LMFDB - Embedded newform 7935.2.a.bk.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
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} - 18x^{8} + 111x^{6} - 4x^{5} - 270x^{4} + 32x^{3} + 218x^{2} - 60x - 18 $ x^10 - 18x^8 + 111x^6 - 4x^5 - 270x^4 + 32x^3 + 218x^2 - 60*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-2.55225$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55225 q^{2} -1.00000 q^{3} +4.51396 q^{4} +1.00000 q^{5} +2.55225 q^{6} +4.92817 q^{7} -6.41625 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.55225 q^{2} -1.00000 q^{3} +4.51396 q^{4} +1.00000 q^{5} +2.55225 q^{6} +4.92817 q^{7} -6.41625 q^{8} +1.00000 q^{9} -2.55225 q^{10} -0.347228 q^{11} -4.51396 q^{12} -2.97779 q^{13} -12.5779 q^{14} -1.00000 q^{15} +7.34792 q^{16} +6.49175 q^{17} -2.55225 q^{18} +6.17701 q^{19} +4.51396 q^{20} -4.92817 q^{21} +0.886213 q^{22} +6.41625 q^{24} +1.00000 q^{25} +7.60005 q^{26} -1.00000 q^{27} +22.2456 q^{28} -4.05211 q^{29} +2.55225 q^{30} +7.03074 q^{31} -5.92122 q^{32} +0.347228 q^{33} -16.5685 q^{34} +4.92817 q^{35} +4.51396 q^{36} -2.11853 q^{37} -15.7653 q^{38} +2.97779 q^{39} -6.41625 q^{40} -3.94227 q^{41} +12.5779 q^{42} +3.20454 q^{43} -1.56738 q^{44} +1.00000 q^{45} +5.11730 q^{47} -7.34792 q^{48} +17.2869 q^{49} -2.55225 q^{50} -6.49175 q^{51} -13.4416 q^{52} -10.7841 q^{53} +2.55225 q^{54} -0.347228 q^{55} -31.6204 q^{56} -6.17701 q^{57} +10.3420 q^{58} +10.5166 q^{59} -4.51396 q^{60} -7.32970 q^{61} -17.9442 q^{62} +4.92817 q^{63} +0.416553 q^{64} -2.97779 q^{65} -0.886213 q^{66} +13.0332 q^{67} +29.3035 q^{68} -12.5779 q^{70} -0.401171 q^{71} -6.41625 q^{72} -6.69797 q^{73} +5.40702 q^{74} -1.00000 q^{75} +27.8828 q^{76} -1.71120 q^{77} -7.60005 q^{78} +8.07360 q^{79} +7.34792 q^{80} +1.00000 q^{81} +10.0616 q^{82} -15.1818 q^{83} -22.2456 q^{84} +6.49175 q^{85} -8.17878 q^{86} +4.05211 q^{87} +2.22790 q^{88} +3.25959 q^{89} -2.55225 q^{90} -14.6751 q^{91} -7.03074 q^{93} -13.0606 q^{94} +6.17701 q^{95} +5.92122 q^{96} -15.5410 q^{97} -44.1204 q^{98} -0.347228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9	$ 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9} - 4 q^{11} - 16 q^{12} - 4 q^{13} - 10 q^{15} + 28 q^{16} + 10 q^{17} + 8 q^{19} + 16 q^{20} - 6 q^{21} - 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27} + 76 q^{28} + 2 q^{29} + 2 q^{31} + 20 q^{32} + 4 q^{33} + 8 q^{34} + 6 q^{35} + 16 q^{36} + 2 q^{37} - 56 q^{38} + 4 q^{39} + 6 q^{41} + 44 q^{43} - 24 q^{44} + 10 q^{45} + 8 q^{47} - 28 q^{48} + 12 q^{49} - 10 q^{51} + 2 q^{53} - 4 q^{55} + 8 q^{56} - 8 q^{57} - 20 q^{58} - 14 q^{59} - 16 q^{60} - 8 q^{61} - 28 q^{62} + 6 q^{63} + 40 q^{64} - 4 q^{65} + 4 q^{66} + 2 q^{67} + 84 q^{68} + 6 q^{71} - 12 q^{73} + 40 q^{74} - 10 q^{75} + 44 q^{76} - 16 q^{77} + 8 q^{78} + 28 q^{80} + 10 q^{81} - 4 q^{82} - 62 q^{83} - 76 q^{84} + 10 q^{85} - 4 q^{86} - 2 q^{87} - 12 q^{88} + 56 q^{89} - 2 q^{93} + 20 q^{94} + 8 q^{95} - 20 q^{96} + 56 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) $ 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9 - 4 * q^11 - 16 * q^12 - 4 * q^13 - 10 * q^15 + 28 * q^16 + 10 * q^17 + 8 * q^19 + 16 * q^20 - 6 * q^21 - 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 + 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 + 4 * q^33 + 8 * q^34 + 6 * q^35 + 16 * q^36 + 2 * q^37 - 56 * q^38 + 4 * q^39 + 6 * q^41 + 44 * q^43 - 24 * q^44 + 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 - 10 * q^51 + 2 * q^53 - 4 * q^55 + 8 * q^56 - 8 * q^57 - 20 * q^58 - 14 * q^59 - 16 * q^60 - 8 * q^61 - 28 * q^62 + 6 * q^63 + 40 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 84 * q^68 + 6 * q^71 - 12 * q^73 + 40 * q^74 - 10 * q^75 + 44 * q^76 - 16 * q^77 + 8 * q^78 + 28 * q^80 + 10 * q^81 - 4 * q^82 - 62 * q^83 - 76 * q^84 + 10 * q^85 - 4 * q^86 - 2 * q^87 - 12 * q^88 + 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.55225	−1.80471	−0.902355	−	0.430993i	$-0.858163\pi$
$2$	−2.55225	−1.80471	−0.902355	+	0.430993i	$0.858163\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.51396	2.25698
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.55225	1.04195
$7$	4.92817	1.86268	0.931338	−	0.364157i	$-0.118643\pi$
$7$	4.92817	1.86268	0.931338	+	0.364157i	$0.118643\pi$
$8$	−6.41625	−2.26849
$9$	1.00000	0.333333
$10$	−2.55225	−0.807091
$11$	−0.347228	−0.104693	−0.0523467	−	0.998629i	$-0.516670\pi$
$11$	−0.347228	−0.104693	−0.0523467	+	0.998629i	$0.516670\pi$
$12$	−4.51396	−1.30307
$13$	−2.97779	−0.825890	−0.412945	−	0.910756i	$-0.635500\pi$
$13$	−2.97779	−0.825890	−0.412945	+	0.910756i	$0.635500\pi$
$14$	−12.5779	−3.36159
$15$	−1.00000	−0.258199
$16$	7.34792	1.83698
$17$	6.49175	1.57448	0.787240	−	0.616646i	$-0.211509\pi$
$17$	6.49175	1.57448	0.787240	+	0.616646i	$0.211509\pi$
$18$	−2.55225	−0.601570
$19$	6.17701	1.41710	0.708552	−	0.705659i	$-0.249349\pi$
$19$	6.17701	1.41710	0.708552	+	0.705659i	$0.249349\pi$
$20$	4.51396	1.00935
$21$	−4.92817	−1.07542
$22$	0.886213	0.188941
$23$	0	0
$23$	0	0
$24$	6.41625	1.30971
$25$	1.00000	0.200000
$26$	7.60005	1.49049
$27$	−1.00000	−0.192450
$28$	22.2456	4.20402
$29$	−4.05211	−0.752458	−0.376229	−	0.926527i	$-0.622779\pi$
$29$	−4.05211	−0.752458	−0.376229	+	0.926527i	$0.622779\pi$
$30$	2.55225	0.465974
$31$	7.03074	1.26276	0.631379	−	0.775475i	$-0.282489\pi$
$31$	7.03074	1.26276	0.631379	+	0.775475i	$0.282489\pi$
$32$	−5.92122	−1.04673
$33$	0.347228	0.0604447
$34$	−16.5685	−2.84148
$35$	4.92817	0.833014
$36$	4.51396	0.752327
$37$	−2.11853	−0.348285	−0.174142	−	0.984721i	$-0.555715\pi$
$37$	−2.11853	−0.348285	−0.174142	+	0.984721i	$0.555715\pi$
$38$	−15.7653	−2.55746
$39$	2.97779	0.476828
$40$	−6.41625	−1.01450
$41$	−3.94227	−0.615678	−0.307839	−	0.951438i	$-0.599606\pi$
$41$	−3.94227	−0.615678	−0.307839	+	0.951438i	$0.599606\pi$
$42$	12.5779	1.94081
$43$	3.20454	0.488688	0.244344	−	0.969689i	$-0.421427\pi$
$43$	3.20454	0.488688	0.244344	+	0.969689i	$0.421427\pi$
$44$	−1.56738	−0.236291
$45$	1.00000	0.149071
$46$	0	0
$47$	5.11730	0.746434	0.373217	−	0.927744i	$-0.378255\pi$
$47$	5.11730	0.746434	0.373217	+	0.927744i	$0.378255\pi$
$48$	−7.34792	−1.06058
$49$	17.2869	2.46956
$50$	−2.55225	−0.360942
$51$	−6.49175	−0.909027
$52$	−13.4416	−1.86402
$53$	−10.7841	−1.48130	−0.740652	−	0.671889i	$-0.765483\pi$
$53$	−10.7841	−1.48130	−0.740652	+	0.671889i	$0.765483\pi$
$54$	2.55225	0.347317
$55$	−0.347228	−0.0468203
$56$	−31.6204	−4.22545
$57$	−6.17701	−0.818165
$58$	10.3420	1.35797
$59$	10.5166	1.36914	0.684572	−	0.728945i	$-0.259989\pi$
$59$	10.5166	1.36914	0.684572	+	0.728945i	$0.259989\pi$
$60$	−4.51396	−0.582750
$61$	−7.32970	−0.938472	−0.469236	−	0.883073i	$-0.655471\pi$
$61$	−7.32970	−0.938472	−0.469236	+	0.883073i	$0.655471\pi$
$62$	−17.9442	−2.27891
$63$	4.92817	0.620892
$64$	0.416553	0.0520691
$65$	−2.97779	−0.369349
$66$	−0.886213	−0.109085
$67$	13.0332	1.59226	0.796131	−	0.605124i	$-0.206876\pi$
$67$	13.0332	1.59226	0.796131	+	0.605124i	$0.206876\pi$
$68$	29.3035	3.55357
$69$	0	0
$70$	−12.5779	−1.50335
$71$	−0.401171	−0.0476102	−0.0238051	−	0.999717i	$-0.507578\pi$
$71$	−0.401171	−0.0476102	−0.0238051	+	0.999717i	$0.507578\pi$
$72$	−6.41625	−0.756162
$73$	−6.69797	−0.783938	−0.391969	−	0.919979i	$-0.628206\pi$
$73$	−6.69797	−0.783938	−0.391969	+	0.919979i	$0.628206\pi$
$74$	5.40702	0.628553
$75$	−1.00000	−0.115470
$76$	27.8828	3.19838
$77$	−1.71120	−0.195010
$78$	−7.60005	−0.860537
$79$	8.07360	0.908351	0.454176	−	0.890912i	$-0.349934\pi$
$79$	8.07360	0.908351	0.454176	+	0.890912i	$0.349934\pi$
$80$	7.34792	0.821523
$81$	1.00000	0.111111
$82$	10.0616	1.11112
$83$	−15.1818	−1.66641	−0.833207	−	0.552961i	$-0.813498\pi$
$83$	−15.1818	−1.66641	−0.833207	+	0.552961i	$0.813498\pi$
$84$	−22.2456	−2.42719
$85$	6.49175	0.704129
$86$	−8.17878	−0.881940
$87$	4.05211	0.434432
$88$	2.22790	0.237495
$89$	3.25959	0.345516	0.172758	−	0.984964i	$-0.444732\pi$
$89$	3.25959	0.345516	0.172758	+	0.984964i	$0.444732\pi$
$90$	−2.55225	−0.269030
$91$	−14.6751	−1.53837
$92$	0	0
$93$	−7.03074	−0.729053
$94$	−13.0606	−1.34710
$95$	6.17701	0.633748
$96$	5.92122	0.604332
$97$	−15.5410	−1.57795	−0.788975	−	0.614425i	$-0.789388\pi$
$97$	−15.5410	−1.57795	−0.788975	+	0.614425i	$0.789388\pi$
$98$	−44.1204	−4.45684
$99$	−0.347228	−0.0348978
$100$	4.51396	0.451396
$101$	9.25026	0.920436	0.460218	−	0.887806i	$-0.347771\pi$
$101$	9.25026	0.920436	0.460218	+	0.887806i	$0.347771\pi$
$102$	16.5685	1.64053
$103$	11.6526	1.14817	0.574083	−	0.818797i	$-0.305359\pi$
$103$	11.6526	1.14817	0.574083	+	0.818797i	$0.305359\pi$
$104$	19.1062	1.87352
$105$	−4.92817	−0.480941
$106$	27.5236	2.67333
$107$	−3.10047	−0.299734	−0.149867	−	0.988706i	$-0.547885\pi$
$107$	−3.10047	−0.299734	−0.149867	+	0.988706i	$0.547885\pi$
$108$	−4.51396	−0.434356
$109$	6.34361	0.607608	0.303804	−	0.952735i	$-0.401743\pi$
$109$	6.34361	0.607608	0.303804	+	0.952735i	$0.401743\pi$
$110$	0.886213	0.0844970
$111$	2.11853	0.201082
$112$	36.2119	3.42170
$113$	−20.0574	−1.88684	−0.943419	−	0.331604i	$-0.892410\pi$
$113$	−20.0574	−1.88684	−0.943419	+	0.331604i	$0.892410\pi$
$114$	15.7653	1.47655
$115$	0	0
$116$	−18.2911	−1.69828
$117$	−2.97779	−0.275297
$118$	−26.8410	−2.47091
$119$	31.9925	2.93275
$120$	6.41625	0.585721
$121$	−10.8794	−0.989039
$122$	18.7072	1.69367
$123$	3.94227	0.355462
$124$	31.7365	2.85002
$125$	1.00000	0.0894427
$126$	−12.5779	−1.12053
$127$	17.9214	1.59027	0.795134	−	0.606434i	$-0.207401\pi$
$127$	17.9214	1.59027	0.795134	+	0.606434i	$0.207401\pi$
$128$	10.7793	0.952763
$129$	−3.20454	−0.282144
$130$	7.60005	0.666569
$131$	11.9734	1.04612	0.523062	−	0.852295i	$-0.324790\pi$
$131$	11.9734	1.04612	0.523062	+	0.852295i	$0.324790\pi$
$132$	1.56738	0.136423
$133$	30.4414	2.63960
$134$	−33.2640	−2.87357
$135$	−1.00000	−0.0860663
$136$	−41.6527	−3.57169
$137$	5.10981	0.436561	0.218280	−	0.975886i	$-0.429955\pi$
$137$	5.10981	0.436561	0.218280	+	0.975886i	$0.429955\pi$
$138$	0	0
$139$	10.0757	0.854608	0.427304	−	0.904108i	$-0.359463\pi$
$139$	10.0757	0.854608	0.427304	+	0.904108i	$0.359463\pi$
$140$	22.2456	1.88010
$141$	−5.11730	−0.430954
$142$	1.02389	0.0859226
$143$	1.03397	0.0864652
$144$	7.34792	0.612327
$145$	−4.05211	−0.336509
$146$	17.0949	1.41478
$147$	−17.2869	−1.42580
$148$	−9.56297	−0.786072
$149$	21.2941	1.74448	0.872239	−	0.489079i	$-0.162667\pi$
$149$	21.2941	1.74448	0.872239	+	0.489079i	$0.162667\pi$
$150$	2.55225	0.208390
$151$	16.9639	1.38050	0.690250	−	0.723571i	$-0.257501\pi$
$151$	16.9639	1.38050	0.690250	+	0.723571i	$0.257501\pi$
$152$	−39.6333	−3.21468
$153$	6.49175	0.524827
$154$	4.36741	0.351936
$155$	7.03074	0.564722
$156$	13.4416	1.07619
$157$	13.0403	1.04073	0.520364	−	0.853945i	$-0.325796\pi$
$157$	13.0403	1.04073	0.520364	+	0.853945i	$0.325796\pi$
$158$	−20.6058	−1.63931
$159$	10.7841	0.855231
$160$	−5.92122	−0.468113
$161$	0	0
$162$	−2.55225	−0.200523
$163$	−7.45370	−0.583819	−0.291910	−	0.956446i	$-0.594291\pi$
$163$	−7.45370	−0.583819	−0.291910	+	0.956446i	$0.594291\pi$
$164$	−17.7952	−1.38957
$165$	0.347228	0.0270317
$166$	38.7476	3.00740
$167$	−3.05073	−0.236072	−0.118036	−	0.993009i	$-0.537660\pi$
$167$	−3.05073	−0.236072	−0.118036	+	0.993009i	$0.537660\pi$
$168$	31.6204	2.43957
$169$	−4.13277	−0.317905
$170$	−16.5685	−1.27075
$171$	6.17701	0.472368
$172$	14.4652	1.10296
$173$	−12.8310	−0.975525	−0.487763	−	0.872976i	$-0.662187\pi$
$173$	−12.8310	−0.975525	−0.487763	+	0.872976i	$0.662187\pi$
$174$	−10.3420	−0.784024
$175$	4.92817	0.372535
$176$	−2.55141	−0.192320
$177$	−10.5166	−0.790476
$178$	−8.31929	−0.623557
$179$	−1.98885	−0.148654	−0.0743270	−	0.997234i	$-0.523681\pi$
$179$	−1.98885	−0.148654	−0.0743270	+	0.997234i	$0.523681\pi$
$180$	4.51396	0.336451
$181$	20.1561	1.49819	0.749097	−	0.662461i	$-0.230488\pi$
$181$	20.1561	1.49819	0.749097	+	0.662461i	$0.230488\pi$
$182$	37.4544	2.77630
$183$	7.32970	0.541827
$184$	0	0
$185$	−2.11853	−0.155758
$186$	17.9442	1.31573
$187$	−2.25412	−0.164838
$188$	23.0993	1.68469
$189$	−4.92817	−0.358472
$190$	−15.7653	−1.14373
$191$	−3.66812	−0.265416	−0.132708	−	0.991155i	$-0.542367\pi$
$191$	−3.66812	−0.265416	−0.132708	+	0.991155i	$0.542367\pi$
$192$	−0.416553	−0.0300621
$193$	3.23107	0.232578	0.116289	−	0.993215i	$-0.462900\pi$
$193$	3.23107	0.232578	0.116289	+	0.993215i	$0.462900\pi$
$194$	39.6645	2.84774
$195$	2.97779	0.213244
$196$	78.0324	5.57375
$197$	14.5071	1.03359	0.516793	−	0.856110i	$-0.327126\pi$
$197$	14.5071	1.03359	0.516793	+	0.856110i	$0.327126\pi$
$198$	0.886213	0.0629804
$199$	10.1518	0.719645	0.359823	−	0.933021i	$-0.382837\pi$
$199$	10.1518	0.719645	0.359823	+	0.933021i	$0.382837\pi$
$200$	−6.41625	−0.453697
$201$	−13.0332	−0.919293
$202$	−23.6090	−1.66112
$203$	−19.9695	−1.40158
$204$	−29.3035	−2.05166
$205$	−3.94227	−0.275340
$206$	−29.7403	−2.07211
$207$	0	0
$208$	−21.8806	−1.51714
$209$	−2.14483	−0.148361
$210$	12.5779	0.867959
$211$	−0.267718	−0.0184304	−0.00921522	−	0.999958i	$-0.502933\pi$
$211$	−0.267718	−0.0184304	−0.00921522	+	0.999958i	$0.502933\pi$
$212$	−48.6788	−3.34327
$213$	0.401171	0.0274878
$214$	7.91317	0.540933
$215$	3.20454	0.218548
$216$	6.41625	0.436570
$217$	34.6487	2.35211
$218$	−16.1905	−1.09656
$219$	6.69797	0.452607
$220$	−1.56738	−0.105672
$221$	−19.3311	−1.30035
$222$	−5.40702	−0.362895
$223$	−20.1120	−1.34680	−0.673401	−	0.739277i	$-0.735167\pi$
$223$	−20.1120	−1.34680	−0.673401	+	0.739277i	$0.735167\pi$
$224$	−29.1808	−1.94972
$225$	1.00000	0.0666667
$226$	51.1913	3.40520
$227$	8.51968	0.565471	0.282735	−	0.959198i	$-0.408758\pi$
$227$	8.51968	0.565471	0.282735	+	0.959198i	$0.408758\pi$
$228$	−27.8828	−1.84658
$229$	2.00362	0.132403	0.0662013	−	0.997806i	$-0.478912\pi$
$229$	2.00362	0.132403	0.0662013	+	0.997806i	$0.478912\pi$
$230$	0	0
$231$	1.71120	0.112589
$232$	25.9993	1.70694
$233$	7.38814	0.484013	0.242006	−	0.970275i	$-0.422194\pi$
$233$	7.38814	0.484013	0.242006	+	0.970275i	$0.422194\pi$
$234$	7.60005	0.496831
$235$	5.11730	0.333816
$236$	47.4715	3.09013
$237$	−8.07360	−0.524437
$238$	−81.6527	−5.29276
$239$	−11.5981	−0.750222	−0.375111	−	0.926980i	$-0.622395\pi$
$239$	−11.5981	−0.750222	−0.375111	+	0.926980i	$0.622395\pi$
$240$	−7.34792	−0.474306
$241$	−12.0741	−0.777760	−0.388880	−	0.921288i	$-0.627138\pi$
$241$	−12.0741	−0.777760	−0.388880	+	0.921288i	$0.627138\pi$
$242$	27.7670	1.78493
$243$	−1.00000	−0.0641500
$244$	−33.0860	−2.11811
$245$	17.2869	1.10442
$246$	−10.0616	−0.641506
$247$	−18.3938	−1.17037
$248$	−45.1109	−2.86455
$249$	15.1818	0.962105
$250$	−2.55225	−0.161418
$251$	−21.9404	−1.38486	−0.692432	−	0.721483i	$-0.743461\pi$
$251$	−21.9404	−1.38486	−0.692432	+	0.721483i	$0.743461\pi$
$252$	22.2456	1.40134
$253$	0	0
$254$	−45.7398	−2.86997
$255$	−6.49175	−0.406529
$256$	−28.3445	−1.77153
$257$	−7.28484	−0.454416	−0.227208	−	0.973846i	$-0.572960\pi$
$257$	−7.28484	−0.454416	−0.227208	+	0.973846i	$0.572960\pi$
$258$	8.17878	0.509189
$259$	−10.4405	−0.648741
$260$	−13.4416	−0.833614
$261$	−4.05211	−0.250819
$262$	−30.5592	−1.88795
$263$	−10.9201	−0.673360	−0.336680	−	0.941619i	$-0.609304\pi$
$263$	−10.9201	−0.673360	−0.336680	+	0.941619i	$0.609304\pi$
$264$	−2.22790	−0.137118
$265$	−10.7841	−0.662459
$266$	−77.6940	−4.76372
$267$	−3.25959	−0.199484
$268$	58.8315	3.59371
$269$	−0.447956	−0.0273124	−0.0136562	−	0.999907i	$-0.504347\pi$
$269$	−0.447956	−0.0273124	−0.0136562	+	0.999907i	$0.504347\pi$
$270$	2.55225	0.155325
$271$	5.41224	0.328770	0.164385	−	0.986396i	$-0.447436\pi$
$271$	5.41224	0.328770	0.164385	+	0.986396i	$0.447436\pi$
$272$	47.7009	2.89229
$273$	14.6751	0.888176
$274$	−13.0415	−0.787865
$275$	−0.347228	−0.0209387
$276$	0	0
$277$	−5.11537	−0.307353	−0.153676	−	0.988121i	$-0.549111\pi$
$277$	−5.11537	−0.307353	−0.153676	+	0.988121i	$0.549111\pi$
$278$	−25.7156	−1.54232
$279$	7.03074	0.420919
$280$	−31.6204	−1.88968
$281$	−2.40341	−0.143376	−0.0716878	−	0.997427i	$-0.522839\pi$
$281$	−2.40341	−0.143376	−0.0716878	+	0.997427i	$0.522839\pi$
$282$	13.0606	0.777747
$283$	−18.1873	−1.08112	−0.540562	−	0.841304i	$-0.681788\pi$
$283$	−18.1873	−1.08112	−0.540562	+	0.841304i	$0.681788\pi$
$284$	−1.81087	−0.107455
$285$	−6.17701	−0.365895
$286$	−2.63895	−0.156045
$287$	−19.4282	−1.14681
$288$	−5.92122	−0.348911
$289$	25.1428	1.47899
$290$	10.3420	0.607302
$291$	15.5410	0.911030
$292$	−30.2344	−1.76933
$293$	−20.4141	−1.19261	−0.596303	−	0.802759i	$-0.703364\pi$
$293$	−20.4141	−1.19261	−0.596303	+	0.802759i	$0.703364\pi$
$294$	44.1204	2.57316
$295$	10.5166	0.612300
$296$	13.5930	0.790079
$297$	0.347228	0.0201482
$298$	−54.3477	−3.14828
$299$	0	0
$300$	−4.51396	−0.260614
$301$	15.7925	0.910267
$302$	−43.2960	−2.49140
$303$	−9.25026	−0.531414
$304$	45.3882	2.60319
$305$	−7.32970	−0.419697
$306$	−16.5685	−0.947161
$307$	−28.6801	−1.63686	−0.818431	−	0.574605i	$-0.805156\pi$
$307$	−28.6801	−1.63686	−0.818431	+	0.574605i	$0.805156\pi$
$308$	−7.72430	−0.440133
$309$	−11.6526	−0.662894
$310$	−17.9442	−1.01916
$311$	17.0063	0.964338	0.482169	−	0.876078i	$-0.339849\pi$
$311$	17.0063	0.964338	0.482169	+	0.876078i	$0.339849\pi$
$312$	−19.1062	−1.08168
$313$	3.13697	0.177312	0.0886559	−	0.996062i	$-0.471743\pi$
$313$	3.13697	0.177312	0.0886559	+	0.996062i	$0.471743\pi$
$314$	−33.2820	−1.87821
$315$	4.92817	0.277671
$316$	36.4439	2.05013
$317$	0.372913	0.0209449	0.0104724	−	0.999945i	$-0.496666\pi$
$317$	0.372913	0.0209449	0.0104724	+	0.999945i	$0.496666\pi$
$318$	−27.5236	−1.54345
$319$	1.40701	0.0787773
$320$	0.416553	0.0232860
$321$	3.10047	0.173052
$322$	0	0
$323$	40.0996	2.23120
$324$	4.51396	0.250776
$325$	−2.97779	−0.165178
$326$	19.0237	1.05362
$327$	−6.34361	−0.350803
$328$	25.2946	1.39666
$329$	25.2189	1.39036
$330$	−0.886213	−0.0487844
$331$	0.751471	0.0413046	0.0206523	−	0.999787i	$-0.493426\pi$
$331$	0.751471	0.0413046	0.0206523	+	0.999787i	$0.493426\pi$
$332$	−68.5299	−3.76107
$333$	−2.11853	−0.116095
$334$	7.78621	0.426042
$335$	13.0332	0.712081
$336$	−36.2119	−1.97552
$337$	−19.7996	−1.07856	−0.539278	−	0.842128i	$-0.681303\pi$
$337$	−19.7996	−1.07856	−0.539278	+	0.842128i	$0.681303\pi$
$338$	10.5478	0.573727
$339$	20.0574	1.08937
$340$	29.3035	1.58921
$341$	−2.44127	−0.132202
$342$	−15.7653	−0.852488
$343$	50.6957	2.73731
$344$	−20.5611	−1.10858
$345$	0	0
$346$	32.7480	1.76054
$347$	−0.303278	−0.0162808	−0.00814041	−	0.999967i	$-0.502591\pi$
$347$	−0.303278	−0.0162808	−0.00814041	+	0.999967i	$0.502591\pi$
$348$	18.2911	0.980504
$349$	−5.95511	−0.318770	−0.159385	−	0.987217i	$-0.550951\pi$
$349$	−5.95511	−0.318770	−0.159385	+	0.987217i	$0.550951\pi$
$350$	−12.5779	−0.672318
$351$	2.97779	0.158943
$352$	2.05601	0.109586
$353$	29.4696	1.56851	0.784255	−	0.620438i	$-0.213045\pi$
$353$	29.4696	1.56851	0.784255	+	0.620438i	$0.213045\pi$
$354$	26.8410	1.42658
$355$	−0.401171	−0.0212919
$356$	14.7137	0.779824
$357$	−31.9925	−1.69322
$358$	5.07605	0.268277
$359$	−11.0399	−0.582664	−0.291332	−	0.956622i	$-0.594098\pi$
$359$	−11.0399	−0.582664	−0.291332	+	0.956622i	$0.594098\pi$
$360$	−6.41625	−0.338166
$361$	19.1555	1.00818
$362$	−51.4434	−2.70381
$363$	10.8794	0.571022
$364$	−66.2427	−3.47206
$365$	−6.69797	−0.350588
$366$	−18.7072	−0.977841
$367$	16.0721	0.838956	0.419478	−	0.907765i	$-0.362213\pi$
$367$	16.0721	0.838956	0.419478	+	0.907765i	$0.362213\pi$
$368$	0	0
$369$	−3.94227	−0.205226
$370$	5.40702	0.281097
$371$	−53.1457	−2.75919
$372$	−31.7365	−1.64546
$373$	−3.93982	−0.203996	−0.101998	−	0.994785i	$-0.532524\pi$
$373$	−3.93982	−0.203996	−0.101998	+	0.994785i	$0.532524\pi$
$374$	5.75307	0.297484
$375$	−1.00000	−0.0516398
$376$	−32.8338	−1.69328
$377$	12.0663	0.621448
$378$	12.5779	0.646938
$379$	−21.9502	−1.12751	−0.563754	−	0.825943i	$-0.690643\pi$
$379$	−21.9502	−1.12751	−0.563754	+	0.825943i	$0.690643\pi$
$380$	27.8828	1.43036
$381$	−17.9214	−0.918142
$382$	9.36195	0.478999
$383$	−4.38081	−0.223849	−0.111924	−	0.993717i	$-0.535701\pi$
$383$	−4.38081	−0.223849	−0.111924	+	0.993717i	$0.535701\pi$
$384$	−10.7793	−0.550078
$385$	−1.71120	−0.0872110
$386$	−8.24649	−0.419735
$387$	3.20454	0.162896
$388$	−70.1515	−3.56140
$389$	5.25350	0.266363	0.133181	−	0.991092i	$-0.457481\pi$
$389$	5.25350	0.266363	0.133181	+	0.991092i	$0.457481\pi$
$390$	−7.60005	−0.384844
$391$	0	0
$392$	−110.917	−5.60216
$393$	−11.9734	−0.603980
$394$	−37.0256	−1.86532
$395$	8.07360	0.406227
$396$	−1.56738	−0.0787636
$397$	7.68020	0.385458	0.192729	−	0.981252i	$-0.438266\pi$
$397$	7.68020	0.385458	0.192729	+	0.981252i	$0.438266\pi$
$398$	−25.9100	−1.29875
$399$	−30.4414	−1.52398
$400$	7.34792	0.367396
$401$	9.73950	0.486368	0.243184	−	0.969980i	$-0.421808\pi$
$401$	9.73950	0.486368	0.243184	+	0.969980i	$0.421808\pi$
$402$	33.2640	1.65906
$403$	−20.9361	−1.04290
$404$	41.7553	2.07741
$405$	1.00000	0.0496904
$406$	50.9671	2.52945
$407$	0.735615	0.0364631
$408$	41.6527	2.06212
$409$	−37.0642	−1.83271	−0.916353	−	0.400370i	$-0.868882\pi$
$409$	−37.0642	−1.83271	−0.916353	+	0.400370i	$0.868882\pi$
$410$	10.0616	0.496909
$411$	−5.10981	−0.252048
$412$	52.5994	2.59139
$413$	51.8276	2.55027
$414$	0	0
$415$	−15.1818	−0.745243
$416$	17.6321	0.864487
$417$	−10.0757	−0.493408
$418$	5.47415	0.267749
$419$	−21.7804	−1.06404	−0.532022	−	0.846731i	$-0.678568\pi$
$419$	−21.7804	−1.06404	−0.532022	+	0.846731i	$0.678568\pi$
$420$	−22.2456	−1.08547
$421$	−20.5131	−0.999748	−0.499874	−	0.866098i	$-0.666620\pi$
$421$	−20.5131	−0.999748	−0.499874	+	0.866098i	$0.666620\pi$
$422$	0.683281	0.0332616
$423$	5.11730	0.248811
$424$	69.1932	3.36032
$425$	6.49175	0.314896
$426$	−1.02389	−0.0496075
$427$	−36.1220	−1.74807
$428$	−13.9954	−0.676494
$429$	−1.03397	−0.0499207
$430$	−8.17878	−0.394416
$431$	3.76273	0.181244	0.0906222	−	0.995885i	$-0.471114\pi$
$431$	3.76273	0.181244	0.0906222	+	0.995885i	$0.471114\pi$
$432$	−7.34792	−0.353527
$433$	−29.2854	−1.40737	−0.703683	−	0.710514i	$-0.748463\pi$
$433$	−29.2854	−1.40737	−0.703683	+	0.710514i	$0.748463\pi$
$434$	−88.4320	−4.24487
$435$	4.05211	0.194284
$436$	28.6348	1.37136
$437$	0	0
$438$	−17.0949	−0.816824
$439$	13.5999	0.649089	0.324545	−	0.945870i	$-0.394789\pi$
$439$	13.5999	0.649089	0.324545	+	0.945870i	$0.394789\pi$
$440$	2.22790	0.106211
$441$	17.2869	0.823186
$442$	49.3377	2.34675
$443$	14.4970	0.688771	0.344386	−	0.938828i	$-0.388087\pi$
$443$	14.4970	0.688771	0.344386	+	0.938828i	$0.388087\pi$
$444$	9.56297	0.453839
$445$	3.25959	0.154520
$446$	51.3309	2.43059
$447$	−21.2941	−1.00718
$448$	2.05285	0.0969878
$449$	−24.2879	−1.14622	−0.573108	−	0.819480i	$-0.694262\pi$
$449$	−24.2879	−1.14622	−0.573108	+	0.819480i	$0.694262\pi$
$450$	−2.55225	−0.120314
$451$	1.36887	0.0644574
$452$	−90.5381	−4.25855
$453$	−16.9639	−0.797032
$454$	−21.7443	−1.02051
$455$	−14.6751	−0.687978
$456$	39.6333	1.85600
$457$	21.9240	1.02556	0.512781	−	0.858519i	$-0.328615\pi$
$457$	21.9240	1.02556	0.512781	+	0.858519i	$0.328615\pi$
$458$	−5.11372	−0.238948
$459$	−6.49175	−0.303009
$460$	0	0
$461$	23.0180	1.07206	0.536028	−	0.844201i	$-0.319924\pi$
$461$	23.0180	1.07206	0.536028	+	0.844201i	$0.319924\pi$
$462$	−4.36741	−0.203190
$463$	−19.1149	−0.888344	−0.444172	−	0.895942i	$-0.646502\pi$
$463$	−19.1149	−0.888344	−0.444172	+	0.895942i	$0.646502\pi$
$464$	−29.7746	−1.38225
$465$	−7.03074	−0.326043
$466$	−18.8563	−0.873503
$467$	17.4831	0.809021	0.404510	−	0.914533i	$-0.367442\pi$
$467$	17.4831	0.809021	0.404510	+	0.914533i	$0.367442\pi$
$468$	−13.4416	−0.621339
$469$	64.2300	2.96587
$470$	−13.0606	−0.602441
$471$	−13.0403	−0.600864
$472$	−67.4771	−3.10589
$473$	−1.11271	−0.0511624
$474$	20.6058	0.946457
$475$	6.17701	0.283421
$476$	144.413	6.61915
$477$	−10.7841	−0.493768
$478$	29.6013	1.35393
$479$	19.2430	0.879237	0.439618	−	0.898185i	$-0.355114\pi$
$479$	19.2430	0.879237	0.439618	+	0.898185i	$0.355114\pi$
$480$	5.92122	0.270265
$481$	6.30854	0.287645
$482$	30.8160	1.40363
$483$	0	0
$484$	−49.1093	−2.23224
$485$	−15.5410	−0.705681
$486$	2.55225	0.115772
$487$	16.3625	0.741455	0.370727	−	0.928742i	$-0.379108\pi$
$487$	16.3625	0.741455	0.370727	+	0.928742i	$0.379108\pi$
$488$	47.0292	2.12891
$489$	7.45370	0.337068
$490$	−44.1204	−1.99316
$491$	12.5792	0.567689	0.283845	−	0.958870i	$-0.408390\pi$
$491$	12.5792	0.567689	0.283845	+	0.958870i	$0.408390\pi$
$492$	17.7952	0.802271
$493$	−26.3053	−1.18473
$494$	46.9456	2.11218
$495$	−0.347228	−0.0156068
$496$	51.6613	2.31966
$497$	−1.97704	−0.0886823
$498$	−38.7476	−1.73632
$499$	−4.04982	−0.181295	−0.0906474	−	0.995883i	$-0.528894\pi$
$499$	−4.04982	−0.181295	−0.0906474	+	0.995883i	$0.528894\pi$
$500$	4.51396	0.201870
$501$	3.05073	0.136296
$502$	55.9972	2.49928
$503$	6.03426	0.269054	0.134527	−	0.990910i	$-0.457048\pi$
$503$	6.03426	0.269054	0.134527	+	0.990910i	$0.457048\pi$
$504$	−31.6204	−1.40848
$505$	9.25026	0.411631
$506$	0	0
$507$	4.13277	0.183543
$508$	80.8965	3.58920
$509$	−37.9650	−1.68277	−0.841384	−	0.540437i	$-0.818259\pi$
$509$	−37.9650	−1.68277	−0.841384	+	0.540437i	$0.818259\pi$
$510$	16.5685	0.733668
$511$	−33.0087	−1.46022
$512$	50.7836	2.24434
$513$	−6.17701	−0.272722
$514$	18.5927	0.820089
$515$	11.6526	0.513475
$516$	−14.4652	−0.636794
$517$	−1.77687	−0.0781467
$518$	26.6467	1.17079
$519$	12.8310	0.563220
$520$	19.1062	0.837864
$521$	25.0991	1.09961	0.549805	−	0.835293i	$-0.314702\pi$
$521$	25.0991	1.09961	0.549805	+	0.835293i	$0.314702\pi$
$522$	10.3420	0.452656
$523$	−30.8809	−1.35033	−0.675163	−	0.737669i	$-0.735927\pi$
$523$	−30.8809	−1.35033	−0.675163	+	0.737669i	$0.735927\pi$
$524$	54.0476	2.36108
$525$	−4.92817	−0.215083
$526$	27.8707	1.21522
$527$	45.6418	1.98819
$528$	2.55141	0.111036
$529$	0	0
$530$	27.5236	1.19555
$531$	10.5166	0.456382
$532$	137.411	5.95754
$533$	11.7392	0.508483
$534$	8.31929	0.360011
$535$	−3.10047	−0.134045
$536$	−83.6244	−3.61203
$537$	1.98885	0.0858254
$538$	1.14329	0.0492909
$539$	−6.00251	−0.258546
$540$	−4.51396	−0.194250
$541$	4.86281	0.209068	0.104534	−	0.994521i	$-0.466665\pi$
$541$	4.86281	0.209068	0.104534	+	0.994521i	$0.466665\pi$
$542$	−13.8134	−0.593335
$543$	−20.1561	−0.864982
$544$	−38.4391	−1.64806
$545$	6.34361	0.271731
$546$	−37.4544	−1.60290
$547$	6.33857	0.271018	0.135509	−	0.990776i	$-0.456733\pi$
$547$	6.33857	0.271018	0.135509	+	0.990776i	$0.456733\pi$
$548$	23.0655	0.985309
$549$	−7.32970	−0.312824
$550$	0.886213	0.0377882
$551$	−25.0299	−1.06631
$552$	0	0
$553$	39.7881	1.69196
$554$	13.0557	0.554683
$555$	2.11853	0.0899267
$556$	45.4812	1.92883
$557$	−45.1860	−1.91459	−0.957296	−	0.289110i	$-0.906641\pi$
$557$	−45.1860	−1.91459	−0.957296	+	0.289110i	$0.906641\pi$
$558$	−17.9442	−0.759637
$559$	−9.54245	−0.403603
$560$	36.2119	1.53023
$561$	2.25412	0.0951690
$562$	6.13410	0.258752
$563$	25.3295	1.06751	0.533755	−	0.845639i	$-0.320780\pi$
$563$	25.3295	1.06751	0.533755	+	0.845639i	$0.320780\pi$
$564$	−23.0993	−0.972655
$565$	−20.0574	−0.843819
$566$	46.4185	1.95111
$567$	4.92817	0.206964
$568$	2.57401	0.108003
$569$	23.5150	0.985802	0.492901	−	0.870085i	$-0.335936\pi$
$569$	23.5150	0.985802	0.492901	+	0.870085i	$0.335936\pi$
$570$	15.7653	0.660334
$571$	19.1474	0.801294	0.400647	−	0.916232i	$-0.368785\pi$
$571$	19.1474	0.801294	0.400647	+	0.916232i	$0.368785\pi$
$572$	4.66732	0.195150
$573$	3.66812	0.153238
$574$	49.5855	2.06966
$575$	0	0
$576$	0.416553	0.0173564
$577$	12.3710	0.515011	0.257506	−	0.966277i	$-0.417099\pi$
$577$	12.3710	0.515011	0.257506	+	0.966277i	$0.417099\pi$
$578$	−64.1707	−2.66915
$579$	−3.23107	−0.134279
$580$	−18.2911	−0.759495
$581$	−74.8184	−3.10399
$582$	−39.6645	−1.64415
$583$	3.74453	0.155083
$584$	42.9758	1.77835
$585$	−2.97779	−0.123116
$586$	52.1019	2.15231
$587$	−2.73052	−0.112700	−0.0563502	−	0.998411i	$-0.517946\pi$
$587$	−2.73052	−0.112700	−0.0563502	+	0.998411i	$0.517946\pi$
$588$	−78.0324	−3.21800
$589$	43.4289	1.78946
$590$	−26.8410	−1.10502
$591$	−14.5071	−0.596741
$592$	−15.5668	−0.639792
$593$	−12.5386	−0.514899	−0.257450	−	0.966292i	$-0.582882\pi$
$593$	−12.5386	−0.514899	−0.257450	+	0.966292i	$0.582882\pi$
$594$	−0.886213	−0.0363617
$595$	31.9925	1.31156
$596$	96.1206	3.93725
$597$	−10.1518	−0.415487
$598$	0	0
$599$	40.8492	1.66905	0.834526	−	0.550968i	$-0.185741\pi$
$599$	40.8492	1.66905	0.834526	+	0.550968i	$0.185741\pi$
$600$	6.41625	0.261942
$601$	12.3678	0.504495	0.252247	−	0.967663i	$-0.418830\pi$
$601$	12.3678	0.504495	0.252247	+	0.967663i	$0.418830\pi$
$602$	−40.3065	−1.64277
$603$	13.0332	0.530754
$604$	76.5742	3.11576
$605$	−10.8794	−0.442312
$606$	23.6090	0.959048
$607$	−10.2939	−0.417818	−0.208909	−	0.977935i	$-0.566991\pi$
$607$	−10.2939	−0.417818	−0.208909	+	0.977935i	$0.566991\pi$
$608$	−36.5754	−1.48333
$609$	19.9695	0.809205
$610$	18.7072	0.757433
$611$	−15.2382	−0.616473
$612$	29.3035	1.18452
$613$	−32.2359	−1.30200	−0.650998	−	0.759079i	$-0.725650\pi$
$613$	−32.2359	−1.30200	−0.650998	+	0.759079i	$0.725650\pi$
$614$	73.1988	2.95406
$615$	3.94227	0.158967
$616$	10.9795	0.442377
$617$	2.45879	0.0989874	0.0494937	−	0.998774i	$-0.484239\pi$
$617$	2.45879	0.0989874	0.0494937	+	0.998774i	$0.484239\pi$
$618$	29.7403	1.19633
$619$	−4.04881	−0.162735	−0.0813676	−	0.996684i	$-0.525929\pi$
$619$	−4.04881	−0.162735	−0.0813676	+	0.996684i	$0.525929\pi$
$620$	31.7365	1.27457
$621$	0	0
$622$	−43.4042	−1.74035
$623$	16.0638	0.643585
$624$	21.8806	0.875924
$625$	1.00000	0.0400000
$626$	−8.00631	−0.319996
$627$	2.14483	0.0856565
$628$	58.8633	2.34890
$629$	−13.7530	−0.548367
$630$	−12.5779	−0.501116
$631$	11.6214	0.462640	0.231320	−	0.972878i	$-0.425696\pi$
$631$	11.6214	0.462640	0.231320	+	0.972878i	$0.425696\pi$
$632$	−51.8022	−2.06058
$633$	0.267718	0.0106408
$634$	−0.951766	−0.0377995
$635$	17.9214	0.711189
$636$	48.6788	1.93024
$637$	−51.4768	−2.03958
$638$	−3.59103	−0.142170
$639$	−0.401171	−0.0158701
$640$	10.7793	0.426089
$641$	15.6190	0.616913	0.308457	−	0.951238i	$-0.400188\pi$
$641$	15.6190	0.616913	0.308457	+	0.951238i	$0.400188\pi$
$642$	−7.91317	−0.312308
$643$	−22.8845	−0.902476	−0.451238	−	0.892404i	$-0.649017\pi$
$643$	−22.8845	−0.902476	−0.451238	+	0.892404i	$0.649017\pi$
$644$	0	0
$645$	−3.20454	−0.126179
$646$	−102.344	−4.02668
$647$	43.9091	1.72625	0.863123	−	0.504993i	$-0.168505\pi$
$647$	43.9091	1.72625	0.863123	+	0.504993i	$0.168505\pi$
$648$	−6.41625	−0.252054
$649$	−3.65166	−0.143340
$650$	7.60005	0.298099
$651$	−34.6487	−1.35799
$652$	−33.6457	−1.31767
$653$	−20.7209	−0.810872	−0.405436	−	0.914123i	$-0.632880\pi$
$653$	−20.7209	−0.810872	−0.405436	+	0.914123i	$0.632880\pi$
$654$	16.1905	0.633097
$655$	11.9734	0.467841
$656$	−28.9675	−1.13099
$657$	−6.69797	−0.261313
$658$	−64.3649	−2.50921
$659$	−7.61519	−0.296646	−0.148323	−	0.988939i	$-0.547387\pi$
$659$	−7.61519	−0.296646	−0.148323	+	0.988939i	$0.547387\pi$
$660$	1.56738	0.0610100
$661$	−1.56361	−0.0608173	−0.0304087	−	0.999538i	$-0.509681\pi$
$661$	−1.56361	−0.0608173	−0.0304087	+	0.999538i	$0.509681\pi$
$662$	−1.91794	−0.0745428
$663$	19.3311	0.750757
$664$	97.4099	3.78024
$665$	30.4414	1.18047
$666$	5.40702	0.209518
$667$	0	0
$668$	−13.7709	−0.532811
$669$	20.1120	0.777577
$670$	−33.2640	−1.28510
$671$	2.54508	0.0982517
$672$	29.1808	1.12567
$673$	8.13251	0.313485	0.156743	−	0.987639i	$-0.449901\pi$
$673$	8.13251	0.313485	0.156743	+	0.987639i	$0.449901\pi$
$674$	50.5336	1.94648
$675$	−1.00000	−0.0384900
$676$	−18.6552	−0.717506
$677$	−19.2467	−0.739709	−0.369855	−	0.929090i	$-0.620593\pi$
$677$	−19.2467	−0.739709	−0.369855	+	0.929090i	$0.620593\pi$
$678$	−51.1913	−1.96599
$679$	−76.5888	−2.93921
$680$	−41.6527	−1.59731
$681$	−8.51968	−0.326475
$682$	6.23073	0.238587
$683$	−20.0734	−0.768088	−0.384044	−	0.923315i	$-0.625469\pi$
$683$	−20.0734	−0.768088	−0.384044	+	0.923315i	$0.625469\pi$
$684$	27.8828	1.06613
$685$	5.10981	0.195236
$686$	−129.388	−4.94005
$687$	−2.00362	−0.0764427
$688$	23.5467	0.897711
$689$	32.1127	1.22339
$690$	0	0
$691$	46.9283	1.78523	0.892617	−	0.450815i	$-0.148867\pi$
$691$	46.9283	1.78523	0.892617	+	0.450815i	$0.148867\pi$
$692$	−57.9188	−2.20174
$693$	−1.71120	−0.0650032
$694$	0.774040	0.0293822
$695$	10.0757	0.382192
$696$	−25.9993	−0.985503
$697$	−25.5922	−0.969374
$698$	15.1989	0.575287
$699$	−7.38814	−0.279445
$700$	22.2456	0.840804
$701$	−18.8567	−0.712208	−0.356104	−	0.934446i	$-0.615895\pi$
$701$	−18.8567	−0.712208	−0.356104	+	0.934446i	$0.615895\pi$
$702$	−7.60005	−0.286846
$703$	−13.0862	−0.493556
$704$	−0.144639	−0.00545129
$705$	−5.11730	−0.192729
$706$	−75.2138	−2.83071
$707$	45.5869	1.71447
$708$	−47.4715	−1.78409
$709$	16.1718	0.607344	0.303672	−	0.952777i	$-0.401787\pi$
$709$	16.1718	0.607344	0.303672	+	0.952777i	$0.401787\pi$
$710$	1.02389	0.0384258
$711$	8.07360	0.302784
$712$	−20.9144	−0.783799
$713$	0	0
$714$	81.6527	3.05578
$715$	1.03397	0.0386684
$716$	−8.97761	−0.335509
$717$	11.5981	0.433141
$718$	28.1766	1.05154
$719$	−40.2758	−1.50203	−0.751017	−	0.660283i	$-0.770436\pi$
$719$	−40.2758	−1.50203	−0.751017	+	0.660283i	$0.770436\pi$
$720$	7.34792	0.273841
$721$	57.4261	2.13866
$722$	−48.8896	−1.81948
$723$	12.0741	0.449040
$724$	90.9840	3.38139
$725$	−4.05211	−0.150492
$726$	−27.7670	−1.03053
$727$	−31.9839	−1.18622	−0.593109	−	0.805122i	$-0.702100\pi$
$727$	−31.9839	−1.18622	−0.593109	+	0.805122i	$0.702100\pi$
$728$	94.1589	3.48976
$729$	1.00000	0.0370370
$730$	17.0949	0.632709
$731$	20.8031	0.769430
$732$	33.0860	1.22289
$733$	19.1849	0.708609	0.354305	−	0.935130i	$-0.384718\pi$
$733$	19.1849	0.708609	0.354305	+	0.935130i	$0.384718\pi$
$734$	−41.0199	−1.51407
$735$	−17.2869	−0.637637
$736$	0	0
$737$	−4.52551	−0.166699
$738$	10.0616	0.370374
$739$	−13.4183	−0.493601	−0.246800	−	0.969066i	$-0.579379\pi$
$739$	−13.4183	−0.493601	−0.246800	+	0.969066i	$0.579379\pi$
$740$	−9.56297	−0.351542
$741$	18.3938	0.675715
$742$	135.641	4.97954
$743$	35.6600	1.30824	0.654120	−	0.756391i	$-0.273039\pi$
$743$	35.6600	1.30824	0.654120	+	0.756391i	$0.273039\pi$
$744$	45.1109	1.65385
$745$	21.2941	0.780155
$746$	10.0554	0.368154
$747$	−15.1818	−0.555472
$748$	−10.1750	−0.372035
$749$	−15.2797	−0.558307
$750$	2.55225	0.0931949
$751$	−4.17313	−0.152280	−0.0761399	−	0.997097i	$-0.524260\pi$
$751$	−4.17313	−0.152280	−0.0761399	+	0.997097i	$0.524260\pi$
$752$	37.6015	1.37119
$753$	21.9404	0.799552
$754$	−30.7963	−1.12153
$755$	16.9639	0.617378
$756$	−22.2456	−0.809064
$757$	8.24046	0.299504	0.149752	−	0.988724i	$-0.452152\pi$
$757$	8.24046	0.299504	0.149752	+	0.988724i	$0.452152\pi$
$758$	56.0224	2.03483
$759$	0	0
$760$	−39.6333	−1.43765
$761$	−14.2609	−0.516958	−0.258479	−	0.966017i	$-0.583221\pi$
$761$	−14.2609	−0.516958	−0.258479	+	0.966017i	$0.583221\pi$
$762$	45.7398	1.65698
$763$	31.2624	1.13178
$764$	−16.5578	−0.599039
$765$	6.49175	0.234710
$766$	11.1809	0.403983
$767$	−31.3162	−1.13076
$768$	28.3445	1.02279
$769$	43.7604	1.57804	0.789020	−	0.614368i	$-0.210589\pi$
$769$	43.7604	1.57804	0.789020	+	0.614368i	$0.210589\pi$
$770$	4.36741	0.157391
$771$	7.28484	0.262357
$772$	14.5849	0.524923
$773$	13.1941	0.474560	0.237280	−	0.971441i	$-0.423744\pi$
$773$	13.1941	0.474560	0.237280	+	0.971441i	$0.423744\pi$
$774$	−8.17878	−0.293980
$775$	7.03074	0.252551
$776$	99.7149	3.57956
$777$	10.4405	0.374551
$778$	−13.4082	−0.480708
$779$	−24.3514	−0.872480
$780$	13.4416	0.481287
$781$	0.139298	0.00498447
$782$	0	0
$783$	4.05211	0.144811
$784$	127.023	4.53653
$785$	13.0403	0.465428
$786$	30.5592	1.09001
$787$	18.4237	0.656734	0.328367	−	0.944550i	$-0.393502\pi$
$787$	18.4237	0.656734	0.328367	+	0.944550i	$0.393502\pi$
$788$	65.4844	2.33278
$789$	10.9201	0.388765
$790$	−20.6058	−0.733122
$791$	−98.8461	−3.51456
$792$	2.22790	0.0791651
$793$	21.8263	0.775075
$794$	−19.6018	−0.695640
$795$	10.7841	0.382471
$796$	45.8250	1.62423
$797$	35.6347	1.26225	0.631124	−	0.775682i	$-0.282594\pi$
$797$	35.6347	1.26225	0.631124	+	0.775682i	$0.282594\pi$
$798$	77.6940	2.75034
$799$	33.2202	1.17525
$800$	−5.92122	−0.209347
$801$	3.25959	0.115172
$802$	−24.8576	−0.877753
$803$	2.32572	0.0820730
$804$	−58.8315	−2.07483
$805$	0	0
$806$	53.4340	1.88213
$807$	0.447956	0.0157688
$808$	−59.3520	−2.08800
$809$	−16.5224	−0.580895	−0.290448	−	0.956891i	$-0.593804\pi$
$809$	−16.5224	−0.580895	−0.290448	+	0.956891i	$0.593804\pi$
$810$	−2.55225	−0.0896768
$811$	−52.4110	−1.84040	−0.920200	−	0.391448i	$-0.871974\pi$
$811$	−52.4110	−1.84040	−0.920200	+	0.391448i	$0.871974\pi$
$812$	−90.1416	−3.16335
$813$	−5.41224	−0.189815
$814$	−1.87747	−0.0658053
$815$	−7.45370	−0.261092
$816$	−47.7009	−1.66987
$817$	19.7945	0.692522
$818$	94.5970	3.30751
$819$	−14.6751	−0.512788
$820$	−17.7952	−0.621436
$821$	9.06103	0.316232	0.158116	−	0.987421i	$-0.449458\pi$
$821$	9.06103	0.316232	0.158116	+	0.987421i	$0.449458\pi$
$822$	13.0415	0.454874
$823$	12.8585	0.448219	0.224109	−	0.974564i	$-0.428053\pi$
$823$	12.8585	0.448219	0.224109	+	0.974564i	$0.428053\pi$
$824$	−74.7660	−2.60460
$825$	0.347228	0.0120889
$826$	−132.277	−4.60250
$827$	−25.0762	−0.871985	−0.435992	−	0.899950i	$-0.643603\pi$
$827$	−25.0762	−0.871985	−0.435992	+	0.899950i	$0.643603\pi$
$828$	0	0
$829$	−28.5320	−0.990957	−0.495479	−	0.868620i	$-0.665007\pi$
$829$	−28.5320	−0.990957	−0.495479	+	0.868620i	$0.665007\pi$
$830$	38.7476	1.34495
$831$	5.11537	0.177450
$832$	−1.24041	−0.0430034
$833$	112.222	3.88827
$834$	25.7156	0.890459
$835$	−3.05073	−0.105575
$836$	−9.68170	−0.334849
$837$	−7.03074	−0.243018
$838$	55.5890	1.92029
$839$	28.5162	0.984490	0.492245	−	0.870457i	$-0.336176\pi$
$839$	28.5162	0.984490	0.492245	+	0.870457i	$0.336176\pi$
$840$	31.6204	1.09101
$841$	−12.5804	−0.433807
$842$	52.3545	1.80426
$843$	2.40341	0.0827780
$844$	−1.20847	−0.0415971
$845$	−4.13277	−0.142172
$846$	−13.0606	−0.449033
$847$	−53.6157	−1.84226
$848$	−79.2404	−2.72113
$849$	18.1873	0.624187
$850$	−16.5685	−0.568297
$851$	0	0
$852$	1.81087	0.0620393
$853$	−40.0964	−1.37287	−0.686437	−	0.727189i	$-0.740826\pi$
$853$	−40.0964	−1.37287	−0.686437	+	0.727189i	$0.740826\pi$
$854$	92.1924	3.15476
$855$	6.17701	0.211249
$856$	19.8934	0.679943
$857$	−36.6714	−1.25267	−0.626336	−	0.779553i	$-0.715446\pi$
$857$	−36.6714	−1.25267	−0.626336	+	0.779553i	$0.715446\pi$
$858$	2.63895	0.0900924
$859$	20.4620	0.698155	0.349078	−	0.937094i	$-0.386495\pi$
$859$	20.4620	0.698155	0.349078	+	0.937094i	$0.386495\pi$
$860$	14.4652	0.493258
$861$	19.4282	0.662110
$862$	−9.60341	−0.327094
$863$	52.9186	1.80137	0.900685	−	0.434474i	$-0.143066\pi$
$863$	52.9186	1.80137	0.900685	+	0.434474i	$0.143066\pi$
$864$	5.92122	0.201444
$865$	−12.8310	−0.436268
$866$	74.7436	2.53989
$867$	−25.1428	−0.853895
$868$	156.403	5.30866
$869$	−2.80338	−0.0950983
$870$	−10.3420	−0.350626
$871$	−38.8102	−1.31503
$872$	−40.7022	−1.37835
$873$	−15.5410	−0.525983
$874$	0	0
$875$	4.92817	0.166603
$876$	30.2344	1.02152
$877$	−38.8677	−1.31247	−0.656235	−	0.754557i	$-0.727852\pi$
$877$	−38.8677	−1.31247	−0.656235	+	0.754557i	$0.727852\pi$
$878$	−34.7104	−1.17142
$879$	20.4141	0.688552
$880$	−2.55141	−0.0860080
$881$	0.556123	0.0187363	0.00936813	−	0.999956i	$-0.497018\pi$
$881$	0.556123	0.0187363	0.00936813	+	0.999956i	$0.497018\pi$
$882$	−44.1204	−1.48561
$883$	4.56968	0.153782	0.0768910	−	0.997040i	$-0.475501\pi$
$883$	4.56968	0.153782	0.0768910	+	0.997040i	$0.475501\pi$
$884$	−87.2597	−2.93486
$885$	−10.5166	−0.353512
$886$	−36.9998	−1.24303
$887$	35.0034	1.17530	0.587650	−	0.809115i	$-0.300053\pi$
$887$	35.0034	1.17530	0.587650	+	0.809115i	$0.300053\pi$
$888$	−13.5930	−0.456152
$889$	88.3198	2.96215
$890$	−8.31929	−0.278863
$891$	−0.347228	−0.0116326
$892$	−90.7850	−3.03971
$893$	31.6096	1.05778
$894$	54.3477	1.81766
$895$	−1.98885	−0.0664801
$896$	53.1222	1.77469
$897$	0	0
$898$	61.9886	2.06859
$899$	−28.4893	−0.950172
$900$	4.51396	0.150465
$901$	−70.0074	−2.33229
$902$	−3.49368	−0.116327
$903$	−15.7925	−0.525543
$904$	128.693	4.28026
$905$	20.1561	0.670012
$906$	43.2960	1.43841
$907$	−33.9010	−1.12567	−0.562833	−	0.826571i	$-0.690288\pi$
$907$	−33.9010	−1.12567	−0.562833	+	0.826571i	$0.690288\pi$
$908$	38.4575	1.27626
$909$	9.25026	0.306812
$910$	37.4544	1.24160
$911$	2.27099	0.0752413	0.0376206	−	0.999292i	$-0.488022\pi$
$911$	2.27099	0.0752413	0.0376206	+	0.999292i	$0.488022\pi$
$912$	−45.3882	−1.50295
$913$	5.27154	0.174462
$914$	−55.9555	−1.85084
$915$	7.32970	0.242312
$916$	9.04424	0.298830
$917$	59.0072	1.94859
$918$	16.5685	0.546844
$919$	5.40954	0.178444	0.0892221	−	0.996012i	$-0.471562\pi$
$919$	5.40954	0.178444	0.0892221	+	0.996012i	$0.471562\pi$
$920$	0	0
$921$	28.6801	0.945043
$922$	−58.7476	−1.93475
$923$	1.19460	0.0393208
$924$	7.72430	0.254111
$925$	−2.11853	−0.0696569
$926$	48.7859	1.60320
$927$	11.6526	0.382722
$928$	23.9934	0.787623
$929$	0.526793	0.0172835	0.00864176	−	0.999963i	$-0.497249\pi$
$929$	0.526793	0.0172835	0.00864176	+	0.999963i	$0.497249\pi$
$930$	17.9442	0.588412
$931$	106.781	3.49962
$932$	33.3498	1.09241
$933$	−17.0063	−0.556761
$934$	−44.6211	−1.46005
$935$	−2.25412	−0.0737176
$936$	19.1062	0.624507
$937$	32.6651	1.06712	0.533561	−	0.845761i	$-0.320853\pi$
$937$	32.6651	1.06712	0.533561	+	0.845761i	$0.320853\pi$
$938$	−163.931	−5.35253
$939$	−3.13697	−0.102371
$940$	23.0993	0.753415
$941$	12.2839	0.400442	0.200221	−	0.979751i	$-0.435834\pi$
$941$	12.2839	0.400442	0.200221	+	0.979751i	$0.435834\pi$
$942$	33.2820	1.08439
$943$	0	0
$944$	77.2752	2.51509
$945$	−4.92817	−0.160314
$946$	2.83990	0.0923333
$947$	−58.1464	−1.88950	−0.944752	−	0.327786i	$-0.893698\pi$
$947$	−58.1464	−1.88950	−0.944752	+	0.327786i	$0.893698\pi$
$948$	−36.4439	−1.18364
$949$	19.9451	0.647446
$950$	−15.7653	−0.511493
$951$	−0.372913	−0.0120925
$952$	−205.272	−6.65290
$953$	14.8143	0.479881	0.239940	−	0.970788i	$-0.422872\pi$
$953$	14.8143	0.479881	0.239940	+	0.970788i	$0.422872\pi$
$954$	27.5236	0.891109
$955$	−3.66812	−0.118698
$956$	−52.3536	−1.69324
$957$	−1.40701	−0.0454821
$958$	−49.1130	−1.58677
$959$	25.1820	0.813170
$960$	−0.416553	−0.0134442
$961$	18.4312	0.594556
$962$	−16.1010	−0.519116
$963$	−3.10047	−0.0999113
$964$	−54.5020	−1.75539
$965$	3.23107	0.104012
$966$	0	0
$967$	2.11030	0.0678627	0.0339314	−	0.999424i	$-0.489197\pi$
$967$	2.11030	0.0678627	0.0339314	+	0.999424i	$0.489197\pi$
$968$	69.8051	2.24362
$969$	−40.0996	−1.28819
$970$	39.6645	1.27355
$971$	−7.87869	−0.252839	−0.126420	−	0.991977i	$-0.540349\pi$
$971$	−7.87869	−0.252839	−0.126420	+	0.991977i	$0.540349\pi$
$972$	−4.51396	−0.144785
$973$	49.6547	1.59186
$974$	−41.7611	−1.33811
$975$	2.97779	0.0953656
$976$	−53.8581	−1.72396
$977$	23.8080	0.761687	0.380843	−	0.924640i	$-0.375634\pi$
$977$	23.8080	0.761687	0.380843	+	0.924640i	$0.375634\pi$
$978$	−19.0237	−0.608310
$979$	−1.13182	−0.0361732
$980$	78.0324	2.49265
$981$	6.34361	0.202536
$982$	−32.1051	−1.02452
$983$	22.6289	0.721751	0.360876	−	0.932614i	$-0.382478\pi$
$983$	22.6289	0.721751	0.360876	+	0.932614i	$0.382478\pi$
$984$	−25.2946	−0.806361
$985$	14.5071	0.462234
$986$	67.1376	2.13810
$987$	−25.2189	−0.802727
$988$	−83.0291	−2.64151
$989$	0	0
$990$	0.886213	0.0281657
$991$	56.1913	1.78498	0.892488	−	0.451071i	$-0.148958\pi$
$991$	56.1913	1.78498	0.892488	+	0.451071i	$0.148958\pi$
$992$	−41.6305	−1.32177
$993$	−0.751471	−0.0238472
$994$	5.04589	0.160046
$995$	10.1518	0.321835
$996$	68.5299	2.17145
$997$	48.7556	1.54410	0.772052	−	0.635559i	$-0.219230\pi$
$997$	48.7556	1.54410	0.772052	+	0.635559i	$0.219230\pi$
$998$	10.3361	0.327185
$999$	2.11853	0.0670274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bk.1.2	yes	10
23.22	odd	2		7935.2.a.bj.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bj.1.2	✓	10	23.22	odd	2
7935.2.a.bk.1.2	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55225 q^{2} -1.00000 q^{3} +4.51396 q^{4} +1.00000 q^{5} +2.55225 q^{6} +4.92817 q^{7} -6.41625 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.55225 q^{2} -1.00000 q^{3} +4.51396 q^{4} +1.00000 q^{5} +2.55225 q^{6} +4.92817 q^{7} -6.41625 q^{8} +1.00000 q^{9} -2.55225 q^{10} -0.347228 q^{11} -4.51396 q^{12} -2.97779 q^{13} -12.5779 q^{14} -1.00000 q^{15} +7.34792 q^{16} +6.49175 q^{17} -2.55225 q^{18} +6.17701 q^{19} +4.51396 q^{20} -4.92817 q^{21} +0.886213 q^{22} +6.41625 q^{24} +1.00000 q^{25} +7.60005 q^{26} -1.00000 q^{27} +22.2456 q^{28} -4.05211 q^{29} +2.55225 q^{30} +7.03074 q^{31} -5.92122 q^{32} +0.347228 q^{33} -16.5685 q^{34} +4.92817 q^{35} +4.51396 q^{36} -2.11853 q^{37} -15.7653 q^{38} +2.97779 q^{39} -6.41625 q^{40} -3.94227 q^{41} +12.5779 q^{42} +3.20454 q^{43} -1.56738 q^{44} +1.00000 q^{45} +5.11730 q^{47} -7.34792 q^{48} +17.2869 q^{49} -2.55225 q^{50} -6.49175 q^{51} -13.4416 q^{52} -10.7841 q^{53} +2.55225 q^{54} -0.347228 q^{55} -31.6204 q^{56} -6.17701 q^{57} +10.3420 q^{58} +10.5166 q^{59} -4.51396 q^{60} -7.32970 q^{61} -17.9442 q^{62} +4.92817 q^{63} +0.416553 q^{64} -2.97779 q^{65} -0.886213 q^{66} +13.0332 q^{67} +29.3035 q^{68} -12.5779 q^{70} -0.401171 q^{71} -6.41625 q^{72} -6.69797 q^{73} +5.40702 q^{74} -1.00000 q^{75} +27.8828 q^{76} -1.71120 q^{77} -7.60005 q^{78} +8.07360 q^{79} +7.34792 q^{80} +1.00000 q^{81} +10.0616 q^{82} -15.1818 q^{83} -22.2456 q^{84} +6.49175 q^{85} -8.17878 q^{86} +4.05211 q^{87} +2.22790 q^{88} +3.25959 q^{89} -2.55225 q^{90} -14.6751 q^{91} -7.03074 q^{93} -13.0606 q^{94} +6.17701 q^{95} +5.92122 q^{96} -15.5410 q^{97} -44.1204 q^{98} -0.347228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9	\( 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9} - 4 q^{11} - 16 q^{12} - 4 q^{13} - 10 q^{15} + 28 q^{16} + 10 q^{17} + 8 q^{19} + 16 q^{20} - 6 q^{21} - 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27} + 76 q^{28} + 2 q^{29} + 2 q^{31} + 20 q^{32} + 4 q^{33} + 8 q^{34} + 6 q^{35} + 16 q^{36} + 2 q^{37} - 56 q^{38} + 4 q^{39} + 6 q^{41} + 44 q^{43} - 24 q^{44} + 10 q^{45} + 8 q^{47} - 28 q^{48} + 12 q^{49} - 10 q^{51} + 2 q^{53} - 4 q^{55} + 8 q^{56} - 8 q^{57} - 20 q^{58} - 14 q^{59} - 16 q^{60} - 8 q^{61} - 28 q^{62} + 6 q^{63} + 40 q^{64} - 4 q^{65} + 4 q^{66} + 2 q^{67} + 84 q^{68} + 6 q^{71} - 12 q^{73} + 40 q^{74} - 10 q^{75} + 44 q^{76} - 16 q^{77} + 8 q^{78} + 28 q^{80} + 10 q^{81} - 4 q^{82} - 62 q^{83} - 76 q^{84} + 10 q^{85} - 4 q^{86} - 2 q^{87} - 12 q^{88} + 56 q^{89} - 2 q^{93} + 20 q^{94} + 8 q^{95} - 20 q^{96} + 56 q^{97} - 4 q^{98} - 4 q^{99}+O(q^{100}) \) 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9 - 4 * q^11 - 16 * q^12 - 4 * q^13 - 10 * q^15 + 28 * q^16 + 10 * q^17 + 8 * q^19 + 16 * q^20 - 6 * q^21 - 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 + 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 + 4 * q^33 + 8 * q^34 + 6 * q^35 + 16 * q^36 + 2 * q^37 - 56 * q^38 + 4 * q^39 + 6 * q^41 + 44 * q^43 - 24 * q^44 + 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 - 10 * q^51 + 2 * q^53 - 4 * q^55 + 8 * q^56 - 8 * q^57 - 20 * q^58 - 14 * q^59 - 16 * q^60 - 8 * q^61 - 28 * q^62 + 6 * q^63 + 40 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 84 * q^68 + 6 * q^71 - 12 * q^73 + 40 * q^74 - 10 * q^75 + 44 * q^76 - 16 * q^77 + 8 * q^78 + 28 * q^80 + 10 * q^81 - 4 * q^82 - 62 * q^83 - 76 * q^84 + 10 * q^85 - 4 * q^86 - 2 * q^87 - 12 * q^88 + 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Introduction

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