LMFDB - Embedded newform 216.2.f.a.107.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(107,216)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("216.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.23123460096.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 $ x^8 + 2x^6 + 6x^4 + 8*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			107.1
Root			$1.08766 - 0.903873i$ of defining polynomial
Character	$\chi$	$=$	216.107
Dual form			216.2.f.a.107.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.08766 - 0.903873i) q^{2} +(0.366025 + 1.96622i) q^{4} -1.59245 q^{5} -1.43937i q^{7} +(1.37910 - 2.46943i) q^{8} +(1.73205 + 1.43937i) q^{10} -4.93886i q^{11} -5.37182i q^{13} +(-1.30101 + 1.56555i) q^{14} +(-3.73205 + 1.43937i) q^{16} +1.32336i q^{17} +0.267949 q^{19} +(-0.582877 - 3.13111i) q^{20} +(-4.46410 + 5.37182i) q^{22} +5.94311 q^{23} -2.46410 q^{25} +(-4.85544 + 5.84273i) q^{26} +(2.83013 - 0.526847i) q^{28} -8.70131 q^{29} -7.86488i q^{31} +(5.36023 + 1.80775i) q^{32} +(1.19615 - 1.43937i) q^{34} +2.29213i q^{35} +2.49307i q^{37} +(-0.291439 - 0.242192i) q^{38} +(-2.19615 + 3.93244i) q^{40} +9.87771i q^{41} +2.00000 q^{43} +(9.71088 - 1.80775i) q^{44} +(-6.46410 - 5.37182i) q^{46} +9.12801 q^{47} +4.92820 q^{49} +(2.68011 + 2.22724i) q^{50} +(10.5622 - 1.96622i) q^{52} +5.51641 q^{53} +7.86488i q^{55} +(-3.55443 - 1.98504i) q^{56} +(9.46410 + 7.86488i) q^{58} -4.93886i q^{59} +5.37182i q^{61} +(-7.10886 + 8.55435i) q^{62} +(-4.19615 - 6.81119i) q^{64} +8.55435i q^{65} +1.19615 q^{67} +(-2.60202 + 0.484384i) q^{68} +(2.07180 - 2.49307i) q^{70} -5.51641 q^{71} -7.92820 q^{73} +(2.25342 - 2.71162i) q^{74} +(0.0980762 + 0.526847i) q^{76} -7.10886 q^{77} +12.1830i q^{79} +(5.94311 - 2.29213i) q^{80} +(8.92820 - 10.7436i) q^{82} -7.23099i q^{83} -2.10739i q^{85} +(-2.17533 - 1.80775i) q^{86} +(-12.1962 - 6.81119i) q^{88} -15.7853i q^{89} -7.73205 q^{91} +(2.17533 + 11.6855i) q^{92} +(-9.92820 - 8.25056i) q^{94} -0.426696 q^{95} +9.39230 q^{97} +(-5.36023 - 4.45447i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{4} - 16 q^{16} + 16 q^{19} - 8 q^{22} + 8 q^{25} - 12 q^{28} - 32 q^{34} + 24 q^{40} + 16 q^{43} - 24 q^{46} - 16 q^{49} + 36 q^{52} + 48 q^{58} + 8 q^{64} - 32 q^{67} + 72 q^{70} - 8 q^{73}+ \cdots - 8 q^{97}+O(q^{100}) $ 8 * q - 4 * q^4 - 16 * q^16 + 16 * q^19 - 8 * q^22 + 8 * q^25 - 12 * q^28 - 32 * q^34 + 24 * q^40 + 16 * q^43 - 24 * q^46 - 16 * q^49 + 36 * q^52 + 48 * q^58 + 8 * q^64 - 32 * q^67 + 72 * q^70 - 8 * q^73 - 20 * q^76 + 16 * q^82 - 56 * q^88 - 48 * q^91 - 24 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.08766	−	0.903873i	−0.769095	−	0.639135i
$2$	−1.08766	−	0.903873i	−0.769095	−	0.639135i
$3$		0			0
$3$		0			0
$4$	0.366025	+	1.96622i	0.183013	+	0.983111i
$5$	−1.59245			−0.712165			−0.356083	−	0.934454i	$-0.615888\pi$
$5$	−1.59245			−0.712165			−0.356083	+	0.934454i	$0.615888\pi$
$6$		0			0
$7$		−	1.43937i		−	0.544032i	−0.962293	−	0.272016i	$-0.912310\pi$
$7$		−	1.43937i		−	0.544032i	0.962293	−	0.272016i	$-0.0876904\pi$
$8$	1.37910	−	2.46943i	0.487586	−	0.873075i
$9$		0			0
$10$	1.73205	+	1.43937i	0.547723	+	0.455170i
$11$		−	4.93886i		−	1.48912i	−0.667555	−	0.744561i	$-0.732659\pi$
$11$		−	4.93886i		−	1.48912i	0.667555	−	0.744561i	$-0.267341\pi$
$12$		0			0
$13$		−	5.37182i		−	1.48987i	−0.667135	−	0.744937i	$-0.732480\pi$
$13$		−	5.37182i		−	1.48987i	0.667135	−	0.744937i	$-0.267520\pi$
$14$	−1.30101	+	1.56555i	−0.347710	+	0.418412i
$15$		0			0
$16$	−3.73205	+	1.43937i	−0.933013	+	0.359843i
$17$			1.32336i			0.320963i	0.987039	+	0.160481i	$0.0513046\pi$
$17$			1.32336i			0.320963i	−0.987039	+	0.160481i	$0.948695\pi$
$18$		0			0
$19$	0.267949			0.0614718			0.0307359	−	0.999528i	$-0.490215\pi$
$19$	0.267949			0.0614718			0.0307359	+	0.999528i	$0.490215\pi$
$20$	−0.582877	−	3.13111i	−0.130335	−	0.700137i
$21$		0			0
$22$	−4.46410	+	5.37182i	−0.951750	+	1.14528i
$23$	5.94311			1.23922			0.619612	−	0.784909i	$-0.287290\pi$
$23$	5.94311			1.23922			0.619612	+	0.784909i	$0.287290\pi$
$24$		0			0
$25$	−2.46410			−0.492820
$26$	−4.85544	+	5.84273i	−0.952231	+	1.14585i
$27$		0			0
$28$	2.83013	−	0.526847i	0.534844	−	0.0995648i
$29$	−8.70131			−1.61579			−0.807896	−	0.589324i	$-0.799394\pi$
$29$	−8.70131			−1.61579			−0.807896	+	0.589324i	$0.799394\pi$
$30$		0			0
$31$		−	7.86488i		−	1.41257i	−0.707925	−	0.706287i	$-0.750369\pi$
$31$		−	7.86488i		−	1.41257i	0.707925	−	0.706287i	$-0.249631\pi$
$32$	5.36023	+	1.80775i	0.947564	+	0.319568i
$33$		0			0
$34$	1.19615	−	1.43937i	0.205138	−	0.246851i
$35$			2.29213i			0.387441i
$36$		0			0
$37$			2.49307i			0.409858i	0.978777	+	0.204929i	$0.0656963\pi$
$37$			2.49307i			0.409858i	−0.978777	+	0.204929i	$0.934304\pi$
$38$	−0.291439	−	0.242192i	−0.0472776	−	0.0392888i
$39$		0			0
$40$	−2.19615	+	3.93244i	−0.347242	+	0.621774i
$41$			9.87771i			1.54264i	0.636448	+	0.771320i	$0.280403\pi$
$41$			9.87771i			1.54264i	−0.636448	+	0.771320i	$0.719597\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	9.71088	−	1.80775i	1.46397	−	0.272528i
$45$		0			0
$46$	−6.46410	−	5.37182i	−0.953080	−	0.792031i
$47$	9.12801			1.33146			0.665728	−	0.746194i	$-0.268121\pi$
$47$	9.12801			1.33146			0.665728	+	0.746194i	$0.268121\pi$
$48$		0			0
$49$	4.92820			0.704029
$50$	2.68011	+	2.22724i	0.379025	+	0.314979i
$51$		0			0
$52$	10.5622	−	1.96622i	1.46471	−	0.272666i
$53$	5.51641			0.757737			0.378869	−	0.925450i	$-0.376313\pi$
$53$	5.51641			0.757737			0.378869	+	0.925450i	$0.376313\pi$
$54$		0			0
$55$			7.86488i			1.06050i
$56$	−3.55443	−	1.98504i	−0.474981	−	0.265263i
$57$		0			0
$58$	9.46410	+	7.86488i	1.24270	+	1.03271i
$59$		−	4.93886i		−	0.642984i	−0.946912	−	0.321492i	$-0.895816\pi$
$59$		−	4.93886i		−	0.642984i	0.946912	−	0.321492i	$-0.104184\pi$
$60$		0			0
$61$			5.37182i			0.687791i	0.939008	+	0.343895i	$0.111747\pi$
$61$			5.37182i			0.687791i	−0.939008	+	0.343895i	$0.888253\pi$
$62$	−7.10886	+	8.55435i	−0.902826	+	1.08640i
$63$		0			0
$64$	−4.19615	−	6.81119i	−0.524519	−	0.851399i
$65$			8.55435i			1.06104i
$66$		0			0
$67$	1.19615			0.146133			0.0730666	−	0.997327i	$-0.476721\pi$
$67$	1.19615			0.146133			0.0730666	+	0.997327i	$0.476721\pi$
$68$	−2.60202	+	0.484384i	−0.315542	+	0.0587402i
$69$		0			0
$70$	2.07180	−	2.49307i	0.247627	−	0.297979i
$71$	−5.51641			−0.654677			−0.327339	−	0.944907i	$-0.606152\pi$
$71$	−5.51641			−0.654677			−0.327339	+	0.944907i	$0.606152\pi$
$72$		0			0
$73$	−7.92820			−0.927926			−0.463963	−	0.885855i	$-0.653573\pi$
$73$	−7.92820			−0.927926			−0.463963	+	0.885855i	$0.653573\pi$
$74$	2.25342	−	2.71162i	0.261955	−	0.315219i
$75$		0			0
$76$	0.0980762	+	0.526847i	0.0112501	+	0.0604335i
$77$	−7.10886			−0.810130
$78$		0			0
$79$			12.1830i			1.37070i	0.728216	+	0.685348i	$0.240350\pi$
$79$			12.1830i			1.37070i	−0.728216	+	0.685348i	$0.759650\pi$
$80$	5.94311	−	2.29213i	0.664459	−	0.256268i
$81$		0			0
$82$	8.92820	−	10.7436i	0.985955	−	1.18644i
$83$		−	7.23099i		−	0.793704i	−0.917883	−	0.396852i	$-0.870103\pi$
$83$		−	7.23099i		−	0.793704i	0.917883	−	0.396852i	$-0.129897\pi$
$84$		0			0
$85$		−	2.10739i		−	0.228578i
$86$	−2.17533	−	1.80775i	−0.234572	−	0.194934i
$87$		0			0
$88$	−12.1962	−	6.81119i	−1.30011	−	0.726075i
$89$		−	15.7853i		−	1.67324i	−0.547782	−	0.836621i	$-0.684528\pi$
$89$		−	15.7853i		−	1.67324i	0.547782	−	0.836621i	$-0.315472\pi$
$90$		0			0
$91$	−7.73205			−0.810539
$92$	2.17533	+	11.6855i	0.226794	+	1.21829i
$93$		0			0
$94$	−9.92820	−	8.25056i	−1.02402	−	0.850981i
$95$	−0.426696			−0.0437781
$96$		0			0
$97$	9.39230			0.953644			0.476822	−	0.879000i	$-0.341789\pi$
$97$	9.39230			0.953644			0.476822	+	0.879000i	$0.341789\pi$
$98$	−5.36023	−	4.45447i	−0.541465	−	0.449970i
$99$		0			0
$100$	−0.901924	−	4.84497i	−0.0901924	−	0.484497i
$101$	−3.18490			−0.316909			−0.158455	−	0.987366i	$-0.550651\pi$
$101$	−3.18490			−0.316909			−0.158455	+	0.987366i	$0.550651\pi$
$102$		0			0
$103$			1.43937i			0.141826i	0.997483	+	0.0709129i	$0.0225912\pi$
$103$			1.43937i			0.141826i	−0.997483	+	0.0709129i	$0.977409\pi$
$104$	−13.2653	−	7.40828i	−1.30077	−	0.726442i
$105$		0			0
$106$	−6.00000	−	4.98614i	−0.582772	−	0.484296i
$107$			12.1698i			1.17650i	0.808678	+	0.588252i	$0.200184\pi$
$107$			12.1698i			1.17650i	−0.808678	+	0.588252i	$0.799816\pi$
$108$		0			0
$109$			13.6224i			1.30479i	0.757880	+	0.652394i	$0.226235\pi$
$109$			13.6224i			1.30479i	−0.757880	+	0.652394i	$0.773765\pi$
$110$	7.10886	−	8.55435i	0.677803	−	0.815625i
$111$		0			0
$112$	2.07180	+	5.37182i	0.195766	+	0.507589i
$113$		−	11.2011i		−	1.05371i	−0.849956	−	0.526854i	$-0.823371\pi$
$113$		−	11.2011i		−	1.05371i	0.849956	−	0.526854i	$-0.176629\pi$
$114$		0			0
$115$	−9.46410			−0.882532
$116$	−3.18490	−	17.1087i	−0.295711	−	1.58850i
$117$		0			0
$118$	−4.46410	+	5.37182i	−0.410954	+	0.494516i
$119$	1.90481			0.174614
$120$		0			0
$121$	−13.3923			−1.21748
$122$	4.85544	−	5.84273i	0.439591	−	0.528976i
$123$		0			0
$124$	15.4641	−	2.87875i	1.38872	−	0.258519i
$125$	11.8862			1.06314
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−1.59245	+	11.2011i	−0.140754	+	0.990045i
$129$		0			0
$130$	7.73205	−	9.30426i	0.678146	−	0.816037i
$131$		−	7.23099i		−	0.631774i	−0.948797	−	0.315887i	$-0.897698\pi$
$131$		−	7.23099i		−	0.631774i	0.948797	−	0.315887i	$-0.102302\pi$
$132$		0			0
$133$		−	0.385679i		−	0.0334426i
$134$	−1.30101	−	1.08117i	−0.112390	−	0.0933989i
$135$		0			0
$136$	3.26795	+	1.82505i	0.280224	+	0.156497i
$137$			5.90763i			0.504722i	0.967633	+	0.252361i	$0.0812071\pi$
$137$			5.90763i			0.504722i	−0.967633	+	0.252361i	$0.918793\pi$
$138$		0			0
$139$	7.19615			0.610370			0.305185	−	0.952293i	$-0.401282\pi$
$139$	7.19615			0.610370			0.305185	+	0.952293i	$0.401282\pi$
$140$	−4.50684	+	0.838978i	−0.380897	+	0.0709066i
$141$		0			0
$142$	6.00000	+	4.98614i	0.503509	+	0.418427i
$143$	−26.5306			−2.21860
$144$		0			0
$145$	13.8564			1.15071
$146$	8.62322	+	7.16609i	0.713663	+	0.593070i
$147$		0			0
$148$	−4.90192	+	0.912526i	−0.402936	+	0.0750092i
$149$	3.18490			0.260917			0.130459	−	0.991454i	$-0.458355\pi$
$149$	3.18490			0.260917			0.130459	+	0.991454i	$0.458355\pi$
$150$		0			0
$151$		−	6.42551i		−	0.522901i	−0.965217	−	0.261450i	$-0.915799\pi$
$151$		−	6.42551i		−	0.522901i	0.965217	−	0.261450i	$-0.0842008\pi$
$152$	0.369529	−	0.661681i	0.0299728	−	0.0536694i
$153$		0			0
$154$	7.73205	+	6.42551i	0.623066	+	0.517782i
$155$			12.5244i			1.00599i
$156$		0			0
$157$			2.10739i			0.168188i	0.996458	+	0.0840940i	$0.0267996\pi$
$157$			2.10739i			0.168188i	−0.996458	+	0.0840940i	$0.973200\pi$
$158$	11.0119	−	13.2510i	0.876059	−	1.05419i
$159$		0			0
$160$	−8.53590	−	2.87875i	−0.674822	−	0.227585i
$161$		−	8.55435i		−	0.674177i
$162$		0			0
$163$	19.1962			1.50356			0.751779	−	0.659415i	$-0.229196\pi$
$163$	19.1962			1.50356			0.751779	+	0.659415i	$0.229196\pi$
$164$	−19.4218	+	3.61549i	−1.51659	+	0.282323i
$165$		0			0
$166$	−6.53590	+	7.86488i	−0.507284	+	0.610433i
$167$	−5.08971			−0.393854			−0.196927	−	0.980418i	$-0.563096\pi$
$167$	−5.08971			−0.393854			−0.196927	+	0.980418i	$0.563096\pi$
$168$		0			0
$169$	−15.8564			−1.21972
$170$	−1.90481	+	2.29213i	−0.146093	+	0.175798i
$171$		0			0
$172$	0.732051	+	3.93244i	0.0558184	+	0.299846i
$173$	11.8862			0.903692			0.451846	−	0.892096i	$-0.350766\pi$
$173$	11.8862			0.903692			0.451846	+	0.892096i	$0.350766\pi$
$174$		0			0
$175$			3.54676i			0.268110i
$176$	7.10886	+	18.4321i	0.535851	+	1.38937i
$177$		0			0
$178$	−14.2679	+	17.1691i	−1.06943	+	1.28688i
$179$			9.87771i			0.738295i	0.929371	+	0.369147i	$0.120350\pi$
$179$			9.87771i			0.738295i	−0.929371	+	0.369147i	$0.879650\pi$
$180$		0			0
$181$		−	16.1154i		−	1.19785i	−0.800804	−	0.598926i	$-0.795594\pi$
$181$		−	16.1154i		−	1.19785i	0.800804	−	0.598926i	$-0.204406\pi$
$182$	8.40987	+	6.98880i	0.623381	+	0.518044i
$183$		0			0
$184$	8.19615	−	14.6761i	0.604228	−	1.08193i
$185$		−	3.97009i		−	0.291887i
$186$		0			0
$187$	6.53590			0.477952
$188$	3.34108	+	17.9477i	0.243673	+	1.30897i
$189$		0			0
$190$	0.464102	+	0.385679i	0.0336695	+	0.0279801i
$191$	9.12801			0.660479			0.330240	−	0.943897i	$-0.392870\pi$
$191$	9.12801			0.660479			0.330240	+	0.943897i	$0.392870\pi$
$192$		0			0
$193$	15.3923			1.10796			0.553981	−	0.832529i	$-0.313108\pi$
$193$	15.3923			1.10796			0.553981	+	0.832529i	$0.313108\pi$
$194$	−10.2157	−	8.48946i	−0.733442	−	0.609507i
$195$		0			0
$196$	1.80385	+	9.68994i	0.128846	+	0.692138i
$197$	19.8485			1.41414			0.707072	−	0.707141i	$-0.250016\pi$
$197$	19.8485			1.41414			0.707072	+	0.707141i	$0.250016\pi$
$198$		0			0
$199$		−	14.2904i		−	1.01302i	−0.862234	−	0.506510i	$-0.830935\pi$
$199$		−	14.2904i		−	1.01302i	0.862234	−	0.506510i	$-0.169065\pi$
$200$	−3.39825	+	6.08492i	−0.240292	+	0.430269i
$201$		0			0
$202$	3.46410	+	2.87875i	0.243733	+	0.202548i
$203$			12.5244i			0.879043i
$204$		0			0
$205$		−	15.7298i		−	1.09861i
$206$	1.30101	−	1.56555i	0.0906458	−	0.109077i
$207$		0			0
$208$	7.73205	+	20.0479i	0.536121	+	1.39007i
$209$		−	1.32336i		−	0.0915389i
$210$		0			0
$211$	−17.0526			−1.17395			−0.586973	−	0.809606i	$-0.699681\pi$
$211$	−17.0526			−1.17395			−0.586973	+	0.809606i	$0.699681\pi$
$212$	2.01915	+	10.8465i	0.138676	+	0.744939i
$213$		0			0
$214$	11.0000	−	13.2367i	0.751945	−	0.904842i
$215$	−3.18490			−0.217208
$216$		0			0
$217$	−11.3205			−0.768486
$218$	12.3129	−	14.8166i	0.833935	−	1.00350i
$219$		0			0
$220$	−15.4641	+	2.87875i	−1.04259	+	0.194085i
$221$	7.10886			0.478194
$222$		0			0
$223$		−	19.3799i		−	1.29777i	−0.760885	−	0.648886i	$-0.775235\pi$
$223$		−	19.3799i		−	1.29777i	0.760885	−	0.648886i	$-0.224765\pi$
$224$	2.60202	−	7.71537i	0.173855	−	0.515505i
$225$		0			0
$226$	−10.1244	+	12.1830i	−0.673462	+	0.810401i
$227$			9.87771i			0.655607i	0.944746	+	0.327803i	$0.106308\pi$
$227$			9.87771i			0.655607i	−0.944746	+	0.327803i	$0.893692\pi$
$228$		0			0
$229$			15.7298i			1.03945i	0.854333	+	0.519726i	$0.173966\pi$
$229$			15.7298i			1.03945i	−0.854333	+	0.519726i	$0.826034\pi$
$230$	10.2938	+	8.55435i	0.678751	+	0.564057i
$231$		0			0
$232$	−12.0000	+	21.4873i	−0.787839	+	1.41071i
$233$		−	2.64673i		−	0.173393i	−0.996235	−	0.0866964i	$-0.972369\pi$
$233$		−	2.64673i		−	0.173393i	0.996235	−	0.0866964i	$-0.0276310\pi$
$234$		0			0
$235$	−14.5359			−0.948217
$236$	9.71088	−	1.80775i	0.632125	−	0.117674i
$237$		0			0
$238$	−2.07180	−	1.72171i	−0.134295	−	0.111602i
$239$	−6.36980			−0.412028			−0.206014	−	0.978549i	$-0.566049\pi$
$239$	−6.36980			−0.412028			−0.206014	+	0.978549i	$0.566049\pi$
$240$		0			0
$241$	15.3923			0.991506			0.495753	−	0.868464i	$-0.334892\pi$
$241$	15.3923			0.991506			0.495753	+	0.868464i	$0.334892\pi$
$242$	14.5663	+	12.1049i	0.936359	+	0.778136i
$243$		0			0
$244$	−10.5622	+	1.96622i	−0.676174	+	0.125874i
$245$	−7.84792			−0.501385
$246$		0			0
$247$		−	1.43937i		−	0.0915852i
$248$	−19.4218	−	10.8465i	−1.23328	−	0.688752i
$249$		0			0
$250$	−12.9282	−	10.7436i	−0.817651	−	0.679487i
$251$		−	2.64673i		−	0.167060i	−0.996505	−	0.0835299i	$-0.973381\pi$
$251$		−	2.64673i		−	0.167060i	0.996505	−	0.0835299i	$-0.0266194\pi$
$252$		0			0
$253$		−	29.3521i		−	1.84535i
$254$		0			0
$255$		0			0
$256$	11.8564	−	10.7436i	0.741025	−	0.671477i
$257$			9.87771i			0.616155i	0.951361	+	0.308077i	$0.0996856\pi$
$257$			9.87771i			0.616155i	−0.951361	+	0.308077i	$0.900314\pi$
$258$		0			0
$259$	3.58846			0.222976
$260$	−16.8197	+	3.13111i	−1.04312	+	0.194183i
$261$		0			0
$262$	−6.53590	+	7.86488i	−0.403789	+	0.485894i
$263$	−23.7724			−1.46587			−0.732935	−	0.680298i	$-0.761850\pi$
$263$	−23.7724			−1.46587			−0.732935	+	0.680298i	$0.761850\pi$
$264$		0			0
$265$	−8.78461			−0.539634
$266$	−0.348605	+	0.419489i	−0.0213743	+	0.0257205i
$267$		0			0
$268$	0.437822	+	2.35190i	0.0267442	+	0.143665i
$269$	0.739059			0.0450612			0.0225306	−	0.999746i	$-0.492828\pi$
$269$	0.739059			0.0450612			0.0225306	+	0.999746i	$0.492828\pi$
$270$		0			0
$271$		−	4.31812i		−	0.262307i	−0.991362	−	0.131154i	$-0.958132\pi$
$271$		−	4.31812i		−	0.262307i	0.991362	−	0.131154i	$-0.0418681\pi$
$272$	−1.90481	−	4.93886i	−0.115496	−	0.299462i
$273$		0			0
$274$	5.33975	−	6.42551i	0.322586	−	0.388179i
$275$			12.1698i			0.733869i
$276$		0			0
$277$		−	2.10739i		−	0.126621i	−0.997994	−	0.0633104i	$-0.979834\pi$
$277$		−	2.10739i		−	0.126621i	0.997994	−	0.0633104i	$-0.0201658\pi$
$278$	−7.82700	−	6.50441i	−0.469432	−	0.390109i
$279$		0			0
$280$	5.66025	+	3.16108i	0.338265	+	0.188911i
$281$		−	7.23099i		−	0.431365i	−0.976464	−	0.215682i	$-0.930802\pi$
$281$		−	7.23099i		−	0.431365i	0.976464	−	0.215682i	$-0.0691975\pi$
$282$		0			0
$283$	0.143594			0.00853575			0.00426787	−	0.999991i	$-0.498641\pi$
$283$	0.143594			0.00853575			0.00426787	+	0.999991i	$0.498641\pi$
$284$	−2.01915	−	10.8465i	−0.119814	−	0.643620i
$285$		0			0
$286$	28.8564	+	23.9803i	1.70632	+	1.41799i
$287$	14.2177			0.839246
$288$		0			0
$289$	15.2487			0.896983
$290$	−15.0711	−	12.5244i	−0.885006	−	0.735460i
$291$		0			0
$292$	−2.90192	−	15.5886i	−0.169822	−	0.912254i
$293$	−7.10886			−0.415304			−0.207652	−	0.978203i	$-0.566582\pi$
$293$	−7.10886			−0.415304			−0.207652	+	0.978203i	$0.566582\pi$
$294$		0			0
$295$			7.86488i			0.457911i
$296$	6.15645	+	3.43820i	0.357837	+	0.199841i
$297$		0			0
$298$	−3.46410	−	2.87875i	−0.200670	−	0.166761i
$299$		−	31.9253i		−	1.84629i
$300$		0			0
$301$		−	2.87875i		−	0.165928i
$302$	−5.80785	+	6.98880i	−0.334204	+	0.402160i
$303$		0			0
$304$	−1.00000	+	0.385679i	−0.0573539	+	0.0221202i
$305$		−	8.55435i		−	0.489821i
$306$		0			0
$307$	7.07180			0.403609			0.201804	−	0.979426i	$-0.435319\pi$
$307$	7.07180			0.403609			0.201804	+	0.979426i	$0.435319\pi$
$308$	−2.60202	−	13.9776i	−0.148264	−	0.796447i
$309$		0			0
$310$	11.3205	−	13.6224i	0.642962	−	0.773699i
$311$	16.9759			0.962616			0.481308	−	0.876551i	$-0.340162\pi$
$311$	16.9759			0.962616			0.481308	+	0.876551i	$0.340162\pi$
$312$		0			0
$313$	−11.3923			−0.643931			−0.321966	−	0.946751i	$-0.604344\pi$
$313$	−11.3923			−0.643931			−0.321966	+	0.946751i	$0.604344\pi$
$314$	1.90481	−	2.29213i	0.107495	−	0.129352i
$315$		0			0
$316$	−23.9545	+	4.45929i	−1.34754	+	0.250855i
$317$	2.33151			0.130951			0.0654753	−	0.997854i	$-0.479144\pi$
$317$	2.33151			0.130951			0.0654753	+	0.997854i	$0.479144\pi$
$318$		0			0
$319$			42.9745i			2.40611i
$320$	6.68216	+	10.8465i	0.373544	+	0.606337i
$321$		0			0
$322$	−7.73205	+	9.30426i	−0.430890	+	0.518506i
$323$			0.354594i			0.0197301i
$324$		0			0
$325$			13.2367i			0.734240i
$326$	−20.8790	−	17.3509i	−1.15638	−	0.960977i
$327$		0			0
$328$	24.3923	+	13.6224i	1.34684	+	0.752170i
$329$		−	13.1386i		−	0.724355i
$330$		0			0
$331$	26.1244			1.43592			0.717962	−	0.696082i	$-0.245075\pi$
$331$	26.1244			1.43592			0.717962	+	0.696082i	$0.245075\pi$
$332$	14.2177	−	2.64673i	0.780299	−	0.145258i
$333$		0			0
$334$	5.53590	+	4.60046i	0.302911	+	0.251726i
$335$	−1.90481			−0.104071
$336$		0			0
$337$	9.39230			0.511631			0.255816	−	0.966726i	$-0.417656\pi$
$337$	9.39230			0.511631			0.255816	+	0.966726i	$0.417656\pi$
$338$	17.2464	+	14.3322i	0.938083	+	0.779568i
$339$		0			0
$340$	4.14359	−	0.771358i	0.224718	−	0.0418328i
$341$	−38.8435			−2.10350
$342$		0			0
$343$		−	17.1691i		−	0.927047i
$344$	2.75821	−	4.93886i	0.148712	−	0.266285i
$345$		0			0
$346$	−12.9282	−	10.7436i	−0.695025	−	0.577581i
$347$		−	19.7554i		−	1.06053i	−0.847833	−	0.530263i	$-0.822093\pi$
$347$		−	19.7554i		−	1.06053i	0.847833	−	0.530263i	$-0.177907\pi$
$348$		0			0
$349$			23.9803i			1.28364i	0.766856	+	0.641819i	$0.221820\pi$
$349$			23.9803i			1.28364i	−0.766856	+	0.641819i	$0.778180\pi$
$350$	3.20583	−	3.85769i	0.171359	−	0.206202i
$351$		0			0
$352$	8.92820	−	26.4734i	0.475875	−	1.41104i
$353$		−	19.7554i		−	1.05148i	−0.850647	−	0.525738i	$-0.823789\pi$
$353$		−	19.7554i		−	1.05148i	0.850647	−	0.525738i	$-0.176211\pi$
$354$		0			0
$355$	8.78461			0.466239
$356$	31.0375	−	5.77783i	1.64498	−	0.306225i
$357$		0			0
$358$	8.92820	−	10.7436i	0.471870	−	0.567819i
$359$	6.79650			0.358705			0.179353	−	0.983785i	$-0.442600\pi$
$359$	6.79650			0.358705			0.179353	+	0.983785i	$0.442600\pi$
$360$		0			0
$361$	−18.9282			−0.996221
$362$	−14.5663	+	17.5282i	−0.765589	+	0.921261i
$363$		0			0
$364$	−2.83013	−	15.2029i	−0.148339	−	0.796850i
$365$	12.6253			0.660837
$366$		0			0
$367$		−	16.3978i		−	0.855957i	−0.903789	−	0.427979i	$-0.859226\pi$
$367$		−	16.3978i		−	0.855957i	0.903789	−	0.427979i	$-0.140774\pi$
$368$	−22.1800	+	8.55435i	−1.15621	+	0.445926i
$369$		0			0
$370$	−3.58846	+	4.31812i	−0.186555	+	0.224488i
$371$		−	7.94018i		−	0.412233i
$372$		0			0
$373$			18.2228i			0.943543i	0.881721	+	0.471771i	$0.156385\pi$
$373$			18.2228i			0.943543i	−0.881721	+	0.471771i	$0.843615\pi$
$374$	−7.10886	−	5.90763i	−0.367590	−	0.305476i
$375$		0			0
$376$	12.5885	−	22.5410i	0.649200	−	1.16246i
$377$			46.7418i			2.40733i
$378$		0			0
$379$	−29.7321			−1.52723			−0.763616	−	0.645670i	$-0.776578\pi$
$379$	−29.7321			−1.52723			−0.763616	+	0.645670i	$0.776578\pi$
$380$	−0.156182	−	0.838978i	−0.00801194	−	0.0430387i
$381$		0			0
$382$	−9.92820	−	8.25056i	−0.507971	−	0.422136i
$383$	−11.8862			−0.607357			−0.303679	−	0.952775i	$-0.598215\pi$
$383$	−11.8862			−0.607357			−0.303679	+	0.952775i	$0.598215\pi$
$384$		0			0
$385$	11.3205			0.576947
$386$	−16.7417	−	13.9127i	−0.852128	−	0.708138i
$387$		0			0
$388$	3.43782	+	18.4673i	0.174529	+	0.937538i
$389$	−7.96225			−0.403702			−0.201851	−	0.979416i	$-0.564696\pi$
$389$	−7.96225			−0.403702			−0.201851	+	0.979416i	$0.564696\pi$
$390$		0			0
$391$			7.86488i			0.397744i
$392$	6.79650	−	12.1698i	0.343275	−	0.614670i
$393$		0			0
$394$	−21.5885	−	17.9405i	−1.08761	−	0.903829i
$395$		−	19.4008i		−	0.976162i
$396$		0			0
$397$			13.6224i			0.683688i	0.939757	+	0.341844i	$0.111051\pi$
$397$			13.6224i			0.683688i	−0.939757	+	0.341844i	$0.888949\pi$
$398$	−12.9167	+	15.5431i	−0.647456	+	0.779108i
$399$		0			0
$400$	9.19615	−	3.54676i	0.459808	−	0.177338i
$401$			39.5109i			1.97308i	0.163527	+	0.986539i	$0.447713\pi$
$401$			39.5109i			1.97308i	−0.163527	+	0.986539i	$0.552287\pi$
$402$		0			0
$403$	−42.2487			−2.10456
$404$	−1.16575	−	6.26222i	−0.0579985	−	0.311557i
$405$		0			0
$406$	11.3205	−	13.6224i	0.561827	−	0.676067i
$407$	12.3129			0.610328
$408$		0			0
$409$	−29.3923			−1.45336			−0.726678	−	0.686978i	$-0.758937\pi$
$409$	−29.3923			−1.45336			−0.726678	+	0.686978i	$0.758937\pi$
$410$	−14.2177	+	17.1087i	−0.702163	+	0.844939i
$411$		0			0
$412$	−2.83013	+	0.526847i	−0.139430	+	0.0259559i
$413$	−7.10886			−0.349804
$414$		0			0
$415$			11.5150i			0.565249i
$416$	9.71088	−	28.7942i	0.476115	−	1.41175i
$417$		0			0
$418$	−1.19615	+	1.43937i	−0.0585057	+	0.0704021i
$419$		−	0.354594i		−	0.0173230i	−0.999962	−	0.00866152i	$-0.997243\pi$
$419$		−	0.354594i		−	0.0173230i	0.999962	−	0.00866152i	$-0.00275708\pi$
$420$		0			0
$421$		−	13.2367i		−	0.645117i	−0.946549	−	0.322559i	$-0.895457\pi$
$421$		−	13.2367i		−	0.645117i	0.946549	−	0.322559i	$-0.104543\pi$
$422$	18.5475	+	15.4134i	0.902876	+	0.750310i
$423$		0			0
$424$	7.60770	−	13.6224i	0.369462	−	0.661561i
$425$		−	3.26090i		−	0.158177i
$426$		0			0
$427$	7.73205			0.374180
$428$	−23.9286	+	4.45447i	−1.15663	+	0.215315i
$429$		0			0
$430$	3.46410	+	2.87875i	0.167054	+	0.138826i
$431$	38.4168			1.85047			0.925237	−	0.379390i	$-0.123866\pi$
$431$	38.4168			1.85047			0.925237	+	0.379390i	$0.123866\pi$
$432$		0			0
$433$	11.4641			0.550930			0.275465	−	0.961311i	$-0.411168\pi$
$433$	11.4641			0.550930			0.275465	+	0.961311i	$0.411168\pi$
$434$	12.3129	+	10.2323i	0.591038	+	0.491166i
$435$		0			0
$436$	−26.7846	+	4.98614i	−1.28275	+	0.238793i
$437$	1.59245			0.0761772
$438$		0			0
$439$			35.1096i			1.67569i	0.545907	+	0.837846i	$0.316185\pi$
$439$			35.1096i			1.67569i	−0.545907	+	0.837846i	$0.683815\pi$
$440$	19.4218	+	10.8465i	0.925896	+	0.517086i
$441$		0			0
$442$	−7.73205	−	6.42551i	−0.367776	−	0.305630i
$443$			31.5707i			1.49997i	0.661456	+	0.749984i	$0.269939\pi$
$443$			31.5707i			1.49997i	−0.661456	+	0.749984i	$0.730061\pi$
$444$		0			0
$445$			25.1374i			1.19163i
$446$	−17.5170	+	21.0788i	−0.829452	+	0.998110i
$447$		0			0
$448$	−9.80385	+	6.03983i	−0.463188	+	0.285355i
$449$			23.0163i			1.08621i	0.839666	+	0.543104i	$0.182751\pi$
$449$			23.0163i			1.08621i	−0.839666	+	0.543104i	$0.817249\pi$
$450$		0			0
$451$	48.7846			2.29718
$452$	22.0238	−	4.09988i	1.03591	−	0.192842i
$453$		0			0
$454$	8.92820	−	10.7436i	0.419021	−	0.504224i
$455$	12.3129			0.577238
$456$		0			0
$457$	−14.3923			−0.673244			−0.336622	−	0.941640i	$-0.609284\pi$
$457$	−14.3923			−0.673244			−0.336622	+	0.941640i	$0.609284\pi$
$458$	14.2177	−	17.1087i	0.664350	−	0.799437i
$459$		0			0
$460$	−3.46410	−	18.6085i	−0.161515	−	0.867627i
$461$	−18.9951			−0.884689			−0.442344	−	0.896845i	$-0.645853\pi$
$461$	−18.9951			−0.884689			−0.442344	+	0.896845i	$0.645853\pi$
$462$		0			0
$463$		−	30.7915i		−	1.43100i	−0.698611	−	0.715502i	$-0.746198\pi$
$463$		−	30.7915i		−	1.43100i	0.698611	−	0.715502i	$-0.253802\pi$
$464$	32.4737	−	12.5244i	1.50756	−	0.581432i
$465$		0			0
$466$	−2.39230	+	2.87875i	−0.110821	+	0.133355i
$467$		−	17.4633i		−	0.808105i	−0.914736	−	0.404052i	$-0.867601\pi$
$467$		−	17.4633i		−	0.808105i	0.914736	−	0.404052i	$-0.132399\pi$
$468$		0			0
$469$		−	1.72171i		−	0.0795012i
$470$	15.8102	+	13.1386i	0.729269	+	0.606039i
$471$		0			0
$472$	−12.1962	−	6.81119i	−0.561373	−	0.313510i
$473$		−	9.87771i		−	0.454178i
$474$		0			0
$475$	−0.660254			−0.0302945
$476$	0.697210	+	3.74528i	0.0319566	+	0.171665i
$477$		0			0
$478$	6.92820	+	5.75749i	0.316889	+	0.263342i
$479$	−3.18490			−0.145522			−0.0727609	−	0.997349i	$-0.523181\pi$
$479$	−3.18490			−0.145522			−0.0727609	+	0.997349i	$0.523181\pi$
$480$		0			0
$481$	13.3923			0.610637
$482$	−16.7417	−	13.9127i	−0.762561	−	0.633706i
$483$		0			0
$484$	−4.90192	−	26.3322i	−0.222815	−	1.19692i
$485$	−14.9568			−0.679152
$486$		0			0
$487$			37.8850i			1.71674i	0.513035	+	0.858368i	$0.328521\pi$
$487$			37.8850i			1.71674i	−0.513035	+	0.858368i	$0.671479\pi$
$488$	13.2653	+	7.40828i	0.600493	+	0.335357i
$489$		0			0
$490$	8.53590	+	7.09353i	0.385613	+	0.320453i
$491$			16.7541i			0.756102i	0.925785	+	0.378051i	$0.123406\pi$
$491$			16.7541i			0.756102i	−0.925785	+	0.378051i	$0.876594\pi$
$492$		0			0
$493$		−	11.5150i		−	0.518609i
$494$	−1.30101	+	1.56555i	−0.0585353	+	0.0704376i
$495$		0			0
$496$	11.3205	+	29.3521i	0.508306	+	1.31795i
$497$			7.94018i			0.356166i
$498$		0			0
$499$	−26.3923			−1.18148			−0.590741	−	0.806861i	$-0.701164\pi$
$499$	−26.3923			−1.18148			−0.590741	+	0.806861i	$0.701164\pi$
$500$	4.35066	+	23.3709i	0.194567	+	1.04518i
$501$		0			0
$502$	−2.39230	+	2.87875i	−0.106774	+	0.128485i
$503$	34.3785			1.53286			0.766432	−	0.642326i	$-0.222030\pi$
$503$	34.3785			1.53286			0.766432	+	0.642326i	$0.222030\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	−26.5306	+	31.9253i	−1.17943	+	1.41925i
$507$		0			0
$508$		0			0
$509$	−22.1800			−0.983110			−0.491555	−	0.870847i	$-0.663571\pi$
$509$	−22.1800			−0.983110			−0.491555	+	0.870847i	$0.663571\pi$
$510$		0			0
$511$			11.4116i			0.504822i
$512$	−22.6067	+	0.968769i	−0.999083	+	0.0428139i
$513$		0			0
$514$	8.92820	−	10.7436i	0.393806	−	0.473881i
$515$		−	2.29213i		−	0.101003i
$516$		0			0
$517$		−	45.0819i		−	1.98270i
$518$	−3.90304	−	3.24351i	−0.171490	−	0.142512i
$519$		0			0
$520$	21.1244	+	11.7973i	0.926364	+	0.517347i
$521$			1.32336i			0.0579776i	0.999580	+	0.0289888i	$0.00922871\pi$
$521$			1.32336i			0.0579776i	−0.999580	+	0.0289888i	$0.990771\pi$
$522$		0			0
$523$	−6.41154			−0.280357			−0.140179	−	0.990126i	$-0.544768\pi$
$523$	−6.41154			−0.280357			−0.140179	+	0.990126i	$0.544768\pi$
$524$	14.2177	−	2.64673i	0.621104	−	0.115623i
$525$		0			0
$526$	25.8564	+	21.4873i	1.12739	+	0.936889i
$527$	10.4081			0.453384
$528$		0			0
$529$	12.3205			0.535674
$530$	9.55470	+	7.94018i	0.415030	+	0.344899i
$531$		0			0
$532$	0.758330	−	0.141168i	0.0328778	−	0.00612042i
$533$	53.0613			2.29834
$534$		0			0
$535$		−	19.3799i		−	0.837865i
$536$	1.64962	−	2.95381i	0.0712526	−	0.127585i
$537$		0			0
$538$	−0.803848	−	0.668016i	−0.0346563	−	0.0288002i
$539$		−	24.3397i		−	1.04838i
$540$		0			0
$541$			12.4653i			0.535927i	0.963429	+	0.267963i	$0.0863506\pi$
$541$			12.4653i			0.535927i	−0.963429	+	0.267963i	$0.913649\pi$
$542$	−3.90304	+	4.69666i	−0.167650	+	0.201739i
$543$		0			0
$544$	−2.39230	+	7.09353i	−0.102569	+	0.304132i
$545$		−	21.6930i		−	0.929224i
$546$		0			0
$547$	−0.411543			−0.0175963			−0.00879815	−	0.999961i	$-0.502801\pi$
$547$	−0.411543			−0.0175963			−0.00879815	+	0.999961i	$0.502801\pi$
$548$	−11.6157	+	2.16234i	−0.496198	+	0.0923706i
$549$		0			0
$550$	11.0000	−	13.2367i	0.469042	−	0.564415i
$551$	−2.33151			−0.0993256
$552$		0			0
$553$	17.5359			0.745702
$554$	−1.90481	+	2.29213i	−0.0809278	+	0.0973833i
$555$		0			0
$556$	2.63397	+	14.1492i	0.111705	+	0.600061i
$557$	−36.3977			−1.54222			−0.771110	−	0.636702i	$-0.780298\pi$
$557$	−36.3977			−1.54222			−0.771110	+	0.636702i	$0.780298\pi$
$558$		0			0
$559$		−	10.7436i		−	0.454407i
$560$	−3.29923	−	8.55435i	−0.139418	−	0.361487i
$561$		0			0
$562$	−6.53590	+	7.86488i	−0.275700	+	0.331760i
$563$		−	11.8153i		−	0.497953i	−0.968509	−	0.248977i	$-0.919906\pi$
$563$		−	11.8153i		−	0.497953i	0.968509	−	0.248977i	$-0.0800943\pi$
$564$		0			0
$565$			17.8372i			0.750415i
$566$	−0.156182	−	0.129790i	−0.00656480	−	0.00545550i
$567$		0			0
$568$	−7.60770	+	13.6224i	−0.319212	+	0.571582i
$569$			35.5408i			1.48995i	0.667094	+	0.744973i	$0.267538\pi$
$569$			35.5408i			1.48995i	−0.667094	+	0.744973i	$0.732462\pi$
$570$		0			0
$571$	7.19615			0.301150			0.150575	−	0.988599i	$-0.451888\pi$
$571$	7.19615			0.301150			0.150575	+	0.988599i	$0.451888\pi$
$572$	−9.71088	−	52.1651i	−0.406032	−	2.18113i
$573$		0			0
$574$	−15.4641	−	12.8510i	−0.645459	−	0.536391i
$575$	−14.6444			−0.610714
$576$		0			0
$577$	−1.92820			−0.0802722			−0.0401361	−	0.999194i	$-0.512779\pi$
$577$	−1.92820			−0.0802722			−0.0401361	+	0.999194i	$0.512779\pi$
$578$	−16.5855	−	13.7829i	−0.689865	−	0.573293i
$579$		0			0
$580$	5.07180	+	27.2448i	0.210595	+	1.13128i
$581$	−10.4081			−0.431801
$582$		0			0
$583$		−	27.2448i		−	1.12836i
$584$	−10.9338	+	19.5781i	−0.452444	+	0.810149i
$585$		0			0
$586$	7.73205	+	6.42551i	0.319408	+	0.265435i
$587$			16.7541i			0.691516i	0.938324	+	0.345758i	$0.112378\pi$
$587$			16.7541i			0.691516i	−0.938324	+	0.345758i	$0.887622\pi$
$588$		0			0
$589$		−	2.10739i		−	0.0868335i
$590$	7.10886	−	8.55435i	0.292667	−	0.352177i
$591$		0			0
$592$	−3.58846	−	9.30426i	−0.147485	−	0.382403i
$593$			1.93754i			0.0795651i	0.999208	+	0.0397826i	$0.0126665\pi$
$593$			1.93754i			0.0795651i	−0.999208	+	0.0397826i	$0.987333\pi$
$594$		0			0
$595$	−3.03332			−0.124354
$596$	1.16575	+	6.26222i	0.0477512	+	0.256510i
$597$		0			0
$598$	−28.8564	+	34.7240i	−1.18003	+	1.41997i
$599$	−43.5066			−1.77763			−0.888815	−	0.458267i	$-0.848471\pi$
$599$	−43.5066			−1.77763			−0.888815	+	0.458267i	$0.848471\pi$
$600$		0			0
$601$	9.60770			0.391906			0.195953	−	0.980613i	$-0.437220\pi$
$601$	9.60770			0.391906			0.195953	+	0.980613i	$0.437220\pi$
$602$	−2.60202	+	3.13111i	−0.106051	+	0.127615i
$603$		0			0
$604$	12.6340	−	2.35190i	0.514069	−	0.0956975i
$605$	21.3266			0.867049
$606$		0			0
$607$		−	27.1414i		−	1.10164i	−0.834625	−	0.550818i	$-0.814316\pi$
$607$		−	27.1414i		−	1.10164i	0.834625	−	0.550818i	$-0.185684\pi$
$608$	1.43627	+	0.484384i	0.0582484	+	0.0196444i
$609$		0			0
$610$	−7.73205	+	9.30426i	−0.313062	+	0.376718i
$611$		−	49.0340i		−	1.98370i
$612$		0			0
$613$		−	2.49307i		−	0.100694i	−0.998732	−	0.0503470i	$-0.983967\pi$
$613$		−	2.49307i		−	0.100694i	0.998732	−	0.0503470i	$-0.0160327\pi$
$614$	−7.69174	−	6.39201i	−0.310413	−	0.257961i
$615$		0			0
$616$	−9.80385	+	17.5548i	−0.395008	+	0.707304i
$617$		−	23.7255i		−	0.955153i	−0.878590	−	0.477577i	$-0.841515\pi$
$617$		−	23.7255i		−	0.955153i	0.878590	−	0.477577i	$-0.158485\pi$
$618$		0			0
$619$	26.8038			1.07734			0.538669	−	0.842518i	$-0.318927\pi$
$619$	26.8038			1.07734			0.538669	+	0.842518i	$0.318927\pi$
$620$	−24.6258	+	4.58426i	−0.988997	+	0.184108i
$621$		0			0
$622$	−18.4641	−	15.3441i	−0.740343	−	0.615242i
$623$	−22.7210			−0.910298
$624$		0			0
$625$	−6.60770			−0.264308
$626$	12.3910	+	10.2972i	0.495244	+	0.411559i
$627$		0			0
$628$	−4.14359	+	0.771358i	−0.165347	+	0.0307805i
$629$	−3.29923			−0.131549
$630$		0			0
$631$		−	17.9405i		−	0.714200i	−0.934066	−	0.357100i	$-0.883766\pi$
$631$		−	17.9405i		−	0.714200i	0.934066	−	0.357100i	$-0.116234\pi$
$632$	30.0851	+	16.8016i	1.19672	+	0.668332i
$633$		0			0
$634$	−2.53590	−	2.10739i	−0.100713	−	0.0836951i
$635$		0			0
$636$		0			0
$637$		−	26.4734i		−	1.04891i
$638$	38.8435	−	46.7418i	1.53783	−	1.85053i
$639$		0			0
$640$	2.53590	−	17.8372i	0.100240	−	0.705076i
$641$		−	11.8153i		−	0.466674i	−0.972396	−	0.233337i	$-0.925035\pi$
$641$		−	11.8153i		−	0.466674i	0.972396	−	0.233337i	$-0.0749646\pi$
$642$		0			0
$643$	22.7846			0.898537			0.449269	−	0.893397i	$-0.351685\pi$
$643$	22.7846			0.898537			0.449269	+	0.893397i	$0.351685\pi$
$644$	16.8197	−	3.13111i	0.662791	−	0.123383i
$645$		0			0
$646$	0.320508	−	0.385679i	0.0126102	−	0.0151743i
$647$	1.47812			0.0581108			0.0290554	−	0.999578i	$-0.490750\pi$
$647$	1.47812			0.0581108			0.0290554	+	0.999578i	$0.490750\pi$
$648$		0			0
$649$	−24.3923			−0.957482
$650$	11.9643	−	14.3971i	0.469279	−	0.564700i
$651$		0			0
$652$	7.02628	+	37.7439i	0.275170	+	1.47816i
$653$	27.8107			1.08832			0.544159	−	0.838982i	$-0.316849\pi$
$653$	27.8107			1.08832			0.544159	+	0.838982i	$0.316849\pi$
$654$		0			0
$655$			11.5150i			0.449928i
$656$	−14.2177	−	36.8641i	−0.555109	−	1.43930i
$657$		0			0
$658$	−11.8756	+	14.2904i	−0.462961	+	0.557098i
$659$			22.4022i			0.872664i	0.899786	+	0.436332i	$0.143723\pi$
$659$			22.4022i			0.872664i	−0.899786	+	0.436332i	$0.856277\pi$
$660$		0			0
$661$		−	41.2528i		−	1.60455i	−0.596956	−	0.802274i	$-0.703623\pi$
$661$		−	41.2528i		−	1.60455i	0.596956	−	0.802274i	$-0.296377\pi$
$662$	−28.4145	−	23.6131i	−1.10436	−	0.917750i
$663$		0			0
$664$	−17.8564	−	9.97227i	−0.692963	−	0.386999i
$665$			0.614175i			0.0238167i
$666$		0			0
$667$	−51.7128			−2.00233
$668$	−1.86296	−	10.0075i	−0.0720803	−	0.387202i
$669$		0			0
$670$	2.07180	+	1.72171i	0.0800405	+	0.0665155i
$671$	26.5306			1.02420
$672$		0			0
$673$	−13.2487			−0.510700			−0.255350	−	0.966849i	$-0.582191\pi$
$673$	−13.2487			−0.510700			−0.255350	+	0.966849i	$0.582191\pi$
$674$	−10.2157	−	8.48946i	−0.393493	−	0.327002i
$675$		0			0
$676$	−5.80385	−	31.1772i	−0.223225	−	1.19912i
$677$	−12.0005			−0.461218			−0.230609	−	0.973046i	$-0.574072\pi$
$677$	−12.0005			−0.461218			−0.230609	+	0.973046i	$0.574072\pi$
$678$		0			0
$679$		−	13.5190i		−	0.518813i
$680$	−5.20405	−	2.90631i	−0.199566	−	0.111452i
$681$		0			0
$682$	42.2487	+	35.1096i	1.61779	+	1.34442i
$683$			34.9266i			1.33643i	0.743969	+	0.668214i	$0.232941\pi$
$683$			34.9266i			1.33643i	−0.743969	+	0.668214i	$0.767059\pi$
$684$		0			0
$685$		−	9.40760i		−	0.359446i
$686$	−15.5187	+	18.6743i	−0.592508	+	0.712986i
$687$		0			0
$688$	−7.46410	+	2.87875i	−0.284566	+	0.109751i
$689$		−	29.6331i		−	1.12893i
$690$		0			0
$691$	−23.8564			−0.907540			−0.453770	−	0.891119i	$-0.649921\pi$
$691$	−23.8564			−0.907540			−0.453770	+	0.891119i	$0.649921\pi$
$692$	4.35066	+	23.3709i	0.165387	+	0.888429i
$693$		0			0
$694$	−17.8564	+	21.4873i	−0.677820	+	0.815645i
$695$	−11.4595			−0.434684
$696$		0			0
$697$	−13.0718			−0.495130
$698$	21.6752	−	26.0825i	0.820418	−	0.987239i
$699$		0			0
$700$	−6.97372	+	1.29821i	−0.263582	+	0.0490676i
$701$	−17.2883			−0.652970			−0.326485	−	0.945202i	$-0.605864\pi$
$701$	−17.2883			−0.652970			−0.326485	+	0.945202i	$0.605864\pi$
$702$		0			0
$703$			0.668016i			0.0251947i
$704$	−33.6395	+	20.7242i	−1.26784	+	0.781072i
$705$		0			0
$706$	−17.8564	+	21.4873i	−0.672035	+	0.808684i
$707$			4.58426i			0.172409i
$708$		0			0
$709$			27.6304i			1.03768i	0.854870	+	0.518841i	$0.173636\pi$
$709$			27.6304i			1.03768i	−0.854870	+	0.518841i	$0.826364\pi$
$710$	−9.55470	−	7.94018i	−0.358582	−	0.297989i
$711$		0			0
$712$	−38.9808	−	21.7696i	−1.46087	−	0.815850i
$713$		−	46.7418i		−	1.75050i
$714$		0			0
$715$	42.2487			1.58001
$716$	−19.4218	+	3.61549i	−0.725826	+	0.135117i
$717$		0			0
$718$	−7.39230	−	6.14317i	−0.275878	−	0.229261i
$719$	15.0711			0.562058			0.281029	−	0.959699i	$-0.409324\pi$
$719$	15.0711			0.562058			0.281029	+	0.959699i	$0.409324\pi$
$720$		0			0
$721$	2.07180			0.0771577
$722$	20.5875	+	17.1087i	0.766188	+	0.636720i
$723$		0			0
$724$	31.6865	−	5.89866i	1.17762	−	0.219222i
$725$	21.4409			0.796296
$726$		0			0
$727$		−	19.3799i		−	0.718760i	−0.933191	−	0.359380i	$-0.882988\pi$
$727$		−	19.3799i		−	0.718760i	0.933191	−	0.359380i	$-0.117012\pi$
$728$	−10.6633	+	19.0937i	−0.395208	+	0.707661i
$729$		0			0
$730$	−13.7321	−	11.4116i	−0.508246	−	0.422364i
$731$			2.64673i			0.0978927i
$732$		0			0
$733$		−	45.0819i		−	1.66514i	−0.553921	−	0.832569i	$-0.686869\pi$
$733$		−	45.0819i		−	1.66514i	0.553921	−	0.832569i	$-0.313131\pi$
$734$	−14.8215	+	17.8353i	−0.547072	+	0.658312i
$735$		0			0
$736$	31.8564	+	10.7436i	1.17424	+	0.396016i
$737$		−	5.90763i		−	0.217610i
$738$		0			0
$739$	48.6410			1.78929			0.894644	−	0.446779i	$-0.147429\pi$
$739$	48.6410			1.78929			0.894644	+	0.446779i	$0.147429\pi$
$740$	7.80607	−	1.45315i	0.286957	−	0.0534190i
$741$		0			0
$742$	−7.17691	+	8.63624i	−0.263473	+	0.317046i
$743$	−43.3085			−1.58884			−0.794418	−	0.607372i	$-0.792224\pi$
$743$	−43.3085			−1.58884			−0.794418	+	0.607372i	$0.792224\pi$
$744$		0			0
$745$	−5.07180			−0.185816
$746$	16.4711	−	19.8203i	0.603051	−	0.725674i
$747$		0			0
$748$	2.39230	+	12.8510i	0.0874713	+	0.469880i
$749$	17.5170			0.640056
$750$		0			0
$751$		−	7.19687i		−	0.262617i	−0.991342	−	0.131309i	$-0.958082\pi$
$751$		−	7.19687i		−	0.262617i	0.991342	−	0.131309i	$-0.0419179\pi$
$752$	−34.0662	+	13.1386i	−1.24227	+	0.479116i
$753$		0			0
$754$	42.2487	−	50.8394i	1.53861	−	1.85146i
$755$			10.2323i			0.372392i
$756$		0			0
$757$			36.0600i			1.31062i	0.755359	+	0.655311i	$0.227463\pi$
$757$			36.0600i			1.31062i	−0.755359	+	0.655311i	$0.772537\pi$
$758$	32.3385	+	26.8740i	1.17459	+	0.976108i
$759$		0			0
$760$	−0.588457	+	1.05369i	−0.0213456	+	0.0382215i
$761$			26.3722i			0.955993i	0.878362	+	0.477996i	$0.158637\pi$
$761$			26.3722i			0.955993i	−0.878362	+	0.477996i	$0.841363\pi$
$762$		0			0
$763$	19.6077			0.709846
$764$	3.34108	+	17.9477i	0.120876	+	0.649324i
$765$		0			0
$766$	12.9282	+	10.7436i	0.467115	+	0.388183i
$767$	−26.5306			−0.957965
$768$		0			0
$769$	17.9282			0.646508			0.323254	−	0.946312i	$-0.395223\pi$
$769$	17.9282			0.646508			0.323254	+	0.946312i	$0.395223\pi$
$770$	−12.3129	−	10.2323i	−0.443726	−	0.368747i
$771$		0			0
$772$	5.63397	+	30.2647i	0.202771	+	1.08925i
$773$	34.1805			1.22939			0.614694	−	0.788766i	$-0.289280\pi$
$773$	34.1805			1.22939			0.614694	+	0.788766i	$0.289280\pi$
$774$		0			0
$775$			19.3799i			0.696146i
$776$	12.9530	−	23.1936i	0.464984	−	0.832603i
$777$		0			0
$778$	8.66025	+	7.19687i	0.310485	+	0.258020i
$779$			2.64673i			0.0948288i
$780$		0			0
$781$			27.2448i			0.974894i
$782$	7.10886	−	8.55435i	0.254212	−	0.305903i
$783$		0			0
$784$	−18.3923	+	7.09353i	−0.656868	+	0.253340i
$785$		−	3.35591i		−	0.119778i
$786$		0			0
$787$	−51.4449			−1.83381			−0.916906	−	0.399104i	$-0.869321\pi$
$787$	−51.4449			−1.83381			−0.916906	+	0.399104i	$0.869321\pi$
$788$	7.26504	+	39.0265i	0.258806	+	1.39026i
$789$		0			0
$790$	−17.5359	+	21.1016i	−0.623899	+	0.750761i
$791$	−16.1225			−0.573251
$792$		0			0
$793$	28.8564			1.02472
$794$	12.3129	−	14.8166i	0.436969	−	0.525820i
$795$		0			0
$796$	28.0981	−	5.23065i	0.995910	−	0.185395i
$797$	−7.84792			−0.277988			−0.138994	−	0.990293i	$-0.544387\pi$
$797$	−7.84792			−0.277988			−0.138994	+	0.990293i	$0.544387\pi$
$798$		0			0
$799$			12.0797i			0.427348i
$800$	−13.2081	−	4.45447i	−0.466979	−	0.157489i
$801$		0			0
$802$	35.7128	−	42.9745i	1.26106	−	1.51748i
$803$			39.1563i			1.38179i
$804$		0			0
$805$			13.6224i			0.480126i
$806$	45.9524	+	38.1875i	1.61860	+	1.34510i
$807$		0			0
$808$	−4.39230	+	7.86488i	−0.154521	+	0.276686i
$809$		−	2.64673i		−	0.0930539i	−0.998917	−	0.0465270i	$-0.985185\pi$
$809$		−	2.64673i		−	0.0930539i	0.998917	−	0.0465270i	$-0.0148153\pi$
$810$		0			0
$811$	−40.9282			−1.43718			−0.718592	−	0.695432i	$-0.755213\pi$
$811$	−40.9282			−1.43718			−0.718592	+	0.695432i	$0.755213\pi$
$812$	−24.6258	+	4.58426i	−0.864197	+	0.160876i
$813$		0			0
$814$	−13.3923	−	11.1293i	−0.469400	−	0.390082i
$815$	−30.5689			−1.07078
$816$		0			0
$817$	0.535898			0.0187487
$818$	31.9689	+	26.5669i	1.11777	+	0.928891i
$819$		0			0
$820$	30.9282	−	5.75749i	1.08006	−	0.201060i
$821$	16.6636			0.581562			0.290781	−	0.956790i	$-0.406085\pi$
$821$	16.6636			0.581562			0.290781	+	0.956790i	$0.406085\pi$
$822$		0			0
$823$			28.6841i			0.999866i	0.866064	+	0.499933i	$0.166642\pi$
$823$			28.6841i			0.999866i	−0.866064	+	0.499933i	$0.833358\pi$
$824$	3.55443	+	1.98504i	0.123824	+	0.0691523i
$825$		0			0
$826$	7.73205	+	6.42551i	0.269032	+	0.223572i
$827$			3.00132i			0.104366i	0.998638	+	0.0521830i	$0.0166179\pi$
$827$			3.00132i			0.104366i	−0.998638	+	0.0521830i	$0.983382\pi$
$828$		0			0
$829$		−	12.4653i		−	0.432939i	−0.976289	−	0.216470i	$-0.930546\pi$
$829$		−	12.4653i		−	0.432939i	0.976289	−	0.216470i	$-0.0694542\pi$
$830$	10.4081	−	12.5244i	0.361270	−	0.434730i
$831$		0			0
$832$	−36.5885	+	22.5410i	−1.26848	+	0.781467i
$833$			6.52180i			0.225967i
$834$		0			0
$835$	8.10512			0.280489
$836$	2.60202	−	0.484384i	0.0899929	−	0.0167528i
$837$		0			0
$838$	−0.320508	+	0.385679i	−0.0110718	+	0.0133231i
$839$	57.0996			1.97130			0.985648	−	0.168815i	$-0.0539942\pi$
$839$	57.0996			1.97130			0.985648	+	0.168815i	$0.0539942\pi$
$840$		0			0
$841$	46.7128			1.61079
$842$	−11.9643	+	14.3971i	−0.412317	+	0.496156i
$843$		0			0
$844$	−6.24167	−	33.5291i	−0.214847	−	1.15412i
$845$	25.2505			0.868645
$846$		0			0
$847$			19.2765i			0.662349i
$848$	−20.5875	+	7.94018i	−0.706978	+	0.272667i
$849$		0			0
$850$	−2.94744	+	3.54676i	−0.101096	+	0.121653i
$851$			14.8166i			0.507905i
$852$		0			0
$853$			0.385679i			0.0132054i	0.999978	+	0.00660270i	$0.00210172\pi$
$853$			0.385679i			0.0132054i	−0.999978	+	0.00660270i	$0.997898\pi$
$854$	−8.40987	−	6.98880i	−0.287780	−	0.239152i
$855$		0			0
$856$	30.0526	+	16.7835i	1.02718	+	0.573647i
$857$		−	36.8641i		−	1.25925i	−0.776897	−	0.629627i	$-0.783208\pi$
$857$		−	36.8641i		−	1.25925i	0.776897	−	0.629627i	$-0.216792\pi$
$858$		0			0
$859$	−19.5885			−0.668350			−0.334175	−	0.942511i	$-0.608458\pi$
$859$	−19.5885			−0.668350			−0.334175	+	0.942511i	$0.608458\pi$
$860$	−1.16575	−	6.26222i	−0.0397519	−	0.213540i
$861$		0			0
$862$	−41.7846	−	34.7240i	−1.42319	−	1.18270i
$863$	−8.27462			−0.281671			−0.140836	−	0.990033i	$-0.544979\pi$
$863$	−8.27462			−0.281671			−0.140836	+	0.990033i	$0.544979\pi$
$864$		0			0
$865$	−18.9282			−0.643578
$866$	−12.4691	−	10.3621i	−0.423717	−	0.352118i
$867$		0			0
$868$	−4.14359	−	22.2586i	−0.140643	−	0.755507i
$869$	60.1701			2.04113
$870$		0			0
$871$		−	6.42551i		−	0.217720i
$872$	33.6395	+	18.7867i	1.13918	+	0.636197i
$873$		0			0
$874$	−1.73205	−	1.43937i	−0.0585875	−	0.0486875i
$875$		−	17.1087i		−	0.578380i
$876$		0			0
$877$			21.8729i			0.738597i	0.929311	+	0.369298i	$0.120402\pi$
$877$			21.8729i			0.738597i	−0.929311	+	0.369298i	$0.879598\pi$
$878$	31.7347	−	38.1875i	1.07099	−	1.28877i
$879$		0			0
$880$	−11.3205	−	29.3521i	−0.381614	−	0.989461i
$881$			35.5408i			1.19740i	0.800974	+	0.598699i	$0.204316\pi$
$881$			35.5408i			1.19740i	−0.800974	+	0.598699i	$0.795684\pi$
$882$		0			0
$883$	19.8756			0.668869			0.334434	−	0.942419i	$-0.391455\pi$
$883$	19.8756			0.668869			0.334434	+	0.942419i	$0.391455\pi$
$884$	2.60202	+	13.9776i	0.0875155	+	0.470117i
$885$		0			0
$886$	28.5359	−	34.3383i	0.958682	−	1.15362i
$887$	19.7341			0.662607			0.331304	−	0.943524i	$-0.392512\pi$
$887$	19.7341			0.662607			0.331304	+	0.943524i	$0.392512\pi$
$888$		0			0
$889$		0			0
$890$	22.7210	−	27.3410i	0.761610	−	0.916473i
$891$		0			0
$892$	38.1051	−	7.09353i	1.27585	−	0.237509i
$893$	2.44584			0.0818470
$894$		0			0
$895$		−	15.7298i		−	0.525788i
$896$	16.1225	+	2.29213i	0.538616	+	0.0765747i
$897$		0			0
$898$	20.8038	−	25.0340i	0.694233	−	0.835396i
$899$			68.4348i			2.28243i
$900$		0			0
$901$			7.30021i			0.243205i
$902$	−53.0613	−	44.0951i	−1.76675	−	1.46821i
$903$		0			0
$904$	−27.6603	−	15.4474i	−0.919966	−	0.513774i
$905$			25.6631i			0.853069i
$906$		0			0
$907$	26.3731			0.875703			0.437852	−	0.899047i	$-0.355740\pi$
$907$	26.3731			0.875703			0.437852	+	0.899047i	$0.355740\pi$
$908$	−19.4218	+	3.61549i	−0.644534	+	0.119984i
$909$		0			0
$910$	−13.3923	−	11.1293i	−0.443951	−	0.368933i
$911$	−44.3599			−1.46971			−0.734855	−	0.678224i	$-0.762750\pi$
$911$	−44.3599			−1.46971			−0.734855	+	0.678224i	$0.762750\pi$
$912$		0			0
$913$	−35.7128			−1.18192
$914$	15.6540	+	13.0088i	0.517788	+	0.430294i
$915$		0			0
$916$	−30.9282	+	5.75749i	−1.02190	+	0.190233i
$917$	−10.4081			−0.343706
$918$		0			0
$919$			30.8949i			1.01913i	0.860433	+	0.509564i	$0.170193\pi$
$919$			30.8949i			1.01913i	−0.860433	+	0.509564i	$0.829807\pi$
$920$	−13.0520	+	23.3709i	−0.430311	+	0.770516i
$921$		0			0
$922$	20.6603	+	17.1691i	0.680409	+	0.565436i
$923$			29.6331i			0.975387i
$924$		0			0
$925$		−	6.14317i		−	0.201986i
$926$	−27.8316	+	33.4908i	−0.914604	+	1.10058i
$927$		0			0
$928$	−46.6410	−	15.7298i	−1.53107	−	0.516355i
$929$			14.4620i			0.474482i	0.971451	+	0.237241i	$0.0762431\pi$
$929$			14.4620i			0.474482i	−0.971451	+	0.237241i	$0.923757\pi$
$930$		0			0
$931$	1.32051			0.0432779
$932$	5.20405	−	0.968769i	0.170464	−	0.0317331i
$933$		0			0
$934$	−15.7846	+	18.9942i	−0.516488	+	0.621509i
$935$	−10.4081			−0.340381
$936$		0			0
$937$	−2.60770			−0.0851897			−0.0425948	−	0.999092i	$-0.513562\pi$
$937$	−2.60770			−0.0851897			−0.0425948	+	0.999092i	$0.513562\pi$
$938$	−1.55621	+	1.87264i	−0.0508120	+	0.0611439i
$939$		0			0
$940$	−5.32051	−	28.5808i	−0.173536	−	0.932203i
$941$	−31.7347			−1.03452			−0.517260	−	0.855828i	$-0.673048\pi$
$941$	−31.7347			−1.03452			−0.517260	+	0.855828i	$0.673048\pi$
$942$		0			0
$943$			58.7043i			1.91167i
$944$	7.10886	+	18.4321i	0.231374	+	0.599913i
$945$		0			0
$946$	−8.92820	+	10.7436i	−0.290281	+	0.349306i
$947$		−	26.6318i		−	0.865418i	−0.901534	−	0.432709i	$-0.857558\pi$
$947$		−	26.6318i		−	0.865418i	0.901534	−	0.432709i	$-0.142442\pi$
$948$		0			0
$949$			42.5888i			1.38249i
$950$	0.718134	+	0.596786i	0.0232994	+	0.0193623i
$951$		0			0
$952$	2.62693	−	4.70380i	0.0851394	−	0.152451i
$953$		−	57.9429i		−	1.87696i	−0.345340	−	0.938478i	$-0.612236\pi$
$953$		−	57.9429i		−	1.87696i	0.345340	−	0.938478i	$-0.387764\pi$
$954$		0			0
$955$	−14.5359			−0.470371
$956$	−2.33151	−	12.5244i	−0.0754064	−	0.405069i
$957$		0			0
$958$	3.46410	+	2.87875i	0.111920	+	0.0930081i
$959$	8.50328			0.274585
$960$		0			0
$961$	−30.8564			−0.995368
$962$	−14.5663	−	12.1049i	−0.469637	−	0.390279i
$963$		0			0
$964$	5.63397	+	30.2647i	0.181458	+	0.974760i
$965$	−24.5115			−0.789053
$966$		0			0
$967$			6.42551i			0.206630i	0.994649	+	0.103315i	$0.0329451\pi$
$967$			6.42551i			0.206630i	−0.994649	+	0.103315i	$0.967055\pi$
$968$	−18.4694	+	33.0713i	−0.593628	+	1.06295i
$969$		0			0
$970$	16.2679	+	13.5190i	0.522332	+	0.434070i
$971$		−	42.5122i		−	1.36428i	−0.731221	−	0.682140i	$-0.761049\pi$
$971$		−	42.5122i		−	1.36428i	0.731221	−	0.682140i	$-0.238951\pi$
$972$		0			0
$973$		−	10.3580i		−	0.332061i
$974$	34.2433	−	41.2062i	1.09723	−	1.32033i
$975$		0			0
$976$	−7.73205	−	20.0479i	−0.247497	−	0.641717i
$977$		−	41.4484i		−	1.32605i	−0.748597	−	0.663026i	$-0.769272\pi$
$977$		−	41.4484i		−	1.32605i	0.748597	−	0.663026i	$-0.230728\pi$
$978$		0			0
$979$	−77.9615			−2.49166
$980$	−2.87254	−	15.4307i	−0.0917599	−	0.492917i
$981$		0			0
$982$	15.1436	−	18.2228i	0.483251	−	0.581514i
$983$	−54.1127			−1.72593			−0.862963	−	0.505267i	$-0.831394\pi$
$983$	−54.1127			−1.72593			−0.862963	+	0.505267i	$0.831394\pi$
$984$		0			0
$985$	−31.6077			−1.00710
$986$	−10.4081	+	12.5244i	−0.331461	+	0.398859i
$987$		0			0
$988$	2.83013	−	0.526847i	0.0900383	−	0.0167612i
$989$	11.8862			0.377960
$990$		0			0
$991$		−	0.668016i		−	0.0212202i	−0.999944	−	0.0106101i	$-0.996623\pi$
$991$		−	0.668016i		−	0.0212202i	0.999944	−	0.0106101i	$-0.00337737\pi$
$992$	14.2177	−	42.1576i	0.451413	−	1.33850i
$993$		0			0
$994$	7.17691	−	8.63624i	0.227638	−	0.273925i
$995$			22.7567i			0.721437i
$996$		0			0
$997$		−	29.3521i		−	0.929592i	−0.885418	−	0.464796i	$-0.846128\pi$
$997$		−	29.3521i		−	0.929592i	0.885418	−	0.464796i	$-0.153872\pi$
$998$	28.7060	+	23.8553i	0.908671	+	0.755126i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.f.a.107.1	✓	8
3.2	odd	2	inner	216.2.f.a.107.8	yes	8
4.3	odd	2		864.2.f.a.431.4		8
8.3	odd	2	inner	216.2.f.a.107.7	yes	8
8.5	even	2		864.2.f.a.431.5		8
9.2	odd	6		648.2.l.f.539.5		16
9.4	even	3		648.2.l.f.107.7		16
9.5	odd	6		648.2.l.f.107.2		16
9.7	even	3		648.2.l.f.539.4		16
12.11	even	2		864.2.f.a.431.6		8
24.5	odd	2		864.2.f.a.431.3		8
24.11	even	2	inner	216.2.f.a.107.2	yes	8
36.7	odd	6		2592.2.p.f.2159.6		16
36.11	even	6		2592.2.p.f.2159.4		16
36.23	even	6		2592.2.p.f.431.3		16
36.31	odd	6		2592.2.p.f.431.5		16
72.5	odd	6		2592.2.p.f.431.6		16
72.11	even	6		648.2.l.f.539.7		16
72.13	even	6		2592.2.p.f.431.4		16
72.29	odd	6		2592.2.p.f.2159.5		16
72.43	odd	6		648.2.l.f.539.2		16
72.59	even	6		648.2.l.f.107.4		16
72.61	even	6		2592.2.p.f.2159.3		16
72.67	odd	6		648.2.l.f.107.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.f.a.107.1	✓	8	1.1	even	1	trivial
216.2.f.a.107.2	yes	8	24.11	even	2	inner
216.2.f.a.107.7	yes	8	8.3	odd	2	inner
216.2.f.a.107.8	yes	8	3.2	odd	2	inner
648.2.l.f.107.2		16	9.5	odd	6
648.2.l.f.107.4		16	72.59	even	6
648.2.l.f.107.5		16	72.67	odd	6
648.2.l.f.107.7		16	9.4	even	3
648.2.l.f.539.2		16	72.43	odd	6
648.2.l.f.539.4		16	9.7	even	3
648.2.l.f.539.5		16	9.2	odd	6
648.2.l.f.539.7		16	72.11	even	6
864.2.f.a.431.3		8	24.5	odd	2
864.2.f.a.431.4		8	4.3	odd	2
864.2.f.a.431.5		8	8.5	even	2
864.2.f.a.431.6		8	12.11	even	2
2592.2.p.f.431.3		16	36.23	even	6
2592.2.p.f.431.4		16	72.13	even	6
2592.2.p.f.431.5		16	36.31	odd	6
2592.2.p.f.431.6		16	72.5	odd	6
2592.2.p.f.2159.3		16	72.61	even	6
2592.2.p.f.2159.4		16	36.11	even	6
2592.2.p.f.2159.5		16	72.29	odd	6
2592.2.p.f.2159.6		16	36.7	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08766 - 0.903873i) q^{2} +(0.366025 + 1.96622i) q^{4} -1.59245 q^{5} -1.43937i q^{7} +(1.37910 - 2.46943i) q^{8} +(1.73205 + 1.43937i) q^{10} -4.93886i q^{11} -5.37182i q^{13} +(-1.30101 + 1.56555i) q^{14} +(-3.73205 + 1.43937i) q^{16} +1.32336i q^{17} +0.267949 q^{19} +(-0.582877 - 3.13111i) q^{20} +(-4.46410 + 5.37182i) q^{22} +5.94311 q^{23} -2.46410 q^{25} +(-4.85544 + 5.84273i) q^{26} +(2.83013 - 0.526847i) q^{28} -8.70131 q^{29} -7.86488i q^{31} +(5.36023 + 1.80775i) q^{32} +(1.19615 - 1.43937i) q^{34} +2.29213i q^{35} +2.49307i q^{37} +(-0.291439 - 0.242192i) q^{38} +(-2.19615 + 3.93244i) q^{40} +9.87771i q^{41} +2.00000 q^{43} +(9.71088 - 1.80775i) q^{44} +(-6.46410 - 5.37182i) q^{46} +9.12801 q^{47} +4.92820 q^{49} +(2.68011 + 2.22724i) q^{50} +(10.5622 - 1.96622i) q^{52} +5.51641 q^{53} +7.86488i q^{55} +(-3.55443 - 1.98504i) q^{56} +(9.46410 + 7.86488i) q^{58} -4.93886i q^{59} +5.37182i q^{61} +(-7.10886 + 8.55435i) q^{62} +(-4.19615 - 6.81119i) q^{64} +8.55435i q^{65} +1.19615 q^{67} +(-2.60202 + 0.484384i) q^{68} +(2.07180 - 2.49307i) q^{70} -5.51641 q^{71} -7.92820 q^{73} +(2.25342 - 2.71162i) q^{74} +(0.0980762 + 0.526847i) q^{76} -7.10886 q^{77} +12.1830i q^{79} +(5.94311 - 2.29213i) q^{80} +(8.92820 - 10.7436i) q^{82} -7.23099i q^{83} -2.10739i q^{85} +(-2.17533 - 1.80775i) q^{86} +(-12.1962 - 6.81119i) q^{88} -15.7853i q^{89} -7.73205 q^{91} +(2.17533 + 11.6855i) q^{92} +(-9.92820 - 8.25056i) q^{94} -0.426696 q^{95} +9.39230 q^{97} +(-5.36023 - 4.45447i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{4} - 16 q^{16} + 16 q^{19} - 8 q^{22} + 8 q^{25} - 12 q^{28} - 32 q^{34} + 24 q^{40} + 16 q^{43} - 24 q^{46} - 16 q^{49} + 36 q^{52} + 48 q^{58} + 8 q^{64} - 32 q^{67} + 72 q^{70} - 8 q^{73}+ \cdots - 8 q^{97}+O(q^{100}) \) 8 * q - 4 * q^4 - 16 * q^16 + 16 * q^19 - 8 * q^22 + 8 * q^25 - 12 * q^28 - 32 * q^34 + 24 * q^40 + 16 * q^43 - 24 * q^46 - 16 * q^49 + 36 * q^52 + 48 * q^58 + 8 * q^64 - 32 * q^67 + 72 * q^70 - 8 * q^73 - 20 * q^76 + 16 * q^82 - 56 * q^88 - 48 * q^91 - 24 * q^94 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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