LMFDB - Embedded newform 8026.2.a.d.1.1

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:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.38260 q^{3} +1.00000 q^{4} +3.86577 q^{5} -3.38260 q^{6} +1.67092 q^{7} +1.00000 q^{8} +8.44195 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.38260 q^{3} +1.00000 q^{4} +3.86577 q^{5} -3.38260 q^{6} +1.67092 q^{7} +1.00000 q^{8} +8.44195 q^{9} +3.86577 q^{10} +2.15757 q^{11} -3.38260 q^{12} -2.91490 q^{13} +1.67092 q^{14} -13.0764 q^{15} +1.00000 q^{16} +5.91379 q^{17} +8.44195 q^{18} +1.02993 q^{19} +3.86577 q^{20} -5.65203 q^{21} +2.15757 q^{22} -5.99490 q^{23} -3.38260 q^{24} +9.94422 q^{25} -2.91490 q^{26} -18.4079 q^{27} +1.67092 q^{28} +5.62652 q^{29} -13.0764 q^{30} +8.09005 q^{31} +1.00000 q^{32} -7.29819 q^{33} +5.91379 q^{34} +6.45938 q^{35} +8.44195 q^{36} -2.48992 q^{37} +1.02993 q^{38} +9.85994 q^{39} +3.86577 q^{40} -9.09150 q^{41} -5.65203 q^{42} +3.04207 q^{43} +2.15757 q^{44} +32.6347 q^{45} -5.99490 q^{46} +2.29639 q^{47} -3.38260 q^{48} -4.20804 q^{49} +9.94422 q^{50} -20.0040 q^{51} -2.91490 q^{52} +11.8631 q^{53} -18.4079 q^{54} +8.34068 q^{55} +1.67092 q^{56} -3.48382 q^{57} +5.62652 q^{58} -4.51133 q^{59} -13.0764 q^{60} +10.7581 q^{61} +8.09005 q^{62} +14.1058 q^{63} +1.00000 q^{64} -11.2684 q^{65} -7.29819 q^{66} -3.06536 q^{67} +5.91379 q^{68} +20.2783 q^{69} +6.45938 q^{70} +7.58472 q^{71} +8.44195 q^{72} +16.9583 q^{73} -2.48992 q^{74} -33.6373 q^{75} +1.02993 q^{76} +3.60512 q^{77} +9.85994 q^{78} -11.3570 q^{79} +3.86577 q^{80} +36.9407 q^{81} -9.09150 q^{82} -1.79781 q^{83} -5.65203 q^{84} +22.8614 q^{85} +3.04207 q^{86} -19.0322 q^{87} +2.15757 q^{88} -12.6568 q^{89} +32.6347 q^{90} -4.87056 q^{91} -5.99490 q^{92} -27.3654 q^{93} +2.29639 q^{94} +3.98146 q^{95} -3.38260 q^{96} -5.57549 q^{97} -4.20804 q^{98} +18.2141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−3.38260	−1.95294	−0.976471	−	0.215648i	$-0.930814\pi$
$3$	−3.38260	−1.95294	−0.976471	+	0.215648i	$0.930814\pi$
$4$	1.00000	0.500000
$5$	3.86577	1.72883	0.864414	−	0.502781i	$-0.167690\pi$
$5$	3.86577	1.72883	0.864414	+	0.502781i	$0.167690\pi$
$6$	−3.38260	−1.38094
$7$	1.67092	0.631547	0.315773	−	0.948835i	$-0.397736\pi$
$7$	1.67092	0.631547	0.315773	+	0.948835i	$0.397736\pi$
$8$	1.00000	0.353553
$9$	8.44195	2.81398
$10$	3.86577	1.22247
$11$	2.15757	0.650532	0.325266	−	0.945623i	$-0.394546\pi$
$11$	2.15757	0.650532	0.325266	+	0.945623i	$0.394546\pi$
$12$	−3.38260	−0.976471
$13$	−2.91490	−0.808449	−0.404224	−	0.914660i	$-0.632459\pi$
$13$	−2.91490	−0.808449	−0.404224	+	0.914660i	$0.632459\pi$
$14$	1.67092	0.446571
$15$	−13.0764	−3.37630
$16$	1.00000	0.250000
$17$	5.91379	1.43430	0.717152	−	0.696917i	$-0.245445\pi$
$17$	5.91379	1.43430	0.717152	+	0.696917i	$0.245445\pi$
$18$	8.44195	1.98979
$19$	1.02993	0.236281	0.118141	−	0.992997i	$-0.462307\pi$
$19$	1.02993	0.236281	0.118141	+	0.992997i	$0.462307\pi$
$20$	3.86577	0.864414
$21$	−5.65203	−1.23337
$22$	2.15757	0.459996
$23$	−5.99490	−1.25002	−0.625011	−	0.780616i	$-0.714906\pi$
$23$	−5.99490	−1.25002	−0.625011	+	0.780616i	$0.714906\pi$
$24$	−3.38260	−0.690469
$25$	9.94422	1.98884
$26$	−2.91490	−0.571660
$27$	−18.4079	−3.54260
$28$	1.67092	0.315773
$29$	5.62652	1.04482	0.522409	−	0.852695i	$-0.325033\pi$
$29$	5.62652	1.04482	0.522409	+	0.852695i	$0.325033\pi$
$30$	−13.0764	−2.38740
$31$	8.09005	1.45302	0.726508	−	0.687158i	$-0.241142\pi$
$31$	8.09005	1.45302	0.726508	+	0.687158i	$0.241142\pi$
$32$	1.00000	0.176777
$33$	−7.29819	−1.27045
$34$	5.91379	1.01421
$35$	6.45938	1.09184
$36$	8.44195	1.40699
$37$	−2.48992	−0.409341	−0.204670	−	0.978831i	$-0.565612\pi$
$37$	−2.48992	−0.409341	−0.204670	+	0.978831i	$0.565612\pi$
$38$	1.02993	0.167076
$39$	9.85994	1.57885
$40$	3.86577	0.611233
$41$	−9.09150	−1.41985	−0.709927	−	0.704275i	$-0.751272\pi$
$41$	−9.09150	−1.41985	−0.709927	+	0.704275i	$0.751272\pi$
$42$	−5.65203	−0.872127
$43$	3.04207	0.463911	0.231955	−	0.972726i	$-0.425488\pi$
$43$	3.04207	0.463911	0.231955	+	0.972726i	$0.425488\pi$
$44$	2.15757	0.325266
$45$	32.6347	4.86489
$46$	−5.99490	−0.883899
$47$	2.29639	0.334962	0.167481	−	0.985875i	$-0.446437\pi$
$47$	2.29639	0.334962	0.167481	+	0.985875i	$0.446437\pi$
$48$	−3.38260	−0.488236
$49$	−4.20804	−0.601149
$50$	9.94422	1.40632
$51$	−20.0040	−2.80111
$52$	−2.91490	−0.404224
$53$	11.8631	1.62952	0.814758	−	0.579801i	$-0.196870\pi$
$53$	11.8631	1.62952	0.814758	+	0.579801i	$0.196870\pi$
$54$	−18.4079	−2.50500
$55$	8.34068	1.12466
$56$	1.67092	0.223286
$57$	−3.48382	−0.461444
$58$	5.62652	0.738798
$59$	−4.51133	−0.587326	−0.293663	−	0.955909i	$-0.594874\pi$
$59$	−4.51133	−0.587326	−0.293663	+	0.955909i	$0.594874\pi$
$60$	−13.0764	−1.68815
$61$	10.7581	1.37743	0.688715	−	0.725032i	$-0.258175\pi$
$61$	10.7581	1.37743	0.688715	+	0.725032i	$0.258175\pi$
$62$	8.09005	1.02744
$63$	14.1058	1.77716
$64$	1.00000	0.125000
$65$	−11.2684	−1.39767
$66$	−7.29819	−0.898345
$67$	−3.06536	−0.374493	−0.187246	−	0.982313i	$-0.559956\pi$
$67$	−3.06536	−0.374493	−0.187246	+	0.982313i	$0.559956\pi$
$68$	5.91379	0.717152
$69$	20.2783	2.44122
$70$	6.45938	0.772044
$71$	7.58472	0.900141	0.450070	−	0.892993i	$-0.351399\pi$
$71$	7.58472	0.900141	0.450070	+	0.892993i	$0.351399\pi$
$72$	8.44195	0.994893
$73$	16.9583	1.98482	0.992411	−	0.122967i	$-0.0392410\pi$
$73$	16.9583	1.98482	0.992411	+	0.122967i	$0.0392410\pi$
$74$	−2.48992	−0.289448
$75$	−33.6373	−3.88410
$76$	1.02993	0.118141
$77$	3.60512	0.410841
$78$	9.85994	1.11642
$79$	−11.3570	−1.27777	−0.638884	−	0.769303i	$-0.720603\pi$
$79$	−11.3570	−1.27777	−0.638884	+	0.769303i	$0.720603\pi$
$80$	3.86577	0.432207
$81$	36.9407	4.10452
$82$	−9.09150	−1.00399
$83$	−1.79781	−0.197336	−0.0986679	−	0.995120i	$-0.531458\pi$
$83$	−1.79781	−0.197336	−0.0986679	+	0.995120i	$0.531458\pi$
$84$	−5.65203	−0.616687
$85$	22.8614	2.47966
$86$	3.04207	0.328034
$87$	−19.0322	−2.04047
$88$	2.15757	0.229998
$89$	−12.6568	−1.34162	−0.670810	−	0.741630i	$-0.734053\pi$
$89$	−12.6568	−1.34162	−0.670810	+	0.741630i	$0.734053\pi$
$90$	32.6347	3.44000
$91$	−4.87056	−0.510573
$92$	−5.99490	−0.625011
$93$	−27.3654	−2.83765
$94$	2.29639	0.236854
$95$	3.98146	0.408489
$96$	−3.38260	−0.345235
$97$	−5.57549	−0.566106	−0.283053	−	0.959104i	$-0.591347\pi$
$97$	−5.57549	−0.566106	−0.283053	+	0.959104i	$0.591347\pi$
$98$	−4.20804	−0.425076
$99$	18.2141	1.83059
$100$	9.94422	0.994422
$101$	15.4725	1.53957	0.769785	−	0.638303i	$-0.220363\pi$
$101$	15.4725	1.53957	0.769785	+	0.638303i	$0.220363\pi$
$102$	−20.0040	−1.98069
$103$	−4.17558	−0.411432	−0.205716	−	0.978612i	$-0.565952\pi$
$103$	−4.17558	−0.411432	−0.205716	+	0.978612i	$0.565952\pi$
$104$	−2.91490	−0.285830
$105$	−21.8495	−2.13229
$106$	11.8631	1.15224
$107$	−1.22521	−0.118446	−0.0592228	−	0.998245i	$-0.518862\pi$
$107$	−1.22521	−0.118446	−0.0592228	+	0.998245i	$0.518862\pi$
$108$	−18.4079	−1.77130
$109$	6.61263	0.633375	0.316688	−	0.948530i	$-0.397429\pi$
$109$	6.61263	0.633375	0.316688	+	0.948530i	$0.397429\pi$
$110$	8.34068	0.795253
$111$	8.42240	0.799419
$112$	1.67092	0.157887
$113$	1.88321	0.177157	0.0885786	−	0.996069i	$-0.471768\pi$
$113$	1.88321	0.177157	0.0885786	+	0.996069i	$0.471768\pi$
$114$	−3.48382	−0.326290
$115$	−23.1749	−2.16107
$116$	5.62652	0.522409
$117$	−24.6075	−2.27496
$118$	−4.51133	−0.415302
$119$	9.88144	0.905831
$120$	−13.0764	−1.19370
$121$	−6.34489	−0.576808
$122$	10.7581	0.973991
$123$	30.7529	2.77289
$124$	8.09005	0.726508
$125$	19.1132	1.70954
$126$	14.1058	1.25664
$127$	−16.5846	−1.47165	−0.735824	−	0.677173i	$-0.763205\pi$
$127$	−16.5846	−1.47165	−0.735824	+	0.677173i	$0.763205\pi$
$128$	1.00000	0.0883883
$129$	−10.2901	−0.905991
$130$	−11.2684	−0.988301
$131$	19.1778	1.67557	0.837785	−	0.546000i	$-0.183850\pi$
$131$	19.1778	1.67557	0.837785	+	0.546000i	$0.183850\pi$
$132$	−7.29819	−0.635226
$133$	1.72092	0.149223
$134$	−3.06536	−0.264806
$135$	−71.1608	−6.12455
$136$	5.91379	0.507103
$137$	4.55843	0.389453	0.194727	−	0.980858i	$-0.437618\pi$
$137$	4.55843	0.389453	0.194727	+	0.980858i	$0.437618\pi$
$138$	20.2783	1.72620
$139$	−20.9024	−1.77292	−0.886458	−	0.462810i	$-0.846841\pi$
$139$	−20.9024	−1.77292	−0.886458	+	0.462810i	$0.846841\pi$
$140$	6.45938	0.545918
$141$	−7.76775	−0.654162
$142$	7.58472	0.636496
$143$	−6.28911	−0.525922
$144$	8.44195	0.703496
$145$	21.7509	1.80631
$146$	16.9583	1.40348
$147$	14.2341	1.17401
$148$	−2.48992	−0.204670
$149$	−7.90441	−0.647555	−0.323777	−	0.946133i	$-0.604953\pi$
$149$	−7.90441	−0.647555	−0.323777	+	0.946133i	$0.604953\pi$
$150$	−33.6373	−2.74647
$151$	−8.62330	−0.701754	−0.350877	−	0.936422i	$-0.614116\pi$
$151$	−8.62330	−0.701754	−0.350877	+	0.936422i	$0.614116\pi$
$152$	1.02993	0.0835380
$153$	49.9239	4.03611
$154$	3.60512	0.290509
$155$	31.2743	2.51201
$156$	9.85994	0.789427
$157$	−6.17010	−0.492427	−0.246214	−	0.969216i	$-0.579187\pi$
$157$	−6.17010	−0.492427	−0.246214	+	0.969216i	$0.579187\pi$
$158$	−11.3570	−0.903518
$159$	−40.1279	−3.18235
$160$	3.86577	0.305616
$161$	−10.0170	−0.789448
$162$	36.9407	2.90233
$163$	−18.3823	−1.43981	−0.719906	−	0.694072i	$-0.755815\pi$
$163$	−18.3823	−1.43981	−0.719906	+	0.694072i	$0.755815\pi$
$164$	−9.09150	−0.709927
$165$	−28.2132	−2.19639
$166$	−1.79781	−0.139537
$167$	7.82402	0.605441	0.302721	−	0.953079i	$-0.402105\pi$
$167$	7.82402	0.605441	0.302721	+	0.953079i	$0.402105\pi$
$168$	−5.65203	−0.436064
$169$	−4.50333	−0.346410
$170$	22.8614	1.75339
$171$	8.69458	0.664891
$172$	3.04207	0.231955
$173$	−15.0734	−1.14601	−0.573006	−	0.819551i	$-0.694223\pi$
$173$	−15.0734	−1.14601	−0.573006	+	0.819551i	$0.694223\pi$
$174$	−19.0322	−1.44283
$175$	16.6159	1.25605
$176$	2.15757	0.162633
$177$	15.2600	1.14701
$178$	−12.6568	−0.948668
$179$	−2.98856	−0.223375	−0.111688	−	0.993743i	$-0.535626\pi$
$179$	−2.98856	−0.223375	−0.111688	+	0.993743i	$0.535626\pi$
$180$	32.6347	2.43245
$181$	−11.4031	−0.847585	−0.423792	−	0.905759i	$-0.639301\pi$
$181$	−11.4031	−0.847585	−0.423792	+	0.905759i	$0.639301\pi$
$182$	−4.87056	−0.361030
$183$	−36.3902	−2.69004
$184$	−5.99490	−0.441950
$185$	−9.62548	−0.707680
$186$	−27.3654	−2.00653
$187$	12.7594	0.933061
$188$	2.29639	0.167481
$189$	−30.7581	−2.23732
$190$	3.98146	0.288846
$191$	5.21307	0.377205	0.188602	−	0.982054i	$-0.439604\pi$
$191$	5.21307	0.377205	0.188602	+	0.982054i	$0.439604\pi$
$192$	−3.38260	−0.244118
$193$	−3.20977	−0.231044	−0.115522	−	0.993305i	$-0.536854\pi$
$193$	−3.20977	−0.231044	−0.115522	+	0.993305i	$0.536854\pi$
$194$	−5.57549	−0.400297
$195$	38.1163	2.72957
$196$	−4.20804	−0.300574
$197$	−21.0140	−1.49718	−0.748591	−	0.663032i	$-0.769269\pi$
$197$	−21.0140	−1.49718	−0.748591	+	0.663032i	$0.769269\pi$
$198$	18.2141	1.29442
$199$	21.0741	1.49390	0.746950	−	0.664880i	$-0.231517\pi$
$199$	21.0741	1.49390	0.746950	+	0.664880i	$0.231517\pi$
$200$	9.94422	0.703162
$201$	10.3689	0.731363
$202$	15.4725	1.08864
$203$	9.40144	0.659852
$204$	−20.0040	−1.40056
$205$	−35.1457	−2.45468
$206$	−4.17558	−0.290926
$207$	−50.6086	−3.51754
$208$	−2.91490	−0.202112
$209$	2.22214	0.153709
$210$	−21.8495	−1.50776
$211$	2.83394	0.195096	0.0975482	−	0.995231i	$-0.468900\pi$
$211$	2.83394	0.195096	0.0975482	+	0.995231i	$0.468900\pi$
$212$	11.8631	0.814758
$213$	−25.6560	−1.75792
$214$	−1.22521	−0.0837537
$215$	11.7599	0.802021
$216$	−18.4079	−1.25250
$217$	13.5178	0.917647
$218$	6.61263	0.447864
$219$	−57.3631	−3.87624
$220$	8.34068	0.562329
$221$	−17.2381	−1.15956
$222$	8.42240	0.565275
$223$	17.9004	1.19870	0.599349	−	0.800488i	$-0.295426\pi$
$223$	17.9004	1.19870	0.599349	+	0.800488i	$0.295426\pi$
$224$	1.67092	0.111643
$225$	83.9486	5.59657
$226$	1.88321	0.125269
$227$	−10.1415	−0.673116	−0.336558	−	0.941663i	$-0.609263\pi$
$227$	−10.1415	−0.673116	−0.336558	+	0.941663i	$0.609263\pi$
$228$	−3.48382	−0.230722
$229$	8.84925	0.584775	0.292387	−	0.956300i	$-0.405550\pi$
$229$	8.84925	0.584775	0.292387	+	0.956300i	$0.405550\pi$
$230$	−23.1749	−1.52811
$231$	−12.1947	−0.802350
$232$	5.62652	0.369399
$233$	−13.0895	−0.857520	−0.428760	−	0.903418i	$-0.641049\pi$
$233$	−13.0895	−0.857520	−0.428760	+	0.903418i	$0.641049\pi$
$234$	−24.6075	−1.60864
$235$	8.87731	0.579092
$236$	−4.51133	−0.293663
$237$	38.4163	2.49541
$238$	9.88144	0.640519
$239$	13.9662	0.903397	0.451699	−	0.892171i	$-0.350818\pi$
$239$	13.9662	0.903397	0.451699	+	0.892171i	$0.350818\pi$
$240$	−13.0764	−0.844075
$241$	19.9722	1.28652	0.643261	−	0.765647i	$-0.277581\pi$
$241$	19.9722	1.28652	0.643261	+	0.765647i	$0.277581\pi$
$242$	−6.34489	−0.407865
$243$	−69.7316	−4.47328
$244$	10.7581	0.688715
$245$	−16.2673	−1.03928
$246$	30.7529	1.96073
$247$	−3.00214	−0.191021
$248$	8.09005	0.513718
$249$	6.08128	0.385385
$250$	19.1132	1.20883
$251$	1.62451	0.102538	0.0512691	−	0.998685i	$-0.483673\pi$
$251$	1.62451	0.102538	0.0512691	+	0.998685i	$0.483673\pi$
$252$	14.1058	0.888581
$253$	−12.9344	−0.813180
$254$	−16.5846	−1.04061
$255$	−77.3308	−4.84264
$256$	1.00000	0.0625000
$257$	−15.2337	−0.950254	−0.475127	−	0.879917i	$-0.657598\pi$
$257$	−15.2337	−0.950254	−0.475127	+	0.879917i	$0.657598\pi$
$258$	−10.2901	−0.640632
$259$	−4.16045	−0.258518
$260$	−11.2684	−0.698834
$261$	47.4988	2.94010
$262$	19.1778	1.18481
$263$	−1.62176	−0.100002	−0.0500011	−	0.998749i	$-0.515922\pi$
$263$	−1.62176	−0.100002	−0.0500011	+	0.998749i	$0.515922\pi$
$264$	−7.29819	−0.449172
$265$	45.8599	2.81715
$266$	1.72092	0.105516
$267$	42.8129	2.62011
$268$	−3.06536	−0.187246
$269$	3.45638	0.210739	0.105370	−	0.994433i	$-0.466397\pi$
$269$	3.45638	0.210739	0.105370	+	0.994433i	$0.466397\pi$
$270$	−71.1608	−4.33071
$271$	23.1218	1.40455	0.702274	−	0.711906i	$-0.252168\pi$
$271$	23.1218	1.40455	0.702274	+	0.711906i	$0.252168\pi$
$272$	5.91379	0.358576
$273$	16.4751	0.997120
$274$	4.55843	0.275385
$275$	21.4553	1.29381
$276$	20.2783	1.22061
$277$	10.5492	0.633839	0.316920	−	0.948452i	$-0.397351\pi$
$277$	10.5492	0.633839	0.316920	+	0.948452i	$0.397351\pi$
$278$	−20.9024	−1.25364
$279$	68.2958	4.08876
$280$	6.45938	0.386022
$281$	−22.1367	−1.32057	−0.660283	−	0.751017i	$-0.729564\pi$
$281$	−22.1367	−1.32057	−0.660283	+	0.751017i	$0.729564\pi$
$282$	−7.76775	−0.462562
$283$	−17.6782	−1.05086	−0.525430	−	0.850837i	$-0.676096\pi$
$283$	−17.6782	−1.05086	−0.525430	+	0.850837i	$0.676096\pi$
$284$	7.58472	0.450070
$285$	−13.4677	−0.797756
$286$	−6.28911	−0.371883
$287$	−15.1911	−0.896704
$288$	8.44195	0.497447
$289$	17.9729	1.05723
$290$	21.7509	1.27725
$291$	18.8596	1.10557
$292$	16.9583	0.992411
$293$	−6.09461	−0.356051	−0.178025	−	0.984026i	$-0.556971\pi$
$293$	−6.09461	−0.356051	−0.178025	+	0.984026i	$0.556971\pi$
$294$	14.2341	0.830149
$295$	−17.4398	−1.01538
$296$	−2.48992	−0.144724
$297$	−39.7164	−2.30458
$298$	−7.90441	−0.457890
$299$	17.4746	1.01058
$300$	−33.6373	−1.94205
$301$	5.08304	0.292981
$302$	−8.62330	−0.496215
$303$	−52.3372	−3.00669
$304$	1.02993	0.0590703
$305$	41.5883	2.38134
$306$	49.9239	2.85396
$307$	15.2429	0.869958	0.434979	−	0.900440i	$-0.356756\pi$
$307$	15.2429	0.869958	0.434979	+	0.900440i	$0.356756\pi$
$308$	3.60512	0.205421
$309$	14.1243	0.803502
$310$	31.2743	1.77626
$311$	−6.26809	−0.355431	−0.177715	−	0.984082i	$-0.556871\pi$
$311$	−6.26809	−0.355431	−0.177715	+	0.984082i	$0.556871\pi$
$312$	9.85994	0.558209
$313$	29.7243	1.68012	0.840060	−	0.542494i	$-0.182520\pi$
$313$	29.7243	1.68012	0.840060	+	0.542494i	$0.182520\pi$
$314$	−6.17010	−0.348199
$315$	54.5298	3.07241
$316$	−11.3570	−0.638884
$317$	−33.8163	−1.89931	−0.949655	−	0.313297i	$-0.898566\pi$
$317$	−33.8163	−1.89931	−0.949655	+	0.313297i	$0.898566\pi$
$318$	−40.1279	−2.25026
$319$	12.1396	0.679688
$320$	3.86577	0.216103
$321$	4.14439	0.231317
$322$	−10.0170	−0.558224
$323$	6.09076	0.338899
$324$	36.9407	2.05226
$325$	−28.9864	−1.60788
$326$	−18.3823	−1.01810
$327$	−22.3679	−1.23695
$328$	−9.09150	−0.501994
$329$	3.83707	0.211544
$330$	−28.2132	−1.55308
$331$	9.76837	0.536918	0.268459	−	0.963291i	$-0.413486\pi$
$331$	9.76837	0.536918	0.268459	+	0.963291i	$0.413486\pi$
$332$	−1.79781	−0.0986679
$333$	−21.0198	−1.15188
$334$	7.82402	0.428111
$335$	−11.8500	−0.647433
$336$	−5.65203	−0.308344
$337$	29.3530	1.59896	0.799481	−	0.600692i	$-0.205108\pi$
$337$	29.3530	1.59896	0.799481	+	0.600692i	$0.205108\pi$
$338$	−4.50333	−0.244949
$339$	−6.37013	−0.345978
$340$	22.8614	1.23983
$341$	17.4548	0.945233
$342$	8.69458	0.470149
$343$	−18.7277	−1.01120
$344$	3.04207	0.164017
$345$	78.3914	4.22045
$346$	−15.0734	−0.810353
$347$	15.9147	0.854347	0.427174	−	0.904170i	$-0.359509\pi$
$347$	15.9147	0.854347	0.427174	+	0.904170i	$0.359509\pi$
$348$	−19.0322	−1.02023
$349$	13.2405	0.708750	0.354375	−	0.935103i	$-0.384694\pi$
$349$	13.2405	0.708750	0.354375	+	0.935103i	$0.384694\pi$
$350$	16.6159	0.888160
$351$	53.6573	2.86401
$352$	2.15757	0.114999
$353$	15.9651	0.849738	0.424869	−	0.905255i	$-0.360320\pi$
$353$	15.9651	0.849738	0.424869	+	0.905255i	$0.360320\pi$
$354$	15.2600	0.811061
$355$	29.3208	1.55619
$356$	−12.6568	−0.670810
$357$	−33.4249	−1.76903
$358$	−2.98856	−0.157950
$359$	−4.36754	−0.230510	−0.115255	−	0.993336i	$-0.536768\pi$
$359$	−4.36754	−0.230510	−0.115255	+	0.993336i	$0.536768\pi$
$360$	32.6347	1.72000
$361$	−17.9393	−0.944171
$362$	−11.4031	−0.599333
$363$	21.4622	1.12647
$364$	−4.87056	−0.255287
$365$	65.5571	3.43141
$366$	−36.3902	−1.90215
$367$	−6.52571	−0.340640	−0.170320	−	0.985389i	$-0.554480\pi$
$367$	−6.52571	−0.340640	−0.170320	+	0.985389i	$0.554480\pi$
$368$	−5.99490	−0.312506
$369$	−76.7500	−3.99545
$370$	−9.62548	−0.500405
$371$	19.8222	1.02912
$372$	−27.3654	−1.41883
$373$	−7.89577	−0.408828	−0.204414	−	0.978885i	$-0.565529\pi$
$373$	−7.89577	−0.408828	−0.204414	+	0.978885i	$0.565529\pi$
$374$	12.7594	0.659774
$375$	−64.6523	−3.33863
$376$	2.29639	0.118427
$377$	−16.4008	−0.844682
$378$	−30.7581	−1.58202
$379$	−5.96534	−0.306419	−0.153209	−	0.988194i	$-0.548961\pi$
$379$	−5.96534	−0.306419	−0.153209	+	0.988194i	$0.548961\pi$
$380$	3.98146	0.204245
$381$	56.0991	2.87404
$382$	5.21307	0.266724
$383$	−14.1703	−0.724067	−0.362033	−	0.932165i	$-0.617917\pi$
$383$	−14.1703	−0.724067	−0.362033	+	0.932165i	$0.617917\pi$
$384$	−3.38260	−0.172617
$385$	13.9366	0.710274
$386$	−3.20977	−0.163373
$387$	25.6810	1.30544
$388$	−5.57549	−0.283053
$389$	15.8277	0.802498	0.401249	−	0.915969i	$-0.368576\pi$
$389$	15.8277	0.802498	0.401249	+	0.915969i	$0.368576\pi$
$390$	38.1163	1.93009
$391$	−35.4526	−1.79291
$392$	−4.20804	−0.212538
$393$	−64.8706	−3.27229
$394$	−21.0140	−1.05867
$395$	−43.9038	−2.20904
$396$	18.2141	0.915293
$397$	−27.3488	−1.37260	−0.686298	−	0.727320i	$-0.740766\pi$
$397$	−27.3488	−1.37260	−0.686298	+	0.727320i	$0.740766\pi$
$398$	21.0741	1.05635
$399$	−5.82117	−0.291423
$400$	9.94422	0.497211
$401$	31.6616	1.58111	0.790553	−	0.612393i	$-0.209793\pi$
$401$	31.6616	1.58111	0.790553	+	0.612393i	$0.209793\pi$
$402$	10.3689	0.517152
$403$	−23.5817	−1.17469
$404$	15.4725	0.769785
$405$	142.804	7.09600
$406$	9.40144	0.466586
$407$	−5.37219	−0.266289
$408$	−20.0040	−0.990343
$409$	14.0012	0.692313	0.346157	−	0.938177i	$-0.387487\pi$
$409$	14.0012	0.692313	0.346157	+	0.938177i	$0.387487\pi$
$410$	−35.1457	−1.73572
$411$	−15.4193	−0.760579
$412$	−4.17558	−0.205716
$413$	−7.53806	−0.370924
$414$	−50.6086	−2.48728
$415$	−6.94995	−0.341159
$416$	−2.91490	−0.142915
$417$	70.7042	3.46240
$418$	2.22214	0.108688
$419$	−2.47696	−0.121007	−0.0605036	−	0.998168i	$-0.519271\pi$
$419$	−2.47696	−0.121007	−0.0605036	+	0.998168i	$0.519271\pi$
$420$	−21.8495	−1.06615
$421$	−1.84058	−0.0897045	−0.0448523	−	0.998994i	$-0.514282\pi$
$421$	−1.84058	−0.0897045	−0.0448523	+	0.998994i	$0.514282\pi$
$422$	2.83394	0.137954
$423$	19.3860	0.942578
$424$	11.8631	0.576121
$425$	58.8080	2.85261
$426$	−25.6560	−1.24304
$427$	17.9758	0.869912
$428$	−1.22521	−0.0592228
$429$	21.2735	1.02710
$430$	11.7599	0.567115
$431$	−32.9571	−1.58749	−0.793744	−	0.608252i	$-0.791871\pi$
$431$	−32.9571	−1.58749	−0.793744	+	0.608252i	$0.791871\pi$
$432$	−18.4079	−0.885651
$433$	16.7380	0.804375	0.402188	−	0.915557i	$-0.368250\pi$
$433$	16.7380	0.804375	0.402188	+	0.915557i	$0.368250\pi$
$434$	13.5178	0.648875
$435$	−73.5743	−3.52762
$436$	6.61263	0.316688
$437$	−6.17430	−0.295357
$438$	−57.3631	−2.74092
$439$	26.6471	1.27180	0.635899	−	0.771772i	$-0.280630\pi$
$439$	26.6471	1.27180	0.635899	+	0.771772i	$0.280630\pi$
$440$	8.34068	0.397626
$441$	−35.5241	−1.69162
$442$	−17.2381	−0.819934
$443$	24.1801	1.14883	0.574415	−	0.818564i	$-0.305229\pi$
$443$	24.1801	1.14883	0.574415	+	0.818564i	$0.305229\pi$
$444$	8.42240	0.399710
$445$	−48.9284	−2.31943
$446$	17.9004	0.847607
$447$	26.7374	1.26464
$448$	1.67092	0.0789434
$449$	10.9953	0.518901	0.259451	−	0.965756i	$-0.416458\pi$
$449$	10.9953	0.518901	0.259451	+	0.965756i	$0.416458\pi$
$450$	83.9486	3.95737
$451$	−19.6156	−0.923660
$452$	1.88321	0.0885786
$453$	29.1691	1.37049
$454$	−10.1415	−0.475965
$455$	−18.8285	−0.882693
$456$	−3.48382	−0.163145
$457$	34.3179	1.60533	0.802663	−	0.596433i	$-0.203416\pi$
$457$	34.3179	1.60533	0.802663	+	0.596433i	$0.203416\pi$
$458$	8.84925	0.413498
$459$	−108.861	−5.08117
$460$	−23.1749	−1.08054
$461$	−5.41907	−0.252391	−0.126196	−	0.992005i	$-0.540277\pi$
$461$	−5.41907	−0.252391	−0.126196	+	0.992005i	$0.540277\pi$
$462$	−12.1947	−0.567347
$463$	−12.8124	−0.595441	−0.297721	−	0.954653i	$-0.596226\pi$
$463$	−12.8124	−0.595441	−0.297721	+	0.954653i	$0.596226\pi$
$464$	5.62652	0.261205
$465$	−105.788	−4.90581
$466$	−13.0895	−0.606358
$467$	−16.8815	−0.781182	−0.390591	−	0.920564i	$-0.627729\pi$
$467$	−16.8815	−0.781182	−0.390591	+	0.920564i	$0.627729\pi$
$468$	−24.6075	−1.13748
$469$	−5.12195	−0.236510
$470$	8.87731	0.409480
$471$	20.8709	0.961682
$472$	−4.51133	−0.207651
$473$	6.56347	0.301789
$474$	38.4163	1.76452
$475$	10.2418	0.469926
$476$	9.88144	0.452915
$477$	100.147	4.58543
$478$	13.9662	0.638798
$479$	−26.5512	−1.21315	−0.606577	−	0.795025i	$-0.707458\pi$
$479$	−26.5512	−1.21315	−0.606577	+	0.795025i	$0.707458\pi$
$480$	−13.0764	−0.596851
$481$	7.25789	0.330931
$482$	19.9722	0.909708
$483$	33.8834	1.54175
$484$	−6.34489	−0.288404
$485$	−21.5536	−0.978699
$486$	−69.7316	−3.16309
$487$	39.2615	1.77911	0.889554	−	0.456831i	$-0.151015\pi$
$487$	39.2615	1.77911	0.889554	+	0.456831i	$0.151015\pi$
$488$	10.7581	0.486995
$489$	62.1798	2.81187
$490$	−16.2673	−0.734883
$491$	−25.5084	−1.15118	−0.575589	−	0.817739i	$-0.695227\pi$
$491$	−25.5084	−1.15118	−0.575589	+	0.817739i	$0.695227\pi$
$492$	30.7529	1.38645
$493$	33.2740	1.49859
$494$	−3.00214	−0.135072
$495$	70.4116	3.16477
$496$	8.09005	0.363254
$497$	12.6734	0.568481
$498$	6.08128	0.272509
$499$	3.34183	0.149601	0.0748004	−	0.997199i	$-0.476168\pi$
$499$	3.34183	0.149601	0.0748004	+	0.997199i	$0.476168\pi$
$500$	19.1132	0.854769
$501$	−26.4655	−1.18239
$502$	1.62451	0.0725054
$503$	12.6795	0.565351	0.282676	−	0.959216i	$-0.408778\pi$
$503$	12.6795	0.565351	0.282676	+	0.959216i	$0.408778\pi$
$504$	14.1058	0.628322
$505$	59.8132	2.66165
$506$	−12.9344	−0.575005
$507$	15.2330	0.676519
$508$	−16.5846	−0.735824
$509$	−19.5250	−0.865428	−0.432714	−	0.901531i	$-0.642444\pi$
$509$	−19.5250	−0.865428	−0.432714	+	0.901531i	$0.642444\pi$
$510$	−77.3308	−3.42426
$511$	28.3359	1.25351
$512$	1.00000	0.0441942
$513$	−18.9588	−0.837051
$514$	−15.2337	−0.671931
$515$	−16.1418	−0.711294
$516$	−10.2901	−0.452995
$517$	4.95462	0.217904
$518$	−4.16045	−0.182800
$519$	50.9873	2.23810
$520$	−11.2684	−0.494150
$521$	35.0644	1.53620	0.768099	−	0.640331i	$-0.221203\pi$
$521$	35.0644	1.53620	0.768099	+	0.640331i	$0.221203\pi$
$522$	47.4988	2.07897
$523$	−33.2486	−1.45386	−0.726930	−	0.686711i	$-0.759054\pi$
$523$	−33.2486	−1.45386	−0.726930	+	0.686711i	$0.759054\pi$
$524$	19.1778	0.837785
$525$	−56.2050	−2.45299
$526$	−1.62176	−0.0707123
$527$	47.8428	2.08407
$528$	−7.29819	−0.317613
$529$	12.9388	0.562556
$530$	45.8599	1.99203
$531$	−38.0845	−1.65272
$532$	1.72092	0.0746113
$533$	26.5009	1.14788
$534$	42.8129	1.85269
$535$	−4.73639	−0.204772
$536$	−3.06536	−0.132403
$537$	10.1091	0.436239
$538$	3.45638	0.149015
$539$	−9.07914	−0.391066
$540$	−71.1608	−3.06228
$541$	8.80302	0.378471	0.189236	−	0.981932i	$-0.439399\pi$
$541$	8.80302	0.378471	0.189236	+	0.981932i	$0.439399\pi$
$542$	23.1218	0.993166
$543$	38.5720	1.65528
$544$	5.91379	0.253552
$545$	25.5629	1.09500
$546$	16.4751	0.705071
$547$	0.897014	0.0383535	0.0191768	−	0.999816i	$-0.493895\pi$
$547$	0.897014	0.0383535	0.0191768	+	0.999816i	$0.493895\pi$
$548$	4.55843	0.194727
$549$	90.8192	3.87607
$550$	21.4553	0.914859
$551$	5.79490	0.246871
$552$	20.2783	0.863102
$553$	−18.9767	−0.806970
$554$	10.5492	0.448192
$555$	32.5591	1.38206
$556$	−20.9024	−0.886458
$557$	−16.8182	−0.712608	−0.356304	−	0.934370i	$-0.615963\pi$
$557$	−16.8182	−0.712608	−0.356304	+	0.934370i	$0.615963\pi$
$558$	68.2958	2.89119
$559$	−8.86733	−0.375048
$560$	6.45938	0.272959
$561$	−43.1599	−1.82221
$562$	−22.1367	−0.933781
$563$	6.35968	0.268028	0.134014	−	0.990979i	$-0.457213\pi$
$563$	6.35968	0.268028	0.134014	+	0.990979i	$0.457213\pi$
$564$	−7.76775	−0.327081
$565$	7.28006	0.306274
$566$	−17.6782	−0.743070
$567$	61.7247	2.59220
$568$	7.58472	0.318248
$569$	27.5707	1.15582	0.577912	−	0.816099i	$-0.303868\pi$
$569$	27.5707	1.15582	0.577912	+	0.816099i	$0.303868\pi$
$570$	−13.4677	−0.564099
$571$	10.8876	0.455633	0.227817	−	0.973704i	$-0.426841\pi$
$571$	10.8876	0.455633	0.227817	+	0.973704i	$0.426841\pi$
$572$	−6.28911	−0.262961
$573$	−17.6337	−0.736659
$574$	−15.1911	−0.634066
$575$	−59.6146	−2.48610
$576$	8.44195	0.351748
$577$	−20.6643	−0.860265	−0.430132	−	0.902766i	$-0.641533\pi$
$577$	−20.6643	−0.860265	−0.430132	+	0.902766i	$0.641533\pi$
$578$	17.9729	0.747574
$579$	10.8574	0.451216
$580$	21.7509	0.903155
$581$	−3.00400	−0.124627
$582$	18.8596	0.781757
$583$	25.5954	1.06005
$584$	16.9583	0.701740
$585$	−95.1270	−3.93302
$586$	−6.09461	−0.251766
$587$	17.2227	0.710856	0.355428	−	0.934704i	$-0.384335\pi$
$587$	17.2227	0.710856	0.355428	+	0.934704i	$0.384335\pi$
$588$	14.2341	0.587004
$589$	8.33215	0.343320
$590$	−17.4398	−0.717985
$591$	71.0817	2.92391
$592$	−2.48992	−0.102335
$593$	−12.2002	−0.501003	−0.250502	−	0.968116i	$-0.580596\pi$
$593$	−12.2002	−0.501003	−0.250502	+	0.968116i	$0.580596\pi$
$594$	−39.7164	−1.62958
$595$	38.1994	1.56602
$596$	−7.90441	−0.323777
$597$	−71.2850	−2.91750
$598$	17.4746	0.714588
$599$	−25.9391	−1.05984	−0.529922	−	0.848046i	$-0.677779\pi$
$599$	−25.9391	−1.05984	−0.529922	+	0.848046i	$0.677779\pi$
$600$	−33.6373	−1.37324
$601$	38.7940	1.58244	0.791219	−	0.611532i	$-0.209447\pi$
$601$	38.7940	1.58244	0.791219	+	0.611532i	$0.209447\pi$
$602$	5.08304	0.207169
$603$	−25.8776	−1.05382
$604$	−8.62330	−0.350877
$605$	−24.5279	−0.997201
$606$	−52.3372	−2.12605
$607$	4.55705	0.184965	0.0924825	−	0.995714i	$-0.470520\pi$
$607$	4.55705	0.184965	0.0924825	+	0.995714i	$0.470520\pi$
$608$	1.02993	0.0417690
$609$	−31.8013	−1.28865
$610$	41.5883	1.68386
$611$	−6.69375	−0.270800
$612$	49.9239	2.01805
$613$	17.3195	0.699527	0.349763	−	0.936838i	$-0.386262\pi$
$613$	17.3195	0.699527	0.349763	+	0.936838i	$0.386262\pi$
$614$	15.2429	0.615153
$615$	118.884	4.79385
$616$	3.60512	0.145254
$617$	22.8724	0.920809	0.460404	−	0.887709i	$-0.347704\pi$
$617$	22.8724	0.920809	0.460404	+	0.887709i	$0.347704\pi$
$618$	14.1243	0.568162
$619$	38.1361	1.53282	0.766409	−	0.642353i	$-0.222042\pi$
$619$	38.1361	1.53282	0.766409	+	0.642353i	$0.222042\pi$
$620$	31.2743	1.25601
$621$	110.354	4.42834
$622$	−6.26809	−0.251327
$623$	−21.1485	−0.847296
$624$	9.85994	0.394714
$625$	24.1663	0.966654
$626$	29.7243	1.18802
$627$	−7.51659	−0.300184
$628$	−6.17010	−0.246214
$629$	−14.7249	−0.587120
$630$	54.5298	2.17252
$631$	33.4833	1.33295	0.666474	−	0.745528i	$-0.267803\pi$
$631$	33.4833	1.33295	0.666474	+	0.745528i	$0.267803\pi$
$632$	−11.3570	−0.451759
$633$	−9.58607	−0.381012
$634$	−33.8163	−1.34302
$635$	−64.1125	−2.54423
$636$	−40.1279	−1.59117
$637$	12.2660	0.485998
$638$	12.1396	0.480612
$639$	64.0298	2.53298
$640$	3.86577	0.152808
$641$	6.04365	0.238710	0.119355	−	0.992852i	$-0.461917\pi$
$641$	6.04365	0.238710	0.119355	+	0.992852i	$0.461917\pi$
$642$	4.14439	0.163566
$643$	−16.0087	−0.631322	−0.315661	−	0.948872i	$-0.602226\pi$
$643$	−16.0087	−0.631322	−0.315661	+	0.948872i	$0.602226\pi$
$644$	−10.0170	−0.394724
$645$	−39.7791	−1.56630
$646$	6.09076	0.239638
$647$	−27.4463	−1.07903	−0.539513	−	0.841977i	$-0.681392\pi$
$647$	−27.4463	−1.07903	−0.539513	+	0.841977i	$0.681392\pi$
$648$	36.9407	1.45117
$649$	−9.73352	−0.382074
$650$	−28.9864	−1.13694
$651$	−45.7252	−1.79211
$652$	−18.3823	−0.719906
$653$	−20.0334	−0.783966	−0.391983	−	0.919972i	$-0.628211\pi$
$653$	−20.0334	−0.783966	−0.391983	+	0.919972i	$0.628211\pi$
$654$	−22.3679	−0.874652
$655$	74.1370	2.89677
$656$	−9.09150	−0.354963
$657$	143.161	5.58525
$658$	3.83707	0.149585
$659$	−18.1687	−0.707751	−0.353876	−	0.935293i	$-0.615136\pi$
$659$	−18.1687	−0.707751	−0.353876	+	0.935293i	$0.615136\pi$
$660$	−28.2132	−1.09820
$661$	40.7159	1.58366	0.791832	−	0.610738i	$-0.209127\pi$
$661$	40.7159	1.58366	0.791832	+	0.610738i	$0.209127\pi$
$662$	9.76837	0.379658
$663$	58.3096	2.26456
$664$	−1.79781	−0.0697687
$665$	6.65269	0.257980
$666$	−21.0198	−0.814501
$667$	−33.7304	−1.30605
$668$	7.82402	0.302721
$669$	−60.5497	−2.34099
$670$	−11.8500	−0.457804
$671$	23.2113	0.896063
$672$	−5.65203	−0.218032
$673$	−24.1295	−0.930124	−0.465062	−	0.885278i	$-0.653968\pi$
$673$	−24.1295	−0.930124	−0.465062	+	0.885278i	$0.653968\pi$
$674$	29.3530	1.13064
$675$	−183.052	−7.04568
$676$	−4.50333	−0.173205
$677$	43.9708	1.68994	0.844968	−	0.534818i	$-0.179620\pi$
$677$	43.9708	1.68994	0.844968	+	0.534818i	$0.179620\pi$
$678$	−6.37013	−0.244643
$679$	−9.31618	−0.357522
$680$	22.8614	0.876694
$681$	34.3047	1.31456
$682$	17.4548	0.668381
$683$	5.39133	0.206294	0.103147	−	0.994666i	$-0.467109\pi$
$683$	5.39133	0.206294	0.103147	+	0.994666i	$0.467109\pi$
$684$	8.69458	0.332446
$685$	17.6219	0.673297
$686$	−18.7277	−0.715027
$687$	−29.9334	−1.14203
$688$	3.04207	0.115978
$689$	−34.5797	−1.31738
$690$	78.3914	2.98431
$691$	−32.2836	−1.22812	−0.614062	−	0.789258i	$-0.710466\pi$
$691$	−32.2836	−1.22812	−0.614062	+	0.789258i	$0.710466\pi$
$692$	−15.0734	−0.573006
$693$	30.4342	1.15610
$694$	15.9147	0.604115
$695$	−80.8038	−3.06506
$696$	−19.0322	−0.721415
$697$	−53.7652	−2.03650
$698$	13.2405	0.501162
$699$	44.2764	1.67469
$700$	16.6159	0.628024
$701$	19.0766	0.720514	0.360257	−	0.932853i	$-0.382689\pi$
$701$	19.0766	0.720514	0.360257	+	0.932853i	$0.382689\pi$
$702$	53.6573	2.02516
$703$	−2.56444	−0.0967196
$704$	2.15757	0.0813165
$705$	−30.0284	−1.13093
$706$	15.9651	0.600856
$707$	25.8532	0.972311
$708$	15.2600	0.573507
$709$	−28.6948	−1.07766	−0.538828	−	0.842416i	$-0.681133\pi$
$709$	−28.6948	−1.07766	−0.538828	+	0.842416i	$0.681133\pi$
$710$	29.3208	1.10039
$711$	−95.8756	−3.59562
$712$	−12.6568	−0.474334
$713$	−48.4990	−1.81630
$714$	−33.4249	−1.25090
$715$	−24.3123	−0.909228
$716$	−2.98856	−0.111688
$717$	−47.2419	−1.76428
$718$	−4.36754	−0.162995
$719$	−11.0746	−0.413011	−0.206506	−	0.978445i	$-0.566209\pi$
$719$	−11.0746	−0.413011	−0.206506	+	0.978445i	$0.566209\pi$
$720$	32.6347	1.21622
$721$	−6.97704	−0.259838
$722$	−17.9393	−0.667630
$723$	−67.5578	−2.51250
$724$	−11.4031	−0.423792
$725$	55.9513	2.07798
$726$	21.4622	0.796537
$727$	9.86957	0.366042	0.183021	−	0.983109i	$-0.441412\pi$
$727$	9.86957	0.366042	0.183021	+	0.983109i	$0.441412\pi$
$728$	−4.87056	−0.180515
$729$	125.052	4.63154
$730$	65.5571	2.42638
$731$	17.9901	0.665389
$732$	−36.3902	−1.34502
$733$	−17.9760	−0.663959	−0.331980	−	0.943287i	$-0.607717\pi$
$733$	−17.9760	−0.663959	−0.331980	+	0.943287i	$0.607717\pi$
$734$	−6.52571	−0.240869
$735$	55.0258	2.02966
$736$	−5.99490	−0.220975
$737$	−6.61372	−0.243620
$738$	−76.7500	−2.82521
$739$	28.7182	1.05642	0.528209	−	0.849115i	$-0.322864\pi$
$739$	28.7182	1.05642	0.528209	+	0.849115i	$0.322864\pi$
$740$	−9.62548	−0.353840
$741$	10.1550	0.373054
$742$	19.8222	0.727695
$743$	−20.2300	−0.742165	−0.371083	−	0.928600i	$-0.621013\pi$
$743$	−20.2300	−0.742165	−0.371083	+	0.928600i	$0.621013\pi$
$744$	−27.3654	−1.00326
$745$	−30.5567	−1.11951
$746$	−7.89577	−0.289085
$747$	−15.1771	−0.555299
$748$	12.7594	0.466531
$749$	−2.04722	−0.0748039
$750$	−64.6523	−2.36077
$751$	−23.3435	−0.851816	−0.425908	−	0.904767i	$-0.640045\pi$
$751$	−23.3435	−0.851816	−0.425908	+	0.904767i	$0.640045\pi$
$752$	2.29639	0.0837406
$753$	−5.49506	−0.200251
$754$	−16.4008	−0.597281
$755$	−33.3357	−1.21321
$756$	−30.7581	−1.11866
$757$	−24.6851	−0.897196	−0.448598	−	0.893734i	$-0.648076\pi$
$757$	−24.6851	−0.897196	−0.448598	+	0.893734i	$0.648076\pi$
$758$	−5.96534	−0.216671
$759$	43.7519	1.58809
$760$	3.98146	0.144423
$761$	43.9679	1.59384	0.796918	−	0.604088i	$-0.206462\pi$
$761$	43.9679	1.59384	0.796918	+	0.604088i	$0.206462\pi$
$762$	56.0991	2.03226
$763$	11.0492	0.400006
$764$	5.21307	0.188602
$765$	192.995	6.97773
$766$	−14.1703	−0.511992
$767$	13.1501	0.474823
$768$	−3.38260	−0.122059
$769$	−33.7726	−1.21787	−0.608936	−	0.793219i	$-0.708403\pi$
$769$	−33.7726	−1.21787	−0.608936	+	0.793219i	$0.708403\pi$
$770$	13.9366	0.502239
$771$	51.5296	1.85579
$772$	−3.20977	−0.115522
$773$	−23.5056	−0.845439	−0.422719	−	0.906261i	$-0.638924\pi$
$773$	−23.5056	−0.845439	−0.422719	+	0.906261i	$0.638924\pi$
$774$	25.6810	0.923083
$775$	80.4492	2.88982
$776$	−5.57549	−0.200149
$777$	14.0731	0.504871
$778$	15.8277	0.567452
$779$	−9.36357	−0.335485
$780$	38.1163	1.36478
$781$	16.3646	0.585570
$782$	−35.4526	−1.26778
$783$	−103.572	−3.70138
$784$	−4.20804	−0.150287
$785$	−23.8522	−0.851322
$786$	−64.8706	−2.31386
$787$	−15.0623	−0.536912	−0.268456	−	0.963292i	$-0.586513\pi$
$787$	−15.0623	−0.536912	−0.268456	+	0.963292i	$0.586513\pi$
$788$	−21.0140	−0.748591
$789$	5.48577	0.195299
$790$	−43.9038	−1.56203
$791$	3.14668	0.111883
$792$	18.2141	0.647210
$793$	−31.3588	−1.11358
$794$	−27.3488	−0.970572
$795$	−155.125	−5.50173
$796$	21.0741	0.746950
$797$	−39.7880	−1.40936	−0.704682	−	0.709523i	$-0.748910\pi$
$797$	−39.7880	−1.40936	−0.704682	+	0.709523i	$0.748910\pi$
$798$	−5.82117	−0.206067
$799$	13.5803	0.480438
$800$	9.94422	0.351581
$801$	−106.848	−3.77529
$802$	31.6616	1.11801
$803$	36.5888	1.29119
$804$	10.3689	0.365681
$805$	−38.7234	−1.36482
$806$	−23.5817	−0.830630
$807$	−11.6915	−0.411561
$808$	15.4725	0.544320
$809$	−7.83055	−0.275307	−0.137654	−	0.990480i	$-0.543956\pi$
$809$	−7.83055	−0.275307	−0.137654	+	0.990480i	$0.543956\pi$
$810$	142.804	5.01763
$811$	20.6505	0.725136	0.362568	−	0.931957i	$-0.381900\pi$
$811$	20.6505	0.725136	0.362568	+	0.931957i	$0.381900\pi$
$812$	9.40144	0.329926
$813$	−78.2117	−2.74300
$814$	−5.37219	−0.188295
$815$	−71.0618	−2.48918
$816$	−20.0040	−0.700278
$817$	3.13310	0.109613
$818$	14.0012	0.489539
$819$	−41.1170	−1.43674
$820$	−35.1457	−1.22734
$821$	−45.0509	−1.57229	−0.786144	−	0.618044i	$-0.787925\pi$
$821$	−45.0509	−1.57229	−0.786144	+	0.618044i	$0.787925\pi$
$822$	−15.4193	−0.537811
$823$	41.4924	1.44633	0.723167	−	0.690674i	$-0.242686\pi$
$823$	41.4924	1.44633	0.723167	+	0.690674i	$0.242686\pi$
$824$	−4.17558	−0.145463
$825$	−72.5748	−2.52673
$826$	−7.53806	−0.262283
$827$	−21.5740	−0.750202	−0.375101	−	0.926984i	$-0.622392\pi$
$827$	−21.5740	−0.750202	−0.375101	+	0.926984i	$0.622392\pi$
$828$	−50.6086	−1.75877
$829$	−37.2058	−1.29221	−0.646106	−	0.763248i	$-0.723603\pi$
$829$	−37.2058	−1.29221	−0.646106	+	0.763248i	$0.723603\pi$
$830$	−6.94995	−0.241236
$831$	−35.6836	−1.23785
$832$	−2.91490	−0.101056
$833$	−24.8855	−0.862230
$834$	70.7042	2.44829
$835$	30.2459	1.04670
$836$	2.22214	0.0768543
$837$	−148.921	−5.14746
$838$	−2.47696	−0.0855651
$839$	55.4985	1.91602	0.958011	−	0.286731i	$-0.0925685\pi$
$839$	55.4985	1.91602	0.958011	+	0.286731i	$0.0925685\pi$
$840$	−21.8495	−0.753879
$841$	2.65772	0.0916455
$842$	−1.84058	−0.0634307
$843$	74.8795	2.57899
$844$	2.83394	0.0975482
$845$	−17.4089	−0.598883
$846$	19.3860	0.666504
$847$	−10.6018	−0.364281
$848$	11.8631	0.407379
$849$	59.7982	2.05227
$850$	58.8080	2.01710
$851$	14.9268	0.511685
$852$	−25.6560	−0.878961
$853$	−48.2463	−1.65192	−0.825960	−	0.563728i	$-0.809367\pi$
$853$	−48.2463	−1.65192	−0.825960	+	0.563728i	$0.809367\pi$
$854$	17.9758	0.615121
$855$	33.6113	1.14948
$856$	−1.22521	−0.0418768
$857$	46.5353	1.58962	0.794808	−	0.606862i	$-0.207572\pi$
$857$	46.5353	1.58962	0.794808	+	0.606862i	$0.207572\pi$
$858$	21.2735	0.726266
$859$	−49.9280	−1.70352	−0.851761	−	0.523931i	$-0.824465\pi$
$859$	−49.9280	−1.70352	−0.851761	+	0.523931i	$0.824465\pi$
$860$	11.7599	0.401011
$861$	51.3855	1.75121
$862$	−32.9571	−1.12252
$863$	−18.1923	−0.619273	−0.309637	−	0.950855i	$-0.600207\pi$
$863$	−18.1923	−0.619273	−0.309637	+	0.950855i	$0.600207\pi$
$864$	−18.4079	−0.626250
$865$	−58.2705	−1.98126
$866$	16.7380	0.568779
$867$	−60.7950	−2.06471
$868$	13.5178	0.458824
$869$	−24.5036	−0.831229
$870$	−73.5743	−2.49440
$871$	8.93522	0.302758
$872$	6.61263	0.223932
$873$	−47.0680	−1.59301
$874$	−6.17430	−0.208849
$875$	31.9366	1.07965
$876$	−57.3631	−1.93812
$877$	21.9778	0.742136	0.371068	−	0.928606i	$-0.378992\pi$
$877$	21.9778	0.742136	0.371068	+	0.928606i	$0.378992\pi$
$878$	26.6471	0.899297
$879$	20.6156	0.695346
$880$	8.34068	0.281164
$881$	−24.3571	−0.820611	−0.410305	−	0.911948i	$-0.634578\pi$
$881$	−24.3571	−0.820611	−0.410305	+	0.911948i	$0.634578\pi$
$882$	−35.5241	−1.19616
$883$	−21.0077	−0.706964	−0.353482	−	0.935441i	$-0.615002\pi$
$883$	−21.0077	−0.706964	−0.353482	+	0.935441i	$0.615002\pi$
$884$	−17.2381	−0.579781
$885$	58.9918	1.98299
$886$	24.1801	0.812346
$887$	−14.7527	−0.495346	−0.247673	−	0.968844i	$-0.579666\pi$
$887$	−14.7527	−0.495346	−0.247673	+	0.968844i	$0.579666\pi$
$888$	8.42240	0.282637
$889$	−27.7115	−0.929415
$890$	−48.9284	−1.64008
$891$	79.7021	2.67012
$892$	17.9004	0.599349
$893$	2.36511	0.0791453
$894$	26.7374	0.894234
$895$	−11.5531	−0.386177
$896$	1.67092	0.0558214
$897$	−59.1093	−1.97360
$898$	10.9953	0.366919
$899$	45.5188	1.51814
$900$	83.9486	2.79829
$901$	70.1556	2.33722
$902$	−19.6156	−0.653127
$903$	−17.1939	−0.572176
$904$	1.88321	0.0626345
$905$	−44.0818	−1.46533
$906$	29.1691	0.969079
$907$	−0.738541	−0.0245228	−0.0122614	−	0.999925i	$-0.503903\pi$
$907$	−0.738541	−0.0245228	−0.0122614	+	0.999925i	$0.503903\pi$
$908$	−10.1415	−0.336558
$909$	130.618	4.33232
$910$	−18.8285	−0.624158
$911$	48.8007	1.61684	0.808419	−	0.588607i	$-0.200323\pi$
$911$	48.8007	1.61684	0.808419	+	0.588607i	$0.200323\pi$
$912$	−3.48382	−0.115361
$913$	−3.87891	−0.128373
$914$	34.3179	1.13514
$915$	−140.676	−4.65062
$916$	8.84925	0.292387
$917$	32.0445	1.05820
$918$	−108.861	−3.59293
$919$	19.8624	0.655199	0.327599	−	0.944817i	$-0.393760\pi$
$919$	19.8624	0.655199	0.327599	+	0.944817i	$0.393760\pi$
$920$	−23.1749	−0.764055
$921$	−51.5606	−1.69898
$922$	−5.41907	−0.178468
$923$	−22.1087	−0.727718
$924$	−12.1947	−0.401175
$925$	−24.7603	−0.814115
$926$	−12.8124	−0.421041
$927$	−35.2500	−1.15776
$928$	5.62652	0.184700
$929$	−11.5679	−0.379530	−0.189765	−	0.981830i	$-0.560773\pi$
$929$	−11.5679	−0.379530	−0.189765	+	0.981830i	$0.560773\pi$
$930$	−105.788	−3.46893
$931$	−4.33397	−0.142040
$932$	−13.0895	−0.428760
$933$	21.2024	0.694135
$934$	−16.8815	−0.552379
$935$	49.3250	1.61310
$936$	−24.6075	−0.804320
$937$	42.4226	1.38589	0.692943	−	0.720992i	$-0.256314\pi$
$937$	42.4226	1.38589	0.692943	+	0.720992i	$0.256314\pi$
$938$	−5.12195	−0.167238
$939$	−100.545	−3.28118
$940$	8.87731	0.289546
$941$	32.9620	1.07453	0.537266	−	0.843413i	$-0.319457\pi$
$941$	32.9620	1.07453	0.537266	+	0.843413i	$0.319457\pi$
$942$	20.8709	0.680012
$943$	54.5026	1.77485
$944$	−4.51133	−0.146831
$945$	−118.904	−3.86794
$946$	6.56347	0.213397
$947$	−56.4798	−1.83535	−0.917674	−	0.397335i	$-0.869935\pi$
$947$	−56.4798	−1.83535	−0.917674	+	0.397335i	$0.869935\pi$
$948$	38.4163	1.24770
$949$	−49.4319	−1.60463
$950$	10.2418	0.332288
$951$	114.387	3.70924
$952$	9.88144	0.320259
$953$	−22.7905	−0.738256	−0.369128	−	0.929379i	$-0.620344\pi$
$953$	−22.7905	−0.738256	−0.369128	+	0.929379i	$0.620344\pi$
$954$	100.147	3.24239
$955$	20.1526	0.652122
$956$	13.9662	0.451699
$957$	−41.0634	−1.32739
$958$	−26.5512	−0.857829
$959$	7.61676	0.245958
$960$	−13.0764	−0.422037
$961$	34.4489	1.11125
$962$	7.25789	0.234004
$963$	−10.3432	−0.333304
$964$	19.9722	0.643261
$965$	−12.4083	−0.399436
$966$	33.8834	1.09018
$967$	−38.5835	−1.24076	−0.620380	−	0.784301i	$-0.713022\pi$
$967$	−38.5835	−1.24076	−0.620380	+	0.784301i	$0.713022\pi$
$968$	−6.34489	−0.203932
$969$	−20.6026	−0.661851
$970$	−21.5536	−0.692044
$971$	7.03751	0.225845	0.112922	−	0.993604i	$-0.463979\pi$
$971$	7.03751	0.225845	0.112922	+	0.993604i	$0.463979\pi$
$972$	−69.7316	−2.23664
$973$	−34.9261	−1.11968
$974$	39.2615	1.25802
$975$	98.0494	3.14009
$976$	10.7581	0.344358
$977$	−13.1383	−0.420333	−0.210166	−	0.977666i	$-0.567401\pi$
$977$	−13.1383	−0.420333	−0.210166	+	0.977666i	$0.567401\pi$
$978$	62.1798	1.98829
$979$	−27.3080	−0.872766
$980$	−16.2673	−0.519641
$981$	55.8235	1.78231
$982$	−25.5084	−0.814006
$983$	−55.7644	−1.77861	−0.889304	−	0.457316i	$-0.848811\pi$
$983$	−55.7644	−1.77861	−0.889304	+	0.457316i	$0.848811\pi$
$984$	30.7529	0.980366
$985$	−81.2352	−2.58837
$986$	33.2740	1.05966
$987$	−12.9792	−0.413134
$988$	−3.00214	−0.0955106
$989$	−18.2369	−0.579899
$990$	70.4116	2.23783
$991$	57.0044	1.81080	0.905402	−	0.424555i	$-0.139569\pi$
$991$	57.0044	1.81080	0.905402	+	0.424555i	$0.139569\pi$
$992$	8.09005	0.256859
$993$	−33.0424	−1.04857
$994$	12.6734	0.401977
$995$	81.4676	2.58270
$996$	6.08128	0.192693
$997$	−37.0768	−1.17423	−0.587116	−	0.809503i	$-0.699737\pi$
$997$	−37.0768	−1.17423	−0.587116	+	0.809503i	$0.699737\pi$
$998$	3.34183	0.105784
$999$	45.8343	1.45013

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.1	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.1	✓	96	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.38260 q^{3} +1.00000 q^{4} +3.86577 q^{5} -3.38260 q^{6} +1.67092 q^{7} +1.00000 q^{8} +8.44195 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.38260 q^{3} +1.00000 q^{4} +3.86577 q^{5} -3.38260 q^{6} +1.67092 q^{7} +1.00000 q^{8} +8.44195 q^{9} +3.86577 q^{10} +2.15757 q^{11} -3.38260 q^{12} -2.91490 q^{13} +1.67092 q^{14} -13.0764 q^{15} +1.00000 q^{16} +5.91379 q^{17} +8.44195 q^{18} +1.02993 q^{19} +3.86577 q^{20} -5.65203 q^{21} +2.15757 q^{22} -5.99490 q^{23} -3.38260 q^{24} +9.94422 q^{25} -2.91490 q^{26} -18.4079 q^{27} +1.67092 q^{28} +5.62652 q^{29} -13.0764 q^{30} +8.09005 q^{31} +1.00000 q^{32} -7.29819 q^{33} +5.91379 q^{34} +6.45938 q^{35} +8.44195 q^{36} -2.48992 q^{37} +1.02993 q^{38} +9.85994 q^{39} +3.86577 q^{40} -9.09150 q^{41} -5.65203 q^{42} +3.04207 q^{43} +2.15757 q^{44} +32.6347 q^{45} -5.99490 q^{46} +2.29639 q^{47} -3.38260 q^{48} -4.20804 q^{49} +9.94422 q^{50} -20.0040 q^{51} -2.91490 q^{52} +11.8631 q^{53} -18.4079 q^{54} +8.34068 q^{55} +1.67092 q^{56} -3.48382 q^{57} +5.62652 q^{58} -4.51133 q^{59} -13.0764 q^{60} +10.7581 q^{61} +8.09005 q^{62} +14.1058 q^{63} +1.00000 q^{64} -11.2684 q^{65} -7.29819 q^{66} -3.06536 q^{67} +5.91379 q^{68} +20.2783 q^{69} +6.45938 q^{70} +7.58472 q^{71} +8.44195 q^{72} +16.9583 q^{73} -2.48992 q^{74} -33.6373 q^{75} +1.02993 q^{76} +3.60512 q^{77} +9.85994 q^{78} -11.3570 q^{79} +3.86577 q^{80} +36.9407 q^{81} -9.09150 q^{82} -1.79781 q^{83} -5.65203 q^{84} +22.8614 q^{85} +3.04207 q^{86} -19.0322 q^{87} +2.15757 q^{88} -12.6568 q^{89} +32.6347 q^{90} -4.87056 q^{91} -5.99490 q^{92} -27.3654 q^{93} +2.29639 q^{94} +3.98146 q^{95} -3.38260 q^{96} -5.57549 q^{97} -4.20804 q^{98} +18.2141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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