LMFDB - Embedded newform 2842.2.a.t.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:	$1$
Dimension:	$5$
Coefficient field:	5.5.974241.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} - 2x^{2} + 11x + 3 $ x^5 - x^4 - 9x^3 - 2x^2 + 11*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$3.47364$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -3.09718 q^{3} +1.00000 q^{4} +2.78950 q^{5} +3.09718 q^{6} -1.00000 q^{8} +6.59255 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.09718 q^{3} +1.00000 q^{4} +2.78950 q^{5} +3.09718 q^{6} -1.00000 q^{8} +6.59255 q^{9} -2.78950 q^{10} +2.80305 q^{11} -3.09718 q^{12} +3.76778 q^{13} -8.63960 q^{15} +1.00000 q^{16} -6.21609 q^{17} -6.59255 q^{18} +1.46546 q^{19} +2.78950 q^{20} -2.80305 q^{22} -6.75033 q^{23} +3.09718 q^{24} +2.78132 q^{25} -3.76778 q^{26} -11.1268 q^{27} -1.00000 q^{29} +8.63960 q^{30} -8.37388 q^{31} -1.00000 q^{32} -8.68156 q^{33} +6.21609 q^{34} +6.59255 q^{36} +2.28596 q^{37} -1.46546 q^{38} -11.6695 q^{39} -2.78950 q^{40} -8.55060 q^{41} +7.71375 q^{43} +2.80305 q^{44} +18.3899 q^{45} +6.75033 q^{46} -12.2347 q^{47} -3.09718 q^{48} -2.78132 q^{50} +19.2524 q^{51} +3.76778 q^{52} -1.12428 q^{53} +11.1268 q^{54} +7.81911 q^{55} -4.53881 q^{57} +1.00000 q^{58} -3.38006 q^{59} -8.63960 q^{60} -3.70947 q^{61} +8.37388 q^{62} +1.00000 q^{64} +10.5102 q^{65} +8.68156 q^{66} -6.57312 q^{67} -6.21609 q^{68} +20.9070 q^{69} +8.45620 q^{71} -6.59255 q^{72} +1.41841 q^{73} -2.28596 q^{74} -8.61427 q^{75} +1.46546 q^{76} +11.6695 q^{78} -12.8464 q^{79} +2.78950 q^{80} +14.6841 q^{81} +8.55060 q^{82} -7.72073 q^{83} -17.3398 q^{85} -7.71375 q^{86} +3.09718 q^{87} -2.80305 q^{88} +9.99993 q^{89} -18.3899 q^{90} -6.75033 q^{92} +25.9354 q^{93} +12.2347 q^{94} +4.08792 q^{95} +3.09718 q^{96} -1.13474 q^{97} +18.4792 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * 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
$3$	−3.09718	−1.78816	−0.894080	−	0.447907i	$-0.852170\pi$
$3$	−3.09718	−1.78816	−0.894080	+	0.447907i	$0.852170\pi$
$4$	1.00000	0.500000
$5$	2.78950	1.24750	0.623752	−	0.781623i	$-0.285608\pi$
$5$	2.78950	1.24750	0.623752	+	0.781623i	$0.285608\pi$
$6$	3.09718	1.26442
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	6.59255	2.19752
$10$	−2.78950	−0.882118
$11$	2.80305	0.845151	0.422575	−	0.906328i	$-0.361126\pi$
$11$	2.80305	0.845151	0.422575	+	0.906328i	$0.361126\pi$
$12$	−3.09718	−0.894080
$13$	3.76778	1.04499	0.522497	−	0.852641i	$-0.325001\pi$
$13$	3.76778	1.04499	0.522497	+	0.852641i	$0.325001\pi$
$14$	0	0
$15$	−8.63960	−2.23074
$16$	1.00000	0.250000
$17$	−6.21609	−1.50762	−0.753812	−	0.657090i	$-0.771787\pi$
$17$	−6.21609	−1.50762	−0.753812	+	0.657090i	$0.771787\pi$
$18$	−6.59255	−1.55388
$19$	1.46546	0.336201	0.168100	−	0.985770i	$-0.446237\pi$
$19$	1.46546	0.336201	0.168100	+	0.985770i	$0.446237\pi$
$20$	2.78950	0.623752
$21$	0	0
$22$	−2.80305	−0.597612
$23$	−6.75033	−1.40754	−0.703771	−	0.710427i	$-0.748502\pi$
$23$	−6.75033	−1.40754	−0.703771	+	0.710427i	$0.748502\pi$
$24$	3.09718	0.632210
$25$	2.78132	0.556265
$26$	−3.76778	−0.738922
$27$	−11.1268	−2.14135
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	8.63960	1.57737
$31$	−8.37388	−1.50399	−0.751996	−	0.659167i	$-0.770909\pi$
$31$	−8.37388	−1.50399	−0.751996	+	0.659167i	$0.770909\pi$
$32$	−1.00000	−0.176777
$33$	−8.68156	−1.51127
$34$	6.21609	1.06605
$35$	0	0
$36$	6.59255	1.09876
$37$	2.28596	0.375809	0.187905	−	0.982187i	$-0.439830\pi$
$37$	2.28596	0.375809	0.187905	+	0.982187i	$0.439830\pi$
$38$	−1.46546	−0.237730
$39$	−11.6695	−1.86862
$40$	−2.78950	−0.441059
$41$	−8.55060	−1.33538	−0.667689	−	0.744440i	$-0.732717\pi$
$41$	−8.55060	−1.33538	−0.667689	+	0.744440i	$0.732717\pi$
$42$	0	0
$43$	7.71375	1.17634	0.588168	−	0.808739i	$-0.299849\pi$
$43$	7.71375	1.17634	0.588168	+	0.808739i	$0.299849\pi$
$44$	2.80305	0.422575
$45$	18.3899	2.74141
$46$	6.75033	0.995282
$47$	−12.2347	−1.78462	−0.892310	−	0.451423i	$-0.850916\pi$
$47$	−12.2347	−1.78462	−0.892310	+	0.451423i	$0.850916\pi$
$48$	−3.09718	−0.447040
$49$	0	0
$50$	−2.78132	−0.393339
$51$	19.2524	2.69587
$52$	3.76778	0.522497
$53$	−1.12428	−0.154431	−0.0772156	−	0.997014i	$-0.524603\pi$
$53$	−1.12428	−0.154431	−0.0772156	+	0.997014i	$0.524603\pi$
$54$	11.1268	1.51416
$55$	7.81911	1.05433
$56$	0	0
$57$	−4.53881	−0.601181
$58$	1.00000	0.131306
$59$	−3.38006	−0.440047	−0.220023	−	0.975495i	$-0.570613\pi$
$59$	−3.38006	−0.440047	−0.220023	+	0.975495i	$0.570613\pi$
$60$	−8.63960	−1.11537
$61$	−3.70947	−0.474949	−0.237474	−	0.971394i	$-0.576320\pi$
$61$	−3.70947	−0.474949	−0.237474	+	0.971394i	$0.576320\pi$
$62$	8.37388	1.06348
$63$	0	0
$64$	1.00000	0.125000
$65$	10.5102	1.30363
$66$	8.68156	1.06863
$67$	−6.57312	−0.803034	−0.401517	−	0.915852i	$-0.631517\pi$
$67$	−6.57312	−0.803034	−0.401517	+	0.915852i	$0.631517\pi$
$68$	−6.21609	−0.753812
$69$	20.9070	2.51691
$70$	0	0
$71$	8.45620	1.00357	0.501783	−	0.864994i	$-0.332678\pi$
$71$	8.45620	1.00357	0.501783	+	0.864994i	$0.332678\pi$
$72$	−6.59255	−0.776940
$73$	1.41841	0.166013	0.0830063	−	0.996549i	$-0.473548\pi$
$73$	1.41841	0.166013	0.0830063	+	0.996549i	$0.473548\pi$
$74$	−2.28596	−0.265737
$75$	−8.61427	−0.994691
$76$	1.46546	0.168100
$77$	0	0
$78$	11.6695	1.32131
$79$	−12.8464	−1.44534	−0.722668	−	0.691195i	$-0.757084\pi$
$79$	−12.8464	−1.44534	−0.722668	+	0.691195i	$0.757084\pi$
$80$	2.78950	0.311876
$81$	14.6841	1.63156
$82$	8.55060	0.944256
$83$	−7.72073	−0.847460	−0.423730	−	0.905789i	$-0.639279\pi$
$83$	−7.72073	−0.847460	−0.423730	+	0.905789i	$0.639279\pi$
$84$	0	0
$85$	−17.3398	−1.88077
$86$	−7.71375	−0.831795
$87$	3.09718	0.332053
$88$	−2.80305	−0.298806
$89$	9.99993	1.05999	0.529995	−	0.848001i	$-0.322194\pi$
$89$	9.99993	1.05999	0.529995	+	0.848001i	$0.322194\pi$
$90$	−18.3899	−1.93847
$91$	0	0
$92$	−6.75033	−0.703771
$93$	25.9354	2.68938
$94$	12.2347	1.26192
$95$	4.08792	0.419411
$96$	3.09718	0.316105
$97$	−1.13474	−0.115216	−0.0576078	−	0.998339i	$-0.518347\pi$
$97$	−1.13474	−0.115216	−0.0576078	+	0.998339i	$0.518347\pi$
$98$	0	0
$99$	18.4792	1.85723
$100$	2.78132	0.278132
$101$	13.7492	1.36810	0.684050	−	0.729435i	$-0.260217\pi$
$101$	13.7492	1.36810	0.684050	+	0.729435i	$0.260217\pi$
$102$	−19.2524	−1.90627
$103$	−3.31557	−0.326692	−0.163346	−	0.986569i	$-0.552229\pi$
$103$	−3.31557	−0.326692	−0.163346	+	0.986569i	$0.552229\pi$
$104$	−3.76778	−0.369461
$105$	0	0
$106$	1.12428	0.109199
$107$	6.61427	0.639426	0.319713	−	0.947514i	$-0.396413\pi$
$107$	6.61427	0.639426	0.319713	+	0.947514i	$0.396413\pi$
$108$	−11.1268	−1.07068
$109$	14.7237	1.41028	0.705139	−	0.709069i	$-0.250885\pi$
$109$	14.7237	1.41028	0.705139	+	0.709069i	$0.250885\pi$
$110$	−7.81911	−0.745523
$111$	−7.08003	−0.672007
$112$	0	0
$113$	−3.56133	−0.335022	−0.167511	−	0.985870i	$-0.553573\pi$
$113$	−3.56133	−0.335022	−0.167511	+	0.985870i	$0.553573\pi$
$114$	4.53881	0.425099
$115$	−18.8301	−1.75591
$116$	−1.00000	−0.0928477
$117$	24.8393	2.29639
$118$	3.38006	0.311160
$119$	0	0
$120$	8.63960	0.788684
$121$	−3.14292	−0.285720
$122$	3.70947	0.335840
$123$	26.4828	2.38787
$124$	−8.37388	−0.751996
$125$	−6.18900	−0.553561
$126$	0	0
$127$	−9.10668	−0.808087	−0.404044	−	0.914740i	$-0.632396\pi$
$127$	−9.10668	−0.808087	−0.404044	+	0.914740i	$0.632396\pi$
$128$	−1.00000	−0.0883883
$129$	−23.8909	−2.10348
$130$	−10.5102	−0.921808
$131$	−1.86931	−0.163322	−0.0816611	−	0.996660i	$-0.526023\pi$
$131$	−1.86931	−0.163322	−0.0816611	+	0.996660i	$0.526023\pi$
$132$	−8.68156	−0.755633
$133$	0	0
$134$	6.57312	0.567831
$135$	−31.0382	−2.67134
$136$	6.21609	0.533026
$137$	13.5477	1.15746	0.578730	−	0.815519i	$-0.303549\pi$
$137$	13.5477	1.15746	0.578730	+	0.815519i	$0.303549\pi$
$138$	−20.9070	−1.77972
$139$	−4.55837	−0.386636	−0.193318	−	0.981136i	$-0.561925\pi$
$139$	−4.55837	−0.386636	−0.193318	+	0.981136i	$0.561925\pi$
$140$	0	0
$141$	37.8932	3.19119
$142$	−8.45620	−0.709628
$143$	10.5613	0.883177
$144$	6.59255	0.549379
$145$	−2.78950	−0.231656
$146$	−1.41841	−0.117389
$147$	0	0
$148$	2.28596	0.187905
$149$	15.6004	1.27804	0.639019	−	0.769191i	$-0.279341\pi$
$149$	15.6004	1.27804	0.639019	+	0.769191i	$0.279341\pi$
$150$	8.61427	0.703353
$151$	−7.61559	−0.619748	−0.309874	−	0.950778i	$-0.600287\pi$
$151$	−7.61559	−0.619748	−0.309874	+	0.950778i	$0.600287\pi$
$152$	−1.46546	−0.118865
$153$	−40.9799	−3.31303
$154$	0	0
$155$	−23.3589	−1.87624
$156$	−11.6695	−0.934308
$157$	−18.7723	−1.49819	−0.749096	−	0.662462i	$-0.769512\pi$
$157$	−18.7723	−1.49819	−0.749096	+	0.662462i	$0.769512\pi$
$158$	12.8464	1.02201
$159$	3.48209	0.276148
$160$	−2.78950	−0.220530
$161$	0	0
$162$	−14.6841	−1.15369
$163$	−8.47804	−0.664051	−0.332026	−	0.943270i	$-0.607732\pi$
$163$	−8.47804	−0.664051	−0.332026	+	0.943270i	$0.607732\pi$
$164$	−8.55060	−0.667689
$165$	−24.2172	−1.88531
$166$	7.72073	0.599245
$167$	−17.6261	−1.36395	−0.681973	−	0.731378i	$-0.738878\pi$
$167$	−17.6261	−1.36395	−0.681973	+	0.731378i	$0.738878\pi$
$168$	0	0
$169$	1.19616	0.0920121
$170$	17.3398	1.32990
$171$	9.66115	0.738807
$172$	7.71375	0.588168
$173$	−18.4928	−1.40598	−0.702990	−	0.711200i	$-0.748152\pi$
$173$	−18.4928	−1.40598	−0.702990	+	0.711200i	$0.748152\pi$
$174$	−3.09718	−0.234797
$175$	0	0
$176$	2.80305	0.211288
$177$	10.4687	0.786874
$178$	−9.99993	−0.749527
$179$	−13.8700	−1.03670	−0.518348	−	0.855170i	$-0.673453\pi$
$179$	−13.8700	−1.03670	−0.518348	+	0.855170i	$0.673453\pi$
$180$	18.3899	1.37070
$181$	22.3876	1.66406	0.832030	−	0.554730i	$-0.187178\pi$
$181$	22.3876	1.66406	0.832030	+	0.554730i	$0.187178\pi$
$182$	0	0
$183$	11.4889	0.849285
$184$	6.75033	0.497641
$185$	6.37669	0.468823
$186$	−25.9354	−1.90168
$187$	−17.4240	−1.27417
$188$	−12.2347	−0.892310
$189$	0	0
$190$	−4.08792	−0.296569
$191$	−7.97033	−0.576713	−0.288356	−	0.957523i	$-0.593109\pi$
$191$	−7.97033	−0.576713	−0.288356	+	0.957523i	$0.593109\pi$
$192$	−3.09718	−0.223520
$193$	−11.4871	−0.826861	−0.413431	−	0.910536i	$-0.635670\pi$
$193$	−11.4871	−0.826861	−0.413431	+	0.910536i	$0.635670\pi$
$194$	1.13474	0.0814698
$195$	−32.5521	−2.33111
$196$	0	0
$197$	−6.59563	−0.469919	−0.234960	−	0.972005i	$-0.575496\pi$
$197$	−6.59563	−0.469919	−0.234960	+	0.972005i	$0.575496\pi$
$198$	−18.4792	−1.31326
$199$	12.3980	0.878871	0.439436	−	0.898274i	$-0.355178\pi$
$199$	12.3980	0.878871	0.439436	+	0.898274i	$0.355178\pi$
$200$	−2.78132	−0.196669
$201$	20.3582	1.43595
$202$	−13.7492	−0.967393
$203$	0	0
$204$	19.2524	1.34794
$205$	−23.8519	−1.66589
$206$	3.31557	0.231006
$207$	−44.5019	−3.09310
$208$	3.76778	0.261248
$209$	4.10777	0.284140
$210$	0	0
$211$	24.3981	1.67964	0.839818	−	0.542868i	$-0.182662\pi$
$211$	24.3981	1.67964	0.839818	+	0.542868i	$0.182662\pi$
$212$	−1.12428	−0.0772156
$213$	−26.1904	−1.79454
$214$	−6.61427	−0.452142
$215$	21.5175	1.46748
$216$	11.1268	0.757082
$217$	0	0
$218$	−14.7237	−0.997217
$219$	−4.39308	−0.296857
$220$	7.81911	0.527164
$221$	−23.4209	−1.57546
$222$	7.08003	0.475181
$223$	12.1316	0.812391	0.406196	−	0.913786i	$-0.366855\pi$
$223$	12.1316	0.812391	0.406196	+	0.913786i	$0.366855\pi$
$224$	0	0
$225$	18.3360	1.22240
$226$	3.56133	0.236896
$227$	−11.8788	−0.788424	−0.394212	−	0.919020i	$-0.628982\pi$
$227$	−11.8788	−0.788424	−0.394212	+	0.919020i	$0.628982\pi$
$228$	−4.53881	−0.300590
$229$	11.5572	0.763719	0.381859	−	0.924220i	$-0.375284\pi$
$229$	11.5572	0.763719	0.381859	+	0.924220i	$0.375284\pi$
$230$	18.8301	1.24162
$231$	0	0
$232$	1.00000	0.0656532
$233$	−16.8242	−1.10219	−0.551095	−	0.834442i	$-0.685790\pi$
$233$	−16.8242	−1.10219	−0.551095	+	0.834442i	$0.685790\pi$
$234$	−24.8393	−1.62379
$235$	−34.1288	−2.22632
$236$	−3.38006	−0.220023
$237$	39.7878	2.58449
$238$	0	0
$239$	−7.97828	−0.516072	−0.258036	−	0.966135i	$-0.583075\pi$
$239$	−7.97828	−0.516072	−0.258036	+	0.966135i	$0.583075\pi$
$240$	−8.63960	−0.557684
$241$	−12.9498	−0.834170	−0.417085	−	0.908867i	$-0.636948\pi$
$241$	−12.9498	−0.834170	−0.417085	+	0.908867i	$0.636948\pi$
$242$	3.14292	0.202035
$243$	−12.0989	−0.776145
$244$	−3.70947	−0.237474
$245$	0	0
$246$	−26.4828	−1.68848
$247$	5.52155	0.351328
$248$	8.37388	0.531742
$249$	23.9125	1.51539
$250$	6.18900	0.391427
$251$	0.655438	0.0413709	0.0206854	−	0.999786i	$-0.493415\pi$
$251$	0.655438	0.0413709	0.0206854	+	0.999786i	$0.493415\pi$
$252$	0	0
$253$	−18.9215	−1.18959
$254$	9.10668	0.571404
$255$	53.7046	3.36311
$256$	1.00000	0.0625000
$257$	−17.1143	−1.06756	−0.533781	−	0.845622i	$-0.679230\pi$
$257$	−17.1143	−1.06756	−0.533781	+	0.845622i	$0.679230\pi$
$258$	23.8909	1.48738
$259$	0	0
$260$	10.5102	0.651817
$261$	−6.59255	−0.408069
$262$	1.86931	0.115486
$263$	11.8065	0.728022	0.364011	−	0.931395i	$-0.381407\pi$
$263$	11.8065	0.728022	0.364011	+	0.931395i	$0.381407\pi$
$264$	8.68156	0.534313
$265$	−3.13617	−0.192653
$266$	0	0
$267$	−30.9716	−1.89543
$268$	−6.57312	−0.401517
$269$	−31.9259	−1.94656	−0.973279	−	0.229624i	$-0.926250\pi$
$269$	−31.9259	−1.94656	−0.973279	+	0.229624i	$0.926250\pi$
$270$	31.0382	1.88893
$271$	−5.43740	−0.330299	−0.165149	−	0.986269i	$-0.552811\pi$
$271$	−5.43740	−0.330299	−0.165149	+	0.986269i	$0.552811\pi$
$272$	−6.21609	−0.376906
$273$	0	0
$274$	−13.5477	−0.818448
$275$	7.79619	0.470128
$276$	20.9070	1.25846
$277$	14.2018	0.853301	0.426650	−	0.904417i	$-0.359693\pi$
$277$	14.2018	0.853301	0.426650	+	0.904417i	$0.359693\pi$
$278$	4.55837	0.273393
$279$	−55.2052	−3.30505
$280$	0	0
$281$	−3.11893	−0.186060	−0.0930300	−	0.995663i	$-0.529655\pi$
$281$	−3.11893	−0.186060	−0.0930300	+	0.995663i	$0.529655\pi$
$282$	−37.8932	−2.25651
$283$	9.65027	0.573649	0.286825	−	0.957983i	$-0.407400\pi$
$283$	9.65027	0.573649	0.286825	+	0.957983i	$0.407400\pi$
$284$	8.45620	0.501783
$285$	−12.6610	−0.749975
$286$	−10.5613	−0.624501
$287$	0	0
$288$	−6.59255	−0.388470
$289$	21.6398	1.27293
$290$	2.78950	0.163805
$291$	3.51451	0.206024
$292$	1.41841	0.0830063
$293$	−19.6730	−1.14931	−0.574654	−	0.818396i	$-0.694863\pi$
$293$	−19.6730	−1.14931	−0.574654	+	0.818396i	$0.694863\pi$
$294$	0	0
$295$	−9.42870	−0.548960
$296$	−2.28596	−0.132869
$297$	−31.1889	−1.80977
$298$	−15.6004	−0.903709
$299$	−25.4338	−1.47087
$300$	−8.61427	−0.497345
$301$	0	0
$302$	7.61559	0.438228
$303$	−42.5839	−2.44638
$304$	1.46546	0.0840502
$305$	−10.3476	−0.592500
$306$	40.9799	2.34267
$307$	18.2644	1.04240	0.521202	−	0.853433i	$-0.325484\pi$
$307$	18.2644	1.04240	0.521202	+	0.853433i	$0.325484\pi$
$308$	0	0
$309$	10.2689	0.584178
$310$	23.3589	1.32670
$311$	30.3270	1.71969	0.859843	−	0.510559i	$-0.170562\pi$
$311$	30.3270	1.71969	0.859843	+	0.510559i	$0.170562\pi$
$312$	11.6695	0.660656
$313$	18.6417	1.05369	0.526846	−	0.849961i	$-0.323374\pi$
$313$	18.6417	1.05369	0.526846	+	0.849961i	$0.323374\pi$
$314$	18.7723	1.05938
$315$	0	0
$316$	−12.8464	−0.722668
$317$	14.9125	0.837570	0.418785	−	0.908085i	$-0.362456\pi$
$317$	14.9125	0.837570	0.418785	+	0.908085i	$0.362456\pi$
$318$	−3.48209	−0.195266
$319$	−2.80305	−0.156941
$320$	2.78950	0.155938
$321$	−20.4856	−1.14340
$322$	0	0
$323$	−9.10946	−0.506864
$324$	14.6841	0.815782
$325$	10.4794	0.581293
$326$	8.47804	0.469555
$327$	−45.6021	−2.52180
$328$	8.55060	0.472128
$329$	0	0
$330$	24.2172	1.33311
$331$	−19.0518	−1.04718	−0.523592	−	0.851969i	$-0.675408\pi$
$331$	−19.0518	−1.04718	−0.523592	+	0.851969i	$0.675408\pi$
$332$	−7.72073	−0.423730
$333$	15.0703	0.825847
$334$	17.6261	0.964455
$335$	−18.3357	−1.00179
$336$	0	0
$337$	−14.7396	−0.802916	−0.401458	−	0.915878i	$-0.631496\pi$
$337$	−14.7396	−0.802916	−0.401458	+	0.915878i	$0.631496\pi$
$338$	−1.19616	−0.0650624
$339$	11.0301	0.599073
$340$	−17.3398	−0.940383
$341$	−23.4724	−1.27110
$342$	−9.66115	−0.522415
$343$	0	0
$344$	−7.71375	−0.415897
$345$	58.3202	3.13985
$346$	18.4928	0.994178
$347$	11.1550	0.598830	0.299415	−	0.954123i	$-0.403208\pi$
$347$	11.1550	0.598830	0.299415	+	0.954123i	$0.403208\pi$
$348$	3.09718	0.166027
$349$	31.8123	1.70288	0.851438	−	0.524456i	$-0.175731\pi$
$349$	31.8123	1.70288	0.851438	+	0.524456i	$0.175731\pi$
$350$	0	0
$351$	−41.9233	−2.23770
$352$	−2.80305	−0.149403
$353$	−1.86046	−0.0990221	−0.0495111	−	0.998774i	$-0.515766\pi$
$353$	−1.86046	−0.0990221	−0.0495111	+	0.998774i	$0.515766\pi$
$354$	−10.4687	−0.556404
$355$	23.5886	1.25195
$356$	9.99993	0.529995
$357$	0	0
$358$	13.8700	0.733054
$359$	−31.2924	−1.65155	−0.825775	−	0.564000i	$-0.809262\pi$
$359$	−31.2924	−1.65155	−0.825775	+	0.564000i	$0.809262\pi$
$360$	−18.3899	−0.969235
$361$	−16.8524	−0.886969
$362$	−22.3876	−1.17667
$363$	9.73420	0.510913
$364$	0	0
$365$	3.95666	0.207101
$366$	−11.4889	−0.600535
$367$	0.872346	0.0455361	0.0227681	−	0.999741i	$-0.492752\pi$
$367$	0.872346	0.0455361	0.0227681	+	0.999741i	$0.492752\pi$
$368$	−6.75033	−0.351885
$369$	−56.3702	−2.93452
$370$	−6.37669	−0.331508
$371$	0	0
$372$	25.9354	1.34469
$373$	11.3493	0.587644	0.293822	−	0.955860i	$-0.405073\pi$
$373$	11.3493	0.587644	0.293822	+	0.955860i	$0.405073\pi$
$374$	17.4240	0.900974
$375$	19.1685	0.989856
$376$	12.2347	0.630958
$377$	−3.76778	−0.194050
$378$	0	0
$379$	−21.3212	−1.09519	−0.547597	−	0.836742i	$-0.684457\pi$
$379$	−21.3212	−1.09519	−0.547597	+	0.836742i	$0.684457\pi$
$380$	4.08792	0.209706
$381$	28.2051	1.44499
$382$	7.97033	0.407797
$383$	−11.6863	−0.597140	−0.298570	−	0.954388i	$-0.596510\pi$
$383$	−11.6863	−0.597140	−0.298570	+	0.954388i	$0.596510\pi$
$384$	3.09718	0.158053
$385$	0	0
$386$	11.4871	0.584679
$387$	50.8533	2.58502
$388$	−1.13474	−0.0576078
$389$	8.79559	0.445954	0.222977	−	0.974824i	$-0.428422\pi$
$389$	8.79559	0.445954	0.222977	+	0.974824i	$0.428422\pi$
$390$	32.5521	1.64834
$391$	41.9607	2.12204
$392$	0	0
$393$	5.78959	0.292046
$394$	6.59563	0.332283
$395$	−35.8351	−1.80306
$396$	18.4792	0.928617
$397$	−24.4533	−1.22728	−0.613639	−	0.789587i	$-0.710295\pi$
$397$	−24.4533	−1.22728	−0.613639	+	0.789587i	$0.710295\pi$
$398$	−12.3980	−0.621456
$399$	0	0
$400$	2.78132	0.139066
$401$	−22.6628	−1.13173	−0.565863	−	0.824499i	$-0.691457\pi$
$401$	−22.6628	−1.13173	−0.565863	+	0.824499i	$0.691457\pi$
$402$	−20.3582	−1.01537
$403$	−31.5509	−1.57166
$404$	13.7492	0.684050
$405$	40.9613	2.03538
$406$	0	0
$407$	6.40765	0.317615
$408$	−19.2524	−0.953135
$409$	−1.81284	−0.0896390	−0.0448195	−	0.998995i	$-0.514271\pi$
$409$	−1.81284	−0.0896390	−0.0448195	+	0.998995i	$0.514271\pi$
$410$	23.8519	1.17796
$411$	−41.9598	−2.06972
$412$	−3.31557	−0.163346
$413$	0	0
$414$	44.5019	2.18715
$415$	−21.5370	−1.05721
$416$	−3.76778	−0.184731
$417$	14.1181	0.691367
$418$	−4.10777	−0.200917
$419$	−14.4468	−0.705773	−0.352887	−	0.935666i	$-0.614800\pi$
$419$	−14.4468	−0.705773	−0.352887	+	0.935666i	$0.614800\pi$
$420$	0	0
$421$	−13.8483	−0.674925	−0.337463	−	0.941339i	$-0.609569\pi$
$421$	−13.8483	−0.674925	−0.337463	+	0.941339i	$0.609569\pi$
$422$	−24.3981	−1.18768
$423$	−80.6581	−3.92173
$424$	1.12428	0.0545997
$425$	−17.2890	−0.838638
$426$	26.1904	1.26893
$427$	0	0
$428$	6.61427	0.319713
$429$	−32.7102	−1.57926
$430$	−21.5175	−1.03767
$431$	−12.5908	−0.606476	−0.303238	−	0.952915i	$-0.598068\pi$
$431$	−12.5908	−0.606476	−0.303238	+	0.952915i	$0.598068\pi$
$432$	−11.1268	−0.535338
$433$	9.09118	0.436894	0.218447	−	0.975849i	$-0.429901\pi$
$433$	9.09118	0.436894	0.218447	+	0.975849i	$0.429901\pi$
$434$	0	0
$435$	8.63960	0.414237
$436$	14.7237	0.705139
$437$	−9.89237	−0.473216
$438$	4.39308	0.209910
$439$	23.9511	1.14312	0.571561	−	0.820560i	$-0.306338\pi$
$439$	23.9511	1.14312	0.571561	+	0.820560i	$0.306338\pi$
$440$	−7.81911	−0.372761
$441$	0	0
$442$	23.4209	1.11402
$443$	26.2769	1.24845	0.624225	−	0.781244i	$-0.285415\pi$
$443$	26.2769	1.24845	0.624225	+	0.781244i	$0.285415\pi$
$444$	−7.08003	−0.336004
$445$	27.8948	1.32234
$446$	−12.1316	−0.574448
$447$	−48.3174	−2.28534
$448$	0	0
$449$	3.06619	0.144703	0.0723513	−	0.997379i	$-0.476950\pi$
$449$	3.06619	0.144703	0.0723513	+	0.997379i	$0.476950\pi$
$450$	−18.3360	−0.864368
$451$	−23.9677	−1.12860
$452$	−3.56133	−0.167511
$453$	23.5869	1.10821
$454$	11.8788	0.557500
$455$	0	0
$456$	4.53881	0.212549
$457$	15.6802	0.733488	0.366744	−	0.930322i	$-0.380473\pi$
$457$	15.6802	0.733488	0.366744	+	0.930322i	$0.380473\pi$
$458$	−11.5572	−0.540031
$459$	69.1652	3.22835
$460$	−18.8301	−0.877957
$461$	1.66602	0.0775941	0.0387971	−	0.999247i	$-0.487647\pi$
$461$	1.66602	0.0775941	0.0387971	+	0.999247i	$0.487647\pi$
$462$	0	0
$463$	17.2509	0.801718	0.400859	−	0.916140i	$-0.368712\pi$
$463$	17.2509	0.801718	0.400859	+	0.916140i	$0.368712\pi$
$464$	−1.00000	−0.0464238
$465$	72.3470	3.35501
$466$	16.8242	0.779366
$467$	11.1793	0.517317	0.258659	−	0.965969i	$-0.416720\pi$
$467$	11.1793	0.517317	0.258659	+	0.965969i	$0.416720\pi$
$468$	24.8393	1.14820
$469$	0	0
$470$	34.1288	1.57425
$471$	58.1412	2.67901
$472$	3.38006	0.155580
$473$	21.6220	0.994181
$474$	−39.7878	−1.82751
$475$	4.07593	0.187017
$476$	0	0
$477$	−7.41184	−0.339365
$478$	7.97828	0.364918
$479$	13.0826	0.597760	0.298880	−	0.954291i	$-0.403387\pi$
$479$	13.0826	0.597760	0.298880	+	0.954291i	$0.403387\pi$
$480$	8.63960	0.394342
$481$	8.61298	0.392718
$482$	12.9498	0.589847
$483$	0	0
$484$	−3.14292	−0.142860
$485$	−3.16537	−0.143732
$486$	12.0989	0.548818
$487$	6.75769	0.306220	0.153110	−	0.988209i	$-0.451071\pi$
$487$	6.75769	0.306220	0.153110	+	0.988209i	$0.451071\pi$
$488$	3.70947	0.167920
$489$	26.2580	1.18743
$490$	0	0
$491$	9.53271	0.430205	0.215103	−	0.976591i	$-0.430991\pi$
$491$	9.53271	0.430205	0.215103	+	0.976591i	$0.430991\pi$
$492$	26.4828	1.19394
$493$	6.21609	0.279959
$494$	−5.52155	−0.248426
$495$	51.5479	2.31690
$496$	−8.37388	−0.375998
$497$	0	0
$498$	−23.9125	−1.07155
$499$	−21.0060	−0.940358	−0.470179	−	0.882571i	$-0.655811\pi$
$499$	−21.0060	−0.940358	−0.470179	+	0.882571i	$0.655811\pi$
$500$	−6.18900	−0.276781
$501$	54.5912	2.43895
$502$	−0.655438	−0.0292536
$503$	43.2476	1.92831	0.964157	−	0.265333i	$-0.0854820\pi$
$503$	43.2476	1.92831	0.964157	+	0.265333i	$0.0854820\pi$
$504$	0	0
$505$	38.3536	1.70671
$506$	18.9215	0.841164
$507$	−3.70472	−0.164532
$508$	−9.10668	−0.404044
$509$	8.51537	0.377437	0.188719	−	0.982031i	$-0.439567\pi$
$509$	8.51537	0.377437	0.188719	+	0.982031i	$0.439567\pi$
$510$	−53.7046	−2.37808
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−16.3059	−0.719924
$514$	17.1143	0.754881
$515$	−9.24878	−0.407550
$516$	−23.8909	−1.05174
$517$	−34.2946	−1.50827
$518$	0	0
$519$	57.2756	2.51412
$520$	−10.5102	−0.460904
$521$	16.6592	0.729855	0.364927	−	0.931036i	$-0.381094\pi$
$521$	16.6592	0.729855	0.364927	+	0.931036i	$0.381094\pi$
$522$	6.59255	0.288548
$523$	−5.33917	−0.233466	−0.116733	−	0.993163i	$-0.537242\pi$
$523$	−5.33917	−0.233466	−0.116733	+	0.993163i	$0.537242\pi$
$524$	−1.86931	−0.0816611
$525$	0	0
$526$	−11.8065	−0.514789
$527$	52.0528	2.26745
$528$	−8.68156	−0.377816
$529$	22.5670	0.981174
$530$	3.13617	0.136227
$531$	−22.2832	−0.967010
$532$	0	0
$533$	−32.2168	−1.39546
$534$	30.9716	1.34027
$535$	18.4505	0.797686
$536$	6.57312	0.283915
$537$	42.9581	1.85378
$538$	31.9259	1.37643
$539$	0	0
$540$	−31.0382	−1.33567
$541$	−15.5363	−0.667956	−0.333978	−	0.942581i	$-0.608391\pi$
$541$	−15.5363	−0.667956	−0.333978	+	0.942581i	$0.608391\pi$
$542$	5.43740	0.233556
$543$	−69.3387	−2.97561
$544$	6.21609	0.266513
$545$	41.0719	1.75933
$546$	0	0
$547$	−37.2836	−1.59413	−0.797067	−	0.603891i	$-0.793616\pi$
$547$	−37.2836	−1.59413	−0.797067	+	0.603891i	$0.793616\pi$
$548$	13.5477	0.578730
$549$	−24.4549	−1.04371
$550$	−7.79619	−0.332431
$551$	−1.46546	−0.0624309
$552$	−20.9070	−0.889862
$553$	0	0
$554$	−14.2018	−0.603375
$555$	−19.7498	−0.838331
$556$	−4.55837	−0.193318
$557$	5.64481	0.239178	0.119589	−	0.992823i	$-0.461842\pi$
$557$	5.64481	0.239178	0.119589	+	0.992823i	$0.461842\pi$
$558$	55.2052	2.33702
$559$	29.0637	1.22926
$560$	0	0
$561$	53.9654	2.27842
$562$	3.11893	0.131564
$563$	−17.3517	−0.731286	−0.365643	−	0.930755i	$-0.619151\pi$
$563$	−17.3517	−0.731286	−0.365643	+	0.930755i	$0.619151\pi$
$564$	37.8932	1.59559
$565$	−9.93435	−0.417941
$566$	−9.65027	−0.405631
$567$	0	0
$568$	−8.45620	−0.354814
$569$	7.88927	0.330735	0.165368	−	0.986232i	$-0.447119\pi$
$569$	7.88927	0.330735	0.165368	+	0.986232i	$0.447119\pi$
$570$	12.6610	0.530312
$571$	15.5879	0.652332	0.326166	−	0.945313i	$-0.394243\pi$
$571$	15.5879	0.652332	0.326166	+	0.945313i	$0.394243\pi$
$572$	10.5613	0.441589
$573$	24.6856	1.03125
$574$	0	0
$575$	−18.7749	−0.782966
$576$	6.59255	0.274690
$577$	28.9405	1.20481	0.602405	−	0.798191i	$-0.294209\pi$
$577$	28.9405	1.20481	0.602405	+	0.798191i	$0.294209\pi$
$578$	−21.6398	−0.900097
$579$	35.5777	1.47856
$580$	−2.78950	−0.115828
$581$	0	0
$582$	−3.51451	−0.145681
$583$	−3.15140	−0.130518
$584$	−1.41841	−0.0586943
$585$	69.2892	2.86476
$586$	19.6730	0.812684
$587$	39.0368	1.61122	0.805611	−	0.592444i	$-0.201837\pi$
$587$	39.0368	1.61122	0.805611	+	0.592444i	$0.201837\pi$
$588$	0	0
$589$	−12.2716	−0.505643
$590$	9.42870	0.388173
$591$	20.4279	0.840291
$592$	2.28596	0.0939523
$593$	−29.2986	−1.20315	−0.601576	−	0.798816i	$-0.705460\pi$
$593$	−29.2986	−1.20315	−0.601576	+	0.798816i	$0.705460\pi$
$594$	31.1889	1.27970
$595$	0	0
$596$	15.6004	0.639019
$597$	−38.3989	−1.57156
$598$	25.4338	1.04006
$599$	−4.87633	−0.199241	−0.0996207	−	0.995025i	$-0.531763\pi$
$599$	−4.87633	−0.199241	−0.0996207	+	0.995025i	$0.531763\pi$
$600$	8.61427	0.351676
$601$	13.4240	0.547578	0.273789	−	0.961790i	$-0.411723\pi$
$601$	13.4240	0.547578	0.273789	+	0.961790i	$0.411723\pi$
$602$	0	0
$603$	−43.3336	−1.76468
$604$	−7.61559	−0.309874
$605$	−8.76719	−0.356437
$606$	42.5839	1.72985
$607$	27.3793	1.11129	0.555645	−	0.831420i	$-0.312471\pi$
$607$	27.3793	1.11129	0.555645	+	0.831420i	$0.312471\pi$
$608$	−1.46546	−0.0594324
$609$	0	0
$610$	10.3476	0.418961
$611$	−46.0978	−1.86492
$612$	−40.9799	−1.65651
$613$	−10.0025	−0.403998	−0.201999	−	0.979386i	$-0.564744\pi$
$613$	−10.0025	−0.403998	−0.201999	+	0.979386i	$0.564744\pi$
$614$	−18.2644	−0.737091
$615$	73.8738	2.97888
$616$	0	0
$617$	−27.0833	−1.09033	−0.545167	−	0.838327i	$-0.683534\pi$
$617$	−27.0833	−1.09033	−0.545167	+	0.838327i	$0.683534\pi$
$618$	−10.2689	−0.413076
$619$	30.5470	1.22779	0.613894	−	0.789388i	$-0.289602\pi$
$619$	30.5470	1.22779	0.613894	+	0.789388i	$0.289602\pi$
$620$	−23.3589	−0.938118
$621$	75.1096	3.01404
$622$	−30.3270	−1.21600
$623$	0	0
$624$	−11.6695	−0.467154
$625$	−31.1709	−1.24683
$626$	−18.6417	−0.745073
$627$	−12.7225	−0.508088
$628$	−18.7723	−0.749096
$629$	−14.2097	−0.566579
$630$	0	0
$631$	15.0961	0.600965	0.300483	−	0.953787i	$-0.402852\pi$
$631$	15.0961	0.600965	0.300483	+	0.953787i	$0.402852\pi$
$632$	12.8464	0.511004
$633$	−75.5655	−3.00346
$634$	−14.9125	−0.592251
$635$	−25.4031	−1.00809
$636$	3.48209	0.138074
$637$	0	0
$638$	2.80305	0.110974
$639$	55.7479	2.20535
$640$	−2.78950	−0.110265
$641$	−47.6686	−1.88280	−0.941398	−	0.337297i	$-0.890487\pi$
$641$	−47.6686	−1.88280	−0.941398	+	0.337297i	$0.890487\pi$
$642$	20.4856	0.808503
$643$	−22.5917	−0.890929	−0.445465	−	0.895299i	$-0.646962\pi$
$643$	−22.5917	−0.890929	−0.445465	+	0.895299i	$0.646962\pi$
$644$	0	0
$645$	−66.6437	−2.62409
$646$	9.10946	0.358407
$647$	40.6976	1.59999	0.799994	−	0.600008i	$-0.204836\pi$
$647$	40.6976	1.59999	0.799994	+	0.600008i	$0.204836\pi$
$648$	−14.6841	−0.576845
$649$	−9.47448	−0.371906
$650$	−10.4794	−0.411036
$651$	0	0
$652$	−8.47804	−0.332026
$653$	−11.8914	−0.465346	−0.232673	−	0.972555i	$-0.574747\pi$
$653$	−11.8914	−0.465346	−0.232673	+	0.972555i	$0.574747\pi$
$654$	45.6021	1.78318
$655$	−5.21444	−0.203745
$656$	−8.55060	−0.333845
$657$	9.35095	0.364815
$658$	0	0
$659$	36.2919	1.41373	0.706866	−	0.707348i	$-0.250108\pi$
$659$	36.2919	1.41373	0.706866	+	0.707348i	$0.250108\pi$
$660$	−24.2172	−0.942654
$661$	−23.6776	−0.920952	−0.460476	−	0.887672i	$-0.652321\pi$
$661$	−23.6776	−0.920952	−0.460476	+	0.887672i	$0.652321\pi$
$662$	19.0518	0.740470
$663$	72.5387	2.81717
$664$	7.72073	0.299622
$665$	0	0
$666$	−15.0703	−0.583962
$667$	6.75033	0.261374
$668$	−17.6261	−0.681973
$669$	−37.5738	−1.45269
$670$	18.3357	0.708371
$671$	−10.3978	−0.401403
$672$	0	0
$673$	−32.1605	−1.23970	−0.619848	−	0.784722i	$-0.712806\pi$
$673$	−32.1605	−1.23970	−0.619848	+	0.784722i	$0.712806\pi$
$674$	14.7396	0.567747
$675$	−30.9472	−1.19116
$676$	1.19616	0.0460060
$677$	−6.02635	−0.231611	−0.115806	−	0.993272i	$-0.536945\pi$
$677$	−6.02635	−0.231611	−0.115806	+	0.993272i	$0.536945\pi$
$678$	−11.0301	−0.423609
$679$	0	0
$680$	17.3398	0.664951
$681$	36.7908	1.40983
$682$	23.4724	0.898804
$683$	−16.1649	−0.618534	−0.309267	−	0.950975i	$-0.600084\pi$
$683$	−16.1649	−0.618534	−0.309267	+	0.950975i	$0.600084\pi$
$684$	9.66115	0.369403
$685$	37.7914	1.44394
$686$	0	0
$687$	−35.7947	−1.36565
$688$	7.71375	0.294084
$689$	−4.23602	−0.161380
$690$	−58.3202	−2.22021
$691$	−6.25698	−0.238027	−0.119013	−	0.992893i	$-0.537973\pi$
$691$	−6.25698	−0.238027	−0.119013	+	0.992893i	$0.537973\pi$
$692$	−18.4928	−0.702990
$693$	0	0
$694$	−11.1550	−0.423437
$695$	−12.7156	−0.482330
$696$	−3.09718	−0.117398
$697$	53.1513	2.01325
$698$	−31.8123	−1.20411
$699$	52.1077	1.97089
$700$	0	0
$701$	−32.7051	−1.23525	−0.617627	−	0.786471i	$-0.711906\pi$
$701$	−32.7051	−1.23525	−0.617627	+	0.786471i	$0.711906\pi$
$702$	41.9233	1.58229
$703$	3.34999	0.126347
$704$	2.80305	0.105644
$705$	105.703	3.98102
$706$	1.86046	0.0700192
$707$	0	0
$708$	10.4687	0.393437
$709$	7.02322	0.263763	0.131881	−	0.991266i	$-0.457898\pi$
$709$	7.02322	0.263763	0.131881	+	0.991266i	$0.457898\pi$
$710$	−23.5886	−0.885264
$711$	−84.6907	−3.17615
$712$	−9.99993	−0.374763
$713$	56.5265	2.11693
$714$	0	0
$715$	29.4607	1.10177
$716$	−13.8700	−0.518348
$717$	24.7102	0.922819
$718$	31.2924	1.16782
$719$	−2.25327	−0.0840326	−0.0420163	−	0.999117i	$-0.513378\pi$
$719$	−2.25327	−0.0840326	−0.0420163	+	0.999117i	$0.513378\pi$
$720$	18.3899	0.685352
$721$	0	0
$722$	16.8524	0.627182
$723$	40.1079	1.49163
$724$	22.3876	0.832030
$725$	−2.78132	−0.103296
$726$	−9.73420	−0.361270
$727$	−34.0513	−1.26289	−0.631447	−	0.775419i	$-0.717539\pi$
$727$	−34.0513	−1.26289	−0.631447	+	0.775419i	$0.717539\pi$
$728$	0	0
$729$	−6.57968	−0.243692
$730$	−3.95666	−0.146443
$731$	−47.9494	−1.77347
$732$	11.4889	0.424642
$733$	11.3601	0.419595	0.209797	−	0.977745i	$-0.432720\pi$
$733$	11.3601	0.419595	0.209797	+	0.977745i	$0.432720\pi$
$734$	−0.872346	−0.0321989
$735$	0	0
$736$	6.75033	0.248821
$737$	−18.4248	−0.678685
$738$	56.3702	2.07502
$739$	11.8858	0.437227	0.218614	−	0.975811i	$-0.429847\pi$
$739$	11.8858	0.437227	0.218614	+	0.975811i	$0.429847\pi$
$740$	6.37669	0.234412
$741$	−17.1012	−0.628230
$742$	0	0
$743$	−26.1441	−0.959133	−0.479566	−	0.877506i	$-0.659206\pi$
$743$	−26.1441	−0.959133	−0.479566	+	0.877506i	$0.659206\pi$
$744$	−25.9354	−0.950839
$745$	43.5175	1.59436
$746$	−11.3493	−0.415527
$747$	−50.8993	−1.86231
$748$	−17.4240	−0.637085
$749$	0	0
$750$	−19.1685	−0.699934
$751$	−0.657023	−0.0239751	−0.0119875	−	0.999928i	$-0.503816\pi$
$751$	−0.657023	−0.0239751	−0.0119875	+	0.999928i	$0.503816\pi$
$752$	−12.2347	−0.446155
$753$	−2.03001	−0.0739778
$754$	3.76778	0.137214
$755$	−21.2437	−0.773138
$756$	0	0
$757$	30.6633	1.11448	0.557239	−	0.830352i	$-0.311861\pi$
$757$	30.6633	1.11448	0.557239	+	0.830352i	$0.311861\pi$
$758$	21.3212	0.774419
$759$	58.6034	2.12717
$760$	−4.08792	−0.148284
$761$	−11.4045	−0.413411	−0.206706	−	0.978403i	$-0.566274\pi$
$761$	−11.4045	−0.413411	−0.206706	+	0.978403i	$0.566274\pi$
$762$	−28.2051	−1.02176
$763$	0	0
$764$	−7.97033	−0.288356
$765$	−114.314	−4.13302
$766$	11.6863	0.422241
$767$	−12.7353	−0.459846
$768$	−3.09718	−0.111760
$769$	−26.3916	−0.951704	−0.475852	−	0.879525i	$-0.657860\pi$
$769$	−26.3916	−0.951704	−0.475852	+	0.879525i	$0.657860\pi$
$770$	0	0
$771$	53.0063	1.90897
$772$	−11.4871	−0.413431
$773$	−36.2068	−1.30227	−0.651134	−	0.758962i	$-0.725707\pi$
$773$	−36.2068	−1.30227	−0.651134	+	0.758962i	$0.725707\pi$
$774$	−50.8533	−1.82788
$775$	−23.2905	−0.836618
$776$	1.13474	0.0407349
$777$	0	0
$778$	−8.79559	−0.315337
$779$	−12.5306	−0.448955
$780$	−32.5521	−1.16555
$781$	23.7031	0.848165
$782$	−41.9607	−1.50051
$783$	11.1268	0.397639
$784$	0	0
$785$	−52.3653	−1.86900
$786$	−5.78959	−0.206508
$787$	18.9730	0.676314	0.338157	−	0.941090i	$-0.390196\pi$
$787$	18.9730	0.676314	0.338157	+	0.941090i	$0.390196\pi$
$788$	−6.59563	−0.234960
$789$	−36.5670	−1.30182
$790$	35.8351	1.27496
$791$	0	0
$792$	−18.4792	−0.656631
$793$	−13.9765	−0.496319
$794$	24.4533	0.867817
$795$	9.71330	0.344495
$796$	12.3980	0.439436
$797$	−2.45142	−0.0868339	−0.0434169	−	0.999057i	$-0.513824\pi$
$797$	−2.45142	−0.0868339	−0.0434169	+	0.999057i	$0.513824\pi$
$798$	0	0
$799$	76.0523	2.69054
$800$	−2.78132	−0.0983347
$801$	65.9251	2.32935
$802$	22.6628	0.800251
$803$	3.97588	0.140306
$804$	20.3582	0.717977
$805$	0	0
$806$	31.5509	1.11133
$807$	98.8805	3.48076
$808$	−13.7492	−0.483697
$809$	−42.7136	−1.50173	−0.750866	−	0.660455i	$-0.770363\pi$
$809$	−42.7136	−1.50173	−0.750866	+	0.660455i	$0.770363\pi$
$810$	−40.9613	−1.43923
$811$	−13.4951	−0.473878	−0.236939	−	0.971524i	$-0.576144\pi$
$811$	−13.4951	−0.473878	−0.236939	+	0.971524i	$0.576144\pi$
$812$	0	0
$813$	16.8406	0.590627
$814$	−6.40765	−0.224588
$815$	−23.6495	−0.828406
$816$	19.2524	0.673968
$817$	11.3042	0.395485
$818$	1.81284	0.0633844
$819$	0	0
$820$	−23.8519	−0.832945
$821$	5.48451	0.191411	0.0957054	−	0.995410i	$-0.469489\pi$
$821$	5.48451	0.191411	0.0957054	+	0.995410i	$0.469489\pi$
$822$	41.9598	1.46352
$823$	2.39007	0.0833124	0.0416562	−	0.999132i	$-0.486737\pi$
$823$	2.39007	0.0833124	0.0416562	+	0.999132i	$0.486737\pi$
$824$	3.31557	0.115503
$825$	−24.1462	−0.840664
$826$	0	0
$827$	−17.6211	−0.612745	−0.306372	−	0.951912i	$-0.599115\pi$
$827$	−17.6211	−0.612745	−0.306372	+	0.951912i	$0.599115\pi$
$828$	−44.5019	−1.54655
$829$	−3.99053	−0.138597	−0.0692984	−	0.997596i	$-0.522076\pi$
$829$	−3.99053	−0.138597	−0.0692984	+	0.997596i	$0.522076\pi$
$830$	21.5370	0.747560
$831$	−43.9855	−1.52584
$832$	3.76778	0.130624
$833$	0	0
$834$	−14.1181	−0.488870
$835$	−49.1679	−1.70153
$836$	4.10777	0.142070
$837$	93.1744	3.22058
$838$	14.4468	0.499057
$839$	−52.4049	−1.80922	−0.904610	−	0.426241i	$-0.859838\pi$
$839$	−52.4049	−1.80922	−0.904610	+	0.426241i	$0.859838\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	13.8483	0.477244
$843$	9.65991	0.332705
$844$	24.3981	0.839818
$845$	3.33668	0.114785
$846$	80.6581	2.77308
$847$	0	0
$848$	−1.12428	−0.0386078
$849$	−29.8887	−1.02578
$850$	17.2890	0.593007
$851$	−15.4310	−0.528967
$852$	−26.1904	−0.897268
$853$	−23.3084	−0.798064	−0.399032	−	0.916937i	$-0.630654\pi$
$853$	−23.3084	−0.798064	−0.399032	+	0.916937i	$0.630654\pi$
$854$	0	0
$855$	26.9498	0.921664
$856$	−6.61427	−0.226071
$857$	42.7990	1.46199	0.730993	−	0.682385i	$-0.239057\pi$
$857$	42.7990	1.46199	0.730993	+	0.682385i	$0.239057\pi$
$858$	32.7102	1.11671
$859$	−28.9445	−0.987575	−0.493788	−	0.869583i	$-0.664388\pi$
$859$	−28.9445	−0.987575	−0.493788	+	0.869583i	$0.664388\pi$
$860$	21.5175	0.733741
$861$	0	0
$862$	12.5908	0.428843
$863$	−53.6213	−1.82529	−0.912644	−	0.408755i	$-0.865963\pi$
$863$	−53.6213	−1.82529	−0.912644	+	0.408755i	$0.865963\pi$
$864$	11.1268	0.378541
$865$	−51.5857	−1.75397
$866$	−9.09118	−0.308931
$867$	−67.0225	−2.27620
$868$	0	0
$869$	−36.0092	−1.22153
$870$	−8.63960	−0.292910
$871$	−24.7660	−0.839165
$872$	−14.7237	−0.498609
$873$	−7.48085	−0.253188
$874$	9.89237	0.334615
$875$	0	0
$876$	−4.39308	−0.148429
$877$	28.6402	0.967110	0.483555	−	0.875314i	$-0.339345\pi$
$877$	28.6402	0.967110	0.483555	+	0.875314i	$0.339345\pi$
$878$	−23.9511	−0.808309
$879$	60.9309	2.05515
$880$	7.81911	0.263582
$881$	−13.6171	−0.458773	−0.229386	−	0.973335i	$-0.573672\pi$
$881$	−13.6171	−0.458773	−0.229386	+	0.973335i	$0.573672\pi$
$882$	0	0
$883$	−38.8344	−1.30688	−0.653441	−	0.756978i	$-0.726675\pi$
$883$	−38.8344	−1.30688	−0.653441	+	0.756978i	$0.726675\pi$
$884$	−23.4209	−0.787729
$885$	29.2024	0.981628
$886$	−26.2769	−0.882788
$887$	33.4467	1.12303	0.561515	−	0.827467i	$-0.310219\pi$
$887$	33.4467	1.12303	0.561515	+	0.827467i	$0.310219\pi$
$888$	7.08003	0.237590
$889$	0	0
$890$	−27.8948	−0.935037
$891$	41.1602	1.37892
$892$	12.1316	0.406196
$893$	−17.9296	−0.599990
$894$	48.3174	1.61598
$895$	−38.6905	−1.29328
$896$	0	0
$897$	78.7731	2.63016
$898$	−3.06619	−0.102320
$899$	8.37388	0.279284
$900$	18.3360	0.611201
$901$	6.98860	0.232824
$902$	23.9677	0.798038
$903$	0	0
$904$	3.56133	0.118448
$905$	62.4504	2.07592
$906$	−23.5869	−0.783622
$907$	−6.20968	−0.206189	−0.103095	−	0.994672i	$-0.532874\pi$
$907$	−6.20968	−0.206189	−0.103095	+	0.994672i	$0.532874\pi$
$908$	−11.8788	−0.394212
$909$	90.6426	3.00643
$910$	0	0
$911$	−55.9816	−1.85475	−0.927377	−	0.374127i	$-0.877942\pi$
$911$	−55.9816	−1.85475	−0.927377	+	0.374127i	$0.877942\pi$
$912$	−4.53881	−0.150295
$913$	−21.6416	−0.716231
$914$	−15.6802	−0.518654
$915$	32.0483	1.05949
$916$	11.5572	0.381859
$917$	0	0
$918$	−69.1652	−2.28279
$919$	−33.8594	−1.11692	−0.558460	−	0.829532i	$-0.688607\pi$
$919$	−33.8594	−1.11692	−0.558460	+	0.829532i	$0.688607\pi$
$920$	18.8301	0.620809
$921$	−56.5682	−1.86399
$922$	−1.66602	−0.0548673
$923$	31.8611	1.04872
$924$	0	0
$925$	6.35799	0.209049
$926$	−17.2509	−0.566900
$927$	−21.8580	−0.717912
$928$	1.00000	0.0328266
$929$	−59.7885	−1.96160	−0.980798	−	0.195025i	$-0.937521\pi$
$929$	−59.7885	−1.96160	−0.980798	+	0.195025i	$0.937521\pi$
$930$	−72.3470	−2.37235
$931$	0	0
$932$	−16.8242	−0.551095
$933$	−93.9283	−3.07507
$934$	−11.1793	−0.365799
$935$	−48.6043	−1.58953
$936$	−24.8393	−0.811897
$937$	27.6720	0.904004	0.452002	−	0.892017i	$-0.350710\pi$
$937$	27.6720	0.904004	0.452002	+	0.892017i	$0.350710\pi$
$938$	0	0
$939$	−57.7368	−1.88417
$940$	−34.1288	−1.11316
$941$	−20.2724	−0.660862	−0.330431	−	0.943830i	$-0.607194\pi$
$941$	−20.2724	−0.660862	−0.330431	+	0.943830i	$0.607194\pi$
$942$	−58.1412	−1.89434
$943$	57.7194	1.87960
$944$	−3.38006	−0.110012
$945$	0	0
$946$	−21.6220	−0.702992
$947$	40.4969	1.31597	0.657986	−	0.753030i	$-0.271409\pi$
$947$	40.4969	1.31597	0.657986	+	0.753030i	$0.271409\pi$
$948$	39.7878	1.29225
$949$	5.34426	0.173482
$950$	−4.07593	−0.132241
$951$	−46.1868	−1.49771
$952$	0	0
$953$	30.5977	0.991156	0.495578	−	0.868564i	$-0.334956\pi$
$953$	30.5977	0.991156	0.495578	+	0.868564i	$0.334956\pi$
$954$	7.41184	0.239967
$955$	−22.2332	−0.719451
$956$	−7.97828	−0.258036
$957$	8.68156	0.280635
$958$	−13.0826	−0.422680
$959$	0	0
$960$	−8.63960	−0.278842
$961$	39.1218	1.26199
$962$	−8.61298	−0.277694
$963$	43.6049	1.40515
$964$	−12.9498	−0.417085
$965$	−32.0434	−1.03151
$966$	0	0
$967$	19.5129	0.627491	0.313746	−	0.949507i	$-0.398416\pi$
$967$	19.5129	0.627491	0.313746	+	0.949507i	$0.398416\pi$
$968$	3.14292	0.101017
$969$	28.2137	0.906354
$970$	3.16537	0.101634
$971$	27.5801	0.885087	0.442543	−	0.896747i	$-0.354076\pi$
$971$	27.5801	0.885087	0.442543	+	0.896747i	$0.354076\pi$
$972$	−12.0989	−0.388073
$973$	0	0
$974$	−6.75769	−0.216530
$975$	−32.4567	−1.03945
$976$	−3.70947	−0.118737
$977$	−19.7213	−0.630940	−0.315470	−	0.948936i	$-0.602162\pi$
$977$	−19.7213	−0.630940	−0.315470	+	0.948936i	$0.602162\pi$
$978$	−26.2580	−0.839640
$979$	28.0303	0.895852
$980$	0	0
$981$	97.0670	3.09911
$982$	−9.53271	−0.304201
$983$	−8.91791	−0.284437	−0.142219	−	0.989835i	$-0.545424\pi$
$983$	−8.91791	−0.284437	−0.142219	+	0.989835i	$0.545424\pi$
$984$	−26.4828	−0.844240
$985$	−18.3985	−0.586226
$986$	−6.21609	−0.197961
$987$	0	0
$988$	5.52155	0.175664
$989$	−52.0704	−1.65574
$990$	−51.5479	−1.63830
$991$	55.1794	1.75283	0.876416	−	0.481555i	$-0.159928\pi$
$991$	55.1794	1.75283	0.876416	+	0.481555i	$0.159928\pi$
$992$	8.37388	0.265871
$993$	59.0070	1.87253
$994$	0	0
$995$	34.5843	1.09639
$996$	23.9125	0.757697
$997$	−45.0444	−1.42657	−0.713285	−	0.700874i	$-0.752793\pi$
$997$	−45.0444	−1.42657	−0.713285	+	0.700874i	$0.752793\pi$
$998$	21.0060	0.664933
$999$	−25.4354	−0.804740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.t.1.1		5
7.2	even	3		406.2.e.d.291.5	yes	10
7.4	even	3		406.2.e.d.233.5	✓	10
7.6	odd	2		2842.2.a.u.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.d.233.5	✓	10	7.4	even	3
406.2.e.d.291.5	yes	10	7.2	even	3
2842.2.a.t.1.1		5	1.1	even	1	trivial
2842.2.a.u.1.5		5	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.09718 q^{3} +1.00000 q^{4} +2.78950 q^{5} +3.09718 q^{6} -1.00000 q^{8} +6.59255 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.09718 q^{3} +1.00000 q^{4} +2.78950 q^{5} +3.09718 q^{6} -1.00000 q^{8} +6.59255 q^{9} -2.78950 q^{10} +2.80305 q^{11} -3.09718 q^{12} +3.76778 q^{13} -8.63960 q^{15} +1.00000 q^{16} -6.21609 q^{17} -6.59255 q^{18} +1.46546 q^{19} +2.78950 q^{20} -2.80305 q^{22} -6.75033 q^{23} +3.09718 q^{24} +2.78132 q^{25} -3.76778 q^{26} -11.1268 q^{27} -1.00000 q^{29} +8.63960 q^{30} -8.37388 q^{31} -1.00000 q^{32} -8.68156 q^{33} +6.21609 q^{34} +6.59255 q^{36} +2.28596 q^{37} -1.46546 q^{38} -11.6695 q^{39} -2.78950 q^{40} -8.55060 q^{41} +7.71375 q^{43} +2.80305 q^{44} +18.3899 q^{45} +6.75033 q^{46} -12.2347 q^{47} -3.09718 q^{48} -2.78132 q^{50} +19.2524 q^{51} +3.76778 q^{52} -1.12428 q^{53} +11.1268 q^{54} +7.81911 q^{55} -4.53881 q^{57} +1.00000 q^{58} -3.38006 q^{59} -8.63960 q^{60} -3.70947 q^{61} +8.37388 q^{62} +1.00000 q^{64} +10.5102 q^{65} +8.68156 q^{66} -6.57312 q^{67} -6.21609 q^{68} +20.9070 q^{69} +8.45620 q^{71} -6.59255 q^{72} +1.41841 q^{73} -2.28596 q^{74} -8.61427 q^{75} +1.46546 q^{76} +11.6695 q^{78} -12.8464 q^{79} +2.78950 q^{80} +14.6841 q^{81} +8.55060 q^{82} -7.72073 q^{83} -17.3398 q^{85} -7.71375 q^{86} +3.09718 q^{87} -2.80305 q^{88} +9.99993 q^{89} -18.3899 q^{90} -6.75033 q^{92} +25.9354 q^{93} +12.2347 q^{94} +4.08792 q^{95} +3.09718 q^{96} -1.13474 q^{97} +18.4792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * q^99

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