LMFDB - Embedded newform 931.2.a.q.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:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 $ x^10 - 2x^9 - 13x^8 + 24x^7 + 57x^6 - 98x^5 - 93x^4 + 152x^3 + 39x^2 - 58*x - 7
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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	$-0.586641\pi$
$3$	−0.931300	−0.537687	−0.268843	+	0.963184i	$0.586641\pi$
$4$	1.05694	0.528471
$5$	4.09480	1.83125	0.915625	−	0.402033i	$-0.131696\pi$
$5$	4.09480	1.83125	0.915625	+	0.402033i	$0.131696\pi$
$6$	−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	$-0.438958\pi$
$13$	1.37441	0.381193	0.190597	+	0.981668i	$0.438958\pi$
$14$	0	0
$15$	−3.81349	−0.984638
$16$	−4.99676	−1.24919
$17$	8.12248	1.96999	0.984996	−	0.172578i	$-0.0552098\pi$
$17$	8.12248	1.96999	0.984996	+	0.172578i	$0.0552098\pi$
$18$	−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	$-0.737043\pi$
$31$	−7.54706	−1.35549	−0.677746	+	0.735297i	$0.737043\pi$
$32$	−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	$-0.573270\pi$
$41$	−2.92184	−0.456316	−0.228158	+	0.973624i	$0.573270\pi$
$42$	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	$-0.351222\pi$
$47$	6.17786	0.901133	0.450567	+	0.892743i	$0.351222\pi$
$48$	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	$-0.497159\pi$
$59$	0.137102	0.0178492	0.00892458	+	0.999960i	$0.497159\pi$
$60$	−4.03064	−0.520353
$61$	2.60019	0.332920	0.166460	−	0.986048i	$-0.446766\pi$
$61$	2.60019	0.332920	0.166460	+	0.986048i	$0.446766\pi$
$62$	−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	$-0.473791\pi$
$73$	1.40542	0.164492	0.0822459	+	0.996612i	$0.473791\pi$
$74$	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	$-0.784687\pi$
$83$	−14.2089	−1.55963	−0.779814	+	0.626011i	$0.784687\pi$
$84$	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	$-0.677843\pi$
$89$	−10.0018	−1.06019	−0.530093	+	0.847939i	$0.677843\pi$
$90$	−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	$-0.655680\pi$
$97$	−9.25433	−0.939635	−0.469818	+	0.882764i	$0.655680\pi$
$98$	0	0
$99$	−7.34007	−0.737705
$100$	12.4374	1.24374
$101$	4.67402	0.465083	0.232541	−	0.972587i	$-0.425296\pi$
$101$	4.67402	0.465083	0.232541	+	0.972587i	$0.425296\pi$
$102$	−13.2258	−1.30955
$103$	8.08612	0.796750	0.398375	−	0.917223i	$-0.369574\pi$
$103$	8.08612	0.796750	0.398375	+	0.917223i	$0.369574\pi$
$104$	−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	$-0.532186\pi$
$131$	−2.31069	−0.201886	−0.100943	+	0.994892i	$0.532186\pi$
$132$	−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	$-0.414895\pi$
$139$	6.22957	0.528385	0.264192	+	0.964470i	$0.414895\pi$
$140$	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	$-0.729126\pi$
$157$	−16.5208	−1.31850	−0.659250	+	0.751924i	$0.729126\pi$
$158$	−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	$-0.546051\pi$
$167$	−3.72614	−0.288337	−0.144169	+	0.989553i	$0.546051\pi$
$168$	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	$-0.492464\pi$
$173$	0.622758	0.0473475	0.0236737	+	0.999720i	$0.492464\pi$
$174$	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	$-0.466077\pi$
$181$	2.86217	0.212743	0.106372	+	0.994326i	$0.466077\pi$
$182$	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	$-0.133444\pi$
$199$	25.7703	1.82681	0.913404	+	0.407054i	$0.133444\pi$
$200$	−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	$-0.731650\pi$
$223$	−19.8668	−1.33038	−0.665190	+	0.746674i	$0.731650\pi$
$224$	0	0
$225$	−25.0961	−1.67307
$226$	6.96254	0.463141
$227$	−13.0317	−0.864947	−0.432473	−	0.901647i	$-0.642359\pi$
$227$	−13.0317	−0.864947	−0.432473	+	0.901647i	$0.642359\pi$
$228$	−0.984331	−0.0651889
$229$	19.8847	1.31402	0.657008	−	0.753883i	$-0.271822\pi$
$229$	19.8847	1.31402	0.657008	+	0.753883i	$0.271822\pi$
$230$	−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	$-0.341545\pi$
$241$	14.8254	0.954987	0.477494	+	0.878635i	$0.341545\pi$
$242$	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	$-0.462641\pi$
$251$	3.71032	0.234193	0.117097	+	0.993121i	$0.462641\pi$
$252$	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	$-0.261954\pi$
$257$	21.8044	1.36012	0.680060	+	0.733157i	$0.261954\pi$
$258$	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	$-0.398846\pi$
$269$	10.2495	0.624925	0.312463	+	0.949930i	$0.398846\pi$
$270$	34.2224	2.08271
$271$	16.5844	1.00743	0.503714	−	0.863871i	$-0.331967\pi$
$271$	16.5844	1.00743	0.503714	+	0.863871i	$0.331967\pi$
$272$	−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	$-0.557935\pi$
$283$	−6.08992	−0.362008	−0.181004	+	0.983482i	$0.557935\pi$
$284$	−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	$-0.451322\pi$
$293$	5.21502	0.304665	0.152332	+	0.988329i	$0.451322\pi$
$294$	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	$-0.692533\pi$
$307$	−19.9270	−1.13730	−0.568648	+	0.822581i	$0.692533\pi$
$308$	0	0
$309$	−7.53061	−0.428402
$310$	−54.0323	−3.06883
$311$	10.2086	0.578878	0.289439	−	0.957196i	$-0.406531\pi$
$311$	10.2086	0.578878	0.289439	+	0.957196i	$0.406531\pi$
$312$	2.11051	0.119484
$313$	8.46451	0.478443	0.239221	−	0.970965i	$-0.423108\pi$
$313$	8.46451	0.478443	0.239221	+	0.970965i	$0.423108\pi$
$314$	−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	$-0.525128\pi$
$349$	−2.94644	−0.157719	−0.0788597	+	0.996886i	$0.525128\pi$
$350$	0	0
$351$	6.56978	0.350669
$352$	−18.7184	−0.997693
$353$	11.3809	0.605746	0.302873	−	0.953031i	$-0.402054\pi$
$353$	11.3809	0.605746	0.302873	+	0.953031i	$0.402054\pi$
$354$	−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	$-0.270842\pi$
$367$	25.2617	1.31865	0.659325	+	0.751858i	$0.270842\pi$
$368$	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	$-0.464095\pi$
$383$	4.40566	0.225119	0.112559	+	0.993645i	$0.464095\pi$
$384$	−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	$-0.348942\pi$
$397$	18.2093	0.913899	0.456949	+	0.889493i	$0.348942\pi$
$398$	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	$-0.648056\pi$
$409$	−18.1424	−0.897082	−0.448541	+	0.893762i	$0.648056\pi$
$410$	−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	$-0.296891\pi$
$419$	24.3857	1.19132	0.595659	+	0.803237i	$0.296891\pi$
$420$	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	$-0.610390\pi$
$433$	−14.1453	−0.679779	−0.339890	+	0.940465i	$0.610390\pi$
$434$	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	$-0.498789\pi$
$439$	0.159456	0.00761044	0.00380522	+	0.999993i	$0.498789\pi$
$440$	−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	$-0.554842\pi$
$461$	−7.36193	−0.342879	−0.171440	+	0.985195i	$0.554842\pi$
$462$	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	$-0.616642\pi$
$467$	−15.4857	−0.716591	−0.358296	+	0.933608i	$0.616642\pi$
$468$	−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	$-0.426361\pi$
$479$	10.0363	0.458569	0.229284	+	0.973359i	$0.426361\pi$
$480$	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	$-0.836187\pi$
$503$	−39.0453	−1.74095	−0.870473	+	0.492216i	$0.836187\pi$
$504$	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	$-0.140260\pi$
$509$	40.8120	1.80896	0.904479	+	0.426518i	$0.140260\pi$
$510$	−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	$-0.656769\pi$
$521$	−21.5853	−0.945669	−0.472835	+	0.881151i	$0.656769\pi$
$522$	19.1660	0.838873
$523$	−31.9796	−1.39837	−0.699184	−	0.714942i	$-0.746453\pi$
$523$	−31.9796	−1.39837	−0.699184	+	0.714942i	$0.746453\pi$
$524$	−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	$-0.171613\pi$
$563$	40.7238	1.71630	0.858151	+	0.513398i	$0.171613\pi$
$564$	−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	$-0.564591\pi$
$577$	−9.68176	−0.403057	−0.201529	+	0.979483i	$0.564591\pi$
$578$	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	$-0.208481\pi$
$587$	38.4292	1.58614	0.793071	+	0.609129i	$0.208481\pi$
$588$	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	$-0.328493\pi$
$593$	24.9901	1.02622	0.513110	+	0.858323i	$0.328493\pi$
$594$	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	$-0.805487\pi$
$601$	−40.1575	−1.63806	−0.819028	+	0.573753i	$0.805487\pi$
$602$	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	$-0.674946\pi$
$607$	−25.7388	−1.04471	−0.522353	+	0.852730i	$0.674946\pi$
$608$	−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	$-0.416051\pi$
$619$	12.9716	0.521373	0.260687	+	0.965423i	$0.416051\pi$
$620$	−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	$-0.583099\pi$
$643$	−13.0899	−0.516213	−0.258107	+	0.966116i	$0.583099\pi$
$644$	0	0
$645$	26.9790	1.06230
$646$	14.2014	0.558748
$647$	−7.06482	−0.277747	−0.138873	−	0.990310i	$-0.544348\pi$
$647$	−7.06482	−0.277747	−0.138873	+	0.990310i	$0.544348\pi$
$648$	−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	$-0.595362\pi$
$661$	−15.1754	−0.590253	−0.295127	+	0.955458i	$0.595362\pi$
$662$	−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	$-0.432935\pi$
$677$	10.8831	0.418271	0.209135	+	0.977887i	$0.432935\pi$
$678$	−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	$-0.558044\pi$
$691$	−9.53380	−0.362683	−0.181341	+	0.983420i	$0.558044\pi$
$692$	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	$-0.436068\pi$
$719$	10.6990	0.399004	0.199502	+	0.979897i	$0.436068\pi$
$720$	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	$-0.437814\pi$
$727$	10.4682	0.388243	0.194121	+	0.980977i	$0.437814\pi$
$728$	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	$-0.707811\pi$
$733$	−32.8927	−1.21492	−0.607459	+	0.794351i	$0.707811\pi$
$734$	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	$-0.600379\pi$
$761$	−17.1118	−0.620301	−0.310151	+	0.950687i	$0.600379\pi$
$762$	−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	$-0.570498\pi$
$769$	−12.1832	−0.439339	−0.219669	+	0.975574i	$0.570498\pi$
$770$	0	0
$771$	−20.3064	−0.731318
$772$	18.5155	0.666389
$773$	2.53553	0.0911968	0.0455984	−	0.998960i	$-0.485481\pi$
$773$	2.53553	0.0911968	0.0455984	+	0.998960i	$0.485481\pi$
$774$	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	$-0.366637\pi$
$787$	22.8256	0.813644	0.406822	+	0.913507i	$0.366637\pi$
$788$	−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	$-0.500014\pi$
$797$	−0.00256630	−9.09031e−5 0	−4.54516e−5		1.00000i	$0.500014\pi$
$798$	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	$-0.549001\pi$
$811$	−8.73329	−0.306667	−0.153334	+	0.988174i	$0.549001\pi$
$812$	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	$-0.572831\pi$
$829$	−13.0611	−0.453629	−0.226815	+	0.973938i	$0.572831\pi$
$830$	−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	$-0.604596\pi$
$839$	−18.6953	−0.645434	−0.322717	+	0.946496i	$0.604596\pi$
$840$	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	$-0.355447\pi$
$853$	25.6242	0.877357	0.438678	+	0.898644i	$0.355447\pi$
$854$	0	0
$855$	−8.73290	−0.298659
$856$	12.0945	0.413382
$857$	−17.2083	−0.587825	−0.293913	−	0.955832i	$-0.594957\pi$
$857$	−17.2083	−0.587825	−0.293913	+	0.955832i	$0.594957\pi$
$858$	−7.70238	−0.262955
$859$	0.234782	0.00801065	0.00400533	−	0.999992i	$-0.498725\pi$
$859$	0.234782	0.00801065	0.00400533	+	0.999992i	$0.498725\pi$
$860$	−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	$-0.715356\pi$
$881$	−37.1682	−1.25223	−0.626114	+	0.779731i	$0.715356\pi$
$882$	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	$-0.669649\pi$
$887$	−30.2645	−1.01618	−0.508091	+	0.861303i	$0.669649\pi$
$888$	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	$-0.462637\pi$
$929$	7.13882	0.234217	0.117109	+	0.993119i	$0.462637\pi$
$930$	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	$-0.440817\pi$
$937$	11.3172	0.369717	0.184859	+	0.982765i	$0.440817\pi$
$938$	0	0
$939$	−7.88301	−0.257252
$940$	26.7376	0.872083
$941$	48.8659	1.59298	0.796492	−	0.604649i	$-0.206687\pi$
$941$	48.8659	1.59298	0.796492	+	0.604649i	$0.206687\pi$
$942$	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	$-0.334696\pi$
$971$	30.9295	0.992575	0.496288	+	0.868158i	$0.334696\pi$
$972$	−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	$-0.510051\pi$
$983$	−1.97961	−0.0631397	−0.0315699	+	0.999502i	$0.510051\pi$
$984$	−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	$-0.681268\pi$
$997$	−34.0500	−1.07837	−0.539187	+	0.842186i	$0.681268\pi$
$998$	−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.q.1.8	yes	10
3.2	odd	2		8379.2.a.cs.1.3		10
7.2	even	3		931.2.f.q.704.3		20
7.3	odd	6		931.2.f.r.324.3		20
7.4	even	3		931.2.f.q.324.3		20
7.5	odd	6		931.2.f.r.704.3		20
7.6	odd	2		931.2.a.p.1.8	✓	10
21.20	even	2		8379.2.a.ct.1.3		10

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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

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