LMFDB - Embedded newform 936.2.ed.a.19.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(19,936)] 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("936.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.ed (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	936.19
Dual form			936.2.ed.a.739.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(0.366025 + 0.366025i) q^{5} +(2.36603 + 0.633975i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.366025 - 0.633975i) q^{10} +(3.36603 - 0.901924i) q^{11} +(3.50000 + 0.866025i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-0.232051 + 0.133975i) q^{17} +(-4.09808 - 1.09808i) q^{19} +(0.267949 + 1.00000i) q^{20} -4.92820 q^{22} +(-0.366025 + 0.633975i) q^{23} -4.73205i q^{25} +(-4.46410 - 2.46410i) q^{26} +(3.46410 + 3.46410i) q^{28} +(2.59808 + 1.50000i) q^{29} +(4.00000 + 4.00000i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(0.366025 - 0.0980762i) q^{34} +(0.633975 + 1.09808i) q^{35} +(-1.86603 - 6.96410i) q^{37} +(5.19615 + 3.00000i) q^{38} -1.46410i q^{40} +(2.50000 + 9.33013i) q^{41} +(-0.633975 + 0.366025i) q^{43} +(6.73205 + 1.80385i) q^{44} +(0.732051 - 0.732051i) q^{46} +(-2.26795 + 2.26795i) q^{47} +(-0.866025 - 0.500000i) q^{49} +(-1.73205 + 6.46410i) q^{50} +(5.19615 + 5.00000i) q^{52} +8.66025i q^{53} +(1.56218 + 0.901924i) q^{55} +(-3.46410 - 6.00000i) q^{56} +(-3.00000 - 3.00000i) q^{58} +(2.80385 - 10.4641i) q^{59} +(1.66987 - 0.964102i) q^{61} +(-4.00000 - 6.92820i) q^{62} +8.00000i q^{64} +(0.964102 + 1.59808i) q^{65} +(-1.56218 - 5.83013i) q^{67} -0.535898 q^{68} +(-0.464102 - 1.73205i) q^{70} +(-1.83013 + 6.83013i) q^{71} +(7.83013 + 7.83013i) q^{73} +10.1962i q^{74} +(-6.00000 - 6.00000i) q^{76} +8.53590 q^{77} -1.07180i q^{79} +(-0.535898 + 2.00000i) q^{80} -13.6603i q^{82} +(7.92820 - 7.92820i) q^{83} +(-0.133975 - 0.0358984i) q^{85} +(1.00000 - 0.267949i) q^{86} +(-8.53590 - 4.92820i) q^{88} +(12.5622 - 3.36603i) q^{89} +(7.73205 + 4.26795i) q^{91} +(-1.26795 + 0.732051i) q^{92} +(3.92820 - 2.26795i) q^{94} +(-1.09808 - 1.90192i) q^{95} +(15.2942 + 4.09808i) q^{97} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{5} + 6 q^{7} - 8 q^{8} + 2 q^{10} + 10 q^{11} + 14 q^{13} - 12 q^{14} + 8 q^{16} + 6 q^{17} - 6 q^{19} + 8 q^{20} + 8 q^{22} + 2 q^{23} - 4 q^{26} + 16 q^{31} + 8 q^{32} - 2 q^{34}+ \cdots + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^5 + 6 * q^7 - 8 * q^8 + 2 * q^10 + 10 * q^11 + 14 * q^13 - 12 * q^14 + 8 * q^16 + 6 * q^17 - 6 * q^19 + 8 * q^20 + 8 * q^22 + 2 * q^23 - 4 * q^26 + 16 * q^31 + 8 * q^32 - 2 * q^34 + 6 * q^35 - 4 * q^37 + 10 * q^41 - 6 * q^43 + 20 * q^44 - 4 * q^46 - 16 * q^47 - 18 * q^55 - 12 * q^58 + 32 * q^59 + 24 * q^61 - 16 * q^62 - 10 * q^65 + 18 * q^67 - 16 * q^68 + 12 * q^70 + 10 * q^71 + 14 * q^73 - 24 * q^76 + 48 * q^77 - 16 * q^80 + 4 * q^83 - 4 * q^85 + 4 * q^86 - 48 * q^88 + 26 * q^89 + 24 * q^91 - 12 * q^92 - 12 * q^94 + 6 * q^95 + 30 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$2$	−1.36603	−	0.366025i	−0.965926	−	0.258819i
$3$		0			0
$3$		0			0
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	0.366025	+	0.366025i	0.163692	+	0.163692i	0.784200	−	0.620508i	$-0.213074\pi$
$5$	0.366025	+	0.366025i	0.163692	+	0.163692i	−0.620508	+	0.784200i	$0.713074\pi$
$6$		0			0
$7$	2.36603	+	0.633975i	0.894274	+	0.239620i	0.676555	−	0.736392i	$-0.263472\pi$
$7$	2.36603	+	0.633975i	0.894274	+	0.239620i	0.217718	+	0.976012i	$0.430139\pi$
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	−0.366025	−	0.633975i	−0.115747	−	0.200480i
$11$	3.36603	−	0.901924i	1.01489	−	0.271940i	0.287222	−	0.957864i	$-0.407268\pi$
$11$	3.36603	−	0.901924i	1.01489	−	0.271940i	0.727673	+	0.685924i	$0.240602\pi$
$12$		0			0
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	−3.00000	−	1.73205i	−0.801784	−	0.462910i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−0.232051	+	0.133975i	−0.0562806	+	0.0324936i	−0.527876	−	0.849321i	$-0.677012\pi$
$17$	−0.232051	+	0.133975i	−0.0562806	+	0.0324936i	0.471596	+	0.881815i	$0.343678\pi$
$18$		0			0
$19$	−4.09808	−	1.09808i	−0.940163	−	0.251916i	−0.243980	−	0.969780i	$-0.578453\pi$
$19$	−4.09808	−	1.09808i	−0.940163	−	0.251916i	−0.696183	+	0.717864i	$0.745120\pi$
$20$	0.267949	+	1.00000i	0.0599153	+	0.223607i
$21$		0			0
$22$	−4.92820			−1.05070
$23$	−0.366025	+	0.633975i	−0.0763216	+	0.132193i	−0.901660	−	0.432445i	$-0.857651\pi$
$23$	−0.366025	+	0.633975i	−0.0763216	+	0.132193i	0.825339	+	0.564638i	$0.190984\pi$
$24$		0			0
$25$		−	4.73205i		−	0.946410i
$26$	−4.46410	−	2.46410i	−0.875482	−	0.483250i
$27$		0			0
$28$	3.46410	+	3.46410i	0.654654	+	0.654654i
$29$	2.59808	+	1.50000i	0.482451	+	0.278543i	0.721437	−	0.692480i	$-0.243482\pi$
$29$	2.59808	+	1.50000i	0.482451	+	0.278543i	−0.238987	+	0.971023i	$0.576815\pi$
$30$		0			0
$31$	4.00000	+	4.00000i	0.718421	+	0.718421i	0.968282	−	0.249861i	$-0.0803848\pi$
$31$	4.00000	+	4.00000i	0.718421	+	0.718421i	−0.249861	+	0.968282i	$0.580385\pi$
$32$	−1.46410	−	5.46410i	−0.258819	−	0.965926i
$33$		0			0
$34$	0.366025	−	0.0980762i	0.0627728	−	0.0168199i
$35$	0.633975	+	1.09808i	0.107161	+	0.185609i
$36$		0			0
$37$	−1.86603	−	6.96410i	−0.306773	−	1.14489i	−0.931409	−	0.363975i	$-0.881419\pi$
$37$	−1.86603	−	6.96410i	−0.306773	−	1.14489i	0.624636	−	0.780916i	$-0.285247\pi$
$38$	5.19615	+	3.00000i	0.842927	+	0.486664i
$39$		0			0
$40$		−	1.46410i		−	0.231495i
$41$	2.50000	+	9.33013i	0.390434	+	1.45712i	0.829419	+	0.558627i	$0.188671\pi$
$41$	2.50000	+	9.33013i	0.390434	+	1.45712i	−0.438985	+	0.898494i	$0.644662\pi$
$42$		0			0
$43$	−0.633975	+	0.366025i	−0.0966802	+	0.0558184i	−0.547561	−	0.836766i	$-0.684443\pi$
$43$	−0.633975	+	0.366025i	−0.0966802	+	0.0558184i	0.450880	+	0.892584i	$0.351110\pi$
$44$	6.73205	+	1.80385i	1.01489	+	0.271940i
$45$		0			0
$46$	0.732051	−	0.732051i	0.107935	−	0.107935i
$47$	−2.26795	+	2.26795i	−0.330814	+	0.330814i	−0.852896	−	0.522081i	$-0.825156\pi$
$47$	−2.26795	+	2.26795i	−0.330814	+	0.330814i	0.522081	+	0.852896i	$0.325156\pi$
$48$		0			0
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−1.73205	+	6.46410i	−0.244949	+	0.914162i
$51$		0			0
$52$	5.19615	+	5.00000i	0.720577	+	0.693375i
$53$			8.66025i			1.18958i	0.803882	+	0.594789i	$0.202764\pi$
$53$			8.66025i			1.18958i	−0.803882	+	0.594789i	$0.797236\pi$
$54$		0			0
$55$	1.56218	+	0.901924i	0.210644	+	0.121615i
$56$	−3.46410	−	6.00000i	−0.462910	−	0.801784i
$57$		0			0
$58$	−3.00000	−	3.00000i	−0.393919	−	0.393919i
$59$	2.80385	−	10.4641i	0.365030	−	1.36231i	−0.502350	−	0.864664i	$-0.667531\pi$
$59$	2.80385	−	10.4641i	0.365030	−	1.36231i	0.867380	−	0.497646i	$-0.165802\pi$
$60$		0			0
$61$	1.66987	−	0.964102i	0.213805	−	0.123441i	−0.389273	−	0.921122i	$-0.627274\pi$
$61$	1.66987	−	0.964102i	0.213805	−	0.123441i	0.603079	+	0.797682i	$0.293941\pi$
$62$	−4.00000	−	6.92820i	−0.508001	−	0.879883i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	0.964102	+	1.59808i	0.119582	+	0.198217i
$66$		0			0
$67$	−1.56218	−	5.83013i	−0.190850	−	0.712263i	−0.993302	−	0.115546i	$-0.963138\pi$
$67$	−1.56218	−	5.83013i	−0.190850	−	0.712263i	0.802452	−	0.596717i	$-0.203529\pi$
$68$	−0.535898			−0.0649872
$69$		0			0
$70$	−0.464102	−	1.73205i	−0.0554708	−	0.207020i
$71$	−1.83013	+	6.83013i	−0.217196	+	0.810587i	0.768186	+	0.640227i	$0.221160\pi$
$71$	−1.83013	+	6.83013i	−0.217196	+	0.810587i	−0.985382	+	0.170360i	$0.945507\pi$
$72$		0			0
$73$	7.83013	+	7.83013i	0.916447	+	0.916447i	0.996769	−	0.0803219i	$-0.0255948\pi$
$73$	7.83013	+	7.83013i	0.916447	+	0.916447i	−0.0803219	+	0.996769i	$0.525595\pi$
$74$			10.1962i			1.18528i
$75$		0			0
$76$	−6.00000	−	6.00000i	−0.688247	−	0.688247i
$77$	8.53590			0.972756
$78$		0			0
$79$		−	1.07180i		−	0.120587i	−0.998181	−	0.0602933i	$-0.980796\pi$
$79$		−	1.07180i		−	0.120587i	0.998181	−	0.0602933i	$-0.0192036\pi$
$80$	−0.535898	+	2.00000i	−0.0599153	+	0.223607i
$81$		0			0
$82$		−	13.6603i		−	1.50852i
$83$	7.92820	−	7.92820i	0.870233	−	0.870233i	−0.122264	−	0.992498i	$-0.539016\pi$
$83$	7.92820	−	7.92820i	0.870233	−	0.870233i	0.992498	+	0.122264i	$0.0390155\pi$
$84$		0			0
$85$	−0.133975	−	0.0358984i	−0.0145316	−	0.00389373i
$86$	1.00000	−	0.267949i	0.107833	−	0.0288937i
$87$		0			0
$88$	−8.53590	−	4.92820i	−0.909930	−	0.525348i
$89$	12.5622	−	3.36603i	1.33159	−	0.356798i	0.478281	−	0.878207i	$-0.341260\pi$
$89$	12.5622	−	3.36603i	1.33159	−	0.356798i	0.853307	+	0.521409i	$0.174593\pi$
$90$		0			0
$91$	7.73205	+	4.26795i	0.810539	+	0.447403i
$92$	−1.26795	+	0.732051i	−0.132193	+	0.0763216i
$93$		0			0
$94$	3.92820	−	2.26795i	0.405163	−	0.233921i
$95$	−1.09808	−	1.90192i	−0.112660	−	0.195133i
$96$		0			0
$97$	15.2942	+	4.09808i	1.55289	+	0.416097i	0.930405	−	0.366532i	$-0.119455\pi$
$97$	15.2942	+	4.09808i	1.55289	+	0.416097i	0.622488	+	0.782629i	$0.286122\pi$
$98$	1.00000	+	1.00000i	0.101015	+	0.101015i
$99$		0			0
$100$	4.73205	−	8.19615i	0.473205	−	0.819615i
$101$	6.42820	−	11.1340i	0.639630	−	1.10787i	−0.345884	−	0.938277i	$-0.612421\pi$
$101$	6.42820	−	11.1340i	0.639630	−	1.10787i	0.985514	−	0.169595i	$-0.0542458\pi$
$102$		0			0
$103$	−12.1962			−1.20172			−0.600861	−	0.799353i	$-0.705176\pi$
$103$	−12.1962			−1.20172			−0.600861	+	0.799353i	$0.705176\pi$
$104$	−5.26795	−	8.73205i	−0.516565	−	0.856248i
$105$		0			0
$106$	3.16987	−	11.8301i	0.307885	−	1.14904i
$107$	1.90192	−	3.29423i	0.183866	−	0.318465i	−0.759328	−	0.650708i	$-0.774472\pi$
$107$	1.90192	−	3.29423i	0.183866	−	0.318465i	0.943194	+	0.332243i	$0.107805\pi$
$108$		0			0
$109$	14.1244	+	14.1244i	1.35287	+	1.35287i	0.882437	+	0.470431i	$0.155902\pi$
$109$	14.1244	+	14.1244i	1.35287	+	1.35287i	0.470431	+	0.882437i	$0.344098\pi$
$110$	−1.80385	−	1.80385i	−0.171990	−	0.171990i
$111$		0			0
$112$	2.53590	+	9.46410i	0.239620	+	0.894274i
$113$	1.96410	+	3.40192i	0.184767	+	0.320026i	0.943498	−	0.331378i	$-0.107514\pi$
$113$	1.96410	+	3.40192i	0.184767	+	0.320026i	−0.758731	+	0.651404i	$0.774180\pi$
$114$		0			0
$115$	−0.366025	+	0.0980762i	−0.0341320	+	0.00914565i
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$		0			0
$118$	−7.66025	+	13.2679i	−0.705184	+	1.22141i
$119$	−0.633975	+	0.169873i	−0.0581164	+	0.0155722i
$120$		0			0
$121$	0.990381	−	0.571797i	0.0900346	−	0.0519815i
$122$	−2.63397	+	0.705771i	−0.238469	+	0.0638975i
$123$		0			0
$124$	2.92820	+	10.9282i	0.262960	+	0.981382i
$125$	3.56218	−	3.56218i	0.318611	−	0.318611i
$126$		0			0
$127$	0.267949	−	0.464102i	0.0237766	−	0.0411824i	−0.853892	−	0.520450i	$-0.825764\pi$
$127$	0.267949	−	0.464102i	0.0237766	−	0.0411824i	0.877669	+	0.479267i	$0.159098\pi$
$128$	2.92820	−	10.9282i	0.258819	−	0.965926i
$129$		0			0
$130$	−0.732051	−	2.53590i	−0.0642051	−	0.222413i
$131$	−13.8564			−1.21064			−0.605320	−	0.795982i	$-0.706955\pi$
$131$	−13.8564			−1.21064			−0.605320	+	0.795982i	$0.706955\pi$
$132$		0			0
$133$	−9.00000	−	5.19615i	−0.780399	−	0.450564i
$134$			8.53590i			0.737389i
$135$		0			0
$136$	0.732051	+	0.196152i	0.0627728	+	0.0168199i
$137$	1.33013	−	4.96410i	0.113640	−	0.424112i	−0.885541	−	0.464561i	$-0.846212\pi$
$137$	1.33013	−	4.96410i	0.113640	−	0.424112i	0.999182	+	0.0404491i	$0.0128788\pi$
$138$		0			0
$139$	−7.66025	−	13.2679i	−0.649734	−	1.12537i	−0.983186	−	0.182606i	$-0.941547\pi$
$139$	−7.66025	−	13.2679i	−0.649734	−	1.12537i	0.333452	−	0.942767i	$-0.391786\pi$
$140$			2.53590i			0.214323i
$141$		0			0
$142$	5.00000	−	8.66025i	0.419591	−	0.726752i
$143$	12.5622	−	0.241670i	1.05050	−	0.0202094i
$144$		0			0
$145$	0.401924	+	1.50000i	0.0333780	+	0.124568i
$146$	−7.83013	−	13.5622i	−0.648026	−	1.12241i
$147$		0			0
$148$	3.73205	−	13.9282i	0.306773	−	1.14489i
$149$	−4.30385	+	16.0622i	−0.352585	+	1.31586i	0.530912	+	0.847427i	$0.321850\pi$
$149$	−4.30385	+	16.0622i	−0.352585	+	1.31586i	−0.883497	+	0.468438i	$0.844817\pi$
$150$		0			0
$151$	−14.6603	+	14.6603i	−1.19303	+	1.19303i	−0.216824	+	0.976211i	$0.569570\pi$
$151$	−14.6603	+	14.6603i	−1.19303	+	1.19303i	−0.976211	+	0.216824i	$0.930430\pi$
$152$	6.00000	+	10.3923i	0.486664	+	0.842927i
$153$		0			0
$154$	−11.6603	−	3.12436i	−0.939610	−	0.251768i
$155$			2.92820i			0.235199i
$156$		0			0
$157$		−	0.803848i		−	0.0641540i	−0.999485	−	0.0320770i	$-0.989788\pi$
$157$		−	0.803848i		−	0.0641540i	0.999485	−	0.0320770i	$-0.0102122\pi$
$158$	−0.392305	+	1.46410i	−0.0312101	+	0.116478i
$159$		0			0
$160$	1.46410	−	2.53590i	0.115747	−	0.200480i
$161$	−1.26795	+	1.26795i	−0.0999284	+	0.0999284i
$162$		0			0
$163$	−2.26795	+	8.46410i	−0.177639	+	0.662960i	0.818447	+	0.574581i	$0.194835\pi$
$163$	−2.26795	+	8.46410i	−0.177639	+	0.662960i	−0.996087	+	0.0883783i	$0.971832\pi$
$164$	−5.00000	+	18.6603i	−0.390434	+	1.45712i
$165$		0			0
$166$	−13.7321	+	7.92820i	−1.06581	+	0.615348i
$167$	−5.26795	−	19.6603i	−0.407646	−	1.52136i	−0.799123	−	0.601168i	$-0.794702\pi$
$167$	−5.26795	−	19.6603i	−0.407646	−	1.52136i	0.391476	−	0.920188i	$-0.371964\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	0.169873	+	0.0980762i	0.0130287	+	0.00752210i
$171$		0			0
$172$	−1.46410			−0.111637
$173$	−9.46410	−	16.3923i	−0.719542	−	1.24628i	−0.961181	−	0.275918i	$-0.911018\pi$
$173$	−9.46410	−	16.3923i	−0.719542	−	1.24628i	0.241639	−	0.970366i	$-0.422315\pi$
$174$		0			0
$175$	3.00000	−	11.1962i	0.226779	−	0.846350i
$176$	9.85641	+	9.85641i	0.742955	+	0.742955i
$177$		0			0
$178$	−18.3923			−1.37856
$179$	1.09808	+	0.633975i	0.0820741	+	0.0473855i	0.540475	−	0.841360i	$-0.318244\pi$
$179$	1.09808	+	0.633975i	0.0820741	+	0.0473855i	−0.458401	+	0.888745i	$0.651578\pi$
$180$		0			0
$181$	1.92820			0.143322			0.0716611	−	0.997429i	$-0.477170\pi$
$181$	1.92820			0.143322			0.0716611	+	0.997429i	$0.477170\pi$
$182$	−9.00000	−	8.66025i	−0.667124	−	0.641941i
$183$		0			0
$184$	2.00000	−	0.535898i	0.147442	−	0.0395070i
$185$	1.86603	−	3.23205i	0.137193	−	0.237625i
$186$		0			0
$187$	−0.660254	+	0.660254i	−0.0482826	+	0.0482826i
$188$	−6.19615	+	1.66025i	−0.451901	+	0.121086i
$189$		0			0
$190$	0.803848	+	3.00000i	0.0583172	+	0.217643i
$191$	−16.3923	+	9.46410i	−1.18611	+	0.684798i	−0.957419	−	0.288702i	$-0.906776\pi$
$191$	−16.3923	+	9.46410i	−1.18611	+	0.684798i	−0.228686	+	0.973500i	$0.573443\pi$
$192$		0			0
$193$	−16.0622	+	4.30385i	−1.15618	+	0.309798i	−0.785440	−	0.618938i	$-0.787563\pi$
$193$	−16.0622	+	4.30385i	−1.15618	+	0.309798i	−0.370741	+	0.928736i	$0.620896\pi$
$194$	−19.3923	−	11.1962i	−1.39229	−	0.803837i
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−9.56218	+	2.56218i	−0.681277	+	0.182548i	−0.582829	−	0.812595i	$-0.698054\pi$
$197$	−9.56218	+	2.56218i	−0.681277	+	0.182548i	−0.0984477	+	0.995142i	$0.531388\pi$
$198$		0			0
$199$	5.36603	+	9.29423i	0.380387	+	0.658850i	0.991118	−	0.132988i	$-0.0424573\pi$
$199$	5.36603	+	9.29423i	0.380387	+	0.658850i	−0.610730	+	0.791839i	$0.709124\pi$
$200$	−9.46410	+	9.46410i	−0.669213	+	0.669213i
$201$		0			0
$202$	−12.8564	+	12.8564i	−0.904574	+	0.904574i
$203$	5.19615	+	5.19615i	0.364698	+	0.364698i
$204$		0			0
$205$	−2.50000	+	4.33013i	−0.174608	+	0.302429i
$206$	16.6603	+	4.46410i	1.16077	+	0.311029i
$207$		0			0
$208$	4.00000	+	13.8564i	0.277350	+	0.960769i
$209$	−14.7846			−1.02267
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	−8.66025	+	15.0000i	−0.594789	+	1.03020i
$213$		0			0
$214$	−3.80385	+	3.80385i	−0.260026	+	0.260026i
$215$	−0.366025	−	0.0980762i	−0.0249627	−	0.00668874i
$216$		0			0
$217$	6.92820	+	12.0000i	0.470317	+	0.814613i
$218$	−14.1244	−	24.4641i	−0.956622	−	1.65692i
$219$		0			0
$220$	1.80385	+	3.12436i	0.121615	+	0.210644i
$221$	−0.928203	+	0.267949i	−0.0624377	+	0.0180242i
$222$		0			0
$223$	−17.9282	+	4.80385i	−1.20056	+	0.321689i	−0.803052	−	0.595909i	$-0.796792\pi$
$223$	−17.9282	+	4.80385i	−1.20056	+	0.321689i	−0.397509	+	0.917598i	$0.630125\pi$
$224$		−	13.8564i		−	0.925820i
$225$		0			0
$226$	−1.43782	−	5.36603i	−0.0956425	−	0.356943i
$227$	−1.09808	−	0.294229i	−0.0728819	−	0.0195286i	0.222194	−	0.975003i	$-0.428678\pi$
$227$	−1.09808	−	0.294229i	−0.0728819	−	0.0195286i	−0.295076	+	0.955474i	$0.595345\pi$
$228$		0			0
$229$	5.00000	−	5.00000i	0.330409	−	0.330409i	−0.522333	−	0.852742i	$-0.674938\pi$
$229$	5.00000	−	5.00000i	0.330409	−	0.330409i	0.852742	+	0.522333i	$0.174938\pi$
$230$	0.535898			0.0353361
$231$		0			0
$232$	−2.19615	−	8.19615i	−0.144184	−	0.538104i
$233$		−	9.07180i		−	0.594313i	−0.954829	−	0.297157i	$-0.903962\pi$
$233$		−	9.07180i		−	0.594313i	0.954829	−	0.297157i	$-0.0960383\pi$
$234$		0			0
$235$	−1.66025			−0.108303
$236$	15.3205	−	15.3205i	0.997280	−	0.997280i
$237$		0			0
$238$	0.928203			0.0601665
$239$	13.0000	+	13.0000i	0.840900	+	0.840900i	0.988976	−	0.148076i	$-0.0473080\pi$
$239$	13.0000	+	13.0000i	0.840900	+	0.840900i	−0.148076	+	0.988976i	$0.547308\pi$
$240$		0			0
$241$	−3.83975	+	14.3301i	−0.247340	+	0.923085i	0.724853	+	0.688903i	$0.241908\pi$
$241$	−3.83975	+	14.3301i	−0.247340	+	0.923085i	−0.972193	+	0.234181i	$0.924759\pi$
$242$	−1.56218	+	0.418584i	−0.100421	+	0.0269076i
$243$		0			0
$244$	3.85641			0.246881
$245$	−0.133975	−	0.500000i	−0.00855932	−	0.0319438i
$246$		0			0
$247$	−13.3923	−	7.39230i	−0.852132	−	0.470361i
$248$		−	16.0000i		−	1.01600i
$249$		0			0
$250$	−6.16987	+	3.56218i	−0.390217	+	0.225292i
$251$	−24.9282	+	14.3923i	−1.57345	+	0.908434i	−0.577713	+	0.816240i	$0.696055\pi$
$251$	−24.9282	+	14.3923i	−1.57345	+	0.908434i	−0.995741	+	0.0921944i	$0.970612\pi$
$252$		0			0
$253$	−0.660254	+	2.46410i	−0.0415098	+	0.154917i
$254$	−0.535898	+	0.535898i	−0.0336253	+	0.0336253i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−2.13397	−	1.23205i	−0.133114	−	0.0768532i	0.431964	−	0.901891i	$-0.357821\pi$
$257$	−2.13397	−	1.23205i	−0.133114	−	0.0768532i	−0.565078	+	0.825037i	$0.691154\pi$
$258$		0			0
$259$		−	17.6603i		−	1.09735i
$260$	0.0717968	+	3.73205i	0.00445265	+	0.231452i
$261$		0			0
$262$	18.9282	+	5.07180i	1.16939	+	0.313337i
$263$	1.56218	+	0.901924i	0.0963280	+	0.0556150i	0.547390	−	0.836878i	$-0.315621\pi$
$263$	1.56218	+	0.901924i	0.0963280	+	0.0556150i	−0.451062	+	0.892493i	$0.648955\pi$
$264$		0			0
$265$	−3.16987	+	3.16987i	−0.194724	+	0.194724i
$266$	10.3923	+	10.3923i	0.637193	+	0.637193i
$267$		0			0
$268$	3.12436	−	11.6603i	0.190850	−	0.712263i
$269$	−7.85641	+	4.53590i	−0.479014	+	0.276559i	−0.720005	−	0.693969i	$-0.755861\pi$
$269$	−7.85641	+	4.53590i	−0.479014	+	0.276559i	0.240992	+	0.970527i	$0.422527\pi$
$270$		0			0
$271$	0.196152	+	0.732051i	0.0119154	+	0.0444689i	0.971628	−	0.236516i	$-0.0760056\pi$
$271$	0.196152	+	0.732051i	0.0119154	+	0.0444689i	−0.959712	+	0.280985i	$0.909339\pi$
$272$	−0.928203	−	0.535898i	−0.0562806	−	0.0324936i
$273$		0			0
$274$	−3.63397	+	6.29423i	−0.219536	+	0.380248i
$275$	−4.26795	−	15.9282i	−0.257367	−	0.960507i
$276$		0			0
$277$	−14.0622	−	24.3564i	−0.844914	−	1.46343i	−0.885696	−	0.464267i	$-0.846318\pi$
$277$	−14.0622	−	24.3564i	−0.844914	−	1.46343i	0.0407812	−	0.999168i	$-0.487015\pi$
$278$	5.60770	+	20.9282i	0.336327	+	1.25519i
$279$		0			0
$280$	0.928203	−	3.46410i	0.0554708	−	0.207020i
$281$	13.2942	+	13.2942i	0.793067	+	0.793067i	0.981992	−	0.188924i	$-0.0605001\pi$
$281$	13.2942	+	13.2942i	0.793067	+	0.793067i	−0.188924	+	0.981992i	$0.560500\pi$
$282$		0			0
$283$	−27.2942	−	15.7583i	−1.62247	−	0.936736i	−0.986256	−	0.165226i	$-0.947165\pi$
$283$	−27.2942	−	15.7583i	−1.62247	−	0.936736i	−0.636218	−	0.771510i	$-0.719502\pi$
$284$	−10.0000	+	10.0000i	−0.593391	+	0.593391i
$285$		0			0
$286$	−17.2487	−	4.26795i	−1.01994	−	0.252369i
$287$			23.6603i			1.39662i
$288$		0			0
$289$	−8.46410	+	14.6603i	−0.497888	+	0.862368i
$290$		−	2.19615i		−	0.128963i
$291$		0			0
$292$	5.73205	+	21.3923i	0.335443	+	1.25189i
$293$	6.59808	+	1.76795i	0.385464	+	0.103285i	0.446346	−	0.894860i	$-0.352725\pi$
$293$	6.59808	+	1.76795i	0.385464	+	0.103285i	−0.0608827	+	0.998145i	$0.519392\pi$
$294$		0			0
$295$	4.85641	−	2.80385i	0.282751	−	0.163246i
$296$	−10.1962	+	17.6603i	−0.592639	+	1.02648i
$297$		0			0
$298$	11.7583	−	20.3660i	0.681142	−	1.17977i
$299$	−1.83013	+	1.90192i	−0.105839	+	0.109991i
$300$		0			0
$301$	−1.73205	+	0.464102i	−0.0998337	+	0.0267504i
$302$	25.3923	−	14.6603i	1.46116	−	0.843603i
$303$		0			0
$304$	−4.39230	−	16.3923i	−0.251916	−	0.940163i
$305$	0.964102	+	0.258330i	0.0552043	+	0.0147919i
$306$		0			0
$307$	−7.73205	−	7.73205i	−0.441291	−	0.441291i	0.451154	−	0.892446i	$-0.351012\pi$
$307$	−7.73205	−	7.73205i	−0.441291	−	0.441291i	−0.892446	+	0.451154i	$0.851012\pi$
$308$	14.7846	+	8.53590i	0.842431	+	0.486378i
$309$		0			0
$310$	1.07180	−	4.00000i	0.0608740	−	0.227185i
$311$	−10.7321			−0.608559			−0.304279	−	0.952583i	$-0.598416\pi$
$311$	−10.7321			−0.608559			−0.304279	+	0.952583i	$0.598416\pi$
$312$		0			0
$313$	−19.8564			−1.12235			−0.561175	−	0.827697i	$-0.689651\pi$
$313$	−19.8564			−1.12235			−0.561175	+	0.827697i	$0.689651\pi$
$314$	−0.294229	+	1.09808i	−0.0166043	+	0.0619680i
$315$		0			0
$316$	1.07180	−	1.85641i	0.0602933	−	0.104431i
$317$	−21.3660	−	21.3660i	−1.20004	−	1.20004i	−0.974155	−	0.225881i	$-0.927474\pi$
$317$	−21.3660	−	21.3660i	−1.20004	−	1.20004i	−0.225881	−	0.974155i	$-0.572526\pi$
$318$		0			0
$319$	10.0981	+	2.70577i	0.565384	+	0.151494i
$320$	−2.92820	+	2.92820i	−0.163692	+	0.163692i
$321$		0			0
$322$	2.19615	−	1.26795i	0.122387	−	0.0706600i
$323$	1.09808	−	0.294229i	0.0610986	−	0.0163713i
$324$		0			0
$325$	4.09808	−	16.5622i	0.227320	−	0.918704i
$326$	6.19615	−	10.7321i	0.343173	−	0.594393i
$327$		0			0
$328$	13.6603	−	23.6603i	0.754261	−	1.30642i
$329$	−6.80385	+	3.92820i	−0.375108	+	0.216569i
$330$		0			0
$331$	12.6603	+	3.39230i	0.695870	+	0.186458i	0.589380	−	0.807856i	$-0.299372\pi$
$331$	12.6603	+	3.39230i	0.695870	+	0.186458i	0.106490	+	0.994314i	$0.466039\pi$
$332$	21.6603	−	5.80385i	1.18876	−	0.318528i
$333$		0			0
$334$			28.7846i			1.57502i
$335$	1.56218	−	2.70577i	0.0853509	−	0.147832i
$336$		0			0
$337$		−	20.8564i		−	1.13612i	−0.822987	−	0.568060i	$-0.807694\pi$
$337$		−	20.8564i		−	1.13612i	0.822987	−	0.568060i	$-0.192306\pi$
$338$	−13.4904	−	12.4904i	−0.733780	−	0.679387i
$339$		0			0
$340$	−0.196152	−	0.196152i	−0.0106379	−	0.0106379i
$341$	17.0718	+	9.85641i	0.924490	+	0.533754i
$342$		0			0
$343$	−13.8564	−	13.8564i	−0.748176	−	0.748176i
$344$	2.00000	+	0.535898i	0.107833	+	0.0288937i
$345$		0			0
$346$	6.92820	+	25.8564i	0.372463	+	1.39005i
$347$	2.36603	+	4.09808i	0.127015	+	0.219996i	0.922519	−	0.385952i	$-0.126127\pi$
$347$	2.36603	+	4.09808i	0.127015	+	0.219996i	−0.795504	+	0.605949i	$0.792794\pi$
$348$		0			0
$349$	4.68653	+	17.4904i	0.250864	+	0.936239i	0.970345	+	0.241726i	$0.0777134\pi$
$349$	4.68653	+	17.4904i	0.250864	+	0.936239i	−0.719480	+	0.694513i	$0.755620\pi$
$350$	−8.19615	+	14.1962i	−0.438103	+	0.758816i
$351$		0			0
$352$	−9.85641	−	17.0718i	−0.525348	−	0.909930i
$353$	0.866025	+	3.23205i	0.0460939	+	0.172025i	0.985136	−	0.171779i	$-0.0549513\pi$
$353$	0.866025	+	3.23205i	0.0460939	+	0.172025i	−0.939042	+	0.343803i	$0.888285\pi$
$354$		0			0
$355$	−3.16987	+	1.83013i	−0.168239	+	0.0971331i
$356$	25.1244	+	6.73205i	1.33159	+	0.356798i
$357$		0			0
$358$	−1.26795	−	1.26795i	−0.0670132	−	0.0670132i
$359$	−4.07180	+	4.07180i	−0.214901	+	0.214901i	−0.806346	−	0.591444i	$-0.798558\pi$
$359$	−4.07180	+	4.07180i	−0.214901	+	0.214901i	0.591444	+	0.806346i	$0.298558\pi$
$360$		0			0
$361$	−0.866025	−	0.500000i	−0.0455803	−	0.0263158i
$362$	−2.63397	−	0.705771i	−0.138439	−	0.0370945i
$363$		0			0
$364$	9.12436	+	15.1244i	0.478246	+	0.792732i
$365$			5.73205i			0.300029i
$366$		0			0
$367$	6.16987	+	3.56218i	0.322065	+	0.185944i	0.652313	−	0.757950i	$-0.273799\pi$
$367$	6.16987	+	3.56218i	0.322065	+	0.185944i	−0.330248	+	0.943894i	$0.607132\pi$
$368$	−2.92820			−0.152643
$369$		0			0
$370$	−3.73205	+	3.73205i	−0.194020	+	0.194020i
$371$	−5.49038	+	20.4904i	−0.285046	+	1.06381i
$372$		0			0
$373$	14.3038	−	8.25833i	0.740625	−	0.427600i	−0.0816714	−	0.996659i	$-0.526026\pi$
$373$	14.3038	−	8.25833i	0.740625	−	0.427600i	0.822297	+	0.569059i	$0.192692\pi$
$374$	1.14359	−	0.660254i	0.0591338	−	0.0341409i
$375$		0			0
$376$	9.07180			0.467842
$377$	7.79423	+	7.50000i	0.401423	+	0.386270i
$378$		0			0
$379$	−6.07180	−	22.6603i	−0.311887	−	1.16398i	−0.926853	−	0.375425i	$-0.877497\pi$
$379$	−6.07180	−	22.6603i	−0.311887	−	1.16398i	0.614966	−	0.788554i	$-0.289170\pi$
$380$		−	4.39230i		−	0.225320i
$381$		0			0
$382$	25.8564	−	6.92820i	1.32293	−	0.354478i
$383$	4.19615	−	15.6603i	0.214413	−	0.800202i	−0.771959	−	0.635672i	$-0.780723\pi$
$383$	4.19615	−	15.6603i	0.214413	−	0.800202i	0.986372	−	0.164529i	$-0.0526104\pi$
$384$		0			0
$385$	3.12436	+	3.12436i	0.159232	+	0.159232i
$386$	23.5167			1.19697
$387$		0			0
$388$	22.3923	+	22.3923i	1.13680	+	1.13680i
$389$	1.73205			0.0878185			0.0439092	−	0.999036i	$-0.486019\pi$
$389$	1.73205			0.0878185			0.0439092	+	0.999036i	$0.486019\pi$
$390$		0			0
$391$		−	0.196152i		−	0.00991985i
$392$	0.732051	+	2.73205i	0.0369741	+	0.137989i
$393$		0			0
$394$	14.0000			0.705310
$395$	0.392305	−	0.392305i	0.0197390	−	0.0197390i
$396$		0			0
$397$	7.29423	+	1.95448i	0.366087	+	0.0980927i	0.437173	−	0.899378i	$-0.355980\pi$
$397$	7.29423	+	1.95448i	0.366087	+	0.0980927i	−0.0710860	+	0.997470i	$0.522646\pi$
$398$	−3.92820	−	14.6603i	−0.196903	−	0.734852i
$399$		0			0
$400$	16.3923	−	9.46410i	0.819615	−	0.473205i
$401$	−2.13397	+	0.571797i	−0.106566	+	0.0285542i	−0.311708	−	0.950178i	$-0.600901\pi$
$401$	−2.13397	+	0.571797i	−0.106566	+	0.0285542i	0.205142	+	0.978732i	$0.434234\pi$
$402$		0			0
$403$	10.5359	+	17.4641i	0.524830	+	0.869949i
$404$	22.2679	−	12.8564i	1.10787	−	0.639630i
$405$		0			0
$406$	−5.19615	−	9.00000i	−0.257881	−	0.446663i
$407$	−12.5622	−	21.7583i	−0.622684	−	1.07852i
$408$		0			0
$409$	−2.33013	−	0.624356i	−0.115217	−	0.0308724i	0.200750	−	0.979643i	$-0.435662\pi$
$409$	−2.33013	−	0.624356i	−0.115217	−	0.0308724i	−0.315967	+	0.948770i	$0.602329\pi$
$410$	5.00000	−	5.00000i	0.246932	−	0.246932i
$411$		0			0
$412$	−21.1244	−	12.1962i	−1.04072	−	0.600861i
$413$	13.2679	−	22.9808i	0.652873	−	1.13081i
$414$		0			0
$415$	5.80385			0.284900
$416$	−0.392305	−	20.3923i	−0.0192343	−	0.999815i
$417$		0			0
$418$	20.1962	+	5.41154i	0.987826	+	0.264687i
$419$	−4.80385	+	8.32051i	−0.234683	+	0.406483i	−0.959181	−	0.282794i	$-0.908739\pi$
$419$	−4.80385	+	8.32051i	−0.234683	+	0.406483i	0.724497	+	0.689278i	$0.242072\pi$
$420$		0			0
$421$	26.3660	+	26.3660i	1.28500	+	1.28500i	0.937785	+	0.347216i	$0.112873\pi$
$421$	26.3660	+	26.3660i	1.28500	+	1.28500i	0.347216	+	0.937785i	$0.387127\pi$
$422$	−22.0000	+	22.0000i	−1.07094	+	1.07094i
$423$		0			0
$424$	17.3205	−	17.3205i	0.841158	−	0.841158i
$425$	0.633975	+	1.09808i	0.0307523	+	0.0532645i
$426$		0			0
$427$	4.56218	−	1.22243i	0.220779	−	0.0591576i
$428$	6.58846	−	3.80385i	0.318465	−	0.183866i
$429$		0			0
$430$	0.464102	+	0.267949i	0.0223810	+	0.0129217i
$431$	39.4186	−	10.5622i	1.89873	−	0.508762i	0.901639	−	0.432488i	$-0.142364\pi$
$431$	39.4186	−	10.5622i	1.89873	−	0.508762i	0.997087	−	0.0762738i	$-0.0243023\pi$
$432$		0			0
$433$	−8.42820	+	4.86603i	−0.405034	+	0.233846i	−0.688654	−	0.725090i	$-0.741798\pi$
$433$	−8.42820	+	4.86603i	−0.405034	+	0.233846i	0.283620	+	0.958937i	$0.408465\pi$
$434$	−5.07180	−	18.9282i	−0.243454	−	0.908583i
$435$		0			0
$436$	10.3397	+	38.5885i	0.495184	+	1.84805i
$437$	2.19615	−	2.19615i	0.105056	−	0.105056i
$438$		0			0
$439$	16.8301	−	29.1506i	0.803258	−	1.39128i	−0.114203	−	0.993457i	$-0.536431\pi$
$439$	16.8301	−	29.1506i	0.803258	−	1.39128i	0.917461	−	0.397826i	$-0.130235\pi$
$440$	−1.32051	−	4.92820i	−0.0629528	−	0.234943i
$441$		0			0
$442$	1.36603	−	0.0262794i	0.0649752	−	0.00124999i
$443$	−12.1436			−0.576960			−0.288480	−	0.957486i	$-0.593150\pi$
$443$	−12.1436			−0.576960			−0.288480	+	0.957486i	$0.593150\pi$
$444$		0			0
$445$	5.83013	+	3.36603i	0.276375	+	0.159565i
$446$	26.2487			1.24291
$447$		0			0
$448$	−5.07180	+	18.9282i	−0.239620	+	0.894274i
$449$	7.02628	−	26.2224i	0.331591	−	1.23751i	−0.575928	−	0.817501i	$-0.695359\pi$
$449$	7.02628	−	26.2224i	0.331591	−	1.23751i	0.907518	−	0.420012i	$-0.137974\pi$
$450$		0			0
$451$	16.8301	+	29.1506i	0.792500	+	1.37265i
$452$			7.85641i			0.369534i
$453$		0			0
$454$	1.39230	+	0.803848i	0.0653441	+	0.0377264i
$455$	1.26795	+	4.39230i	0.0594424	+	0.205914i
$456$		0			0
$457$	−1.59808	−	5.96410i	−0.0747549	−	0.278989i	0.918423	−	0.395600i	$-0.129463\pi$
$457$	−1.59808	−	5.96410i	−0.0747549	−	0.278989i	−0.993178	+	0.116611i	$0.962797\pi$
$458$	−8.66025	+	5.00000i	−0.404667	+	0.233635i
$459$		0			0
$460$	−0.732051	−	0.196152i	−0.0341320	−	0.00914565i
$461$	7.28461	−	27.1865i	0.339278	−	1.26620i	−0.559878	−	0.828575i	$-0.689152\pi$
$461$	7.28461	−	27.1865i	0.339278	−	1.26620i	0.899156	−	0.437628i	$-0.144181\pi$
$462$		0			0
$463$	−0.660254	+	0.660254i	−0.0306846	+	0.0306846i	−0.722283	−	0.691598i	$-0.756907\pi$
$463$	−0.660254	+	0.660254i	−0.0306846	+	0.0306846i	0.691598	+	0.722283i	$0.256907\pi$
$464$			12.0000i			0.557086i
$465$		0			0
$466$	−3.32051	+	12.3923i	−0.153820	+	0.574062i
$467$			14.1962i			0.656920i	0.944518	+	0.328460i	$0.106530\pi$
$467$			14.1962i			0.656920i	−0.944518	+	0.328460i	$0.893470\pi$
$468$		0			0
$469$		−	14.7846i		−	0.682690i
$470$	2.26795	+	0.607695i	0.104613	+	0.0280309i
$471$		0			0
$472$	−26.5359	+	15.3205i	−1.22141	+	0.705184i
$473$	−1.80385	+	1.80385i	−0.0829410	+	0.0829410i
$474$		0			0
$475$	−5.19615	+	19.3923i	−0.238416	+	0.889780i
$476$	−1.26795	−	0.339746i	−0.0581164	−	0.0155722i
$477$		0			0
$478$	−13.0000	−	22.5167i	−0.594606	−	1.02989i
$479$	−10.1244	−	37.7846i	−0.462594	−	1.72642i	−0.664747	−	0.747069i	$-0.731460\pi$
$479$	−10.1244	−	37.7846i	−0.462594	−	1.72642i	0.202153	−	0.979354i	$-0.435206\pi$
$480$		0			0
$481$	−0.500000	−	25.9904i	−0.0227980	−	1.18506i
$482$	10.4904	−	18.1699i	0.477824	−	0.827615i
$483$		0			0
$484$	2.28719			0.103963
$485$	4.09808	+	7.09808i	0.186084	+	0.322307i
$486$		0			0
$487$	3.29423	−	12.2942i	0.149276	−	0.557105i	−0.850252	−	0.526376i	$-0.823550\pi$
$487$	3.29423	−	12.2942i	0.149276	−	0.557105i	0.999528	−	0.0307288i	$-0.00978283\pi$
$488$	−5.26795	−	1.41154i	−0.238469	−	0.0638975i
$489$		0			0
$490$			0.732051i			0.0330707i
$491$	4.09808	+	2.36603i	0.184944	+	0.106777i	0.589613	−	0.807686i	$-0.299280\pi$
$491$	4.09808	+	2.36603i	0.184944	+	0.106777i	−0.404670	+	0.914463i	$0.632613\pi$
$492$		0			0
$493$	−0.803848			−0.0362035
$494$	15.5885	+	15.0000i	0.701358	+	0.674882i
$495$		0			0
$496$	−5.85641	+	21.8564i	−0.262960	+	0.981382i
$497$	−8.66025	+	15.0000i	−0.388465	+	0.672842i
$498$		0			0
$499$	−13.0718	+	13.0718i	−0.585174	+	0.585174i	−0.936321	−	0.351147i	$-0.885792\pi$
$499$	−13.0718	+	13.0718i	−0.585174	+	0.585174i	0.351147	+	0.936321i	$0.385792\pi$
$500$	9.73205	−	2.60770i	0.435231	−	0.116620i
$501$		0			0
$502$	39.3205	−	10.5359i	1.75496	−	0.470240i
$503$	−22.8109	+	13.1699i	−1.01709	+	0.587216i	−0.913259	−	0.407380i	$-0.866443\pi$
$503$	−22.8109	+	13.1699i	−1.01709	+	0.587216i	−0.103828	+	0.994595i	$0.533109\pi$
$504$		0			0
$505$	6.42820	−	1.72243i	0.286051	−	0.0766472i
$506$	1.80385	−	3.12436i	0.0801908	−	0.138895i
$507$		0			0
$508$	0.928203	−	0.535898i	0.0411824	−	0.0237766i
$509$	−29.4545	+	7.89230i	−1.30555	+	0.349820i	−0.843545	−	0.537059i	$-0.819535\pi$
$509$	−29.4545	+	7.89230i	−1.30555	+	0.349820i	−0.462002	+	0.886879i	$0.652869\pi$
$510$		0			0
$511$	13.5622	+	23.4904i	0.599955	+	1.03915i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$	2.46410	+	2.46410i	0.108687	+	0.108687i
$515$	−4.46410	−	4.46410i	−0.196712	−	0.196712i
$516$		0			0
$517$	−5.58846	+	9.67949i	−0.245780	+	0.425704i
$518$	−6.46410	+	24.1244i	−0.284016	+	1.05996i
$519$		0			0
$520$	1.26795	−	5.12436i	0.0556033	−	0.224718i
$521$	−34.7128			−1.52080			−0.760398	−	0.649457i	$-0.774996\pi$
$521$	−34.7128			−1.52080			−0.760398	+	0.649457i	$0.774996\pi$
$522$		0			0
$523$	−5.36603	+	9.29423i	−0.234640	+	0.406408i	−0.959168	−	0.282837i	$-0.908724\pi$
$523$	−5.36603	+	9.29423i	−0.234640	+	0.406408i	0.724528	+	0.689245i	$0.242058\pi$
$524$	−24.0000	−	13.8564i	−1.04844	−	0.605320i
$525$		0			0
$526$	−1.80385	−	1.80385i	−0.0786515	−	0.0786515i
$527$	−1.46410	−	0.392305i	−0.0637773	−	0.0170891i
$528$		0			0
$529$	11.2321	+	19.4545i	0.488350	+	0.845847i
$530$	5.49038	−	3.16987i	0.238487	−	0.137690i
$531$		0			0
$532$	−10.3923	−	18.0000i	−0.450564	−	0.780399i
$533$	0.669873	+	34.8205i	0.0290154	+	1.50824i
$534$		0			0
$535$	1.90192	−	0.509619i	0.0822273	−	0.0220327i
$536$	−8.53590	+	14.7846i	−0.368695	+	0.638598i
$537$		0			0
$538$	12.3923	−	3.32051i	0.534270	−	0.143157i
$539$	−3.36603	−	0.901924i	−0.144985	−	0.0388486i
$540$		0			0
$541$	−20.2942	+	20.2942i	−0.872517	+	0.872517i	−0.992746	−	0.120229i	$-0.961637\pi$
$541$	−20.2942	+	20.2942i	−0.872517	+	0.872517i	0.120229	+	0.992746i	$0.461637\pi$
$542$		−	1.07180i		−	0.0460376i
$543$		0			0
$544$	1.07180	+	1.07180i	0.0459529	+	0.0459529i
$545$			10.3397i			0.442906i
$546$		0			0
$547$	−4.33975			−0.185554			−0.0927771	−	0.995687i	$-0.529574\pi$
$547$	−4.33975			−0.185554			−0.0927771	+	0.995687i	$0.529574\pi$
$548$	7.26795	−	7.26795i	0.310471	−	0.310471i
$549$		0			0
$550$			23.3205i			0.994390i
$551$	−9.00000	−	9.00000i	−0.383413	−	0.383413i
$552$		0			0
$553$	0.679492	−	2.53590i	0.0288949	−	0.107837i
$554$	10.2942	+	38.4186i	0.437360	+	1.63225i
$555$		0			0
$556$		−	30.6410i		−	1.29947i
$557$	−4.13397	−	15.4282i	−0.175162	−	0.653714i	−0.996524	−	0.0833065i	$-0.973452\pi$
$557$	−4.13397	−	15.4282i	−0.175162	−	0.653714i	0.821362	−	0.570407i	$-0.193215\pi$
$558$		0			0
$559$	−2.53590	+	0.732051i	−0.107257	+	0.0309625i
$560$	−2.53590	+	4.39230i	−0.107161	+	0.185609i
$561$		0			0
$562$	−13.2942	−	23.0263i	−0.560783	−	0.971305i
$563$	35.7846	−	20.6603i	1.50814	−	0.870726i	0.508186	−	0.861247i	$-0.330316\pi$
$563$	35.7846	−	20.6603i	1.50814	−	0.870726i	0.999955	−	0.00947879i	$-0.00301724\pi$
$564$		0			0
$565$	−0.526279	+	1.96410i	−0.0221407	+	0.0826304i
$566$	31.5167	+	31.5167i	1.32474	+	1.32474i
$567$		0			0
$568$	17.3205	−	10.0000i	0.726752	−	0.419591i
$569$	−35.1962	−	20.3205i	−1.47550	−	0.851880i	−0.475881	−	0.879510i	$-0.657871\pi$
$569$	−35.1962	−	20.3205i	−1.47550	−	0.851880i	−0.999618	+	0.0276295i	$0.991204\pi$
$570$		0			0
$571$			25.6603i			1.07385i	0.843631	+	0.536924i	$0.180414\pi$
$571$			25.6603i			1.07385i	−0.843631	+	0.536924i	$0.819586\pi$
$572$	22.0000	+	12.1436i	0.919866	+	0.507749i
$573$		0			0
$574$	8.66025	−	32.3205i	0.361472	−	1.34903i
$575$	3.00000	+	1.73205i	0.125109	+	0.0722315i
$576$		0			0
$577$	29.0263	−	29.0263i	1.20838	−	1.20838i	0.236828	−	0.971552i	$-0.423892\pi$
$577$	29.0263	−	29.0263i	1.20838	−	1.20838i	0.971552	−	0.236828i	$-0.0761079\pi$
$578$	16.9282	−	16.9282i	0.704120	−	0.704120i
$579$		0			0
$580$	−0.803848	+	3.00000i	−0.0333780	+	0.124568i
$581$	23.7846	−	13.7321i	0.986752	−	0.569701i
$582$		0			0
$583$	7.81089	+	29.1506i	0.323494	+	1.20730i
$584$		−	31.3205i		−	1.29605i
$585$		0			0
$586$	−8.36603	−	4.83013i	−0.345597	−	0.199531i
$587$	−9.58846	−	35.7846i	−0.395758	−	1.47699i	−0.820485	−	0.571668i	$-0.806297\pi$
$587$	−9.58846	−	35.7846i	−0.395758	−	1.47699i	0.424727	−	0.905321i	$-0.360370\pi$
$588$		0			0
$589$	−12.0000	−	20.7846i	−0.494451	−	0.856415i
$590$	−7.66025	+	2.05256i	−0.315368	+	0.0845025i
$591$		0			0
$592$	20.3923	−	20.3923i	0.838119	−	0.838119i
$593$	−5.75833	−	5.75833i	−0.236466	−	0.236466i	0.578919	−	0.815385i	$-0.303475\pi$
$593$	−5.75833	−	5.75833i	−0.236466	−	0.236466i	−0.815385	+	0.578919i	$0.803475\pi$
$594$		0			0
$595$	−0.294229	−	0.169873i	−0.0120622	−	0.00696411i
$596$	−23.5167	+	23.5167i	−0.963280	+	0.963280i
$597$		0			0
$598$	3.19615	−	1.92820i	0.130700	−	0.0788501i
$599$			18.5359i			0.757356i	0.925528	+	0.378678i	$0.123621\pi$
$599$			18.5359i			0.757356i	−0.925528	+	0.378678i	$0.876379\pi$
$600$		0			0
$601$	−0.205771	+	0.356406i	−0.00839359	+	0.0145381i	−0.870192	−	0.492713i	$-0.836005\pi$
$601$	−0.205771	+	0.356406i	−0.00839359	+	0.0145381i	0.861798	+	0.507251i	$0.169338\pi$
$602$	2.53590			0.103356
$603$		0			0
$604$	−40.0526	+	10.7321i	−1.62972	+	0.436681i
$605$	0.571797	+	0.153212i	0.0232468	+	0.00622897i
$606$		0			0
$607$	28.0526	−	16.1962i	1.13862	−	0.657382i	0.192530	−	0.981291i	$-0.438331\pi$
$607$	28.0526	−	16.1962i	1.13862	−	0.657382i	0.946088	+	0.323910i	$0.104997\pi$
$608$			24.0000i			0.973329i
$609$		0			0
$610$	−1.22243	−	0.705771i	−0.0494948	−	0.0285758i
$611$	−9.90192	+	5.97372i	−0.400589	+	0.241671i
$612$		0			0
$613$	−29.2583	+	7.83975i	−1.18173	+	0.316644i	−0.795614	−	0.605805i	$-0.792851\pi$
$613$	−29.2583	+	7.83975i	−1.18173	+	0.316644i	−0.386119	+	0.922449i	$0.626185\pi$
$614$	7.73205	+	13.3923i	0.312040	+	0.540469i
$615$		0			0
$616$	−17.0718	−	17.0718i	−0.687842	−	0.687842i
$617$	−2.33013	−	0.624356i	−0.0938074	−	0.0251356i	0.211610	−	0.977354i	$-0.432129\pi$
$617$	−2.33013	−	0.624356i	−0.0938074	−	0.0251356i	−0.305417	+	0.952219i	$0.598796\pi$
$618$		0			0
$619$	17.1244	+	17.1244i	0.688286	+	0.688286i	0.961853	−	0.273567i	$-0.0882035\pi$
$619$	17.1244	+	17.1244i	0.688286	+	0.688286i	−0.273567	+	0.961853i	$0.588204\pi$
$620$	−2.92820	+	5.07180i	−0.117599	+	0.203688i
$621$		0			0
$622$	14.6603	+	3.92820i	0.587823	+	0.157507i
$623$	31.8564			1.27630
$624$		0			0
$625$	−21.0526			−0.842102
$626$	27.1244	+	7.26795i	1.08411	+	0.290486i
$627$		0			0
$628$	0.803848	−	1.39230i	0.0320770	−	0.0555590i
$629$	1.36603	+	1.36603i	0.0544670	+	0.0544670i
$630$		0			0
$631$	−32.5167	−	8.71281i	−1.29447	−	0.346852i	−0.455112	−	0.890434i	$-0.650401\pi$
$631$	−32.5167	−	8.71281i	−1.29447	−	0.346852i	−0.839356	+	0.543583i	$0.817067\pi$
$632$	−2.14359	+	2.14359i	−0.0852676	+	0.0852676i
$633$		0			0
$634$	21.3660	+	37.0070i	0.848553	+	1.46974i
$635$	0.267949	−	0.0717968i	0.0106332	−	0.00284917i
$636$		0			0
$637$	−2.59808	−	2.50000i	−0.102940	−	0.0990536i
$638$	−12.8038	−	7.39230i	−0.506909	−	0.292664i
$639$		0			0
$640$	5.07180	−	2.92820i	0.200480	−	0.115747i
$641$	14.5526	−	8.40192i	0.574792	−	0.331856i	−0.184269	−	0.982876i	$-0.558992\pi$
$641$	14.5526	−	8.40192i	0.574792	−	0.331856i	0.759061	+	0.651020i	$0.225659\pi$
$642$		0			0
$643$	−16.1962	−	4.33975i	−0.638714	−	0.171143i	−0.0750931	−	0.997177i	$-0.523925\pi$
$643$	−16.1962	−	4.33975i	−0.638714	−	0.171143i	−0.563621	+	0.826034i	$0.690592\pi$
$644$	−3.46410	+	0.928203i	−0.136505	+	0.0365763i
$645$		0			0
$646$	−1.60770			−0.0632539
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	−0.745622	−	0.666369i	$-0.767847\pi$
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	0.949904	+	0.312543i	$0.101181\pi$
$648$		0			0
$649$		−	37.7513i		−	1.48187i
$650$	−11.6603	+	21.1244i	−0.457353	+	0.828565i
$651$		0			0
$652$	−12.3923	+	12.3923i	−0.485320	+	0.485320i
$653$	36.2487	+	20.9282i	1.41852	+	0.818984i	0.996169	−	0.0874477i	$-0.0278711\pi$
$653$	36.2487	+	20.9282i	1.41852	+	0.818984i	0.422353	+	0.906432i	$0.361204\pi$
$654$		0			0
$655$	−5.07180	−	5.07180i	−0.198171	−	0.198171i
$656$	−27.3205	+	27.3205i	−1.06669	+	1.06669i
$657$		0			0
$658$	10.7321	−	2.87564i	0.418379	−	0.112104i
$659$	−1.92820	−	3.33975i	−0.0751121	−	0.130098i	0.826023	−	0.563637i	$-0.190598\pi$
$659$	−1.92820	−	3.33975i	−0.0751121	−	0.130098i	−0.901135	+	0.433539i	$0.857265\pi$
$660$		0			0
$661$	−9.59808	−	35.8205i	−0.373322	−	1.39326i	−0.855781	−	0.517338i	$-0.826923\pi$
$661$	−9.59808	−	35.8205i	−0.373322	−	1.39326i	0.482459	−	0.875918i	$-0.339744\pi$
$662$	−16.0526	−	9.26795i	−0.623900	−	0.360209i
$663$		0			0
$664$	−31.7128			−1.23070
$665$	−1.39230	−	5.19615i	−0.0539913	−	0.201498i
$666$		0			0
$667$	−1.90192	+	1.09808i	−0.0736428	+	0.0425177i
$668$	10.5359	−	39.3205i	0.407646	−	1.52136i
$669$		0			0
$670$	−3.12436	+	3.12436i	−0.120704	+	0.120704i
$671$	4.75129	−	4.75129i	0.183421	−	0.183421i
$672$		0			0
$673$	15.0622	+	8.69615i	0.580604	+	0.335212i	0.761373	−	0.648314i	$-0.224525\pi$
$673$	15.0622	+	8.69615i	0.580604	+	0.335212i	−0.180769	+	0.983526i	$0.557859\pi$
$674$	−7.63397	+	28.4904i	−0.294050	+	1.09741i
$675$		0			0
$676$	13.8564	+	22.0000i	0.532939	+	0.846154i
$677$			36.2487i			1.39315i	0.717483	+	0.696576i	$0.245294\pi$
$677$			36.2487i			1.39315i	−0.717483	+	0.696576i	$0.754706\pi$
$678$		0			0
$679$	33.5885	+	19.3923i	1.28901	+	0.744208i
$680$	0.196152	+	0.339746i	0.00752210	+	0.0130287i
$681$		0			0
$682$	−19.7128	−	19.7128i	−0.754843	−	0.754843i
$683$	−4.12436	+	15.3923i	−0.157814	+	0.588970i	0.841034	+	0.540983i	$0.181947\pi$
$683$	−4.12436	+	15.3923i	−0.157814	+	0.588970i	−0.998848	+	0.0479877i	$0.984719\pi$
$684$		0			0
$685$	2.30385	−	1.33013i	0.0880255	−	0.0508215i
$686$	13.8564	+	24.0000i	0.529040	+	0.916324i
$687$		0			0
$688$	−2.53590	−	1.46410i	−0.0966802	−	0.0558184i
$689$	−7.50000	+	30.3109i	−0.285727	+	1.15475i
$690$		0			0
$691$	0.241670	+	0.901924i	0.00919355	+	0.0343108i	0.970370	−	0.241623i	$-0.0776797\pi$
$691$	0.241670	+	0.901924i	0.00919355	+	0.0343108i	−0.961177	+	0.275934i	$0.911013\pi$
$692$		−	37.8564i		−	1.43908i
$693$		0			0
$694$	−1.73205	−	6.46410i	−0.0657477	−	0.245374i
$695$	2.05256	−	7.66025i	0.0778580	−	0.290570i
$696$		0			0
$697$	−1.83013	−	1.83013i	−0.0693210	−	0.0693210i
$698$		−	25.6077i		−	0.969266i
$699$		0			0
$700$	16.3923	−	16.3923i	0.619571	−	0.619571i
$701$	−36.6410			−1.38391			−0.691956	−	0.721940i	$-0.743251\pi$
$701$	−36.6410			−1.38391			−0.691956	+	0.721940i	$0.743251\pi$
$702$		0			0
$703$			30.5885i			1.15367i
$704$	7.21539	+	26.9282i	0.271940	+	1.01489i
$705$		0			0
$706$		−	4.73205i		−	0.178093i
$707$	22.2679	−	22.2679i	0.837472	−	0.837472i
$708$		0			0
$709$	−14.3301	−	3.83975i	−0.538179	−	0.144205i	−0.0205166	−	0.999790i	$-0.506531\pi$
$709$	−14.3301	−	3.83975i	−0.538179	−	0.144205i	−0.517663	+	0.855585i	$0.673198\pi$
$710$	5.00000	−	1.33975i	0.187647	−	0.0502798i
$711$		0			0
$712$	−31.8564	−	18.3923i	−1.19387	−	0.689281i
$713$	−4.00000	+	1.07180i	−0.149801	+	0.0401391i
$714$		0			0
$715$	4.68653	+	4.50962i	0.175266	+	0.168650i
$716$	1.26795	+	2.19615i	0.0473855	+	0.0820741i
$717$		0			0
$718$	7.05256	−	4.07180i	0.263199	−	0.151958i
$719$	19.4641	+	33.7128i	0.725889	+	1.25728i	0.958607	+	0.284732i	$0.0919045\pi$
$719$	19.4641	+	33.7128i	0.725889	+	1.25728i	−0.232719	+	0.972544i	$0.574762\pi$
$720$		0			0
$721$	−28.8564	−	7.73205i	−1.07467	−	0.287957i
$722$	1.00000	+	1.00000i	0.0372161	+	0.0372161i
$723$		0			0
$724$	3.33975	+	1.92820i	0.124121	+	0.0716611i
$725$	7.09808	−	12.2942i	0.263616	−	0.456596i
$726$		0			0
$727$	−32.5885			−1.20864			−0.604319	−	0.796742i	$-0.706555\pi$
$727$	−32.5885			−1.20864			−0.604319	+	0.796742i	$0.706555\pi$
$728$	−6.92820	−	24.0000i	−0.256776	−	0.889499i
$729$		0			0
$730$	2.09808	−	7.83013i	0.0776533	−	0.289806i
$731$	0.0980762	−	0.169873i	0.00362748	−	0.00628298i
$732$		0			0
$733$	4.68653	+	4.68653i	0.173101	+	0.173101i	0.788340	−	0.615239i	$-0.210941\pi$
$733$	4.68653	+	4.68653i	0.173101	+	0.173101i	−0.615239	+	0.788340i	$0.710941\pi$
$734$	−7.12436	−	7.12436i	−0.262965	−	0.262965i
$735$		0			0
$736$	4.00000	+	1.07180i	0.147442	+	0.0395070i
$737$	−10.5167	−	18.2154i	−0.387386	−	0.670973i
$738$		0			0
$739$	24.5885	−	6.58846i	0.904501	−	0.242360i	0.223553	−	0.974692i	$-0.428235\pi$
$739$	24.5885	−	6.58846i	0.904501	−	0.242360i	0.680948	+	0.732332i	$0.261568\pi$
$740$	6.46410	−	3.73205i	0.237625	−	0.137193i
$741$		0			0
$742$	15.0000	−	25.9808i	0.550667	−	0.953784i
$743$	−47.7846	+	12.8038i	−1.75305	+	0.469728i	−0.985272	−	0.170992i	$-0.945303\pi$
$743$	−47.7846	+	12.8038i	−1.75305	+	0.469728i	−0.767775	+	0.640720i	$0.778636\pi$
$744$		0			0
$745$	−7.45448	+	4.30385i	−0.273111	+	0.157681i
$746$	−22.5622	+	6.04552i	−0.826060	+	0.221342i
$747$		0			0
$748$	−1.80385	+	0.483340i	−0.0659552	+	0.0176726i
$749$	6.58846	−	6.58846i	0.240737	−	0.240737i
$750$		0			0
$751$	22.9545	−	39.7583i	0.837621	−	1.45080i	−0.0542575	−	0.998527i	$-0.517279\pi$
$751$	22.9545	−	39.7583i	0.837621	−	1.45080i	0.891878	−	0.452275i	$-0.149387\pi$
$752$	−12.3923	−	3.32051i	−0.451901	−	0.121086i
$753$		0			0
$754$	−7.90192	−	13.0981i	−0.287771	−	0.477004i
$755$	−10.7321			−0.390579
$756$		0			0
$757$	−11.6603	−	6.73205i	−0.423799	−	0.244681i	0.272902	−	0.962042i	$-0.412016\pi$
$757$	−11.6603	−	6.73205i	−0.423799	−	0.244681i	−0.696701	+	0.717361i	$0.745350\pi$
$758$			33.1769i			1.20504i
$759$		0			0
$760$	−1.60770	+	6.00000i	−0.0583172	+	0.217643i
$761$	−11.9545	+	44.6147i	−0.433350	+	1.61728i	0.311635	+	0.950202i	$0.399123\pi$
$761$	−11.9545	+	44.6147i	−0.433350	+	1.61728i	−0.744985	+	0.667081i	$0.767543\pi$
$762$		0			0
$763$	24.4641	+	42.3731i	0.885660	+	1.53401i
$764$	−37.8564			−1.36960
$765$		0			0
$766$	−11.4641	+	19.8564i	−0.414215	+	0.717441i
$767$	18.8756	−	34.1962i	0.681560	−	1.23475i
$768$		0			0
$769$	−5.95448	−	22.2224i	−0.214724	−	0.801361i	−0.986263	−	0.165180i	$-0.947180\pi$
$769$	−5.95448	−	22.2224i	−0.214724	−	0.801361i	0.771539	−	0.636182i	$-0.219487\pi$
$770$	−3.12436	−	5.41154i	−0.112594	−	0.195018i
$771$		0			0
$772$	−32.1244	−	8.60770i	−1.15618	−	0.309798i
$773$	−3.95448	+	14.7583i	−0.142233	+	0.530820i	0.857630	+	0.514267i	$0.171936\pi$
$773$	−3.95448	+	14.7583i	−0.142233	+	0.530820i	−0.999863	+	0.0165532i	$0.994731\pi$
$774$		0			0
$775$	18.9282	−	18.9282i	0.679921	−	0.679921i
$776$	−22.3923	−	38.7846i	−0.803837	−	1.39229i
$777$		0			0
$778$	−2.36603	−	0.633975i	−0.0848261	−	0.0227291i
$779$		−	40.9808i		−	1.46829i
$780$		0			0
$781$			24.6410i			0.881725i
$782$	−0.0717968	+	0.267949i	−0.00256745	+	0.00958184i
$783$		0			0
$784$		−	4.00000i		−	0.142857i
$785$	0.294229	−	0.294229i	0.0105015	−	0.0105015i
$786$		0			0
$787$	−2.87564	+	10.7321i	−0.102506	+	0.382556i	−0.998050	−	0.0624155i	$-0.980120\pi$
$787$	−2.87564	+	10.7321i	−0.102506	+	0.382556i	0.895545	+	0.444972i	$0.146786\pi$
$788$	−19.1244	−	5.12436i	−0.681277	−	0.182548i
$789$		0			0
$790$	−0.679492	+	0.392305i	−0.0241752	+	0.0139576i
$791$	2.49038	+	9.29423i	0.0885478	+	0.330465i
$792$		0			0
$793$	6.67949	−	1.92820i	0.237196	−	0.0684725i
$794$	−9.24871	−	5.33975i	−0.328224	−	0.189500i
$795$		0			0
$796$			21.4641i			0.760775i
$797$	−1.85641	−	3.21539i	−0.0657573	−	0.113895i	0.831272	−	0.555865i	$-0.187613\pi$
$797$	−1.85641	−	3.21539i	−0.0657573	−	0.113895i	−0.897030	+	0.441970i	$0.854280\pi$
$798$		0			0
$799$	0.222432	−	0.830127i	0.00786907	−	0.0293678i
$800$	−25.8564	+	6.92820i	−0.914162	+	0.244949i
$801$		0			0
$802$	3.12436			0.110325
$803$	33.4186	+	19.2942i	1.17932	+	0.680879i
$804$		0			0
$805$	−0.928203			−0.0327149
$806$	−8.00000	−	27.7128i	−0.281788	−	0.976142i
$807$		0			0
$808$	−35.1244	+	9.41154i	−1.23567	+	0.331097i
$809$	22.0885	−	38.2583i	0.776589	−	1.34509i	−0.157308	−	0.987550i	$-0.550282\pi$
$809$	22.0885	−	38.2583i	0.776589	−	1.34509i	0.933897	−	0.357542i	$-0.116385\pi$
$810$		0			0
$811$	16.9808	−	16.9808i	0.596275	−	0.596275i	−0.343044	−	0.939319i	$-0.611458\pi$
$811$	16.9808	−	16.9808i	0.596275	−	0.596275i	0.939319	+	0.343044i	$0.111458\pi$
$812$	3.80385	+	14.1962i	0.133489	+	0.498187i
$813$		0			0
$814$	9.19615	+	34.3205i	0.322325	+	1.20293i
$815$	−3.92820	+	2.26795i	−0.137599	+	0.0794428i
$816$		0			0
$817$	3.00000	−	0.803848i	0.104957	−	0.0281231i
$818$	2.95448	+	1.70577i	0.103301	+	0.0596409i
$819$		0			0
$820$	−8.66025	+	5.00000i	−0.302429	+	0.174608i
$821$	−34.4186	+	9.22243i	−1.20122	+	0.321865i	−0.803310	−	0.595561i	$-0.796930\pi$
$821$	−34.4186	+	9.22243i	−1.20122	+	0.321865i	−0.397907	+	0.917426i	$0.630263\pi$
$822$		0			0
$823$	18.2679	+	31.6410i	0.636781	+	1.10294i	0.986135	+	0.165946i	$0.0530677\pi$
$823$	18.2679	+	31.6410i	0.636781	+	1.10294i	−0.349354	+	0.936991i	$0.613599\pi$
$824$	24.3923	+	24.3923i	0.849746	+	0.849746i
$825$		0			0
$826$	−26.5359	+	26.5359i	−0.923302	+	0.923302i
$827$	30.1962	+	30.1962i	1.05002	+	1.05002i	0.998681	+	0.0513420i	$0.0163498\pi$
$827$	30.1962	+	30.1962i	1.05002	+	1.05002i	0.0513420	+	0.998681i	$0.483650\pi$
$828$		0			0
$829$	−24.4545	+	42.3564i	−0.849339	+	1.47110i	0.0324595	+	0.999473i	$0.489666\pi$
$829$	−24.4545	+	42.3564i	−0.849339	+	1.47110i	−0.881799	+	0.471626i	$0.843667\pi$
$830$	−7.92820	−	2.12436i	−0.275192	−	0.0737375i
$831$		0			0
$832$	−6.92820	+	28.0000i	−0.240192	+	0.970725i
$833$	0.267949			0.00928389
$834$		0			0
$835$	5.26795	−	9.12436i	0.182305	−	0.315761i
$836$	−25.6077	−	14.7846i	−0.885661	−	0.511336i
$837$		0			0
$838$	9.60770	−	9.60770i	0.331892	−	0.331892i
$839$	−38.3205	−	10.2679i	−1.32297	−	0.354489i	−0.472881	−	0.881126i	$-0.656786\pi$
$839$	−38.3205	−	10.2679i	−1.32297	−	0.354489i	−0.850090	+	0.526637i	$0.823453\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	−26.3660	−	45.6673i	−0.908633	−	1.57380i
$843$		0			0
$844$	38.1051	−	22.0000i	1.31163	−	0.757271i
$845$	1.99038	+	6.42820i	0.0684712	+	0.221137i
$846$		0			0
$847$	2.70577	−	0.725009i	0.0929714	−	0.0249116i
$848$	−30.0000	+	17.3205i	−1.03020	+	0.594789i
$849$		0			0
$850$	−0.464102	−	1.73205i	−0.0159186	−	0.0594089i
$851$	5.09808	+	1.36603i	0.174760	+	0.0468267i
$852$		0			0
$853$	−7.77757	+	7.77757i	−0.266299	+	0.266299i	−0.827607	−	0.561308i	$-0.810298\pi$
$853$	−7.77757	+	7.77757i	−0.266299	+	0.266299i	0.561308	+	0.827607i	$0.310298\pi$
$854$	−6.67949			−0.228568
$855$		0			0
$856$	−10.3923	+	2.78461i	−0.355202	+	0.0951760i
$857$			3.39230i			0.115879i	0.998320	+	0.0579395i	$0.0184530\pi$
$857$			3.39230i			0.115879i	−0.998320	+	0.0579395i	$0.981547\pi$
$858$		0			0
$859$	−33.6603			−1.14847			−0.574237	−	0.818689i	$-0.694701\pi$
$859$	−33.6603			−1.14847			−0.574237	+	0.818689i	$0.694701\pi$
$860$	−0.535898	−	0.535898i	−0.0182740	−	0.0182740i
$861$		0			0
$862$	−57.7128			−1.96571
$863$	33.6410	+	33.6410i	1.14515	+	1.14515i	0.987493	+	0.157660i	$0.0503950\pi$
$863$	33.6410	+	33.6410i	1.14515	+	1.14515i	0.157660	+	0.987493i	$0.449605\pi$
$864$		0			0
$865$	2.53590	−	9.46410i	0.0862231	−	0.321789i
$866$	13.2942	−	3.56218i	0.451756	−	0.121048i
$867$		0			0
$868$			27.7128i			0.940634i
$869$	−0.966679	−	3.60770i	−0.0327923	−	0.122383i
$870$		0			0
$871$	−0.418584	−	21.7583i	−0.0141832	−	0.737253i
$872$		−	56.4974i		−	1.91324i
$873$		0			0
$874$	−3.80385	+	2.19615i	−0.128667	+	0.0742860i
$875$	10.6865	−	6.16987i	0.361271	−	0.208580i
$876$		0			0
$877$	2.83975	−	10.5981i	0.0958914	−	0.357872i	−0.901262	−	0.433275i	$-0.857358\pi$
$877$	2.83975	−	10.5981i	0.0958914	−	0.357872i	0.997153	+	0.0754036i	$0.0240245\pi$
$878$	−33.6603	+	33.6603i	−1.13598	+	1.13598i
$879$		0			0
$880$			7.21539i			0.243231i
$881$	37.7942	+	21.8205i	1.27332	+	0.735152i	0.975611	−	0.219505i	$-0.0704443\pi$
$881$	37.7942	+	21.8205i	1.27332	+	0.735152i	0.297709	+	0.954657i	$0.403778\pi$
$882$		0			0
$883$			12.7846i			0.430236i	0.976588	+	0.215118i	$0.0690137\pi$
$883$			12.7846i			0.430236i	−0.976588	+	0.215118i	$0.930986\pi$
$884$	−1.87564	−	0.464102i	−0.0630847	−	0.0156094i
$885$		0			0
$886$	16.5885	+	4.44486i	0.557300	+	0.149328i
$887$	−24.8038	−	14.3205i	−0.832832	−	0.480836i	0.0219895	−	0.999758i	$-0.493000\pi$
$887$	−24.8038	−	14.3205i	−0.832832	−	0.480836i	−0.854821	+	0.518923i	$0.826333\pi$
$888$		0			0
$889$	0.928203	−	0.928203i	0.0311309	−	0.0311309i
$890$	−6.73205	−	6.73205i	−0.225659	−	0.225659i
$891$		0			0
$892$	−35.8564	−	9.60770i	−1.20056	−	0.321689i
$893$	11.7846	−	6.80385i	0.394357	−	0.227682i
$894$		0			0
$895$	0.169873	+	0.633975i	0.00567823	+	0.0211914i
$896$	13.8564	−	24.0000i	0.462910	−	0.801784i
$897$		0			0
$898$	−19.1962	+	33.2487i	−0.640584	+	1.10952i
$899$	4.39230	+	16.3923i	0.146492	+	0.546714i
$900$		0			0
$901$	−1.16025	−	2.00962i	−0.0386537	−	0.0669501i
$902$	−12.3205	−	45.9808i	−0.410228	−	1.53099i
$903$		0			0
$904$	2.87564	−	10.7321i	0.0956425	−	0.356943i
$905$	0.705771	+	0.705771i	0.0234606	+	0.0234606i
$906$		0			0
$907$	1.85641	+	1.07180i	0.0616410	+	0.0355884i	0.530504	−	0.847683i	$-0.322003\pi$
$907$	1.85641	+	1.07180i	0.0616410	+	0.0355884i	−0.468863	+	0.883271i	$0.655336\pi$
$908$	−1.60770	−	1.60770i	−0.0533532	−	0.0533532i
$909$		0			0
$910$	−0.124356	−	6.46410i	−0.00412235	−	0.214283i
$911$			50.7846i			1.68257i	0.540592	+	0.841285i	$0.318200\pi$
$911$			50.7846i			1.68257i	−0.540592	+	0.841285i	$0.681800\pi$
$912$		0			0
$913$	19.5359	−	33.8372i	0.646544	−	1.11985i
$914$			8.73205i			0.288831i
$915$		0			0
$916$	13.6603	−	3.66025i	0.451347	−	0.120938i
$917$	−32.7846	−	8.78461i	−1.08264	−	0.290093i
$918$		0			0
$919$	−30.9282	+	17.8564i	−1.02023	+	0.589028i	−0.914170	−	0.405331i	$-0.867156\pi$
$919$	−30.9282	+	17.8564i	−1.02023	+	0.589028i	−0.106058	+	0.994360i	$0.533823\pi$
$920$	0.928203	+	0.535898i	0.0306020	+	0.0176680i
$921$		0			0
$922$	−19.9019	+	34.4711i	−0.655435	+	1.13525i
$923$	−12.3205	+	22.3205i	−0.405534	+	0.734688i
$924$		0			0
$925$	−32.9545	+	8.83013i	−1.08354	+	0.290333i
$926$	1.14359	−	0.660254i	0.0375808	−	0.0216973i
$927$		0			0
$928$	4.39230	−	16.3923i	0.144184	−	0.538104i
$929$	27.3564	+	7.33013i	0.897535	+	0.240494i	0.677957	−	0.735101i	$-0.262865\pi$
$929$	27.3564	+	7.33013i	0.897535	+	0.240494i	0.219577	+	0.975595i	$0.429532\pi$
$930$		0			0
$931$	3.00000	+	3.00000i	0.0983210	+	0.0983210i
$932$	9.07180	−	15.7128i	0.297157	−	0.514690i
$933$		0			0
$934$	5.19615	−	19.3923i	0.170023	−	0.634536i
$935$	−0.483340			−0.0158069
$936$		0			0
$937$	−46.7128			−1.52604			−0.763021	−	0.646374i	$-0.776285\pi$
$937$	−46.7128			−1.52604			−0.763021	+	0.646374i	$0.776285\pi$
$938$	−5.41154	+	20.1962i	−0.176693	+	0.659428i
$939$		0			0
$940$	−2.87564	−	1.66025i	−0.0937932	−	0.0541515i
$941$	5.19615	+	5.19615i	0.169390	+	0.169390i	0.786711	−	0.617321i	$-0.211782\pi$
$941$	5.19615	+	5.19615i	0.169390	+	0.169390i	−0.617321	+	0.786711i	$0.711782\pi$
$942$		0			0
$943$	−6.83013	−	1.83013i	−0.222420	−	0.0595971i
$944$	41.8564	−	11.2154i	1.36231	−	0.365030i
$945$		0			0
$946$	3.12436	−	1.80385i	0.101582	−	0.0586481i
$947$	12.3923	−	3.32051i	0.402696	−	0.107902i	−0.0517856	−	0.998658i	$-0.516491\pi$
$947$	12.3923	−	3.32051i	0.402696	−	0.107902i	0.454481	+	0.890756i	$0.349825\pi$
$948$		0			0
$949$	20.6244	+	34.1865i	0.669495	+	1.10974i
$950$	14.1962	−	24.5885i	0.460584	−	0.797755i
$951$		0			0
$952$	1.60770	+	0.928203i	0.0521057	+	0.0300832i
$953$	34.2679	−	19.7846i	1.11005	−	0.640886i	0.171206	−	0.985235i	$-0.445234\pi$
$953$	34.2679	−	19.7846i	1.11005	−	0.640886i	0.938842	+	0.344349i	$0.111900\pi$
$954$		0			0
$955$	−9.46410	−	2.53590i	−0.306251	−	0.0820597i
$956$	9.51666	+	35.5167i	0.307791	+	1.14869i
$957$		0			0
$958$			55.3205i			1.78732i
$959$	6.29423	−	10.9019i	0.203251	−	0.352041i
$960$		0			0
$961$			1.00000i			0.0322581i
$962$	−8.83013	+	35.6865i	−0.284695	+	1.15058i
$963$		0			0
$964$	−20.9808	+	20.9808i	−0.675745	+	0.675745i
$965$	−7.45448	−	4.30385i	−0.239968	−	0.138546i
$966$		0			0
$967$	−19.0526	−	19.0526i	−0.612689	−	0.612689i	0.330957	−	0.943646i	$-0.392629\pi$
$967$	−19.0526	−	19.0526i	−0.612689	−	0.612689i	−0.943646	+	0.330957i	$0.892629\pi$
$968$	−3.12436	−	0.837169i	−0.100421	−	0.0269076i
$969$		0			0
$970$	−3.00000	−	11.1962i	−0.0963242	−	0.359487i
$971$	20.1244	+	34.8564i	0.645821	+	1.11860i	0.984111	+	0.177553i	$0.0568182\pi$
$971$	20.1244	+	34.8564i	0.645821	+	1.11860i	−0.338290	+	0.941042i	$0.609848\pi$
$972$		0			0
$973$	−9.71281	−	36.2487i	−0.311378	−	1.16208i
$974$	−9.00000	+	15.5885i	−0.288379	+	0.499486i
$975$		0			0
$976$	6.67949	+	3.85641i	0.213805	+	0.123441i
$977$	−11.8397	−	44.1865i	−0.378787	−	1.41365i	−0.847732	−	0.530425i	$-0.822032\pi$
$977$	−11.8397	−	44.1865i	−0.378787	−	1.41365i	0.468945	−	0.883227i	$-0.344634\pi$
$978$		0			0
$979$	39.2487	−	22.6603i	1.25439	−	0.724225i
$980$	0.267949	−	1.00000i	0.00855932	−	0.0319438i
$981$		0			0
$982$	−4.73205	−	4.73205i	−0.151006	−	0.151006i
$983$	−6.33975	+	6.33975i	−0.202206	+	0.202206i	−0.800945	−	0.598738i	$-0.795669\pi$
$983$	−6.33975	+	6.33975i	−0.202206	+	0.202206i	0.598738	+	0.800945i	$0.295669\pi$
$984$		0			0
$985$	−4.43782	−	2.56218i	−0.141401	−	0.0816378i
$986$	1.09808	+	0.294229i	0.0349699	+	0.00937015i
$987$		0			0
$988$	−15.8038	−	26.1962i	−0.502787	−	0.833411i
$989$		−	0.535898i		−	0.0170406i
$990$		0			0
$991$	34.8109	+	20.0981i	1.10580	+	0.638436i	0.937739	−	0.347340i	$-0.112915\pi$
$991$	34.8109	+	20.0981i	1.10580	+	0.638436i	0.168065	+	0.985776i	$0.446248\pi$
$992$	16.0000	−	27.7128i	0.508001	−	0.879883i
$993$		0			0
$994$	17.3205	−	17.3205i	0.549373	−	0.549373i
$995$	−1.43782	+	5.36603i	−0.0455820	+	0.170114i
$996$		0			0
$997$	6.86603	−	3.96410i	0.217449	−	0.125544i	−0.387319	−	0.921946i	$-0.626599\pi$
$997$	6.86603	−	3.96410i	0.217449	−	0.125544i	0.604769	+	0.796401i	$0.293266\pi$
$998$	22.6410	−	13.0718i	0.716689	−	0.413780i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.ed.a.19.1		4
3.2	odd	2		312.2.bt.b.19.1	yes	4
8.3	odd	2		936.2.ed.b.19.1		4
13.11	odd	12		936.2.ed.b.739.1		4
24.11	even	2		312.2.bt.a.19.1	✓	4
39.11	even	12		312.2.bt.a.115.1	yes	4
104.11	even	12	inner	936.2.ed.a.739.1		4
312.11	odd	12		312.2.bt.b.115.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.a.19.1	✓	4	24.11	even	2
312.2.bt.a.115.1	yes	4	39.11	even	12
312.2.bt.b.19.1	yes	4	3.2	odd	2
312.2.bt.b.115.1	yes	4	312.11	odd	12
936.2.ed.a.19.1		4	1.1	even	1	trivial
936.2.ed.a.739.1		4	104.11	even	12	inner
936.2.ed.b.19.1		4	8.3	odd	2
936.2.ed.b.739.1		4	13.11	odd	12

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.ed (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 0.366025i) q^{2} +(1.73205 + 1.00000i) q^{4} +(0.366025 + 0.366025i) q^{5} +(2.36603 + 0.633975i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.366025 - 0.633975i) q^{10} +(3.36603 - 0.901924i) q^{11} +(3.50000 + 0.866025i) q^{13} +(-3.00000 - 1.73205i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-0.232051 + 0.133975i) q^{17} +(-4.09808 - 1.09808i) q^{19} +(0.267949 + 1.00000i) q^{20} -4.92820 q^{22} +(-0.366025 + 0.633975i) q^{23} -4.73205i q^{25} +(-4.46410 - 2.46410i) q^{26} +(3.46410 + 3.46410i) q^{28} +(2.59808 + 1.50000i) q^{29} +(4.00000 + 4.00000i) q^{31} +(-1.46410 - 5.46410i) q^{32} +(0.366025 - 0.0980762i) q^{34} +(0.633975 + 1.09808i) q^{35} +(-1.86603 - 6.96410i) q^{37} +(5.19615 + 3.00000i) q^{38} -1.46410i q^{40} +(2.50000 + 9.33013i) q^{41} +(-0.633975 + 0.366025i) q^{43} +(6.73205 + 1.80385i) q^{44} +(0.732051 - 0.732051i) q^{46} +(-2.26795 + 2.26795i) q^{47} +(-0.866025 - 0.500000i) q^{49} +(-1.73205 + 6.46410i) q^{50} +(5.19615 + 5.00000i) q^{52} +8.66025i q^{53} +(1.56218 + 0.901924i) q^{55} +(-3.46410 - 6.00000i) q^{56} +(-3.00000 - 3.00000i) q^{58} +(2.80385 - 10.4641i) q^{59} +(1.66987 - 0.964102i) q^{61} +(-4.00000 - 6.92820i) q^{62} +8.00000i q^{64} +(0.964102 + 1.59808i) q^{65} +(-1.56218 - 5.83013i) q^{67} -0.535898 q^{68} +(-0.464102 - 1.73205i) q^{70} +(-1.83013 + 6.83013i) q^{71} +(7.83013 + 7.83013i) q^{73} +10.1962i q^{74} +(-6.00000 - 6.00000i) q^{76} +8.53590 q^{77} -1.07180i q^{79} +(-0.535898 + 2.00000i) q^{80} -13.6603i q^{82} +(7.92820 - 7.92820i) q^{83} +(-0.133975 - 0.0358984i) q^{85} +(1.00000 - 0.267949i) q^{86} +(-8.53590 - 4.92820i) q^{88} +(12.5622 - 3.36603i) q^{89} +(7.73205 + 4.26795i) q^{91} +(-1.26795 + 0.732051i) q^{92} +(3.92820 - 2.26795i) q^{94} +(-1.09808 - 1.90192i) q^{95} +(15.2942 + 4.09808i) q^{97} +(1.00000 + 1.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{5} + 6 q^{7} - 8 q^{8} + 2 q^{10} + 10 q^{11} + 14 q^{13} - 12 q^{14} + 8 q^{16} + 6 q^{17} - 6 q^{19} + 8 q^{20} + 8 q^{22} + 2 q^{23} - 4 q^{26} + 16 q^{31} + 8 q^{32} - 2 q^{34}+ \cdots + 4 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^5 + 6 * q^7 - 8 * q^8 + 2 * q^10 + 10 * q^11 + 14 * q^13 - 12 * q^14 + 8 * q^16 + 6 * q^17 - 6 * q^19 + 8 * q^20 + 8 * q^22 + 2 * q^23 - 4 * q^26 + 16 * q^31 + 8 * q^32 - 2 * q^34 + 6 * q^35 - 4 * q^37 + 10 * q^41 - 6 * q^43 + 20 * q^44 - 4 * q^46 - 16 * q^47 - 18 * q^55 - 12 * q^58 + 32 * q^59 + 24 * q^61 - 16 * q^62 - 10 * q^65 + 18 * q^67 - 16 * q^68 + 12 * q^70 + 10 * q^71 + 14 * q^73 - 24 * q^76 + 48 * q^77 - 16 * q^80 + 4 * q^83 - 4 * q^85 + 4 * q^86 - 48 * q^88 + 26 * q^89 + 24 * q^91 - 12 * q^92 - 12 * q^94 + 6 * q^95 + 30 * q^97 + 4 * q^98

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