LMFDB - Embedded newform 931.2.a.q.1.6

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.115985$ 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)

$f(q)$	$=$	$q+0.115985 q^{2} +2.98171 q^{3} -1.98655 q^{4} +0.455421 q^{5} +0.345835 q^{6} -0.462382 q^{8} +5.89060 q^{9} +O(q^{10})$	\(q+0.115985 q^{2} +2.98171 q^{3} -1.98655 q^{4} +0.455421 q^{5} +0.345835 q^{6} -0.462382 q^{8} +5.89060 q^{9} +0.0528223 q^{10} +3.02258 q^{11} -5.92331 q^{12} -0.114243 q^{13} +1.35793 q^{15} +3.91947 q^{16} -0.380139 q^{17} +0.683224 q^{18} +1.00000 q^{19} -0.904716 q^{20} +0.350576 q^{22} +7.55172 q^{23} -1.37869 q^{24} -4.79259 q^{25} -0.0132505 q^{26} +8.61892 q^{27} -7.78449 q^{29} +0.157501 q^{30} +6.78918 q^{31} +1.37936 q^{32} +9.01247 q^{33} -0.0440906 q^{34} -11.7020 q^{36} -1.55658 q^{37} +0.115985 q^{38} -0.340638 q^{39} -0.210578 q^{40} -6.21830 q^{41} +9.25945 q^{43} -6.00450 q^{44} +2.68270 q^{45} +0.875890 q^{46} +11.1835 q^{47} +11.6867 q^{48} -0.555871 q^{50} -1.13346 q^{51} +0.226948 q^{52} -8.04637 q^{53} +0.999670 q^{54} +1.37655 q^{55} +2.98171 q^{57} -0.902887 q^{58} -7.35760 q^{59} -2.69760 q^{60} +12.5155 q^{61} +0.787446 q^{62} -7.67894 q^{64} -0.0520285 q^{65} +1.04532 q^{66} -2.62315 q^{67} +0.755164 q^{68} +22.5170 q^{69} +3.18872 q^{71} -2.72370 q^{72} -9.01050 q^{73} -0.180541 q^{74} -14.2901 q^{75} -1.98655 q^{76} -0.0395091 q^{78} -10.8324 q^{79} +1.78501 q^{80} +8.02734 q^{81} -0.721232 q^{82} -3.10584 q^{83} -0.173123 q^{85} +1.07396 q^{86} -23.2111 q^{87} -1.39759 q^{88} +4.12195 q^{89} +0.311155 q^{90} -15.0019 q^{92} +20.2434 q^{93} +1.29712 q^{94} +0.455421 q^{95} +4.11286 q^{96} -15.6426 q^{97} +17.8048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	$ 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) $ 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * 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 $

$2$	0.115985	0.0820141	0.0410071	−	0.999159i	$-0.486943\pi$
$2$	0.115985	0.0820141	0.0410071	+	0.999159i	$0.486943\pi$
$3$	2.98171	1.72149	0.860746	−	0.509035i	$-0.169998\pi$
$3$	2.98171	1.72149	0.860746	+	0.509035i	$0.169998\pi$
$4$	−1.98655	−0.993274
$5$	0.455421	0.203671	0.101835	−	0.994801i	$-0.467529\pi$
$5$	0.455421	0.203671	0.101835	+	0.994801i	$0.467529\pi$
$6$	0.345835	0.141187
$7$	0	0
$7$	0	0
$8$	−0.462382	−0.163477
$9$	5.89060	1.96353
$10$	0.0528223	0.0167039
$11$	3.02258	0.911343	0.455671	−	0.890148i	$-0.349399\pi$
$11$	3.02258	0.911343	0.455671	+	0.890148i	$0.349399\pi$
$12$	−5.92331	−1.70991
$13$	−0.114243	−0.0316852	−0.0158426	−	0.999874i	$-0.505043\pi$
$13$	−0.114243	−0.0316852	−0.0158426	+	0.999874i	$0.505043\pi$
$14$	0	0
$15$	1.35793	0.350617
$16$	3.91947	0.979866
$17$	−0.380139	−0.0921973	−0.0460986	−	0.998937i	$-0.514679\pi$
$17$	−0.380139	−0.0921973	−0.0460986	+	0.998937i	$0.514679\pi$
$18$	0.683224	0.161037
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.904716	−0.202301
$21$	0	0
$22$	0.350576	0.0747430
$23$	7.55172	1.57464	0.787321	−	0.616543i	$-0.211467\pi$
$23$	7.55172	1.57464	0.787321	+	0.616543i	$0.211467\pi$
$24$	−1.37869	−0.281423
$25$	−4.79259	−0.958518
$26$	−0.0132505	−0.00259863
$27$	8.61892	1.65871
$28$	0	0
$29$	−7.78449	−1.44554	−0.722772	−	0.691087i	$-0.757132\pi$
$29$	−7.78449	−1.44554	−0.722772	+	0.691087i	$0.757132\pi$
$30$	0.157501	0.0287556
$31$	6.78918	1.21937	0.609686	−	0.792643i	$-0.291295\pi$
$31$	6.78918	1.21937	0.609686	+	0.792643i	$0.291295\pi$
$32$	1.37936	0.243839
$33$	9.01247	1.56887
$34$	−0.0440906	−0.00756148
$35$	0	0
$36$	−11.7020	−1.95033
$37$	−1.55658	−0.255901	−0.127950	−	0.991781i	$-0.540840\pi$
$37$	−1.55658	−0.255901	−0.127950	+	0.991781i	$0.540840\pi$
$38$	0.115985	0.0188153
$39$	−0.340638	−0.0545458
$40$	−0.210578	−0.0332954
$41$	−6.21830	−0.971135	−0.485567	−	0.874199i	$-0.661387\pi$
$41$	−6.21830	−0.971135	−0.485567	+	0.874199i	$0.661387\pi$
$42$	0	0
$43$	9.25945	1.41205	0.706027	−	0.708185i	$-0.250486\pi$
$43$	9.25945	1.41205	0.706027	+	0.708185i	$0.250486\pi$
$44$	−6.00450	−0.905213
$45$	2.68270	0.399914
$46$	0.875890	0.129143
$47$	11.1835	1.63128	0.815638	−	0.578562i	$-0.196386\pi$
$47$	11.1835	1.63128	0.815638	+	0.578562i	$0.196386\pi$
$48$	11.6867	1.68683
$49$	0	0
$50$	−0.555871	−0.0786120
$51$	−1.13346	−0.158717
$52$	0.226948	0.0314721
$53$	−8.04637	−1.10525	−0.552627	−	0.833429i	$-0.686375\pi$
$53$	−8.04637	−1.10525	−0.552627	+	0.833429i	$0.686375\pi$
$54$	0.999670	0.136038
$55$	1.37655	0.185614
$56$	0	0
$57$	2.98171	0.394937
$58$	−0.902887	−0.118555
$59$	−7.35760	−0.957878	−0.478939	−	0.877848i	$-0.658978\pi$
$59$	−7.35760	−0.957878	−0.478939	+	0.877848i	$0.658978\pi$
$60$	−2.69760	−0.348259
$61$	12.5155	1.60245	0.801225	−	0.598363i	$-0.204182\pi$
$61$	12.5155	1.60245	0.801225	+	0.598363i	$0.204182\pi$
$62$	0.787446	0.100006
$63$	0	0
$64$	−7.67894	−0.959868
$65$	−0.0520285	−0.00645334
$66$	1.04532	0.128669
$67$	−2.62315	−0.320469	−0.160234	−	0.987079i	$-0.551225\pi$
$67$	−2.62315	−0.320469	−0.160234	+	0.987079i	$0.551225\pi$
$68$	0.755164	0.0915771
$69$	22.5170	2.71073
$70$	0	0
$71$	3.18872	0.378431	0.189216	−	0.981936i	$-0.439405\pi$
$71$	3.18872	0.378431	0.189216	+	0.981936i	$0.439405\pi$
$72$	−2.72370	−0.320992
$73$	−9.01050	−1.05460	−0.527299	−	0.849680i	$-0.676795\pi$
$73$	−9.01050	−1.05460	−0.527299	+	0.849680i	$0.676795\pi$
$74$	−0.180541	−0.0209875
$75$	−14.2901	−1.65008
$76$	−1.98655	−0.227873
$77$	0	0
$78$	−0.0395091	−0.00447352
$79$	−10.8324	−1.21874	−0.609371	−	0.792885i	$-0.708578\pi$
$79$	−10.8324	−1.21874	−0.609371	+	0.792885i	$0.708578\pi$
$80$	1.78501	0.199570
$81$	8.02734	0.891927
$82$	−0.721232	−0.0796468
$83$	−3.10584	−0.340910	−0.170455	−	0.985365i	$-0.554524\pi$
$83$	−3.10584	−0.340910	−0.170455	+	0.985365i	$0.554524\pi$
$84$	0	0
$85$	−0.173123	−0.0187779
$86$	1.07396	0.115808
$87$	−23.2111	−2.48849
$88$	−1.39759	−0.148983
$89$	4.12195	0.436926	0.218463	−	0.975845i	$-0.429896\pi$
$89$	4.12195	0.436926	0.218463	+	0.975845i	$0.429896\pi$
$90$	0.311155	0.0327986
$91$	0	0
$92$	−15.0019	−1.56405
$93$	20.2434	2.09914
$94$	1.29712	0.133788
$95$	0.455421	0.0467253
$96$	4.11286	0.419767
$97$	−15.6426	−1.58827	−0.794134	−	0.607743i	$-0.792075\pi$
$97$	−15.6426	−1.58827	−0.794134	+	0.607743i	$0.792075\pi$
$98$	0	0
$99$	17.8048	1.78945
$100$	9.52071	0.952071
$101$	12.1520	1.20916	0.604582	−	0.796543i	$-0.293340\pi$
$101$	12.1520	1.20916	0.604582	+	0.796543i	$0.293340\pi$
$102$	−0.131465	−0.0130170
$103$	−4.01637	−0.395745	−0.197872	−	0.980228i	$-0.563403\pi$
$103$	−4.01637	−0.395745	−0.197872	+	0.980228i	$0.563403\pi$
$104$	0.0528236	0.00517978
$105$	0	0
$106$	−0.933262	−0.0906464
$107$	−11.8670	−1.14723	−0.573615	−	0.819125i	$-0.694459\pi$
$107$	−11.8670	−1.14723	−0.573615	+	0.819125i	$0.694459\pi$
$108$	−17.1219	−1.64756
$109$	−19.0795	−1.82749	−0.913744	−	0.406290i	$-0.866822\pi$
$109$	−19.0795	−1.82749	−0.913744	+	0.406290i	$0.866822\pi$
$110$	0.159660	0.0152230
$111$	−4.64128	−0.440531
$112$	0	0
$113$	−17.4660	−1.64306	−0.821532	−	0.570163i	$-0.806880\pi$
$113$	−17.4660	−1.64306	−0.821532	+	0.570163i	$0.806880\pi$
$114$	0.345835	0.0323904
$115$	3.43922	0.320709
$116$	15.4643	1.43582
$117$	−0.672957	−0.0622149
$118$	−0.853375	−0.0785595
$119$	0	0
$120$	−0.627884	−0.0573177
$121$	−1.86399	−0.169454
$122$	1.45162	0.131424
$123$	−18.5412	−1.67180
$124$	−13.4870	−1.21117
$125$	−4.45976	−0.398893
$126$	0	0
$127$	2.72063	0.241417	0.120709	−	0.992688i	$-0.461483\pi$
$127$	2.72063	0.241417	0.120709	+	0.992688i	$0.461483\pi$
$128$	−3.64937	−0.322562
$129$	27.6090	2.43084
$130$	−0.00603455	−0.000529265 0
$131$	−10.2547	−0.895958	−0.447979	−	0.894044i	$-0.647856\pi$
$131$	−10.2547	−0.895958	−0.447979	+	0.894044i	$0.647856\pi$
$132$	−17.9037	−1.55832
$133$	0	0
$134$	−0.304247	−0.0262829
$135$	3.92524	0.337831
$136$	0.175769	0.0150721
$137$	11.6246	0.993159	0.496580	−	0.867991i	$-0.334589\pi$
$137$	11.6246	0.993159	0.496580	+	0.867991i	$0.334589\pi$
$138$	2.61165	0.222318
$139$	10.0142	0.849396	0.424698	−	0.905335i	$-0.360380\pi$
$139$	10.0142	0.849396	0.424698	+	0.905335i	$0.360380\pi$
$140$	0	0
$141$	33.3459	2.80823
$142$	0.369845	0.0310367
$143$	−0.345308	−0.0288761
$144$	23.0880	1.92400
$145$	−3.54522	−0.294415
$146$	−1.04509	−0.0864920
$147$	0	0
$148$	3.09223	0.254180
$149$	−7.42994	−0.608684	−0.304342	−	0.952563i	$-0.598437\pi$
$149$	−7.42994	−0.608684	−0.304342	+	0.952563i	$0.598437\pi$
$150$	−1.65745	−0.135330
$151$	9.94873	0.809616	0.404808	−	0.914402i	$-0.367338\pi$
$151$	9.94873	0.809616	0.404808	+	0.914402i	$0.367338\pi$
$152$	−0.462382	−0.0375041
$153$	−2.23925	−0.181032
$154$	0	0
$155$	3.09194	0.248350
$156$	0.676694	0.0541789
$157$	11.8823	0.948307	0.474153	−	0.880442i	$-0.342754\pi$
$157$	11.8823	0.948307	0.474153	+	0.880442i	$0.342754\pi$
$158$	−1.25640	−0.0999540
$159$	−23.9919	−1.90269
$160$	0.628192	0.0496629
$161$	0	0
$162$	0.931055	0.0731506
$163$	18.4620	1.44605	0.723026	−	0.690821i	$-0.242751\pi$
$163$	18.4620	1.44605	0.723026	+	0.690821i	$0.242751\pi$
$164$	12.3529	0.964603
$165$	4.10447	0.319533
$166$	−0.360232	−0.0279594
$167$	−3.66385	−0.283517	−0.141759	−	0.989901i	$-0.545276\pi$
$167$	−3.66385	−0.283517	−0.141759	+	0.989901i	$0.545276\pi$
$168$	0	0
$169$	−12.9869	−0.998996
$170$	−0.0200798	−0.00154005
$171$	5.89060	0.450465
$172$	−18.3943	−1.40256
$173$	7.68083	0.583962	0.291981	−	0.956424i	$-0.405686\pi$
$173$	7.68083	0.583962	0.291981	+	0.956424i	$0.405686\pi$
$174$	−2.69215	−0.204091
$175$	0	0
$176$	11.8469	0.892994
$177$	−21.9382	−1.64898
$178$	0.478086	0.0358341
$179$	4.03847	0.301850	0.150925	−	0.988545i	$-0.451775\pi$
$179$	4.03847	0.301850	0.150925	+	0.988545i	$0.451775\pi$
$180$	−5.32932	−0.397224
$181$	−3.44276	−0.255898	−0.127949	−	0.991781i	$-0.540839\pi$
$181$	−3.44276	−0.255898	−0.127949	+	0.991781i	$0.540839\pi$
$182$	0	0
$183$	37.3177	2.75861
$184$	−3.49178	−0.257417
$185$	−0.708902	−0.0521195
$186$	2.34794	0.172159
$187$	−1.14900	−0.0840233
$188$	−22.2165	−1.62030
$189$	0	0
$190$	0.0528223	0.00383213
$191$	−4.31904	−0.312514	−0.156257	−	0.987716i	$-0.549943\pi$
$191$	−4.31904	−0.312514	−0.156257	+	0.987716i	$0.549943\pi$
$192$	−22.8964	−1.65240
$193$	−4.14084	−0.298064	−0.149032	−	0.988832i	$-0.547616\pi$
$193$	−4.14084	−0.298064	−0.149032	+	0.988832i	$0.547616\pi$
$194$	−1.81432	−0.130260
$195$	−0.155134	−0.0111094
$196$	0	0
$197$	−8.20993	−0.584933	−0.292467	−	0.956276i	$-0.594476\pi$
$197$	−8.20993	−0.584933	−0.292467	+	0.956276i	$0.594476\pi$
$198$	2.06510	0.146760
$199$	14.2507	1.01021	0.505104	−	0.863058i	$-0.331454\pi$
$199$	14.2507	1.01021	0.505104	+	0.863058i	$0.331454\pi$
$200$	2.21601	0.156695
$201$	−7.82147	−0.551684
$202$	1.40945	0.0991686
$203$	0	0
$204$	2.25168	0.157649
$205$	−2.83195	−0.197792
$206$	−0.465840	−0.0324566
$207$	44.4842	3.09186
$208$	−0.447770	−0.0310472
$209$	3.02258	0.209076
$210$	0	0
$211$	−22.6622	−1.56013	−0.780066	−	0.625697i	$-0.784815\pi$
$211$	−22.6622	−1.56013	−0.780066	+	0.625697i	$0.784815\pi$
$212$	15.9845	1.09782
$213$	9.50784	0.651466
$214$	−1.37640	−0.0940890
$215$	4.21695	0.287594
$216$	−3.98523	−0.271161
$217$	0	0
$218$	−2.21295	−0.149880
$219$	−26.8667	−1.81548
$220$	−2.73458	−0.184365
$221$	0.0434281	0.00292129
$222$	−0.538322	−0.0361298
$223$	−1.67370	−0.112079	−0.0560395	−	0.998429i	$-0.517847\pi$
$223$	−1.67370	−0.112079	−0.0560395	+	0.998429i	$0.517847\pi$
$224$	0	0
$225$	−28.2312	−1.88208
$226$	−2.02580	−0.134754
$227$	−1.53304	−0.101751	−0.0508756	−	0.998705i	$-0.516201\pi$
$227$	−1.53304	−0.101751	−0.0508756	+	0.998705i	$0.516201\pi$
$228$	−5.92331	−0.392281
$229$	5.29451	0.349871	0.174936	−	0.984580i	$-0.444028\pi$
$229$	5.29451	0.349871	0.174936	+	0.984580i	$0.444028\pi$
$230$	0.398899	0.0263026
$231$	0	0
$232$	3.59940	0.236312
$233$	−15.6497	−1.02525	−0.512623	−	0.858614i	$-0.671326\pi$
$233$	−15.6497	−1.02525	−0.512623	+	0.858614i	$0.671326\pi$
$234$	−0.0780532	−0.00510250
$235$	5.09319	0.332243
$236$	14.6162	0.951435
$237$	−32.2991	−2.09805
$238$	0	0
$239$	−23.5090	−1.52067	−0.760335	−	0.649531i	$-0.774965\pi$
$239$	−23.5090	−1.52067	−0.760335	+	0.649531i	$0.774965\pi$
$240$	5.32238	0.343558
$241$	−28.6329	−1.84441	−0.922205	−	0.386702i	$-0.873614\pi$
$241$	−28.6329	−1.84441	−0.922205	+	0.386702i	$0.873614\pi$
$242$	−0.216196	−0.0138976
$243$	−1.92156	−0.123268
$244$	−24.8627	−1.59167
$245$	0	0
$246$	−2.15051	−0.137111
$247$	−0.114243	−0.00726908
$248$	−3.13919	−0.199339
$249$	−9.26070	−0.586873
$250$	−0.517267	−0.0327148
$251$	14.7590	0.931579	0.465790	−	0.884896i	$-0.345770\pi$
$251$	14.7590	0.931579	0.465790	+	0.884896i	$0.345770\pi$
$252$	0	0
$253$	22.8257	1.43504
$254$	0.315554	0.0197996
$255$	−0.516204	−0.0323260
$256$	14.9346	0.933413
$257$	27.8291	1.73593	0.867965	−	0.496625i	$-0.165428\pi$
$257$	27.8291	1.73593	0.867965	+	0.496625i	$0.165428\pi$
$258$	3.20224	0.199363
$259$	0	0
$260$	0.103357	0.00640993
$261$	−45.8553	−2.83837
$262$	−1.18940	−0.0734812
$263$	6.85894	0.422941	0.211470	−	0.977384i	$-0.432175\pi$
$263$	6.85894	0.422941	0.211470	+	0.977384i	$0.432175\pi$
$264$	−4.16720	−0.256473
$265$	−3.66449	−0.225108
$266$	0	0
$267$	12.2905	0.752164
$268$	5.21101	0.318313
$269$	21.9415	1.33780	0.668898	−	0.743354i	$-0.266766\pi$
$269$	21.9415	1.33780	0.668898	+	0.743354i	$0.266766\pi$
$270$	0.455271	0.0277069
$271$	−13.4749	−0.818544	−0.409272	−	0.912412i	$-0.634217\pi$
$271$	−13.4749	−0.818544	−0.409272	+	0.912412i	$0.634217\pi$
$272$	−1.48994	−0.0903410
$273$	0	0
$274$	1.34829	0.0814531
$275$	−14.4860	−0.873539
$276$	−44.7312	−2.69250
$277$	−3.49572	−0.210037	−0.105019	−	0.994470i	$-0.533490\pi$
$277$	−3.49572	−0.210037	−0.105019	+	0.994470i	$0.533490\pi$
$278$	1.16151	0.0696625
$279$	39.9923	2.39428
$280$	0	0
$281$	28.9931	1.72958	0.864792	−	0.502130i	$-0.167450\pi$
$281$	28.9931	1.72958	0.864792	+	0.502130i	$0.167450\pi$
$282$	3.86764	0.230314
$283$	−24.6530	−1.46547	−0.732736	−	0.680513i	$-0.761757\pi$
$283$	−24.6530	−1.46547	−0.732736	+	0.680513i	$0.761757\pi$
$284$	−6.33454	−0.375886
$285$	1.35793	0.0804371
$286$	−0.0400507	−0.00236824
$287$	0	0
$288$	8.12528	0.478787
$289$	−16.8555	−0.991500
$290$	−0.411194	−0.0241462
$291$	−46.6418	−2.73419
$292$	17.8998	1.04751
$293$	25.0343	1.46252	0.731260	−	0.682099i	$-0.238933\pi$
$293$	25.0343	1.46252	0.731260	+	0.682099i	$0.238933\pi$
$294$	0	0
$295$	−3.35081	−0.195092
$296$	0.719736	0.0418338
$297$	26.0514	1.51166
$298$	−0.861765	−0.0499207
$299$	−0.862728	−0.0498928
$300$	28.3880	1.63898
$301$	0	0
$302$	1.15391	0.0663999
$303$	36.2336	2.08157
$304$	3.91947	0.224797
$305$	5.69985	0.326372
$306$	−0.259720	−0.0148472
$307$	28.2511	1.61237	0.806187	−	0.591660i	$-0.201527\pi$
$307$	28.2511	1.61237	0.806187	+	0.591660i	$0.201527\pi$
$308$	0	0
$309$	−11.9756	−0.681271
$310$	0.358620	0.0203682
$311$	18.7579	1.06366	0.531831	−	0.846850i	$-0.321504\pi$
$311$	18.7579	1.06366	0.531831	+	0.846850i	$0.321504\pi$
$312$	0.157505	0.00891695
$313$	−8.97055	−0.507045	−0.253523	−	0.967329i	$-0.581589\pi$
$313$	−8.97055	−0.507045	−0.253523	+	0.967329i	$0.581589\pi$
$314$	1.37817	0.0777745
$315$	0	0
$316$	21.5191	1.21054
$317$	−16.9808	−0.953736	−0.476868	−	0.878975i	$-0.658228\pi$
$317$	−16.9808	−0.953736	−0.476868	+	0.878975i	$0.658228\pi$
$318$	−2.78272	−0.156047
$319$	−23.5293	−1.31739
$320$	−3.49716	−0.195497
$321$	−35.3841	−1.97495
$322$	0	0
$323$	−0.380139	−0.0211515
$324$	−15.9467	−0.885928
$325$	0.547518	0.0303708
$326$	2.14132	0.118597
$327$	−56.8897	−3.14601
$328$	2.87523	0.158758
$329$	0	0
$330$	0.476059	0.0262062
$331$	−9.60909	−0.528163	−0.264082	−	0.964500i	$-0.585069\pi$
$331$	−9.60909	−0.528163	−0.264082	+	0.964500i	$0.585069\pi$
$332$	6.16989	0.338617
$333$	−9.16921	−0.502470
$334$	−0.424953	−0.0232524
$335$	−1.19464	−0.0652700
$336$	0	0
$337$	4.23997	0.230966	0.115483	−	0.993309i	$-0.463158\pi$
$337$	4.23997	0.230966	0.115483	+	0.993309i	$0.463158\pi$
$338$	−1.50630	−0.0819318
$339$	−52.0786	−2.82852
$340$	0.343918	0.0186516
$341$	20.5209	1.11127
$342$	0.683224	0.0369445
$343$	0	0
$344$	−4.28140	−0.230838
$345$	10.2547	0.552097
$346$	0.890864	0.0478931
$347$	−13.2060	−0.708938	−0.354469	−	0.935068i	$-0.615338\pi$
$347$	−13.2060	−0.708938	−0.354469	+	0.935068i	$0.615338\pi$
$348$	46.1099	2.47175
$349$	−20.3782	−1.09082	−0.545410	−	0.838169i	$-0.683626\pi$
$349$	−20.3782	−1.09082	−0.545410	+	0.838169i	$0.683626\pi$
$350$	0	0
$351$	−0.984648	−0.0525566
$352$	4.16924	0.222221
$353$	−17.9841	−0.957194	−0.478597	−	0.878035i	$-0.658855\pi$
$353$	−17.9841	−0.957194	−0.478597	+	0.878035i	$0.658855\pi$
$354$	−2.54452	−0.135239
$355$	1.45221	0.0770754
$356$	−8.18845	−0.433987
$357$	0	0
$358$	0.468404	0.0247559
$359$	24.9674	1.31773	0.658864	−	0.752262i	$-0.271037\pi$
$359$	24.9674	1.31773	0.658864	+	0.752262i	$0.271037\pi$
$360$	−1.24043	−0.0653766
$361$	1.00000	0.0526316
$362$	−0.399310	−0.0209873
$363$	−5.55789	−0.291714
$364$	0	0
$365$	−4.10357	−0.214791
$366$	4.32831	0.226245
$367$	−12.3958	−0.647053	−0.323527	−	0.946219i	$-0.604869\pi$
$367$	−12.3958	−0.647053	−0.323527	+	0.946219i	$0.604869\pi$
$368$	29.5987	1.54294
$369$	−36.6295	−1.90685
$370$	−0.0822223	−0.00427453
$371$	0	0
$372$	−40.2144	−2.08502
$373$	6.62794	0.343182	0.171591	−	0.985168i	$-0.445109\pi$
$373$	6.62794	0.343182	0.171591	+	0.985168i	$0.445109\pi$
$374$	−0.133267	−0.00689110
$375$	−13.2977	−0.686690
$376$	−5.17103	−0.266676
$377$	0.889320	0.0458023
$378$	0	0
$379$	5.75107	0.295412	0.147706	−	0.989031i	$-0.452811\pi$
$379$	5.75107	0.295412	0.147706	+	0.989031i	$0.452811\pi$
$380$	−0.904716	−0.0464110
$381$	8.11214	0.415597
$382$	−0.500945	−0.0256306
$383$	35.0424	1.79058	0.895290	−	0.445483i	$-0.146968\pi$
$383$	35.0424	1.79058	0.895290	+	0.445483i	$0.146968\pi$
$384$	−10.8814	−0.555288
$385$	0	0
$386$	−0.480277	−0.0244455
$387$	54.5437	2.77261
$388$	31.0748	1.57758
$389$	−2.71717	−0.137766	−0.0688829	−	0.997625i	$-0.521943\pi$
$389$	−2.71717	−0.137766	−0.0688829	+	0.997625i	$0.521943\pi$
$390$	−0.0179933	−0.000911125 0
$391$	−2.87070	−0.145178
$392$	0	0
$393$	−30.5766	−1.54238
$394$	−0.952232	−0.0479728
$395$	−4.93331	−0.248222
$396$	−35.3701	−1.77742
$397$	−27.0074	−1.35546	−0.677730	−	0.735311i	$-0.737036\pi$
$397$	−27.0074	−1.35546	−0.677730	+	0.735311i	$0.737036\pi$
$398$	1.65288	0.0828513
$399$	0	0
$400$	−18.7844	−0.939220
$401$	3.95183	0.197345	0.0986725	−	0.995120i	$-0.468540\pi$
$401$	3.95183	0.197345	0.0986725	+	0.995120i	$0.468540\pi$
$402$	−0.907177	−0.0452459
$403$	−0.775613	−0.0386360
$404$	−24.1404	−1.20103
$405$	3.65582	0.181659
$406$	0	0
$407$	−4.70491	−0.233214
$408$	0.524093	0.0259465
$409$	2.25833	0.111667	0.0558335	−	0.998440i	$-0.482218\pi$
$409$	2.25833	0.111667	0.0558335	+	0.998440i	$0.482218\pi$
$410$	−0.328465	−0.0162217
$411$	34.6613	1.70972
$412$	7.97871	0.393083
$413$	0	0
$414$	5.15951	0.253576
$415$	−1.41446	−0.0694333
$416$	−0.157582	−0.00772610
$417$	29.8595	1.46223
$418$	0.350576	0.0171472
$419$	29.9598	1.46363	0.731816	−	0.681502i	$-0.238673\pi$
$419$	29.9598	1.46363	0.731816	+	0.681502i	$0.238673\pi$
$420$	0	0
$421$	−13.5814	−0.661918	−0.330959	−	0.943645i	$-0.607372\pi$
$421$	−13.5814	−0.661918	−0.330959	+	0.943645i	$0.607372\pi$
$422$	−2.62849	−0.127953
$423$	65.8773	3.20307
$424$	3.72049	0.180683
$425$	1.82185	0.0883728
$426$	1.10277	0.0534294
$427$	0	0
$428$	23.5744	1.13951
$429$	−1.02961	−0.0497099
$430$	0.489105	0.0235867
$431$	15.1464	0.729576	0.364788	−	0.931091i	$-0.381141\pi$
$431$	15.1464	0.729576	0.364788	+	0.931091i	$0.381141\pi$
$432$	33.7816	1.62532
$433$	−2.31299	−0.111155	−0.0555775	−	0.998454i	$-0.517700\pi$
$433$	−2.31299	−0.111155	−0.0555775	+	0.998454i	$0.517700\pi$
$434$	0	0
$435$	−10.5708	−0.506832
$436$	37.9024	1.81520
$437$	7.55172	0.361248
$438$	−3.11615	−0.148895
$439$	−23.0598	−1.10059	−0.550293	−	0.834972i	$-0.685484\pi$
$439$	−23.0598	−1.10059	−0.550293	+	0.834972i	$0.685484\pi$
$440$	−0.636491	−0.0303435
$441$	0	0
$442$	0.00503702	0.000239587 0
$443$	13.4276	0.637964	0.318982	−	0.947761i	$-0.396659\pi$
$443$	13.4276	0.637964	0.318982	+	0.947761i	$0.396659\pi$
$444$	9.22013	0.437568
$445$	1.87722	0.0889890
$446$	−0.194124	−0.00919206
$447$	−22.1539	−1.04784
$448$	0	0
$449$	20.5036	0.967625	0.483812	−	0.875172i	$-0.339252\pi$
$449$	20.5036	0.967625	0.483812	+	0.875172i	$0.339252\pi$
$450$	−3.27441	−0.154357
$451$	−18.7953	−0.885037
$452$	34.6970	1.63201
$453$	29.6642	1.39375
$454$	−0.177810	−0.00834503
$455$	0	0
$456$	−1.37869	−0.0645630
$457$	24.7132	1.15604	0.578018	−	0.816024i	$-0.303826\pi$
$457$	24.7132	1.15604	0.578018	+	0.816024i	$0.303826\pi$
$458$	0.614086	0.0286944
$459$	−3.27639	−0.152929
$460$	−6.83217	−0.318551
$461$	6.18673	0.288145	0.144072	−	0.989567i	$-0.453980\pi$
$461$	6.18673	0.288145	0.144072	+	0.989567i	$0.453980\pi$
$462$	0	0
$463$	27.8718	1.29531	0.647656	−	0.761933i	$-0.275749\pi$
$463$	27.8718	1.29531	0.647656	+	0.761933i	$0.275749\pi$
$464$	−30.5110	−1.41644
$465$	9.21926	0.427533
$466$	−1.81514	−0.0840846
$467$	−9.50940	−0.440042	−0.220021	−	0.975495i	$-0.570613\pi$
$467$	−9.50940	−0.440042	−0.220021	+	0.975495i	$0.570613\pi$
$468$	1.33686	0.0617964
$469$	0	0
$470$	0.590736	0.0272486
$471$	35.4294	1.63250
$472$	3.40202	0.156591
$473$	27.9875	1.28686
$474$	−3.74623	−0.172070
$475$	−4.79259	−0.219899
$476$	0	0
$477$	−47.3979	−2.17020
$478$	−2.72670	−0.124716
$479$	33.6904	1.53935	0.769677	−	0.638433i	$-0.220417\pi$
$479$	33.6904	1.53935	0.769677	+	0.638433i	$0.220417\pi$
$480$	1.87309	0.0854943
$481$	0.177828	0.00810827
$482$	−3.32100	−0.151268
$483$	0	0
$484$	3.70291	0.168314
$485$	−7.12399	−0.323484
$486$	−0.222872	−0.0101097
$487$	−13.6711	−0.619495	−0.309747	−	0.950819i	$-0.600244\pi$
$487$	−13.6711	−0.619495	−0.309747	+	0.950819i	$0.600244\pi$
$488$	−5.78695	−0.261963
$489$	55.0482	2.48937
$490$	0	0
$491$	−10.3779	−0.468350	−0.234175	−	0.972195i	$-0.575239\pi$
$491$	−10.3779	−0.468350	−0.234175	+	0.972195i	$0.575239\pi$
$492$	36.8329	1.66056
$493$	2.95919	0.133275
$494$	−0.0132505	−0.000596167 0
$495$	8.10870	0.364459
$496$	26.6100	1.19482
$497$	0	0
$498$	−1.07411	−0.0481319
$499$	30.3124	1.35697	0.678485	−	0.734614i	$-0.262637\pi$
$499$	30.3124	1.35697	0.678485	+	0.734614i	$0.262637\pi$
$500$	8.85952	0.396210
$501$	−10.9245	−0.488072
$502$	1.71183	0.0764026
$503$	2.15307	0.0960005	0.0480003	−	0.998847i	$-0.484715\pi$
$503$	2.15307	0.0960005	0.0480003	+	0.998847i	$0.484715\pi$
$504$	0	0
$505$	5.53426	0.246271
$506$	2.64745	0.117693
$507$	−38.7233	−1.71976
$508$	−5.40466	−0.239793
$509$	23.3130	1.03333	0.516665	−	0.856188i	$-0.327173\pi$
$509$	23.3130	1.03333	0.516665	+	0.856188i	$0.327173\pi$
$510$	−0.0598722	−0.00265118
$511$	0	0
$512$	9.03095	0.399115
$513$	8.61892	0.380535
$514$	3.22777	0.142371
$515$	−1.82914	−0.0806016
$516$	−54.8466	−2.41449
$517$	33.8030	1.48665
$518$	0	0
$519$	22.9020	1.00529
$520$	0.0240570	0.00105497
$521$	8.92838	0.391159	0.195580	−	0.980688i	$-0.437341\pi$
$521$	8.92838	0.391159	0.195580	+	0.980688i	$0.437341\pi$
$522$	−5.31855	−0.232786
$523$	45.3629	1.98358	0.991790	−	0.127877i	$-0.0408162\pi$
$523$	45.3629	1.98358	0.991790	+	0.127877i	$0.0408162\pi$
$524$	20.3715	0.889932
$525$	0	0
$526$	0.795538	0.0346871
$527$	−2.58083	−0.112423
$528$	35.3240	1.53728
$529$	34.0285	1.47950
$530$	−0.425027	−0.0184620
$531$	−43.3407	−1.88082
$532$	0	0
$533$	0.710394	0.0307706
$534$	1.42552	0.0616881
$535$	−5.40450	−0.233657
$536$	1.21290	0.0523891
$537$	12.0416	0.519632
$538$	2.54489	0.109718
$539$	0	0
$540$	−7.79768	−0.335559
$541$	3.96287	0.170377	0.0851886	−	0.996365i	$-0.472851\pi$
$541$	3.96287	0.170377	0.0851886	+	0.996365i	$0.472851\pi$
$542$	−1.56290	−0.0671322
$543$	−10.2653	−0.440527
$544$	−0.524350	−0.0224813
$545$	−8.68923	−0.372206
$546$	0	0
$547$	2.84859	0.121797	0.0608985	−	0.998144i	$-0.480603\pi$
$547$	2.84859	0.121797	0.0608985	+	0.998144i	$0.480603\pi$
$548$	−23.0929	−0.986479
$549$	73.7240	3.14646
$550$	−1.68017	−0.0716425
$551$	−7.78449	−0.331630
$552$	−10.4115	−0.443141
$553$	0	0
$554$	−0.405452	−0.0172260
$555$	−2.11374	−0.0897233
$556$	−19.8937	−0.843683
$557$	5.82803	0.246942	0.123471	−	0.992348i	$-0.460597\pi$
$557$	5.82803	0.246942	0.123471	+	0.992348i	$0.460597\pi$
$558$	4.63853	0.196365
$559$	−1.05782	−0.0447412
$560$	0	0
$561$	−3.42599	−0.144645
$562$	3.36278	0.141850
$563$	−3.56682	−0.150324	−0.0751618	−	0.997171i	$-0.523947\pi$
$563$	−3.56682	−0.150324	−0.0751618	+	0.997171i	$0.523947\pi$
$564$	−66.2432	−2.78934
$565$	−7.95439	−0.334644
$566$	−2.85940	−0.120189
$567$	0	0
$568$	−1.47441	−0.0618647
$569$	−12.7110	−0.532874	−0.266437	−	0.963852i	$-0.585846\pi$
$569$	−12.7110	−0.532874	−0.266437	+	0.963852i	$0.585846\pi$
$570$	0.157501	0.00659698
$571$	−4.56560	−0.191064	−0.0955322	−	0.995426i	$-0.530455\pi$
$571$	−4.56560	−0.191064	−0.0955322	+	0.995426i	$0.530455\pi$
$572$	0.685970	0.0286818
$573$	−12.8781	−0.537991
$574$	0	0
$575$	−36.1923	−1.50932
$576$	−45.2336	−1.88473
$577$	−29.4497	−1.22601	−0.613004	−	0.790080i	$-0.710039\pi$
$577$	−29.4497	−1.22601	−0.613004	+	0.790080i	$0.710039\pi$
$578$	−1.95499	−0.0813170
$579$	−12.3468	−0.513115
$580$	7.04275	0.292434
$581$	0	0
$582$	−5.40977	−0.224242
$583$	−24.3208	−1.00727
$584$	4.16629	0.172402
$585$	−0.306479	−0.0126713
$586$	2.90362	0.119947
$587$	5.52421	0.228009	0.114004	−	0.993480i	$-0.463632\pi$
$587$	5.52421	0.228009	0.114004	+	0.993480i	$0.463632\pi$
$588$	0	0
$589$	6.78918	0.279743
$590$	−0.388645	−0.0160003
$591$	−24.4796	−1.00696
$592$	−6.10098	−0.250749
$593$	38.6333	1.58648	0.793241	−	0.608908i	$-0.208392\pi$
$593$	38.6333	1.58648	0.793241	+	0.608908i	$0.208392\pi$
$594$	3.02158	0.123977
$595$	0	0
$596$	14.7599	0.604590
$597$	42.4916	1.73907
$598$	−0.100064	−0.00409192
$599$	16.4316	0.671376	0.335688	−	0.941973i	$-0.391031\pi$
$599$	16.4316	0.671376	0.335688	+	0.941973i	$0.391031\pi$
$600$	6.60749	0.269750
$601$	−14.9427	−0.609524	−0.304762	−	0.952429i	$-0.598577\pi$
$601$	−14.9427	−0.609524	−0.304762	+	0.952429i	$0.598577\pi$
$602$	0	0
$603$	−15.4519	−0.629250
$604$	−19.7636	−0.804170
$605$	−0.848903	−0.0345128
$606$	4.20257	0.170718
$607$	2.60839	0.105871	0.0529356	−	0.998598i	$-0.483142\pi$
$607$	2.60839	0.105871	0.0529356	+	0.998598i	$0.483142\pi$
$608$	1.37936	0.0559406
$609$	0	0
$610$	0.661099	0.0267671
$611$	−1.27763	−0.0516873
$612$	4.44837	0.179815
$613$	16.5528	0.668561	0.334280	−	0.942474i	$-0.391507\pi$
$613$	16.5528	0.668561	0.334280	+	0.942474i	$0.391507\pi$
$614$	3.27672	0.132237
$615$	−8.44404	−0.340497
$616$	0	0
$617$	−8.91874	−0.359055	−0.179527	−	0.983753i	$-0.557457\pi$
$617$	−8.91874	−0.359055	−0.179527	+	0.983753i	$0.557457\pi$
$618$	−1.38900	−0.0558738
$619$	−17.3727	−0.698269	−0.349134	−	0.937073i	$-0.613524\pi$
$619$	−17.3727	−0.698269	−0.349134	+	0.937073i	$0.613524\pi$
$620$	−6.14228	−0.246680
$621$	65.0877	2.61188
$622$	2.17564	0.0872354
$623$	0	0
$624$	−1.33512	−0.0534476
$625$	21.9319	0.877276
$626$	−1.04045	−0.0415849
$627$	9.01247	0.359923
$628$	−23.6047	−0.941928
$629$	0.591719	0.0235934
$630$	0	0
$631$	−21.0077	−0.836304	−0.418152	−	0.908377i	$-0.637322\pi$
$631$	−21.0077	−0.836304	−0.418152	+	0.908377i	$0.637322\pi$
$632$	5.00871	0.199236
$633$	−67.5722	−2.68575
$634$	−1.96953	−0.0782198
$635$	1.23903	0.0491696
$636$	47.6611	1.88989
$637$	0	0
$638$	−2.72905	−0.108044
$639$	18.7835	0.743062
$640$	−1.66200	−0.0656964
$641$	−36.0443	−1.42367	−0.711833	−	0.702349i	$-0.752135\pi$
$641$	−36.0443	−1.42367	−0.711833	+	0.702349i	$0.752135\pi$
$642$	−4.10404	−0.161973
$643$	34.8200	1.37317	0.686584	−	0.727051i	$-0.259109\pi$
$643$	34.8200	1.37317	0.686584	+	0.727051i	$0.259109\pi$
$644$	0	0
$645$	12.5737	0.495090
$646$	−0.0440906	−0.00173472
$647$	−32.6329	−1.28293	−0.641466	−	0.767151i	$-0.721674\pi$
$647$	−32.6329	−1.28293	−0.641466	+	0.767151i	$0.721674\pi$
$648$	−3.71170	−0.145809
$649$	−22.2390	−0.872955
$650$	0.0635041	0.00249084
$651$	0	0
$652$	−36.6755	−1.43633
$653$	3.82264	0.149592	0.0747958	−	0.997199i	$-0.476170\pi$
$653$	3.82264	0.149592	0.0747958	+	0.997199i	$0.476170\pi$
$654$	−6.59837	−0.258017
$655$	−4.67022	−0.182480
$656$	−24.3724	−0.951582
$657$	−53.0772	−2.07074
$658$	0	0
$659$	15.9751	0.622302	0.311151	−	0.950360i	$-0.399285\pi$
$659$	15.9751	0.622302	0.311151	+	0.950360i	$0.399285\pi$
$660$	−8.15372	−0.317383
$661$	−2.90081	−0.112829	−0.0564143	−	0.998407i	$-0.517967\pi$
$661$	−2.90081	−0.112829	−0.0564143	+	0.998407i	$0.517967\pi$
$662$	−1.11451	−0.0433168
$663$	0.129490	0.00502897
$664$	1.43608	0.0557307
$665$	0	0
$666$	−1.06350	−0.0412096
$667$	−58.7863	−2.27621
$668$	7.27841	0.281610
$669$	−4.99048	−0.192943
$670$	−0.138561	−0.00535306
$671$	37.8293	1.46038
$672$	0	0
$673$	−12.5385	−0.483325	−0.241663	−	0.970360i	$-0.577693\pi$
$673$	−12.5385	−0.483325	−0.241663	+	0.970360i	$0.577693\pi$
$674$	0.491775	0.0189425
$675$	−41.3070	−1.58991
$676$	25.7992	0.992276
$677$	−16.6607	−0.640322	−0.320161	−	0.947363i	$-0.603737\pi$
$677$	−16.6607	−0.640322	−0.320161	+	0.947363i	$0.603737\pi$
$678$	−6.04036	−0.231978
$679$	0	0
$680$	0.0800491	0.00306974
$681$	−4.57107	−0.175164
$682$	2.38012	0.0911395
$683$	25.0821	0.959739	0.479869	−	0.877340i	$-0.340684\pi$
$683$	25.0821	0.959739	0.479869	+	0.877340i	$0.340684\pi$
$684$	−11.7020	−0.447435
$685$	5.29411	0.202277
$686$	0	0
$687$	15.7867	0.602300
$688$	36.2921	1.38362
$689$	0.919238	0.0350202
$690$	1.18940	0.0452797
$691$	−22.4076	−0.852427	−0.426213	−	0.904623i	$-0.640153\pi$
$691$	−22.4076	−0.852427	−0.426213	+	0.904623i	$0.640153\pi$
$692$	−15.2583	−0.580034
$693$	0	0
$694$	−1.53171	−0.0581429
$695$	4.56070	0.172997
$696$	10.7324	0.406810
$697$	2.36382	0.0895360
$698$	−2.36358	−0.0894627
$699$	−46.6629	−1.76495
$700$	0	0
$701$	16.1548	0.610160	0.305080	−	0.952327i	$-0.401317\pi$
$701$	16.1548	0.610160	0.305080	+	0.952327i	$0.401317\pi$
$702$	−0.114205	−0.00431038
$703$	−1.55658	−0.0587077
$704$	−23.2102	−0.874769
$705$	15.1864	0.571954
$706$	−2.08589	−0.0785034
$707$	0	0
$708$	43.5813	1.63789
$709$	−22.9006	−0.860049	−0.430025	−	0.902817i	$-0.641495\pi$
$709$	−22.9006	−0.860049	−0.430025	+	0.902817i	$0.641495\pi$
$710$	0.168435	0.00632127
$711$	−63.8094	−2.39304
$712$	−1.90591	−0.0714271
$713$	51.2700	1.92008
$714$	0	0
$715$	−0.157260	−0.00588121
$716$	−8.02262	−0.299819
$717$	−70.0970	−2.61782
$718$	2.89585	0.108072
$719$	−6.52984	−0.243522	−0.121761	−	0.992559i	$-0.538854\pi$
$719$	−6.52984	−0.243522	−0.121761	+	0.992559i	$0.538854\pi$
$720$	10.5148	0.391862
$721$	0	0
$722$	0.115985	0.00431653
$723$	−85.3751	−3.17513
$724$	6.83920	0.254177
$725$	37.3079	1.38558
$726$	−0.644635	−0.0239246
$727$	−32.4672	−1.20414	−0.602071	−	0.798443i	$-0.705658\pi$
$727$	−32.4672	−1.20414	−0.602071	+	0.798443i	$0.705658\pi$
$728$	0	0
$729$	−29.8116	−1.10413
$730$	−0.475955	−0.0176159
$731$	−3.51988	−0.130187
$732$	−74.1334	−2.74005
$733$	16.1067	0.594914	0.297457	−	0.954735i	$-0.403862\pi$
$733$	16.1067	0.594914	0.297457	+	0.954735i	$0.403862\pi$
$734$	−1.43773	−0.0530675
$735$	0	0
$736$	10.4166	0.383960
$737$	−7.92868	−0.292057
$738$	−4.24849	−0.156389
$739$	−31.0575	−1.14247	−0.571234	−	0.820788i	$-0.693535\pi$
$739$	−31.0575	−1.14247	−0.571234	+	0.820788i	$0.693535\pi$
$740$	1.40827	0.0517689
$741$	−0.340638	−0.0125137
$742$	0	0
$743$	33.5645	1.23136	0.615681	−	0.787995i	$-0.288881\pi$
$743$	33.5645	1.23136	0.615681	+	0.787995i	$0.288881\pi$
$744$	−9.36016	−0.343160
$745$	−3.38375	−0.123971
$746$	0.768744	0.0281457
$747$	−18.2952	−0.669387
$748$	2.28255	0.0834582
$749$	0	0
$750$	−1.54234	−0.0563183
$751$	−5.09207	−0.185812	−0.0929062	−	0.995675i	$-0.529616\pi$
$751$	−5.09207	−0.185812	−0.0929062	+	0.995675i	$0.529616\pi$
$752$	43.8332	1.59843
$753$	44.0070	1.60371
$754$	0.103148	0.00375643
$755$	4.53086	0.164895
$756$	0	0
$757$	23.6010	0.857792	0.428896	−	0.903354i	$-0.358903\pi$
$757$	23.6010	0.857792	0.428896	+	0.903354i	$0.358903\pi$
$758$	0.667040	0.0242280
$759$	68.0596	2.47041
$760$	−0.210578	−0.00763848
$761$	15.4115	0.558665	0.279333	−	0.960194i	$-0.409887\pi$
$761$	15.4115	0.558665	0.279333	+	0.960194i	$0.409887\pi$
$762$	0.940890	0.0340848
$763$	0	0
$764$	8.57997	0.310412
$765$	−1.01980	−0.0368710
$766$	4.06440	0.146853
$767$	0.840551	0.0303505
$768$	44.5307	1.60686
$769$	5.46467	0.197061	0.0985305	−	0.995134i	$-0.468586\pi$
$769$	5.46467	0.197061	0.0985305	+	0.995134i	$0.468586\pi$
$770$	0	0
$771$	82.9783	2.98839
$772$	8.22597	0.296059
$773$	−29.7542	−1.07019	−0.535093	−	0.844793i	$-0.679723\pi$
$773$	−29.7542	−1.07019	−0.535093	+	0.844793i	$0.679723\pi$
$774$	6.32628	0.227393
$775$	−32.5378	−1.16879
$776$	7.23286	0.259645
$777$	0	0
$778$	−0.315152	−0.0112987
$779$	−6.21830	−0.222794
$780$	0.308181	0.0110346
$781$	9.63817	0.344881
$782$	−0.332960	−0.0119066
$783$	−67.0939	−2.39774
$784$	0	0
$785$	5.41143	0.193142
$786$	−3.54644	−0.126497
$787$	−14.8486	−0.529296	−0.264648	−	0.964345i	$-0.585256\pi$
$787$	−14.8486	−0.529296	−0.264648	+	0.964345i	$0.585256\pi$
$788$	16.3094	0.580999
$789$	20.4514	0.728089
$790$	−0.572193	−0.0203577
$791$	0	0
$792$	−8.23262	−0.292533
$793$	−1.42981	−0.0507739
$794$	−3.13246	−0.111167
$795$	−10.9264	−0.387521
$796$	−28.3098	−1.00341
$797$	29.7181	1.05267	0.526334	−	0.850278i	$-0.323566\pi$
$797$	29.7181	1.05267	0.526334	+	0.850278i	$0.323566\pi$
$798$	0	0
$799$	−4.25127	−0.150399
$800$	−6.61073	−0.233725
$801$	24.2808	0.857918
$802$	0.458355	0.0161851
$803$	−27.2350	−0.961101
$804$	15.5377	0.547973
$805$	0	0
$806$	−0.0899598	−0.00316870
$807$	65.4232	2.30300
$808$	−5.61884	−0.197670
$809$	−42.3066	−1.48742	−0.743710	−	0.668502i	$-0.766936\pi$
$809$	−42.3066	−1.48742	−0.743710	+	0.668502i	$0.766936\pi$
$810$	0.424022	0.0148986
$811$	−38.8133	−1.36292	−0.681460	−	0.731855i	$-0.738655\pi$
$811$	−38.8133	−1.36292	−0.681460	+	0.731855i	$0.738655\pi$
$812$	0	0
$813$	−40.1784	−1.40912
$814$	−0.545701	−0.0191268
$815$	8.40797	0.294518
$816$	−4.44257	−0.155521
$817$	9.25945	0.323947
$818$	0.261933	0.00915828
$819$	0	0
$820$	5.62579	0.196461
$821$	47.0318	1.64142	0.820710	−	0.571345i	$-0.193578\pi$
$821$	47.0318	1.64142	0.820710	+	0.571345i	$0.193578\pi$
$822$	4.02021	0.140221
$823$	−19.2051	−0.669446	−0.334723	−	0.942316i	$-0.608643\pi$
$823$	−19.2051	−0.669446	−0.334723	+	0.942316i	$0.608643\pi$
$824$	1.85709	0.0646950
$825$	−43.1931	−1.50379
$826$	0	0
$827$	−45.0176	−1.56542	−0.782708	−	0.622389i	$-0.786162\pi$
$827$	−45.0176	−1.56542	−0.782708	+	0.622389i	$0.786162\pi$
$828$	−88.3699	−3.07107
$829$	4.62639	0.160681	0.0803407	−	0.996767i	$-0.474399\pi$
$829$	4.62639	0.160681	0.0803407	+	0.996767i	$0.474399\pi$
$830$	−0.164057	−0.00569451
$831$	−10.4232	−0.361577
$832$	0.877262	0.0304136
$833$	0	0
$834$	3.46327	0.119923
$835$	−1.66860	−0.0577441
$836$	−6.00450	−0.207670
$837$	58.5154	2.02259
$838$	3.47490	0.120038
$839$	−51.4784	−1.77723	−0.888616	−	0.458653i	$-0.848332\pi$
$839$	−51.4784	−1.77723	−0.888616	+	0.458653i	$0.848332\pi$
$840$	0	0
$841$	31.5983	1.08960
$842$	−1.57525	−0.0542866
$843$	86.4491	2.97747
$844$	45.0196	1.54964
$845$	−5.91453	−0.203466
$846$	7.64081	0.262697
$847$	0	0
$848$	−31.5375	−1.08300
$849$	−73.5083	−2.52280
$850$	0.211308	0.00724781
$851$	−11.7549	−0.402953
$852$	−18.8878	−0.647084
$853$	−20.2256	−0.692510	−0.346255	−	0.938140i	$-0.612547\pi$
$853$	−20.2256	−0.692510	−0.346255	+	0.938140i	$0.612547\pi$
$854$	0	0
$855$	2.68270	0.0917465
$856$	5.48710	0.187545
$857$	16.7793	0.573171	0.286585	−	0.958055i	$-0.407480\pi$
$857$	16.7793	0.573171	0.286585	+	0.958055i	$0.407480\pi$
$858$	−0.119419	−0.00407691
$859$	28.1017	0.958818	0.479409	−	0.877592i	$-0.340851\pi$
$859$	28.1017	0.958818	0.479409	+	0.877592i	$0.340851\pi$
$860$	−8.37718	−0.285659
$861$	0	0
$862$	1.75676	0.0598355
$863$	0.110636	0.00376609	0.00188305	−	0.999998i	$-0.499401\pi$
$863$	0.110636	0.00376609	0.00188305	+	0.999998i	$0.499401\pi$
$864$	11.8886	0.404460
$865$	3.49801	0.118936
$866$	−0.268273	−0.00911628
$867$	−50.2582	−1.70686
$868$	0	0
$869$	−32.7419	−1.11069
$870$	−1.22606	−0.0415674
$871$	0.299675	0.0101541
$872$	8.82203	0.298752
$873$	−92.1444	−3.11862
$874$	0.875890	0.0296274
$875$	0	0
$876$	53.3720	1.80327
$877$	−15.9499	−0.538590	−0.269295	−	0.963058i	$-0.586791\pi$
$877$	−15.9499	−0.538590	−0.269295	+	0.963058i	$0.586791\pi$
$878$	−2.67461	−0.0902636
$879$	74.6450	2.51771
$880$	5.39534	0.181877
$881$	26.1322	0.880415	0.440208	−	0.897896i	$-0.354905\pi$
$881$	26.1322	0.880415	0.440208	+	0.897896i	$0.354905\pi$
$882$	0	0
$883$	13.7510	0.462758	0.231379	−	0.972864i	$-0.425676\pi$
$883$	13.7510	0.462758	0.231379	+	0.972864i	$0.425676\pi$
$884$	−0.0862719	−0.00290164
$885$	−9.99114	−0.335849
$886$	1.55740	0.0523220
$887$	14.6047	0.490378	0.245189	−	0.969475i	$-0.421150\pi$
$887$	14.6047	0.490378	0.245189	+	0.969475i	$0.421150\pi$
$888$	2.14604	0.0720165
$889$	0	0
$890$	0.217731	0.00729835
$891$	24.2633	0.812852
$892$	3.32488	0.111325
$893$	11.1835	0.374241
$894$	−2.56953	−0.0859380
$895$	1.83921	0.0614779
$896$	0	0
$897$	−2.57241	−0.0858901
$898$	2.37812	0.0793589
$899$	−52.8503	−1.76266
$900$	56.0827	1.86942
$901$	3.05874	0.101901
$902$	−2.17998	−0.0725855
$903$	0	0
$904$	8.07596	0.268602
$905$	−1.56791	−0.0521190
$906$	3.44062	0.114307
$907$	35.6929	1.18516	0.592581	−	0.805511i	$-0.298109\pi$
$907$	35.6929	1.18516	0.592581	+	0.805511i	$0.298109\pi$
$908$	3.04545	0.101067
$909$	71.5823	2.37423
$910$	0	0
$911$	−30.9668	−1.02598	−0.512988	−	0.858396i	$-0.671462\pi$
$911$	−30.9668	−1.02598	−0.512988	+	0.858396i	$0.671462\pi$
$912$	11.6867	0.386986
$913$	−9.38764	−0.310686
$914$	2.86637	0.0948112
$915$	16.9953	0.561847
$916$	−10.5178	−0.347518
$917$	0	0
$918$	−0.380014	−0.0125423
$919$	16.2032	0.534495	0.267248	−	0.963628i	$-0.413886\pi$
$919$	16.2032	0.534495	0.267248	+	0.963628i	$0.413886\pi$
$920$	−1.59023	−0.0524283
$921$	84.2366	2.77569
$922$	0.717571	0.0236319
$923$	−0.364287	−0.0119907
$924$	0	0
$925$	7.46007	0.245286
$926$	3.23272	0.106234
$927$	−23.6588	−0.777057
$928$	−10.7376	−0.352480
$929$	25.4330	0.834430	0.417215	−	0.908808i	$-0.363006\pi$
$929$	25.4330	0.834430	0.417215	+	0.908808i	$0.363006\pi$
$930$	1.06930	0.0350637
$931$	0	0
$932$	31.0889	1.01835
$933$	55.9306	1.83109
$934$	−1.10295	−0.0360897
$935$	−0.523280	−0.0171131
$936$	0.311163	0.0101707
$937$	−27.4028	−0.895209	−0.447604	−	0.894232i	$-0.647723\pi$
$937$	−27.4028	−0.895209	−0.447604	+	0.894232i	$0.647723\pi$
$938$	0	0
$939$	−26.7476	−0.872874
$940$	−10.1179	−0.330008
$941$	10.7287	0.349746	0.174873	−	0.984591i	$-0.444049\pi$
$941$	10.7287	0.349746	0.174873	+	0.984591i	$0.444049\pi$
$942$	4.10930	0.133888
$943$	−46.9589	−1.52919
$944$	−28.8379	−0.938592
$945$	0	0
$946$	3.24614	0.105541
$947$	−33.1329	−1.07667	−0.538337	−	0.842730i	$-0.680947\pi$
$947$	−33.1329	−1.07667	−0.538337	+	0.842730i	$0.680947\pi$
$948$	64.1637	2.08394
$949$	1.02938	0.0334152
$950$	−0.555871	−0.0180348
$951$	−50.6318	−1.64185
$952$	0	0
$953$	13.0094	0.421417	0.210709	−	0.977549i	$-0.432423\pi$
$953$	13.0094	0.421417	0.210709	+	0.977549i	$0.432423\pi$
$954$	−5.49747	−0.177987
$955$	−1.96698	−0.0636500
$956$	46.7017	1.51044
$957$	−70.1574	−2.26787
$958$	3.90760	0.126249
$959$	0	0
$960$	−10.4275	−0.336546
$961$	15.0930	0.486870
$962$	0.0206255	0.000664992 0
$963$	−69.9039	−2.25262
$964$	56.8807	1.83200
$965$	−1.88583	−0.0607069
$966$	0	0
$967$	25.4242	0.817587	0.408793	−	0.912627i	$-0.365950\pi$
$967$	25.4242	0.817587	0.408793	+	0.912627i	$0.365950\pi$
$968$	0.861876	0.0277018
$969$	−1.13346	−0.0364121
$970$	−0.826279	−0.0265302
$971$	−14.3770	−0.461381	−0.230691	−	0.973027i	$-0.574099\pi$
$971$	−14.3770	−0.461381	−0.230691	+	0.973027i	$0.574099\pi$
$972$	3.81726	0.122439
$973$	0	0
$974$	−1.58564	−0.0508073
$975$	1.63254	0.0522831
$976$	49.0542	1.57019
$977$	37.4276	1.19741	0.598707	−	0.800968i	$-0.295681\pi$
$977$	37.4276	1.19741	0.598707	+	0.800968i	$0.295681\pi$
$978$	6.38479	0.204163
$979$	12.4589	0.398189
$980$	0	0
$981$	−112.390	−3.58833
$982$	−1.20369	−0.0384113
$983$	−15.6188	−0.498162	−0.249081	−	0.968483i	$-0.580128\pi$
$983$	−15.6188	−0.498162	−0.249081	+	0.968483i	$0.580128\pi$
$984$	8.57309	0.273300
$985$	−3.73898	−0.119134
$986$	0.343223	0.0109304
$987$	0	0
$988$	0.226948	0.00722018
$989$	69.9248	2.22348
$990$	0.940491	0.0298908
$991$	16.9606	0.538770	0.269385	−	0.963033i	$-0.413180\pi$
$991$	16.9606	0.538770	0.269385	+	0.963033i	$0.413180\pi$
$992$	9.36475	0.297331
$993$	−28.6515	−0.909229
$994$	0	0
$995$	6.49009	0.205750
$996$	18.3968	0.582926
$997$	−48.3424	−1.53102	−0.765510	−	0.643425i	$-0.777513\pi$
$997$	−48.3424	−1.53102	−0.765510	+	0.643425i	$0.777513\pi$
$998$	3.51580	0.111291
$999$	−13.4161	−0.424466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.q.1.6	yes	10
3.2	odd	2		8379.2.a.cs.1.5		10
7.2	even	3		931.2.f.q.704.5		20
7.3	odd	6		931.2.f.r.324.5		20
7.4	even	3		931.2.f.q.324.5		20
7.5	odd	6		931.2.f.r.704.5		20
7.6	odd	2		931.2.a.p.1.6	✓	10
21.20	even	2		8379.2.a.ct.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.6	✓	10	7.6	odd	2
931.2.a.q.1.6	yes	10	1.1	even	1	trivial
931.2.f.q.324.5		20	7.4	even	3
931.2.f.q.704.5		20	7.2	even	3
931.2.f.r.324.5		20	7.3	odd	6
931.2.f.r.704.5		20	7.5	odd	6
8379.2.a.cs.1.5		10	3.2	odd	2
8379.2.a.ct.1.5		10	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)

\(f(q)\)	\(=\)	\(q+0.115985 q^{2} +2.98171 q^{3} -1.98655 q^{4} +0.455421 q^{5} +0.345835 q^{6} -0.462382 q^{8} +5.89060 q^{9} +O(q^{10})\)	\(q+0.115985 q^{2} +2.98171 q^{3} -1.98655 q^{4} +0.455421 q^{5} +0.345835 q^{6} -0.462382 q^{8} +5.89060 q^{9} +0.0528223 q^{10} +3.02258 q^{11} -5.92331 q^{12} -0.114243 q^{13} +1.35793 q^{15} +3.91947 q^{16} -0.380139 q^{17} +0.683224 q^{18} +1.00000 q^{19} -0.904716 q^{20} +0.350576 q^{22} +7.55172 q^{23} -1.37869 q^{24} -4.79259 q^{25} -0.0132505 q^{26} +8.61892 q^{27} -7.78449 q^{29} +0.157501 q^{30} +6.78918 q^{31} +1.37936 q^{32} +9.01247 q^{33} -0.0440906 q^{34} -11.7020 q^{36} -1.55658 q^{37} +0.115985 q^{38} -0.340638 q^{39} -0.210578 q^{40} -6.21830 q^{41} +9.25945 q^{43} -6.00450 q^{44} +2.68270 q^{45} +0.875890 q^{46} +11.1835 q^{47} +11.6867 q^{48} -0.555871 q^{50} -1.13346 q^{51} +0.226948 q^{52} -8.04637 q^{53} +0.999670 q^{54} +1.37655 q^{55} +2.98171 q^{57} -0.902887 q^{58} -7.35760 q^{59} -2.69760 q^{60} +12.5155 q^{61} +0.787446 q^{62} -7.67894 q^{64} -0.0520285 q^{65} +1.04532 q^{66} -2.62315 q^{67} +0.755164 q^{68} +22.5170 q^{69} +3.18872 q^{71} -2.72370 q^{72} -9.01050 q^{73} -0.180541 q^{74} -14.2901 q^{75} -1.98655 q^{76} -0.0395091 q^{78} -10.8324 q^{79} +1.78501 q^{80} +8.02734 q^{81} -0.721232 q^{82} -3.10584 q^{83} -0.173123 q^{85} +1.07396 q^{86} -23.2111 q^{87} -1.39759 q^{88} +4.12195 q^{89} +0.311155 q^{90} -15.0019 q^{92} +20.2434 q^{93} +1.29712 q^{94} +0.455421 q^{95} +4.11286 q^{96} -15.6426 q^{97} +17.8048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 4 q^{3} + 10 q^{4} + 16 q^{5} + 8 q^{6} - 6 q^{8} + 10 q^{9} - 12 q^{10} + 12 q^{12} + 12 q^{13} + 2 q^{16} + 16 q^{17} + 2 q^{18} + 10 q^{19} + 32 q^{20} + 4 q^{22} + 12 q^{23} - 8 q^{24} + 14 q^{25} + 24 q^{26} + 16 q^{27} - 12 q^{29} - 12 q^{30} + 8 q^{31} - 34 q^{32} - 4 q^{33} + 16 q^{34} - 6 q^{36} + 4 q^{37} - 2 q^{38} - 4 q^{39} - 20 q^{40} + 40 q^{41} + 4 q^{43} - 20 q^{44} + 24 q^{45} - 32 q^{46} + 16 q^{47} + 12 q^{48} - 34 q^{50} - 28 q^{51} - 40 q^{52} + 8 q^{54} + 16 q^{55} + 4 q^{57} - 8 q^{58} + 36 q^{59} + 32 q^{60} + 16 q^{61} - 16 q^{62} + 18 q^{64} + 8 q^{65} + 8 q^{66} - 28 q^{67} + 40 q^{68} + 48 q^{69} - 12 q^{71} + 34 q^{72} + 24 q^{74} - 32 q^{75} + 10 q^{76} + 28 q^{78} - 8 q^{79} + 8 q^{80} + 14 q^{81} - 8 q^{82} + 40 q^{85} - 52 q^{86} - 8 q^{87} - 4 q^{88} + 48 q^{89} - 64 q^{90} + 28 q^{92} + 40 q^{93} - 36 q^{94} + 16 q^{95} - 8 q^{96} - 16 q^{97} - 8 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 4 * q^3 + 10 * q^4 + 16 * q^5 + 8 * q^6 - 6 * q^8 + 10 * q^9 - 12 * q^10 + 12 * q^12 + 12 * q^13 + 2 * q^16 + 16 * q^17 + 2 * q^18 + 10 * q^19 + 32 * q^20 + 4 * q^22 + 12 * q^23 - 8 * q^24 + 14 * q^25 + 24 * q^26 + 16 * q^27 - 12 * q^29 - 12 * q^30 + 8 * q^31 - 34 * q^32 - 4 * q^33 + 16 * q^34 - 6 * q^36 + 4 * q^37 - 2 * q^38 - 4 * q^39 - 20 * q^40 + 40 * q^41 + 4 * q^43 - 20 * q^44 + 24 * q^45 - 32 * q^46 + 16 * q^47 + 12 * q^48 - 34 * q^50 - 28 * q^51 - 40 * q^52 + 8 * q^54 + 16 * q^55 + 4 * q^57 - 8 * q^58 + 36 * q^59 + 32 * q^60 + 16 * q^61 - 16 * q^62 + 18 * q^64 + 8 * q^65 + 8 * q^66 - 28 * q^67 + 40 * q^68 + 48 * q^69 - 12 * q^71 + 34 * q^72 + 24 * q^74 - 32 * q^75 + 10 * q^76 + 28 * q^78 - 8 * q^79 + 8 * q^80 + 14 * q^81 - 8 * q^82 + 40 * q^85 - 52 * q^86 - 8 * q^87 - 4 * q^88 + 48 * q^89 - 64 * q^90 + 28 * q^92 + 40 * q^93 - 36 * q^94 + 16 * q^95 - 8 * q^96 - 16 * q^97 - 8 * q^99

Introduction

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