LMFDB - Embedded newform 5929.2.a.bi.1.4

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:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$2.46673$ 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)

$f(q)$	$=$	$q+2.46673 q^{2} +1.61803 q^{3} +4.08477 q^{4} +3.46673 q^{5} +3.99126 q^{6} +5.14256 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q+2.46673 q^{2} +1.61803 q^{3} +4.08477 q^{4} +3.46673 q^{5} +3.99126 q^{6} +5.14256 q^{8} -0.381966 q^{9} +8.55150 q^{10} +6.60929 q^{12} +0.653752 q^{13} +5.60929 q^{15} +4.51578 q^{16} +1.13715 q^{17} -0.942208 q^{18} +6.07602 q^{19} +14.1608 q^{20} -6.66708 q^{23} +8.32083 q^{24} +7.01823 q^{25} +1.61263 q^{26} -5.47214 q^{27} -4.57357 q^{29} +13.8366 q^{30} -2.79631 q^{31} +0.854102 q^{32} +2.80505 q^{34} -1.56024 q^{36} -0.439758 q^{37} +14.9879 q^{38} +1.05779 q^{39} +17.8279 q^{40} +5.90315 q^{41} +8.70820 q^{43} -1.32417 q^{45} -16.4459 q^{46} +0.604703 q^{47} +7.30669 q^{48} +17.3121 q^{50} +1.83995 q^{51} +2.67042 q^{52} +9.82247 q^{53} -13.4983 q^{54} +9.83121 q^{57} -11.2818 q^{58} -1.69406 q^{59} +22.9126 q^{60} -6.85818 q^{61} -6.89775 q^{62} -6.92472 q^{64} +2.26638 q^{65} -6.17828 q^{67} +4.64501 q^{68} -10.7876 q^{69} -5.41687 q^{71} -1.96428 q^{72} -6.70198 q^{73} -1.08477 q^{74} +11.3557 q^{75} +24.8191 q^{76} +2.60929 q^{78} +2.65375 q^{79} +15.6550 q^{80} -7.70820 q^{81} +14.5615 q^{82} -6.69658 q^{83} +3.94221 q^{85} +21.4808 q^{86} -7.40020 q^{87} +0.698213 q^{89} -3.26638 q^{90} -27.2335 q^{92} -4.52452 q^{93} +1.49164 q^{94} +21.0639 q^{95} +1.38197 q^{96} +14.8587 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9} + 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} + 3 q^{17} - 3 q^{18} - 3 q^{19} + 17 q^{20} - 8 q^{23} + 12 q^{24} + 12 q^{26} - 4 q^{27} + 3 q^{29} + 12 q^{30} + 3 q^{31} - 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} + 5 q^{39} + 13 q^{40} - 4 q^{41} + 8 q^{43} - 9 q^{45} - 3 q^{46} + 14 q^{47} + 3 q^{48} + 33 q^{50} - 11 q^{51} + 17 q^{52} - 9 q^{53} - 2 q^{54} + 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} + 19 q^{61} - 10 q^{62} + 3 q^{64} + 12 q^{65} - 15 q^{67} + q^{68} - 14 q^{69} - 7 q^{71} - 6 q^{72} + 11 q^{73} + 8 q^{74} + 5 q^{75} + 26 q^{76} - 9 q^{78} + 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} + q^{83} + 15 q^{85} + 4 q^{86} - 6 q^{87} + 17 q^{89} - 16 q^{90} - 17 q^{92} - 11 q^{93} + 20 q^{94} + 17 q^{95} + 10 q^{96} + 15 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9 + 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 + 3 * q^17 - 3 * q^18 - 3 * q^19 + 17 * q^20 - 8 * q^23 + 12 * q^24 + 12 * q^26 - 4 * q^27 + 3 * q^29 + 12 * q^30 + 3 * q^31 - 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 + 5 * q^39 + 13 * q^40 - 4 * q^41 + 8 * q^43 - 9 * q^45 - 3 * q^46 + 14 * q^47 + 3 * q^48 + 33 * q^50 - 11 * q^51 + 17 * q^52 - 9 * q^53 - 2 * q^54 + 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 + 19 * q^61 - 10 * q^62 + 3 * q^64 + 12 * q^65 - 15 * q^67 + q^68 - 14 * q^69 - 7 * q^71 - 6 * q^72 + 11 * q^73 + 8 * q^74 + 5 * q^75 + 26 * q^76 - 9 * q^78 + 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 + q^83 + 15 * q^85 + 4 * q^86 - 6 * q^87 + 17 * q^89 - 16 * q^90 - 17 * q^92 - 11 * q^93 + 20 * q^94 + 17 * q^95 + 10 * q^96 + 15 * 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 $

$2$	2.46673	1.74424	0.872121	−	0.489290i	$-0.162744\pi$
$2$	2.46673	1.74424	0.872121	+	0.489290i	$0.162744\pi$
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	4.08477	2.04238
$5$	3.46673	1.55037	0.775185	−	0.631735i	$-0.217657\pi$
$5$	3.46673	1.55037	0.775185	+	0.631735i	$0.217657\pi$
$6$	3.99126	1.62942
$7$	0	0
$7$	0	0
$8$	5.14256	1.81817
$9$	−0.381966	−0.127322
$10$	8.55150	2.70422
$11$	0	0
$11$	0	0
$12$	6.60929	1.90794
$13$	0.653752	0.181318	0.0906590	−	0.995882i	$-0.471103\pi$
$13$	0.653752	0.181318	0.0906590	+	0.995882i	$0.471103\pi$
$14$	0	0
$15$	5.60929	1.44831
$16$	4.51578	1.12894
$17$	1.13715	0.275800	0.137900	−	0.990446i	$-0.455965\pi$
$17$	1.13715	0.275800	0.137900	+	0.990446i	$0.455965\pi$
$18$	−0.942208	−0.222080
$19$	6.07602	1.39393	0.696967	−	0.717103i	$-0.254532\pi$
$19$	6.07602	1.39393	0.696967	+	0.717103i	$0.254532\pi$
$20$	14.1608	3.16645
$21$	0	0
$22$	0	0
$23$	−6.66708	−1.39018	−0.695091	−	0.718921i	$-0.744636\pi$
$23$	−6.66708	−1.39018	−0.695091	+	0.718921i	$0.744636\pi$
$24$	8.32083	1.69848
$25$	7.01823	1.40365
$26$	1.61263	0.316263
$27$	−5.47214	−1.05311
$28$	0	0
$29$	−4.57357	−0.849291	−0.424646	−	0.905360i	$-0.639601\pi$
$29$	−4.57357	−0.849291	−0.424646	+	0.905360i	$0.639601\pi$
$30$	13.8366	2.52621
$31$	−2.79631	−0.502232	−0.251116	−	0.967957i	$-0.580798\pi$
$31$	−2.79631	−0.502232	−0.251116	+	0.967957i	$0.580798\pi$
$32$	0.854102	0.150985
$33$	0	0
$34$	2.80505	0.481063
$35$	0	0
$36$	−1.56024	−0.260040
$37$	−0.439758	−0.0722958	−0.0361479	−	0.999346i	$-0.511509\pi$
$37$	−0.439758	−0.0722958	−0.0361479	+	0.999346i	$0.511509\pi$
$38$	14.9879	2.43136
$39$	1.05779	0.169382
$40$	17.8279	2.81883
$41$	5.90315	0.921917	0.460959	−	0.887422i	$-0.347506\pi$
$41$	5.90315	0.921917	0.460959	+	0.887422i	$0.347506\pi$
$42$	0	0
$43$	8.70820	1.32799	0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820	1.32799	0.663994	+	0.747738i	$0.268860\pi$
$44$	0	0
$45$	−1.32417	−0.197396
$46$	−16.4459	−2.42482
$47$	0.604703	0.0882051	0.0441025	−	0.999027i	$-0.485957\pi$
$47$	0.604703	0.0882051	0.0441025	+	0.999027i	$0.485957\pi$
$48$	7.30669	1.05463
$49$	0	0
$50$	17.3121	2.44830
$51$	1.83995	0.257645
$52$	2.67042	0.370321
$53$	9.82247	1.34922	0.674610	−	0.738175i	$-0.264312\pi$
$53$	9.82247	1.34922	0.674610	+	0.738175i	$0.264312\pi$
$54$	−13.4983	−1.83688
$55$	0	0
$56$	0	0
$57$	9.83121	1.30218
$58$	−11.2818	−1.48137
$59$	−1.69406	−0.220547	−0.110274	−	0.993901i	$-0.535173\pi$
$59$	−1.69406	−0.220547	−0.110274	+	0.993901i	$0.535173\pi$
$60$	22.9126	2.95801
$61$	−6.85818	−0.878100	−0.439050	−	0.898463i	$-0.644685\pi$
$61$	−6.85818	−0.878100	−0.439050	+	0.898463i	$0.644685\pi$
$62$	−6.89775	−0.876015
$63$	0	0
$64$	−6.92472	−0.865590
$65$	2.26638	0.281110
$66$	0	0
$67$	−6.17828	−0.754797	−0.377398	−	0.926051i	$-0.623181\pi$
$67$	−6.17828	−0.754797	−0.377398	+	0.926051i	$0.623181\pi$
$68$	4.64501	0.563290
$69$	−10.7876	−1.29867
$70$	0	0
$71$	−5.41687	−0.642864	−0.321432	−	0.946933i	$-0.604164\pi$
$71$	−5.41687	−0.642864	−0.321432	+	0.946933i	$0.604164\pi$
$72$	−1.96428	−0.231493
$73$	−6.70198	−0.784408	−0.392204	−	0.919878i	$-0.628287\pi$
$73$	−6.70198	−0.784408	−0.392204	+	0.919878i	$0.628287\pi$
$74$	−1.08477	−0.126101
$75$	11.3557	1.31125
$76$	24.8191	2.84695
$77$	0	0
$78$	2.60929	0.295444
$79$	2.65375	0.298570	0.149285	−	0.988794i	$-0.452303\pi$
$79$	2.65375	0.298570	0.149285	+	0.988794i	$0.452303\pi$
$80$	15.6550	1.75028
$81$	−7.70820	−0.856467
$82$	14.5615	1.60805
$83$	−6.69658	−0.735045	−0.367522	−	0.930015i	$-0.619794\pi$
$83$	−6.69658	−0.735045	−0.367522	+	0.930015i	$0.619794\pi$
$84$	0	0
$85$	3.94221	0.427592
$86$	21.4808	2.31633
$87$	−7.40020	−0.793384
$88$	0	0
$89$	0.698213	0.0740105	0.0370052	−	0.999315i	$-0.488218\pi$
$89$	0.698213	0.0740105	0.0370052	+	0.999315i	$0.488218\pi$
$90$	−3.26638	−0.344307
$91$	0	0
$92$	−27.2335	−2.83929
$93$	−4.52452	−0.469171
$94$	1.49164	0.153851
$95$	21.0639	2.16111
$96$	1.38197	0.141046
$97$	14.8587	1.50867	0.754336	−	0.656489i	$-0.227959\pi$
$97$	14.8587	1.50867	0.754336	+	0.656489i	$0.227959\pi$
$98$	0	0
$99$	0	0
$100$	28.6678	2.86678
$101$	−8.61959	−0.857682	−0.428841	−	0.903380i	$-0.641078\pi$
$101$	−8.61959	−0.857682	−0.428841	+	0.903380i	$0.641078\pi$
$102$	4.53867	0.449396
$103$	0.932958	0.0919271	0.0459636	−	0.998943i	$-0.485364\pi$
$103$	0.932958	0.0919271	0.0459636	+	0.998943i	$0.485364\pi$
$104$	3.36196	0.329667
$105$	0	0
$106$	24.2294	2.35337
$107$	6.62212	0.640184	0.320092	−	0.947386i	$-0.396286\pi$
$107$	6.62212	0.640184	0.320092	+	0.947386i	$0.396286\pi$
$108$	−22.3524	−2.15086
$109$	−4.12507	−0.395110	−0.197555	−	0.980292i	$-0.563300\pi$
$109$	−4.12507	−0.395110	−0.197555	+	0.980292i	$0.563300\pi$
$110$	0	0
$111$	−0.711544	−0.0675368
$112$	0	0
$113$	−18.8258	−1.77098	−0.885491	−	0.464656i	$-0.846178\pi$
$113$	−18.8258	−1.77098	−0.885491	+	0.464656i	$0.846178\pi$
$114$	24.2510	2.27131
$115$	−23.1130	−2.15530
$116$	−18.6820	−1.73458
$117$	−0.249711	−0.0230858
$118$	−4.17878	−0.384688
$119$	0	0
$120$	28.8461	2.63328
$121$	0	0
$122$	−16.9173	−1.53162
$123$	9.55150	0.861230
$124$	−11.4223	−1.02575
$125$	6.99666	0.625800
$126$	0	0
$127$	−7.96635	−0.706899	−0.353449	−	0.935454i	$-0.614991\pi$
$127$	−7.96635	−0.706899	−0.353449	+	0.935454i	$0.614991\pi$
$128$	−18.7896	−1.66078
$129$	14.0902	1.24057
$130$	5.59056	0.490324
$131$	4.80505	0.419819	0.209910	−	0.977721i	$-0.432683\pi$
$131$	4.80505	0.419819	0.209910	+	0.977721i	$0.432683\pi$
$132$	0	0
$133$	0	0
$134$	−15.2401	−1.31655
$135$	−18.9704	−1.63271
$136$	5.84788	0.501452
$137$	−21.8777	−1.86914	−0.934571	−	0.355778i	$-0.884216\pi$
$137$	−21.8777	−1.86914	−0.934571	+	0.355778i	$0.884216\pi$
$138$	−26.6100	−2.26520
$139$	19.8137	1.68058	0.840289	−	0.542139i	$-0.182385\pi$
$139$	19.8137	1.68058	0.840289	+	0.542139i	$0.182385\pi$
$140$	0	0
$141$	0.978431	0.0823987
$142$	−13.3620	−1.12131
$143$	0	0
$144$	−1.72487	−0.143740
$145$	−15.8553	−1.31672
$146$	−16.5320	−1.36820
$147$	0	0
$148$	−1.79631	−0.147656
$149$	3.16211	0.259050	0.129525	−	0.991576i	$-0.458655\pi$
$149$	3.16211	0.259050	0.129525	+	0.991576i	$0.458655\pi$
$150$	28.0115	2.28713
$151$	8.92806	0.726555	0.363278	−	0.931681i	$-0.381658\pi$
$151$	8.92806	0.726555	0.363278	+	0.931681i	$0.381658\pi$
$152$	31.2463	2.53441
$153$	−0.434354	−0.0351155
$154$	0	0
$155$	−9.69406	−0.778645
$156$	4.32083	0.345944
$157$	−1.13968	−0.0909561	−0.0454780	−	0.998965i	$-0.514481\pi$
$157$	−1.13968	−0.0909561	−0.0454780	+	0.998965i	$0.514481\pi$
$158$	6.54609	0.520779
$159$	15.8931	1.26040
$160$	2.96094	0.234083
$161$	0	0
$162$	−19.0141	−1.49389
$163$	−5.06728	−0.396900	−0.198450	−	0.980111i	$-0.563591\pi$
$163$	−5.06728	−0.396900	−0.198450	+	0.980111i	$0.563591\pi$
$164$	24.1130	1.88291
$165$	0	0
$166$	−16.5187	−1.28210
$167$	19.7069	1.52496	0.762482	−	0.647009i	$-0.223981\pi$
$167$	19.7069	1.52496	0.762482	+	0.647009i	$0.223981\pi$
$168$	0	0
$169$	−12.5726	−0.967124
$170$	9.72437	0.745825
$171$	−2.32083	−0.177479
$172$	35.5710	2.71226
$173$	14.3948	1.09442	0.547208	−	0.836997i	$-0.315691\pi$
$173$	14.3948	1.09442	0.547208	+	0.836997i	$0.315691\pi$
$174$	−18.2543	−1.38385
$175$	0	0
$176$	0	0
$177$	−2.74104	−0.206029
$178$	1.72230	0.129092
$179$	−4.66420	−0.348619	−0.174309	−	0.984691i	$-0.555769\pi$
$179$	−4.66420	−0.348619	−0.174309	+	0.984691i	$0.555769\pi$
$180$	−5.40894	−0.403159
$181$	−9.90805	−0.736459	−0.368230	−	0.929735i	$-0.620036\pi$
$181$	−9.90805	−0.736459	−0.368230	+	0.929735i	$0.620036\pi$
$182$	0	0
$183$	−11.0968	−0.820297
$184$	−34.2859	−2.52759
$185$	−1.52452	−0.112085
$186$	−11.1608	−0.818349
$187$	0	0
$188$	2.47007	0.180148
$189$	0	0
$190$	51.9591	3.76951
$191$	9.94295	0.719447	0.359723	−	0.933059i	$-0.382871\pi$
$191$	9.94295	0.719447	0.359723	+	0.933059i	$0.382871\pi$
$192$	−11.2044	−0.808610
$193$	3.70665	0.266810	0.133405	−	0.991062i	$-0.457409\pi$
$193$	3.70665	0.266810	0.133405	+	0.991062i	$0.457409\pi$
$194$	36.6524	2.63149
$195$	3.66708	0.262605
$196$	0	0
$197$	5.91982	0.421770	0.210885	−	0.977511i	$-0.432365\pi$
$197$	5.91982	0.421770	0.210885	+	0.977511i	$0.432365\pi$
$198$	0	0
$199$	−11.4842	−0.814095	−0.407047	−	0.913407i	$-0.633442\pi$
$199$	−11.4842	−0.814095	−0.407047	+	0.913407i	$0.633442\pi$
$200$	36.0917	2.55207
$201$	−9.99666	−0.705110
$202$	−21.2622	−1.49600
$203$	0	0
$204$	7.51578	0.526210
$205$	20.4646	1.42931
$206$	2.30136	0.160343
$207$	2.54660	0.177001
$208$	2.95220	0.204698
$209$	0	0
$210$	0	0
$211$	8.72487	0.600645	0.300323	−	0.953838i	$-0.402906\pi$
$211$	8.72487	0.600645	0.300323	+	0.953838i	$0.402906\pi$
$212$	40.1225	2.75562
$213$	−8.76467	−0.600546
$214$	16.3350	1.11664
$215$	30.1890	2.05887
$216$	−28.1408	−1.91474
$217$	0	0
$218$	−10.1754	−0.689168
$219$	−10.8440	−0.732772
$220$	0	0
$221$	0.743416	0.0500076
$222$	−1.75519	−0.117801
$223$	−10.3328	−0.691938	−0.345969	−	0.938246i	$-0.612450\pi$
$223$	−10.3328	−0.691938	−0.345969	+	0.938246i	$0.612450\pi$
$224$	0	0
$225$	−2.68073	−0.178715
$226$	−46.4382	−3.08902
$227$	13.2690	0.880691	0.440346	−	0.897828i	$-0.354856\pi$
$227$	13.2690	0.880691	0.440346	+	0.897828i	$0.354856\pi$
$228$	40.1582	2.65954
$229$	2.49623	0.164955	0.0824777	−	0.996593i	$-0.473717\pi$
$229$	2.49623	0.164955	0.0824777	+	0.996593i	$0.473717\pi$
$230$	−57.0135	−3.75936
$231$	0	0
$232$	−23.5199	−1.54415
$233$	−9.60389	−0.629171	−0.314586	−	0.949229i	$-0.601866\pi$
$233$	−9.60389	−0.629171	−0.314586	+	0.949229i	$0.601866\pi$
$234$	−0.615970	−0.0402672
$235$	2.09634	0.136750
$236$	−6.91982	−0.450442
$237$	4.29386	0.278916
$238$	0	0
$239$	5.56327	0.359858	0.179929	−	0.983680i	$-0.442413\pi$
$239$	5.56327	0.359858	0.179929	+	0.983680i	$0.442413\pi$
$240$	25.3303	1.63507
$241$	−15.0208	−0.967572	−0.483786	−	0.875186i	$-0.660739\pi$
$241$	−15.0208	−0.967572	−0.483786	+	0.875186i	$0.660739\pi$
$242$	0	0
$243$	3.94427	0.253025
$244$	−28.0141	−1.79342
$245$	0	0
$246$	23.5610	1.50219
$247$	3.97221	0.252746
$248$	−14.3802	−0.913143
$249$	−10.8353	−0.686659
$250$	17.2589	1.09155
$251$	−27.6131	−1.74292	−0.871460	−	0.490466i	$-0.836827\pi$
$251$	−27.6131	−1.74292	−0.871460	+	0.490466i	$0.836827\pi$
$252$	0	0
$253$	0	0
$254$	−19.6508	−1.23300
$255$	6.37863	0.399445
$256$	−32.4995	−2.03122
$257$	28.4680	1.77578	0.887892	−	0.460052i	$-0.152169\pi$
$257$	28.4680	1.77578	0.887892	+	0.460052i	$0.152169\pi$
$258$	34.7567	2.16386
$259$	0	0
$260$	9.25764	0.574134
$261$	1.74695	0.108133
$262$	11.8528	0.732267
$263$	14.1803	0.874397	0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803	0.874397	0.437199	+	0.899365i	$0.355971\pi$
$264$	0	0
$265$	34.0519	2.09179
$266$	0	0
$267$	1.12973	0.0691385
$268$	−25.2368	−1.54158
$269$	24.1937	1.47511	0.737557	−	0.675285i	$-0.235979\pi$
$269$	24.1937	1.47511	0.737557	+	0.675285i	$0.235979\pi$
$270$	−46.7950	−2.84785
$271$	−7.44975	−0.452540	−0.226270	−	0.974065i	$-0.572653\pi$
$271$	−7.44975	−0.452540	−0.226270	+	0.974065i	$0.572653\pi$
$272$	5.13514	0.311363
$273$	0	0
$274$	−53.9665	−3.26024
$275$	0	0
$276$	−44.0647	−2.65238
$277$	−19.1890	−1.15296	−0.576478	−	0.817113i	$-0.695573\pi$
$277$	−19.1890	−1.15296	−0.576478	+	0.817113i	$0.695573\pi$
$278$	48.8751	2.93134
$279$	1.06810	0.0639452
$280$	0	0
$281$	−1.90063	−0.113382	−0.0566910	−	0.998392i	$-0.518055\pi$
$281$	−1.90063	−0.113382	−0.0566910	+	0.998392i	$0.518055\pi$
$282$	2.41353	0.143723
$283$	−7.25178	−0.431073	−0.215537	−	0.976496i	$-0.569150\pi$
$283$	−7.25178	−0.431073	−0.215537	+	0.976496i	$0.569150\pi$
$284$	−22.1266	−1.31297
$285$	34.0822	2.01885
$286$	0	0
$287$	0	0
$288$	−0.326238	−0.0192238
$289$	−15.7069	−0.923934
$290$	−39.1109	−2.29667
$291$	24.0419	1.40936
$292$	−27.3760	−1.60206
$293$	3.27097	0.191092	0.0955460	−	0.995425i	$-0.469540\pi$
$293$	3.27097	0.191092	0.0955460	+	0.995425i	$0.469540\pi$
$294$	0	0
$295$	−5.87284	−0.341930
$296$	−2.26148	−0.131446
$297$	0	0
$298$	7.80008	0.451846
$299$	−4.35862	−0.252065
$300$	46.3855	2.67807
$301$	0	0
$302$	22.0231	1.26729
$303$	−13.9468	−0.801222
$304$	27.4380	1.57368
$305$	−23.7755	−1.36138
$306$	−1.07144	−0.0612499
$307$	−31.6121	−1.80420	−0.902099	−	0.431530i	$-0.857974\pi$
$307$	−31.6121	−1.80420	−0.902099	+	0.431530i	$0.857974\pi$
$308$	0	0
$309$	1.50956	0.0858758
$310$	−23.9126	−1.35815
$311$	9.03829	0.512514	0.256257	−	0.966609i	$-0.417511\pi$
$311$	9.03829	0.512514	0.256257	+	0.966609i	$0.417511\pi$
$312$	5.43976	0.307966
$313$	−14.4990	−0.819534	−0.409767	−	0.912190i	$-0.634390\pi$
$313$	−14.4990	−0.819534	−0.409767	+	0.912190i	$0.634390\pi$
$314$	−2.81128	−0.158649
$315$	0	0
$316$	10.8400	0.609795
$317$	−18.4174	−1.03442	−0.517211	−	0.855858i	$-0.673030\pi$
$317$	−18.4174	−1.03442	−0.517211	+	0.855858i	$0.673030\pi$
$318$	39.2040	2.19845
$319$	0	0
$320$	−24.0061	−1.34198
$321$	10.7148	0.598042
$322$	0	0
$323$	6.90937	0.384448
$324$	−31.4862	−1.74923
$325$	4.58818	0.254506
$326$	−12.4996	−0.692290
$327$	−6.67450	−0.369101
$328$	30.3573	1.67620
$329$	0	0
$330$	0	0
$331$	−6.47653	−0.355982	−0.177991	−	0.984032i	$-0.556960\pi$
$331$	−6.47653	−0.355982	−0.177991	+	0.984032i	$0.556960\pi$
$332$	−27.3540	−1.50124
$333$	0.167973	0.00920485
$334$	48.6116	2.65991
$335$	−21.4184	−1.17021
$336$	0	0
$337$	6.25682	0.340831	0.170415	−	0.985372i	$-0.445489\pi$
$337$	6.25682	0.340831	0.170415	+	0.985372i	$0.445489\pi$
$338$	−31.0133	−1.68690
$339$	−30.4608	−1.65440
$340$	16.1030	0.873308
$341$	0	0
$342$	−5.72487	−0.309566
$343$	0	0
$344$	44.7824	2.41451
$345$	−37.3976	−2.01342
$346$	35.5081	1.90893
$347$	22.7156	1.21944	0.609719	−	0.792617i	$-0.291282\pi$
$347$	22.7156	1.21944	0.609719	+	0.792617i	$0.291282\pi$
$348$	−30.2281	−1.62039
$349$	−29.6941	−1.58949	−0.794743	−	0.606946i	$-0.792394\pi$
$349$	−29.6941	−1.58949	−0.794743	+	0.606946i	$0.792394\pi$
$350$	0	0
$351$	−3.57742	−0.190948
$352$	0	0
$353$	6.82506	0.363262	0.181631	−	0.983367i	$-0.441862\pi$
$353$	6.82506	0.363262	0.181631	+	0.983367i	$0.441862\pi$
$354$	−6.76141	−0.359365
$355$	−18.7788	−0.996676
$356$	2.85204	0.151158
$357$	0	0
$358$	−11.5053	−0.608076
$359$	−7.25970	−0.383152	−0.191576	−	0.981478i	$-0.561360\pi$
$359$	−7.25970	−0.383152	−0.191576	+	0.981478i	$0.561360\pi$
$360$	−6.80964	−0.358900
$361$	17.9180	0.943055
$362$	−24.4405	−1.28456
$363$	0	0
$364$	0	0
$365$	−23.2340	−1.21612
$366$	−27.3728	−1.43080
$367$	36.3366	1.89676	0.948378	−	0.317143i	$-0.102723\pi$
$367$	36.3366	1.89676	0.948378	+	0.317143i	$0.102723\pi$
$368$	−30.1071	−1.56944
$369$	−2.25480	−0.117380
$370$	−3.76059	−0.195504
$371$	0	0
$372$	−18.4816	−0.958227
$373$	−14.2913	−0.739977	−0.369989	−	0.929036i	$-0.620638\pi$
$373$	−14.2913	−0.739977	−0.369989	+	0.929036i	$0.620638\pi$
$374$	0	0
$375$	11.3208	0.584605
$376$	3.10972	0.160372
$377$	−2.98998	−0.153992
$378$	0	0
$379$	−2.54528	−0.130742	−0.0653710	−	0.997861i	$-0.520823\pi$
$379$	−2.54528	−0.130742	−0.0653710	+	0.997861i	$0.520823\pi$
$380$	86.0413	4.41382
$381$	−12.8898	−0.660365
$382$	24.5266	1.25489
$383$	23.1367	1.18223	0.591115	−	0.806587i	$-0.298688\pi$
$383$	23.1367	1.18223	0.591115	+	0.806587i	$0.298688\pi$
$384$	−30.4023	−1.55146
$385$	0	0
$386$	9.14330	0.465382
$387$	−3.32624	−0.169082
$388$	60.6943	3.08128
$389$	30.2615	1.53432	0.767158	−	0.641458i	$-0.221670\pi$
$389$	30.2615	1.53432	0.767158	+	0.641458i	$0.221670\pi$
$390$	9.04571	0.458047
$391$	−7.58150	−0.383413
$392$	0	0
$393$	7.77474	0.392184
$394$	14.6026	0.735669
$395$	9.19985	0.462894
$396$	0	0
$397$	22.6740	1.13798	0.568989	−	0.822345i	$-0.307335\pi$
$397$	22.6740	1.13798	0.568989	+	0.822345i	$0.307335\pi$
$398$	−28.3285	−1.41998
$399$	0	0
$400$	31.6928	1.58464
$401$	−16.2186	−0.809917	−0.404959	−	0.914335i	$-0.632714\pi$
$401$	−16.2186	−0.809917	−0.404959	+	0.914335i	$0.632714\pi$
$402$	−24.6591	−1.22988
$403$	−1.82809	−0.0910637
$404$	−35.2090	−1.75171
$405$	−26.7223	−1.32784
$406$	0	0
$407$	0	0
$408$	9.46207	0.468442
$409$	35.0614	1.73368	0.866838	−	0.498590i	$-0.166149\pi$
$409$	35.0614	1.73368	0.866838	+	0.498590i	$0.166149\pi$
$410$	50.4808	2.49307
$411$	−35.3989	−1.74610
$412$	3.81092	0.187750
$413$	0	0
$414$	6.28178	0.308732
$415$	−23.2152	−1.13959
$416$	0.558371	0.0273764
$417$	32.0593	1.56995
$418$	0	0
$419$	−28.2633	−1.38075	−0.690376	−	0.723451i	$-0.742555\pi$
$419$	−28.2633	−1.38075	−0.690376	+	0.723451i	$0.742555\pi$
$420$	0	0
$421$	−13.7947	−0.672311	−0.336156	−	0.941806i	$-0.609127\pi$
$421$	−13.7947	−0.672311	−0.336156	+	0.941806i	$0.609127\pi$
$422$	21.5219	1.04767
$423$	−0.230976	−0.0112304
$424$	50.5126	2.45311
$425$	7.98081	0.387126
$426$	−21.6201	−1.04750
$427$	0	0
$428$	27.0498	1.30750
$429$	0	0
$430$	74.4682	3.59117
$431$	28.1700	1.35690	0.678451	−	0.734645i	$-0.262651\pi$
$431$	28.1700	1.35690	0.678451	+	0.734645i	$0.262651\pi$
$432$	−24.7110	−1.18891
$433$	−14.1793	−0.681415	−0.340708	−	0.940169i	$-0.610667\pi$
$433$	−14.1793	−0.681415	−0.340708	+	0.940169i	$0.610667\pi$
$434$	0	0
$435$	−25.6545	−1.23004
$436$	−16.8499	−0.806966
$437$	−40.5093	−1.93782
$438$	−26.7493	−1.27813
$439$	−28.0185	−1.33725	−0.668625	−	0.743599i	$-0.733117\pi$
$439$	−28.0185	−1.33725	−0.668625	+	0.743599i	$0.733117\pi$
$440$	0	0
$441$	0	0
$442$	1.83381	0.0872254
$443$	17.3370	0.823706	0.411853	−	0.911250i	$-0.364882\pi$
$443$	17.3370	0.823706	0.411853	+	0.911250i	$0.364882\pi$
$444$	−2.90649	−0.137936
$445$	2.42052	0.114744
$446$	−25.4883	−1.20691
$447$	5.11640	0.241998
$448$	0	0
$449$	−29.5215	−1.39321	−0.696603	−	0.717457i	$-0.745306\pi$
$449$	−29.5215	−1.39321	−0.696603	+	0.717457i	$0.745306\pi$
$450$	−6.61263	−0.311722
$451$	0	0
$452$	−76.8990	−3.61702
$453$	14.4459	0.678728
$454$	32.7309	1.53614
$455$	0	0
$456$	50.5576	2.36757
$457$	9.69725	0.453618	0.226809	−	0.973939i	$-0.427171\pi$
$457$	9.69725	0.453618	0.226809	+	0.973939i	$0.427171\pi$
$458$	6.15752	0.287722
$459$	−6.22266	−0.290449
$460$	−94.4111	−4.40194
$461$	19.2216	0.895240	0.447620	−	0.894224i	$-0.352272\pi$
$461$	19.2216	0.895240	0.447620	+	0.894224i	$0.352272\pi$
$462$	0	0
$463$	20.5327	0.954235	0.477117	−	0.878840i	$-0.341682\pi$
$463$	20.5327	0.954235	0.477117	+	0.878840i	$0.341682\pi$
$464$	−20.6532	−0.958803
$465$	−15.6853	−0.727389
$466$	−23.6902	−1.09743
$467$	−33.6714	−1.55813	−0.779064	−	0.626944i	$-0.784305\pi$
$467$	−33.6714	−1.55813	−0.779064	+	0.626944i	$0.784305\pi$
$468$	−1.02001	−0.0471500
$469$	0	0
$470$	5.17112	0.238526
$471$	−1.84403	−0.0849686
$472$	−8.71178	−0.400992
$473$	0	0
$474$	10.5918	0.486498
$475$	42.6429	1.95659
$476$	0	0
$477$	−3.75185	−0.171785
$478$	13.7231	0.627680
$479$	−14.1708	−0.647479	−0.323740	−	0.946146i	$-0.604940\pi$
$479$	−14.1708	−0.647479	−0.323740	+	0.946146i	$0.604940\pi$
$480$	4.79091	0.218674
$481$	−0.287493	−0.0131085
$482$	−37.0522	−1.68768
$483$	0	0
$484$	0	0
$485$	51.5111	2.33900
$486$	9.72946	0.441337
$487$	27.7415	1.25709	0.628543	−	0.777775i	$-0.283652\pi$
$487$	27.7415	1.25709	0.628543	+	0.777775i	$0.283652\pi$
$488$	−35.2686	−1.59653
$489$	−8.19903	−0.370773
$490$	0	0
$491$	−3.44295	−0.155378	−0.0776891	−	0.996978i	$-0.524754\pi$
$491$	−3.44295	−0.155378	−0.0776891	+	0.996978i	$0.524754\pi$
$492$	39.0156	1.75896
$493$	−5.20086	−0.234235
$494$	9.79837	0.440850
$495$	0	0
$496$	−12.6275	−0.566992
$497$	0	0
$498$	−26.7278	−1.19770
$499$	−2.58923	−0.115910	−0.0579550	−	0.998319i	$-0.518458\pi$
$499$	−2.58923	−0.115910	−0.0579550	+	0.998319i	$0.518458\pi$
$500$	28.5797	1.27812
$501$	31.8864	1.42458
$502$	−68.1140	−3.04008
$503$	22.9026	1.02118	0.510589	−	0.859825i	$-0.329427\pi$
$503$	22.9026	1.02118	0.510589	+	0.859825i	$0.329427\pi$
$504$	0	0
$505$	−29.8818	−1.32972
$506$	0	0
$507$	−20.3429	−0.903460
$508$	−32.5407	−1.44376
$509$	24.0985	1.06815	0.534074	−	0.845438i	$-0.320660\pi$
$509$	24.0985	1.06815	0.534074	+	0.845438i	$0.320660\pi$
$510$	15.7344	0.696729
$511$	0	0
$512$	−42.5884	−1.88216
$513$	−33.2488	−1.46797
$514$	70.2229	3.09740
$515$	3.23432	0.142521
$516$	57.5550	2.53372
$517$	0	0
$518$	0	0
$519$	23.2913	1.02237
$520$	11.6550	0.511105
$521$	33.5057	1.46791	0.733956	−	0.679197i	$-0.237672\pi$
$521$	33.5057	1.46791	0.733956	+	0.679197i	$0.237672\pi$
$522$	4.30926	0.188611
$523$	31.1574	1.36242	0.681208	−	0.732090i	$-0.261455\pi$
$523$	31.1574	1.36242	0.681208	+	0.732090i	$0.261455\pi$
$524$	19.6275	0.857432
$525$	0	0
$526$	34.9791	1.52516
$527$	−3.17983	−0.138516
$528$	0	0
$529$	21.4500	0.932608
$530$	83.9968	3.64859
$531$	0.647072	0.0280805
$532$	0	0
$533$	3.85919	0.167160
$534$	2.78675	0.120594
$535$	22.9571	0.992522
$536$	−31.7721	−1.37235
$537$	−7.54683	−0.325670
$538$	59.6793	2.57296
$539$	0	0
$540$	−77.4898	−3.33463
$541$	22.6071	0.971957	0.485979	−	0.873971i	$-0.338463\pi$
$541$	22.6071	0.971957	0.485979	+	0.873971i	$0.338463\pi$
$542$	−18.3765	−0.789340
$543$	−16.0316	−0.687980
$544$	0.971245	0.0416418
$545$	−14.3005	−0.612567
$546$	0	0
$547$	−27.4442	−1.17343	−0.586715	−	0.809794i	$-0.699579\pi$
$547$	−27.4442	−1.17343	−0.586715	+	0.809794i	$0.699579\pi$
$548$	−89.3654	−3.81750
$549$	2.61959	0.111801
$550$	0	0
$551$	−27.7891	−1.18386
$552$	−55.4757	−2.36120
$553$	0	0
$554$	−47.3341	−2.01103
$555$	−2.46673	−0.104707
$556$	80.9344	3.43238
$557$	−30.2504	−1.28175	−0.640875	−	0.767645i	$-0.721428\pi$
$557$	−30.2504	−1.28175	−0.640875	+	0.767645i	$0.721428\pi$
$558$	2.63470	0.111536
$559$	5.69300	0.240788
$560$	0	0
$561$	0	0
$562$	−4.68834	−0.197766
$563$	−7.46234	−0.314500	−0.157250	−	0.987559i	$-0.550263\pi$
$563$	−7.46234	−0.314500	−0.157250	+	0.987559i	$0.550263\pi$
$564$	3.99666	0.168290
$565$	−65.2640	−2.74568
$566$	−17.8882	−0.751896
$567$	0	0
$568$	−27.8565	−1.16883
$569$	35.6483	1.49446	0.747228	−	0.664568i	$-0.231384\pi$
$569$	35.6483	1.49446	0.747228	+	0.664568i	$0.231384\pi$
$570$	84.0716	3.52137
$571$	25.8902	1.08347	0.541737	−	0.840548i	$-0.317767\pi$
$571$	25.8902	1.08347	0.541737	+	0.840548i	$0.317767\pi$
$572$	0	0
$573$	16.0880	0.672087
$574$	0	0
$575$	−46.7911	−1.95132
$576$	2.64501	0.110209
$577$	−8.16382	−0.339864	−0.169932	−	0.985456i	$-0.554355\pi$
$577$	−8.16382	−0.339864	−0.169932	+	0.985456i	$0.554355\pi$
$578$	−38.7447	−1.61157
$579$	5.99748	0.249247
$580$	−64.7654	−2.68924
$581$	0	0
$582$	59.3048	2.45826
$583$	0	0
$584$	−34.4653	−1.42619
$585$	−0.865681	−0.0357915
$586$	8.06860	0.333311
$587$	12.4634	0.514419	0.257210	−	0.966356i	$-0.417197\pi$
$587$	12.4634	0.514419	0.257210	+	0.966356i	$0.417197\pi$
$588$	0	0
$589$	−16.9904	−0.700079
$590$	−14.4867	−0.596409
$591$	9.57847	0.394006
$592$	−1.98585	−0.0816180
$593$	23.6707	0.972037	0.486019	−	0.873948i	$-0.338449\pi$
$593$	23.6707	0.972037	0.486019	+	0.873948i	$0.338449\pi$
$594$	0	0
$595$	0	0
$596$	12.9165	0.529080
$597$	−18.5819	−0.760505
$598$	−10.7515	−0.439663
$599$	38.9809	1.59272	0.796358	−	0.604826i	$-0.206757\pi$
$599$	38.9809	1.59272	0.796358	+	0.604826i	$0.206757\pi$
$600$	58.3975	2.38407
$601$	−30.5510	−1.24620	−0.623100	−	0.782142i	$-0.714127\pi$
$601$	−30.5510	−1.24620	−0.623100	+	0.782142i	$0.714127\pi$
$602$	0	0
$603$	2.35989	0.0961022
$604$	36.4690	1.48390
$605$	0	0
$606$	−34.4030	−1.39753
$607$	−37.6173	−1.52684	−0.763420	−	0.645903i	$-0.776481\pi$
$607$	−37.6173	−1.52684	−0.763420	+	0.645903i	$0.776481\pi$
$608$	5.18954	0.210464
$609$	0	0
$610$	−58.6477	−2.37458
$611$	0.395326	0.0159932
$612$	−1.77423	−0.0717192
$613$	17.6272	0.711956	0.355978	−	0.934494i	$-0.384148\pi$
$613$	17.6272	0.711956	0.355978	+	0.934494i	$0.384148\pi$
$614$	−77.9786	−3.14696
$615$	33.1125	1.33522
$616$	0	0
$617$	−44.4849	−1.79089	−0.895447	−	0.445168i	$-0.853144\pi$
$617$	−44.4849	−1.79089	−0.895447	+	0.445168i	$0.853144\pi$
$618$	3.72368	0.149788
$619$	6.20424	0.249369	0.124685	−	0.992196i	$-0.460208\pi$
$619$	6.20424	0.249369	0.124685	+	0.992196i	$0.460208\pi$
$620$	−39.5979	−1.59029
$621$	36.4832	1.46402
$622$	22.2950	0.893949
$623$	0	0
$624$	4.77676	0.191223
$625$	−10.8356	−0.433424
$626$	−35.7652	−1.42947
$627$	0	0
$628$	−4.65531	−0.185767
$629$	−0.500073	−0.0199392
$630$	0	0
$631$	44.8057	1.78369	0.891844	−	0.452344i	$-0.149412\pi$
$631$	44.8057	1.78369	0.891844	+	0.452344i	$0.149412\pi$
$632$	13.6471	0.542851
$633$	14.1171	0.561106
$634$	−45.4307	−1.80428
$635$	−27.6172	−1.09595
$636$	64.9195	2.57423
$637$	0	0
$638$	0	0
$639$	2.06906	0.0818507
$640$	−65.1386	−2.57483
$641$	−10.2756	−0.405863	−0.202932	−	0.979193i	$-0.565047\pi$
$641$	−10.2756	−0.405863	−0.202932	+	0.979193i	$0.565047\pi$
$642$	26.4306	1.04313
$643$	16.4446	0.648511	0.324255	−	0.945970i	$-0.394886\pi$
$643$	16.4446	0.648511	0.324255	+	0.945970i	$0.394886\pi$
$644$	0	0
$645$	48.8468	1.92334
$646$	17.0436	0.670570
$647$	26.9686	1.06025	0.530123	−	0.847920i	$-0.322146\pi$
$647$	26.9686	1.06025	0.530123	+	0.847920i	$0.322146\pi$
$648$	−39.6399	−1.55720
$649$	0	0
$650$	11.3178	0.443921
$651$	0	0
$652$	−20.6986	−0.810621
$653$	7.10602	0.278080	0.139040	−	0.990287i	$-0.455598\pi$
$653$	7.10602	0.278080	0.139040	+	0.990287i	$0.455598\pi$
$654$	−16.4642	−0.643802
$655$	16.6578	0.650875
$656$	26.6573	1.04079
$657$	2.55993	0.0998724
$658$	0	0
$659$	−32.6279	−1.27100	−0.635502	−	0.772099i	$-0.719207\pi$
$659$	−32.6279	−1.27100	−0.635502	+	0.772099i	$0.719207\pi$
$660$	0	0
$661$	33.8165	1.31531	0.657654	−	0.753320i	$-0.271549\pi$
$661$	33.8165	1.31531	0.657654	+	0.753320i	$0.271549\pi$
$662$	−15.9759	−0.620919
$663$	1.20287	0.0467157
$664$	−34.4375	−1.33644
$665$	0	0
$666$	0.414344	0.0160555
$667$	30.4924	1.18067
$668$	80.4980	3.11456
$669$	−16.7189	−0.646390
$670$	−52.8335	−2.04114
$671$	0	0
$672$	0	0
$673$	23.7496	0.915478	0.457739	−	0.889087i	$-0.348659\pi$
$673$	23.7496	0.915478	0.457739	+	0.889087i	$0.348659\pi$
$674$	15.4339	0.594491
$675$	−38.4047	−1.47820
$676$	−51.3562	−1.97524
$677$	45.6311	1.75375	0.876874	−	0.480721i	$-0.159625\pi$
$677$	45.6311	1.75375	0.876874	+	0.480721i	$0.159625\pi$
$678$	−75.1386	−2.88568
$679$	0	0
$680$	20.2730	0.777435
$681$	21.4696	0.822717
$682$	0	0
$683$	−28.8727	−1.10478	−0.552392	−	0.833585i	$-0.686285\pi$
$683$	−28.8727	−1.10478	−0.552392	+	0.833585i	$0.686285\pi$
$684$	−9.48006	−0.362479
$685$	−75.8442	−2.89786
$686$	0	0
$687$	4.03898	0.154097
$688$	39.3243	1.49923
$689$	6.42145	0.244638
$690$	−92.2498	−3.51189
$691$	27.0635	1.02954	0.514772	−	0.857327i	$-0.327877\pi$
$691$	27.0635	1.02954	0.514772	+	0.857327i	$0.327877\pi$
$692$	58.7994	2.23522
$693$	0	0
$694$	56.0334	2.12700
$695$	68.6889	2.60552
$696$	−38.0559	−1.44251
$697$	6.71279	0.254265
$698$	−73.2473	−2.77245
$699$	−15.5394	−0.587755
$700$	0	0
$701$	38.5156	1.45471	0.727357	−	0.686259i	$-0.240748\pi$
$701$	38.5156	1.45471	0.727357	+	0.686259i	$0.240748\pi$
$702$	−8.82453	−0.333060
$703$	−2.67198	−0.100776
$704$	0	0
$705$	3.39196	0.127748
$706$	16.8356	0.633616
$707$	0	0
$708$	−11.1965	−0.420790
$709$	−1.89464	−0.0711548	−0.0355774	−	0.999367i	$-0.511327\pi$
$709$	−1.89464	−0.0711548	−0.0355774	+	0.999367i	$0.511327\pi$
$710$	−46.3223	−1.73845
$711$	−1.01364	−0.0380146
$712$	3.59060	0.134564
$713$	18.6432	0.698194
$714$	0	0
$715$	0	0
$716$	−19.0522	−0.712013
$717$	9.00156	0.336169
$718$	−17.9077	−0.668311
$719$	−14.5772	−0.543639	−0.271819	−	0.962348i	$-0.587625\pi$
$719$	−14.5772	−0.543639	−0.271819	+	0.962348i	$0.587625\pi$
$720$	−5.97968	−0.222849
$721$	0	0
$722$	44.1990	1.64492
$723$	−24.3041	−0.903879
$724$	−40.4721	−1.50413
$725$	−32.0984	−1.19210
$726$	0	0
$727$	−4.04780	−0.150125	−0.0750623	−	0.997179i	$-0.523916\pi$
$727$	−4.04780	−0.150125	−0.0750623	+	0.997179i	$0.523916\pi$
$728$	0	0
$729$	29.5066	1.09284
$730$	−57.3120	−2.12121
$731$	9.90257	0.366260
$732$	−45.3277	−1.67536
$733$	23.5012	0.868036	0.434018	−	0.900904i	$-0.357095\pi$
$733$	23.5012	0.868036	0.434018	+	0.900904i	$0.357095\pi$
$734$	89.6327	3.30840
$735$	0	0
$736$	−5.69437	−0.209897
$737$	0	0
$738$	−5.56199	−0.204740
$739$	−32.6786	−1.20210	−0.601051	−	0.799210i	$-0.705251\pi$
$739$	−32.6786	−1.20210	−0.601051	+	0.799210i	$0.705251\pi$
$740$	−6.22732	−0.228921
$741$	6.42717	0.236108
$742$	0	0
$743$	−18.1058	−0.664237	−0.332119	−	0.943238i	$-0.607763\pi$
$743$	−18.1058	−0.664237	−0.332119	+	0.943238i	$0.607763\pi$
$744$	−23.2676	−0.853033
$745$	10.9622	0.401624
$746$	−35.2529	−1.29070
$747$	2.55787	0.0935874
$748$	0	0
$749$	0	0
$750$	27.9255	1.01969
$751$	9.14357	0.333654	0.166827	−	0.985986i	$-0.446648\pi$
$751$	9.14357	0.333654	0.166827	+	0.985986i	$0.446648\pi$
$752$	2.73071	0.0995787
$753$	−44.6789	−1.62819
$754$	−7.37548	−0.268599
$755$	30.9512	1.12643
$756$	0	0
$757$	47.3509	1.72100	0.860499	−	0.509452i	$-0.170152\pi$
$757$	47.3509	1.72100	0.860499	+	0.509452i	$0.170152\pi$
$758$	−6.27851	−0.228046
$759$	0	0
$760$	108.323	3.92927
$761$	−3.44828	−0.125000	−0.0625000	−	0.998045i	$-0.519907\pi$
$761$	−3.44828	−0.125000	−0.0625000	+	0.998045i	$0.519907\pi$
$762$	−31.7957	−1.15184
$763$	0	0
$764$	40.6146	1.46939
$765$	−1.50579	−0.0544419
$766$	57.0720	2.06210
$767$	−1.10749	−0.0399892
$768$	−52.5854	−1.89751
$769$	−34.9787	−1.26137	−0.630683	−	0.776041i	$-0.717225\pi$
$769$	−34.9787	−1.26137	−0.630683	+	0.776041i	$0.717225\pi$
$770$	0	0
$771$	46.0622	1.65889
$772$	15.1408	0.544928
$773$	−25.3794	−0.912832	−0.456416	−	0.889766i	$-0.650867\pi$
$773$	−25.3794	−0.912832	−0.456416	+	0.889766i	$0.650867\pi$
$774$	−8.20494	−0.294920
$775$	−19.6251	−0.704956
$776$	76.4117	2.74302
$777$	0	0
$778$	74.6469	2.67622
$779$	35.8677	1.28509
$780$	14.9792	0.536340
$781$	0	0
$782$	−18.7015	−0.668765
$783$	25.0272	0.894399
$784$	0	0
$785$	−3.95095	−0.141016
$786$	19.1782	0.684064
$787$	−29.7552	−1.06066	−0.530329	−	0.847792i	$-0.677932\pi$
$787$	−29.7552	−1.06066	−0.530329	+	0.847792i	$0.677932\pi$
$788$	24.1811	0.861415
$789$	22.9443	0.816838
$790$	22.6936	0.807400
$791$	0	0
$792$	0	0
$793$	−4.48355	−0.159215
$794$	55.9308	1.98491
$795$	55.0971	1.95409
$796$	−46.9103	−1.66269
$797$	6.24330	0.221149	0.110575	−	0.993868i	$-0.464731\pi$
$797$	6.24330	0.221149	0.110575	+	0.993868i	$0.464731\pi$
$798$	0	0
$799$	0.687641	0.0243270
$800$	5.99428	0.211930
$801$	−0.266694	−0.00942316
$802$	−40.0069	−1.41269
$803$	0	0
$804$	−40.8340	−1.44010
$805$	0	0
$806$	−4.50941	−0.158837
$807$	39.1462	1.37801
$808$	−44.3268	−1.55941
$809$	39.1860	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$809$	39.1860	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$810$	−65.9167	−2.31608
$811$	12.3809	0.434753	0.217376	−	0.976088i	$-0.430250\pi$
$811$	12.3809	0.434753	0.217376	+	0.976088i	$0.430250\pi$
$812$	0	0
$813$	−12.0539	−0.422750
$814$	0	0
$815$	−17.5669	−0.615341
$816$	8.30883	0.290867
$817$	52.9112	1.85113
$818$	86.4871	3.02395
$819$	0	0
$820$	83.5933	2.91920
$821$	47.6987	1.66470	0.832349	−	0.554252i	$-0.186996\pi$
$821$	47.6987	1.66470	0.832349	+	0.554252i	$0.186996\pi$
$822$	−87.3196	−3.04562
$823$	−14.5207	−0.506161	−0.253080	−	0.967445i	$-0.581444\pi$
$823$	−14.5207	−0.506161	−0.253080	+	0.967445i	$0.581444\pi$
$824$	4.79779	0.167139
$825$	0	0
$826$	0	0
$827$	−30.9372	−1.07579	−0.537896	−	0.843011i	$-0.680781\pi$
$827$	−30.9372	−1.07579	−0.537896	+	0.843011i	$0.680781\pi$
$828$	10.4023	0.361504
$829$	−0.0858057	−0.00298015	−0.00149008	−	0.999999i	$-0.500474\pi$
$829$	−0.0858057	−0.00298015	−0.00149008	+	0.999999i	$0.500474\pi$
$830$	−57.2658	−1.98772
$831$	−31.0485	−1.07706
$832$	−4.52705	−0.156947
$833$	0	0
$834$	79.0816	2.73837
$835$	68.3185	2.36426
$836$	0	0
$837$	15.3018	0.528907
$838$	−69.7179	−2.40837
$839$	−10.6905	−0.369078	−0.184539	−	0.982825i	$-0.559079\pi$
$839$	−10.6905	−0.369078	−0.184539	+	0.982825i	$0.559079\pi$
$840$	0	0
$841$	−8.08244	−0.278705
$842$	−34.0278	−1.17267
$843$	−3.07528	−0.105918
$844$	35.6391	1.22675
$845$	−43.5859	−1.49940
$846$	−0.569756	−0.0195886
$847$	0	0
$848$	44.3561	1.52319
$849$	−11.7336	−0.402697
$850$	19.6865	0.675242
$851$	2.93190	0.100504
$852$	−35.8016	−1.22654
$853$	−21.2003	−0.725884	−0.362942	−	0.931812i	$-0.618228\pi$
$853$	−21.2003	−0.725884	−0.362942	+	0.931812i	$0.618228\pi$
$854$	0	0
$855$	−8.04571	−0.275157
$856$	34.0546	1.16396
$857$	9.45359	0.322929	0.161464	−	0.986879i	$-0.448378\pi$
$857$	9.45359	0.322929	0.161464	+	0.986879i	$0.448378\pi$
$858$	0	0
$859$	38.8261	1.32473	0.662365	−	0.749181i	$-0.269553\pi$
$859$	38.8261	1.32473	0.662365	+	0.749181i	$0.269553\pi$
$860$	123.315	4.20501
$861$	0	0
$862$	69.4879	2.36677
$863$	−37.6046	−1.28008	−0.640038	−	0.768343i	$-0.721081\pi$
$863$	−37.6046	−1.28008	−0.640038	+	0.768343i	$0.721081\pi$
$864$	−4.67376	−0.159005
$865$	49.9029	1.69675
$866$	−34.9766	−1.18855
$867$	−25.4143	−0.863114
$868$	0	0
$869$	0	0
$870$	−63.2828	−2.14549
$871$	−4.03906	−0.136858
$872$	−21.2134	−0.718377
$873$	−5.67551	−0.192087
$874$	−99.9257	−3.38004
$875$	0	0
$876$	−44.2953	−1.49660
$877$	22.0086	0.743178	0.371589	−	0.928397i	$-0.378813\pi$
$877$	22.0086	0.743178	0.371589	+	0.928397i	$0.378813\pi$
$878$	−69.1142	−2.33249
$879$	5.29254	0.178513
$880$	0	0
$881$	6.92969	0.233467	0.116734	−	0.993163i	$-0.462758\pi$
$881$	6.92969	0.233467	0.116734	+	0.993163i	$0.462758\pi$
$882$	0	0
$883$	42.3388	1.42481	0.712407	−	0.701767i	$-0.247605\pi$
$883$	42.3388	1.42481	0.712407	+	0.701767i	$0.247605\pi$
$884$	3.03668	0.102135
$885$	−9.50245	−0.319421
$886$	42.7657	1.43674
$887$	−8.05647	−0.270510	−0.135255	−	0.990811i	$-0.543185\pi$
$887$	−8.05647	−0.270510	−0.135255	+	0.990811i	$0.543185\pi$
$888$	−3.65916	−0.122793
$889$	0	0
$890$	5.97077	0.200141
$891$	0	0
$892$	−42.2072	−1.41320
$893$	3.67419	0.122952
$894$	12.6208	0.422102
$895$	−16.1695	−0.540488
$896$	0	0
$897$	−7.05239	−0.235472
$898$	−72.8216	−2.43009
$899$	12.7891	0.426541
$900$	−10.9501	−0.365004
$901$	11.1697	0.372115
$902$	0	0
$903$	0	0
$904$	−96.8128	−3.21995
$905$	−34.3485	−1.14178
$906$	35.6342	1.18387
$907$	2.89429	0.0961033	0.0480517	−	0.998845i	$-0.484699\pi$
$907$	2.89429	0.0961033	0.0480517	+	0.998845i	$0.484699\pi$
$908$	54.2006	1.79871
$909$	3.29239	0.109202
$910$	0	0
$911$	−20.2500	−0.670912	−0.335456	−	0.942056i	$-0.608890\pi$
$911$	−20.2500	−0.670912	−0.335456	+	0.942056i	$0.608890\pi$
$912$	44.3956	1.47008
$913$	0	0
$914$	23.9205	0.791220
$915$	−38.4695	−1.27176
$916$	10.1965	0.336902
$917$	0	0
$918$	−15.3496	−0.506613
$919$	18.7261	0.617718	0.308859	−	0.951108i	$-0.400053\pi$
$919$	18.7261	0.617718	0.308859	+	0.951108i	$0.400053\pi$
$920$	−118.860	−3.91869
$921$	−51.1494	−1.68543
$922$	47.4146	1.56152
$923$	−3.54128	−0.116563
$924$	0	0
$925$	−3.08632	−0.101478
$926$	50.6486	1.66442
$927$	−0.356358	−0.0117043
$928$	−3.90630	−0.128230
$929$	45.2701	1.48526	0.742631	−	0.669700i	$-0.233577\pi$
$929$	45.2701	1.48526	0.742631	+	0.669700i	$0.233577\pi$
$930$	−38.6915	−1.26874
$931$	0	0
$932$	−39.2296	−1.28501
$933$	14.6243	0.478777
$934$	−83.0584	−2.71775
$935$	0	0
$936$	−1.28415	−0.0419738
$937$	−29.4599	−0.962413	−0.481207	−	0.876607i	$-0.659801\pi$
$937$	−29.4599	−0.962413	−0.481207	+	0.876607i	$0.659801\pi$
$938$	0	0
$939$	−23.4599	−0.765586
$940$	8.56308	0.279297
$941$	−58.2346	−1.89839	−0.949197	−	0.314683i	$-0.898102\pi$
$941$	−58.2346	−1.89839	−0.949197	+	0.314683i	$0.898102\pi$
$942$	−4.54874	−0.148206
$943$	−39.3568	−1.28163
$944$	−7.64998	−0.248986
$945$	0	0
$946$	0	0
$947$	45.3642	1.47414	0.737069	−	0.675818i	$-0.236209\pi$
$947$	45.3642	1.47414	0.737069	+	0.675818i	$0.236209\pi$
$948$	17.5394	0.569654
$949$	−4.38143	−0.142227
$950$	105.189	3.41277
$951$	−29.7999	−0.966329
$952$	0	0
$953$	−41.3375	−1.33905	−0.669527	−	0.742788i	$-0.733503\pi$
$953$	−41.3375	−1.33905	−0.669527	+	0.742788i	$0.733503\pi$
$954$	−9.25480	−0.299635
$955$	34.4695	1.11541
$956$	22.7247	0.734968
$957$	0	0
$958$	−34.9555	−1.12936
$959$	0	0
$960$	−38.8428	−1.25364
$961$	−23.1807	−0.747763
$962$	−0.709167	−0.0228645
$963$	−2.52942	−0.0815095
$964$	−61.3563	−1.97615
$965$	12.8499	0.413654
$966$	0	0
$967$	−6.52818	−0.209932	−0.104966	−	0.994476i	$-0.533473\pi$
$967$	−6.52818	−0.209932	−0.104966	+	0.994476i	$0.533473\pi$
$968$	0	0
$969$	11.1796	0.359140
$970$	127.064	4.07978
$971$	−28.8587	−0.926119	−0.463060	−	0.886327i	$-0.653248\pi$
$971$	−28.8587	−0.926119	−0.463060	+	0.886327i	$0.653248\pi$
$972$	16.1114	0.516774
$973$	0	0
$974$	68.4308	2.19266
$975$	7.42383	0.237753
$976$	−30.9700	−0.991327
$977$	−8.98453	−0.287441	−0.143720	−	0.989618i	$-0.545907\pi$
$977$	−8.98453	−0.287441	−0.143720	+	0.989618i	$0.545907\pi$
$978$	−20.2248	−0.646718
$979$	0	0
$980$	0	0
$981$	1.57564	0.0503062
$982$	−8.49284	−0.271017
$983$	−36.8819	−1.17635	−0.588175	−	0.808734i	$-0.700153\pi$
$983$	−36.8819	−1.17635	−0.588175	+	0.808734i	$0.700153\pi$
$984$	49.1191	1.56586
$985$	20.5224	0.653899
$986$	−12.8291	−0.408562
$987$	0	0
$988$	16.2255	0.516203
$989$	−58.0583	−1.84615
$990$	0	0
$991$	−2.98352	−0.0947746	−0.0473873	−	0.998877i	$-0.515089\pi$
$991$	−2.98352	−0.0947746	−0.0473873	+	0.998877i	$0.515089\pi$
$992$	−2.38833	−0.0758297
$993$	−10.4792	−0.332549
$994$	0	0
$995$	−39.8127	−1.26215
$996$	−44.2596	−1.40242
$997$	−62.8553	−1.99065	−0.995324	−	0.0965930i	$-0.969205\pi$
$997$	−62.8553	−1.99065	−0.995324	+	0.0965930i	$0.969205\pi$
$998$	−6.38694	−0.202175
$999$	2.40642	0.0761357

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bi.1.4		4
7.6	odd	2		847.2.a.l.1.4		4
11.5	even	5		539.2.f.d.344.1		8
11.9	even	5		539.2.f.d.246.1		8
11.10	odd	2		5929.2.a.bb.1.1		4
21.20	even	2		7623.2.a.ch.1.1		4
77.5	odd	30		539.2.q.c.410.2		16
77.6	even	10		847.2.f.q.729.2		8
77.9	even	15		539.2.q.b.312.1		16
77.13	even	10		847.2.f.q.323.2		8
77.16	even	15		539.2.q.b.410.2		16
77.20	odd	10		77.2.f.a.15.1	✓	8
77.27	odd	10		77.2.f.a.36.1	yes	8
77.31	odd	30		539.2.q.c.422.2		16
77.38	odd	30		539.2.q.c.520.1		16
77.41	even	10		847.2.f.s.372.1		8
77.48	odd	10		847.2.f.p.148.2		8
77.53	even	15		539.2.q.b.422.2		16
77.60	even	15		539.2.q.b.520.1		16
77.62	even	10		847.2.f.s.148.1		8
77.69	odd	10		847.2.f.p.372.2		8
77.75	odd	30		539.2.q.c.312.1		16
77.76	even	2		847.2.a.k.1.1		4
231.20	even	10		693.2.m.g.631.2		8
231.104	even	10		693.2.m.g.190.2		8
231.230	odd	2		7623.2.a.co.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.1	✓	8	77.20	odd	10
77.2.f.a.36.1	yes	8	77.27	odd	10
539.2.f.d.246.1		8	11.9	even	5
539.2.f.d.344.1		8	11.5	even	5
539.2.q.b.312.1		16	77.9	even	15
539.2.q.b.410.2		16	77.16	even	15
539.2.q.b.422.2		16	77.53	even	15
539.2.q.b.520.1		16	77.60	even	15
539.2.q.c.312.1		16	77.75	odd	30
539.2.q.c.410.2		16	77.5	odd	30
539.2.q.c.422.2		16	77.31	odd	30
539.2.q.c.520.1		16	77.38	odd	30
693.2.m.g.190.2		8	231.104	even	10
693.2.m.g.631.2		8	231.20	even	10
847.2.a.k.1.1		4	77.76	even	2
847.2.a.l.1.4		4	7.6	odd	2
847.2.f.p.148.2		8	77.48	odd	10
847.2.f.p.372.2		8	77.69	odd	10
847.2.f.q.323.2		8	77.13	even	10
847.2.f.q.729.2		8	77.6	even	10
847.2.f.s.148.1		8	77.62	even	10
847.2.f.s.372.1		8	77.41	even	10
5929.2.a.bb.1.1		4	11.10	odd	2
5929.2.a.bi.1.4		4	1.1	even	1	trivial
7623.2.a.ch.1.1		4	21.20	even	2
7623.2.a.co.1.4		4	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)

\(f(q)\)	\(=\)	\(q+2.46673 q^{2} +1.61803 q^{3} +4.08477 q^{4} +3.46673 q^{5} +3.99126 q^{6} +5.14256 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q+2.46673 q^{2} +1.61803 q^{3} +4.08477 q^{4} +3.46673 q^{5} +3.99126 q^{6} +5.14256 q^{8} -0.381966 q^{9} +8.55150 q^{10} +6.60929 q^{12} +0.653752 q^{13} +5.60929 q^{15} +4.51578 q^{16} +1.13715 q^{17} -0.942208 q^{18} +6.07602 q^{19} +14.1608 q^{20} -6.66708 q^{23} +8.32083 q^{24} +7.01823 q^{25} +1.61263 q^{26} -5.47214 q^{27} -4.57357 q^{29} +13.8366 q^{30} -2.79631 q^{31} +0.854102 q^{32} +2.80505 q^{34} -1.56024 q^{36} -0.439758 q^{37} +14.9879 q^{38} +1.05779 q^{39} +17.8279 q^{40} +5.90315 q^{41} +8.70820 q^{43} -1.32417 q^{45} -16.4459 q^{46} +0.604703 q^{47} +7.30669 q^{48} +17.3121 q^{50} +1.83995 q^{51} +2.67042 q^{52} +9.82247 q^{53} -13.4983 q^{54} +9.83121 q^{57} -11.2818 q^{58} -1.69406 q^{59} +22.9126 q^{60} -6.85818 q^{61} -6.89775 q^{62} -6.92472 q^{64} +2.26638 q^{65} -6.17828 q^{67} +4.64501 q^{68} -10.7876 q^{69} -5.41687 q^{71} -1.96428 q^{72} -6.70198 q^{73} -1.08477 q^{74} +11.3557 q^{75} +24.8191 q^{76} +2.60929 q^{78} +2.65375 q^{79} +15.6550 q^{80} -7.70820 q^{81} +14.5615 q^{82} -6.69658 q^{83} +3.94221 q^{85} +21.4808 q^{86} -7.40020 q^{87} +0.698213 q^{89} -3.26638 q^{90} -27.2335 q^{92} -4.52452 q^{93} +1.49164 q^{94} +21.0639 q^{95} +1.38197 q^{96} +14.8587 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9} + 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} + 3 q^{17} - 3 q^{18} - 3 q^{19} + 17 q^{20} - 8 q^{23} + 12 q^{24} + 12 q^{26} - 4 q^{27} + 3 q^{29} + 12 q^{30} + 3 q^{31} - 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} + 5 q^{39} + 13 q^{40} - 4 q^{41} + 8 q^{43} - 9 q^{45} - 3 q^{46} + 14 q^{47} + 3 q^{48} + 33 q^{50} - 11 q^{51} + 17 q^{52} - 9 q^{53} - 2 q^{54} + 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} + 19 q^{61} - 10 q^{62} + 3 q^{64} + 12 q^{65} - 15 q^{67} + q^{68} - 14 q^{69} - 7 q^{71} - 6 q^{72} + 11 q^{73} + 8 q^{74} + 5 q^{75} + 26 q^{76} - 9 q^{78} + 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} + q^{83} + 15 q^{85} + 4 q^{86} - 6 q^{87} + 17 q^{89} - 16 q^{90} - 17 q^{92} - 11 q^{93} + 20 q^{94} + 17 q^{95} + 10 q^{96} + 15 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 + q^6 + 9 * q^8 - 6 * q^9 + 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 + 3 * q^17 - 3 * q^18 - 3 * q^19 + 17 * q^20 - 8 * q^23 + 12 * q^24 + 12 * q^26 - 4 * q^27 + 3 * q^29 + 12 * q^30 + 3 * q^31 - 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 + 5 * q^39 + 13 * q^40 - 4 * q^41 + 8 * q^43 - 9 * q^45 - 3 * q^46 + 14 * q^47 + 3 * q^48 + 33 * q^50 - 11 * q^51 + 17 * q^52 - 9 * q^53 - 2 * q^54 + 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 + 19 * q^61 - 10 * q^62 + 3 * q^64 + 12 * q^65 - 15 * q^67 + q^68 - 14 * q^69 - 7 * q^71 - 6 * q^72 + 11 * q^73 + 8 * q^74 + 5 * q^75 + 26 * q^76 - 9 * q^78 + 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 + q^83 + 15 * q^85 + 4 * q^86 - 6 * q^87 + 17 * q^89 - 16 * q^90 - 17 * q^92 - 11 * q^93 + 20 * q^94 + 17 * q^95 + 10 * q^96 + 15 * q^97

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