LMFDB - Embedded newform 931.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.43407242818$
Analytic rank:	$1$
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			1.1
Root			$2.76052$ 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)

$f(q)$	$=$	$q-2.76052 q^{2} +0.148409 q^{3} +5.62048 q^{4} -2.53457 q^{5} -0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} +O(q^{10})$	\(q-2.76052 q^{2} +0.148409 q^{3} +5.62048 q^{4} -2.53457 q^{5} -0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} +6.99673 q^{10} +1.58351 q^{11} +0.834129 q^{12} +6.17112 q^{13} -0.376152 q^{15} +16.3488 q^{16} -3.03303 q^{17} +8.22076 q^{18} -1.00000 q^{19} -14.2455 q^{20} -4.37132 q^{22} +6.07217 q^{23} -1.48326 q^{24} +1.42404 q^{25} -17.0355 q^{26} -0.887185 q^{27} +1.46356 q^{29} +1.03838 q^{30} -7.46482 q^{31} -25.1424 q^{32} +0.235007 q^{33} +8.37274 q^{34} -16.7376 q^{36} -0.493725 q^{37} +2.76052 q^{38} +0.915849 q^{39} +25.3315 q^{40} -6.46929 q^{41} +0.636828 q^{43} +8.90010 q^{44} +7.54788 q^{45} -16.7624 q^{46} +3.56543 q^{47} +2.42631 q^{48} -3.93108 q^{50} -0.450128 q^{51} +34.6846 q^{52} +11.0835 q^{53} +2.44909 q^{54} -4.01352 q^{55} -0.148409 q^{57} -4.04019 q^{58} -13.7225 q^{59} -2.11416 q^{60} -3.53613 q^{61} +20.6068 q^{62} +36.7086 q^{64} -15.6411 q^{65} -0.648743 q^{66} -4.76008 q^{67} -17.0471 q^{68} +0.901165 q^{69} -0.975752 q^{71} +29.7631 q^{72} +1.26338 q^{73} +1.36294 q^{74} +0.211340 q^{75} -5.62048 q^{76} -2.52822 q^{78} -16.2898 q^{79} -41.4372 q^{80} +8.80226 q^{81} +17.8586 q^{82} -0.284058 q^{83} +7.68741 q^{85} -1.75798 q^{86} +0.217205 q^{87} -15.8263 q^{88} -6.16563 q^{89} -20.8361 q^{90} +34.1285 q^{92} -1.10785 q^{93} -9.84245 q^{94} +2.53457 q^{95} -3.73136 q^{96} -13.9410 q^{97} -4.71566 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76052	−1.95198	−0.975992	−	0.217808i	$-0.930109\pi$
$2$	−2.76052	−1.95198	−0.975992	+	0.217808i	$0.930109\pi$
$3$	0.148409	0.0856839	0.0428420	−	0.999082i	$-0.486359\pi$
$3$	0.148409	0.0856839	0.0428420	+	0.999082i	$0.486359\pi$
$4$	5.62048	2.81024
$5$	−2.53457	−1.13349	−0.566747	−	0.823892i	$-0.691798\pi$
$5$	−2.53457	−1.13349	−0.566747	+	0.823892i	$0.691798\pi$
$6$	−0.409686	−0.167254
$7$	0	0
$7$	0	0
$8$	−9.99440	−3.53355
$9$	−2.97797	−0.992658
$10$	6.99673	2.21256
$11$	1.58351	0.477447	0.238724	−	0.971088i	$-0.423271\pi$
$11$	1.58351	0.477447	0.238724	+	0.971088i	$0.423271\pi$
$12$	0.834129	0.240792
$13$	6.17112	1.71156	0.855780	−	0.517340i	$-0.173078\pi$
$13$	6.17112	1.71156	0.855780	+	0.517340i	$0.173078\pi$
$14$	0	0
$15$	−0.376152	−0.0971221
$16$	16.3488	4.08720
$17$	−3.03303	−0.735617	−0.367809	−	0.929902i	$-0.619892\pi$
$17$	−3.03303	−0.735617	−0.367809	+	0.929902i	$0.619892\pi$
$18$	8.22076	1.93765
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−14.2455	−3.18539
$21$	0	0
$22$	−4.37132	−0.931969
$23$	6.07217	1.26614	0.633068	−	0.774096i	$-0.281795\pi$
$23$	6.07217	1.26614	0.633068	+	0.774096i	$0.281795\pi$
$24$	−1.48326	−0.302769
$25$	1.42404	0.284807
$26$	−17.0355	−3.34094
$27$	−0.887185	−0.170739
$28$	0	0
$29$	1.46356	0.271776	0.135888	−	0.990724i	$-0.456611\pi$
$29$	1.46356	0.271776	0.135888	+	0.990724i	$0.456611\pi$
$30$	1.03838	0.189581
$31$	−7.46482	−1.34072	−0.670361	−	0.742035i	$-0.733861\pi$
$31$	−7.46482	−1.34072	−0.670361	+	0.742035i	$0.733861\pi$
$32$	−25.1424	−4.44459
$33$	0.235007	0.0409095
$34$	8.37274	1.43591
$35$	0	0
$36$	−16.7376	−2.78961
$37$	−0.493725	−0.0811678	−0.0405839	−	0.999176i	$-0.512922\pi$
$37$	−0.493725	−0.0811678	−0.0405839	+	0.999176i	$0.512922\pi$
$38$	2.76052	0.447816
$39$	0.915849	0.146653
$40$	25.3315	4.00526
$41$	−6.46929	−1.01033	−0.505166	−	0.863022i	$-0.668569\pi$
$41$	−6.46929	−1.01033	−0.505166	+	0.863022i	$0.668569\pi$
$42$	0	0
$43$	0.636828	0.0971153	0.0485576	−	0.998820i	$-0.484538\pi$
$43$	0.636828	0.0971153	0.0485576	+	0.998820i	$0.484538\pi$
$44$	8.90010	1.34174
$45$	7.54788	1.12517
$46$	−16.7624	−2.47148
$47$	3.56543	0.520072	0.260036	−	0.965599i	$-0.416266\pi$
$47$	3.56543	0.520072	0.260036	+	0.965599i	$0.416266\pi$
$48$	2.42631	0.350207
$49$	0	0
$50$	−3.93108	−0.555939
$51$	−0.450128	−0.0630306
$52$	34.6846	4.80989
$53$	11.0835	1.52244	0.761219	−	0.648495i	$-0.224601\pi$
$53$	11.0835	1.52244	0.761219	+	0.648495i	$0.224601\pi$
$54$	2.44909	0.333279
$55$	−4.01352	−0.541183
$56$	0	0
$57$	−0.148409	−0.0196572
$58$	−4.04019	−0.530502
$59$	−13.7225	−1.78652	−0.893260	−	0.449539i	$-0.851588\pi$
$59$	−13.7225	−1.78652	−0.893260	+	0.449539i	$0.851588\pi$
$60$	−2.11416	−0.272936
$61$	−3.53613	−0.452754	−0.226377	−	0.974040i	$-0.572688\pi$
$61$	−3.53613	−0.452754	−0.226377	+	0.974040i	$0.572688\pi$
$62$	20.6068	2.61707
$63$	0	0
$64$	36.7086	4.58857
$65$	−15.6411	−1.94004
$66$	−0.648743	−0.0798547
$67$	−4.76008	−0.581537	−0.290768	−	0.956793i	$-0.593911\pi$
$67$	−4.76008	−0.581537	−0.290768	+	0.956793i	$0.593911\pi$
$68$	−17.0471	−2.06726
$69$	0.901165	0.108487
$70$	0	0
$71$	−0.975752	−0.115800	−0.0579002	−	0.998322i	$-0.518441\pi$
$71$	−0.975752	−0.115800	−0.0579002	+	0.998322i	$0.518441\pi$
$72$	29.7631	3.50761
$73$	1.26338	0.147868	0.0739339	−	0.997263i	$-0.476445\pi$
$73$	1.26338	0.147868	0.0739339	+	0.997263i	$0.476445\pi$
$74$	1.36294	0.158438
$75$	0.211340	0.0244034
$76$	−5.62048	−0.644713
$77$	0	0
$78$	−2.52822	−0.286264
$79$	−16.2898	−1.83275	−0.916373	−	0.400327i	$-0.868897\pi$
$79$	−16.2898	−1.83275	−0.916373	+	0.400327i	$0.868897\pi$
$80$	−41.4372	−4.63282
$81$	8.80226	0.978029
$82$	17.8586	1.97215
$83$	−0.284058	−0.0311794	−0.0155897	−	0.999878i	$-0.504963\pi$
$83$	−0.284058	−0.0311794	−0.0155897	+	0.999878i	$0.504963\pi$
$84$	0	0
$85$	7.68741	0.833817
$86$	−1.75798	−0.189567
$87$	0.217205	0.0232868
$88$	−15.8263	−1.68709
$89$	−6.16563	−0.653556	−0.326778	−	0.945101i	$-0.605963\pi$
$89$	−6.16563	−0.653556	−0.326778	+	0.945101i	$0.605963\pi$
$90$	−20.8361	−2.19632
$91$	0	0
$92$	34.1285	3.55814
$93$	−1.10785	−0.114878
$94$	−9.84245	−1.01517
$95$	2.53457	0.260041
$96$	−3.73136	−0.380830
$97$	−13.9410	−1.41549	−0.707747	−	0.706466i	$-0.750288\pi$
$97$	−13.9410	−1.41549	−0.707747	+	0.706466i	$0.750288\pi$
$98$	0	0
$99$	−4.71566	−0.473942
$100$	8.00376	0.800376
$101$	−16.2153	−1.61348	−0.806740	−	0.590907i	$-0.798770\pi$
$101$	−16.2153	−1.61348	−0.806740	+	0.590907i	$0.798770\pi$
$102$	1.24259	0.123035
$103$	−7.62785	−0.751595	−0.375797	−	0.926702i	$-0.622631\pi$
$103$	−7.62785	−0.751595	−0.375797	+	0.926702i	$0.622631\pi$
$104$	−61.6766	−6.04789
$105$	0	0
$106$	−30.5963	−2.97177
$107$	2.72492	0.263428	0.131714	−	0.991288i	$-0.457952\pi$
$107$	2.72492	0.263428	0.131714	+	0.991288i	$0.457952\pi$
$108$	−4.98640	−0.479817
$109$	2.84550	0.272549	0.136275	−	0.990671i	$-0.456487\pi$
$109$	2.84550	0.272549	0.136275	+	0.990671i	$0.456487\pi$
$110$	11.0794	1.05638
$111$	−0.0732731	−0.00695478
$112$	0	0
$113$	−6.07066	−0.571080	−0.285540	−	0.958367i	$-0.592173\pi$
$113$	−6.07066	−0.571080	−0.285540	+	0.958367i	$0.592173\pi$
$114$	0.409686	0.0383706
$115$	−15.3903	−1.43516
$116$	8.22590	0.763756
$117$	−18.3774	−1.69899
$118$	37.8813	3.48726
$119$	0	0
$120$	3.75942	0.343186
$121$	−8.49249	−0.772044
$122$	9.76155	0.883769
$123$	−0.960100	−0.0865693
$124$	−41.9559	−3.76775
$125$	9.06353	0.810666
$126$	0	0
$127$	−11.4368	−1.01485	−0.507426	−	0.861695i	$-0.669403\pi$
$127$	−11.4368	−1.01485	−0.507426	+	0.861695i	$0.669403\pi$
$128$	−51.0499	−4.51222
$129$	0.0945109	0.00832122
$130$	43.1776	3.78693
$131$	11.9389	1.04311	0.521554	−	0.853218i	$-0.325353\pi$
$131$	11.9389	1.04311	0.521554	+	0.853218i	$0.325353\pi$
$132$	1.32085	0.114966
$133$	0	0
$134$	13.1403	1.13515
$135$	2.24863	0.193531
$136$	30.3133	2.59934
$137$	−9.26003	−0.791138	−0.395569	−	0.918436i	$-0.629453\pi$
$137$	−9.26003	−0.791138	−0.395569	+	0.918436i	$0.629453\pi$
$138$	−2.48768	−0.211766
$139$	−6.14306	−0.521048	−0.260524	−	0.965467i	$-0.583895\pi$
$139$	−6.14306	−0.521048	−0.260524	+	0.965467i	$0.583895\pi$
$140$	0	0
$141$	0.529142	0.0445618
$142$	2.69358	0.226040
$143$	9.77204	0.817179
$144$	−48.6863	−4.05719
$145$	−3.70949	−0.308056
$146$	−3.48759	−0.288635
$147$	0	0
$148$	−2.77497	−0.228101
$149$	12.0740	0.989141	0.494571	−	0.869138i	$-0.335325\pi$
$149$	12.0740	0.989141	0.494571	+	0.869138i	$0.335325\pi$
$150$	−0.583407	−0.0476350
$151$	6.45109	0.524983	0.262491	−	0.964934i	$-0.415456\pi$
$151$	6.45109	0.524983	0.262491	+	0.964934i	$0.415456\pi$
$152$	9.99440	0.810653
$153$	9.03228	0.730217
$154$	0	0
$155$	18.9201	1.51970
$156$	5.14751	0.412130
$157$	−4.02184	−0.320977	−0.160489	−	0.987038i	$-0.551307\pi$
$157$	−4.02184	−0.320977	−0.160489	+	0.987038i	$0.551307\pi$
$158$	44.9683	3.57749
$159$	1.64489	0.130448
$160$	63.7252	5.03792
$161$	0	0
$162$	−24.2988	−1.90910
$163$	−11.9800	−0.938346	−0.469173	−	0.883106i	$-0.655448\pi$
$163$	−11.9800	−0.938346	−0.469173	+	0.883106i	$0.655448\pi$
$164$	−36.3605	−2.83928
$165$	−0.595642	−0.0463707
$166$	0.784147	0.0608616
$167$	−15.1250	−1.17041	−0.585204	−	0.810886i	$-0.698985\pi$
$167$	−15.1250	−1.17041	−0.585204	+	0.810886i	$0.698985\pi$
$168$	0	0
$169$	25.0827	1.92944
$170$	−21.2213	−1.62760
$171$	2.97797	0.227731
$172$	3.57927	0.272917
$173$	−14.8273	−1.12730	−0.563649	−	0.826014i	$-0.690603\pi$
$173$	−14.8273	−1.12730	−0.563649	+	0.826014i	$0.690603\pi$
$174$	−0.599600	−0.0454555
$175$	0	0
$176$	25.8885	1.95142
$177$	−2.03655	−0.153076
$178$	17.0204	1.27573
$179$	−16.2947	−1.21792	−0.608961	−	0.793200i	$-0.708414\pi$
$179$	−16.2947	−1.21792	−0.608961	+	0.793200i	$0.708414\pi$
$180$	42.4227	3.16200
$181$	−1.03994	−0.0772982	−0.0386491	−	0.999253i	$-0.512305\pi$
$181$	−1.03994	−0.0772982	−0.0386491	+	0.999253i	$0.512305\pi$
$182$	0	0
$183$	−0.524792	−0.0387938
$184$	−60.6878	−4.47396
$185$	1.25138	0.0920032
$186$	3.05823	0.224240
$187$	−4.80284	−0.351218
$188$	20.0394	1.46153
$189$	0	0
$190$	−6.99673	−0.507596
$191$	3.77831	0.273389	0.136694	−	0.990613i	$-0.456352\pi$
$191$	3.77831	0.273389	0.136694	+	0.990613i	$0.456352\pi$
$192$	5.44788	0.393167
$193$	10.4678	0.753491	0.376746	−	0.926317i	$-0.377043\pi$
$193$	10.4678	0.753491	0.376746	+	0.926317i	$0.377043\pi$
$194$	38.4844	2.76302
$195$	−2.32128	−0.166230
$196$	0	0
$197$	−13.4885	−0.961014	−0.480507	−	0.876991i	$-0.659547\pi$
$197$	−13.4885	−0.961014	−0.480507	+	0.876991i	$0.659547\pi$
$198$	13.0177	0.925126
$199$	17.9294	1.27098	0.635491	−	0.772109i	$-0.280798\pi$
$199$	17.9294	1.27098	0.635491	+	0.772109i	$0.280798\pi$
$200$	−14.2324	−1.00638
$201$	−0.706439	−0.0498284
$202$	44.7626	3.14949
$203$	0	0
$204$	−2.52994	−0.177131
$205$	16.3968	1.14521
$206$	21.0568	1.46710
$207$	−18.0828	−1.25684
$208$	100.890	6.99549
$209$	−1.58351	−0.109534
$210$	0	0
$211$	7.90422	0.544149	0.272074	−	0.962276i	$-0.412290\pi$
$211$	7.90422	0.544149	0.272074	+	0.962276i	$0.412290\pi$
$212$	62.2946	4.27841
$213$	−0.144810	−0.00992223
$214$	−7.52221	−0.514208
$215$	−1.61408	−0.110080
$216$	8.86688	0.603315
$217$	0	0
$218$	−7.85506	−0.532012
$219$	0.187497	0.0126699
$220$	−22.5579	−1.52085
$221$	−18.7172	−1.25905
$222$	0.202272	0.0135756
$223$	−4.22024	−0.282608	−0.141304	−	0.989966i	$-0.545130\pi$
$223$	−4.22024	−0.282608	−0.141304	+	0.989966i	$0.545130\pi$
$224$	0	0
$225$	−4.24074	−0.282716
$226$	16.7582	1.11474
$227$	16.1145	1.06956	0.534778	−	0.844993i	$-0.320395\pi$
$227$	16.1145	1.06956	0.534778	+	0.844993i	$0.320395\pi$
$228$	−0.834129	−0.0552415
$229$	−13.2448	−0.875240	−0.437620	−	0.899160i	$-0.644179\pi$
$229$	−13.2448	−0.875240	−0.437620	+	0.899160i	$0.644179\pi$
$230$	42.4854	2.80140
$231$	0	0
$232$	−14.6274	−0.960336
$233$	16.9074	1.10764	0.553821	−	0.832636i	$-0.313169\pi$
$233$	16.9074	1.10764	0.553821	+	0.832636i	$0.313169\pi$
$234$	50.7313	3.31641
$235$	−9.03683	−0.589498
$236$	−77.1272	−5.02055
$237$	−2.41755	−0.157037
$238$	0	0
$239$	−6.77655	−0.438338	−0.219169	−	0.975687i	$-0.570335\pi$
$239$	−6.77655	−0.438338	−0.219169	+	0.975687i	$0.570335\pi$
$240$	−6.14964	−0.396958
$241$	−22.6252	−1.45742	−0.728708	−	0.684824i	$-0.759879\pi$
$241$	−22.6252	−1.45742	−0.728708	+	0.684824i	$0.759879\pi$
$242$	23.4437	1.50702
$243$	3.96789	0.254540
$244$	−19.8747	−1.27235
$245$	0	0
$246$	2.65038	0.168982
$247$	−6.17112	−0.392659
$248$	74.6064	4.73751
$249$	−0.0421567	−0.00267157
$250$	−25.0201	−1.58241
$251$	−11.3603	−0.717053	−0.358527	−	0.933520i	$-0.616721\pi$
$251$	−11.3603	−0.717053	−0.358527	+	0.933520i	$0.616721\pi$
$252$	0	0
$253$	9.61537	0.604513
$254$	31.5715	1.98097
$255$	1.14088	0.0714447
$256$	67.5073	4.21921
$257$	17.5409	1.09417	0.547085	−	0.837077i	$-0.315737\pi$
$257$	17.5409	1.09417	0.547085	+	0.837077i	$0.315737\pi$
$258$	−0.260899	−0.0162429
$259$	0	0
$260$	−87.9105	−5.45198
$261$	−4.35844	−0.269781
$262$	−32.9576	−2.03613
$263$	−15.3999	−0.949596	−0.474798	−	0.880095i	$-0.657479\pi$
$263$	−15.3999	−0.949596	−0.474798	+	0.880095i	$0.657479\pi$
$264$	−2.34876	−0.144556
$265$	−28.0919	−1.72567
$266$	0	0
$267$	−0.915035	−0.0559992
$268$	−26.7539	−1.63426
$269$	−7.92775	−0.483363	−0.241682	−	0.970356i	$-0.577699\pi$
$269$	−7.92775	−0.483363	−0.241682	+	0.970356i	$0.577699\pi$
$270$	−6.20739	−0.377770
$271$	8.75327	0.531723	0.265862	−	0.964011i	$-0.414344\pi$
$271$	8.75327	0.531723	0.265862	+	0.964011i	$0.414344\pi$
$272$	−49.5864	−3.00662
$273$	0	0
$274$	25.5625	1.54429
$275$	2.25498	0.135980
$276$	5.06498	0.304876
$277$	18.4795	1.11032	0.555162	−	0.831742i	$-0.312656\pi$
$277$	18.4795	1.11032	0.555162	+	0.831742i	$0.312656\pi$
$278$	16.9581	1.01708
$279$	22.2300	1.33088
$280$	0	0
$281$	−3.48167	−0.207699	−0.103850	−	0.994593i	$-0.533116\pi$
$281$	−3.48167	−0.207699	−0.103850	+	0.994593i	$0.533116\pi$
$282$	−1.46071	−0.0869839
$283$	11.3181	0.672791	0.336395	−	0.941721i	$-0.390792\pi$
$283$	11.3181	0.672791	0.336395	+	0.941721i	$0.390792\pi$
$284$	−5.48419	−0.325427
$285$	0.376152	0.0222813
$286$	−26.9759	−1.59512
$287$	0	0
$288$	74.8735	4.41196
$289$	−7.80074	−0.458867
$290$	10.2401	0.601321
$291$	−2.06897	−0.121285
$292$	7.10081	0.415544
$293$	15.0868	0.881381	0.440691	−	0.897659i	$-0.354734\pi$
$293$	15.0868	0.881381	0.440691	+	0.897659i	$0.354734\pi$
$294$	0	0
$295$	34.7807	2.02501
$296$	4.93448	0.286811
$297$	−1.40487	−0.0815187
$298$	−33.3305	−1.93079
$299$	37.4721	2.16707
$300$	1.18783	0.0685793
$301$	0	0
$302$	−17.8084	−1.02476
$303$	−2.40649	−0.138249
$304$	−16.3488	−0.937668
$305$	8.96255	0.513194
$306$	−24.9338	−1.42537
$307$	6.07516	0.346728	0.173364	−	0.984858i	$-0.444536\pi$
$307$	6.07516	0.346728	0.173364	+	0.984858i	$0.444536\pi$
$308$	0	0
$309$	−1.13204	−0.0643996
$310$	−52.2293	−2.96643
$311$	−18.5023	−1.04917	−0.524586	−	0.851358i	$-0.675780\pi$
$311$	−18.5023	−1.04917	−0.524586	+	0.851358i	$0.675780\pi$
$312$	−9.15336	−0.518207
$313$	11.8582	0.670263	0.335131	−	0.942171i	$-0.391219\pi$
$313$	11.8582	0.670263	0.335131	+	0.942171i	$0.391219\pi$
$314$	11.1024	0.626543
$315$	0	0
$316$	−91.5564	−5.15045
$317$	−2.28430	−0.128299	−0.0641495	−	0.997940i	$-0.520433\pi$
$317$	−2.28430	−0.128299	−0.0641495	+	0.997940i	$0.520433\pi$
$318$	−4.54076	−0.254633
$319$	2.31756	0.129759
$320$	−93.0404	−5.20111
$321$	0.404403	0.0225716
$322$	0	0
$323$	3.03303	0.168762
$324$	49.4729	2.74849
$325$	8.78789	0.487464
$326$	33.0710	1.83163
$327$	0.422297	0.0233531
$328$	64.6567	3.57007
$329$	0	0
$330$	1.64428	0.0905148
$331$	21.2867	1.17002	0.585011	−	0.811026i	$-0.301090\pi$
$331$	21.2867	1.17002	0.585011	+	0.811026i	$0.301090\pi$
$332$	−1.59654	−0.0876215
$333$	1.47030	0.0805719
$334$	41.7529	2.28462
$335$	12.0648	0.659168
$336$	0	0
$337$	17.1088	0.931978	0.465989	−	0.884791i	$-0.345699\pi$
$337$	17.1088	0.931978	0.465989	+	0.884791i	$0.345699\pi$
$338$	−69.2413	−3.76623
$339$	−0.900941	−0.0489324
$340$	43.2069	2.34323
$341$	−11.8206	−0.640124
$342$	−8.22076	−0.444528
$343$	0	0
$344$	−6.36471	−0.343162
$345$	−2.28406	−0.122970
$346$	40.9311	2.20047
$347$	10.7992	0.579729	0.289865	−	0.957068i	$-0.406390\pi$
$347$	10.7992	0.579729	0.289865	+	0.957068i	$0.406390\pi$
$348$	1.22080	0.0654416
$349$	20.7117	1.10867	0.554336	−	0.832293i	$-0.312972\pi$
$349$	20.7117	1.10867	0.554336	+	0.832293i	$0.312972\pi$
$350$	0	0
$351$	−5.47492	−0.292230
$352$	−39.8133	−2.12206
$353$	−16.9047	−0.899749	−0.449874	−	0.893092i	$-0.648531\pi$
$353$	−16.9047	−0.899749	−0.449874	+	0.893092i	$0.648531\pi$
$354$	5.62193	0.298802
$355$	2.47311	0.131259
$356$	−34.6538	−1.83665
$357$	0	0
$358$	44.9819	2.37736
$359$	15.5071	0.818433	0.409217	−	0.912437i	$-0.365802\pi$
$359$	15.5071	0.818433	0.409217	+	0.912437i	$0.365802\pi$
$360$	−75.4366	−3.97586
$361$	1.00000	0.0526316
$362$	2.87078	0.150885
$363$	−1.26036	−0.0661518
$364$	0	0
$365$	−3.20213	−0.167607
$366$	1.44870	0.0757248
$367$	−2.71781	−0.141869	−0.0709343	−	0.997481i	$-0.522598\pi$
$367$	−2.71781	−0.141869	−0.0709343	+	0.997481i	$0.522598\pi$
$368$	99.2728	5.17495
$369$	19.2654	1.00292
$370$	−3.45446	−0.179589
$371$	0	0
$372$	−6.22662	−0.322835
$373$	−16.3916	−0.848727	−0.424364	−	0.905492i	$-0.639502\pi$
$373$	−16.3916	−0.848727	−0.424364	+	0.905492i	$0.639502\pi$
$374$	13.2583	0.685572
$375$	1.34511	0.0694611
$376$	−35.6344	−1.83770
$377$	9.03179	0.465161
$378$	0	0
$379$	−26.4759	−1.35998	−0.679988	−	0.733223i	$-0.738015\pi$
$379$	−26.4759	−1.35998	−0.679988	+	0.733223i	$0.738015\pi$
$380$	14.2455	0.730778
$381$	−1.69732	−0.0869565
$382$	−10.4301	−0.533650
$383$	8.97673	0.458689	0.229345	−	0.973345i	$-0.426342\pi$
$383$	8.97673	0.458689	0.229345	+	0.973345i	$0.426342\pi$
$384$	−7.57627	−0.386625
$385$	0	0
$386$	−28.8967	−1.47080
$387$	−1.89646	−0.0964023
$388$	−78.3551	−3.97788
$389$	−22.0155	−1.11623	−0.558115	−	0.829763i	$-0.688475\pi$
$389$	−22.0155	−1.11623	−0.558115	+	0.829763i	$0.688475\pi$
$390$	6.40794	0.324479
$391$	−18.4171	−0.931391
$392$	0	0
$393$	1.77184	0.0893775
$394$	37.2352	1.87588
$395$	41.2876	2.07740
$396$	−26.5043	−1.33189
$397$	3.35484	0.168374	0.0841872	−	0.996450i	$-0.473171\pi$
$397$	3.35484	0.168374	0.0841872	+	0.996450i	$0.473171\pi$
$398$	−49.4945	−2.48093
$399$	0	0
$400$	23.2813	1.16406
$401$	−20.1098	−1.00423	−0.502117	−	0.864800i	$-0.667445\pi$
$401$	−20.1098	−1.00423	−0.502117	+	0.864800i	$0.667445\pi$
$402$	1.95014	0.0972641
$403$	−46.0663	−2.29472
$404$	−91.1376	−4.53426
$405$	−22.3099	−1.10859
$406$	0	0
$407$	−0.781819	−0.0387533
$408$	4.49876	0.222722
$409$	2.44826	0.121059	0.0605294	−	0.998166i	$-0.480721\pi$
$409$	2.44826	0.121059	0.0605294	+	0.998166i	$0.480721\pi$
$410$	−45.2638	−2.23542
$411$	−1.37427	−0.0677878
$412$	−42.8722	−2.11216
$413$	0	0
$414$	49.9179	2.45333
$415$	0.719963	0.0353416
$416$	−155.157	−7.60719
$417$	−0.911685	−0.0446454
$418$	4.37132	0.213808
$419$	36.0307	1.76022	0.880108	−	0.474774i	$-0.157470\pi$
$419$	36.0307	1.76022	0.880108	+	0.474774i	$0.157470\pi$
$420$	0	0
$421$	−21.2289	−1.03463	−0.517316	−	0.855795i	$-0.673069\pi$
$421$	−21.2289	−1.03463	−0.517316	+	0.855795i	$0.673069\pi$
$422$	−21.8198	−1.06217
$423$	−10.6178	−0.516254
$424$	−110.773	−5.37962
$425$	−4.31914	−0.209509
$426$	0.399752	0.0193680
$427$	0	0
$428$	15.3154	0.740297
$429$	1.45026	0.0700191
$430$	4.45571	0.214873
$431$	−11.3811	−0.548208	−0.274104	−	0.961700i	$-0.588381\pi$
$431$	−11.3811	−0.548208	−0.274104	+	0.961700i	$0.588381\pi$
$432$	−14.5044	−0.697844
$433$	−23.1101	−1.11060	−0.555300	−	0.831650i	$-0.687396\pi$
$433$	−23.1101	−1.11060	−0.555300	+	0.831650i	$0.687396\pi$
$434$	0	0
$435$	−0.550521	−0.0263955
$436$	15.9931	0.765929
$437$	−6.07217	−0.290471
$438$	−0.517590	−0.0247314
$439$	27.9702	1.33494	0.667472	−	0.744635i	$-0.267376\pi$
$439$	27.9702	1.33494	0.667472	+	0.744635i	$0.267376\pi$
$440$	40.1127	1.91230
$441$	0	0
$442$	51.6691	2.45765
$443$	28.6352	1.36050	0.680249	−	0.732981i	$-0.261872\pi$
$443$	28.6352	1.36050	0.680249	+	0.732981i	$0.261872\pi$
$444$	−0.411830	−0.0195446
$445$	15.6272	0.740801
$446$	11.6501	0.551646
$447$	1.79189	0.0847535
$448$	0	0
$449$	1.51721	0.0716016	0.0358008	−	0.999359i	$-0.488602\pi$
$449$	1.51721	0.0716016	0.0358008	+	0.999359i	$0.488602\pi$
$450$	11.7067	0.551857
$451$	−10.2442	−0.482380
$452$	−34.1200	−1.60487
$453$	0.957400	0.0449826
$454$	−44.4844	−2.08776
$455$	0	0
$456$	1.48326	0.0694599
$457$	8.02405	0.375349	0.187675	−	0.982231i	$-0.439905\pi$
$457$	8.02405	0.375349	0.187675	+	0.982231i	$0.439905\pi$
$458$	36.5625	1.70845
$459$	2.69086	0.125598
$460$	−86.5010	−4.03313
$461$	−19.3393	−0.900719	−0.450360	−	0.892847i	$-0.648704\pi$
$461$	−19.3393	−0.900719	−0.450360	+	0.892847i	$0.648704\pi$
$462$	0	0
$463$	32.2738	1.49989	0.749946	−	0.661499i	$-0.230080\pi$
$463$	32.2738	1.49989	0.749946	+	0.661499i	$0.230080\pi$
$464$	23.9274	1.11080
$465$	2.80791	0.130214
$466$	−46.6733	−2.16210
$467$	−32.1680	−1.48856	−0.744278	−	0.667870i	$-0.767206\pi$
$467$	−32.1680	−1.48856	−0.744278	+	0.667870i	$0.767206\pi$
$468$	−103.290	−4.77458
$469$	0	0
$470$	24.9464	1.15069
$471$	−0.596876	−0.0275026
$472$	137.148	6.31277
$473$	1.00842	0.0463674
$474$	6.67370	0.306533
$475$	−1.42404	−0.0653392
$476$	0	0
$477$	−33.0064	−1.51126
$478$	18.7068	0.855629
$479$	7.81799	0.357213	0.178606	−	0.983921i	$-0.442841\pi$
$479$	7.81799	0.357213	0.178606	+	0.983921i	$0.442841\pi$
$480$	9.45738	0.431669
$481$	−3.04683	−0.138924
$482$	62.4573	2.84485
$483$	0	0
$484$	−47.7318	−2.16963
$485$	35.3344	1.60445
$486$	−10.9534	−0.496858
$487$	−29.7980	−1.35027	−0.675137	−	0.737692i	$-0.735916\pi$
$487$	−29.7980	−1.35027	−0.675137	+	0.737692i	$0.735916\pi$
$488$	35.3415	1.59983
$489$	−1.77794	−0.0804011
$490$	0	0
$491$	19.8290	0.894872	0.447436	−	0.894316i	$-0.352337\pi$
$491$	19.8290	0.894872	0.447436	+	0.894316i	$0.352337\pi$
$492$	−5.39622	−0.243280
$493$	−4.43901	−0.199923
$494$	17.0355	0.766463
$495$	11.9522	0.537210
$496$	−122.041	−5.47980
$497$	0	0
$498$	0.116374	0.00521486
$499$	−30.6722	−1.37308	−0.686539	−	0.727093i	$-0.740871\pi$
$499$	−30.6722	−1.37308	−0.686539	+	0.727093i	$0.740871\pi$
$500$	50.9413	2.27817
$501$	−2.24468	−0.100285
$502$	31.3602	1.39968
$503$	36.5009	1.62750	0.813748	−	0.581218i	$-0.197424\pi$
$503$	36.5009	1.62750	0.813748	+	0.581218i	$0.197424\pi$
$504$	0	0
$505$	41.0987	1.82887
$506$	−26.5434	−1.18000
$507$	3.72249	0.165322
$508$	−64.2802	−2.85197
$509$	−4.95937	−0.219820	−0.109910	−	0.993942i	$-0.535056\pi$
$509$	−4.95937	−0.219820	−0.109910	+	0.993942i	$0.535056\pi$
$510$	−3.14943	−0.139459
$511$	0	0
$512$	−84.2554	−3.72360
$513$	0.887185	0.0391702
$514$	−48.4220	−2.13580
$515$	19.3333	0.851928
$516$	0.531196	0.0233846
$517$	5.64591	0.248307
$518$	0	0
$519$	−2.20050	−0.0965914
$520$	156.324	6.85524
$521$	33.8799	1.48431	0.742153	−	0.670231i	$-0.233805\pi$
$521$	33.8799	1.48431	0.742153	+	0.670231i	$0.233805\pi$
$522$	12.0316	0.526608
$523$	25.7088	1.12417	0.562083	−	0.827081i	$-0.310000\pi$
$523$	25.7088	1.12417	0.562083	+	0.827081i	$0.310000\pi$
$524$	67.1024	2.93138
$525$	0	0
$526$	42.5116	1.85360
$527$	22.6410	0.986258
$528$	3.84209	0.167206
$529$	13.8713	0.603100
$530$	77.5483	3.36848
$531$	40.8653	1.77340
$532$	0	0
$533$	−39.9227	−1.72924
$534$	2.52597	0.109310
$535$	−6.90651	−0.298594
$536$	47.5742	2.05489
$537$	−2.41828	−0.104356
$538$	21.8847	0.943517
$539$	0	0
$540$	12.6384	0.543869
$541$	21.7172	0.933697	0.466849	−	0.884337i	$-0.345389\pi$
$541$	21.7172	0.933697	0.466849	+	0.884337i	$0.345389\pi$
$542$	−24.1636	−1.03791
$543$	−0.154336	−0.00662321
$544$	76.2576	3.26952
$545$	−7.21211	−0.308933
$546$	0	0
$547$	26.1501	1.11810	0.559049	−	0.829135i	$-0.311166\pi$
$547$	26.1501	1.11810	0.559049	+	0.829135i	$0.311166\pi$
$548$	−52.0458	−2.22329
$549$	10.5305	0.449430
$550$	−6.22492	−0.265431
$551$	−1.46356	−0.0623497
$552$	−9.00660	−0.383346
$553$	0	0
$554$	−51.0130	−2.16733
$555$	0.185716	0.00788319
$556$	−34.5269	−1.46427
$557$	−17.5350	−0.742983	−0.371492	−	0.928436i	$-0.621154\pi$
$557$	−17.5350	−0.742983	−0.371492	+	0.928436i	$0.621154\pi$
$558$	−61.3665	−2.59785
$559$	3.92994	0.166219
$560$	0	0
$561$	−0.712784	−0.0300938
$562$	9.61123	0.405425
$563$	23.0311	0.970644	0.485322	−	0.874335i	$-0.338702\pi$
$563$	23.0311	0.970644	0.485322	+	0.874335i	$0.338702\pi$
$564$	2.97403	0.125229
$565$	15.3865	0.647315
$566$	−31.2438	−1.31328
$567$	0	0
$568$	9.75205	0.409187
$569$	−41.3636	−1.73405	−0.867027	−	0.498261i	$-0.833972\pi$
$569$	−41.3636	−1.73405	−0.867027	+	0.498261i	$0.833972\pi$
$570$	−1.03838	−0.0434928
$571$	−28.2907	−1.18393	−0.591964	−	0.805965i	$-0.701647\pi$
$571$	−28.2907	−1.18393	−0.591964	+	0.805965i	$0.701647\pi$
$572$	54.9235	2.29647
$573$	0.560734	0.0234250
$574$	0	0
$575$	8.64699	0.360604
$576$	−109.317	−4.55488
$577$	−29.7398	−1.23808	−0.619041	−	0.785359i	$-0.712479\pi$
$577$	−29.7398	−1.23808	−0.619041	+	0.785359i	$0.712479\pi$
$578$	21.5341	0.895701
$579$	1.55352	0.0645621
$580$	−20.8491	−0.865712
$581$	0	0
$582$	5.71143	0.236746
$583$	17.5509	0.726883
$584$	−12.6268	−0.522499
$585$	46.5788	1.92580
$586$	−41.6475	−1.72044
$587$	−7.21249	−0.297691	−0.148846	−	0.988860i	$-0.547556\pi$
$587$	−7.21249	−0.297691	−0.148846	+	0.988860i	$0.547556\pi$
$588$	0	0
$589$	7.46482	0.307583
$590$	−96.0128	−3.95278
$591$	−2.00181	−0.0823435
$592$	−8.07181	−0.331749
$593$	−5.16126	−0.211948	−0.105974	−	0.994369i	$-0.533796\pi$
$593$	−5.16126	−0.211948	−0.105974	+	0.994369i	$0.533796\pi$
$594$	3.87817	0.159123
$595$	0	0
$596$	67.8617	2.77972
$597$	2.66088	0.108903
$598$	−103.442	−4.23008
$599$	32.8017	1.34024	0.670121	−	0.742252i	$-0.266242\pi$
$599$	32.8017	1.34024	0.670121	+	0.742252i	$0.266242\pi$
$600$	−2.11221	−0.0862307
$601$	24.6906	1.00715	0.503576	−	0.863951i	$-0.332017\pi$
$601$	24.6906	1.00715	0.503576	+	0.863951i	$0.332017\pi$
$602$	0	0
$603$	14.1754	0.577267
$604$	36.2582	1.47533
$605$	21.5248	0.875107
$606$	6.64317	0.269860
$607$	17.4222	0.707146	0.353573	−	0.935407i	$-0.384967\pi$
$607$	17.4222	0.707146	0.353573	+	0.935407i	$0.384967\pi$
$608$	25.1424	1.01966
$609$	0	0
$610$	−24.7413	−1.00175
$611$	22.0027	0.890134
$612$	50.7657	2.05208
$613$	−28.0331	−1.13225	−0.566123	−	0.824321i	$-0.691557\pi$
$613$	−28.0331	−1.13225	−0.566123	+	0.824321i	$0.691557\pi$
$614$	−16.7706	−0.676806
$615$	2.43344	0.0981257
$616$	0	0
$617$	−7.79442	−0.313791	−0.156896	−	0.987615i	$-0.550149\pi$
$617$	−7.79442	−0.313791	−0.156896	+	0.987615i	$0.550149\pi$
$618$	3.12502	0.125707
$619$	21.1086	0.848424	0.424212	−	0.905563i	$-0.360551\pi$
$619$	21.1086	0.848424	0.424212	+	0.905563i	$0.360551\pi$
$620$	106.340	4.27072
$621$	−5.38714	−0.216178
$622$	51.0761	2.04797
$623$	0	0
$624$	14.9730	0.599401
$625$	−30.0923	−1.20369
$626$	−32.7347	−1.30834
$627$	−0.235007	−0.00938529
$628$	−22.6046	−0.902023
$629$	1.49748	0.0597084
$630$	0	0
$631$	27.8768	1.10976	0.554880	−	0.831931i	$-0.312764\pi$
$631$	27.8768	1.10976	0.554880	+	0.831931i	$0.312764\pi$
$632$	162.807	6.47611
$633$	1.17306	0.0466248
$634$	6.30585	0.250437
$635$	28.9873	1.15033
$636$	9.24507	0.366591
$637$	0	0
$638$	−6.39769	−0.253287
$639$	2.90576	0.114950
$640$	129.390	5.11457
$641$	22.5527	0.890780	0.445390	−	0.895337i	$-0.353065\pi$
$641$	22.5527	0.890780	0.445390	+	0.895337i	$0.353065\pi$
$642$	−1.11636	−0.0440593
$643$	−16.1900	−0.638472	−0.319236	−	0.947675i	$-0.603426\pi$
$643$	−16.1900	−0.638472	−0.319236	+	0.947675i	$0.603426\pi$
$644$	0	0
$645$	−0.239544	−0.00943205
$646$	−8.37274	−0.329421
$647$	29.3233	1.15282	0.576408	−	0.817162i	$-0.304454\pi$
$647$	29.3233	1.15282	0.576408	+	0.817162i	$0.304454\pi$
$648$	−87.9733	−3.45592
$649$	−21.7298	−0.852969
$650$	−24.2592	−0.951522
$651$	0	0
$652$	−67.3333	−2.63697
$653$	−6.28876	−0.246098	−0.123049	−	0.992401i	$-0.539267\pi$
$653$	−6.28876	−0.246098	−0.123049	+	0.992401i	$0.539267\pi$
$654$	−1.16576	−0.0455849
$655$	−30.2600	−1.18236
$656$	−105.765	−4.12943
$657$	−3.76232	−0.146782
$658$	0	0
$659$	−8.10004	−0.315533	−0.157766	−	0.987476i	$-0.550429\pi$
$659$	−8.10004	−0.315533	−0.157766	+	0.987476i	$0.550429\pi$
$660$	−3.34779	−0.130313
$661$	9.95412	0.387170	0.193585	−	0.981083i	$-0.437988\pi$
$661$	9.95412	0.387170	0.193585	+	0.981083i	$0.437988\pi$
$662$	−58.7623	−2.28386
$663$	−2.77779	−0.107881
$664$	2.83899	0.110174
$665$	0	0
$666$	−4.05879	−0.157275
$667$	8.88699	0.344105
$668$	−85.0097	−3.28912
$669$	−0.626321	−0.0242150
$670$	−33.3050	−1.28668
$671$	−5.59950	−0.216166
$672$	0	0
$673$	−35.7331	−1.37741	−0.688704	−	0.725042i	$-0.741820\pi$
$673$	−35.7331	−1.37741	−0.688704	+	0.725042i	$0.741820\pi$
$674$	−47.2293	−1.81920
$675$	−1.26338	−0.0486276
$676$	140.977	5.42218
$677$	−5.43480	−0.208876	−0.104438	−	0.994531i	$-0.533304\pi$
$677$	−5.43480	−0.208876	−0.104438	+	0.994531i	$0.533304\pi$
$678$	2.48707	0.0955152
$679$	0	0
$680$	−76.8311	−2.94634
$681$	2.39153	0.0916437
$682$	32.6311	1.24951
$683$	20.9587	0.801963	0.400982	−	0.916086i	$-0.368669\pi$
$683$	20.9587	0.801963	0.400982	+	0.916086i	$0.368669\pi$
$684$	16.7376	0.639980
$685$	23.4702	0.896749
$686$	0	0
$687$	−1.96564	−0.0749940
$688$	10.4114	0.396930
$689$	68.3976	2.60574
$690$	6.30520	0.240035
$691$	−41.0627	−1.56210	−0.781049	−	0.624470i	$-0.785315\pi$
$691$	−41.0627	−1.56210	−0.781049	+	0.624470i	$0.785315\pi$
$692$	−83.3365	−3.16798
$693$	0	0
$694$	−29.8113	−1.13162
$695$	15.5700	0.590604
$696$	−2.17084	−0.0822853
$697$	19.6215	0.743218
$698$	−57.1751	−2.16411
$699$	2.50921	0.0949071
$700$	0	0
$701$	−39.6574	−1.49784	−0.748920	−	0.662661i	$-0.769427\pi$
$701$	−39.6574	−1.49784	−0.748920	+	0.662661i	$0.769427\pi$
$702$	15.1136	0.570427
$703$	0.493725	0.0186212
$704$	58.1285	2.19080
$705$	−1.34115	−0.0505105
$706$	46.6659	1.75629
$707$	0	0
$708$	−11.4464	−0.430180
$709$	−38.7028	−1.45351	−0.726757	−	0.686894i	$-0.758973\pi$
$709$	−38.7028	−1.45351	−0.726757	+	0.686894i	$0.758973\pi$
$710$	−6.82707	−0.256215
$711$	48.5106	1.81929
$712$	61.6218	2.30937
$713$	−45.3277	−1.69754
$714$	0	0
$715$	−24.7679	−0.926267
$716$	−91.5840	−3.42265
$717$	−1.00570	−0.0375585
$718$	−42.8077	−1.59757
$719$	−25.4944	−0.950781	−0.475390	−	0.879775i	$-0.657693\pi$
$719$	−25.4944	−0.950781	−0.475390	+	0.879775i	$0.657693\pi$
$720$	123.399	4.59880
$721$	0	0
$722$	−2.76052	−0.102736
$723$	−3.35778	−0.124877
$724$	−5.84496	−0.217226
$725$	2.08416	0.0774038
$726$	3.47925	0.129127
$727$	−22.6721	−0.840860	−0.420430	−	0.907325i	$-0.638121\pi$
$727$	−22.6721	−0.840860	−0.420430	+	0.907325i	$0.638121\pi$
$728$	0	0
$729$	−25.8179	−0.956219
$730$	8.83955	0.327166
$731$	−1.93152	−0.0714397
$732$	−2.94958	−0.109020
$733$	9.50433	0.351050	0.175525	−	0.984475i	$-0.443838\pi$
$733$	9.50433	0.351050	0.175525	+	0.984475i	$0.443838\pi$
$734$	7.50258	0.276925
$735$	0	0
$736$	−152.669	−5.62746
$737$	−7.53765	−0.277653
$738$	−53.1825	−1.95767
$739$	14.2287	0.523410	0.261705	−	0.965148i	$-0.415715\pi$
$739$	14.2287	0.523410	0.261705	+	0.965148i	$0.415715\pi$
$740$	7.03334	0.258551
$741$	−0.915849	−0.0336445
$742$	0	0
$743$	−32.0267	−1.17494	−0.587472	−	0.809244i	$-0.699877\pi$
$743$	−32.0267	−1.17494	−0.587472	+	0.809244i	$0.699877\pi$
$744$	11.0723	0.405929
$745$	−30.6024	−1.12118
$746$	45.2495	1.65670
$747$	0.845916	0.0309505
$748$	−26.9942	−0.987007
$749$	0	0
$750$	−3.71320	−0.135587
$751$	−7.55357	−0.275634	−0.137817	−	0.990458i	$-0.544009\pi$
$751$	−7.55357	−0.275634	−0.137817	+	0.990458i	$0.544009\pi$
$752$	58.2906	2.12564
$753$	−1.68596	−0.0614399
$754$	−24.9325	−0.907986
$755$	−16.3507	−0.595064
$756$	0	0
$757$	−25.3179	−0.920193	−0.460097	−	0.887869i	$-0.652185\pi$
$757$	−25.3179	−0.920193	−0.460097	+	0.887869i	$0.652185\pi$
$758$	73.0873	2.65465
$759$	1.42701	0.0517970
$760$	−25.3315	−0.918870
$761$	−5.14945	−0.186667	−0.0933337	−	0.995635i	$-0.529752\pi$
$761$	−5.14945	−0.186667	−0.0933337	+	0.995635i	$0.529752\pi$
$762$	4.68549	0.169738
$763$	0	0
$764$	21.2359	0.768287
$765$	−22.8929	−0.827696
$766$	−24.7804	−0.895354
$767$	−84.6833	−3.05774
$768$	10.0187	0.361518
$769$	30.5976	1.10338	0.551689	−	0.834050i	$-0.313983\pi$
$769$	30.5976	1.10338	0.551689	+	0.834050i	$0.313983\pi$
$770$	0	0
$771$	2.60322	0.0937528
$772$	58.8342	2.11749
$773$	−49.6897	−1.78721	−0.893606	−	0.448851i	$-0.851833\pi$
$773$	−49.6897	−1.78721	−0.893606	+	0.448851i	$0.851833\pi$
$774$	5.23521	0.188176
$775$	−10.6302	−0.381847
$776$	139.332	5.00173
$777$	0	0
$778$	60.7743	2.17886
$779$	6.46929	0.231786
$780$	−13.0467	−0.467147
$781$	−1.54512	−0.0552886
$782$	50.8407	1.81806
$783$	−1.29845	−0.0464027
$784$	0	0
$785$	10.1936	0.363826
$786$	−4.89120	−0.174463
$787$	−13.4645	−0.479957	−0.239978	−	0.970778i	$-0.577140\pi$
$787$	−13.4645	−0.479957	−0.239978	+	0.970778i	$0.577140\pi$
$788$	−75.8117	−2.70068
$789$	−2.28548	−0.0813651
$790$	−113.975	−4.05506
$791$	0	0
$792$	47.1302	1.67470
$793$	−21.8218	−0.774916
$794$	−9.26110	−0.328664
$795$	−4.16909	−0.147862
$796$	100.772	3.57176
$797$	−10.9902	−0.389293	−0.194647	−	0.980873i	$-0.562356\pi$
$797$	−10.9902	−0.389293	−0.194647	+	0.980873i	$0.562356\pi$
$798$	0	0
$799$	−10.8141	−0.382574
$800$	−35.8037	−1.26585
$801$	18.3611	0.648757
$802$	55.5134	1.96025
$803$	2.00058	0.0705990
$804$	−3.97052	−0.140030
$805$	0	0
$806$	127.167	4.47926
$807$	−1.17655	−0.0414165
$808$	162.062	5.70132
$809$	20.0635	0.705396	0.352698	−	0.935737i	$-0.385264\pi$
$809$	20.0635	0.705396	0.352698	+	0.935737i	$0.385264\pi$
$810$	61.5870	2.16395
$811$	−1.57184	−0.0551948	−0.0275974	−	0.999619i	$-0.508786\pi$
$811$	−1.57184	−0.0551948	−0.0275974	+	0.999619i	$0.508786\pi$
$812$	0	0
$813$	1.29906	0.0455601
$814$	2.15823	0.0756459
$815$	30.3641	1.06361
$816$	−7.35906	−0.257619
$817$	−0.636828	−0.0222798
$818$	−6.75848	−0.236305
$819$	0	0
$820$	92.1581	3.21830
$821$	3.08159	0.107548	0.0537742	−	0.998553i	$-0.482875\pi$
$821$	3.08159	0.107548	0.0537742	+	0.998553i	$0.482875\pi$
$822$	3.79370	0.132321
$823$	49.4005	1.72199	0.860996	−	0.508612i	$-0.169841\pi$
$823$	49.4005	1.72199	0.860996	+	0.508612i	$0.169841\pi$
$824$	76.2358	2.65580
$825$	0.334659	0.0116513
$826$	0	0
$827$	19.8375	0.689817	0.344909	−	0.938636i	$-0.387910\pi$
$827$	19.8375	0.689817	0.344909	+	0.938636i	$0.387910\pi$
$828$	−101.634	−3.53202
$829$	−40.6536	−1.41196	−0.705979	−	0.708233i	$-0.749493\pi$
$829$	−40.6536	−1.41196	−0.705979	+	0.708233i	$0.749493\pi$
$830$	−1.98747	−0.0689862
$831$	2.74252	0.0951369
$832$	226.533	7.85361
$833$	0	0
$834$	2.51673	0.0871471
$835$	38.3353	1.32665
$836$	−8.90010	−0.307816
$837$	6.62268	0.228913
$838$	−99.4635	−3.43591
$839$	−21.7950	−0.752448	−0.376224	−	0.926529i	$-0.622778\pi$
$839$	−21.7950	−0.752448	−0.376224	+	0.926529i	$0.622778\pi$
$840$	0	0
$841$	−26.8580	−0.926138
$842$	58.6027	2.01958
$843$	−0.516711	−0.0177965
$844$	44.4255	1.52919
$845$	−63.5737	−2.18700
$846$	29.3106	1.00772
$847$	0	0
$848$	181.202	6.22251
$849$	1.67971	0.0576474
$850$	11.9231	0.408958
$851$	−2.99798	−0.102769
$852$	−0.813902	−0.0278838
$853$	−52.6727	−1.80348	−0.901740	−	0.432280i	$-0.857709\pi$
$853$	−52.6727	−1.80348	−0.901740	+	0.432280i	$0.857709\pi$
$854$	0	0
$855$	−7.54788	−0.258132
$856$	−27.2340	−0.930839
$857$	−25.9375	−0.886007	−0.443003	−	0.896520i	$-0.646087\pi$
$857$	−25.9375	−0.886007	−0.443003	+	0.896520i	$0.646087\pi$
$858$	−4.00347	−0.136676
$859$	41.6061	1.41958	0.709791	−	0.704413i	$-0.248790\pi$
$859$	41.6061	1.41958	0.709791	+	0.704413i	$0.248790\pi$
$860$	−9.07191	−0.309350
$861$	0	0
$862$	31.4178	1.07009
$863$	26.6445	0.906990	0.453495	−	0.891259i	$-0.350177\pi$
$863$	26.6445	0.906990	0.453495	+	0.891259i	$0.350177\pi$
$864$	22.3060	0.758864
$865$	37.5808	1.27779
$866$	63.7959	2.16787
$867$	−1.15770	−0.0393175
$868$	0	0
$869$	−25.7951	−0.875039
$870$	1.51973	0.0515235
$871$	−29.3750	−0.995335
$872$	−28.4391	−0.963068
$873$	41.5159	1.40510
$874$	16.7624	0.566995
$875$	0	0
$876$	1.05382	0.0356054
$877$	−21.6320	−0.730461	−0.365230	−	0.930917i	$-0.619010\pi$
$877$	−21.6320	−0.730461	−0.365230	+	0.930917i	$0.619010\pi$
$878$	−77.2123	−2.60579
$879$	2.23902	0.0755202
$880$	−65.6163	−2.21192
$881$	36.3647	1.22516	0.612579	−	0.790409i	$-0.290132\pi$
$881$	36.3647	1.22516	0.612579	+	0.790409i	$0.290132\pi$
$882$	0	0
$883$	−45.8156	−1.54182	−0.770908	−	0.636946i	$-0.780197\pi$
$883$	−45.8156	−1.54182	−0.770908	+	0.636946i	$0.780197\pi$
$884$	−105.199	−3.53824
$885$	5.16176	0.173511
$886$	−79.0479	−2.65567
$887$	20.6252	0.692526	0.346263	−	0.938138i	$-0.387451\pi$
$887$	20.6252	0.692526	0.346263	+	0.938138i	$0.387451\pi$
$888$	0.732321	0.0245751
$889$	0	0
$890$	−43.1393	−1.44603
$891$	13.9385	0.466957
$892$	−23.7198	−0.794196
$893$	−3.56543	−0.119313
$894$	−4.94655	−0.165437
$895$	41.3000	1.38051
$896$	0	0
$897$	5.56119	0.185683
$898$	−4.18829	−0.139765
$899$	−10.9252	−0.364376
$900$	−23.8350	−0.794500
$901$	−33.6166	−1.11993
$902$	28.2793	0.941599
$903$	0	0
$904$	60.6727	2.01794
$905$	2.63580	0.0876169
$906$	−2.64292	−0.0878052
$907$	8.54091	0.283596	0.141798	−	0.989896i	$-0.454712\pi$
$907$	8.54091	0.283596	0.141798	+	0.989896i	$0.454712\pi$
$908$	90.5711	3.00571
$909$	48.2887	1.60163
$910$	0	0
$911$	−43.6287	−1.44548	−0.722742	−	0.691118i	$-0.757119\pi$
$911$	−43.6287	−1.44548	−0.722742	+	0.691118i	$0.757119\pi$
$912$	−2.42631	−0.0803431
$913$	−0.449809	−0.0148865
$914$	−22.1505	−0.732675
$915$	1.33012	0.0439725
$916$	−74.4420	−2.45963
$917$	0	0
$918$	−7.42816	−0.245166
$919$	−49.8066	−1.64297	−0.821484	−	0.570231i	$-0.806854\pi$
$919$	−49.8066	−1.64297	−0.821484	+	0.570231i	$0.806854\pi$
$920$	153.817	5.07120
$921$	0.901607	0.0297090
$922$	53.3864	1.75819
$923$	−6.02148	−0.198199
$924$	0	0
$925$	−0.703081	−0.0231172
$926$	−89.0926	−2.92776
$927$	22.7156	0.746077
$928$	−36.7974	−1.20793
$929$	−44.5895	−1.46293	−0.731467	−	0.681876i	$-0.761164\pi$
$929$	−44.5895	−1.46293	−0.731467	+	0.681876i	$0.761164\pi$
$930$	−7.75130	−0.254175
$931$	0	0
$932$	95.0277	3.11274
$933$	−2.74591	−0.0898971
$934$	88.8004	2.90564
$935$	12.1731	0.398104
$936$	183.671	6.00349
$937$	52.7172	1.72219	0.861097	−	0.508440i	$-0.169778\pi$
$937$	52.7172	1.72219	0.861097	+	0.508440i	$0.169778\pi$
$938$	0	0
$939$	1.75986	0.0574307
$940$	−50.7913	−1.65663
$941$	−15.0751	−0.491436	−0.245718	−	0.969341i	$-0.579024\pi$
$941$	−15.0751	−0.491436	−0.245718	+	0.969341i	$0.579024\pi$
$942$	1.64769	0.0536846
$943$	−39.2826	−1.27922
$944$	−224.347	−7.30187
$945$	0	0
$946$	−2.78378	−0.0905084
$947$	−12.9216	−0.419895	−0.209948	−	0.977713i	$-0.567329\pi$
$947$	−12.9216	−0.419895	−0.209948	+	0.977713i	$0.567329\pi$
$948$	−13.5878	−0.441311
$949$	7.79648	0.253085
$950$	3.93108	0.127541
$951$	−0.339010	−0.0109932
$952$	0	0
$953$	−16.3314	−0.529026	−0.264513	−	0.964382i	$-0.585211\pi$
$953$	−16.3314	−0.529026	−0.264513	+	0.964382i	$0.585211\pi$
$954$	91.1149	2.94995
$955$	−9.57638	−0.309884
$956$	−38.0874	−1.23184
$957$	0.343947	0.0111182
$958$	−21.5817	−0.697274
$959$	0	0
$960$	−13.8080	−0.445652
$961$	24.7236	0.797534
$962$	8.41084	0.271176
$963$	−8.11476	−0.261494
$964$	−127.164	−4.09569
$965$	−26.5314	−0.854077
$966$	0	0
$967$	56.7625	1.82536	0.912679	−	0.408678i	$-0.134010\pi$
$967$	56.7625	1.82536	0.912679	+	0.408678i	$0.134010\pi$
$968$	84.8773	2.72806
$969$	0.450128	0.0144602
$970$	−97.5414	−3.13187
$971$	6.73556	0.216154	0.108077	−	0.994143i	$-0.465531\pi$
$971$	6.73556	0.216154	0.108077	+	0.994143i	$0.465531\pi$
$972$	22.3014	0.715318
$973$	0	0
$974$	82.2579	2.63571
$975$	1.30420	0.0417679
$976$	−57.8114	−1.85050
$977$	21.3172	0.681997	0.340999	−	0.940064i	$-0.389235\pi$
$977$	21.3172	0.681997	0.340999	+	0.940064i	$0.389235\pi$
$978$	4.90804	0.156942
$979$	−9.76336	−0.312038
$980$	0	0
$981$	−8.47382	−0.270548
$982$	−54.7385	−1.74678
$983$	21.2637	0.678206	0.339103	−	0.940749i	$-0.389876\pi$
$983$	21.2637	0.678206	0.339103	+	0.940749i	$0.389876\pi$
$984$	9.59562	0.305897
$985$	34.1875	1.08930
$986$	12.2540	0.390247
$987$	0	0
$988$	−34.6846	−1.10346
$989$	3.86693	0.122961
$990$	−32.9942	−1.04862
$991$	−43.6356	−1.38613	−0.693065	−	0.720875i	$-0.743740\pi$
$991$	−43.6356	−1.38613	−0.693065	+	0.720875i	$0.743740\pi$
$992$	187.684	5.95896
$993$	3.15913	0.100252
$994$	0	0
$995$	−45.4433	−1.44065
$996$	−0.236941	−0.00750775
$997$	−51.7772	−1.63980	−0.819901	−	0.572506i	$-0.805971\pi$
$997$	−51.7772	−1.63980	−0.819901	+	0.572506i	$0.805971\pi$
$998$	84.6714	2.68023
$999$	0.438025	0.0138585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.p.1.1	✓	10
3.2	odd	2		8379.2.a.ct.1.10		10
7.2	even	3		931.2.f.r.704.10		20
7.3	odd	6		931.2.f.q.324.10		20
7.4	even	3		931.2.f.r.324.10		20
7.5	odd	6		931.2.f.q.704.10		20
7.6	odd	2		931.2.a.q.1.1	yes	10
21.20	even	2		8379.2.a.cs.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.1	✓	10	1.1	even	1	trivial
931.2.a.q.1.1	yes	10	7.6	odd	2
931.2.f.q.324.10		20	7.3	odd	6
931.2.f.q.704.10		20	7.5	odd	6
931.2.f.r.324.10		20	7.4	even	3
931.2.f.r.704.10		20	7.2	even	3
8379.2.a.cs.1.10		10	21.20	even	2
8379.2.a.ct.1.10		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)

\(f(q)\)	\(=\)	\(q-2.76052 q^{2} +0.148409 q^{3} +5.62048 q^{4} -2.53457 q^{5} -0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} +O(q^{10})\)	\(q-2.76052 q^{2} +0.148409 q^{3} +5.62048 q^{4} -2.53457 q^{5} -0.409686 q^{6} -9.99440 q^{8} -2.97797 q^{9} +6.99673 q^{10} +1.58351 q^{11} +0.834129 q^{12} +6.17112 q^{13} -0.376152 q^{15} +16.3488 q^{16} -3.03303 q^{17} +8.22076 q^{18} -1.00000 q^{19} -14.2455 q^{20} -4.37132 q^{22} +6.07217 q^{23} -1.48326 q^{24} +1.42404 q^{25} -17.0355 q^{26} -0.887185 q^{27} +1.46356 q^{29} +1.03838 q^{30} -7.46482 q^{31} -25.1424 q^{32} +0.235007 q^{33} +8.37274 q^{34} -16.7376 q^{36} -0.493725 q^{37} +2.76052 q^{38} +0.915849 q^{39} +25.3315 q^{40} -6.46929 q^{41} +0.636828 q^{43} +8.90010 q^{44} +7.54788 q^{45} -16.7624 q^{46} +3.56543 q^{47} +2.42631 q^{48} -3.93108 q^{50} -0.450128 q^{51} +34.6846 q^{52} +11.0835 q^{53} +2.44909 q^{54} -4.01352 q^{55} -0.148409 q^{57} -4.04019 q^{58} -13.7225 q^{59} -2.11416 q^{60} -3.53613 q^{61} +20.6068 q^{62} +36.7086 q^{64} -15.6411 q^{65} -0.648743 q^{66} -4.76008 q^{67} -17.0471 q^{68} +0.901165 q^{69} -0.975752 q^{71} +29.7631 q^{72} +1.26338 q^{73} +1.36294 q^{74} +0.211340 q^{75} -5.62048 q^{76} -2.52822 q^{78} -16.2898 q^{79} -41.4372 q^{80} +8.80226 q^{81} +17.8586 q^{82} -0.284058 q^{83} +7.68741 q^{85} -1.75798 q^{86} +0.217205 q^{87} -15.8263 q^{88} -6.16563 q^{89} -20.8361 q^{90} +34.1285 q^{92} -1.10785 q^{93} -9.84245 q^{94} +2.53457 q^{95} -3.73136 q^{96} -13.9410 q^{97} -4.71566 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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

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