LMFDB - Embedded newform 2793.2.a.be.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1240016.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 2x^{2} + 16x + 6 $ x^5 - x^4 - 8x^3 + 2x^2 + 16*x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.89281$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.47552 q^{2} -1.00000 q^{3} +4.12820 q^{4} +2.79287 q^{5} -2.47552 q^{6} +5.26839 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.47552 q^{2} -1.00000 q^{3} +4.12820 q^{4} +2.79287 q^{5} -2.47552 q^{6} +5.26839 q^{8} +1.00000 q^{9} +6.91381 q^{10} +3.78561 q^{11} -4.12820 q^{12} +2.95104 q^{13} -2.79287 q^{15} +4.78561 q^{16} +3.46352 q^{17} +2.47552 q^{18} -1.00000 q^{19} +11.5295 q^{20} +9.37135 q^{22} -3.78561 q^{23} -5.26839 q^{24} +2.80013 q^{25} +7.30535 q^{26} -1.00000 q^{27} -6.57848 q^{29} -6.91381 q^{30} -5.78561 q^{31} +1.31009 q^{32} -3.78561 q^{33} +8.57401 q^{34} +4.12820 q^{36} -9.84214 q^{37} -2.47552 q^{38} -2.95104 q^{39} +14.7139 q^{40} -1.30535 q^{41} +10.0565 q^{43} +15.6277 q^{44} +2.79287 q^{45} -9.37135 q^{46} +6.99274 q^{47} -4.78561 q^{48} +6.93178 q^{50} -3.46352 q^{51} +12.1825 q^{52} -4.63843 q^{53} -2.47552 q^{54} +10.5727 q^{55} +1.00000 q^{57} -16.2852 q^{58} -7.57122 q^{59} -11.5295 q^{60} -2.67065 q^{61} -14.3224 q^{62} -6.32806 q^{64} +8.24187 q^{65} -9.37135 q^{66} +10.0660 q^{67} +14.2981 q^{68} +3.78561 q^{69} +10.2147 q^{71} +5.26839 q^{72} -5.64569 q^{73} -24.3644 q^{74} -2.80013 q^{75} -4.12820 q^{76} -7.30535 q^{78} +16.3224 q^{79} +13.3656 q^{80} +1.00000 q^{81} -3.23143 q^{82} +8.65295 q^{83} +9.67317 q^{85} +24.8951 q^{86} +6.57848 q^{87} +19.9441 q^{88} -12.4768 q^{89} +6.91381 q^{90} -15.6277 q^{92} +5.78561 q^{93} +17.3107 q^{94} -2.79287 q^{95} -1.31009 q^{96} +16.6622 q^{97} +3.78561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * 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 $

$2$	2.47552	1.75046	0.875228	−	0.483710i	$-0.160711\pi$
$2$	2.47552	1.75046	0.875228	+	0.483710i	$0.160711\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.12820	2.06410
$5$	2.79287	1.24901	0.624505	−	0.781021i	$-0.285301\pi$
$5$	2.79287	1.24901	0.624505	+	0.781021i	$0.285301\pi$
$6$	−2.47552	−1.01063
$7$	0	0
$7$	0	0
$8$	5.26839	1.86266
$9$	1.00000	0.333333
$10$	6.91381	2.18634
$11$	3.78561	1.14140	0.570702	−	0.821157i	$-0.306671\pi$
$11$	3.78561	1.14140	0.570702	+	0.821157i	$0.306671\pi$
$12$	−4.12820	−1.19171
$13$	2.95104	0.818471	0.409235	−	0.912429i	$-0.365795\pi$
$13$	2.95104	0.818471	0.409235	+	0.912429i	$0.365795\pi$
$14$	0	0
$15$	−2.79287	−0.721116
$16$	4.78561	1.19640
$17$	3.46352	0.840027	0.420014	−	0.907518i	$-0.362025\pi$
$17$	3.46352	0.840027	0.420014	+	0.907518i	$0.362025\pi$
$18$	2.47552	0.583486
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	11.5295	2.57808
$21$	0	0
$22$	9.37135	1.99798
$23$	−3.78561	−0.789355	−0.394677	−	0.918820i	$-0.629144\pi$
$23$	−3.78561	−0.789355	−0.394677	+	0.918820i	$0.629144\pi$
$24$	−5.26839	−1.07541
$25$	2.80013	0.560026
$26$	7.30535	1.43270
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−6.57848	−1.22159	−0.610797	−	0.791787i	$-0.709151\pi$
$29$	−6.57848	−1.22159	−0.610797	+	0.791787i	$0.709151\pi$
$30$	−6.91381	−1.26228
$31$	−5.78561	−1.03913	−0.519563	−	0.854432i	$-0.673905\pi$
$31$	−5.78561	−1.03913	−0.519563	+	0.854432i	$0.673905\pi$
$32$	1.31009	0.231594
$33$	−3.78561	−0.658990
$34$	8.57401	1.47043
$35$	0	0
$36$	4.12820	0.688033
$37$	−9.84214	−1.61804	−0.809019	−	0.587783i	$-0.800001\pi$
$37$	−9.84214	−1.61804	−0.809019	+	0.587783i	$0.800001\pi$
$38$	−2.47552	−0.401582
$39$	−2.95104	−0.472544
$40$	14.7139	2.32648
$41$	−1.30535	−0.203862	−0.101931	−	0.994791i	$-0.532502\pi$
$41$	−1.30535	−0.203862	−0.101931	+	0.994791i	$0.532502\pi$
$42$	0	0
$43$	10.0565	1.53361	0.766803	−	0.641883i	$-0.221846\pi$
$43$	10.0565	1.53361	0.766803	+	0.641883i	$0.221846\pi$
$44$	15.6277	2.35597
$45$	2.79287	0.416337
$46$	−9.37135	−1.38173
$47$	6.99274	1.02000	0.509998	−	0.860176i	$-0.329646\pi$
$47$	6.99274	1.02000	0.509998	+	0.860176i	$0.329646\pi$
$48$	−4.78561	−0.690744
$49$	0	0
$50$	6.93178	0.980302
$51$	−3.46352	−0.484990
$52$	12.1825	1.68940
$53$	−4.63843	−0.637137	−0.318568	−	0.947900i	$-0.603202\pi$
$53$	−4.63843	−0.637137	−0.318568	+	0.947900i	$0.603202\pi$
$54$	−2.47552	−0.336876
$55$	10.5727	1.42563
$56$	0	0
$57$	1.00000	0.132453
$58$	−16.2852	−2.13835
$59$	−7.57122	−0.985689	−0.492845	−	0.870117i	$-0.664043\pi$
$59$	−7.57122	−0.985689	−0.492845	+	0.870117i	$0.664043\pi$
$60$	−11.5295	−1.48845
$61$	−2.67065	−0.341942	−0.170971	−	0.985276i	$-0.554690\pi$
$61$	−2.67065	−0.341942	−0.170971	+	0.985276i	$0.554690\pi$
$62$	−14.3224	−1.81895
$63$	0	0
$64$	−6.32806	−0.791008
$65$	8.24187	1.02228
$66$	−9.37135	−1.15353
$67$	10.0660	1.22976	0.614879	−	0.788622i	$-0.289205\pi$
$67$	10.0660	1.22976	0.614879	+	0.788622i	$0.289205\pi$
$68$	14.2981	1.73390
$69$	3.78561	0.455734
$70$	0	0
$71$	10.2147	1.21226	0.606130	−	0.795365i	$-0.292721\pi$
$71$	10.2147	1.21226	0.606130	+	0.795365i	$0.292721\pi$
$72$	5.26839	0.620886
$73$	−5.64569	−0.660777	−0.330389	−	0.943845i	$-0.607180\pi$
$73$	−5.64569	−0.660777	−0.330389	+	0.943845i	$0.607180\pi$
$74$	−24.3644	−2.83230
$75$	−2.80013	−0.323331
$76$	−4.12820	−0.473537
$77$	0	0
$78$	−7.30535	−0.827168
$79$	16.3224	1.83641	0.918206	−	0.396102i	$-0.129637\pi$
$79$	16.3224	1.83641	0.918206	+	0.396102i	$0.129637\pi$
$80$	13.3656	1.49432
$81$	1.00000	0.111111
$82$	−3.23143	−0.356852
$83$	8.65295	0.949784	0.474892	−	0.880044i	$-0.342487\pi$
$83$	8.65295	0.949784	0.474892	+	0.880044i	$0.342487\pi$
$84$	0	0
$85$	9.67317	1.04920
$86$	24.8951	2.68451
$87$	6.57848	0.705287
$88$	19.9441	2.12605
$89$	−12.4768	−1.32254	−0.661271	−	0.750147i	$-0.729983\pi$
$89$	−12.4768	−1.32254	−0.661271	+	0.750147i	$0.729983\pi$
$90$	6.91381	0.728779
$91$	0	0
$92$	−15.6277	−1.62931
$93$	5.78561	0.599940
$94$	17.3107	1.78546
$95$	−2.79287	−0.286543
$96$	−1.31009	−0.133711
$97$	16.6622	1.69179	0.845894	−	0.533350i	$-0.179067\pi$
$97$	16.6622	1.69179	0.845894	+	0.533350i	$0.179067\pi$
$98$	0	0
$99$	3.78561	0.380468
$100$	11.5595	1.15595
$101$	4.10770	0.408732	0.204366	−	0.978895i	$-0.434487\pi$
$101$	4.10770	0.408732	0.204366	+	0.978895i	$0.434487\pi$
$102$	−8.57401	−0.848954
$103$	−18.4149	−1.81447	−0.907235	−	0.420624i	$-0.861811\pi$
$103$	−18.4149	−1.81447	−0.907235	+	0.420624i	$0.861811\pi$
$104$	15.5472	1.52453
$105$	0	0
$106$	−11.4825	−1.11528
$107$	−3.61292	−0.349275	−0.174637	−	0.984633i	$-0.555875\pi$
$107$	−3.61292	−0.349275	−0.174637	+	0.984633i	$0.555875\pi$
$108$	−4.12820	−0.397236
$109$	3.98548	0.381740	0.190870	−	0.981615i	$-0.438869\pi$
$109$	3.98548	0.381740	0.190870	+	0.981615i	$0.438869\pi$
$110$	26.1730	2.49550
$111$	9.84214	0.934174
$112$	0	0
$113$	−1.61797	−0.152206	−0.0761028	−	0.997100i	$-0.524248\pi$
$113$	−1.61797	−0.152206	−0.0761028	+	0.997100i	$0.524248\pi$
$114$	2.47552	0.231854
$115$	−10.5727	−0.985912
$116$	−27.1573	−2.52149
$117$	2.95104	0.272824
$118$	−18.7427	−1.72541
$119$	0	0
$120$	−14.7139	−1.34319
$121$	3.33085	0.302805
$122$	−6.61124	−0.598554
$123$	1.30535	0.117700
$124$	−23.8841	−2.14486
$125$	−6.14395	−0.549532
$126$	0	0
$127$	−18.5788	−1.64860	−0.824300	−	0.566153i	$-0.808431\pi$
$127$	−18.5788	−1.64860	−0.824300	+	0.566153i	$0.808431\pi$
$128$	−18.2854	−1.61622
$129$	−10.0565	−0.885428
$130$	20.4029	1.78945
$131$	5.67791	0.496081	0.248041	−	0.968750i	$-0.420213\pi$
$131$	5.67791	0.496081	0.248041	+	0.968750i	$0.420213\pi$
$132$	−15.6277	−1.36022
$133$	0	0
$134$	24.9186	2.15264
$135$	−2.79287	−0.240372
$136$	18.2472	1.56468
$137$	−8.84364	−0.755563	−0.377782	−	0.925895i	$-0.623313\pi$
$137$	−8.84364	−0.755563	−0.377782	+	0.925895i	$0.623313\pi$
$138$	9.37135	0.797743
$139$	7.64569	0.648499	0.324249	−	0.945972i	$-0.394888\pi$
$139$	7.64569	0.648499	0.324249	+	0.945972i	$0.394888\pi$
$140$	0	0
$141$	−6.99274	−0.588895
$142$	25.2867	2.12201
$143$	11.1715	0.934207
$144$	4.78561	0.398801
$145$	−18.3729	−1.52578
$146$	−13.9760	−1.15666
$147$	0	0
$148$	−40.6303	−3.33979
$149$	4.01452	0.328882	0.164441	−	0.986387i	$-0.447418\pi$
$149$	4.01452	0.328882	0.164441	+	0.986387i	$0.447418\pi$
$150$	−6.93178	−0.565977
$151$	13.0675	1.06342	0.531709	−	0.846927i	$-0.321550\pi$
$151$	13.0675	1.06342	0.531709	+	0.846927i	$0.321550\pi$
$152$	−5.26839	−0.427323
$153$	3.46352	0.280009
$154$	0	0
$155$	−16.1585	−1.29788
$156$	−12.1825	−0.975378
$157$	−23.7442	−1.89499	−0.947497	−	0.319764i	$-0.896396\pi$
$157$	−23.7442	−1.89499	−0.947497	+	0.319764i	$0.896396\pi$
$158$	40.4064	3.21456
$159$	4.63843	0.367851
$160$	3.65892	0.289263
$161$	0	0
$162$	2.47552	0.194495
$163$	15.0170	1.17623	0.588113	−	0.808779i	$-0.299871\pi$
$163$	15.0170	1.17623	0.588113	+	0.808779i	$0.299871\pi$
$164$	−5.38876	−0.420791
$165$	−10.5727	−0.823086
$166$	21.4205	1.66256
$167$	−3.48782	−0.269896	−0.134948	−	0.990853i	$-0.543087\pi$
$167$	−3.48782	−0.269896	−0.134948	+	0.990853i	$0.543087\pi$
$168$	0	0
$169$	−4.29137	−0.330105
$170$	23.9461	1.83658
$171$	−1.00000	−0.0764719
$172$	41.5153	3.16551
$173$	−8.87658	−0.674874	−0.337437	−	0.941348i	$-0.609560\pi$
$173$	−8.87658	−0.674874	−0.337437	+	0.941348i	$0.609560\pi$
$174$	16.2852	1.23457
$175$	0	0
$176$	18.1165	1.36558
$177$	7.57122	0.569088
$178$	−30.8867	−2.31505
$179$	−24.0423	−1.79701	−0.898503	−	0.438967i	$-0.855344\pi$
$179$	−24.0423	−1.79701	−0.898503	+	0.438967i	$0.855344\pi$
$180$	11.5295	0.859360
$181$	18.1645	1.35016	0.675079	−	0.737745i	$-0.264109\pi$
$181$	18.1645	1.35016	0.675079	+	0.737745i	$0.264109\pi$
$182$	0	0
$183$	2.67065	0.197420
$184$	−19.9441	−1.47030
$185$	−27.4878	−2.02094
$186$	14.3224	1.05017
$187$	13.1115	0.958811
$188$	28.8674	2.10537
$189$	0	0
$190$	−6.91381	−0.501580
$191$	5.05502	0.365768	0.182884	−	0.983134i	$-0.441457\pi$
$191$	5.05502	0.365768	0.182884	+	0.983134i	$0.441457\pi$
$192$	6.32806	0.456689
$193$	−17.4134	−1.25344	−0.626720	−	0.779244i	$-0.715603\pi$
$193$	−17.4134	−1.25344	−0.626720	+	0.779244i	$0.715603\pi$
$194$	41.2476	2.96140
$195$	−8.24187	−0.590213
$196$	0	0
$197$	−18.7457	−1.33558	−0.667789	−	0.744351i	$-0.732759\pi$
$197$	−18.7457	−1.33558	−0.667789	+	0.744351i	$0.732759\pi$
$198$	9.37135	0.665993
$199$	17.1570	1.21623	0.608113	−	0.793851i	$-0.291927\pi$
$199$	17.1570	1.21623	0.608113	+	0.793851i	$0.291927\pi$
$200$	14.7522	1.04314
$201$	−10.0660	−0.710001
$202$	10.1687	0.715467
$203$	0	0
$204$	−14.2981	−1.00107
$205$	−3.64569	−0.254626
$206$	−45.5863	−3.17615
$207$	−3.78561	−0.263118
$208$	14.1225	0.979221
$209$	−3.78561	−0.261856
$210$	0	0
$211$	3.49070	0.240310	0.120155	−	0.992755i	$-0.461661\pi$
$211$	3.49070	0.240310	0.120155	+	0.992755i	$0.461661\pi$
$212$	−19.1483	−1.31511
$213$	−10.2147	−0.699899
$214$	−8.94386	−0.611390
$215$	28.0866	1.91549
$216$	−5.26839	−0.358469
$217$	0	0
$218$	9.86613	0.668219
$219$	5.64569	0.381500
$220$	43.6463	2.94263
$221$	10.2210	0.687538
$222$	24.3644	1.63523
$223$	7.55569	0.505966	0.252983	−	0.967471i	$-0.418588\pi$
$223$	7.55569	0.505966	0.252983	+	0.967471i	$0.418588\pi$
$224$	0	0
$225$	2.80013	0.186675
$226$	−4.00531	−0.266429
$227$	14.4983	0.962284	0.481142	−	0.876643i	$-0.340222\pi$
$227$	14.4983	0.962284	0.481142	+	0.876643i	$0.340222\pi$
$228$	4.12820	0.273396
$229$	−4.97504	−0.328760	−0.164380	−	0.986397i	$-0.552562\pi$
$229$	−4.97504	−0.328760	−0.164380	+	0.986397i	$0.552562\pi$
$230$	−26.1730	−1.72580
$231$	0	0
$232$	−34.6580	−2.27541
$233$	7.70563	0.504812	0.252406	−	0.967621i	$-0.418778\pi$
$233$	7.70563	0.504812	0.252406	+	0.967621i	$0.418778\pi$
$234$	7.30535	0.477566
$235$	19.5298	1.27399
$236$	−31.2555	−2.03456
$237$	−16.3224	−1.06025
$238$	0	0
$239$	16.6438	1.07660	0.538298	−	0.842755i	$-0.319067\pi$
$239$	16.6438	1.07660	0.538298	+	0.842755i	$0.319067\pi$
$240$	−13.3656	−0.862746
$241$	−25.6227	−1.65050	−0.825252	−	0.564765i	$-0.808967\pi$
$241$	−25.6227	−1.65050	−0.825252	+	0.564765i	$0.808967\pi$
$242$	8.24559	0.530047
$243$	−1.00000	−0.0641500
$244$	−11.0250	−0.705801
$245$	0	0
$246$	3.23143	0.206028
$247$	−2.95104	−0.187770
$248$	−30.4809	−1.93554
$249$	−8.65295	−0.548358
$250$	−15.2095	−0.961931
$251$	−22.9933	−1.45133	−0.725664	−	0.688050i	$-0.758467\pi$
$251$	−22.9933	−1.45133	−0.725664	+	0.688050i	$0.758467\pi$
$252$	0	0
$253$	−14.3309	−0.900973
$254$	−45.9921	−2.88580
$255$	−9.67317	−0.605757
$256$	−32.6098	−2.03811
$257$	−18.8911	−1.17839	−0.589197	−	0.807989i	$-0.700556\pi$
$257$	−18.8911	−1.17839	−0.589197	+	0.807989i	$0.700556\pi$
$258$	−24.8951	−1.54990
$259$	0	0
$260$	34.0241	2.11008
$261$	−6.57848	−0.407198
$262$	14.0558	0.868369
$263$	10.7127	0.660570	0.330285	−	0.943881i	$-0.392855\pi$
$263$	10.7127	0.660570	0.330285	+	0.943881i	$0.392855\pi$
$264$	−19.9441	−1.22747
$265$	−12.9545	−0.795790
$266$	0	0
$267$	12.4768	0.763570
$268$	41.5544	2.53834
$269$	19.4039	1.18308	0.591538	−	0.806277i	$-0.298521\pi$
$269$	19.4039	1.18308	0.591538	+	0.806277i	$0.298521\pi$
$270$	−6.91381	−0.420761
$271$	−0.289866	−0.0176081	−0.00880407	−	0.999961i	$-0.502802\pi$
$271$	−0.289866	−0.0176081	−0.00880407	+	0.999961i	$0.502802\pi$
$272$	16.5751	1.00501
$273$	0	0
$274$	−21.8926	−1.32258
$275$	10.6002	0.639217
$276$	15.6277	0.940680
$277$	1.47228	0.0884610	0.0442305	−	0.999021i	$-0.485916\pi$
$277$	1.47228	0.0884610	0.0442305	+	0.999021i	$0.485916\pi$
$278$	18.9270	1.13517
$279$	−5.78561	−0.346376
$280$	0	0
$281$	22.8494	1.36308	0.681540	−	0.731781i	$-0.261310\pi$
$281$	22.8494	1.36308	0.681540	+	0.731781i	$0.261310\pi$
$282$	−17.3107	−1.03083
$283$	1.04392	0.0620545	0.0310272	−	0.999519i	$-0.490122\pi$
$283$	1.04392	0.0620545	0.0310272	+	0.999519i	$0.490122\pi$
$284$	42.1682	2.50223
$285$	2.79287	0.165435
$286$	27.6552	1.63529
$287$	0	0
$288$	1.31009	0.0771979
$289$	−5.00402	−0.294354
$290$	−45.4824	−2.67082
$291$	−16.6622	−0.976755
$292$	−23.3065	−1.36391
$293$	23.5062	1.37325	0.686625	−	0.727012i	$-0.259092\pi$
$293$	23.5062	1.37325	0.686625	+	0.727012i	$0.259092\pi$
$294$	0	0
$295$	−21.1455	−1.23114
$296$	−51.8522	−3.01385
$297$	−3.78561	−0.219663
$298$	9.93802	0.575694
$299$	−11.1715	−0.646064
$300$	−11.5595	−0.667388
$301$	0	0
$302$	32.3489	1.86147
$303$	−4.10770	−0.235981
$304$	−4.78561	−0.274474
$305$	−7.45878	−0.427089
$306$	8.57401	0.490144
$307$	−25.5898	−1.46049	−0.730243	−	0.683188i	$-0.760593\pi$
$307$	−25.5898	−1.46049	−0.730243	+	0.683188i	$0.760593\pi$
$308$	0	0
$309$	18.4149	1.04758
$310$	−40.0006	−2.27188
$311$	6.94732	0.393946	0.196973	−	0.980409i	$-0.436889\pi$
$311$	6.94732	0.393946	0.196973	+	0.980409i	$0.436889\pi$
$312$	−15.5472	−0.880188
$313$	6.24187	0.352811	0.176406	−	0.984318i	$-0.443553\pi$
$313$	6.24187	0.352811	0.176406	+	0.984318i	$0.443553\pi$
$314$	−58.7793	−3.31711
$315$	0	0
$316$	67.3820	3.79054
$317$	−18.8114	−1.05655	−0.528277	−	0.849072i	$-0.677162\pi$
$317$	−18.8114	−1.05655	−0.528277	+	0.849072i	$0.677162\pi$
$318$	11.4825	0.643907
$319$	−24.9036	−1.39433
$320$	−17.6735	−0.987977
$321$	3.61292	0.201654
$322$	0	0
$323$	−3.46352	−0.192715
$324$	4.12820	0.229344
$325$	8.26330	0.458365
$326$	37.1750	2.05893
$327$	−3.98548	−0.220398
$328$	−6.87711	−0.379725
$329$	0	0
$330$	−26.1730	−1.44078
$331$	−27.2974	−1.50040	−0.750201	−	0.661210i	$-0.770043\pi$
$331$	−27.2974	−1.50040	−0.750201	+	0.661210i	$0.770043\pi$
$332$	35.7211	1.96045
$333$	−9.84214	−0.539346
$334$	−8.63417	−0.472441
$335$	28.1130	1.53598
$336$	0	0
$337$	7.56679	0.412189	0.206095	−	0.978532i	$-0.433925\pi$
$337$	7.56679	0.412189	0.206095	+	0.978532i	$0.433925\pi$
$338$	−10.6234	−0.577835
$339$	1.61797	0.0878759
$340$	39.9327	2.16566
$341$	−21.9021	−1.18606
$342$	−2.47552	−0.133861
$343$	0	0
$344$	52.9817	2.85658
$345$	10.5727	0.569216
$346$	−21.9741	−1.18134
$347$	−14.0331	−0.753334	−0.376667	−	0.926349i	$-0.622930\pi$
$347$	−14.0331	−0.753334	−0.376667	+	0.926349i	$0.622930\pi$
$348$	27.1573	1.45578
$349$	18.5608	0.993536	0.496768	−	0.867883i	$-0.334520\pi$
$349$	18.5608	0.993536	0.496768	+	0.867883i	$0.334520\pi$
$350$	0	0
$351$	−2.95104	−0.157515
$352$	4.95950	0.264342
$353$	−33.2917	−1.77194	−0.885970	−	0.463742i	$-0.846506\pi$
$353$	−33.2917	−1.77194	−0.885970	+	0.463742i	$0.846506\pi$
$354$	18.7427	0.996164
$355$	28.5283	1.51413
$356$	−51.5068	−2.72986
$357$	0	0
$358$	−59.5172	−3.14558
$359$	−13.1560	−0.694345	−0.347172	−	0.937801i	$-0.612858\pi$
$359$	−13.1560	−0.694345	−0.347172	+	0.937801i	$0.612858\pi$
$360$	14.7139	0.775493
$361$	1.00000	0.0526316
$362$	44.9666	2.36339
$363$	−3.33085	−0.174825
$364$	0	0
$365$	−15.7677	−0.825318
$366$	6.61124	0.345575
$367$	10.4143	0.543620	0.271810	−	0.962351i	$-0.412378\pi$
$367$	10.4143	0.543620	0.271810	+	0.962351i	$0.412378\pi$
$368$	−18.1165	−0.944386
$369$	−1.30535	−0.0679540
$370$	−68.0466	−3.53758
$371$	0	0
$372$	23.8841	1.23833
$373$	34.6157	1.79234	0.896168	−	0.443715i	$-0.146340\pi$
$373$	34.6157	1.79234	0.896168	+	0.443715i	$0.146340\pi$
$374$	32.4579	1.67836
$375$	6.14395	0.317272
$376$	36.8405	1.89990
$377$	−19.4134	−0.999839
$378$	0	0
$379$	−24.2100	−1.24358	−0.621791	−	0.783183i	$-0.713595\pi$
$379$	−24.2100	−1.24358	−0.621791	+	0.783183i	$0.713595\pi$
$380$	−11.5295	−0.591452
$381$	18.5788	0.951820
$382$	12.5138	0.640262
$383$	−3.48782	−0.178219	−0.0891097	−	0.996022i	$-0.528402\pi$
$383$	−3.48782	−0.178219	−0.0891097	+	0.996022i	$0.528402\pi$
$384$	18.2854	0.933124
$385$	0	0
$386$	−43.1071	−2.19409
$387$	10.0565	0.511202
$388$	68.7848	3.49202
$389$	6.16741	0.312700	0.156350	−	0.987702i	$-0.450027\pi$
$389$	6.16741	0.312700	0.156350	+	0.987702i	$0.450027\pi$
$390$	−20.4029	−1.03314
$391$	−13.1115	−0.663079
$392$	0	0
$393$	−5.67791	−0.286413
$394$	−46.4054	−2.33787
$395$	45.5863	2.29370
$396$	15.6277	0.785324
$397$	11.5023	0.577286	0.288643	−	0.957437i	$-0.406796\pi$
$397$	11.5023	0.577286	0.288643	+	0.957437i	$0.406796\pi$
$398$	42.4724	2.12895
$399$	0	0
$400$	13.4003	0.670017
$401$	15.9942	0.798714	0.399357	−	0.916795i	$-0.369233\pi$
$401$	15.9942	0.798714	0.399357	+	0.916795i	$0.369233\pi$
$402$	−24.9186	−1.24283
$403$	−17.0736	−0.850495
$404$	16.9574	0.843662
$405$	2.79287	0.138779
$406$	0	0
$407$	−37.2585	−1.84684
$408$	−18.2472	−0.903370
$409$	6.62319	0.327496	0.163748	−	0.986502i	$-0.447642\pi$
$409$	6.62319	0.327496	0.163748	+	0.986502i	$0.447642\pi$
$410$	−9.02496	−0.445711
$411$	8.84364	0.436225
$412$	−76.0202	−3.74524
$413$	0	0
$414$	−9.37135	−0.460577
$415$	24.1666	1.18629
$416$	3.86613	0.189553
$417$	−7.64569	−0.374411
$418$	−9.37135	−0.458368
$419$	35.8219	1.75001	0.875006	−	0.484112i	$-0.160857\pi$
$419$	35.8219	1.75001	0.875006	+	0.484112i	$0.160857\pi$
$420$	0	0
$421$	−11.2959	−0.550527	−0.275264	−	0.961369i	$-0.588765\pi$
$421$	−11.2959	−0.550527	−0.275264	+	0.961369i	$0.588765\pi$
$422$	8.64130	0.420652
$423$	6.99274	0.339999
$424$	−24.4370	−1.18677
$425$	9.69831	0.470437
$426$	−25.2867	−1.22514
$427$	0	0
$428$	−14.9149	−0.720937
$429$	−11.1715	−0.539364
$430$	69.5289	3.35298
$431$	−3.26118	−0.157086	−0.0785428	−	0.996911i	$-0.525027\pi$
$431$	−3.26118	−0.157086	−0.0785428	+	0.996911i	$0.525027\pi$
$432$	−4.78561	−0.230248
$433$	12.9242	0.621096	0.310548	−	0.950558i	$-0.399488\pi$
$433$	12.9242	0.621096	0.310548	+	0.950558i	$0.399488\pi$
$434$	0	0
$435$	18.3729	0.880911
$436$	16.4528	0.787948
$437$	3.78561	0.181090
$438$	13.9760	0.667799
$439$	10.3464	0.493806	0.246903	−	0.969040i	$-0.420587\pi$
$439$	10.3464	0.493806	0.246903	+	0.969040i	$0.420587\pi$
$440$	55.7013	2.65545
$441$	0	0
$442$	25.3022	1.20351
$443$	−18.5996	−0.883694	−0.441847	−	0.897090i	$-0.645677\pi$
$443$	−18.5996	−0.883694	−0.441847	+	0.897090i	$0.645677\pi$
$444$	40.6303	1.92823
$445$	−34.8462	−1.65187
$446$	18.7042	0.885672
$447$	−4.01452	−0.189880
$448$	0	0
$449$	−8.75147	−0.413008	−0.206504	−	0.978446i	$-0.566209\pi$
$449$	−8.75147	−0.413008	−0.206504	+	0.978446i	$0.566209\pi$
$450$	6.93178	0.326767
$451$	−4.94156	−0.232689
$452$	−6.67929	−0.314167
$453$	−13.0675	−0.613965
$454$	35.8907	1.68444
$455$	0	0
$456$	5.26839	0.246715
$457$	−13.6043	−0.636382	−0.318191	−	0.948027i	$-0.603075\pi$
$457$	−13.6043	−0.636382	−0.318191	+	0.948027i	$0.603075\pi$
$458$	−12.3158	−0.575479
$459$	−3.46352	−0.161663
$460$	−43.6463	−2.03502
$461$	41.6461	1.93965	0.969825	−	0.243802i	$-0.0783946\pi$
$461$	41.6461	1.93965	0.969825	+	0.243802i	$0.0783946\pi$
$462$	0	0
$463$	20.5128	0.953310	0.476655	−	0.879090i	$-0.341849\pi$
$463$	20.5128	0.953310	0.476655	+	0.879090i	$0.341849\pi$
$464$	−31.4821	−1.46152
$465$	16.1585	0.749331
$466$	19.0754	0.883652
$467$	−0.604951	−0.0279938	−0.0139969	−	0.999902i	$-0.504455\pi$
$467$	−0.604951	−0.0279938	−0.0139969	+	0.999902i	$0.504455\pi$
$468$	12.1825	0.563135
$469$	0	0
$470$	48.3465	2.23006
$471$	23.7442	1.09408
$472$	−39.8882	−1.83600
$473$	38.0701	1.75046
$474$	−40.4064	−1.85593
$475$	−2.80013	−0.128479
$476$	0	0
$477$	−4.63843	−0.212379
$478$	41.2020	1.88453
$479$	−22.2962	−1.01874	−0.509370	−	0.860547i	$-0.670122\pi$
$479$	−22.2962	−1.01874	−0.509370	+	0.860547i	$0.670122\pi$
$480$	−3.65892	−0.167006
$481$	−29.0445	−1.32432
$482$	−63.4295	−2.88913
$483$	0	0
$484$	13.7504	0.625019
$485$	46.5354	2.11306
$486$	−2.47552	−0.112292
$487$	40.9102	1.85382	0.926910	−	0.375283i	$-0.122455\pi$
$487$	40.9102	1.85382	0.926910	+	0.375283i	$0.122455\pi$
$488$	−14.0700	−0.636920
$489$	−15.0170	−0.679094
$490$	0	0
$491$	20.9135	0.943815	0.471907	−	0.881648i	$-0.343566\pi$
$491$	20.9135	0.943815	0.471907	+	0.881648i	$0.343566\pi$
$492$	5.38876	0.242944
$493$	−22.7847	−1.02617
$494$	−7.30535	−0.328683
$495$	10.5727	0.475209
$496$	−27.6877	−1.24321
$497$	0	0
$498$	−21.4205	−0.959877
$499$	−43.8882	−1.96470	−0.982352	−	0.187042i	$-0.940110\pi$
$499$	−43.8882	−1.96470	−0.982352	+	0.187042i	$0.940110\pi$
$500$	−25.3634	−1.13429
$501$	3.48782	0.155824
$502$	−56.9205	−2.54049
$503$	11.6749	0.520558	0.260279	−	0.965533i	$-0.416185\pi$
$503$	11.6749	0.520558	0.260279	+	0.965533i	$0.416185\pi$
$504$	0	0
$505$	11.4723	0.510510
$506$	−35.4763	−1.57711
$507$	4.29137	0.190586
$508$	−76.6969	−3.40287
$509$	6.89110	0.305442	0.152721	−	0.988269i	$-0.451196\pi$
$509$	6.89110	0.305442	0.152721	+	0.988269i	$0.451196\pi$
$510$	−23.9461	−1.06035
$511$	0	0
$512$	−44.1554	−1.95141
$513$	1.00000	0.0441511
$514$	−46.7653	−2.06273
$515$	−51.4303	−2.26629
$516$	−41.5153	−1.82761
$517$	26.4718	1.16423
$518$	0	0
$519$	8.87658	0.389638
$520$	43.4214	1.90415
$521$	−13.1929	−0.577992	−0.288996	−	0.957330i	$-0.593321\pi$
$521$	−13.1929	−0.577992	−0.288996	+	0.957330i	$0.593321\pi$
$522$	−16.2852	−0.712782
$523$	24.4334	1.06840	0.534199	−	0.845359i	$-0.320613\pi$
$523$	24.4334	1.06840	0.534199	+	0.845359i	$0.320613\pi$
$524$	23.4395	1.02396
$525$	0	0
$526$	26.5194	1.15630
$527$	−20.0386	−0.872895
$528$	−18.1165	−0.788418
$529$	−8.66915	−0.376919
$530$	−32.0692	−1.39300
$531$	−7.57122	−0.328563
$532$	0	0
$533$	−3.85215	−0.166855
$534$	30.8867	1.33660
$535$	−10.0904	−0.436247
$536$	53.0316	2.29062
$537$	24.0423	1.03750
$538$	48.0347	2.07092
$539$	0	0
$540$	−11.5295	−0.496152
$541$	−18.3639	−0.789524	−0.394762	−	0.918783i	$-0.629173\pi$
$541$	−18.3639	−0.789524	−0.394762	+	0.918783i	$0.629173\pi$
$542$	−0.717570	−0.0308223
$543$	−18.1645	−0.779515
$544$	4.53753	0.194545
$545$	11.1309	0.476797
$546$	0	0
$547$	24.4423	1.04508	0.522538	−	0.852616i	$-0.324985\pi$
$547$	24.4423	1.04508	0.522538	+	0.852616i	$0.324985\pi$
$548$	−36.5083	−1.55956
$549$	−2.67065	−0.113981
$550$	26.2410	1.11892
$551$	6.57848	0.280253
$552$	19.9441	0.848876
$553$	0	0
$554$	3.64467	0.154847
$555$	27.4878	1.16679
$556$	31.5629	1.33856
$557$	25.1431	1.06535	0.532673	−	0.846321i	$-0.321188\pi$
$557$	25.1431	1.06535	0.532673	+	0.846321i	$0.321188\pi$
$558$	−14.3224	−0.606315
$559$	29.6772	1.25521
$560$	0	0
$561$	−13.1115	−0.553570
$562$	56.5641	2.38601
$563$	−41.8547	−1.76396	−0.881982	−	0.471282i	$-0.843791\pi$
$563$	−41.8547	−1.76396	−0.881982	+	0.471282i	$0.843791\pi$
$564$	−28.8674	−1.21554
$565$	−4.51878	−0.190106
$566$	2.58424	0.108624
$567$	0	0
$568$	53.8150	2.25803
$569$	−13.5087	−0.566314	−0.283157	−	0.959074i	$-0.591382\pi$
$569$	−13.5087	−0.566314	−0.283157	+	0.959074i	$0.591382\pi$
$570$	6.91381	0.289588
$571$	−18.2950	−0.765621	−0.382811	−	0.923827i	$-0.625044\pi$
$571$	−18.2950	−0.765621	−0.382811	+	0.923827i	$0.625044\pi$
$572$	46.1181	1.92829
$573$	−5.05502	−0.211177
$574$	0	0
$575$	−10.6002	−0.442059
$576$	−6.32806	−0.263669
$577$	−6.36176	−0.264843	−0.132422	−	0.991193i	$-0.542275\pi$
$577$	−6.36176	−0.264843	−0.132422	+	0.991193i	$0.542275\pi$
$578$	−12.3876	−0.515254
$579$	17.4134	0.723674
$580$	−75.8468	−3.14937
$581$	0	0
$582$	−41.2476	−1.70977
$583$	−17.5593	−0.727231
$584$	−29.7437	−1.23080
$585$	8.24187	0.340759
$586$	58.1901	2.40381
$587$	−6.03283	−0.249002	−0.124501	−	0.992220i	$-0.539733\pi$
$587$	−6.03283	−0.249002	−0.124501	+	0.992220i	$0.539733\pi$
$588$	0	0
$589$	5.78561	0.238392
$590$	−52.3460	−2.15505
$591$	18.7457	0.771096
$592$	−47.1006	−1.93582
$593$	−1.72675	−0.0709091	−0.0354545	−	0.999371i	$-0.511288\pi$
$593$	−1.72675	−0.0709091	−0.0354545	+	0.999371i	$0.511288\pi$
$594$	−9.37135	−0.384511
$595$	0	0
$596$	16.5727	0.678845
$597$	−17.1570	−0.702188
$598$	−27.6552	−1.13091
$599$	−15.6426	−0.639138	−0.319569	−	0.947563i	$-0.603538\pi$
$599$	−15.6426	−0.639138	−0.319569	+	0.947563i	$0.603538\pi$
$600$	−14.7522	−0.602256
$601$	−6.52825	−0.266293	−0.133146	−	0.991096i	$-0.542508\pi$
$601$	−6.52825	−0.266293	−0.133146	+	0.991096i	$0.542508\pi$
$602$	0	0
$603$	10.0660	0.409919
$604$	53.9452	2.19500
$605$	9.30265	0.378206
$606$	−10.1687	−0.413075
$607$	−15.5712	−0.632016	−0.316008	−	0.948756i	$-0.602343\pi$
$607$	−15.5712	−0.632016	−0.316008	+	0.948756i	$0.602343\pi$
$608$	−1.31009	−0.0531313
$609$	0	0
$610$	−18.4644	−0.747600
$611$	20.6358	0.834837
$612$	14.2981	0.577966
$613$	−15.7931	−0.637875	−0.318938	−	0.947776i	$-0.603326\pi$
$613$	−15.7931	−0.637875	−0.318938	+	0.947776i	$0.603326\pi$
$614$	−63.3480	−2.55652
$615$	3.64569	0.147008
$616$	0	0
$617$	−9.95201	−0.400653	−0.200326	−	0.979729i	$-0.564200\pi$
$617$	−9.95201	−0.400653	−0.200326	+	0.979729i	$0.564200\pi$
$618$	45.5863	1.83375
$619$	−24.6183	−0.989494	−0.494747	−	0.869037i	$-0.664739\pi$
$619$	−24.6183	−0.989494	−0.494747	+	0.869037i	$0.664739\pi$
$620$	−66.7053	−2.67895
$621$	3.78561	0.151911
$622$	17.1982	0.689586
$623$	0	0
$624$	−14.1225	−0.565353
$625$	−31.1599	−1.24640
$626$	15.4519	0.617581
$627$	3.78561	0.151183
$628$	−98.0208	−3.91145
$629$	−34.0884	−1.35920
$630$	0	0
$631$	−20.1186	−0.800908	−0.400454	−	0.916317i	$-0.631148\pi$
$631$	−20.1186	−0.800908	−0.400454	+	0.916317i	$0.631148\pi$
$632$	85.9927	3.42061
$633$	−3.49070	−0.138743
$634$	−46.5680	−1.84945
$635$	−51.8882	−2.05912
$636$	19.1483	0.759281
$637$	0	0
$638$	−61.6493	−2.44072
$639$	10.2147	0.404087
$640$	−51.0689	−2.01867
$641$	19.1271	0.755477	0.377738	−	0.925912i	$-0.376702\pi$
$641$	19.1271	0.755477	0.377738	+	0.925912i	$0.376702\pi$
$642$	8.94386	0.352986
$643$	16.5614	0.653117	0.326559	−	0.945177i	$-0.394111\pi$
$643$	16.5614	0.653117	0.326559	+	0.945177i	$0.394111\pi$
$644$	0	0
$645$	−28.0866	−1.10591
$646$	−8.57401	−0.337340
$647$	−14.8735	−0.584736	−0.292368	−	0.956306i	$-0.594443\pi$
$647$	−14.8735	−0.584736	−0.292368	+	0.956306i	$0.594443\pi$
$648$	5.26839	0.206962
$649$	−28.6617	−1.12507
$650$	20.4560	0.802348
$651$	0	0
$652$	61.9933	2.42784
$653$	29.6843	1.16164	0.580818	−	0.814034i	$-0.302733\pi$
$653$	29.6843	1.16164	0.580818	+	0.814034i	$0.302733\pi$
$654$	−9.86613	−0.385796
$655$	15.8577	0.619611
$656$	−6.24692	−0.243901
$657$	−5.64569	−0.220259
$658$	0	0
$659$	44.9939	1.75271	0.876356	−	0.481663i	$-0.159967\pi$
$659$	44.9939	1.75271	0.876356	+	0.481663i	$0.159967\pi$
$660$	−43.6463	−1.69893
$661$	−10.2994	−0.400601	−0.200300	−	0.979735i	$-0.564192\pi$
$661$	−10.2994	−0.400601	−0.200300	+	0.979735i	$0.564192\pi$
$662$	−67.5753	−2.62639
$663$	−10.2210	−0.396950
$664$	45.5871	1.76912
$665$	0	0
$666$	−24.3644	−0.944101
$667$	24.9036	0.964271
$668$	−14.3984	−0.557091
$669$	−7.55569	−0.292120
$670$	69.5944	2.68867
$671$	−10.1100	−0.390294
$672$	0	0
$673$	−34.4268	−1.32706	−0.663528	−	0.748151i	$-0.730942\pi$
$673$	−34.4268	−1.32706	−0.663528	+	0.748151i	$0.730942\pi$
$674$	18.7317	0.721519
$675$	−2.80013	−0.107777
$676$	−17.7156	−0.681370
$677$	24.0845	0.925644	0.462822	−	0.886451i	$-0.346837\pi$
$677$	24.0845	0.925644	0.462822	+	0.886451i	$0.346837\pi$
$678$	4.00531	0.153823
$679$	0	0
$680$	50.9620	1.95430
$681$	−14.4983	−0.555575
$682$	−54.2190	−2.07615
$683$	27.7740	1.06274	0.531371	−	0.847139i	$-0.321677\pi$
$683$	27.7740	1.06274	0.531371	+	0.847139i	$0.321677\pi$
$684$	−4.12820	−0.157846
$685$	−24.6991	−0.943706
$686$	0	0
$687$	4.97504	0.189809
$688$	48.1266	1.83481
$689$	−13.6882	−0.521478
$690$	26.1730	0.996389
$691$	−10.3108	−0.392240	−0.196120	−	0.980580i	$-0.562834\pi$
$691$	−10.3108	−0.392240	−0.196120	+	0.980580i	$0.562834\pi$
$692$	−36.6443	−1.39301
$693$	0	0
$694$	−34.7391	−1.31868
$695$	21.3534	0.809981
$696$	34.6580	1.31371
$697$	−4.52112	−0.171250
$698$	45.9476	1.73914
$699$	−7.70563	−0.291454
$700$	0	0
$701$	44.5279	1.68180	0.840898	−	0.541194i	$-0.182027\pi$
$701$	44.5279	1.68180	0.840898	+	0.541194i	$0.182027\pi$
$702$	−7.30535	−0.275723
$703$	9.84214	0.371203
$704$	−23.9556	−0.902860
$705$	−19.5298	−0.735536
$706$	−82.4144	−3.10171
$707$	0	0
$708$	31.2555	1.17465
$709$	−4.54968	−0.170867	−0.0854333	−	0.996344i	$-0.527227\pi$
$709$	−4.54968	−0.170867	−0.0854333	+	0.996344i	$0.527227\pi$
$710$	70.6224	2.65041
$711$	16.3224	0.612138
$712$	−65.7329	−2.46344
$713$	21.9021	0.820239
$714$	0	0
$715$	31.2005	1.16683
$716$	−99.2514	−3.70920
$717$	−16.6438	−0.621573
$718$	−32.5678	−1.21542
$719$	−41.8280	−1.55992	−0.779961	−	0.625828i	$-0.784761\pi$
$719$	−41.8280	−1.55992	−0.779961	+	0.625828i	$0.784761\pi$
$720$	13.3656	0.498106
$721$	0	0
$722$	2.47552	0.0921293
$723$	25.6227	0.952919
$724$	74.9867	2.78686
$725$	−18.4206	−0.684125
$726$	−8.24559	−0.306023
$727$	14.0599	0.521454	0.260727	−	0.965413i	$-0.416038\pi$
$727$	14.0599	0.521454	0.260727	+	0.965413i	$0.416038\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−39.0332	−1.44468
$731$	34.8310	1.28827
$732$	11.0250	0.407494
$733$	48.0247	1.77383	0.886916	−	0.461931i	$-0.152843\pi$
$733$	48.0247	1.77383	0.886916	+	0.461931i	$0.152843\pi$
$734$	25.7807	0.951583
$735$	0	0
$736$	−4.95950	−0.182810
$737$	38.1060	1.40365
$738$	−3.23143	−0.118951
$739$	−16.4354	−0.604585	−0.302292	−	0.953215i	$-0.597752\pi$
$739$	−16.4354	−0.604585	−0.302292	+	0.953215i	$0.597752\pi$
$740$	−113.475	−4.17143
$741$	2.95104	0.108409
$742$	0	0
$743$	−0.154749	−0.00567720	−0.00283860	−	0.999996i	$-0.500904\pi$
$743$	−0.154749	−0.00567720	−0.00283860	+	0.999996i	$0.500904\pi$
$744$	30.4809	1.11748
$745$	11.2120	0.410777
$746$	85.6920	3.13741
$747$	8.65295	0.316595
$748$	54.1270	1.97908
$749$	0	0
$750$	15.2095	0.555371
$751$	19.4162	0.708509	0.354254	−	0.935149i	$-0.384735\pi$
$751$	19.4162	0.708509	0.354254	+	0.935149i	$0.384735\pi$
$752$	33.4645	1.22033
$753$	22.9933	0.837924
$754$	−48.0581	−1.75017
$755$	36.4959	1.32822
$756$	0	0
$757$	22.8406	0.830157	0.415078	−	0.909786i	$-0.363754\pi$
$757$	22.8406	0.830157	0.415078	+	0.909786i	$0.363754\pi$
$758$	−59.9322	−2.17684
$759$	14.3309	0.520177
$760$	−14.7139	−0.533731
$761$	4.80800	0.174290	0.0871449	−	0.996196i	$-0.472226\pi$
$761$	4.80800	0.174290	0.0871449	+	0.996196i	$0.472226\pi$
$762$	45.9921	1.66612
$763$	0	0
$764$	20.8681	0.754982
$765$	9.67317	0.349734
$766$	−8.63417	−0.311965
$767$	−22.3430	−0.806758
$768$	32.6098	1.17671
$769$	−22.6638	−0.817278	−0.408639	−	0.912696i	$-0.633996\pi$
$769$	−22.6638	−0.817278	−0.408639	+	0.912696i	$0.633996\pi$
$770$	0	0
$771$	18.8911	0.680346
$772$	−71.8858	−2.58723
$773$	−14.8266	−0.533277	−0.266639	−	0.963797i	$-0.585913\pi$
$773$	−14.8266	−0.533277	−0.266639	+	0.963797i	$0.585913\pi$
$774$	24.8951	0.894837
$775$	−16.2005	−0.581938
$776$	87.7829	3.15122
$777$	0	0
$778$	15.2675	0.547368
$779$	1.30535	0.0467691
$780$	−34.0241	−1.21826
$781$	38.6689	1.38368
$782$	−32.4579	−1.16069
$783$	6.57848	0.235096
$784$	0	0
$785$	−66.3145	−2.36687
$786$	−14.0558	−0.501353
$787$	−15.9675	−0.569181	−0.284591	−	0.958649i	$-0.591858\pi$
$787$	−15.9675	−0.569181	−0.284591	+	0.958649i	$0.591858\pi$
$788$	−77.3860	−2.75676
$789$	−10.7127	−0.381381
$790$	112.850	4.01502
$791$	0	0
$792$	19.9441	0.708682
$793$	−7.88119	−0.279869
$794$	28.4743	1.01051
$795$	12.9545	0.459450
$796$	70.8273	2.51041
$797$	10.7855	0.382042	0.191021	−	0.981586i	$-0.438820\pi$
$797$	10.7855	0.382042	0.191021	+	0.981586i	$0.438820\pi$
$798$	0	0
$799$	24.2195	0.856824
$800$	3.66843	0.129699
$801$	−12.4768	−0.440847
$802$	39.5941	1.39811
$803$	−21.3724	−0.754215
$804$	−41.5544	−1.46551
$805$	0	0
$806$	−42.2659	−1.48875
$807$	−19.4039	−0.683049
$808$	21.6410	0.761327
$809$	−46.8418	−1.64687	−0.823436	−	0.567410i	$-0.807946\pi$
$809$	−46.8418	−1.64687	−0.823436	+	0.567410i	$0.807946\pi$
$810$	6.91381	0.242926
$811$	5.30542	0.186299	0.0931493	−	0.995652i	$-0.470307\pi$
$811$	5.30542	0.186299	0.0931493	+	0.995652i	$0.470307\pi$
$812$	0	0
$813$	0.289866	0.0101661
$814$	−92.2341	−3.23281
$815$	41.9407	1.46912
$816$	−16.5751	−0.580243
$817$	−10.0565	−0.351833
$818$	16.3958	0.573267
$819$	0	0
$820$	−15.0501	−0.525572
$821$	22.5962	0.788612	0.394306	−	0.918979i	$-0.370985\pi$
$821$	22.5962	0.788612	0.394306	+	0.918979i	$0.370985\pi$
$822$	21.8926	0.763592
$823$	−33.6648	−1.17348	−0.586741	−	0.809775i	$-0.699589\pi$
$823$	−33.6648	−1.17348	−0.586741	+	0.809775i	$0.699589\pi$
$824$	−97.0167	−3.37974
$825$	−10.6002	−0.369052
$826$	0	0
$827$	41.4891	1.44272	0.721359	−	0.692561i	$-0.243518\pi$
$827$	41.4891	1.44272	0.721359	+	0.692561i	$0.243518\pi$
$828$	−15.6277	−0.543102
$829$	−29.8076	−1.03526	−0.517631	−	0.855604i	$-0.673186\pi$
$829$	−29.8076	−1.03526	−0.517631	+	0.855604i	$0.673186\pi$
$830$	59.8248	2.07655
$831$	−1.47228	−0.0510730
$832$	−18.6744	−0.647417
$833$	0	0
$834$	−18.9270	−0.655390
$835$	−9.74104	−0.337102
$836$	−15.6277	−0.540497
$837$	5.78561	0.199980
$838$	88.6777	3.06332
$839$	−16.7167	−0.577124	−0.288562	−	0.957461i	$-0.593177\pi$
$839$	−16.7167	−0.577124	−0.288562	+	0.957461i	$0.593177\pi$
$840$	0	0
$841$	14.2764	0.492291
$842$	−27.9632	−0.963674
$843$	−22.8494	−0.786975
$844$	14.4103	0.496023
$845$	−11.9852	−0.412305
$846$	17.3107	0.595153
$847$	0	0
$848$	−22.1977	−0.762272
$849$	−1.04392	−0.0358272
$850$	24.0084	0.823480
$851$	37.2585	1.27720
$852$	−42.1682	−1.44466
$853$	39.4543	1.35089	0.675446	−	0.737410i	$-0.263951\pi$
$853$	39.4543	1.35089	0.675446	+	0.737410i	$0.263951\pi$
$854$	0	0
$855$	−2.79287	−0.0955142
$856$	−19.0343	−0.650579
$857$	32.5858	1.11311	0.556555	−	0.830811i	$-0.312123\pi$
$857$	32.5858	1.11311	0.556555	+	0.830811i	$0.312123\pi$
$858$	−27.6552	−0.944134
$859$	−39.2555	−1.33938	−0.669690	−	0.742641i	$-0.733573\pi$
$859$	−39.2555	−1.33938	−0.669690	+	0.742641i	$0.733573\pi$
$860$	115.947	3.95376
$861$	0	0
$862$	−8.07312	−0.274972
$863$	47.8390	1.62846	0.814230	−	0.580543i	$-0.197160\pi$
$863$	47.8390	1.62846	0.814230	+	0.580543i	$0.197160\pi$
$864$	−1.31009	−0.0445702
$865$	−24.7911	−0.842924
$866$	31.9940	1.08720
$867$	5.00402	0.169946
$868$	0	0
$869$	61.7902	2.09609
$870$	45.4824	1.54200
$871$	29.7052	1.00652
$872$	20.9971	0.711050
$873$	16.6622	0.563930
$874$	9.37135	0.316991
$875$	0	0
$876$	23.3065	0.787454
$877$	−27.6813	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$877$	−27.6813	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$878$	25.6127	0.864386
$879$	−23.5062	−0.792846
$880$	50.5970	1.70562
$881$	17.7320	0.597407	0.298704	−	0.954346i	$-0.403446\pi$
$881$	17.7320	0.597407	0.298704	+	0.954346i	$0.403446\pi$
$882$	0	0
$883$	−6.03408	−0.203063	−0.101531	−	0.994832i	$-0.532374\pi$
$883$	−6.03408	−0.203063	−0.101531	+	0.994832i	$0.532374\pi$
$884$	42.1942	1.41915
$885$	21.1455	0.710797
$886$	−46.0437	−1.54687
$887$	27.1890	0.912918	0.456459	−	0.889745i	$-0.349118\pi$
$887$	27.1890	0.912918	0.456459	+	0.889745i	$0.349118\pi$
$888$	51.8522	1.74005
$889$	0	0
$890$	−86.2625	−2.89152
$891$	3.78561	0.126823
$892$	31.1914	1.04436
$893$	−6.99274	−0.234003
$894$	−9.93802	−0.332377
$895$	−67.1471	−2.24448
$896$	0	0
$897$	11.1715	0.373005
$898$	−21.6644	−0.722952
$899$	38.0605	1.26939
$900$	11.5595	0.385316
$901$	−16.0653	−0.535212
$902$	−12.2329	−0.407312
$903$	0	0
$904$	−8.52408	−0.283507
$905$	50.7312	1.68636
$906$	−32.3489	−1.07472
$907$	15.9316	0.529000	0.264500	−	0.964386i	$-0.414793\pi$
$907$	15.9316	0.529000	0.264500	+	0.964386i	$0.414793\pi$
$908$	59.8517	1.98625
$909$	4.10770	0.136244
$910$	0	0
$911$	35.4625	1.17493	0.587463	−	0.809251i	$-0.300127\pi$
$911$	35.4625	1.17493	0.587463	+	0.809251i	$0.300127\pi$
$912$	4.78561	0.158467
$913$	32.7567	1.08409
$914$	−33.6777	−1.11396
$915$	7.45878	0.246580
$916$	−20.5379	−0.678592
$917$	0	0
$918$	−8.57401	−0.282985
$919$	−24.2261	−0.799145	−0.399573	−	0.916702i	$-0.630841\pi$
$919$	−24.2261	−0.799145	−0.399573	+	0.916702i	$0.630841\pi$
$920$	−55.7013	−1.83642
$921$	25.5898	0.843211
$922$	103.096	3.39527
$923$	30.1439	0.992200
$924$	0	0
$925$	−27.5593	−0.906143
$926$	50.7798	1.66873
$927$	−18.4149	−0.604823
$928$	−8.61842	−0.282913
$929$	−18.5294	−0.607930	−0.303965	−	0.952683i	$-0.598311\pi$
$929$	−18.5294	−0.607930	−0.303965	+	0.952683i	$0.598311\pi$
$930$	40.0006	1.31167
$931$	0	0
$932$	31.8103	1.04198
$933$	−6.94732	−0.227445
$934$	−1.49757	−0.0490019
$935$	36.6189	1.19756
$936$	15.5472	0.508177
$937$	12.3309	0.402831	0.201416	−	0.979506i	$-0.435446\pi$
$937$	12.3309	0.402831	0.201416	+	0.979506i	$0.435446\pi$
$938$	0	0
$939$	−6.24187	−0.203696
$940$	80.6229	2.62963
$941$	54.8991	1.78966	0.894830	−	0.446406i	$-0.147296\pi$
$941$	54.8991	1.78966	0.894830	+	0.446406i	$0.147296\pi$
$942$	58.7793	1.91513
$943$	4.94156	0.160919
$944$	−36.2329	−1.17928
$945$	0	0
$946$	94.2433	3.06411
$947$	−21.9497	−0.713268	−0.356634	−	0.934244i	$-0.616076\pi$
$947$	−21.9497	−0.713268	−0.356634	+	0.934244i	$0.616076\pi$
$948$	−67.3820	−2.18847
$949$	−16.6606	−0.540827
$950$	−6.93178	−0.224897
$951$	18.8114	0.610002
$952$	0	0
$953$	50.8141	1.64603	0.823015	−	0.568019i	$-0.192290\pi$
$953$	50.8141	1.64603	0.823015	+	0.568019i	$0.192290\pi$
$954$	−11.4825	−0.371760
$955$	14.1180	0.456848
$956$	68.7088	2.22220
$957$	24.9036	0.805018
$958$	−55.1947	−1.78326
$959$	0	0
$960$	17.6735	0.570409
$961$	2.47330	0.0797839
$962$	−71.9003	−2.31816
$963$	−3.61292	−0.116425
$964$	−105.776	−3.40680
$965$	−48.6333	−1.56556
$966$	0	0
$967$	−58.6185	−1.88504	−0.942522	−	0.334144i	$-0.891553\pi$
$967$	−58.6185	−1.88504	−0.942522	+	0.334144i	$0.891553\pi$
$968$	17.5482	0.564022
$969$	3.46352	0.111264
$970$	115.199	3.69882
$971$	37.0086	1.18766	0.593832	−	0.804589i	$-0.297614\pi$
$971$	37.0086	1.18766	0.593832	+	0.804589i	$0.297614\pi$
$972$	−4.12820	−0.132412
$973$	0	0
$974$	101.274	3.24503
$975$	−8.26330	−0.264637
$976$	−12.7807	−0.409100
$977$	35.7076	1.14239	0.571193	−	0.820816i	$-0.306481\pi$
$977$	35.7076	1.14239	0.571193	+	0.820816i	$0.306481\pi$
$978$	−37.1750	−1.18872
$979$	−47.2325	−1.50956
$980$	0	0
$981$	3.98548	0.127247
$982$	51.7719	1.65211
$983$	36.6380	1.16857	0.584285	−	0.811549i	$-0.301375\pi$
$983$	36.6380	1.16857	0.584285	+	0.811549i	$0.301375\pi$
$984$	6.87711	0.219234
$985$	−52.3544	−1.66815
$986$	−56.4040	−1.79627
$987$	0	0
$988$	−12.1825	−0.387576
$989$	−38.0701	−1.21056
$990$	26.1730	0.831832
$991$	28.2364	0.896959	0.448480	−	0.893793i	$-0.351966\pi$
$991$	28.2364	0.896959	0.448480	+	0.893793i	$0.351966\pi$
$992$	−7.57968	−0.240655
$993$	27.2974	0.866258
$994$	0	0
$995$	47.9172	1.51908
$996$	−35.7211	−1.13186
$997$	43.4285	1.37539	0.687697	−	0.725998i	$-0.258622\pi$
$997$	43.4285	1.37539	0.687697	+	0.725998i	$0.258622\pi$
$998$	−108.646	−3.43913
$999$	9.84214	0.311391

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.be.1.5		5
3.2	odd	2		8379.2.a.ce.1.1		5
7.6	odd	2		399.2.a.f.1.5	✓	5
21.20	even	2		1197.2.a.p.1.1		5
28.27	even	2		6384.2.a.cc.1.2		5
35.34	odd	2		9975.2.a.bq.1.1		5
133.132	even	2		7581.2.a.x.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.f.1.5	✓	5	7.6	odd	2
1197.2.a.p.1.1		5	21.20	even	2
2793.2.a.be.1.5		5	1.1	even	1	trivial
6384.2.a.cc.1.2		5	28.27	even	2
7581.2.a.x.1.1		5	133.132	even	2
8379.2.a.ce.1.1		5	3.2	odd	2
9975.2.a.bq.1.1		5	35.34	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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q+2.47552 q^{2} -1.00000 q^{3} +4.12820 q^{4} +2.79287 q^{5} -2.47552 q^{6} +5.26839 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.47552 q^{2} -1.00000 q^{3} +4.12820 q^{4} +2.79287 q^{5} -2.47552 q^{6} +5.26839 q^{8} +1.00000 q^{9} +6.91381 q^{10} +3.78561 q^{11} -4.12820 q^{12} +2.95104 q^{13} -2.79287 q^{15} +4.78561 q^{16} +3.46352 q^{17} +2.47552 q^{18} -1.00000 q^{19} +11.5295 q^{20} +9.37135 q^{22} -3.78561 q^{23} -5.26839 q^{24} +2.80013 q^{25} +7.30535 q^{26} -1.00000 q^{27} -6.57848 q^{29} -6.91381 q^{30} -5.78561 q^{31} +1.31009 q^{32} -3.78561 q^{33} +8.57401 q^{34} +4.12820 q^{36} -9.84214 q^{37} -2.47552 q^{38} -2.95104 q^{39} +14.7139 q^{40} -1.30535 q^{41} +10.0565 q^{43} +15.6277 q^{44} +2.79287 q^{45} -9.37135 q^{46} +6.99274 q^{47} -4.78561 q^{48} +6.93178 q^{50} -3.46352 q^{51} +12.1825 q^{52} -4.63843 q^{53} -2.47552 q^{54} +10.5727 q^{55} +1.00000 q^{57} -16.2852 q^{58} -7.57122 q^{59} -11.5295 q^{60} -2.67065 q^{61} -14.3224 q^{62} -6.32806 q^{64} +8.24187 q^{65} -9.37135 q^{66} +10.0660 q^{67} +14.2981 q^{68} +3.78561 q^{69} +10.2147 q^{71} +5.26839 q^{72} -5.64569 q^{73} -24.3644 q^{74} -2.80013 q^{75} -4.12820 q^{76} -7.30535 q^{78} +16.3224 q^{79} +13.3656 q^{80} +1.00000 q^{81} -3.23143 q^{82} +8.65295 q^{83} +9.67317 q^{85} +24.8951 q^{86} +6.57848 q^{87} +19.9441 q^{88} -12.4768 q^{89} +6.91381 q^{90} -15.6277 q^{92} +5.78561 q^{93} +17.3107 q^{94} -2.79287 q^{95} -1.31009 q^{96} +16.6622 q^{97} +3.78561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} - 2 q^{11} - 7 q^{12} - 8 q^{13} - 2 q^{15} + 3 q^{16} + 2 q^{17} + q^{18} - 5 q^{19} + 2 q^{20} + 2 q^{22} + 2 q^{23} - 3 q^{24} + 11 q^{25} + 32 q^{26} - 5 q^{27} - 8 q^{31} - 3 q^{32} + 2 q^{33} + 8 q^{34} + 7 q^{36} + 2 q^{37} - q^{38} + 8 q^{39} + 36 q^{40} - 2 q^{41} + 20 q^{43} + 6 q^{44} + 2 q^{45} - 2 q^{46} + 26 q^{47} - 3 q^{48} - q^{50} - 2 q^{51} - 4 q^{52} + 4 q^{53} - q^{54} + 4 q^{55} + 5 q^{57} - 2 q^{58} + 4 q^{59} - 2 q^{60} - 10 q^{61} - 4 q^{62} - 21 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} + 58 q^{68} - 2 q^{69} + 10 q^{71} + 3 q^{72} - 10 q^{73} - 6 q^{74} - 11 q^{75} - 7 q^{76} - 32 q^{78} + 14 q^{79} + 6 q^{80} + 5 q^{81} + 26 q^{82} + 34 q^{83} - 36 q^{85} + 8 q^{86} + 6 q^{88} - 10 q^{89} - 6 q^{92} + 8 q^{93} + 8 q^{94} - 2 q^{95} + 3 q^{96} + 16 q^{97} - 2 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 7 * q^4 + 2 * q^5 - q^6 + 3 * q^8 + 5 * q^9 - 2 * q^11 - 7 * q^12 - 8 * q^13 - 2 * q^15 + 3 * q^16 + 2 * q^17 + q^18 - 5 * q^19 + 2 * q^20 + 2 * q^22 + 2 * q^23 - 3 * q^24 + 11 * q^25 + 32 * q^26 - 5 * q^27 - 8 * q^31 - 3 * q^32 + 2 * q^33 + 8 * q^34 + 7 * q^36 + 2 * q^37 - q^38 + 8 * q^39 + 36 * q^40 - 2 * q^41 + 20 * q^43 + 6 * q^44 + 2 * q^45 - 2 * q^46 + 26 * q^47 - 3 * q^48 - q^50 - 2 * q^51 - 4 * q^52 + 4 * q^53 - q^54 + 4 * q^55 + 5 * q^57 - 2 * q^58 + 4 * q^59 - 2 * q^60 - 10 * q^61 - 4 * q^62 - 21 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 + 58 * q^68 - 2 * q^69 + 10 * q^71 + 3 * q^72 - 10 * q^73 - 6 * q^74 - 11 * q^75 - 7 * q^76 - 32 * q^78 + 14 * q^79 + 6 * q^80 + 5 * q^81 + 26 * q^82 + 34 * q^83 - 36 * q^85 + 8 * q^86 + 6 * q^88 - 10 * q^89 - 6 * q^92 + 8 * q^93 + 8 * q^94 - 2 * q^95 + 3 * q^96 + 16 * q^97 - 2 * q^99

Introduction

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