LMFDB - Embedded newform 931.2.a.p.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:	$1$
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	$-0.830002\pi$
$3$	−2.98171	−1.72149	−0.860746	+	0.509035i	$0.830002\pi$
$4$	−1.98655	−0.993274
$5$	−0.455421	−0.203671	−0.101835	−	0.994801i	$-0.532471\pi$
$5$	−0.455421	−0.203671	−0.101835	+	0.994801i	$0.532471\pi$
$6$	−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	$-0.494957\pi$
$13$	0.114243	0.0316852	0.0158426	+	0.999874i	$0.494957\pi$
$14$	0	0
$15$	1.35793	0.350617
$16$	3.91947	0.979866
$17$	0.380139	0.0921973	0.0460986	−	0.998937i	$-0.485321\pi$
$17$	0.380139	0.0921973	0.0460986	+	0.998937i	$0.485321\pi$
$18$	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	$-0.708705\pi$
$31$	−6.78918	−1.21937	−0.609686	+	0.792643i	$0.708705\pi$
$32$	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	$-0.338613\pi$
$41$	6.21830	0.971135	0.485567	+	0.874199i	$0.338613\pi$
$42$	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	$-0.803614\pi$
$47$	−11.1835	−1.63128	−0.815638	+	0.578562i	$0.803614\pi$
$48$	−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	$-0.341022\pi$
$59$	7.35760	0.957878	0.478939	+	0.877848i	$0.341022\pi$
$60$	−2.69760	−0.348259
$61$	−12.5155	−1.60245	−0.801225	−	0.598363i	$-0.795818\pi$
$61$	−12.5155	−1.60245	−0.801225	+	0.598363i	$0.795818\pi$
$62$	−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	$-0.323205\pi$
$73$	9.01050	1.05460	0.527299	+	0.849680i	$0.323205\pi$
$74$	−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	$-0.445476\pi$
$83$	3.10584	0.340910	0.170455	+	0.985365i	$0.445476\pi$
$84$	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	$-0.570104\pi$
$89$	−4.12195	−0.436926	−0.218463	+	0.975845i	$0.570104\pi$
$90$	−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	$-0.207925\pi$
$97$	15.6426	1.58827	0.794134	+	0.607743i	$0.207925\pi$
$98$	0	0
$99$	17.8048	1.78945
$100$	9.52071	0.952071
$101$	−12.1520	−1.20916	−0.604582	−	0.796543i	$-0.706660\pi$
$101$	−12.1520	−1.20916	−0.604582	+	0.796543i	$0.706660\pi$
$102$	−0.131465	−0.0130170
$103$	4.01637	0.395745	0.197872	−	0.980228i	$-0.436597\pi$
$103$	4.01637	0.395745	0.197872	+	0.980228i	$0.436597\pi$
$104$	−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	$-0.352144\pi$
$131$	10.2547	0.895958	0.447979	+	0.894044i	$0.352144\pi$
$132$	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	$-0.639620\pi$
$139$	−10.0142	−0.849396	−0.424698	+	0.905335i	$0.639620\pi$
$140$	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	$-0.657246\pi$
$157$	−11.8823	−0.948307	−0.474153	+	0.880442i	$0.657246\pi$
$158$	−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	$-0.454724\pi$
$167$	3.66385	0.283517	0.141759	+	0.989901i	$0.454724\pi$
$168$	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	$-0.594314\pi$
$173$	−7.68083	−0.583962	−0.291981	+	0.956424i	$0.594314\pi$
$174$	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	$-0.459161\pi$
$181$	3.44276	0.255898	0.127949	+	0.991781i	$0.459161\pi$
$182$	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	$-0.668546\pi$
$199$	−14.2507	−1.01021	−0.505104	+	0.863058i	$0.668546\pi$
$200$	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	$-0.482153\pi$
$223$	1.67370	0.112079	0.0560395	+	0.998429i	$0.482153\pi$
$224$	0	0
$225$	−28.2312	−1.88208
$226$	−2.02580	−0.134754
$227$	1.53304	0.101751	0.0508756	−	0.998705i	$-0.483799\pi$
$227$	1.53304	0.101751	0.0508756	+	0.998705i	$0.483799\pi$
$228$	−5.92331	−0.392281
$229$	−5.29451	−0.349871	−0.174936	−	0.984580i	$-0.555972\pi$
$229$	−5.29451	−0.349871	−0.174936	+	0.984580i	$0.555972\pi$
$230$	−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	$-0.126386\pi$
$241$	28.6329	1.84441	0.922205	+	0.386702i	$0.126386\pi$
$242$	−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	$-0.654230\pi$
$251$	−14.7590	−0.931579	−0.465790	+	0.884896i	$0.654230\pi$
$252$	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	$-0.834572\pi$
$257$	−27.8291	−1.73593	−0.867965	+	0.496625i	$0.834572\pi$
$258$	−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	$-0.733234\pi$
$269$	−21.9415	−1.33780	−0.668898	+	0.743354i	$0.733234\pi$
$270$	0.455271	0.0277069
$271$	13.4749	0.818544	0.409272	−	0.912412i	$-0.365783\pi$
$271$	13.4749	0.818544	0.409272	+	0.912412i	$0.365783\pi$
$272$	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	$-0.238243\pi$
$283$	24.6530	1.46547	0.732736	+	0.680513i	$0.238243\pi$
$284$	−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	$-0.761067\pi$
$293$	−25.0343	−1.46252	−0.731260	+	0.682099i	$0.761067\pi$
$294$	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	$-0.798473\pi$
$307$	−28.2511	−1.61237	−0.806187	+	0.591660i	$0.798473\pi$
$308$	0	0
$309$	−11.9756	−0.681271
$310$	0.358620	0.0203682
$311$	−18.7579	−1.06366	−0.531831	−	0.846850i	$-0.678496\pi$
$311$	−18.7579	−1.06366	−0.531831	+	0.846850i	$0.678496\pi$
$312$	0.157505	0.00891695
$313$	8.97055	0.507045	0.253523	−	0.967329i	$-0.418411\pi$
$313$	8.97055	0.507045	0.253523	+	0.967329i	$0.418411\pi$
$314$	−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	$-0.316374\pi$
$349$	20.3782	1.09082	0.545410	+	0.838169i	$0.316374\pi$
$350$	0	0
$351$	−0.984648	−0.0525566
$352$	4.16924	0.222221
$353$	17.9841	0.957194	0.478597	−	0.878035i	$-0.341145\pi$
$353$	17.9841	0.957194	0.478597	+	0.878035i	$0.341145\pi$
$354$	−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	$-0.395131\pi$
$367$	12.3958	0.647053	0.323527	+	0.946219i	$0.395131\pi$
$368$	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	$-0.853032\pi$
$383$	−35.0424	−1.79058	−0.895290	+	0.445483i	$0.853032\pi$
$384$	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	$-0.262964\pi$
$397$	27.0074	1.35546	0.677730	+	0.735311i	$0.262964\pi$
$398$	−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	$-0.517782\pi$
$409$	−2.25833	−0.111667	−0.0558335	+	0.998440i	$0.517782\pi$
$410$	−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	$-0.761327\pi$
$419$	−29.9598	−1.46363	−0.731816	+	0.681502i	$0.761327\pi$
$420$	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	$-0.482300\pi$
$433$	2.31299	0.111155	0.0555775	+	0.998454i	$0.482300\pi$
$434$	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	$-0.314516\pi$
$439$	23.0598	1.10059	0.550293	+	0.834972i	$0.314516\pi$
$440$	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	$-0.546020\pi$
$461$	−6.18673	−0.288145	−0.144072	+	0.989567i	$0.546020\pi$
$462$	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	$-0.429387\pi$
$467$	9.50940	0.440042	0.220021	+	0.975495i	$0.429387\pi$
$468$	−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	$-0.779583\pi$
$479$	−33.6904	−1.53935	−0.769677	+	0.638433i	$0.779583\pi$
$480$	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	$-0.515285\pi$
$503$	−2.15307	−0.0960005	−0.0480003	+	0.998847i	$0.515285\pi$
$504$	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	$-0.672827\pi$
$509$	−23.3130	−1.03333	−0.516665	+	0.856188i	$0.672827\pi$
$510$	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	$-0.562659\pi$
$521$	−8.92838	−0.391159	−0.195580	+	0.980688i	$0.562659\pi$
$522$	−5.31855	−0.232786
$523$	−45.3629	−1.98358	−0.991790	−	0.127877i	$-0.959184\pi$
$523$	−45.3629	−1.98358	−0.991790	+	0.127877i	$0.959184\pi$
$524$	−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	$-0.476053\pi$
$563$	3.56682	0.150324	0.0751618	+	0.997171i	$0.476053\pi$
$564$	−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	$-0.289961\pi$
$577$	29.4497	1.22601	0.613004	+	0.790080i	$0.289961\pi$
$578$	−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	$-0.536368\pi$
$587$	−5.52421	−0.228009	−0.114004	+	0.993480i	$0.536368\pi$
$588$	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	$-0.791608\pi$
$593$	−38.6333	−1.58648	−0.793241	+	0.608908i	$0.791608\pi$
$594$	−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	$-0.401423\pi$
$601$	14.9427	0.609524	0.304762	+	0.952429i	$0.401423\pi$
$602$	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	$-0.516858\pi$
$607$	−2.60839	−0.105871	−0.0529356	+	0.998598i	$0.516858\pi$
$608$	−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	$-0.386476\pi$
$619$	17.3727	0.698269	0.349134	+	0.937073i	$0.386476\pi$
$620$	−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	$-0.740891\pi$
$643$	−34.8200	−1.37317	−0.686584	+	0.727051i	$0.740891\pi$
$644$	0	0
$645$	12.5737	0.495090
$646$	−0.0440906	−0.00173472
$647$	32.6329	1.28293	0.641466	−	0.767151i	$-0.278326\pi$
$647$	32.6329	1.28293	0.641466	+	0.767151i	$0.278326\pi$
$648$	−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	$-0.482033\pi$
$661$	2.90081	0.112829	0.0564143	+	0.998407i	$0.482033\pi$
$662$	−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	$-0.396263\pi$
$677$	16.6607	0.640322	0.320161	+	0.947363i	$0.396263\pi$
$678$	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	$-0.359847\pi$
$691$	22.4076	0.852427	0.426213	+	0.904623i	$0.359847\pi$
$692$	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	$-0.461146\pi$
$719$	6.52984	0.243522	0.121761	+	0.992559i	$0.461146\pi$
$720$	−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	$-0.294342\pi$
$727$	32.4672	1.20414	0.602071	+	0.798443i	$0.294342\pi$
$728$	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	$-0.596138\pi$
$733$	−16.1067	−0.594914	−0.297457	+	0.954735i	$0.596138\pi$
$734$	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	$-0.590113\pi$
$761$	−15.4115	−0.558665	−0.279333	+	0.960194i	$0.590113\pi$
$762$	−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	$-0.531414\pi$
$769$	−5.46467	−0.197061	−0.0985305	+	0.995134i	$0.531414\pi$
$770$	0	0
$771$	82.9783	2.98839
$772$	8.22597	0.296059
$773$	29.7542	1.07019	0.535093	−	0.844793i	$-0.320277\pi$
$773$	29.7542	1.07019	0.535093	+	0.844793i	$0.320277\pi$
$774$	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	$-0.414744\pi$
$787$	14.8486	0.529296	0.264648	+	0.964345i	$0.414744\pi$
$788$	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	$-0.676434\pi$
$797$	−29.7181	−1.05267	−0.526334	+	0.850278i	$0.676434\pi$
$798$	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	$-0.261345\pi$
$811$	38.8133	1.36292	0.681460	+	0.731855i	$0.261345\pi$
$812$	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	$-0.525601\pi$
$829$	−4.62639	−0.160681	−0.0803407	+	0.996767i	$0.525601\pi$
$830$	−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	$-0.151668\pi$
$839$	51.4784	1.77723	0.888616	+	0.458653i	$0.151668\pi$
$840$	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	$-0.387453\pi$
$853$	20.2256	0.692510	0.346255	+	0.938140i	$0.387453\pi$
$854$	0	0
$855$	2.68270	0.0917465
$856$	5.48710	0.187545
$857$	−16.7793	−0.573171	−0.286585	−	0.958055i	$-0.592520\pi$
$857$	−16.7793	−0.573171	−0.286585	+	0.958055i	$0.592520\pi$
$858$	−0.119419	−0.00407691
$859$	−28.1017	−0.958818	−0.479409	−	0.877592i	$-0.659149\pi$
$859$	−28.1017	−0.958818	−0.479409	+	0.877592i	$0.659149\pi$
$860$	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	$-0.645095\pi$
$881$	−26.1322	−0.880415	−0.440208	+	0.897896i	$0.645095\pi$
$882$	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	$-0.578850\pi$
$887$	−14.6047	−0.490378	−0.245189	+	0.969475i	$0.578850\pi$
$888$	−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	$-0.636994\pi$
$929$	−25.4330	−0.834430	−0.417215	+	0.908808i	$0.636994\pi$
$930$	−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	$-0.352277\pi$
$937$	27.4028	0.895209	0.447604	+	0.894232i	$0.352277\pi$
$938$	0	0
$939$	−26.7476	−0.872874
$940$	−10.1179	−0.330008
$941$	−10.7287	−0.349746	−0.174873	−	0.984591i	$-0.555951\pi$
$941$	−10.7287	−0.349746	−0.174873	+	0.984591i	$0.555951\pi$
$942$	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	$-0.425901\pi$
$971$	14.3770	0.461381	0.230691	+	0.973027i	$0.425901\pi$
$972$	−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	$-0.419872\pi$
$983$	15.6188	0.498162	0.249081	+	0.968483i	$0.419872\pi$
$984$	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	$-0.222487\pi$
$997$	48.3424	1.53102	0.765510	+	0.643425i	$0.222487\pi$
$998$	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.p.1.6	✓	10
3.2	odd	2		8379.2.a.ct.1.5		10
7.2	even	3		931.2.f.r.704.5		20
7.3	odd	6		931.2.f.q.324.5		20
7.4	even	3		931.2.f.r.324.5		20
7.5	odd	6		931.2.f.q.704.5		20
7.6	odd	2		931.2.a.q.1.6	yes	10
21.20	even	2		8379.2.a.cs.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.6	✓	10	1.1	even	1	trivial
931.2.a.q.1.6	yes	10	7.6	odd	2
931.2.f.q.324.5		20	7.3	odd	6
931.2.f.q.704.5		20	7.5	odd	6
931.2.f.r.324.5		20	7.4	even	3
931.2.f.r.704.5		20	7.2	even	3
8379.2.a.cs.1.5		10	21.20	even	2
8379.2.a.ct.1.5		10	3.2	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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
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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