LMFDB - Embedded newform 8007.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.19134 q^{2} -1.00000 q^{3} -0.580715 q^{4} -1.39828 q^{5} +1.19134 q^{6} -2.85096 q^{7} +3.07450 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.19134 q^{2} -1.00000 q^{3} -0.580715 q^{4} -1.39828 q^{5} +1.19134 q^{6} -2.85096 q^{7} +3.07450 q^{8} +1.00000 q^{9} +1.66582 q^{10} +1.44709 q^{11} +0.580715 q^{12} +4.76174 q^{13} +3.39646 q^{14} +1.39828 q^{15} -2.50134 q^{16} +1.00000 q^{17} -1.19134 q^{18} -0.218764 q^{19} +0.812000 q^{20} +2.85096 q^{21} -1.72398 q^{22} +0.569474 q^{23} -3.07450 q^{24} -3.04483 q^{25} -5.67284 q^{26} -1.00000 q^{27} +1.65560 q^{28} -9.06102 q^{29} -1.66582 q^{30} +5.73900 q^{31} -3.16906 q^{32} -1.44709 q^{33} -1.19134 q^{34} +3.98643 q^{35} -0.580715 q^{36} -10.9257 q^{37} +0.260621 q^{38} -4.76174 q^{39} -4.29900 q^{40} +12.5006 q^{41} -3.39646 q^{42} -0.483360 q^{43} -0.840349 q^{44} -1.39828 q^{45} -0.678436 q^{46} -9.82697 q^{47} +2.50134 q^{48} +1.12798 q^{49} +3.62741 q^{50} -1.00000 q^{51} -2.76522 q^{52} -1.52293 q^{53} +1.19134 q^{54} -2.02343 q^{55} -8.76529 q^{56} +0.218764 q^{57} +10.7947 q^{58} +1.65879 q^{59} -0.812000 q^{60} +2.71148 q^{61} -6.83709 q^{62} -2.85096 q^{63} +8.77811 q^{64} -6.65823 q^{65} +1.72398 q^{66} +7.18516 q^{67} -0.580715 q^{68} -0.569474 q^{69} -4.74918 q^{70} -5.67185 q^{71} +3.07450 q^{72} -4.78669 q^{73} +13.0162 q^{74} +3.04483 q^{75} +0.127039 q^{76} -4.12561 q^{77} +5.67284 q^{78} +13.2506 q^{79} +3.49756 q^{80} +1.00000 q^{81} -14.8925 q^{82} +0.389976 q^{83} -1.65560 q^{84} -1.39828 q^{85} +0.575845 q^{86} +9.06102 q^{87} +4.44909 q^{88} -3.31786 q^{89} +1.66582 q^{90} -13.5755 q^{91} -0.330702 q^{92} -5.73900 q^{93} +11.7072 q^{94} +0.305892 q^{95} +3.16906 q^{96} +6.87720 q^{97} -1.34381 q^{98} +1.44709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * 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 $

$2$	−1.19134	−0.842403	−0.421201	−	0.906967i	$-0.638391\pi$
$2$	−1.19134	−0.842403	−0.421201	+	0.906967i	$0.638391\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.580715	−0.290357
$5$	−1.39828	−0.625328	−0.312664	−	0.949864i	$-0.601221\pi$
$5$	−1.39828	−0.625328	−0.312664	+	0.949864i	$0.601221\pi$
$6$	1.19134	0.486361
$7$	−2.85096	−1.07756	−0.538781	−	0.842446i	$-0.681115\pi$
$7$	−2.85096	−1.07756	−0.538781	+	0.842446i	$0.681115\pi$
$8$	3.07450	1.08700
$9$	1.00000	0.333333
$10$	1.66582	0.526778
$11$	1.44709	0.436315	0.218157	−	0.975914i	$-0.429995\pi$
$11$	1.44709	0.436315	0.218157	+	0.975914i	$0.429995\pi$
$12$	0.580715	0.167638
$13$	4.76174	1.32067	0.660335	−	0.750971i	$-0.270414\pi$
$13$	4.76174	1.32067	0.660335	+	0.750971i	$0.270414\pi$
$14$	3.39646	0.907742
$15$	1.39828	0.361033
$16$	−2.50134	−0.625335
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.19134	−0.280801
$19$	−0.218764	−0.0501878	−0.0250939	−	0.999685i	$-0.507988\pi$
$19$	−0.218764	−0.0501878	−0.0250939	+	0.999685i	$0.507988\pi$
$20$	0.812000	0.181569
$21$	2.85096	0.622131
$22$	−1.72398	−0.367553
$23$	0.569474	0.118744	0.0593718	−	0.998236i	$-0.481090\pi$
$23$	0.569474	0.118744	0.0593718	+	0.998236i	$0.481090\pi$
$24$	−3.07450	−0.627580
$25$	−3.04483	−0.608965
$26$	−5.67284	−1.11254
$27$	−1.00000	−0.192450
$28$	1.65560	0.312878
$29$	−9.06102	−1.68259	−0.841295	−	0.540576i	$-0.818206\pi$
$29$	−9.06102	−1.68259	−0.841295	+	0.540576i	$0.818206\pi$
$30$	−1.66582	−0.304135
$31$	5.73900	1.03076	0.515378	−	0.856963i	$-0.327652\pi$
$31$	5.73900	1.03076	0.515378	+	0.856963i	$0.327652\pi$
$32$	−3.16906	−0.560217
$33$	−1.44709	−0.251907
$34$	−1.19134	−0.204313
$35$	3.98643	0.673830
$36$	−0.580715	−0.0967858
$37$	−10.9257	−1.79618	−0.898088	−	0.439816i	$-0.855044\pi$
$37$	−10.9257	−1.79618	−0.898088	+	0.439816i	$0.855044\pi$
$38$	0.260621	0.0422784
$39$	−4.76174	−0.762489
$40$	−4.29900	−0.679732
$41$	12.5006	1.95227	0.976135	−	0.217164i	$-0.0696806\pi$
$41$	12.5006	1.95227	0.976135	+	0.217164i	$0.0696806\pi$
$42$	−3.39646	−0.524085
$43$	−0.483360	−0.0737117	−0.0368559	−	0.999321i	$-0.511734\pi$
$43$	−0.483360	−0.0737117	−0.0368559	+	0.999321i	$0.511734\pi$
$44$	−0.840349	−0.126687
$45$	−1.39828	−0.208443
$46$	−0.678436	−0.100030
$47$	−9.82697	−1.43341	−0.716706	−	0.697376i	$-0.754351\pi$
$47$	−9.82697	−1.43341	−0.716706	+	0.697376i	$0.754351\pi$
$48$	2.50134	0.361037
$49$	1.12798	0.161141
$50$	3.62741	0.512994
$51$	−1.00000	−0.140028
$52$	−2.76522	−0.383466
$53$	−1.52293	−0.209190	−0.104595	−	0.994515i	$-0.533355\pi$
$53$	−1.52293	−0.209190	−0.104595	+	0.994515i	$0.533355\pi$
$54$	1.19134	0.162120
$55$	−2.02343	−0.272840
$56$	−8.76529	−1.17131
$57$	0.218764	0.0289760
$58$	10.7947	1.41742
$59$	1.65879	0.215957	0.107978	−	0.994153i	$-0.465562\pi$
$59$	1.65879	0.215957	0.107978	+	0.994153i	$0.465562\pi$
$60$	−0.812000	−0.104829
$61$	2.71148	0.347170	0.173585	−	0.984819i	$-0.444465\pi$
$61$	2.71148	0.347170	0.173585	+	0.984819i	$0.444465\pi$
$62$	−6.83709	−0.868311
$63$	−2.85096	−0.359187
$64$	8.77811	1.09726
$65$	−6.65823	−0.825852
$66$	1.72398	0.212207
$67$	7.18516	0.877807	0.438904	−	0.898534i	$-0.355367\pi$
$67$	7.18516	0.877807	0.438904	+	0.898534i	$0.355367\pi$
$68$	−0.580715	−0.0704220
$69$	−0.569474	−0.0685566
$70$	−4.74918	−0.567636
$71$	−5.67185	−0.673124	−0.336562	−	0.941661i	$-0.609264\pi$
$71$	−5.67185	−0.673124	−0.336562	+	0.941661i	$0.609264\pi$
$72$	3.07450	0.362334
$73$	−4.78669	−0.560240	−0.280120	−	0.959965i	$-0.590374\pi$
$73$	−4.78669	−0.560240	−0.280120	+	0.959965i	$0.590374\pi$
$74$	13.0162	1.51310
$75$	3.04483	0.351586
$76$	0.127039	0.0145724
$77$	−4.12561	−0.470157
$78$	5.67284	0.642323
$79$	13.2506	1.49081	0.745405	−	0.666612i	$-0.232256\pi$
$79$	13.2506	1.49081	0.745405	+	0.666612i	$0.232256\pi$
$80$	3.49756	0.391039
$81$	1.00000	0.111111
$82$	−14.8925	−1.64460
$83$	0.389976	0.0428055	0.0214027	−	0.999771i	$-0.493187\pi$
$83$	0.389976	0.0428055	0.0214027	+	0.999771i	$0.493187\pi$
$84$	−1.65560	−0.180640
$85$	−1.39828	−0.151664
$86$	0.575845	0.0620950
$87$	9.06102	0.971444
$88$	4.44909	0.474275
$89$	−3.31786	−0.351692	−0.175846	−	0.984418i	$-0.556266\pi$
$89$	−3.31786	−0.351692	−0.175846	+	0.984418i	$0.556266\pi$
$90$	1.66582	0.175593
$91$	−13.5755	−1.42310
$92$	−0.330702	−0.0344781
$93$	−5.73900	−0.595107
$94$	11.7072	1.20751
$95$	0.305892	0.0313838
$96$	3.16906	0.323441
$97$	6.87720	0.698274	0.349137	−	0.937072i	$-0.386475\pi$
$97$	6.87720	0.698274	0.349137	+	0.937072i	$0.386475\pi$
$98$	−1.34381	−0.135745
$99$	1.44709	0.145438
$100$	1.76818	0.176818
$101$	−2.48008	−0.246778	−0.123389	−	0.992358i	$-0.539376\pi$
$101$	−2.48008	−0.246778	−0.123389	+	0.992358i	$0.539376\pi$
$102$	1.19134	0.117960
$103$	−0.0292218	−0.00287931	−0.00143965	−	0.999999i	$-0.500458\pi$
$103$	−0.0292218	−0.00287931	−0.00143965	+	0.999999i	$0.500458\pi$
$104$	14.6400	1.43557
$105$	−3.98643	−0.389036
$106$	1.81432	0.176222
$107$	16.7470	1.61899	0.809497	−	0.587124i	$-0.199740\pi$
$107$	16.7470	1.61899	0.809497	+	0.587124i	$0.199740\pi$
$108$	0.580715	0.0558793
$109$	17.4938	1.67560	0.837802	−	0.545974i	$-0.183840\pi$
$109$	17.4938	1.67560	0.837802	+	0.545974i	$0.183840\pi$
$110$	2.41059	0.229841
$111$	10.9257	1.03702
$112$	7.13123	0.673837
$113$	7.22937	0.680081	0.340041	−	0.940411i	$-0.389559\pi$
$113$	7.22937	0.680081	0.340041	+	0.940411i	$0.389559\pi$
$114$	−0.260621	−0.0244094
$115$	−0.796281	−0.0742536
$116$	5.26187	0.488553
$117$	4.76174	0.440223
$118$	−1.97618	−0.181923
$119$	−2.85096	−0.261347
$120$	4.29900	0.392443
$121$	−8.90592	−0.809629
$122$	−3.23029	−0.292457
$123$	−12.5006	−1.12714
$124$	−3.33272	−0.299288
$125$	11.2489	1.00613
$126$	3.39646	0.302581
$127$	−14.6205	−1.29736	−0.648680	−	0.761062i	$-0.724678\pi$
$127$	−14.6205	−1.29736	−0.648680	+	0.761062i	$0.724678\pi$
$128$	−4.11956	−0.364121
$129$	0.483360	0.0425575
$130$	7.93220	0.695700
$131$	−8.89591	−0.777239	−0.388619	−	0.921398i	$-0.627048\pi$
$131$	−8.89591	−0.777239	−0.388619	+	0.921398i	$0.627048\pi$
$132$	0.840349	0.0731430
$133$	0.623687	0.0540805
$134$	−8.55995	−0.739467
$135$	1.39828	0.120344
$136$	3.07450	0.263636
$137$	12.4773	1.06601	0.533006	−	0.846112i	$-0.321062\pi$
$137$	12.4773	1.06601	0.533006	+	0.846112i	$0.321062\pi$
$138$	0.678436	0.0577523
$139$	−11.9857	−1.01662	−0.508309	−	0.861175i	$-0.669729\pi$
$139$	−11.9857	−1.01662	−0.508309	+	0.861175i	$0.669729\pi$
$140$	−2.31498	−0.195652
$141$	9.82697	0.827580
$142$	6.75708	0.567042
$143$	6.89069	0.576228
$144$	−2.50134	−0.208445
$145$	12.6698	1.05217
$146$	5.70257	0.471948
$147$	−1.12798	−0.0930346
$148$	6.34472	0.521533
$149$	4.96040	0.406372	0.203186	−	0.979140i	$-0.434870\pi$
$149$	4.96040	0.406372	0.203186	+	0.979140i	$0.434870\pi$
$150$	−3.62741	−0.296177
$151$	8.80681	0.716688	0.358344	−	0.933590i	$-0.383341\pi$
$151$	8.80681	0.716688	0.358344	+	0.933590i	$0.383341\pi$
$152$	−0.672589	−0.0545542
$153$	1.00000	0.0808452
$154$	4.91499	0.396061
$155$	−8.02471	−0.644560
$156$	2.76522	0.221394
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−15.7859	−1.25586
$159$	1.52293	0.120776
$160$	4.43123	0.350319
$161$	−1.62355	−0.127954
$162$	−1.19134	−0.0936003
$163$	−0.856753	−0.0671061	−0.0335530	−	0.999437i	$-0.510682\pi$
$163$	−0.856753	−0.0671061	−0.0335530	+	0.999437i	$0.510682\pi$
$164$	−7.25930	−0.566856
$165$	2.02343	0.157524
$166$	−0.464594	−0.0360595
$167$	13.3828	1.03559	0.517796	−	0.855504i	$-0.326753\pi$
$167$	13.3828	1.03559	0.517796	+	0.855504i	$0.326753\pi$
$168$	8.76529	0.676257
$169$	9.67420	0.744169
$170$	1.66582	0.127762
$171$	−0.218764	−0.0167293
$172$	0.280694	0.0214028
$173$	−0.949222	−0.0721680	−0.0360840	−	0.999349i	$-0.511488\pi$
$173$	−0.949222	−0.0721680	−0.0360840	+	0.999349i	$0.511488\pi$
$174$	−10.7947	−0.818347
$175$	8.68068	0.656198
$176$	−3.61967	−0.272843
$177$	−1.65879	−0.124683
$178$	3.95269	0.296267
$179$	10.6289	0.794438	0.397219	−	0.917724i	$-0.369975\pi$
$179$	10.6289	0.794438	0.397219	+	0.917724i	$0.369975\pi$
$180$	0.812000	0.0605229
$181$	14.4191	1.07176	0.535882	−	0.844293i	$-0.319979\pi$
$181$	14.4191	1.07176	0.535882	+	0.844293i	$0.319979\pi$
$182$	16.1731	1.19883
$183$	−2.71148	−0.200439
$184$	1.75085	0.129074
$185$	15.2772	1.12320
$186$	6.83709	0.501320
$187$	1.44709	0.105822
$188$	5.70667	0.416202
$189$	2.85096	0.207377
$190$	−0.364420	−0.0264378
$191$	13.8309	1.00077	0.500383	−	0.865804i	$-0.333193\pi$
$191$	13.8309	1.00077	0.500383	+	0.865804i	$0.333193\pi$
$192$	−8.77811	−0.633505
$193$	−3.20089	−0.230405	−0.115203	−	0.993342i	$-0.536752\pi$
$193$	−3.20089	−0.230405	−0.115203	+	0.993342i	$0.536752\pi$
$194$	−8.19307	−0.588228
$195$	6.65823	0.476806
$196$	−0.655037	−0.0467884
$197$	−5.37817	−0.383178	−0.191589	−	0.981475i	$-0.561364\pi$
$197$	−5.37817	−0.383178	−0.191589	+	0.981475i	$0.561364\pi$
$198$	−1.72398	−0.122518
$199$	−13.4715	−0.954971	−0.477485	−	0.878640i	$-0.658452\pi$
$199$	−13.4715	−0.954971	−0.477485	+	0.878640i	$0.658452\pi$
$200$	−9.36132	−0.661946
$201$	−7.18516	−0.506802
$202$	2.95462	0.207886
$203$	25.8326	1.81310
$204$	0.580715	0.0406582
$205$	−17.4793	−1.22081
$206$	0.0348130	0.00242554
$207$	0.569474	0.0395812
$208$	−11.9107	−0.825861
$209$	−0.316571	−0.0218977
$210$	4.74918	0.327725
$211$	−8.33660	−0.573915	−0.286958	−	0.957943i	$-0.592644\pi$
$211$	−8.33660	−0.573915	−0.286958	+	0.957943i	$0.592644\pi$
$212$	0.884386	0.0607399
$213$	5.67185	0.388628
$214$	−19.9513	−1.36384
$215$	0.675871	0.0460940
$216$	−3.07450	−0.209193
$217$	−16.3617	−1.11070
$218$	−20.8411	−1.41153
$219$	4.78669	0.323455
$220$	1.17504	0.0792211
$221$	4.76174	0.320310
$222$	−13.0162	−0.873591
$223$	−23.5273	−1.57550	−0.787751	−	0.615993i	$-0.788755\pi$
$223$	−23.5273	−1.57550	−0.787751	+	0.615993i	$0.788755\pi$
$224$	9.03488	0.603668
$225$	−3.04483	−0.202988
$226$	−8.61261	−0.572903
$227$	−18.7461	−1.24422	−0.622112	−	0.782929i	$-0.713725\pi$
$227$	−18.7461	−1.24422	−0.622112	+	0.782929i	$0.713725\pi$
$228$	−0.127039	−0.00841339
$229$	13.2865	0.877996	0.438998	−	0.898488i	$-0.355334\pi$
$229$	13.2865	0.877996	0.438998	+	0.898488i	$0.355334\pi$
$230$	0.948640	0.0625515
$231$	4.12561	0.271445
$232$	−27.8581	−1.82898
$233$	−8.94158	−0.585782	−0.292891	−	0.956146i	$-0.594617\pi$
$233$	−8.94158	−0.585782	−0.292891	+	0.956146i	$0.594617\pi$
$234$	−5.67284	−0.370845
$235$	13.7408	0.896352
$236$	−0.963287	−0.0627046
$237$	−13.2506	−0.860720
$238$	3.39646	0.220160
$239$	0.880442	0.0569511	0.0284755	−	0.999594i	$-0.490935\pi$
$239$	0.880442	0.0569511	0.0284755	+	0.999594i	$0.490935\pi$
$240$	−3.49756	−0.225767
$241$	−9.29638	−0.598832	−0.299416	−	0.954123i	$-0.596792\pi$
$241$	−9.29638	−0.598832	−0.299416	+	0.954123i	$0.596792\pi$
$242$	10.6100	0.682034
$243$	−1.00000	−0.0641500
$244$	−1.57460	−0.100803
$245$	−1.57723	−0.100766
$246$	14.8925	0.949509
$247$	−1.04170	−0.0662816
$248$	17.6446	1.12043
$249$	−0.389976	−0.0247138
$250$	−13.4012	−0.847567
$251$	−25.8183	−1.62964	−0.814818	−	0.579717i	$-0.803163\pi$
$251$	−25.8183	−1.62964	−0.814818	+	0.579717i	$0.803163\pi$
$252$	1.65560	0.104293
$253$	0.824082	0.0518096
$254$	17.4179	1.09290
$255$	1.39828	0.0875634
$256$	−12.6484	−0.790527
$257$	−29.0500	−1.81209	−0.906044	−	0.423184i	$-0.860913\pi$
$257$	−29.0500	−1.81209	−0.906044	+	0.423184i	$0.860913\pi$
$258$	−0.575845	−0.0358506
$259$	31.1488	1.93549
$260$	3.86653	0.239792
$261$	−9.06102	−0.560863
$262$	10.5980	0.654748
$263$	27.6035	1.70211	0.851053	−	0.525080i	$-0.175965\pi$
$263$	27.6035	1.70211	0.851053	+	0.525080i	$0.175965\pi$
$264$	−4.44909	−0.273823
$265$	2.12947	0.130812
$266$	−0.743022	−0.0455576
$267$	3.31786	0.203050
$268$	−4.17253	−0.254878
$269$	19.9668	1.21740	0.608700	−	0.793401i	$-0.291691\pi$
$269$	19.9668	1.21740	0.608700	+	0.793401i	$0.291691\pi$
$270$	−1.66582	−0.101378
$271$	−22.3238	−1.35608	−0.678038	−	0.735027i	$-0.737170\pi$
$271$	−22.3238	−1.35608	−0.678038	+	0.735027i	$0.737170\pi$
$272$	−2.50134	−0.151666
$273$	13.5755	0.821630
$274$	−14.8647	−0.898011
$275$	−4.40615	−0.265701
$276$	0.330702	0.0199059
$277$	8.02210	0.482001	0.241001	−	0.970525i	$-0.422524\pi$
$277$	8.02210	0.482001	0.241001	+	0.970525i	$0.422524\pi$
$278$	14.2791	0.856402
$279$	5.73900	0.343585
$280$	12.2563	0.732453
$281$	−2.32948	−0.138965	−0.0694824	−	0.997583i	$-0.522135\pi$
$281$	−2.32948	−0.138965	−0.0694824	+	0.997583i	$0.522135\pi$
$282$	−11.7072	−0.697156
$283$	15.9459	0.947885	0.473942	−	0.880556i	$-0.342830\pi$
$283$	15.9459	0.947885	0.473942	+	0.880556i	$0.342830\pi$
$284$	3.29373	0.195447
$285$	−0.305892	−0.0181195
$286$	−8.20913	−0.485416
$287$	−35.6388	−2.10369
$288$	−3.16906	−0.186739
$289$	1.00000	0.0588235
$290$	−15.0940	−0.886351
$291$	−6.87720	−0.403149
$292$	2.77970	0.162670
$293$	11.0931	0.648064	0.324032	−	0.946046i	$-0.394961\pi$
$293$	11.0931	0.648064	0.324032	+	0.946046i	$0.394961\pi$
$294$	1.34381	0.0783726
$295$	−2.31945	−0.135044
$296$	−33.5911	−1.95244
$297$	−1.44709	−0.0839689
$298$	−5.90951	−0.342329
$299$	2.71169	0.156821
$300$	−1.76818	−0.102086
$301$	1.37804	0.0794290
$302$	−10.4919	−0.603740
$303$	2.48008	0.142477
$304$	0.547202	0.0313842
$305$	−3.79140	−0.217095
$306$	−1.19134	−0.0681042
$307$	−8.86982	−0.506228	−0.253114	−	0.967437i	$-0.581455\pi$
$307$	−8.86982	−0.506228	−0.253114	+	0.967437i	$0.581455\pi$
$308$	2.39580	0.136513
$309$	0.0292218	0.00166237
$310$	9.56013	0.542979
$311$	17.8346	1.01131	0.505654	−	0.862736i	$-0.331251\pi$
$311$	17.8346	1.01131	0.505654	+	0.862736i	$0.331251\pi$
$312$	−14.6400	−0.828826
$313$	7.59030	0.429029	0.214515	−	0.976721i	$-0.431183\pi$
$313$	7.59030	0.429029	0.214515	+	0.976721i	$0.431183\pi$
$314$	−1.19134	−0.0672311
$315$	3.98643	0.224610
$316$	−7.69483	−0.432868
$317$	−31.4411	−1.76591	−0.882955	−	0.469458i	$-0.844449\pi$
$317$	−31.4411	−1.76591	−0.882955	+	0.469458i	$0.844449\pi$
$318$	−1.81432	−0.101742
$319$	−13.1121	−0.734139
$320$	−12.2742	−0.686149
$321$	−16.7470	−0.934726
$322$	1.93419	0.107788
$323$	−0.218764	−0.0121723
$324$	−0.580715	−0.0322619
$325$	−14.4987	−0.804242
$326$	1.02068	0.0565303
$327$	−17.4938	−0.967411
$328$	38.4332	2.12212
$329$	28.0163	1.54459
$330$	−2.41059	−0.132699
$331$	−26.9797	−1.48294	−0.741470	−	0.670986i	$-0.765871\pi$
$331$	−26.9797	−1.48294	−0.741470	+	0.670986i	$0.765871\pi$
$332$	−0.226465	−0.0124289
$333$	−10.9257	−0.598725
$334$	−15.9434	−0.872385
$335$	−10.0468	−0.548917
$336$	−7.13123	−0.389040
$337$	0.895336	0.0487720	0.0243860	−	0.999703i	$-0.492237\pi$
$337$	0.895336	0.0487720	0.0243860	+	0.999703i	$0.492237\pi$
$338$	−11.5252	−0.626890
$339$	−7.22937	−0.392645
$340$	0.812000	0.0440369
$341$	8.30487	0.449734
$342$	0.260621	0.0140928
$343$	16.7409	0.903923
$344$	−1.48609	−0.0801247
$345$	0.796281	0.0428704
$346$	1.13084	0.0607945
$347$	6.90556	0.370710	0.185355	−	0.982672i	$-0.440657\pi$
$347$	6.90556	0.370710	0.185355	+	0.982672i	$0.440657\pi$
$348$	−5.26187	−0.282066
$349$	0.342945	0.0183574	0.00917872	−	0.999958i	$-0.497078\pi$
$349$	0.342945	0.0183574	0.00917872	+	0.999958i	$0.497078\pi$
$350$	−10.3416	−0.552783
$351$	−4.76174	−0.254163
$352$	−4.58593	−0.244431
$353$	−32.0701	−1.70692	−0.853461	−	0.521157i	$-0.825500\pi$
$353$	−32.0701	−1.70692	−0.853461	+	0.521157i	$0.825500\pi$
$354$	1.97618	0.105033
$355$	7.93080	0.420923
$356$	1.92673	0.102117
$357$	2.85096	0.150889
$358$	−12.6626	−0.669237
$359$	−11.0700	−0.584254	−0.292127	−	0.956380i	$-0.594363\pi$
$359$	−11.0700	−0.584254	−0.292127	+	0.956380i	$0.594363\pi$
$360$	−4.29900	−0.226577
$361$	−18.9521	−0.997481
$362$	−17.1780	−0.902857
$363$	8.90592	0.467440
$364$	7.88352	0.413209
$365$	6.69311	0.350334
$366$	3.23029	0.168850
$367$	−2.94778	−0.153873	−0.0769365	−	0.997036i	$-0.524514\pi$
$367$	−2.94778	−0.153873	−0.0769365	+	0.997036i	$0.524514\pi$
$368$	−1.42445	−0.0742545
$369$	12.5006	0.650757
$370$	−18.2003	−0.946186
$371$	4.34181	0.225415
$372$	3.33272	0.172794
$373$	15.8757	0.822014	0.411007	−	0.911632i	$-0.365177\pi$
$373$	15.8757	0.822014	0.411007	+	0.911632i	$0.365177\pi$
$374$	−1.72398	−0.0891447
$375$	−11.2489	−0.580890
$376$	−30.2131	−1.55812
$377$	−43.1463	−2.22215
$378$	−3.39646	−0.174695
$379$	14.8230	0.761407	0.380703	−	0.924697i	$-0.375682\pi$
$379$	14.8230	0.761407	0.380703	+	0.924697i	$0.375682\pi$
$380$	−0.177636	−0.00911253
$381$	14.6205	0.749031
$382$	−16.4772	−0.843048
$383$	20.7188	1.05868	0.529341	−	0.848409i	$-0.322439\pi$
$383$	20.7188	1.05868	0.529341	+	0.848409i	$0.322439\pi$
$384$	4.11956	0.210225
$385$	5.76874	0.294002
$386$	3.81334	0.194094
$387$	−0.483360	−0.0245706
$388$	−3.99369	−0.202749
$389$	16.4909	0.836124	0.418062	−	0.908418i	$-0.362709\pi$
$389$	16.4909	0.836124	0.418062	+	0.908418i	$0.362709\pi$
$390$	−7.93220	−0.401662
$391$	0.569474	0.0287995
$392$	3.46799	0.175160
$393$	8.89591	0.448739
$394$	6.40721	0.322791
$395$	−18.5280	−0.932245
$396$	−0.840349	−0.0422291
$397$	−24.7138	−1.24035	−0.620175	−	0.784463i	$-0.712939\pi$
$397$	−24.7138	−1.24035	−0.620175	+	0.784463i	$0.712939\pi$
$398$	16.0491	0.804470
$399$	−0.623687	−0.0312234
$400$	7.61614	0.380807
$401$	26.4524	1.32097	0.660484	−	0.750840i	$-0.270351\pi$
$401$	26.4524	1.32097	0.660484	+	0.750840i	$0.270351\pi$
$402$	8.55995	0.426932
$403$	27.3277	1.36129
$404$	1.44022	0.0716537
$405$	−1.39828	−0.0694809
$406$	−30.7754	−1.52736
$407$	−15.8105	−0.783699
$408$	−3.07450	−0.152211
$409$	−25.1503	−1.24360	−0.621801	−	0.783176i	$-0.713599\pi$
$409$	−25.1503	−1.24360	−0.621801	+	0.783176i	$0.713599\pi$
$410$	20.8238	1.02841
$411$	−12.4773	−0.615462
$412$	0.0169695	0.000836028 0
$413$	−4.72916	−0.232707
$414$	−0.678436	−0.0333433
$415$	−0.545295	−0.0267675
$416$	−15.0903	−0.739861
$417$	11.9857	0.586944
$418$	0.377143	0.0184467
$419$	7.67148	0.374776	0.187388	−	0.982286i	$-0.439998\pi$
$419$	7.67148	0.374776	0.187388	+	0.982286i	$0.439998\pi$
$420$	2.31498	0.112959
$421$	−20.9359	−1.02035	−0.510176	−	0.860070i	$-0.670420\pi$
$421$	−20.9359	−1.02035	−0.510176	+	0.860070i	$0.670420\pi$
$422$	9.93171	0.483468
$423$	−9.82697	−0.477804
$424$	−4.68224	−0.227390
$425$	−3.04483	−0.147696
$426$	−6.75708	−0.327382
$427$	−7.73034	−0.374097
$428$	−9.72523	−0.470087
$429$	−6.89069	−0.332685
$430$	−0.805190	−0.0388297
$431$	16.6439	0.801709	0.400855	−	0.916142i	$-0.368713\pi$
$431$	16.6439	0.801709	0.400855	+	0.916142i	$0.368713\pi$
$432$	2.50134	0.120346
$433$	−23.8045	−1.14397	−0.571984	−	0.820264i	$-0.693826\pi$
$433$	−23.8045	−1.14397	−0.571984	+	0.820264i	$0.693826\pi$
$434$	19.4923	0.935659
$435$	−12.6698	−0.607471
$436$	−10.1589	−0.486524
$437$	−0.124580	−0.00595948
$438$	−5.70257	−0.272479
$439$	−9.79132	−0.467314	−0.233657	−	0.972319i	$-0.575069\pi$
$439$	−9.79132	−0.467314	−0.233657	+	0.972319i	$0.575069\pi$
$440$	−6.22106	−0.296577
$441$	1.12798	0.0537135
$442$	−5.67284	−0.269830
$443$	19.6597	0.934063	0.467031	−	0.884241i	$-0.345323\pi$
$443$	19.6597	0.934063	0.467031	+	0.884241i	$0.345323\pi$
$444$	−6.34472	−0.301107
$445$	4.63928	0.219923
$446$	28.0289	1.32721
$447$	−4.96040	−0.234619
$448$	−25.0260	−1.18237
$449$	−23.5723	−1.11245	−0.556224	−	0.831033i	$-0.687750\pi$
$449$	−23.5723	−1.11245	−0.556224	+	0.831033i	$0.687750\pi$
$450$	3.62741	0.170998
$451$	18.0896	0.851805
$452$	−4.19820	−0.197467
$453$	−8.80681	−0.413780
$454$	22.3329	1.04814
$455$	18.9824	0.889907
$456$	0.672589	0.0314969
$457$	−20.5261	−0.960172	−0.480086	−	0.877221i	$-0.659395\pi$
$457$	−20.5261	−0.960172	−0.480086	+	0.877221i	$0.659395\pi$
$458$	−15.8287	−0.739626
$459$	−1.00000	−0.0466760
$460$	0.462413	0.0215601
$461$	26.3899	1.22910	0.614551	−	0.788877i	$-0.289337\pi$
$461$	26.3899	1.22910	0.614551	+	0.788877i	$0.289337\pi$
$462$	−4.91499	−0.228666
$463$	34.2618	1.59228	0.796141	−	0.605111i	$-0.206871\pi$
$463$	34.2618	1.59228	0.796141	+	0.605111i	$0.206871\pi$
$464$	22.6647	1.05218
$465$	8.02471	0.372137
$466$	10.6524	0.493465
$467$	14.8912	0.689081	0.344540	−	0.938772i	$-0.388035\pi$
$467$	14.8912	0.689081	0.344540	+	0.938772i	$0.388035\pi$
$468$	−2.76522	−0.127822
$469$	−20.4846	−0.945892
$470$	−16.3699	−0.755089
$471$	−1.00000	−0.0460776
$472$	5.09997	0.234745
$473$	−0.699467	−0.0321615
$474$	15.7859	0.725073
$475$	0.666097	0.0305626
$476$	1.65560	0.0758841
$477$	−1.52293	−0.0697300
$478$	−1.04890	−0.0479757
$479$	18.1180	0.827832	0.413916	−	0.910315i	$-0.364161\pi$
$479$	18.1180	0.827832	0.413916	+	0.910315i	$0.364161\pi$
$480$	−4.43123	−0.202257
$481$	−52.0254	−2.37216
$482$	11.0751	0.504458
$483$	1.62355	0.0738740
$484$	5.17180	0.235082
$485$	−9.61623	−0.436650
$486$	1.19134	0.0540402
$487$	14.6005	0.661614	0.330807	−	0.943698i	$-0.392679\pi$
$487$	14.6005	0.661614	0.330807	+	0.943698i	$0.392679\pi$
$488$	8.33646	0.377374
$489$	0.856753	0.0387437
$490$	1.87902	0.0848853
$491$	−16.7100	−0.754113	−0.377057	−	0.926190i	$-0.623064\pi$
$491$	−16.7100	−0.754113	−0.377057	+	0.926190i	$0.623064\pi$
$492$	7.25930	0.327275
$493$	−9.06102	−0.408088
$494$	1.24101	0.0558358
$495$	−2.02343	−0.0909466
$496$	−14.3552	−0.644567
$497$	16.1702	0.725333
$498$	0.464594	0.0208189
$499$	−25.1245	−1.12473	−0.562363	−	0.826891i	$-0.690108\pi$
$499$	−25.1245	−1.12473	−0.562363	+	0.826891i	$0.690108\pi$
$500$	−6.53239	−0.292138
$501$	−13.3828	−0.597899
$502$	30.7583	1.37281
$503$	4.31823	0.192541	0.0962703	−	0.995355i	$-0.469309\pi$
$503$	4.31823	0.192541	0.0962703	+	0.995355i	$0.469309\pi$
$504$	−8.76529	−0.390437
$505$	3.46784	0.154317
$506$	−0.981759	−0.0436445
$507$	−9.67420	−0.429646
$508$	8.49034	0.376698
$509$	21.9992	0.975097	0.487548	−	0.873096i	$-0.337891\pi$
$509$	21.9992	0.975097	0.487548	+	0.873096i	$0.337891\pi$
$510$	−1.66582	−0.0737637
$511$	13.6467	0.603693
$512$	23.3077	1.03006
$513$	0.218764	0.00965865
$514$	34.6083	1.52651
$515$	0.0408601	0.00180051
$516$	−0.280694	−0.0123569
$517$	−14.2205	−0.625419
$518$	−37.1087	−1.63046
$519$	0.949222	0.0416662
$520$	−20.4707	−0.897701
$521$	17.4581	0.764854	0.382427	−	0.923986i	$-0.375088\pi$
$521$	17.4581	0.764854	0.382427	+	0.923986i	$0.375088\pi$
$522$	10.7947	0.472473
$523$	13.2429	0.579070	0.289535	−	0.957167i	$-0.406499\pi$
$523$	13.2429	0.579070	0.289535	+	0.957167i	$0.406499\pi$
$524$	5.16599	0.225677
$525$	−8.68068	−0.378856
$526$	−32.8851	−1.43386
$527$	5.73900	0.249995
$528$	3.61967	0.157526
$529$	−22.6757	−0.985900
$530$	−2.53692	−0.110197
$531$	1.65879	0.0719856
$532$	−0.362184	−0.0157027
$533$	59.5248	2.57830
$534$	−3.95269	−0.171050
$535$	−23.4169	−1.01240
$536$	22.0908	0.954177
$537$	−10.6289	−0.458669
$538$	−23.7872	−1.02554
$539$	1.63230	0.0703081
$540$	−0.812000	−0.0349429
$541$	−25.4042	−1.09221	−0.546106	−	0.837716i	$-0.683890\pi$
$541$	−25.4042	−1.09221	−0.546106	+	0.837716i	$0.683890\pi$
$542$	26.5952	1.14236
$543$	−14.4191	−0.618783
$544$	−3.16906	−0.135873
$545$	−24.4612	−1.04780
$546$	−16.1731	−0.692143
$547$	−3.27648	−0.140092	−0.0700462	−	0.997544i	$-0.522315\pi$
$547$	−3.27648	−0.140092	−0.0700462	+	0.997544i	$0.522315\pi$
$548$	−7.24578	−0.309524
$549$	2.71148	0.115723
$550$	5.24921	0.223827
$551$	1.98222	0.0844455
$552$	−1.75085	−0.0745211
$553$	−37.7770	−1.60644
$554$	−9.55703	−0.406039
$555$	−15.2772	−0.648479
$556$	6.96030	0.295183
$557$	−6.76026	−0.286441	−0.143221	−	0.989691i	$-0.545746\pi$
$557$	−6.76026	−0.286441	−0.143221	+	0.989691i	$0.545746\pi$
$558$	−6.83709	−0.289437
$559$	−2.30164	−0.0973489
$560$	−9.97142	−0.421369
$561$	−1.44709	−0.0610963
$562$	2.77519	0.117064
$563$	−17.6352	−0.743233	−0.371617	−	0.928386i	$-0.621196\pi$
$563$	−17.6352	−0.743233	−0.371617	+	0.928386i	$0.621196\pi$
$564$	−5.70667	−0.240294
$565$	−10.1086	−0.425274
$566$	−18.9969	−0.798501
$567$	−2.85096	−0.119729
$568$	−17.4381	−0.731687
$569$	−3.44843	−0.144566	−0.0722828	−	0.997384i	$-0.523028\pi$
$569$	−3.44843	−0.144566	−0.0722828	+	0.997384i	$0.523028\pi$
$570$	0.364420	0.0152639
$571$	−19.8965	−0.832641	−0.416320	−	0.909218i	$-0.636681\pi$
$571$	−19.8965	−0.832641	−0.416320	+	0.909218i	$0.636681\pi$
$572$	−4.00152	−0.167312
$573$	−13.8309	−0.577792
$574$	42.4579	1.77216
$575$	−1.73395	−0.0723107
$576$	8.77811	0.365754
$577$	6.68801	0.278426	0.139213	−	0.990262i	$-0.455543\pi$
$577$	6.68801	0.278426	0.139213	+	0.990262i	$0.455543\pi$
$578$	−1.19134	−0.0495531
$579$	3.20089	0.133025
$580$	−7.35755	−0.305506
$581$	−1.11181	−0.0461256
$582$	8.19307	0.339614
$583$	−2.20382	−0.0912728
$584$	−14.7167	−0.608981
$585$	−6.65823	−0.275284
$586$	−13.2156	−0.545931
$587$	34.1475	1.40942	0.704709	−	0.709497i	$-0.251078\pi$
$587$	34.1475	1.40942	0.704709	+	0.709497i	$0.251078\pi$
$588$	0.655037	0.0270133
$589$	−1.25549	−0.0517314
$590$	2.76325	0.113761
$591$	5.37817	0.221228
$592$	27.3289	1.12321
$593$	−9.70200	−0.398413	−0.199207	−	0.979957i	$-0.563837\pi$
$593$	−9.70200	−0.398413	−0.199207	+	0.979957i	$0.563837\pi$
$594$	1.72398	0.0707356
$595$	3.98643	0.163428
$596$	−2.88058	−0.117993
$597$	13.4715	0.551353
$598$	−3.23054	−0.132106
$599$	9.71081	0.396773	0.198386	−	0.980124i	$-0.436430\pi$
$599$	9.71081	0.396773	0.198386	+	0.980124i	$0.436430\pi$
$600$	9.36132	0.382174
$601$	1.22217	0.0498535	0.0249267	−	0.999689i	$-0.492065\pi$
$601$	1.22217	0.0498535	0.0249267	+	0.999689i	$0.492065\pi$
$602$	−1.64171	−0.0669112
$603$	7.18516	0.292602
$604$	−5.11425	−0.208096
$605$	12.4529	0.506284
$606$	−2.95462	−0.120023
$607$	−23.2923	−0.945407	−0.472703	−	0.881222i	$-0.656722\pi$
$607$	−23.2923	−0.945407	−0.472703	+	0.881222i	$0.656722\pi$
$608$	0.693276	0.0281161
$609$	−25.8326	−1.04679
$610$	4.51684	0.182881
$611$	−46.7935	−1.89306
$612$	−0.580715	−0.0234740
$613$	−11.3368	−0.457890	−0.228945	−	0.973439i	$-0.573528\pi$
$613$	−11.3368	−0.457890	−0.228945	+	0.973439i	$0.573528\pi$
$614$	10.5670	0.426447
$615$	17.4793	0.704834
$616$	−12.6842	−0.511061
$617$	−36.7762	−1.48056	−0.740278	−	0.672301i	$-0.765306\pi$
$617$	−36.7762	−1.48056	−0.740278	+	0.672301i	$0.765306\pi$
$618$	−0.0348130	−0.00140038
$619$	13.7345	0.552037	0.276018	−	0.961152i	$-0.410985\pi$
$619$	13.7345	0.552037	0.276018	+	0.961152i	$0.410985\pi$
$620$	4.66007	0.187153
$621$	−0.569474	−0.0228522
$622$	−21.2470	−0.851929
$623$	9.45909	0.378971
$624$	11.9107	0.476811
$625$	−0.504911	−0.0201964
$626$	−9.04261	−0.361415
$627$	0.316571	0.0126426
$628$	−0.580715	−0.0231730
$629$	−10.9257	−0.435637
$630$	−4.74918	−0.189212
$631$	17.1548	0.682922	0.341461	−	0.939896i	$-0.389078\pi$
$631$	17.1548	0.682922	0.341461	+	0.939896i	$0.389078\pi$
$632$	40.7390	1.62051
$633$	8.33660	0.331350
$634$	37.4570	1.48761
$635$	20.4435	0.811275
$636$	−0.884386	−0.0350682
$637$	5.37117	0.212814
$638$	15.6210	0.618441
$639$	−5.67185	−0.224375
$640$	5.76028	0.227695
$641$	14.4970	0.572598	0.286299	−	0.958140i	$-0.407575\pi$
$641$	14.4970	0.572598	0.286299	+	0.958140i	$0.407575\pi$
$642$	19.9513	0.787416
$643$	−34.0152	−1.34143	−0.670714	−	0.741716i	$-0.734012\pi$
$643$	−34.0152	−1.34143	−0.670714	+	0.741716i	$0.734012\pi$
$644$	0.942819	0.0371523
$645$	−0.675871	−0.0266124
$646$	0.260621	0.0102540
$647$	46.3234	1.82116	0.910581	−	0.413330i	$-0.135634\pi$
$647$	46.3234	1.82116	0.910581	+	0.413330i	$0.135634\pi$
$648$	3.07450	0.120778
$649$	2.40043	0.0942251
$650$	17.2728	0.677496
$651$	16.3617	0.641265
$652$	0.497529	0.0194847
$653$	−3.82490	−0.149680	−0.0748400	−	0.997196i	$-0.523845\pi$
$653$	−3.82490	−0.149680	−0.0748400	+	0.997196i	$0.523845\pi$
$654$	20.8411	0.814950
$655$	12.4389	0.486029
$656$	−31.2683	−1.22082
$657$	−4.78669	−0.186747
$658$	−33.3769	−1.30117
$659$	−6.70870	−0.261334	−0.130667	−	0.991426i	$-0.541712\pi$
$659$	−6.70870	−0.261334	−0.130667	+	0.991426i	$0.541712\pi$
$660$	−1.17504	−0.0457383
$661$	−35.4219	−1.37775	−0.688877	−	0.724879i	$-0.741896\pi$
$661$	−35.4219	−1.37775	−0.688877	+	0.724879i	$0.741896\pi$
$662$	32.1420	1.24923
$663$	−4.76174	−0.184931
$664$	1.19898	0.0465296
$665$	−0.872086	−0.0338181
$666$	13.0162	0.504368
$667$	−5.16002	−0.199797
$668$	−7.77159	−0.300692
$669$	23.5273	0.909617
$670$	11.9692	0.462410
$671$	3.92377	0.151475
$672$	−9.03488	−0.348528
$673$	4.14453	0.159760	0.0798800	−	0.996804i	$-0.474546\pi$
$673$	4.14453	0.159760	0.0798800	+	0.996804i	$0.474546\pi$
$674$	−1.06665	−0.0410857
$675$	3.04483	0.117195
$676$	−5.61795	−0.216075
$677$	−2.75375	−0.105835	−0.0529177	−	0.998599i	$-0.516852\pi$
$677$	−2.75375	−0.105835	−0.0529177	+	0.998599i	$0.516852\pi$
$678$	8.61261	0.330765
$679$	−19.6066	−0.752434
$680$	−4.29900	−0.164859
$681$	18.7461	0.718353
$682$	−9.89390	−0.378857
$683$	14.7394	0.563987	0.281993	−	0.959416i	$-0.409004\pi$
$683$	14.7394	0.563987	0.281993	+	0.959416i	$0.409004\pi$
$684$	0.127039	0.00485747
$685$	−17.4468	−0.666607
$686$	−19.9441	−0.761468
$687$	−13.2865	−0.506911
$688$	1.20905	0.0460945
$689$	−7.25179	−0.276271
$690$	−0.948640	−0.0361141
$691$	−34.5874	−1.31577	−0.657883	−	0.753120i	$-0.728548\pi$
$691$	−34.5874	−1.31577	−0.657883	+	0.753120i	$0.728548\pi$
$692$	0.551227	0.0209545
$693$	−4.12561	−0.156719
$694$	−8.22685	−0.312287
$695$	16.7594	0.635719
$696$	27.8581	1.05596
$697$	12.5006	0.473495
$698$	−0.408564	−0.0154644
$699$	8.94158	0.338202
$700$	−5.04100	−0.190532
$701$	−14.5551	−0.549738	−0.274869	−	0.961482i	$-0.588634\pi$
$701$	−14.5551	−0.549738	−0.274869	+	0.961482i	$0.588634\pi$
$702$	5.67284	0.214108
$703$	2.39015	0.0901462
$704$	12.7027	0.478752
$705$	−13.7408	−0.517509
$706$	38.2064	1.43792
$707$	7.07063	0.265918
$708$	0.963287	0.0362025
$709$	25.1798	0.945646	0.472823	−	0.881157i	$-0.343235\pi$
$709$	25.1798	0.945646	0.472823	+	0.881157i	$0.343235\pi$
$710$	−9.44826	−0.354587
$711$	13.2506	0.496937
$712$	−10.2008	−0.382290
$713$	3.26821	0.122396
$714$	−3.39646	−0.127109
$715$	−9.63508	−0.360331
$716$	−6.17234	−0.230671
$717$	−0.880442	−0.0328807
$718$	13.1881	0.492177
$719$	29.0504	1.08340	0.541699	−	0.840572i	$-0.317781\pi$
$719$	29.0504	1.08340	0.541699	+	0.840572i	$0.317781\pi$
$720$	3.49756	0.130346
$721$	0.0833101	0.00310263
$722$	22.5784	0.840281
$723$	9.29638	0.345736
$724$	−8.37340	−0.311195
$725$	27.5892	1.02464
$726$	−10.6100	−0.393772
$727$	−40.7904	−1.51283	−0.756415	−	0.654092i	$-0.773051\pi$
$727$	−40.7904	−1.51283	−0.756415	+	0.654092i	$0.773051\pi$
$728$	−41.7381	−1.54692
$729$	1.00000	0.0370370
$730$	−7.97376	−0.295122
$731$	−0.483360	−0.0178777
$732$	1.57460	0.0581989
$733$	−38.1943	−1.41074	−0.705370	−	0.708840i	$-0.749219\pi$
$733$	−38.1943	−1.41074	−0.705370	+	0.708840i	$0.749219\pi$
$734$	3.51180	0.129623
$735$	1.57723	0.0581771
$736$	−1.80470	−0.0665221
$737$	10.3976	0.383001
$738$	−14.8925	−0.548199
$739$	−2.56431	−0.0943296	−0.0471648	−	0.998887i	$-0.515019\pi$
$739$	−2.56431	−0.0943296	−0.0471648	+	0.998887i	$0.515019\pi$
$740$	−8.87167	−0.326129
$741$	1.04170	0.0382677
$742$	−5.17256	−0.189891
$743$	22.9683	0.842624	0.421312	−	0.906916i	$-0.361570\pi$
$743$	22.9683	0.842624	0.421312	+	0.906916i	$0.361570\pi$
$744$	−17.6446	−0.646882
$745$	−6.93600	−0.254115
$746$	−18.9133	−0.692467
$747$	0.389976	0.0142685
$748$	−0.840349	−0.0307262
$749$	−47.7451	−1.74457
$750$	13.4012	0.489343
$751$	−8.91482	−0.325306	−0.162653	−	0.986683i	$-0.552005\pi$
$751$	−8.91482	−0.325306	−0.162653	+	0.986683i	$0.552005\pi$
$752$	24.5806	0.896362
$753$	25.8183	0.940871
$754$	51.4018	1.87194
$755$	−12.3144	−0.448165
$756$	−1.65560	−0.0602135
$757$	21.5700	0.783975	0.391988	−	0.919970i	$-0.371788\pi$
$757$	21.5700	0.783975	0.391988	+	0.919970i	$0.371788\pi$
$758$	−17.6592	−0.641411
$759$	−0.824082	−0.0299123
$760$	0.940465	0.0341143
$761$	−37.8485	−1.37201	−0.686004	−	0.727598i	$-0.740637\pi$
$761$	−37.8485	−1.37201	−0.686004	+	0.727598i	$0.740637\pi$
$762$	−17.4179	−0.630986
$763$	−49.8742	−1.80557
$764$	−8.03179	−0.290580
$765$	−1.39828	−0.0505548
$766$	−24.6831	−0.891836
$767$	7.89875	0.285207
$768$	12.6484	0.456411
$769$	5.76472	0.207881	0.103941	−	0.994584i	$-0.466855\pi$
$769$	5.76472	0.207881	0.103941	+	0.994584i	$0.466855\pi$
$770$	−6.87251	−0.247668
$771$	29.0500	1.04621
$772$	1.85881	0.0668999
$773$	−34.4380	−1.23865	−0.619324	−	0.785135i	$-0.712593\pi$
$773$	−34.4380	−1.23865	−0.619324	+	0.785135i	$0.712593\pi$
$774$	0.575845	0.0206983
$775$	−17.4743	−0.627694
$776$	21.1440	0.759025
$777$	−31.1488	−1.11746
$778$	−19.6463	−0.704353
$779$	−2.73468	−0.0979802
$780$	−3.86653	−0.138444
$781$	−8.20769	−0.293694
$782$	−0.678436	−0.0242608
$783$	9.06102	0.323815
$784$	−2.82147	−0.100767
$785$	−1.39828	−0.0499066
$786$	−10.5980	−0.378019
$787$	5.05693	0.180260	0.0901301	−	0.995930i	$-0.471272\pi$
$787$	5.05693	0.180260	0.0901301	+	0.995930i	$0.471272\pi$
$788$	3.12318	0.111259
$789$	−27.6035	−0.982711
$790$	22.0731	0.785326
$791$	−20.6106	−0.732830
$792$	4.44909	0.158092
$793$	12.9114	0.458497
$794$	29.4425	1.04487
$795$	−2.12947	−0.0755246
$796$	7.82311	0.277283
$797$	−12.5727	−0.445347	−0.222674	−	0.974893i	$-0.571478\pi$
$797$	−12.5727	−0.445347	−0.222674	+	0.974893i	$0.571478\pi$
$798$	0.743022	0.0263027
$799$	−9.82697	−0.347653
$800$	9.64925	0.341152
$801$	−3.31786	−0.117231
$802$	−31.5137	−1.11279
$803$	−6.92679	−0.244441
$804$	4.17253	0.147154
$805$	2.27017	0.0800129
$806$	−32.5565	−1.14675
$807$	−19.9668	−0.702866
$808$	−7.62503	−0.268248
$809$	−7.27908	−0.255919	−0.127959	−	0.991779i	$-0.540843\pi$
$809$	−7.27908	−0.255919	−0.127959	+	0.991779i	$0.540843\pi$
$810$	1.66582	0.0585309
$811$	−20.2287	−0.710325	−0.355163	−	0.934805i	$-0.615575\pi$
$811$	−20.2287	−0.710325	−0.355163	+	0.934805i	$0.615575\pi$
$812$	−15.0014	−0.526446
$813$	22.3238	0.782931
$814$	18.8357	0.660190
$815$	1.19798	0.0419633
$816$	2.50134	0.0875644
$817$	0.105742	0.00369943
$818$	29.9625	1.04761
$819$	−13.5755	−0.474368
$820$	10.1505	0.354471
$821$	−7.19768	−0.251201	−0.125600	−	0.992081i	$-0.540086\pi$
$821$	−7.19768	−0.251201	−0.125600	+	0.992081i	$0.540086\pi$
$822$	14.8647	0.518467
$823$	11.1047	0.387087	0.193543	−	0.981092i	$-0.438002\pi$
$823$	11.1047	0.387087	0.193543	+	0.981092i	$0.438002\pi$
$824$	−0.0898424	−0.00312981
$825$	4.40615	0.153402
$826$	5.63403	0.196033
$827$	−27.2121	−0.946256	−0.473128	−	0.880994i	$-0.656875\pi$
$827$	−27.2121	−0.946256	−0.473128	+	0.880994i	$0.656875\pi$
$828$	−0.330702	−0.0114927
$829$	16.6533	0.578392	0.289196	−	0.957270i	$-0.406612\pi$
$829$	16.6533	0.578392	0.289196	+	0.957270i	$0.406612\pi$
$830$	0.649630	0.0225490
$831$	−8.02210	−0.278283
$832$	41.7991	1.44912
$833$	1.12798	0.0390823
$834$	−14.2791	−0.494444
$835$	−18.7128	−0.647584
$836$	0.183838	0.00635816
$837$	−5.73900	−0.198369
$838$	−9.13933	−0.315713
$839$	−26.3257	−0.908863	−0.454431	−	0.890782i	$-0.650157\pi$
$839$	−26.3257	−0.908863	−0.454431	+	0.890782i	$0.650157\pi$
$840$	−12.2563	−0.422882
$841$	53.1021	1.83111
$842$	24.9417	0.859548
$843$	2.32948	0.0802314
$844$	4.84119	0.166641
$845$	−13.5272	−0.465350
$846$	11.7072	0.402503
$847$	25.3904	0.872426
$848$	3.80936	0.130814
$849$	−15.9459	−0.547262
$850$	3.62741	0.124419
$851$	−6.22191	−0.213284
$852$	−3.29373	−0.112841
$853$	23.4588	0.803212	0.401606	−	0.915812i	$-0.368452\pi$
$853$	23.4588	0.803212	0.401606	+	0.915812i	$0.368452\pi$
$854$	9.20944	0.315141
$855$	0.305892	0.0104613
$856$	51.4887	1.75985
$857$	−40.9244	−1.39795	−0.698976	−	0.715145i	$-0.746361\pi$
$857$	−40.9244	−1.39795	−0.698976	+	0.715145i	$0.746361\pi$
$858$	8.20913	0.280255
$859$	−14.4393	−0.492663	−0.246331	−	0.969186i	$-0.579225\pi$
$859$	−14.4393	−0.492663	−0.246331	+	0.969186i	$0.579225\pi$
$860$	−0.392488	−0.0133837
$861$	35.6388	1.21457
$862$	−19.8285	−0.675362
$863$	19.2082	0.653856	0.326928	−	0.945049i	$-0.393986\pi$
$863$	19.2082	0.653856	0.326928	+	0.945049i	$0.393986\pi$
$864$	3.16906	0.107814
$865$	1.32727	0.0451287
$866$	28.3591	0.963683
$867$	−1.00000	−0.0339618
$868$	9.50147	0.322501
$869$	19.1749	0.650463
$870$	15.0940	0.511735
$871$	34.2139	1.15929
$872$	53.7848	1.82138
$873$	6.87720	0.232758
$874$	0.148417	0.00502028
$875$	−32.0701	−1.08417
$876$	−2.77970	−0.0939175
$877$	−6.04207	−0.204026	−0.102013	−	0.994783i	$-0.532528\pi$
$877$	−6.04207	−0.204026	−0.102013	+	0.994783i	$0.532528\pi$
$878$	11.6648	0.393667
$879$	−11.0931	−0.374160
$880$	5.06130	0.170616
$881$	4.86732	0.163984	0.0819921	−	0.996633i	$-0.473872\pi$
$881$	4.86732	0.163984	0.0819921	+	0.996633i	$0.473872\pi$
$882$	−1.34381	−0.0452484
$883$	−14.9703	−0.503790	−0.251895	−	0.967755i	$-0.581054\pi$
$883$	−14.9703	−0.503790	−0.251895	+	0.967755i	$0.581054\pi$
$884$	−2.76522	−0.0930043
$885$	2.31945	0.0779675
$886$	−23.4214	−0.786857
$887$	8.52967	0.286398	0.143199	−	0.989694i	$-0.454261\pi$
$887$	8.52967	0.286398	0.143199	+	0.989694i	$0.454261\pi$
$888$	33.5911	1.12724
$889$	41.6825	1.39799
$890$	−5.52695	−0.185264
$891$	1.44709	0.0484794
$892$	13.6626	0.457459
$893$	2.14978	0.0719398
$894$	5.90951	0.197643
$895$	−14.8621	−0.496784
$896$	11.7447	0.392363
$897$	−2.71169	−0.0905406
$898$	28.0826	0.937129
$899$	−52.0012	−1.73434
$900$	1.76818	0.0589392
$901$	−1.52293	−0.0507360
$902$	−21.5508	−0.717563
$903$	−1.37804	−0.0458583
$904$	22.2267	0.739249
$905$	−20.1619	−0.670204
$906$	10.4919	0.348570
$907$	23.5979	0.783557	0.391778	−	0.920060i	$-0.371860\pi$
$907$	23.5979	0.783557	0.391778	+	0.920060i	$0.371860\pi$
$908$	10.8861	0.361270
$909$	−2.48008	−0.0822592
$910$	−22.6144	−0.749660
$911$	42.0953	1.39468	0.697339	−	0.716741i	$-0.254367\pi$
$911$	42.0953	1.39468	0.697339	+	0.716741i	$0.254367\pi$
$912$	−0.547202	−0.0181197
$913$	0.564332	0.0186767
$914$	24.4535	0.808851
$915$	3.79140	0.125340
$916$	−7.71566	−0.254933
$917$	25.3619	0.837523
$918$	1.19134	0.0393200
$919$	−52.7067	−1.73863	−0.869316	−	0.494257i	$-0.835440\pi$
$919$	−52.7067	−1.73863	−0.869316	+	0.494257i	$0.835440\pi$
$920$	−2.44817	−0.0807138
$921$	8.86982	0.292271
$922$	−31.4393	−1.03540
$923$	−27.0079	−0.888975
$924$	−2.39580	−0.0788161
$925$	33.2669	1.09381
$926$	−40.8174	−1.34134
$927$	−0.0292218	−0.000959769 0
$928$	28.7150	0.942615
$929$	34.6377	1.13643	0.568213	−	0.822881i	$-0.307635\pi$
$929$	34.6377	1.13643	0.568213	+	0.822881i	$0.307635\pi$
$930$	−9.56013	−0.313489
$931$	−0.246762	−0.00808730
$932$	5.19251	0.170086
$933$	−17.8346	−0.583879
$934$	−17.7404	−0.580484
$935$	−2.02343	−0.0661734
$936$	14.6400	0.478523
$937$	−27.5677	−0.900597	−0.450298	−	0.892878i	$-0.648682\pi$
$937$	−27.5677	−0.900597	−0.450298	+	0.892878i	$0.648682\pi$
$938$	24.4041	0.796822
$939$	−7.59030	−0.247700
$940$	−7.97950	−0.260262
$941$	−1.97969	−0.0645360	−0.0322680	−	0.999479i	$-0.510273\pi$
$941$	−1.97969	−0.0645360	−0.0322680	+	0.999479i	$0.510273\pi$
$942$	1.19134	0.0388159
$943$	7.11878	0.231819
$944$	−4.14921	−0.135045
$945$	−3.98643	−0.129679
$946$	0.833301	0.0270930
$947$	−36.7555	−1.19439	−0.597197	−	0.802095i	$-0.703719\pi$
$947$	−36.7555	−1.19439	−0.597197	+	0.802095i	$0.703719\pi$
$948$	7.69483	0.249916
$949$	−22.7930	−0.739892
$950$	−0.793547	−0.0257461
$951$	31.4411	1.01955
$952$	−8.76529	−0.284085
$953$	−49.2206	−1.59441	−0.797206	−	0.603707i	$-0.793690\pi$
$953$	−49.2206	−1.59441	−0.797206	+	0.603707i	$0.793690\pi$
$954$	1.81432	0.0587408
$955$	−19.3394	−0.625807
$956$	−0.511286	−0.0165362
$957$	13.1121	0.423855
$958$	−21.5846	−0.697368
$959$	−35.5724	−1.14869
$960$	12.2742	0.396148
$961$	1.93615	0.0624564
$962$	61.9799	1.99831
$963$	16.7470	0.539665
$964$	5.39855	0.173875
$965$	4.47573	0.144079
$966$	−1.93419	−0.0622317
$967$	−17.5265	−0.563615	−0.281807	−	0.959471i	$-0.590934\pi$
$967$	−17.5265	−0.563615	−0.281807	+	0.959471i	$0.590934\pi$
$968$	−27.3813	−0.880068
$969$	0.218764	0.00702770
$970$	11.4562	0.367835
$971$	13.8099	0.443182	0.221591	−	0.975140i	$-0.428875\pi$
$971$	13.8099	0.443182	0.221591	+	0.975140i	$0.428875\pi$
$972$	0.580715	0.0186264
$973$	34.1709	1.09547
$974$	−17.3942	−0.557345
$975$	14.4987	0.464329
$976$	−6.78234	−0.217097
$977$	−59.9829	−1.91902	−0.959511	−	0.281671i	$-0.909111\pi$
$977$	−59.9829	−1.91902	−0.959511	+	0.281671i	$0.909111\pi$
$978$	−1.02068	−0.0326378
$979$	−4.80125	−0.153449
$980$	0.915923	0.0292581
$981$	17.4938	0.558535
$982$	19.9073	0.635267
$983$	−12.6314	−0.402879	−0.201439	−	0.979501i	$-0.564562\pi$
$983$	−12.6314	−0.402879	−0.201439	+	0.979501i	$0.564562\pi$
$984$	−38.4332	−1.22521
$985$	7.52016	0.239612
$986$	10.7947	0.343774
$987$	−28.0163	−0.891769
$988$	0.604929	0.0192453
$989$	−0.275261	−0.00875279
$990$	2.41059	0.0766137
$991$	35.8154	1.13772	0.568858	−	0.822436i	$-0.307386\pi$
$991$	35.8154	1.13772	0.568858	+	0.822436i	$0.307386\pi$
$992$	−18.1873	−0.577446
$993$	26.9797	0.856176
$994$	−19.2642	−0.611023
$995$	18.8369	0.597170
$996$	0.226465	0.00717582
$997$	−0.919257	−0.0291132	−0.0145566	−	0.999894i	$-0.504634\pi$
$997$	−0.919257	−0.0291132	−0.0145566	+	0.999894i	$0.504634\pi$
$998$	29.9317	0.947472
$999$	10.9257	0.345674

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.12	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.12	✓	39	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-1.19134 q^{2} -1.00000 q^{3} -0.580715 q^{4} -1.39828 q^{5} +1.19134 q^{6} -2.85096 q^{7} +3.07450 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.19134 q^{2} -1.00000 q^{3} -0.580715 q^{4} -1.39828 q^{5} +1.19134 q^{6} -2.85096 q^{7} +3.07450 q^{8} +1.00000 q^{9} +1.66582 q^{10} +1.44709 q^{11} +0.580715 q^{12} +4.76174 q^{13} +3.39646 q^{14} +1.39828 q^{15} -2.50134 q^{16} +1.00000 q^{17} -1.19134 q^{18} -0.218764 q^{19} +0.812000 q^{20} +2.85096 q^{21} -1.72398 q^{22} +0.569474 q^{23} -3.07450 q^{24} -3.04483 q^{25} -5.67284 q^{26} -1.00000 q^{27} +1.65560 q^{28} -9.06102 q^{29} -1.66582 q^{30} +5.73900 q^{31} -3.16906 q^{32} -1.44709 q^{33} -1.19134 q^{34} +3.98643 q^{35} -0.580715 q^{36} -10.9257 q^{37} +0.260621 q^{38} -4.76174 q^{39} -4.29900 q^{40} +12.5006 q^{41} -3.39646 q^{42} -0.483360 q^{43} -0.840349 q^{44} -1.39828 q^{45} -0.678436 q^{46} -9.82697 q^{47} +2.50134 q^{48} +1.12798 q^{49} +3.62741 q^{50} -1.00000 q^{51} -2.76522 q^{52} -1.52293 q^{53} +1.19134 q^{54} -2.02343 q^{55} -8.76529 q^{56} +0.218764 q^{57} +10.7947 q^{58} +1.65879 q^{59} -0.812000 q^{60} +2.71148 q^{61} -6.83709 q^{62} -2.85096 q^{63} +8.77811 q^{64} -6.65823 q^{65} +1.72398 q^{66} +7.18516 q^{67} -0.580715 q^{68} -0.569474 q^{69} -4.74918 q^{70} -5.67185 q^{71} +3.07450 q^{72} -4.78669 q^{73} +13.0162 q^{74} +3.04483 q^{75} +0.127039 q^{76} -4.12561 q^{77} +5.67284 q^{78} +13.2506 q^{79} +3.49756 q^{80} +1.00000 q^{81} -14.8925 q^{82} +0.389976 q^{83} -1.65560 q^{84} -1.39828 q^{85} +0.575845 q^{86} +9.06102 q^{87} +4.44909 q^{88} -3.31786 q^{89} +1.66582 q^{90} -13.5755 q^{91} -0.330702 q^{92} -5.73900 q^{93} +11.7072 q^{94} +0.305892 q^{95} +3.16906 q^{96} +6.87720 q^{97} -1.34381 q^{98} +1.44709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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