LMFDB - Embedded newform 931.2.a.p.1.2

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			1.2
Root			$2.20114$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20114 q^{2} -2.62563 q^{3} +2.84501 q^{4} -4.23731 q^{5} +5.77938 q^{6} -1.86000 q^{8} +3.89394 q^{9} +O(q^{10})$	\(q-2.20114 q^{2} -2.62563 q^{3} +2.84501 q^{4} -4.23731 q^{5} +5.77938 q^{6} -1.86000 q^{8} +3.89394 q^{9} +9.32690 q^{10} -4.54922 q^{11} -7.46996 q^{12} -0.667049 q^{13} +11.1256 q^{15} -1.59592 q^{16} +1.86633 q^{17} -8.57111 q^{18} -1.00000 q^{19} -12.0552 q^{20} +10.0135 q^{22} +9.29601 q^{23} +4.88366 q^{24} +12.9548 q^{25} +1.46827 q^{26} -2.34716 q^{27} -1.31070 q^{29} -24.4890 q^{30} +3.90360 q^{31} +7.23283 q^{32} +11.9446 q^{33} -4.10806 q^{34} +11.0783 q^{36} +3.00492 q^{37} +2.20114 q^{38} +1.75143 q^{39} +7.88137 q^{40} -5.48606 q^{41} +4.44567 q^{43} -12.9426 q^{44} -16.4998 q^{45} -20.4618 q^{46} -5.81459 q^{47} +4.19030 q^{48} -28.5152 q^{50} -4.90030 q^{51} -1.89777 q^{52} -9.95130 q^{53} +5.16642 q^{54} +19.2764 q^{55} +2.62563 q^{57} +2.88503 q^{58} +2.07940 q^{59} +31.6525 q^{60} +10.1390 q^{61} -8.59238 q^{62} -12.7286 q^{64} +2.82649 q^{65} -26.2917 q^{66} -0.523489 q^{67} +5.30974 q^{68} -24.4079 q^{69} -4.03304 q^{71} -7.24271 q^{72} +5.38666 q^{73} -6.61425 q^{74} -34.0144 q^{75} -2.84501 q^{76} -3.85513 q^{78} -2.64530 q^{79} +6.76240 q^{80} -5.51905 q^{81} +12.0756 q^{82} +2.83415 q^{83} -7.90822 q^{85} -9.78554 q^{86} +3.44141 q^{87} +8.46152 q^{88} -14.0986 q^{89} +36.3184 q^{90} +26.4473 q^{92} -10.2494 q^{93} +12.7987 q^{94} +4.23731 q^{95} -18.9908 q^{96} -3.71220 q^{97} -17.7144 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.20114	−1.55644	−0.778220	−	0.627991i	$-0.783877\pi$
$2$	−2.20114	−1.55644	−0.778220	+	0.627991i	$0.783877\pi$
$3$	−2.62563	−1.51591	−0.757955	−	0.652307i	$-0.773801\pi$
$3$	−2.62563	−1.51591	−0.757955	+	0.652307i	$0.773801\pi$
$4$	2.84501	1.42251
$5$	−4.23731	−1.89498	−0.947490	−	0.319784i	$-0.896390\pi$
$5$	−4.23731	−1.89498	−0.947490	+	0.319784i	$0.896390\pi$
$6$	5.77938	2.35942
$7$	0	0
$7$	0	0
$8$	−1.86000	−0.657608
$9$	3.89394	1.29798
$10$	9.32690	2.94942
$11$	−4.54922	−1.37164	−0.685821	−	0.727771i	$-0.740556\pi$
$11$	−4.54922	−1.37164	−0.685821	+	0.727771i	$0.740556\pi$
$12$	−7.46996	−2.15639
$13$	−0.667049	−0.185006	−0.0925031	−	0.995712i	$-0.529487\pi$
$13$	−0.667049	−0.185006	−0.0925031	+	0.995712i	$0.529487\pi$
$14$	0	0
$15$	11.1256	2.87262
$16$	−1.59592	−0.398980
$17$	1.86633	0.452652	0.226326	−	0.974052i	$-0.427329\pi$
$17$	1.86633	0.452652	0.226326	+	0.974052i	$0.427329\pi$
$18$	−8.57111	−2.02023
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−12.0552	−2.69562
$21$	0	0
$22$	10.0135	2.13488
$23$	9.29601	1.93835	0.969176	−	0.246369i	$-0.0792375\pi$
$23$	9.29601	1.93835	0.969176	+	0.246369i	$0.0792375\pi$
$24$	4.88366	0.996873
$25$	12.9548	2.59095
$26$	1.46827	0.287951
$27$	−2.34716	−0.451711
$28$	0	0
$29$	−1.31070	−0.243390	−0.121695	−	0.992568i	$-0.538833\pi$
$29$	−1.31070	−0.243390	−0.121695	+	0.992568i	$0.538833\pi$
$30$	−24.4890	−4.47106
$31$	3.90360	0.701108	0.350554	−	0.936542i	$-0.385993\pi$
$31$	3.90360	0.701108	0.350554	+	0.936542i	$0.385993\pi$
$32$	7.23283	1.27860
$33$	11.9446	2.07928
$34$	−4.10806	−0.704526
$35$	0	0
$36$	11.0783	1.84639
$37$	3.00492	0.494006	0.247003	−	0.969015i	$-0.420554\pi$
$37$	3.00492	0.494006	0.247003	+	0.969015i	$0.420554\pi$
$38$	2.20114	0.357072
$39$	1.75143	0.280453
$40$	7.88137	1.24615
$41$	−5.48606	−0.856779	−0.428390	−	0.903594i	$-0.640919\pi$
$41$	−5.48606	−0.856779	−0.428390	+	0.903594i	$0.640919\pi$
$42$	0	0
$43$	4.44567	0.677958	0.338979	−	0.940794i	$-0.389918\pi$
$43$	4.44567	0.677958	0.338979	+	0.940794i	$0.389918\pi$
$44$	−12.9426	−1.95117
$45$	−16.4998	−2.45965
$46$	−20.4618	−3.01693
$47$	−5.81459	−0.848146	−0.424073	−	0.905628i	$-0.639400\pi$
$47$	−5.81459	−0.848146	−0.424073	+	0.905628i	$0.639400\pi$
$48$	4.19030	0.604818
$49$	0	0
$50$	−28.5152	−4.03266
$51$	−4.90030	−0.686179
$52$	−1.89777	−0.263173
$53$	−9.95130	−1.36692	−0.683458	−	0.729990i	$-0.739525\pi$
$53$	−9.95130	−1.36692	−0.683458	+	0.729990i	$0.739525\pi$
$54$	5.16642	0.703061
$55$	19.2764	2.59923
$56$	0	0
$57$	2.62563	0.347773
$58$	2.88503	0.378823
$59$	2.07940	0.270714	0.135357	−	0.990797i	$-0.456782\pi$
$59$	2.07940	0.270714	0.135357	+	0.990797i	$0.456782\pi$
$60$	31.6525	4.08632
$61$	10.1390	1.29816	0.649080	−	0.760720i	$-0.275154\pi$
$61$	10.1390	1.29816	0.649080	+	0.760720i	$0.275154\pi$
$62$	−8.59238	−1.09123
$63$	0	0
$64$	−12.7286	−1.59108
$65$	2.82649	0.350583
$66$	−26.2917	−3.23628
$67$	−0.523489	−0.0639544	−0.0319772	−	0.999489i	$-0.510180\pi$
$67$	−0.523489	−0.0639544	−0.0319772	+	0.999489i	$0.510180\pi$
$68$	5.30974	0.643901
$69$	−24.4079	−2.93837
$70$	0	0
$71$	−4.03304	−0.478634	−0.239317	−	0.970942i	$-0.576923\pi$
$71$	−4.03304	−0.478634	−0.239317	+	0.970942i	$0.576923\pi$
$72$	−7.24271	−0.853562
$73$	5.38666	0.630461	0.315230	−	0.949015i	$-0.397918\pi$
$73$	5.38666	0.630461	0.315230	+	0.949015i	$0.397918\pi$
$74$	−6.61425	−0.768891
$75$	−34.0144	−3.92765
$76$	−2.84501	−0.326346
$77$	0	0
$78$	−3.85513	−0.436508
$79$	−2.64530	−0.297619	−0.148810	−	0.988866i	$-0.547544\pi$
$79$	−2.64530	−0.297619	−0.148810	+	0.988866i	$0.547544\pi$
$80$	6.76240	0.756060
$81$	−5.51905	−0.613228
$82$	12.0756	1.33353
$83$	2.83415	0.311088	0.155544	−	0.987829i	$-0.450287\pi$
$83$	2.83415	0.311088	0.155544	+	0.987829i	$0.450287\pi$
$84$	0	0
$85$	−7.90822	−0.857767
$86$	−9.78554	−1.05520
$87$	3.44141	0.368958
$88$	8.46152	0.902002
$89$	−14.0986	−1.49445	−0.747225	−	0.664572i	$-0.768614\pi$
$89$	−14.0986	−1.49445	−0.747225	+	0.664572i	$0.768614\pi$
$90$	36.3184	3.82829
$91$	0	0
$92$	26.4473	2.75732
$93$	−10.2494	−1.06282
$94$	12.7987	1.32009
$95$	4.23731	0.434738
$96$	−18.9908	−1.93824
$97$	−3.71220	−0.376917	−0.188459	−	0.982081i	$-0.560349\pi$
$97$	−3.71220	−0.376917	−0.188459	+	0.982081i	$0.560349\pi$
$98$	0	0
$99$	−17.7144	−1.78036
$100$	36.8565	3.68565
$101$	−3.14167	−0.312608	−0.156304	−	0.987709i	$-0.549958\pi$
$101$	−3.14167	−0.312608	−0.156304	+	0.987709i	$0.549958\pi$
$102$	10.7862	1.06800
$103$	11.4811	1.13127	0.565633	−	0.824657i	$-0.308632\pi$
$103$	11.4811	1.13127	0.565633	+	0.824657i	$0.308632\pi$
$104$	1.24071	0.121662
$105$	0	0
$106$	21.9042	2.12752
$107$	2.13866	0.206752	0.103376	−	0.994642i	$-0.467035\pi$
$107$	2.13866	0.206752	0.103376	+	0.994642i	$0.467035\pi$
$108$	−6.67770	−0.642562
$109$	−7.02420	−0.672796	−0.336398	−	0.941720i	$-0.609209\pi$
$109$	−7.02420	−0.672796	−0.336398	+	0.941720i	$0.609209\pi$
$110$	−42.4301	−4.04555
$111$	−7.88982	−0.748868
$112$	0	0
$113$	6.54272	0.615487	0.307744	−	0.951469i	$-0.400426\pi$
$113$	6.54272	0.615487	0.307744	+	0.951469i	$0.400426\pi$
$114$	−5.77938	−0.541289
$115$	−39.3900	−3.67314
$116$	−3.72895	−0.346225
$117$	−2.59745	−0.240134
$118$	−4.57704	−0.421351
$119$	0	0
$120$	−20.6936	−1.88906
$121$	9.69539	0.881399
$122$	−22.3173	−2.02051
$123$	14.4044	1.29880
$124$	11.1058	0.997332
$125$	−33.7067	−3.01482
$126$	0	0
$127$	−19.8356	−1.76012	−0.880061	−	0.474860i	$-0.842499\pi$
$127$	−19.8356	−1.76012	−0.880061	+	0.474860i	$0.842499\pi$
$128$	13.5518	1.19782
$129$	−11.6727	−1.02772
$130$	−6.22150	−0.545662
$131$	10.7068	0.935456	0.467728	−	0.883872i	$-0.345073\pi$
$131$	10.7068	0.935456	0.467728	+	0.883872i	$0.345073\pi$
$132$	33.9825	2.95780
$133$	0	0
$134$	1.15227	0.0995412
$135$	9.94563	0.855983
$136$	−3.47137	−0.297667
$137$	18.2869	1.56235	0.781177	−	0.624310i	$-0.214620\pi$
$137$	18.2869	1.56235	0.781177	+	0.624310i	$0.214620\pi$
$138$	53.7252	4.57339
$139$	6.71739	0.569762	0.284881	−	0.958563i	$-0.408046\pi$
$139$	6.71739	0.569762	0.284881	+	0.958563i	$0.408046\pi$
$140$	0	0
$141$	15.2670	1.28571
$142$	8.87728	0.744965
$143$	3.03455	0.253762
$144$	−6.21442	−0.517868
$145$	5.55383	0.461220
$146$	−11.8568	−0.981275
$147$	0	0
$148$	8.54905	0.702727
$149$	15.9572	1.30727	0.653633	−	0.756812i	$-0.273244\pi$
$149$	15.9572	1.30727	0.653633	+	0.756812i	$0.273244\pi$
$150$	74.8705	6.11315
$151$	−19.1129	−1.55539	−0.777694	−	0.628643i	$-0.783611\pi$
$151$	−19.1129	−1.55539	−0.777694	+	0.628643i	$0.783611\pi$
$152$	1.86000	0.150866
$153$	7.26738	0.587533
$154$	0	0
$155$	−16.5408	−1.32859
$156$	4.98283	0.398946
$157$	−3.10148	−0.247525	−0.123763	−	0.992312i	$-0.539496\pi$
$157$	−3.10148	−0.247525	−0.123763	+	0.992312i	$0.539496\pi$
$158$	5.82267	0.463226
$159$	26.1284	2.07212
$160$	−30.6477	−2.42292
$161$	0	0
$162$	12.1482	0.954452
$163$	−4.45275	−0.348766	−0.174383	−	0.984678i	$-0.555793\pi$
$163$	−4.45275	−0.348766	−0.174383	+	0.984678i	$0.555793\pi$
$164$	−15.6079	−1.21877
$165$	−50.6128	−3.94020
$166$	−6.23835	−0.484190
$167$	18.9814	1.46883	0.734413	−	0.678703i	$-0.237458\pi$
$167$	18.9814	1.46883	0.734413	+	0.678703i	$0.237458\pi$
$168$	0	0
$169$	−12.5550	−0.965773
$170$	17.4071	1.33506
$171$	−3.89394	−0.297777
$172$	12.6480	0.964400
$173$	4.37027	0.332266	0.166133	−	0.986103i	$-0.446872\pi$
$173$	4.37027	0.332266	0.166133	+	0.986103i	$0.446872\pi$
$174$	−7.57502	−0.574261
$175$	0	0
$176$	7.26019	0.547258
$177$	−5.45973	−0.410379
$178$	31.0330	2.32602
$179$	−5.77456	−0.431611	−0.215806	−	0.976436i	$-0.569238\pi$
$179$	−5.77456	−0.431611	−0.215806	+	0.976436i	$0.569238\pi$
$180$	−46.9422	−3.49887
$181$	−8.85069	−0.657867	−0.328933	−	0.944353i	$-0.606689\pi$
$181$	−8.85069	−0.657867	−0.328933	+	0.944353i	$0.606689\pi$
$182$	0	0
$183$	−26.6212	−1.96789
$184$	−17.2905	−1.27468
$185$	−12.7328	−0.936132
$186$	22.5604	1.65421
$187$	−8.49035	−0.620876
$188$	−16.5426	−1.20649
$189$	0	0
$190$	−9.32690	−0.676644
$191$	5.50278	0.398167	0.199084	−	0.979983i	$-0.436203\pi$
$191$	5.50278	0.398167	0.199084	+	0.979983i	$0.436203\pi$
$192$	33.4207	2.41193
$193$	−18.5258	−1.33352	−0.666758	−	0.745274i	$-0.732319\pi$
$193$	−18.5258	−1.33352	−0.666758	+	0.745274i	$0.732319\pi$
$194$	8.17108	0.586649
$195$	−7.42133	−0.531452
$196$	0	0
$197$	7.47529	0.532593	0.266296	−	0.963891i	$-0.414200\pi$
$197$	7.47529	0.532593	0.266296	+	0.963891i	$0.414200\pi$
$198$	38.9918	2.77103
$199$	22.1007	1.56668	0.783338	−	0.621596i	$-0.213515\pi$
$199$	22.1007	1.56668	0.783338	+	0.621596i	$0.213515\pi$
$200$	−24.0958	−1.70383
$201$	1.37449	0.0969490
$202$	6.91525	0.486555
$203$	0	0
$204$	−13.9414	−0.976095
$205$	23.2461	1.62358
$206$	−25.2715	−1.76075
$207$	36.1981	2.51594
$208$	1.06456	0.0738138
$209$	4.54922	0.314676
$210$	0	0
$211$	10.3344	0.711449	0.355724	−	0.934591i	$-0.384234\pi$
$211$	10.3344	0.711449	0.355724	+	0.934591i	$0.384234\pi$
$212$	−28.3116	−1.94445
$213$	10.5893	0.725565
$214$	−4.70749	−0.321797
$215$	−18.8377	−1.28472
$216$	4.36570	0.297048
$217$	0	0
$218$	15.4612	1.04717
$219$	−14.1434	−0.955721
$220$	54.8417	3.69743
$221$	−1.24494	−0.0837434
$222$	17.3666	1.16557
$223$	17.9428	1.20154	0.600768	−	0.799423i	$-0.294862\pi$
$223$	17.9428	1.20154	0.600768	+	0.799423i	$0.294862\pi$
$224$	0	0
$225$	50.4451	3.36300
$226$	−14.4014	−0.957970
$227$	14.5072	0.962875	0.481437	−	0.876481i	$-0.340115\pi$
$227$	14.5072	0.962875	0.481437	+	0.876481i	$0.340115\pi$
$228$	7.46996	0.494710
$229$	−4.81034	−0.317876	−0.158938	−	0.987289i	$-0.550807\pi$
$229$	−4.81034	−0.317876	−0.158938	+	0.987289i	$0.550807\pi$
$230$	86.7030	5.71702
$231$	0	0
$232$	2.43789	0.160055
$233$	−19.2611	−1.26184	−0.630920	−	0.775848i	$-0.717322\pi$
$233$	−19.2611	−1.26184	−0.630920	+	0.775848i	$0.717322\pi$
$234$	5.71735	0.373755
$235$	24.6382	1.60722
$236$	5.91592	0.385093
$237$	6.94557	0.451163
$238$	0	0
$239$	6.84407	0.442706	0.221353	−	0.975194i	$-0.428953\pi$
$239$	6.84407	0.442706	0.221353	+	0.975194i	$0.428953\pi$
$240$	−17.7556	−1.14612
$241$	0.589968	0.0380032	0.0190016	−	0.999819i	$-0.493951\pi$
$241$	0.589968	0.0380032	0.0190016	+	0.999819i	$0.493951\pi$
$242$	−21.3409	−1.37185
$243$	21.5325	1.38131
$244$	28.8455	1.84664
$245$	0	0
$246$	−31.7060	−2.02150
$247$	0.667049	0.0424433
$248$	−7.26069	−0.461054
$249$	−7.44142	−0.471581
$250$	74.1932	4.69239
$251$	−7.77752	−0.490913	−0.245456	−	0.969408i	$-0.578938\pi$
$251$	−7.77752	−0.490913	−0.245456	+	0.969408i	$0.578938\pi$
$252$	0	0
$253$	−42.2896	−2.65872
$254$	43.6609	2.73953
$255$	20.7641	1.30030
$256$	−4.37220	−0.273263
$257$	5.16184	0.321987	0.160993	−	0.986955i	$-0.448530\pi$
$257$	5.16184	0.321987	0.160993	+	0.986955i	$0.448530\pi$
$258$	25.6932	1.59959
$259$	0	0
$260$	8.04141	0.498707
$261$	−5.10378	−0.315916
$262$	−23.5671	−1.45598
$263$	21.2984	1.31331	0.656657	−	0.754190i	$-0.271970\pi$
$263$	21.2984	1.31331	0.656657	+	0.754190i	$0.271970\pi$
$264$	−22.2168	−1.36735
$265$	42.1667	2.59028
$266$	0	0
$267$	37.0177	2.26545
$268$	−1.48933	−0.0909756
$269$	−10.2840	−0.627025	−0.313512	−	0.949584i	$-0.601506\pi$
$269$	−10.2840	−0.627025	−0.313512	+	0.949584i	$0.601506\pi$
$270$	−21.8917	−1.33229
$271$	−25.2222	−1.53214	−0.766069	−	0.642758i	$-0.777790\pi$
$271$	−25.2222	−1.53214	−0.766069	+	0.642758i	$0.777790\pi$
$272$	−2.97852	−0.180599
$273$	0	0
$274$	−40.2520	−2.43171
$275$	−58.9340	−3.55386
$276$	−69.4408	−4.17985
$277$	11.2653	0.676864	0.338432	−	0.940991i	$-0.390104\pi$
$277$	11.2653	0.676864	0.338432	+	0.940991i	$0.390104\pi$
$278$	−14.7859	−0.886800
$279$	15.2004	0.910024
$280$	0	0
$281$	−7.07464	−0.422038	−0.211019	−	0.977482i	$-0.567678\pi$
$281$	−7.07464	−0.422038	−0.211019	+	0.977482i	$0.567678\pi$
$282$	−33.6047	−2.00113
$283$	−24.3703	−1.44866	−0.724331	−	0.689453i	$-0.757851\pi$
$283$	−24.3703	−1.44866	−0.724331	+	0.689453i	$0.757851\pi$
$284$	−11.4741	−0.680860
$285$	−11.1256	−0.659024
$286$	−6.67948	−0.394966
$287$	0	0
$288$	28.1642	1.65959
$289$	−13.5168	−0.795106
$290$	−12.2247	−0.717862
$291$	9.74688	0.571372
$292$	15.3251	0.896835
$293$	−16.0761	−0.939177	−0.469588	−	0.882886i	$-0.655598\pi$
$293$	−16.0761	−0.939177	−0.469588	+	0.882886i	$0.655598\pi$
$294$	0	0
$295$	−8.81104	−0.512999
$296$	−5.58914	−0.324862
$297$	10.6777	0.619585
$298$	−35.1241	−2.03468
$299$	−6.20090	−0.358607
$300$	−96.7715	−5.58711
$301$	0	0
$302$	42.0702	2.42087
$303$	8.24887	0.473885
$304$	1.59592	0.0915323
$305$	−42.9619	−2.45999
$306$	−15.9965	−0.914460
$307$	13.1085	0.748142	0.374071	−	0.927400i	$-0.377962\pi$
$307$	13.1085	0.748142	0.374071	+	0.927400i	$0.377962\pi$
$308$	0	0
$309$	−30.1451	−1.71490
$310$	36.4085	2.06787
$311$	28.0359	1.58977	0.794885	−	0.606760i	$-0.207531\pi$
$311$	28.0359	1.58977	0.794885	+	0.606760i	$0.207531\pi$
$312$	−3.25764	−0.184428
$313$	−9.53490	−0.538945	−0.269472	−	0.963008i	$-0.586849\pi$
$313$	−9.53490	−0.538945	−0.269472	+	0.963008i	$0.586849\pi$
$314$	6.82680	0.385258
$315$	0	0
$316$	−7.52591	−0.423365
$317$	−11.1347	−0.625389	−0.312694	−	0.949854i	$-0.601232\pi$
$317$	−11.1347	−0.625389	−0.312694	+	0.949854i	$0.601232\pi$
$318$	−57.5124	−3.22513
$319$	5.96265	0.333844
$320$	53.9351	3.01506
$321$	−5.61533	−0.313417
$322$	0	0
$323$	−1.86633	−0.103845
$324$	−15.7018	−0.872321
$325$	−8.64146	−0.479342
$326$	9.80113	0.542834
$327$	18.4429	1.01990
$328$	10.2040	0.563424
$329$	0	0
$330$	111.406	6.13269
$331$	−0.894117	−0.0491451	−0.0245726	−	0.999698i	$-0.507822\pi$
$331$	−0.894117	−0.0491451	−0.0245726	+	0.999698i	$0.507822\pi$
$332$	8.06319	0.442525
$333$	11.7010	0.641210
$334$	−41.7807	−2.28614
$335$	2.21818	0.121192
$336$	0	0
$337$	−10.4880	−0.571315	−0.285658	−	0.958332i	$-0.592212\pi$
$337$	−10.4880	−0.571315	−0.285658	+	0.958332i	$0.592212\pi$
$338$	27.6354	1.50317
$339$	−17.1788	−0.933023
$340$	−22.4990	−1.22018
$341$	−17.7584	−0.961669
$342$	8.57111	0.463472
$343$	0	0
$344$	−8.26892	−0.445830
$345$	103.424	5.56815
$346$	−9.61958	−0.517152
$347$	9.44400	0.506981	0.253490	−	0.967338i	$-0.418421\pi$
$347$	9.44400	0.506981	0.253490	+	0.967338i	$0.418421\pi$
$348$	9.79086	0.524845
$349$	−21.5964	−1.15603	−0.578015	−	0.816026i	$-0.696173\pi$
$349$	−21.5964	−1.15603	−0.578015	+	0.816026i	$0.696173\pi$
$350$	0	0
$351$	1.56567	0.0835693
$352$	−32.9037	−1.75378
$353$	0.973443	0.0518112	0.0259056	−	0.999664i	$-0.491753\pi$
$353$	0.973443	0.0518112	0.0259056	+	0.999664i	$0.491753\pi$
$354$	12.0176	0.638730
$355$	17.0892	0.907002
$356$	−40.1107	−2.12586
$357$	0	0
$358$	12.7106	0.671777
$359$	−4.13501	−0.218238	−0.109119	−	0.994029i	$-0.534803\pi$
$359$	−4.13501	−0.218238	−0.109119	+	0.994029i	$0.534803\pi$
$360$	30.6896	1.61748
$361$	1.00000	0.0526316
$362$	19.4816	1.02393
$363$	−25.4565	−1.33612
$364$	0	0
$365$	−22.8249	−1.19471
$366$	58.5969	3.06291
$367$	−31.0923	−1.62301	−0.811503	−	0.584348i	$-0.801350\pi$
$367$	−31.0923	−1.62301	−0.811503	+	0.584348i	$0.801350\pi$
$368$	−14.8357	−0.773364
$369$	−21.3624	−1.11208
$370$	28.0266	1.45703
$371$	0	0
$372$	−29.1598	−1.51186
$373$	−16.6976	−0.864569	−0.432285	−	0.901737i	$-0.642292\pi$
$373$	−16.6976	−0.864569	−0.432285	+	0.901737i	$0.642292\pi$
$374$	18.6884	0.966356
$375$	88.5015	4.57020
$376$	10.8151	0.557747
$377$	0.874300	0.0450287
$378$	0	0
$379$	−6.93613	−0.356285	−0.178142	−	0.984005i	$-0.557009\pi$
$379$	−6.93613	−0.356285	−0.178142	+	0.984005i	$0.557009\pi$
$380$	12.0552	0.618419
$381$	52.0809	2.66819
$382$	−12.1124	−0.619723
$383$	−26.4779	−1.35296	−0.676478	−	0.736463i	$-0.736495\pi$
$383$	−26.4779	−1.35296	−0.676478	+	0.736463i	$0.736495\pi$
$384$	−35.5821	−1.81579
$385$	0	0
$386$	40.7779	2.07554
$387$	17.3112	0.879976
$388$	−10.5613	−0.536168
$389$	19.4236	0.984813	0.492407	−	0.870365i	$-0.336117\pi$
$389$	19.4236	0.984813	0.492407	+	0.870365i	$0.336117\pi$
$390$	16.3354	0.827174
$391$	17.3494	0.877399
$392$	0	0
$393$	−28.1121	−1.41807
$394$	−16.4542	−0.828949
$395$	11.2089	0.563982
$396$	−50.3977	−2.53258
$397$	−6.44353	−0.323392	−0.161696	−	0.986841i	$-0.551696\pi$
$397$	−6.44353	−0.323392	−0.161696	+	0.986841i	$0.551696\pi$
$398$	−48.6467	−2.43844
$399$	0	0
$400$	−20.6748	−1.03374
$401$	−19.1953	−0.958570	−0.479285	−	0.877659i	$-0.659104\pi$
$401$	−19.1953	−0.958570	−0.479285	+	0.877659i	$0.659104\pi$
$402$	−3.02544	−0.150895
$403$	−2.60390	−0.129709
$404$	−8.93810	−0.444687
$405$	23.3859	1.16205
$406$	0	0
$407$	−13.6700	−0.677599
$408$	9.11453	0.451237
$409$	−21.7829	−1.07709	−0.538547	−	0.842595i	$-0.681027\pi$
$409$	−21.7829	−1.07709	−0.538547	+	0.842595i	$0.681027\pi$
$410$	−51.1680	−2.52701
$411$	−48.0146	−2.36839
$412$	32.6639	1.60924
$413$	0	0
$414$	−79.6771	−3.91592
$415$	−12.0091	−0.589506
$416$	−4.82466	−0.236548
$417$	−17.6374	−0.863707
$418$	−10.0135	−0.489775
$419$	12.7698	0.623844	0.311922	−	0.950108i	$-0.399027\pi$
$419$	12.7698	0.623844	0.311922	+	0.950108i	$0.399027\pi$
$420$	0	0
$421$	30.1544	1.46963	0.734817	−	0.678266i	$-0.237268\pi$
$421$	30.1544	1.46963	0.734817	+	0.678266i	$0.237268\pi$
$422$	−22.7474	−1.10733
$423$	−22.6417	−1.10088
$424$	18.5094	0.898895
$425$	24.1779	1.17280
$426$	−23.3085	−1.12930
$427$	0	0
$428$	6.08452	0.294106
$429$	−7.96762	−0.384680
$430$	41.4643	1.99959
$431$	2.95699	0.142433	0.0712165	−	0.997461i	$-0.477312\pi$
$431$	2.95699	0.142433	0.0712165	+	0.997461i	$0.477312\pi$
$432$	3.74588	0.180224
$433$	1.44760	0.0695674	0.0347837	−	0.999395i	$-0.488926\pi$
$433$	1.44760	0.0695674	0.0347837	+	0.999395i	$0.488926\pi$
$434$	0	0
$435$	−14.5823	−0.699168
$436$	−19.9839	−0.957057
$437$	−9.29601	−0.444689
$438$	31.1316	1.48752
$439$	−2.08826	−0.0996671	−0.0498336	−	0.998758i	$-0.515869\pi$
$439$	−2.08826	−0.0996671	−0.0498336	+	0.998758i	$0.515869\pi$
$440$	−35.8541	−1.70928
$441$	0	0
$442$	2.74028	0.130342
$443$	−27.9091	−1.32600	−0.663001	−	0.748618i	$-0.730718\pi$
$443$	−27.9091	−1.32600	−0.663001	+	0.748618i	$0.730718\pi$
$444$	−22.4466	−1.06527
$445$	59.7401	2.83195
$446$	−39.4945	−1.87012
$447$	−41.8978	−1.98170
$448$	0	0
$449$	34.9394	1.64889	0.824446	−	0.565941i	$-0.191487\pi$
$449$	34.9394	1.64889	0.824446	+	0.565941i	$0.191487\pi$
$450$	−111.037	−5.23432
$451$	24.9573	1.17519
$452$	18.6141	0.875535
$453$	50.1835	2.35783
$454$	−31.9323	−1.49866
$455$	0	0
$456$	−4.88366	−0.228698
$457$	−19.1491	−0.895759	−0.447879	−	0.894094i	$-0.647821\pi$
$457$	−19.1491	−0.895759	−0.447879	+	0.894094i	$0.647821\pi$
$458$	10.5882	0.494755
$459$	−4.38058	−0.204468
$460$	−112.065	−5.22507
$461$	−30.7840	−1.43375	−0.716877	−	0.697200i	$-0.754429\pi$
$461$	−30.7840	−1.43375	−0.716877	+	0.697200i	$0.754429\pi$
$462$	0	0
$463$	−9.88109	−0.459213	−0.229607	−	0.973284i	$-0.573744\pi$
$463$	−9.88109	−0.459213	−0.229607	+	0.973284i	$0.573744\pi$
$464$	2.09177	0.0971079
$465$	43.4300	2.01402
$466$	42.3965	1.96398
$467$	10.5101	0.486349	0.243174	−	0.969983i	$-0.421811\pi$
$467$	10.5101	0.486349	0.243174	+	0.969983i	$0.421811\pi$
$468$	−7.38979	−0.341593
$469$	0	0
$470$	−54.2321	−2.50154
$471$	8.14335	0.375226
$472$	−3.86767	−0.178024
$473$	−20.2243	−0.929915
$474$	−15.2882	−0.702209
$475$	−12.9548	−0.594405
$476$	0	0
$477$	−38.7498	−1.77423
$478$	−15.0648	−0.689046
$479$	21.1885	0.968127	0.484063	−	0.875033i	$-0.339160\pi$
$479$	21.1885	0.968127	0.484063	+	0.875033i	$0.339160\pi$
$480$	80.4696	3.67292
$481$	−2.00443	−0.0913942
$482$	−1.29860	−0.0591497
$483$	0	0
$484$	27.5835	1.25380
$485$	15.7297	0.714251
$486$	−47.3960	−2.14992
$487$	−2.06595	−0.0936171	−0.0468085	−	0.998904i	$-0.514905\pi$
$487$	−2.06595	−0.0936171	−0.0468085	+	0.998904i	$0.514905\pi$
$488$	−18.8584	−0.853680
$489$	11.6913	0.528698
$490$	0	0
$491$	17.6735	0.797594	0.398797	−	0.917039i	$-0.369428\pi$
$491$	17.6735	0.797594	0.398797	+	0.917039i	$0.369428\pi$
$492$	40.9807	1.84755
$493$	−2.44620	−0.110171
$494$	−1.46827	−0.0660605
$495$	75.0613	3.37375
$496$	−6.22984	−0.279728
$497$	0	0
$498$	16.3796	0.733988
$499$	8.94463	0.400417	0.200208	−	0.979753i	$-0.435838\pi$
$499$	8.94463	0.400417	0.200208	+	0.979753i	$0.435838\pi$
$500$	−95.8962	−4.28861
$501$	−49.8382	−2.22661
$502$	17.1194	0.764077
$503$	−18.8431	−0.840171	−0.420085	−	0.907485i	$-0.638000\pi$
$503$	−18.8431	−0.840171	−0.420085	+	0.907485i	$0.638000\pi$
$504$	0	0
$505$	13.3122	0.592386
$506$	93.0853	4.13815
$507$	32.9649	1.46402
$508$	−56.4325	−2.50379
$509$	10.7558	0.476743	0.238371	−	0.971174i	$-0.423386\pi$
$509$	10.7558	0.476743	0.238371	+	0.971174i	$0.423386\pi$
$510$	−45.7046	−2.02383
$511$	0	0
$512$	−17.4798	−0.772507
$513$	2.34716	0.103630
$514$	−11.3619	−0.501153
$515$	−48.6489	−2.14373
$516$	−33.2090	−1.46194
$517$	26.4519	1.16335
$518$	0	0
$519$	−11.4747	−0.503684
$520$	−5.25726	−0.230546
$521$	−3.90860	−0.171239	−0.0856194	−	0.996328i	$-0.527287\pi$
$521$	−3.90860	−0.171239	−0.0856194	+	0.996328i	$0.527287\pi$
$522$	11.2341	0.491704
$523$	34.5912	1.51257	0.756284	−	0.654243i	$-0.227013\pi$
$523$	34.5912	1.51257	0.756284	+	0.654243i	$0.227013\pi$
$524$	30.4610	1.33069
$525$	0	0
$526$	−46.8807	−2.04409
$527$	7.28542	0.317358
$528$	−19.0626	−0.829593
$529$	63.4158	2.75721
$530$	−92.8148	−4.03162
$531$	8.09705	0.351382
$532$	0	0
$533$	3.65947	0.158509
$534$	−81.4812	−3.52604
$535$	−9.06216	−0.391791
$536$	0.973687	0.0420569
$537$	15.1619	0.654283
$538$	22.6365	0.975927
$539$	0	0
$540$	28.2955	1.21764
$541$	0.256694	0.0110361	0.00551807	−	0.999985i	$-0.498244\pi$
$541$	0.256694	0.0110361	0.00551807	+	0.999985i	$0.498244\pi$
$542$	55.5175	2.38468
$543$	23.2387	0.997266
$544$	13.4989	0.578759
$545$	29.7637	1.27494
$546$	0	0
$547$	−8.24778	−0.352650	−0.176325	−	0.984332i	$-0.556421\pi$
$547$	−8.24778	−0.352650	−0.176325	+	0.984332i	$0.556421\pi$
$548$	52.0265	2.22246
$549$	39.4805	1.68499
$550$	129.722	5.53137
$551$	1.31070	0.0558376
$552$	45.3986	1.93229
$553$	0	0
$554$	−24.7964	−1.05350
$555$	33.4316	1.41909
$556$	19.1111	0.810490
$557$	−3.18844	−0.135098	−0.0675492	−	0.997716i	$-0.521518\pi$
$557$	−3.18844	−0.135098	−0.0675492	+	0.997716i	$0.521518\pi$
$558$	−33.4582	−1.41640
$559$	−2.96548	−0.125426
$560$	0	0
$561$	22.2925	0.941191
$562$	15.5723	0.656876
$563$	−32.5758	−1.37291	−0.686453	−	0.727175i	$-0.740833\pi$
$563$	−32.5758	−1.37291	−0.686453	+	0.727175i	$0.740833\pi$
$564$	43.4348	1.82893
$565$	−27.7235	−1.16634
$566$	53.6423	2.25476
$567$	0	0
$568$	7.50143	0.314753
$569$	−39.5612	−1.65849	−0.829246	−	0.558884i	$-0.811230\pi$
$569$	−39.5612	−1.65849	−0.829246	+	0.558884i	$0.811230\pi$
$570$	24.4890	1.02573
$571$	−6.55004	−0.274111	−0.137055	−	0.990563i	$-0.543764\pi$
$571$	−6.55004	−0.274111	−0.137055	+	0.990563i	$0.543764\pi$
$572$	8.63335	0.360978
$573$	−14.4483	−0.603585
$574$	0	0
$575$	120.428	5.02218
$576$	−49.5645	−2.06519
$577$	17.5603	0.731045	0.365522	−	0.930803i	$-0.380890\pi$
$577$	17.5603	0.731045	0.365522	+	0.930803i	$0.380890\pi$
$578$	29.7524	1.23754
$579$	48.6419	2.02149
$580$	15.8007	0.656089
$581$	0	0
$582$	−21.4542	−0.889307
$583$	45.2706	1.87492
$584$	−10.0192	−0.414596
$585$	11.0062	0.455050
$586$	35.3858	1.46177
$587$	30.2766	1.24965	0.624825	−	0.780765i	$-0.285170\pi$
$587$	30.2766	1.24965	0.624825	+	0.780765i	$0.285170\pi$
$588$	0	0
$589$	−3.90360	−0.160845
$590$	19.3943	0.798452
$591$	−19.6274	−0.807362
$592$	−4.79562	−0.197099
$593$	−24.8433	−1.02019	−0.510097	−	0.860117i	$-0.670390\pi$
$593$	−24.8433	−1.02019	−0.510097	+	0.860117i	$0.670390\pi$
$594$	−23.5032	−0.964347
$595$	0	0
$596$	45.3985	1.85960
$597$	−58.0282	−2.37494
$598$	13.6490	0.558151
$599$	−29.8211	−1.21846	−0.609228	−	0.792995i	$-0.708521\pi$
$599$	−29.8211	−1.21846	−0.609228	+	0.792995i	$0.708521\pi$
$600$	63.2667	2.58285
$601$	−43.8767	−1.78977	−0.894884	−	0.446298i	$-0.852742\pi$
$601$	−43.8767	−1.78977	−0.894884	+	0.446298i	$0.852742\pi$
$602$	0	0
$603$	−2.03844	−0.0830115
$604$	−54.3765	−2.21255
$605$	−41.0823	−1.67023
$606$	−18.1569	−0.737574
$607$	−6.47053	−0.262631	−0.131315	−	0.991341i	$-0.541920\pi$
$607$	−6.47053	−0.262631	−0.131315	+	0.991341i	$0.541920\pi$
$608$	−7.23283	−0.293330
$609$	0	0
$610$	94.5651	3.82883
$611$	3.87862	0.156912
$612$	20.6758	0.835770
$613$	−40.0247	−1.61658	−0.808291	−	0.588783i	$-0.799607\pi$
$613$	−40.0247	−1.61658	−0.808291	+	0.588783i	$0.799607\pi$
$614$	−28.8536	−1.16444
$615$	−61.0358	−2.46120
$616$	0	0
$617$	−17.7730	−0.715513	−0.357757	−	0.933815i	$-0.616458\pi$
$617$	−17.7730	−0.715513	−0.357757	+	0.933815i	$0.616458\pi$
$618$	66.3537	2.66914
$619$	−20.5165	−0.824628	−0.412314	−	0.911042i	$-0.635279\pi$
$619$	−20.5165	−0.824628	−0.412314	+	0.911042i	$0.635279\pi$
$620$	−47.0587	−1.88992
$621$	−21.8192	−0.875575
$622$	−61.7109	−2.47438
$623$	0	0
$624$	−2.79514	−0.111895
$625$	78.0520	3.12208
$626$	20.9877	0.838835
$627$	−11.9446	−0.477020
$628$	−8.82376	−0.352106
$629$	5.60818	0.223613
$630$	0	0
$631$	−2.78970	−0.111056	−0.0555281	−	0.998457i	$-0.517684\pi$
$631$	−2.78970	−0.111056	−0.0555281	+	0.998457i	$0.517684\pi$
$632$	4.92024	0.195717
$633$	−27.1343	−1.07849
$634$	24.5091	0.973380
$635$	84.0494	3.33540
$636$	74.3358	2.94761
$637$	0	0
$638$	−13.1246	−0.519609
$639$	−15.7044	−0.621257
$640$	−57.4233	−2.26985
$641$	−34.5824	−1.36592	−0.682961	−	0.730455i	$-0.739308\pi$
$641$	−34.5824	−1.36592	−0.682961	+	0.730455i	$0.739308\pi$
$642$	12.3601	0.487815
$643$	20.5081	0.808761	0.404381	−	0.914591i	$-0.367487\pi$
$643$	20.5081	0.808761	0.404381	+	0.914591i	$0.367487\pi$
$644$	0	0
$645$	49.4607	1.94751
$646$	4.10806	0.161629
$647$	18.5977	0.731153	0.365576	−	0.930781i	$-0.380872\pi$
$647$	18.5977	0.731153	0.365576	+	0.930781i	$0.380872\pi$
$648$	10.2654	0.403263
$649$	−9.45963	−0.371323
$650$	19.0211	0.746068
$651$	0	0
$652$	−12.6681	−0.496123
$653$	−42.3665	−1.65793	−0.828964	−	0.559302i	$-0.811069\pi$
$653$	−42.3665	−1.65793	−0.828964	+	0.559302i	$0.811069\pi$
$654$	−40.5955	−1.58741
$655$	−45.3679	−1.77267
$656$	8.75532	0.341838
$657$	20.9753	0.818326
$658$	0	0
$659$	37.3476	1.45486	0.727429	−	0.686183i	$-0.240715\pi$
$659$	37.3476	1.45486	0.727429	+	0.686183i	$0.240715\pi$
$660$	−143.994	−5.60496
$661$	41.0123	1.59519	0.797596	−	0.603192i	$-0.206105\pi$
$661$	41.0123	1.59519	0.797596	+	0.603192i	$0.206105\pi$
$662$	1.96808	0.0764915
$663$	3.26874	0.126947
$664$	−5.27150	−0.204574
$665$	0	0
$666$	−25.7555	−0.998005
$667$	−12.1843	−0.471776
$668$	54.0024	2.08942
$669$	−47.1111	−1.82142
$670$	−4.88253	−0.188629
$671$	−46.1243	−1.78061
$672$	0	0
$673$	42.3029	1.63066	0.815329	−	0.578998i	$-0.196556\pi$
$673$	42.3029	1.63066	0.815329	+	0.578998i	$0.196556\pi$
$674$	23.0855	0.889219
$675$	−30.4069	−1.17036
$676$	−35.7193	−1.37382
$677$	36.5041	1.40297	0.701483	−	0.712686i	$-0.252522\pi$
$677$	36.5041	1.40297	0.701483	+	0.712686i	$0.252522\pi$
$678$	37.8129	1.45219
$679$	0	0
$680$	14.7092	0.564074
$681$	−38.0905	−1.45963
$682$	39.0886	1.49678
$683$	27.0271	1.03416	0.517082	−	0.855936i	$-0.327018\pi$
$683$	27.0271	1.03416	0.517082	+	0.855936i	$0.327018\pi$
$684$	−11.0783	−0.423590
$685$	−77.4871	−2.96063
$686$	0	0
$687$	12.6302	0.481871
$688$	−7.09493	−0.270492
$689$	6.63801	0.252888
$690$	−227.650	−8.66649
$691$	5.49793	0.209151	0.104576	−	0.994517i	$-0.466652\pi$
$691$	5.49793	0.209151	0.104576	+	0.994517i	$0.466652\pi$
$692$	12.4335	0.472650
$693$	0	0
$694$	−20.7876	−0.789085
$695$	−28.4636	−1.07969
$696$	−6.40100	−0.242629
$697$	−10.2388	−0.387823
$698$	47.5368	1.79929
$699$	50.5727	1.91283
$700$	0	0
$701$	−32.8214	−1.23965	−0.619824	−	0.784741i	$-0.712796\pi$
$701$	−32.8214	−1.23965	−0.619824	+	0.784741i	$0.712796\pi$
$702$	−3.44626	−0.130071
$703$	−3.00492	−0.113333
$704$	57.9053	2.18239
$705$	−64.6908	−2.43640
$706$	−2.14268	−0.0806410
$707$	0	0
$708$	−15.5330	−0.583766
$709$	4.93049	0.185168	0.0925842	−	0.995705i	$-0.470487\pi$
$709$	4.93049	0.185168	0.0925842	+	0.995705i	$0.470487\pi$
$710$	−37.6158	−1.41169
$711$	−10.3006	−0.386304
$712$	26.2233	0.982761
$713$	36.2880	1.35899
$714$	0	0
$715$	−12.8583	−0.480874
$716$	−16.4287	−0.613970
$717$	−17.9700	−0.671102
$718$	9.10174	0.339674
$719$	−15.6062	−0.582014	−0.291007	−	0.956721i	$-0.593990\pi$
$719$	−15.6062	−0.582014	−0.291007	+	0.956721i	$0.593990\pi$
$720$	26.3324	0.981350
$721$	0	0
$722$	−2.20114	−0.0819179
$723$	−1.54904	−0.0576094
$724$	−25.1803	−0.935820
$725$	−16.9798	−0.630613
$726$	56.0333	2.07959
$727$	−26.5642	−0.985213	−0.492606	−	0.870252i	$-0.663956\pi$
$727$	−26.5642	−0.985213	−0.492606	+	0.870252i	$0.663956\pi$
$728$	0	0
$729$	−39.9792	−1.48071
$730$	50.2408	1.85950
$731$	8.29709	0.306879
$732$	−75.7376	−2.79934
$733$	−37.8191	−1.39688	−0.698440	−	0.715668i	$-0.746122\pi$
$733$	−37.8191	−1.39688	−0.698440	+	0.715668i	$0.746122\pi$
$734$	68.4385	2.52611
$735$	0	0
$736$	67.2365	2.47837
$737$	2.38147	0.0877224
$738$	47.0216	1.73089
$739$	42.8341	1.57568	0.787839	−	0.615881i	$-0.211200\pi$
$739$	42.8341	1.57568	0.787839	+	0.615881i	$0.211200\pi$
$740$	−36.2249	−1.33165
$741$	−1.75143	−0.0643402
$742$	0	0
$743$	−35.0205	−1.28478	−0.642389	−	0.766379i	$-0.722057\pi$
$743$	−35.0205	−1.28478	−0.642389	+	0.766379i	$0.722057\pi$
$744$	19.0639	0.698916
$745$	−67.6156	−2.47724
$746$	36.7538	1.34565
$747$	11.0360	0.403786
$748$	−24.1552	−0.883201
$749$	0	0
$750$	−194.804	−7.11324
$751$	−11.6655	−0.425679	−0.212839	−	0.977087i	$-0.568271\pi$
$751$	−11.6655	−0.425679	−0.212839	+	0.977087i	$0.568271\pi$
$752$	9.27963	0.338393
$753$	20.4209	0.744179
$754$	−1.92446	−0.0700846
$755$	80.9873	2.94743
$756$	0	0
$757$	−13.5376	−0.492031	−0.246016	−	0.969266i	$-0.579121\pi$
$757$	−13.5376	−0.492031	−0.246016	+	0.969266i	$0.579121\pi$
$758$	15.2674	0.554536
$759$	111.037	4.03038
$760$	−7.88137	−0.285887
$761$	−46.4300	−1.68309	−0.841543	−	0.540190i	$-0.818352\pi$
$761$	−46.4300	−1.68309	−0.841543	+	0.540190i	$0.818352\pi$
$762$	−114.637	−4.15287
$763$	0	0
$764$	15.6555	0.566396
$765$	−30.7941	−1.11336
$766$	58.2815	2.10580
$767$	−1.38706	−0.0500839
$768$	11.4798	0.414241
$769$	12.0896	0.435963	0.217981	−	0.975953i	$-0.430053\pi$
$769$	12.0896	0.435963	0.217981	+	0.975953i	$0.430053\pi$
$770$	0	0
$771$	−13.5531	−0.488103
$772$	−52.7062	−1.89694
$773$	−41.3224	−1.48627	−0.743133	−	0.669144i	$-0.766661\pi$
$773$	−41.3224	−1.48627	−0.743133	+	0.669144i	$0.766661\pi$
$774$	−38.1043	−1.36963
$775$	50.5703	1.81654
$776$	6.90468	0.247864
$777$	0	0
$778$	−42.7540	−1.53280
$779$	5.48606	0.196559
$780$	−21.1138	−0.755995
$781$	18.3472	0.656514
$782$	−38.1885	−1.36562
$783$	3.07641	0.109942
$784$	0	0
$785$	13.1419	0.469056
$786$	61.8786	2.20714
$787$	12.6708	0.451664	0.225832	−	0.974166i	$-0.427490\pi$
$787$	12.6708	0.451664	0.225832	+	0.974166i	$0.427490\pi$
$788$	21.2673	0.757617
$789$	−55.9217	−1.99086
$790$	−24.6724	−0.877805
$791$	0	0
$792$	32.9487	1.17078
$793$	−6.76319	−0.240168
$794$	14.1831	0.503340
$795$	−110.714	−3.92663
$796$	62.8768	2.22861
$797$	−8.94088	−0.316702	−0.158351	−	0.987383i	$-0.550618\pi$
$797$	−8.94088	−0.316702	−0.158351	+	0.987383i	$0.550618\pi$
$798$	0	0
$799$	−10.8520	−0.383915
$800$	93.6996	3.31278
$801$	−54.8991	−1.93977
$802$	42.2516	1.49196
$803$	−24.5051	−0.864766
$804$	3.91044	0.137911
$805$	0	0
$806$	5.73154	0.201885
$807$	27.0019	0.950513
$808$	5.84349	0.205573
$809$	19.5233	0.686404	0.343202	−	0.939262i	$-0.388488\pi$
$809$	19.5233	0.686404	0.343202	+	0.939262i	$0.388488\pi$
$810$	−51.4756	−1.80867
$811$	−22.4029	−0.786671	−0.393336	−	0.919395i	$-0.628679\pi$
$811$	−22.4029	−0.786671	−0.393336	+	0.919395i	$0.628679\pi$
$812$	0	0
$813$	66.2241	2.32258
$814$	30.0897	1.05464
$815$	18.8677	0.660906
$816$	7.82049	0.273772
$817$	−4.44567	−0.155534
$818$	47.9472	1.67643
$819$	0	0
$820$	66.1356	2.30955
$821$	52.6094	1.83608	0.918040	−	0.396487i	$-0.129771\pi$
$821$	52.6094	1.83608	0.918040	+	0.396487i	$0.129771\pi$
$822$	105.687	3.68625
$823$	9.72070	0.338842	0.169421	−	0.985544i	$-0.445810\pi$
$823$	9.72070	0.338842	0.169421	+	0.985544i	$0.445810\pi$
$824$	−21.3548	−0.743930
$825$	154.739	5.38732
$826$	0	0
$827$	52.0766	1.81088	0.905440	−	0.424473i	$-0.139541\pi$
$827$	52.0766	1.81088	0.905440	+	0.424473i	$0.139541\pi$
$828$	102.984	3.57895
$829$	−6.02902	−0.209396	−0.104698	−	0.994504i	$-0.533388\pi$
$829$	−6.02902	−0.209396	−0.104698	+	0.994504i	$0.533388\pi$
$830$	26.4338	0.917531
$831$	−29.5784	−1.02606
$832$	8.49063	0.294360
$833$	0	0
$834$	38.8224	1.34431
$835$	−80.4300	−2.78340
$836$	12.9426	0.447629
$837$	−9.16238	−0.316698
$838$	−28.1080	−0.970976
$839$	−52.1776	−1.80137	−0.900685	−	0.434473i	$-0.856935\pi$
$839$	−52.1776	−1.80137	−0.900685	+	0.434473i	$0.856935\pi$
$840$	0	0
$841$	−27.2821	−0.940761
$842$	−66.3740	−2.28740
$843$	18.5754	0.639770
$844$	29.4015	1.01204
$845$	53.1996	1.83012
$846$	49.8375	1.71345
$847$	0	0
$848$	15.8815	0.545372
$849$	63.9873	2.19604
$850$	−53.2189	−1.82539
$851$	27.9338	0.957558
$852$	30.1266	1.03212
$853$	−32.7787	−1.12232	−0.561161	−	0.827707i	$-0.689645\pi$
$853$	−32.7787	−1.12232	−0.561161	+	0.827707i	$0.689645\pi$
$854$	0	0
$855$	16.4998	0.564282
$856$	−3.97790	−0.135962
$857$	52.7222	1.80095	0.900477	−	0.434903i	$-0.143217\pi$
$857$	52.7222	1.80095	0.900477	+	0.434903i	$0.143217\pi$
$858$	17.5378	0.598732
$859$	38.9499	1.32895	0.664476	−	0.747309i	$-0.268655\pi$
$859$	38.9499	1.32895	0.664476	+	0.747309i	$0.268655\pi$
$860$	−53.5934	−1.82752
$861$	0	0
$862$	−6.50874	−0.221689
$863$	−42.4625	−1.44544	−0.722721	−	0.691140i	$-0.757109\pi$
$863$	−42.4625	−1.44544	−0.722721	+	0.691140i	$0.757109\pi$
$864$	−16.9766	−0.577556
$865$	−18.5182	−0.629637
$866$	−3.18638	−0.108278
$867$	35.4902	1.20531
$868$	0	0
$869$	12.0340	0.408227
$870$	32.0977	1.08821
$871$	0.349193	0.0118320
$872$	13.0650	0.442436
$873$	−14.4551	−0.489231
$874$	20.4618	0.692131
$875$	0	0
$876$	−40.2381	−1.35952
$877$	34.0068	1.14833	0.574163	−	0.818741i	$-0.305327\pi$
$877$	34.0068	1.14833	0.574163	+	0.818741i	$0.305327\pi$
$878$	4.59655	0.155126
$879$	42.2099	1.42371
$880$	−30.7637	−1.03704
$881$	19.0580	0.642079	0.321040	−	0.947066i	$-0.395968\pi$
$881$	19.0580	0.642079	0.321040	+	0.947066i	$0.395968\pi$
$882$	0	0
$883$	−40.7499	−1.37134	−0.685671	−	0.727911i	$-0.740491\pi$
$883$	−40.7499	−1.37134	−0.685671	+	0.727911i	$0.740491\pi$
$884$	−3.54186	−0.119126
$885$	23.1346	0.777659
$886$	61.4319	2.06384
$887$	−6.28833	−0.211141	−0.105571	−	0.994412i	$-0.533667\pi$
$887$	−6.28833	−0.211141	−0.105571	+	0.994412i	$0.533667\pi$
$888$	14.6750	0.492461
$889$	0	0
$890$	−131.496	−4.40777
$891$	25.1074	0.841128
$892$	51.0474	1.70919
$893$	5.81459	0.194578
$894$	92.2228	3.08439
$895$	24.4686	0.817895
$896$	0	0
$897$	16.2813	0.543616
$898$	−76.9064	−2.56640
$899$	−5.11644	−0.170643
$900$	143.517	4.78390
$901$	−18.5724	−0.618737
$902$	−54.9345	−1.82912
$903$	0	0
$904$	−12.1694	−0.404749
$905$	37.5031	1.24664
$906$	−110.461	−3.66982
$907$	−25.7603	−0.855355	−0.427678	−	0.903931i	$-0.640668\pi$
$907$	−25.7603	−0.855355	−0.427678	+	0.903931i	$0.640668\pi$
$908$	41.2731	1.36970
$909$	−12.2335	−0.405759
$910$	0	0
$911$	−30.3836	−1.00665	−0.503327	−	0.864096i	$-0.667891\pi$
$911$	−30.3836	−1.00665	−0.503327	+	0.864096i	$0.667891\pi$
$912$	−4.19030	−0.138755
$913$	−12.8932	−0.426701
$914$	42.1499	1.39420
$915$	112.802	3.72912
$916$	−13.6855	−0.452181
$917$	0	0
$918$	9.64226	0.318242
$919$	16.3148	0.538174	0.269087	−	0.963116i	$-0.413278\pi$
$919$	16.3148	0.538174	0.269087	+	0.963116i	$0.413278\pi$
$920$	73.2653	2.41548
$921$	−34.4181	−1.13411
$922$	67.7599	2.23155
$923$	2.69024	0.0885502
$924$	0	0
$925$	38.9280	1.27995
$926$	21.7497	0.714738
$927$	44.7067	1.46836
$928$	−9.48006	−0.311198
$929$	−35.3308	−1.15917	−0.579583	−	0.814913i	$-0.696784\pi$
$929$	−35.3308	−1.15917	−0.579583	+	0.814913i	$0.696784\pi$
$930$	−95.5954	−3.13470
$931$	0	0
$932$	−54.7982	−1.79498
$933$	−73.6119	−2.40995
$934$	−23.1342	−0.756973
$935$	35.9762	1.17655
$936$	4.83125	0.157914
$937$	−28.5431	−0.932461	−0.466231	−	0.884663i	$-0.654388\pi$
$937$	−28.5431	−0.932461	−0.466231	+	0.884663i	$0.654388\pi$
$938$	0	0
$939$	25.0351	0.816991
$940$	70.0961	2.28628
$941$	−51.9012	−1.69193	−0.845966	−	0.533237i	$-0.820975\pi$
$941$	−51.9012	−1.69193	−0.845966	+	0.533237i	$0.820975\pi$
$942$	−17.9246	−0.584017
$943$	−50.9985	−1.66074
$944$	−3.31855	−0.108010
$945$	0	0
$946$	44.5165	1.44736
$947$	29.9686	0.973848	0.486924	−	0.873444i	$-0.338119\pi$
$947$	29.9686	0.973848	0.486924	+	0.873444i	$0.338119\pi$
$948$	19.7603	0.641783
$949$	−3.59317	−0.116639
$950$	28.5152	0.925156
$951$	29.2357	0.948032
$952$	0	0
$953$	10.6441	0.344796	0.172398	−	0.985027i	$-0.444848\pi$
$953$	10.6441	0.344796	0.172398	+	0.985027i	$0.444848\pi$
$954$	85.2937	2.76148
$955$	−23.3170	−0.754519
$956$	19.4715	0.629753
$957$	−15.6557	−0.506077
$958$	−46.6388	−1.50683
$959$	0	0
$960$	−141.614	−4.57056
$961$	−15.7619	−0.508447
$962$	4.41203	0.142250
$963$	8.32782	0.268360
$964$	1.67847	0.0540598
$965$	78.4995	2.52699
$966$	0	0
$967$	45.3775	1.45924	0.729620	−	0.683852i	$-0.239697\pi$
$967$	45.3775	1.45924	0.729620	+	0.683852i	$0.239697\pi$
$968$	−18.0334	−0.579615
$969$	4.90030	0.157420
$970$	−34.6234	−1.11169
$971$	10.6259	0.341000	0.170500	−	0.985358i	$-0.445462\pi$
$971$	10.6259	0.341000	0.170500	+	0.985358i	$0.445462\pi$
$972$	61.2602	1.96492
$973$	0	0
$974$	4.54744	0.145709
$975$	22.6893	0.726639
$976$	−16.1810	−0.517940
$977$	34.7509	1.11178	0.555890	−	0.831256i	$-0.312378\pi$
$977$	34.7509	1.11178	0.555890	+	0.831256i	$0.312378\pi$
$978$	−25.7341	−0.822887
$979$	64.1376	2.04985
$980$	0	0
$981$	−27.3518	−0.873276
$982$	−38.9019	−1.24141
$983$	31.8461	1.01573	0.507867	−	0.861436i	$-0.330434\pi$
$983$	31.8461	1.01573	0.507867	+	0.861436i	$0.330434\pi$
$984$	−26.7921	−0.854100
$985$	−31.6751	−1.00925
$986$	5.38442	0.171475
$987$	0	0
$988$	1.89777	0.0603760
$989$	41.3270	1.31412
$990$	−165.220	−5.25105
$991$	−20.2572	−0.643490	−0.321745	−	0.946826i	$-0.604269\pi$
$991$	−20.2572	−0.643490	−0.321745	+	0.946826i	$0.604269\pi$
$992$	28.2341	0.896434
$993$	2.34762	0.0744995
$994$	0	0
$995$	−93.6473	−2.96882
$996$	−21.1710	−0.670828
$997$	28.8629	0.914096	0.457048	−	0.889442i	$-0.348907\pi$
$997$	28.8629	0.914096	0.457048	+	0.889442i	$0.348907\pi$
$998$	−19.6884	−0.623225
$999$	−7.05303	−0.223148

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.p.1.2	✓	10
3.2	odd	2		8379.2.a.ct.1.9		10
7.2	even	3		931.2.f.r.704.9		20
7.3	odd	6		931.2.f.q.324.9		20
7.4	even	3		931.2.f.r.324.9		20
7.5	odd	6		931.2.f.q.704.9		20
7.6	odd	2		931.2.a.q.1.2	yes	10
21.20	even	2		8379.2.a.cs.1.9		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.2	✓	10	1.1	even	1	trivial
931.2.a.q.1.2	yes	10	7.6	odd	2
931.2.f.q.324.9		20	7.3	odd	6
931.2.f.q.704.9		20	7.5	odd	6
931.2.f.r.324.9		20	7.4	even	3
931.2.f.r.704.9		20	7.2	even	3
8379.2.a.cs.1.9		10	21.20	even	2
8379.2.a.ct.1.9		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)

\(f(q)\)	\(=\)	\(q-2.20114 q^{2} -2.62563 q^{3} +2.84501 q^{4} -4.23731 q^{5} +5.77938 q^{6} -1.86000 q^{8} +3.89394 q^{9} +O(q^{10})\)	\(q-2.20114 q^{2} -2.62563 q^{3} +2.84501 q^{4} -4.23731 q^{5} +5.77938 q^{6} -1.86000 q^{8} +3.89394 q^{9} +9.32690 q^{10} -4.54922 q^{11} -7.46996 q^{12} -0.667049 q^{13} +11.1256 q^{15} -1.59592 q^{16} +1.86633 q^{17} -8.57111 q^{18} -1.00000 q^{19} -12.0552 q^{20} +10.0135 q^{22} +9.29601 q^{23} +4.88366 q^{24} +12.9548 q^{25} +1.46827 q^{26} -2.34716 q^{27} -1.31070 q^{29} -24.4890 q^{30} +3.90360 q^{31} +7.23283 q^{32} +11.9446 q^{33} -4.10806 q^{34} +11.0783 q^{36} +3.00492 q^{37} +2.20114 q^{38} +1.75143 q^{39} +7.88137 q^{40} -5.48606 q^{41} +4.44567 q^{43} -12.9426 q^{44} -16.4998 q^{45} -20.4618 q^{46} -5.81459 q^{47} +4.19030 q^{48} -28.5152 q^{50} -4.90030 q^{51} -1.89777 q^{52} -9.95130 q^{53} +5.16642 q^{54} +19.2764 q^{55} +2.62563 q^{57} +2.88503 q^{58} +2.07940 q^{59} +31.6525 q^{60} +10.1390 q^{61} -8.59238 q^{62} -12.7286 q^{64} +2.82649 q^{65} -26.2917 q^{66} -0.523489 q^{67} +5.30974 q^{68} -24.4079 q^{69} -4.03304 q^{71} -7.24271 q^{72} +5.38666 q^{73} -6.61425 q^{74} -34.0144 q^{75} -2.84501 q^{76} -3.85513 q^{78} -2.64530 q^{79} +6.76240 q^{80} -5.51905 q^{81} +12.0756 q^{82} +2.83415 q^{83} -7.90822 q^{85} -9.78554 q^{86} +3.44141 q^{87} +8.46152 q^{88} -14.0986 q^{89} +36.3184 q^{90} +26.4473 q^{92} -10.2494 q^{93} +12.7987 q^{94} +4.23731 q^{95} -18.9908 q^{96} -3.71220 q^{97} -17.7144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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