LMFDB - Embedded newform 495.2.n.h.361.3

Newspace parameters

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

Self dual:	no
Analytic conductor:	$3.95259490005$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
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} - 172 x^{7} + 471 x^{6} - 430 x^{5} + 383 x^{4} + 70 x^{3} + 17 x^{2} + 4 x + 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			361.3
Root			$0.735494 + 0.534368i$ of defining polynomial
Character	$\chi$	$=$	495.361
Dual form			495.2.n.h.181.3

$q$-expansion

$f(q)$	$=$	$q+(-0.0280832 + 0.0864312i) q^{2} +(1.61135 + 1.17072i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.98801 + 1.44438i) q^{7} +(-0.293484 + 0.213228i) q^{8} +O(q^{10})$	\(q+(-0.0280832 + 0.0864312i) q^{2} +(1.61135 + 1.17072i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(1.98801 + 1.44438i) q^{7} +(-0.293484 + 0.213228i) q^{8} +0.0908791 q^{10} +(0.242484 + 3.30775i) q^{11} +(0.0999755 - 0.307693i) q^{13} +(-0.180669 + 0.131264i) q^{14} +(1.22078 + 3.75716i) q^{16} +(-1.13260 - 3.48579i) q^{17} +(-0.437853 + 0.318119i) q^{19} +(0.615482 - 1.89426i) q^{20} +(-0.292702 - 0.0719339i) q^{22} +4.62543 q^{23} +(-0.809017 + 0.587785i) q^{25} +(0.0237866 + 0.0172820i) q^{26} +(1.51244 + 4.65480i) q^{28} +(1.19403 + 0.867515i) q^{29} +(0.275312 - 0.847323i) q^{31} -1.08455 q^{32} +0.333088 q^{34} +(0.759354 - 2.33705i) q^{35} +(1.84899 + 1.34337i) q^{37} +(-0.0151991 - 0.0467779i) q^{38} +(0.293484 + 0.213228i) q^{40} +(-7.26541 + 5.27863i) q^{41} +6.31964 q^{43} +(-3.48171 + 5.61383i) q^{44} +(-0.129897 + 0.399782i) q^{46} +(-1.18347 + 0.859844i) q^{47} +(-0.297142 - 0.914509i) q^{49} +(-0.0280832 - 0.0864312i) q^{50} +(0.521317 - 0.378759i) q^{52} +(3.19196 - 9.82385i) q^{53} +(3.07092 - 1.25277i) q^{55} -0.891432 q^{56} +(-0.108513 + 0.0788390i) q^{58} +(5.09137 + 3.69910i) q^{59} +(-2.00101 - 6.15847i) q^{61} +(0.0655035 + 0.0475911i) q^{62} +(-2.41109 + 7.42059i) q^{64} -0.323527 q^{65} -7.05634 q^{67} +(2.25585 - 6.94279i) q^{68} +(0.180669 + 0.131264i) q^{70} +(2.87940 + 8.86188i) q^{71} +(-5.01044 - 3.64030i) q^{73} +(-0.168034 + 0.122084i) q^{74} -1.07796 q^{76} +(-4.29557 + 6.92609i) q^{77} +(3.58612 - 11.0369i) q^{79} +(3.19603 - 2.32205i) q^{80} +(-0.252202 - 0.776199i) q^{82} +(-5.36887 - 16.5237i) q^{83} +(-2.96519 + 2.15434i) q^{85} +(-0.177476 + 0.546214i) q^{86} +(-0.776471 - 0.919066i) q^{88} -4.70270 q^{89} +(0.643177 - 0.467296i) q^{91} +(7.45320 + 5.41507i) q^{92} +(-0.0410816 - 0.126436i) q^{94} +(0.437853 + 0.318119i) q^{95} +(3.40155 - 10.4689i) q^{97} +0.0873867 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/495\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$397$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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	−0.960494	−	0.278299i	$-0.910229\pi$
$2$	−0.0280832	+	0.0864312i	−0.0198578	+	0.0611161i	0.940637	+	0.339415i	$0.110229\pi$
$3$		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	0.896260	−	0.443529i	$-0.146274\pi$
$7$	1.98801	+	1.44438i	0.751399	+	0.545923i	−0.144861	+	0.989452i	$0.546274\pi$
$8$	−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	−0.936235	−	0.351375i	$-0.885714\pi$
$13$	0.0999755	−	0.307693i	0.0277282	−	0.0853386i	0.963963	+	0.266037i	$0.0857142\pi$
$14$	−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	−0.989300	−	0.145898i	$-0.953393\pi$
$17$	−1.13260	−	3.48579i	−0.274696	−	0.845428i	0.714604	−	0.699530i	$-0.246607\pi$
$18$		0			0
$19$	−0.437853	+	0.318119i	−0.100450	+	0.0729815i	−0.636877	−	0.770966i	$-0.719774\pi$
$19$	−0.437853	+	0.318119i	−0.100450	+	0.0729815i	0.536426	+	0.843947i	$0.319774\pi$
$20$	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	0.693103	−	0.720838i	$-0.256243\pi$
$29$	1.19403	+	0.867515i	0.221726	+	0.161094i	−0.471377	+	0.881932i	$0.656243\pi$
$30$		0			0
$31$	0.275312	−	0.847323i	0.0494475	−	0.152184i	−0.923284	−	0.384118i	$-0.874506\pi$
$31$	0.275312	−	0.847323i	0.0494475	−	0.152184i	0.972731	+	0.231935i	$0.0745055\pi$
$32$	−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	0.729305	−	0.684188i	$-0.239843\pi$
$37$	1.84899	+	1.34337i	0.303971	+	0.220848i	−0.425334	+	0.905036i	$0.639843\pi$
$38$	−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	−0.986367	−	0.164559i	$-0.947380\pi$
$41$	−7.26541	+	5.27863i	−1.13467	+	0.824384i	−0.148299	+	0.988943i	$0.547380\pi$
$42$		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	−0.670744	−	0.741689i	$-0.734025\pi$
$47$	−1.18347	+	0.859844i	−0.172627	+	0.125421i	0.498117	+	0.867110i	$0.334025\pi$
$48$		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	−0.451060	−	0.892494i	$-0.648954\pi$
$53$	3.19196	−	9.82385i	0.438450	−	1.34941i	0.889510	−	0.456916i	$-0.151046\pi$
$54$		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	0.867621	−	0.497227i	$-0.165648\pi$
$59$	5.09137	+	3.69910i	0.662840	+	0.481581i	−0.204781	+	0.978808i	$0.565648\pi$
$60$		0			0
$61$	−2.00101	−	6.15847i	−0.256203	−	0.788511i	−0.993590	−	0.113041i	$-0.963941\pi$
$61$	−2.00101	−	6.15847i	−0.256203	−	0.788511i	0.737388	−	0.675470i	$-0.236059\pi$
$62$	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	0.963315	+	0.268372i	$0.0864855\pi$
$71$	2.87940	+	8.86188i	0.341722	+	1.05171i	−0.621594	+	0.783340i	$0.713515\pi$
$72$		0			0
$73$	−5.01044	−	3.64030i	−0.586428	−	0.426065i	0.254608	−	0.967044i	$-0.418054\pi$
$73$	−5.01044	−	3.64030i	−0.586428	−	0.426065i	−0.841036	+	0.540980i	$0.818054\pi$
$74$	−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	−0.518697	−	0.854958i	$-0.673583\pi$
$79$	3.58612	−	11.0369i	0.403470	−	1.24175i	0.922166	−	0.386793i	$-0.126417\pi$
$80$	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	−0.581223	−	0.813744i	$-0.697426\pi$
$83$	−5.36887	−	16.5237i	−0.589311	−	1.81371i	−0.00808702	−	0.999967i	$-0.502574\pi$
$84$		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	−0.616007	−	0.787741i	$-0.711251\pi$
$97$	3.40155	−	10.4689i	0.345375	−	1.06296i	0.961383	−	0.275216i	$-0.0887492\pi$
$98$	0.0873867			0.00882739
$99$		0			0
$100$	−1.99174			−0.199174
$101$	−2.07395	+	6.38296i	−0.206366	+	0.635129i	0.793289	+	0.608846i	$0.208367\pi$
$101$	−2.07395	+	6.38296i	−0.206366	+	0.635129i	−0.999655	+	0.0262830i	$0.991633\pi$
$102$		0			0
$103$	−12.6233	−	9.17139i	−1.24381	−	0.903684i	−0.245968	−	0.969278i	$-0.579106\pi$
$103$	−12.6233	−	9.17139i	−1.24381	−	0.903684i	−0.997846	+	0.0655935i	$0.979106\pi$
$104$	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	−0.880796	−	0.473496i	$-0.842992\pi$
$107$	−7.26833	+	5.28075i	−0.702656	+	0.510509i	0.178140	+	0.984005i	$0.442992\pi$
$108$		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	0.549812	−	0.835288i	$-0.314699\pi$
$113$	16.0953	−	11.6939i	1.51412	−	1.10007i	0.964308	−	0.264784i	$-0.0853007\pi$
$114$		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	−0.968147	−	0.250381i	$-0.919444\pi$
$127$	−3.74224	−	11.5174i	−0.332070	−	1.02201i	0.636078	−	0.771625i	$-0.280556\pi$
$128$	−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	0.910674	+	0.413125i	$0.135563\pi$
$137$	4.87796	+	15.0128i	0.416752	+	1.28263i	−0.493922	+	0.869506i	$0.664437\pi$
$138$		0			0
$139$	−11.1932	−	8.13233i	−0.949395	−	0.689776i	0.00126895	−	0.999999i	$-0.499596\pi$
$139$	−11.1932	−	8.13233i	−0.949395	−	0.689776i	−0.950664	+	0.310224i	$0.899596\pi$
$140$	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	−0.997883	−	0.0650280i	$-0.979286\pi$
$149$	−2.79288	−	8.59559i	−0.228801	−	0.704178i	0.769082	−	0.639150i	$-0.220714\pi$
$150$		0			0
$151$	7.16102	−	5.20278i	0.582755	−	0.423397i	−0.256961	−	0.966422i	$-0.582721\pi$
$151$	7.16102	−	5.20278i	0.582755	−	0.423397i	0.839716	+	0.543025i	$0.182721\pi$
$152$	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	−0.898282	−	0.439419i	$-0.855184\pi$
$157$	−9.49715	+	6.90008i	−0.757955	+	0.550686i	0.140328	+	0.990105i	$0.455184\pi$
$158$	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	−0.815499	−	0.578759i	$-0.803537\pi$
$163$	2.35476	−	7.24722i	0.184439	−	0.567646i	0.999938	+	0.0111126i	$0.00353731\pi$
$164$	−17.8869			−1.39673
$165$		0			0
$166$	1.57894			0.122549
$167$	−3.12640	+	9.62208i	−0.241928	+	0.744579i	0.754198	+	0.656647i	$0.228026\pi$
$167$	−3.12640	+	9.62208i	−0.241928	+	0.744579i	−0.996126	+	0.0879319i	$0.971974\pi$
$168$		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	−0.248241	−	0.968698i	$-0.579852\pi$
$173$	7.84357	−	5.69869i	0.596335	−	0.433263i	0.844576	+	0.535435i	$0.179852\pi$
$174$		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	0.117276	−	0.993099i	$-0.462584\pi$
$179$	14.6904	−	10.6732i	1.09801	−	0.797751i	0.980734	+	0.195348i	$0.0625837\pi$
$180$		0			0
$181$	−1.36254	−	4.19346i	−0.101277	−	0.311697i	0.887562	−	0.460688i	$-0.152397\pi$
$181$	−1.36254	−	4.19346i	−0.101277	−	0.311697i	−0.988839	+	0.148991i	$0.952397\pi$
$182$	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	0.886125	−	0.463446i	$-0.153387\pi$
$191$	9.93939	+	7.22139i	0.719189	+	0.522521i	−0.166936	+	0.985968i	$0.553387\pi$
$192$		0			0
$193$	7.19896	+	22.1561i	0.518193	+	1.59483i	0.777397	+	0.629010i	$0.216540\pi$
$193$	7.19896	+	22.1561i	0.518193	+	1.59483i	−0.259204	+	0.965823i	$0.583460\pi$
$194$	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	0.712469	+	0.701704i	$0.247577\pi$
$211$	−4.01468	+	12.3559i	−0.276382	+	0.850616i	−0.988850	+	0.148912i	$0.952423\pi$
$212$	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	0.228968	−	0.973434i	$-0.426465\pi$
$223$	18.3008	−	13.2963i	1.22551	−	0.890387i	0.996546	+	0.0830466i	$0.0264650\pi$
$224$	−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	0.923700	−	0.383118i	$-0.125150\pi$
$227$	12.7278	+	9.24727i	0.844772	+	0.613763i	−0.0789276	+	0.996880i	$0.525150\pi$
$228$		0			0
$229$	−7.50944	+	23.1117i	−0.496238	+	1.52726i	0.318781	+	0.947828i	$0.396727\pi$
$229$	−7.50944	+	23.1117i	−0.496238	+	1.52726i	−0.815019	+	0.579434i	$0.803273\pi$
$230$	0.420355			0.0277174
$231$		0			0
$232$	−0.535408			−0.0351513
$233$	1.65556	−	5.09529i	0.108459	−	0.333804i	−0.882067	−	0.471123i	$-0.843849\pi$
$233$	1.65556	−	5.09529i	0.108459	−	0.333804i	0.990527	+	0.137319i	$0.0438487\pi$
$234$		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	−0.563408	−	0.826179i	$-0.690510\pi$
$239$	0.745637	−	0.541737i	0.0482312	−	0.0350420i	0.611640	+	0.791136i	$0.290510\pi$
$240$		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	−0.942005	−	0.335599i	$-0.891061\pi$
$251$	0.274926	−	0.846135i	0.0173532	−	0.0534076i	0.959358	+	0.282191i	$0.0910613\pi$
$252$		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	0.105196	−	0.994452i	$-0.466453\pi$
$257$	−12.9545	−	9.41196i	−0.808077	−	0.587102i	−0.913272	+	0.407349i	$0.866453\pi$
$258$		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	0.650783	+	0.759264i	$0.274441\pi$
$269$	9.35808	+	28.8012i	0.570572	+	1.75604i	−0.0802108	+	0.996778i	$0.525559\pi$
$270$		0			0
$271$	−4.86915	−	3.53764i	−0.295780	−	0.214897i	0.429991	−	0.902833i	$-0.358517\pi$
$271$	−4.86915	−	3.53764i	−0.295780	−	0.214897i	−0.725771	+	0.687937i	$0.758517\pi$
$272$	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	0.252369	+	0.967631i	$0.418790\pi$
$277$	−8.66386	+	26.6646i	−0.520561	+	1.60212i	−0.772930	+	0.634491i	$0.781210\pi$
$278$	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	−0.834117	−	0.551588i	$-0.814022\pi$
$281$	−8.10523	−	24.9453i	−0.483517	−	1.48811i	0.350599	−	0.936526i	$-0.385978\pi$
$282$		0			0
$283$	−10.0324	+	7.28897i	−0.596365	+	0.433284i	−0.844587	−	0.535419i	$-0.820154\pi$
$283$	−10.0324	+	7.28897i	−0.596365	+	0.433284i	0.248222	+	0.968703i	$0.420154\pi$
$284$	−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	0.993685	+	0.112202i	$0.0357902\pi$
$293$	24.0919	+	17.5038i	1.40746	+	1.02258i	0.413776	+	0.910379i	$0.364210\pi$
$294$		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	−0.368652	−	0.929567i	$-0.620181\pi$
$311$	7.08052	−	5.14430i	0.401499	−	0.291706i	0.770151	+	0.637861i	$0.220181\pi$
$312$		0			0
$313$	5.00966	+	15.4181i	0.283162	+	0.871484i	0.986943	+	0.161067i	$0.0514936\pi$
$313$	5.00966	+	15.4181i	0.283162	+	0.871484i	−0.703781	+	0.710417i	$0.748506\pi$
$314$	−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	−0.886940	−	0.461885i	$-0.847173\pi$
$317$	1.81782	−	5.59467i	0.102099	−	0.314228i	0.989039	+	0.147657i	$0.0471732\pi$
$318$		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	0.869394	−	0.494119i	$-0.164509\pi$
$337$	12.2650	+	8.91103i	0.668116	+	0.485415i	−0.201278	+	0.979534i	$0.564509\pi$
$338$	−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	−0.985497	−	0.169690i	$-0.945723\pi$
$347$	−5.36400	−	16.5087i	−0.287955	−	0.886233i	0.697543	−	0.716543i	$-0.254277\pi$
$348$		0			0
$349$	3.95801	−	2.87566i	0.211867	−	0.153931i	−0.476791	−	0.879017i	$-0.658200\pi$
$349$	3.95801	−	2.87566i	0.211867	−	0.153931i	0.688658	+	0.725086i	$0.258200\pi$
$350$	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	0.997411	−	0.0719119i	$-0.0229101\pi$
$359$	23.4423	+	17.0318i	1.23724	+	0.898904i	0.239825	+	0.970816i	$0.422910\pi$
$360$		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	0.841962	−	0.539537i	$-0.181401\pi$
$367$	11.2839	+	8.19820i	0.589013	+	0.427943i	−0.252949	+	0.967480i	$0.581401\pi$
$368$	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	0.934894	−	0.354928i	$-0.115495\pi$
$379$	−0.585450	−	1.80183i	−0.0300726	−	0.0925538i	−0.964966	+	0.262374i	$0.915495\pi$
$380$	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	−0.958341	−	0.285628i	$-0.907798\pi$
$383$	−0.296274	+	0.911838i	−0.0151389	+	0.0465928i	0.943202	+	0.332221i	$0.107798\pi$
$384$		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	0.445778	−	0.895143i	$-0.352927\pi$
$389$	−5.28186	−	3.83750i	−0.267801	−	0.194569i	−0.713579	+	0.700575i	$0.752927\pi$
$390$		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	−0.999974	−	0.00726766i	$-0.997687\pi$
$401$	−3.90987	−	12.0334i	−0.195250	−	0.600917i	0.804724	−	0.593649i	$-0.202313\pi$
$402$		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	−0.905481	−	0.424386i	$-0.860490\pi$
$409$	1.54745	−	4.76256i	0.0765164	−	0.235493i	0.981998	+	0.188893i	$0.0604899\pi$
$410$	−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	−0.946876	−	0.321600i	$-0.895780\pi$
$421$	−19.1562	+	13.9178i	−0.933617	+	0.678313i	0.0132587	+	0.999912i	$0.495780\pi$
$422$	−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	−0.555532	−	0.831495i	$-0.687485\pi$
$431$	7.94388	−	24.4488i	0.382643	−	1.17765i	0.938176	−	0.346160i	$-0.112515\pi$
$432$		0			0
$433$	−16.0949	−	11.6937i	−0.773474	−	0.561962i	0.129539	−	0.991574i	$-0.458650\pi$
$433$	−16.0949	−	11.6937i	−0.773474	−	0.561962i	−0.903013	+	0.429613i	$0.858650\pi$
$434$	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	−0.970559	−	0.240862i	$-0.922570\pi$
$443$	−21.9190	+	15.9251i	−1.04141	+	0.756625i	−0.0708460	+	0.997487i	$0.522570\pi$
$444$		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	−0.557751	−	0.830009i	$-0.688335\pi$
$449$	8.08057	−	24.8694i	0.381346	−	1.17366i	0.939097	−	0.343653i	$-0.111665\pi$
$450$		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	−0.999763	−	0.0217820i	$-0.993066\pi$
$457$	−4.35548	−	13.4048i	−0.203741	−	0.627050i	0.796022	−	0.605268i	$-0.206934\pi$
$458$	−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	0.899613	−	0.436688i	$-0.143849\pi$
$467$	−1.83401	−	5.64451i	−0.0848679	−	0.261197i	−0.984481	+	0.175491i	$0.943849\pi$
$468$		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	−0.894837	−	0.446394i	$-0.852708\pi$
$479$	−9.48284	−	29.1852i	−0.433282	−	1.33351i	0.461555	−	0.887112i	$-0.347292\pi$
$480$		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	−0.487038	+	0.873381i	$0.661923\pi$
$487$	−32.3998	+	23.5398i	−1.46818	+	1.06669i	−0.981138	+	0.193311i	$0.938077\pi$
$488$	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	0.884048	−	0.467397i	$-0.154808\pi$
$491$	15.7927	+	11.4740i	0.712713	+	0.517816i	−0.171335	+	0.985213i	$0.554808\pi$
$492$		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	0.406941	−	0.913455i	$-0.366596\pi$
$499$	−7.50690	−	5.45408i	−0.336055	−	0.244158i	−0.742995	+	0.669296i	$0.766596\pi$
$500$	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	−0.881119	−	0.472894i	$-0.843209\pi$
$503$	−15.7812	+	11.4657i	−0.703651	+	0.511232i	0.177468	+	0.984126i	$0.443209\pi$
$504$		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	−0.381835	−	0.924231i	$-0.624708\pi$
$509$	8.55440	−	6.21513i	0.379167	−	0.275481i	0.761002	+	0.648750i	$0.224708\pi$
$510$		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	0.429366	−	0.903131i	$-0.358737\pi$
$521$	−6.77644	−	4.92337i	−0.296881	−	0.215697i	−0.726247	+	0.687434i	$0.758737\pi$
$522$		0			0
$523$	10.6523	+	32.7846i	0.465795	+	1.43357i	0.857980	+	0.513683i	$0.171719\pi$
$523$	10.6523	+	32.7846i	0.465795	+	1.43357i	−0.392186	+	0.919886i	$0.628281\pi$
$524$	−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	0.654108	+	0.756402i	$0.273044\pi$
$541$	−7.43553	+	22.8842i	−0.319678	+	0.983868i	−0.973786	+	0.227467i	$0.926956\pi$
$542$	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	−0.134506	−	0.990913i	$-0.542945\pi$
$547$	17.9233	−	13.0220i	0.766343	−	0.556781i	0.900849	+	0.434132i	$0.142945\pi$
$548$	−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	0.448030	−	0.894018i	$-0.352126\pi$
$557$	−6.22550	−	4.52309i	−0.263783	−	0.191649i	−0.711813	+	0.702369i	$0.752126\pi$
$558$		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	0.477705	+	0.878520i	$0.341469\pi$
$563$	−10.0877	+	31.0469i	−0.425148	+	1.30847i	−0.902853	+	0.429950i	$0.858531\pi$
$564$		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	−0.274489	−	0.961590i	$-0.588509\pi$
$569$	13.2440	−	9.62230i	0.555215	−	0.403388i	0.829705	+	0.558203i	$0.188509\pi$
$570$		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	0.987526	+	0.157457i	$0.0503295\pi$
$577$	6.75349	+	20.7851i	0.281151	+	0.865295i	−0.706374	+	0.707838i	$0.749671\pi$
$578$	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	0.999738	−	0.0229093i	$-0.00729289\pi$
$587$	31.1788	+	22.6527i	1.28689	+	0.934977i	0.287148	+	0.957886i	$0.407293\pi$
$588$		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	−0.843939	−	0.536439i	$-0.819769\pi$
$599$	−11.6618	−	35.8914i	−0.476489	−	1.46648i	0.367451	−	0.930043i	$-0.380231\pi$
$600$		0			0
$601$	18.5724	+	13.4937i	0.757585	+	0.550417i	0.898169	−	0.439651i	$-0.144898\pi$
$601$	18.5724	+	13.4937i	0.757585	+	0.550417i	−0.140584	+	0.990069i	$0.544898\pi$
$602$	−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	−0.855365	−	0.518027i	$-0.826667\pi$
$607$	3.47703	−	10.7012i	0.141128	−	0.434348i	0.996493	+	0.0836784i	$0.0266668\pi$
$608$	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	−0.480390	+	0.877055i	$0.659505\pi$
$613$	−36.2214	+	26.3164i	−1.46297	+	1.06291i	−0.982578	+	0.185853i	$0.940495\pi$
$614$	−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	−0.612017	−	0.790844i	$-0.709642\pi$
$619$	−1.21920	+	0.885800i	−0.0490037	+	0.0356033i	0.563014	+	0.826448i	$0.309642\pi$
$620$	−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	0.976686	−	0.214674i	$-0.0688688\pi$
$631$	26.9869	+	19.6071i	1.07433	+	0.780548i	0.0976458	+	0.995221i	$0.468869\pi$
$632$	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	−0.441697	−	0.897164i	$-0.645623\pi$
$641$	6.96411	−	5.05972i	0.275066	−	0.199847i	0.716762	+	0.697318i	$0.245623\pi$
$642$		0			0
$643$	−3.66045	−	11.2657i	−0.144354	−	0.444276i	0.852573	−	0.522608i	$-0.175041\pi$
$643$	−3.66045	−	11.2657i	−0.144354	−	0.444276i	−0.996927	+	0.0783317i	$0.975041\pi$
$644$	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	−0.720615	−	0.693335i	$-0.756141\pi$
$647$	6.86541	−	21.1295i	0.269907	−	0.830688i	0.990522	−	0.137353i	$-0.0438595\pi$
$648$		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	0.690918	−	0.722933i	$-0.257207\pi$
$653$	5.54195	+	4.02646i	0.216873	+	0.157568i	−0.474045	+	0.880501i	$0.657207\pi$
$654$		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	−0.510530	−	0.859860i	$-0.670551\pi$
$673$	10.5821	−	32.5684i	0.407910	−	1.25542i	0.918441	−	0.395559i	$-0.129449\pi$
$674$	−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	0.999447	+	0.0332415i	$0.0105831\pi$
$677$	5.47487	+	16.8499i	0.210416	+	0.647595i	−0.789031	+	0.614353i	$0.789417\pi$
$678$		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	0.652791	+	0.757538i	$0.273598\pi$
$691$	−8.42752	+	25.9372i	−0.320598	+	0.986699i	−0.973389	+	0.229161i	$0.926402\pi$
$692$	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	−0.994111	−	0.108369i	$-0.965437\pi$
$701$	−31.7252	+	23.0497i	−1.19824	+	0.870574i	−0.204132	+	0.978943i	$0.565437\pi$
$702$		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	0.970226	+	0.242200i	$0.0778691\pi$
$709$	8.72458	+	26.8515i	0.327658	+	1.00843i	−0.642568	+	0.766229i	$0.722131\pi$
$710$	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	0.999348	−	0.0361078i	$-0.0114960\pi$
$719$	34.1565	+	24.8162i	1.27382	+	0.925486i	0.274475	+	0.961594i	$0.411496\pi$
$720$		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	0.837347	−	0.546672i	$-0.184106\pi$
$733$	15.5996	+	11.3338i	0.576185	+	0.418623i	−0.261162	+	0.965295i	$0.584106\pi$
$734$	−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	0.510187	+	0.860064i	$0.329576\pi$
$739$	−11.0939	+	34.1435i	−0.408096	+	1.25599i	−0.918282	+	0.395926i	$0.870424\pi$
$740$	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	0.856455	−	0.516221i	$-0.172662\pi$
$743$	−3.81228	−	11.7330i	−0.139859	−	0.430442i	−0.996314	+	0.0857798i	$0.972662\pi$
$744$		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	−0.683599	−	0.729858i	$-0.739586\pi$
$751$	−5.50024	+	3.99616i	−0.200707	+	0.145822i	0.482892	+	0.875680i	$0.339586\pi$
$752$	−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	−0.991922	−	0.126846i	$-0.959515\pi$
$757$	−3.16082	+	9.72801i	−0.114882	+	0.353571i	0.877040	+	0.480417i	$0.159515\pi$
$758$	0.172176			0.00625370
$759$		0			0
$760$	−0.196335			−0.00712181
$761$	−7.57503	+	23.3136i	−0.274595	+	0.845116i	0.714732	+	0.699399i	$0.246549\pi$
$761$	−7.57503	+	23.3136i	−0.274595	+	0.845116i	−0.989326	+	0.145717i	$0.953451\pi$
$762$		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	−0.706809	−	0.707404i	$-0.749866\pi$
$773$	−7.01865	+	5.09935i	−0.252443	+	0.183411i	0.454366	+	0.890815i	$0.349866\pi$
$774$		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

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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