LMFDB - Embedded newform 891.2.f.f.487.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, minimal)

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:	no
Analytic conductor:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.3
Character	$\chi$	$=$	891.487
Dual form			891.2.f.f.730.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16387 + 0.845603i) q^{2} +(0.0215212 - 0.0662354i) q^{4} +(2.82229 + 2.05051i) q^{5} +(-0.104399 + 0.321307i) q^{7} +(-0.858159 - 2.64114i) q^{8} +O(q^{10})$	\(q+(-1.16387 + 0.845603i) q^{2} +(0.0215212 - 0.0662354i) q^{4} +(2.82229 + 2.05051i) q^{5} +(-0.104399 + 0.321307i) q^{7} +(-0.858159 - 2.64114i) q^{8} -5.01870 q^{10} +(2.70377 - 1.92084i) q^{11} +(-0.935670 + 0.679804i) q^{13} +(-0.150191 - 0.462240i) q^{14} +(3.34483 + 2.43016i) q^{16} +(3.32650 + 2.41684i) q^{17} +(1.38230 + 4.25428i) q^{19} +(0.196555 - 0.142806i) q^{20} +(-1.52258 + 4.52193i) q^{22} +5.28243 q^{23} +(2.21562 + 6.81898i) q^{25} +(0.514156 - 1.58241i) q^{26} +(0.0190351 + 0.0138298i) q^{28} +(1.63104 - 5.01982i) q^{29} +(-4.57436 + 3.32347i) q^{31} -0.393789 q^{32} -5.91531 q^{34} +(-0.953487 + 0.692749i) q^{35} +(1.10852 - 3.41166i) q^{37} +(-5.20626 - 3.78257i) q^{38} +(2.99372 - 9.21372i) q^{40} +(-3.45020 - 10.6186i) q^{41} -1.50787 q^{43} +(-0.0690391 - 0.220424i) q^{44} +(-6.14808 + 4.46684i) q^{46} +(2.72593 + 8.38956i) q^{47} +(5.57078 + 4.04741i) q^{49} +(-8.34485 - 6.06289i) q^{50} +(0.0248904 + 0.0766047i) q^{52} +(-1.63163 + 1.18545i) q^{53} +(11.5695 + 0.122962i) q^{55} +0.938208 q^{56} +(2.34645 + 7.22164i) q^{58} +(-3.56887 + 10.9839i) q^{59} +(-6.37211 - 4.62961i) q^{61} +(2.51364 - 7.73619i) q^{62} +(-6.23134 + 4.52733i) q^{64} -4.03468 q^{65} -4.18422 q^{67} +(0.231671 - 0.168319i) q^{68} +(0.523947 - 1.61254i) q^{70} +(-1.95860 - 1.42300i) q^{71} +(-1.04183 + 3.20643i) q^{73} +(1.59474 + 4.90810i) q^{74} +0.311533 q^{76} +(0.334907 + 1.06927i) q^{77} +(-6.90716 + 5.01835i) q^{79} +(4.45700 + 13.7172i) q^{80} +(12.9947 + 9.44124i) q^{82} +(9.17143 + 6.66344i) q^{83} +(4.43257 + 13.6421i) q^{85} +(1.75497 - 1.27506i) q^{86} +(-7.39347 - 5.49266i) q^{88} -3.45994 q^{89} +(-0.120743 - 0.371608i) q^{91} +(0.113684 - 0.349884i) q^{92} +(-10.2669 - 7.45932i) q^{94} +(-4.82221 + 14.8412i) q^{95} +(10.5482 - 7.66375i) q^{97} -9.90618 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8}+O(q^{10}) $ 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8	$ 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{11} + 11 q^{13} + 10 q^{14} + 9 q^{16} - 10 q^{17} + 4 q^{19} + 45 q^{20} + 16 q^{22} - 20 q^{23} - 11 q^{25} - 6 q^{26} - 27 q^{28} + 23 q^{29} - 3 q^{31} - 18 q^{32} - 8 q^{34} + 9 q^{35} - 21 q^{37} + q^{38} + 25 q^{40} - 10 q^{41} + 8 q^{43} + 19 q^{44} - 9 q^{46} + 34 q^{47} - q^{49} + 27 q^{52} + 2 q^{53} + 9 q^{55} - 114 q^{56} - q^{58} + 16 q^{59} + 3 q^{61} + 92 q^{62} + 13 q^{64} - 84 q^{65} - 10 q^{67} + 23 q^{68} + 46 q^{70} - 24 q^{71} - 20 q^{73} - 68 q^{74} - 16 q^{76} + 26 q^{77} - 19 q^{79} - 28 q^{80} + 47 q^{82} - 7 q^{83} - 25 q^{85} + 77 q^{86} - 18 q^{88} - 28 q^{89} + 10 q^{91} - 50 q^{92} + 63 q^{94} + 77 q^{95} + 33 q^{97} - 164 q^{98}+O(q^{100}) $ 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8 - 4 * q^10 + 2 * q^11 + 11 * q^13 + 10 * q^14 + 9 * q^16 - 10 * q^17 + 4 * q^19 + 45 * q^20 + 16 * q^22 - 20 * q^23 - 11 * q^25 - 6 * q^26 - 27 * q^28 + 23 * q^29 - 3 * q^31 - 18 * q^32 - 8 * q^34 + 9 * q^35 - 21 * q^37 + q^38 + 25 * q^40 - 10 * q^41 + 8 * q^43 + 19 * q^44 - 9 * q^46 + 34 * q^47 - q^49 + 27 * q^52 + 2 * q^53 + 9 * q^55 - 114 * q^56 - q^58 + 16 * q^59 + 3 * q^61 + 92 * q^62 + 13 * q^64 - 84 * q^65 - 10 * q^67 + 23 * q^68 + 46 * q^70 - 24 * q^71 - 20 * q^73 - 68 * q^74 - 16 * q^76 + 26 * q^77 - 19 * q^79 - 28 * q^80 + 47 * q^82 - 7 * q^83 - 25 * q^85 + 77 * q^86 - 18 * q^88 - 28 * q^89 + 10 * q^91 - 50 * q^92 + 63 * q^94 + 77 * q^95 + 33 * q^97 - 164 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−1.16387	+	0.845603i	−0.822982	+	0.597932i	−0.917565	−	0.397585i	$-0.869848\pi$
$2$	−1.16387	+	0.845603i	−0.822982	+	0.597932i	0.0945829	+	0.995517i	$0.469848\pi$
$3$		0			0
$3$		0			0
$4$	0.0215212	−	0.0662354i	0.0107606	−	0.0331177i
$5$	2.82229	+	2.05051i	1.26216	+	0.917017i	0.998862	−	0.0476966i	$-0.0151881\pi$
$5$	2.82229	+	2.05051i	1.26216	+	0.917017i	0.263303	+	0.964713i	$0.415188\pi$
$6$		0			0
$7$	−0.104399	+	0.321307i	−0.0394591	+	0.121443i	−0.968846	−	0.247665i	$-0.920337\pi$
$7$	−0.104399	+	0.321307i	−0.0394591	+	0.121443i	0.929387	+	0.369108i	$0.120337\pi$
$8$	−0.858159	−	2.64114i	−0.303405	−	0.933784i
$9$		0			0
$10$	−5.01870			−1.58705
$11$	2.70377	−	1.92084i	0.815218	−	0.579154i
$11$	2.70377	−	1.92084i	0.815218	−	0.579154i
$12$		0			0
$13$	−0.935670	+	0.679804i	−0.259508	+	0.188544i	−0.709930	−	0.704272i	$-0.751274\pi$
$13$	−0.935670	+	0.679804i	−0.259508	+	0.188544i	0.450422	+	0.892816i	$0.351274\pi$
$14$	−0.150191	−	0.462240i	−0.0401402	−	0.123539i
$15$		0			0
$16$	3.34483	+	2.43016i	0.836208	+	0.607540i
$17$	3.32650	+	2.41684i	0.806795	+	0.586171i	0.912900	−	0.408184i	$-0.133838\pi$
$17$	3.32650	+	2.41684i	0.806795	+	0.586171i	−0.106105	+	0.994355i	$0.533838\pi$
$18$		0			0
$19$	1.38230	+	4.25428i	0.317121	+	0.976000i	0.974872	+	0.222764i	$0.0715080\pi$
$19$	1.38230	+	4.25428i	0.317121	+	0.976000i	−0.657751	+	0.753236i	$0.728492\pi$
$20$	0.196555	−	0.142806i	0.0439511	−	0.0319324i
$21$		0			0
$22$	−1.52258	+	4.52193i	−0.324615	+	0.964078i
$23$	5.28243			1.10146			0.550731	−	0.834683i	$-0.314349\pi$
$23$	5.28243			1.10146			0.550731	+	0.834683i	$0.314349\pi$
$24$		0			0
$25$	2.21562	+	6.81898i	0.443124	+	1.36380i
$26$	0.514156	−	1.58241i	0.100834	−	0.310336i
$27$		0			0
$28$	0.0190351	+	0.0138298i	0.00359730	+	0.00261359i
$29$	1.63104	−	5.01982i	0.302876	−	0.932157i	−0.677585	−	0.735444i	$-0.736973\pi$
$29$	1.63104	−	5.01982i	0.302876	−	0.932157i	0.980461	−	0.196713i	$-0.0630266\pi$
$30$		0			0
$31$	−4.57436	+	3.32347i	−0.821579	+	0.596912i	−0.917164	−	0.398509i	$-0.869528\pi$
$31$	−4.57436	+	3.32347i	−0.821579	+	0.596912i	0.0955850	+	0.995421i	$0.469528\pi$
$32$	−0.393789			−0.0696127
$33$		0			0
$34$	−5.91531			−1.01447
$35$	−0.953487	+	0.692749i	−0.161169	+	0.117096i
$36$		0			0
$37$	1.10852	−	3.41166i	0.182239	−	0.560874i	−0.817651	−	0.575714i	$-0.804724\pi$
$37$	1.10852	−	3.41166i	0.182239	−	0.560874i	0.999890	+	0.0148406i	$0.00472409\pi$
$38$	−5.20626	−	3.78257i	−0.844566	−	0.613613i
$39$		0			0
$40$	2.99372	−	9.21372i	0.473349	−	1.45682i
$41$	−3.45020	−	10.6186i	−0.538831	−	1.65835i	−0.735222	−	0.677826i	$-0.762922\pi$
$41$	−3.45020	−	10.6186i	−0.538831	−	1.65835i	0.196391	−	0.980526i	$-0.437078\pi$
$42$		0			0
$43$	−1.50787			−0.229948			−0.114974	−	0.993369i	$-0.536678\pi$
$43$	−1.50787			−0.229948			−0.114974	+	0.993369i	$0.536678\pi$
$44$	−0.0690391	−	0.220424i	−0.0104080	−	0.0332302i
$45$		0			0
$46$	−6.14808	+	4.46684i	−0.906484	+	0.658599i
$47$	2.72593	+	8.38956i	0.397618	+	1.22374i	0.926904	+	0.375299i	$0.122460\pi$
$47$	2.72593	+	8.38956i	0.397618	+	1.22374i	−0.529286	+	0.848444i	$0.677540\pi$
$48$		0			0
$49$	5.57078	+	4.04741i	0.795826	+	0.578201i
$50$	−8.34485	−	6.06289i	−1.18014	−	0.857422i
$51$		0			0
$52$	0.0248904	+	0.0766047i	0.00345167	+	0.0106232i
$53$	−1.63163	+	1.18545i	−0.224122	+	0.162834i	−0.694180	−	0.719801i	$-0.744233\pi$
$53$	−1.63163	+	1.18545i	−0.224122	+	0.162834i	0.470058	+	0.882635i	$0.344233\pi$
$54$		0			0
$55$	11.5695	+	0.122962i	1.56003	+	0.0165802i
$56$	0.938208			0.125373
$57$		0			0
$58$	2.34645	+	7.22164i	0.308104	+	0.948248i
$59$	−3.56887	+	10.9839i	−0.464628	+	1.42998i	0.394823	+	0.918757i	$0.370806\pi$
$59$	−3.56887	+	10.9839i	−0.464628	+	1.42998i	−0.859450	+	0.511219i	$0.829194\pi$
$60$		0			0
$61$	−6.37211	−	4.62961i	−0.815865	−	0.592761i	0.0996599	−	0.995022i	$-0.468225\pi$
$61$	−6.37211	−	4.62961i	−0.815865	−	0.592761i	−0.915525	+	0.402261i	$0.868225\pi$
$62$	2.51364	−	7.73619i	0.319233	−	0.982497i
$63$		0			0
$64$	−6.23134	+	4.52733i	−0.778918	+	0.565917i
$65$	−4.03468			−0.500440
$66$		0			0
$67$	−4.18422			−0.511184			−0.255592	−	0.966785i	$-0.582270\pi$
$67$	−4.18422			−0.511184			−0.255592	+	0.966785i	$0.582270\pi$
$68$	0.231671	−	0.168319i	0.0280942	−	0.0204116i
$69$		0			0
$70$	0.523947	−	1.61254i	0.0626237	−	0.192736i
$71$	−1.95860	−	1.42300i	−0.232442	−	0.168879i	0.465467	−	0.885065i	$-0.345886\pi$
$71$	−1.95860	−	1.42300i	−0.232442	−	0.168879i	−0.697910	+	0.716186i	$0.745886\pi$
$72$		0			0
$73$	−1.04183	+	3.20643i	−0.121937	+	0.375284i	−0.993331	−	0.115301i	$-0.963217\pi$
$73$	−1.04183	+	3.20643i	−0.121937	+	0.375284i	0.871394	+	0.490585i	$0.163217\pi$
$74$	1.59474	+	4.90810i	0.185385	+	0.570555i
$75$		0			0
$76$	0.311533			0.0357353
$77$	0.334907	+	1.06927i	0.0381662	+	0.121855i
$78$		0			0
$79$	−6.90716	+	5.01835i	−0.777117	+	0.564608i	−0.904112	−	0.427295i	$-0.859467\pi$
$79$	−6.90716	+	5.01835i	−0.777117	+	0.564608i	0.126996	+	0.991903i	$0.459467\pi$
$80$	4.45700	+	13.7172i	0.498307	+	1.53363i
$81$		0			0
$82$	12.9947	+	9.44124i	1.43503	+	1.04261i
$83$	9.17143	+	6.66344i	1.00670	+	0.731407i	0.963513	−	0.267660i	$-0.0862504\pi$
$83$	9.17143	+	6.66344i	1.00670	+	0.731407i	0.0431823	+	0.999067i	$0.486250\pi$
$84$		0			0
$85$	4.43257	+	13.6421i	0.480780	+	1.47969i
$86$	1.75497	−	1.27506i	0.189243	−	0.137493i
$87$		0			0
$88$	−7.39347	−	5.49266i	−0.788146	−	0.585519i
$89$	−3.45994			−0.366753			−0.183376	−	0.983043i	$-0.558703\pi$
$89$	−3.45994			−0.366753			−0.183376	+	0.983043i	$0.558703\pi$
$90$		0			0
$91$	−0.120743	−	0.371608i	−0.0126573	−	0.0389551i
$92$	0.113684	−	0.349884i	0.0118524	−	0.0364779i
$93$		0			0
$94$	−10.2669	−	7.45932i	−1.05895	−	0.769370i
$95$	−4.82221	+	14.8412i	−0.494748	+	1.52268i
$96$		0			0
$97$	10.5482	−	7.66375i	1.07101	−	0.778136i	0.0949183	−	0.995485i	$-0.469741\pi$
$97$	10.5482	−	7.66375i	1.07101	−	0.778136i	0.976094	+	0.217349i	$0.0697410\pi$
$98$	−9.90618			−1.00068
$99$		0			0
$100$	0.499341			0.0499341
$101$	1.76641	−	1.28337i	0.175764	−	0.127700i	−0.496425	−	0.868080i	$-0.665354\pi$
$101$	1.76641	−	1.28337i	0.175764	−	0.127700i	0.672189	+	0.740379i	$0.265354\pi$
$102$		0			0
$103$	0.269323	−	0.828891i	0.0265372	−	0.0816731i	−0.936911	−	0.349569i	$-0.886328\pi$
$103$	0.269323	−	0.828891i	0.0265372	−	0.0816731i	0.963448	+	0.267895i	$0.0863282\pi$
$104$	2.59841	+	1.88786i	0.254795	+	0.185120i
$105$		0			0
$106$	0.896592	−	2.75943i	0.0870847	−	0.268019i
$107$	1.90401	+	5.85995i	0.184068	+	0.566502i	0.999931	−	0.0117425i	$-0.00373784\pi$
$107$	1.90401	+	5.85995i	0.184068	+	0.566502i	−0.815863	+	0.578245i	$0.803738\pi$
$108$		0			0
$109$	−11.7010			−1.12075			−0.560376	−	0.828238i	$-0.689343\pi$
$109$	−11.7010			−1.12075			−0.560376	+	0.828238i	$0.689343\pi$
$110$	−13.5694	+	9.64011i	−1.29379	+	0.919148i
$111$		0			0
$112$	−1.13002	+	0.821011i	−0.106777	+	0.0775782i
$113$	−0.129331	−	0.398040i	−0.0121664	−	0.0374444i	0.944789	−	0.327679i	$-0.106267\pi$
$113$	−0.129331	−	0.398040i	−0.0121664	−	0.0374444i	−0.956955	+	0.290235i	$0.906267\pi$
$114$		0			0
$115$	14.9085	+	10.8317i	1.39023	+	1.01006i
$116$	−0.297388	−	0.216065i	−0.0276118	−	0.0200611i
$117$		0			0
$118$	−5.13427	−	15.8017i	−0.472648	−	1.45466i
$119$	−1.12383	+	0.816512i	−0.103021	+	0.0748495i
$120$		0			0
$121$	3.62077	−	10.3870i	0.329161	−	0.944274i
$122$	11.3311			1.02587
$123$		0			0
$124$	0.121686	+	0.374510i	0.0109277	+	0.0336320i
$125$	−2.33919	+	7.19928i	−0.209223	+	0.643924i
$126$		0			0
$127$	−7.46315	−	5.42229i	−0.662247	−	0.481151i	0.205174	−	0.978726i	$-0.434224\pi$
$127$	−7.46315	−	5.42229i	−0.662247	−	0.481151i	−0.867421	+	0.497575i	$0.834224\pi$
$128$	3.66753	−	11.2875i	0.324167	−	0.997685i
$129$		0			0
$130$	4.69585	−	3.41173i	0.411853	−	0.299229i
$131$	−15.3755			−1.34336			−0.671680	−	0.740841i	$-0.734427\pi$
$131$	−15.3755			−1.34336			−0.671680	+	0.740841i	$0.734427\pi$
$132$		0			0
$133$	−1.51124			−0.131041
$134$	4.86990	−	3.53819i	0.420695	−	0.305653i
$135$		0			0
$136$	3.52856	−	10.8598i	0.302571	−	0.931219i
$137$	−1.58692	−	1.15297i	−0.135580	−	0.0985047i	0.517928	−	0.855424i	$-0.326703\pi$
$137$	−1.58692	−	1.15297i	−0.135580	−	0.0985047i	−0.653508	+	0.756919i	$0.726703\pi$
$138$		0			0
$139$	5.45316	−	16.7831i	0.462531	−	1.42352i	−0.399531	−	0.916720i	$-0.630827\pi$
$139$	5.45316	−	16.7831i	0.462531	−	1.42352i	0.862062	−	0.506803i	$-0.169173\pi$
$140$	0.0253643	+	0.0780634i	0.00214368	+	0.00659756i
$141$		0			0
$142$	3.48285			0.292274
$143$	−1.22405	+	3.63531i	−0.102360	+	0.304000i
$144$		0			0
$145$	14.8965	−	10.8229i	1.23708	−	0.898794i
$146$	−1.49880	−	4.61285i	−0.124042	−	0.381762i
$147$		0			0
$148$	−0.202116	−	0.146846i	−0.0166139	−	0.0120707i
$149$	−0.545729	−	0.396496i	−0.0447079	−	0.0324822i	0.565207	−	0.824949i	$-0.308796\pi$
$149$	−0.545729	−	0.396496i	−0.0447079	−	0.0324822i	−0.609915	+	0.792467i	$0.708796\pi$
$150$		0			0
$151$	1.70703	+	5.25369i	0.138916	+	0.427540i	0.996179	−	0.0873400i	$-0.0278367\pi$
$151$	1.70703	+	5.25369i	0.138916	+	0.427540i	−0.857263	+	0.514880i	$0.827837\pi$
$152$	10.0499	−	7.30170i	0.815157	−	0.592246i
$153$		0			0
$154$	−1.29397	−	0.961300i	−0.104271	−	0.0774638i
$155$	−19.7250			−1.58435
$156$		0			0
$157$	0.245613	+	0.755920i	0.0196021	+	0.0603290i	0.960379	−	0.278697i	$-0.0899025\pi$
$157$	0.245613	+	0.755920i	0.0196021	+	0.0603290i	−0.940777	+	0.339026i	$0.889903\pi$
$158$	3.79553	−	11.6814i	0.301956	−	0.929325i
$159$		0			0
$160$	−1.11139	−	0.807469i	−0.0878628	−	0.0638360i
$161$	−0.551480	+	1.69728i	−0.0434627	+	0.133765i
$162$		0			0
$163$	−11.6538	+	8.46700i	−0.912799	+	0.663187i	−0.941721	−	0.336395i	$-0.890792\pi$
$163$	−11.6538	+	8.46700i	−0.912799	+	0.663187i	0.0289225	+	0.999582i	$0.490792\pi$
$164$	−0.777582			−0.0607190
$165$		0			0
$166$	−16.3090			−1.26582
$167$	10.9791	−	7.97675i	0.849585	−	0.617260i	−0.0754466	−	0.997150i	$-0.524038\pi$
$167$	10.9791	−	7.97675i	0.849585	−	0.617260i	0.925032	+	0.379890i	$0.124038\pi$
$168$		0			0
$169$	−3.60388	+	11.0916i	−0.277221	+	0.853199i
$170$	−16.6947	−	12.1294i	−1.28043	−	0.930284i
$171$		0			0
$172$	−0.0324512	+	0.0998744i	−0.00247438	+	0.00761535i
$173$	−5.43454	−	16.7258i	−0.413180	−	1.27164i	−0.913868	−	0.406011i	$-0.866920\pi$
$173$	−5.43454	−	16.7258i	−0.413180	−	1.27164i	0.500688	−	0.865628i	$-0.333080\pi$
$174$		0			0
$175$	−2.42229			−0.183108
$176$	13.7116	+	0.145728i	1.03355	+	0.0109847i
$177$		0			0
$178$	4.02693	−	2.92573i	0.301831	−	0.219293i
$179$	−4.96972	−	15.2952i	−0.371454	−	1.14322i	−0.945840	−	0.324634i	$-0.894759\pi$
$179$	−4.96972	−	15.2952i	−0.371454	−	1.14322i	0.574386	−	0.818585i	$-0.305241\pi$
$180$		0			0
$181$	12.0200	+	8.73306i	0.893441	+	0.649123i	0.936773	−	0.349938i	$-0.113797\pi$
$181$	12.0200	+	8.73306i	0.893441	+	0.649123i	−0.0433317	+	0.999061i	$0.513797\pi$
$182$	0.454762	+	0.330404i	0.0337092	+	0.0244912i
$183$		0			0
$184$	−4.53316	−	13.9516i	−0.334189	−	1.02853i
$185$	10.1242	−	7.35566i	0.744346	−	0.540799i
$186$		0			0
$187$	13.6365	+	0.144929i	0.997197	+	0.0105983i
$188$	0.614351			0.0448062
$189$		0			0
$190$	−6.93735	−	21.3510i	−0.503288	−	1.54896i
$191$	−0.418559	+	1.28819i	−0.0302859	+	0.0932104i	−0.965057	−	0.262041i	$-0.915605\pi$
$191$	−0.418559	+	1.28819i	−0.0302859	+	0.0932104i	0.934771	+	0.355251i	$0.115605\pi$
$192$		0			0
$193$	18.0722	+	13.1302i	1.30086	+	0.945132i	0.999964	−	0.00852400i	$-0.00271331\pi$
$193$	18.0722	+	13.1302i	1.30086	+	0.945132i	0.300899	+	0.953656i	$0.402713\pi$
$194$	−5.79633	+	17.8393i	−0.416152	+	1.28078i
$195$		0			0
$196$	0.387972	−	0.281878i	0.0277123	−	0.0201341i
$197$	8.74655			0.623166			0.311583	−	0.950219i	$-0.399141\pi$
$197$	8.74655			0.623166			0.311583	+	0.950219i	$0.399141\pi$
$198$		0			0
$199$	6.39133			0.453070			0.226535	−	0.974003i	$-0.427260\pi$
$199$	6.39133			0.453070			0.226535	+	0.974003i	$0.427260\pi$
$200$	16.1085	−	11.7035i	1.13905	−	0.827565i
$201$		0			0
$202$	−0.970653	+	2.98736i	−0.0682949	+	0.210190i
$203$	1.44262	+	1.04813i	0.101252	+	0.0735642i
$204$		0			0
$205$	12.0362	−	37.0435i	0.840642	−	2.58723i
$206$	0.387455	+	1.19246i	0.0269953	+	0.0830829i
$207$		0			0
$208$	−4.78169			−0.331551
$209$	11.9092	+	8.84744i	0.823777	+	0.611990i
$210$		0			0
$211$	−5.33472	+	3.87590i	−0.367257	+	0.266828i	−0.756073	−	0.654488i	$-0.772884\pi$
$211$	−5.33472	+	3.87590i	−0.367257	+	0.266828i	0.388816	+	0.921316i	$0.372884\pi$
$212$	0.0434041	+	0.133584i	0.00298101	+	0.00917460i
$213$		0			0
$214$	−7.17122	−	5.21019i	−0.490214	−	0.356161i
$215$	−4.25564	−	3.09190i	−0.290232	−	0.210866i
$216$		0			0
$217$	−0.590295	−	1.81674i	−0.0400718	−	0.123328i
$218$	13.6185	−	9.89439i	0.922359	−	0.670133i
$219$		0			0
$220$	0.257134	−	0.763666i	0.0173360	−	0.0514863i
$221$	−4.75549			−0.319889
$222$		0			0
$223$	−2.06946	−	6.36915i	−0.138581	−	0.426510i	0.857548	−	0.514403i	$-0.171987\pi$
$223$	−2.06946	−	6.36915i	−0.138581	−	0.426510i	−0.996130	+	0.0878934i	$0.971987\pi$
$224$	0.0411112	−	0.126527i	0.00274686	−	0.00845395i
$225$		0			0
$226$	0.487108	+	0.353905i	0.0324020	+	0.0235414i
$227$	−1.89964	+	5.84648i	−0.126083	+	0.388045i	−0.994097	−	0.108496i	$-0.965397\pi$
$227$	−1.89964	+	5.84648i	−0.126083	+	0.388045i	0.868014	+	0.496541i	$0.165397\pi$
$228$		0			0
$229$	18.5392	−	13.4695i	1.22511	−	0.890092i	0.228593	−	0.973522i	$-0.426587\pi$
$229$	18.5392	−	13.4695i	1.22511	−	0.890092i	0.996514	+	0.0834295i	$0.0265873\pi$
$230$	−26.5109			−1.74808
$231$		0			0
$232$	−14.6577			−0.962328
$233$	9.54280	−	6.93325i	0.625170	−	0.454212i	−0.229554	−	0.973296i	$-0.573727\pi$
$233$	9.54280	−	6.93325i	0.625170	−	0.454212i	0.854724	+	0.519084i	$0.173727\pi$
$234$		0			0
$235$	−9.50952	+	29.2673i	−0.620333	+	1.90919i
$236$	0.650714	+	0.472772i	0.0423579	+	0.0307748i
$237$		0			0
$238$	0.617552	−	1.90063i	0.0400300	−	0.123200i
$239$	−2.98286	−	9.18031i	−0.192945	−	0.593825i	−0.999994	−	0.00334057i	$-0.998937\pi$
$239$	−2.98286	−	9.18031i	−0.192945	−	0.593825i	0.807049	−	0.590485i	$-0.201063\pi$
$240$		0			0
$241$	−7.26689			−0.468102			−0.234051	−	0.972224i	$-0.575198\pi$
$241$	−7.26689			−0.468102			−0.234051	+	0.972224i	$0.575198\pi$
$242$	4.56918	+	15.1509i	0.293718	+	0.973936i
$243$		0			0
$244$	−0.443780	+	0.322425i	−0.0284101	+	0.0206411i
$245$	7.42308	+	22.8459i	0.474243	+	1.45957i
$246$		0			0
$247$	−4.18546	−	3.04091i	−0.266314	−	0.193489i
$248$	12.7033	+	9.22947i	0.806659	+	0.586072i
$249$		0			0
$250$	−3.36522	−	10.3571i	−0.212835	−	0.655039i
$251$	10.6325	−	7.72498i	0.671119	−	0.487597i	−0.199280	−	0.979943i	$-0.563860\pi$
$251$	10.6325	−	7.72498i	0.671119	−	0.487597i	0.870400	+	0.492346i	$0.163860\pi$
$252$		0			0
$253$	14.2825	−	10.1467i	0.897932	−	0.637917i
$254$	13.2713			0.832713
$255$		0			0
$256$	0.515890	+	1.58774i	0.0322431	+	0.0992341i
$257$	−0.564349	+	1.73689i	−0.0352031	+	0.108344i	−0.967114	−	0.254343i	$-0.918141\pi$
$257$	−0.564349	+	1.73689i	−0.0352031	+	0.108344i	0.931911	+	0.362687i	$0.118141\pi$
$258$		0			0
$259$	0.980463	+	0.712348i	0.0609230	+	0.0442631i
$260$	−0.0868310	+	0.267238i	−0.00538503	+	0.0165734i
$261$		0			0
$262$	17.8951	−	13.0015i	1.10556	−	0.803238i
$263$	5.27436			0.325231			0.162616	−	0.986690i	$-0.448007\pi$
$263$	5.27436			0.325231			0.162616	+	0.986690i	$0.448007\pi$
$264$		0			0
$265$	−7.03571			−0.432201
$266$	1.75889	−	1.27791i	0.107845	−	0.0783537i
$267$		0			0
$268$	−0.0900494	+	0.277144i	−0.00550064	+	0.0169292i
$269$	14.0391	+	10.2000i	0.855982	+	0.621907i	0.926789	−	0.375583i	$-0.122557\pi$
$269$	14.0391	+	10.2000i	0.855982	+	0.621907i	−0.0708069	+	0.997490i	$0.522557\pi$
$270$		0			0
$271$	2.50681	−	7.71516i	0.152278	−	0.468662i	−0.845597	−	0.533821i	$-0.820755\pi$
$271$	2.50681	−	7.71516i	0.152278	−	0.468662i	0.997875	+	0.0651590i	$0.0207555\pi$
$272$	5.25326	+	16.1679i	0.318526	+	0.980321i
$273$		0			0
$274$	2.82193			0.170479
$275$	19.0887	+	14.1811i	1.15109	+	0.855154i
$276$		0			0
$277$	15.7453	−	11.4396i	0.946042	−	0.687340i	−0.00382512	−	0.999993i	$-0.501218\pi$
$277$	15.7453	−	11.4396i	0.946042	−	0.687340i	0.949868	+	0.312653i	$0.101218\pi$
$278$	7.84505	+	24.1446i	0.470515	+	1.44810i
$279$		0			0
$280$	2.64789	+	1.92381i	0.158242	+	0.114969i
$281$	−23.4526	−	17.0393i	−1.39907	−	1.01648i	−0.994801	−	0.101838i	$-0.967528\pi$
$281$	−23.4526	−	17.0393i	−1.39907	−	1.01648i	−0.404265	−	0.914642i	$-0.632472\pi$
$282$		0			0
$283$	3.02068	+	9.29671i	0.179561	+	0.552632i	0.999812	−	0.0193713i	$-0.00616646\pi$
$283$	3.02068	+	9.29671i	0.179561	+	0.552632i	−0.820251	+	0.572003i	$0.806166\pi$
$284$	−0.136404	+	0.0991037i	−0.00809412	+	0.00588072i
$285$		0			0
$286$	−1.64939	−	5.26609i	−0.0975306	−	0.311390i
$287$	3.77204			0.222656
$288$		0			0
$289$	−0.0288211	−	0.0887023i	−0.00169536	−	0.00521778i
$290$	−8.18569	+	25.1930i	−0.480680	+	1.47938i
$291$		0			0
$292$	0.189958	+	0.138012i	0.0111164	+	0.00807655i
$293$	7.78996	−	23.9750i	0.455095	−	1.40064i	−0.415929	−	0.909397i	$-0.636544\pi$
$293$	7.78996	−	23.9750i	0.455095	−	1.40064i	0.871024	−	0.491240i	$-0.163456\pi$
$294$		0			0
$295$	−32.5949	+	23.6816i	−1.89775	+	1.37880i
$296$	−9.96196			−0.579027
$297$		0			0
$298$	0.970438			0.0562159
$299$	−4.94261	+	3.59102i	−0.285839	+	0.207674i
$300$		0			0
$301$	0.157420	−	0.484489i	0.00907354	−	0.0279255i
$302$	−6.42930	−	4.67116i	−0.369965	−	0.268795i
$303$		0			0
$304$	−5.71504	+	17.5891i	−0.327780	+	1.00880i
$305$	−8.49086	−	26.1322i	−0.486185	−	1.49632i
$306$		0			0
$307$	4.47659			0.255492			0.127746	−	0.991807i	$-0.459226\pi$
$307$	4.47659			0.255492			0.127746	+	0.991807i	$0.459226\pi$
$308$	0.0780314		0.000829324i	0.00444625		4.72551e-5i
$309$		0			0
$310$	22.9573	−	16.6795i	1.30389	−	0.947331i
$311$	−7.00281	−	21.5524i	−0.397093	−	1.22213i	−0.927320	−	0.374270i	$-0.877893\pi$
$311$	−7.00281	−	21.5524i	−0.397093	−	1.22213i	0.530227	−	0.847856i	$-0.322107\pi$
$312$		0			0
$313$	−13.4966	−	9.80585i	−0.762873	−	0.554259i	0.136917	−	0.990582i	$-0.456281\pi$
$313$	−13.4966	−	9.80585i	−0.762873	−	0.554259i	−0.899790	+	0.436323i	$0.856281\pi$
$314$	−0.925071	−	0.672104i	−0.0522048	−	0.0379290i
$315$		0			0
$316$	0.183742	+	0.565500i	0.0103363	+	0.0318118i
$317$	20.5229	−	14.9108i	1.15268	−	0.837472i	0.163846	−	0.986486i	$-0.447610\pi$
$317$	20.5229	−	14.9108i	1.15268	−	0.837472i	0.988835	+	0.149014i	$0.0476100\pi$
$318$		0			0
$319$	−5.23230	−	16.7054i	−0.292953	−	0.935323i
$320$	−26.8700			−1.50208
$321$		0			0
$322$	−0.793374	−	2.44175i	−0.0442130	−	0.136074i
$323$	−5.68372	+	17.4927i	−0.316250	+	0.973319i
$324$		0			0
$325$	−6.70866	−	4.87413i	−0.372129	−	0.270368i
$326$	6.40385	−	19.7090i	0.354677	−	1.09158i
$327$		0			0
$328$	−25.0845	+	18.2249i	−1.38506	+	1.00630i
$329$	−2.98021			−0.164304
$330$		0			0
$331$	7.58836			0.417094			0.208547	−	0.978012i	$-0.433127\pi$
$331$	7.58836			0.417094			0.208547	+	0.978012i	$0.433127\pi$
$332$	0.638736	−	0.464069i	0.0350552	−	0.0254691i
$333$		0			0
$334$	−6.03306	+	18.5678i	−0.330114	+	1.01599i
$335$	−11.8091	−	8.57979i	−0.645198	−	0.468764i
$336$		0			0
$337$	−4.45301	+	13.7050i	−0.242571	+	0.746557i	0.753455	+	0.657499i	$0.228386\pi$
$337$	−4.45301	+	13.7050i	−0.242571	+	0.746557i	−0.996026	+	0.0890579i	$0.971614\pi$
$338$	−5.18463	−	15.9566i	−0.282007	−	0.867927i
$339$		0			0
$340$	0.998981			0.0541774
$341$	−5.98419	+	17.7725i	−0.324062	+	0.962435i
$342$		0			0
$343$	−3.79528	+	2.75744i	−0.204926	+	0.148888i
$344$	1.29399	+	3.98250i	0.0697673	+	0.214722i
$345$		0			0
$346$	20.4685	+	14.8712i	1.10039	+	0.799482i
$347$	13.6257	+	9.89961i	0.731463	+	0.531439i	0.890026	−	0.455910i	$-0.150686\pi$
$347$	13.6257	+	9.89961i	0.731463	+	0.531439i	−0.158563	+	0.987349i	$0.550686\pi$
$348$		0			0
$349$	9.44937	+	29.0822i	0.505813	+	1.55673i	0.799399	+	0.600801i	$0.205151\pi$
$349$	9.44937	+	29.0822i	0.505813	+	1.55673i	−0.293586	+	0.955933i	$0.594849\pi$
$350$	2.81924	−	2.04830i	0.150695	−	0.109486i
$351$		0			0
$352$	−1.06472	+	0.756405i	−0.0567496	+	0.0403165i
$353$	0.486485			0.0258930			0.0129465	−	0.999916i	$-0.495879\pi$
$353$	0.486485			0.0258930			0.0129465	+	0.999916i	$0.495879\pi$
$354$		0			0
$355$	−2.60983	−	8.03224i	−0.138516	−	0.426307i
$356$	−0.0744620	+	0.229171i	−0.00394648	+	0.0121460i
$357$		0			0
$358$	18.7178	+	13.5993i	0.989266	+	0.718744i
$359$	10.5622	−	32.5072i	0.557453	−	1.71566i	−0.131924	−	0.991260i	$-0.542116\pi$
$359$	10.5622	−	32.5072i	0.557453	−	1.71566i	0.689377	−	0.724403i	$-0.257884\pi$
$360$		0			0
$361$	−0.816851	+	0.593477i	−0.0429921	+	0.0312356i
$362$	−21.3745			−1.12342
$363$		0			0
$364$	−0.0272122			−0.00142630
$365$	−9.51516	+	6.91317i	−0.498046	+	0.361852i
$366$		0			0
$367$	−0.730389	+	2.24791i	−0.0381260	+	0.117340i	−0.968308	−	0.249759i	$-0.919649\pi$
$367$	−0.730389	+	2.24791i	−0.0381260	+	0.117340i	0.930182	+	0.367098i	$0.119649\pi$
$368$	17.6688	+	12.8372i	0.921052	+	0.669183i
$369$		0			0
$370$	−5.56331	+	17.1221i	−0.289223	+	0.890136i
$371$	−0.210553	−	0.648015i	−0.0109314	−	0.0336432i
$372$		0			0
$373$	−22.8663			−1.18397			−0.591987	−	0.805948i	$-0.701656\pi$
$373$	−22.8663			−1.18397			−0.591987	+	0.805948i	$0.701656\pi$
$374$	−15.9937	+	11.3624i	−0.827012	+	0.587533i
$375$		0			0
$376$	19.8187	−	14.3991i	1.02207	−	0.742579i
$377$	1.88638	+	5.80568i	0.0971535	+	0.299008i
$378$		0			0
$379$	−21.9257	−	15.9299i	−1.12625	−	0.818266i	−0.141102	−	0.989995i	$-0.545065\pi$
$379$	−21.9257	−	15.9299i	−1.12625	−	0.818266i	−0.985144	+	0.171729i	$0.945065\pi$
$380$	0.879236	+	0.638802i	0.0451038	+	0.0327699i
$381$		0			0
$382$	−0.602150	−	1.85323i	−0.0308087	−	0.0948194i
$383$	−16.9860	+	12.3411i	−0.867945	+	0.630599i	−0.930035	−	0.367472i	$-0.880223\pi$
$383$	−16.9860	+	12.3411i	−0.867945	+	0.630599i	0.0620899	+	0.998071i	$0.480223\pi$
$384$		0			0
$385$	−1.24735	+	3.70453i	−0.0635711	+	0.188800i
$386$	−32.1366			−1.63571
$387$		0			0
$388$	−0.280601	−	0.863601i	−0.0142454	−	0.0438427i
$389$	2.17985	−	6.70889i	0.110523	−	0.340154i	−0.880464	−	0.474113i	$-0.842769\pi$
$389$	2.17985	−	6.70889i	0.110523	−	0.340154i	0.990987	+	0.133958i	$0.0427689\pi$
$390$		0			0
$391$	17.5720	+	12.7668i	0.888654	+	0.645645i
$392$	5.90916	−	18.1865i	0.298458	−	0.918559i
$393$		0			0
$394$	−10.1799	+	7.39611i	−0.512855	+	0.372611i
$395$	−29.7842			−1.49860
$396$		0			0
$397$	1.54426			0.0775042			0.0387521	−	0.999249i	$-0.487662\pi$
$397$	1.54426			0.0775042			0.0387521	+	0.999249i	$0.487662\pi$
$398$	−7.43870	+	5.40453i	−0.372868	+	0.270905i
$399$		0			0
$400$	−9.16035	+	28.1926i	−0.458017	+	1.40963i
$401$	−17.9298	−	13.0268i	−0.895374	−	0.650527i	0.0419000	−	0.999122i	$-0.486659\pi$
$401$	−17.9298	−	13.0268i	−0.895374	−	0.650527i	−0.937274	+	0.348595i	$0.886659\pi$
$402$		0			0
$403$	2.02079	−	6.21934i	0.100662	−	0.309807i
$404$	−0.0469894	−	0.144619i	−0.00233781	−	0.00719505i
$405$		0			0
$406$	−2.56533			−0.127315
$407$	−3.55607	−	11.3536i	−0.176268	−	0.562779i
$408$		0			0
$409$	3.83167	−	2.78387i	0.189464	−	0.137654i	−0.489010	−	0.872278i	$-0.662642\pi$
$409$	3.83167	−	2.78387i	0.189464	−	0.137654i	0.678474	+	0.734625i	$0.262642\pi$
$410$	17.3155	+	53.2918i	0.855154	+	2.63189i
$411$		0			0
$412$	−0.0491058	−	0.0356775i	−0.00241927	−	0.00175770i
$413$	−3.15660	−	2.29341i	−0.155326	−	0.112851i
$414$		0			0
$415$	12.2210	+	37.6123i	0.599904	+	1.84631i
$416$	0.368457	−	0.267699i	0.0180651	−	0.0131250i
$417$		0			0
$418$	−21.3422	−	0.226827i	−1.04388	−	0.0110945i
$419$	40.2948			1.96853			0.984265	−	0.176697i	$-0.0565412\pi$
$419$	40.2948			1.96853			0.984265	+	0.176697i	$0.0565412\pi$
$420$		0			0
$421$	−4.20385	−	12.9381i	−0.204883	−	0.630566i	−0.999718	−	0.0237401i	$-0.992443\pi$
$421$	−4.20385	−	12.9381i	−0.204883	−	0.630566i	0.794835	−	0.606826i	$-0.207557\pi$
$422$	2.93146	−	9.02210i	0.142701	−	0.439189i
$423$		0			0
$424$	4.53114	+	3.29207i	0.220052	+	0.159877i
$425$	−9.11014	+	28.0381i	−0.441907	+	1.36005i
$426$		0			0
$427$	2.15277	−	1.56408i	0.104180	−	0.0756910i
$428$	0.429113			0.0207419
$429$		0			0
$430$	7.56755			0.364940
$431$	−6.35439	+	4.61673i	−0.306080	+	0.222380i	−0.730213	−	0.683220i	$-0.760579\pi$
$431$	−6.35439	+	4.61673i	−0.306080	+	0.222380i	0.424133	+	0.905600i	$0.360579\pi$
$432$		0			0
$433$	0.426664	−	1.31314i	0.0205041	−	0.0631053i	−0.940281	−	0.340400i	$-0.889438\pi$
$433$	0.426664	−	1.31314i	0.0205041	−	0.0631053i	0.960785	+	0.277294i	$0.0894377\pi$
$434$	2.22327	+	1.61530i	0.106720	+	0.0775369i
$435$		0			0
$436$	−0.251819	+	0.775020i	−0.0120600	+	0.0371167i
$437$	7.30191	+	22.4730i	0.349298	+	1.07503i
$438$		0			0
$439$	−5.50930			−0.262945			−0.131472	−	0.991320i	$-0.541970\pi$
$439$	−5.50930			−0.262945			−0.131472	+	0.991320i	$0.541970\pi$
$440$	−9.60372	−	30.6622i	−0.457840	−	1.46177i
$441$		0			0
$442$	5.53478	−	4.02125i	0.263263	−	0.191272i
$443$	0.340950	+	1.04934i	0.0161990	+	0.0498555i	0.958829	−	0.283983i	$-0.0916560\pi$
$443$	0.340950	+	1.04934i	0.0161990	+	0.0498555i	−0.942630	+	0.333839i	$0.891656\pi$
$444$		0			0
$445$	−9.76494	−	7.09464i	−0.462902	−	0.336318i
$446$	7.79436	+	5.66294i	0.369074	+	0.268148i
$447$		0			0
$448$	−0.804118	−	2.47482i	−0.0379910	−	0.116924i
$449$	−1.16721	+	0.848031i	−0.0550843	+	0.0400211i	−0.614987	−	0.788538i	$-0.710839\pi$
$449$	−1.16721	+	0.848031i	−0.0550843	+	0.0400211i	0.559902	+	0.828559i	$0.310839\pi$
$450$		0			0
$451$	−29.7252	−	22.0831i	−1.39971	−	1.03985i
$452$	−0.0291477			−0.00137099
$453$		0			0
$454$	−2.73287	−	8.41090i	−0.128260	−	0.394743i
$455$	0.421216	−	1.29637i	0.0197469	−	0.0607747i
$456$		0			0
$457$	24.4060	+	17.7320i	1.14166	+	0.829467i	0.987350	−	0.158555i	$-0.0506835\pi$
$457$	24.4060	+	17.7320i	1.14166	+	0.829467i	0.154313	+	0.988022i	$0.450684\pi$
$458$	−10.1874	+	31.3537i	−0.476027	+	1.46506i
$459$		0			0
$460$	1.03829	−	0.754362i	0.0484105	−	0.0351723i
$461$	−26.6770			−1.24247			−0.621237	−	0.783623i	$-0.713369\pi$
$461$	−26.6770			−1.24247			−0.621237	+	0.783623i	$0.713369\pi$
$462$		0			0
$463$	0.697479			0.0324146			0.0162073	−	0.999869i	$-0.494841\pi$
$463$	0.697479			0.0324146			0.0162073	+	0.999869i	$0.494841\pi$
$464$	17.6545	−	12.8268i	0.819590	−	0.595467i
$465$		0			0
$466$	−5.24383	+	16.1388i	−0.242916	+	0.747618i
$467$	−25.9087	−	18.8238i	−1.19891	−	0.871061i	−0.204736	−	0.978817i	$-0.565633\pi$
$467$	−25.9087	−	18.8238i	−1.19891	−	0.871061i	−0.994177	+	0.107756i	$0.965633\pi$
$468$		0			0
$469$	0.436828	−	1.34442i	0.0201709	−	0.0620795i
$470$	−13.6806	−	42.1047i	−0.631041	−	1.94214i
$471$		0			0
$472$	32.0726			1.47626
$473$	−4.07694	+	2.89637i	−0.187458	+	0.133175i
$474$		0			0
$475$	−25.9472	+	18.8518i	−1.19054	+	0.864978i
$476$	0.0298958	+	0.0920098i	0.00137027	+	0.00421726i
$477$		0			0
$478$	11.2346	+	8.16240i	0.513858	+	0.373339i
$479$	17.7890	+	12.9245i	0.812801	+	0.590534i	0.914641	−	0.404266i	$-0.132473\pi$
$479$	17.7890	+	12.9245i	0.812801	+	0.590534i	−0.101840	+	0.994801i	$0.532473\pi$
$480$		0			0
$481$	1.28206	+	3.94576i	0.0584567	+	0.179911i
$482$	8.45774	−	6.14490i	0.385239	−	0.279893i
$483$		0			0
$484$	−0.610065	−	0.463364i	−0.0277302	−	0.0210620i
$485$	45.4848			2.06536
$486$		0			0
$487$	5.41429	+	16.6635i	0.245345	+	0.755094i	0.995580	+	0.0939221i	$0.0299405\pi$
$487$	5.41429	+	16.6635i	0.245345	+	0.755094i	−0.750235	+	0.661172i	$0.770060\pi$
$488$	−6.75917	+	20.8026i	−0.305973	+	0.941689i
$489$		0			0
$490$	−27.9581	−	20.3127i	−1.26302	−	0.917636i
$491$	−0.0621973	+	0.191424i	−0.00280692	+	0.00863883i	−0.952450	−	0.304694i	$-0.901446\pi$
$491$	−0.0621973	+	0.191424i	−0.00280692	+	0.00863883i	0.949643	+	0.313333i	$0.101446\pi$
$492$		0			0
$493$	17.5578	−	12.7565i	0.790762	−	0.574522i
$494$	7.44274			0.334865
$495$		0			0
$496$	−23.3770			−1.04966
$497$	0.661696	−	0.480750i	0.0296811	−	0.0215646i
$498$		0			0
$499$	−7.54093	+	23.2086i	−0.337578	+	1.03896i	0.627860	+	0.778327i	$0.283931\pi$
$499$	−7.54093	+	23.2086i	−0.337578	+	1.03896i	−0.965438	+	0.260633i	$0.916069\pi$
$500$	0.426505	+	0.309874i	0.0190739	+	0.0138580i
$501$		0			0
$502$	−5.84264	+	17.9818i	−0.260770	+	0.802567i
$503$	−5.13640	−	15.8082i	−0.229021	−	0.704853i	−0.997859	−	0.0654093i	$-0.979165\pi$
$503$	−5.13640	−	15.8082i	−0.229021	−	0.704853i	0.768838	−	0.639444i	$-0.220835\pi$
$504$		0			0
$505$	7.61689			0.338947
$506$	−8.04293	+	23.8868i	−0.357552	+	1.06190i
$507$		0			0
$508$	−0.519764	+	0.377630i	−0.0230608	+	0.0167546i
$509$	5.21844	+	16.0607i	0.231303	+	0.711879i	0.997590	+	0.0693800i	$0.0221021\pi$
$509$	5.21844	+	16.0607i	0.231303	+	0.711879i	−0.766287	+	0.642498i	$0.777898\pi$
$510$		0			0
$511$	−0.921481	−	0.669495i	−0.0407639	−	0.0296167i
$512$	17.2604	+	12.5404i	0.762810	+	0.554214i
$513$		0			0
$514$	−0.811886	−	2.49873i	−0.0358108	−	0.110214i
$515$	2.45976	−	1.78712i	0.108390	−	0.0787499i
$516$		0			0
$517$	23.4853	+	17.4474i	1.03288	+	0.767335i
$518$	−1.74350			−0.0766049
$519$		0			0
$520$	3.46239	+	10.6561i	0.151836	+	0.467303i
$521$	−5.89465	+	18.1419i	−0.258249	+	0.794809i	0.734923	+	0.678151i	$0.237218\pi$
$521$	−5.89465	+	18.1419i	−0.258249	+	0.794809i	−0.993172	+	0.116658i	$0.962782\pi$
$522$		0			0
$523$	12.1874	+	8.85469i	0.532919	+	0.387189i	0.821449	−	0.570283i	$-0.193166\pi$
$523$	12.1874	+	8.85469i	0.532919	+	0.387189i	−0.288529	+	0.957471i	$0.593166\pi$
$524$	−0.330898	+	1.01840i	−0.0144554	+	0.0444890i
$525$		0			0
$526$	−6.13868	+	4.46002i	−0.267659	+	0.194466i
$527$	−23.2489			−1.01274
$528$		0			0
$529$	4.90407			0.213220
$530$	8.18868	−	5.94942i	0.355693	−	0.258426i
$531$		0			0
$532$	−0.0325237	+	0.100098i	−0.00141008	+	0.00433979i
$533$	10.4468	+	7.59008i	0.452503	+	0.328763i
$534$		0			0
$535$	−6.64222	+	20.4426i	−0.287168	+	0.883813i
$536$	3.59072	+	11.0511i	0.155096	+	0.477335i
$537$		0			0
$538$	−24.9650			−1.07632
$539$	22.8365	+	0.242708i	0.983639	+	0.0104542i
$540$		0			0
$541$	5.44671	−	3.95727i	0.234172	−	0.170136i	−0.464511	−	0.885568i	$-0.653770\pi$
$541$	5.44671	−	3.95727i	0.234172	−	0.170136i	0.698683	+	0.715431i	$0.253770\pi$
$542$	3.60636	+	11.0992i	0.154906	+	0.476752i
$543$		0			0
$544$	−1.30994	−	0.951727i	−0.0561632	−	0.0408049i
$545$	−33.0236	−	23.9930i	−1.41457	−	1.02775i
$546$		0			0
$547$	2.87154	+	8.83768i	0.122778	+	0.377872i	0.993490	−	0.113922i	$-0.0363413\pi$
$547$	2.87154	+	8.83768i	0.122778	+	0.377872i	−0.870712	+	0.491794i	$0.836341\pi$
$548$	−0.110520	+	0.0802974i	−0.00472117	+	0.00343013i
$549$		0			0
$550$	−34.2084	−	0.363569i	−1.45865	−	0.0155027i
$551$	23.6103			1.00583
$552$		0			0
$553$	−0.891329	−	2.74323i	−0.0379032	−	0.116654i
$554$	−8.65213	+	26.6285i	−0.367594	+	1.13134i
$555$		0			0
$556$	−0.994277	−	0.722384i	−0.0421667	−	0.0306359i
$557$	−10.5763	+	32.5504i	−0.448131	+	1.37921i	0.430882	+	0.902408i	$0.358203\pi$
$557$	−10.5763	+	32.5504i	−0.448131	+	1.37921i	−0.879013	+	0.476798i	$0.841797\pi$
$558$		0			0
$559$	1.41087	−	1.02506i	0.0596734	−	0.0433553i
$560$	−4.87275			−0.205911
$561$		0			0
$562$	41.7044			1.75919
$563$	8.41171	−	6.11146i	0.354511	−	0.257567i	−0.396248	−	0.918144i	$-0.629688\pi$
$563$	8.41171	−	6.11146i	0.354511	−	0.257567i	0.750759	+	0.660576i	$0.229688\pi$
$564$		0			0
$565$	0.451176	−	1.38858i	0.0189811	−	0.0584178i
$566$	−11.3770	−	8.26589i	−0.478212	−	0.347441i
$567$		0			0
$568$	−2.07757	+	6.39409i	−0.0871727	+	0.268290i
$569$	−5.87646	−	18.0859i	−0.246354	−	0.758200i	−0.995411	−	0.0956940i	$-0.969493\pi$
$569$	−5.87646	−	18.0859i	−0.246354	−	0.758200i	0.749057	−	0.662506i	$-0.230507\pi$
$570$		0			0
$571$	−31.1105			−1.30193			−0.650966	−	0.759107i	$-0.725636\pi$
$571$	−31.1105			−1.30193			−0.650966	+	0.759107i	$0.725636\pi$
$572$	0.214443	+	0.159311i	0.00896632	+	0.00666114i
$573$		0			0
$574$	−4.39017	+	3.18965i	−0.183242	+	0.133133i
$575$	11.7039	+	36.0208i	0.488085	+	1.50217i
$576$		0			0
$577$	−8.81901	−	6.40738i	−0.367140	−	0.266743i	0.388884	−	0.921287i	$-0.372861\pi$
$577$	−8.81901	−	6.40738i	−0.367140	−	0.266743i	−0.756024	+	0.654544i	$0.772861\pi$
$578$	0.108551	+	0.0788670i	0.00451513	+	0.00328043i
$579$		0			0
$580$	−0.396270	−	1.21959i	−0.0164542	−	0.0506409i
$581$	−3.09850	+	2.25119i	−0.128547	+	0.0933951i
$582$		0			0
$583$	−2.13451	+	6.33929i	−0.0884022	+	0.262547i
$584$	9.36268			0.387430
$585$		0			0
$586$	11.2068	+	34.4911i	0.462950	+	1.42482i
$587$	6.96460	−	21.4348i	0.287460	−	0.884710i	−0.698191	−	0.715912i	$-0.746011\pi$
$587$	6.96460	−	21.4348i	0.287460	−	0.884710i	0.985651	−	0.168799i	$-0.0539887\pi$
$588$		0			0
$589$	−20.4621	−	14.8666i	−0.843127	−	0.612567i
$590$	17.9111	−	55.1247i	0.737389	−	2.26945i
$591$		0			0
$592$	11.9987	−	8.71755i	0.493143	−	0.358289i
$593$	−39.7293			−1.63148			−0.815742	−	0.578415i	$-0.803671\pi$
$593$	−39.7293			−1.63148			−0.815742	+	0.578415i	$0.803671\pi$
$594$		0			0
$595$	−4.84604			−0.198668
$596$	−0.0380068	+	0.0276136i	−0.00155682	+	0.00113110i
$597$		0			0
$598$	2.71600	−	8.35898i	0.111065	−	0.341824i
$599$	−6.65672	−	4.83639i	−0.271986	−	0.197610i	0.443428	−	0.896310i	$-0.353762\pi$
$599$	−6.65672	−	4.83639i	−0.271986	−	0.197610i	−0.715414	+	0.698700i	$0.753762\pi$
$600$		0			0
$601$	−7.10571	+	21.8691i	−0.289848	+	0.892061i	0.695055	+	0.718956i	$0.255380\pi$
$601$	−7.10571	+	21.8691i	−0.289848	+	0.892061i	−0.984903	+	0.173105i	$0.944620\pi$
$602$	0.226469	+	0.696998i	0.00923017	+	0.0284075i
$603$		0			0
$604$	0.384718			0.0156539
$605$	31.5175	−	21.8907i	1.28137	−	0.889984i
$606$		0			0
$607$	−0.0354023	+	0.0257213i	−0.00143694	+	0.00104399i	−0.588503	−	0.808495i	$-0.700283\pi$
$607$	−0.0354023	+	0.0257213i	−0.00143694	+	0.00104399i	0.587067	+	0.809539i	$0.300283\pi$
$608$	−0.544335	−	1.67529i	−0.0220757	−	0.0679420i
$609$		0			0
$610$	31.9797	+	23.2346i	1.29482	+	0.940743i
$611$	−8.25383	−	5.99676i	−0.333914	−	0.242603i
$612$		0			0
$613$	−9.45678	−	29.1050i	−0.381956	−	1.17554i	−0.938665	−	0.344832i	$-0.887936\pi$
$613$	−9.45678	−	29.1050i	−0.381956	−	1.17554i	0.556709	−	0.830708i	$-0.312064\pi$
$614$	−5.21018	+	3.78542i	−0.210266	+	0.152767i
$615$		0			0
$616$	2.53670	−	1.80214i	0.102207	−	0.0726105i
$617$	−8.64528			−0.348046			−0.174023	−	0.984742i	$-0.555677\pi$
$617$	−8.64528			−0.348046			−0.174023	+	0.984742i	$0.555677\pi$
$618$		0			0
$619$	−10.4157	−	32.0562i	−0.418642	−	1.28845i	−0.908952	−	0.416900i	$-0.863116\pi$
$619$	−10.4157	−	32.0562i	−0.418642	−	1.28845i	0.490310	−	0.871548i	$-0.336884\pi$
$620$	−0.424505	+	1.30649i	−0.0170485	+	0.0524700i
$621$		0			0
$622$	26.3752	+	19.1627i	1.05755	+	0.768354i
$623$	0.361214	−	1.11170i	0.0144717	−	0.0445394i
$624$		0			0
$625$	7.63877	−	5.54989i	0.305551	−	0.221996i
$626$	24.0002			0.959240
$627$		0			0
$628$	0.0553546			0.00220889
$629$	11.9329	−	8.66978i	0.475797	−	0.345687i
$630$		0			0
$631$	4.15555	−	12.7895i	0.165430	−	0.509140i	−0.833638	−	0.552311i	$-0.813746\pi$
$631$	4.15555	−	12.7895i	0.165430	−	0.509140i	0.999068	+	0.0431710i	$0.0137460\pi$
$632$	19.1816	+	13.9363i	0.763003	+	0.554354i
$633$		0			0
$634$	−11.2775	+	34.7085i	−0.447885	+	1.37845i
$635$	−9.94466	−	30.6065i	−0.394642	−	1.21458i
$636$		0			0
$637$	−7.96386			−0.315540
$638$	20.2159	+	15.0185i	0.800354	+	0.594589i
$639$		0			0
$640$	33.4960	−	24.3363i	1.32405	−	0.961976i
$641$	−4.64437	−	14.2939i	−0.183442	−	0.564575i	0.816477	−	0.577379i	$-0.195924\pi$
$641$	−4.64437	−	14.2939i	−0.183442	−	0.564575i	−0.999918	+	0.0128037i	$0.995924\pi$
$642$		0			0
$643$	−10.4101	−	7.56336i	−0.410533	−	0.298270i	0.363284	−	0.931678i	$-0.381655\pi$
$643$	−10.4101	−	7.56336i	−0.410533	−	0.298270i	−0.773818	+	0.633408i	$0.781655\pi$
$644$	0.100552	+	0.0730551i	0.00396229	+	0.00287877i
$645$		0			0
$646$	−8.17674	−	25.1654i	−0.321709	−	0.990120i
$647$	15.1827	−	11.0309i	0.596894	−	0.433669i	−0.247881	−	0.968791i	$-0.579734\pi$
$647$	15.1827	−	11.0309i	0.596894	−	0.433669i	0.844775	+	0.535121i	$0.179734\pi$
$648$		0			0
$649$	11.4488	+	36.5531i	0.449404	+	1.43483i
$650$	11.9296			0.467917
$651$		0			0
$652$	0.310011	+	0.954117i	0.0121410	+	0.0373661i
$653$	−5.29700	+	16.3025i	−0.207287	+	0.637965i	0.792324	+	0.610100i	$0.208871\pi$
$653$	−5.29700	+	16.3025i	−0.207287	+	0.637965i	−0.999612	+	0.0278650i	$0.991129\pi$
$654$		0			0
$655$	−43.3940	−	31.5276i	−1.69554	−	1.23188i
$656$	14.2647	−	43.9021i	0.556941	−	1.71409i
$657$		0			0
$658$	3.46858	−	2.52007i	0.135219	−	0.0982427i
$659$	−40.4572			−1.57599			−0.787995	−	0.615681i	$-0.788881\pi$
$659$	−40.4572			−1.57599			−0.787995	+	0.615681i	$0.788881\pi$
$660$		0			0
$661$	26.4035			1.02698			0.513489	−	0.858096i	$-0.328353\pi$
$661$	26.4035			1.02698			0.513489	+	0.858096i	$0.328353\pi$
$662$	−8.83189	+	6.41674i	−0.343261	+	0.249394i
$663$		0			0
$664$	9.72853	−	29.9413i	0.377540	−	1.16195i
$665$	−4.26516	−	3.09882i	−0.165396	−	0.120167i
$666$		0			0
$667$	8.61585	−	26.5168i	0.333607	−	1.02674i
$668$	−0.292061	−	0.898872i	−0.0113002	−	0.0347784i
$669$		0			0
$670$	20.9993			0.811276
$671$	−26.1215	−	0.277621i	−1.00841	−	0.0107174i
$672$		0			0
$673$	17.9571	−	13.0466i	0.692195	−	0.502909i	−0.185186	−	0.982704i	$-0.559289\pi$
$673$	17.9571	−	13.0466i	0.692195	−	0.502909i	0.877381	+	0.479794i	$0.159289\pi$
$674$	−6.40622	−	19.7163i	−0.246758	−	0.759444i
$675$		0			0
$676$	0.657096	+	0.477409i	0.0252729	+	0.0183619i
$677$	29.9538	+	21.7627i	1.15122	+	0.836408i	0.988642	−	0.150289i	$-0.0480203\pi$
$677$	29.9538	+	21.7627i	1.15122	+	0.836408i	0.162574	+	0.986696i	$0.448020\pi$
$678$		0			0
$679$	1.36119	+	4.18931i	0.0522377	+	0.160771i
$680$	32.2267	−	23.4141i	1.23584	−	0.897889i
$681$		0			0
$682$	−8.06365	−	25.7452i	−0.308773	−	0.985834i
$683$	27.2029			1.04089			0.520445	−	0.853895i	$-0.325766\pi$
$683$	27.2029			1.04089			0.520445	+	0.853895i	$0.325766\pi$
$684$		0			0
$685$	−2.11458	−	6.50801i	−0.0807940	−	0.248658i
$686$	2.08553	−	6.41861i	0.0796260	−	0.245064i
$687$		0			0
$688$	−5.04357	−	3.66437i	−0.192284	−	0.139703i
$689$	0.720796	−	2.21838i	0.0274601	−	0.0845136i
$690$		0			0
$691$	−12.0550	+	8.75846i	−0.458593	+	0.333188i	−0.792979	−	0.609249i	$-0.791471\pi$
$691$	−12.0550	+	8.75846i	−0.458593	+	0.333188i	0.334386	+	0.942436i	$0.391471\pi$
$692$	−1.22480			−0.0465598
$693$		0			0
$694$	−24.2297			−0.919746
$695$	49.8043	−	36.1849i	1.88918	−	1.37257i
$696$		0			0
$697$	14.1865	−	43.6615i	0.537351	−	1.65380i
$698$	−35.5898	−	25.8575i	−1.34710	−	0.978722i
$699$		0			0
$700$	−0.0521307	+	0.160442i	−0.00197035	+	0.00606412i
$701$	−1.74688	−	5.37634i	−0.0659787	−	0.203062i	0.912632	−	0.408782i	$-0.134046\pi$
$701$	−1.74688	−	5.37634i	−0.0659787	−	0.203062i	−0.978611	+	0.205720i	$0.934046\pi$
$702$		0			0
$703$	16.0465			0.605204
$704$	−8.15185	+	24.2103i	−0.307235	+	0.912459i
$705$		0			0
$706$	−0.566207	+	0.411374i	−0.0213095	+	0.0154822i
$707$	0.227945	+	0.701543i	0.00857276	+	0.0263842i
$708$		0			0
$709$	−38.3804	−	27.8850i	−1.44140	−	1.04724i	−0.987747	−	0.156066i	$-0.950119\pi$
$709$	−38.3804	−	27.8850i	−1.44140	−	1.04724i	−0.453658	−	0.891176i	$-0.649881\pi$
$710$	9.82960	+	7.14163i	0.368898	+	0.268020i
$711$		0			0
$712$	2.96918	+	9.13819i	0.111275	+	0.342468i
$713$	−24.1637	+	17.5560i	−0.904939	+	0.657477i
$714$		0			0
$715$	−10.9088	+	7.74995i	−0.407968	+	0.289832i
$716$	−1.12004			−0.0418578
$717$		0			0
$718$	15.1951	+	46.7657i	0.567075	+	1.74528i
$719$	6.92225	−	21.3045i	0.258157	−	0.794524i	−0.735035	−	0.678029i	$-0.762834\pi$
$719$	6.92225	−	21.3045i	0.258157	−	0.794524i	0.993191	−	0.116495i	$-0.0371658\pi$
$720$		0			0
$721$	0.238212	+	0.173071i	0.00887146	+	0.00644549i
$722$	0.448865	−	1.38146i	0.0167050	−	0.0514127i
$723$		0			0
$724$	0.837123	−	0.608205i	0.0311114	−	0.0226038i
$725$	37.8438			1.40548
$726$		0			0
$727$	19.2627			0.714413			0.357207	−	0.934025i	$-0.383729\pi$
$727$	19.2627			0.714413			0.357207	+	0.934025i	$0.383729\pi$
$728$	−0.877853	+	0.637798i	−0.0325354	+	0.0236383i
$729$		0			0
$730$	5.22864	−	16.0921i	0.193521	−	0.595595i
$731$	−5.01593	−	3.64429i	−0.185521	−	0.134789i
$732$		0			0
$733$	11.4626	−	35.2781i	0.423379	−	1.30303i	−0.481158	−	0.876634i	$-0.659784\pi$
$733$	11.4626	−	35.2781i	0.423379	−	1.30303i	0.904538	−	0.426394i	$-0.140216\pi$
$734$	−1.05076	−	3.23389i	−0.0387841	−	0.119365i
$735$		0			0
$736$	−2.08016			−0.0766758
$737$	−11.3132	+	8.03721i	−0.416726	+	0.296054i
$738$		0			0
$739$	−24.2184	+	17.5957i	−0.890888	+	0.647268i	−0.936109	−	0.351709i	$-0.885601\pi$
$739$	−24.2184	+	17.5957i	−0.890888	+	0.647268i	0.0452217	+	0.998977i	$0.485601\pi$
$740$	−0.269320	−	0.828883i	−0.00990042	−	0.0304704i
$741$		0			0
$742$	0.793020	+	0.576163i	0.0291127	+	0.0211516i
$743$	5.02010	+	3.64731i	0.184169	+	0.133807i	0.676050	−	0.736856i	$-0.263690\pi$
$743$	5.02010	+	3.64731i	0.184169	+	0.133807i	−0.491881	+	0.870663i	$0.663690\pi$
$744$		0			0
$745$	−0.727186	−	2.23805i	−0.0266420	−	0.0819958i
$746$	26.6135	−	19.3358i	0.974389	−	0.707935i
$747$		0			0
$748$	0.303072	−	0.900098i	0.0110814	−	0.0329108i
$749$	−2.08162			−0.0760607
$750$		0			0
$751$	0.148564	+	0.457233i	0.00542117	+	0.0166847i	0.953731	−	0.300663i	$-0.0972079\pi$
$751$	0.148564	+	0.457233i	0.00542117	+	0.0166847i	−0.948309	+	0.317347i	$0.897208\pi$
$752$	−11.2702	+	34.6861i	−0.410982	+	1.26487i
$753$		0			0
$754$	−7.10481	−	5.16195i	−0.258742	−	0.187987i
$755$	−5.95503	+	18.3277i	−0.216726	+	0.667014i
$756$		0			0
$757$	−7.65001	+	5.55806i	−0.278045	+	0.202011i	−0.718064	−	0.695977i	$-0.754972\pi$
$757$	−7.65001	+	5.55806i	−0.278045	+	0.202011i	0.440020	+	0.897988i	$0.354972\pi$
$758$	38.9891			1.41615
$759$		0			0
$760$	43.3360			1.57196
$761$	−0.455821	+	0.331173i	−0.0165235	+	0.0120050i	−0.596016	−	0.802972i	$-0.703251\pi$
$761$	−0.455821	+	0.331173i	−0.0165235	+	0.0120050i	0.579493	+	0.814977i	$0.303251\pi$
$762$		0			0
$763$	1.22157	−	3.75961i	0.0442239	−	0.136107i
$764$	0.0763161	+	0.0554469i	0.00276102	+	0.00200600i
$765$		0			0
$766$	9.33392	−	28.7268i	0.337248	−	1.03794i
$767$	−4.12759	−	12.7034i	−0.149038	−	0.458693i
$768$		0			0
$769$	−45.8516			−1.65345			−0.826725	−	0.562606i	$-0.809799\pi$
$769$	−45.8516			−1.65345			−0.826725	+	0.562606i	$0.809799\pi$
$770$	−1.68080	−	5.36637i	−0.0605718	−	0.193390i
$771$		0			0
$772$	1.25862	−	0.914440i	0.0452987	−	0.0329114i
$773$	−14.6681	−	45.1438i	−0.527575	−	1.62371i	−0.759166	−	0.650897i	$-0.774393\pi$
$773$	−14.6681	−	45.1438i	−0.527575	−	1.62371i	0.231591	−	0.972813i	$-0.425607\pi$
$774$		0			0
$775$	−32.7977	−	23.8289i	−1.17813	−	0.855960i
$776$	−29.2931	−	21.2827i	−1.05156	−	0.764004i
$777$		0			0
$778$	3.13599	+	9.65159i	0.112431	+	0.346026i
$779$	40.4055	−	29.3563i	1.44768	−	1.05180i
$780$		0			0
$781$	−8.02895	−	0.0853323i	−0.287299	−	0.00305343i
$782$	−31.2472			−1.11740
$783$		0			0
$784$	8.79746	+	27.0758i	0.314195	+	0.966993i
$785$	−0.856832	+	2.63706i	−0.0305816	+	0.0941206i
$786$		0			0
$787$	19.9410	+	14.4880i	0.710818	+	0.516440i	0.883438	−	0.468549i	$-0.155223\pi$
$787$	19.9410	+	14.4880i	0.710818	+	0.516440i	−0.172619	+	0.984989i	$0.555223\pi$
$788$	0.188236	−	0.579332i	0.00670564	−	0.0206378i
$789$		0			0
$790$	34.6650	−	25.1856i	1.23332	−	0.896063i
$791$	0.141395			0.00502742
$792$		0			0
$793$	9.10942			0.323485
$794$	−1.79732	+	1.30583i	−0.0637845	+	0.0463422i
$795$		0			0
$796$	0.137549	−	0.423333i	0.00487530	−	0.0150046i
$797$	32.6967	+	23.7556i	1.15818	+	0.841465i	0.989546	−	0.144214i	$-0.0460655\pi$
$797$	32.6967	+	23.7556i	1.15818	+	0.841465i	0.168631	+	0.985679i	$0.446066\pi$
$798$		0			0
$799$	−11.2084	+	34.4960i	−0.396526	+	1.22038i
$800$	−0.872487	−	2.68524i	−0.0308471	−	0.0949376i
$801$		0			0
$802$	31.8835			1.12585
$803$	3.34215	+	10.6706i	0.117942	+	0.376558i
$804$		0			0
$805$	−5.03673	+	3.65940i	−0.177521	+	0.128977i
$806$	2.90715	+	8.94730i	0.102400	+	0.315155i
$807$		0			0
$808$	−4.90543	−	3.56400i	−0.172572	−	0.125381i
$809$	−10.3850	−	7.54517i	−0.365119	−	0.265274i	0.390065	−	0.920787i	$-0.372452\pi$
$809$	−10.3850	−	7.54517i	−0.365119	−	0.265274i	−0.755184	+	0.655513i	$0.772452\pi$
$810$		0			0
$811$	11.5743	+	35.6220i	0.406428	+	1.25086i	0.919697	+	0.392629i	$0.128434\pi$
$811$	11.5743	+	35.6220i	0.406428	+	1.25086i	−0.513269	+	0.858228i	$0.671566\pi$
$812$	0.100470	−	0.0729959i	0.00352581	−	0.00256165i
$813$		0			0
$814$	13.7395	+	10.2072i	0.481569	+	0.357761i
$815$	−50.2521			−1.76026
$816$		0			0
$817$	−2.08433	−	6.41491i	−0.0729214	−	0.224429i
$818$	−2.10553	+	6.48015i	−0.0736180	+	0.226573i
$819$		0			0
$820$	−2.19456	−	1.59444i	−0.0766374	−	0.0556803i
$821$	−14.6996	+	45.2406i	−0.513018	+	1.57891i	0.273840	+	0.961775i	$0.411706\pi$
$821$	−14.6996	+	45.2406i	−0.513018	+	1.57891i	−0.786859	+	0.617133i	$0.788294\pi$
$822$		0			0
$823$	−32.5265	+	23.6319i	−1.13380	+	0.823756i	−0.986244	−	0.165297i	$-0.947142\pi$
$823$	−32.5265	+	23.6319i	−1.13380	+	0.823756i	−0.147559	+	0.989053i	$0.547142\pi$
$824$	−2.42034			−0.0843166
$825$		0			0
$826$	5.61320			0.195308
$827$	−22.4362	+	16.3008i	−0.780182	+	0.566835i	−0.905034	−	0.425340i	$-0.860154\pi$
$827$	−22.4362	+	16.3008i	−0.780182	+	0.566835i	0.124852	+	0.992175i	$0.460154\pi$
$828$		0			0
$829$	15.8416	−	48.7555i	0.550202	−	1.69335i	−0.158087	−	0.987425i	$-0.550533\pi$
$829$	15.8416	−	48.7555i	0.550202	−	1.69335i	0.708289	−	0.705923i	$-0.249467\pi$
$830$	−46.0287	−	33.4418i	−1.59768	−	1.16078i
$831$		0			0
$832$	2.75278	−	8.47218i	0.0954354	−	0.293720i
$833$	8.74924	+	26.9274i	0.303143	+	0.932979i
$834$		0			0
$835$	47.3425			1.63835
$836$	0.842314	−	0.598404i	0.0291320	−	0.0206962i
$837$		0			0
$838$	−46.8980	+	34.0734i	−1.62007	+	1.17705i
$839$	0.0425467	+	0.130945i	0.00146888	+	0.00452074i	0.951788	−	0.306756i	$-0.0992435\pi$
$839$	0.0425467	+	0.130945i	0.00146888	+	0.00452074i	−0.950319	+	0.311276i	$0.899243\pi$
$840$		0			0
$841$	0.923189	+	0.670736i	0.0318341	+	0.0231288i
$842$	15.8333	+	11.5035i	0.545650	+	0.396438i
$843$		0			0
$844$	0.141912	+	0.436761i	0.00488482	+	0.0150339i
$845$	−32.9146	+	23.9139i	−1.13230	+	0.822662i
$846$		0			0
$847$	2.95942	+	2.24777i	0.101687	+	0.0772343i
$848$	−8.33837			−0.286341
$849$		0			0
$850$	−13.1061	−	40.3364i	−0.449535	−	1.38353i
$851$	5.85566	−	18.0219i	0.200729	−	0.617781i
$852$		0			0
$853$	−12.4273	−	9.02895i	−0.425502	−	0.309145i	0.354346	−	0.935114i	$-0.384704\pi$
$853$	−12.4273	−	9.02895i	−0.425502	−	0.309145i	−0.779848	+	0.625969i	$0.784704\pi$
$854$	−1.18296	+	3.64077i	−0.0404800	+	0.124585i
$855$		0			0
$856$	13.8430	−	10.0575i	0.473144	−	0.343759i
$857$	−23.0550			−0.787545			−0.393773	−	0.919208i	$-0.628830\pi$
$857$	−23.0550			−0.787545			−0.393773	+	0.919208i	$0.628830\pi$
$858$		0			0
$859$	−54.1194			−1.84653			−0.923265	−	0.384164i	$-0.874490\pi$
$859$	−54.1194			−1.84653			−0.923265	+	0.384164i	$0.874490\pi$
$860$	−0.296380	+	0.215333i	−0.0101065	+	0.00734278i
$861$		0			0
$862$	3.49178	−	10.7466i	0.118930	−	0.366030i
$863$	34.3062	+	24.9249i	1.16780	+	0.848453i	0.990743	−	0.135748i	$-0.0433439\pi$
$863$	34.3062	+	24.9249i	1.16780	+	0.848453i	0.177052	+	0.984201i	$0.443344\pi$
$864$		0			0
$865$	18.9586	−	58.3486i	0.644612	−	1.98391i
$866$	0.613809	+	1.88911i	0.0208581	+	0.0641946i
$867$		0			0
$868$	−0.133036			−0.00451555
$869$	−9.03596	+	26.8360i	−0.306524	+	0.910349i
$870$		0			0
$871$	3.91505	−	2.84445i	0.132656	−	0.0963805i
$872$	10.0413	+	30.9040i	0.340042	+	1.04654i
$873$		0			0
$874$	−27.5017	−	19.9811i	−0.930258	−	0.675872i
$875$	−2.06897	−	1.50320i	−0.0699440	−	0.0508173i
$876$		0			0
$877$	−15.7051	−	48.3354i	−0.530325	−	1.63217i	−0.753540	−	0.657402i	$-0.771655\pi$
$877$	−15.7051	−	48.3354i	−0.530325	−	1.63217i	0.223215	−	0.974769i	$-0.428345\pi$
$878$	6.41212	−	4.65868i	0.216399	−	0.157223i
$879$		0			0
$880$	38.3993	+	28.5271i	1.29444	+	0.961648i
$881$	−33.9359			−1.14333			−0.571665	−	0.820487i	$-0.693702\pi$
$881$	−33.9359			−1.14333			−0.571665	+	0.820487i	$0.693702\pi$
$882$		0			0
$883$	−14.3560	−	44.1833i	−0.483119	−	1.48689i	−0.834687	−	0.550725i	$-0.814351\pi$
$883$	−14.3560	−	44.1833i	−0.483119	−	1.48689i	0.351568	−	0.936162i	$-0.385649\pi$
$884$	−0.102344	+	0.314982i	−0.00344219	+	0.0105940i
$885$		0			0
$886$	−1.28414	−	0.932986i	−0.0431417	−	0.0313443i
$887$	−7.56473	+	23.2818i	−0.253999	+	0.781728i	0.740026	+	0.672578i	$0.234813\pi$
$887$	−7.56473	+	23.2818i	−0.253999	+	0.781728i	−0.994025	+	0.109150i	$0.965187\pi$
$888$		0			0
$889$	2.52137	−	1.83188i	0.0845639	−	0.0614393i
$890$	17.3644			0.582056
$891$		0			0
$892$	−0.466401			−0.0156162
$893$	−31.9235	+	23.1938i	−1.06828	+	0.776150i
$894$		0			0
$895$	17.3370	−	53.3580i	0.579514	−	1.78356i
$896$	3.24387	+	2.35681i	0.108370	+	0.0787355i
$897$		0			0
$898$	0.641392	−	1.97400i	0.0214035	−	0.0658732i
$899$	9.22225	+	28.3832i	0.307579	+	0.946632i
$900$		0			0
$901$	−8.29267			−0.276269
$902$	53.2699	+	0.566157i	1.77369	+	0.0188510i
$903$		0			0
$904$	−0.940292	+	0.683162i	−0.0312737	+	0.0227216i
$905$	16.0167	+	49.2944i	0.532414	+	1.63860i
$906$		0			0
$907$	27.8234	+	20.2149i	0.923862	+	0.671225i	0.944482	−	0.328563i	$-0.106564\pi$
$907$	27.8234	+	20.2149i	0.923862	+	0.671225i	−0.0206206	+	0.999787i	$0.506564\pi$
$908$	0.346362	+	0.251647i	0.0114944	+	0.00835118i
$909$		0			0
$910$	0.605972	+	1.86499i	0.0200878	+	0.0618238i
$911$	12.7596	−	9.27037i	0.422743	−	0.307141i	−0.355997	−	0.934487i	$-0.615859\pi$
$911$	12.7596	−	9.27037i	0.422743	−	0.307141i	0.778741	+	0.627346i	$0.215859\pi$
$912$		0			0
$913$	37.5968	+	0.399582i	1.24427	+	0.0132242i
$914$	−43.3997			−1.43553
$915$		0			0
$916$	−0.493174	−	1.51783i	−0.0162949	−	0.0501507i
$917$	1.60518	−	4.94024i	0.0530078	−	0.163141i
$918$		0			0
$919$	−24.4677	−	17.7768i	−0.807115	−	0.586403i	0.105878	−	0.994379i	$-0.466235\pi$
$919$	−24.4677	−	17.7768i	−0.807115	−	0.586403i	−0.912993	+	0.407976i	$0.866235\pi$
$920$	15.8141	−	48.6708i	0.521376	−	1.60463i
$921$		0			0
$922$	31.0487	−	22.5582i	1.02253	−	0.742914i
$923$	2.79996			0.0921619
$924$		0			0
$925$	25.7201			0.845672
$926$	−0.811777	+	0.589790i	−0.0266766	+	0.0193817i
$927$		0			0
$928$	−0.642285	+	1.97675i	−0.0210840	+	0.0648900i
$929$	−0.248201	−	0.180328i	−0.00814320	−	0.00591638i	0.583706	−	0.811965i	$-0.301602\pi$
$929$	−0.248201	−	0.180328i	−0.00814320	−	0.00591638i	−0.591849	+	0.806049i	$0.701602\pi$
$930$		0			0
$931$	−9.51833	+	29.2944i	−0.311951	+	0.960086i
$932$	−0.253854	−	0.781283i	−0.00831528	−	0.0255918i
$933$		0			0
$934$	46.0719			1.50752
$935$	38.1888	+	28.3707i	1.24891	+	0.927823i
$936$		0			0
$937$	−11.1295	+	8.08603i	−0.363584	+	0.264159i	−0.754545	−	0.656248i	$-0.772143\pi$
$937$	−11.1295	+	8.08603i	−0.363584	+	0.264159i	0.390962	+	0.920407i	$0.372143\pi$
$938$	0.628432	+	1.93412i	0.0205190	+	0.0631511i
$939$		0			0
$940$	1.73388	+	1.25973i	0.0565528	+	0.0410880i
$941$	−2.01357	−	1.46295i	−0.0656406	−	0.0476907i	0.554481	−	0.832196i	$-0.312917\pi$
$941$	−2.01357	−	1.46295i	−0.0656406	−	0.0476907i	−0.620122	+	0.784506i	$0.712917\pi$
$942$		0			0
$943$	−18.2255	−	56.0922i	−0.593503	−	1.82661i
$944$	−38.6298	+	28.0662i	−1.25729	+	0.913477i
$945$		0			0
$946$	2.29585	−	6.81848i	0.0746446	−	0.221688i
$947$	−15.1620			−0.492698			−0.246349	−	0.969181i	$-0.579231\pi$
$947$	−15.1620			−0.492698			−0.246349	+	0.969181i	$0.579231\pi$
$948$		0			0
$949$	−1.20493	−	3.70840i	−0.0391137	−	0.120380i
$950$	14.2582	−	43.8821i	0.462596	−	1.42372i
$951$		0			0
$952$	3.12095	+	2.26750i	0.101151	+	0.0734901i
$953$	6.45470	−	19.8655i	0.209088	−	0.643507i	−0.790433	−	0.612549i	$-0.790144\pi$
$953$	6.45470	−	19.8655i	0.209088	−	0.643507i	0.999521	−	0.0309580i	$-0.00985581\pi$
$954$		0			0
$955$	−3.82275	+	2.77739i	−0.123701	+	0.0898742i
$956$	−0.672257			−0.0217423
$957$		0			0
$958$	−31.6331			−1.02202
$959$	0.536130	−	0.389521i	0.0173125	−	0.0125783i
$960$		0			0
$961$	0.299812	−	0.922728i	0.00967137	−	0.0297654i
$962$	−4.82870	−	3.50825i	−0.155683	−	0.113111i
$963$		0			0
$964$	−0.156392	+	0.481326i	−0.00503705	+	0.0155025i
$965$	24.0812	+	74.1143i	0.775202	+	2.38583i
$966$		0			0
$967$	57.3736			1.84501			0.922505	−	0.385985i	$-0.126138\pi$
$967$	57.3736			1.84501			0.922505	+	0.385985i	$0.126138\pi$
$968$	−30.5408	−	0.649252i	−0.981617	−	0.0208678i
$969$		0			0
$970$	−52.9385	+	38.4621i	−1.69975	+	1.23494i
$971$	1.39820	+	4.30322i	0.0448704	+	0.138097i	0.970982	−	0.239153i	$-0.0768698\pi$
$971$	1.39820	+	4.30322i	0.0448704	+	0.138097i	−0.926111	+	0.377250i	$0.876870\pi$
$972$		0			0
$973$	4.82322	+	3.50427i	0.154625	+	0.112342i
$974$	−20.3922	−	14.8158i	−0.653409	−	0.474729i
$975$		0			0
$976$	−10.0629	−	30.9705i	−0.322107	−	0.991342i
$977$	14.5162	−	10.5466i	0.464414	−	0.337417i	−0.330846	−	0.943685i	$-0.607334\pi$
$977$	14.5162	−	10.5466i	0.464414	−	0.337417i	0.795260	+	0.606268i	$0.207334\pi$
$978$		0			0
$979$	−9.35489	+	6.64598i	−0.298983	+	0.212406i
$980$	1.67296			0.0534408
$981$		0			0
$982$	−0.0894786	−	0.275387i	−0.00285538	−	0.00878795i
$983$	−1.99527	+	6.14080i	−0.0636391	+	0.195861i	−0.977821	−	0.209444i	$-0.932835\pi$
$983$	−1.99527	+	6.14080i	−0.0636391	+	0.195861i	0.914182	+	0.405305i	$0.132835\pi$
$984$		0			0
$985$	24.6853	+	17.9349i	0.786538	+	0.571454i
$986$	−9.64810	+	29.6938i	−0.307258	+	0.945643i
$987$		0			0
$988$	−0.291492	+	0.211781i	−0.00927360	+	0.00673766i
$989$	−7.96522			−0.253279
$990$		0			0
$991$	12.2590			0.389420			0.194710	−	0.980861i	$-0.437623\pi$
$991$	12.2590			0.389420			0.194710	+	0.980861i	$0.437623\pi$
$992$	1.80133	−	1.30875i	0.0571924	−	0.0415527i
$993$		0			0
$994$	−0.363606	+	1.11906i	−0.0115329	+	0.0354946i
$995$	18.0382	+	13.1055i	0.571849	+	0.415472i
$996$		0			0
$997$	3.77110	−	11.6062i	0.119432	−	0.367574i	−0.873414	−	0.486979i	$-0.838099\pi$
$997$	3.77110	−	11.6062i	0.119432	−	0.367574i	0.992846	+	0.119405i	$0.0380988\pi$
$998$	−10.8486	−	33.3885i	−0.343406	−	1.05689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.f.487.3		36
3.2	odd	2		891.2.f.e.487.7		36
9.2	odd	6		297.2.n.b.91.3		72
9.4	even	3		99.2.m.b.25.3	yes	72
9.5	odd	6		297.2.n.b.289.7		72
9.7	even	3		99.2.m.b.58.7	yes	72
11.2	odd	10		9801.2.a.co.1.5		18
11.4	even	5	inner	891.2.f.f.730.3		36
11.9	even	5		9801.2.a.cm.1.14		18
33.2	even	10		9801.2.a.cn.1.14		18
33.20	odd	10		9801.2.a.cp.1.5		18
33.26	odd	10		891.2.f.e.730.7		36
99.4	even	15		99.2.m.b.70.7	yes	72
99.13	odd	30		1089.2.e.o.727.14		36
99.31	even	15		1089.2.e.p.727.5		36
99.59	odd	30		297.2.n.b.235.3		72
99.70	even	15		99.2.m.b.4.3	✓	72
99.79	odd	30		1089.2.e.o.364.14		36
99.92	odd	30		297.2.n.b.37.7		72
99.97	even	15		1089.2.e.p.364.5		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.3	✓	72	99.70	even	15
99.2.m.b.25.3	yes	72	9.4	even	3
99.2.m.b.58.7	yes	72	9.7	even	3
99.2.m.b.70.7	yes	72	99.4	even	15
297.2.n.b.37.7		72	99.92	odd	30
297.2.n.b.91.3		72	9.2	odd	6
297.2.n.b.235.3		72	99.59	odd	30
297.2.n.b.289.7		72	9.5	odd	6
891.2.f.e.487.7		36	3.2	odd	2
891.2.f.e.730.7		36	33.26	odd	10
891.2.f.f.487.3		36	1.1	even	1	trivial
891.2.f.f.730.3		36	11.4	even	5	inner
1089.2.e.o.364.14		36	99.79	odd	30
1089.2.e.o.727.14		36	99.13	odd	30
1089.2.e.p.364.5		36	99.97	even	15
1089.2.e.p.727.5		36	99.31	even	15
9801.2.a.cm.1.14		18	11.9	even	5
9801.2.a.cn.1.14		18	33.2	even	10
9801.2.a.co.1.5		18	11.2	odd	10
9801.2.a.cp.1.5		18	33.20	odd	10

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16387 + 0.845603i) q^{2} +(0.0215212 - 0.0662354i) q^{4} +(2.82229 + 2.05051i) q^{5} +(-0.104399 + 0.321307i) q^{7} +(-0.858159 - 2.64114i) q^{8} +O(q^{10})\)	\(q+(-1.16387 + 0.845603i) q^{2} +(0.0215212 - 0.0662354i) q^{4} +(2.82229 + 2.05051i) q^{5} +(-0.104399 + 0.321307i) q^{7} +(-0.858159 - 2.64114i) q^{8} -5.01870 q^{10} +(2.70377 - 1.92084i) q^{11} +(-0.935670 + 0.679804i) q^{13} +(-0.150191 - 0.462240i) q^{14} +(3.34483 + 2.43016i) q^{16} +(3.32650 + 2.41684i) q^{17} +(1.38230 + 4.25428i) q^{19} +(0.196555 - 0.142806i) q^{20} +(-1.52258 + 4.52193i) q^{22} +5.28243 q^{23} +(2.21562 + 6.81898i) q^{25} +(0.514156 - 1.58241i) q^{26} +(0.0190351 + 0.0138298i) q^{28} +(1.63104 - 5.01982i) q^{29} +(-4.57436 + 3.32347i) q^{31} -0.393789 q^{32} -5.91531 q^{34} +(-0.953487 + 0.692749i) q^{35} +(1.10852 - 3.41166i) q^{37} +(-5.20626 - 3.78257i) q^{38} +(2.99372 - 9.21372i) q^{40} +(-3.45020 - 10.6186i) q^{41} -1.50787 q^{43} +(-0.0690391 - 0.220424i) q^{44} +(-6.14808 + 4.46684i) q^{46} +(2.72593 + 8.38956i) q^{47} +(5.57078 + 4.04741i) q^{49} +(-8.34485 - 6.06289i) q^{50} +(0.0248904 + 0.0766047i) q^{52} +(-1.63163 + 1.18545i) q^{53} +(11.5695 + 0.122962i) q^{55} +0.938208 q^{56} +(2.34645 + 7.22164i) q^{58} +(-3.56887 + 10.9839i) q^{59} +(-6.37211 - 4.62961i) q^{61} +(2.51364 - 7.73619i) q^{62} +(-6.23134 + 4.52733i) q^{64} -4.03468 q^{65} -4.18422 q^{67} +(0.231671 - 0.168319i) q^{68} +(0.523947 - 1.61254i) q^{70} +(-1.95860 - 1.42300i) q^{71} +(-1.04183 + 3.20643i) q^{73} +(1.59474 + 4.90810i) q^{74} +0.311533 q^{76} +(0.334907 + 1.06927i) q^{77} +(-6.90716 + 5.01835i) q^{79} +(4.45700 + 13.7172i) q^{80} +(12.9947 + 9.44124i) q^{82} +(9.17143 + 6.66344i) q^{83} +(4.43257 + 13.6421i) q^{85} +(1.75497 - 1.27506i) q^{86} +(-7.39347 - 5.49266i) q^{88} -3.45994 q^{89} +(-0.120743 - 0.371608i) q^{91} +(0.113684 - 0.349884i) q^{92} +(-10.2669 - 7.45932i) q^{94} +(-4.82221 + 14.8412i) q^{95} +(10.5482 - 7.66375i) q^{97} -9.90618 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8}+O(q^{10}) \) 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8	\( 36 q + q^{2} - 11 q^{4} + 8 q^{5} + 2 q^{7} + 3 q^{8} - 4 q^{10} + 2 q^{11} + 11 q^{13} + 10 q^{14} + 9 q^{16} - 10 q^{17} + 4 q^{19} + 45 q^{20} + 16 q^{22} - 20 q^{23} - 11 q^{25} - 6 q^{26} - 27 q^{28} + 23 q^{29} - 3 q^{31} - 18 q^{32} - 8 q^{34} + 9 q^{35} - 21 q^{37} + q^{38} + 25 q^{40} - 10 q^{41} + 8 q^{43} + 19 q^{44} - 9 q^{46} + 34 q^{47} - q^{49} + 27 q^{52} + 2 q^{53} + 9 q^{55} - 114 q^{56} - q^{58} + 16 q^{59} + 3 q^{61} + 92 q^{62} + 13 q^{64} - 84 q^{65} - 10 q^{67} + 23 q^{68} + 46 q^{70} - 24 q^{71} - 20 q^{73} - 68 q^{74} - 16 q^{76} + 26 q^{77} - 19 q^{79} - 28 q^{80} + 47 q^{82} - 7 q^{83} - 25 q^{85} + 77 q^{86} - 18 q^{88} - 28 q^{89} + 10 q^{91} - 50 q^{92} + 63 q^{94} + 77 q^{95} + 33 q^{97} - 164 q^{98}+O(q^{100}) \) 36 * q + q^2 - 11 * q^4 + 8 * q^5 + 2 * q^7 + 3 * q^8 - 4 * q^10 + 2 * q^11 + 11 * q^13 + 10 * q^14 + 9 * q^16 - 10 * q^17 + 4 * q^19 + 45 * q^20 + 16 * q^22 - 20 * q^23 - 11 * q^25 - 6 * q^26 - 27 * q^28 + 23 * q^29 - 3 * q^31 - 18 * q^32 - 8 * q^34 + 9 * q^35 - 21 * q^37 + q^38 + 25 * q^40 - 10 * q^41 + 8 * q^43 + 19 * q^44 - 9 * q^46 + 34 * q^47 - q^49 + 27 * q^52 + 2 * q^53 + 9 * q^55 - 114 * q^56 - q^58 + 16 * q^59 + 3 * q^61 + 92 * q^62 + 13 * q^64 - 84 * q^65 - 10 * q^67 + 23 * q^68 + 46 * q^70 - 24 * q^71 - 20 * q^73 - 68 * q^74 - 16 * q^76 + 26 * q^77 - 19 * q^79 - 28 * q^80 + 47 * q^82 - 7 * q^83 - 25 * q^85 + 77 * q^86 - 18 * q^88 - 28 * q^89 + 10 * q^91 - 50 * q^92 + 63 * q^94 + 77 * q^95 + 33 * q^97 - 164 * q^98

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