LMFDB - Embedded newform 8026.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.53693 q^{3} +1.00000 q^{4} +0.430224 q^{5} +2.53693 q^{6} +2.70951 q^{7} -1.00000 q^{8} +3.43604 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.53693 q^{3} +1.00000 q^{4} +0.430224 q^{5} +2.53693 q^{6} +2.70951 q^{7} -1.00000 q^{8} +3.43604 q^{9} -0.430224 q^{10} +1.84301 q^{11} -2.53693 q^{12} +4.78290 q^{13} -2.70951 q^{14} -1.09145 q^{15} +1.00000 q^{16} -3.44461 q^{17} -3.43604 q^{18} -0.168024 q^{19} +0.430224 q^{20} -6.87386 q^{21} -1.84301 q^{22} +9.12483 q^{23} +2.53693 q^{24} -4.81491 q^{25} -4.78290 q^{26} -1.10620 q^{27} +2.70951 q^{28} -6.67499 q^{29} +1.09145 q^{30} +6.88555 q^{31} -1.00000 q^{32} -4.67560 q^{33} +3.44461 q^{34} +1.16570 q^{35} +3.43604 q^{36} -1.65400 q^{37} +0.168024 q^{38} -12.1339 q^{39} -0.430224 q^{40} +1.99108 q^{41} +6.87386 q^{42} -12.4682 q^{43} +1.84301 q^{44} +1.47827 q^{45} -9.12483 q^{46} -0.771079 q^{47} -2.53693 q^{48} +0.341471 q^{49} +4.81491 q^{50} +8.73874 q^{51} +4.78290 q^{52} -4.18969 q^{53} +1.10620 q^{54} +0.792907 q^{55} -2.70951 q^{56} +0.426267 q^{57} +6.67499 q^{58} -7.95297 q^{59} -1.09145 q^{60} +4.20081 q^{61} -6.88555 q^{62} +9.30999 q^{63} +1.00000 q^{64} +2.05772 q^{65} +4.67560 q^{66} -15.4904 q^{67} -3.44461 q^{68} -23.1491 q^{69} -1.16570 q^{70} -0.199219 q^{71} -3.43604 q^{72} -10.8856 q^{73} +1.65400 q^{74} +12.2151 q^{75} -0.168024 q^{76} +4.99366 q^{77} +12.1339 q^{78} -7.86915 q^{79} +0.430224 q^{80} -7.50176 q^{81} -1.99108 q^{82} -5.01016 q^{83} -6.87386 q^{84} -1.48195 q^{85} +12.4682 q^{86} +16.9340 q^{87} -1.84301 q^{88} +4.71744 q^{89} -1.47827 q^{90} +12.9593 q^{91} +9.12483 q^{92} -17.4682 q^{93} +0.771079 q^{94} -0.0722881 q^{95} +2.53693 q^{96} +1.64242 q^{97} -0.341471 q^{98} +6.33265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * 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
$3$	−2.53693	−1.46470	−0.732350	−	0.680928i	$-0.761576\pi$
$3$	−2.53693	−1.46470	−0.732350	+	0.680928i	$0.761576\pi$
$4$	1.00000	0.500000
$5$	0.430224	0.192402	0.0962010	−	0.995362i	$-0.469331\pi$
$5$	0.430224	0.192402	0.0962010	+	0.995362i	$0.469331\pi$
$6$	2.53693	1.03570
$7$	2.70951	1.02410	0.512050	−	0.858956i	$-0.328886\pi$
$7$	2.70951	1.02410	0.512050	+	0.858956i	$0.328886\pi$
$8$	−1.00000	−0.353553
$9$	3.43604	1.14535
$10$	−0.430224	−0.136049
$11$	1.84301	0.555688	0.277844	−	0.960626i	$-0.410380\pi$
$11$	1.84301	0.555688	0.277844	+	0.960626i	$0.410380\pi$
$12$	−2.53693	−0.732350
$13$	4.78290	1.32654	0.663269	−	0.748381i	$-0.269168\pi$
$13$	4.78290	1.32654	0.663269	+	0.748381i	$0.269168\pi$
$14$	−2.70951	−0.724148
$15$	−1.09145	−0.281811
$16$	1.00000	0.250000
$17$	−3.44461	−0.835440	−0.417720	−	0.908576i	$-0.637171\pi$
$17$	−3.44461	−0.835440	−0.417720	+	0.908576i	$0.637171\pi$
$18$	−3.43604	−0.809882
$19$	−0.168024	−0.0385474	−0.0192737	−	0.999814i	$-0.506135\pi$
$19$	−0.168024	−0.0385474	−0.0192737	+	0.999814i	$0.506135\pi$
$20$	0.430224	0.0962010
$21$	−6.87386	−1.50000
$22$	−1.84301	−0.392931
$23$	9.12483	1.90266	0.951329	−	0.308178i	$-0.0997191\pi$
$23$	9.12483	1.90266	0.951329	+	0.308178i	$0.0997191\pi$
$24$	2.53693	0.517850
$25$	−4.81491	−0.962981
$26$	−4.78290	−0.938004
$27$	−1.10620	−0.212888
$28$	2.70951	0.512050
$29$	−6.67499	−1.23951	−0.619757	−	0.784793i	$-0.712769\pi$
$29$	−6.67499	−1.23951	−0.619757	+	0.784793i	$0.712769\pi$
$30$	1.09145	0.199271
$31$	6.88555	1.23668	0.618341	−	0.785910i	$-0.287805\pi$
$31$	6.88555	1.23668	0.618341	+	0.785910i	$0.287805\pi$
$32$	−1.00000	−0.176777
$33$	−4.67560	−0.813917
$34$	3.44461	0.590745
$35$	1.16570	0.197039
$36$	3.43604	0.572673
$37$	−1.65400	−0.271915	−0.135958	−	0.990715i	$-0.543411\pi$
$37$	−1.65400	−0.271915	−0.135958	+	0.990715i	$0.543411\pi$
$38$	0.168024	0.0272572
$39$	−12.1339	−1.94298
$40$	−0.430224	−0.0680244
$41$	1.99108	0.310955	0.155477	−	0.987839i	$-0.450308\pi$
$41$	1.99108	0.310955	0.155477	+	0.987839i	$0.450308\pi$
$42$	6.87386	1.06066
$43$	−12.4682	−1.90138	−0.950692	−	0.310136i	$-0.899625\pi$
$43$	−12.4682	−1.90138	−0.950692	+	0.310136i	$0.899625\pi$
$44$	1.84301	0.277844
$45$	1.47827	0.220367
$46$	−9.12483	−1.34538
$47$	−0.771079	−0.112473	−0.0562367	−	0.998417i	$-0.517910\pi$
$47$	−0.771079	−0.112473	−0.0562367	+	0.998417i	$0.517910\pi$
$48$	−2.53693	−0.366175
$49$	0.341471	0.0487815
$50$	4.81491	0.680931
$51$	8.73874	1.22367
$52$	4.78290	0.663269
$53$	−4.18969	−0.575498	−0.287749	−	0.957706i	$-0.592907\pi$
$53$	−4.18969	−0.575498	−0.287749	+	0.957706i	$0.592907\pi$
$54$	1.10620	0.150535
$55$	0.792907	0.106916
$56$	−2.70951	−0.362074
$57$	0.426267	0.0564604
$58$	6.67499	0.876469
$59$	−7.95297	−1.03539	−0.517694	−	0.855566i	$-0.673209\pi$
$59$	−7.95297	−1.03539	−0.517694	+	0.855566i	$0.673209\pi$
$60$	−1.09145	−0.140906
$61$	4.20081	0.537858	0.268929	−	0.963160i	$-0.413330\pi$
$61$	4.20081	0.537858	0.268929	+	0.963160i	$0.413330\pi$
$62$	−6.88555	−0.874466
$63$	9.30999	1.17295
$64$	1.00000	0.125000
$65$	2.05772	0.255229
$66$	4.67560	0.575526
$67$	−15.4904	−1.89246	−0.946229	−	0.323498i	$-0.895141\pi$
$67$	−15.4904	−1.89246	−0.946229	+	0.323498i	$0.895141\pi$
$68$	−3.44461	−0.417720
$69$	−23.1491	−2.78682
$70$	−1.16570	−0.139328
$71$	−0.199219	−0.0236430	−0.0118215	−	0.999930i	$-0.503763\pi$
$71$	−0.199219	−0.0236430	−0.0118215	+	0.999930i	$0.503763\pi$
$72$	−3.43604	−0.404941
$73$	−10.8856	−1.27407	−0.637034	−	0.770836i	$-0.719839\pi$
$73$	−10.8856	−1.27407	−0.637034	+	0.770836i	$0.719839\pi$
$74$	1.65400	0.192273
$75$	12.2151	1.41048
$76$	−0.168024	−0.0192737
$77$	4.99366	0.569081
$78$	12.1339	1.37389
$79$	−7.86915	−0.885348	−0.442674	−	0.896683i	$-0.645970\pi$
$79$	−7.86915	−0.885348	−0.442674	+	0.896683i	$0.645970\pi$
$80$	0.430224	0.0481005
$81$	−7.50176	−0.833529
$82$	−1.99108	−0.219878
$83$	−5.01016	−0.549936	−0.274968	−	0.961453i	$-0.588667\pi$
$83$	−5.01016	−0.549936	−0.274968	+	0.961453i	$0.588667\pi$
$84$	−6.87386	−0.750000
$85$	−1.48195	−0.160740
$86$	12.4682	1.34448
$87$	16.9340	1.81552
$88$	−1.84301	−0.196466
$89$	4.71744	0.500048	0.250024	−	0.968240i	$-0.419562\pi$
$89$	4.71744	0.500048	0.250024	+	0.968240i	$0.419562\pi$
$90$	−1.47827	−0.155823
$91$	12.9593	1.35851
$92$	9.12483	0.951329
$93$	−17.4682	−1.81137
$94$	0.771079	0.0795307
$95$	−0.0722881	−0.00741660
$96$	2.53693	0.258925
$97$	1.64242	0.166762	0.0833812	−	0.996518i	$-0.473428\pi$
$97$	1.64242	0.166762	0.0833812	+	0.996518i	$0.473428\pi$
$98$	−0.341471	−0.0344937
$99$	6.33265	0.636455
$100$	−4.81491	−0.481491
$101$	−8.84635	−0.880245	−0.440123	−	0.897938i	$-0.645065\pi$
$101$	−8.84635	−0.880245	−0.440123	+	0.897938i	$0.645065\pi$
$102$	−8.73874	−0.865265
$103$	−2.93468	−0.289163	−0.144581	−	0.989493i	$-0.546184\pi$
$103$	−2.93468	−0.289163	−0.144581	+	0.989493i	$0.546184\pi$
$104$	−4.78290	−0.469002
$105$	−2.95730	−0.288603
$106$	4.18969	0.406939
$107$	−10.0895	−0.975388	−0.487694	−	0.873015i	$-0.662162\pi$
$107$	−10.0895	−0.975388	−0.487694	+	0.873015i	$0.662162\pi$
$108$	−1.10620	−0.106444
$109$	−4.60903	−0.441465	−0.220732	−	0.975334i	$-0.570845\pi$
$109$	−4.60903	−0.441465	−0.220732	+	0.975334i	$0.570845\pi$
$110$	−0.792907	−0.0756007
$111$	4.19608	0.398274
$112$	2.70951	0.256025
$113$	−14.0213	−1.31902	−0.659509	−	0.751697i	$-0.729236\pi$
$113$	−14.0213	−1.31902	−0.659509	+	0.751697i	$0.729236\pi$
$114$	−0.426267	−0.0399235
$115$	3.92572	0.366075
$116$	−6.67499	−0.619757
$117$	16.4342	1.51935
$118$	7.95297	0.732130
$119$	−9.33322	−0.855574
$120$	1.09145	0.0996353
$121$	−7.60331	−0.691210
$122$	−4.20081	−0.380323
$123$	−5.05125	−0.455456
$124$	6.88555	0.618341
$125$	−4.22261	−0.377682
$126$	−9.30999	−0.829400
$127$	17.0627	1.51407	0.757036	−	0.653373i	$-0.226647\pi$
$127$	17.0627	1.51407	0.757036	+	0.653373i	$0.226647\pi$
$128$	−1.00000	−0.0883883
$129$	31.6310	2.78496
$130$	−2.05772	−0.180474
$131$	−15.3038	−1.33710	−0.668549	−	0.743668i	$-0.733084\pi$
$131$	−15.3038	−1.33710	−0.668549	+	0.743668i	$0.733084\pi$
$132$	−4.67560	−0.406958
$133$	−0.455265	−0.0394764
$134$	15.4904	1.33817
$135$	−0.475913	−0.0409601
$136$	3.44461	0.295373
$137$	17.0227	1.45435	0.727175	−	0.686453i	$-0.240833\pi$
$137$	17.0227	1.45435	0.727175	+	0.686453i	$0.240833\pi$
$138$	23.1491	1.97058
$139$	5.17044	0.438551	0.219276	−	0.975663i	$-0.429631\pi$
$139$	5.17044	0.438551	0.219276	+	0.975663i	$0.429631\pi$
$140$	1.16570	0.0985195
$141$	1.95618	0.164740
$142$	0.199219	0.0167181
$143$	8.81494	0.737142
$144$	3.43604	0.286336
$145$	−2.87174	−0.238485
$146$	10.8856	0.900902
$147$	−0.866289	−0.0714503
$148$	−1.65400	−0.135958
$149$	−21.7243	−1.77972	−0.889860	−	0.456233i	$-0.849198\pi$
$149$	−21.7243	−1.77972	−0.889860	+	0.456233i	$0.849198\pi$
$150$	−12.2151	−0.997359
$151$	−10.1938	−0.829561	−0.414781	−	0.909921i	$-0.636142\pi$
$151$	−10.1938	−0.829561	−0.414781	+	0.909921i	$0.636142\pi$
$152$	0.168024	0.0136286
$153$	−11.8358	−0.956868
$154$	−4.99366	−0.402401
$155$	2.96233	0.237940
$156$	−12.1339	−0.971490
$157$	12.0569	0.962249	0.481124	−	0.876652i	$-0.340229\pi$
$157$	12.0569	0.962249	0.481124	+	0.876652i	$0.340229\pi$
$158$	7.86915	0.626036
$159$	10.6290	0.842932
$160$	−0.430224	−0.0340122
$161$	24.7239	1.94851
$162$	7.50176	0.589394
$163$	−0.371930	−0.0291318	−0.0145659	−	0.999894i	$-0.504637\pi$
$163$	−0.371930	−0.0291318	−0.0145659	+	0.999894i	$0.504637\pi$
$164$	1.99108	0.155477
$165$	−2.01155	−0.156599
$166$	5.01016	0.388864
$167$	0.0538349	0.00416587	0.00208293	−	0.999998i	$-0.499337\pi$
$167$	0.0538349	0.00416587	0.00208293	+	0.999998i	$0.499337\pi$
$168$	6.87386	0.530330
$169$	9.87616	0.759705
$170$	1.48195	0.113661
$171$	−0.577338	−0.0441501
$172$	−12.4682	−0.950692
$173$	−2.99274	−0.227534	−0.113767	−	0.993507i	$-0.536292\pi$
$173$	−2.99274	−0.227534	−0.113767	+	0.993507i	$0.536292\pi$
$174$	−16.9340	−1.28376
$175$	−13.0461	−0.986190
$176$	1.84301	0.138922
$177$	20.1762	1.51653
$178$	−4.71744	−0.353587
$179$	−17.0184	−1.27201	−0.636006	−	0.771684i	$-0.719415\pi$
$179$	−17.0184	−1.27201	−0.636006	+	0.771684i	$0.719415\pi$
$180$	1.47827	0.110183
$181$	18.1555	1.34949	0.674746	−	0.738050i	$-0.264253\pi$
$181$	18.1555	1.34949	0.674746	+	0.738050i	$0.264253\pi$
$182$	−12.9593	−0.960611
$183$	−10.6572	−0.787801
$184$	−9.12483	−0.672691
$185$	−0.711589	−0.0523170
$186$	17.4682	1.28083
$187$	−6.34845	−0.464244
$188$	−0.771079	−0.0562367
$189$	−2.99726	−0.218019
$190$	0.0722881	0.00524433
$191$	−21.7467	−1.57354	−0.786769	−	0.617247i	$-0.788248\pi$
$191$	−21.7467	−1.57354	−0.786769	+	0.617247i	$0.788248\pi$
$192$	−2.53693	−0.183087
$193$	15.9196	1.14591	0.572957	−	0.819585i	$-0.305796\pi$
$193$	15.9196	1.14591	0.572957	+	0.819585i	$0.305796\pi$
$194$	−1.64242	−0.117919
$195$	−5.22030	−0.373833
$196$	0.341471	0.0243908
$197$	5.74588	0.409377	0.204688	−	0.978827i	$-0.434382\pi$
$197$	5.74588	0.409377	0.204688	+	0.978827i	$0.434382\pi$
$198$	−6.33265	−0.450042
$199$	−2.58966	−0.183576	−0.0917879	−	0.995779i	$-0.529258\pi$
$199$	−2.58966	−0.183576	−0.0917879	+	0.995779i	$0.529258\pi$
$200$	4.81491	0.340465
$201$	39.2982	2.77188
$202$	8.84635	0.622427
$203$	−18.0860	−1.26939
$204$	8.73874	0.611834
$205$	0.856612	0.0598284
$206$	2.93468	0.204469
$207$	31.3532	2.17920
$208$	4.78290	0.331635
$209$	−0.309671	−0.0214204
$210$	2.95730	0.204073
$211$	21.1181	1.45383	0.726914	−	0.686729i	$-0.240954\pi$
$211$	21.1181	1.45383	0.726914	+	0.686729i	$0.240954\pi$
$212$	−4.18969	−0.287749
$213$	0.505406	0.0346299
$214$	10.0895	0.689703
$215$	−5.36412	−0.365830
$216$	1.10620	0.0752673
$217$	18.6565	1.26649
$218$	4.60903	0.312163
$219$	27.6162	1.86613
$220$	0.792907	0.0534578
$221$	−16.4752	−1.10824
$222$	−4.19608	−0.281622
$223$	21.2262	1.42141	0.710707	−	0.703488i	$-0.248375\pi$
$223$	21.2262	1.42141	0.710707	+	0.703488i	$0.248375\pi$
$224$	−2.70951	−0.181037
$225$	−16.5442	−1.10295
$226$	14.0213	0.932686
$227$	−17.5121	−1.16232	−0.581159	−	0.813790i	$-0.697400\pi$
$227$	−17.5121	−1.16232	−0.581159	+	0.813790i	$0.697400\pi$
$228$	0.426267	0.0282302
$229$	13.8706	0.916593	0.458297	−	0.888799i	$-0.348460\pi$
$229$	13.8706	0.916593	0.458297	+	0.888799i	$0.348460\pi$
$230$	−3.92572	−0.258854
$231$	−12.6686	−0.833532
$232$	6.67499	0.438235
$233$	−12.5545	−0.822473	−0.411237	−	0.911529i	$-0.634903\pi$
$233$	−12.5545	−0.822473	−0.411237	+	0.911529i	$0.634903\pi$
$234$	−16.4342	−1.07434
$235$	−0.331737	−0.0216401
$236$	−7.95297	−0.517694
$237$	19.9635	1.29677
$238$	9.33322	0.604983
$239$	22.7727	1.47305	0.736523	−	0.676413i	$-0.236466\pi$
$239$	22.7727	1.47305	0.736523	+	0.676413i	$0.236466\pi$
$240$	−1.09145	−0.0704528
$241$	−12.0780	−0.778014	−0.389007	−	0.921235i	$-0.627182\pi$
$241$	−12.0780	−0.778014	−0.389007	+	0.921235i	$0.627182\pi$
$242$	7.60331	0.488760
$243$	22.3501	1.43376
$244$	4.20081	0.268929
$245$	0.146909	0.00938566
$246$	5.05125	0.322056
$247$	−0.803644	−0.0511347
$248$	−6.88555	−0.437233
$249$	12.7104	0.805491
$250$	4.22261	0.267061
$251$	6.53636	0.412572	0.206286	−	0.978492i	$-0.433862\pi$
$251$	6.53636	0.412572	0.206286	+	0.978492i	$0.433862\pi$
$252$	9.30999	0.586475
$253$	16.8171	1.05728
$254$	−17.0627	−1.07061
$255$	3.75962	0.235436
$256$	1.00000	0.0625000
$257$	−1.80159	−0.112380	−0.0561901	−	0.998420i	$-0.517895\pi$
$257$	−1.80159	−0.112380	−0.0561901	+	0.998420i	$0.517895\pi$
$258$	−31.6310	−1.96926
$259$	−4.48153	−0.278469
$260$	2.05772	0.127614
$261$	−22.9355	−1.41967
$262$	15.3038	0.945471
$263$	−26.0948	−1.60907	−0.804536	−	0.593904i	$-0.797586\pi$
$263$	−26.0948	−1.60907	−0.804536	+	0.593904i	$0.797586\pi$
$264$	4.67560	0.287763
$265$	−1.80250	−0.110727
$266$	0.455265	0.0279141
$267$	−11.9678	−0.732420
$268$	−15.4904	−0.946229
$269$	1.01775	0.0620531	0.0310265	−	0.999519i	$-0.490122\pi$
$269$	1.01775	0.0620531	0.0310265	+	0.999519i	$0.490122\pi$
$270$	0.475913	0.0289631
$271$	−3.23828	−0.196711	−0.0983557	−	0.995151i	$-0.531358\pi$
$271$	−3.23828	−0.196711	−0.0983557	+	0.995151i	$0.531358\pi$
$272$	−3.44461	−0.208860
$273$	−32.8770	−1.98981
$274$	−17.0227	−1.02838
$275$	−8.87392	−0.535118
$276$	−23.1491	−1.39341
$277$	22.4992	1.35184	0.675922	−	0.736974i	$-0.263746\pi$
$277$	22.4992	1.35184	0.675922	+	0.736974i	$0.263746\pi$
$278$	−5.17044	−0.310102
$279$	23.6590	1.41643
$280$	−1.16570	−0.0696638
$281$	11.9100	0.710492	0.355246	−	0.934773i	$-0.384397\pi$
$281$	11.9100	0.710492	0.355246	+	0.934773i	$0.384397\pi$
$282$	−1.95618	−0.116489
$283$	−17.8477	−1.06094	−0.530469	−	0.847704i	$-0.677984\pi$
$283$	−17.8477	−1.06094	−0.530469	+	0.847704i	$0.677984\pi$
$284$	−0.199219	−0.0118215
$285$	0.183390	0.0108631
$286$	−8.81494	−0.521238
$287$	5.39487	0.318449
$288$	−3.43604	−0.202470
$289$	−5.13468	−0.302040
$290$	2.87174	0.168634
$291$	−4.16671	−0.244257
$292$	−10.8856	−0.637034
$293$	8.61555	0.503326	0.251663	−	0.967815i	$-0.419023\pi$
$293$	8.61555	0.503326	0.251663	+	0.967815i	$0.419023\pi$
$294$	0.866289	0.0505230
$295$	−3.42156	−0.199211
$296$	1.65400	0.0961366
$297$	−2.03873	−0.118299
$298$	21.7243	1.25845
$299$	43.6432	2.52395
$300$	12.2151	0.705239
$301$	−33.7828	−1.94721
$302$	10.1938	0.586588
$303$	22.4426	1.28929
$304$	−0.168024	−0.00963686
$305$	1.80729	0.103485
$306$	11.8358	0.676608
$307$	7.30680	0.417021	0.208511	−	0.978020i	$-0.433138\pi$
$307$	7.30680	0.417021	0.208511	+	0.978020i	$0.433138\pi$
$308$	4.99366	0.284540
$309$	7.44510	0.423537
$310$	−2.96233	−0.168249
$311$	−14.9369	−0.846994	−0.423497	−	0.905898i	$-0.639198\pi$
$311$	−14.9369	−0.846994	−0.423497	+	0.905898i	$0.639198\pi$
$312$	12.1339	0.686947
$313$	26.8296	1.51650	0.758249	−	0.651965i	$-0.226055\pi$
$313$	26.8296	1.51650	0.758249	+	0.651965i	$0.226055\pi$
$314$	−12.0569	−0.680413
$315$	4.00538	0.225678
$316$	−7.86915	−0.442674
$317$	−13.2564	−0.744552	−0.372276	−	0.928122i	$-0.621423\pi$
$317$	−13.2564	−0.744552	−0.372276	+	0.928122i	$0.621423\pi$
$318$	−10.6290	−0.596043
$319$	−12.3021	−0.688784
$320$	0.430224	0.0240502
$321$	25.5964	1.42865
$322$	−24.7239	−1.37781
$323$	0.578778	0.0322041
$324$	−7.50176	−0.416764
$325$	−23.0292	−1.27743
$326$	0.371930	0.0205993
$327$	11.6928	0.646613
$328$	−1.99108	−0.109939
$329$	−2.08925	−0.115184
$330$	2.01155	0.110732
$331$	14.2918	0.785548	0.392774	−	0.919635i	$-0.371515\pi$
$331$	14.2918	0.785548	0.392774	+	0.919635i	$0.371515\pi$
$332$	−5.01016	−0.274968
$333$	−5.68319	−0.311437
$334$	−0.0538349	−0.00294571
$335$	−6.66436	−0.364113
$336$	−6.87386	−0.375000
$337$	7.48646	0.407814	0.203907	−	0.978990i	$-0.434636\pi$
$337$	7.48646	0.407814	0.203907	+	0.978990i	$0.434636\pi$
$338$	−9.87616	−0.537192
$339$	35.5712	1.93196
$340$	−1.48195	−0.0803702
$341$	12.6901	0.687210
$342$	0.577338	0.0312189
$343$	−18.0414	−0.974143
$344$	12.4682	0.672241
$345$	−9.95929	−0.536190
$346$	2.99274	0.160891
$347$	21.9665	1.17922	0.589611	−	0.807687i	$-0.299281\pi$
$347$	21.9665	1.17922	0.589611	+	0.807687i	$0.299281\pi$
$348$	16.9340	0.907759
$349$	21.3753	1.14419	0.572096	−	0.820186i	$-0.306130\pi$
$349$	21.3753	1.14419	0.572096	+	0.820186i	$0.306130\pi$
$350$	13.0461	0.697341
$351$	−5.29084	−0.282404
$352$	−1.84301	−0.0982328
$353$	−8.37870	−0.445953	−0.222977	−	0.974824i	$-0.571577\pi$
$353$	−8.37870	−0.445953	−0.222977	+	0.974824i	$0.571577\pi$
$354$	−20.1762	−1.07235
$355$	−0.0857089	−0.00454896
$356$	4.71744	0.250024
$357$	23.6778	1.25316
$358$	17.0184	0.899448
$359$	−12.2276	−0.645350	−0.322675	−	0.946510i	$-0.604582\pi$
$359$	−12.2276	−0.645350	−0.322675	+	0.946510i	$0.604582\pi$
$360$	−1.47827	−0.0779114
$361$	−18.9718	−0.998514
$362$	−18.1555	−0.954234
$363$	19.2891	1.01242
$364$	12.9593	0.679254
$365$	−4.68326	−0.245133
$366$	10.6572	0.557060
$367$	−22.3638	−1.16738	−0.583691	−	0.811976i	$-0.698392\pi$
$367$	−22.3638	−1.16738	−0.583691	+	0.811976i	$0.698392\pi$
$368$	9.12483	0.475664
$369$	6.84144	0.356151
$370$	0.711589	0.0369937
$371$	−11.3520	−0.589368
$372$	−17.4682	−0.905684
$373$	−16.3308	−0.845574	−0.422787	−	0.906229i	$-0.638948\pi$
$373$	−16.3308	−0.845574	−0.422787	+	0.906229i	$0.638948\pi$
$374$	6.34845	0.328270
$375$	10.7125	0.553190
$376$	0.771079	0.0397654
$377$	−31.9258	−1.64426
$378$	2.99726	0.154162
$379$	−16.2814	−0.836319	−0.418159	−	0.908374i	$-0.637325\pi$
$379$	−16.2814	−0.836319	−0.418159	+	0.908374i	$0.637325\pi$
$380$	−0.0722881	−0.00370830
$381$	−43.2870	−2.21766
$382$	21.7467	1.11266
$383$	19.8643	1.01502	0.507509	−	0.861647i	$-0.330567\pi$
$383$	19.8643	1.01502	0.507509	+	0.861647i	$0.330567\pi$
$384$	2.53693	0.129462
$385$	2.14839	0.109492
$386$	−15.9196	−0.810284
$387$	−42.8412	−2.17774
$388$	1.64242	0.0833812
$389$	19.0456	0.965652	0.482826	−	0.875716i	$-0.339610\pi$
$389$	19.0456	0.965652	0.482826	+	0.875716i	$0.339610\pi$
$390$	5.22030	0.264340
$391$	−31.4314	−1.58956
$392$	−0.341471	−0.0172469
$393$	38.8247	1.95845
$394$	−5.74588	−0.289473
$395$	−3.38550	−0.170343
$396$	6.33265	0.318228
$397$	−0.385802	−0.0193629	−0.00968143	−	0.999953i	$-0.503082\pi$
$397$	−0.385802	−0.0193629	−0.00968143	+	0.999953i	$0.503082\pi$
$398$	2.58966	0.129808
$399$	1.15498	0.0578211
$400$	−4.81491	−0.240745
$401$	16.5767	0.827798	0.413899	−	0.910323i	$-0.364167\pi$
$401$	16.5767	0.827798	0.413899	+	0.910323i	$0.364167\pi$
$402$	−39.2982	−1.96002
$403$	32.9329	1.64051
$404$	−8.84635	−0.440123
$405$	−3.22744	−0.160373
$406$	18.0860	0.897592
$407$	−3.04833	−0.151100
$408$	−8.73874	−0.432632
$409$	5.65773	0.279757	0.139878	−	0.990169i	$-0.455329\pi$
$409$	5.65773	0.279757	0.139878	+	0.990169i	$0.455329\pi$
$410$	−0.856612	−0.0423050
$411$	−43.1855	−2.13018
$412$	−2.93468	−0.144581
$413$	−21.5487	−1.06034
$414$	−31.3532	−1.54093
$415$	−2.15549	−0.105809
$416$	−4.78290	−0.234501
$417$	−13.1171	−0.642346
$418$	0.309671	0.0151465
$419$	−25.9626	−1.26836	−0.634178	−	0.773187i	$-0.718661\pi$
$419$	−25.9626	−1.26836	−0.634178	+	0.773187i	$0.718661\pi$
$420$	−2.95730	−0.144301
$421$	15.4706	0.753991	0.376996	−	0.926215i	$-0.376957\pi$
$421$	15.4706	0.753991	0.376996	+	0.926215i	$0.376957\pi$
$422$	−21.1181	−1.02801
$423$	−2.64946	−0.128821
$424$	4.18969	0.203469
$425$	16.5855	0.804513
$426$	−0.505406	−0.0244870
$427$	11.3822	0.550821
$428$	−10.0895	−0.487694
$429$	−22.3629	−1.07969
$430$	5.36412	0.258681
$431$	−38.1870	−1.83940	−0.919702	−	0.392618i	$-0.871569\pi$
$431$	−38.1870	−1.83940	−0.919702	+	0.392618i	$0.871569\pi$
$432$	−1.10620	−0.0532220
$433$	−29.3382	−1.40990	−0.704952	−	0.709255i	$-0.749032\pi$
$433$	−29.3382	−1.40990	−0.704952	+	0.709255i	$0.749032\pi$
$434$	−18.6565	−0.895541
$435$	7.28542	0.349309
$436$	−4.60903	−0.220732
$437$	−1.53319	−0.0733426
$438$	−27.6162	−1.31955
$439$	−24.7242	−1.18002	−0.590011	−	0.807395i	$-0.700876\pi$
$439$	−24.7242	−1.18002	−0.590011	+	0.807395i	$0.700876\pi$
$440$	−0.792907	−0.0378004
$441$	1.17331	0.0558717
$442$	16.4752	0.783646
$443$	−3.15508	−0.149902	−0.0749511	−	0.997187i	$-0.523880\pi$
$443$	−3.15508	−0.149902	−0.0749511	+	0.997187i	$0.523880\pi$
$444$	4.19608	0.199137
$445$	2.02956	0.0962102
$446$	−21.2262	−1.00509
$447$	55.1130	2.60676
$448$	2.70951	0.128013
$449$	−36.4107	−1.71833	−0.859164	−	0.511700i	$-0.829016\pi$
$449$	−36.4107	−1.71833	−0.859164	+	0.511700i	$0.829016\pi$
$450$	16.5442	0.779901
$451$	3.66959	0.172794
$452$	−14.0213	−0.659509
$453$	25.8611	1.21506
$454$	17.5121	0.821883
$455$	5.57542	0.261380
$456$	−0.426267	−0.0199618
$457$	7.67716	0.359123	0.179561	−	0.983747i	$-0.442532\pi$
$457$	7.67716	0.359123	0.179561	+	0.983747i	$0.442532\pi$
$458$	−13.8706	−0.648129
$459$	3.81042	0.177855
$460$	3.92572	0.183038
$461$	10.0942	0.470136	0.235068	−	0.971979i	$-0.424469\pi$
$461$	10.0942	0.470136	0.235068	+	0.971979i	$0.424469\pi$
$462$	12.6686	0.589396
$463$	4.63210	0.215272	0.107636	−	0.994190i	$-0.465672\pi$
$463$	4.63210	0.215272	0.107636	+	0.994190i	$0.465672\pi$
$464$	−6.67499	−0.309879
$465$	−7.51524	−0.348511
$466$	12.5545	0.581576
$467$	−35.7367	−1.65370	−0.826849	−	0.562424i	$-0.809869\pi$
$467$	−35.7367	−1.65370	−0.826849	+	0.562424i	$0.809869\pi$
$468$	16.4342	0.759673
$469$	−41.9716	−1.93807
$470$	0.331737	0.0153019
$471$	−30.5877	−1.40941
$472$	7.95297	0.366065
$473$	−22.9790	−1.05658
$474$	−19.9635	−0.916955
$475$	0.809022	0.0371205
$476$	−9.33322	−0.427787
$477$	−14.3959	−0.659144
$478$	−22.7727	−1.04160
$479$	−22.6696	−1.03580	−0.517901	−	0.855441i	$-0.673286\pi$
$479$	−22.6696	−1.03580	−0.517901	+	0.855441i	$0.673286\pi$
$480$	1.09145	0.0498176
$481$	−7.91090	−0.360706
$482$	12.0780	0.550139
$483$	−62.7228	−2.85399
$484$	−7.60331	−0.345605
$485$	0.706608	0.0320854
$486$	−22.3501	−1.01382
$487$	−11.6083	−0.526024	−0.263012	−	0.964793i	$-0.584716\pi$
$487$	−11.6083	−0.526024	−0.263012	+	0.964793i	$0.584716\pi$
$488$	−4.20081	−0.190162
$489$	0.943562	0.0426694
$490$	−0.146909	−0.00663666
$491$	13.1988	0.595654	0.297827	−	0.954620i	$-0.403738\pi$
$491$	13.1988	0.595654	0.297827	+	0.954620i	$0.403738\pi$
$492$	−5.05125	−0.227728
$493$	22.9927	1.03554
$494$	0.803644	0.0361577
$495$	2.72446	0.122455
$496$	6.88555	0.309171
$497$	−0.539788	−0.0242128
$498$	−12.7104	−0.569568
$499$	13.8151	0.618447	0.309224	−	0.950989i	$-0.399931\pi$
$499$	13.8151	0.618447	0.309224	+	0.950989i	$0.399931\pi$
$500$	−4.22261	−0.188841
$501$	−0.136576	−0.00610175
$502$	−6.53636	−0.291732
$503$	22.3892	0.998286	0.499143	−	0.866520i	$-0.333648\pi$
$503$	22.3892	0.998286	0.499143	+	0.866520i	$0.333648\pi$
$504$	−9.30999	−0.414700
$505$	−3.80591	−0.169361
$506$	−16.8171	−0.747613
$507$	−25.0552	−1.11274
$508$	17.0627	0.757036
$509$	−25.5318	−1.13168	−0.565839	−	0.824516i	$-0.691448\pi$
$509$	−25.5318	−1.13168	−0.565839	+	0.824516i	$0.691448\pi$
$510$	−3.75962	−0.166479
$511$	−29.4948	−1.30477
$512$	−1.00000	−0.0441942
$513$	0.185868	0.00820629
$514$	1.80159	0.0794648
$515$	−1.26257	−0.0556355
$516$	31.6310	1.39248
$517$	−1.42111	−0.0625002
$518$	4.48153	0.196907
$519$	7.59239	0.333269
$520$	−2.05772	−0.0902370
$521$	−10.3189	−0.452080	−0.226040	−	0.974118i	$-0.572578\pi$
$521$	−10.3189	−0.452080	−0.226040	+	0.974118i	$0.572578\pi$
$522$	22.9355	1.00386
$523$	20.0078	0.874879	0.437439	−	0.899248i	$-0.355885\pi$
$523$	20.0078	0.874879	0.437439	+	0.899248i	$0.355885\pi$
$524$	−15.3038	−0.668549
$525$	33.0970	1.44447
$526$	26.0948	1.13779
$527$	−23.7180	−1.03317
$528$	−4.67560	−0.203479
$529$	60.2624	2.62011
$530$	1.80250	0.0782958
$531$	−27.3267	−1.18588
$532$	−0.455265	−0.0197382
$533$	9.52316	0.412494
$534$	11.9678	0.517899
$535$	−4.34074	−0.187667
$536$	15.4904	0.669085
$537$	43.1744	1.86312
$538$	−1.01775	−0.0438782
$539$	0.629334	0.0271073
$540$	−0.475913	−0.0204800
$541$	21.8368	0.938836	0.469418	−	0.882976i	$-0.344464\pi$
$541$	21.8368	0.938836	0.469418	+	0.882976i	$0.344464\pi$
$542$	3.23828	0.139096
$543$	−46.0594	−1.97660
$544$	3.44461	0.147686
$545$	−1.98291	−0.0849387
$546$	32.8770	1.40701
$547$	−1.59033	−0.0679975	−0.0339987	−	0.999422i	$-0.510824\pi$
$547$	−1.59033	−0.0679975	−0.0339987	+	0.999422i	$0.510824\pi$
$548$	17.0227	0.727175
$549$	14.4341	0.616034
$550$	8.87392	0.378385
$551$	1.12156	0.0477801
$552$	23.1491	0.985291
$553$	−21.3216	−0.906686
$554$	−22.4992	−0.955897
$555$	1.80525	0.0766288
$556$	5.17044	0.219276
$557$	13.3836	0.567080	0.283540	−	0.958960i	$-0.408491\pi$
$557$	13.3836	0.567080	0.283540	+	0.958960i	$0.408491\pi$
$558$	−23.6590	−1.00157
$559$	−59.6342	−2.52226
$560$	1.16570	0.0492597
$561$	16.1056	0.679979
$562$	−11.9100	−0.502394
$563$	4.57302	0.192730	0.0963650	−	0.995346i	$-0.469278\pi$
$563$	4.57302	0.192730	0.0963650	+	0.995346i	$0.469278\pi$
$564$	1.95618	0.0823699
$565$	−6.03232	−0.253782
$566$	17.8477	0.750197
$567$	−20.3261	−0.853617
$568$	0.199219	0.00835906
$569$	29.4349	1.23398	0.616988	−	0.786972i	$-0.288352\pi$
$569$	29.4349	1.23398	0.616988	+	0.786972i	$0.288352\pi$
$570$	−0.183390	−0.00768137
$571$	7.52208	0.314789	0.157395	−	0.987536i	$-0.449691\pi$
$571$	7.52208	0.314789	0.157395	+	0.987536i	$0.449691\pi$
$572$	8.81494	0.368571
$573$	55.1701	2.30476
$574$	−5.39487	−0.225178
$575$	−43.9352	−1.83222
$576$	3.43604	0.143168
$577$	−0.132548	−0.00551806	−0.00275903	−	0.999996i	$-0.500878\pi$
$577$	−0.132548	−0.00551806	−0.00275903	+	0.999996i	$0.500878\pi$
$578$	5.13468	0.213574
$579$	−40.3869	−1.67842
$580$	−2.87174	−0.119243
$581$	−13.5751	−0.563190
$582$	4.16671	0.172716
$583$	−7.72164	−0.319798
$584$	10.8856	0.450451
$585$	7.07040	0.292325
$586$	−8.61555	−0.355905
$587$	−11.9967	−0.495155	−0.247578	−	0.968868i	$-0.579634\pi$
$587$	−11.9967	−0.495155	−0.247578	+	0.968868i	$0.579634\pi$
$588$	−0.866289	−0.0357251
$589$	−1.15694	−0.0476709
$590$	3.42156	0.140863
$591$	−14.5769	−0.599614
$592$	−1.65400	−0.0679788
$593$	19.2312	0.789730	0.394865	−	0.918739i	$-0.370791\pi$
$593$	19.2312	0.789730	0.394865	+	0.918739i	$0.370791\pi$
$594$	2.03873	0.0836503
$595$	−4.01537	−0.164614
$596$	−21.7243	−0.889860
$597$	6.56979	0.268884
$598$	−43.6432	−1.78470
$599$	27.9860	1.14348	0.571739	−	0.820436i	$-0.306269\pi$
$599$	27.9860	1.14348	0.571739	+	0.820436i	$0.306269\pi$
$600$	−12.2151	−0.498680
$601$	9.08081	0.370414	0.185207	−	0.982700i	$-0.440704\pi$
$601$	9.08081	0.370414	0.185207	+	0.982700i	$0.440704\pi$
$602$	33.7828	1.37688
$603$	−53.2257	−2.16752
$604$	−10.1938	−0.414781
$605$	−3.27113	−0.132990
$606$	−22.4426	−0.911669
$607$	11.6633	0.473400	0.236700	−	0.971583i	$-0.423934\pi$
$607$	11.6633	0.473400	0.236700	+	0.971583i	$0.423934\pi$
$608$	0.168024	0.00681429
$609$	45.8830	1.85927
$610$	−1.80729	−0.0731750
$611$	−3.68800	−0.149200
$612$	−11.8358	−0.478434
$613$	−1.57527	−0.0636246	−0.0318123	−	0.999494i	$-0.510128\pi$
$613$	−1.57527	−0.0636246	−0.0318123	+	0.999494i	$0.510128\pi$
$614$	−7.30680	−0.294879
$615$	−2.17317	−0.0876306
$616$	−4.99366	−0.201200
$617$	39.7210	1.59911	0.799554	−	0.600594i	$-0.205069\pi$
$617$	39.7210	1.59911	0.799554	+	0.600594i	$0.205069\pi$
$618$	−7.44510	−0.299486
$619$	−17.3692	−0.698128	−0.349064	−	0.937099i	$-0.613500\pi$
$619$	−17.3692	−0.698128	−0.349064	+	0.937099i	$0.613500\pi$
$620$	2.96233	0.118970
$621$	−10.0939	−0.405053
$622$	14.9369	0.598915
$623$	12.7820	0.512099
$624$	−12.1339	−0.485745
$625$	22.2579	0.890315
$626$	−26.8296	−1.07233
$627$	0.785614	0.0313744
$628$	12.0569	0.481124
$629$	5.69737	0.227169
$630$	−4.00538	−0.159578
$631$	8.51089	0.338813	0.169407	−	0.985546i	$-0.445815\pi$
$631$	8.51089	0.338813	0.169407	+	0.985546i	$0.445815\pi$
$632$	7.86915	0.313018
$633$	−53.5752	−2.12942
$634$	13.2564	0.526478
$635$	7.34079	0.291310
$636$	10.6290	0.421466
$637$	1.63322	0.0647106
$638$	12.3021	0.487044
$639$	−0.684525	−0.0270794
$640$	−0.430224	−0.0170061
$641$	−2.63793	−0.104192	−0.0520961	−	0.998642i	$-0.516590\pi$
$641$	−2.63793	−0.104192	−0.0520961	+	0.998642i	$0.516590\pi$
$642$	−25.5964	−1.01021
$643$	−2.03128	−0.0801057	−0.0400529	−	0.999198i	$-0.512753\pi$
$643$	−2.03128	−0.0801057	−0.0400529	+	0.999198i	$0.512753\pi$
$644$	24.7239	0.974256
$645$	13.6084	0.535831
$646$	−0.578778	−0.0227717
$647$	11.9481	0.469730	0.234865	−	0.972028i	$-0.424535\pi$
$647$	11.9481	0.469730	0.234865	+	0.972028i	$0.424535\pi$
$648$	7.50176	0.294697
$649$	−14.6574	−0.575353
$650$	23.0292	0.903281
$651$	−47.3304	−1.85502
$652$	−0.371930	−0.0145659
$653$	−14.4121	−0.563989	−0.281994	−	0.959416i	$-0.590996\pi$
$653$	−14.4121	−0.563989	−0.281994	+	0.959416i	$0.590996\pi$
$654$	−11.6928	−0.457225
$655$	−6.58406	−0.257260
$656$	1.99108	0.0777387
$657$	−37.4035	−1.45925
$658$	2.08925	0.0814474
$659$	−10.2630	−0.399792	−0.199896	−	0.979817i	$-0.564060\pi$
$659$	−10.2630	−0.399792	−0.199896	+	0.979817i	$0.564060\pi$
$660$	−2.01155	−0.0782996
$661$	−30.5539	−1.18841	−0.594204	−	0.804315i	$-0.702533\pi$
$661$	−30.5539	−1.18841	−0.594204	+	0.804315i	$0.702533\pi$
$662$	−14.2918	−0.555466
$663$	41.7966	1.62324
$664$	5.01016	0.194432
$665$	−0.195866	−0.00759535
$666$	5.68319	0.220219
$667$	−60.9081	−2.35837
$668$	0.0538349	0.00208293
$669$	−53.8496	−2.08195
$670$	6.66436	0.257467
$671$	7.74213	0.298882
$672$	6.87386	0.265165
$673$	−3.40313	−0.131181	−0.0655906	−	0.997847i	$-0.520893\pi$
$673$	−3.40313	−0.131181	−0.0655906	+	0.997847i	$0.520893\pi$
$674$	−7.48646	−0.288368
$675$	5.32624	0.205007
$676$	9.87616	0.379852
$677$	−8.64977	−0.332438	−0.166219	−	0.986089i	$-0.553156\pi$
$677$	−8.64977	−0.332438	−0.166219	+	0.986089i	$0.553156\pi$
$678$	−35.5712	−1.36611
$679$	4.45016	0.170781
$680$	1.48195	0.0568303
$681$	44.4270	1.70245
$682$	−12.6901	−0.485931
$683$	−42.6429	−1.63168	−0.815842	−	0.578275i	$-0.803726\pi$
$683$	−42.6429	−1.63168	−0.815842	+	0.578275i	$0.803726\pi$
$684$	−0.577338	−0.0220751
$685$	7.32358	0.279820
$686$	18.0414	0.688823
$687$	−35.1887	−1.34253
$688$	−12.4682	−0.475346
$689$	−20.0389	−0.763421
$690$	9.95929	0.379144
$691$	−21.5296	−0.819024	−0.409512	−	0.912305i	$-0.634301\pi$
$691$	−21.5296	−0.819024	−0.409512	+	0.912305i	$0.634301\pi$
$692$	−2.99274	−0.113767
$693$	17.1584	0.651794
$694$	−21.9665	−0.833836
$695$	2.22445	0.0843781
$696$	−16.9340	−0.641882
$697$	−6.85850	−0.259784
$698$	−21.3753	−0.809067
$699$	31.8500	1.20468
$700$	−13.0461	−0.493095
$701$	−36.9185	−1.39439	−0.697197	−	0.716880i	$-0.745570\pi$
$701$	−36.9185	−1.39439	−0.697197	+	0.716880i	$0.745570\pi$
$702$	5.29084	0.199690
$703$	0.277912	0.0104816
$704$	1.84301	0.0694611
$705$	0.841594	0.0316963
$706$	8.37870	0.315337
$707$	−23.9693	−0.901459
$708$	20.1762	0.758266
$709$	−18.8295	−0.707155	−0.353578	−	0.935405i	$-0.615035\pi$
$709$	−18.8295	−0.707155	−0.353578	+	0.935405i	$0.615035\pi$
$710$	0.0857089	0.00321660
$711$	−27.0387	−1.01403
$712$	−4.71744	−0.176794
$713$	62.8295	2.35298
$714$	−23.6778	−0.886118
$715$	3.79240	0.141828
$716$	−17.0184	−0.636006
$717$	−57.7729	−2.15757
$718$	12.2276	0.456331
$719$	−18.7166	−0.698013	−0.349006	−	0.937120i	$-0.613481\pi$
$719$	−18.7166	−0.698013	−0.349006	+	0.937120i	$0.613481\pi$
$720$	1.47827	0.0550917
$721$	−7.95157	−0.296132
$722$	18.9718	0.706056
$723$	30.6411	1.13956
$724$	18.1555	0.674746
$725$	32.1395	1.19363
$726$	−19.2891	−0.715886
$727$	−35.0765	−1.30092	−0.650459	−	0.759542i	$-0.725423\pi$
$727$	−35.0765	−1.30092	−0.650459	+	0.759542i	$0.725423\pi$
$728$	−12.9593	−0.480305
$729$	−34.1954	−1.26650
$730$	4.68326	0.173335
$731$	42.9481	1.58849
$732$	−10.6572	−0.393901
$733$	−6.62709	−0.244777	−0.122389	−	0.992482i	$-0.539055\pi$
$733$	−6.62709	−0.244777	−0.122389	+	0.992482i	$0.539055\pi$
$734$	22.3638	0.825464
$735$	−0.372698	−0.0137472
$736$	−9.12483	−0.336346
$737$	−28.5490	−1.05162
$738$	−6.84144	−0.251837
$739$	28.4346	1.04598	0.522992	−	0.852338i	$-0.324816\pi$
$739$	28.4346	1.04598	0.522992	+	0.852338i	$0.324816\pi$
$740$	−0.711589	−0.0261585
$741$	2.03879	0.0748969
$742$	11.3520	0.416746
$743$	20.5060	0.752291	0.376145	−	0.926561i	$-0.377249\pi$
$743$	20.5060	0.752291	0.376145	+	0.926561i	$0.377249\pi$
$744$	17.4682	0.640415
$745$	−9.34630	−0.342422
$746$	16.3308	0.597911
$747$	−17.2151	−0.629867
$748$	−6.34845	−0.232122
$749$	−27.3376	−0.998895
$750$	−10.7125	−0.391164
$751$	11.0789	0.404274	0.202137	−	0.979357i	$-0.435211\pi$
$751$	11.0789	0.404274	0.202137	+	0.979357i	$0.435211\pi$
$752$	−0.771079	−0.0281184
$753$	−16.5823	−0.604294
$754$	31.9258	1.16267
$755$	−4.38562	−0.159609
$756$	−2.99726	−0.109009
$757$	25.0710	0.911223	0.455611	−	0.890179i	$-0.349421\pi$
$757$	25.0710	0.911223	0.455611	+	0.890179i	$0.349421\pi$
$758$	16.2814	0.591366
$759$	−42.6640	−1.54861
$760$	0.0722881	0.00262217
$761$	−4.95062	−0.179460	−0.0897299	−	0.995966i	$-0.528600\pi$
$761$	−4.95062	−0.179460	−0.0897299	+	0.995966i	$0.528600\pi$
$762$	43.2870	1.56812
$763$	−12.4882	−0.452104
$764$	−21.7467	−0.786769
$765$	−5.09204	−0.184103
$766$	−19.8643	−0.717726
$767$	−38.0383	−1.37348
$768$	−2.53693	−0.0915437
$769$	40.2594	1.45179	0.725896	−	0.687804i	$-0.241425\pi$
$769$	40.2594	1.45179	0.725896	+	0.687804i	$0.241425\pi$
$770$	−2.14839	−0.0774227
$771$	4.57052	0.164603
$772$	15.9196	0.572957
$773$	−22.7439	−0.818042	−0.409021	−	0.912525i	$-0.634130\pi$
$773$	−22.7439	−0.818042	−0.409021	+	0.912525i	$0.634130\pi$
$774$	42.8412	1.53990
$775$	−33.1533	−1.19090
$776$	−1.64242	−0.0589594
$777$	11.3693	0.407873
$778$	−19.0456	−0.682819
$779$	−0.334551	−0.0119865
$780$	−5.22030	−0.186917
$781$	−0.367163	−0.0131381
$782$	31.4314	1.12399
$783$	7.38387	0.263878
$784$	0.341471	0.0121954
$785$	5.18718	0.185139
$786$	−38.8247	−1.38483
$787$	14.9974	0.534601	0.267300	−	0.963613i	$-0.413868\pi$
$787$	14.9974	0.534601	0.267300	+	0.963613i	$0.413868\pi$
$788$	5.74588	0.204688
$789$	66.2007	2.35681
$790$	3.38550	0.120451
$791$	−37.9910	−1.35081
$792$	−6.33265	−0.225021
$793$	20.0921	0.713490
$794$	0.385802	0.0136916
$795$	4.57284	0.162182
$796$	−2.58966	−0.0917879
$797$	27.0740	0.959009	0.479505	−	0.877539i	$-0.340816\pi$
$797$	27.0740	0.959009	0.479505	+	0.877539i	$0.340816\pi$
$798$	−1.15498	−0.0408857
$799$	2.65606	0.0939648
$800$	4.81491	0.170233
$801$	16.2093	0.572728
$802$	−16.5767	−0.585342
$803$	−20.0623	−0.707985
$804$	39.2982	1.38594
$805$	10.6368	0.374898
$806$	−32.9329	−1.16001
$807$	−2.58196	−0.0908891
$808$	8.84635	0.311214
$809$	7.87258	0.276785	0.138393	−	0.990377i	$-0.455806\pi$
$809$	7.87258	0.276785	0.138393	+	0.990377i	$0.455806\pi$
$810$	3.22744	0.113401
$811$	−39.8557	−1.39952	−0.699762	−	0.714376i	$-0.746710\pi$
$811$	−39.8557	−1.39952	−0.699762	+	0.714376i	$0.746710\pi$
$812$	−18.0860	−0.634694
$813$	8.21530	0.288123
$814$	3.04833	0.106844
$815$	−0.160013	−0.00560502
$816$	8.73874	0.305917
$817$	2.09496	0.0732935
$818$	−5.65773	−0.197818
$819$	44.5288	1.55596
$820$	0.856612	0.0299142
$821$	−18.8290	−0.657136	−0.328568	−	0.944480i	$-0.606566\pi$
$821$	−18.8290	−0.657136	−0.328568	+	0.944480i	$0.606566\pi$
$822$	43.1855	1.50627
$823$	3.42596	0.119422	0.0597108	−	0.998216i	$-0.480982\pi$
$823$	3.42596	0.119422	0.0597108	+	0.998216i	$0.480982\pi$
$824$	2.93468	0.102235
$825$	22.5126	0.783787
$826$	21.5487	0.749775
$827$	−9.19256	−0.319657	−0.159828	−	0.987145i	$-0.551094\pi$
$827$	−9.19256	−0.319657	−0.159828	+	0.987145i	$0.551094\pi$
$828$	31.3532	1.08960
$829$	−26.6336	−0.925021	−0.462511	−	0.886614i	$-0.653051\pi$
$829$	−26.6336	−0.925021	−0.462511	+	0.886614i	$0.653051\pi$
$830$	2.15549	0.0748181
$831$	−57.0789	−1.98004
$832$	4.78290	0.165817
$833$	−1.17623	−0.0407540
$834$	13.1171	0.454207
$835$	0.0231611	0.000801521 0
$836$	−0.309671	−0.0107102
$837$	−7.61679	−0.263275
$838$	25.9626	0.896863
$839$	2.27461	0.0785284	0.0392642	−	0.999229i	$-0.487499\pi$
$839$	2.27461	0.0785284	0.0392642	+	0.999229i	$0.487499\pi$
$840$	2.95730	0.102037
$841$	15.5555	0.536397
$842$	−15.4706	−0.533152
$843$	−30.2149	−1.04066
$844$	21.1181	0.726914
$845$	4.24896	0.146169
$846$	2.64946	0.0910902
$847$	−20.6013	−0.707869
$848$	−4.18969	−0.143875
$849$	45.2786	1.55396
$850$	−16.5855	−0.568877
$851$	−15.0924	−0.517362
$852$	0.505406	0.0173149
$853$	−12.1298	−0.415318	−0.207659	−	0.978201i	$-0.566584\pi$
$853$	−12.1298	−0.415318	−0.207659	+	0.978201i	$0.566584\pi$
$854$	−11.3822	−0.389489
$855$	−0.248385	−0.00849458
$856$	10.0895	0.344852
$857$	−38.7915	−1.32509	−0.662546	−	0.749021i	$-0.730524\pi$
$857$	−38.7915	−1.32509	−0.662546	+	0.749021i	$0.730524\pi$
$858$	22.3629	0.763458
$859$	−55.7809	−1.90322	−0.951609	−	0.307310i	$-0.900571\pi$
$859$	−55.7809	−1.90322	−0.951609	+	0.307310i	$0.900571\pi$
$860$	−5.36412	−0.182915
$861$	−13.6864	−0.466432
$862$	38.1870	1.30065
$863$	−43.8966	−1.49426	−0.747128	−	0.664680i	$-0.768568\pi$
$863$	−43.8966	−1.49426	−0.747128	+	0.664680i	$0.768568\pi$
$864$	1.10620	0.0376336
$865$	−1.28755	−0.0437780
$866$	29.3382	0.996953
$867$	13.0263	0.442398
$868$	18.6565	0.633243
$869$	−14.5029	−0.491978
$870$	−7.28542	−0.246999
$871$	−74.0892	−2.51042
$872$	4.60903	0.156081
$873$	5.64341	0.191001
$874$	1.53319	0.0518610
$875$	−11.4412	−0.386784
$876$	27.6162	0.933063
$877$	30.2715	1.02220	0.511098	−	0.859523i	$-0.329239\pi$
$877$	30.2715	1.02220	0.511098	+	0.859523i	$0.329239\pi$
$878$	24.7242	0.834401
$879$	−21.8571	−0.737221
$880$	0.792907	0.0267289
$881$	−45.7372	−1.54093	−0.770463	−	0.637484i	$-0.779975\pi$
$881$	−45.7372	−1.54093	−0.770463	+	0.637484i	$0.779975\pi$
$882$	−1.17331	−0.0395073
$883$	−29.2148	−0.983156	−0.491578	−	0.870833i	$-0.663580\pi$
$883$	−29.2148	−0.983156	−0.491578	+	0.870833i	$0.663580\pi$
$884$	−16.4752	−0.554122
$885$	8.68027	0.291784
$886$	3.15508	0.105997
$887$	44.4347	1.49197	0.745985	−	0.665963i	$-0.231979\pi$
$887$	44.4347	1.49197	0.745985	+	0.665963i	$0.231979\pi$
$888$	−4.19608	−0.140811
$889$	46.2317	1.55056
$890$	−2.02956	−0.0680309
$891$	−13.8258	−0.463182
$892$	21.2262	0.710707
$893$	0.129560	0.00433556
$894$	−55.1130	−1.84326
$895$	−7.32170	−0.244738
$896$	−2.70951	−0.0905185
$897$	−110.720	−3.69683
$898$	36.4107	1.21504
$899$	−45.9610	−1.53289
$900$	−16.5442	−0.551473
$901$	14.4318	0.480794
$902$	−3.66959	−0.122184
$903$	85.7048	2.85208
$904$	14.0213	0.466343
$905$	7.81095	0.259645
$906$	−25.8611	−0.859176
$907$	28.6717	0.952028	0.476014	−	0.879438i	$-0.342081\pi$
$907$	28.6717	0.952028	0.476014	+	0.879438i	$0.342081\pi$
$908$	−17.5121	−0.581159
$909$	−30.3964	−1.00819
$910$	−5.57542	−0.184823
$911$	17.2229	0.570620	0.285310	−	0.958435i	$-0.407903\pi$
$911$	17.2229	0.570620	0.285310	+	0.958435i	$0.407903\pi$
$912$	0.426267	0.0141151
$913$	−9.23377	−0.305593
$914$	−7.67716	−0.253938
$915$	−4.58497	−0.151575
$916$	13.8706	0.458297
$917$	−41.4659	−1.36932
$918$	−3.81042	−0.125763
$919$	43.6102	1.43857	0.719284	−	0.694717i	$-0.244470\pi$
$919$	43.6102	1.43857	0.719284	+	0.694717i	$0.244470\pi$
$920$	−3.92572	−0.129427
$921$	−18.5369	−0.610811
$922$	−10.0942	−0.332436
$923$	−0.952847	−0.0313633
$924$	−12.6686	−0.416766
$925$	7.96384	0.261849
$926$	−4.63210	−0.152220
$927$	−10.0837	−0.331192
$928$	6.67499	0.219117
$929$	6.38382	0.209446	0.104723	−	0.994501i	$-0.466604\pi$
$929$	6.38382	0.209446	0.104723	+	0.994501i	$0.466604\pi$
$930$	7.51524	0.246434
$931$	−0.0573754	−0.00188040
$932$	−12.5545	−0.411237
$933$	37.8939	1.24059
$934$	35.7367	1.16934
$935$	−2.73125	−0.0893215
$936$	−16.4342	−0.537170
$937$	22.8385	0.746101	0.373050	−	0.927811i	$-0.378312\pi$
$937$	22.8385	0.746101	0.373050	+	0.927811i	$0.378312\pi$
$938$	41.9716	1.37042
$939$	−68.0649	−2.22121
$940$	−0.331737	−0.0108201
$941$	−30.1998	−0.984484	−0.492242	−	0.870458i	$-0.663822\pi$
$941$	−30.1998	−0.984484	−0.492242	+	0.870458i	$0.663822\pi$
$942$	30.5877	0.996600
$943$	18.1683	0.591641
$944$	−7.95297	−0.258847
$945$	−1.28949	−0.0419472
$946$	22.9790	0.747113
$947$	35.7877	1.16295	0.581473	−	0.813566i	$-0.302477\pi$
$947$	35.7877	1.16295	0.581473	+	0.813566i	$0.302477\pi$
$948$	19.9635	0.648385
$949$	−52.0650	−1.69010
$950$	−0.809022	−0.0262481
$951$	33.6305	1.09055
$952$	9.33322	0.302491
$953$	11.1649	0.361665	0.180833	−	0.983514i	$-0.442121\pi$
$953$	11.1649	0.361665	0.180833	+	0.983514i	$0.442121\pi$
$954$	14.3959	0.466086
$955$	−9.35597	−0.302752
$956$	22.7727	0.736523
$957$	31.2096	1.00886
$958$	22.6696	0.732422
$959$	46.1233	1.48940
$960$	−1.09145	−0.0352264
$961$	16.4109	0.529383
$962$	7.91090	0.255058
$963$	−34.6679	−1.11716
$964$	−12.0780	−0.389007
$965$	6.84897	0.220476
$966$	62.7228	2.01807
$967$	26.8188	0.862434	0.431217	−	0.902248i	$-0.358084\pi$
$967$	26.8188	0.862434	0.431217	+	0.902248i	$0.358084\pi$
$968$	7.60331	0.244380
$969$	−1.46832	−0.0471693
$970$	−0.706608	−0.0226878
$971$	10.5077	0.337209	0.168605	−	0.985684i	$-0.446074\pi$
$971$	10.5077	0.337209	0.168605	+	0.985684i	$0.446074\pi$
$972$	22.3501	0.716879
$973$	14.0094	0.449120
$974$	11.6083	0.371955
$975$	58.4237	1.87105
$976$	4.20081	0.134465
$977$	22.9897	0.735504	0.367752	−	0.929924i	$-0.380127\pi$
$977$	22.9897	0.735504	0.367752	+	0.929924i	$0.380127\pi$
$978$	−0.943562	−0.0301718
$979$	8.69429	0.277871
$980$	0.146909	0.00469283
$981$	−15.8368	−0.505630
$982$	−13.1988	−0.421191
$983$	60.3613	1.92523	0.962613	−	0.270879i	$-0.0873142\pi$
$983$	60.3613	1.92523	0.962613	+	0.270879i	$0.0873142\pi$
$984$	5.05125	0.161028
$985$	2.47201	0.0787649
$986$	−22.9927	−0.732238
$987$	5.30029	0.168710
$988$	−0.803644	−0.0255673
$989$	−113.770	−3.61768
$990$	−2.72446	−0.0865890
$991$	20.1288	0.639411	0.319706	−	0.947517i	$-0.396416\pi$
$991$	20.1288	0.639411	0.319706	+	0.947517i	$0.396416\pi$
$992$	−6.88555	−0.218617
$993$	−36.2573	−1.15059
$994$	0.539788	0.0171210
$995$	−1.11413	−0.0353204
$996$	12.7104	0.402746
$997$	−24.8240	−0.786185	−0.393092	−	0.919499i	$-0.628595\pi$
$997$	−24.8240	−0.786185	−0.393092	+	0.919499i	$0.628595\pi$
$998$	−13.8151	−0.437308
$999$	1.82965	0.0578875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.11	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.11	✓	81	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.53693 q^{3} +1.00000 q^{4} +0.430224 q^{5} +2.53693 q^{6} +2.70951 q^{7} -1.00000 q^{8} +3.43604 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.53693 q^{3} +1.00000 q^{4} +0.430224 q^{5} +2.53693 q^{6} +2.70951 q^{7} -1.00000 q^{8} +3.43604 q^{9} -0.430224 q^{10} +1.84301 q^{11} -2.53693 q^{12} +4.78290 q^{13} -2.70951 q^{14} -1.09145 q^{15} +1.00000 q^{16} -3.44461 q^{17} -3.43604 q^{18} -0.168024 q^{19} +0.430224 q^{20} -6.87386 q^{21} -1.84301 q^{22} +9.12483 q^{23} +2.53693 q^{24} -4.81491 q^{25} -4.78290 q^{26} -1.10620 q^{27} +2.70951 q^{28} -6.67499 q^{29} +1.09145 q^{30} +6.88555 q^{31} -1.00000 q^{32} -4.67560 q^{33} +3.44461 q^{34} +1.16570 q^{35} +3.43604 q^{36} -1.65400 q^{37} +0.168024 q^{38} -12.1339 q^{39} -0.430224 q^{40} +1.99108 q^{41} +6.87386 q^{42} -12.4682 q^{43} +1.84301 q^{44} +1.47827 q^{45} -9.12483 q^{46} -0.771079 q^{47} -2.53693 q^{48} +0.341471 q^{49} +4.81491 q^{50} +8.73874 q^{51} +4.78290 q^{52} -4.18969 q^{53} +1.10620 q^{54} +0.792907 q^{55} -2.70951 q^{56} +0.426267 q^{57} +6.67499 q^{58} -7.95297 q^{59} -1.09145 q^{60} +4.20081 q^{61} -6.88555 q^{62} +9.30999 q^{63} +1.00000 q^{64} +2.05772 q^{65} +4.67560 q^{66} -15.4904 q^{67} -3.44461 q^{68} -23.1491 q^{69} -1.16570 q^{70} -0.199219 q^{71} -3.43604 q^{72} -10.8856 q^{73} +1.65400 q^{74} +12.2151 q^{75} -0.168024 q^{76} +4.99366 q^{77} +12.1339 q^{78} -7.86915 q^{79} +0.430224 q^{80} -7.50176 q^{81} -1.99108 q^{82} -5.01016 q^{83} -6.87386 q^{84} -1.48195 q^{85} +12.4682 q^{86} +16.9340 q^{87} -1.84301 q^{88} +4.71744 q^{89} -1.47827 q^{90} +12.9593 q^{91} +9.12483 q^{92} -17.4682 q^{93} +0.771079 q^{94} -0.0722881 q^{95} +2.53693 q^{96} +1.64242 q^{97} -0.341471 q^{98} +6.33265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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