LMFDB - Embedded newform 8042.2.a.a.1.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, 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("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$1$
Dimension:	$67$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.42
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.606281 q^{3} +1.00000 q^{4} +2.83620 q^{5} +0.606281 q^{6} -0.506576 q^{7} +1.00000 q^{8} -2.63242 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.606281 q^{3} +1.00000 q^{4} +2.83620 q^{5} +0.606281 q^{6} -0.506576 q^{7} +1.00000 q^{8} -2.63242 q^{9} +2.83620 q^{10} -2.31628 q^{11} +0.606281 q^{12} -5.13920 q^{13} -0.506576 q^{14} +1.71953 q^{15} +1.00000 q^{16} +2.32259 q^{17} -2.63242 q^{18} +1.99379 q^{19} +2.83620 q^{20} -0.307128 q^{21} -2.31628 q^{22} -5.75059 q^{23} +0.606281 q^{24} +3.04402 q^{25} -5.13920 q^{26} -3.41483 q^{27} -0.506576 q^{28} -2.59333 q^{29} +1.71953 q^{30} +2.87237 q^{31} +1.00000 q^{32} -1.40431 q^{33} +2.32259 q^{34} -1.43675 q^{35} -2.63242 q^{36} -11.5175 q^{37} +1.99379 q^{38} -3.11580 q^{39} +2.83620 q^{40} -4.91187 q^{41} -0.307128 q^{42} -9.07959 q^{43} -2.31628 q^{44} -7.46607 q^{45} -5.75059 q^{46} +7.72806 q^{47} +0.606281 q^{48} -6.74338 q^{49} +3.04402 q^{50} +1.40814 q^{51} -5.13920 q^{52} +1.33235 q^{53} -3.41483 q^{54} -6.56942 q^{55} -0.506576 q^{56} +1.20880 q^{57} -2.59333 q^{58} +8.08349 q^{59} +1.71953 q^{60} +9.91408 q^{61} +2.87237 q^{62} +1.33352 q^{63} +1.00000 q^{64} -14.5758 q^{65} -1.40431 q^{66} -8.87706 q^{67} +2.32259 q^{68} -3.48647 q^{69} -1.43675 q^{70} -8.34287 q^{71} -2.63242 q^{72} -0.534805 q^{73} -11.5175 q^{74} +1.84553 q^{75} +1.99379 q^{76} +1.17337 q^{77} -3.11580 q^{78} +11.1366 q^{79} +2.83620 q^{80} +5.82692 q^{81} -4.91187 q^{82} -6.89561 q^{83} -0.307128 q^{84} +6.58732 q^{85} -9.07959 q^{86} -1.57229 q^{87} -2.31628 q^{88} -9.04322 q^{89} -7.46607 q^{90} +2.60340 q^{91} -5.75059 q^{92} +1.74147 q^{93} +7.72806 q^{94} +5.65478 q^{95} +0.606281 q^{96} +9.89069 q^{97} -6.74338 q^{98} +6.09742 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) $ 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * 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
$3$	0.606281	0.350037	0.175018	−	0.984565i	$-0.444002\pi$
$3$	0.606281	0.350037	0.175018	+	0.984565i	$0.444002\pi$
$4$	1.00000	0.500000
$5$	2.83620	1.26839	0.634193	−	0.773175i	$-0.281332\pi$
$5$	2.83620	1.26839	0.634193	+	0.773175i	$0.281332\pi$
$6$	0.606281	0.247513
$7$	−0.506576	−0.191468	−0.0957339	−	0.995407i	$-0.530520\pi$
$7$	−0.506576	−0.191468	−0.0957339	+	0.995407i	$0.530520\pi$
$8$	1.00000	0.353553
$9$	−2.63242	−0.877474
$10$	2.83620	0.896884
$11$	−2.31628	−0.698384	−0.349192	−	0.937051i	$-0.613544\pi$
$11$	−2.31628	−0.698384	−0.349192	+	0.937051i	$0.613544\pi$
$12$	0.606281	0.175018
$13$	−5.13920	−1.42536	−0.712679	−	0.701490i	$-0.752518\pi$
$13$	−5.13920	−1.42536	−0.712679	+	0.701490i	$0.752518\pi$
$14$	−0.506576	−0.135388
$15$	1.71953	0.443981
$16$	1.00000	0.250000
$17$	2.32259	0.563311	0.281655	−	0.959516i	$-0.409117\pi$
$17$	2.32259	0.563311	0.281655	+	0.959516i	$0.409117\pi$
$18$	−2.63242	−0.620468
$19$	1.99379	0.457406	0.228703	−	0.973496i	$-0.426551\pi$
$19$	1.99379	0.457406	0.228703	+	0.973496i	$0.426551\pi$
$20$	2.83620	0.634193
$21$	−0.307128	−0.0670207
$22$	−2.31628	−0.493832
$23$	−5.75059	−1.19908	−0.599541	−	0.800344i	$-0.704650\pi$
$23$	−5.75059	−1.19908	−0.599541	+	0.800344i	$0.704650\pi$
$24$	0.606281	0.123757
$25$	3.04402	0.608804
$26$	−5.13920	−1.00788
$27$	−3.41483	−0.657185
$28$	−0.506576	−0.0957339
$29$	−2.59333	−0.481569	−0.240784	−	0.970579i	$-0.577405\pi$
$29$	−2.59333	−0.481569	−0.240784	+	0.970579i	$0.577405\pi$
$30$	1.71953	0.313942
$31$	2.87237	0.515894	0.257947	−	0.966159i	$-0.416954\pi$
$31$	2.87237	0.515894	0.257947	+	0.966159i	$0.416954\pi$
$32$	1.00000	0.176777
$33$	−1.40431	−0.244460
$34$	2.32259	0.398321
$35$	−1.43675	−0.242855
$36$	−2.63242	−0.438737
$37$	−11.5175	−1.89347	−0.946734	−	0.322017i	$-0.895639\pi$
$37$	−11.5175	−1.89347	−0.946734	+	0.322017i	$0.895639\pi$
$38$	1.99379	0.323435
$39$	−3.11580	−0.498927
$40$	2.83620	0.448442
$41$	−4.91187	−0.767106	−0.383553	−	0.923519i	$-0.625300\pi$
$41$	−4.91187	−0.767106	−0.383553	+	0.923519i	$0.625300\pi$
$42$	−0.307128	−0.0473908
$43$	−9.07959	−1.38463	−0.692313	−	0.721598i	$-0.743408\pi$
$43$	−9.07959	−1.38463	−0.692313	+	0.721598i	$0.743408\pi$
$44$	−2.31628	−0.349192
$45$	−7.46607	−1.11298
$46$	−5.75059	−0.847878
$47$	7.72806	1.12725	0.563627	−	0.826030i	$-0.309406\pi$
$47$	7.72806	1.12725	0.563627	+	0.826030i	$0.309406\pi$
$48$	0.606281	0.0875091
$49$	−6.74338	−0.963340
$50$	3.04402	0.430489
$51$	1.40814	0.197179
$52$	−5.13920	−0.712679
$53$	1.33235	0.183012	0.0915059	−	0.995805i	$-0.470832\pi$
$53$	1.33235	0.183012	0.0915059	+	0.995805i	$0.470832\pi$
$54$	−3.41483	−0.464700
$55$	−6.56942	−0.885820
$56$	−0.506576	−0.0676941
$57$	1.20880	0.160109
$58$	−2.59333	−0.340521
$59$	8.08349	1.05238	0.526191	−	0.850367i	$-0.323620\pi$
$59$	8.08349	1.05238	0.526191	+	0.850367i	$0.323620\pi$
$60$	1.71953	0.221991
$61$	9.91408	1.26937	0.634684	−	0.772772i	$-0.281130\pi$
$61$	9.91408	1.26937	0.634684	+	0.772772i	$0.281130\pi$
$62$	2.87237	0.364792
$63$	1.33352	0.168008
$64$	1.00000	0.125000
$65$	−14.5758	−1.80790
$66$	−1.40431	−0.172859
$67$	−8.87706	−1.08451	−0.542253	−	0.840215i	$-0.682429\pi$
$67$	−8.87706	−1.08451	−0.542253	+	0.840215i	$0.682429\pi$
$68$	2.32259	0.281655
$69$	−3.48647	−0.419722
$70$	−1.43675	−0.171724
$71$	−8.34287	−0.990117	−0.495058	−	0.868860i	$-0.664853\pi$
$71$	−8.34287	−0.990117	−0.495058	+	0.868860i	$0.664853\pi$
$72$	−2.63242	−0.310234
$73$	−0.534805	−0.0625942	−0.0312971	−	0.999510i	$-0.509964\pi$
$73$	−0.534805	−0.0625942	−0.0312971	+	0.999510i	$0.509964\pi$
$74$	−11.5175	−1.33888
$75$	1.84553	0.213103
$76$	1.99379	0.228703
$77$	1.17337	0.133718
$78$	−3.11580	−0.352795
$79$	11.1366	1.25296	0.626481	−	0.779437i	$-0.284495\pi$
$79$	11.1366	1.25296	0.626481	+	0.779437i	$0.284495\pi$
$80$	2.83620	0.317097
$81$	5.82692	0.647436
$82$	−4.91187	−0.542426
$83$	−6.89561	−0.756891	−0.378446	−	0.925623i	$-0.623541\pi$
$83$	−6.89561	−0.756891	−0.378446	+	0.925623i	$0.623541\pi$
$84$	−0.307128	−0.0335104
$85$	6.58732	0.714496
$86$	−9.07959	−0.979078
$87$	−1.57229	−0.168567
$88$	−2.31628	−0.246916
$89$	−9.04322	−0.958579	−0.479290	−	0.877657i	$-0.659106\pi$
$89$	−9.04322	−0.958579	−0.479290	+	0.877657i	$0.659106\pi$
$90$	−7.46607	−0.786993
$91$	2.60340	0.272910
$92$	−5.75059	−0.599541
$93$	1.74147	0.180582
$94$	7.72806	0.797089
$95$	5.65478	0.580168
$96$	0.606281	0.0618783
$97$	9.89069	1.00425	0.502123	−	0.864796i	$-0.332552\pi$
$97$	9.89069	1.00425	0.502123	+	0.864796i	$0.332552\pi$
$98$	−6.74338	−0.681184
$99$	6.09742	0.612814
$100$	3.04402	0.304402
$101$	16.7639	1.66807	0.834036	−	0.551709i	$-0.186024\pi$
$101$	16.7639	1.66807	0.834036	+	0.551709i	$0.186024\pi$
$102$	1.40814	0.139427
$103$	−11.8307	−1.16571	−0.582857	−	0.812574i	$-0.698065\pi$
$103$	−11.8307	−1.16571	−0.582857	+	0.812574i	$0.698065\pi$
$104$	−5.13920	−0.503940
$105$	−0.871074	−0.0850082
$106$	1.33235	0.129409
$107$	−14.9779	−1.44796	−0.723982	−	0.689819i	$-0.757690\pi$
$107$	−14.9779	−1.44796	−0.723982	+	0.689819i	$0.757690\pi$
$108$	−3.41483	−0.328592
$109$	7.55838	0.723962	0.361981	−	0.932186i	$-0.382101\pi$
$109$	7.55838	0.723962	0.361981	+	0.932186i	$0.382101\pi$
$110$	−6.56942	−0.626370
$111$	−6.98285	−0.662783
$112$	−0.506576	−0.0478670
$113$	0.621916	0.0585049	0.0292524	−	0.999572i	$-0.490687\pi$
$113$	0.621916	0.0585049	0.0292524	+	0.999572i	$0.490687\pi$
$114$	1.20880	0.113214
$115$	−16.3098	−1.52090
$116$	−2.59333	−0.240784
$117$	13.5286	1.25072
$118$	8.08349	0.744146
$119$	−1.17657	−0.107856
$120$	1.71953	0.156971
$121$	−5.63486	−0.512260
$122$	9.91408	0.897579
$123$	−2.97798	−0.268515
$124$	2.87237	0.257947
$125$	−5.54755	−0.496188
$126$	1.33352	0.118800
$127$	4.21630	0.374137	0.187068	−	0.982347i	$-0.440101\pi$
$127$	4.21630	0.374137	0.187068	+	0.982347i	$0.440101\pi$
$128$	1.00000	0.0883883
$129$	−5.50479	−0.484669
$130$	−14.5758	−1.27838
$131$	−20.3847	−1.78102	−0.890510	−	0.454965i	$-0.849652\pi$
$131$	−20.3847	−1.78102	−0.890510	+	0.454965i	$0.849652\pi$
$132$	−1.40431	−0.122230
$133$	−1.01001	−0.0875786
$134$	−8.87706	−0.766861
$135$	−9.68514	−0.833564
$136$	2.32259	0.199160
$137$	15.4768	1.32228	0.661138	−	0.750264i	$-0.270074\pi$
$137$	15.4768	1.32228	0.661138	+	0.750264i	$0.270074\pi$
$138$	−3.48647	−0.296788
$139$	−12.5978	−1.06853	−0.534265	−	0.845317i	$-0.679412\pi$
$139$	−12.5978	−1.06853	−0.534265	+	0.845317i	$0.679412\pi$
$140$	−1.43675	−0.121428
$141$	4.68538	0.394580
$142$	−8.34287	−0.700118
$143$	11.9038	0.995447
$144$	−2.63242	−0.219369
$145$	−7.35519	−0.610815
$146$	−0.534805	−0.0442608
$147$	−4.08838	−0.337204
$148$	−11.5175	−0.946734
$149$	−21.9706	−1.79990	−0.899950	−	0.435992i	$-0.856398\pi$
$149$	−21.9706	−1.79990	−0.899950	+	0.435992i	$0.856398\pi$
$150$	1.84553	0.150687
$151$	6.14178	0.499811	0.249906	−	0.968270i	$-0.419600\pi$
$151$	6.14178	0.499811	0.249906	+	0.968270i	$0.419600\pi$
$152$	1.99379	0.161718
$153$	−6.11404	−0.494291
$154$	1.17337	0.0945529
$155$	8.14662	0.654352
$156$	−3.11580	−0.249464
$157$	−3.24619	−0.259074	−0.129537	−	0.991575i	$-0.541349\pi$
$157$	−3.24619	−0.259074	−0.129537	+	0.991575i	$0.541349\pi$
$158$	11.1366	0.885978
$159$	0.807776	0.0640608
$160$	2.83620	0.224221
$161$	2.91311	0.229585
$162$	5.82692	0.457806
$163$	8.00402	0.626923	0.313462	−	0.949601i	$-0.398511\pi$
$163$	8.00402	0.626923	0.313462	+	0.949601i	$0.398511\pi$
$164$	−4.91187	−0.383553
$165$	−3.98291	−0.310070
$166$	−6.89561	−0.535203
$167$	−7.06916	−0.547028	−0.273514	−	0.961868i	$-0.588186\pi$
$167$	−7.06916	−0.547028	−0.273514	+	0.961868i	$0.588186\pi$
$168$	−0.307128	−0.0236954
$169$	13.4114	1.03165
$170$	6.58732	0.505225
$171$	−5.24849	−0.401362
$172$	−9.07959	−0.692313
$173$	−2.74118	−0.208408	−0.104204	−	0.994556i	$-0.533229\pi$
$173$	−2.74118	−0.208408	−0.104204	+	0.994556i	$0.533229\pi$
$174$	−1.57229	−0.119195
$175$	−1.54203	−0.116566
$176$	−2.31628	−0.174596
$177$	4.90087	0.368372
$178$	−9.04322	−0.677818
$179$	8.44117	0.630923	0.315461	−	0.948938i	$-0.397841\pi$
$179$	8.44117	0.630923	0.315461	+	0.948938i	$0.397841\pi$
$180$	−7.46607	−0.556488
$181$	22.2468	1.65359	0.826796	−	0.562502i	$-0.190161\pi$
$181$	22.2468	1.65359	0.826796	+	0.562502i	$0.190161\pi$
$182$	2.60340	0.192977
$183$	6.01072	0.444325
$184$	−5.75059	−0.423939
$185$	−32.6659	−2.40165
$186$	1.74147	0.127690
$187$	−5.37976	−0.393407
$188$	7.72806	0.563627
$189$	1.72987	0.125830
$190$	5.65478	0.410241
$191$	−2.84506	−0.205861	−0.102931	−	0.994689i	$-0.532822\pi$
$191$	−2.84506	−0.205861	−0.102931	+	0.994689i	$0.532822\pi$
$192$	0.606281	0.0437546
$193$	−14.8685	−1.07025	−0.535127	−	0.844771i	$-0.679736\pi$
$193$	−14.8685	−1.07025	−0.535127	+	0.844771i	$0.679736\pi$
$194$	9.89069	0.710110
$195$	−8.83703	−0.632833
$196$	−6.74338	−0.481670
$197$	7.31057	0.520856	0.260428	−	0.965493i	$-0.416136\pi$
$197$	7.31057	0.520856	0.260428	+	0.965493i	$0.416136\pi$
$198$	6.09742	0.433325
$199$	−3.44497	−0.244208	−0.122104	−	0.992517i	$-0.538964\pi$
$199$	−3.44497	−0.244208	−0.122104	+	0.992517i	$0.538964\pi$
$200$	3.04402	0.215245
$201$	−5.38199	−0.379617
$202$	16.7639	1.17951
$203$	1.31372	0.0922049
$204$	1.40814	0.0985897
$205$	−13.9310	−0.972987
$206$	−11.8307	−0.824285
$207$	15.1380	1.05216
$208$	−5.13920	−0.356340
$209$	−4.61816	−0.319445
$210$	−0.871074	−0.0601098
$211$	21.5727	1.48513	0.742563	−	0.669777i	$-0.233610\pi$
$211$	21.5727	1.48513	0.742563	+	0.669777i	$0.233610\pi$
$212$	1.33235	0.0915059
$213$	−5.05813	−0.346577
$214$	−14.9779	−1.02387
$215$	−25.7515	−1.75624
$216$	−3.41483	−0.232350
$217$	−1.45508	−0.0987770
$218$	7.55838	0.511918
$219$	−0.324242	−0.0219103
$220$	−6.56942	−0.442910
$221$	−11.9363	−0.802920
$222$	−6.98285	−0.468658
$223$	−24.3866	−1.63304	−0.816522	−	0.577314i	$-0.804101\pi$
$223$	−24.3866	−1.63304	−0.816522	+	0.577314i	$0.804101\pi$
$224$	−0.506576	−0.0338470
$225$	−8.01314	−0.534210
$226$	0.621916	0.0413692
$227$	−28.0437	−1.86132	−0.930662	−	0.365879i	$-0.880768\pi$
$227$	−28.0437	−1.86132	−0.930662	+	0.365879i	$0.880768\pi$
$228$	1.20880	0.0800544
$229$	−7.69372	−0.508415	−0.254208	−	0.967150i	$-0.581815\pi$
$229$	−7.69372	−0.508415	−0.254208	+	0.967150i	$0.581815\pi$
$230$	−16.3098	−1.07544
$231$	0.711393	0.0468062
$232$	−2.59333	−0.170260
$233$	−3.68905	−0.241678	−0.120839	−	0.992672i	$-0.538558\pi$
$233$	−3.68905	−0.241678	−0.120839	+	0.992672i	$0.538558\pi$
$234$	13.5286	0.884389
$235$	21.9183	1.42979
$236$	8.08349	0.526191
$237$	6.75189	0.438582
$238$	−1.17657	−0.0762656
$239$	14.7129	0.951700	0.475850	−	0.879526i	$-0.342141\pi$
$239$	14.7129	0.951700	0.475850	+	0.879526i	$0.342141\pi$
$240$	1.71953	0.110995
$241$	2.19480	0.141380	0.0706899	−	0.997498i	$-0.477480\pi$
$241$	2.19480	0.141380	0.0706899	+	0.997498i	$0.477480\pi$
$242$	−5.63486	−0.362223
$243$	13.7772	0.883811
$244$	9.91408	0.634684
$245$	−19.1256	−1.22189
$246$	−2.97798	−0.189869
$247$	−10.2465	−0.651968
$248$	2.87237	0.182396
$249$	−4.18068	−0.264940
$250$	−5.54755	−0.350858
$251$	27.6709	1.74657	0.873287	−	0.487206i	$-0.161984\pi$
$251$	27.6709	1.74657	0.873287	+	0.487206i	$0.161984\pi$
$252$	1.33352	0.0840041
$253$	13.3200	0.837419
$254$	4.21630	0.264555
$255$	3.99377	0.250100
$256$	1.00000	0.0625000
$257$	−19.2990	−1.20384	−0.601920	−	0.798557i	$-0.705597\pi$
$257$	−19.2990	−1.20384	−0.601920	+	0.798557i	$0.705597\pi$
$258$	−5.50479	−0.342713
$259$	5.83450	0.362538
$260$	−14.5758	−0.903952
$261$	6.82674	0.422564
$262$	−20.3847	−1.25937
$263$	22.0731	1.36109	0.680544	−	0.732707i	$-0.261743\pi$
$263$	22.0731	1.36109	0.680544	+	0.732707i	$0.261743\pi$
$264$	−1.40431	−0.0864296
$265$	3.77880	0.232130
$266$	−1.01001	−0.0619274
$267$	−5.48273	−0.335538
$268$	−8.87706	−0.542253
$269$	13.3919	0.816518	0.408259	−	0.912866i	$-0.366136\pi$
$269$	13.3919	0.816518	0.408259	+	0.912866i	$0.366136\pi$
$270$	−9.68514	−0.589419
$271$	11.2432	0.682978	0.341489	−	0.939886i	$-0.389069\pi$
$271$	11.2432	0.682978	0.341489	+	0.939886i	$0.389069\pi$
$272$	2.32259	0.140828
$273$	1.57839	0.0955285
$274$	15.4768	0.934990
$275$	−7.05079	−0.425179
$276$	−3.48647	−0.209861
$277$	−7.38661	−0.443818	−0.221909	−	0.975067i	$-0.571229\pi$
$277$	−7.38661	−0.443818	−0.221909	+	0.975067i	$0.571229\pi$
$278$	−12.5978	−0.755565
$279$	−7.56130	−0.452683
$280$	−1.43675	−0.0858622
$281$	26.4726	1.57922	0.789610	−	0.613609i	$-0.210283\pi$
$281$	26.4726	1.57922	0.789610	+	0.613609i	$0.210283\pi$
$282$	4.68538	0.279010
$283$	21.8382	1.29815	0.649073	−	0.760726i	$-0.275157\pi$
$283$	21.8382	1.29815	0.649073	+	0.760726i	$0.275157\pi$
$284$	−8.34287	−0.495058
$285$	3.42838	0.203080
$286$	11.9038	0.703888
$287$	2.48824	0.146876
$288$	−2.63242	−0.155117
$289$	−11.6056	−0.682681
$290$	−7.35519	−0.431912
$291$	5.99653	0.351523
$292$	−0.534805	−0.0312971
$293$	−17.2723	−1.00906	−0.504528	−	0.863395i	$-0.668334\pi$
$293$	−17.2723	−1.00906	−0.504528	+	0.863395i	$0.668334\pi$
$294$	−4.08838	−0.238439
$295$	22.9264	1.33483
$296$	−11.5175	−0.669442
$297$	7.90970	0.458967
$298$	−21.9706	−1.27272
$299$	29.5535	1.70912
$300$	1.84553	0.106552
$301$	4.59951	0.265111
$302$	6.14178	0.353420
$303$	10.1636	0.583886
$304$	1.99379	0.114352
$305$	28.1183	1.61005
$306$	−6.11404	−0.349516
$307$	15.4679	0.882802	0.441401	−	0.897310i	$-0.354482\pi$
$307$	15.4679	0.882802	0.441401	+	0.897310i	$0.354482\pi$
$308$	1.17337	0.0668590
$309$	−7.17274	−0.408043
$310$	8.14662	0.462697
$311$	−20.4803	−1.16133	−0.580664	−	0.814143i	$-0.697207\pi$
$311$	−20.4803	−1.16133	−0.580664	+	0.814143i	$0.697207\pi$
$312$	−3.11580	−0.176398
$313$	−30.8101	−1.74149	−0.870746	−	0.491733i	$-0.836364\pi$
$313$	−30.8101	−1.74149	−0.870746	+	0.491733i	$0.836364\pi$
$314$	−3.24619	−0.183193
$315$	3.78213	0.213099
$316$	11.1366	0.626481
$317$	28.3244	1.59086	0.795428	−	0.606048i	$-0.207246\pi$
$317$	28.3244	1.59086	0.795428	+	0.606048i	$0.207246\pi$
$318$	0.807776	0.0452978
$319$	6.00687	0.336320
$320$	2.83620	0.158548
$321$	−9.08079	−0.506840
$322$	2.91311	0.162341
$323$	4.63075	0.257662
$324$	5.82692	0.323718
$325$	−15.6438	−0.867763
$326$	8.00402	0.443302
$327$	4.58250	0.253413
$328$	−4.91187	−0.271213
$329$	−3.91485	−0.215833
$330$	−3.98291	−0.219252
$331$	19.7108	1.08341	0.541703	−	0.840570i	$-0.317780\pi$
$331$	19.7108	1.08341	0.541703	+	0.840570i	$0.317780\pi$
$332$	−6.89561	−0.378446
$333$	30.3190	1.66147
$334$	−7.06916	−0.386807
$335$	−25.1771	−1.37557
$336$	−0.307128	−0.0167552
$337$	18.9578	1.03270	0.516348	−	0.856379i	$-0.327291\pi$
$337$	18.9578	1.03270	0.516348	+	0.856379i	$0.327291\pi$
$338$	13.4114	0.729484
$339$	0.377056	0.0204789
$340$	6.58732	0.357248
$341$	−6.65321	−0.360292
$342$	−5.24849	−0.283806
$343$	6.96207	0.375916
$344$	−9.07959	−0.489539
$345$	−9.88833	−0.532370
$346$	−2.74118	−0.147367
$347$	21.3952	1.14855	0.574277	−	0.818661i	$-0.305283\pi$
$347$	21.3952	1.14855	0.574277	+	0.818661i	$0.305283\pi$
$348$	−1.57229	−0.0842834
$349$	−14.9750	−0.801591	−0.400796	−	0.916167i	$-0.631266\pi$
$349$	−14.9750	−0.801591	−0.400796	+	0.916167i	$0.631266\pi$
$350$	−1.54203	−0.0824248
$351$	17.5495	0.936724
$352$	−2.31628	−0.123458
$353$	−30.1792	−1.60628	−0.803138	−	0.595794i	$-0.796838\pi$
$353$	−30.1792	−1.60628	−0.803138	+	0.595794i	$0.796838\pi$
$354$	4.90087	0.260478
$355$	−23.6620	−1.25585
$356$	−9.04322	−0.479290
$357$	−0.713331	−0.0377535
$358$	8.44117	0.446130
$359$	2.53928	0.134018	0.0670090	−	0.997752i	$-0.478654\pi$
$359$	2.53928	0.134018	0.0670090	+	0.997752i	$0.478654\pi$
$360$	−7.46607	−0.393497
$361$	−15.0248	−0.790780
$362$	22.2468	1.16927
$363$	−3.41631	−0.179310
$364$	2.60340	0.136455
$365$	−1.51681	−0.0793937
$366$	6.01072	0.314185
$367$	−34.2313	−1.78686	−0.893429	−	0.449203i	$-0.851708\pi$
$367$	−34.2313	−1.78686	−0.893429	+	0.449203i	$0.851708\pi$
$368$	−5.75059	−0.299770
$369$	12.9301	0.673116
$370$	−32.6659	−1.69822
$371$	−0.674935	−0.0350409
$372$	1.74147	0.0902908
$373$	−11.0437	−0.571819	−0.285910	−	0.958257i	$-0.592296\pi$
$373$	−11.0437	−0.571819	−0.285910	+	0.958257i	$0.592296\pi$
$374$	−5.37976	−0.278181
$375$	−3.36338	−0.173684
$376$	7.72806	0.398544
$377$	13.3276	0.686408
$378$	1.72987	0.0889750
$379$	−7.30810	−0.375392	−0.187696	−	0.982227i	$-0.560102\pi$
$379$	−7.30810	−0.375392	−0.187696	+	0.982227i	$0.560102\pi$
$380$	5.65478	0.290084
$381$	2.55627	0.130961
$382$	−2.84506	−0.145566
$383$	24.7122	1.26273	0.631366	−	0.775485i	$-0.282494\pi$
$383$	24.7122	1.26273	0.631366	+	0.775485i	$0.282494\pi$
$384$	0.606281	0.0309391
$385$	3.32791	0.169606
$386$	−14.8685	−0.756784
$387$	23.9013	1.21497
$388$	9.89069	0.502123
$389$	11.2213	0.568943	0.284471	−	0.958685i	$-0.408182\pi$
$389$	11.2213	0.568943	0.284471	+	0.958685i	$0.408182\pi$
$390$	−8.83703	−0.447480
$391$	−13.3563	−0.675455
$392$	−6.74338	−0.340592
$393$	−12.3589	−0.623422
$394$	7.31057	0.368301
$395$	31.5855	1.58924
$396$	6.09742	0.306407
$397$	−35.8478	−1.79915	−0.899576	−	0.436765i	$-0.856124\pi$
$397$	−35.8478	−1.79915	−0.899576	+	0.436765i	$0.856124\pi$
$398$	−3.44497	−0.172681
$399$	−0.612347	−0.0306557
$400$	3.04402	0.152201
$401$	29.5883	1.47757	0.738784	−	0.673942i	$-0.235400\pi$
$401$	29.5883	1.47757	0.738784	+	0.673942i	$0.235400\pi$
$402$	−5.38199	−0.268429
$403$	−14.7617	−0.735333
$404$	16.7639	0.834036
$405$	16.5263	0.821199
$406$	1.31372	0.0651987
$407$	26.6778	1.32237
$408$	1.40814	0.0697134
$409$	35.8856	1.77443	0.887214	−	0.461359i	$-0.152638\pi$
$409$	35.8856	1.77443	0.887214	+	0.461359i	$0.152638\pi$
$410$	−13.9310	−0.688005
$411$	9.38331	0.462845
$412$	−11.8307	−0.582857
$413$	−4.09490	−0.201497
$414$	15.1380	0.743992
$415$	−19.5573	−0.960031
$416$	−5.13920	−0.251970
$417$	−7.63780	−0.374025
$418$	−4.61816	−0.225882
$419$	6.58220	0.321562	0.160781	−	0.986990i	$-0.448599\pi$
$419$	6.58220	0.321562	0.160781	+	0.986990i	$0.448599\pi$
$420$	−0.871074	−0.0425041
$421$	27.4147	1.33611	0.668055	−	0.744112i	$-0.267127\pi$
$421$	27.4147	1.33611	0.668055	+	0.744112i	$0.267127\pi$
$422$	21.5727	1.05014
$423$	−20.3435	−0.989136
$424$	1.33235	0.0647044
$425$	7.07000	0.342946
$426$	−5.05813	−0.245067
$427$	−5.02224	−0.243043
$428$	−14.9779	−0.723982
$429$	7.21706	0.348443
$430$	−25.7515	−1.24185
$431$	−4.38215	−0.211081	−0.105540	−	0.994415i	$-0.533657\pi$
$431$	−4.38215	−0.211081	−0.105540	+	0.994415i	$0.533657\pi$
$432$	−3.41483	−0.164296
$433$	−5.82602	−0.279980	−0.139990	−	0.990153i	$-0.544707\pi$
$433$	−5.82602	−0.279980	−0.139990	+	0.990153i	$0.544707\pi$
$434$	−1.45508	−0.0698459
$435$	−4.45931	−0.213808
$436$	7.55838	0.361981
$437$	−11.4655	−0.548467
$438$	−0.324242	−0.0154929
$439$	21.9844	1.04926	0.524629	−	0.851331i	$-0.324204\pi$
$439$	21.9844	1.04926	0.524629	+	0.851331i	$0.324204\pi$
$440$	−6.56942	−0.313185
$441$	17.7514	0.845306
$442$	−11.9363	−0.567750
$443$	−3.95742	−0.188023	−0.0940113	−	0.995571i	$-0.529969\pi$
$443$	−3.95742	−0.188023	−0.0940113	+	0.995571i	$0.529969\pi$
$444$	−6.98285	−0.331391
$445$	−25.6484	−1.21585
$446$	−24.3866	−1.15474
$447$	−13.3204	−0.630031
$448$	−0.506576	−0.0239335
$449$	−26.1503	−1.23411	−0.617054	−	0.786921i	$-0.711674\pi$
$449$	−26.1503	−1.23411	−0.617054	+	0.786921i	$0.711674\pi$
$450$	−8.01314	−0.377743
$451$	11.3773	0.535734
$452$	0.621916	0.0292524
$453$	3.72365	0.174952
$454$	−28.0437	−1.31616
$455$	7.38375	0.346156
$456$	1.20880	0.0566070
$457$	−31.5086	−1.47391	−0.736956	−	0.675941i	$-0.763737\pi$
$457$	−31.5086	−1.47391	−0.736956	+	0.675941i	$0.763737\pi$
$458$	−7.69372	−0.359504
$459$	−7.93125	−0.370199
$460$	−16.3098	−0.760449
$461$	−34.7480	−1.61838	−0.809189	−	0.587549i	$-0.800093\pi$
$461$	−34.7480	−1.61838	−0.809189	+	0.587549i	$0.800093\pi$
$462$	0.711393	0.0330970
$463$	31.5590	1.46667	0.733335	−	0.679868i	$-0.237963\pi$
$463$	31.5590	1.46667	0.733335	+	0.679868i	$0.237963\pi$
$464$	−2.59333	−0.120392
$465$	4.93914	0.229047
$466$	−3.68905	−0.170892
$467$	27.9018	1.29114	0.645571	−	0.763700i	$-0.276619\pi$
$467$	27.9018	1.29114	0.645571	+	0.763700i	$0.276619\pi$
$468$	13.5286	0.625358
$469$	4.49691	0.207648
$470$	21.9183	1.01102
$471$	−1.96810	−0.0906854
$472$	8.08349	0.372073
$473$	21.0309	0.967000
$474$	6.75189	0.310125
$475$	6.06912	0.278471
$476$	−1.17657	−0.0539279
$477$	−3.50730	−0.160588
$478$	14.7129	0.672953
$479$	−11.6765	−0.533511	−0.266755	−	0.963764i	$-0.585952\pi$
$479$	−11.6765	−0.533511	−0.266755	+	0.963764i	$0.585952\pi$
$480$	1.71953	0.0784856
$481$	59.1908	2.69887
$482$	2.19480	0.0999706
$483$	1.76616	0.0803633
$484$	−5.63486	−0.256130
$485$	28.0519	1.27377
$486$	13.7772	0.624949
$487$	3.85271	0.174583	0.0872916	−	0.996183i	$-0.472179\pi$
$487$	3.85271	0.174583	0.0872916	+	0.996183i	$0.472179\pi$
$488$	9.91408	0.448789
$489$	4.85269	0.219446
$490$	−19.1256	−0.864005
$491$	−23.0154	−1.03867	−0.519334	−	0.854571i	$-0.673820\pi$
$491$	−23.0154	−1.03867	−0.519334	+	0.854571i	$0.673820\pi$
$492$	−2.97798	−0.134258
$493$	−6.02324	−0.271273
$494$	−10.2465	−0.461011
$495$	17.2935	0.777285
$496$	2.87237	0.128973
$497$	4.22630	0.189575
$498$	−4.18068	−0.187341
$499$	4.68051	0.209529	0.104764	−	0.994497i	$-0.466591\pi$
$499$	4.68051	0.209529	0.104764	+	0.994497i	$0.466591\pi$
$500$	−5.54755	−0.248094
$501$	−4.28590	−0.191480
$502$	27.6709	1.23501
$503$	16.6960	0.744436	0.372218	−	0.928145i	$-0.378597\pi$
$503$	16.6960	0.744436	0.372218	+	0.928145i	$0.378597\pi$
$504$	1.33352	0.0593998
$505$	47.5458	2.11576
$506$	13.3200	0.592145
$507$	8.13108	0.361114
$508$	4.21630	0.187068
$509$	15.9856	0.708549	0.354274	−	0.935142i	$-0.384728\pi$
$509$	15.9856	0.708549	0.354274	+	0.935142i	$0.384728\pi$
$510$	3.99377	0.176847
$511$	0.270920	0.0119848
$512$	1.00000	0.0441942
$513$	−6.80845	−0.300600
$514$	−19.2990	−0.851243
$515$	−33.5542	−1.47858
$516$	−5.50479	−0.242335
$517$	−17.9003	−0.787256
$518$	5.83450	0.256353
$519$	−1.66193	−0.0729504
$520$	−14.5758	−0.639191
$521$	8.16111	0.357545	0.178772	−	0.983890i	$-0.442787\pi$
$521$	8.16111	0.357545	0.178772	+	0.983890i	$0.442787\pi$
$522$	6.82674	0.298798
$523$	−15.5703	−0.680842	−0.340421	−	0.940273i	$-0.610570\pi$
$523$	−15.5703	−0.680842	−0.340421	+	0.940273i	$0.610570\pi$
$524$	−20.3847	−0.890510
$525$	−0.934902	−0.0408025
$526$	22.0731	0.962435
$527$	6.67135	0.290608
$528$	−1.40431	−0.0611150
$529$	10.0693	0.437796
$530$	3.77880	0.164140
$531$	−21.2792	−0.923437
$532$	−1.01001	−0.0437893
$533$	25.2431	1.09340
$534$	−5.48273	−0.237261
$535$	−42.4802	−1.83658
$536$	−8.87706	−0.383431
$537$	5.11772	0.220846
$538$	13.3919	0.577366
$539$	15.6195	0.672781
$540$	−9.68514	−0.416782
$541$	−3.83247	−0.164771	−0.0823853	−	0.996601i	$-0.526254\pi$
$541$	−3.83247	−0.164771	−0.0823853	+	0.996601i	$0.526254\pi$
$542$	11.2432	0.482938
$543$	13.4878	0.578818
$544$	2.32259	0.0995802
$545$	21.4371	0.918263
$546$	1.57839	0.0675489
$547$	−3.56550	−0.152450	−0.0762248	−	0.997091i	$-0.524287\pi$
$547$	−3.56550	−0.152450	−0.0762248	+	0.997091i	$0.524287\pi$
$548$	15.4768	0.661138
$549$	−26.0981	−1.11384
$550$	−7.05079	−0.300647
$551$	−5.17054	−0.220273
$552$	−3.48647	−0.148394
$553$	−5.64152	−0.239902
$554$	−7.38661	−0.313827
$555$	−19.8047	−0.840665
$556$	−12.5978	−0.534265
$557$	−33.2500	−1.40885	−0.704423	−	0.709780i	$-0.748794\pi$
$557$	−33.2500	−1.40885	−0.704423	+	0.709780i	$0.748794\pi$
$558$	−7.56130	−0.320096
$559$	46.6619	1.97359
$560$	−1.43675	−0.0607138
$561$	−3.26165	−0.137707
$562$	26.4726	1.11668
$563$	−10.0736	−0.424552	−0.212276	−	0.977210i	$-0.568088\pi$
$563$	−10.0736	−0.424552	−0.212276	+	0.977210i	$0.568088\pi$
$564$	4.68538	0.197290
$565$	1.76388	0.0742068
$566$	21.8382	0.917928
$567$	−2.95178	−0.123963
$568$	−8.34287	−0.350059
$569$	−15.3273	−0.642552	−0.321276	−	0.946986i	$-0.604112\pi$
$569$	−15.3273	−0.642552	−0.321276	+	0.946986i	$0.604112\pi$
$570$	3.42838	0.143599
$571$	7.47962	0.313012	0.156506	−	0.987677i	$-0.449977\pi$
$571$	7.47962	0.313012	0.156506	+	0.987677i	$0.449977\pi$
$572$	11.9038	0.497724
$573$	−1.72490	−0.0720589
$574$	2.48824	0.103857
$575$	−17.5049	−0.730005
$576$	−2.63242	−0.109684
$577$	13.0447	0.543058	0.271529	−	0.962430i	$-0.412471\pi$
$577$	13.0447	0.543058	0.271529	+	0.962430i	$0.412471\pi$
$578$	−11.6056	−0.482728
$579$	−9.01446	−0.374628
$580$	−7.35519	−0.305408
$581$	3.49315	0.144920
$582$	5.99653	0.248564
$583$	−3.08608	−0.127812
$584$	−0.534805	−0.0221304
$585$	38.3697	1.58639
$586$	−17.2723	−0.713511
$587$	41.1069	1.69666	0.848332	−	0.529465i	$-0.177607\pi$
$587$	41.1069	1.69666	0.848332	+	0.529465i	$0.177607\pi$
$588$	−4.08838	−0.168602
$589$	5.72690	0.235973
$590$	22.9264	0.943864
$591$	4.43226	0.182319
$592$	−11.5175	−0.473367
$593$	−20.9216	−0.859146	−0.429573	−	0.903032i	$-0.641336\pi$
$593$	−20.9216	−0.859146	−0.429573	+	0.903032i	$0.641336\pi$
$594$	7.90970	0.324539
$595$	−3.33698	−0.136803
$596$	−21.9706	−0.899950
$597$	−2.08862	−0.0854816
$598$	29.5535	1.20853
$599$	−43.3206	−1.77003	−0.885016	−	0.465560i	$-0.845853\pi$
$599$	−43.3206	−1.77003	−0.885016	+	0.465560i	$0.845853\pi$
$600$	1.84553	0.0753435
$601$	16.1755	0.659814	0.329907	−	0.944013i	$-0.392983\pi$
$601$	16.1755	0.659814	0.329907	+	0.944013i	$0.392983\pi$
$602$	4.59951	0.187462
$603$	23.3682	0.951626
$604$	6.14178	0.249906
$605$	−15.9816	−0.649743
$606$	10.1636	0.412870
$607$	33.8663	1.37459	0.687295	−	0.726378i	$-0.258798\pi$
$607$	33.8663	1.37459	0.687295	+	0.726378i	$0.258798\pi$
$608$	1.99379	0.0808588
$609$	0.796482	0.0322751
$610$	28.1183	1.13848
$611$	−39.7161	−1.60674
$612$	−6.11404	−0.247145
$613$	17.2881	0.698258	0.349129	−	0.937075i	$-0.386477\pi$
$613$	17.2881	0.698258	0.349129	+	0.937075i	$0.386477\pi$
$614$	15.4679	0.624235
$615$	−8.44613	−0.340581
$616$	1.17337	0.0472765
$617$	−41.1566	−1.65690	−0.828450	−	0.560062i	$-0.810777\pi$
$617$	−41.1566	−1.65690	−0.828450	+	0.560062i	$0.810777\pi$
$618$	−7.17274	−0.288530
$619$	−8.98902	−0.361299	−0.180650	−	0.983548i	$-0.557820\pi$
$619$	−8.98902	−0.361299	−0.180650	+	0.983548i	$0.557820\pi$
$620$	8.14662	0.327176
$621$	19.6373	0.788018
$622$	−20.4803	−0.821183
$623$	4.58108	0.183537
$624$	−3.11580	−0.124732
$625$	−30.9540	−1.23816
$626$	−30.8101	−1.23142
$627$	−2.79991	−0.111817
$628$	−3.24619	−0.129537
$629$	−26.7505	−1.06661
$630$	3.78213	0.150684
$631$	−30.4844	−1.21357	−0.606783	−	0.794868i	$-0.707540\pi$
$631$	−30.4844	−1.21357	−0.606783	+	0.794868i	$0.707540\pi$
$632$	11.1366	0.442989
$633$	13.0791	0.519848
$634$	28.3244	1.12491
$635$	11.9583	0.474550
$636$	0.807776	0.0320304
$637$	34.6556	1.37310
$638$	6.00687	0.237814
$639$	21.9620	0.868802
$640$	2.83620	0.112111
$641$	−2.35829	−0.0931469	−0.0465735	−	0.998915i	$-0.514830\pi$
$641$	−2.35829	−0.0931469	−0.0465735	+	0.998915i	$0.514830\pi$
$642$	−9.08079	−0.358390
$643$	14.7441	0.581449	0.290725	−	0.956807i	$-0.406104\pi$
$643$	14.7441	0.581449	0.290725	+	0.956807i	$0.406104\pi$
$644$	2.91311	0.114793
$645$	−15.6127	−0.614748
$646$	4.63075	0.182194
$647$	−34.3863	−1.35187	−0.675933	−	0.736963i	$-0.736259\pi$
$647$	−34.3863	−1.35187	−0.675933	+	0.736963i	$0.736259\pi$
$648$	5.82692	0.228903
$649$	−18.7236	−0.734966
$650$	−15.6438	−0.613601
$651$	−0.882185	−0.0345756
$652$	8.00402	0.313462
$653$	−47.5448	−1.86057	−0.930285	−	0.366837i	$-0.880441\pi$
$653$	−47.5448	−1.86057	−0.930285	+	0.366837i	$0.880441\pi$
$654$	4.58250	0.179190
$655$	−57.8150	−2.25902
$656$	−4.91187	−0.191776
$657$	1.40783	0.0549248
$658$	−3.91485	−0.152617
$659$	−3.87275	−0.150861	−0.0754305	−	0.997151i	$-0.524033\pi$
$659$	−3.87275	−0.150861	−0.0754305	+	0.997151i	$0.524033\pi$
$660$	−3.98291	−0.155035
$661$	14.4534	0.562171	0.281085	−	0.959683i	$-0.409306\pi$
$661$	14.4534	0.562171	0.281085	+	0.959683i	$0.409306\pi$
$662$	19.7108	0.766084
$663$	−7.23673	−0.281051
$664$	−6.89561	−0.267602
$665$	−2.86457	−0.111083
$666$	30.3190	1.17484
$667$	14.9132	0.577440
$668$	−7.06916	−0.273514
$669$	−14.7851	−0.571625
$670$	−25.1771	−0.972676
$671$	−22.9638	−0.886506
$672$	−0.307128	−0.0118477
$673$	−12.3841	−0.477371	−0.238686	−	0.971097i	$-0.576717\pi$
$673$	−12.3841	−0.477371	−0.238686	+	0.971097i	$0.576717\pi$
$674$	18.9578	0.730227
$675$	−10.3948	−0.400096
$676$	13.4114	0.515823
$677$	−33.8151	−1.29962	−0.649810	−	0.760097i	$-0.725151\pi$
$677$	−33.8151	−1.29962	−0.649810	+	0.760097i	$0.725151\pi$
$678$	0.377056	0.0144807
$679$	−5.01039	−0.192281
$680$	6.58732	0.252612
$681$	−17.0024	−0.651532
$682$	−6.65321	−0.254765
$683$	15.9786	0.611405	0.305703	−	0.952127i	$-0.401109\pi$
$683$	15.9786	0.611405	0.305703	+	0.952127i	$0.401109\pi$
$684$	−5.24849	−0.200681
$685$	43.8954	1.67716
$686$	6.96207	0.265813
$687$	−4.66455	−0.177964
$688$	−9.07959	−0.346156
$689$	−6.84720	−0.260857
$690$	−9.88833	−0.376442
$691$	−3.91747	−0.149028	−0.0745139	−	0.997220i	$-0.523741\pi$
$691$	−3.91747	−0.149028	−0.0745139	+	0.997220i	$0.523741\pi$
$692$	−2.74118	−0.104204
$693$	−3.08881	−0.117334
$694$	21.3952	0.812150
$695$	−35.7298	−1.35531
$696$	−1.57229	−0.0595973
$697$	−11.4083	−0.432119
$698$	−14.9750	−0.566811
$699$	−2.23660	−0.0845960
$700$	−1.54203	−0.0582831
$701$	22.2993	0.842234	0.421117	−	0.907006i	$-0.361638\pi$
$701$	22.2993	0.842234	0.421117	+	0.907006i	$0.361638\pi$
$702$	17.5495	0.662364
$703$	−22.9635	−0.866084
$704$	−2.31628	−0.0872980
$705$	13.2887	0.500480
$706$	−30.1792	−1.13581
$707$	−8.49220	−0.319382
$708$	4.90087	0.184186
$709$	−13.8744	−0.521066	−0.260533	−	0.965465i	$-0.583898\pi$
$709$	−13.8744	−0.521066	−0.260533	+	0.965465i	$0.583898\pi$
$710$	−23.6620	−0.888020
$711$	−29.3162	−1.09944
$712$	−9.04322	−0.338909
$713$	−16.5179	−0.618598
$714$	−0.713331	−0.0266958
$715$	33.7616	1.26261
$716$	8.44117	0.315461
$717$	8.92017	0.333130
$718$	2.53928	0.0947650
$719$	40.6715	1.51679	0.758395	−	0.651795i	$-0.225984\pi$
$719$	40.6715	1.51679	0.758395	+	0.651795i	$0.225984\pi$
$720$	−7.46607	−0.278244
$721$	5.99316	0.223197
$722$	−15.0248	−0.559166
$723$	1.33067	0.0494881
$724$	22.2468	0.826796
$725$	−7.89414	−0.293181
$726$	−3.41631	−0.126791
$727$	37.1695	1.37854	0.689271	−	0.724504i	$-0.257931\pi$
$727$	37.1695	1.37854	0.689271	+	0.724504i	$0.257931\pi$
$728$	2.60340	0.0964883
$729$	−9.12788	−0.338070
$730$	−1.51681	−0.0561398
$731$	−21.0882	−0.779974
$732$	6.01072	0.222163
$733$	−41.8369	−1.54528	−0.772640	−	0.634845i	$-0.781064\pi$
$733$	−41.8369	−1.54528	−0.772640	+	0.634845i	$0.781064\pi$
$734$	−34.2313	−1.26350
$735$	−11.5955	−0.427705
$736$	−5.75059	−0.211970
$737$	20.5617	0.757401
$738$	12.9301	0.475965
$739$	−45.4052	−1.67026	−0.835128	−	0.550055i	$-0.814607\pi$
$739$	−45.4052	−1.67026	−0.835128	+	0.550055i	$0.814607\pi$
$740$	−32.6659	−1.20082
$741$	−6.21225	−0.228213
$742$	−0.674935	−0.0247776
$743$	−45.5343	−1.67049	−0.835245	−	0.549877i	$-0.814674\pi$
$743$	−45.5343	−1.67049	−0.835245	+	0.549877i	$0.814674\pi$
$744$	1.74147	0.0638452
$745$	−62.3129	−2.28297
$746$	−11.0437	−0.404337
$747$	18.1522	0.664153
$748$	−5.37976	−0.196704
$749$	7.58743	0.277239
$750$	−3.36338	−0.122813
$751$	3.83131	0.139807	0.0699033	−	0.997554i	$-0.477731\pi$
$751$	3.83131	0.139807	0.0699033	+	0.997554i	$0.477731\pi$
$752$	7.72806	0.281813
$753$	16.7764	0.611365
$754$	13.3276	0.485364
$755$	17.4193	0.633954
$756$	1.72987	0.0629148
$757$	50.9991	1.85359	0.926797	−	0.375563i	$-0.122551\pi$
$757$	50.9991	1.85359	0.926797	+	0.375563i	$0.122551\pi$
$758$	−7.30810	−0.265442
$759$	8.07564	0.293127
$760$	5.65478	0.205120
$761$	2.35731	0.0854523	0.0427261	−	0.999087i	$-0.486396\pi$
$761$	2.35731	0.0854523	0.0427261	+	0.999087i	$0.486396\pi$
$762$	2.55627	0.0926037
$763$	−3.82890	−0.138615
$764$	−2.84506	−0.102931
$765$	−17.3406	−0.626952
$766$	24.7122	0.892887
$767$	−41.5427	−1.50002
$768$	0.606281	0.0218773
$769$	−41.4269	−1.49389	−0.746946	−	0.664885i	$-0.768481\pi$
$769$	−41.4269	−1.49389	−0.746946	+	0.664885i	$0.768481\pi$
$770$	3.32791	0.119930
$771$	−11.7006	−0.421388
$772$	−14.8685	−0.535127
$773$	−4.46622	−0.160639	−0.0803194	−	0.996769i	$-0.525594\pi$
$773$	−4.46622	−0.160639	−0.0803194	+	0.996769i	$0.525594\pi$
$774$	23.9013	0.859116
$775$	8.74356	0.314078
$776$	9.89069	0.355055
$777$	3.53735	0.126902
$778$	11.2213	0.402303
$779$	−9.79323	−0.350879
$780$	−8.83703	−0.316416
$781$	19.3244	0.691482
$782$	−13.3563	−0.477619
$783$	8.85578	0.316480
$784$	−6.74338	−0.240835
$785$	−9.20684	−0.328606
$786$	−12.3589	−0.440826
$787$	28.3992	1.01232	0.506161	−	0.862439i	$-0.331064\pi$
$787$	28.3992	1.01232	0.506161	+	0.862439i	$0.331064\pi$
$788$	7.31057	0.260428
$789$	13.3825	0.476431
$790$	31.5855	1.12376
$791$	−0.315048	−0.0112018
$792$	6.09742	0.216662
$793$	−50.9505	−1.80930
$794$	−35.8478	−1.27219
$795$	2.29101	0.0812538
$796$	−3.44497	−0.122104
$797$	−12.9540	−0.458856	−0.229428	−	0.973326i	$-0.573686\pi$
$797$	−12.9540	−0.458856	−0.229428	+	0.973326i	$0.573686\pi$
$798$	−0.612347	−0.0216769
$799$	17.9491	0.634994
$800$	3.04402	0.107622
$801$	23.8056	0.841129
$802$	29.5883	1.04480
$803$	1.23876	0.0437148
$804$	−5.38199	−0.189808
$805$	8.26216	0.291203
$806$	−14.7617	−0.519959
$807$	8.11925	0.285811
$808$	16.7639	0.589753
$809$	−15.6364	−0.549747	−0.274874	−	0.961480i	$-0.588636\pi$
$809$	−15.6364	−0.549747	−0.274874	+	0.961480i	$0.588636\pi$
$810$	16.5263	0.580675
$811$	50.0830	1.75865	0.879325	−	0.476222i	$-0.157994\pi$
$811$	50.0830	1.75865	0.879325	+	0.476222i	$0.157994\pi$
$812$	1.31372	0.0461025
$813$	6.81656	0.239067
$814$	26.6778	0.935055
$815$	22.7010	0.795181
$816$	1.40814	0.0492948
$817$	−18.1028	−0.633336
$818$	35.8856	1.25471
$819$	−6.85324	−0.239472
$820$	−13.9310	−0.486493
$821$	17.5211	0.611489	0.305745	−	0.952114i	$-0.401095\pi$
$821$	17.5211	0.611489	0.305745	+	0.952114i	$0.401095\pi$
$822$	9.38331	0.327281
$823$	29.0554	1.01281	0.506404	−	0.862296i	$-0.330974\pi$
$823$	29.0554	1.01281	0.506404	+	0.862296i	$0.330974\pi$
$824$	−11.8307	−0.412142
$825$	−4.27476	−0.148828
$826$	−4.09490	−0.142480
$827$	39.7099	1.38085	0.690425	−	0.723404i	$-0.257424\pi$
$827$	39.7099	1.38085	0.690425	+	0.723404i	$0.257424\pi$
$828$	15.1380	0.526082
$829$	52.5437	1.82492	0.912460	−	0.409166i	$-0.134180\pi$
$829$	52.5437	1.82492	0.912460	+	0.409166i	$0.134180\pi$
$830$	−19.5573	−0.678844
$831$	−4.47836	−0.155353
$832$	−5.13920	−0.178170
$833$	−15.6621	−0.542660
$834$	−7.63780	−0.264475
$835$	−20.0495	−0.693842
$836$	−4.61816	−0.159723
$837$	−9.80867	−0.339037
$838$	6.58220	0.227378
$839$	−49.2979	−1.70195	−0.850977	−	0.525203i	$-0.823989\pi$
$839$	−49.2979	−1.70195	−0.850977	+	0.525203i	$0.823989\pi$
$840$	−0.871074	−0.0300549
$841$	−22.2747	−0.768091
$842$	27.4147	0.944773
$843$	16.0498	0.552785
$844$	21.5727	0.742563
$845$	38.0374	1.30853
$846$	−20.3435	−0.699425
$847$	2.85449	0.0980813
$848$	1.33235	0.0457529
$849$	13.2401	0.454399
$850$	7.07000	0.242499
$851$	66.2325	2.27042
$852$	−5.05813	−0.173289
$853$	−54.3701	−1.86160	−0.930798	−	0.365535i	$-0.880886\pi$
$853$	−54.3701	−1.86160	−0.930798	+	0.365535i	$0.880886\pi$
$854$	−5.02224	−0.171857
$855$	−14.8858	−0.509082
$856$	−14.9779	−0.511933
$857$	−19.0440	−0.650529	−0.325265	−	0.945623i	$-0.605453\pi$
$857$	−19.0440	−0.650529	−0.325265	+	0.945623i	$0.605453\pi$
$858$	7.21706	0.246386
$859$	32.6700	1.11469	0.557344	−	0.830282i	$-0.311821\pi$
$859$	32.6700	1.11469	0.557344	+	0.830282i	$0.311821\pi$
$860$	−25.7515	−0.878120
$861$	1.50857	0.0514120
$862$	−4.38215	−0.149257
$863$	−50.9338	−1.73381	−0.866904	−	0.498475i	$-0.833894\pi$
$863$	−50.9338	−1.73381	−0.866904	+	0.498475i	$0.833894\pi$
$864$	−3.41483	−0.116175
$865$	−7.77453	−0.264342
$866$	−5.82602	−0.197976
$867$	−7.03624	−0.238963
$868$	−1.45508	−0.0493885
$869$	−25.7954	−0.875048
$870$	−4.45931	−0.151185
$871$	45.6210	1.54581
$872$	7.55838	0.255959
$873$	−26.0365	−0.881201
$874$	−11.4655	−0.387825
$875$	2.81026	0.0950041
$876$	−0.324242	−0.0109551
$877$	31.3442	1.05842	0.529210	−	0.848491i	$-0.322488\pi$
$877$	31.3442	1.05842	0.529210	+	0.848491i	$0.322488\pi$
$878$	21.9844	0.741937
$879$	−10.4718	−0.353207
$880$	−6.56942	−0.221455
$881$	11.4636	0.386218	0.193109	−	0.981177i	$-0.438143\pi$
$881$	11.4636	0.386218	0.193109	+	0.981177i	$0.438143\pi$
$882$	17.7514	0.597722
$883$	3.37582	0.113606	0.0568028	−	0.998385i	$-0.481909\pi$
$883$	3.37582	0.113606	0.0568028	+	0.998385i	$0.481909\pi$
$884$	−11.9363	−0.401460
$885$	13.8998	0.467238
$886$	−3.95742	−0.132952
$887$	−1.76783	−0.0593581	−0.0296790	−	0.999559i	$-0.509449\pi$
$887$	−1.76783	−0.0593581	−0.0296790	+	0.999559i	$0.509449\pi$
$888$	−6.98285	−0.234329
$889$	−2.13588	−0.0716351
$890$	−25.6484	−0.859735
$891$	−13.4968	−0.452159
$892$	−24.3866	−0.816522
$893$	15.4081	0.515613
$894$	−13.3204	−0.445499
$895$	23.9408	0.800254
$896$	−0.506576	−0.0169235
$897$	17.9177	0.598255
$898$	−26.1503	−0.872646
$899$	−7.44901	−0.248438
$900$	−8.01314	−0.267105
$901$	3.09449	0.103093
$902$	11.3773	0.378821
$903$	2.78859	0.0927986
$904$	0.621916	0.0206846
$905$	63.0964	2.09739
$906$	3.72365	0.123710
$907$	12.5595	0.417033	0.208516	−	0.978019i	$-0.433137\pi$
$907$	12.5595	0.417033	0.208516	+	0.978019i	$0.433137\pi$
$908$	−28.0437	−0.930662
$909$	−44.1297	−1.46369
$910$	7.38375	0.244769
$911$	−7.16701	−0.237454	−0.118727	−	0.992927i	$-0.537881\pi$
$911$	−7.16701	−0.237454	−0.118727	+	0.992927i	$0.537881\pi$
$912$	1.20880	0.0400272
$913$	15.9721	0.528601
$914$	−31.5086	−1.04221
$915$	17.0476	0.563576
$916$	−7.69372	−0.254208
$917$	10.3264	0.341008
$918$	−7.93125	−0.261770
$919$	14.8261	0.489067	0.244533	−	0.969641i	$-0.421365\pi$
$919$	14.8261	0.489067	0.244533	+	0.969641i	$0.421365\pi$
$920$	−16.3098	−0.537719
$921$	9.37792	0.309013
$922$	−34.7480	−1.14437
$923$	42.8757	1.41127
$924$	0.711393	0.0234031
$925$	−35.0595	−1.15275
$926$	31.5590	1.03709
$927$	31.1434	1.02288
$928$	−2.59333	−0.0851302
$929$	−26.5293	−0.870397	−0.435198	−	0.900335i	$-0.643322\pi$
$929$	−26.5293	−0.870397	−0.435198	+	0.900335i	$0.643322\pi$
$930$	4.93914	0.161961
$931$	−13.4449	−0.440638
$932$	−3.68905	−0.120839
$933$	−12.4168	−0.406507
$934$	27.9018	0.912975
$935$	−15.2581	−0.498992
$936$	13.5286	0.442195
$937$	0.156956	0.00512752	0.00256376	−	0.999997i	$-0.499184\pi$
$937$	0.156956	0.00512752	0.00256376	+	0.999997i	$0.499184\pi$
$938$	4.49691	0.146829
$939$	−18.6796	−0.609586
$940$	21.9183	0.714897
$941$	4.66962	0.152225	0.0761127	−	0.997099i	$-0.475749\pi$
$941$	4.66962	0.152225	0.0761127	+	0.997099i	$0.475749\pi$
$942$	−1.96810	−0.0641243
$943$	28.2462	0.919822
$944$	8.08349	0.263095
$945$	4.90626	0.159601
$946$	21.0309	0.683772
$947$	−25.3870	−0.824968	−0.412484	−	0.910965i	$-0.635339\pi$
$947$	−25.3870	−0.824968	−0.412484	+	0.910965i	$0.635339\pi$
$948$	6.75189	0.219291
$949$	2.74847	0.0892192
$950$	6.06912	0.196908
$951$	17.1725	0.556858
$952$	−1.17657	−0.0381328
$953$	−10.0087	−0.324212	−0.162106	−	0.986773i	$-0.551829\pi$
$953$	−10.0087	−0.324212	−0.162106	+	0.986773i	$0.551829\pi$
$954$	−3.50730	−0.113553
$955$	−8.06914	−0.261111
$956$	14.7129	0.475850
$957$	3.64185	0.117724
$958$	−11.6765	−0.377249
$959$	−7.84020	−0.253173
$960$	1.71953	0.0554977
$961$	−22.7495	−0.733854
$962$	59.1908	1.90839
$963$	39.4281	1.27055
$964$	2.19480	0.0706899
$965$	−42.1699	−1.35750
$966$	1.76616	0.0568254
$967$	35.6485	1.14638	0.573189	−	0.819423i	$-0.305706\pi$
$967$	35.6485	1.14638	0.573189	+	0.819423i	$0.305706\pi$
$968$	−5.63486	−0.181111
$969$	2.80754	0.0901911
$970$	28.0519	0.900693
$971$	−9.43207	−0.302690	−0.151345	−	0.988481i	$-0.548360\pi$
$971$	−9.43207	−0.302690	−0.151345	+	0.988481i	$0.548360\pi$
$972$	13.7772	0.441905
$973$	6.38174	0.204589
$974$	3.85271	0.123449
$975$	−9.48455	−0.303749
$976$	9.91408	0.317342
$977$	24.6853	0.789753	0.394876	−	0.918734i	$-0.370787\pi$
$977$	24.6853	0.789753	0.394876	+	0.918734i	$0.370787\pi$
$978$	4.85269	0.155172
$979$	20.9466	0.669456
$980$	−19.1256	−0.610944
$981$	−19.8969	−0.635258
$982$	−23.0154	−0.734450
$983$	12.7612	0.407019	0.203510	−	0.979073i	$-0.434765\pi$
$983$	12.7612	0.407019	0.203510	+	0.979073i	$0.434765\pi$
$984$	−2.97798	−0.0949344
$985$	20.7342	0.660647
$986$	−6.02324	−0.191819
$987$	−2.37350	−0.0755494
$988$	−10.2465	−0.325984
$989$	52.2130	1.66028
$990$	17.2935	0.549623
$991$	9.01446	0.286354	0.143177	−	0.989697i	$-0.454268\pi$
$991$	9.01446	0.286354	0.143177	+	0.989697i	$0.454268\pi$
$992$	2.87237	0.0911980
$993$	11.9503	0.379232
$994$	4.22630	0.134050
$995$	−9.77062	−0.309749
$996$	−4.18068	−0.132470
$997$	−18.7956	−0.595261	−0.297631	−	0.954681i	$-0.596196\pi$
$997$	−18.7956	−0.595261	−0.297631	+	0.954681i	$0.596196\pi$
$998$	4.68051	0.148159
$999$	39.3304	1.24436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.a.1.42	✓	67

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.a.1.42	✓	67	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.606281 q^{3} +1.00000 q^{4} +2.83620 q^{5} +0.606281 q^{6} -0.506576 q^{7} +1.00000 q^{8} -2.63242 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.606281 q^{3} +1.00000 q^{4} +2.83620 q^{5} +0.606281 q^{6} -0.506576 q^{7} +1.00000 q^{8} -2.63242 q^{9} +2.83620 q^{10} -2.31628 q^{11} +0.606281 q^{12} -5.13920 q^{13} -0.506576 q^{14} +1.71953 q^{15} +1.00000 q^{16} +2.32259 q^{17} -2.63242 q^{18} +1.99379 q^{19} +2.83620 q^{20} -0.307128 q^{21} -2.31628 q^{22} -5.75059 q^{23} +0.606281 q^{24} +3.04402 q^{25} -5.13920 q^{26} -3.41483 q^{27} -0.506576 q^{28} -2.59333 q^{29} +1.71953 q^{30} +2.87237 q^{31} +1.00000 q^{32} -1.40431 q^{33} +2.32259 q^{34} -1.43675 q^{35} -2.63242 q^{36} -11.5175 q^{37} +1.99379 q^{38} -3.11580 q^{39} +2.83620 q^{40} -4.91187 q^{41} -0.307128 q^{42} -9.07959 q^{43} -2.31628 q^{44} -7.46607 q^{45} -5.75059 q^{46} +7.72806 q^{47} +0.606281 q^{48} -6.74338 q^{49} +3.04402 q^{50} +1.40814 q^{51} -5.13920 q^{52} +1.33235 q^{53} -3.41483 q^{54} -6.56942 q^{55} -0.506576 q^{56} +1.20880 q^{57} -2.59333 q^{58} +8.08349 q^{59} +1.71953 q^{60} +9.91408 q^{61} +2.87237 q^{62} +1.33352 q^{63} +1.00000 q^{64} -14.5758 q^{65} -1.40431 q^{66} -8.87706 q^{67} +2.32259 q^{68} -3.48647 q^{69} -1.43675 q^{70} -8.34287 q^{71} -2.63242 q^{72} -0.534805 q^{73} -11.5175 q^{74} +1.84553 q^{75} +1.99379 q^{76} +1.17337 q^{77} -3.11580 q^{78} +11.1366 q^{79} +2.83620 q^{80} +5.82692 q^{81} -4.91187 q^{82} -6.89561 q^{83} -0.307128 q^{84} +6.58732 q^{85} -9.07959 q^{86} -1.57229 q^{87} -2.31628 q^{88} -9.04322 q^{89} -7.46607 q^{90} +2.60340 q^{91} -5.75059 q^{92} +1.74147 q^{93} +7.72806 q^{94} +5.65478 q^{95} +0.606281 q^{96} +9.89069 q^{97} -6.74338 q^{98} +6.09742 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9}+O(q^{10}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9	\( 67 q + 67 q^{2} - 11 q^{3} + 67 q^{4} - 20 q^{5} - 11 q^{6} - 40 q^{7} + 67 q^{8} + 24 q^{9} - 20 q^{10} - 13 q^{11} - 11 q^{12} - 51 q^{13} - 40 q^{14} - 31 q^{15} + 67 q^{16} - 34 q^{17} + 24 q^{18} - 33 q^{19} - 20 q^{20} - 39 q^{21} - 13 q^{22} - 43 q^{23} - 11 q^{24} - 9 q^{25} - 51 q^{26} - 29 q^{27} - 40 q^{28} - 63 q^{29} - 31 q^{30} - 43 q^{31} + 67 q^{32} - 49 q^{33} - 34 q^{34} - 20 q^{35} + 24 q^{36} - 77 q^{37} - 33 q^{38} - 40 q^{39} - 20 q^{40} - 50 q^{41} - 39 q^{42} - 56 q^{43} - 13 q^{44} - 48 q^{45} - 43 q^{46} - 48 q^{47} - 11 q^{48} + q^{49} - 9 q^{50} - 18 q^{51} - 51 q^{52} - 91 q^{53} - 29 q^{54} - 58 q^{55} - 40 q^{56} - 65 q^{57} - 63 q^{58} - 17 q^{59} - 31 q^{60} - 45 q^{61} - 43 q^{62} - 67 q^{63} + 67 q^{64} - 65 q^{65} - 49 q^{66} - 112 q^{67} - 34 q^{68} - 57 q^{69} - 20 q^{70} - 75 q^{71} + 24 q^{72} - 79 q^{73} - 77 q^{74} - 5 q^{75} - 33 q^{76} - 85 q^{77} - 40 q^{78} - 80 q^{79} - 20 q^{80} - 77 q^{81} - 50 q^{82} - 22 q^{83} - 39 q^{84} - 134 q^{85} - 56 q^{86} - 49 q^{87} - 13 q^{88} - 77 q^{89} - 48 q^{90} - 17 q^{91} - 43 q^{92} - 97 q^{93} - 48 q^{94} - 73 q^{95} - 11 q^{96} - 87 q^{97} + q^{98} - 44 q^{99}+O(q^{100}) \) 67 * q + 67 * q^2 - 11 * q^3 + 67 * q^4 - 20 * q^5 - 11 * q^6 - 40 * q^7 + 67 * q^8 + 24 * q^9 - 20 * q^10 - 13 * q^11 - 11 * q^12 - 51 * q^13 - 40 * q^14 - 31 * q^15 + 67 * q^16 - 34 * q^17 + 24 * q^18 - 33 * q^19 - 20 * q^20 - 39 * q^21 - 13 * q^22 - 43 * q^23 - 11 * q^24 - 9 * q^25 - 51 * q^26 - 29 * q^27 - 40 * q^28 - 63 * q^29 - 31 * q^30 - 43 * q^31 + 67 * q^32 - 49 * q^33 - 34 * q^34 - 20 * q^35 + 24 * q^36 - 77 * q^37 - 33 * q^38 - 40 * q^39 - 20 * q^40 - 50 * q^41 - 39 * q^42 - 56 * q^43 - 13 * q^44 - 48 * q^45 - 43 * q^46 - 48 * q^47 - 11 * q^48 + q^49 - 9 * q^50 - 18 * q^51 - 51 * q^52 - 91 * q^53 - 29 * q^54 - 58 * q^55 - 40 * q^56 - 65 * q^57 - 63 * q^58 - 17 * q^59 - 31 * q^60 - 45 * q^61 - 43 * q^62 - 67 * q^63 + 67 * q^64 - 65 * q^65 - 49 * q^66 - 112 * q^67 - 34 * q^68 - 57 * q^69 - 20 * q^70 - 75 * q^71 + 24 * q^72 - 79 * q^73 - 77 * q^74 - 5 * q^75 - 33 * q^76 - 85 * q^77 - 40 * q^78 - 80 * q^79 - 20 * q^80 - 77 * q^81 - 50 * q^82 - 22 * q^83 - 39 * q^84 - 134 * q^85 - 56 * q^86 - 49 * q^87 - 13 * q^88 - 77 * q^89 - 48 * q^90 - 17 * q^91 - 43 * q^92 - 97 * q^93 - 48 * q^94 - 73 * q^95 - 11 * q^96 - 87 * q^97 + q^98 - 44 * q^99

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