LMFDB - Embedded newform 5929.2.a.bm.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, 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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.7674048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 2 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 847)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.879640$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.120360 q^{2} -2.76784 q^{3} -1.98551 q^{4} +2.80853 q^{5} -0.333137 q^{6} -0.479696 q^{8} +4.66094 q^{9} +O(q^{10})$	\(q+0.120360 q^{2} -2.76784 q^{3} -1.98551 q^{4} +2.80853 q^{5} -0.333137 q^{6} -0.479696 q^{8} +4.66094 q^{9} +0.338034 q^{10} +5.49558 q^{12} -1.07967 q^{13} -7.77355 q^{15} +3.91329 q^{16} -6.95828 q^{17} +0.560990 q^{18} -7.54411 q^{19} -5.57636 q^{20} +4.82552 q^{23} +1.32772 q^{24} +2.88781 q^{25} -0.129949 q^{26} -4.59720 q^{27} +1.22726 q^{29} -0.935623 q^{30} +8.07409 q^{31} +1.43040 q^{32} -0.837498 q^{34} -9.25435 q^{36} +1.53525 q^{37} -0.908009 q^{38} +2.98836 q^{39} -1.34724 q^{40} -9.29986 q^{41} -5.23402 q^{43} +13.0904 q^{45} +0.580799 q^{46} +1.89387 q^{47} -10.8314 q^{48} +0.347577 q^{50} +19.2594 q^{51} +2.14371 q^{52} -3.82552 q^{53} -0.553319 q^{54} +20.8809 q^{57} +0.147713 q^{58} +6.66349 q^{59} +15.4345 q^{60} +9.79952 q^{61} +0.971796 q^{62} -7.65442 q^{64} -3.03229 q^{65} -2.06100 q^{67} +13.8158 q^{68} -13.3563 q^{69} +12.5212 q^{71} -2.23583 q^{72} -2.56708 q^{73} +0.184783 q^{74} -7.99301 q^{75} +14.9789 q^{76} +0.359679 q^{78} -15.3283 q^{79} +10.9906 q^{80} -1.25848 q^{81} -1.11933 q^{82} -2.04602 q^{83} -19.5425 q^{85} -0.629967 q^{86} -3.39687 q^{87} -4.76119 q^{89} +1.57555 q^{90} -9.58114 q^{92} -22.3478 q^{93} +0.227945 q^{94} -21.1878 q^{95} -3.95910 q^{96} -9.11512 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9}+O(q^{10}) $ 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9	$ 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9} + 8 q^{10} + 14 q^{12} - 4 q^{13} + 2 q^{15} + 8 q^{16} - 22 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{23} + 20 q^{24} + 4 q^{25} - 6 q^{26} + 2 q^{27} + 12 q^{29} + 20 q^{30} + 2 q^{31} + 8 q^{32} - 24 q^{34} + 18 q^{36} + 14 q^{37} + 22 q^{38} + 20 q^{39} - 18 q^{40} - 26 q^{41} - 4 q^{43} + 36 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 32 q^{54} + 20 q^{57} - 2 q^{58} + 4 q^{59} + 24 q^{60} + 8 q^{61} - 20 q^{62} + 26 q^{64} + 24 q^{65} + 6 q^{67} - 12 q^{68} + 14 q^{69} + 22 q^{71} + 16 q^{72} - 14 q^{73} + 44 q^{74} + 20 q^{75} + 30 q^{76} + 32 q^{78} - 28 q^{79} + 4 q^{80} - 6 q^{81} + 4 q^{82} - 22 q^{83} - 24 q^{85} - 30 q^{86} - 22 q^{87} + 22 q^{90} + 10 q^{92} - 50 q^{93} + 38 q^{94} - 24 q^{95} + 62 q^{96} + 4 q^{97}+O(q^{100}) $ 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9 + 8 * q^10 + 14 * q^12 - 4 * q^13 + 2 * q^15 + 8 * q^16 - 22 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^23 + 20 * q^24 + 4 * q^25 - 6 * q^26 + 2 * q^27 + 12 * q^29 + 20 * q^30 + 2 * q^31 + 8 * q^32 - 24 * q^34 + 18 * q^36 + 14 * q^37 + 22 * q^38 + 20 * q^39 - 18 * q^40 - 26 * q^41 - 4 * q^43 + 36 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 32 * q^54 + 20 * q^57 - 2 * q^58 + 4 * q^59 + 24 * q^60 + 8 * q^61 - 20 * q^62 + 26 * q^64 + 24 * q^65 + 6 * q^67 - 12 * q^68 + 14 * q^69 + 22 * q^71 + 16 * q^72 - 14 * q^73 + 44 * q^74 + 20 * q^75 + 30 * q^76 + 32 * q^78 - 28 * q^79 + 4 * q^80 - 6 * q^81 + 4 * q^82 - 22 * q^83 - 24 * q^85 - 30 * q^86 - 22 * q^87 + 22 * q^90 + 10 * q^92 - 50 * q^93 + 38 * q^94 - 24 * q^95 + 62 * q^96 + 4 * q^97

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 $

$2$	0.120360	0.0851073	0.0425536	−	0.999094i	$-0.486451\pi$
$2$	0.120360	0.0851073	0.0425536	+	0.999094i	$0.486451\pi$
$3$	−2.76784	−1.59801	−0.799006	−	0.601322i	$-0.794641\pi$
$3$	−2.76784	−1.59801	−0.799006	+	0.601322i	$0.794641\pi$
$4$	−1.98551	−0.992757
$5$	2.80853	1.25601	0.628005	−	0.778209i	$-0.283872\pi$
$5$	2.80853	1.25601	0.628005	+	0.778209i	$0.283872\pi$
$6$	−0.333137	−0.136003
$7$	0	0
$7$	0	0
$8$	−0.479696	−0.169598
$9$	4.66094	1.55365
$10$	0.338034	0.106896
$11$	0	0
$11$	0	0
$12$	5.49558	1.58644
$13$	−1.07967	−0.299448	−0.149724	−	0.988728i	$-0.547838\pi$
$13$	−1.07967	−0.299448	−0.149724	+	0.988728i	$0.547838\pi$
$14$	0	0
$15$	−7.77355	−2.00712
$16$	3.91329	0.978323
$17$	−6.95828	−1.68763	−0.843816	−	0.536633i	$-0.819696\pi$
$17$	−6.95828	−1.68763	−0.843816	+	0.536633i	$0.819696\pi$
$18$	0.560990	0.132227
$19$	−7.54411	−1.73074	−0.865369	−	0.501135i	$-0.832916\pi$
$19$	−7.54411	−1.73074	−0.865369	+	0.501135i	$0.832916\pi$
$20$	−5.57636	−1.24691
$21$	0	0
$22$	0	0
$23$	4.82552	1.00619	0.503095	−	0.864231i	$-0.332194\pi$
$23$	4.82552	1.00619	0.503095	+	0.864231i	$0.332194\pi$
$24$	1.32772	0.271020
$25$	2.88781	0.577563
$26$	−0.129949	−0.0254852
$27$	−4.59720	−0.884732
$28$	0	0
$29$	1.22726	0.227897	0.113949	−	0.993487i	$-0.463650\pi$
$29$	1.22726	0.227897	0.113949	+	0.993487i	$0.463650\pi$
$30$	−0.935623	−0.170821
$31$	8.07409	1.45015	0.725074	−	0.688671i	$-0.241805\pi$
$31$	8.07409	1.45015	0.725074	+	0.688671i	$0.241805\pi$
$32$	1.43040	0.252861
$33$	0	0
$34$	−0.837498	−0.143630
$35$	0	0
$36$	−9.25435	−1.54239
$37$	1.53525	0.252394	0.126197	−	0.992005i	$-0.459723\pi$
$37$	1.53525	0.252394	0.126197	+	0.992005i	$0.459723\pi$
$38$	−0.908009	−0.147298
$39$	2.98836	0.478521
$40$	−1.34724	−0.213017
$41$	−9.29986	−1.45239	−0.726197	−	0.687487i	$-0.758714\pi$
$41$	−9.29986	−1.45239	−0.726197	+	0.687487i	$0.758714\pi$
$42$	0	0
$43$	−5.23402	−0.798181	−0.399091	−	0.916912i	$-0.630674\pi$
$43$	−5.23402	−0.798181	−0.399091	+	0.916912i	$0.630674\pi$
$44$	0	0
$45$	13.0904	1.95140
$46$	0.580799	0.0856341
$47$	1.89387	0.276249	0.138124	−	0.990415i	$-0.455893\pi$
$47$	1.89387	0.276249	0.138124	+	0.990415i	$0.455893\pi$
$48$	−10.8314	−1.56337
$49$	0	0
$50$	0.347577	0.0491548
$51$	19.2594	2.69686
$52$	2.14371	0.297279
$53$	−3.82552	−0.525476	−0.262738	−	0.964867i	$-0.584625\pi$
$53$	−3.82552	−0.525476	−0.262738	+	0.964867i	$0.584625\pi$
$54$	−0.553319	−0.0752972
$55$	0	0
$56$	0	0
$57$	20.8809	2.76574
$58$	0.147713	0.0193957
$59$	6.66349	0.867513	0.433756	−	0.901030i	$-0.357188\pi$
$59$	6.66349	0.867513	0.433756	+	0.901030i	$0.357188\pi$
$60$	15.4345	1.99258
$61$	9.79952	1.25470	0.627350	−	0.778737i	$-0.284139\pi$
$61$	9.79952	1.25470	0.627350	+	0.778737i	$0.284139\pi$
$62$	0.971796	0.123418
$63$	0	0
$64$	−7.65442	−0.956802
$65$	−3.03229	−0.376110
$66$	0	0
$67$	−2.06100	−0.251792	−0.125896	−	0.992043i	$-0.540181\pi$
$67$	−2.06100	−0.251792	−0.125896	+	0.992043i	$0.540181\pi$
$68$	13.8158	1.67541
$69$	−13.3563	−1.60791
$70$	0	0
$71$	12.5212	1.48599	0.742996	−	0.669296i	$-0.233404\pi$
$71$	12.5212	1.48599	0.742996	+	0.669296i	$0.233404\pi$
$72$	−2.23583	−0.263495
$73$	−2.56708	−0.300454	−0.150227	−	0.988652i	$-0.548000\pi$
$73$	−2.56708	−0.300454	−0.150227	+	0.988652i	$0.548000\pi$
$74$	0.184783	0.0214806
$75$	−7.99301	−0.922953
$76$	14.9789	1.71820
$77$	0	0
$78$	0.359679	0.0407257
$79$	−15.3283	−1.72457	−0.862287	−	0.506420i	$-0.830969\pi$
$79$	−15.3283	−1.72457	−0.862287	+	0.506420i	$0.830969\pi$
$80$	10.9906	1.22878
$81$	−1.25848	−0.139832
$82$	−1.11933	−0.123609
$83$	−2.04602	−0.224580	−0.112290	−	0.993675i	$-0.535819\pi$
$83$	−2.04602	−0.224580	−0.112290	+	0.993675i	$0.535819\pi$
$84$	0	0
$85$	−19.5425	−2.11968
$86$	−0.629967	−0.0679310
$87$	−3.39687	−0.364183
$88$	0	0
$89$	−4.76119	−0.504685	−0.252342	−	0.967638i	$-0.581201\pi$
$89$	−4.76119	−0.504685	−0.252342	+	0.967638i	$0.581201\pi$
$90$	1.57555	0.166078
$91$	0	0
$92$	−9.58114	−0.998902
$93$	−22.3478	−2.31736
$94$	0.227945	0.0235108
$95$	−21.1878	−2.17383
$96$	−3.95910	−0.404074
$97$	−9.11512	−0.925500	−0.462750	−	0.886489i	$-0.653137\pi$
$97$	−9.11512	−0.925500	−0.462750	+	0.886489i	$0.653137\pi$
$98$	0	0
$99$	0	0
$100$	−5.73379	−0.573379
$101$	4.74385	0.472031	0.236015	−	0.971749i	$-0.424158\pi$
$101$	4.74385	0.472031	0.236015	+	0.971749i	$0.424158\pi$
$102$	2.31806	0.229522
$103$	−0.350901	−0.0345753	−0.0172876	−	0.999851i	$-0.505503\pi$
$103$	−0.350901	−0.0345753	−0.0172876	+	0.999851i	$0.505503\pi$
$104$	0.517915	0.0507858
$105$	0	0
$106$	−0.460439	−0.0447218
$107$	2.54774	0.246299	0.123149	−	0.992388i	$-0.460701\pi$
$107$	2.54774	0.246299	0.123149	+	0.992388i	$0.460701\pi$
$108$	9.12781	0.878324
$109$	−3.81522	−0.365432	−0.182716	−	0.983166i	$-0.558489\pi$
$109$	−3.81522	−0.365432	−0.182716	+	0.983166i	$0.558489\pi$
$110$	0	0
$111$	−4.24933	−0.403329
$112$	0	0
$113$	2.31468	0.217747	0.108873	−	0.994056i	$-0.465276\pi$
$113$	2.31468	0.217747	0.108873	+	0.994056i	$0.465276\pi$
$114$	2.51322	0.235385
$115$	13.5526	1.26379
$116$	−2.43675	−0.226246
$117$	−5.03229	−0.465236
$118$	0.802017	0.0738316
$119$	0	0
$120$	3.72894	0.340404
$121$	0	0
$122$	1.17947	0.106784
$123$	25.7405	2.32094
$124$	−16.0312	−1.43964
$125$	−5.93213	−0.530586
$126$	0	0
$127$	9.84644	0.873730	0.436865	−	0.899527i	$-0.356089\pi$
$127$	9.84644	0.873730	0.436865	+	0.899527i	$0.356089\pi$
$128$	−3.78208	−0.334291
$129$	14.4869	1.27550
$130$	−0.364966	−0.0320097
$131$	−16.3782	−1.43097	−0.715484	−	0.698629i	$-0.753794\pi$
$131$	−16.3782	−1.43097	−0.715484	+	0.698629i	$0.753794\pi$
$132$	0	0
$133$	0	0
$134$	−0.248062	−0.0214293
$135$	−12.9114	−1.11123
$136$	3.33786	0.286219
$137$	−14.2142	−1.21440	−0.607199	−	0.794550i	$-0.707707\pi$
$137$	−14.2142	−1.21440	−0.607199	+	0.794550i	$0.707707\pi$
$138$	−1.60756	−0.136844
$139$	9.17942	0.778588	0.389294	−	0.921114i	$-0.372719\pi$
$139$	9.17942	0.778588	0.389294	+	0.921114i	$0.372719\pi$
$140$	0	0
$141$	−5.24192	−0.441449
$142$	1.50705	0.126469
$143$	0	0
$144$	18.2396	1.51997
$145$	3.44680	0.286241
$146$	−0.308974	−0.0255708
$147$	0	0
$148$	−3.04827	−0.250566
$149$	11.6200	0.951947	0.475973	−	0.879460i	$-0.342096\pi$
$149$	11.6200	0.951947	0.475973	+	0.879460i	$0.342096\pi$
$150$	−0.962037	−0.0785500
$151$	17.9150	1.45790	0.728952	−	0.684565i	$-0.240008\pi$
$151$	17.9150	1.45790	0.728952	+	0.684565i	$0.240008\pi$
$152$	3.61888	0.293530
$153$	−32.4321	−2.62198
$154$	0	0
$155$	22.6763	1.82140
$156$	−5.93344	−0.475055
$157$	−7.42805	−0.592823	−0.296412	−	0.955060i	$-0.595790\pi$
$157$	−7.42805	−0.592823	−0.296412	+	0.955060i	$0.595790\pi$
$158$	−1.84492	−0.146774
$159$	10.5884	0.839717
$160$	4.01730	0.317596
$161$	0	0
$162$	−0.151471	−0.0119007
$163$	7.85296	0.615091	0.307546	−	0.951533i	$-0.400492\pi$
$163$	7.85296	0.615091	0.307546	+	0.951533i	$0.400492\pi$
$164$	18.4650	1.44187
$165$	0	0
$166$	−0.246259	−0.0191134
$167$	5.40259	0.418065	0.209032	−	0.977909i	$-0.432969\pi$
$167$	5.40259	0.418065	0.209032	+	0.977909i	$0.432969\pi$
$168$	0	0
$169$	−11.8343	−0.910331
$170$	−2.35214	−0.180401
$171$	−35.1626	−2.68895
$172$	10.3922	0.792400
$173$	19.7211	1.49937	0.749685	−	0.661795i	$-0.230205\pi$
$173$	19.7211	1.49937	0.749685	+	0.661795i	$0.230205\pi$
$174$	−0.408847	−0.0309946
$175$	0	0
$176$	0	0
$177$	−18.4435	−1.38630
$178$	−0.573056	−0.0429524
$179$	−23.3292	−1.74370	−0.871851	−	0.489770i	$-0.837081\pi$
$179$	−23.3292	−1.74370	−0.871851	+	0.489770i	$0.837081\pi$
$180$	−25.9911	−1.93726
$181$	−3.08500	−0.229306	−0.114653	−	0.993406i	$-0.536576\pi$
$181$	−3.08500	−0.229306	−0.114653	+	0.993406i	$0.536576\pi$
$182$	0	0
$183$	−27.1235	−2.00503
$184$	−2.31478	−0.170648
$185$	4.31180	0.317010
$186$	−2.68978	−0.197224
$187$	0	0
$188$	−3.76030	−0.274248
$189$	0	0
$190$	−2.55017	−0.185008
$191$	12.5715	0.909640	0.454820	−	0.890583i	$-0.349704\pi$
$191$	12.5715	0.909640	0.454820	+	0.890583i	$0.349704\pi$
$192$	21.1862	1.52898
$193$	−20.6685	−1.48775	−0.743877	−	0.668317i	$-0.767015\pi$
$193$	−20.6685	−1.48775	−0.743877	+	0.668317i	$0.767015\pi$
$194$	−1.09709	−0.0787668
$195$	8.39290	0.601028
$196$	0	0
$197$	6.27954	0.447399	0.223699	−	0.974658i	$-0.428187\pi$
$197$	6.27954	0.447399	0.223699	+	0.974658i	$0.428187\pi$
$198$	0	0
$199$	6.86896	0.486927	0.243464	−	0.969910i	$-0.421716\pi$
$199$	6.86896	0.486927	0.243464	+	0.969910i	$0.421716\pi$
$200$	−1.38527	−0.0979536
$201$	5.70453	0.402366
$202$	0.570969	0.0401733
$203$	0	0
$204$	−38.2398	−2.67732
$205$	−26.1189	−1.82422
$206$	−0.0422344	−0.00294261
$207$	22.4914	1.56326
$208$	−4.22508	−0.292957
$209$	0	0
$210$	0	0
$211$	10.2586	0.706232	0.353116	−	0.935580i	$-0.385122\pi$
$211$	10.2586	0.706232	0.353116	+	0.935580i	$0.385122\pi$
$212$	7.59562	0.521669
$213$	−34.6567	−2.37463
$214$	0.306645	0.0209618
$215$	−14.6999	−1.00252
$216$	2.20526	0.150049
$217$	0	0
$218$	−0.459199	−0.0311009
$219$	7.10527	0.480130
$220$	0	0
$221$	7.51268	0.505358
$222$	−0.511449	−0.0343262
$223$	13.5221	0.905506	0.452753	−	0.891636i	$-0.350442\pi$
$223$	13.5221	0.905506	0.452753	+	0.891636i	$0.350442\pi$
$224$	0	0
$225$	13.4599	0.897328
$226$	0.278595	0.0185319
$227$	−13.5764	−0.901100	−0.450550	−	0.892751i	$-0.648772\pi$
$227$	−13.5764	−0.901100	−0.450550	+	0.892751i	$0.648772\pi$
$228$	−41.4593	−2.74571
$229$	1.45296	0.0960141	0.0480070	−	0.998847i	$-0.484713\pi$
$229$	1.45296	0.0960141	0.0480070	+	0.998847i	$0.484713\pi$
$230$	1.63119	0.107557
$231$	0	0
$232$	−0.588713	−0.0386509
$233$	8.20387	0.537453	0.268727	−	0.963216i	$-0.413397\pi$
$233$	8.20387	0.537453	0.268727	+	0.963216i	$0.413397\pi$
$234$	−0.605686	−0.0395949
$235$	5.31897	0.346971
$236$	−13.2305	−0.861229
$237$	42.4264	2.75589
$238$	0	0
$239$	10.3835	0.671655	0.335827	−	0.941924i	$-0.390984\pi$
$239$	10.3835	0.671655	0.335827	+	0.941924i	$0.390984\pi$
$240$	−30.4202	−1.96361
$241$	8.20445	0.528495	0.264248	−	0.964455i	$-0.414876\pi$
$241$	8.20445	0.528495	0.264248	+	0.964455i	$0.414876\pi$
$242$	0	0
$243$	17.2749	1.10818
$244$	−19.4571	−1.24561
$245$	0	0
$246$	3.09813	0.197529
$247$	8.14519	0.518266
$248$	−3.87311	−0.245943
$249$	5.66306	0.358882
$250$	−0.713990	−0.0451567
$251$	16.4452	1.03801	0.519005	−	0.854771i	$-0.326302\pi$
$251$	16.4452	1.03801	0.519005	+	0.854771i	$0.326302\pi$
$252$	0	0
$253$	0	0
$254$	1.18512	0.0743608
$255$	54.0906	3.38728
$256$	14.8536	0.928352
$257$	12.0440	0.751282	0.375641	−	0.926765i	$-0.377423\pi$
$257$	12.0440	0.751282	0.375641	+	0.926765i	$0.377423\pi$
$258$	1.74365	0.108555
$259$	0	0
$260$	6.02066	0.373385
$261$	5.72020	0.354071
$262$	−1.97127	−0.121786
$263$	1.87602	0.115681	0.0578403	−	0.998326i	$-0.481579\pi$
$263$	1.87602	0.115681	0.0578403	+	0.998326i	$0.481579\pi$
$264$	0	0
$265$	−10.7441	−0.660003
$266$	0	0
$267$	13.1782	0.806493
$268$	4.09215	0.249968
$269$	14.0290	0.855362	0.427681	−	0.903930i	$-0.359331\pi$
$269$	14.0290	0.855362	0.427681	+	0.903930i	$0.359331\pi$
$270$	−1.55401	−0.0945741
$271$	−1.35328	−0.0822056	−0.0411028	−	0.999155i	$-0.513087\pi$
$271$	−1.35328	−0.0822056	−0.0411028	+	0.999155i	$0.513087\pi$
$272$	−27.2298	−1.65105
$273$	0	0
$274$	−1.71081	−0.103354
$275$	0	0
$276$	26.5190	1.59626
$277$	−13.3835	−0.804138	−0.402069	−	0.915609i	$-0.631709\pi$
$277$	−13.3835	−0.804138	−0.402069	+	0.915609i	$0.631709\pi$
$278$	1.10483	0.0662635
$279$	37.6328	2.25302
$280$	0	0
$281$	2.31887	0.138332	0.0691661	−	0.997605i	$-0.477966\pi$
$281$	2.31887	0.138332	0.0691661	+	0.997605i	$0.477966\pi$
$282$	−0.630916	−0.0375705
$283$	22.2679	1.32369	0.661845	−	0.749641i	$-0.269774\pi$
$283$	22.2679	1.32369	0.661845	+	0.749641i	$0.269774\pi$
$284$	−24.8610	−1.47523
$285$	58.6445	3.47380
$286$	0	0
$287$	0	0
$288$	6.66698	0.392856
$289$	31.4177	1.84810
$290$	0.414857	0.0243612
$291$	25.2292	1.47896
$292$	5.09698	0.298278
$293$	2.43981	0.142535	0.0712675	−	0.997457i	$-0.477296\pi$
$293$	2.43981	0.142535	0.0712675	+	0.997457i	$0.477296\pi$
$294$	0	0
$295$	18.7146	1.08961
$296$	−0.736455	−0.0428056
$297$	0	0
$298$	1.39858	0.0810176
$299$	−5.20999	−0.301301
$300$	15.8702	0.916268
$301$	0	0
$302$	2.15625	0.124078
$303$	−13.1302	−0.754311
$304$	−29.5223	−1.69322
$305$	27.5222	1.57592
$306$	−3.90353	−0.223150
$307$	8.89055	0.507410	0.253705	−	0.967282i	$-0.418351\pi$
$307$	8.89055	0.507410	0.253705	+	0.967282i	$0.418351\pi$
$308$	0	0
$309$	0.971237	0.0552517
$310$	2.72931	0.155015
$311$	11.8347	0.671085	0.335543	−	0.942025i	$-0.391080\pi$
$311$	11.8347	0.671085	0.335543	+	0.942025i	$0.391080\pi$
$312$	−1.43351	−0.0811563
$313$	29.5406	1.66973	0.834865	−	0.550454i	$-0.185545\pi$
$313$	29.5406	1.66973	0.834865	+	0.550454i	$0.185545\pi$
$314$	−0.894039	−0.0504536
$315$	0	0
$316$	30.4346	1.71208
$317$	−25.1545	−1.41282	−0.706409	−	0.707804i	$-0.749686\pi$
$317$	−25.1545	−1.41282	−0.706409	+	0.707804i	$0.749686\pi$
$318$	1.27442	0.0714660
$319$	0	0
$320$	−21.4976	−1.20175
$321$	−7.05172	−0.393589
$322$	0	0
$323$	52.4941	2.92085
$324$	2.49874	0.138819
$325$	−3.11790	−0.172950
$326$	0.945181	0.0523488
$327$	10.5599	0.583964
$328$	4.46110	0.246323
$329$	0	0
$330$	0	0
$331$	−9.46333	−0.520152	−0.260076	−	0.965588i	$-0.583748\pi$
$331$	−9.46333	−0.520152	−0.260076	+	0.965588i	$0.583748\pi$
$332$	4.06241	0.222954
$333$	7.15572	0.392131
$334$	0.650255	0.0355804
$335$	−5.78838	−0.316253
$336$	0	0
$337$	−17.2248	−0.938297	−0.469148	−	0.883119i	$-0.655439\pi$
$337$	−17.2248	−0.938297	−0.469148	+	0.883119i	$0.655439\pi$
$338$	−1.42438	−0.0774758
$339$	−6.40667	−0.347962
$340$	38.8019	2.10433
$341$	0	0
$342$	−4.23217	−0.228850
$343$	0	0
$344$	2.51074	0.135370
$345$	−37.5114	−2.01955
$346$	2.37363	0.127607
$347$	−8.73485	−0.468911	−0.234456	−	0.972127i	$-0.575331\pi$
$347$	−8.73485	−0.468911	−0.234456	+	0.972127i	$0.575331\pi$
$348$	6.74453	0.361545
$349$	29.9851	1.60506	0.802532	−	0.596609i	$-0.203486\pi$
$349$	29.9851	1.60506	0.802532	+	0.596609i	$0.203486\pi$
$350$	0	0
$351$	4.96348	0.264931
$352$	0	0
$353$	−7.31999	−0.389604	−0.194802	−	0.980843i	$-0.562406\pi$
$353$	−7.31999	−0.389604	−0.194802	+	0.980843i	$0.562406\pi$
$354$	−2.21985	−0.117984
$355$	35.1661	1.86642
$356$	9.45340	0.501029
$357$	0	0
$358$	−2.80789	−0.148402
$359$	4.96996	0.262304	0.131152	−	0.991362i	$-0.458132\pi$
$359$	4.96996	0.262304	0.131152	+	0.991362i	$0.458132\pi$
$360$	−6.27939	−0.330953
$361$	37.9137	1.99546
$362$	−0.371311	−0.0195156
$363$	0	0
$364$	0	0
$365$	−7.20971	−0.377374
$366$	−3.26458	−0.170642
$367$	14.2042	0.741455	0.370727	−	0.928742i	$-0.379108\pi$
$367$	14.2042	0.741455	0.370727	+	0.928742i	$0.379108\pi$
$368$	18.8837	0.984379
$369$	−43.3460	−2.25650
$370$	0.518967	0.0269798
$371$	0	0
$372$	44.3718	2.30057
$373$	8.97781	0.464853	0.232427	−	0.972614i	$-0.425333\pi$
$373$	8.97781	0.464853	0.232427	+	0.972614i	$0.425333\pi$
$374$	0	0
$375$	16.4192	0.847883
$376$	−0.908480	−0.0468513
$377$	−1.32504	−0.0682433
$378$	0	0
$379$	10.7896	0.554223	0.277112	−	0.960838i	$-0.410623\pi$
$379$	10.7896	0.554223	0.277112	+	0.960838i	$0.410623\pi$
$380$	42.0687	2.15808
$381$	−27.2534	−1.39623
$382$	1.51310	0.0774170
$383$	23.5100	1.20130	0.600652	−	0.799511i	$-0.294908\pi$
$383$	23.5100	1.20130	0.600652	+	0.799511i	$0.294908\pi$
$384$	10.4682	0.534202
$385$	0	0
$386$	−2.48766	−0.126619
$387$	−24.3954	−1.24009
$388$	18.0982	0.918797
$389$	−11.8745	−0.602063	−0.301032	−	0.953614i	$-0.597331\pi$
$389$	−11.8745	−0.602063	−0.301032	+	0.953614i	$0.597331\pi$
$390$	1.01017	0.0511519
$391$	−33.5773	−1.69808
$392$	0	0
$393$	45.3322	2.28670
$394$	0.755804	0.0380769
$395$	−43.0501	−2.16608
$396$	0	0
$397$	23.7264	1.19079	0.595397	−	0.803431i	$-0.296995\pi$
$397$	23.7264	1.19079	0.595397	+	0.803431i	$0.296995\pi$
$398$	0.826747	0.0414411
$399$	0	0
$400$	11.3009	0.565043
$401$	−3.80121	−0.189823	−0.0949117	−	0.995486i	$-0.530257\pi$
$401$	−3.80121	−0.189823	−0.0949117	+	0.995486i	$0.530257\pi$
$402$	0.686596	0.0342443
$403$	−8.71738	−0.434244
$404$	−9.41898	−0.468612
$405$	−3.53448	−0.175630
$406$	0	0
$407$	0	0
$408$	−9.23866	−0.457382
$409$	5.98291	0.295836	0.147918	−	0.989000i	$-0.452743\pi$
$409$	5.98291	0.295836	0.147918	+	0.989000i	$0.452743\pi$
$410$	−3.14367	−0.155255
$411$	39.3425	1.94062
$412$	0.696718	0.0343248
$413$	0	0
$414$	2.70707	0.133045
$415$	−5.74631	−0.282075
$416$	−1.54436	−0.0757185
$417$	−25.4072	−1.24419
$418$	0	0
$419$	4.16889	0.203664	0.101832	−	0.994802i	$-0.467530\pi$
$419$	4.16889	0.203664	0.101832	+	0.994802i	$0.467530\pi$
$420$	0	0
$421$	23.4555	1.14315	0.571575	−	0.820550i	$-0.306333\pi$
$421$	23.4555	1.14315	0.571575	+	0.820550i	$0.306333\pi$
$422$	1.23473	0.0601055
$423$	8.82719	0.429192
$424$	1.83509	0.0891197
$425$	−20.0942	−0.974713
$426$	−4.17127	−0.202099
$427$	0	0
$428$	−5.05856	−0.244515
$429$	0	0
$430$	−1.76928	−0.0853221
$431$	37.2730	1.79538	0.897689	−	0.440630i	$-0.145245\pi$
$431$	37.2730	1.79538	0.897689	+	0.440630i	$0.145245\pi$
$432$	−17.9902	−0.865554
$433$	22.7863	1.09504	0.547520	−	0.836793i	$-0.315572\pi$
$433$	22.7863	1.09504	0.547520	+	0.836793i	$0.315572\pi$
$434$	0	0
$435$	−9.54019	−0.457417
$436$	7.57517	0.362785
$437$	−36.4043	−1.74145
$438$	0.855190	0.0408625
$439$	1.42974	0.0682379	0.0341189	−	0.999418i	$-0.489137\pi$
$439$	1.42974	0.0682379	0.0341189	+	0.999418i	$0.489137\pi$
$440$	0	0
$441$	0	0
$442$	0.904225	0.0430096
$443$	−26.4301	−1.25573	−0.627866	−	0.778321i	$-0.716072\pi$
$443$	−26.4301	−1.25573	−0.627866	+	0.778321i	$0.716072\pi$
$444$	8.43711	0.400408
$445$	−13.3719	−0.633890
$446$	1.62752	0.0770651
$447$	−32.1623	−1.52122
$448$	0	0
$449$	14.0870	0.664806	0.332403	−	0.943137i	$-0.392141\pi$
$449$	14.0870	0.664806	0.332403	+	0.943137i	$0.392141\pi$
$450$	1.62003	0.0763691
$451$	0	0
$452$	−4.59583	−0.216170
$453$	−49.5859	−2.32975
$454$	−1.63406	−0.0766902
$455$	0	0
$456$	−10.0165	−0.469065
$457$	29.4829	1.37915	0.689575	−	0.724214i	$-0.257797\pi$
$457$	29.4829	1.37915	0.689575	+	0.724214i	$0.257797\pi$
$458$	0.174878	0.00817150
$459$	31.9887	1.49310
$460$	−26.9089	−1.25463
$461$	−31.7282	−1.47773	−0.738866	−	0.673853i	$-0.764638\pi$
$461$	−31.7282	−1.47773	−0.738866	+	0.673853i	$0.764638\pi$
$462$	0	0
$463$	−12.7839	−0.594117	−0.297059	−	0.954859i	$-0.596006\pi$
$463$	−12.7839	−0.594117	−0.297059	+	0.954859i	$0.596006\pi$
$464$	4.80264	0.222957
$465$	−62.7643	−2.91062
$466$	0.987417	0.0457412
$467$	−29.5768	−1.36865	−0.684325	−	0.729177i	$-0.739903\pi$
$467$	−29.5768	−1.36865	−0.684325	+	0.729177i	$0.739903\pi$
$468$	9.99168	0.461866
$469$	0	0
$470$	0.640191	0.0295298
$471$	20.5597	0.947339
$472$	−3.19645	−0.147129
$473$	0	0
$474$	5.10644	0.234546
$475$	−21.7860	−0.999610
$476$	0	0
$477$	−17.8305	−0.816403
$478$	1.24976	0.0571627
$479$	28.5574	1.30482	0.652411	−	0.757866i	$-0.273758\pi$
$479$	28.5574	1.30482	0.652411	+	0.757866i	$0.273758\pi$
$480$	−11.1192	−0.507522
$481$	−1.65757	−0.0755788
$482$	0.987487	0.0449788
$483$	0	0
$484$	0	0
$485$	−25.6000	−1.16244
$486$	2.07920	0.0943146
$487$	1.05828	0.0479552	0.0239776	−	0.999712i	$-0.492367\pi$
$487$	1.05828	0.0479552	0.0239776	+	0.999712i	$0.492367\pi$
$488$	−4.70079	−0.212795
$489$	−21.7357	−0.982924
$490$	0	0
$491$	18.4489	0.832586	0.416293	−	0.909230i	$-0.363329\pi$
$491$	18.4489	0.832586	0.416293	+	0.909230i	$0.363329\pi$
$492$	−51.1081	−2.30413
$493$	−8.53965	−0.384606
$494$	0.980354	0.0441082
$495$	0	0
$496$	31.5962	1.41871
$497$	0	0
$498$	0.681606	0.0305435
$499$	31.7293	1.42040	0.710199	−	0.704001i	$-0.248605\pi$
$499$	31.7293	1.42040	0.710199	+	0.704001i	$0.248605\pi$
$500$	11.7783	0.526742
$501$	−14.9535	−0.668073
$502$	1.97934	0.0883423
$503$	29.0283	1.29431	0.647154	−	0.762359i	$-0.275959\pi$
$503$	29.0283	1.29431	0.647154	+	0.762359i	$0.275959\pi$
$504$	0	0
$505$	13.3232	0.592876
$506$	0	0
$507$	32.7555	1.45472
$508$	−19.5502	−0.867401
$509$	−2.88831	−0.128022	−0.0640110	−	0.997949i	$-0.520389\pi$
$509$	−2.88831	−0.128022	−0.0640110	+	0.997949i	$0.520389\pi$
$510$	6.51033	0.288282
$511$	0	0
$512$	9.35193	0.413301
$513$	34.6818	1.53124
$514$	1.44961	0.0639396
$515$	−0.985513	−0.0434269
$516$	−28.7640	−1.26626
$517$	0	0
$518$	0	0
$519$	−54.5849	−2.39601
$520$	1.45458	0.0637875
$521$	−31.6708	−1.38752	−0.693762	−	0.720204i	$-0.744048\pi$
$521$	−31.6708	−1.38752	−0.693762	+	0.720204i	$0.744048\pi$
$522$	0.688482	0.0301340
$523$	16.0380	0.701295	0.350647	−	0.936508i	$-0.385962\pi$
$523$	16.0380	0.701295	0.350647	+	0.936508i	$0.385962\pi$
$524$	32.5191	1.42060
$525$	0	0
$526$	0.225798	0.00984526
$527$	−56.1818	−2.44732
$528$	0	0
$529$	0.285644	0.0124193
$530$	−1.29316	−0.0561711
$531$	31.0581	1.34781
$532$	0	0
$533$	10.0408	0.434916
$534$	1.58613	0.0686384
$535$	7.15538	0.309354
$536$	0.988655	0.0427034
$537$	64.5714	2.78646
$538$	1.68853	0.0727976
$539$	0	0
$540$	25.6357	1.10318
$541$	13.5946	0.584480	0.292240	−	0.956345i	$-0.405599\pi$
$541$	13.5946	0.584480	0.292240	+	0.956345i	$0.405599\pi$
$542$	−0.162880	−0.00699630
$543$	8.53879	0.366435
$544$	−9.95310	−0.426735
$545$	−10.7151	−0.458986
$546$	0	0
$547$	−8.82486	−0.377324	−0.188662	−	0.982042i	$-0.560415\pi$
$547$	−8.82486	−0.377324	−0.188662	+	0.982042i	$0.560415\pi$
$548$	28.2224	1.20560
$549$	45.6749	1.94936
$550$	0	0
$551$	−9.25862	−0.394430
$552$	6.40695	0.272698
$553$	0	0
$554$	−1.61084	−0.0684380
$555$	−11.9344	−0.506586
$556$	−18.2259	−0.772949
$557$	33.9920	1.44029	0.720145	−	0.693824i	$-0.244075\pi$
$557$	33.9920	1.44029	0.720145	+	0.693824i	$0.244075\pi$
$558$	4.52948	0.191748
$559$	5.65104	0.239014
$560$	0	0
$561$	0	0
$562$	0.279099	0.0117731
$563$	20.2256	0.852406	0.426203	−	0.904628i	$-0.359851\pi$
$563$	20.2256	0.852406	0.426203	+	0.904628i	$0.359851\pi$
$564$	10.4079	0.438251
$565$	6.50084	0.273492
$566$	2.68016	0.112656
$567$	0	0
$568$	−6.00637	−0.252022
$569$	28.9330	1.21293	0.606467	−	0.795109i	$-0.292586\pi$
$569$	28.9330	1.21293	0.606467	+	0.795109i	$0.292586\pi$
$570$	7.05845	0.295646
$571$	−7.51312	−0.314414	−0.157207	−	0.987566i	$-0.550249\pi$
$571$	−7.51312	−0.314414	−0.157207	+	0.987566i	$0.550249\pi$
$572$	0	0
$573$	−34.7958	−1.45362
$574$	0	0
$575$	13.9352	0.581138
$576$	−35.6768	−1.48653
$577$	−34.3748	−1.43104	−0.715521	−	0.698592i	$-0.753810\pi$
$577$	−34.3748	−1.43104	−0.715521	+	0.698592i	$0.753810\pi$
$578$	3.78143	0.157287
$579$	57.2072	2.37745
$580$	−6.84367	−0.284168
$581$	0	0
$582$	3.03658	0.125870
$583$	0	0
$584$	1.23142	0.0509565
$585$	−14.1333	−0.584341
$586$	0.293655	0.0121308
$587$	−42.0392	−1.73514	−0.867571	−	0.497313i	$-0.834320\pi$
$587$	−42.0392	−1.73514	−0.867571	+	0.497313i	$0.834320\pi$
$588$	0	0
$589$	−60.9118	−2.50983
$590$	2.25249	0.0927333
$591$	−17.3808	−0.714949
$592$	6.00789	0.246923
$593$	−29.2867	−1.20266	−0.601331	−	0.799000i	$-0.705363\pi$
$593$	−29.2867	−1.20266	−0.601331	+	0.799000i	$0.705363\pi$
$594$	0	0
$595$	0	0
$596$	−23.0716	−0.945051
$597$	−19.0122	−0.778116
$598$	−0.627074	−0.0256430
$599$	−15.1577	−0.619327	−0.309663	−	0.950846i	$-0.600216\pi$
$599$	−15.1577	−0.619327	−0.309663	+	0.950846i	$0.600216\pi$
$600$	3.83421	0.156531
$601$	−31.8735	−1.30015	−0.650073	−	0.759872i	$-0.725262\pi$
$601$	−31.8735	−1.30015	−0.650073	+	0.759872i	$0.725262\pi$
$602$	0	0
$603$	−9.60621	−0.391195
$604$	−35.5705	−1.44734
$605$	0	0
$606$	−1.58035	−0.0641974
$607$	20.1463	0.817714	0.408857	−	0.912598i	$-0.365927\pi$
$607$	20.1463	0.817714	0.408857	+	0.912598i	$0.365927\pi$
$608$	−10.7911	−0.437635
$609$	0	0
$610$	3.31257	0.134122
$611$	−2.04476	−0.0827220
$612$	64.3944	2.60299
$613$	−3.89132	−0.157169	−0.0785844	−	0.996907i	$-0.525040\pi$
$613$	−3.89132	−0.157169	−0.0785844	+	0.996907i	$0.525040\pi$
$614$	1.07007	0.0431843
$615$	72.2929	2.91513
$616$	0	0
$617$	28.6122	1.15189	0.575943	−	0.817490i	$-0.304635\pi$
$617$	28.6122	1.15189	0.575943	+	0.817490i	$0.304635\pi$
$618$	0.116898	0.00470233
$619$	26.1546	1.05124	0.525621	−	0.850719i	$-0.323833\pi$
$619$	26.1546	1.05124	0.525621	+	0.850719i	$0.323833\pi$
$620$	−45.0240	−1.80821
$621$	−22.1839	−0.890209
$622$	1.42443	0.0571143
$623$	0	0
$624$	11.6943	0.468148
$625$	−31.0996	−1.24398
$626$	3.55550	0.142106
$627$	0	0
$628$	14.7485	0.588529
$629$	−10.6827	−0.425948
$630$	0	0
$631$	−5.68272	−0.226225	−0.113113	−	0.993582i	$-0.536082\pi$
$631$	−5.68272	−0.226225	−0.113113	+	0.993582i	$0.536082\pi$
$632$	7.35295	0.292485
$633$	−28.3942	−1.12857
$634$	−3.02759	−0.120241
$635$	27.6540	1.09741
$636$	−21.0235	−0.833635
$637$	0	0
$638$	0	0
$639$	58.3605	2.30870
$640$	−10.6221	−0.419874
$641$	−20.7292	−0.818756	−0.409378	−	0.912365i	$-0.634254\pi$
$641$	−20.7292	−0.818756	−0.409378	+	0.912365i	$0.634254\pi$
$642$	−0.848744	−0.0334973
$643$	−21.2756	−0.839029	−0.419515	−	0.907749i	$-0.637800\pi$
$643$	−21.2756	−0.839029	−0.419515	+	0.907749i	$0.637800\pi$
$644$	0	0
$645$	40.6869	1.60205
$646$	6.31818	0.248586
$647$	17.2718	0.679023	0.339512	−	0.940602i	$-0.389738\pi$
$647$	17.2718	0.679023	0.339512	+	0.940602i	$0.389738\pi$
$648$	0.603690	0.0237152
$649$	0	0
$650$	−0.375270	−0.0147193
$651$	0	0
$652$	−15.5922	−0.610636
$653$	41.0788	1.60754	0.803768	−	0.594942i	$-0.202825\pi$
$653$	41.0788	1.60754	0.803768	+	0.594942i	$0.202825\pi$
$654$	1.27099	0.0496996
$655$	−45.9985	−1.79731
$656$	−36.3930	−1.42091
$657$	−11.9650	−0.466799
$658$	0	0
$659$	6.00410	0.233887	0.116943	−	0.993139i	$-0.462690\pi$
$659$	6.00410	0.233887	0.116943	+	0.993139i	$0.462690\pi$
$660$	0	0
$661$	1.83502	0.0713739	0.0356870	−	0.999363i	$-0.488638\pi$
$661$	1.83502	0.0713739	0.0356870	+	0.999363i	$0.488638\pi$
$662$	−1.13901	−0.0442687
$663$	−20.7939	−0.807568
$664$	0.981469	0.0380884
$665$	0	0
$666$	0.861261	0.0333732
$667$	5.92218	0.229308
$668$	−10.7269	−0.415037
$669$	−37.4270	−1.44701
$670$	−0.696689	−0.0269154
$671$	0	0
$672$	0	0
$673$	44.4403	1.71305	0.856524	−	0.516107i	$-0.172619\pi$
$673$	44.4403	1.71305	0.856524	+	0.516107i	$0.172619\pi$
$674$	−2.07318	−0.0798559
$675$	−13.2759	−0.510989
$676$	23.4972	0.903737
$677$	−15.5471	−0.597525	−0.298762	−	0.954327i	$-0.596574\pi$
$677$	−15.5471	−0.597525	−0.298762	+	0.954327i	$0.596574\pi$
$678$	−0.771106	−0.0296141
$679$	0	0
$680$	9.37447	0.359494
$681$	37.5774	1.43997
$682$	0	0
$683$	−36.8979	−1.41186	−0.705930	−	0.708282i	$-0.749471\pi$
$683$	−36.8979	−1.41186	−0.705930	+	0.708282i	$0.749471\pi$
$684$	69.8159	2.66948
$685$	−39.9208	−1.52530
$686$	0	0
$687$	−4.02155	−0.153432
$688$	−20.4823	−0.780879
$689$	4.13032	0.157352
$690$	−4.51487	−0.171878
$691$	18.6726	0.710339	0.355169	−	0.934802i	$-0.384423\pi$
$691$	18.6726	0.710339	0.355169	+	0.934802i	$0.384423\pi$
$692$	−39.1566	−1.48851
$693$	0	0
$694$	−1.05133	−0.0399078
$695$	25.7806	0.977915
$696$	1.62946	0.0617647
$697$	64.7110	2.45111
$698$	3.60900	0.136603
$699$	−22.7070	−0.858857
$700$	0	0
$701$	−26.1328	−0.987022	−0.493511	−	0.869739i	$-0.664287\pi$
$701$	−26.1328	−0.987022	−0.493511	+	0.869739i	$0.664287\pi$
$702$	0.597404	0.0225476
$703$	−11.5821	−0.436828
$704$	0	0
$705$	−14.7221	−0.554465
$706$	−0.881033	−0.0331581
$707$	0	0
$708$	36.6198	1.37626
$709$	−16.4449	−0.617602	−0.308801	−	0.951127i	$-0.599928\pi$
$709$	−16.4449	−0.617602	−0.308801	+	0.951127i	$0.599928\pi$
$710$	4.23259	0.158846
$711$	−71.4445	−2.67938
$712$	2.28392	0.0855936
$713$	38.9617	1.45913
$714$	0	0
$715$	0	0
$716$	46.3204	1.73107
$717$	−28.7400	−1.07331
$718$	0.598184	0.0223240
$719$	9.34913	0.348664	0.174332	−	0.984687i	$-0.444223\pi$
$719$	9.34913	0.348664	0.174332	+	0.984687i	$0.444223\pi$
$720$	51.2264	1.90909
$721$	0	0
$722$	4.56328	0.169828
$723$	−22.7086	−0.844542
$724$	6.12531	0.227646
$725$	3.54411	0.131625
$726$	0	0
$727$	−27.7523	−1.02928	−0.514638	−	0.857408i	$-0.672073\pi$
$727$	−27.7523	−1.02928	−0.514638	+	0.857408i	$0.672073\pi$
$728$	0	0
$729$	−44.0387	−1.63106
$730$	−0.867760	−0.0321173
$731$	36.4198	1.34704
$732$	53.8541	1.99050
$733$	−1.45630	−0.0537896	−0.0268948	−	0.999638i	$-0.508562\pi$
$733$	−1.45630	−0.0537896	−0.0268948	+	0.999638i	$0.508562\pi$
$734$	1.70962	0.0631032
$735$	0	0
$736$	6.90240	0.254426
$737$	0	0
$738$	−5.21712	−0.192045
$739$	−27.5966	−1.01516	−0.507579	−	0.861605i	$-0.669459\pi$
$739$	−27.5966	−1.01516	−0.507579	+	0.861605i	$0.669459\pi$
$740$	−8.56113	−0.314713
$741$	−22.5446	−0.828195
$742$	0	0
$743$	27.9773	1.02639	0.513194	−	0.858273i	$-0.328462\pi$
$743$	27.9773	1.02639	0.513194	+	0.858273i	$0.328462\pi$
$744$	10.7201	0.393019
$745$	32.6350	1.19566
$746$	1.08057	0.0395624
$747$	−9.53638	−0.348918
$748$	0	0
$749$	0	0
$750$	1.97621	0.0721610
$751$	34.0957	1.24417	0.622085	−	0.782950i	$-0.286286\pi$
$751$	34.0957	1.24417	0.622085	+	0.782950i	$0.286286\pi$
$752$	7.41125	0.270260
$753$	−45.5176	−1.65875
$754$	−0.159482	−0.00580800
$755$	50.3148	1.83114
$756$	0	0
$757$	−39.7629	−1.44521	−0.722604	−	0.691262i	$-0.757055\pi$
$757$	−39.7629	−1.44521	−0.722604	+	0.691262i	$0.757055\pi$
$758$	1.29863	0.0471684
$759$	0	0
$760$	10.1637	0.368677
$761$	3.82415	0.138625	0.0693127	−	0.997595i	$-0.477919\pi$
$761$	3.82415	0.138625	0.0693127	+	0.997595i	$0.477919\pi$
$762$	−3.28021	−0.118830
$763$	0	0
$764$	−24.9608	−0.903051
$765$	−91.0864	−3.29324
$766$	2.82966	0.102240
$767$	−7.19440	−0.259775
$768$	−41.1125	−1.48352
$769$	19.6583	0.708897	0.354449	−	0.935075i	$-0.384669\pi$
$769$	19.6583	0.708897	0.354449	+	0.935075i	$0.384669\pi$
$770$	0	0
$771$	−33.3358	−1.20056
$772$	41.0376	1.47698
$773$	17.5966	0.632905	0.316452	−	0.948608i	$-0.397508\pi$
$773$	17.5966	0.632905	0.316452	+	0.948608i	$0.397508\pi$
$774$	−2.93623	−0.105541
$775$	23.3165	0.837552
$776$	4.37249	0.156963
$777$	0	0
$778$	−1.42922	−0.0512400
$779$	70.1592	2.51371
$780$	−16.6642	−0.596675
$781$	0	0
$782$	−4.04136	−0.144519
$783$	−5.64198	−0.201628
$784$	0	0
$785$	−20.8619	−0.744592
$786$	5.45617	0.194615
$787$	54.0967	1.92834	0.964169	−	0.265287i	$-0.0854667\pi$
$787$	54.0967	1.92834	0.964169	+	0.265287i	$0.0854667\pi$
$788$	−12.4681	−0.444158
$789$	−5.19253	−0.184859
$790$	−5.18150	−0.184349
$791$	0	0
$792$	0	0
$793$	−10.5803	−0.375717
$794$	2.85571	0.101345
$795$	29.7379	1.05469
$796$	−13.6384	−0.483401
$797$	−36.5244	−1.29376	−0.646881	−	0.762591i	$-0.723927\pi$
$797$	−36.5244	−1.29376	−0.646881	+	0.762591i	$0.723927\pi$
$798$	0	0
$799$	−13.1781	−0.466206
$800$	4.13072	0.146043
$801$	−22.1916	−0.784101
$802$	−0.457513	−0.0161554
$803$	0	0
$804$	−11.3264	−0.399452
$805$	0	0
$806$	−1.04922	−0.0369573
$807$	−38.8300	−1.36688
$808$	−2.27561	−0.0800555
$809$	46.9354	1.65016	0.825081	−	0.565015i	$-0.191130\pi$
$809$	46.9354	1.65016	0.825081	+	0.565015i	$0.191130\pi$
$810$	−0.425410	−0.0149474
$811$	12.6615	0.444605	0.222303	−	0.974978i	$-0.428643\pi$
$811$	12.6615	0.444605	0.222303	+	0.974978i	$0.428643\pi$
$812$	0	0
$813$	3.74565	0.131366
$814$	0	0
$815$	22.0552	0.772561
$816$	75.3677	2.63840
$817$	39.4861	1.38144
$818$	0.720103	0.0251778
$819$	0	0
$820$	51.8594	1.81101
$821$	−49.2938	−1.72037	−0.860183	−	0.509986i	$-0.829651\pi$
$821$	−49.2938	−1.72037	−0.860183	+	0.509986i	$0.829651\pi$
$822$	4.73526	0.165161
$823$	19.2259	0.670173	0.335087	−	0.942187i	$-0.391234\pi$
$823$	19.2259	0.670173	0.335087	+	0.942187i	$0.391234\pi$
$824$	0.168326	0.00586390
$825$	0	0
$826$	0	0
$827$	43.6419	1.51758	0.758789	−	0.651337i	$-0.225792\pi$
$827$	43.6419	1.51758	0.758789	+	0.651337i	$0.225792\pi$
$828$	−44.6571	−1.55194
$829$	36.7072	1.27489	0.637447	−	0.770494i	$-0.279990\pi$
$829$	36.7072	1.27489	0.637447	+	0.770494i	$0.279990\pi$
$830$	−0.691625	−0.0240067
$831$	37.0434	1.28502
$832$	8.26428	0.286512
$833$	0	0
$834$	−3.05800	−0.105890
$835$	15.1733	0.525094
$836$	0	0
$837$	−37.1182	−1.28299
$838$	0.501768	0.0173333
$839$	−40.4545	−1.39665	−0.698323	−	0.715783i	$-0.746070\pi$
$839$	−40.4545	−1.39665	−0.698323	+	0.715783i	$0.746070\pi$
$840$	0	0
$841$	−27.4938	−0.948063
$842$	2.82310	0.0972904
$843$	−6.41826	−0.221057
$844$	−20.3686	−0.701117
$845$	−33.2369	−1.14339
$846$	1.06244	0.0365274
$847$	0	0
$848$	−14.9704	−0.514085
$849$	−61.6340	−2.11527
$850$	−2.41854	−0.0829552
$851$	7.40840	0.253957
$852$	68.8113	2.35743
$853$	−25.4948	−0.872927	−0.436463	−	0.899722i	$-0.643769\pi$
$853$	−25.4948	−0.872927	−0.436463	+	0.899722i	$0.643769\pi$
$854$	0	0
$855$	−98.7552	−3.37735
$856$	−1.22214	−0.0417718
$857$	−49.4756	−1.69005	−0.845027	−	0.534723i	$-0.820416\pi$
$857$	−49.4756	−1.69005	−0.845027	+	0.534723i	$0.820416\pi$
$858$	0	0
$859$	−21.6779	−0.739641	−0.369821	−	0.929103i	$-0.620581\pi$
$859$	−21.6779	−0.739641	−0.369821	+	0.929103i	$0.620581\pi$
$860$	29.1868	0.995262
$861$	0	0
$862$	4.48618	0.152800
$863$	13.6398	0.464306	0.232153	−	0.972679i	$-0.425423\pi$
$863$	13.6398	0.464306	0.232153	+	0.972679i	$0.425423\pi$
$864$	−6.57582	−0.223714
$865$	55.3873	1.88322
$866$	2.74256	0.0931959
$867$	−86.9592	−2.95329
$868$	0	0
$869$	0	0
$870$	−1.14826	−0.0389295
$871$	2.22521	0.0753985
$872$	1.83014	0.0619765
$873$	−42.4850	−1.43790
$874$	−4.38161	−0.148210
$875$	0	0
$876$	−14.1076	−0.476652
$877$	29.1290	0.983618	0.491809	−	0.870703i	$-0.336336\pi$
$877$	29.1290	0.983618	0.491809	+	0.870703i	$0.336336\pi$
$878$	0.172084	0.00580754
$879$	−6.75299	−0.227773
$880$	0	0
$881$	48.8256	1.64498	0.822488	−	0.568783i	$-0.192586\pi$
$881$	48.8256	1.64498	0.822488	+	0.568783i	$0.192586\pi$
$882$	0	0
$883$	−24.2131	−0.814837	−0.407419	−	0.913242i	$-0.633571\pi$
$883$	−24.2131	−0.814837	−0.407419	+	0.913242i	$0.633571\pi$
$884$	−14.9165	−0.501697
$885$	−51.7990	−1.74120
$886$	−3.18113	−0.106872
$887$	−6.64749	−0.223201	−0.111600	−	0.993753i	$-0.535598\pi$
$887$	−6.64749	−0.223201	−0.111600	+	0.993753i	$0.535598\pi$
$888$	2.03839	0.0684038
$889$	0	0
$890$	−1.60944	−0.0539486
$891$	0	0
$892$	−26.8483	−0.898947
$893$	−14.2875	−0.478114
$894$	−3.87105	−0.129467
$895$	−65.5205	−2.19011
$896$	0	0
$897$	14.4204	0.481484
$898$	1.69551	0.0565799
$899$	9.90903	0.330485
$900$	−26.7248	−0.890828
$901$	26.6191	0.886809
$902$	0	0
$903$	0	0
$904$	−1.11034	−0.0369295
$905$	−8.66431	−0.288011
$906$	−5.96815	−0.198279
$907$	−8.37806	−0.278189	−0.139094	−	0.990279i	$-0.544419\pi$
$907$	−8.37806	−0.278189	−0.139094	+	0.990279i	$0.544419\pi$
$908$	26.9562	0.894573
$909$	22.1108	0.733368
$910$	0	0
$911$	−18.7868	−0.622434	−0.311217	−	0.950339i	$-0.600737\pi$
$911$	−18.7868	−0.622434	−0.311217	+	0.950339i	$0.600737\pi$
$912$	81.7130	2.70579
$913$	0	0
$914$	3.54856	0.117376
$915$	−76.1771	−2.51834
$916$	−2.88486	−0.0953186
$917$	0	0
$918$	3.85015	0.127074
$919$	18.0039	0.593894	0.296947	−	0.954894i	$-0.404032\pi$
$919$	18.0039	0.593894	0.296947	+	0.954894i	$0.404032\pi$
$920$	−6.50113	−0.214336
$921$	−24.6076	−0.810848
$922$	−3.81881	−0.125766
$923$	−13.5188	−0.444977
$924$	0	0
$925$	4.43353	0.145773
$926$	−1.53867	−0.0505637
$927$	−1.63553	−0.0537177
$928$	1.75547	0.0576262
$929$	10.1225	0.332109	0.166054	−	0.986117i	$-0.446897\pi$
$929$	10.1225	0.332109	0.166054	+	0.986117i	$0.446897\pi$
$930$	−7.55430	−0.247715
$931$	0	0
$932$	−16.2889	−0.533560
$933$	−32.7566	−1.07240
$934$	−3.55986	−0.116482
$935$	0	0
$936$	2.41397	0.0789031
$937$	28.2113	0.921622	0.460811	−	0.887498i	$-0.347559\pi$
$937$	28.2113	0.921622	0.460811	+	0.887498i	$0.347559\pi$
$938$	0	0
$939$	−81.7635	−2.66825
$940$	−10.5609	−0.344458
$941$	20.1501	0.656875	0.328437	−	0.944526i	$-0.393478\pi$
$941$	20.1501	0.656875	0.328437	+	0.944526i	$0.393478\pi$
$942$	2.47456	0.0806255
$943$	−44.8766	−1.46138
$944$	26.0762	0.848707
$945$	0	0
$946$	0	0
$947$	0.125141	0.00406653	0.00203326	−	0.999998i	$-0.499353\pi$
$947$	0.125141	0.00406653	0.00203326	+	0.999998i	$0.499353\pi$
$948$	−84.2382	−2.73593
$949$	2.77161	0.0899703
$950$	−2.62216	−0.0850741
$951$	69.6236	2.25770
$952$	0	0
$953$	−29.3495	−0.950723	−0.475362	−	0.879790i	$-0.657683\pi$
$953$	−29.3495	−0.950723	−0.475362	+	0.879790i	$0.657683\pi$
$954$	−2.14608	−0.0694818
$955$	35.3073	1.14252
$956$	−20.6166	−0.666790
$957$	0	0
$958$	3.43717	0.111050
$959$	0	0
$960$	59.5020	1.92042
$961$	34.1909	1.10293
$962$	−0.199505	−0.00643231
$963$	11.8748	0.382661
$964$	−16.2900	−0.524667
$965$	−58.0481	−1.86863
$966$	0	0
$967$	−51.9463	−1.67048	−0.835240	−	0.549885i	$-0.814672\pi$
$967$	−51.9463	−1.67048	−0.835240	+	0.549885i	$0.814672\pi$
$968$	0	0
$969$	−145.295	−4.66756
$970$	−3.08122	−0.0989320
$971$	25.0066	0.802500	0.401250	−	0.915969i	$-0.368576\pi$
$971$	25.0066	0.802500	0.401250	+	0.915969i	$0.368576\pi$
$972$	−34.2995	−1.10016
$973$	0	0
$974$	0.127374	0.00408134
$975$	8.62984	0.276376
$976$	38.3484	1.22750
$977$	−17.4156	−0.557176	−0.278588	−	0.960411i	$-0.589866\pi$
$977$	−17.4156	−0.557176	−0.278588	+	0.960411i	$0.589866\pi$
$978$	−2.61611	−0.0836540
$979$	0	0
$980$	0	0
$981$	−17.7825	−0.567751
$982$	2.22051	0.0708592
$983$	42.3349	1.35028	0.675138	−	0.737692i	$-0.264084\pi$
$983$	42.3349	1.35028	0.675138	+	0.737692i	$0.264084\pi$
$984$	−12.3476	−0.393628
$985$	17.6362	0.561937
$986$	−1.02783	−0.0327328
$987$	0	0
$988$	−16.1724	−0.514512
$989$	−25.2569	−0.803122
$990$	0	0
$991$	55.6263	1.76703	0.883513	−	0.468406i	$-0.155172\pi$
$991$	55.6263	1.76703	0.883513	+	0.468406i	$0.155172\pi$
$992$	11.5491	0.366685
$993$	26.1930	0.831209
$994$	0	0
$995$	19.2916	0.611586
$996$	−11.2441	−0.356283
$997$	16.4267	0.520240	0.260120	−	0.965576i	$-0.416238\pi$
$997$	16.4267	0.520240	0.260120	+	0.965576i	$0.416238\pi$
$998$	3.81894	0.120886
$999$	−7.05787	−0.223301

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bm.1.3		6
7.6	odd	2		847.2.a.n.1.3	yes	6
11.10	odd	2		5929.2.a.bj.1.4		6
21.20	even	2		7623.2.a.cp.1.4		6
77.6	even	10		847.2.f.z.729.3		24
77.13	even	10		847.2.f.z.323.3		24
77.20	odd	10		847.2.f.y.323.4		24
77.27	odd	10		847.2.f.y.729.4		24
77.41	even	10		847.2.f.z.372.4		24
77.48	odd	10		847.2.f.y.148.3		24
77.62	even	10		847.2.f.z.148.4		24
77.69	odd	10		847.2.f.y.372.3		24
77.76	even	2		847.2.a.m.1.4	✓	6
231.230	odd	2		7623.2.a.cs.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.4	✓	6	77.76	even	2
847.2.a.n.1.3	yes	6	7.6	odd	2
847.2.f.y.148.3		24	77.48	odd	10
847.2.f.y.323.4		24	77.20	odd	10
847.2.f.y.372.3		24	77.69	odd	10
847.2.f.y.729.4		24	77.27	odd	10
847.2.f.z.148.4		24	77.62	even	10
847.2.f.z.323.3		24	77.13	even	10
847.2.f.z.372.4		24	77.41	even	10
847.2.f.z.729.3		24	77.6	even	10
5929.2.a.bj.1.4		6	11.10	odd	2
5929.2.a.bm.1.3		6	1.1	even	1	trivial
7623.2.a.cp.1.4		6	21.20	even	2
7623.2.a.cs.1.3		6	231.230	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+0.120360 q^{2} -2.76784 q^{3} -1.98551 q^{4} +2.80853 q^{5} -0.333137 q^{6} -0.479696 q^{8} +4.66094 q^{9} +O(q^{10})\)	\(q+0.120360 q^{2} -2.76784 q^{3} -1.98551 q^{4} +2.80853 q^{5} -0.333137 q^{6} -0.479696 q^{8} +4.66094 q^{9} +0.338034 q^{10} +5.49558 q^{12} -1.07967 q^{13} -7.77355 q^{15} +3.91329 q^{16} -6.95828 q^{17} +0.560990 q^{18} -7.54411 q^{19} -5.57636 q^{20} +4.82552 q^{23} +1.32772 q^{24} +2.88781 q^{25} -0.129949 q^{26} -4.59720 q^{27} +1.22726 q^{29} -0.935623 q^{30} +8.07409 q^{31} +1.43040 q^{32} -0.837498 q^{34} -9.25435 q^{36} +1.53525 q^{37} -0.908009 q^{38} +2.98836 q^{39} -1.34724 q^{40} -9.29986 q^{41} -5.23402 q^{43} +13.0904 q^{45} +0.580799 q^{46} +1.89387 q^{47} -10.8314 q^{48} +0.347577 q^{50} +19.2594 q^{51} +2.14371 q^{52} -3.82552 q^{53} -0.553319 q^{54} +20.8809 q^{57} +0.147713 q^{58} +6.66349 q^{59} +15.4345 q^{60} +9.79952 q^{61} +0.971796 q^{62} -7.65442 q^{64} -3.03229 q^{65} -2.06100 q^{67} +13.8158 q^{68} -13.3563 q^{69} +12.5212 q^{71} -2.23583 q^{72} -2.56708 q^{73} +0.184783 q^{74} -7.99301 q^{75} +14.9789 q^{76} +0.359679 q^{78} -15.3283 q^{79} +10.9906 q^{80} -1.25848 q^{81} -1.11933 q^{82} -2.04602 q^{83} -19.5425 q^{85} -0.629967 q^{86} -3.39687 q^{87} -4.76119 q^{89} +1.57555 q^{90} -9.58114 q^{92} -22.3478 q^{93} +0.227945 q^{94} -21.1878 q^{95} -3.95910 q^{96} -9.11512 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9	\( 6 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 4 q^{5} + 6 q^{6} + 12 q^{8} + 8 q^{9} + 8 q^{10} + 14 q^{12} - 4 q^{13} + 2 q^{15} + 8 q^{16} - 22 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} + 2 q^{23} + 20 q^{24} + 4 q^{25} - 6 q^{26} + 2 q^{27} + 12 q^{29} + 20 q^{30} + 2 q^{31} + 8 q^{32} - 24 q^{34} + 18 q^{36} + 14 q^{37} + 22 q^{38} + 20 q^{39} - 18 q^{40} - 26 q^{41} - 4 q^{43} + 36 q^{45} + 12 q^{46} + 16 q^{47} + 24 q^{48} - 4 q^{50} - 4 q^{51} - 12 q^{52} + 4 q^{53} + 32 q^{54} + 20 q^{57} - 2 q^{58} + 4 q^{59} + 24 q^{60} + 8 q^{61} - 20 q^{62} + 26 q^{64} + 24 q^{65} + 6 q^{67} - 12 q^{68} + 14 q^{69} + 22 q^{71} + 16 q^{72} - 14 q^{73} + 44 q^{74} + 20 q^{75} + 30 q^{76} + 32 q^{78} - 28 q^{79} + 4 q^{80} - 6 q^{81} + 4 q^{82} - 22 q^{83} - 24 q^{85} - 30 q^{86} - 22 q^{87} + 22 q^{90} + 10 q^{92} - 50 q^{93} + 38 q^{94} - 24 q^{95} + 62 q^{96} + 4 q^{97}+O(q^{100}) \) 6 * q + 4 * q^2 + 2 * q^3 + 4 * q^4 + 4 * q^5 + 6 * q^6 + 12 * q^8 + 8 * q^9 + 8 * q^10 + 14 * q^12 - 4 * q^13 + 2 * q^15 + 8 * q^16 - 22 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 + 2 * q^23 + 20 * q^24 + 4 * q^25 - 6 * q^26 + 2 * q^27 + 12 * q^29 + 20 * q^30 + 2 * q^31 + 8 * q^32 - 24 * q^34 + 18 * q^36 + 14 * q^37 + 22 * q^38 + 20 * q^39 - 18 * q^40 - 26 * q^41 - 4 * q^43 + 36 * q^45 + 12 * q^46 + 16 * q^47 + 24 * q^48 - 4 * q^50 - 4 * q^51 - 12 * q^52 + 4 * q^53 + 32 * q^54 + 20 * q^57 - 2 * q^58 + 4 * q^59 + 24 * q^60 + 8 * q^61 - 20 * q^62 + 26 * q^64 + 24 * q^65 + 6 * q^67 - 12 * q^68 + 14 * q^69 + 22 * q^71 + 16 * q^72 - 14 * q^73 + 44 * q^74 + 20 * q^75 + 30 * q^76 + 32 * q^78 - 28 * q^79 + 4 * q^80 - 6 * q^81 + 4 * q^82 - 22 * q^83 - 24 * q^85 - 30 * q^86 - 22 * q^87 + 22 * q^90 + 10 * q^92 - 50 * q^93 + 38 * q^94 - 24 * q^95 + 62 * q^96 + 4 * q^97

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