LMFDB - Embedded newform 2842.2.a.y.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.345065.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 7x^{3} + 8x^{2} + 14x - 3 $ x^5 - 2x^4 - 7x^3 + 8x^2 + 14x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.196248$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.803752 q^{3} +1.00000 q^{4} +0.712284 q^{5} +0.803752 q^{6} +1.00000 q^{8} -2.35398 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.803752 q^{3} +1.00000 q^{4} +0.712284 q^{5} +0.803752 q^{6} +1.00000 q^{8} -2.35398 q^{9} +0.712284 q^{10} +2.61731 q^{11} +0.803752 q^{12} +1.95573 q^{13} +0.572499 q^{15} +1.00000 q^{16} -3.59099 q^{17} -2.35398 q^{18} +7.06276 q^{19} +0.712284 q^{20} +2.61731 q^{22} +3.24920 q^{23} +0.803752 q^{24} -4.49265 q^{25} +1.95573 q^{26} -4.30327 q^{27} +1.00000 q^{29} +0.572499 q^{30} +8.32767 q^{31} +1.00000 q^{32} +2.10366 q^{33} -3.59099 q^{34} -2.35398 q^{36} +0.815948 q^{37} +7.06276 q^{38} +1.57192 q^{39} +0.712284 q^{40} +5.79075 q^{41} +3.35398 q^{43} +2.61731 q^{44} -1.67670 q^{45} +3.24920 q^{46} +0.930224 q^{47} +0.803752 q^{48} -4.49265 q^{50} -2.88626 q^{51} +1.95573 q^{52} -5.55733 q^{53} -4.30327 q^{54} +1.86426 q^{55} +5.67670 q^{57} +1.00000 q^{58} +8.89202 q^{59} +0.572499 q^{60} +1.48103 q^{61} +8.32767 q^{62} +1.00000 q^{64} +1.39304 q^{65} +2.10366 q^{66} -6.82170 q^{67} -3.59099 q^{68} +2.61155 q^{69} +6.03069 q^{71} -2.35398 q^{72} -7.83070 q^{73} +0.815948 q^{74} -3.61098 q^{75} +7.06276 q^{76} +1.57192 q^{78} -16.4665 q^{79} +0.712284 q^{80} +3.60319 q^{81} +5.79075 q^{82} +14.3623 q^{83} -2.55780 q^{85} +3.35398 q^{86} +0.803752 q^{87} +2.61731 q^{88} -3.96596 q^{89} -1.67670 q^{90} +3.24920 q^{92} +6.69338 q^{93} +0.930224 q^{94} +5.03069 q^{95} +0.803752 q^{96} +13.4920 q^{97} -6.16110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9} + 7 q^{10} + 3 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 16 q^{17} + 4 q^{18} + 2 q^{19} + 7 q^{20} - 5 q^{23} + 3 q^{24} + 4 q^{25} + 8 q^{26} + 9 q^{27} + 5 q^{29} + 4 q^{30} + 5 q^{31} + 5 q^{32} + 3 q^{33} + 16 q^{34} + 4 q^{36} + 2 q^{38} - 20 q^{39} + 7 q^{40} + 17 q^{41} + q^{43} + 14 q^{45} - 5 q^{46} - 4 q^{47} + 3 q^{48} + 4 q^{50} - 3 q^{51} + 8 q^{52} + 5 q^{53} + 9 q^{54} + 12 q^{55} + 6 q^{57} + 5 q^{58} + 17 q^{59} + 4 q^{60} + 13 q^{61} + 5 q^{62} + 5 q^{64} - 7 q^{65} + 3 q^{66} - 14 q^{67} + 16 q^{68} + 16 q^{69} - 8 q^{71} + 4 q^{72} + 6 q^{73} + 8 q^{75} + 2 q^{76} - 20 q^{78} + 11 q^{79} + 7 q^{80} - 19 q^{81} + 17 q^{82} + 2 q^{83} + 39 q^{85} + q^{86} + 3 q^{87} + 9 q^{89} + 14 q^{90} - 5 q^{92} - 3 q^{93} - 4 q^{94} - 13 q^{95} + 3 q^{96} + 12 q^{97} + 10 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9 + 7 * q^10 + 3 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 16 * q^17 + 4 * q^18 + 2 * q^19 + 7 * q^20 - 5 * q^23 + 3 * q^24 + 4 * q^25 + 8 * q^26 + 9 * q^27 + 5 * q^29 + 4 * q^30 + 5 * q^31 + 5 * q^32 + 3 * q^33 + 16 * q^34 + 4 * q^36 + 2 * q^38 - 20 * q^39 + 7 * q^40 + 17 * q^41 + q^43 + 14 * q^45 - 5 * q^46 - 4 * q^47 + 3 * q^48 + 4 * q^50 - 3 * q^51 + 8 * q^52 + 5 * q^53 + 9 * q^54 + 12 * q^55 + 6 * q^57 + 5 * q^58 + 17 * q^59 + 4 * q^60 + 13 * q^61 + 5 * q^62 + 5 * q^64 - 7 * q^65 + 3 * q^66 - 14 * q^67 + 16 * q^68 + 16 * q^69 - 8 * q^71 + 4 * q^72 + 6 * q^73 + 8 * q^75 + 2 * q^76 - 20 * q^78 + 11 * q^79 + 7 * q^80 - 19 * q^81 + 17 * q^82 + 2 * q^83 + 39 * q^85 + q^86 + 3 * q^87 + 9 * q^89 + 14 * q^90 - 5 * q^92 - 3 * q^93 - 4 * q^94 - 13 * q^95 + 3 * q^96 + 12 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.803752	0.464046	0.232023	−	0.972710i	$-0.425465\pi$
$3$	0.803752	0.464046	0.232023	+	0.972710i	$0.425465\pi$
$4$	1.00000	0.500000
$5$	0.712284	0.318543	0.159271	−	0.987235i	$-0.449085\pi$
$5$	0.712284	0.318543	0.159271	+	0.987235i	$0.449085\pi$
$6$	0.803752	0.328130
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.35398	−0.784661
$10$	0.712284	0.225244
$11$	2.61731	0.789148	0.394574	−	0.918864i	$-0.370892\pi$
$11$	2.61731	0.789148	0.394574	+	0.918864i	$0.370892\pi$
$12$	0.803752	0.232023
$13$	1.95573	0.542423	0.271211	−	0.962520i	$-0.412576\pi$
$13$	1.95573	0.542423	0.271211	+	0.962520i	$0.412576\pi$
$14$	0	0
$15$	0.572499	0.147819
$16$	1.00000	0.250000
$17$	−3.59099	−0.870943	−0.435471	−	0.900203i	$-0.643418\pi$
$17$	−3.59099	−0.870943	−0.435471	+	0.900203i	$0.643418\pi$
$18$	−2.35398	−0.554839
$19$	7.06276	1.62031	0.810154	−	0.586217i	$-0.199384\pi$
$19$	7.06276	1.62031	0.810154	+	0.586217i	$0.199384\pi$
$20$	0.712284	0.159271
$21$	0	0
$22$	2.61731	0.558012
$23$	3.24920	0.677506	0.338753	−	0.940875i	$-0.389995\pi$
$23$	3.24920	0.677506	0.338753	+	0.940875i	$0.389995\pi$
$24$	0.803752	0.164065
$25$	−4.49265	−0.898530
$26$	1.95573	0.383551
$27$	−4.30327	−0.828165
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.572499	0.104524
$31$	8.32767	1.49569	0.747847	−	0.663872i	$-0.231088\pi$
$31$	8.32767	1.49569	0.747847	+	0.663872i	$0.231088\pi$
$32$	1.00000	0.176777
$33$	2.10366	0.366201
$34$	−3.59099	−0.615850
$35$	0	0
$36$	−2.35398	−0.392331
$37$	0.815948	0.134141	0.0670705	−	0.997748i	$-0.478635\pi$
$37$	0.815948	0.134141	0.0670705	+	0.997748i	$0.478635\pi$
$38$	7.06276	1.14573
$39$	1.57192	0.251709
$40$	0.712284	0.112622
$41$	5.79075	0.904363	0.452181	−	0.891926i	$-0.350646\pi$
$41$	5.79075	0.904363	0.452181	+	0.891926i	$0.350646\pi$
$42$	0	0
$43$	3.35398	0.511478	0.255739	−	0.966746i	$-0.417681\pi$
$43$	3.35398	0.511478	0.255739	+	0.966746i	$0.417681\pi$
$44$	2.61731	0.394574
$45$	−1.67670	−0.249948
$46$	3.24920	0.479069
$47$	0.930224	0.135687	0.0678436	−	0.997696i	$-0.478388\pi$
$47$	0.930224	0.135687	0.0678436	+	0.997696i	$0.478388\pi$
$48$	0.803752	0.116012
$49$	0	0
$50$	−4.49265	−0.635357
$51$	−2.88626	−0.404158
$52$	1.95573	0.271211
$53$	−5.55733	−0.763358	−0.381679	−	0.924295i	$-0.624654\pi$
$53$	−5.55733	−0.763358	−0.381679	+	0.924295i	$0.624654\pi$
$54$	−4.30327	−0.585601
$55$	1.86426	0.251377
$56$	0	0
$57$	5.67670	0.751898
$58$	1.00000	0.131306
$59$	8.89202	1.15764	0.578821	−	0.815455i	$-0.303513\pi$
$59$	8.89202	1.15764	0.578821	+	0.815455i	$0.303513\pi$
$60$	0.572499	0.0739093
$61$	1.48103	0.189627	0.0948133	−	0.995495i	$-0.469775\pi$
$61$	1.48103	0.189627	0.0948133	+	0.995495i	$0.469775\pi$
$62$	8.32767	1.05761
$63$	0	0
$64$	1.00000	0.125000
$65$	1.39304	0.172785
$66$	2.10366	0.258943
$67$	−6.82170	−0.833404	−0.416702	−	0.909043i	$-0.636814\pi$
$67$	−6.82170	−0.833404	−0.416702	+	0.909043i	$0.636814\pi$
$68$	−3.59099	−0.435471
$69$	2.61155	0.314394
$70$	0	0
$71$	6.03069	0.715711	0.357855	−	0.933777i	$-0.383508\pi$
$71$	6.03069	0.715711	0.357855	+	0.933777i	$0.383508\pi$
$72$	−2.35398	−0.277420
$73$	−7.83070	−0.916514	−0.458257	−	0.888820i	$-0.651526\pi$
$73$	−7.83070	−0.916514	−0.458257	+	0.888820i	$0.651526\pi$
$74$	0.815948	0.0948521
$75$	−3.61098	−0.416960
$76$	7.06276	0.810154
$77$	0	0
$78$	1.57192	0.177985
$79$	−16.4665	−1.85263	−0.926313	−	0.376756i	$-0.877040\pi$
$79$	−16.4665	−1.85263	−0.926313	+	0.376756i	$0.877040\pi$
$80$	0.712284	0.0796357
$81$	3.60319	0.400354
$82$	5.79075	0.639481
$83$	14.3623	1.57647	0.788233	−	0.615377i	$-0.210996\pi$
$83$	14.3623	1.57647	0.788233	+	0.615377i	$0.210996\pi$
$84$	0	0
$85$	−2.55780	−0.277433
$86$	3.35398	0.361669
$87$	0.803752	0.0861712
$88$	2.61731	0.279006
$89$	−3.96596	−0.420391	−0.210196	−	0.977659i	$-0.567410\pi$
$89$	−3.96596	−0.420391	−0.210196	+	0.977659i	$0.567410\pi$
$90$	−1.67670	−0.176740
$91$	0	0
$92$	3.24920	0.338753
$93$	6.69338	0.694071
$94$	0.930224	0.0959453
$95$	5.03069	0.516138
$96$	0.803752	0.0820326
$97$	13.4920	1.36990	0.684951	−	0.728589i	$-0.259824\pi$
$97$	13.4920	1.36990	0.684951	+	0.728589i	$0.259824\pi$
$98$	0	0
$99$	−6.16110	−0.619213
$100$	−4.49265	−0.449265
$101$	−4.35974	−0.433810	−0.216905	−	0.976193i	$-0.569596\pi$
$101$	−4.35974	−0.433810	−0.216905	+	0.976193i	$0.569596\pi$
$102$	−2.88626	−0.285783
$103$	9.17815	0.904350	0.452175	−	0.891929i	$-0.350648\pi$
$103$	9.17815	0.904350	0.452175	+	0.891929i	$0.350648\pi$
$104$	1.95573	0.191775
$105$	0	0
$106$	−5.55733	−0.539776
$107$	16.5515	1.60010	0.800048	−	0.599936i	$-0.204807\pi$
$107$	16.5515	1.60010	0.800048	+	0.599936i	$0.204807\pi$
$108$	−4.30327	−0.414083
$109$	−15.1757	−1.45357	−0.726784	−	0.686867i	$-0.758986\pi$
$109$	−15.1757	−1.45357	−0.726784	+	0.686867i	$0.758986\pi$
$110$	1.86426	0.177751
$111$	0.655820	0.0622477
$112$	0	0
$113$	−9.46144	−0.890057	−0.445028	−	0.895516i	$-0.646806\pi$
$113$	−9.46144	−0.890057	−0.445028	+	0.895516i	$0.646806\pi$
$114$	5.67670	0.531672
$115$	2.31435	0.215815
$116$	1.00000	0.0928477
$117$	−4.60376	−0.425618
$118$	8.89202	0.818577
$119$	0	0
$120$	0.572499	0.0522618
$121$	−4.14971	−0.377246
$122$	1.48103	0.134086
$123$	4.65432	0.419666
$124$	8.32767	0.747847
$125$	−6.76146	−0.604763
$126$	0	0
$127$	9.28047	0.823508	0.411754	−	0.911295i	$-0.364916\pi$
$127$	9.28047	0.823508	0.411754	+	0.911295i	$0.364916\pi$
$128$	1.00000	0.0883883
$129$	2.69577	0.237349
$130$	1.39304	0.122177
$131$	0.712284	0.0622325	0.0311163	−	0.999516i	$-0.490094\pi$
$131$	0.712284	0.0622325	0.0311163	+	0.999516i	$0.490094\pi$
$132$	2.10366	0.183101
$133$	0	0
$134$	−6.82170	−0.589305
$135$	−3.06515	−0.263806
$136$	−3.59099	−0.307925
$137$	−2.58662	−0.220990	−0.110495	−	0.993877i	$-0.535244\pi$
$137$	−2.58662	−0.220990	−0.110495	+	0.993877i	$0.535244\pi$
$138$	2.61155	0.222310
$139$	−9.84174	−0.834765	−0.417383	−	0.908731i	$-0.637052\pi$
$139$	−9.84174	−0.834765	−0.417383	+	0.908731i	$0.637052\pi$
$140$	0	0
$141$	0.747669	0.0629651
$142$	6.03069	0.506084
$143$	5.11875	0.428052
$144$	−2.35398	−0.196165
$145$	0.712284	0.0591519
$146$	−7.83070	−0.648073
$147$	0	0
$148$	0.815948	0.0670705
$149$	4.13604	0.338838	0.169419	−	0.985544i	$-0.445811\pi$
$149$	4.13604	0.338838	0.169419	+	0.985544i	$0.445811\pi$
$150$	−3.61098	−0.294835
$151$	−14.4979	−1.17983	−0.589913	−	0.807467i	$-0.700838\pi$
$151$	−14.4979	−1.17983	−0.589913	+	0.807467i	$0.700838\pi$
$152$	7.06276	0.572865
$153$	8.45313	0.683395
$154$	0	0
$155$	5.93166	0.476442
$156$	1.57192	0.125855
$157$	14.3121	1.14223	0.571116	−	0.820870i	$-0.306511\pi$
$157$	14.3121	1.14223	0.571116	+	0.820870i	$0.306511\pi$
$158$	−16.4665	−1.31000
$159$	−4.46672	−0.354234
$160$	0.712284	0.0563110
$161$	0	0
$162$	3.60319	0.283093
$163$	1.94624	0.152441	0.0762205	−	0.997091i	$-0.475715\pi$
$163$	1.94624	0.152441	0.0762205	+	0.997091i	$0.475715\pi$
$164$	5.79075	0.452181
$165$	1.49841	0.116651
$166$	14.3623	1.11473
$167$	−15.4641	−1.19665	−0.598324	−	0.801254i	$-0.704166\pi$
$167$	−15.4641	−1.19665	−0.598324	+	0.801254i	$0.704166\pi$
$168$	0	0
$169$	−9.17511	−0.705778
$170$	−2.55780	−0.196175
$171$	−16.6256	−1.27139
$172$	3.35398	0.255739
$173$	−10.1790	−0.773899	−0.386949	−	0.922101i	$-0.626471\pi$
$173$	−10.1790	−0.773899	−0.386949	+	0.922101i	$0.626471\pi$
$174$	0.803752	0.0609323
$175$	0	0
$176$	2.61731	0.197287
$177$	7.14697	0.537200
$178$	−3.96596	−0.297261
$179$	−20.3169	−1.51856	−0.759278	−	0.650766i	$-0.774448\pi$
$179$	−20.3169	−1.51856	−0.759278	+	0.650766i	$0.774448\pi$
$180$	−1.67670	−0.124974
$181$	15.8077	1.17497	0.587487	−	0.809234i	$-0.300117\pi$
$181$	15.8077	1.17497	0.587487	+	0.809234i	$0.300117\pi$
$182$	0	0
$183$	1.19038	0.0879955
$184$	3.24920	0.239534
$185$	0.581187	0.0427297
$186$	6.69338	0.490782
$187$	−9.39872	−0.687302
$188$	0.930224	0.0678436
$189$	0	0
$190$	5.03069	0.364964
$191$	−20.5463	−1.48668	−0.743341	−	0.668913i	$-0.766760\pi$
$191$	−20.5463	−1.48668	−0.743341	+	0.668913i	$0.766760\pi$
$192$	0.803752	0.0580058
$193$	−10.7648	−0.774868	−0.387434	−	0.921897i	$-0.626639\pi$
$193$	−10.7648	−0.774868	−0.387434	+	0.921897i	$0.626639\pi$
$194$	13.4920	0.968667
$195$	1.11966	0.0801802
$196$	0	0
$197$	25.4431	1.81274	0.906372	−	0.422481i	$-0.138841\pi$
$197$	25.4431	1.81274	0.906372	+	0.422481i	$0.138841\pi$
$198$	−6.16110	−0.437850
$199$	−25.3328	−1.79580	−0.897899	−	0.440202i	$-0.854907\pi$
$199$	−25.3328	−1.79580	−0.897899	+	0.440202i	$0.854907\pi$
$200$	−4.49265	−0.317678
$201$	−5.48295	−0.386738
$202$	−4.35974	−0.306750
$203$	0	0
$204$	−2.88626	−0.202079
$205$	4.12465	0.288078
$206$	9.17815	0.639472
$207$	−7.64857	−0.531612
$208$	1.95573	0.135606
$209$	18.4854	1.27866
$210$	0	0
$211$	26.4015	1.81755	0.908776	−	0.417285i	$-0.137018\pi$
$211$	26.4015	1.81755	0.908776	+	0.417285i	$0.137018\pi$
$212$	−5.55733	−0.381679
$213$	4.84718	0.332123
$214$	16.5515	1.13144
$215$	2.38899	0.162928
$216$	−4.30327	−0.292801
$217$	0	0
$218$	−15.1757	−1.02783
$219$	−6.29394	−0.425305
$220$	1.86426	0.125689
$221$	−7.02302	−0.472419
$222$	0.655820	0.0440157
$223$	−9.13324	−0.611607	−0.305803	−	0.952095i	$-0.598925\pi$
$223$	−9.13324	−0.611607	−0.305803	+	0.952095i	$0.598925\pi$
$224$	0	0
$225$	10.5756	0.705042
$226$	−9.46144	−0.629365
$227$	4.53792	0.301192	0.150596	−	0.988595i	$-0.451881\pi$
$227$	4.53792	0.301192	0.150596	+	0.988595i	$0.451881\pi$
$228$	5.67670	0.375949
$229$	1.01540	0.0670994	0.0335497	−	0.999437i	$-0.489319\pi$
$229$	1.01540	0.0670994	0.0335497	+	0.999437i	$0.489319\pi$
$230$	2.31435	0.152604
$231$	0	0
$232$	1.00000	0.0656532
$233$	9.28302	0.608151	0.304075	−	0.952648i	$-0.401653\pi$
$233$	9.28302	0.608151	0.304075	+	0.952648i	$0.401653\pi$
$234$	−4.60376	−0.300957
$235$	0.662583	0.0432222
$236$	8.89202	0.578821
$237$	−13.2350	−0.859704
$238$	0	0
$239$	−7.42704	−0.480416	−0.240208	−	0.970721i	$-0.577216\pi$
$239$	−7.42704	−0.480416	−0.240208	+	0.970721i	$0.577216\pi$
$240$	0.572499	0.0369547
$241$	−15.7233	−1.01283	−0.506413	−	0.862291i	$-0.669029\pi$
$241$	−15.7233	−1.01283	−0.506413	+	0.862291i	$0.669029\pi$
$242$	−4.14971	−0.266753
$243$	15.8059	1.01395
$244$	1.48103	0.0948133
$245$	0	0
$246$	4.65432	0.296749
$247$	13.8129	0.878892
$248$	8.32767	0.528807
$249$	11.5437	0.731553
$250$	−6.76146	−0.427632
$251$	8.44770	0.533214	0.266607	−	0.963805i	$-0.414097\pi$
$251$	8.44770	0.533214	0.266607	+	0.963805i	$0.414097\pi$
$252$	0	0
$253$	8.50416	0.534652
$254$	9.28047	0.582308
$255$	−2.05584	−0.128742
$256$	1.00000	0.0625000
$257$	−26.1241	−1.62958	−0.814788	−	0.579759i	$-0.803147\pi$
$257$	−26.1241	−1.62958	−0.814788	+	0.579759i	$0.803147\pi$
$258$	2.69577	0.167831
$259$	0	0
$260$	1.39304	0.0863925
$261$	−2.35398	−0.145708
$262$	0.712284	0.0440050
$263$	−3.41075	−0.210316	−0.105158	−	0.994456i	$-0.533535\pi$
$263$	−3.41075	−0.210316	−0.105158	+	0.994456i	$0.533535\pi$
$264$	2.10366	0.129472
$265$	−3.95840	−0.243162
$266$	0	0
$267$	−3.18765	−0.195081
$268$	−6.82170	−0.416702
$269$	−3.22211	−0.196455	−0.0982277	−	0.995164i	$-0.531317\pi$
$269$	−3.22211	−0.196455	−0.0982277	+	0.995164i	$0.531317\pi$
$270$	−3.06515	−0.186539
$271$	−10.8198	−0.657259	−0.328629	−	0.944459i	$-0.606587\pi$
$271$	−10.8198	−0.657259	−0.328629	+	0.944459i	$0.606587\pi$
$272$	−3.59099	−0.217736
$273$	0	0
$274$	−2.58662	−0.156263
$275$	−11.7586	−0.709073
$276$	2.61155	0.157197
$277$	−27.1495	−1.63126	−0.815628	−	0.578576i	$-0.803609\pi$
$277$	−27.1495	−1.63126	−0.815628	+	0.578576i	$0.803609\pi$
$278$	−9.84174	−0.590268
$279$	−19.6032	−1.17361
$280$	0	0
$281$	−22.1541	−1.32160	−0.660802	−	0.750560i	$-0.729784\pi$
$281$	−22.1541	−1.32160	−0.660802	+	0.750560i	$0.729784\pi$
$282$	0.747669	0.0445231
$283$	−14.5383	−0.864210	−0.432105	−	0.901823i	$-0.642229\pi$
$283$	−14.5383	−0.864210	−0.432105	+	0.901823i	$0.642229\pi$
$284$	6.03069	0.357855
$285$	4.04342	0.239512
$286$	5.11875	0.302678
$287$	0	0
$288$	−2.35398	−0.138710
$289$	−4.10479	−0.241458
$290$	0.712284	0.0418267
$291$	10.8442	0.635698
$292$	−7.83070	−0.458257
$293$	9.06141	0.529373	0.264687	−	0.964334i	$-0.414731\pi$
$293$	9.06141	0.529373	0.264687	+	0.964334i	$0.414731\pi$
$294$	0	0
$295$	6.33364	0.368759
$296$	0.815948	0.0474260
$297$	−11.2630	−0.653545
$298$	4.13604	0.239595
$299$	6.35457	0.367494
$300$	−3.61098	−0.208480
$301$	0	0
$302$	−14.4979	−0.834262
$303$	−3.50415	−0.201308
$304$	7.06276	0.405077
$305$	1.05491	0.0604042
$306$	8.45313	0.483233
$307$	11.8381	0.675636	0.337818	−	0.941211i	$-0.390311\pi$
$307$	11.8381	0.675636	0.337818	+	0.941211i	$0.390311\pi$
$308$	0	0
$309$	7.37695	0.419660
$310$	5.93166	0.336896
$311$	11.3041	0.640999	0.320499	−	0.947249i	$-0.396149\pi$
$311$	11.3041	0.640999	0.320499	+	0.947249i	$0.396149\pi$
$312$	1.57192	0.0889926
$313$	11.8533	0.669987	0.334993	−	0.942221i	$-0.391266\pi$
$313$	11.8533	0.669987	0.334993	+	0.942221i	$0.391266\pi$
$314$	14.3121	0.807680
$315$	0	0
$316$	−16.4665	−0.926313
$317$	7.41663	0.416559	0.208280	−	0.978069i	$-0.433214\pi$
$317$	7.41663	0.416559	0.208280	+	0.978069i	$0.433214\pi$
$318$	−4.46672	−0.250481
$319$	2.61731	0.146541
$320$	0.712284	0.0398179
$321$	13.3033	0.742518
$322$	0	0
$323$	−25.3623	−1.41120
$324$	3.60319	0.200177
$325$	−8.78643	−0.487383
$326$	1.94624	0.107792
$327$	−12.1975	−0.674522
$328$	5.79075	0.319741
$329$	0	0
$330$	1.49841	0.0824845
$331$	29.4239	1.61728	0.808642	−	0.588302i	$-0.200203\pi$
$331$	29.4239	1.61728	0.808642	+	0.588302i	$0.200203\pi$
$332$	14.3623	0.788233
$333$	−1.92073	−0.105255
$334$	−15.4641	−0.846158
$335$	−4.85899	−0.265475
$336$	0	0
$337$	25.7213	1.40113	0.700565	−	0.713589i	$-0.252931\pi$
$337$	25.7213	1.40113	0.700565	+	0.713589i	$0.252931\pi$
$338$	−9.17511	−0.499060
$339$	−7.60464	−0.413028
$340$	−2.55780	−0.138716
$341$	21.7961	1.18032
$342$	−16.6256	−0.899010
$343$	0	0
$344$	3.35398	0.180835
$345$	1.86017	0.100148
$346$	−10.1790	−0.547229
$347$	17.1022	0.918092	0.459046	−	0.888412i	$-0.348191\pi$
$347$	17.1022	0.918092	0.459046	+	0.888412i	$0.348191\pi$
$348$	0.803752	0.0430856
$349$	2.58512	0.138378	0.0691892	−	0.997604i	$-0.477959\pi$
$349$	2.58512	0.138378	0.0691892	+	0.997604i	$0.477959\pi$
$350$	0	0
$351$	−8.41605	−0.449216
$352$	2.61731	0.139503
$353$	7.84366	0.417476	0.208738	−	0.977972i	$-0.433064\pi$
$353$	7.84366	0.417476	0.208738	+	0.977972i	$0.433064\pi$
$354$	7.14697	0.379857
$355$	4.29556	0.227985
$356$	−3.96596	−0.210196
$357$	0	0
$358$	−20.3169	−1.07378
$359$	−3.86388	−0.203928	−0.101964	−	0.994788i	$-0.532513\pi$
$359$	−3.86388	−0.203928	−0.101964	+	0.994788i	$0.532513\pi$
$360$	−1.67670	−0.0883700
$361$	30.8825	1.62540
$362$	15.8077	0.830832
$363$	−3.33533	−0.175060
$364$	0	0
$365$	−5.57768	−0.291949
$366$	1.19038	0.0622222
$367$	−4.01795	−0.209735	−0.104868	−	0.994486i	$-0.533442\pi$
$367$	−4.01795	−0.209735	−0.104868	+	0.994486i	$0.533442\pi$
$368$	3.24920	0.169376
$369$	−13.6313	−0.709618
$370$	0.581187	0.0302145
$371$	0	0
$372$	6.69338	0.347035
$373$	21.5426	1.11544	0.557718	−	0.830031i	$-0.311677\pi$
$373$	21.5426	1.11544	0.557718	+	0.830031i	$0.311677\pi$
$374$	−9.39872	−0.485996
$375$	−5.43454	−0.280638
$376$	0.930224	0.0479726
$377$	1.95573	0.100725
$378$	0	0
$379$	−5.88638	−0.302363	−0.151182	−	0.988506i	$-0.548308\pi$
$379$	−5.88638	−0.302363	−0.151182	+	0.988506i	$0.548308\pi$
$380$	5.03069	0.258069
$381$	7.45919	0.382146
$382$	−20.5463	−1.05124
$383$	−10.9954	−0.561838	−0.280919	−	0.959731i	$-0.590639\pi$
$383$	−10.9954	−0.561838	−0.280919	+	0.959731i	$0.590639\pi$
$384$	0.803752	0.0410163
$385$	0	0
$386$	−10.7648	−0.547914
$387$	−7.89522	−0.401337
$388$	13.4920	0.684951
$389$	23.1125	1.17185	0.585925	−	0.810365i	$-0.300731\pi$
$389$	23.1125	1.17185	0.585925	+	0.810365i	$0.300731\pi$
$390$	1.11966	0.0566960
$391$	−11.6679	−0.590069
$392$	0	0
$393$	0.572499	0.0288788
$394$	25.4431	1.28180
$395$	−11.7288	−0.590141
$396$	−6.16110	−0.309607
$397$	−10.5634	−0.530164	−0.265082	−	0.964226i	$-0.585399\pi$
$397$	−10.5634	−0.530164	−0.265082	+	0.964226i	$0.585399\pi$
$398$	−25.3328	−1.26982
$399$	0	0
$400$	−4.49265	−0.224633
$401$	−26.0088	−1.29882	−0.649408	−	0.760440i	$-0.724983\pi$
$401$	−26.0088	−1.29882	−0.649408	+	0.760440i	$0.724983\pi$
$402$	−5.48295	−0.273465
$403$	16.2867	0.811298
$404$	−4.35974	−0.216905
$405$	2.56649	0.127530
$406$	0	0
$407$	2.13559	0.105857
$408$	−2.88626	−0.142891
$409$	−5.31114	−0.262619	−0.131309	−	0.991341i	$-0.541918\pi$
$409$	−5.31114	−0.262619	−0.131309	+	0.991341i	$0.541918\pi$
$410$	4.12465	0.203702
$411$	−2.07900	−0.102550
$412$	9.17815	0.452175
$413$	0	0
$414$	−7.64857	−0.375907
$415$	10.2300	0.502172
$416$	1.95573	0.0958877
$417$	−7.91031	−0.387370
$418$	18.4854	0.904151
$419$	−40.6199	−1.98441	−0.992205	−	0.124614i	$-0.960231\pi$
$419$	−40.6199	−1.98441	−0.992205	+	0.124614i	$0.960231\pi$
$420$	0	0
$421$	−23.6874	−1.15446	−0.577228	−	0.816583i	$-0.695865\pi$
$421$	−23.6874	−1.15446	−0.577228	+	0.816583i	$0.695865\pi$
$422$	26.4015	1.28520
$423$	−2.18973	−0.106468
$424$	−5.55733	−0.269888
$425$	16.1331	0.782569
$426$	4.84718	0.234846
$427$	0	0
$428$	16.5515	0.800048
$429$	4.11421	0.198636
$430$	2.38899	0.115207
$431$	23.0287	1.10925	0.554626	−	0.832100i	$-0.312862\pi$
$431$	23.0287	1.10925	0.554626	+	0.832100i	$0.312862\pi$
$432$	−4.30327	−0.207041
$433$	−3.59018	−0.172533	−0.0862666	−	0.996272i	$-0.527494\pi$
$433$	−3.59018	−0.172533	−0.0862666	+	0.996272i	$0.527494\pi$
$434$	0	0
$435$	0.572499	0.0274492
$436$	−15.1757	−0.726784
$437$	22.9483	1.09777
$438$	−6.29394	−0.300736
$439$	−21.6037	−1.03109	−0.515545	−	0.856862i	$-0.672411\pi$
$439$	−21.6037	−1.03109	−0.515545	+	0.856862i	$0.672411\pi$
$440$	1.86426	0.0888753
$441$	0	0
$442$	−7.02302	−0.334051
$443$	−19.4926	−0.926120	−0.463060	−	0.886327i	$-0.653249\pi$
$443$	−19.4926	−0.926120	−0.463060	+	0.886327i	$0.653249\pi$
$444$	0.655820	0.0311238
$445$	−2.82489	−0.133913
$446$	−9.13324	−0.432471
$447$	3.32435	0.157236
$448$	0	0
$449$	−27.1804	−1.28272	−0.641361	−	0.767239i	$-0.721630\pi$
$449$	−27.1804	−1.28272	−0.641361	+	0.767239i	$0.721630\pi$
$450$	10.5756	0.498540
$451$	15.1562	0.713676
$452$	−9.46144	−0.445028
$453$	−11.6527	−0.547494
$454$	4.53792	0.212975
$455$	0	0
$456$	5.67670	0.265836
$457$	−15.2998	−0.715695	−0.357847	−	0.933780i	$-0.616489\pi$
$457$	−15.2998	−0.715695	−0.357847	+	0.933780i	$0.616489\pi$
$458$	1.01540	0.0474464
$459$	15.4530	0.721285
$460$	2.31435	0.107907
$461$	−0.636183	−0.0296300	−0.0148150	−	0.999890i	$-0.504716\pi$
$461$	−0.636183	−0.0296300	−0.0148150	+	0.999890i	$0.504716\pi$
$462$	0	0
$463$	4.26588	0.198252	0.0991260	−	0.995075i	$-0.468395\pi$
$463$	4.26588	0.198252	0.0991260	+	0.995075i	$0.468395\pi$
$464$	1.00000	0.0464238
$465$	4.76758	0.221091
$466$	9.28302	0.430027
$467$	−28.9386	−1.33912	−0.669559	−	0.742759i	$-0.733517\pi$
$467$	−28.9386	−1.33912	−0.669559	+	0.742759i	$0.733517\pi$
$468$	−4.60376	−0.212809
$469$	0	0
$470$	0.662583	0.0305627
$471$	11.5034	0.530048
$472$	8.89202	0.409288
$473$	8.77840	0.403631
$474$	−13.2350	−0.607902
$475$	−31.7305	−1.45590
$476$	0	0
$477$	13.0819	0.598978
$478$	−7.42704	−0.339705
$479$	−25.0280	−1.14356	−0.571778	−	0.820408i	$-0.693746\pi$
$479$	−25.0280	−1.14356	−0.571778	+	0.820408i	$0.693746\pi$
$480$	0.572499	0.0261309
$481$	1.59578	0.0727612
$482$	−15.7233	−0.716176
$483$	0	0
$484$	−4.14971	−0.188623
$485$	9.61011	0.436372
$486$	15.8059	0.716970
$487$	−27.1123	−1.22858	−0.614288	−	0.789082i	$-0.710557\pi$
$487$	−27.1123	−1.22858	−0.614288	+	0.789082i	$0.710557\pi$
$488$	1.48103	0.0670431
$489$	1.56429	0.0707397
$490$	0	0
$491$	4.79882	0.216568	0.108284	−	0.994120i	$-0.465464\pi$
$491$	4.79882	0.216568	0.108284	+	0.994120i	$0.465464\pi$
$492$	4.65432	0.209833
$493$	−3.59099	−0.161730
$494$	13.8129	0.621470
$495$	−4.38845	−0.197246
$496$	8.32767	0.373923
$497$	0	0
$498$	11.5437	0.517286
$499$	37.7156	1.68838	0.844192	−	0.536042i	$-0.180081\pi$
$499$	37.7156	1.68838	0.844192	+	0.536042i	$0.180081\pi$
$500$	−6.76146	−0.302382
$501$	−12.4293	−0.555300
$502$	8.44770	0.377039
$503$	9.49123	0.423193	0.211596	−	0.977357i	$-0.432134\pi$
$503$	9.49123	0.423193	0.211596	+	0.977357i	$0.432134\pi$
$504$	0	0
$505$	−3.10537	−0.138187
$506$	8.50416	0.378056
$507$	−7.37451	−0.327514
$508$	9.28047	0.411754
$509$	29.2451	1.29627	0.648134	−	0.761527i	$-0.275550\pi$
$509$	29.2451	1.29627	0.648134	+	0.761527i	$0.275550\pi$
$510$	−2.05584	−0.0910341
$511$	0	0
$512$	1.00000	0.0441942
$513$	−30.3930	−1.34188
$514$	−26.1241	−1.15228
$515$	6.53745	0.288074
$516$	2.69577	0.118675
$517$	2.43468	0.107077
$518$	0	0
$519$	−8.18143	−0.359125
$520$	1.39304	0.0610887
$521$	−7.17634	−0.314401	−0.157201	−	0.987567i	$-0.550247\pi$
$521$	−7.17634	−0.314401	−0.157201	+	0.987567i	$0.550247\pi$
$522$	−2.35398	−0.103031
$523$	−6.18687	−0.270533	−0.135266	−	0.990809i	$-0.543189\pi$
$523$	−6.18687	−0.270533	−0.135266	+	0.990809i	$0.543189\pi$
$524$	0.712284	0.0311163
$525$	0	0
$526$	−3.41075	−0.148716
$527$	−29.9046	−1.30266
$528$	2.10366	0.0915503
$529$	−12.4427	−0.540986
$530$	−3.95840	−0.171942
$531$	−20.9317	−0.908357
$532$	0	0
$533$	11.3252	0.490547
$534$	−3.18765	−0.137943
$535$	11.7894	0.509699
$536$	−6.82170	−0.294653
$537$	−16.3297	−0.704681
$538$	−3.22211	−0.138915
$539$	0	0
$540$	−3.06515	−0.131903
$541$	−12.7303	−0.547317	−0.273659	−	0.961827i	$-0.588234\pi$
$541$	−12.7303	−0.547317	−0.273659	+	0.961827i	$0.588234\pi$
$542$	−10.8198	−0.464752
$543$	12.7054	0.545242
$544$	−3.59099	−0.153962
$545$	−10.8094	−0.463024
$546$	0	0
$547$	−6.92270	−0.295993	−0.147997	−	0.988988i	$-0.547283\pi$
$547$	−6.92270	−0.295993	−0.147997	+	0.988988i	$0.547283\pi$
$548$	−2.58662	−0.110495
$549$	−3.48632	−0.148793
$550$	−11.7586	−0.501390
$551$	7.06276	0.300884
$552$	2.61155	0.111155
$553$	0	0
$554$	−27.1495	−1.15347
$555$	0.467130	0.0198286
$556$	−9.84174	−0.417383
$557$	−23.4698	−0.994447	−0.497224	−	0.867622i	$-0.665647\pi$
$557$	−23.4698	−0.994447	−0.497224	+	0.867622i	$0.665647\pi$
$558$	−19.6032	−0.829869
$559$	6.55949	0.277437
$560$	0	0
$561$	−7.55424	−0.318940
$562$	−22.1541	−0.934515
$563$	23.2630	0.980420	0.490210	−	0.871604i	$-0.336920\pi$
$563$	23.2630	0.980420	0.490210	+	0.871604i	$0.336920\pi$
$564$	0.747669	0.0314826
$565$	−6.73923	−0.283521
$566$	−14.5383	−0.611089
$567$	0	0
$568$	6.03069	0.253042
$569$	−35.4013	−1.48410	−0.742049	−	0.670345i	$-0.766146\pi$
$569$	−35.4013	−1.48410	−0.742049	+	0.670345i	$0.766146\pi$
$570$	4.04342	0.169360
$571$	13.7138	0.573904	0.286952	−	0.957945i	$-0.407358\pi$
$571$	13.7138	0.573904	0.286952	+	0.957945i	$0.407358\pi$
$572$	5.11875	0.214026
$573$	−16.5142	−0.689889
$574$	0	0
$575$	−14.5975	−0.608759
$576$	−2.35398	−0.0980826
$577$	−17.7644	−0.739541	−0.369771	−	0.929123i	$-0.620564\pi$
$577$	−17.7644	−0.739541	−0.369771	+	0.929123i	$0.620564\pi$
$578$	−4.10479	−0.170737
$579$	−8.65224	−0.359575
$580$	0.712284	0.0295760
$581$	0	0
$582$	10.8442	0.449506
$583$	−14.5452	−0.602402
$584$	−7.83070	−0.324037
$585$	−3.27918	−0.135578
$586$	9.06141	0.374323
$587$	−14.7467	−0.608661	−0.304330	−	0.952567i	$-0.598433\pi$
$587$	−14.7467	−0.608661	−0.304330	+	0.952567i	$0.598433\pi$
$588$	0	0
$589$	58.8163	2.42348
$590$	6.33364	0.260752
$591$	20.4499	0.841197
$592$	0.815948	0.0335353
$593$	39.6988	1.63023	0.815117	−	0.579296i	$-0.196672\pi$
$593$	39.6988	1.63023	0.815117	+	0.579296i	$0.196672\pi$
$594$	−11.2630	−0.462126
$595$	0	0
$596$	4.13604	0.169419
$597$	−20.3613	−0.833333
$598$	6.35457	0.259858
$599$	31.1739	1.27373	0.636865	−	0.770975i	$-0.280231\pi$
$599$	31.1739	1.27373	0.636865	+	0.770975i	$0.280231\pi$
$600$	−3.61098	−0.147418
$601$	−48.4991	−1.97832	−0.989160	−	0.146841i	$-0.953090\pi$
$601$	−48.4991	−1.97832	−0.989160	+	0.146841i	$0.953090\pi$
$602$	0	0
$603$	16.0582	0.653939
$604$	−14.4979	−0.589913
$605$	−2.95577	−0.120169
$606$	−3.50415	−0.142346
$607$	−39.3662	−1.59783	−0.798913	−	0.601447i	$-0.794591\pi$
$607$	−39.3662	−1.59783	−0.798913	+	0.601447i	$0.794591\pi$
$608$	7.06276	0.286433
$609$	0	0
$610$	1.05491	0.0427122
$611$	1.81927	0.0735998
$612$	8.45313	0.341697
$613$	1.23234	0.0497736	0.0248868	−	0.999690i	$-0.492077\pi$
$613$	1.23234	0.0497736	0.0248868	+	0.999690i	$0.492077\pi$
$614$	11.8381	0.477747
$615$	3.31520	0.133682
$616$	0	0
$617$	8.21864	0.330870	0.165435	−	0.986221i	$-0.447097\pi$
$617$	8.21864	0.330870	0.165435	+	0.986221i	$0.447097\pi$
$618$	7.37695	0.296745
$619$	−28.2731	−1.13639	−0.568196	−	0.822893i	$-0.692358\pi$
$619$	−28.2731	−1.13639	−0.568196	+	0.822893i	$0.692358\pi$
$620$	5.93166	0.238221
$621$	−13.9822	−0.561087
$622$	11.3041	0.453254
$623$	0	0
$624$	1.57192	0.0629273
$625$	17.6472	0.705887
$626$	11.8533	0.473752
$627$	14.8577	0.593358
$628$	14.3121	0.571116
$629$	−2.93006	−0.116829
$630$	0	0
$631$	17.9943	0.716340	0.358170	−	0.933656i	$-0.383401\pi$
$631$	17.9943	0.716340	0.358170	+	0.933656i	$0.383401\pi$
$632$	−16.4665	−0.655002
$633$	21.2202	0.843428
$634$	7.41663	0.294552
$635$	6.61032	0.262323
$636$	−4.46672	−0.177117
$637$	0	0
$638$	2.61731	0.103620
$639$	−14.1961	−0.561590
$640$	0.712284	0.0281555
$641$	5.57617	0.220246	0.110123	−	0.993918i	$-0.464876\pi$
$641$	5.57617	0.220246	0.110123	+	0.993918i	$0.464876\pi$
$642$	13.3033	0.525040
$643$	2.67709	0.105574	0.0527870	−	0.998606i	$-0.483190\pi$
$643$	2.67709	0.105574	0.0527870	+	0.998606i	$0.483190\pi$
$644$	0	0
$645$	1.92015	0.0756059
$646$	−25.3623	−0.997866
$647$	−5.45673	−0.214526	−0.107263	−	0.994231i	$-0.534209\pi$
$647$	−5.45673	−0.214526	−0.107263	+	0.994231i	$0.534209\pi$
$648$	3.60319	0.141547
$649$	23.2731	0.913551
$650$	−8.78643	−0.344632
$651$	0	0
$652$	1.94624	0.0762205
$653$	26.4149	1.03369	0.516847	−	0.856078i	$-0.327105\pi$
$653$	26.4149	1.03369	0.516847	+	0.856078i	$0.327105\pi$
$654$	−12.1975	−0.476959
$655$	0.507348	0.0198237
$656$	5.79075	0.226091
$657$	18.4333	0.719153
$658$	0	0
$659$	−8.36863	−0.325996	−0.162998	−	0.986626i	$-0.552116\pi$
$659$	−8.36863	−0.325996	−0.162998	+	0.986626i	$0.552116\pi$
$660$	1.49841	0.0583254
$661$	8.21307	0.319451	0.159726	−	0.987161i	$-0.448939\pi$
$661$	8.21307	0.319451	0.159726	+	0.987161i	$0.448939\pi$
$662$	29.4239	1.14359
$663$	−5.64476	−0.219224
$664$	14.3623	0.557365
$665$	0	0
$666$	−1.92073	−0.0744267
$667$	3.24920	0.125810
$668$	−15.4641	−0.598324
$669$	−7.34085	−0.283814
$670$	−4.85899	−0.187719
$671$	3.87631	0.149643
$672$	0	0
$673$	−42.1365	−1.62424	−0.812121	−	0.583490i	$-0.801687\pi$
$673$	−42.1365	−1.62424	−0.812121	+	0.583490i	$0.801687\pi$
$674$	25.7213	0.990749
$675$	19.3331	0.744132
$676$	−9.17511	−0.352889
$677$	46.2136	1.77613	0.888066	−	0.459717i	$-0.152049\pi$
$677$	46.2136	1.77613	0.888066	+	0.459717i	$0.152049\pi$
$678$	−7.60464	−0.292055
$679$	0	0
$680$	−2.55780	−0.0980873
$681$	3.64736	0.139767
$682$	21.7961	0.834614
$683$	49.5140	1.89460	0.947300	−	0.320348i	$-0.103800\pi$
$683$	49.5140	1.89460	0.947300	+	0.320348i	$0.103800\pi$
$684$	−16.6256	−0.635696
$685$	−1.84241	−0.0703947
$686$	0	0
$687$	0.816128	0.0311372
$688$	3.35398	0.127869
$689$	−10.8687	−0.414063
$690$	1.86017	0.0708153
$691$	−23.3055	−0.886584	−0.443292	−	0.896377i	$-0.646189\pi$
$691$	−23.3055	−0.886584	−0.443292	+	0.896377i	$0.646189\pi$
$692$	−10.1790	−0.386949
$693$	0	0
$694$	17.1022	0.649189
$695$	−7.01011	−0.265909
$696$	0.803752	0.0304661
$697$	−20.7945	−0.787648
$698$	2.58512	0.0978483
$699$	7.46124	0.282210
$700$	0	0
$701$	43.6611	1.64906	0.824528	−	0.565822i	$-0.191441\pi$
$701$	43.6611	1.64906	0.824528	+	0.565822i	$0.191441\pi$
$702$	−8.41605	−0.317643
$703$	5.76284	0.217350
$704$	2.61731	0.0986434
$705$	0.532553	0.0200571
$706$	7.84366	0.295200
$707$	0	0
$708$	7.14697	0.268600
$709$	−23.7611	−0.892368	−0.446184	−	0.894941i	$-0.647217\pi$
$709$	−23.7611	−0.892368	−0.446184	+	0.894941i	$0.647217\pi$
$710$	4.29556	0.161209
$711$	38.7618	1.45368
$712$	−3.96596	−0.148631
$713$	27.0583	1.01334
$714$	0	0
$715$	3.64600	0.136353
$716$	−20.3169	−0.759278
$717$	−5.96950	−0.222935
$718$	−3.86388	−0.144199
$719$	21.7328	0.810496	0.405248	−	0.914207i	$-0.367185\pi$
$719$	21.7328	0.810496	0.405248	+	0.914207i	$0.367185\pi$
$720$	−1.67670	−0.0624871
$721$	0	0
$722$	30.8825	1.14933
$723$	−12.6376	−0.469998
$724$	15.8077	0.587487
$725$	−4.49265	−0.166853
$726$	−3.33533	−0.123786
$727$	1.15990	0.0430182	0.0215091	−	0.999769i	$-0.493153\pi$
$727$	1.15990	0.0430182	0.0215091	+	0.999769i	$0.493153\pi$
$728$	0	0
$729$	1.89445	0.0701648
$730$	−5.57768	−0.206439
$731$	−12.0441	−0.445468
$732$	1.19038	0.0439978
$733$	−18.8946	−0.697887	−0.348943	−	0.937144i	$-0.613459\pi$
$733$	−18.8946	−0.697887	−0.348943	+	0.937144i	$0.613459\pi$
$734$	−4.01795	−0.148305
$735$	0	0
$736$	3.24920	0.119767
$737$	−17.8545	−0.657678
$738$	−13.6313	−0.501776
$739$	−25.7529	−0.947337	−0.473669	−	0.880703i	$-0.657071\pi$
$739$	−25.7529	−0.947337	−0.473669	+	0.880703i	$0.657071\pi$
$740$	0.581187	0.0213648
$741$	11.1021	0.407846
$742$	0	0
$743$	−32.5708	−1.19491	−0.597454	−	0.801903i	$-0.703821\pi$
$743$	−32.5708	−1.19491	−0.597454	+	0.801903i	$0.703821\pi$
$744$	6.69338	0.245391
$745$	2.94604	0.107934
$746$	21.5426	0.788732
$747$	−33.8086	−1.23699
$748$	−9.39872	−0.343651
$749$	0	0
$750$	−5.43454	−0.198441
$751$	10.1689	0.371070	0.185535	−	0.982638i	$-0.440598\pi$
$751$	10.1689	0.371070	0.185535	+	0.982638i	$0.440598\pi$
$752$	0.930224	0.0339218
$753$	6.78985	0.247436
$754$	1.95573	0.0712236
$755$	−10.3266	−0.375825
$756$	0	0
$757$	0.875300	0.0318133	0.0159067	−	0.999873i	$-0.494937\pi$
$757$	0.875300	0.0318133	0.0159067	+	0.999873i	$0.494937\pi$
$758$	−5.88638	−0.213803
$759$	6.83523	0.248103
$760$	5.03069	0.182482
$761$	−34.6165	−1.25485	−0.627424	−	0.778678i	$-0.715891\pi$
$761$	−34.6165	−1.25485	−0.627424	+	0.778678i	$0.715891\pi$
$762$	7.45919	0.270218
$763$	0	0
$764$	−20.5463	−0.743341
$765$	6.02103	0.217691
$766$	−10.9954	−0.397279
$767$	17.3904	0.627931
$768$	0.803752	0.0290029
$769$	−28.8545	−1.04052	−0.520260	−	0.854008i	$-0.674165\pi$
$769$	−28.8545	−1.04052	−0.520260	+	0.854008i	$0.674165\pi$
$770$	0	0
$771$	−20.9973	−0.756199
$772$	−10.7648	−0.387434
$773$	42.3750	1.52412	0.762062	−	0.647504i	$-0.224187\pi$
$773$	42.3750	1.52412	0.762062	+	0.647504i	$0.224187\pi$
$774$	−7.89522	−0.283788
$775$	−37.4133	−1.34393
$776$	13.4920	0.484333
$777$	0	0
$778$	23.1125	0.828624
$779$	40.8986	1.46535
$780$	1.11966	0.0400901
$781$	15.7842	0.564801
$782$	−11.6679	−0.417242
$783$	−4.30327	−0.153786
$784$	0	0
$785$	10.1943	0.363850
$786$	0.572499	0.0204204
$787$	−14.8097	−0.527908	−0.263954	−	0.964535i	$-0.585027\pi$
$787$	−14.8097	−0.527908	−0.263954	+	0.964535i	$0.585027\pi$
$788$	25.4431	0.906372
$789$	−2.74140	−0.0975964
$790$	−11.7288	−0.417292
$791$	0	0
$792$	−6.16110	−0.218925
$793$	2.89650	0.102858
$794$	−10.5634	−0.374882
$795$	−3.18157	−0.112839
$796$	−25.3328	−0.897899
$797$	−16.8780	−0.597848	−0.298924	−	0.954277i	$-0.596628\pi$
$797$	−16.8780	−0.597848	−0.298924	+	0.954277i	$0.596628\pi$
$798$	0	0
$799$	−3.34042	−0.118176
$800$	−4.49265	−0.158839
$801$	9.33581	0.329865
$802$	−26.0088	−0.918402
$803$	−20.4953	−0.723265
$804$	−5.48295	−0.193369
$805$	0	0
$806$	16.2867	0.573674
$807$	−2.58978	−0.0911644
$808$	−4.35974	−0.153375
$809$	4.54640	0.159843	0.0799215	−	0.996801i	$-0.474533\pi$
$809$	4.54640	0.159843	0.0799215	+	0.996801i	$0.474533\pi$
$810$	2.56649	0.0901773
$811$	−16.0486	−0.563542	−0.281771	−	0.959482i	$-0.590922\pi$
$811$	−16.0486	−0.563542	−0.281771	+	0.959482i	$0.590922\pi$
$812$	0	0
$813$	−8.69647	−0.304999
$814$	2.13559	0.0748523
$815$	1.38627	0.0485590
$816$	−2.88626	−0.101039
$817$	23.6884	0.828751
$818$	−5.31114	−0.185700
$819$	0	0
$820$	4.12465	0.144039
$821$	16.9317	0.590921	0.295461	−	0.955355i	$-0.404527\pi$
$821$	16.9317	0.590921	0.295461	+	0.955355i	$0.404527\pi$
$822$	−2.07900	−0.0725135
$823$	−46.2841	−1.61336	−0.806681	−	0.590987i	$-0.798738\pi$
$823$	−46.2841	−1.61336	−0.806681	+	0.590987i	$0.798738\pi$
$824$	9.17815	0.319736
$825$	−9.45103	−0.329043
$826$	0	0
$827$	−23.7632	−0.826329	−0.413164	−	0.910656i	$-0.635576\pi$
$827$	−23.7632	−0.826329	−0.413164	+	0.910656i	$0.635576\pi$
$828$	−7.64857	−0.265806
$829$	33.1727	1.15214	0.576068	−	0.817402i	$-0.304586\pi$
$829$	33.1727	1.15214	0.576068	+	0.817402i	$0.304586\pi$
$830$	10.2300	0.355089
$831$	−21.8215	−0.756979
$832$	1.95573	0.0678028
$833$	0	0
$834$	−7.91031	−0.273912
$835$	−11.0148	−0.381184
$836$	18.4854	0.639331
$837$	−35.8362	−1.23868
$838$	−40.6199	−1.40319
$839$	49.0237	1.69249	0.846243	−	0.532796i	$-0.178859\pi$
$839$	49.0237	1.69249	0.846243	+	0.532796i	$0.178859\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−23.6874	−0.816323
$843$	−17.8064	−0.613285
$844$	26.4015	0.908776
$845$	−6.53528	−0.224820
$846$	−2.18973	−0.0752845
$847$	0	0
$848$	−5.55733	−0.190840
$849$	−11.6852	−0.401034
$850$	16.1331	0.553360
$851$	2.65118	0.0908813
$852$	4.84718	0.166061
$853$	37.2710	1.27613	0.638067	−	0.769981i	$-0.279734\pi$
$853$	37.2710	1.27613	0.638067	+	0.769981i	$0.279734\pi$
$854$	0	0
$855$	−11.8422	−0.404993
$856$	16.5515	0.565719
$857$	26.9065	0.919109	0.459554	−	0.888150i	$-0.348009\pi$
$857$	26.9065	0.919109	0.459554	+	0.888150i	$0.348009\pi$
$858$	4.11421	0.140457
$859$	6.14826	0.209776	0.104888	−	0.994484i	$-0.466552\pi$
$859$	6.14826	0.209776	0.104888	+	0.994484i	$0.466552\pi$
$860$	2.38899	0.0814638
$861$	0	0
$862$	23.0287	0.784359
$863$	−39.3606	−1.33985	−0.669925	−	0.742429i	$-0.733674\pi$
$863$	−39.3606	−1.33985	−0.669925	+	0.742429i	$0.733674\pi$
$864$	−4.30327	−0.146400
$865$	−7.25037	−0.246520
$866$	−3.59018	−0.121999
$867$	−3.29924	−0.112048
$868$	0	0
$869$	−43.0979	−1.46199
$870$	0.572499	0.0194095
$871$	−13.3414	−0.452057
$872$	−15.1757	−0.513914
$873$	−31.7599	−1.07491
$874$	22.9483	0.776239
$875$	0	0
$876$	−6.29394	−0.212652
$877$	−31.5677	−1.06597	−0.532983	−	0.846126i	$-0.678929\pi$
$877$	−31.5677	−1.06597	−0.532983	+	0.846126i	$0.678929\pi$
$878$	−21.6037	−0.729091
$879$	7.28312	0.245654
$880$	1.86426	0.0628443
$881$	19.2740	0.649357	0.324679	−	0.945824i	$-0.394744\pi$
$881$	19.2740	0.649357	0.324679	+	0.945824i	$0.394744\pi$
$882$	0	0
$883$	−44.5134	−1.49800	−0.748998	−	0.662573i	$-0.769465\pi$
$883$	−44.5134	−1.49800	−0.748998	+	0.662573i	$0.769465\pi$
$884$	−7.02302	−0.236210
$885$	5.09067	0.171121
$886$	−19.4926	−0.654866
$887$	51.1613	1.71783	0.858914	−	0.512120i	$-0.171140\pi$
$887$	51.1613	1.71783	0.858914	+	0.512120i	$0.171140\pi$
$888$	0.655820	0.0220079
$889$	0	0
$890$	−2.82489	−0.0946905
$891$	9.43064	0.315938
$892$	−9.13324	−0.305803
$893$	6.56995	0.219855
$894$	3.32435	0.111183
$895$	−14.4714	−0.483726
$896$	0	0
$897$	5.10750	0.170534
$898$	−27.1804	−0.907021
$899$	8.32767	0.277743
$900$	10.5756	0.352521
$901$	19.9563	0.664842
$902$	15.1562	0.504645
$903$	0	0
$904$	−9.46144	−0.314683
$905$	11.2595	0.374280
$906$	−11.6527	−0.387136
$907$	35.8581	1.19065	0.595324	−	0.803486i	$-0.297024\pi$
$907$	35.8581	1.19065	0.595324	+	0.803486i	$0.297024\pi$
$908$	4.53792	0.150596
$909$	10.2627	0.340394
$910$	0	0
$911$	−11.9973	−0.397490	−0.198745	−	0.980051i	$-0.563686\pi$
$911$	−11.9973	−0.397490	−0.198745	+	0.980051i	$0.563686\pi$
$912$	5.67670	0.187974
$913$	37.5905	1.24406
$914$	−15.2998	−0.506073
$915$	0.847889	0.0280304
$916$	1.01540	0.0335497
$917$	0	0
$918$	15.4530	0.510025
$919$	26.5885	0.877073	0.438537	−	0.898713i	$-0.355497\pi$
$919$	26.5885	0.877073	0.438537	+	0.898713i	$0.355497\pi$
$920$	2.31435	0.0763020
$921$	9.51490	0.313527
$922$	−0.636183	−0.0209516
$923$	11.7944	0.388218
$924$	0	0
$925$	−3.66577	−0.120530
$926$	4.26588	0.140185
$927$	−21.6052	−0.709608
$928$	1.00000	0.0328266
$929$	44.9197	1.47377	0.736883	−	0.676020i	$-0.236297\pi$
$929$	44.9197	1.47377	0.736883	+	0.676020i	$0.236297\pi$
$930$	4.76758	0.156335
$931$	0	0
$932$	9.28302	0.304075
$933$	9.08572	0.297453
$934$	−28.9386	−0.946899
$935$	−6.69455	−0.218935
$936$	−4.60376	−0.150479
$937$	1.43861	0.0469972	0.0234986	−	0.999724i	$-0.492519\pi$
$937$	1.43861	0.0469972	0.0234986	+	0.999724i	$0.492519\pi$
$938$	0	0
$939$	9.52709	0.310905
$940$	0.662583	0.0216111
$941$	−52.4734	−1.71058	−0.855292	−	0.518146i	$-0.826623\pi$
$941$	−52.4734	−1.71058	−0.855292	+	0.518146i	$0.826623\pi$
$942$	11.5034	0.374801
$943$	18.8153	0.612711
$944$	8.89202	0.289411
$945$	0	0
$946$	8.77840	0.285410
$947$	16.6447	0.540880	0.270440	−	0.962737i	$-0.412831\pi$
$947$	16.6447	0.540880	0.270440	+	0.962737i	$0.412831\pi$
$948$	−13.2350	−0.429852
$949$	−15.3147	−0.497138
$950$	−31.7305	−1.02947
$951$	5.96113	0.193303
$952$	0	0
$953$	−27.1846	−0.880595	−0.440297	−	0.897852i	$-0.645127\pi$
$953$	−27.1846	−0.880595	−0.440297	+	0.897852i	$0.645127\pi$
$954$	13.0819	0.423541
$955$	−14.6348	−0.473572
$956$	−7.42704	−0.240208
$957$	2.10366	0.0680018
$958$	−25.0280	−0.808617
$959$	0	0
$960$	0.572499	0.0184773
$961$	38.3500	1.23710
$962$	1.59578	0.0514499
$963$	−38.9620	−1.25553
$964$	−15.7233	−0.506413
$965$	−7.66760	−0.246829
$966$	0	0
$967$	22.3331	0.718185	0.359092	−	0.933302i	$-0.383086\pi$
$967$	22.3331	0.718185	0.359092	+	0.933302i	$0.383086\pi$
$968$	−4.14971	−0.133377
$969$	−20.3850	−0.654860
$970$	9.61011	0.308562
$971$	31.3365	1.00564	0.502818	−	0.864392i	$-0.332297\pi$
$971$	31.3365	1.00564	0.502818	+	0.864392i	$0.332297\pi$
$972$	15.8059	0.506974
$973$	0	0
$974$	−27.1123	−0.868735
$975$	−7.06211	−0.226168
$976$	1.48103	0.0474067
$977$	−14.3324	−0.458535	−0.229267	−	0.973364i	$-0.573633\pi$
$977$	−14.3324	−0.458535	−0.229267	+	0.973364i	$0.573633\pi$
$978$	1.56429	0.0500205
$979$	−10.3801	−0.331751
$980$	0	0
$981$	35.7233	1.14056
$982$	4.79882	0.153136
$983$	37.6298	1.20020	0.600102	−	0.799924i	$-0.295127\pi$
$983$	37.6298	1.20020	0.600102	+	0.799924i	$0.295127\pi$
$984$	4.65432	0.148374
$985$	18.1227	0.577437
$986$	−3.59099	−0.114360
$987$	0	0
$988$	13.8129	0.439446
$989$	10.8978	0.346529
$990$	−4.38845	−0.139474
$991$	7.53280	0.239287	0.119644	−	0.992817i	$-0.461825\pi$
$991$	7.53280	0.239287	0.119644	+	0.992817i	$0.461825\pi$
$992$	8.32767	0.264404
$993$	23.6495	0.750494
$994$	0	0
$995$	−18.0442	−0.572039
$996$	11.5437	0.365777
$997$	−40.4803	−1.28202	−0.641012	−	0.767531i	$-0.721485\pi$
$997$	−40.4803	−1.28202	−0.641012	+	0.767531i	$0.721485\pi$
$998$	37.7156	1.19387
$999$	−3.51125	−0.111091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.y.1.3		5
7.3	odd	6		406.2.e.b.233.3	✓	10
7.5	odd	6		406.2.e.b.291.3	yes	10
7.6	odd	2		2842.2.a.w.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.b.233.3	✓	10	7.3	odd	6
406.2.e.b.291.3	yes	10	7.5	odd	6
2842.2.a.w.1.3		5	7.6	odd	2
2842.2.a.y.1.3		5	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.803752 q^{3} +1.00000 q^{4} +0.712284 q^{5} +0.803752 q^{6} +1.00000 q^{8} -2.35398 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.803752 q^{3} +1.00000 q^{4} +0.712284 q^{5} +0.803752 q^{6} +1.00000 q^{8} -2.35398 q^{9} +0.712284 q^{10} +2.61731 q^{11} +0.803752 q^{12} +1.95573 q^{13} +0.572499 q^{15} +1.00000 q^{16} -3.59099 q^{17} -2.35398 q^{18} +7.06276 q^{19} +0.712284 q^{20} +2.61731 q^{22} +3.24920 q^{23} +0.803752 q^{24} -4.49265 q^{25} +1.95573 q^{26} -4.30327 q^{27} +1.00000 q^{29} +0.572499 q^{30} +8.32767 q^{31} +1.00000 q^{32} +2.10366 q^{33} -3.59099 q^{34} -2.35398 q^{36} +0.815948 q^{37} +7.06276 q^{38} +1.57192 q^{39} +0.712284 q^{40} +5.79075 q^{41} +3.35398 q^{43} +2.61731 q^{44} -1.67670 q^{45} +3.24920 q^{46} +0.930224 q^{47} +0.803752 q^{48} -4.49265 q^{50} -2.88626 q^{51} +1.95573 q^{52} -5.55733 q^{53} -4.30327 q^{54} +1.86426 q^{55} +5.67670 q^{57} +1.00000 q^{58} +8.89202 q^{59} +0.572499 q^{60} +1.48103 q^{61} +8.32767 q^{62} +1.00000 q^{64} +1.39304 q^{65} +2.10366 q^{66} -6.82170 q^{67} -3.59099 q^{68} +2.61155 q^{69} +6.03069 q^{71} -2.35398 q^{72} -7.83070 q^{73} +0.815948 q^{74} -3.61098 q^{75} +7.06276 q^{76} +1.57192 q^{78} -16.4665 q^{79} +0.712284 q^{80} +3.60319 q^{81} +5.79075 q^{82} +14.3623 q^{83} -2.55780 q^{85} +3.35398 q^{86} +0.803752 q^{87} +2.61731 q^{88} -3.96596 q^{89} -1.67670 q^{90} +3.24920 q^{92} +6.69338 q^{93} +0.930224 q^{94} +5.03069 q^{95} +0.803752 q^{96} +13.4920 q^{97} -6.16110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9} + 7 q^{10} + 3 q^{12} + 8 q^{13} + 4 q^{15} + 5 q^{16} + 16 q^{17} + 4 q^{18} + 2 q^{19} + 7 q^{20} - 5 q^{23} + 3 q^{24} + 4 q^{25} + 8 q^{26} + 9 q^{27} + 5 q^{29} + 4 q^{30} + 5 q^{31} + 5 q^{32} + 3 q^{33} + 16 q^{34} + 4 q^{36} + 2 q^{38} - 20 q^{39} + 7 q^{40} + 17 q^{41} + q^{43} + 14 q^{45} - 5 q^{46} - 4 q^{47} + 3 q^{48} + 4 q^{50} - 3 q^{51} + 8 q^{52} + 5 q^{53} + 9 q^{54} + 12 q^{55} + 6 q^{57} + 5 q^{58} + 17 q^{59} + 4 q^{60} + 13 q^{61} + 5 q^{62} + 5 q^{64} - 7 q^{65} + 3 q^{66} - 14 q^{67} + 16 q^{68} + 16 q^{69} - 8 q^{71} + 4 q^{72} + 6 q^{73} + 8 q^{75} + 2 q^{76} - 20 q^{78} + 11 q^{79} + 7 q^{80} - 19 q^{81} + 17 q^{82} + 2 q^{83} + 39 q^{85} + q^{86} + 3 q^{87} + 9 q^{89} + 14 q^{90} - 5 q^{92} - 3 q^{93} - 4 q^{94} - 13 q^{95} + 3 q^{96} + 12 q^{97} + 10 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 4 * q^9 + 7 * q^10 + 3 * q^12 + 8 * q^13 + 4 * q^15 + 5 * q^16 + 16 * q^17 + 4 * q^18 + 2 * q^19 + 7 * q^20 - 5 * q^23 + 3 * q^24 + 4 * q^25 + 8 * q^26 + 9 * q^27 + 5 * q^29 + 4 * q^30 + 5 * q^31 + 5 * q^32 + 3 * q^33 + 16 * q^34 + 4 * q^36 + 2 * q^38 - 20 * q^39 + 7 * q^40 + 17 * q^41 + q^43 + 14 * q^45 - 5 * q^46 - 4 * q^47 + 3 * q^48 + 4 * q^50 - 3 * q^51 + 8 * q^52 + 5 * q^53 + 9 * q^54 + 12 * q^55 + 6 * q^57 + 5 * q^58 + 17 * q^59 + 4 * q^60 + 13 * q^61 + 5 * q^62 + 5 * q^64 - 7 * q^65 + 3 * q^66 - 14 * q^67 + 16 * q^68 + 16 * q^69 - 8 * q^71 + 4 * q^72 + 6 * q^73 + 8 * q^75 + 2 * q^76 - 20 * q^78 + 11 * q^79 + 7 * q^80 - 19 * q^81 + 17 * q^82 + 2 * q^83 + 39 * q^85 + q^86 + 3 * q^87 + 9 * q^89 + 14 * q^90 - 5 * q^92 - 3 * q^93 - 4 * q^94 - 13 * q^95 + 3 * q^96 + 12 * q^97 + 10 * q^99

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