LMFDB - Embedded newform 4011.2.a.i.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
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} - 3 x^{18} - 20 x^{17} + 63 x^{16} + 156 x^{15} - 531 x^{14} - 597 x^{13} + 2313 x^{12} + \cdots + 18 $ x^19 - 3x^18 - 20x^17 + 63x^16 + 156x^15 - 531x^14 - 597x^13 + 2313x^12 + 1149x^11 - 5631x^10 - 951x^9 + 7819x^8 - 87x^7 - 6025x^6 + 649x^5 + 2354x^4 - 342x^3 - 384x^2 + 45x + 18
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			1.18
Root			$2.30694$ of defining polynomial
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.30694 q^{2} -1.00000 q^{3} +3.32198 q^{4} -0.793515 q^{5} -2.30694 q^{6} +1.00000 q^{7} +3.04973 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.30694 q^{2} -1.00000 q^{3} +3.32198 q^{4} -0.793515 q^{5} -2.30694 q^{6} +1.00000 q^{7} +3.04973 q^{8} +1.00000 q^{9} -1.83059 q^{10} -0.906431 q^{11} -3.32198 q^{12} -1.05756 q^{13} +2.30694 q^{14} +0.793515 q^{15} +0.391582 q^{16} -0.469936 q^{17} +2.30694 q^{18} -7.20245 q^{19} -2.63604 q^{20} -1.00000 q^{21} -2.09108 q^{22} -7.64783 q^{23} -3.04973 q^{24} -4.37033 q^{25} -2.43973 q^{26} -1.00000 q^{27} +3.32198 q^{28} +8.06467 q^{29} +1.83059 q^{30} -1.21140 q^{31} -5.19610 q^{32} +0.906431 q^{33} -1.08411 q^{34} -0.793515 q^{35} +3.32198 q^{36} -4.45278 q^{37} -16.6156 q^{38} +1.05756 q^{39} -2.42000 q^{40} +2.73281 q^{41} -2.30694 q^{42} +9.83416 q^{43} -3.01114 q^{44} -0.793515 q^{45} -17.6431 q^{46} -6.30891 q^{47} -0.391582 q^{48} +1.00000 q^{49} -10.0821 q^{50} +0.469936 q^{51} -3.51319 q^{52} -6.10349 q^{53} -2.30694 q^{54} +0.719266 q^{55} +3.04973 q^{56} +7.20245 q^{57} +18.6047 q^{58} +4.52116 q^{59} +2.63604 q^{60} -9.48144 q^{61} -2.79463 q^{62} +1.00000 q^{63} -12.7702 q^{64} +0.839190 q^{65} +2.09108 q^{66} +9.61556 q^{67} -1.56112 q^{68} +7.64783 q^{69} -1.83059 q^{70} -3.40931 q^{71} +3.04973 q^{72} -10.0328 q^{73} -10.2723 q^{74} +4.37033 q^{75} -23.9264 q^{76} -0.906431 q^{77} +2.43973 q^{78} +16.4960 q^{79} -0.310726 q^{80} +1.00000 q^{81} +6.30443 q^{82} -14.1189 q^{83} -3.32198 q^{84} +0.372901 q^{85} +22.6868 q^{86} -8.06467 q^{87} -2.76436 q^{88} -5.19413 q^{89} -1.83059 q^{90} -1.05756 q^{91} -25.4059 q^{92} +1.21140 q^{93} -14.5543 q^{94} +5.71525 q^{95} +5.19610 q^{96} -8.73387 q^{97} +2.30694 q^{98} -0.906431 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9} - 12 q^{10} + q^{11} - 11 q^{12} - 25 q^{13} + 3 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 29 q^{19} - 14 q^{20} - 19 q^{21} - 5 q^{22} + 18 q^{23} - 6 q^{24} + 3 q^{25} - 15 q^{26} - 19 q^{27} + 11 q^{28} + 2 q^{29} + 12 q^{30} - 24 q^{31} + 15 q^{32} - q^{33} - 16 q^{34} - 12 q^{35} + 11 q^{36} - 24 q^{37} - 26 q^{38} + 25 q^{39} - 44 q^{40} - 14 q^{41} - 3 q^{42} - 17 q^{43} - 6 q^{44} - 12 q^{45} - 16 q^{46} + 7 q^{47} - 3 q^{48} + 19 q^{49} + 7 q^{50} + 9 q^{51} - 64 q^{52} + 4 q^{53} - 3 q^{54} - 15 q^{55} + 6 q^{56} + 29 q^{57} - 15 q^{58} - 23 q^{59} + 14 q^{60} - 38 q^{61} - 4 q^{62} + 19 q^{63} + 33 q^{65} + 5 q^{66} - 20 q^{67} - 27 q^{68} - 18 q^{69} - 12 q^{70} + 14 q^{71} + 6 q^{72} - 19 q^{73} - 11 q^{74} - 3 q^{75} - 33 q^{76} + q^{77} + 15 q^{78} - 16 q^{79} - 10 q^{80} + 19 q^{81} - 25 q^{82} - 11 q^{83} - 11 q^{84} - 5 q^{85} + 5 q^{86} - 2 q^{87} - 25 q^{88} - 19 q^{89} - 12 q^{90} - 25 q^{91} + 22 q^{92} + 24 q^{93} - 35 q^{94} + 26 q^{95} - 15 q^{96} - 57 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9 - 12 * q^10 + q^11 - 11 * q^12 - 25 * q^13 + 3 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 29 * q^19 - 14 * q^20 - 19 * q^21 - 5 * q^22 + 18 * q^23 - 6 * q^24 + 3 * q^25 - 15 * q^26 - 19 * q^27 + 11 * q^28 + 2 * q^29 + 12 * q^30 - 24 * q^31 + 15 * q^32 - q^33 - 16 * q^34 - 12 * q^35 + 11 * q^36 - 24 * q^37 - 26 * q^38 + 25 * q^39 - 44 * q^40 - 14 * q^41 - 3 * q^42 - 17 * q^43 - 6 * q^44 - 12 * q^45 - 16 * q^46 + 7 * q^47 - 3 * q^48 + 19 * q^49 + 7 * q^50 + 9 * q^51 - 64 * q^52 + 4 * q^53 - 3 * q^54 - 15 * q^55 + 6 * q^56 + 29 * q^57 - 15 * q^58 - 23 * q^59 + 14 * q^60 - 38 * q^61 - 4 * q^62 + 19 * q^63 + 33 * q^65 + 5 * q^66 - 20 * q^67 - 27 * q^68 - 18 * q^69 - 12 * q^70 + 14 * q^71 + 6 * q^72 - 19 * q^73 - 11 * q^74 - 3 * q^75 - 33 * q^76 + q^77 + 15 * q^78 - 16 * q^79 - 10 * q^80 + 19 * q^81 - 25 * q^82 - 11 * q^83 - 11 * q^84 - 5 * q^85 + 5 * q^86 - 2 * q^87 - 25 * q^88 - 19 * q^89 - 12 * q^90 - 25 * q^91 + 22 * q^92 + 24 * q^93 - 35 * q^94 + 26 * q^95 - 15 * q^96 - 57 * q^97 + 3 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.30694	1.63125	0.815627	−	0.578578i	$-0.196392\pi$
$2$	2.30694	1.63125	0.815627	+	0.578578i	$0.196392\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.32198	1.66099
$5$	−0.793515	−0.354871	−0.177435	−	0.984132i	$-0.556780\pi$
$5$	−0.793515	−0.354871	−0.177435	+	0.984132i	$0.556780\pi$
$6$	−2.30694	−0.941805
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.04973	1.07824
$9$	1.00000	0.333333
$10$	−1.83059	−0.578884
$11$	−0.906431	−0.273299	−0.136650	−	0.990619i	$-0.543633\pi$
$11$	−0.906431	−0.273299	−0.136650	+	0.990619i	$0.543633\pi$
$12$	−3.32198	−0.958972
$13$	−1.05756	−0.293314	−0.146657	−	0.989187i	$-0.546851\pi$
$13$	−1.05756	−0.293314	−0.146657	+	0.989187i	$0.546851\pi$
$14$	2.30694	0.616556
$15$	0.793515	0.204885
$16$	0.391582	0.0978954
$17$	−0.469936	−0.113976	−0.0569881	−	0.998375i	$-0.518150\pi$
$17$	−0.469936	−0.113976	−0.0569881	+	0.998375i	$0.518150\pi$
$18$	2.30694	0.543751
$19$	−7.20245	−1.65236	−0.826178	−	0.563409i	$-0.809489\pi$
$19$	−7.20245	−1.65236	−0.826178	+	0.563409i	$0.809489\pi$
$20$	−2.63604	−0.589436
$21$	−1.00000	−0.218218
$22$	−2.09108	−0.445820
$23$	−7.64783	−1.59468	−0.797342	−	0.603528i	$-0.793761\pi$
$23$	−7.64783	−1.59468	−0.797342	+	0.603528i	$0.793761\pi$
$24$	−3.04973	−0.622523
$25$	−4.37033	−0.874067
$26$	−2.43973	−0.478470
$27$	−1.00000	−0.192450
$28$	3.32198	0.627795
$29$	8.06467	1.49757	0.748786	−	0.662812i	$-0.230637\pi$
$29$	8.06467	1.49757	0.748786	+	0.662812i	$0.230637\pi$
$30$	1.83059	0.334219
$31$	−1.21140	−0.217574	−0.108787	−	0.994065i	$-0.534697\pi$
$31$	−1.21140	−0.217574	−0.108787	+	0.994065i	$0.534697\pi$
$32$	−5.19610	−0.918549
$33$	0.906431	0.157789
$34$	−1.08411	−0.185924
$35$	−0.793515	−0.134129
$36$	3.32198	0.553663
$37$	−4.45278	−0.732032	−0.366016	−	0.930608i	$-0.619279\pi$
$37$	−4.45278	−0.732032	−0.366016	+	0.930608i	$0.619279\pi$
$38$	−16.6156	−2.69541
$39$	1.05756	0.169345
$40$	−2.42000	−0.382636
$41$	2.73281	0.426793	0.213396	−	0.976966i	$-0.431547\pi$
$41$	2.73281	0.426793	0.213396	+	0.976966i	$0.431547\pi$
$42$	−2.30694	−0.355969
$43$	9.83416	1.49970	0.749848	−	0.661610i	$-0.230127\pi$
$43$	9.83416	1.49970	0.749848	+	0.661610i	$0.230127\pi$
$44$	−3.01114	−0.453947
$45$	−0.793515	−0.118290
$46$	−17.6431	−2.60133
$47$	−6.30891	−0.920249	−0.460124	−	0.887854i	$-0.652195\pi$
$47$	−6.30891	−0.920249	−0.460124	+	0.887854i	$0.652195\pi$
$48$	−0.391582	−0.0565200
$49$	1.00000	0.142857
$50$	−10.0821	−1.42582
$51$	0.469936	0.0658042
$52$	−3.51319	−0.487192
$53$	−6.10349	−0.838379	−0.419189	−	0.907899i	$-0.637686\pi$
$53$	−6.10349	−0.838379	−0.419189	+	0.907899i	$0.637686\pi$
$54$	−2.30694	−0.313935
$55$	0.719266	0.0969858
$56$	3.04973	0.407537
$57$	7.20245	0.953988
$58$	18.6047	2.44292
$59$	4.52116	0.588605	0.294303	−	0.955712i	$-0.404913\pi$
$59$	4.52116	0.588605	0.294303	+	0.955712i	$0.404913\pi$
$60$	2.63604	0.340311
$61$	−9.48144	−1.21397	−0.606987	−	0.794712i	$-0.707622\pi$
$61$	−9.48144	−1.21397	−0.606987	+	0.794712i	$0.707622\pi$
$62$	−2.79463	−0.354919
$63$	1.00000	0.125988
$64$	−12.7702	−1.59628
$65$	0.839190	0.104089
$66$	2.09108	0.257394
$67$	9.61556	1.17473	0.587364	−	0.809323i	$-0.300166\pi$
$67$	9.61556	1.17473	0.587364	+	0.809323i	$0.300166\pi$
$68$	−1.56112	−0.189313
$69$	7.64783	0.920691
$70$	−1.83059	−0.218798
$71$	−3.40931	−0.404610	−0.202305	−	0.979323i	$-0.564843\pi$
$71$	−3.40931	−0.404610	−0.202305	+	0.979323i	$0.564843\pi$
$72$	3.04973	0.359414
$73$	−10.0328	−1.17425	−0.587126	−	0.809495i	$-0.699741\pi$
$73$	−10.0328	−1.17425	−0.587126	+	0.809495i	$0.699741\pi$
$74$	−10.2723	−1.19413
$75$	4.37033	0.504643
$76$	−23.9264	−2.74454
$77$	−0.906431	−0.103297
$78$	2.43973	0.276245
$79$	16.4960	1.85594	0.927971	−	0.372653i	$-0.121552\pi$
$79$	16.4960	1.85594	0.927971	+	0.372653i	$0.121552\pi$
$80$	−0.310726	−0.0347402
$81$	1.00000	0.111111
$82$	6.30443	0.696207
$83$	−14.1189	−1.54975	−0.774875	−	0.632115i	$-0.782187\pi$
$83$	−14.1189	−1.54975	−0.774875	+	0.632115i	$0.782187\pi$
$84$	−3.32198	−0.362458
$85$	0.372901	0.0404468
$86$	22.6868	2.44638
$87$	−8.06467	−0.864624
$88$	−2.76436	−0.294682
$89$	−5.19413	−0.550576	−0.275288	−	0.961362i	$-0.588773\pi$
$89$	−5.19413	−0.550576	−0.275288	+	0.961362i	$0.588773\pi$
$90$	−1.83059	−0.192961
$91$	−1.05756	−0.110862
$92$	−25.4059	−2.64875
$93$	1.21140	0.125616
$94$	−14.5543	−1.50116
$95$	5.71525	0.586373
$96$	5.19610	0.530324
$97$	−8.73387	−0.886790	−0.443395	−	0.896326i	$-0.646226\pi$
$97$	−8.73387	−0.886790	−0.443395	+	0.896326i	$0.646226\pi$
$98$	2.30694	0.233036
$99$	−0.906431	−0.0910997
$100$	−14.5182	−1.45182
$101$	−7.38830	−0.735163	−0.367581	−	0.929991i	$-0.619814\pi$
$101$	−7.38830	−0.735163	−0.367581	+	0.929991i	$0.619814\pi$
$102$	1.08411	0.107343
$103$	8.06475	0.794644	0.397322	−	0.917679i	$-0.369940\pi$
$103$	8.06475	0.794644	0.397322	+	0.917679i	$0.369940\pi$
$104$	−3.22527	−0.316264
$105$	0.793515	0.0774391
$106$	−14.0804	−1.36761
$107$	3.80673	0.368010	0.184005	−	0.982925i	$-0.441094\pi$
$107$	3.80673	0.368010	0.184005	+	0.982925i	$0.441094\pi$
$108$	−3.32198	−0.319657
$109$	−5.43365	−0.520449	−0.260224	−	0.965548i	$-0.583797\pi$
$109$	−5.43365	−0.520449	−0.260224	+	0.965548i	$0.583797\pi$
$110$	1.65931	0.158209
$111$	4.45278	0.422639
$112$	0.391582	0.0370010
$113$	11.1286	1.04689	0.523445	−	0.852060i	$-0.324647\pi$
$113$	11.1286	1.04689	0.523445	+	0.852060i	$0.324647\pi$
$114$	16.6156	1.55620
$115$	6.06867	0.565907
$116$	26.7907	2.48745
$117$	−1.05756	−0.0977715
$118$	10.4301	0.960165
$119$	−0.469936	−0.0430789
$120$	2.42000	0.220915
$121$	−10.1784	−0.925308
$122$	−21.8731	−1.98030
$123$	−2.73281	−0.246409
$124$	−4.02425	−0.361388
$125$	7.43550	0.665051
$126$	2.30694	0.205519
$127$	10.7571	0.954538	0.477269	−	0.878757i	$-0.341627\pi$
$127$	10.7571	0.954538	0.477269	+	0.878757i	$0.341627\pi$
$128$	−19.0680	−1.68539
$129$	−9.83416	−0.865850
$130$	1.93596	0.169795
$131$	−8.39209	−0.733221	−0.366610	−	0.930375i	$-0.619482\pi$
$131$	−8.39209	−0.733221	−0.366610	+	0.930375i	$0.619482\pi$
$132$	3.01114	0.262086
$133$	−7.20245	−0.624532
$134$	22.1825	1.91628
$135$	0.793515	0.0682949
$136$	−1.43317	−0.122894
$137$	14.2063	1.21373	0.606865	−	0.794805i	$-0.292427\pi$
$137$	14.2063	1.21373	0.606865	+	0.794805i	$0.292427\pi$
$138$	17.6431	1.50188
$139$	4.54774	0.385735	0.192867	−	0.981225i	$-0.438221\pi$
$139$	4.54774	0.385735	0.192867	+	0.981225i	$0.438221\pi$
$140$	−2.63604	−0.222786
$141$	6.30891	0.531306
$142$	−7.86507	−0.660022
$143$	0.958605	0.0801626
$144$	0.391582	0.0326318
$145$	−6.39944	−0.531445
$146$	−23.1451	−1.91550
$147$	−1.00000	−0.0824786
$148$	−14.7920	−1.21590
$149$	−2.50733	−0.205409	−0.102704	−	0.994712i	$-0.532750\pi$
$149$	−2.50733	−0.205409	−0.102704	+	0.994712i	$0.532750\pi$
$150$	10.0821	0.823200
$151$	−16.7717	−1.36486	−0.682432	−	0.730949i	$-0.739078\pi$
$151$	−16.7717	−1.36486	−0.682432	+	0.730949i	$0.739078\pi$
$152$	−21.9655	−1.78164
$153$	−0.469936	−0.0379920
$154$	−2.09108	−0.168504
$155$	0.961265	0.0772107
$156$	3.51319	0.281280
$157$	20.6735	1.64992	0.824962	−	0.565188i	$-0.191196\pi$
$157$	20.6735	1.64992	0.824962	+	0.565188i	$0.191196\pi$
$158$	38.0552	3.02751
$159$	6.10349	0.484038
$160$	4.12318	0.325966
$161$	−7.64783	−0.602734
$162$	2.30694	0.181250
$163$	−11.8403	−0.927405	−0.463703	−	0.885991i	$-0.653479\pi$
$163$	−11.8403	−0.927405	−0.463703	+	0.885991i	$0.653479\pi$
$164$	9.07833	0.708898
$165$	−0.719266	−0.0559948
$166$	−32.5714	−2.52803
$167$	−13.9957	−1.08302	−0.541509	−	0.840695i	$-0.682147\pi$
$167$	−13.9957	−1.08302	−0.541509	+	0.840695i	$0.682147\pi$
$168$	−3.04973	−0.235291
$169$	−11.8816	−0.913967
$170$	0.860261	0.0659790
$171$	−7.20245	−0.550785
$172$	32.6689	2.49098
$173$	−18.3641	−1.39620	−0.698098	−	0.716002i	$-0.745970\pi$
$173$	−18.3641	−1.39620	−0.698098	+	0.716002i	$0.745970\pi$
$174$	−18.6047	−1.41042
$175$	−4.37033	−0.330366
$176$	−0.354942	−0.0267547
$177$	−4.52116	−0.339832
$178$	−11.9825	−0.898130
$179$	15.0612	1.12573	0.562864	−	0.826550i	$-0.309700\pi$
$179$	15.0612	1.12573	0.562864	+	0.826550i	$0.309700\pi$
$180$	−2.63604	−0.196479
$181$	−15.9500	−1.18555	−0.592777	−	0.805367i	$-0.701968\pi$
$181$	−15.9500	−1.18555	−0.592777	+	0.805367i	$0.701968\pi$
$182$	−2.43973	−0.180845
$183$	9.48144	0.700888
$184$	−23.3238	−1.71945
$185$	3.53335	0.259777
$186$	2.79463	0.204912
$187$	0.425964	0.0311496
$188$	−20.9581	−1.52852
$189$	−1.00000	−0.0727393
$190$	13.1848	0.956523
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	12.7702	0.921613
$193$	−16.6139	−1.19589	−0.597946	−	0.801536i	$-0.704016\pi$
$193$	−16.6139	−1.19589	−0.597946	+	0.801536i	$0.704016\pi$
$194$	−20.1485	−1.44658
$195$	−0.839190	−0.0600956
$196$	3.32198	0.237284
$197$	9.13172	0.650608	0.325304	−	0.945609i	$-0.394533\pi$
$197$	9.13172	0.650608	0.325304	+	0.945609i	$0.394533\pi$
$198$	−2.09108	−0.148607
$199$	13.9548	0.989229	0.494615	−	0.869112i	$-0.335309\pi$
$199$	13.9548	0.989229	0.494615	+	0.869112i	$0.335309\pi$
$200$	−13.3283	−0.942454
$201$	−9.61556	−0.678230
$202$	−17.0444	−1.19924
$203$	8.06467	0.566029
$204$	1.56112	0.109300
$205$	−2.16852	−0.151456
$206$	18.6049	1.29627
$207$	−7.64783	−0.531561
$208$	−0.414121	−0.0287141
$209$	6.52852	0.451587
$210$	1.83059	0.126323
$211$	4.02086	0.276808	0.138404	−	0.990376i	$-0.455803\pi$
$211$	4.02086	0.276808	0.138404	+	0.990376i	$0.455803\pi$
$212$	−20.2757	−1.39254
$213$	3.40931	0.233602
$214$	8.78190	0.600318
$215$	−7.80355	−0.532198
$216$	−3.04973	−0.207508
$217$	−1.21140	−0.0822353
$218$	−12.5351	−0.848984
$219$	10.0328	0.677955
$220$	2.38939	0.161092
$221$	0.496985	0.0334309
$222$	10.2723	0.689432
$223$	−6.10934	−0.409112	−0.204556	−	0.978855i	$-0.565575\pi$
$223$	−6.10934	−0.409112	−0.204556	+	0.978855i	$0.565575\pi$
$224$	−5.19610	−0.347179
$225$	−4.37033	−0.291356
$226$	25.6730	1.70774
$227$	14.7359	0.978054	0.489027	−	0.872269i	$-0.337352\pi$
$227$	14.7359	0.978054	0.489027	+	0.872269i	$0.337352\pi$
$228$	23.9264	1.58456
$229$	−20.5311	−1.35673	−0.678366	−	0.734724i	$-0.737312\pi$
$229$	−20.5311	−1.35673	−0.678366	+	0.734724i	$0.737312\pi$
$230$	14.0001	0.923137
$231$	0.906431	0.0596388
$232$	24.5950	1.61474
$233$	12.2818	0.804607	0.402303	−	0.915506i	$-0.368210\pi$
$233$	12.2818	0.804607	0.402303	+	0.915506i	$0.368210\pi$
$234$	−2.43973	−0.159490
$235$	5.00621	0.326569
$236$	15.0192	0.977667
$237$	−16.4960	−1.07153
$238$	−1.08411	−0.0702727
$239$	−12.2474	−0.792219	−0.396109	−	0.918203i	$-0.629640\pi$
$239$	−12.2474	−0.792219	−0.396109	+	0.918203i	$0.629640\pi$
$240$	0.310726	0.0200573
$241$	−17.5836	−1.13266	−0.566329	−	0.824179i	$-0.691637\pi$
$241$	−17.5836	−1.13266	−0.566329	+	0.824179i	$0.691637\pi$
$242$	−23.4809	−1.50941
$243$	−1.00000	−0.0641500
$244$	−31.4971	−2.01640
$245$	−0.793515	−0.0506958
$246$	−6.30443	−0.401956
$247$	7.61703	0.484660
$248$	−3.69444	−0.234597
$249$	14.1189	0.894748
$250$	17.1533	1.08487
$251$	8.92233	0.563173	0.281586	−	0.959536i	$-0.409139\pi$
$251$	8.92233	0.563173	0.281586	+	0.959536i	$0.409139\pi$
$252$	3.32198	0.209265
$253$	6.93223	0.435826
$254$	24.8160	1.55709
$255$	−0.372901	−0.0233520
$256$	−18.4483	−1.15302
$257$	9.41821	0.587492	0.293746	−	0.955884i	$-0.405098\pi$
$257$	9.41821	0.587492	0.293746	+	0.955884i	$0.405098\pi$
$258$	−22.6868	−1.41242
$259$	−4.45278	−0.276682
$260$	2.78777	0.172890
$261$	8.06467	0.499191
$262$	−19.3601	−1.19607
$263$	13.3832	0.825241	0.412620	−	0.910903i	$-0.364614\pi$
$263$	13.3832	0.825241	0.412620	+	0.910903i	$0.364614\pi$
$264$	2.76436	0.170135
$265$	4.84321	0.297516
$266$	−16.6156	−1.01877
$267$	5.19413	0.317875
$268$	31.9427	1.95121
$269$	−14.8861	−0.907619	−0.453810	−	0.891099i	$-0.649935\pi$
$269$	−14.8861	−0.907619	−0.453810	+	0.891099i	$0.649935\pi$
$270$	1.83059	0.111406
$271$	13.5588	0.823639	0.411820	−	0.911265i	$-0.364893\pi$
$271$	13.5588	0.823639	0.411820	+	0.911265i	$0.364893\pi$
$272$	−0.184018	−0.0111577
$273$	1.05756	0.0640065
$274$	32.7732	1.97990
$275$	3.96140	0.238882
$276$	25.4059	1.52926
$277$	12.2341	0.735077	0.367539	−	0.930008i	$-0.380201\pi$
$277$	12.2341	0.735077	0.367539	+	0.930008i	$0.380201\pi$
$278$	10.4914	0.629231
$279$	−1.21140	−0.0725247
$280$	−2.42000	−0.144623
$281$	17.3998	1.03799	0.518994	−	0.854778i	$-0.326307\pi$
$281$	17.3998	1.03799	0.518994	+	0.854778i	$0.326307\pi$
$282$	14.5543	0.866695
$283$	−16.8291	−1.00039	−0.500194	−	0.865913i	$-0.666738\pi$
$283$	−16.8291	−1.00039	−0.500194	+	0.865913i	$0.666738\pi$
$284$	−11.3256	−0.672054
$285$	−5.71525	−0.338542
$286$	2.21145	0.130766
$287$	2.73281	0.161313
$288$	−5.19610	−0.306183
$289$	−16.7792	−0.987009
$290$	−14.7631	−0.866921
$291$	8.73387	0.511989
$292$	−33.3288	−1.95042
$293$	31.5316	1.84210	0.921048	−	0.389450i	$-0.127335\pi$
$293$	31.5316	1.84210	0.921048	+	0.389450i	$0.127335\pi$
$294$	−2.30694	−0.134544
$295$	−3.58761	−0.208879
$296$	−13.5798	−0.789307
$297$	0.906431	0.0525964
$298$	−5.78427	−0.335074
$299$	8.08805	0.467744
$300$	14.5182	0.838206
$301$	9.83416	0.566832
$302$	−38.6914	−2.22644
$303$	7.38830	0.424446
$304$	−2.82035	−0.161758
$305$	7.52367	0.430804
$306$	−1.08411	−0.0619747
$307$	15.2096	0.868055	0.434028	−	0.900900i	$-0.357092\pi$
$307$	15.2096	0.868055	0.434028	+	0.900900i	$0.357092\pi$
$308$	−3.01114	−0.171576
$309$	−8.06475	−0.458788
$310$	2.21758	0.125950
$311$	32.6689	1.85248	0.926241	−	0.376932i	$-0.123021\pi$
$311$	32.6689	1.85248	0.926241	+	0.376932i	$0.123021\pi$
$312$	3.22527	0.182595
$313$	30.7810	1.73984	0.869922	−	0.493190i	$-0.164169\pi$
$313$	30.7810	1.73984	0.869922	+	0.493190i	$0.164169\pi$
$314$	47.6925	2.69144
$315$	−0.793515	−0.0447095
$316$	54.7993	3.08270
$317$	−26.8469	−1.50787	−0.753936	−	0.656948i	$-0.771847\pi$
$317$	−26.8469	−1.50787	−0.753936	+	0.656948i	$0.771847\pi$
$318$	14.0804	0.789589
$319$	−7.31007	−0.409285
$320$	10.1334	0.566473
$321$	−3.80673	−0.212471
$322$	−17.6431	−0.983212
$323$	3.38469	0.188329
$324$	3.32198	0.184554
$325$	4.62189	0.256376
$326$	−27.3149	−1.51283
$327$	5.43365	0.300481
$328$	8.33431	0.460185
$329$	−6.30891	−0.347821
$330$	−1.65931	−0.0913417
$331$	−29.3241	−1.61180	−0.805899	−	0.592054i	$-0.798317\pi$
$331$	−29.3241	−1.61180	−0.805899	+	0.592054i	$0.798317\pi$
$332$	−46.9026	−2.57412
$333$	−4.45278	−0.244011
$334$	−32.2872	−1.76668
$335$	−7.63009	−0.416877
$336$	−0.391582	−0.0213625
$337$	12.2751	0.668669	0.334334	−	0.942455i	$-0.391489\pi$
$337$	12.2751	0.668669	0.334334	+	0.942455i	$0.391489\pi$
$338$	−27.4101	−1.49091
$339$	−11.1286	−0.604422
$340$	1.23877	0.0671817
$341$	1.09805	0.0594628
$342$	−16.6156	−0.898471
$343$	1.00000	0.0539949
$344$	29.9915	1.61703
$345$	−6.06867	−0.326726
$346$	−42.3649	−2.27755
$347$	20.8771	1.12074	0.560371	−	0.828242i	$-0.310659\pi$
$347$	20.8771	1.12074	0.560371	+	0.828242i	$0.310659\pi$
$348$	−26.7907	−1.43613
$349$	3.49505	0.187086	0.0935429	−	0.995615i	$-0.470181\pi$
$349$	3.49505	0.187086	0.0935429	+	0.995615i	$0.470181\pi$
$350$	−10.0821	−0.538911
$351$	1.05756	0.0564484
$352$	4.70990	0.251038
$353$	9.32062	0.496087	0.248043	−	0.968749i	$-0.420212\pi$
$353$	9.32062	0.496087	0.248043	+	0.968749i	$0.420212\pi$
$354$	−10.4301	−0.554351
$355$	2.70534	0.143584
$356$	−17.2548	−0.914501
$357$	0.469936	0.0248716
$358$	34.7453	1.83635
$359$	−3.37627	−0.178193	−0.0890964	−	0.996023i	$-0.528398\pi$
$359$	−3.37627	−0.178193	−0.0890964	+	0.996023i	$0.528398\pi$
$360$	−2.42000	−0.127545
$361$	32.8753	1.73028
$362$	−36.7957	−1.93394
$363$	10.1784	0.534227
$364$	−3.51319	−0.184141
$365$	7.96119	0.416708
$366$	21.8731	1.14333
$367$	−4.24524	−0.221600	−0.110800	−	0.993843i	$-0.535341\pi$
$367$	−4.24524	−0.221600	−0.110800	+	0.993843i	$0.535341\pi$
$368$	−2.99475	−0.156112
$369$	2.73281	0.142264
$370$	8.15122	0.423762
$371$	−6.10349	−0.316877
$372$	4.02425	0.208648
$373$	−28.9405	−1.49848	−0.749240	−	0.662299i	$-0.769581\pi$
$373$	−28.9405	−1.49848	−0.749240	+	0.662299i	$0.769581\pi$
$374$	0.982674	0.0508129
$375$	−7.43550	−0.383968
$376$	−19.2404	−0.992250
$377$	−8.52888	−0.439260
$378$	−2.30694	−0.118656
$379$	−24.6245	−1.26488	−0.632439	−	0.774610i	$-0.717946\pi$
$379$	−24.6245	−1.26488	−0.632439	+	0.774610i	$0.717946\pi$
$380$	18.9859	0.973959
$381$	−10.7571	−0.551103
$382$	2.30694	0.118033
$383$	21.3909	1.09302	0.546511	−	0.837452i	$-0.315956\pi$
$383$	21.3909	1.09302	0.546511	+	0.837452i	$0.315956\pi$
$384$	19.0680	0.973061
$385$	0.719266	0.0366572
$386$	−38.3272	−1.95080
$387$	9.83416	0.499898
$388$	−29.0137	−1.47295
$389$	11.0153	0.558497	0.279248	−	0.960219i	$-0.409915\pi$
$389$	11.0153	0.558497	0.279248	+	0.960219i	$0.409915\pi$
$390$	−1.93596	−0.0980313
$391$	3.59399	0.181756
$392$	3.04973	0.154034
$393$	8.39209	0.423325
$394$	21.0663	1.06131
$395$	−13.0898	−0.658619
$396$	−3.01114	−0.151316
$397$	8.29907	0.416518	0.208259	−	0.978074i	$-0.433220\pi$
$397$	8.29907	0.416518	0.208259	+	0.978074i	$0.433220\pi$
$398$	32.1929	1.61368
$399$	7.20245	0.360574
$400$	−1.71134	−0.0855671
$401$	9.16859	0.457857	0.228929	−	0.973443i	$-0.426478\pi$
$401$	9.16859	0.457857	0.228929	+	0.973443i	$0.426478\pi$
$402$	−22.1825	−1.10636
$403$	1.28113	0.0638176
$404$	−24.5438	−1.22110
$405$	−0.793515	−0.0394301
$406$	18.6047	0.923337
$407$	4.03614	0.200064
$408$	1.43317	0.0709527
$409$	30.9098	1.52839	0.764196	−	0.644984i	$-0.223136\pi$
$409$	30.9098	1.52839	0.764196	+	0.644984i	$0.223136\pi$
$410$	−5.00266	−0.247064
$411$	−14.2063	−0.700747
$412$	26.7909	1.31989
$413$	4.52116	0.222472
$414$	−17.6431	−0.867111
$415$	11.2036	0.549961
$416$	5.49518	0.269424
$417$	−4.54774	−0.222704
$418$	15.0609	0.736654
$419$	−5.45063	−0.266281	−0.133140	−	0.991097i	$-0.542506\pi$
$419$	−5.45063	−0.266281	−0.133140	+	0.991097i	$0.542506\pi$
$420$	2.63604	0.128626
$421$	−2.15241	−0.104902	−0.0524510	−	0.998623i	$-0.516703\pi$
$421$	−2.15241	−0.104902	−0.0524510	+	0.998623i	$0.516703\pi$
$422$	9.27590	0.451544
$423$	−6.30891	−0.306750
$424$	−18.6140	−0.903974
$425$	2.05378	0.0996228
$426$	7.86507	0.381064
$427$	−9.48144	−0.458839
$428$	12.6459	0.611261
$429$	−0.958605	−0.0462819
$430$	−18.0023	−0.868150
$431$	−11.3127	−0.544912	−0.272456	−	0.962168i	$-0.587836\pi$
$431$	−11.3127	−0.544912	−0.272456	+	0.962168i	$0.587836\pi$
$432$	−0.391582	−0.0188400
$433$	−30.7225	−1.47643	−0.738214	−	0.674567i	$-0.764330\pi$
$433$	−30.7225	−1.47643	−0.738214	+	0.674567i	$0.764330\pi$
$434$	−2.79463	−0.134147
$435$	6.39944	0.306830
$436$	−18.0505	−0.864460
$437$	55.0832	2.63499
$438$	23.1451	1.10592
$439$	26.8430	1.28115	0.640574	−	0.767897i	$-0.278697\pi$
$439$	26.8430	1.28115	0.640574	+	0.767897i	$0.278697\pi$
$440$	2.19356	0.104574
$441$	1.00000	0.0476190
$442$	1.14652	0.0545342
$443$	38.0659	1.80856	0.904282	−	0.426935i	$-0.140407\pi$
$443$	38.0659	1.80856	0.904282	+	0.426935i	$0.140407\pi$
$444$	14.7920	0.701999
$445$	4.12162	0.195383
$446$	−14.0939	−0.667365
$447$	2.50733	0.118593
$448$	−12.7702	−0.603338
$449$	16.9190	0.798456	0.399228	−	0.916852i	$-0.369278\pi$
$449$	16.9190	0.798456	0.399228	+	0.916852i	$0.369278\pi$
$450$	−10.0821	−0.475275
$451$	−2.47710	−0.116642
$452$	36.9689	1.73887
$453$	16.7717	0.788004
$454$	33.9948	1.59545
$455$	0.839190	0.0393418
$456$	21.9655	1.02863
$457$	−5.24503	−0.245352	−0.122676	−	0.992447i	$-0.539148\pi$
$457$	−5.24503	−0.245352	−0.122676	+	0.992447i	$0.539148\pi$
$458$	−47.3640	−2.21318
$459$	0.469936	0.0219347
$460$	20.1600	0.939965
$461$	−6.95458	−0.323907	−0.161954	−	0.986798i	$-0.551779\pi$
$461$	−6.95458	−0.323907	−0.161954	+	0.986798i	$0.551779\pi$
$462$	2.09108	0.0972859
$463$	−18.1343	−0.842771	−0.421386	−	0.906882i	$-0.638456\pi$
$463$	−18.1343	−0.842771	−0.421386	+	0.906882i	$0.638456\pi$
$464$	3.15798	0.146605
$465$	−0.961265	−0.0445776
$466$	28.3334	1.31252
$467$	13.7654	0.636987	0.318494	−	0.947925i	$-0.396823\pi$
$467$	13.7654	0.636987	0.318494	+	0.947925i	$0.396823\pi$
$468$	−3.51319	−0.162397
$469$	9.61556	0.444005
$470$	11.5490	0.532718
$471$	−20.6735	−0.952584
$472$	13.7883	0.634658
$473$	−8.91398	−0.409865
$474$	−38.0552	−1.74793
$475$	31.4771	1.44427
$476$	−1.56112	−0.0715536
$477$	−6.10349	−0.279460
$478$	−28.2541	−1.29231
$479$	−8.18228	−0.373858	−0.186929	−	0.982373i	$-0.559853\pi$
$479$	−8.18228	−0.373858	−0.186929	+	0.982373i	$0.559853\pi$
$480$	−4.12318	−0.188197
$481$	4.70908	0.214716
$482$	−40.5643	−1.84765
$483$	7.64783	0.347989
$484$	−33.8124	−1.53693
$485$	6.93046	0.314696
$486$	−2.30694	−0.104645
$487$	−15.3929	−0.697517	−0.348759	−	0.937213i	$-0.613397\pi$
$487$	−15.3929	−0.697517	−0.348759	+	0.937213i	$0.613397\pi$
$488$	−28.9158	−1.30896
$489$	11.8403	0.535438
$490$	−1.83059	−0.0826977
$491$	−35.8142	−1.61627	−0.808136	−	0.588996i	$-0.799523\pi$
$491$	−35.8142	−1.61627	−0.808136	+	0.588996i	$0.799523\pi$
$492$	−9.07833	−0.409283
$493$	−3.78988	−0.170687
$494$	17.5720	0.790603
$495$	0.719266	0.0323286
$496$	−0.474363	−0.0212995
$497$	−3.40931	−0.152928
$498$	32.5714	1.45956
$499$	−25.6615	−1.14877	−0.574383	−	0.818587i	$-0.694758\pi$
$499$	−25.6615	−1.14877	−0.574383	+	0.818587i	$0.694758\pi$
$500$	24.7006	1.10464
$501$	13.9957	0.625281
$502$	20.5833	0.918677
$503$	5.13332	0.228884	0.114442	−	0.993430i	$-0.463492\pi$
$503$	5.13332	0.228884	0.114442	+	0.993430i	$0.463492\pi$
$504$	3.04973	0.135846
$505$	5.86272	0.260888
$506$	15.9922	0.710942
$507$	11.8816	0.527679
$508$	35.7349	1.58548
$509$	−36.7174	−1.62747	−0.813736	−	0.581234i	$-0.802570\pi$
$509$	−36.7174	−1.62747	−0.813736	+	0.581234i	$0.802570\pi$
$510$	−0.860261	−0.0380930
$511$	−10.0328	−0.443826
$512$	−4.42313	−0.195477
$513$	7.20245	0.317996
$514$	21.7273	0.958348
$515$	−6.39950	−0.281996
$516$	−32.6689	−1.43817
$517$	5.71859	0.251503
$518$	−10.2723	−0.451339
$519$	18.3641	0.806094
$520$	2.55930	0.112233
$521$	20.3400	0.891112	0.445556	−	0.895254i	$-0.353006\pi$
$521$	20.3400	0.891112	0.445556	+	0.895254i	$0.353006\pi$
$522$	18.6047	0.814307
$523$	2.42045	0.105839	0.0529195	−	0.998599i	$-0.483147\pi$
$523$	2.42045	0.105839	0.0529195	+	0.998599i	$0.483147\pi$
$524$	−27.8784	−1.21787
$525$	4.37033	0.190737
$526$	30.8742	1.34618
$527$	0.569281	0.0247983
$528$	0.354942	0.0154469
$529$	35.4894	1.54302
$530$	11.1730	0.485324
$531$	4.52116	0.196202
$532$	−23.9264	−1.03734
$533$	−2.89011	−0.125185
$534$	11.9825	0.518535
$535$	−3.02070	−0.130596
$536$	29.3248	1.26664
$537$	−15.0612	−0.649939
$538$	−34.3413	−1.48056
$539$	−0.906431	−0.0390427
$540$	2.63604	0.113437
$541$	11.6562	0.501140	0.250570	−	0.968099i	$-0.419382\pi$
$541$	11.6562	0.501140	0.250570	+	0.968099i	$0.419382\pi$
$542$	31.2794	1.34357
$543$	15.9500	0.684480
$544$	2.44183	0.104693
$545$	4.31168	0.184692
$546$	2.43973	0.104411
$547$	32.4156	1.38599	0.692996	−	0.720941i	$-0.256290\pi$
$547$	32.4156	1.38599	0.692996	+	0.720941i	$0.256290\pi$
$548$	47.1932	2.01599
$549$	−9.48144	−0.404658
$550$	9.13873	0.389677
$551$	−58.0854	−2.47452
$552$	23.3238	0.992727
$553$	16.4960	0.701480
$554$	28.2234	1.19910
$555$	−3.53335	−0.149982
$556$	15.1075	0.640701
$557$	8.67609	0.367618	0.183809	−	0.982962i	$-0.441157\pi$
$557$	8.67609	0.367618	0.183809	+	0.982962i	$0.441157\pi$
$558$	−2.79463	−0.118306
$559$	−10.4002	−0.439882
$560$	−0.310726	−0.0131306
$561$	−0.425964	−0.0179842
$562$	40.1404	1.69322
$563$	24.9462	1.05136	0.525678	−	0.850683i	$-0.323812\pi$
$563$	24.9462	1.05136	0.525678	+	0.850683i	$0.323812\pi$
$564$	20.9581	0.882493
$565$	−8.83070	−0.371510
$566$	−38.8238	−1.63189
$567$	1.00000	0.0419961
$568$	−10.3975	−0.436268
$569$	37.5503	1.57419	0.787096	−	0.616831i	$-0.211584\pi$
$569$	37.5503	1.57419	0.787096	+	0.616831i	$0.211584\pi$
$570$	−13.1848	−0.552249
$571$	26.6709	1.11614	0.558071	−	0.829793i	$-0.311542\pi$
$571$	26.6709	1.11614	0.558071	+	0.829793i	$0.311542\pi$
$572$	3.18446	0.133149
$573$	−1.00000	−0.0417756
$574$	6.30443	0.263142
$575$	33.4236	1.39386
$576$	−12.7702	−0.532094
$577$	−15.4830	−0.644564	−0.322282	−	0.946644i	$-0.604450\pi$
$577$	−15.4830	−0.644564	−0.322282	+	0.946644i	$0.604450\pi$
$578$	−38.7085	−1.61006
$579$	16.6139	0.690448
$580$	−21.2588	−0.882723
$581$	−14.1189	−0.585750
$582$	20.1485	0.835183
$583$	5.53239	0.229128
$584$	−30.5973	−1.26613
$585$	0.839190	0.0346962
$586$	72.7415	3.00493
$587$	−38.6819	−1.59657	−0.798286	−	0.602278i	$-0.794260\pi$
$587$	−38.6819	−1.59657	−0.798286	+	0.602278i	$0.794260\pi$
$588$	−3.32198	−0.136996
$589$	8.72506	0.359510
$590$	−8.27641	−0.340734
$591$	−9.13172	−0.375629
$592$	−1.74363	−0.0716626
$593$	−39.3449	−1.61570	−0.807851	−	0.589386i	$-0.799370\pi$
$593$	−39.3449	−1.61570	−0.807851	+	0.589386i	$0.799370\pi$
$594$	2.09108	0.0857981
$595$	0.372901	0.0152875
$596$	−8.32931	−0.341182
$597$	−13.9548	−0.571132
$598$	18.6586	0.763009
$599$	25.6621	1.04853	0.524263	−	0.851557i	$-0.324341\pi$
$599$	25.6621	1.04853	0.524263	+	0.851557i	$0.324341\pi$
$600$	13.3283	0.544126
$601$	2.23226	0.0910556	0.0455278	−	0.998963i	$-0.485503\pi$
$601$	2.23226	0.0910556	0.0455278	+	0.998963i	$0.485503\pi$
$602$	22.6868	0.924646
$603$	9.61556	0.391576
$604$	−55.7153	−2.26702
$605$	8.07670	0.328365
$606$	17.0444	0.692380
$607$	−5.39854	−0.219120	−0.109560	−	0.993980i	$-0.534944\pi$
$607$	−5.39854	−0.219120	−0.109560	+	0.993980i	$0.534944\pi$
$608$	37.4246	1.51777
$609$	−8.06467	−0.326797
$610$	17.3567	0.702750
$611$	6.67205	0.269922
$612$	−1.56112	−0.0631044
$613$	−20.0225	−0.808701	−0.404351	−	0.914604i	$-0.632502\pi$
$613$	−20.0225	−0.808701	−0.404351	+	0.914604i	$0.632502\pi$
$614$	35.0875	1.41602
$615$	2.16852	0.0874433
$616$	−2.76436	−0.111379
$617$	−30.0465	−1.20963	−0.604813	−	0.796367i	$-0.706752\pi$
$617$	−30.0465	−1.20963	−0.604813	+	0.796367i	$0.706752\pi$
$618$	−18.6049	−0.748399
$619$	−29.2166	−1.17431	−0.587157	−	0.809473i	$-0.699753\pi$
$619$	−29.2166	−1.17431	−0.587157	+	0.809473i	$0.699753\pi$
$620$	3.19330	0.128246
$621$	7.64783	0.306897
$622$	75.3652	3.02187
$623$	−5.19413	−0.208098
$624$	0.414121	0.0165781
$625$	15.9515	0.638060
$626$	71.0099	2.83813
$627$	−6.52852	−0.260724
$628$	68.6769	2.74051
$629$	2.09252	0.0834342
$630$	−1.83059	−0.0729326
$631$	−24.2793	−0.966543	−0.483272	−	0.875470i	$-0.660552\pi$
$631$	−24.2793	−0.966543	−0.483272	+	0.875470i	$0.660552\pi$
$632$	50.3082	2.00115
$633$	−4.02086	−0.159815
$634$	−61.9342	−2.45972
$635$	−8.53592	−0.338738
$636$	20.2757	0.803982
$637$	−1.05756	−0.0419021
$638$	−16.8639	−0.667648
$639$	−3.40931	−0.134870
$640$	15.1308	0.598096
$641$	−30.5757	−1.20767	−0.603834	−	0.797110i	$-0.706361\pi$
$641$	−30.5757	−1.20767	−0.603834	+	0.797110i	$0.706361\pi$
$642$	−8.78190	−0.346594
$643$	5.40911	0.213314	0.106657	−	0.994296i	$-0.465985\pi$
$643$	5.40911	0.213314	0.106657	+	0.994296i	$0.465985\pi$
$644$	−25.4059	−1.00113
$645$	7.80355	0.307265
$646$	7.80828	0.307213
$647$	−25.8156	−1.01491	−0.507457	−	0.861677i	$-0.669415\pi$
$647$	−25.8156	−1.01491	−0.507457	+	0.861677i	$0.669415\pi$
$648$	3.04973	0.119805
$649$	−4.09812	−0.160865
$650$	10.6624	0.418215
$651$	1.21140	0.0474786
$652$	−39.3333	−1.54041
$653$	−9.35700	−0.366168	−0.183084	−	0.983097i	$-0.558608\pi$
$653$	−9.35700	−0.366168	−0.183084	+	0.983097i	$0.558608\pi$
$654$	12.5351	0.490161
$655$	6.65925	0.260199
$656$	1.07012	0.0417811
$657$	−10.0328	−0.391418
$658$	−14.5543	−0.567385
$659$	−42.3538	−1.64987	−0.824934	−	0.565228i	$-0.808788\pi$
$659$	−42.3538	−1.64987	−0.824934	+	0.565228i	$0.808788\pi$
$660$	−2.38939	−0.0930068
$661$	−27.8308	−1.08249	−0.541247	−	0.840864i	$-0.682048\pi$
$661$	−27.8308	−1.08249	−0.541247	+	0.840864i	$0.682048\pi$
$662$	−67.6489	−2.62925
$663$	−0.496985	−0.0193013
$664$	−43.0587	−1.67100
$665$	5.71525	0.221628
$666$	−10.2723	−0.398044
$667$	−61.6773	−2.38815
$668$	−46.4934	−1.79888
$669$	6.10934	0.236201
$670$	−17.6022	−0.680031
$671$	8.59427	0.331778
$672$	5.19610	0.200444
$673$	−33.2591	−1.28204	−0.641022	−	0.767523i	$-0.721489\pi$
$673$	−33.2591	−1.28204	−0.641022	+	0.767523i	$0.721489\pi$
$674$	28.3180	1.09077
$675$	4.37033	0.168214
$676$	−39.4703	−1.51809
$677$	−45.0738	−1.73233	−0.866164	−	0.499760i	$-0.833422\pi$
$677$	−45.0738	−1.73233	−0.866164	+	0.499760i	$0.833422\pi$
$678$	−25.6730	−0.985965
$679$	−8.73387	−0.335175
$680$	1.13725	0.0436114
$681$	−14.7359	−0.564680
$682$	2.53314	0.0969989
$683$	11.3949	0.436013	0.218006	−	0.975947i	$-0.430045\pi$
$683$	11.3949	0.436013	0.218006	+	0.975947i	$0.430045\pi$
$684$	−23.9264	−0.914848
$685$	−11.2729	−0.430717
$686$	2.30694	0.0880794
$687$	20.5311	0.783310
$688$	3.85088	0.146813
$689$	6.45481	0.245909
$690$	−14.0001	−0.532974
$691$	20.8400	0.792793	0.396396	−	0.918080i	$-0.370261\pi$
$691$	20.8400	0.792793	0.396396	+	0.918080i	$0.370261\pi$
$692$	−61.0051	−2.31907
$693$	−0.906431	−0.0344324
$694$	48.1623	1.82822
$695$	−3.60870	−0.136886
$696$	−24.5950	−0.932273
$697$	−1.28424	−0.0486442
$698$	8.06288	0.305184
$699$	−12.2818	−0.464540
$700$	−14.5182	−0.548735
$701$	19.2377	0.726596	0.363298	−	0.931673i	$-0.381651\pi$
$701$	19.2377	0.726596	0.363298	+	0.931673i	$0.381651\pi$
$702$	2.43973	0.0920817
$703$	32.0709	1.20958
$704$	11.5753	0.436262
$705$	−5.00621	−0.188545
$706$	21.5021	0.809243
$707$	−7.38830	−0.277865
$708$	−15.0192	−0.564456
$709$	−3.84591	−0.144436	−0.0722181	−	0.997389i	$-0.523008\pi$
$709$	−3.84591	−0.144436	−0.0722181	+	0.997389i	$0.523008\pi$
$710$	6.24106	0.234223
$711$	16.4960	0.618647
$712$	−15.8407	−0.593654
$713$	9.26460	0.346962
$714$	1.08411	0.0405719
$715$	−0.760668	−0.0284474
$716$	50.0330	1.86982
$717$	12.2474	0.457388
$718$	−7.78886	−0.290678
$719$	41.6750	1.55422	0.777108	−	0.629367i	$-0.216686\pi$
$719$	41.6750	1.55422	0.777108	+	0.629367i	$0.216686\pi$
$720$	−0.310726	−0.0115801
$721$	8.06475	0.300347
$722$	75.8414	2.82253
$723$	17.5836	0.653940
$724$	−52.9855	−1.96919
$725$	−35.2453	−1.30898
$726$	23.4809	0.871459
$727$	−33.0308	−1.22505	−0.612523	−	0.790453i	$-0.709845\pi$
$727$	−33.0308	−1.22505	−0.612523	+	0.790453i	$0.709845\pi$
$728$	−3.22527	−0.119536
$729$	1.00000	0.0370370
$730$	18.3660	0.679756
$731$	−4.62142	−0.170929
$732$	31.4971	1.16417
$733$	40.1369	1.48249	0.741246	−	0.671234i	$-0.234235\pi$
$733$	40.1369	1.48249	0.741246	+	0.671234i	$0.234235\pi$
$734$	−9.79353	−0.361486
$735$	0.793515	0.0292692
$736$	39.7389	1.46479
$737$	−8.71584	−0.321052
$738$	6.30443	0.232069
$739$	−10.1180	−0.372198	−0.186099	−	0.982531i	$-0.559585\pi$
$739$	−10.1180	−0.372198	−0.186099	+	0.982531i	$0.559585\pi$
$740$	11.7377	0.431487
$741$	−7.61703	−0.279819
$742$	−14.0804	−0.516907
$743$	−23.7149	−0.870017	−0.435008	−	0.900426i	$-0.643255\pi$
$743$	−23.7149	−0.870017	−0.435008	+	0.900426i	$0.643255\pi$
$744$	3.69444	0.135445
$745$	1.98961	0.0728936
$746$	−66.7639	−2.44440
$747$	−14.1189	−0.516583
$748$	1.41504	0.0517391
$749$	3.80673	0.139095
$750$	−17.1533	−0.626349
$751$	−35.1856	−1.28394	−0.641971	−	0.766729i	$-0.721883\pi$
$751$	−35.1856	−1.28394	−0.641971	+	0.766729i	$0.721883\pi$
$752$	−2.47045	−0.0900882
$753$	−8.92233	−0.325148
$754$	−19.6756	−0.716544
$755$	13.3086	0.484350
$756$	−3.32198	−0.120819
$757$	−3.06786	−0.111503	−0.0557517	−	0.998445i	$-0.517756\pi$
$757$	−3.06786	−0.111503	−0.0557517	+	0.998445i	$0.517756\pi$
$758$	−56.8074	−2.06334
$759$	−6.93223	−0.251624
$760$	17.4300	0.632251
$761$	7.04343	0.255324	0.127662	−	0.991818i	$-0.459253\pi$
$761$	7.04343	0.255324	0.127662	+	0.991818i	$0.459253\pi$
$762$	−24.8160	−0.898989
$763$	−5.43365	−0.196711
$764$	3.32198	0.120185
$765$	0.372901	0.0134823
$766$	49.3475	1.78300
$767$	−4.78140	−0.172646
$768$	18.4483	0.665696
$769$	−23.3077	−0.840497	−0.420249	−	0.907409i	$-0.638057\pi$
$769$	−23.3077	−0.840497	−0.420249	+	0.907409i	$0.638057\pi$
$770$	1.65931	0.0597972
$771$	−9.41821	−0.339189
$772$	−55.1909	−1.98636
$773$	7.15108	0.257206	0.128603	−	0.991696i	$-0.458951\pi$
$773$	7.15108	0.257206	0.128603	+	0.991696i	$0.458951\pi$
$774$	22.6868	0.815461
$775$	5.29423	0.190174
$776$	−26.6359	−0.956173
$777$	4.45278	0.159743
$778$	25.4116	0.911050
$779$	−19.6829	−0.705214
$780$	−2.78777	−0.0998182
$781$	3.09030	0.110580
$782$	8.29112	0.296490
$783$	−8.06467	−0.288208
$784$	0.391582	0.0139851
$785$	−16.4047	−0.585510
$786$	19.3601	0.690551
$787$	−8.69954	−0.310105	−0.155053	−	0.987906i	$-0.549555\pi$
$787$	−8.69954	−0.310105	−0.155053	+	0.987906i	$0.549555\pi$
$788$	30.3354	1.08065
$789$	−13.3832	−0.476453
$790$	−30.1974	−1.07438
$791$	11.1286	0.395687
$792$	−2.76436	−0.0982274
$793$	10.0272	0.356076
$794$	19.1455	0.679447
$795$	−4.84321	−0.171771
$796$	46.3575	1.64310
$797$	−23.4196	−0.829566	−0.414783	−	0.909920i	$-0.636143\pi$
$797$	−23.4196	−0.829566	−0.414783	+	0.909920i	$0.636143\pi$
$798$	16.6156	0.588187
$799$	2.96478	0.104886
$800$	22.7087	0.802873
$801$	−5.19413	−0.183525
$802$	21.1514	0.746882
$803$	9.09405	0.320922
$804$	−31.9427	−1.12653
$805$	6.06867	0.213893
$806$	2.95549	0.104103
$807$	14.8861	0.524014
$808$	−22.5323	−0.792683
$809$	24.4987	0.861328	0.430664	−	0.902512i	$-0.358279\pi$
$809$	24.4987	0.861328	0.430664	+	0.902512i	$0.358279\pi$
$810$	−1.83059	−0.0643205
$811$	2.98769	0.104912	0.0524560	−	0.998623i	$-0.483295\pi$
$811$	2.98769	0.104912	0.0524560	+	0.998623i	$0.483295\pi$
$812$	26.7907	0.940168
$813$	−13.5588	−0.475528
$814$	9.31113	0.326355
$815$	9.39547	0.329109
$816$	0.184018	0.00644193
$817$	−70.8301	−2.47803
$818$	71.3071	2.49320
$819$	−1.05756	−0.0369541
$820$	−7.20379	−0.251567
$821$	−1.22627	−0.0427972	−0.0213986	−	0.999771i	$-0.506812\pi$
$821$	−1.22627	−0.0427972	−0.0213986	+	0.999771i	$0.506812\pi$
$822$	−32.7732	−1.14310
$823$	−31.4985	−1.09797	−0.548984	−	0.835833i	$-0.684985\pi$
$823$	−31.4985	−1.09797	−0.548984	+	0.835833i	$0.684985\pi$
$824$	24.5953	0.856817
$825$	−3.96140	−0.137918
$826$	10.4301	0.362908
$827$	12.9226	0.449364	0.224682	−	0.974432i	$-0.427866\pi$
$827$	12.9226	0.449364	0.224682	+	0.974432i	$0.427866\pi$
$828$	−25.4059	−0.882917
$829$	25.9020	0.899614	0.449807	−	0.893126i	$-0.351493\pi$
$829$	25.9020	0.899614	0.449807	+	0.893126i	$0.351493\pi$
$830$	25.8459	0.897125
$831$	−12.2341	−0.424397
$832$	13.5053	0.468212
$833$	−0.469936	−0.0162823
$834$	−10.4914	−0.363287
$835$	11.1058	0.384332
$836$	21.6876	0.750082
$837$	1.21140	0.0418721
$838$	−12.5743	−0.434371
$839$	−9.07181	−0.313194	−0.156597	−	0.987663i	$-0.550052\pi$
$839$	−9.07181	−0.313194	−0.156597	+	0.987663i	$0.550052\pi$
$840$	2.42000	0.0834980
$841$	36.0390	1.24272
$842$	−4.96549	−0.171122
$843$	−17.3998	−0.599282
$844$	13.3572	0.459775
$845$	9.42820	0.324340
$846$	−14.5543	−0.500387
$847$	−10.1784	−0.349733
$848$	−2.39002	−0.0820735
$849$	16.8291	0.577574
$850$	4.73794	0.162510
$851$	34.0541	1.16736
$852$	11.3256	0.388010
$853$	38.1987	1.30790	0.653950	−	0.756538i	$-0.273111\pi$
$853$	38.1987	1.30790	0.653950	+	0.756538i	$0.273111\pi$
$854$	−21.8731	−0.748483
$855$	5.71525	0.195458
$856$	11.6095	0.396804
$857$	0.526837	0.0179964	0.00899820	−	0.999960i	$-0.497136\pi$
$857$	0.526837	0.0179964	0.00899820	+	0.999960i	$0.497136\pi$
$858$	−2.21145	−0.0754975
$859$	13.7982	0.470787	0.235394	−	0.971900i	$-0.424362\pi$
$859$	13.7982	0.470787	0.235394	+	0.971900i	$0.424362\pi$
$860$	−25.9232	−0.883975
$861$	−2.73281	−0.0931338
$862$	−26.0977	−0.888890
$863$	13.6869	0.465906	0.232953	−	0.972488i	$-0.425161\pi$
$863$	13.6869	0.465906	0.232953	+	0.972488i	$0.425161\pi$
$864$	5.19610	0.176775
$865$	14.5722	0.495469
$866$	−70.8749	−2.40843
$867$	16.7792	0.569850
$868$	−4.02425	−0.136592
$869$	−14.9525	−0.507227
$870$	14.7631	0.500517
$871$	−10.1690	−0.344565
$872$	−16.5711	−0.561169
$873$	−8.73387	−0.295597
$874$	127.074	4.29833
$875$	7.43550	0.251366
$876$	33.3288	1.12608
$877$	−21.0484	−0.710754	−0.355377	−	0.934723i	$-0.615647\pi$
$877$	−21.0484	−0.710754	−0.355377	+	0.934723i	$0.615647\pi$
$878$	61.9253	2.08988
$879$	−31.5316	−1.06353
$880$	0.281652	0.00949447
$881$	−32.7084	−1.10198	−0.550988	−	0.834513i	$-0.685749\pi$
$881$	−32.7084	−1.10198	−0.550988	+	0.834513i	$0.685749\pi$
$882$	2.30694	0.0776788
$883$	56.0820	1.88731	0.943655	−	0.330931i	$-0.107363\pi$
$883$	56.0820	1.88731	0.943655	+	0.330931i	$0.107363\pi$
$884$	1.65097	0.0555283
$885$	3.58761	0.120596
$886$	87.8157	2.95023
$887$	5.32881	0.178924	0.0894619	−	0.995990i	$-0.471485\pi$
$887$	5.32881	0.178924	0.0894619	+	0.995990i	$0.471485\pi$
$888$	13.5798	0.455707
$889$	10.7571	0.360782
$890$	9.50833	0.318720
$891$	−0.906431	−0.0303666
$892$	−20.2951	−0.679530
$893$	45.4396	1.52058
$894$	5.78427	0.193455
$895$	−11.9513	−0.399488
$896$	−19.0680	−0.637018
$897$	−8.08805	−0.270052
$898$	39.0311	1.30248
$899$	−9.76955	−0.325833
$900$	−14.5182	−0.483938
$901$	2.86825	0.0955552
$902$	−5.71452	−0.190273
$903$	−9.83416	−0.327260
$904$	33.9391	1.12880
$905$	12.6566	0.420718
$906$	38.6914	1.28544
$907$	−43.5774	−1.44696	−0.723482	−	0.690344i	$-0.757459\pi$
$907$	−43.5774	−1.44696	−0.723482	+	0.690344i	$0.757459\pi$
$908$	48.9522	1.62454
$909$	−7.38830	−0.245054
$910$	1.93596	0.0641765
$911$	58.5961	1.94137	0.970687	−	0.240345i	$-0.0772607\pi$
$911$	58.5961	1.94137	0.970687	+	0.240345i	$0.0772607\pi$
$912$	2.82035	0.0933911
$913$	12.7978	0.423545
$914$	−12.1000	−0.400232
$915$	−7.52367	−0.248725
$916$	−68.2038	−2.25352
$917$	−8.39209	−0.277131
$918$	1.08411	0.0357811
$919$	40.1555	1.32461	0.662305	−	0.749235i	$-0.269579\pi$
$919$	40.1555	1.32461	0.662305	+	0.749235i	$0.269579\pi$
$920$	18.5078	0.610184
$921$	−15.2096	−0.501172
$922$	−16.0438	−0.528375
$923$	3.60555	0.118678
$924$	3.01114	0.0990593
$925$	19.4601	0.639845
$926$	−41.8347	−1.37477
$927$	8.06475	0.264881
$928$	−41.9048	−1.37559
$929$	14.6359	0.480187	0.240094	−	0.970750i	$-0.422822\pi$
$929$	14.6359	0.480187	0.240094	+	0.970750i	$0.422822\pi$
$930$	−2.21758	−0.0727174
$931$	−7.20245	−0.236051
$932$	40.7998	1.33644
$933$	−32.6689	−1.06953
$934$	31.7560	1.03909
$935$	−0.338009	−0.0110541
$936$	−3.22527	−0.105421
$937$	−39.4590	−1.28907	−0.644535	−	0.764574i	$-0.722949\pi$
$937$	−39.4590	−1.28907	−0.644535	+	0.764574i	$0.722949\pi$
$938$	22.1825	0.724286
$939$	−30.7810	−1.00450
$940$	16.6305	0.542428
$941$	50.5334	1.64734	0.823671	−	0.567067i	$-0.191922\pi$
$941$	50.5334	1.64734	0.823671	+	0.567067i	$0.191922\pi$
$942$	−47.6925	−1.55391
$943$	−20.9001	−0.680600
$944$	1.77041	0.0576218
$945$	0.793515	0.0258130
$946$	−20.5640	−0.668594
$947$	7.80568	0.253650	0.126825	−	0.991925i	$-0.459521\pi$
$947$	7.80568	0.253650	0.126825	+	0.991925i	$0.459521\pi$
$948$	−54.7993	−1.77980
$949$	10.6103	0.344425
$950$	72.6159	2.35597
$951$	26.8469	0.870570
$952$	−1.43317	−0.0464495
$953$	−9.55857	−0.309632	−0.154816	−	0.987943i	$-0.549479\pi$
$953$	−9.55857	−0.309632	−0.154816	+	0.987943i	$0.549479\pi$
$954$	−14.0804	−0.455870
$955$	−0.793515	−0.0256775
$956$	−40.6856	−1.31587
$957$	7.31007	0.236301
$958$	−18.8760	−0.609857
$959$	14.2063	0.458747
$960$	−10.1334	−0.327054
$961$	−29.5325	−0.952662
$962$	10.8636	0.350256
$963$	3.80673	0.122670
$964$	−58.4123	−1.88133
$965$	13.1833	0.424387
$966$	17.6431	0.567658
$967$	−37.3276	−1.20038	−0.600188	−	0.799859i	$-0.704907\pi$
$967$	−37.3276	−1.20038	−0.600188	+	0.799859i	$0.704907\pi$
$968$	−31.0413	−0.997704
$969$	−3.38469	−0.108732
$970$	15.9882	0.513349
$971$	−54.1453	−1.73760	−0.868802	−	0.495159i	$-0.835110\pi$
$971$	−54.1453	−1.73760	−0.868802	+	0.495159i	$0.835110\pi$
$972$	−3.32198	−0.106552
$973$	4.54774	0.145794
$974$	−35.5104	−1.13783
$975$	−4.62189	−0.148019
$976$	−3.71276	−0.118843
$977$	−13.6322	−0.436132	−0.218066	−	0.975934i	$-0.569975\pi$
$977$	−13.6322	−0.436132	−0.218066	+	0.975934i	$0.569975\pi$
$978$	27.3149	0.873435
$979$	4.70812	0.150472
$980$	−2.63604	−0.0842052
$981$	−5.43365	−0.173483
$982$	−82.6213	−2.63655
$983$	42.6160	1.35924	0.679620	−	0.733564i	$-0.262145\pi$
$983$	42.6160	1.35924	0.679620	+	0.733564i	$0.262145\pi$
$984$	−8.33431	−0.265688
$985$	−7.24616	−0.230882
$986$	−8.74302	−0.278435
$987$	6.30891	0.200815
$988$	25.3036	0.805015
$989$	−75.2100	−2.39154
$990$	1.65931	0.0527362
$991$	−14.5169	−0.461144	−0.230572	−	0.973055i	$-0.574060\pi$
$991$	−14.5169	−0.461144	−0.230572	+	0.973055i	$0.574060\pi$
$992$	6.29456	0.199852
$993$	29.3241	0.930572
$994$	−7.86507	−0.249465
$995$	−11.0733	−0.351048
$996$	46.9026	1.48617
$997$	12.4310	0.393695	0.196847	−	0.980434i	$-0.436930\pi$
$997$	12.4310	0.393695	0.196847	+	0.980434i	$0.436930\pi$
$998$	−59.1996	−1.87393
$999$	4.45278	0.140880

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.i.1.18	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.i.1.18	✓	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+2.30694 q^{2} -1.00000 q^{3} +3.32198 q^{4} -0.793515 q^{5} -2.30694 q^{6} +1.00000 q^{7} +3.04973 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.30694 q^{2} -1.00000 q^{3} +3.32198 q^{4} -0.793515 q^{5} -2.30694 q^{6} +1.00000 q^{7} +3.04973 q^{8} +1.00000 q^{9} -1.83059 q^{10} -0.906431 q^{11} -3.32198 q^{12} -1.05756 q^{13} +2.30694 q^{14} +0.793515 q^{15} +0.391582 q^{16} -0.469936 q^{17} +2.30694 q^{18} -7.20245 q^{19} -2.63604 q^{20} -1.00000 q^{21} -2.09108 q^{22} -7.64783 q^{23} -3.04973 q^{24} -4.37033 q^{25} -2.43973 q^{26} -1.00000 q^{27} +3.32198 q^{28} +8.06467 q^{29} +1.83059 q^{30} -1.21140 q^{31} -5.19610 q^{32} +0.906431 q^{33} -1.08411 q^{34} -0.793515 q^{35} +3.32198 q^{36} -4.45278 q^{37} -16.6156 q^{38} +1.05756 q^{39} -2.42000 q^{40} +2.73281 q^{41} -2.30694 q^{42} +9.83416 q^{43} -3.01114 q^{44} -0.793515 q^{45} -17.6431 q^{46} -6.30891 q^{47} -0.391582 q^{48} +1.00000 q^{49} -10.0821 q^{50} +0.469936 q^{51} -3.51319 q^{52} -6.10349 q^{53} -2.30694 q^{54} +0.719266 q^{55} +3.04973 q^{56} +7.20245 q^{57} +18.6047 q^{58} +4.52116 q^{59} +2.63604 q^{60} -9.48144 q^{61} -2.79463 q^{62} +1.00000 q^{63} -12.7702 q^{64} +0.839190 q^{65} +2.09108 q^{66} +9.61556 q^{67} -1.56112 q^{68} +7.64783 q^{69} -1.83059 q^{70} -3.40931 q^{71} +3.04973 q^{72} -10.0328 q^{73} -10.2723 q^{74} +4.37033 q^{75} -23.9264 q^{76} -0.906431 q^{77} +2.43973 q^{78} +16.4960 q^{79} -0.310726 q^{80} +1.00000 q^{81} +6.30443 q^{82} -14.1189 q^{83} -3.32198 q^{84} +0.372901 q^{85} +22.6868 q^{86} -8.06467 q^{87} -2.76436 q^{88} -5.19413 q^{89} -1.83059 q^{90} -1.05756 q^{91} -25.4059 q^{92} +1.21140 q^{93} -14.5543 q^{94} +5.71525 q^{95} +5.19610 q^{96} -8.73387 q^{97} +2.30694 q^{98} -0.906431 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9	\( 19 q + 3 q^{2} - 19 q^{3} + 11 q^{4} - 12 q^{5} - 3 q^{6} + 19 q^{7} + 6 q^{8} + 19 q^{9} - 12 q^{10} + q^{11} - 11 q^{12} - 25 q^{13} + 3 q^{14} + 12 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 29 q^{19} - 14 q^{20} - 19 q^{21} - 5 q^{22} + 18 q^{23} - 6 q^{24} + 3 q^{25} - 15 q^{26} - 19 q^{27} + 11 q^{28} + 2 q^{29} + 12 q^{30} - 24 q^{31} + 15 q^{32} - q^{33} - 16 q^{34} - 12 q^{35} + 11 q^{36} - 24 q^{37} - 26 q^{38} + 25 q^{39} - 44 q^{40} - 14 q^{41} - 3 q^{42} - 17 q^{43} - 6 q^{44} - 12 q^{45} - 16 q^{46} + 7 q^{47} - 3 q^{48} + 19 q^{49} + 7 q^{50} + 9 q^{51} - 64 q^{52} + 4 q^{53} - 3 q^{54} - 15 q^{55} + 6 q^{56} + 29 q^{57} - 15 q^{58} - 23 q^{59} + 14 q^{60} - 38 q^{61} - 4 q^{62} + 19 q^{63} + 33 q^{65} + 5 q^{66} - 20 q^{67} - 27 q^{68} - 18 q^{69} - 12 q^{70} + 14 q^{71} + 6 q^{72} - 19 q^{73} - 11 q^{74} - 3 q^{75} - 33 q^{76} + q^{77} + 15 q^{78} - 16 q^{79} - 10 q^{80} + 19 q^{81} - 25 q^{82} - 11 q^{83} - 11 q^{84} - 5 q^{85} + 5 q^{86} - 2 q^{87} - 25 q^{88} - 19 q^{89} - 12 q^{90} - 25 q^{91} + 22 q^{92} + 24 q^{93} - 35 q^{94} + 26 q^{95} - 15 q^{96} - 57 q^{97} + 3 q^{98} + q^{99}+O(q^{100}) \) 19 * q + 3 * q^2 - 19 * q^3 + 11 * q^4 - 12 * q^5 - 3 * q^6 + 19 * q^7 + 6 * q^8 + 19 * q^9 - 12 * q^10 + q^11 - 11 * q^12 - 25 * q^13 + 3 * q^14 + 12 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 29 * q^19 - 14 * q^20 - 19 * q^21 - 5 * q^22 + 18 * q^23 - 6 * q^24 + 3 * q^25 - 15 * q^26 - 19 * q^27 + 11 * q^28 + 2 * q^29 + 12 * q^30 - 24 * q^31 + 15 * q^32 - q^33 - 16 * q^34 - 12 * q^35 + 11 * q^36 - 24 * q^37 - 26 * q^38 + 25 * q^39 - 44 * q^40 - 14 * q^41 - 3 * q^42 - 17 * q^43 - 6 * q^44 - 12 * q^45 - 16 * q^46 + 7 * q^47 - 3 * q^48 + 19 * q^49 + 7 * q^50 + 9 * q^51 - 64 * q^52 + 4 * q^53 - 3 * q^54 - 15 * q^55 + 6 * q^56 + 29 * q^57 - 15 * q^58 - 23 * q^59 + 14 * q^60 - 38 * q^61 - 4 * q^62 + 19 * q^63 + 33 * q^65 + 5 * q^66 - 20 * q^67 - 27 * q^68 - 18 * q^69 - 12 * q^70 + 14 * q^71 + 6 * q^72 - 19 * q^73 - 11 * q^74 - 3 * q^75 - 33 * q^76 + q^77 + 15 * q^78 - 16 * q^79 - 10 * q^80 + 19 * q^81 - 25 * q^82 - 11 * q^83 - 11 * q^84 - 5 * q^85 + 5 * q^86 - 2 * q^87 - 25 * q^88 - 19 * q^89 - 12 * q^90 - 25 * q^91 + 22 * q^92 + 24 * q^93 - 35 * q^94 + 26 * q^95 - 15 * q^96 - 57 * q^97 + 3 * q^98 + q^99

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