LMFDB - Embedded newform 8006.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.63641 q^{3} +1.00000 q^{4} -3.89748 q^{5} -1.63641 q^{6} +0.627952 q^{7} +1.00000 q^{8} -0.322178 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.63641 q^{3} +1.00000 q^{4} -3.89748 q^{5} -1.63641 q^{6} +0.627952 q^{7} +1.00000 q^{8} -0.322178 q^{9} -3.89748 q^{10} -3.73459 q^{11} -1.63641 q^{12} -4.01386 q^{13} +0.627952 q^{14} +6.37785 q^{15} +1.00000 q^{16} +5.37624 q^{17} -0.322178 q^{18} +5.53191 q^{19} -3.89748 q^{20} -1.02758 q^{21} -3.73459 q^{22} -6.27819 q^{23} -1.63641 q^{24} +10.1903 q^{25} -4.01386 q^{26} +5.43643 q^{27} +0.627952 q^{28} +7.65966 q^{29} +6.37785 q^{30} -1.61550 q^{31} +1.00000 q^{32} +6.11131 q^{33} +5.37624 q^{34} -2.44743 q^{35} -0.322178 q^{36} +8.63546 q^{37} +5.53191 q^{38} +6.56830 q^{39} -3.89748 q^{40} -6.35516 q^{41} -1.02758 q^{42} -7.36296 q^{43} -3.73459 q^{44} +1.25568 q^{45} -6.27819 q^{46} +7.87796 q^{47} -1.63641 q^{48} -6.60568 q^{49} +10.1903 q^{50} -8.79771 q^{51} -4.01386 q^{52} +5.97655 q^{53} +5.43643 q^{54} +14.5555 q^{55} +0.627952 q^{56} -9.05244 q^{57} +7.65966 q^{58} -0.290523 q^{59} +6.37785 q^{60} +4.60589 q^{61} -1.61550 q^{62} -0.202312 q^{63} +1.00000 q^{64} +15.6439 q^{65} +6.11131 q^{66} +2.20116 q^{67} +5.37624 q^{68} +10.2737 q^{69} -2.44743 q^{70} +11.7865 q^{71} -0.322178 q^{72} +8.39674 q^{73} +8.63546 q^{74} -16.6755 q^{75} +5.53191 q^{76} -2.34514 q^{77} +6.56830 q^{78} -13.1409 q^{79} -3.89748 q^{80} -7.92967 q^{81} -6.35516 q^{82} -12.0767 q^{83} -1.02758 q^{84} -20.9538 q^{85} -7.36296 q^{86} -12.5343 q^{87} -3.73459 q^{88} +0.966188 q^{89} +1.25568 q^{90} -2.52051 q^{91} -6.27819 q^{92} +2.64361 q^{93} +7.87796 q^{94} -21.5605 q^{95} -1.63641 q^{96} -10.8090 q^{97} -6.60568 q^{98} +1.20320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9 - 9 * q^10 - 48 * q^11 - 15 * q^12 - 30 * q^13 - 29 * q^14 - 51 * q^15 + 69 * q^16 - 37 * q^17 + 40 * q^18 - 72 * q^19 - 9 * q^20 - 38 * q^21 - 48 * q^22 - 75 * q^23 - 15 * q^24 + 18 * q^25 - 30 * q^26 - 48 * q^27 - 29 * q^28 - 27 * q^29 - 51 * q^30 - 61 * q^31 + 69 * q^32 - 29 * q^33 - 37 * q^34 - 64 * q^35 + 40 * q^36 - 42 * q^37 - 72 * q^38 - 68 * q^39 - 9 * q^40 - 49 * q^41 - 38 * q^42 - 95 * q^43 - 48 * q^44 - 20 * q^45 - 75 * q^46 - 62 * q^47 - 15 * q^48 - 4 * q^49 + 18 * q^50 - 76 * q^51 - 30 * q^52 - 28 * q^53 - 48 * q^54 - 76 * q^55 - 29 * q^56 - 44 * q^57 - 27 * q^58 - 68 * q^59 - 51 * q^60 - 62 * q^61 - 61 * q^62 - 91 * q^63 + 69 * q^64 - 79 * q^65 - 29 * q^66 - 116 * q^67 - 37 * q^68 - 23 * q^69 - 64 * q^70 - 89 * q^71 + 40 * q^72 - 60 * q^73 - 42 * q^74 - 47 * q^75 - 72 * q^76 + 5 * q^77 - 68 * q^78 - 170 * q^79 - 9 * q^80 - 3 * q^81 - 49 * q^82 - 82 * q^83 - 38 * q^84 - 81 * q^85 - 95 * q^86 - 51 * q^87 - 48 * q^88 - 78 * q^89 - 20 * q^90 - 85 * q^91 - 75 * q^92 - 21 * q^93 - 62 * q^94 - 70 * q^95 - 15 * q^96 - 60 * q^97 - 4 * q^98 - 148 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.63641	−0.944779	−0.472389	−	0.881390i	$-0.656608\pi$
$3$	−1.63641	−0.944779	−0.472389	+	0.881390i	$0.656608\pi$
$4$	1.00000	0.500000
$5$	−3.89748	−1.74300	−0.871502	−	0.490391i	$-0.836854\pi$
$5$	−3.89748	−1.74300	−0.871502	+	0.490391i	$0.836854\pi$
$6$	−1.63641	−0.668060
$7$	0.627952	0.237343	0.118672	−	0.992934i	$-0.462136\pi$
$7$	0.627952	0.237343	0.118672	+	0.992934i	$0.462136\pi$
$8$	1.00000	0.353553
$9$	−0.322178	−0.107393
$10$	−3.89748	−1.23249
$11$	−3.73459	−1.12602	−0.563011	−	0.826449i	$-0.690357\pi$
$11$	−3.73459	−1.12602	−0.563011	+	0.826449i	$0.690357\pi$
$12$	−1.63641	−0.472389
$13$	−4.01386	−1.11324	−0.556622	−	0.830766i	$-0.687903\pi$
$13$	−4.01386	−1.11324	−0.556622	+	0.830766i	$0.687903\pi$
$14$	0.627952	0.167827
$15$	6.37785	1.64675
$16$	1.00000	0.250000
$17$	5.37624	1.30393	0.651965	−	0.758249i	$-0.273945\pi$
$17$	5.37624	1.30393	0.651965	+	0.758249i	$0.273945\pi$
$18$	−0.322178	−0.0759381
$19$	5.53191	1.26911	0.634553	−	0.772879i	$-0.281184\pi$
$19$	5.53191	1.26911	0.634553	+	0.772879i	$0.281184\pi$
$20$	−3.89748	−0.871502
$21$	−1.02758	−0.224237
$22$	−3.73459	−0.796218
$23$	−6.27819	−1.30909	−0.654547	−	0.756021i	$-0.727141\pi$
$23$	−6.27819	−1.30909	−0.654547	+	0.756021i	$0.727141\pi$
$24$	−1.63641	−0.334030
$25$	10.1903	2.03807
$26$	−4.01386	−0.787183
$27$	5.43643	1.04624
$28$	0.627952	0.118672
$29$	7.65966	1.42236	0.711181	−	0.703009i	$-0.248161\pi$
$29$	7.65966	1.42236	0.711181	+	0.703009i	$0.248161\pi$
$30$	6.37785	1.16443
$31$	−1.61550	−0.290152	−0.145076	−	0.989421i	$-0.546343\pi$
$31$	−1.61550	−0.290152	−0.145076	+	0.989421i	$0.546343\pi$
$32$	1.00000	0.176777
$33$	6.11131	1.06384
$34$	5.37624	0.922018
$35$	−2.44743	−0.413691
$36$	−0.322178	−0.0536963
$37$	8.63546	1.41966	0.709831	−	0.704372i	$-0.248771\pi$
$37$	8.63546	1.41966	0.709831	+	0.704372i	$0.248771\pi$
$38$	5.53191	0.897394
$39$	6.56830	1.05177
$40$	−3.89748	−0.616245
$41$	−6.35516	−0.992510	−0.496255	−	0.868177i	$-0.665292\pi$
$41$	−6.35516	−0.992510	−0.496255	+	0.868177i	$0.665292\pi$
$42$	−1.02758	−0.158560
$43$	−7.36296	−1.12284	−0.561420	−	0.827531i	$-0.689745\pi$
$43$	−7.36296	−1.12284	−0.561420	+	0.827531i	$0.689745\pi$
$44$	−3.73459	−0.563011
$45$	1.25568	0.187186
$46$	−6.27819	−0.925669
$47$	7.87796	1.14912	0.574559	−	0.818463i	$-0.305173\pi$
$47$	7.87796	1.14912	0.574559	+	0.818463i	$0.305173\pi$
$48$	−1.63641	−0.236195
$49$	−6.60568	−0.943668
$50$	10.1903	1.44113
$51$	−8.79771	−1.23193
$52$	−4.01386	−0.556622
$53$	5.97655	0.820942	0.410471	−	0.911874i	$-0.365364\pi$
$53$	5.97655	0.820942	0.410471	+	0.911874i	$0.365364\pi$
$54$	5.43643	0.739804
$55$	14.5555	1.96266
$56$	0.627952	0.0839136
$57$	−9.05244	−1.19902
$58$	7.65966	1.00576
$59$	−0.290523	−0.0378229	−0.0189115	−	0.999821i	$-0.506020\pi$
$59$	−0.290523	−0.0378229	−0.0189115	+	0.999821i	$0.506020\pi$
$60$	6.37785	0.823377
$61$	4.60589	0.589724	0.294862	−	0.955540i	$-0.404726\pi$
$61$	4.60589	0.589724	0.294862	+	0.955540i	$0.404726\pi$
$62$	−1.61550	−0.205168
$63$	−0.202312	−0.0254889
$64$	1.00000	0.125000
$65$	15.6439	1.94039
$66$	6.11131	0.752250
$67$	2.20116	0.268914	0.134457	−	0.990919i	$-0.457071\pi$
$67$	2.20116	0.268914	0.134457	+	0.990919i	$0.457071\pi$
$68$	5.37624	0.651965
$69$	10.2737	1.23680
$70$	−2.44743	−0.292524
$71$	11.7865	1.39880	0.699399	−	0.714731i	$-0.253451\pi$
$71$	11.7865	1.39880	0.699399	+	0.714731i	$0.253451\pi$
$72$	−0.322178	−0.0379690
$73$	8.39674	0.982764	0.491382	−	0.870944i	$-0.336492\pi$
$73$	8.39674	0.982764	0.491382	+	0.870944i	$0.336492\pi$
$74$	8.63546	1.00385
$75$	−16.6755	−1.92552
$76$	5.53191	0.634553
$77$	−2.34514	−0.267254
$78$	6.56830	0.743714
$79$	−13.1409	−1.47847	−0.739233	−	0.673450i	$-0.764812\pi$
$79$	−13.1409	−1.47847	−0.739233	+	0.673450i	$0.764812\pi$
$80$	−3.89748	−0.435751
$81$	−7.92967	−0.881074
$82$	−6.35516	−0.701810
$83$	−12.0767	−1.32559	−0.662794	−	0.748802i	$-0.730629\pi$
$83$	−12.0767	−1.32559	−0.662794	+	0.748802i	$0.730629\pi$
$84$	−1.02758	−0.112119
$85$	−20.9538	−2.27276
$86$	−7.36296	−0.793968
$87$	−12.5343	−1.34382
$88$	−3.73459	−0.398109
$89$	0.966188	0.102416	0.0512079	−	0.998688i	$-0.483693\pi$
$89$	0.966188	0.102416	0.0512079	+	0.998688i	$0.483693\pi$
$90$	1.25568	0.132360
$91$	−2.52051	−0.264221
$92$	−6.27819	−0.654547
$93$	2.64361	0.274129
$94$	7.87796	0.812550
$95$	−21.5605	−2.21206
$96$	−1.63641	−0.167015
$97$	−10.8090	−1.09749	−0.548745	−	0.835989i	$-0.684894\pi$
$97$	−10.8090	−1.09749	−0.548745	+	0.835989i	$0.684894\pi$
$98$	−6.60568	−0.667274
$99$	1.20320	0.120926
$100$	10.1903	1.01903
$101$	6.02038	0.599050	0.299525	−	0.954088i	$-0.403172\pi$
$101$	6.02038	0.599050	0.299525	+	0.954088i	$0.403172\pi$
$102$	−8.79771	−0.871103
$103$	−7.21104	−0.710525	−0.355263	−	0.934767i	$-0.615609\pi$
$103$	−7.21104	−0.710525	−0.355263	+	0.934767i	$0.615609\pi$
$104$	−4.01386	−0.393591
$105$	4.00498	0.390846
$106$	5.97655	0.580494
$107$	−2.90040	−0.280392	−0.140196	−	0.990124i	$-0.544773\pi$
$107$	−2.90040	−0.280392	−0.140196	+	0.990124i	$0.544773\pi$
$108$	5.43643	0.523121
$109$	1.73499	0.166182	0.0830911	−	0.996542i	$-0.473521\pi$
$109$	1.73499	0.166182	0.0830911	+	0.996542i	$0.473521\pi$
$110$	14.5555	1.38781
$111$	−14.1311	−1.34127
$112$	0.627952	0.0593359
$113$	16.2173	1.52560	0.762798	−	0.646637i	$-0.223825\pi$
$113$	16.2173	1.52560	0.762798	+	0.646637i	$0.223825\pi$
$114$	−9.05244	−0.847839
$115$	24.4691	2.28176
$116$	7.65966	0.711181
$117$	1.29318	0.119554
$118$	−0.290523	−0.0267448
$119$	3.37602	0.309479
$120$	6.37785	0.582216
$121$	2.94718	0.267925
$122$	4.60589	0.416998
$123$	10.3996	0.937703
$124$	−1.61550	−0.145076
$125$	−20.2292	−1.80935
$126$	−0.202312	−0.0180234
$127$	−7.08793	−0.628952	−0.314476	−	0.949265i	$-0.601829\pi$
$127$	−7.08793	−0.628952	−0.314476	+	0.949265i	$0.601829\pi$
$128$	1.00000	0.0883883
$129$	12.0488	1.06084
$130$	15.6439	1.37206
$131$	10.5518	0.921917	0.460958	−	0.887422i	$-0.347506\pi$
$131$	10.5518	0.921917	0.460958	+	0.887422i	$0.347506\pi$
$132$	6.11131	0.531921
$133$	3.47377	0.301214
$134$	2.20116	0.190151
$135$	−21.1884	−1.82360
$136$	5.37624	0.461009
$137$	−21.3039	−1.82011	−0.910056	−	0.414486i	$-0.863961\pi$
$137$	−21.3039	−1.82011	−0.910056	+	0.414486i	$0.863961\pi$
$138$	10.2737	0.874553
$139$	−5.41061	−0.458922	−0.229461	−	0.973318i	$-0.573696\pi$
$139$	−5.41061	−0.458922	−0.229461	+	0.973318i	$0.573696\pi$
$140$	−2.44743	−0.206845
$141$	−12.8915	−1.08566
$142$	11.7865	0.989100
$143$	14.9901	1.25354
$144$	−0.322178	−0.0268482
$145$	−29.8533	−2.47918
$146$	8.39674	0.694919
$147$	10.8096	0.891558
$148$	8.63546	0.709831
$149$	16.3043	1.33570	0.667850	−	0.744296i	$-0.267215\pi$
$149$	16.3043	1.33570	0.667850	+	0.744296i	$0.267215\pi$
$150$	−16.6755	−1.36155
$151$	−22.5972	−1.83894	−0.919469	−	0.393163i	$-0.871381\pi$
$151$	−22.5972	−1.83894	−0.919469	+	0.393163i	$0.871381\pi$
$152$	5.53191	0.448697
$153$	−1.73211	−0.140033
$154$	−2.34514	−0.188977
$155$	6.29636	0.505736
$156$	6.56830	0.525885
$157$	−21.8354	−1.74266	−0.871329	−	0.490699i	$-0.836741\pi$
$157$	−21.8354	−1.74266	−0.871329	+	0.490699i	$0.836741\pi$
$158$	−13.1409	−1.04543
$159$	−9.78006	−0.775609
$160$	−3.89748	−0.308123
$161$	−3.94240	−0.310705
$162$	−7.92967	−0.623014
$163$	12.7450	0.998262	0.499131	−	0.866527i	$-0.333653\pi$
$163$	12.7450	0.998262	0.499131	+	0.866527i	$0.333653\pi$
$164$	−6.35516	−0.496255
$165$	−23.8187	−1.85428
$166$	−12.0767	−0.937332
$167$	13.6043	1.05273	0.526366	−	0.850258i	$-0.323554\pi$
$167$	13.6043	1.05273	0.526366	+	0.850258i	$0.323554\pi$
$168$	−1.02758	−0.0792798
$169$	3.11107	0.239313
$170$	−20.9538	−1.60708
$171$	−1.78226	−0.136293
$172$	−7.36296	−0.561420
$173$	13.5776	1.03229	0.516143	−	0.856503i	$-0.327367\pi$
$173$	13.5776	1.03229	0.516143	+	0.856503i	$0.327367\pi$
$174$	−12.5343	−0.950223
$175$	6.39903	0.483721
$176$	−3.73459	−0.281505
$177$	0.475414	0.0357343
$178$	0.966188	0.0724189
$179$	21.0500	1.57335	0.786676	−	0.617365i	$-0.211800\pi$
$179$	21.0500	1.57335	0.786676	+	0.617365i	$0.211800\pi$
$180$	1.25568	0.0935930
$181$	−14.7773	−1.09839	−0.549194	−	0.835695i	$-0.685065\pi$
$181$	−14.7773	−1.09839	−0.549194	+	0.835695i	$0.685065\pi$
$182$	−2.52051	−0.186833
$183$	−7.53710	−0.557159
$184$	−6.27819	−0.462835
$185$	−33.6565	−2.47448
$186$	2.64361	0.193839
$187$	−20.0781	−1.46825
$188$	7.87796	0.574559
$189$	3.41381	0.248318
$190$	−21.5605	−1.56416
$191$	−23.6401	−1.71053	−0.855267	−	0.518188i	$-0.826607\pi$
$191$	−23.6401	−1.71053	−0.855267	+	0.518188i	$0.826607\pi$
$192$	−1.63641	−0.118097
$193$	−22.3508	−1.60885	−0.804425	−	0.594055i	$-0.797526\pi$
$193$	−22.3508	−1.60885	−0.804425	+	0.594055i	$0.797526\pi$
$194$	−10.8090	−0.776043
$195$	−25.5998	−1.83324
$196$	−6.60568	−0.471834
$197$	−21.3992	−1.52463	−0.762316	−	0.647205i	$-0.775938\pi$
$197$	−21.3992	−1.52463	−0.762316	+	0.647205i	$0.775938\pi$
$198$	1.20320	0.0855079
$199$	7.93988	0.562843	0.281421	−	0.959584i	$-0.409194\pi$
$199$	7.93988	0.562843	0.281421	+	0.959584i	$0.409194\pi$
$200$	10.1903	0.720565
$201$	−3.60199	−0.254065
$202$	6.02038	0.423592
$203$	4.80989	0.337588
$204$	−8.79771	−0.615963
$205$	24.7691	1.72995
$206$	−7.21104	−0.502417
$207$	2.02270	0.140587
$208$	−4.01386	−0.278311
$209$	−20.6594	−1.42904
$210$	4.00498	0.276370
$211$	0.885911	0.0609886	0.0304943	−	0.999535i	$-0.490292\pi$
$211$	0.885911	0.0609886	0.0304943	+	0.999535i	$0.490292\pi$
$212$	5.97655	0.410471
$213$	−19.2875	−1.32155
$214$	−2.90040	−0.198267
$215$	28.6970	1.95712
$216$	5.43643	0.369902
$217$	−1.01445	−0.0688656
$218$	1.73499	0.117509
$219$	−13.7405	−0.928495
$220$	14.5555	0.981331
$221$	−21.5795	−1.45159
$222$	−14.1311	−0.948418
$223$	−2.20454	−0.147627	−0.0738135	−	0.997272i	$-0.523517\pi$
$223$	−2.20454	−0.147627	−0.0738135	+	0.997272i	$0.523517\pi$
$224$	0.627952	0.0419568
$225$	−3.28310	−0.218873
$226$	16.2173	1.07876
$227$	3.12712	0.207554	0.103777	−	0.994601i	$-0.466907\pi$
$227$	3.12712	0.207554	0.103777	+	0.994601i	$0.466907\pi$
$228$	−9.05244	−0.599512
$229$	−4.66998	−0.308601	−0.154301	−	0.988024i	$-0.549312\pi$
$229$	−4.66998	−0.308601	−0.154301	+	0.988024i	$0.549312\pi$
$230$	24.4691	1.61345
$231$	3.83760	0.252496
$232$	7.65966	0.502881
$233$	−14.2310	−0.932307	−0.466153	−	0.884704i	$-0.654361\pi$
$233$	−14.2310	−0.932307	−0.466153	+	0.884704i	$0.654361\pi$
$234$	1.29318	0.0845376
$235$	−30.7042	−2.00292
$236$	−0.290523	−0.0189115
$237$	21.5038	1.39682
$238$	3.37602	0.218835
$239$	17.6226	1.13991	0.569957	−	0.821675i	$-0.306960\pi$
$239$	17.6226	1.13991	0.569957	+	0.821675i	$0.306960\pi$
$240$	6.37785	0.411689
$241$	−0.720136	−0.0463880	−0.0231940	−	0.999731i	$-0.507384\pi$
$241$	−0.720136	−0.0463880	−0.0231940	+	0.999731i	$0.507384\pi$
$242$	2.94718	0.189452
$243$	−3.33314	−0.213821
$244$	4.60589	0.294862
$245$	25.7455	1.64482
$246$	10.3996	0.663056
$247$	−22.2043	−1.41283
$248$	−1.61550	−0.102584
$249$	19.7623	1.25239
$250$	−20.2292	−1.27941
$251$	15.3805	0.970811	0.485406	−	0.874289i	$-0.338672\pi$
$251$	15.3805	0.970811	0.485406	+	0.874289i	$0.338672\pi$
$252$	−0.202312	−0.0127445
$253$	23.4465	1.47407
$254$	−7.08793	−0.444736
$255$	34.2889	2.14725
$256$	1.00000	0.0625000
$257$	4.85813	0.303042	0.151521	−	0.988454i	$-0.451583\pi$
$257$	4.85813	0.303042	0.151521	+	0.988454i	$0.451583\pi$
$258$	12.0488	0.750125
$259$	5.42265	0.336947
$260$	15.6439	0.970195
$261$	−2.46777	−0.152751
$262$	10.5518	0.651894
$263$	−17.7487	−1.09443	−0.547217	−	0.836991i	$-0.684313\pi$
$263$	−17.7487	−1.09443	−0.547217	+	0.836991i	$0.684313\pi$
$264$	6.11131	0.376125
$265$	−23.2935	−1.43091
$266$	3.47377	0.212990
$267$	−1.58108	−0.0967602
$268$	2.20116	0.134457
$269$	−18.8930	−1.15193	−0.575963	−	0.817476i	$-0.695373\pi$
$269$	−18.8930	−1.15193	−0.575963	+	0.817476i	$0.695373\pi$
$270$	−21.1884	−1.28948
$271$	−2.92406	−0.177624	−0.0888120	−	0.996048i	$-0.528307\pi$
$271$	−2.92406	−0.177624	−0.0888120	+	0.996048i	$0.528307\pi$
$272$	5.37624	0.325983
$273$	4.12458	0.249631
$274$	−21.3039	−1.28701
$275$	−38.0567	−2.29491
$276$	10.2737	0.618402
$277$	−4.17430	−0.250809	−0.125405	−	0.992106i	$-0.540023\pi$
$277$	−4.17430	−0.250809	−0.125405	+	0.992106i	$0.540023\pi$
$278$	−5.41061	−0.324507
$279$	0.520477	0.0311602
$280$	−2.44743	−0.146262
$281$	28.1277	1.67796	0.838979	−	0.544163i	$-0.183153\pi$
$281$	28.1277	1.67796	0.838979	+	0.544163i	$0.183153\pi$
$282$	−12.8915	−0.767680
$283$	27.0615	1.60864	0.804319	−	0.594198i	$-0.202531\pi$
$283$	27.0615	1.60864	0.804319	+	0.594198i	$0.202531\pi$
$284$	11.7865	0.699399
$285$	35.2817	2.08991
$286$	14.9901	0.886385
$287$	−3.99074	−0.235566
$288$	−0.322178	−0.0189845
$289$	11.9040	0.700235
$290$	−29.8533	−1.75305
$291$	17.6880	1.03689
$292$	8.39674	0.491382
$293$	18.3293	1.07081	0.535404	−	0.844596i	$-0.320159\pi$
$293$	18.3293	1.07081	0.535404	+	0.844596i	$0.320159\pi$
$294$	10.8096	0.630427
$295$	1.13231	0.0659255
$296$	8.63546	0.501926
$297$	−20.3028	−1.17809
$298$	16.3043	0.944482
$299$	25.1998	1.45734
$300$	−16.6755	−0.962761
$301$	−4.62358	−0.266499
$302$	−22.5972	−1.30033
$303$	−9.85177	−0.565970
$304$	5.53191	0.317277
$305$	−17.9514	−1.02789
$306$	−1.73211	−0.0990180
$307$	13.3167	0.760024	0.380012	−	0.924982i	$-0.375920\pi$
$307$	13.3167	0.760024	0.380012	+	0.924982i	$0.375920\pi$
$308$	−2.34514	−0.133627
$309$	11.8002	0.671289
$310$	6.29636	0.357609
$311$	−15.1564	−0.859441	−0.429721	−	0.902962i	$-0.641388\pi$
$311$	−15.1564	−0.859441	−0.429721	+	0.902962i	$0.641388\pi$
$312$	6.56830	0.371857
$313$	−26.9868	−1.52539	−0.762693	−	0.646760i	$-0.776123\pi$
$313$	−26.9868	−1.52539	−0.762693	+	0.646760i	$0.776123\pi$
$314$	−21.8354	−1.23225
$315$	0.788507	0.0444273
$316$	−13.1409	−0.739233
$317$	21.1410	1.18740	0.593700	−	0.804687i	$-0.297667\pi$
$317$	21.1410	1.18740	0.593700	+	0.804687i	$0.297667\pi$
$318$	−9.78006	−0.548438
$319$	−28.6057	−1.60161
$320$	−3.89748	−0.217876
$321$	4.74622	0.264908
$322$	−3.94240	−0.219701
$323$	29.7409	1.65483
$324$	−7.92967	−0.440537
$325$	−40.9025	−2.26887
$326$	12.7450	0.705878
$327$	−2.83915	−0.157005
$328$	−6.35516	−0.350905
$329$	4.94698	0.272736
$330$	−23.8187	−1.31117
$331$	0.707561	0.0388911	0.0194455	−	0.999811i	$-0.493810\pi$
$331$	0.707561	0.0388911	0.0194455	+	0.999811i	$0.493810\pi$
$332$	−12.0767	−0.662794
$333$	−2.78216	−0.152461
$334$	13.6043	0.744394
$335$	−8.57897	−0.468719
$336$	−1.02758	−0.0560593
$337$	−13.5812	−0.739813	−0.369906	−	0.929069i	$-0.620610\pi$
$337$	−13.5812	−0.739813	−0.369906	+	0.929069i	$0.620610\pi$
$338$	3.11107	0.169220
$339$	−26.5381	−1.44135
$340$	−20.9538	−1.13638
$341$	6.03322	0.326717
$342$	−1.78226	−0.0963735
$343$	−8.54371	−0.461317
$344$	−7.36296	−0.396984
$345$	−40.0414	−2.15576
$346$	13.5776	0.729936
$347$	5.09502	0.273515	0.136757	−	0.990605i	$-0.456332\pi$
$347$	5.09502	0.273515	0.136757	+	0.990605i	$0.456332\pi$
$348$	−12.5343	−0.671909
$349$	−26.1492	−1.39974	−0.699868	−	0.714273i	$-0.746758\pi$
$349$	−26.1492	−1.39974	−0.699868	+	0.714273i	$0.746758\pi$
$350$	6.39903	0.342043
$351$	−21.8211	−1.16472
$352$	−3.73459	−0.199054
$353$	24.9017	1.32538	0.662691	−	0.748893i	$-0.269414\pi$
$353$	24.9017	1.32538	0.662691	+	0.748893i	$0.269414\pi$
$354$	0.475414	0.0252680
$355$	−45.9375	−2.43811
$356$	0.966188	0.0512079
$357$	−5.52454	−0.292390
$358$	21.0500	1.11253
$359$	−11.6026	−0.612360	−0.306180	−	0.951974i	$-0.599051\pi$
$359$	−11.6026	−0.612360	−0.306180	+	0.951974i	$0.599051\pi$
$360$	1.25568	0.0661802
$361$	11.6020	0.610631
$362$	−14.7773	−0.776677
$363$	−4.82277	−0.253130
$364$	−2.52051	−0.132111
$365$	−32.7261	−1.71296
$366$	−7.53710	−0.393971
$367$	−36.7928	−1.92057	−0.960284	−	0.279025i	$-0.909989\pi$
$367$	−36.7928	−1.92057	−0.960284	+	0.279025i	$0.909989\pi$
$368$	−6.27819	−0.327273
$369$	2.04749	0.106588
$370$	−33.6565	−1.74972
$371$	3.75299	0.194845
$372$	2.64361	0.137065
$373$	29.4915	1.52701	0.763505	−	0.645802i	$-0.223477\pi$
$373$	29.4915	1.52701	0.763505	+	0.645802i	$0.223477\pi$
$374$	−20.0781	−1.03821
$375$	33.1031	1.70944
$376$	7.87796	0.406275
$377$	−30.7448	−1.58344
$378$	3.41381	0.175588
$379$	−32.9400	−1.69201	−0.846006	−	0.533173i	$-0.820999\pi$
$379$	−32.9400	−1.69201	−0.846006	+	0.533173i	$0.820999\pi$
$380$	−21.5605	−1.10603
$381$	11.5987	0.594221
$382$	−23.6401	−1.20953
$383$	26.7052	1.36457	0.682286	−	0.731085i	$-0.260986\pi$
$383$	26.7052	1.36457	0.682286	+	0.731085i	$0.260986\pi$
$384$	−1.63641	−0.0835075
$385$	9.14014	0.465825
$386$	−22.3508	−1.13763
$387$	2.37218	0.120585
$388$	−10.8090	−0.548745
$389$	−20.2008	−1.02422	−0.512112	−	0.858919i	$-0.671137\pi$
$389$	−20.2008	−1.02422	−0.512112	+	0.858919i	$0.671137\pi$
$390$	−25.5998	−1.29630
$391$	−33.7531	−1.70697
$392$	−6.60568	−0.333637
$393$	−17.2671	−0.871008
$394$	−21.3992	−1.07808
$395$	51.2163	2.57697
$396$	1.20320	0.0604632
$397$	39.0424	1.95948	0.979741	−	0.200271i	$-0.0641823\pi$
$397$	39.0424	1.95948	0.979741	+	0.200271i	$0.0641823\pi$
$398$	7.93988	0.397990
$399$	−5.68449	−0.284581
$400$	10.1903	0.509516
$401$	14.7834	0.738248	0.369124	−	0.929380i	$-0.379658\pi$
$401$	14.7834	0.738248	0.369124	+	0.929380i	$0.379658\pi$
$402$	−3.60199	−0.179651
$403$	6.48437	0.323010
$404$	6.02038	0.299525
$405$	30.9057	1.53572
$406$	4.80989	0.238711
$407$	−32.2499	−1.59857
$408$	−8.79771	−0.435552
$409$	32.6849	1.61617	0.808083	−	0.589068i	$-0.200505\pi$
$409$	32.6849	1.61617	0.808083	+	0.589068i	$0.200505\pi$
$410$	24.7691	1.22326
$411$	34.8617	1.71960
$412$	−7.21104	−0.355263
$413$	−0.182435	−0.00897702
$414$	2.02270	0.0994101
$415$	47.0686	2.31050
$416$	−4.01386	−0.196796
$417$	8.85394	0.433580
$418$	−20.6594	−1.01048
$419$	−14.2528	−0.696297	−0.348148	−	0.937439i	$-0.613189\pi$
$419$	−14.2528	−0.696297	−0.348148	+	0.937439i	$0.613189\pi$
$420$	4.00498	0.195423
$421$	1.45142	0.0707381	0.0353690	−	0.999374i	$-0.488739\pi$
$421$	1.45142	0.0707381	0.0353690	+	0.999374i	$0.488739\pi$
$422$	0.885911	0.0431255
$423$	−2.53811	−0.123407
$424$	5.97655	0.290247
$425$	54.7857	2.65750
$426$	−19.2875	−0.934480
$427$	2.89228	0.139967
$428$	−2.90040	−0.140196
$429$	−24.5299	−1.18432
$430$	28.6970	1.38389
$431$	2.36731	0.114029	0.0570146	−	0.998373i	$-0.481842\pi$
$431$	2.36731	0.114029	0.0570146	+	0.998373i	$0.481842\pi$
$432$	5.43643	0.261560
$433$	25.8715	1.24330	0.621652	−	0.783294i	$-0.286462\pi$
$433$	25.8715	1.24330	0.621652	+	0.783294i	$0.286462\pi$
$434$	−1.01445	−0.0486953
$435$	48.8521	2.34228
$436$	1.73499	0.0830911
$437$	−34.7304	−1.66138
$438$	−13.7405	−0.656545
$439$	−28.1313	−1.34263	−0.671317	−	0.741171i	$-0.734271\pi$
$439$	−28.1313	−1.34263	−0.671317	+	0.741171i	$0.734271\pi$
$440$	14.5555	0.693906
$441$	2.12820	0.101343
$442$	−21.5795	−1.02643
$443$	−32.8354	−1.56006	−0.780029	−	0.625744i	$-0.784796\pi$
$443$	−32.8354	−1.56006	−0.780029	+	0.625744i	$0.784796\pi$
$444$	−14.1311	−0.670633
$445$	−3.76570	−0.178511
$446$	−2.20454	−0.104388
$447$	−26.6804	−1.26194
$448$	0.627952	0.0296679
$449$	2.39995	0.113260	0.0566302	−	0.998395i	$-0.481964\pi$
$449$	2.39995	0.113260	0.0566302	+	0.998395i	$0.481964\pi$
$450$	−3.28310	−0.154767
$451$	23.7339	1.11759
$452$	16.2173	0.762798
$453$	36.9782	1.73739
$454$	3.12712	0.146763
$455$	9.82363	0.460539
$456$	−9.05244	−0.423919
$457$	−23.5438	−1.10133	−0.550667	−	0.834725i	$-0.685627\pi$
$457$	−23.5438	−1.10133	−0.550667	+	0.834725i	$0.685627\pi$
$458$	−4.66998	−0.218214
$459$	29.2276	1.36423
$460$	24.4691	1.14088
$461$	7.98259	0.371786	0.185893	−	0.982570i	$-0.440482\pi$
$461$	7.98259	0.371786	0.185893	+	0.982570i	$0.440482\pi$
$462$	3.83760	0.178542
$463$	−13.7279	−0.637992	−0.318996	−	0.947756i	$-0.603346\pi$
$463$	−13.7279	−0.637992	−0.318996	+	0.947756i	$0.603346\pi$
$464$	7.65966	0.355591
$465$	−10.3034	−0.477808
$466$	−14.2310	−0.659241
$467$	2.29133	0.106030	0.0530150	−	0.998594i	$-0.483117\pi$
$467$	2.29133	0.106030	0.0530150	+	0.998594i	$0.483117\pi$
$468$	1.29318	0.0597771
$469$	1.38222	0.0638251
$470$	−30.7042	−1.41628
$471$	35.7316	1.64643
$472$	−0.290523	−0.0133724
$473$	27.4977	1.26434
$474$	21.5038	0.987703
$475$	56.3719	2.58652
$476$	3.37602	0.154740
$477$	−1.92551	−0.0881632
$478$	17.6226	0.806041
$479$	4.79410	0.219048	0.109524	−	0.993984i	$-0.465067\pi$
$479$	4.79410	0.219048	0.109524	+	0.993984i	$0.465067\pi$
$480$	6.37785	0.291108
$481$	−34.6615	−1.58043
$482$	−0.720136	−0.0328013
$483$	6.45137	0.293547
$484$	2.94718	0.133963
$485$	42.1280	1.91293
$486$	−3.33314	−0.151194
$487$	−35.0467	−1.58812	−0.794058	−	0.607842i	$-0.792035\pi$
$487$	−35.0467	−1.58812	−0.794058	+	0.607842i	$0.792035\pi$
$488$	4.60589	0.208499
$489$	−20.8559	−0.943137
$490$	25.7455	1.16306
$491$	−1.38704	−0.0625963	−0.0312981	−	0.999510i	$-0.509964\pi$
$491$	−1.38704	−0.0625963	−0.0312981	+	0.999510i	$0.509964\pi$
$492$	10.3996	0.468851
$493$	41.1802	1.85466
$494$	−22.2043	−0.999018
$495$	−4.68946	−0.210775
$496$	−1.61550	−0.0725379
$497$	7.40134	0.331996
$498$	19.7623	0.885571
$499$	−15.4828	−0.693103	−0.346552	−	0.938031i	$-0.612647\pi$
$499$	−15.4828	−0.693103	−0.346552	+	0.938031i	$0.612647\pi$
$500$	−20.2292	−0.904677
$501$	−22.2622	−0.994600
$502$	15.3805	0.686467
$503$	23.2507	1.03670	0.518349	−	0.855169i	$-0.326547\pi$
$503$	23.2507	1.03670	0.518349	+	0.855169i	$0.326547\pi$
$504$	−0.202312	−0.00901170
$505$	−23.4643	−1.04415
$506$	23.4465	1.04232
$507$	−5.09097	−0.226098
$508$	−7.08793	−0.314476
$509$	−33.9166	−1.50332	−0.751662	−	0.659548i	$-0.770748\pi$
$509$	−33.9166	−1.50332	−0.751662	+	0.659548i	$0.770748\pi$
$510$	34.2889	1.51834
$511$	5.27275	0.233253
$512$	1.00000	0.0441942
$513$	30.0738	1.32779
$514$	4.85813	0.214283
$515$	28.1049	1.23845
$516$	12.0488	0.530418
$517$	−29.4210	−1.29393
$518$	5.42265	0.238258
$519$	−22.2184	−0.975281
$520$	15.6439	0.686032
$521$	−24.1250	−1.05693	−0.528467	−	0.848954i	$-0.677233\pi$
$521$	−24.1250	−1.05693	−0.528467	+	0.848954i	$0.677233\pi$
$522$	−2.46777	−0.108011
$523$	−30.5533	−1.33600	−0.668002	−	0.744160i	$-0.732850\pi$
$523$	−30.5533	−1.33600	−0.668002	+	0.744160i	$0.732850\pi$
$524$	10.5518	0.460958
$525$	−10.4714	−0.457010
$526$	−17.7487	−0.773882
$527$	−8.68530	−0.378338
$528$	6.11131	0.265960
$529$	16.4157	0.713727
$530$	−23.2935	−1.01180
$531$	0.0936002	0.00406190
$532$	3.47377	0.150607
$533$	25.5087	1.10491
$534$	−1.58108	−0.0684198
$535$	11.3042	0.488725
$536$	2.20116	0.0950756
$537$	−34.4464	−1.48647
$538$	−18.8930	−0.814535
$539$	24.6695	1.06259
$540$	−21.1884	−0.911802
$541$	21.8960	0.941384	0.470692	−	0.882298i	$-0.344004\pi$
$541$	21.8960	0.941384	0.470692	+	0.882298i	$0.344004\pi$
$542$	−2.92406	−0.125599
$543$	24.1816	1.03773
$544$	5.37624	0.230505
$545$	−6.76209	−0.289656
$546$	4.12458	0.176516
$547$	−8.19703	−0.350479	−0.175240	−	0.984526i	$-0.556070\pi$
$547$	−8.19703	−0.350479	−0.175240	+	0.984526i	$0.556070\pi$
$548$	−21.3039	−0.910056
$549$	−1.48392	−0.0633320
$550$	−38.0567	−1.62274
$551$	42.3725	1.80513
$552$	10.2737	0.437276
$553$	−8.25185	−0.350904
$554$	−4.17430	−0.177349
$555$	55.0757	2.33783
$556$	−5.41061	−0.229461
$557$	−34.9159	−1.47943	−0.739717	−	0.672918i	$-0.765041\pi$
$557$	−34.9159	−1.47943	−0.739717	+	0.672918i	$0.765041\pi$
$558$	0.520477	0.0220336
$559$	29.5539	1.25000
$560$	−2.44743	−0.103423
$561$	32.8559	1.38718
$562$	28.1277	1.18650
$563$	−44.2324	−1.86417	−0.932086	−	0.362238i	$-0.882013\pi$
$563$	−44.2324	−1.86417	−0.932086	+	0.362238i	$0.882013\pi$
$564$	−12.8915	−0.542832
$565$	−63.2066	−2.65912
$566$	27.0615	1.13748
$567$	−4.97945	−0.209117
$568$	11.7865	0.494550
$569$	−31.3520	−1.31435	−0.657173	−	0.753740i	$-0.728248\pi$
$569$	−31.3520	−1.31435	−0.657173	+	0.753740i	$0.728248\pi$
$570$	35.2817	1.47779
$571$	−5.97336	−0.249977	−0.124989	−	0.992158i	$-0.539889\pi$
$571$	−5.97336	−0.249977	−0.124989	+	0.992158i	$0.539889\pi$
$572$	14.9901	0.626769
$573$	38.6847	1.61608
$574$	−3.99074	−0.166570
$575$	−63.9769	−2.66802
$576$	−0.322178	−0.0134241
$577$	15.2948	0.636732	0.318366	−	0.947968i	$-0.396866\pi$
$577$	15.2948	0.636732	0.318366	+	0.947968i	$0.396866\pi$
$578$	11.9040	0.495141
$579$	36.5750	1.52001
$580$	−29.8533	−1.23959
$581$	−7.58357	−0.314619
$582$	17.6880	0.733189
$583$	−22.3200	−0.924399
$584$	8.39674	0.347459
$585$	−5.04013	−0.208384
$586$	18.3293	0.757176
$587$	−20.9379	−0.864199	−0.432099	−	0.901826i	$-0.642227\pi$
$587$	−20.9379	−0.864199	−0.432099	+	0.901826i	$0.642227\pi$
$588$	10.8096	0.445779
$589$	−8.93677	−0.368233
$590$	1.13231	0.0466164
$591$	35.0178	1.44044
$592$	8.63546	0.354915
$593$	−45.0487	−1.84993	−0.924964	−	0.380055i	$-0.875905\pi$
$593$	−45.0487	−1.84993	−0.924964	+	0.380055i	$0.875905\pi$
$594$	−20.3028	−0.833036
$595$	−13.1580	−0.539424
$596$	16.3043	0.667850
$597$	−12.9929	−0.531762
$598$	25.1998	1.03050
$599$	20.4517	0.835632	0.417816	−	0.908532i	$-0.362796\pi$
$599$	20.4517	0.835632	0.417816	+	0.908532i	$0.362796\pi$
$600$	−16.6755	−0.680775
$601$	32.4798	1.32488	0.662440	−	0.749115i	$-0.269521\pi$
$601$	32.4798	1.32488	0.662440	+	0.749115i	$0.269521\pi$
$602$	−4.62358	−0.188443
$603$	−0.709165	−0.0288794
$604$	−22.5972	−0.919469
$605$	−11.4865	−0.466995
$606$	−9.85177	−0.400201
$607$	−11.0973	−0.450427	−0.225213	−	0.974309i	$-0.572308\pi$
$607$	−11.0973	−0.450427	−0.225213	+	0.974309i	$0.572308\pi$
$608$	5.53191	0.224348
$609$	−7.87093	−0.318946
$610$	−17.9514	−0.726829
$611$	−31.6210	−1.27925
$612$	−1.73211	−0.0700163
$613$	−17.3653	−0.701376	−0.350688	−	0.936492i	$-0.614052\pi$
$613$	−17.3653	−0.701376	−0.350688	+	0.936492i	$0.614052\pi$
$614$	13.3167	0.537418
$615$	−40.5323	−1.63442
$616$	−2.34514	−0.0944885
$617$	−43.7905	−1.76294	−0.881469	−	0.472242i	$-0.843445\pi$
$617$	−43.7905	−1.76294	−0.881469	+	0.472242i	$0.843445\pi$
$618$	11.8002	0.474673
$619$	43.2459	1.73820	0.869100	−	0.494637i	$-0.164699\pi$
$619$	43.2459	1.73820	0.869100	+	0.494637i	$0.164699\pi$
$620$	6.29636	0.252868
$621$	−34.1310	−1.36963
$622$	−15.1564	−0.607717
$623$	0.606719	0.0243077
$624$	6.56830	0.262942
$625$	27.8912	1.11565
$626$	−26.9868	−1.07861
$627$	33.8072	1.35013
$628$	−21.8354	−0.871329
$629$	46.4263	1.85114
$630$	0.788507	0.0314149
$631$	−9.75750	−0.388440	−0.194220	−	0.980958i	$-0.562218\pi$
$631$	−9.75750	−0.388440	−0.194220	+	0.980958i	$0.562218\pi$
$632$	−13.1409	−0.522717
$633$	−1.44971	−0.0576208
$634$	21.1410	0.839618
$635$	27.6250	1.09627
$636$	−9.78006	−0.387805
$637$	26.5143	1.05053
$638$	−28.6057	−1.13251
$639$	−3.79735	−0.150221
$640$	−3.89748	−0.154061
$641$	−40.2386	−1.58933	−0.794664	−	0.607050i	$-0.792353\pi$
$641$	−40.2386	−1.58933	−0.794664	+	0.607050i	$0.792353\pi$
$642$	4.74622	0.187319
$643$	25.4424	1.00335	0.501675	−	0.865056i	$-0.332717\pi$
$643$	25.4424	1.00335	0.501675	+	0.865056i	$0.332717\pi$
$644$	−3.94240	−0.155352
$645$	−46.9599	−1.84904
$646$	29.7409	1.17014
$647$	3.90642	0.153577	0.0767887	−	0.997047i	$-0.475533\pi$
$647$	3.90642	0.153577	0.0767887	+	0.997047i	$0.475533\pi$
$648$	−7.92967	−0.311507
$649$	1.08499	0.0425894
$650$	−40.9025	−1.60433
$651$	1.66006	0.0650628
$652$	12.7450	0.499131
$653$	18.9527	0.741678	0.370839	−	0.928697i	$-0.379070\pi$
$653$	18.9527	0.741678	0.370839	+	0.928697i	$0.379070\pi$
$654$	−2.83915	−0.111020
$655$	−41.1255	−1.60691
$656$	−6.35516	−0.248127
$657$	−2.70524	−0.105542
$658$	4.94698	0.192853
$659$	−19.9078	−0.775499	−0.387750	−	0.921765i	$-0.626747\pi$
$659$	−19.9078	−0.775499	−0.387750	+	0.921765i	$0.626747\pi$
$660$	−23.8187	−0.927141
$661$	−0.140789	−0.00547606	−0.00273803	−	0.999996i	$-0.500872\pi$
$661$	−0.140789	−0.00547606	−0.00273803	+	0.999996i	$0.500872\pi$
$662$	0.707561	0.0275002
$663$	35.3128	1.37143
$664$	−12.0767	−0.468666
$665$	−13.5389	−0.525017
$666$	−2.78216	−0.107806
$667$	−48.0888	−1.86201
$668$	13.6043	0.526366
$669$	3.60752	0.139475
$670$	−8.57897	−0.331434
$671$	−17.2011	−0.664042
$672$	−1.02758	−0.0396399
$673$	18.0451	0.695586	0.347793	−	0.937571i	$-0.386931\pi$
$673$	18.0451	0.695586	0.347793	+	0.937571i	$0.386931\pi$
$674$	−13.5812	−0.523127
$675$	55.3990	2.13231
$676$	3.11107	0.119657
$677$	−18.8267	−0.723568	−0.361784	−	0.932262i	$-0.617832\pi$
$677$	−18.8267	−0.723568	−0.361784	+	0.932262i	$0.617832\pi$
$678$	−26.5381	−1.01919
$679$	−6.78755	−0.260482
$680$	−20.9538	−0.803541
$681$	−5.11723	−0.196093
$682$	6.03322	0.231024
$683$	20.2960	0.776607	0.388303	−	0.921532i	$-0.373061\pi$
$683$	20.2960	0.776607	0.388303	+	0.921532i	$0.373061\pi$
$684$	−1.78226	−0.0681463
$685$	83.0313	3.17246
$686$	−8.54371	−0.326200
$687$	7.64198	0.291560
$688$	−7.36296	−0.280710
$689$	−23.9890	−0.913910
$690$	−40.0414	−1.52435
$691$	29.5015	1.12229	0.561146	−	0.827717i	$-0.310361\pi$
$691$	29.5015	1.12229	0.561146	+	0.827717i	$0.310361\pi$
$692$	13.5776	0.516143
$693$	0.755553	0.0287011
$694$	5.09502	0.193404
$695$	21.0877	0.799903
$696$	−12.5343	−0.475111
$697$	−34.1669	−1.29416
$698$	−26.1492	−0.989762
$699$	23.2878	0.880824
$700$	6.39903	0.241861
$701$	10.4180	0.393484	0.196742	−	0.980455i	$-0.436964\pi$
$701$	10.4180	0.393484	0.196742	+	0.980455i	$0.436964\pi$
$702$	−21.8211	−0.823583
$703$	47.7706	1.80170
$704$	−3.73459	−0.140753
$705$	50.2445	1.89232
$706$	24.9017	0.937187
$707$	3.78051	0.142181
$708$	0.475414	0.0178672
$709$	13.4713	0.505926	0.252963	−	0.967476i	$-0.418595\pi$
$709$	13.4713	0.505926	0.252963	+	0.967476i	$0.418595\pi$
$710$	−45.9375	−1.72401
$711$	4.23371	0.158776
$712$	0.966188	0.0362094
$713$	10.1424	0.379836
$714$	−5.52454	−0.206751
$715$	−58.4237	−2.18492
$716$	21.0500	0.786676
$717$	−28.8378	−1.07697
$718$	−11.6026	−0.433004
$719$	−10.6508	−0.397209	−0.198605	−	0.980080i	$-0.563641\pi$
$719$	−10.6508	−0.397209	−0.198605	+	0.980080i	$0.563641\pi$
$720$	1.25568	0.0467965
$721$	−4.52819	−0.168638
$722$	11.6020	0.431781
$723$	1.17843	0.0438265
$724$	−14.7773	−0.549194
$725$	78.0544	2.89887
$726$	−4.82277	−0.178990
$727$	36.7123	1.36159	0.680793	−	0.732476i	$-0.261635\pi$
$727$	36.7123	1.36159	0.680793	+	0.732476i	$0.261635\pi$
$728$	−2.52051	−0.0934163
$729$	29.2434	1.08309
$730$	−32.7261	−1.21125
$731$	−39.5851	−1.46411
$732$	−7.53710	−0.278579
$733$	−38.2833	−1.41402	−0.707012	−	0.707201i	$-0.749958\pi$
$733$	−38.2833	−1.41402	−0.707012	+	0.707201i	$0.749958\pi$
$734$	−36.7928	−1.35805
$735$	−42.1300	−1.55399
$736$	−6.27819	−0.231417
$737$	−8.22043	−0.302803
$738$	2.04749	0.0753693
$739$	−22.7006	−0.835056	−0.417528	−	0.908664i	$-0.637103\pi$
$739$	−22.7006	−0.835056	−0.417528	+	0.908664i	$0.637103\pi$
$740$	−33.6565	−1.23724
$741$	36.3352	1.33481
$742$	3.75299	0.137776
$743$	−31.7397	−1.16442	−0.582209	−	0.813039i	$-0.697811\pi$
$743$	−31.7397	−1.16442	−0.582209	+	0.813039i	$0.697811\pi$
$744$	2.64361	0.0969193
$745$	−63.5456	−2.32813
$746$	29.4915	1.07976
$747$	3.89084	0.142358
$748$	−20.0781	−0.734127
$749$	−1.82131	−0.0665492
$750$	33.1031	1.20876
$751$	−7.57702	−0.276490	−0.138245	−	0.990398i	$-0.544146\pi$
$751$	−7.57702	−0.276490	−0.138245	+	0.990398i	$0.544146\pi$
$752$	7.87796	0.287280
$753$	−25.1688	−0.917202
$754$	−30.7448	−1.11966
$755$	88.0722	3.20528
$756$	3.41381	0.124159
$757$	31.3605	1.13982	0.569909	−	0.821708i	$-0.306979\pi$
$757$	31.3605	1.13982	0.569909	+	0.821708i	$0.306979\pi$
$758$	−32.9400	−1.19643
$759$	−38.3680	−1.39267
$760$	−21.5605	−0.782081
$761$	−43.8574	−1.58983	−0.794915	−	0.606721i	$-0.792484\pi$
$761$	−43.8574	−1.58983	−0.794915	+	0.606721i	$0.792484\pi$
$762$	11.5987	0.420178
$763$	1.08949	0.0394422
$764$	−23.6401	−0.855267
$765$	6.75085	0.244077
$766$	26.7052	0.964898
$767$	1.16612	0.0421062
$768$	−1.63641	−0.0590487
$769$	47.3576	1.70776	0.853879	−	0.520471i	$-0.174244\pi$
$769$	47.3576	1.70776	0.853879	+	0.520471i	$0.174244\pi$
$770$	9.14014	0.329388
$771$	−7.94987	−0.286307
$772$	−22.3508	−0.804425
$773$	−4.35599	−0.156674	−0.0783371	−	0.996927i	$-0.524961\pi$
$773$	−4.35599	−0.156674	−0.0783371	+	0.996927i	$0.524961\pi$
$774$	2.37218	0.0852664
$775$	−16.4624	−0.591348
$776$	−10.8090	−0.388022
$777$	−8.87366	−0.318341
$778$	−20.2008	−0.724235
$779$	−35.1562	−1.25960
$780$	−25.5998	−0.916620
$781$	−44.0177	−1.57508
$782$	−33.7531	−1.20701
$783$	41.6412	1.48813
$784$	−6.60568	−0.235917
$785$	85.1032	3.03746
$786$	−17.2671	−0.615896
$787$	−35.1907	−1.25441	−0.627206	−	0.778854i	$-0.715801\pi$
$787$	−35.1907	−1.25441	−0.627206	+	0.778854i	$0.715801\pi$
$788$	−21.3992	−0.762316
$789$	29.0441	1.03400
$790$	51.2163	1.82220
$791$	10.1837	0.362090
$792$	1.20320	0.0427540
$793$	−18.4874	−0.656507
$794$	39.0424	1.38556
$795$	38.1176	1.35189
$796$	7.93988	0.281421
$797$	16.5566	0.586464	0.293232	−	0.956041i	$-0.405269\pi$
$797$	16.5566	0.586464	0.293232	+	0.956041i	$0.405269\pi$
$798$	−5.68449	−0.201229
$799$	42.3538	1.49837
$800$	10.1903	0.360283
$801$	−0.311285	−0.0109987
$802$	14.7834	0.522020
$803$	−31.3584	−1.10661
$804$	−3.60199	−0.127032
$805$	15.3654	0.541560
$806$	6.48437	0.228402
$807$	30.9166	1.08832
$808$	6.02038	0.211796
$809$	−34.1589	−1.20096	−0.600481	−	0.799639i	$-0.705024\pi$
$809$	−34.1589	−1.20096	−0.600481	+	0.799639i	$0.705024\pi$
$810$	30.9057	1.08592
$811$	−33.7413	−1.18482	−0.592409	−	0.805637i	$-0.701823\pi$
$811$	−33.7413	−1.18482	−0.592409	+	0.805637i	$0.701823\pi$
$812$	4.80989	0.168794
$813$	4.78494	0.167815
$814$	−32.2499	−1.13036
$815$	−49.6732	−1.73998
$816$	−8.79771	−0.307982
$817$	−40.7312	−1.42500
$818$	32.6849	1.14280
$819$	0.812053	0.0283754
$820$	24.7691	0.864975
$821$	−33.3700	−1.16462	−0.582310	−	0.812967i	$-0.697851\pi$
$821$	−33.3700	−1.16462	−0.582310	+	0.812967i	$0.697851\pi$
$822$	34.8617	1.21594
$823$	14.4096	0.502287	0.251143	−	0.967950i	$-0.419193\pi$
$823$	14.4096	0.502287	0.251143	+	0.967950i	$0.419193\pi$
$824$	−7.21104	−0.251209
$825$	62.2762	2.16818
$826$	−0.182435	−0.00634771
$827$	1.66737	0.0579800	0.0289900	−	0.999580i	$-0.490771\pi$
$827$	1.66737	0.0579800	0.0289900	+	0.999580i	$0.490771\pi$
$828$	2.02270	0.0702935
$829$	20.6252	0.716342	0.358171	−	0.933656i	$-0.383401\pi$
$829$	20.6252	0.716342	0.358171	+	0.933656i	$0.383401\pi$
$830$	47.0686	1.63377
$831$	6.83084	0.236959
$832$	−4.01386	−0.139156
$833$	−35.5137	−1.23048
$834$	8.85394	0.306587
$835$	−53.0225	−1.83492
$836$	−20.6594	−0.714521
$837$	−8.78253	−0.303569
$838$	−14.2528	−0.492356
$839$	41.2979	1.42576	0.712880	−	0.701286i	$-0.247390\pi$
$839$	41.2979	1.42576	0.712880	+	0.701286i	$0.247390\pi$
$840$	4.00498	0.138185
$841$	29.6703	1.02311
$842$	1.45142	0.0500194
$843$	−46.0283	−1.58530
$844$	0.885911	0.0304943
$845$	−12.1253	−0.417124
$846$	−2.53811	−0.0872619
$847$	1.85068	0.0635902
$848$	5.97655	0.205236
$849$	−44.2835	−1.51981
$850$	54.7857	1.87913
$851$	−54.2151	−1.85847
$852$	−19.2875	−0.660777
$853$	18.5632	0.635593	0.317797	−	0.948159i	$-0.397057\pi$
$853$	18.5632	0.635593	0.317797	+	0.948159i	$0.397057\pi$
$854$	2.89228	0.0989717
$855$	6.94631	0.237559
$856$	−2.90040	−0.0991335
$857$	29.6391	1.01245	0.506227	−	0.862400i	$-0.331040\pi$
$857$	29.6391	1.01245	0.506227	+	0.862400i	$0.331040\pi$
$858$	−24.5299	−0.837438
$859$	−41.4945	−1.41578	−0.707888	−	0.706325i	$-0.750352\pi$
$859$	−41.4945	−1.41578	−0.707888	+	0.706325i	$0.750352\pi$
$860$	28.6970	0.978559
$861$	6.53046	0.222558
$862$	2.36731	0.0806309
$863$	19.6886	0.670209	0.335105	−	0.942181i	$-0.391228\pi$
$863$	19.6886	0.670209	0.335105	+	0.942181i	$0.391228\pi$
$864$	5.43643	0.184951
$865$	−52.9184	−1.79928
$866$	25.8715	0.879149
$867$	−19.4798	−0.661567
$868$	−1.01445	−0.0344328
$869$	49.0759	1.66478
$870$	48.8521	1.65624
$871$	−8.83515	−0.299367
$872$	1.73499	0.0587543
$873$	3.48243	0.117862
$874$	−34.7304	−1.17477
$875$	−12.7030	−0.429438
$876$	−13.7405	−0.464247
$877$	−13.4636	−0.454633	−0.227317	−	0.973821i	$-0.572995\pi$
$877$	−13.4636	−0.454633	−0.227317	+	0.973821i	$0.572995\pi$
$878$	−28.1313	−0.949385
$879$	−29.9942	−1.01168
$880$	14.5555	0.490665
$881$	−17.8798	−0.602386	−0.301193	−	0.953563i	$-0.597385\pi$
$881$	−17.8798	−0.602386	−0.301193	+	0.953563i	$0.597385\pi$
$882$	2.12820	0.0716603
$883$	19.5330	0.657337	0.328669	−	0.944445i	$-0.393400\pi$
$883$	19.5330	0.657337	0.328669	+	0.944445i	$0.393400\pi$
$884$	−21.5795	−0.725797
$885$	−1.85292	−0.0622851
$886$	−32.8354	−1.10313
$887$	18.2583	0.613053	0.306527	−	0.951862i	$-0.400833\pi$
$887$	18.2583	0.613053	0.306527	+	0.951862i	$0.400833\pi$
$888$	−14.1311	−0.474209
$889$	−4.45088	−0.149278
$890$	−3.76570	−0.126226
$891$	29.6141	0.992109
$892$	−2.20454	−0.0738135
$893$	43.5801	1.45835
$894$	−26.6804	−0.892327
$895$	−82.0420	−2.74236
$896$	0.627952	0.0209784
$897$	−41.2371	−1.37687
$898$	2.39995	0.0800873
$899$	−12.3741	−0.412701
$900$	−3.28310	−0.109437
$901$	32.1314	1.07045
$902$	23.7339	0.790254
$903$	7.56606	0.251783
$904$	16.2173	0.539379
$905$	57.5942	1.91449
$906$	36.9782	1.22852
$907$	33.7969	1.12221	0.561103	−	0.827746i	$-0.310377\pi$
$907$	33.7969	1.12221	0.561103	+	0.827746i	$0.310377\pi$
$908$	3.12712	0.103777
$909$	−1.93963	−0.0643336
$910$	9.82363	0.325650
$911$	53.4343	1.77036	0.885179	−	0.465251i	$-0.154036\pi$
$911$	53.4343	1.77036	0.885179	+	0.465251i	$0.154036\pi$
$912$	−9.05244	−0.299756
$913$	45.1014	1.49264
$914$	−23.5438	−0.778761
$915$	29.3757	0.971130
$916$	−4.66998	−0.154301
$917$	6.62603	0.218811
$918$	29.2276	0.964653
$919$	8.70482	0.287146	0.143573	−	0.989640i	$-0.454141\pi$
$919$	8.70482	0.287146	0.143573	+	0.989640i	$0.454141\pi$
$920$	24.4691	0.806723
$921$	−21.7915	−0.718054
$922$	7.98259	0.262893
$923$	−47.3093	−1.55720
$924$	3.83760	0.126248
$925$	87.9982	2.89336
$926$	−13.7279	−0.451128
$927$	2.32324	0.0763052
$928$	7.65966	0.251441
$929$	36.4246	1.19505	0.597527	−	0.801849i	$-0.296150\pi$
$929$	36.4246	1.19505	0.597527	+	0.801849i	$0.296150\pi$
$930$	−10.3034	−0.337862
$931$	−36.5420	−1.19762
$932$	−14.2310	−0.466153
$933$	24.8020	0.811982
$934$	2.29133	0.0749746
$935$	78.2538	2.55917
$936$	1.29318	0.0422688
$937$	−23.3184	−0.761780	−0.380890	−	0.924620i	$-0.624382\pi$
$937$	−23.3184	−0.761780	−0.380890	+	0.924620i	$0.624382\pi$
$938$	1.38222	0.0451311
$939$	44.1614	1.44115
$940$	−30.7042	−1.00146
$941$	27.9548	0.911301	0.455651	−	0.890159i	$-0.349407\pi$
$941$	27.9548	0.911301	0.455651	+	0.890159i	$0.349407\pi$
$942$	35.7316	1.16420
$943$	39.8990	1.29929
$944$	−0.290523	−0.00945573
$945$	−13.3053	−0.432820
$946$	27.4977	0.894026
$947$	6.62548	0.215299	0.107650	−	0.994189i	$-0.465668\pi$
$947$	6.62548	0.215299	0.107650	+	0.994189i	$0.465668\pi$
$948$	21.5038	0.698412
$949$	−33.7033	−1.09406
$950$	56.3719	1.82895
$951$	−34.5953	−1.12183
$952$	3.37602	0.109417
$953$	−5.82898	−0.188819	−0.0944097	−	0.995533i	$-0.530096\pi$
$953$	−5.82898	−0.188819	−0.0944097	+	0.995533i	$0.530096\pi$
$954$	−1.92551	−0.0623408
$955$	92.1366	2.98147
$956$	17.6226	0.569957
$957$	46.8105	1.51317
$958$	4.79410	0.154890
$959$	−13.3778	−0.431991
$960$	6.37785	0.205844
$961$	−28.3902	−0.915812
$962$	−34.6615	−1.11753
$963$	0.934444	0.0301120
$964$	−0.720136	−0.0231940
$965$	87.1119	2.80423
$966$	6.45137	0.207569
$967$	−38.5729	−1.24042	−0.620210	−	0.784436i	$-0.712953\pi$
$967$	−38.5729	−1.24042	−0.620210	+	0.784436i	$0.712953\pi$
$968$	2.94718	0.0947258
$969$	−48.6681	−1.56345
$970$	42.1280	1.35265
$971$	−36.0239	−1.15606	−0.578031	−	0.816015i	$-0.696179\pi$
$971$	−36.0239	−1.15606	−0.578031	+	0.816015i	$0.696179\pi$
$972$	−3.33314	−0.106910
$973$	−3.39760	−0.108922
$974$	−35.0467	−1.12297
$975$	66.9331	2.14358
$976$	4.60589	0.147431
$977$	39.9093	1.27681	0.638406	−	0.769700i	$-0.279594\pi$
$977$	39.9093	1.27681	0.638406	+	0.769700i	$0.279594\pi$
$978$	−20.8559	−0.666899
$979$	−3.60832	−0.115322
$980$	25.7455	0.822409
$981$	−0.558976	−0.0178467
$982$	−1.38704	−0.0442623
$983$	12.1798	0.388474	0.194237	−	0.980955i	$-0.437777\pi$
$983$	12.1798	0.388474	0.194237	+	0.980955i	$0.437777\pi$
$984$	10.3996	0.331528
$985$	83.4030	2.65744
$986$	41.1802	1.31144
$987$	−8.09526	−0.257675
$988$	−22.2043	−0.706413
$989$	46.2261	1.46990
$990$	−4.68946	−0.149041
$991$	24.6468	0.782931	0.391466	−	0.920193i	$-0.371968\pi$
$991$	24.6468	0.782931	0.391466	+	0.920193i	$0.371968\pi$
$992$	−1.61550	−0.0512920
$993$	−1.15786	−0.0367435
$994$	7.40134	0.234756
$995$	−30.9455	−0.981038
$996$	19.7623	0.626194
$997$	−16.8976	−0.535154	−0.267577	−	0.963537i	$-0.586223\pi$
$997$	−16.8976	−0.535154	−0.267577	+	0.963537i	$0.586223\pi$
$998$	−15.4828	−0.490098
$999$	46.9461	1.48531

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.a.1.20	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.a.1.20	✓	69	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.63641 q^{3} +1.00000 q^{4} -3.89748 q^{5} -1.63641 q^{6} +0.627952 q^{7} +1.00000 q^{8} -0.322178 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.63641 q^{3} +1.00000 q^{4} -3.89748 q^{5} -1.63641 q^{6} +0.627952 q^{7} +1.00000 q^{8} -0.322178 q^{9} -3.89748 q^{10} -3.73459 q^{11} -1.63641 q^{12} -4.01386 q^{13} +0.627952 q^{14} +6.37785 q^{15} +1.00000 q^{16} +5.37624 q^{17} -0.322178 q^{18} +5.53191 q^{19} -3.89748 q^{20} -1.02758 q^{21} -3.73459 q^{22} -6.27819 q^{23} -1.63641 q^{24} +10.1903 q^{25} -4.01386 q^{26} +5.43643 q^{27} +0.627952 q^{28} +7.65966 q^{29} +6.37785 q^{30} -1.61550 q^{31} +1.00000 q^{32} +6.11131 q^{33} +5.37624 q^{34} -2.44743 q^{35} -0.322178 q^{36} +8.63546 q^{37} +5.53191 q^{38} +6.56830 q^{39} -3.89748 q^{40} -6.35516 q^{41} -1.02758 q^{42} -7.36296 q^{43} -3.73459 q^{44} +1.25568 q^{45} -6.27819 q^{46} +7.87796 q^{47} -1.63641 q^{48} -6.60568 q^{49} +10.1903 q^{50} -8.79771 q^{51} -4.01386 q^{52} +5.97655 q^{53} +5.43643 q^{54} +14.5555 q^{55} +0.627952 q^{56} -9.05244 q^{57} +7.65966 q^{58} -0.290523 q^{59} +6.37785 q^{60} +4.60589 q^{61} -1.61550 q^{62} -0.202312 q^{63} +1.00000 q^{64} +15.6439 q^{65} +6.11131 q^{66} +2.20116 q^{67} +5.37624 q^{68} +10.2737 q^{69} -2.44743 q^{70} +11.7865 q^{71} -0.322178 q^{72} +8.39674 q^{73} +8.63546 q^{74} -16.6755 q^{75} +5.53191 q^{76} -2.34514 q^{77} +6.56830 q^{78} -13.1409 q^{79} -3.89748 q^{80} -7.92967 q^{81} -6.35516 q^{82} -12.0767 q^{83} -1.02758 q^{84} -20.9538 q^{85} -7.36296 q^{86} -12.5343 q^{87} -3.73459 q^{88} +0.966188 q^{89} +1.25568 q^{90} -2.52051 q^{91} -6.27819 q^{92} +2.64361 q^{93} +7.87796 q^{94} -21.5605 q^{95} -1.63641 q^{96} -10.8090 q^{97} -6.60568 q^{98} +1.20320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9 - 9 * q^10 - 48 * q^11 - 15 * q^12 - 30 * q^13 - 29 * q^14 - 51 * q^15 + 69 * q^16 - 37 * q^17 + 40 * q^18 - 72 * q^19 - 9 * q^20 - 38 * q^21 - 48 * q^22 - 75 * q^23 - 15 * q^24 + 18 * q^25 - 30 * q^26 - 48 * q^27 - 29 * q^28 - 27 * q^29 - 51 * q^30 - 61 * q^31 + 69 * q^32 - 29 * q^33 - 37 * q^34 - 64 * q^35 + 40 * q^36 - 42 * q^37 - 72 * q^38 - 68 * q^39 - 9 * q^40 - 49 * q^41 - 38 * q^42 - 95 * q^43 - 48 * q^44 - 20 * q^45 - 75 * q^46 - 62 * q^47 - 15 * q^48 - 4 * q^49 + 18 * q^50 - 76 * q^51 - 30 * q^52 - 28 * q^53 - 48 * q^54 - 76 * q^55 - 29 * q^56 - 44 * q^57 - 27 * q^58 - 68 * q^59 - 51 * q^60 - 62 * q^61 - 61 * q^62 - 91 * q^63 + 69 * q^64 - 79 * q^65 - 29 * q^66 - 116 * q^67 - 37 * q^68 - 23 * q^69 - 64 * q^70 - 89 * q^71 + 40 * q^72 - 60 * q^73 - 42 * q^74 - 47 * q^75 - 72 * q^76 + 5 * q^77 - 68 * q^78 - 170 * q^79 - 9 * q^80 - 3 * q^81 - 49 * q^82 - 82 * q^83 - 38 * q^84 - 81 * q^85 - 95 * q^86 - 51 * q^87 - 48 * q^88 - 78 * q^89 - 20 * q^90 - 85 * q^91 - 75 * q^92 - 21 * q^93 - 62 * q^94 - 70 * q^95 - 15 * q^96 - 60 * q^97 - 4 * q^98 - 148 * q^99

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