LMFDB - Embedded newform 495.2.n.h.181.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [495,2,Mod(91,495)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(495, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("495.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 495 = 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	495.n (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:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 5 x^{14} - 8 x^{13} + 47 x^{12} + 32 x^{11} + 171 x^{10} + 26 x^{9} + 360 x^{8} + \cdots + 1 $ x^16 - 2x^15 + 5x^14 - 8x^13 + 47x^12 + 32x^11 + 171x^10 + 26x^9 + 360x^8 - 172x^7 + 471x^6 - 430x^5 + 383x^4 + 70x^3 + 17x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			181.3
Root			$0.735494 - 0.534368i$ of defining polynomial
Character	$\chi$	$=$	495.181
Dual form			495.2.n.h.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0280832 - 0.0864312i) q^{2} +(1.61135 - 1.17072i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(1.98801 - 1.44438i) q^{7} +(-0.293484 - 0.213228i) q^{8} +O(q^{10})$	\(q+(-0.0280832 - 0.0864312i) q^{2} +(1.61135 - 1.17072i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(1.98801 - 1.44438i) q^{7} +(-0.293484 - 0.213228i) q^{8} +0.0908791 q^{10} +(0.242484 - 3.30775i) q^{11} +(0.0999755 + 0.307693i) q^{13} +(-0.180669 - 0.131264i) q^{14} +(1.22078 - 3.75716i) q^{16} +(-1.13260 + 3.48579i) q^{17} +(-0.437853 - 0.318119i) q^{19} +(0.615482 + 1.89426i) q^{20} +(-0.292702 + 0.0719339i) q^{22} +4.62543 q^{23} +(-0.809017 - 0.587785i) q^{25} +(0.0237866 - 0.0172820i) q^{26} +(1.51244 - 4.65480i) q^{28} +(1.19403 - 0.867515i) q^{29} +(0.275312 + 0.847323i) q^{31} -1.08455 q^{32} +0.333088 q^{34} +(0.759354 + 2.33705i) q^{35} +(1.84899 - 1.34337i) q^{37} +(-0.0151991 + 0.0467779i) q^{38} +(0.293484 - 0.213228i) q^{40} +(-7.26541 - 5.27863i) q^{41} +6.31964 q^{43} +(-3.48171 - 5.61383i) q^{44} +(-0.129897 - 0.399782i) q^{46} +(-1.18347 - 0.859844i) q^{47} +(-0.297142 + 0.914509i) q^{49} +(-0.0280832 + 0.0864312i) q^{50} +(0.521317 + 0.378759i) q^{52} +(3.19196 + 9.82385i) q^{53} +(3.07092 + 1.25277i) q^{55} -0.891432 q^{56} +(-0.108513 - 0.0788390i) q^{58} +(5.09137 - 3.69910i) q^{59} +(-2.00101 + 6.15847i) q^{61} +(0.0655035 - 0.0475911i) q^{62} +(-2.41109 - 7.42059i) q^{64} -0.323527 q^{65} -7.05634 q^{67} +(2.25585 + 6.94279i) q^{68} +(0.180669 - 0.131264i) q^{70} +(2.87940 - 8.86188i) q^{71} +(-5.01044 + 3.64030i) q^{73} +(-0.168034 - 0.122084i) q^{74} -1.07796 q^{76} +(-4.29557 - 6.92609i) q^{77} +(3.58612 + 11.0369i) q^{79} +(3.19603 + 2.32205i) q^{80} +(-0.252202 + 0.776199i) q^{82} +(-5.36887 + 16.5237i) q^{83} +(-2.96519 - 2.15434i) q^{85} +(-0.177476 - 0.546214i) q^{86} +(-0.776471 + 0.919066i) q^{88} -4.70270 q^{89} +(0.643177 + 0.467296i) q^{91} +(7.45320 - 5.41507i) q^{92} +(-0.0410816 + 0.126436i) q^{94} +(0.437853 - 0.318119i) q^{95} +(3.40155 + 10.4689i) q^{97} +0.0873867 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	$ 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) $ 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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 $

$2$	−0.0280832	−	0.0864312i	−0.0198578	−	0.0611161i	0.940637	−	0.339415i	$-0.110229\pi$
$2$	−0.0280832	−	0.0864312i	−0.0198578	−	0.0611161i	−0.960494	+	0.278299i	$0.910229\pi$
$3$		0			0
$3$		0			0
$4$	1.61135	−	1.17072i	0.805676	−	0.585358i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$		0			0
$7$	1.98801	−	1.44438i	0.751399	−	0.545923i	−0.144861	−	0.989452i	$-0.546274\pi$
$7$	1.98801	−	1.44438i	0.751399	−	0.545923i	0.896260	+	0.443529i	$0.146274\pi$
$8$	−0.293484	−	0.213228i	−0.103762	−	0.0753876i
$9$		0			0
$10$	0.0908791			0.0287385
$11$	0.242484	−	3.30775i	0.0731117	−	0.997324i
$11$	0.242484	−	3.30775i	0.0731117	−	0.997324i
$12$		0			0
$13$	0.0999755	+	0.307693i	0.0277282	+	0.0853386i	0.963963	−	0.266037i	$-0.0857142\pi$
$13$	0.0999755	+	0.307693i	0.0277282	+	0.0853386i	−0.936235	+	0.351375i	$0.885714\pi$
$14$	−0.180669	−	0.131264i	−0.0482858	−	0.0350817i
$15$		0			0
$16$	1.22078	−	3.75716i	0.305194	−	0.939291i
$17$	−1.13260	+	3.48579i	−0.274696	+	0.845428i	0.714604	+	0.699530i	$0.246607\pi$
$17$	−1.13260	+	3.48579i	−0.274696	+	0.845428i	−0.989300	+	0.145898i	$0.953393\pi$
$18$		0			0
$19$	−0.437853	−	0.318119i	−0.100450	−	0.0729815i	0.536426	−	0.843947i	$-0.319774\pi$
$19$	−0.437853	−	0.318119i	−0.100450	−	0.0729815i	−0.636877	+	0.770966i	$0.719774\pi$
$20$	0.615482	+	1.89426i	0.137626	+	0.423569i
$21$		0			0
$22$	−0.292702	+	0.0719339i	−0.0624043	+	0.0153364i
$23$	4.62543			0.964470			0.482235	−	0.876042i	$-0.339825\pi$
$23$	4.62543			0.964470			0.482235	+	0.876042i	$0.339825\pi$
$24$		0			0
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	0.0237866	−	0.0172820i	0.00466494	−	0.00338928i
$27$		0			0
$28$	1.51244	−	4.65480i	0.285824	−	0.879675i
$29$	1.19403	−	0.867515i	0.221726	−	0.161094i	−0.471377	−	0.881932i	$-0.656243\pi$
$29$	1.19403	−	0.867515i	0.221726	−	0.161094i	0.693103	+	0.720838i	$0.256243\pi$
$30$		0			0
$31$	0.275312	+	0.847323i	0.0494475	+	0.152184i	0.972731	−	0.231935i	$-0.0745055\pi$
$31$	0.275312	+	0.847323i	0.0494475	+	0.152184i	−0.923284	+	0.384118i	$0.874506\pi$
$32$	−1.08455			−0.191723
$33$		0			0
$34$	0.333088			0.0571241
$35$	0.759354	+	2.33705i	0.128354	+	0.395034i
$36$		0			0
$37$	1.84899	−	1.34337i	0.303971	−	0.220848i	−0.425334	−	0.905036i	$-0.639843\pi$
$37$	1.84899	−	1.34337i	0.303971	−	0.220848i	0.729305	+	0.684188i	$0.239843\pi$
$38$	−0.0151991	+	0.0467779i	−0.00246562	+	0.00758838i
$39$		0			0
$40$	0.293484	−	0.213228i	0.0464038	−	0.0337144i
$41$	−7.26541	−	5.27863i	−1.13467	−	0.824384i	−0.148299	−	0.988943i	$-0.547380\pi$
$41$	−7.26541	−	5.27863i	−1.13467	−	0.824384i	−0.986367	+	0.164559i	$0.947380\pi$
$42$		0			0
$43$	6.31964			0.963736			0.481868	−	0.876244i	$-0.339959\pi$
$43$	6.31964			0.963736			0.481868	+	0.876244i	$0.339959\pi$
$44$	−3.48171	−	5.61383i	−0.524887	−	0.846317i
$45$		0			0
$46$	−0.129897	−	0.399782i	−0.0191523	−	0.0589446i
$47$	−1.18347	−	0.859844i	−0.172627	−	0.125421i	0.498117	−	0.867110i	$-0.334025\pi$
$47$	−1.18347	−	0.859844i	−0.172627	−	0.125421i	−0.670744	+	0.741689i	$0.734025\pi$
$48$		0			0
$49$	−0.297142	+	0.914509i	−0.0424488	+	0.130644i
$50$	−0.0280832	+	0.0864312i	−0.00397156	+	0.0122232i
$51$		0			0
$52$	0.521317	+	0.378759i	0.0722936	+	0.0525244i
$53$	3.19196	+	9.82385i	0.438450	+	1.34941i	0.889510	+	0.456916i	$0.151046\pi$
$53$	3.19196	+	9.82385i	0.438450	+	1.34941i	−0.451060	+	0.892494i	$0.648954\pi$
$54$		0			0
$55$	3.07092	+	1.25277i	0.414083	+	0.168923i
$56$	−0.891432			−0.119123
$57$		0			0
$58$	−0.108513	−	0.0788390i	−0.0142484	−	0.0103521i
$59$	5.09137	−	3.69910i	0.662840	−	0.481581i	−0.204781	−	0.978808i	$-0.565648\pi$
$59$	5.09137	−	3.69910i	0.662840	−	0.481581i	0.867621	+	0.497227i	$0.165648\pi$
$60$		0			0
$61$	−2.00101	+	6.15847i	−0.256203	+	0.788511i	0.737388	+	0.675470i	$0.236059\pi$
$61$	−2.00101	+	6.15847i	−0.256203	+	0.788511i	−0.993590	+	0.113041i	$0.963941\pi$
$62$	0.0655035	−	0.0475911i	0.00831895	−	0.00604407i
$63$		0			0
$64$	−2.41109	−	7.42059i	−0.301387	−	0.927573i
$65$	−0.323527			−0.0401286
$66$		0			0
$67$	−7.05634			−0.862069			−0.431035	−	0.902335i	$-0.641851\pi$
$67$	−7.05634			−0.862069			−0.431035	+	0.902335i	$0.641851\pi$
$68$	2.25585	+	6.94279i	0.273562	+	0.841936i
$69$		0			0
$70$	0.180669	−	0.131264i	0.0215941	−	0.0156890i
$71$	2.87940	−	8.86188i	0.341722	−	1.05171i	−0.621594	−	0.783340i	$-0.713515\pi$
$71$	2.87940	−	8.86188i	0.341722	−	1.05171i	0.963315	−	0.268372i	$-0.0864855\pi$
$72$		0			0
$73$	−5.01044	+	3.64030i	−0.586428	+	0.426065i	−0.841036	−	0.540980i	$-0.818054\pi$
$73$	−5.01044	+	3.64030i	−0.586428	+	0.426065i	0.254608	+	0.967044i	$0.418054\pi$
$74$	−0.168034	−	0.122084i	−0.0195336	−	0.0141920i
$75$		0			0
$76$	−1.07796			−0.123651
$77$	−4.29557	−	6.92609i	−0.489526	−	0.789301i
$78$		0			0
$79$	3.58612	+	11.0369i	0.403470	+	1.24175i	0.922166	+	0.386793i	$0.126417\pi$
$79$	3.58612	+	11.0369i	0.403470	+	1.24175i	−0.518697	+	0.854958i	$0.673583\pi$
$80$	3.19603	+	2.32205i	0.357327	+	0.259614i
$81$		0			0
$82$	−0.252202	+	0.776199i	−0.0278511	+	0.0857168i
$83$	−5.36887	+	16.5237i	−0.589311	+	1.81371i	−0.00808702	+	0.999967i	$0.502574\pi$
$83$	−5.36887	+	16.5237i	−0.589311	+	1.81371i	−0.581223	+	0.813744i	$0.697426\pi$
$84$		0			0
$85$	−2.96519	−	2.15434i	−0.321620	−	0.233670i
$86$	−0.177476	−	0.546214i	−0.0191377	−	0.0588997i
$87$		0			0
$88$	−0.776471	+	0.919066i	−0.0827721	+	0.0979727i
$89$	−4.70270			−0.498485			−0.249242	−	0.968441i	$-0.580182\pi$
$89$	−4.70270			−0.498485			−0.249242	+	0.968441i	$0.580182\pi$
$90$		0			0
$91$	0.643177	+	0.467296i	0.0674233	+	0.0489859i
$92$	7.45320	−	5.41507i	0.777050	−	0.564560i
$93$		0			0
$94$	−0.0410816	+	0.126436i	−0.00423724	+	0.0130409i
$95$	0.437853	−	0.318119i	0.0449228	−	0.0326383i
$96$		0			0
$97$	3.40155	+	10.4689i	0.345375	+	1.06296i	0.961383	+	0.275216i	$0.0887492\pi$
$97$	3.40155	+	10.4689i	0.345375	+	1.06296i	−0.616007	+	0.787741i	$0.711251\pi$
$98$	0.0873867			0.00882739
$99$		0			0
$100$	−1.99174			−0.199174
$101$	−2.07395	−	6.38296i	−0.206366	−	0.635129i	−0.999655	−	0.0262830i	$-0.991633\pi$
$101$	−2.07395	−	6.38296i	−0.206366	−	0.635129i	0.793289	−	0.608846i	$-0.208367\pi$
$102$		0			0
$103$	−12.6233	+	9.17139i	−1.24381	+	0.903684i	−0.997846	−	0.0655935i	$-0.979106\pi$
$103$	−12.6233	+	9.17139i	−1.24381	+	0.903684i	−0.245968	+	0.969278i	$0.579106\pi$
$104$	0.0362677	−	0.111620i	0.00355634	−	0.0109453i
$105$		0			0
$106$	0.759446	−	0.551770i	0.0737640	−	0.0535926i
$107$	−7.26833	−	5.28075i	−0.702656	−	0.510509i	0.178140	−	0.984005i	$-0.442992\pi$
$107$	−7.26833	−	5.28075i	−0.702656	−	0.510509i	−0.880796	+	0.473496i	$0.842992\pi$
$108$		0			0
$109$	−10.7685			−1.03144			−0.515719	−	0.856758i	$-0.672475\pi$
$109$	−10.7685			−1.03144			−0.515719	+	0.856758i	$0.672475\pi$
$110$	0.0220367	−	0.300605i	0.00210112	−	0.0286616i
$111$		0			0
$112$	−2.99984	−	9.23256i	−0.283458	−	0.872394i
$113$	16.0953	+	11.6939i	1.51412	+	1.10007i	0.964308	+	0.264784i	$0.0853007\pi$
$113$	16.0953	+	11.6939i	1.51412	+	1.10007i	0.549812	+	0.835288i	$0.314699\pi$
$114$		0			0
$115$	−1.42934	+	4.39905i	−0.133286	+	0.410213i
$116$	0.908393	−	2.79575i	0.0843422	−	0.259578i
$117$		0			0
$118$	−0.462699	−	0.336170i	−0.0425949	−	0.0309470i
$119$	2.78316	+	8.56570i	0.255132	+	0.785216i
$120$		0			0
$121$	−10.8824	−	1.60415i	−0.989309	−	0.145832i
$122$	0.588478			0.0532783
$123$		0			0
$124$	1.43560	+	1.04302i	0.128921	+	0.0936663i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$		0			0
$127$	−3.74224	+	11.5174i	−0.332070	+	1.02201i	0.636078	+	0.771625i	$0.280556\pi$
$127$	−3.74224	+	11.5174i	−0.332070	+	1.02201i	−0.968147	+	0.250381i	$0.919444\pi$
$128$	−2.32850	+	1.69175i	−0.205812	+	0.149531i
$129$		0			0
$130$	0.00908568	+	0.0279628i	0.000796867	+	0.00245250i
$131$	−18.7043			−1.63420			−0.817099	−	0.576497i	$-0.804419\pi$
$131$	−18.7043			−1.63420			−0.817099	+	0.576497i	$0.804419\pi$
$132$		0			0
$133$	−1.32994			−0.115321
$134$	0.198165	+	0.609888i	0.0171188	+	0.0526863i
$135$		0			0
$136$	1.07567	−	0.781519i	0.0922378	−	0.0670147i
$137$	4.87796	−	15.0128i	0.416752	−	1.28263i	−0.493922	−	0.869506i	$-0.664437\pi$
$137$	4.87796	−	15.0128i	0.416752	−	1.28263i	0.910674	−	0.413125i	$-0.135563\pi$
$138$		0			0
$139$	−11.1932	+	8.13233i	−0.949395	+	0.689776i	−0.950664	−	0.310224i	$-0.899596\pi$
$139$	−11.1932	+	8.13233i	−0.949395	+	0.689776i	0.00126895	+	0.999999i	$0.499596\pi$
$140$	3.95961	+	2.87683i	0.334648	+	0.243136i
$141$		0			0
$142$	−0.846805			−0.0710623
$143$	1.04201	−	0.256083i	0.0871375	−	0.0214147i
$144$		0			0
$145$	0.456080	+	1.40367i	0.0378754	+	0.116568i
$146$	0.455344	+	0.330827i	0.0376846	+	0.0273794i
$147$		0			0
$148$	1.40667	−	4.32927i	0.115627	−	0.355864i
$149$	−2.79288	+	8.59559i	−0.228801	+	0.704178i	0.769082	+	0.639150i	$0.220714\pi$
$149$	−2.79288	+	8.59559i	−0.228801	+	0.704178i	−0.997883	+	0.0650280i	$0.979286\pi$
$150$		0			0
$151$	7.16102	+	5.20278i	0.582755	+	0.423397i	0.839716	−	0.543025i	$-0.182721\pi$
$151$	7.16102	+	5.20278i	0.582755	+	0.423397i	−0.256961	+	0.966422i	$0.582721\pi$
$152$	0.0606708	+	0.186725i	0.00492105	+	0.0151454i
$153$		0			0
$154$	−0.477997	+	0.565778i	−0.0385181	+	0.0455917i
$155$	−0.890928			−0.0715611
$156$		0			0
$157$	−9.49715	−	6.90008i	−0.757955	−	0.550686i	0.140328	−	0.990105i	$-0.455184\pi$
$157$	−9.49715	−	6.90008i	−0.757955	−	0.550686i	−0.898282	+	0.439419i	$0.855184\pi$
$158$	0.853225	−	0.619904i	0.0678789	−	0.0493169i
$159$		0			0
$160$	0.335145	−	1.03147i	0.0264955	−	0.0815448i
$161$	9.19543	−	6.68087i	0.724701	−	0.526526i
$162$		0			0
$163$	2.35476	+	7.24722i	0.184439	+	0.567646i	0.999938	−	0.0111126i	$-0.00353731\pi$
$163$	2.35476	+	7.24722i	0.184439	+	0.567646i	−0.815499	+	0.578759i	$0.803537\pi$
$164$	−17.8869			−1.39673
$165$		0			0
$166$	1.57894			0.122549
$167$	−3.12640	−	9.62208i	−0.241928	−	0.744579i	−0.996126	−	0.0879319i	$-0.971974\pi$
$167$	−3.12640	−	9.62208i	−0.241928	−	0.744579i	0.754198	−	0.656647i	$-0.228026\pi$
$168$		0			0
$169$	10.4325	−	7.57968i	0.802503	−	0.583053i
$170$	−0.102930	+	0.316785i	−0.00789435	+	0.0242963i
$171$		0			0
$172$	10.1832	−	7.39850i	0.776459	−	0.564130i
$173$	7.84357	+	5.69869i	0.596335	+	0.433263i	0.844576	−	0.535435i	$-0.179852\pi$
$173$	7.84357	+	5.69869i	0.596335	+	0.433263i	−0.248241	+	0.968698i	$0.579852\pi$
$174$		0			0
$175$	−2.45732			−0.185756
$176$	−12.1317	−	4.94907i	−0.914464	−	0.373050i
$177$		0			0
$178$	0.132067	+	0.406459i	0.00989882	+	0.0304654i
$179$	14.6904	+	10.6732i	1.09801	+	0.797751i	0.980734	−	0.195348i	$-0.0625837\pi$
$179$	14.6904	+	10.6732i	1.09801	+	0.797751i	0.117276	+	0.993099i	$0.462584\pi$
$180$		0			0
$181$	−1.36254	+	4.19346i	−0.101277	+	0.311697i	−0.988839	−	0.148991i	$-0.952397\pi$
$181$	−1.36254	+	4.19346i	−0.101277	+	0.311697i	0.887562	+	0.460688i	$0.152397\pi$
$182$	0.0223264	−	0.0687137i	0.00165495	−	0.00509340i
$183$		0			0
$184$	−1.35749	−	0.986274i	−0.100075	−	0.0727091i
$185$	0.706250	+	2.17361i	0.0519245	+	0.159807i
$186$		0			0
$187$	11.2555	+	4.59161i	0.823082	+	0.335772i
$188$	−2.91363			−0.212498
$189$		0			0
$190$	−0.0397917	−	0.0289104i	−0.00288679	−	0.00209738i
$191$	9.93939	−	7.22139i	0.719189	−	0.522521i	−0.166936	−	0.985968i	$-0.553387\pi$
$191$	9.93939	−	7.22139i	0.719189	−	0.522521i	0.886125	+	0.463446i	$0.153387\pi$
$192$		0			0
$193$	7.19896	−	22.1561i	0.518193	−	1.59483i	−0.259204	−	0.965823i	$-0.583460\pi$
$193$	7.19896	−	22.1561i	0.518193	−	1.59483i	0.777397	−	0.629010i	$-0.216540\pi$
$194$	0.809313	−	0.588000i	0.0581053	−	0.0422160i
$195$		0			0
$196$	0.591830	+	1.82146i	0.0422736	+	0.130105i
$197$	−19.6929			−1.40306			−0.701532	−	0.712638i	$-0.747500\pi$
$197$	−19.6929			−1.40306			−0.701532	+	0.712638i	$0.747500\pi$
$198$		0			0
$199$	22.2083			1.57431			0.787154	−	0.616757i	$-0.211554\pi$
$199$	22.2083			1.57431			0.787154	+	0.616757i	$0.211554\pi$
$200$	0.112101	+	0.345011i	0.00792672	+	0.0243959i
$201$		0			0
$202$	−0.493444	+	0.358508i	−0.0347186	+	0.0252245i
$203$	1.12073	−	3.44927i	0.0786601	−	0.242091i
$204$		0			0
$205$	7.26541	−	5.27863i	0.507438	−	0.368676i
$206$	1.14720	+	0.833488i	0.0799291	+	0.0580719i
$207$		0			0
$208$	1.27810			0.0886203
$209$	−1.15843	+	1.37117i	−0.0801303	+	0.0948458i
$210$		0			0
$211$	−4.01468	−	12.3559i	−0.276382	−	0.850616i	−0.988850	−	0.148912i	$-0.952423\pi$
$211$	−4.01468	−	12.3559i	−0.276382	−	0.850616i	0.712469	−	0.701704i	$-0.247577\pi$
$212$	16.6443	+	12.0928i	1.14314	+	0.830537i
$213$		0			0
$214$	−0.252304	+	0.776510i	−0.0172471	+	0.0530812i
$215$	−1.95288	+	6.01033i	−0.133185	+	0.409901i
$216$		0			0
$217$	1.77118	+	1.28684i	0.120235	+	0.0873561i
$218$	0.302415	+	0.930736i	0.0204821	+	0.0630374i
$219$		0			0
$220$	6.41497	−	1.57653i	0.432498	−	0.106290i
$221$	−1.18578			−0.0797645
$222$		0			0
$223$	18.3008	+	13.2963i	1.22551	+	0.890387i	0.996546	−	0.0830466i	$-0.0264650\pi$
$223$	18.3008	+	13.2963i	1.22551	+	0.890387i	0.228968	+	0.973434i	$0.426465\pi$
$224$	−2.15610	+	1.56650i	−0.144061	+	0.104666i
$225$		0			0
$226$	0.558712	−	1.71954i	0.0371650	−	0.114382i
$227$	12.7278	−	9.24727i	0.844772	−	0.613763i	−0.0789276	−	0.996880i	$-0.525150\pi$
$227$	12.7278	−	9.24727i	0.844772	−	0.613763i	0.923700	+	0.383118i	$0.125150\pi$
$228$		0			0
$229$	−7.50944	−	23.1117i	−0.496238	−	1.52726i	−0.815019	−	0.579434i	$-0.803273\pi$
$229$	−7.50944	−	23.1117i	−0.496238	−	1.52726i	0.318781	−	0.947828i	$-0.396727\pi$
$230$	0.420355			0.0277174
$231$		0			0
$232$	−0.535408			−0.0351513
$233$	1.65556	+	5.09529i	0.108459	+	0.333804i	0.990527	−	0.137319i	$-0.0438487\pi$
$233$	1.65556	+	5.09529i	0.108459	+	0.333804i	−0.882067	+	0.471123i	$0.843849\pi$
$234$		0			0
$235$	1.18347	−	0.859844i	0.0772013	−	0.0560901i
$236$	3.87340	−	11.9211i	0.252137	−	0.775997i
$237$		0			0
$238$	0.662183	−	0.481104i	0.0429230	−	0.0311854i
$239$	0.745637	+	0.541737i	0.0482312	+	0.0350420i	0.611640	−	0.791136i	$-0.290510\pi$
$239$	0.745637	+	0.541737i	0.0482312	+	0.0350420i	−0.563408	+	0.826179i	$0.690510\pi$
$240$		0			0
$241$	11.4029			0.734523			0.367262	−	0.930118i	$-0.380295\pi$
$241$	11.4029			0.734523			0.367262	+	0.930118i	$0.380295\pi$
$242$	0.166964	+	0.985628i	0.0107328	+	0.0633586i
$243$		0			0
$244$	3.98549	+	12.2661i	0.255145	+	0.785255i
$245$	−0.777928	−	0.565198i	−0.0497000	−	0.0361091i
$246$		0			0
$247$	0.0541084	−	0.166528i	0.00344283	−	0.0105959i
$248$	0.0998738	−	0.307380i	0.00634199	−	0.0195186i
$249$		0			0
$250$	−0.0735227	−	0.0534174i	−0.00464999	−	0.00337841i
$251$	0.274926	+	0.846135i	0.0173532	+	0.0534076i	0.959358	−	0.282191i	$-0.0910613\pi$
$251$	0.274926	+	0.846135i	0.0173532	+	0.0534076i	−0.942005	+	0.335599i	$0.891061\pi$
$252$		0			0
$253$	1.12159	−	15.2998i	0.0705140	−	0.961888i
$254$	1.10056			0.0690551
$255$		0			0
$256$	−12.4130	−	9.01860i	−0.775815	−	0.563663i
$257$	−12.9545	+	9.41196i	−0.808077	+	0.587102i	−0.913272	−	0.407349i	$-0.866453\pi$
$257$	−12.9545	+	9.41196i	−0.808077	+	0.587102i	0.105196	+	0.994452i	$0.466453\pi$
$258$		0			0
$259$	1.73548	−	5.34127i	0.107838	−	0.331890i
$260$	−0.521317	+	0.378759i	−0.0323307	+	0.0234896i
$261$		0			0
$262$	0.525275	+	1.61663i	0.0324516	+	0.0998757i
$263$	−21.2954			−1.31313			−0.656565	−	0.754269i	$-0.727991\pi$
$263$	−21.2954			−1.31313			−0.656565	+	0.754269i	$0.727991\pi$
$264$		0			0
$265$	−10.3294			−0.634531
$266$	0.0373490	+	0.114948i	0.00229001	+	0.00704794i
$267$		0			0
$268$	−11.3703	+	8.26097i	−0.694549	+	0.504619i
$269$	9.35808	−	28.8012i	0.570572	−	1.75604i	−0.0802108	−	0.996778i	$-0.525559\pi$
$269$	9.35808	−	28.8012i	0.570572	−	1.75604i	0.650783	−	0.759264i	$-0.274441\pi$
$270$		0			0
$271$	−4.86915	+	3.53764i	−0.295780	+	0.214897i	−0.725771	−	0.687937i	$-0.758517\pi$
$271$	−4.86915	+	3.53764i	−0.295780	+	0.214897i	0.429991	+	0.902833i	$0.358517\pi$
$272$	11.7140	+	8.51073i	0.710267	+	0.516039i
$273$		0			0
$274$	−1.43456			−0.0866651
$275$	−2.14042	+	2.53350i	−0.129072	+	0.152776i
$276$		0			0
$277$	−8.66386	−	26.6646i	−0.520561	−	1.60212i	−0.772930	−	0.634491i	$-0.781210\pi$
$277$	−8.66386	−	26.6646i	−0.520561	−	1.60212i	0.252369	−	0.967631i	$-0.418790\pi$
$278$	1.01723	+	0.739059i	0.0610093	+	0.0443258i
$279$		0			0
$280$	0.275468	−	0.847802i	0.0164623	−	0.0506659i
$281$	−8.10523	+	24.9453i	−0.483517	+	1.48811i	0.350599	+	0.936526i	$0.385978\pi$
$281$	−8.10523	+	24.9453i	−0.483517	+	1.48811i	−0.834117	+	0.551588i	$0.814022\pi$
$282$		0			0
$283$	−10.0324	−	7.28897i	−0.596365	−	0.433284i	0.248222	−	0.968703i	$-0.420154\pi$
$283$	−10.0324	−	7.28897i	−0.596365	−	0.433284i	−0.844587	+	0.535419i	$0.820154\pi$
$284$	−5.73502	−	17.6506i	−0.340311	−	1.04737i
$285$		0			0
$286$	−0.0513966	−	0.0828708i	−0.00303915	−	0.00490025i
$287$	−22.0681			−1.30264
$288$		0			0
$289$	2.88536	+	2.09634i	0.169727	+	0.123314i
$290$	0.108513	−	0.0788390i	0.00637208	−	0.00462959i
$291$		0			0
$292$	−3.81183	+	11.7316i	−0.223071	+	0.686540i
$293$	24.0919	−	17.5038i	1.40746	−	1.02258i	0.413776	−	0.910379i	$-0.364210\pi$
$293$	24.0919	−	17.5038i	1.40746	−	1.02258i	0.993685	−	0.112202i	$-0.0357902\pi$
$294$		0			0
$295$	1.94473	+	5.98526i	0.113227	+	0.348475i
$296$	−0.829091			−0.0481899
$297$		0			0
$298$	0.821359			0.0475801
$299$	0.462430	+	1.42321i	0.0267430	+	0.0823065i
$300$		0			0
$301$	12.5635	−	9.12794i	0.724150	−	0.526126i
$302$	0.248578	−	0.765046i	0.0143041	−	0.0440234i
$303$		0			0
$304$	−1.72974	+	1.25673i	−0.0992077	+	0.0720786i
$305$	−5.23871	−	3.80614i	−0.299967	−	0.217939i
$306$		0			0
$307$	13.5474			0.773194			0.386597	−	0.922249i	$-0.373650\pi$
$307$	13.5474			0.773194			0.386597	+	0.922249i	$0.373650\pi$
$308$	−15.0302	−	6.13148i	−0.856423	−	0.349373i
$309$		0			0
$310$	0.0250201	+	0.0770039i	0.00142105	+	0.00437353i
$311$	7.08052	+	5.14430i	0.401499	+	0.291706i	0.770151	−	0.637861i	$-0.220181\pi$
$311$	7.08052	+	5.14430i	0.401499	+	0.291706i	−0.368652	+	0.929567i	$0.620181\pi$
$312$		0			0
$313$	5.00966	−	15.4181i	0.283162	−	0.871484i	−0.703781	−	0.710417i	$-0.748506\pi$
$313$	5.00966	−	15.4181i	0.283162	−	0.871484i	0.986943	−	0.161067i	$-0.0514936\pi$
$314$	−0.329672	+	1.01463i	−0.0186045	+	0.0572586i
$315$		0			0
$316$	18.6996	+	13.5861i	1.05193	+	0.764275i
$317$	1.81782	+	5.59467i	0.102099	+	0.314228i	0.989039	−	0.147657i	$-0.0471732\pi$
$317$	1.81782	+	5.59467i	0.102099	+	0.314228i	−0.886940	+	0.461885i	$0.847173\pi$
$318$		0			0
$319$	−2.57999	−	4.15992i	−0.144452	−	0.232911i
$320$	7.80247			0.436171
$321$		0			0
$322$	−0.835672	−	0.607152i	−0.0465702	−	0.0338352i
$323$	1.60481	−	1.16596i	0.0892939	−	0.0648758i
$324$		0			0
$325$	0.0999755	−	0.307693i	0.00554564	−	0.0170677i
$326$	0.560256	−	0.407050i	0.0310297	−	0.0225444i
$327$		0			0
$328$	1.00673	+	3.09838i	0.0555871	+	0.171080i
$329$	−3.59470			−0.198182
$330$		0			0
$331$	13.4772			0.740775			0.370387	−	0.928877i	$-0.379225\pi$
$331$	13.4772			0.740775			0.370387	+	0.928877i	$0.379225\pi$
$332$	10.6934	+	32.9109i	0.586877	+	1.80622i
$333$		0			0
$334$	−0.743848	+	0.540437i	−0.0407016	+	0.0295714i
$335$	2.18053	−	6.71098i	0.119135	−	0.366660i
$336$		0			0
$337$	12.2650	−	8.91103i	0.668116	−	0.485415i	−0.201278	−	0.979534i	$-0.564509\pi$
$337$	12.2650	−	8.91103i	0.668116	−	0.485415i	0.869394	+	0.494119i	$0.164509\pi$
$338$	−0.948100	−	0.688835i	−0.0515698	−	0.0374677i
$339$		0			0
$340$	−7.30008			−0.395902
$341$	2.86949	−	0.705200i	0.155392	−	0.0381887i
$342$		0			0
$343$	6.04565	+	18.6066i	0.326435	+	1.00466i
$344$	−1.85471	−	1.34753i	−0.0999993	−	0.0726537i
$345$		0			0
$346$	0.272272	−	0.837966i	0.0146374	−	0.0450493i
$347$	−5.36400	+	16.5087i	−0.287955	+	0.886233i	0.697543	+	0.716543i	$0.254277\pi$
$347$	−5.36400	+	16.5087i	−0.287955	+	0.886233i	−0.985497	+	0.169690i	$0.945723\pi$
$348$		0			0
$349$	3.95801	+	2.87566i	0.211867	+	0.153931i	0.688658	−	0.725086i	$-0.258200\pi$
$349$	3.95801	+	2.87566i	0.211867	+	0.153931i	−0.476791	+	0.879017i	$0.658200\pi$
$350$	0.0690094	+	0.212389i	0.00368871	+	0.0113527i
$351$		0			0
$352$	−0.262986	+	3.58742i	−0.0140172	+	0.191210i
$353$	−9.32665			−0.496408			−0.248204	−	0.968708i	$-0.579840\pi$
$353$	−9.32665			−0.496408			−0.248204	+	0.968708i	$0.579840\pi$
$354$		0			0
$355$	7.53836	+	5.47694i	0.400095	+	0.290686i
$356$	−7.57770	+	5.50552i	−0.401617	+	0.291792i
$357$		0			0
$358$	0.509943	−	1.56944i	0.0269513	−	0.0829477i
$359$	23.4423	−	17.0318i	1.23724	−	0.898904i	0.239825	−	0.970816i	$-0.422910\pi$
$359$	23.4423	−	17.0318i	1.23724	−	0.898904i	0.997411	+	0.0719119i	$0.0229101\pi$
$360$		0			0
$361$	−5.78081	−	17.7915i	−0.304253	−	0.936394i
$362$	0.400710			0.0210608
$363$		0			0
$364$	1.58346			0.0829956
$365$	−1.91382	−	5.89013i	−0.100174	−	0.308303i
$366$		0			0
$367$	11.2839	−	8.19820i	0.589013	−	0.427943i	−0.252949	−	0.967480i	$-0.581401\pi$
$367$	11.2839	−	8.19820i	0.589013	−	0.427943i	0.841962	+	0.539537i	$0.181401\pi$
$368$	5.64662	−	17.3785i	0.294350	−	0.905917i
$369$		0			0
$370$	0.168034	−	0.122084i	0.00873568	−	0.00634684i
$371$	20.5350	+	14.9196i	1.06612	+	0.774585i
$372$		0			0
$373$	−22.0121			−1.13974			−0.569871	−	0.821734i	$-0.693007\pi$
$373$	−22.0121			−1.13974			−0.569871	+	0.821734i	$0.693007\pi$
$374$	0.0807685	−	1.10177i	0.00417644	−	0.0569712i
$375$		0			0
$376$	0.163987	+	0.504701i	0.00845699	+	0.0260279i
$377$	0.386302	+	0.280665i	0.0198956	+	0.0144550i
$378$		0			0
$379$	−0.585450	+	1.80183i	−0.0300726	+	0.0925538i	−0.964966	−	0.262374i	$-0.915495\pi$
$379$	−0.585450	+	1.80183i	−0.0300726	+	0.0925538i	0.934894	+	0.354928i	$0.115495\pi$
$380$	0.333109	−	1.02520i	0.0170881	−	0.0525918i
$381$		0			0
$382$	−0.903283	−	0.656273i	−0.0462160	−	0.0335779i
$383$	−0.296274	−	0.911838i	−0.0151389	−	0.0465928i	0.943202	−	0.332221i	$-0.107798\pi$
$383$	−0.296274	−	0.911838i	−0.0151389	−	0.0465928i	−0.958341	+	0.285628i	$0.907798\pi$
$384$		0			0
$385$	7.91451	−	1.94505i	0.403361	−	0.0991292i
$386$	−2.11715			−0.107760
$387$		0			0
$388$	17.7372	+	12.8868i	0.900471	+	0.654230i
$389$	−5.28186	+	3.83750i	−0.267801	+	0.194569i	−0.713579	−	0.700575i	$-0.752927\pi$
$389$	−5.28186	+	3.83750i	−0.267801	+	0.194569i	0.445778	+	0.895143i	$0.352927\pi$
$390$		0			0
$391$	−5.23877	+	16.1233i	−0.264936	+	0.815389i
$392$	0.282206	−	0.205034i	0.0142535	−	0.0103558i
$393$		0			0
$394$	0.553040	+	1.70208i	0.0278618	+	0.0857497i
$395$	−11.6049			−0.583907
$396$		0			0
$397$	−21.3621			−1.07213			−0.536066	−	0.844176i	$-0.680090\pi$
$397$	−21.3621			−1.07213			−0.536066	+	0.844176i	$0.680090\pi$
$398$	−0.623681	−	1.91949i	−0.0312623	−	0.0962155i
$399$		0			0
$400$	−3.19603	+	2.32205i	−0.159802	+	0.116103i
$401$	−3.90987	+	12.0334i	−0.195250	+	0.600917i	0.804724	+	0.593649i	$0.202313\pi$
$401$	−3.90987	+	12.0334i	−0.195250	+	0.600917i	−0.999974	+	0.00726766i	$0.997687\pi$
$402$		0			0
$403$	−0.233191	+	0.169423i	−0.0116161	+	0.00843956i
$404$	−10.8145	−	7.85719i	−0.538042	−	0.390910i
$405$		0			0
$406$	−0.329598			−0.0163577
$407$	−3.99517	−	6.44173i	−0.198033	−	0.319305i
$408$		0			0
$409$	1.54745	+	4.76256i	0.0765164	+	0.235493i	0.981998	−	0.188893i	$-0.0604899\pi$
$409$	1.54745	+	4.76256i	0.0765164	+	0.235493i	−0.905481	+	0.424386i	$0.860490\pi$
$410$	−0.660274	−	0.479717i	−0.0326086	−	0.0236915i
$411$		0			0
$412$	−9.60355	+	29.5567i	−0.473133	+	1.45615i
$413$	4.77883	−	14.7077i	0.235151	−	0.723719i
$414$		0			0
$415$	−14.0559	−	10.2122i	−0.689977	−	0.501297i
$416$	−0.108428	−	0.333709i	−0.00531614	−	0.0163614i
$417$		0			0
$418$	0.151044	+	0.0616176i	0.00738781	+	0.00301382i
$419$	9.31728			0.455179			0.227589	−	0.973757i	$-0.426916\pi$
$419$	9.31728			0.455179			0.227589	+	0.973757i	$0.426916\pi$
$420$		0			0
$421$	−19.1562	−	13.9178i	−0.933617	−	0.678313i	0.0132587	−	0.999912i	$-0.495780\pi$
$421$	−19.1562	−	13.9178i	−0.933617	−	0.678313i	−0.946876	+	0.321600i	$0.895780\pi$
$422$	−0.955191	+	0.693987i	−0.0464980	+	0.0337827i
$423$		0			0
$424$	1.15794	−	3.56376i	0.0562343	−	0.173071i
$425$	2.96519	−	2.15434i	0.143833	−	0.104501i
$426$		0			0
$427$	4.91712	+	15.1333i	0.237956	+	0.732353i
$428$	−17.8941			−0.864944
$429$		0			0
$430$	0.574323			0.0276963
$431$	7.94388	+	24.4488i	0.382643	+	1.17765i	0.938176	+	0.346160i	$0.112515\pi$
$431$	7.94388	+	24.4488i	0.382643	+	1.17765i	−0.555532	+	0.831495i	$0.687485\pi$
$432$		0			0
$433$	−16.0949	+	11.6937i	−0.773474	+	0.561962i	−0.903013	−	0.429613i	$-0.858650\pi$
$433$	−16.0949	+	11.6937i	−0.773474	+	0.561962i	0.129539	+	0.991574i	$0.458650\pi$
$434$	0.0614824	−	0.189223i	0.00295125	−	0.00908302i
$435$		0			0
$436$	−17.3519	+	12.6069i	−0.831005	+	0.603761i
$437$	−2.02526	−	1.47144i	−0.0968814	−	0.0703884i
$438$		0			0
$439$	−2.83831			−0.135465			−0.0677327	−	0.997704i	$-0.521577\pi$
$439$	−2.83831			−0.135465			−0.0677327	+	0.997704i	$0.521577\pi$
$440$	−0.634141	−	1.02247i	−0.0302315	−	0.0487446i
$441$		0			0
$442$	0.0333006	+	0.102489i	0.00158395	+	0.00487489i
$443$	−21.9190	−	15.9251i	−1.04141	−	0.756625i	−0.0708460	−	0.997487i	$-0.522570\pi$
$443$	−21.9190	−	15.9251i	−1.04141	−	0.756625i	−0.970559	+	0.240862i	$0.922570\pi$
$444$		0			0
$445$	1.45321	−	4.47253i	0.0688889	−	0.212018i
$446$	0.635271	−	1.95516i	0.0300810	−	0.0925797i
$447$		0			0
$448$	−15.5114	−	11.2697i	−0.732846	−	0.532443i
$449$	8.08057	+	24.8694i	0.381346	+	1.17366i	0.939097	+	0.343653i	$0.111665\pi$
$449$	8.08057	+	24.8694i	0.381346	+	1.17366i	−0.557751	+	0.830009i	$0.688335\pi$
$450$		0			0
$451$	−19.2221	+	22.7522i	−0.905135	+	1.07136i
$452$	39.6255			1.86383
$453$		0			0
$454$	−1.15669	−	0.840383i	−0.0542861	−	0.0394412i
$455$	−0.643177	+	0.467296i	−0.0301526	+	0.0219072i
$456$		0			0
$457$	−4.35548	+	13.4048i	−0.203741	+	0.627050i	0.796022	+	0.605268i	$0.206934\pi$
$457$	−4.35548	+	13.4048i	−0.203741	+	0.627050i	−0.999763	+	0.0217820i	$0.993066\pi$
$458$	−1.78668	+	1.29810i	−0.0834861	+	0.0606562i
$459$		0			0
$460$	2.84687	+	8.76177i	0.132736	+	0.408519i
$461$	0.212479			0.00989612			0.00494806	−	0.999988i	$-0.498425\pi$
$461$	0.212479			0.00989612			0.00494806	+	0.999988i	$0.498425\pi$
$462$		0			0
$463$	−9.01059			−0.418758			−0.209379	−	0.977835i	$-0.567144\pi$
$463$	−9.01059			−0.418758			−0.209379	+	0.977835i	$0.567144\pi$
$464$	−1.80175	−	5.54522i	−0.0836441	−	0.257430i
$465$		0			0
$466$	0.393899	−	0.286184i	0.0182470	−	0.0132572i
$467$	−1.83401	+	5.64451i	−0.0848679	+	0.261197i	−0.984481	−	0.175491i	$-0.943849\pi$
$467$	−1.83401	+	5.64451i	−0.0848679	+	0.261197i	0.899613	+	0.436688i	$0.143849\pi$
$468$		0			0
$469$	−14.0281	+	10.1920i	−0.647758	+	0.470624i
$470$	−0.107553	−	0.0781419i	−0.00496105	−	0.00360442i
$471$		0			0
$472$	−2.28299			−0.105083
$473$	1.53241	−	20.9038i	0.0704604	−	0.961156i
$474$		0			0
$475$	0.167245	+	0.514727i	0.00767373	+	0.0236173i
$476$	14.5127	+	10.5441i	0.665187	+	0.483286i
$477$		0			0
$478$	0.0258831	−	0.0796599i	0.00118386	−	0.00364356i
$479$	−9.48284	+	29.1852i	−0.433282	+	1.33351i	0.461555	+	0.887112i	$0.347292\pi$
$479$	−9.48284	+	29.1852i	−0.433282	+	1.33351i	−0.894837	+	0.446394i	$0.852708\pi$
$480$		0			0
$481$	0.598198	+	0.434616i	0.0272755	+	0.0198168i
$482$	−0.320229	−	0.985563i	−0.0145860	−	0.0448912i
$483$		0			0
$484$	−19.4134	+	10.1553i	−0.882427	+	0.461607i
$485$	−11.0077			−0.499832
$486$		0			0
$487$	−32.3998	−	23.5398i	−1.46818	−	1.06669i	−0.981138	−	0.193311i	$-0.938077\pi$
$487$	−32.3998	−	23.5398i	−1.46818	−	1.06669i	−0.487038	−	0.873381i	$-0.661923\pi$
$488$	1.90042	−	1.38074i	0.0860281	−	0.0625031i
$489$		0			0
$490$	−0.0270040	+	0.0831097i	−0.00121992	+	0.00375452i
$491$	15.7927	−	11.4740i	0.712713	−	0.517816i	−0.171335	−	0.985213i	$-0.554808\pi$
$491$	15.7927	−	11.4740i	0.712713	−	0.517816i	0.884048	+	0.467397i	$0.154808\pi$
$492$		0			0
$493$	1.67161	+	5.14469i	0.0752856	+	0.231705i
$494$	−0.0159128			−0.000715950
$495$		0			0
$496$	3.51962			0.158036
$497$	−7.07561	−	21.7765i	−0.317384	−	0.976809i
$498$		0			0
$499$	−7.50690	+	5.45408i	−0.336055	+	0.244158i	−0.742995	−	0.669296i	$-0.766596\pi$
$499$	−7.50690	+	5.45408i	−0.336055	+	0.244158i	0.406941	+	0.913455i	$0.366596\pi$
$500$	0.615482	−	1.89426i	0.0275252	−	0.0847138i
$501$		0			0
$502$	0.0654117	−	0.0475243i	0.00291946	−	0.00212112i
$503$	−15.7812	−	11.4657i	−0.703651	−	0.511232i	0.177468	−	0.984126i	$-0.443209\pi$
$503$	−15.7812	−	11.4657i	−0.703651	−	0.511232i	−0.881119	+	0.472894i	$0.843209\pi$
$504$		0			0
$505$	6.71144			0.298655
$506$	−1.35387	+	0.332726i	−0.0601871	+	0.0147915i
$507$		0			0
$508$	7.45356	+	22.9397i	0.330698	+	1.01779i
$509$	8.55440	+	6.21513i	0.379167	+	0.275481i	0.761002	−	0.648750i	$-0.224708\pi$
$509$	8.55440	+	6.21513i	0.379167	+	0.275481i	−0.381835	+	0.924231i	$0.624708\pi$
$510$		0			0
$511$	−4.70287	+	14.4739i	−0.208043	+	0.640289i
$512$	−2.20971	+	6.80077i	−0.0976561	+	0.300555i
$513$		0			0
$514$	1.17729	+	0.855351i	0.0519280	+	0.0377279i
$515$	−4.82169	−	14.8396i	−0.212469	−	0.653912i
$516$		0			0
$517$	−3.13112	+	3.70614i	−0.137707	+	0.162996i
$518$	−0.510390			−0.0224252
$519$		0			0
$520$	0.0949500	+	0.0689852i	0.00416383	+	0.00302520i
$521$	−6.77644	+	4.92337i	−0.296881	+	0.215697i	−0.726247	−	0.687434i	$-0.758737\pi$
$521$	−6.77644	+	4.92337i	−0.296881	+	0.215697i	0.429366	+	0.903131i	$0.358737\pi$
$522$		0			0
$523$	10.6523	−	32.7846i	0.465795	−	1.43357i	−0.392186	−	0.919886i	$-0.628281\pi$
$523$	10.6523	−	32.7846i	0.465795	−	1.43357i	0.857980	−	0.513683i	$-0.171719\pi$
$524$	−30.1391	+	21.8974i	−1.31663	+	0.956591i
$525$		0			0
$526$	0.598043	+	1.84059i	0.0260759	+	0.0802534i
$527$	−3.26541			−0.142243
$528$		0			0
$529$	−1.60536			−0.0697983
$530$	0.290083	+	0.892783i	0.0126004	+	0.0387800i
$531$		0			0
$532$	−2.14301	+	1.55698i	−0.0929111	+	0.0675038i
$533$	0.897834	−	2.76325i	0.0388895	−	0.119690i
$534$		0			0
$535$	7.26833	−	5.28075i	0.314237	−	0.228307i
$536$	2.07092	+	1.50461i	0.0894502	+	0.0649894i
$537$		0			0
$538$	−2.75213			−0.118653
$539$	2.95291	+	1.20462i	0.127191	+	0.0518869i
$540$		0			0
$541$	−7.43553	−	22.8842i	−0.319678	−	0.983868i	−0.973786	−	0.227467i	$-0.926956\pi$
$541$	−7.43553	−	22.8842i	−0.319678	−	0.983868i	0.654108	−	0.756402i	$-0.273044\pi$
$542$	0.442504	+	0.321498i	0.0190072	+	0.0138095i
$543$		0			0
$544$	1.22836	−	3.78051i	0.0526656	−	0.162088i
$545$	3.32766	−	10.2415i	0.142541	−	0.438697i
$546$		0			0
$547$	17.9233	+	13.0220i	0.766343	+	0.556781i	0.900849	−	0.434132i	$-0.142945\pi$
$547$	17.9233	+	13.0220i	0.766343	+	0.556781i	−0.134506	+	0.990913i	$0.542945\pi$
$548$	−9.71563	−	29.9016i	−0.415031	−	1.27733i
$549$		0			0
$550$	0.279083	+	0.113850i	0.0119001	+	0.00485459i
$551$	−0.798784			−0.0340293
$552$		0			0
$553$	23.0707	+	16.7619i	0.981068	+	0.712787i
$554$	−2.06135	+	1.49766i	−0.0875782	+	0.0636293i
$555$		0			0
$556$	−8.51553	+	26.2081i	−0.361139	+	1.11147i
$557$	−6.22550	+	4.52309i	−0.263783	+	0.191649i	−0.711813	−	0.702369i	$-0.752126\pi$
$557$	−6.22550	+	4.52309i	−0.263783	+	0.191649i	0.448030	+	0.894018i	$0.352126\pi$
$558$		0			0
$559$	0.631809	+	1.94451i	0.0267227	+	0.0822439i
$560$	9.70768			0.410224
$561$		0			0
$562$	2.38367			0.100549
$563$	−10.0877	−	31.0469i	−0.425148	−	1.30847i	−0.902853	−	0.429950i	$-0.858531\pi$
$563$	−10.0877	−	31.0469i	−0.425148	−	1.30847i	0.477705	−	0.878520i	$-0.341469\pi$
$564$		0			0
$565$	−16.0953	+	11.6939i	−0.677135	+	0.491967i
$566$	−0.348252	+	1.07181i	−0.0146381	+	0.0450515i
$567$		0			0
$568$	−2.73466	+	1.98685i	−0.114744	+	0.0833662i
$569$	13.2440	+	9.62230i	0.555215	+	0.403388i	0.829705	−	0.558203i	$-0.188509\pi$
$569$	13.2440	+	9.62230i	0.555215	+	0.403388i	−0.274489	+	0.961590i	$0.588509\pi$
$570$		0			0
$571$	14.2204			0.595107			0.297554	−	0.954705i	$-0.403829\pi$
$571$	14.2204			0.595107			0.297554	+	0.954705i	$0.403829\pi$
$572$	1.37925	−	1.63254i	0.0576693	−	0.0682600i
$573$		0			0
$574$	0.619742	+	1.90737i	0.0258675	+	0.0796121i
$575$	−3.74205	−	2.71876i	−0.156054	−	0.113380i
$576$		0			0
$577$	6.75349	−	20.7851i	0.281151	−	0.865295i	−0.706374	−	0.707838i	$-0.749671\pi$
$577$	6.75349	−	20.7851i	0.281151	−	0.865295i	0.987526	−	0.157457i	$-0.0503295\pi$
$578$	0.100159	−	0.308257i	0.00416605	−	0.0128218i
$579$		0			0
$580$	2.37820	+	1.72787i	0.0987495	+	0.0717457i
$581$	13.1930	+	40.6040i	0.547340	+	1.68454i
$582$		0			0
$583$	33.2688	−	8.17608i	1.37785	−	0.338619i
$584$	2.24670			0.0929690
$585$		0			0
$586$	−2.18945	−	1.59073i	−0.0904452	−	0.0657123i
$587$	31.1788	−	22.6527i	1.28689	−	0.934977i	0.287148	−	0.957886i	$-0.407293\pi$
$587$	31.1788	−	22.6527i	1.28689	−	0.934977i	0.999738	+	0.0229093i	$0.00729289\pi$
$588$		0			0
$589$	0.149003	−	0.458585i	0.00613957	−	0.0188957i
$590$	0.462699	−	0.336170i	0.0190490	−	0.0138399i
$591$		0			0
$592$	−2.79005	−	8.58689i	−0.114670	−	0.352919i
$593$	30.7989			1.26476			0.632379	−	0.774659i	$-0.282079\pi$
$593$	30.7989			1.26476			0.632379	+	0.774659i	$0.282079\pi$
$594$		0			0
$595$	−9.00651			−0.369231
$596$	5.56268	+	17.1202i	0.227856	+	0.701270i
$597$		0			0
$598$	0.110023	−	0.0799367i	0.00449919	−	0.00326886i
$599$	−11.6618	+	35.8914i	−0.476489	+	1.46648i	0.367451	+	0.930043i	$0.380231\pi$
$599$	−11.6618	+	35.8914i	−0.476489	+	1.46648i	−0.843939	+	0.536439i	$0.819769\pi$
$600$		0			0
$601$	18.5724	−	13.4937i	0.757585	−	0.550417i	−0.140584	−	0.990069i	$-0.544898\pi$
$601$	18.5724	−	13.4937i	0.757585	−	0.550417i	0.898169	+	0.439651i	$0.144898\pi$
$602$	−1.14176	−	0.829539i	−0.0465348	−	0.0338095i
$603$		0			0
$604$	17.6299			0.717351
$605$	4.88849	−	9.85407i	0.198745	−	0.400625i
$606$		0			0
$607$	3.47703	+	10.7012i	0.141128	+	0.434348i	0.996493	−	0.0836784i	$-0.0266668\pi$
$607$	3.47703	+	10.7012i	0.141128	+	0.434348i	−0.855365	+	0.518027i	$0.826667\pi$
$608$	0.474874	+	0.345016i	0.0192587	+	0.0139923i
$609$		0			0
$610$	−0.181850	+	0.559676i	−0.00736288	+	0.0226606i
$611$	0.146250	−	0.450110i	0.00591662	−	0.0182095i
$612$		0			0
$613$	−36.2214	−	26.3164i	−1.46297	−	1.06291i	−0.982578	−	0.185853i	$-0.940495\pi$
$613$	−36.2214	−	26.3164i	−1.46297	−	1.06291i	−0.480390	−	0.877055i	$-0.659505\pi$
$614$	−0.380455	−	1.17092i	−0.0153539	−	0.0472545i
$615$		0			0
$616$	−0.216158	+	2.94863i	−0.00870926	+	0.118804i
$617$	−16.4108			−0.660673			−0.330337	−	0.943863i	$-0.607162\pi$
$617$	−16.4108			−0.660673			−0.330337	+	0.943863i	$0.607162\pi$
$618$		0			0
$619$	−1.21920	−	0.885800i	−0.0490037	−	0.0356033i	0.563014	−	0.826448i	$-0.309642\pi$
$619$	−1.21920	−	0.885800i	−0.0490037	−	0.0356033i	−0.612017	+	0.790844i	$0.709642\pi$
$620$	−1.43560	+	1.04302i	−0.0576550	+	0.0418888i
$621$		0			0
$622$	0.245784	−	0.756446i	0.00985505	−	0.0303307i
$623$	−9.34903	+	6.79247i	−0.374561	+	0.272134i
$624$		0			0
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−1.47329			−0.0588847
$627$		0			0
$628$	−23.3813			−0.933015
$629$	2.58853	+	7.96667i	0.103211	+	0.317652i
$630$		0			0
$631$	26.9869	−	19.6071i	1.07433	−	0.780548i	0.0976458	−	0.995221i	$-0.468869\pi$
$631$	26.9869	−	19.6071i	1.07433	−	0.780548i	0.976686	+	0.214674i	$0.0688688\pi$
$632$	1.30092	−	4.00382i	0.0517478	−	0.159263i
$633$		0			0
$634$	0.432504	−	0.314232i	0.0171769	−	0.0124798i
$635$	−9.79730	−	7.11816i	−0.388794	−	0.282475i
$636$		0			0
$637$	−0.311095			−0.0123260
$638$	−0.287092	+	0.339815i	−0.0113661	+	0.0134534i
$639$		0			0
$640$	−0.889407	−	2.73731i	−0.0351569	−	0.108202i
$641$	6.96411	+	5.05972i	0.275066	+	0.199847i	0.716762	−	0.697318i	$-0.245623\pi$
$641$	6.96411	+	5.05972i	0.275066	+	0.199847i	−0.441697	+	0.897164i	$0.645623\pi$
$642$		0			0
$643$	−3.66045	+	11.2657i	−0.144354	+	0.444276i	−0.996927	−	0.0783317i	$-0.975041\pi$
$643$	−3.66045	+	11.2657i	−0.144354	+	0.444276i	0.852573	+	0.522608i	$0.175041\pi$
$644$	6.99568	−	21.5305i	0.275668	−	0.848420i
$645$		0			0
$646$	−0.145843	−	0.105961i	−0.00573813	−	0.00416900i
$647$	6.86541	+	21.1295i	0.269907	+	0.830688i	0.990522	+	0.137353i	$0.0438595\pi$
$647$	6.86541	+	21.1295i	0.269907	+	0.830688i	−0.720615	+	0.693335i	$0.756141\pi$
$648$		0			0
$649$	−11.0011	−	17.7379i	−0.431831	−	0.696275i
$650$	−0.0294019			−0.00115324
$651$		0			0
$652$	12.2788	+	8.92107i	0.480875	+	0.349376i
$653$	5.54195	−	4.02646i	0.216873	−	0.157568i	−0.474045	−	0.880501i	$-0.657207\pi$
$653$	5.54195	−	4.02646i	0.216873	−	0.157568i	0.690918	+	0.722933i	$0.257207\pi$
$654$		0			0
$655$	5.77993	−	17.7888i	0.225841	−	0.695066i
$656$	−28.7021	+	20.8533i	−1.12063	+	0.814185i
$657$		0			0
$658$	0.100951	+	0.310694i	0.00393547	+	0.0121121i
$659$	10.7882			0.420248			0.210124	−	0.977675i	$-0.432613\pi$
$659$	10.7882			0.420248			0.210124	+	0.977675i	$0.432613\pi$
$660$		0			0
$661$	24.3271			0.946214			0.473107	−	0.881005i	$-0.343132\pi$
$661$	24.3271			0.946214			0.473107	+	0.881005i	$0.343132\pi$
$662$	−0.378483	−	1.16485i	−0.0147102	−	0.0452732i
$663$		0			0
$664$	5.09900	−	3.70464i	0.197880	−	0.143768i
$665$	0.410975	−	1.26485i	0.0159369	−	0.0490488i
$666$		0			0
$667$	5.52292	−	4.01263i	0.213848	−	0.155370i
$668$	−16.3025	−	11.8444i	−0.630761	−	0.458275i
$669$		0			0
$670$	−0.641274			−0.0247746
$671$	19.8855	+	8.11216i	0.767669	+	0.313167i
$672$		0			0
$673$	10.5821	+	32.5684i	0.407910	+	1.25542i	0.918441	+	0.395559i	$0.129449\pi$
$673$	10.5821	+	32.5684i	0.407910	+	1.25542i	−0.510530	+	0.859860i	$0.670551\pi$
$674$	−1.11463	−	0.809826i	−0.0429340	−	0.0311933i
$675$		0			0
$676$	7.93684	−	24.4271i	0.305263	−	0.939503i
$677$	5.47487	−	16.8499i	0.210416	−	0.647595i	−0.789031	−	0.614353i	$-0.789417\pi$
$677$	5.47487	−	16.8499i	0.210416	−	0.647595i	0.999447	−	0.0332415i	$-0.0105831\pi$
$678$		0			0
$679$	21.8834	+	15.8992i	0.839807	+	0.610156i
$680$	0.410869	+	1.26452i	0.0157561	+	0.0484923i
$681$		0			0
$682$	−0.141536	−	0.228209i	−0.00541968	−	0.00873858i
$683$	−19.2788			−0.737683			−0.368842	−	0.929492i	$-0.620246\pi$
$683$	−19.2788			−0.737683			−0.368842	+	0.929492i	$0.620246\pi$
$684$		0			0
$685$	12.7707	+	9.27843i	0.487942	+	0.354511i
$686$	1.43841	−	1.04507i	0.0549187	−	0.0399008i
$687$		0			0
$688$	7.71486	−	23.7439i	0.294126	−	0.905228i
$689$	−2.70361	+	1.96429i	−0.102999	+	0.0748334i
$690$		0			0
$691$	−8.42752	−	25.9372i	−0.320598	−	0.986699i	−0.973389	−	0.229161i	$-0.926402\pi$
$691$	−8.42752	−	25.9372i	−0.320598	−	0.986699i	0.652791	−	0.757538i	$-0.273598\pi$
$692$	19.3103			0.734067
$693$		0			0
$694$	1.57750			0.0598812
$695$	−4.27542	−	13.1584i	−0.162176	−	0.499126i
$696$		0			0
$697$	26.6290	−	19.3471i	1.00865	−	0.732824i
$698$	0.137393	−	0.422853i	0.00520041	−	0.0160052i
$699$		0			0
$700$	−3.95961	+	2.87683i	−0.149659	+	0.108734i
$701$	−31.7252	−	23.0497i	−1.19824	−	0.870574i	−0.204132	−	0.978943i	$-0.565437\pi$
$701$	−31.7252	−	23.0497i	−1.19824	−	0.870574i	−0.994111	+	0.108369i	$0.965437\pi$
$702$		0			0
$703$	−1.23693			−0.0466519
$704$	−25.1301	+	6.17592i	−0.947126	+	0.232764i
$705$		0			0
$706$	0.261922	+	0.806113i	0.00985757	+	0.0303385i
$707$	−13.3425	−	9.69386i	−0.501794	−	0.364575i
$708$		0			0
$709$	8.72458	−	26.8515i	0.327658	−	1.00843i	−0.642568	−	0.766229i	$-0.722131\pi$
$709$	8.72458	−	26.8515i	0.327658	−	1.00843i	0.970226	−	0.242200i	$-0.0778691\pi$
$710$	0.261677	−	0.805359i	0.00982057	−	0.0302246i
$711$		0			0
$712$	1.38016	+	1.00275i	0.0517239	+	0.0375796i
$713$	1.27344	+	3.91924i	0.0476906	+	0.146777i
$714$		0			0
$715$	−0.0784503	+	1.07015i	−0.00293387	+	0.0400212i
$716$	36.1666			1.35161
$717$		0			0
$718$	−2.13041	−	1.54784i	−0.0795063	−	0.0577647i
$719$	34.1565	−	24.8162i	1.27382	−	0.925486i	0.274475	−	0.961594i	$-0.411496\pi$
$719$	34.1565	−	24.8162i	1.27382	−	0.925486i	0.999348	+	0.0361078i	$0.0114960\pi$
$720$		0			0
$721$	−11.8484	+	36.4657i	−0.441259	+	1.35806i
$722$	−1.37540	+	0.999284i	−0.0511869	+	0.0371895i
$723$		0			0
$724$	2.71382	+	8.35228i	0.100858	+	0.310410i
$725$	−1.47591			−0.0548137
$726$		0			0
$727$	5.10543			0.189350			0.0946750	−	0.995508i	$-0.469819\pi$
$727$	5.10543			0.189350			0.0946750	+	0.995508i	$0.469819\pi$
$728$	−0.0891214	−	0.274287i	−0.00330306	−	0.0101658i
$729$		0			0
$730$	−0.455344	+	0.330827i	−0.0168531	+	0.0122445i
$731$	−7.15763	+	22.0289i	−0.264734	+	0.814769i
$732$		0			0
$733$	15.5996	−	11.3338i	0.576185	−	0.418623i	−0.261162	−	0.965295i	$-0.584106\pi$
$733$	15.5996	−	11.3338i	0.576185	−	0.418623i	0.837347	+	0.546672i	$0.184106\pi$
$734$	−1.02547	−	0.745045i	−0.0378507	−	0.0275001i
$735$		0			0
$736$	−5.01652			−0.184911
$737$	−1.71105	+	23.3406i	−0.0630274	+	0.859762i
$738$		0			0
$739$	−11.0939	−	34.1435i	−0.408096	−	1.25599i	−0.918282	−	0.395926i	$-0.870424\pi$
$739$	−11.0939	−	34.1435i	−0.408096	−	1.25599i	0.510187	−	0.860064i	$-0.329576\pi$
$740$	3.68270	+	2.67564i	0.135379	+	0.0983584i
$741$		0			0
$742$	0.712826	−	2.19385i	0.0261687	−	0.0805389i
$743$	−3.81228	+	11.7330i	−0.139859	+	0.430442i	−0.996314	−	0.0857798i	$-0.972662\pi$
$743$	−3.81228	+	11.7330i	−0.139859	+	0.430442i	0.856455	+	0.516221i	$0.172662\pi$
$744$		0			0
$745$	−7.31184	−	5.31236i	−0.267885	−	0.194630i
$746$	0.618169	+	1.90253i	0.0226328	+	0.0696565i
$747$		0			0
$748$	23.5120	−	5.77826i	0.859684	−	0.211274i
$749$	−22.0769			−0.806674
$750$		0			0
$751$	−5.50024	−	3.99616i	−0.200707	−	0.145822i	0.482892	−	0.875680i	$-0.339586\pi$
$751$	−5.50024	−	3.99616i	−0.200707	−	0.145822i	−0.683599	+	0.729858i	$0.739586\pi$
$752$	−4.67533	+	3.39683i	−0.170492	+	0.123870i
$753$		0			0
$754$	0.0134096	−	0.0412705i	0.000488349	−	0.00150298i
$755$	−7.16102	+	5.20278i	−0.260616	+	0.189349i
$756$		0			0
$757$	−3.16082	−	9.72801i	−0.114882	−	0.353571i	0.877040	−	0.480417i	$-0.159515\pi$
$757$	−3.16082	−	9.72801i	−0.114882	−	0.353571i	−0.991922	+	0.126846i	$0.959515\pi$
$758$	0.172176			0.00625370
$759$		0			0
$760$	−0.196335			−0.00712181
$761$	−7.57503	−	23.3136i	−0.274595	−	0.845116i	−0.989326	−	0.145717i	$-0.953451\pi$
$761$	−7.57503	−	23.3136i	−0.274595	−	0.845116i	0.714732	−	0.699399i	$-0.246549\pi$
$762$		0			0
$763$	−21.4080	+	15.5538i	−0.775022	+	0.563086i
$764$	7.56166	−	23.2724i	0.273571	−	0.841966i
$765$		0			0
$766$	−0.0704909	+	0.0512147i	−0.00254694	+	0.00185046i
$767$	1.64720	+	1.19676i	0.0594768	+	0.0432125i
$768$		0			0
$769$	27.2852			0.983930			0.491965	−	0.870615i	$-0.336279\pi$
$769$	27.2852			0.983930			0.491965	+	0.870615i	$0.336279\pi$
$770$	−0.390378	−	0.629437i	−0.0140682	−	0.0226833i
$771$		0			0
$772$	−14.3385	−	44.1293i	−0.516053	−	1.58825i
$773$	−7.01865	−	5.09935i	−0.252443	−	0.183411i	0.454366	−	0.890815i	$-0.349866\pi$
$773$	−7.01865	−	5.09935i	−0.252443	−	0.183411i	−0.706809	+	0.707404i	$0.749866\pi$
$774$		0			0
$775$	0.275312	−	0.847323i	0.00988950	−	0.0304367i
$776$	1.23397	−	3.79776i	0.0442968	−	0.136332i
$777$		0			0
$778$	0.480011	+	0.348748i	0.0172092	+	0.0125032i
$779$	1.50195	+	4.62253i	0.0538130	+	0.165619i
$780$		0			0
$781$	−28.6147	−	11.6732i	−1.02391	−	0.417700i
$782$	1.54067			0.0550944
$783$		0			0
$784$	3.07321	+	2.23282i	0.109758	+	0.0797436i
$785$	9.49715	−	6.90008i	0.338968	−	0.246274i
$786$		0			0
$787$	−9.29945	+	28.6208i	−0.331490	+	1.02022i	0.636936	+	0.770917i	$0.280202\pi$
$787$	−9.29945	+	28.6208i	−0.331490	+	1.02022i	−0.968425	+	0.249303i	$0.919798\pi$
$788$	−31.7323	+	23.0548i	−1.13041	+	0.821294i
$789$		0			0
$790$	0.325903	+	1.00303i	0.0115951	+	0.0356861i
$791$	48.8882			1.73826
$792$		0			0
$793$	−2.09497			−0.0743945
$794$	0.599915	+	1.84635i	0.0212902	+	0.0655245i
$795$		0			0
$796$	35.7855	−	25.9997i	1.26838	−	0.921533i
$797$	−9.94562	+	30.6095i	−0.352292	+	1.08424i	0.605271	+	0.796019i	$0.293065\pi$
$797$	−9.94562	+	30.6095i	−0.352292	+	1.08424i	−0.957563	+	0.288224i	$0.906935\pi$
$798$		0			0
$799$	4.33764	−	3.15148i	0.153455	−	0.111491i
$800$	0.877420	+	0.637483i	0.0310215	+	0.0225384i
$801$		0			0
$802$	1.14986			0.0406029
$803$	10.8262	+	17.4560i	0.382050	+	0.616009i
$804$		0			0
$805$	3.51234	+	10.8099i	0.123794	+	0.380998i
$806$	0.0211922	+	0.0153970i	0.000746462	+	0.000542337i
$807$		0			0
$808$	−0.752358	+	2.31552i	−0.0264679	+	0.0814597i
$809$	13.0540	−	40.1760i	0.458953	−	1.41251i	−0.407477	−	0.913215i	$-0.633591\pi$
$809$	13.0540	−	40.1760i	0.458953	−	1.41251i	0.866431	−	0.499297i	$-0.166409\pi$
$810$		0			0
$811$	38.2700	+	27.8047i	1.34384	+	0.976357i	0.999293	+	0.0375875i	$0.0119673\pi$
$811$	38.2700	+	27.8047i	1.34384	+	0.976357i	0.344546	+	0.938769i	$0.388033\pi$
$812$	−2.23221	−	6.87005i	−0.0783353	−	0.241091i
$813$		0			0
$814$	−0.444569	+	0.526211i	−0.0155821	+	0.0184437i
$815$	−7.62018			−0.266923
$816$		0			0
$817$	−2.76707	−	2.01040i	−0.0968076	−	0.0703349i
$818$	0.368176	−	0.267496i	0.0128730	−	0.00935276i
$819$		0			0
$820$	5.52736	−	17.0115i	0.193024	−	0.594066i
$821$	−21.6295	+	15.7148i	−0.754876	+	0.548449i	−0.897334	−	0.441351i	$-0.854499\pi$
$821$	−21.6295	+	15.7148i	−0.754876	+	0.548449i	0.142458	+	0.989801i	$0.454499\pi$
$822$		0			0
$823$	−5.75152	−	17.7014i	−0.200485	−	0.617031i	−0.999869	−	0.0162092i	$-0.994840\pi$
$823$	−5.75152	−	17.7014i	−0.200485	−	0.617031i	0.799383	−	0.600822i	$-0.205160\pi$
$824$	5.66035			0.197188
$825$		0			0
$826$	−1.40541			−0.0489004
$827$	1.38068	+	4.24930i	0.0480110	+	0.147763i	0.972188	−	0.234202i	$-0.0752476\pi$
$827$	1.38068	+	4.24930i	0.0480110	+	0.147763i	−0.924177	+	0.381965i	$0.875248\pi$
$828$		0			0
$829$	−30.3591	+	22.0572i	−1.05441	+	0.766077i	−0.973047	−	0.230607i	$-0.925929\pi$
$829$	−30.3591	+	22.0572i	−1.05441	+	0.766077i	−0.0813673	+	0.996684i	$0.525929\pi$
$830$	−0.487918	+	1.50166i	−0.0169359	+	0.0521233i
$831$		0			0
$832$	2.04221	−	1.48375i	0.0708009	−	0.0514399i
$833$	−2.85124	−	2.07155i	−0.0987896	−	0.0717749i
$834$		0			0
$835$	10.1173			0.350122
$836$	−0.261389	+	3.56563i	−0.00904032	+	0.123320i
$837$		0			0
$838$	−0.261659	−	0.805303i	−0.00903885	−	0.0278187i
$839$	−25.8181	−	18.7579i	−0.891339	−	0.647595i	0.0448882	−	0.998992i	$-0.485707\pi$
$839$	−25.8181	−	18.7579i	−0.891339	−	0.647595i	−0.936227	+	0.351397i	$0.885707\pi$
$840$		0			0
$841$	−8.28836	+	25.5090i	−0.285806	+	0.879619i
$842$	−0.664965	+	2.04655i	−0.0229162	+	0.0705288i
$843$		0			0
$844$	−20.9343	−	15.2097i	−0.720589	−	0.523539i
$845$	3.98488	+	12.2642i	0.137084	+	0.421901i
$846$		0			0
$847$	−23.9514	+	12.5292i	−0.822979	+	0.430509i
$848$	40.8065			1.40130
$849$		0			0
$850$	−0.269474	−	0.195784i	−0.00924287	−	0.00671534i
$851$	8.55236	−	6.21365i	0.293171	−	0.213001i
$852$		0			0
$853$	16.3512	−	50.3237i	0.559853	−	1.72305i	−0.122916	−	0.992417i	$-0.539224\pi$
$853$	16.3512	−	50.3237i	0.559853	−	1.72305i	0.682769	−	0.730634i	$-0.260776\pi$
$854$	1.16990	−	0.849985i	0.0400333	−	0.0290859i
$855$		0			0
$856$	1.00713	+	3.09963i	0.0344230	+	0.105943i
$857$	17.8209			0.608750			0.304375	−	0.952552i	$-0.401552\pi$
$857$	17.8209			0.608750			0.304375	+	0.952552i	$0.401552\pi$
$858$		0			0
$859$	7.61904			0.259958			0.129979	−	0.991517i	$-0.458509\pi$
$859$	7.61904			0.259958			0.129979	+	0.991517i	$0.458509\pi$
$860$	3.88962	+	11.9710i	0.132635	+	0.408209i
$861$		0			0
$862$	1.89004	−	1.37320i	0.0643752	−	0.0467713i
$863$	−0.623314	+	1.91836i	−0.0212178	+	0.0653018i	−0.961105	−	0.276184i	$-0.910930\pi$
$863$	−0.623314	+	1.91836i	−0.0212178	+	0.0653018i	0.939887	+	0.341486i	$0.110930\pi$
$864$		0			0
$865$	−7.84357	+	5.69869i	−0.266689	+	0.193761i
$866$	1.46269	+	1.06271i	0.0497044	+	0.0361123i
$867$		0			0
$868$	4.36051			0.148005
$869$	37.3770	−	9.18569i	1.26793	−	0.311603i
$870$		0			0
$871$	−0.705461	−	2.17119i	−0.0239036	−	0.0735678i
$872$	3.16039	+	2.29616i	0.107024	+	0.0777577i
$873$		0			0
$874$	−0.0703023	+	0.216368i	−0.00237801	+	0.00731877i
$875$	0.759354	−	2.33705i	0.0256709	−	0.0790068i
$876$		0			0
$877$	−0.929313	−	0.675185i	−0.0313807	−	0.0227994i	0.571984	−	0.820265i	$-0.306174\pi$
$877$	−0.929313	−	0.675185i	−0.0313807	−	0.0227994i	−0.603365	+	0.797465i	$0.706174\pi$
$878$	0.0797089	+	0.245319i	0.00269005	+	0.00827911i
$879$		0			0
$880$	8.45576	−	10.0086i	0.285044	−	0.337390i
$881$	−36.3252			−1.22383			−0.611913	−	0.790925i	$-0.709600\pi$
$881$	−36.3252			−1.22383			−0.611913	+	0.790925i	$0.709600\pi$
$882$		0			0
$883$	18.5815	+	13.5002i	0.625316	+	0.454319i	0.854774	−	0.519000i	$-0.173695\pi$
$883$	18.5815	+	13.5002i	0.625316	+	0.454319i	−0.229458	+	0.973318i	$0.573695\pi$
$884$	−1.91072	+	1.38822i	−0.0642643	+	0.0466908i
$885$		0			0
$886$	−0.760870	+	2.34172i	−0.0255619	+	0.0786715i
$887$	−15.9618	+	11.5969i	−0.535946	+	0.389387i	−0.822577	−	0.568654i	$-0.807464\pi$
$887$	−15.9618	+	11.5969i	−0.535946	+	0.389387i	0.286631	+	0.958041i	$0.407464\pi$
$888$		0			0
$889$	9.19588	+	28.3020i	0.308420	+	0.949219i
$890$	−0.427377			−0.0143257
$891$		0			0
$892$	45.0553			1.50856
$893$	0.244655	+	0.752971i	0.00818707	+	0.0251972i
$894$		0			0
$895$	−14.6904	+	10.6732i	−0.491045	+	0.356765i
$896$	−2.18556	+	6.72646i	−0.0730144	+	0.224715i
$897$		0			0
$898$	1.92257	−	1.39683i	0.0641569	−	0.0466127i
$899$	1.06380	+	0.772894i	0.0354796	+	0.0257775i
$900$		0			0
$901$	−37.8591			−1.26127
$902$	2.50632	+	1.02244i	0.0834512	+	0.0340434i
$903$		0			0
$904$	−2.23023	−	6.86396i	−0.0741765	−	0.228292i
$905$	−3.56717	−	2.59170i	−0.118577	−	0.0861510i
$906$		0			0
$907$	2.34427	−	7.21492i	0.0778402	−	0.239567i	−0.904563	−	0.426340i	$-0.859803\pi$
$907$	2.34427	−	7.21492i	0.0778402	−	0.239567i	0.982403	+	0.186773i	$0.0598027\pi$
$908$	9.68300	−	29.8012i	0.321342	−	0.988988i
$909$		0			0
$910$	0.0584514	+	0.0424674i	0.00193764	+	0.00140778i
$911$	−9.97431	−	30.6978i	−0.330464	−	1.01706i	−0.968914	−	0.247399i	$-0.920424\pi$
$911$	−9.97431	−	30.6978i	−0.330464	−	1.01706i	0.638450	−	0.769663i	$-0.279576\pi$
$912$		0			0
$913$	53.3544	+	21.7656i	1.76577	+	0.720337i
$914$	1.28091			0.0423687
$915$		0			0
$916$	−39.1576	−	28.4496i	−1.29380	−	0.940003i
$917$	−37.1843	+	27.0160i	−1.22793	+	0.892147i
$918$		0			0
$919$	−2.20447	+	6.78467i	−0.0727188	+	0.223805i	−0.980810	−	0.194968i	$-0.937540\pi$
$919$	−2.20447	+	6.78467i	−0.0727188	+	0.223805i	0.908091	+	0.418773i	$0.137540\pi$
$920$	1.35749	−	0.986274i	0.0447551	−	0.0325165i
$921$		0			0
$922$	−0.00596708	−	0.0183648i	−0.000196515	−	0.000604812i
$923$	3.01461			0.0992269
$924$		0			0
$925$	−2.28547			−0.0751459
$926$	0.253046	+	0.778796i	0.00831561	+	0.0255928i
$927$		0			0
$928$	−1.29499	+	0.940864i	−0.0425101	+	0.0308854i
$929$	−16.0259	+	49.3227i	−0.525793	+	1.61823i	0.236948	+	0.971522i	$0.423853\pi$
$929$	−16.0259	+	49.3227i	−0.525793	+	1.61823i	−0.762742	+	0.646703i	$0.776147\pi$
$930$		0			0
$931$	0.421027	−	0.305894i	0.0137986	−	0.0100253i
$932$	8.63284	+	6.27212i	0.282778	+	0.205450i
$933$		0			0
$934$	0.539366			0.0176486
$935$	−7.84501	+	9.28570i	−0.256559	+	0.303675i
$936$		0			0
$937$	13.4538	+	41.4066i	0.439517	+	1.35269i	0.888387	+	0.459096i	$0.151827\pi$
$937$	13.4538	+	41.4066i	0.439517	+	1.35269i	−0.448870	+	0.893597i	$0.648173\pi$
$938$	1.27486	+	0.926242i	0.0416257	+	0.0302429i
$939$		0			0
$940$	0.900360	−	2.77102i	0.0293665	−	0.0903808i
$941$	4.84617	−	14.9150i	0.157981	−	0.486215i	−0.840470	−	0.541858i	$-0.817721\pi$
$941$	4.84617	−	14.9150i	0.157981	−	0.486215i	0.998451	+	0.0556434i	$0.0177210\pi$
$942$		0			0
$943$	−33.6057	−	24.4160i	−1.09435	−	0.795093i
$944$	−7.68268	−	23.6449i	−0.250050	−	0.769575i
$945$		0			0
$946$	−1.84977	+	0.454596i	−0.0601413	+	0.0147802i
$947$	10.8305			0.351944			0.175972	−	0.984395i	$-0.443693\pi$
$947$	10.8305			0.351944			0.175972	+	0.984395i	$0.443693\pi$
$948$		0			0
$949$	−1.62102	−	1.17774i	−0.0526204	−	0.0382309i
$950$	0.0397917	−	0.0289104i	0.00129101	−	0.000937976i
$951$		0			0
$952$	1.00964	−	3.10734i	0.0327225	−	0.100710i
$953$	26.6128	−	19.3353i	0.862073	−	0.626332i	−0.0663755	−	0.997795i	$-0.521144\pi$
$953$	26.6128	−	19.3353i	0.862073	−	0.626332i	0.928448	+	0.371462i	$0.121144\pi$
$954$		0			0
$955$	3.79651	+	11.6845i	0.122852	+	0.378100i
$956$	1.83570			0.0593709
$957$		0			0
$958$	2.78882			0.0901026
$959$	−11.9867	−	36.8913i	−0.387071	−	1.19128i
$960$		0			0
$961$	24.4374	−	17.7548i	0.788302	−	0.572735i
$962$	0.0207651	−	0.0639083i	0.000669493	−	0.00206049i
$963$		0			0
$964$	18.3740	−	13.3495i	0.591788	−	0.429959i
$965$	18.8471	+	13.6932i	0.606711	+	0.440801i
$966$		0			0
$967$	−7.65301			−0.246104			−0.123052	−	0.992400i	$-0.539268\pi$
$967$	−7.65301			−0.246104			−0.123052	+	0.992400i	$0.539268\pi$
$968$	2.85176	+	2.79123i	0.0916589	+	0.0897135i
$969$		0			0
$970$	0.309130	+	0.951405i	0.00992557	+	0.0305478i
$971$	−34.9602	−	25.4001i	−1.12193	−	0.815127i	−0.137426	−	0.990512i	$-0.543883\pi$
$971$	−34.9602	−	25.4001i	−1.12193	−	0.815127i	−0.984500	+	0.175385i	$0.943883\pi$
$972$		0			0
$973$	−10.5061	+	32.3344i	−0.336810	+	1.03659i
$974$	−1.12469	+	3.46143i	−0.0360373	+	0.110911i
$975$		0			0
$976$	20.6956	+	15.0362i	0.662449	+	0.481298i
$977$	−5.45581	−	16.7913i	−0.174547	−	0.537200i	0.825066	−	0.565037i	$-0.191138\pi$
$977$	−5.45581	−	16.7913i	−0.174547	−	0.537200i	−0.999612	+	0.0278370i	$0.991138\pi$
$978$		0			0
$979$	−1.14033	+	15.5553i	−0.0364451	+	0.497151i
$980$	−1.91520			−0.0611789
$981$		0			0
$982$	−1.43522	−	1.04275i	−0.0457998	−	0.0332755i
$983$	−9.78842	+	7.11170i	−0.312202	+	0.226828i	−0.732841	−	0.680400i	$-0.761806\pi$
$983$	−9.78842	+	7.11170i	−0.312202	+	0.226828i	0.420639	+	0.907228i	$0.361806\pi$
$984$		0			0
$985$	6.08545	−	18.7291i	0.193899	−	0.596758i
$986$	0.397717	−	0.288959i	0.0126659	−	0.00920232i
$987$		0			0
$988$	−0.107770	−	0.331681i	−0.00342861	−	0.0105522i
$989$	29.2311			0.929494
$990$		0			0
$991$	−8.45499			−0.268581			−0.134291	−	0.990942i	$-0.542876\pi$
$991$	−8.45499			−0.268581			−0.134291	+	0.990942i	$0.542876\pi$
$992$	−0.298590	−	0.918965i	−0.00948023	−	0.0291772i
$993$		0			0
$994$	−1.68346	+	1.22311i	−0.0533961	+	0.0387946i
$995$	−6.86275	+	21.1214i	−0.217564	+	0.669593i
$996$		0			0
$997$	−44.1402	+	32.0697i	−1.39793	+	1.01566i	−0.402992	+	0.915204i	$0.632030\pi$
$997$	−44.1402	+	32.0697i	−1.39793	+	1.01566i	−0.994942	+	0.100455i	$0.967970\pi$
$998$	0.682220	+	0.495662i	0.0215953	+	0.0156899i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	495.2.n.h.181.3	yes	16
3.2	odd	2		495.2.n.g.181.2	✓	16
11.3	even	5		5445.2.a.ca.1.5		8
11.8	odd	10		5445.2.a.cc.1.4		8
11.9	even	5	inner	495.2.n.h.361.3	yes	16
33.8	even	10		5445.2.a.cb.1.5		8
33.14	odd	10		5445.2.a.cd.1.4		8
33.20	odd	10		495.2.n.g.361.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
495.2.n.g.181.2	✓	16	3.2	odd	2
495.2.n.g.361.2	yes	16	33.20	odd	10
495.2.n.h.181.3	yes	16	1.1	even	1	trivial
495.2.n.h.361.3	yes	16	11.9	even	5	inner
5445.2.a.ca.1.5		8	11.3	even	5
5445.2.a.cb.1.5		8	33.8	even	10
5445.2.a.cc.1.4		8	11.8	odd	10
5445.2.a.cd.1.4		8	33.14	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:	\( N \)	\(=\)	\( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	495.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0280832 - 0.0864312i) q^{2} +(1.61135 - 1.17072i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(1.98801 - 1.44438i) q^{7} +(-0.293484 - 0.213228i) q^{8} +O(q^{10})\)	\(q+(-0.0280832 - 0.0864312i) q^{2} +(1.61135 - 1.17072i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(1.98801 - 1.44438i) q^{7} +(-0.293484 - 0.213228i) q^{8} +0.0908791 q^{10} +(0.242484 - 3.30775i) q^{11} +(0.0999755 + 0.307693i) q^{13} +(-0.180669 - 0.131264i) q^{14} +(1.22078 - 3.75716i) q^{16} +(-1.13260 + 3.48579i) q^{17} +(-0.437853 - 0.318119i) q^{19} +(0.615482 + 1.89426i) q^{20} +(-0.292702 + 0.0719339i) q^{22} +4.62543 q^{23} +(-0.809017 - 0.587785i) q^{25} +(0.0237866 - 0.0172820i) q^{26} +(1.51244 - 4.65480i) q^{28} +(1.19403 - 0.867515i) q^{29} +(0.275312 + 0.847323i) q^{31} -1.08455 q^{32} +0.333088 q^{34} +(0.759354 + 2.33705i) q^{35} +(1.84899 - 1.34337i) q^{37} +(-0.0151991 + 0.0467779i) q^{38} +(0.293484 - 0.213228i) q^{40} +(-7.26541 - 5.27863i) q^{41} +6.31964 q^{43} +(-3.48171 - 5.61383i) q^{44} +(-0.129897 - 0.399782i) q^{46} +(-1.18347 - 0.859844i) q^{47} +(-0.297142 + 0.914509i) q^{49} +(-0.0280832 + 0.0864312i) q^{50} +(0.521317 + 0.378759i) q^{52} +(3.19196 + 9.82385i) q^{53} +(3.07092 + 1.25277i) q^{55} -0.891432 q^{56} +(-0.108513 - 0.0788390i) q^{58} +(5.09137 - 3.69910i) q^{59} +(-2.00101 + 6.15847i) q^{61} +(0.0655035 - 0.0475911i) q^{62} +(-2.41109 - 7.42059i) q^{64} -0.323527 q^{65} -7.05634 q^{67} +(2.25585 + 6.94279i) q^{68} +(0.180669 - 0.131264i) q^{70} +(2.87940 - 8.86188i) q^{71} +(-5.01044 + 3.64030i) q^{73} +(-0.168034 - 0.122084i) q^{74} -1.07796 q^{76} +(-4.29557 - 6.92609i) q^{77} +(3.58612 + 11.0369i) q^{79} +(3.19603 + 2.32205i) q^{80} +(-0.252202 + 0.776199i) q^{82} +(-5.36887 + 16.5237i) q^{83} +(-2.96519 - 2.15434i) q^{85} +(-0.177476 - 0.546214i) q^{86} +(-0.776471 + 0.919066i) q^{88} -4.70270 q^{89} +(0.643177 + 0.467296i) q^{91} +(7.45320 - 5.41507i) q^{92} +(-0.0410816 + 0.126436i) q^{94} +(0.437853 - 0.318119i) q^{95} +(3.40155 + 10.4689i) q^{97} +0.0873867 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8}+O(q^{10}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8	\( 16 q + 2 q^{2} - 8 q^{4} + 4 q^{5} - 4 q^{7} + 6 q^{8} + 8 q^{10} - 4 q^{11} + 2 q^{13} + 22 q^{14} + 8 q^{16} + 4 q^{17} - 4 q^{19} - 2 q^{20} - 28 q^{22} - 8 q^{23} - 4 q^{25} - 6 q^{26} - 2 q^{28} + 26 q^{29} - 10 q^{31} - 56 q^{32} - 4 q^{34} + 4 q^{35} + 22 q^{37} + 30 q^{38} - 6 q^{40} + 6 q^{41} + 28 q^{43} - 68 q^{44} + 16 q^{46} + 20 q^{47} + 10 q^{49} + 2 q^{50} + 30 q^{52} - 14 q^{53} - 6 q^{55} - 68 q^{56} - 6 q^{58} + 16 q^{59} - 38 q^{61} + 20 q^{62} + 10 q^{64} - 12 q^{65} + 20 q^{67} + 48 q^{68} - 22 q^{70} + 54 q^{71} + 2 q^{73} - 28 q^{74} - 44 q^{76} - 34 q^{77} - 12 q^{79} + 22 q^{80} + 30 q^{82} + 28 q^{83} - 4 q^{85} - 74 q^{86} + 46 q^{88} - 76 q^{89} - 34 q^{91} + 8 q^{92} - 10 q^{94} + 4 q^{95} - 18 q^{97} - 8 q^{98}+O(q^{100}) \) 16 * q + 2 * q^2 - 8 * q^4 + 4 * q^5 - 4 * q^7 + 6 * q^8 + 8 * q^10 - 4 * q^11 + 2 * q^13 + 22 * q^14 + 8 * q^16 + 4 * q^17 - 4 * q^19 - 2 * q^20 - 28 * q^22 - 8 * q^23 - 4 * q^25 - 6 * q^26 - 2 * q^28 + 26 * q^29 - 10 * q^31 - 56 * q^32 - 4 * q^34 + 4 * q^35 + 22 * q^37 + 30 * q^38 - 6 * q^40 + 6 * q^41 + 28 * q^43 - 68 * q^44 + 16 * q^46 + 20 * q^47 + 10 * q^49 + 2 * q^50 + 30 * q^52 - 14 * q^53 - 6 * q^55 - 68 * q^56 - 6 * q^58 + 16 * q^59 - 38 * q^61 + 20 * q^62 + 10 * q^64 - 12 * q^65 + 20 * q^67 + 48 * q^68 - 22 * q^70 + 54 * q^71 + 2 * q^73 - 28 * q^74 - 44 * q^76 - 34 * q^77 - 12 * q^79 + 22 * q^80 + 30 * q^82 + 28 * q^83 - 4 * q^85 - 74 * q^86 + 46 * q^88 - 76 * q^89 - 34 * q^91 + 8 * q^92 - 10 * q^94 + 4 * q^95 - 18 * q^97 - 8 * q^98

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