LMFDB - Embedded newform 8007.2.a.d.1.20

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			1.20
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)

$f(q)$	$=$	$q-0.422786 q^{2} +1.00000 q^{3} -1.82125 q^{4} -3.08259 q^{5} -0.422786 q^{6} -4.30268 q^{7} +1.61557 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.422786 q^{2} +1.00000 q^{3} -1.82125 q^{4} -3.08259 q^{5} -0.422786 q^{6} -4.30268 q^{7} +1.61557 q^{8} +1.00000 q^{9} +1.30328 q^{10} -2.58617 q^{11} -1.82125 q^{12} -1.28681 q^{13} +1.81911 q^{14} -3.08259 q^{15} +2.95946 q^{16} +1.00000 q^{17} -0.422786 q^{18} -3.31065 q^{19} +5.61417 q^{20} -4.30268 q^{21} +1.09340 q^{22} +0.151219 q^{23} +1.61557 q^{24} +4.50235 q^{25} +0.544045 q^{26} +1.00000 q^{27} +7.83626 q^{28} +2.45690 q^{29} +1.30328 q^{30} +2.00542 q^{31} -4.48236 q^{32} -2.58617 q^{33} -0.422786 q^{34} +13.2634 q^{35} -1.82125 q^{36} +4.30468 q^{37} +1.39970 q^{38} -1.28681 q^{39} -4.98014 q^{40} +8.90849 q^{41} +1.81911 q^{42} +1.16968 q^{43} +4.71007 q^{44} -3.08259 q^{45} -0.0639333 q^{46} +6.67070 q^{47} +2.95946 q^{48} +11.5130 q^{49} -1.90353 q^{50} +1.00000 q^{51} +2.34360 q^{52} +7.99597 q^{53} -0.422786 q^{54} +7.97211 q^{55} -6.95129 q^{56} -3.31065 q^{57} -1.03874 q^{58} +0.837472 q^{59} +5.61417 q^{60} -12.7603 q^{61} -0.847865 q^{62} -4.30268 q^{63} -4.02384 q^{64} +3.96670 q^{65} +1.09340 q^{66} +6.68173 q^{67} -1.82125 q^{68} +0.151219 q^{69} -5.60757 q^{70} +7.71606 q^{71} +1.61557 q^{72} +7.41421 q^{73} -1.81996 q^{74} +4.50235 q^{75} +6.02952 q^{76} +11.1275 q^{77} +0.544045 q^{78} -8.32771 q^{79} -9.12280 q^{80} +1.00000 q^{81} -3.76639 q^{82} -15.3180 q^{83} +7.83626 q^{84} -3.08259 q^{85} -0.494526 q^{86} +2.45690 q^{87} -4.17815 q^{88} -13.0409 q^{89} +1.30328 q^{90} +5.53672 q^{91} -0.275408 q^{92} +2.00542 q^{93} -2.82028 q^{94} +10.2054 q^{95} -4.48236 q^{96} +6.86021 q^{97} -4.86755 q^{98} -2.58617 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.422786	−0.298955	−0.149477	−	0.988765i	$-0.547759\pi$
$2$	−0.422786	−0.298955	−0.149477	+	0.988765i	$0.547759\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.82125	−0.910626
$5$	−3.08259	−1.37858	−0.689288	−	0.724488i	$-0.742076\pi$
$5$	−3.08259	−1.37858	−0.689288	+	0.724488i	$0.742076\pi$
$6$	−0.422786	−0.172602
$7$	−4.30268	−1.62626	−0.813130	−	0.582083i	$-0.802238\pi$
$7$	−4.30268	−1.62626	−0.813130	+	0.582083i	$0.802238\pi$
$8$	1.61557	0.571191
$9$	1.00000	0.333333
$10$	1.30328	0.412132
$11$	−2.58617	−0.779761	−0.389880	−	0.920866i	$-0.627484\pi$
$11$	−2.58617	−0.779761	−0.389880	+	0.920866i	$0.627484\pi$
$12$	−1.82125	−0.525750
$13$	−1.28681	−0.356897	−0.178448	−	0.983949i	$-0.557108\pi$
$13$	−1.28681	−0.356897	−0.178448	+	0.983949i	$0.557108\pi$
$14$	1.81911	0.486178
$15$	−3.08259	−0.795921
$16$	2.95946	0.739865
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.422786	−0.0996517
$19$	−3.31065	−0.759514	−0.379757	−	0.925086i	$-0.623992\pi$
$19$	−3.31065	−0.759514	−0.379757	+	0.925086i	$0.623992\pi$
$20$	5.61417	1.25537
$21$	−4.30268	−0.938921
$22$	1.09340	0.233113
$23$	0.151219	0.0315313	0.0157657	−	0.999876i	$-0.494981\pi$
$23$	0.151219	0.0315313	0.0157657	+	0.999876i	$0.494981\pi$
$24$	1.61557	0.329777
$25$	4.50235	0.900470
$26$	0.544045	0.106696
$27$	1.00000	0.192450
$28$	7.83626	1.48091
$29$	2.45690	0.456236	0.228118	−	0.973634i	$-0.426743\pi$
$29$	2.45690	0.456236	0.228118	+	0.973634i	$0.426743\pi$
$30$	1.30328	0.237944
$31$	2.00542	0.360185	0.180092	−	0.983650i	$-0.442360\pi$
$31$	2.00542	0.360185	0.180092	+	0.983650i	$0.442360\pi$
$32$	−4.48236	−0.792378
$33$	−2.58617	−0.450195
$34$	−0.422786	−0.0725072
$35$	13.2634	2.24192
$36$	−1.82125	−0.303542
$37$	4.30468	0.707685	0.353843	−	0.935305i	$-0.384875\pi$
$37$	4.30468	0.707685	0.353843	+	0.935305i	$0.384875\pi$
$38$	1.39970	0.227061
$39$	−1.28681	−0.206054
$40$	−4.98014	−0.787430
$41$	8.90849	1.39127	0.695636	−	0.718394i	$-0.255123\pi$
$41$	8.90849	1.39127	0.695636	+	0.718394i	$0.255123\pi$
$42$	1.81911	0.280695
$43$	1.16968	0.178375	0.0891876	−	0.996015i	$-0.471573\pi$
$43$	1.16968	0.178375	0.0891876	+	0.996015i	$0.471573\pi$
$44$	4.71007	0.710070
$45$	−3.08259	−0.459525
$46$	−0.0639333	−0.00942645
$47$	6.67070	0.973021	0.486511	−	0.873675i	$-0.338270\pi$
$47$	6.67070	0.973021	0.486511	+	0.873675i	$0.338270\pi$
$48$	2.95946	0.427162
$49$	11.5130	1.64472
$50$	−1.90353	−0.269200
$51$	1.00000	0.140028
$52$	2.34360	0.324999
$53$	7.99597	1.09833	0.549166	−	0.835713i	$-0.314946\pi$
$53$	7.99597	1.09833	0.549166	+	0.835713i	$0.314946\pi$
$54$	−0.422786	−0.0575339
$55$	7.97211	1.07496
$56$	−6.95129	−0.928905
$57$	−3.31065	−0.438506
$58$	−1.03874	−0.136394
$59$	0.837472	0.109030	0.0545148	−	0.998513i	$-0.482639\pi$
$59$	0.837472	0.109030	0.0545148	+	0.998513i	$0.482639\pi$
$60$	5.61417	0.724786
$61$	−12.7603	−1.63379	−0.816896	−	0.576785i	$-0.804307\pi$
$61$	−12.7603	−1.63379	−0.816896	+	0.576785i	$0.804307\pi$
$62$	−0.847865	−0.107679
$63$	−4.30268	−0.542086
$64$	−4.02384	−0.502980
$65$	3.96670	0.492009
$66$	1.09340	0.134588
$67$	6.68173	0.816303	0.408151	−	0.912914i	$-0.366174\pi$
$67$	6.68173	0.816303	0.408151	+	0.912914i	$0.366174\pi$
$68$	−1.82125	−0.220859
$69$	0.151219	0.0182046
$70$	−5.60757	−0.670233
$71$	7.71606	0.915728	0.457864	−	0.889022i	$-0.348615\pi$
$71$	7.71606	0.915728	0.457864	+	0.889022i	$0.348615\pi$
$72$	1.61557	0.190397
$73$	7.41421	0.867768	0.433884	−	0.900969i	$-0.357143\pi$
$73$	7.41421	0.867768	0.433884	+	0.900969i	$0.357143\pi$
$74$	−1.81996	−0.211566
$75$	4.50235	0.519887
$76$	6.02952	0.691633
$77$	11.1275	1.26809
$78$	0.544045	0.0616010
$79$	−8.32771	−0.936941	−0.468470	−	0.883479i	$-0.655195\pi$
$79$	−8.32771	−0.936941	−0.468470	+	0.883479i	$0.655195\pi$
$80$	−9.12280	−1.01996
$81$	1.00000	0.111111
$82$	−3.76639	−0.415928
$83$	−15.3180	−1.68137	−0.840687	−	0.541521i	$-0.817849\pi$
$83$	−15.3180	−1.68137	−0.840687	+	0.541521i	$0.817849\pi$
$84$	7.83626	0.855006
$85$	−3.08259	−0.334354
$86$	−0.494526	−0.0533261
$87$	2.45690	0.263408
$88$	−4.17815	−0.445392
$89$	−13.0409	−1.38234	−0.691168	−	0.722695i	$-0.742903\pi$
$89$	−13.0409	−1.38234	−0.691168	+	0.722695i	$0.742903\pi$
$90$	1.30328	0.137377
$91$	5.53672	0.580406
$92$	−0.275408	−0.0287133
$93$	2.00542	0.207953
$94$	−2.82028	−0.290889
$95$	10.2054	1.04705
$96$	−4.48236	−0.457479
$97$	6.86021	0.696548	0.348274	−	0.937393i	$-0.386768\pi$
$97$	6.86021	0.696548	0.348274	+	0.937393i	$0.386768\pi$
$98$	−4.86755	−0.491697
$99$	−2.58617	−0.259920
$100$	−8.19991	−0.819991
$101$	−7.45233	−0.741535	−0.370767	−	0.928726i	$-0.620905\pi$
$101$	−7.45233	−0.741535	−0.370767	+	0.928726i	$0.620905\pi$
$102$	−0.422786	−0.0418621
$103$	8.28026	0.815879	0.407939	−	0.913009i	$-0.366248\pi$
$103$	8.28026	0.815879	0.407939	+	0.913009i	$0.366248\pi$
$104$	−2.07893	−0.203856
$105$	13.2634	1.29437
$106$	−3.38059	−0.328352
$107$	4.70409	0.454762	0.227381	−	0.973806i	$-0.426984\pi$
$107$	4.70409	0.454762	0.227381	+	0.973806i	$0.426984\pi$
$108$	−1.82125	−0.175250
$109$	4.39400	0.420869	0.210434	−	0.977608i	$-0.432512\pi$
$109$	4.39400	0.420869	0.210434	+	0.977608i	$0.432512\pi$
$110$	−3.37050	−0.321364
$111$	4.30468	0.408582
$112$	−12.7336	−1.20321
$113$	−5.29195	−0.497825	−0.248912	−	0.968526i	$-0.580073\pi$
$113$	−5.29195	−0.497825	−0.248912	+	0.968526i	$0.580073\pi$
$114$	1.39970	0.131093
$115$	−0.466146	−0.0434683
$116$	−4.47464	−0.415460
$117$	−1.28681	−0.118966
$118$	−0.354072	−0.0325949
$119$	−4.30268	−0.394426
$120$	−4.98014	−0.454623
$121$	−4.31171	−0.391973
$122$	5.39489	0.488430
$123$	8.90849	0.803252
$124$	−3.65238	−0.327994
$125$	1.53405	0.137210
$126$	1.81911	0.162059
$127$	−6.53366	−0.579769	−0.289884	−	0.957062i	$-0.593617\pi$
$127$	−6.53366	−0.579769	−0.289884	+	0.957062i	$0.593617\pi$
$128$	10.6660	0.942746
$129$	1.16968	0.102985
$130$	−1.67707	−0.147088
$131$	−16.7576	−1.46412	−0.732059	−	0.681242i	$-0.761440\pi$
$131$	−16.7576	−1.46412	−0.732059	+	0.681242i	$0.761440\pi$
$132$	4.71007	0.409959
$133$	14.2446	1.23517
$134$	−2.82494	−0.244038
$135$	−3.08259	−0.265307
$136$	1.61557	0.138534
$137$	−20.2186	−1.72739	−0.863697	−	0.504012i	$-0.831857\pi$
$137$	−20.2186	−1.72739	−0.863697	+	0.504012i	$0.831857\pi$
$138$	−0.0639333	−0.00544236
$139$	−7.06689	−0.599405	−0.299703	−	0.954033i	$-0.596887\pi$
$139$	−7.06689	−0.599405	−0.299703	+	0.954033i	$0.596887\pi$
$140$	−24.1560	−2.04155
$141$	6.67070	0.561774
$142$	−3.26224	−0.273761
$143$	3.32791	0.278294
$144$	2.95946	0.246622
$145$	−7.57362	−0.628955
$146$	−3.13463	−0.259423
$147$	11.5130	0.949579
$148$	−7.83991	−0.644437
$149$	5.84768	0.479060	0.239530	−	0.970889i	$-0.423007\pi$
$149$	5.84768	0.479060	0.239530	+	0.970889i	$0.423007\pi$
$150$	−1.90353	−0.155423
$151$	3.53625	0.287776	0.143888	−	0.989594i	$-0.454040\pi$
$151$	3.53625	0.287776	0.143888	+	0.989594i	$0.454040\pi$
$152$	−5.34859	−0.433828
$153$	1.00000	0.0808452
$154$	−4.70454	−0.379103
$155$	−6.18189	−0.496542
$156$	2.34360	0.187638
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	3.52084	0.280103
$159$	7.99597	0.634122
$160$	13.8173	1.09235
$161$	−0.650646	−0.0512781
$162$	−0.422786	−0.0332172
$163$	10.4238	0.816458	0.408229	−	0.912880i	$-0.366147\pi$
$163$	10.4238	0.816458	0.408229	+	0.912880i	$0.366147\pi$
$164$	−16.2246	−1.26693
$165$	7.97211	0.620628
$166$	6.47626	0.502655
$167$	19.5661	1.51407	0.757035	−	0.653374i	$-0.226647\pi$
$167$	19.5661	1.51407	0.757035	+	0.653374i	$0.226647\pi$
$168$	−6.95129	−0.536303
$169$	−11.3441	−0.872625
$170$	1.30328	0.0999567
$171$	−3.31065	−0.253171
$172$	−2.13029	−0.162433
$173$	18.0039	1.36881	0.684405	−	0.729102i	$-0.260062\pi$
$173$	18.0039	1.36881	0.684405	+	0.729102i	$0.260062\pi$
$174$	−1.03874	−0.0787470
$175$	−19.3722	−1.46440
$176$	−7.65368	−0.576918
$177$	0.837472	0.0629483
$178$	5.51352	0.413256
$179$	9.45241	0.706506	0.353253	−	0.935528i	$-0.385075\pi$
$179$	9.45241	0.706506	0.353253	+	0.935528i	$0.385075\pi$
$180$	5.61417	0.418455
$181$	−10.8859	−0.809140	−0.404570	−	0.914507i	$-0.632579\pi$
$181$	−10.8859	−0.809140	−0.404570	+	0.914507i	$0.632579\pi$
$182$	−2.34085	−0.173515
$183$	−12.7603	−0.943270
$184$	0.244305	0.0180104
$185$	−13.2696	−0.975598
$186$	−0.847865	−0.0621685
$187$	−2.58617	−0.189120
$188$	−12.1490	−0.886058
$189$	−4.30268	−0.312974
$190$	−4.31468	−0.313020
$191$	14.4755	1.04741	0.523706	−	0.851899i	$-0.324549\pi$
$191$	14.4755	1.04741	0.523706	+	0.851899i	$0.324549\pi$
$192$	−4.02384	−0.290396
$193$	−6.39596	−0.460391	−0.230196	−	0.973144i	$-0.573937\pi$
$193$	−6.39596	−0.460391	−0.230196	+	0.973144i	$0.573937\pi$
$194$	−2.90040	−0.208237
$195$	3.96670	0.284061
$196$	−20.9681	−1.49772
$197$	6.06415	0.432053	0.216026	−	0.976388i	$-0.430690\pi$
$197$	6.06415	0.432053	0.216026	+	0.976388i	$0.430690\pi$
$198$	1.09340	0.0777044
$199$	4.92760	0.349308	0.174654	−	0.984630i	$-0.444119\pi$
$199$	4.92760	0.349308	0.174654	+	0.984630i	$0.444119\pi$
$200$	7.27387	0.514340
$201$	6.68173	0.471293
$202$	3.15074	0.221686
$203$	−10.5713	−0.741957
$204$	−1.82125	−0.127513
$205$	−27.4612	−1.91797
$206$	−3.50078	−0.243911
$207$	0.151219	0.0105104
$208$	−3.80826	−0.264055
$209$	8.56190	0.592239
$210$	−5.60757	−0.386959
$211$	21.5691	1.48488	0.742438	−	0.669915i	$-0.233670\pi$
$211$	21.5691	1.48488	0.742438	+	0.669915i	$0.233670\pi$
$212$	−14.5627	−1.00017
$213$	7.71606	0.528696
$214$	−1.98882	−0.135953
$215$	−3.60565	−0.245904
$216$	1.61557	0.109926
$217$	−8.62869	−0.585754
$218$	−1.85772	−0.125821
$219$	7.41421	0.501006
$220$	−14.5192	−0.978885
$221$	−1.28681	−0.0865601
$222$	−1.81996	−0.122148
$223$	15.8358	1.06044	0.530221	−	0.847859i	$-0.322109\pi$
$223$	15.8358	1.06044	0.530221	+	0.847859i	$0.322109\pi$
$224$	19.2862	1.28861
$225$	4.50235	0.300157
$226$	2.23736	0.148827
$227$	13.7770	0.914410	0.457205	−	0.889361i	$-0.348851\pi$
$227$	13.7770	0.914410	0.457205	+	0.889361i	$0.348851\pi$
$228$	6.02952	0.399315
$229$	−2.27341	−0.150231	−0.0751157	−	0.997175i	$-0.523933\pi$
$229$	−2.27341	−0.150231	−0.0751157	+	0.997175i	$0.523933\pi$
$230$	0.197080	0.0129951
$231$	11.1275	0.732134
$232$	3.96931	0.260598
$233$	−5.99326	−0.392632	−0.196316	−	0.980541i	$-0.562898\pi$
$233$	−5.99326	−0.392632	−0.196316	+	0.980541i	$0.562898\pi$
$234$	0.544045	0.0355653
$235$	−20.5630	−1.34138
$236$	−1.52525	−0.0992852
$237$	−8.32771	−0.540943
$238$	1.81911	0.117916
$239$	−18.3428	−1.18649	−0.593247	−	0.805020i	$-0.702154\pi$
$239$	−18.3428	−1.18649	−0.593247	+	0.805020i	$0.702154\pi$
$240$	−9.12280	−0.588874
$241$	−0.558209	−0.0359574	−0.0179787	−	0.999838i	$-0.505723\pi$
$241$	−0.558209	−0.0359574	−0.0179787	+	0.999838i	$0.505723\pi$
$242$	1.82293	0.117182
$243$	1.00000	0.0641500
$244$	23.2398	1.48777
$245$	−35.4899	−2.26737
$246$	−3.76639	−0.240136
$247$	4.26017	0.271068
$248$	3.23991	0.205734
$249$	−15.3180	−0.970742
$250$	−0.648576	−0.0410195
$251$	−13.8345	−0.873225	−0.436613	−	0.899650i	$-0.643822\pi$
$251$	−13.8345	−0.873225	−0.436613	+	0.899650i	$0.643822\pi$
$252$	7.83626	0.493638
$253$	−0.391079	−0.0245869
$254$	2.76234	0.173325
$255$	−3.08259	−0.193039
$256$	3.53827	0.221142
$257$	−10.8395	−0.676152	−0.338076	−	0.941119i	$-0.609776\pi$
$257$	−10.8395	−0.676152	−0.338076	+	0.941119i	$0.609776\pi$
$258$	−0.494526	−0.0307879
$259$	−18.5217	−1.15088
$260$	−7.22436	−0.448036
$261$	2.45690	0.152079
$262$	7.08488	0.437705
$263$	−12.5915	−0.776423	−0.388211	−	0.921570i	$-0.626907\pi$
$263$	−12.5915	−0.776423	−0.388211	+	0.921570i	$0.626907\pi$
$264$	−4.17815	−0.257147
$265$	−24.6483	−1.51413
$266$	−6.02244	−0.369259
$267$	−13.0409	−0.798091
$268$	−12.1691	−0.743347
$269$	6.37761	0.388850	0.194425	−	0.980917i	$-0.437716\pi$
$269$	6.37761	0.388850	0.194425	+	0.980917i	$0.437716\pi$
$270$	1.30328	0.0793148
$271$	9.63410	0.585230	0.292615	−	0.956230i	$-0.405475\pi$
$271$	9.63410	0.585230	0.292615	+	0.956230i	$0.405475\pi$
$272$	2.95946	0.179444
$273$	5.53672	0.335098
$274$	8.54816	0.516413
$275$	−11.6439	−0.702151
$276$	−0.275408	−0.0165776
$277$	−9.31494	−0.559681	−0.279840	−	0.960047i	$-0.590282\pi$
$277$	−9.31494	−0.559681	−0.279840	+	0.960047i	$0.590282\pi$
$278$	2.98778	0.179195
$279$	2.00542	0.120062
$280$	21.4280	1.28057
$281$	11.7797	0.702716	0.351358	−	0.936241i	$-0.385720\pi$
$281$	11.7797	0.702716	0.351358	+	0.936241i	$0.385720\pi$
$282$	−2.82028	−0.167945
$283$	8.29362	0.493004	0.246502	−	0.969142i	$-0.420719\pi$
$283$	8.29362	0.493004	0.246502	+	0.969142i	$0.420719\pi$
$284$	−14.0529	−0.833885
$285$	10.2054	0.604513
$286$	−1.40699	−0.0831973
$287$	−38.3304	−2.26257
$288$	−4.48236	−0.264126
$289$	1.00000	0.0588235
$290$	3.20202	0.188029
$291$	6.86021	0.402152
$292$	−13.5031	−0.790212
$293$	29.5502	1.72634	0.863170	−	0.504914i	$-0.168476\pi$
$293$	29.5502	1.72634	0.863170	+	0.504914i	$0.168476\pi$
$294$	−4.86755	−0.283881
$295$	−2.58158	−0.150306
$296$	6.95453	0.404224
$297$	−2.58617	−0.150065
$298$	−2.47232	−0.143217
$299$	−0.194590	−0.0112534
$300$	−8.19991	−0.473422
$301$	−5.03277	−0.290084
$302$	−1.49508	−0.0860320
$303$	−7.45233	−0.428125
$304$	−9.79773	−0.561938
$305$	39.3348	2.25231
$306$	−0.422786	−0.0241691
$307$	15.0788	0.860592	0.430296	−	0.902688i	$-0.358409\pi$
$307$	15.0788	0.860592	0.430296	+	0.902688i	$0.358409\pi$
$308$	−20.2659	−1.15476
$309$	8.28026	0.471048
$310$	2.61362	0.148444
$311$	8.04754	0.456334	0.228167	−	0.973622i	$-0.426727\pi$
$311$	8.04754	0.456334	0.228167	+	0.973622i	$0.426727\pi$
$312$	−2.07893	−0.117696
$313$	−13.5319	−0.764866	−0.382433	−	0.923983i	$-0.624914\pi$
$313$	−13.5319	−0.764866	−0.382433	+	0.923983i	$0.624914\pi$
$314$	0.422786	0.0238592
$315$	13.2634	0.747307
$316$	15.1669	0.853203
$317$	−21.2672	−1.19448	−0.597241	−	0.802062i	$-0.703736\pi$
$317$	−21.2672	−1.19448	−0.597241	+	0.802062i	$0.703736\pi$
$318$	−3.38059	−0.189574
$319$	−6.35398	−0.355755
$320$	12.4038	0.693396
$321$	4.70409	0.262557
$322$	0.275084	0.0153298
$323$	−3.31065	−0.184209
$324$	−1.82125	−0.101181
$325$	−5.79366	−0.321375
$326$	−4.40705	−0.244084
$327$	4.39400	0.242989
$328$	14.3923	0.794683
$329$	−28.7019	−1.58238
$330$	−3.37050	−0.185540
$331$	8.98849	0.494052	0.247026	−	0.969009i	$-0.420547\pi$
$331$	8.98849	0.494052	0.247026	+	0.969009i	$0.420547\pi$
$332$	27.8980	1.53110
$333$	4.30468	0.235895
$334$	−8.27228	−0.452639
$335$	−20.5970	−1.12534
$336$	−12.7336	−0.694675
$337$	−15.3731	−0.837423	−0.418712	−	0.908119i	$-0.637518\pi$
$337$	−15.3731	−0.837423	−0.418712	+	0.908119i	$0.637518\pi$
$338$	4.79614	0.260876
$339$	−5.29195	−0.287419
$340$	5.61417	0.304471
$341$	−5.18637	−0.280858
$342$	1.39970	0.0756868
$343$	−19.4181	−1.04848
$344$	1.88971	0.101886
$345$	−0.466146	−0.0250964
$346$	−7.61179	−0.409213
$347$	−14.1186	−0.757927	−0.378964	−	0.925412i	$-0.623719\pi$
$347$	−14.1186	−0.757927	−0.378964	+	0.925412i	$0.623719\pi$
$348$	−4.47464	−0.239866
$349$	25.7632	1.37907	0.689537	−	0.724250i	$-0.257814\pi$
$349$	25.7632	1.37907	0.689537	+	0.724250i	$0.257814\pi$
$350$	8.19028	0.437789
$351$	−1.28681	−0.0686848
$352$	11.5922	0.617865
$353$	−13.2249	−0.703892	−0.351946	−	0.936020i	$-0.614480\pi$
$353$	−13.2249	−0.703892	−0.351946	+	0.936020i	$0.614480\pi$
$354$	−0.354072	−0.0188187
$355$	−23.7854	−1.26240
$356$	23.7508	1.25879
$357$	−4.30268	−0.227722
$358$	−3.99635	−0.211214
$359$	−18.5428	−0.978651	−0.489325	−	0.872101i	$-0.662757\pi$
$359$	−18.5428	−0.978651	−0.489325	+	0.872101i	$0.662757\pi$
$360$	−4.98014	−0.262477
$361$	−8.03963	−0.423138
$362$	4.60239	0.241897
$363$	−4.31171	−0.226306
$364$	−10.0838	−0.528533
$365$	−22.8550	−1.19628
$366$	5.39489	0.281995
$367$	−18.4204	−0.961539	−0.480769	−	0.876847i	$-0.659643\pi$
$367$	−18.4204	−0.961539	−0.480769	+	0.876847i	$0.659643\pi$
$368$	0.447527	0.0233289
$369$	8.90849	0.463757
$370$	5.61019	0.291660
$371$	−34.4041	−1.78617
$372$	−3.65238	−0.189367
$373$	26.1586	1.35444	0.677222	−	0.735779i	$-0.263184\pi$
$373$	26.1586	1.35444	0.677222	+	0.735779i	$0.263184\pi$
$374$	1.09340	0.0565383
$375$	1.53405	0.0792181
$376$	10.7770	0.555781
$377$	−3.16156	−0.162829
$378$	1.81911	0.0935651
$379$	−3.03298	−0.155794	−0.0778969	−	0.996961i	$-0.524821\pi$
$379$	−3.03298	−0.155794	−0.0778969	+	0.996961i	$0.524821\pi$
$380$	−18.5865	−0.953468
$381$	−6.53366	−0.334730
$382$	−6.12005	−0.313129
$383$	−4.69009	−0.239653	−0.119826	−	0.992795i	$-0.538234\pi$
$383$	−4.69009	−0.239653	−0.119826	+	0.992795i	$0.538234\pi$
$384$	10.6660	0.544295
$385$	−34.3014	−1.74816
$386$	2.70412	0.137636
$387$	1.16968	0.0594584
$388$	−12.4942	−0.634295
$389$	1.81359	0.0919526	0.0459763	−	0.998943i	$-0.485360\pi$
$389$	1.81359	0.0919526	0.0459763	+	0.998943i	$0.485360\pi$
$390$	−1.67707	−0.0849216
$391$	0.151219	0.00764747
$392$	18.6001	0.939449
$393$	−16.7576	−0.845309
$394$	−2.56384	−0.129164
$395$	25.6709	1.29164
$396$	4.71007	0.236690
$397$	−34.5011	−1.73156	−0.865781	−	0.500422i	$-0.833178\pi$
$397$	−34.5011	−1.73156	−0.865781	+	0.500422i	$0.833178\pi$
$398$	−2.08332	−0.104428
$399$	14.2446	0.713124
$400$	13.3245	0.666227
$401$	−17.8511	−0.891444	−0.445722	−	0.895171i	$-0.647053\pi$
$401$	−17.8511	−0.891444	−0.445722	+	0.895171i	$0.647053\pi$
$402$	−2.82494	−0.140895
$403$	−2.58060	−0.128549
$404$	13.5726	0.675261
$405$	−3.08259	−0.153175
$406$	4.46938	0.221812
$407$	−11.1327	−0.551825
$408$	1.61557	0.0799828
$409$	32.4253	1.60333	0.801664	−	0.597775i	$-0.203948\pi$
$409$	32.4253	1.60333	0.801664	+	0.597775i	$0.203948\pi$
$410$	11.6102	0.573388
$411$	−20.2186	−0.997311
$412$	−15.0804	−0.742960
$413$	−3.60337	−0.177310
$414$	−0.0639333	−0.00314215
$415$	47.2192	2.31790
$416$	5.76795	0.282797
$417$	−7.06689	−0.346067
$418$	−3.61985	−0.177053
$419$	31.9318	1.55997	0.779985	−	0.625798i	$-0.215227\pi$
$419$	31.9318	1.55997	0.779985	+	0.625798i	$0.215227\pi$
$420$	−24.1560	−1.17869
$421$	−25.2035	−1.22834	−0.614172	−	0.789172i	$-0.710510\pi$
$421$	−25.2035	−1.22834	−0.614172	+	0.789172i	$0.710510\pi$
$422$	−9.11910	−0.443911
$423$	6.67070	0.324340
$424$	12.9181	0.627357
$425$	4.50235	0.218396
$426$	−3.26224	−0.158056
$427$	54.9035	2.65697
$428$	−8.56733	−0.414118
$429$	3.32791	0.160673
$430$	1.52442	0.0735141
$431$	−6.63035	−0.319373	−0.159686	−	0.987168i	$-0.551048\pi$
$431$	−6.63035	−0.319373	−0.159686	+	0.987168i	$0.551048\pi$
$432$	2.95946	0.142387
$433$	3.35815	0.161382	0.0806911	−	0.996739i	$-0.474287\pi$
$433$	3.35815	0.161382	0.0806911	+	0.996739i	$0.474287\pi$
$434$	3.64809	0.175114
$435$	−7.57362	−0.363127
$436$	−8.00258	−0.383254
$437$	−0.500632	−0.0239485
$438$	−3.13463	−0.149778
$439$	−5.56038	−0.265382	−0.132691	−	0.991157i	$-0.542362\pi$
$439$	−5.56038	−0.265382	−0.132691	+	0.991157i	$0.542362\pi$
$440$	12.8795	0.614007
$441$	11.5130	0.548240
$442$	0.544045	0.0258776
$443$	−29.9902	−1.42488	−0.712438	−	0.701735i	$-0.752409\pi$
$443$	−29.9902	−1.42488	−0.712438	+	0.701735i	$0.752409\pi$
$444$	−7.83991	−0.372066
$445$	40.1998	1.90565
$446$	−6.69515	−0.317025
$447$	5.84768	0.276586
$448$	17.3133	0.817976
$449$	−21.5833	−1.01858	−0.509289	−	0.860596i	$-0.670091\pi$
$449$	−21.5833	−1.01858	−0.509289	+	0.860596i	$0.670091\pi$
$450$	−1.90353	−0.0897333
$451$	−23.0389	−1.08486
$452$	9.63797	0.453332
$453$	3.53625	0.166147
$454$	−5.82472	−0.273367
$455$	−17.0674	−0.800134
$456$	−5.34859	−0.250471
$457$	−29.9769	−1.40226	−0.701129	−	0.713034i	$-0.747320\pi$
$457$	−29.9769	−1.40226	−0.701129	+	0.713034i	$0.747320\pi$
$458$	0.961168	0.0449124
$459$	1.00000	0.0466760
$460$	0.848969	0.0395834
$461$	−14.5472	−0.677530	−0.338765	−	0.940871i	$-0.610009\pi$
$461$	−14.5472	−0.677530	−0.338765	+	0.940871i	$0.610009\pi$
$462$	−4.70454	−0.218875
$463$	14.9157	0.693189	0.346595	−	0.938015i	$-0.387338\pi$
$463$	14.9157	0.693189	0.346595	+	0.938015i	$0.387338\pi$
$464$	7.27111	0.337553
$465$	−6.18189	−0.286678
$466$	2.53387	0.117379
$467$	−20.8752	−0.965989	−0.482995	−	0.875623i	$-0.660451\pi$
$467$	−20.8752	−0.965989	−0.482995	+	0.875623i	$0.660451\pi$
$468$	2.34360	0.108333
$469$	−28.7493	−1.32752
$470$	8.69376	0.401013
$471$	−1.00000	−0.0460776
$472$	1.35300	0.0622767
$473$	−3.02501	−0.139090
$474$	3.52084	0.161718
$475$	−14.9057	−0.683920
$476$	7.83626	0.359174
$477$	7.99597	0.366111
$478$	7.75507	0.354709
$479$	19.1828	0.876482	0.438241	−	0.898857i	$-0.355602\pi$
$479$	19.1828	0.876482	0.438241	+	0.898857i	$0.355602\pi$
$480$	13.8173	0.630670
$481$	−5.53930	−0.252570
$482$	0.236003	0.0107496
$483$	−0.650646	−0.0296054
$484$	7.85270	0.356941
$485$	−21.1472	−0.960244
$486$	−0.422786	−0.0191780
$487$	−2.74504	−0.124390	−0.0621949	−	0.998064i	$-0.519810\pi$
$487$	−2.74504	−0.124390	−0.0621949	+	0.998064i	$0.519810\pi$
$488$	−20.6152	−0.933207
$489$	10.4238	0.471382
$490$	15.0047	0.677841
$491$	−43.0535	−1.94298	−0.971489	−	0.237086i	$-0.923808\pi$
$491$	−43.0535	−1.94298	−0.971489	+	0.237086i	$0.923808\pi$
$492$	−16.2246	−0.731462
$493$	2.45690	0.110653
$494$	−1.80114	−0.0810371
$495$	7.97211	0.358320
$496$	5.93497	0.266488
$497$	−33.1997	−1.48921
$498$	6.47626	0.290208
$499$	7.06361	0.316211	0.158105	−	0.987422i	$-0.449461\pi$
$499$	7.06361	0.316211	0.158105	+	0.987422i	$0.449461\pi$
$500$	−2.79389	−0.124947
$501$	19.5661	0.874149
$502$	5.84903	0.261055
$503$	−16.6327	−0.741616	−0.370808	−	0.928710i	$-0.620919\pi$
$503$	−16.6327	−0.741616	−0.370808	+	0.928710i	$0.620919\pi$
$504$	−6.95129	−0.309635
$505$	22.9725	1.02226
$506$	0.165343	0.00735037
$507$	−11.3441	−0.503810
$508$	11.8994	0.527953
$509$	−19.2037	−0.851191	−0.425595	−	0.904914i	$-0.639935\pi$
$509$	−19.2037	−0.851191	−0.425595	+	0.904914i	$0.639935\pi$
$510$	1.30328	0.0577100
$511$	−31.9010	−1.41122
$512$	−22.8278	−1.00886
$513$	−3.31065	−0.146169
$514$	4.58281	0.202139
$515$	−25.5246	−1.12475
$516$	−2.13029	−0.0937808
$517$	−17.2516	−0.758724
$518$	7.83070	0.344061
$519$	18.0039	0.790283
$520$	6.40849	0.281031
$521$	−40.6313	−1.78009	−0.890044	−	0.455875i	$-0.849326\pi$
$521$	−40.6313	−1.78009	−0.890044	+	0.455875i	$0.849326\pi$
$522$	−1.03874	−0.0454646
$523$	−10.1075	−0.441970	−0.220985	−	0.975277i	$-0.570927\pi$
$523$	−10.1075	−0.441970	−0.220985	+	0.975277i	$0.570927\pi$
$524$	30.5198	1.33326
$525$	−19.3722	−0.845470
$526$	5.32349	0.232115
$527$	2.00542	0.0873576
$528$	−7.65368	−0.333084
$529$	−22.9771	−0.999006
$530$	10.4210	0.452658
$531$	0.837472	0.0363432
$532$	−25.9431	−1.12477
$533$	−11.4635	−0.496540
$534$	5.51352	0.238593
$535$	−14.5008	−0.626923
$536$	10.7948	0.466265
$537$	9.45241	0.407901
$538$	−2.69637	−0.116249
$539$	−29.7747	−1.28249
$540$	5.61417	0.241595
$541$	−3.61464	−0.155405	−0.0777027	−	0.996977i	$-0.524758\pi$
$541$	−3.61464	−0.155405	−0.0777027	+	0.996977i	$0.524758\pi$
$542$	−4.07316	−0.174957
$543$	−10.8859	−0.467157
$544$	−4.48236	−0.192180
$545$	−13.5449	−0.580199
$546$	−2.34085	−0.100179
$547$	29.2135	1.24908	0.624540	−	0.780993i	$-0.285286\pi$
$547$	29.2135	1.24908	0.624540	+	0.780993i	$0.285286\pi$
$548$	36.8232	1.57301
$549$	−12.7603	−0.544597
$550$	4.92286	0.209912
$551$	−8.13394	−0.346517
$552$	0.244305	0.0103983
$553$	35.8315	1.52371
$554$	3.93823	0.167319
$555$	−13.2696	−0.563261
$556$	12.8706	0.545834
$557$	−4.89361	−0.207349	−0.103675	−	0.994611i	$-0.533060\pi$
$557$	−4.89361	−0.207349	−0.103675	+	0.994611i	$0.533060\pi$
$558$	−0.847865	−0.0358930
$559$	−1.50516	−0.0636615
$560$	39.2525	1.65872
$561$	−2.58617	−0.109188
$562$	−4.98028	−0.210081
$563$	32.5788	1.37303	0.686517	−	0.727114i	$-0.259139\pi$
$563$	32.5788	1.37303	0.686517	+	0.727114i	$0.259139\pi$
$564$	−12.1490	−0.511566
$565$	16.3129	0.686289
$566$	−3.50643	−0.147386
$567$	−4.30268	−0.180695
$568$	12.4658	0.523055
$569$	−8.86181	−0.371506	−0.185753	−	0.982596i	$-0.559472\pi$
$569$	−8.86181	−0.371506	−0.185753	+	0.982596i	$0.559472\pi$
$570$	−4.31468	−0.180722
$571$	26.1342	1.09368	0.546842	−	0.837236i	$-0.315830\pi$
$571$	26.1342	1.09368	0.546842	+	0.837236i	$0.315830\pi$
$572$	−6.06096	−0.253422
$573$	14.4755	0.604723
$574$	16.2055	0.676406
$575$	0.680841	0.0283930
$576$	−4.02384	−0.167660
$577$	−42.2641	−1.75948	−0.879740	−	0.475456i	$-0.842283\pi$
$577$	−42.2641	−1.75948	−0.879740	+	0.475456i	$0.842283\pi$
$578$	−0.422786	−0.0175856
$579$	−6.39596	−0.265807
$580$	13.7935	0.572743
$581$	65.9086	2.73435
$582$	−2.90040	−0.120225
$583$	−20.6790	−0.856436
$584$	11.9782	0.495661
$585$	3.96670	0.164003
$586$	−12.4934	−0.516098
$587$	−11.7494	−0.484952	−0.242476	−	0.970157i	$-0.577959\pi$
$587$	−11.7494	−0.484952	−0.242476	+	0.970157i	$0.577959\pi$
$588$	−20.9681	−0.864711
$589$	−6.63925	−0.273565
$590$	1.09146	0.0449346
$591$	6.06415	0.249446
$592$	12.7395	0.523592
$593$	−17.5574	−0.720995	−0.360497	−	0.932760i	$-0.617393\pi$
$593$	−17.5574	−0.720995	−0.360497	+	0.932760i	$0.617393\pi$
$594$	1.09340	0.0448627
$595$	13.2634	0.543746
$596$	−10.6501	−0.436245
$597$	4.92760	0.201673
$598$	0.0822699	0.00336427
$599$	20.0171	0.817878	0.408939	−	0.912562i	$-0.365899\pi$
$599$	20.0171	0.817878	0.408939	+	0.912562i	$0.365899\pi$
$600$	7.27387	0.296955
$601$	1.75683	0.0716627	0.0358313	−	0.999358i	$-0.488592\pi$
$601$	1.75683	0.0716627	0.0358313	+	0.999358i	$0.488592\pi$
$602$	2.12779	0.0867221
$603$	6.68173	0.272101
$604$	−6.44040	−0.262056
$605$	13.2912	0.540365
$606$	3.15074	0.127990
$607$	42.7296	1.73434	0.867171	−	0.498011i	$-0.165936\pi$
$607$	42.7296	1.73434	0.867171	+	0.498011i	$0.165936\pi$
$608$	14.8395	0.601822
$609$	−10.5713	−0.428369
$610$	−16.6302	−0.673338
$611$	−8.58391	−0.347268
$612$	−1.82125	−0.0736197
$613$	19.3137	0.780075	0.390037	−	0.920799i	$-0.372462\pi$
$613$	19.3137	0.780075	0.390037	+	0.920799i	$0.372462\pi$
$614$	−6.37511	−0.257278
$615$	−27.4612	−1.10734
$616$	17.9772	0.724323
$617$	−26.1454	−1.05257	−0.526287	−	0.850307i	$-0.676416\pi$
$617$	−26.1454	−1.05257	−0.526287	+	0.850307i	$0.676416\pi$
$618$	−3.50078	−0.140822
$619$	13.2768	0.533640	0.266820	−	0.963746i	$-0.414027\pi$
$619$	13.2768	0.533640	0.266820	+	0.963746i	$0.414027\pi$
$620$	11.2588	0.452164
$621$	0.151219	0.00606821
$622$	−3.40239	−0.136423
$623$	56.1109	2.24803
$624$	−3.80826	−0.152452
$625$	−27.2406	−1.08962
$626$	5.72109	0.228661
$627$	8.56190	0.341929
$628$	1.82125	0.0726759
$629$	4.30468	0.171639
$630$	−5.60757	−0.223411
$631$	−3.16777	−0.126107	−0.0630535	−	0.998010i	$-0.520084\pi$
$631$	−3.16777	−0.126107	−0.0630535	+	0.998010i	$0.520084\pi$
$632$	−13.4540	−0.535172
$633$	21.5691	0.857293
$634$	8.99146	0.357096
$635$	20.1406	0.799255
$636$	−14.5627	−0.577448
$637$	−14.8151	−0.586994
$638$	2.68637	0.106355
$639$	7.71606	0.305243
$640$	−32.8787	−1.29965
$641$	−8.85339	−0.349688	−0.174844	−	0.984596i	$-0.555942\pi$
$641$	−8.85339	−0.349688	−0.174844	+	0.984596i	$0.555942\pi$
$642$	−1.98882	−0.0784926
$643$	26.5831	1.04833	0.524167	−	0.851616i	$-0.324377\pi$
$643$	26.5831	1.04833	0.524167	+	0.851616i	$0.324377\pi$
$644$	1.18499	0.0466952
$645$	−3.60565	−0.141972
$646$	1.39970	0.0550703
$647$	11.0243	0.433410	0.216705	−	0.976237i	$-0.430469\pi$
$647$	11.0243	0.433410	0.216705	+	0.976237i	$0.430469\pi$
$648$	1.61557	0.0634657
$649$	−2.16585	−0.0850170
$650$	2.44948	0.0960765
$651$	−8.62869	−0.338185
$652$	−18.9844	−0.743488
$653$	−17.2417	−0.674720	−0.337360	−	0.941376i	$-0.609534\pi$
$653$	−17.2417	−0.674720	−0.337360	+	0.941376i	$0.609534\pi$
$654$	−1.85772	−0.0726427
$655$	51.6567	2.01840
$656$	26.3643	1.02935
$657$	7.41421	0.289256
$658$	12.1347	0.473062
$659$	−23.7591	−0.925525	−0.462762	−	0.886482i	$-0.653142\pi$
$659$	−23.7591	−0.925525	−0.462762	+	0.886482i	$0.653142\pi$
$660$	−14.5192	−0.565160
$661$	−0.845957	−0.0329039	−0.0164520	−	0.999865i	$-0.505237\pi$
$661$	−0.845957	−0.0329039	−0.0164520	+	0.999865i	$0.505237\pi$
$662$	−3.80021	−0.147699
$663$	−1.28681	−0.0499755
$664$	−24.7474	−0.960386
$665$	−43.9104	−1.70277
$666$	−1.81996	−0.0705220
$667$	0.371530	0.0143857
$668$	−35.6348	−1.37875
$669$	15.8358	0.612247
$670$	8.70813	0.336425
$671$	33.0004	1.27397
$672$	19.2862	0.743980
$673$	20.8022	0.801868	0.400934	−	0.916107i	$-0.368686\pi$
$673$	20.8022	0.801868	0.400934	+	0.916107i	$0.368686\pi$
$674$	6.49951	0.250352
$675$	4.50235	0.173296
$676$	20.6605	0.794635
$677$	15.0844	0.579739	0.289870	−	0.957066i	$-0.406388\pi$
$677$	15.0844	0.579739	0.289870	+	0.957066i	$0.406388\pi$
$678$	2.23736	0.0859254
$679$	−29.5173	−1.13277
$680$	−4.98014	−0.190980
$681$	13.7770	0.527935
$682$	2.19273	0.0839639
$683$	38.8580	1.48686	0.743429	−	0.668815i	$-0.233198\pi$
$683$	38.8580	1.48686	0.743429	+	0.668815i	$0.233198\pi$
$684$	6.02952	0.230544
$685$	62.3257	2.38134
$686$	8.20971	0.313448
$687$	−2.27341	−0.0867362
$688$	3.46164	0.131974
$689$	−10.2893	−0.391991
$690$	0.197080	0.00750271
$691$	18.0309	0.685928	0.342964	−	0.939348i	$-0.388569\pi$
$691$	18.0309	0.685928	0.342964	+	0.939348i	$0.388569\pi$
$692$	−32.7896	−1.24647
$693$	11.1275	0.422698
$694$	5.96916	0.226586
$695$	21.7843	0.826326
$696$	3.96931	0.150456
$697$	8.90849	0.337433
$698$	−10.8923	−0.412281
$699$	−5.99326	−0.226686
$700$	35.2816	1.33352
$701$	2.36557	0.0893464	0.0446732	−	0.999002i	$-0.485775\pi$
$701$	2.36557	0.0893464	0.0446732	+	0.999002i	$0.485775\pi$
$702$	0.544045	0.0205337
$703$	−14.2513	−0.537497
$704$	10.4064	0.392204
$705$	−20.5630	−0.774448
$706$	5.59132	0.210432
$707$	32.0650	1.20593
$708$	−1.52525	−0.0573223
$709$	16.4810	0.618958	0.309479	−	0.950906i	$-0.399845\pi$
$709$	16.4810	0.618958	0.309479	+	0.950906i	$0.399845\pi$
$710$	10.0561	0.377401
$711$	−8.32771	−0.312314
$712$	−21.0686	−0.789578
$713$	0.303258	0.0113571
$714$	1.81911	0.0680786
$715$	−10.2586	−0.383649
$716$	−17.2152	−0.643363
$717$	−18.3428	−0.685023
$718$	7.83963	0.292572
$719$	4.07058	0.151807	0.0759035	−	0.997115i	$-0.475816\pi$
$719$	4.07058	0.151807	0.0759035	+	0.997115i	$0.475816\pi$
$720$	−9.12280	−0.339987
$721$	−35.6273	−1.32683
$722$	3.39904	0.126499
$723$	−0.558209	−0.0207600
$724$	19.8259	0.736824
$725$	11.0618	0.410826
$726$	1.82293	0.0676553
$727$	−14.7876	−0.548443	−0.274222	−	0.961666i	$-0.588420\pi$
$727$	−14.7876	−0.548443	−0.274222	+	0.961666i	$0.588420\pi$
$728$	8.94498	0.331523
$729$	1.00000	0.0370370
$730$	9.66276	0.357635
$731$	1.16968	0.0432623
$732$	23.2398	0.858966
$733$	20.3437	0.751411	0.375705	−	0.926739i	$-0.377400\pi$
$733$	20.3437	0.751411	0.375705	+	0.926739i	$0.377400\pi$
$734$	7.78791	0.287457
$735$	−35.4899	−1.30907
$736$	−0.677819	−0.0249847
$737$	−17.2801	−0.636521
$738$	−3.76639	−0.138643
$739$	40.2859	1.48194	0.740970	−	0.671538i	$-0.234366\pi$
$739$	40.2859	1.48194	0.740970	+	0.671538i	$0.234366\pi$
$740$	24.1672	0.888404
$741$	4.26017	0.156501
$742$	14.5456	0.533985
$743$	−7.79512	−0.285975	−0.142988	−	0.989724i	$-0.545671\pi$
$743$	−7.79512	−0.285975	−0.142988	+	0.989724i	$0.545671\pi$
$744$	3.23991	0.118781
$745$	−18.0260	−0.660421
$746$	−11.0595	−0.404918
$747$	−15.3180	−0.560458
$748$	4.71007	0.172217
$749$	−20.2402	−0.739560
$750$	−0.648576	−0.0236826
$751$	33.2156	1.21205	0.606027	−	0.795444i	$-0.292762\pi$
$751$	33.2156	1.21205	0.606027	+	0.795444i	$0.292762\pi$
$752$	19.7417	0.719905
$753$	−13.8345	−0.504157
$754$	1.33667	0.0486785
$755$	−10.9008	−0.396721
$756$	7.83626	0.285002
$757$	−2.03362	−0.0739132	−0.0369566	−	0.999317i	$-0.511766\pi$
$757$	−2.03362	−0.0739132	−0.0369566	+	0.999317i	$0.511766\pi$
$758$	1.28230	0.0465754
$759$	−0.391079	−0.0141953
$760$	16.4875	0.598064
$761$	−10.1663	−0.368529	−0.184264	−	0.982877i	$-0.558990\pi$
$761$	−10.1663	−0.368529	−0.184264	+	0.982877i	$0.558990\pi$
$762$	2.76234	0.100069
$763$	−18.9060	−0.684442
$764$	−26.3636	−0.953800
$765$	−3.08259	−0.111451
$766$	1.98291	0.0716454
$767$	−1.07767	−0.0389123
$768$	3.53827	0.127676
$769$	13.6894	0.493651	0.246826	−	0.969060i	$-0.420612\pi$
$769$	13.6894	0.493651	0.246826	+	0.969060i	$0.420612\pi$
$770$	14.5022	0.522622
$771$	−10.8395	−0.390377
$772$	11.6487	0.419244
$773$	5.10177	0.183498	0.0917490	−	0.995782i	$-0.470754\pi$
$773$	5.10177	0.183498	0.0917490	+	0.995782i	$0.470754\pi$
$774$	−0.494526	−0.0177754
$775$	9.02912	0.324335
$776$	11.0832	0.397862
$777$	−18.5217	−0.664461
$778$	−0.766760	−0.0274897
$779$	−29.4929	−1.05669
$780$	−7.22436	−0.258674
$781$	−19.9551	−0.714048
$782$	−0.0639333	−0.00228625
$783$	2.45690	0.0878026
$784$	34.0724	1.21687
$785$	3.08259	0.110022
$786$	7.08488	0.252709
$787$	10.5493	0.376043	0.188022	−	0.982165i	$-0.439792\pi$
$787$	10.5493	0.376043	0.188022	+	0.982165i	$0.439792\pi$
$788$	−11.0443	−0.393438
$789$	−12.5915	−0.448268
$790$	−10.8533	−0.386143
$791$	22.7695	0.809592
$792$	−4.17815	−0.148464
$793$	16.4201	0.583095
$794$	14.5866	0.517659
$795$	−24.6483	−0.874185
$796$	−8.97440	−0.318089
$797$	−6.46442	−0.228982	−0.114491	−	0.993424i	$-0.536524\pi$
$797$	−6.46442	−0.228982	−0.114491	+	0.993424i	$0.536524\pi$
$798$	−6.02244	−0.213192
$799$	6.67070	0.235992
$800$	−20.1812	−0.713512
$801$	−13.0409	−0.460778
$802$	7.54722	0.266502
$803$	−19.1744	−0.676651
$804$	−12.1691	−0.429171
$805$	2.00567	0.0706908
$806$	1.09104	0.0384303
$807$	6.37761	0.224503
$808$	−12.0398	−0.423558
$809$	52.5022	1.84588	0.922939	−	0.384945i	$-0.125780\pi$
$809$	52.5022	1.84588	0.922939	+	0.384945i	$0.125780\pi$
$810$	1.30328	0.0457924
$811$	−10.6798	−0.375018	−0.187509	−	0.982263i	$-0.560041\pi$
$811$	−10.6798	−0.375018	−0.187509	+	0.982263i	$0.560041\pi$
$812$	19.2529	0.675645
$813$	9.63410	0.337883
$814$	4.70673	0.164971
$815$	−32.1324	−1.12555
$816$	2.95946	0.103602
$817$	−3.87241	−0.135478
$818$	−13.7090	−0.479323
$819$	5.53672	0.193469
$820$	50.0138	1.74656
$821$	31.0956	1.08524	0.542621	−	0.839978i	$-0.317432\pi$
$821$	31.0956	1.08524	0.542621	+	0.839978i	$0.317432\pi$
$822$	8.54816	0.298151
$823$	−21.7239	−0.757247	−0.378624	−	0.925551i	$-0.623603\pi$
$823$	−21.7239	−0.757247	−0.378624	+	0.925551i	$0.623603\pi$
$824$	13.3774	0.466023
$825$	−11.6439	−0.405387
$826$	1.52346	0.0530078
$827$	−22.8303	−0.793887	−0.396944	−	0.917843i	$-0.629929\pi$
$827$	−22.8303	−0.793887	−0.396944	+	0.917843i	$0.629929\pi$
$828$	−0.275408	−0.00957108
$829$	−13.9725	−0.485287	−0.242643	−	0.970116i	$-0.578014\pi$
$829$	−13.9725	−0.485287	−0.242643	+	0.970116i	$0.578014\pi$
$830$	−19.9636	−0.692948
$831$	−9.31494	−0.323132
$832$	5.17792	0.179512
$833$	11.5130	0.398903
$834$	2.98778	0.103458
$835$	−60.3142	−2.08726
$836$	−15.5934	−0.539308
$837$	2.00542	0.0693176
$838$	−13.5003	−0.466361
$839$	−46.1380	−1.59286	−0.796430	−	0.604730i	$-0.793281\pi$
$839$	−46.1380	−1.59286	−0.796430	+	0.604730i	$0.793281\pi$
$840$	21.4280	0.739335
$841$	−22.9636	−0.791849
$842$	10.6557	0.367219
$843$	11.7797	0.405713
$844$	−39.2827	−1.35217
$845$	34.9693	1.20298
$846$	−2.82028	−0.0969632
$847$	18.5519	0.637450
$848$	23.6638	0.812618
$849$	8.29362	0.284636
$850$	−1.90353	−0.0652906
$851$	0.650950	0.0223143
$852$	−14.0529	−0.481444
$853$	24.8327	0.850255	0.425127	−	0.905134i	$-0.360229\pi$
$853$	24.8327	0.850255	0.425127	+	0.905134i	$0.360229\pi$
$854$	−23.2125	−0.794314
$855$	10.2054	0.349016
$856$	7.59980	0.259756
$857$	−33.8862	−1.15753	−0.578765	−	0.815494i	$-0.696465\pi$
$857$	−33.8862	−1.15753	−0.578765	+	0.815494i	$0.696465\pi$
$858$	−1.40699	−0.0480340
$859$	21.5940	0.736778	0.368389	−	0.929672i	$-0.379910\pi$
$859$	21.5940	0.736778	0.368389	+	0.929672i	$0.379910\pi$
$860$	6.56680	0.223926
$861$	−38.3304	−1.30630
$862$	2.80322	0.0954780
$863$	29.9198	1.01848	0.509240	−	0.860624i	$-0.329926\pi$
$863$	29.9198	1.01848	0.509240	+	0.860624i	$0.329926\pi$
$864$	−4.48236	−0.152493
$865$	−55.4986	−1.88701
$866$	−1.41978	−0.0482460
$867$	1.00000	0.0339618
$868$	15.7150	0.533402
$869$	21.5369	0.730590
$870$	3.20202	0.108559
$871$	−8.59811	−0.291336
$872$	7.09883	0.240397
$873$	6.86021	0.232183
$874$	0.211660	0.00715952
$875$	−6.60053	−0.223139
$876$	−13.5031	−0.456229
$877$	−24.6063	−0.830895	−0.415448	−	0.909617i	$-0.636375\pi$
$877$	−24.6063	−0.830895	−0.415448	+	0.909617i	$0.636375\pi$
$878$	2.35085	0.0793374
$879$	29.5502	0.996702
$880$	23.5932	0.795325
$881$	−56.6976	−1.91019	−0.955095	−	0.296301i	$-0.904247\pi$
$881$	−56.6976	−1.91019	−0.955095	+	0.296301i	$0.904247\pi$
$882$	−4.86755	−0.163899
$883$	28.6235	0.963257	0.481629	−	0.876375i	$-0.340045\pi$
$883$	28.6235	0.963257	0.481629	+	0.876375i	$0.340045\pi$
$884$	2.34360	0.0788239
$885$	−2.58158	−0.0867789
$886$	12.6794	0.425974
$887$	26.5639	0.891929	0.445965	−	0.895051i	$-0.352861\pi$
$887$	26.5639	0.891929	0.445965	+	0.895051i	$0.352861\pi$
$888$	6.95453	0.233379
$889$	28.1122	0.942855
$890$	−16.9959	−0.569704
$891$	−2.58617	−0.0866401
$892$	−28.8410	−0.965667
$893$	−22.0843	−0.739023
$894$	−2.47232	−0.0826866
$895$	−29.1379	−0.973972
$896$	−45.8922	−1.53315
$897$	−0.194590	−0.00649717
$898$	9.12511	0.304509
$899$	4.92713	0.164329
$900$	−8.19991	−0.273330
$901$	7.99597	0.266385
$902$	9.74053	0.324324
$903$	−5.03277	−0.167480
$904$	−8.54953	−0.284353
$905$	33.5566	1.11546
$906$	−1.49508	−0.0496706
$907$	4.05719	0.134717	0.0673584	−	0.997729i	$-0.478543\pi$
$907$	4.05719	0.134717	0.0673584	+	0.997729i	$0.478543\pi$
$908$	−25.0913	−0.832686
$909$	−7.45233	−0.247178
$910$	7.21588	0.239204
$911$	−12.4646	−0.412969	−0.206485	−	0.978450i	$-0.566202\pi$
$911$	−12.4646	−0.412969	−0.206485	+	0.978450i	$0.566202\pi$
$912$	−9.79773	−0.324435
$913$	39.6151	1.31107
$914$	12.6738	0.419212
$915$	39.3348	1.30037
$916$	4.14046	0.136805
$917$	72.1025	2.38103
$918$	−0.422786	−0.0139540
$919$	36.6737	1.20975	0.604876	−	0.796319i	$-0.293222\pi$
$919$	36.6737	1.20975	0.604876	+	0.796319i	$0.293222\pi$
$920$	−0.753092	−0.0248287
$921$	15.0788	0.496863
$922$	6.15035	0.202551
$923$	−9.92909	−0.326820
$924$	−20.2659	−0.666700
$925$	19.3812	0.637249
$926$	−6.30613	−0.207232
$927$	8.28026	0.271960
$928$	−11.0127	−0.361511
$929$	9.86519	0.323666	0.161833	−	0.986818i	$-0.448259\pi$
$929$	9.86519	0.323666	0.161833	+	0.986818i	$0.448259\pi$
$930$	2.61362	0.0857040
$931$	−38.1156	−1.24919
$932$	10.9152	0.357541
$933$	8.04754	0.263465
$934$	8.82575	0.288787
$935$	7.97211	0.260716
$936$	−2.07893	−0.0679520
$937$	35.3426	1.15459	0.577296	−	0.816535i	$-0.304108\pi$
$937$	35.3426	1.15459	0.577296	+	0.816535i	$0.304108\pi$
$938$	12.1548	0.396869
$939$	−13.5319	−0.441596
$940$	37.4504	1.22150
$941$	60.1731	1.96159	0.980793	−	0.195050i	$-0.0624868\pi$
$941$	60.1731	1.96159	0.980793	+	0.195050i	$0.0624868\pi$
$942$	0.422786	0.0137751
$943$	1.34713	0.0438687
$944$	2.47847	0.0806672
$945$	13.2634	0.431458
$946$	1.27893	0.0415816
$947$	−52.9523	−1.72072	−0.860359	−	0.509689i	$-0.829760\pi$
$947$	−52.9523	−1.72072	−0.860359	+	0.509689i	$0.829760\pi$
$948$	15.1669	0.492597
$949$	−9.54067	−0.309703
$950$	6.30192	0.204461
$951$	−21.2672	−0.689635
$952$	−6.95129	−0.225293
$953$	−13.5606	−0.439269	−0.219635	−	0.975582i	$-0.570487\pi$
$953$	−13.5606	−0.439269	−0.219635	+	0.975582i	$0.570487\pi$
$954$	−3.38059	−0.109451
$955$	−44.6221	−1.44394
$956$	33.4068	1.08045
$957$	−6.35398	−0.205395
$958$	−8.11020	−0.262029
$959$	86.9942	2.80919
$960$	12.4038	0.400332
$961$	−26.9783	−0.870267
$962$	2.34194	0.0755072
$963$	4.70409	0.151587
$964$	1.01664	0.0327438
$965$	19.7161	0.634684
$966$	0.275084	0.00885069
$967$	−27.3834	−0.880590	−0.440295	−	0.897853i	$-0.645126\pi$
$967$	−27.3834	−0.880590	−0.440295	+	0.897853i	$0.645126\pi$
$968$	−6.96587	−0.223892
$969$	−3.31065	−0.106353
$970$	8.94074	0.287070
$971$	−24.1045	−0.773550	−0.386775	−	0.922174i	$-0.626411\pi$
$971$	−24.1045	−0.773550	−0.386775	+	0.922174i	$0.626411\pi$
$972$	−1.82125	−0.0584167
$973$	30.4065	0.974789
$974$	1.16057	0.0371869
$975$	−5.79366	−0.185546
$976$	−37.7637	−1.20879
$977$	−19.1844	−0.613765	−0.306882	−	0.951747i	$-0.599286\pi$
$977$	−19.1844	−0.613765	−0.306882	+	0.951747i	$0.599286\pi$
$978$	−4.40705	−0.140922
$979$	33.7261	1.07789
$980$	64.6361	2.06472
$981$	4.39400	0.140290
$982$	18.2024	0.580863
$983$	−20.0726	−0.640216	−0.320108	−	0.947381i	$-0.603719\pi$
$983$	−20.0726	−0.640216	−0.320108	+	0.947381i	$0.603719\pi$
$984$	14.3923	0.458810
$985$	−18.6933	−0.595617
$986$	−1.03874	−0.0330804
$987$	−28.7019	−0.913590
$988$	−7.75884	−0.246842
$989$	0.176878	0.00562441
$990$	−3.37050	−0.107121
$991$	36.0039	1.14370	0.571850	−	0.820358i	$-0.306226\pi$
$991$	36.0039	1.14370	0.571850	+	0.820358i	$0.306226\pi$
$992$	−8.98904	−0.285402
$993$	8.98849	0.285241
$994$	14.0364	0.445207
$995$	−15.1898	−0.481548
$996$	27.8980	0.883983
$997$	25.1694	0.797123	0.398561	−	0.917142i	$-0.369510\pi$
$997$	25.1694	0.797123	0.398561	+	0.917142i	$0.369510\pi$
$998$	−2.98640	−0.0945328
$999$	4.30468	0.136194

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.20	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-0.422786 q^{2} +1.00000 q^{3} -1.82125 q^{4} -3.08259 q^{5} -0.422786 q^{6} -4.30268 q^{7} +1.61557 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.422786 q^{2} +1.00000 q^{3} -1.82125 q^{4} -3.08259 q^{5} -0.422786 q^{6} -4.30268 q^{7} +1.61557 q^{8} +1.00000 q^{9} +1.30328 q^{10} -2.58617 q^{11} -1.82125 q^{12} -1.28681 q^{13} +1.81911 q^{14} -3.08259 q^{15} +2.95946 q^{16} +1.00000 q^{17} -0.422786 q^{18} -3.31065 q^{19} +5.61417 q^{20} -4.30268 q^{21} +1.09340 q^{22} +0.151219 q^{23} +1.61557 q^{24} +4.50235 q^{25} +0.544045 q^{26} +1.00000 q^{27} +7.83626 q^{28} +2.45690 q^{29} +1.30328 q^{30} +2.00542 q^{31} -4.48236 q^{32} -2.58617 q^{33} -0.422786 q^{34} +13.2634 q^{35} -1.82125 q^{36} +4.30468 q^{37} +1.39970 q^{38} -1.28681 q^{39} -4.98014 q^{40} +8.90849 q^{41} +1.81911 q^{42} +1.16968 q^{43} +4.71007 q^{44} -3.08259 q^{45} -0.0639333 q^{46} +6.67070 q^{47} +2.95946 q^{48} +11.5130 q^{49} -1.90353 q^{50} +1.00000 q^{51} +2.34360 q^{52} +7.99597 q^{53} -0.422786 q^{54} +7.97211 q^{55} -6.95129 q^{56} -3.31065 q^{57} -1.03874 q^{58} +0.837472 q^{59} +5.61417 q^{60} -12.7603 q^{61} -0.847865 q^{62} -4.30268 q^{63} -4.02384 q^{64} +3.96670 q^{65} +1.09340 q^{66} +6.68173 q^{67} -1.82125 q^{68} +0.151219 q^{69} -5.60757 q^{70} +7.71606 q^{71} +1.61557 q^{72} +7.41421 q^{73} -1.81996 q^{74} +4.50235 q^{75} +6.02952 q^{76} +11.1275 q^{77} +0.544045 q^{78} -8.32771 q^{79} -9.12280 q^{80} +1.00000 q^{81} -3.76639 q^{82} -15.3180 q^{83} +7.83626 q^{84} -3.08259 q^{85} -0.494526 q^{86} +2.45690 q^{87} -4.17815 q^{88} -13.0409 q^{89} +1.30328 q^{90} +5.53672 q^{91} -0.275408 q^{92} +2.00542 q^{93} -2.82028 q^{94} +10.2054 q^{95} -4.48236 q^{96} +6.86021 q^{97} -4.86755 q^{98} -2.58617 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 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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