LMFDB - Embedded newform 8002.2.a.g.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.22371 q^{3} +1.00000 q^{4} +3.47056 q^{5} -2.22371 q^{6} +3.09791 q^{7} +1.00000 q^{8} +1.94489 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.22371 q^{3} +1.00000 q^{4} +3.47056 q^{5} -2.22371 q^{6} +3.09791 q^{7} +1.00000 q^{8} +1.94489 q^{9} +3.47056 q^{10} -6.20898 q^{11} -2.22371 q^{12} +6.03269 q^{13} +3.09791 q^{14} -7.71751 q^{15} +1.00000 q^{16} +7.75233 q^{17} +1.94489 q^{18} +7.05840 q^{19} +3.47056 q^{20} -6.88885 q^{21} -6.20898 q^{22} +8.59775 q^{23} -2.22371 q^{24} +7.04476 q^{25} +6.03269 q^{26} +2.34626 q^{27} +3.09791 q^{28} -3.09526 q^{29} -7.71751 q^{30} -5.40326 q^{31} +1.00000 q^{32} +13.8070 q^{33} +7.75233 q^{34} +10.7515 q^{35} +1.94489 q^{36} -1.57501 q^{37} +7.05840 q^{38} -13.4150 q^{39} +3.47056 q^{40} +3.78686 q^{41} -6.88885 q^{42} -8.38549 q^{43} -6.20898 q^{44} +6.74985 q^{45} +8.59775 q^{46} +4.74091 q^{47} -2.22371 q^{48} +2.59704 q^{49} +7.04476 q^{50} -17.2389 q^{51} +6.03269 q^{52} +2.44928 q^{53} +2.34626 q^{54} -21.5486 q^{55} +3.09791 q^{56} -15.6958 q^{57} -3.09526 q^{58} -12.6294 q^{59} -7.71751 q^{60} +6.88577 q^{61} -5.40326 q^{62} +6.02509 q^{63} +1.00000 q^{64} +20.9368 q^{65} +13.8070 q^{66} +0.628138 q^{67} +7.75233 q^{68} -19.1189 q^{69} +10.7515 q^{70} -7.76794 q^{71} +1.94489 q^{72} -8.98898 q^{73} -1.57501 q^{74} -15.6655 q^{75} +7.05840 q^{76} -19.2348 q^{77} -13.4150 q^{78} +8.10357 q^{79} +3.47056 q^{80} -11.0521 q^{81} +3.78686 q^{82} -0.793705 q^{83} -6.88885 q^{84} +26.9049 q^{85} -8.38549 q^{86} +6.88296 q^{87} -6.20898 q^{88} -6.92112 q^{89} +6.74985 q^{90} +18.6887 q^{91} +8.59775 q^{92} +12.0153 q^{93} +4.74091 q^{94} +24.4966 q^{95} -2.22371 q^{96} -5.04057 q^{97} +2.59704 q^{98} -12.0758 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.22371	−1.28386	−0.641930	−	0.766763i	$-0.721866\pi$
$3$	−2.22371	−1.28386	−0.641930	+	0.766763i	$0.721866\pi$
$4$	1.00000	0.500000
$5$	3.47056	1.55208	0.776040	−	0.630684i	$-0.217226\pi$
$5$	3.47056	1.55208	0.776040	+	0.630684i	$0.217226\pi$
$6$	−2.22371	−0.907826
$7$	3.09791	1.17090	0.585450	−	0.810709i	$-0.300918\pi$
$7$	3.09791	1.17090	0.585450	+	0.810709i	$0.300918\pi$
$8$	1.00000	0.353553
$9$	1.94489	0.648296
$10$	3.47056	1.09749
$11$	−6.20898	−1.87208	−0.936038	−	0.351898i	$-0.885536\pi$
$11$	−6.20898	−1.87208	−0.936038	+	0.351898i	$0.885536\pi$
$12$	−2.22371	−0.641930
$13$	6.03269	1.67317	0.836584	−	0.547838i	$-0.184549\pi$
$13$	6.03269	1.67317	0.836584	+	0.547838i	$0.184549\pi$
$14$	3.09791	0.827951
$15$	−7.71751	−1.99265
$16$	1.00000	0.250000
$17$	7.75233	1.88022	0.940109	−	0.340875i	$-0.110723\pi$
$17$	7.75233	1.88022	0.940109	+	0.340875i	$0.110723\pi$
$18$	1.94489	0.458415
$19$	7.05840	1.61931	0.809654	−	0.586907i	$-0.199655\pi$
$19$	7.05840	1.61931	0.809654	+	0.586907i	$0.199655\pi$
$20$	3.47056	0.776040
$21$	−6.88885	−1.50327
$22$	−6.20898	−1.32376
$23$	8.59775	1.79276	0.896378	−	0.443291i	$-0.146189\pi$
$23$	8.59775	1.79276	0.896378	+	0.443291i	$0.146189\pi$
$24$	−2.22371	−0.453913
$25$	7.04476	1.40895
$26$	6.03269	1.18311
$27$	2.34626	0.451538
$28$	3.09791	0.585450
$29$	−3.09526	−0.574775	−0.287387	−	0.957814i	$-0.592787\pi$
$29$	−3.09526	−0.574775	−0.287387	+	0.957814i	$0.592787\pi$
$30$	−7.71751	−1.40902
$31$	−5.40326	−0.970455	−0.485227	−	0.874388i	$-0.661263\pi$
$31$	−5.40326	−0.970455	−0.485227	+	0.874388i	$0.661263\pi$
$32$	1.00000	0.176777
$33$	13.8070	2.40348
$34$	7.75233	1.32951
$35$	10.7515	1.81733
$36$	1.94489	0.324148
$37$	−1.57501	−0.258929	−0.129465	−	0.991584i	$-0.541326\pi$
$37$	−1.57501	−0.258929	−0.129465	+	0.991584i	$0.541326\pi$
$38$	7.05840	1.14502
$39$	−13.4150	−2.14811
$40$	3.47056	0.548743
$41$	3.78686	0.591408	0.295704	−	0.955280i	$-0.404446\pi$
$41$	3.78686	0.591408	0.295704	+	0.955280i	$0.404446\pi$
$42$	−6.88885	−1.06297
$43$	−8.38549	−1.27878	−0.639388	−	0.768885i	$-0.720812\pi$
$43$	−8.38549	−1.27878	−0.639388	+	0.768885i	$0.720812\pi$
$44$	−6.20898	−0.936038
$45$	6.74985	1.00621
$46$	8.59775	1.26767
$47$	4.74091	0.691533	0.345766	−	0.938321i	$-0.387619\pi$
$47$	4.74091	0.691533	0.345766	+	0.938321i	$0.387619\pi$
$48$	−2.22371	−0.320965
$49$	2.59704	0.371005
$50$	7.04476	0.996279
$51$	−17.2389	−2.41394
$52$	6.03269	0.836584
$53$	2.44928	0.336435	0.168218	−	0.985750i	$-0.446199\pi$
$53$	2.44928	0.336435	0.168218	+	0.985750i	$0.446199\pi$
$54$	2.34626	0.319286
$55$	−21.5486	−2.90561
$56$	3.09791	0.413975
$57$	−15.6958	−2.07896
$58$	−3.09526	−0.406427
$59$	−12.6294	−1.64421	−0.822106	−	0.569334i	$-0.807201\pi$
$59$	−12.6294	−1.64421	−0.822106	+	0.569334i	$0.807201\pi$
$60$	−7.71751	−0.996327
$61$	6.88577	0.881632	0.440816	−	0.897597i	$-0.354689\pi$
$61$	6.88577	0.881632	0.440816	+	0.897597i	$0.354689\pi$
$62$	−5.40326	−0.686215
$63$	6.02509	0.759090
$64$	1.00000	0.125000
$65$	20.9368	2.59689
$66$	13.8070	1.69952
$67$	0.628138	0.0767392	0.0383696	−	0.999264i	$-0.487784\pi$
$67$	0.628138	0.0767392	0.0383696	+	0.999264i	$0.487784\pi$
$68$	7.75233	0.940109
$69$	−19.1189	−2.30165
$70$	10.7515	1.28505
$71$	−7.76794	−0.921885	−0.460943	−	0.887430i	$-0.652489\pi$
$71$	−7.76794	−0.921885	−0.460943	+	0.887430i	$0.652489\pi$
$72$	1.94489	0.229207
$73$	−8.98898	−1.05208	−0.526040	−	0.850460i	$-0.676324\pi$
$73$	−8.98898	−1.05208	−0.526040	+	0.850460i	$0.676324\pi$
$74$	−1.57501	−0.183091
$75$	−15.6655	−1.80890
$76$	7.05840	0.809654
$77$	−19.2348	−2.19201
$78$	−13.4150	−1.51895
$79$	8.10357	0.911723	0.455861	−	0.890051i	$-0.349331\pi$
$79$	8.10357	0.911723	0.455861	+	0.890051i	$0.349331\pi$
$80$	3.47056	0.388020
$81$	−11.0521	−1.22801
$82$	3.78686	0.418189
$83$	−0.793705	−0.0871205	−0.0435602	−	0.999051i	$-0.513870\pi$
$83$	−0.793705	−0.0871205	−0.0435602	+	0.999051i	$0.513870\pi$
$84$	−6.88885	−0.751635
$85$	26.9049	2.91825
$86$	−8.38549	−0.904231
$87$	6.88296	0.737930
$88$	−6.20898	−0.661879
$89$	−6.92112	−0.733638	−0.366819	−	0.930292i	$-0.619553\pi$
$89$	−6.92112	−0.733638	−0.366819	+	0.930292i	$0.619553\pi$
$90$	6.74985	0.711496
$91$	18.6887	1.95911
$92$	8.59775	0.896378
$93$	12.0153	1.24593
$94$	4.74091	0.488987
$95$	24.4966	2.51330
$96$	−2.22371	−0.226957
$97$	−5.04057	−0.511792	−0.255896	−	0.966704i	$-0.582370\pi$
$97$	−5.04057	−0.511792	−0.255896	+	0.966704i	$0.582370\pi$
$98$	2.59704	0.262340
$99$	−12.0758	−1.21366
$100$	7.04476	0.704476
$101$	16.3394	1.62583	0.812914	−	0.582383i	$-0.197880\pi$
$101$	16.3394	1.62583	0.812914	+	0.582383i	$0.197880\pi$
$102$	−17.2389	−1.70691
$103$	−18.1148	−1.78490	−0.892451	−	0.451144i	$-0.851016\pi$
$103$	−18.1148	−1.78490	−0.892451	+	0.451144i	$0.851016\pi$
$104$	6.03269	0.591554
$105$	−23.9081	−2.33320
$106$	2.44928	0.237896
$107$	−1.58922	−0.153636	−0.0768179	−	0.997045i	$-0.524476\pi$
$107$	−1.58922	−0.153636	−0.0768179	+	0.997045i	$0.524476\pi$
$108$	2.34626	0.225769
$109$	−2.70795	−0.259375	−0.129687	−	0.991555i	$-0.541397\pi$
$109$	−2.70795	−0.259375	−0.129687	+	0.991555i	$0.541397\pi$
$110$	−21.5486	−2.05458
$111$	3.50236	0.332429
$112$	3.09791	0.292725
$113$	−12.7783	−1.20208	−0.601041	−	0.799218i	$-0.705247\pi$
$113$	−12.7783	−1.20208	−0.601041	+	0.799218i	$0.705247\pi$
$114$	−15.6958	−1.47005
$115$	29.8390	2.78250
$116$	−3.09526	−0.287387
$117$	11.7329	1.08471
$118$	−12.6294	−1.16263
$119$	24.0160	2.20154
$120$	−7.71751	−0.704509
$121$	27.5514	2.50467
$122$	6.88577	0.623408
$123$	−8.42088	−0.759285
$124$	−5.40326	−0.485227
$125$	7.09645	0.634725
$126$	6.02509	0.536758
$127$	−3.77097	−0.334619	−0.167310	−	0.985904i	$-0.553508\pi$
$127$	−3.77097	−0.334619	−0.167310	+	0.985904i	$0.553508\pi$
$128$	1.00000	0.0883883
$129$	18.6469	1.64177
$130$	20.9368	1.83628
$131$	3.61372	0.315732	0.157866	−	0.987461i	$-0.449539\pi$
$131$	3.61372	0.315732	0.157866	+	0.987461i	$0.449539\pi$
$132$	13.8070	1.20174
$133$	21.8663	1.89605
$134$	0.628138	0.0542628
$135$	8.14283	0.700823
$136$	7.75233	0.664757
$137$	16.0502	1.37126	0.685631	−	0.727949i	$-0.259526\pi$
$137$	16.0502	1.37126	0.685631	+	0.727949i	$0.259526\pi$
$138$	−19.1189	−1.62751
$139$	17.4761	1.48231	0.741153	−	0.671336i	$-0.234279\pi$
$139$	17.4761	1.48231	0.741153	+	0.671336i	$0.234279\pi$
$140$	10.7515	0.908665
$141$	−10.5424	−0.887831
$142$	−7.76794	−0.651871
$143$	−37.4569	−3.13230
$144$	1.94489	0.162074
$145$	−10.7423	−0.892096
$146$	−8.98898	−0.743933
$147$	−5.77506	−0.476319
$148$	−1.57501	−0.129465
$149$	−8.07936	−0.661887	−0.330943	−	0.943651i	$-0.607367\pi$
$149$	−8.07936	−0.661887	−0.330943	+	0.943651i	$0.607367\pi$
$150$	−15.6655	−1.27908
$151$	−18.7749	−1.52788	−0.763939	−	0.645288i	$-0.776737\pi$
$151$	−18.7749	−1.52788	−0.763939	+	0.645288i	$0.776737\pi$
$152$	7.05840	0.572512
$153$	15.0774	1.21894
$154$	−19.2348	−1.54999
$155$	−18.7523	−1.50622
$156$	−13.4150	−1.07406
$157$	−15.6564	−1.24952	−0.624760	−	0.780817i	$-0.714803\pi$
$157$	−15.6564	−1.24952	−0.624760	+	0.780817i	$0.714803\pi$
$158$	8.10357	0.644685
$159$	−5.44650	−0.431936
$160$	3.47056	0.274372
$161$	26.6350	2.09914
$162$	−11.0521	−0.868333
$163$	13.1248	1.02801	0.514007	−	0.857786i	$-0.328161\pi$
$163$	13.1248	1.02801	0.514007	+	0.857786i	$0.328161\pi$
$164$	3.78686	0.295704
$165$	47.9179	3.73040
$166$	−0.793705	−0.0616035
$167$	−14.0834	−1.08980	−0.544902	−	0.838500i	$-0.683433\pi$
$167$	−14.0834	−1.08980	−0.544902	+	0.838500i	$0.683433\pi$
$168$	−6.88885	−0.531486
$169$	23.3934	1.79949
$170$	26.9049	2.06351
$171$	13.7278	1.04979
$172$	−8.38549	−0.639388
$173$	−22.6454	−1.72169	−0.860847	−	0.508863i	$-0.830066\pi$
$173$	−22.6454	−1.72169	−0.860847	+	0.508863i	$0.830066\pi$
$174$	6.88296	0.521796
$175$	21.8240	1.64974
$176$	−6.20898	−0.468019
$177$	28.0842	2.11094
$178$	−6.92112	−0.518760
$179$	−1.70707	−0.127593	−0.0637963	−	0.997963i	$-0.520321\pi$
$179$	−1.70707	−0.127593	−0.0637963	+	0.997963i	$0.520321\pi$
$180$	6.74985	0.503104
$181$	4.52532	0.336364	0.168182	−	0.985756i	$-0.446210\pi$
$181$	4.52532	0.336364	0.168182	+	0.985756i	$0.446210\pi$
$182$	18.6887	1.38530
$183$	−15.3120	−1.13189
$184$	8.59775	0.633835
$185$	−5.46615	−0.401879
$186$	12.0153	0.881004
$187$	−48.1341	−3.51991
$188$	4.74091	0.345766
$189$	7.26850	0.528706
$190$	24.4966	1.77717
$191$	−1.60159	−0.115887	−0.0579436	−	0.998320i	$-0.518454\pi$
$191$	−1.60159	−0.115887	−0.0579436	+	0.998320i	$0.518454\pi$
$192$	−2.22371	−0.160482
$193$	8.67377	0.624351	0.312176	−	0.950024i	$-0.398942\pi$
$193$	8.67377	0.624351	0.312176	+	0.950024i	$0.398942\pi$
$194$	−5.04057	−0.361892
$195$	−46.5574	−3.33404
$196$	2.59704	0.185503
$197$	18.0242	1.28417	0.642085	−	0.766633i	$-0.278070\pi$
$197$	18.0242	1.28417	0.642085	+	0.766633i	$0.278070\pi$
$198$	−12.0758	−0.858188
$199$	−27.6877	−1.96273	−0.981365	−	0.192155i	$-0.938452\pi$
$199$	−27.6877	−1.96273	−0.981365	+	0.192155i	$0.938452\pi$
$200$	7.04476	0.498140
$201$	−1.39680	−0.0985224
$202$	16.3394	1.14963
$203$	−9.58882	−0.673003
$204$	−17.2389	−1.20697
$205$	13.1425	0.917912
$206$	−18.1148	−1.26212
$207$	16.7217	1.16224
$208$	6.03269	0.418292
$209$	−43.8254	−3.03147
$210$	−23.9081	−1.64982
$211$	−16.3928	−1.12853	−0.564263	−	0.825595i	$-0.690840\pi$
$211$	−16.3928	−1.12853	−0.564263	+	0.825595i	$0.690840\pi$
$212$	2.44928	0.168218
$213$	17.2737	1.18357
$214$	−1.58922	−0.108637
$215$	−29.1023	−1.98476
$216$	2.34626	0.159643
$217$	−16.7388	−1.13630
$218$	−2.70795	−0.183406
$219$	19.9889	1.35072
$220$	−21.5486	−1.45281
$221$	46.7675	3.14592
$222$	3.50236	0.235063
$223$	−18.3250	−1.22713	−0.613565	−	0.789644i	$-0.710265\pi$
$223$	−18.3250	−1.22713	−0.613565	+	0.789644i	$0.710265\pi$
$224$	3.09791	0.206988
$225$	13.7013	0.913418
$226$	−12.7783	−0.850000
$227$	17.7934	1.18099	0.590495	−	0.807041i	$-0.298932\pi$
$227$	17.7934	1.18099	0.590495	+	0.807041i	$0.298932\pi$
$228$	−15.6958	−1.03948
$229$	−17.9285	−1.18475	−0.592376	−	0.805662i	$-0.701810\pi$
$229$	−17.9285	−1.18475	−0.592376	+	0.805662i	$0.701810\pi$
$230$	29.8390	1.96752
$231$	42.7727	2.81424
$232$	−3.09526	−0.203214
$233$	−27.3935	−1.79461	−0.897304	−	0.441414i	$-0.854477\pi$
$233$	−27.3935	−1.79461	−0.897304	+	0.441414i	$0.854477\pi$
$234$	11.7329	0.767005
$235$	16.4536	1.07331
$236$	−12.6294	−0.822106
$237$	−18.0200	−1.17052
$238$	24.0160	1.55673
$239$	−7.06148	−0.456769	−0.228385	−	0.973571i	$-0.573344\pi$
$239$	−7.06148	−0.456769	−0.228385	+	0.973571i	$0.573344\pi$
$240$	−7.71751	−0.498163
$241$	5.69098	0.366588	0.183294	−	0.983058i	$-0.441324\pi$
$241$	5.69098	0.366588	0.183294	+	0.983058i	$0.441324\pi$
$242$	27.5514	1.77107
$243$	17.5378	1.12505
$244$	6.88577	0.440816
$245$	9.01316	0.575830
$246$	−8.42088	−0.536896
$247$	42.5812	2.70937
$248$	−5.40326	−0.343108
$249$	1.76497	0.111850
$250$	7.09645	0.448819
$251$	4.49059	0.283444	0.141722	−	0.989907i	$-0.454736\pi$
$251$	4.49059	0.283444	0.141722	+	0.989907i	$0.454736\pi$
$252$	6.02509	0.379545
$253$	−53.3832	−3.35618
$254$	−3.77097	−0.236612
$255$	−59.8287	−3.74662
$256$	1.00000	0.0625000
$257$	−6.16427	−0.384516	−0.192258	−	0.981344i	$-0.561581\pi$
$257$	−6.16427	−0.384516	−0.192258	+	0.981344i	$0.561581\pi$
$258$	18.6469	1.16091
$259$	−4.87923	−0.303180
$260$	20.9368	1.29845
$261$	−6.01993	−0.372624
$262$	3.61372	0.223256
$263$	9.59560	0.591690	0.295845	−	0.955236i	$-0.404399\pi$
$263$	9.59560	0.591690	0.295845	+	0.955236i	$0.404399\pi$
$264$	13.8070	0.849760
$265$	8.50038	0.522174
$266$	21.8663	1.34071
$267$	15.3906	0.941888
$268$	0.628138	0.0383696
$269$	6.93524	0.422849	0.211425	−	0.977394i	$-0.432190\pi$
$269$	6.93524	0.422849	0.211425	+	0.977394i	$0.432190\pi$
$270$	8.14283	0.495557
$271$	−22.4141	−1.36156	−0.680779	−	0.732489i	$-0.738359\pi$
$271$	−22.4141	−1.36156	−0.680779	+	0.732489i	$0.738359\pi$
$272$	7.75233	0.470054
$273$	−41.5583	−2.51523
$274$	16.0502	0.969629
$275$	−43.7407	−2.63767
$276$	−19.1189	−1.15082
$277$	16.2654	0.977291	0.488645	−	0.872483i	$-0.337491\pi$
$277$	16.2654	0.977291	0.488645	+	0.872483i	$0.337491\pi$
$278$	17.4761	1.04815
$279$	−10.5087	−0.629142
$280$	10.7515	0.642523
$281$	−10.1095	−0.603082	−0.301541	−	0.953453i	$-0.597501\pi$
$281$	−10.1095	−0.603082	−0.301541	+	0.953453i	$0.597501\pi$
$282$	−10.5424	−0.627791
$283$	6.55771	0.389815	0.194908	−	0.980822i	$-0.437559\pi$
$283$	6.55771	0.389815	0.194908	+	0.980822i	$0.437559\pi$
$284$	−7.76794	−0.460943
$285$	−54.4733	−3.22672
$286$	−37.4569	−2.21487
$287$	11.7313	0.692479
$288$	1.94489	0.114604
$289$	43.0987	2.53522
$290$	−10.7423	−0.630807
$291$	11.2088	0.657070
$292$	−8.98898	−0.526040
$293$	13.5905	0.793965	0.396983	−	0.917826i	$-0.370057\pi$
$293$	13.5905	0.793965	0.396983	+	0.917826i	$0.370057\pi$
$294$	−5.77506	−0.336808
$295$	−43.8311	−2.55195
$296$	−1.57501	−0.0915454
$297$	−14.5679	−0.845314
$298$	−8.07936	−0.468025
$299$	51.8676	2.99958
$300$	−15.6655	−0.904448
$301$	−25.9775	−1.49732
$302$	−18.7749	−1.08037
$303$	−36.3340	−2.08734
$304$	7.05840	0.404827
$305$	23.8974	1.36836
$306$	15.0774	0.861919
$307$	32.5757	1.85919	0.929597	−	0.368577i	$-0.120155\pi$
$307$	32.5757	1.85919	0.929597	+	0.368577i	$0.120155\pi$
$308$	−19.2348	−1.09601
$309$	40.2820	2.29156
$310$	−18.7523	−1.06506
$311$	11.5684	0.655983	0.327991	−	0.944681i	$-0.393628\pi$
$311$	11.5684	0.655983	0.327991	+	0.944681i	$0.393628\pi$
$312$	−13.4150	−0.759473
$313$	2.47719	0.140019	0.0700095	−	0.997546i	$-0.477697\pi$
$313$	2.47719	0.140019	0.0700095	+	0.997546i	$0.477697\pi$
$314$	−15.6564	−0.883544
$315$	20.9104	1.17817
$316$	8.10357	0.455861
$317$	−12.8562	−0.722074	−0.361037	−	0.932552i	$-0.617577\pi$
$317$	−12.8562	−0.722074	−0.361037	+	0.932552i	$0.617577\pi$
$318$	−5.44650	−0.305425
$319$	19.2184	1.07602
$320$	3.47056	0.194010
$321$	3.53397	0.197247
$322$	26.6350	1.48431
$323$	54.7191	3.04465
$324$	−11.0521	−0.614004
$325$	42.4989	2.35741
$326$	13.1248	0.726915
$327$	6.02171	0.333001
$328$	3.78686	0.209094
$329$	14.6869	0.809715
$330$	47.9179	2.63779
$331$	−15.8020	−0.868555	−0.434277	−	0.900779i	$-0.642996\pi$
$331$	−15.8020	−0.868555	−0.434277	+	0.900779i	$0.642996\pi$
$332$	−0.793705	−0.0435602
$333$	−3.06321	−0.167863
$334$	−14.0834	−0.770608
$335$	2.17999	0.119105
$336$	−6.88885	−0.375818
$337$	15.4049	0.839159	0.419579	−	0.907719i	$-0.362178\pi$
$337$	15.4049	0.839159	0.419579	+	0.907719i	$0.362178\pi$
$338$	23.3934	1.27243
$339$	28.4153	1.54331
$340$	26.9049	1.45912
$341$	33.5487	1.81677
$342$	13.7278	0.742315
$343$	−13.6400	−0.736490
$344$	−8.38549	−0.452115
$345$	−66.3533	−3.57234
$346$	−22.6454	−1.21742
$347$	14.1929	0.761914	0.380957	−	0.924593i	$-0.375595\pi$
$347$	14.1929	0.761914	0.380957	+	0.924593i	$0.375595\pi$
$348$	6.88296	0.368965
$349$	3.12593	0.167327	0.0836635	−	0.996494i	$-0.473338\pi$
$349$	3.12593	0.167327	0.0836635	+	0.996494i	$0.473338\pi$
$350$	21.8240	1.16654
$351$	14.1543	0.755499
$352$	−6.20898	−0.330940
$353$	−8.85222	−0.471156	−0.235578	−	0.971855i	$-0.575698\pi$
$353$	−8.85222	−0.471156	−0.235578	+	0.971855i	$0.575698\pi$
$354$	28.0842	1.49266
$355$	−26.9591	−1.43084
$356$	−6.92112	−0.366819
$357$	−53.4047	−2.82648
$358$	−1.70707	−0.0902216
$359$	−3.68243	−0.194351	−0.0971756	−	0.995267i	$-0.530981\pi$
$359$	−3.68243	−0.194351	−0.0971756	+	0.995267i	$0.530981\pi$
$360$	6.74985	0.355748
$361$	30.8210	1.62216
$362$	4.52532	0.237845
$363$	−61.2663	−3.21565
$364$	18.6887	0.979556
$365$	−31.1967	−1.63291
$366$	−15.3120	−0.800369
$367$	−24.6758	−1.28807	−0.644033	−	0.764997i	$-0.722740\pi$
$367$	−24.6758	−1.28807	−0.644033	+	0.764997i	$0.722740\pi$
$368$	8.59775	0.448189
$369$	7.36502	0.383408
$370$	−5.46615	−0.284171
$371$	7.58766	0.393932
$372$	12.0153	0.622964
$373$	−19.7244	−1.02129	−0.510646	−	0.859791i	$-0.670594\pi$
$373$	−19.7244	−1.02129	−0.510646	+	0.859791i	$0.670594\pi$
$374$	−48.1341	−2.48895
$375$	−15.7804	−0.814899
$376$	4.74091	0.244494
$377$	−18.6727	−0.961695
$378$	7.26850	0.373851
$379$	19.9912	1.02688	0.513440	−	0.858125i	$-0.328371\pi$
$379$	19.9912	1.02688	0.513440	+	0.858125i	$0.328371\pi$
$380$	24.4966	1.25665
$381$	8.38555	0.429605
$382$	−1.60159	−0.0819446
$383$	29.4611	1.50539	0.752697	−	0.658367i	$-0.228752\pi$
$383$	29.4611	1.50539	0.752697	+	0.658367i	$0.228752\pi$
$384$	−2.22371	−0.113478
$385$	−66.7556	−3.40218
$386$	8.67377	0.441483
$387$	−16.3088	−0.829025
$388$	−5.04057	−0.255896
$389$	18.3449	0.930125	0.465062	−	0.885278i	$-0.346032\pi$
$389$	18.3449	0.930125	0.465062	+	0.885278i	$0.346032\pi$
$390$	−46.5574	−2.35753
$391$	66.6526	3.37077
$392$	2.59704	0.131170
$393$	−8.03587	−0.405356
$394$	18.0242	0.908046
$395$	28.1239	1.41507
$396$	−12.0758	−0.606830
$397$	16.7070	0.838502	0.419251	−	0.907870i	$-0.362293\pi$
$397$	16.7070	0.838502	0.419251	+	0.907870i	$0.362293\pi$
$398$	−27.6877	−1.38786
$399$	−48.6243	−2.43426
$400$	7.04476	0.352238
$401$	28.9430	1.44535	0.722673	−	0.691190i	$-0.242913\pi$
$401$	28.9430	1.44535	0.722673	+	0.691190i	$0.242913\pi$
$402$	−1.39680	−0.0696659
$403$	−32.5962	−1.62373
$404$	16.3394	0.812914
$405$	−38.3568	−1.90597
$406$	−9.58882	−0.475885
$407$	9.77918	0.484736
$408$	−17.2389	−0.853455
$409$	26.5842	1.31450	0.657252	−	0.753671i	$-0.271719\pi$
$409$	26.5842	1.31450	0.657252	+	0.753671i	$0.271719\pi$
$410$	13.1425	0.649062
$411$	−35.6910	−1.76051
$412$	−18.1148	−0.892451
$413$	−39.1248	−1.92521
$414$	16.7217	0.821825
$415$	−2.75460	−0.135218
$416$	6.03269	0.295777
$417$	−38.8618	−1.90307
$418$	−43.8254	−2.14357
$419$	18.1843	0.888362	0.444181	−	0.895937i	$-0.353495\pi$
$419$	18.1843	0.888362	0.444181	+	0.895937i	$0.353495\pi$
$420$	−23.9081	−1.16660
$421$	−27.6219	−1.34621	−0.673105	−	0.739547i	$-0.735040\pi$
$421$	−27.6219	−1.34621	−0.673105	+	0.739547i	$0.735040\pi$
$422$	−16.3928	−0.797988
$423$	9.22054	0.448318
$424$	2.44928	0.118948
$425$	54.6133	2.64913
$426$	17.2737	0.836912
$427$	21.3315	1.03230
$428$	−1.58922	−0.0768179
$429$	83.2932	4.02143
$430$	−29.1023	−1.40344
$431$	−27.4125	−1.32041	−0.660206	−	0.751084i	$-0.729531\pi$
$431$	−27.4125	−1.32041	−0.660206	+	0.751084i	$0.729531\pi$
$432$	2.34626	0.112885
$433$	−22.2689	−1.07018	−0.535088	−	0.844797i	$-0.679721\pi$
$433$	−22.2689	−1.07018	−0.535088	+	0.844797i	$0.679721\pi$
$434$	−16.7388	−0.803489
$435$	23.8877	1.14533
$436$	−2.70795	−0.129687
$437$	60.6864	2.90302
$438$	19.9889	0.955106
$439$	−0.375616	−0.0179272	−0.00896359	−	0.999960i	$-0.502853\pi$
$439$	−0.375616	−0.0179272	−0.00896359	+	0.999960i	$0.502853\pi$
$440$	−21.5486	−1.02729
$441$	5.05095	0.240521
$442$	46.7675	2.22450
$443$	8.14557	0.387008	0.193504	−	0.981100i	$-0.438015\pi$
$443$	8.14557	0.387008	0.193504	+	0.981100i	$0.438015\pi$
$444$	3.50236	0.166215
$445$	−24.0202	−1.13866
$446$	−18.3250	−0.867712
$447$	17.9662	0.849770
$448$	3.09791	0.146362
$449$	16.5710	0.782033	0.391016	−	0.920384i	$-0.372124\pi$
$449$	16.5710	0.782033	0.391016	+	0.920384i	$0.372124\pi$
$450$	13.7013	0.645884
$451$	−23.5125	−1.10716
$452$	−12.7783	−0.601041
$453$	41.7499	1.96158
$454$	17.7934	0.835086
$455$	64.8603	3.04070
$456$	−15.6958	−0.735025
$457$	−0.581644	−0.0272081	−0.0136041	−	0.999907i	$-0.504330\pi$
$457$	−0.581644	−0.0272081	−0.0136041	+	0.999907i	$0.504330\pi$
$458$	−17.9285	−0.837746
$459$	18.1890	0.848990
$460$	29.8390	1.39125
$461$	32.5519	1.51610	0.758048	−	0.652199i	$-0.226153\pi$
$461$	32.5519	1.51610	0.758048	+	0.652199i	$0.226153\pi$
$462$	42.7727	1.98997
$463$	−21.3808	−0.993648	−0.496824	−	0.867851i	$-0.665501\pi$
$463$	−21.3808	−0.993648	−0.496824	+	0.867851i	$0.665501\pi$
$464$	−3.09526	−0.143694
$465$	41.6998	1.93378
$466$	−27.3935	−1.26898
$467$	−10.1851	−0.471311	−0.235656	−	0.971837i	$-0.575724\pi$
$467$	−10.1851	−0.471311	−0.235656	+	0.971837i	$0.575724\pi$
$468$	11.7329	0.542355
$469$	1.94591	0.0898539
$470$	16.4536	0.758947
$471$	34.8154	1.60421
$472$	−12.6294	−0.581317
$473$	52.0653	2.39397
$474$	−18.0200	−0.827686
$475$	49.7247	2.28153
$476$	24.0160	1.10077
$477$	4.76359	0.218110
$478$	−7.06148	−0.322985
$479$	−19.8799	−0.908336	−0.454168	−	0.890916i	$-0.650063\pi$
$479$	−19.8799	−0.908336	−0.454168	+	0.890916i	$0.650063\pi$
$480$	−7.71751	−0.352255
$481$	−9.50153	−0.433233
$482$	5.69098	0.259217
$483$	−59.2286	−2.69500
$484$	27.5514	1.25234
$485$	−17.4936	−0.794342
$486$	17.5378	0.795532
$487$	7.26347	0.329139	0.164570	−	0.986365i	$-0.447376\pi$
$487$	7.26347	0.329139	0.164570	+	0.986365i	$0.447376\pi$
$488$	6.88577	0.311704
$489$	−29.1858	−1.31983
$490$	9.01316	0.407173
$491$	31.6545	1.42855	0.714273	−	0.699867i	$-0.246757\pi$
$491$	31.6545	1.42855	0.714273	+	0.699867i	$0.246757\pi$
$492$	−8.42088	−0.379643
$493$	−23.9955	−1.08070
$494$	42.5812	1.91582
$495$	−41.9096	−1.88370
$496$	−5.40326	−0.242614
$497$	−24.0644	−1.07943
$498$	1.76497	0.0790902
$499$	−3.03935	−0.136060	−0.0680299	−	0.997683i	$-0.521671\pi$
$499$	−3.03935	−0.136060	−0.0680299	+	0.997683i	$0.521671\pi$
$500$	7.09645	0.317363
$501$	31.3173	1.39916
$502$	4.49059	0.200425
$503$	−31.4053	−1.40029	−0.700146	−	0.714000i	$-0.746882\pi$
$503$	−31.4053	−1.40029	−0.700146	+	0.714000i	$0.746882\pi$
$504$	6.02509	0.268379
$505$	56.7067	2.52342
$506$	−53.3832	−2.37317
$507$	−52.0202	−2.31030
$508$	−3.77097	−0.167310
$509$	−10.3480	−0.458668	−0.229334	−	0.973348i	$-0.573655\pi$
$509$	−10.3480	−0.458668	−0.229334	+	0.973348i	$0.573655\pi$
$510$	−59.8287	−2.64926
$511$	−27.8470	−1.23188
$512$	1.00000	0.0441942
$513$	16.5608	0.731179
$514$	−6.16427	−0.271894
$515$	−62.8684	−2.77031
$516$	18.6469	0.820884
$517$	−29.4362	−1.29460
$518$	−4.87923	−0.214381
$519$	50.3567	2.21042
$520$	20.9368	0.918140
$521$	−28.6659	−1.25588	−0.627939	−	0.778263i	$-0.716101\pi$
$521$	−28.6659	−1.25588	−0.627939	+	0.778263i	$0.716101\pi$
$522$	−6.01993	−0.263485
$523$	−24.4214	−1.06787	−0.533937	−	0.845525i	$-0.679288\pi$
$523$	−24.4214	−1.06787	−0.533937	+	0.845525i	$0.679288\pi$
$524$	3.61372	0.157866
$525$	−48.5303	−2.11804
$526$	9.59560	0.418388
$527$	−41.8879	−1.82467
$528$	13.8070	0.600871
$529$	50.9213	2.21397
$530$	8.50038	0.369233
$531$	−24.5628	−1.06594
$532$	21.8663	0.948023
$533$	22.8450	0.989525
$534$	15.3906	0.666015
$535$	−5.51548	−0.238455
$536$	0.628138	0.0271314
$537$	3.79604	0.163811
$538$	6.93524	0.298999
$539$	−16.1249	−0.694550
$540$	8.14283	0.350412
$541$	12.3329	0.530234	0.265117	−	0.964216i	$-0.414589\pi$
$541$	12.3329	0.530234	0.265117	+	0.964216i	$0.414589\pi$
$542$	−22.4141	−0.962767
$543$	−10.0630	−0.431845
$544$	7.75233	0.332379
$545$	−9.39811	−0.402571
$546$	−41.5583	−1.77853
$547$	−18.8758	−0.807071	−0.403536	−	0.914964i	$-0.632219\pi$
$547$	−18.8758	−0.807071	−0.403536	+	0.914964i	$0.632219\pi$
$548$	16.0502	0.685631
$549$	13.3921	0.571559
$550$	−43.7407	−1.86511
$551$	−21.8476	−0.930737
$552$	−19.1189	−0.813755
$553$	25.1041	1.06754
$554$	16.2654	0.691049
$555$	12.1551	0.515957
$556$	17.4761	0.741153
$557$	9.02085	0.382225	0.191113	−	0.981568i	$-0.438790\pi$
$557$	9.02085	0.382225	0.191113	+	0.981568i	$0.438790\pi$
$558$	−10.5087	−0.444871
$559$	−50.5871	−2.13961
$560$	10.7515	0.454332
$561$	107.036	4.51907
$562$	−10.1095	−0.426443
$563$	21.0091	0.885428	0.442714	−	0.896663i	$-0.354016\pi$
$563$	21.0091	0.885428	0.442714	+	0.896663i	$0.354016\pi$
$564$	−10.5424	−0.443915
$565$	−44.3478	−1.86573
$566$	6.55771	0.275641
$567$	−34.2383	−1.43787
$568$	−7.76794	−0.325936
$569$	−21.9590	−0.920567	−0.460284	−	0.887772i	$-0.652252\pi$
$569$	−21.9590	−0.920567	−0.460284	+	0.887772i	$0.652252\pi$
$570$	−54.4733	−2.28164
$571$	27.5496	1.15292	0.576458	−	0.817127i	$-0.304434\pi$
$571$	27.5496	1.15292	0.576458	+	0.817127i	$0.304434\pi$
$572$	−37.4569	−1.56615
$573$	3.56148	0.148783
$574$	11.7313	0.489657
$575$	60.5691	2.52591
$576$	1.94489	0.0810371
$577$	10.9857	0.457339	0.228670	−	0.973504i	$-0.426562\pi$
$577$	10.9857	0.457339	0.228670	+	0.973504i	$0.426562\pi$
$578$	43.0987	1.79267
$579$	−19.2879	−0.801580
$580$	−10.7423	−0.446048
$581$	−2.45883	−0.102009
$582$	11.2088	0.464618
$583$	−15.2076	−0.629832
$584$	−8.98898	−0.371967
$585$	40.7198	1.68355
$586$	13.5905	0.561418
$587$	27.7402	1.14496	0.572480	−	0.819918i	$-0.305981\pi$
$587$	27.7402	1.14496	0.572480	+	0.819918i	$0.305981\pi$
$588$	−5.77506	−0.238159
$589$	−38.1384	−1.57147
$590$	−43.8311	−1.80450
$591$	−40.0806	−1.64869
$592$	−1.57501	−0.0647324
$593$	8.21322	0.337277	0.168638	−	0.985678i	$-0.446063\pi$
$593$	8.21322	0.337277	0.168638	+	0.985678i	$0.446063\pi$
$594$	−14.5679	−0.597727
$595$	83.3489	3.41697
$596$	−8.07936	−0.330943
$597$	61.5694	2.51987
$598$	51.8676	2.12102
$599$	2.60863	0.106586	0.0532929	−	0.998579i	$-0.483028\pi$
$599$	2.60863	0.106586	0.0532929	+	0.998579i	$0.483028\pi$
$600$	−15.6655	−0.639542
$601$	2.54168	0.103677	0.0518387	−	0.998655i	$-0.483492\pi$
$601$	2.54168	0.103677	0.0518387	+	0.998655i	$0.483492\pi$
$602$	−25.9775	−1.05876
$603$	1.22166	0.0497498
$604$	−18.7749	−0.763939
$605$	95.6186	3.88745
$606$	−36.3340	−1.47597
$607$	−27.8667	−1.13107	−0.565537	−	0.824723i	$-0.691331\pi$
$607$	−27.8667	−1.13107	−0.565537	+	0.824723i	$0.691331\pi$
$608$	7.05840	0.286256
$609$	21.3228	0.864042
$610$	23.8974	0.967579
$611$	28.6004	1.15705
$612$	15.0774	0.609469
$613$	3.90383	0.157674	0.0788372	−	0.996888i	$-0.474879\pi$
$613$	3.90383	0.157674	0.0788372	+	0.996888i	$0.474879\pi$
$614$	32.5757	1.31465
$615$	−29.2251	−1.17847
$616$	−19.2348	−0.774994
$617$	28.7113	1.15587	0.577937	−	0.816081i	$-0.303858\pi$
$617$	28.7113	1.15587	0.577937	+	0.816081i	$0.303858\pi$
$618$	40.2820	1.62038
$619$	−23.3767	−0.939587	−0.469793	−	0.882776i	$-0.655672\pi$
$619$	−23.3767	−0.939587	−0.469793	+	0.882776i	$0.655672\pi$
$620$	−18.7523	−0.753112
$621$	20.1726	0.809497
$622$	11.5684	0.463850
$623$	−21.4410	−0.859016
$624$	−13.4150	−0.537028
$625$	−10.5952	−0.423807
$626$	2.47719	0.0990084
$627$	97.4551	3.89198
$628$	−15.6564	−0.624760
$629$	−12.2100	−0.486844
$630$	20.9104	0.833091
$631$	−28.3919	−1.13026	−0.565131	−	0.825001i	$-0.691174\pi$
$631$	−28.3919	−1.13026	−0.565131	+	0.825001i	$0.691174\pi$
$632$	8.10357	0.322343
$633$	36.4528	1.44887
$634$	−12.8562	−0.510583
$635$	−13.0874	−0.519356
$636$	−5.44650	−0.215968
$637$	15.6671	0.620754
$638$	19.2184	0.760863
$639$	−15.1078	−0.597655
$640$	3.47056	0.137186
$641$	−12.5925	−0.497373	−0.248687	−	0.968584i	$-0.579999\pi$
$641$	−12.5925	−0.497373	−0.248687	+	0.968584i	$0.579999\pi$
$642$	3.53397	0.139475
$643$	−22.5159	−0.887941	−0.443971	−	0.896041i	$-0.646431\pi$
$643$	−22.5159	−0.887941	−0.443971	+	0.896041i	$0.646431\pi$
$644$	26.6350	1.04957
$645$	64.7151	2.54816
$646$	54.7191	2.15289
$647$	34.5550	1.35850	0.679248	−	0.733909i	$-0.262306\pi$
$647$	34.5550	1.35850	0.679248	+	0.733909i	$0.262306\pi$
$648$	−11.0521	−0.434166
$649$	78.4158	3.07809
$650$	42.4989	1.66694
$651$	37.2223	1.45886
$652$	13.1248	0.514007
$653$	11.3061	0.442442	0.221221	−	0.975224i	$-0.428996\pi$
$653$	11.3061	0.442442	0.221221	+	0.975224i	$0.428996\pi$
$654$	6.02171	0.235467
$655$	12.5416	0.490042
$656$	3.78686	0.147852
$657$	−17.4826	−0.682060
$658$	14.6869	0.572555
$659$	36.7891	1.43310	0.716551	−	0.697535i	$-0.245720\pi$
$659$	36.7891	1.43310	0.716551	+	0.697535i	$0.245720\pi$
$660$	47.9179	1.86520
$661$	35.8989	1.39630	0.698152	−	0.715949i	$-0.254006\pi$
$661$	35.8989	1.39630	0.698152	+	0.715949i	$0.254006\pi$
$662$	−15.8020	−0.614161
$663$	−103.997	−4.03892
$664$	−0.793705	−0.0308017
$665$	75.8881	2.94282
$666$	−3.06321	−0.118697
$667$	−26.6123	−1.03043
$668$	−14.0834	−0.544902
$669$	40.7494	1.57546
$670$	2.17999	0.0842202
$671$	−42.7536	−1.65048
$672$	−6.88885	−0.265743
$673$	−9.15071	−0.352734	−0.176367	−	0.984324i	$-0.556435\pi$
$673$	−9.15071	−0.352734	−0.176367	+	0.984324i	$0.556435\pi$
$674$	15.4049	0.593375
$675$	16.5288	0.636195
$676$	23.3934	0.899746
$677$	−24.1701	−0.928933	−0.464467	−	0.885591i	$-0.653754\pi$
$677$	−24.1701	−0.928933	−0.464467	+	0.885591i	$0.653754\pi$
$678$	28.4153	1.09128
$679$	−15.6152	−0.599257
$680$	26.9049	1.03176
$681$	−39.5674	−1.51623
$682$	33.5487	1.28465
$683$	−5.81172	−0.222379	−0.111190	−	0.993799i	$-0.535466\pi$
$683$	−5.81172	−0.222379	−0.111190	+	0.993799i	$0.535466\pi$
$684$	13.7278	0.524896
$685$	55.7032	2.12831
$686$	−13.6400	−0.520777
$687$	39.8679	1.52105
$688$	−8.38549	−0.319694
$689$	14.7758	0.562913
$690$	−66.3533	−2.52603
$691$	5.19429	0.197600	0.0988001	−	0.995107i	$-0.468500\pi$
$691$	5.19429	0.197600	0.0988001	+	0.995107i	$0.468500\pi$
$692$	−22.6454	−0.860847
$693$	−37.4096	−1.42107
$694$	14.1929	0.538754
$695$	60.6519	2.30066
$696$	6.88296	0.260898
$697$	29.3570	1.11198
$698$	3.12593	0.118318
$699$	60.9152	2.30402
$700$	21.8240	0.824870
$701$	−24.6505	−0.931035	−0.465518	−	0.885039i	$-0.654132\pi$
$701$	−24.6505	−0.931035	−0.465518	+	0.885039i	$0.654132\pi$
$702$	14.1543	0.534219
$703$	−11.1170	−0.419287
$704$	−6.20898	−0.234010
$705$	−36.5880	−1.37798
$706$	−8.85222	−0.333158
$707$	50.6179	1.90368
$708$	28.0842	1.05547
$709$	−29.0992	−1.09284	−0.546421	−	0.837510i	$-0.684010\pi$
$709$	−29.0992	−1.09284	−0.546421	+	0.837510i	$0.684010\pi$
$710$	−26.9591	−1.01176
$711$	15.7605	0.591067
$712$	−6.92112	−0.259380
$713$	−46.4559	−1.73979
$714$	−53.4047	−1.99862
$715$	−129.996	−4.86158
$716$	−1.70707	−0.0637963
$717$	15.7027	0.586428
$718$	−3.68243	−0.137427
$719$	−37.7956	−1.40954	−0.704768	−	0.709437i	$-0.748949\pi$
$719$	−37.7956	−1.40954	−0.704768	+	0.709437i	$0.748949\pi$
$720$	6.74985	0.251552
$721$	−56.1179	−2.08994
$722$	30.8210	1.14704
$723$	−12.6551	−0.470648
$724$	4.52532	0.168182
$725$	−21.8053	−0.809830
$726$	−61.2663	−2.27381
$727$	8.73138	0.323829	0.161914	−	0.986805i	$-0.448233\pi$
$727$	8.73138	0.323829	0.161914	+	0.986805i	$0.448233\pi$
$728$	18.6887	0.692651
$729$	−5.84284	−0.216402
$730$	−31.1967	−1.15464
$731$	−65.0071	−2.40437
$732$	−15.3120	−0.565946
$733$	−53.7323	−1.98465	−0.992324	−	0.123669i	$-0.960534\pi$
$733$	−53.7323	−1.98465	−0.992324	+	0.123669i	$0.960534\pi$
$734$	−24.6758	−0.910801
$735$	−20.0427	−0.739285
$736$	8.59775	0.316917
$737$	−3.90009	−0.143662
$738$	7.36502	0.271110
$739$	28.2807	1.04032	0.520161	−	0.854068i	$-0.325872\pi$
$739$	28.2807	1.04032	0.520161	+	0.854068i	$0.325872\pi$
$740$	−5.46615	−0.200940
$741$	−94.6882	−3.47846
$742$	7.58766	0.278552
$743$	−1.87617	−0.0688301	−0.0344151	−	0.999408i	$-0.510957\pi$
$743$	−1.87617	−0.0688301	−0.0344151	+	0.999408i	$0.510957\pi$
$744$	12.0153	0.440502
$745$	−28.0399	−1.02730
$746$	−19.7244	−0.722162
$747$	−1.54367	−0.0564799
$748$	−48.1341	−1.75996
$749$	−4.92326	−0.179892
$750$	−15.7804	−0.576220
$751$	0.249246	0.00909511	0.00454756	−	0.999990i	$-0.498552\pi$
$751$	0.249246	0.00909511	0.00454756	+	0.999990i	$0.498552\pi$
$752$	4.74091	0.172883
$753$	−9.98578	−0.363902
$754$	−18.6727	−0.680021
$755$	−65.1593	−2.37139
$756$	7.26850	0.264353
$757$	−34.2184	−1.24369	−0.621844	−	0.783141i	$-0.713616\pi$
$757$	−34.2184	−1.24369	−0.621844	+	0.783141i	$0.713616\pi$
$758$	19.9912	0.726114
$759$	118.709	4.30886
$760$	24.4966	0.888584
$761$	30.8103	1.11687	0.558435	−	0.829548i	$-0.311402\pi$
$761$	30.8103	1.11687	0.558435	+	0.829548i	$0.311402\pi$
$762$	8.38555	0.303776
$763$	−8.38899	−0.303702
$764$	−1.60159	−0.0579436
$765$	52.3271	1.89189
$766$	29.4611	1.06447
$767$	−76.1895	−2.75104
$768$	−2.22371	−0.0802412
$769$	0.901069	0.0324934	0.0162467	−	0.999868i	$-0.494828\pi$
$769$	0.901069	0.0324934	0.0162467	+	0.999868i	$0.494828\pi$
$770$	−66.7556	−2.40570
$771$	13.7075	0.493665
$772$	8.67377	0.312176
$773$	−44.1639	−1.58846	−0.794232	−	0.607614i	$-0.792127\pi$
$773$	−44.1639	−1.58846	−0.794232	+	0.607614i	$0.792127\pi$
$774$	−16.3088	−0.586209
$775$	−38.0647	−1.36732
$776$	−5.04057	−0.180946
$777$	10.8500	0.389241
$778$	18.3449	0.657698
$779$	26.7292	0.957672
$780$	−46.5574	−1.66702
$781$	48.2310	1.72584
$782$	66.6526	2.38349
$783$	−7.26228	−0.259533
$784$	2.59704	0.0927513
$785$	−54.3365	−1.93935
$786$	−8.03587	−0.286630
$787$	17.5968	0.627260	0.313630	−	0.949545i	$-0.398455\pi$
$787$	17.5968	0.627260	0.313630	+	0.949545i	$0.398455\pi$
$788$	18.0242	0.642085
$789$	−21.3378	−0.759647
$790$	28.1239	1.00060
$791$	−39.5860	−1.40752
$792$	−12.0758	−0.429094
$793$	41.5397	1.47512
$794$	16.7070	0.592911
$795$	−18.9024	−0.670399
$796$	−27.6877	−0.981365
$797$	19.5698	0.693199	0.346599	−	0.938013i	$-0.387336\pi$
$797$	19.5698	0.693199	0.346599	+	0.938013i	$0.387336\pi$
$798$	−48.6243	−1.72128
$799$	36.7531	1.30023
$800$	7.04476	0.249070
$801$	−13.4608	−0.475615
$802$	28.9430	1.02201
$803$	55.8123	1.96957
$804$	−1.39680	−0.0492612
$805$	92.4384	3.25803
$806$	−32.5962	−1.14815
$807$	−15.4220	−0.542879
$808$	16.3394	0.574817
$809$	32.9884	1.15981	0.579904	−	0.814684i	$-0.303090\pi$
$809$	32.9884	1.15981	0.579904	+	0.814684i	$0.303090\pi$
$810$	−38.3568	−1.34772
$811$	−11.7819	−0.413719	−0.206860	−	0.978371i	$-0.566324\pi$
$811$	−11.7819	−0.413719	−0.206860	+	0.978371i	$0.566324\pi$
$812$	−9.58882	−0.336502
$813$	49.8424	1.74805
$814$	9.77918	0.342760
$815$	45.5503	1.59556
$816$	−17.2389	−0.603484
$817$	−59.1881	−2.07073
$818$	26.5842	0.929495
$819$	36.3475	1.27009
$820$	13.1425	0.458956
$821$	−38.9105	−1.35799	−0.678993	−	0.734145i	$-0.737583\pi$
$821$	−38.9105	−1.35799	−0.678993	+	0.734145i	$0.737583\pi$
$822$	−35.6910	−1.24487
$823$	23.5755	0.821789	0.410895	−	0.911683i	$-0.365216\pi$
$823$	23.5755	0.821789	0.410895	+	0.911683i	$0.365216\pi$
$824$	−18.1148	−0.631058
$825$	97.2667	3.38639
$826$	−39.1248	−1.36133
$827$	10.0064	0.347956	0.173978	−	0.984750i	$-0.444338\pi$
$827$	10.0064	0.347956	0.173978	+	0.984750i	$0.444338\pi$
$828$	16.7217	0.581118
$829$	31.8871	1.10748	0.553742	−	0.832688i	$-0.313199\pi$
$829$	31.8871	1.10748	0.553742	+	0.832688i	$0.313199\pi$
$830$	−2.75460	−0.0956135
$831$	−36.1694	−1.25470
$832$	6.03269	0.209146
$833$	20.1331	0.697570
$834$	−38.8618	−1.34568
$835$	−48.8771	−1.69146
$836$	−43.8254	−1.51573
$837$	−12.6775	−0.438197
$838$	18.1843	0.628167
$839$	13.5018	0.466135	0.233068	−	0.972461i	$-0.425124\pi$
$839$	13.5018	0.466135	0.233068	+	0.972461i	$0.425124\pi$
$840$	−23.9081	−0.824909
$841$	−19.4194	−0.669634
$842$	−27.6219	−0.951914
$843$	22.4806	0.774273
$844$	−16.3928	−0.564263
$845$	81.1881	2.79296
$846$	9.22054	0.317009
$847$	85.3517	2.93272
$848$	2.44928	0.0841088
$849$	−14.5824	−0.500468
$850$	54.6133	1.87322
$851$	−13.5415	−0.464197
$852$	17.2737	0.591786
$853$	21.8433	0.747899	0.373950	−	0.927449i	$-0.378003\pi$
$853$	21.8433	0.747899	0.373950	+	0.927449i	$0.378003\pi$
$854$	21.3315	0.729948
$855$	47.6431	1.62936
$856$	−1.58922	−0.0543184
$857$	30.0428	1.02624	0.513121	−	0.858316i	$-0.328489\pi$
$857$	30.0428	1.02624	0.513121	+	0.858316i	$0.328489\pi$
$858$	83.2932	2.84358
$859$	6.85206	0.233789	0.116895	−	0.993144i	$-0.462706\pi$
$859$	6.85206	0.233789	0.116895	+	0.993144i	$0.462706\pi$
$860$	−29.1023	−0.992381
$861$	−26.0871	−0.889046
$862$	−27.4125	−0.933673
$863$	−23.4477	−0.798170	−0.399085	−	0.916914i	$-0.630672\pi$
$863$	−23.4477	−0.798170	−0.399085	+	0.916914i	$0.630672\pi$
$864$	2.34626	0.0798214
$865$	−78.5920	−2.67221
$866$	−22.2689	−0.756728
$867$	−95.8390	−3.25486
$868$	−16.7388	−0.568152
$869$	−50.3149	−1.70682
$870$	23.8877	0.809868
$871$	3.78936	0.128398
$872$	−2.70795	−0.0917029
$873$	−9.80335	−0.331793
$874$	60.6864	2.05275
$875$	21.9841	0.743200
$876$	19.9889	0.675362
$877$	−47.7248	−1.61155	−0.805775	−	0.592221i	$-0.798251\pi$
$877$	−47.7248	−1.61155	−0.805775	+	0.592221i	$0.798251\pi$
$878$	−0.375616	−0.0126764
$879$	−30.2213	−1.01934
$880$	−21.5486	−0.726403
$881$	−32.8548	−1.10691	−0.553453	−	0.832881i	$-0.686690\pi$
$881$	−32.8548	−1.10691	−0.553453	+	0.832881i	$0.686690\pi$
$882$	5.05095	0.170074
$883$	−8.74291	−0.294222	−0.147111	−	0.989120i	$-0.546998\pi$
$883$	−8.74291	−0.294222	−0.147111	+	0.989120i	$0.546998\pi$
$884$	46.7675	1.57296
$885$	97.4678	3.27634
$886$	8.14557	0.273656
$887$	43.6623	1.46604	0.733018	−	0.680209i	$-0.238111\pi$
$887$	43.6623	1.46604	0.733018	+	0.680209i	$0.238111\pi$
$888$	3.50236	0.117531
$889$	−11.6821	−0.391806
$890$	−24.0202	−0.805157
$891$	68.6221	2.29893
$892$	−18.3250	−0.613565
$893$	33.4632	1.11980
$894$	17.9662	0.600878
$895$	−5.92449	−0.198034
$896$	3.09791	0.103494
$897$	−115.339	−3.85104
$898$	16.5710	0.552981
$899$	16.7245	0.557793
$900$	13.7013	0.456709
$901$	18.9877	0.632571
$902$	−23.5125	−0.782881
$903$	57.7664	1.92235
$904$	−12.7783	−0.425000
$905$	15.7054	0.522064
$906$	41.7499	1.38705
$907$	42.8322	1.42222	0.711110	−	0.703081i	$-0.248193\pi$
$907$	42.8322	1.42222	0.711110	+	0.703081i	$0.248193\pi$
$908$	17.7934	0.590495
$909$	31.7783	1.05402
$910$	64.8603	2.15010
$911$	22.7221	0.752818	0.376409	−	0.926454i	$-0.377159\pi$
$911$	22.7221	0.752818	0.376409	+	0.926454i	$0.377159\pi$
$912$	−15.6958	−0.519741
$913$	4.92810	0.163096
$914$	−0.581644	−0.0192391
$915$	−53.1410	−1.75679
$916$	−17.9285	−0.592376
$917$	11.1950	0.369691
$918$	18.1890	0.600326
$919$	6.26722	0.206737	0.103368	−	0.994643i	$-0.467038\pi$
$919$	6.26722	0.206737	0.103368	+	0.994643i	$0.467038\pi$
$920$	29.8390	0.983762
$921$	−72.4390	−2.38695
$922$	32.5519	1.07204
$923$	−46.8616	−1.54247
$924$	42.7727	1.40712
$925$	−11.0955	−0.364819
$926$	−21.3808	−0.702615
$927$	−35.2312	−1.15715
$928$	−3.09526	−0.101607
$929$	−27.6328	−0.906603	−0.453302	−	0.891357i	$-0.649754\pi$
$929$	−27.6328	−0.906603	−0.453302	+	0.891357i	$0.649754\pi$
$930$	41.6998	1.36739
$931$	18.3309	0.600772
$932$	−27.3935	−0.897304
$933$	−25.7247	−0.842190
$934$	−10.1851	−0.333268
$935$	−167.052	−5.46318
$936$	11.7329	0.383503
$937$	−12.2582	−0.400458	−0.200229	−	0.979749i	$-0.564169\pi$
$937$	−12.2582	−0.400458	−0.200229	+	0.979749i	$0.564169\pi$
$938$	1.94591	0.0635363
$939$	−5.50855	−0.179765
$940$	16.4536	0.536657
$941$	−28.2289	−0.920236	−0.460118	−	0.887858i	$-0.652193\pi$
$941$	−28.2289	−0.920236	−0.460118	+	0.887858i	$0.652193\pi$
$942$	34.8154	1.13435
$943$	32.5585	1.06025
$944$	−12.6294	−0.411053
$945$	25.2257	0.820593
$946$	52.0653	1.69279
$947$	18.3064	0.594879	0.297440	−	0.954741i	$-0.403867\pi$
$947$	18.3064	0.594879	0.297440	+	0.954741i	$0.403867\pi$
$948$	−18.0200	−0.585262
$949$	−54.2277	−1.76031
$950$	49.7247	1.61328
$951$	28.5884	0.927041
$952$	24.0160	0.778364
$953$	−35.1796	−1.13958	−0.569789	−	0.821791i	$-0.692975\pi$
$953$	−35.1796	−1.13958	−0.569789	+	0.821791i	$0.692975\pi$
$954$	4.76359	0.154227
$955$	−5.55842	−0.179866
$956$	−7.06148	−0.228385
$957$	−42.7361	−1.38146
$958$	−19.8799	−0.642291
$959$	49.7221	1.60561
$960$	−7.71751	−0.249082
$961$	−1.80474	−0.0582174
$962$	−9.50153	−0.306342
$963$	−3.09086	−0.0996015
$964$	5.69098	0.183294
$965$	30.1028	0.969043
$966$	−59.2286	−1.90565
$967$	−54.5412	−1.75393	−0.876963	−	0.480558i	$-0.840434\pi$
$967$	−54.5412	−1.75393	−0.876963	+	0.480558i	$0.840434\pi$
$968$	27.5514	0.885535
$969$	−121.679	−3.90891
$970$	−17.4936	−0.561685
$971$	27.3297	0.877052	0.438526	−	0.898719i	$-0.355501\pi$
$971$	27.3297	0.877052	0.438526	+	0.898719i	$0.355501\pi$
$972$	17.5378	0.562526
$973$	54.1394	1.73563
$974$	7.26347	0.232737
$975$	−94.5052	−3.02659
$976$	6.88577	0.220408
$977$	21.8504	0.699056	0.349528	−	0.936926i	$-0.386342\pi$
$977$	21.8504	0.699056	0.349528	+	0.936926i	$0.386342\pi$
$978$	−29.1858	−0.933257
$979$	42.9731	1.37343
$980$	9.01316	0.287915
$981$	−5.26667	−0.168152
$982$	31.6545	1.01014
$983$	11.3591	0.362297	0.181149	−	0.983456i	$-0.442018\pi$
$983$	11.3591	0.362297	0.181149	+	0.983456i	$0.442018\pi$
$984$	−8.42088	−0.268448
$985$	62.5540	1.99313
$986$	−23.9955	−0.764171
$987$	−32.6594	−1.03956
$988$	42.5812	1.35469
$989$	−72.0964	−2.29253
$990$	−41.9096	−1.33198
$991$	−21.0575	−0.668912	−0.334456	−	0.942411i	$-0.608553\pi$
$991$	−21.0575	−0.668912	−0.334456	+	0.942411i	$0.608553\pi$
$992$	−5.40326	−0.171554
$993$	35.1390	1.11510
$994$	−24.0644	−0.763276
$995$	−96.0917	−3.04631
$996$	1.76497	0.0559252
$997$	20.0333	0.634461	0.317231	−	0.948348i	$-0.397247\pi$
$997$	20.0333	0.634461	0.317231	+	0.948348i	$0.397247\pi$
$998$	−3.03935	−0.0962088
$999$	−3.69538	−0.116917

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.15	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.15	✓	95	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.22371 q^{3} +1.00000 q^{4} +3.47056 q^{5} -2.22371 q^{6} +3.09791 q^{7} +1.00000 q^{8} +1.94489 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.22371 q^{3} +1.00000 q^{4} +3.47056 q^{5} -2.22371 q^{6} +3.09791 q^{7} +1.00000 q^{8} +1.94489 q^{9} +3.47056 q^{10} -6.20898 q^{11} -2.22371 q^{12} +6.03269 q^{13} +3.09791 q^{14} -7.71751 q^{15} +1.00000 q^{16} +7.75233 q^{17} +1.94489 q^{18} +7.05840 q^{19} +3.47056 q^{20} -6.88885 q^{21} -6.20898 q^{22} +8.59775 q^{23} -2.22371 q^{24} +7.04476 q^{25} +6.03269 q^{26} +2.34626 q^{27} +3.09791 q^{28} -3.09526 q^{29} -7.71751 q^{30} -5.40326 q^{31} +1.00000 q^{32} +13.8070 q^{33} +7.75233 q^{34} +10.7515 q^{35} +1.94489 q^{36} -1.57501 q^{37} +7.05840 q^{38} -13.4150 q^{39} +3.47056 q^{40} +3.78686 q^{41} -6.88885 q^{42} -8.38549 q^{43} -6.20898 q^{44} +6.74985 q^{45} +8.59775 q^{46} +4.74091 q^{47} -2.22371 q^{48} +2.59704 q^{49} +7.04476 q^{50} -17.2389 q^{51} +6.03269 q^{52} +2.44928 q^{53} +2.34626 q^{54} -21.5486 q^{55} +3.09791 q^{56} -15.6958 q^{57} -3.09526 q^{58} -12.6294 q^{59} -7.71751 q^{60} +6.88577 q^{61} -5.40326 q^{62} +6.02509 q^{63} +1.00000 q^{64} +20.9368 q^{65} +13.8070 q^{66} +0.628138 q^{67} +7.75233 q^{68} -19.1189 q^{69} +10.7515 q^{70} -7.76794 q^{71} +1.94489 q^{72} -8.98898 q^{73} -1.57501 q^{74} -15.6655 q^{75} +7.05840 q^{76} -19.2348 q^{77} -13.4150 q^{78} +8.10357 q^{79} +3.47056 q^{80} -11.0521 q^{81} +3.78686 q^{82} -0.793705 q^{83} -6.88885 q^{84} +26.9049 q^{85} -8.38549 q^{86} +6.88296 q^{87} -6.20898 q^{88} -6.92112 q^{89} +6.74985 q^{90} +18.6887 q^{91} +8.59775 q^{92} +12.0153 q^{93} +4.74091 q^{94} +24.4966 q^{95} -2.22371 q^{96} -5.04057 q^{97} +2.59704 q^{98} -12.0758 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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