LMFDB - Embedded newform 931.2.a.p.1.8

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			1.8
Root			$-1.74841$ 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)

$f(q)$	$=$	$q+1.74841 q^{2} +0.931300 q^{3} +1.05694 q^{4} -4.09480 q^{5} +1.62830 q^{6} -1.64885 q^{8} -2.13268 q^{9} +O(q^{10})$	\(q+1.74841 q^{2} +0.931300 q^{3} +1.05694 q^{4} -4.09480 q^{5} +1.62830 q^{6} -1.64885 q^{8} -2.13268 q^{9} -7.15939 q^{10} +3.44171 q^{11} +0.984331 q^{12} -1.37441 q^{13} -3.81349 q^{15} -4.99676 q^{16} -8.12248 q^{17} -3.72880 q^{18} -1.00000 q^{19} -4.32797 q^{20} +6.01753 q^{22} -0.950330 q^{23} -1.53558 q^{24} +11.7674 q^{25} -2.40304 q^{26} -4.78007 q^{27} -5.13999 q^{29} -6.66755 q^{30} +7.54706 q^{31} -5.43868 q^{32} +3.20527 q^{33} -14.2014 q^{34} -2.25412 q^{36} +7.05154 q^{37} -1.74841 q^{38} -1.27999 q^{39} +6.75172 q^{40} +2.92184 q^{41} -7.07463 q^{43} +3.63769 q^{44} +8.73290 q^{45} -1.66157 q^{46} -6.17786 q^{47} -4.65348 q^{48} +20.5742 q^{50} -7.56447 q^{51} -1.45267 q^{52} +0.559023 q^{53} -8.35752 q^{54} -14.0931 q^{55} -0.931300 q^{57} -8.98682 q^{58} -0.137102 q^{59} -4.03064 q^{60} -2.60019 q^{61} +13.1954 q^{62} +0.484460 q^{64} +5.62794 q^{65} +5.60413 q^{66} +8.47952 q^{67} -8.58500 q^{68} -0.885043 q^{69} -9.89746 q^{71} +3.51647 q^{72} -1.40542 q^{73} +12.3290 q^{74} +10.9590 q^{75} -1.05694 q^{76} -2.23795 q^{78} -14.6016 q^{79} +20.4607 q^{80} +1.94636 q^{81} +5.10859 q^{82} +14.2089 q^{83} +33.2599 q^{85} -12.3694 q^{86} -4.78687 q^{87} -5.67488 q^{88} +10.0018 q^{89} +15.2687 q^{90} -1.00444 q^{92} +7.02858 q^{93} -10.8014 q^{94} +4.09480 q^{95} -5.06505 q^{96} +9.25433 q^{97} -7.34007 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.74841	1.23631	0.618157	−	0.786055i	$-0.287880\pi$
$2$	1.74841	1.23631	0.618157	+	0.786055i	$0.287880\pi$
$3$	0.931300	0.537687	0.268843	−	0.963184i	$-0.413359\pi$
$3$	0.931300	0.537687	0.268843	+	0.963184i	$0.413359\pi$
$4$	1.05694	0.528471
$5$	−4.09480	−1.83125	−0.915625	−	0.402033i	$-0.868304\pi$
$5$	−4.09480	−1.83125	−0.915625	+	0.402033i	$0.868304\pi$
$6$	1.62830	0.664749
$7$	0	0
$7$	0	0
$8$	−1.64885	−0.582957
$9$	−2.13268	−0.710893
$10$	−7.15939	−2.26400
$11$	3.44171	1.03772	0.518858	−	0.854861i	$-0.326357\pi$
$11$	3.44171	1.03772	0.518858	+	0.854861i	$0.326357\pi$
$12$	0.984331	0.284152
$13$	−1.37441	−0.381193	−0.190597	−	0.981668i	$-0.561042\pi$
$13$	−1.37441	−0.381193	−0.190597	+	0.981668i	$0.561042\pi$
$14$	0	0
$15$	−3.81349	−0.984638
$16$	−4.99676	−1.24919
$17$	−8.12248	−1.96999	−0.984996	−	0.172578i	$-0.944790\pi$
$17$	−8.12248	−1.96999	−0.984996	+	0.172578i	$0.944790\pi$
$18$	−3.72880	−0.878887
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.32797	−0.967763
$21$	0	0
$22$	6.01753	1.28294
$23$	−0.950330	−0.198158	−0.0990788	−	0.995080i	$-0.531590\pi$
$23$	−0.950330	−0.198158	−0.0990788	+	0.995080i	$0.531590\pi$
$24$	−1.53558	−0.313448
$25$	11.7674	2.35348
$26$	−2.40304	−0.471274
$27$	−4.78007	−0.919924
$28$	0	0
$29$	−5.13999	−0.954472	−0.477236	−	0.878775i	$-0.658361\pi$
$29$	−5.13999	−0.954472	−0.477236	+	0.878775i	$0.658361\pi$
$30$	−6.66755	−1.21732
$31$	7.54706	1.35549	0.677746	−	0.735297i	$-0.262957\pi$
$31$	7.54706	1.35549	0.677746	+	0.735297i	$0.262957\pi$
$32$	−5.43868	−0.961432
$33$	3.20527	0.557966
$34$	−14.2014	−2.43553
$35$	0	0
$36$	−2.25412	−0.375687
$37$	7.05154	1.15927	0.579633	−	0.814877i	$-0.303196\pi$
$37$	7.05154	1.15927	0.579633	+	0.814877i	$0.303196\pi$
$38$	−1.74841	−0.283630
$39$	−1.27999	−0.204962
$40$	6.75172	1.06754
$41$	2.92184	0.456316	0.228158	−	0.973624i	$-0.426730\pi$
$41$	2.92184	0.456316	0.228158	+	0.973624i	$0.426730\pi$
$42$	0	0
$43$	−7.07463	−1.07887	−0.539436	−	0.842027i	$-0.681362\pi$
$43$	−7.07463	−1.07887	−0.539436	+	0.842027i	$0.681362\pi$
$44$	3.63769	0.548403
$45$	8.73290	1.30182
$46$	−1.66157	−0.244985
$47$	−6.17786	−0.901133	−0.450567	−	0.892743i	$-0.648778\pi$
$47$	−6.17786	−0.901133	−0.450567	+	0.892743i	$0.648778\pi$
$48$	−4.65348	−0.671672
$49$	0	0
$50$	20.5742	2.90964
$51$	−7.56447	−1.05924
$52$	−1.45267	−0.201450
$53$	0.559023	0.0767877	0.0383939	−	0.999263i	$-0.487776\pi$
$53$	0.559023	0.0767877	0.0383939	+	0.999263i	$0.487776\pi$
$54$	−8.35752	−1.13731
$55$	−14.0931	−1.90032
$56$	0	0
$57$	−0.931300	−0.123354
$58$	−8.98682	−1.18003
$59$	−0.137102	−0.0178492	−0.00892458	−	0.999960i	$-0.502841\pi$
$59$	−0.137102	−0.0178492	−0.00892458	+	0.999960i	$0.502841\pi$
$60$	−4.03064	−0.520353
$61$	−2.60019	−0.332920	−0.166460	−	0.986048i	$-0.553234\pi$
$61$	−2.60019	−0.332920	−0.166460	+	0.986048i	$0.553234\pi$
$62$	13.1954	1.67581
$63$	0	0
$64$	0.484460	0.0605575
$65$	5.62794	0.698060
$66$	5.60413	0.689820
$67$	8.47952	1.03594	0.517969	−	0.855399i	$-0.326688\pi$
$67$	8.47952	1.03594	0.517969	+	0.855399i	$0.326688\pi$
$68$	−8.58500	−1.04108
$69$	−0.885043	−0.106547
$70$	0	0
$71$	−9.89746	−1.17461	−0.587306	−	0.809365i	$-0.699812\pi$
$71$	−9.89746	−1.17461	−0.587306	+	0.809365i	$0.699812\pi$
$72$	3.51647	0.414420
$73$	−1.40542	−0.164492	−0.0822459	−	0.996612i	$-0.526209\pi$
$73$	−1.40542	−0.164492	−0.0822459	+	0.996612i	$0.526209\pi$
$74$	12.3290	1.43322
$75$	10.9590	1.26543
$76$	−1.05694	−0.121240
$77$	0	0
$78$	−2.23795	−0.253398
$79$	−14.6016	−1.64280	−0.821402	−	0.570350i	$-0.806808\pi$
$79$	−14.6016	−1.64280	−0.821402	+	0.570350i	$0.806808\pi$
$80$	20.4607	2.28758
$81$	1.94636	0.216262
$82$	5.10859	0.564149
$83$	14.2089	1.55963	0.779814	−	0.626011i	$-0.215313\pi$
$83$	14.2089	1.55963	0.779814	+	0.626011i	$0.215313\pi$
$84$	0	0
$85$	33.2599	3.60755
$86$	−12.3694	−1.33382
$87$	−4.78687	−0.513207
$88$	−5.67488	−0.604944
$89$	10.0018	1.06019	0.530093	−	0.847939i	$-0.322157\pi$
$89$	10.0018	1.06019	0.530093	+	0.847939i	$0.322157\pi$
$90$	15.2687	1.60946
$91$	0	0
$92$	−1.00444	−0.104721
$93$	7.02858	0.728829
$94$	−10.8014	−1.11408
$95$	4.09480	0.420118
$96$	−5.06505	−0.516949
$97$	9.25433	0.939635	0.469818	−	0.882764i	$-0.344320\pi$
$97$	9.25433	0.939635	0.469818	+	0.882764i	$0.344320\pi$
$98$	0	0
$99$	−7.34007	−0.737705
$100$	12.4374	1.24374
$101$	−4.67402	−0.465083	−0.232541	−	0.972587i	$-0.574704\pi$
$101$	−4.67402	−0.465083	−0.232541	+	0.972587i	$0.574704\pi$
$102$	−13.2258	−1.30955
$103$	−8.08612	−0.796750	−0.398375	−	0.917223i	$-0.630426\pi$
$103$	−8.08612	−0.796750	−0.398375	+	0.917223i	$0.630426\pi$
$104$	2.26620	0.222219
$105$	0	0
$106$	0.977402	0.0949337
$107$	−7.33512	−0.709112	−0.354556	−	0.935035i	$-0.615368\pi$
$107$	−7.33512	−0.709112	−0.354556	+	0.935035i	$0.615368\pi$
$108$	−5.05226	−0.486153
$109$	−10.8749	−1.04163	−0.520814	−	0.853670i	$-0.674371\pi$
$109$	−10.8749	−1.04163	−0.520814	+	0.853670i	$0.674371\pi$
$110$	−24.6406	−2.34939
$111$	6.56711	0.623322
$112$	0	0
$113$	3.98221	0.374615	0.187307	−	0.982301i	$-0.440024\pi$
$113$	3.98221	0.374615	0.187307	+	0.982301i	$0.440024\pi$
$114$	−1.62830	−0.152504
$115$	3.89141	0.362876
$116$	−5.43267	−0.504411
$117$	2.93118	0.270988
$118$	−0.239711	−0.0220672
$119$	0	0
$120$	6.28788	0.574002
$121$	0.845386	0.0768533
$122$	−4.54620	−0.411594
$123$	2.72112	0.245355
$124$	7.97680	0.716338
$125$	−27.7111	−2.47855
$126$	0	0
$127$	5.67953	0.503977	0.251988	−	0.967730i	$-0.418916\pi$
$127$	5.67953	0.503977	0.251988	+	0.967730i	$0.418916\pi$
$128$	11.7244	1.03630
$129$	−6.58861	−0.580094
$130$	9.83995	0.863021
$131$	2.31069	0.201886	0.100943	−	0.994892i	$-0.467814\pi$
$131$	2.31069	0.201886	0.100943	+	0.994892i	$0.467814\pi$
$132$	3.38778	0.294869
$133$	0	0
$134$	14.8257	1.28074
$135$	19.5734	1.68461
$136$	13.3928	1.14842
$137$	−14.7845	−1.26313	−0.631564	−	0.775323i	$-0.717587\pi$
$137$	−14.7845	−1.26313	−0.631564	+	0.775323i	$0.717587\pi$
$138$	−1.54742	−0.131725
$139$	−6.22957	−0.528385	−0.264192	−	0.964470i	$-0.585105\pi$
$139$	−6.22957	−0.528385	−0.264192	+	0.964470i	$0.585105\pi$
$140$	0	0
$141$	−5.75344	−0.484527
$142$	−17.3048	−1.45219
$143$	−4.73033	−0.395570
$144$	10.6565	0.888040
$145$	21.0472	1.74788
$146$	−2.45725	−0.203364
$147$	0	0
$148$	7.45308	0.612639
$149$	−2.48948	−0.203946	−0.101973	−	0.994787i	$-0.532516\pi$
$149$	−2.48948	−0.203946	−0.101973	+	0.994787i	$0.532516\pi$
$150$	19.1608	1.56447
$151$	13.1124	1.06708	0.533538	−	0.845776i	$-0.320862\pi$
$151$	13.1124	1.06708	0.533538	+	0.845776i	$0.320862\pi$
$152$	1.64885	0.133740
$153$	17.3227	1.40045
$154$	0	0
$155$	−30.9037	−2.48224
$156$	−1.35288	−0.108317
$157$	16.5208	1.31850	0.659250	−	0.751924i	$-0.270874\pi$
$157$	16.5208	1.31850	0.659250	+	0.751924i	$0.270874\pi$
$158$	−25.5295	−2.03102
$159$	0.520618	0.0412877
$160$	22.2703	1.76062
$161$	0	0
$162$	3.40304	0.267368
$163$	−7.02181	−0.549991	−0.274995	−	0.961446i	$-0.588676\pi$
$163$	−7.02181	−0.549991	−0.274995	+	0.961446i	$0.588676\pi$
$164$	3.08822	0.241150
$165$	−13.1249	−1.02177
$166$	24.8430	1.92819
$167$	3.72614	0.288337	0.144169	−	0.989553i	$-0.453949\pi$
$167$	3.72614	0.288337	0.144169	+	0.989553i	$0.453949\pi$
$168$	0	0
$169$	−11.1110	−0.854692
$170$	58.1521	4.46006
$171$	2.13268	0.163090
$172$	−7.47748	−0.570152
$173$	−0.622758	−0.0473475	−0.0236737	−	0.999720i	$-0.507536\pi$
$173$	−0.622758	−0.0473475	−0.0236737	+	0.999720i	$0.507536\pi$
$174$	−8.36943	−0.634485
$175$	0	0
$176$	−17.1974	−1.29630
$177$	−0.127683	−0.00959725
$178$	17.4872	1.31072
$179$	−21.0084	−1.57024	−0.785121	−	0.619343i	$-0.787399\pi$
$179$	−21.0084	−1.57024	−0.785121	+	0.619343i	$0.787399\pi$
$180$	9.23017	0.687976
$181$	−2.86217	−0.212743	−0.106372	−	0.994326i	$-0.533923\pi$
$181$	−2.86217	−0.212743	−0.106372	+	0.994326i	$0.533923\pi$
$182$	0	0
$183$	−2.42156	−0.179007
$184$	1.56695	0.115517
$185$	−28.8747	−2.12291
$186$	12.2888	0.901062
$187$	−27.9553	−2.04429
$188$	−6.52964	−0.476223
$189$	0	0
$190$	7.15939	0.519397
$191$	−13.9148	−1.00684	−0.503418	−	0.864043i	$-0.667924\pi$
$191$	−13.9148	−1.00684	−0.503418	+	0.864043i	$0.667924\pi$
$192$	0.451178	0.0325610
$193$	17.5180	1.26097	0.630487	−	0.776200i	$-0.282855\pi$
$193$	17.5180	1.26097	0.630487	+	0.776200i	$0.282855\pi$
$194$	16.1804	1.16168
$195$	5.24130	0.375337
$196$	0	0
$197$	−16.3074	−1.16185	−0.580926	−	0.813956i	$-0.697309\pi$
$197$	−16.3074	−1.16185	−0.580926	+	0.813956i	$0.697309\pi$
$198$	−12.8335	−0.912034
$199$	−25.7703	−1.82681	−0.913404	−	0.407054i	$-0.866556\pi$
$199$	−25.7703	−1.82681	−0.913404	+	0.407054i	$0.866556\pi$
$200$	−19.4027	−1.37198
$201$	7.89698	0.557010
$202$	−8.17211	−0.574988
$203$	0	0
$204$	−7.99521	−0.559777
$205$	−11.9644	−0.835628
$206$	−14.1379	−0.985032
$207$	2.02675	0.140869
$208$	6.86760	0.476182
$209$	−3.44171	−0.238068
$210$	0	0
$211$	−16.0100	−1.10217	−0.551087	−	0.834448i	$-0.685787\pi$
$211$	−16.0100	−1.10217	−0.551087	+	0.834448i	$0.685787\pi$
$212$	0.590855	0.0405801
$213$	−9.21751	−0.631573
$214$	−12.8248	−0.876685
$215$	28.9692	1.97568
$216$	7.88162	0.536277
$217$	0	0
$218$	−19.0138	−1.28778
$219$	−1.30887	−0.0884451
$220$	−14.8956	−1.00426
$221$	11.1636	0.750947
$222$	11.4820	0.770622
$223$	19.8668	1.33038	0.665190	−	0.746674i	$-0.268350\pi$
$223$	19.8668	1.33038	0.665190	+	0.746674i	$0.268350\pi$
$224$	0	0
$225$	−25.0961	−1.67307
$226$	6.96254	0.463141
$227$	13.0317	0.864947	0.432473	−	0.901647i	$-0.357641\pi$
$227$	13.0317	0.864947	0.432473	+	0.901647i	$0.357641\pi$
$228$	−0.984331	−0.0651889
$229$	−19.8847	−1.31402	−0.657008	−	0.753883i	$-0.728178\pi$
$229$	−19.8847	−1.31402	−0.657008	+	0.753883i	$0.728178\pi$
$230$	6.80379	0.448629
$231$	0	0
$232$	8.47509	0.556417
$233$	4.04569	0.265042	0.132521	−	0.991180i	$-0.457693\pi$
$233$	4.04569	0.265042	0.132521	+	0.991180i	$0.457693\pi$
$234$	5.12491	0.335026
$235$	25.2971	1.65020
$236$	−0.144909	−0.00943277
$237$	−13.5984	−0.883313
$238$	0	0
$239$	−2.88288	−0.186478	−0.0932391	−	0.995644i	$-0.529722\pi$
$239$	−2.88288	−0.186478	−0.0932391	+	0.995644i	$0.529722\pi$
$240$	19.0551	1.23000
$241$	−14.8254	−0.954987	−0.477494	−	0.878635i	$-0.658455\pi$
$241$	−14.8254	−0.954987	−0.477494	+	0.878635i	$0.658455\pi$
$242$	1.47808	0.0950148
$243$	16.1528	1.03621
$244$	−2.74825	−0.175939
$245$	0	0
$246$	4.75763	0.303335
$247$	1.37441	0.0874517
$248$	−12.4440	−0.790194
$249$	13.2327	0.838591
$250$	−48.4504	−3.06427
$251$	−3.71032	−0.234193	−0.117097	−	0.993121i	$-0.537359\pi$
$251$	−3.71032	−0.234193	−0.117097	+	0.993121i	$0.537359\pi$
$252$	0	0
$253$	−3.27076	−0.205631
$254$	9.93016	0.623073
$255$	30.9750	1.93973
$256$	19.5302	1.22063
$257$	−21.8044	−1.36012	−0.680060	−	0.733157i	$-0.738046\pi$
$257$	−21.8044	−1.36012	−0.680060	+	0.733157i	$0.738046\pi$
$258$	−11.5196	−0.717179
$259$	0	0
$260$	5.94841	0.368905
$261$	10.9620	0.678528
$262$	4.04003	0.249594
$263$	−8.17378	−0.504017	−0.252008	−	0.967725i	$-0.581091\pi$
$263$	−8.17378	−0.504017	−0.252008	+	0.967725i	$0.581091\pi$
$264$	−5.28502	−0.325270
$265$	−2.28909	−0.140618
$266$	0	0
$267$	9.31466	0.570048
$268$	8.96237	0.547464
$269$	−10.2495	−0.624925	−0.312463	−	0.949930i	$-0.601154\pi$
$269$	−10.2495	−0.624925	−0.312463	+	0.949930i	$0.601154\pi$
$270$	34.2224	2.08271
$271$	−16.5844	−1.00743	−0.503714	−	0.863871i	$-0.668033\pi$
$271$	−16.5844	−1.00743	−0.503714	+	0.863871i	$0.668033\pi$
$272$	40.5861	2.46089
$273$	0	0
$274$	−25.8495	−1.56162
$275$	40.5000	2.44224
$276$	−0.935440	−0.0563068
$277$	−2.21811	−0.133273	−0.0666367	−	0.997777i	$-0.521227\pi$
$277$	−2.21811	−0.133273	−0.0666367	+	0.997777i	$0.521227\pi$
$278$	−10.8918	−0.653249
$279$	−16.0955	−0.963609
$280$	0	0
$281$	31.3128	1.86797	0.933983	−	0.357319i	$-0.116309\pi$
$281$	31.3128	1.86797	0.933983	+	0.357319i	$0.116309\pi$
$282$	−10.0594	−0.599027
$283$	6.08992	0.362008	0.181004	−	0.983482i	$-0.442065\pi$
$283$	6.08992	0.362008	0.181004	+	0.983482i	$0.442065\pi$
$284$	−10.4610	−0.620749
$285$	3.81349	0.225892
$286$	−8.27056	−0.489049
$287$	0	0
$288$	11.5990	0.683476
$289$	48.9747	2.88087
$290$	36.7992	2.16092
$291$	8.61856	0.505229
$292$	−1.48545	−0.0869292
$293$	−5.21502	−0.304665	−0.152332	−	0.988329i	$-0.548678\pi$
$293$	−5.21502	−0.304665	−0.152332	+	0.988329i	$0.548678\pi$
$294$	0	0
$295$	0.561405	0.0326863
$296$	−11.6270	−0.675803
$297$	−16.4516	−0.954620
$298$	−4.35263	−0.252141
$299$	1.30614	0.0755363
$300$	11.5830	0.668745
$301$	0	0
$302$	22.9259	1.31924
$303$	−4.35292	−0.250069
$304$	4.99676	0.286584
$305$	10.6473	0.609660
$306$	30.2871	1.73140
$307$	19.9270	1.13730	0.568648	−	0.822581i	$-0.307467\pi$
$307$	19.9270	1.13730	0.568648	+	0.822581i	$0.307467\pi$
$308$	0	0
$309$	−7.53061	−0.428402
$310$	−54.0323	−3.06883
$311$	−10.2086	−0.578878	−0.289439	−	0.957196i	$-0.593469\pi$
$311$	−10.2086	−0.578878	−0.289439	+	0.957196i	$0.593469\pi$
$312$	2.11051	0.119484
$313$	−8.46451	−0.478443	−0.239221	−	0.970965i	$-0.576892\pi$
$313$	−8.46451	−0.478443	−0.239221	+	0.970965i	$0.576892\pi$
$314$	28.8851	1.63008
$315$	0	0
$316$	−15.4330	−0.868174
$317$	12.5058	0.702394	0.351197	−	0.936302i	$-0.385775\pi$
$317$	12.5058	0.702394	0.351197	+	0.936302i	$0.385775\pi$
$318$	0.910255	0.0510446
$319$	−17.6904	−0.990471
$320$	−1.98377	−0.110896
$321$	−6.83120	−0.381280
$322$	0	0
$323$	8.12248	0.451947
$324$	2.05719	0.114288
$325$	−16.1732	−0.897129
$326$	−12.2770	−0.679961
$327$	−10.1278	−0.560069
$328$	−4.81769	−0.266013
$329$	0	0
$330$	−22.9478	−1.26323
$331$	−16.5678	−0.910651	−0.455326	−	0.890325i	$-0.650477\pi$
$331$	−16.5678	−0.910651	−0.455326	+	0.890325i	$0.650477\pi$
$332$	15.0180	0.824219
$333$	−15.0387	−0.824115
$334$	6.51482	0.356475
$335$	−34.7219	−1.89706
$336$	0	0
$337$	25.5559	1.39212	0.696061	−	0.717983i	$-0.254935\pi$
$337$	25.5559	1.39212	0.696061	+	0.717983i	$0.254935\pi$
$338$	−19.4266	−1.05667
$339$	3.70863	0.201425
$340$	35.1538	1.90648
$341$	25.9748	1.40661
$342$	3.72880	0.201630
$343$	0	0
$344$	11.6650	0.628936
$345$	3.62407	0.195114
$346$	−1.08884	−0.0585363
$347$	−17.8803	−0.959862	−0.479931	−	0.877306i	$-0.659338\pi$
$347$	−17.8803	−0.959862	−0.479931	+	0.877306i	$0.659338\pi$
$348$	−5.05945	−0.271215
$349$	2.94644	0.157719	0.0788597	−	0.996886i	$-0.474872\pi$
$349$	2.94644	0.157719	0.0788597	+	0.996886i	$0.474872\pi$
$350$	0	0
$351$	6.56978	0.350669
$352$	−18.7184	−0.997693
$353$	−11.3809	−0.605746	−0.302873	−	0.953031i	$-0.597946\pi$
$353$	−11.3809	−0.605746	−0.302873	+	0.953031i	$0.597946\pi$
$354$	−0.223243	−0.0118652
$355$	40.5281	2.15101
$356$	10.5713	0.560278
$357$	0	0
$358$	−36.7313	−1.94131
$359$	25.1364	1.32665	0.663325	−	0.748332i	$-0.269145\pi$
$359$	25.1364	1.32665	0.663325	+	0.748332i	$0.269145\pi$
$360$	−14.3993	−0.758908
$361$	1.00000	0.0526316
$362$	−5.00425	−0.263017
$363$	0.787309	0.0413230
$364$	0	0
$365$	5.75491	0.301226
$366$	−4.23388	−0.221309
$367$	−25.2617	−1.31865	−0.659325	−	0.751858i	$-0.729158\pi$
$367$	−25.2617	−1.31865	−0.659325	+	0.751858i	$0.729158\pi$
$368$	4.74857	0.247536
$369$	−6.23136	−0.324392
$370$	−50.4848	−2.62458
$371$	0	0
$372$	7.42880	0.385165
$373$	8.37003	0.433384	0.216692	−	0.976240i	$-0.430473\pi$
$373$	8.37003	0.433384	0.216692	+	0.976240i	$0.430473\pi$
$374$	−48.8773	−2.52738
$375$	−25.8073	−1.33269
$376$	10.1864	0.525322
$377$	7.06446	0.363838
$378$	0	0
$379$	27.0316	1.38852	0.694260	−	0.719724i	$-0.255732\pi$
$379$	27.0316	1.38852	0.694260	+	0.719724i	$0.255732\pi$
$380$	4.32797	0.222020
$381$	5.28935	0.270982
$382$	−24.3287	−1.24477
$383$	−4.40566	−0.225119	−0.112559	−	0.993645i	$-0.535905\pi$
$383$	−4.40566	−0.225119	−0.112559	+	0.993645i	$0.535905\pi$
$384$	10.9189	0.557205
$385$	0	0
$386$	30.6287	1.55896
$387$	15.0879	0.766962
$388$	9.78130	0.496570
$389$	0.0107108	0.000543061 0	0.000271530	−	1.00000i	$-0.499914\pi$
$389$	0.0107108	0.000543061 0	0.000271530		1.00000i	$0.499914\pi$
$390$	9.16395	0.464035
$391$	7.71904	0.390369
$392$	0	0
$393$	2.15194	0.108551
$394$	−28.5120	−1.43641
$395$	59.7905	3.00838
$396$	−7.75803	−0.389856
$397$	−18.2093	−0.913899	−0.456949	−	0.889493i	$-0.651058\pi$
$397$	−18.2093	−0.913899	−0.456949	+	0.889493i	$0.651058\pi$
$398$	−45.0571	−2.25851
$399$	0	0
$400$	−58.7988	−2.93994
$401$	−34.3564	−1.71568	−0.857839	−	0.513919i	$-0.828193\pi$
$401$	−34.3564	−1.71568	−0.857839	+	0.513919i	$0.828193\pi$
$402$	13.8072	0.688639
$403$	−10.3728	−0.516704
$404$	−4.94017	−0.245783
$405$	−7.96996	−0.396030
$406$	0	0
$407$	24.2694	1.20299
$408$	12.4727	0.617491
$409$	18.1424	0.897082	0.448541	−	0.893762i	$-0.351944\pi$
$409$	18.1424	0.897082	0.448541	+	0.893762i	$0.351944\pi$
$410$	−20.9186	−1.03310
$411$	−13.7689	−0.679167
$412$	−8.54657	−0.421059
$413$	0	0
$414$	3.54359	0.174158
$415$	−58.1826	−2.85607
$416$	7.47499	0.366491
$417$	−5.80160	−0.284105
$418$	−6.01753	−0.294327
$419$	−24.3857	−1.19132	−0.595659	−	0.803237i	$-0.703109\pi$
$419$	−24.3857	−1.19132	−0.595659	+	0.803237i	$0.703109\pi$
$420$	0	0
$421$	5.58958	0.272420	0.136210	−	0.990680i	$-0.456508\pi$
$421$	5.58958	0.272420	0.136210	+	0.990680i	$0.456508\pi$
$422$	−27.9921	−1.36263
$423$	13.1754	0.640609
$424$	−0.921747	−0.0447640
$425$	−95.5804	−4.63633
$426$	−16.1160	−0.780823
$427$	0	0
$428$	−7.75280	−0.374746
$429$	−4.40536	−0.212693
$430$	50.6501	2.44256
$431$	33.6327	1.62003	0.810016	−	0.586408i	$-0.199458\pi$
$431$	33.6327	1.62003	0.810016	+	0.586408i	$0.199458\pi$
$432$	23.8848	1.14916
$433$	14.1453	0.679779	0.339890	−	0.940465i	$-0.389610\pi$
$433$	14.1453	0.679779	0.339890	+	0.940465i	$0.389610\pi$
$434$	0	0
$435$	19.6013	0.939810
$436$	−11.4942	−0.550470
$437$	0.950330	0.0454605
$438$	−2.28844	−0.109346
$439$	−0.159456	−0.00761044	−0.00380522	−	0.999993i	$-0.501211\pi$
$439$	−0.159456	−0.00761044	−0.00380522	+	0.999993i	$0.501211\pi$
$440$	23.2375	1.10780
$441$	0	0
$442$	19.5186	0.928406
$443$	35.3725	1.68060	0.840299	−	0.542123i	$-0.182379\pi$
$443$	35.3725	1.68060	0.840299	+	0.542123i	$0.182379\pi$
$444$	6.94105	0.329408
$445$	−40.9553	−1.94147
$446$	34.7354	1.64477
$447$	−2.31845	−0.109659
$448$	0	0
$449$	22.1023	1.04307	0.521537	−	0.853229i	$-0.325359\pi$
$449$	22.1023	1.04307	0.521537	+	0.853229i	$0.325359\pi$
$450$	−43.8782	−2.06844
$451$	10.0562	0.473526
$452$	4.20897	0.197973
$453$	12.2116	0.573752
$454$	22.7848	1.06935
$455$	0	0
$456$	1.53558	0.0719100
$457$	8.65281	0.404761	0.202381	−	0.979307i	$-0.435132\pi$
$457$	8.65281	0.404761	0.202381	+	0.979307i	$0.435132\pi$
$458$	−34.7666	−1.62454
$459$	38.8260	1.81224
$460$	4.11300	0.191770
$461$	7.36193	0.342879	0.171440	−	0.985195i	$-0.445158\pi$
$461$	7.36193	0.342879	0.171440	+	0.985195i	$0.445158\pi$
$462$	0	0
$463$	−41.4461	−1.92617	−0.963083	−	0.269206i	$-0.913239\pi$
$463$	−41.4461	−1.92617	−0.963083	+	0.269206i	$0.913239\pi$
$464$	25.6833	1.19232
$465$	−28.7806	−1.33467
$466$	7.07353	0.327675
$467$	15.4857	0.716591	0.358296	−	0.933608i	$-0.383358\pi$
$467$	15.4857	0.716591	0.358296	+	0.933608i	$0.383358\pi$
$468$	3.09809	0.143209
$469$	0	0
$470$	44.2297	2.04016
$471$	15.3858	0.708940
$472$	0.226061	0.0104053
$473$	−24.3488	−1.11956
$474$	−23.7757	−1.09205
$475$	−11.7674	−0.539925
$476$	0	0
$477$	−1.19222	−0.0545879
$478$	−5.04047	−0.230546
$479$	−10.0363	−0.458569	−0.229284	−	0.973359i	$-0.573639\pi$
$479$	−10.0363	−0.458569	−0.229284	+	0.973359i	$0.573639\pi$
$480$	20.7404	0.946663
$481$	−9.69172	−0.441904
$482$	−25.9209	−1.18066
$483$	0	0
$484$	0.893525	0.0406148
$485$	−37.8946	−1.72071
$486$	28.2418	1.28107
$487$	8.32169	0.377092	0.188546	−	0.982064i	$-0.439623\pi$
$487$	8.32169	0.377092	0.188546	+	0.982064i	$0.439623\pi$
$488$	4.28733	0.194078
$489$	−6.53941	−0.295723
$490$	0	0
$491$	−1.98289	−0.0894864	−0.0447432	−	0.998999i	$-0.514247\pi$
$491$	−1.98289	−0.0894864	−0.0447432	+	0.998999i	$0.514247\pi$
$492$	2.87606	0.129663
$493$	41.7495	1.88030
$494$	2.40304	0.108118
$495$	30.0561	1.35092
$496$	−37.7108	−1.69327
$497$	0	0
$498$	23.1363	1.03676
$499$	−22.5527	−1.00960	−0.504798	−	0.863238i	$-0.668433\pi$
$499$	−22.5527	−1.00960	−0.504798	+	0.863238i	$0.668433\pi$
$500$	−29.2890	−1.30984
$501$	3.47015	0.155035
$502$	−6.48717	−0.289536
$503$	39.0453	1.74095	0.870473	−	0.492216i	$-0.163813\pi$
$503$	39.0453	1.74095	0.870473	+	0.492216i	$0.163813\pi$
$504$	0	0
$505$	19.1392	0.851682
$506$	−5.71864	−0.254225
$507$	−10.3477	−0.459556
$508$	6.00294	0.266337
$509$	−40.8120	−1.80896	−0.904479	−	0.426518i	$-0.859740\pi$
$509$	−40.8120	−1.80896	−0.904479	+	0.426518i	$0.859740\pi$
$510$	54.1570	2.39811
$511$	0	0
$512$	10.6979	0.472787
$513$	4.78007	0.211045
$514$	−38.1230	−1.68153
$515$	33.1111	1.45905
$516$	−6.96378	−0.306563
$517$	−21.2624	−0.935120
$518$	0	0
$519$	−0.579975	−0.0254581
$520$	−9.27964	−0.406939
$521$	21.5853	0.945669	0.472835	−	0.881151i	$-0.343231\pi$
$521$	21.5853	0.945669	0.472835	+	0.881151i	$0.343231\pi$
$522$	19.1660	0.838873
$523$	31.9796	1.39837	0.699184	−	0.714942i	$-0.253547\pi$
$523$	31.9796	1.39837	0.699184	+	0.714942i	$0.253547\pi$
$524$	2.44226	0.106691
$525$	0	0
$526$	−14.2911	−0.623123
$527$	−61.3008	−2.67031
$528$	−16.0159	−0.697005
$529$	−22.0969	−0.960734
$530$	−4.00227	−0.173847
$531$	0.292395	0.0126888
$532$	0	0
$533$	−4.01582	−0.173944
$534$	16.2859	0.704758
$535$	30.0358	1.29856
$536$	−13.9815	−0.603908
$537$	−19.5651	−0.844298
$538$	−17.9204	−0.772603
$539$	0	0
$540$	20.6880	0.890269
$541$	−4.07963	−0.175397	−0.0876984	−	0.996147i	$-0.527951\pi$
$541$	−4.07963	−0.175397	−0.0876984	+	0.996147i	$0.527951\pi$
$542$	−28.9963	−1.24550
$543$	−2.66554	−0.114389
$544$	44.1756	1.89401
$545$	44.5306	1.90748
$546$	0	0
$547$	−1.15349	−0.0493198	−0.0246599	−	0.999696i	$-0.507850\pi$
$547$	−1.15349	−0.0493198	−0.0246599	+	0.999696i	$0.507850\pi$
$548$	−15.6264	−0.667527
$549$	5.54537	0.236671
$550$	70.8106	3.01937
$551$	5.13999	0.218971
$552$	1.45931	0.0621122
$553$	0	0
$554$	−3.87817	−0.164768
$555$	−26.8910	−1.14146
$556$	−6.58429	−0.279236
$557$	−36.2638	−1.53655	−0.768273	−	0.640122i	$-0.778884\pi$
$557$	−36.2638	−1.53655	−0.768273	+	0.640122i	$0.778884\pi$
$558$	−28.1415	−1.19132
$559$	9.72345	0.411258
$560$	0	0
$561$	−26.0347	−1.09919
$562$	54.7477	2.30939
$563$	−40.7238	−1.71630	−0.858151	−	0.513398i	$-0.828387\pi$
$563$	−40.7238	−1.71630	−0.858151	+	0.513398i	$0.828387\pi$
$564$	−6.08106	−0.256059
$565$	−16.3064	−0.686013
$566$	10.6477	0.447556
$567$	0	0
$568$	16.3195	0.684749
$569$	2.99949	0.125745	0.0628726	−	0.998022i	$-0.479974\pi$
$569$	2.99949	0.125745	0.0628726	+	0.998022i	$0.479974\pi$
$570$	6.66755	0.279273
$571$	13.4885	0.564475	0.282237	−	0.959345i	$-0.408923\pi$
$571$	13.4885	0.564475	0.282237	+	0.959345i	$0.408923\pi$
$572$	−4.99969	−0.209047
$573$	−12.9588	−0.541362
$574$	0	0
$575$	−11.1829	−0.466359
$576$	−1.03320	−0.0430499
$577$	9.68176	0.403057	0.201529	−	0.979483i	$-0.435409\pi$
$577$	9.68176	0.403057	0.201529	+	0.979483i	$0.435409\pi$
$578$	85.6280	3.56165
$579$	16.3145	0.678009
$580$	22.2457	0.923703
$581$	0	0
$582$	15.0688	0.624622
$583$	1.92400	0.0796838
$584$	2.31733	0.0958918
$585$	−12.0026	−0.496246
$586$	−9.11800	−0.376661
$587$	−38.4292	−1.58614	−0.793071	−	0.609129i	$-0.791519\pi$
$587$	−38.4292	−1.58614	−0.793071	+	0.609129i	$0.791519\pi$
$588$	0	0
$589$	−7.54706	−0.310971
$590$	0.981567	0.0404105
$591$	−15.1871	−0.624712
$592$	−35.2349	−1.44814
$593$	−24.9901	−1.02622	−0.513110	−	0.858323i	$-0.671507\pi$
$593$	−24.9901	−1.02622	−0.513110	+	0.858323i	$0.671507\pi$
$594$	−28.7642	−1.18021
$595$	0	0
$596$	−2.63124	−0.107780
$597$	−23.9999	−0.982250
$598$	2.28368	0.0933866
$599$	−27.1748	−1.11033	−0.555166	−	0.831740i	$-0.687345\pi$
$599$	−27.1748	−1.11033	−0.555166	+	0.831740i	$0.687345\pi$
$600$	−18.0697	−0.737693
$601$	40.1575	1.63806	0.819028	−	0.573753i	$-0.194513\pi$
$601$	40.1575	1.63806	0.819028	+	0.573753i	$0.194513\pi$
$602$	0	0
$603$	−18.0841	−0.736442
$604$	13.8591	0.563919
$605$	−3.46169	−0.140738
$606$	−7.61069	−0.309163
$607$	25.7388	1.04471	0.522353	−	0.852730i	$-0.325054\pi$
$607$	25.7388	1.04471	0.522353	+	0.852730i	$0.325054\pi$
$608$	5.43868	0.220568
$609$	0	0
$610$	18.6158	0.753732
$611$	8.49092	0.343506
$612$	18.3090	0.740099
$613$	39.3334	1.58866	0.794330	−	0.607487i	$-0.207822\pi$
$613$	39.3334	1.58866	0.794330	+	0.607487i	$0.207822\pi$
$614$	34.8407	1.40605
$615$	−11.1424	−0.449306
$616$	0	0
$617$	43.8168	1.76400	0.881999	−	0.471252i	$-0.156198\pi$
$617$	43.8168	1.76400	0.881999	+	0.471252i	$0.156198\pi$
$618$	−13.1666	−0.529639
$619$	−12.9716	−0.521373	−0.260687	−	0.965423i	$-0.583949\pi$
$619$	−12.9716	−0.521373	−0.260687	+	0.965423i	$0.583949\pi$
$620$	−32.6634	−1.31179
$621$	4.54264	0.182290
$622$	−17.8489	−0.715675
$623$	0	0
$624$	6.39580	0.256037
$625$	54.6344	2.18538
$626$	−14.7995	−0.591505
$627$	−3.20527	−0.128006
$628$	17.4615	0.696789
$629$	−57.2760	−2.28375
$630$	0	0
$631$	−12.3388	−0.491198	−0.245599	−	0.969371i	$-0.578985\pi$
$631$	−12.3388	−0.491198	−0.245599	+	0.969371i	$0.578985\pi$
$632$	24.0758	0.957685
$633$	−14.9101	−0.592625
$634$	21.8652	0.868379
$635$	−23.2565	−0.922908
$636$	0.550264	0.0218194
$637$	0	0
$638$	−30.9300	−1.22453
$639$	21.1081	0.835024
$640$	−48.0091	−1.89773
$641$	−9.46213	−0.373732	−0.186866	−	0.982385i	$-0.559833\pi$
$641$	−9.46213	−0.373732	−0.186866	+	0.982385i	$0.559833\pi$
$642$	−11.9437	−0.471382
$643$	13.0899	0.516213	0.258107	−	0.966116i	$-0.416901\pi$
$643$	13.0899	0.516213	0.258107	+	0.966116i	$0.416901\pi$
$644$	0	0
$645$	26.9790	1.06230
$646$	14.2014	0.558748
$647$	7.06482	0.277747	0.138873	−	0.990310i	$-0.455652\pi$
$647$	7.06482	0.277747	0.138873	+	0.990310i	$0.455652\pi$
$648$	−3.20926	−0.126072
$649$	−0.471866	−0.0185224
$650$	−28.2775	−1.10913
$651$	0	0
$652$	−7.42165	−0.290654
$653$	−13.2843	−0.519857	−0.259928	−	0.965628i	$-0.583699\pi$
$653$	−13.2843	−0.519857	−0.259928	+	0.965628i	$0.583699\pi$
$654$	−17.7076	−0.692421
$655$	−9.46180	−0.369703
$656$	−14.5998	−0.570025
$657$	2.99731	0.116936
$658$	0	0
$659$	−11.6633	−0.454339	−0.227169	−	0.973855i	$-0.572947\pi$
$659$	−11.6633	−0.454339	−0.227169	+	0.973855i	$0.572947\pi$
$660$	−13.8723	−0.539978
$661$	15.1754	0.590253	0.295127	−	0.955458i	$-0.404638\pi$
$661$	15.1754	0.590253	0.295127	+	0.955458i	$0.404638\pi$
$662$	−28.9674	−1.12585
$663$	10.3967	0.403774
$664$	−23.4284	−0.909197
$665$	0	0
$666$	−26.2938	−1.01886
$667$	4.88469	0.189136
$668$	3.93831	0.152378
$669$	18.5020	0.715328
$670$	−60.7082	−2.34536
$671$	−8.94911	−0.345477
$672$	0	0
$673$	−21.2864	−0.820530	−0.410265	−	0.911966i	$-0.634564\pi$
$673$	−21.2864	−0.820530	−0.410265	+	0.911966i	$0.634564\pi$
$674$	44.6823	1.72110
$675$	−56.2489	−2.16502
$676$	−11.7437	−0.451680
$677$	−10.8831	−0.418271	−0.209135	−	0.977887i	$-0.567065\pi$
$677$	−10.8831	−0.418271	−0.209135	+	0.977887i	$0.567065\pi$
$678$	6.48422	0.249025
$679$	0	0
$680$	−54.8407	−2.10305
$681$	12.1365	0.465070
$682$	45.4146	1.73902
$683$	4.61105	0.176437	0.0882184	−	0.996101i	$-0.471883\pi$
$683$	4.61105	0.176437	0.0882184	+	0.996101i	$0.471883\pi$
$684$	2.25412	0.0861884
$685$	60.5397	2.31310
$686$	0	0
$687$	−18.5186	−0.706529
$688$	35.3502	1.34771
$689$	−0.768328	−0.0292710
$690$	6.33637	0.241222
$691$	9.53380	0.362683	0.181341	−	0.983420i	$-0.441956\pi$
$691$	9.53380	0.362683	0.181341	+	0.983420i	$0.441956\pi$
$692$	−0.658220	−0.0250218
$693$	0	0
$694$	−31.2620	−1.18669
$695$	25.5088	0.967605
$696$	7.89285	0.299178
$697$	−23.7326	−0.898938
$698$	5.15159	0.194991
$699$	3.76775	0.142509
$700$	0	0
$701$	−27.4493	−1.03675	−0.518374	−	0.855154i	$-0.673462\pi$
$701$	−27.4493	−1.03675	−0.518374	+	0.855154i	$0.673462\pi$
$702$	11.4867	0.433537
$703$	−7.05154	−0.265954
$704$	1.66737	0.0628415
$705$	23.5592	0.887290
$706$	−19.8985	−0.748892
$707$	0	0
$708$	−0.134954	−0.00507187
$709$	−45.7994	−1.72003	−0.860016	−	0.510267i	$-0.829546\pi$
$709$	−45.7994	−1.72003	−0.860016	+	0.510267i	$0.829546\pi$
$710$	70.8598	2.65932
$711$	31.1404	1.16786
$712$	−16.4915	−0.618043
$713$	−7.17220	−0.268601
$714$	0	0
$715$	19.3697	0.724388
$716$	−22.2047	−0.829828
$717$	−2.68483	−0.100267
$718$	43.9488	1.64016
$719$	−10.6990	−0.399004	−0.199502	−	0.979897i	$-0.563932\pi$
$719$	−10.6990	−0.399004	−0.199502	+	0.979897i	$0.563932\pi$
$720$	−43.6362	−1.62622
$721$	0	0
$722$	1.74841	0.0650691
$723$	−13.8069	−0.513484
$724$	−3.02515	−0.112429
$725$	−60.4842	−2.24633
$726$	1.37654	0.0510882
$727$	−10.4682	−0.388243	−0.194121	−	0.980977i	$-0.562186\pi$
$727$	−10.4682	−0.388243	−0.194121	+	0.980977i	$0.562186\pi$
$728$	0	0
$729$	9.20407	0.340891
$730$	10.0620	0.372409
$731$	57.4636	2.12537
$732$	−2.55945	−0.0945999
$733$	32.8927	1.21492	0.607459	−	0.794351i	$-0.292189\pi$
$733$	32.8927	1.21492	0.607459	+	0.794351i	$0.292189\pi$
$734$	−44.1679	−1.63027
$735$	0	0
$736$	5.16855	0.190515
$737$	29.1841	1.07501
$738$	−10.8950	−0.401050
$739$	47.5332	1.74854	0.874269	−	0.485443i	$-0.161342\pi$
$739$	47.5332	1.74854	0.874269	+	0.485443i	$0.161342\pi$
$740$	−30.5189	−1.12190
$741$	1.27999	0.0470216
$742$	0	0
$743$	43.4955	1.59569	0.797847	−	0.602860i	$-0.205972\pi$
$743$	43.4955	1.59569	0.797847	+	0.602860i	$0.205972\pi$
$744$	−11.5891	−0.424876
$745$	10.1939	0.373476
$746$	14.6343	0.535798
$747$	−30.3030	−1.10873
$748$	−29.5471	−1.08035
$749$	0	0
$750$	−45.1218	−1.64762
$751$	30.1100	1.09873	0.549364	−	0.835583i	$-0.314870\pi$
$751$	30.1100	1.09873	0.549364	+	0.835583i	$0.314870\pi$
$752$	30.8693	1.12569
$753$	−3.45542	−0.125923
$754$	12.3516	0.449818
$755$	−53.6928	−1.95408
$756$	0	0
$757$	−1.55964	−0.0566862	−0.0283431	−	0.999598i	$-0.509023\pi$
$757$	−1.55964	−0.0566862	−0.0283431	+	0.999598i	$0.509023\pi$
$758$	47.2624	1.71665
$759$	−3.04606	−0.110565
$760$	−6.75172	−0.244911
$761$	17.1118	0.620301	0.310151	−	0.950687i	$-0.399621\pi$
$761$	17.1118	0.620301	0.310151	+	0.950687i	$0.399621\pi$
$762$	9.24796	0.335018
$763$	0	0
$764$	−14.7071	−0.532084
$765$	−70.9328	−2.56458
$766$	−7.70291	−0.278318
$767$	0.188435	0.00680398
$768$	18.1884	0.656319
$769$	12.1832	0.439339	0.219669	−	0.975574i	$-0.429502\pi$
$769$	12.1832	0.439339	0.219669	+	0.975574i	$0.429502\pi$
$770$	0	0
$771$	−20.3064	−0.731318
$772$	18.5155	0.666389
$773$	−2.53553	−0.0911968	−0.0455984	−	0.998960i	$-0.514519\pi$
$773$	−2.53553	−0.0911968	−0.0455984	+	0.998960i	$0.514519\pi$
$774$	26.3799	0.948206
$775$	88.8091	3.19012
$776$	−15.2590	−0.547767
$777$	0	0
$778$	0.0187269	0.000671394 0
$779$	−2.92184	−0.104686
$780$	5.53975	0.198355
$781$	−34.0642	−1.21891
$782$	13.4961	0.482618
$783$	24.5695	0.878042
$784$	0	0
$785$	−67.6492	−2.41450
$786$	3.76248	0.134203
$787$	−22.8256	−0.813644	−0.406822	−	0.913507i	$-0.633363\pi$
$787$	−22.8256	−0.813644	−0.406822	+	0.913507i	$0.633363\pi$
$788$	−17.2360	−0.614005
$789$	−7.61224	−0.271003
$790$	104.538	3.71931
$791$	0	0
$792$	12.1027	0.430051
$793$	3.57373	0.126907
$794$	−31.8374	−1.12987
$795$	−2.13183	−0.0756082
$796$	−27.2377	−0.965415
$797$	0.00256630	9.09031e−5 0	4.54516e−5	−	1.00000i	$-0.499986\pi$
$797$	0.00256630	9.09031e−5 0	4.54516e−5		1.00000i	$0.499986\pi$
$798$	0	0
$799$	50.1795	1.77522
$800$	−63.9991	−2.26271
$801$	−21.3306	−0.753679
$802$	−60.0691	−2.12111
$803$	−4.83705	−0.170696
$804$	8.34665	0.294364
$805$	0	0
$806$	−18.1358	−0.638808
$807$	−9.54539	−0.336014
$808$	7.70677	0.271123
$809$	37.3543	1.31331	0.656654	−	0.754192i	$-0.271971\pi$
$809$	37.3543	1.31331	0.656654	+	0.754192i	$0.271971\pi$
$810$	−13.9348	−0.489618
$811$	8.73329	0.306667	0.153334	−	0.988174i	$-0.450999\pi$
$811$	8.73329	0.306667	0.153334	+	0.988174i	$0.450999\pi$
$812$	0	0
$813$	−15.4450	−0.541680
$814$	42.4329	1.48727
$815$	28.7529	1.00717
$816$	37.7978	1.32319
$817$	7.07463	0.247510
$818$	31.7203	1.10908
$819$	0	0
$820$	−12.6457	−0.441605
$821$	0.587201	0.0204935	0.0102467	−	0.999948i	$-0.496738\pi$
$821$	0.587201	0.0204935	0.0102467	+	0.999948i	$0.496738\pi$
$822$	−24.0736	−0.839664
$823$	−37.9346	−1.32232	−0.661158	−	0.750247i	$-0.729935\pi$
$823$	−37.9346	−1.32232	−0.661158	+	0.750247i	$0.729935\pi$
$824$	13.3328	0.464471
$825$	37.7176	1.31316
$826$	0	0
$827$	42.2454	1.46902	0.734509	−	0.678599i	$-0.237413\pi$
$827$	42.2454	1.46902	0.734509	+	0.678599i	$0.237413\pi$
$828$	2.14216	0.0744452
$829$	13.0611	0.453629	0.226815	−	0.973938i	$-0.427169\pi$
$829$	13.0611	0.453629	0.226815	+	0.973938i	$0.427169\pi$
$830$	−101.727	−3.53100
$831$	−2.06573	−0.0716593
$832$	−0.665848	−0.0230841
$833$	0	0
$834$	−10.1436	−0.351243
$835$	−15.2578	−0.528017
$836$	−3.63769	−0.125812
$837$	−36.0754	−1.24695
$838$	−42.6362	−1.47284
$839$	18.6953	0.645434	0.322717	−	0.946496i	$-0.395404\pi$
$839$	18.6953	0.645434	0.322717	+	0.946496i	$0.395404\pi$
$840$	0	0
$841$	−2.58050	−0.0889827
$842$	9.77289	0.336796
$843$	29.1616	1.00438
$844$	−16.9217	−0.582468
$845$	45.4973	1.56515
$846$	23.0360	0.791994
$847$	0	0
$848$	−2.79330	−0.0959224
$849$	5.67155	0.194647
$850$	−167.114	−5.73196
$851$	−6.70130	−0.229717
$852$	−9.74238	−0.333768
$853$	−25.6242	−0.877357	−0.438678	−	0.898644i	$-0.644553\pi$
$853$	−25.6242	−0.877357	−0.438678	+	0.898644i	$0.644553\pi$
$854$	0	0
$855$	−8.73290	−0.298659
$856$	12.0945	0.413382
$857$	17.2083	0.587825	0.293913	−	0.955832i	$-0.405043\pi$
$857$	17.2083	0.587825	0.293913	+	0.955832i	$0.405043\pi$
$858$	−7.70238	−0.262955
$859$	−0.234782	−0.00801065	−0.00400533	−	0.999992i	$-0.501275\pi$
$859$	−0.234782	−0.00801065	−0.00400533	+	0.999992i	$0.501275\pi$
$860$	30.6188	1.04409
$861$	0	0
$862$	58.8038	2.00287
$863$	−16.3767	−0.557469	−0.278735	−	0.960368i	$-0.589915\pi$
$863$	−16.3767	−0.557469	−0.278735	+	0.960368i	$0.589915\pi$
$864$	25.9973	0.884445
$865$	2.55007	0.0867050
$866$	24.7318	0.840420
$867$	45.6102	1.54900
$868$	0	0
$869$	−50.2544	−1.70476
$870$	34.2711	1.16190
$871$	−11.6543	−0.394893
$872$	17.9311	0.607224
$873$	−19.7365	−0.667980
$874$	1.66157	0.0562034
$875$	0	0
$876$	−1.38340	−0.0467407
$877$	45.5680	1.53872	0.769361	−	0.638814i	$-0.220575\pi$
$877$	45.5680	1.53872	0.769361	+	0.638814i	$0.220575\pi$
$878$	−0.278795	−0.00940889
$879$	−4.85675	−0.163814
$880$	70.4199	2.37386
$881$	37.1682	1.25223	0.626114	−	0.779731i	$-0.284644\pi$
$881$	37.1682	1.25223	0.626114	+	0.779731i	$0.284644\pi$
$882$	0	0
$883$	9.76685	0.328681	0.164340	−	0.986404i	$-0.447450\pi$
$883$	9.76685	0.328681	0.164340	+	0.986404i	$0.447450\pi$
$884$	11.7993	0.396854
$885$	0.522837	0.0175750
$886$	61.8457	2.07775
$887$	30.2645	1.01618	0.508091	−	0.861303i	$-0.330351\pi$
$887$	30.2645	1.01618	0.508091	+	0.861303i	$0.330351\pi$
$888$	−10.8282	−0.363370
$889$	0	0
$890$	−71.6067	−2.40026
$891$	6.69882	0.224419
$892$	20.9981	0.703068
$893$	6.17786	0.206734
$894$	−4.05361	−0.135573
$895$	86.0252	2.87551
$896$	0	0
$897$	1.21641	0.0406149
$898$	38.6440	1.28957
$899$	−38.7918	−1.29378
$900$	−26.5251	−0.884170
$901$	−4.54066	−0.151271
$902$	17.5823	0.585426
$903$	0	0
$904$	−6.56608	−0.218385
$905$	11.7200	0.389586
$906$	21.3509	0.709338
$907$	−14.4688	−0.480429	−0.240214	−	0.970720i	$-0.577218\pi$
$907$	−14.4688	−0.480429	−0.240214	+	0.970720i	$0.577218\pi$
$908$	13.7738	0.457099
$909$	9.96819	0.330624
$910$	0	0
$911$	7.05854	0.233860	0.116930	−	0.993140i	$-0.462695\pi$
$911$	7.05854	0.233860	0.116930	+	0.993140i	$0.462695\pi$
$912$	4.65348	0.154092
$913$	48.9029	1.61845
$914$	15.1287	0.500412
$915$	9.91580	0.327806
$916$	−21.0170	−0.694420
$917$	0	0
$918$	67.8838	2.24050
$919$	−11.2365	−0.370657	−0.185328	−	0.982677i	$-0.559335\pi$
$919$	−11.2365	−0.370657	−0.185328	+	0.982677i	$0.559335\pi$
$920$	−6.41637	−0.211541
$921$	18.5581	0.611509
$922$	12.8717	0.423906
$923$	13.6032	0.447754
$924$	0	0
$925$	82.9782	2.72831
$926$	−72.4649	−2.38134
$927$	17.2451	0.566404
$928$	27.9548	0.917661
$929$	−7.13882	−0.234217	−0.117109	−	0.993119i	$-0.537363\pi$
$929$	−7.13882	−0.234217	−0.117109	+	0.993119i	$0.537363\pi$
$930$	−50.3203	−1.65007
$931$	0	0
$932$	4.27606	0.140067
$933$	−9.50730	−0.311255
$934$	27.0753	0.885932
$935$	114.471	3.74361
$936$	−4.83308	−0.157974
$937$	−11.3172	−0.369717	−0.184859	−	0.982765i	$-0.559183\pi$
$937$	−11.3172	−0.369717	−0.184859	+	0.982765i	$0.559183\pi$
$938$	0	0
$939$	−7.88301	−0.257252
$940$	26.7376	0.872083
$941$	−48.8659	−1.59298	−0.796492	−	0.604649i	$-0.793313\pi$
$941$	−48.8659	−1.59298	−0.796492	+	0.604649i	$0.793313\pi$
$942$	26.9007	0.876472
$943$	−2.77672	−0.0904224
$944$	0.685066	0.0222970
$945$	0	0
$946$	−42.5718	−1.38413
$947$	−8.66650	−0.281623	−0.140812	−	0.990036i	$-0.544971\pi$
$947$	−8.66650	−0.281623	−0.140812	+	0.990036i	$0.544971\pi$
$948$	−14.3728	−0.466806
$949$	1.93162	0.0627032
$950$	−20.5742	−0.667516
$951$	11.6466	0.377668
$952$	0	0
$953$	−28.3474	−0.918263	−0.459131	−	0.888368i	$-0.651839\pi$
$953$	−28.3474	−0.918263	−0.459131	+	0.888368i	$0.651839\pi$
$954$	−2.08449	−0.0674877
$955$	56.9781	1.84377
$956$	−3.04704	−0.0985484
$957$	−16.4750	−0.532563
$958$	−17.5475	−0.566935
$959$	0	0
$960$	−1.84748	−0.0596273
$961$	25.9580	0.837356
$962$	−16.9451	−0.546333
$963$	15.6435	0.504103
$964$	−15.6696	−0.504683
$965$	−71.7328	−2.30916
$966$	0	0
$967$	−23.9566	−0.770392	−0.385196	−	0.922835i	$-0.625866\pi$
$967$	−23.9566	−0.770392	−0.385196	+	0.922835i	$0.625866\pi$
$968$	−1.39392	−0.0448022
$969$	7.56447	0.243006
$970$	−66.2554	−2.12733
$971$	−30.9295	−0.992575	−0.496288	−	0.868158i	$-0.665304\pi$
$971$	−30.9295	−0.992575	−0.496288	+	0.868158i	$0.665304\pi$
$972$	17.0726	0.547605
$973$	0	0
$974$	14.5497	0.466204
$975$	−15.0621	−0.482374
$976$	12.9925	0.415881
$977$	0.236820	0.00757654	0.00378827	−	0.999993i	$-0.498794\pi$
$977$	0.236820	0.00757654	0.00378827	+	0.999993i	$0.498794\pi$
$978$	−11.4336	−0.365606
$979$	34.4232	1.10017
$980$	0	0
$981$	23.1927	0.740486
$982$	−3.46690	−0.110633
$983$	1.97961	0.0631397	0.0315699	−	0.999502i	$-0.489949\pi$
$983$	1.97961	0.0631397	0.0315699	+	0.999502i	$0.489949\pi$
$984$	−4.48672	−0.143031
$985$	66.7754	2.12764
$986$	72.9953	2.32464
$987$	0	0
$988$	1.45267	0.0462157
$989$	6.72324	0.213786
$990$	52.5505	1.67016
$991$	50.7952	1.61356	0.806781	−	0.590850i	$-0.201208\pi$
$991$	50.7952	1.61356	0.806781	+	0.590850i	$0.201208\pi$
$992$	−41.0460	−1.30321
$993$	−15.4296	−0.489645
$994$	0	0
$995$	105.524	3.34534
$996$	13.9863	0.443171
$997$	34.0500	1.07837	0.539187	−	0.842186i	$-0.318732\pi$
$997$	34.0500	1.07837	0.539187	+	0.842186i	$0.318732\pi$
$998$	−39.4313	−1.24818
$999$	−33.7068	−1.06644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.p.1.8	✓	10
3.2	odd	2		8379.2.a.ct.1.3		10
7.2	even	3		931.2.f.r.704.3		20
7.3	odd	6		931.2.f.q.324.3		20
7.4	even	3		931.2.f.r.324.3		20
7.5	odd	6		931.2.f.q.704.3		20
7.6	odd	2		931.2.a.q.1.8	yes	10
21.20	even	2		8379.2.a.cs.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.a.p.1.8	✓	10	1.1	even	1	trivial
931.2.a.q.1.8	yes	10	7.6	odd	2
931.2.f.q.324.3		20	7.3	odd	6
931.2.f.q.704.3		20	7.5	odd	6
931.2.f.r.324.3		20	7.4	even	3
931.2.f.r.704.3		20	7.2	even	3
8379.2.a.cs.1.3		10	21.20	even	2
8379.2.a.ct.1.3		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)

\(f(q)\)	\(=\)	\(q+1.74841 q^{2} +0.931300 q^{3} +1.05694 q^{4} -4.09480 q^{5} +1.62830 q^{6} -1.64885 q^{8} -2.13268 q^{9} +O(q^{10})\)	\(q+1.74841 q^{2} +0.931300 q^{3} +1.05694 q^{4} -4.09480 q^{5} +1.62830 q^{6} -1.64885 q^{8} -2.13268 q^{9} -7.15939 q^{10} +3.44171 q^{11} +0.984331 q^{12} -1.37441 q^{13} -3.81349 q^{15} -4.99676 q^{16} -8.12248 q^{17} -3.72880 q^{18} -1.00000 q^{19} -4.32797 q^{20} +6.01753 q^{22} -0.950330 q^{23} -1.53558 q^{24} +11.7674 q^{25} -2.40304 q^{26} -4.78007 q^{27} -5.13999 q^{29} -6.66755 q^{30} +7.54706 q^{31} -5.43868 q^{32} +3.20527 q^{33} -14.2014 q^{34} -2.25412 q^{36} +7.05154 q^{37} -1.74841 q^{38} -1.27999 q^{39} +6.75172 q^{40} +2.92184 q^{41} -7.07463 q^{43} +3.63769 q^{44} +8.73290 q^{45} -1.66157 q^{46} -6.17786 q^{47} -4.65348 q^{48} +20.5742 q^{50} -7.56447 q^{51} -1.45267 q^{52} +0.559023 q^{53} -8.35752 q^{54} -14.0931 q^{55} -0.931300 q^{57} -8.98682 q^{58} -0.137102 q^{59} -4.03064 q^{60} -2.60019 q^{61} +13.1954 q^{62} +0.484460 q^{64} +5.62794 q^{65} +5.60413 q^{66} +8.47952 q^{67} -8.58500 q^{68} -0.885043 q^{69} -9.89746 q^{71} +3.51647 q^{72} -1.40542 q^{73} +12.3290 q^{74} +10.9590 q^{75} -1.05694 q^{76} -2.23795 q^{78} -14.6016 q^{79} +20.4607 q^{80} +1.94636 q^{81} +5.10859 q^{82} +14.2089 q^{83} +33.2599 q^{85} -12.3694 q^{86} -4.78687 q^{87} -5.67488 q^{88} +10.0018 q^{89} +15.2687 q^{90} -1.00444 q^{92} +7.02858 q^{93} -10.8014 q^{94} +4.09480 q^{95} -5.06505 q^{96} +9.25433 q^{97} -7.34007 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 4 q^{3} + 10 q^{4} - 16 q^{5} - 8 q^{6} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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