LMFDB - Embedded newform 2842.2.a.y.1.1

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			1.1
Root			$2.94688$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.94688 q^{3} +1.00000 q^{4} +3.27192 q^{5} -1.94688 q^{6} +1.00000 q^{8} +0.790361 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.94688 q^{3} +1.00000 q^{4} +3.27192 q^{5} -1.94688 q^{6} +1.00000 q^{8} +0.790361 q^{9} +3.27192 q^{10} +3.28288 q^{11} -1.94688 q^{12} +5.52251 q^{13} -6.37005 q^{15} +1.00000 q^{16} +7.57383 q^{17} +0.790361 q^{18} -0.726289 q^{19} +3.27192 q^{20} +3.28288 q^{22} -7.95605 q^{23} -1.94688 q^{24} +5.70546 q^{25} +5.52251 q^{26} +4.30191 q^{27} +1.00000 q^{29} -6.37005 q^{30} -6.64707 q^{31} +1.00000 q^{32} -6.39138 q^{33} +7.57383 q^{34} +0.790361 q^{36} -5.11946 q^{37} -0.726289 q^{38} -10.7517 q^{39} +3.27192 q^{40} +4.58090 q^{41} +0.209639 q^{43} +3.28288 q^{44} +2.58600 q^{45} -7.95605 q^{46} -5.68941 q^{47} -1.94688 q^{48} +5.70546 q^{50} -14.7454 q^{51} +5.52251 q^{52} -5.77012 q^{53} +4.30191 q^{54} +10.7413 q^{55} +1.41400 q^{57} +1.00000 q^{58} +8.53874 q^{59} -6.37005 q^{60} -0.151247 q^{61} -6.64707 q^{62} +1.00000 q^{64} +18.0692 q^{65} -6.39138 q^{66} +11.3261 q^{67} +7.57383 q^{68} +15.4895 q^{69} -1.37636 q^{71} +0.790361 q^{72} +5.79425 q^{73} -5.11946 q^{74} -11.1079 q^{75} -0.726289 q^{76} -10.7517 q^{78} +0.715154 q^{79} +3.27192 q^{80} -10.7464 q^{81} +4.58090 q^{82} -5.49921 q^{83} +24.7810 q^{85} +0.209639 q^{86} -1.94688 q^{87} +3.28288 q^{88} -9.01553 q^{89} +2.58600 q^{90} -7.95605 q^{92} +12.9411 q^{93} -5.68941 q^{94} -2.37636 q^{95} -1.94688 q^{96} -17.9462 q^{97} +2.59466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.94688	−1.12403	−0.562017	−	0.827125i	$-0.689975\pi$
$3$	−1.94688	−1.12403	−0.562017	+	0.827125i	$0.689975\pi$
$4$	1.00000	0.500000
$5$	3.27192	1.46325	0.731624	−	0.681709i	$-0.238763\pi$
$5$	3.27192	1.46325	0.731624	+	0.681709i	$0.238763\pi$
$6$	−1.94688	−0.794812
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	0.790361	0.263454
$10$	3.27192	1.03467
$11$	3.28288	0.989825	0.494912	−	0.868943i	$-0.335200\pi$
$11$	3.28288	0.989825	0.494912	+	0.868943i	$0.335200\pi$
$12$	−1.94688	−0.562017
$13$	5.52251	1.53167	0.765834	−	0.643038i	$-0.222326\pi$
$13$	5.52251	1.53167	0.765834	+	0.643038i	$0.222326\pi$
$14$	0	0
$15$	−6.37005	−1.64474
$16$	1.00000	0.250000
$17$	7.57383	1.83692	0.918462	−	0.395509i	$-0.129432\pi$
$17$	7.57383	1.83692	0.918462	+	0.395509i	$0.129432\pi$
$18$	0.790361	0.186290
$19$	−0.726289	−0.166622	−0.0833111	−	0.996524i	$-0.526550\pi$
$19$	−0.726289	−0.166622	−0.0833111	+	0.996524i	$0.526550\pi$
$20$	3.27192	0.731624
$21$	0	0
$22$	3.28288	0.699912
$23$	−7.95605	−1.65895	−0.829476	−	0.558543i	$-0.811361\pi$
$23$	−7.95605	−1.65895	−0.829476	+	0.558543i	$0.811361\pi$
$24$	−1.94688	−0.397406
$25$	5.70546	1.14109
$26$	5.52251	1.08305
$27$	4.30191	0.827903
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−6.37005	−1.16301
$31$	−6.64707	−1.19385	−0.596925	−	0.802297i	$-0.703611\pi$
$31$	−6.64707	−1.19385	−0.596925	+	0.802297i	$0.703611\pi$
$32$	1.00000	0.176777
$33$	−6.39138	−1.11260
$34$	7.57383	1.29890
$35$	0	0
$36$	0.790361	0.131727
$37$	−5.11946	−0.841635	−0.420817	−	0.907145i	$-0.638257\pi$
$37$	−5.11946	−0.841635	−0.420817	+	0.907145i	$0.638257\pi$
$38$	−0.726289	−0.117820
$39$	−10.7517	−1.72165
$40$	3.27192	0.517336
$41$	4.58090	0.715416	0.357708	−	0.933833i	$-0.383558\pi$
$41$	4.58090	0.715416	0.357708	+	0.933833i	$0.383558\pi$
$42$	0	0
$43$	0.209639	0.0319696	0.0159848	−	0.999872i	$-0.494912\pi$
$43$	0.209639	0.0319696	0.0159848	+	0.999872i	$0.494912\pi$
$44$	3.28288	0.494912
$45$	2.58600	0.385498
$46$	−7.95605	−1.17306
$47$	−5.68941	−0.829885	−0.414943	−	0.909848i	$-0.636198\pi$
$47$	−5.68941	−0.829885	−0.414943	+	0.909848i	$0.636198\pi$
$48$	−1.94688	−0.281009
$49$	0	0
$50$	5.70546	0.806874
$51$	−14.7454	−2.06477
$52$	5.52251	0.765834
$53$	−5.77012	−0.792587	−0.396293	−	0.918124i	$-0.629704\pi$
$53$	−5.77012	−0.792587	−0.396293	+	0.918124i	$0.629704\pi$
$54$	4.30191	0.585416
$55$	10.7413	1.44836
$56$	0	0
$57$	1.41400	0.187289
$58$	1.00000	0.131306
$59$	8.53874	1.11165	0.555825	−	0.831299i	$-0.312403\pi$
$59$	8.53874	1.11165	0.555825	+	0.831299i	$0.312403\pi$
$60$	−6.37005	−0.822370
$61$	−0.151247	−0.0193652	−0.00968262	−	0.999953i	$-0.503082\pi$
$61$	−0.151247	−0.0193652	−0.00968262	+	0.999953i	$0.503082\pi$
$62$	−6.64707	−0.844179
$63$	0	0
$64$	1.00000	0.125000
$65$	18.0692	2.24121
$66$	−6.39138	−0.786725
$67$	11.3261	1.38370	0.691852	−	0.722039i	$-0.256795\pi$
$67$	11.3261	1.38370	0.691852	+	0.722039i	$0.256795\pi$
$68$	7.57383	0.918462
$69$	15.4895	1.86472
$70$	0	0
$71$	−1.37636	−0.163344	−0.0816719	−	0.996659i	$-0.526026\pi$
$71$	−1.37636	−0.163344	−0.0816719	+	0.996659i	$0.526026\pi$
$72$	0.790361	0.0931450
$73$	5.79425	0.678166	0.339083	−	0.940756i	$-0.389883\pi$
$73$	5.79425	0.678166	0.339083	+	0.940756i	$0.389883\pi$
$74$	−5.11946	−0.595126
$75$	−11.1079	−1.28263
$76$	−0.726289	−0.0833111
$77$	0	0
$78$	−10.7517	−1.21739
$79$	0.715154	0.0804611	0.0402306	−	0.999190i	$-0.487191\pi$
$79$	0.715154	0.0804611	0.0402306	+	0.999190i	$0.487191\pi$
$80$	3.27192	0.365812
$81$	−10.7464	−1.19405
$82$	4.58090	0.505876
$83$	−5.49921	−0.603617	−0.301808	−	0.953369i	$-0.597590\pi$
$83$	−5.49921	−0.603617	−0.301808	+	0.953369i	$0.597590\pi$
$84$	0	0
$85$	24.7810	2.68787
$86$	0.209639	0.0226059
$87$	−1.94688	−0.208728
$88$	3.28288	0.349956
$89$	−9.01553	−0.955644	−0.477822	−	0.878457i	$-0.658574\pi$
$89$	−9.01553	−0.955644	−0.477822	+	0.878457i	$0.658574\pi$
$90$	2.58600	0.272588
$91$	0	0
$92$	−7.95605	−0.829476
$93$	12.9411	1.34193
$94$	−5.68941	−0.586818
$95$	−2.37636	−0.243809
$96$	−1.94688	−0.198703
$97$	−17.9462	−1.82216	−0.911078	−	0.412233i	$-0.864749\pi$
$97$	−17.9462	−1.82216	−0.911078	+	0.412233i	$0.864749\pi$
$98$	0	0
$99$	2.59466	0.260773
$100$	5.70546	0.570546
$101$	10.9970	1.09424	0.547121	−	0.837053i	$-0.315724\pi$
$101$	10.9970	1.09424	0.547121	+	0.837053i	$0.315724\pi$
$102$	−14.7454	−1.46001
$103$	17.2608	1.70076	0.850381	−	0.526168i	$-0.176372\pi$
$103$	17.2608	1.70076	0.850381	+	0.526168i	$0.176372\pi$
$104$	5.52251	0.541527
$105$	0	0
$106$	−5.77012	−0.560443
$107$	−14.9680	−1.44701	−0.723507	−	0.690318i	$-0.757471\pi$
$107$	−14.9680	−1.44701	−0.723507	+	0.690318i	$0.757471\pi$
$108$	4.30191	0.413952
$109$	6.11647	0.585851	0.292926	−	0.956135i	$-0.405371\pi$
$109$	6.11647	0.585851	0.292926	+	0.956135i	$0.405371\pi$
$110$	10.7413	1.02414
$111$	9.96701	0.946027
$112$	0	0
$113$	9.72278	0.914643	0.457321	−	0.889302i	$-0.348809\pi$
$113$	9.72278	0.914643	0.457321	+	0.889302i	$0.348809\pi$
$114$	1.41400	0.132433
$115$	−26.0316	−2.42746
$116$	1.00000	0.0928477
$117$	4.36478	0.403524
$118$	8.53874	0.786055
$119$	0	0
$120$	−6.37005	−0.581504
$121$	−0.222715	−0.0202468
$122$	−0.151247	−0.0136933
$123$	−8.91849	−0.804153
$124$	−6.64707	−0.596925
$125$	2.30822	0.206453
$126$	0	0
$127$	−3.95078	−0.350575	−0.175287	−	0.984517i	$-0.556085\pi$
$127$	−3.95078	−0.350575	−0.175287	+	0.984517i	$0.556085\pi$
$128$	1.00000	0.0883883
$129$	−0.408143	−0.0359350
$130$	18.0692	1.58477
$131$	3.27192	0.285869	0.142935	−	0.989732i	$-0.454346\pi$
$131$	3.27192	0.285869	0.142935	+	0.989732i	$0.454346\pi$
$132$	−6.39138	−0.556299
$133$	0	0
$134$	11.3261	0.978426
$135$	14.0755	1.21143
$136$	7.57383	0.649451
$137$	−10.6592	−0.910680	−0.455340	−	0.890318i	$-0.650482\pi$
$137$	−10.6592	−0.910680	−0.455340	+	0.890318i	$0.650482\pi$
$138$	15.4895	1.31856
$139$	0.656434	0.0556780	0.0278390	−	0.999612i	$-0.491137\pi$
$139$	0.656434	0.0556780	0.0278390	+	0.999612i	$0.491137\pi$
$140$	0	0
$141$	11.0766	0.932820
$142$	−1.37636	−0.115502
$143$	18.1297	1.51608
$144$	0.790361	0.0658634
$145$	3.27192	0.271718
$146$	5.79425	0.479536
$147$	0	0
$148$	−5.11946	−0.420817
$149$	10.1710	0.833238	0.416619	−	0.909081i	$-0.363215\pi$
$149$	10.1710	0.833238	0.416619	+	0.909081i	$0.363215\pi$
$150$	−11.1079	−0.906955
$151$	−19.6390	−1.59820	−0.799099	−	0.601199i	$-0.794690\pi$
$151$	−19.6390	−1.59820	−0.799099	+	0.601199i	$0.794690\pi$
$152$	−0.726289	−0.0589098
$153$	5.98606	0.483945
$154$	0	0
$155$	−21.7487	−1.74690
$156$	−10.7517	−0.860824
$157$	0.164679	0.0131428	0.00657142	−	0.999978i	$-0.497908\pi$
$157$	0.164679	0.0131428	0.00657142	+	0.999978i	$0.497908\pi$
$158$	0.715154	0.0568946
$159$	11.2338	0.890895
$160$	3.27192	0.258668
$161$	0	0
$162$	−10.7464	−0.844318
$163$	14.2581	1.11678	0.558392	−	0.829577i	$-0.311419\pi$
$163$	14.2581	1.11678	0.558392	+	0.829577i	$0.311419\pi$
$164$	4.58090	0.357708
$165$	−20.9121	−1.62801
$166$	−5.49921	−0.426821
$167$	−7.63407	−0.590742	−0.295371	−	0.955383i	$-0.595443\pi$
$167$	−7.63407	−0.590742	−0.295371	+	0.955383i	$0.595443\pi$
$168$	0	0
$169$	17.4981	1.34601
$170$	24.7810	1.90061
$171$	−0.574031	−0.0438972
$172$	0.209639	0.0159848
$173$	13.9739	1.06241	0.531207	−	0.847242i	$-0.321739\pi$
$173$	13.9739	1.06241	0.531207	+	0.847242i	$0.321739\pi$
$174$	−1.94688	−0.147593
$175$	0	0
$176$	3.28288	0.247456
$177$	−16.6239	−1.24953
$178$	−9.01553	−0.675743
$179$	12.5338	0.936818	0.468409	−	0.883512i	$-0.344827\pi$
$179$	12.5338	0.936818	0.468409	+	0.883512i	$0.344827\pi$
$180$	2.58600	0.192749
$181$	21.3711	1.58850	0.794252	−	0.607588i	$-0.207863\pi$
$181$	21.3711	1.58850	0.794252	+	0.607588i	$0.207863\pi$
$182$	0	0
$183$	0.294461	0.0217672
$184$	−7.95605	−0.586528
$185$	−16.7505	−1.23152
$186$	12.9411	0.948886
$187$	24.8640	1.81823
$188$	−5.68941	−0.414943
$189$	0	0
$190$	−2.37636	−0.172399
$191$	−6.62026	−0.479025	−0.239512	−	0.970893i	$-0.576988\pi$
$191$	−6.62026	−0.479025	−0.239512	+	0.970893i	$0.576988\pi$
$192$	−1.94688	−0.140504
$193$	−4.05261	−0.291713	−0.145857	−	0.989306i	$-0.546594\pi$
$193$	−4.05261	−0.291713	−0.145857	+	0.989306i	$0.546594\pi$
$194$	−17.9462	−1.28846
$195$	−35.1787	−2.51920
$196$	0	0
$197$	21.1218	1.50487	0.752434	−	0.658668i	$-0.228880\pi$
$197$	21.1218	1.50487	0.752434	+	0.658668i	$0.228880\pi$
$198$	2.59466	0.184394
$199$	7.23535	0.512900	0.256450	−	0.966557i	$-0.417447\pi$
$199$	7.23535	0.512900	0.256450	+	0.966557i	$0.417447\pi$
$200$	5.70546	0.403437
$201$	−22.0506	−1.55533
$202$	10.9970	0.773746
$203$	0	0
$204$	−14.7454	−1.03238
$205$	14.9883	1.04683
$206$	17.2608	1.20262
$207$	−6.28815	−0.437057
$208$	5.52251	0.382917
$209$	−2.38432	−0.164927
$210$	0	0
$211$	6.76446	0.465684	0.232842	−	0.972515i	$-0.425197\pi$
$211$	6.76446	0.465684	0.232842	+	0.972515i	$0.425197\pi$
$212$	−5.77012	−0.396293
$213$	2.67961	0.183604
$214$	−14.9680	−1.02319
$215$	0.685922	0.0467795
$216$	4.30191	0.292708
$217$	0	0
$218$	6.11647	0.414259
$219$	−11.2807	−0.762282
$220$	10.7413	0.724179
$221$	41.8266	2.81356
$222$	9.96701	0.668942
$223$	23.3248	1.56195	0.780973	−	0.624565i	$-0.214724\pi$
$223$	23.3248	1.56195	0.780973	+	0.624565i	$0.214724\pi$
$224$	0	0
$225$	4.50938	0.300625
$226$	9.72278	0.646750
$227$	26.9250	1.78708	0.893538	−	0.448988i	$-0.148215\pi$
$227$	26.9250	1.78708	0.893538	+	0.448988i	$0.148215\pi$
$228$	1.41400	0.0936445
$229$	−9.87701	−0.652691	−0.326346	−	0.945250i	$-0.605817\pi$
$229$	−9.87701	−0.652691	−0.326346	+	0.945250i	$0.605817\pi$
$230$	−26.0316	−1.71647
$231$	0	0
$232$	1.00000	0.0656532
$233$	−8.45298	−0.553773	−0.276887	−	0.960903i	$-0.589303\pi$
$233$	−8.45298	−0.553773	−0.276887	+	0.960903i	$0.589303\pi$
$234$	4.36478	0.285334
$235$	−18.6153	−1.21433
$236$	8.53874	0.555825
$237$	−1.39232	−0.0904411
$238$	0	0
$239$	10.6075	0.686141	0.343071	−	0.939310i	$-0.388533\pi$
$239$	10.6075	0.686141	0.343071	+	0.939310i	$0.388533\pi$
$240$	−6.37005	−0.411185
$241$	−27.2035	−1.75233	−0.876167	−	0.482008i	$-0.839908\pi$
$241$	−27.2035	−1.75233	−0.876167	+	0.482008i	$0.839908\pi$
$242$	−0.222715	−0.0143167
$243$	8.01629	0.514245
$244$	−0.151247	−0.00968262
$245$	0	0
$246$	−8.91849	−0.568622
$247$	−4.01094	−0.255210
$248$	−6.64707	−0.422089
$249$	10.7063	0.678486
$250$	2.30822	0.145985
$251$	−19.4237	−1.22601	−0.613005	−	0.790079i	$-0.710040\pi$
$251$	−19.4237	−1.22601	−0.613005	+	0.790079i	$0.710040\pi$
$252$	0	0
$253$	−26.1187	−1.64207
$254$	−3.95078	−0.247894
$255$	−48.2457	−3.02126
$256$	1.00000	0.0625000
$257$	−26.3885	−1.64607	−0.823034	−	0.567993i	$-0.807720\pi$
$257$	−26.3885	−1.64607	−0.823034	+	0.567993i	$0.807720\pi$
$258$	−0.408143	−0.0254099
$259$	0	0
$260$	18.0692	1.12060
$261$	0.790361	0.0489221
$262$	3.27192	0.202140
$263$	−8.42683	−0.519621	−0.259810	−	0.965660i	$-0.583660\pi$
$263$	−8.42683	−0.519621	−0.259810	+	0.965660i	$0.583660\pi$
$264$	−6.39138	−0.393363
$265$	−18.8794	−1.15975
$266$	0	0
$267$	17.5522	1.07418
$268$	11.3261	0.691852
$269$	7.17395	0.437403	0.218702	−	0.975792i	$-0.429818\pi$
$269$	7.17395	0.437403	0.218702	+	0.975792i	$0.429818\pi$
$270$	14.0755	0.856609
$271$	−13.1986	−0.801756	−0.400878	−	0.916132i	$-0.631295\pi$
$271$	−13.1986	−0.801756	−0.400878	+	0.916132i	$0.631295\pi$
$272$	7.57383	0.459231
$273$	0	0
$274$	−10.6592	−0.643948
$275$	18.7303	1.12948
$276$	15.4895	0.932359
$277$	1.12616	0.0676642	0.0338321	−	0.999428i	$-0.489229\pi$
$277$	1.12616	0.0676642	0.0338321	+	0.999428i	$0.489229\pi$
$278$	0.656434	0.0393703
$279$	−5.25359	−0.314524
$280$	0	0
$281$	−23.4326	−1.39787	−0.698935	−	0.715185i	$-0.746342\pi$
$281$	−23.4326	−1.39787	−0.698935	+	0.715185i	$0.746342\pi$
$282$	11.0766	0.659603
$283$	−13.5923	−0.807976	−0.403988	−	0.914764i	$-0.632376\pi$
$283$	−13.5923	−0.807976	−0.403988	+	0.914764i	$0.632376\pi$
$284$	−1.37636	−0.0816719
$285$	4.62650	0.274050
$286$	18.1297	1.07203
$287$	0	0
$288$	0.790361	0.0465725
$289$	40.3629	2.37429
$290$	3.27192	0.192134
$291$	34.9391	2.04817
$292$	5.79425	0.339083
$293$	−11.5465	−0.674555	−0.337278	−	0.941405i	$-0.609506\pi$
$293$	−11.5465	−0.674555	−0.337278	+	0.941405i	$0.609506\pi$
$294$	0	0
$295$	27.9381	1.62662
$296$	−5.11946	−0.297563
$297$	14.1227	0.819479
$298$	10.1710	0.589188
$299$	−43.9374	−2.54096
$300$	−11.1079	−0.641314
$301$	0	0
$302$	−19.6390	−1.13010
$303$	−21.4099	−1.22997
$304$	−0.726289	−0.0416555
$305$	−0.494869	−0.0283361
$306$	5.98606	0.342200
$307$	13.7316	0.783705	0.391853	−	0.920028i	$-0.371834\pi$
$307$	13.7316	0.783705	0.391853	+	0.920028i	$0.371834\pi$
$308$	0	0
$309$	−33.6049	−1.91171
$310$	−21.7487	−1.23524
$311$	−23.7428	−1.34633	−0.673166	−	0.739491i	$-0.735066\pi$
$311$	−23.7428	−1.34633	−0.673166	+	0.739491i	$0.735066\pi$
$312$	−10.7517	−0.608695
$313$	6.59145	0.372571	0.186285	−	0.982496i	$-0.440355\pi$
$313$	6.59145	0.372571	0.186285	+	0.982496i	$0.440355\pi$
$314$	0.164679	0.00929339
$315$	0	0
$316$	0.715154	0.0402306
$317$	−19.3757	−1.08825	−0.544124	−	0.839005i	$-0.683138\pi$
$317$	−19.3757	−1.08825	−0.544124	+	0.839005i	$0.683138\pi$
$318$	11.2338	0.629958
$319$	3.28288	0.183806
$320$	3.27192	0.182906
$321$	29.1410	1.62649
$322$	0	0
$323$	−5.50079	−0.306072
$324$	−10.7464	−0.597023
$325$	31.5085	1.74778
$326$	14.2581	0.789685
$327$	−11.9081	−0.658517
$328$	4.58090	0.252938
$329$	0	0
$330$	−20.9121	−1.15117
$331$	8.08490	0.444386	0.222193	−	0.975003i	$-0.428678\pi$
$331$	8.08490	0.444386	0.222193	+	0.975003i	$0.428678\pi$
$332$	−5.49921	−0.301808
$333$	−4.04623	−0.221732
$334$	−7.63407	−0.417718
$335$	37.0581	2.02470
$336$	0	0
$337$	4.71806	0.257009	0.128505	−	0.991709i	$-0.458982\pi$
$337$	4.71806	0.257009	0.128505	+	0.991709i	$0.458982\pi$
$338$	17.4981	0.951771
$339$	−18.9291	−1.02809
$340$	24.7810	1.34394
$341$	−21.8215	−1.18170
$342$	−0.574031	−0.0310400
$343$	0	0
$344$	0.209639	0.0113030
$345$	50.6805	2.72854
$346$	13.9739	0.751240
$347$	−14.2769	−0.766423	−0.383212	−	0.923661i	$-0.625182\pi$
$347$	−14.2769	−0.766423	−0.383212	+	0.923661i	$0.625182\pi$
$348$	−1.94688	−0.104364
$349$	−12.2263	−0.654457	−0.327228	−	0.944945i	$-0.606115\pi$
$349$	−12.2263	−0.654457	−0.327228	+	0.944945i	$0.606115\pi$
$350$	0	0
$351$	23.7574	1.26807
$352$	3.28288	0.174978
$353$	−31.7650	−1.69068	−0.845339	−	0.534230i	$-0.820602\pi$
$353$	−31.7650	−1.69068	−0.845339	+	0.534230i	$0.820602\pi$
$354$	−16.6239	−0.883553
$355$	−4.50334	−0.239012
$356$	−9.01553	−0.477822
$357$	0	0
$358$	12.5338	0.662431
$359$	−6.41290	−0.338460	−0.169230	−	0.985577i	$-0.554128\pi$
$359$	−6.41290	−0.338460	−0.169230	+	0.985577i	$0.554128\pi$
$360$	2.58600	0.136294
$361$	−18.4725	−0.972237
$362$	21.3711	1.12324
$363$	0.433601	0.0227581
$364$	0	0
$365$	18.9583	0.992324
$366$	0.294461	0.0153917
$367$	11.3792	0.593990	0.296995	−	0.954879i	$-0.404015\pi$
$367$	11.3792	0.593990	0.296995	+	0.954879i	$0.404015\pi$
$368$	−7.95605	−0.414738
$369$	3.62057	0.188479
$370$	−16.7505	−0.870816
$371$	0	0
$372$	12.9411	0.670964
$373$	1.35919	0.0703762	0.0351881	−	0.999381i	$-0.488797\pi$
$373$	1.35919	0.0703762	0.0351881	+	0.999381i	$0.488797\pi$
$374$	24.8640	1.28569
$375$	−4.49384	−0.232061
$376$	−5.68941	−0.293409
$377$	5.52251	0.284424
$378$	0	0
$379$	1.85052	0.0950550	0.0475275	−	0.998870i	$-0.484866\pi$
$379$	1.85052	0.0950550	0.0475275	+	0.998870i	$0.484866\pi$
$380$	−2.37636	−0.121905
$381$	7.69170	0.394058
$382$	−6.62026	−0.338722
$383$	17.9832	0.918897	0.459448	−	0.888204i	$-0.348047\pi$
$383$	17.9832	0.918897	0.459448	+	0.888204i	$0.348047\pi$
$384$	−1.94688	−0.0993516
$385$	0	0
$386$	−4.05261	−0.206272
$387$	0.165690	0.00842252
$388$	−17.9462	−0.911078
$389$	9.07521	0.460131	0.230066	−	0.973175i	$-0.426106\pi$
$389$	9.07521	0.460131	0.230066	+	0.973175i	$0.426106\pi$
$390$	−35.1787	−1.78134
$391$	−60.2578	−3.04737
$392$	0	0
$393$	−6.37005	−0.321327
$394$	21.1218	1.06410
$395$	2.33993	0.117735
$396$	2.59466	0.130387
$397$	9.39171	0.471357	0.235678	−	0.971831i	$-0.424269\pi$
$397$	9.39171	0.471357	0.235678	+	0.971831i	$0.424269\pi$
$398$	7.23535	0.362675
$399$	0	0
$400$	5.70546	0.285273
$401$	18.2599	0.911858	0.455929	−	0.890016i	$-0.349307\pi$
$401$	18.2599	0.911858	0.455929	+	0.890016i	$0.349307\pi$
$402$	−22.0506	−1.09979
$403$	−36.7085	−1.82858
$404$	10.9970	0.547121
$405$	−35.1614	−1.74718
$406$	0	0
$407$	−16.8066	−0.833071
$408$	−14.7454	−0.730005
$409$	−37.2015	−1.83950	−0.919748	−	0.392509i	$-0.871607\pi$
$409$	−37.2015	−1.83950	−0.919748	+	0.392509i	$0.871607\pi$
$410$	14.9883	0.740221
$411$	20.7523	1.02364
$412$	17.2608	0.850381
$413$	0	0
$414$	−6.28815	−0.309046
$415$	−17.9930	−0.883240
$416$	5.52251	0.270763
$417$	−1.27800	−0.0625840
$418$	−2.38432	−0.116621
$419$	15.7480	0.769339	0.384669	−	0.923054i	$-0.374315\pi$
$419$	15.7480	0.769339	0.384669	+	0.923054i	$0.374315\pi$
$420$	0	0
$421$	−17.7989	−0.867463	−0.433732	−	0.901042i	$-0.642803\pi$
$421$	−17.7989	−0.867463	−0.433732	+	0.901042i	$0.642803\pi$
$422$	6.76446	0.329289
$423$	−4.49669	−0.218636
$424$	−5.77012	−0.280222
$425$	43.2122	2.09610
$426$	2.67961	0.129828
$427$	0	0
$428$	−14.9680	−0.723507
$429$	−35.2965	−1.70413
$430$	0.685922	0.0330781
$431$	−18.4373	−0.888093	−0.444047	−	0.896004i	$-0.646458\pi$
$431$	−18.4373	−0.888093	−0.444047	+	0.896004i	$0.646458\pi$
$432$	4.30191	0.206976
$433$	9.21863	0.443019	0.221509	−	0.975158i	$-0.428902\pi$
$433$	9.21863	0.443019	0.221509	+	0.975158i	$0.428902\pi$
$434$	0	0
$435$	−6.37005	−0.305421
$436$	6.11647	0.292926
$437$	5.77839	0.276418
$438$	−11.2807	−0.539015
$439$	−13.2108	−0.630516	−0.315258	−	0.949006i	$-0.602091\pi$
$439$	−13.2108	−0.630516	−0.315258	+	0.949006i	$0.602091\pi$
$440$	10.7413	0.512072
$441$	0	0
$442$	41.8266	1.98949
$443$	−17.8784	−0.849428	−0.424714	−	0.905327i	$-0.639625\pi$
$443$	−17.8784	−0.849428	−0.424714	+	0.905327i	$0.639625\pi$
$444$	9.96701	0.473013
$445$	−29.4981	−1.39834
$446$	23.3248	1.10446
$447$	−19.8017	−0.936588
$448$	0	0
$449$	−15.8464	−0.747836	−0.373918	−	0.927462i	$-0.621986\pi$
$449$	−15.8464	−0.747836	−0.373918	+	0.927462i	$0.621986\pi$
$450$	4.50938	0.212574
$451$	15.0385	0.708137
$452$	9.72278	0.457321
$453$	38.2349	1.79643
$454$	26.9250	1.26365
$455$	0	0
$456$	1.41400	0.0662167
$457$	11.5218	0.538967	0.269484	−	0.963005i	$-0.413147\pi$
$457$	11.5218	0.538967	0.269484	+	0.963005i	$0.413147\pi$
$458$	−9.87701	−0.461522
$459$	32.5820	1.52080
$460$	−26.0316	−1.21373
$461$	16.6699	0.776394	0.388197	−	0.921576i	$-0.373098\pi$
$461$	16.6699	0.776394	0.388197	+	0.921576i	$0.373098\pi$
$462$	0	0
$463$	3.57103	0.165960	0.0829800	−	0.996551i	$-0.473556\pi$
$463$	3.57103	0.165960	0.0829800	+	0.996551i	$0.473556\pi$
$464$	1.00000	0.0464238
$465$	42.3422	1.96357
$466$	−8.45298	−0.391577
$467$	−30.0447	−1.39030	−0.695151	−	0.718864i	$-0.744662\pi$
$467$	−30.0447	−1.39030	−0.695151	+	0.718864i	$0.744662\pi$
$468$	4.36478	0.201762
$469$	0	0
$470$	−18.6153	−0.858659
$471$	−0.320612	−0.0147730
$472$	8.53874	0.393027
$473$	0.688219	0.0316443
$474$	−1.39232	−0.0639515
$475$	−4.14382	−0.190131
$476$	0	0
$477$	−4.56048	−0.208810
$478$	10.6075	0.485175
$479$	7.44127	0.340000	0.170000	−	0.985444i	$-0.445623\pi$
$479$	7.44127	0.340000	0.170000	+	0.985444i	$0.445623\pi$
$480$	−6.37005	−0.290752
$481$	−28.2723	−1.28911
$482$	−27.2035	−1.23909
$483$	0	0
$484$	−0.222715	−0.0101234
$485$	−58.7184	−2.66627
$486$	8.01629	0.363626
$487$	11.2737	0.510858	0.255429	−	0.966828i	$-0.417783\pi$
$487$	11.2737	0.510858	0.255429	+	0.966828i	$0.417783\pi$
$488$	−0.151247	−0.00684665
$489$	−27.7590	−1.25530
$490$	0	0
$491$	−36.6241	−1.65282	−0.826411	−	0.563067i	$-0.809621\pi$
$491$	−36.6241	−1.65282	−0.826411	+	0.563067i	$0.809621\pi$
$492$	−8.91849	−0.402076
$493$	7.57383	0.341108
$494$	−4.01094	−0.180461
$495$	8.48952	0.381575
$496$	−6.64707	−0.298462
$497$	0	0
$498$	10.7063	0.479762
$499$	17.9127	0.801881	0.400940	−	0.916104i	$-0.368683\pi$
$499$	17.9127	0.801881	0.400940	+	0.916104i	$0.368683\pi$
$500$	2.30822	0.103227
$501$	14.8627	0.664015
$502$	−19.4237	−0.866920
$503$	15.1356	0.674862	0.337431	−	0.941350i	$-0.390442\pi$
$503$	15.1356	0.674862	0.337431	+	0.941350i	$0.390442\pi$
$504$	0	0
$505$	35.9813	1.60115
$506$	−26.1187	−1.16112
$507$	−34.0668	−1.51296
$508$	−3.95078	−0.175287
$509$	5.45446	0.241765	0.120882	−	0.992667i	$-0.461428\pi$
$509$	5.45446	0.241765	0.120882	+	0.992667i	$0.461428\pi$
$510$	−48.2457	−2.13636
$511$	0	0
$512$	1.00000	0.0441942
$513$	−3.12443	−0.137947
$514$	−26.3885	−1.16395
$515$	56.4761	2.48863
$516$	−0.408143	−0.0179675
$517$	−18.6776	−0.821441
$518$	0	0
$519$	−27.2055	−1.19419
$520$	18.0692	0.792387
$521$	22.5369	0.987361	0.493680	−	0.869643i	$-0.335651\pi$
$521$	22.5369	0.987361	0.493680	+	0.869643i	$0.335651\pi$
$522$	0.790361	0.0345932
$523$	−33.5416	−1.46667	−0.733335	−	0.679867i	$-0.762038\pi$
$523$	−33.5416	−1.46667	−0.733335	+	0.679867i	$0.762038\pi$
$524$	3.27192	0.142935
$525$	0	0
$526$	−8.42683	−0.367427
$527$	−50.3438	−2.19301
$528$	−6.39138	−0.278149
$529$	40.2988	1.75212
$530$	−18.8794	−0.820067
$531$	6.74869	0.292868
$532$	0	0
$533$	25.2981	1.09578
$534$	17.5522	0.759558
$535$	−48.9742	−2.11734
$536$	11.3261	0.489213
$537$	−24.4018	−1.05302
$538$	7.17395	0.309291
$539$	0	0
$540$	14.0755	0.605714
$541$	−24.3356	−1.04627	−0.523135	−	0.852250i	$-0.675238\pi$
$541$	−24.3356	−1.04627	−0.523135	+	0.852250i	$0.675238\pi$
$542$	−13.1986	−0.566927
$543$	−41.6072	−1.78553
$544$	7.57383	0.324725
$545$	20.0126	0.857245
$546$	0	0
$547$	0.837618	0.0358139	0.0179070	−	0.999840i	$-0.494300\pi$
$547$	0.837618	0.0358139	0.0179070	+	0.999840i	$0.494300\pi$
$548$	−10.6592	−0.455340
$549$	−0.119540	−0.00510184
$550$	18.7303	0.798664
$551$	−0.726289	−0.0309410
$552$	15.4895	0.659278
$553$	0	0
$554$	1.12616	0.0478458
$555$	32.6113	1.38427
$556$	0.656434	0.0278390
$557$	−31.5131	−1.33525	−0.667627	−	0.744496i	$-0.732690\pi$
$557$	−31.5131	−1.33525	−0.667627	+	0.744496i	$0.732690\pi$
$558$	−5.25359	−0.222402
$559$	1.15773	0.0489669
$560$	0	0
$561$	−48.4073	−2.04376
$562$	−23.4326	−0.988443
$563$	6.94272	0.292601	0.146300	−	0.989240i	$-0.453263\pi$
$563$	6.94272	0.292601	0.146300	+	0.989240i	$0.453263\pi$
$564$	11.0766	0.466410
$565$	31.8122	1.33835
$566$	−13.5923	−0.571325
$567$	0	0
$568$	−1.37636	−0.0577508
$569$	8.58441	0.359877	0.179939	−	0.983678i	$-0.442410\pi$
$569$	8.58441	0.359877	0.179939	+	0.983678i	$0.442410\pi$
$570$	4.62650	0.193783
$571$	−13.3712	−0.559568	−0.279784	−	0.960063i	$-0.590263\pi$
$571$	−13.3712	−0.559568	−0.279784	+	0.960063i	$0.590263\pi$
$572$	18.1297	0.758042
$573$	12.8889	0.538441
$574$	0	0
$575$	−45.3930	−1.89302
$576$	0.790361	0.0329317
$577$	−10.5180	−0.437870	−0.218935	−	0.975739i	$-0.570258\pi$
$577$	−10.5180	−0.437870	−0.218935	+	0.975739i	$0.570258\pi$
$578$	40.3629	1.67888
$579$	7.88996	0.327896
$580$	3.27192	0.135859
$581$	0	0
$582$	34.9391	1.44827
$583$	−18.9426	−0.784522
$584$	5.79425	0.239768
$585$	14.2812	0.590455
$586$	−11.5465	−0.476982
$587$	0.917043	0.0378504	0.0189252	−	0.999821i	$-0.493976\pi$
$587$	0.917043	0.0378504	0.0189252	+	0.999821i	$0.493976\pi$
$588$	0	0
$589$	4.82770	0.198922
$590$	27.9381	1.15019
$591$	−41.1218	−1.69152
$592$	−5.11946	−0.210409
$593$	−0.679688	−0.0279114	−0.0139557	−	0.999903i	$-0.504442\pi$
$593$	−0.679688	−0.0279114	−0.0139557	+	0.999903i	$0.504442\pi$
$594$	14.1227	0.579459
$595$	0	0
$596$	10.1710	0.416619
$597$	−14.0864	−0.576518
$598$	−43.9374	−1.79673
$599$	2.32249	0.0948943	0.0474471	−	0.998874i	$-0.484891\pi$
$599$	2.32249	0.0948943	0.0474471	+	0.998874i	$0.484891\pi$
$600$	−11.1079	−0.453477
$601$	10.4183	0.424971	0.212485	−	0.977164i	$-0.431844\pi$
$601$	10.4183	0.424971	0.212485	+	0.977164i	$0.431844\pi$
$602$	0	0
$603$	8.95171	0.364542
$604$	−19.6390	−0.799099
$605$	−0.728706	−0.0296261
$606$	−21.4099	−0.869718
$607$	−4.95135	−0.200969	−0.100484	−	0.994939i	$-0.532039\pi$
$607$	−4.95135	−0.200969	−0.100484	+	0.994939i	$0.532039\pi$
$608$	−0.726289	−0.0294549
$609$	0	0
$610$	−0.494869	−0.0200367
$611$	−31.4198	−1.27111
$612$	5.98606	0.241972
$613$	7.69663	0.310864	0.155432	−	0.987847i	$-0.450323\pi$
$613$	7.69663	0.310864	0.155432	+	0.987847i	$0.450323\pi$
$614$	13.7316	0.554163
$615$	−29.1806	−1.17667
$616$	0	0
$617$	−15.1756	−0.610947	−0.305473	−	0.952201i	$-0.598815\pi$
$617$	−15.1756	−0.610947	−0.305473	+	0.952201i	$0.598815\pi$
$618$	−33.6049	−1.35179
$619$	−8.58872	−0.345210	−0.172605	−	0.984991i	$-0.555218\pi$
$619$	−8.58872	−0.345210	−0.172605	+	0.984991i	$0.555218\pi$
$620$	−21.7487	−0.873448
$621$	−34.2262	−1.37345
$622$	−23.7428	−0.952001
$623$	0	0
$624$	−10.7517	−0.430412
$625$	−20.9750	−0.839000
$626$	6.59145	0.263447
$627$	4.64199	0.185383
$628$	0.164679	0.00657142
$629$	−38.7740	−1.54602
$630$	0	0
$631$	−22.3220	−0.888625	−0.444312	−	0.895872i	$-0.646552\pi$
$631$	−22.3220	−0.888625	−0.444312	+	0.895872i	$0.646552\pi$
$632$	0.715154	0.0284473
$633$	−13.1696	−0.523445
$634$	−19.3757	−0.769508
$635$	−12.9266	−0.512977
$636$	11.2338	0.445447
$637$	0	0
$638$	3.28288	0.129970
$639$	−1.08782	−0.0430336
$640$	3.27192	0.129334
$641$	−36.6256	−1.44662	−0.723312	−	0.690522i	$-0.757381\pi$
$641$	−36.6256	−1.44662	−0.723312	+	0.690522i	$0.757381\pi$
$642$	29.1410	1.15010
$643$	4.74242	0.187023	0.0935114	−	0.995618i	$-0.470191\pi$
$643$	4.74242	0.187023	0.0935114	+	0.995618i	$0.470191\pi$
$644$	0	0
$645$	−1.33541	−0.0525817
$646$	−5.50079	−0.216426
$647$	23.6856	0.931177	0.465589	−	0.885001i	$-0.345843\pi$
$647$	23.6856	0.931177	0.465589	+	0.885001i	$0.345843\pi$
$648$	−10.7464	−0.422159
$649$	28.0316	1.10034
$650$	31.5085	1.23586
$651$	0	0
$652$	14.2581	0.558392
$653$	−16.5206	−0.646502	−0.323251	−	0.946313i	$-0.604776\pi$
$653$	−16.5206	−0.646502	−0.323251	+	0.946313i	$0.604776\pi$
$654$	−11.9081	−0.465642
$655$	10.7055	0.418297
$656$	4.58090	0.178854
$657$	4.57955	0.178665
$658$	0	0
$659$	−36.6326	−1.42700	−0.713502	−	0.700653i	$-0.752892\pi$
$659$	−36.6326	−1.42700	−0.713502	+	0.700653i	$0.752892\pi$
$660$	−20.9121	−0.814003
$661$	31.5392	1.22673	0.613367	−	0.789798i	$-0.289815\pi$
$661$	31.5392	1.22673	0.613367	+	0.789798i	$0.289815\pi$
$662$	8.08490	0.314229
$663$	−81.4315	−3.16254
$664$	−5.49921	−0.213411
$665$	0	0
$666$	−4.04623	−0.156788
$667$	−7.95605	−0.308060
$668$	−7.63407	−0.295371
$669$	−45.4107	−1.75568
$670$	37.0581	1.43168
$671$	−0.496527	−0.0191682
$672$	0	0
$673$	8.46574	0.326330	0.163165	−	0.986599i	$-0.447830\pi$
$673$	8.46574	0.326330	0.163165	+	0.986599i	$0.447830\pi$
$674$	4.71806	0.181733
$675$	24.5444	0.944715
$676$	17.4981	0.673004
$677$	31.5517	1.21263	0.606314	−	0.795225i	$-0.292647\pi$
$677$	31.5517	1.21263	0.606314	+	0.795225i	$0.292647\pi$
$678$	−18.9291	−0.726969
$679$	0	0
$680$	24.7810	0.950307
$681$	−52.4199	−2.00873
$682$	−21.8215	−0.835589
$683$	−36.6890	−1.40386	−0.701932	−	0.712244i	$-0.747679\pi$
$683$	−36.6890	−1.40386	−0.701932	+	0.712244i	$0.747679\pi$
$684$	−0.574031	−0.0219486
$685$	−34.8762	−1.33255
$686$	0	0
$687$	19.2294	0.733648
$688$	0.209639	0.00799241
$689$	−31.8655	−1.21398
$690$	50.6805	1.92937
$691$	−42.5940	−1.62035	−0.810176	−	0.586187i	$-0.800629\pi$
$691$	−42.5940	−1.62035	−0.810176	+	0.586187i	$0.800629\pi$
$692$	13.9739	0.531207
$693$	0	0
$694$	−14.2769	−0.541943
$695$	2.14780	0.0814707
$696$	−1.94688	−0.0737965
$697$	34.6950	1.31417
$698$	−12.2263	−0.462771
$699$	16.4570	0.622460
$700$	0	0
$701$	19.1484	0.723227	0.361613	−	0.932328i	$-0.382226\pi$
$701$	19.1484	0.723227	0.361613	+	0.932328i	$0.382226\pi$
$702$	23.7574	0.896663
$703$	3.71821	0.140235
$704$	3.28288	0.123728
$705$	36.2418	1.36495
$706$	−31.7650	−1.19549
$707$	0	0
$708$	−16.6239	−0.624766
$709$	2.64868	0.0994734	0.0497367	−	0.998762i	$-0.484162\pi$
$709$	2.64868	0.0994734	0.0497367	+	0.998762i	$0.484162\pi$
$710$	−4.50334	−0.169007
$711$	0.565230	0.0211978
$712$	−9.01553	−0.337871
$713$	52.8844	1.98054
$714$	0	0
$715$	59.3190	2.21840
$716$	12.5338	0.468409
$717$	−20.6516	−0.771247
$718$	−6.41290	−0.239327
$719$	24.4679	0.912499	0.456249	−	0.889852i	$-0.349192\pi$
$719$	24.4679	0.912499	0.456249	+	0.889852i	$0.349192\pi$
$720$	2.58600	0.0963745
$721$	0	0
$722$	−18.4725	−0.687475
$723$	52.9622	1.96968
$724$	21.3711	0.794252
$725$	5.70546	0.211896
$726$	0.433601	0.0160924
$727$	−10.3496	−0.383847	−0.191923	−	0.981410i	$-0.561472\pi$
$727$	−10.3496	−0.383847	−0.191923	+	0.981410i	$0.561472\pi$
$728$	0	0
$729$	16.6324	0.616016
$730$	18.9583	0.701679
$731$	1.58777	0.0587258
$732$	0.294461	0.0108836
$733$	−14.0365	−0.518451	−0.259226	−	0.965817i	$-0.583467\pi$
$733$	−14.0365	−0.518451	−0.259226	+	0.965817i	$0.583467\pi$
$734$	11.3792	0.420015
$735$	0	0
$736$	−7.95605	−0.293264
$737$	37.1822	1.36962
$738$	3.62057	0.133275
$739$	3.53574	0.130064	0.0650322	−	0.997883i	$-0.479285\pi$
$739$	3.53574	0.130064	0.0650322	+	0.997883i	$0.479285\pi$
$740$	−16.7505	−0.615760
$741$	7.80883	0.286865
$742$	0	0
$743$	1.52701	0.0560204	0.0280102	−	0.999608i	$-0.491083\pi$
$743$	1.52701	0.0560204	0.0280102	+	0.999608i	$0.491083\pi$
$744$	12.9411	0.474443
$745$	33.2786	1.21923
$746$	1.35919	0.0497635
$747$	−4.34636	−0.159025
$748$	24.8640	0.909117
$749$	0	0
$750$	−4.49384	−0.164092
$751$	−40.2810	−1.46988	−0.734938	−	0.678134i	$-0.762789\pi$
$751$	−40.2810	−1.46988	−0.734938	+	0.678134i	$0.762789\pi$
$752$	−5.68941	−0.207471
$753$	37.8156	1.37808
$754$	5.52251	0.201118
$755$	−64.2572	−2.33856
$756$	0	0
$757$	1.02370	0.0372071	0.0186036	−	0.999827i	$-0.494078\pi$
$757$	1.02370	0.0372071	0.0186036	+	0.999827i	$0.494078\pi$
$758$	1.85052	0.0672140
$759$	50.8502	1.84574
$760$	−2.37636	−0.0861996
$761$	24.1088	0.873943	0.436972	−	0.899475i	$-0.356051\pi$
$761$	24.1088	0.873943	0.436972	+	0.899475i	$0.356051\pi$
$762$	7.69170	0.278641
$763$	0	0
$764$	−6.62026	−0.239512
$765$	19.5859	0.708131
$766$	17.9832	0.649758
$767$	47.1553	1.70268
$768$	−1.94688	−0.0702522
$769$	26.1822	0.944155	0.472077	−	0.881557i	$-0.343504\pi$
$769$	26.1822	0.944155	0.472077	+	0.881557i	$0.343504\pi$
$770$	0	0
$771$	51.3753	1.85024
$772$	−4.05261	−0.145857
$773$	30.5037	1.09714	0.548570	−	0.836105i	$-0.315172\pi$
$773$	30.5037	1.09714	0.548570	+	0.836105i	$0.315172\pi$
$774$	0.165690	0.00595562
$775$	−37.9246	−1.36229
$776$	−17.9462	−0.644230
$777$	0	0
$778$	9.07521	0.325362
$779$	−3.32706	−0.119204
$780$	−35.1787	−1.25960
$781$	−4.51842	−0.161682
$782$	−60.2578	−2.15481
$783$	4.30191	0.153738
$784$	0	0
$785$	0.538818	0.0192312
$786$	−6.37005	−0.227212
$787$	42.6169	1.51913	0.759564	−	0.650432i	$-0.225412\pi$
$787$	42.6169	1.51913	0.759564	+	0.650432i	$0.225412\pi$
$788$	21.1218	0.752434
$789$	16.4061	0.584072
$790$	2.33993	0.0832509
$791$	0	0
$792$	2.59466	0.0921972
$793$	−0.835265	−0.0296611
$794$	9.39171	0.333299
$795$	36.7560	1.30360
$796$	7.23535	0.256450
$797$	26.5763	0.941379	0.470690	−	0.882299i	$-0.344005\pi$
$797$	26.5763	0.941379	0.470690	+	0.882299i	$0.344005\pi$
$798$	0	0
$799$	−43.0906	−1.52444
$800$	5.70546	0.201719
$801$	−7.12553	−0.251768
$802$	18.2599	0.644781
$803$	19.0218	0.671265
$804$	−22.0506	−0.777665
$805$	0	0
$806$	−36.7085	−1.29300
$807$	−13.9668	−0.491656
$808$	10.9970	0.386873
$809$	34.5650	1.21524	0.607621	−	0.794227i	$-0.292124\pi$
$809$	34.5650	1.21524	0.607621	+	0.794227i	$0.292124\pi$
$810$	−35.1614	−1.23545
$811$	−51.5669	−1.81076	−0.905379	−	0.424605i	$-0.860413\pi$
$811$	−51.5669	−1.81076	−0.905379	+	0.424605i	$0.860413\pi$
$812$	0	0
$813$	25.6961	0.901201
$814$	−16.8066	−0.589070
$815$	46.6515	1.63413
$816$	−14.7454	−0.516192
$817$	−0.152258	−0.00532685
$818$	−37.2015	−1.30072
$819$	0	0
$820$	14.9883	0.523416
$821$	33.1961	1.15855	0.579276	−	0.815132i	$-0.303335\pi$
$821$	33.1961	1.15855	0.579276	+	0.815132i	$0.303335\pi$
$822$	20.7523	0.723820
$823$	31.2919	1.09077	0.545384	−	0.838187i	$-0.316384\pi$
$823$	31.2919	1.09077	0.545384	+	0.838187i	$0.316384\pi$
$824$	17.2608	0.601310
$825$	−36.4658	−1.26958
$826$	0	0
$827$	−22.8284	−0.793821	−0.396910	−	0.917857i	$-0.629918\pi$
$827$	−22.8284	−0.793821	−0.396910	+	0.917857i	$0.629918\pi$
$828$	−6.28815	−0.218528
$829$	−3.65073	−0.126795	−0.0633975	−	0.997988i	$-0.520194\pi$
$829$	−3.65073	−0.126795	−0.0633975	+	0.997988i	$0.520194\pi$
$830$	−17.9930	−0.624545
$831$	−2.19250	−0.0760569
$832$	5.52251	0.191459
$833$	0	0
$834$	−1.27800	−0.0442536
$835$	−24.9781	−0.864402
$836$	−2.38432	−0.0824634
$837$	−28.5951	−0.988392
$838$	15.7480	0.544005
$839$	10.9777	0.378991	0.189495	−	0.981882i	$-0.439315\pi$
$839$	10.9777	0.378991	0.189495	+	0.981882i	$0.439315\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−17.7989	−0.613389
$843$	45.6205	1.57125
$844$	6.76446	0.232842
$845$	57.2524	1.96954
$846$	−4.49669	−0.154599
$847$	0	0
$848$	−5.77012	−0.198147
$849$	26.4626	0.908193
$850$	43.2122	1.48217
$851$	40.7307	1.39623
$852$	2.67961	0.0918021
$853$	−24.9620	−0.854683	−0.427342	−	0.904090i	$-0.640550\pi$
$853$	−24.9620	−0.854683	−0.427342	+	0.904090i	$0.640550\pi$
$854$	0	0
$855$	−1.87818	−0.0642325
$856$	−14.9680	−0.511596
$857$	−18.9158	−0.646151	−0.323076	−	0.946373i	$-0.604717\pi$
$857$	−18.9158	−0.646151	−0.323076	+	0.946373i	$0.604717\pi$
$858$	−35.2965	−1.20500
$859$	−48.7485	−1.66328	−0.831639	−	0.555317i	$-0.812597\pi$
$859$	−48.7485	−1.66328	−0.831639	+	0.555317i	$0.812597\pi$
$860$	0.685922	0.0233897
$861$	0	0
$862$	−18.4373	−0.627977
$863$	49.1728	1.67386	0.836930	−	0.547310i	$-0.184348\pi$
$863$	49.1728	1.67386	0.836930	+	0.547310i	$0.184348\pi$
$864$	4.30191	0.146354
$865$	45.7214	1.55457
$866$	9.21863	0.313262
$867$	−78.5820	−2.66879
$868$	0	0
$869$	2.34776	0.0796424
$870$	−6.37005	−0.215965
$871$	62.5485	2.11938
$872$	6.11647	0.207130
$873$	−14.1840	−0.480054
$874$	5.77839	0.195457
$875$	0	0
$876$	−11.2807	−0.381141
$877$	55.9351	1.88879	0.944397	−	0.328808i	$-0.106647\pi$
$877$	55.9351	1.88879	0.944397	+	0.328808i	$0.106647\pi$
$878$	−13.2108	−0.445842
$879$	22.4798	0.758223
$880$	10.7413	0.362090
$881$	−17.2684	−0.581789	−0.290894	−	0.956755i	$-0.593953\pi$
$881$	−17.2684	−0.581789	−0.290894	+	0.956755i	$0.593953\pi$
$882$	0	0
$883$	−5.45803	−0.183677	−0.0918386	−	0.995774i	$-0.529274\pi$
$883$	−5.45803	−0.183677	−0.0918386	+	0.995774i	$0.529274\pi$
$884$	41.8266	1.40678
$885$	−54.3922	−1.82838
$886$	−17.8784	−0.600637
$887$	24.9605	0.838090	0.419045	−	0.907965i	$-0.362365\pi$
$887$	24.9605	0.838090	0.419045	+	0.907965i	$0.362365\pi$
$888$	9.96701	0.334471
$889$	0	0
$890$	−29.4981	−0.988779
$891$	−35.2792	−1.18190
$892$	23.3248	0.780973
$893$	4.13215	0.138277
$894$	−19.8017	−0.662268
$895$	41.0095	1.37080
$896$	0	0
$897$	85.5410	2.85613
$898$	−15.8464	−0.528800
$899$	−6.64707	−0.221692
$900$	4.50938	0.150313
$901$	−43.7019	−1.45592
$902$	15.0385	0.500728
$903$	0	0
$904$	9.72278	0.323375
$905$	69.9247	2.32437
$906$	38.2349	1.27027
$907$	6.67476	0.221632	0.110816	−	0.993841i	$-0.464654\pi$
$907$	6.67476	0.221632	0.110816	+	0.993841i	$0.464654\pi$
$908$	26.9250	0.893538
$909$	8.69160	0.288282
$910$	0	0
$911$	16.4305	0.544368	0.272184	−	0.962245i	$-0.412254\pi$
$911$	16.4305	0.544368	0.272184	+	0.962245i	$0.412254\pi$
$912$	1.41400	0.0468223
$913$	−18.0532	−0.597475
$914$	11.5218	0.381107
$915$	0.963454	0.0318508
$916$	−9.87701	−0.326346
$917$	0	0
$918$	32.5820	1.07537
$919$	−8.15734	−0.269086	−0.134543	−	0.990908i	$-0.542957\pi$
$919$	−8.15734	−0.269086	−0.134543	+	0.990908i	$0.542957\pi$
$920$	−26.0316	−0.858235
$921$	−26.7339	−0.880912
$922$	16.6699	0.548994
$923$	−7.60096	−0.250189
$924$	0	0
$925$	−29.2089	−0.960383
$926$	3.57103	0.117351
$927$	13.6423	0.448072
$928$	1.00000	0.0328266
$929$	−50.1252	−1.64455	−0.822277	−	0.569087i	$-0.807297\pi$
$929$	−50.1252	−1.64455	−0.822277	+	0.569087i	$0.807297\pi$
$930$	42.3422	1.38846
$931$	0	0
$932$	−8.45298	−0.276887
$933$	46.2246	1.51332
$934$	−30.0447	−0.983092
$935$	81.3529	2.66052
$936$	4.36478	0.142667
$937$	38.3790	1.25379	0.626893	−	0.779105i	$-0.284326\pi$
$937$	38.3790	1.25379	0.626893	+	0.779105i	$0.284326\pi$
$938$	0	0
$939$	−12.8328	−0.418783
$940$	−18.6153	−0.607164
$941$	−6.33133	−0.206395	−0.103198	−	0.994661i	$-0.532907\pi$
$941$	−6.33133	−0.206395	−0.103198	+	0.994661i	$0.532907\pi$
$942$	−0.320612	−0.0104461
$943$	−36.4459	−1.18684
$944$	8.53874	0.277912
$945$	0	0
$946$	0.688219	0.0223759
$947$	−15.3218	−0.497891	−0.248946	−	0.968517i	$-0.580084\pi$
$947$	−15.3218	−0.497891	−0.248946	+	0.968517i	$0.580084\pi$
$948$	−1.39232	−0.0452205
$949$	31.9988	1.03873
$950$	−4.14382	−0.134443
$951$	37.7223	1.22323
$952$	0	0
$953$	5.44368	0.176338	0.0881690	−	0.996106i	$-0.471898\pi$
$953$	5.44368	0.176338	0.0881690	+	0.996106i	$0.471898\pi$
$954$	−4.56048	−0.147651
$955$	−21.6610	−0.700932
$956$	10.6075	0.343071
$957$	−6.39138	−0.206604
$958$	7.44127	0.240416
$959$	0	0
$960$	−6.37005	−0.205593
$961$	13.1836	0.425276
$962$	−28.2723	−0.911535
$963$	−11.8301	−0.381221
$964$	−27.2035	−0.876167
$965$	−13.2598	−0.426848
$966$	0	0
$967$	−24.9842	−0.803439	−0.401719	−	0.915763i	$-0.631587\pi$
$967$	−24.9842	−0.803439	−0.401719	+	0.915763i	$0.631587\pi$
$968$	−0.222715	−0.00715833
$969$	10.7094	0.344036
$970$	−58.7184	−1.88533
$971$	−3.46409	−0.111168	−0.0555840	−	0.998454i	$-0.517702\pi$
$971$	−3.46409	−0.111168	−0.0555840	+	0.998454i	$0.517702\pi$
$972$	8.01629	0.257123
$973$	0	0
$974$	11.2737	0.361232
$975$	−61.3434	−1.96456
$976$	−0.151247	−0.00484131
$977$	−33.7587	−1.08004	−0.540018	−	0.841654i	$-0.681583\pi$
$977$	−33.7587	−1.08004	−0.540018	+	0.841654i	$0.681583\pi$
$978$	−27.7590	−0.887634
$979$	−29.5969	−0.945921
$980$	0	0
$981$	4.83422	0.154345
$982$	−36.6241	−1.16872
$983$	55.8164	1.78027	0.890133	−	0.455701i	$-0.150611\pi$
$983$	55.8164	1.78027	0.890133	+	0.455701i	$0.150611\pi$
$984$	−8.91849	−0.284311
$985$	69.1089	2.20199
$986$	7.57383	0.241200
$987$	0	0
$988$	−4.01094	−0.127605
$989$	−1.66790	−0.0530361
$990$	8.48952	0.269815
$991$	−16.0274	−0.509127	−0.254564	−	0.967056i	$-0.581932\pi$
$991$	−16.0274	−0.509127	−0.254564	+	0.967056i	$0.581932\pi$
$992$	−6.64707	−0.211045
$993$	−15.7404	−0.499506
$994$	0	0
$995$	23.6735	0.750500
$996$	10.7063	0.339243
$997$	−3.90000	−0.123514	−0.0617572	−	0.998091i	$-0.519670\pi$
$997$	−3.90000	−0.123514	−0.0617572	+	0.998091i	$0.519670\pi$
$998$	17.9127	0.567015
$999$	−22.0235	−0.696792

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.y.1.1		5
7.3	odd	6		406.2.e.b.233.1	✓	10
7.5	odd	6		406.2.e.b.291.1	yes	10
7.6	odd	2		2842.2.a.w.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.b.233.1	✓	10	7.3	odd	6
406.2.e.b.291.1	yes	10	7.5	odd	6
2842.2.a.w.1.5		5	7.6	odd	2
2842.2.a.y.1.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.94688 q^{3} +1.00000 q^{4} +3.27192 q^{5} -1.94688 q^{6} +1.00000 q^{8} +0.790361 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.94688 q^{3} +1.00000 q^{4} +3.27192 q^{5} -1.94688 q^{6} +1.00000 q^{8} +0.790361 q^{9} +3.27192 q^{10} +3.28288 q^{11} -1.94688 q^{12} +5.52251 q^{13} -6.37005 q^{15} +1.00000 q^{16} +7.57383 q^{17} +0.790361 q^{18} -0.726289 q^{19} +3.27192 q^{20} +3.28288 q^{22} -7.95605 q^{23} -1.94688 q^{24} +5.70546 q^{25} +5.52251 q^{26} +4.30191 q^{27} +1.00000 q^{29} -6.37005 q^{30} -6.64707 q^{31} +1.00000 q^{32} -6.39138 q^{33} +7.57383 q^{34} +0.790361 q^{36} -5.11946 q^{37} -0.726289 q^{38} -10.7517 q^{39} +3.27192 q^{40} +4.58090 q^{41} +0.209639 q^{43} +3.28288 q^{44} +2.58600 q^{45} -7.95605 q^{46} -5.68941 q^{47} -1.94688 q^{48} +5.70546 q^{50} -14.7454 q^{51} +5.52251 q^{52} -5.77012 q^{53} +4.30191 q^{54} +10.7413 q^{55} +1.41400 q^{57} +1.00000 q^{58} +8.53874 q^{59} -6.37005 q^{60} -0.151247 q^{61} -6.64707 q^{62} +1.00000 q^{64} +18.0692 q^{65} -6.39138 q^{66} +11.3261 q^{67} +7.57383 q^{68} +15.4895 q^{69} -1.37636 q^{71} +0.790361 q^{72} +5.79425 q^{73} -5.11946 q^{74} -11.1079 q^{75} -0.726289 q^{76} -10.7517 q^{78} +0.715154 q^{79} +3.27192 q^{80} -10.7464 q^{81} +4.58090 q^{82} -5.49921 q^{83} +24.7810 q^{85} +0.209639 q^{86} -1.94688 q^{87} +3.28288 q^{88} -9.01553 q^{89} +2.58600 q^{90} -7.95605 q^{92} +12.9411 q^{93} -5.68941 q^{94} -2.37636 q^{95} -1.94688 q^{96} -17.9462 q^{97} +2.59466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 4 q^{9}+O(q^{10}) \) 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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