LMFDB - Embedded newform 855.2.cj.d.658.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [855,2,Mod(217,855)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(855, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("855.217"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.cj (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,6,0,0,4,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.82720937282$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			658.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	855.658
Dual form			855.2.cj.d.217.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.633975 - 2.36603i) q^{2} +(-3.46410 - 2.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-3.46410 + 3.46410i) q^{8} +(5.36603 + 1.09808i) q^{10} +5.00000 q^{11} +(3.46410 + 6.00000i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.73205 + 0.732051i) q^{17} +(4.33013 + 0.500000i) q^{19} +(4.00000 - 8.00000i) q^{20} +(3.16987 - 11.8301i) q^{22} +(4.09808 - 1.09808i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(10.9282 - 2.92820i) q^{28} +(0.866025 - 1.50000i) q^{29} +5.19615i q^{31} +(3.46410 - 6.00000i) q^{34} +(-4.73205 - 4.19615i) q^{35} +(1.73205 + 1.73205i) q^{37} +(3.92820 - 9.92820i) q^{38} +(-8.19615 - 7.26795i) q^{40} +(3.00000 - 1.73205i) q^{41} +(2.56218 - 9.56218i) q^{43} +(-17.3205 - 10.0000i) q^{44} -10.3923i q^{46} +(2.19615 + 8.19615i) q^{47} -1.00000i q^{49} +(-1.73205 + 12.1244i) q^{50} +(1.90192 + 7.09808i) q^{53} +(0.669873 + 11.1603i) q^{55} -13.8564i q^{56} +(-3.00000 - 3.00000i) q^{58} +(2.59808 + 4.50000i) q^{59} +(2.50000 - 4.33013i) q^{61} +(12.2942 + 3.29423i) q^{62} +8.00000i q^{64} +(-9.46410 + 2.53590i) q^{67} +(-8.00000 - 8.00000i) q^{68} +(-12.9282 + 8.53590i) q^{70} +(4.50000 - 2.59808i) q^{71} +(-0.366025 + 1.36603i) q^{73} +(5.19615 - 3.00000i) q^{74} +(-14.0000 - 10.3923i) q^{76} +(-10.0000 + 10.0000i) q^{77} +(-0.866025 - 1.50000i) q^{79} +(-7.46410 + 4.92820i) q^{80} +(-2.19615 - 8.19615i) q^{82} +(-5.00000 - 5.00000i) q^{83} +(-1.26795 + 6.19615i) q^{85} +(-21.0000 - 12.1244i) q^{86} +(-17.3205 + 17.3205i) q^{88} +(2.59808 - 4.50000i) q^{89} +(-16.3923 - 4.39230i) q^{92} +20.7846 q^{94} +(-0.535898 + 9.73205i) q^{95} +(-1.90192 + 7.09808i) q^{97} +(-2.36603 - 0.633975i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} + 4 q^{5} - 8 q^{7} + 18 q^{10} + 20 q^{11} + 8 q^{16} + 4 q^{17} + 16 q^{20} + 30 q^{22} + 6 q^{23} - 6 q^{25} + 16 q^{28} - 12 q^{35} - 12 q^{38} - 12 q^{40} + 12 q^{41} - 14 q^{43} - 12 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) $ 4 * q + 6 * q^2 + 4 * q^5 - 8 * q^7 + 18 * q^10 + 20 * q^11 + 8 * q^16 + 4 * q^17 + 16 * q^20 + 30 * q^22 + 6 * q^23 - 6 * q^25 + 16 * q^28 - 12 * q^35 - 12 * q^38 - 12 * q^40 + 12 * q^41 - 14 * q^43 - 12 * q^47 + 18 * q^53 + 20 * q^55 - 12 * q^58 + 10 * q^61 + 18 * q^62 - 24 * q^67 - 32 * q^68 - 24 * q^70 + 18 * q^71 + 2 * q^73 - 56 * q^76 - 40 * q^77 - 16 * q^80 + 12 * q^82 - 20 * q^83 - 12 * q^85 - 84 * q^86 - 24 * q^92 - 16 * q^95 - 18 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.633975	−	2.36603i	0.448288	−	1.67303i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	0.633975	−	2.36603i	0.448288	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$3$		0			0
$3$		0			0
$4$	−3.46410	−	2.00000i	−1.73205	−	1.00000i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		0			0
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	−0.975579	−	0.219650i	$-0.929509\pi$
$7$	−2.00000	+	2.00000i	−0.755929	+	0.755929i	0.219650	+	0.975579i	$0.429509\pi$
$8$	−3.46410	+	3.46410i	−1.22474	+	1.22474i
$9$		0			0
$10$	5.36603	+	1.09808i	1.69689	+	0.347242i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$13$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$14$	3.46410	+	6.00000i	0.925820	+	1.60357i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.574428	−	0.818555i	$-0.305225\pi$
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.0881917	+	0.996104i	$0.471891\pi$
$18$		0			0
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$19$	4.33013	+	0.500000i	0.993399	+	0.114708i
$20$	4.00000	−	8.00000i	0.894427	−	1.78885i
$21$		0			0
$22$	3.16987	−	11.8301i	0.675819	−	2.52219i
$23$	4.09808	−	1.09808i	0.854508	−	0.228965i	0.195131	−	0.980777i	$-0.437487\pi$
$23$	4.09808	−	1.09808i	0.854508	−	0.228965i	0.659377	+	0.751812i	$0.270820\pi$
$24$		0			0
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$		0			0
$27$		0			0
$28$	10.9282	−	2.92820i	2.06524	−	0.553378i
$29$	0.866025	−	1.50000i	0.160817	−	0.278543i	−0.774345	−	0.632764i	$-0.781920\pi$
$29$	0.866025	−	1.50000i	0.160817	−	0.278543i	0.935162	+	0.354221i	$0.115254\pi$
$30$		0			0
$31$			5.19615i			0.933257i	0.884454	+	0.466628i	$0.154531\pi$
$31$			5.19615i			0.933257i	−0.884454	+	0.466628i	$0.845469\pi$
$32$		0			0
$33$		0			0
$34$	3.46410	−	6.00000i	0.594089	−	1.02899i
$35$	−4.73205	−	4.19615i	−0.799863	−	0.709279i
$36$		0			0
$37$	1.73205	+	1.73205i	0.284747	+	0.284747i	0.834999	−	0.550252i	$-0.185468\pi$
$37$	1.73205	+	1.73205i	0.284747	+	0.284747i	−0.550252	+	0.834999i	$0.685468\pi$
$38$	3.92820	−	9.92820i	0.637239	−	1.61057i
$39$		0			0
$40$	−8.19615	−	7.26795i	−1.29593	−	1.14916i
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	−0.247099	−	0.968990i	$-0.579477\pi$
$41$	3.00000	−	1.73205i	0.468521	−	0.270501i	0.715621	+	0.698489i	$0.246144\pi$
$42$		0			0
$43$	2.56218	−	9.56218i	0.390728	−	1.45822i	−0.438207	−	0.898874i	$-0.644386\pi$
$43$	2.56218	−	9.56218i	0.390728	−	1.45822i	0.828935	−	0.559344i	$-0.188947\pi$
$44$	−17.3205	−	10.0000i	−2.61116	−	1.50756i
$45$		0			0
$46$		−	10.3923i		−	1.53226i
$47$	2.19615	+	8.19615i	0.320342	+	1.19553i	0.918912	+	0.394462i	$0.129069\pi$
$47$	2.19615	+	8.19615i	0.320342	+	1.19553i	−0.598571	+	0.801070i	$0.704264\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$	−1.73205	+	12.1244i	−0.244949	+	1.71464i
$51$		0			0
$52$		0			0
$53$	1.90192	+	7.09808i	0.261249	+	0.974996i	0.964506	+	0.264060i	$0.0850617\pi$
$53$	1.90192	+	7.09808i	0.261249	+	0.974996i	−0.703257	+	0.710936i	$0.748272\pi$
$54$		0			0
$55$	0.669873	+	11.1603i	0.0903257	+	1.50485i
$56$		−	13.8564i		−	1.85164i
$57$		0			0
$58$	−3.00000	−	3.00000i	−0.393919	−	0.393919i
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	0.984102	−	0.177605i	$-0.0568349\pi$
$59$	2.59808	+	4.50000i	0.338241	+	0.585850i	−0.645861	+	0.763455i	$0.723502\pi$
$60$		0			0
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	12.2942	+	3.29423i	1.56137	+	0.418367i
$63$		0			0
$64$			8.00000i			1.00000i
$65$		0			0
$66$		0			0
$67$	−9.46410	+	2.53590i	−1.15622	+	0.309809i	−0.785457	−	0.618917i	$-0.787572\pi$
$67$	−9.46410	+	2.53590i	−1.15622	+	0.309809i	−0.370767	+	0.928726i	$0.620905\pi$
$68$	−8.00000	−	8.00000i	−0.970143	−	0.970143i
$69$		0			0
$70$	−12.9282	+	8.53590i	−1.54522	+	1.02023i
$71$	4.50000	−	2.59808i	0.534052	−	0.308335i	−0.208613	−	0.977998i	$-0.566895\pi$
$71$	4.50000	−	2.59808i	0.534052	−	0.308335i	0.742665	+	0.669663i	$0.233562\pi$
$72$		0			0
$73$	−0.366025	+	1.36603i	−0.0428400	+	0.159881i	−0.984032	−	0.177991i	$-0.943040\pi$
$73$	−0.366025	+	1.36603i	−0.0428400	+	0.159881i	0.941192	+	0.337872i	$0.109707\pi$
$74$	5.19615	−	3.00000i	0.604040	−	0.348743i
$75$		0			0
$76$	−14.0000	−	10.3923i	−1.60591	−	1.19208i
$77$	−10.0000	+	10.0000i	−1.13961	+	1.13961i
$78$		0			0
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	0.813187	−	0.582003i	$-0.197731\pi$
$79$	−0.866025	−	1.50000i	−0.0974355	−	0.168763i	−0.910622	+	0.413239i	$0.864397\pi$
$80$	−7.46410	+	4.92820i	−0.834512	+	0.550990i
$81$		0			0
$82$	−2.19615	−	8.19615i	−0.242524	−	0.905114i
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	0.377279	−	0.926100i	$-0.376860\pi$
$83$	−5.00000	−	5.00000i	−0.548821	−	0.548821i	−0.926100	+	0.377279i	$0.876860\pi$
$84$		0			0
$85$	−1.26795	+	6.19615i	−0.137528	+	0.672067i
$86$	−21.0000	−	12.1244i	−2.26449	−	1.30740i
$87$		0			0
$88$	−17.3205	+	17.3205i	−1.84637	+	1.84637i
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	−0.694839	−	0.719165i	$-0.744525\pi$
$89$	2.59808	−	4.50000i	0.275396	−	0.476999i	0.970235	+	0.242166i	$0.0778579\pi$
$90$		0			0
$91$		0			0
$92$	−16.3923	−	4.39230i	−1.70902	−	0.457929i
$93$		0			0
$94$	20.7846			2.14377
$95$	−0.535898	+	9.73205i	−0.0549820	+	0.998487i
$96$		0			0
$97$	−1.90192	+	7.09808i	−0.193111	+	0.720700i	0.799637	+	0.600484i	$0.205025\pi$
$97$	−1.90192	+	7.09808i	−0.193111	+	0.720700i	−0.992748	+	0.120216i	$0.961641\pi$
$98$	−2.36603	−	0.633975i	−0.239005	−	0.0640411i
$99$		0			0
$100$	18.3923	+	7.85641i	1.83923	+	0.785641i
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	−0.714423	−	0.699715i	$-0.753311\pi$
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	0.963182	+	0.268851i	$0.0866439\pi$
$102$		0			0
$103$	−6.92820	+	6.92820i	−0.682656	+	0.682656i	−0.960598	−	0.277942i	$-0.910348\pi$
$103$	−6.92820	+	6.92820i	−0.682656	+	0.682656i	0.277942	+	0.960598i	$0.410348\pi$
$104$		0			0
$105$		0			0
$106$	18.0000			1.74831
$107$	−1.73205	−	1.73205i	−0.167444	−	0.167444i	0.618411	−	0.785855i	$-0.287777\pi$
$107$	−1.73205	−	1.73205i	−0.167444	−	0.167444i	−0.785855	+	0.618411i	$0.787777\pi$
$108$		0			0
$109$	−0.866025	−	1.50000i	−0.0829502	−	0.143674i	0.821566	−	0.570114i	$-0.193101\pi$
$109$	−0.866025	−	1.50000i	−0.0829502	−	0.143674i	−0.904516	+	0.426440i	$0.859768\pi$
$110$	26.8301	+	5.49038i	2.55815	+	0.523487i
$111$		0			0
$112$	−10.9282	−	2.92820i	−1.03262	−	0.276689i
$113$	−1.73205	+	1.73205i	−0.162938	+	0.162938i	−0.783867	−	0.620929i	$-0.786755\pi$
$113$	−1.73205	+	1.73205i	−0.162938	+	0.162938i	0.620929	+	0.783867i	$0.286755\pi$
$114$		0			0
$115$	3.00000	+	9.00000i	0.279751	+	0.839254i
$116$	−6.00000	+	3.46410i	−0.557086	+	0.321634i
$117$		0			0
$118$	12.2942	−	3.29423i	1.13178	−	0.303258i
$119$	−6.92820	+	4.00000i	−0.635107	+	0.366679i
$120$		0			0
$121$	14.0000			1.27273
$122$	−8.66025	−	8.66025i	−0.784063	−	0.784063i
$123$		0			0
$124$	10.3923	−	18.0000i	0.933257	−	1.61645i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$		0			0
$127$	−9.46410	+	2.53590i	−0.839803	+	0.225025i	−0.652986	−	0.757370i	$-0.726484\pi$
$127$	−9.46410	+	2.53590i	−0.839803	+	0.225025i	−0.186817	+	0.982395i	$0.559817\pi$
$128$	18.9282	+	5.07180i	1.67303	+	0.448288i
$129$		0			0
$130$		0			0
$131$	5.00000	+	8.66025i	0.436852	+	0.756650i	0.997445	−	0.0714417i	$-0.0227600\pi$
$131$	5.00000	+	8.66025i	0.436852	+	0.756650i	−0.560593	+	0.828092i	$0.689427\pi$
$132$		0			0
$133$	−9.66025	+	7.66025i	−0.837650	+	0.664228i
$134$			24.0000i			2.07328i
$135$		0			0
$136$	−12.0000	+	6.92820i	−1.02899	+	0.594089i
$137$	−2.92820	−	10.9282i	−0.250173	−	0.933659i	−0.970712	−	0.240245i	$-0.922772\pi$
$137$	−2.92820	−	10.9282i	−0.250173	−	0.933659i	0.720539	−	0.693414i	$-0.243894\pi$
$138$		0			0
$139$	−15.5885	−	9.00000i	−1.32220	−	0.763370i	−0.338117	−	0.941104i	$-0.609790\pi$
$139$	−15.5885	−	9.00000i	−1.32220	−	0.763370i	−0.984079	+	0.177734i	$0.943123\pi$
$140$	8.00000	+	24.0000i	0.676123	+	2.02837i
$141$		0			0
$142$	−3.29423	−	12.2942i	−0.276446	−	1.03171i
$143$		0			0
$144$		0			0
$145$	3.46410	+	1.73205i	0.287678	+	0.143839i
$146$	3.00000	+	1.73205i	0.248282	+	0.143346i
$147$		0			0
$148$	−2.53590	−	9.46410i	−0.208450	−	0.777944i
$149$	16.4545	−	9.50000i	1.34800	−	0.778270i	0.360037	−	0.932938i	$-0.382764\pi$
$149$	16.4545	−	9.50000i	1.34800	−	0.778270i	0.987967	+	0.154668i	$0.0494307\pi$
$150$		0			0
$151$		−	15.5885i		−	1.26857i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$		−	15.5885i		−	1.26857i	0.773099	−	0.634285i	$-0.218706\pi$
$152$	−16.7321	+	13.2679i	−1.35715	+	1.07617i
$153$		0			0
$154$	17.3205	+	30.0000i	1.39573	+	2.41747i
$155$	−11.5981	+	0.696152i	−0.931580	+	0.0559163i
$156$		0			0
$157$	9.56218	+	2.56218i	0.763145	+	0.204484i	0.619341	−	0.785122i	$-0.287400\pi$
$157$	9.56218	+	2.56218i	0.763145	+	0.204484i	0.143804	+	0.989606i	$0.454067\pi$
$158$	−4.09808	+	1.09808i	−0.326025	+	0.0873583i
$159$		0			0
$160$		0			0
$161$	−6.00000	+	10.3923i	−0.472866	+	0.819028i
$162$		0			0
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	0.129936	−	0.991522i	$-0.458523\pi$
$163$	−11.0000	−	11.0000i	−0.861586	−	0.861586i	−0.991522	+	0.129936i	$0.958523\pi$
$164$	−13.8564			−1.08200
$165$		0			0
$166$	−15.0000	+	8.66025i	−1.16423	+	0.672166i
$167$	−18.9282	+	5.07180i	−1.46471	+	0.392467i	−0.901113	−	0.433584i	$-0.857249\pi$
$167$	−18.9282	+	5.07180i	−1.46471	+	0.392467i	−0.563595	+	0.826051i	$0.690582\pi$
$168$		0			0
$169$	11.2583	−	6.50000i	0.866025	−	0.500000i
$170$	13.8564	+	6.92820i	1.06274	+	0.531369i
$171$		0			0
$172$	−28.0000	+	28.0000i	−2.13498	+	2.13498i
$173$	−4.73205	−	1.26795i	−0.359771	−	0.0964004i	0.0744057	−	0.997228i	$-0.476294\pi$
$173$	−4.73205	−	1.26795i	−0.359771	−	0.0964004i	−0.434177	+	0.900828i	$0.642961\pi$
$174$		0			0
$175$	8.73205	−	11.1244i	0.660081	−	0.840922i
$176$	10.0000	+	17.3205i	0.753778	+	1.30558i
$177$		0			0
$178$	−9.00000	−	9.00000i	−0.674579	−	0.674579i
$179$	−19.0526			−1.42406			−0.712028	−	0.702152i	$-0.752223\pi$
$179$	−19.0526			−1.42406			−0.712028	+	0.702152i	$0.752223\pi$
$180$		0			0
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	0.706129	−	0.708083i	$-0.250440\pi$
$181$	6.00000	+	3.46410i	0.445976	+	0.257485i	−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$		0			0
$184$	−10.3923	+	18.0000i	−0.766131	+	1.32698i
$185$	−3.63397	+	4.09808i	−0.267175	+	0.301297i
$186$		0			0
$187$	13.6603	+	3.66025i	0.998937	+	0.267664i
$188$	8.78461	−	32.7846i	0.640684	−	2.39106i
$189$		0			0
$190$	22.6865	+	7.43782i	1.64585	+	0.539596i
$191$	7.00000			0.506502			0.253251	−	0.967401i	$-0.418500\pi$
$191$	7.00000			0.506502			0.253251	+	0.967401i	$0.418500\pi$
$192$		0			0
$193$	−9.46410	−	2.53590i	−0.681241	−	0.182538i	−0.0984278	−	0.995144i	$-0.531381\pi$
$193$	−9.46410	−	2.53590i	−0.681241	−	0.182538i	−0.582813	+	0.812606i	$0.698048\pi$
$194$	15.5885	+	9.00000i	1.11919	+	0.646162i
$195$		0			0
$196$	−2.00000	+	3.46410i	−0.142857	+	0.247436i
$197$	6.00000	−	6.00000i	0.427482	−	0.427482i	−0.460288	−	0.887770i	$-0.652254\pi$
$197$	6.00000	−	6.00000i	0.427482	−	0.427482i	0.887770	+	0.460288i	$0.152254\pi$
$198$		0			0
$199$	12.9904	+	7.50000i	0.920864	+	0.531661i	0.883911	−	0.467656i	$-0.154901\pi$
$199$	12.9904	+	7.50000i	0.920864	+	0.531661i	0.0369532	+	0.999317i	$0.488235\pi$
$200$	15.1244	−	19.2679i	1.06945	−	1.36245i
$201$		0			0
$202$	−8.66025	−	8.66025i	−0.609333	−	0.609333i
$203$	1.26795	+	4.73205i	0.0889926	+	0.332125i
$204$		0			0
$205$	4.26795	+	6.46410i	0.298087	+	0.451472i
$206$	12.0000	+	20.7846i	0.836080	+	1.44813i
$207$		0			0
$208$		0			0
$209$	21.6506	+	2.50000i	1.49761	+	0.172929i
$210$		0			0
$211$	−22.5000	+	12.9904i	−1.54896	+	0.894295i	−0.550743	+	0.834675i	$0.685655\pi$
$211$	−22.5000	+	12.9904i	−1.54896	+	0.894295i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	7.60770	−	28.3923i	0.522499	−	1.94999i
$213$		0			0
$214$	−5.19615	+	3.00000i	−0.355202	+	0.205076i
$215$	21.6865	+	4.43782i	1.47901	+	0.302657i
$216$		0			0
$217$	−10.3923	−	10.3923i	−0.705476	−	0.705476i
$218$	−4.09808	+	1.09808i	−0.277557	+	0.0743711i
$219$		0			0
$220$	20.0000	−	40.0000i	1.34840	−	2.69680i
$221$		0			0
$222$		0			0
$223$	26.0263	+	6.97372i	1.74285	+	0.466995i	0.983077	−	0.183195i	$-0.0586439\pi$
$223$	26.0263	+	6.97372i	1.74285	+	0.466995i	0.759772	+	0.650190i	$0.225311\pi$
$224$		0			0
$225$		0			0
$226$	3.00000	+	5.19615i	0.199557	+	0.345643i
$227$	−8.66025	−	8.66025i	−0.574801	−	0.574801i	0.358665	−	0.933466i	$-0.383232\pi$
$227$	−8.66025	−	8.66025i	−0.574801	−	0.574801i	−0.933466	+	0.358665i	$0.883232\pi$
$228$		0			0
$229$		−	9.00000i		−	0.594737i	−0.954763	−	0.297368i	$-0.903891\pi$
$229$		−	9.00000i		−	0.594737i	0.954763	−	0.297368i	$-0.0961089\pi$
$230$	23.1962	−	1.39230i	1.52951	−	0.0918059i
$231$		0			0
$232$	2.19615	+	8.19615i	0.144184	+	0.538104i
$233$	3.29423	−	12.2942i	0.215812	−	0.805422i	−0.770067	−	0.637963i	$-0.779777\pi$
$233$	3.29423	−	12.2942i	0.215812	−	0.805422i	0.985879	−	0.167459i	$-0.0535561\pi$
$234$		0			0
$235$	−18.0000	+	6.00000i	−1.17419	+	0.391397i
$236$		−	20.7846i		−	1.35296i
$237$		0			0
$238$	5.07180	+	18.9282i	0.328756	+	1.22693i
$239$		−	11.0000i		−	0.711531i	−0.934575	−	0.355765i	$-0.884220\pi$
$239$		−	11.0000i		−	0.711531i	0.934575	−	0.355765i	$-0.115780\pi$
$240$		0			0
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	0.122119	−	0.992515i	$-0.461031\pi$
$241$	−10.5000	−	6.06218i	−0.676364	−	0.390499i	−0.798484	+	0.602016i	$0.794364\pi$
$242$	8.87564	−	33.1244i	0.570548	−	2.12931i
$243$		0			0
$244$	−17.3205	+	10.0000i	−1.10883	+	0.640184i
$245$	2.23205	−	0.133975i	0.142600	−	0.00855932i
$246$		0			0
$247$		0			0
$248$	−18.0000	−	18.0000i	−1.14300	−	1.14300i
$249$		0			0
$250$	−27.2942	−	2.24167i	−1.72624	−	0.141776i
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	−0.934075	−	0.357078i	$-0.883773\pi$
$251$	−2.50000	+	4.33013i	−0.157799	+	0.273315i	0.776276	+	0.630393i	$0.217106\pi$
$252$		0			0
$253$	20.4904	−	5.49038i	1.28822	−	0.345177i
$254$			24.0000i			1.50589i
$255$		0			0
$256$	16.0000	−	27.7128i	1.00000	−	1.73205i
$257$	23.6603	−	6.33975i	1.47589	−	0.395462i	0.570941	−	0.820991i	$-0.306578\pi$
$257$	23.6603	−	6.33975i	1.47589	−	0.395462i	0.904945	+	0.425529i	$0.139912\pi$
$258$		0			0
$259$	−6.92820			−0.430498
$260$		0			0
$261$		0			0
$262$	23.6603	−	6.33975i	1.46174	−	0.391671i
$263$	−4.75833	+	17.7583i	−0.293411	+	1.09503i	0.649060	+	0.760737i	$0.275163\pi$
$263$	−4.75833	+	17.7583i	−0.293411	+	1.09503i	−0.942471	+	0.334288i	$0.891504\pi$
$264$		0			0
$265$	−15.5885	+	5.19615i	−0.957591	+	0.319197i
$266$	12.0000	+	27.7128i	0.735767	+	1.69918i
$267$		0			0
$268$	37.8564	+	10.1436i	2.31245	+	0.619619i
$269$	0.866025	+	1.50000i	0.0528025	+	0.0914566i	0.891219	−	0.453574i	$-0.149851\pi$
$269$	0.866025	+	1.50000i	0.0528025	+	0.0914566i	−0.838416	+	0.545031i	$0.816518\pi$
$270$		0			0
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	0.998722	−	0.0505395i	$-0.0160941\pi$
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	−0.543130	+	0.839649i	$0.682761\pi$
$272$	2.92820	+	10.9282i	0.177548	+	0.662620i
$273$		0			0
$274$	−27.7128			−1.67419
$275$	−24.8205	+	2.99038i	−1.49673	+	0.180327i
$276$		0			0
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	−0.576653	−	0.816989i	$-0.695641\pi$
$277$	4.00000	−	4.00000i	0.240337	−	0.240337i	0.816989	+	0.576653i	$0.195641\pi$
$278$	−31.1769	+	31.1769i	−1.86987	+	1.86987i
$279$		0			0
$280$	30.9282	−	1.85641i	1.84831	−	0.110942i
$281$	3.00000	+	1.73205i	0.178965	+	0.103325i	0.586806	−	0.809727i	$-0.300385\pi$
$281$	3.00000	+	1.73205i	0.178965	+	0.103325i	−0.407841	+	0.913053i	$0.633718\pi$
$282$		0			0
$283$	1.46410	−	5.46410i	0.0870318	−	0.324807i	−0.908659	−	0.417538i	$-0.862893\pi$
$283$	1.46410	−	5.46410i	0.0870318	−	0.324807i	0.995691	+	0.0927310i	$0.0295597\pi$
$284$	−20.7846			−1.23334
$285$		0			0
$286$		0			0
$287$	−2.53590	+	9.46410i	−0.149689	+	0.558648i
$288$		0			0
$289$	−7.79423	−	4.50000i	−0.458484	−	0.264706i
$290$	6.29423	−	7.09808i	0.369610	−	0.416813i
$291$		0			0
$292$	4.00000	−	4.00000i	0.234082	−	0.234082i
$293$	−6.92820	+	6.92820i	−0.404750	+	0.404750i	−0.879903	−	0.475153i	$-0.842393\pi$
$293$	−6.92820	+	6.92820i	−0.404750	+	0.404750i	0.475153	+	0.879903i	$0.342393\pi$
$294$		0			0
$295$	−9.69615	+	6.40192i	−0.564532	+	0.372734i
$296$	−12.0000			−0.697486
$297$		0			0
$298$	−12.0455	−	44.9545i	−0.697778	−	2.60414i
$299$		0			0
$300$		0			0
$301$	14.0000	+	24.2487i	0.806947	+	1.39767i
$302$	−36.8827	−	9.88269i	−2.12236	−	0.568685i
$303$		0			0
$304$	6.92820	+	16.0000i	0.397360	+	0.917663i
$305$	10.0000	+	5.00000i	0.572598	+	0.286299i
$306$		0			0
$307$	3.16987	−	11.8301i	0.180914	−	0.675181i	−0.814554	−	0.580088i	$-0.803018\pi$
$307$	3.16987	−	11.8301i	0.180914	−	0.675181i	0.995468	−	0.0950935i	$-0.0303150\pi$
$308$	54.6410	−	14.6410i	3.11346	−	0.834249i
$309$		0			0
$310$	−5.70577	+	27.8827i	−0.324066	+	1.58363i
$311$	20.0000			1.13410			0.567048	−	0.823685i	$-0.308085\pi$
$311$	20.0000			1.13410			0.567048	+	0.823685i	$0.308085\pi$
$312$		0			0
$313$	−27.3205	+	7.32051i	−1.54425	+	0.413780i	−0.927635	−	0.373488i	$-0.878162\pi$
$313$	−27.3205	+	7.32051i	−1.54425	+	0.413780i	−0.616611	+	0.787268i	$0.711495\pi$
$314$	12.1244	−	21.0000i	0.684217	−	1.18510i
$315$		0			0
$316$			6.92820i			0.389742i
$317$	−21.2942	+	5.70577i	−1.19600	+	0.320468i	−0.801256	−	0.598322i	$-0.795834\pi$
$317$	−21.2942	+	5.70577i	−1.19600	+	0.320468i	−0.394747	+	0.918790i	$0.629168\pi$
$318$		0			0
$319$	4.33013	−	7.50000i	0.242441	−	0.419919i
$320$	−17.8564	+	1.07180i	−0.998203	+	0.0599153i
$321$		0			0
$322$	20.7846	+	20.7846i	1.15828	+	1.15828i
$323$	11.4641	+	4.53590i	0.637880	+	0.252384i
$324$		0			0
$325$		0			0
$326$	−33.0000	+	19.0526i	−1.82770	+	1.05522i
$327$		0			0
$328$	−4.39230	+	16.3923i	−0.242524	+	0.905114i
$329$	−20.7846	−	12.0000i	−1.14589	−	0.661581i
$330$		0			0
$331$		0			0		1.00000			$0$
$331$		0			0		−1.00000			$\pi$
$332$	7.32051	+	27.3205i	0.401765	+	1.49941i
$333$		0			0
$334$			48.0000i			2.62644i
$335$	−6.92820	−	20.7846i	−0.378528	−	1.13558i
$336$		0			0
$337$	−4.43782	+	16.5622i	−0.241744	+	0.902199i	0.733249	+	0.679961i	$0.238003\pi$
$337$	−4.43782	+	16.5622i	−0.241744	+	0.902199i	−0.974992	+	0.222239i	$0.928664\pi$
$338$	−8.24167	−	30.7583i	−0.448288	−	1.67303i
$339$		0			0
$340$	16.7846	−	18.9282i	0.910273	−	1.02653i
$341$			25.9808i			1.40694i
$342$		0			0
$343$	−12.0000	−	12.0000i	−0.647939	−	0.647939i
$344$	24.2487	+	42.0000i	1.30740	+	2.26449i
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	10.9282	+	2.92820i	0.586657	+	0.157194i	0.539925	−	0.841713i	$-0.318453\pi$
$347$	10.9282	+	2.92820i	0.586657	+	0.157194i	0.0467319	+	0.998907i	$0.485119\pi$
$348$		0			0
$349$		−	18.0000i		−	0.963518i	−0.876304	−	0.481759i	$-0.839998\pi$
$349$		−	18.0000i		−	0.963518i	0.876304	−	0.481759i	$-0.160002\pi$
$350$	−20.7846	−	27.7128i	−1.11098	−	1.48131i
$351$		0			0
$352$		0			0
$353$	−6.00000	−	6.00000i	−0.319348	−	0.319348i	0.529169	−	0.848517i	$-0.322504\pi$
$353$	−6.00000	−	6.00000i	−0.319348	−	0.319348i	−0.848517	+	0.529169i	$0.822504\pi$
$354$		0			0
$355$	6.40192	+	9.69615i	0.339779	+	0.514618i
$356$	−18.0000	+	10.3923i	−0.953998	+	0.550791i
$357$		0			0
$358$	−12.0788	+	45.0788i	−0.638386	+	2.38249i
$359$	−29.4449	+	17.0000i	−1.55404	+	0.897226i	−0.556234	+	0.831026i	$0.687754\pi$
$359$	−29.4449	+	17.0000i	−1.55404	+	0.897226i	−0.997806	+	0.0662000i	$0.978912\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$	12.0000	−	12.0000i	0.630706	−	0.630706i
$363$		0			0
$364$		0			0
$365$	−3.09808	−	0.633975i	−0.162161	−	0.0331837i
$366$		0			0
$367$	−8.05256	−	30.0526i	−0.420340	−	1.56873i	−0.773893	−	0.633316i	$-0.781693\pi$
$367$	−8.05256	−	30.0526i	−0.420340	−	1.56873i	0.353553	−	0.935415i	$-0.384973\pi$
$368$	12.0000	+	12.0000i	0.625543	+	0.625543i
$369$		0			0
$370$	7.39230	+	11.1962i	0.384308	+	0.582060i
$371$	−18.0000	−	10.3923i	−0.934513	−	0.539542i
$372$		0			0
$373$	−6.92820	+	6.92820i	−0.358729	+	0.358729i	−0.863344	−	0.504615i	$-0.831634\pi$
$373$	−6.92820	+	6.92820i	−0.358729	+	0.358729i	0.504615	+	0.863344i	$0.331634\pi$
$374$	17.3205	−	30.0000i	0.895622	−	1.55126i
$375$		0			0
$376$	−36.0000	−	20.7846i	−1.85656	−	1.07188i
$377$		0			0
$378$		0			0
$379$	−32.9090			−1.69042			−0.845210	−	0.534434i	$-0.820525\pi$
$379$	−32.9090			−1.69042			−0.845210	+	0.534434i	$0.820525\pi$
$380$	21.3205	−	32.6410i	1.09372	−	1.67445i
$381$		0			0
$382$	4.43782	−	16.5622i	0.227059	−	0.847395i
$383$	−28.3923	−	7.60770i	−1.45078	−	0.388735i	−0.554484	−	0.832194i	$-0.687084\pi$
$383$	−28.3923	−	7.60770i	−1.45078	−	0.388735i	−0.896295	+	0.443459i	$0.853751\pi$
$384$		0			0
$385$	−23.6603	−	20.9808i	−1.20584	−	1.06928i
$386$	−12.0000	+	20.7846i	−0.610784	+	1.05791i
$387$		0			0
$388$	20.7846	−	20.7846i	1.05518	−	1.05518i
$389$	19.9186	+	11.5000i	1.00991	+	0.583073i	0.911166	−	0.412039i	$-0.135183\pi$
$389$	19.9186	+	11.5000i	1.00991	+	0.583073i	0.0987463	+	0.995113i	$0.468517\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	3.46410	+	3.46410i	0.174964	+	0.174964i
$393$		0			0
$394$	−10.3923	−	18.0000i	−0.523557	−	0.906827i
$395$	3.23205	−	2.13397i	0.162622	−	0.107372i
$396$		0			0
$397$	−5.46410	−	1.46410i	−0.274235	−	0.0734812i	0.119080	−	0.992885i	$-0.462005\pi$
$397$	−5.46410	−	1.46410i	−0.274235	−	0.0734812i	−0.393316	+	0.919403i	$0.628672\pi$
$398$	25.9808	−	25.9808i	1.30230	−	1.30230i
$399$		0			0
$400$	−12.0000	−	16.0000i	−0.600000	−	0.800000i
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.577241	−	0.816574i	$-0.304129\pi$
$401$	31.5000	−	18.1865i	1.57303	−	0.908192i	0.995794	−	0.0916181i	$-0.0292039\pi$
$402$		0			0
$403$		0			0
$404$	−17.3205	+	10.0000i	−0.861727	+	0.497519i
$405$		0			0
$406$	12.0000			0.595550
$407$	8.66025	+	8.66025i	0.429273	+	0.429273i
$408$		0			0
$409$	16.4545	−	28.5000i	0.813622	−	1.40923i	−0.0966915	−	0.995314i	$-0.530826\pi$
$409$	16.4545	−	28.5000i	0.813622	−	1.40923i	0.910313	−	0.413920i	$-0.135841\pi$
$410$	18.0000	−	6.00000i	0.888957	−	0.296319i
$411$		0			0
$412$	37.8564	−	10.1436i	1.86505	−	0.499739i
$413$	−14.1962	−	3.80385i	−0.698547	−	0.187175i
$414$		0			0
$415$	10.4904	−	11.8301i	0.514953	−	0.580718i
$416$		0			0
$417$		0			0
$418$	19.6410	−	49.6410i	0.960674	−	2.42802i
$419$		−	31.0000i		−	1.51445i	−0.653155	−	0.757225i	$-0.726555\pi$
$419$		−	31.0000i		−	1.51445i	0.653155	−	0.757225i	$-0.273445\pi$
$420$		0			0
$421$	−10.5000	+	6.06218i	−0.511739	+	0.295452i	−0.733548	−	0.679638i	$-0.762137\pi$
$421$	−10.5000	+	6.06218i	−0.511739	+	0.295452i	0.221809	+	0.975090i	$0.428804\pi$
$422$	16.4711	+	61.4711i	0.801803	+	2.99237i
$423$		0			0
$424$	−31.1769	−	18.0000i	−1.51408	−	0.874157i
$425$	−14.0000	−	2.00000i	−0.679100	−	0.0970143i
$426$		0			0
$427$	3.66025	+	13.6603i	0.177132	+	0.661066i
$428$	2.53590	+	9.46410i	0.122577	+	0.457465i
$429$		0			0
$430$	24.2487	−	48.4974i	1.16938	−	2.33875i
$431$	−19.5000	−	11.2583i	−0.939282	−	0.542295i	−0.0495468	−	0.998772i	$-0.515778\pi$
$431$	−19.5000	−	11.2583i	−0.939282	−	0.542295i	−0.889735	+	0.456477i	$0.849111\pi$
$432$		0			0
$433$	−2.53590	−	9.46410i	−0.121867	−	0.454816i	0.877841	−	0.478952i	$-0.158983\pi$
$433$	−2.53590	−	9.46410i	−0.121867	−	0.454816i	−0.999709	+	0.0241361i	$0.992316\pi$
$434$	−31.1769	+	18.0000i	−1.49654	+	0.864028i
$435$		0			0
$436$			6.92820i			0.331801i
$437$	18.2942	−	2.70577i	0.875132	−	0.129435i
$438$		0			0
$439$	14.7224	+	25.5000i	0.702663	+	1.21705i	0.967528	+	0.252763i	$0.0813393\pi$
$439$	14.7224	+	25.5000i	0.702663	+	1.21705i	−0.264865	+	0.964286i	$0.585327\pi$
$440$	−40.9808	−	36.3397i	−1.95368	−	1.73243i
$441$		0			0
$442$		0			0
$443$	8.19615	−	2.19615i	0.389411	−	0.104342i	−0.0588009	−	0.998270i	$-0.518728\pi$
$443$	8.19615	−	2.19615i	0.389411	−	0.104342i	0.448212	+	0.893927i	$0.352061\pi$
$444$		0			0
$445$	10.3923	+	5.19615i	0.492642	+	0.246321i
$446$	33.0000	−	57.1577i	1.56260	−	2.70649i
$447$		0			0
$448$	−16.0000	−	16.0000i	−0.755929	−	0.755929i
$449$	−15.5885			−0.735665			−0.367832	−	0.929892i	$-0.619900\pi$
$449$	−15.5885			−0.735665			−0.367832	+	0.929892i	$0.619900\pi$
$450$		0			0
$451$	15.0000	−	8.66025i	0.706322	−	0.407795i
$452$	9.46410	−	2.53590i	0.445154	−	0.119279i
$453$		0			0
$454$	−25.9808	+	15.0000i	−1.21934	+	0.703985i
$455$		0			0
$456$		0			0
$457$	−10.0000	+	10.0000i	−0.467780	+	0.467780i	−0.901195	−	0.433414i	$-0.857309\pi$
$457$	−10.0000	+	10.0000i	−0.467780	+	0.467780i	0.433414	+	0.901195i	$0.357309\pi$
$458$	−21.2942	−	5.70577i	−0.995014	−	0.266613i
$459$		0			0
$460$	7.60770	−	37.1769i	0.354711	−	1.73338i
$461$	−2.50000	−	4.33013i	−0.116437	−	0.201674i	0.801917	−	0.597436i	$-0.203814\pi$
$461$	−2.50000	−	4.33013i	−0.116437	−	0.201674i	−0.918353	+	0.395762i	$0.870481\pi$
$462$		0			0
$463$	8.00000	+	8.00000i	0.371792	+	0.371792i	0.868129	−	0.496338i	$-0.165322\pi$
$463$	8.00000	+	8.00000i	0.371792	+	0.371792i	−0.496338	+	0.868129i	$0.665322\pi$
$464$	6.92820			0.321634
$465$		0			0
$466$	−27.0000	−	15.5885i	−1.25075	−	0.722121i
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$	13.8564	−	24.0000i	0.639829	−	1.10822i
$470$	2.78461	+	46.3923i	0.128444	+	2.13992i
$471$		0			0
$472$	−24.5885	−	6.58846i	−1.13178	−	0.303258i
$473$	12.8109	−	47.8109i	0.589045	−	2.19835i
$474$		0			0
$475$	−21.7942	+	0.107695i	−0.999988	+	0.00494139i
$476$	32.0000			1.46672
$477$		0			0
$478$	−26.0263	−	6.97372i	−1.19041	−	0.318971i
$479$	−11.2583	−	6.50000i	−0.514406	−	0.296993i	0.220237	−	0.975446i	$-0.429317\pi$
$479$	−11.2583	−	6.50000i	−0.514406	−	0.296993i	−0.734643	+	0.678454i	$0.762650\pi$
$480$		0			0
$481$		0			0
$482$	−21.0000	+	21.0000i	−0.956524	+	0.956524i
$483$		0			0
$484$	−48.4974	−	28.0000i	−2.20443	−	1.27273i
$485$	−16.0981	−	3.29423i	−0.730976	−	0.149583i
$486$		0			0
$487$	6.92820	+	6.92820i	0.313947	+	0.313947i	0.846437	−	0.532490i	$-0.178743\pi$
$487$	6.92820	+	6.92820i	0.313947	+	0.313947i	−0.532490	+	0.846437i	$0.678743\pi$
$488$	6.33975	+	23.6603i	0.286987	+	1.07105i
$489$		0			0
$490$	1.09808	−	5.36603i	0.0496060	−	0.242412i
$491$	18.5000	+	32.0429i	0.834893	+	1.44608i	0.894117	+	0.447833i	$0.147804\pi$
$491$	18.5000	+	32.0429i	0.834893	+	1.44608i	−0.0592240	+	0.998245i	$0.518863\pi$
$492$		0			0
$493$	3.46410	−	3.46410i	0.156015	−	0.156015i
$494$		0			0
$495$		0			0
$496$	−18.0000	+	10.3923i	−0.808224	+	0.466628i
$497$	−3.80385	+	14.1962i	−0.170626	+	0.636784i
$498$		0			0
$499$	−5.19615	+	3.00000i	−0.232612	+	0.134298i	−0.611776	−	0.791031i	$-0.709545\pi$
$499$	−5.19615	+	3.00000i	−0.232612	+	0.134298i	0.379165	+	0.925329i	$0.376211\pi$
$500$	−15.0718	+	42.1051i	−0.674031	+	1.88300i
$501$		0			0
$502$	8.66025	+	8.66025i	0.386526	+	0.386526i
$503$	−13.6603	+	3.66025i	−0.609081	+	0.163203i	−0.550159	−	0.835060i	$-0.685433\pi$
$503$	−13.6603	+	3.66025i	−0.609081	+	0.163203i	−0.0589217	+	0.998263i	$0.518766\pi$
$504$		0			0
$505$	10.0000	+	5.00000i	0.444994	+	0.222497i
$506$		−	51.9615i		−	2.30997i
$507$		0			0
$508$	37.8564	+	10.1436i	1.67961	+	0.450049i
$509$	−15.5885	+	27.0000i	−0.690946	+	1.19675i	0.280582	+	0.959830i	$0.409473\pi$
$509$	−15.5885	+	27.0000i	−0.690946	+	1.19675i	−0.971528	+	0.236924i	$0.923861\pi$
$510$		0			0
$511$	−2.00000	−	3.46410i	−0.0884748	−	0.153243i
$512$	−27.7128	−	27.7128i	−1.22474	−	1.22474i
$513$		0			0
$514$		−	60.0000i		−	2.64649i
$515$	−16.3923	−	14.5359i	−0.722331	−	0.640528i
$516$		0			0
$517$	10.9808	+	40.9808i	0.482933	+	1.80233i
$518$	−4.39230	+	16.3923i	−0.192987	+	0.720237i
$519$		0			0
$520$		0			0
$521$			1.73205i			0.0758825i	0.999280	+	0.0379413i	$0.0120800\pi$
$521$			1.73205i			0.0758825i	−0.999280	+	0.0379413i	$0.987920\pi$
$522$		0			0
$523$	−3.16987	−	11.8301i	−0.138609	−	0.517295i	−0.999957	−	0.00928008i	$-0.997046\pi$
$523$	−3.16987	−	11.8301i	−0.138609	−	0.517295i	0.861348	−	0.508015i	$-0.169621\pi$
$524$		−	40.0000i		−	1.74741i
$525$		0			0
$526$	39.0000	+	22.5167i	1.70048	+	0.981773i
$527$	−3.80385	+	14.1962i	−0.165698	+	0.618394i
$528$		0			0
$529$	−4.33013	+	2.50000i	−0.188266	+	0.108696i
$530$	2.41154	+	40.1769i	0.104751	+	1.74517i
$531$		0			0
$532$	48.7846	−	7.21539i	2.11508	−	0.312827i
$533$		0			0
$534$		0			0
$535$	3.63397	−	4.09808i	0.157110	−	0.177175i
$536$	24.0000	−	41.5692i	1.03664	−	1.79552i
$537$		0			0
$538$	4.09808	−	1.09808i	0.176681	−	0.0473414i
$539$		−	5.00000i		−	0.215365i
$540$		0			0
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	−0.255693	−	0.966758i	$-0.582304\pi$
$541$	16.5000	−	28.5788i	0.709390	−	1.22870i	0.965084	−	0.261942i	$-0.0843630\pi$
$542$	35.4904	−	9.50962i	1.52444	−	0.408473i
$543$		0			0
$544$		0			0
$545$	3.23205	−	2.13397i	0.138446	−	0.0914094i
$546$		0			0
$547$	−35.4904	+	9.50962i	−1.51746	+	0.406602i	−0.918905	−	0.394480i	$-0.870925\pi$
$547$	−35.4904	+	9.50962i	−1.51746	+	0.406602i	−0.598555	+	0.801082i	$0.704258\pi$
$548$	−11.7128	+	43.7128i	−0.500347	+	1.86732i
$549$		0			0
$550$	−8.66025	+	60.6218i	−0.369274	+	2.58492i
$551$	4.50000	−	6.06218i	0.191706	−	0.258257i
$552$		0			0
$553$	4.73205	+	1.26795i	0.201227	+	0.0539187i
$554$	−6.92820	−	12.0000i	−0.294351	−	0.509831i
$555$		0			0
$556$	36.0000	+	62.3538i	1.52674	+	2.64439i
$557$	−12.0788	−	45.0788i	−0.511797	−	1.91005i	−0.400599	−	0.916253i	$-0.631198\pi$
$557$	−12.0788	−	45.0788i	−0.511797	−	1.91005i	−0.111198	−	0.993798i	$-0.535469\pi$
$558$		0			0
$559$		0			0
$560$	5.07180	−	24.7846i	0.214323	−	1.04734i
$561$		0			0
$562$	6.00000	−	6.00000i	0.253095	−	0.253095i
$563$	19.0526	−	19.0526i	0.802970	−	0.802970i	−0.180589	−	0.983559i	$-0.557800\pi$
$563$	19.0526	−	19.0526i	0.802970	−	0.802970i	0.983559	+	0.180589i	$0.0578004\pi$
$564$		0			0
$565$	−4.09808	−	3.63397i	−0.172407	−	0.152882i
$566$	−12.0000	−	6.92820i	−0.504398	−	0.291214i
$567$		0			0
$568$	−6.58846	+	24.5885i	−0.276446	+	1.03171i
$569$	−1.73205			−0.0726113			−0.0363057	−	0.999341i	$-0.511559\pi$
$569$	−1.73205			−0.0726113			−0.0363057	+	0.999341i	$0.511559\pi$
$570$		0			0
$571$	9.00000			0.376638			0.188319	−	0.982108i	$-0.439696\pi$
$571$	9.00000			0.376638			0.188319	+	0.982108i	$0.439696\pi$
$572$		0			0
$573$		0			0
$574$	20.7846	+	12.0000i	0.867533	+	0.500870i
$575$	−19.6865	+	7.90192i	−0.820985	+	0.329533i
$576$		0			0
$577$	−7.00000	+	7.00000i	−0.291414	+	0.291414i	−0.837639	−	0.546225i	$-0.816064\pi$
$577$	−7.00000	+	7.00000i	−0.291414	+	0.291414i	0.546225	+	0.837639i	$0.316064\pi$
$578$	−15.5885	+	15.5885i	−0.648394	+	0.648394i
$579$		0			0
$580$	−8.53590	−	12.9282i	−0.354434	−	0.536814i
$581$	20.0000			0.829740
$582$		0			0
$583$	9.50962	+	35.4904i	0.393848	+	1.46986i
$584$	−3.46410	−	6.00000i	−0.143346	−	0.248282i
$585$		0			0
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	24.5885	+	6.58846i	1.01487	+	0.271935i	0.727665	−	0.685933i	$-0.240606\pi$
$587$	24.5885	+	6.58846i	1.01487	+	0.271935i	0.287210	+	0.957868i	$0.407272\pi$
$588$		0			0
$589$	−2.59808	+	22.5000i	−0.107052	+	0.927096i
$590$	9.00000	+	27.0000i	0.370524	+	1.11157i
$591$		0			0
$592$	−2.53590	+	9.46410i	−0.104225	+	0.388972i
$593$	38.2487	−	10.2487i	1.57069	−	0.420864i	0.634659	−	0.772792i	$-0.281140\pi$
$593$	38.2487	−	10.2487i	1.57069	−	0.420864i	0.936027	+	0.351928i	$0.114474\pi$
$594$		0			0
$595$	−9.85641	−	14.9282i	−0.404073	−	0.611997i
$596$	−76.0000			−3.11308
$597$		0			0
$598$		0			0
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	−0.430784	−	0.902455i	$-0.641763\pi$
$599$	13.8564	−	24.0000i	0.566157	−	0.980613i	0.996941	−	0.0781581i	$-0.0249039\pi$
$600$		0			0
$601$		−	22.5167i		−	0.918474i	−0.888314	−	0.459237i	$-0.848123\pi$
$601$		−	22.5167i		−	0.918474i	0.888314	−	0.459237i	$-0.151877\pi$
$602$	66.2487	−	17.7513i	2.70010	−	0.723489i
$603$		0			0
$604$	−31.1769	+	54.0000i	−1.26857	+	2.19723i
$605$	1.87564	+	31.2487i	0.0762558	+	1.27044i
$606$		0			0
$607$	−3.46410	−	3.46410i	−0.140604	−	0.140604i	0.633302	−	0.773905i	$-0.281699\pi$
$607$	−3.46410	−	3.46410i	−0.140604	−	0.140604i	−0.773905	+	0.633302i	$0.781699\pi$
$608$		0			0
$609$		0			0
$610$	18.1699	−	20.4904i	0.735677	−	0.829631i
$611$		0			0
$612$		0			0
$613$	4.02628	−	15.0263i	0.162620	−	0.606906i	−0.835712	−	0.549168i	$-0.814945\pi$
$613$	4.02628	−	15.0263i	0.162620	−	0.606906i	0.998332	−	0.0577376i	$-0.0183887\pi$
$614$	−25.9808	−	15.0000i	−1.04850	−	0.605351i
$615$		0			0
$616$		−	69.2820i		−	2.79145i
$617$	1.83013	+	6.83013i	0.0736781	+	0.274971i	0.992930	−	0.118699i	$-0.0378722\pi$
$617$	1.83013	+	6.83013i	0.0736781	+	0.274971i	−0.919252	+	0.393669i	$0.871206\pi$
$618$		0			0
$619$		−	30.0000i		−	1.20580i	−0.797816	−	0.602901i	$-0.794011\pi$
$619$		−	30.0000i		−	1.20580i	0.797816	−	0.602901i	$-0.205989\pi$
$620$	41.5692	+	20.7846i	1.66946	+	0.834730i
$621$		0			0
$622$	12.6795	−	47.3205i	0.508401	−	1.89738i
$623$	3.80385	+	14.1962i	0.152398	+	0.568757i
$624$		0			0
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$			69.2820i			2.76907i
$627$		0			0
$628$	−28.0000	−	28.0000i	−1.11732	−	1.11732i
$629$	3.46410	+	6.00000i	0.138123	+	0.239236i
$630$		0			0
$631$	−20.5000	+	35.5070i	−0.816092	+	1.41351i	0.0924489	+	0.995717i	$0.470531\pi$
$631$	−20.5000	+	35.5070i	−0.816092	+	1.41351i	−0.908541	+	0.417796i	$0.862803\pi$
$632$	8.19615	+	2.19615i	0.326025	+	0.0873583i
$633$		0			0
$634$			54.0000i			2.14461i
$635$	−6.92820	−	20.7846i	−0.274937	−	0.824812i
$636$		0			0
$637$		0			0
$638$	−15.0000	−	15.0000i	−0.593856	−	0.593856i
$639$		0			0
$640$	−8.78461	+	42.9282i	−0.347242	+	1.69689i
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	−0.344517	−	0.938780i	$-0.611957\pi$
$641$	7.50000	−	4.33013i	0.296232	−	0.171030i	0.640749	+	0.767750i	$0.278624\pi$
$642$		0			0
$643$	7.32051	−	27.3205i	0.288693	−	1.07742i	−0.657406	−	0.753537i	$-0.728346\pi$
$643$	7.32051	−	27.3205i	0.288693	−	1.07742i	0.946099	−	0.323879i	$-0.104987\pi$
$644$	41.5692	−	24.0000i	1.63806	−	0.945732i
$645$		0			0
$646$	18.0000	−	24.2487i	0.708201	−	0.954053i
$647$	−10.0000	+	10.0000i	−0.393141	+	0.393141i	−0.875805	−	0.482665i	$-0.839669\pi$
$647$	−10.0000	+	10.0000i	−0.393141	+	0.393141i	0.482665	+	0.875805i	$0.339669\pi$
$648$		0			0
$649$	12.9904	+	22.5000i	0.509917	+	0.883202i
$650$		0			0
$651$		0			0
$652$	16.1051	+	60.1051i	0.630725	+	2.35390i
$653$	23.0000	+	23.0000i	0.900060	+	0.900060i	0.995441	−	0.0953813i	$-0.0304070\pi$
$653$	23.0000	+	23.0000i	0.900060	+	0.900060i	−0.0953813	+	0.995441i	$0.530407\pi$
$654$		0			0
$655$	−18.6603	+	12.3205i	−0.729116	+	0.481402i
$656$	12.0000	+	6.92820i	0.468521	+	0.270501i
$657$		0			0
$658$	−41.5692	+	41.5692i	−1.62054	+	1.62054i
$659$	1.73205	−	3.00000i	0.0674711	−	0.116863i	−0.830316	−	0.557292i	$-0.811840\pi$
$659$	1.73205	−	3.00000i	0.0674711	−	0.116863i	0.897787	+	0.440429i	$0.145174\pi$
$660$		0			0
$661$	25.5000	+	14.7224i	0.991835	+	0.572636i	0.905822	−	0.423658i	$-0.139254\pi$
$661$	25.5000	+	14.7224i	0.991835	+	0.572636i	0.0860127	+	0.996294i	$0.472587\pi$
$662$		0			0
$663$		0			0
$664$	34.6410			1.34433
$665$	−18.3923	−	20.5359i	−0.713223	−	0.796348i
$666$		0			0
$667$	1.90192	−	7.09808i	0.0736428	−	0.274839i
$668$	75.7128	+	20.2872i	2.92942	+	0.784935i
$669$		0			0
$670$	−53.5692	+	3.21539i	−2.06956	+	0.124221i
$671$	12.5000	−	21.6506i	0.482557	−	0.835813i
$672$		0			0
$673$	13.8564	−	13.8564i	0.534125	−	0.534125i	−0.387672	−	0.921797i	$-0.626721\pi$
$673$	13.8564	−	13.8564i	0.534125	−	0.534125i	0.921797	+	0.387672i	$0.126721\pi$
$674$	36.3731	+	21.0000i	1.40104	+	0.808890i
$675$		0			0
$676$	−52.0000			−2.00000
$677$	31.1769	+	31.1769i	1.19823	+	1.19823i	0.974697	+	0.223529i	$0.0717577\pi$
$677$	31.1769	+	31.1769i	1.19823	+	1.19823i	0.223529	+	0.974697i	$0.428242\pi$
$678$		0			0
$679$	−10.3923	−	18.0000i	−0.398820	−	0.690777i
$680$	−17.0718	−	25.8564i	−0.654674	−	0.991548i
$681$		0			0
$682$	61.4711	+	16.4711i	2.35385	+	0.630713i
$683$	27.7128	−	27.7128i	1.06040	−	1.06040i	0.0623468	−	0.998055i	$-0.480142\pi$
$683$	27.7128	−	27.7128i	1.06040	−	1.06040i	0.998055	−	0.0623468i	$-0.0198585\pi$
$684$		0			0
$685$	24.0000	−	8.00000i	0.916993	−	0.305664i
$686$	−36.0000	+	20.7846i	−1.37449	+	0.793560i
$687$		0			0
$688$	38.2487	−	10.2487i	1.45822	−	0.390728i
$689$		0			0
$690$		0			0
$691$	15.0000			0.570627			0.285313	−	0.958434i	$-0.407902\pi$
$691$	15.0000			0.570627			0.285313	+	0.958434i	$0.407902\pi$
$692$	13.8564	+	13.8564i	0.526742	+	0.526742i
$693$		0			0
$694$	13.8564	−	24.0000i	0.525982	−	0.911028i
$695$	18.0000	−	36.0000i	0.682779	−	1.36556i
$696$		0			0
$697$	9.46410	−	2.53590i	0.358478	−	0.0960540i
$698$	−42.5885	−	11.4115i	−1.61200	−	0.431933i
$699$		0			0
$700$	−52.4974	+	21.0718i	−1.98422	+	0.796439i
$701$	−11.0000	−	19.0526i	−0.415464	−	0.719605i	0.580013	−	0.814607i	$-0.303048\pi$
$701$	−11.0000	−	19.0526i	−0.415464	−	0.719605i	−0.995477	+	0.0950021i	$0.969714\pi$
$702$		0			0
$703$	6.63397	+	8.36603i	0.250205	+	0.315531i
$704$			40.0000i			1.50756i
$705$		0			0
$706$	−18.0000	+	10.3923i	−0.677439	+	0.391120i
$707$	3.66025	+	13.6603i	0.137658	+	0.513747i
$708$		0			0
$709$	12.9904	+	7.50000i	0.487864	+	0.281668i	0.723688	−	0.690127i	$-0.242446\pi$
$709$	12.9904	+	7.50000i	0.487864	+	0.281668i	−0.235824	+	0.971796i	$0.575779\pi$
$710$	27.0000	−	9.00000i	1.01329	−	0.337764i
$711$		0			0
$712$	6.58846	+	24.5885i	0.246913	+	0.921491i
$713$	5.70577	+	21.2942i	0.213683	+	0.797475i
$714$		0			0
$715$		0			0
$716$	66.0000	+	38.1051i	2.46654	+	1.42406i
$717$		0			0
$718$	21.5551	+	80.4449i	0.804431	+	3.00218i
$719$	6.06218	−	3.50000i	0.226081	−	0.130528i	−0.382682	−	0.923880i	$-0.624999\pi$
$719$	6.06218	−	3.50000i	0.226081	−	0.130528i	0.608763	+	0.793352i	$0.291666\pi$
$720$		0			0
$721$		−	27.7128i		−	1.03208i
$722$	21.9737	−	41.0263i	0.817777	−	1.52684i
$723$		0			0
$724$	−13.8564	−	24.0000i	−0.514969	−	0.891953i
$725$	−3.40192	+	7.96410i	−0.126344	+	0.295779i
$726$		0			0
$727$	−25.9545	−	6.95448i	−0.962598	−	0.257927i	−0.256899	−	0.966438i	$-0.582701\pi$
$727$	−25.9545	−	6.95448i	−0.962598	−	0.257927i	−0.705700	+	0.708511i	$0.749367\pi$
$728$		0			0
$729$		0			0
$730$	−3.46410	+	6.92820i	−0.128212	+	0.256424i
$731$	14.0000	−	24.2487i	0.517809	−	0.896871i
$732$		0			0
$733$	19.0000	+	19.0000i	0.701781	+	0.701781i	0.964793	−	0.263012i	$-0.0847158\pi$
$733$	19.0000	+	19.0000i	0.701781	+	0.701781i	−0.263012	+	0.964793i	$0.584716\pi$
$734$	−76.2102			−2.81297
$735$		0			0
$736$		0			0
$737$	−47.3205	+	12.6795i	−1.74307	+	0.467055i
$738$		0			0
$739$	−16.4545	+	9.50000i	−0.605288	+	0.349463i	−0.771119	−	0.636691i	$-0.780303\pi$
$739$	−16.4545	+	9.50000i	−0.605288	+	0.349463i	0.165831	+	0.986154i	$0.446969\pi$
$740$	20.7846	−	6.92820i	0.764057	−	0.254686i
$741$		0			0
$742$	−36.0000	+	36.0000i	−1.32160	+	1.32160i
$743$	21.2942	+	5.70577i	0.781209	+	0.209324i	0.627318	−	0.778763i	$-0.284153\pi$
$743$	21.2942	+	5.70577i	0.781209	+	0.209324i	0.153892	+	0.988088i	$0.450819\pi$
$744$		0			0
$745$	23.4090	+	35.4545i	0.857638	+	1.29895i
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$		0			0
$748$	−40.0000	−	40.0000i	−1.46254	−	1.46254i
$749$	6.92820			0.253151
$750$		0			0
$751$	7.50000	+	4.33013i	0.273679	+	0.158009i	0.630558	−	0.776142i	$-0.282826\pi$
$751$	7.50000	+	4.33013i	0.273679	+	0.158009i	−0.356879	+	0.934150i	$0.616159\pi$
$752$	−24.0000	+	24.0000i	−0.875190	+	0.875190i
$753$		0			0
$754$		0			0
$755$	34.7942	−	2.08846i	1.26629	−	0.0760067i
$756$		0			0
$757$	−19.1244	−	5.12436i	−0.695087	−	0.186248i	−0.106058	−	0.994360i	$-0.533823\pi$
$757$	−19.1244	−	5.12436i	−0.695087	−	0.186248i	−0.589029	+	0.808112i	$0.700490\pi$
$758$	−20.8634	+	77.8634i	−0.757795	+	2.82813i
$759$		0			0
$760$	−31.8564	−	35.5692i	−1.15555	−	1.29023i
$761$	−34.0000			−1.23250			−0.616250	−	0.787551i	$-0.711349\pi$
$761$	−34.0000			−1.23250			−0.616250	+	0.787551i	$0.711349\pi$
$762$		0			0
$763$	4.73205	+	1.26795i	0.171312	+	0.0459028i
$764$	−24.2487	−	14.0000i	−0.877288	−	0.506502i
$765$		0			0
$766$	−36.0000	+	62.3538i	−1.30073	+	2.25294i
$767$		0			0
$768$		0			0
$769$	18.1865	+	10.5000i	0.655823	+	0.378640i	0.790684	−	0.612225i	$-0.209725\pi$
$769$	18.1865	+	10.5000i	0.655823	+	0.378640i	−0.134860	+	0.990865i	$0.543059\pi$
$770$	−64.6410	+	42.6795i	−2.32950	+	1.53806i
$771$		0			0
$772$	27.7128	+	27.7128i	0.997406	+	0.997406i
$773$	−2.53590	−	9.46410i	−0.0912099	−	0.340400i	0.905208	−	0.424970i	$-0.139715\pi$
$773$	−2.53590	−	9.46410i	−0.0912099	−	0.340400i	−0.996418	+	0.0845694i	$0.973049\pi$
$774$		0			0
$775$	−3.10770	−	25.7942i	−0.111632	−	0.926556i
$776$	−18.0000	−	31.1769i	−0.646162	−	1.11919i
$777$		0			0
$778$	39.8372	−	39.8372i	1.42823	−	1.42823i
$779$	13.8564	−	6.00000i	0.496457	−	0.214972i
$780$		0			0
$781$	22.5000	−	12.9904i	0.805113	−	0.464832i
$782$	7.60770	−	28.3923i	0.272051	−	1.01531i
$783$		0			0
$784$	3.46410	−	2.00000i	0.123718	−	0.0714286i
$785$	−4.43782	+	21.6865i	−0.158393	+	0.774026i
$786$		0			0
$787$	24.2487	+	24.2487i	0.864373	+	0.864373i	0.991843	−	0.127469i	$-0.0406854\pi$
$787$	24.2487	+	24.2487i	0.864373	+	0.864373i	−0.127469	+	0.991843i	$0.540685\pi$
$788$	−32.7846	+	8.78461i	−1.16790	+	0.312939i
$789$		0			0
$790$	−3.00000	−	9.00000i	−0.106735	−	0.320206i
$791$		−	6.92820i		−	0.246339i
$792$		0			0
$793$		0			0
$794$	−6.92820	+	12.0000i	−0.245873	+	0.425864i
$795$		0			0
$796$	−30.0000	−	51.9615i	−1.06332	−	1.84173i
$797$	1.73205	+	1.73205i	0.0613524	+	0.0613524i	0.737117	−	0.675765i	$-0.236187\pi$
$797$	1.73205	+	1.73205i	0.0613524	+	0.0613524i	−0.675765	+	0.737117i	$0.736187\pi$
$798$		0			0
$799$			24.0000i			0.849059i
$800$		0			0
$801$		0			0
$802$	−23.0596	−	86.0596i	−0.814263	−	3.03887i
$803$	−1.83013	+	6.83013i	−0.0645838	+	0.241030i
$804$		0			0
$805$	−24.0000	−	12.0000i	−0.845889	−	0.422944i
$806$		0			0
$807$		0			0
$808$	6.33975	+	23.6603i	0.223031	+	0.832365i
$809$			35.0000i			1.23053i	0.788319	+	0.615267i	$0.210952\pi$
$809$			35.0000i			1.23053i	−0.788319	+	0.615267i	$0.789048\pi$
$810$		0			0
$811$	−34.5000	−	19.9186i	−1.21146	−	0.699436i	−0.248382	−	0.968662i	$-0.579899\pi$
$811$	−34.5000	−	19.9186i	−1.21146	−	0.699436i	−0.963077	+	0.269226i	$0.913232\pi$
$812$	5.07180	−	18.9282i	0.177985	−	0.664250i
$813$		0			0
$814$	25.9808	−	15.0000i	0.910625	−	0.525750i
$815$	23.0788	−	26.0263i	0.808416	−	0.911661i
$816$		0			0
$817$	15.8756	−	40.1244i	0.555418	−	1.40377i
$818$	−57.0000	−	57.0000i	−1.99296	−	1.99296i
$819$		0			0
$820$	−1.85641	−	30.9282i	−0.0648285	−	1.08006i
$821$	−14.5000	+	25.1147i	−0.506053	+	0.876510i	0.493922	+	0.869506i	$0.335563\pi$
$821$	−14.5000	+	25.1147i	−0.506053	+	0.876510i	−0.999975	+	0.00700413i	$0.997770\pi$
$822$		0			0
$823$	2.73205	−	0.732051i	0.0952333	−	0.0255177i	−0.210888	−	0.977510i	$-0.567635\pi$
$823$	2.73205	−	0.732051i	0.0952333	−	0.0255177i	0.306121	+	0.951993i	$0.400969\pi$
$824$		−	48.0000i		−	1.67216i
$825$		0			0
$826$	−18.0000	+	31.1769i	−0.626300	+	1.08478i
$827$	−23.6603	+	6.33975i	−0.822748	+	0.220455i	−0.645547	−	0.763720i	$-0.723371\pi$
$827$	−23.6603	+	6.33975i	−0.822748	+	0.220455i	−0.177200	+	0.984175i	$0.556704\pi$
$828$		0			0
$829$	−17.3205			−0.601566			−0.300783	−	0.953693i	$-0.597248\pi$
$829$	−17.3205			−0.601566			−0.300783	+	0.953693i	$0.597248\pi$
$830$	−21.3397	−	32.3205i	−0.740713	−	1.12186i
$831$		0			0
$832$		0			0
$833$	0.732051	−	2.73205i	0.0253641	−	0.0946600i
$834$		0			0
$835$	−13.8564	−	41.5692i	−0.479521	−	1.43856i
$836$	−70.0000	−	51.9615i	−2.42100	−	1.79713i
$837$		0			0
$838$	−73.3468	−	19.6532i	−2.53372	−	0.678909i
$839$	13.8564	+	24.0000i	0.478376	+	0.828572i	0.999693	−	0.0247915i	$-0.00789218\pi$
$839$	13.8564	+	24.0000i	0.478376	+	0.828572i	−0.521316	+	0.853363i	$0.674559\pi$
$840$		0			0
$841$	13.0000	+	22.5167i	0.448276	+	0.776437i
$842$	7.68653	+	28.6865i	0.264895	+	0.988603i
$843$		0			0
$844$	103.923			3.57718
$845$	16.0167	+	24.2583i	0.550990	+	0.834512i
$846$		0			0
$847$	−28.0000	+	28.0000i	−0.962091	+	0.962091i
$848$	−20.7846	+	20.7846i	−0.713746	+	0.713746i
$849$		0			0
$850$	−13.6077	+	31.8564i	−0.466740	+	1.09267i
$851$	9.00000	+	5.19615i	0.308516	+	0.178122i
$852$		0			0
$853$	6.22243	−	23.2224i	0.213052	−	0.795121i	−0.773791	−	0.633441i	$-0.781642\pi$
$853$	6.22243	−	23.2224i	0.213052	−	0.795121i	0.986843	−	0.161680i	$-0.0516913\pi$
$854$	34.6410			1.18539
$855$		0			0
$856$	12.0000			0.410152
$857$	14.5814	−	54.4186i	0.498092	−	1.85890i	−0.0138842	−	0.999904i	$-0.504420\pi$
$857$	14.5814	−	54.4186i	0.498092	−	1.85890i	0.511976	−	0.859000i	$-0.328914\pi$
$858$		0			0
$859$	45.8993	+	26.5000i	1.56607	+	0.904168i	0.996621	+	0.0821386i	$0.0261750\pi$
$859$	45.8993	+	26.5000i	1.56607	+	0.904168i	0.569445	+	0.822030i	$0.307158\pi$
$860$	−66.2487	−	58.7461i	−2.25906	−	2.00323i
$861$		0			0
$862$	−39.0000	+	39.0000i	−1.32835	+	1.32835i
$863$	−22.5167	+	22.5167i	−0.766476	+	0.766476i	−0.977484	−	0.211008i	$-0.932325\pi$
$863$	−22.5167	+	22.5167i	−0.766476	+	0.766476i	0.211008	+	0.977484i	$0.432325\pi$
$864$		0			0
$865$	2.19615	−	10.7321i	0.0746714	−	0.364901i
$866$	−24.0000			−0.815553
$867$		0			0
$868$	15.2154	+	56.7846i	0.516444	+	1.92740i
$869$	−4.33013	−	7.50000i	−0.146889	−	0.254420i
$870$		0			0
$871$		0			0
$872$	8.19615	+	2.19615i	0.277557	+	0.0743711i
$873$		0			0
$874$	5.19615	−	45.0000i	0.175762	−	1.52215i
$875$	26.0000	+	18.0000i	0.878960	+	0.608511i
$876$		0			0
$877$	1.90192	−	7.09808i	0.0642234	−	0.239685i	−0.926351	−	0.376662i	$-0.877072\pi$
$877$	1.90192	−	7.09808i	0.0642234	−	0.239685i	0.990574	+	0.136977i	$0.0437386\pi$
$878$	69.6673	−	18.6673i	2.35116	−	0.629991i
$879$		0			0
$880$	−37.3205	+	24.6410i	−1.25807	+	0.830648i
$881$	−47.0000			−1.58347			−0.791735	−	0.610865i	$-0.790822\pi$
$881$	−47.0000			−1.58347			−0.791735	+	0.610865i	$0.790822\pi$
$882$		0			0
$883$	−19.1244	+	5.12436i	−0.643586	+	0.172448i	−0.565827	−	0.824524i	$-0.691443\pi$
$883$	−19.1244	+	5.12436i	−0.643586	+	0.172448i	−0.0777587	+	0.996972i	$0.524776\pi$
$884$		0			0
$885$		0			0
$886$		−	20.7846i		−	0.698273i
$887$	−42.5885	+	11.4115i	−1.42998	+	0.383162i	−0.889013	−	0.457882i	$-0.848608\pi$
$887$	−42.5885	+	11.4115i	−1.42998	+	0.383162i	−0.540967	+	0.841044i	$0.681942\pi$
$888$		0			0
$889$	13.8564	−	24.0000i	0.464729	−	0.804934i
$890$	18.8827	−	21.2942i	0.632949	−	0.713784i
$891$		0			0
$892$	−76.2102	−	76.2102i	−2.55171	−	2.55171i
$893$	5.41154	+	36.5885i	0.181090	+	1.22439i
$894$		0			0
$895$	−2.55256	−	42.5263i	−0.0853226	−	1.42150i
$896$	−48.0000	+	27.7128i	−1.60357	+	0.925820i
$897$		0			0
$898$	−9.88269	+	36.8827i	−0.329789	+	1.23079i
$899$	7.79423	+	4.50000i	0.259952	+	0.150083i
$900$		0			0
$901$			20.7846i			0.692436i
$902$	−10.9808	−	40.9808i	−0.365619	−	1.36451i
$903$		0			0
$904$		−	12.0000i		−	0.399114i
$905$	−6.92820	+	13.8564i	−0.230301	+	0.460603i
$906$		0			0
$907$	−1.26795	+	4.73205i	−0.0421016	+	0.157125i	−0.983776	−	0.179399i	$-0.942585\pi$
$907$	−1.26795	+	4.73205i	−0.0421016	+	0.157125i	0.941675	+	0.336524i	$0.109251\pi$
$908$	12.6795	+	47.3205i	0.420784	+	1.57039i
$909$		0			0
$910$		0			0
$911$		−	29.4449i		−	0.975552i	−0.872969	−	0.487776i	$-0.837808\pi$
$911$		−	29.4449i		−	0.975552i	0.872969	−	0.487776i	$-0.162192\pi$
$912$		0			0
$913$	−25.0000	−	25.0000i	−0.827379	−	0.827379i
$914$	17.3205	+	30.0000i	0.572911	+	0.992312i
$915$		0			0
$916$	−18.0000	+	31.1769i	−0.594737	+	1.03011i
$917$	−27.3205	−	7.32051i	−0.902203	−	0.241744i
$918$		0			0
$919$			22.0000i			0.725713i	0.931845	+	0.362857i	$0.118198\pi$
$919$			22.0000i			0.725713i	−0.931845	+	0.362857i	$0.881802\pi$
$920$	−41.5692	−	20.7846i	−1.37050	−	0.685248i
$921$		0			0
$922$	−11.8301	+	3.16987i	−0.389604	+	0.104394i
$923$		0			0
$924$		0			0
$925$	−9.63397	−	7.56218i	−0.316763	−	0.248643i
$926$	24.0000	−	13.8564i	0.788689	−	0.455350i
$927$		0			0
$928$		0			0
$929$	6.06218	−	3.50000i	0.198894	−	0.114831i	−0.397246	−	0.917712i	$-0.630034\pi$
$929$	6.06218	−	3.50000i	0.198894	−	0.114831i	0.596139	+	0.802881i	$0.296701\pi$
$930$		0			0
$931$	0.500000	−	4.33013i	0.0163868	−	0.141914i
$932$	−36.0000	+	36.0000i	−1.17922	+	1.17922i
$933$		0			0
$934$	15.5885	+	27.0000i	0.510070	+	0.883467i
$935$	−6.33975	+	30.9808i	−0.207332	+	1.01318i
$936$		0			0
$937$	6.22243	+	23.2224i	0.203278	+	0.758644i	0.989968	+	0.141295i	$0.0451266\pi$
$937$	6.22243	+	23.2224i	0.203278	+	0.758644i	−0.786690	+	0.617349i	$0.788207\pi$
$938$	−48.0000	−	48.0000i	−1.56726	−	1.56726i
$939$		0			0
$940$	74.3538	+	15.2154i	2.42515	+	0.496271i
$941$	28.5000	+	16.4545i	0.929073	+	0.536401i	0.886518	−	0.462693i	$-0.153117\pi$
$941$	28.5000	+	16.4545i	0.929073	+	0.536401i	0.0425550	+	0.999094i	$0.486450\pi$
$942$		0			0
$943$	10.3923	−	10.3923i	0.338420	−	0.338420i
$944$	−10.3923	+	18.0000i	−0.338241	+	0.585850i
$945$		0			0
$946$	−105.000	−	60.6218i	−3.41384	−	1.97098i
$947$	−5.46410	−	1.46410i	−0.177559	−	0.0475769i	0.168944	−	0.985626i	$-0.445964\pi$
$947$	−5.46410	−	1.46410i	−0.177559	−	0.0475769i	−0.346503	+	0.938049i	$0.612631\pi$
$948$		0			0
$949$		0			0
$950$	−13.5622	+	51.6340i	−0.440015	+	1.67523i
$951$		0			0
$952$	10.1436	−	37.8564i	0.328756	−	1.22693i
$953$	33.1244	+	8.87564i	1.07300	+	0.287510i	0.751726	−	0.659475i	$-0.229221\pi$
$953$	33.1244	+	8.87564i	1.07300	+	0.287510i	0.321277	+	0.946985i	$0.395888\pi$
$954$		0			0
$955$	0.937822	+	15.6244i	0.0303472	+	0.505592i
$956$	−22.0000	+	38.1051i	−0.711531	+	1.23241i
$957$		0			0
$958$	−22.5167	+	22.5167i	−0.727480	+	0.727480i
$959$	27.7128	+	16.0000i	0.894893	+	0.516667i
$960$		0			0
$961$	4.00000			0.129032
$962$		0			0
$963$		0			0
$964$	24.2487	+	42.0000i	0.780998	+	1.35273i
$965$	4.39230	−	21.4641i	0.141393	−	0.690954i
$966$		0			0
$967$	−34.1506	−	9.15064i	−1.09821	−	0.294265i	−0.336175	−	0.941800i	$-0.609133\pi$
$967$	−34.1506	−	9.15064i	−1.09821	−	0.294265i	−0.762036	+	0.647535i	$0.775800\pi$
$968$	−48.4974	+	48.4974i	−1.55877	+	1.55877i
$969$		0			0
$970$	−18.0000	+	36.0000i	−0.577945	+	1.15589i
$971$	45.0000	−	25.9808i	1.44412	−	0.833762i	0.445998	−	0.895034i	$-0.352849\pi$
$971$	45.0000	−	25.9808i	1.44412	−	0.833762i	0.998121	+	0.0612718i	$0.0195156\pi$
$972$		0			0
$973$	49.1769	−	13.1769i	1.57654	−	0.422432i
$974$	20.7846	−	12.0000i	0.665982	−	0.384505i
$975$		0			0
$976$	20.0000			0.640184
$977$	31.1769	+	31.1769i	0.997438	+	0.997438i	0.999997	−	0.00255886i	$-0.000814512\pi$
$977$	31.1769	+	31.1769i	0.997438	+	0.997438i	−0.00255886	+	0.999997i	$0.500815\pi$
$978$		0			0
$979$	12.9904	−	22.5000i	0.415174	−	0.719103i
$980$	−8.00000	−	4.00000i	−0.255551	−	0.127775i
$981$		0			0
$982$	87.5429	−	23.4571i	2.79361	−	0.748545i
$983$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$983$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$984$		0			0
$985$	14.1962	+	12.5885i	0.452327	+	0.401102i
$986$	−6.00000	−	10.3923i	−0.191079	−	0.330958i
$987$		0			0
$988$		0			0
$989$		−	42.0000i		−	1.33552i
$990$		0			0
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	−0.757863	−	0.652413i	$-0.773757\pi$
$991$	−18.0000	+	10.3923i	−0.571789	+	0.330122i	0.186075	+	0.982536i	$0.440423\pi$
$992$		0			0
$993$		0			0
$994$	31.1769	+	18.0000i	0.988872	+	0.570925i
$995$	−15.0000	+	30.0000i	−0.475532	+	0.951064i
$996$		0			0
$997$	−2.92820	−	10.9282i	−0.0927371	−	0.346100i	0.903930	−	0.427681i	$-0.140669\pi$
$997$	−2.92820	−	10.9282i	−0.0927371	−	0.346100i	−0.996667	+	0.0815818i	$0.974003\pi$
$998$	3.80385	+	14.1962i	0.120409	+	0.449371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.cj.d.658.1		4
3.2	odd	2		95.2.l.a.88.1	yes	4
5.2	odd	4	inner	855.2.cj.d.487.1		4
15.2	even	4		95.2.l.a.12.1	yes	4
15.8	even	4		475.2.p.d.107.1		4
15.14	odd	2		475.2.p.d.468.1		4
19.8	odd	6	inner	855.2.cj.d.388.1		4
57.8	even	6		95.2.l.a.8.1	✓	4
95.27	even	12	inner	855.2.cj.d.217.1		4
285.8	odd	12		475.2.p.d.407.1		4
285.122	odd	12		95.2.l.a.27.1	yes	4
285.179	even	6		475.2.p.d.293.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.l.a.8.1	✓	4	57.8	even	6
95.2.l.a.12.1	yes	4	15.2	even	4
95.2.l.a.27.1	yes	4	285.122	odd	12
95.2.l.a.88.1	yes	4	3.2	odd	2
475.2.p.d.107.1		4	15.8	even	4
475.2.p.d.293.1		4	285.179	even	6
475.2.p.d.407.1		4	285.8	odd	12
475.2.p.d.468.1		4	15.14	odd	2
855.2.cj.d.217.1		4	95.27	even	12	inner
855.2.cj.d.388.1		4	19.8	odd	6	inner
855.2.cj.d.487.1		4	5.2	odd	4	inner
855.2.cj.d.658.1		4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.cj (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.633975 - 2.36603i) q^{2} +(-3.46410 - 2.00000i) q^{4} +(0.133975 + 2.23205i) q^{5} +(-2.00000 + 2.00000i) q^{7} +(-3.46410 + 3.46410i) q^{8} +(5.36603 + 1.09808i) q^{10} +5.00000 q^{11} +(3.46410 + 6.00000i) q^{14} +(2.00000 + 3.46410i) q^{16} +(2.73205 + 0.732051i) q^{17} +(4.33013 + 0.500000i) q^{19} +(4.00000 - 8.00000i) q^{20} +(3.16987 - 11.8301i) q^{22} +(4.09808 - 1.09808i) q^{23} +(-4.96410 + 0.598076i) q^{25} +(10.9282 - 2.92820i) q^{28} +(0.866025 - 1.50000i) q^{29} +5.19615i q^{31} +(3.46410 - 6.00000i) q^{34} +(-4.73205 - 4.19615i) q^{35} +(1.73205 + 1.73205i) q^{37} +(3.92820 - 9.92820i) q^{38} +(-8.19615 - 7.26795i) q^{40} +(3.00000 - 1.73205i) q^{41} +(2.56218 - 9.56218i) q^{43} +(-17.3205 - 10.0000i) q^{44} -10.3923i q^{46} +(2.19615 + 8.19615i) q^{47} -1.00000i q^{49} +(-1.73205 + 12.1244i) q^{50} +(1.90192 + 7.09808i) q^{53} +(0.669873 + 11.1603i) q^{55} -13.8564i q^{56} +(-3.00000 - 3.00000i) q^{58} +(2.59808 + 4.50000i) q^{59} +(2.50000 - 4.33013i) q^{61} +(12.2942 + 3.29423i) q^{62} +8.00000i q^{64} +(-9.46410 + 2.53590i) q^{67} +(-8.00000 - 8.00000i) q^{68} +(-12.9282 + 8.53590i) q^{70} +(4.50000 - 2.59808i) q^{71} +(-0.366025 + 1.36603i) q^{73} +(5.19615 - 3.00000i) q^{74} +(-14.0000 - 10.3923i) q^{76} +(-10.0000 + 10.0000i) q^{77} +(-0.866025 - 1.50000i) q^{79} +(-7.46410 + 4.92820i) q^{80} +(-2.19615 - 8.19615i) q^{82} +(-5.00000 - 5.00000i) q^{83} +(-1.26795 + 6.19615i) q^{85} +(-21.0000 - 12.1244i) q^{86} +(-17.3205 + 17.3205i) q^{88} +(2.59808 - 4.50000i) q^{89} +(-16.3923 - 4.39230i) q^{92} +20.7846 q^{94} +(-0.535898 + 9.73205i) q^{95} +(-1.90192 + 7.09808i) q^{97} +(-2.36603 - 0.633975i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} + 4 q^{5} - 8 q^{7} + 18 q^{10} + 20 q^{11} + 8 q^{16} + 4 q^{17} + 16 q^{20} + 30 q^{22} + 6 q^{23} - 6 q^{25} + 16 q^{28} - 12 q^{35} - 12 q^{38} - 12 q^{40} + 12 q^{41} - 14 q^{43} - 12 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) \) 4 * q + 6 * q^2 + 4 * q^5 - 8 * q^7 + 18 * q^10 + 20 * q^11 + 8 * q^16 + 4 * q^17 + 16 * q^20 + 30 * q^22 + 6 * q^23 - 6 * q^25 + 16 * q^28 - 12 * q^35 - 12 * q^38 - 12 * q^40 + 12 * q^41 - 14 * q^43 - 12 * q^47 + 18 * q^53 + 20 * q^55 - 12 * q^58 + 10 * q^61 + 18 * q^62 - 24 * q^67 - 32 * q^68 - 24 * q^70 + 18 * q^71 + 2 * q^73 - 56 * q^76 - 40 * q^77 - 16 * q^80 + 12 * q^82 - 20 * q^83 - 12 * q^85 - 84 * q^86 - 24 * q^92 - 16 * q^95 - 18 * q^97 - 6 * q^98

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