1.00000	0.0924500
$118$	−8.76303	−0.806702
$119$	−6.83306	−0.626385
$120$	−5.35833	−0.489146
$121$	28.4726	2.58842
$122$	9.87223	0.893789
$123$	8.88389	0.801033
$124$	−0.549523	−0.0493486
$125$	12.1002	1.08227
$126$	−1.59487	−0.142083
$127$	−15.7212	−1.39503	−0.697515	−	0.716570i	$-0.745711\pi$
$127$	−15.7212	−1.39503	−0.697515	+	0.716570i	$0.745711\pi$
$128$	−11.9938	−1.06011
$129$	−2.49165	−0.219378
$130$	2.80071	0.245639
$131$	3.83008	0.334636	0.167318	−	0.985903i	$-0.446489\pi$
$131$	3.83008	0.334636	0.167318	+	0.985903i	$0.446489\pi$
$132$	0.545327	0.0474646
$133$	−0.698453	−0.0605636
$134$	8.51145	0.735277
$135$	−1.93878	−0.166863
$136$	−17.1053	−1.46676
$137$	−13.2421	−1.13135	−0.565674	−	0.824629i	$-0.691384\pi$
$137$	−13.2421	−1.13135	−0.565674	+	0.824629i	$0.691384\pi$
$138$	11.7616	1.00122
$139$	−7.84581	−0.665473	−0.332737	−	0.943020i	$-0.607972\pi$
$139$	−7.84581	−0.665473	−0.332737	+	0.943020i	$0.607972\pi$
$140$	−0.185790	−0.0157022
$141$	−11.8048	−0.994140
$142$	−15.7364	−1.32057
$143$	6.28272	0.525388
$144$	−4.16606	−0.347172
$145$	−11.9875	−0.995505
$146$	6.23686	0.516166
$147$	−5.78109	−0.476816
$148$	0.201414	0.0165561
$149$	−5.25848	−0.430792	−0.215396	−	0.976527i	$-0.569104\pi$
$149$	−5.25848	−0.430792	−0.215396	+	0.976527i	$0.569104\pi$
$150$	1.79292	0.146391
$151$	13.6992	1.11483	0.557413	−	0.830235i	$-0.311794\pi$
$151$	13.6992	1.11483	0.557413	+	0.830235i	$0.311794\pi$
$152$	−1.74845	−0.141818
$153$	−6.18912	−0.500361
$154$	−10.0202	−0.807447
$155$	12.2745	0.985914
$156$	0.0867978	0.00694939
$157$	−6.42612	−0.512860	−0.256430	−	0.966563i	$-0.582546\pi$
$157$	−6.42612	−0.512860	−0.256430	+	0.966563i	$0.582546\pi$
$158$	−13.9325	−1.10841
$159$	−7.40229	−0.587040
$160$	−0.951282	−0.0752055
$161$	−8.98904	−0.708436
$162$	−1.44458	−0.113497
$163$	−18.4115	−1.44210	−0.721049	−	0.692884i	$-0.756340\pi$
$163$	−18.4115	−1.44210	−0.721049	+	0.692884i	$0.756340\pi$
$164$	0.771102	0.0602129
$165$	−12.1808	−0.948275
$166$	10.4266	0.809262
$167$	2.72353	0.210753	0.105376	−	0.994432i	$-0.466395\pi$
$167$	2.72353	0.210753	0.105376	+	0.994432i	$0.466395\pi$
$168$	3.05132	0.235414
$169$	1.00000	0.0769231
$170$	−17.3339	−1.32945
$171$	−0.632632	−0.0483786
$172$	−0.216270	−0.0164904
$173$	21.6568	1.64654	0.823268	−	0.567653i	$-0.192149\pi$
$173$	21.6568	1.64654	0.823268	+	0.567653i	$0.192149\pi$
$174$	−8.93181	−0.677119
$175$	−1.37027	−0.103583
$176$	−26.1742	−1.97296
$177$	6.06616	0.455961
$178$	−11.2694	−0.844675
$179$	−9.24215	−0.690791	−0.345396	−	0.938457i	$-0.612255\pi$
$179$	−9.24215	−0.690791	−0.345396	+	0.938457i	$0.612255\pi$
$180$	−0.168282	−0.0125430
$181$	−10.7918	−0.802151	−0.401075	−	0.916045i	$-0.631363\pi$
$181$	−10.7918	−0.802151	−0.401075	+	0.916045i	$0.631363\pi$
$182$	−1.59487	−0.118220
$183$	−6.83400	−0.505184
$184$	−22.5024	−1.65890
$185$	−4.49893	−0.330768
$186$	9.14570	0.670595
$187$	−38.8845	−2.84352
$188$	−1.02463	−0.0747286
$189$	1.10404	0.0803074
$190$	−1.77182	−0.128541
$191$	18.6799	1.35163	0.675815	−	0.737071i	$-0.263792\pi$
$191$	18.6799	1.35163	0.675815	+	0.737071i	$0.263792\pi$
$192$	7.62333	0.550166
$193$	−5.17612	−0.372585	−0.186293	−	0.982494i	$-0.559647\pi$
$193$	−5.17612	−0.372585	−0.186293	+	0.982494i	$0.559647\pi$
$194$	−1.12824	−0.0810031
$195$	−1.93878	−0.138839
$196$	−0.501786	−0.0358418
$197$	−9.33972	−0.665428	−0.332714	−	0.943028i	$-0.607964\pi$
$197$	−9.33972	−0.665428	−0.332714	+	0.943028i	$0.607964\pi$
$198$	−9.07587	−0.644994
$199$	−16.7658	−1.18849	−0.594247	−	0.804283i	$-0.702550\pi$
$199$	−16.7658	−1.18849	−0.594247	+	0.804283i	$0.702550\pi$
$200$	−3.43021	−0.242553
$201$	−5.89201	−0.415590
$202$	−9.97121	−0.701572
$203$	6.82630	0.479113
$204$	−0.537202	−0.0376116
$205$	−17.2239	−1.20297
$206$	1.44458	0.100648
$207$	−8.14192	−0.565903
$208$	−4.16606	−0.288864
$209$	−3.97465	−0.274932
$210$	3.09211	0.213376
$211$	−20.4014	−1.40449	−0.702244	−	0.711936i	$-0.747818\pi$
$211$	−20.4014	−1.40449	−0.702244	+	0.711936i	$0.747818\pi$
$212$	−0.642503	−0.0441273
$213$	10.8934	0.746406
$214$	20.2119	1.38166
$215$	4.83076	0.329455
$216$	2.76376	0.188050
$217$	−6.98977	−0.474497
$218$	20.9897	1.42160
$219$	−4.31744	−0.291745
$220$	−1.05727	−0.0712810
$221$	−6.18912	−0.416325
$222$	−3.35213	−0.224980
$223$	12.4356	0.832750	0.416375	−	0.909193i	$-0.363300\pi$
$223$	12.4356	0.832750	0.416375	+	0.909193i	$0.363300\pi$
$224$	0.541711	0.0361946
$225$	−1.24114	−0.0827425
$226$	−13.9608	−0.928661
$227$	14.2066	0.942928	0.471464	−	0.881885i	$-0.343726\pi$
$227$	14.2066	0.942928	0.471464	+	0.881885i	$0.343726\pi$
$228$	−0.0549111	−0.00363657
$229$	−7.12485	−0.470823	−0.235412	−	0.971896i	$-0.575644\pi$
$229$	−7.12485	−0.470823	−0.235412	+	0.971896i	$0.575644\pi$
$230$	−22.8032	−1.50360
$231$	6.93640	0.456382
$232$	17.0884	1.12191
$233$	−8.88768	−0.582251	−0.291126	−	0.956685i	$-0.594030\pi$
$233$	−8.88768	−0.582251	−0.291126	+	0.956685i	$0.594030\pi$
$234$	−1.44458	−0.0944348
$235$	22.8868	1.49297
$236$	0.526530	0.0342742
$237$	9.64471	0.626491
$238$	9.87087	0.639833
$239$	−16.2076	−1.04838	−0.524190	−	0.851601i	$-0.675632\pi$
$239$	−16.2076	−1.04838	−0.524190	+	0.851601i	$0.675632\pi$
$240$	8.07707	0.521373
$241$	−4.30406	−0.277249	−0.138624	−	0.990345i	$-0.544268\pi$
$241$	−4.30406	−0.277249	−0.138624	+	0.990345i	$0.544268\pi$
$242$	−41.1309	−2.64399
$243$	1.00000	0.0641500
$244$	−0.593176	−0.0379742
$245$	11.2082	0.716069
$246$	−12.8334	−0.818230
$247$	−0.632632	−0.0402534
$248$	−17.4976	−1.11110
$249$	−7.21777	−0.457407
$250$	−17.4796	−1.10551
$251$	20.8582	1.31655	0.658277	−	0.752775i	$-0.271285\pi$
$251$	20.8582	1.31655	0.658277	+	0.752775i	$0.271285\pi$
$252$	0.0958286	0.00603663
$253$	−51.1535	−3.21599
$254$	22.7105	1.42498
$255$	11.9993	0.751427
$256$	2.07928	0.129955
$257$	−8.27155	−0.515965	−0.257983	−	0.966150i	$-0.583058\pi$
$257$	−8.27155	−0.515965	−0.257983	+	0.966150i	$0.583058\pi$
$258$	3.59938	0.224088
$259$	2.56193	0.159191
$260$	−0.168282	−0.0104364
$261$	6.18300	0.382718
$262$	−5.53284	−0.341820
$263$	−16.3681	−1.00930	−0.504652	−	0.863323i	$-0.668379\pi$
$263$	−16.3681	−1.00930	−0.504652	+	0.863323i	$0.668379\pi$
$264$	17.3640	1.06868
$265$	14.3514	0.881600
$266$	1.00897	0.0618638
$267$	7.80116	0.477424
$268$	−0.511413	−0.0312395
$269$	8.17422	0.498391	0.249195	−	0.968453i	$-0.419834\pi$
$269$	8.17422	0.498391	0.249195	+	0.968453i	$0.419834\pi$
$270$	2.80071	0.170446
$271$	−31.2231	−1.89667	−0.948333	−	0.317275i	$-0.897232\pi$
$271$	−31.2231	−1.89667	−0.948333	+	0.317275i	$0.897232\pi$
$272$	25.7842	1.56340
$273$	1.10404	0.0668198
$274$	19.1292	1.15564
$275$	−7.79773	−0.470221
$276$	−0.706701	−0.0425384
$277$	−18.0708	−1.08577	−0.542886	−	0.839806i	$-0.682668\pi$
$277$	−18.0708	−1.08577	−0.542886	+	0.839806i	$0.682668\pi$
$278$	11.3339	0.679760
$279$	−6.33107	−0.379031
$280$	−5.91583	−0.353538
$281$	9.61403	0.573525	0.286762	−	0.958002i	$-0.407421\pi$
$281$	9.61403	0.573525	0.286762	+	0.958002i	$0.407421\pi$
$282$	17.0529	1.01548
$283$	32.1679	1.91219	0.956093	−	0.293063i	$-0.0946747\pi$
$283$	32.1679	1.91219	0.956093	+	0.293063i	$0.0946747\pi$
$284$	0.945527	0.0561067
$285$	1.22653	0.0726535
$286$	−9.07587	−0.536667
$287$	9.80820	0.578960
$288$	0.490661	0.0289125
$289$	21.3052	1.25325
$290$	17.3168	1.01688
$291$	0.781021	0.0457842
$292$	−0.374744	−0.0219302
$293$	−30.8380	−1.80157	−0.900787	−	0.434262i	$-0.857009\pi$
$293$	−30.8380	−1.80157	−0.900787	+	0.434262i	$0.857009\pi$
$294$	8.35122	0.487053
$295$	−11.7609	−0.684749
$296$	6.41331	0.372766
$297$	6.28272	0.364561
$298$	7.59627	0.440040
$299$	−8.14192	−0.470860
$300$	−0.107728	−0.00621968
$301$	−2.75089	−0.158559
$302$	−19.7895	−1.13876
$303$	6.90252	0.396539
$304$	2.63558	0.151161
$305$	13.2496	0.758670
$306$	8.94065	0.511103
$307$	−4.49872	−0.256756	−0.128378	−	0.991725i	$-0.540977\pi$
$307$	−4.49872	−0.256756	−0.128378	+	0.991725i	$0.540977\pi$
$308$	0.602064	0.0343058
$309$	−1.00000	−0.0568880
$310$	−17.7315	−1.00708
$311$	−12.0426	−0.682872	−0.341436	−	0.939905i	$-0.610913\pi$
$311$	−12.0426	−0.682872	−0.341436	+	0.939905i	$0.610913\pi$
$312$	2.76376	0.156467
$313$	−3.08385	−0.174309	−0.0871547	−	0.996195i	$-0.527777\pi$
$313$	−3.08385	−0.174309	−0.0871547	+	0.996195i	$0.527777\pi$
$314$	9.28301	0.523871
$315$	−2.14050	−0.120603
$316$	0.837140	0.0470928
$317$	−33.1324	−1.86090	−0.930450	−	0.366420i	$-0.880583\pi$
$317$	−33.1324	−1.86090	−0.930450	+	0.366420i	$0.880583\pi$
$318$	10.6932	0.599643
$319$	38.8461	2.17496
$320$	−14.7799	−0.826224
$321$	−13.9916	−0.780935
$322$	12.9853	0.723645
$323$	3.91543	0.217861
$324$	0.0867978	0.00482210
$325$	−1.24114	−0.0688460
$326$	26.5967	1.47306
$327$	−14.5300	−0.803512
$328$	24.5530	1.35571
$329$	−13.0330	−0.718531
$330$	17.5961	0.968633
$331$	−26.0189	−1.43013	−0.715065	−	0.699058i	$-0.753603\pi$
$331$	−26.0189	−1.43013	−0.715065	+	0.699058i	$0.753603\pi$
$332$	−0.626486	−0.0343829
$333$	2.32050	0.127162
$334$	−3.93434	−0.215277
$335$	11.4233	0.624121
$336$	−4.59951	−0.250924
$337$	−13.1359	−0.715560	−0.357780	−	0.933806i	$-0.616466\pi$
$337$	−13.1359	−0.715560	−0.357780	+	0.933806i	$0.616466\pi$
$338$	−1.44458	−0.0785745
$339$	9.66432	0.524894
$340$	1.04152	0.0564841
$341$	−39.7763	−2.15401
$342$	0.913884	0.0494172
$343$	−14.1109	−0.761916
$344$	−6.88634	−0.371287
$345$	15.7854	0.849857
$346$	−31.2849	−1.68188
$347$	17.2354	0.925244	0.462622	−	0.886556i	$-0.346909\pi$
$347$	17.2354	0.925244	0.462622	+	0.886556i	$0.346909\pi$
$348$	0.536671	0.0287686
$349$	10.5927	0.567012	0.283506	−	0.958970i	$-0.408502\pi$
$349$	10.5927	0.567012	0.283506	+	0.958970i	$0.408502\pi$
$350$	1.97946	0.105807
$351$	1.00000	0.0533761
$352$	3.08269	0.164308
$353$	32.8773	1.74988	0.874942	−	0.484227i	$-0.160899\pi$
$353$	32.8773	1.74988	0.874942	+	0.484227i	$0.160899\pi$
$354$	−8.76303	−0.465750
$355$	−21.1200	−1.12093
$356$	0.677124	0.0358875
$357$	−6.83306	−0.361644
$358$	13.3510	0.705622
$359$	13.0290	0.687642	0.343821	−	0.939035i	$-0.388279\pi$
$359$	13.0290	0.687642	0.343821	+	0.939035i	$0.388279\pi$
$360$	−5.35833	−0.282409
$361$	−18.5998	−0.978936
$362$	15.5896	0.819372
$363$	28.4726	1.49443
$364$	0.0958286	0.00502278
$365$	8.37055	0.438135
$366$	9.87223	0.516030
$367$	23.5880	1.23129	0.615643	−	0.788026i	$-0.288897\pi$
$367$	23.5880	1.23129	0.615643	+	0.788026i	$0.288897\pi$
$368$	33.9198	1.76819
$369$	8.88389	0.462477
$370$	6.49904	0.337869
$371$	−8.17246	−0.424293
$372$	−0.549523	−0.0284914
$373$	−31.5884	−1.63559	−0.817794	−	0.575512i	$-0.804803\pi$
$373$	−31.5884	−1.63559	−0.817794	+	0.575512i	$0.804803\pi$
$374$	56.1716	2.90457
$375$	12.1002	0.624851
$376$	−32.6256	−1.68254
$377$	6.18300	0.318441
$378$	−1.59487	−0.0820315
$379$	22.0652	1.13341	0.566706	−	0.823920i	$-0.308217\pi$
$379$	22.0652	1.13341	0.566706	+	0.823920i	$0.308217\pi$
$380$	0.106460	0.00546130
$381$	−15.7212	−0.805421
$382$	−26.9845	−1.38065
$383$	6.15510	0.314511	0.157255	−	0.987558i	$-0.449735\pi$
$383$	6.15510	0.314511	0.157255	+	0.987558i	$0.449735\pi$
$384$	−11.9938	−0.612056
$385$	−13.4481	−0.685381
$386$	7.47730	0.380584
$387$	−2.49165	−0.126658
$388$	0.0677909	0.00344156
$389$	−12.0152	−0.609196	−0.304598	−	0.952481i	$-0.598522\pi$
$389$	−12.0152	−0.609196	−0.304598	+	0.952481i	$0.598522\pi$
$390$	2.80071	0.141820
$391$	50.3913	2.54840
$392$	−15.9776	−0.806989
$393$	3.83008	0.193202
$394$	13.4919	0.679714
$395$	−18.6990	−0.940847
$396$	0.545327	0.0274037
$397$	−3.84669	−0.193060	−0.0965298	−	0.995330i	$-0.530774\pi$
$397$	−3.84669	−0.193060	−0.0965298	+	0.995330i	$0.530774\pi$
$398$	24.2194	1.21401
$399$	−0.698453	−0.0349664
$400$	5.17066	0.258533
$401$	26.4522	1.32096	0.660480	−	0.750843i	$-0.270353\pi$
$401$	26.4522	1.32096	0.660480	+	0.750843i	$0.270353\pi$
$402$	8.51145	0.424512
$403$	−6.33107	−0.315373
$404$	0.599124	0.0298075
$405$	−1.93878	−0.0963387
$406$	−9.86111	−0.489399
$407$	14.5790	0.722656
$408$	−17.1053	−0.846837
$409$	−26.6464	−1.31758	−0.658790	−	0.752327i	$-0.728932\pi$
$409$	−26.6464	−1.31758	−0.658790	+	0.752327i	$0.728932\pi$
$410$	24.8812	1.22879
$411$	−13.2421	−0.653184
$412$	−0.0867978	−0.00427622
$413$	6.69731	0.329553
$414$	11.7616	0.578052
$415$	13.9937	0.686921
$416$	0.490661	0.0240566
$417$	−7.84581	−0.384211
$418$	5.74168	0.280835
$419$	13.8060	0.674466	0.337233	−	0.941421i	$-0.390509\pi$
$419$	13.8060	0.674466	0.337233	+	0.941421i	$0.390509\pi$
$420$	−0.185790	−0.00906564
$421$	17.1181	0.834285	0.417142	−	0.908841i	$-0.363032\pi$
$421$	17.1181	0.834285	0.417142	+	0.908841i	$0.363032\pi$
$422$	29.4713	1.43464
$423$	−11.8048	−0.573967
$424$	−20.4582	−0.993538
$425$	7.68155	0.372610
$426$	−15.7364	−0.762431
$427$	−7.54503	−0.365130
$428$	−1.21444	−0.0587022
$429$	6.28272	0.303333
$430$	−6.97840	−0.336528
$431$	−25.0006	−1.20423	−0.602117	−	0.798408i	$-0.705676\pi$
$431$	−25.0006	−1.20423	−0.602117	+	0.798408i	$0.705676\pi$
$432$	−4.16606	−0.200440
$433$	26.5781	1.27726	0.638630	−	0.769514i	$-0.279501\pi$
$433$	26.5781	1.27726	0.638630	+	0.769514i	$0.279501\pi$
$434$	10.0973	0.484684
$435$	−11.9875	−0.574755
$436$	−1.26117	−0.0603993
$437$	5.15084	0.246398
$438$	6.23686	0.298009
$439$	−1.50959	−0.0720489	−0.0360245	−	0.999351i	$-0.511469\pi$
$439$	−1.50959	−0.0720489	−0.0360245	+	0.999351i	$0.511469\pi$
$440$	−33.6649	−1.60491
$441$	−5.78109	−0.275290
$442$	8.94065	0.425263
$443$	6.85462	0.325673	0.162836	−	0.986653i	$-0.447936\pi$
$443$	6.85462	0.325673	0.162836	+	0.986653i	$0.447936\pi$
$444$	0.201414	0.00955869
$445$	−15.1247	−0.716981
$446$	−17.9642	−0.850629
$447$	−5.25848	−0.248718
$448$	8.41649	0.397642
$449$	−9.92211	−0.468253	−0.234127	−	0.972206i	$-0.575223\pi$
$449$	−9.92211	−0.468253	−0.234127	+	0.972206i	$0.575223\pi$
$450$	1.79292	0.0845189
$451$	55.8150	2.62823
$452$	0.838842	0.0394558
$453$	13.6992	0.643645
$454$	−20.5226	−0.963172
$455$	−2.14050	−0.100348
$456$	−1.74845	−0.0818785
$457$	−32.3313	−1.51240	−0.756198	−	0.654343i	$-0.772945\pi$
$457$	−32.3313	−1.51240	−0.756198	+	0.654343i	$0.772945\pi$
$458$	10.2924	0.480932
$459$	−6.18912	−0.288883
$460$	1.37014	0.0638830
$461$	−12.6810	−0.590612	−0.295306	−	0.955403i	$-0.595422\pi$
$461$	−12.6810	−0.590612	−0.295306	+	0.955403i	$0.595422\pi$
$462$	−10.0202	−0.466180
$463$	23.3661	1.08592	0.542958	−	0.839760i	$-0.317304\pi$
$463$	23.3661	1.08592	0.542958	+	0.839760i	$0.317304\pi$
$464$	−25.7588	−1.19582
$465$	12.2745	0.569218
$466$	12.8389	0.594751
$467$	28.0441	1.29773	0.648864	−	0.760904i	$-0.275244\pi$
$467$	28.0441	1.29773	0.648864	+	0.760904i	$0.275244\pi$
$468$	0.0867978	0.00401223
$469$	−6.50503	−0.300374
$470$	−33.0617	−1.52502
$471$	−6.42612	−0.296100
$472$	16.7654	0.771692
$473$	−15.6544	−0.719789
$474$	−13.9325	−0.639941
$475$	0.785184	0.0360267
$476$	−0.593094	−0.0271844
$477$	−7.40229	−0.338928
$478$	23.4130	1.07089
$479$	−27.3460	−1.24947	−0.624734	−	0.780837i	$-0.714793\pi$
$479$	−27.3460	−1.24947	−0.624734	+	0.780837i	$0.714793\pi$
$480$	−0.951282	−0.0434199
$481$	2.32050	0.105806
$482$	6.21753	0.283201
$483$	−8.98904	−0.409016
$484$	2.47136	0.112335
$485$	−1.51423	−0.0687575
$486$	−1.44458	−0.0655273
$487$	−37.0900	−1.68071	−0.840354	−	0.542038i	$-0.817653\pi$
$487$	−37.0900	−1.68071	−0.840354	+	0.542038i	$0.817653\pi$
$488$	−18.8876	−0.855000
$489$	−18.4115	−0.832595
$490$	−16.1912	−0.731442
$491$	−3.67398	−0.165804	−0.0829021	−	0.996558i	$-0.526419\pi$
$491$	−3.67398	−0.165804	−0.0829021	+	0.996558i	$0.526419\pi$
$492$	0.771102	0.0347639
$493$	−38.2673	−1.72347
$494$	0.913884	0.0411176
$495$	−12.1808	−0.547487
$496$	26.3756	1.18430
$497$	12.0268	0.539477
$498$	10.4266	0.467228
$499$	38.5925	1.72764	0.863820	−	0.503801i	$-0.168066\pi$
$499$	38.5925	1.72764	0.863820	+	0.503801i	$0.168066\pi$
$500$	1.05027	0.0469695
$501$	2.72353	0.121678
$502$	−30.1312	−1.34482
$503$	−0.191633	−0.00854450	−0.00427225	−	0.999991i	$-0.501360\pi$
$503$	−0.191633	−0.00854450	−0.00427225	+	0.999991i	$0.501360\pi$
$504$	3.05132	0.135916
$505$	−13.3825	−0.595512
$506$	73.8950	3.28503
$507$	1.00000	0.0444116
$508$	−1.36457	−0.0605428
$509$	18.9933	0.841864	0.420932	−	0.907092i	$-0.361703\pi$
$509$	18.9933	0.841864	0.420932	+	0.907092i	$0.361703\pi$
$510$	−17.3339	−0.767559
$511$	−4.76664	−0.210864
$512$	20.9839	0.927366
$513$	−0.632632	−0.0279314
$514$	11.9489	0.527042
$515$	1.93878	0.0854328
$516$	−0.216270	−0.00952076
$517$	−74.1660	−3.26182
$518$	−3.70090	−0.162608
$519$	21.6568	0.950628
$520$	−5.35833	−0.234978
$521$	−33.7455	−1.47842	−0.739208	−	0.673477i	$-0.764800\pi$
$521$	−33.7455	−1.47842	−0.739208	+	0.673477i	$0.764800\pi$
$522$	−8.93181	−0.390935
$523$	12.7221	0.556299	0.278150	−	0.960538i	$-0.410279\pi$
$523$	12.7221	0.556299	0.278150	+	0.960538i	$0.410279\pi$
$524$	0.332443	0.0145228
$525$	−1.37027	−0.0598035
$526$	23.6450	1.03097
$527$	39.1837	1.70687
$528$	−26.1742	−1.13909
$529$	43.2909	1.88221
$530$	−20.7317	−0.900527
$531$	6.06616	0.263249
$532$	−0.0606242	−0.00262839
$533$	8.88389	0.384804
$534$	−11.2694	−0.487673
$535$	27.1266	1.17279
$536$	−16.2841	−0.703367
$537$	−9.24215	−0.398828
$538$	−11.8083	−0.509091
$539$	−36.3210	−1.56446
$540$	−0.168282	−0.00724169
$541$	31.9091	1.37188	0.685940	−	0.727658i	$-0.259391\pi$
$541$	31.9091	1.37188	0.685940	+	0.727658i	$0.259391\pi$
$542$	45.1041	1.93739
$543$	−10.7918	−0.463122
$544$	−3.03676	−0.130200
$545$	28.1705	1.20669
$546$	−1.59487	−0.0682543
$547$	2.78715	0.119170	0.0595850	−	0.998223i	$-0.481022\pi$
$547$	2.78715	0.119170	0.0595850	+	0.998223i	$0.481022\pi$
$548$	−1.14938	−0.0490993
$549$	−6.83400	−0.291668
$550$	11.2644	0.480316
$551$	−3.91156	−0.166638
$552$	−22.5024	−0.957764
$553$	10.6482	0.452807
$554$	26.1047	1.10908
$555$	−4.49893	−0.190969
$556$	−0.680999	−0.0288808
$557$	−12.5226	−0.530599	−0.265300	−	0.964166i	$-0.585471\pi$
$557$	−12.5226	−0.530599	−0.265300	+	0.964166i	$0.585471\pi$
$558$	9.14570	0.387168
$559$	−2.49165	−0.105386
$560$	8.91744	0.376831
$561$	−38.8845	−1.64171
$562$	−13.8882	−0.585838
$563$	−27.4876	−1.15846	−0.579231	−	0.815163i	$-0.696647\pi$
$563$	−27.4876	−1.15846	−0.579231	+	0.815163i	$0.696647\pi$
$564$	−1.02463	−0.0431446
$565$	−18.7370	−0.788271
$566$	−46.4690	−1.95324
$567$	1.10404	0.0463655
$568$	30.1069	1.26326
$569$	10.6015	0.444440	0.222220	−	0.974997i	$-0.428670\pi$
$569$	10.6015	0.444440	0.222220	+	0.974997i	$0.428670\pi$
$570$	−1.77182	−0.0742133
$571$	−15.2677	−0.638935	−0.319467	−	0.947597i	$-0.603504\pi$
$571$	−15.2677	−0.638935	−0.319467	+	0.947597i	$0.603504\pi$
$572$	0.545327	0.0228013
$573$	18.6799	0.780364
$574$	−14.1687	−0.591389
$575$	10.1053	0.421418
$576$	7.62333	0.317639
$577$	−20.9495	−0.872140	−0.436070	−	0.899913i	$-0.643630\pi$
$577$	−20.9495	−0.872140	−0.436070	+	0.899913i	$0.643630\pi$
$578$	−30.7769	−1.28015
$579$	−5.17612	−0.215112
$580$	−1.04049	−0.0432038
$581$	−7.96873	−0.330599
$582$	−1.12824	−0.0467672
$583$	−46.5066	−1.92611
$584$	−11.9324	−0.493765
$585$	−1.93878	−0.0801586
$586$	44.5478	1.84025
$587$	−12.1296	−0.500641	−0.250321	−	0.968163i	$-0.580536\pi$
$587$	−12.1296	−0.500641	−0.250321	+	0.968163i	$0.580536\pi$
$588$	−0.501786	−0.0206933
$589$	4.00523	0.165033
$590$	16.9896	0.699450
$591$	−9.33972	−0.384185
$592$	−9.66733	−0.397325
$593$	22.3995	0.919837	0.459918	−	0.887961i	$-0.347879\pi$
$593$	22.3995	0.919837	0.459918	+	0.887961i	$0.347879\pi$
$594$	−9.07587	−0.372387
$595$	13.2478	0.543106
$596$	−0.456425	−0.0186959
$597$	−16.7658	−0.686177
$598$	11.7616	0.480969
$599$	−12.8181	−0.523733	−0.261867	−	0.965104i	$-0.584338\pi$
$599$	−12.8181	−0.523733	−0.261867	+	0.965104i	$0.584338\pi$
$600$	−3.43021	−0.140038
$601$	8.72395	0.355857	0.177929	−	0.984043i	$-0.443060\pi$
$601$	8.72395	0.355857	0.177929	+	0.984043i	$0.443060\pi$
$602$	3.97387	0.161963
$603$	−5.89201	−0.239941
$604$	1.18906	0.0483822
$605$	−55.2021	−2.24429
$606$	−9.97121	−0.405053
$607$	36.3808	1.47665	0.738326	−	0.674444i	$-0.235617\pi$
$607$	36.3808	1.47665	0.738326	+	0.674444i	$0.235617\pi$
$608$	−0.310408	−0.0125887
$609$	6.82630	0.276616
$610$	−19.1401	−0.774958
$611$	−11.8048	−0.477569
$612$	−0.537202	−0.0217151
$613$	−16.6729	−0.673413	−0.336707	−	0.941610i	$-0.609313\pi$
$613$	−16.6729	−0.673413	−0.336707	+	0.941610i	$0.609313\pi$
$614$	6.49874	0.262268
$615$	−17.2239	−0.694534
$616$	19.1706	0.772405
$617$	8.63683	0.347706	0.173853	−	0.984772i	$-0.444378\pi$
$617$	8.63683	0.347706	0.173853	+	0.984772i	$0.444378\pi$
$618$	1.44458	0.0581093
$619$	17.3091	0.695711	0.347856	−	0.937548i	$-0.386910\pi$
$619$	17.3091	0.695711	0.347856	+	0.937548i	$0.386910\pi$
$620$	1.06540	0.0427876
$621$	−8.14192	−0.326724
$622$	17.3964	0.697533
$623$	8.61283	0.345066
$624$	−4.16606	−0.166776
$625$	−17.2539	−0.690155
$626$	4.45485	0.178052
$627$	−3.97465	−0.158732
$628$	−0.557773	−0.0222576
$629$	−14.3618	−0.572644
$630$	3.09211	0.123193
$631$	−31.9316	−1.27118	−0.635589	−	0.772027i	$-0.719243\pi$
$631$	−31.9316	−1.27118	−0.635589	+	0.772027i	$0.719243\pi$
$632$	26.6557	1.06031
$633$	−20.4014	−0.810881
$634$	47.8622	1.90085
$635$	30.4799	1.20956
$636$	−0.642503	−0.0254769
$637$	−5.78109	−0.229055
$638$	−56.1161	−2.22166
$639$	10.8934	0.430938
$640$	23.2533	0.919168
$641$	−33.4283	−1.32034	−0.660169	−	0.751117i	$-0.729515\pi$
$641$	−33.4283	−1.32034	−0.660169	+	0.751117i	$0.729515\pi$
$642$	20.2119	0.797701
$643$	18.6871	0.736948	0.368474	−	0.929638i	$-0.379880\pi$
$643$	18.6871	0.736948	0.368474	+	0.929638i	$0.379880\pi$
$644$	−0.780229	−0.0307453
$645$	4.83076	0.190211
$646$	−5.65614	−0.222538
$647$	−1.10233	−0.0433370	−0.0216685	−	0.999765i	$-0.506898\pi$
$647$	−1.10233	−0.0433370	−0.0216685	+	0.999765i	$0.506898\pi$
$648$	2.76376	0.108571
$649$	38.1120	1.49603
$650$	1.79292	0.0703240
$651$	−6.98977	−0.273951
$652$	−1.59807	−0.0625854
$653$	−40.7194	−1.59347	−0.796737	−	0.604326i	$-0.793442\pi$
$653$	−40.7194	−1.59347	−0.796737	+	0.604326i	$0.793442\pi$
$654$	20.9897	0.820763
$655$	−7.42568	−0.290145
$656$	−37.0108	−1.44503
$657$	−4.31744	−0.168439
$658$	18.8271	0.733957
$659$	−45.9095	−1.78838	−0.894191	−	0.447686i	$-0.852248\pi$
$659$	−45.9095	−1.78838	−0.894191	+	0.447686i	$0.852248\pi$
$660$	−1.05727	−0.0411541
$661$	−43.9648	−1.71003	−0.855016	−	0.518602i	$-0.826453\pi$
$661$	−43.9648	−1.71003	−0.855016	+	0.518602i	$0.826453\pi$
$662$	37.5863	1.46083
$663$	−6.18912	−0.240365
$664$	−19.9482	−0.774141
$665$	1.35415	0.0525115
$666$	−3.35213	−0.129892
$667$	−50.3415	−1.94923
$668$	0.236396	0.00914644
$669$	12.4356	0.480789
$670$	−16.5018	−0.637520
$671$	−42.9361	−1.65753
$672$	0.541711	0.0208969
$673$	31.1192	1.19956	0.599779	−	0.800166i	$-0.295255\pi$
$673$	31.1192	1.19956	0.599779	+	0.800166i	$0.295255\pi$
$674$	18.9758	0.730922
$675$	−1.24114	−0.0477714
$676$	0.0867978	0.00333838
$677$	−6.95505	−0.267304	−0.133652	−	0.991028i	$-0.542671\pi$
$677$	−6.95505	−0.267304	−0.133652	+	0.991028i	$0.542671\pi$
$678$	−13.9608	−0.536163
$679$	0.862281	0.0330913
$680$	33.1633	1.27176
$681$	14.2066	0.544400
$682$	57.4599	2.20025
$683$	11.6383	0.445328	0.222664	−	0.974895i	$-0.428525\pi$
$683$	11.6383	0.445328	0.222664	+	0.974895i	$0.428525\pi$
$684$	−0.0549111	−0.00209958
$685$	25.6735	0.980933
$686$	20.3842	0.778273
$687$	−7.12485	−0.271830
$688$	10.3804	0.395748
$689$	−7.40229	−0.282005
$690$	−22.8032	−0.868102
$691$	−31.3475	−1.19252	−0.596258	−	0.802793i	$-0.703347\pi$
$691$	−31.3475	−1.19252	−0.596258	+	0.802793i	$0.703347\pi$
$692$	1.87976	0.0714578
$693$	6.93640	0.263492
$694$	−24.8978	−0.945108
$695$	15.2113	0.576997
$696$	17.0884	0.647733
$697$	−54.9834	−2.08265
$698$	−15.3019	−0.579185
$699$	−8.88768	−0.336163
$700$	−0.118937	−0.00449538
$701$	26.4961	1.00075	0.500373	−	0.865810i	$-0.333196\pi$
$701$	26.4961	1.00075	0.500373	+	0.865810i	$0.333196\pi$
$702$	−1.44458	−0.0545220
$703$	−1.46802	−0.0553674
$704$	47.8953	1.80512
$705$	22.8868	0.861967
$706$	−47.4938	−1.78745
$707$	7.62068	0.286605
$708$	0.526530	0.0197882
$709$	−40.9326	−1.53726	−0.768628	−	0.639696i	$-0.779060\pi$
$709$	−40.9326	−1.53726	−0.768628	+	0.639696i	$0.779060\pi$
$710$	30.5094	1.14500
$711$	9.64471	0.361705
$712$	21.5606	0.808017
$713$	51.5471	1.93045
$714$	9.87087	0.369408
$715$	−12.1808	−0.455536
$716$	−0.802199	−0.0299796
$717$	−16.2076	−0.605282
$718$	−18.8213	−0.702405
$719$	−16.1523	−0.602378	−0.301189	−	0.953564i	$-0.597384\pi$
$719$	−16.1523	−0.602378	−0.301189	+	0.953564i	$0.597384\pi$
$720$	8.07707	0.301015
$721$	−1.10404	−0.0411167
$722$	26.8688	0.999952
$723$	−4.30406	−0.160070
$724$	−0.936707	−0.0348125
$725$	−7.67396	−0.285004
$726$	−41.1309	−1.52651
$727$	38.0571	1.41146	0.705729	−	0.708482i	$-0.250620\pi$
$727$	38.0571	1.41146	0.705729	+	0.708482i	$0.250620\pi$
$728$	3.05132	0.113089
$729$	1.00000	0.0370370
$730$	−12.0919	−0.447541
$731$	15.4211	0.570371
$732$	−0.593176	−0.0219244
$733$	4.50693	0.166467	0.0832337	−	0.996530i	$-0.473475\pi$
$733$	4.50693	0.166467	0.0832337	+	0.996530i	$0.473475\pi$
$734$	−34.0747	−1.25772
$735$	11.2082	0.413422
$736$	−3.99492	−0.147255
$737$	−37.0178	−1.36357
$738$	−12.8334	−0.472405
$739$	−27.2827	−1.00361	−0.501804	−	0.864981i	$-0.667330\pi$
$739$	−27.2827	−1.00361	−0.501804	+	0.864981i	$0.667330\pi$
$740$	−0.390497	−0.0143550
$741$	−0.632632	−0.0232403
$742$	11.8057	0.433402
$743$	33.5491	1.23080	0.615398	−	0.788217i	$-0.288995\pi$
$743$	33.5491	1.23080	0.615398	+	0.788217i	$0.288995\pi$
$744$	−17.4976	−0.641492
$745$	10.1950	0.373517
$746$	45.6319	1.67070
$747$	−7.21777	−0.264084
$748$	−3.37509	−0.123406
$749$	−15.4473	−0.564434
$750$	−17.4796	−0.638266
$751$	22.9644	0.837983	0.418991	−	0.907990i	$-0.362384\pi$
$751$	22.9644	0.837983	0.418991	+	0.907990i	$0.362384\pi$
$752$	49.1793	1.79339
$753$	20.8582	0.760113
$754$	−8.93181	−0.325277
$755$	−26.5597	−0.966607
$756$	0.0958286	0.00348525
$757$	7.61994	0.276951	0.138476	−	0.990366i	$-0.455780\pi$
$757$	7.61994	0.276951	0.138476	+	0.990366i	$0.455780\pi$
$758$	−31.8748	−1.15775
$759$	−51.1535	−1.85675
$760$	3.38985	0.122963
$761$	16.3025	0.590965	0.295482	−	0.955348i	$-0.404520\pi$
$761$	16.3025	0.590965	0.295482	+	0.955348i	$0.404520\pi$
$762$	22.7105	0.822713
$763$	−16.0418	−0.580751
$764$	1.62137	0.0586593
$765$	11.9993	0.433837
$766$	−8.89150	−0.321263
$767$	6.06616	0.219036
$768$	2.07928	0.0750296
$769$	41.6392	1.50155	0.750774	−	0.660559i	$-0.229681\pi$
$769$	41.6392	1.50155	0.750774	+	0.660559i	$0.229681\pi$
$770$	19.4269	0.700096
$771$	−8.27155	−0.297893
$772$	−0.449276	−0.0161698
$773$	20.6725	0.743539	0.371769	−	0.928325i	$-0.378751\pi$
$773$	20.6725	0.743539	0.371769	+	0.928325i	$0.378751\pi$
$774$	3.59938	0.129377
$775$	7.85773	0.282258
$776$	2.15856	0.0774877
$777$	2.56193	0.0919087
$778$	17.3569	0.622275
$779$	−5.62023	−0.201366
$780$	−0.168282	−0.00602545
$781$	68.4405	2.44899
$782$	−72.7941	−2.60311
$783$	6.18300	0.220962
$784$	24.0844	0.860156
$785$	12.4588	0.444674
$786$	−5.53284	−0.197350
$787$	18.6403	0.664454	0.332227	−	0.943199i	$-0.392200\pi$
$787$	18.6403	0.664454	0.332227	+	0.943199i	$0.392200\pi$
$788$	−0.810667	−0.0288788
$789$	−16.3681	−0.582722
$790$	27.0121	0.961046
$791$	10.6698	0.379376
$792$	17.3640	0.617002
$793$	−6.83400	−0.242682
$794$	5.55683	0.197204
$795$	14.3514	0.508992
$796$	−1.45523	−0.0515793
$797$	21.9582	0.777800	0.388900	−	0.921280i	$-0.372855\pi$
$797$	21.9582	0.777800	0.388900	+	0.921280i	$0.372855\pi$
$798$	1.00897	0.0357171
$799$	73.0610	2.58471
$800$	−0.608978	−0.0215306
$801$	7.80116	0.275641
$802$	−38.2122	−1.34932
$803$	−27.1253	−0.957230
$804$	−0.511413	−0.0180362
$805$	17.4278	0.614248
$806$	9.14570	0.322144
$807$	8.17422	0.287746
$808$	19.0769	0.671124
$809$	20.4049	0.717397	0.358698	−	0.933453i	$-0.383221\pi$
$809$	20.4049	0.717397	0.358698	+	0.933453i	$0.383221\pi$
$810$	2.80071	0.0984070
$811$	−38.5422	−1.35340	−0.676700	−	0.736259i	$-0.736591\pi$
$811$	−38.5422	−1.35340	−0.676700	+	0.736259i	$0.736591\pi$
$812$	0.592508	0.0207930
$813$	−31.2231	−1.09504
$814$	−21.0605	−0.738171
$815$	35.6958	1.25037
$816$	25.7842	0.902629
$817$	1.57630	0.0551477
$818$	38.4928	1.34587
$819$	1.10404	0.0385784
$820$	−1.49500	−0.0522075
$821$	10.2770	0.358668	0.179334	−	0.983788i	$-0.442606\pi$
$821$	10.2770	0.358668	0.179334	+	0.983788i	$0.442606\pi$
$822$	19.1292	0.667207
$823$	42.3808	1.47730	0.738651	−	0.674088i	$-0.235463\pi$
$823$	42.3808	1.47730	0.738651	+	0.674088i	$0.235463\pi$
$824$	−2.76376	−0.0962803
$825$	−7.79773	−0.271482
$826$	−9.67477	−0.336628
$827$	33.6641	1.17061	0.585307	−	0.810812i	$-0.300974\pi$
$827$	33.6641	1.17061	0.585307	+	0.810812i	$0.300974\pi$
$828$	−0.706701	−0.0245596
$829$	−31.8872	−1.10749	−0.553744	−	0.832687i	$-0.686801\pi$
$829$	−31.8872	−1.10749	−0.553744	+	0.832687i	$0.686801\pi$
$830$	−20.2149	−0.701669
$831$	−18.0708	−0.626871
$832$	7.62333	0.264291
$833$	35.7798	1.23970
$834$	11.3339	0.392460
$835$	−5.28031	−0.182733
$836$	−0.344991	−0.0119318
$837$	−6.33107	−0.218834
$838$	−19.9438	−0.688946
$839$	−45.2070	−1.56072	−0.780359	−	0.625332i	$-0.784964\pi$
$839$	−45.2070	−1.56072	−0.780359	+	0.625332i	$0.784964\pi$
$840$	−5.91583	−0.204115
$841$	9.22950	0.318259
$842$	−24.7284	−0.852196
$843$	9.61403	0.331125
$844$	−1.77079	−0.0609532
$845$	−1.93878	−0.0666960
$846$	17.0529	0.586289
$847$	31.4350	1.08012
$848$	30.8384	1.05900
$849$	32.1679	1.10400
$850$	−11.0966	−0.380609
$851$	−18.8933	−0.647654
$852$	0.945527	0.0323932
$853$	−1.95643	−0.0669868	−0.0334934	−	0.999439i	$-0.510663\pi$
$853$	−1.95643	−0.0669868	−0.0334934	+	0.999439i	$0.510663\pi$
$854$	10.8994	0.372969
$855$	1.22653	0.0419465
$856$	−38.6695	−1.32170
$857$	31.1500	1.06406	0.532031	−	0.846725i	$-0.321429\pi$
$857$	31.1500	1.06406	0.532031	+	0.846725i	$0.321429\pi$
$858$	−9.07587	−0.309845
$859$	21.9842	0.750093	0.375046	−	0.927006i	$-0.377627\pi$
$859$	21.9842	0.750093	0.375046	+	0.927006i	$0.377627\pi$
$860$	0.419300	0.0142980
$861$	9.80820	0.334262
$862$	36.1152	1.23009
$863$	7.81830	0.266138	0.133069	−	0.991107i	$-0.457517\pi$
$863$	7.81830	0.266138	0.133069	+	0.991107i	$0.457517\pi$
$864$	0.490661	0.0166926
$865$	−41.9877	−1.42763
$866$	−38.3940	−1.30468
$867$	21.3052	0.723562
$868$	−0.606697	−0.0205926
$869$	60.5951	2.05555
$870$	17.3168	0.587095
$871$	−5.89201	−0.199643
$872$	−40.1576	−1.35991
$873$	0.781021	0.0264335
$874$	−7.44078	−0.251688
$875$	13.3591	0.451621
$876$	−0.374744	−0.0126614
$877$	52.7282	1.78050	0.890252	−	0.455468i	$-0.150528\pi$
$877$	52.7282	1.78050	0.890252	+	0.455468i	$0.150528\pi$
$878$	2.18072	0.0735957
$879$	−30.8380	−1.04014
$880$	50.7460	1.71065
$881$	36.3607	1.22502	0.612512	−	0.790461i	$-0.290159\pi$
$881$	36.3607	1.22502	0.612512	+	0.790461i	$0.290159\pi$
$882$	8.35122	0.281200
$883$	39.1778	1.31844	0.659219	−	0.751951i	$-0.270887\pi$
$883$	39.1778	1.31844	0.659219	+	0.751951i	$0.270887\pi$
$884$	−0.537202	−0.0180681
$885$	−11.7609	−0.395340
$886$	−9.90201	−0.332665
$887$	−41.4385	−1.39137	−0.695683	−	0.718348i	$-0.744898\pi$
$887$	−41.4385	−1.39137	−0.695683	+	0.718348i	$0.744898\pi$
$888$	6.41331	0.215216
$889$	−17.3569	−0.582131
$890$	21.8488	0.732374
$891$	6.28272	0.210479
$892$	1.07938	0.0361404
$893$	7.46806	0.249909
$894$	7.59627	0.254057
$895$	17.9185	0.598949
$896$	−13.2417	−0.442373
$897$	−8.14192	−0.271851
$898$	14.3332	0.478306
$899$	−39.1450	−1.30556
$900$	−0.107728	−0.00359094
$901$	45.8137	1.52627
$902$	−80.6290	−2.68465
$903$	−2.75089	−0.0915440
$904$	26.7099	0.888358
$905$	20.9230	0.695503
$906$	−19.7895	−0.657463
$907$	−38.3207	−1.27242	−0.636208	−	0.771517i	$-0.719498\pi$
$907$	−38.3207	−1.27242	−0.636208	+	0.771517i	$0.719498\pi$
$908$	1.23311	0.0409221
$909$	6.90252	0.228942
$910$	3.09211	0.102502
$911$	−42.7009	−1.41474	−0.707372	−	0.706842i	$-0.750119\pi$
$911$	−42.7009	−1.41474	−0.707372	+	0.706842i	$0.750119\pi$
$912$	2.63558	0.0872729
$913$	−45.3472	−1.50077
$914$	46.7050	1.54486
$915$	13.2496	0.438019
$916$	−0.618421	−0.0204332
$917$	4.22858	0.139640
$918$	8.94065	0.295085
$919$	−28.0516	−0.925338	−0.462669	−	0.886531i	$-0.653108\pi$
$919$	−28.0516	−0.925338	−0.462669	+	0.886531i	$0.653108\pi$
$920$	43.6271	1.43834
$921$	−4.49872	−0.148238
$922$	18.3186	0.603292
$923$	10.8934	0.358562
$924$	0.602064	0.0198065
$925$	−2.88006	−0.0946957
$926$	−33.7541	−1.10923
$927$	−1.00000	−0.0328443
$928$	3.03375	0.0995879
$929$	22.2976	0.731561	0.365780	−	0.930701i	$-0.380802\pi$
$929$	22.2976	0.731561	0.365780	+	0.930701i	$0.380802\pi$
$930$	−17.7315	−0.581438
$931$	3.65730	0.119863
$932$	−0.771431	−0.0252691
$933$	−12.0426	−0.394256
$934$	−40.5119	−1.32559
$935$	75.3885	2.46547
$936$	2.76376	0.0903365
$937$	3.18662	0.104102	0.0520512	−	0.998644i	$-0.483424\pi$
$937$	3.18662	0.104102	0.0520512	+	0.998644i	$0.483424\pi$
$938$	9.39701	0.306823
$939$	−3.08385	−0.100638
$940$	1.98652	0.0647933
$941$	−38.7577	−1.26346	−0.631732	−	0.775187i	$-0.717656\pi$
$941$	−38.7577	−1.26346	−0.631732	+	0.775187i	$0.717656\pi$
$942$	9.28301	0.302457
$943$	−72.3319	−2.35545
$944$	−25.2720	−0.822534
$945$	−2.14050	−0.0696303
$946$	22.6139	0.735242
$947$	−59.8819	−1.94590	−0.972950	−	0.231016i	$-0.925795\pi$
$947$	−59.8819	−1.94590	−0.972950	+	0.231016i	$0.925795\pi$
$948$	0.837140	0.0271890
$949$	−4.31744	−0.140150
$950$	−1.13426	−0.0368002
$951$	−33.1324	−1.07439
$952$	−18.8850	−0.612065
$953$	7.55700	0.244795	0.122398	−	0.992481i	$-0.460942\pi$
$953$	7.55700	0.244795	0.122398	+	0.992481i	$0.460942\pi$
$954$	10.6932	0.346204
$955$	−36.2162	−1.17193
$956$	−1.40678	−0.0454985
$957$	38.8461	1.25572
$958$	39.5033	1.27629
$959$	−14.6198	−0.472100
$960$	−14.7799	−0.477021
$961$	9.08239	0.292980
$962$	−3.35213	−0.108077
$963$	−13.9916	−0.450873
$964$	−0.373583	−0.0120323
$965$	10.0354	0.323049
$966$	12.9853	0.417797
$967$	2.46894	0.0793956	0.0396978	−	0.999212i	$-0.487360\pi$
$967$	2.46894	0.0793956	0.0396978	+	0.999212i	$0.487360\pi$
$968$	78.6916	2.52925
$969$	3.91543	0.125782
$970$	2.18741	0.0702336
$971$	6.82148	0.218912	0.109456	−	0.993992i	$-0.465089\pi$
$971$	6.82148	0.218912	0.109456	+	0.993992i	$0.465089\pi$
$972$	0.0867978	0.00278404
$973$	−8.66212	−0.277695
$974$	53.5793	1.71679
$975$	−1.24114	−0.0397482
$976$	28.4709	0.911330
$977$	−18.5394	−0.593129	−0.296564	−	0.955013i	$-0.595841\pi$
$977$	−18.5394	−0.593129	−0.296564	+	0.955013i	$0.595841\pi$
$978$	26.5967	0.850470
$979$	49.0126	1.56645
$980$	0.972851	0.0310766
$981$	−14.5300	−0.463908
$982$	5.30733	0.169364
$983$	−34.6598	−1.10548	−0.552738	−	0.833355i	$-0.686417\pi$
$983$	−34.6598	−1.10548	−0.552738	+	0.833355i	$0.686417\pi$
$984$	24.5530	0.782720
$985$	18.1077	0.576958
$986$	55.2800	1.76047
$987$	−13.0330	−0.414844
$988$	−0.0549111	−0.00174695
$989$	20.2869	0.645084
$990$	17.5961	0.559241
$991$	33.7659	1.07261	0.536304	−	0.844025i	$-0.319820\pi$
$991$	33.7659	1.07261	0.536304	+	0.844025i	$0.319820\pi$
$992$	−3.10640	−0.0986284
$993$	−26.0189	−0.825686
$994$	−17.3737	−0.551059
$995$	32.5051	1.03048
$996$	−0.626486	−0.0198510
$997$	40.2706	1.27538	0.637691	−	0.770293i	$-0.279890\pi$
$997$	40.2706	1.27538	0.637691	+	0.770293i	$0.279890\pi$
$998$	−55.7498	−1.76473
$999$	2.32050	0.0734173

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.f.1.6	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.f.1.6	✓	19	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)

\(f(q)\)	\(=\)	\(q-1.44458 q^{2} +1.00000 q^{3} +0.0867978 q^{4} -1.93878 q^{5} -1.44458 q^{6} +1.10404 q^{7} +2.76376 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.44458 q^{2} +1.00000 q^{3} +0.0867978 q^{4} -1.93878 q^{5} -1.44458 q^{6} +1.10404 q^{7} +2.76376 q^{8} +1.00000 q^{9} +2.80071 q^{10} +6.28272 q^{11} +0.0867978 q^{12} +1.00000 q^{13} -1.59487 q^{14} -1.93878 q^{15} -4.16606 q^{16} -6.18912 q^{17} -1.44458 q^{18} -0.632632 q^{19} -0.168282 q^{20} +1.10404 q^{21} -9.07587 q^{22} -8.14192 q^{23} +2.76376 q^{24} -1.24114 q^{25} -1.44458 q^{26} +1.00000 q^{27} +0.0958286 q^{28} +6.18300 q^{29} +2.80071 q^{30} -6.33107 q^{31} +0.490661 q^{32} +6.28272 q^{33} +8.94065 q^{34} -2.14050 q^{35} +0.0867978 q^{36} +2.32050 q^{37} +0.913884 q^{38} +1.00000 q^{39} -5.35833 q^{40} +8.88389 q^{41} -1.59487 q^{42} -2.49165 q^{43} +0.545327 q^{44} -1.93878 q^{45} +11.7616 q^{46} -11.8048 q^{47} -4.16606 q^{48} -5.78109 q^{49} +1.79292 q^{50} -6.18912 q^{51} +0.0867978 q^{52} -7.40229 q^{53} -1.44458 q^{54} -12.1808 q^{55} +3.05132 q^{56} -0.632632 q^{57} -8.93181 q^{58} +6.06616 q^{59} -0.168282 q^{60} -6.83400 q^{61} +9.14570 q^{62} +1.10404 q^{63} +7.62333 q^{64} -1.93878 q^{65} -9.07587 q^{66} -5.89201 q^{67} -0.537202 q^{68} -8.14192 q^{69} +3.09211 q^{70} +10.8934 q^{71} +2.76376 q^{72} -4.31744 q^{73} -3.35213 q^{74} -1.24114 q^{75} -0.0549111 q^{76} +6.93640 q^{77} -1.44458 q^{78} +9.64471 q^{79} +8.07707 q^{80} +1.00000 q^{81} -12.8334 q^{82} -7.21777 q^{83} +0.0958286 q^{84} +11.9993 q^{85} +3.59938 q^{86} +6.18300 q^{87} +17.3640 q^{88} +7.80116 q^{89} +2.80071 q^{90} +1.10404 q^{91} -0.706701 q^{92} -6.33107 q^{93} +17.0529 q^{94} +1.22653 q^{95} +0.490661 q^{96} +0.781021 q^{97} +8.35122 q^{98} +6.28272 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9	\( 19 q - 4 q^{2} + 19 q^{3} + 10 q^{4} - 3 q^{5} - 4 q^{6} - 23 q^{7} - 9 q^{8} + 19 q^{9} - 6 q^{10} - 15 q^{11} + 10 q^{12} + 19 q^{13} - 4 q^{14} - 3 q^{15} - 4 q^{16} - 4 q^{18} - 32 q^{19} - 8 q^{20} - 23 q^{21} - 9 q^{22} - 23 q^{23} - 9 q^{24} - 8 q^{25} - 4 q^{26} + 19 q^{27} - 22 q^{28} + 4 q^{29} - 6 q^{30} - 50 q^{31} - 2 q^{32} - 15 q^{33} - 35 q^{34} - 4 q^{35} + 10 q^{36} - 38 q^{37} + 20 q^{38} + 19 q^{39} - 30 q^{40} - 11 q^{41} - 4 q^{42} - 17 q^{43} - 29 q^{44} - 3 q^{45} - 5 q^{46} - 38 q^{47} - 4 q^{48} - 6 q^{49} - 9 q^{50} + 10 q^{52} - 12 q^{53} - 4 q^{54} - 22 q^{55} + 12 q^{56} - 32 q^{57} - 23 q^{58} - 8 q^{59} - 8 q^{60} - 31 q^{61} + 31 q^{62} - 23 q^{63} + 15 q^{64} - 3 q^{65} - 9 q^{66} - 48 q^{67} + 44 q^{68} - 23 q^{69} + 13 q^{70} - 14 q^{71} - 9 q^{72} - 50 q^{73} - 10 q^{74} - 8 q^{75} - 64 q^{76} + 23 q^{77} - 4 q^{78} - 21 q^{79} + 8 q^{80} + 19 q^{81} - 10 q^{82} - 15 q^{83} - 22 q^{84} - 29 q^{85} + 9 q^{86} + 4 q^{87} + 3 q^{88} - 10 q^{89} - 6 q^{90} - 23 q^{91} - 17 q^{92} - 50 q^{93} - 22 q^{94} - 25 q^{95} - 2 q^{96} - 42 q^{97} - q^{98} - 15 q^{99}+O(q^{100}) \) 19 * q - 4 * q^2 + 19 * q^3 + 10 * q^4 - 3 * q^5 - 4 * q^6 - 23 * q^7 - 9 * q^8 + 19 * q^9 - 6 * q^10 - 15 * q^11 + 10 * q^12 + 19 * q^13 - 4 * q^14 - 3 * q^15 - 4 * q^16 - 4 * q^18 - 32 * q^19 - 8 * q^20 - 23 * q^21 - 9 * q^22 - 23 * q^23 - 9 * q^24 - 8 * q^25 - 4 * q^26 + 19 * q^27 - 22 * q^28 + 4 * q^29 - 6 * q^30 - 50 * q^31 - 2 * q^32 - 15 * q^33 - 35 * q^34 - 4 * q^35 + 10 * q^36 - 38 * q^37 + 20 * q^38 + 19 * q^39 - 30 * q^40 - 11 * q^41 - 4 * q^42 - 17 * q^43 - 29 * q^44 - 3 * q^45 - 5 * q^46 - 38 * q^47 - 4 * q^48 - 6 * q^49 - 9 * q^50 + 10 * q^52 - 12 * q^53 - 4 * q^54 - 22 * q^55 + 12 * q^56 - 32 * q^57 - 23 * q^58 - 8 * q^59 - 8 * q^60 - 31 * q^61 + 31 * q^62 - 23 * q^63 + 15 * q^64 - 3 * q^65 - 9 * q^66 - 48 * q^67 + 44 * q^68 - 23 * q^69 + 13 * q^70 - 14 * q^71 - 9 * q^72 - 50 * q^73 - 10 * q^74 - 8 * q^75 - 64 * q^76 + 23 * q^77 - 4 * q^78 - 21 * q^79 + 8 * q^80 + 19 * q^81 - 10 * q^82 - 15 * q^83 - 22 * q^84 - 29 * q^85 + 9 * q^86 + 4 * q^87 + 3 * q^88 - 10 * q^89 - 6 * q^90 - 23 * q^91 - 17 * q^92 - 50 * q^93 - 22 * q^94 - 25 * q^95 - 2 * q^96 - 42 * q^97 - q^98 - 15 * q^99

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