LMFDB - Embedded newform 8039.2.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54048 q^{2} -0.00862555 q^{3} +4.45405 q^{4} +1.93048 q^{5} +0.0219131 q^{6} +2.12668 q^{7} -6.23447 q^{8} -2.99993 q^{9} +O(q^{10})$	\(q-2.54048 q^{2} -0.00862555 q^{3} +4.45405 q^{4} +1.93048 q^{5} +0.0219131 q^{6} +2.12668 q^{7} -6.23447 q^{8} -2.99993 q^{9} -4.90434 q^{10} -0.144312 q^{11} -0.0384187 q^{12} +2.86114 q^{13} -5.40279 q^{14} -0.0166514 q^{15} +6.93047 q^{16} +1.80936 q^{17} +7.62126 q^{18} +3.49192 q^{19} +8.59845 q^{20} -0.0183438 q^{21} +0.366622 q^{22} +1.30149 q^{23} +0.0537758 q^{24} -1.27326 q^{25} -7.26867 q^{26} +0.0517527 q^{27} +9.47234 q^{28} -0.377288 q^{29} +0.0423027 q^{30} -5.88875 q^{31} -5.13779 q^{32} +0.00124477 q^{33} -4.59666 q^{34} +4.10551 q^{35} -13.3618 q^{36} -1.50531 q^{37} -8.87116 q^{38} -0.0246789 q^{39} -12.0355 q^{40} +2.50853 q^{41} +0.0466021 q^{42} -9.47492 q^{43} -0.642773 q^{44} -5.79129 q^{45} -3.30642 q^{46} -10.8460 q^{47} -0.0597791 q^{48} -2.47723 q^{49} +3.23468 q^{50} -0.0156068 q^{51} +12.7437 q^{52} -3.56950 q^{53} -0.131477 q^{54} -0.278591 q^{55} -13.2587 q^{56} -0.0301197 q^{57} +0.958494 q^{58} +9.54789 q^{59} -0.0741664 q^{60} -11.5950 q^{61} +14.9603 q^{62} -6.37988 q^{63} -0.808476 q^{64} +5.52336 q^{65} -0.00316232 q^{66} -10.2713 q^{67} +8.05900 q^{68} -0.0112261 q^{69} -10.4300 q^{70} +0.327858 q^{71} +18.7030 q^{72} +5.36406 q^{73} +3.82420 q^{74} +0.0109825 q^{75} +15.5532 q^{76} -0.306906 q^{77} +0.0626963 q^{78} -0.109829 q^{79} +13.3791 q^{80} +8.99933 q^{81} -6.37287 q^{82} +7.32759 q^{83} -0.0817042 q^{84} +3.49294 q^{85} +24.0709 q^{86} +0.00325432 q^{87} +0.899710 q^{88} -13.4748 q^{89} +14.7127 q^{90} +6.08472 q^{91} +5.79692 q^{92} +0.0507938 q^{93} +27.5541 q^{94} +6.74107 q^{95} +0.0443163 q^{96} -5.56865 q^{97} +6.29336 q^{98} +0.432925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.54048	−1.79639	−0.898196	−	0.439595i	$-0.855122\pi$
$2$	−2.54048	−1.79639	−0.898196	+	0.439595i	$0.855122\pi$
$3$	−0.00862555	−0.00497997	−0.00248998	−	0.999997i	$-0.500793\pi$
$3$	−0.00862555	−0.00497997	−0.00248998	+	0.999997i	$0.500793\pi$
$4$	4.45405	2.22703
$5$	1.93048	0.863336	0.431668	−	0.902033i	$-0.357925\pi$
$5$	1.93048	0.863336	0.431668	+	0.902033i	$0.357925\pi$
$6$	0.0219131	0.00894597
$7$	2.12668	0.803810	0.401905	−	0.915681i	$-0.368348\pi$
$7$	2.12668	0.803810	0.401905	+	0.915681i	$0.368348\pi$
$8$	−6.23447	−2.20422
$9$	−2.99993	−0.999975
$10$	−4.90434	−1.55089
$11$	−0.144312	−0.0435117	−0.0217559	−	0.999763i	$-0.506926\pi$
$11$	−0.144312	−0.0435117	−0.0217559	+	0.999763i	$0.506926\pi$
$12$	−0.0384187	−0.0110905
$13$	2.86114	0.793537	0.396768	−	0.917919i	$-0.370132\pi$
$13$	2.86114	0.793537	0.396768	+	0.917919i	$0.370132\pi$
$14$	−5.40279	−1.44396
$15$	−0.0166514	−0.00429938
$16$	6.93047	1.73262
$17$	1.80936	0.438835	0.219418	−	0.975631i	$-0.429584\pi$
$17$	1.80936	0.438835	0.219418	+	0.975631i	$0.429584\pi$
$18$	7.62126	1.79635
$19$	3.49192	0.801101	0.400550	−	0.916275i	$-0.368819\pi$
$19$	3.49192	0.801101	0.400550	+	0.916275i	$0.368819\pi$
$20$	8.59845	1.92267
$21$	−0.0183438	−0.00400294
$22$	0.366622	0.0781641
$23$	1.30149	0.271380	0.135690	−	0.990751i	$-0.456675\pi$
$23$	1.30149	0.271380	0.135690	+	0.990751i	$0.456675\pi$
$24$	0.0537758	0.0109769
$25$	−1.27326	−0.254651
$26$	−7.26867	−1.42550
$27$	0.0517527	0.00995981
$28$	9.47234	1.79010
$29$	−0.377288	−0.0700606	−0.0350303	−	0.999386i	$-0.511153\pi$
$29$	−0.377288	−0.0700606	−0.0350303	+	0.999386i	$0.511153\pi$
$30$	0.0423027	0.00772338
$31$	−5.88875	−1.05765	−0.528826	−	0.848730i	$-0.677367\pi$
$31$	−5.88875	−1.05765	−0.528826	+	0.848730i	$0.677367\pi$
$32$	−5.13779	−0.908241
$33$	0.00124477	0.000216687 0
$34$	−4.59666	−0.788320
$35$	4.10551	0.693958
$36$	−13.3618	−2.22697
$37$	−1.50531	−0.247471	−0.123735	−	0.992315i	$-0.539487\pi$
$37$	−1.50531	−0.247471	−0.123735	+	0.992315i	$0.539487\pi$
$38$	−8.87116	−1.43909
$39$	−0.0246789	−0.00395179
$40$	−12.0355	−1.90298
$41$	2.50853	0.391766	0.195883	−	0.980627i	$-0.437243\pi$
$41$	2.50853	0.391766	0.195883	+	0.980627i	$0.437243\pi$
$42$	0.0466021	0.00719086
$43$	−9.47492	−1.44491	−0.722456	−	0.691417i	$-0.756987\pi$
$43$	−9.47492	−1.44491	−0.722456	+	0.691417i	$0.756987\pi$
$44$	−0.642773	−0.0969017
$45$	−5.79129	−0.863314
$46$	−3.30642	−0.487505
$47$	−10.8460	−1.58205	−0.791026	−	0.611782i	$-0.790453\pi$
$47$	−10.8460	−1.58205	−0.791026	+	0.611782i	$0.790453\pi$
$48$	−0.0597791	−0.00862838
$49$	−2.47723	−0.353890
$50$	3.23468	0.457453
$51$	−0.0156068	−0.00218538
$52$	12.7437	1.76723
$53$	−3.56950	−0.490309	−0.245154	−	0.969484i	$-0.578839\pi$
$53$	−3.56950	−0.490309	−0.245154	+	0.969484i	$0.578839\pi$
$54$	−0.131477	−0.0178917
$55$	−0.278591	−0.0375652
$56$	−13.2587	−1.77177
$57$	−0.0301197	−0.00398945
$58$	0.958494	0.125856
$59$	9.54789	1.24303	0.621515	−	0.783403i	$-0.286518\pi$
$59$	9.54789	1.24303	0.621515	+	0.783403i	$0.286518\pi$
$60$	−0.0741664	−0.00957484
$61$	−11.5950	−1.48459	−0.742293	−	0.670076i	$-0.766262\pi$
$61$	−11.5950	−1.48459	−0.742293	+	0.670076i	$0.766262\pi$
$62$	14.9603	1.89996
$63$	−6.37988	−0.803790
$64$	−0.808476	−0.101060
$65$	5.52336	0.685089
$66$	−0.00316232	−0.000389255 0
$67$	−10.2713	−1.25484	−0.627422	−	0.778680i	$-0.715890\pi$
$67$	−10.2713	−1.25484	−0.627422	+	0.778680i	$0.715890\pi$
$68$	8.05900	0.977297
$69$	−0.0112261	−0.00135146
$70$	−10.4300	−1.24662
$71$	0.327858	0.0389096	0.0194548	−	0.999811i	$-0.493807\pi$
$71$	0.327858	0.0389096	0.0194548	+	0.999811i	$0.493807\pi$
$72$	18.7030	2.20416
$73$	5.36406	0.627816	0.313908	−	0.949453i	$-0.398362\pi$
$73$	5.36406	0.627816	0.313908	+	0.949453i	$0.398362\pi$
$74$	3.82420	0.444555
$75$	0.0109825	0.00126815
$76$	15.5532	1.78407
$77$	−0.306906	−0.0349751
$78$	0.0626963	0.00709896
$79$	−0.109829	−0.0123567	−0.00617837	−	0.999981i	$-0.501967\pi$
$79$	−0.109829	−0.0123567	−0.00617837	+	0.999981i	$0.501967\pi$
$80$	13.3791	1.49583
$81$	8.99933	0.999926
$82$	−6.37287	−0.703765
$83$	7.32759	0.804307	0.402154	−	0.915572i	$-0.368262\pi$
$83$	7.32759	0.804307	0.402154	+	0.915572i	$0.368262\pi$
$84$	−0.0817042	−0.00891466
$85$	3.49294	0.378862
$86$	24.0709	2.59563
$87$	0.00325432	0.000348899 0
$88$	0.899710	0.0959094
$89$	−13.4748	−1.42832	−0.714161	−	0.699982i	$-0.753191\pi$
$89$	−13.4748	−1.42832	−0.714161	+	0.699982i	$0.753191\pi$
$90$	14.7127	1.55085
$91$	6.08472	0.637852
$92$	5.79692	0.604370
$93$	0.0507938	0.00526707
$94$	27.5541	2.84199
$95$	6.74107	0.691619
$96$	0.0443163	0.00452301
$97$	−5.56865	−0.565410	−0.282705	−	0.959207i	$-0.591232\pi$
$97$	−5.56865	−0.565410	−0.282705	+	0.959207i	$0.591232\pi$
$98$	6.29336	0.635725
$99$	0.432925	0.0435106
$100$	−5.67115	−0.567115
$101$	−3.49165	−0.347432	−0.173716	−	0.984796i	$-0.555577\pi$
$101$	−3.49165	−0.347432	−0.173716	+	0.984796i	$0.555577\pi$
$102$	0.0396487	0.00392581
$103$	−13.5366	−1.33380	−0.666900	−	0.745147i	$-0.732379\pi$
$103$	−13.5366	−1.33380	−0.666900	+	0.745147i	$0.732379\pi$
$104$	−17.8377	−1.74913
$105$	−0.0354123	−0.00345589
$106$	9.06825	0.880786
$107$	−11.1123	−1.07427	−0.537136	−	0.843496i	$-0.680494\pi$
$107$	−11.1123	−1.07427	−0.537136	+	0.843496i	$0.680494\pi$
$108$	0.230509	0.0221807
$109$	14.1403	1.35439	0.677196	−	0.735802i	$-0.263195\pi$
$109$	14.1403	1.35439	0.677196	+	0.735802i	$0.263195\pi$
$110$	0.707756	0.0674819
$111$	0.0129841	0.00123240
$112$	14.7389	1.39269
$113$	−13.2073	−1.24244	−0.621221	−	0.783635i	$-0.713363\pi$
$113$	−13.2073	−1.24244	−0.621221	+	0.783635i	$0.713363\pi$
$114$	0.0765186	0.00716663
$115$	2.51250	0.234292
$116$	−1.68046	−0.156027
$117$	−8.58320	−0.793517
$118$	−24.2562	−2.23297
$119$	3.84794	0.352740
$120$	0.103813	0.00947678
$121$	−10.9792	−0.998107
$122$	29.4568	2.66690
$123$	−0.0216374	−0.00195098
$124$	−26.2288	−2.35542
$125$	−12.1104	−1.08319
$126$	16.2080	1.44392
$127$	9.38944	0.833178	0.416589	−	0.909095i	$-0.363225\pi$
$127$	9.38944	0.833178	0.416589	+	0.909095i	$0.363225\pi$
$128$	12.3295	1.08978
$129$	0.0817264	0.00719561
$130$	−14.0320	−1.23069
$131$	12.6649	1.10654	0.553268	−	0.833003i	$-0.313381\pi$
$131$	12.6649	1.10654	0.553268	+	0.833003i	$0.313381\pi$
$132$	0.00554427	0.000482567 0
$133$	7.42619	0.643933
$134$	26.0942	2.25419
$135$	0.0999074	0.00859866
$136$	−11.2804	−0.967289
$137$	13.2498	1.13201	0.566004	−	0.824402i	$-0.308489\pi$
$137$	13.2498	1.13201	0.566004	+	0.824402i	$0.308489\pi$
$138$	0.0285197	0.00242776
$139$	−8.72781	−0.740283	−0.370142	−	0.928975i	$-0.620691\pi$
$139$	−8.72781	−0.740283	−0.370142	+	0.928975i	$0.620691\pi$
$140$	18.2861	1.54546
$141$	0.0935528	0.00787856
$142$	−0.832917	−0.0698968
$143$	−0.412897	−0.0345281
$144$	−20.7909	−1.73257
$145$	−0.728346	−0.0604858
$146$	−13.6273	−1.12780
$147$	0.0213675	0.00176236
$148$	−6.70471	−0.551124
$149$	8.95272	0.733436	0.366718	−	0.930332i	$-0.380481\pi$
$149$	8.95272	0.733436	0.366718	+	0.930332i	$0.380481\pi$
$150$	−0.0279009	−0.00227810
$151$	−10.5189	−0.856013	−0.428006	−	0.903776i	$-0.640784\pi$
$151$	−10.5189	−0.856013	−0.428006	+	0.903776i	$0.640784\pi$
$152$	−21.7703	−1.76580
$153$	−5.42796	−0.438824
$154$	0.779688	0.0628291
$155$	−11.3681	−0.913108
$156$	−0.109921	−0.00880073
$157$	−10.6721	−0.851729	−0.425865	−	0.904787i	$-0.640030\pi$
$157$	−10.6721	−0.851729	−0.425865	+	0.904787i	$0.640030\pi$
$158$	0.279019	0.0221975
$159$	0.0307889	0.00244172
$160$	−9.91839	−0.784117
$161$	2.76786	0.218138
$162$	−22.8626	−1.79626
$163$	−7.59286	−0.594718	−0.297359	−	0.954766i	$-0.596106\pi$
$163$	−7.59286	−0.594718	−0.297359	+	0.954766i	$0.596106\pi$
$164$	11.1731	0.872473
$165$	0.00240300	0.000187074 0
$166$	−18.6156	−1.44485
$167$	6.54233	0.506261	0.253130	−	0.967432i	$-0.418540\pi$
$167$	6.54233	0.506261	0.253130	+	0.967432i	$0.418540\pi$
$168$	0.114364	0.00882337
$169$	−4.81389	−0.370300
$170$	−8.87374	−0.680585
$171$	−10.4755	−0.801081
$172$	−42.2018	−3.21785
$173$	−5.30273	−0.403159	−0.201580	−	0.979472i	$-0.564607\pi$
$173$	−5.30273	−0.403159	−0.201580	+	0.979472i	$0.564607\pi$
$174$	−0.00826754	−0.000626760 0
$175$	−2.70781	−0.204691
$176$	−1.00015	−0.0753892
$177$	−0.0823558	−0.00619024
$178$	34.2324	2.56583
$179$	−11.6946	−0.874098	−0.437049	−	0.899438i	$-0.643976\pi$
$179$	−11.6946	−0.874098	−0.437049	+	0.899438i	$0.643976\pi$
$180$	−25.7947	−1.92262
$181$	−18.5211	−1.37667	−0.688333	−	0.725395i	$-0.741657\pi$
$181$	−18.5211	−1.37667	−0.688333	+	0.725395i	$0.741657\pi$
$182$	−15.4581	−1.14583
$183$	0.100013	0.00739318
$184$	−8.11412	−0.598181
$185$	−2.90596	−0.213650
$186$	−0.129041	−0.00946172
$187$	−0.261113	−0.0190945
$188$	−48.3087	−3.52327
$189$	0.110061	0.00800579
$190$	−17.1256	−1.24242
$191$	4.70844	0.340691	0.170345	−	0.985384i	$-0.445512\pi$
$191$	4.70844	0.340691	0.170345	+	0.985384i	$0.445512\pi$
$192$	0.00697356	0.000503273 0
$193$	−17.0877	−1.23000	−0.614999	−	0.788528i	$-0.710844\pi$
$193$	−17.0877	−1.23000	−0.614999	+	0.788528i	$0.710844\pi$
$194$	14.1470	1.01570
$195$	−0.0476420	−0.00341172
$196$	−11.0337	−0.788122
$197$	7.20480	0.513321	0.256660	−	0.966502i	$-0.417378\pi$
$197$	7.20480	0.513321	0.256660	+	0.966502i	$0.417378\pi$
$198$	−1.09984	−0.0781622
$199$	7.68247	0.544596	0.272298	−	0.962213i	$-0.412216\pi$
$199$	7.68247	0.544596	0.272298	+	0.962213i	$0.412216\pi$
$200$	7.93808	0.561307
$201$	0.0885960	0.00624908
$202$	8.87047	0.624124
$203$	−0.802371	−0.0563154
$204$	−0.0695133	−0.00486691
$205$	4.84265	0.338226
$206$	34.3895	2.39603
$207$	−3.90438	−0.271373
$208$	19.8290	1.37490
$209$	−0.503926	−0.0348573
$210$	0.0899643	0.00620813
$211$	−8.06448	−0.555182	−0.277591	−	0.960699i	$-0.589536\pi$
$211$	−8.06448	−0.555182	−0.277591	+	0.960699i	$0.589536\pi$
$212$	−15.8987	−1.09193
$213$	−0.00282795	−0.000193768 0
$214$	28.2307	1.92981
$215$	−18.2911	−1.24744
$216$	−0.322651	−0.0219536
$217$	−12.5235	−0.850150
$218$	−35.9231	−2.43302
$219$	−0.0462680	−0.00312650
$220$	−1.24086	−0.0836587
$221$	5.17684	0.348232
$222$	−0.0329859	−0.00221387
$223$	−10.5079	−0.703660	−0.351830	−	0.936064i	$-0.614440\pi$
$223$	−10.5079	−0.703660	−0.351830	+	0.936064i	$0.614440\pi$
$224$	−10.9264	−0.730053
$225$	3.81967	0.254645
$226$	33.5530	2.23191
$227$	−2.96218	−0.196607	−0.0983033	−	0.995157i	$-0.531342\pi$
$227$	−2.96218	−0.196607	−0.0983033	+	0.995157i	$0.531342\pi$
$228$	−0.134155	−0.00888462
$229$	4.68822	0.309806	0.154903	−	0.987930i	$-0.450493\pi$
$229$	4.68822	0.309806	0.154903	+	0.987930i	$0.450493\pi$
$230$	−6.38297	−0.420880
$231$	0.00264723	0.000174175 0
$232$	2.35219	0.154429
$233$	6.38035	0.417991	0.208995	−	0.977917i	$-0.432981\pi$
$233$	6.38035	0.417991	0.208995	+	0.977917i	$0.432981\pi$
$234$	21.8055	1.42547
$235$	−20.9380	−1.36584
$236$	42.5268	2.76826
$237$	0.000947336 0	6.15361e−5 0
$238$	−9.77562	−0.633659
$239$	−1.52955	−0.0989385	−0.0494693	−	0.998776i	$-0.515753\pi$
$239$	−1.52955	−0.0989385	−0.0494693	+	0.998776i	$0.515753\pi$
$240$	−0.115402	−0.00744919
$241$	23.7655	1.53087	0.765437	−	0.643511i	$-0.222523\pi$
$241$	23.7655	1.53087	0.765437	+	0.643511i	$0.222523\pi$
$242$	27.8924	1.79299
$243$	−0.232882	−0.0149394
$244$	−51.6446	−3.30621
$245$	−4.78224	−0.305526
$246$	0.0549695	0.00350473
$247$	9.99085	0.635703
$248$	36.7133	2.33130
$249$	−0.0632045	−0.00400542
$250$	30.7662	1.94583
$251$	7.79778	0.492192	0.246096	−	0.969246i	$-0.420852\pi$
$251$	7.79778	0.492192	0.246096	+	0.969246i	$0.420852\pi$
$252$	−28.4163	−1.79006
$253$	−0.187821	−0.0118082
$254$	−23.8537	−1.49671
$255$	−0.0301285	−0.00188672
$256$	−29.7059	−1.85662
$257$	−6.54419	−0.408216	−0.204108	−	0.978948i	$-0.565429\pi$
$257$	−6.54419	−0.408216	−0.204108	+	0.978948i	$0.565429\pi$
$258$	−0.207624	−0.0129261
$259$	−3.20130	−0.198919
$260$	24.6013	1.52571
$261$	1.13184	0.0700589
$262$	−32.1749	−1.98777
$263$	12.2007	0.752326	0.376163	−	0.926553i	$-0.377243\pi$
$263$	12.2007	0.752326	0.376163	+	0.926553i	$0.377243\pi$
$264$	−0.00776049	−0.000477625 0
$265$	−6.89084	−0.423301
$266$	−18.8661	−1.15676
$267$	0.116227	0.00711299
$268$	−45.7491	−2.79457
$269$	0.416636	0.0254027	0.0127014	−	0.999919i	$-0.495957\pi$
$269$	0.416636	0.0254027	0.0127014	+	0.999919i	$0.495957\pi$
$270$	−0.253813	−0.0154466
$271$	−0.956559	−0.0581068	−0.0290534	−	0.999578i	$-0.509249\pi$
$271$	−0.956559	−0.0581068	−0.0290534	+	0.999578i	$0.509249\pi$
$272$	12.5397	0.760333
$273$	−0.0524841	−0.00317648
$274$	−33.6609	−2.03353
$275$	0.183746	0.0110803
$276$	−0.0500016	−0.00300974
$277$	−6.76847	−0.406678	−0.203339	−	0.979108i	$-0.565179\pi$
$277$	−6.76847	−0.406678	−0.203339	+	0.979108i	$0.565179\pi$
$278$	22.1729	1.32984
$279$	17.6658	1.05763
$280$	−25.5957	−1.52964
$281$	−14.8744	−0.887335	−0.443668	−	0.896191i	$-0.646323\pi$
$281$	−14.8744	−0.887335	−0.443668	+	0.896191i	$0.646323\pi$
$282$	−0.237669	−0.0141530
$283$	−16.4350	−0.976959	−0.488480	−	0.872575i	$-0.662448\pi$
$283$	−16.4350	−0.976959	−0.488480	+	0.872575i	$0.662448\pi$
$284$	1.46030	0.0866526
$285$	−0.0581454	−0.00344424
$286$	1.04896	0.0620261
$287$	5.33483	0.314905
$288$	15.4130	0.908219
$289$	−13.7262	−0.807424
$290$	1.85035	0.108656
$291$	0.0480326	0.00281572
$292$	23.8918	1.39816
$293$	22.0688	1.28927	0.644635	−	0.764490i	$-0.277009\pi$
$293$	22.0688	1.28927	0.644635	+	0.764490i	$0.277009\pi$
$294$	−0.0542837	−0.00316589
$295$	18.4320	1.07315
$296$	9.38479	0.545480
$297$	−0.00746853	−0.000433368 0
$298$	−22.7442	−1.31754
$299$	3.72375	0.215350
$300$	0.0489168	0.00282421
$301$	−20.1501	−1.16143
$302$	26.7230	1.53773
$303$	0.0301174	0.00173020
$304$	24.2006	1.38800
$305$	−22.3839	−1.28170
$306$	13.7896	0.788301
$307$	31.4494	1.79491	0.897457	−	0.441101i	$-0.145412\pi$
$307$	31.4494	1.79491	0.897457	+	0.441101i	$0.145412\pi$
$308$	−1.36697	−0.0778905
$309$	0.116761	0.00664228
$310$	28.8805	1.64030
$311$	−12.9946	−0.736854	−0.368427	−	0.929657i	$-0.620103\pi$
$311$	−12.9946	−0.736854	−0.368427	+	0.929657i	$0.620103\pi$
$312$	0.153860	0.00871060
$313$	11.9896	0.677695	0.338848	−	0.940841i	$-0.389963\pi$
$313$	11.9896	0.677695	0.338848	+	0.940841i	$0.389963\pi$
$314$	27.1124	1.53004
$315$	−12.3162	−0.693941
$316$	−0.489184	−0.0275188
$317$	−17.7924	−0.999322	−0.499661	−	0.866221i	$-0.666542\pi$
$317$	−17.7924	−0.999322	−0.499661	+	0.866221i	$0.666542\pi$
$318$	−0.0782187	−0.00438629
$319$	0.0544472	0.00304846
$320$	−1.56075	−0.0872483
$321$	0.0958501	0.00534983
$322$	−7.03170	−0.391861
$323$	6.31815	0.351551
$324$	40.0835	2.22686
$325$	−3.64296	−0.202075
$326$	19.2895	1.06835
$327$	−0.121968	−0.00674483
$328$	−15.6393	−0.863538
$329$	−23.0660	−1.27167
$330$	−0.00610479	−0.000336057 0
$331$	18.7174	1.02880	0.514401	−	0.857550i	$-0.328014\pi$
$331$	18.7174	1.02880	0.514401	+	0.857550i	$0.328014\pi$
$332$	32.6375	1.79121
$333$	4.51580	0.247465
$334$	−16.6207	−0.909443
$335$	−19.8286	−1.08335
$336$	−0.127131	−0.00693557
$337$	24.8019	1.35105	0.675524	−	0.737338i	$-0.263918\pi$
$337$	24.8019	1.35105	0.675524	+	0.737338i	$0.263918\pi$
$338$	12.2296	0.665203
$339$	0.113921	0.00618732
$340$	15.5577	0.843736
$341$	0.849818	0.0460202
$342$	26.6128	1.43906
$343$	−20.1550	−1.08827
$344$	59.0711	3.18490
$345$	−0.0216717	−0.00116677
$346$	13.4715	0.724232
$347$	−0.845146	−0.0453698	−0.0226849	−	0.999743i	$-0.507221\pi$
$347$	−0.845146	−0.0453698	−0.0226849	+	0.999743i	$0.507221\pi$
$348$	0.0144949	0.000777008 0
$349$	3.49424	0.187042	0.0935212	−	0.995617i	$-0.470188\pi$
$349$	3.49424	0.187042	0.0935212	+	0.995617i	$0.470188\pi$
$350$	6.87914	0.367706
$351$	0.148072	0.00790347
$352$	0.741445	0.0395191
$353$	18.4724	0.983184	0.491592	−	0.870826i	$-0.336415\pi$
$353$	18.4724	0.983184	0.491592	+	0.870826i	$0.336415\pi$
$354$	0.209224	0.0111201
$355$	0.632922	0.0335920
$356$	−60.0173	−3.18091
$357$	−0.0331906	−0.00175663
$358$	29.7100	1.57022
$359$	−4.29168	−0.226506	−0.113253	−	0.993566i	$-0.536127\pi$
$359$	−4.29168	−0.226506	−0.113253	+	0.993566i	$0.536127\pi$
$360$	36.1056	1.90293
$361$	−6.80651	−0.358237
$362$	47.0526	2.47303
$363$	0.0947014	0.00497054
$364$	27.1017	1.42051
$365$	10.3552	0.542016
$366$	−0.254082	−0.0132811
$367$	22.9254	1.19670	0.598348	−	0.801236i	$-0.295824\pi$
$367$	22.9254	1.19670	0.598348	+	0.801236i	$0.295824\pi$
$368$	9.01996	0.470198
$369$	−7.52539	−0.391756
$370$	7.38254	0.383800
$371$	−7.59119	−0.394115
$372$	0.226238	0.0117299
$373$	−12.9639	−0.671243	−0.335621	−	0.941997i	$-0.608946\pi$
$373$	−12.9639	−0.671243	−0.335621	+	0.941997i	$0.608946\pi$
$374$	0.663353	0.0343012
$375$	0.104459	0.00539423
$376$	67.6191	3.48719
$377$	−1.07947	−0.0555957
$378$	−0.279609	−0.0143815
$379$	−9.14406	−0.469699	−0.234849	−	0.972032i	$-0.575460\pi$
$379$	−9.14406	−0.469699	−0.234849	+	0.972032i	$0.575460\pi$
$380$	30.0251	1.54025
$381$	−0.0809891	−0.00414920
$382$	−11.9617	−0.612014
$383$	33.3798	1.70563	0.852814	−	0.522214i	$-0.174894\pi$
$383$	33.3798	1.70563	0.852814	+	0.522214i	$0.174894\pi$
$384$	−0.106349	−0.00542709
$385$	−0.592474	−0.0301953
$386$	43.4109	2.20956
$387$	28.4240	1.44488
$388$	−24.8030	−1.25918
$389$	3.92447	0.198979	0.0994893	−	0.995039i	$-0.468279\pi$
$389$	3.92447	0.198979	0.0994893	+	0.995039i	$0.468279\pi$
$390$	0.121034	0.00612878
$391$	2.35487	0.119091
$392$	15.4442	0.780051
$393$	−0.109242	−0.00551051
$394$	−18.3037	−0.922125
$395$	−0.212022	−0.0106680
$396$	1.92827	0.0968993
$397$	−14.5511	−0.730300	−0.365150	−	0.930949i	$-0.618982\pi$
$397$	−14.5511	−0.730300	−0.365150	+	0.930949i	$0.618982\pi$
$398$	−19.5172	−0.978308
$399$	−0.0640550	−0.00320676
$400$	−8.82426	−0.441213
$401$	4.19975	0.209725	0.104863	−	0.994487i	$-0.466560\pi$
$401$	4.19975	0.209725	0.104863	+	0.994487i	$0.466560\pi$
$402$	−0.225077	−0.0112258
$403$	−16.8485	−0.839285
$404$	−15.5520	−0.773740
$405$	17.3730	0.863272
$406$	2.03841	0.101165
$407$	0.217234	0.0107679
$408$	0.0973000	0.00481707
$409$	−1.64734	−0.0814555	−0.0407278	−	0.999170i	$-0.512968\pi$
$409$	−1.64734	−0.0814555	−0.0407278	+	0.999170i	$0.512968\pi$
$410$	−12.3027	−0.607586
$411$	−0.114287	−0.00563736
$412$	−60.2927	−2.97041
$413$	20.3053	0.999159
$414$	9.91901	0.487493
$415$	14.1457	0.694387
$416$	−14.6999	−0.720723
$417$	0.0752822	0.00368659
$418$	1.28021	0.0626173
$419$	−6.13362	−0.299647	−0.149823	−	0.988713i	$-0.547871\pi$
$419$	−6.13362	−0.299647	−0.149823	+	0.988713i	$0.547871\pi$
$420$	−0.157728	−0.00769635
$421$	33.5268	1.63400	0.816998	−	0.576640i	$-0.195636\pi$
$421$	33.5268	1.63400	0.816998	+	0.576640i	$0.195636\pi$
$422$	20.4877	0.997324
$423$	32.5372	1.58201
$424$	22.2540	1.08075
$425$	−2.30378	−0.111750
$426$	0.00718437	0.000348084 0
$427$	−24.6588	−1.19332
$428$	−49.4950	−2.39243
$429$	0.00356146	0.000171949 0
$430$	46.4683	2.24090
$431$	−31.8747	−1.53535	−0.767675	−	0.640839i	$-0.778586\pi$
$431$	−31.8747	−1.53535	−0.767675	+	0.640839i	$0.778586\pi$
$432$	0.358670	0.0172565
$433$	26.8118	1.28849	0.644245	−	0.764819i	$-0.277172\pi$
$433$	26.8118	1.28849	0.644245	+	0.764819i	$0.277172\pi$
$434$	31.8157	1.52720
$435$	0.00628239	0.000301217 0
$436$	62.9815	3.01627
$437$	4.54471	0.217403
$438$	0.117543	0.00561642
$439$	0.718863	0.0343095	0.0171547	−	0.999853i	$-0.494539\pi$
$439$	0.718863	0.0343095	0.0171547	+	0.999853i	$0.494539\pi$
$440$	1.73687	0.0828020
$441$	7.43150	0.353881
$442$	−13.1517	−0.625561
$443$	−26.9391	−1.27992	−0.639959	−	0.768409i	$-0.721049\pi$
$443$	−26.9391	−1.27992	−0.639959	+	0.768409i	$0.721049\pi$
$444$	0.0578318	0.00274458
$445$	−26.0127	−1.23312
$446$	26.6951	1.26405
$447$	−0.0772222	−0.00365248
$448$	−1.71937	−0.0812326
$449$	8.75025	0.412950	0.206475	−	0.978452i	$-0.433801\pi$
$449$	8.75025	0.412950	0.206475	+	0.978452i	$0.433801\pi$
$450$	−9.70381	−0.457442
$451$	−0.362010	−0.0170464
$452$	−58.8262	−2.76695
$453$	0.0907310	0.00426291
$454$	7.52536	0.353182
$455$	11.7464	0.550681
$456$	0.187781	0.00879363
$457$	−20.8606	−0.975816	−0.487908	−	0.872895i	$-0.662240\pi$
$457$	−20.8606	−0.975816	−0.487908	+	0.872895i	$0.662240\pi$
$458$	−11.9103	−0.556533
$459$	0.0936394	0.00437071
$460$	11.1908	0.521774
$461$	34.7934	1.62049	0.810245	−	0.586091i	$-0.199334\pi$
$461$	34.7934	1.62049	0.810245	+	0.586091i	$0.199334\pi$
$462$	−0.00672524	−0.000312887 0
$463$	7.19820	0.334529	0.167264	−	0.985912i	$-0.446507\pi$
$463$	7.19820	0.334529	0.167264	+	0.985912i	$0.446507\pi$
$464$	−2.61478	−0.121388
$465$	0.0980562	0.00454725
$466$	−16.2092	−0.750875
$467$	15.0353	0.695752	0.347876	−	0.937540i	$-0.386903\pi$
$467$	15.0353	0.695752	0.347876	+	0.937540i	$0.386903\pi$
$468$	−38.2300	−1.76718
$469$	−21.8439	−1.00866
$470$	53.1925	2.45359
$471$	0.0920531	0.00424158
$472$	−59.5261	−2.73991
$473$	1.36734	0.0628706
$474$	−0.00240669	−0.000110543 0
$475$	−4.44610	−0.204001
$476$	17.1389	0.785561
$477$	10.7082	0.490296
$478$	3.88580	0.177732
$479$	30.0359	1.37238	0.686189	−	0.727424i	$-0.259282\pi$
$479$	30.0359	1.37238	0.686189	+	0.727424i	$0.259282\pi$
$480$	0.0855516	0.00390488
$481$	−4.30689	−0.196377
$482$	−60.3760	−2.75005
$483$	−0.0238743	−0.00108632
$484$	−48.9018	−2.22281
$485$	−10.7501	−0.488139
$486$	0.591633	0.0268370
$487$	−1.35562	−0.0614291	−0.0307146	−	0.999528i	$-0.509778\pi$
$487$	−1.35562	−0.0614291	−0.0307146	+	0.999528i	$0.509778\pi$
$488$	72.2886	3.27235
$489$	0.0654926	0.00296168
$490$	12.1492	0.548844
$491$	0.334387	0.0150907	0.00754534	−	0.999972i	$-0.497598\pi$
$491$	0.334387	0.0150907	0.00754534	+	0.999972i	$0.497598\pi$
$492$	−0.0963742	−0.00434488
$493$	−0.682651	−0.0307451
$494$	−25.3816	−1.14197
$495$	0.835753	0.0375643
$496$	−40.8118	−1.83251
$497$	0.697249	0.0312759
$498$	0.160570	0.00719531
$499$	15.3214	0.685882	0.342941	−	0.939357i	$-0.388577\pi$
$499$	15.3214	0.685882	0.342941	+	0.939357i	$0.388577\pi$
$500$	−53.9403	−2.41228
$501$	−0.0564312	−0.00252116
$502$	−19.8101	−0.884169
$503$	−6.94253	−0.309552	−0.154776	−	0.987950i	$-0.549466\pi$
$503$	−6.94253	−0.309552	−0.154776	+	0.987950i	$0.549466\pi$
$504$	39.7752	1.77173
$505$	−6.74055	−0.299951
$506$	0.477156	0.0212122
$507$	0.0415225	0.00184408
$508$	41.8210	1.85551
$509$	−17.6350	−0.781657	−0.390828	−	0.920464i	$-0.627811\pi$
$509$	−17.6350	−0.781657	−0.390828	+	0.920464i	$0.627811\pi$
$510$	0.0765409	0.00338929
$511$	11.4076	0.504644
$512$	50.8084	2.24543
$513$	0.180716	0.00797881
$514$	16.6254	0.733315
$515$	−26.1321	−1.15152
$516$	0.364014	0.0160248
$517$	1.56521	0.0688378
$518$	8.13286	0.357337
$519$	0.0457390	0.00200772
$520$	−34.4353	−1.51009
$521$	38.3611	1.68063	0.840314	−	0.542099i	$-0.182370\pi$
$521$	38.3611	1.68063	0.840314	+	0.542099i	$0.182370\pi$
$522$	−2.87541	−0.125853
$523$	36.4435	1.59356	0.796781	−	0.604268i	$-0.206534\pi$
$523$	36.4435	1.59356	0.796781	+	0.604268i	$0.206534\pi$
$524$	56.4100	2.46428
$525$	0.0233563	0.00101935
$526$	−30.9956	−1.35147
$527$	−10.6549	−0.464135
$528$	0.00862685	0.000375435 0
$529$	−21.3061	−0.926353
$530$	17.5061	0.760415
$531$	−28.6430	−1.24300
$532$	33.0766	1.43405
$533$	7.17724	0.310881
$534$	−0.295273	−0.0127777
$535$	−21.4521	−0.927457
$536$	64.0364	2.76595
$537$	0.100873	0.00435298
$538$	−1.05846	−0.0456333
$539$	0.357494	0.0153984
$540$	0.444993	0.0191494
$541$	−31.2189	−1.34220	−0.671102	−	0.741365i	$-0.734179\pi$
$541$	−31.2189	−1.34220	−0.671102	+	0.741365i	$0.734179\pi$
$542$	2.43012	0.104383
$543$	0.159755	0.00685574
$544$	−9.29613	−0.398568
$545$	27.2975	1.16930
$546$	0.133335	0.00570621
$547$	20.4524	0.874480	0.437240	−	0.899345i	$-0.355956\pi$
$547$	20.4524	0.874480	0.437240	+	0.899345i	$0.355956\pi$
$548$	59.0154	2.52101
$549$	34.7841	1.48455
$550$	−0.466804	−0.0199046
$551$	−1.31746	−0.0561256
$552$	0.0699888	0.00297892
$553$	−0.233571	−0.00993246
$554$	17.1952	0.730553
$555$	0.0250655	0.00106397
$556$	−38.8741	−1.64863
$557$	17.9004	0.758466	0.379233	−	0.925301i	$-0.376188\pi$
$557$	17.9004	0.758466	0.379233	+	0.925301i	$0.376188\pi$
$558$	−44.8797	−1.89991
$559$	−27.1090	−1.14659
$560$	28.4531	1.20236
$561$	0.00225224	9.50898e−5 0
$562$	37.7883	1.59400
$563$	−21.2873	−0.897155	−0.448577	−	0.893744i	$-0.648069\pi$
$563$	−21.2873	−0.897155	−0.448577	+	0.893744i	$0.648069\pi$
$564$	0.416689	0.0175458
$565$	−25.4965	−1.07265
$566$	41.7528	1.75500
$567$	19.1387	0.803750
$568$	−2.04402	−0.0857652
$569$	−32.5512	−1.36462	−0.682309	−	0.731064i	$-0.739024\pi$
$569$	−32.5512	−1.36462	−0.682309	+	0.731064i	$0.739024\pi$
$570$	0.147717	0.00618720
$571$	−18.3217	−0.766738	−0.383369	−	0.923595i	$-0.625236\pi$
$571$	−18.3217	−0.766738	−0.383369	+	0.923595i	$0.625236\pi$
$572$	−1.83906	−0.0768951
$573$	−0.0406129	−0.00169663
$574$	−13.5530	−0.565693
$575$	−1.65713	−0.0691072
$576$	2.42537	0.101057
$577$	−33.8511	−1.40924	−0.704619	−	0.709586i	$-0.748882\pi$
$577$	−33.8511	−1.40924	−0.704619	+	0.709586i	$0.748882\pi$
$578$	34.8712	1.45045
$579$	0.147391	0.00612535
$580$	−3.24409	−0.134704
$581$	15.5834	0.646510
$582$	−0.122026	−0.00505814
$583$	0.515122	0.0213342
$584$	−33.4421	−1.38384
$585$	−16.5697	−0.685072
$586$	−56.0653	−2.31604
$587$	−44.7998	−1.84909	−0.924543	−	0.381077i	$-0.875553\pi$
$587$	−44.7998	−1.84909	−0.924543	+	0.381077i	$0.875553\pi$
$588$	0.0951718	0.00392482
$589$	−20.5630	−0.847285
$590$	−46.8261	−1.92780
$591$	−0.0621454	−0.00255632
$592$	−10.4325	−0.428772
$593$	−10.0209	−0.411511	−0.205755	−	0.978603i	$-0.565965\pi$
$593$	−10.0209	−0.411511	−0.205755	+	0.978603i	$0.565965\pi$
$594$	0.0189737	0.000778500 0
$595$	7.42836	0.304533
$596$	39.8759	1.63338
$597$	−0.0662656	−0.00271207
$598$	−9.46012	−0.386853
$599$	−30.6017	−1.25035	−0.625176	−	0.780484i	$-0.714973\pi$
$599$	−30.6017	−1.25035	−0.625176	+	0.780484i	$0.714973\pi$
$600$	−0.0684703	−0.00279529
$601$	3.73330	0.152284	0.0761422	−	0.997097i	$-0.475740\pi$
$601$	3.73330	0.152284	0.0761422	+	0.997097i	$0.475740\pi$
$602$	51.1910	2.08639
$603$	30.8133	1.25481
$604$	−46.8515	−1.90636
$605$	−21.1951	−0.861701
$606$	−0.0765127	−0.00310812
$607$	22.3584	0.907499	0.453750	−	0.891129i	$-0.350086\pi$
$607$	22.3584	0.907499	0.453750	+	0.891129i	$0.350086\pi$
$608$	−17.9407	−0.727593
$609$	0.00692089	0.000280449 0
$610$	56.8658	2.30243
$611$	−31.0319	−1.25542
$612$	−24.1764	−0.977273
$613$	41.2539	1.66623	0.833115	−	0.553100i	$-0.186555\pi$
$613$	41.2539	1.66623	0.833115	+	0.553100i	$0.186555\pi$
$614$	−79.8968	−3.22437
$615$	−0.0417706	−0.00168435
$616$	1.91340	0.0770929
$617$	40.9533	1.64872	0.824358	−	0.566068i	$-0.191536\pi$
$617$	40.9533	1.64872	0.824358	+	0.566068i	$0.191536\pi$
$618$	−0.296628	−0.0119321
$619$	−35.0309	−1.40801	−0.704005	−	0.710195i	$-0.748607\pi$
$619$	−35.0309	−1.40801	−0.704005	+	0.710195i	$0.748607\pi$
$620$	−50.6341	−2.03352
$621$	0.0673557	0.00270289
$622$	33.0124	1.32368
$623$	−28.6565	−1.14810
$624$	−0.171036	−0.00684693
$625$	−17.0125	−0.680502
$626$	−30.4595	−1.21741
$627$	0.00434664	0.000173588 0
$628$	−47.5342	−1.89682
$629$	−2.72365	−0.108599
$630$	31.2891	1.24659
$631$	−2.63451	−0.104878	−0.0524390	−	0.998624i	$-0.516700\pi$
$631$	−2.63451	−0.104878	−0.0524390	+	0.998624i	$0.516700\pi$
$632$	0.684726	0.0272369
$633$	0.0695606	0.00276479
$634$	45.2013	1.79517
$635$	18.1261	0.719313
$636$	0.137135	0.00543777
$637$	−7.08769	−0.280825
$638$	−0.138322	−0.00547623
$639$	−0.983549	−0.0389086
$640$	23.8018	0.940850
$641$	19.7702	0.780876	0.390438	−	0.920629i	$-0.372324\pi$
$641$	19.7702	0.780876	0.390438	+	0.920629i	$0.372324\pi$
$642$	−0.243506	−0.00961040
$643$	10.8105	0.426324	0.213162	−	0.977017i	$-0.431624\pi$
$643$	10.8105	0.426324	0.213162	+	0.977017i	$0.431624\pi$
$644$	12.3282	0.485799
$645$	0.157771	0.00621223
$646$	−16.0511	−0.631524
$647$	−21.8033	−0.857176	−0.428588	−	0.903500i	$-0.640989\pi$
$647$	−21.8033	−0.857176	−0.428588	+	0.903500i	$0.640989\pi$
$648$	−56.1061	−2.20406
$649$	−1.37788	−0.0540863
$650$	9.25488	0.363006
$651$	0.108022	0.00423372
$652$	−33.8190	−1.32445
$653$	8.29490	0.324604	0.162302	−	0.986741i	$-0.448108\pi$
$653$	8.29490	0.324604	0.162302	+	0.986741i	$0.448108\pi$
$654$	0.309857	0.0121164
$655$	24.4493	0.955312
$656$	17.3853	0.678780
$657$	−16.0918	−0.627800
$658$	58.5987	2.28442
$659$	−23.6372	−0.920773	−0.460386	−	0.887719i	$-0.652289\pi$
$659$	−23.6372	−0.920773	−0.460386	+	0.887719i	$0.652289\pi$
$660$	0.0107031	0.000416618 0
$661$	−24.4857	−0.952385	−0.476192	−	0.879341i	$-0.657983\pi$
$661$	−24.4857	−0.952385	−0.476192	+	0.879341i	$0.657983\pi$
$662$	−47.5513	−1.84813
$663$	−0.0446531	−0.00173418
$664$	−45.6837	−1.77287
$665$	14.3361	0.555930
$666$	−11.4723	−0.444543
$667$	−0.491038	−0.0190130
$668$	29.1399	1.12746
$669$	0.0906363	0.00350420
$670$	50.3742	1.94612
$671$	1.67330	0.0645969
$672$	0.0942466	0.00363564
$673$	0.727731	0.0280520	0.0140260	−	0.999902i	$-0.495535\pi$
$673$	0.727731	0.0280520	0.0140260	+	0.999902i	$0.495535\pi$
$674$	−63.0089	−2.42701
$675$	−0.0658944	−0.00253628
$676$	−21.4413	−0.824667
$677$	−6.17378	−0.237278	−0.118639	−	0.992937i	$-0.537853\pi$
$677$	−6.17378	−0.237278	−0.118639	+	0.992937i	$0.537853\pi$
$678$	−0.289413	−0.0111149
$679$	−11.8427	−0.454482
$680$	−21.7766	−0.835095
$681$	0.0255504	0.000979094 0
$682$	−2.15895	−0.0826704
$683$	−22.5235	−0.861838	−0.430919	−	0.902391i	$-0.641811\pi$
$683$	−22.5235	−0.861838	−0.430919	+	0.902391i	$0.641811\pi$
$684$	−46.6584	−1.78403
$685$	25.5785	0.977304
$686$	51.2035	1.95496
$687$	−0.0404385	−0.00154282
$688$	−65.6656	−2.50348
$689$	−10.2128	−0.389078
$690$	0.0550566	0.00209597
$691$	−13.8238	−0.525883	−0.262941	−	0.964812i	$-0.584693\pi$
$691$	−13.8238	−0.525883	−0.262941	+	0.964812i	$0.584693\pi$
$692$	−23.6186	−0.897846
$693$	0.920694	0.0349743
$694$	2.14708	0.0815020
$695$	−16.8488	−0.639113
$696$	−0.0202890	−0.000769051 0
$697$	4.53884	0.171921
$698$	−8.87706	−0.336002
$699$	−0.0550341	−0.00208158
$700$	−12.0607	−0.455852
$701$	−36.9826	−1.39681	−0.698407	−	0.715701i	$-0.746107\pi$
$701$	−36.9826	−1.39681	−0.698407	+	0.715701i	$0.746107\pi$
$702$	−0.376173	−0.0141977
$703$	−5.25640	−0.198249
$704$	0.116673	0.00439727
$705$	0.180602	0.00680185
$706$	−46.9287	−1.76618
$707$	−7.42562	−0.279269
$708$	−0.366817	−0.0137858
$709$	38.5230	1.44676	0.723381	−	0.690449i	$-0.242587\pi$
$709$	38.5230	1.44676	0.723381	+	0.690449i	$0.242587\pi$
$710$	−1.60793	−0.0603444
$711$	0.329479	0.0123564
$712$	84.0080	3.14833
$713$	−7.66417	−0.287025
$714$	0.0843201	0.00315560
$715$	−0.797088	−0.0298094
$716$	−52.0885	−1.94664
$717$	0.0131932	0.000492710 0
$718$	10.9030	0.406894
$719$	−1.58342	−0.0590515	−0.0295257	−	0.999564i	$-0.509400\pi$
$719$	−1.58342	−0.0590515	−0.0295257	+	0.999564i	$0.509400\pi$
$720$	−40.1364	−1.49579
$721$	−28.7880	−1.07212
$722$	17.2918	0.643535
$723$	−0.204991	−0.00762370
$724$	−82.4941	−3.06587
$725$	0.480384	0.0178410
$726$	−0.240587	−0.00892903
$727$	−3.28651	−0.121890	−0.0609449	−	0.998141i	$-0.519411\pi$
$727$	−3.28651	−0.121890	−0.0609449	+	0.998141i	$0.519411\pi$
$728$	−37.9351	−1.40597
$729$	−26.9960	−0.999851
$730$	−26.3072	−0.973673
$731$	−17.1436	−0.634078
$732$	0.445464	0.0164648
$733$	−3.41915	−0.126289	−0.0631446	−	0.998004i	$-0.520113\pi$
$733$	−3.41915	−0.126289	−0.0631446	+	0.998004i	$0.520113\pi$
$734$	−58.2416	−2.14974
$735$	0.0412494	0.00152151
$736$	−6.68680	−0.246479
$737$	1.48228	0.0546004
$738$	19.1181	0.703748
$739$	25.1496	0.925145	0.462572	−	0.886582i	$-0.346927\pi$
$739$	25.1496	0.925145	0.462572	+	0.886582i	$0.346927\pi$
$740$	−12.9433	−0.475805
$741$	−0.0861766	−0.00316578
$742$	19.2853	0.707985
$743$	0.445394	0.0163399	0.00816996	−	0.999967i	$-0.497399\pi$
$743$	0.445394	0.0163399	0.00816996	+	0.999967i	$0.497399\pi$
$744$	−0.316672	−0.0116098
$745$	17.2830	0.633201
$746$	32.9344	1.20582
$747$	−21.9822	−0.804287
$748$	−1.16301	−0.0425239
$749$	−23.6324	−0.863509
$750$	−0.265376	−0.00969015
$751$	16.2337	0.592374	0.296187	−	0.955130i	$-0.404285\pi$
$751$	16.2337	0.592374	0.296187	+	0.955130i	$0.404285\pi$
$752$	−75.1679	−2.74109
$753$	−0.0672602	−0.00245110
$754$	2.74238	0.0998716
$755$	−20.3064	−0.739026
$756$	0.490219	0.0178291
$757$	42.4560	1.54309	0.771545	−	0.636174i	$-0.219484\pi$
$757$	42.4560	1.54309	0.771545	+	0.636174i	$0.219484\pi$
$758$	23.2303	0.843763
$759$	0.00162006	5.88045e−5 0
$760$	−42.0270	−1.52448
$761$	−8.06197	−0.292246	−0.146123	−	0.989266i	$-0.546680\pi$
$761$	−8.06197	−0.292246	−0.146123	+	0.989266i	$0.546680\pi$
$762$	0.205751	0.00745359
$763$	30.0718	1.08867
$764$	20.9716	0.758727
$765$	−10.4785	−0.378853
$766$	−84.8008	−3.06398
$767$	27.3178	0.986389
$768$	0.256230	0.00924590
$769$	24.6000	0.887099	0.443549	−	0.896250i	$-0.353719\pi$
$769$	24.6000	0.887099	0.443549	+	0.896250i	$0.353719\pi$
$770$	1.50517	0.0542426
$771$	0.0564473	0.00203290
$772$	−76.1094	−2.73924
$773$	5.46534	0.196575	0.0982873	−	0.995158i	$-0.468664\pi$
$773$	5.46534	0.196575	0.0982873	+	0.995158i	$0.468664\pi$
$774$	−72.2108	−2.59556
$775$	7.49789	0.269332
$776$	34.7176	1.24629
$777$	0.0276130	0.000990612 0
$778$	−9.97005	−0.357443
$779$	8.75956	0.313844
$780$	−0.212200	−0.00759798
$781$	−0.0473138	−0.00169302
$782$	−5.98252	−0.213934
$783$	−0.0195257	−0.000697790 0
$784$	−17.1684	−0.613156
$785$	−20.6023	−0.735328
$786$	0.277526	0.00989904
$787$	17.6987	0.630890	0.315445	−	0.948944i	$-0.397846\pi$
$787$	17.6987	0.630890	0.315445	+	0.948944i	$0.397846\pi$
$788$	32.0905	1.14318
$789$	−0.105238	−0.00374656
$790$	0.538639	0.0191639
$791$	−28.0878	−0.998687
$792$	−2.69906	−0.0959070
$793$	−33.1748	−1.17807
$794$	36.9669	1.31190
$795$	0.0594373	0.00210802
$796$	34.2181	1.21283
$797$	−14.9799	−0.530617	−0.265308	−	0.964164i	$-0.585474\pi$
$797$	−14.9799	−0.530617	−0.265308	+	0.964164i	$0.585474\pi$
$798$	0.162731	0.00576060
$799$	−19.6244	−0.694260
$800$	6.54172	0.231285
$801$	40.4233	1.42829
$802$	−10.6694	−0.376749
$803$	−0.774099	−0.0273173
$804$	0.394611	0.0139169
$805$	5.34329	0.188326
$806$	42.8034	1.50769
$807$	−0.00359372	−0.000126505 0
$808$	21.7686	0.765817
$809$	18.0084	0.633143	0.316571	−	0.948569i	$-0.397468\pi$
$809$	18.0084	0.633143	0.316571	+	0.948569i	$0.397468\pi$
$810$	−44.1358	−1.55077
$811$	−37.0608	−1.30138	−0.650691	−	0.759343i	$-0.725521\pi$
$811$	−37.0608	−1.30138	−0.650691	+	0.759343i	$0.725521\pi$
$812$	−3.57380	−0.125416
$813$	0.00825085	0.000289370 0
$814$	−0.551879	−0.0193433
$815$	−14.6578	−0.513442
$816$	−0.108162	−0.00378643
$817$	−33.0856	−1.15752
$818$	4.18503	0.146326
$819$	−18.2537	−0.637837
$820$	21.5694	0.753237
$821$	−33.4687	−1.16807	−0.584033	−	0.811730i	$-0.698526\pi$
$821$	−33.4687	−1.16807	−0.584033	+	0.811730i	$0.698526\pi$
$822$	0.290344	0.0101269
$823$	41.5560	1.44855	0.724275	−	0.689511i	$-0.242175\pi$
$823$	41.5560	1.44855	0.724275	+	0.689511i	$0.242175\pi$
$824$	84.3936	2.93999
$825$	−0.00158491	−5.51796e−5 0
$826$	−51.5853	−1.79488
$827$	12.6586	0.440184	0.220092	−	0.975479i	$-0.429364\pi$
$827$	12.6586	0.440184	0.220092	+	0.975479i	$0.429364\pi$
$828$	−17.3903	−0.604355
$829$	−7.16890	−0.248986	−0.124493	−	0.992220i	$-0.539730\pi$
$829$	−7.16890	−0.248986	−0.124493	+	0.992220i	$0.539730\pi$
$830$	−35.9370	−1.24739
$831$	0.0583818	0.00202524
$832$	−2.31316	−0.0801944
$833$	−4.48221	−0.155299
$834$	−0.191253	−0.00662255
$835$	12.6298	0.437073
$836$	−2.24451	−0.0776280
$837$	−0.304759	−0.0105340
$838$	15.5824	0.538284
$839$	19.9198	0.687710	0.343855	−	0.939023i	$-0.388267\pi$
$839$	19.9198	0.687710	0.343855	+	0.939023i	$0.388267\pi$
$840$	0.220777	0.00761753
$841$	−28.8577	−0.995092
$842$	−85.1743	−2.93530
$843$	0.128300	0.00441890
$844$	−35.9196	−1.23640
$845$	−9.29312	−0.319693
$846$	−82.6602	−2.84192
$847$	−23.3492	−0.802288
$848$	−24.7383	−0.849517
$849$	0.141761	0.00486522
$850$	5.85272	0.200747
$851$	−1.95914	−0.0671586
$852$	−0.0125959	−0.000431527 0
$853$	−27.1149	−0.928396	−0.464198	−	0.885731i	$-0.653657\pi$
$853$	−27.1149	−0.928396	−0.464198	+	0.885731i	$0.653657\pi$
$854$	62.6453	2.14368
$855$	−20.2227	−0.691602
$856$	69.2796	2.36793
$857$	16.1305	0.551006	0.275503	−	0.961300i	$-0.411156\pi$
$857$	16.1305	0.551006	0.275503	+	0.961300i	$0.411156\pi$
$858$	−0.00904783	−0.000308888 0
$859$	30.1033	1.02711	0.513555	−	0.858056i	$-0.328328\pi$
$859$	30.1033	1.02711	0.513555	+	0.858056i	$0.328328\pi$
$860$	−81.4696	−2.77809
$861$	−0.0460159	−0.00156822
$862$	80.9771	2.75809
$863$	14.4271	0.491105	0.245553	−	0.969383i	$-0.421031\pi$
$863$	14.4271	0.491105	0.245553	+	0.969383i	$0.421031\pi$
$864$	−0.265894	−0.00904591
$865$	−10.2368	−0.348062
$866$	−68.1148	−2.31464
$867$	0.118396	0.00402094
$868$	−55.7803	−1.89331
$869$	0.0158497	0.000537663 0
$870$	−0.0159603	−0.000541105 0
$871$	−29.3877	−0.995765
$872$	−88.1572	−2.98538
$873$	16.7055	0.565396
$874$	−11.5457	−0.390541
$875$	−25.7549	−0.870675
$876$	−0.206080	−0.00696280
$877$	11.4273	0.385873	0.192937	−	0.981211i	$-0.438199\pi$
$877$	11.4273	0.385873	0.192937	+	0.981211i	$0.438199\pi$
$878$	−1.82626	−0.0616332
$879$	−0.190355	−0.00642052
$880$	−1.93077	−0.0650862
$881$	−39.1727	−1.31976	−0.659881	−	0.751371i	$-0.729393\pi$
$881$	−39.1727	−1.31976	−0.659881	+	0.751371i	$0.729393\pi$
$882$	−18.8796	−0.635709
$883$	−57.3561	−1.93019	−0.965094	−	0.261904i	$-0.915650\pi$
$883$	−57.3561	−1.93019	−0.965094	+	0.261904i	$0.915650\pi$
$884$	23.0579	0.775521
$885$	−0.158986	−0.00534426
$886$	68.4384	2.29923
$887$	31.0344	1.04203	0.521016	−	0.853547i	$-0.325553\pi$
$887$	31.0344	1.04203	0.521016	+	0.853547i	$0.325553\pi$
$888$	−0.0809490	−0.00271647
$889$	19.9683	0.669717
$890$	66.0849	2.21517
$891$	−1.29871	−0.0435085
$892$	−46.8026	−1.56707
$893$	−37.8733	−1.26738
$894$	0.196182	0.00656129
$895$	−22.5762	−0.754640
$896$	26.2209	0.875979
$897$	−0.0321194	−0.00107244
$898$	−22.2299	−0.741820
$899$	2.22176	0.0740997
$900$	17.0130	0.567101
$901$	−6.45852	−0.215165
$902$	0.919681	0.0306220
$903$	0.173806	0.00578390
$904$	82.3409	2.73862
$905$	−35.7546	−1.18852
$906$	−0.230500	−0.00765787
$907$	22.4956	0.746953	0.373477	−	0.927640i	$-0.378166\pi$
$907$	22.4956	0.746953	0.373477	+	0.927640i	$0.378166\pi$
$908$	−13.1937	−0.437848
$909$	10.4747	0.347423
$910$	−29.8416	−0.989239
$911$	−8.50656	−0.281835	−0.140918	−	0.990021i	$-0.545005\pi$
$911$	−8.50656	−0.281835	−0.140918	+	0.990021i	$0.545005\pi$
$912$	−0.208744	−0.00691220
$913$	−1.05746	−0.0349968
$914$	52.9959	1.75295
$915$	0.193073	0.00638280
$916$	20.8816	0.689946
$917$	26.9342	0.889444
$918$	−0.237889	−0.00785152
$919$	−47.2331	−1.55808	−0.779038	−	0.626977i	$-0.784292\pi$
$919$	−47.2331	−1.55808	−0.779038	+	0.626977i	$0.784292\pi$
$920$	−15.6641	−0.516431
$921$	−0.271269	−0.00893861
$922$	−88.3921	−2.91104
$923$	0.938046	0.0308762
$924$	0.0117909	0.000387892 0
$925$	1.91664	0.0630187
$926$	−18.2869	−0.600945
$927$	40.6088	1.33377
$928$	1.93843	0.0636320
$929$	−28.4625	−0.933826	−0.466913	−	0.884303i	$-0.654634\pi$
$929$	−28.4625	−0.933826	−0.466913	+	0.884303i	$0.654634\pi$
$930$	−0.249110	−0.00816864
$931$	−8.65028	−0.283502
$932$	28.4184	0.930876
$933$	0.112085	0.00366951
$934$	−38.1970	−1.24984
$935$	−0.504073	−0.0164849
$936$	53.5117	1.74909
$937$	−34.1367	−1.11520	−0.557598	−	0.830111i	$-0.688277\pi$
$937$	−34.1367	−1.11520	−0.557598	+	0.830111i	$0.688277\pi$
$938$	55.4939	1.81194
$939$	−0.103417	−0.00337490
$940$	−93.2588	−3.04177
$941$	26.5538	0.865629	0.432814	−	0.901483i	$-0.357521\pi$
$941$	26.5538	0.865629	0.432814	+	0.901483i	$0.357521\pi$
$942$	−0.233859	−0.00761955
$943$	3.26483	0.106317
$944$	66.1714	2.15369
$945$	0.212471	0.00691169
$946$	−3.47371	−0.112940
$947$	23.3411	0.758484	0.379242	−	0.925298i	$-0.376185\pi$
$947$	23.3411	0.758484	0.379242	+	0.925298i	$0.376185\pi$
$948$	0.00421948	0.000137042 0
$949$	15.3473	0.498195
$950$	11.2953	0.366466
$951$	0.153469	0.00497659
$952$	−23.9899	−0.777516
$953$	−17.4574	−0.565502	−0.282751	−	0.959193i	$-0.591247\pi$
$953$	−17.4574	−0.565502	−0.282751	+	0.959193i	$0.591247\pi$
$954$	−27.2041	−0.880765
$955$	9.08953	0.294130
$956$	−6.81271	−0.220339
$957$	−0.000469637 0	−1.51812e−5 0
$958$	−76.3058	−2.46533
$959$	28.1781	0.909920
$960$	0.0134623	0.000434494 0
$961$	3.67742	0.118626
$962$	10.9416	0.352770
$963$	33.3362	1.07424
$964$	105.853	3.40929
$965$	−32.9874	−1.06190
$966$	0.0606523	0.00195146
$967$	−6.07349	−0.195310	−0.0976552	−	0.995220i	$-0.531134\pi$
$967$	−6.07349	−0.195310	−0.0976552	+	0.995220i	$0.531134\pi$
$968$	68.4494	2.20005
$969$	−0.0544975	−0.00175071
$970$	27.3106	0.876889
$971$	27.7521	0.890607	0.445304	−	0.895380i	$-0.353096\pi$
$971$	27.7521	0.890607	0.445304	+	0.895380i	$0.353096\pi$
$972$	−1.03727	−0.0332704
$973$	−18.5613	−0.595047
$974$	3.44394	0.110351
$975$	0.0314225	0.00100633
$976$	−80.3587	−2.57222
$977$	−5.31634	−0.170085	−0.0850424	−	0.996377i	$-0.527103\pi$
$977$	−5.31634	−0.170085	−0.0850424	+	0.996377i	$0.527103\pi$
$978$	−0.166383	−0.00532033
$979$	1.94457	0.0621487
$980$	−21.3003	−0.680414
$981$	−42.4198	−1.35436
$982$	−0.849505	−0.0271088
$983$	41.5899	1.32651	0.663255	−	0.748393i	$-0.269174\pi$
$983$	41.5899	1.32651	0.663255	+	0.748393i	$0.269174\pi$
$984$	0.134898	0.00430039
$985$	13.9087	0.443168
$986$	1.73426	0.0552302
$987$	0.198957	0.00633287
$988$	44.4998	1.41573
$989$	−12.3315	−0.392120
$990$	−2.12322	−0.0674802
$991$	28.9636	0.920059	0.460029	−	0.887904i	$-0.347839\pi$
$991$	28.9636	0.920059	0.460029	+	0.887904i	$0.347839\pi$
$992$	30.2552	0.960603
$993$	−0.161448	−0.00512340
$994$	−1.77135	−0.0561838
$995$	14.8308	0.470169
$996$	−0.281516	−0.00892018
$997$	−15.9593	−0.505437	−0.252718	−	0.967540i	$-0.581325\pi$
$997$	−15.9593	−0.505437	−0.252718	+	0.967540i	$0.581325\pi$
$998$	−38.9239	−1.23211
$999$	−0.0779036	−0.00246476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.17	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.17	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54048 q^{2} -0.00862555 q^{3} +4.45405 q^{4} +1.93048 q^{5} +0.0219131 q^{6} +2.12668 q^{7} -6.23447 q^{8} -2.99993 q^{9} +O(q^{10})\)	\(q-2.54048 q^{2} -0.00862555 q^{3} +4.45405 q^{4} +1.93048 q^{5} +0.0219131 q^{6} +2.12668 q^{7} -6.23447 q^{8} -2.99993 q^{9} -4.90434 q^{10} -0.144312 q^{11} -0.0384187 q^{12} +2.86114 q^{13} -5.40279 q^{14} -0.0166514 q^{15} +6.93047 q^{16} +1.80936 q^{17} +7.62126 q^{18} +3.49192 q^{19} +8.59845 q^{20} -0.0183438 q^{21} +0.366622 q^{22} +1.30149 q^{23} +0.0537758 q^{24} -1.27326 q^{25} -7.26867 q^{26} +0.0517527 q^{27} +9.47234 q^{28} -0.377288 q^{29} +0.0423027 q^{30} -5.88875 q^{31} -5.13779 q^{32} +0.00124477 q^{33} -4.59666 q^{34} +4.10551 q^{35} -13.3618 q^{36} -1.50531 q^{37} -8.87116 q^{38} -0.0246789 q^{39} -12.0355 q^{40} +2.50853 q^{41} +0.0466021 q^{42} -9.47492 q^{43} -0.642773 q^{44} -5.79129 q^{45} -3.30642 q^{46} -10.8460 q^{47} -0.0597791 q^{48} -2.47723 q^{49} +3.23468 q^{50} -0.0156068 q^{51} +12.7437 q^{52} -3.56950 q^{53} -0.131477 q^{54} -0.278591 q^{55} -13.2587 q^{56} -0.0301197 q^{57} +0.958494 q^{58} +9.54789 q^{59} -0.0741664 q^{60} -11.5950 q^{61} +14.9603 q^{62} -6.37988 q^{63} -0.808476 q^{64} +5.52336 q^{65} -0.00316232 q^{66} -10.2713 q^{67} +8.05900 q^{68} -0.0112261 q^{69} -10.4300 q^{70} +0.327858 q^{71} +18.7030 q^{72} +5.36406 q^{73} +3.82420 q^{74} +0.0109825 q^{75} +15.5532 q^{76} -0.306906 q^{77} +0.0626963 q^{78} -0.109829 q^{79} +13.3791 q^{80} +8.99933 q^{81} -6.37287 q^{82} +7.32759 q^{83} -0.0817042 q^{84} +3.49294 q^{85} +24.0709 q^{86} +0.00325432 q^{87} +0.899710 q^{88} -13.4748 q^{89} +14.7127 q^{90} +6.08472 q^{91} +5.79692 q^{92} +0.0507938 q^{93} +27.5541 q^{94} +6.74107 q^{95} +0.0443163 q^{96} -5.56865 q^{97} +6.29336 q^{98} +0.432925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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