LMFDB - Embedded newform 1056.2.y.c.97.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1056,2,Mod(97,1056)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1056.97"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1056, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1056 = 2^{5} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1056.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,2,0,8,0,-2,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.43220245345$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
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			97.1
Root			$1.73855 + 1.26313i$ of defining polynomial
Character	$\chi$	$=$	1056.97
Dual form			1056.2.y.c.577.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.973083 - 2.99484i) q^{5} +(3.85658 + 2.80197i) q^{7} +(0.309017 - 0.951057i) q^{9} +(1.73855 - 2.82444i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(2.54756 + 1.85091i) q^{15} +(0.837466 + 2.57746i) q^{17} +(-0.234536 + 0.170401i) q^{19} -4.76700 q^{21} -1.90794 q^{23} +(-3.97709 + 2.88953i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-7.09513 - 5.15491i) q^{29} +(2.27276 - 6.99485i) q^{31} +(0.253650 + 3.30691i) q^{33} +(4.63868 - 14.2764i) q^{35} +(8.19405 + 5.95332i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(6.27100 - 4.55615i) q^{41} +11.7212 q^{43} -3.14896 q^{45} +(3.50554 - 2.54692i) q^{47} +(4.85906 + 14.9546i) q^{49} +(-2.19251 - 1.59296i) q^{51} +(1.51429 - 4.66051i) q^{53} +(-10.1505 - 2.45825i) q^{55} +(0.0895849 - 0.275714i) q^{57} +(6.75919 + 4.91084i) q^{59} +(-2.83264 - 8.71798i) q^{61} +(3.85658 - 2.80197i) q^{63} +3.14896 q^{65} -1.88431 q^{67} +(1.54355 - 1.12146i) q^{69} +(1.83841 + 5.65805i) q^{71} +(-8.38503 - 6.09208i) q^{73} +(1.51911 - 4.67535i) q^{75} +(14.6188 - 6.02132i) q^{77} +(3.41925 - 10.5234i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.53575 + 10.8819i) q^{83} +(6.90414 - 5.01615i) q^{85} +8.77006 q^{87} -7.62768 q^{89} +(-3.85658 + 2.80197i) q^{91} +(2.27276 + 6.99485i) q^{93} +(0.738546 + 0.536585i) q^{95} +(-0.686745 + 2.11358i) q^{97} +(-2.14896 - 2.52626i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{5} + 8 q^{7} - 2 q^{9} + 2 q^{13} + 2 q^{15} - 10 q^{17} - 6 q^{19} - 12 q^{21} - 8 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{29} + 10 q^{31} + 26 q^{37} + 2 q^{39} + 6 q^{41} + 12 q^{43}+ \cdots + 30 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^5 + 8 * q^7 - 2 * q^9 + 2 * q^13 + 2 * q^15 - 10 * q^17 - 6 * q^19 - 12 * q^21 - 8 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^29 + 10 * q^31 + 26 * q^37 + 2 * q^39 + 6 * q^41 + 12 * q^43 - 8 * q^45 - 12 * q^47 + 20 * q^49 + 14 * q^53 - 42 * q^55 + 4 * q^57 + 12 * q^59 - 14 * q^61 + 8 * q^63 + 8 * q^65 - 12 * q^67 + 12 * q^69 + 24 * q^71 - 32 * q^73 + 6 * q^75 + 8 * q^77 - 2 * q^79 - 2 * q^81 + 12 * q^83 + 14 * q^85 - 36 * q^89 - 8 * q^91 + 10 * q^93 - 8 * q^95 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1056\mathbb{Z}\right)^\times$.

$n$	$133$	$353$	$673$	$991$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$		0			0
$5$	−0.973083	−	2.99484i	−0.435176	−	1.33933i	−0.892906	−	0.450242i	$-0.851338\pi$
$5$	−0.973083	−	2.99484i	−0.435176	−	1.33933i	0.457731	−	0.889091i	$-0.348662\pi$
$6$		0			0
$7$	3.85658	+	2.80197i	1.45765	+	1.05904i	0.983967	+	0.178350i	$0.0570758\pi$
$7$	3.85658	+	2.80197i	1.45765	+	1.05904i	0.473683	+	0.880695i	$0.342924\pi$
$8$		0			0
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	1.73855	−	2.82444i	0.524191	−	0.851600i
$11$	1.73855	−	2.82444i	0.524191	−	0.851600i
$12$		0			0
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	−0.984720	−	0.174143i	$-0.944284\pi$
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	0.899014	+	0.437919i	$0.144284\pi$
$14$		0			0
$15$	2.54756	+	1.85091i	0.657778	+	0.477904i
$16$		0			0
$17$	0.837466	+	2.57746i	0.203115	+	0.625125i	0.999786	+	0.0207105i	$0.00659282\pi$
$17$	0.837466	+	2.57746i	0.203115	+	0.625125i	−0.796670	+	0.604414i	$0.793407\pi$
$18$		0			0
$19$	−0.234536	+	0.170401i	−0.0538063	+	0.0390926i	−0.614363	−	0.789023i	$-0.710587\pi$
$19$	−0.234536	+	0.170401i	−0.0538063	+	0.0390926i	0.560557	+	0.828116i	$0.310587\pi$
$20$		0			0
$21$	−4.76700			−1.04024
$22$		0			0
$23$	−1.90794			−0.397832			−0.198916	−	0.980017i	$-0.563742\pi$
$23$	−1.90794			−0.397832			−0.198916	+	0.980017i	$0.563742\pi$
$24$		0			0
$25$	−3.97709	+	2.88953i	−0.795418	+	0.577905i
$26$		0			0
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$		0			0
$29$	−7.09513	−	5.15491i	−1.31753	−	0.957243i	−0.999959	−	0.00900891i	$-0.997132\pi$
$29$	−7.09513	−	5.15491i	−1.31753	−	0.957243i	−0.317572	−	0.948234i	$-0.602868\pi$
$30$		0			0
$31$	2.27276	−	6.99485i	0.408201	−	1.25631i	−0.509992	−	0.860179i	$-0.670352\pi$
$31$	2.27276	−	6.99485i	0.408201	−	1.25631i	0.918193	−	0.396133i	$-0.129648\pi$
$32$		0			0
$33$	0.253650	+	3.30691i	0.0441549	+	0.575659i
$34$		0			0
$35$	4.63868	−	14.2764i	0.784080	−	2.41315i
$36$		0			0
$37$	8.19405	+	5.95332i	1.34709	+	0.978720i	0.999151	+	0.0412043i	$0.0131194\pi$
$37$	8.19405	+	5.95332i	1.34709	+	0.978720i	0.347942	+	0.937516i	$0.386881\pi$
$38$		0			0
$39$	−0.309017	−	0.951057i	−0.0494823	−	0.152291i
$40$		0			0
$41$	6.27100	−	4.55615i	0.979366	−	0.711551i	0.0217995	−	0.999762i	$-0.493060\pi$
$41$	6.27100	−	4.55615i	0.979366	−	0.711551i	0.957567	+	0.288211i	$0.0930605\pi$
$42$		0			0
$43$	11.7212			1.78746			0.893732	−	0.448602i	$-0.148078\pi$
$43$	11.7212			1.78746			0.893732	+	0.448602i	$0.148078\pi$
$44$		0			0
$45$	−3.14896			−0.469419
$46$		0			0
$47$	3.50554	−	2.54692i	0.511336	−	0.371507i	−0.301994	−	0.953310i	$-0.597652\pi$
$47$	3.50554	−	2.54692i	0.511336	−	0.371507i	0.813330	+	0.581803i	$0.197652\pi$
$48$		0			0
$49$	4.85906	+	14.9546i	0.694151	+	2.13638i
$50$		0			0
$51$	−2.19251	−	1.59296i	−0.307013	−	0.223058i
$52$		0			0
$53$	1.51429	−	4.66051i	0.208004	−	0.640170i	−0.791573	−	0.611075i	$-0.790737\pi$
$53$	1.51429	−	4.66051i	0.208004	−	0.640170i	0.999577	−	0.0290952i	$-0.00926261\pi$
$54$		0			0
$55$	−10.1505	−	2.45825i	−1.36869	−	0.331471i
$56$		0			0
$57$	0.0895849	−	0.275714i	0.0118658	−	0.0365192i
$58$		0			0
$59$	6.75919	+	4.91084i	0.879972	+	0.639337i	0.933244	−	0.359243i	$-0.116965\pi$
$59$	6.75919	+	4.91084i	0.879972	+	0.639337i	−0.0532722	+	0.998580i	$0.516965\pi$
$60$		0			0
$61$	−2.83264	−	8.71798i	−0.362683	−	1.11622i	−0.951419	−	0.307898i	$-0.900374\pi$
$61$	−2.83264	−	8.71798i	−0.362683	−	1.11622i	0.588737	−	0.808325i	$-0.299626\pi$
$62$		0			0
$63$	3.85658	−	2.80197i	0.485883	−	0.353015i
$64$		0			0
$65$	3.14896			0.390581
$66$		0			0
$67$	−1.88431			−0.230205			−0.115103	−	0.993354i	$-0.536720\pi$
$67$	−1.88431			−0.230205			−0.115103	+	0.993354i	$0.536720\pi$
$68$		0			0
$69$	1.54355	−	1.12146i	0.185822	−	0.135008i
$70$		0			0
$71$	1.83841	+	5.65805i	0.218179	+	0.671487i	0.998913	+	0.0466227i	$0.0148458\pi$
$71$	1.83841	+	5.65805i	0.218179	+	0.671487i	−0.780733	+	0.624865i	$0.785154\pi$
$72$		0			0
$73$	−8.38503	−	6.09208i	−0.981393	−	0.713024i	−0.0233738	−	0.999727i	$-0.507441\pi$
$73$	−8.38503	−	6.09208i	−0.981393	−	0.713024i	−0.958020	+	0.286703i	$0.907441\pi$
$74$		0			0
$75$	1.51911	−	4.67535i	0.175412	−	0.539863i
$76$		0			0
$77$	14.6188	−	6.02132i	1.66597	−	0.686193i
$78$		0			0
$79$	3.41925	−	10.5234i	0.384695	−	1.18397i	−0.552006	−	0.833840i	$-0.686137\pi$
$79$	3.41925	−	10.5234i	0.384695	−	1.18397i	0.936701	−	0.350130i	$-0.113863\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$		0			0
$83$	3.53575	+	10.8819i	0.388099	+	1.19445i	0.934207	+	0.356731i	$0.116109\pi$
$83$	3.53575	+	10.8819i	0.388099	+	1.19445i	−0.546108	+	0.837715i	$0.683891\pi$
$84$		0			0
$85$	6.90414	−	5.01615i	0.748859	−	0.544078i
$86$		0			0
$87$	8.77006			0.940249
$88$		0			0
$89$	−7.62768			−0.808532			−0.404266	−	0.914641i	$-0.632473\pi$
$89$	−7.62768			−0.808532			−0.404266	+	0.914641i	$0.632473\pi$
$90$		0			0
$91$	−3.85658	+	2.80197i	−0.404279	+	0.293726i
$92$		0			0
$93$	2.27276	+	6.99485i	0.235675	+	0.725332i
$94$		0			0
$95$	0.738546	+	0.536585i	0.0757732	+	0.0550525i
$96$		0			0
$97$	−0.686745	+	2.11358i	−0.0697284	+	0.214602i	−0.979848	−	0.199743i	$-0.935989\pi$
$97$	−0.686745	+	2.11358i	−0.0697284	+	0.214602i	0.910120	+	0.414345i	$0.135989\pi$
$98$		0			0
$99$	−2.14896	−	2.52626i	−0.215979	−	0.253898i
$100$		0			0
$101$	4.36510	−	13.4344i	0.434344	−	1.33677i	−0.459414	−	0.888222i	$-0.651940\pi$
$101$	4.36510	−	13.4344i	0.434344	−	1.33677i	0.893757	−	0.448551i	$-0.148060\pi$
$102$		0			0
$103$	4.70514	+	3.41848i	0.463611	+	0.336833i	0.794946	−	0.606680i	$-0.207499\pi$
$103$	4.70514	+	3.41848i	0.463611	+	0.336833i	−0.331335	+	0.943513i	$0.607499\pi$
$104$		0			0
$105$	4.63868	+	14.2764i	0.452689	+	1.39323i
$106$		0			0
$107$	−3.63868	+	2.64366i	−0.351764	+	0.255572i	−0.749609	−	0.661881i	$-0.769758\pi$
$107$	−3.63868	+	2.64366i	−0.351764	+	0.255572i	0.397844	+	0.917453i	$0.369758\pi$
$108$		0			0
$109$	−13.1757			−1.26200			−0.630999	−	0.775783i	$-0.717355\pi$
$109$	−13.1757			−1.26200			−0.630999	+	0.775783i	$0.717355\pi$
$110$		0			0
$111$	−10.1284			−0.961345
$112$		0			0
$113$	9.02998	−	6.56066i	0.849469	−	0.617175i	−0.0755305	−	0.997143i	$-0.524065\pi$
$113$	9.02998	−	6.56066i	0.849469	−	0.617175i	0.925000	+	0.379968i	$0.124065\pi$
$114$		0			0
$115$	1.85658	+	5.71397i	0.173127	+	0.532830i
$116$		0			0
$117$	0.809017	+	0.587785i	0.0747936	+	0.0543408i
$118$		0			0
$119$	−3.99220	+	12.2867i	−0.365964	+	1.12632i
$120$		0			0
$121$	−4.95492	−	9.82084i	−0.450447	−	0.892803i
$122$		0			0
$123$	−2.39531	+	7.37201i	−0.215978	+	0.664712i
$124$		0			0
$125$	−0.214107	−	0.155558i	−0.0191503	−	0.0139135i
$126$		0			0
$127$	−0.385029	−	1.18500i	−0.0341658	−	0.105152i	0.932519	−	0.361120i	$-0.117606\pi$
$127$	−0.385029	−	1.18500i	−0.0341658	−	0.105152i	−0.966685	+	0.255969i	$0.917606\pi$
$128$		0			0
$129$	−9.48263	+	6.88954i	−0.834899	+	0.606590i
$130$		0			0
$131$	3.08711			0.269722			0.134861	−	0.990865i	$-0.456941\pi$
$131$	3.08711			0.269722			0.134861	+	0.990865i	$0.456941\pi$
$132$		0			0
$133$	−1.38197			−0.119832
$134$		0			0
$135$	2.54756	−	1.85091i	0.219259	−	0.159301i
$136$		0			0
$137$	4.88801	+	15.0437i	0.417611	+	1.28527i	0.909895	+	0.414839i	$0.136162\pi$
$137$	4.88801	+	15.0437i	0.417611	+	1.28527i	−0.492284	+	0.870435i	$0.663838\pi$
$138$		0			0
$139$	4.29391	+	3.11971i	0.364205	+	0.264610i	0.754804	−	0.655951i	$-0.227732\pi$
$139$	4.29391	+	3.11971i	0.364205	+	0.264610i	−0.390599	+	0.920561i	$0.627732\pi$
$140$		0			0
$141$	−1.33900	+	4.12101i	−0.112764	+	0.347052i
$142$		0			0
$143$	2.14896	+	2.52626i	0.179705	+	0.211256i
$144$		0			0
$145$	−8.53399	+	26.2649i	−0.708709	+	2.18118i
$146$		0			0
$147$	−12.7212	−	9.24248i	−1.04923	−	0.762307i
$148$		0			0
$149$	1.77232	+	5.45464i	0.145194	+	0.446862i	0.997036	−	0.0769376i	$-0.0245142\pi$
$149$	1.77232	+	5.45464i	0.145194	+	0.446862i	−0.851842	+	0.523799i	$0.824514\pi$
$150$		0			0
$151$	4.94121	−	3.59000i	0.402110	−	0.292150i	−0.368290	−	0.929711i	$-0.620057\pi$
$151$	4.94121	−	3.59000i	0.402110	−	0.292150i	0.770400	+	0.637561i	$0.220057\pi$
$152$		0			0
$153$	2.71010			0.219098
$154$		0			0
$155$	−23.1600			−1.86026
$156$		0			0
$157$	−14.6371	+	10.6345i	−1.16817	+	0.848726i	−0.990789	−	0.135416i	$-0.956763\pi$
$157$	−14.6371	+	10.6345i	−1.16817	+	0.848726i	−0.177382	+	0.984142i	$0.556763\pi$
$158$		0			0
$159$	1.51429	+	4.66051i	0.120091	+	0.369602i
$160$		0			0
$161$	−7.35811	−	5.34598i	−0.579900	−	0.421322i
$162$		0			0
$163$	0.781070	−	2.40389i	0.0611782	−	0.188287i	−0.915796	−	0.401643i	$-0.868439\pi$
$163$	0.781070	−	2.40389i	0.0611782	−	0.188287i	0.976975	+	0.213356i	$0.0684393\pi$
$164$		0			0
$165$	9.65685	−	3.97754i	0.751785	−	0.309651i
$166$		0			0
$167$	1.26267	−	3.88611i	0.0977087	−	0.300717i	−0.890241	−	0.455489i	$-0.849464\pi$
$167$	1.26267	−	3.88611i	0.0977087	−	0.300717i	0.987950	+	0.154772i	$0.0494644\pi$
$168$		0			0
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$		0			0
$171$	0.0895849	+	0.275714i	0.00685073	+	0.0210844i
$172$		0			0
$173$	5.84549	−	4.24699i	0.444424	−	0.322893i	−0.342966	−	0.939348i	$-0.611432\pi$
$173$	5.84549	−	4.24699i	0.444424	−	0.322893i	0.787390	+	0.616455i	$0.211432\pi$
$174$		0			0
$175$	−23.4343			−1.77147
$176$		0			0
$177$	−8.35482			−0.627987
$178$		0			0
$179$	−8.76239	+	6.36625i	−0.654932	+	0.475836i	−0.864948	−	0.501862i	$-0.832648\pi$
$179$	−8.76239	+	6.36625i	−0.654932	+	0.475836i	0.210016	+	0.977698i	$0.432648\pi$
$180$		0			0
$181$	−5.81938	−	17.9102i	−0.432551	−	1.33126i	−0.895575	−	0.444910i	$-0.853236\pi$
$181$	−5.81938	−	17.9102i	−0.432551	−	1.33126i	0.463024	−	0.886346i	$-0.346764\pi$
$182$		0			0
$183$	7.41596	+	5.38801i	0.548203	+	0.398293i
$184$		0			0
$185$	9.85577	−	30.3329i	0.724610	−	2.23012i
$186$		0			0
$187$	8.73584	+	2.11565i	0.638828	+	0.154712i
$188$		0			0
$189$	−1.47308	+	4.53368i	−0.107151	+	0.329777i
$190$		0			0
$191$	19.4706	+	14.1462i	1.40884	+	1.02358i	0.993489	+	0.113924i	$0.0363420\pi$
$191$	19.4706	+	14.1462i	1.40884	+	1.02358i	0.415353	+	0.909660i	$0.363658\pi$
$192$		0			0
$193$	1.97520	+	6.07904i	0.142178	+	0.437579i	0.996637	−	0.0819395i	$-0.0261114\pi$
$193$	1.97520	+	6.07904i	0.142178	+	0.437579i	−0.854459	+	0.519518i	$0.826111\pi$
$194$		0			0
$195$	−2.54756	+	1.85091i	−0.182435	+	0.132547i
$196$		0			0
$197$	−25.4390			−1.81246			−0.906228	−	0.422790i	$-0.861051\pi$
$197$	−25.4390			−1.81246			−0.906228	+	0.422790i	$0.861051\pi$
$198$		0			0
$199$	−18.0252			−1.27777			−0.638887	−	0.769300i	$-0.720605\pi$
$199$	−18.0252			−1.27777			−0.638887	+	0.769300i	$0.720605\pi$
$200$		0			0
$201$	1.52444	−	1.10757i	0.107526	−	0.0781220i
$202$		0			0
$203$	−12.9190	−	39.7607i	−0.906737	−	2.79065i
$204$		0			0
$205$	−19.7472	−	14.3471i	−1.37920	−	1.00205i
$206$		0			0
$207$	−0.589585	+	1.81456i	−0.0409790	+	0.126120i
$208$		0			0
$209$	0.0735340	+	0.958683i	0.00508645	+	0.0663135i
$210$		0			0
$211$	−4.04165	+	12.4389i	−0.278239	+	0.856331i	0.710105	+	0.704095i	$0.248647\pi$
$211$	−4.04165	+	12.4389i	−0.278239	+	0.856331i	−0.988344	+	0.152236i	$0.951353\pi$
$212$		0			0
$213$	−4.81303	−	3.49687i	−0.329783	−	0.239601i
$214$		0			0
$215$	−11.4057	−	35.1031i	−0.777861	−	2.39401i
$216$		0			0
$217$	28.3645	−	20.6080i	1.92550	−	1.39896i
$218$		0			0
$219$	10.3645			0.700366
$220$		0			0
$221$	−2.71010			−0.182301
$222$		0			0
$223$	−8.14648	+	5.91877i	−0.545529	+	0.396350i	−0.826134	−	0.563473i	$-0.809465\pi$
$223$	−8.14648	+	5.91877i	−0.545529	+	0.396350i	0.280605	+	0.959823i	$0.409465\pi$
$224$		0			0
$225$	1.51911	+	4.67535i	0.101274	+	0.311690i
$226$		0			0
$227$	−9.41369	−	6.83945i	−0.624809	−	0.453950i	0.229789	−	0.973240i	$-0.426196\pi$
$227$	−9.41369	−	6.83945i	−0.624809	−	0.453950i	−0.854598	+	0.519290i	$0.826196\pi$
$228$		0			0
$229$	−1.21550	+	3.74094i	−0.0803228	+	0.247208i	−0.983152	−	0.182792i	$-0.941487\pi$
$229$	−1.21550	+	3.74094i	−0.0803228	+	0.247208i	0.902829	+	0.430000i	$0.141487\pi$
$230$		0			0
$231$	−8.28764	+	13.4641i	−0.545287	+	0.885872i
$232$		0			0
$233$	−1.35009	+	4.15516i	−0.0884475	+	0.272213i	−0.985491	−	0.169729i	$-0.945711\pi$
$233$	−1.35009	+	4.15516i	−0.0884475	+	0.272213i	0.897043	+	0.441943i	$0.145711\pi$
$234$		0			0
$235$	−11.0388	−	8.02017i	−0.720093	−	0.523178i
$236$		0			0
$237$	3.41925	+	10.5234i	0.222104	+	0.683566i
$238$		0			0
$239$	−3.51852	+	2.55635i	−0.227594	+	0.165357i	−0.695738	−	0.718295i	$-0.744923\pi$
$239$	−3.51852	+	2.55635i	−0.227594	+	0.165357i	0.468144	+	0.883652i	$0.344923\pi$
$240$		0			0
$241$	5.48061			0.353037			0.176519	−	0.984297i	$-0.443516\pi$
$241$	5.48061			0.353037			0.176519	+	0.984297i	$0.443516\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	40.0585	−	29.1042i	2.55924	−	1.85940i
$246$		0			0
$247$	−0.0895849	−	0.275714i	−0.00570015	−	0.0175433i
$248$		0			0
$249$	−9.25671	−	6.72540i	−0.586620	−	0.426205i
$250$		0			0
$251$	−8.21076	+	25.2701i	−0.518259	+	1.59504i	0.259014	+	0.965873i	$0.416602\pi$
$251$	−8.21076	+	25.2701i	−0.518259	+	1.59504i	−0.777273	+	0.629163i	$0.783398\pi$
$252$		0			0
$253$	−3.31704	+	5.38885i	−0.208540	+	0.338794i
$254$		0			0
$255$	−2.63715	+	8.11631i	−0.165145	+	0.508263i
$256$		0			0
$257$	5.16064	+	3.74943i	0.321912	+	0.233883i	0.736991	−	0.675903i	$-0.236246\pi$
$257$	5.16064	+	3.74943i	0.321912	+	0.233883i	−0.415079	+	0.909785i	$0.636246\pi$
$258$		0			0
$259$	14.9200	+	45.9189i	0.927082	+	2.85326i
$260$		0			0
$261$	−7.09513	+	5.15491i	−0.439177	+	0.319081i
$262$		0			0
$263$	−26.4473			−1.63081			−0.815406	−	0.578890i	$-0.803486\pi$
$263$	−26.4473			−1.63081			−0.815406	+	0.578890i	$0.803486\pi$
$264$		0			0
$265$	−15.4310			−0.947919
$266$		0			0
$267$	6.17092	−	4.48344i	0.377654	−	0.274382i
$268$		0			0
$269$	1.41713	+	4.36148i	0.0864040	+	0.265924i	0.984918	−	0.173020i	$-0.0553526\pi$
$269$	1.41713	+	4.36148i	0.0864040	+	0.265924i	−0.898514	+	0.438944i	$0.855353\pi$
$270$		0			0
$271$	−10.8736	−	7.90011i	−0.660522	−	0.479897i	0.206317	−	0.978485i	$-0.433852\pi$
$271$	−10.8736	−	7.90011i	−0.660522	−	0.479897i	−0.866839	+	0.498588i	$0.833852\pi$
$272$		0			0
$273$	1.47308	−	4.53368i	0.0891550	−	0.274391i
$274$		0			0
$275$	1.24693	+	16.2566i	0.0751930	+	0.980312i
$276$		0			0
$277$	−9.04960	+	27.8518i	−0.543738	+	1.67345i	0.180235	+	0.983624i	$0.442314\pi$
$277$	−9.04960	+	27.8518i	−0.543738	+	1.67345i	−0.723973	+	0.689829i	$0.757686\pi$
$278$		0			0
$279$	−5.95017	−	4.32305i	−0.356228	−	0.258815i
$280$		0			0
$281$	−2.76889	−	8.52176i	−0.165178	−	0.508366i	0.833871	−	0.551959i	$-0.186119\pi$
$281$	−2.76889	−	8.52176i	−0.165178	−	0.508366i	−0.999049	+	0.0435932i	$0.986119\pi$
$282$		0			0
$283$	−5.67493	+	4.12308i	−0.337340	+	0.245092i	−0.743539	−	0.668693i	$-0.766854\pi$
$283$	−5.67493	+	4.12308i	−0.337340	+	0.245092i	0.406199	+	0.913785i	$0.366854\pi$
$284$		0			0
$285$	−0.912893			−0.0540751
$286$		0			0
$287$	36.9508			2.18114
$288$		0			0
$289$	7.81136	−	5.67529i	0.459492	−	0.333840i
$290$		0			0
$291$	−0.686745	−	2.11358i	−0.0402577	−	0.123901i
$292$		0			0
$293$	−2.48797	−	1.80762i	−0.145349	−	0.105602i	0.512734	−	0.858547i	$-0.328633\pi$
$293$	−2.48797	−	1.80762i	−0.145349	−	0.105602i	−0.658083	+	0.752945i	$0.728633\pi$
$294$		0			0
$295$	8.12993	−	25.0214i	0.473343	−	1.45680i
$296$		0			0
$297$	3.22344	+	0.780656i	0.187043	+	0.0452982i
$298$		0			0
$299$	0.589585	−	1.81456i	0.0340966	−	0.104938i
$300$		0			0
$301$	45.2037	+	32.8424i	2.60550	+	1.89300i
$302$		0			0
$303$	4.36510	+	13.4344i	0.250769	+	0.771786i
$304$		0			0
$305$	−23.3526	+	16.9666i	−1.33716	+	0.971506i
$306$		0			0
$307$	−10.1281			−0.578043			−0.289021	−	0.957323i	$-0.593330\pi$
$307$	−10.1281			−0.578043			−0.289021	+	0.957323i	$0.593330\pi$
$308$		0			0
$309$	−5.81587			−0.330854
$310$		0			0
$311$	−8.45951	+	6.14619i	−0.479695	+	0.348519i	−0.801208	−	0.598387i	$-0.795809\pi$
$311$	−8.45951	+	6.14619i	−0.479695	+	0.348519i	0.321513	+	0.946905i	$0.395809\pi$
$312$		0			0
$313$	2.10316	+	6.47285i	0.118878	+	0.365867i	0.992736	−	0.120313i	$-0.0383898\pi$
$313$	2.10316	+	6.47285i	0.118878	+	0.365867i	−0.873859	+	0.486180i	$0.838390\pi$
$314$		0			0
$315$	−12.1442	−	8.82329i	−0.684249	−	0.497136i
$316$		0			0
$317$	−3.58061	+	11.0200i	−0.201107	+	0.618943i	0.798744	+	0.601671i	$0.205498\pi$
$317$	−3.58061	+	11.0200i	−0.201107	+	0.618943i	−0.999851	+	0.0172723i	$0.994502\pi$
$318$		0			0
$319$	−26.8949	+	11.0777i	−1.50583	+	0.620232i
$320$		0			0
$321$	1.38985	−	4.27752i	0.0775740	−	0.238748i
$322$		0			0
$323$	−0.635616	−	0.461802i	−0.0353666	−	0.0256954i
$324$		0			0
$325$	−1.51911	−	4.67535i	−0.0842653	−	0.259342i
$326$		0			0
$327$	10.6593	−	7.74445i	0.589462	−	0.428269i
$328$		0			0
$329$	20.6558			1.13879
$330$		0			0
$331$	31.9488			1.75606			0.878032	−	0.478603i	$-0.158857\pi$
$331$	31.9488			1.75606			0.878032	+	0.478603i	$0.158857\pi$
$332$		0			0
$333$	8.19405	−	5.95332i	0.449031	−	0.326240i
$334$		0			0
$335$	1.83359	+	5.64321i	0.100180	+	0.308321i
$336$		0			0
$337$	11.8782	+	8.62999i	0.647045	+	0.470105i	0.862263	−	0.506460i	$-0.169046\pi$
$337$	11.8782	+	8.62999i	0.647045	+	0.470105i	−0.215219	+	0.976566i	$0.569046\pi$
$338$		0			0
$339$	−3.44915	+	10.6154i	−0.187332	+	0.576548i
$340$		0			0
$341$	−15.8052	−	18.5802i	−0.855901	−	1.00617i
$342$		0			0
$343$	−12.8515	+	39.5529i	−0.693917	+	2.13566i
$344$		0			0
$345$	−4.86059	−	3.53143i	−0.261685	−	0.190126i
$346$		0			0
$347$	4.49270	+	13.8271i	0.241181	+	0.742278i	0.996241	+	0.0866228i	$0.0276075\pi$
$347$	4.49270	+	13.8271i	0.241181	+	0.742278i	−0.755060	+	0.655655i	$0.772393\pi$
$348$		0			0
$349$	−10.9790	+	7.97669i	−0.587691	+	0.426982i	−0.841489	−	0.540275i	$-0.818320\pi$
$349$	−10.9790	+	7.97669i	−0.587691	+	0.426982i	0.253798	+	0.967257i	$0.418320\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−17.5713			−0.935228			−0.467614	−	0.883933i	$-0.654886\pi$
$353$	−17.5713			−0.935228			−0.467614	+	0.883933i	$0.654886\pi$
$354$		0			0
$355$	15.1560	−	11.0115i	0.804399	−	0.584430i
$356$		0			0
$357$	−3.99220	−	12.2867i	−0.211289	−	0.650282i
$358$		0			0
$359$	12.1983	+	8.86256i	0.643800	+	0.467748i	0.861154	−	0.508345i	$-0.169742\pi$
$359$	12.1983	+	8.86256i	0.643800	+	0.467748i	−0.217353	+	0.976093i	$0.569742\pi$
$360$		0			0
$361$	−5.84535	+	17.9901i	−0.307650	+	0.946850i
$362$		0			0
$363$	9.78115	+	5.03280i	0.513377	+	0.264153i
$364$		0			0
$365$	−10.0855	+	31.0399i	−0.527898	+	1.62470i
$366$		0			0
$367$	−17.8259	−	12.9512i	−0.930502	−	0.676049i	0.0156136	−	0.999878i	$-0.495030\pi$
$367$	−17.8259	−	12.9512i	−0.930502	−	0.676049i	−0.946116	+	0.323829i	$0.895030\pi$
$368$		0			0
$369$	−2.39531	−	7.37201i	−0.124695	−	0.383771i
$370$		0			0
$371$	18.8986	−	13.7306i	0.981166	−	0.712859i
$372$		0			0
$373$	34.3215			1.77710			0.888551	−	0.458779i	$-0.151713\pi$
$373$	34.3215			1.77710			0.888551	+	0.458779i	$0.151713\pi$
$374$		0			0
$375$	0.264650			0.0136665
$376$		0			0
$377$	7.09513	−	5.15491i	0.365418	−	0.265491i
$378$		0			0
$379$	−1.72854	−	5.31991i	−0.0887893	−	0.273265i	0.896796	−	0.442444i	$-0.145889\pi$
$379$	−1.72854	−	5.31991i	−0.0887893	−	0.273265i	−0.985585	+	0.169179i	$0.945889\pi$
$380$		0			0
$381$	1.00802	+	0.732369i	0.0516424	+	0.0375204i
$382$		0			0
$383$	−7.32637	+	22.5483i	−0.374360	+	1.15216i	0.569549	+	0.821957i	$0.307118\pi$
$383$	−7.32637	+	22.5483i	−0.374360	+	1.15216i	−0.943909	+	0.330205i	$0.892882\pi$
$384$		0			0
$385$	−32.2582	−	37.9218i	−1.64403	−	1.93268i
$386$		0			0
$387$	3.62204	−	11.1475i	0.184119	−	0.566659i
$388$		0			0
$389$	5.69486	+	4.13756i	0.288741	+	0.209782i	0.722721	−	0.691140i	$-0.242891\pi$
$389$	5.69486	+	4.13756i	0.288741	+	0.209782i	−0.433980	+	0.900922i	$0.642891\pi$
$390$		0			0
$391$	−1.59783	−	4.91762i	−0.0808059	−	0.248695i
$392$		0			0
$393$	−2.49752	+	1.81456i	−0.125983	+	0.0915322i
$394$		0			0
$395$	−34.8430			−1.75314
$396$		0			0
$397$	13.7388			0.689533			0.344766	−	0.938689i	$-0.387958\pi$
$397$	13.7388			0.689533			0.344766	+	0.938689i	$0.387958\pi$
$398$		0			0
$399$	1.11803	−	0.812299i	0.0559717	−	0.0406658i
$400$		0			0
$401$	−11.9241	−	36.6987i	−0.595462	−	1.83264i	−0.552413	−	0.833571i	$-0.686293\pi$
$401$	−11.9241	−	36.6987i	−0.595462	−	1.83264i	−0.0430489	−	0.999073i	$-0.513707\pi$
$402$		0			0
$403$	5.95017	+	4.32305i	0.296399	+	0.215347i
$404$		0			0
$405$	−0.973083	+	2.99484i	−0.0483529	+	0.148815i
$406$		0			0
$407$	31.0605	−	12.7935i	1.53961	−	0.634148i
$408$		0			0
$409$	3.97882	−	12.2455i	0.196740	−	0.605503i	−0.803212	−	0.595693i	$-0.796877\pi$
$409$	3.97882	−	12.2455i	0.196740	−	0.605503i	0.999952	−	0.00980963i	$-0.00312255\pi$
$410$		0			0
$411$	−12.7970	−	9.29755i	−0.631228	−	0.458614i
$412$		0			0
$413$	12.3073	+	37.8781i	0.605605	+	1.86386i
$414$		0			0
$415$	29.1490	−	21.1780i	1.43087	−	1.03959i
$416$		0			0
$417$	−5.30757			−0.259913
$418$		0			0
$419$	−20.8582			−1.01899			−0.509494	−	0.860474i	$-0.670167\pi$
$419$	−20.8582			−1.01899			−0.509494	+	0.860474i	$0.670167\pi$
$420$		0			0
$421$	25.5092	−	18.5335i	1.24324	−	0.903268i	0.245432	−	0.969414i	$-0.421070\pi$
$421$	25.5092	−	18.5335i	1.24324	−	0.903268i	0.997810	+	0.0661458i	$0.0210702\pi$
$422$		0			0
$423$	−1.33900	−	4.12101i	−0.0651043	−	0.200370i
$424$		0			0
$425$	−10.7783	−	7.83090i	−0.522825	−	0.379854i
$426$		0			0
$427$	13.5032	−	41.5586i	0.653465	−	2.01116i
$428$		0			0
$429$	−3.22344	−	0.780656i	−0.155629	−	0.0376904i
$430$		0			0
$431$	−5.77291	+	17.7672i	−0.278071	+	0.855815i	0.710319	+	0.703880i	$0.248551\pi$
$431$	−5.77291	+	17.7672i	−0.278071	+	0.855815i	−0.988390	+	0.151935i	$0.951449\pi$
$432$		0			0
$433$	0.871335	+	0.633062i	0.0418737	+	0.0304230i	0.608525	−	0.793535i	$-0.291761\pi$
$433$	0.871335	+	0.633062i	0.0418737	+	0.0304230i	−0.566652	+	0.823958i	$0.691761\pi$
$434$		0			0
$435$	−8.53399	−	26.2649i	−0.409174	−	1.25931i
$436$		0			0
$437$	0.447481	−	0.325114i	0.0214059	−	0.0155523i
$438$		0			0
$439$	6.98032			0.333153			0.166576	−	0.986029i	$-0.446729\pi$
$439$	6.98032			0.333153			0.166576	+	0.986029i	$0.446729\pi$
$440$		0			0
$441$	15.7242			0.748773
$442$		0			0
$443$	13.4721	−	9.78808i	0.640080	−	0.465046i	−0.219797	−	0.975546i	$-0.570540\pi$
$443$	13.4721	−	9.78808i	0.640080	−	0.465046i	0.859878	+	0.510500i	$0.170540\pi$
$444$		0			0
$445$	7.42236	+	22.8437i	0.351854	+	1.08289i
$446$		0			0
$447$	−4.64000	−	3.37115i	−0.219464	−	0.159450i
$448$		0			0
$449$	−3.47826	+	10.7050i	−0.164149	+	0.505200i	−0.998973	−	0.0453183i	$-0.985570\pi$
$449$	−3.47826	+	10.7050i	−0.164149	+	0.505200i	0.834823	+	0.550518i	$0.185570\pi$
$450$		0			0
$451$	−1.96614	−	25.6332i	−0.0925821	−	1.20702i
$452$		0			0
$453$	−1.88737	+	5.80874i	−0.0886766	+	0.272918i
$454$		0			0
$455$	12.1442	+	8.82329i	0.569330	+	0.413642i
$456$		0			0
$457$	−7.02028	−	21.6062i	−0.328395	−	1.01069i	−0.969885	−	0.243564i	$-0.921684\pi$
$457$	−7.02028	−	21.6062i	−0.328395	−	1.01069i	0.641490	−	0.767131i	$-0.278316\pi$
$458$		0			0
$459$	−2.19251	+	1.59296i	−0.102338	+	0.0743528i
$460$		0			0
$461$	−12.0229			−0.559962			−0.279981	−	0.960005i	$-0.590328\pi$
$461$	−12.0229			−0.559962			−0.279981	+	0.960005i	$0.590328\pi$
$462$		0			0
$463$	36.2618			1.68523			0.842613	−	0.538519i	$-0.181016\pi$
$463$	36.2618			1.68523			0.842613	+	0.538519i	$0.181016\pi$
$464$		0			0
$465$	18.7369	−	13.6131i	0.868901	−	0.631294i
$466$		0			0
$467$	−5.72294	−	17.6134i	−0.264826	−	0.815051i	−0.991733	−	0.128315i	$-0.959043\pi$
$467$	−5.72294	−	17.6134i	−0.264826	−	0.815051i	0.726907	−	0.686736i	$-0.240957\pi$
$468$		0			0
$469$	−7.26700	−	5.27978i	−0.335559	−	0.243798i
$470$		0			0
$471$	5.59089	−	17.2070i	0.257615	−	0.792856i
$472$		0			0
$473$	20.3778	−	33.1058i	0.936973	−	1.52220i
$474$		0			0
$475$	0.440396	−	1.35540i	0.0202067	−	0.0621899i
$476$		0			0
$477$	−3.96447	−	2.88035i	−0.181520	−	0.131882i
$478$		0			0
$479$	−7.06470	−	21.7429i	−0.322794	−	0.993459i	−0.972426	−	0.233210i	$-0.925077\pi$
$479$	−7.06470	−	21.7429i	−0.322794	−	0.993459i	0.649632	−	0.760249i	$-0.274923\pi$
$480$		0			0
$481$	−8.19405	+	5.95332i	−0.373616	+	0.271448i
$482$		0			0
$483$	9.09513			0.413843
$484$		0			0
$485$	6.99811			0.317768
$486$		0			0
$487$	1.04214	−	0.757161i	0.0472240	−	0.0343102i	−0.563923	−	0.825827i	$-0.690708\pi$
$487$	1.04214	−	0.757161i	0.0472240	−	0.0343102i	0.611147	+	0.791517i	$0.290708\pi$
$488$		0			0
$489$	0.781070	+	2.40389i	0.0353212	+	0.108708i
$490$		0			0
$491$	19.3570	+	14.0637i	0.873570	+	0.634686i	0.931542	−	0.363633i	$-0.118464\pi$
$491$	19.3570	+	14.0637i	0.873570	+	0.634686i	−0.0579727	+	0.998318i	$0.518464\pi$
$492$		0			0
$493$	7.34463	−	22.6044i	0.330785	−	1.01805i
$494$		0			0
$495$	−5.47461	+	8.89405i	−0.246066	+	0.399758i
$496$		0			0
$497$	−8.76370	+	26.9719i	−0.393106	+	1.20986i
$498$		0			0
$499$	6.58366	+	4.78331i	0.294725	+	0.214130i	0.725315	−	0.688418i	$-0.241694\pi$
$499$	6.58366	+	4.78331i	0.294725	+	0.214130i	−0.430589	+	0.902548i	$0.641694\pi$
$500$		0			0
$501$	1.26267	+	3.88611i	0.0564122	+	0.173619i
$502$		0			0
$503$	−8.41524	+	6.11403i	−0.375217	+	0.272611i	−0.759371	−	0.650658i	$-0.774493\pi$
$503$	−8.41524	+	6.11403i	−0.375217	+	0.272611i	0.384154	+	0.923269i	$0.374493\pi$
$504$		0			0
$505$	−44.4815			−1.97940
$506$		0			0
$507$	−12.0000			−0.532939
$508$		0			0
$509$	−11.3705	+	8.26114i	−0.503988	+	0.366169i	−0.810538	−	0.585686i	$-0.800825\pi$
$509$	−11.3705	+	8.26114i	−0.503988	+	0.366169i	0.306550	+	0.951855i	$0.400825\pi$
$510$		0			0
$511$	−15.2677	−	46.9892i	−0.675404	−	2.07868i
$512$		0			0
$513$	−0.234536	−	0.170401i	−0.0103550	−	0.00752337i
$514$		0			0
$515$	5.65933	−	17.4176i	0.249380	−	0.767512i
$516$		0			0
$517$	−1.09909	−	14.3291i	−0.0483379	−	0.630195i
$518$		0			0
$519$	−2.23278	+	6.87178i	−0.0980080	+	0.301638i
$520$		0			0
$521$	18.0883	+	13.1419i	0.792462	+	0.575757i	0.908693	−	0.417465i	$-0.137081\pi$
$521$	18.0883	+	13.1419i	0.792462	+	0.575757i	−0.116231	+	0.993222i	$0.537081\pi$
$522$		0			0
$523$	6.59288	+	20.2908i	0.288286	+	0.887254i	0.985394	+	0.170288i	$0.0544698\pi$
$523$	6.59288	+	20.2908i	0.288286	+	0.887254i	−0.697108	+	0.716966i	$0.745530\pi$
$524$		0			0
$525$	18.9588	−	13.7744i	0.827429	−	0.601162i
$526$		0			0
$527$	19.9323			0.868264
$528$		0			0
$529$	−19.3598			−0.841729
$530$		0			0
$531$	6.75919	−	4.91084i	0.293324	−	0.213112i
$532$		0			0
$533$	2.39531	+	7.37201i	0.103752	+	0.319317i
$534$		0			0
$535$	11.4581	+	8.32477i	0.495375	+	0.359911i
$536$		0			0
$537$	3.34693	−	10.3008i	0.144431	−	0.444513i
$538$		0			0
$539$	50.6862	+	12.2752i	2.18321	+	0.528731i
$540$		0			0
$541$	−11.4320	+	35.1841i	−0.491500	+	1.51268i	0.330840	+	0.943687i	$0.392668\pi$
$541$	−11.4320	+	35.1841i	−0.491500	+	1.51268i	−0.822340	+	0.568996i	$0.807332\pi$
$542$		0			0
$543$	15.2353	+	11.0691i	0.653811	+	0.475021i
$544$		0			0
$545$	12.8210	+	39.4590i	0.549191	+	1.69024i
$546$		0			0
$547$	−31.0148	+	22.5336i	−1.32610	+	0.963467i	−0.326264	+	0.945279i	$0.605790\pi$
$547$	−31.0148	+	22.5336i	−1.32610	+	0.963467i	−0.999835	+	0.0181879i	$0.994210\pi$
$548$		0			0
$549$	−9.16663			−0.391222
$550$		0			0
$551$	2.54247			0.108313
$552$		0			0
$553$	42.6727	−	31.0036i	1.81463	−	1.31841i
$554$		0			0
$555$	9.85577	+	30.3329i	0.418354	+	1.28756i
$556$		0			0
$557$	−5.92720	−	4.30637i	−0.251144	−	0.182467i	0.455090	−	0.890446i	$-0.349607\pi$
$557$	−5.92720	−	4.30637i	−0.251144	−	0.182467i	−0.706234	+	0.707979i	$0.749607\pi$
$558$		0			0
$559$	−3.62204	+	11.1475i	−0.153196	+	0.471489i
$560$		0			0
$561$	−8.31099	+	3.42320i	−0.350890	+	0.144528i
$562$		0			0
$563$	9.31924	−	28.6817i	0.392759	−	1.20879i	−0.537934	−	0.842987i	$-0.680795\pi$
$563$	9.31924	−	28.6817i	0.392759	−	1.20879i	0.930693	−	0.365801i	$-0.119205\pi$
$564$		0			0
$565$	−28.4351	−	20.6593i	−1.19627	−	0.869142i
$566$		0			0
$567$	−1.47308	−	4.53368i	−0.0618637	−	0.190397i
$568$		0			0
$569$	−13.1650	+	9.56493i	−0.551906	+	0.400983i	−0.828488	−	0.560007i	$-0.810798\pi$
$569$	−13.1650	+	9.56493i	−0.551906	+	0.400983i	0.276582	+	0.960990i	$0.410798\pi$
$570$		0			0
$571$	−10.1020			−0.422755			−0.211378	−	0.977404i	$-0.567795\pi$
$571$	−10.1020			−0.422755			−0.211378	+	0.977404i	$0.567795\pi$
$572$		0			0
$573$	−24.0670			−1.00541
$574$		0			0
$575$	7.58804	−	5.51303i	0.316443	−	0.229909i
$576$		0			0
$577$	−12.9426	−	39.8334i	−0.538809	−	1.65828i	−0.735271	−	0.677773i	$-0.762945\pi$
$577$	−12.9426	−	39.8334i	−0.538809	−	1.65828i	0.196462	−	0.980512i	$-0.437055\pi$
$578$		0			0
$579$	−5.17114	−	3.75705i	−0.214905	−	0.156138i
$580$		0			0
$581$	−16.8549	+	51.8741i	−0.699259	+	2.15210i
$582$		0			0
$583$	−10.5307	−	12.3795i	−0.436135	−	0.512708i
$584$		0			0
$585$	0.973083	−	2.99484i	0.0402320	−	0.123821i
$586$		0			0
$587$	−3.58441	−	2.60423i	−0.147945	−	0.107488i	0.511351	−	0.859372i	$-0.329145\pi$
$587$	−3.58441	−	2.60423i	−0.147945	−	0.107488i	−0.659295	+	0.751884i	$0.729145\pi$
$588$		0			0
$589$	0.658881	+	2.02783i	0.0271487	+	0.0835552i
$590$		0			0
$591$	20.5806	−	14.9527i	0.846573	−	0.615071i
$592$		0			0
$593$	−10.6225			−0.436215			−0.218108	−	0.975925i	$-0.569988\pi$
$593$	−10.6225			−0.436215			−0.218108	+	0.975925i	$0.569988\pi$
$594$		0			0
$595$	40.6815			1.66778
$596$		0			0
$597$	14.5827	−	10.5950i	0.596831	−	0.433623i
$598$		0			0
$599$	2.06537	+	6.35657i	0.0843889	+	0.259722i	0.984343	−	0.176262i	$-0.0564005\pi$
$599$	2.06537	+	6.35657i	0.0843889	+	0.259722i	−0.899954	+	0.435984i	$0.856400\pi$
$600$		0			0
$601$	−5.91975	−	4.30095i	−0.241472	−	0.175439i	0.460467	−	0.887677i	$-0.347682\pi$
$601$	−5.91975	−	4.30095i	−0.241472	−	0.175439i	−0.701939	+	0.712237i	$0.747682\pi$
$602$		0			0
$603$	−0.582284	+	1.79209i	−0.0237124	+	0.0729794i
$604$		0			0
$605$	−24.5903	+	24.3957i	−0.999737	+	0.991825i
$606$		0			0
$607$	9.48781	−	29.2005i	0.385098	−	1.18521i	−0.551310	−	0.834300i	$-0.685872\pi$
$607$	9.48781	−	29.2005i	0.385098	−	1.18521i	0.936409	−	0.350911i	$-0.114128\pi$
$608$		0			0
$609$	33.8224	+	24.5734i	1.37055	+	0.995766i
$610$		0			0
$611$	1.33900	+	4.12101i	0.0541700	+	0.166718i
$612$		0			0
$613$	−25.0524	+	18.2016i	−1.01186	+	0.735156i	−0.964598	−	0.263726i	$-0.915048\pi$
$613$	−25.0524	+	18.2016i	−1.01186	+	0.735156i	−0.0472583	+	0.998883i	$0.515048\pi$
$614$		0			0
$615$	24.4088			0.984259
$616$		0			0
$617$	−27.3227			−1.09997			−0.549986	−	0.835174i	$-0.685367\pi$
$617$	−27.3227			−1.09997			−0.549986	+	0.835174i	$0.685367\pi$
$618$		0			0
$619$	−21.7248	+	15.7840i	−0.873195	+	0.634413i	−0.931442	−	0.363889i	$-0.881449\pi$
$619$	−21.7248	+	15.7840i	−0.873195	+	0.634413i	0.0582477	+	0.998302i	$0.481449\pi$
$620$		0			0
$621$	−0.589585	−	1.81456i	−0.0236592	−	0.0728156i
$622$		0			0
$623$	−29.4168	−	21.3725i	−1.17856	−	0.856272i
$624$		0			0
$625$	−7.85310	+	24.1693i	−0.314124	+	0.966774i
$626$		0			0
$627$	−0.622990	−	0.732369i	−0.0248798	−	0.0292480i
$628$		0			0
$629$	−8.48219	+	26.1055i	−0.338207	+	1.04089i
$630$		0			0
$631$	38.1798	+	27.7393i	1.51991	+	1.10428i	0.961530	+	0.274701i	$0.0885788\pi$
$631$	38.1798	+	27.7393i	1.51991	+	1.10428i	0.558385	+	0.829582i	$0.311421\pi$
$632$		0			0
$633$	−4.04165	−	12.4389i	−0.160641	−	0.494403i
$634$		0			0
$635$	−3.17421	+	2.30620i	−0.125965	+	0.0915188i
$636$		0			0
$637$	−15.7242			−0.623017
$638$		0			0
$639$	5.94923			0.235348
$640$		0			0
$641$	24.9991	−	18.1629i	0.987407	−	0.717393i	0.0280549	−	0.999606i	$-0.491069\pi$
$641$	24.9991	−	18.1629i	0.987407	−	0.717393i	0.959352	+	0.282214i	$0.0910687\pi$
$642$		0			0
$643$	14.8648	+	45.7492i	0.586211	+	1.80417i	0.594350	+	0.804206i	$0.297409\pi$
$643$	14.8648	+	45.7492i	0.586211	+	1.80417i	−0.00813892	+	0.999967i	$0.502591\pi$
$644$		0			0
$645$	29.8604	+	21.6949i	1.17575	+	0.854235i
$646$		0			0
$647$	−2.09185	+	6.43804i	−0.0822390	+	0.253106i	−0.983719	−	0.179716i	$-0.942482\pi$
$647$	−2.09185	+	6.43804i	−0.0822390	+	0.253106i	0.901480	+	0.432822i	$0.142482\pi$
$648$		0			0
$649$	25.6215	−	10.5532i	1.00573	−	0.414250i
$650$		0			0
$651$	−10.8343	+	33.3444i	−0.424628	+	1.30687i
$652$		0			0
$653$	0.463747	+	0.336932i	0.0181478	+	0.0131852i	0.596822	−	0.802374i	$-0.296430\pi$
$653$	0.463747	+	0.336932i	0.0181478	+	0.0131852i	−0.578674	+	0.815559i	$0.696430\pi$
$654$		0			0
$655$	−3.00401	−	9.24539i	−0.117376	−	0.361247i
$656$		0			0
$657$	−8.38503	+	6.09208i	−0.327131	+	0.237675i
$658$		0			0
$659$	30.5486			1.19000			0.595002	−	0.803724i	$-0.297151\pi$
$659$	30.5486			1.19000			0.595002	+	0.803724i	$0.297151\pi$
$660$		0			0
$661$	−1.25682			−0.0488847			−0.0244423	−	0.999701i	$-0.507781\pi$
$661$	−1.25682			−0.0488847			−0.0244423	+	0.999701i	$0.507781\pi$
$662$		0			0
$663$	2.19251	−	1.59296i	0.0851502	−	0.0618652i
$664$		0			0
$665$	1.34477	+	4.13877i	0.0521478	+	0.160495i
$666$		0			0
$667$	13.5371	+	9.83524i	0.524157	+	0.380822i
$668$		0			0
$669$	3.11168	−	9.57677i	0.120304	−	0.370259i
$670$		0			0
$671$	−29.5481	−	7.15598i	−1.14069	−	0.276254i
$672$		0			0
$673$	8.33164	−	25.6421i	0.321161	−	0.988432i	−0.651983	−	0.758234i	$-0.726063\pi$
$673$	8.33164	−	25.6421i	0.321161	−	0.988432i	0.973144	−	0.230198i	$-0.0739375\pi$
$674$		0			0
$675$	−3.97709	−	2.88953i	−0.153078	−	0.111218i
$676$		0			0
$677$	−1.23607	−	3.80423i	−0.0475060	−	0.146208i	0.924490	−	0.381207i	$-0.124491\pi$
$677$	−1.23607	−	3.80423i	−0.0475060	−	0.146208i	−0.971996	+	0.234999i	$0.924491\pi$
$678$		0			0
$679$	−8.57069	+	6.22697i	−0.328913	+	0.238969i
$680$		0			0
$681$	11.6360			0.445891
$682$		0			0
$683$	−28.8819			−1.10514			−0.552568	−	0.833468i	$-0.686352\pi$
$683$	−28.8819			−1.10514			−0.552568	+	0.833468i	$0.686352\pi$
$684$		0			0
$685$	40.2972	−	29.2776i	1.53968	−	1.11864i
$686$		0			0
$687$	−1.21550	−	3.74094i	−0.0463744	−	0.142726i
$688$		0			0
$689$	3.96447	+	2.88035i	0.151034	+	0.109733i
$690$		0			0
$691$	−5.42264	+	16.6892i	−0.206287	+	0.634885i	0.793371	+	0.608738i	$0.208324\pi$
$691$	−5.42264	+	16.6892i	−0.206287	+	0.634885i	−0.999658	+	0.0261475i	$0.991676\pi$
$692$		0			0
$693$	−1.20915	−	15.7640i	−0.0459318	−	0.598826i
$694$		0			0
$695$	5.16470	−	15.8953i	0.195908	−	0.602944i
$696$		0			0
$697$	16.9950	+	12.3476i	0.643733	+	0.467699i
$698$		0			0
$699$	−1.35009	−	4.15516i	−0.0510652	−	0.157162i
$700$		0			0
$701$	10.2829	−	7.47097i	0.388380	−	0.282175i	−0.376411	−	0.926453i	$-0.622842\pi$
$701$	10.2829	−	7.47097i	0.388380	−	0.282175i	0.764791	+	0.644278i	$0.222842\pi$
$702$		0			0
$703$	−2.93625			−0.110743
$704$		0			0
$705$	13.6447			0.513890
$706$		0			0
$707$	54.4772	−	39.5800i	2.04882	−	1.48856i
$708$		0			0
$709$	−13.8659	−	42.6749i	−0.520745	−	1.60269i	−0.772580	−	0.634918i	$-0.781034\pi$
$709$	−13.8659	−	42.6749i	−0.520745	−	1.60269i	0.251835	−	0.967770i	$-0.418966\pi$
$710$		0			0
$711$	−8.95171	−	6.50380i	−0.335715	−	0.243911i
$712$		0			0
$713$	−4.33629	+	13.3457i	−0.162395	+	0.499802i
$714$		0			0
$715$	5.47461	−	8.89405i	0.204739	−	0.332619i
$716$		0			0
$717$	1.34395	−	4.13626i	0.0501909	−	0.154472i
$718$		0			0
$719$	−16.1425	−	11.7282i	−0.602012	−	0.437387i	0.244580	−	0.969629i	$-0.421350\pi$
$719$	−16.1425	−	11.7282i	−0.602012	−	0.437387i	−0.846593	+	0.532242i	$0.821350\pi$
$720$		0			0
$721$	8.56726	+	26.3673i	0.319062	+	0.981970i
$722$		0			0
$723$	−4.43391	+	3.22142i	−0.164899	+	0.119806i
$724$		0			0
$725$	43.1132			1.60118
$726$		0			0
$727$	10.4418			0.387264			0.193632	−	0.981074i	$-0.437973\pi$
$727$	10.4418			0.387264			0.193632	+	0.981074i	$0.437973\pi$
$728$		0			0
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	9.81609	+	30.2108i	0.363061	+	1.11739i
$732$		0			0
$733$	−11.3867	−	8.27289i	−0.420576	−	0.305566i	0.357294	−	0.933992i	$-0.383700\pi$
$733$	−11.3867	−	8.27289i	−0.420576	−	0.305566i	−0.777869	+	0.628426i	$0.783700\pi$
$734$		0			0
$735$	−15.3010	+	47.0916i	−0.564385	+	1.73700i
$736$		0			0
$737$	−3.27596	+	5.32212i	−0.120672	+	0.196043i
$738$		0			0
$739$	13.0488	−	40.1601i	0.480009	−	1.47731i	−0.359073	−	0.933309i	$-0.616907\pi$
$739$	13.0488	−	40.1601i	0.480009	−	1.47731i	0.839082	−	0.544005i	$-0.183093\pi$
$740$		0			0
$741$	0.234536	+	0.170401i	0.00861591	+	0.00625983i
$742$		0			0
$743$	−11.6338	−	35.8051i	−0.426802	−	1.31356i	−0.901258	−	0.433282i	$-0.857355\pi$
$743$	−11.6338	−	35.8051i	−0.426802	−	1.31356i	0.474457	−	0.880279i	$-0.342645\pi$
$744$		0			0
$745$	14.6112	−	10.6156i	0.535312	−	0.388927i
$746$		0			0
$747$	11.4419			0.418638
$748$		0			0
$749$	−21.4403			−0.783412
$750$		0			0
$751$	−37.6857	+	27.3802i	−1.37517	+	0.999119i	−0.377856	+	0.925864i	$0.623338\pi$
$751$	−37.6857	+	27.3802i	−1.37517	+	0.999119i	−0.997313	+	0.0732543i	$0.976662\pi$
$752$		0			0
$753$	−8.21076	−	25.2701i	−0.299217	−	0.920895i
$754$		0			0
$755$	−15.5597	−	11.3048i	−0.566275	−	0.411423i
$756$		0			0
$757$	13.4316	−	41.3381i	0.488178	−	1.50246i	−0.339146	−	0.940734i	$-0.610138\pi$
$757$	13.4316	−	41.3381i	0.488178	−	1.50246i	0.827324	−	0.561724i	$-0.189862\pi$
$758$		0			0
$759$	−0.483949	−	6.30938i	−0.0175662	−	0.229016i
$760$		0			0
$761$	−4.06529	+	12.5117i	−0.147367	+	0.453548i	−0.997308	−	0.0733300i	$-0.976637\pi$
$761$	−4.06529	+	12.5117i	−0.147367	+	0.453548i	0.849941	+	0.526878i	$0.176637\pi$
$762$		0			0
$763$	−50.8130	−	36.9178i	−1.83955	−	1.33651i
$764$		0			0
$765$	−2.63715	−	8.11631i	−0.0953463	−	0.293446i
$766$		0			0
$767$	−6.75919	+	4.91084i	−0.244060	+	0.177320i
$768$		0			0
$769$	19.9646			0.719944			0.359972	−	0.932963i	$-0.382786\pi$
$769$	19.9646			0.719944			0.359972	+	0.932963i	$0.382786\pi$
$770$		0			0
$771$	−6.37890			−0.229731
$772$		0			0
$773$	3.22638	−	2.34410i	0.116045	−	0.0843116i	−0.528249	−	0.849089i	$-0.677151\pi$
$773$	3.22638	−	2.34410i	0.116045	−	0.0843116i	0.644294	+	0.764778i	$0.277151\pi$
$774$		0			0
$775$	11.1728	+	34.3864i	0.401339	+	1.23520i
$776$		0			0
$777$	−39.0610	−	28.3795i	−1.40130	−	1.01811i
$778$		0			0
$779$	−0.694408	+	2.13717i	−0.0248797	+	0.0765720i
$780$		0			0
$781$	19.1770	+	4.64430i	0.686207	+	0.166186i
$782$		0			0
$783$	2.71010	−	8.34082i	0.0968510	−	0.298077i
$784$		0			0
$785$	46.0918	+	33.4876i	1.64509	+	1.19522i
$786$		0			0
$787$	−1.22425	−	3.76785i	−0.0436397	−	0.134309i	0.926863	−	0.375400i	$-0.122495\pi$
$787$	−1.22425	−	3.76785i	−0.0436397	−	0.134309i	−0.970502	+	0.241091i	$0.922495\pi$
$788$		0			0
$789$	21.3963	−	15.5453i	0.761729	−	0.553429i
$790$		0			0
$791$	53.2076			1.89185
$792$		0			0
$793$	9.16663			0.325516
$794$		0			0
$795$	12.4839	−	9.07012i	0.442760	−	0.321684i
$796$		0			0
$797$	3.54553	+	10.9120i	0.125589	+	0.386523i	0.994008	−	0.109308i	$-0.0348634\pi$
$797$	3.54553	+	10.9120i	0.125589	+	0.386523i	−0.868419	+	0.495831i	$0.834863\pi$
$798$		0			0
$799$	9.50036	+	6.90241i	0.336098	+	0.244190i
$800$		0			0
$801$	−2.35708	+	7.25435i	−0.0832834	+	0.256320i
$802$		0			0
$803$	−31.7845	+	13.0916i	−1.12165	+	0.461994i
$804$		0			0
$805$	−8.85031	+	27.2384i	−0.311932	+	0.960029i
$806$		0			0
$807$	−3.71010	−	2.69554i	−0.130602	−	0.0948876i
$808$		0			0
$809$	−11.4845	−	35.3455i	−0.403772	−	1.24268i	−0.921916	−	0.387389i	$-0.873377\pi$
$809$	−11.4845	−	35.3455i	−0.403772	−	1.24268i	0.518145	−	0.855293i	$-0.326623\pi$
$810$		0			0
$811$	−11.7817	+	8.55987i	−0.413710	+	0.300578i	−0.775102	−	0.631836i	$-0.782302\pi$
$811$	−11.7817	+	8.55987i	−0.413710	+	0.300578i	0.361392	+	0.932414i	$0.382302\pi$
$812$		0			0
$813$	13.4405			0.471378
$814$		0			0
$815$	−7.95931			−0.278802
$816$		0			0
$817$	−2.74904	+	1.99730i	−0.0961769	+	0.0698766i
$818$		0			0
$819$	1.47308	+	4.53368i	0.0514737	+	0.158420i
$820$		0			0
$821$	1.41997	+	1.03167i	0.0495572	+	0.0360054i	0.612288	−	0.790635i	$-0.290249\pi$
$821$	1.41997	+	1.03167i	0.0495572	+	0.0360054i	−0.562731	+	0.826640i	$0.690249\pi$
$822$		0			0
$823$	11.6140	−	35.7443i	0.404839	−	1.24597i	−0.516190	−	0.856474i	$-0.672650\pi$
$823$	11.6140	−	35.7443i	0.404839	−	1.24597i	0.921029	−	0.389493i	$-0.127350\pi$
$824$		0			0
$825$	−10.5642	−	12.4190i	−0.367798	−	0.432373i
$826$		0			0
$827$	5.55556	−	17.0983i	0.193186	−	0.594564i	−0.806807	−	0.590815i	$-0.798806\pi$
$827$	5.55556	−	17.0983i	0.193186	−	0.594564i	0.999993	−	0.00374973i	$-0.00119358\pi$
$828$		0			0
$829$	1.21959	+	0.886081i	0.0423579	+	0.0307749i	0.608763	−	0.793352i	$-0.291666\pi$
$829$	1.21959	+	0.886081i	0.0423579	+	0.0307749i	−0.566405	+	0.824127i	$0.691666\pi$
$830$		0			0
$831$	−9.04960	−	27.8518i	−0.313927	−	0.966168i
$832$		0			0
$833$	−34.4756	+	25.0480i	−1.19451	+	0.867862i
$834$		0			0
$835$	−12.8670			−0.445280
$836$		0			0
$837$	7.35482			0.254220
$838$		0			0
$839$	−35.1429	+	25.5328i	−1.21327	+	0.881490i	−0.995523	−	0.0945156i	$-0.969870\pi$
$839$	−35.1429	+	25.5328i	−1.21327	+	0.881490i	−0.217744	+	0.976006i	$0.569870\pi$
$840$		0			0
$841$	14.8062	+	45.5688i	0.510559	+	1.57134i
$842$		0			0
$843$	7.24904	+	5.26674i	0.249670	+	0.181396i
$844$		0			0
$845$	11.6770	−	35.9381i	0.401701	−	1.23631i
$846$		0			0
$847$	8.40866	−	51.7584i	0.288925	−	1.77844i
$848$		0			0
$849$	2.16763	−	6.67128i	0.0743929	−	0.228958i
$850$		0			0
$851$	−15.6337	−	11.3586i	−0.535917	−	0.389367i
$852$		0			0
$853$	12.7068	+	39.1074i	0.435071	+	1.33901i	0.893014	+	0.450029i	$0.148586\pi$
$853$	12.7068	+	39.1074i	0.435071	+	1.33901i	−0.457943	+	0.888982i	$0.651414\pi$
$854$		0			0
$855$	0.738546	−	0.536585i	0.0252577	−	0.0183508i
$856$		0			0
$857$	−57.3388			−1.95865			−0.979327	−	0.202282i	$-0.935164\pi$
$857$	−57.3388			−1.95865			−0.979327	+	0.202282i	$0.935164\pi$
$858$		0			0
$859$	−35.3444			−1.20594			−0.602968	−	0.797765i	$-0.706015\pi$
$859$	−35.3444			−1.20594			−0.602968	+	0.797765i	$0.706015\pi$
$860$		0			0
$861$	−29.8938	+	21.7192i	−1.01878	+	0.740187i
$862$		0			0
$863$	9.72001	+	29.9151i	0.330873	+	1.01832i	0.968719	+	0.248159i	$0.0798254\pi$
$863$	9.72001	+	29.9151i	0.330873	+	1.01832i	−0.637846	+	0.770164i	$0.720175\pi$
$864$		0			0
$865$	−18.4072	−	13.3736i	−0.625864	−	0.454717i
$866$		0			0
$867$	−2.98367	+	9.18281i	−0.101331	+	0.311864i
$868$		0			0
$869$	−23.7781	−	27.9528i	−0.806616	−	0.948234i
$870$		0			0
$871$	0.582284	−	1.79209i	0.0197299	−	0.0607225i
$872$		0			0
$873$	1.79792	+	1.30627i	0.0608504	+	0.0442104i
$874$		0			0
$875$	−0.389852	−	1.19984i	−0.0131794	−	0.0405620i
$876$		0			0
$877$	−14.2731	+	10.3700i	−0.481969	+	0.350171i	−0.802088	−	0.597206i	$-0.796277\pi$
$877$	−14.2731	+	10.3700i	−0.481969	+	0.350171i	0.320118	+	0.947378i	$0.396277\pi$
$878$		0			0
$879$	3.07530			0.103727
$880$		0			0
$881$	−9.21345			−0.310409			−0.155204	−	0.987882i	$-0.549604\pi$
$881$	−9.21345			−0.310409			−0.155204	+	0.987882i	$0.549604\pi$
$882$		0			0
$883$	5.08711	−	3.69600i	0.171195	−	0.124380i	−0.498889	−	0.866666i	$-0.666258\pi$
$883$	5.08711	−	3.69600i	0.171195	−	0.124380i	0.670083	+	0.742286i	$0.266258\pi$
$884$		0			0
$885$	8.12993	+	25.0214i	0.273285	+	0.841083i
$886$		0			0
$887$	−11.0131	−	8.00145i	−0.369782	−	0.268663i	0.387338	−	0.921938i	$-0.373395\pi$
$887$	−11.0131	−	8.00145i	−0.369782	−	0.268663i	−0.757121	+	0.653275i	$0.773395\pi$
$888$		0			0
$889$	1.83543	−	5.64888i	0.0615584	−	0.189457i
$890$		0			0
$891$	−3.06668	+	1.26313i	−0.102738	+	0.0423164i
$892$		0			0
$893$	−0.388179	+	1.19469i	−0.0129899	+	0.0399789i
$894$		0			0
$895$	27.5924	+	20.0471i	0.922313	+	0.670100i
$896$		0			0
$897$	0.589585	+	1.81456i	0.0196857	+	0.0605863i
$898$		0			0
$899$	−52.1834	+	37.9134i	−1.74041	+	1.26448i
$900$		0			0
$901$	13.2804			0.442435
$902$		0			0
$903$	−55.8748			−1.85940
$904$		0			0
$905$	−47.9755	+	34.8562i	−1.59476	+	1.15866i
$906$		0			0
$907$	1.18751	+	3.65477i	0.0394305	+	0.121355i	0.968834	−	0.247710i	$-0.0796780\pi$
$907$	1.18751	+	3.65477i	0.0394305	+	0.121355i	−0.929404	+	0.369065i	$0.879678\pi$
$908$		0			0
$909$	−11.4280	−	8.30292i	−0.379042	−	0.275390i
$910$		0			0
$911$	−10.0334	+	30.8796i	−0.332422	+	1.02309i	0.635557	+	0.772054i	$0.280771\pi$
$911$	−10.0334	+	30.8796i	−0.332422	+	1.02309i	−0.967978	+	0.251034i	$0.919229\pi$
$912$		0			0
$913$	36.8824	+	8.93221i	1.22063	+	0.295613i
$914$		0			0
$915$	8.91988	−	27.4526i	0.294882	−	0.907554i
$916$		0			0
$917$	11.9057	+	8.64998i	0.393160	+	0.285647i
$918$		0			0
$919$	14.4862	+	44.5840i	0.477856	+	1.47069i	0.842066	+	0.539374i	$0.181339\pi$
$919$	14.4862	+	44.5840i	0.477856	+	1.47069i	−0.364210	+	0.931317i	$0.618661\pi$
$920$		0			0
$921$	8.19383	−	5.95317i	0.269996	−	0.196163i
$922$		0			0
$923$	−5.94923			−0.195821
$924$		0			0
$925$	−49.7908			−1.63711
$926$		0			0
$927$	4.70514	−	3.41848i	0.154537	−	0.112278i
$928$		0			0
$929$	14.7218	+	45.3091i	0.483007	+	1.48654i	0.834847	+	0.550483i	$0.185556\pi$
$929$	14.7218	+	45.3091i	0.483007	+	1.48654i	−0.351840	+	0.936060i	$0.614444\pi$
$930$		0			0
$931$	−3.68791	−	2.67942i	−0.120866	−	0.0878145i
$932$		0			0
$933$	3.23125	−	9.94475i	0.105786	−	0.325577i
$934$		0			0
$935$	−2.16465	−	28.2211i	−0.0707916	−	0.922930i
$936$		0			0
$937$	10.1917	−	31.3668i	0.332948	−	1.02471i	−0.634775	−	0.772697i	$-0.718907\pi$
$937$	10.1917	−	31.3668i	0.332948	−	1.02471i	0.967724	−	0.252013i	$-0.0810926\pi$
$938$		0			0
$939$	−5.50614	−	4.00044i	−0.179686	−	0.130550i
$940$		0			0
$941$	1.11339	+	3.42666i	0.0362954	+	0.111706i	0.967563	−	0.252631i	$-0.0812958\pi$
$941$	1.11339	+	3.42666i	0.0362954	+	0.111706i	−0.931267	+	0.364337i	$0.881296\pi$
$942$		0			0
$943$	−11.9647	+	8.69285i	−0.389624	+	0.283078i
$944$		0			0
$945$	15.0111			0.488311
$946$		0			0
$947$	−21.1512			−0.687322			−0.343661	−	0.939094i	$-0.611667\pi$
$947$	−21.1512			−0.687322			−0.343661	+	0.939094i	$0.611667\pi$
$948$		0			0
$949$	8.38503	−	6.09208i	0.272190	−	0.197757i
$950$		0			0
$951$	−3.58061	−	11.0200i	−0.116109	−	0.357347i
$952$		0			0
$953$	13.2977	+	9.66131i	0.430753	+	0.312961i	0.781950	−	0.623341i	$-0.214225\pi$
$953$	13.2977	+	9.66131i	0.430753	+	0.312961i	−0.351197	+	0.936302i	$0.614225\pi$
$954$		0			0
$955$	23.4192	−	72.0767i	0.757826	−	2.33235i
$956$		0			0
$957$	15.2472	−	24.7705i	0.492870	−	0.800716i
$958$		0			0
$959$	−23.3011	+	71.7135i	−0.752432	+	2.31575i
$960$		0			0
$961$	−18.6829	−	13.5739i	−0.602675	−	0.437869i
$962$		0			0
$963$	1.38985	+	4.27752i	0.0447874	+	0.137841i
$964$		0			0
$965$	16.2837	−	11.8308i	0.524191	−	0.380847i
$966$		0			0
$967$	0.0359806			0.00115706			0.000578529	−	1.00000i	$-0.499816\pi$
$967$	0.0359806			0.00115706			0.000578529		1.00000i	$0.499816\pi$
$968$		0			0
$969$	0.785665			0.0252392
$970$		0			0
$971$	−10.6501	+	7.73776i	−0.341778	+	0.248316i	−0.745412	−	0.666604i	$-0.767747\pi$
$971$	−10.6501	+	7.73776i	−0.341778	+	0.248316i	0.403633	+	0.914921i	$0.367747\pi$
$972$		0			0
$973$	7.81849	+	24.0628i	0.250649	+	0.771419i
$974$		0			0
$975$	3.97709	+	2.88953i	0.127369	+	0.0925389i
$976$		0			0
$977$	1.76809	−	5.44161i	0.0565661	−	0.174093i	−0.918782	−	0.394766i	$-0.870826\pi$
$977$	1.76809	−	5.44161i	0.0565661	−	0.174093i	0.975348	+	0.220674i	$0.0708256\pi$
$978$		0			0
$979$	−13.2611	+	21.5439i	−0.423826	+	0.688547i
$980$		0			0
$981$	−4.07150	+	12.5308i	−0.129993	+	0.400077i
$982$		0			0
$983$	18.5444	+	13.4733i	0.591474	+	0.429731i	0.842842	−	0.538161i	$-0.180881\pi$
$983$	18.5444	+	13.4733i	0.591474	+	0.429731i	−0.251369	+	0.967891i	$0.580881\pi$
$984$		0			0
$985$	24.7543	+	76.1858i	0.788737	+	2.42748i
$986$		0			0
$987$	−16.7109	+	12.1412i	−0.531914	+	0.386458i
$988$		0			0
$989$	−22.3633			−0.711111
$990$		0			0
$991$	14.8537			0.471842			0.235921	−	0.971772i	$-0.424189\pi$
$991$	14.8537			0.471842			0.235921	+	0.971772i	$0.424189\pi$
$992$		0			0
$993$	−25.8471	+	18.7790i	−0.820233	+	0.595934i
$994$		0			0
$995$	17.5400	+	53.9827i	0.556056	+	1.71137i
$996$		0			0
$997$	−13.2315	−	9.61326i	−0.419047	−	0.304455i	0.358208	−	0.933642i	$-0.383388\pi$
$997$	−13.2315	−	9.61326i	−0.419047	−	0.304455i	−0.777254	+	0.629187i	$0.783388\pi$
$998$		0			0
$999$	−3.12985	+	9.63268i	−0.0990240	+	0.304764i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1056.2.y.c.97.1	✓	8
4.3	odd	2		1056.2.y.d.97.1	yes	8
11.5	even	5	inner	1056.2.y.c.577.1	yes	8
44.27	odd	10		1056.2.y.d.577.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1056.2.y.c.97.1	✓	8	1.1	even	1	trivial
1056.2.y.c.577.1	yes	8	11.5	even	5	inner
1056.2.y.d.97.1	yes	8	4.3	odd	2
1056.2.y.d.577.1	yes	8	44.27	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1056 = 2^{5} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1056.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{3} +(-0.973083 - 2.99484i) q^{5} +(3.85658 + 2.80197i) q^{7} +(0.309017 - 0.951057i) q^{9} +(1.73855 - 2.82444i) q^{11} +(-0.309017 + 0.951057i) q^{13} +(2.54756 + 1.85091i) q^{15} +(0.837466 + 2.57746i) q^{17} +(-0.234536 + 0.170401i) q^{19} -4.76700 q^{21} -1.90794 q^{23} +(-3.97709 + 2.88953i) q^{25} +(0.309017 + 0.951057i) q^{27} +(-7.09513 - 5.15491i) q^{29} +(2.27276 - 6.99485i) q^{31} +(0.253650 + 3.30691i) q^{33} +(4.63868 - 14.2764i) q^{35} +(8.19405 + 5.95332i) q^{37} +(-0.309017 - 0.951057i) q^{39} +(6.27100 - 4.55615i) q^{41} +11.7212 q^{43} -3.14896 q^{45} +(3.50554 - 2.54692i) q^{47} +(4.85906 + 14.9546i) q^{49} +(-2.19251 - 1.59296i) q^{51} +(1.51429 - 4.66051i) q^{53} +(-10.1505 - 2.45825i) q^{55} +(0.0895849 - 0.275714i) q^{57} +(6.75919 + 4.91084i) q^{59} +(-2.83264 - 8.71798i) q^{61} +(3.85658 - 2.80197i) q^{63} +3.14896 q^{65} -1.88431 q^{67} +(1.54355 - 1.12146i) q^{69} +(1.83841 + 5.65805i) q^{71} +(-8.38503 - 6.09208i) q^{73} +(1.51911 - 4.67535i) q^{75} +(14.6188 - 6.02132i) q^{77} +(3.41925 - 10.5234i) q^{79} +(-0.809017 - 0.587785i) q^{81} +(3.53575 + 10.8819i) q^{83} +(6.90414 - 5.01615i) q^{85} +8.77006 q^{87} -7.62768 q^{89} +(-3.85658 + 2.80197i) q^{91} +(2.27276 + 6.99485i) q^{93} +(0.738546 + 0.536585i) q^{95} +(-0.686745 + 2.11358i) q^{97} +(-2.14896 - 2.52626i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{5} + 8 q^{7} - 2 q^{9} + 2 q^{13} + 2 q^{15} - 10 q^{17} - 6 q^{19} - 12 q^{21} - 8 q^{23} - 4 q^{25} - 2 q^{27} - 20 q^{29} + 10 q^{31} + 26 q^{37} + 2 q^{39} + 6 q^{41} + 12 q^{43}+ \cdots + 30 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^5 + 8 * q^7 - 2 * q^9 + 2 * q^13 + 2 * q^15 - 10 * q^17 - 6 * q^19 - 12 * q^21 - 8 * q^23 - 4 * q^25 - 2 * q^27 - 20 * q^29 + 10 * q^31 + 26 * q^37 + 2 * q^39 + 6 * q^41 + 12 * q^43 - 8 * q^45 - 12 * q^47 + 20 * q^49 + 14 * q^53 - 42 * q^55 + 4 * q^57 + 12 * q^59 - 14 * q^61 + 8 * q^63 + 8 * q^65 - 12 * q^67 + 12 * q^69 + 24 * q^71 - 32 * q^73 + 6 * q^75 + 8 * q^77 - 2 * q^79 - 2 * q^81 + 12 * q^83 + 14 * q^85 - 36 * q^89 - 8 * q^91 + 10 * q^93 - 8 * q^95 + 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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