LMFDB - Embedded newform 912.2.bh.f.767.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(239,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))

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

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

chi := DirichletCharacter("912.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bh (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			767.7
Character	$\chi$	$=$	912.767
Dual form			912.2.bh.f.239.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.325205 - 1.70125i) q^{3} +(-0.164566 + 0.0950122i) q^{5} +0.883190i q^{7} +(-2.78848 - 1.10651i) q^{9} -3.88483 q^{11} +(-2.04597 + 3.54372i) q^{13} +(0.108122 + 0.310866i) q^{15} +(-3.97390 + 2.29433i) q^{17} +(-3.03184 - 3.13176i) q^{19} +(1.50252 + 0.287218i) q^{21} +(1.39463 - 2.41558i) q^{23} +(-2.48195 + 4.29886i) q^{25} +(-2.78927 + 4.38406i) q^{27} +(-2.80681 - 1.62051i) q^{29} -4.38406i q^{31} +(-1.26337 + 6.60906i) q^{33} +(-0.0839138 - 0.145343i) q^{35} +0.128042 q^{37} +(5.36338 + 4.63313i) q^{39} +(-1.63972 + 0.946691i) q^{41} +(3.36531 - 1.94296i) q^{43} +(0.564021 - 0.0828466i) q^{45} +(2.07366 - 3.59168i) q^{47} +6.21998 q^{49} +(2.61089 + 7.50671i) q^{51} +(-11.2845 - 6.51511i) q^{53} +(0.639311 - 0.369107i) q^{55} +(-6.31387 + 4.13945i) q^{57} +(4.94684 + 8.56818i) q^{59} +(-3.04597 + 5.27577i) q^{61} +(0.977256 - 2.46276i) q^{63} -0.777567i q^{65} +(-12.7119 - 7.33924i) q^{67} +(-3.65595 - 3.15818i) q^{69} +(4.43262 + 7.67752i) q^{71} +(2.37196 + 4.10835i) q^{73} +(6.50628 + 5.62041i) q^{75} -3.43105i q^{77} +(0.305846 - 0.176580i) q^{79} +(6.55129 + 6.17095i) q^{81} +1.00091 q^{83} +(0.435979 - 0.755138i) q^{85} +(-3.66968 + 4.24808i) q^{87} +(-0.493698 - 0.285037i) q^{89} +(-3.12978 - 1.80698i) q^{91} +(-7.45837 - 1.42572i) q^{93} +(0.796493 + 0.227320i) q^{95} +(0.981945 + 1.70078i) q^{97} +(10.8328 + 4.29860i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) $ 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.325205	−	1.70125i	0.187757	−	0.982216i
$3$	0.325205	−	1.70125i	0.187757	−	0.982216i
$4$		0			0
$5$	−0.164566	+	0.0950122i	−0.0735961	+	0.0424907i	−0.536346	−	0.843998i	$-0.680196\pi$
$5$	−0.164566	+	0.0950122i	−0.0735961	+	0.0424907i	0.462750	+	0.886489i	$0.346863\pi$
$6$		0			0
$7$			0.883190i			0.333814i	0.985973	+	0.166907i	$0.0533780\pi$
$7$			0.883190i			0.333814i	−0.985973	+	0.166907i	$0.946622\pi$
$8$		0			0
$9$	−2.78848	−	1.10651i	−0.929495	−	0.368836i
$10$		0			0
$11$	−3.88483			−1.17132			−0.585661	−	0.810556i	$-0.699165\pi$
$11$	−3.88483			−1.17132			−0.585661	+	0.810556i	$0.699165\pi$
$12$		0			0
$13$	−2.04597	+	3.54372i	−0.567449	+	0.982851i	0.429368	+	0.903130i	$0.358736\pi$
$13$	−2.04597	+	3.54372i	−0.567449	+	0.982851i	−0.996817	+	0.0797210i	$0.974597\pi$
$14$		0			0
$15$	0.108122	+	0.310866i	0.0279169	+	0.0802652i
$16$		0			0
$17$	−3.97390	+	2.29433i	−0.963812	+	0.556457i	−0.897344	−	0.441332i	$-0.854506\pi$
$17$	−3.97390	+	2.29433i	−0.963812	+	0.556457i	−0.0664678	+	0.997789i	$0.521173\pi$
$18$		0			0
$19$	−3.03184	−	3.13176i	−0.695552	−	0.718476i
$19$	−3.03184	−	3.13176i	−0.695552	−	0.718476i
$20$		0			0
$21$	1.50252	+	0.287218i	0.327878	+	0.0626760i
$22$		0			0
$23$	1.39463	−	2.41558i	0.290801	−	0.503683i	−0.683198	−	0.730233i	$-0.739411\pi$
$23$	1.39463	−	2.41558i	0.290801	−	0.503683i	0.973999	+	0.226550i	$0.0727448\pi$
$24$		0			0
$25$	−2.48195	+	4.29886i	−0.496389	+	0.859771i
$26$		0			0
$27$	−2.78927	+	4.38406i	−0.536795	+	0.843713i
$28$		0			0
$29$	−2.80681	−	1.62051i	−0.521211	−	0.300921i	0.216219	−	0.976345i	$-0.430628\pi$
$29$	−2.80681	−	1.62051i	−0.521211	−	0.300921i	−0.737430	+	0.675424i	$0.763961\pi$
$30$		0			0
$31$		−	4.38406i		−	0.787400i	−0.919239	−	0.393700i	$-0.871195\pi$
$31$		−	4.38406i		−	0.787400i	0.919239	−	0.393700i	$-0.128805\pi$
$32$		0			0
$33$	−1.26337	+	6.60906i	−0.219924	+	1.15049i
$34$		0			0
$35$	−0.0839138	−	0.145343i	−0.0141840	−	0.0245675i
$36$		0			0
$37$	0.128042			0.0210500			0.0105250	−	0.999945i	$-0.496650\pi$
$37$	0.128042			0.0210500			0.0105250	+	0.999945i	$0.496650\pi$
$38$		0			0
$39$	5.36338	+	4.63313i	0.858829	+	0.741894i
$40$		0			0
$41$	−1.63972	+	0.946691i	−0.256081	+	0.147848i	−0.622545	−	0.782584i	$-0.713901\pi$
$41$	−1.63972	+	0.946691i	−0.256081	+	0.147848i	0.366465	+	0.930432i	$0.380568\pi$
$42$		0			0
$43$	3.36531	−	1.94296i	0.513204	−	0.296299i	−0.220945	−	0.975286i	$-0.570914\pi$
$43$	3.36531	−	1.94296i	0.513204	−	0.296299i	0.734150	+	0.678987i	$0.237581\pi$
$44$		0			0
$45$	0.564021	−	0.0828466i	0.0840793	−	0.0123500i
$46$		0			0
$47$	2.07366	−	3.59168i	0.302474	−	0.523901i	−0.674221	−	0.738529i	$-0.735521\pi$
$47$	2.07366	−	3.59168i	0.302474	−	0.523901i	0.976696	+	0.214628i	$0.0688540\pi$
$48$		0			0
$49$	6.21998			0.888568
$50$		0			0
$51$	2.61089	+	7.50671i	0.365598	+	1.05115i
$52$		0			0
$53$	−11.2845	−	6.51511i	−1.55005	−	0.894919i	−0.998137	−	0.0610148i	$-0.980566\pi$
$53$	−11.2845	−	6.51511i	−1.55005	−	0.894919i	−0.551909	−	0.833904i	$-0.686100\pi$
$54$		0			0
$55$	0.639311	−	0.369107i	0.0862047	−	0.0497703i
$56$		0			0
$57$	−6.31387	+	4.13945i	−0.836293	+	0.548283i
$58$		0			0
$59$	4.94684	+	8.56818i	0.644024	+	1.11548i	0.984526	+	0.175239i	$0.0560697\pi$
$59$	4.94684	+	8.56818i	0.644024	+	1.11548i	−0.340502	+	0.940244i	$0.610597\pi$
$60$		0			0
$61$	−3.04597	+	5.27577i	−0.389996	+	0.675493i	−0.992449	−	0.122662i	$-0.960857\pi$
$61$	−3.04597	+	5.27577i	−0.389996	+	0.675493i	0.602452	+	0.798155i	$0.294190\pi$
$62$		0			0
$63$	0.977256	−	2.46276i	0.123123	−	0.310279i
$64$		0			0
$65$		−	0.777567i		−	0.0964453i
$66$		0			0
$67$	−12.7119	−	7.33924i	−1.55301	−	0.896631i	−0.997894	−	0.0648581i	$-0.979341\pi$
$67$	−12.7119	−	7.33924i	−1.55301	−	0.896631i	−0.555116	−	0.831773i	$-0.687326\pi$
$68$		0			0
$69$	−3.65595	−	3.15818i	−0.440125	−	0.380200i
$70$		0			0
$71$	4.43262	+	7.67752i	0.526055	+	0.911153i	0.999539	+	0.0303514i	$0.00966263\pi$
$71$	4.43262	+	7.67752i	0.526055	+	0.911153i	−0.473485	+	0.880802i	$0.657004\pi$
$72$		0			0
$73$	2.37196	+	4.10835i	0.277617	+	0.480846i	0.970792	−	0.239923i	$-0.0771222\pi$
$73$	2.37196	+	4.10835i	0.277617	+	0.480846i	−0.693175	+	0.720769i	$0.743789\pi$
$74$		0			0
$75$	6.50628	+	5.62041i	0.751280	+	0.648989i
$76$		0			0
$77$		−	3.43105i		−	0.391004i
$78$		0			0
$79$	0.305846	−	0.176580i	0.0344104	−	0.0198669i	−0.482696	−	0.875788i	$-0.660342\pi$
$79$	0.305846	−	0.176580i	0.0344104	−	0.0198669i	0.517107	+	0.855921i	$0.327009\pi$
$80$		0			0
$81$	6.55129	+	6.17095i	0.727921	+	0.685661i
$82$		0			0
$83$	1.00091			0.109864			0.0549318	−	0.998490i	$-0.482506\pi$
$83$	1.00091			0.109864			0.0549318	+	0.998490i	$0.482506\pi$
$84$		0			0
$85$	0.435979	−	0.755138i	0.0472885	−	0.0819062i
$86$		0			0
$87$	−3.66968	+	4.24808i	−0.393431	+	0.455442i
$88$		0			0
$89$	−0.493698	−	0.285037i	−0.0523319	−	0.0302138i	0.473606	−	0.880737i	$-0.342952\pi$
$89$	−0.493698	−	0.285037i	−0.0523319	−	0.0302138i	−0.525938	+	0.850523i	$0.676285\pi$
$90$		0			0
$91$	−3.12978	−	1.80698i	−0.328090	−	0.189423i
$92$		0			0
$93$	−7.45837	−	1.42572i	−0.773397	−	0.147840i
$94$		0			0
$95$	0.796493	+	0.227320i	0.0817185	+	0.0233225i
$96$		0			0
$97$	0.981945	+	1.70078i	0.0997014	+	0.172688i	0.911561	−	0.411165i	$-0.134878\pi$
$97$	0.981945	+	1.70078i	0.0997014	+	0.172688i	−0.811860	+	0.583853i	$0.801545\pi$
$98$		0			0
$99$	10.8328	+	4.29860i	1.08874	+	0.432025i
$100$		0			0
$101$	13.5976	+	7.85059i	1.35301	+	0.781162i	0.988670	−	0.150103i	$-0.0479604\pi$
$101$	13.5976	+	7.85059i	1.35301	+	0.781162i	0.364343	+	0.931265i	$0.381294\pi$
$102$		0			0
$103$		−	7.88493i		−	0.776925i	−0.921465	−	0.388463i	$-0.873006\pi$
$103$		−	7.88493i		−	0.776925i	0.921465	−	0.388463i	$-0.126994\pi$
$104$		0			0
$105$	−0.274554	+	0.0954919i	−0.0267937	+	0.00931906i
$106$		0			0
$107$	−7.76967			−0.751122			−0.375561	−	0.926798i	$-0.622550\pi$
$107$	−7.76967			−0.751122			−0.375561	+	0.926798i	$0.622550\pi$
$108$		0			0
$109$	−7.07388	−	12.2523i	−0.677555	−	1.17356i	−0.975715	−	0.219043i	$-0.929706\pi$
$109$	−7.07388	−	12.2523i	−0.677555	−	1.17356i	0.298160	−	0.954516i	$-0.403627\pi$
$110$		0			0
$111$	0.0416399	−	0.217832i	0.00395229	−	0.0206757i
$112$		0			0
$113$			16.6513i			1.56642i	0.621756	+	0.783211i	$0.286420\pi$
$113$			16.6513i			1.56642i	−0.621756	+	0.783211i	$0.713580\pi$
$114$		0			0
$115$			0.530029i			0.0494255i
$116$		0			0
$117$	9.62629	−	7.61772i	0.889951	−	0.704259i
$118$		0			0
$119$	−2.02633	−	3.50971i	−0.185753	−	0.321734i
$120$		0			0
$121$	4.09193			0.371994
$122$		0			0
$123$	1.07731	+	3.09743i	0.0971379	+	0.279286i
$124$		0			0
$125$		−	1.89338i		−	0.169349i
$126$		0			0
$127$	3.49086	+	2.01545i	0.309764	+	0.178842i	0.646821	−	0.762642i	$-0.276098\pi$
$127$	3.49086	+	2.01545i	0.309764	+	0.178842i	−0.337057	+	0.941484i	$0.609432\pi$
$128$		0			0
$129$	−2.21104	−	6.35708i	−0.194671	−	0.559710i
$130$		0			0
$131$	−8.14962	−	14.1156i	−0.712036	−	1.23328i	−0.964092	−	0.265569i	$-0.914440\pi$
$131$	−8.14962	−	14.1156i	−0.712036	−	1.23328i	0.252056	−	0.967713i	$-0.418893\pi$
$132$		0			0
$133$	2.76594	−	2.67769i	0.239838	−	0.232185i
$134$		0			0
$135$	0.0424797	−	0.986481i	0.00365607	−	0.0849028i
$136$		0			0
$137$	−6.81691	−	3.93574i	−0.582408	−	0.336253i	0.179682	−	0.983725i	$-0.442493\pi$
$137$	−6.81691	−	3.93574i	−0.582408	−	0.336253i	−0.762090	+	0.647472i	$0.775826\pi$
$138$		0			0
$139$	−14.2141	−	8.20649i	−1.20562	−	0.696065i	−0.243821	−	0.969820i	$-0.578401\pi$
$139$	−14.2141	−	8.20649i	−1.20562	−	0.696065i	−0.961799	+	0.273755i	$0.911734\pi$
$140$		0			0
$141$	−5.43598	−	4.69584i	−0.457792	−	0.395461i
$142$		0			0
$143$	7.94824	−	13.7668i	0.664665	−	1.15123i
$144$		0			0
$145$	0.615873			0.0511455
$146$		0			0
$147$	2.02276	−	10.5817i	0.166835	−	0.872765i
$148$		0			0
$149$	17.8855	−	10.3262i	1.46524	−	0.845956i	0.465993	−	0.884789i	$-0.345697\pi$
$149$	17.8855	−	10.3262i	1.46524	−	0.845956i	0.999246	+	0.0388328i	$0.0123640\pi$
$150$		0			0
$151$		−	8.28797i		−	0.674465i	−0.941421	−	0.337233i	$-0.890509\pi$
$151$		−	8.28797i		−	0.674465i	0.941421	−	0.337233i	$-0.109491\pi$
$152$		0			0
$153$	13.6198	−	2.00056i	1.10110	−	0.161736i
$154$		0			0
$155$	0.416539	+	0.721467i	0.0334572	+	0.0579496i
$156$		0			0
$157$	−6.46389	−	11.1958i	−0.515875	−	0.893521i	−0.999830	−	0.0184285i	$-0.994134\pi$
$157$	−6.46389	−	11.1958i	−0.515875	−	0.893521i	0.483956	−	0.875093i	$-0.339200\pi$
$158$		0			0
$159$	−14.7536	+	17.0790i	−1.17004	+	1.35445i
$160$		0			0
$161$	2.13341	+	1.23173i	0.168137	+	0.0970737i
$162$		0			0
$163$			1.17314i			0.0918877i	0.998944	+	0.0459439i	$0.0146295\pi$
$163$			1.17314i			0.0918877i	−0.998944	+	0.0459439i	$0.985370\pi$
$164$		0			0
$165$	−0.420034	−	1.20766i	−0.0326996	−	0.0940163i
$166$		0			0
$167$	−8.33122	+	14.4301i	−0.644689	+	1.11663i	0.339684	+	0.940540i	$0.389680\pi$
$167$	−8.33122	+	14.4301i	−0.644689	+	1.11663i	−0.984373	+	0.176095i	$0.943653\pi$
$168$		0			0
$169$	−1.87196	−	3.24233i	−0.143997	−	0.249410i
$170$		0			0
$171$	4.98892	+	12.0876i	0.381513	+	0.924364i
$172$		0			0
$173$	15.7521	−	9.09448i	1.19761	−	0.691440i	0.237588	−	0.971366i	$-0.423643\pi$
$173$	15.7521	−	9.09448i	1.19761	−	0.691440i	0.960022	+	0.279926i	$0.0903098\pi$
$174$		0			0
$175$	−3.79671	−	2.19203i	−0.287004	−	0.165702i
$176$		0			0
$177$	16.1853	−	5.62939i	1.21656	−	0.423131i
$178$		0			0
$179$	0.833078			0.0622672			0.0311336	−	0.999515i	$-0.490088\pi$
$179$	0.833078			0.0622672			0.0311336	+	0.999515i	$0.490088\pi$
$180$		0			0
$181$	5.07388	−	8.78822i	0.377138	−	0.653223i	−0.613506	−	0.789690i	$-0.710241\pi$
$181$	5.07388	−	8.78822i	0.377138	−	0.653223i	0.990645	+	0.136467i	$0.0435748\pi$
$182$		0			0
$183$	7.98482	+	6.89765i	0.590255	+	0.509889i
$184$		0			0
$185$	−0.0210714	+	0.0121656i	−0.00154920	+	0.000894431i
$186$		0			0
$187$	15.4379	−	8.91310i	1.12893	−	0.651790i
$188$		0			0
$189$	−3.87196	−	2.46346i	−0.281643	−	0.179190i
$190$		0			0
$191$	−20.6144			−1.49160			−0.745802	−	0.666167i	$-0.767934\pi$
$191$	−20.6144			−1.49160			−0.745802	+	0.666167i	$0.767934\pi$
$192$		0			0
$193$	−0.0820758	−	0.142159i	−0.00590794	−	0.0102329i	0.863056	−	0.505108i	$-0.168547\pi$
$193$	−0.0820758	−	0.142159i	−0.00590794	−	0.0102329i	−0.868964	+	0.494875i	$0.835214\pi$
$194$		0			0
$195$	−1.32283	−	0.252868i	−0.0947301	−	0.0181083i
$196$		0			0
$197$			16.4787i			1.17406i	0.809565	+	0.587031i	$0.199703\pi$
$197$			16.4787i			1.17406i	−0.809565	+	0.587031i	$0.800297\pi$
$198$		0			0
$199$	−13.6024	−	7.85332i	−0.964246	−	0.556707i	−0.0667685	−	0.997768i	$-0.521269\pi$
$199$	−13.6024	−	7.85332i	−0.964246	−	0.556707i	−0.897477	+	0.441061i	$0.854602\pi$
$200$		0			0
$201$	−16.6198	+	19.2394i	−1.17227	+	1.35704i
$202$		0			0
$203$	1.43122	−	2.47894i	0.100452	−	0.173988i
$204$		0			0
$205$	0.179894	−	0.311586i	0.0125644	−	0.0217621i
$206$		0			0
$207$	−6.56177	+	5.19263i	−0.456075	+	0.360913i
$208$		0			0
$209$	11.7782	+	12.1664i	0.814715	+	0.841566i
$210$		0			0
$211$	−5.09091	+	2.93924i	−0.350472	+	0.202345i	−0.664893	−	0.746938i	$-0.731523\pi$
$211$	−5.09091	+	2.93924i	−0.350472	+	0.202345i	0.314421	+	0.949284i	$0.398190\pi$
$212$		0			0
$213$	14.5029	−	5.04421i	0.993720	−	0.345624i
$214$		0			0
$215$	−0.369210	+	0.639490i	−0.0251799	+	0.0436129i
$216$		0			0
$217$	3.87196			0.262846
$218$		0			0
$219$	7.76069	−	2.69923i	0.524419	−	0.182397i
$220$		0			0
$221$		−	18.7765i		−	1.26304i
$222$		0			0
$223$	7.48344	−	4.32056i	0.501128	−	0.289326i	−0.228051	−	0.973649i	$-0.573235\pi$
$223$	7.48344	−	4.32056i	0.501128	−	0.289326i	0.729179	+	0.684323i	$0.239902\pi$
$224$		0			0
$225$	11.6776	−	9.24100i	0.778505	−	0.616067i
$226$		0			0
$227$	15.5608			1.03281			0.516404	−	0.856345i	$-0.327270\pi$
$227$	15.5608			1.03281			0.516404	+	0.856345i	$0.327270\pi$
$228$		0			0
$229$	−17.6599			−1.16700			−0.583500	−	0.812113i	$-0.698317\pi$
$229$	−17.6599			−1.16700			−0.583500	+	0.812113i	$0.698317\pi$
$230$		0			0
$231$	−5.83706	−	1.11579i	−0.384050	−	0.0734137i
$232$		0			0
$233$	−0.981453	+	0.566642i	−0.0642971	+	0.0371220i	−0.531804	−	0.846868i	$-0.678486\pi$
$233$	−0.981453	+	0.566642i	−0.0642971	+	0.0371220i	0.467507	+	0.883989i	$0.345152\pi$
$234$		0			0
$235$			0.788092i			0.0514094i
$236$		0			0
$237$	−0.200944	−	0.577745i	−0.0130527	−	0.0375286i
$238$		0			0
$239$	12.8508			0.831248			0.415624	−	0.909537i	$-0.363563\pi$
$239$	12.8508			0.831248			0.415624	+	0.909537i	$0.363563\pi$
$240$		0			0
$241$	10.4639	−	18.1240i	0.674038	−	1.16747i	−0.302710	−	0.953083i	$-0.597892\pi$
$241$	10.4639	−	18.1240i	0.674038	−	1.16747i	0.976749	−	0.214386i	$-0.0687751\pi$
$242$		0			0
$243$	12.6288	−	9.13853i	0.810140	−	0.586237i
$244$		0			0
$245$	−1.02360	+	0.590973i	−0.0653952	+	0.0377559i
$246$		0			0
$247$	17.3011	−	4.33651i	1.10084	−	0.275926i
$248$		0			0
$249$	0.325499	−	1.70279i	0.0206277	−	0.107910i
$250$		0			0
$251$	−5.19555	+	8.99896i	−0.327941	+	0.568010i	−0.982103	−	0.188344i	$-0.939688\pi$
$251$	−5.19555	+	8.99896i	−0.327941	+	0.568010i	0.654163	+	0.756354i	$0.273021\pi$
$252$		0			0
$253$	−5.41792	+	9.38412i	−0.340622	+	0.589975i
$254$		0			0
$255$	−1.14289	−	0.987282i	−0.0715708	−	0.0618260i
$256$		0			0
$257$	−6.00002	−	3.46411i	−0.374271	−	0.216085i	0.301052	−	0.953608i	$-0.402662\pi$
$257$	−6.00002	−	3.46411i	−0.374271	−	0.216085i	−0.675323	+	0.737522i	$0.735996\pi$
$258$		0			0
$259$			0.113086i			0.00702680i
$260$		0			0
$261$	6.03363	+	7.62452i	0.373472	+	0.471946i
$262$		0			0
$263$	12.4648	+	21.5896i	0.768611	+	1.33127i	0.938316	+	0.345778i	$0.112385\pi$
$263$	12.4648	+	21.5896i	0.768611	+	1.33127i	−0.169706	+	0.985495i	$0.554282\pi$
$264$		0			0
$265$	2.47606			0.152103
$266$		0			0
$267$	−0.645470	+	0.747207i	−0.0395022	+	0.0457283i
$268$		0			0
$269$	22.5117	−	12.9972i	1.37256	−	0.792451i	0.381314	−	0.924445i	$-0.375472\pi$
$269$	22.5117	−	12.9972i	1.37256	−	0.792451i	0.991250	+	0.131995i	$0.0421383\pi$
$270$		0			0
$271$	5.02059	−	2.89864i	0.304979	−	0.176080i	−0.339698	−	0.940534i	$-0.610325\pi$
$271$	5.02059	−	2.89864i	0.304979	−	0.176080i	0.644678	+	0.764455i	$0.276992\pi$
$272$		0			0
$273$	−4.09193	+	4.73689i	−0.247655	+	0.286689i
$274$		0			0
$275$	9.64195	−	16.7003i	0.581431	−	1.00707i
$276$		0			0
$277$	11.0919			0.666450			0.333225	−	0.942847i	$-0.391863\pi$
$277$	11.0919			0.666450			0.333225	+	0.942847i	$0.391863\pi$
$278$		0			0
$279$	−4.85099	+	12.2249i	−0.290421	+	0.731884i
$280$		0			0
$281$	−8.44149	−	4.87370i	−0.503577	−	0.290741i	0.226612	−	0.973985i	$-0.427235\pi$
$281$	−8.44149	−	4.87370i	−0.503577	−	0.290741i	−0.730190	+	0.683245i	$0.760568\pi$
$282$		0			0
$283$	−26.1064	+	15.0725i	−1.55186	+	0.895969i	−0.553873	+	0.832601i	$0.686851\pi$
$283$	−26.1064	+	15.0725i	−1.55186	+	0.895969i	−0.997990	+	0.0633678i	$0.979816\pi$
$284$		0			0
$285$	0.645750	−	1.28111i	0.0382509	−	0.0758862i
$286$		0			0
$287$	−0.836108	−	1.44818i	−0.0493539	−	0.0854835i
$288$		0			0
$289$	2.02791	−	3.51245i	0.119289	−	0.206614i
$290$		0			0
$291$	3.21278	−	1.11743i	0.188336	−	0.0655049i
$292$		0			0
$293$			9.93742i			0.580550i	0.956943	+	0.290275i	$0.0937469\pi$
$293$			9.93742i			0.580550i	−0.956943	+	0.290275i	$0.906253\pi$
$294$		0			0
$295$	−1.62816	−	0.940021i	−0.0947954	−	0.0547301i
$296$		0			0
$297$	10.8358	−	17.0313i	0.628760	−	0.988259i
$298$		0			0
$299$	5.70675	+	9.88438i	0.330030	+	0.571629i
$300$		0			0
$301$	1.71600	+	2.97221i	0.0989088	+	0.171315i
$302$		0			0
$303$	17.7778	−	20.5799i	1.02131	−	1.18228i
$304$		0			0
$305$		−	1.15762i		−	0.0662849i
$306$		0			0
$307$	−21.0978	+	12.1808i	−1.20412	+	0.695197i	−0.961468	−	0.274917i	$-0.911350\pi$
$307$	−21.0978	+	12.1808i	−1.20412	+	0.695197i	−0.242649	+	0.970114i	$0.578016\pi$
$308$		0			0
$309$	−13.4142	−	2.56422i	−0.763108	−	0.145873i
$310$		0			0
$311$	−24.1911			−1.37175			−0.685876	−	0.727718i	$-0.740581\pi$
$311$	−24.1911			−1.37175			−0.685876	+	0.727718i	$0.740581\pi$
$312$		0			0
$313$	0.0180546	−	0.0312715i	0.00102051	−	0.00176757i	−0.865515	−	0.500884i	$-0.833008\pi$
$313$	0.0180546	−	0.0312715i	0.00102051	−	0.00176757i	0.866535	+	0.499116i	$0.166342\pi$
$314$		0			0
$315$	0.0731693	+	0.498138i	0.00412262	+	0.0280669i
$316$		0			0
$317$	−19.2323	−	11.1038i	−1.08019	−	0.623650i	−0.149245	−	0.988800i	$-0.547684\pi$
$317$	−19.2323	−	11.1038i	−1.08019	−	0.623650i	−0.930949	+	0.365150i	$0.881018\pi$
$318$		0			0
$319$	10.9040	+	6.29542i	0.610506	+	0.352476i
$320$		0			0
$321$	−2.52673	+	13.2181i	−0.141028	+	0.737764i
$322$		0			0
$323$	19.2335	+	5.48926i	1.07018	+	0.305430i
$324$		0			0
$325$	−10.1560	−	17.5906i	−0.563351	−	0.975753i
$326$		0			0
$327$	−23.1447	+	8.04991i	−1.27990	+	0.445161i
$328$		0			0
$329$	3.17214	+	1.83144i	0.174886	+	0.100970i
$330$		0			0
$331$			10.3895i			0.571060i	0.958370	+	0.285530i	$0.0921696\pi$
$331$			10.3895i			0.571060i	−0.958370	+	0.285530i	$0.907830\pi$
$332$		0			0
$333$	−0.357044	−	0.141680i	−0.0195659	−	0.00776400i
$334$		0			0
$335$	2.78927			0.152394
$336$		0			0
$337$	4.13790	+	7.16705i	0.225406	+	0.390414i	0.956441	−	0.291925i	$-0.0942959\pi$
$337$	4.13790	+	7.16705i	0.225406	+	0.390414i	−0.731035	+	0.682340i	$0.760963\pi$
$338$		0			0
$339$	28.3280	+	5.41508i	1.53856	+	0.294107i
$340$		0			0
$341$			17.0313i			0.922299i
$342$		0			0
$343$			11.6758i			0.630431i
$344$		0			0
$345$	0.901711	+	0.172368i	0.0485465	+	0.00927998i
$346$		0			0
$347$	5.11467	+	8.85887i	0.274570	+	0.475569i	0.970027	−	0.242999i	$-0.0781312\pi$
$347$	5.11467	+	8.85887i	0.274570	+	0.475569i	−0.695457	+	0.718568i	$0.744798\pi$
$348$		0			0
$349$	−20.6356			−1.10460			−0.552299	−	0.833646i	$-0.686249\pi$
$349$	−20.6356			−1.10460			−0.552299	+	0.833646i	$0.686249\pi$
$350$		0			0
$351$	−9.82912	−	18.8540i	−0.524639	−	1.00635i
$352$		0			0
$353$			25.4486i			1.35449i	0.735757	+	0.677245i	$0.236826\pi$
$353$			25.4486i			1.35449i	−0.735757	+	0.677245i	$0.763174\pi$
$354$		0			0
$355$	−1.45892	−	0.842305i	−0.0774312	−	0.0447049i
$356$		0			0
$357$	−6.62985	+	2.30592i	−0.350889	+	0.122042i
$358$		0			0
$359$	−8.07948	−	13.9941i	−0.426419	−	0.738579i	0.570133	−	0.821552i	$-0.306892\pi$
$359$	−8.07948	−	13.9941i	−0.426419	−	0.738579i	−0.996552	+	0.0829734i	$0.973558\pi$
$360$		0			0
$361$	−0.615873	+	18.9900i	−0.0324144	+	0.999475i
$362$		0			0
$363$	1.33072	−	6.96139i	0.0698445	−	0.365378i
$364$		0			0
$365$	−0.780687	−	0.450730i	−0.0408630	−	0.0235923i
$366$		0			0
$367$	20.0266	+	11.5624i	1.04538	+	0.603551i	0.921353	−	0.388727i	$-0.127085\pi$
$367$	20.0266	+	11.5624i	1.04538	+	0.603551i	0.124029	+	0.992279i	$0.460419\pi$
$368$		0			0
$369$	5.61984	−	0.825475i	0.292557	−	0.0429725i
$370$		0			0
$371$	5.75408	−	9.96636i	0.298737	−	0.517428i
$372$		0			0
$373$	21.4597			1.11114			0.555570	−	0.831470i	$-0.312500\pi$
$373$	21.4597			1.11114			0.555570	+	0.831470i	$0.312500\pi$
$374$		0			0
$375$	−3.22111	−	0.615737i	−0.166337	−	0.0317965i
$376$		0			0
$377$	11.4853	−	6.63102i	0.591521	−	0.341515i
$378$		0			0
$379$		−	32.0384i		−	1.64570i	−0.568256	−	0.822852i	$-0.692382\pi$
$379$		−	32.0384i		−	1.64570i	0.568256	−	0.822852i	$-0.307618\pi$
$380$		0			0
$381$	4.56402	−	5.28338i	0.233822	−	0.270676i
$382$		0			0
$383$	−8.82865	−	15.2917i	−0.451123	−	0.781368i	0.547333	−	0.836915i	$-0.315643\pi$
$383$	−8.82865	−	15.2917i	−0.451123	−	0.781368i	−0.998456	+	0.0555472i	$0.982310\pi$
$384$		0			0
$385$	0.325991	+	0.564633i	0.0166141	+	0.0287764i
$386$		0			0
$387$	−11.5340	+	1.69418i	−0.586306	+	0.0861200i
$388$		0			0
$389$	−6.10731	−	3.52606i	−0.309653	−	0.178778i	0.337118	−	0.941462i	$-0.390548\pi$
$389$	−6.10731	−	3.52606i	−0.309653	−	0.178778i	−0.646771	+	0.762684i	$0.723881\pi$
$390$		0			0
$391$			12.7990i			0.647274i
$392$		0			0
$393$	−26.6643	+	9.27408i	−1.34504	+	0.467815i
$394$		0			0
$395$	−0.0335546	+	0.0581183i	−0.00168831	+	0.00292425i
$396$		0			0
$397$	7.26594	+	12.5850i	0.364667	+	0.631622i	0.988723	−	0.149758i	$-0.0478494\pi$
$397$	7.26594	+	12.5850i	0.364667	+	0.631622i	−0.624056	+	0.781380i	$0.714516\pi$
$398$		0			0
$399$	−3.65592	−	5.57635i	−0.183025	−	0.279167i
$400$		0			0
$401$	−16.7487	+	9.66986i	−0.836389	+	0.482890i	−0.856035	−	0.516917i	$-0.827079\pi$
$401$	−16.7487	+	9.66986i	−0.836389	+	0.482890i	0.0196460	+	0.999807i	$0.493746\pi$
$402$		0			0
$403$	15.5359	+	8.96964i	0.773897	+	0.446810i
$404$		0			0
$405$	−1.66443	−	0.393077i	−0.0827064	−	0.0195321i
$406$		0			0
$407$	−0.497423			−0.0246563
$408$		0			0
$409$	−12.3300	+	21.3561i	−0.609677	+	1.05599i	0.381616	+	0.924321i	$0.375368\pi$
$409$	−12.3300	+	21.3561i	−0.609677	+	1.05599i	−0.991293	+	0.131671i	$0.957966\pi$
$410$		0			0
$411$	−8.91256	+	10.3173i	−0.439624	+	0.508916i
$412$		0			0
$413$	−7.56734	+	4.36900i	−0.372364	+	0.214985i
$414$		0			0
$415$	−0.164715	+	0.0950983i	−0.00808554	+	0.00466819i
$416$		0			0
$417$	−18.5837	+	21.5128i	−0.910049	+	1.05349i
$418$		0			0
$419$	−27.0536			−1.32165			−0.660826	−	0.750539i	$-0.729794\pi$
$419$	−27.0536			−1.32165			−0.660826	+	0.750539i	$0.729794\pi$
$420$		0			0
$421$	8.81779	+	15.2729i	0.429753	+	0.744354i	0.996851	−	0.0792963i	$-0.0252673\pi$
$421$	8.81779	+	15.2729i	0.429753	+	0.744354i	−0.567098	+	0.823650i	$0.691934\pi$
$422$		0			0
$423$	−9.75659	+	7.72083i	−0.474382	+	0.375400i
$424$		0			0
$425$		−	22.7776i		−	1.10488i
$426$		0			0
$427$	−4.65951	−	2.69017i	−0.225489	−	0.130186i
$428$		0			0
$429$	−20.8358	−	17.9989i	−1.00596	−	0.868997i
$430$		0			0
$431$	−8.84242	+	15.3155i	−0.425924	+	0.737723i	−0.996506	−	0.0835180i	$-0.973384\pi$
$431$	−8.84242	+	15.3155i	−0.425924	+	0.737723i	0.570582	+	0.821241i	$0.306718\pi$
$432$		0			0
$433$	−4.00986	+	6.94528i	−0.192701	+	0.333769i	−0.946145	−	0.323744i	$-0.895058\pi$
$433$	−4.00986	+	6.94528i	−0.192701	+	0.333769i	0.753443	+	0.657513i	$0.228392\pi$
$434$		0			0
$435$	0.200285	−	1.04775i	0.00960292	−	0.0502359i
$436$		0			0
$437$	−11.7933	+	2.95599i	−0.564151	+	0.141404i
$438$		0			0
$439$	32.2680	−	18.6299i	1.54007	−	0.889159i	0.541234	−	0.840872i	$-0.317957\pi$
$439$	32.2680	−	18.6299i	1.54007	−	0.889159i	0.998834	−	0.0482867i	$-0.0153761\pi$
$440$		0			0
$441$	−17.3443	−	6.88245i	−0.825919	−	0.327735i
$442$		0			0
$443$	10.1760	−	17.6253i	0.483474	−	0.837402i	−0.516346	−	0.856380i	$-0.672708\pi$
$443$	10.1760	−	17.6253i	0.483474	−	0.837402i	0.999820	+	0.0189785i	$0.00604140\pi$
$444$		0			0
$445$	0.108328			0.00513523
$446$		0			0
$447$	−11.7510	−	33.7858i	−0.555802	−	1.59801i
$448$		0			0
$449$		−	19.9098i		−	0.939601i	−0.882773	−	0.469800i	$-0.844326\pi$
$449$		−	19.9098i		−	0.939601i	0.882773	−	0.469800i	$-0.155674\pi$
$450$		0			0
$451$	6.37003	−	3.67774i	0.299953	−	0.173178i
$452$		0			0
$453$	−14.0999	−	2.69529i	−0.662470	−	0.126636i
$454$		0			0
$455$	0.686740			0.0321948
$456$		0			0
$457$	−6.52394			−0.305177			−0.152589	−	0.988290i	$-0.548761\pi$
$457$	−6.52394			−0.305177			−0.152589	+	0.988290i	$0.548761\pi$
$458$		0			0
$459$	1.02579	−	23.8213i	0.0478798	−	1.11188i
$460$		0			0
$461$	−31.5193	+	18.1977i	−1.46800	+	0.847551i	−0.999358	−	0.0358363i	$-0.988591\pi$
$461$	−31.5193	+	18.1977i	−1.46800	+	0.847551i	−0.468644	+	0.883387i	$0.655257\pi$
$462$		0			0
$463$			32.5227i			1.51146i	0.654885	+	0.755728i	$0.272717\pi$
$463$			32.5227i			1.51146i	−0.654885	+	0.755728i	$0.727283\pi$
$464$		0			0
$465$	1.36285	−	0.474012i	0.0632008	−	0.0219818i
$466$		0			0
$467$	−36.7062			−1.69856			−0.849281	−	0.527941i	$-0.822964\pi$
$467$	−36.7062			−1.69856			−0.849281	+	0.527941i	$0.822964\pi$
$468$		0			0
$469$	6.48195	−	11.2271i	0.299308	−	0.518417i
$470$		0			0
$471$	−21.1489	+	7.35575i	−0.974489	+	0.338935i
$472$		0			0
$473$	−13.0737	+	7.54808i	−0.601127	+	0.347061i
$474$		0			0
$475$	20.9879	−	5.26059i	0.962989	−	0.241372i
$476$		0			0
$477$	24.2576	+	30.6537i	1.11068	+	1.40353i
$478$		0			0
$479$	2.90674	−	5.03462i	0.132812	−	0.230038i	−0.791947	−	0.610589i	$-0.790933\pi$
$479$	2.90674	−	5.03462i	0.132812	−	0.230038i	0.924760	+	0.380552i	$0.124266\pi$
$480$		0			0
$481$	−0.261970	+	0.453746i	−0.0119448	+	0.0206890i
$482$		0			0
$483$	2.78927	−	3.22890i	0.126916	−	0.146920i
$484$		0			0
$485$	−0.323190	−	0.186594i	−0.0146753	−	0.00847278i
$486$		0			0
$487$			13.0072i			0.589413i	0.955588	+	0.294706i	$0.0952218\pi$
$487$			13.0072i			0.589413i	−0.955588	+	0.294706i	$0.904778\pi$
$488$		0			0
$489$	1.99581	+	0.381512i	0.0902536	+	0.0172526i
$490$		0			0
$491$	11.2960	+	19.5653i	0.509783	+	0.882970i	0.999936	+	0.0113335i	$0.00360763\pi$
$491$	11.2960	+	19.5653i	0.509783	+	0.882970i	−0.490153	+	0.871637i	$0.663059\pi$
$492$		0			0
$493$	14.8720			0.669799
$494$		0			0
$495$	−2.19113	+	0.321845i	−0.0984839	+	0.0144659i
$496$		0			0
$497$	−6.78071	+	3.91484i	−0.304156	+	0.175605i
$498$		0			0
$499$	−30.9030	+	17.8418i	−1.38341	+	0.798711i	−0.992561	−	0.121745i	$-0.961151\pi$
$499$	−30.9030	+	17.8418i	−1.38341	+	0.798711i	−0.390846	+	0.920456i	$0.627818\pi$
$500$		0			0
$501$	21.8398	+	18.8662i	0.975731	+	0.842880i
$502$		0			0
$503$	13.5573	−	23.4819i	0.604490	−	1.04701i	−0.387642	−	0.921810i	$-0.626710\pi$
$503$	13.5573	−	23.4819i	0.604490	−	1.04701i	0.992132	−	0.125198i	$-0.0399565\pi$
$504$		0			0
$505$	−2.98361			−0.132769
$506$		0			0
$507$	−6.12477	+	2.13024i	−0.272010	+	0.0946074i
$508$		0			0
$509$	−14.7344	−	8.50694i	−0.653093	−	0.377063i	0.136547	−	0.990634i	$-0.456399\pi$
$509$	−14.7344	−	8.50694i	−0.653093	−	0.377063i	−0.789640	+	0.613570i	$0.789733\pi$
$510$		0			0
$511$	−3.62846	+	2.09489i	−0.160513	+	0.0926725i
$512$		0			0
$513$	22.1865	−	4.55644i	0.979556	−	0.201172i
$514$		0			0
$515$	0.749164	+	1.29759i	0.0330121	+	0.0571787i
$516$		0			0
$517$	−8.05582	+	13.9531i	−0.354295	+	0.613656i
$518$		0			0
$519$	−10.3493	−	29.7558i	−0.454284	−	1.30613i
$520$		0			0
$521$		−	7.42530i		−	0.325309i	−0.986683	−	0.162654i	$-0.947994\pi$
$521$		−	7.42530i		−	0.325309i	0.986683	−	0.162654i	$-0.0520055\pi$
$522$		0			0
$523$	−28.4010	−	16.3973i	−1.24189	−	0.717004i	−0.272410	−	0.962181i	$-0.587821\pi$
$523$	−28.4010	−	16.3973i	−1.24189	−	0.717004i	−0.969478	+	0.245177i	$0.921154\pi$
$524$		0			0
$525$	−4.96389	+	5.74628i	−0.216642	+	0.250788i
$526$		0			0
$527$	10.0585	+	17.4218i	0.438154	+	0.758906i
$528$		0			0
$529$	7.60999	+	13.1809i	0.330869	+	0.573082i
$530$		0			0
$531$	−4.31344	−	29.3660i	−0.187187	−	1.27437i
$532$		0			0
$533$		−	7.74759i		−	0.335586i
$534$		0			0
$535$	1.27862	−	0.738213i	0.0552797	−	0.0319157i
$536$		0			0
$537$	0.270921	−	1.41727i	0.0116911	−	0.0611598i
$538$		0			0
$539$	−24.1636			−1.04080
$540$		0			0
$541$	−4.55582	+	7.89092i	−0.195870	+	0.339257i	−0.947185	−	0.320686i	$-0.896086\pi$
$541$	−4.55582	+	7.89092i	−0.195870	+	0.339257i	0.751315	+	0.659943i	$0.229420\pi$
$542$		0			0
$543$	−13.3009	−	11.4899i	−0.570795	−	0.493078i
$544$		0			0
$545$	2.32824	+	1.34421i	0.0997308	+	0.0575796i
$546$		0			0
$547$	19.6108	+	11.3223i	0.838497	+	0.484107i	0.856753	−	0.515727i	$-0.172478\pi$
$547$	19.6108	+	11.3223i	0.838497	+	0.484107i	−0.0182558	+	0.999833i	$0.505811\pi$
$548$		0			0
$549$	14.3313	−	11.3410i	0.611645	−	0.484023i
$550$		0			0
$551$	3.43474	+	13.7034i	0.146325	+	0.583784i
$552$		0			0
$553$	0.155954	+	0.270120i	0.00663184	+	0.0114867i
$554$		0			0
$555$	0.0138441	+	0.0398039i	0.000587651	+	0.00168958i
$556$		0			0
$557$	−6.78665	−	3.91827i	−0.287560	−	0.166023i	0.349281	−	0.937018i	$-0.386426\pi$
$557$	−6.78665	−	3.91827i	−0.287560	−	0.166023i	−0.636841	+	0.770995i	$0.719759\pi$
$558$		0			0
$559$			15.9009i			0.672538i
$560$		0			0
$561$	−10.1429	−	29.1623i	−0.428233	−	1.23123i
$562$		0			0
$563$	8.10532			0.341599			0.170799	−	0.985306i	$-0.445365\pi$
$563$	8.10532			0.341599			0.170799	+	0.985306i	$0.445365\pi$
$564$		0			0
$565$	−1.58208	−	2.74024i	−0.0665584	−	0.115283i
$566$		0			0
$567$	−5.45012	+	5.78603i	−0.228884	+	0.242990i
$568$		0			0
$569$		−	28.8796i		−	1.21070i	−0.795961	−	0.605348i	$-0.793034\pi$
$569$		−	28.8796i		−	1.21070i	0.795961	−	0.605348i	$-0.206966\pi$
$570$		0			0
$571$			17.2330i			0.721177i	0.932725	+	0.360588i	$0.117424\pi$
$571$			17.2330i			0.721177i	−0.932725	+	0.360588i	$0.882576\pi$
$572$		0			0
$573$	−6.70390	+	35.0702i	−0.280059	+	1.46508i
$574$		0			0
$575$	6.92281	+	11.9907i	0.288701	+	0.500045i
$576$		0			0
$577$	2.32368			0.0967360			0.0483680	−	0.998830i	$-0.484598\pi$
$577$	2.32368			0.0967360			0.0483680	+	0.998830i	$0.484598\pi$
$578$		0			0
$579$	−0.268540	+	0.0934003i	−0.0111601	+	0.00388158i
$580$		0			0
$581$			0.883990i			0.0366741i
$582$		0			0
$583$	43.8384	+	25.3101i	1.81560	+	1.04824i
$584$		0			0
$585$	−0.860383	+	2.16823i	−0.0355725	+	0.0896454i
$586$		0			0
$587$	−19.7447	−	34.1989i	−0.814952	−	1.41154i	−0.909362	−	0.416005i	$-0.863430\pi$
$587$	−19.7447	−	34.1989i	−0.814952	−	1.41154i	0.0944101	−	0.995533i	$-0.469904\pi$
$588$		0			0
$589$	−13.7298	+	13.2918i	−0.565728	+	0.547678i
$590$		0			0
$591$	28.0344	+	5.35896i	1.15318	+	0.220438i
$592$		0			0
$593$	8.44149	+	4.87370i	0.346651	+	0.200139i	0.663209	−	0.748434i	$-0.269194\pi$
$593$	8.44149	+	4.87370i	0.346651	+	0.200139i	−0.316558	+	0.948573i	$0.602527\pi$
$594$		0			0
$595$	0.666930	+	0.385052i	0.0273415	+	0.0157856i
$596$		0			0
$597$	−17.7840	+	20.5870i	−0.727851	+	0.842571i
$598$		0			0
$599$	17.1233	−	29.6584i	0.699639	−	1.21181i	−0.268953	−	0.963153i	$-0.586678\pi$
$599$	17.1233	−	29.6584i	0.699639	−	1.21181i	0.968592	−	0.248656i	$-0.0799889\pi$
$600$		0			0
$601$	−33.7716			−1.37757			−0.688786	−	0.724965i	$-0.741856\pi$
$601$	−33.7716			−1.37757			−0.688786	+	0.724965i	$0.741856\pi$
$602$		0			0
$603$	27.3261	+	34.5312i	1.11281	+	1.40622i
$604$		0			0
$605$	−0.673393	+	0.388784i	−0.0273773	+	0.0158063i
$606$		0			0
$607$		−	2.20131i		−	0.0893485i	−0.999002	−	0.0446742i	$-0.985775\pi$
$607$		−	2.20131i		−	0.0893485i	0.999002	−	0.0446742i	$-0.0142250\pi$
$608$		0			0
$609$	−3.75186	−	3.24102i	−0.152033	−	0.131333i
$610$		0			0
$611$	8.48528	+	14.6969i	0.343278	+	0.594574i
$612$		0			0
$613$	17.3497	+	30.0505i	0.700747	+	1.21373i	0.968205	+	0.250160i	$0.0804831\pi$
$613$	17.3497	+	30.0505i	0.700747	+	1.21373i	−0.267458	+	0.963570i	$0.586184\pi$
$614$		0			0
$615$	−0.471583	−	0.407374i	−0.0190160	−	0.0164269i
$616$		0			0
$617$	−1.61865	−	0.934526i	−0.0651642	−	0.0376226i	0.467064	−	0.884224i	$-0.345312\pi$
$617$	−1.61865	−	0.934526i	−0.0651642	−	0.0376226i	−0.532228	+	0.846601i	$0.678645\pi$
$618$		0			0
$619$			31.0103i			1.24641i	0.782059	+	0.623204i	$0.214169\pi$
$619$			31.0103i			1.24641i	−0.782059	+	0.623204i	$0.785831\pi$
$620$		0			0
$621$	6.70003	+	12.8519i	0.268863	+	0.515727i
$622$		0			0
$623$	0.251741	−	0.436029i	0.0100858	−	0.0174691i
$624$		0			0
$625$	−12.2298	−	21.1827i	−0.489193	−	0.847308i
$626$		0			0
$627$	24.5283	−	16.0811i	0.979568	−	0.642216i
$628$		0			0
$629$	−0.508827	+	0.293771i	−0.0202883	+	0.0117134i
$630$		0			0
$631$	−1.86320	−	1.07572i	−0.0741726	−	0.0428236i	0.462455	−	0.886643i	$-0.346969\pi$
$631$	−1.86320	−	1.07572i	−0.0741726	−	0.0428236i	−0.536628	+	0.843819i	$0.680302\pi$
$632$		0			0
$633$	3.34478	+	9.61674i	0.132943	+	0.382231i
$634$		0			0
$635$	−0.765969			−0.0303966
$636$		0			0
$637$	−12.7259	+	22.0418i	−0.504217	+	0.873329i
$638$		0			0
$639$	−3.86505	−	26.3133i	−0.152899	−	1.04094i
$640$		0			0
$641$	−4.30303	+	2.48436i	−0.169959	+	0.0981261i	−0.582567	−	0.812783i	$-0.697952\pi$
$641$	−4.30303	+	2.48436i	−0.169959	+	0.0981261i	0.412607	+	0.910909i	$0.364618\pi$
$642$		0			0
$643$	4.56207	−	2.63391i	0.179910	−	0.103871i	−0.407340	−	0.913277i	$-0.633544\pi$
$643$	4.56207	−	2.63391i	0.179910	−	0.103871i	0.587251	+	0.809405i	$0.300210\pi$
$644$		0			0
$645$	0.967862	+	0.836082i	0.0381095	+	0.0329207i
$646$		0			0
$647$	34.8017			1.36820			0.684099	−	0.729389i	$-0.260196\pi$
$647$	34.8017			1.36820			0.684099	+	0.729389i	$0.260196\pi$
$648$		0			0
$649$	−19.2177	−	33.2860i	−0.754359	−	1.30659i
$650$		0			0
$651$	1.25918	−	6.58716i	0.0493511	−	0.258171i
$652$		0			0
$653$			22.0175i			0.861612i	0.902445	+	0.430806i	$0.141771\pi$
$653$			22.0175i			0.861612i	−0.902445	+	0.430806i	$0.858229\pi$
$654$		0			0
$655$	2.68230	+	1.54863i	0.104806	+	0.0605099i
$656$		0			0
$657$	−2.06825	−	14.0807i	−0.0806900	−	0.549339i
$658$		0			0
$659$	−23.1076	+	40.0236i	−0.900145	+	1.55910i	−0.0728403	+	0.997344i	$0.523206\pi$
$659$	−23.1076	+	40.0236i	−0.900145	+	1.55910i	−0.827305	+	0.561753i	$0.810127\pi$
$660$		0			0
$661$	16.7118	−	28.9456i	0.650013	−	1.12586i	−0.333106	−	0.942889i	$-0.608097\pi$
$661$	16.7118	−	28.9456i	0.650013	−	1.12586i	0.983119	−	0.182966i	$-0.0585698\pi$
$662$		0			0
$663$	−31.9435	−	6.10620i	−1.24058	−	0.237145i
$664$		0			0
$665$	−0.200766	+	0.703455i	−0.00778539	+	0.0272788i
$666$		0			0
$667$	−7.82894	+	4.52004i	−0.303138	+	0.175017i
$668$		0			0
$669$	−4.91670	−	14.1362i	−0.190091	−	0.546539i
$670$		0			0
$671$	11.8331	−	20.4955i	0.456811	−	0.791219i
$672$		0			0
$673$	18.9639			0.731004			0.365502	−	0.930811i	$-0.380897\pi$
$673$	18.9639			0.731004			0.365502	+	0.930811i	$0.380897\pi$
$674$		0			0
$675$	−11.9236	−	22.8717i	−0.458940	−	0.880331i
$676$		0			0
$677$			36.3779i			1.39812i	0.715065	+	0.699058i	$0.246397\pi$
$677$			36.3779i			1.39812i	−0.715065	+	0.699058i	$0.753603\pi$
$678$		0			0
$679$	−1.50211	+	0.867244i	−0.0576457	+	0.0332818i
$680$		0			0
$681$	5.06045	−	26.4728i	0.193917	−	1.01444i
$682$		0			0
$683$	38.0643			1.45649			0.728245	−	0.685317i	$-0.240336\pi$
$683$	38.0643			1.45649			0.728245	+	0.685317i	$0.240336\pi$
$684$		0			0
$685$	1.49577			0.0571506
$686$		0			0
$687$	−5.74309	+	30.0439i	−0.219113	+	1.14625i
$688$		0			0
$689$	46.1754	−	26.6594i	1.75914	−	1.01564i
$690$		0			0
$691$			22.2914i			0.848007i	0.905661	+	0.424003i	$0.139375\pi$
$691$			22.2914i			0.848007i	−0.905661	+	0.424003i	$0.860625\pi$
$692$		0			0
$693$	−3.79648	+	9.56742i	−0.144216	+	0.363436i
$694$		0			0
$695$	3.11886			0.118305
$696$		0			0
$697$	4.34405	−	7.52411i	0.164542	−	0.284996i
$698$		0			0
$699$	0.644826	+	1.85397i	0.0243895	+	0.0701236i
$700$		0			0
$701$	−18.0231	+	10.4056i	−0.680722	+	0.393015i	−0.800127	−	0.599831i	$-0.795235\pi$
$701$	−18.0231	+	10.4056i	−0.680722	+	0.393015i	0.119405	+	0.992846i	$0.461901\pi$
$702$		0			0
$703$	−0.388204	−	0.400998i	−0.0146414	−	0.0151239i
$704$		0			0
$705$	1.34074	+	0.256291i	0.0504952	+	0.00965248i
$706$		0			0
$707$	−6.93356	+	12.0093i	−0.260763	+	0.451655i
$708$		0			0
$709$	5.97375	−	10.3468i	0.224349	−	0.388584i	−0.731775	−	0.681546i	$-0.761308\pi$
$709$	5.97375	−	10.3468i	0.224349	−	0.388584i	0.956124	+	0.292963i	$0.0946412\pi$
$710$		0			0
$711$	−1.04823	+	0.153971i	−0.0393119	+	0.00577435i
$712$		0			0
$713$	−10.5900	−	6.11416i	−0.396600	−	0.228977i
$714$		0			0
$715$			3.02072i			0.112968i
$716$		0			0
$717$	4.17913	−	21.8624i	0.156073	−	0.816465i
$718$		0			0
$719$	3.34780	+	5.79855i	0.124852	+	0.216250i	0.921675	−	0.387963i	$-0.126821\pi$
$719$	3.34780	+	5.79855i	0.124852	+	0.216250i	−0.796823	+	0.604212i	$0.793488\pi$
$720$		0			0
$721$	6.96389			0.259349
$722$		0			0
$723$	−27.4305	−	23.6957i	−1.02015	−	0.881251i
$724$		0			0
$725$	13.9327	−	8.04404i	0.517447	−	0.298748i
$726$		0			0
$727$	39.8338	−	22.9981i	1.47735	−	0.852951i	0.477681	−	0.878533i	$-0.341477\pi$
$727$	39.8338	−	22.9981i	1.47735	−	0.852951i	0.999673	+	0.0255827i	$0.00814412\pi$
$728$		0			0
$729$	−11.4400	−	24.4566i	−0.423702	−	0.905802i
$730$		0			0
$731$	−8.91559	+	15.4423i	−0.329755	+	0.571152i
$732$		0			0
$733$	44.7636			1.65338			0.826691	−	0.562656i	$-0.190220\pi$
$733$	44.7636			1.65338			0.826691	+	0.562656i	$0.190220\pi$
$734$		0			0
$735$	0.672514	+	1.93358i	0.0248060	+	0.0713211i
$736$		0			0
$737$	49.3838	+	28.5117i	1.81907	+	1.05024i
$738$		0			0
$739$	−30.1266	+	17.3936i	−1.10822	+	0.639834i	−0.938369	−	0.345635i	$-0.887663\pi$
$739$	−30.1266	+	17.3936i	−1.10822	+	0.639834i	−0.169855	+	0.985469i	$0.554330\pi$
$740$		0			0
$741$	−1.75107	−	30.8438i	−0.0643271	−	1.13307i
$742$		0			0
$743$	20.4831	+	35.4779i	0.751454	+	1.30156i	0.947118	+	0.320885i	$0.103980\pi$
$743$	20.4831	+	35.4779i	0.751454	+	1.30156i	−0.195664	+	0.980671i	$0.562686\pi$
$744$		0			0
$745$	−1.96223	+	3.39868i	−0.0718906	+	0.124518i
$746$		0			0
$747$	−2.79101	−	1.10751i	−0.102118	−	0.0405216i
$748$		0			0
$749$		−	6.86209i		−	0.250735i
$750$		0			0
$751$	−27.5382	−	15.8992i	−1.00488	−	0.580169i	−0.0951932	−	0.995459i	$-0.530347\pi$
$751$	−27.5382	−	15.8992i	−1.00488	−	0.580169i	−0.909689	+	0.415290i	$0.863680\pi$
$752$		0			0
$753$	13.6198	+	11.7654i	0.496335	+	0.428756i
$754$		0			0
$755$	0.787458	+	1.36392i	0.0286585	+	0.0496380i
$756$		0			0
$757$	16.3579	+	28.3327i	0.594537	+	1.02977i	0.993612	+	0.112850i	$0.0359980\pi$
$757$	16.3579	+	28.3327i	0.594537	+	1.02977i	−0.399075	+	0.916918i	$0.630669\pi$
$758$		0			0
$759$	14.2028	+	12.2690i	0.515528	+	0.445336i
$760$		0			0
$761$			3.68720i			0.133661i	0.997764	+	0.0668305i	$0.0212887\pi$
$761$			3.68720i			0.133661i	−0.997764	+	0.0668305i	$0.978711\pi$
$762$		0			0
$763$	10.8211	−	6.24758i	0.391751	−	0.226178i
$764$		0			0
$765$	−2.05129	+	1.62328i	−0.0741644	+	0.0586896i
$766$		0			0
$767$	−40.4843			−1.46180
$768$		0			0
$769$	16.7397	−	28.9940i	0.603649	−	1.04555i	−0.388615	−	0.921400i	$-0.627046\pi$
$769$	16.7397	−	28.9940i	0.603649	−	1.04555i	0.992263	−	0.124150i	$-0.0396203\pi$
$770$		0			0
$771$	−7.84455	+	9.08097i	−0.282514	+	0.327043i
$772$		0			0
$773$	18.1936	+	10.5041i	0.654377	+	0.377805i	0.790131	−	0.612938i	$-0.210012\pi$
$773$	18.1936	+	10.5041i	0.654377	+	0.377805i	−0.135754	+	0.990743i	$0.543346\pi$
$774$		0			0
$775$	18.8464	+	10.8810i	0.676984	+	0.390857i
$776$		0			0
$777$	0.192387	+	0.0367760i	0.00690183	+	0.00131933i
$778$		0			0
$779$	7.93617	+	2.26499i	0.284343	+	0.0811516i
$780$		0			0
$781$	−17.2200	−	29.8259i	−0.616179	−	1.06725i
$782$		0			0
$783$	14.9334	−	7.78517i	0.533675	−	0.278219i
$784$		0			0
$785$	2.12747	+	1.22830i	0.0759328	+	0.0438398i
$786$		0			0
$787$			4.64212i			0.165474i	0.996571	+	0.0827369i	$0.0263661\pi$
$787$			4.64212i			0.165474i	−0.996571	+	0.0827369i	$0.973634\pi$
$788$		0			0
$789$	40.7829	−	14.1846i	1.45191	−	0.504986i
$790$		0			0
$791$	−14.7063			−0.522894
$792$		0			0
$793$	−12.4639	−	21.5881i	−0.442606	−	0.766616i
$794$		0			0
$795$	0.805226	−	4.21239i	0.0285584	−	0.149398i
$796$		0			0
$797$		−	17.8020i		−	0.630581i	−0.948995	−	0.315290i	$-0.897898\pi$
$797$		−	17.8020i		−	0.630581i	0.948995	−	0.315290i	$-0.102102\pi$
$798$		0			0
$799$			19.0307i			0.673256i
$800$		0			0
$801$	1.06127	+	1.34110i	0.0374983	+	0.0473854i
$802$		0			0
$803$	−9.21466	−	15.9603i	−0.325178	−	0.563225i
$804$		0			0
$805$	−0.468117			−0.0164989
$806$		0			0
$807$	−14.7905	−	42.5248i	−0.520649	−	1.49694i
$808$		0			0
$809$		−	19.4705i		−	0.684545i	−0.939601	−	0.342273i	$-0.888803\pi$
$809$		−	19.4705i		−	0.684545i	0.939601	−	0.342273i	$-0.111197\pi$
$810$		0			0
$811$	30.4997	+	17.6090i	1.07099	+	0.618336i	0.928452	−	0.371453i	$-0.121140\pi$
$811$	30.4997	+	17.6090i	1.07099	+	0.618336i	0.142538	+	0.989789i	$0.454474\pi$
$812$		0			0
$813$	−3.29858	−	9.48392i	−0.115686	−	0.332615i
$814$		0			0
$815$	−0.111463	−	0.193060i	−0.00390438	−	0.00676258i
$816$		0			0
$817$	−16.2880	−	4.64859i	−0.569844	−	0.162634i
$818$		0			0
$819$	6.72790	+	8.50185i	0.235092	+	0.297079i
$820$		0			0
$821$	42.5458	+	24.5638i	1.48486	+	0.857283i	0.999852	−	0.0172271i	$-0.00548381\pi$
$821$	42.5458	+	24.5638i	1.48486	+	0.857283i	0.485007	+	0.874510i	$0.338817\pi$
$822$		0			0
$823$	−38.9007	−	22.4593i	−1.35599	−	0.782883i	−0.366912	−	0.930256i	$-0.619585\pi$
$823$	−38.9007	−	22.4593i	−1.35599	−	0.782883i	−0.989081	+	0.147373i	$0.952918\pi$
$824$		0			0
$825$	−25.2758	−	21.8344i	−0.879990	−	0.760175i
$826$		0			0
$827$	26.0724	−	45.1588i	0.906627	−	1.57032i	0.0879094	−	0.996128i	$-0.471981\pi$
$827$	26.0724	−	45.1588i	0.906627	−	1.57032i	0.818718	−	0.574196i	$-0.194685\pi$
$828$		0			0
$829$	−33.3316			−1.15766			−0.578828	−	0.815450i	$-0.696490\pi$
$829$	−33.3316			−1.15766			−0.578828	+	0.815450i	$0.696490\pi$
$830$		0			0
$831$	3.60715	−	18.8701i	0.125131	−	0.654597i
$832$		0			0
$833$	−24.7175	+	14.2707i	−0.856412	+	0.494450i
$834$		0			0
$835$		−	3.16627i		−	0.109573i
$836$		0			0
$837$	19.2200	+	12.2283i	0.664340	+	0.422673i
$838$		0			0
$839$	−21.9144	−	37.9568i	−0.756568	−	1.31041i	−0.944591	−	0.328250i	$-0.893541\pi$
$839$	−21.9144	−	37.9568i	−0.756568	−	1.31041i	0.188023	−	0.982165i	$-0.439792\pi$
$840$		0			0
$841$	−9.24789	−	16.0178i	−0.318893	−	0.552338i
$842$		0			0
$843$	−11.0366	+	12.7761i	−0.380120	+	0.440033i
$844$		0			0
$845$	0.616121	+	0.355718i	0.0211952	+	0.0122371i
$846$		0			0
$847$			3.61395i			0.124177i
$848$		0			0
$849$	17.1522	+	49.3151i	0.588661	+	1.69249i
$850$		0			0
$851$	0.178572	−	0.309296i	0.00612138	−	0.0106025i
$852$		0			0
$853$	−1.88413	−	3.26340i	−0.0645113	−	0.111737i	0.831966	−	0.554827i	$-0.187216\pi$
$853$	−1.88413	−	3.26340i	−0.0645113	−	0.111737i	−0.896477	+	0.443090i	$0.853882\pi$
$854$		0			0
$855$	−1.96948	−	1.51520i	−0.0673547	−	0.0518188i
$856$		0			0
$857$	23.9869	−	13.8488i	0.819376	−	0.473067i	−0.0308250	−	0.999525i	$-0.509813\pi$
$857$	23.9869	−	13.8488i	0.819376	−	0.473067i	0.850201	+	0.526458i	$0.176480\pi$
$858$		0			0
$859$	−10.8759	−	6.27918i	−0.371080	−	0.214243i	0.302850	−	0.953038i	$-0.402062\pi$
$859$	−10.8759	−	6.27918i	−0.371080	−	0.214243i	−0.673930	+	0.738795i	$0.735395\pi$
$860$		0			0
$861$	−2.73562	+	0.951471i	−0.0932297	+	0.0324261i
$862$		0			0
$863$	−49.9994			−1.70200			−0.850999	−	0.525167i	$-0.824003\pi$
$863$	−49.9994			−1.70200			−0.850999	+	0.525167i	$0.824003\pi$
$864$		0			0
$865$	−1.72817	+	2.99328i	−0.0587596	+	0.101775i
$866$		0			0
$867$	−5.31605	−	4.59224i	−0.180543	−	0.155961i
$868$		0			0
$869$	−1.18816	+	0.685986i	−0.0403056	+	0.0232705i
$870$		0			0
$871$	52.0164	−	30.0317i	1.76251	−	1.01758i
$872$		0			0
$873$	−0.856215	−	5.82912i	−0.0289785	−	0.197286i
$874$		0			0
$875$	1.67222			0.0565312
$876$		0			0
$877$	−21.7758	−	37.7168i	−0.735316	−	1.27361i	−0.954584	−	0.297941i	$-0.903700\pi$
$877$	−21.7758	−	37.7168i	−0.735316	−	1.27361i	0.219268	−	0.975665i	$-0.429633\pi$
$878$		0			0
$879$	16.9060	+	3.23170i	0.570226	+	0.109002i
$880$		0			0
$881$		−	34.8820i		−	1.17521i	−0.809149	−	0.587603i	$-0.800072\pi$
$881$		−	34.8820i		−	1.17521i	0.809149	−	0.587603i	$-0.199928\pi$
$882$		0			0
$883$	−11.1546	−	6.44011i	−0.375382	−	0.216727i	0.300425	−	0.953805i	$-0.402871\pi$
$883$	−11.1546	−	6.44011i	−0.375382	−	0.216727i	−0.675807	+	0.737079i	$0.736205\pi$
$884$		0			0
$885$	−2.12869	+	2.46421i	−0.0715553	+	0.0828335i
$886$		0			0
$887$	−7.89788	+	13.6795i	−0.265185	+	0.459314i	−0.967612	−	0.252442i	$-0.918766\pi$
$887$	−7.89788	+	13.6795i	−0.265185	+	0.459314i	0.702427	+	0.711756i	$0.252100\pi$
$888$		0			0
$889$	−1.78002	+	3.08309i	−0.0597001	+	0.103404i
$890$		0			0
$891$	−25.4507	−	23.9731i	−0.852629	−	0.803130i
$892$		0			0
$893$	−17.5353	+	4.39521i	−0.586797	+	0.147080i
$894$		0			0
$895$	−0.137096	+	0.0791526i	−0.00458262	+	0.00264578i
$896$		0			0
$897$	18.6716	−	6.49415i	0.623428	−	0.216833i
$898$		0			0
$899$	−7.10442	+	12.3052i	−0.236946	+	0.410402i
$900$		0			0
$901$	59.7913			1.99194
$902$		0			0
$903$	5.61451	−	1.95277i	0.186839	−	0.0649842i
$904$		0			0
$905$			1.92832i			0.0640996i
$906$		0			0
$907$	33.8957	−	19.5697i	1.12549	−	0.649800i	0.182691	−	0.983170i	$-0.441519\pi$
$907$	33.8957	−	19.5697i	1.12549	−	0.649800i	0.942796	+	0.333370i	$0.108186\pi$
$908$		0			0
$909$	−29.2300	−	36.9371i	−0.969498	−	1.22513i
$910$		0			0
$911$	49.1938			1.62986			0.814932	−	0.579556i	$-0.196774\pi$
$911$	49.1938			1.62986			0.814932	+	0.579556i	$0.196774\pi$
$912$		0			0
$913$	−3.88835			−0.128686
$914$		0			0
$915$	−1.96939	−	0.376462i	−0.0651060	−	0.0124455i
$916$		0			0
$917$	12.4667	−	7.19767i	0.411687	−	0.237688i
$918$		0			0
$919$			44.1810i			1.45740i	0.684835	+	0.728698i	$0.259874\pi$
$919$			44.1810i			1.45740i	−0.684835	+	0.728698i	$0.740126\pi$
$920$		0			0
$921$	13.8615	+	39.8539i	0.456752	+	1.31323i
$922$		0			0
$923$	−36.2759			−1.19404
$924$		0			0
$925$	−0.317794	+	0.550435i	−0.0104490	+	0.0180982i
$926$		0			0
$927$	−8.72473	+	21.9870i	−0.286558	+	0.722148i
$928$		0			0
$929$	50.5147	−	29.1647i	1.65733	−	0.956861i	0.683393	−	0.730050i	$-0.260503\pi$
$929$	50.5147	−	29.1647i	1.65733	−	0.956861i	0.973939	−	0.226811i	$-0.0728299\pi$
$930$		0			0
$931$	−18.8580	−	19.4795i	−0.618045	−	0.638414i
$932$		0			0
$933$	−7.86706	+	41.1551i	−0.257556	+	1.34736i
$934$		0			0
$935$	−1.69371	+	2.93358i	−0.0553901	+	0.0959385i
$936$		0			0
$937$	−8.26594	+	14.3170i	−0.270037	+	0.467717i	−0.968871	−	0.247567i	$-0.920369\pi$
$937$	−8.26594	+	14.3170i	−0.270037	+	0.467717i	0.698834	+	0.715284i	$0.253702\pi$
$938$		0			0
$939$	−0.0473292	−	0.0408850i	−0.00154453	−	0.00133423i
$940$		0			0
$941$	52.1695	+	30.1201i	1.70068	+	0.981886i	0.945074	+	0.326857i	$0.105990\pi$
$941$	52.1695	+	30.1201i	1.70068	+	0.981886i	0.755604	+	0.655029i	$0.227344\pi$
$942$		0			0
$943$			5.28115i			0.171978i
$944$		0			0
$945$	0.871251	+	0.0375177i	0.0283418	+	0.00122045i
$946$		0			0
$947$	4.95759	+	8.58679i	0.161100	+	0.279033i	0.935263	−	0.353952i	$-0.115163\pi$
$947$	4.95759	+	8.58679i	0.161100	+	0.279033i	−0.774163	+	0.632986i	$0.781829\pi$
$948$		0			0
$949$	−19.4118			−0.630133
$950$		0			0
$951$	−25.1447	+	29.1079i	−0.815373	+	0.943888i
$952$		0			0
$953$	−38.3422	+	22.1369i	−1.24202	+	0.717083i	−0.969506	−	0.245067i	$-0.921190\pi$
$953$	−38.3422	+	22.1369i	−1.24202	+	0.717083i	−0.272519	+	0.962150i	$0.587857\pi$
$954$		0			0
$955$	3.39243	−	1.95862i	0.109776	−	0.0633794i
$956$		0			0
$957$	14.2561	−	16.5031i	0.460834	−	0.533468i
$958$		0			0
$959$	3.47601	−	6.02062i	0.112246	−	0.194416i
$960$		0			0
$961$	11.7800			0.380001
$962$		0			0
$963$	21.6656	+	8.59719i	0.698164	+	0.277041i
$964$		0			0
$965$	0.0270137	+	0.0155964i	0.000869603	+	0.000502066i
$966$		0			0
$967$	9.17788	−	5.29885i	0.295141	−	0.170400i	−0.345117	−	0.938560i	$-0.612161\pi$
$967$	9.17788	−	5.29885i	0.295141	−	0.170400i	0.640258	+	0.768160i	$0.278827\pi$
$968$		0			0
$969$	15.5934	−	30.9359i	0.500933	−	0.993803i
$970$		0			0
$971$	−20.0666	−	34.7564i	−0.643968	−	1.11539i	−0.984539	−	0.175167i	$-0.943954\pi$
$971$	−20.0666	−	34.7564i	−0.643968	−	1.11539i	0.340571	−	0.940219i	$-0.389380\pi$
$972$		0			0
$973$	7.24789	−	12.5537i	0.232357	−	0.402453i
$974$		0			0
$975$	−33.2288	+	11.5572i	−1.06417	+	0.370128i
$976$		0			0
$977$			5.89450i			0.188582i	0.995545	+	0.0942909i	$0.0300584\pi$
$977$			5.89450i			0.188582i	−0.995545	+	0.0942909i	$0.969942\pi$
$978$		0			0
$979$	1.91793	+	1.10732i	0.0612974	+	0.0353901i
$980$		0			0
$981$	6.16812	+	41.9927i	0.196933	+	1.34072i
$982$		0			0
$983$	−12.2862	−	21.2803i	−0.391869	−	0.678737i	0.600827	−	0.799379i	$-0.294838\pi$
$983$	−12.2862	−	21.2803i	−0.391869	−	0.678737i	−0.992696	+	0.120642i	$0.961505\pi$
$984$		0			0
$985$	−1.56568	−	2.71184i	−0.0498867	−	0.0864064i
$986$		0			0
$987$	4.14732	−	4.80100i	0.132011	−	0.152818i
$988$		0			0
$989$		−	10.8389i		−	0.344656i
$990$		0			0
$991$	−24.3959	+	14.0850i	−0.774960	+	0.447423i	−0.834641	−	0.550794i	$-0.814325\pi$
$991$	−24.3959	+	14.0850i	−0.774960	+	0.447423i	0.0596810	+	0.998217i	$0.480992\pi$
$992$		0			0
$993$	17.6751	+	3.37872i	0.560904	+	0.107220i
$994$		0			0
$995$	2.98465			0.0946197
$996$		0			0
$997$	25.3917	−	43.9797i	0.804162	−	1.39285i	−0.112693	−	0.993630i	$-0.535948\pi$
$997$	25.3917	−	43.9797i	0.804162	−	1.39285i	0.916855	−	0.399220i	$-0.130719\pi$
$998$		0			0
$999$	−0.357144	+	0.561345i	−0.0112995	+	0.0177602i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bh.f.767.7	yes	24
3.2	odd	2	inner	912.2.bh.f.767.12	yes	24
4.3	odd	2	inner	912.2.bh.f.767.6	yes	24
12.11	even	2	inner	912.2.bh.f.767.1	yes	24
19.11	even	3	inner	912.2.bh.f.239.1	✓	24
57.11	odd	6	inner	912.2.bh.f.239.6	yes	24
76.11	odd	6	inner	912.2.bh.f.239.12	yes	24
228.11	even	6	inner	912.2.bh.f.239.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
912.2.bh.f.239.1	✓	24	19.11	even	3	inner
912.2.bh.f.239.6	yes	24	57.11	odd	6	inner
912.2.bh.f.239.7	yes	24	228.11	even	6	inner
912.2.bh.f.239.12	yes	24	76.11	odd	6	inner
912.2.bh.f.767.1	yes	24	12.11	even	2	inner
912.2.bh.f.767.6	yes	24	4.3	odd	2	inner
912.2.bh.f.767.7	yes	24	1.1	even	1	trivial
912.2.bh.f.767.12	yes	24	3.2	odd	2	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.325205 - 1.70125i) q^{3} +(-0.164566 + 0.0950122i) q^{5} +0.883190i q^{7} +(-2.78848 - 1.10651i) q^{9} -3.88483 q^{11} +(-2.04597 + 3.54372i) q^{13} +(0.108122 + 0.310866i) q^{15} +(-3.97390 + 2.29433i) q^{17} +(-3.03184 - 3.13176i) q^{19} +(1.50252 + 0.287218i) q^{21} +(1.39463 - 2.41558i) q^{23} +(-2.48195 + 4.29886i) q^{25} +(-2.78927 + 4.38406i) q^{27} +(-2.80681 - 1.62051i) q^{29} -4.38406i q^{31} +(-1.26337 + 6.60906i) q^{33} +(-0.0839138 - 0.145343i) q^{35} +0.128042 q^{37} +(5.36338 + 4.63313i) q^{39} +(-1.63972 + 0.946691i) q^{41} +(3.36531 - 1.94296i) q^{43} +(0.564021 - 0.0828466i) q^{45} +(2.07366 - 3.59168i) q^{47} +6.21998 q^{49} +(2.61089 + 7.50671i) q^{51} +(-11.2845 - 6.51511i) q^{53} +(0.639311 - 0.369107i) q^{55} +(-6.31387 + 4.13945i) q^{57} +(4.94684 + 8.56818i) q^{59} +(-3.04597 + 5.27577i) q^{61} +(0.977256 - 2.46276i) q^{63} -0.777567i q^{65} +(-12.7119 - 7.33924i) q^{67} +(-3.65595 - 3.15818i) q^{69} +(4.43262 + 7.67752i) q^{71} +(2.37196 + 4.10835i) q^{73} +(6.50628 + 5.62041i) q^{75} -3.43105i q^{77} +(0.305846 - 0.176580i) q^{79} +(6.55129 + 6.17095i) q^{81} +1.00091 q^{83} +(0.435979 - 0.755138i) q^{85} +(-3.66968 + 4.24808i) q^{87} +(-0.493698 - 0.285037i) q^{89} +(-3.12978 - 1.80698i) q^{91} +(-7.45837 - 1.42572i) q^{93} +(0.796493 + 0.227320i) q^{95} +(0.981945 + 1.70078i) q^{97} +(10.8328 + 4.29860i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9} + 12 q^{13} + 12 q^{21} + 8 q^{25} + 16 q^{37} + 20 q^{45} + 40 q^{49} + 18 q^{57} - 12 q^{61} + 28 q^{69} + 44 q^{73} - 22 q^{81} + 4 q^{85} + 8 q^{93} - 44 q^{97}+O(q^{100}) \) 24 * q - 2 * q^9 + 12 * q^13 + 12 * q^21 + 8 * q^25 + 16 * q^37 + 20 * q^45 + 40 * q^49 + 18 * q^57 - 12 * q^61 + 28 * q^69 + 44 * q^73 - 22 * q^81 + 4 * q^85 + 8 * q^93 - 44 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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