LMFDB - Embedded newform 8035.2.a.e.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29854 q^{2} +0.376180 q^{3} +3.28327 q^{4} +1.00000 q^{5} -0.864664 q^{6} -1.95111 q^{7} -2.94965 q^{8} -2.85849 q^{9} +O(q^{10})$	\(q-2.29854 q^{2} +0.376180 q^{3} +3.28327 q^{4} +1.00000 q^{5} -0.864664 q^{6} -1.95111 q^{7} -2.94965 q^{8} -2.85849 q^{9} -2.29854 q^{10} +2.60450 q^{11} +1.23510 q^{12} -2.36574 q^{13} +4.48469 q^{14} +0.376180 q^{15} +0.213337 q^{16} -1.73671 q^{17} +6.57034 q^{18} +1.91328 q^{19} +3.28327 q^{20} -0.733968 q^{21} -5.98655 q^{22} -4.02247 q^{23} -1.10960 q^{24} +1.00000 q^{25} +5.43775 q^{26} -2.20385 q^{27} -6.40602 q^{28} -2.38367 q^{29} -0.864664 q^{30} +4.76604 q^{31} +5.40894 q^{32} +0.979762 q^{33} +3.99189 q^{34} -1.95111 q^{35} -9.38520 q^{36} -9.22691 q^{37} -4.39774 q^{38} -0.889945 q^{39} -2.94965 q^{40} -5.94952 q^{41} +1.68705 q^{42} +10.4144 q^{43} +8.55130 q^{44} -2.85849 q^{45} +9.24579 q^{46} +0.872904 q^{47} +0.0802530 q^{48} -3.19318 q^{49} -2.29854 q^{50} -0.653316 q^{51} -7.76738 q^{52} -2.14307 q^{53} +5.06562 q^{54} +2.60450 q^{55} +5.75509 q^{56} +0.719737 q^{57} +5.47896 q^{58} +9.38810 q^{59} +1.23510 q^{60} +0.990473 q^{61} -10.9549 q^{62} +5.57722 q^{63} -12.8593 q^{64} -2.36574 q^{65} -2.25202 q^{66} -3.56243 q^{67} -5.70209 q^{68} -1.51317 q^{69} +4.48469 q^{70} +9.58765 q^{71} +8.43154 q^{72} +0.651431 q^{73} +21.2084 q^{74} +0.376180 q^{75} +6.28182 q^{76} -5.08167 q^{77} +2.04557 q^{78} -6.54717 q^{79} +0.213337 q^{80} +7.74642 q^{81} +13.6752 q^{82} -12.9789 q^{83} -2.40982 q^{84} -1.73671 q^{85} -23.9378 q^{86} -0.896691 q^{87} -7.68238 q^{88} -10.2616 q^{89} +6.57034 q^{90} +4.61582 q^{91} -13.2069 q^{92} +1.79289 q^{93} -2.00640 q^{94} +1.91328 q^{95} +2.03474 q^{96} +2.88823 q^{97} +7.33964 q^{98} -7.44494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.29854	−1.62531	−0.812656	−	0.582744i	$-0.801979\pi$
$2$	−2.29854	−1.62531	−0.812656	+	0.582744i	$0.801979\pi$
$3$	0.376180	0.217188	0.108594	−	0.994086i	$-0.465365\pi$
$3$	0.376180	0.217188	0.108594	+	0.994086i	$0.465365\pi$
$4$	3.28327	1.64164
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.864664	−0.352998
$7$	−1.95111	−0.737449	−0.368725	−	0.929539i	$-0.620205\pi$
$7$	−1.95111	−0.737449	−0.368725	+	0.929539i	$0.620205\pi$
$8$	−2.94965	−1.04286
$9$	−2.85849	−0.952830
$10$	−2.29854	−0.726861
$11$	2.60450	0.785287	0.392644	−	0.919691i	$-0.371561\pi$
$11$	2.60450	0.785287	0.392644	+	0.919691i	$0.371561\pi$
$12$	1.23510	0.356543
$13$	−2.36574	−0.656139	−0.328069	−	0.944654i	$-0.606398\pi$
$13$	−2.36574	−0.656139	−0.328069	+	0.944654i	$0.606398\pi$
$14$	4.48469	1.19858
$15$	0.376180	0.0971293
$16$	0.213337	0.0533342
$17$	−1.73671	−0.421214	−0.210607	−	0.977571i	$-0.567544\pi$
$17$	−1.73671	−0.421214	−0.210607	+	0.977571i	$0.567544\pi$
$18$	6.57034	1.54864
$19$	1.91328	0.438936	0.219468	−	0.975620i	$-0.429568\pi$
$19$	1.91328	0.438936	0.219468	+	0.975620i	$0.429568\pi$
$20$	3.28327	0.734162
$21$	−0.733968	−0.160165
$22$	−5.98655	−1.27634
$23$	−4.02247	−0.838742	−0.419371	−	0.907815i	$-0.637749\pi$
$23$	−4.02247	−0.838742	−0.419371	+	0.907815i	$0.637749\pi$
$24$	−1.10960	−0.226496
$25$	1.00000	0.200000
$26$	5.43775	1.06643
$27$	−2.20385	−0.424130
$28$	−6.40602	−1.21062
$29$	−2.38367	−0.442637	−0.221319	−	0.975202i	$-0.571036\pi$
$29$	−2.38367	−0.442637	−0.221319	+	0.975202i	$0.571036\pi$
$30$	−0.864664	−0.157865
$31$	4.76604	0.856006	0.428003	−	0.903777i	$-0.359217\pi$
$31$	4.76604	0.856006	0.428003	+	0.903777i	$0.359217\pi$
$32$	5.40894	0.956175
$33$	0.979762	0.170555
$34$	3.99189	0.684604
$35$	−1.95111	−0.329797
$36$	−9.38520	−1.56420
$37$	−9.22691	−1.51689	−0.758447	−	0.651735i	$-0.774042\pi$
$37$	−9.22691	−1.51689	−0.758447	+	0.651735i	$0.774042\pi$
$38$	−4.39774	−0.713408
$39$	−0.889945	−0.142505
$40$	−2.94965	−0.466381
$41$	−5.94952	−0.929159	−0.464580	−	0.885531i	$-0.653795\pi$
$41$	−5.94952	−0.929159	−0.464580	+	0.885531i	$0.653795\pi$
$42$	1.68705	0.260318
$43$	10.4144	1.58818	0.794088	−	0.607803i	$-0.207949\pi$
$43$	10.4144	1.58818	0.794088	+	0.607803i	$0.207949\pi$
$44$	8.55130	1.28916
$45$	−2.85849	−0.426118
$46$	9.24579	1.36322
$47$	0.872904	0.127326	0.0636631	−	0.997971i	$-0.479722\pi$
$47$	0.872904	0.127326	0.0636631	+	0.997971i	$0.479722\pi$
$48$	0.0802530	0.0115835
$49$	−3.19318	−0.456168
$50$	−2.29854	−0.325062
$51$	−0.653316	−0.0914825
$52$	−7.76738	−1.07714
$53$	−2.14307	−0.294373	−0.147186	−	0.989109i	$-0.547022\pi$
$53$	−2.14307	−0.294373	−0.147186	+	0.989109i	$0.547022\pi$
$54$	5.06562	0.689344
$55$	2.60450	0.351191
$56$	5.75509	0.769056
$57$	0.719737	0.0953315
$58$	5.47896	0.719423
$59$	9.38810	1.22223	0.611113	−	0.791543i	$-0.290722\pi$
$59$	9.38810	1.22223	0.611113	+	0.791543i	$0.290722\pi$
$60$	1.23510	0.159451
$61$	0.990473	0.126817	0.0634085	−	0.997988i	$-0.479803\pi$
$61$	0.990473	0.126817	0.0634085	+	0.997988i	$0.479803\pi$
$62$	−10.9549	−1.39128
$63$	5.57722	0.702664
$64$	−12.8593	−1.60742
$65$	−2.36574	−0.293434
$66$	−2.25202	−0.277205
$67$	−3.56243	−0.435220	−0.217610	−	0.976036i	$-0.569826\pi$
$67$	−3.56243	−0.435220	−0.217610	+	0.976036i	$0.569826\pi$
$68$	−5.70209	−0.691480
$69$	−1.51317	−0.182164
$70$	4.48469	0.536023
$71$	9.58765	1.13784	0.568922	−	0.822391i	$-0.307360\pi$
$71$	9.58765	1.13784	0.568922	+	0.822391i	$0.307360\pi$
$72$	8.43154	0.993667
$73$	0.651431	0.0762442	0.0381221	−	0.999273i	$-0.487862\pi$
$73$	0.651431	0.0762442	0.0381221	+	0.999273i	$0.487862\pi$
$74$	21.2084	2.46543
$75$	0.376180	0.0434375
$76$	6.28182	0.720574
$77$	−5.08167	−0.579110
$78$	2.04557	0.231615
$79$	−6.54717	−0.736614	−0.368307	−	0.929704i	$-0.620063\pi$
$79$	−6.54717	−0.736614	−0.368307	+	0.929704i	$0.620063\pi$
$80$	0.213337	0.0238518
$81$	7.74642	0.860714
$82$	13.6752	1.51017
$83$	−12.9789	−1.42462	−0.712308	−	0.701867i	$-0.752350\pi$
$83$	−12.9789	−1.42462	−0.712308	+	0.701867i	$0.752350\pi$
$84$	−2.40982	−0.262933
$85$	−1.73671	−0.188373
$86$	−23.9378	−2.58128
$87$	−0.896691	−0.0961353
$88$	−7.68238	−0.818944
$89$	−10.2616	−1.08773	−0.543865	−	0.839173i	$-0.683040\pi$
$89$	−10.2616	−1.08773	−0.543865	+	0.839173i	$0.683040\pi$
$90$	6.57034	0.692575
$91$	4.61582	0.483869
$92$	−13.2069	−1.37691
$93$	1.79289	0.185914
$94$	−2.00640	−0.206945
$95$	1.91328	0.196298
$96$	2.03474	0.207669
$97$	2.88823	0.293255	0.146628	−	0.989192i	$-0.453158\pi$
$97$	2.88823	0.293255	0.146628	+	0.989192i	$0.453158\pi$
$98$	7.33964	0.741416
$99$	−7.44494	−0.748245
$100$	3.28327	0.328327
$101$	8.78531	0.874171	0.437085	−	0.899420i	$-0.356011\pi$
$101$	8.78531	0.874171	0.437085	+	0.899420i	$0.356011\pi$
$102$	1.50167	0.148687
$103$	6.97491	0.687258	0.343629	−	0.939105i	$-0.388344\pi$
$103$	6.97491	0.687258	0.343629	+	0.939105i	$0.388344\pi$
$104$	6.97811	0.684260
$105$	−0.733968	−0.0716279
$106$	4.92592	0.478448
$107$	−19.2765	−1.86353	−0.931765	−	0.363062i	$-0.881731\pi$
$107$	−19.2765	−1.86353	−0.931765	+	0.363062i	$0.881731\pi$
$108$	−7.23583	−0.696268
$109$	6.38519	0.611590	0.305795	−	0.952097i	$-0.401078\pi$
$109$	6.38519	0.611590	0.305795	+	0.952097i	$0.401078\pi$
$110$	−5.98655	−0.570795
$111$	−3.47098	−0.329451
$112$	−0.416243	−0.0393313
$113$	−4.68261	−0.440503	−0.220252	−	0.975443i	$-0.570688\pi$
$113$	−4.68261	−0.440503	−0.220252	+	0.975443i	$0.570688\pi$
$114$	−1.65434	−0.154943
$115$	−4.02247	−0.375097
$116$	−7.82625	−0.726649
$117$	6.76245	0.625188
$118$	−21.5789	−1.98650
$119$	3.38851	0.310624
$120$	−1.10960	−0.101292
$121$	−4.21656	−0.383324
$122$	−2.27664	−0.206117
$123$	−2.23809	−0.201802
$124$	15.6482	1.40525
$125$	1.00000	0.0894427
$126$	−12.8194	−1.14205
$127$	−4.92805	−0.437294	−0.218647	−	0.975804i	$-0.570164\pi$
$127$	−4.92805	−0.437294	−0.218647	+	0.975804i	$0.570164\pi$
$128$	18.7398	1.65638
$129$	3.91768	0.344932
$130$	5.43775	0.476922
$131$	7.78352	0.680050	0.340025	−	0.940416i	$-0.389565\pi$
$131$	7.78352	0.680050	0.340025	+	0.940416i	$0.389565\pi$
$132$	3.21683	0.279989
$133$	−3.73301	−0.323693
$134$	8.18838	0.707369
$135$	−2.20385	−0.189677
$136$	5.12269	0.439267
$137$	10.9217	0.933104	0.466552	−	0.884494i	$-0.345496\pi$
$137$	10.9217	0.933104	0.466552	+	0.884494i	$0.345496\pi$
$138$	3.47808	0.296074
$139$	0.978402	0.0829870	0.0414935	−	0.999139i	$-0.486788\pi$
$139$	0.978402	0.0829870	0.0414935	+	0.999139i	$0.486788\pi$
$140$	−6.40602	−0.541407
$141$	0.328369	0.0276537
$142$	−22.0376	−1.84935
$143$	−6.16159	−0.515258
$144$	−0.609821	−0.0508184
$145$	−2.38367	−0.197953
$146$	−1.49734	−0.123921
$147$	−1.20121	−0.0990742
$148$	−30.2945	−2.49019
$149$	−10.5078	−0.860833	−0.430416	−	0.902630i	$-0.641633\pi$
$149$	−10.5078	−0.860833	−0.430416	+	0.902630i	$0.641633\pi$
$150$	−0.864664	−0.0705995
$151$	15.1205	1.23049	0.615243	−	0.788337i	$-0.289058\pi$
$151$	15.1205	1.23049	0.615243	+	0.788337i	$0.289058\pi$
$152$	−5.64351	−0.457749
$153$	4.96436	0.401345
$154$	11.6804	0.941234
$155$	4.76604	0.382818
$156$	−2.92193	−0.233942
$157$	−3.11282	−0.248430	−0.124215	−	0.992255i	$-0.539641\pi$
$157$	−3.11282	−0.248430	−0.124215	+	0.992255i	$0.539641\pi$
$158$	15.0489	1.19723
$159$	−0.806179	−0.0639342
$160$	5.40894	0.427614
$161$	7.84827	0.618530
$162$	−17.8054	−1.39893
$163$	23.8189	1.86564	0.932818	−	0.360347i	$-0.117342\pi$
$163$	23.8189	1.86564	0.932818	+	0.360347i	$0.117342\pi$
$164$	−19.5339	−1.52534
$165$	0.979762	0.0762744
$166$	29.8324	2.31545
$167$	9.31260	0.720631	0.360315	−	0.932831i	$-0.382669\pi$
$167$	9.31260	0.720631	0.360315	+	0.932831i	$0.382669\pi$
$168$	2.16495	0.167029
$169$	−7.40326	−0.569482
$170$	3.99189	0.306164
$171$	−5.46909	−0.418231
$172$	34.1932	2.60721
$173$	−12.9195	−0.982250	−0.491125	−	0.871089i	$-0.663414\pi$
$173$	−12.9195	−0.982250	−0.491125	+	0.871089i	$0.663414\pi$
$174$	2.06108	0.156250
$175$	−1.95111	−0.147490
$176$	0.555637	0.0418827
$177$	3.53162	0.265452
$178$	23.5867	1.76790
$179$	19.9484	1.49102	0.745508	−	0.666496i	$-0.232207\pi$
$179$	19.9484	1.49102	0.745508	+	0.666496i	$0.232207\pi$
$180$	−9.38520	−0.699531
$181$	2.89998	0.215554	0.107777	−	0.994175i	$-0.465627\pi$
$181$	2.89998	0.215554	0.107777	+	0.994175i	$0.465627\pi$
$182$	−10.6096	−0.786438
$183$	0.372596	0.0275431
$184$	11.8649	0.874690
$185$	−9.22691	−0.678376
$186$	−4.12102	−0.302168
$187$	−4.52327	−0.330774
$188$	2.86598	0.209023
$189$	4.29994	0.312775
$190$	−4.39774	−0.319046
$191$	7.42378	0.537166	0.268583	−	0.963257i	$-0.413445\pi$
$191$	7.42378	0.537166	0.268583	+	0.963257i	$0.413445\pi$
$192$	−4.83742	−0.349111
$193$	−14.5476	−1.04716	−0.523578	−	0.851978i	$-0.675403\pi$
$193$	−14.5476	−1.04716	−0.523578	+	0.851978i	$0.675403\pi$
$194$	−6.63870	−0.476631
$195$	−0.889945	−0.0637303
$196$	−10.4841	−0.748863
$197$	12.4089	0.884100	0.442050	−	0.896990i	$-0.354251\pi$
$197$	12.4089	0.884100	0.442050	+	0.896990i	$0.354251\pi$
$198$	17.1125	1.21613
$199$	−15.8896	−1.12638	−0.563190	−	0.826327i	$-0.690426\pi$
$199$	−15.8896	−1.12638	−0.563190	+	0.826327i	$0.690426\pi$
$200$	−2.94965	−0.208572
$201$	−1.34012	−0.0945245
$202$	−20.1934	−1.42080
$203$	4.65081	0.326423
$204$	−2.14501	−0.150181
$205$	−5.94952	−0.415533
$206$	−16.0321	−1.11701
$207$	11.4982	0.799178
$208$	−0.504700	−0.0349946
$209$	4.98314	0.344691
$210$	1.68705	0.116418
$211$	20.4900	1.41059	0.705295	−	0.708914i	$-0.250815\pi$
$211$	20.4900	1.41059	0.705295	+	0.708914i	$0.250815\pi$
$212$	−7.03627	−0.483253
$213$	3.60668	0.247126
$214$	44.3078	3.02882
$215$	10.4144	0.710254
$216$	6.50058	0.442308
$217$	−9.29906	−0.631261
$218$	−14.6766	−0.994025
$219$	0.245055	0.0165593
$220$	8.55130	0.576528
$221$	4.10861	0.276375
$222$	7.97817	0.535460
$223$	−1.03739	−0.0694686	−0.0347343	−	0.999397i	$-0.511059\pi$
$223$	−1.03739	−0.0694686	−0.0347343	+	0.999397i	$0.511059\pi$
$224$	−10.5534	−0.705130
$225$	−2.85849	−0.190566
$226$	10.7632	0.715954
$227$	18.2544	1.21158	0.605792	−	0.795623i	$-0.292856\pi$
$227$	18.2544	1.21158	0.605792	+	0.795623i	$0.292856\pi$
$228$	2.36309	0.156500
$229$	4.56970	0.301974	0.150987	−	0.988536i	$-0.451755\pi$
$229$	4.56970	0.301974	0.150987	+	0.988536i	$0.451755\pi$
$230$	9.24579	0.609649
$231$	−1.91162	−0.125775
$232$	7.03101	0.461608
$233$	−18.1220	−1.18721	−0.593605	−	0.804757i	$-0.702296\pi$
$233$	−18.1220	−1.18721	−0.593605	+	0.804757i	$0.702296\pi$
$234$	−15.5437	−1.01613
$235$	0.872904	0.0569420
$236$	30.8237	2.00645
$237$	−2.46291	−0.159984
$238$	−7.78861	−0.504861
$239$	21.3923	1.38375	0.691875	−	0.722017i	$-0.256785\pi$
$239$	21.3923	1.38375	0.691875	+	0.722017i	$0.256785\pi$
$240$	0.0802530	0.00518031
$241$	18.8211	1.21237	0.606186	−	0.795323i	$-0.292699\pi$
$241$	18.8211	1.21237	0.606186	+	0.795323i	$0.292699\pi$
$242$	9.69192	0.623020
$243$	9.52559	0.611067
$244$	3.25199	0.208188
$245$	−3.19318	−0.204005
$246$	5.14434	0.327991
$247$	−4.52632	−0.288003
$248$	−14.0582	−0.892694
$249$	−4.88239	−0.309409
$250$	−2.29854	−0.145372
$251$	−17.9267	−1.13152	−0.565762	−	0.824569i	$-0.691418\pi$
$251$	−17.9267	−1.13152	−0.565762	+	0.824569i	$0.691418\pi$
$252$	18.3115	1.15352
$253$	−10.4765	−0.658654
$254$	11.3273	0.710739
$255$	−0.653316	−0.0409122
$256$	−17.3554	−1.08471
$257$	−4.84913	−0.302481	−0.151240	−	0.988497i	$-0.548327\pi$
$257$	−4.84913	−0.302481	−0.151240	+	0.988497i	$0.548327\pi$
$258$	−9.00493	−0.560622
$259$	18.0027	1.11863
$260$	−7.76738	−0.481712
$261$	6.81371	0.421758
$262$	−17.8907	−1.10529
$263$	17.8484	1.10058	0.550290	−	0.834974i	$-0.314517\pi$
$263$	17.8484	1.10058	0.550290	+	0.834974i	$0.314517\pi$
$264$	−2.88996	−0.177865
$265$	−2.14307	−0.131648
$266$	8.58047	0.526102
$267$	−3.86022	−0.236241
$268$	−11.6964	−0.714474
$269$	14.1203	0.860929	0.430464	−	0.902608i	$-0.358350\pi$
$269$	14.1203	0.860929	0.430464	+	0.902608i	$0.358350\pi$
$270$	5.06562	0.308284
$271$	−20.9217	−1.27090	−0.635450	−	0.772142i	$-0.719185\pi$
$271$	−20.9217	−1.27090	−0.635450	+	0.772142i	$0.719185\pi$
$272$	−0.370504	−0.0224651
$273$	1.73638	0.105090
$274$	−25.1039	−1.51658
$275$	2.60450	0.157057
$276$	−4.96816	−0.299048
$277$	2.54785	0.153086	0.0765428	−	0.997066i	$-0.475612\pi$
$277$	2.54785	0.153086	0.0765428	+	0.997066i	$0.475612\pi$
$278$	−2.24889	−0.134880
$279$	−13.6237	−0.815628
$280$	5.75509	0.343932
$281$	14.9393	0.891203	0.445601	−	0.895232i	$-0.352990\pi$
$281$	14.9393	0.891203	0.445601	+	0.895232i	$0.352990\pi$
$282$	−0.754769	−0.0449458
$283$	11.3429	0.674265	0.337133	−	0.941457i	$-0.390543\pi$
$283$	11.3429	0.674265	0.337133	+	0.941457i	$0.390543\pi$
$284$	31.4789	1.86793
$285$	0.719737	0.0426336
$286$	14.1626	0.837454
$287$	11.6082	0.685208
$288$	−15.4614	−0.911071
$289$	−13.9838	−0.822579
$290$	5.47896	0.321736
$291$	1.08649	0.0636914
$292$	2.13882	0.125165
$293$	2.48272	0.145042	0.0725210	−	0.997367i	$-0.476896\pi$
$293$	2.48272	0.145042	0.0725210	+	0.997367i	$0.476896\pi$
$294$	2.76103	0.161026
$295$	9.38810	0.546596
$296$	27.2162	1.58191
$297$	−5.73993	−0.333064
$298$	24.1526	1.39912
$299$	9.51612	0.550331
$300$	1.23510	0.0713086
$301$	−20.3195	−1.17120
$302$	−34.7550	−1.99992
$303$	3.30486	0.189859
$304$	0.408173	0.0234103
$305$	0.990473	0.0567143
$306$	−11.4108	−0.652311
$307$	−4.73084	−0.270003	−0.135002	−	0.990845i	$-0.543104\pi$
$307$	−4.73084	−0.270003	−0.135002	+	0.990845i	$0.543104\pi$
$308$	−16.6845	−0.950688
$309$	2.62382	0.149264
$310$	−10.9549	−0.622198
$311$	12.2261	0.693281	0.346641	−	0.937998i	$-0.387322\pi$
$311$	12.2261	0.693281	0.346641	+	0.937998i	$0.387322\pi$
$312$	2.62503	0.148613
$313$	−2.86569	−0.161978	−0.0809892	−	0.996715i	$-0.525808\pi$
$313$	−2.86569	−0.161978	−0.0809892	+	0.996715i	$0.525808\pi$
$314$	7.15492	0.403776
$315$	5.57722	0.314241
$316$	−21.4962	−1.20925
$317$	5.70421	0.320381	0.160190	−	0.987086i	$-0.448789\pi$
$317$	5.70421	0.320381	0.160190	+	0.987086i	$0.448789\pi$
$318$	1.85303	0.103913
$319$	−6.20829	−0.347597
$320$	−12.8593	−0.718858
$321$	−7.25144	−0.404736
$322$	−18.0395	−1.00530
$323$	−3.32281	−0.184886
$324$	25.4336	1.41298
$325$	−2.36574	−0.131228
$326$	−54.7485	−3.03224
$327$	2.40198	0.132830
$328$	17.5490	0.968982
$329$	−1.70313	−0.0938966
$330$	−2.25202	−0.123970
$331$	24.5839	1.35126	0.675628	−	0.737243i	$-0.263873\pi$
$331$	24.5839	1.35126	0.675628	+	0.737243i	$0.263873\pi$
$332$	−42.6132	−2.33870
$333$	26.3750	1.44534
$334$	−21.4054	−1.17125
$335$	−3.56243	−0.194636
$336$	−0.156582	−0.00854227
$337$	25.4913	1.38860	0.694299	−	0.719686i	$-0.255714\pi$
$337$	25.4913	1.38860	0.694299	+	0.719686i	$0.255714\pi$
$338$	17.0167	0.925585
$339$	−1.76150	−0.0956718
$340$	−5.70209	−0.309239
$341$	12.4132	0.672211
$342$	12.5709	0.679756
$343$	19.8880	1.07385
$344$	−30.7188	−1.65624
$345$	−1.51317	−0.0814664
$346$	29.6959	1.59646
$347$	−9.16249	−0.491868	−0.245934	−	0.969287i	$-0.579095\pi$
$347$	−9.16249	−0.491868	−0.245934	+	0.969287i	$0.579095\pi$
$348$	−2.94408	−0.157819
$349$	−5.70889	−0.305590	−0.152795	−	0.988258i	$-0.548827\pi$
$349$	−5.70889	−0.305590	−0.152795	+	0.988258i	$0.548827\pi$
$350$	4.48469	0.239717
$351$	5.21373	0.278288
$352$	14.0876	0.750872
$353$	27.0334	1.43885	0.719423	−	0.694573i	$-0.244407\pi$
$353$	27.0334	1.43885	0.719423	+	0.694573i	$0.244407\pi$
$354$	−8.11755	−0.431443
$355$	9.58765	0.508860
$356$	−33.6917	−1.78566
$357$	1.27469	0.0674637
$358$	−45.8522	−2.42337
$359$	27.7654	1.46540	0.732700	−	0.680552i	$-0.238260\pi$
$359$	27.7654	1.46540	0.732700	+	0.680552i	$0.238260\pi$
$360$	8.43154	0.444381
$361$	−15.3394	−0.807335
$362$	−6.66571	−0.350342
$363$	−1.58619	−0.0832531
$364$	15.1550	0.794337
$365$	0.651431	0.0340974
$366$	−0.856426	−0.0447661
$367$	−30.8849	−1.61218	−0.806090	−	0.591793i	$-0.798420\pi$
$367$	−30.8849	−1.61218	−0.806090	+	0.591793i	$0.798420\pi$
$368$	−0.858140	−0.0447336
$369$	17.0066	0.885330
$370$	21.2084	1.10257
$371$	4.18135	0.217085
$372$	5.88655	0.305203
$373$	−16.2769	−0.842787	−0.421394	−	0.906878i	$-0.638459\pi$
$373$	−16.2769	−0.842787	−0.421394	+	0.906878i	$0.638459\pi$
$374$	10.3969	0.537611
$375$	0.376180	0.0194259
$376$	−2.57476	−0.132783
$377$	5.63916	0.290431
$378$	−9.88358	−0.508356
$379$	−2.25071	−0.115611	−0.0578056	−	0.998328i	$-0.518410\pi$
$379$	−2.25071	−0.115611	−0.0578056	+	0.998328i	$0.518410\pi$
$380$	6.28182	0.322250
$381$	−1.85384	−0.0949749
$382$	−17.0638	−0.873062
$383$	−12.8723	−0.657744	−0.328872	−	0.944375i	$-0.606668\pi$
$383$	−12.8723	−0.657744	−0.328872	+	0.944375i	$0.606668\pi$
$384$	7.04952	0.359744
$385$	−5.08167	−0.258986
$386$	33.4381	1.70195
$387$	−29.7693	−1.51326
$388$	9.48284	0.481418
$389$	−26.7313	−1.35533	−0.677666	−	0.735369i	$-0.737009\pi$
$389$	−26.7313	−1.35533	−0.677666	+	0.735369i	$0.737009\pi$
$390$	2.04557	0.103582
$391$	6.98586	0.353290
$392$	9.41877	0.475719
$393$	2.92801	0.147698
$394$	−28.5224	−1.43694
$395$	−6.54717	−0.329424
$396$	−24.4438	−1.22835
$397$	−22.6527	−1.13691	−0.568453	−	0.822716i	$-0.692458\pi$
$397$	−22.6527	−1.13691	−0.568453	+	0.822716i	$0.692458\pi$
$398$	36.5227	1.83072
$399$	−1.40428	−0.0703022
$400$	0.213337	0.0106668
$401$	−26.0469	−1.30072	−0.650359	−	0.759627i	$-0.725382\pi$
$401$	−26.0469	−1.30072	−0.650359	+	0.759627i	$0.725382\pi$
$402$	3.08031	0.153632
$403$	−11.2752	−0.561659
$404$	28.8446	1.43507
$405$	7.74642	0.384923
$406$	−10.6900	−0.530538
$407$	−24.0315	−1.19120
$408$	1.92705	0.0954033
$409$	14.7319	0.728444	0.364222	−	0.931312i	$-0.381335\pi$
$409$	14.7319	0.728444	0.364222	+	0.931312i	$0.381335\pi$
$410$	13.6752	0.675370
$411$	4.10853	0.202659
$412$	22.9005	1.12823
$413$	−18.3172	−0.901330
$414$	−26.4290	−1.29891
$415$	−12.9789	−0.637108
$416$	−12.7962	−0.627383
$417$	0.368055	0.0180237
$418$	−11.4539	−0.560230
$419$	28.8541	1.40961	0.704807	−	0.709399i	$-0.251034\pi$
$419$	28.8541	1.40961	0.704807	+	0.709399i	$0.251034\pi$
$420$	−2.40982	−0.117587
$421$	−9.21410	−0.449068	−0.224534	−	0.974466i	$-0.572086\pi$
$421$	−9.21410	−0.449068	−0.224534	+	0.974466i	$0.572086\pi$
$422$	−47.0970	−2.29265
$423$	−2.49519	−0.121320
$424$	6.32130	0.306989
$425$	−1.73671	−0.0842428
$426$	−8.29009	−0.401656
$427$	−1.93252	−0.0935212
$428$	−63.2900	−3.05924
$429$	−2.31787	−0.111908
$430$	−23.9378	−1.15438
$431$	−10.5288	−0.507154	−0.253577	−	0.967315i	$-0.581607\pi$
$431$	−10.5288	−0.507154	−0.253577	+	0.967315i	$0.581607\pi$
$432$	−0.470162	−0.0226207
$433$	28.1946	1.35495	0.677473	−	0.735548i	$-0.263075\pi$
$433$	28.1946	1.35495	0.677473	+	0.735548i	$0.263075\pi$
$434$	21.3742	1.02600
$435$	−0.896691	−0.0429930
$436$	20.9643	1.00401
$437$	−7.69610	−0.368154
$438$	−0.563269	−0.0269140
$439$	−13.2147	−0.630702	−0.315351	−	0.948975i	$-0.602122\pi$
$439$	−13.2147	−0.630702	−0.315351	+	0.948975i	$0.602122\pi$
$440$	−7.68238	−0.366243
$441$	9.12767	0.434651
$442$	−9.44379	−0.449195
$443$	−13.5025	−0.641521	−0.320761	−	0.947160i	$-0.603939\pi$
$443$	−13.5025	−0.641521	−0.320761	+	0.947160i	$0.603939\pi$
$444$	−11.3962	−0.540838
$445$	−10.2616	−0.486447
$446$	2.38448	0.112908
$447$	−3.95283	−0.186962
$448$	25.0899	1.18539
$449$	−16.9881	−0.801720	−0.400860	−	0.916139i	$-0.631289\pi$
$449$	−16.9881	−0.801720	−0.400860	+	0.916139i	$0.631289\pi$
$450$	6.57034	0.309729
$451$	−15.4956	−0.729657
$452$	−15.3743	−0.723146
$453$	5.68802	0.267246
$454$	−41.9583	−1.96920
$455$	4.61582	0.216393
$456$	−2.12297	−0.0994174
$457$	−24.7197	−1.15634	−0.578169	−	0.815917i	$-0.696233\pi$
$457$	−24.7197	−1.15634	−0.578169	+	0.815917i	$0.696233\pi$
$458$	−10.5036	−0.490802
$459$	3.82744	0.178650
$460$	−13.2069	−0.615773
$461$	19.1287	0.890911	0.445456	−	0.895304i	$-0.353042\pi$
$461$	19.1287	0.890911	0.445456	+	0.895304i	$0.353042\pi$
$462$	4.39393	0.204424
$463$	27.8284	1.29330	0.646649	−	0.762788i	$-0.276170\pi$
$463$	27.8284	1.29330	0.646649	+	0.762788i	$0.276170\pi$
$464$	−0.508525	−0.0236077
$465$	1.79289	0.0831433
$466$	41.6540	1.92959
$467$	19.9731	0.924245	0.462122	−	0.886816i	$-0.347088\pi$
$467$	19.9731	0.924245	0.462122	+	0.886816i	$0.347088\pi$
$468$	22.2030	1.02633
$469$	6.95069	0.320953
$470$	−2.00640	−0.0925485
$471$	−1.17098	−0.0539559
$472$	−27.6916	−1.27461
$473$	27.1243	1.24717
$474$	5.66110	0.260023
$475$	1.91328	0.0877873
$476$	11.1254	0.509932
$477$	6.12593	0.280487
$478$	−49.1709	−2.24903
$479$	15.3382	0.700822	0.350411	−	0.936596i	$-0.386042\pi$
$479$	15.3382	0.700822	0.350411	+	0.936596i	$0.386042\pi$
$480$	2.03474	0.0928725
$481$	21.8285	0.995293
$482$	−43.2610	−1.97048
$483$	2.95236	0.134337
$484$	−13.8441	−0.629278
$485$	2.88823	0.131148
$486$	−21.8949	−0.993174
$487$	18.8145	0.852565	0.426282	−	0.904590i	$-0.359823\pi$
$487$	18.8145	0.852565	0.426282	+	0.904590i	$0.359823\pi$
$488$	−2.92155	−0.132252
$489$	8.96018	0.405193
$490$	7.33964	0.331571
$491$	43.7329	1.97364	0.986819	−	0.161827i	$-0.0517387\pi$
$491$	43.7329	1.97364	0.986819	+	0.161827i	$0.0517387\pi$
$492$	−7.34827	−0.331285
$493$	4.13975	0.186445
$494$	10.4039	0.468095
$495$	−7.44494	−0.334625
$496$	1.01677	0.0456544
$497$	−18.7065	−0.839103
$498$	11.2224	0.502886
$499$	−33.6518	−1.50646	−0.753230	−	0.657757i	$-0.771505\pi$
$499$	−33.6518	−1.50646	−0.753230	+	0.657757i	$0.771505\pi$
$500$	3.28327	0.146832
$501$	3.50322	0.156512
$502$	41.2052	1.83908
$503$	12.8581	0.573314	0.286657	−	0.958033i	$-0.407456\pi$
$503$	12.8581	0.573314	0.286657	+	0.958033i	$0.407456\pi$
$504$	−16.4509	−0.732779
$505$	8.78531	0.390941
$506$	24.0807	1.07052
$507$	−2.78496	−0.123684
$508$	−16.1801	−0.717878
$509$	33.2470	1.47365	0.736824	−	0.676084i	$-0.236325\pi$
$509$	33.2470	1.47365	0.736824	+	0.676084i	$0.236325\pi$
$510$	1.50167	0.0664951
$511$	−1.27101	−0.0562262
$512$	2.41246	0.106617
$513$	−4.21657	−0.186166
$514$	11.1459	0.491625
$515$	6.97491	0.307351
$516$	12.8628	0.566253
$517$	2.27348	0.0999877
$518$	−41.3798	−1.81813
$519$	−4.86005	−0.213333
$520$	6.97811	0.306011
$521$	17.2371	0.755170	0.377585	−	0.925975i	$-0.376755\pi$
$521$	17.2371	0.755170	0.377585	+	0.925975i	$0.376755\pi$
$522$	−15.6616	−0.685488
$523$	−38.4753	−1.68241	−0.841204	−	0.540718i	$-0.818153\pi$
$523$	−38.4753	−1.68241	−0.841204	+	0.540718i	$0.818153\pi$
$524$	25.5554	1.11639
$525$	−0.733968	−0.0320330
$526$	−41.0252	−1.78878
$527$	−8.27723	−0.360562
$528$	0.209019	0.00909640
$529$	−6.81976	−0.296511
$530$	4.92592	0.213968
$531$	−26.8358	−1.16457
$532$	−12.2565	−0.531387
$533$	14.0750	0.609657
$534$	8.87285	0.383966
$535$	−19.2765	−0.833396
$536$	10.5079	0.453874
$537$	7.50421	0.323830
$538$	−32.4560	−1.39928
$539$	−8.31665	−0.358223
$540$	−7.23583	−0.311381
$541$	3.80320	0.163512	0.0817561	−	0.996652i	$-0.473947\pi$
$541$	3.80320	0.163512	0.0817561	+	0.996652i	$0.473947\pi$
$542$	48.0892	2.06561
$543$	1.09091	0.0468156
$544$	−9.39376	−0.402754
$545$	6.38519	0.273512
$546$	−3.99113	−0.170805
$547$	−5.70834	−0.244071	−0.122035	−	0.992526i	$-0.538942\pi$
$547$	−5.70834	−0.244071	−0.122035	+	0.992526i	$0.538942\pi$
$548$	35.8589	1.53182
$549$	−2.83126	−0.120835
$550$	−5.98655	−0.255267
$551$	−4.56063	−0.194290
$552$	4.46333	0.189972
$553$	12.7742	0.543216
$554$	−5.85633	−0.248812
$555$	−3.47098	−0.147335
$556$	3.21236	0.136234
$557$	−13.9051	−0.589179	−0.294589	−	0.955624i	$-0.595183\pi$
$557$	−13.9051	−0.589179	−0.294589	+	0.955624i	$0.595183\pi$
$558$	31.3145	1.32565
$559$	−24.6377	−1.04206
$560$	−0.416243	−0.0175895
$561$	−1.70156	−0.0718400
$562$	−34.3385	−1.44848
$563$	−31.4288	−1.32457	−0.662283	−	0.749254i	$-0.730412\pi$
$563$	−31.4288	−1.32457	−0.662283	+	0.749254i	$0.730412\pi$
$564$	1.07813	0.0453973
$565$	−4.68261	−0.196999
$566$	−26.0721	−1.09589
$567$	−15.1141	−0.634733
$568$	−28.2802	−1.18661
$569$	−33.5490	−1.40645	−0.703223	−	0.710969i	$-0.748257\pi$
$569$	−33.5490	−1.40645	−0.703223	+	0.710969i	$0.748257\pi$
$570$	−1.65434	−0.0692928
$571$	15.4601	0.646984	0.323492	−	0.946231i	$-0.395143\pi$
$571$	15.4601	0.646984	0.323492	+	0.946231i	$0.395143\pi$
$572$	−20.2302	−0.845866
$573$	2.79268	0.116666
$574$	−26.6818	−1.11368
$575$	−4.02247	−0.167748
$576$	36.7582	1.53159
$577$	−11.2214	−0.467153	−0.233576	−	0.972338i	$-0.575043\pi$
$577$	−11.2214	−0.467153	−0.233576	+	0.972338i	$0.575043\pi$
$578$	32.1424	1.33695
$579$	−5.47250	−0.227429
$580$	−7.82625	−0.324968
$581$	25.3232	1.05058
$582$	−2.49735	−0.103518
$583$	−5.58163	−0.231167
$584$	−1.92149	−0.0795120
$585$	6.76245	0.279593
$586$	−5.70662	−0.235738
$587$	−8.10118	−0.334372	−0.167186	−	0.985925i	$-0.553468\pi$
$587$	−8.10118	−0.334372	−0.167186	+	0.985925i	$0.553468\pi$
$588$	−3.94390	−0.162644
$589$	9.11876	0.375732
$590$	−21.5789	−0.888389
$591$	4.66799	0.192016
$592$	−1.96844	−0.0809023
$593$	31.2125	1.28174	0.640871	−	0.767649i	$-0.278573\pi$
$593$	31.2125	1.28174	0.640871	+	0.767649i	$0.278573\pi$
$594$	13.1934	0.541333
$595$	3.38851	0.138915
$596$	−34.5000	−1.41317
$597$	−5.97733	−0.244636
$598$	−21.8732	−0.894460
$599$	28.3034	1.15645	0.578223	−	0.815879i	$-0.303746\pi$
$599$	28.3034	1.15645	0.578223	+	0.815879i	$0.303746\pi$
$600$	−1.10960	−0.0452992
$601$	−27.7590	−1.13231	−0.566157	−	0.824298i	$-0.691570\pi$
$601$	−27.7590	−1.13231	−0.566157	+	0.824298i	$0.691570\pi$
$602$	46.7052	1.90356
$603$	10.1832	0.414691
$604$	49.6446	2.02001
$605$	−4.21656	−0.171428
$606$	−7.59634	−0.308580
$607$	−33.7033	−1.36798	−0.683988	−	0.729493i	$-0.739756\pi$
$607$	−33.7033	−1.36798	−0.683988	+	0.729493i	$0.739756\pi$
$608$	10.3488	0.419700
$609$	1.74954	0.0708949
$610$	−2.27664	−0.0921784
$611$	−2.06507	−0.0835437
$612$	16.2994	0.658863
$613$	29.7111	1.20002	0.600010	−	0.799992i	$-0.295163\pi$
$613$	29.7111	1.20002	0.600010	+	0.799992i	$0.295163\pi$
$614$	10.8740	0.438840
$615$	−2.23809	−0.0902486
$616$	14.9891	0.603930
$617$	−20.4746	−0.824275	−0.412138	−	0.911122i	$-0.635218\pi$
$617$	−20.4746	−0.824275	−0.412138	+	0.911122i	$0.635218\pi$
$618$	−6.03095	−0.242600
$619$	−11.8611	−0.476740	−0.238370	−	0.971174i	$-0.576613\pi$
$619$	−11.8611	−0.476740	−0.238370	+	0.971174i	$0.576613\pi$
$620$	15.6482	0.628447
$621$	8.86490	0.355736
$622$	−28.1022	−1.12680
$623$	20.0215	0.802145
$624$	−0.189858	−0.00760040
$625$	1.00000	0.0400000
$626$	6.58690	0.263265
$627$	1.87456	0.0748627
$628$	−10.2202	−0.407831
$629$	16.0245	0.638937
$630$	−12.8194	−0.510739
$631$	−0.920878	−0.0366596	−0.0183298	−	0.999832i	$-0.505835\pi$
$631$	−0.920878	−0.0366596	−0.0183298	+	0.999832i	$0.505835\pi$
$632$	19.3119	0.768185
$633$	7.70793	0.306363
$634$	−13.1113	−0.520718
$635$	−4.92805	−0.195564
$636$	−2.64691	−0.104957
$637$	7.55424	0.299310
$638$	14.2700	0.564954
$639$	−27.4062	−1.08417
$640$	18.7398	0.740754
$641$	1.90133	0.0750982	0.0375491	−	0.999295i	$-0.488045\pi$
$641$	1.90133	0.0750982	0.0375491	+	0.999295i	$0.488045\pi$
$642$	16.6677	0.657821
$643$	−27.1665	−1.07134	−0.535672	−	0.844426i	$-0.679942\pi$
$643$	−27.1665	−1.07134	−0.535672	+	0.844426i	$0.679942\pi$
$644$	25.7680	1.01540
$645$	3.91768	0.154258
$646$	7.63760	0.300497
$647$	11.7455	0.461762	0.230881	−	0.972982i	$-0.425839\pi$
$647$	11.7455	0.461762	0.230881	+	0.972982i	$0.425839\pi$
$648$	−22.8492	−0.897603
$649$	24.4513	0.959799
$650$	5.43775	0.213286
$651$	−3.49812	−0.137102
$652$	78.2038	3.06270
$653$	16.3182	0.638581	0.319291	−	0.947657i	$-0.396555\pi$
$653$	16.3182	0.638581	0.319291	+	0.947657i	$0.396555\pi$
$654$	−5.52104	−0.215890
$655$	7.78352	0.304127
$656$	−1.26925	−0.0495560
$657$	−1.86211	−0.0726477
$658$	3.91471	0.152611
$659$	27.2824	1.06277	0.531386	−	0.847130i	$-0.321672\pi$
$659$	27.2824	1.06277	0.531386	+	0.847130i	$0.321672\pi$
$660$	3.21683	0.125215
$661$	16.4119	0.638351	0.319175	−	0.947696i	$-0.396594\pi$
$661$	16.4119	0.638351	0.319175	+	0.947696i	$0.396594\pi$
$662$	−56.5071	−2.19621
$663$	1.54558	0.0600252
$664$	38.2832	1.48567
$665$	−3.73301	−0.144760
$666$	−60.6239	−2.34913
$667$	9.58825	0.371259
$668$	30.5758	1.18301
$669$	−0.390245	−0.0150877
$670$	8.18838	0.316345
$671$	2.57969	0.0995879
$672$	−3.96999	−0.153146
$673$	24.1836	0.932210	0.466105	−	0.884729i	$-0.345657\pi$
$673$	24.1836	0.932210	0.466105	+	0.884729i	$0.345657\pi$
$674$	−58.5927	−2.25691
$675$	−2.20385	−0.0848261
$676$	−24.3069	−0.934882
$677$	17.8432	0.685769	0.342885	−	0.939377i	$-0.388596\pi$
$677$	17.8432	0.685769	0.342885	+	0.939377i	$0.388596\pi$
$678$	4.04888	0.155496
$679$	−5.63524	−0.216261
$680$	5.12269	0.196446
$681$	6.86693	0.263141
$682$	−28.5321	−1.09255
$683$	−14.4024	−0.551092	−0.275546	−	0.961288i	$-0.588859\pi$
$683$	−14.4024	−0.551092	−0.275546	+	0.961288i	$0.588859\pi$
$684$	−17.9565	−0.686584
$685$	10.9217	0.417297
$686$	−45.7133	−1.74534
$687$	1.71903	0.0655850
$688$	2.22177	0.0847041
$689$	5.06994	0.193149
$690$	3.47808	0.132408
$691$	24.6527	0.937834	0.468917	−	0.883242i	$-0.344644\pi$
$691$	24.6527	0.937834	0.468917	+	0.883242i	$0.344644\pi$
$692$	−42.4182	−1.61250
$693$	14.5259	0.551793
$694$	21.0603	0.799439
$695$	0.978402	0.0371129
$696$	2.64493	0.100256
$697$	10.3326	0.391375
$698$	13.1221	0.496679
$699$	−6.81712	−0.257847
$700$	−6.40602	−0.242125
$701$	16.0053	0.604512	0.302256	−	0.953227i	$-0.402260\pi$
$701$	16.0053	0.604512	0.302256	+	0.953227i	$0.402260\pi$
$702$	−11.9840	−0.452305
$703$	−17.6536	−0.665820
$704$	−33.4922	−1.26228
$705$	0.328369	0.0123671
$706$	−62.1374	−2.33857
$707$	−17.1411	−0.644657
$708$	11.5953	0.435776
$709$	30.3372	1.13934	0.569668	−	0.821875i	$-0.307072\pi$
$709$	30.3372	1.13934	0.569668	+	0.821875i	$0.307072\pi$
$710$	−22.0376	−0.827055
$711$	18.7150	0.701868
$712$	30.2682	1.13435
$713$	−19.1712	−0.717969
$714$	−2.92992	−0.109649
$715$	−6.16159	−0.230430
$716$	65.4962	2.44771
$717$	8.04734	0.300534
$718$	−63.8197	−2.38173
$719$	12.1768	0.454117	0.227059	−	0.973881i	$-0.427089\pi$
$719$	12.1768	0.454117	0.227059	+	0.973881i	$0.427089\pi$
$720$	−0.609821	−0.0227267
$721$	−13.6088	−0.506818
$722$	35.2581	1.31217
$723$	7.08012	0.263312
$724$	9.52143	0.353861
$725$	−2.38367	−0.0885274
$726$	3.64591	0.135312
$727$	−26.0568	−0.966393	−0.483197	−	0.875512i	$-0.660524\pi$
$727$	−26.0568	−0.966393	−0.483197	+	0.875512i	$0.660524\pi$
$728$	−13.6151	−0.504607
$729$	−19.6559	−0.727997
$730$	−1.49734	−0.0554189
$731$	−18.0867	−0.668962
$732$	1.22334	0.0452158
$733$	43.0593	1.59043	0.795217	−	0.606325i	$-0.207357\pi$
$733$	43.0593	1.59043	0.795217	+	0.606325i	$0.207357\pi$
$734$	70.9902	2.62029
$735$	−1.20121	−0.0443073
$736$	−21.7573	−0.801984
$737$	−9.27837	−0.341773
$738$	−39.0904	−1.43894
$739$	42.0281	1.54603	0.773015	−	0.634388i	$-0.218748\pi$
$739$	42.0281	1.54603	0.773015	+	0.634388i	$0.218748\pi$
$740$	−30.2945	−1.11365
$741$	−1.70271	−0.0625507
$742$	−9.61100	−0.352831
$743$	20.3625	0.747026	0.373513	−	0.927625i	$-0.378153\pi$
$743$	20.3625	0.747026	0.373513	+	0.927625i	$0.378153\pi$
$744$	−5.28840	−0.193882
$745$	−10.5078	−0.384976
$746$	37.4131	1.36979
$747$	37.1000	1.35742
$748$	−14.8511	−0.543011
$749$	37.6105	1.37426
$750$	−0.864664	−0.0315731
$751$	28.5759	1.04275	0.521375	−	0.853327i	$-0.325419\pi$
$751$	28.5759	1.04275	0.521375	+	0.853327i	$0.325419\pi$
$752$	0.186223	0.00679084
$753$	−6.74367	−0.245753
$754$	−12.9618	−0.472042
$755$	15.1205	0.550290
$756$	14.1179	0.513462
$757$	3.89635	0.141615	0.0708077	−	0.997490i	$-0.477442\pi$
$757$	3.89635	0.141615	0.0708077	+	0.997490i	$0.477442\pi$
$758$	5.17334	0.187904
$759$	−3.94106	−0.143051
$760$	−5.64351	−0.204711
$761$	25.7963	0.935114	0.467557	−	0.883963i	$-0.345134\pi$
$761$	25.7963	0.935114	0.467557	+	0.883963i	$0.345134\pi$
$762$	4.26111	0.154364
$763$	−12.4582	−0.451017
$764$	24.3743	0.881832
$765$	4.96436	0.179487
$766$	29.5875	1.06904
$767$	−22.2098	−0.801950
$768$	−6.52875	−0.235586
$769$	−21.4791	−0.774557	−0.387279	−	0.921963i	$-0.626585\pi$
$769$	−21.4791	−0.774557	−0.387279	+	0.921963i	$0.626585\pi$
$770$	11.6804	0.420932
$771$	−1.82415	−0.0656951
$772$	−47.7636	−1.71905
$773$	30.0115	1.07944	0.539719	−	0.841846i	$-0.318531\pi$
$773$	30.0115	1.07944	0.539719	+	0.841846i	$0.318531\pi$
$774$	68.4260	2.45952
$775$	4.76604	0.171201
$776$	−8.51927	−0.305824
$777$	6.77225	0.242953
$778$	61.4430	2.20284
$779$	−11.3831	−0.407842
$780$	−2.92193	−0.104622
$781$	24.9711	0.893535
$782$	−16.0573	−0.574206
$783$	5.25325	0.187736
$784$	−0.681223	−0.0243294
$785$	−3.11282	−0.111101
$786$	−6.73013	−0.240056
$787$	37.3021	1.32968	0.664839	−	0.746987i	$-0.268500\pi$
$787$	37.3021	1.32968	0.664839	+	0.746987i	$0.268500\pi$
$788$	40.7419	1.45137
$789$	6.71421	0.239032
$790$	15.0489	0.535416
$791$	9.13628	0.324849
$792$	21.9600	0.780314
$793$	−2.34320	−0.0832096
$794$	52.0680	1.84783
$795$	−0.806179	−0.0285922
$796$	−52.1697	−1.84911
$797$	27.6704	0.980136	0.490068	−	0.871684i	$-0.336972\pi$
$797$	27.6704	0.980136	0.490068	+	0.871684i	$0.336972\pi$
$798$	3.22780	0.114263
$799$	−1.51598	−0.0536316
$800$	5.40894	0.191235
$801$	29.3327	1.03642
$802$	59.8697	2.11407
$803$	1.69665	0.0598736
$804$	−4.39997	−0.155175
$805$	7.84827	0.276615
$806$	25.9165	0.912871
$807$	5.31177	0.186983
$808$	−25.9136	−0.911637
$809$	3.26796	0.114895	0.0574476	−	0.998349i	$-0.481704\pi$
$809$	3.26796	0.114895	0.0574476	+	0.998349i	$0.481704\pi$
$810$	−17.8054	−0.625619
$811$	6.83258	0.239924	0.119962	−	0.992778i	$-0.461723\pi$
$811$	6.83258	0.239924	0.119962	+	0.992778i	$0.461723\pi$
$812$	15.2699	0.535867
$813$	−7.87031	−0.276024
$814$	55.2373	1.93607
$815$	23.8189	0.834338
$816$	−0.139376	−0.00487914
$817$	19.9256	0.697108
$818$	−33.8618	−1.18395
$819$	−13.1943	−0.461045
$820$	−19.5339	−0.682154
$821$	2.52040	0.0879625	0.0439812	−	0.999032i	$-0.485996\pi$
$821$	2.52040	0.0879625	0.0439812	+	0.999032i	$0.485996\pi$
$822$	−9.44360	−0.329383
$823$	2.49335	0.0869128	0.0434564	−	0.999055i	$-0.486163\pi$
$823$	2.49335	0.0869128	0.0434564	+	0.999055i	$0.486163\pi$
$824$	−20.5735	−0.716713
$825$	0.979762	0.0341109
$826$	42.1027	1.46494
$827$	−6.46025	−0.224645	−0.112322	−	0.993672i	$-0.535829\pi$
$827$	−6.46025	−0.224645	−0.112322	+	0.993672i	$0.535829\pi$
$828$	37.7517	1.31196
$829$	38.0882	1.32286	0.661429	−	0.750007i	$-0.269950\pi$
$829$	38.0882	1.32286	0.661429	+	0.750007i	$0.269950\pi$
$830$	29.8324	1.03550
$831$	0.958451	0.0332483
$832$	30.4218	1.05469
$833$	5.54563	0.192145
$834$	−0.845989	−0.0292942
$835$	9.31260	0.322276
$836$	16.3610	0.565858
$837$	−10.5036	−0.363058
$838$	−66.3221	−2.29106
$839$	34.3699	1.18658	0.593291	−	0.804988i	$-0.297829\pi$
$839$	34.3699	1.18658	0.593291	+	0.804988i	$0.297829\pi$
$840$	2.16495	0.0746978
$841$	−23.3181	−0.804072
$842$	21.1790	0.729875
$843$	5.61986	0.193558
$844$	67.2743	2.31568
$845$	−7.40326	−0.254680
$846$	5.73528	0.197183
$847$	8.22696	0.282682
$848$	−0.457195	−0.0157001
$849$	4.26697	0.146442
$850$	3.99189	0.136921
$851$	37.1149	1.27228
$852$	11.8417	0.405691
$853$	8.62729	0.295393	0.147696	−	0.989033i	$-0.452814\pi$
$853$	8.62729	0.295393	0.147696	+	0.989033i	$0.452814\pi$
$854$	4.44197	0.152001
$855$	−5.46909	−0.187039
$856$	56.8590	1.94340
$857$	6.94918	0.237380	0.118690	−	0.992931i	$-0.462131\pi$
$857$	6.94918	0.237380	0.118690	+	0.992931i	$0.462131\pi$
$858$	5.32770	0.181885
$859$	6.32976	0.215969	0.107984	−	0.994153i	$-0.465560\pi$
$859$	6.32976	0.215969	0.107984	+	0.994153i	$0.465560\pi$
$860$	34.1932	1.16598
$861$	4.36676	0.148819
$862$	24.2008	0.824284
$863$	41.7850	1.42238	0.711189	−	0.703001i	$-0.248157\pi$
$863$	41.7850	1.42238	0.711189	+	0.703001i	$0.248157\pi$
$864$	−11.9205	−0.405543
$865$	−12.9195	−0.439276
$866$	−64.8063	−2.20221
$867$	−5.26044	−0.178654
$868$	−30.5313	−1.03630
$869$	−17.0521	−0.578454
$870$	2.06108	0.0698771
$871$	8.42780	0.285565
$872$	−18.8341	−0.637803
$873$	−8.25597	−0.279422
$874$	17.6898	0.598365
$875$	−1.95111	−0.0659595
$876$	0.804583	0.0271843
$877$	−8.53029	−0.288047	−0.144024	−	0.989574i	$-0.546004\pi$
$877$	−8.53029	−0.288047	−0.144024	+	0.989574i	$0.546004\pi$
$878$	30.3744	1.02509
$879$	0.933949	0.0315013
$880$	0.555637	0.0187305
$881$	27.2786	0.919040	0.459520	−	0.888167i	$-0.348021\pi$
$881$	27.2786	0.919040	0.459520	+	0.888167i	$0.348021\pi$
$882$	−20.9803	−0.706443
$883$	−25.7131	−0.865314	−0.432657	−	0.901559i	$-0.642424\pi$
$883$	−25.7131	−0.865314	−0.432657	+	0.901559i	$0.642424\pi$
$884$	13.4897	0.453707
$885$	3.53162	0.118714
$886$	31.0359	1.04267
$887$	8.70465	0.292273	0.146137	−	0.989264i	$-0.453316\pi$
$887$	8.70465	0.292273	0.146137	+	0.989264i	$0.453316\pi$
$888$	10.2382	0.343571
$889$	9.61516	0.322482
$890$	23.5867	0.790628
$891$	20.1756	0.675908
$892$	−3.40603	−0.114042
$893$	1.67011	0.0558881
$894$	9.08572	0.303872
$895$	19.9484	0.666803
$896$	−36.5633	−1.22149
$897$	3.57977	0.119525
$898$	39.0479	1.30304
$899$	−11.3607	−0.378900
$900$	−9.38520	−0.312840
$901$	3.72188	0.123994
$902$	35.6171	1.18592
$903$	−7.64381	−0.254370
$904$	13.8121	0.459383
$905$	2.89998	0.0963986
$906$	−13.0741	−0.434359
$907$	−32.2856	−1.07203	−0.536013	−	0.844210i	$-0.680070\pi$
$907$	−32.2856	−1.07203	−0.536013	+	0.844210i	$0.680070\pi$
$908$	59.9341	1.98898
$909$	−25.1127	−0.832936
$910$	−10.6096	−0.351706
$911$	60.2092	1.99482	0.997410	−	0.0719291i	$-0.0229155\pi$
$911$	60.2092	1.99482	0.997410	+	0.0719291i	$0.0229155\pi$
$912$	0.153546	0.00508443
$913$	−33.8035	−1.11873
$914$	56.8192	1.87941
$915$	0.372596	0.0123177
$916$	15.0036	0.495732
$917$	−15.1865	−0.501502
$918$	−8.79752	−0.290361
$919$	52.9782	1.74759	0.873795	−	0.486294i	$-0.161652\pi$
$919$	52.9782	1.74759	0.873795	+	0.486294i	$0.161652\pi$
$920$	11.8649	0.391173
$921$	−1.77965	−0.0586414
$922$	−43.9680	−1.44801
$923$	−22.6819	−0.746584
$924$	−6.27638	−0.206478
$925$	−9.22691	−0.303379
$926$	−63.9647	−2.10201
$927$	−19.9377	−0.654840
$928$	−12.8932	−0.423238
$929$	23.2960	0.764315	0.382158	−	0.924097i	$-0.375181\pi$
$929$	23.2960	0.764315	0.382158	+	0.924097i	$0.375181\pi$
$930$	−4.12102	−0.135134
$931$	−6.10944	−0.200229
$932$	−59.4994	−1.94897
$933$	4.59923	0.150572
$934$	−45.9089	−1.50219
$935$	−4.52327	−0.147927
$936$	−19.9469	−0.651984
$937$	−4.65031	−0.151919	−0.0759595	−	0.997111i	$-0.524202\pi$
$937$	−4.65031	−0.151919	−0.0759595	+	0.997111i	$0.524202\pi$
$938$	−15.9764	−0.521649
$939$	−1.07802	−0.0351797
$940$	2.86598	0.0934781
$941$	8.53668	0.278288	0.139144	−	0.990272i	$-0.455565\pi$
$941$	8.53668	0.278288	0.139144	+	0.990272i	$0.455565\pi$
$942$	2.69154	0.0876951
$943$	23.9318	0.779325
$944$	2.00283	0.0651865
$945$	4.29994	0.139877
$946$	−62.3461	−2.02705
$947$	−44.2799	−1.43890	−0.719452	−	0.694542i	$-0.755607\pi$
$947$	−44.2799	−1.43890	−0.719452	+	0.694542i	$0.755607\pi$
$948$	−8.08642	−0.262635
$949$	−1.54112	−0.0500268
$950$	−4.39774	−0.142682
$951$	2.14581	0.0695827
$952$	−9.99492	−0.323937
$953$	54.6411	1.77000	0.885000	−	0.465591i	$-0.154158\pi$
$953$	54.6411	1.77000	0.885000	+	0.465591i	$0.154158\pi$
$954$	−14.0807	−0.455879
$955$	7.42378	0.240228
$956$	70.2367	2.27162
$957$	−2.33543	−0.0754939
$958$	−35.2555	−1.13905
$959$	−21.3094	−0.688117
$960$	−4.83742	−0.156127
$961$	−8.28486	−0.267253
$962$	−50.1736	−1.61766
$963$	55.1017	1.77563
$964$	61.7948	1.99028
$965$	−14.5476	−0.468302
$966$	−6.78611	−0.218340
$967$	−42.7889	−1.37600	−0.687998	−	0.725712i	$-0.741510\pi$
$967$	−42.7889	−1.37600	−0.687998	+	0.725712i	$0.741510\pi$
$968$	12.4374	0.399753
$969$	−1.24997	−0.0401550
$970$	−6.63870	−0.213156
$971$	−41.8328	−1.34248	−0.671239	−	0.741241i	$-0.734238\pi$
$971$	−41.8328	−1.34248	−0.671239	+	0.741241i	$0.734238\pi$
$972$	31.2751	1.00315
$973$	−1.90897	−0.0611987
$974$	−43.2457	−1.38568
$975$	−0.889945	−0.0285011
$976$	0.211304	0.00676369
$977$	−1.50352	−0.0481020	−0.0240510	−	0.999711i	$-0.507656\pi$
$977$	−1.50352	−0.0481020	−0.0240510	+	0.999711i	$0.507656\pi$
$978$	−20.5953	−0.658565
$979$	−26.7264	−0.854180
$980$	−10.4841	−0.334902
$981$	−18.2520	−0.582741
$982$	−100.522	−3.20778
$983$	10.7313	0.342275	0.171138	−	0.985247i	$-0.445256\pi$
$983$	10.7313	0.342275	0.171138	+	0.985247i	$0.445256\pi$
$984$	6.60159	0.210451
$985$	12.4089	0.395381
$986$	−9.51537	−0.303031
$987$	−0.640684	−0.0203932
$988$	−14.8612	−0.472796
$989$	−41.8914	−1.33207
$990$	17.1125	0.543870
$991$	18.3111	0.581670	0.290835	−	0.956773i	$-0.406067\pi$
$991$	18.3111	0.581670	0.290835	+	0.956773i	$0.406067\pi$
$992$	25.7792	0.818491
$993$	9.24799	0.293476
$994$	42.9977	1.36380
$995$	−15.8896	−0.503733
$996$	−16.0302	−0.507937
$997$	−8.65852	−0.274218	−0.137109	−	0.990556i	$-0.543781\pi$
$997$	−8.65852	−0.274218	−0.137109	+	0.990556i	$0.543781\pi$
$998$	77.3499	2.44847
$999$	20.3347	0.643361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.18	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.18	✓	153	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29854 q^{2} +0.376180 q^{3} +3.28327 q^{4} +1.00000 q^{5} -0.864664 q^{6} -1.95111 q^{7} -2.94965 q^{8} -2.85849 q^{9} +O(q^{10})\)	\(q-2.29854 q^{2} +0.376180 q^{3} +3.28327 q^{4} +1.00000 q^{5} -0.864664 q^{6} -1.95111 q^{7} -2.94965 q^{8} -2.85849 q^{9} -2.29854 q^{10} +2.60450 q^{11} +1.23510 q^{12} -2.36574 q^{13} +4.48469 q^{14} +0.376180 q^{15} +0.213337 q^{16} -1.73671 q^{17} +6.57034 q^{18} +1.91328 q^{19} +3.28327 q^{20} -0.733968 q^{21} -5.98655 q^{22} -4.02247 q^{23} -1.10960 q^{24} +1.00000 q^{25} +5.43775 q^{26} -2.20385 q^{27} -6.40602 q^{28} -2.38367 q^{29} -0.864664 q^{30} +4.76604 q^{31} +5.40894 q^{32} +0.979762 q^{33} +3.99189 q^{34} -1.95111 q^{35} -9.38520 q^{36} -9.22691 q^{37} -4.39774 q^{38} -0.889945 q^{39} -2.94965 q^{40} -5.94952 q^{41} +1.68705 q^{42} +10.4144 q^{43} +8.55130 q^{44} -2.85849 q^{45} +9.24579 q^{46} +0.872904 q^{47} +0.0802530 q^{48} -3.19318 q^{49} -2.29854 q^{50} -0.653316 q^{51} -7.76738 q^{52} -2.14307 q^{53} +5.06562 q^{54} +2.60450 q^{55} +5.75509 q^{56} +0.719737 q^{57} +5.47896 q^{58} +9.38810 q^{59} +1.23510 q^{60} +0.990473 q^{61} -10.9549 q^{62} +5.57722 q^{63} -12.8593 q^{64} -2.36574 q^{65} -2.25202 q^{66} -3.56243 q^{67} -5.70209 q^{68} -1.51317 q^{69} +4.48469 q^{70} +9.58765 q^{71} +8.43154 q^{72} +0.651431 q^{73} +21.2084 q^{74} +0.376180 q^{75} +6.28182 q^{76} -5.08167 q^{77} +2.04557 q^{78} -6.54717 q^{79} +0.213337 q^{80} +7.74642 q^{81} +13.6752 q^{82} -12.9789 q^{83} -2.40982 q^{84} -1.73671 q^{85} -23.9378 q^{86} -0.896691 q^{87} -7.68238 q^{88} -10.2616 q^{89} +6.57034 q^{90} +4.61582 q^{91} -13.2069 q^{92} +1.79289 q^{93} -2.00640 q^{94} +1.91328 q^{95} +2.03474 q^{96} +2.88823 q^{97} +7.33964 q^{98} -7.44494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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