LMFDB - Embedded newform 864.2.bh.b.239.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(47,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 7]))

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

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

chi := DirichletCharacter("864.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bh (of order $18$, degree $6$, not 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			239.1
Character	$\chi$	$=$	864.239
Dual form			864.2.bh.b.47.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71829 + 0.217923i) q^{3} +(-0.693543 + 3.93328i) q^{5} +(2.05979 + 2.45476i) q^{7} +(2.90502 - 0.748909i) q^{9} +O(q^{10})$	\(q+(-1.71829 + 0.217923i) q^{3} +(-0.693543 + 3.93328i) q^{5} +(2.05979 + 2.45476i) q^{7} +(2.90502 - 0.748909i) q^{9} +(4.77912 - 0.842688i) q^{11} +(0.246151 + 0.676295i) q^{13} +(0.334553 - 6.90964i) q^{15} +(0.707869 + 0.408688i) q^{17} +(0.653550 + 1.13198i) q^{19} +(-4.07426 - 3.76911i) q^{21} +(2.96174 + 2.48519i) q^{23} +(-10.2912 - 3.74569i) q^{25} +(-4.82845 + 1.91991i) q^{27} +(5.23351 + 1.90484i) q^{29} +(-0.511632 + 0.609740i) q^{31} +(-8.02826 + 2.48946i) q^{33} +(-11.0838 + 6.39925i) q^{35} +(-2.71792 - 1.56919i) q^{37} +(-0.570338 - 1.10843i) q^{39} +(3.40768 + 9.36253i) q^{41} +(-2.01090 - 11.4044i) q^{43} +(0.930912 + 11.9456i) q^{45} +(-3.89967 + 3.27222i) q^{47} +(-0.567588 + 3.21895i) q^{49} +(-1.30538 - 0.547982i) q^{51} -0.181698 q^{53} +19.3820i q^{55} +(-1.36967 - 1.80265i) q^{57} +(-0.908057 - 0.160115i) q^{59} +(-0.975724 - 1.16282i) q^{61} +(7.82213 + 5.58854i) q^{63} +(-2.83077 + 0.499141i) q^{65} +(-5.95586 + 2.16776i) q^{67} +(-5.63069 - 3.62484i) q^{69} +(4.91251 - 8.50871i) q^{71} +(-0.606035 - 1.04968i) q^{73} +(18.4995 + 4.19348i) q^{75} +(11.9126 + 9.99585i) q^{77} +(-0.336165 + 0.923605i) q^{79} +(7.87827 - 4.35119i) q^{81} +(-0.517786 + 1.42261i) q^{83} +(-2.09842 + 2.50080i) q^{85} +(-9.40778 - 2.13256i) q^{87} +(-5.93630 + 3.42732i) q^{89} +(-1.15312 + 1.99727i) q^{91} +(0.746255 - 1.15920i) q^{93} +(-4.90566 + 1.78551i) q^{95} +(-1.47950 - 8.39068i) q^{97} +(13.2523 - 6.02715i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) $ 192 * q + 12 * q^3 - 12 * q^9	$ 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) $ 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.71829	+	0.217923i	−0.992053	+	0.125818i
$3$	−1.71829	+	0.217923i	−0.992053	+	0.125818i
$4$		0			0
$5$	−0.693543	+	3.93328i	−0.310162	+	1.75901i	0.287992	+	0.957633i	$0.407012\pi$
$5$	−0.693543	+	3.93328i	−0.310162	+	1.75901i	−0.598153	+	0.801382i	$0.704099\pi$
$6$		0			0
$7$	2.05979	+	2.45476i	0.778528	+	0.927814i	0.998866	−	0.0476099i	$-0.0151604\pi$
$7$	2.05979	+	2.45476i	0.778528	+	0.927814i	−0.220338	+	0.975424i	$0.570716\pi$
$8$		0			0
$9$	2.90502	−	0.748909i	0.968340	−	0.249636i
$10$		0			0
$11$	4.77912	−	0.842688i	1.44096	−	0.254080i	0.602096	−	0.798423i	$-0.294332\pi$
$11$	4.77912	−	0.842688i	1.44096	−	0.254080i	0.838862	+	0.544343i	$0.183221\pi$
$12$		0			0
$13$	0.246151	+	0.676295i	0.0682700	+	0.187570i	0.969136	−	0.246527i	$-0.0792895\pi$
$13$	0.246151	+	0.676295i	0.0682700	+	0.187570i	−0.900866	+	0.434098i	$0.857067\pi$
$14$		0			0
$15$	0.334553	−	6.90964i	0.0863813	−	1.78406i
$16$		0			0
$17$	0.707869	+	0.408688i	0.171683	+	0.0991214i	0.583379	−	0.812200i	$-0.301730\pi$
$17$	0.707869	+	0.408688i	0.171683	+	0.0991214i	−0.411696	+	0.911321i	$0.635063\pi$
$18$		0			0
$19$	0.653550	+	1.13198i	0.149935	+	0.259694i	0.931203	−	0.364501i	$-0.118760\pi$
$19$	0.653550	+	1.13198i	0.149935	+	0.259694i	−0.781268	+	0.624195i	$0.785427\pi$
$20$		0			0
$21$	−4.07426	−	3.76911i	−0.889077	−	0.822488i
$22$		0			0
$23$	2.96174	+	2.48519i	0.617565	+	0.518198i	0.897037	−	0.441955i	$-0.145715\pi$
$23$	2.96174	+	2.48519i	0.617565	+	0.518198i	−0.279472	+	0.960154i	$0.590160\pi$
$24$		0			0
$25$	−10.2912	−	3.74569i	−2.05824	−	0.749138i
$26$		0			0
$27$	−4.82845	+	1.91991i	−0.929236	+	0.369487i
$28$		0			0
$29$	5.23351	+	1.90484i	0.971838	+	0.353720i	0.778662	−	0.627444i	$-0.215899\pi$
$29$	5.23351	+	1.90484i	0.971838	+	0.353720i	0.193177	+	0.981164i	$0.438121\pi$
$30$		0			0
$31$	−0.511632	+	0.609740i	−0.0918919	+	0.109512i	−0.810031	−	0.586387i	$-0.800550\pi$
$31$	−0.511632	+	0.609740i	−0.0918919	+	0.109512i	0.718139	+	0.695900i	$0.244994\pi$
$32$		0			0
$33$	−8.02826	+	2.48946i	−1.39754	+	0.433359i
$34$		0			0
$35$	−11.0838	+	6.39925i	−1.87351	+	1.08167i
$36$		0			0
$37$	−2.71792	−	1.56919i	−0.446823	−	0.257974i	0.259664	−	0.965699i	$-0.416388\pi$
$37$	−2.71792	−	1.56919i	−0.446823	−	0.257974i	−0.706488	+	0.707725i	$0.749721\pi$
$38$		0			0
$39$	−0.570338	−	1.10843i	−0.0913272	−	0.177490i
$40$		0			0
$41$	3.40768	+	9.36253i	0.532191	+	1.46218i	0.856458	+	0.516216i	$0.172660\pi$
$41$	3.40768	+	9.36253i	0.532191	+	1.46218i	−0.324268	+	0.945965i	$0.605118\pi$
$42$		0			0
$43$	−2.01090	−	11.4044i	−0.306660	−	1.73915i	−0.615587	−	0.788069i	$-0.711081\pi$
$43$	−2.01090	−	11.4044i	−0.306660	−	1.73915i	0.308927	−	0.951086i	$-0.400030\pi$
$44$		0			0
$45$	0.930912	+	11.9456i	0.138772	+	1.78075i
$46$		0			0
$47$	−3.89967	+	3.27222i	−0.568826	+	0.477302i	−0.881256	−	0.472639i	$-0.843301\pi$
$47$	−3.89967	+	3.27222i	−0.568826	+	0.477302i	0.312430	+	0.949941i	$0.398857\pi$
$48$		0			0
$49$	−0.567588	+	3.21895i	−0.0810840	+	0.459850i
$50$		0			0
$51$	−1.30538	−	0.547982i	−0.182790	−	0.0767329i
$52$		0			0
$53$	−0.181698			−0.0249581			−0.0124790	−	0.999922i	$-0.503972\pi$
$53$	−0.181698			−0.0249581			−0.0124790	+	0.999922i	$0.503972\pi$
$54$		0			0
$55$			19.3820i			2.61347i
$56$		0			0
$57$	−1.36967	−	1.80265i	−0.181417	−	0.238766i
$58$		0			0
$59$	−0.908057	−	0.160115i	−0.118219	−	0.0208452i	0.114226	−	0.993455i	$-0.463561\pi$
$59$	−0.908057	−	0.160115i	−0.118219	−	0.0208452i	−0.232445	+	0.972610i	$0.574672\pi$
$60$		0			0
$61$	−0.975724	−	1.16282i	−0.124929	−	0.148884i	0.699954	−	0.714187i	$-0.253204\pi$
$61$	−0.975724	−	1.16282i	−0.124929	−	0.148884i	−0.824883	+	0.565303i	$0.808759\pi$
$62$		0			0
$63$	7.82213	+	5.58854i	0.985496	+	0.704090i
$64$		0			0
$65$	−2.83077	+	0.499141i	−0.351114	+	0.0619108i
$66$		0			0
$67$	−5.95586	+	2.16776i	−0.727624	+	0.264834i	−0.679159	−	0.733991i	$-0.737655\pi$
$67$	−5.95586	+	2.16776i	−0.727624	+	0.264834i	−0.0484653	+	0.998825i	$0.515433\pi$
$68$		0			0
$69$	−5.63069	−	3.62484i	−0.677856	−	0.436380i
$70$		0			0
$71$	4.91251	−	8.50871i	0.583008	−	1.00980i	−0.412113	−	0.911133i	$-0.635209\pi$
$71$	4.91251	−	8.50871i	0.583008	−	1.00980i	0.995121	−	0.0986659i	$-0.0314575\pi$
$72$		0			0
$73$	−0.606035	−	1.04968i	−0.0709311	−	0.122856i	0.828379	−	0.560169i	$-0.189264\pi$
$73$	−0.606035	−	1.04968i	−0.0709311	−	0.122856i	−0.899310	+	0.437313i	$0.855930\pi$
$74$		0			0
$75$	18.4995	+	4.19348i	2.13614	+	0.484221i
$76$		0			0
$77$	11.9126	+	9.99585i	1.35757	+	1.13913i
$78$		0			0
$79$	−0.336165	+	0.923605i	−0.0378215	+	0.103914i	−0.957166	−	0.289540i	$-0.906498\pi$
$79$	−0.336165	+	0.923605i	−0.0378215	+	0.103914i	0.919344	+	0.393454i	$0.128720\pi$
$80$		0			0
$81$	7.87827	−	4.35119i	0.875363	−	0.483466i
$82$		0			0
$83$	−0.517786	+	1.42261i	−0.0568344	+	0.156151i	−0.964861	−	0.262762i	$-0.915367\pi$
$83$	−0.517786	+	1.42261i	−0.0568344	+	0.156151i	0.908026	+	0.418913i	$0.137589\pi$
$84$		0			0
$85$	−2.09842	+	2.50080i	−0.227606	+	0.271250i
$86$		0			0
$87$	−9.40778	−	2.13256i	−1.00862	−	0.228635i
$88$		0			0
$89$	−5.93630	+	3.42732i	−0.629246	+	0.363296i	−0.780460	−	0.625206i	$-0.785015\pi$
$89$	−5.93630	+	3.42732i	−0.629246	+	0.363296i	0.151214	+	0.988501i	$0.451682\pi$
$90$		0			0
$91$	−1.15312	+	1.99727i	−0.120880	+	0.209371i
$92$		0			0
$93$	0.746255	−	1.15920i	0.0773830	−	0.120204i
$94$		0			0
$95$	−4.90566	+	1.78551i	−0.503310	+	0.183190i
$96$		0			0
$97$	−1.47950	−	8.39068i	−0.150221	−	0.851945i	−0.963026	−	0.269409i	$-0.913172\pi$
$97$	−1.47950	−	8.39068i	−0.150221	−	0.851945i	0.812805	−	0.582536i	$-0.197939\pi$
$98$		0			0
$99$	13.2523	−	6.02715i	1.33191	−	0.605751i
$100$		0			0
$101$	13.0625	−	10.9607i	1.29976	−	1.09063i	0.309577	−	0.950875i	$-0.399813\pi$
$101$	13.0625	−	10.9607i	1.29976	−	1.09063i	0.990186	−	0.139756i	$-0.0446317\pi$
$102$		0			0
$103$	−11.4111	−	2.01208i	−1.12437	−	0.198256i	−0.419610	−	0.907705i	$-0.637833\pi$
$103$	−11.4111	−	2.01208i	−1.12437	−	0.198256i	−0.704757	+	0.709448i	$0.748944\pi$
$104$		0			0
$105$	17.6506	−	13.4112i	1.72253	−	1.30880i
$106$		0			0
$107$			6.92250i			0.669223i	0.942356	+	0.334612i	$0.108605\pi$
$107$			6.92250i			0.669223i	−0.942356	+	0.334612i	$0.891395\pi$
$108$		0			0
$109$			3.45030i			0.330479i	0.986253	+	0.165239i	$0.0528397\pi$
$109$			3.45030i			0.330479i	−0.986253	+	0.165239i	$0.947160\pi$
$110$		0			0
$111$	5.01213	+	2.10402i	0.475730	+	0.199705i
$112$		0			0
$113$	−14.4711	−	2.55165i	−1.36133	−	0.240039i	−0.555170	−	0.831737i	$-0.687347\pi$
$113$	−14.4711	−	2.55165i	−1.36133	−	0.240039i	−0.806160	+	0.591698i	$0.798458\pi$
$114$		0			0
$115$	−11.8290	+	9.92574i	−1.10306	+	0.925580i
$116$		0			0
$117$	1.22156	+	1.78030i	0.112933	+	0.164589i
$118$		0			0
$119$	0.454829	+	2.57946i	0.0416941	+	0.236459i
$120$		0			0
$121$	11.7932	−	4.29239i	1.07211	−	0.390217i
$122$		0			0
$123$	−7.89569	−	15.3449i	−0.711930	−	1.38360i
$124$		0			0
$125$	11.8853	−	20.5860i	1.06306	−	1.84127i
$126$		0			0
$127$	−1.53630	+	0.886983i	−0.136325	+	0.0787070i	−0.566611	−	0.823985i	$-0.691746\pi$
$127$	−1.53630	+	0.886983i	−0.136325	+	0.0787070i	0.430287	+	0.902692i	$0.358412\pi$
$128$		0			0
$129$	5.94059	+	19.1578i	0.523040	+	1.68675i
$130$		0			0
$131$	1.60193	−	1.90910i	0.139961	−	0.166799i	−0.691510	−	0.722366i	$-0.743054\pi$
$131$	1.60193	−	1.90910i	0.139961	−	0.166799i	0.831472	+	0.555567i	$0.187499\pi$
$132$		0			0
$133$	−1.43257	+	3.93596i	−0.124220	+	0.341291i
$134$		0			0
$135$	−4.20281	−	20.3232i	−0.361720	−	1.74914i
$136$		0			0
$137$	5.54495	−	15.2346i	0.473737	−	1.30158i	−0.440992	−	0.897511i	$-0.645373\pi$
$137$	5.54495	−	15.2346i	0.473737	−	1.30158i	0.914728	−	0.404069i	$-0.132405\pi$
$138$		0			0
$139$	0.802121	+	0.673059i	0.0680350	+	0.0570881i	0.676171	−	0.736745i	$-0.263638\pi$
$139$	0.802121	+	0.673059i	0.0680350	+	0.0570881i	−0.608136	+	0.793833i	$0.708082\pi$
$140$		0			0
$141$	5.98767	−	6.47243i	0.504253	−	0.545077i
$142$		0			0
$143$	1.74629	+	3.02466i	0.146032	+	0.252935i
$144$		0			0
$145$	−11.1219	+	19.2638i	−0.923626	+	1.59977i
$146$		0			0
$147$	0.273795	−	5.65477i	0.0225822	−	0.466398i
$148$		0			0
$149$	−20.8730	+	7.59715i	−1.70998	+	0.622383i	−0.996899	−	0.0786947i	$-0.974925\pi$
$149$	−20.8730	+	7.59715i	−1.70998	+	0.622383i	−0.713085	+	0.701078i	$0.752703\pi$
$150$		0			0
$151$	−5.72685	+	1.00980i	−0.466045	+	0.0821762i	−0.401739	−	0.915754i	$-0.631594\pi$
$151$	−5.72685	+	1.00980i	−0.466045	+	0.0821762i	−0.0643052	+	0.997930i	$0.520483\pi$
$152$		0			0
$153$	2.36244	+	0.657118i	0.190992	+	0.0531248i
$154$		0			0
$155$	−2.04344	−	2.43527i	−0.164133	−	0.195606i
$156$		0			0
$157$	−10.1064	−	1.78204i	−0.806582	−	0.142222i	−0.244871	−	0.969556i	$-0.578746\pi$
$157$	−10.1064	−	1.78204i	−0.806582	−	0.142222i	−0.561711	+	0.827334i	$0.689857\pi$
$158$		0			0
$159$	0.312209	−	0.0395961i	0.0247598	−	0.00314018i
$160$		0			0
$161$			12.3893i			0.976417i
$162$		0			0
$163$	11.7405			0.919590			0.459795	−	0.888025i	$-0.347923\pi$
$163$	11.7405			0.919590			0.459795	+	0.888025i	$0.347923\pi$
$164$		0			0
$165$	−4.22380	−	33.3039i	−0.328822	−	2.59271i
$166$		0			0
$167$	2.71920	−	15.4214i	0.210418	−	1.19334i	−0.678265	−	0.734818i	$-0.737268\pi$
$167$	2.71920	−	15.4214i	0.210418	−	1.19334i	0.888683	−	0.458523i	$-0.151621\pi$
$168$		0			0
$169$	9.56179	−	8.02330i	0.735523	−	0.617177i
$170$		0			0
$171$	2.74633	+	2.79898i	0.210017	+	0.214043i
$172$		0			0
$173$	−1.41091	−	8.00169i	−0.107270	−	0.608357i	−0.990289	−	0.139021i	$-0.955604\pi$
$173$	−1.41091	−	8.00169i	−0.107270	−	0.608357i	0.883020	−	0.469336i	$-0.155507\pi$
$174$		0			0
$175$	−12.0029	−	32.9778i	−0.907337	−	2.49289i
$176$		0			0
$177$	1.59519	+	0.0772367i	0.119902	+	0.00580547i
$178$		0			0
$179$	13.3490	+	7.70708i	0.997755	+	0.576054i	0.907583	−	0.419872i	$-0.137925\pi$
$179$	13.3490	+	7.70708i	0.997755	+	0.576054i	0.0901716	+	0.995926i	$0.471258\pi$
$180$		0			0
$181$	12.4342	−	7.17888i	0.924226	−	0.533602i	0.0392449	−	0.999230i	$-0.487505\pi$
$181$	12.4342	−	7.17888i	0.924226	−	0.533602i	0.884981	+	0.465628i	$0.154171\pi$
$182$		0			0
$183$	1.92998	+	1.78543i	0.142668	+	0.131983i
$184$		0			0
$185$	8.05706	−	9.60203i	0.592367	−	0.705955i
$186$		0			0
$187$	3.72739	+	1.35666i	0.272573	+	0.0992086i
$188$		0			0
$189$	−14.6585	−	7.89809i	−1.06625	−	0.574502i
$190$		0			0
$191$	−10.3786	−	3.77752i	−0.750972	−	0.273332i	−0.0619574	−	0.998079i	$-0.519734\pi$
$191$	−10.3786	−	3.77752i	−0.750972	−	0.273332i	−0.689015	+	0.724747i	$0.741957\pi$
$192$		0			0
$193$	−4.41602	−	3.70548i	−0.317872	−	0.266726i	0.469865	−	0.882738i	$-0.344303\pi$
$193$	−4.41602	−	3.70548i	−0.317872	−	0.266726i	−0.787737	+	0.616012i	$0.788747\pi$
$194$		0			0
$195$	4.75530	−	1.47456i	0.340534	−	0.105595i
$196$		0			0
$197$	9.38881	+	16.2619i	0.668925	+	1.15861i	0.978205	+	0.207641i	$0.0665785\pi$
$197$	9.38881	+	16.2619i	0.668925	+	1.15861i	−0.309280	+	0.950971i	$0.600088\pi$
$198$		0			0
$199$	10.5780	+	6.10722i	0.749856	+	0.432930i	0.825642	−	0.564194i	$-0.190813\pi$
$199$	10.5780	+	6.10722i	0.749856	+	0.432930i	−0.0757858	+	0.997124i	$0.524147\pi$
$200$		0			0
$201$	9.76147	−	5.02275i	0.688521	−	0.354277i
$202$		0			0
$203$	6.10400	+	16.7706i	0.428417	+	1.17707i
$204$		0			0
$205$	−39.1888	+	6.91004i	−2.73706	+	0.482618i
$206$		0			0
$207$	10.4651	+	5.00146i	0.727373	+	0.347625i
$208$		0			0
$209$	4.07730	+	4.85914i	0.282033	+	0.336113i
$210$		0			0
$211$	3.21591	−	18.2383i	0.221393	−	1.25558i	−0.648070	−	0.761581i	$-0.724424\pi$
$211$	3.21591	−	18.2383i	0.221393	−	1.25558i	0.869463	−	0.493999i	$-0.164465\pi$
$212$		0			0
$213$	−6.58685	+	15.6910i	−0.451324	+	1.07513i
$214$		0			0
$215$	46.2513			3.15431
$216$		0			0
$217$	−2.55062			−0.173148
$218$		0			0
$219$	1.27009	+	1.67159i	0.0858249	+	0.112956i
$220$		0			0
$221$	−0.102151	+	0.579327i	−0.00687142	+	0.0389697i
$222$		0			0
$223$	7.23856	+	8.62658i	0.484730	+	0.577679i	0.951869	−	0.306505i	$-0.0991597\pi$
$223$	7.23856	+	8.62658i	0.484730	+	0.577679i	−0.467139	+	0.884184i	$0.654715\pi$
$224$		0			0
$225$	−32.7013	−	3.17413i	−2.18009	−	0.211609i
$226$		0			0
$227$	8.98787	−	1.58480i	0.596546	−	0.105187i	0.132781	−	0.991145i	$-0.457609\pi$
$227$	8.98787	−	1.58480i	0.596546	−	0.105187i	0.463765	+	0.885958i	$0.346498\pi$
$228$		0			0
$229$	6.36470	+	17.4869i	0.420591	+	1.15557i	0.951369	+	0.308054i	$0.0996778\pi$
$229$	6.36470	+	17.4869i	0.420591	+	1.15557i	−0.530777	+	0.847511i	$0.678100\pi$
$230$		0			0
$231$	−22.6476	−	14.5797i	−1.49010	−	0.959274i
$232$		0			0
$233$	19.2286	+	11.1016i	1.25971	+	0.727291i	0.973017	−	0.230732i	$-0.0741122\pi$
$233$	19.2286	+	11.1016i	1.25971	+	0.727291i	0.286688	+	0.958024i	$0.407446\pi$
$234$		0			0
$235$	−10.1659	−	17.6079i	−0.663153	−	1.14861i
$236$		0			0
$237$	0.376352	−	1.66028i	0.0244467	−	0.107847i
$238$		0			0
$239$	13.4989	+	11.3269i	0.873169	+	0.732676i	0.964763	−	0.263121i	$-0.0847517\pi$
$239$	13.4989	+	11.3269i	0.873169	+	0.732676i	−0.0915939	+	0.995796i	$0.529196\pi$
$240$		0			0
$241$	8.85508	+	3.22299i	0.570406	+	0.207611i	0.611090	−	0.791561i	$-0.290731\pi$
$241$	8.85508	+	3.22299i	0.570406	+	0.207611i	−0.0406839	+	0.999172i	$0.512954\pi$
$242$		0			0
$243$	−12.5889	+	9.19345i	−0.807578	+	0.589760i
$244$		0			0
$245$	−12.2674	−	4.46496i	−0.783734	−	0.285256i
$246$		0			0
$247$	−0.604681	+	0.720631i	−0.0384749	+	0.0458526i
$248$		0			0
$249$	0.579686	−	2.55728i	0.0367361	−	0.162061i
$250$		0			0
$251$	26.8008	−	15.4735i	1.69165	−	0.976676i	0.738468	−	0.674288i	$-0.235549\pi$
$251$	26.8008	−	15.4735i	1.69165	−	0.976676i	0.953185	−	0.302388i	$-0.0977840\pi$
$252$		0			0
$253$	16.2487	+	9.38121i	1.02155	+	0.589792i
$254$		0			0
$255$	3.06071	−	4.75439i	0.191669	−	0.297731i
$256$		0			0
$257$	3.14184	+	8.63213i	0.195982	+	0.538457i	0.998290	−	0.0584533i	$-0.0186169\pi$
$257$	3.14184	+	8.63213i	0.195982	+	0.538457i	−0.802308	+	0.596911i	$0.796395\pi$
$258$		0			0
$259$	−1.74635	−	9.90406i	−0.108513	−	0.615408i
$260$		0			0
$261$	16.6300	+	1.61418i	1.02937	+	0.0999151i
$262$		0			0
$263$	−3.59765	+	3.01879i	−0.221841	+	0.186147i	−0.746934	−	0.664898i	$-0.768475\pi$
$263$	−3.59765	+	3.01879i	−0.221841	+	0.186147i	0.525093	+	0.851045i	$0.324030\pi$
$264$		0			0
$265$	0.126015	−	0.714667i	0.00774104	−	0.0439016i
$266$		0			0
$267$	9.45337	−	7.18278i	0.578537	−	0.439579i
$268$		0			0
$269$	−28.2139			−1.72023			−0.860115	−	0.510100i	$-0.829608\pi$
$269$	−28.2139			−1.72023			−0.860115	+	0.510100i	$0.829608\pi$
$270$		0			0
$271$		−	15.1576i		−	0.920757i	−0.887723	−	0.460378i	$-0.847714\pi$
$271$		−	15.1576i		−	0.920757i	0.887723	−	0.460378i	$-0.152286\pi$
$272$		0			0
$273$	1.54615	−	3.68317i	0.0935770	−	0.222916i
$274$		0			0
$275$	−52.3393	−	9.22883i	−3.15618	−	0.556520i
$276$		0			0
$277$	9.43735	+	11.2470i	0.567035	+	0.675766i	0.971020	−	0.239000i	$-0.0768195\pi$
$277$	9.43735	+	11.2470i	0.567035	+	0.675766i	−0.403984	+	0.914766i	$0.632375\pi$
$278$		0			0
$279$	−1.02966	+	2.15447i	−0.0616443	+	0.128985i
$280$		0			0
$281$	3.57405	−	0.630201i	0.213210	−	0.0375946i	−0.0660229	−	0.997818i	$-0.521031\pi$
$281$	3.57405	−	0.630201i	0.213210	−	0.0375946i	0.279233	+	0.960223i	$0.409920\pi$
$282$		0			0
$283$	6.78947	−	2.47116i	0.403592	−	0.146895i	−0.132245	−	0.991217i	$-0.542218\pi$
$283$	6.78947	−	2.47116i	0.403592	−	0.146895i	0.535837	+	0.844322i	$0.319996\pi$
$284$		0			0
$285$	8.04023	−	4.13708i	0.476262	−	0.245060i
$286$		0			0
$287$	−15.9637	+	27.6499i	−0.942307	+	1.63212i
$288$		0			0
$289$	−8.16595	−	14.1438i	−0.480350	−	0.831990i
$290$		0			0
$291$	4.37074	+	14.0952i	0.256217	+	0.826274i
$292$		0			0
$293$	6.40067	+	5.37080i	0.373931	+	0.313765i	0.810314	−	0.585996i	$-0.199296\pi$
$293$	6.40067	+	5.37080i	0.373931	+	0.313765i	−0.436383	+	0.899761i	$0.643741\pi$
$294$		0			0
$295$	1.25955	−	3.46059i	0.0733340	−	0.201483i
$296$		0			0
$297$	−21.4579	+	13.2444i	−1.24511	+	0.768516i
$298$		0			0
$299$	−0.951687	+	2.61474i	−0.0550375	+	0.151214i
$300$		0			0
$301$	23.8531	−	28.4270i	1.37487	−	1.63850i
$302$		0			0
$303$	−20.0564	+	21.6802i	−1.15221	+	1.24550i
$304$		0			0
$305$	5.25041	−	3.03133i	0.300638	−	0.173573i
$306$		0			0
$307$	−14.2168	+	24.6242i	−0.811393	+	1.40537i	0.100495	+	0.994938i	$0.467957\pi$
$307$	−14.2168	+	24.6242i	−0.811393	+	1.40537i	−0.911889	+	0.410437i	$0.865376\pi$
$308$		0			0
$309$	20.0460	+	0.970593i	1.14038	+	0.0552151i
$310$		0			0
$311$	−10.5053	+	3.82361i	−0.595701	+	0.216817i	−0.622235	−	0.782831i	$-0.713775\pi$
$311$	−10.5053	+	3.82361i	−0.595701	+	0.216817i	0.0265343	+	0.999648i	$0.491553\pi$
$312$		0			0
$313$	−1.64149	−	9.30937i	−0.0927827	−	0.526197i	−0.995404	−	0.0957617i	$-0.969471\pi$
$313$	−1.64149	−	9.30937i	−0.0927827	−	0.526197i	0.902622	−	0.430435i	$-0.141640\pi$
$314$		0			0
$315$	−27.4063	+	26.8907i	−1.54417	+	1.51512i
$316$		0			0
$317$	−16.2563	+	13.6406i	−0.913043	+	0.766134i	−0.972695	−	0.232085i	$-0.925445\pi$
$317$	−16.2563	+	13.6406i	−0.913043	+	0.766134i	0.0596524	+	0.998219i	$0.481001\pi$
$318$		0			0
$319$	26.6168	+	4.69325i	1.49025	+	0.262772i
$320$		0			0
$321$	−1.50857	−	11.8948i	−0.0842003	−	0.663905i
$322$		0			0
$323$			1.06839i			0.0594469i
$324$		0			0
$325$		−	7.88189i		−	0.437208i
$326$		0			0
$327$	−0.751900	−	5.92860i	−0.0415802	−	0.327853i
$328$		0			0
$329$	−16.0650	−	2.83270i	−0.885694	−	0.156172i
$330$		0			0
$331$	7.45482	−	6.25534i	0.409754	−	0.343825i	−0.414495	−	0.910051i	$-0.636042\pi$
$331$	7.45482	−	6.25534i	0.409754	−	0.343825i	0.824249	+	0.566227i	$0.191597\pi$
$332$		0			0
$333$	−9.07079	−	2.52306i	−0.497076	−	0.138263i
$334$		0			0
$335$	−4.39574	−	24.9295i	−0.240165	−	1.36204i
$336$		0			0
$337$	17.8549	−	6.49864i	0.972617	−	0.354004i	0.193652	−	0.981070i	$-0.437967\pi$
$337$	17.8549	−	6.49864i	0.972617	−	0.354004i	0.778966	+	0.627067i	$0.215745\pi$
$338$		0			0
$339$	25.4216	+	1.23087i	1.38071	+	0.0668518i
$340$		0			0
$341$	−1.93133	+	3.34517i	−0.104588	+	0.181151i
$342$		0			0
$343$	10.3552	−	5.97856i	0.559126	−	0.322812i
$344$		0			0
$345$	18.1626	−	19.6331i	0.977843	−	1.05701i
$346$		0			0
$347$	7.03596	−	8.38513i	0.377710	−	0.450137i	−0.543380	−	0.839487i	$-0.682856\pi$
$347$	7.03596	−	8.38513i	0.377710	−	0.450137i	0.921090	+	0.389350i	$0.127300\pi$
$348$		0			0
$349$	−8.70795	+	23.9249i	−0.466126	+	1.28067i	0.454682	+	0.890654i	$0.349753\pi$
$349$	−8.70795	+	23.9249i	−0.466126	+	1.28067i	−0.920808	+	0.390017i	$0.872469\pi$
$350$		0			0
$351$	−2.48695	−	2.79287i	−0.132744	−	0.149072i
$352$		0			0
$353$	−3.42693	+	9.41540i	−0.182397	+	0.501131i	−0.996869	−	0.0790715i	$-0.974804\pi$
$353$	−3.42693	+	9.41540i	−0.182397	+	0.501131i	0.814472	+	0.580203i	$0.197027\pi$
$354$		0			0
$355$	30.0601	+	25.2234i	1.59542	+	1.33872i
$356$		0			0
$357$	−1.34365	−	4.33314i	−0.0711136	−	0.229334i
$358$		0			0
$359$	−2.79690	−	4.84437i	−0.147615	−	0.255676i	0.782731	−	0.622360i	$-0.213826\pi$
$359$	−2.79690	−	4.84437i	−0.147615	−	0.255676i	−0.930345	+	0.366685i	$0.880493\pi$
$360$		0			0
$361$	8.64575	−	14.9749i	0.455039	−	0.788151i
$362$		0			0
$363$	−19.3288	+	9.94558i	−1.01450	+	0.522007i
$364$		0			0
$365$	4.54901	−	1.65570i	0.238106	−	0.0866635i
$366$		0			0
$367$	−30.7502	+	5.42209i	−1.60515	+	0.283031i	−0.903207	−	0.429205i	$-0.858794\pi$
$367$	−30.7502	+	5.42209i	−1.60515	+	0.283031i	−0.701940	+	0.712236i	$0.747683\pi$
$368$		0			0
$369$	16.9111	+	24.6463i	0.880355	+	1.28303i
$370$		0			0
$371$	−0.374259	−	0.446025i	−0.0194306	−	0.0231565i
$372$		0			0
$373$	13.5451	+	2.38837i	0.701340	+	0.123665i	0.512936	−	0.858427i	$-0.328558\pi$
$373$	13.5451	+	2.38837i	0.701340	+	0.123665i	0.188403	+	0.982092i	$0.439669\pi$
$374$		0			0
$375$	−15.9362	+	37.9627i	−0.822944	+	1.96039i
$376$		0			0
$377$			4.00827i			0.206437i
$378$		0			0
$379$	−31.9660			−1.64199			−0.820993	−	0.570939i	$-0.806579\pi$
$379$	−31.9660			−1.64199			−0.820993	+	0.570939i	$0.806579\pi$
$380$		0			0
$381$	2.44651	−	1.85889i	0.125338	−	0.0952337i
$382$		0			0
$383$	−1.30024	+	7.37403i	−0.0664392	+	0.376795i	0.933400	+	0.358839i	$0.116827\pi$
$383$	−1.30024	+	7.37403i	−0.0664392	+	0.376795i	−0.999839	+	0.0179566i	$0.994284\pi$
$384$		0			0
$385$	−47.5783	+	39.9230i	−2.42482	+	2.03466i
$386$		0			0
$387$	−14.3826	−	31.6240i	−0.731107	−	1.60754i
$388$		0			0
$389$	−4.61608	−	26.1791i	−0.234044	−	1.32733i	−0.844617	−	0.535371i	$-0.820172\pi$
$389$	−4.61608	−	26.1791i	−0.234044	−	1.32733i	0.610572	−	0.791960i	$-0.290939\pi$
$390$		0			0
$391$	1.08085	+	2.96962i	0.0546610	+	0.150180i
$392$		0			0
$393$	−2.33654	+	3.62949i	−0.117863	+	0.183083i
$394$		0			0
$395$	−3.39965	−	1.96279i	−0.171055	−	0.0987586i
$396$		0			0
$397$	25.7004	−	14.8381i	1.28986	−	0.744704i	0.311235	−	0.950333i	$-0.399257\pi$
$397$	25.7004	−	14.8381i	1.28986	−	0.744704i	0.978630	+	0.205629i	$0.0659241\pi$
$398$		0			0
$399$	1.60383	−	7.07529i	0.0802920	−	0.354208i
$400$		0			0
$401$	−15.5172	+	18.4927i	−0.774891	+	0.923480i	−0.998691	−	0.0511557i	$-0.983710\pi$
$401$	−15.5172	+	18.4927i	−0.774891	+	0.923480i	0.223799	+	0.974635i	$0.428154\pi$
$402$		0			0
$403$	−0.538303	−	0.195926i	−0.0268148	−	0.00975977i
$404$		0			0
$405$	11.6505	+	34.0052i	0.578919	+	1.68973i
$406$		0			0
$407$	−14.3116	−	5.20900i	−0.709400	−	0.258200i
$408$		0			0
$409$	−7.17989	−	6.02464i	−0.355023	−	0.297899i	0.447781	−	0.894143i	$-0.352215\pi$
$409$	−7.17989	−	6.02464i	−0.355023	−	0.297899i	−0.802803	+	0.596244i	$0.796659\pi$
$410$		0			0
$411$	−6.20783	+	27.3858i	−0.306210	+	1.35084i
$412$		0			0
$413$	−1.47736	−	2.55887i	−0.0726963	−	0.125914i
$414$		0			0
$415$	−5.23640	−	3.02323i	−0.257045	−	0.148405i
$416$		0			0
$417$	−1.52495	−	0.981708i	−0.0746771	−	0.0480745i
$418$		0			0
$419$	−6.17961	−	16.9783i	−0.301894	−	0.829446i	−0.994171	−	0.107814i	$-0.965615\pi$
$419$	−6.17961	−	16.9783i	−0.301894	−	0.829446i	0.692277	−	0.721631i	$-0.256607\pi$
$420$		0			0
$421$	−10.9086	+	1.92348i	−0.531653	+	0.0937447i	−0.433029	−	0.901380i	$-0.642555\pi$
$421$	−10.9086	+	1.92348i	−0.531653	+	0.0937447i	−0.0986239	+	0.995125i	$0.531444\pi$
$422$		0			0
$423$	−8.87804	+	12.4264i	−0.431665	+	0.604190i
$424$		0			0
$425$	−5.75400	−	6.85735i	−0.279110	−	0.332630i
$426$		0			0
$427$	0.844667	−	4.79035i	0.0408763	−	0.231821i
$428$		0			0
$429$	−3.65977	−	4.81668i	−0.176695	−	0.232552i
$430$		0			0
$431$	24.5183			1.18101			0.590503	−	0.807036i	$-0.298930\pi$
$431$	24.5183			1.18101			0.590503	+	0.807036i	$0.298930\pi$
$432$		0			0
$433$	−8.35856			−0.401687			−0.200843	−	0.979623i	$-0.564368\pi$
$433$	−8.35856			−0.401687			−0.200843	+	0.979623i	$0.564368\pi$
$434$		0			0
$435$	14.9127	−	35.5244i	0.715007	−	1.70326i
$436$		0			0
$437$	−0.877549	+	4.97683i	−0.0419789	+	0.238074i
$438$		0			0
$439$	6.95815	+	8.29240i	0.332094	+	0.395775i	0.906091	−	0.423083i	$-0.139052\pi$
$439$	6.95815	+	8.29240i	0.332094	+	0.395775i	−0.573997	+	0.818858i	$0.694608\pi$
$440$		0			0
$441$	0.761848	+	9.77619i	0.0362785	+	0.465533i
$442$		0			0
$443$	0.0932147	−	0.0164363i	0.00442876	−	0.000780910i	−0.171433	−	0.985196i	$-0.554840\pi$
$443$	0.0932147	−	0.0164363i	0.00442876	−	0.000780910i	0.175862	+	0.984415i	$0.443729\pi$
$444$		0			0
$445$	−9.36353	−	25.7261i	−0.443874	−	1.21953i
$446$		0			0
$447$	34.2102	−	17.6028i	1.61809	−	0.832584i
$448$		0			0
$449$	−22.5438	−	13.0157i	−1.06391	−	0.614247i	−0.137397	−	0.990516i	$-0.543874\pi$
$449$	−22.5438	−	13.0157i	−1.06391	−	0.614247i	−0.926511	+	0.376269i	$0.877207\pi$
$450$		0			0
$451$	24.1754	+	41.8730i	1.13838	+	1.97172i
$452$		0			0
$453$	9.62032	−	2.98314i	0.452002	−	0.140160i
$454$		0			0
$455$	−7.05607	−	5.92075i	−0.330794	−	0.277569i
$456$		0			0
$457$	29.3356	+	10.6773i	1.37226	+	0.499463i	0.919823	−	0.392333i	$-0.128332\pi$
$457$	29.3356	+	10.6773i	1.37226	+	0.499463i	0.452439	+	0.891795i	$0.350554\pi$
$458$		0			0
$459$	−4.20255	−	0.614285i	−0.196158	−	0.0286724i
$460$		0			0
$461$	−29.8177	−	10.8528i	−1.38875	−	0.505464i	−0.463931	−	0.885871i	$-0.653562\pi$
$461$	−29.8177	−	10.8528i	−1.38875	−	0.505464i	−0.924819	+	0.380407i	$0.875784\pi$
$462$		0			0
$463$	4.54519	−	5.41674i	0.211233	−	0.251737i	−0.650017	−	0.759920i	$-0.725238\pi$
$463$	4.54519	−	5.41674i	0.211233	−	0.251737i	0.861249	+	0.508183i	$0.169683\pi$
$464$		0			0
$465$	4.04191	+	3.73918i	0.187439	+	0.173400i
$466$		0			0
$467$	−22.4420	+	12.9569i	−1.03849	+	0.599572i	−0.919405	−	0.393312i	$-0.871329\pi$
$467$	−22.4420	+	12.9569i	−1.03849	+	0.599572i	−0.119085	+	0.992884i	$0.537996\pi$
$468$		0			0
$469$	−17.5892	−	10.1551i	−0.812192	−	0.468919i
$470$		0			0
$471$	17.7541	+	0.859624i	0.818066	+	0.0396094i
$472$		0			0
$473$	−19.2207	−	52.8084i	−0.883768	−	2.42813i
$474$		0			0
$475$	−2.48576	−	14.0974i	−0.114054	−	0.646835i
$476$		0			0
$477$	−0.527835	+	0.136075i	−0.0241679	+	0.00623045i
$478$		0			0
$479$	−0.164361	+	0.137915i	−0.00750983	+	0.00630150i	−0.646535	−	0.762884i	$-0.723782\pi$
$479$	−0.164361	+	0.137915i	−0.00750983	+	0.00630150i	0.639025	+	0.769186i	$0.279338\pi$
$480$		0			0
$481$	0.392217	−	2.22437i	0.0178836	−	0.101423i
$482$		0			0
$483$	−2.69992	−	21.2884i	−0.122851	−	0.968658i
$484$		0			0
$485$	34.0290			1.54518
$486$		0			0
$487$			0.392983i			0.0178078i	0.999960	+	0.00890388i	$0.00283423\pi$
$487$			0.392983i			0.0178078i	−0.999960	+	0.00890388i	$0.997166\pi$
$488$		0			0
$489$	−20.1736	+	2.55854i	−0.912282	+	0.115701i
$490$		0			0
$491$	13.4296	+	2.36800i	0.606070	+	0.106866i	0.468258	−	0.883592i	$-0.344882\pi$
$491$	13.4296	+	2.36800i	0.606070	+	0.106866i	0.137812	+	0.990458i	$0.455993\pi$
$492$		0			0
$493$	2.92615	+	3.48725i	0.131787	+	0.157058i
$494$		0			0
$495$	14.5154	+	56.3052i	0.652418	+	2.53073i
$496$		0			0
$497$	31.0056	−	5.46713i	1.39079	−	0.245234i
$498$		0			0
$499$	24.6543	−	8.97345i	1.10368	−	0.401707i	0.275008	−	0.961442i	$-0.411319\pi$
$499$	24.6543	−	8.97345i	1.10368	−	0.401707i	0.828672	+	0.559735i	$0.189097\pi$
$500$		0			0
$501$	−1.31170	+	27.0909i	−0.0586023	+	1.21033i
$502$		0			0
$503$	−8.03410	+	13.9155i	−0.358223	+	0.620460i	−0.987664	−	0.156588i	$-0.949950\pi$
$503$	−8.03410	+	13.9155i	−0.358223	+	0.620460i	0.629441	+	0.777048i	$0.283284\pi$
$504$		0			0
$505$	34.0521	+	58.9799i	1.51530	+	2.62457i
$506$		0			0
$507$	−14.6814	+	15.8701i	−0.652026	+	0.704814i
$508$		0			0
$509$	14.1393	+	11.8643i	0.626714	+	0.525875i	0.899906	−	0.436084i	$-0.143635\pi$
$509$	14.1393	+	11.8643i	0.626714	+	0.525875i	−0.273192	+	0.961959i	$0.588079\pi$
$510$		0			0
$511$	1.32842	−	3.64980i	0.0587658	−	0.161458i
$512$		0			0
$513$	−5.32894	−	4.21096i	−0.235278	−	0.185918i
$514$		0			0
$515$	15.8281	−	43.4875i	0.697471	−	1.91629i
$516$		0			0
$517$	−15.8796	+	18.9245i	−0.698382	+	0.832299i
$518$		0			0
$519$	4.16811	+	13.4417i	0.182960	+	0.590026i
$520$		0			0
$521$	22.1275	−	12.7753i	0.969421	−	0.559696i	0.0703617	−	0.997522i	$-0.477585\pi$
$521$	22.1275	−	12.7753i	0.969421	−	0.559696i	0.899060	+	0.437826i	$0.144251\pi$
$522$		0			0
$523$	−1.67576	+	2.90250i	−0.0732759	+	0.126918i	−0.900335	−	0.435197i	$-0.856679\pi$
$523$	−1.67576	+	2.90250i	−0.0732759	+	0.126918i	0.827059	+	0.562115i	$0.190012\pi$
$524$		0			0
$525$	27.8111	+	54.0496i	1.21378	+	2.35892i
$526$		0			0
$527$	−0.611362	+	0.222518i	−0.0266313	+	0.00969302i
$528$		0			0
$529$	−1.39821	−	7.92962i	−0.0607915	−	0.344766i
$530$		0			0
$531$	−2.75783	+	0.214915i	−0.119680	+	0.00932652i
$532$		0			0
$533$	−5.49302	+	4.60919i	−0.237929	+	0.199646i
$534$		0			0
$535$	−27.2281	−	4.80105i	−1.17717	−	0.207567i
$536$		0			0
$537$	−24.6170	−	10.3339i	−1.06230	−	0.445941i
$538$		0			0
$539$			15.8621i			0.683227i
$540$		0			0
$541$			25.0374i			1.07644i	0.842804	+	0.538221i	$0.180903\pi$
$541$			25.0374i			1.07644i	−0.842804	+	0.538221i	$0.819097\pi$
$542$		0			0
$543$	−19.8010	+	15.0451i	−0.849744	+	0.645646i
$544$		0			0
$545$	−13.5710	−	2.39293i	−0.581317	−	0.102502i
$546$		0			0
$547$	−2.10713	+	1.76810i	−0.0900946	+	0.0755983i	−0.686723	−	0.726920i	$-0.740951\pi$
$547$	−2.10713	+	1.76810i	−0.0900946	+	0.0755983i	0.596628	+	0.802518i	$0.296507\pi$
$548$		0			0
$549$	−3.70535	−	2.64729i	−0.158140	−	0.112984i
$550$		0			0
$551$	1.26411	+	7.16914i	0.0538531	+	0.305416i
$552$		0			0
$553$	−2.95966	+	1.07723i	−0.125858	+	0.0458084i
$554$		0			0
$555$	−11.7518	+	18.2549i	−0.498838	+	0.774876i
$556$		0			0
$557$	16.8751	−	29.2285i	0.715019	−	1.23845i	−0.247933	−	0.968777i	$-0.579751\pi$
$557$	16.8751	−	29.2285i	0.715019	−	1.23845i	0.962952	−	0.269673i	$-0.0869155\pi$
$558$		0			0
$559$	7.21775	−	4.16717i	0.305278	−	0.176252i
$560$		0			0
$561$	−6.70036	−	1.51884i	−0.282890	−	0.0641256i
$562$		0			0
$563$	−5.43652	+	6.47899i	−0.229122	+	0.273057i	−0.868341	−	0.495968i	$-0.834813\pi$
$563$	−5.43652	+	6.47899i	−0.229122	+	0.273057i	0.639219	+	0.769025i	$0.279258\pi$
$564$		0			0
$565$	20.0727	−	55.1493i	0.844465	−	2.32015i
$566$		0			0
$567$	26.9087	+	10.3768i	1.13006	+	0.435783i
$568$		0			0
$569$	−1.75562	+	4.82354i	−0.0735996	+	0.202213i	−0.971037	−	0.238928i	$-0.923204\pi$
$569$	−1.75562	+	4.82354i	−0.0735996	+	0.202213i	0.897438	+	0.441141i	$0.145426\pi$
$570$		0			0
$571$	−2.13892	−	1.79477i	−0.0895112	−	0.0751088i	0.596934	−	0.802290i	$-0.296385\pi$
$571$	−2.13892	−	1.79477i	−0.0895112	−	0.0751088i	−0.686445	+	0.727182i	$0.740830\pi$
$572$		0			0
$573$	18.6567	+	4.22911i	0.779395	+	0.176674i
$574$		0			0
$575$	−21.1711	−	36.6693i	−0.882894	−	1.52922i
$576$		0			0
$577$	−4.57149	+	7.91805i	−0.190314	+	0.329633i	−0.945354	−	0.326045i	$-0.894284\pi$
$577$	−4.57149	+	7.91805i	−0.190314	+	0.329633i	0.755041	+	0.655678i	$0.227617\pi$
$578$		0			0
$579$	8.39549	+	5.40472i	0.348905	+	0.224613i
$580$		0			0
$581$	−4.55869	+	1.65923i	−0.189127	+	0.0688364i
$582$		0			0
$583$	−0.868355	+	0.153114i	−0.0359636	+	0.00634135i
$584$		0			0
$585$	−7.84963	+	3.57000i	−0.324542	+	0.147601i
$586$		0			0
$587$	1.90264	+	2.26748i	0.0785303	+	0.0935887i	0.803879	−	0.594793i	$-0.202766\pi$
$587$	1.90264	+	2.26748i	0.0785303	+	0.0935887i	−0.725349	+	0.688382i	$0.758321\pi$
$588$		0			0
$589$	−1.02459	−	0.180663i	−0.0422175	−	0.00744409i
$590$		0			0
$591$	−19.6765	−	25.8966i	−0.809383	−	1.06524i
$592$		0			0
$593$			1.86981i			0.0767837i	0.999263	+	0.0383919i	$0.0122235\pi$
$593$			1.86981i			0.0767837i	−0.999263	+	0.0383919i	$0.987776\pi$
$594$		0			0
$595$	−10.4612			−0.428867
$596$		0			0
$597$	−19.5070	−	8.18877i	−0.798368	−	0.335144i
$598$		0			0
$599$	−5.09545	+	28.8978i	−0.208195	+	1.18073i	0.684138	+	0.729352i	$0.260179\pi$
$599$	−5.09545	+	28.8978i	−0.208195	+	1.18073i	−0.892333	+	0.451378i	$0.850933\pi$
$600$		0			0
$601$	3.02633	−	2.53939i	0.123447	−	0.103584i	−0.578974	−	0.815346i	$-0.696547\pi$
$601$	3.02633	−	2.53939i	0.123447	−	0.103584i	0.702421	+	0.711762i	$0.252102\pi$
$602$		0			0
$603$	−15.6784	+	10.7578i	−0.638475	+	0.438090i
$604$		0			0
$605$	8.70404	+	49.3630i	0.353869	+	2.00689i
$606$		0			0
$607$	7.61399	+	20.9193i	0.309042	+	0.849087i	0.992844	+	0.119419i	$0.0381031\pi$
$607$	7.61399	+	20.9193i	0.309042	+	0.849087i	−0.683802	+	0.729668i	$0.739675\pi$
$608$		0			0
$609$	−14.1431	−	27.4865i	−0.573109	−	1.11381i
$610$		0			0
$611$	−3.17289	−	1.83187i	−0.128361	−	0.0741095i
$612$		0			0
$613$	−32.5675	+	18.8029i	−1.31539	+	0.759441i	−0.982983	−	0.183695i	$-0.941194\pi$
$613$	−32.5675	+	18.8029i	−1.31539	+	0.759441i	−0.332407	+	0.943136i	$0.607861\pi$
$614$		0			0
$615$	65.8317	−	20.4136i	2.65459	−	0.823155i
$616$		0			0
$617$	18.4585	−	21.9980i	0.743111	−	0.885605i	−0.253544	−	0.967324i	$-0.581596\pi$
$617$	18.4585	−	21.9980i	0.743111	−	0.885605i	0.996655	+	0.0817186i	$0.0260409\pi$
$618$		0			0
$619$	−24.3178	−	8.85094i	−0.977413	−	0.355749i	−0.196579	−	0.980488i	$-0.562983\pi$
$619$	−24.3178	−	8.85094i	−0.977413	−	0.355749i	−0.780834	+	0.624738i	$0.785206\pi$
$620$		0			0
$621$	−19.0719	−	6.31335i	−0.765331	−	0.253346i
$622$		0			0
$623$	−20.6408	−	7.51264i	−0.826956	−	0.300988i
$624$		0			0
$625$	30.7801	+	25.8276i	1.23121	+	1.03310i
$626$		0			0
$627$	−8.06489	−	7.46085i	−0.322081	−	0.297958i
$628$		0			0
$629$	−1.28262	−	2.22156i	−0.0511414	−	0.0885795i
$630$		0			0
$631$	12.0456	+	6.95454i	0.479528	+	0.276856i	0.720220	−	0.693746i	$-0.244041\pi$
$631$	12.0456	+	6.95454i	0.479528	+	0.276856i	−0.240692	+	0.970602i	$0.577374\pi$
$632$		0			0
$633$	−1.55130	+	32.0395i	−0.0616587	+	1.27346i
$634$		0			0
$635$	−2.42326	−	6.65785i	−0.0961642	−	0.264209i
$636$		0			0
$637$	−2.31667	+	0.408492i	−0.0917899	+	0.0161850i
$638$		0			0
$639$	7.89868	−	28.3970i	0.312467	−	1.12337i
$640$		0			0
$641$	1.21478	+	1.44771i	0.0479808	+	0.0571813i	0.789501	−	0.613749i	$-0.210339\pi$
$641$	1.21478	+	1.44771i	0.0479808	+	0.0571813i	−0.741520	+	0.670930i	$0.765895\pi$
$642$		0			0
$643$	−2.69381	+	15.2774i	−0.106234	+	0.602480i	0.884487	+	0.466565i	$0.154509\pi$
$643$	−2.69381	+	15.2774i	−0.106234	+	0.602480i	−0.990720	+	0.135915i	$0.956602\pi$
$644$		0			0
$645$	−79.4730	+	10.0792i	−3.12925	+	0.396869i
$646$		0			0
$647$	−29.1611			−1.14644			−0.573221	−	0.819401i	$-0.694306\pi$
$647$	−29.1611			−1.14644			−0.573221	+	0.819401i	$0.694306\pi$
$648$		0			0
$649$	−4.47464			−0.175645
$650$		0			0
$651$	4.38270	−	0.555840i	0.171772	−	0.0217851i
$652$		0			0
$653$	−1.67688	+	9.51004i	−0.0656212	+	0.372157i	0.934258	+	0.356599i	$0.116064\pi$
$653$	−1.67688	+	9.51004i	−0.0656212	+	0.372157i	−0.999879	+	0.0155580i	$0.995048\pi$
$654$		0			0
$655$	6.39803	+	7.62488i	0.249992	+	0.297929i
$656$		0			0
$657$	−2.54666	−	2.59549i	−0.0993547	−	0.101260i
$658$		0			0
$659$	−40.5315	+	7.14680i	−1.57888	+	0.278400i	−0.893254	−	0.449551i	$-0.851584\pi$
$659$	−40.5315	+	7.14680i	−1.57888	+	0.278400i	−0.685629	+	0.727951i	$0.740473\pi$
$660$		0			0
$661$	−12.8126	−	35.2022i	−0.498351	−	1.36921i	−0.892868	−	0.450319i	$-0.851310\pi$
$661$	−12.8126	−	35.2022i	−0.498351	−	1.36921i	0.394516	−	0.918889i	$-0.370912\pi$
$662$		0			0
$663$	0.0492759	−	1.01771i	0.00191372	−	0.0395246i
$664$		0			0
$665$	−14.4877	−	8.36445i	−0.561807	−	0.324360i
$666$		0			0
$667$	10.7664	+	18.6479i	0.416876	+	0.722050i
$668$		0			0
$669$	−14.3179	−	13.2455i	−0.553560	−	0.512100i
$670$		0			0
$671$	−5.64300	−	4.73504i	−0.217846	−	0.182794i
$672$		0			0
$673$	11.9812	+	4.36081i	0.461842	+	0.168097i	0.562453	−	0.826829i	$-0.309858\pi$
$673$	11.9812	+	4.36081i	0.461842	+	0.168097i	−0.100611	+	0.994926i	$0.532080\pi$
$674$		0			0
$675$	56.8819	−	1.67231i	2.18939	−	0.0643673i
$676$		0			0
$677$	20.8147	+	7.57594i	0.799974	+	0.291167i	0.709476	−	0.704730i	$-0.248932\pi$
$677$	20.8147	+	7.57594i	0.799974	+	0.291167i	0.0904985	+	0.995897i	$0.471154\pi$
$678$		0			0
$679$	17.5497	−	20.9149i	0.673495	−	0.802640i
$680$		0			0
$681$	−15.0984	+	4.68181i	−0.578571	+	0.179408i
$682$		0			0
$683$	9.46338	−	5.46368i	0.362106	−	0.209062i	−0.307898	−	0.951419i	$-0.599626\pi$
$683$	9.46338	−	5.46368i	0.362106	−	0.209062i	0.670004	+	0.742357i	$0.266292\pi$
$684$		0			0
$685$	56.0763	+	32.3757i	2.14256	+	1.23701i
$686$		0			0
$687$	−14.7472	−	28.6605i	−0.562640	−	1.09346i
$688$		0			0
$689$	−0.0447251	−	0.122881i	−0.00170389	−	0.00468140i
$690$		0			0
$691$	3.31599	+	18.8059i	0.126146	+	0.715410i	0.980621	+	0.195917i	$0.0627683\pi$
$691$	3.31599	+	18.8059i	0.126146	+	0.715410i	−0.854474	+	0.519494i	$0.826121\pi$
$692$		0			0
$693$	42.0923	+	20.1167i	1.59895	+	0.764170i
$694$		0			0
$695$	−3.20363	+	2.68817i	−0.121521	+	0.101968i
$696$		0			0
$697$	−1.41416	+	8.02012i	−0.0535653	+	0.303784i
$698$		0			0
$699$	−35.4595	−	14.8854i	−1.34120	−	0.563018i
$700$		0			0
$701$	−23.5901			−0.890985			−0.445493	−	0.895286i	$-0.646971\pi$
$701$	−23.5901			−0.890985			−0.445493	+	0.895286i	$0.646971\pi$
$702$		0			0
$703$		−	4.10218i		−	0.154717i
$704$		0			0
$705$	21.3052	+	28.0401i	0.802399	+	1.05605i
$706$		0			0
$707$	53.8119	+	9.48848i	2.02380	+	0.356851i
$708$		0			0
$709$	12.3497	+	14.7178i	0.463804	+	0.552740i	0.946355	−	0.323128i	$-0.104734\pi$
$709$	12.3497	+	14.7178i	0.463804	+	0.552740i	−0.482551	+	0.875868i	$0.660290\pi$
$710$		0			0
$711$	−0.284869	+	2.93485i	−0.0106834	+	0.110065i
$712$		0			0
$713$	−3.03064	+	0.534384i	−0.113498	+	0.0200128i
$714$		0			0
$715$	−13.1080	+	4.77091i	−0.490210	+	0.178422i
$716$		0			0
$717$	−25.6633	−	16.5211i	−0.958414	−	0.616993i
$718$		0			0
$719$	14.2201	−	24.6300i	0.530321	−	0.918542i	−0.469054	−	0.883170i	$-0.655405\pi$
$719$	14.2201	−	24.6300i	0.530321	−	0.918542i	0.999374	−	0.0353726i	$-0.0112618\pi$
$720$		0			0
$721$	−18.5653	−	32.1560i	−0.691406	−	1.19755i
$722$		0			0
$723$	−15.9179	−	3.60829i	−0.591994	−	0.134194i
$724$		0			0
$725$	−46.7241	−	39.2062i	−1.73529	−	1.45608i
$726$		0			0
$727$	17.4790	−	48.0230i	0.648259	−	1.78108i	0.0241888	−	0.999707i	$-0.492300\pi$
$727$	17.4790	−	48.0230i	0.648259	−	1.78108i	0.624070	−	0.781369i	$-0.285478\pi$
$728$		0			0
$729$	19.6279	−	18.5404i	0.726958	−	0.686681i
$730$		0			0
$731$	3.23739	−	8.89465i	0.119739	−	0.328980i
$732$		0			0
$733$	23.4532	−	27.9504i	0.866264	−	1.03237i	−0.132886	−	0.991131i	$-0.542424\pi$
$733$	23.4532	−	27.9504i	0.866264	−	1.03237i	0.999149	−	0.0412414i	$-0.0131313\pi$
$734$		0			0
$735$	22.0519	+	4.99874i	0.813397	+	0.184381i
$736$		0			0
$737$	−26.6370	+	15.3789i	−0.981187	+	0.566489i
$738$		0			0
$739$	14.3403	−	24.8381i	0.527516	−	0.913684i	−0.471970	−	0.881615i	$-0.656457\pi$
$739$	14.3403	−	24.8381i	0.527516	−	0.913684i	0.999486	−	0.0320692i	$-0.0102097\pi$
$740$		0			0
$741$	0.881973	−	1.37002i	0.0324001	−	0.0503291i
$742$		0			0
$743$	−34.8288	+	12.6767i	−1.27775	+	0.465061i	−0.889686	−	0.456573i	$-0.849077\pi$
$743$	−34.8288	+	12.6767i	−1.27775	+	0.465061i	−0.388060	+	0.921634i	$0.626855\pi$
$744$		0			0
$745$	−15.4054	−	87.3683i	−0.564410	−	3.20093i
$746$		0			0
$747$	−0.438776	+	4.52047i	−0.0160540	+	0.165395i
$748$		0			0
$749$	−16.9931	+	14.2589i	−0.620914	+	0.521009i
$750$		0			0
$751$	35.3512	+	6.23338i	1.28998	+	0.227459i	0.776215	−	0.630469i	$-0.217137\pi$
$751$	35.3512	+	6.23338i	1.28998	+	0.227459i	0.513770	+	0.857928i	$0.328248\pi$
$752$		0			0
$753$	−42.6795	+	32.4284i	−1.55533	+	1.18176i
$754$		0			0
$755$		−	23.2256i		−	0.845267i
$756$		0			0
$757$		−	40.0043i		−	1.45398i	−0.686647	−	0.726991i	$-0.740918\pi$
$757$		−	40.0043i		−	1.45398i	0.686647	−	0.726991i	$-0.259082\pi$
$758$		0			0
$759$	−29.9644	−	12.5786i	−1.08764	−	0.456575i
$760$		0			0
$761$	49.8212	+	8.78482i	1.80602	+	0.318449i	0.972299	−	0.233741i	$-0.0750969\pi$
$761$	49.8212	+	8.78482i	1.80602	+	0.318449i	0.833718	+	0.552191i	$0.186208\pi$
$762$		0			0
$763$	−8.46967	+	7.10690i	−0.306623	+	0.257287i
$764$		0			0
$765$	−4.22308	+	8.83640i	−0.152686	+	0.319481i
$766$		0			0
$767$	−0.115234	−	0.653526i	−0.00416087	−	0.0235975i
$768$		0			0
$769$	22.5878	−	8.22128i	0.814536	−	0.296467i	0.0990400	−	0.995083i	$-0.468423\pi$
$769$	22.5878	−	8.22128i	0.814536	−	0.296467i	0.715496	+	0.698616i	$0.246201\pi$
$770$		0			0
$771$	−7.27972	−	14.1478i	−0.262173	−	0.509520i
$772$		0			0
$773$	−2.65158	+	4.59267i	−0.0953707	+	0.165187i	−0.909763	−	0.415127i	$-0.863737\pi$
$773$	−2.65158	+	4.59267i	−0.0953707	+	0.165187i	0.814393	+	0.580314i	$0.197070\pi$
$774$		0			0
$775$	7.54921	−	4.35854i	0.271175	−	0.156563i
$776$		0			0
$777$	5.15906	+	16.6374i	0.185080	+	0.596865i
$778$		0			0
$779$	−8.37112	+	9.97631i	−0.299927	+	0.357439i
$780$		0			0
$781$	16.3073	−	44.8039i	0.583520	−	1.60321i
$782$		0			0
$783$	−28.9269	+	0.850441i	−1.03376	+	0.0303923i
$784$		0			0
$785$	14.0185	−	38.5155i	0.500341	−	1.37468i
$786$		0			0
$787$	−21.0660	−	17.6764i	−0.750921	−	0.630097i	0.184826	−	0.982771i	$-0.440828\pi$
$787$	−21.0660	−	17.6764i	−0.750921	−	0.630097i	−0.935746	+	0.352674i	$0.885272\pi$
$788$		0			0
$789$	5.52394	−	5.97116i	0.196657	−	0.212579i
$790$		0			0
$791$	−23.5438	−	40.7791i	−0.837122	−	1.44994i
$792$		0			0
$793$	0.546235	−	0.946107i	0.0193974	−	0.0335973i
$794$		0			0
$795$	−0.0607875	+	1.25546i	−0.00215591	+	0.0445267i
$796$		0			0
$797$	26.4946	−	9.64326i	0.938488	−	0.341582i	0.172919	−	0.984936i	$-0.444680\pi$
$797$	26.4946	−	9.64326i	0.938488	−	0.341582i	0.765569	+	0.643354i	$0.222458\pi$
$798$		0			0
$799$	−4.09777	+	0.722548i	−0.144969	+	0.0255619i
$800$		0			0
$801$	−14.6783	+	14.4022i	−0.518632	+	0.508876i
$802$		0			0
$803$	−3.78087	−	4.50587i	−0.133424	−	0.159009i
$804$		0			0
$805$	−48.7307	−	8.59254i	−1.71753	−	0.302847i
$806$		0			0
$807$	48.4795	−	6.14846i	1.70656	−	0.216436i
$808$		0			0
$809$			53.0126i			1.86382i	0.362683	+	0.931912i	$0.381861\pi$
$809$			53.0126i			1.86382i	−0.362683	+	0.931912i	$0.618139\pi$
$810$		0			0
$811$	54.1169			1.90030			0.950150	−	0.311792i	$-0.100929\pi$
$811$	54.1169			1.90030			0.950150	+	0.311792i	$0.100929\pi$
$812$		0			0
$813$	3.30319	+	26.0451i	0.115848	+	0.913440i
$814$		0			0
$815$	−8.14256	+	46.1788i	−0.285222	+	1.61757i
$816$		0			0
$817$	11.5953	−	9.72965i	0.405670	−	0.340397i
$818$		0			0
$819$	−1.85407	+	6.66569i	−0.0647866	+	0.232918i
$820$		0			0
$821$	−7.33356	−	41.5907i	−0.255943	−	1.45152i	−0.793640	−	0.608387i	$-0.791817\pi$
$821$	−7.33356	−	41.5907i	−0.255943	−	1.45152i	0.537697	−	0.843138i	$-0.319294\pi$
$822$		0			0
$823$	3.41874	+	9.39291i	0.119170	+	0.327416i	0.984907	−	0.173082i	$-0.0553725\pi$
$823$	3.41874	+	9.39291i	0.119170	+	0.327416i	−0.865738	+	0.500498i	$0.833150\pi$
$824$		0			0
$825$	91.9451	+	4.45183i	3.20112	+	0.154993i
$826$		0			0
$827$	24.9490	+	14.4043i	0.867561	+	0.500886i	0.866537	−	0.499113i	$-0.166341\pi$
$827$	24.9490	+	14.4043i	0.867561	+	0.500886i	0.00102385	+	0.999999i	$0.499674\pi$
$828$		0			0
$829$	−25.8979	+	14.9522i	−0.899473	+	0.519311i	−0.877029	−	0.480437i	$-0.840478\pi$
$829$	−25.8979	+	14.9522i	−0.899473	+	0.519311i	−0.0224435	+	0.999748i	$0.507145\pi$
$830$		0			0
$831$	−18.6670	−	17.2689i	−0.647553	−	0.599053i
$832$		0			0
$833$	−1.71733	+	2.04663i	−0.0595018	+	0.0709115i
$834$		0			0
$835$	58.7706	+	21.3907i	2.03384	+	0.740257i
$836$		0			0
$837$	1.29975	−	3.92639i	0.0449258	−	0.135716i
$838$		0			0
$839$	25.4014	+	9.24535i	0.876954	+	0.319185i	0.740980	−	0.671527i	$-0.234361\pi$
$839$	25.4014	+	9.24535i	0.876954	+	0.319185i	0.135974	+	0.990712i	$0.456584\pi$
$840$		0			0
$841$	1.54592	+	1.29718i	0.0533074	+	0.0447302i
$842$		0			0
$843$	−6.00390	+	1.86173i	−0.206785	+	0.0641215i
$844$		0			0
$845$	24.9263	+	43.1737i	0.857492	+	1.48522i
$846$		0			0
$847$	34.8284	+	20.1082i	1.19672	+	0.690926i
$848$		0			0
$849$	−11.1277	+	5.72575i	−0.381903	+	0.196507i
$850$		0			0
$851$	−4.15002	−	11.4021i	−0.142261	−	0.390858i
$852$		0			0
$853$	39.4657	−	6.95887i	1.35128	−	0.238267i	0.549304	−	0.835623i	$-0.314893\pi$
$853$	39.4657	−	6.95887i	1.35128	−	0.238267i	0.801977	+	0.597355i	$0.203782\pi$
$854$		0			0
$855$	−12.9138	+	8.86085i	−0.441644	+	0.303035i
$856$		0			0
$857$	−21.1106	−	25.1586i	−0.721123	−	0.859401i	0.273616	−	0.961839i	$-0.411780\pi$
$857$	−21.1106	−	25.1586i	−0.721123	−	0.859401i	−0.994739	+	0.102438i	$0.967336\pi$
$858$		0			0
$859$	5.44881	−	30.9017i	0.185911	−	1.05435i	−0.738868	−	0.673850i	$-0.764640\pi$
$859$	5.44881	−	30.9017i	0.185911	−	1.05435i	0.924779	−	0.380504i	$-0.124249\pi$
$860$		0			0
$861$	21.4046	−	50.9894i	0.729468	−	1.73771i
$862$		0			0
$863$	−23.6646			−0.805553			−0.402777	−	0.915298i	$-0.631955\pi$
$863$	−23.6646			−0.805553			−0.402777	+	0.915298i	$0.631955\pi$
$864$		0			0
$865$	32.4514			1.10338
$866$		0			0
$867$	17.1137	+	22.5236i	0.581212	+	0.764942i
$868$		0			0
$869$	−0.828261	+	4.69730i	−0.0280968	+	0.159345i
$870$		0			0
$871$	−2.93208	−	3.49432i	−0.0993498	−	0.118401i
$872$		0			0
$873$	−10.5818	−	23.2671i	−0.358141	−	0.787471i
$874$		0			0
$875$	75.0151	−	13.2272i	2.53597	−	0.447161i
$876$		0			0
$877$	−7.18418	−	19.7384i	−0.242592	−	0.666517i	−0.999909	−	0.0134696i	$-0.995712\pi$
$877$	−7.18418	−	19.7384i	−0.242592	−	0.666517i	0.757317	−	0.653048i	$-0.226510\pi$
$878$		0			0
$879$	−12.1686	−	7.83372i	−0.410437	−	0.264225i
$880$		0			0
$881$	22.9740	+	13.2641i	0.774014	+	0.446877i	0.834305	−	0.551303i	$-0.185869\pi$
$881$	22.9740	+	13.2641i	0.774014	+	0.446877i	−0.0602904	+	0.998181i	$0.519203\pi$
$882$		0			0
$883$	−10.5094	−	18.2028i	−0.353669	−	0.612573i	0.633220	−	0.773972i	$-0.281733\pi$
$883$	−10.5094	−	18.2028i	−0.353669	−	0.612573i	−0.986889	+	0.161399i	$0.948399\pi$
$884$		0			0
$885$	−1.41013	+	6.22078i	−0.0474010	+	0.209109i
$886$		0			0
$887$	−20.1742	−	16.9281i	−0.677382	−	0.568391i	0.237858	−	0.971300i	$-0.423555\pi$
$887$	−20.1742	−	16.9281i	−0.677382	−	0.568391i	−0.915240	+	0.402909i	$0.867999\pi$
$888$		0			0
$889$	−5.34179	−	1.94425i	−0.179158	−	0.0652082i
$890$		0			0
$891$	33.9845	−	27.4338i	1.13852	−	0.919066i
$892$		0			0
$893$	−6.25272	−	2.27580i	−0.209239	−	0.0761569i
$894$		0			0
$895$	−39.5722	+	47.1603i	−1.32275	+	1.57640i
$896$		0			0
$897$	1.06546	−	4.70027i	0.0355746	−	0.156937i
$898$		0			0
$899$	−3.83909	+	2.21650i	−0.128041	+	0.0739244i
$900$		0			0
$901$	−0.128618	−	0.0742576i	−0.00428489	−	0.00247388i
$902$		0			0
$903$	−34.7915	+	54.0438i	−1.15779	+	1.79847i
$904$		0			0
$905$	19.6129	+	53.8859i	0.651954	+	1.79123i
$906$		0			0
$907$	−9.92172	−	56.2689i	−0.329445	−	1.86838i	−0.476393	−	0.879233i	$-0.658056\pi$
$907$	−9.92172	−	56.2689i	−0.329445	−	1.86838i	0.146948	−	0.989144i	$-0.453055\pi$
$908$		0			0
$909$	29.7381	−	41.6236i	0.986351	−	1.38057i
$910$		0			0
$911$	42.5909	−	35.7380i	1.41110	−	1.18405i	0.455189	−	0.890395i	$-0.349572\pi$
$911$	42.5909	−	35.7380i	1.41110	−	1.18405i	0.955911	−	0.293658i	$-0.0948726\pi$
$912$		0			0
$913$	−1.27575	+	7.23514i	−0.0422212	+	0.239448i
$914$		0			0
$915$	−8.36111	+	6.35287i	−0.276410	+	0.210020i
$916$		0			0
$917$	7.98604			0.263722
$918$		0			0
$919$		−	44.1041i		−	1.45486i	−0.686182	−	0.727430i	$-0.740715\pi$
$919$		−	44.1041i		−	1.45486i	0.686182	−	0.727430i	$-0.259285\pi$
$920$		0			0
$921$	19.0623	−	45.4095i	0.628124	−	1.49629i
$922$		0			0
$923$	6.96362	+	1.22787i	0.229210	+	0.0404160i
$924$		0			0
$925$	22.0929	+	26.3294i	0.726412	+	0.865704i
$926$		0			0
$927$	−34.6563	+	2.70073i	−1.13826	+	0.0887035i
$928$		0			0
$929$	30.7854	−	5.42829i	1.01004	−	0.178096i	0.355940	−	0.934509i	$-0.384161\pi$
$929$	30.7854	−	5.42829i	1.01004	−	0.178096i	0.654095	+	0.756412i	$0.273050\pi$
$930$		0			0
$931$	−4.01474	+	1.46125i	−0.131578	+	0.0478904i
$932$		0			0
$933$	17.2179	−	8.85941i	0.563687	−	0.290044i
$934$		0			0
$935$	−7.92121	+	13.7199i	−0.259051	+	0.448690i
$936$		0			0
$937$	10.1116	+	17.5138i	0.330332	+	0.572152i	0.982577	−	0.185856i	$-0.0595059\pi$
$937$	10.1116	+	17.5138i	0.330332	+	0.572152i	−0.652245	+	0.758008i	$0.726173\pi$
$938$		0			0
$939$	4.84928	+	15.6384i	0.158250	+	0.510341i
$940$		0			0
$941$	−17.1063	−	14.3539i	−0.557650	−	0.467924i	0.319872	−	0.947461i	$-0.396360\pi$
$941$	−17.1063	−	14.3539i	−0.557650	−	0.467924i	−0.877522	+	0.479537i	$0.840805\pi$
$942$		0			0
$943$	−13.1750	+	36.1981i	−0.429038	+	1.17877i
$944$		0			0
$945$	41.2317	−	52.1784i	1.34127	−	1.69736i
$946$		0			0
$947$	−9.78332	+	26.8794i	−0.317915	+	0.873465i	0.673080	+	0.739569i	$0.264971\pi$
$947$	−9.78332	+	26.8794i	−0.317915	+	0.873465i	−0.990995	+	0.133895i	$0.957251\pi$
$948$		0			0
$949$	0.560719	−	0.668239i	0.0182017	−	0.0216920i
$950$		0			0
$951$	24.9603	−	26.9811i	0.809394	−	0.874923i
$952$		0			0
$953$	−11.8170	+	6.82255i	−0.382790	+	0.221004i	−0.679032	−	0.734109i	$-0.737600\pi$
$953$	−11.8170	+	6.82255i	−0.382790	+	0.221004i	0.296241	+	0.955113i	$0.404267\pi$
$954$		0			0
$955$	22.0561	−	38.2022i	0.713717	−	1.23619i
$956$		0			0
$957$	−46.7580	−	2.26394i	−1.51147	−	0.0731829i
$958$		0			0
$959$	48.8188	−	17.7686i	1.57644	−	0.573778i
$960$		0			0
$961$	5.27308	+	29.9051i	0.170099	+	0.964681i
$962$		0			0
$963$	5.18432	+	20.1100i	0.167062	+	0.648035i
$964$		0			0
$965$	17.6374	−	14.7995i	0.567767	−	0.476413i
$966$		0			0
$967$	−35.2023	−	6.20712i	−1.13203	−	0.199607i	−0.423913	−	0.905703i	$-0.639344\pi$
$967$	−35.2023	−	6.20712i	−1.13203	−	0.199607i	−0.708117	+	0.706095i	$0.750455\pi$
$968$		0			0
$969$	−0.232827	−	1.83580i	−0.00747949	−	0.0589745i
$970$		0			0
$971$			2.58655i			0.0830062i	0.999138	+	0.0415031i	$0.0132146\pi$
$971$			2.58655i			0.0830062i	−0.999138	+	0.0415031i	$0.986785\pi$
$972$		0			0
$973$			3.35538i			0.107569i
$974$		0			0
$975$	1.71765	+	13.5433i	0.0550087	+	0.433734i
$976$		0			0
$977$	6.01215	+	1.06011i	0.192346	+	0.0339158i	0.268991	−	0.963143i	$-0.413310\pi$
$977$	6.01215	+	1.06011i	0.192346	+	0.0339158i	−0.0766452	+	0.997058i	$0.524421\pi$
$978$		0			0
$979$	−25.4821	+	21.3820i	−0.814412	+	0.683373i
$980$		0			0
$981$	2.58396	+	10.0232i	0.0824995	+	0.320016i
$982$		0			0
$983$	−1.84783	−	10.4796i	−0.0589367	−	0.334247i	0.941055	−	0.338253i	$-0.109836\pi$
$983$	−1.84783	−	10.4796i	−0.0589367	−	0.334247i	−0.999992	+	0.00400613i	$0.998725\pi$
$984$		0			0
$985$	−70.4740	+	25.6505i	−2.24549	+	0.817291i
$986$		0			0
$987$	28.2217	+	1.36645i	0.898305	+	0.0434944i
$988$		0			0
$989$	22.3864	−	38.7743i	0.711845	−	1.23295i
$990$		0			0
$991$	−27.4598	+	15.8539i	−0.872288	+	0.503616i	−0.868108	−	0.496375i	$-0.834664\pi$
$991$	−27.4598	+	15.8539i	−0.872288	+	0.503616i	−0.00418044	+	0.999991i	$0.501331\pi$
$992$		0			0
$993$	−11.4463	+	12.3730i	−0.363239	+	0.392647i
$994$		0			0
$995$	−31.3577	+	37.3707i	−0.994106	+	1.18473i
$996$		0			0
$997$	3.77204	−	10.3636i	0.119462	−	0.328218i	−0.865521	−	0.500873i	$-0.833012\pi$
$997$	3.77204	−	10.3636i	0.119462	−	0.328218i	0.984982	+	0.172655i	$0.0552345\pi$
$998$		0			0
$999$	16.1361	+	2.35860i	0.510522	+	0.0746228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bh.b.239.1		192
4.3	odd	2		216.2.v.b.131.30	yes	192
8.3	odd	2	inner	864.2.bh.b.239.2		192
8.5	even	2		216.2.v.b.131.12	✓	192
12.11	even	2		648.2.v.b.179.3		192
24.5	odd	2		648.2.v.b.179.21		192
27.20	odd	18	inner	864.2.bh.b.47.2		192
108.7	odd	18		648.2.v.b.467.21		192
108.47	even	18		216.2.v.b.155.12	yes	192
216.61	even	18		648.2.v.b.467.3		192
216.101	odd	18		216.2.v.b.155.30	yes	192
216.155	even	18	inner	864.2.bh.b.47.1		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.131.12	✓	192	8.5	even	2
216.2.v.b.131.30	yes	192	4.3	odd	2
216.2.v.b.155.12	yes	192	108.47	even	18
216.2.v.b.155.30	yes	192	216.101	odd	18
648.2.v.b.179.3		192	12.11	even	2
648.2.v.b.179.21		192	24.5	odd	2
648.2.v.b.467.3		192	216.61	even	18
648.2.v.b.467.21		192	108.7	odd	18
864.2.bh.b.47.1		192	216.155	even	18	inner
864.2.bh.b.47.2		192	27.20	odd	18	inner
864.2.bh.b.239.1		192	1.1	even	1	trivial
864.2.bh.b.239.2		192	8.3	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bh (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71829 + 0.217923i) q^{3} +(-0.693543 + 3.93328i) q^{5} +(2.05979 + 2.45476i) q^{7} +(2.90502 - 0.748909i) q^{9} +O(q^{10})\)	\(q+(-1.71829 + 0.217923i) q^{3} +(-0.693543 + 3.93328i) q^{5} +(2.05979 + 2.45476i) q^{7} +(2.90502 - 0.748909i) q^{9} +(4.77912 - 0.842688i) q^{11} +(0.246151 + 0.676295i) q^{13} +(0.334553 - 6.90964i) q^{15} +(0.707869 + 0.408688i) q^{17} +(0.653550 + 1.13198i) q^{19} +(-4.07426 - 3.76911i) q^{21} +(2.96174 + 2.48519i) q^{23} +(-10.2912 - 3.74569i) q^{25} +(-4.82845 + 1.91991i) q^{27} +(5.23351 + 1.90484i) q^{29} +(-0.511632 + 0.609740i) q^{31} +(-8.02826 + 2.48946i) q^{33} +(-11.0838 + 6.39925i) q^{35} +(-2.71792 - 1.56919i) q^{37} +(-0.570338 - 1.10843i) q^{39} +(3.40768 + 9.36253i) q^{41} +(-2.01090 - 11.4044i) q^{43} +(0.930912 + 11.9456i) q^{45} +(-3.89967 + 3.27222i) q^{47} +(-0.567588 + 3.21895i) q^{49} +(-1.30538 - 0.547982i) q^{51} -0.181698 q^{53} +19.3820i q^{55} +(-1.36967 - 1.80265i) q^{57} +(-0.908057 - 0.160115i) q^{59} +(-0.975724 - 1.16282i) q^{61} +(7.82213 + 5.58854i) q^{63} +(-2.83077 + 0.499141i) q^{65} +(-5.95586 + 2.16776i) q^{67} +(-5.63069 - 3.62484i) q^{69} +(4.91251 - 8.50871i) q^{71} +(-0.606035 - 1.04968i) q^{73} +(18.4995 + 4.19348i) q^{75} +(11.9126 + 9.99585i) q^{77} +(-0.336165 + 0.923605i) q^{79} +(7.87827 - 4.35119i) q^{81} +(-0.517786 + 1.42261i) q^{83} +(-2.09842 + 2.50080i) q^{85} +(-9.40778 - 2.13256i) q^{87} +(-5.93630 + 3.42732i) q^{89} +(-1.15312 + 1.99727i) q^{91} +(0.746255 - 1.15920i) q^{93} +(-4.90566 + 1.78551i) q^{95} +(-1.47950 - 8.39068i) q^{97} +(13.2523 - 6.02715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 12 q^{3} - 12 q^{9}+O(q^{10}) \) 192 * q + 12 * q^3 - 12 * q^9	\( 192 q + 12 q^{3} - 12 q^{9} + 30 q^{11} - 18 q^{17} + 6 q^{19} - 12 q^{25} - 18 q^{27} - 30 q^{33} + 18 q^{35} + 18 q^{41} + 42 q^{43} - 12 q^{49} + 18 q^{51} - 36 q^{57} + 84 q^{59} - 12 q^{65} - 30 q^{67} - 6 q^{73} + 96 q^{75} - 12 q^{81} + 72 q^{83} + 144 q^{89} + 6 q^{91} - 42 q^{97} + 12 q^{99}+O(q^{100}) \) 192 * q + 12 * q^3 - 12 * q^9 + 30 * q^11 - 18 * q^17 + 6 * q^19 - 12 * q^25 - 18 * q^27 - 30 * q^33 + 18 * q^35 + 18 * q^41 + 42 * q^43 - 12 * q^49 + 18 * q^51 - 36 * q^57 + 84 * q^59 - 12 * q^65 - 30 * q^67 - 6 * q^73 + 96 * q^75 - 12 * q^81 + 72 * q^83 + 144 * q^89 + 6 * q^91 - 42 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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