LMFDB - Embedded newform 5929.2.a.bi.1.1

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			1.1
Root			$-1.46673$ 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)

$f(q)$	$=$	$q-1.46673 q^{2} +1.61803 q^{3} +0.151302 q^{4} -0.466732 q^{5} -2.37322 q^{6} +2.71154 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-1.46673 q^{2} +1.61803 q^{3} +0.151302 q^{4} -0.466732 q^{5} -2.37322 q^{6} +2.71154 q^{8} -0.381966 q^{9} +0.684570 q^{10} +0.244812 q^{12} +1.58232 q^{13} -0.755188 q^{15} -4.27971 q^{16} -5.22732 q^{17} +0.560242 q^{18} -4.22192 q^{19} -0.0706175 q^{20} -1.80505 q^{23} +4.38737 q^{24} -4.78216 q^{25} -2.32083 q^{26} -5.47214 q^{27} +2.71947 q^{29} +1.10766 q^{30} -1.29386 q^{31} +0.854102 q^{32} +7.66708 q^{34} -0.0577923 q^{36} -1.94221 q^{37} +6.19242 q^{38} +2.56024 q^{39} -1.26556 q^{40} +1.04112 q^{41} +8.70820 q^{43} +0.178276 q^{45} +2.64753 q^{46} +6.39530 q^{47} -6.92472 q^{48} +7.01415 q^{50} -8.45799 q^{51} +0.239408 q^{52} -13.2044 q^{53} +8.02616 q^{54} -6.83121 q^{57} -3.98873 q^{58} +8.60389 q^{59} -0.114262 q^{60} +15.2401 q^{61} +1.89775 q^{62} +7.30669 q^{64} -0.738517 q^{65} -4.67583 q^{67} -0.790906 q^{68} -2.92064 q^{69} +9.74310 q^{71} -1.03572 q^{72} +13.3200 q^{73} +2.84870 q^{74} -7.73770 q^{75} -0.638786 q^{76} -3.75519 q^{78} +3.58232 q^{79} +1.99748 q^{80} -7.70820 q^{81} -1.52705 q^{82} +17.2589 q^{83} +2.43976 q^{85} -12.7726 q^{86} +4.40020 q^{87} +8.91982 q^{89} -0.261483 q^{90} -0.273109 q^{92} -2.09351 q^{93} -9.38018 q^{94} +1.97050 q^{95} +1.38197 q^{96} +2.70362 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.46673	−1.03714	−0.518568	−	0.855036i	$-0.673535\pi$
$2$	−1.46673	−1.03714	−0.518568	+	0.855036i	$0.673535\pi$
$3$	1.61803	0.934172	0.467086	−	0.884212i	$-0.345304\pi$
$3$	1.61803	0.934172	0.467086	+	0.884212i	$0.345304\pi$
$4$	0.151302	0.0756511
$5$	−0.466732	−0.208729	−0.104364	−	0.994539i	$-0.533281\pi$
$5$	−0.466732	−0.208729	−0.104364	+	0.994539i	$0.533281\pi$
$6$	−2.37322	−0.968864
$7$	0	0
$7$	0	0
$8$	2.71154	0.958676
$9$	−0.381966	−0.127322
$10$	0.684570	0.216480
$11$	0	0
$11$	0	0
$12$	0.244812	0.0706712
$13$	1.58232	0.438856	0.219428	−	0.975629i	$-0.429581\pi$
$13$	1.58232	0.438856	0.219428	+	0.975629i	$0.429581\pi$
$14$	0	0
$15$	−0.755188	−0.194989
$16$	−4.27971	−1.06993
$17$	−5.22732	−1.26781	−0.633906	−	0.773410i	$-0.718549\pi$
$17$	−5.22732	−1.26781	−0.633906	+	0.773410i	$0.718549\pi$
$18$	0.560242	0.132050
$19$	−4.22192	−0.968575	−0.484287	−	0.874909i	$-0.660921\pi$
$19$	−4.22192	−0.968575	−0.484287	+	0.874909i	$0.660921\pi$
$20$	−0.0706175	−0.0157906
$21$	0	0
$22$	0	0
$23$	−1.80505	−0.376380	−0.188190	−	0.982133i	$-0.560262\pi$
$23$	−1.80505	−0.376380	−0.188190	+	0.982133i	$0.560262\pi$
$24$	4.38737	0.895568
$25$	−4.78216	−0.956432
$26$	−2.32083	−0.455153
$27$	−5.47214	−1.05311
$28$	0	0
$29$	2.71947	0.504993	0.252496	−	0.967598i	$-0.418748\pi$
$29$	2.71947	0.504993	0.252496	+	0.967598i	$0.418748\pi$
$30$	1.10766	0.202230
$31$	−1.29386	−0.232384	−0.116192	−	0.993227i	$-0.537069\pi$
$31$	−1.29386	−0.232384	−0.116192	+	0.993227i	$0.537069\pi$
$32$	0.854102	0.150985
$33$	0	0
$34$	7.66708	1.31489
$35$	0	0
$36$	−0.0577923	−0.00963205
$37$	−1.94221	−0.319297	−0.159648	−	0.987174i	$-0.551036\pi$
$37$	−1.94221	−0.319297	−0.159648	+	0.987174i	$0.551036\pi$
$38$	6.19242	1.00454
$39$	2.56024	0.409967
$40$	−1.26556	−0.200103
$41$	1.04112	0.162596	0.0812980	−	0.996690i	$-0.474093\pi$
$41$	1.04112	0.162596	0.0812980	+	0.996690i	$0.474093\pi$
$42$	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
$45$	0.178276	0.0265758
$46$	2.64753	0.390357
$47$	6.39530	0.932850	0.466425	−	0.884561i	$-0.345542\pi$
$47$	6.39530	0.932850	0.466425	+	0.884561i	$0.345542\pi$
$48$	−6.92472	−0.999497
$49$	0	0
$50$	7.01415	0.991950
$51$	−8.45799	−1.18436
$52$	0.239408	0.0331999
$53$	−13.2044	−1.81377	−0.906884	−	0.421380i	$-0.861546\pi$
$53$	−13.2044	−1.81377	−0.906884	+	0.421380i	$0.861546\pi$
$54$	8.02616	1.09222
$55$	0	0
$56$	0	0
$57$	−6.83121	−0.904816
$58$	−3.98873	−0.523746
$59$	8.60389	1.12013	0.560065	−	0.828448i	$-0.310776\pi$
$59$	8.60389	1.12013	0.560065	+	0.828448i	$0.310776\pi$
$60$	−0.114262	−0.0147511
$61$	15.2401	1.95130	0.975651	−	0.219331i	$-0.0703874\pi$
$61$	15.2401	1.95130	0.975651	+	0.219331i	$0.0703874\pi$
$62$	1.89775	0.241014
$63$	0	0
$64$	7.30669	0.913336
$65$	−0.738517	−0.0916018
$66$	0	0
$67$	−4.67583	−0.571243	−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583	−0.571243	−0.285622	+	0.958342i	$0.592200\pi$
$68$	−0.790906	−0.0959114
$69$	−2.92064	−0.351604
$70$	0	0
$71$	9.74310	1.15629	0.578147	−	0.815933i	$-0.303776\pi$
$71$	9.74310	1.15629	0.578147	+	0.815933i	$0.303776\pi$
$72$	−1.03572	−0.122060
$73$	13.3200	1.55899	0.779495	−	0.626408i	$-0.215476\pi$
$73$	13.3200	1.55899	0.779495	+	0.626408i	$0.215476\pi$
$74$	2.84870	0.331154
$75$	−7.73770	−0.893473
$76$	−0.638786	−0.0732737
$77$	0	0
$78$	−3.75519	−0.425191
$79$	3.58232	0.403042	0.201521	−	0.979484i	$-0.435412\pi$
$79$	3.58232	0.403042	0.201521	+	0.979484i	$0.435412\pi$
$80$	1.99748	0.223325
$81$	−7.70820	−0.856467
$82$	−1.52705	−0.168634
$83$	17.2589	1.89441	0.947204	−	0.320631i	$-0.103895\pi$
$83$	17.2589	1.89441	0.947204	+	0.320631i	$0.103895\pi$
$84$	0	0
$85$	2.43976	0.264629
$86$	−12.7726	−1.37730
$87$	4.40020	0.471750
$88$	0	0
$89$	8.91982	0.945499	0.472750	−	0.881197i	$-0.343262\pi$
$89$	8.91982	0.945499	0.472750	+	0.881197i	$0.343262\pi$
$90$	−0.261483	−0.0275627
$91$	0	0
$92$	−0.273109	−0.0284735
$93$	−2.09351	−0.217087
$94$	−9.38018	−0.967492
$95$	1.97050	0.202169
$96$	1.38197	0.141046
$97$	2.70362	0.274511	0.137255	−	0.990536i	$-0.456172\pi$
$97$	2.70362	0.274511	0.137255	+	0.990536i	$0.456172\pi$
$98$	0	0
$99$	0	0
$100$	−0.723551	−0.0723551
$101$	−0.178781	−0.0177894	−0.00889469	−	0.999960i	$-0.502831\pi$
$101$	−0.178781	−0.0177894	−0.00889469	+	0.999960i	$0.502831\pi$
$102$	12.4056	1.22834
$103$	−16.8772	−1.66296	−0.831481	−	0.555553i	$-0.812507\pi$
$103$	−16.8772	−1.66296	−0.831481	+	0.555553i	$0.812507\pi$
$104$	4.29052	0.420720
$105$	0	0
$106$	19.3674	1.88112
$107$	−15.4762	−1.49614	−0.748071	−	0.663618i	$-0.769020\pi$
$107$	−15.4762	−1.49614	−0.748071	+	0.663618i	$0.769020\pi$
$108$	−0.827946	−0.0796692
$109$	11.0349	1.05695	0.528476	−	0.848948i	$-0.322764\pi$
$109$	11.0349	1.05695	0.528476	+	0.848948i	$0.322764\pi$
$110$	0	0
$111$	−3.14256	−0.298278
$112$	0	0
$113$	1.77008	0.166515	0.0832574	−	0.996528i	$-0.473468\pi$
$113$	1.77008	0.166515	0.0832574	+	0.996528i	$0.473468\pi$
$114$	10.0196	0.938417
$115$	0.842476	0.0785613
$116$	0.411462	0.0382033
$117$	−0.604391	−0.0558760
$118$	−12.6196	−1.16173
$119$	0	0
$120$	−2.04773	−0.186931
$121$	0	0
$122$	−22.3532	−2.02376
$123$	1.68457	0.151893
$124$	−0.195764	−0.0175801
$125$	4.56565	0.408364
$126$	0	0
$127$	−8.54023	−0.757823	−0.378911	−	0.925433i	$-0.623702\pi$
$127$	−8.54023	−0.757823	−0.378911	+	0.925433i	$0.623702\pi$
$128$	−12.4252	−1.09824
$129$	14.0902	1.24057
$130$	1.08321	0.0950035
$131$	9.66708	0.844617	0.422308	−	0.906452i	$-0.361220\pi$
$131$	9.66708	0.844617	0.422308	+	0.906452i	$0.361220\pi$
$132$	0	0
$133$	0	0
$134$	6.85818	0.592457
$135$	2.55402	0.219815
$136$	−14.1741	−1.21542
$137$	−14.0108	−1.19702	−0.598512	−	0.801114i	$-0.704241\pi$
$137$	−14.0108	−1.19702	−0.598512	+	0.801114i	$0.704241\pi$
$138$	4.28379	0.364661
$139$	−9.57765	−0.812366	−0.406183	−	0.913792i	$-0.633140\pi$
$139$	−9.57765	−0.812366	−0.406183	+	0.913792i	$0.633140\pi$
$140$	0	0
$141$	10.3478	0.871443
$142$	−14.2905	−1.19923
$143$	0	0
$144$	1.63470	0.136225
$145$	−1.26926	−0.105407
$146$	−19.5369	−1.61688
$147$	0	0
$148$	−0.293860	−0.0241552
$149$	14.9625	1.22578	0.612888	−	0.790170i	$-0.290008\pi$
$149$	14.9625	1.22578	0.612888	+	0.790170i	$0.290008\pi$
$150$	11.3491	0.926653
$151$	−2.87233	−0.233747	−0.116874	−	0.993147i	$-0.537287\pi$
$151$	−2.87233	−0.233747	−0.116874	+	0.993147i	$0.537287\pi$
$152$	−11.4479	−0.928549
$153$	1.99666	0.161420
$154$	0	0
$155$	0.603886	0.0485053
$156$	0.387370	0.0310144
$157$	18.8823	1.50697	0.753487	−	0.657463i	$-0.228370\pi$
$157$	18.8823	1.50697	0.753487	+	0.657463i	$0.228370\pi$
$158$	−5.25430	−0.418009
$159$	−21.3652	−1.69437
$160$	−0.398637	−0.0315150
$161$	0	0
$162$	11.3059	0.888273
$163$	11.5951	0.908202	0.454101	−	0.890950i	$-0.349961\pi$
$163$	11.5951	0.908202	0.454101	+	0.890950i	$0.349961\pi$
$164$	0.157524	0.0123006
$165$	0	0
$166$	−25.3142	−1.96476
$167$	−6.32491	−0.489437	−0.244718	−	0.969594i	$-0.578695\pi$
$167$	−6.32491	−0.489437	−0.244718	+	0.969594i	$0.578695\pi$
$168$	0	0
$169$	−10.4963	−0.807406
$170$	−3.57847	−0.274456
$171$	1.61263	0.123321
$172$	1.31757	0.100464
$173$	−1.33906	−0.101807	−0.0509035	−	0.998704i	$-0.516210\pi$
$173$	−1.33906	−0.101807	−0.0509035	+	0.998704i	$0.516210\pi$
$174$	−6.45391	−0.489269
$175$	0	0
$176$	0	0
$177$	13.9214	1.04639
$178$	−13.0830	−0.980611
$179$	17.7888	1.32960	0.664799	−	0.747022i	$-0.268517\pi$
$179$	17.7888	1.32960	0.664799	+	0.747022i	$0.268517\pi$
$180$	0.0269735	0.00201049
$181$	0.963777	0.0716370	0.0358185	−	0.999358i	$-0.488596\pi$
$181$	0.963777	0.0716370	0.0358185	+	0.999358i	$0.488596\pi$
$182$	0	0
$183$	24.6591	1.82285
$184$	−4.89448	−0.360826
$185$	0.906490	0.0666465
$186$	3.07062	0.225149
$187$	0	0
$188$	0.967622	0.0705711
$189$	0	0
$190$	−2.89020	−0.209677
$191$	−16.0888	−1.16415	−0.582074	−	0.813136i	$-0.697759\pi$
$191$	−16.0888	−1.16415	−0.582074	+	0.813136i	$0.697759\pi$
$192$	11.8225	0.853213
$193$	12.1475	0.874393	0.437197	−	0.899366i	$-0.355971\pi$
$193$	12.1475	0.874393	0.437197	+	0.899366i	$0.355971\pi$
$194$	−3.96548	−0.284705
$195$	−1.19495	−0.0855719
$196$	0	0
$197$	−2.30179	−0.163996	−0.0819978	−	0.996633i	$-0.526130\pi$
$197$	−2.30179	−0.163996	−0.0819978	+	0.996633i	$0.526130\pi$
$198$	0	0
$199$	−20.2797	−1.43759	−0.718795	−	0.695222i	$-0.755306\pi$
$199$	−20.2797	−1.43759	−0.718795	+	0.695222i	$0.755306\pi$
$200$	−12.9670	−0.916908
$201$	−7.56565	−0.533640
$202$	0.262224	0.0184500
$203$	0	0
$204$	−1.27971	−0.0895978
$205$	−0.485925	−0.0339384
$206$	24.7544	1.72472
$207$	0.689469	0.0479214
$208$	−6.77186	−0.469544
$209$	0	0
$210$	0	0
$211$	5.36530	0.369362	0.184681	−	0.982799i	$-0.440875\pi$
$211$	5.36530	0.369362	0.184681	+	0.982799i	$0.440875\pi$
$212$	−1.99786	−0.137214
$213$	15.7647	1.08018
$214$	22.6995	1.55170
$215$	−4.06440	−0.277189
$216$	−14.8379	−1.00959
$217$	0	0
$218$	−16.1852	−1.09620
$219$	21.5522	1.45637
$220$	0	0
$221$	−8.27128	−0.556387
$222$	4.60929	0.309355
$223$	25.4230	1.70245	0.851225	−	0.524800i	$-0.175860\pi$
$223$	25.4230	1.70245	0.851225	+	0.524800i	$0.175860\pi$
$224$	0	0
$225$	1.82662	0.121775
$226$	−2.59623	−0.172699
$227$	21.7098	1.44093	0.720464	−	0.693493i	$-0.243929\pi$
$227$	21.7098	1.44093	0.720464	+	0.693493i	$0.243929\pi$
$228$	−1.03358	−0.0684503
$229$	−20.5307	−1.35670	−0.678352	−	0.734737i	$-0.737306\pi$
$229$	−20.5307	−1.35670	−0.678352	+	0.734737i	$0.737306\pi$
$230$	−1.23569	−0.0814787
$231$	0	0
$232$	7.37396	0.484124
$233$	0.694056	0.0454691	0.0227345	−	0.999742i	$-0.492763\pi$
$233$	0.694056	0.0454691	0.0227345	+	0.999742i	$0.492763\pi$
$234$	0.886480	0.0579510
$235$	−2.98489	−0.194713
$236$	1.30179	0.0847391
$237$	5.79631	0.376511
$238$	0	0
$239$	0.346561	0.0224171	0.0112086	−	0.999937i	$-0.496432\pi$
$239$	0.346561	0.0224171	0.0112086	+	0.999937i	$0.496432\pi$
$240$	3.23199	0.208624
$241$	10.4372	0.672317	0.336158	−	0.941806i	$-0.390872\pi$
$241$	10.4372	0.672317	0.336158	+	0.941806i	$0.390872\pi$
$242$	0	0
$243$	3.94427	0.253025
$244$	2.30587	0.147618
$245$	0	0
$246$	−2.47081	−0.157533
$247$	−6.68041	−0.425064
$248$	−3.50836	−0.222781
$249$	27.9255	1.76970
$250$	−6.69658	−0.423529
$251$	6.99502	0.441522	0.220761	−	0.975328i	$-0.429146\pi$
$251$	6.99502	0.441522	0.220761	+	0.975328i	$0.429146\pi$
$252$	0	0
$253$	0	0
$254$	12.5262	0.785965
$255$	3.94761	0.247209
$256$	3.61099	0.225687
$257$	9.94843	0.620566	0.310283	−	0.950644i	$-0.399576\pi$
$257$	9.94843	0.620566	0.310283	+	0.950644i	$0.399576\pi$
$258$	−20.6665	−1.28664
$259$	0	0
$260$	−0.111739	−0.00692978
$261$	−1.03875	−0.0642967
$262$	−14.1790	−0.875983
$263$	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
$265$	6.16293	0.378586
$266$	0	0
$267$	14.4326	0.883259
$268$	−0.707463	−0.0432152
$269$	18.4031	1.12206	0.561028	−	0.827797i	$-0.310406\pi$
$269$	18.4031	1.12206	0.561028	+	0.827797i	$0.310406\pi$
$270$	−3.74606	−0.227978
$271$	−0.730591	−0.0443802	−0.0221901	−	0.999754i	$-0.507064\pi$
$271$	−0.730591	−0.0443802	−0.0221901	+	0.999754i	$0.507064\pi$
$272$	22.3714	1.35647
$273$	0	0
$274$	20.5501	1.24148
$275$	0	0
$276$	−0.441899	−0.0265992
$277$	15.0644	0.905132	0.452566	−	0.891731i	$-0.350509\pi$
$277$	15.0644	0.905132	0.452566	+	0.891731i	$0.350509\pi$
$278$	14.0478	0.842534
$279$	0.494211	0.0295876
$280$	0	0
$281$	−10.6961	−0.638077	−0.319039	−	0.947742i	$-0.603360\pi$
$281$	−10.6961	−0.638077	−0.319039	+	0.947742i	$0.603360\pi$
$282$	−15.1775	−0.903804
$283$	−9.10890	−0.541468	−0.270734	−	0.962654i	$-0.587266\pi$
$283$	−9.10890	−0.541468	−0.270734	+	0.962654i	$0.587266\pi$
$284$	1.47415	0.0874749
$285$	3.18834	0.188861
$286$	0	0
$287$	0	0
$288$	−0.326238	−0.0192238
$289$	10.3249	0.607348
$290$	1.86167	0.109321
$291$	4.37454	0.256440
$292$	2.01535	0.117939
$293$	−11.8890	−0.694563	−0.347281	−	0.937761i	$-0.612895\pi$
$293$	−11.8890	−0.694563	−0.347281	+	0.937761i	$0.612895\pi$
$294$	0	0
$295$	−4.01571	−0.233804
$296$	−5.26638	−0.306102
$297$	0	0
$298$	−21.9460	−1.27130
$299$	−2.85617	−0.165176
$300$	−1.17073	−0.0675922
$301$	0	0
$302$	4.21294	0.242427
$303$	−0.289274	−0.0166183
$304$	18.0686	1.03631
$305$	−7.11306	−0.407293
$306$	−2.92856	−0.167415
$307$	−2.22072	−0.126743	−0.0633716	−	0.997990i	$-0.520185\pi$
$307$	−2.22072	−0.126743	−0.0633716	+	0.997990i	$0.520185\pi$
$308$	0	0
$309$	−27.3079	−1.55349
$310$	−0.885738	−0.0503066
$311$	21.4126	1.21420	0.607098	−	0.794627i	$-0.292334\pi$
$311$	21.4126	1.21420	0.607098	+	0.794627i	$0.292334\pi$
$312$	6.94221	0.393025
$313$	31.5548	1.78358	0.891790	−	0.452449i	$-0.149450\pi$
$313$	31.5548	1.78358	0.891790	+	0.452449i	$0.149450\pi$
$314$	−27.6953	−1.56294
$315$	0	0
$316$	0.542012	0.0304906
$317$	−13.2007	−0.741423	−0.370712	−	0.928748i	$-0.620886\pi$
$317$	−13.2007	−0.741423	−0.370712	+	0.928748i	$0.620886\pi$
$318$	31.3370	1.75729
$319$	0	0
$320$	−3.41026	−0.190639
$321$	−25.0410	−1.39765
$322$	0	0
$323$	22.0693	1.22797
$324$	−1.16627	−0.0647927
$325$	−7.56689	−0.419736
$326$	−17.0070	−0.941929
$327$	17.8548	0.987375
$328$	2.82305	0.155877
$329$	0	0
$330$	0	0
$331$	9.47653	0.520877	0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653	0.520877	0.260439	+	0.965490i	$0.416133\pi$
$332$	2.61131	0.143314
$333$	0.741857	0.0406535
$334$	9.27695	0.507612
$335$	2.18236	0.119235
$336$	0	0
$337$	−19.2011	−1.04595	−0.522975	−	0.852348i	$-0.675178\pi$
$337$	−19.2011	−1.04595	−0.522975	+	0.852348i	$0.675178\pi$
$338$	15.3952	0.837390
$339$	2.86405	0.155554
$340$	0.369141	0.0200195
$341$	0	0
$342$	−2.36530	−0.127901
$343$	0	0
$344$	23.6127	1.27311
$345$	1.36315	0.0733898
$346$	1.96405	0.105588
$347$	3.04831	0.163642	0.0818208	−	0.996647i	$-0.473926\pi$
$347$	3.04831	0.163642	0.0818208	+	0.996647i	$0.473926\pi$
$348$	0.665759	0.0356884
$349$	−19.3961	−1.03825	−0.519125	−	0.854698i	$-0.673742\pi$
$349$	−19.3961	−1.03825	−0.519125	+	0.854698i	$0.673742\pi$
$350$	0	0
$351$	−8.65865	−0.462165
$352$	0	0
$353$	10.7585	0.572619	0.286309	−	0.958137i	$-0.407572\pi$
$353$	10.7585	0.572619	0.286309	+	0.958137i	$0.407572\pi$
$354$	−20.4189	−1.08525
$355$	−4.54742	−0.241352
$356$	1.34959	0.0715280
$357$	0	0
$358$	−26.0914	−1.37897
$359$	0.607226	0.0320481	0.0160241	−	0.999872i	$-0.494899\pi$
$359$	0.607226	0.0320481	0.0160241	+	0.999872i	$0.494899\pi$
$360$	0.483402	0.0254775
$361$	−1.17539	−0.0618628
$362$	−1.41360	−0.0742973
$363$	0	0
$364$	0	0
$365$	−6.21688	−0.325406
$366$	−36.1683	−1.89055
$367$	−27.6628	−1.44399	−0.721994	−	0.691899i	$-0.756774\pi$
$367$	−27.6628	−1.44399	−0.721994	+	0.691899i	$0.756774\pi$
$368$	7.72511	0.402699
$369$	−0.397673	−0.0207020
$370$	−1.32958	−0.0691215
$371$	0	0
$372$	−0.316753	−0.0164229
$373$	−29.4513	−1.52493	−0.762465	−	0.647029i	$-0.776011\pi$
$373$	−29.4513	−1.52493	−0.762465	+	0.647029i	$0.776011\pi$
$374$	0	0
$375$	7.38737	0.381482
$376$	17.3411	0.894300
$377$	4.30306	0.221619
$378$	0	0
$379$	25.3436	1.30182	0.650908	−	0.759157i	$-0.274388\pi$
$379$	25.3436	1.30182	0.650908	+	0.759157i	$0.274388\pi$
$380$	0.298142	0.0152943
$381$	−13.8184	−0.707937
$382$	23.5980	1.20738
$383$	31.9322	1.63166	0.815829	−	0.578293i	$-0.196281\pi$
$383$	31.9322	1.63166	0.815829	+	0.578293i	$0.196281\pi$
$384$	−20.1043	−1.02594
$385$	0	0
$386$	−17.8171	−0.906865
$387$	−3.32624	−0.169082
$388$	0.409063	0.0207670
$389$	17.7517	0.900047	0.450024	−	0.893017i	$-0.351416\pi$
$389$	17.7517	0.900047	0.450024	+	0.893017i	$0.351416\pi$
$390$	1.75267	0.0887497
$391$	9.43560	0.477179
$392$	0	0
$393$	15.6417	0.789018
$394$	3.37610	0.170086
$395$	−1.67198	−0.0841265
$396$	0	0
$397$	13.3047	0.667742	0.333871	−	0.942619i	$-0.391645\pi$
$397$	13.3047	0.667742	0.333871	+	0.942619i	$0.391645\pi$
$398$	29.7449	1.49098
$399$	0	0
$400$	20.4663	1.02331
$401$	−3.48962	−0.174264	−0.0871318	−	0.996197i	$-0.527770\pi$
$401$	−3.48962	−0.174264	−0.0871318	+	0.996197i	$0.527770\pi$
$402$	11.0968	0.553457
$403$	−2.04730	−0.101983
$404$	−0.0270500	−0.00134579
$405$	3.59766	0.178769
$406$	0	0
$407$	0	0
$408$	−22.9342	−1.13541
$409$	29.6255	1.46489	0.732443	−	0.680828i	$-0.238380\pi$
$409$	29.6255	1.46489	0.732443	+	0.680828i	$0.238380\pi$
$410$	0.712721	0.0351988
$411$	−22.6700	−1.11823
$412$	−2.55356	−0.125805
$413$	0	0
$414$	−1.01127	−0.0497010
$415$	−8.05527	−0.395418
$416$	1.35146	0.0662608
$417$	−15.4970	−0.758890
$418$	0	0
$419$	11.6452	0.568907	0.284454	−	0.958690i	$-0.408188\pi$
$419$	11.6452	0.568907	0.284454	+	0.958690i	$0.408188\pi$
$420$	0	0
$421$	19.8848	0.969128	0.484564	−	0.874756i	$-0.338978\pi$
$421$	19.8848	0.969128	0.484564	+	0.874756i	$0.338978\pi$
$422$	−7.86945	−0.383079
$423$	−2.44279	−0.118772
$424$	−35.8044	−1.73882
$425$	24.9979	1.21258
$426$	−23.1225	−1.12029
$427$	0	0
$428$	−2.34159	−0.113185
$429$	0	0
$430$	5.96138	0.287483
$431$	30.2464	1.45692	0.728458	−	0.685090i	$-0.240237\pi$
$431$	30.2464	1.45692	0.728458	+	0.685090i	$0.240237\pi$
$432$	23.4192	1.12676
$433$	5.70719	0.274270	0.137135	−	0.990552i	$-0.456211\pi$
$433$	5.70719	0.274270	0.137135	+	0.990552i	$0.456211\pi$
$434$	0	0
$435$	−2.05371	−0.0984679
$436$	1.66960	0.0799596
$437$	7.62079	0.364552
$438$	−31.6114	−1.51045
$439$	−6.84875	−0.326873	−0.163436	−	0.986554i	$-0.552258\pi$
$439$	−6.84875	−0.326873	−0.163436	+	0.986554i	$0.552258\pi$
$440$	0	0
$441$	0	0
$442$	12.1317	0.577048
$443$	0.100695	0.00478417	0.00239209	−	0.999997i	$-0.499239\pi$
$443$	0.100695	0.00478417	0.00239209	+	0.999997i	$0.499239\pi$
$444$	−0.475476	−0.0225651
$445$	−4.16316	−0.197353
$446$	−37.2887	−1.76567
$447$	24.2098	1.14509
$448$	0	0
$449$	−30.8047	−1.45377	−0.726883	−	0.686762i	$-0.759032\pi$
$449$	−30.8047	−1.45377	−0.726883	+	0.686762i	$0.759032\pi$
$450$	−2.67917	−0.126297
$451$	0	0
$452$	0.267817	0.0125970
$453$	−4.64753	−0.218360
$454$	−31.8424	−1.49444
$455$	0	0
$456$	−18.5231	−0.867425
$457$	23.1356	1.08224	0.541118	−	0.840947i	$-0.318001\pi$
$457$	23.1356	1.08224	0.541118	+	0.840947i	$0.318001\pi$
$458$	30.1130	1.40709
$459$	28.6046	1.33515
$460$	0.127468	0.00594325
$461$	2.77839	0.129403	0.0647013	−	0.997905i	$-0.479391\pi$
$461$	2.77839	0.129403	0.0647013	+	0.997905i	$0.479391\pi$
$462$	0	0
$463$	−26.0950	−1.21274	−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950	−1.21274	−0.606369	+	0.795184i	$0.707374\pi$
$464$	−11.6385	−0.540306
$465$	0.977108	0.0453123
$466$	−1.01799	−0.0471576
$467$	2.65829	0.123011	0.0615055	−	0.998107i	$-0.480410\pi$
$467$	2.65829	0.123011	0.0615055	+	0.998107i	$0.480410\pi$
$468$	−0.0914457	−0.00422708
$469$	0	0
$470$	4.37803	0.201943
$471$	30.5522	1.40777
$472$	23.3298	1.07384
$473$	0	0
$474$	−8.50163	−0.390493
$475$	20.1899	0.926376
$476$	0	0
$477$	5.04364	0.230933
$478$	−0.508312	−0.0232496
$479$	8.28223	0.378425	0.189212	−	0.981936i	$-0.439407\pi$
$479$	8.28223	0.378425	0.189212	+	0.981936i	$0.439407\pi$
$480$	−0.645007	−0.0294404
$481$	−3.07319	−0.140125
$482$	−15.3085	−0.697284
$483$	0	0
$484$	0	0
$485$	−1.26186	−0.0572983
$486$	−5.78519	−0.262422
$487$	−19.5956	−0.887960	−0.443980	−	0.896037i	$-0.646434\pi$
$487$	−19.5956	−0.887960	−0.443980	+	0.896037i	$0.646434\pi$
$488$	41.3243	1.87066
$489$	18.7613	0.848417
$490$	0	0
$491$	−28.6817	−1.29439	−0.647193	−	0.762327i	$-0.724057\pi$
$491$	−28.6817	−1.29439	−0.647193	+	0.762327i	$0.724057\pi$
$492$	0.254879	0.0114908
$493$	−14.2156	−0.640236
$494$	9.79837	0.440850
$495$	0	0
$496$	5.53735	0.248634
$497$	0	0
$498$	−40.9592	−1.83542
$499$	27.9499	1.25121	0.625605	−	0.780140i	$-0.284852\pi$
$499$	27.9499	1.25121	0.625605	+	0.780140i	$0.284852\pi$
$500$	0.690792	0.0308932
$501$	−10.2339	−0.457218
$502$	−10.2598	−0.457918
$503$	8.09736	0.361043	0.180522	−	0.983571i	$-0.442221\pi$
$503$	8.09736	0.361043	0.180522	+	0.983571i	$0.442221\pi$
$504$	0	0
$505$	0.0834428	0.00371316
$506$	0	0
$507$	−16.9833	−0.754256
$508$	−1.29216	−0.0573301
$509$	−16.3002	−0.722492	−0.361246	−	0.932471i	$-0.617648\pi$
$509$	−16.3002	−0.722492	−0.361246	+	0.932471i	$0.617648\pi$
$510$	−5.79009	−0.256389
$511$	0	0
$512$	19.5539	0.864170
$513$	23.1029	1.02002
$514$	−14.5917	−0.643611
$515$	7.87714	0.347108
$516$	2.13187	0.0938505
$517$	0	0
$518$	0	0
$519$	−2.16665	−0.0951054
$520$	−2.00252	−0.0878164
$521$	−7.68605	−0.336732	−0.168366	−	0.985725i	$-0.553849\pi$
$521$	−7.68605	−0.336732	−0.168366	+	0.985725i	$0.553849\pi$
$522$	1.52356	0.0666844
$523$	−26.1229	−1.14228	−0.571138	−	0.820854i	$-0.693498\pi$
$523$	−26.1229	−1.14228	−0.571138	+	0.820854i	$0.693498\pi$
$524$	1.46265	0.0638962
$525$	0	0
$526$	−20.7988	−0.906869
$527$	6.76343	0.294619
$528$	0	0
$529$	−19.7418	−0.858338
$530$	−9.03936	−0.392645
$531$	−3.28639	−0.142617
$532$	0	0
$533$	1.64738	0.0713561
$534$	−21.1687	−0.916060
$535$	7.22324	0.312288
$536$	−12.6787	−0.547637
$537$	28.7829	1.24207
$538$	−26.9924	−1.16372
$539$	0	0
$540$	0.386429	0.0166292
$541$	−25.8777	−1.11257	−0.556284	−	0.830992i	$-0.687773\pi$
$541$	−25.8777	−1.11257	−0.556284	+	0.830992i	$0.687773\pi$
$542$	1.07158	0.0460283
$543$	1.55942	0.0669213
$544$	−4.46467	−0.191421
$545$	−5.15034	−0.220616
$546$	0	0
$547$	−38.0968	−1.62890	−0.814451	−	0.580232i	$-0.802962\pi$
$547$	−38.0968	−1.62890	−0.814451	+	0.580232i	$0.802962\pi$
$548$	−2.11987	−0.0905562
$549$	−5.82122	−0.248444
$550$	0	0
$551$	−11.4814	−0.489123
$552$	−7.91944	−0.337074
$553$	0	0
$554$	−22.0954	−0.938745
$555$	1.46673	0.0622593
$556$	−1.44912	−0.0614564
$557$	34.5422	1.46360	0.731799	−	0.681520i	$-0.238681\pi$
$557$	34.5422	1.46360	0.731799	+	0.681520i	$0.238681\pi$
$558$	−0.724874	−0.0306864
$559$	13.7791	0.582795
$560$	0	0
$561$	0	0
$562$	15.6883	0.661773
$563$	−19.4819	−0.821066	−0.410533	−	0.911846i	$-0.634657\pi$
$563$	−19.4819	−0.821066	−0.410533	+	0.911846i	$0.634657\pi$
$564$	1.56565	0.0659256
$565$	−0.826151	−0.0347565
$566$	13.3603	0.561576
$567$	0	0
$568$	26.4189	1.10851
$569$	17.1288	0.718075	0.359038	−	0.933323i	$-0.383105\pi$
$569$	17.1288	0.718075	0.359038	+	0.933323i	$0.383105\pi$
$570$	−4.67644	−0.195875
$571$	−3.85581	−0.161360	−0.0806802	−	0.996740i	$-0.525709\pi$
$571$	−3.85581	−0.161360	−0.0806802	+	0.996740i	$0.525709\pi$
$572$	0	0
$573$	−26.0323	−1.08751
$574$	0	0
$575$	8.63206	0.359982
$576$	−2.79091	−0.116288
$577$	9.78185	0.407224	0.203612	−	0.979052i	$-0.434732\pi$
$577$	9.78185	0.407224	0.203612	+	0.979052i	$0.434732\pi$
$578$	−15.1439	−0.629902
$579$	19.6550	0.816834
$580$	−0.192042	−0.00797412
$581$	0	0
$582$	−6.41628	−0.265964
$583$	0	0
$584$	36.1178	1.49457
$585$	0.282089	0.0116629
$586$	17.4380	0.720356
$587$	6.09891	0.251729	0.125865	−	0.992047i	$-0.459830\pi$
$587$	6.09891	0.251729	0.125865	+	0.992047i	$0.459830\pi$
$588$	0	0
$589$	5.46257	0.225081
$590$	5.88997	0.242486
$591$	−3.72437	−0.153200
$592$	8.31209	0.341625
$593$	−13.2330	−0.543413	−0.271706	−	0.962380i	$-0.587588\pi$
$593$	−13.2330	−0.543413	−0.271706	+	0.962380i	$0.587588\pi$
$594$	0	0
$595$	0	0
$596$	2.26386	0.0927313
$597$	−32.8133	−1.34296
$598$	4.18923	0.171310
$599$	−5.92515	−0.242095	−0.121048	−	0.992647i	$-0.538625\pi$
$599$	−5.92515	−0.242095	−0.121048	+	0.992647i	$0.538625\pi$
$600$	−20.9811	−0.856550
$601$	−12.7408	−0.519708	−0.259854	−	0.965648i	$-0.583674\pi$
$601$	−12.7408	−0.519708	−0.259854	+	0.965648i	$0.583674\pi$
$602$	0	0
$603$	1.78601	0.0727318
$604$	−0.434590	−0.0176832
$605$	0	0
$606$	0.424287	0.0172355
$607$	−8.36141	−0.339379	−0.169690	−	0.985498i	$-0.554276\pi$
$607$	−8.36141	−0.339379	−0.169690	+	0.985498i	$0.554276\pi$
$608$	−3.60595	−0.146241
$609$	0	0
$610$	10.4330	0.422418
$611$	10.1194	0.409386
$612$	0.302099	0.0122116
$613$	−6.68294	−0.269921	−0.134961	−	0.990851i	$-0.543091\pi$
$613$	−6.68294	−0.269921	−0.134961	+	0.990851i	$0.543091\pi$
$614$	3.25720	0.131450
$615$	−0.786243	−0.0317044
$616$	0	0
$617$	11.8669	0.477741	0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669	0.477741	0.238871	+	0.971051i	$0.423223\pi$
$618$	40.0534	1.61118
$619$	−20.6206	−0.828814	−0.414407	−	0.910092i	$-0.636011\pi$
$619$	−20.6206	−0.828814	−0.414407	+	0.910092i	$0.636011\pi$
$620$	0.0913692	0.00366948
$621$	9.87750	0.396370
$622$	−31.4065	−1.25929
$623$	0	0
$624$	−10.9571	−0.438635
$625$	21.7799	0.871195
$626$	−46.2824	−1.84982
$627$	0	0
$628$	2.85694	0.114004
$629$	10.1525	0.404809
$630$	0	0
$631$	−15.4795	−0.616228	−0.308114	−	0.951349i	$-0.599698\pi$
$631$	−15.4795	−0.616228	−0.308114	+	0.951349i	$0.599698\pi$
$632$	9.71361	0.386387
$633$	8.68123	0.345048
$634$	19.3618	0.768957
$635$	3.98600	0.158179
$636$	−3.23260	−0.128181
$637$	0	0
$638$	0	0
$639$	−3.72153	−0.147222
$640$	5.79921	0.229234
$641$	−23.5785	−0.931294	−0.465647	−	0.884971i	$-0.654178\pi$
$641$	−23.5785	−0.931294	−0.465647	+	0.884971i	$0.654178\pi$
$642$	36.7285	1.44956
$643$	−28.6806	−1.13105	−0.565527	−	0.824730i	$-0.691327\pi$
$643$	−28.6806	−1.13105	−0.565527	+	0.824730i	$0.691327\pi$
$644$	0	0
$645$	−6.57633	−0.258943
$646$	−32.3698	−1.27357
$647$	−5.42763	−0.213382	−0.106691	−	0.994292i	$-0.534026\pi$
$647$	−5.42763	−0.213382	−0.106691	+	0.994292i	$0.534026\pi$
$648$	−20.9011	−0.821074
$649$	0	0
$650$	11.0986	0.435323
$651$	0	0
$652$	1.75437	0.0687064
$653$	−12.3421	−0.482983	−0.241492	−	0.970403i	$-0.577637\pi$
$653$	−12.3421	−0.482983	−0.241492	+	0.970403i	$0.577637\pi$
$654$	−26.1883	−1.02404
$655$	−4.51193	−0.176296
$656$	−4.45570	−0.173966
$657$	−5.08779	−0.198494
$658$	0	0
$659$	16.2115	0.631512	0.315756	−	0.948840i	$-0.397742\pi$
$659$	16.2115	0.631512	0.315756	+	0.948840i	$0.397742\pi$
$660$	0	0
$661$	−43.7050	−1.69993	−0.849964	−	0.526840i	$-0.823377\pi$
$661$	−43.7050	−1.69993	−0.849964	+	0.526840i	$0.823377\pi$
$662$	−13.8995	−0.540220
$663$	−13.3832	−0.519761
$664$	46.7982	1.81612
$665$	0	0
$666$	−1.08811	−0.0421632
$667$	−4.90879	−0.190069
$668$	−0.956973	−0.0370264
$669$	41.1353	1.59038
$670$	−3.20093	−0.123663
$671$	0	0
$672$	0	0
$673$	−5.86102	−0.225926	−0.112963	−	0.993599i	$-0.536034\pi$
$673$	−5.86102	−0.225926	−0.112963	+	0.993599i	$0.536034\pi$
$674$	28.1629	1.08479
$675$	26.1686	1.00723
$676$	−1.58811	−0.0610811
$677$	20.5279	0.788952	0.394476	−	0.918906i	$-0.370926\pi$
$677$	20.5279	0.788952	0.394476	+	0.918906i	$0.370926\pi$
$678$	−4.20079	−0.161330
$679$	0	0
$680$	6.61551	0.253693
$681$	35.1271	1.34607
$682$	0	0
$683$	38.7055	1.48103	0.740513	−	0.672042i	$-0.234583\pi$
$683$	38.7055	1.48103	0.740513	+	0.672042i	$0.234583\pi$
$684$	0.243994	0.00932936
$685$	6.53929	0.249853
$686$	0	0
$687$	−33.2193	−1.26740
$688$	−37.2686	−1.42085
$689$	−20.8936	−0.795982
$690$	−1.99938	−0.0761152
$691$	23.1300	0.879907	0.439954	−	0.898020i	$-0.354995\pi$
$691$	23.1300	0.879907	0.439954	+	0.898020i	$0.354995\pi$
$692$	−0.202603	−0.00770182
$693$	0	0
$694$	−4.47105	−0.169719
$695$	4.47020	0.169564
$696$	11.9313	0.452256
$697$	−5.44228	−0.206141
$698$	28.4489	1.07681
$699$	1.12301	0.0424760
$700$	0	0
$701$	35.5107	1.34122	0.670610	−	0.741810i	$-0.266032\pi$
$701$	35.5107	1.34122	0.670610	+	0.741810i	$0.266032\pi$
$702$	12.6999	0.479328
$703$	8.19985	0.309263
$704$	0	0
$705$	−4.82965	−0.181895
$706$	−15.7799	−0.593883
$707$	0	0
$708$	2.10634	0.0791609
$709$	43.8045	1.64511	0.822556	−	0.568684i	$-0.192547\pi$
$709$	43.8045	1.64511	0.822556	+	0.568684i	$0.192547\pi$
$710$	6.66984	0.250315
$711$	−1.36832	−0.0513161
$712$	24.1865	0.906427
$713$	2.33549	0.0874647
$714$	0	0
$715$	0	0
$716$	2.69149	0.100586
$717$	0.560747	0.0209415
$718$	−0.890637	−0.0332383
$719$	−15.8605	−0.591496	−0.295748	−	0.955266i	$-0.595569\pi$
$719$	−15.8605	−0.591496	−0.295748	+	0.955266i	$0.595569\pi$
$720$	−0.762969	−0.0284342
$721$	0	0
$722$	1.72399	0.0641602
$723$	16.8877	0.628060
$724$	0.145822	0.00541942
$725$	−13.0049	−0.482992
$726$	0	0
$727$	−13.7719	−0.510770	−0.255385	−	0.966839i	$-0.582202\pi$
$727$	−13.7719	−0.510770	−0.255385	+	0.966839i	$0.582202\pi$
$728$	0	0
$729$	29.5066	1.09284
$730$	9.11849	0.337490
$731$	−45.5206	−1.68364
$732$	3.73097	0.137901
$733$	19.5677	0.722750	0.361375	−	0.932421i	$-0.382307\pi$
$733$	19.5677	0.722750	0.361375	+	0.932421i	$0.382307\pi$
$734$	40.5740	1.49761
$735$	0	0
$736$	−1.54170	−0.0568278
$737$	0	0
$738$	0.583280	0.0214708
$739$	−11.1542	−0.410313	−0.205157	−	0.978729i	$-0.565770\pi$
$739$	−11.1542	−0.410313	−0.205157	+	0.978729i	$0.565770\pi$
$740$	0.137154	0.00504188
$741$	−10.8091	−0.397083
$742$	0	0
$743$	20.6550	0.757757	0.378878	−	0.925446i	$-0.376310\pi$
$743$	20.6550	0.757757	0.378878	+	0.925446i	$0.376310\pi$
$744$	−5.67664	−0.208116
$745$	−6.98348	−0.255855
$746$	43.1972	1.58156
$747$	−6.59231	−0.241200
$748$	0	0
$749$	0	0
$750$	−10.8353	−0.395649
$751$	26.5991	0.970614	0.485307	−	0.874344i	$-0.338708\pi$
$751$	26.5991	0.970614	0.485307	+	0.874344i	$0.338708\pi$
$752$	−27.3700	−0.998082
$753$	11.3182	0.412458
$754$	−6.31144	−0.229849
$755$	1.34061	0.0487897
$756$	0	0
$757$	21.0999	0.766890	0.383445	−	0.923564i	$-0.374738\pi$
$757$	21.0999	0.766890	0.383445	+	0.923564i	$0.374738\pi$
$758$	−37.1723	−1.35016
$759$	0	0
$760$	5.34311	0.193815
$761$	7.99743	0.289907	0.144953	−	0.989438i	$-0.453697\pi$
$761$	7.99743	0.289907	0.144953	+	0.989438i	$0.453697\pi$
$762$	20.2679	0.734227
$763$	0	0
$764$	−2.43428	−0.0880691
$765$	−0.931905	−0.0336931
$766$	−46.8360	−1.69225
$767$	13.6141	0.491576
$768$	5.84271	0.210831
$769$	52.0476	1.87689	0.938443	−	0.345435i	$-0.112269\pi$
$769$	52.0476	1.87689	0.938443	+	0.345435i	$0.112269\pi$
$770$	0	0
$771$	16.0969	0.579716
$772$	1.83794	0.0661488
$773$	1.58099	0.0568644	0.0284322	−	0.999596i	$-0.490949\pi$
$773$	1.58099	0.0568644	0.0284322	+	0.999596i	$0.490949\pi$
$774$	4.87870	0.175361
$775$	6.18745	0.222260
$776$	7.33098	0.263167
$777$	0	0
$778$	−26.0370	−0.933471
$779$	−4.39553	−0.157486
$780$	−0.180798	−0.00647361
$781$	0	0
$782$	−13.8395	−0.494899
$783$	−14.8813	−0.531815
$784$	0	0
$785$	−8.81298	−0.314549
$786$	−22.9421	−0.818319
$787$	−23.3907	−0.833789	−0.416894	−	0.908955i	$-0.636882\pi$
$787$	−23.3907	−0.833789	−0.416894	+	0.908955i	$0.636882\pi$
$788$	−0.348265	−0.0124064
$789$	22.9443	0.816838
$790$	2.45235	0.0872506
$791$	0	0
$792$	0	0
$793$	24.1147	0.856339
$794$	−19.5144	−0.692539
$795$	9.97183	0.353664
$796$	−3.06836	−0.108755
$797$	46.1518	1.63478	0.817391	−	0.576084i	$-0.195420\pi$
$797$	46.1518	1.63478	0.817391	+	0.576084i	$0.195420\pi$
$798$	0	0
$799$	−33.4303	−1.18268
$800$	−4.08445	−0.144407
$801$	−3.40707	−0.120383
$802$	5.11834	0.180735
$803$	0	0
$804$	−1.14470	−0.0403704
$805$	0	0
$806$	3.00283	0.105770
$807$	29.7768	1.04819
$808$	−0.484773	−0.0170542
$809$	33.7501	1.18659	0.593295	−	0.804985i	$-0.297827\pi$
$809$	33.7501	1.18659	0.593295	+	0.804985i	$0.297827\pi$
$810$	−5.27681	−0.185408
$811$	30.7650	1.08030	0.540152	−	0.841567i	$-0.318367\pi$
$811$	30.7650	1.08030	0.540152	+	0.841567i	$0.318367\pi$
$812$	0	0
$813$	−1.18212	−0.0414588
$814$	0	0
$815$	−5.41182	−0.189568
$816$	36.1978	1.26717
$817$	−36.7653	−1.28626
$818$	−43.4527	−1.51929
$819$	0	0
$820$	−0.0735215	−0.00256748
$821$	12.0784	0.421538	0.210769	−	0.977536i	$-0.432403\pi$
$821$	12.0784	0.421538	0.210769	+	0.977536i	$0.432403\pi$
$822$	33.2508	1.15975
$823$	−24.8187	−0.865124	−0.432562	−	0.901604i	$-0.642390\pi$
$823$	−24.8187	−0.865124	−0.432562	+	0.901604i	$0.642390\pi$
$824$	−45.7634	−1.59424
$825$	0	0
$826$	0	0
$827$	5.17330	0.179893	0.0899466	−	0.995947i	$-0.471330\pi$
$827$	5.17330	0.179893	0.0899466	+	0.995947i	$0.471330\pi$
$828$	0.104318	0.00362531
$829$	−31.5535	−1.09590	−0.547949	−	0.836511i	$-0.684591\pi$
$829$	−31.5535	−1.09590	−0.547949	+	0.836511i	$0.684591\pi$
$830$	11.8149	0.410102
$831$	24.3747	0.845549
$832$	11.5615	0.400822
$833$	0	0
$834$	22.7299	0.787072
$835$	2.95204	0.102160
$836$	0	0
$837$	7.08018	0.244727
$838$	−17.0804	−0.590034
$839$	5.83642	0.201496	0.100748	−	0.994912i	$-0.467876\pi$
$839$	5.83642	0.201496	0.100748	+	0.994912i	$0.467876\pi$
$840$	0	0
$841$	−21.6045	−0.744982
$842$	−29.1657	−1.00512
$843$	−17.3067	−0.596074
$844$	0.811781	0.0279427
$845$	4.89895	0.168529
$846$	3.58291	0.123183
$847$	0	0
$848$	56.5112	1.94060
$849$	−14.7385	−0.505825
$850$	−36.6652	−1.25761
$851$	3.50579	0.120177
$852$	2.38523	0.0817166
$853$	20.3462	0.696640	0.348320	−	0.937376i	$-0.386752\pi$
$853$	20.3462	0.696640	0.348320	+	0.937376i	$0.386752\pi$
$854$	0	0
$855$	−0.752666	−0.0257406
$856$	−41.9644	−1.43432
$857$	15.1087	0.516104	0.258052	−	0.966131i	$-0.416919\pi$
$857$	15.1087	0.516104	0.258052	+	0.966131i	$0.416919\pi$
$858$	0	0
$859$	33.9641	1.15884	0.579420	−	0.815029i	$-0.303279\pi$
$859$	33.9641	1.15884	0.579420	+	0.815029i	$0.303279\pi$
$860$	−0.614952	−0.0209697
$861$	0	0
$862$	−44.3633	−1.51102
$863$	−2.77734	−0.0945417	−0.0472709	−	0.998882i	$-0.515052\pi$
$863$	−2.77734	−0.0945417	−0.0472709	+	0.998882i	$0.515052\pi$
$864$	−4.67376	−0.159005
$865$	0.624983	0.0212501
$866$	−8.37092	−0.284456
$867$	16.7061	0.567368
$868$	0	0
$869$	0	0
$870$	3.01224	0.102125
$871$	−7.39864	−0.250693
$872$	29.9216	1.01327
$873$	−1.03269	−0.0349513
$874$	−11.1777	−0.378090
$875$	0	0
$876$	3.26090	0.110176
$877$	49.6783	1.67752	0.838759	−	0.544503i	$-0.183282\pi$
$877$	49.6783	1.67752	0.838759	+	0.544503i	$0.183282\pi$
$878$	10.0453	0.339012
$879$	−19.2368	−0.648841
$880$	0	0
$881$	27.3064	0.919975	0.459988	−	0.887925i	$-0.347854\pi$
$881$	27.3064	0.919975	0.459988	+	0.887925i	$0.347854\pi$
$882$	0	0
$883$	−17.8109	−0.599386	−0.299693	−	0.954036i	$-0.596884\pi$
$883$	−17.8109	−0.599386	−0.299693	+	0.954036i	$0.596884\pi$
$884$	−1.25146	−0.0420912
$885$	−6.49755	−0.218413
$886$	−0.147693	−0.00496184
$887$	16.4729	0.553105	0.276553	−	0.960999i	$-0.410808\pi$
$887$	16.4729	0.553105	0.276553	+	0.960999i	$0.410808\pi$
$888$	−8.52118	−0.285952
$889$	0	0
$890$	6.10625	0.204682
$891$	0	0
$892$	3.84656	0.128792
$893$	−27.0004	−0.903535
$894$	−35.5093	−1.18761
$895$	−8.30260	−0.277525
$896$	0	0
$897$	−4.62137	−0.154303
$898$	45.1823	1.50775
$899$	−3.51861	−0.117352
$900$	0.276372	0.00921240
$901$	69.0238	2.29952
$902$	0	0
$903$	0	0
$904$	4.79964	0.159634
$905$	−0.449825	−0.0149527
$906$	6.81668	0.226469
$907$	28.4877	0.945918	0.472959	−	0.881084i	$-0.343186\pi$
$907$	28.4877	0.945918	0.472959	+	0.881084i	$0.343186\pi$
$908$	3.28473	0.109008
$909$	0.0682883	0.00226498
$910$	0	0
$911$	−11.2353	−0.372242	−0.186121	−	0.982527i	$-0.559592\pi$
$911$	−11.2353	−0.372242	−0.186121	+	0.982527i	$0.559592\pi$
$912$	29.2356	0.968088
$913$	0	0
$914$	−33.9337	−1.12243
$915$	−11.5092	−0.380482
$916$	−3.10634	−0.102636
$917$	0	0
$918$	−41.9553	−1.38473
$919$	0.780457	0.0257449	0.0128724	−	0.999917i	$-0.495902\pi$
$919$	0.780457	0.0257449	0.0128724	+	0.999917i	$0.495902\pi$
$920$	2.28441	0.0753148
$921$	−3.59320	−0.118400
$922$	−4.07516	−0.134208
$923$	15.4167	0.507446
$924$	0	0
$925$	9.28795	0.305386
$926$	38.2744	1.25777
$927$	6.44653	0.211732
$928$	2.32270	0.0762465
$929$	−26.5963	−0.872597	−0.436298	−	0.899802i	$-0.643711\pi$
$929$	−26.5963	−0.872597	−0.436298	+	0.899802i	$0.643711\pi$
$930$	−1.43315	−0.0469950
$931$	0	0
$932$	0.105012	0.00343979
$933$	34.6463	1.13427
$934$	−3.89900	−0.127579
$935$	0	0
$936$	−1.63883	−0.0535669
$937$	−41.9697	−1.37109	−0.685544	−	0.728031i	$-0.740436\pi$
$937$	−41.9697	−1.37109	−0.685544	+	0.728031i	$0.740436\pi$
$938$	0	0
$939$	51.0567	1.66617
$940$	−0.451620	−0.0147302
$941$	49.0330	1.59843	0.799215	−	0.601046i	$-0.205249\pi$
$941$	49.0330	1.59843	0.799215	+	0.601046i	$0.205249\pi$
$942$	−44.8119	−1.46005
$943$	−1.87928	−0.0611978
$944$	−36.8222	−1.19846
$945$	0	0
$946$	0	0
$947$	−27.2953	−0.886978	−0.443489	−	0.896280i	$-0.646259\pi$
$947$	−27.2953	−0.886978	−0.443489	+	0.896280i	$0.646259\pi$
$948$	0.876994	0.0284835
$949$	21.0765	0.684171
$950$	−29.6132	−0.960778
$951$	−21.3591	−0.692617
$952$	0	0
$953$	19.7408	0.639466	0.319733	−	0.947508i	$-0.396407\pi$
$953$	19.7408	0.639466	0.319733	+	0.947508i	$0.396407\pi$
$954$	−7.39767	−0.239509
$955$	7.50918	0.242991
$956$	0.0524354	0.00169588
$957$	0	0
$958$	−12.1478	−0.392478
$959$	0	0
$960$	−5.51792	−0.178090
$961$	−29.3259	−0.945998
$962$	4.50754	0.145329
$963$	5.91139	0.190492
$964$	1.57917	0.0508615
$965$	−5.66960	−0.182511
$966$	0	0
$967$	−12.6734	−0.407551	−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734	−0.407551	−0.203775	+	0.979018i	$0.565321\pi$
$968$	0	0
$969$	35.7089	1.14714
$970$	1.85082	0.0594261
$971$	−16.7036	−0.536045	−0.268022	−	0.963413i	$-0.586370\pi$
$971$	−16.7036	−0.536045	−0.268022	+	0.963413i	$0.586370\pi$
$972$	0.596777	0.0191416
$973$	0	0
$974$	28.7414	0.920935
$975$	−12.2435	−0.392105
$976$	−65.2234	−2.08775
$977$	27.3452	0.874851	0.437425	−	0.899255i	$-0.355890\pi$
$977$	27.3452	0.874851	0.437425	+	0.899255i	$0.355890\pi$
$978$	−27.5178	−0.879924
$979$	0	0
$980$	0	0
$981$	−4.21496	−0.134573
$982$	42.0683	1.34245
$983$	55.0065	1.75443	0.877217	−	0.480093i	$-0.159397\pi$
$983$	55.0065	1.75443	0.877217	+	0.480093i	$0.159397\pi$
$984$	4.56779	0.145616
$985$	1.07432	0.0342306
$986$	20.8504	0.664012
$987$	0	0
$988$	−1.01076	−0.0321566
$989$	−15.7188	−0.499828
$990$	0	0
$991$	53.2327	1.69099	0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327	1.69099	0.845497	+	0.533980i	$0.179304\pi$
$992$	−1.10509	−0.0350866
$993$	15.3333	0.486589
$994$	0	0
$995$	9.46519	0.300067
$996$	4.22518	0.133880
$997$	−32.7546	−1.03735	−0.518674	−	0.854972i	$-0.673574\pi$
$997$	−32.7546	−1.03735	−0.518674	+	0.854972i	$0.673574\pi$
$998$	−40.9950	−1.29767
$999$	10.6280	0.336256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bi.1.1		4
7.6	odd	2		847.2.a.l.1.1		4
11.5	even	5		539.2.f.d.344.2		8
11.9	even	5		539.2.f.d.246.2		8
11.10	odd	2		5929.2.a.bb.1.4		4
21.20	even	2		7623.2.a.ch.1.4		4
77.5	odd	30		539.2.q.c.410.1		16
77.6	even	10		847.2.f.q.729.1		8
77.9	even	15		539.2.q.b.312.2		16
77.13	even	10		847.2.f.q.323.1		8
77.16	even	15		539.2.q.b.410.1		16
77.20	odd	10		77.2.f.a.15.2	✓	8
77.27	odd	10		77.2.f.a.36.2	yes	8
77.31	odd	30		539.2.q.c.422.1		16
77.38	odd	30		539.2.q.c.520.2		16
77.41	even	10		847.2.f.s.372.2		8
77.48	odd	10		847.2.f.p.148.1		8
77.53	even	15		539.2.q.b.422.1		16
77.60	even	15		539.2.q.b.520.2		16
77.62	even	10		847.2.f.s.148.2		8
77.69	odd	10		847.2.f.p.372.1		8
77.75	odd	30		539.2.q.c.312.2		16
77.76	even	2		847.2.a.k.1.4		4
231.20	even	10		693.2.m.g.631.1		8
231.104	even	10		693.2.m.g.190.1		8
231.230	odd	2		7623.2.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	77.20	odd	10
77.2.f.a.36.2	yes	8	77.27	odd	10
539.2.f.d.246.2		8	11.9	even	5
539.2.f.d.344.2		8	11.5	even	5
539.2.q.b.312.2		16	77.9	even	15
539.2.q.b.410.1		16	77.16	even	15
539.2.q.b.422.1		16	77.53	even	15
539.2.q.b.520.2		16	77.60	even	15
539.2.q.c.312.2		16	77.75	odd	30
539.2.q.c.410.1		16	77.5	odd	30
539.2.q.c.422.1		16	77.31	odd	30
539.2.q.c.520.2		16	77.38	odd	30
693.2.m.g.190.1		8	231.104	even	10
693.2.m.g.631.1		8	231.20	even	10
847.2.a.k.1.4		4	77.76	even	2
847.2.a.l.1.1		4	7.6	odd	2
847.2.f.p.148.1		8	77.48	odd	10
847.2.f.p.372.1		8	77.69	odd	10
847.2.f.q.323.1		8	77.13	even	10
847.2.f.q.729.1		8	77.6	even	10
847.2.f.s.148.2		8	77.62	even	10
847.2.f.s.372.2		8	77.41	even	10
5929.2.a.bb.1.4		4	11.10	odd	2
5929.2.a.bi.1.1		4	1.1	even	1	trivial
7623.2.a.ch.1.4		4	21.20	even	2
7623.2.a.co.1.1		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)

\(f(q)\)	\(=\)	\(q-1.46673 q^{2} +1.61803 q^{3} +0.151302 q^{4} -0.466732 q^{5} -2.37322 q^{6} +2.71154 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-1.46673 q^{2} +1.61803 q^{3} +0.151302 q^{4} -0.466732 q^{5} -2.37322 q^{6} +2.71154 q^{8} -0.381966 q^{9} +0.684570 q^{10} +0.244812 q^{12} +1.58232 q^{13} -0.755188 q^{15} -4.27971 q^{16} -5.22732 q^{17} +0.560242 q^{18} -4.22192 q^{19} -0.0706175 q^{20} -1.80505 q^{23} +4.38737 q^{24} -4.78216 q^{25} -2.32083 q^{26} -5.47214 q^{27} +2.71947 q^{29} +1.10766 q^{30} -1.29386 q^{31} +0.854102 q^{32} +7.66708 q^{34} -0.0577923 q^{36} -1.94221 q^{37} +6.19242 q^{38} +2.56024 q^{39} -1.26556 q^{40} +1.04112 q^{41} +8.70820 q^{43} +0.178276 q^{45} +2.64753 q^{46} +6.39530 q^{47} -6.92472 q^{48} +7.01415 q^{50} -8.45799 q^{51} +0.239408 q^{52} -13.2044 q^{53} +8.02616 q^{54} -6.83121 q^{57} -3.98873 q^{58} +8.60389 q^{59} -0.114262 q^{60} +15.2401 q^{61} +1.89775 q^{62} +7.30669 q^{64} -0.738517 q^{65} -4.67583 q^{67} -0.790906 q^{68} -2.92064 q^{69} +9.74310 q^{71} -1.03572 q^{72} +13.3200 q^{73} +2.84870 q^{74} -7.73770 q^{75} -0.638786 q^{76} -3.75519 q^{78} +3.58232 q^{79} +1.99748 q^{80} -7.70820 q^{81} -1.52705 q^{82} +17.2589 q^{83} +2.43976 q^{85} -12.7726 q^{86} +4.40020 q^{87} +8.91982 q^{89} -0.261483 q^{90} -0.273109 q^{92} -2.09351 q^{93} -9.38018 q^{94} +1.97050 q^{95} +1.38197 q^{96} +2.70362 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} + q^{6} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 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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