LMFDB - Embedded newform 1216.2.s.h.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1216,2,Mod(31,1216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1216, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 5]))

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

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

chi := DirichletCharacter("1216.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1216 = 2^{6} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1216.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$9.70980888579$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 18 x^{10} - 18 x^{9} + 11 x^{8} - 36 x^{7} + 180 x^{6} - 120 x^{5} + 31 x^{4} + \cdots + 9 $ x^12 - 6x^11 + 18x^10 - 18x^9 + 11x^8 - 36x^7 + 180x^6 - 120x^5 + 31x^4 + 18x^3 + 162x^2 - 54*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$-0.649007 - 0.649007i$ of defining polynomial
Character	$\chi$	$=$	1216.31
Dual form			1216.2.s.h.863.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.121621 - 0.0702177i) q^{3} +(1.50000 - 0.866025i) q^{5} +2.00000i q^{7} +(-1.49014 + 2.58100i) q^{9} +(-2.13057 + 3.69026i) q^{13} +(0.121621 - 0.210653i) q^{15} +(1.99014 + 3.44702i) q^{17} +(-4.31305 + 0.630574i) q^{19} +(0.140435 + 0.243241i) q^{21} +(-6.40996 - 3.70079i) q^{23} +(-1.00000 + 1.73205i) q^{25} +0.839843i q^{27} +(1.99014 - 3.44702i) q^{29} -8.62609 q^{31} +(1.73205 + 3.00000i) q^{35} +7.26115 q^{37} +0.598416i q^{39} +(-6.39172 + 3.69026i) q^{41} +(6.16672 + 10.6811i) q^{43} +5.16199i q^{45} +(0.364862 + 0.210653i) q^{47} +3.00000 q^{49} +(0.484084 + 0.279486i) q^{51} +(5.48028 - 9.49212i) q^{53} +(-0.480278 + 0.379543i) q^{57} +(-1.21381 + 0.700792i) q^{59} +(-1.92131 - 1.10927i) q^{61} +(-5.16199 - 2.98028i) q^{63} +7.38053i q^{65} +(-1.81951 - 1.05050i) q^{67} -1.03944 q^{69} +(-0.970566 - 1.68107i) q^{71} +(2.50000 + 4.33013i) q^{73} +0.280871i q^{75} +(2.70262 + 4.68107i) q^{79} +(-4.41145 - 7.64085i) q^{81} +8.62609 q^{83} +(5.97042 + 3.44702i) q^{85} -0.558972i q^{87} +(14.5491 + 8.39993i) q^{89} +(-7.38053 - 4.26115i) q^{91} +(-1.04911 + 0.605704i) q^{93} +(-5.92348 + 4.68107i) q^{95} +(-6.39172 + 3.69026i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 18 q^{5} + 12 q^{9} + 2 q^{13} - 6 q^{17} + 4 q^{21} - 12 q^{25} - 6 q^{29} + 32 q^{37} + 6 q^{41} + 36 q^{49} + 6 q^{53} + 54 q^{57} - 30 q^{61} - 132 q^{69} + 30 q^{73} - 30 q^{81} - 18 q^{85}+ \cdots + 6 q^{97}+O(q^{100}) $ 12 * q + 18 * q^5 + 12 * q^9 + 2 * q^13 - 6 * q^17 + 4 * q^21 - 12 * q^25 - 6 * q^29 + 32 * q^37 + 6 * q^41 + 36 * q^49 + 6 * q^53 + 54 * q^57 - 30 * q^61 - 132 * q^69 + 30 * q^73 - 30 * q^81 - 18 * q^85 + 78 * q^89 + 84 * q^93 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times$.

$n$	$191$	$705$	$837$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.121621	−	0.0702177i	0.0702177	−	0.0405402i	−0.464480	−	0.885584i	$-0.653759\pi$
$3$	0.121621	−	0.0702177i	0.0702177	−	0.0405402i	0.534698	+	0.845043i	$0.320425\pi$
$4$		0			0
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	−0.125567	−	0.992085i	$-0.540075\pi$
$5$	1.50000	−	0.866025i	0.670820	−	0.387298i	0.796387	+	0.604787i	$0.206742\pi$
$6$		0			0
$7$			2.00000i			0.755929i	0.925820	+	0.377964i	$0.123376\pi$
$7$			2.00000i			0.755929i	−0.925820	+	0.377964i	$0.876624\pi$
$8$		0			0
$9$	−1.49014	+	2.58100i	−0.496713	+	0.860332i
$10$		0			0
$11$		0			0			−	1.00000i	$-0.5\pi$
$11$		0			0				1.00000i	$0.5\pi$
$12$		0			0
$13$	−2.13057	+	3.69026i	−0.590915	+	1.02349i	0.403194	+	0.915114i	$0.367900\pi$
$13$	−2.13057	+	3.69026i	−0.590915	+	1.02349i	−0.994109	+	0.108380i	$0.965434\pi$
$14$		0			0
$15$	0.121621	−	0.210653i	0.0314023	−	0.0543904i
$16$		0			0
$17$	1.99014	+	3.44702i	0.482680	+	0.836026i	0.999802	−	0.0198857i	$-0.00633024\pi$
$17$	1.99014	+	3.44702i	0.482680	+	0.836026i	−0.517123	+	0.855911i	$0.672997\pi$
$18$		0			0
$19$	−4.31305	+	0.630574i	−0.989481	+	0.144664i
$19$	−4.31305	+	0.630574i	−0.989481	+	0.144664i
$20$		0			0
$21$	0.140435	+	0.243241i	0.0306455	+	0.0530796i
$22$		0			0
$23$	−6.40996	−	3.70079i	−1.33657	−	0.771668i	−0.350272	−	0.936648i	$-0.613911\pi$
$23$	−6.40996	−	3.70079i	−1.33657	−	0.771668i	−0.986297	+	0.164980i	$0.947244\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$			0.839843i			0.161628i
$28$		0			0
$29$	1.99014	−	3.44702i	0.369560	−	0.640096i	−0.619937	−	0.784651i	$-0.712842\pi$
$29$	1.99014	−	3.44702i	0.369560	−	0.640096i	0.989497	+	0.144556i	$0.0461753\pi$
$30$		0			0
$31$	−8.62609			−1.54929			−0.774646	−	0.632395i	$-0.782072\pi$
$31$	−8.62609			−1.54929			−0.774646	+	0.632395i	$0.782072\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.73205	+	3.00000i	0.292770	+	0.507093i
$36$		0			0
$37$	7.26115			1.19373			0.596863	−	0.802343i	$-0.296414\pi$
$37$	7.26115			1.19373			0.596863	+	0.802343i	$0.296414\pi$
$38$		0			0
$39$			0.598416i			0.0958232i
$40$		0			0
$41$	−6.39172	+	3.69026i	−0.998219	+	0.576322i	−0.907721	−	0.419574i	$-0.862179\pi$
$41$	−6.39172	+	3.69026i	−0.998219	+	0.576322i	−0.0904984	+	0.995897i	$0.528846\pi$
$42$		0			0
$43$	6.16672	+	10.6811i	0.940416	+	1.62885i	0.764680	+	0.644411i	$0.222897\pi$
$43$	6.16672	+	10.6811i	0.940416	+	1.62885i	0.175736	+	0.984437i	$0.443769\pi$
$44$		0			0
$45$			5.16199i			0.769504i
$46$		0			0
$47$	0.364862	+	0.210653i	0.0532206	+	0.0307269i	0.526374	−	0.850253i	$-0.323551\pi$
$47$	0.364862	+	0.210653i	0.0532206	+	0.0307269i	−0.473154	+	0.880980i	$0.656884\pi$
$48$		0			0
$49$	3.00000			0.428571
$50$		0			0
$51$	0.484084	+	0.279486i	0.0677853	+	0.0391359i
$52$		0			0
$53$	5.48028	−	9.49212i	0.752774	−	1.30384i	−0.193699	−	0.981061i	$-0.562049\pi$
$53$	5.48028	−	9.49212i	0.752774	−	1.30384i	0.946473	−	0.322782i	$-0.104618\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.480278	+	0.379543i	−0.0636144	+	0.0502717i
$58$		0			0
$59$	−1.21381	+	0.700792i	−0.158024	+	0.0912353i	−0.576927	−	0.816796i	$-0.695748\pi$
$59$	−1.21381	+	0.700792i	−0.158024	+	0.0912353i	0.418903	+	0.908031i	$0.362415\pi$
$60$		0			0
$61$	−1.92131	−	1.10927i	−0.245998	−	0.142027i	0.371932	−	0.928260i	$-0.378695\pi$
$61$	−1.92131	−	1.10927i	−0.245998	−	0.142027i	−0.617930	+	0.786233i	$0.712029\pi$
$62$		0			0
$63$	−5.16199	−	2.98028i	−0.650350	−	0.375480i
$64$		0			0
$65$			7.38053i			0.915442i
$66$		0			0
$67$	−1.81951	−	1.05050i	−0.222289	−	0.128338i	0.384721	−	0.923033i	$-0.374298\pi$
$67$	−1.81951	−	1.05050i	−0.222289	−	0.128338i	−0.607010	+	0.794695i	$0.707631\pi$
$68$		0			0
$69$	−1.03944			−0.125134
$70$		0			0
$71$	−0.970566	−	1.68107i	−0.115185	−	0.199506i	0.802669	−	0.596425i	$-0.203413\pi$
$71$	−0.970566	−	1.68107i	−0.115185	−	0.199506i	−0.917854	+	0.396919i	$0.870079\pi$
$72$		0			0
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	0.974424	−	0.224716i	$-0.0721453\pi$
$73$	2.50000	+	4.33013i	0.292603	+	0.506803i	−0.681822	+	0.731519i	$0.738812\pi$
$74$		0			0
$75$			0.280871i			0.0324322i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	2.70262	+	4.68107i	0.304068	+	0.526662i	0.977053	−	0.212994i	$-0.0683216\pi$
$79$	2.70262	+	4.68107i	0.304068	+	0.526662i	−0.672985	+	0.739656i	$0.734988\pi$
$80$		0			0
$81$	−4.41145	−	7.64085i	−0.490161	−	0.848983i
$82$		0			0
$83$	8.62609			0.946837			0.473418	−	0.880838i	$-0.343020\pi$
$83$	8.62609			0.946837			0.473418	+	0.880838i	$0.343020\pi$
$84$		0			0
$85$	5.97042	+	3.44702i	0.647583	+	0.373882i
$86$		0			0
$87$		−	0.558972i		−	0.0599281i
$88$		0			0
$89$	14.5491	+	8.39993i	1.54220	+	0.890391i	0.998699	+	0.0509840i	$0.0162358\pi$
$89$	14.5491	+	8.39993i	1.54220	+	0.890391i	0.543503	+	0.839407i	$0.317098\pi$
$90$		0			0
$91$	−7.38053	−	4.26115i	−0.773689	−	0.446690i
$92$		0			0
$93$	−1.04911	+	0.605704i	−0.108788	+	0.0628086i
$94$		0			0
$95$	−5.92348	+	4.68107i	−0.607736	+	0.480268i
$96$		0			0
$97$	−6.39172	+	3.69026i	−0.648981	+	0.374689i	−0.788066	−	0.615591i	$-0.788917\pi$
$97$	−6.39172	+	3.69026i	−0.648981	+	0.374689i	0.139085	+	0.990280i	$0.455584\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.0295831	−	0.0170798i	−0.00294363	−	0.00169951i	0.498527	−	0.866874i	$-0.333874\pi$
$101$	−0.0295831	−	0.0170798i	−0.00294363	−	0.00169951i	−0.501471	+	0.865174i	$0.667208\pi$
$102$		0			0
$103$	−3.95058			−0.389263			−0.194631	−	0.980876i	$-0.562351\pi$
$103$	−3.95058			−0.389263			−0.194631	+	0.980876i	$0.562351\pi$
$104$		0			0
$105$	0.421306	+	0.243241i	0.0411153	+	0.0237379i
$106$		0			0
$107$		−	7.96056i		−	0.769576i	−0.923005	−	0.384788i	$-0.874275\pi$
$107$		−	7.96056i		−	0.769576i	0.923005	−	0.384788i	$-0.125725\pi$
$108$		0			0
$109$	7.70927	+	13.3528i	0.738414	+	1.27897i	0.953209	+	0.302311i	$0.0977583\pi$
$109$	7.70927	+	13.3528i	0.738414	+	1.27897i	−0.214795	+	0.976659i	$0.568908\pi$
$110$		0			0
$111$	0.883105	−	0.509861i	0.0838206	−	0.0483939i
$112$		0			0
$113$			13.0632i			1.22888i	0.788964	+	0.614439i	$0.210618\pi$
$113$			13.0632i			1.22888i	−0.788964	+	0.614439i	$0.789382\pi$
$114$		0			0
$115$	−12.8199			−1.19546
$116$		0			0
$117$	−6.34970	−	10.9980i	−0.587030	−	1.01677i
$118$		0			0
$119$	−6.89404	+	3.98028i	−0.631976	+	0.364871i
$120$		0			0
$121$	−11.0000			−1.00000
$122$		0			0
$123$	−0.518243	+	0.897624i	−0.0467284	+	0.0809360i
$124$		0			0
$125$			12.1244i			1.08444i
$126$		0			0
$127$	6.40996	−	11.1024i	0.568792	−	0.985177i	−0.427894	−	0.903829i	$-0.640744\pi$
$127$	6.40996	−	11.1024i	0.568792	−	0.985177i	0.996686	−	0.0813476i	$-0.0259224\pi$
$128$		0			0
$129$	1.50000	+	0.866025i	0.132068	+	0.0762493i
$130$		0			0
$131$	8.99096	+	15.5728i	0.785543	+	1.36060i	0.928674	+	0.370897i	$0.120950\pi$
$131$	8.99096	+	15.5728i	0.785543	+	1.36060i	−0.143130	+	0.989704i	$0.545717\pi$
$132$		0			0
$133$	−1.26115	−	8.62609i	−0.109355	−	0.747977i
$134$		0			0
$135$	0.727325	+	1.25976i	0.0625982	+	0.108423i
$136$		0			0
$137$	7.99014	−	13.8393i	0.682644	−	1.18237i	−0.291527	−	0.956562i	$-0.594163\pi$
$137$	7.99014	−	13.8393i	0.682644	−	1.18237i	0.974171	−	0.225811i	$-0.0725032\pi$
$138$		0			0
$139$	2.45938	−	4.25976i	0.208602	−	0.361308i	−0.742673	−	0.669655i	$-0.766442\pi$
$139$	2.45938	−	4.25976i	0.208602	−	0.361308i	0.951274	+	0.308346i	$0.0997755\pi$
$140$		0			0
$141$	0.0591663			0.00498270
$142$		0			0
$143$		0			0
$144$		0			0
$145$		−	6.89404i		−	0.572519i
$146$		0			0
$147$	0.364862	−	0.210653i	0.0300933	−	0.0173744i
$148$		0			0
$149$	−0.0295831	+	0.0170798i	−0.00242355	+	0.00139923i	−0.501211	−	0.865325i	$-0.667112\pi$
$149$	−0.0295831	+	0.0170798i	−0.00242355	+	0.00139923i	0.498788	+	0.866724i	$0.333779\pi$
$150$		0			0
$151$	9.90582			0.806124			0.403062	−	0.915173i	$-0.367946\pi$
$151$	9.90582			0.806124			0.403062	+	0.915173i	$0.367946\pi$
$152$		0			0
$153$	−11.8623			−0.959013
$154$		0			0
$155$	−12.9391	+	7.47042i	−1.03930	+	0.600038i
$156$		0			0
$157$	−16.8621	+	9.73536i	−1.34575	+	0.776966i	−0.987644	−	0.156716i	$-0.949909\pi$
$157$	−16.8621	+	9.73536i	−1.34575	+	0.776966i	−0.358102	+	0.933683i	$0.616576\pi$
$158$		0			0
$159$		−	1.53925i		−	0.122070i
$160$		0			0
$161$	7.40158	−	12.8199i	0.583327	−	1.01035i
$162$		0			0
$163$	−2.97762			−0.233225			−0.116613	−	0.993177i	$-0.537204\pi$
$163$	−2.97762			−0.233225			−0.116613	+	0.993177i	$0.537204\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	0.121621	−	0.210653i	0.00941128	−	0.0163008i	−0.861281	−	0.508128i	$-0.830338\pi$
$167$	0.121621	−	0.210653i	0.00941128	−	0.0163008i	0.870693	+	0.491827i	$0.163671\pi$
$168$		0			0
$169$	−2.57869	−	4.46643i	−0.198361	−	0.343571i
$170$		0			0
$171$	4.79953	−	12.0716i	0.367029	−	0.923139i
$172$		0			0
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	0.803354	−	0.595502i	$-0.203047\pi$
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	−0.917397	+	0.397974i	$0.869713\pi$
$174$		0			0
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$		0			0
$177$	−0.0984160	+	0.170461i	−0.00739740	+	0.0128127i
$178$		0			0
$179$		−	11.1574i		−	0.833942i	−0.908920	−	0.416971i	$-0.863092\pi$
$179$		−	11.1574i		−	0.833942i	0.908920	−	0.416971i	$-0.136908\pi$
$180$		0			0
$181$	5.76115	−	9.97860i	0.428223	−	0.741704i	−0.568493	−	0.822688i	$-0.692473\pi$
$181$	5.76115	−	9.97860i	0.428223	−	0.741704i	0.996715	+	0.0809848i	$0.0258065\pi$
$182$		0			0
$183$	−0.311561			−0.0230312
$184$		0			0
$185$	10.8917	−	6.28834i	0.800775	−	0.462328i
$186$		0			0
$187$		0			0
$188$		0			0
$189$	−1.67969			−0.122179
$190$		0			0
$191$			13.1179i			0.949181i	0.880207	+	0.474591i	$0.157404\pi$
$191$			13.1179i			0.949181i	−0.880207	+	0.474591i	$0.842596\pi$
$192$		0			0
$193$	2.34261	−	1.35251i	0.168625	−	0.0973556i	−0.413312	−	0.910589i	$-0.635628\pi$
$193$	2.34261	−	1.35251i	0.168625	−	0.0973556i	0.581937	+	0.813234i	$0.302295\pi$
$194$		0			0
$195$	0.518243	+	0.897624i	0.0371122	+	0.0642802i
$196$		0			0
$197$		−	12.0902i		−	0.861391i	−0.902497	−	0.430695i	$-0.858268\pi$
$197$		−	12.0902i		−	0.861391i	0.902497	−	0.430695i	$-0.141732\pi$
$198$		0			0
$199$	−0.637465	−	0.368041i	−0.0451887	−	0.0260897i	0.477235	−	0.878775i	$-0.341639\pi$
$199$	−0.637465	−	0.368041i	−0.0451887	−	0.0260897i	−0.522424	+	0.852686i	$0.674972\pi$
$200$		0			0
$201$	−0.295053			−0.0208115
$202$		0			0
$203$	6.89404	+	3.98028i	0.483867	+	0.279361i
$204$		0			0
$205$	−6.39172	+	11.0708i	−0.446417	+	0.773217i
$206$		0			0
$207$	19.1035	−	11.0294i	1.32778	−	0.766596i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	18.1377	−	10.4718i	1.24865	−	0.720909i	0.277810	−	0.960636i	$-0.410391\pi$
$211$	18.1377	−	10.4718i	1.24865	−	0.720909i	0.970840	+	0.239727i	$0.0770581\pi$
$212$		0			0
$213$	−0.236082	−	0.136302i	−0.0161760	−	0.00933925i
$214$		0			0
$215$	18.5002	+	10.6811i	1.26170	+	0.728443i
$216$		0			0
$217$		−	17.2522i		−	1.17115i
$218$		0			0
$219$	0.608103	+	0.351088i	0.0410918	+	0.0237244i
$220$		0			0
$221$	−16.9606			−1.14089
$222$		0			0
$223$	5.52685	+	9.57279i	0.370106	+	0.641042i	0.989581	−	0.143974i	$-0.0459882\pi$
$223$	5.52685	+	9.57279i	0.370106	+	0.641042i	−0.619476	+	0.785016i	$0.712655\pi$
$224$		0			0
$225$	−2.98028	−	5.16199i	−0.198685	−	0.344133i
$226$		0			0
$227$		−	19.9606i		−	1.32483i	−0.749138	−	0.662414i	$-0.769532\pi$
$227$		−	19.9606i		−	1.32483i	0.749138	−	0.662414i	$-0.230468\pi$
$228$		0			0
$229$		−	11.1172i		−	0.734647i	−0.930093	−	0.367324i	$-0.880274\pi$
$229$		−	11.1172i		−	0.734647i	0.930093	−	0.367324i	$-0.119726\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.39172	+	11.0708i	0.418736	+	0.725271i	0.995813	−	0.0914183i	$-0.0291400\pi$
$233$	6.39172	+	11.0708i	0.418736	+	0.725271i	−0.577077	+	0.816690i	$0.695807\pi$
$234$		0			0
$235$	0.729724			0.0476019
$236$		0			0
$237$	0.657388	+	0.379543i	0.0427019	+	0.0246540i
$238$		0			0
$239$			17.7440i			1.14776i	0.818938	+	0.573882i	$0.194563\pi$
$239$			17.7440i			1.14776i	−0.818938	+	0.573882i	$0.805437\pi$
$240$		0			0
$241$	−3.81303	−	2.20145i	−0.245619	−	0.141808i	0.372138	−	0.928178i	$-0.378625\pi$
$241$	−3.81303	−	2.20145i	−0.245619	−	0.141808i	−0.617756	+	0.786369i	$0.711958\pi$
$242$		0			0
$243$	−3.25502	−	1.87929i	−0.208810	−	0.120556i
$244$		0			0
$245$	4.50000	−	2.59808i	0.287494	−	0.165985i
$246$		0			0
$247$	6.86228	−	17.2598i	0.436637	−	1.09821i
$248$		0			0
$249$	1.04911	−	0.605704i	0.0664847	−	0.0383850i
$250$		0			0
$251$	−8.14201	+	14.1024i	−0.513919	+	0.890134i	0.485950	+	0.873986i	$0.338474\pi$
$251$	−8.14201	+	14.1024i	−0.513919	+	0.890134i	−0.999870	+	0.0161477i	$0.994860\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	0.968168			0.0606290
$256$		0			0
$257$	−13.0787	−	7.55099i	−0.815827	−	0.471018i	0.0331486	−	0.999450i	$-0.489447\pi$
$257$	−13.0787	−	7.55099i	−0.815827	−	0.471018i	−0.848975	+	0.528433i	$0.822780\pi$
$258$		0			0
$259$			14.5223i			0.902372i
$260$		0			0
$261$	5.93117	+	10.2731i	0.367130	+	0.635888i
$262$		0			0
$263$	10.0274	−	5.78935i	0.618319	−	0.356986i	−0.157895	−	0.987456i	$-0.550471\pi$
$263$	10.0274	−	5.78935i	0.618319	−	0.356986i	0.776214	+	0.630469i	$0.217138\pi$
$264$		0			0
$265$		−	18.9842i		−	1.16619i
$266$		0			0
$267$	2.35930			0.144387
$268$		0			0
$269$	−9.39172	−	16.2669i	−0.572623	−	0.991813i	−0.996295	−	0.0859972i	$-0.972592\pi$
$269$	−9.39172	−	16.2669i	−0.572623	−	0.991813i	0.423672	−	0.905816i	$-0.360741\pi$
$270$		0			0
$271$	24.5111	−	14.1515i	1.48894	−	0.859642i	0.489023	−	0.872271i	$-0.337354\pi$
$271$	24.5111	−	14.1515i	1.48894	−	0.859642i	0.999920	+	0.0126295i	$0.00402019\pi$
$272$		0			0
$273$	−1.19683			−0.0724356
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	3.15734i		−	0.189706i	−0.995491	−	0.0948530i	$-0.969762\pi$
$277$		−	3.15734i		−	0.189706i	0.995491	−	0.0948530i	$-0.0302381\pi$
$278$		0			0
$279$	12.8541	−	22.2639i	0.769554	−	1.33291i
$280$		0			0
$281$	−5.34261	−	3.08456i	−0.318714	−	0.184009i	0.332105	−	0.943242i	$-0.392241\pi$
$281$	−5.34261	−	3.08456i	−0.318714	−	0.184009i	−0.650819	+	0.759233i	$0.725574\pi$
$282$		0			0
$283$	−7.25891	−	12.5728i	−0.431497	−	0.747375i	0.565505	−	0.824745i	$-0.308681\pi$
$283$	−7.25891	−	12.5728i	−0.431497	−	0.747375i	−0.997002	+	0.0773697i	$0.975348\pi$
$284$		0			0
$285$	−0.391723	+	0.985247i	−0.0232037	+	0.0583610i
$286$		0			0
$287$	−7.38053	−	12.7834i	−0.435659	−	0.754583i
$288$		0			0
$289$	0.578694	−	1.00233i	0.0340408	−	0.0589604i
$290$		0			0
$291$	−0.518243	+	0.897624i	−0.0303800	+	0.0526196i
$292$		0			0
$293$	30.5866			1.78689			0.893445	−	0.449174i	$-0.148282\pi$
$293$	30.5866			1.78689			0.893445	+	0.449174i	$0.148282\pi$
$294$		0			0
$295$	−1.21381	+	2.10238i	−0.0706706	+	0.122405i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	27.3138	−	15.7696i	1.57960	−	0.911981i
$300$		0			0
$301$	−21.3621	+	12.3334i	−1.23129	+	0.710888i
$302$		0			0
$303$	−0.00479723			−0.000275593
$304$		0			0
$305$	−3.84261			−0.220027
$306$		0			0
$307$	−14.8611	+	8.58008i	−0.848170	+	0.489691i	−0.860033	−	0.510239i	$-0.829557\pi$
$307$	−14.8611	+	8.58008i	−0.848170	+	0.489691i	0.0118632	+	0.999930i	$0.496224\pi$
$308$		0			0
$309$	−0.480472	+	0.277401i	−0.0273331	+	0.0157808i
$310$		0			0
$311$			29.7440i			1.68663i	0.537421	+	0.843314i	$0.319398\pi$
$311$			29.7440i			1.68663i	−0.537421	+	0.843314i	$0.680602\pi$
$312$		0			0
$313$	5.81303	−	10.0685i	0.328572	−	0.569103i	−0.653657	−	0.756791i	$-0.726766\pi$
$313$	5.81303	−	10.0685i	0.328572	−	0.569103i	0.982229	+	0.187688i	$0.0600994\pi$
$314$		0			0
$315$	−10.3240			−0.581691
$316$		0			0
$317$	−8.41145	+	14.5691i	−0.472434	+	0.818279i	−0.999502	−	0.0315434i	$-0.989958\pi$
$317$	−8.41145	+	14.5691i	−0.472434	+	0.818279i	0.527069	+	0.849823i	$0.323291\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.558972	−	0.968168i	−0.0311988	−	0.0540378i
$322$		0			0
$323$	−10.7572	−	13.6122i	−0.598545	−	0.757405i
$324$		0			0
$325$	−4.26115	−	7.38053i	−0.236366	−	0.409398i
$326$		0			0
$327$	1.87521	+	1.08265i	0.103699	+	0.0598709i
$328$		0			0
$329$	−0.421306	+	0.729724i	−0.0232274	+	0.0402310i
$330$		0			0
$331$		−	33.3594i		−	1.83360i	−0.399350	−	0.916798i	$-0.630764\pi$
$331$		−	33.3594i		−	1.83360i	0.399350	−	0.916798i	$-0.369236\pi$
$332$		0			0
$333$	−10.8201	+	18.7410i	−0.592939	+	1.02700i
$334$		0			0
$335$	−3.63902			−0.198821
$336$		0			0
$337$	−11.5491	+	6.66788i	−0.629120	+	0.363223i	−0.780411	−	0.625267i	$-0.784990\pi$
$337$	−11.5491	+	6.66788i	−0.629120	+	0.363223i	0.151291	+	0.988489i	$0.451657\pi$
$338$		0			0
$339$	0.917265	+	1.58875i	0.0498190	+	0.0862890i
$340$		0			0
$341$		0			0
$342$		0			0
$343$			20.0000i			1.07990i
$344$		0			0
$345$	−1.55917	+	0.900185i	−0.0839427	+	0.0484643i
$346$		0			0
$347$	3.98235	+	6.89762i	0.213783	+	0.370284i	0.952896	−	0.303299i	$-0.0980880\pi$
$347$	3.98235	+	6.89762i	0.213783	+	0.370284i	−0.739112	+	0.673582i	$0.764755\pi$
$348$		0			0
$349$		−	6.13496i		−	0.328397i	−0.986427	−	0.164198i	$-0.947496\pi$
$349$		−	6.13496i		−	0.328397i	0.986427	−	0.164198i	$-0.0525037\pi$
$350$		0			0
$351$	−3.09924	−	1.78935i	−0.165425	−	0.0955083i
$352$		0			0
$353$	12.9803			0.690870			0.345435	−	0.938443i	$-0.387731\pi$
$353$	12.9803			0.690870			0.345435	+	0.938443i	$0.387731\pi$
$354$		0			0
$355$	−2.91170	−	1.68107i	−0.154537	−	0.0892219i
$356$		0			0
$357$	−0.558972	+	0.968168i	−0.0295839	+	0.0512409i
$358$		0			0
$359$	−23.4746	+	13.5531i	−1.23894	+	0.715304i	−0.968878	−	0.247539i	$-0.920378\pi$
$359$	−23.4746	+	13.5531i	−1.23894	+	0.715304i	−0.270064	+	0.962842i	$0.587045\pi$
$360$		0			0
$361$	18.2048	−	5.43939i	0.958145	−	0.286284i
$362$		0			0
$363$	−1.33783	+	0.772395i	−0.0702177	+	0.0405402i
$364$		0			0
$365$	7.50000	+	4.33013i	0.392568	+	0.226649i
$366$		0			0
$367$	3.82896	+	2.21065i	0.199870	+	0.115395i	0.596595	−	0.802542i	$-0.296520\pi$
$367$	3.82896	+	2.21065i	0.199870	+	0.115395i	−0.396725	+	0.917938i	$0.629853\pi$
$368$		0			0
$369$		−	21.9960i		−	1.14507i
$370$		0			0
$371$	18.9842	+	10.9606i	0.985613	+	0.569044i
$372$		0			0
$373$	−13.6797			−0.708307			−0.354154	−	0.935187i	$-0.615231\pi$
$373$	−13.6797			−0.708307			−0.354154	+	0.935187i	$0.615231\pi$
$374$		0			0
$375$	0.851344	+	1.47457i	0.0439632	+	0.0761465i
$376$		0			0
$377$	8.48028	+	14.6883i	0.436757	+	0.756485i
$378$		0			0
$379$			23.0446i			1.18372i	0.806040	+	0.591861i	$0.201606\pi$
$379$			23.0446i			1.18372i	−0.806040	+	0.591861i	$0.798394\pi$
$380$		0			0
$381$		−	1.80037i		−	0.0922358i
$382$		0			0
$383$	3.98235	+	6.89762i	0.203488	+	0.352452i	0.949650	−	0.313313i	$-0.101439\pi$
$383$	3.98235	+	6.89762i	0.203488	+	0.352452i	−0.746162	+	0.665765i	$0.768105\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−36.7571			−1.86847
$388$		0			0
$389$	−17.7048	−	10.2218i	−0.897667	−	0.518268i	−0.0212242	−	0.999775i	$-0.506756\pi$
$389$	−17.7048	−	10.2218i	−0.897667	−	0.518268i	−0.876442	+	0.481507i	$0.840090\pi$
$390$		0			0
$391$		−	29.4604i		−	1.48987i
$392$		0			0
$393$	2.18697	+	1.26265i	0.110318	+	0.0636922i
$394$		0			0
$395$	8.10785	+	4.68107i	0.407950	+	0.235530i
$396$		0			0
$397$	−13.0787	+	7.55099i	−0.656401	+	0.378973i	−0.790904	−	0.611940i	$-0.790389\pi$
$397$	−13.0787	+	7.55099i	−0.656401	+	0.378973i	0.134503	+	0.990913i	$0.457056\pi$
$398$		0			0
$399$	−0.759086	−	0.960556i	−0.0380018	−	0.0480879i
$400$		0			0
$401$	26.9113	−	15.5372i	1.34388	−	0.775892i	0.356509	−	0.934292i	$-0.383967\pi$
$401$	26.9113	−	15.5372i	1.34388	−	0.775892i	0.987375	+	0.158400i	$0.0506337\pi$
$402$		0			0
$403$	18.3785	−	31.8326i	0.915500	−	1.58569i
$404$		0			0
$405$	−13.2343	−	7.64085i	−0.657619	−	0.379677i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	1.13786	+	0.656944i	0.0562636	+	0.0324838i	0.527868	−	0.849326i	$-0.322992\pi$
$409$	1.13786	+	0.656944i	0.0562636	+	0.0324838i	−0.471604	+	0.881810i	$0.656325\pi$
$410$		0			0
$411$		−	2.24420i		−	0.110698i
$412$		0			0
$413$	−1.40158	−	2.42761i	−0.0689674	−	0.119455i
$414$		0			0
$415$	12.9391	−	7.47042i	0.635157	−	0.366708i
$416$		0			0
$417$		−	0.690767i		−	0.0338270i
$418$		0			0
$419$	−15.2475			−0.744891			−0.372445	−	0.928054i	$-0.621481\pi$
$419$	−15.2475			−0.744891			−0.372445	+	0.928054i	$0.621481\pi$
$420$		0			0
$421$	−6.23885	−	10.8060i	−0.304063	−	0.526653i	0.672989	−	0.739652i	$-0.265010\pi$
$421$	−6.23885	−	10.8060i	−0.304063	−	0.526653i	−0.977052	+	0.213000i	$0.931677\pi$
$422$		0			0
$423$	−1.08739	+	0.627805i	−0.0528707	+	0.0305249i
$424$		0			0
$425$	−7.96056			−0.386144
$426$		0			0
$427$	2.21853	−	3.84261i	0.107362	−	0.185957i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.8175	+	22.2006i	−0.617398	+	1.06937i	0.372560	+	0.928008i	$0.378480\pi$
$431$	−12.8175	+	22.2006i	−0.617398	+	1.06937i	−0.989959	+	0.141357i	$0.954853\pi$
$432$		0			0
$433$	−2.76392	−	1.59575i	−0.132825	−	0.0766868i	0.432115	−	0.901819i	$-0.357767\pi$
$433$	−2.76392	−	1.59575i	−0.132825	−	0.0766868i	−0.564940	+	0.825132i	$0.691101\pi$
$434$		0			0
$435$	−0.484084	−	0.838458i	−0.0232100	−	0.0402010i
$436$		0			0
$437$	29.9801	+	11.9197i	1.43414	+	0.570198i
$438$		0			0
$439$	−1.24797	−	2.16154i	−0.0595622	−	0.103165i	0.834707	−	0.550695i	$-0.185637\pi$
$439$	−1.24797	−	2.16154i	−0.0595622	−	0.103165i	−0.894269	+	0.447530i	$0.852304\pi$
$440$		0			0
$441$	−4.47042	+	7.74299i	−0.212877	+	0.368714i
$442$		0			0
$443$	−14.3063	+	24.7793i	−0.679714	+	1.17730i	0.295353	+	0.955388i	$0.404563\pi$
$443$	−14.3063	+	24.7793i	−0.679714	+	1.17730i	−0.975067	+	0.221911i	$0.928770\pi$
$444$		0			0
$445$	29.0982			1.37939
$446$		0			0
$447$	−0.00239861	+	0.00415452i	−0.000113450	+	0.000196502i
$448$		0			0
$449$			5.58016i			0.263344i	0.991293	+	0.131672i	$0.0420345\pi$
$449$			5.58016i			0.263344i	−0.991293	+	0.131672i	$0.957965\pi$
$450$		0			0
$451$		0			0
$452$		0			0
$453$	1.20475	−	0.695564i	0.0566042	−	0.0326804i
$454$		0			0
$455$	−14.7611			−0.692009
$456$		0			0
$457$	−38.7243			−1.81145			−0.905723	−	0.423871i	$-0.860671\pi$
$457$	−38.7243			−1.81145			−0.905723	+	0.423871i	$0.860671\pi$
$458$		0			0
$459$	−2.89496	+	1.67140i	−0.135125	+	0.0780144i
$460$		0			0
$461$	13.1752	−	7.60669i	0.613629	−	0.354279i	−0.160756	−	0.986994i	$-0.551393\pi$
$461$	13.1752	−	7.60669i	0.613629	−	0.354279i	0.774384	+	0.632716i	$0.218060\pi$
$462$		0			0
$463$		−	11.7834i		−	0.547623i	−0.961783	−	0.273812i	$-0.911716\pi$
$463$		−	11.7834i		−	0.547623i	0.961783	−	0.273812i	$-0.0882845\pi$
$464$		0			0
$465$	−1.04911	+	1.81711i	−0.0486513	+	0.0842666i
$466$		0			0
$467$	36.0321			1.66737			0.833684	−	0.552241i	$-0.186227\pi$
$467$	36.0321			1.66737			0.833684	+	0.552241i	$0.186227\pi$
$468$		0			0
$469$	2.10099	−	3.63902i	0.0970148	−	0.168034i
$470$		0			0
$471$	−1.36719	+	2.36804i	−0.0629967	+	0.109114i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	3.22086	−	8.10099i	0.147783	−	0.371699i
$476$		0			0
$477$	16.3328	+	28.2892i	0.747825	+	1.29527i
$478$		0			0
$479$	9.29772	+	5.36804i	0.424824	+	0.245272i	0.697139	−	0.716936i	$-0.254456\pi$
$479$	9.29772	+	5.36804i	0.424824	+	0.245272i	−0.272315	+	0.962208i	$0.587789\pi$
$480$		0			0
$481$	−15.4704	+	26.7955i	−0.705390	+	1.22177i
$482$		0			0
$483$		−	2.07889i		−	0.0945927i
$484$		0			0
$485$	−6.39172	+	11.0708i	−0.290233	+	0.502699i
$486$		0			0
$487$	28.5491			1.29368			0.646842	−	0.762624i	$-0.276089\pi$
$487$	28.5491			1.29368			0.646842	+	0.762624i	$0.276089\pi$
$488$		0			0
$489$	−0.362140	+	0.209082i	−0.0163765	+	0.00945499i
$490$		0			0
$491$	17.6171	+	30.5136i	0.795046	+	1.37706i	0.922810	+	0.385256i	$0.125887\pi$
$491$	17.6171	+	30.5136i	0.795046	+	1.37706i	−0.127763	+	0.991805i	$0.540780\pi$
$492$		0			0
$493$	15.8426			0.713515
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.36214	−	1.94113i	0.150813	−	0.0870717i
$498$		0			0
$499$	6.16672	+	10.6811i	0.276060	+	0.478150i	0.970402	−	0.241495i	$-0.0776377\pi$
$499$	6.16672	+	10.6811i	0.276060	+	0.478150i	−0.694342	+	0.719645i	$0.744304\pi$
$500$		0			0
$501$		−	0.0341597i		−	0.00152614i
$502$		0			0
$503$	−20.1980	−	11.6613i	−0.900586	−	0.519954i	−0.0231960	−	0.999731i	$-0.507384\pi$
$503$	−20.1980	−	11.6613i	−0.900586	−	0.519954i	−0.877390	+	0.479777i	$0.840718\pi$
$504$		0			0
$505$	−0.0591663			−0.00263286
$506$		0			0
$507$	−0.627245	−	0.362140i	−0.0278569	−	0.0160832i
$508$		0			0
$509$	17.5491	−	30.3960i	0.777851	−	1.34728i	−0.155328	−	0.987863i	$-0.549643\pi$
$509$	17.5491	−	30.3960i	0.777851	−	1.34728i	0.933178	−	0.359414i	$-0.117023\pi$
$510$		0			0
$511$	−8.66025	+	5.00000i	−0.383107	+	0.221187i
$512$		0			0
$513$	−0.529583	−	3.62228i	−0.0233817	−	0.159928i
$514$		0			0
$515$	−5.92588	+	3.42131i	−0.261125	+	0.150761i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−0.364862	−	0.210653i	−0.0160157	−	0.00924664i
$520$		0			0
$521$			29.5221i			1.29339i	0.762750	+	0.646693i	$0.223849\pi$
$521$			29.5221i			1.29339i	−0.762750	+	0.646693i	$0.776151\pi$
$522$		0			0
$523$	−1.19227	−	0.688356i	−0.0521342	−	0.0300997i	0.473706	−	0.880683i	$-0.342916\pi$
$523$	−1.19227	−	0.688356i	−0.0521342	−	0.0300997i	−0.525841	+	0.850583i	$0.676249\pi$
$524$		0			0
$525$	−0.561741			−0.0245164
$526$		0			0
$527$	−17.1671	−	29.7343i	−0.747812	−	1.29525i
$528$		0			0
$529$	15.8917	+	27.5253i	0.690944	+	1.19675i
$530$		0			0
$531$		−	4.17711i		−	0.181271i
$532$		0			0
$533$		−	31.4495i		−	1.36223i
$534$		0			0
$535$	−6.89404	−	11.9408i	−0.298055	−	0.516247i
$536$		0			0
$537$	−0.783446	−	1.35697i	−0.0338082	−	0.0585575i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	0.450889	+	0.260321i	0.0193852	+	0.0111921i	0.509661	−	0.860375i	$-0.329771\pi$
$541$	0.450889	+	0.260321i	0.0193852	+	0.0111921i	−0.490276	+	0.871567i	$0.663104\pi$
$542$		0			0
$543$		−	1.61814i		−	0.0694410i
$544$		0			0
$545$	23.1278	+	13.3528i	0.990686	+	0.571973i
$546$		0			0
$547$	−9.66498	−	5.58008i	−0.413245	−	0.238587i	0.278938	−	0.960309i	$-0.410018\pi$
$547$	−9.66498	−	5.58008i	−0.413245	−	0.238587i	−0.692183	+	0.721722i	$0.743351\pi$
$548$		0			0
$549$	5.72603	−	3.30592i	0.244381	−	0.141093i
$550$		0			0
$551$	−6.40996	+	16.1221i	−0.273073	+	0.686824i
$552$		0			0
$553$	−9.36214	+	5.40523i	−0.398119	+	0.229854i
$554$		0			0
$555$	0.883105	−	1.52958i	0.0374857	−	0.0649272i
$556$		0			0
$557$	−27.1769	−	15.6906i	−1.15152	−	0.664832i	−0.202265	−	0.979331i	$-0.564830\pi$
$557$	−27.1769	−	15.6906i	−1.15152	−	0.664832i	−0.949258	+	0.314499i	$0.898164\pi$
$558$		0			0
$559$	−52.5546			−2.22282
$560$		0			0
$561$		0			0
$562$		0			0
$563$			42.7243i			1.80061i	0.435256	+	0.900307i	$0.356658\pi$
$563$			42.7243i			1.80061i	−0.435256	+	0.900307i	$0.643342\pi$
$564$		0			0
$565$	11.3130	+	19.5947i	0.475943	+	0.824357i
$566$		0			0
$567$	15.2817	−	8.82289i	0.641771	−	0.370527i
$568$		0			0
$569$			19.8547i			0.832353i	0.909284	+	0.416177i	$0.136630\pi$
$569$			19.8547i			0.832353i	−0.909284	+	0.416177i	$0.863370\pi$
$570$		0			0
$571$	−39.0098			−1.63251			−0.816254	−	0.577693i	$-0.803953\pi$
$571$	−39.0098			−1.63251			−0.816254	+	0.577693i	$0.803953\pi$
$572$		0			0
$573$	0.921112	+	1.59541i	0.0384800	+	0.0666493i
$574$		0			0
$575$	12.8199	−	7.40158i	0.534628	−	0.308667i
$576$		0			0
$577$	−12.0982			−0.503656			−0.251828	−	0.967772i	$-0.581032\pi$
$577$	−12.0982			−0.503656			−0.251828	+	0.967772i	$0.581032\pi$
$578$		0			0
$579$	0.189940	−	0.328986i	0.00789363	−	0.0136722i
$580$		0			0
$581$			17.2522i			0.715741i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−19.0491	−	10.9980i	−0.787584	−	0.454712i
$586$		0			0
$587$	−6.56334	−	11.3680i	−0.270898	−	0.469209i	0.698194	−	0.715909i	$-0.253987\pi$
$587$	−6.56334	−	11.3680i	−0.270898	−	0.469209i	−0.969092	+	0.246699i	$0.920654\pi$
$588$		0			0
$589$	37.2048	−	5.43939i	1.53300	−	0.224126i
$590$		0			0
$591$	−0.848946	−	1.47042i	−0.0349210	−	0.0604849i
$592$		0			0
$593$	−3.39172	+	5.87464i	−0.139281	+	0.241242i	−0.927225	−	0.374505i	$-0.877813\pi$
$593$	−3.39172	+	5.87464i	−0.139281	+	0.241242i	0.787943	+	0.615748i	$0.211146\pi$
$594$		0			0
$595$	−6.89404	+	11.9408i	−0.282628	+	0.489526i
$596$		0			0
$597$	−0.103372			−0.00423073
$598$		0			0
$599$	−11.1196	+	19.2598i	−0.454336	+	0.786933i	−0.998650	−	0.0519490i	$-0.983457\pi$
$599$	−11.1196	+	19.2598i	−0.454336	+	0.786933i	0.544314	+	0.838882i	$0.316790\pi$
$600$		0			0
$601$			25.9466i			1.05838i	0.848502	+	0.529192i	$0.177505\pi$
$601$			25.9466i			1.05838i	−0.848502	+	0.529192i	$0.822495\pi$
$602$		0			0
$603$	5.42265	−	3.13077i	0.220827	−	0.127495i
$604$		0			0
$605$	−16.5000	+	9.52628i	−0.670820	+	0.387298i
$606$		0			0
$607$	−12.8834			−0.522923			−0.261461	−	0.965214i	$-0.584204\pi$
$607$	−12.8834			−0.522923			−0.261461	+	0.965214i	$0.584204\pi$
$608$		0			0
$609$	1.11794			0.0453014
$610$		0			0
$611$	−1.55473	+	0.897624i	−0.0628977	+	0.0363140i
$612$		0			0
$613$	−26.9704	+	15.5714i	−1.08932	+	0.628922i	−0.933397	−	0.358846i	$-0.883170\pi$
$613$	−26.9704	+	15.5714i	−1.08932	+	0.628922i	−0.155928	+	0.987768i	$0.549837\pi$
$614$		0			0
$615$			1.79525i			0.0723914i
$616$		0			0
$617$	−8.54911	+	14.8075i	−0.344174	+	0.596127i	−0.985203	−	0.171389i	$-0.945174\pi$
$617$	−8.54911	+	14.8075i	−0.344174	+	0.596127i	0.641029	+	0.767517i	$0.278508\pi$
$618$		0			0
$619$	42.4055			1.70442			0.852211	−	0.523198i	$-0.175261\pi$
$619$	42.4055			1.70442			0.852211	+	0.523198i	$0.175261\pi$
$620$		0			0
$621$	3.10808	−	5.38336i	0.124723	−	0.216027i
$622$		0			0
$623$	−16.7999	+	29.0982i	−0.673072	+	1.16580i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	14.4507	+	25.0293i	0.576187	+	0.997985i
$630$		0			0
$631$	−29.4346	−	16.9941i	−1.17177	−	0.676524i	−0.217677	−	0.976021i	$-0.569848\pi$
$631$	−29.4346	−	16.9941i	−1.17177	−	0.676524i	−0.954097	+	0.299496i	$0.903181\pi$
$632$		0			0
$633$	1.47061	−	2.54717i	0.0584516	−	0.101241i
$634$		0			0
$635$		−	22.2048i		−	0.881169i
$636$		0			0
$637$	−6.39172	+	11.0708i	−0.253249	+	0.438641i
$638$		0			0
$639$	5.78511			0.228856
$640$		0			0
$641$	25.8621	−	14.9315i	1.02149	−	0.589759i	0.106957	−	0.994264i	$-0.465889\pi$
$641$	25.8621	−	14.9315i	1.02149	−	0.589759i	0.914536	+	0.404504i	$0.132556\pi$
$642$		0			0
$643$	22.7233	+	39.3580i	0.896121	+	1.55213i	0.832411	+	0.554159i	$0.186960\pi$
$643$	22.7233	+	39.3580i	0.896121	+	1.55213i	0.0637103	+	0.997968i	$0.479707\pi$
$644$		0			0
$645$	3.00000			0.118125
$646$		0			0
$647$			2.35422i			0.0925539i	0.998929	+	0.0462770i	$0.0147357\pi$
$647$			2.35422i			0.0925539i	−0.998929	+	0.0462770i	$0.985264\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$	−1.21141	−	2.09822i	−0.0474789	−	0.0822358i
$652$		0			0
$653$		−	27.9513i		−	1.09382i	−0.837192	−	0.546909i	$-0.815805\pi$
$653$		−	27.9513i		−	1.09382i	0.837192	−	0.546909i	$-0.184195\pi$
$654$		0			0
$655$	26.9729	+	15.5728i	1.05392	+	0.608479i
$656$		0			0
$657$	−14.9014			−0.581359
$658$		0			0
$659$	16.9215	+	9.76962i	0.659168	+	0.380571i	0.791960	−	0.610573i	$-0.209061\pi$
$659$	16.9215	+	9.76962i	0.659168	+	0.380571i	−0.132792	+	0.991144i	$0.542394\pi$
$660$		0			0
$661$	1.29073	−	2.23561i	0.0502036	−	0.0869553i	−0.839832	−	0.542847i	$-0.817346\pi$
$661$	1.29073	−	2.23561i	0.0502036	−	0.0869553i	0.890035	+	0.455892i	$0.150680\pi$
$662$		0			0
$663$	−2.06275	+	1.19093i	−0.0801107	+	0.0462519i
$664$		0			0
$665$	−9.36214	−	11.8470i	−0.363048	−	0.459405i
$666$		0			0
$667$	−25.5134	+	14.7302i	−0.987884	+	0.570355i
$668$		0			0
$669$	1.34436	+	0.776166i	0.0519759	+	0.0300083i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		−	36.8254i		−	1.41951i	−0.704446	−	0.709757i	$-0.748805\pi$
$673$		−	36.8254i		−	1.41951i	0.704446	−	0.709757i	$-0.251195\pi$
$674$		0			0
$675$	−1.45465	−	0.839843i	−0.0559895	−	0.0323256i
$676$		0			0
$677$	31.8229			1.22305			0.611527	−	0.791224i	$-0.290556\pi$
$677$	31.8229			1.22305			0.611527	+	0.791224i	$0.290556\pi$
$678$		0			0
$679$	−7.38053	−	12.7834i	−0.283239	−	0.490584i
$680$		0			0
$681$	−1.40158	−	2.42761i	−0.0537088	−	0.0930264i
$682$		0			0
$683$		−	27.7834i		−	1.06310i	−0.847026	−	0.531552i	$-0.821609\pi$
$683$		−	27.7834i		−	1.06310i	0.847026	−	0.531552i	$-0.178391\pi$
$684$		0			0
$685$		−	27.6787i		−	1.05755i
$686$		0			0
$687$	−0.780626	−	1.35208i	−0.0297827	−	0.0515852i
$688$		0			0
$689$	23.3523	+	40.4473i	0.889651	+	1.54092i
$690$		0			0
$691$	−20.7846			−0.790684			−0.395342	−	0.918534i	$-0.629374\pi$
$691$	−20.7846			−0.790684			−0.395342	+	0.918534i	$0.629374\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		−	8.51953i		−	0.323164i
$696$		0			0
$697$	−25.4408	−	14.6883i	−0.963640	−	0.556358i
$698$		0			0
$699$	1.55473	+	0.897624i	0.0588053	+	0.0339513i
$700$		0			0
$701$	23.4391	−	13.5326i	0.885282	−	0.511118i	0.0128857	−	0.999917i	$-0.495898\pi$
$701$	23.4391	−	13.5326i	0.885282	−	0.511118i	0.872396	+	0.488799i	$0.162565\pi$
$702$		0			0
$703$	−31.3177	+	4.57869i	−1.18117	+	0.172689i
$704$		0			0
$705$	0.0887494	−	0.0512395i	0.00334250	−	0.00192979i
$706$		0			0
$707$	0.0341597	−	0.0591663i	0.00128471	−	0.00222518i
$708$		0			0
$709$	−10.8621	−	6.27126i	−0.407936	−	0.235522i	0.281966	−	0.959424i	$-0.409013\pi$
$709$	−10.8621	−	6.27126i	−0.407936	−	0.235522i	−0.689903	+	0.723902i	$0.742347\pi$
$710$		0			0
$711$	−16.1091			−0.604138
$712$		0			0
$713$	55.2929	+	31.9234i	2.07074	+	1.19554i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.24594	+	2.15804i	0.0465306	+	0.0805933i
$718$		0			0
$719$	−14.1529	+	8.17121i	−0.527816	+	0.304735i	−0.740127	−	0.672468i	$-0.765234\pi$
$719$	−14.1529	+	8.17121i	−0.527816	+	0.304735i	0.212311	+	0.977202i	$0.431901\pi$
$720$		0			0
$721$		−	7.90117i		−	0.294255i
$722$		0			0
$723$	−0.618324			−0.0229957
$724$		0			0
$725$	3.98028	+	6.89404i	0.147824	+	0.256038i
$726$		0			0
$727$	−34.6308	+	19.9941i	−1.28439	+	0.741540i	−0.977647	−	0.210254i	$-0.932571\pi$
$727$	−34.6308	+	19.9941i	−1.28439	+	0.741540i	−0.306738	+	0.951794i	$0.599238\pi$
$728$		0			0
$729$	25.9408			0.960772
$730$		0			0
$731$	−24.5453	+	42.5136i	−0.907839	+	1.57242i
$732$		0			0
$733$			6.55312i			0.242045i	0.992650	+	0.121023i	$0.0386173\pi$
$733$			6.55312i			0.242045i	−0.992650	+	0.121023i	$0.961383\pi$
$734$		0			0
$735$	0.364862	−	0.631959i	0.0134581	−	0.0233102i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−2.66846	−	4.62190i	−0.0981608	−	0.170019i	0.812763	−	0.582595i	$-0.197963\pi$
$739$	−2.66846	−	4.62190i	−0.0981608	−	0.170019i	−0.910923	+	0.412576i	$0.864629\pi$
$740$		0			0
$741$	−0.377346	−	2.58100i	−0.0138621	−	0.0948153i
$742$		0			0
$743$	10.2707	+	17.7893i	0.376795	+	0.652628i	0.990594	−	0.136834i	$-0.0436928\pi$
$743$	10.2707	+	17.7893i	0.376795	+	0.652628i	−0.613799	+	0.789462i	$0.710360\pi$
$744$		0			0
$745$	−0.0295831	+	0.0512395i	−0.00108384	+	0.00187727i
$746$		0			0
$747$	−12.8541	+	22.2639i	−0.470306	+	0.814594i
$748$		0			0
$749$	15.9211			0.581745
$750$		0			0
$751$	15.5225	−	26.8858i	0.566425	−	0.981078i	−0.430490	−	0.902595i	$-0.641659\pi$
$751$	15.5225	−	26.8858i	0.566425	−	0.981078i	0.996916	−	0.0784823i	$-0.0250074\pi$
$752$		0			0
$753$			2.28685i			0.0833375i
$754$		0			0
$755$	14.8587	−	8.57869i	0.540765	−	0.312211i
$756$		0			0
$757$	−44.1651	+	25.4987i	−1.60521	+	0.926767i	−0.614786	+	0.788694i	$0.710758\pi$
$757$	−44.1651	+	25.4987i	−1.60521	+	0.926767i	−0.990422	+	0.138074i	$0.955909\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	13.7046			0.496790			0.248395	−	0.968659i	$-0.420097\pi$
$761$	13.7046			0.496790			0.248395	+	0.968659i	$0.420097\pi$
$762$		0			0
$763$	−26.7057	+	15.4185i	−0.966811	+	0.558188i
$764$		0			0
$765$	−17.7935	+	10.2731i	−0.643325	+	0.371424i
$766$		0			0
$767$		−	5.97236i		−	0.215649i
$768$		0			0
$769$	−21.8621	+	37.8663i	−0.788369	+	1.36550i	0.138597	+	0.990349i	$0.455741\pi$
$769$	−21.8621	+	37.8663i	−0.788369	+	1.36550i	−0.926966	+	0.375146i	$0.877593\pi$
$770$		0			0
$771$	−2.12085			−0.0763806
$772$		0			0
$773$	−21.4606	+	37.1708i	−0.771883	+	1.33694i	0.164648	+	0.986352i	$0.447351\pi$
$773$	−21.4606	+	37.1708i	−0.771883	+	1.33694i	−0.936530	+	0.350587i	$0.885982\pi$
$774$		0			0
$775$	8.62609	−	14.9408i	0.309858	−	0.536691i
$776$		0			0
$777$	1.01972	+	1.76621i	0.0365823	+	0.0633624i
$778$		0			0
$779$	25.2408	−	19.9467i	0.904346	−	0.714666i
$780$		0			0
$781$		0			0
$782$		0			0
$783$	2.89496	+	1.67140i	0.103457	+	0.0597311i
$784$		0			0
$785$	−16.8621	+	29.2061i	−0.601836	+	1.04241i
$786$		0			0
$787$		−	25.6797i		−	0.915382i	−0.889111	−	0.457691i	$-0.848677\pi$
$787$		−	25.6797i		−	0.915382i	0.889111	−	0.457691i	$-0.151323\pi$
$788$		0			0
$789$	0.813029	−	1.40821i	0.0289446	−	0.0501335i
$790$		0			0
$791$	−26.1263			−0.928945
$792$		0			0
$793$	8.18697	−	4.72675i	0.290728	−	0.167852i
$794$		0			0
$795$	−1.33303	−	2.30887i	−0.0472777	−	0.0818873i
$796$		0			0
$797$	1.70456			0.0603785			0.0301893	−	0.999544i	$-0.490389\pi$
$797$	1.70456			0.0603785			0.0301893	+	0.999544i	$0.490389\pi$
$798$		0			0
$799$			1.67692i			0.0593250i
$800$		0			0
$801$	−43.3604	+	25.0341i	−1.53206	+	0.884538i
$802$		0			0
$803$		0			0
$804$		0			0
$805$		−	25.6398i		−	0.903686i
$806$		0			0
$807$	−2.28445	−	1.31893i	−0.0804166	−	0.0464285i
$808$		0			0
$809$	4.17711			0.146859			0.0734297	−	0.997300i	$-0.476606\pi$
$809$	4.17711			0.146859			0.0734297	+	0.997300i	$0.476606\pi$
$810$		0			0
$811$	42.6590	+	24.6292i	1.49796	+	0.864848i	0.999997	−	0.00235039i	$-0.000748154\pi$
$811$	42.6590	+	24.6292i	1.49796	+	0.864848i	0.497963	+	0.867198i	$0.334081\pi$
$812$		0			0
$813$	1.98737	−	3.44222i	0.0697001	−	0.120724i
$814$		0			0
$815$	−4.46643	+	2.57869i	−0.156452	+	0.0903277i
$816$		0			0
$817$	−33.3326	−	42.1794i	−1.16616	−	1.47567i
$818$		0			0
$819$	21.9960	−	12.6994i	0.768603	−	0.443753i
$820$		0			0
$821$	43.1752	+	24.9272i	1.50682	+	0.869965i	0.999969	+	0.00793394i	$0.00252548\pi$
$821$	43.1752	+	24.9272i	1.50682	+	0.869965i	0.506855	+	0.862031i	$0.330808\pi$
$822$		0			0
$823$	24.6136	+	14.2107i	0.857975	+	0.495352i	0.863334	−	0.504633i	$-0.168372\pi$
$823$	24.6136	+	14.2107i	0.857975	+	0.495352i	−0.00535850	+	0.999986i	$0.501706\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−32.0498	−	18.5040i	−1.11448	−	0.643446i	−0.174494	−	0.984658i	$-0.555829\pi$
$827$	−32.0498	−	18.5040i	−1.11448	−	0.643446i	−0.939986	+	0.341212i	$0.889162\pi$
$828$		0			0
$829$	23.0446			0.800372			0.400186	−	0.916434i	$-0.368946\pi$
$829$	23.0446			0.800372			0.400186	+	0.916434i	$0.368946\pi$
$830$		0			0
$831$	−0.221701	−	0.383997i	−0.00769072	−	0.0133207i
$832$		0			0
$833$	5.97042	+	10.3411i	0.206863	+	0.358297i
$834$		0			0
$835$		−	0.421306i		−	0.0145799i
$836$		0			0
$837$		−	7.24456i		−	0.250409i
$838$		0			0
$839$	24.5453	+	42.5136i	0.847396	+	1.46773i	0.883524	+	0.468386i	$0.155164\pi$
$839$	24.5453	+	42.5136i	0.847396	+	1.46773i	−0.0361276	+	0.999347i	$0.511502\pi$
$840$		0			0
$841$	6.57869	+	11.3946i	0.226852	+	0.392918i
$842$		0			0
$843$	−0.866362			−0.0298391
$844$		0			0
$845$	−7.73608	−	4.46643i	−0.266129	−	0.153650i
$846$		0			0
$847$		−	22.0000i		−	0.755929i
$848$		0			0
$849$	−1.76566	−	1.01941i	−0.0605975	−	0.0349860i
$850$		0			0
$851$	−46.5437	−	26.8720i	−1.59550	−	0.921160i
$852$		0			0
$853$	−7.92131	+	4.57337i	−0.271220	+	0.156589i	−0.629442	−	0.777047i	$-0.716717\pi$
$853$	−7.92131	+	4.57337i	−0.271220	+	0.156589i	0.358222	+	0.933637i	$0.383383\pi$
$854$		0			0
$855$	−3.25502	−	22.2639i	−0.111319	−	0.761410i
$856$		0			0
$857$	−4.50000	+	2.59808i	−0.153717	+	0.0887486i	−0.574886	−	0.818234i	$-0.694953\pi$
$857$	−4.50000	+	2.59808i	−0.153717	+	0.0887486i	0.421168	+	0.906982i	$0.361620\pi$
$858$		0			0
$859$	−1.85367	+	3.21065i	−0.0632465	+	0.109546i	−0.895915	−	0.444226i	$-0.853479\pi$
$859$	−1.85367	+	3.21065i	−0.0632465	+	0.109546i	0.832668	+	0.553772i	$0.186812\pi$
$860$		0			0
$861$	−1.79525	−	1.03649i	−0.0611819	−	0.0353234i
$862$		0			0
$863$	2.67086			0.0909170			0.0454585	−	0.998966i	$-0.485525\pi$
$863$	2.67086			0.0909170			0.0454585	+	0.998966i	$0.485525\pi$
$864$		0			0
$865$	−4.50000	−	2.59808i	−0.153005	−	0.0883372i
$866$		0			0
$867$		−	0.162538i		−	0.00552009i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	7.75321	−	4.47632i	0.262707	−	0.151674i
$872$		0			0
$873$		−	21.9960i		−	0.744452i
$874$		0			0
$875$	−24.2487			−0.819756
$876$		0			0
$877$	−7.71204	−	13.3576i	−0.260417	−	0.451056i	0.705936	−	0.708276i	$-0.250527\pi$
$877$	−7.71204	−	13.3576i	−0.260417	−	0.451056i	−0.966353	+	0.257220i	$0.917193\pi$
$878$		0			0
$879$	3.71996	−	2.14772i	0.125471	−	0.0724408i
$880$		0			0
$881$	−11.4687			−0.386389			−0.193195	−	0.981160i	$-0.561885\pi$
$881$	−11.4687			−0.386389			−0.193195	+	0.981160i	$0.561885\pi$
$882$		0			0
$883$	19.9890	−	34.6219i	0.672682	−	1.16512i	−0.304458	−	0.952526i	$-0.598475\pi$
$883$	19.9890	−	34.6219i	0.672682	−	1.16512i	0.977141	−	0.212594i	$-0.0681912\pi$
$884$		0			0
$885$			0.340923i			0.0114600i
$886$		0			0
$887$	29.2549	−	50.6710i	0.982284	−	1.70137i	0.328851	−	0.944382i	$-0.393339\pi$
$887$	29.2549	−	50.6710i	0.982284	−	1.70137i	0.653433	−	0.756984i	$-0.273328\pi$
$888$		0			0
$889$	22.2048	+	12.8199i	0.744723	+	0.429966i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.70650	−	0.678484i	−0.0571058	−	0.0227046i
$894$		0			0
$895$	−9.66258	−	16.7361i	−0.322984	−	0.559426i
$896$		0			0
$897$	2.21461	−	3.83582i	0.0739438	−	0.128074i
$898$		0			0
$899$	−17.1671	+	29.7343i	−0.572556	+	0.991696i
$900$		0			0
$901$	43.6261			1.45339
$902$		0			0
$903$	−1.73205	+	3.00000i	−0.0576390	+	0.0998337i
$904$		0			0
$905$		−	19.9572i		−	0.663400i
$906$		0			0
$907$	45.9356	−	26.5209i	1.52527	−	0.880612i	0.525714	−	0.850661i	$-0.323798\pi$
$907$	45.9356	−	26.5209i	1.52527	−	0.880612i	0.999551	−	0.0299511i	$-0.00953517\pi$
$908$		0			0
$909$	0.0881660	−	0.0509027i	0.00292428	−	0.00168833i
$910$		0			0
$911$	−30.6904			−1.01682			−0.508410	−	0.861115i	$-0.669766\pi$
$911$	−30.6904			−1.01682			−0.508410	+	0.861115i	$0.669766\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	−0.467341	+	0.269819i	−0.0154498	+	0.00891995i
$916$		0			0
$917$	−31.1456	+	17.9819i	−1.02852	+	0.593815i
$918$		0			0
$919$			32.8426i			1.08338i	0.840579	+	0.541689i	$0.182215\pi$
$919$			32.8426i			1.08338i	−0.840579	+	0.541689i	$0.817785\pi$
$920$		0			0
$921$	−1.20495	+	2.08703i	−0.0397043	+	0.0687699i
$922$		0			0
$923$	8.27145			0.272258
$924$		0			0
$925$	−7.26115	+	12.5767i	−0.238745	+	0.413519i
$926$		0			0
$927$	5.88692	−	10.1964i	0.193352	−	0.334895i
$928$		0			0
$929$	−6.88186	−	11.9197i	−0.225787	−	0.391074i	0.730769	−	0.682625i	$-0.239162\pi$
$929$	−6.88186	−	11.9197i	−0.225787	−	0.391074i	−0.956555	+	0.291551i	$0.905829\pi$
$930$		0			0
$931$	−12.9391	+	1.89172i	−0.424063	+	0.0619987i
$932$		0			0
$933$	2.08855	+	3.61748i	0.0683762	+	0.118431i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	21.2243	−	36.7615i	0.693367	−	1.20095i	−0.277361	−	0.960766i	$-0.589460\pi$
$937$	21.2243	−	36.7615i	0.693367	−	1.20095i	0.970728	−	0.240181i	$-0.0772068\pi$
$938$		0			0
$939$		−	1.63271i		−	0.0532815i
$940$		0			0
$941$	28.2440	−	48.9200i	0.920728	−	1.59475i	0.122437	−	0.992476i	$-0.460929\pi$
$941$	28.2440	−	48.9200i	0.920728	−	1.59475i	0.798291	−	0.602272i	$-0.205738\pi$
$942$		0			0
$943$	54.6276			1.77892
$944$		0			0
$945$	−2.51953	+	1.45465i	−0.0819602	+	0.0473198i
$946$		0			0
$947$	19.5366	+	33.8385i	0.634856	+	1.09960i	0.986546	+	0.163486i	$0.0522737\pi$
$947$	19.5366	+	33.8385i	0.634856	+	1.09960i	−0.351690	+	0.936116i	$0.614393\pi$
$948$		0			0
$949$	−21.3057			−0.691614
$950$		0			0
$951$			2.36253i			0.0766102i
$952$		0			0
$953$	−15.1769	+	8.76240i	−0.491629	+	0.283842i	−0.725250	−	0.688486i	$-0.758276\pi$
$953$	−15.1769	+	8.76240i	−0.491629	+	0.283842i	0.233621	+	0.972328i	$0.424942\pi$
$954$		0			0
$955$	11.3605	+	19.6769i	0.367616	+	0.636730i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.6787	+	15.9803i	0.893790	+	0.516030i
$960$		0			0
$961$	43.4095			1.40031
$962$		0			0
$963$	20.5462	+	11.8623i	0.662091	+	0.382258i
$964$		0			0
$965$	2.34261	−	4.05752i	0.0754114	−	0.130616i
$966$		0			0
$967$	18.1251	−	10.4645i	0.582863	−	0.336516i	−0.179407	−	0.983775i	$-0.557418\pi$
$967$	18.1251	−	10.4645i	0.582863	−	0.336516i	0.762270	+	0.647259i	$0.224085\pi$
$968$		0			0
$969$	−2.26411	−	0.900185i	−0.0727338	−	0.0289181i
$970$		0			0
$971$	41.3715	−	23.8858i	1.32767	−	0.766533i	0.342734	−	0.939433i	$-0.388647\pi$
$971$	41.3715	−	23.8858i	1.32767	−	0.766533i	0.984939	+	0.172900i	$0.0553138\pi$
$972$		0			0
$973$	8.51953	+	4.91875i	0.273124	+	0.157688i
$974$		0			0
$975$	−1.03649	−	0.598416i	−0.0331941	−	0.0191646i
$976$		0			0
$977$		−	48.1223i		−	1.53957i	−0.638303	−	0.769785i	$-0.720363\pi$
$977$		−	48.1223i		−	1.53957i	0.638303	−	0.769785i	$-0.279637\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−45.9515			−1.46712
$982$		0			0
$983$	−18.9866	−	32.8858i	−0.605580	−	1.04889i	−0.991960	−	0.126555i	$-0.959608\pi$
$983$	−18.9866	−	32.8858i	−0.605580	−	1.04889i	0.386380	−	0.922340i	$-0.373725\pi$
$984$		0			0
$985$	−10.4704	−	18.1353i	−0.333615	−	0.577839i
$986$		0			0
$987$			0.118333i			0.00376657i
$988$		0			0
$989$		−	91.2870i		−	2.90276i
$990$		0			0
$991$	22.4166	+	38.8267i	0.712086	+	1.23337i	0.964073	+	0.265639i	$0.0855828\pi$
$991$	22.4166	+	38.8267i	0.712086	+	1.23337i	−0.251987	+	0.967731i	$0.581084\pi$
$992$		0			0
$993$	−2.34242	−	4.05719i	−0.0743344	−	0.128751i
$994$		0			0
$995$	−1.27493			−0.0404180
$996$		0			0
$997$	12.6574	+	7.30775i	0.400863	+	0.231439i	0.686856	−	0.726793i	$-0.258990\pi$
$997$	12.6574	+	7.30775i	0.400863	+	0.231439i	−0.285993	+	0.958232i	$0.592323\pi$
$998$		0			0
$999$			6.09822i			0.192939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1216.2.s.h.31.4	yes	12
4.3	odd	2	inner	1216.2.s.h.31.3	yes	12
8.3	odd	2		1216.2.s.g.31.4	yes	12
8.5	even	2		1216.2.s.g.31.3	✓	12
19.8	odd	6		1216.2.s.g.863.4	yes	12
76.27	even	6		1216.2.s.g.863.3	yes	12
152.27	even	6	inner	1216.2.s.h.863.4	yes	12
152.141	odd	6	inner	1216.2.s.h.863.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1216.2.s.g.31.3	✓	12	8.5	even	2
1216.2.s.g.31.4	yes	12	8.3	odd	2
1216.2.s.g.863.3	yes	12	76.27	even	6
1216.2.s.g.863.4	yes	12	19.8	odd	6
1216.2.s.h.31.3	yes	12	4.3	odd	2	inner
1216.2.s.h.31.4	yes	12	1.1	even	1	trivial
1216.2.s.h.863.3	yes	12	152.141	odd	6	inner
1216.2.s.h.863.4	yes	12	152.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1216 = 2^{6} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1216.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.121621 - 0.0702177i) q^{3} +(1.50000 - 0.866025i) q^{5} +2.00000i q^{7} +(-1.49014 + 2.58100i) q^{9} +(-2.13057 + 3.69026i) q^{13} +(0.121621 - 0.210653i) q^{15} +(1.99014 + 3.44702i) q^{17} +(-4.31305 + 0.630574i) q^{19} +(0.140435 + 0.243241i) q^{21} +(-6.40996 - 3.70079i) q^{23} +(-1.00000 + 1.73205i) q^{25} +0.839843i q^{27} +(1.99014 - 3.44702i) q^{29} -8.62609 q^{31} +(1.73205 + 3.00000i) q^{35} +7.26115 q^{37} +0.598416i q^{39} +(-6.39172 + 3.69026i) q^{41} +(6.16672 + 10.6811i) q^{43} +5.16199i q^{45} +(0.364862 + 0.210653i) q^{47} +3.00000 q^{49} +(0.484084 + 0.279486i) q^{51} +(5.48028 - 9.49212i) q^{53} +(-0.480278 + 0.379543i) q^{57} +(-1.21381 + 0.700792i) q^{59} +(-1.92131 - 1.10927i) q^{61} +(-5.16199 - 2.98028i) q^{63} +7.38053i q^{65} +(-1.81951 - 1.05050i) q^{67} -1.03944 q^{69} +(-0.970566 - 1.68107i) q^{71} +(2.50000 + 4.33013i) q^{73} +0.280871i q^{75} +(2.70262 + 4.68107i) q^{79} +(-4.41145 - 7.64085i) q^{81} +8.62609 q^{83} +(5.97042 + 3.44702i) q^{85} -0.558972i q^{87} +(14.5491 + 8.39993i) q^{89} +(-7.38053 - 4.26115i) q^{91} +(-1.04911 + 0.605704i) q^{93} +(-5.92348 + 4.68107i) q^{95} +(-6.39172 + 3.69026i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 18 q^{5} + 12 q^{9} + 2 q^{13} - 6 q^{17} + 4 q^{21} - 12 q^{25} - 6 q^{29} + 32 q^{37} + 6 q^{41} + 36 q^{49} + 6 q^{53} + 54 q^{57} - 30 q^{61} - 132 q^{69} + 30 q^{73} - 30 q^{81} - 18 q^{85}+ \cdots + 6 q^{97}+O(q^{100}) \) 12 * q + 18 * q^5 + 12 * q^9 + 2 * q^13 - 6 * q^17 + 4 * q^21 - 12 * q^25 - 6 * q^29 + 32 * q^37 + 6 * q^41 + 36 * q^49 + 6 * q^53 + 54 * q^57 - 30 * q^61 - 132 * q^69 + 30 * q^73 - 30 * q^81 - 18 * q^85 + 78 * q^89 + 84 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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