LMFDB - Embedded newform 5929.2.a.bx.1.9

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 14x^{8} + 14x^{7} + 61x^{6} - 57x^{5} - 84x^{4} + 63x^{3} + 20x^{2} - 15x + 1 $ x^10 - x^9 - 14x^8 + 14x^7 + 61x^6 - 57x^5 - 84x^4 + 63x^3 + 20x^2 - 15x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			1.9
Root			$-2.23710$ 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)

$f(q)$	$=$	$q+2.23710 q^{2} -1.33493 q^{3} +3.00462 q^{4} +0.866333 q^{5} -2.98638 q^{6} +2.24744 q^{8} -1.21795 q^{9} +O(q^{10})$	\(q+2.23710 q^{2} -1.33493 q^{3} +3.00462 q^{4} +0.866333 q^{5} -2.98638 q^{6} +2.24744 q^{8} -1.21795 q^{9} +1.93808 q^{10} -4.01098 q^{12} +3.38113 q^{13} -1.15650 q^{15} -0.981487 q^{16} +2.19568 q^{17} -2.72468 q^{18} +3.58857 q^{19} +2.60300 q^{20} +1.66967 q^{23} -3.00019 q^{24} -4.24947 q^{25} +7.56393 q^{26} +5.63069 q^{27} +1.53233 q^{29} -2.58720 q^{30} +8.87690 q^{31} -6.69057 q^{32} +4.91197 q^{34} -3.65948 q^{36} +3.08531 q^{37} +8.02800 q^{38} -4.51359 q^{39} +1.94703 q^{40} -0.657599 q^{41} -9.76359 q^{43} -1.05515 q^{45} +3.73523 q^{46} -13.1955 q^{47} +1.31022 q^{48} -9.50649 q^{50} -2.93109 q^{51} +10.1590 q^{52} +6.56376 q^{53} +12.5964 q^{54} -4.79051 q^{57} +3.42799 q^{58} +14.5692 q^{59} -3.47484 q^{60} -5.79638 q^{61} +19.8585 q^{62} -13.0045 q^{64} +2.92919 q^{65} +5.28376 q^{67} +6.59720 q^{68} -2.22891 q^{69} +7.83420 q^{71} -2.73727 q^{72} +5.91734 q^{73} +6.90214 q^{74} +5.67276 q^{75} +10.7823 q^{76} -10.0974 q^{78} +11.7544 q^{79} -0.850295 q^{80} -3.86275 q^{81} -1.47112 q^{82} +0.563588 q^{83} +1.90219 q^{85} -21.8421 q^{86} -2.04557 q^{87} -3.52203 q^{89} -2.36048 q^{90} +5.01674 q^{92} -11.8501 q^{93} -29.5197 q^{94} +3.10890 q^{95} +8.93148 q^{96} +13.9139 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} + 3 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} + 3 q^{8} + 9 q^{9}+O(q^{10}) $ 10 * q - q^2 + 3 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 + 3 * q^8 + 9 * q^9	$ 10 q - q^{2} + 3 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} + 3 q^{8} + 9 q^{9} + 7 q^{10} - 9 q^{12} + q^{13} - q^{15} + 15 q^{16} + 19 q^{17} - 17 q^{18} + 28 q^{19} + 5 q^{20} + 7 q^{23} + 19 q^{24} - 8 q^{25} + 5 q^{26} - 6 q^{27} + 15 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} - 12 q^{34} + 16 q^{36} + 13 q^{37} - 24 q^{38} - 4 q^{39} + 10 q^{40} + 35 q^{41} - 18 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} + 33 q^{48} - 6 q^{50} + 21 q^{51} - 4 q^{52} - 9 q^{53} + 17 q^{54} - 4 q^{57} - 9 q^{58} - 12 q^{59} - 21 q^{60} + 20 q^{61} + 38 q^{62} - 29 q^{64} + 20 q^{65} + 19 q^{67} + 56 q^{68} - 9 q^{69} + 15 q^{71} + 4 q^{72} + 3 q^{73} - 42 q^{74} + 27 q^{75} + 24 q^{76} - 25 q^{78} + 32 q^{79} + 6 q^{80} - 46 q^{81} + 18 q^{82} + 29 q^{83} + 23 q^{85} + 9 q^{86} + 24 q^{87} - 5 q^{89} + 12 q^{90} + 15 q^{92} - q^{93} - 19 q^{94} - q^{95} + 46 q^{96} - 4 q^{97}+O(q^{100}) $ 10 * q - q^2 + 3 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 + 3 * q^8 + 9 * q^9 + 7 * q^10 - 9 * q^12 + q^13 - q^15 + 15 * q^16 + 19 * q^17 - 17 * q^18 + 28 * q^19 + 5 * q^20 + 7 * q^23 + 19 * q^24 - 8 * q^25 + 5 * q^26 - 6 * q^27 + 15 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 - 12 * q^34 + 16 * q^36 + 13 * q^37 - 24 * q^38 - 4 * q^39 + 10 * q^40 + 35 * q^41 - 18 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 + 33 * q^48 - 6 * q^50 + 21 * q^51 - 4 * q^52 - 9 * q^53 + 17 * q^54 - 4 * q^57 - 9 * q^58 - 12 * q^59 - 21 * q^60 + 20 * q^61 + 38 * q^62 - 29 * q^64 + 20 * q^65 + 19 * q^67 + 56 * q^68 - 9 * q^69 + 15 * q^71 + 4 * q^72 + 3 * q^73 - 42 * q^74 + 27 * q^75 + 24 * q^76 - 25 * q^78 + 32 * q^79 + 6 * q^80 - 46 * q^81 + 18 * q^82 + 29 * q^83 + 23 * q^85 + 9 * q^86 + 24 * q^87 - 5 * q^89 + 12 * q^90 + 15 * q^92 - q^93 - 19 * q^94 - q^95 + 46 * 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 $

$2$	2.23710	1.58187	0.790935	−	0.611900i	$-0.209595\pi$
$2$	2.23710	1.58187	0.790935	+	0.611900i	$0.209595\pi$
$3$	−1.33493	−0.770725	−0.385362	−	0.922765i	$-0.625924\pi$
$3$	−1.33493	−0.770725	−0.385362	+	0.922765i	$0.625924\pi$
$4$	3.00462	1.50231
$5$	0.866333	0.387436	0.193718	−	0.981057i	$-0.437945\pi$
$5$	0.866333	0.387436	0.193718	+	0.981057i	$0.437945\pi$
$6$	−2.98638	−1.21919
$7$	0	0
$7$	0	0
$8$	2.24744	0.794591
$9$	−1.21795	−0.405983
$10$	1.93808	0.612873
$11$	0	0
$11$	0	0
$12$	−4.01098	−1.15787
$13$	3.38113	0.937757	0.468878	−	0.883263i	$-0.344658\pi$
$13$	3.38113	0.937757	0.468878	+	0.883263i	$0.344658\pi$
$14$	0	0
$15$	−1.15650	−0.298607
$16$	−0.981487	−0.245372
$17$	2.19568	0.532531	0.266266	−	0.963900i	$-0.414210\pi$
$17$	2.19568	0.532531	0.266266	+	0.963900i	$0.414210\pi$
$18$	−2.72468	−0.642213
$19$	3.58857	0.823275	0.411637	−	0.911348i	$-0.364957\pi$
$19$	3.58857	0.823275	0.411637	+	0.911348i	$0.364957\pi$
$20$	2.60300	0.582050
$21$	0	0
$22$	0	0
$23$	1.66967	0.348151	0.174076	−	0.984732i	$-0.444306\pi$
$23$	1.66967	0.348151	0.174076	+	0.984732i	$0.444306\pi$
$24$	−3.00019	−0.612411
$25$	−4.24947	−0.849893
$26$	7.56393	1.48341
$27$	5.63069	1.08363
$28$	0	0
$29$	1.53233	0.284547	0.142274	−	0.989827i	$-0.454559\pi$
$29$	1.53233	0.284547	0.142274	+	0.989827i	$0.454559\pi$
$30$	−2.58720	−0.472357
$31$	8.87690	1.59434	0.797169	−	0.603757i	$-0.206330\pi$
$31$	8.87690	1.59434	0.797169	+	0.603757i	$0.206330\pi$
$32$	−6.69057	−1.18274
$33$	0	0
$34$	4.91197	0.842395
$35$	0	0
$36$	−3.65948	−0.609913
$37$	3.08531	0.507221	0.253611	−	0.967306i	$-0.418382\pi$
$37$	3.08531	0.507221	0.253611	+	0.967306i	$0.418382\pi$
$38$	8.02800	1.30231
$39$	−4.51359	−0.722752
$40$	1.94703	0.307853
$41$	−0.657599	−0.102700	−0.0513498	−	0.998681i	$-0.516352\pi$
$41$	−0.657599	−0.102700	−0.0513498	+	0.998681i	$0.516352\pi$
$42$	0	0
$43$	−9.76359	−1.48893	−0.744467	−	0.667660i	$-0.767296\pi$
$43$	−9.76359	−1.48893	−0.744467	+	0.667660i	$0.767296\pi$
$44$	0	0
$45$	−1.05515	−0.157293
$46$	3.73523	0.550730
$47$	−13.1955	−1.92476	−0.962382	−	0.271701i	$-0.912414\pi$
$47$	−13.1955	−1.92476	−0.962382	+	0.271701i	$0.912414\pi$
$48$	1.31022	0.189114
$49$	0	0
$50$	−9.50649	−1.34442
$51$	−2.93109	−0.410435
$52$	10.1590	1.40880
$53$	6.56376	0.901602	0.450801	−	0.892625i	$-0.351138\pi$
$53$	6.56376	0.901602	0.450801	+	0.892625i	$0.351138\pi$
$54$	12.5964	1.71416
$55$	0	0
$56$	0	0
$57$	−4.79051	−0.634518
$58$	3.42799	0.450117
$59$	14.5692	1.89675	0.948373	−	0.317156i	$-0.102728\pi$
$59$	14.5692	1.89675	0.948373	+	0.317156i	$0.102728\pi$
$60$	−3.47484	−0.448600
$61$	−5.79638	−0.742150	−0.371075	−	0.928603i	$-0.621011\pi$
$61$	−5.79638	−0.742150	−0.371075	+	0.928603i	$0.621011\pi$
$62$	19.8585	2.52203
$63$	0	0
$64$	−13.0045	−1.62556
$65$	2.92919	0.363321
$66$	0	0
$67$	5.28376	0.645514	0.322757	−	0.946482i	$-0.395390\pi$
$67$	5.28376	0.645514	0.322757	+	0.946482i	$0.395390\pi$
$68$	6.59720	0.800028
$69$	−2.22891	−0.268329
$70$	0	0
$71$	7.83420	0.929749	0.464874	−	0.885377i	$-0.346099\pi$
$71$	7.83420	0.929749	0.464874	+	0.885377i	$0.346099\pi$
$72$	−2.73727	−0.322591
$73$	5.91734	0.692572	0.346286	−	0.938129i	$-0.387443\pi$
$73$	5.91734	0.692572	0.346286	+	0.938129i	$0.387443\pi$
$74$	6.90214	0.802358
$75$	5.67276	0.655034
$76$	10.7823	1.23682
$77$	0	0
$78$	−10.0974	−1.14330
$79$	11.7544	1.32247	0.661237	−	0.750177i	$-0.270032\pi$
$79$	11.7544	1.32247	0.661237	+	0.750177i	$0.270032\pi$
$80$	−0.850295	−0.0950658
$81$	−3.86275	−0.429194
$82$	−1.47112	−0.162458
$83$	0.563588	0.0618619	0.0309309	−	0.999522i	$-0.490153\pi$
$83$	0.563588	0.0618619	0.0309309	+	0.999522i	$0.490153\pi$
$84$	0	0
$85$	1.90219	0.206322
$86$	−21.8421	−2.35530
$87$	−2.04557	−0.219308
$88$	0	0
$89$	−3.52203	−0.373334	−0.186667	−	0.982423i	$-0.559769\pi$
$89$	−3.52203	−0.373334	−0.186667	+	0.982423i	$0.559769\pi$
$90$	−2.36048	−0.248816
$91$	0	0
$92$	5.01674	0.523031
$93$	−11.8501	−1.22880
$94$	−29.5197	−3.04472
$95$	3.10890	0.318966
$96$	8.93148	0.911565
$97$	13.9139	1.41274	0.706370	−	0.707842i	$-0.250331\pi$
$97$	13.9139	1.41274	0.706370	+	0.707842i	$0.250331\pi$
$98$	0	0
$99$	0	0
$100$	−12.7680	−1.27680
$101$	12.1379	1.20777	0.603884	−	0.797073i	$-0.293619\pi$
$101$	12.1379	1.20777	0.603884	+	0.797073i	$0.293619\pi$
$102$	−6.55715	−0.649255
$103$	−2.88094	−0.283867	−0.141934	−	0.989876i	$-0.545332\pi$
$103$	−2.88094	−0.283867	−0.141934	+	0.989876i	$0.545332\pi$
$104$	7.59890	0.745133
$105$	0	0
$106$	14.6838	1.42622
$107$	−0.933493	−0.0902442	−0.0451221	−	0.998981i	$-0.514368\pi$
$107$	−0.933493	−0.0902442	−0.0451221	+	0.998981i	$0.514368\pi$
$108$	16.9181	1.62794
$109$	12.1673	1.16542	0.582708	−	0.812682i	$-0.301993\pi$
$109$	12.1673	1.16542	0.582708	+	0.812682i	$0.301993\pi$
$110$	0	0
$111$	−4.11868	−0.390928
$112$	0	0
$113$	12.7946	1.20362	0.601810	−	0.798640i	$-0.294447\pi$
$113$	12.7946	1.20362	0.601810	+	0.798640i	$0.294447\pi$
$114$	−10.7169	−1.00373
$115$	1.44649	0.134886
$116$	4.60409	0.427479
$117$	−4.11805	−0.380713
$118$	32.5928	3.00041
$119$	0	0
$120$	−2.59916	−0.237270
$121$	0	0
$122$	−12.9671	−1.17398
$123$	0.877852	0.0791532
$124$	26.6717	2.39519
$125$	−8.01312	−0.716715
$126$	0	0
$127$	2.21879	0.196886	0.0984430	−	0.995143i	$-0.468614\pi$
$127$	2.21879	0.196886	0.0984430	+	0.995143i	$0.468614\pi$
$128$	−15.7113	−1.38869
$129$	13.0337	1.14756
$130$	6.55288	0.574726
$131$	−1.26676	−0.110678	−0.0553388	−	0.998468i	$-0.517624\pi$
$131$	−1.26676	−0.110678	−0.0553388	+	0.998468i	$0.517624\pi$
$132$	0	0
$133$	0	0
$134$	11.8203	1.02112
$135$	4.87805	0.419836
$136$	4.93467	0.423145
$137$	6.52288	0.557287	0.278644	−	0.960395i	$-0.410115\pi$
$137$	6.52288	0.557287	0.278644	+	0.960395i	$0.410115\pi$
$138$	−4.98629	−0.424461
$139$	14.2162	1.20580	0.602900	−	0.797817i	$-0.294012\pi$
$139$	14.2162	1.20580	0.602900	+	0.797817i	$0.294012\pi$
$140$	0	0
$141$	17.6151	1.48346
$142$	17.5259	1.47074
$143$	0	0
$144$	1.19540	0.0996168
$145$	1.32751	0.110244
$146$	13.2377	1.09556
$147$	0	0
$148$	9.27018	0.762004
$149$	3.67613	0.301161	0.150580	−	0.988598i	$-0.451886\pi$
$149$	3.67613	0.301161	0.150580	+	0.988598i	$0.451886\pi$
$150$	12.6905	1.03618
$151$	−8.84747	−0.719997	−0.359998	−	0.932953i	$-0.617223\pi$
$151$	−8.84747	−0.719997	−0.359998	+	0.932953i	$0.617223\pi$
$152$	8.06511	0.654167
$153$	−2.67423	−0.216199
$154$	0	0
$155$	7.69035	0.617704
$156$	−13.5616	−1.08580
$157$	−2.30667	−0.184093	−0.0920463	−	0.995755i	$-0.529341\pi$
$157$	−2.30667	−0.184093	−0.0920463	+	0.995755i	$0.529341\pi$
$158$	26.2958	2.09198
$159$	−8.76219	−0.694887
$160$	−5.79627	−0.458235
$161$	0	0
$162$	−8.64136	−0.678930
$163$	−5.73214	−0.448976	−0.224488	−	0.974477i	$-0.572071\pi$
$163$	−5.73214	−0.448976	−0.224488	+	0.974477i	$0.572071\pi$
$164$	−1.97584	−0.154287
$165$	0	0
$166$	1.26080	0.0978574
$167$	−3.22436	−0.249508	−0.124754	−	0.992188i	$-0.539814\pi$
$167$	−3.22436	−0.249508	−0.124754	+	0.992188i	$0.539814\pi$
$168$	0	0
$169$	−1.56796	−0.120612
$170$	4.25540	0.326374
$171$	−4.37070	−0.334236
$172$	−29.3359	−2.23684
$173$	8.40040	0.638670	0.319335	−	0.947642i	$-0.396540\pi$
$173$	8.40040	0.638670	0.319335	+	0.947642i	$0.396540\pi$
$174$	−4.57614	−0.346916
$175$	0	0
$176$	0	0
$177$	−19.4489	−1.46187
$178$	−7.87913	−0.590566
$179$	−2.56784	−0.191930	−0.0959648	−	0.995385i	$-0.530594\pi$
$179$	−2.56784	−0.191930	−0.0959648	+	0.995385i	$0.530594\pi$
$180$	−3.17033	−0.236302
$181$	−1.77336	−0.131813	−0.0659063	−	0.997826i	$-0.520994\pi$
$181$	−1.77336	−0.131813	−0.0659063	+	0.997826i	$0.520994\pi$
$182$	0	0
$183$	7.73778	0.571993
$184$	3.75250	0.276638
$185$	2.67290	0.196516
$186$	−26.5098	−1.94379
$187$	0	0
$188$	−39.6475	−2.89159
$189$	0	0
$190$	6.95492	0.504563
$191$	−8.28086	−0.599182	−0.299591	−	0.954068i	$-0.596850\pi$
$191$	−8.28086	−0.599182	−0.299591	+	0.954068i	$0.596850\pi$
$192$	17.3602	1.25286
$193$	−19.0258	−1.36951	−0.684754	−	0.728774i	$-0.740091\pi$
$193$	−19.0258	−1.36951	−0.684754	+	0.728774i	$0.740091\pi$
$194$	31.1268	2.23477
$195$	−3.91027	−0.280020
$196$	0	0
$197$	15.1831	1.08175	0.540877	−	0.841102i	$-0.318093\pi$
$197$	15.1831	1.08175	0.540877	+	0.841102i	$0.318093\pi$
$198$	0	0
$199$	24.6046	1.74417	0.872086	−	0.489352i	$-0.162767\pi$
$199$	24.6046	1.74417	0.872086	+	0.489352i	$0.162767\pi$
$200$	−9.55044	−0.675318
$201$	−7.05348	−0.497514
$202$	27.1537	1.91053
$203$	0	0
$204$	−8.80683	−0.616601
$205$	−0.569700	−0.0397896
$206$	−6.44495	−0.449041
$207$	−2.03358	−0.141344
$208$	−3.31853	−0.230099
$209$	0	0
$210$	0	0
$211$	−17.3971	−1.19766	−0.598832	−	0.800875i	$-0.704368\pi$
$211$	−17.3971	−1.19766	−0.598832	+	0.800875i	$0.704368\pi$
$212$	19.7216	1.35449
$213$	−10.4581	−0.716581
$214$	−2.08832	−0.142755
$215$	−8.45852	−0.576866
$216$	12.6547	0.861040
$217$	0	0
$218$	27.2195	1.84354
$219$	−7.89926	−0.533782
$220$	0	0
$221$	7.42389	0.499385
$222$	−9.21391	−0.618397
$223$	−2.69266	−0.180314	−0.0901568	−	0.995928i	$-0.528737\pi$
$223$	−2.69266	−0.180314	−0.0901568	+	0.995928i	$0.528737\pi$
$224$	0	0
$225$	5.17564	0.345042
$226$	28.6229	1.90397
$227$	23.0048	1.52688	0.763441	−	0.645878i	$-0.223508\pi$
$227$	23.0048	1.52688	0.763441	+	0.645878i	$0.223508\pi$
$228$	−14.3937	−0.953244
$229$	−17.9076	−1.18337	−0.591685	−	0.806169i	$-0.701537\pi$
$229$	−17.9076	−1.18337	−0.591685	+	0.806169i	$0.701537\pi$
$230$	3.23595	0.213372
$231$	0	0
$232$	3.44384	0.226099
$233$	−20.4638	−1.34063	−0.670313	−	0.742079i	$-0.733840\pi$
$233$	−20.4638	−1.34063	−0.670313	+	0.742079i	$0.733840\pi$
$234$	−9.21249	−0.602239
$235$	−11.4317	−0.745723
$236$	43.7749	2.84950
$237$	−15.6914	−1.01926
$238$	0	0
$239$	7.01657	0.453864	0.226932	−	0.973911i	$-0.427130\pi$
$239$	7.01657	0.453864	0.226932	+	0.973911i	$0.427130\pi$
$240$	1.13509	0.0732696
$241$	−11.1317	−0.717054	−0.358527	−	0.933519i	$-0.616721\pi$
$241$	−11.1317	−0.717054	−0.358527	+	0.933519i	$0.616721\pi$
$242$	0	0
$243$	−11.7355	−0.752835
$244$	−17.4159	−1.11494
$245$	0	0
$246$	1.96384	0.125210
$247$	12.1334	0.772032
$248$	19.9503	1.26685
$249$	−0.752354	−0.0476785
$250$	−17.9262	−1.13375
$251$	−10.5902	−0.668448	−0.334224	−	0.942494i	$-0.608474\pi$
$251$	−10.5902	−0.668448	−0.334224	+	0.942494i	$0.608474\pi$
$252$	0	0
$253$	0	0
$254$	4.96366	0.311448
$255$	−2.53930	−0.159017
$256$	−9.13869	−0.571168
$257$	−0.601305	−0.0375084	−0.0187542	−	0.999824i	$-0.505970\pi$
$257$	−0.601305	−0.0375084	−0.0187542	+	0.999824i	$0.505970\pi$
$258$	29.1578	1.81529
$259$	0	0
$260$	8.80110	0.545821
$261$	−1.86631	−0.115521
$262$	−2.83388	−0.175078
$263$	−17.2138	−1.06145	−0.530723	−	0.847545i	$-0.678080\pi$
$263$	−17.2138	−1.06145	−0.530723	+	0.847545i	$0.678080\pi$
$264$	0	0
$265$	5.68640	0.349313
$266$	0	0
$267$	4.70167	0.287738
$268$	15.8757	0.969764
$269$	−20.8280	−1.26991	−0.634953	−	0.772551i	$-0.718981\pi$
$269$	−20.8280	−1.26991	−0.634953	+	0.772551i	$0.718981\pi$
$270$	10.9127	0.664125
$271$	23.2245	1.41079	0.705395	−	0.708814i	$-0.250770\pi$
$271$	23.2245	1.41079	0.705395	+	0.708814i	$0.250770\pi$
$272$	−2.15503	−0.130668
$273$	0	0
$274$	14.5923	0.881556
$275$	0	0
$276$	−6.69702	−0.403113
$277$	7.92612	0.476234	0.238117	−	0.971236i	$-0.423470\pi$
$277$	7.92612	0.476234	0.238117	+	0.971236i	$0.423470\pi$
$278$	31.8030	1.90742
$279$	−10.8116	−0.647274
$280$	0	0
$281$	9.70387	0.578884	0.289442	−	0.957196i	$-0.406530\pi$
$281$	9.70387	0.578884	0.289442	+	0.957196i	$0.406530\pi$
$282$	39.4069	2.34664
$283$	−12.5422	−0.745558	−0.372779	−	0.927920i	$-0.621595\pi$
$283$	−12.5422	−0.745558	−0.372779	+	0.927920i	$0.621595\pi$
$284$	23.5388	1.39677
$285$	−4.15018	−0.245835
$286$	0	0
$287$	0	0
$288$	8.14878	0.480172
$289$	−12.1790	−0.716410
$290$	2.96978	0.174391
$291$	−18.5741	−1.08883
$292$	17.7794	1.04046
$293$	6.66180	0.389186	0.194593	−	0.980884i	$-0.437661\pi$
$293$	6.66180	0.389186	0.194593	+	0.980884i	$0.437661\pi$
$294$	0	0
$295$	12.6218	0.734868
$296$	6.93405	0.403033
$297$	0	0
$298$	8.22388	0.476397
$299$	5.64539	0.326481
$300$	17.0445	0.984065
$301$	0	0
$302$	−19.7927	−1.13894
$303$	−16.2033	−0.930856
$304$	−3.52214	−0.202008
$305$	−5.02159	−0.287536
$306$	−5.98253	−0.341998
$307$	2.06252	0.117714	0.0588572	−	0.998266i	$-0.481254\pi$
$307$	2.06252	0.117714	0.0588572	+	0.998266i	$0.481254\pi$
$308$	0	0
$309$	3.84586	0.218784
$310$	17.2041	0.977127
$311$	−3.54411	−0.200968	−0.100484	−	0.994939i	$-0.532039\pi$
$311$	−3.54411	−0.200968	−0.100484	+	0.994939i	$0.532039\pi$
$312$	−10.1440	−0.574293
$313$	15.5555	0.879246	0.439623	−	0.898182i	$-0.355112\pi$
$313$	15.5555	0.879246	0.439623	+	0.898182i	$0.355112\pi$
$314$	−5.16026	−0.291211
$315$	0	0
$316$	35.3175	1.98677
$317$	−16.6211	−0.933534	−0.466767	−	0.884380i	$-0.654581\pi$
$317$	−16.6211	−0.933534	−0.466767	+	0.884380i	$0.654581\pi$
$318$	−19.6019	−1.09922
$319$	0	0
$320$	−11.2662	−0.629802
$321$	1.24615	0.0695534
$322$	0	0
$323$	7.87937	0.438420
$324$	−11.6061	−0.644784
$325$	−14.3680	−0.796993
$326$	−12.8234	−0.710221
$327$	−16.2425	−0.898215
$328$	−1.47792	−0.0816043
$329$	0	0
$330$	0	0
$331$	21.0406	1.15650	0.578249	−	0.815860i	$-0.303736\pi$
$331$	21.0406	1.15650	0.578249	+	0.815860i	$0.303736\pi$
$332$	1.69337	0.0929358
$333$	−3.75775	−0.205923
$334$	−7.21322	−0.394690
$335$	4.57750	0.250096
$336$	0	0
$337$	−30.2679	−1.64880	−0.824399	−	0.566009i	$-0.808487\pi$
$337$	−30.2679	−1.64880	−0.824399	+	0.566009i	$0.808487\pi$
$338$	−3.50769	−0.190793
$339$	−17.0800	−0.927659
$340$	5.71537	0.309960
$341$	0	0
$342$	−9.77770	−0.528717
$343$	0	0
$344$	−21.9431	−1.18309
$345$	−1.93098	−0.103960
$346$	18.7925	1.01029
$347$	26.2201	1.40757	0.703783	−	0.710415i	$-0.251493\pi$
$347$	26.2201	1.40757	0.703783	+	0.710415i	$0.251493\pi$
$348$	−6.14616	−0.329469
$349$	10.6788	0.571624	0.285812	−	0.958286i	$-0.407737\pi$
$349$	10.6788	0.571624	0.285812	+	0.958286i	$0.407737\pi$
$350$	0	0
$351$	19.0381	1.01618
$352$	0	0
$353$	−3.89859	−0.207501	−0.103751	−	0.994603i	$-0.533084\pi$
$353$	−3.89859	−0.207501	−0.103751	+	0.994603i	$0.533084\pi$
$354$	−43.5092	−2.31249
$355$	6.78703	0.360218
$356$	−10.5824	−0.560864
$357$	0	0
$358$	−5.74452	−0.303608
$359$	−21.3341	−1.12597	−0.562984	−	0.826468i	$-0.690347\pi$
$359$	−21.3341	−1.12597	−0.562984	+	0.826468i	$0.690347\pi$
$360$	−2.37139	−0.124983
$361$	−6.12215	−0.322218
$362$	−3.96718	−0.208510
$363$	0	0
$364$	0	0
$365$	5.12638	0.268327
$366$	17.3102	0.904819
$367$	−0.588016	−0.0306942	−0.0153471	−	0.999882i	$-0.504885\pi$
$367$	−0.588016	−0.0306942	−0.0153471	+	0.999882i	$0.504885\pi$
$368$	−1.63876	−0.0854264
$369$	0.800922	0.0416944
$370$	5.97955	0.310862
$371$	0	0
$372$	−35.6050	−1.84603
$373$	−13.3157	−0.689460	−0.344730	−	0.938702i	$-0.612030\pi$
$373$	−13.3157	−0.689460	−0.344730	+	0.938702i	$0.612030\pi$
$374$	0	0
$375$	10.6970	0.552390
$376$	−29.6562	−1.52940
$377$	5.18102	0.266836
$378$	0	0
$379$	8.69504	0.446634	0.223317	−	0.974746i	$-0.428311\pi$
$379$	8.69504	0.446634	0.223317	+	0.974746i	$0.428311\pi$
$380$	9.34107	0.479187
$381$	−2.96194	−0.151745
$382$	−18.5251	−0.947827
$383$	−30.8626	−1.57700	−0.788502	−	0.615032i	$-0.789143\pi$
$383$	−30.8626	−1.57700	−0.788502	+	0.615032i	$0.789143\pi$
$384$	20.9735	1.07030
$385$	0	0
$386$	−42.5627	−2.16638
$387$	11.8916	0.604482
$388$	41.8060	2.12238
$389$	5.12780	0.259990	0.129995	−	0.991515i	$-0.458504\pi$
$389$	5.12780	0.259990	0.129995	+	0.991515i	$0.458504\pi$
$390$	−8.74767	−0.442956
$391$	3.66608	0.185401
$392$	0	0
$393$	1.69105	0.0853020
$394$	33.9662	1.71119
$395$	10.1832	0.512374
$396$	0	0
$397$	29.2532	1.46818	0.734088	−	0.679054i	$-0.237610\pi$
$397$	29.2532	1.46818	0.734088	+	0.679054i	$0.237610\pi$
$398$	55.0429	2.75905
$399$	0	0
$400$	4.17080	0.208540
$401$	14.5228	0.725233	0.362617	−	0.931938i	$-0.381883\pi$
$401$	14.5228	0.725233	0.362617	+	0.931938i	$0.381883\pi$
$402$	−15.7793	−0.787002
$403$	30.0139	1.49510
$404$	36.4698	1.81444
$405$	−3.34643	−0.166285
$406$	0	0
$407$	0	0
$408$	−6.58747	−0.326128
$409$	−11.9348	−0.590136	−0.295068	−	0.955476i	$-0.595342\pi$
$409$	−11.9348	−0.590136	−0.295068	+	0.955476i	$0.595342\pi$
$410$	−1.27448	−0.0629419
$411$	−8.70762	−0.429515
$412$	−8.65613	−0.426457
$413$	0	0
$414$	−4.54932	−0.223587
$415$	0.488255	0.0239675
$416$	−22.6217	−1.10912
$417$	−18.9777	−0.929340
$418$	0	0
$419$	15.3521	0.749999	0.374999	−	0.927025i	$-0.377643\pi$
$419$	15.3521	0.749999	0.374999	+	0.927025i	$0.377643\pi$
$420$	0	0
$421$	−7.59342	−0.370081	−0.185040	−	0.982731i	$-0.559242\pi$
$421$	−7.59342	−0.370081	−0.185040	+	0.982731i	$0.559242\pi$
$422$	−38.9190	−1.89455
$423$	16.0715	0.781422
$424$	14.7517	0.716405
$425$	−9.33048	−0.452595
$426$	−23.3959	−1.13354
$427$	0	0
$428$	−2.80480	−0.135575
$429$	0	0
$430$	−18.9226	−0.912527
$431$	26.3474	1.26911	0.634556	−	0.772877i	$-0.281183\pi$
$431$	26.3474	1.26911	0.634556	+	0.772877i	$0.281183\pi$
$432$	−5.52645	−0.265891
$433$	−7.43107	−0.357114	−0.178557	−	0.983930i	$-0.557143\pi$
$433$	−7.43107	−0.357114	−0.178557	+	0.983930i	$0.557143\pi$
$434$	0	0
$435$	−1.77214	−0.0849677
$436$	36.5581	1.75082
$437$	5.99175	0.286624
$438$	−17.6714	−0.844374
$439$	−18.9874	−0.906221	−0.453111	−	0.891454i	$-0.649686\pi$
$439$	−18.9874	−0.906221	−0.453111	+	0.891454i	$0.649686\pi$
$440$	0	0
$441$	0	0
$442$	16.6080	0.789962
$443$	−5.23013	−0.248491	−0.124246	−	0.992251i	$-0.539651\pi$
$443$	−5.23013	−0.248491	−0.124246	+	0.992251i	$0.539651\pi$
$444$	−12.3751	−0.587295
$445$	−3.05125	−0.144643
$446$	−6.02375	−0.285233
$447$	−4.90740	−0.232112
$448$	0	0
$449$	−14.2076	−0.670498	−0.335249	−	0.942130i	$-0.608820\pi$
$449$	−14.2076	−0.670498	−0.335249	+	0.942130i	$0.608820\pi$
$450$	11.5784	0.545812
$451$	0	0
$452$	38.4431	1.80821
$453$	11.8108	0.554919
$454$	51.4640	2.41533
$455$	0	0
$456$	−10.7664	−0.504183
$457$	−31.2442	−1.46154	−0.730771	−	0.682623i	$-0.760839\pi$
$457$	−31.2442	−1.46154	−0.730771	+	0.682623i	$0.760839\pi$
$458$	−40.0612	−1.87194
$459$	12.3632	0.577065
$460$	4.34617	0.202641
$461$	24.4883	1.14053	0.570266	−	0.821460i	$-0.306840\pi$
$461$	24.4883	1.14053	0.570266	+	0.821460i	$0.306840\pi$
$462$	0	0
$463$	−4.68038	−0.217516	−0.108758	−	0.994068i	$-0.534687\pi$
$463$	−4.68038	−0.217516	−0.108758	+	0.994068i	$0.534687\pi$
$464$	−1.50397	−0.0698199
$465$	−10.2661	−0.476080
$466$	−45.7795	−2.12069
$467$	−34.9981	−1.61952	−0.809758	−	0.586763i	$-0.800402\pi$
$467$	−34.9981	−1.61952	−0.809758	+	0.586763i	$0.800402\pi$
$468$	−12.3732	−0.571950
$469$	0	0
$470$	−25.5739	−1.17964
$471$	3.07926	0.141885
$472$	32.7434	1.50714
$473$	0	0
$474$	−35.1032	−1.61234
$475$	−15.2495	−0.699696
$476$	0	0
$477$	−7.99433	−0.366035
$478$	15.6968	0.717954
$479$	42.5459	1.94397	0.971986	−	0.235040i	$-0.0755220\pi$
$479$	42.5459	1.94397	0.971986	+	0.235040i	$0.0755220\pi$
$480$	7.73763	0.353173
$481$	10.4318	0.475650
$482$	−24.9027	−1.13429
$483$	0	0
$484$	0	0
$485$	12.0541	0.547347
$486$	−26.2536	−1.19089
$487$	−20.9103	−0.947534	−0.473767	−	0.880650i	$-0.657106\pi$
$487$	−20.9103	−0.947534	−0.473767	+	0.880650i	$0.657106\pi$
$488$	−13.0270	−0.589706
$489$	7.65203	0.346037
$490$	0	0
$491$	12.0253	0.542695	0.271348	−	0.962481i	$-0.412531\pi$
$491$	12.0253	0.542695	0.271348	+	0.962481i	$0.412531\pi$
$492$	2.63761	0.118913
$493$	3.36452	0.151530
$494$	27.1437	1.22125
$495$	0	0
$496$	−8.71256	−0.391205
$497$	0	0
$498$	−1.68309	−0.0754211
$499$	20.1707	0.902966	0.451483	−	0.892280i	$-0.350895\pi$
$499$	20.1707	0.902966	0.451483	+	0.892280i	$0.350895\pi$
$500$	−24.0764	−1.07673
$501$	4.30431	0.192302
$502$	−23.6914	−1.05740
$503$	−3.35049	−0.149391	−0.0746955	−	0.997206i	$-0.523798\pi$
$503$	−3.35049	−0.149391	−0.0746955	+	0.997206i	$0.523798\pi$
$504$	0	0
$505$	10.5155	0.467932
$506$	0	0
$507$	2.09312	0.0929589
$508$	6.66664	0.295784
$509$	−29.2137	−1.29487	−0.647437	−	0.762119i	$-0.724159\pi$
$509$	−29.2137	−1.29487	−0.647437	+	0.762119i	$0.724159\pi$
$510$	−5.68068	−0.251545
$511$	0	0
$512$	10.9784	0.485181
$513$	20.2061	0.892122
$514$	−1.34518	−0.0593333
$515$	−2.49585	−0.109980
$516$	39.1615	1.72399
$517$	0	0
$518$	0	0
$519$	−11.2140	−0.492239
$520$	6.58318	0.288691
$521$	−38.0049	−1.66502	−0.832512	−	0.554008i	$-0.813098\pi$
$521$	−38.0049	−1.66502	−0.832512	+	0.554008i	$0.813098\pi$
$522$	−4.17512	−0.182740
$523$	−0.602925	−0.0263640	−0.0131820	−	0.999913i	$-0.504196\pi$
$523$	−0.602925	−0.0263640	−0.0131820	+	0.999913i	$0.504196\pi$
$524$	−3.80615	−0.166272
$525$	0	0
$526$	−38.5089	−1.67907
$527$	19.4908	0.849035
$528$	0	0
$529$	−20.2122	−0.878791
$530$	12.7211	0.552567
$531$	−17.7445	−0.770047
$532$	0	0
$533$	−2.22343	−0.0963073
$534$	10.5181	0.455164
$535$	−0.808716	−0.0349638
$536$	11.8750	0.512920
$537$	3.42790	0.147925
$538$	−46.5944	−2.00883
$539$	0	0
$540$	14.6567	0.630724
$541$	−6.28767	−0.270328	−0.135164	−	0.990823i	$-0.543156\pi$
$541$	−6.28767	−0.270328	−0.135164	+	0.990823i	$0.543156\pi$
$542$	51.9556	2.23169
$543$	2.36732	0.101591
$544$	−14.6904	−0.629845
$545$	10.5409	0.451524
$546$	0	0
$547$	3.04781	0.130315	0.0651574	−	0.997875i	$-0.479245\pi$
$547$	3.04781	0.130315	0.0651574	+	0.997875i	$0.479245\pi$
$548$	19.5988	0.837219
$549$	7.05970	0.301300
$550$	0	0
$551$	5.49889	0.234261
$552$	−5.00934	−0.213212
$553$	0	0
$554$	17.7315	0.753341
$555$	−3.56815	−0.151460
$556$	42.7142	1.81149
$557$	−33.9843	−1.43996	−0.719980	−	0.693995i	$-0.755849\pi$
$557$	−33.9843	−1.43996	−0.719980	+	0.693995i	$0.755849\pi$
$558$	−24.1867	−1.02390
$559$	−33.0120	−1.39626
$560$	0	0
$561$	0	0
$562$	21.7085	0.915719
$563$	42.1279	1.77548	0.887740	−	0.460344i	$-0.152274\pi$
$563$	42.1279	1.77548	0.887740	+	0.460344i	$0.152274\pi$
$564$	52.9269	2.22862
$565$	11.0844	0.466325
$566$	−28.0582	−1.17938
$567$	0	0
$568$	17.6069	0.738770
$569$	22.3590	0.937338	0.468669	−	0.883374i	$-0.344734\pi$
$569$	22.3590	0.937338	0.468669	+	0.883374i	$0.344734\pi$
$570$	−9.28437	−0.388879
$571$	18.9838	0.794448	0.397224	−	0.917722i	$-0.369974\pi$
$571$	18.9838	0.794448	0.397224	+	0.917722i	$0.369974\pi$
$572$	0	0
$573$	11.0544	0.461804
$574$	0	0
$575$	−7.09523	−0.295891
$576$	15.8388	0.659952
$577$	−27.6589	−1.15145	−0.575727	−	0.817642i	$-0.695281\pi$
$577$	−27.6589	−1.15145	−0.575727	+	0.817642i	$0.695281\pi$
$578$	−27.2456	−1.13327
$579$	25.3982	1.05551
$580$	3.98867	0.165621
$581$	0	0
$582$	−41.5522	−1.72239
$583$	0	0
$584$	13.2989	0.550311
$585$	−3.56760	−0.147502
$586$	14.9031	0.615642
$587$	22.1556	0.914458	0.457229	−	0.889349i	$-0.348842\pi$
$587$	22.1556	0.914458	0.457229	+	0.889349i	$0.348842\pi$
$588$	0	0
$589$	31.8554	1.31258
$590$	28.2362	1.16247
$591$	−20.2685	−0.833734
$592$	−3.02819	−0.124458
$593$	12.2341	0.502395	0.251198	−	0.967936i	$-0.419176\pi$
$593$	12.2341	0.502395	0.251198	+	0.967936i	$0.419176\pi$
$594$	0	0
$595$	0	0
$596$	11.0454	0.452437
$597$	−32.8455	−1.34428
$598$	12.6293	0.516450
$599$	−7.65027	−0.312582	−0.156291	−	0.987711i	$-0.549954\pi$
$599$	−7.65027	−0.312582	−0.156291	+	0.987711i	$0.549954\pi$
$600$	12.7492	0.520484
$601$	2.75876	0.112532	0.0562661	−	0.998416i	$-0.482080\pi$
$601$	2.75876	0.112532	0.0562661	+	0.998416i	$0.482080\pi$
$602$	0	0
$603$	−6.43536	−0.262068
$604$	−26.5833	−1.08166
$605$	0	0
$606$	−36.2485	−1.47249
$607$	−2.97295	−0.120668	−0.0603341	−	0.998178i	$-0.519217\pi$
$607$	−2.97295	−0.120668	−0.0603341	+	0.998178i	$0.519217\pi$
$608$	−24.0096	−0.973718
$609$	0	0
$610$	−11.2338	−0.454844
$611$	−44.6157	−1.80496
$612$	−8.03506	−0.324798
$613$	−14.6145	−0.590275	−0.295137	−	0.955455i	$-0.595365\pi$
$613$	−14.6145	−0.590275	−0.295137	+	0.955455i	$0.595365\pi$
$614$	4.61407	0.186209
$615$	0.760512	0.0306668
$616$	0	0
$617$	−8.43040	−0.339395	−0.169697	−	0.985496i	$-0.554279\pi$
$617$	−8.43040	−0.339395	−0.169697	+	0.985496i	$0.554279\pi$
$618$	8.60359	0.346087
$619$	−44.3978	−1.78450	−0.892250	−	0.451542i	$-0.850874\pi$
$619$	−44.3978	−1.78450	−0.892250	+	0.451542i	$0.850874\pi$
$620$	23.1066	0.927983
$621$	9.40141	0.377266
$622$	−7.92854	−0.317905
$623$	0	0
$624$	4.43003	0.177343
$625$	14.3053	0.572212
$626$	34.7991	1.39085
$627$	0	0
$628$	−6.93069	−0.276565
$629$	6.77435	0.270111
$630$	0	0
$631$	−38.9464	−1.55043	−0.775217	−	0.631696i	$-0.782359\pi$
$631$	−38.9464	−1.55043	−0.775217	+	0.631696i	$0.782359\pi$
$632$	26.4174	1.05083
$633$	23.2239	0.923069
$634$	−37.1831	−1.47673
$635$	1.92221	0.0762807
$636$	−26.3271	−1.04394
$637$	0	0
$638$	0	0
$639$	−9.54167	−0.377462
$640$	−13.6112	−0.538030
$641$	−11.3840	−0.449642	−0.224821	−	0.974400i	$-0.572180\pi$
$641$	−11.3840	−0.449642	−0.224821	+	0.974400i	$0.572180\pi$
$642$	2.78777	0.110024
$643$	−19.0640	−0.751809	−0.375905	−	0.926658i	$-0.622668\pi$
$643$	−19.0640	−0.751809	−0.375905	+	0.926658i	$0.622668\pi$
$644$	0	0
$645$	11.2916	0.444605
$646$	17.6269	0.693523
$647$	−27.5833	−1.08441	−0.542205	−	0.840246i	$-0.682410\pi$
$647$	−27.5833	−1.08441	−0.542205	+	0.840246i	$0.682410\pi$
$648$	−8.68131	−0.341034
$649$	0	0
$650$	−32.1427	−1.26074
$651$	0	0
$652$	−17.2229	−0.674502
$653$	−3.43062	−0.134251	−0.0671253	−	0.997745i	$-0.521383\pi$
$653$	−3.43062	−0.134251	−0.0671253	+	0.997745i	$0.521383\pi$
$654$	−36.3362	−1.42086
$655$	−1.09744	−0.0428805
$656$	0.645425	0.0251996
$657$	−7.20702	−0.281173
$658$	0	0
$659$	12.7090	0.495073	0.247536	−	0.968879i	$-0.420379\pi$
$659$	12.7090	0.495073	0.247536	+	0.968879i	$0.420379\pi$
$660$	0	0
$661$	2.50316	0.0973617	0.0486808	−	0.998814i	$-0.484498\pi$
$661$	2.50316	0.0973617	0.0486808	+	0.998814i	$0.484498\pi$
$662$	47.0700	1.82943
$663$	−9.91041	−0.384888
$664$	1.26663	0.0491549
$665$	0	0
$666$	−8.40646	−0.325744
$667$	2.55850	0.0990655
$668$	−9.68798	−0.374839
$669$	3.59452	0.138972
$670$	10.2403	0.395619
$671$	0	0
$672$	0	0
$673$	−28.3874	−1.09425	−0.547126	−	0.837050i	$-0.684278\pi$
$673$	−28.3874	−1.09425	−0.547126	+	0.837050i	$0.684278\pi$
$674$	−67.7124	−2.60818
$675$	−23.9274	−0.920967
$676$	−4.71113	−0.181197
$677$	−26.6763	−1.02525	−0.512627	−	0.858611i	$-0.671328\pi$
$677$	−26.6763	−1.02525	−0.512627	+	0.858611i	$0.671328\pi$
$678$	−38.2097	−1.46744
$679$	0	0
$680$	4.27507	0.163941
$681$	−30.7099	−1.17681
$682$	0	0
$683$	4.61681	0.176657	0.0883286	−	0.996091i	$-0.471847\pi$
$683$	4.61681	0.176657	0.0883286	+	0.996091i	$0.471847\pi$
$684$	−13.1323	−0.502126
$685$	5.65099	0.215913
$686$	0	0
$687$	23.9055	0.912053
$688$	9.58283	0.365342
$689$	22.1929	0.845483
$690$	−4.31979	−0.164451
$691$	20.3735	0.775045	0.387523	−	0.921860i	$-0.373331\pi$
$691$	20.3735	0.775045	0.387523	+	0.921860i	$0.373331\pi$
$692$	25.2400	0.959482
$693$	0	0
$694$	58.6570	2.22659
$695$	12.3159	0.467170
$696$	−4.59729	−0.174260
$697$	−1.44388	−0.0546908
$698$	23.8896	0.904234
$699$	27.3178	1.03325
$700$	0	0
$701$	−43.0910	−1.62752	−0.813762	−	0.581198i	$-0.802584\pi$
$701$	−43.0910	−1.62752	−0.813762	+	0.581198i	$0.802584\pi$
$702$	42.5901	1.60746
$703$	11.0718	0.417582
$704$	0	0
$705$	15.2606	0.574747
$706$	−8.72155	−0.328240
$707$	0	0
$708$	−58.4367	−2.19618
$709$	−19.6482	−0.737905	−0.368952	−	0.929448i	$-0.620283\pi$
$709$	−19.6482	−0.737905	−0.368952	+	0.929448i	$0.620283\pi$
$710$	15.1833	0.569818
$711$	−14.3163	−0.536902
$712$	−7.91555	−0.296648
$713$	14.8215	0.555070
$714$	0	0
$715$	0	0
$716$	−7.71540	−0.288338
$717$	−9.36666	−0.349804
$718$	−47.7265	−1.78114
$719$	−16.9516	−0.632188	−0.316094	−	0.948728i	$-0.602371\pi$
$719$	−16.9516	−0.632188	−0.316094	+	0.948728i	$0.602371\pi$
$720$	1.03562	0.0385951
$721$	0	0
$722$	−13.6959	−0.509707
$723$	14.8601	0.552651
$724$	−5.32827	−0.198024
$725$	−6.51160	−0.241835
$726$	0	0
$727$	4.90596	0.181952	0.0909760	−	0.995853i	$-0.471001\pi$
$727$	4.90596	0.181952	0.0909760	+	0.995853i	$0.471001\pi$
$728$	0	0
$729$	27.2544	1.00942
$730$	11.4682	0.424459
$731$	−21.4377	−0.792903
$732$	23.2491	0.859312
$733$	−15.5202	−0.573253	−0.286627	−	0.958042i	$-0.592534\pi$
$733$	−15.5202	−0.573253	−0.286627	+	0.958042i	$0.592534\pi$
$734$	−1.31545	−0.0485542
$735$	0	0
$736$	−11.1711	−0.411771
$737$	0	0
$738$	1.79174	0.0659550
$739$	−14.7932	−0.544177	−0.272089	−	0.962272i	$-0.587714\pi$
$739$	−14.7932	−0.544177	−0.272089	+	0.962272i	$0.587714\pi$
$740$	8.03106	0.295228
$741$	−16.1973	−0.595024
$742$	0	0
$743$	−1.51600	−0.0556165	−0.0278082	−	0.999613i	$-0.508853\pi$
$743$	−1.51600	−0.0556165	−0.0278082	+	0.999613i	$0.508853\pi$
$744$	−26.6324	−0.976390
$745$	3.18476	0.116680
$746$	−29.7886	−1.09064
$747$	−0.686422	−0.0251149
$748$	0	0
$749$	0	0
$750$	23.9303	0.873809
$751$	42.0819	1.53559	0.767795	−	0.640695i	$-0.221354\pi$
$751$	42.0819	1.53559	0.767795	+	0.640695i	$0.221354\pi$
$752$	12.9512	0.472283
$753$	14.1372	0.515190
$754$	11.5905	0.422100
$755$	−7.66485	−0.278953
$756$	0	0
$757$	42.9210	1.55999	0.779996	−	0.625785i	$-0.215221\pi$
$757$	42.9210	1.55999	0.779996	+	0.625785i	$0.215221\pi$
$758$	19.4517	0.706517
$759$	0	0
$760$	6.98707	0.253448
$761$	41.4958	1.50422	0.752112	−	0.659036i	$-0.229035\pi$
$761$	41.4958	1.50422	0.752112	+	0.659036i	$0.229035\pi$
$762$	−6.62617	−0.240041
$763$	0	0
$764$	−24.8809	−0.900158
$765$	−2.31678	−0.0837632
$766$	−69.0427	−2.49462
$767$	49.2603	1.77869
$768$	12.1995	0.440213
$769$	−36.1695	−1.30430	−0.652152	−	0.758088i	$-0.726134\pi$
$769$	−36.1695	−1.30430	−0.652152	+	0.758088i	$0.726134\pi$
$770$	0	0
$771$	0.802702	0.0289086
$772$	−57.1654	−2.05743
$773$	−1.34792	−0.0484813	−0.0242406	−	0.999706i	$-0.507717\pi$
$773$	−1.34792	−0.0484813	−0.0242406	+	0.999706i	$0.507717\pi$
$774$	26.6026	0.956211
$775$	−37.7221	−1.35502
$776$	31.2707	1.12255
$777$	0	0
$778$	11.4714	0.411270
$779$	−2.35984	−0.0845501
$780$	−11.7489	−0.420678
$781$	0	0
$782$	8.20138	0.293281
$783$	8.62810	0.308343
$784$	0	0
$785$	−1.99835	−0.0713241
$786$	3.78304	0.134937
$787$	20.4025	0.727271	0.363635	−	0.931541i	$-0.381535\pi$
$787$	20.4025	0.727271	0.363635	+	0.931541i	$0.381535\pi$
$788$	45.6196	1.62513
$789$	22.9793	0.818083
$790$	22.7809	0.810509
$791$	0	0
$792$	0	0
$793$	−19.5983	−0.695956
$794$	65.4424	2.32246
$795$	−7.59097	−0.269224
$796$	73.9275	2.62029
$797$	−54.7927	−1.94086	−0.970429	−	0.241386i	$-0.922398\pi$
$797$	−54.7927	−1.94086	−0.970429	+	0.241386i	$0.922398\pi$
$798$	0	0
$799$	−28.9732	−1.02500
$800$	28.4314	1.00520
$801$	4.28965	0.151567
$802$	32.4889	1.14722
$803$	0	0
$804$	−21.1930	−0.747421
$805$	0	0
$806$	67.1442	2.36505
$807$	27.8040	0.978748
$808$	27.2793	0.959681
$809$	23.7544	0.835161	0.417580	−	0.908640i	$-0.362878\pi$
$809$	23.7544	0.835161	0.417580	+	0.908640i	$0.362878\pi$
$810$	−7.48630	−0.263042
$811$	29.2078	1.02562	0.512812	−	0.858501i	$-0.328604\pi$
$811$	29.2078	1.02562	0.512812	+	0.858501i	$0.328604\pi$
$812$	0	0
$813$	−31.0032	−1.08733
$814$	0	0
$815$	−4.96594	−0.173949
$816$	2.87683	0.100709
$817$	−35.0373	−1.22580
$818$	−26.6993	−0.933519
$819$	0	0
$820$	−1.71173	−0.0597763
$821$	−11.4389	−0.399222	−0.199611	−	0.979875i	$-0.563968\pi$
$821$	−11.4389	−0.399222	−0.199611	+	0.979875i	$0.563968\pi$
$822$	−19.4798	−0.679437
$823$	−11.5842	−0.403801	−0.201901	−	0.979406i	$-0.564712\pi$
$823$	−11.5842	−0.403801	−0.201901	+	0.979406i	$0.564712\pi$
$824$	−6.47475	−0.225558
$825$	0	0
$826$	0	0
$827$	−27.8602	−0.968793	−0.484397	−	0.874848i	$-0.660961\pi$
$827$	−27.8602	−0.968793	−0.484397	+	0.874848i	$0.660961\pi$
$828$	−6.11014	−0.212342
$829$	−12.7352	−0.442313	−0.221157	−	0.975238i	$-0.570983\pi$
$829$	−12.7352	−0.442313	−0.221157	+	0.975238i	$0.570983\pi$
$830$	1.09228	0.0379135
$831$	−10.5808	−0.367046
$832$	−43.9700	−1.52438
$833$	0	0
$834$	−42.4549	−1.47009
$835$	−2.79337	−0.0966685
$836$	0	0
$837$	49.9830	1.72767
$838$	34.3442	1.18640
$839$	−3.61968	−0.124965	−0.0624826	−	0.998046i	$-0.519902\pi$
$839$	−3.61968	−0.124965	−0.0624826	+	0.998046i	$0.519902\pi$
$840$	0	0
$841$	−26.6520	−0.919033
$842$	−16.9872	−0.585419
$843$	−12.9540	−0.446160
$844$	−52.2716	−1.79926
$845$	−1.35838	−0.0467295
$846$	35.9535	1.23611
$847$	0	0
$848$	−6.44224	−0.221228
$849$	16.7431	0.574620
$850$	−20.8732	−0.715946
$851$	5.15146	0.176590
$852$	−31.4228	−1.07653
$853$	49.2391	1.68591	0.842957	−	0.537981i	$-0.180813\pi$
$853$	49.2391	1.68591	0.842957	+	0.537981i	$0.180813\pi$
$854$	0	0
$855$	−3.78648	−0.129495
$856$	−2.09797	−0.0717073
$857$	24.1385	0.824556	0.412278	−	0.911058i	$-0.364733\pi$
$857$	24.1385	0.824556	0.412278	+	0.911058i	$0.364733\pi$
$858$	0	0
$859$	0.185297	0.00632225	0.00316113	−	0.999995i	$-0.498994\pi$
$859$	0.185297	0.00632225	0.00316113	+	0.999995i	$0.498994\pi$
$860$	−25.4147	−0.866633
$861$	0	0
$862$	58.9419	2.00757
$863$	38.3281	1.30471	0.652353	−	0.757916i	$-0.273782\pi$
$863$	38.3281	1.30471	0.652353	+	0.757916i	$0.273782\pi$
$864$	−37.6725	−1.28165
$865$	7.27754	0.247444
$866$	−16.6241	−0.564908
$867$	16.2581	0.552155
$868$	0	0
$869$	0	0
$870$	−3.96446	−0.134408
$871$	17.8651	0.605336
$872$	27.3453	0.926029
$873$	−16.9464	−0.573549
$874$	13.4041	0.453402
$875$	0	0
$876$	−23.7343	−0.801907
$877$	−26.5947	−0.898039	−0.449020	−	0.893522i	$-0.648227\pi$
$877$	−26.5947	−0.898039	−0.449020	+	0.893522i	$0.648227\pi$
$878$	−42.4768	−1.43352
$879$	−8.89307	−0.299956
$880$	0	0
$881$	−1.78266	−0.0600595	−0.0300297	−	0.999549i	$-0.509560\pi$
$881$	−1.78266	−0.0600595	−0.0300297	+	0.999549i	$0.509560\pi$
$882$	0	0
$883$	45.0879	1.51733	0.758664	−	0.651483i	$-0.225853\pi$
$883$	45.0879	1.51733	0.758664	+	0.651483i	$0.225853\pi$
$884$	22.3060	0.750232
$885$	−16.8492	−0.566381
$886$	−11.7003	−0.393081
$887$	18.5072	0.621411	0.310706	−	0.950506i	$-0.399435\pi$
$887$	18.5072	0.621411	0.310706	+	0.950506i	$0.399435\pi$
$888$	−9.25650	−0.310628
$889$	0	0
$890$	−6.82595	−0.228806
$891$	0	0
$892$	−8.09042	−0.270887
$893$	−47.3531	−1.58461
$894$	−10.9783	−0.367171
$895$	−2.22461	−0.0743604
$896$	0	0
$897$	−7.53622	−0.251627
$898$	−31.7838	−1.06064
$899$	13.6024	0.453665
$900$	15.5508	0.518361
$901$	14.4119	0.480131
$902$	0	0
$903$	0	0
$904$	28.7552	0.956385
$905$	−1.53632	−0.0510689
$906$	26.4219	0.877810
$907$	15.1773	0.503955	0.251978	−	0.967733i	$-0.418919\pi$
$907$	15.1773	0.503955	0.251978	+	0.967733i	$0.418919\pi$
$908$	69.1207	2.29385
$909$	−14.7834	−0.490333
$910$	0	0
$911$	−31.7996	−1.05357	−0.526783	−	0.850000i	$-0.676602\pi$
$911$	−31.7996	−1.05357	−0.526783	+	0.850000i	$0.676602\pi$
$912$	4.70182	0.155693
$913$	0	0
$914$	−69.8964	−2.31197
$915$	6.70350	0.221611
$916$	−53.8057	−1.77779
$917$	0	0
$918$	27.6577	0.912841
$919$	21.8677	0.721351	0.360675	−	0.932691i	$-0.382546\pi$
$919$	21.8677	0.721351	0.360675	+	0.932691i	$0.382546\pi$
$920$	3.25091	0.107179
$921$	−2.75333	−0.0907254
$922$	54.7827	1.80417
$923$	26.4885	0.871878
$924$	0	0
$925$	−13.1109	−0.431084
$926$	−10.4705	−0.344082
$927$	3.50884	0.115245
$928$	−10.2522	−0.336545
$929$	30.7231	1.00799	0.503996	−	0.863706i	$-0.331863\pi$
$929$	30.7231	1.00799	0.503996	+	0.863706i	$0.331863\pi$
$930$	−22.9663	−0.753096
$931$	0	0
$932$	−61.4859	−2.01404
$933$	4.73116	0.154891
$934$	−78.2942	−2.56186
$935$	0	0
$936$	−9.25508	−0.302512
$937$	−44.3186	−1.44783	−0.723913	−	0.689892i	$-0.757658\pi$
$937$	−44.3186	−1.44783	−0.723913	+	0.689892i	$0.757658\pi$
$938$	0	0
$939$	−20.7655	−0.677657
$940$	−34.3480	−1.12031
$941$	−24.4111	−0.795779	−0.397890	−	0.917433i	$-0.630257\pi$
$941$	−24.4111	−0.795779	−0.397890	+	0.917433i	$0.630257\pi$
$942$	6.88862	0.224443
$943$	−1.09798	−0.0357550
$944$	−14.2995	−0.465408
$945$	0	0
$946$	0	0
$947$	−52.9342	−1.72013	−0.860066	−	0.510184i	$-0.829577\pi$
$947$	−52.9342	−1.72013	−0.860066	+	0.510184i	$0.829577\pi$
$948$	−47.1466	−1.53125
$949$	20.0073	0.649464
$950$	−34.1147	−1.10683
$951$	22.1881	0.719498
$952$	0	0
$953$	−4.80198	−0.155551	−0.0777756	−	0.996971i	$-0.524782\pi$
$953$	−4.80198	−0.155551	−0.0777756	+	0.996971i	$0.524782\pi$
$954$	−17.8841	−0.579020
$955$	−7.17398	−0.232145
$956$	21.0821	0.681845
$957$	0	0
$958$	95.1795	3.07511
$959$	0	0
$960$	15.0397	0.485404
$961$	47.7993	1.54191
$962$	23.3370	0.752416
$963$	1.13695	0.0366376
$964$	−33.4465	−1.07724
$965$	−16.4827	−0.530597
$966$	0	0
$967$	10.0231	0.322320	0.161160	−	0.986928i	$-0.448477\pi$
$967$	10.0231	0.322320	0.161160	+	0.986928i	$0.448477\pi$
$968$	0	0
$969$	−10.5184	−0.337901
$970$	26.9662	0.865831
$971$	−1.51293	−0.0485524	−0.0242762	−	0.999705i	$-0.507728\pi$
$971$	−1.51293	−0.0485524	−0.0242762	+	0.999705i	$0.507728\pi$
$972$	−35.2609	−1.13099
$973$	0	0
$974$	−46.7784	−1.49888
$975$	19.1803	0.614262
$976$	5.68907	0.182103
$977$	−18.3330	−0.586525	−0.293262	−	0.956032i	$-0.594741\pi$
$977$	−18.3330	−0.586525	−0.293262	+	0.956032i	$0.594741\pi$
$978$	17.1184	0.547385
$979$	0	0
$980$	0	0
$981$	−14.8192	−0.473139
$982$	26.9019	0.858473
$983$	29.2145	0.931797	0.465898	−	0.884838i	$-0.345731\pi$
$983$	29.2145	0.931797	0.465898	+	0.884838i	$0.345731\pi$
$984$	1.97292	0.0628944
$985$	13.1537	0.419110
$986$	7.52677	0.239701
$987$	0	0
$988$	36.4564	1.15983
$989$	−16.3020	−0.518374
$990$	0	0
$991$	−45.2375	−1.43702	−0.718508	−	0.695519i	$-0.755175\pi$
$991$	−45.2375	−1.43702	−0.718508	+	0.695519i	$0.755175\pi$
$992$	−59.3915	−1.88568
$993$	−28.0879	−0.891342
$994$	0	0
$995$	21.3158	0.675755
$996$	−2.26054	−0.0716279
$997$	14.0812	0.445955	0.222978	−	0.974824i	$-0.428422\pi$
$997$	14.0812	0.445955	0.222978	+	0.974824i	$0.428422\pi$
$998$	45.1240	1.42837
$999$	17.3724	0.549638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bx.1.9		10
7.3	odd	6		847.2.e.i.485.2		20
7.5	odd	6		847.2.e.i.606.2		20
7.6	odd	2		5929.2.a.bw.1.9		10
11.5	even	5		539.2.f.g.344.1		20
11.9	even	5		539.2.f.g.246.1		20
11.10	odd	2		5929.2.a.bz.1.2		10
77.3	odd	30		847.2.n.i.9.5		40
77.5	odd	30		77.2.m.b.25.5	yes	40
77.9	even	15		539.2.q.h.312.1		40
77.10	even	6		847.2.e.h.485.9		20
77.16	even	15		539.2.q.h.410.5		40
77.17	even	30		847.2.n.j.366.5		40
77.19	even	30		847.2.n.h.130.5		40
77.20	odd	10		539.2.f.h.246.1		20
77.24	even	30		847.2.n.j.807.1		40
77.26	odd	30		847.2.n.i.753.5		40
77.27	odd	10		539.2.f.h.344.1		20
77.31	odd	30		77.2.m.b.37.5	yes	40
77.38	odd	30		77.2.m.b.58.1	yes	40
77.40	even	30		847.2.n.h.753.1		40
77.47	odd	30		847.2.n.i.130.1		40
77.52	even	30		847.2.n.h.9.1		40
77.53	even	15		539.2.q.h.422.5		40
77.54	even	6		847.2.e.h.606.9		20
77.59	odd	30		847.2.n.i.632.1		40
77.60	even	15		539.2.q.h.520.1		40
77.61	even	30		847.2.n.j.487.1		40
77.68	even	30		847.2.n.j.81.5		40
77.73	even	30		847.2.n.h.632.5		40
77.75	odd	30		77.2.m.b.4.1	✓	40
77.76	even	2		5929.2.a.by.1.2		10
231.5	even	30		693.2.by.b.487.1		40
231.38	even	30		693.2.by.b.289.5		40
231.152	even	30		693.2.by.b.235.5		40
231.185	even	30		693.2.by.b.37.1		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.m.b.4.1	✓	40	77.75	odd	30
77.2.m.b.25.5	yes	40	77.5	odd	30
77.2.m.b.37.5	yes	40	77.31	odd	30
77.2.m.b.58.1	yes	40	77.38	odd	30
539.2.f.g.246.1		20	11.9	even	5
539.2.f.g.344.1		20	11.5	even	5
539.2.f.h.246.1		20	77.20	odd	10
539.2.f.h.344.1		20	77.27	odd	10
539.2.q.h.312.1		40	77.9	even	15
539.2.q.h.410.5		40	77.16	even	15
539.2.q.h.422.5		40	77.53	even	15
539.2.q.h.520.1		40	77.60	even	15
693.2.by.b.37.1		40	231.185	even	30
693.2.by.b.235.5		40	231.152	even	30
693.2.by.b.289.5		40	231.38	even	30
693.2.by.b.487.1		40	231.5	even	30
847.2.e.h.485.9		20	77.10	even	6
847.2.e.h.606.9		20	77.54	even	6
847.2.e.i.485.2		20	7.3	odd	6
847.2.e.i.606.2		20	7.5	odd	6
847.2.n.h.9.1		40	77.52	even	30
847.2.n.h.130.5		40	77.19	even	30
847.2.n.h.632.5		40	77.73	even	30
847.2.n.h.753.1		40	77.40	even	30
847.2.n.i.9.5		40	77.3	odd	30
847.2.n.i.130.1		40	77.47	odd	30
847.2.n.i.632.1		40	77.59	odd	30
847.2.n.i.753.5		40	77.26	odd	30
847.2.n.j.81.5		40	77.68	even	30
847.2.n.j.366.5		40	77.17	even	30
847.2.n.j.487.1		40	77.61	even	30
847.2.n.j.807.1		40	77.24	even	30
5929.2.a.bw.1.9		10	7.6	odd	2
5929.2.a.bx.1.9		10	1.1	even	1	trivial
5929.2.a.by.1.2		10	77.76	even	2
5929.2.a.bz.1.2		10	11.10	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)

\(f(q)\)	\(=\)	\(q+2.23710 q^{2} -1.33493 q^{3} +3.00462 q^{4} +0.866333 q^{5} -2.98638 q^{6} +2.24744 q^{8} -1.21795 q^{9} +O(q^{10})\)	\(q+2.23710 q^{2} -1.33493 q^{3} +3.00462 q^{4} +0.866333 q^{5} -2.98638 q^{6} +2.24744 q^{8} -1.21795 q^{9} +1.93808 q^{10} -4.01098 q^{12} +3.38113 q^{13} -1.15650 q^{15} -0.981487 q^{16} +2.19568 q^{17} -2.72468 q^{18} +3.58857 q^{19} +2.60300 q^{20} +1.66967 q^{23} -3.00019 q^{24} -4.24947 q^{25} +7.56393 q^{26} +5.63069 q^{27} +1.53233 q^{29} -2.58720 q^{30} +8.87690 q^{31} -6.69057 q^{32} +4.91197 q^{34} -3.65948 q^{36} +3.08531 q^{37} +8.02800 q^{38} -4.51359 q^{39} +1.94703 q^{40} -0.657599 q^{41} -9.76359 q^{43} -1.05515 q^{45} +3.73523 q^{46} -13.1955 q^{47} +1.31022 q^{48} -9.50649 q^{50} -2.93109 q^{51} +10.1590 q^{52} +6.56376 q^{53} +12.5964 q^{54} -4.79051 q^{57} +3.42799 q^{58} +14.5692 q^{59} -3.47484 q^{60} -5.79638 q^{61} +19.8585 q^{62} -13.0045 q^{64} +2.92919 q^{65} +5.28376 q^{67} +6.59720 q^{68} -2.22891 q^{69} +7.83420 q^{71} -2.73727 q^{72} +5.91734 q^{73} +6.90214 q^{74} +5.67276 q^{75} +10.7823 q^{76} -10.0974 q^{78} +11.7544 q^{79} -0.850295 q^{80} -3.86275 q^{81} -1.47112 q^{82} +0.563588 q^{83} +1.90219 q^{85} -21.8421 q^{86} -2.04557 q^{87} -3.52203 q^{89} -2.36048 q^{90} +5.01674 q^{92} -11.8501 q^{93} -29.5197 q^{94} +3.10890 q^{95} +8.93148 q^{96} +13.9139 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} + 3 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 10 * q - q^2 + 3 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 + 3 * q^8 + 9 * q^9	\( 10 q - q^{2} + 3 q^{3} + 9 q^{4} + 2 q^{5} + 9 q^{6} + 3 q^{8} + 9 q^{9} + 7 q^{10} - 9 q^{12} + q^{13} - q^{15} + 15 q^{16} + 19 q^{17} - 17 q^{18} + 28 q^{19} + 5 q^{20} + 7 q^{23} + 19 q^{24} - 8 q^{25} + 5 q^{26} - 6 q^{27} + 15 q^{29} + 22 q^{30} + 14 q^{31} + 15 q^{32} - 12 q^{34} + 16 q^{36} + 13 q^{37} - 24 q^{38} - 4 q^{39} + 10 q^{40} + 35 q^{41} - 18 q^{43} - 8 q^{45} - 9 q^{46} - 16 q^{47} + 33 q^{48} - 6 q^{50} + 21 q^{51} - 4 q^{52} - 9 q^{53} + 17 q^{54} - 4 q^{57} - 9 q^{58} - 12 q^{59} - 21 q^{60} + 20 q^{61} + 38 q^{62} - 29 q^{64} + 20 q^{65} + 19 q^{67} + 56 q^{68} - 9 q^{69} + 15 q^{71} + 4 q^{72} + 3 q^{73} - 42 q^{74} + 27 q^{75} + 24 q^{76} - 25 q^{78} + 32 q^{79} + 6 q^{80} - 46 q^{81} + 18 q^{82} + 29 q^{83} + 23 q^{85} + 9 q^{86} + 24 q^{87} - 5 q^{89} + 12 q^{90} + 15 q^{92} - q^{93} - 19 q^{94} - q^{95} + 46 q^{96} - 4 q^{97}+O(q^{100}) \) 10 * q - q^2 + 3 * q^3 + 9 * q^4 + 2 * q^5 + 9 * q^6 + 3 * q^8 + 9 * q^9 + 7 * q^10 - 9 * q^12 + q^13 - q^15 + 15 * q^16 + 19 * q^17 - 17 * q^18 + 28 * q^19 + 5 * q^20 + 7 * q^23 + 19 * q^24 - 8 * q^25 + 5 * q^26 - 6 * q^27 + 15 * q^29 + 22 * q^30 + 14 * q^31 + 15 * q^32 - 12 * q^34 + 16 * q^36 + 13 * q^37 - 24 * q^38 - 4 * q^39 + 10 * q^40 + 35 * q^41 - 18 * q^43 - 8 * q^45 - 9 * q^46 - 16 * q^47 + 33 * q^48 - 6 * q^50 + 21 * q^51 - 4 * q^52 - 9 * q^53 + 17 * q^54 - 4 * q^57 - 9 * q^58 - 12 * q^59 - 21 * q^60 + 20 * q^61 + 38 * q^62 - 29 * q^64 + 20 * q^65 + 19 * q^67 + 56 * q^68 - 9 * q^69 + 15 * q^71 + 4 * q^72 + 3 * q^73 - 42 * q^74 + 27 * q^75 + 24 * q^76 - 25 * q^78 + 32 * q^79 + 6 * q^80 - 46 * q^81 + 18 * q^82 + 29 * q^83 + 23 * q^85 + 9 * q^86 + 24 * q^87 - 5 * q^89 + 12 * q^90 + 15 * q^92 - q^93 - 19 * q^94 - q^95 + 46 * q^96 - 4 * q^97

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