LMFDB - Embedded newform 8470.2.a.bu.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{33}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 8 $ x^2 - x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 770)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.37228$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.00000 q^{12} -6.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +6.74456 q^{17} -1.00000 q^{18} +6.74456 q^{19} +1.00000 q^{20} -2.00000 q^{21} -6.74456 q^{23} -2.00000 q^{24} +1.00000 q^{25} +6.74456 q^{26} -4.00000 q^{27} -1.00000 q^{28} -8.74456 q^{29} -2.00000 q^{30} +4.74456 q^{31} -1.00000 q^{32} -6.74456 q^{34} -1.00000 q^{35} +1.00000 q^{36} +0.744563 q^{37} -6.74456 q^{38} -13.4891 q^{39} -1.00000 q^{40} +4.00000 q^{41} +2.00000 q^{42} -4.00000 q^{43} +1.00000 q^{45} +6.74456 q^{46} +4.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +13.4891 q^{51} -6.74456 q^{52} -12.7446 q^{53} +4.00000 q^{54} +1.00000 q^{56} +13.4891 q^{57} +8.74456 q^{58} -8.74456 q^{59} +2.00000 q^{60} -1.25544 q^{61} -4.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.74456 q^{65} -4.00000 q^{67} +6.74456 q^{68} -13.4891 q^{69} +1.00000 q^{70} -4.00000 q^{71} -1.00000 q^{72} -10.7446 q^{73} -0.744563 q^{74} +2.00000 q^{75} +6.74456 q^{76} +13.4891 q^{78} -6.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} -8.00000 q^{83} -2.00000 q^{84} +6.74456 q^{85} +4.00000 q^{86} -17.4891 q^{87} +15.4891 q^{89} -1.00000 q^{90} +6.74456 q^{91} -6.74456 q^{92} +9.48913 q^{93} -4.74456 q^{94} +6.74456 q^{95} -2.00000 q^{96} -16.7446 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 2 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 6 q^{29} - 4 q^{30} - 2 q^{31} - 2 q^{32} - 2 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{37} - 2 q^{38} - 4 q^{39} - 2 q^{40} + 8 q^{41} + 4 q^{42} - 8 q^{43} + 2 q^{45} + 2 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{49} - 2 q^{50} + 4 q^{51} - 2 q^{52} - 14 q^{53} + 8 q^{54} + 2 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} + 4 q^{60} - 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 8 q^{67} + 2 q^{68} - 4 q^{69} + 2 q^{70} - 8 q^{71} - 2 q^{72} - 10 q^{73} + 10 q^{74} + 4 q^{75} + 2 q^{76} + 4 q^{78} - 2 q^{79} + 2 q^{80} - 22 q^{81} - 8 q^{82} - 16 q^{83} - 4 q^{84} + 2 q^{85} + 8 q^{86} - 12 q^{87} + 8 q^{89} - 2 q^{90} + 2 q^{91} - 2 q^{92} - 4 q^{93} + 2 q^{94} + 2 q^{95} - 4 q^{96} - 22 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^12 - 2 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 2 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 6 * q^29 - 4 * q^30 - 2 * q^31 - 2 * q^32 - 2 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^37 - 2 * q^38 - 4 * q^39 - 2 * q^40 + 8 * q^41 + 4 * q^42 - 8 * q^43 + 2 * q^45 + 2 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^49 - 2 * q^50 + 4 * q^51 - 2 * q^52 - 14 * q^53 + 8 * q^54 + 2 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 + 4 * q^60 - 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 8 * q^67 + 2 * q^68 - 4 * q^69 + 2 * q^70 - 8 * q^71 - 2 * q^72 - 10 * q^73 + 10 * q^74 + 4 * q^75 + 2 * q^76 + 4 * q^78 - 2 * q^79 + 2 * q^80 - 22 * q^81 - 8 * q^82 - 16 * q^83 - 4 * q^84 + 2 * q^85 + 8 * q^86 - 12 * q^87 + 8 * q^89 - 2 * q^90 + 2 * q^91 - 2 * q^92 - 4 * q^93 + 2 * q^94 + 2 * q^95 - 4 * q^96 - 22 * q^97 - 2 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.00000	1.15470	0.577350	−	0.816497i	$-0.304087\pi$
$3$	2.00000	1.15470	0.577350	+	0.816497i	$0.304087\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.00000	−0.816497
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	2.00000	0.577350
$13$	−6.74456	−1.87061	−0.935303	−	0.353849i	$-0.884873\pi$
$13$	−6.74456	−1.87061	−0.935303	+	0.353849i	$0.884873\pi$
$14$	1.00000	0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	6.74456	1.63580	0.817898	−	0.575363i	$-0.195139\pi$
$17$	6.74456	1.63580	0.817898	+	0.575363i	$0.195139\pi$
$18$	−1.00000	−0.235702
$19$	6.74456	1.54731	0.773654	−	0.633608i	$-0.218427\pi$
$19$	6.74456	1.54731	0.773654	+	0.633608i	$0.218427\pi$
$20$	1.00000	0.223607
$21$	−2.00000	−0.436436
$22$	0	0
$23$	−6.74456	−1.40634	−0.703169	−	0.711022i	$-0.748232\pi$
$23$	−6.74456	−1.40634	−0.703169	+	0.711022i	$0.748232\pi$
$24$	−2.00000	−0.408248
$25$	1.00000	0.200000
$26$	6.74456	1.32272
$27$	−4.00000	−0.769800
$28$	−1.00000	−0.188982
$29$	−8.74456	−1.62382	−0.811912	−	0.583779i	$-0.801573\pi$
$29$	−8.74456	−1.62382	−0.811912	+	0.583779i	$0.801573\pi$
$30$	−2.00000	−0.365148
$31$	4.74456	0.852149	0.426074	−	0.904688i	$-0.359896\pi$
$31$	4.74456	0.852149	0.426074	+	0.904688i	$0.359896\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−6.74456	−1.15668
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	0.744563	0.122405	0.0612027	−	0.998125i	$-0.480506\pi$
$37$	0.744563	0.122405	0.0612027	+	0.998125i	$0.480506\pi$
$38$	−6.74456	−1.09411
$39$	−13.4891	−2.15999
$40$	−1.00000	−0.158114
$41$	4.00000	0.624695	0.312348	−	0.949968i	$-0.398885\pi$
$41$	4.00000	0.624695	0.312348	+	0.949968i	$0.398885\pi$
$42$	2.00000	0.308607
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	6.74456	0.994432
$47$	4.74456	0.692066	0.346033	−	0.938222i	$-0.387529\pi$
$47$	4.74456	0.692066	0.346033	+	0.938222i	$0.387529\pi$
$48$	2.00000	0.288675
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	13.4891	1.88886
$52$	−6.74456	−0.935303
$53$	−12.7446	−1.75060	−0.875300	−	0.483580i	$-0.839336\pi$
$53$	−12.7446	−1.75060	−0.875300	+	0.483580i	$0.839336\pi$
$54$	4.00000	0.544331
$55$	0	0
$56$	1.00000	0.133631
$57$	13.4891	1.78668
$58$	8.74456	1.14822
$59$	−8.74456	−1.13845	−0.569223	−	0.822183i	$-0.692756\pi$
$59$	−8.74456	−1.13845	−0.569223	+	0.822183i	$0.692756\pi$
$60$	2.00000	0.258199
$61$	−1.25544	−0.160742	−0.0803711	−	0.996765i	$-0.525611\pi$
$61$	−1.25544	−0.160742	−0.0803711	+	0.996765i	$0.525611\pi$
$62$	−4.74456	−0.602560
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−6.74456	−0.836560
$66$	0	0
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	6.74456	0.817898
$69$	−13.4891	−1.62390
$70$	1.00000	0.119523
$71$	−4.00000	−0.474713	−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000	−0.474713	−0.237356	+	0.971423i	$0.576281\pi$
$72$	−1.00000	−0.117851
$73$	−10.7446	−1.25756	−0.628778	−	0.777585i	$-0.716445\pi$
$73$	−10.7446	−1.25756	−0.628778	+	0.777585i	$0.716445\pi$
$74$	−0.744563	−0.0865536
$75$	2.00000	0.230940
$76$	6.74456	0.773654
$77$	0	0
$78$	13.4891	1.52734
$79$	−6.74456	−0.758823	−0.379411	−	0.925228i	$-0.623873\pi$
$79$	−6.74456	−0.758823	−0.379411	+	0.925228i	$0.623873\pi$
$80$	1.00000	0.111803
$81$	−11.0000	−1.22222
$82$	−4.00000	−0.441726
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	−2.00000	−0.218218
$85$	6.74456	0.731551
$86$	4.00000	0.431331
$87$	−17.4891	−1.87503
$88$	0	0
$89$	15.4891	1.64184	0.820922	−	0.571040i	$-0.193460\pi$
$89$	15.4891	1.64184	0.820922	+	0.571040i	$0.193460\pi$
$90$	−1.00000	−0.105409
$91$	6.74456	0.707022
$92$	−6.74456	−0.703169
$93$	9.48913	0.983976
$94$	−4.74456	−0.489364
$95$	6.74456	0.691978
$96$	−2.00000	−0.204124
$97$	−16.7446	−1.70015	−0.850076	−	0.526659i	$-0.823444\pi$
$97$	−16.7446	−1.70015	−0.850076	+	0.526659i	$0.823444\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−2.74456	−0.273094	−0.136547	−	0.990634i	$-0.543601\pi$
$101$	−2.74456	−0.273094	−0.136547	+	0.990634i	$0.543601\pi$
$102$	−13.4891	−1.33562
$103$	−0.744563	−0.0733639	−0.0366820	−	0.999327i	$-0.511679\pi$
$103$	−0.744563	−0.0733639	−0.0366820	+	0.999327i	$0.511679\pi$
$104$	6.74456	0.661359
$105$	−2.00000	−0.195180
$106$	12.7446	1.23786
$107$	12.0000	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$108$	−4.00000	−0.384900
$109$	18.2337	1.74647	0.873235	−	0.487299i	$-0.162018\pi$
$109$	18.2337	1.74647	0.873235	+	0.487299i	$0.162018\pi$
$110$	0	0
$111$	1.48913	0.141342
$112$	−1.00000	−0.0944911
$113$	10.0000	0.940721	0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000	0.940721	0.470360	+	0.882474i	$0.344124\pi$
$114$	−13.4891	−1.26337
$115$	−6.74456	−0.628934
$116$	−8.74456	−0.811912
$117$	−6.74456	−0.623535
$118$	8.74456	0.805002
$119$	−6.74456	−0.618273
$120$	−2.00000	−0.182574
$121$	0	0
$122$	1.25544	0.113662
$123$	8.00000	0.721336
$124$	4.74456	0.426074
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	0	0		−	1.00000i	$-0.5\pi$
$127$	0	0			1.00000i	$0.5\pi$
$128$	−1.00000	−0.0883883
$129$	−8.00000	−0.704361
$130$	6.74456	0.591537
$131$	2.74456	0.239794	0.119897	−	0.992786i	$-0.461744\pi$
$131$	2.74456	0.239794	0.119897	+	0.992786i	$0.461744\pi$
$132$	0	0
$133$	−6.74456	−0.584828
$134$	4.00000	0.345547
$135$	−4.00000	−0.344265
$136$	−6.74456	−0.578341
$137$	3.48913	0.298096	0.149048	−	0.988830i	$-0.452379\pi$
$137$	3.48913	0.298096	0.149048	+	0.988830i	$0.452379\pi$
$138$	13.4891	1.14827
$139$	−14.7446	−1.25062	−0.625309	−	0.780377i	$-0.715027\pi$
$139$	−14.7446	−1.25062	−0.625309	+	0.780377i	$0.715027\pi$
$140$	−1.00000	−0.0845154
$141$	9.48913	0.799129
$142$	4.00000	0.335673
$143$	0	0
$144$	1.00000	0.0833333
$145$	−8.74456	−0.726196
$146$	10.7446	0.889226
$147$	2.00000	0.164957
$148$	0.744563	0.0612027
$149$	0.744563	0.0609969	0.0304985	−	0.999535i	$-0.490291\pi$
$149$	0.744563	0.0609969	0.0304985	+	0.999535i	$0.490291\pi$
$150$	−2.00000	−0.163299
$151$	9.25544	0.753197	0.376598	−	0.926377i	$-0.377094\pi$
$151$	9.25544	0.753197	0.376598	+	0.926377i	$0.377094\pi$
$152$	−6.74456	−0.547056
$153$	6.74456	0.545266
$154$	0	0
$155$	4.74456	0.381092
$156$	−13.4891	−1.07999
$157$	0.510875	0.0407722	0.0203861	−	0.999792i	$-0.493510\pi$
$157$	0.510875	0.0407722	0.0203861	+	0.999792i	$0.493510\pi$
$158$	6.74456	0.536569
$159$	−25.4891	−2.02142
$160$	−1.00000	−0.0790569
$161$	6.74456	0.531546
$162$	11.0000	0.864242
$163$	−4.00000	−0.313304	−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000	−0.313304	−0.156652	+	0.987654i	$0.550070\pi$
$164$	4.00000	0.312348
$165$	0	0
$166$	8.00000	0.620920
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	2.00000	0.154303
$169$	32.4891	2.49916
$170$	−6.74456	−0.517284
$171$	6.74456	0.515770
$172$	−4.00000	−0.304997
$173$	−20.2337	−1.53834	−0.769169	−	0.639045i	$-0.779330\pi$
$173$	−20.2337	−1.53834	−0.769169	+	0.639045i	$0.779330\pi$
$174$	17.4891	1.32585
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−17.4891	−1.31456
$178$	−15.4891	−1.16096
$179$	−4.00000	−0.298974	−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000	−0.298974	−0.149487	+	0.988764i	$0.547762\pi$
$180$	1.00000	0.0745356
$181$	−19.4891	−1.44862	−0.724308	−	0.689477i	$-0.757840\pi$
$181$	−19.4891	−1.44862	−0.724308	+	0.689477i	$0.757840\pi$
$182$	−6.74456	−0.499940
$183$	−2.51087	−0.185609
$184$	6.74456	0.497216
$185$	0.744563	0.0547413
$186$	−9.48913	−0.695776
$187$	0	0
$188$	4.74456	0.346033
$189$	4.00000	0.290957
$190$	−6.74456	−0.489302
$191$	−16.0000	−1.15772	−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000	−1.15772	−0.578860	+	0.815427i	$0.696502\pi$
$192$	2.00000	0.144338
$193$	2.00000	0.143963	0.0719816	−	0.997406i	$-0.477068\pi$
$193$	2.00000	0.143963	0.0719816	+	0.997406i	$0.477068\pi$
$194$	16.7446	1.20219
$195$	−13.4891	−0.965976
$196$	1.00000	0.0714286
$197$	−10.0000	−0.712470	−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000	−0.712470	−0.356235	+	0.934396i	$0.615940\pi$
$198$	0	0
$199$	3.25544	0.230772	0.115386	−	0.993321i	$-0.463190\pi$
$199$	3.25544	0.230772	0.115386	+	0.993321i	$0.463190\pi$
$200$	−1.00000	−0.0707107
$201$	−8.00000	−0.564276
$202$	2.74456	0.193107
$203$	8.74456	0.613748
$204$	13.4891	0.944428
$205$	4.00000	0.279372
$206$	0.744563	0.0518761
$207$	−6.74456	−0.468780
$208$	−6.74456	−0.467651
$209$	0	0
$210$	2.00000	0.138013
$211$	12.0000	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$212$	−12.7446	−0.875300
$213$	−8.00000	−0.548151
$214$	−12.0000	−0.820303
$215$	−4.00000	−0.272798
$216$	4.00000	0.272166
$217$	−4.74456	−0.322082
$218$	−18.2337	−1.23494
$219$	−21.4891	−1.45210
$220$	0	0
$221$	−45.4891	−3.05993
$222$	−1.48913	−0.0999435
$223$	15.2554	1.02158	0.510790	−	0.859706i	$-0.329353\pi$
$223$	15.2554	1.02158	0.510790	+	0.859706i	$0.329353\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−10.0000	−0.665190
$227$	−20.0000	−1.32745	−0.663723	−	0.747978i	$-0.731025\pi$
$227$	−20.0000	−1.32745	−0.663723	+	0.747978i	$0.731025\pi$
$228$	13.4891	0.893339
$229$	−6.00000	−0.396491	−0.198246	−	0.980152i	$-0.563524\pi$
$229$	−6.00000	−0.396491	−0.198246	+	0.980152i	$0.563524\pi$
$230$	6.74456	0.444723
$231$	0	0
$232$	8.74456	0.574109
$233$	24.9783	1.63638	0.818190	−	0.574948i	$-0.194978\pi$
$233$	24.9783	1.63638	0.818190	+	0.574948i	$0.194978\pi$
$234$	6.74456	0.440906
$235$	4.74456	0.309501
$236$	−8.74456	−0.569223
$237$	−13.4891	−0.876213
$238$	6.74456	0.437185
$239$	14.7446	0.953746	0.476873	−	0.878972i	$-0.341770\pi$
$239$	14.7446	0.953746	0.476873	+	0.878972i	$0.341770\pi$
$240$	2.00000	0.129099
$241$	−20.0000	−1.28831	−0.644157	−	0.764894i	$-0.722792\pi$
$241$	−20.0000	−1.28831	−0.644157	+	0.764894i	$0.722792\pi$
$242$	0	0
$243$	−10.0000	−0.641500
$244$	−1.25544	−0.0803711
$245$	1.00000	0.0638877
$246$	−8.00000	−0.510061
$247$	−45.4891	−2.89440
$248$	−4.74456	−0.301280
$249$	−16.0000	−1.01396
$250$	−1.00000	−0.0632456
$251$	−26.2337	−1.65586	−0.827928	−	0.560835i	$-0.810480\pi$
$251$	−26.2337	−1.65586	−0.827928	+	0.560835i	$0.810480\pi$
$252$	−1.00000	−0.0629941
$253$	0	0
$254$	0	0
$255$	13.4891	0.844722
$256$	1.00000	0.0625000
$257$	−10.2337	−0.638360	−0.319180	−	0.947694i	$-0.603407\pi$
$257$	−10.2337	−0.638360	−0.319180	+	0.947694i	$0.603407\pi$
$258$	8.00000	0.498058
$259$	−0.744563	−0.0462649
$260$	−6.74456	−0.418280
$261$	−8.74456	−0.541275
$262$	−2.74456	−0.169560
$263$	−26.9783	−1.66355	−0.831775	−	0.555113i	$-0.812675\pi$
$263$	−26.9783	−1.66355	−0.831775	+	0.555113i	$0.812675\pi$
$264$	0	0
$265$	−12.7446	−0.782892
$266$	6.74456	0.413536
$267$	30.9783	1.89584
$268$	−4.00000	−0.244339
$269$	20.9783	1.27907	0.639533	−	0.768763i	$-0.279128\pi$
$269$	20.9783	1.27907	0.639533	+	0.768763i	$0.279128\pi$
$270$	4.00000	0.243432
$271$	−14.9783	−0.909864	−0.454932	−	0.890526i	$-0.650336\pi$
$271$	−14.9783	−0.909864	−0.454932	+	0.890526i	$0.650336\pi$
$272$	6.74456	0.408949
$273$	13.4891	0.816399
$274$	−3.48913	−0.210786
$275$	0	0
$276$	−13.4891	−0.811950
$277$	−15.4891	−0.930651	−0.465326	−	0.885140i	$-0.654063\pi$
$277$	−15.4891	−0.930651	−0.465326	+	0.885140i	$0.654063\pi$
$278$	14.7446	0.884320
$279$	4.74456	0.284050
$280$	1.00000	0.0597614
$281$	−14.0000	−0.835170	−0.417585	−	0.908638i	$-0.637123\pi$
$281$	−14.0000	−0.835170	−0.417585	+	0.908638i	$0.637123\pi$
$282$	−9.48913	−0.565069
$283$	−28.0000	−1.66443	−0.832214	−	0.554455i	$-0.812927\pi$
$283$	−28.0000	−1.66443	−0.832214	+	0.554455i	$0.812927\pi$
$284$	−4.00000	−0.237356
$285$	13.4891	0.799027
$286$	0	0
$287$	−4.00000	−0.236113
$288$	−1.00000	−0.0589256
$289$	28.4891	1.67583
$290$	8.74456	0.513498
$291$	−33.4891	−1.96317
$292$	−10.7446	−0.628778
$293$	−13.2554	−0.774391	−0.387195	−	0.921998i	$-0.626556\pi$
$293$	−13.2554	−0.774391	−0.387195	+	0.921998i	$0.626556\pi$
$294$	−2.00000	−0.116642
$295$	−8.74456	−0.509128
$296$	−0.744563	−0.0432768
$297$	0	0
$298$	−0.744563	−0.0431314
$299$	45.4891	2.63070
$300$	2.00000	0.115470
$301$	4.00000	0.230556
$302$	−9.25544	−0.532591
$303$	−5.48913	−0.315342
$304$	6.74456	0.386827
$305$	−1.25544	−0.0718861
$306$	−6.74456	−0.385561
$307$	1.48913	0.0849889	0.0424944	−	0.999097i	$-0.486470\pi$
$307$	1.48913	0.0849889	0.0424944	+	0.999097i	$0.486470\pi$
$308$	0	0
$309$	−1.48913	−0.0847134
$310$	−4.74456	−0.269473
$311$	−20.7446	−1.17632	−0.588158	−	0.808746i	$-0.700147\pi$
$311$	−20.7446	−1.17632	−0.588158	+	0.808746i	$0.700147\pi$
$312$	13.4891	0.763671
$313$	−2.23369	−0.126256	−0.0631278	−	0.998005i	$-0.520108\pi$
$313$	−2.23369	−0.126256	−0.0631278	+	0.998005i	$0.520108\pi$
$314$	−0.510875	−0.0288303
$315$	−1.00000	−0.0563436
$316$	−6.74456	−0.379411
$317$	2.23369	0.125456	0.0627282	−	0.998031i	$-0.480020\pi$
$317$	2.23369	0.125456	0.0627282	+	0.998031i	$0.480020\pi$
$318$	25.4891	1.42936
$319$	0	0
$320$	1.00000	0.0559017
$321$	24.0000	1.33955
$322$	−6.74456	−0.375860
$323$	45.4891	2.53108
$324$	−11.0000	−0.611111
$325$	−6.74456	−0.374121
$326$	4.00000	0.221540
$327$	36.4674	2.01665
$328$	−4.00000	−0.220863
$329$	−4.74456	−0.261576
$330$	0	0
$331$	14.9783	0.823279	0.411640	−	0.911347i	$-0.364956\pi$
$331$	14.9783	0.823279	0.411640	+	0.911347i	$0.364956\pi$
$332$	−8.00000	−0.439057
$333$	0.744563	0.0408018
$334$	0	0
$335$	−4.00000	−0.218543
$336$	−2.00000	−0.109109
$337$	−26.0000	−1.41631	−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000	−1.41631	−0.708155	+	0.706057i	$0.750472\pi$
$338$	−32.4891	−1.76718
$339$	20.0000	1.08625
$340$	6.74456	0.365775
$341$	0	0
$342$	−6.74456	−0.364704
$343$	−1.00000	−0.0539949
$344$	4.00000	0.215666
$345$	−13.4891	−0.726230
$346$	20.2337	1.08777
$347$	22.9783	1.23354	0.616769	−	0.787145i	$-0.288441\pi$
$347$	22.9783	1.23354	0.616769	+	0.787145i	$0.288441\pi$
$348$	−17.4891	−0.937516
$349$	−30.7446	−1.64572	−0.822859	−	0.568245i	$-0.807623\pi$
$349$	−30.7446	−1.64572	−0.822859	+	0.568245i	$0.807623\pi$
$350$	1.00000	0.0534522
$351$	26.9783	1.43999
$352$	0	0
$353$	8.74456	0.465426	0.232713	−	0.972545i	$-0.425240\pi$
$353$	8.74456	0.465426	0.232713	+	0.972545i	$0.425240\pi$
$354$	17.4891	0.929537
$355$	−4.00000	−0.212298
$356$	15.4891	0.820922
$357$	−13.4891	−0.713920
$358$	4.00000	0.211407
$359$	1.25544	0.0662594	0.0331297	−	0.999451i	$-0.489453\pi$
$359$	1.25544	0.0662594	0.0331297	+	0.999451i	$0.489453\pi$
$360$	−1.00000	−0.0527046
$361$	26.4891	1.39416
$362$	19.4891	1.02433
$363$	0	0
$364$	6.74456	0.353511
$365$	−10.7446	−0.562396
$366$	2.51087	0.131246
$367$	−8.74456	−0.456462	−0.228231	−	0.973607i	$-0.573294\pi$
$367$	−8.74456	−0.456462	−0.228231	+	0.973607i	$0.573294\pi$
$368$	−6.74456	−0.351585
$369$	4.00000	0.208232
$370$	−0.744563	−0.0387080
$371$	12.7446	0.661665
$372$	9.48913	0.491988
$373$	16.9783	0.879100	0.439550	−	0.898218i	$-0.355138\pi$
$373$	16.9783	0.879100	0.439550	+	0.898218i	$0.355138\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	−4.74456	−0.244682
$377$	58.9783	3.03753
$378$	−4.00000	−0.205738
$379$	−37.4891	−1.92569	−0.962844	−	0.270060i	$-0.912956\pi$
$379$	−37.4891	−1.92569	−0.962844	+	0.270060i	$0.912956\pi$
$380$	6.74456	0.345989
$381$	0	0
$382$	16.0000	0.818631
$383$	19.7228	1.00779	0.503894	−	0.863765i	$-0.331900\pi$
$383$	19.7228	1.00779	0.503894	+	0.863765i	$0.331900\pi$
$384$	−2.00000	−0.102062
$385$	0	0
$386$	−2.00000	−0.101797
$387$	−4.00000	−0.203331
$388$	−16.7446	−0.850076
$389$	−7.48913	−0.379714	−0.189857	−	0.981812i	$-0.560802\pi$
$389$	−7.48913	−0.379714	−0.189857	+	0.981812i	$0.560802\pi$
$390$	13.4891	0.683048
$391$	−45.4891	−2.30048
$392$	−1.00000	−0.0505076
$393$	5.48913	0.276890
$394$	10.0000	0.503793
$395$	−6.74456	−0.339356
$396$	0	0
$397$	35.4891	1.78115	0.890574	−	0.454838i	$-0.150303\pi$
$397$	35.4891	1.78115	0.890574	+	0.454838i	$0.150303\pi$
$398$	−3.25544	−0.163180
$399$	−13.4891	−0.675301
$400$	1.00000	0.0500000
$401$	23.4891	1.17299	0.586495	−	0.809953i	$-0.300507\pi$
$401$	23.4891	1.17299	0.586495	+	0.809953i	$0.300507\pi$
$402$	8.00000	0.399004
$403$	−32.0000	−1.59403
$404$	−2.74456	−0.136547
$405$	−11.0000	−0.546594
$406$	−8.74456	−0.433985
$407$	0	0
$408$	−13.4891	−0.667811
$409$	21.4891	1.06257	0.531284	−	0.847194i	$-0.321710\pi$
$409$	21.4891	1.06257	0.531284	+	0.847194i	$0.321710\pi$
$410$	−4.00000	−0.197546
$411$	6.97825	0.344212
$412$	−0.744563	−0.0366820
$413$	8.74456	0.430292
$414$	6.74456	0.331477
$415$	−8.00000	−0.392705
$416$	6.74456	0.330679
$417$	−29.4891	−1.44409
$418$	0	0
$419$	−0.744563	−0.0363743	−0.0181871	−	0.999835i	$-0.505789\pi$
$419$	−0.744563	−0.0363743	−0.0181871	+	0.999835i	$0.505789\pi$
$420$	−2.00000	−0.0975900
$421$	4.51087	0.219847	0.109923	−	0.993940i	$-0.464939\pi$
$421$	4.51087	0.219847	0.109923	+	0.993940i	$0.464939\pi$
$422$	−12.0000	−0.584151
$423$	4.74456	0.230689
$424$	12.7446	0.618931
$425$	6.74456	0.327159
$426$	8.00000	0.387601
$427$	1.25544	0.0607549
$428$	12.0000	0.580042
$429$	0	0
$430$	4.00000	0.192897
$431$	17.2554	0.831165	0.415583	−	0.909555i	$-0.363578\pi$
$431$	17.2554	0.831165	0.415583	+	0.909555i	$0.363578\pi$
$432$	−4.00000	−0.192450
$433$	36.7446	1.76583	0.882915	−	0.469532i	$-0.155577\pi$
$433$	36.7446	1.76583	0.882915	+	0.469532i	$0.155577\pi$
$434$	4.74456	0.227746
$435$	−17.4891	−0.838539
$436$	18.2337	0.873235
$437$	−45.4891	−2.17604
$438$	21.4891	1.02679
$439$	−14.9783	−0.714873	−0.357436	−	0.933937i	$-0.616349\pi$
$439$	−14.9783	−0.714873	−0.357436	+	0.933937i	$0.616349\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	45.4891	2.16370
$443$	−29.4891	−1.40107	−0.700535	−	0.713618i	$-0.747055\pi$
$443$	−29.4891	−1.40107	−0.700535	+	0.713618i	$0.747055\pi$
$444$	1.48913	0.0706708
$445$	15.4891	0.734255
$446$	−15.2554	−0.722366
$447$	1.48913	0.0704332
$448$	−1.00000	−0.0472456
$449$	−4.97825	−0.234938	−0.117469	−	0.993077i	$-0.537478\pi$
$449$	−4.97825	−0.234938	−0.117469	+	0.993077i	$0.537478\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	10.0000	0.470360
$453$	18.5109	0.869717
$454$	20.0000	0.938647
$455$	6.74456	0.316190
$456$	−13.4891	−0.631686
$457$	−3.48913	−0.163214	−0.0816072	−	0.996665i	$-0.526005\pi$
$457$	−3.48913	−0.163214	−0.0816072	+	0.996665i	$0.526005\pi$
$458$	6.00000	0.280362
$459$	−26.9783	−1.25924
$460$	−6.74456	−0.314467
$461$	−33.7228	−1.57063	−0.785314	−	0.619098i	$-0.787498\pi$
$461$	−33.7228	−1.57063	−0.785314	+	0.619098i	$0.787498\pi$
$462$	0	0
$463$	1.25544	0.0583451	0.0291726	−	0.999574i	$-0.490713\pi$
$463$	1.25544	0.0583451	0.0291726	+	0.999574i	$0.490713\pi$
$464$	−8.74456	−0.405956
$465$	9.48913	0.440048
$466$	−24.9783	−1.15710
$467$	16.9783	0.785660	0.392830	−	0.919611i	$-0.371496\pi$
$467$	16.9783	0.785660	0.392830	+	0.919611i	$0.371496\pi$
$468$	−6.74456	−0.311768
$469$	4.00000	0.184703
$470$	−4.74456	−0.218850
$471$	1.02175	0.0470797
$472$	8.74456	0.402501
$473$	0	0
$474$	13.4891	0.619576
$475$	6.74456	0.309462
$476$	−6.74456	−0.309137
$477$	−12.7446	−0.583533
$478$	−14.7446	−0.674401
$479$	41.4891	1.89569	0.947843	−	0.318737i	$-0.103259\pi$
$479$	41.4891	1.89569	0.947843	+	0.318737i	$0.103259\pi$
$480$	−2.00000	−0.0912871
$481$	−5.02175	−0.228972
$482$	20.0000	0.910975
$483$	13.4891	0.613776
$484$	0	0
$485$	−16.7446	−0.760331
$486$	10.0000	0.453609
$487$	9.25544	0.419404	0.209702	−	0.977765i	$-0.432751\pi$
$487$	9.25544	0.419404	0.209702	+	0.977765i	$0.432751\pi$
$488$	1.25544	0.0568310
$489$	−8.00000	−0.361773
$490$	−1.00000	−0.0451754
$491$	−30.9783	−1.39803	−0.699014	−	0.715108i	$-0.746378\pi$
$491$	−30.9783	−1.39803	−0.699014	+	0.715108i	$0.746378\pi$
$492$	8.00000	0.360668
$493$	−58.9783	−2.65625
$494$	45.4891	2.04665
$495$	0	0
$496$	4.74456	0.213037
$497$	4.00000	0.179425
$498$	16.0000	0.716977
$499$	−13.4891	−0.603856	−0.301928	−	0.953331i	$-0.597630\pi$
$499$	−13.4891	−0.603856	−0.301928	+	0.953331i	$0.597630\pi$
$500$	1.00000	0.0447214
$501$	0	0
$502$	26.2337	1.17087
$503$	−6.51087	−0.290306	−0.145153	−	0.989409i	$-0.546367\pi$
$503$	−6.51087	−0.290306	−0.145153	+	0.989409i	$0.546367\pi$
$504$	1.00000	0.0445435
$505$	−2.74456	−0.122131
$506$	0	0
$507$	64.9783	2.88579
$508$	0	0
$509$	−35.4891	−1.57303	−0.786514	−	0.617573i	$-0.788116\pi$
$509$	−35.4891	−1.57303	−0.786514	+	0.617573i	$0.788116\pi$
$510$	−13.4891	−0.597309
$511$	10.7446	0.475311
$512$	−1.00000	−0.0441942
$513$	−26.9783	−1.19112
$514$	10.2337	0.451389
$515$	−0.744563	−0.0328094
$516$	−8.00000	−0.352180
$517$	0	0
$518$	0.744563	0.0327142
$519$	−40.4674	−1.77632
$520$	6.74456	0.295769
$521$	−2.00000	−0.0876216	−0.0438108	−	0.999040i	$-0.513950\pi$
$521$	−2.00000	−0.0876216	−0.0438108	+	0.999040i	$0.513950\pi$
$522$	8.74456	0.382739
$523$	17.4891	0.764746	0.382373	−	0.924008i	$-0.375107\pi$
$523$	17.4891	0.764746	0.382373	+	0.924008i	$0.375107\pi$
$524$	2.74456	0.119897
$525$	−2.00000	−0.0872872
$526$	26.9783	1.17631
$527$	32.0000	1.39394
$528$	0	0
$529$	22.4891	0.977788
$530$	12.7446	0.553588
$531$	−8.74456	−0.379482
$532$	−6.74456	−0.292414
$533$	−26.9783	−1.16856
$534$	−30.9783	−1.34056
$535$	12.0000	0.518805
$536$	4.00000	0.172774
$537$	−8.00000	−0.345225
$538$	−20.9783	−0.904437
$539$	0	0
$540$	−4.00000	−0.172133
$541$	−1.76631	−0.0759397	−0.0379698	−	0.999279i	$-0.512089\pi$
$541$	−1.76631	−0.0759397	−0.0379698	+	0.999279i	$0.512089\pi$
$542$	14.9783	0.643371
$543$	−38.9783	−1.67272
$544$	−6.74456	−0.289171
$545$	18.2337	0.781045
$546$	−13.4891	−0.577281
$547$	−14.9783	−0.640424	−0.320212	−	0.947346i	$-0.603754\pi$
$547$	−14.9783	−0.640424	−0.320212	+	0.947346i	$0.603754\pi$
$548$	3.48913	0.149048
$549$	−1.25544	−0.0535808
$550$	0	0
$551$	−58.9783	−2.51256
$552$	13.4891	0.574135
$553$	6.74456	0.286808
$554$	15.4891	0.658070
$555$	1.48913	0.0632098
$556$	−14.7446	−0.625309
$557$	0.978251	0.0414498	0.0207249	−	0.999785i	$-0.493403\pi$
$557$	0.978251	0.0414498	0.0207249	+	0.999785i	$0.493403\pi$
$558$	−4.74456	−0.200853
$559$	26.9783	1.14106
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	14.0000	0.590554
$563$	−5.48913	−0.231339	−0.115670	−	0.993288i	$-0.536901\pi$
$563$	−5.48913	−0.231339	−0.115670	+	0.993288i	$0.536901\pi$
$564$	9.48913	0.399564
$565$	10.0000	0.420703
$566$	28.0000	1.17693
$567$	11.0000	0.461957
$568$	4.00000	0.167836
$569$	−16.5109	−0.692172	−0.346086	−	0.938203i	$-0.612489\pi$
$569$	−16.5109	−0.692172	−0.346086	+	0.938203i	$0.612489\pi$
$570$	−13.4891	−0.564997
$571$	17.4891	0.731897	0.365949	−	0.930635i	$-0.380745\pi$
$571$	17.4891	0.731897	0.365949	+	0.930635i	$0.380745\pi$
$572$	0	0
$573$	−32.0000	−1.33682
$574$	4.00000	0.166957
$575$	−6.74456	−0.281268
$576$	1.00000	0.0416667
$577$	−8.74456	−0.364041	−0.182020	−	0.983295i	$-0.558264\pi$
$577$	−8.74456	−0.364041	−0.182020	+	0.983295i	$0.558264\pi$
$578$	−28.4891	−1.18499
$579$	4.00000	0.166234
$580$	−8.74456	−0.363098
$581$	8.00000	0.331896
$582$	33.4891	1.38817
$583$	0	0
$584$	10.7446	0.444613
$585$	−6.74456	−0.278853
$586$	13.2554	0.547577
$587$	−4.97825	−0.205474	−0.102737	−	0.994709i	$-0.532760\pi$
$587$	−4.97825	−0.205474	−0.102737	+	0.994709i	$0.532760\pi$
$588$	2.00000	0.0824786
$589$	32.0000	1.31854
$590$	8.74456	0.360008
$591$	−20.0000	−0.822690
$592$	0.744563	0.0306013
$593$	40.2337	1.65220	0.826100	−	0.563524i	$-0.190555\pi$
$593$	40.2337	1.65220	0.826100	+	0.563524i	$0.190555\pi$
$594$	0	0
$595$	−6.74456	−0.276500
$596$	0.744563	0.0304985
$597$	6.51087	0.266472
$598$	−45.4891	−1.86019
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	−2.00000	−0.0816497
$601$	33.4891	1.36605	0.683025	−	0.730395i	$-0.260664\pi$
$601$	33.4891	1.36605	0.683025	+	0.730395i	$0.260664\pi$
$602$	−4.00000	−0.163028
$603$	−4.00000	−0.162893
$604$	9.25544	0.376598
$605$	0	0
$606$	5.48913	0.222980
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	−6.74456	−0.273528
$609$	17.4891	0.708695
$610$	1.25544	0.0508312
$611$	−32.0000	−1.29458
$612$	6.74456	0.272633
$613$	−11.4891	−0.464041	−0.232021	−	0.972711i	$-0.574534\pi$
$613$	−11.4891	−0.464041	−0.232021	+	0.972711i	$0.574534\pi$
$614$	−1.48913	−0.0600962
$615$	8.00000	0.322591
$616$	0	0
$617$	−10.0000	−0.402585	−0.201292	−	0.979531i	$-0.564514\pi$
$617$	−10.0000	−0.402585	−0.201292	+	0.979531i	$0.564514\pi$
$618$	1.48913	0.0599014
$619$	0.744563	0.0299265	0.0149632	−	0.999888i	$-0.495237\pi$
$619$	0.744563	0.0299265	0.0149632	+	0.999888i	$0.495237\pi$
$620$	4.74456	0.190546
$621$	26.9783	1.08260
$622$	20.7446	0.831781
$623$	−15.4891	−0.620559
$624$	−13.4891	−0.539997
$625$	1.00000	0.0400000
$626$	2.23369	0.0892761
$627$	0	0
$628$	0.510875	0.0203861
$629$	5.02175	0.200230
$630$	1.00000	0.0398410
$631$	−2.97825	−0.118562	−0.0592811	−	0.998241i	$-0.518881\pi$
$631$	−2.97825	−0.118562	−0.0592811	+	0.998241i	$0.518881\pi$
$632$	6.74456	0.268284
$633$	24.0000	0.953914
$634$	−2.23369	−0.0887111
$635$	0	0
$636$	−25.4891	−1.01071
$637$	−6.74456	−0.267229
$638$	0	0
$639$	−4.00000	−0.158238
$640$	−1.00000	−0.0395285
$641$	11.4891	0.453793	0.226897	−	0.973919i	$-0.427142\pi$
$641$	11.4891	0.453793	0.226897	+	0.973919i	$0.427142\pi$
$642$	−24.0000	−0.947204
$643$	46.4674	1.83249	0.916247	−	0.400613i	$-0.131203\pi$
$643$	46.4674	1.83249	0.916247	+	0.400613i	$0.131203\pi$
$644$	6.74456	0.265773
$645$	−8.00000	−0.315000
$646$	−45.4891	−1.78975
$647$	8.74456	0.343784	0.171892	−	0.985116i	$-0.445012\pi$
$647$	8.74456	0.343784	0.171892	+	0.985116i	$0.445012\pi$
$648$	11.0000	0.432121
$649$	0	0
$650$	6.74456	0.264544
$651$	−9.48913	−0.371908
$652$	−4.00000	−0.156652
$653$	15.7228	0.615281	0.307641	−	0.951503i	$-0.400461\pi$
$653$	15.7228	0.615281	0.307641	+	0.951503i	$0.400461\pi$
$654$	−36.4674	−1.42599
$655$	2.74456	0.107239
$656$	4.00000	0.156174
$657$	−10.7446	−0.419185
$658$	4.74456	0.184962
$659$	41.4891	1.61619	0.808093	−	0.589054i	$-0.200500\pi$
$659$	41.4891	1.61619	0.808093	+	0.589054i	$0.200500\pi$
$660$	0	0
$661$	22.0000	0.855701	0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000	0.855701	0.427850	+	0.903850i	$0.359271\pi$
$662$	−14.9783	−0.582146
$663$	−90.9783	−3.53330
$664$	8.00000	0.310460
$665$	−6.74456	−0.261543
$666$	−0.744563	−0.0288512
$667$	58.9783	2.28365
$668$	0	0
$669$	30.5109	1.17962
$670$	4.00000	0.154533
$671$	0	0
$672$	2.00000	0.0771517
$673$	−20.9783	−0.808652	−0.404326	−	0.914615i	$-0.632494\pi$
$673$	−20.9783	−0.808652	−0.404326	+	0.914615i	$0.632494\pi$
$674$	26.0000	1.00148
$675$	−4.00000	−0.153960
$676$	32.4891	1.24958
$677$	−36.2337	−1.39257	−0.696287	−	0.717764i	$-0.745166\pi$
$677$	−36.2337	−1.39257	−0.696287	+	0.717764i	$0.745166\pi$
$678$	−20.0000	−0.768095
$679$	16.7446	0.642597
$680$	−6.74456	−0.258642
$681$	−40.0000	−1.53280
$682$	0	0
$683$	0	0		−	1.00000i	$-0.5\pi$
$683$	0	0			1.00000i	$0.5\pi$
$684$	6.74456	0.257885
$685$	3.48913	0.133313
$686$	1.00000	0.0381802
$687$	−12.0000	−0.457829
$688$	−4.00000	−0.152499
$689$	85.9565	3.27468
$690$	13.4891	0.513522
$691$	1.76631	0.0671937	0.0335968	−	0.999435i	$-0.489304\pi$
$691$	1.76631	0.0671937	0.0335968	+	0.999435i	$0.489304\pi$
$692$	−20.2337	−0.769169
$693$	0	0
$694$	−22.9783	−0.872242
$695$	−14.7446	−0.559293
$696$	17.4891	0.662924
$697$	26.9783	1.02187
$698$	30.7446	1.16370
$699$	49.9565	1.88953
$700$	−1.00000	−0.0377964
$701$	−22.2337	−0.839755	−0.419877	−	0.907581i	$-0.637927\pi$
$701$	−22.2337	−0.839755	−0.419877	+	0.907581i	$0.637927\pi$
$702$	−26.9783	−1.01823
$703$	5.02175	0.189399
$704$	0	0
$705$	9.48913	0.357381
$706$	−8.74456	−0.329106
$707$	2.74456	0.103220
$708$	−17.4891	−0.657282
$709$	0.510875	0.0191863	0.00959315	−	0.999954i	$-0.496946\pi$
$709$	0.510875	0.0191863	0.00959315	+	0.999954i	$0.496946\pi$
$710$	4.00000	0.150117
$711$	−6.74456	−0.252941
$712$	−15.4891	−0.580480
$713$	−32.0000	−1.19841
$714$	13.4891	0.504818
$715$	0	0
$716$	−4.00000	−0.149487
$717$	29.4891	1.10129
$718$	−1.25544	−0.0468525
$719$	7.72281	0.288012	0.144006	−	0.989577i	$-0.454001\pi$
$719$	7.72281	0.288012	0.144006	+	0.989577i	$0.454001\pi$
$720$	1.00000	0.0372678
$721$	0.744563	0.0277290
$722$	−26.4891	−0.985823
$723$	−40.0000	−1.48762
$724$	−19.4891	−0.724308
$725$	−8.74456	−0.324765
$726$	0	0
$727$	14.2337	0.527898	0.263949	−	0.964537i	$-0.414975\pi$
$727$	14.2337	0.527898	0.263949	+	0.964537i	$0.414975\pi$
$728$	−6.74456	−0.249970
$729$	13.0000	0.481481
$730$	10.7446	0.397674
$731$	−26.9783	−0.997827
$732$	−2.51087	−0.0928046
$733$	16.2337	0.599605	0.299802	−	0.954001i	$-0.403079\pi$
$733$	16.2337	0.599605	0.299802	+	0.954001i	$0.403079\pi$
$734$	8.74456	0.322768
$735$	2.00000	0.0737711
$736$	6.74456	0.248608
$737$	0	0
$738$	−4.00000	−0.147242
$739$	30.9783	1.13955	0.569777	−	0.821800i	$-0.307030\pi$
$739$	30.9783	1.13955	0.569777	+	0.821800i	$0.307030\pi$
$740$	0.744563	0.0273707
$741$	−90.9783	−3.34217
$742$	−12.7446	−0.467868
$743$	−26.9783	−0.989736	−0.494868	−	0.868968i	$-0.664784\pi$
$743$	−26.9783	−0.989736	−0.494868	+	0.868968i	$0.664784\pi$
$744$	−9.48913	−0.347888
$745$	0.744563	0.0272787
$746$	−16.9783	−0.621618
$747$	−8.00000	−0.292705
$748$	0	0
$749$	−12.0000	−0.438470
$750$	−2.00000	−0.0730297
$751$	20.0000	0.729810	0.364905	−	0.931045i	$-0.381101\pi$
$751$	20.0000	0.729810	0.364905	+	0.931045i	$0.381101\pi$
$752$	4.74456	0.173016
$753$	−52.4674	−1.91202
$754$	−58.9783	−2.14786
$755$	9.25544	0.336840
$756$	4.00000	0.145479
$757$	−19.2554	−0.699851	−0.349925	−	0.936778i	$-0.613793\pi$
$757$	−19.2554	−0.699851	−0.349925	+	0.936778i	$0.613793\pi$
$758$	37.4891	1.36167
$759$	0	0
$760$	−6.74456	−0.244651
$761$	29.4891	1.06898	0.534490	−	0.845175i	$-0.320504\pi$
$761$	29.4891	1.06898	0.534490	+	0.845175i	$0.320504\pi$
$762$	0	0
$763$	−18.2337	−0.660104
$764$	−16.0000	−0.578860
$765$	6.74456	0.243850
$766$	−19.7228	−0.712614
$767$	58.9783	2.12958
$768$	2.00000	0.0721688
$769$	8.00000	0.288487	0.144244	−	0.989542i	$-0.453925\pi$
$769$	8.00000	0.288487	0.144244	+	0.989542i	$0.453925\pi$
$770$	0	0
$771$	−20.4674	−0.737115
$772$	2.00000	0.0719816
$773$	−51.4891	−1.85194	−0.925968	−	0.377603i	$-0.876748\pi$
$773$	−51.4891	−1.85194	−0.925968	+	0.377603i	$0.876748\pi$
$774$	4.00000	0.143777
$775$	4.74456	0.170430
$776$	16.7446	0.601095
$777$	−1.48913	−0.0534221
$778$	7.48913	0.268498
$779$	26.9783	0.966596
$780$	−13.4891	−0.482988
$781$	0	0
$782$	45.4891	1.62669
$783$	34.9783	1.25002
$784$	1.00000	0.0357143
$785$	0.510875	0.0182339
$786$	−5.48913	−0.195791
$787$	−5.48913	−0.195666	−0.0978331	−	0.995203i	$-0.531191\pi$
$787$	−5.48913	−0.195666	−0.0978331	+	0.995203i	$0.531191\pi$
$788$	−10.0000	−0.356235
$789$	−53.9565	−1.92090
$790$	6.74456	0.239961
$791$	−10.0000	−0.355559
$792$	0	0
$793$	8.46738	0.300685
$794$	−35.4891	−1.25946
$795$	−25.4891	−0.904006
$796$	3.25544	0.115386
$797$	−42.4674	−1.50427	−0.752136	−	0.659008i	$-0.770976\pi$
$797$	−42.4674	−1.50427	−0.752136	+	0.659008i	$0.770976\pi$
$798$	13.4891	0.477510
$799$	32.0000	1.13208
$800$	−1.00000	−0.0353553
$801$	15.4891	0.547281
$802$	−23.4891	−0.829430
$803$	0	0
$804$	−8.00000	−0.282138
$805$	6.74456	0.237715
$806$	32.0000	1.12715
$807$	41.9565	1.47694
$808$	2.74456	0.0965534
$809$	−34.4674	−1.21181	−0.605904	−	0.795538i	$-0.707189\pi$
$809$	−34.4674	−1.21181	−0.605904	+	0.795538i	$0.707189\pi$
$810$	11.0000	0.386501
$811$	18.7446	0.658211	0.329105	−	0.944293i	$-0.393253\pi$
$811$	18.7446	0.658211	0.329105	+	0.944293i	$0.393253\pi$
$812$	8.74456	0.306874
$813$	−29.9565	−1.05062
$814$	0	0
$815$	−4.00000	−0.140114
$816$	13.4891	0.472214
$817$	−26.9783	−0.943850
$818$	−21.4891	−0.751350
$819$	6.74456	0.235674
$820$	4.00000	0.139686
$821$	−7.72281	−0.269528	−0.134764	−	0.990878i	$-0.543028\pi$
$821$	−7.72281	−0.269528	−0.134764	+	0.990878i	$0.543028\pi$
$822$	−6.97825	−0.243394
$823$	7.76631	0.270717	0.135358	−	0.990797i	$-0.456781\pi$
$823$	7.76631	0.270717	0.135358	+	0.990797i	$0.456781\pi$
$824$	0.744563	0.0259381
$825$	0	0
$826$	−8.74456	−0.304262
$827$	−4.00000	−0.139094	−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000	−0.139094	−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−6.74456	−0.234390
$829$	14.4674	0.502473	0.251236	−	0.967926i	$-0.419163\pi$
$829$	14.4674	0.502473	0.251236	+	0.967926i	$0.419163\pi$
$830$	8.00000	0.277684
$831$	−30.9783	−1.07462
$832$	−6.74456	−0.233826
$833$	6.74456	0.233685
$834$	29.4891	1.02112
$835$	0	0
$836$	0	0
$837$	−18.9783	−0.655984
$838$	0.744563	0.0257205
$839$	−3.25544	−0.112390	−0.0561951	−	0.998420i	$-0.517897\pi$
$839$	−3.25544	−0.112390	−0.0561951	+	0.998420i	$0.517897\pi$
$840$	2.00000	0.0690066
$841$	47.4674	1.63681
$842$	−4.51087	−0.155455
$843$	−28.0000	−0.964371
$844$	12.0000	0.413057
$845$	32.4891	1.11766
$846$	−4.74456	−0.163121
$847$	0	0
$848$	−12.7446	−0.437650
$849$	−56.0000	−1.92192
$850$	−6.74456	−0.231337
$851$	−5.02175	−0.172143
$852$	−8.00000	−0.274075
$853$	22.7446	0.778759	0.389379	−	0.921077i	$-0.372689\pi$
$853$	22.7446	0.778759	0.389379	+	0.921077i	$0.372689\pi$
$854$	−1.25544	−0.0429602
$855$	6.74456	0.230659
$856$	−12.0000	−0.410152
$857$	43.2119	1.47609	0.738046	−	0.674751i	$-0.235749\pi$
$857$	43.2119	1.47609	0.738046	+	0.674751i	$0.235749\pi$
$858$	0	0
$859$	−29.2119	−0.996698	−0.498349	−	0.866976i	$-0.666060\pi$
$859$	−29.2119	−0.996698	−0.498349	+	0.866976i	$0.666060\pi$
$860$	−4.00000	−0.136399
$861$	−8.00000	−0.272639
$862$	−17.2554	−0.587723
$863$	−40.2337	−1.36957	−0.684785	−	0.728745i	$-0.740104\pi$
$863$	−40.2337	−1.36957	−0.684785	+	0.728745i	$0.740104\pi$
$864$	4.00000	0.136083
$865$	−20.2337	−0.687966
$866$	−36.7446	−1.24863
$867$	56.9783	1.93508
$868$	−4.74456	−0.161041
$869$	0	0
$870$	17.4891	0.592937
$871$	26.9783	0.914123
$872$	−18.2337	−0.617471
$873$	−16.7446	−0.566718
$874$	45.4891	1.53869
$875$	−1.00000	−0.0338062
$876$	−21.4891	−0.726050
$877$	26.4674	0.893740	0.446870	−	0.894599i	$-0.352539\pi$
$877$	26.4674	0.893740	0.446870	+	0.894599i	$0.352539\pi$
$878$	14.9783	0.505491
$879$	−26.5109	−0.894190
$880$	0	0
$881$	−55.4891	−1.86948	−0.934738	−	0.355338i	$-0.884366\pi$
$881$	−55.4891	−1.86948	−0.934738	+	0.355338i	$0.884366\pi$
$882$	−1.00000	−0.0336718
$883$	−8.00000	−0.269221	−0.134611	−	0.990899i	$-0.542978\pi$
$883$	−8.00000	−0.269221	−0.134611	+	0.990899i	$0.542978\pi$
$884$	−45.4891	−1.52996
$885$	−17.4891	−0.587891
$886$	29.4891	0.990707
$887$	41.4891	1.39307	0.696534	−	0.717524i	$-0.254724\pi$
$887$	41.4891	1.39307	0.696534	+	0.717524i	$0.254724\pi$
$888$	−1.48913	−0.0499718
$889$	0	0
$890$	−15.4891	−0.519197
$891$	0	0
$892$	15.2554	0.510790
$893$	32.0000	1.07084
$894$	−1.48913	−0.0498038
$895$	−4.00000	−0.133705
$896$	1.00000	0.0334077
$897$	90.9783	3.03768
$898$	4.97825	0.166126
$899$	−41.4891	−1.38374
$900$	1.00000	0.0333333
$901$	−85.9565	−2.86363
$902$	0	0
$903$	8.00000	0.266223
$904$	−10.0000	−0.332595
$905$	−19.4891	−0.647840
$906$	−18.5109	−0.614983
$907$	−14.5109	−0.481826	−0.240913	−	0.970547i	$-0.577447\pi$
$907$	−14.5109	−0.481826	−0.240913	+	0.970547i	$0.577447\pi$
$908$	−20.0000	−0.663723
$909$	−2.74456	−0.0910314
$910$	−6.74456	−0.223580
$911$	20.0000	0.662630	0.331315	−	0.943520i	$-0.392508\pi$
$911$	20.0000	0.662630	0.331315	+	0.943520i	$0.392508\pi$
$912$	13.4891	0.446670
$913$	0	0
$914$	3.48913	0.115410
$915$	−2.51087	−0.0830070
$916$	−6.00000	−0.198246
$917$	−2.74456	−0.0906334
$918$	26.9783	0.890415
$919$	55.2119	1.82127	0.910637	−	0.413207i	$-0.135592\pi$
$919$	55.2119	1.82127	0.910637	+	0.413207i	$0.135592\pi$
$920$	6.74456	0.222362
$921$	2.97825	0.0981367
$922$	33.7228	1.11060
$923$	26.9783	0.888000
$924$	0	0
$925$	0.744563	0.0244811
$926$	−1.25544	−0.0412562
$927$	−0.744563	−0.0244546
$928$	8.74456	0.287054
$929$	−28.9783	−0.950746	−0.475373	−	0.879784i	$-0.657687\pi$
$929$	−28.9783	−0.950746	−0.475373	+	0.879784i	$0.657687\pi$
$930$	−9.48913	−0.311161
$931$	6.74456	0.221044
$932$	24.9783	0.818190
$933$	−41.4891	−1.35829
$934$	−16.9783	−0.555545
$935$	0	0
$936$	6.74456	0.220453
$937$	18.7446	0.612358	0.306179	−	0.951974i	$-0.400949\pi$
$937$	18.7446	0.612358	0.306179	+	0.951974i	$0.400949\pi$
$938$	−4.00000	−0.130605
$939$	−4.46738	−0.145787
$940$	4.74456	0.154751
$941$	−12.2337	−0.398807	−0.199403	−	0.979917i	$-0.563900\pi$
$941$	−12.2337	−0.398807	−0.199403	+	0.979917i	$0.563900\pi$
$942$	−1.02175	−0.0332904
$943$	−26.9783	−0.878533
$944$	−8.74456	−0.284611
$945$	4.00000	0.130120
$946$	0	0
$947$	−8.00000	−0.259965	−0.129983	−	0.991516i	$-0.541492\pi$
$947$	−8.00000	−0.259965	−0.129983	+	0.991516i	$0.541492\pi$
$948$	−13.4891	−0.438106
$949$	72.4674	2.35239
$950$	−6.74456	−0.218823
$951$	4.46738	0.144865
$952$	6.74456	0.218593
$953$	−6.00000	−0.194359	−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000	−0.194359	−0.0971795	+	0.995267i	$0.530982\pi$
$954$	12.7446	0.412620
$955$	−16.0000	−0.517748
$956$	14.7446	0.476873
$957$	0	0
$958$	−41.4891	−1.34045
$959$	−3.48913	−0.112670
$960$	2.00000	0.0645497
$961$	−8.48913	−0.273843
$962$	5.02175	0.161908
$963$	12.0000	0.386695
$964$	−20.0000	−0.644157
$965$	2.00000	0.0643823
$966$	−13.4891	−0.434005
$967$	50.9783	1.63935	0.819675	−	0.572829i	$-0.194154\pi$
$967$	50.9783	1.63935	0.819675	+	0.572829i	$0.194154\pi$
$968$	0	0
$969$	90.9783	2.92264
$970$	16.7446	0.537636
$971$	19.7228	0.632935	0.316468	−	0.948603i	$-0.397503\pi$
$971$	19.7228	0.632935	0.316468	+	0.948603i	$0.397503\pi$
$972$	−10.0000	−0.320750
$973$	14.7446	0.472689
$974$	−9.25544	−0.296563
$975$	−13.4891	−0.431998
$976$	−1.25544	−0.0401856
$977$	12.9783	0.415211	0.207606	−	0.978213i	$-0.433433\pi$
$977$	12.9783	0.415211	0.207606	+	0.978213i	$0.433433\pi$
$978$	8.00000	0.255812
$979$	0	0
$980$	1.00000	0.0319438
$981$	18.2337	0.582157
$982$	30.9783	0.988556
$983$	2.23369	0.0712436	0.0356218	−	0.999365i	$-0.488659\pi$
$983$	2.23369	0.0712436	0.0356218	+	0.999365i	$0.488659\pi$
$984$	−8.00000	−0.255031
$985$	−10.0000	−0.318626
$986$	58.9783	1.87825
$987$	−9.48913	−0.302042
$988$	−45.4891	−1.44720
$989$	26.9783	0.857858
$990$	0	0
$991$	1.48913	0.0473036	0.0236518	−	0.999720i	$-0.492471\pi$
$991$	1.48913	0.0473036	0.0236518	+	0.999720i	$0.492471\pi$
$992$	−4.74456	−0.150640
$993$	29.9565	0.950641
$994$	−4.00000	−0.126872
$995$	3.25544	0.103204
$996$	−16.0000	−0.506979
$997$	−39.2119	−1.24185	−0.620927	−	0.783868i	$-0.713244\pi$
$997$	−39.2119	−1.24185	−0.620927	+	0.783868i	$0.713244\pi$
$998$	13.4891	0.426991
$999$	−2.97825	−0.0942277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.bu.1.1		2
11.10	odd	2		770.2.a.k.1.2	✓	2
33.32	even	2		6930.2.a.bo.1.2		2
44.43	even	2		6160.2.a.r.1.2		2
55.32	even	4		3850.2.c.y.1849.3		4
55.43	even	4		3850.2.c.y.1849.2		4
55.54	odd	2		3850.2.a.bc.1.1		2
77.76	even	2		5390.2.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.a.k.1.2	✓	2	11.10	odd	2
3850.2.a.bc.1.1		2	55.54	odd	2
3850.2.c.y.1849.2		4	55.43	even	4
3850.2.c.y.1849.3		4	55.32	even	4
5390.2.a.bq.1.1		2	77.76	even	2
6160.2.a.r.1.2		2	44.43	even	2
6930.2.a.bo.1.2		2	33.32	even	2
8470.2.a.bu.1.1		2	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.00000 q^{12} -6.74456 q^{13} +1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +6.74456 q^{17} -1.00000 q^{18} +6.74456 q^{19} +1.00000 q^{20} -2.00000 q^{21} -6.74456 q^{23} -2.00000 q^{24} +1.00000 q^{25} +6.74456 q^{26} -4.00000 q^{27} -1.00000 q^{28} -8.74456 q^{29} -2.00000 q^{30} +4.74456 q^{31} -1.00000 q^{32} -6.74456 q^{34} -1.00000 q^{35} +1.00000 q^{36} +0.744563 q^{37} -6.74456 q^{38} -13.4891 q^{39} -1.00000 q^{40} +4.00000 q^{41} +2.00000 q^{42} -4.00000 q^{43} +1.00000 q^{45} +6.74456 q^{46} +4.74456 q^{47} +2.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +13.4891 q^{51} -6.74456 q^{52} -12.7446 q^{53} +4.00000 q^{54} +1.00000 q^{56} +13.4891 q^{57} +8.74456 q^{58} -8.74456 q^{59} +2.00000 q^{60} -1.25544 q^{61} -4.74456 q^{62} -1.00000 q^{63} +1.00000 q^{64} -6.74456 q^{65} -4.00000 q^{67} +6.74456 q^{68} -13.4891 q^{69} +1.00000 q^{70} -4.00000 q^{71} -1.00000 q^{72} -10.7446 q^{73} -0.744563 q^{74} +2.00000 q^{75} +6.74456 q^{76} +13.4891 q^{78} -6.74456 q^{79} +1.00000 q^{80} -11.0000 q^{81} -4.00000 q^{82} -8.00000 q^{83} -2.00000 q^{84} +6.74456 q^{85} +4.00000 q^{86} -17.4891 q^{87} +15.4891 q^{89} -1.00000 q^{90} +6.74456 q^{91} -6.74456 q^{92} +9.48913 q^{93} -4.74456 q^{94} +6.74456 q^{95} -2.00000 q^{96} -16.7446 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 4 q^{3} + 2 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{12} - 2 q^{13} + 2 q^{14} + 4 q^{15} + 2 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} - 4 q^{21} - 2 q^{23} - 4 q^{24} + 2 q^{25} + 2 q^{26} - 8 q^{27} - 2 q^{28} - 6 q^{29} - 4 q^{30} - 2 q^{31} - 2 q^{32} - 2 q^{34} - 2 q^{35} + 2 q^{36} - 10 q^{37} - 2 q^{38} - 4 q^{39} - 2 q^{40} + 8 q^{41} + 4 q^{42} - 8 q^{43} + 2 q^{45} + 2 q^{46} - 2 q^{47} + 4 q^{48} + 2 q^{49} - 2 q^{50} + 4 q^{51} - 2 q^{52} - 14 q^{53} + 8 q^{54} + 2 q^{56} + 4 q^{57} + 6 q^{58} - 6 q^{59} + 4 q^{60} - 14 q^{61} + 2 q^{62} - 2 q^{63} + 2 q^{64} - 2 q^{65} - 8 q^{67} + 2 q^{68} - 4 q^{69} + 2 q^{70} - 8 q^{71} - 2 q^{72} - 10 q^{73} + 10 q^{74} + 4 q^{75} + 2 q^{76} + 4 q^{78} - 2 q^{79} + 2 q^{80} - 22 q^{81} - 8 q^{82} - 16 q^{83} - 4 q^{84} + 2 q^{85} + 8 q^{86} - 12 q^{87} + 8 q^{89} - 2 q^{90} + 2 q^{91} - 2 q^{92} - 4 q^{93} + 2 q^{94} + 2 q^{95} - 4 q^{96} - 22 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 4 * q^3 + 2 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^12 - 2 * q^13 + 2 * q^14 + 4 * q^15 + 2 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 - 4 * q^21 - 2 * q^23 - 4 * q^24 + 2 * q^25 + 2 * q^26 - 8 * q^27 - 2 * q^28 - 6 * q^29 - 4 * q^30 - 2 * q^31 - 2 * q^32 - 2 * q^34 - 2 * q^35 + 2 * q^36 - 10 * q^37 - 2 * q^38 - 4 * q^39 - 2 * q^40 + 8 * q^41 + 4 * q^42 - 8 * q^43 + 2 * q^45 + 2 * q^46 - 2 * q^47 + 4 * q^48 + 2 * q^49 - 2 * q^50 + 4 * q^51 - 2 * q^52 - 14 * q^53 + 8 * q^54 + 2 * q^56 + 4 * q^57 + 6 * q^58 - 6 * q^59 + 4 * q^60 - 14 * q^61 + 2 * q^62 - 2 * q^63 + 2 * q^64 - 2 * q^65 - 8 * q^67 + 2 * q^68 - 4 * q^69 + 2 * q^70 - 8 * q^71 - 2 * q^72 - 10 * q^73 + 10 * q^74 + 4 * q^75 + 2 * q^76 + 4 * q^78 - 2 * q^79 + 2 * q^80 - 22 * q^81 - 8 * q^82 - 16 * q^83 - 4 * q^84 + 2 * q^85 + 8 * q^86 - 12 * q^87 + 8 * q^89 - 2 * q^90 + 2 * q^91 - 2 * q^92 - 4 * q^93 + 2 * q^94 + 2 * q^95 - 4 * q^96 - 22 * q^97 - 2 * q^98

Introduction

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