LMFDB - Embedded newform 931.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 $ x^7 - 3x^6 - 6x^5 + 18x^4 + 4x^3 - 12*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.770405$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46342 q^{2} +3.03216 q^{3} +4.06842 q^{4} +0.527614 q^{5} -7.46948 q^{6} -5.09539 q^{8} +6.19401 q^{9} +O(q^{10})$	\(q-2.46342 q^{2} +3.03216 q^{3} +4.06842 q^{4} +0.527614 q^{5} -7.46948 q^{6} -5.09539 q^{8} +6.19401 q^{9} -1.29973 q^{10} +5.19585 q^{11} +12.3361 q^{12} -0.508647 q^{13} +1.59981 q^{15} +4.41522 q^{16} -2.47239 q^{17} -15.2584 q^{18} -1.00000 q^{19} +2.14656 q^{20} -12.7995 q^{22} +2.60130 q^{23} -15.4501 q^{24} -4.72162 q^{25} +1.25301 q^{26} +9.68476 q^{27} +7.14062 q^{29} -3.94100 q^{30} +8.03152 q^{31} -0.685756 q^{32} +15.7547 q^{33} +6.09052 q^{34} +25.1999 q^{36} -4.76105 q^{37} +2.46342 q^{38} -1.54230 q^{39} -2.68840 q^{40} -4.92683 q^{41} -8.66759 q^{43} +21.1389 q^{44} +3.26804 q^{45} -6.40809 q^{46} +1.54607 q^{47} +13.3877 q^{48} +11.6313 q^{50} -7.49668 q^{51} -2.06939 q^{52} +0.0990139 q^{53} -23.8576 q^{54} +2.74140 q^{55} -3.03216 q^{57} -17.5903 q^{58} +5.64927 q^{59} +6.50871 q^{60} -7.39363 q^{61} -19.7850 q^{62} -7.14114 q^{64} -0.268369 q^{65} -38.8103 q^{66} +10.2020 q^{67} -10.0587 q^{68} +7.88757 q^{69} -0.577091 q^{71} -31.5609 q^{72} -14.9988 q^{73} +11.7285 q^{74} -14.3167 q^{75} -4.06842 q^{76} +3.79933 q^{78} +4.97997 q^{79} +2.32953 q^{80} +10.7837 q^{81} +12.1368 q^{82} -0.753447 q^{83} -1.30446 q^{85} +21.3519 q^{86} +21.6515 q^{87} -26.4749 q^{88} +2.73099 q^{89} -8.05056 q^{90} +10.5832 q^{92} +24.3529 q^{93} -3.80863 q^{94} -0.527614 q^{95} -2.07933 q^{96} +0.0779461 q^{97} +32.1831 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	$ 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.46342	−1.74190	−0.870949	−	0.491373i	$-0.836495\pi$
$2$	−2.46342	−1.74190	−0.870949	+	0.491373i	$0.836495\pi$
$3$	3.03216	1.75062	0.875310	−	0.483562i	$-0.160657\pi$
$3$	3.03216	1.75062	0.875310	+	0.483562i	$0.160657\pi$
$4$	4.06842	2.03421
$5$	0.527614	0.235956	0.117978	−	0.993016i	$-0.462359\pi$
$5$	0.527614	0.235956	0.117978	+	0.993016i	$0.462359\pi$
$6$	−7.46948	−3.04940
$7$	0	0
$7$	0	0
$8$	−5.09539	−1.80149
$9$	6.19401	2.06467
$10$	−1.29973	−0.411011
$11$	5.19585	1.56661	0.783303	−	0.621640i	$-0.213533\pi$
$11$	5.19585	1.56661	0.783303	+	0.621640i	$0.213533\pi$
$12$	12.3361	3.56113
$13$	−0.508647	−0.141073	−0.0705367	−	0.997509i	$-0.522471\pi$
$13$	−0.508647	−0.141073	−0.0705367	+	0.997509i	$0.522471\pi$
$14$	0	0
$15$	1.59981	0.413069
$16$	4.41522	1.10381
$17$	−2.47239	−0.599642	−0.299821	−	0.953996i	$-0.596927\pi$
$17$	−2.47239	−0.599642	−0.299821	+	0.953996i	$0.596927\pi$
$18$	−15.2584	−3.59645
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.14656	0.479984
$21$	0	0
$22$	−12.7995	−2.72887
$23$	2.60130	0.542409	0.271204	−	0.962522i	$-0.412578\pi$
$23$	2.60130	0.542409	0.271204	+	0.962522i	$0.412578\pi$
$24$	−15.4501	−3.15373
$25$	−4.72162	−0.944325
$26$	1.25301	0.245736
$27$	9.68476	1.86383
$28$	0	0
$29$	7.14062	1.32598	0.662990	−	0.748628i	$-0.269287\pi$
$29$	7.14062	1.32598	0.662990	+	0.748628i	$0.269287\pi$
$30$	−3.94100	−0.719525
$31$	8.03152	1.44250	0.721252	−	0.692673i	$-0.243567\pi$
$31$	8.03152	1.44250	0.721252	+	0.692673i	$0.243567\pi$
$32$	−0.685756	−0.121226
$33$	15.7547	2.74253
$34$	6.09052	1.04452
$35$	0	0
$36$	25.1999	4.19998
$37$	−4.76105	−0.782712	−0.391356	−	0.920239i	$-0.627994\pi$
$37$	−4.76105	−0.782712	−0.391356	+	0.920239i	$0.627994\pi$
$38$	2.46342	0.399619
$39$	−1.54230	−0.246966
$40$	−2.68840	−0.425073
$41$	−4.92683	−0.769442	−0.384721	−	0.923033i	$-0.625702\pi$
$41$	−4.92683	−0.769442	−0.384721	+	0.923033i	$0.625702\pi$
$42$	0	0
$43$	−8.66759	−1.32180	−0.660898	−	0.750476i	$-0.729824\pi$
$43$	−8.66759	−1.32180	−0.660898	+	0.750476i	$0.729824\pi$
$44$	21.1389	3.18681
$45$	3.26804	0.487171
$46$	−6.40809	−0.944821
$47$	1.54607	0.225518	0.112759	−	0.993622i	$-0.464031\pi$
$47$	1.54607	0.225518	0.112759	+	0.993622i	$0.464031\pi$
$48$	13.3877	1.93234
$49$	0	0
$50$	11.6313	1.64492
$51$	−7.49668	−1.04974
$52$	−2.06939	−0.286973
$53$	0.0990139	0.0136006	0.00680030	−	0.999977i	$-0.497835\pi$
$53$	0.0990139	0.0136006	0.00680030	+	0.999977i	$0.497835\pi$
$54$	−23.8576	−3.24661
$55$	2.74140	0.369650
$56$	0	0
$57$	−3.03216	−0.401620
$58$	−17.5903	−2.30972
$59$	5.64927	0.735472	0.367736	−	0.929930i	$-0.380133\pi$
$59$	5.64927	0.735472	0.367736	+	0.929930i	$0.380133\pi$
$60$	6.50871	0.840270
$61$	−7.39363	−0.946657	−0.473329	−	0.880886i	$-0.656948\pi$
$61$	−7.39363	−0.946657	−0.473329	+	0.880886i	$0.656948\pi$
$62$	−19.7850	−2.51269
$63$	0	0
$64$	−7.14114	−0.892643
$65$	−0.268369	−0.0332871
$66$	−38.8103	−4.77722
$67$	10.2020	1.24637	0.623184	−	0.782075i	$-0.285839\pi$
$67$	10.2020	1.24637	0.623184	+	0.782075i	$0.285839\pi$
$68$	−10.0587	−1.21980
$69$	7.88757	0.949552
$70$	0	0
$71$	−0.577091	−0.0684881	−0.0342441	−	0.999413i	$-0.510902\pi$
$71$	−0.577091	−0.0684881	−0.0342441	+	0.999413i	$0.510902\pi$
$72$	−31.5609	−3.71949
$73$	−14.9988	−1.75547	−0.877736	−	0.479144i	$-0.840947\pi$
$73$	−14.9988	−1.75547	−0.877736	+	0.479144i	$0.840947\pi$
$74$	11.7285	1.36341
$75$	−14.3167	−1.65315
$76$	−4.06842	−0.466680
$77$	0	0
$78$	3.79933	0.430190
$79$	4.97997	0.560290	0.280145	−	0.959958i	$-0.409617\pi$
$79$	4.97997	0.560290	0.280145	+	0.959958i	$0.409617\pi$
$80$	2.32953	0.260450
$81$	10.7837	1.19819
$82$	12.1368	1.34029
$83$	−0.753447	−0.0827016	−0.0413508	−	0.999145i	$-0.513166\pi$
$83$	−0.753447	−0.0827016	−0.0413508	+	0.999145i	$0.513166\pi$
$84$	0	0
$85$	−1.30446	−0.141489
$86$	21.3519	2.30243
$87$	21.6515	2.32129
$88$	−26.4749	−2.82223
$89$	2.73099	0.289484	0.144742	−	0.989469i	$-0.453765\pi$
$89$	2.73099	0.289484	0.144742	+	0.989469i	$0.453765\pi$
$90$	−8.05056	−0.848603
$91$	0	0
$92$	10.5832	1.10337
$93$	24.3529	2.52528
$94$	−3.80863	−0.392830
$95$	−0.527614	−0.0541320
$96$	−2.07933	−0.212220
$97$	0.0779461	0.00791423	0.00395711	−	0.999992i	$-0.498740\pi$
$97$	0.0779461	0.00791423	0.00395711	+	0.999992i	$0.498740\pi$
$98$	0	0
$99$	32.1831	3.23453
$100$	−19.2096	−1.92096
$101$	−2.38524	−0.237340	−0.118670	−	0.992934i	$-0.537863\pi$
$101$	−2.38524	−0.237340	−0.118670	+	0.992934i	$0.537863\pi$
$102$	18.4674	1.82855
$103$	−7.83303	−0.771811	−0.385906	−	0.922538i	$-0.626111\pi$
$103$	−7.83303	−0.771811	−0.385906	+	0.922538i	$0.626111\pi$
$104$	2.59176	0.254143
$105$	0	0
$106$	−0.243912	−0.0236909
$107$	−1.53768	−0.148653	−0.0743266	−	0.997234i	$-0.523681\pi$
$107$	−1.53768	−0.148653	−0.0743266	+	0.997234i	$0.523681\pi$
$108$	39.4017	3.79143
$109$	10.1265	0.969938	0.484969	−	0.874531i	$-0.338831\pi$
$109$	10.1265	0.969938	0.484969	+	0.874531i	$0.338831\pi$
$110$	−6.75321	−0.643893
$111$	−14.4363	−1.37023
$112$	0	0
$113$	0.843882	0.0793858	0.0396929	−	0.999212i	$-0.487362\pi$
$113$	0.843882	0.0793858	0.0396929	+	0.999212i	$0.487362\pi$
$114$	7.46948	0.699581
$115$	1.37248	0.127985
$116$	29.0511	2.69732
$117$	−3.15057	−0.291270
$118$	−13.9165	−1.28112
$119$	0	0
$120$	−8.15166	−0.744141
$121$	15.9968	1.45426
$122$	18.2136	1.64898
$123$	−14.9390	−1.34700
$124$	32.6756	2.93436
$125$	−5.12926	−0.458775
$126$	0	0
$127$	2.86441	0.254175	0.127087	−	0.991892i	$-0.459437\pi$
$127$	2.86441	0.254175	0.127087	+	0.991892i	$0.459437\pi$
$128$	18.9631	1.67612
$129$	−26.2815	−2.31396
$130$	0.661105	0.0579828
$131$	10.8647	0.949256	0.474628	−	0.880187i	$-0.342583\pi$
$131$	10.8647	0.949256	0.474628	+	0.880187i	$0.342583\pi$
$132$	64.0966	5.57889
$133$	0	0
$134$	−25.1317	−2.17105
$135$	5.10981	0.439782
$136$	12.5978	1.08025
$137$	0.129685	0.0110797	0.00553987	−	0.999985i	$-0.498237\pi$
$137$	0.129685	0.0110797	0.00553987	+	0.999985i	$0.498237\pi$
$138$	−19.4304	−1.65402
$139$	−10.7990	−0.915963	−0.457982	−	0.888962i	$-0.651427\pi$
$139$	−10.7990	−0.915963	−0.457982	+	0.888962i	$0.651427\pi$
$140$	0	0
$141$	4.68795	0.394797
$142$	1.42162	0.119299
$143$	−2.64285	−0.221007
$144$	27.3479	2.27899
$145$	3.76749	0.312873
$146$	36.9482	3.05786
$147$	0	0
$148$	−19.3700	−1.59220
$149$	1.52116	0.124618	0.0623090	−	0.998057i	$-0.480154\pi$
$149$	1.52116	0.124618	0.0623090	+	0.998057i	$0.480154\pi$
$150$	35.2681	2.87963
$151$	−12.3864	−1.00799	−0.503994	−	0.863707i	$-0.668137\pi$
$151$	−12.3864	−1.00799	−0.503994	+	0.863707i	$0.668137\pi$
$152$	5.09539	0.413291
$153$	−15.3140	−1.23806
$154$	0	0
$155$	4.23754	0.340367
$156$	−6.27474	−0.502381
$157$	16.6065	1.32534	0.662670	−	0.748911i	$-0.269423\pi$
$157$	16.6065	1.32534	0.662670	+	0.748911i	$0.269423\pi$
$158$	−12.2677	−0.975968
$159$	0.300226	0.0238095
$160$	−0.361814	−0.0286039
$161$	0	0
$162$	−26.5648	−2.08713
$163$	−4.64033	−0.363459	−0.181729	−	0.983349i	$-0.558169\pi$
$163$	−4.64033	−0.363459	−0.181729	+	0.983349i	$0.558169\pi$
$164$	−20.0444	−1.56521
$165$	8.31237	0.647117
$166$	1.85605	0.144058
$167$	18.3883	1.42293	0.711463	−	0.702723i	$-0.248033\pi$
$167$	18.3883	1.42293	0.711463	+	0.702723i	$0.248033\pi$
$168$	0	0
$169$	−12.7413	−0.980098
$170$	3.21344	0.246460
$171$	−6.19401	−0.473668
$172$	−35.2634	−2.68881
$173$	−15.5058	−1.17889	−0.589443	−	0.807810i	$-0.700653\pi$
$173$	−15.5058	−1.17889	−0.589443	+	0.807810i	$0.700653\pi$
$174$	−53.3367	−4.04345
$175$	0	0
$176$	22.9408	1.72923
$177$	17.1295	1.28753
$178$	−6.72756	−0.504252
$179$	−1.55881	−0.116511	−0.0582554	−	0.998302i	$-0.518554\pi$
$179$	−1.55881	−0.116511	−0.0582554	+	0.998302i	$0.518554\pi$
$180$	13.2958	0.991009
$181$	−6.26096	−0.465373	−0.232687	−	0.972552i	$-0.574752\pi$
$181$	−6.26096	−0.465373	−0.232687	+	0.972552i	$0.574752\pi$
$182$	0	0
$183$	−22.4187	−1.65724
$184$	−13.2546	−0.977146
$185$	−2.51200	−0.184686
$186$	−59.9913	−4.39877
$187$	−12.8461	−0.939403
$188$	6.29009	0.458752
$189$	0	0
$190$	1.29973	0.0942925
$191$	6.19627	0.448346	0.224173	−	0.974549i	$-0.428032\pi$
$191$	6.19627	0.448346	0.224173	+	0.974549i	$0.428032\pi$
$192$	−21.6531	−1.56268
$193$	17.9485	1.29196	0.645980	−	0.763354i	$-0.276449\pi$
$193$	17.9485	1.29196	0.645980	+	0.763354i	$0.276449\pi$
$194$	−0.192014	−0.0137858
$195$	−0.813739	−0.0582731
$196$	0	0
$197$	21.1561	1.50731	0.753654	−	0.657271i	$-0.228289\pi$
$197$	21.1561	1.50731	0.753654	+	0.657271i	$0.228289\pi$
$198$	−79.2805	−5.63422
$199$	22.3762	1.58621	0.793104	−	0.609086i	$-0.208464\pi$
$199$	22.3762	1.58621	0.793104	+	0.609086i	$0.208464\pi$
$200$	24.0585	1.70119
$201$	30.9340	2.18192
$202$	5.87583	0.413422
$203$	0	0
$204$	−30.4997	−2.13540
$205$	−2.59946	−0.181554
$206$	19.2960	1.34442
$207$	16.1125	1.11990
$208$	−2.24579	−0.155718
$209$	−5.19585	−0.359404
$210$	0	0
$211$	−4.06788	−0.280045	−0.140022	−	0.990148i	$-0.544717\pi$
$211$	−4.06788	−0.280045	−0.140022	+	0.990148i	$0.544717\pi$
$212$	0.402830	0.0276665
$213$	−1.74983	−0.119897
$214$	3.78795	0.258939
$215$	−4.57314	−0.311885
$216$	−49.3476	−3.35768
$217$	0	0
$218$	−24.9457	−1.68953
$219$	−45.4787	−3.07317
$220$	11.1532	0.751947
$221$	1.25757	0.0845935
$222$	35.5626	2.38681
$223$	1.88378	0.126147	0.0630735	−	0.998009i	$-0.479910\pi$
$223$	1.88378	0.126147	0.0630735	+	0.998009i	$0.479910\pi$
$224$	0	0
$225$	−29.2458	−1.94972
$226$	−2.07883	−0.138282
$227$	−8.63342	−0.573021	−0.286510	−	0.958077i	$-0.592495\pi$
$227$	−8.63342	−0.573021	−0.286510	+	0.958077i	$0.592495\pi$
$228$	−12.3361	−0.816980
$229$	−21.0382	−1.39024	−0.695121	−	0.718893i	$-0.744649\pi$
$229$	−21.0382	−1.39024	−0.695121	+	0.718893i	$0.744649\pi$
$230$	−3.38100	−0.222936
$231$	0	0
$232$	−36.3842	−2.38874
$233$	−28.8002	−1.88676	−0.943382	−	0.331707i	$-0.892375\pi$
$233$	−28.8002	−1.88676	−0.943382	+	0.331707i	$0.892375\pi$
$234$	7.76116	0.507363
$235$	0.815730	0.0532124
$236$	22.9836	1.49611
$237$	15.1001	0.980855
$238$	0	0
$239$	2.63542	0.170471	0.0852357	−	0.996361i	$-0.472836\pi$
$239$	2.63542	0.170471	0.0852357	+	0.996361i	$0.472836\pi$
$240$	7.06352	0.455948
$241$	−3.01442	−0.194176	−0.0970880	−	0.995276i	$-0.530953\pi$
$241$	−3.01442	−0.194176	−0.0970880	+	0.995276i	$0.530953\pi$
$242$	−39.4069	−2.53317
$243$	3.64376	0.233747
$244$	−30.0804	−1.92570
$245$	0	0
$246$	36.8009	2.34634
$247$	0.508647	0.0323645
$248$	−40.9237	−2.59866
$249$	−2.28457	−0.144779
$250$	12.6355	0.799140
$251$	−16.7424	−1.05677	−0.528387	−	0.849004i	$-0.677203\pi$
$251$	−16.7424	−1.05677	−0.528387	+	0.849004i	$0.677203\pi$
$252$	0	0
$253$	13.5160	0.849742
$254$	−7.05623	−0.442747
$255$	−3.95535	−0.247694
$256$	−32.4318	−2.02699
$257$	−25.9514	−1.61880	−0.809402	−	0.587255i	$-0.800209\pi$
$257$	−25.9514	−1.61880	−0.809402	+	0.587255i	$0.800209\pi$
$258$	64.7424	4.03069
$259$	0	0
$260$	−1.09184	−0.0677130
$261$	44.2291	2.73771
$262$	−26.7644	−1.65351
$263$	16.5601	1.02114	0.510571	−	0.859836i	$-0.329434\pi$
$263$	16.5601	1.02114	0.510571	+	0.859836i	$0.329434\pi$
$264$	−80.2761	−4.94065
$265$	0.0522411	0.00320914
$266$	0	0
$267$	8.28080	0.506776
$268$	41.5059	2.53538
$269$	−30.6880	−1.87108	−0.935542	−	0.353217i	$-0.885088\pi$
$269$	−30.6880	−1.87108	−0.935542	+	0.353217i	$0.885088\pi$
$270$	−12.5876	−0.766057
$271$	−0.997658	−0.0606034	−0.0303017	−	0.999541i	$-0.509647\pi$
$271$	−0.997658	−0.0606034	−0.0303017	+	0.999541i	$0.509647\pi$
$272$	−10.9161	−0.661888
$273$	0	0
$274$	−0.319468	−0.0192998
$275$	−24.5328	−1.47939
$276$	32.0900	1.93159
$277$	4.92326	0.295810	0.147905	−	0.989002i	$-0.452747\pi$
$277$	4.92326	0.295810	0.147905	+	0.989002i	$0.452747\pi$
$278$	26.6026	1.59552
$279$	49.7473	2.97829
$280$	0	0
$281$	10.7113	0.638982	0.319491	−	0.947589i	$-0.396488\pi$
$281$	10.7113	0.638982	0.319491	+	0.947589i	$0.396488\pi$
$282$	−11.5484	−0.687696
$283$	−13.8018	−0.820431	−0.410216	−	0.911989i	$-0.634547\pi$
$283$	−13.8018	−0.820431	−0.410216	+	0.911989i	$0.634547\pi$
$284$	−2.34785	−0.139319
$285$	−1.59981	−0.0947646
$286$	6.51045	0.384971
$287$	0	0
$288$	−4.24758	−0.250291
$289$	−10.8873	−0.640430
$290$	−9.28089	−0.544993
$291$	0.236345	0.0138548
$292$	−61.0213	−3.57100
$293$	−28.5818	−1.66977	−0.834883	−	0.550428i	$-0.814465\pi$
$293$	−28.5818	−1.66977	−0.834883	+	0.550428i	$0.814465\pi$
$294$	0	0
$295$	2.98063	0.173539
$296$	24.2594	1.41005
$297$	50.3205	2.91989
$298$	−3.74724	−0.217072
$299$	−1.32315	−0.0765195
$300$	−58.2465	−3.36286
$301$	0	0
$302$	30.5128	1.75581
$303$	−7.23243	−0.415492
$304$	−4.41522	−0.253230
$305$	−3.90098	−0.223369
$306$	37.7247	2.15658
$307$	14.7160	0.839885	0.419942	−	0.907551i	$-0.362050\pi$
$307$	14.7160	0.839885	0.419942	+	0.907551i	$0.362050\pi$
$308$	0	0
$309$	−23.7510	−1.35115
$310$	−10.4388	−0.592885
$311$	−14.3748	−0.815121	−0.407561	−	0.913178i	$-0.633621\pi$
$311$	−14.3748	−0.815121	−0.407561	+	0.913178i	$0.633621\pi$
$312$	7.85863	0.444907
$313$	−25.1416	−1.42109	−0.710543	−	0.703654i	$-0.751550\pi$
$313$	−25.1416	−1.42109	−0.710543	+	0.703654i	$0.751550\pi$
$314$	−40.9087	−2.30861
$315$	0	0
$316$	20.2606	1.13975
$317$	11.4920	0.645457	0.322729	−	0.946491i	$-0.395400\pi$
$317$	11.4920	0.645457	0.322729	+	0.946491i	$0.395400\pi$
$318$	−0.739582	−0.0414737
$319$	37.1016	2.07729
$320$	−3.76776	−0.210624
$321$	−4.66250	−0.260235
$322$	0	0
$323$	2.47239	0.137567
$324$	43.8728	2.43738
$325$	2.40164	0.133219
$326$	11.4311	0.633108
$327$	30.7051	1.69799
$328$	25.1041	1.38614
$329$	0	0
$330$	−20.4768	−1.12721
$331$	−1.77094	−0.0973398	−0.0486699	−	0.998815i	$-0.515498\pi$
$331$	−1.77094	−0.0973398	−0.0486699	+	0.998815i	$0.515498\pi$
$332$	−3.06534	−0.168232
$333$	−29.4900	−1.61604
$334$	−45.2980	−2.47859
$335$	5.38269	0.294088
$336$	0	0
$337$	−29.8644	−1.62682	−0.813409	−	0.581692i	$-0.802391\pi$
$337$	−29.8644	−1.62682	−0.813409	+	0.581692i	$0.802391\pi$
$338$	31.3871	1.70723
$339$	2.55879	0.138974
$340$	−5.30711	−0.287819
$341$	41.7305	2.25984
$342$	15.2584	0.825081
$343$	0	0
$344$	44.1647	2.38120
$345$	4.16159	0.224052
$346$	38.1973	2.05350
$347$	−9.27053	−0.497668	−0.248834	−	0.968546i	$-0.580047\pi$
$347$	−9.27053	−0.497668	−0.248834	+	0.968546i	$0.580047\pi$
$348$	88.0876	4.72199
$349$	−16.2809	−0.871499	−0.435749	−	0.900068i	$-0.643517\pi$
$349$	−16.2809	−0.871499	−0.435749	+	0.900068i	$0.643517\pi$
$350$	0	0
$351$	−4.92613	−0.262937
$352$	−3.56309	−0.189913
$353$	15.4338	0.821459	0.410729	−	0.911757i	$-0.365274\pi$
$353$	15.4338	0.821459	0.410729	+	0.911757i	$0.365274\pi$
$354$	−42.1971	−2.24275
$355$	−0.304481	−0.0161602
$356$	11.1108	0.588872
$357$	0	0
$358$	3.83999	0.202950
$359$	−9.38974	−0.495571	−0.247786	−	0.968815i	$-0.579703\pi$
$359$	−9.38974	−0.495571	−0.247786	+	0.968815i	$0.579703\pi$
$360$	−16.6520	−0.877635
$361$	1.00000	0.0526316
$362$	15.4234	0.810634
$363$	48.5050	2.54585
$364$	0	0
$365$	−7.91355	−0.414214
$366$	55.2266	2.88674
$367$	0.152199	0.00794475	0.00397237	−	0.999992i	$-0.498736\pi$
$367$	0.152199	0.00794475	0.00397237	+	0.999992i	$0.498736\pi$
$368$	11.4853	0.598714
$369$	−30.5169	−1.58864
$370$	6.18810	0.321704
$371$	0	0
$372$	99.0778	5.13694
$373$	−27.0481	−1.40050	−0.700249	−	0.713898i	$-0.746928\pi$
$373$	−27.0481	−1.40050	−0.700249	+	0.713898i	$0.746928\pi$
$374$	31.6454	1.63635
$375$	−15.5528	−0.803141
$376$	−7.87785	−0.406269
$377$	−3.63206	−0.187060
$378$	0	0
$379$	22.1680	1.13869	0.569347	−	0.822097i	$-0.307196\pi$
$379$	22.1680	1.13869	0.569347	+	0.822097i	$0.307196\pi$
$380$	−2.14656	−0.110116
$381$	8.68535	0.444964
$382$	−15.2640	−0.780974
$383$	−8.17968	−0.417962	−0.208981	−	0.977920i	$-0.567015\pi$
$383$	−8.17968	−0.417962	−0.208981	+	0.977920i	$0.567015\pi$
$384$	57.4993	2.93425
$385$	0	0
$386$	−44.2146	−2.25046
$387$	−53.6871	−2.72907
$388$	0.317118	0.0160992
$389$	35.2542	1.78746	0.893730	−	0.448605i	$-0.148079\pi$
$389$	35.2542	1.78746	0.893730	+	0.448605i	$0.148079\pi$
$390$	2.00458	0.101506
$391$	−6.43142	−0.325251
$392$	0	0
$393$	32.9436	1.66179
$394$	−52.1162	−2.62558
$395$	2.62750	0.132204
$396$	130.935	6.57971
$397$	−21.3720	−1.07263	−0.536316	−	0.844017i	$-0.680184\pi$
$397$	−21.3720	−1.07263	−0.536316	+	0.844017i	$0.680184\pi$
$398$	−55.1219	−2.76301
$399$	0	0
$400$	−20.8470	−1.04235
$401$	−11.8079	−0.589659	−0.294829	−	0.955550i	$-0.595263\pi$
$401$	−11.8079	−0.589659	−0.294829	+	0.955550i	$0.595263\pi$
$402$	−76.2033	−3.80068
$403$	−4.08521	−0.203499
$404$	−9.70416	−0.482800
$405$	5.68964	0.282721
$406$	0	0
$407$	−24.7377	−1.22620
$408$	38.1985	1.89111
$409$	24.0017	1.18681	0.593404	−	0.804905i	$-0.297784\pi$
$409$	24.0017	1.18681	0.593404	+	0.804905i	$0.297784\pi$
$410$	6.40357	0.316250
$411$	0.393226	0.0193964
$412$	−31.8681	−1.57003
$413$	0	0
$414$	−39.6918	−1.95074
$415$	−0.397529	−0.0195139
$416$	0.348808	0.0171017
$417$	−32.7445	−1.60350
$418$	12.7995	0.626046
$419$	14.3794	0.702481	0.351240	−	0.936285i	$-0.385760\pi$
$419$	14.3794	0.702481	0.351240	+	0.936285i	$0.385760\pi$
$420$	0	0
$421$	33.5910	1.63713	0.818563	−	0.574416i	$-0.194771\pi$
$421$	33.5910	1.63713	0.818563	+	0.574416i	$0.194771\pi$
$422$	10.0209	0.487810
$423$	9.57640	0.465621
$424$	−0.504514	−0.0245014
$425$	11.6737	0.566257
$426$	4.31057	0.208848
$427$	0	0
$428$	−6.25594	−0.302392
$429$	−8.01356	−0.386898
$430$	11.2655	0.543273
$431$	−14.5686	−0.701743	−0.350872	−	0.936424i	$-0.614115\pi$
$431$	−14.5686	−0.701743	−0.350872	+	0.936424i	$0.614115\pi$
$432$	42.7604	2.05731
$433$	−10.8118	−0.519583	−0.259791	−	0.965665i	$-0.583654\pi$
$433$	−10.8118	−0.519583	−0.259791	+	0.965665i	$0.583654\pi$
$434$	0	0
$435$	11.4236	0.547721
$436$	41.1987	1.97306
$437$	−2.60130	−0.124437
$438$	112.033	5.35314
$439$	4.99320	0.238312	0.119156	−	0.992876i	$-0.461981\pi$
$439$	4.99320	0.238312	0.119156	+	0.992876i	$0.461981\pi$
$440$	−13.9685	−0.665922
$441$	0	0
$442$	−3.09793	−0.147353
$443$	24.3168	1.15533	0.577663	−	0.816275i	$-0.303965\pi$
$443$	24.3168	1.15533	0.577663	+	0.816275i	$0.303965\pi$
$444$	−58.7329	−2.78734
$445$	1.44091	0.0683055
$446$	−4.64053	−0.219735
$447$	4.61239	0.218159
$448$	0	0
$449$	−8.97068	−0.423353	−0.211676	−	0.977340i	$-0.567892\pi$
$449$	−8.97068	−0.423353	−0.211676	+	0.977340i	$0.567892\pi$
$450$	72.0446	3.39621
$451$	−25.5991	−1.20541
$452$	3.43327	0.161487
$453$	−37.5575	−1.76460
$454$	21.2677	0.998144
$455$	0	0
$456$	15.4501	0.723515
$457$	−21.7708	−1.01840	−0.509198	−	0.860649i	$-0.670058\pi$
$457$	−21.7708	−1.01840	−0.509198	+	0.860649i	$0.670058\pi$
$458$	51.8258	2.42166
$459$	−23.9445	−1.11763
$460$	5.58384	0.260348
$461$	−14.4222	−0.671707	−0.335854	−	0.941914i	$-0.609025\pi$
$461$	−14.4222	−0.671707	−0.335854	+	0.941914i	$0.609025\pi$
$462$	0	0
$463$	22.0398	1.02427	0.512137	−	0.858904i	$-0.328854\pi$
$463$	22.0398	1.02427	0.512137	+	0.858904i	$0.328854\pi$
$464$	31.5274	1.46362
$465$	12.8489	0.595854
$466$	70.9469	3.28655
$467$	−32.6176	−1.50936	−0.754682	−	0.656091i	$-0.772209\pi$
$467$	−32.6176	−1.50936	−0.754682	+	0.656091i	$0.772209\pi$
$468$	−12.8178	−0.592505
$469$	0	0
$470$	−2.00948	−0.0926905
$471$	50.3535	2.32017
$472$	−28.7852	−1.32495
$473$	−45.0355	−2.07073
$474$	−37.1978	−1.70855
$475$	4.72162	0.216643
$476$	0	0
$477$	0.613293	0.0280808
$478$	−6.49215	−0.296944
$479$	−12.5287	−0.572449	−0.286225	−	0.958163i	$-0.592400\pi$
$479$	−12.5287	−0.572449	−0.286225	+	0.958163i	$0.592400\pi$
$480$	−1.09708	−0.0500746
$481$	2.42170	0.110420
$482$	7.42578	0.338235
$483$	0	0
$484$	65.0819	2.95827
$485$	0.0411254	0.00186741
$486$	−8.97609	−0.407164
$487$	17.5463	0.795101	0.397550	−	0.917580i	$-0.369860\pi$
$487$	17.5463	0.795101	0.397550	+	0.917580i	$0.369860\pi$
$488$	37.6734	1.70540
$489$	−14.0702	−0.636278
$490$	0	0
$491$	−37.6290	−1.69817	−0.849086	−	0.528254i	$-0.822847\pi$
$491$	−37.6290	−1.69817	−0.849086	+	0.528254i	$0.822847\pi$
$492$	−60.7780	−2.74009
$493$	−17.6544	−0.795113
$494$	−1.25301	−0.0563756
$495$	16.9803	0.763206
$496$	35.4609	1.59224
$497$	0	0
$498$	5.62786	0.252190
$499$	−32.2474	−1.44359	−0.721797	−	0.692105i	$-0.756683\pi$
$499$	−32.2474	−1.44359	−0.721797	+	0.692105i	$0.756683\pi$
$500$	−20.8680	−0.933246
$501$	55.7562	2.49100
$502$	41.2436	1.84079
$503$	−21.4870	−0.958059	−0.479030	−	0.877799i	$-0.659011\pi$
$503$	−21.4870	−0.958059	−0.479030	+	0.877799i	$0.659011\pi$
$504$	0	0
$505$	−1.25848	−0.0560018
$506$	−33.2955	−1.48016
$507$	−38.6336	−1.71578
$508$	11.6536	0.517046
$509$	41.2922	1.83024	0.915122	−	0.403177i	$-0.132094\pi$
$509$	41.2922	1.83024	0.915122	+	0.403177i	$0.132094\pi$
$510$	9.74367	0.431457
$511$	0	0
$512$	41.9668	1.85469
$513$	−9.68476	−0.427593
$514$	63.9291	2.81979
$515$	−4.13281	−0.182114
$516$	−106.924	−4.70709
$517$	8.03317	0.353298
$518$	0	0
$519$	−47.0162	−2.06378
$520$	1.36745	0.0599665
$521$	−1.39056	−0.0609216	−0.0304608	−	0.999536i	$-0.509697\pi$
$521$	−1.39056	−0.0609216	−0.0304608	+	0.999536i	$0.509697\pi$
$522$	−108.955	−4.76882
$523$	−17.7680	−0.776939	−0.388470	−	0.921462i	$-0.626996\pi$
$523$	−17.7680	−0.776939	−0.388470	+	0.921462i	$0.626996\pi$
$524$	44.2023	1.93099
$525$	0	0
$526$	−40.7945	−1.77873
$527$	−19.8570	−0.864985
$528$	69.5603	3.02722
$529$	−16.2332	−0.705793
$530$	−0.128692	−0.00559000
$531$	34.9916	1.51851
$532$	0	0
$533$	2.50602	0.108548
$534$	−20.3991	−0.882753
$535$	−0.811301	−0.0350756
$536$	−51.9830	−2.24532
$537$	−4.72656	−0.203966
$538$	75.5975	3.25924
$539$	0	0
$540$	20.7889	0.894611
$541$	40.2394	1.73003	0.865013	−	0.501750i	$-0.167310\pi$
$541$	40.2394	1.73003	0.865013	+	0.501750i	$0.167310\pi$
$542$	2.45765	0.105565
$543$	−18.9842	−0.814692
$544$	1.69545	0.0726920
$545$	5.34286	0.228863
$546$	0	0
$547$	38.3840	1.64118	0.820591	−	0.571516i	$-0.193645\pi$
$547$	38.3840	1.64118	0.820591	+	0.571516i	$0.193645\pi$
$548$	0.527614	0.0225385
$549$	−45.7962	−1.95454
$550$	60.4346	2.57694
$551$	−7.14062	−0.304201
$552$	−40.1902	−1.71061
$553$	0	0
$554$	−12.1281	−0.515272
$555$	−7.61678	−0.323314
$556$	−43.9351	−1.86326
$557$	−12.3286	−0.522381	−0.261191	−	0.965287i	$-0.584115\pi$
$557$	−12.3286	−0.522381	−0.261191	+	0.965287i	$0.584115\pi$
$558$	−122.548	−5.18789
$559$	4.40875	0.186470
$560$	0	0
$561$	−38.9516	−1.64454
$562$	−26.3864	−1.11304
$563$	−34.7841	−1.46598	−0.732988	−	0.680241i	$-0.761875\pi$
$563$	−34.7841	−1.46598	−0.732988	+	0.680241i	$0.761875\pi$
$564$	19.0726	0.803100
$565$	0.445244	0.0187315
$566$	33.9996	1.42911
$567$	0	0
$568$	2.94051	0.123381
$569$	38.0403	1.59473	0.797365	−	0.603497i	$-0.206226\pi$
$569$	38.0403	1.59473	0.797365	+	0.603497i	$0.206226\pi$
$570$	3.94100	0.165070
$571$	−30.8478	−1.29094	−0.645469	−	0.763786i	$-0.723338\pi$
$571$	−30.8478	−1.29094	−0.645469	+	0.763786i	$0.723338\pi$
$572$	−10.7522	−0.449574
$573$	18.7881	0.784884
$574$	0	0
$575$	−12.2824	−0.512210
$576$	−44.2323	−1.84301
$577$	24.9724	1.03961	0.519807	−	0.854284i	$-0.326004\pi$
$577$	24.9724	1.03961	0.519807	+	0.854284i	$0.326004\pi$
$578$	26.8200	1.11556
$579$	54.4227	2.26173
$580$	15.3277	0.636450
$581$	0	0
$582$	−0.582217	−0.0241337
$583$	0.514461	0.0213068
$584$	76.4246	3.16247
$585$	−1.66228	−0.0687269
$586$	70.4089	2.90856
$587$	19.1805	0.791665	0.395832	−	0.918323i	$-0.370456\pi$
$587$	19.1805	0.791665	0.395832	+	0.918323i	$0.370456\pi$
$588$	0	0
$589$	−8.03152	−0.330933
$590$	−7.34254	−0.302287
$591$	64.1487	2.63872
$592$	−21.0211	−0.863962
$593$	39.4778	1.62116	0.810579	−	0.585630i	$-0.199153\pi$
$593$	39.4778	1.62116	0.810579	+	0.585630i	$0.199153\pi$
$594$	−123.960	−5.08616
$595$	0	0
$596$	6.18871	0.253499
$597$	67.8483	2.77685
$598$	3.25946	0.133289
$599$	−11.7314	−0.479331	−0.239665	−	0.970856i	$-0.577038\pi$
$599$	−11.7314	−0.479331	−0.239665	+	0.970856i	$0.577038\pi$
$600$	72.9493	2.97814
$601$	36.1638	1.47515	0.737577	−	0.675263i	$-0.235970\pi$
$601$	36.1638	1.47515	0.737577	+	0.675263i	$0.235970\pi$
$602$	0	0
$603$	63.1910	2.57334
$604$	−50.3930	−2.05046
$605$	8.44014	0.343141
$606$	17.8165	0.723745
$607$	3.19619	0.129729	0.0648647	−	0.997894i	$-0.479338\pi$
$607$	3.19619	0.129729	0.0648647	+	0.997894i	$0.479338\pi$
$608$	0.685756	0.0278111
$609$	0	0
$610$	9.60974	0.389087
$611$	−0.786407	−0.0318146
$612$	−62.3038	−2.51848
$613$	−6.91777	−0.279406	−0.139703	−	0.990193i	$-0.544615\pi$
$613$	−6.91777	−0.279406	−0.139703	+	0.990193i	$0.544615\pi$
$614$	−36.2516	−1.46299
$615$	−7.88200	−0.317833
$616$	0	0
$617$	13.3466	0.537312	0.268656	−	0.963236i	$-0.413420\pi$
$617$	13.3466	0.537312	0.268656	+	0.963236i	$0.413420\pi$
$618$	58.5087	2.35356
$619$	−28.4741	−1.14447	−0.572235	−	0.820089i	$-0.693924\pi$
$619$	−28.4741	−1.14447	−0.572235	+	0.820089i	$0.693924\pi$
$620$	17.2401	0.692379
$621$	25.1930	1.01096
$622$	35.4112	1.41986
$623$	0	0
$624$	−6.80961	−0.272602
$625$	20.9019	0.836074
$626$	61.9342	2.47539
$627$	−15.7547	−0.629180
$628$	67.5622	2.69602
$629$	11.7712	0.469347
$630$	0	0
$631$	8.97167	0.357157	0.178578	−	0.983926i	$-0.442850\pi$
$631$	8.97167	0.357157	0.178578	+	0.983926i	$0.442850\pi$
$632$	−25.3749	−1.00936
$633$	−12.3345	−0.490252
$634$	−28.3097	−1.12432
$635$	1.51130	0.0599741
$636$	1.22145	0.0484335
$637$	0	0
$638$	−91.3966	−3.61843
$639$	−3.57451	−0.141405
$640$	10.0052	0.395490
$641$	−18.5533	−0.732811	−0.366405	−	0.930455i	$-0.619412\pi$
$641$	−18.5533	−0.732811	−0.366405	+	0.930455i	$0.619412\pi$
$642$	11.4857	0.453304
$643$	−24.2879	−0.957822	−0.478911	−	0.877863i	$-0.658968\pi$
$643$	−24.2879	−0.957822	−0.478911	+	0.877863i	$0.658968\pi$
$644$	0	0
$645$	−13.8665	−0.545993
$646$	−6.09052	−0.239628
$647$	−24.5862	−0.966582	−0.483291	−	0.875460i	$-0.660559\pi$
$647$	−24.5862	−0.966582	−0.483291	+	0.875460i	$0.660559\pi$
$648$	−54.9473	−2.15853
$649$	29.3527	1.15220
$650$	−5.91624	−0.232054
$651$	0	0
$652$	−18.8788	−0.739352
$653$	−5.87378	−0.229859	−0.114929	−	0.993374i	$-0.536664\pi$
$653$	−5.87378	−0.229859	−0.114929	+	0.993374i	$0.536664\pi$
$654$	−75.6394	−2.95773
$655$	5.73238	0.223983
$656$	−21.7531	−0.849315
$657$	−92.9025	−3.62447
$658$	0	0
$659$	29.9579	1.16699	0.583496	−	0.812116i	$-0.301684\pi$
$659$	29.9579	1.16699	0.583496	+	0.812116i	$0.301684\pi$
$660$	33.8182	1.31637
$661$	0.453535	0.0176405	0.00882023	−	0.999961i	$-0.497192\pi$
$661$	0.453535	0.0176405	0.00882023	+	0.999961i	$0.497192\pi$
$662$	4.36257	0.169556
$663$	3.81317	0.148091
$664$	3.83911	0.148986
$665$	0	0
$666$	72.6462	2.81498
$667$	18.5749	0.719223
$668$	74.8112	2.89453
$669$	5.71192	0.220835
$670$	−13.2598	−0.512271
$671$	−38.4162	−1.48304
$672$	0	0
$673$	6.12498	0.236100	0.118050	−	0.993008i	$-0.462336\pi$
$673$	6.12498	0.236100	0.118050	+	0.993008i	$0.462336\pi$
$674$	73.5685	2.83375
$675$	−45.7278	−1.76006
$676$	−51.8369	−1.99373
$677$	−5.83502	−0.224258	−0.112129	−	0.993694i	$-0.535767\pi$
$677$	−5.83502	−0.224258	−0.112129	+	0.993694i	$0.535767\pi$
$678$	−6.30336	−0.242079
$679$	0	0
$680$	6.64676	0.254891
$681$	−26.1779	−1.00314
$682$	−102.800	−3.93641
$683$	5.89230	0.225463	0.112731	−	0.993626i	$-0.464040\pi$
$683$	5.89230	0.225463	0.112731	+	0.993626i	$0.464040\pi$
$684$	−25.1999	−0.963541
$685$	0.0684236	0.00261433
$686$	0	0
$687$	−63.7912	−2.43378
$688$	−38.2693	−1.45901
$689$	−0.0503631	−0.00191868
$690$	−10.2517	−0.390277
$691$	−13.0336	−0.495821	−0.247911	−	0.968783i	$-0.579744\pi$
$691$	−13.0336	−0.495821	−0.247911	+	0.968783i	$0.579744\pi$
$692$	−63.0843	−2.39810
$693$	0	0
$694$	22.8372	0.866887
$695$	−5.69772	−0.216127
$696$	−110.323	−4.18178
$697$	12.1810	0.461390
$698$	40.1067	1.51806
$699$	−87.3269	−3.30301
$700$	0	0
$701$	36.8143	1.39046	0.695228	−	0.718790i	$-0.255304\pi$
$701$	36.8143	1.39046	0.695228	+	0.718790i	$0.255304\pi$
$702$	12.1351	0.458010
$703$	4.76105	0.179567
$704$	−37.1043	−1.39842
$705$	2.47343	0.0931546
$706$	−38.0199	−1.43090
$707$	0	0
$708$	69.6901	2.61911
$709$	−21.1545	−0.794473	−0.397236	−	0.917716i	$-0.630031\pi$
$709$	−21.1545	−0.794473	−0.397236	+	0.917716i	$0.630031\pi$
$710$	0.750064	0.0281494
$711$	30.8460	1.15681
$712$	−13.9154	−0.521503
$713$	20.8924	0.782427
$714$	0	0
$715$	−1.39441	−0.0521478
$716$	−6.34189	−0.237007
$717$	7.99103	0.298431
$718$	23.1308	0.863235
$719$	51.1306	1.90685	0.953426	−	0.301628i	$-0.0975301\pi$
$719$	51.1306	1.90685	0.953426	+	0.301628i	$0.0975301\pi$
$720$	14.4291	0.537742
$721$	0	0
$722$	−2.46342	−0.0916789
$723$	−9.14022	−0.339928
$724$	−25.4722	−0.946668
$725$	−33.7153	−1.25216
$726$	−119.488	−4.43462
$727$	27.3462	1.01421	0.507107	−	0.861883i	$-0.330715\pi$
$727$	27.3462	1.01421	0.507107	+	0.861883i	$0.330715\pi$
$728$	0	0
$729$	−21.3027	−0.788990
$730$	19.4944	0.721519
$731$	21.4296	0.792604
$732$	−91.2087	−3.37117
$733$	−2.51791	−0.0930013	−0.0465007	−	0.998918i	$-0.514807\pi$
$733$	−2.51791	−0.0930013	−0.0465007	+	0.998918i	$0.514807\pi$
$734$	−0.374931	−0.0138389
$735$	0	0
$736$	−1.78386	−0.0657539
$737$	53.0078	1.95257
$738$	75.1758	2.76726
$739$	−9.41320	−0.346270	−0.173135	−	0.984898i	$-0.555390\pi$
$739$	−9.41320	−0.346270	−0.173135	+	0.984898i	$0.555390\pi$
$740$	−10.2199	−0.375690
$741$	1.54230	0.0566579
$742$	0	0
$743$	−15.0634	−0.552624	−0.276312	−	0.961068i	$-0.589112\pi$
$743$	−15.0634	−0.552624	−0.276312	+	0.961068i	$0.589112\pi$
$744$	−124.087	−4.54926
$745$	0.802583	0.0294044
$746$	66.6308	2.43953
$747$	−4.66686	−0.170751
$748$	−52.2635	−1.91094
$749$	0	0
$750$	38.3129	1.39899
$751$	9.72515	0.354876	0.177438	−	0.984132i	$-0.443219\pi$
$751$	9.72515	0.354876	0.177438	+	0.984132i	$0.443219\pi$
$752$	6.82626	0.248928
$753$	−50.7658	−1.85001
$754$	8.94727	0.325840
$755$	−6.53522	−0.237841
$756$	0	0
$757$	−35.6513	−1.29577	−0.647884	−	0.761739i	$-0.724346\pi$
$757$	−35.6513	−1.29577	−0.647884	+	0.761739i	$0.724346\pi$
$758$	−54.6090	−1.98349
$759$	40.9826	1.48757
$760$	2.68840	0.0975184
$761$	−23.2232	−0.841840	−0.420920	−	0.907098i	$-0.638293\pi$
$761$	−23.2232	−0.841840	−0.420920	+	0.907098i	$0.638293\pi$
$762$	−21.3956	−0.775082
$763$	0	0
$764$	25.2091	0.912032
$765$	−8.07987	−0.292128
$766$	20.1500	0.728048
$767$	−2.87348	−0.103756
$768$	−98.3385	−3.54848
$769$	36.1161	1.30238	0.651189	−	0.758915i	$-0.274270\pi$
$769$	36.1161	1.30238	0.651189	+	0.758915i	$0.274270\pi$
$770$	0	0
$771$	−78.6889	−2.83391
$772$	73.0221	2.62812
$773$	−14.0128	−0.504005	−0.252003	−	0.967727i	$-0.581089\pi$
$773$	−14.0128	−0.504005	−0.252003	+	0.967727i	$0.581089\pi$
$774$	132.254	4.75377
$775$	−37.9218	−1.36219
$776$	−0.397166	−0.0142574
$777$	0	0
$778$	−86.8459	−3.11358
$779$	4.92683	0.176522
$780$	−3.31064	−0.118540
$781$	−2.99848	−0.107294
$782$	15.8433	0.566554
$783$	69.1552	2.47140
$784$	0	0
$785$	8.76180	0.312722
$786$	−81.1539	−2.89466
$787$	42.9804	1.53209	0.766044	−	0.642789i	$-0.222223\pi$
$787$	42.9804	1.53209	0.766044	+	0.642789i	$0.222223\pi$
$788$	86.0719	3.06618
$789$	50.2130	1.78763
$790$	−6.47262	−0.230286
$791$	0	0
$792$	−163.986	−5.82697
$793$	3.76075	0.133548
$794$	52.6482	1.86842
$795$	0.158403	0.00561799
$796$	91.0359	3.22668
$797$	17.6905	0.626630	0.313315	−	0.949649i	$-0.398560\pi$
$797$	17.6905	0.626630	0.313315	+	0.949649i	$0.398560\pi$
$798$	0	0
$799$	−3.82249	−0.135230
$800$	3.23788	0.114476
$801$	16.9158	0.597689
$802$	29.0878	1.02713
$803$	−77.9313	−2.75014
$804$	125.853	4.43848
$805$	0	0
$806$	10.0636	0.354474
$807$	−93.0511	−3.27556
$808$	12.1537	0.427566
$809$	46.9803	1.65174	0.825870	−	0.563861i	$-0.190685\pi$
$809$	46.9803	1.65174	0.825870	+	0.563861i	$0.190685\pi$
$810$	−14.0160	−0.492471
$811$	−12.1883	−0.427988	−0.213994	−	0.976835i	$-0.568647\pi$
$811$	−12.1883	−0.427988	−0.213994	+	0.976835i	$0.568647\pi$
$812$	0	0
$813$	−3.02506	−0.106094
$814$	60.9393	2.13592
$815$	−2.44830	−0.0857602
$816$	−33.0995	−1.15871
$817$	8.66759	0.303241
$818$	−59.1262	−2.06730
$819$	0	0
$820$	−10.5757	−0.369320
$821$	44.4533	1.55143	0.775716	−	0.631082i	$-0.217389\pi$
$821$	44.4533	1.55143	0.775716	+	0.631082i	$0.217389\pi$
$822$	−0.968680	−0.0337866
$823$	−11.9760	−0.417456	−0.208728	−	0.977974i	$-0.566932\pi$
$823$	−11.9760	−0.417456	−0.208728	+	0.977974i	$0.566932\pi$
$824$	39.9123	1.39041
$825$	−74.3876	−2.58984
$826$	0	0
$827$	13.5824	0.472307	0.236154	−	0.971716i	$-0.424113\pi$
$827$	13.5824	0.472307	0.236154	+	0.971716i	$0.424113\pi$
$828$	65.5524	2.27810
$829$	17.7772	0.617428	0.308714	−	0.951155i	$-0.400101\pi$
$829$	17.7772	0.617428	0.308714	+	0.951155i	$0.400101\pi$
$830$	0.979279	0.0339913
$831$	14.9281	0.517851
$832$	3.63232	0.125928
$833$	0	0
$834$	80.6633	2.79314
$835$	9.70190	0.335748
$836$	−21.1389	−0.731104
$837$	77.7833	2.68858
$838$	−35.4225	−1.22365
$839$	49.4432	1.70697	0.853484	−	0.521119i	$-0.174485\pi$
$839$	49.4432	1.70697	0.853484	+	0.521119i	$0.174485\pi$
$840$	0	0
$841$	21.9885	0.758223
$842$	−82.7487	−2.85171
$843$	32.4784	1.11862
$844$	−16.5499	−0.569670
$845$	−6.72247	−0.231260
$846$	−23.5907	−0.811064
$847$	0	0
$848$	0.437168	0.0150124
$849$	−41.8493	−1.43626
$850$	−28.7571	−0.986362
$851$	−12.3849	−0.424550
$852$	−7.11907	−0.243895
$853$	−0.260988	−0.00893607	−0.00446803	−	0.999990i	$-0.501422\pi$
$853$	−0.260988	−0.00893607	−0.00446803	+	0.999990i	$0.501422\pi$
$854$	0	0
$855$	−3.26804	−0.111765
$856$	7.83508	0.267798
$857$	−20.4688	−0.699200	−0.349600	−	0.936899i	$-0.613683\pi$
$857$	−20.4688	−0.699200	−0.349600	+	0.936899i	$0.613683\pi$
$858$	19.7407	0.673938
$859$	−7.08167	−0.241623	−0.120812	−	0.992675i	$-0.538550\pi$
$859$	−7.08167	−0.241623	−0.120812	+	0.992675i	$0.538550\pi$
$860$	−18.6055	−0.634441
$861$	0	0
$862$	35.8885	1.22237
$863$	50.3208	1.71294	0.856470	−	0.516196i	$-0.172653\pi$
$863$	50.3208	1.71294	0.856470	+	0.516196i	$0.172653\pi$
$864$	−6.64139	−0.225945
$865$	−8.18108	−0.278165
$866$	26.6340	0.905061
$867$	−33.0121	−1.12115
$868$	0	0
$869$	25.8751	0.877754
$870$	−28.1412	−0.954075
$871$	−5.18920	−0.175829
$872$	−51.5982	−1.74734
$873$	0.482799	0.0163403
$874$	6.40809	0.216757
$875$	0	0
$876$	−185.027	−6.25147
$877$	−42.1043	−1.42176	−0.710881	−	0.703313i	$-0.751703\pi$
$877$	−42.1043	−1.42176	−0.710881	+	0.703313i	$0.751703\pi$
$878$	−12.3003	−0.415116
$879$	−86.6646	−2.92312
$880$	12.1039	0.408022
$881$	35.5826	1.19881	0.599403	−	0.800447i	$-0.295405\pi$
$881$	35.5826	1.19881	0.599403	+	0.800447i	$0.295405\pi$
$882$	0	0
$883$	15.5303	0.522635	0.261317	−	0.965253i	$-0.415843\pi$
$883$	15.5303	0.522635	0.261317	+	0.965253i	$0.415843\pi$
$884$	5.11634	0.172081
$885$	9.03776	0.303801
$886$	−59.9024	−2.01246
$887$	20.2577	0.680186	0.340093	−	0.940392i	$-0.389541\pi$
$887$	20.2577	0.680186	0.340093	+	0.940392i	$0.389541\pi$
$888$	73.5585	2.46846
$889$	0	0
$890$	−3.54955	−0.118981
$891$	56.0306	1.87710
$892$	7.66400	0.256610
$893$	−1.54607	−0.0517374
$894$	−11.3622	−0.380010
$895$	−0.822448	−0.0274914
$896$	0	0
$897$	−4.01199	−0.133956
$898$	22.0985	0.737438
$899$	57.3500	1.91273
$900$	−118.984	−3.96614
$901$	−0.244801	−0.00815549
$902$	63.0612	2.09971
$903$	0	0
$904$	−4.29991	−0.143013
$905$	−3.30337	−0.109808
$906$	92.5197	3.07376
$907$	−15.5694	−0.516974	−0.258487	−	0.966015i	$-0.583224\pi$
$907$	−15.5694	−0.516974	−0.258487	+	0.966015i	$0.583224\pi$
$908$	−35.1244	−1.16565
$909$	−14.7742	−0.490029
$910$	0	0
$911$	−31.2116	−1.03408	−0.517042	−	0.855960i	$-0.672967\pi$
$911$	−31.2116	−1.03408	−0.517042	+	0.855960i	$0.672967\pi$
$912$	−13.3877	−0.443310
$913$	−3.91480	−0.129561
$914$	53.6306	1.77394
$915$	−11.8284	−0.391035
$916$	−85.5922	−2.82805
$917$	0	0
$918$	58.9852	1.94680
$919$	22.1742	0.731458	0.365729	−	0.930721i	$-0.380820\pi$
$919$	22.1742	0.731458	0.365729	+	0.930721i	$0.380820\pi$
$920$	−6.99333	−0.230563
$921$	44.6212	1.47032
$922$	35.5278	1.17005
$923$	0.293536	0.00966185
$924$	0	0
$925$	22.4799	0.739135
$926$	−54.2931	−1.78418
$927$	−48.5179	−1.59354
$928$	−4.89673	−0.160743
$929$	−46.1337	−1.51360	−0.756798	−	0.653649i	$-0.773237\pi$
$929$	−46.1337	−1.51360	−0.756798	+	0.653649i	$0.773237\pi$
$930$	−31.6522	−1.03792
$931$	0	0
$932$	−117.171	−3.83808
$933$	−43.5868	−1.42697
$934$	80.3508	2.62916
$935$	−6.77780	−0.221658
$936$	16.0534	0.524721
$937$	6.44029	0.210395	0.105198	−	0.994451i	$-0.466452\pi$
$937$	6.44029	0.210395	0.105198	+	0.994451i	$0.466452\pi$
$938$	0	0
$939$	−76.2333	−2.48778
$940$	3.31873	0.108245
$941$	0.318299	0.0103762	0.00518812	−	0.999987i	$-0.498349\pi$
$941$	0.318299	0.0103762	0.00518812	+	0.999987i	$0.498349\pi$
$942$	−124.042	−4.04150
$943$	−12.8162	−0.417352
$944$	24.9428	0.811818
$945$	0	0
$946$	110.941	3.60701
$947$	−48.4088	−1.57308	−0.786538	−	0.617542i	$-0.788128\pi$
$947$	−48.4088	−1.57308	−0.786538	+	0.617542i	$0.788128\pi$
$948$	61.4335	1.99527
$949$	7.62908	0.247650
$950$	−11.6313	−0.377370
$951$	34.8457	1.12995
$952$	0	0
$953$	43.4324	1.40691	0.703457	−	0.710738i	$-0.251639\pi$
$953$	43.4324	1.40691	0.703457	+	0.710738i	$0.251639\pi$
$954$	−1.51080	−0.0489138
$955$	3.26924	0.105790
$956$	10.7220	0.346775
$957$	112.498	3.63654
$958$	30.8633	0.997149
$959$	0	0
$960$	−11.4245	−0.368723
$961$	33.5053	1.08082
$962$	−5.96565	−0.192340
$963$	−9.52441	−0.306920
$964$	−12.2640	−0.394995
$965$	9.46987	0.304846
$966$	0	0
$967$	−27.9195	−0.897829	−0.448915	−	0.893575i	$-0.648189\pi$
$967$	−27.9195	−0.897829	−0.448915	+	0.893575i	$0.648189\pi$
$968$	−81.5101	−2.61983
$969$	7.49668	0.240828
$970$	−0.101309	−0.00325284
$971$	40.0375	1.28486	0.642432	−	0.766343i	$-0.277926\pi$
$971$	40.0375	1.28486	0.642432	+	0.766343i	$0.277926\pi$
$972$	14.8243	0.475491
$973$	0	0
$974$	−43.2240	−1.38498
$975$	7.28217	0.233216
$976$	−32.6445	−1.04493
$977$	−8.54575	−0.273403	−0.136701	−	0.990612i	$-0.543650\pi$
$977$	−8.54575	−0.273403	−0.136701	+	0.990612i	$0.543650\pi$
$978$	34.6609	1.10833
$979$	14.1898	0.453508
$980$	0	0
$981$	62.7234	2.00260
$982$	92.6959	2.95804
$983$	−48.2785	−1.53985	−0.769923	−	0.638137i	$-0.779705\pi$
$983$	−48.2785	−1.53985	−0.769923	+	0.638137i	$0.779705\pi$
$984$	76.1198	2.42661
$985$	11.1622	0.355658
$986$	43.4901	1.38501
$987$	0	0
$988$	2.06939	0.0658362
$989$	−22.5470	−0.716953
$990$	−41.8295	−1.32943
$991$	48.8351	1.55130	0.775648	−	0.631165i	$-0.217423\pi$
$991$	48.8351	1.55130	0.775648	+	0.631165i	$0.217423\pi$
$992$	−5.50767	−0.174869
$993$	−5.36978	−0.170405
$994$	0	0
$995$	11.8060	0.374275
$996$	−9.29461	−0.294511
$997$	29.6600	0.939342	0.469671	−	0.882842i	$-0.344373\pi$
$997$	29.6600	0.939342	0.469671	+	0.882842i	$0.344373\pi$
$998$	79.4389	2.51459
$999$	−46.1097	−1.45884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.o.1.1		7
3.2	odd	2		8379.2.a.ck.1.7		7
7.2	even	3		931.2.f.p.704.7		14
7.3	odd	6		133.2.f.d.58.7	yes	14
7.4	even	3		931.2.f.p.324.7		14
7.5	odd	6		133.2.f.d.39.7	✓	14
7.6	odd	2		931.2.a.n.1.1		7
21.5	even	6		1197.2.j.l.172.1		14
21.17	even	6		1197.2.j.l.856.1		14
21.20	even	2		8379.2.a.cl.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.7	✓	14	7.5	odd	6
133.2.f.d.58.7	yes	14	7.3	odd	6
931.2.a.n.1.1		7	7.6	odd	2
931.2.a.o.1.1		7	1.1	even	1	trivial
931.2.f.p.324.7		14	7.4	even	3
931.2.f.p.704.7		14	7.2	even	3
1197.2.j.l.172.1		14	21.5	even	6
1197.2.j.l.856.1		14	21.17	even	6
8379.2.a.ck.1.7		7	3.2	odd	2
8379.2.a.cl.1.7		7	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46342 q^{2} +3.03216 q^{3} +4.06842 q^{4} +0.527614 q^{5} -7.46948 q^{6} -5.09539 q^{8} +6.19401 q^{9} +O(q^{10})\)	\(q-2.46342 q^{2} +3.03216 q^{3} +4.06842 q^{4} +0.527614 q^{5} -7.46948 q^{6} -5.09539 q^{8} +6.19401 q^{9} -1.29973 q^{10} +5.19585 q^{11} +12.3361 q^{12} -0.508647 q^{13} +1.59981 q^{15} +4.41522 q^{16} -2.47239 q^{17} -15.2584 q^{18} -1.00000 q^{19} +2.14656 q^{20} -12.7995 q^{22} +2.60130 q^{23} -15.4501 q^{24} -4.72162 q^{25} +1.25301 q^{26} +9.68476 q^{27} +7.14062 q^{29} -3.94100 q^{30} +8.03152 q^{31} -0.685756 q^{32} +15.7547 q^{33} +6.09052 q^{34} +25.1999 q^{36} -4.76105 q^{37} +2.46342 q^{38} -1.54230 q^{39} -2.68840 q^{40} -4.92683 q^{41} -8.66759 q^{43} +21.1389 q^{44} +3.26804 q^{45} -6.40809 q^{46} +1.54607 q^{47} +13.3877 q^{48} +11.6313 q^{50} -7.49668 q^{51} -2.06939 q^{52} +0.0990139 q^{53} -23.8576 q^{54} +2.74140 q^{55} -3.03216 q^{57} -17.5903 q^{58} +5.64927 q^{59} +6.50871 q^{60} -7.39363 q^{61} -19.7850 q^{62} -7.14114 q^{64} -0.268369 q^{65} -38.8103 q^{66} +10.2020 q^{67} -10.0587 q^{68} +7.88757 q^{69} -0.577091 q^{71} -31.5609 q^{72} -14.9988 q^{73} +11.7285 q^{74} -14.3167 q^{75} -4.06842 q^{76} +3.79933 q^{78} +4.97997 q^{79} +2.32953 q^{80} +10.7837 q^{81} +12.1368 q^{82} -0.753447 q^{83} -1.30446 q^{85} +21.3519 q^{86} +21.6515 q^{87} -26.4749 q^{88} +2.73099 q^{89} -8.05056 q^{90} +10.5832 q^{92} +24.3529 q^{93} -3.80863 q^{94} -0.527614 q^{95} -2.07933 q^{96} +0.0779461 q^{97} +32.1831 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9	\( 7 q + 2 q^{2} + 2 q^{3} + 10 q^{4} + 2 q^{5} + 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} + 22 q^{12} - 6 q^{13} + 2 q^{15} + 24 q^{16} - 19 q^{17} - 12 q^{18} - 7 q^{19} + 8 q^{20} - 6 q^{22} - q^{23} - 20 q^{24} - 3 q^{25} - 12 q^{26} + 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} + 14 q^{33} - 6 q^{34} + 46 q^{36} + 8 q^{37} - 2 q^{38} + 16 q^{39} + 10 q^{40} + 4 q^{41} + 4 q^{43} + 26 q^{44} - 14 q^{45} - 16 q^{46} - 5 q^{47} + 28 q^{48} + 16 q^{50} - 4 q^{51} - 42 q^{52} + 20 q^{53} + 24 q^{54} + 30 q^{55} - 2 q^{57} + 16 q^{59} - 44 q^{60} - 5 q^{61} - 24 q^{62} + 32 q^{64} + 26 q^{65} - 68 q^{66} - 4 q^{67} - 22 q^{68} + 36 q^{69} + 12 q^{71} - 3 q^{73} - 4 q^{74} - 18 q^{75} - 10 q^{76} - 14 q^{78} - 20 q^{79} + 4 q^{80} + 27 q^{81} + 48 q^{82} + 11 q^{83} + 26 q^{85} + 36 q^{86} + 16 q^{87} - 32 q^{88} + 10 q^{89} - 32 q^{90} - 30 q^{92} - 4 q^{93} - 16 q^{94} - 2 q^{95} + 12 q^{96} + 4 q^{97} + 15 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 + 2 * q^3 + 10 * q^4 + 2 * q^5 + 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 + 22 * q^12 - 6 * q^13 + 2 * q^15 + 24 * q^16 - 19 * q^17 - 12 * q^18 - 7 * q^19 + 8 * q^20 - 6 * q^22 - q^23 - 20 * q^24 - 3 * q^25 - 12 * q^26 + 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 + 14 * q^33 - 6 * q^34 + 46 * q^36 + 8 * q^37 - 2 * q^38 + 16 * q^39 + 10 * q^40 + 4 * q^41 + 4 * q^43 + 26 * q^44 - 14 * q^45 - 16 * q^46 - 5 * q^47 + 28 * q^48 + 16 * q^50 - 4 * q^51 - 42 * q^52 + 20 * q^53 + 24 * q^54 + 30 * q^55 - 2 * q^57 + 16 * q^59 - 44 * q^60 - 5 * q^61 - 24 * q^62 + 32 * q^64 + 26 * q^65 - 68 * q^66 - 4 * q^67 - 22 * q^68 + 36 * q^69 + 12 * q^71 - 3 * q^73 - 4 * q^74 - 18 * q^75 - 10 * q^76 - 14 * q^78 - 20 * q^79 + 4 * q^80 + 27 * q^81 + 48 * q^82 + 11 * q^83 + 26 * q^85 + 36 * q^86 + 16 * q^87 - 32 * q^88 + 10 * q^89 - 32 * q^90 - 30 * q^92 - 4 * q^93 - 16 * q^94 - 2 * q^95 + 12 * q^96 + 4 * q^97 + 15 * q^99

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