LMFDB - Embedded newform 8007.2.a.d.1.1

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.69841 q^{2} +1.00000 q^{3} +5.28144 q^{4} +2.43860 q^{5} -2.69841 q^{6} -1.23437 q^{7} -8.85467 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69841 q^{2} +1.00000 q^{3} +5.28144 q^{4} +2.43860 q^{5} -2.69841 q^{6} -1.23437 q^{7} -8.85467 q^{8} +1.00000 q^{9} -6.58035 q^{10} +3.49260 q^{11} +5.28144 q^{12} -3.44121 q^{13} +3.33083 q^{14} +2.43860 q^{15} +13.3307 q^{16} +1.00000 q^{17} -2.69841 q^{18} +1.20823 q^{19} +12.8793 q^{20} -1.23437 q^{21} -9.42448 q^{22} -4.65555 q^{23} -8.85467 q^{24} +0.946776 q^{25} +9.28580 q^{26} +1.00000 q^{27} -6.51923 q^{28} +7.07562 q^{29} -6.58035 q^{30} -2.33445 q^{31} -18.2624 q^{32} +3.49260 q^{33} -2.69841 q^{34} -3.01013 q^{35} +5.28144 q^{36} +0.712199 q^{37} -3.26030 q^{38} -3.44121 q^{39} -21.5930 q^{40} -3.67468 q^{41} +3.33083 q^{42} -0.770314 q^{43} +18.4459 q^{44} +2.43860 q^{45} +12.5626 q^{46} -12.7908 q^{47} +13.3307 q^{48} -5.47634 q^{49} -2.55479 q^{50} +1.00000 q^{51} -18.1745 q^{52} -8.40319 q^{53} -2.69841 q^{54} +8.51706 q^{55} +10.9299 q^{56} +1.20823 q^{57} -19.0930 q^{58} -10.9635 q^{59} +12.8793 q^{60} -8.90938 q^{61} +6.29932 q^{62} -1.23437 q^{63} +22.6181 q^{64} -8.39174 q^{65} -9.42448 q^{66} +3.74715 q^{67} +5.28144 q^{68} -4.65555 q^{69} +8.12258 q^{70} -3.98956 q^{71} -8.85467 q^{72} +2.71664 q^{73} -1.92181 q^{74} +0.946776 q^{75} +6.38118 q^{76} -4.31115 q^{77} +9.28580 q^{78} +3.31615 q^{79} +32.5082 q^{80} +1.00000 q^{81} +9.91580 q^{82} +0.952567 q^{83} -6.51923 q^{84} +2.43860 q^{85} +2.07862 q^{86} +7.07562 q^{87} -30.9258 q^{88} -15.4572 q^{89} -6.58035 q^{90} +4.24772 q^{91} -24.5880 q^{92} -2.33445 q^{93} +34.5149 q^{94} +2.94639 q^{95} -18.2624 q^{96} +12.0190 q^{97} +14.7774 q^{98} +3.49260 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.69841	−1.90807	−0.954033	−	0.299701i	$-0.903113\pi$
$2$	−2.69841	−1.90807	−0.954033	+	0.299701i	$0.903113\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.28144	2.64072
$5$	2.43860	1.09058	0.545288	−	0.838249i	$-0.316420\pi$
$5$	2.43860	1.09058	0.545288	+	0.838249i	$0.316420\pi$
$6$	−2.69841	−1.10162
$7$	−1.23437	−0.466547	−0.233274	−	0.972411i	$-0.574944\pi$
$7$	−1.23437	−0.466547	−0.233274	+	0.972411i	$0.574944\pi$
$8$	−8.85467	−3.13060
$9$	1.00000	0.333333
$10$	−6.58035	−2.08089
$11$	3.49260	1.05306	0.526529	−	0.850157i	$-0.323493\pi$
$11$	3.49260	1.05306	0.526529	+	0.850157i	$0.323493\pi$
$12$	5.28144	1.52462
$13$	−3.44121	−0.954420	−0.477210	−	0.878789i	$-0.658352\pi$
$13$	−3.44121	−0.954420	−0.477210	+	0.878789i	$0.658352\pi$
$14$	3.33083	0.890203
$15$	2.43860	0.629644
$16$	13.3307	3.33267
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.69841	−0.636022
$19$	1.20823	0.277186	0.138593	−	0.990349i	$-0.455742\pi$
$19$	1.20823	0.277186	0.138593	+	0.990349i	$0.455742\pi$
$20$	12.8793	2.87990
$21$	−1.23437	−0.269361
$22$	−9.42448	−2.00931
$23$	−4.65555	−0.970748	−0.485374	−	0.874307i	$-0.661317\pi$
$23$	−4.65555	−0.970748	−0.485374	+	0.874307i	$0.661317\pi$
$24$	−8.85467	−1.80745
$25$	0.946776	0.189355
$26$	9.28580	1.82110
$27$	1.00000	0.192450
$28$	−6.51923	−1.23202
$29$	7.07562	1.31391	0.656955	−	0.753930i	$-0.271844\pi$
$29$	7.07562	1.31391	0.656955	+	0.753930i	$0.271844\pi$
$30$	−6.58035	−1.20140
$31$	−2.33445	−0.419280	−0.209640	−	0.977779i	$-0.567229\pi$
$31$	−2.33445	−0.419280	−0.209640	+	0.977779i	$0.567229\pi$
$32$	−18.2624	−3.22836
$33$	3.49260	0.607984
$34$	−2.69841	−0.462774
$35$	−3.01013	−0.508805
$36$	5.28144	0.880239
$37$	0.712199	0.117085	0.0585424	−	0.998285i	$-0.481355\pi$
$37$	0.712199	0.117085	0.0585424	+	0.998285i	$0.481355\pi$
$38$	−3.26030	−0.528890
$39$	−3.44121	−0.551034
$40$	−21.5930	−3.41415
$41$	−3.67468	−0.573888	−0.286944	−	0.957947i	$-0.592639\pi$
$41$	−3.67468	−0.573888	−0.286944	+	0.957947i	$0.592639\pi$
$42$	3.33083	0.513959
$43$	−0.770314	−0.117472	−0.0587359	−	0.998274i	$-0.518707\pi$
$43$	−0.770314	−0.117472	−0.0587359	+	0.998274i	$0.518707\pi$
$44$	18.4459	2.78083
$45$	2.43860	0.363525
$46$	12.5626	1.85225
$47$	−12.7908	−1.86573	−0.932865	−	0.360226i	$-0.882700\pi$
$47$	−12.7908	−1.86573	−0.932865	+	0.360226i	$0.882700\pi$
$48$	13.3307	1.92412
$49$	−5.47634	−0.782334
$50$	−2.55479	−0.361302
$51$	1.00000	0.140028
$52$	−18.1745	−2.52035
$53$	−8.40319	−1.15427	−0.577134	−	0.816650i	$-0.695829\pi$
$53$	−8.40319	−1.15427	−0.577134	+	0.816650i	$0.695829\pi$
$54$	−2.69841	−0.367208
$55$	8.51706	1.14844
$56$	10.9299	1.46057
$57$	1.20823	0.160034
$58$	−19.0930	−2.50703
$59$	−10.9635	−1.42732	−0.713661	−	0.700491i	$-0.752964\pi$
$59$	−10.9635	−1.42732	−0.713661	+	0.700491i	$0.752964\pi$
$60$	12.8793	1.66271
$61$	−8.90938	−1.14073	−0.570365	−	0.821392i	$-0.693198\pi$
$61$	−8.90938	−1.14073	−0.570365	+	0.821392i	$0.693198\pi$
$62$	6.29932	0.800014
$63$	−1.23437	−0.155516
$64$	22.6181	2.82726
$65$	−8.39174	−1.04087
$66$	−9.42448	−1.16007
$67$	3.74715	0.457787	0.228894	−	0.973451i	$-0.426489\pi$
$67$	3.74715	0.457787	0.228894	+	0.973451i	$0.426489\pi$
$68$	5.28144	0.640468
$69$	−4.65555	−0.560462
$70$	8.12258	0.970834
$71$	−3.98956	−0.473474	−0.236737	−	0.971574i	$-0.576078\pi$
$71$	−3.98956	−0.473474	−0.236737	+	0.971574i	$0.576078\pi$
$72$	−8.85467	−1.04353
$73$	2.71664	0.317959	0.158980	−	0.987282i	$-0.449180\pi$
$73$	2.71664	0.317959	0.158980	+	0.987282i	$0.449180\pi$
$74$	−1.92181	−0.223406
$75$	0.946776	0.109324
$76$	6.38118	0.731971
$77$	−4.31115	−0.491302
$78$	9.28580	1.05141
$79$	3.31615	0.373096	0.186548	−	0.982446i	$-0.440270\pi$
$79$	3.31615	0.373096	0.186548	+	0.982446i	$0.440270\pi$
$80$	32.5082	3.63453
$81$	1.00000	0.111111
$82$	9.91580	1.09502
$83$	0.952567	0.104558	0.0522789	−	0.998633i	$-0.483352\pi$
$83$	0.952567	0.104558	0.0522789	+	0.998633i	$0.483352\pi$
$84$	−6.51923	−0.711307
$85$	2.43860	0.264503
$86$	2.07862	0.224144
$87$	7.07562	0.758587
$88$	−30.9258	−3.29670
$89$	−15.4572	−1.63846	−0.819231	−	0.573464i	$-0.805599\pi$
$89$	−15.4572	−1.63846	−0.819231	+	0.573464i	$0.805599\pi$
$90$	−6.58035	−0.693630
$91$	4.24772	0.445282
$92$	−24.5880	−2.56347
$93$	−2.33445	−0.242071
$94$	34.5149	3.55994
$95$	2.94639	0.302293
$96$	−18.2624	−1.86390
$97$	12.0190	1.22035	0.610174	−	0.792267i	$-0.291100\pi$
$97$	12.0190	1.22035	0.610174	+	0.792267i	$0.291100\pi$
$98$	14.7774	1.49274
$99$	3.49260	0.351020
$100$	5.00034	0.500034
$101$	−8.82314	−0.877936	−0.438968	−	0.898503i	$-0.644656\pi$
$101$	−8.82314	−0.877936	−0.438968	+	0.898503i	$0.644656\pi$
$102$	−2.69841	−0.267183
$103$	−1.94355	−0.191504	−0.0957519	−	0.995405i	$-0.530526\pi$
$103$	−1.94355	−0.191504	−0.0957519	+	0.995405i	$0.530526\pi$
$104$	30.4708	2.98790
$105$	−3.01013	−0.293759
$106$	22.6753	2.20242
$107$	−8.10470	−0.783511	−0.391755	−	0.920069i	$-0.628132\pi$
$107$	−8.10470	−0.783511	−0.391755	+	0.920069i	$0.628132\pi$
$108$	5.28144	0.508206
$109$	8.59238	0.823001	0.411501	−	0.911410i	$-0.365005\pi$
$109$	8.59238	0.823001	0.411501	+	0.911410i	$0.365005\pi$
$110$	−22.9826	−2.19130
$111$	0.712199	0.0675990
$112$	−16.4550	−1.55485
$113$	2.13171	0.200534	0.100267	−	0.994961i	$-0.468030\pi$
$113$	2.13171	0.200534	0.100267	+	0.994961i	$0.468030\pi$
$114$	−3.26030	−0.305355
$115$	−11.3530	−1.05867
$116$	37.3695	3.46967
$117$	−3.44121	−0.318140
$118$	29.5840	2.72343
$119$	−1.23437	−0.113154
$120$	−21.5930	−1.97116
$121$	1.19826	0.108933
$122$	24.0412	2.17659
$123$	−3.67468	−0.331334
$124$	−12.3293	−1.10720
$125$	−9.88420	−0.884069
$126$	3.33083	0.296734
$127$	3.31701	0.294337	0.147168	−	0.989111i	$-0.452984\pi$
$127$	3.31701	0.294337	0.147168	+	0.989111i	$0.452984\pi$
$128$	−24.5081	−2.16623
$129$	−0.770314	−0.0678223
$130$	22.6444	1.98604
$131$	−6.62419	−0.578758	−0.289379	−	0.957215i	$-0.593449\pi$
$131$	−6.62419	−0.578758	−0.289379	+	0.957215i	$0.593449\pi$
$132$	18.4459	1.60551
$133$	−1.49140	−0.129321
$134$	−10.1114	−0.873489
$135$	2.43860	0.209881
$136$	−8.85467	−0.759282
$137$	−15.3455	−1.31106	−0.655529	−	0.755170i	$-0.727554\pi$
$137$	−15.3455	−1.31106	−0.655529	+	0.755170i	$0.727554\pi$
$138$	12.5626	1.06940
$139$	6.88476	0.583957	0.291979	−	0.956425i	$-0.405686\pi$
$139$	6.88476	0.583957	0.291979	+	0.956425i	$0.405686\pi$
$140$	−15.8978	−1.34361
$141$	−12.7908	−1.07718
$142$	10.7655	0.903420
$143$	−12.0188	−1.00506
$144$	13.3307	1.11089
$145$	17.2546	1.43292
$146$	−7.33063	−0.606687
$147$	−5.47634	−0.451681
$148$	3.76143	0.309188
$149$	13.9620	1.14381	0.571904	−	0.820321i	$-0.306205\pi$
$149$	13.9620	1.14381	0.571904	+	0.820321i	$0.306205\pi$
$150$	−2.55479	−0.208598
$151$	8.66012	0.704751	0.352375	−	0.935859i	$-0.385374\pi$
$151$	8.66012	0.704751	0.352375	+	0.935859i	$0.385374\pi$
$152$	−10.6985	−0.867759
$153$	1.00000	0.0808452
$154$	11.6333	0.937436
$155$	−5.69280	−0.457257
$156$	−18.1745	−1.45513
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−8.94835	−0.711893
$159$	−8.40319	−0.666416
$160$	−44.5347	−3.52077
$161$	5.74666	0.452900
$162$	−2.69841	−0.212007
$163$	−1.59972	−0.125300	−0.0626498	−	0.998036i	$-0.519955\pi$
$163$	−1.59972	−0.125300	−0.0626498	+	0.998036i	$0.519955\pi$
$164$	−19.4076	−1.51548
$165$	8.51706	0.663052
$166$	−2.57042	−0.199503
$167$	10.0057	0.774266	0.387133	−	0.922024i	$-0.373465\pi$
$167$	10.0057	0.774266	0.387133	+	0.922024i	$0.373465\pi$
$168$	10.9299	0.843262
$169$	−1.15808	−0.0890833
$170$	−6.58035	−0.504690
$171$	1.20823	0.0923955
$172$	−4.06836	−0.310210
$173$	6.75933	0.513902	0.256951	−	0.966424i	$-0.417282\pi$
$173$	6.75933	0.513902	0.256951	+	0.966424i	$0.417282\pi$
$174$	−19.0930	−1.44743
$175$	−1.16867	−0.0883431
$176$	46.5588	3.50950
$177$	−10.9635	−0.824065
$178$	41.7100	3.12629
$179$	21.8132	1.63040	0.815198	−	0.579183i	$-0.196628\pi$
$179$	21.8132	1.63040	0.815198	+	0.579183i	$0.196628\pi$
$180$	12.8793	0.959967
$181$	0.906109	0.0673506	0.0336753	−	0.999433i	$-0.489279\pi$
$181$	0.906109	0.0673506	0.0336753	+	0.999433i	$0.489279\pi$
$182$	−11.4621	−0.849627
$183$	−8.90938	−0.658600
$184$	41.2233	3.03902
$185$	1.73677	0.127690
$186$	6.29932	0.461888
$187$	3.49260	0.255404
$188$	−67.5538	−4.92687
$189$	−1.23437	−0.0897871
$190$	−7.95057	−0.576795
$191$	−8.97584	−0.649469	−0.324735	−	0.945805i	$-0.605275\pi$
$191$	−8.97584	−0.649469	−0.324735	+	0.945805i	$0.605275\pi$
$192$	22.6181	1.63232
$193$	−23.4655	−1.68909	−0.844543	−	0.535488i	$-0.820128\pi$
$193$	−23.4655	−1.68909	−0.844543	+	0.535488i	$0.820128\pi$
$194$	−32.4323	−2.32851
$195$	−8.39174	−0.600945
$196$	−28.9229	−2.06592
$197$	−10.4199	−0.742389	−0.371195	−	0.928555i	$-0.621052\pi$
$197$	−10.4199	−0.742389	−0.371195	+	0.928555i	$0.621052\pi$
$198$	−9.42448	−0.669769
$199$	−17.5247	−1.24229	−0.621147	−	0.783694i	$-0.713333\pi$
$199$	−17.5247	−1.24229	−0.621147	+	0.783694i	$0.713333\pi$
$200$	−8.38339	−0.592795
$201$	3.74715	0.264304
$202$	23.8085	1.67516
$203$	−8.73392	−0.613001
$204$	5.28144	0.369774
$205$	−8.96107	−0.625868
$206$	5.24451	0.365402
$207$	−4.65555	−0.323583
$208$	−45.8737	−3.18077
$209$	4.21986	0.291894
$210$	8.12258	0.560511
$211$	10.2134	0.703117	0.351559	−	0.936166i	$-0.385652\pi$
$211$	10.2134	0.703117	0.351559	+	0.936166i	$0.385652\pi$
$212$	−44.3809	−3.04809
$213$	−3.98956	−0.273360
$214$	21.8698	1.49499
$215$	−1.87849	−0.128112
$216$	−8.85467	−0.602484
$217$	2.88157	0.195614
$218$	−23.1858	−1.57034
$219$	2.71664	0.183574
$220$	44.9823	3.03271
$221$	−3.44121	−0.231481
$222$	−1.92181	−0.128983
$223$	−12.0587	−0.807512	−0.403756	−	0.914867i	$-0.632296\pi$
$223$	−12.0587	−0.807512	−0.403756	+	0.914867i	$0.632296\pi$
$224$	22.5425	1.50618
$225$	0.946776	0.0631184
$226$	−5.75223	−0.382632
$227$	−26.5919	−1.76496	−0.882482	−	0.470346i	$-0.844129\pi$
$227$	−26.5919	−1.76496	−0.882482	+	0.470346i	$0.844129\pi$
$228$	6.38118	0.422604
$229$	21.6555	1.43103	0.715516	−	0.698596i	$-0.246191\pi$
$229$	21.6555	1.43103	0.715516	+	0.698596i	$0.246191\pi$
$230$	30.6351	2.02002
$231$	−4.31115	−0.283653
$232$	−62.6523	−4.11333
$233$	−11.1546	−0.730763	−0.365381	−	0.930858i	$-0.619061\pi$
$233$	−11.1546	−0.730763	−0.365381	+	0.930858i	$0.619061\pi$
$234$	9.28580	0.607032
$235$	−31.1917	−2.03472
$236$	−57.9029	−3.76916
$237$	3.31615	0.215407
$238$	3.33083	0.215906
$239$	21.2856	1.37685	0.688426	−	0.725307i	$-0.258302\pi$
$239$	21.2856	1.37685	0.688426	+	0.725307i	$0.258302\pi$
$240$	32.5082	2.09840
$241$	17.7616	1.14413	0.572064	−	0.820209i	$-0.306143\pi$
$241$	17.7616	1.14413	0.572064	+	0.820209i	$0.306143\pi$
$242$	−3.23340	−0.207851
$243$	1.00000	0.0641500
$244$	−47.0543	−3.01234
$245$	−13.3546	−0.853194
$246$	9.91580	0.632208
$247$	−4.15776	−0.264552
$248$	20.6708	1.31260
$249$	0.952567	0.0603665
$250$	26.6717	1.68686
$251$	−11.7952	−0.744506	−0.372253	−	0.928131i	$-0.621415\pi$
$251$	−11.7952	−0.744506	−0.372253	+	0.928131i	$0.621415\pi$
$252$	−6.51923	−0.410673
$253$	−16.2600	−1.02226
$254$	−8.95066	−0.561614
$255$	2.43860	0.152711
$256$	20.8969	1.30606
$257$	−27.8696	−1.73846	−0.869229	−	0.494410i	$-0.835384\pi$
$257$	−27.8696	−1.73846	−0.869229	+	0.494410i	$0.835384\pi$
$258$	2.07862	0.129410
$259$	−0.879116	−0.0546256
$260$	−44.3204	−2.74864
$261$	7.07562	0.437970
$262$	17.8748	1.10431
$263$	14.9920	0.924445	0.462223	−	0.886764i	$-0.347052\pi$
$263$	14.9920	0.924445	0.462223	+	0.886764i	$0.347052\pi$
$264$	−30.9258	−1.90335
$265$	−20.4920	−1.25882
$266$	4.02441	0.246752
$267$	−15.4572	−0.945966
$268$	19.7903	1.20889
$269$	7.65219	0.466562	0.233281	−	0.972409i	$-0.425054\pi$
$269$	7.65219	0.466562	0.233281	+	0.972409i	$0.425054\pi$
$270$	−6.58035	−0.400468
$271$	−9.48291	−0.576046	−0.288023	−	0.957623i	$-0.592998\pi$
$271$	−9.48291	−0.576046	−0.288023	+	0.957623i	$0.592998\pi$
$272$	13.3307	0.808292
$273$	4.24772	0.257084
$274$	41.4086	2.50159
$275$	3.30671	0.199402
$276$	−24.5880	−1.48002
$277$	−20.8006	−1.24979	−0.624893	−	0.780710i	$-0.714858\pi$
$277$	−20.8006	−1.24979	−0.624893	+	0.780710i	$0.714858\pi$
$278$	−18.5779	−1.11423
$279$	−2.33445	−0.139760
$280$	26.6537	1.59286
$281$	−7.22485	−0.430998	−0.215499	−	0.976504i	$-0.569138\pi$
$281$	−7.22485	−0.430998	−0.215499	+	0.976504i	$0.569138\pi$
$282$	34.5149	2.05533
$283$	−13.6067	−0.808835	−0.404418	−	0.914574i	$-0.632526\pi$
$283$	−13.6067	−0.808835	−0.404418	+	0.914574i	$0.632526\pi$
$284$	−21.0706	−1.25031
$285$	2.94639	0.174529
$286$	32.4316	1.91772
$287$	4.53590	0.267746
$288$	−18.2624	−1.07612
$289$	1.00000	0.0588235
$290$	−46.5601	−2.73410
$291$	12.0190	0.704568
$292$	14.3478	0.839640
$293$	−6.17949	−0.361009	−0.180505	−	0.983574i	$-0.557773\pi$
$293$	−6.17949	−0.361009	−0.180505	+	0.983574i	$0.557773\pi$
$294$	14.7774	0.861837
$295$	−26.7355	−1.55660
$296$	−6.30629	−0.366546
$297$	3.49260	0.202661
$298$	−37.6751	−2.18246
$299$	16.0207	0.926501
$300$	5.00034	0.288694
$301$	0.950850	0.0548061
$302$	−23.3686	−1.34471
$303$	−8.82314	−0.506876
$304$	16.1065	0.923772
$305$	−21.7264	−1.24405
$306$	−2.69841	−0.154258
$307$	22.5089	1.28465	0.642324	−	0.766433i	$-0.277970\pi$
$307$	22.5089	1.28465	0.642324	+	0.766433i	$0.277970\pi$
$308$	−22.7691	−1.29739
$309$	−1.94355	−0.110565
$310$	15.3615	0.872476
$311$	17.6395	1.00024	0.500122	−	0.865955i	$-0.333289\pi$
$311$	17.6395	1.00024	0.500122	+	0.865955i	$0.333289\pi$
$312$	30.4708	1.72507
$313$	−25.4311	−1.43745	−0.718726	−	0.695294i	$-0.755274\pi$
$313$	−25.4311	−1.43745	−0.718726	+	0.695294i	$0.755274\pi$
$314$	2.69841	0.152280
$315$	−3.01013	−0.169602
$316$	17.5141	0.985242
$317$	−30.3369	−1.70389	−0.851944	−	0.523633i	$-0.824576\pi$
$317$	−30.3369	−1.70389	−0.851944	+	0.523633i	$0.824576\pi$
$318$	22.6753	1.27157
$319$	24.7123	1.38362
$320$	55.1564	3.08334
$321$	−8.10470	−0.452360
$322$	−15.5069	−0.864163
$323$	1.20823	0.0672276
$324$	5.28144	0.293413
$325$	−3.25805	−0.180724
$326$	4.31670	0.239080
$327$	8.59238	0.475160
$328$	32.5380	1.79661
$329$	15.7886	0.870451
$330$	−22.9826	−1.26515
$331$	13.9712	0.767927	0.383964	−	0.923348i	$-0.374559\pi$
$331$	13.9712	0.767927	0.383964	+	0.923348i	$0.374559\pi$
$332$	5.03092	0.276108
$333$	0.712199	0.0390283
$334$	−26.9996	−1.47735
$335$	9.13781	0.499252
$336$	−16.4550	−0.897693
$337$	−20.7364	−1.12958	−0.564792	−	0.825234i	$-0.691043\pi$
$337$	−20.7364	−1.12958	−0.564792	+	0.825234i	$0.691043\pi$
$338$	3.12499	0.169977
$339$	2.13171	0.115778
$340$	12.8793	0.698479
$341$	−8.15331	−0.441526
$342$	−3.26030	−0.176297
$343$	15.4004	0.831543
$344$	6.82087	0.367757
$345$	−11.3530	−0.611226
$346$	−18.2395	−0.980559
$347$	15.0486	0.807849	0.403924	−	0.914792i	$-0.367646\pi$
$347$	15.0486	0.807849	0.403924	+	0.914792i	$0.367646\pi$
$348$	37.3695	2.00321
$349$	8.69715	0.465548	0.232774	−	0.972531i	$-0.425220\pi$
$349$	8.69715	0.465548	0.232774	+	0.972531i	$0.425220\pi$
$350$	3.15355	0.168565
$351$	−3.44121	−0.183678
$352$	−63.7832	−3.39966
$353$	4.28379	0.228003	0.114002	−	0.993481i	$-0.463633\pi$
$353$	4.28379	0.228003	0.114002	+	0.993481i	$0.463633\pi$
$354$	29.5840	1.57237
$355$	−9.72895	−0.516359
$356$	−81.6363	−4.32672
$357$	−1.23437	−0.0653297
$358$	−58.8610	−3.11090
$359$	19.3018	1.01871	0.509355	−	0.860557i	$-0.329884\pi$
$359$	19.3018	1.01871	0.509355	+	0.860557i	$0.329884\pi$
$360$	−21.5930	−1.13805
$361$	−17.5402	−0.923168
$362$	−2.44506	−0.128509
$363$	1.19826	0.0628923
$364$	22.4340	1.17586
$365$	6.62481	0.346758
$366$	24.0412	1.25665
$367$	15.7004	0.819556	0.409778	−	0.912185i	$-0.365606\pi$
$367$	15.7004	0.819556	0.409778	+	0.912185i	$0.365606\pi$
$368$	−62.0616	−3.23519
$369$	−3.67468	−0.191296
$370$	−4.68652	−0.243641
$371$	10.3726	0.538520
$372$	−12.3293	−0.639242
$373$	29.7952	1.54274	0.771368	−	0.636389i	$-0.219573\pi$
$373$	29.7952	1.54274	0.771368	+	0.636389i	$0.219573\pi$
$374$	−9.42448	−0.487328
$375$	−9.88420	−0.510418
$376$	113.258	5.84085
$377$	−24.3487	−1.25402
$378$	3.33083	0.171320
$379$	−11.3644	−0.583752	−0.291876	−	0.956456i	$-0.594279\pi$
$379$	−11.3644	−0.583752	−0.291876	+	0.956456i	$0.594279\pi$
$380$	15.5611	0.798270
$381$	3.31701	0.169936
$382$	24.2205	1.23923
$383$	5.37138	0.274465	0.137232	−	0.990539i	$-0.456179\pi$
$383$	5.37138	0.274465	0.137232	+	0.990539i	$0.456179\pi$
$384$	−24.5081	−1.25068
$385$	−10.5132	−0.535802
$386$	63.3197	3.22289
$387$	−0.770314	−0.0391572
$388$	63.4778	3.22259
$389$	20.1012	1.01917	0.509586	−	0.860420i	$-0.329799\pi$
$389$	20.1012	1.01917	0.509586	+	0.860420i	$0.329799\pi$
$390$	22.6444	1.14664
$391$	−4.65555	−0.235441
$392$	48.4911	2.44917
$393$	−6.62419	−0.334146
$394$	28.1173	1.41653
$395$	8.08678	0.406890
$396$	18.4459	0.926944
$397$	35.6074	1.78708	0.893541	−	0.448981i	$-0.148213\pi$
$397$	35.6074	1.78708	0.893541	+	0.448981i	$0.148213\pi$
$398$	47.2889	2.37038
$399$	−1.49140	−0.0746633
$400$	12.6212	0.631059
$401$	25.8420	1.29049	0.645243	−	0.763978i	$-0.276756\pi$
$401$	25.8420	1.29049	0.645243	+	0.763978i	$0.276756\pi$
$402$	−10.1114	−0.504309
$403$	8.03334	0.400169
$404$	−46.5989	−2.31838
$405$	2.43860	0.121175
$406$	23.5677	1.16965
$407$	2.48743	0.123297
$408$	−8.85467	−0.438371
$409$	9.22852	0.456321	0.228160	−	0.973624i	$-0.426729\pi$
$409$	9.22852	0.456321	0.228160	+	0.973624i	$0.426729\pi$
$410$	24.1807	1.19420
$411$	−15.3455	−0.756940
$412$	−10.2647	−0.505708
$413$	13.5330	0.665913
$414$	12.5626	0.617418
$415$	2.32293	0.114028
$416$	62.8446	3.08121
$417$	6.88476	0.337148
$418$	−11.3869	−0.556952
$419$	23.3844	1.14240	0.571201	−	0.820810i	$-0.306478\pi$
$419$	23.3844	1.14240	0.571201	+	0.820810i	$0.306478\pi$
$420$	−15.8978	−0.775734
$421$	20.8590	1.01661	0.508303	−	0.861178i	$-0.330273\pi$
$421$	20.8590	1.01661	0.508303	+	0.861178i	$0.330273\pi$
$422$	−27.5599	−1.34159
$423$	−12.7908	−0.621910
$424$	74.4075	3.61355
$425$	0.946776	0.0459254
$426$	10.7655	0.521590
$427$	10.9975	0.532204
$428$	−42.8044	−2.06903
$429$	−12.0188	−0.580272
$430$	5.06894	0.244446
$431$	3.33083	0.160441	0.0802203	−	0.996777i	$-0.474438\pi$
$431$	3.33083	0.160441	0.0802203	+	0.996777i	$0.474438\pi$
$432$	13.3307	0.641373
$433$	29.8702	1.43547	0.717736	−	0.696315i	$-0.245178\pi$
$433$	29.8702	1.43547	0.717736	+	0.696315i	$0.245178\pi$
$434$	−7.77568	−0.373244
$435$	17.2546	0.827296
$436$	45.3801	2.17331
$437$	−5.62496	−0.269078
$438$	−7.33063	−0.350271
$439$	−8.31385	−0.396798	−0.198399	−	0.980121i	$-0.563574\pi$
$439$	−8.31385	−0.396798	−0.198399	+	0.980121i	$0.563574\pi$
$440$	−75.4158	−3.59531
$441$	−5.47634	−0.260778
$442$	9.28580	0.441681
$443$	−18.3306	−0.870911	−0.435456	−	0.900210i	$-0.643413\pi$
$443$	−18.3306	−0.870911	−0.435456	+	0.900210i	$0.643413\pi$
$444$	3.76143	0.178510
$445$	−37.6940	−1.78687
$446$	32.5394	1.54079
$447$	13.9620	0.660378
$448$	−27.9190	−1.31905
$449$	−32.8176	−1.54876	−0.774380	−	0.632721i	$-0.781938\pi$
$449$	−32.8176	−1.54876	−0.774380	+	0.632721i	$0.781938\pi$
$450$	−2.55479	−0.120434
$451$	−12.8342	−0.604338
$452$	11.2585	0.529554
$453$	8.66012	0.406888
$454$	71.7559	3.36767
$455$	10.3585	0.485613
$456$	−10.6985	−0.501001
$457$	27.5574	1.28908	0.644541	−	0.764570i	$-0.277049\pi$
$457$	27.5574	1.28908	0.644541	+	0.764570i	$0.277049\pi$
$458$	−58.4354	−2.73051
$459$	1.00000	0.0466760
$460$	−59.9602	−2.79566
$461$	−19.6367	−0.914570	−0.457285	−	0.889320i	$-0.651178\pi$
$461$	−19.6367	−0.914570	−0.457285	+	0.889320i	$0.651178\pi$
$462$	11.6333	0.541229
$463$	3.00038	0.139440	0.0697198	−	0.997567i	$-0.477789\pi$
$463$	3.00038	0.139440	0.0697198	+	0.997567i	$0.477789\pi$
$464$	94.3230	4.37883
$465$	−5.69280	−0.263997
$466$	30.0997	1.39434
$467$	5.07245	0.234725	0.117362	−	0.993089i	$-0.462556\pi$
$467$	5.07245	0.234725	0.117362	+	0.993089i	$0.462556\pi$
$468$	−18.1745	−0.840118
$469$	−4.62536	−0.213579
$470$	84.1680	3.88238
$471$	−1.00000	−0.0460776
$472$	97.0779	4.46837
$473$	−2.69040	−0.123705
$474$	−8.94835	−0.411012
$475$	1.14392	0.0524867
$476$	−6.51923	−0.298809
$477$	−8.40319	−0.384756
$478$	−57.4374	−2.62713
$479$	11.7667	0.537633	0.268816	−	0.963191i	$-0.413368\pi$
$479$	11.7667	0.537633	0.268816	+	0.963191i	$0.413368\pi$
$480$	−44.5347	−2.03272
$481$	−2.45083	−0.111748
$482$	−47.9283	−2.18307
$483$	5.74666	0.261482
$484$	6.32853	0.287661
$485$	29.3096	1.33088
$486$	−2.69841	−0.122403
$487$	−6.52984	−0.295895	−0.147948	−	0.988995i	$-0.547267\pi$
$487$	−6.52984	−0.295895	−0.147948	+	0.988995i	$0.547267\pi$
$488$	78.8896	3.57116
$489$	−1.59972	−0.0723418
$490$	36.0362	1.62795
$491$	−18.0835	−0.816097	−0.408049	−	0.912960i	$-0.633791\pi$
$491$	−18.0835	−0.816097	−0.408049	+	0.912960i	$0.633791\pi$
$492$	−19.4076	−0.874961
$493$	7.07562	0.318670
$494$	11.2194	0.504783
$495$	8.51706	0.382813
$496$	−31.1199	−1.39732
$497$	4.92459	0.220898
$498$	−2.57042	−0.115183
$499$	−25.8776	−1.15844	−0.579219	−	0.815172i	$-0.696642\pi$
$499$	−25.8776	−1.15844	−0.579219	+	0.815172i	$0.696642\pi$
$500$	−52.2028	−2.33458
$501$	10.0057	0.447023
$502$	31.8283	1.42057
$503$	24.5847	1.09618	0.548089	−	0.836420i	$-0.315355\pi$
$503$	24.5847	1.09618	0.548089	+	0.836420i	$0.315355\pi$
$504$	10.9299	0.486857
$505$	−21.5161	−0.957455
$506$	43.8761	1.95053
$507$	−1.15808	−0.0514323
$508$	17.5186	0.777261
$509$	−14.8936	−0.660145	−0.330073	−	0.943956i	$-0.607073\pi$
$509$	−14.8936	−0.660145	−0.330073	+	0.943956i	$0.607073\pi$
$510$	−6.58035	−0.291383
$511$	−3.35334	−0.148343
$512$	−7.37234	−0.325815
$513$	1.20823	0.0533446
$514$	75.2037	3.31709
$515$	−4.73955	−0.208849
$516$	−4.06836	−0.179100
$517$	−44.6732	−1.96472
$518$	2.37222	0.104229
$519$	6.75933	0.296701
$520$	74.3060	3.25854
$521$	−20.2273	−0.886173	−0.443087	−	0.896479i	$-0.646117\pi$
$521$	−20.2273	−0.886173	−0.443087	+	0.896479i	$0.646117\pi$
$522$	−19.0930	−0.835676
$523$	−6.13209	−0.268138	−0.134069	−	0.990972i	$-0.542804\pi$
$523$	−6.13209	−0.268138	−0.134069	+	0.990972i	$0.542804\pi$
$524$	−34.9852	−1.52834
$525$	−1.16867	−0.0510049
$526$	−40.4546	−1.76390
$527$	−2.33445	−0.101690
$528$	46.5588	2.02621
$529$	−1.32589	−0.0576475
$530$	55.2960	2.40190
$531$	−10.9635	−0.475774
$532$	−7.87672	−0.341499
$533$	12.6453	0.547730
$534$	41.7100	1.80497
$535$	−19.7641	−0.854478
$536$	−33.1798	−1.43315
$537$	21.8132	0.941309
$538$	−20.6488	−0.890232
$539$	−19.1267	−0.823843
$540$	12.8793	0.554237
$541$	6.97721	0.299974	0.149987	−	0.988688i	$-0.452077\pi$
$541$	6.97721	0.299974	0.149987	+	0.988688i	$0.452077\pi$
$542$	25.5888	1.09913
$543$	0.906109	0.0388849
$544$	−18.2624	−0.782993
$545$	20.9534	0.897545
$546$	−11.4621	−0.490533
$547$	−18.4869	−0.790442	−0.395221	−	0.918586i	$-0.629332\pi$
$547$	−18.4869	−0.790442	−0.395221	+	0.918586i	$0.629332\pi$
$548$	−81.0465	−3.46213
$549$	−8.90938	−0.380243
$550$	−8.92287	−0.380472
$551$	8.54896	0.364198
$552$	41.2233	1.75458
$553$	−4.09335	−0.174067
$554$	56.1286	2.38468
$555$	1.73677	0.0737218
$556$	36.3614	1.54207
$557$	−9.42857	−0.399501	−0.199751	−	0.979847i	$-0.564013\pi$
$557$	−9.42857	−0.399501	−0.199751	+	0.979847i	$0.564013\pi$
$558$	6.29932	0.266671
$559$	2.65081	0.112117
$560$	−40.1271	−1.69568
$561$	3.49260	0.147458
$562$	19.4956	0.822373
$563$	−41.0363	−1.72947	−0.864737	−	0.502225i	$-0.832515\pi$
$563$	−41.0363	−1.72947	−0.864737	+	0.502225i	$0.832515\pi$
$564$	−67.5538	−2.84453
$565$	5.19838	0.218698
$566$	36.7165	1.54331
$567$	−1.23437	−0.0518386
$568$	35.3263	1.48226
$569$	25.8530	1.08381	0.541907	−	0.840438i	$-0.317702\pi$
$569$	25.8530	1.08381	0.541907	+	0.840438i	$0.317702\pi$
$570$	−7.95057	−0.333013
$571$	−24.8432	−1.03965	−0.519827	−	0.854272i	$-0.674004\pi$
$571$	−24.8432	−1.03965	−0.519827	+	0.854272i	$0.674004\pi$
$572$	−63.4763	−2.65408
$573$	−8.97584	−0.374971
$574$	−12.2397	−0.510877
$575$	−4.40776	−0.183816
$576$	22.6181	0.942419
$577$	6.87932	0.286390	0.143195	−	0.989694i	$-0.454262\pi$
$577$	6.87932	0.286390	0.143195	+	0.989694i	$0.454262\pi$
$578$	−2.69841	−0.112239
$579$	−23.4655	−0.975194
$580$	91.1292	3.78393
$581$	−1.17582	−0.0487812
$582$	−32.4323	−1.34436
$583$	−29.3490	−1.21551
$584$	−24.0550	−0.995402
$585$	−8.39174	−0.346956
$586$	16.6748	0.688830
$587$	−9.56783	−0.394906	−0.197453	−	0.980312i	$-0.563267\pi$
$587$	−9.56783	−0.394906	−0.197453	+	0.980312i	$0.563267\pi$
$588$	−28.9229	−1.19276
$589$	−2.82055	−0.116219
$590$	72.1435	2.97010
$591$	−10.4199	−0.428619
$592$	9.49411	0.390205
$593$	−0.994619	−0.0408441	−0.0204221	−	0.999791i	$-0.506501\pi$
$593$	−0.994619	−0.0408441	−0.0204221	+	0.999791i	$0.506501\pi$
$594$	−9.42448	−0.386691
$595$	−3.01013	−0.123403
$596$	73.7391	3.02047
$597$	−17.5247	−0.717239
$598$	−43.2305	−1.76783
$599$	−44.2642	−1.80859	−0.904294	−	0.426910i	$-0.859602\pi$
$599$	−44.2642	−1.80859	−0.904294	+	0.426910i	$0.859602\pi$
$600$	−8.38339	−0.342250
$601$	23.2137	0.946907	0.473454	−	0.880819i	$-0.343007\pi$
$601$	23.2137	0.946907	0.473454	+	0.880819i	$0.343007\pi$
$602$	−2.56579	−0.104574
$603$	3.74715	0.152596
$604$	45.7379	1.86105
$605$	2.92208	0.118799
$606$	23.8085	0.967154
$607$	32.5287	1.32030	0.660150	−	0.751133i	$-0.270492\pi$
$607$	32.5287	1.32030	0.660150	+	0.751133i	$0.270492\pi$
$608$	−22.0651	−0.894858
$609$	−8.73392	−0.353916
$610$	58.6269	2.37373
$611$	44.0158	1.78069
$612$	5.28144	0.213489
$613$	−2.59213	−0.104695	−0.0523476	−	0.998629i	$-0.516670\pi$
$613$	−2.59213	−0.104695	−0.0523476	+	0.998629i	$0.516670\pi$
$614$	−60.7382	−2.45119
$615$	−8.96107	−0.361345
$616$	38.1738	1.53807
$617$	25.1653	1.01312	0.506558	−	0.862206i	$-0.330918\pi$
$617$	25.1653	1.01312	0.506558	+	0.862206i	$0.330918\pi$
$618$	5.24451	0.210965
$619$	37.6061	1.51152	0.755759	−	0.654850i	$-0.227268\pi$
$619$	37.6061	1.51152	0.755759	+	0.654850i	$0.227268\pi$
$620$	−30.0661	−1.20749
$621$	−4.65555	−0.186821
$622$	−47.5986	−1.90853
$623$	19.0799	0.764420
$624$	−45.8737	−1.83642
$625$	−28.8375	−1.15350
$626$	68.6237	2.74275
$627$	4.21986	0.168525
$628$	−5.28144	−0.210752
$629$	0.712199	0.0283972
$630$	8.12258	0.323611
$631$	−16.4795	−0.656038	−0.328019	−	0.944671i	$-0.606381\pi$
$631$	−16.4795	−0.656038	−0.328019	+	0.944671i	$0.606381\pi$
$632$	−29.3634	−1.16802
$633$	10.2134	0.405945
$634$	81.8614	3.25113
$635$	8.08886	0.320997
$636$	−44.3809	−1.75982
$637$	18.8452	0.746675
$638$	−66.6841	−2.64005
$639$	−3.98956	−0.157825
$640$	−59.7656	−2.36244
$641$	11.4038	0.450423	0.225211	−	0.974310i	$-0.427693\pi$
$641$	11.4038	0.450423	0.225211	+	0.974310i	$0.427693\pi$
$642$	21.8698	0.863133
$643$	15.0119	0.592012	0.296006	−	0.955186i	$-0.404345\pi$
$643$	15.0119	0.592012	0.296006	+	0.955186i	$0.404345\pi$
$644$	30.3506	1.19598
$645$	−1.87849	−0.0739654
$646$	−3.26030	−0.128275
$647$	17.5787	0.691091	0.345546	−	0.938402i	$-0.387694\pi$
$647$	17.5787	0.691091	0.345546	+	0.938402i	$0.387694\pi$
$648$	−8.85467	−0.347844
$649$	−38.2910	−1.50305
$650$	8.79157	0.344834
$651$	2.88157	0.112938
$652$	−8.44881	−0.330881
$653$	3.97975	0.155740	0.0778698	−	0.996964i	$-0.475188\pi$
$653$	3.97975	0.155740	0.0778698	+	0.996964i	$0.475188\pi$
$654$	−23.1858	−0.906637
$655$	−16.1538	−0.631179
$656$	−48.9860	−1.91258
$657$	2.71664	0.105986
$658$	−42.6041	−1.66088
$659$	−10.3064	−0.401482	−0.200741	−	0.979644i	$-0.564335\pi$
$659$	−10.3064	−0.401482	−0.200741	+	0.979644i	$0.564335\pi$
$660$	44.9823	1.75093
$661$	0.378656	0.0147280	0.00736401	−	0.999973i	$-0.497656\pi$
$661$	0.378656	0.0147280	0.00736401	+	0.999973i	$0.497656\pi$
$662$	−37.7001	−1.46526
$663$	−3.44121	−0.133645
$664$	−8.43467	−0.327329
$665$	−3.63692	−0.141034
$666$	−1.92181	−0.0744685
$667$	−32.9409	−1.27548
$668$	52.8446	2.04462
$669$	−12.0587	−0.466217
$670$	−24.6576	−0.952606
$671$	−31.1169	−1.20125
$672$	22.5425	0.869595
$673$	19.2403	0.741660	0.370830	−	0.928701i	$-0.379073\pi$
$673$	19.2403	0.741660	0.370830	+	0.928701i	$0.379073\pi$
$674$	55.9554	2.15532
$675$	0.946776	0.0364414
$676$	−6.11634	−0.235244
$677$	20.0072	0.768941	0.384470	−	0.923137i	$-0.374384\pi$
$677$	20.0072	0.768941	0.384470	+	0.923137i	$0.374384\pi$
$678$	−5.75223	−0.220913
$679$	−14.8359	−0.569350
$680$	−21.5930	−0.828054
$681$	−26.5919	−1.01900
$682$	22.0010	0.842462
$683$	−47.6894	−1.82479	−0.912393	−	0.409315i	$-0.865768\pi$
$683$	−47.6894	−1.82479	−0.912393	+	0.409315i	$0.865768\pi$
$684$	6.38118	0.243990
$685$	−37.4217	−1.42981
$686$	−41.5566	−1.58664
$687$	21.6555	0.826207
$688$	−10.2688	−0.391495
$689$	28.9171	1.10166
$690$	30.6351	1.16626
$691$	17.3439	0.659792	0.329896	−	0.944017i	$-0.392986\pi$
$691$	17.3439	0.659792	0.329896	+	0.944017i	$0.392986\pi$
$692$	35.6989	1.35707
$693$	−4.31115	−0.163767
$694$	−40.6072	−1.54143
$695$	16.7892	0.636850
$696$	−62.6523	−2.37483
$697$	−3.67468	−0.139188
$698$	−23.4685	−0.888296
$699$	−11.1546	−0.421906
$700$	−6.17225	−0.233289
$701$	−17.4418	−0.658768	−0.329384	−	0.944196i	$-0.606841\pi$
$701$	−17.4418	−0.658768	−0.329384	+	0.944196i	$0.606841\pi$
$702$	9.28580	0.350470
$703$	0.860499	0.0324543
$704$	78.9959	2.97727
$705$	−31.1917	−1.17475
$706$	−11.5594	−0.435046
$707$	10.8910	0.409598
$708$	−57.9029	−2.17612
$709$	46.6728	1.75283	0.876417	−	0.481552i	$-0.159927\pi$
$709$	46.6728	1.75283	0.876417	+	0.481552i	$0.159927\pi$
$710$	26.2527	0.985248
$711$	3.31615	0.124365
$712$	136.869	5.12937
$713$	10.8682	0.407015
$714$	3.33083	0.124653
$715$	−29.3090	−1.09609
$716$	115.205	4.30541
$717$	21.2856	0.794926
$718$	−52.0842	−1.94377
$719$	−27.2284	−1.01545	−0.507724	−	0.861520i	$-0.669513\pi$
$719$	−27.2284	−1.01545	−0.507724	+	0.861520i	$0.669513\pi$
$720$	32.5082	1.21151
$721$	2.39906	0.0893456
$722$	47.3307	1.76147
$723$	17.7616	0.660563
$724$	4.78556	0.177854
$725$	6.69903	0.248796
$726$	−3.23340	−0.120003
$727$	−15.5808	−0.577860	−0.288930	−	0.957350i	$-0.593300\pi$
$727$	−15.5808	−0.577860	−0.288930	+	0.957350i	$0.593300\pi$
$728$	−37.6121	−1.39400
$729$	1.00000	0.0370370
$730$	−17.8765	−0.661638
$731$	−0.770314	−0.0284911
$732$	−47.0543	−1.73918
$733$	24.3282	0.898583	0.449291	−	0.893385i	$-0.351677\pi$
$733$	24.3282	0.898583	0.449291	+	0.893385i	$0.351677\pi$
$734$	−42.3663	−1.56377
$735$	−13.3546	−0.492592
$736$	85.0213	3.13393
$737$	13.0873	0.482077
$738$	9.91580	0.365006
$739$	−29.0304	−1.06790	−0.533950	−	0.845516i	$-0.679293\pi$
$739$	−29.0304	−1.06790	−0.533950	+	0.845516i	$0.679293\pi$
$740$	9.17264	0.337193
$741$	−4.15776	−0.152739
$742$	−27.9896	−1.02753
$743$	−21.8023	−0.799850	−0.399925	−	0.916548i	$-0.630964\pi$
$743$	−21.8023	−0.799850	−0.399925	+	0.916548i	$0.630964\pi$
$744$	20.6708	0.757828
$745$	34.0476	1.24741
$746$	−80.3997	−2.94364
$747$	0.952567	0.0348526
$748$	18.4459	0.674451
$749$	10.0042	0.365545
$750$	26.6717	0.973911
$751$	−18.9991	−0.693288	−0.346644	−	0.937997i	$-0.612679\pi$
$751$	−18.9991	−0.693288	−0.346644	+	0.937997i	$0.612679\pi$
$752$	−170.510	−6.21787
$753$	−11.7952	−0.429841
$754$	65.7029	2.39276
$755$	21.1186	0.768584
$756$	−6.51923	−0.237102
$757$	−8.44855	−0.307068	−0.153534	−	0.988143i	$-0.549065\pi$
$757$	−8.44855	−0.307068	−0.153534	+	0.988143i	$0.549065\pi$
$758$	30.6660	1.11384
$759$	−16.2600	−0.590199
$760$	−26.0893	−0.946357
$761$	6.25727	0.226826	0.113413	−	0.993548i	$-0.463822\pi$
$761$	6.25727	0.226826	0.113413	+	0.993548i	$0.463822\pi$
$762$	−8.95066	−0.324248
$763$	−10.6062	−0.383969
$764$	−47.4053	−1.71506
$765$	2.43860	0.0881678
$766$	−14.4942	−0.523697
$767$	37.7276	1.36226
$768$	20.8969	0.754054
$769$	−29.8427	−1.07616	−0.538078	−	0.842895i	$-0.680849\pi$
$769$	−29.8427	−1.07616	−0.538078	+	0.842895i	$0.680849\pi$
$770$	28.3689	1.02234
$771$	−27.8696	−1.00370
$772$	−123.932	−4.46040
$773$	−6.44045	−0.231647	−0.115823	−	0.993270i	$-0.536951\pi$
$773$	−6.44045	−0.231647	−0.115823	+	0.993270i	$0.536951\pi$
$774$	2.07862	0.0747146
$775$	−2.21020	−0.0793928
$776$	−106.425	−3.82042
$777$	−0.879116	−0.0315381
$778$	−54.2414	−1.94465
$779$	−4.43985	−0.159074
$780$	−44.3204	−1.58693
$781$	−13.9339	−0.498596
$782$	12.5626	0.449237
$783$	7.07562	0.252862
$784$	−73.0033	−2.60726
$785$	−2.43860	−0.0870374
$786$	17.8748	0.637573
$787$	−37.2987	−1.32955	−0.664777	−	0.747041i	$-0.731474\pi$
$787$	−37.2987	−1.32955	−0.664777	+	0.747041i	$0.731474\pi$
$788$	−55.0322	−1.96044
$789$	14.9920	0.533729
$790$	−21.8215	−0.776373
$791$	−2.63131	−0.0935586
$792$	−30.9258	−1.09890
$793$	30.6590	1.08873
$794$	−96.0834	−3.40987
$795$	−20.4920	−0.726778
$796$	−92.5556	−3.28055
$797$	23.2872	0.824876	0.412438	−	0.910986i	$-0.364677\pi$
$797$	23.2872	0.824876	0.412438	+	0.910986i	$0.364677\pi$
$798$	4.02441	0.142462
$799$	−12.7908	−0.452506
$800$	−17.2904	−0.611307
$801$	−15.4572	−0.546154
$802$	−69.7323	−2.46233
$803$	9.48815	0.334830
$804$	19.7903	0.697951
$805$	14.0138	0.493922
$806$	−21.6773	−0.763549
$807$	7.65219	0.269370
$808$	78.1260	2.74846
$809$	−29.0041	−1.01973	−0.509865	−	0.860254i	$-0.670305\pi$
$809$	−29.0041	−1.01973	−0.509865	+	0.860254i	$0.670305\pi$
$810$	−6.58035	−0.231210
$811$	42.7843	1.50236	0.751180	−	0.660098i	$-0.229485\pi$
$811$	42.7843	1.50236	0.751180	+	0.660098i	$0.229485\pi$
$812$	−46.1277	−1.61876
$813$	−9.48291	−0.332580
$814$	−6.71211	−0.235259
$815$	−3.90108	−0.136649
$816$	13.3307	0.466668
$817$	−0.930714	−0.0325616
$818$	−24.9024	−0.870691
$819$	4.24772	0.148427
$820$	−47.3273	−1.65274
$821$	−32.4011	−1.13081	−0.565403	−	0.824815i	$-0.691279\pi$
$821$	−32.4011	−1.13081	−0.565403	+	0.824815i	$0.691279\pi$
$822$	41.4086	1.44429
$823$	−19.4853	−0.679214	−0.339607	−	0.940567i	$-0.610294\pi$
$823$	−19.4853	−0.679214	−0.339607	+	0.940567i	$0.610294\pi$
$824$	17.2095	0.599522
$825$	3.30671	0.115125
$826$	−36.5175	−1.27061
$827$	−2.01554	−0.0700871	−0.0350436	−	0.999386i	$-0.511157\pi$
$827$	−2.01554	−0.0700871	−0.0350436	+	0.999386i	$0.511157\pi$
$828$	−24.5880	−0.854491
$829$	−38.9441	−1.35258	−0.676292	−	0.736634i	$-0.736414\pi$
$829$	−38.9441	−1.35258	−0.676292	+	0.736634i	$0.736414\pi$
$830$	−6.26823	−0.217573
$831$	−20.8006	−0.721565
$832$	−77.8335	−2.69839
$833$	−5.47634	−0.189744
$834$	−18.5779	−0.643301
$835$	24.4000	0.844395
$836$	22.2869	0.770809
$837$	−2.33445	−0.0806905
$838$	−63.1008	−2.17978
$839$	44.2608	1.52805	0.764027	−	0.645184i	$-0.223219\pi$
$839$	44.2608	1.52805	0.764027	+	0.645184i	$0.223219\pi$
$840$	26.6537	0.919641
$841$	21.0645	0.726361
$842$	−56.2862	−1.93975
$843$	−7.22485	−0.248837
$844$	53.9412	1.85673
$845$	−2.82410	−0.0971521
$846$	34.5149	1.18665
$847$	−1.47909	−0.0508222
$848$	−112.020	−3.84679
$849$	−13.6067	−0.466981
$850$	−2.55479	−0.0876287
$851$	−3.31568	−0.113660
$852$	−21.0706	−0.721867
$853$	−33.9978	−1.16406	−0.582032	−	0.813166i	$-0.697742\pi$
$853$	−33.9978	−1.16406	−0.582032	+	0.813166i	$0.697742\pi$
$854$	−29.6757	−1.01548
$855$	2.94639	0.100764
$856$	71.7644	2.45286
$857$	7.45828	0.254770	0.127385	−	0.991853i	$-0.459342\pi$
$857$	7.45828	0.254770	0.127385	+	0.991853i	$0.459342\pi$
$858$	32.4316	1.10720
$859$	24.4095	0.832840	0.416420	−	0.909172i	$-0.363285\pi$
$859$	24.4095	0.832840	0.416420	+	0.909172i	$0.363285\pi$
$860$	−9.92111	−0.338307
$861$	4.53590	0.154583
$862$	−8.98796	−0.306131
$863$	13.9561	0.475072	0.237536	−	0.971379i	$-0.423660\pi$
$863$	13.9561	0.475072	0.237536	+	0.971379i	$0.423660\pi$
$864$	−18.2624	−0.621299
$865$	16.4833	0.560449
$866$	−80.6022	−2.73898
$867$	1.00000	0.0339618
$868$	15.2188	0.516561
$869$	11.5820	0.392892
$870$	−46.5601	−1.57854
$871$	−12.8947	−0.436921
$872$	−76.0827	−2.57649
$873$	12.0190	0.406783
$874$	15.1785	0.513419
$875$	12.2007	0.412460
$876$	14.3478	0.484767
$877$	−14.8461	−0.501318	−0.250659	−	0.968075i	$-0.580647\pi$
$877$	−14.8461	−0.501318	−0.250659	+	0.968075i	$0.580647\pi$
$878$	22.4342	0.757117
$879$	−6.17949	−0.208429
$880$	113.538	3.82738
$881$	−23.7535	−0.800276	−0.400138	−	0.916455i	$-0.631038\pi$
$881$	−23.7535	−0.800276	−0.400138	+	0.916455i	$0.631038\pi$
$882$	14.7774	0.497582
$883$	−11.1298	−0.374548	−0.187274	−	0.982308i	$-0.559965\pi$
$883$	−11.1298	−0.374548	−0.187274	+	0.982308i	$0.559965\pi$
$884$	−18.1745	−0.611275
$885$	−26.7355	−0.898705
$886$	49.4634	1.66176
$887$	26.7810	0.899220	0.449610	−	0.893225i	$-0.351563\pi$
$887$	26.7810	0.899220	0.449610	+	0.893225i	$0.351563\pi$
$888$	−6.30629	−0.211625
$889$	−4.09441	−0.137322
$890$	101.714	3.40946
$891$	3.49260	0.117007
$892$	−63.6874	−2.13241
$893$	−15.4542	−0.517155
$894$	−37.6751	−1.26004
$895$	53.1937	1.77807
$896$	30.2520	1.01065
$897$	16.0207	0.534916
$898$	88.5555	2.95514
$899$	−16.5177	−0.550896
$900$	5.00034	0.166678
$901$	−8.40319	−0.279951
$902$	34.6319	1.15312
$903$	0.950850	0.0316423
$904$	−18.8756	−0.627792
$905$	2.20964	0.0734509
$906$	−23.3686	−0.776369
$907$	2.25209	0.0747795	0.0373897	−	0.999301i	$-0.488096\pi$
$907$	2.25209	0.0747795	0.0373897	+	0.999301i	$0.488096\pi$
$908$	−140.443	−4.66077
$909$	−8.82314	−0.292645
$910$	−27.9515	−0.926583
$911$	4.31651	0.143012	0.0715062	−	0.997440i	$-0.477219\pi$
$911$	4.31651	0.143012	0.0715062	+	0.997440i	$0.477219\pi$
$912$	16.1065	0.533340
$913$	3.32694	0.110106
$914$	−74.3613	−2.45965
$915$	−21.7264	−0.718253
$916$	114.372	3.77895
$917$	8.17669	0.270018
$918$	−2.69841	−0.0890609
$919$	−1.86298	−0.0614540	−0.0307270	−	0.999528i	$-0.509782\pi$
$919$	−1.86298	−0.0614540	−0.0307270	+	0.999528i	$0.509782\pi$
$920$	100.527	3.31429
$921$	22.5089	0.741692
$922$	52.9878	1.74506
$923$	13.7289	0.451893
$924$	−22.7691	−0.749048
$925$	0.674293	0.0221706
$926$	−8.09627	−0.266060
$927$	−1.94355	−0.0638346
$928$	−129.218	−4.24178
$929$	−43.9466	−1.44184	−0.720920	−	0.693018i	$-0.756281\pi$
$929$	−43.9466	−1.44184	−0.720920	+	0.693018i	$0.756281\pi$
$930$	15.3615	0.503724
$931$	−6.61666	−0.216852
$932$	−58.9123	−1.92974
$933$	17.6395	0.577491
$934$	−13.6876	−0.447870
$935$	8.51706	0.278538
$936$	30.4708	0.995968
$937$	−3.43674	−0.112273	−0.0561366	−	0.998423i	$-0.517878\pi$
$937$	−3.43674	−0.112273	−0.0561366	+	0.998423i	$0.517878\pi$
$938$	12.4811	0.407524
$939$	−25.4311	−0.829913
$940$	−164.737	−5.37312
$941$	−45.6384	−1.48777	−0.743885	−	0.668307i	$-0.767019\pi$
$941$	−45.6384	−1.48777	−0.743885	+	0.668307i	$0.767019\pi$
$942$	2.69841	0.0879191
$943$	17.1076	0.557101
$944$	−146.151	−4.75680
$945$	−3.01013	−0.0979196
$946$	7.25981	0.236037
$947$	−12.3422	−0.401068	−0.200534	−	0.979687i	$-0.564268\pi$
$947$	−12.3422	−0.401068	−0.200534	+	0.979687i	$0.564268\pi$
$948$	17.5141	0.568830
$949$	−9.34854	−0.303466
$950$	−3.08677	−0.100148
$951$	−30.3369	−0.983740
$952$	10.9299	0.354241
$953$	19.7758	0.640602	0.320301	−	0.947316i	$-0.396216\pi$
$953$	19.7758	0.640602	0.320301	+	0.947316i	$0.396216\pi$
$954$	22.6753	0.734140
$955$	−21.8885	−0.708295
$956$	112.419	3.63588
$957$	24.7123	0.798836
$958$	−31.7513	−1.02584
$959$	18.9420	0.611670
$960$	55.1564	1.78017
$961$	−25.5503	−0.824204
$962$	6.61334	0.213223
$963$	−8.10470	−0.261170
$964$	93.8070	3.02132
$965$	−57.2231	−1.84208
$966$	−15.5069	−0.498925
$967$	−3.03264	−0.0975232	−0.0487616	−	0.998810i	$-0.515527\pi$
$967$	−3.03264	−0.0975232	−0.0487616	+	0.998810i	$0.515527\pi$
$968$	−10.6102	−0.341025
$969$	1.20823	0.0388139
$970$	−79.0895	−2.53941
$971$	36.2685	1.16391	0.581955	−	0.813221i	$-0.302288\pi$
$971$	36.2685	1.16391	0.581955	+	0.813221i	$0.302288\pi$
$972$	5.28144	0.169402
$973$	−8.49832	−0.272444
$974$	17.6202	0.564588
$975$	−3.25805	−0.104341
$976$	−118.768	−3.80168
$977$	3.32633	0.106419	0.0532093	−	0.998583i	$-0.483055\pi$
$977$	3.32633	0.106419	0.0532093	+	0.998583i	$0.483055\pi$
$978$	4.31670	0.138033
$979$	−53.9859	−1.72540
$980$	−70.5315	−2.25304
$981$	8.59238	0.274334
$982$	48.7968	1.55717
$983$	56.4765	1.80132	0.900660	−	0.434525i	$-0.143084\pi$
$983$	56.4765	1.80132	0.900660	+	0.434525i	$0.143084\pi$
$984$	32.5380	1.03728
$985$	−25.4100	−0.809631
$986$	−19.0930	−0.608044
$987$	15.7886	0.502555
$988$	−21.9590	−0.698608
$989$	3.58623	0.114036
$990$	−22.9826	−0.730433
$991$	2.95518	0.0938745	0.0469373	−	0.998898i	$-0.485054\pi$
$991$	2.95518	0.0938745	0.0469373	+	0.998898i	$0.485054\pi$
$992$	42.6326	1.35359
$993$	13.9712	0.443363
$994$	−13.2886	−0.421488
$995$	−42.7358	−1.35482
$996$	5.03092	0.159411
$997$	8.46808	0.268187	0.134093	−	0.990969i	$-0.457188\pi$
$997$	8.46808	0.268187	0.134093	+	0.990969i	$0.457188\pi$
$998$	69.8283	2.21038
$999$	0.712199	0.0225330

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.1	✓	40	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)

\(f(q)\)	\(=\)	\(q-2.69841 q^{2} +1.00000 q^{3} +5.28144 q^{4} +2.43860 q^{5} -2.69841 q^{6} -1.23437 q^{7} -8.85467 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69841 q^{2} +1.00000 q^{3} +5.28144 q^{4} +2.43860 q^{5} -2.69841 q^{6} -1.23437 q^{7} -8.85467 q^{8} +1.00000 q^{9} -6.58035 q^{10} +3.49260 q^{11} +5.28144 q^{12} -3.44121 q^{13} +3.33083 q^{14} +2.43860 q^{15} +13.3307 q^{16} +1.00000 q^{17} -2.69841 q^{18} +1.20823 q^{19} +12.8793 q^{20} -1.23437 q^{21} -9.42448 q^{22} -4.65555 q^{23} -8.85467 q^{24} +0.946776 q^{25} +9.28580 q^{26} +1.00000 q^{27} -6.51923 q^{28} +7.07562 q^{29} -6.58035 q^{30} -2.33445 q^{31} -18.2624 q^{32} +3.49260 q^{33} -2.69841 q^{34} -3.01013 q^{35} +5.28144 q^{36} +0.712199 q^{37} -3.26030 q^{38} -3.44121 q^{39} -21.5930 q^{40} -3.67468 q^{41} +3.33083 q^{42} -0.770314 q^{43} +18.4459 q^{44} +2.43860 q^{45} +12.5626 q^{46} -12.7908 q^{47} +13.3307 q^{48} -5.47634 q^{49} -2.55479 q^{50} +1.00000 q^{51} -18.1745 q^{52} -8.40319 q^{53} -2.69841 q^{54} +8.51706 q^{55} +10.9299 q^{56} +1.20823 q^{57} -19.0930 q^{58} -10.9635 q^{59} +12.8793 q^{60} -8.90938 q^{61} +6.29932 q^{62} -1.23437 q^{63} +22.6181 q^{64} -8.39174 q^{65} -9.42448 q^{66} +3.74715 q^{67} +5.28144 q^{68} -4.65555 q^{69} +8.12258 q^{70} -3.98956 q^{71} -8.85467 q^{72} +2.71664 q^{73} -1.92181 q^{74} +0.946776 q^{75} +6.38118 q^{76} -4.31115 q^{77} +9.28580 q^{78} +3.31615 q^{79} +32.5082 q^{80} +1.00000 q^{81} +9.91580 q^{82} +0.952567 q^{83} -6.51923 q^{84} +2.43860 q^{85} +2.07862 q^{86} +7.07562 q^{87} -30.9258 q^{88} -15.4572 q^{89} -6.58035 q^{90} +4.24772 q^{91} -24.5880 q^{92} -2.33445 q^{93} +34.5149 q^{94} +2.94639 q^{95} -18.2624 q^{96} +12.0190 q^{97} +14.7774 q^{98} +3.49260 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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