LMFDB - Embedded newform 2842.2.a.r.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:	$4$
Coefficient field:	4.4.11348.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 5x^{2} + x + 2 $ x^4 - x^3 - 5*x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.589216$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.39434 q^{3} +1.00000 q^{4} +2.65282 q^{5} -3.39434 q^{6} +1.00000 q^{8} +8.52156 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.39434 q^{3} +1.00000 q^{4} +2.65282 q^{5} -3.39434 q^{6} +1.00000 q^{8} +8.52156 q^{9} +2.65282 q^{10} -1.39434 q^{11} -3.39434 q^{12} +7.08465 q^{13} -9.00460 q^{15} +1.00000 q^{16} +0.741518 q^{17} +8.52156 q^{18} +1.17843 q^{19} +2.65282 q^{20} -1.39434 q^{22} +3.17843 q^{23} -3.39434 q^{24} +2.03748 q^{25} +7.08465 q^{26} -18.7421 q^{27} +1.00000 q^{29} -9.00460 q^{30} +7.31429 q^{31} +1.00000 q^{32} +4.73288 q^{33} +0.741518 q^{34} +8.52156 q^{36} +1.61025 q^{37} +1.17843 q^{38} -24.0477 q^{39} +2.65282 q^{40} -11.3528 q^{41} -7.52156 q^{43} -1.39434 q^{44} +22.6062 q^{45} +3.17843 q^{46} +4.95743 q^{47} -3.39434 q^{48} +2.03748 q^{50} -2.51696 q^{51} +7.08465 q^{52} +1.26712 q^{53} -18.7421 q^{54} -3.69895 q^{55} -4.00000 q^{57} +1.00000 q^{58} -4.51187 q^{59} -9.00460 q^{60} -0.915903 q^{61} +7.31429 q^{62} +1.00000 q^{64} +18.7943 q^{65} +4.73288 q^{66} -11.6523 q^{67} +0.741518 q^{68} -10.7887 q^{69} +13.5078 q^{71} +8.52156 q^{72} -0.995954 q^{73} +1.61025 q^{74} -6.91590 q^{75} +1.17843 q^{76} -24.0477 q^{78} -3.68166 q^{79} +2.65282 q^{80} +38.0523 q^{81} -11.3528 q^{82} +11.7324 q^{83} +1.96712 q^{85} -7.52156 q^{86} -3.39434 q^{87} -1.39434 q^{88} -4.56413 q^{89} +22.6062 q^{90} +3.17843 q^{92} -24.8272 q^{93} +4.95743 q^{94} +3.12617 q^{95} -3.39434 q^{96} +11.3528 q^{97} -11.8820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9	$ 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} - q^{12} + 7 q^{13} - 5 q^{15} + 4 q^{16} + 9 q^{18} - 2 q^{19} + q^{20} + 7 q^{22} + 6 q^{23} - q^{24} + 9 q^{25} + 7 q^{26} - 13 q^{27} + 4 q^{29} - 5 q^{30} + 7 q^{31} + 4 q^{32} + 19 q^{33} + 9 q^{36} - 12 q^{37} - 2 q^{38} - 15 q^{39} + q^{40} - 4 q^{41} - 5 q^{43} + 7 q^{44} + 44 q^{45} + 6 q^{46} + 11 q^{47} - q^{48} + 9 q^{50} - 16 q^{51} + 7 q^{52} + 5 q^{53} - 13 q^{54} - 3 q^{55} - 16 q^{57} + 4 q^{58} - 16 q^{59} - 5 q^{60} + 34 q^{61} + 7 q^{62} + 4 q^{64} - q^{65} + 19 q^{66} + 2 q^{67} - 18 q^{69} + 24 q^{71} + 9 q^{72} + 24 q^{73} - 12 q^{74} + 10 q^{75} - 2 q^{76} - 15 q^{78} - 9 q^{79} + q^{80} + 40 q^{81} - 4 q^{82} + 8 q^{83} - 24 q^{85} - 5 q^{86} - q^{87} + 7 q^{88} - 2 q^{89} + 44 q^{90} + 6 q^{92} - 55 q^{93} + 11 q^{94} + 20 q^{95} - q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 - q^12 + 7 * q^13 - 5 * q^15 + 4 * q^16 + 9 * q^18 - 2 * q^19 + q^20 + 7 * q^22 + 6 * q^23 - q^24 + 9 * q^25 + 7 * q^26 - 13 * q^27 + 4 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 + 19 * q^33 + 9 * q^36 - 12 * q^37 - 2 * q^38 - 15 * q^39 + q^40 - 4 * q^41 - 5 * q^43 + 7 * q^44 + 44 * q^45 + 6 * q^46 + 11 * q^47 - q^48 + 9 * q^50 - 16 * q^51 + 7 * q^52 + 5 * q^53 - 13 * q^54 - 3 * q^55 - 16 * q^57 + 4 * q^58 - 16 * q^59 - 5 * q^60 + 34 * q^61 + 7 * q^62 + 4 * q^64 - q^65 + 19 * q^66 + 2 * q^67 - 18 * q^69 + 24 * q^71 + 9 * q^72 + 24 * q^73 - 12 * q^74 + 10 * q^75 - 2 * q^76 - 15 * q^78 - 9 * q^79 + q^80 + 40 * q^81 - 4 * q^82 + 8 * q^83 - 24 * q^85 - 5 * q^86 - q^87 + 7 * q^88 - 2 * q^89 + 44 * q^90 + 6 * q^92 - 55 * q^93 + 11 * q^94 + 20 * q^95 - q^96 + 4 * q^97 + 2 * 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
$3$	−3.39434	−1.95972	−0.979862	−	0.199675i	$-0.936011\pi$
$3$	−3.39434	−1.95972	−0.979862	+	0.199675i	$0.936011\pi$
$4$	1.00000	0.500000
$5$	2.65282	1.18638	0.593190	−	0.805063i	$-0.297868\pi$
$5$	2.65282	1.18638	0.593190	+	0.805063i	$0.297868\pi$
$6$	−3.39434	−1.38573
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	8.52156	2.84052
$10$	2.65282	0.838897
$11$	−1.39434	−0.420410	−0.210205	−	0.977657i	$-0.567413\pi$
$11$	−1.39434	−0.420410	−0.210205	+	0.977657i	$0.567413\pi$
$12$	−3.39434	−0.979862
$13$	7.08465	1.96493	0.982464	−	0.186454i	$-0.0596995\pi$
$13$	7.08465	1.96493	0.982464	+	0.186454i	$0.0596995\pi$
$14$	0	0
$15$	−9.00460	−2.32498
$16$	1.00000	0.250000
$17$	0.741518	0.179844	0.0899222	−	0.995949i	$-0.471338\pi$
$17$	0.741518	0.179844	0.0899222	+	0.995949i	$0.471338\pi$
$18$	8.52156	2.00855
$19$	1.17843	0.270351	0.135175	−	0.990822i	$-0.456840\pi$
$19$	1.17843	0.270351	0.135175	+	0.990822i	$0.456840\pi$
$20$	2.65282	0.593190
$21$	0	0
$22$	−1.39434	−0.297275
$23$	3.17843	0.662749	0.331374	−	0.943499i	$-0.392488\pi$
$23$	3.17843	0.662749	0.331374	+	0.943499i	$0.392488\pi$
$24$	−3.39434	−0.692867
$25$	2.03748	0.407496
$26$	7.08465	1.38941
$27$	−18.7421	−3.60691
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−9.00460	−1.64401
$31$	7.31429	1.31369	0.656843	−	0.754028i	$-0.271892\pi$
$31$	7.31429	1.31369	0.656843	+	0.754028i	$0.271892\pi$
$32$	1.00000	0.176777
$33$	4.73288	0.823888
$34$	0.741518	0.127169
$35$	0	0
$36$	8.52156	1.42026
$37$	1.61025	0.264724	0.132362	−	0.991201i	$-0.457744\pi$
$37$	1.61025	0.264724	0.132362	+	0.991201i	$0.457744\pi$
$38$	1.17843	0.191167
$39$	−24.0477	−3.85072
$40$	2.65282	0.419448
$41$	−11.3528	−1.77301	−0.886506	−	0.462717i	$-0.846875\pi$
$41$	−11.3528	−1.77301	−0.886506	+	0.462717i	$0.846875\pi$
$42$	0	0
$43$	−7.52156	−1.14703	−0.573514	−	0.819196i	$-0.694420\pi$
$43$	−7.52156	−1.14703	−0.573514	+	0.819196i	$0.694420\pi$
$44$	−1.39434	−0.210205
$45$	22.6062	3.36993
$46$	3.17843	0.468634
$47$	4.95743	0.723115	0.361558	−	0.932350i	$-0.382245\pi$
$47$	4.95743	0.723115	0.361558	+	0.932350i	$0.382245\pi$
$48$	−3.39434	−0.489931
$49$	0	0
$50$	2.03748	0.288143
$51$	−2.51696	−0.352446
$52$	7.08465	0.982464
$53$	1.26712	0.174053	0.0870265	−	0.996206i	$-0.472264\pi$
$53$	1.26712	0.174053	0.0870265	+	0.996206i	$0.472264\pi$
$54$	−18.7421	−2.55047
$55$	−3.69895	−0.498766
$56$	0	0
$57$	−4.00000	−0.529813
$58$	1.00000	0.131306
$59$	−4.51187	−0.587396	−0.293698	−	0.955898i	$-0.594886\pi$
$59$	−4.51187	−0.587396	−0.293698	+	0.955898i	$0.594886\pi$
$60$	−9.00460	−1.16249
$61$	−0.915903	−0.117269	−0.0586347	−	0.998280i	$-0.518675\pi$
$61$	−0.915903	−0.117269	−0.0586347	+	0.998280i	$0.518675\pi$
$62$	7.31429	0.928916
$63$	0	0
$64$	1.00000	0.125000
$65$	18.7943	2.33115
$66$	4.73288	0.582577
$67$	−11.6523	−1.42356	−0.711779	−	0.702403i	$-0.752110\pi$
$67$	−11.6523	−1.42356	−0.711779	+	0.702403i	$0.752110\pi$
$68$	0.741518	0.0899222
$69$	−10.7887	−1.29881
$70$	0	0
$71$	13.5078	1.60308	0.801542	−	0.597938i	$-0.204013\pi$
$71$	13.5078	1.60308	0.801542	+	0.597938i	$0.204013\pi$
$72$	8.52156	1.00428
$73$	−0.995954	−0.116568	−0.0582838	−	0.998300i	$-0.518563\pi$
$73$	−0.995954	−0.116568	−0.0582838	+	0.998300i	$0.518563\pi$
$74$	1.61025	0.187188
$75$	−6.91590	−0.798580
$76$	1.17843	0.135175
$77$	0	0
$78$	−24.0477	−2.72287
$79$	−3.68166	−0.414219	−0.207110	−	0.978318i	$-0.566406\pi$
$79$	−3.68166	−0.414219	−0.207110	+	0.978318i	$0.566406\pi$
$80$	2.65282	0.296595
$81$	38.0523	4.22803
$82$	−11.3528	−1.25371
$83$	11.7324	1.28780	0.643898	−	0.765111i	$-0.277316\pi$
$83$	11.7324	1.28780	0.643898	+	0.765111i	$0.277316\pi$
$84$	0	0
$85$	1.96712	0.213364
$86$	−7.52156	−0.811071
$87$	−3.39434	−0.363912
$88$	−1.39434	−0.148637
$89$	−4.56413	−0.483797	−0.241899	−	0.970302i	$-0.577770\pi$
$89$	−4.56413	−0.483797	−0.241899	+	0.970302i	$0.577770\pi$
$90$	22.6062	2.38290
$91$	0	0
$92$	3.17843	0.331374
$93$	−24.8272	−2.57446
$94$	4.95743	0.511320
$95$	3.12617	0.320739
$96$	−3.39434	−0.346434
$97$	11.3528	1.15270	0.576352	−	0.817202i	$-0.304476\pi$
$97$	11.3528	1.15270	0.576352	+	0.817202i	$0.304476\pi$
$98$	0	0
$99$	−11.8820	−1.19418
$100$	2.03748	0.203748
$101$	6.12722	0.609681	0.304840	−	0.952403i	$-0.401397\pi$
$101$	6.12722	0.609681	0.304840	+	0.952403i	$0.401397\pi$
$102$	−2.51696	−0.249217
$103$	−19.3148	−1.90315	−0.951574	−	0.307420i	$-0.900534\pi$
$103$	−19.3148	−1.90315	−0.951574	+	0.307420i	$0.900534\pi$
$104$	7.08465	0.694707
$105$	0	0
$106$	1.26712	0.123074
$107$	8.43182	0.815135	0.407567	−	0.913175i	$-0.366377\pi$
$107$	8.43182	0.815135	0.407567	+	0.913175i	$0.366377\pi$
$108$	−18.7421	−1.80346
$109$	7.16470	0.686254	0.343127	−	0.939289i	$-0.388514\pi$
$109$	7.16470	0.686254	0.343127	+	0.939289i	$0.388514\pi$
$110$	−3.69895	−0.352681
$111$	−5.46575	−0.518786
$112$	0	0
$113$	10.2717	0.966282	0.483141	−	0.875543i	$-0.339496\pi$
$113$	10.2717	0.966282	0.483141	+	0.875543i	$0.339496\pi$
$114$	−4.00000	−0.374634
$115$	8.43182	0.786271
$116$	1.00000	0.0928477
$117$	60.3722	5.58142
$118$	−4.51187	−0.415352
$119$	0	0
$120$	−9.00460	−0.822003
$121$	−9.05581	−0.823255
$122$	−0.915903	−0.0829220
$123$	38.5353	3.47462
$124$	7.31429	0.656843
$125$	−7.85905	−0.702935
$126$	0	0
$127$	6.51696	0.578287	0.289144	−	0.957286i	$-0.406630\pi$
$127$	6.51696	0.578287	0.289144	+	0.957286i	$0.406630\pi$
$128$	1.00000	0.0883883
$129$	25.5308	2.24786
$130$	18.7943	1.64837
$131$	7.07600	0.618233	0.309117	−	0.951024i	$-0.399967\pi$
$131$	7.07600	0.618233	0.309117	+	0.951024i	$0.399967\pi$
$132$	4.73288	0.411944
$133$	0	0
$134$	−11.6523	−1.00661
$135$	−49.7194	−4.27917
$136$	0.741518	0.0635846
$137$	−14.9580	−1.27795	−0.638973	−	0.769229i	$-0.720641\pi$
$137$	−14.9580	−1.27795	−0.638973	+	0.769229i	$0.720641\pi$
$138$	−10.7887	−0.918394
$139$	−11.9199	−1.01104	−0.505518	−	0.862816i	$-0.668699\pi$
$139$	−11.9199	−1.01104	−0.505518	+	0.862816i	$0.668699\pi$
$140$	0	0
$141$	−16.8272	−1.41711
$142$	13.5078	1.13355
$143$	−9.87842	−0.826075
$144$	8.52156	0.710130
$145$	2.65282	0.220305
$146$	−0.995954	−0.0824257
$147$	0	0
$148$	1.61025	0.132362
$149$	−9.36146	−0.766921	−0.383460	−	0.923557i	$-0.625268\pi$
$149$	−9.36146	−0.766921	−0.383460	+	0.923557i	$0.625268\pi$
$150$	−6.91590	−0.564681
$151$	0.212361	0.0172817	0.00864085	−	0.999963i	$-0.497249\pi$
$151$	0.212361	0.0172817	0.00864085	+	0.999963i	$0.497249\pi$
$152$	1.17843	0.0955834
$153$	6.31889	0.510852
$154$	0	0
$155$	19.4035	1.55853
$156$	−24.0477	−1.92536
$157$	−6.83076	−0.545154	−0.272577	−	0.962134i	$-0.587876\pi$
$157$	−6.83076	−0.545154	−0.272577	+	0.962134i	$0.587876\pi$
$158$	−3.68166	−0.292897
$159$	−4.30105	−0.341096
$160$	2.65282	0.209724
$161$	0	0
$162$	38.0523	2.98967
$163$	19.4035	1.51980	0.759901	−	0.650039i	$-0.225247\pi$
$163$	19.4035	1.51980	0.759901	+	0.650039i	$0.225247\pi$
$164$	−11.3528	−0.886506
$165$	12.5555	0.977444
$166$	11.7324	0.910609
$167$	12.5089	0.967966	0.483983	−	0.875078i	$-0.339190\pi$
$167$	12.5089	0.967966	0.483983	+	0.875078i	$0.339190\pi$
$168$	0	0
$169$	37.1922	2.86094
$170$	1.96712	0.150871
$171$	10.0421	0.767937
$172$	−7.52156	−0.573514
$173$	7.84499	0.596444	0.298222	−	0.954497i	$-0.403606\pi$
$173$	7.84499	0.596444	0.298222	+	0.954497i	$0.403606\pi$
$174$	−3.39434	−0.257324
$175$	0	0
$176$	−1.39434	−0.105103
$177$	15.3148	1.15113
$178$	−4.56413	−0.342096
$179$	0.779493	0.0582621	0.0291310	−	0.999576i	$-0.490726\pi$
$179$	0.779493	0.0582621	0.0291310	+	0.999576i	$0.490726\pi$
$180$	22.6062	1.68497
$181$	7.08465	0.526598	0.263299	−	0.964714i	$-0.415189\pi$
$181$	7.08465	0.526598	0.263299	+	0.964714i	$0.415189\pi$
$182$	0	0
$183$	3.10889	0.229816
$184$	3.17843	0.234317
$185$	4.27172	0.314063
$186$	−24.8272	−1.82042
$187$	−1.03393	−0.0756084
$188$	4.95743	0.361558
$189$	0	0
$190$	3.12617	0.226796
$191$	23.3148	1.68700	0.843501	−	0.537127i	$-0.180490\pi$
$191$	23.3148	1.68700	0.843501	+	0.537127i	$0.180490\pi$
$192$	−3.39434	−0.244966
$193$	9.40808	0.677208	0.338604	−	0.940929i	$-0.390045\pi$
$193$	9.40808	0.677208	0.338604	+	0.940929i	$0.390045\pi$
$194$	11.3528	0.815085
$195$	−63.7944	−4.56841
$196$	0	0
$197$	12.1968	0.868983	0.434492	−	0.900676i	$-0.356928\pi$
$197$	12.1968	0.868983	0.434492	+	0.900676i	$0.356928\pi$
$198$	−11.8820	−0.844415
$199$	12.0943	0.857345	0.428672	−	0.903460i	$-0.358981\pi$
$199$	12.0943	0.857345	0.428672	+	0.903460i	$0.358981\pi$
$200$	2.03748	0.144072
$201$	39.5520	2.78978
$202$	6.12722	0.431110
$203$	0	0
$204$	−2.51696	−0.176223
$205$	−30.1170	−2.10346
$206$	−19.3148	−1.34573
$207$	27.0852	1.88255
$208$	7.08465	0.491232
$209$	−1.64314	−0.113658
$210$	0	0
$211$	−6.80783	−0.468671	−0.234335	−	0.972156i	$-0.575291\pi$
$211$	−6.80783	−0.468671	−0.234335	+	0.972156i	$0.575291\pi$
$212$	1.26712	0.0870265
$213$	−45.8502	−3.14160
$214$	8.43182	0.576387
$215$	−19.9534	−1.36081
$216$	−18.7421	−1.27524
$217$	0	0
$218$	7.16470	0.485255
$219$	3.38061	0.228440
$220$	−3.69895	−0.249383
$221$	5.25339	0.353381
$222$	−5.46575	−0.366837
$223$	1.73747	0.116350	0.0581748	−	0.998306i	$-0.481472\pi$
$223$	1.73747	0.116350	0.0581748	+	0.998306i	$0.481472\pi$
$224$	0	0
$225$	17.3625	1.15750
$226$	10.2717	0.683265
$227$	20.4288	1.35591	0.677954	−	0.735104i	$-0.262867\pi$
$227$	20.4288	1.35591	0.677954	+	0.735104i	$0.262867\pi$
$228$	−4.00000	−0.264906
$229$	23.9763	1.58440	0.792200	−	0.610262i	$-0.208936\pi$
$229$	23.9763	1.58440	0.792200	+	0.610262i	$0.208936\pi$
$230$	8.43182	0.555978
$231$	0	0
$232$	1.00000	0.0656532
$233$	8.65792	0.567199	0.283599	−	0.958943i	$-0.408471\pi$
$233$	8.65792	0.567199	0.283599	+	0.958943i	$0.408471\pi$
$234$	60.3722	3.94666
$235$	13.1512	0.857889
$236$	−4.51187	−0.293698
$237$	12.4968	0.811756
$238$	0	0
$239$	−10.1520	−0.656679	−0.328339	−	0.944560i	$-0.606489\pi$
$239$	−10.1520	−0.656679	−0.328339	+	0.944560i	$0.606489\pi$
$240$	−9.00460	−0.581244
$241$	2.12367	0.136797	0.0683987	−	0.997658i	$-0.478211\pi$
$241$	2.12367	0.136797	0.0683987	+	0.997658i	$0.478211\pi$
$242$	−9.05581	−0.582129
$243$	−72.9364	−4.67887
$244$	−0.915903	−0.0586347
$245$	0	0
$246$	38.5353	2.45692
$247$	8.34877	0.531220
$248$	7.31429	0.464458
$249$	−39.8237	−2.52373
$250$	−7.85905	−0.497050
$251$	−14.7750	−0.932587	−0.466293	−	0.884630i	$-0.654411\pi$
$251$	−14.7750	−0.932587	−0.466293	+	0.884630i	$0.654411\pi$
$252$	0	0
$253$	−4.43182	−0.278626
$254$	6.51696	0.408911
$255$	−6.67707	−0.418134
$256$	1.00000	0.0625000
$257$	12.1501	0.757905	0.378953	−	0.925416i	$-0.376284\pi$
$257$	12.1501	0.757905	0.378953	+	0.925416i	$0.376284\pi$
$258$	25.5308	1.58948
$259$	0	0
$260$	18.7943	1.16557
$261$	8.52156	0.527471
$262$	7.07600	0.437157
$263$	−9.86114	−0.608064	−0.304032	−	0.952662i	$-0.598333\pi$
$263$	−9.86114	−0.608064	−0.304032	+	0.952662i	$0.598333\pi$
$264$	4.73288	0.291288
$265$	3.36146	0.206493
$266$	0	0
$267$	15.4922	0.948109
$268$	−11.6523	−0.711779
$269$	−19.4502	−1.18590	−0.592948	−	0.805241i	$-0.702036\pi$
$269$	−19.4502	−1.18590	−0.592948	+	0.805241i	$0.702036\pi$
$270$	−49.7194	−3.02583
$271$	−15.8232	−0.961189	−0.480594	−	0.876943i	$-0.659579\pi$
$271$	−15.8232	−0.961189	−0.480594	+	0.876943i	$0.659579\pi$
$272$	0.741518	0.0449611
$273$	0	0
$274$	−14.9580	−0.903645
$275$	−2.84094	−0.171315
$276$	−10.7887	−0.649403
$277$	−18.8081	−1.13007	−0.565033	−	0.825068i	$-0.691137\pi$
$277$	−18.8081	−1.13007	−0.565033	+	0.825068i	$0.691137\pi$
$278$	−11.9199	−0.714911
$279$	62.3292	3.73155
$280$	0	0
$281$	−10.8968	−0.650046	−0.325023	−	0.945706i	$-0.605372\pi$
$281$	−10.8968	−0.650046	−0.325023	+	0.945706i	$0.605372\pi$
$282$	−16.8272	−1.00205
$283$	−8.62349	−0.512613	−0.256307	−	0.966596i	$-0.582506\pi$
$283$	−8.62349	−0.512613	−0.256307	+	0.966596i	$0.582506\pi$
$284$	13.5078	0.801542
$285$	−10.6113	−0.628559
$286$	−9.87842	−0.584123
$287$	0	0
$288$	8.52156	0.502138
$289$	−16.4502	−0.967656
$290$	2.65282	0.155779
$291$	−38.5353	−2.25898
$292$	−0.995954	−0.0582838
$293$	−10.6534	−0.622377	−0.311188	−	0.950348i	$-0.600727\pi$
$293$	−10.6534	−0.622377	−0.311188	+	0.950348i	$0.600727\pi$
$294$	0	0
$295$	−11.9692	−0.696874
$296$	1.61025	0.0935941
$297$	26.1329	1.51638
$298$	−9.36146	−0.542295
$299$	22.5181	1.30225
$300$	−6.91590	−0.399290
$301$	0	0
$302$	0.212361	0.0122200
$303$	−20.7979	−1.19481
$304$	1.17843	0.0675877
$305$	−2.42973	−0.139126
$306$	6.31889	0.361227
$307$	−11.8262	−0.674955	−0.337477	−	0.941334i	$-0.609574\pi$
$307$	−11.8262	−0.674955	−0.337477	+	0.941334i	$0.609574\pi$
$308$	0	0
$309$	65.5612	3.72965
$310$	19.4035	1.10205
$311$	−26.4040	−1.49724	−0.748618	−	0.663002i	$-0.769282\pi$
$311$	−26.4040	−1.49724	−0.748618	+	0.663002i	$0.769282\pi$
$312$	−24.0477	−1.36143
$313$	−27.0989	−1.53172	−0.765861	−	0.643006i	$-0.777687\pi$
$313$	−27.0989	−1.53172	−0.765861	+	0.643006i	$0.777687\pi$
$314$	−6.83076	−0.385482
$315$	0	0
$316$	−3.68166	−0.207110
$317$	8.86574	0.497949	0.248975	−	0.968510i	$-0.419906\pi$
$317$	8.86574	0.497949	0.248975	+	0.968510i	$0.419906\pi$
$318$	−4.30105	−0.241191
$319$	−1.39434	−0.0780682
$320$	2.65282	0.148297
$321$	−28.6205	−1.59744
$322$	0	0
$323$	0.873828	0.0486211
$324$	38.0523	2.11402
$325$	14.4348	0.800700
$326$	19.4035	1.07466
$327$	−24.3194	−1.34487
$328$	−11.3528	−0.626854
$329$	0	0
$330$	12.5555	0.691157
$331$	−19.7760	−1.08699	−0.543494	−	0.839413i	$-0.682899\pi$
$331$	−19.7760	−1.08699	−0.543494	+	0.839413i	$0.682899\pi$
$332$	11.7324	0.643898
$333$	13.7219	0.751954
$334$	12.5089	0.684455
$335$	−30.9116	−1.68888
$336$	0	0
$337$	5.47494	0.298239	0.149120	−	0.988819i	$-0.452356\pi$
$337$	5.47494	0.298239	0.149120	+	0.988819i	$0.452356\pi$
$338$	37.1922	2.02299
$339$	−34.8657	−1.89365
$340$	1.96712	0.106682
$341$	−10.1986	−0.552287
$342$	10.0421	0.543013
$343$	0	0
$344$	−7.52156	−0.405535
$345$	−28.6205	−1.54088
$346$	7.84499	0.421749
$347$	−1.83071	−0.0982775	−0.0491387	−	0.998792i	$-0.515648\pi$
$347$	−1.83071	−0.0982775	−0.0491387	+	0.998792i	$0.515648\pi$
$348$	−3.39434	−0.181956
$349$	−30.2394	−1.61868	−0.809339	−	0.587342i	$-0.800174\pi$
$349$	−30.2394	−1.61868	−0.809339	+	0.587342i	$0.800174\pi$
$350$	0	0
$351$	−132.781	−7.08732
$352$	−1.39434	−0.0743187
$353$	−3.64314	−0.193905	−0.0969523	−	0.995289i	$-0.530909\pi$
$353$	−3.64314	−0.193905	−0.0969523	+	0.995289i	$0.530909\pi$
$354$	15.3148	0.813975
$355$	35.8339	1.90187
$356$	−4.56413	−0.241899
$357$	0	0
$358$	0.779493	0.0411975
$359$	9.96147	0.525747	0.262873	−	0.964830i	$-0.415330\pi$
$359$	9.96147	0.525747	0.262873	+	0.964830i	$0.415330\pi$
$360$	22.6062	1.19145
$361$	−17.6113	−0.926910
$362$	7.08465	0.372361
$363$	30.7385	1.61335
$364$	0	0
$365$	−2.64209	−0.138293
$366$	3.10889	0.162504
$367$	8.20727	0.428416	0.214208	−	0.976788i	$-0.431283\pi$
$367$	8.20727	0.428416	0.214208	+	0.976788i	$0.431283\pi$
$368$	3.17843	0.165687
$369$	−96.7437	−5.03628
$370$	4.27172	0.222076
$371$	0	0
$372$	−24.8272	−1.28723
$373$	−10.4957	−0.543448	−0.271724	−	0.962375i	$-0.587594\pi$
$373$	−10.4957	−0.543448	−0.271724	+	0.962375i	$0.587594\pi$
$374$	−1.03393	−0.0534632
$375$	26.6763	1.37756
$376$	4.95743	0.255660
$377$	7.08465	0.364878
$378$	0	0
$379$	−6.81615	−0.350122	−0.175061	−	0.984558i	$-0.556012\pi$
$379$	−6.81615	−0.350122	−0.175061	+	0.984558i	$0.556012\pi$
$380$	3.12617	0.160369
$381$	−22.1208	−1.13328
$382$	23.3148	1.19289
$383$	21.1455	1.08049	0.540244	−	0.841509i	$-0.318332\pi$
$383$	21.1455	1.08049	0.540244	+	0.841509i	$0.318332\pi$
$384$	−3.39434	−0.173217
$385$	0	0
$386$	9.40808	0.478858
$387$	−64.0954	−3.25815
$388$	11.3528	0.576352
$389$	−9.17843	−0.465365	−0.232682	−	0.972553i	$-0.574750\pi$
$389$	−9.17843	−0.465365	−0.232682	+	0.972553i	$0.574750\pi$
$390$	−63.7944	−3.23035
$391$	2.35686	0.119192
$392$	0	0
$393$	−24.0184	−1.21157
$394$	12.1968	0.614464
$395$	−9.76681	−0.491421
$396$	−11.8820	−0.597092
$397$	38.1003	1.91220	0.956100	−	0.293042i	$-0.0946675\pi$
$397$	38.1003	1.91220	0.956100	+	0.293042i	$0.0946675\pi$
$398$	12.0943	0.606234
$399$	0	0
$400$	2.03748	0.101874
$401$	−13.5986	−0.679082	−0.339541	−	0.940591i	$-0.610272\pi$
$401$	−13.5986	−0.679082	−0.339541	+	0.940591i	$0.610272\pi$
$402$	39.5520	1.97267
$403$	51.8192	2.58130
$404$	6.12722	0.304840
$405$	100.946	5.01605
$406$	0	0
$407$	−2.24524	−0.111293
$408$	−2.51696	−0.124608
$409$	32.9302	1.62829	0.814146	−	0.580660i	$-0.197205\pi$
$409$	32.9302	1.62829	0.814146	+	0.580660i	$0.197205\pi$
$410$	−30.1170	−1.48737
$411$	50.7725	2.50442
$412$	−19.3148	−0.951574
$413$	0	0
$414$	27.0852	1.33116
$415$	31.1239	1.52781
$416$	7.08465	0.347353
$417$	40.4604	1.98135
$418$	−1.64314	−0.0803685
$419$	−2.24934	−0.109888	−0.0549438	−	0.998489i	$-0.517498\pi$
$419$	−2.24934	−0.109888	−0.0549438	+	0.998489i	$0.517498\pi$
$420$	0	0
$421$	−29.5445	−1.43991	−0.719955	−	0.694021i	$-0.755838\pi$
$421$	−29.5445	−1.43991	−0.719955	+	0.694021i	$0.755838\pi$
$422$	−6.80783	−0.331400
$423$	42.2450	2.05402
$424$	1.26712	0.0615370
$425$	1.51083	0.0732859
$426$	−45.8502	−2.22145
$427$	0	0
$428$	8.43182	0.407567
$429$	33.5308	1.61888
$430$	−19.9534	−0.962238
$431$	−17.4275	−0.839451	−0.419725	−	0.907651i	$-0.637874\pi$
$431$	−17.4275	−0.839451	−0.419725	+	0.907651i	$0.637874\pi$
$432$	−18.7421	−0.901728
$433$	14.3016	0.687291	0.343646	−	0.939099i	$-0.388338\pi$
$433$	14.3016	0.687291	0.343646	+	0.939099i	$0.388338\pi$
$434$	0	0
$435$	−9.00460	−0.431737
$436$	7.16470	0.343127
$437$	3.74556	0.179175
$438$	3.38061	0.161532
$439$	3.65233	0.174316	0.0871581	−	0.996194i	$-0.472221\pi$
$439$	3.65233	0.174316	0.0871581	+	0.996194i	$0.472221\pi$
$440$	−3.69895	−0.176340
$441$	0	0
$442$	5.25339	0.249878
$443$	9.26357	0.440126	0.220063	−	0.975486i	$-0.429374\pi$
$443$	9.26357	0.440126	0.220063	+	0.975486i	$0.429374\pi$
$444$	−5.46575	−0.259393
$445$	−12.1078	−0.573967
$446$	1.73747	0.0822717
$447$	31.7760	1.50295
$448$	0	0
$449$	−9.29756	−0.438779	−0.219389	−	0.975637i	$-0.570407\pi$
$449$	−9.29756	−0.438779	−0.219389	+	0.975637i	$0.570407\pi$
$450$	17.3625	0.818476
$451$	15.8297	0.745392
$452$	10.2717	0.483141
$453$	−0.720826	−0.0338674
$454$	20.4288	0.958772
$455$	0	0
$456$	−4.00000	−0.187317
$457$	−19.8070	−0.926533	−0.463267	−	0.886219i	$-0.653323\pi$
$457$	−19.8070	−0.926533	−0.463267	+	0.886219i	$0.653323\pi$
$458$	23.9763	1.12034
$459$	−13.8976	−0.648683
$460$	8.43182	0.393136
$461$	−19.6388	−0.914671	−0.457336	−	0.889294i	$-0.651196\pi$
$461$	−19.6388	−0.914671	−0.457336	+	0.889294i	$0.651196\pi$
$462$	0	0
$463$	20.8329	0.968185	0.484092	−	0.875017i	$-0.339150\pi$
$463$	20.8329	0.968185	0.484092	+	0.875017i	$0.339150\pi$
$464$	1.00000	0.0464238
$465$	−65.8622	−3.05429
$466$	8.65792	0.401070
$467$	−17.4979	−0.809705	−0.404852	−	0.914382i	$-0.632677\pi$
$467$	−17.4979	−0.809705	−0.404852	+	0.914382i	$0.632677\pi$
$468$	60.3722	2.79071
$469$	0	0
$470$	13.1512	0.606619
$471$	23.1859	1.06835
$472$	−4.51187	−0.207676
$473$	10.4876	0.482222
$474$	12.4968	0.573998
$475$	2.40103	0.110167
$476$	0	0
$477$	10.7979	0.494401
$478$	−10.1520	−0.464342
$479$	27.0711	1.23691	0.618456	−	0.785819i	$-0.287759\pi$
$479$	27.0711	1.23691	0.618456	+	0.785819i	$0.287759\pi$
$480$	−9.00460	−0.411002
$481$	11.4081	0.520164
$482$	2.12367	0.0967304
$483$	0	0
$484$	−9.05581	−0.411628
$485$	30.1170	1.36754
$486$	−72.9364	−3.30846
$487$	−17.0523	−0.772714	−0.386357	−	0.922349i	$-0.626267\pi$
$487$	−17.0523	−0.772714	−0.386357	+	0.922349i	$0.626267\pi$
$488$	−0.915903	−0.0414610
$489$	−65.8622	−2.97839
$490$	0	0
$491$	−7.44451	−0.335966	−0.167983	−	0.985790i	$-0.553725\pi$
$491$	−7.44451	−0.335966	−0.167983	+	0.985790i	$0.553725\pi$
$492$	38.5353	1.73731
$493$	0.741518	0.0333963
$494$	8.34877	0.375629
$495$	−31.5208	−1.41675
$496$	7.31429	0.328421
$497$	0	0
$498$	−39.8237	−1.78454
$499$	10.6184	0.475345	0.237672	−	0.971345i	$-0.423616\pi$
$499$	10.6184	0.475345	0.237672	+	0.971345i	$0.423616\pi$
$500$	−7.85905	−0.351467
$501$	−42.4594	−1.89695
$502$	−14.7750	−0.659438
$503$	33.2291	1.48161	0.740807	−	0.671718i	$-0.234443\pi$
$503$	33.2291	1.48161	0.740807	+	0.671718i	$0.234443\pi$
$504$	0	0
$505$	16.2544	0.723313
$506$	−4.43182	−0.197019
$507$	−126.243	−5.60665
$508$	6.51696	0.289144
$509$	−29.0867	−1.28925	−0.644624	−	0.764500i	$-0.722986\pi$
$509$	−29.0867	−1.28925	−0.644624	+	0.764500i	$0.722986\pi$
$510$	−6.67707	−0.295665
$511$	0	0
$512$	1.00000	0.0441942
$513$	−22.0862	−0.975131
$514$	12.1501	0.535920
$515$	−51.2389	−2.25786
$516$	25.5308	1.12393
$517$	−6.91235	−0.304005
$518$	0	0
$519$	−26.6286	−1.16887
$520$	18.7943	0.824186
$521$	18.4795	0.809603	0.404802	−	0.914405i	$-0.367341\pi$
$521$	18.4795	0.809603	0.404802	+	0.914405i	$0.367341\pi$
$522$	8.52156	0.372979
$523$	10.7755	0.471180	0.235590	−	0.971853i	$-0.424298\pi$
$523$	10.7755	0.471180	0.235590	+	0.971853i	$0.424298\pi$
$524$	7.07600	0.309117
$525$	0	0
$526$	−9.86114	−0.429966
$527$	5.42368	0.236259
$528$	4.73288	0.205972
$529$	−12.8976	−0.560764
$530$	3.36146	0.146012
$531$	−38.4482	−1.66851
$532$	0	0
$533$	−80.4307	−3.48384
$534$	15.4922	0.670414
$535$	22.3681	0.967059
$536$	−11.6523	−0.503304
$537$	−2.64587	−0.114178
$538$	−19.4502	−0.838556
$539$	0	0
$540$	−49.7194	−2.13958
$541$	−24.1137	−1.03673	−0.518365	−	0.855160i	$-0.673459\pi$
$541$	−24.1137	−1.03673	−0.518365	+	0.855160i	$0.673459\pi$
$542$	−15.8232	−0.679663
$543$	−24.0477	−1.03199
$544$	0.741518	0.0317923
$545$	19.0067	0.814157
$546$	0	0
$547$	0.696442	0.0297777	0.0148889	−	0.999889i	$-0.495261\pi$
$547$	0.696442	0.0297777	0.0148889	+	0.999889i	$0.495261\pi$
$548$	−14.9580	−0.638973
$549$	−7.80492	−0.333106
$550$	−2.84094	−0.121138
$551$	1.17843	0.0502029
$552$	−10.7887	−0.459197
$553$	0	0
$554$	−18.8081	−0.799078
$555$	−14.4997	−0.615477
$556$	−11.9199	−0.505518
$557$	−19.8318	−0.840301	−0.420150	−	0.907455i	$-0.638023\pi$
$557$	−19.8318	−0.840301	−0.420150	+	0.907455i	$0.638023\pi$
$558$	62.3292	2.63860
$559$	−53.2876	−2.25383
$560$	0	0
$561$	3.50951	0.148172
$562$	−10.8968	−0.459652
$563$	44.0159	1.85505	0.927525	−	0.373761i	$-0.121932\pi$
$563$	44.0159	1.85505	0.927525	+	0.373761i	$0.121932\pi$
$564$	−16.8272	−0.708553
$565$	27.2491	1.14638
$566$	−8.62349	−0.362472
$567$	0	0
$568$	13.5078	0.566776
$569$	20.6459	0.865520	0.432760	−	0.901509i	$-0.357540\pi$
$569$	20.6459	0.865520	0.432760	+	0.901509i	$0.357540\pi$
$570$	−10.6113	−0.444458
$571$	13.1008	0.548251	0.274126	−	0.961694i	$-0.411612\pi$
$571$	13.1008	0.548251	0.274126	+	0.961694i	$0.411612\pi$
$572$	−9.87842	−0.413038
$573$	−79.1386	−3.30606
$574$	0	0
$575$	6.47599	0.270067
$576$	8.52156	0.355065
$577$	20.8084	0.866264	0.433132	−	0.901330i	$-0.357408\pi$
$577$	20.8084	0.866264	0.433132	+	0.901330i	$0.357408\pi$
$578$	−16.4502	−0.684236
$579$	−31.9342	−1.32714
$580$	2.65282	0.110153
$581$	0	0
$582$	−38.5353	−1.59734
$583$	−1.76681	−0.0731736
$584$	−0.995954	−0.0412129
$585$	160.157	6.62168
$586$	−10.6534	−0.440087
$587$	10.6316	0.438812	0.219406	−	0.975634i	$-0.429588\pi$
$587$	10.6316	0.438812	0.219406	+	0.975634i	$0.429588\pi$
$588$	0	0
$589$	8.61939	0.355156
$590$	−11.9692	−0.492764
$591$	−41.4000	−1.70297
$592$	1.61025	0.0661810
$593$	−40.2445	−1.65264	−0.826321	−	0.563199i	$-0.809570\pi$
$593$	−40.2445	−1.65264	−0.826321	+	0.563199i	$0.809570\pi$
$594$	26.1329	1.07224
$595$	0	0
$596$	−9.36146	−0.383460
$597$	−41.0523	−1.68016
$598$	22.5181	0.920832
$599$	−2.03853	−0.0832919	−0.0416459	−	0.999132i	$-0.513260\pi$
$599$	−2.03853	−0.0832919	−0.0416459	+	0.999132i	$0.513260\pi$
$600$	−6.91590	−0.282341
$601$	32.3949	1.32142	0.660709	−	0.750642i	$-0.270256\pi$
$601$	32.3949	1.32142	0.660709	+	0.750642i	$0.270256\pi$
$602$	0	0
$603$	−99.2960	−4.04365
$604$	0.212361	0.00864085
$605$	−24.0235	−0.976693
$606$	−20.7979	−0.844856
$607$	−0.752575	−0.0305461	−0.0152730	−	0.999883i	$-0.504862\pi$
$607$	−0.752575	−0.0305461	−0.0152730	+	0.999883i	$0.504862\pi$
$608$	1.17843	0.0477917
$609$	0	0
$610$	−2.42973	−0.0983769
$611$	35.1216	1.42087
$612$	6.31889	0.255426
$613$	−11.6909	−0.472189	−0.236095	−	0.971730i	$-0.575868\pi$
$613$	−11.6909	−0.472189	−0.236095	+	0.971730i	$0.575868\pi$
$614$	−11.8262	−0.477265
$615$	102.228	4.12221
$616$	0	0
$617$	23.8043	0.958327	0.479163	−	0.877726i	$-0.340940\pi$
$617$	23.8043	0.958327	0.479163	+	0.877726i	$0.340940\pi$
$618$	65.5612	2.63726
$619$	−16.0908	−0.646743	−0.323372	−	0.946272i	$-0.604816\pi$
$619$	−16.0908	−0.646743	−0.323372	+	0.946272i	$0.604816\pi$
$620$	19.4035	0.779265
$621$	−59.5704	−2.39048
$622$	−26.4040	−1.05871
$623$	0	0
$624$	−24.0477	−0.962679
$625$	−31.0361	−1.24144
$626$	−27.0989	−1.08309
$627$	5.57737	0.222739
$628$	−6.83076	−0.272577
$629$	1.19403	0.0476091
$630$	0	0
$631$	47.9526	1.90896	0.954482	−	0.298269i	$-0.0964094\pi$
$631$	47.9526	1.90896	0.954482	+	0.298269i	$0.0964094\pi$
$632$	−3.68166	−0.146449
$633$	23.1081	0.918465
$634$	8.86574	0.352103
$635$	17.2884	0.686068
$636$	−4.30105	−0.170548
$637$	0	0
$638$	−1.39434	−0.0552025
$639$	115.108	4.55359
$640$	2.65282	0.104862
$641$	−28.3681	−1.12047	−0.560237	−	0.828332i	$-0.689290\pi$
$641$	−28.3681	−1.12047	−0.560237	+	0.828332i	$0.689290\pi$
$642$	−28.6205	−1.12956
$643$	1.93932	0.0764795	0.0382397	−	0.999269i	$-0.487825\pi$
$643$	1.93932	0.0764795	0.0382397	+	0.999269i	$0.487825\pi$
$644$	0	0
$645$	67.7286	2.66681
$646$	0.873828	0.0343803
$647$	−32.7877	−1.28902	−0.644509	−	0.764597i	$-0.722938\pi$
$647$	−32.7877	−1.28902	−0.644509	+	0.764597i	$0.722938\pi$
$648$	38.0523	1.49484
$649$	6.29110	0.246947
$650$	14.4348	0.566180
$651$	0	0
$652$	19.4035	0.759901
$653$	13.3979	0.524300	0.262150	−	0.965027i	$-0.415568\pi$
$653$	13.3979	0.524300	0.262150	+	0.965027i	$0.415568\pi$
$654$	−24.3194	−0.950965
$655$	18.7714	0.733459
$656$	−11.3528	−0.443253
$657$	−8.48708	−0.331113
$658$	0	0
$659$	3.81697	0.148688	0.0743441	−	0.997233i	$-0.476314\pi$
$659$	3.81697	0.148688	0.0743441	+	0.997233i	$0.476314\pi$
$660$	12.5555	0.488722
$661$	−14.6164	−0.568512	−0.284256	−	0.958748i	$-0.591747\pi$
$661$	−14.6164	−0.568512	−0.284256	+	0.958748i	$0.591747\pi$
$662$	−19.7760	−0.768616
$663$	−17.8318	−0.692530
$664$	11.7324	0.455305
$665$	0	0
$666$	13.7219	0.531712
$667$	3.17843	0.123069
$668$	12.5089	0.483983
$669$	−5.89757	−0.228013
$670$	−30.9116	−1.19422
$671$	1.27708	0.0493012
$672$	0	0
$673$	29.2536	1.12764	0.563822	−	0.825896i	$-0.309330\pi$
$673$	29.2536	1.12764	0.563822	+	0.825896i	$0.309330\pi$
$674$	5.47494	0.210887
$675$	−38.1866	−1.46980
$676$	37.1922	1.43047
$677$	0.744518	0.0286141	0.0143071	−	0.999898i	$-0.495446\pi$
$677$	0.744518	0.0286141	0.0143071	+	0.999898i	$0.495446\pi$
$678$	−34.8657	−1.33901
$679$	0	0
$680$	1.96712	0.0754355
$681$	−69.3424	−2.65721
$682$	−10.1986	−0.390526
$683$	−18.1866	−0.695890	−0.347945	−	0.937515i	$-0.613120\pi$
$683$	−18.1866	−0.695890	−0.347945	+	0.937515i	$0.613120\pi$
$684$	10.0421	0.383968
$685$	−39.6809	−1.51613
$686$	0	0
$687$	−81.3838	−3.10499
$688$	−7.52156	−0.286757
$689$	8.97713	0.342001
$690$	−28.6205	−1.08956
$691$	−16.2127	−0.616760	−0.308380	−	0.951263i	$-0.599787\pi$
$691$	−16.2127	−0.616760	−0.308380	+	0.951263i	$0.599787\pi$
$692$	7.84499	0.298222
$693$	0	0
$694$	−1.83071	−0.0694927
$695$	−31.6215	−1.19947
$696$	−3.39434	−0.128662
$697$	−8.41831	−0.318866
$698$	−30.2394	−1.14458
$699$	−29.3879	−1.11155
$700$	0	0
$701$	0.845486	0.0319336	0.0159668	−	0.999873i	$-0.494917\pi$
$701$	0.845486	0.0319336	0.0159668	+	0.999873i	$0.494917\pi$
$702$	−132.781	−5.01149
$703$	1.89757	0.0715683
$704$	−1.39434	−0.0525513
$705$	−44.6396	−1.68123
$706$	−3.64314	−0.137111
$707$	0	0
$708$	15.3148	0.575567
$709$	−4.34854	−0.163313	−0.0816565	−	0.996661i	$-0.526021\pi$
$709$	−4.34854	−0.163313	−0.0816565	+	0.996661i	$0.526021\pi$
$710$	35.8339	1.34482
$711$	−31.3735	−1.17660
$712$	−4.56413	−0.171048
$713$	23.2480	0.870643
$714$	0	0
$715$	−26.2057	−0.980039
$716$	0.779493	0.0291310
$717$	34.4594	1.28691
$718$	9.96147	0.371759
$719$	9.81452	0.366020	0.183010	−	0.983111i	$-0.441416\pi$
$719$	9.81452	0.366020	0.183010	+	0.983111i	$0.441416\pi$
$720$	22.6062	0.842484
$721$	0	0
$722$	−17.6113	−0.655425
$723$	−7.20846	−0.268085
$724$	7.08465	0.263299
$725$	2.03748	0.0756701
$726$	30.7385	1.14081
$727$	−23.1178	−0.857390	−0.428695	−	0.903449i	$-0.641027\pi$
$727$	−23.1178	−0.857390	−0.428695	+	0.903449i	$0.641027\pi$
$728$	0	0
$729$	133.414	4.94126
$730$	−2.64209	−0.0977882
$731$	−5.57737	−0.206286
$732$	3.10889	0.114908
$733$	23.9477	0.884530	0.442265	−	0.896884i	$-0.354175\pi$
$733$	23.9477	0.884530	0.442265	+	0.896884i	$0.354175\pi$
$734$	8.20727	0.302936
$735$	0	0
$736$	3.17843	0.117159
$737$	16.2473	0.598478
$738$	−96.7437	−3.56119
$739$	−30.5647	−1.12434	−0.562170	−	0.827022i	$-0.690033\pi$
$739$	−30.5647	−1.12434	−0.562170	+	0.827022i	$0.690033\pi$
$740$	4.27172	0.157032
$741$	−28.3386	−1.04104
$742$	0	0
$743$	23.6636	0.868134	0.434067	−	0.900881i	$-0.357078\pi$
$743$	23.6636	0.868134	0.434067	+	0.900881i	$0.357078\pi$
$744$	−24.8272	−0.910210
$745$	−24.8343	−0.909859
$746$	−10.4957	−0.384276
$747$	99.9782	3.65801
$748$	−1.03393	−0.0378042
$749$	0	0
$750$	26.6763	0.974081
$751$	44.7321	1.63230	0.816149	−	0.577842i	$-0.196105\pi$
$751$	44.7321	1.63230	0.816149	+	0.577842i	$0.196105\pi$
$752$	4.95743	0.180779
$753$	50.1512	1.82761
$754$	7.08465	0.258008
$755$	0.563356	0.0205026
$756$	0	0
$757$	−4.60379	−0.167328	−0.0836638	−	0.996494i	$-0.526662\pi$
$757$	−4.60379	−0.167328	−0.0836638	+	0.996494i	$0.526662\pi$
$758$	−6.81615	−0.247574
$759$	15.0431	0.546031
$760$	3.12617	0.113398
$761$	−3.81342	−0.138236	−0.0691182	−	0.997608i	$-0.522019\pi$
$761$	−3.81342	−0.138236	−0.0691182	+	0.997608i	$0.522019\pi$
$762$	−22.1208	−0.801352
$763$	0	0
$764$	23.3148	0.843501
$765$	16.7629	0.606064
$766$	21.1455	0.764020
$767$	−31.9650	−1.15419
$768$	−3.39434	−0.122483
$769$	−30.2084	−1.08934	−0.544671	−	0.838650i	$-0.683345\pi$
$769$	−30.2084	−1.08934	−0.544671	+	0.838650i	$0.683345\pi$
$770$	0	0
$771$	−41.2417	−1.48529
$772$	9.40808	0.338604
$773$	−13.4421	−0.483477	−0.241739	−	0.970341i	$-0.577718\pi$
$773$	−13.4421	−0.483477	−0.241739	+	0.970341i	$0.577718\pi$
$774$	−64.0954	−2.30386
$775$	14.9027	0.535321
$776$	11.3528	0.407542
$777$	0	0
$778$	−9.17843	−0.329063
$779$	−13.3785	−0.479335
$780$	−63.7944	−2.28421
$781$	−18.8345	−0.673953
$782$	2.35686	0.0842812
$783$	−18.7421	−0.669787
$784$	0	0
$785$	−18.1208	−0.646759
$786$	−24.0184	−0.856707
$787$	12.0316	0.428879	0.214440	−	0.976737i	$-0.431208\pi$
$787$	12.0316	0.428879	0.214440	+	0.976737i	$0.431208\pi$
$788$	12.1968	0.434492
$789$	33.4721	1.19164
$790$	−9.76681	−0.347487
$791$	0	0
$792$	−11.8820	−0.422208
$793$	−6.48885	−0.230426
$794$	38.1003	1.35213
$795$	−11.4099	−0.404669
$796$	12.0943	0.428672
$797$	44.1924	1.56538	0.782688	−	0.622414i	$-0.213848\pi$
$797$	44.1924	1.56538	0.782688	+	0.622414i	$0.213848\pi$
$798$	0	0
$799$	3.67602	0.130048
$800$	2.03748	0.0720358
$801$	−38.8935	−1.37424
$802$	−13.5986	−0.480184
$803$	1.38870	0.0490062
$804$	39.5520	1.39489
$805$	0	0
$806$	51.8192	1.82525
$807$	66.0205	2.32403
$808$	6.12722	0.215555
$809$	20.7056	0.727971	0.363986	−	0.931405i	$-0.381416\pi$
$809$	20.7056	0.727971	0.363986	+	0.931405i	$0.381416\pi$
$810$	100.946	3.54689
$811$	−32.7776	−1.15098	−0.575488	−	0.817810i	$-0.695188\pi$
$811$	−32.7776	−1.15098	−0.575488	+	0.817810i	$0.695188\pi$
$812$	0	0
$813$	53.7092	1.88367
$814$	−2.24524	−0.0786958
$815$	51.4742	1.80306
$816$	−2.51696	−0.0881114
$817$	−8.86364	−0.310100
$818$	32.9302	1.15138
$819$	0	0
$820$	−30.1170	−1.05173
$821$	−29.3513	−1.02437	−0.512183	−	0.858876i	$-0.671163\pi$
$821$	−29.3513	−1.02437	−0.512183	+	0.858876i	$0.671163\pi$
$822$	50.7725	1.77089
$823$	−33.4567	−1.16623	−0.583113	−	0.812391i	$-0.698166\pi$
$823$	−33.4567	−1.16623	−0.583113	+	0.812391i	$0.698166\pi$
$824$	−19.3148	−0.672864
$825$	9.64314	0.335731
$826$	0	0
$827$	−46.1265	−1.60397	−0.801987	−	0.597342i	$-0.796224\pi$
$827$	−46.1265	−1.60397	−0.801987	+	0.597342i	$0.796224\pi$
$828$	27.0852	0.941276
$829$	−19.7887	−0.687291	−0.343646	−	0.939099i	$-0.611662\pi$
$829$	−19.7887	−0.687291	−0.343646	+	0.939099i	$0.611662\pi$
$830$	31.1239	1.08033
$831$	63.8410	2.21462
$832$	7.08465	0.245616
$833$	0	0
$834$	40.4604	1.40103
$835$	33.1838	1.14837
$836$	−1.64314	−0.0568291
$837$	−137.085	−4.73835
$838$	−2.24934	−0.0777023
$839$	11.0497	0.381477	0.190739	−	0.981641i	$-0.438912\pi$
$839$	11.0497	0.381477	0.190739	+	0.981641i	$0.438912\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−29.5445	−1.01817
$843$	36.9873	1.27391
$844$	−6.80783	−0.234335
$845$	98.6644	3.39416
$846$	42.2450	1.45241
$847$	0	0
$848$	1.26712	0.0435132
$849$	29.2711	1.00458
$850$	1.51083	0.0518209
$851$	5.11808	0.175446
$852$	−45.8502	−1.57080
$853$	9.62963	0.329712	0.164856	−	0.986318i	$-0.447284\pi$
$853$	9.62963	0.329712	0.164856	+	0.986318i	$0.447284\pi$
$854$	0	0
$855$	26.6399	0.911064
$856$	8.43182	0.288194
$857$	24.9398	0.851928	0.425964	−	0.904740i	$-0.359935\pi$
$857$	24.9398	0.851928	0.425964	+	0.904740i	$0.359935\pi$
$858$	33.5308	1.14472
$859$	0.860094	0.0293460	0.0146730	−	0.999892i	$-0.495329\pi$
$859$	0.860094	0.0293460	0.0146730	+	0.999892i	$0.495329\pi$
$860$	−19.9534	−0.680405
$861$	0	0
$862$	−17.4275	−0.593581
$863$	19.7219	0.671340	0.335670	−	0.941980i	$-0.391037\pi$
$863$	19.7219	0.671340	0.335670	+	0.941980i	$0.391037\pi$
$864$	−18.7421	−0.637618
$865$	20.8114	0.707608
$866$	14.3016	0.485988
$867$	55.8374	1.89634
$868$	0	0
$869$	5.13350	0.174142
$870$	−9.00460	−0.305284
$871$	−82.5526	−2.79719
$872$	7.16470	0.242627
$873$	96.7437	3.27428
$874$	3.74556	0.126696
$875$	0	0
$876$	3.38061	0.114220
$877$	17.3453	0.585708	0.292854	−	0.956157i	$-0.405395\pi$
$877$	17.3453	0.585708	0.292854	+	0.956157i	$0.405395\pi$
$878$	3.65233	0.123260
$879$	36.1612	1.21969
$880$	−3.69895	−0.124691
$881$	46.8003	1.57674	0.788371	−	0.615200i	$-0.210925\pi$
$881$	46.8003	1.57674	0.788371	+	0.615200i	$0.210925\pi$
$882$	0	0
$883$	−8.36605	−0.281540	−0.140770	−	0.990042i	$-0.544958\pi$
$883$	−8.36605	−0.281540	−0.140770	+	0.990042i	$0.544958\pi$
$884$	5.25339	0.176691
$885$	40.6276	1.36568
$886$	9.26357	0.311216
$887$	26.3461	0.884616	0.442308	−	0.896863i	$-0.354160\pi$
$887$	26.3461	0.884616	0.442308	+	0.896863i	$0.354160\pi$
$888$	−5.46575	−0.183419
$889$	0	0
$890$	−12.1078	−0.405856
$891$	−53.0580	−1.77751
$892$	1.73747	0.0581748
$893$	5.84199	0.195495
$894$	31.7760	1.06275
$895$	2.06786	0.0691209
$896$	0	0
$897$	−76.4340	−2.55206
$898$	−9.29756	−0.310264
$899$	7.31429	0.243945
$900$	17.3625	0.578750
$901$	0.939595	0.0313024
$902$	15.8297	0.527072
$903$	0	0
$904$	10.2717	0.341632
$905$	18.7943	0.624745
$906$	−0.720826	−0.0239478
$907$	−36.9272	−1.22615	−0.613074	−	0.790026i	$-0.710067\pi$
$907$	−36.9272	−1.22615	−0.613074	+	0.790026i	$0.710067\pi$
$908$	20.4288	0.677954
$909$	52.2135	1.73181
$910$	0	0
$911$	−8.92045	−0.295548	−0.147774	−	0.989021i	$-0.547211\pi$
$911$	−8.92045	−0.295548	−0.147774	+	0.989021i	$0.547211\pi$
$912$	−4.00000	−0.132453
$913$	−16.3590	−0.541402
$914$	−19.8070	−0.655158
$915$	8.24734	0.272649
$916$	23.9763	0.792200
$917$	0	0
$918$	−13.8976	−0.458688
$919$	9.07600	0.299390	0.149695	−	0.988732i	$-0.452171\pi$
$919$	9.07600	0.299390	0.149695	+	0.988732i	$0.452171\pi$
$920$	8.43182	0.277989
$921$	40.1421	1.32273
$922$	−19.6388	−0.646770
$923$	95.6982	3.14994
$924$	0	0
$925$	3.28086	0.107874
$926$	20.8329	0.684610
$927$	−164.593	−5.40593
$928$	1.00000	0.0328266
$929$	−31.9160	−1.04713	−0.523564	−	0.851986i	$-0.675398\pi$
$929$	−31.9160	−1.04713	−0.523564	+	0.851986i	$0.675398\pi$
$930$	−65.8622	−2.15971
$931$	0	0
$932$	8.65792	0.283599
$933$	89.6243	2.93417
$934$	−17.4979	−0.572548
$935$	−2.74283	−0.0897003
$936$	60.3722	1.97333
$937$	−31.4932	−1.02884	−0.514419	−	0.857539i	$-0.671992\pi$
$937$	−31.4932	−1.02884	−0.514419	+	0.857539i	$0.671992\pi$
$938$	0	0
$939$	91.9830	3.00175
$940$	13.1512	0.428945
$941$	−36.3974	−1.18652	−0.593261	−	0.805010i	$-0.702160\pi$
$941$	−36.3974	−1.18652	−0.593261	+	0.805010i	$0.702160\pi$
$942$	23.1859	0.755439
$943$	−36.0842	−1.17506
$944$	−4.51187	−0.146849
$945$	0	0
$946$	10.4876	0.340982
$947$	1.90589	0.0619331	0.0309666	−	0.999520i	$-0.490141\pi$
$947$	1.90589	0.0619331	0.0309666	+	0.999520i	$0.490141\pi$
$948$	12.4968	0.405878
$949$	−7.05598	−0.229047
$950$	2.40103	0.0778997
$951$	−30.0933	−0.975843
$952$	0	0
$953$	18.8693	0.611236	0.305618	−	0.952154i	$-0.401137\pi$
$953$	18.8693	0.611236	0.305618	+	0.952154i	$0.401137\pi$
$954$	10.7979	0.349594
$955$	61.8502	2.00143
$956$	−10.1520	−0.328339
$957$	4.73288	0.152992
$958$	27.0711	0.874629
$959$	0	0
$960$	−9.00460	−0.290622
$961$	22.4989	0.725770
$962$	11.4081	0.367811
$963$	71.8523	2.31541
$964$	2.12367	0.0683987
$965$	24.9580	0.803426
$966$	0	0
$967$	−52.7167	−1.69525	−0.847627	−	0.530592i	$-0.821970\pi$
$967$	−52.7167	−1.69525	−0.847627	+	0.530592i	$0.821970\pi$
$968$	−9.05581	−0.291065
$969$	−2.96607	−0.0952839
$970$	30.1170	0.967000
$971$	−38.0421	−1.22083	−0.610414	−	0.792082i	$-0.708997\pi$
$971$	−38.0421	−1.22083	−0.610414	+	0.792082i	$0.708997\pi$
$972$	−72.9364	−2.33944
$973$	0	0
$974$	−17.0523	−0.546391
$975$	−48.9967	−1.56915
$976$	−0.915903	−0.0293173
$977$	25.9673	0.830769	0.415384	−	0.909646i	$-0.363647\pi$
$977$	25.9673	0.830769	0.415384	+	0.909646i	$0.363647\pi$
$978$	−65.8622	−2.10604
$979$	6.36396	0.203393
$980$	0	0
$981$	61.0544	1.94932
$982$	−7.44451	−0.237564
$983$	−57.1370	−1.82239	−0.911194	−	0.411978i	$-0.864838\pi$
$983$	−57.1370	−1.82239	−0.911194	+	0.411978i	$0.864838\pi$
$984$	38.5353	1.22846
$985$	32.3559	1.03094
$986$	0.741518	0.0236147
$987$	0	0
$988$	8.34877	0.265610
$989$	−23.9068	−0.760191
$990$	−31.5208	−1.00180
$991$	−41.2793	−1.31128	−0.655640	−	0.755074i	$-0.727601\pi$
$991$	−41.2793	−1.31128	−0.655640	+	0.755074i	$0.727601\pi$
$992$	7.31429	0.232229
$993$	67.1265	2.13020
$994$	0	0
$995$	32.0842	1.01714
$996$	−39.8237	−1.26186
$997$	7.89816	0.250137	0.125069	−	0.992148i	$-0.460085\pi$
$997$	7.89816	0.250137	0.125069	+	0.992148i	$0.460085\pi$
$998$	10.6184	0.336120
$999$	−30.1795	−0.954836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.r.1.1		4
7.6	odd	2		406.2.a.g.1.4	✓	4
21.20	even	2		3654.2.a.bg.1.4		4
28.27	even	2		3248.2.a.x.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.a.g.1.4	✓	4	7.6	odd	2
2842.2.a.r.1.1		4	1.1	even	1	trivial
3248.2.a.x.1.1		4	28.27	even	2
3654.2.a.bg.1.4		4	21.20	even	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.39434 q^{3} +1.00000 q^{4} +2.65282 q^{5} -3.39434 q^{6} +1.00000 q^{8} +8.52156 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.39434 q^{3} +1.00000 q^{4} +2.65282 q^{5} -3.39434 q^{6} +1.00000 q^{8} +8.52156 q^{9} +2.65282 q^{10} -1.39434 q^{11} -3.39434 q^{12} +7.08465 q^{13} -9.00460 q^{15} +1.00000 q^{16} +0.741518 q^{17} +8.52156 q^{18} +1.17843 q^{19} +2.65282 q^{20} -1.39434 q^{22} +3.17843 q^{23} -3.39434 q^{24} +2.03748 q^{25} +7.08465 q^{26} -18.7421 q^{27} +1.00000 q^{29} -9.00460 q^{30} +7.31429 q^{31} +1.00000 q^{32} +4.73288 q^{33} +0.741518 q^{34} +8.52156 q^{36} +1.61025 q^{37} +1.17843 q^{38} -24.0477 q^{39} +2.65282 q^{40} -11.3528 q^{41} -7.52156 q^{43} -1.39434 q^{44} +22.6062 q^{45} +3.17843 q^{46} +4.95743 q^{47} -3.39434 q^{48} +2.03748 q^{50} -2.51696 q^{51} +7.08465 q^{52} +1.26712 q^{53} -18.7421 q^{54} -3.69895 q^{55} -4.00000 q^{57} +1.00000 q^{58} -4.51187 q^{59} -9.00460 q^{60} -0.915903 q^{61} +7.31429 q^{62} +1.00000 q^{64} +18.7943 q^{65} +4.73288 q^{66} -11.6523 q^{67} +0.741518 q^{68} -10.7887 q^{69} +13.5078 q^{71} +8.52156 q^{72} -0.995954 q^{73} +1.61025 q^{74} -6.91590 q^{75} +1.17843 q^{76} -24.0477 q^{78} -3.68166 q^{79} +2.65282 q^{80} +38.0523 q^{81} -11.3528 q^{82} +11.7324 q^{83} +1.96712 q^{85} -7.52156 q^{86} -3.39434 q^{87} -1.39434 q^{88} -4.56413 q^{89} +22.6062 q^{90} +3.17843 q^{92} -24.8272 q^{93} +4.95743 q^{94} +3.12617 q^{95} -3.39434 q^{96} +11.3528 q^{97} -11.8820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9	\( 4 q + 4 q^{2} - q^{3} + 4 q^{4} + q^{5} - q^{6} + 4 q^{8} + 9 q^{9} + q^{10} + 7 q^{11} - q^{12} + 7 q^{13} - 5 q^{15} + 4 q^{16} + 9 q^{18} - 2 q^{19} + q^{20} + 7 q^{22} + 6 q^{23} - q^{24} + 9 q^{25} + 7 q^{26} - 13 q^{27} + 4 q^{29} - 5 q^{30} + 7 q^{31} + 4 q^{32} + 19 q^{33} + 9 q^{36} - 12 q^{37} - 2 q^{38} - 15 q^{39} + q^{40} - 4 q^{41} - 5 q^{43} + 7 q^{44} + 44 q^{45} + 6 q^{46} + 11 q^{47} - q^{48} + 9 q^{50} - 16 q^{51} + 7 q^{52} + 5 q^{53} - 13 q^{54} - 3 q^{55} - 16 q^{57} + 4 q^{58} - 16 q^{59} - 5 q^{60} + 34 q^{61} + 7 q^{62} + 4 q^{64} - q^{65} + 19 q^{66} + 2 q^{67} - 18 q^{69} + 24 q^{71} + 9 q^{72} + 24 q^{73} - 12 q^{74} + 10 q^{75} - 2 q^{76} - 15 q^{78} - 9 q^{79} + q^{80} + 40 q^{81} - 4 q^{82} + 8 q^{83} - 24 q^{85} - 5 q^{86} - q^{87} + 7 q^{88} - 2 q^{89} + 44 q^{90} + 6 q^{92} - 55 q^{93} + 11 q^{94} + 20 q^{95} - q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - q^3 + 4 * q^4 + q^5 - q^6 + 4 * q^8 + 9 * q^9 + q^10 + 7 * q^11 - q^12 + 7 * q^13 - 5 * q^15 + 4 * q^16 + 9 * q^18 - 2 * q^19 + q^20 + 7 * q^22 + 6 * q^23 - q^24 + 9 * q^25 + 7 * q^26 - 13 * q^27 + 4 * q^29 - 5 * q^30 + 7 * q^31 + 4 * q^32 + 19 * q^33 + 9 * q^36 - 12 * q^37 - 2 * q^38 - 15 * q^39 + q^40 - 4 * q^41 - 5 * q^43 + 7 * q^44 + 44 * q^45 + 6 * q^46 + 11 * q^47 - q^48 + 9 * q^50 - 16 * q^51 + 7 * q^52 + 5 * q^53 - 13 * q^54 - 3 * q^55 - 16 * q^57 + 4 * q^58 - 16 * q^59 - 5 * q^60 + 34 * q^61 + 7 * q^62 + 4 * q^64 - q^65 + 19 * q^66 + 2 * q^67 - 18 * q^69 + 24 * q^71 + 9 * q^72 + 24 * q^73 - 12 * q^74 + 10 * q^75 - 2 * q^76 - 15 * q^78 - 9 * q^79 + q^80 + 40 * q^81 - 4 * q^82 + 8 * q^83 - 24 * q^85 - 5 * q^86 - q^87 + 7 * q^88 - 2 * q^89 + 44 * q^90 + 6 * q^92 - 55 * q^93 + 11 * q^94 + 20 * q^95 - q^96 + 4 * q^97 + 2 * q^99

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