LMFDB - Embedded newform 864.2.y.a.97.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, 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:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			97.6
Character	$\chi$	$=$	864.97
Dual form			864.2.y.a.481.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.602286 + 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(0.0578408 - 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +O(q^{10})$	\(q+(0.602286 + 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(0.0578408 - 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +(-0.0918319 + 0.0334241i) q^{11} +(-0.709877 + 0.595658i) q^{13} +(-0.0324330 - 5.33160i) q^{15} +(-1.04568 - 1.81118i) q^{17} +(0.0352132 - 0.0609911i) q^{19} +(0.567547 - 0.103638i) q^{21} +(-1.09484 - 6.20915i) q^{23} +(3.42857 + 2.87691i) q^{25} +(-4.54666 - 2.51553i) q^{27} +(-5.42290 - 4.55035i) q^{29} +(-1.69111 - 9.59077i) q^{31} +(-0.109589 - 0.129001i) q^{33} +(-0.512672 + 0.887973i) q^{35} +(2.24591 + 3.89004i) q^{37} +(-1.39487 - 0.794057i) q^{39} +(0.632082 - 0.530380i) q^{41} +(-8.73217 + 3.17825i) q^{43} +(8.63879 - 3.26382i) q^{45} +(0.949958 - 5.38748i) q^{47} +(6.47359 + 2.35619i) q^{49} +(2.31148 - 2.78900i) q^{51} -8.63841 q^{53} +0.300825 q^{55} +(0.120256 + 0.0204508i) q^{57} +(-13.0152 - 4.73715i) q^{59} +(-0.712093 + 4.03848i) q^{61} +(0.510129 + 0.859255i) q^{63} +(2.68053 - 0.975633i) q^{65} +(9.50406 - 7.97485i) q^{67} +(9.42401 - 5.51766i) q^{69} +(2.92034 + 5.05819i) q^{71} +(-2.07395 + 3.59218i) q^{73} +(-2.60702 + 7.30060i) q^{75} +(0.00565252 + 0.0320570i) q^{77} +(4.81366 + 4.03914i) q^{79} +(1.34673 - 8.89867i) q^{81} +(11.4212 + 9.58350i) q^{83} +(1.11791 + 6.33997i) q^{85} +(4.12346 - 11.5472i) q^{87} +(1.08533 - 1.87984i) q^{89} +(0.154335 + 0.267315i) q^{91} +(14.5565 - 8.52268i) q^{93} +(-0.166072 + 0.139351i) q^{95} +(-2.94990 + 1.07368i) q^{97} +(0.143489 - 0.255663i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{9}+O(q^{10}) $ 48 * q - 12 * q^9	$ 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) $ 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.602286	+	1.62396i	0.347730	+	0.937595i
$3$	0.602286	+	1.62396i	0.347730	+	0.937595i
$4$		0			0
$5$	−2.89262	−	1.05283i	−1.29362	−	0.470839i	−0.398705	−	0.917079i	$-0.630540\pi$
$5$	−2.89262	−	1.05283i	−1.29362	−	0.470839i	−0.894913	+	0.446241i	$0.852763\pi$
$6$		0			0
$7$	0.0578408	−	0.328031i	0.0218618	−	0.123984i	−0.971924	−	0.235296i	$-0.924394\pi$
$7$	0.0578408	−	0.328031i	0.0218618	−	0.123984i	0.993786	+	0.111312i	$0.0355052\pi$
$8$		0			0
$9$	−2.27450	+	1.95618i	−0.758168	+	0.652060i
$10$		0			0
$11$	−0.0918319	+	0.0334241i	−0.0276884	+	0.0100777i	−0.355827	−	0.934552i	$-0.615801\pi$
$11$	−0.0918319	+	0.0334241i	−0.0276884	+	0.0100777i	0.328139	+	0.944630i	$0.393579\pi$
$12$		0			0
$13$	−0.709877	+	0.595658i	−0.196885	+	0.165206i	−0.735900	−	0.677090i	$-0.763241\pi$
$13$	−0.709877	+	0.595658i	−0.196885	+	0.165206i	0.539016	+	0.842296i	$0.318796\pi$
$14$		0			0
$15$	−0.0324330	−	5.33160i	−0.00837417	−	1.37661i
$16$		0			0
$17$	−1.04568	−	1.81118i	−0.253616	−	0.439275i	0.710903	−	0.703290i	$-0.248287\pi$
$17$	−1.04568	−	1.81118i	−0.253616	−	0.439275i	−0.964519	+	0.264015i	$0.914953\pi$
$18$		0			0
$19$	0.0352132	−	0.0609911i	0.00807847	−	0.0139923i	−0.861958	−	0.506980i	$-0.830762\pi$
$19$	0.0352132	−	0.0609911i	0.00807847	−	0.0139923i	0.870036	+	0.492988i	$0.164095\pi$
$20$		0			0
$21$	0.567547	−	0.103638i	0.123849	−	0.0226156i
$22$		0			0
$23$	−1.09484	−	6.20915i	−0.228290	−	1.29470i	−0.856295	−	0.516487i	$-0.827239\pi$
$23$	−1.09484	−	6.20915i	−0.228290	−	1.29470i	0.628005	−	0.778209i	$-0.283872\pi$
$24$		0			0
$25$	3.42857	+	2.87691i	0.685715	+	0.575383i
$26$		0			0
$27$	−4.54666	−	2.51553i	−0.875005	−	0.484113i
$28$		0			0
$29$	−5.42290	−	4.55035i	−1.00701	−	0.844979i	−0.0190669	−	0.999818i	$-0.506070\pi$
$29$	−5.42290	−	4.55035i	−1.00701	−	0.844979i	−0.987940	+	0.154839i	$0.950514\pi$
$30$		0			0
$31$	−1.69111	−	9.59077i	−0.303732	−	1.72255i	−0.629412	−	0.777072i	$-0.716704\pi$
$31$	−1.69111	−	9.59077i	−0.303732	−	1.72255i	0.325679	−	0.945480i	$-0.394407\pi$
$32$		0			0
$33$	−0.109589	−	0.129001i	−0.0190769	−	0.0224561i
$34$		0			0
$35$	−0.512672	+	0.887973i	−0.0866573	+	0.150095i
$36$		0			0
$37$	2.24591	+	3.89004i	0.369226	+	0.639518i	0.989445	−	0.144911i	$-0.0462895\pi$
$37$	2.24591	+	3.89004i	0.369226	+	0.639518i	−0.620219	+	0.784429i	$0.712956\pi$
$38$		0			0
$39$	−1.39487	−	0.794057i	−0.223359	−	0.127151i
$40$		0			0
$41$	0.632082	−	0.530380i	0.0987147	−	0.0828314i	−0.592095	−	0.805868i	$-0.701699\pi$
$41$	0.632082	−	0.530380i	0.0987147	−	0.0828314i	0.690809	+	0.723037i	$0.257254\pi$
$42$		0			0
$43$	−8.73217	+	3.17825i	−1.33164	+	0.484679i	−0.907171	−	0.420762i	$-0.861763\pi$
$43$	−8.73217	+	3.17825i	−1.33164	+	0.484679i	−0.424473	+	0.905441i	$0.639541\pi$
$44$		0			0
$45$	8.63879	−	3.26382i	1.28779	−	0.486542i
$46$		0			0
$47$	0.949958	−	5.38748i	0.138566	−	0.785844i	−0.833745	−	0.552150i	$-0.813807\pi$
$47$	0.949958	−	5.38748i	0.138566	−	0.785844i	0.972310	−	0.233694i	$-0.0750814\pi$
$48$		0			0
$49$	6.47359	+	2.35619i	0.924798	+	0.336599i
$50$		0			0
$51$	2.31148	−	2.78900i	0.323672	−	0.390538i
$52$		0			0
$53$	−8.63841			−1.18658			−0.593288	−	0.804990i	$-0.702171\pi$
$53$	−8.63841			−1.18658			−0.593288	+	0.804990i	$0.702171\pi$
$54$		0			0
$55$	0.300825			0.0405632
$56$		0			0
$57$	0.120256	+	0.0204508i	0.0159282	+	0.00270878i
$58$		0			0
$59$	−13.0152	−	4.73715i	−1.69444	−	0.616725i	−0.699265	−	0.714863i	$-0.746489\pi$
$59$	−13.0152	−	4.73715i	−1.69444	−	0.616725i	−0.995173	+	0.0981376i	$0.968711\pi$
$60$		0			0
$61$	−0.712093	+	4.03848i	−0.0911741	+	0.517074i	0.904679	+	0.426095i	$0.140111\pi$
$61$	−0.712093	+	4.03848i	−0.0911741	+	0.517074i	−0.995853	+	0.0909796i	$0.971000\pi$
$62$		0			0
$63$	0.510129	+	0.859255i	0.0642702	+	0.108256i
$64$		0			0
$65$	2.68053	−	0.975633i	0.332479	−	0.121012i
$66$		0			0
$67$	9.50406	−	7.97485i	1.16111	−	0.974283i	0.161185	−	0.986924i	$-0.448468\pi$
$67$	9.50406	−	7.97485i	1.16111	−	0.974283i	0.999920	+	0.0126410i	$0.00402387\pi$
$68$		0			0
$69$	9.42401	−	5.51766i	1.13452	−	0.664248i
$70$		0			0
$71$	2.92034	+	5.05819i	0.346581	+	0.600296i	0.985640	−	0.168862i	$-0.0540092\pi$
$71$	2.92034	+	5.05819i	0.346581	+	0.600296i	−0.639059	+	0.769158i	$0.720676\pi$
$72$		0			0
$73$	−2.07395	+	3.59218i	−0.242737	+	0.420433i	−0.961493	−	0.274829i	$-0.911379\pi$
$73$	−2.07395	+	3.59218i	−0.242737	+	0.420433i	0.718756	+	0.695263i	$0.244712\pi$
$74$		0			0
$75$	−2.60702	+	7.30060i	−0.301032	+	0.843000i
$76$		0			0
$77$	0.00565252	+	0.0320570i	0.000644164	+	0.00365324i
$78$		0			0
$79$	4.81366	+	4.03914i	0.541579	+	0.454438i	0.872077	−	0.489368i	$-0.162773\pi$
$79$	4.81366	+	4.03914i	0.541579	+	0.454438i	−0.330499	+	0.943806i	$0.607217\pi$
$80$		0			0
$81$	1.34673	−	8.89867i	0.149636	−	0.988741i
$82$		0			0
$83$	11.4212	+	9.58350i	1.25364	+	1.05193i	0.996330	+	0.0855956i	$0.0272793\pi$
$83$	11.4212	+	9.58350i	1.25364	+	1.05193i	0.257306	+	0.966330i	$0.417165\pi$
$84$		0			0
$85$	1.11791	+	6.33997i	0.121254	+	0.687667i
$86$		0			0
$87$	4.12346	−	11.5472i	0.442081	−	1.23799i
$88$		0			0
$89$	1.08533	−	1.87984i	0.115044	−	0.199263i	−0.802753	−	0.596312i	$-0.796632\pi$
$89$	1.08533	−	1.87984i	0.115044	−	0.199263i	0.917798	+	0.397049i	$0.129966\pi$
$90$		0			0
$91$	0.154335	+	0.267315i	0.0161787	+	0.0280223i
$92$		0			0
$93$	14.5565	−	8.52268i	1.50944	−	0.883761i
$94$		0			0
$95$	−0.166072	+	0.139351i	−0.0170386	+	0.0142971i
$96$		0			0
$97$	−2.94990	+	1.07368i	−0.299517	+	0.109015i	−0.487407	−	0.873175i	$-0.662057\pi$
$97$	−2.94990	+	1.07368i	−0.299517	+	0.109015i	0.187890	+	0.982190i	$0.439835\pi$
$98$		0			0
$99$	0.143489	−	0.255663i	0.0144211	−	0.0256951i
$100$		0			0
$101$	−2.78788	+	15.8109i	−0.277404	+	1.57324i	0.453815	+	0.891096i	$0.350063\pi$
$101$	−2.78788	+	15.8109i	−0.277404	+	1.57324i	−0.731219	+	0.682142i	$0.761048\pi$
$102$		0			0
$103$	−4.48898	−	1.63386i	−0.442313	−	0.160989i	0.111257	−	0.993792i	$-0.464512\pi$
$103$	−4.48898	−	1.63386i	−0.442313	−	0.160989i	−0.553569	+	0.832803i	$0.686735\pi$
$104$		0			0
$105$	−1.75081	−	0.297745i	−0.170862	−	0.0290569i
$106$		0			0
$107$	5.91001			0.571342			0.285671	−	0.958328i	$-0.407784\pi$
$107$	5.91001			0.571342			0.285671	+	0.958328i	$0.407784\pi$
$108$		0			0
$109$	−10.7056			−1.02541			−0.512706	−	0.858564i	$-0.671357\pi$
$109$	−10.7056			−1.02541			−0.512706	+	0.858564i	$0.671357\pi$
$110$		0			0
$111$	−4.96459	+	5.99019i	−0.471218	+	0.568564i
$112$		0			0
$113$	−5.43312	−	1.97749i	−0.511105	−	0.186027i	0.0735773	−	0.997290i	$-0.476558\pi$
$113$	−5.43312	−	1.97749i	−0.511105	−	0.186027i	−0.584682	+	0.811263i	$0.698781\pi$
$114$		0			0
$115$	−3.37020	+	19.1134i	−0.314273	+	1.78233i
$116$		0			0
$117$	0.449405	−	2.74347i	0.0415475	−	0.253634i
$118$		0			0
$119$	−0.654607	+	0.238257i	−0.0600077	+	0.0218410i
$120$		0			0
$121$	−8.41917	+	7.06452i	−0.765379	+	0.642230i
$122$		0			0
$123$	1.24201	+	0.707037i	0.111988	+	0.0637514i
$124$		0			0
$125$	0.806989	+	1.39775i	0.0721793	+	0.125018i
$126$		0			0
$127$	−1.63144	+	2.82574i	−0.144767	+	0.250744i	−0.929286	−	0.369361i	$-0.879577\pi$
$127$	−1.63144	+	2.82574i	−0.144767	+	0.250744i	0.784519	+	0.620105i	$0.212910\pi$
$128$		0			0
$129$	−10.4206	−	12.2665i	−0.917485	−	1.08000i
$130$		0			0
$131$	−2.51442	−	14.2600i	−0.219686	−	1.24590i	−0.872588	−	0.488457i	$-0.837560\pi$
$131$	−2.51442	−	14.2600i	−0.219686	−	1.24590i	0.652902	−	0.757442i	$-0.273551\pi$
$132$		0			0
$133$	−0.0179702	−	0.0150788i	−0.00155822	−	0.00130750i
$134$		0			0
$135$	10.5033	+	12.0633i	0.903984	+	1.03824i
$136$		0			0
$137$	−14.6111	−	12.2602i	−1.24831	−	1.04746i	−0.996827	−	0.0795971i	$-0.974637\pi$
$137$	−14.6111	−	12.2602i	−1.24831	−	1.04746i	−0.251485	−	0.967861i	$-0.580919\pi$
$138$		0			0
$139$	−0.529619	−	3.00362i	−0.0449217	−	0.254764i	0.954074	−	0.299571i	$-0.0968436\pi$
$139$	−0.529619	−	3.00362i	−0.0449217	−	0.254764i	−0.998996	+	0.0448077i	$0.985733\pi$
$140$		0			0
$141$	9.32120	−	1.70211i	0.784987	−	0.143343i
$142$		0			0
$143$	0.0452801	−	0.0784274i	0.00378651	−	0.00655843i
$144$		0			0
$145$	10.8956	+	18.8718i	0.904833	+	1.56722i
$146$		0			0
$147$	0.0725841	+	11.9320i	0.00598664	+	0.984132i
$148$		0			0
$149$	−12.7296	+	10.6814i	−1.04285	+	0.875055i	−0.992324	−	0.123667i	$-0.960534\pi$
$149$	−12.7296	+	10.6814i	−1.04285	+	0.875055i	−0.0505265	+	0.998723i	$0.516090\pi$
$150$		0			0
$151$	13.5710	−	4.93945i	1.10439	−	0.401966i	0.275460	−	0.961313i	$-0.411170\pi$
$151$	13.5710	−	4.93945i	1.10439	−	0.401966i	0.828934	+	0.559346i	$0.188948\pi$
$152$		0			0
$153$	5.92140	+	2.07399i	0.478717	+	0.167672i
$154$		0			0
$155$	−5.20568	+	29.5229i	−0.418130	+	2.37133i
$156$		0			0
$157$	−12.7462	−	4.63925i	−1.01726	−	0.370253i	−0.221044	−	0.975264i	$-0.570946\pi$
$157$	−12.7462	−	4.63925i	−1.01726	−	0.370253i	−0.796217	+	0.605011i	$0.793169\pi$
$158$		0			0
$159$	−5.20279	−	14.0284i	−0.412608	−	1.11253i
$160$		0			0
$161$	−2.10012			−0.165513
$162$		0			0
$163$	−9.43138			−0.738722			−0.369361	−	0.929286i	$-0.620423\pi$
$163$	−9.43138			−0.738722			−0.369361	+	0.929286i	$0.620423\pi$
$164$		0			0
$165$	0.181182	+	0.488528i	0.0141050	+	0.0380318i
$166$		0			0
$167$	−2.59637	−	0.945002i	−0.200913	−	0.0731264i	0.239604	−	0.970871i	$-0.422983\pi$
$167$	−2.59637	−	0.945002i	−0.200913	−	0.0731264i	−0.440517	+	0.897744i	$0.645205\pi$
$168$		0			0
$169$	−2.10831	+	11.9568i	−0.162178	+	0.919755i
$170$		0			0
$171$	0.0392169	+	0.207608i	0.00299899	+	0.0158762i
$172$		0			0
$173$	8.81604	−	3.20878i	0.670271	−	0.243959i	0.0156064	−	0.999878i	$-0.495032\pi$
$173$	8.81604	−	3.20878i	0.670271	−	0.243959i	0.654665	+	0.755920i	$0.272810\pi$
$174$		0			0
$175$	1.14203	−	0.958277i	0.0863293	−	0.0724389i
$176$		0			0
$177$	−0.145931	−	23.9893i	−0.0109689	−	1.80315i
$178$		0			0
$179$	2.89391	+	5.01240i	0.216301	+	0.374644i	0.953674	−	0.300841i	$-0.0972674\pi$
$179$	2.89391	+	5.01240i	0.216301	+	0.374644i	−0.737373	+	0.675486i	$0.763934\pi$
$180$		0			0
$181$	6.75357	−	11.6975i	0.501989	−	0.869470i	−0.498009	−	0.867172i	$-0.665935\pi$
$181$	6.75357	−	11.6975i	0.501989	−	0.869470i	0.999997	−	0.00229800i	$-0.000731477\pi$
$182$		0			0
$183$	−6.98722	+	1.27591i	−0.516510	+	0.0943178i
$184$		0			0
$185$	−2.40104	−	13.6170i	−0.176528	−	1.00114i
$186$		0			0
$187$	0.156564	+	0.131373i	0.0114491	+	0.00960694i
$188$		0			0
$189$	−1.08815	+	1.34595i	−0.0791516	+	0.0979033i
$190$		0			0
$191$	−11.3363	−	9.51225i	−0.820263	−	0.688282i	0.132771	−	0.991147i	$-0.457613\pi$
$191$	−11.3363	−	9.51225i	−0.820263	−	0.688282i	−0.953034	+	0.302865i	$0.902057\pi$
$192$		0			0
$193$	1.85429	+	10.5162i	0.133475	+	0.756975i	0.975909	+	0.218176i	$0.0700106\pi$
$193$	1.85429	+	10.5162i	0.133475	+	0.756975i	−0.842434	+	0.538799i	$0.818878\pi$
$194$		0			0
$195$	3.19883	+	3.76547i	0.229073	+	0.269651i
$196$		0			0
$197$	−6.17840	+	10.7013i	−0.440193	+	0.762437i	−0.997703	−	0.0677333i	$-0.978423\pi$
$197$	−6.17840	+	10.7013i	−0.440193	+	0.762437i	0.557511	+	0.830170i	$0.311757\pi$
$198$		0			0
$199$	−2.77528	−	4.80693i	−0.196734	−	0.340754i	0.750733	−	0.660605i	$-0.229700\pi$
$199$	−2.77528	−	4.80693i	−0.196734	−	0.340754i	−0.947468	+	0.319851i	$0.896367\pi$
$200$		0			0
$201$	18.6750	+	10.6311i	1.31723	+	0.749859i
$202$		0			0
$203$	−1.80632	+	1.51568i	−0.126779	+	0.106380i
$204$		0			0
$205$	−2.38677	+	0.868714i	−0.166699	+	0.0606736i
$206$		0			0
$207$	14.6364	+	11.9810i	1.01730	+	0.832738i
$208$		0			0
$209$	−0.00119513	+	0.00677790i	−8.26687e−5	+	0.000468837i
$210$		0			0
$211$	23.4853	+	8.54797i	1.61680	+	0.588466i	0.982768	−	0.184843i	$-0.0591776\pi$
$211$	23.4853	+	8.54797i	1.61680	+	0.588466i	0.634029	+	0.773309i	$0.281400\pi$
$212$		0			0
$213$	−6.45542	+	7.78900i	−0.442318	+	0.533694i
$214$		0			0
$215$	28.6050			1.95084
$216$		0			0
$217$	−3.24389			−0.220209
$218$		0			0
$219$	−7.08268	−	1.20449i	−0.478603	−	0.0813919i
$220$		0			0
$221$	1.82115	+	0.662844i	0.122504	+	0.0445877i
$222$		0			0
$223$	−3.05241	+	17.3111i	−0.204404	+	1.15923i	0.693970	+	0.720004i	$0.255860\pi$
$223$	−3.05241	+	17.3111i	−0.204404	+	1.15923i	−0.898374	+	0.439230i	$0.855251\pi$
$224$		0			0
$225$	−13.4261	+	0.163352i	−0.895071	+	0.0108901i
$226$		0			0
$227$	−2.65362	+	0.965838i	−0.176127	+	0.0641049i	−0.428578	−	0.903505i	$-0.640985\pi$
$227$	−2.65362	+	0.965838i	−0.176127	+	0.0641049i	0.252452	+	0.967610i	$0.418763\pi$
$228$		0			0
$229$	18.0037	−	15.1069i	1.18972	−	0.998292i	0.189854	−	0.981812i	$-0.439199\pi$
$229$	18.0037	−	15.1069i	1.18972	−	0.998292i	0.999864	−	0.0164797i	$-0.00524589\pi$
$230$		0			0
$231$	−0.0486550	+	0.0284870i	−0.00320126	+	0.00187431i
$232$		0			0
$233$	−8.78503	−	15.2161i	−0.575527	−	0.996841i	−0.995984	−	0.0895291i	$-0.971464\pi$
$233$	−8.78503	−	15.2161i	−0.575527	−	0.996841i	0.420458	−	0.907312i	$-0.361870\pi$
$234$		0			0
$235$	−8.41995	+	14.5838i	−0.549257	+	0.951340i
$236$		0			0
$237$	−3.66021	+	10.2499i	−0.237756	+	0.665803i
$238$		0			0
$239$	2.75271	+	15.6114i	0.178058	+	1.00982i	0.934555	+	0.355819i	$0.115798\pi$
$239$	2.75271	+	15.6114i	0.178058	+	1.00982i	−0.756497	+	0.653997i	$0.773091\pi$
$240$		0			0
$241$	13.5895	+	11.4030i	0.875379	+	0.734531i	0.965224	−	0.261425i	$-0.0841925\pi$
$241$	13.5895	+	11.4030i	0.875379	+	0.734531i	−0.0898443	+	0.995956i	$0.528637\pi$
$242$		0			0
$243$	15.2622	−	3.17251i	0.979071	−	0.203517i
$244$		0			0
$245$	−16.2450	−	13.6311i	−1.03785	−	0.870861i
$246$		0			0
$247$	0.0113328	+	0.0642712i	0.000721086	+	0.00408948i
$248$		0			0
$249$	−8.68442	+	24.3195i	−0.550353	+	1.54119i
$250$		0			0
$251$	12.7955	−	22.1625i	0.807647	−	1.39889i	−0.106842	−	0.994276i	$-0.534074\pi$
$251$	12.7955	−	22.1625i	0.807647	−	1.39889i	0.914489	−	0.404610i	$-0.132593\pi$
$252$		0			0
$253$	0.308076	+	0.533604i	0.0193686	+	0.0335474i
$254$		0			0
$255$	−9.62257	+	5.63392i	−0.602589	+	0.352810i
$256$		0			0
$257$	8.12359	−	6.81650i	0.506735	−	0.425201i	−0.353243	−	0.935531i	$-0.614921\pi$
$257$	8.12359	−	6.81650i	0.506735	−	0.425201i	0.859979	+	0.510330i	$0.170477\pi$
$258$		0			0
$259$	1.40596	−	0.511728i	0.0873621	−	0.0317972i
$260$		0			0
$261$	21.2357	−	0.258370i	1.31446	−	0.0159927i
$262$		0			0
$263$	−4.02163	+	22.8078i	−0.247984	+	1.40639i	0.565474	+	0.824766i	$0.308693\pi$
$263$	−4.02163	+	22.8078i	−0.247984	+	1.40639i	−0.813459	+	0.581623i	$0.802418\pi$
$264$		0			0
$265$	24.9876	+	9.09475i	1.53498	+	0.558686i
$266$		0			0
$267$	3.70647	+	0.630327i	0.226832	+	0.0385754i
$268$		0			0
$269$	5.67441			0.345975			0.172987	−	0.984924i	$-0.444658\pi$
$269$	5.67441			0.345975			0.172987	+	0.984924i	$0.444658\pi$
$270$		0			0
$271$	−32.2235			−1.95744			−0.978718	−	0.205207i	$-0.934213\pi$
$271$	−32.2235			−1.95744			−0.978718	+	0.205207i	$0.934213\pi$
$272$		0			0
$273$	−0.341156	+	0.411634i	−0.0206477	+	0.0249132i
$274$		0			0
$275$	−0.411011	−	0.149596i	−0.0247849	−	0.00902096i
$276$		0			0
$277$	3.06996	−	17.4106i	0.184456	−	1.04610i	−0.742197	−	0.670182i	$-0.766216\pi$
$277$	3.06996	−	17.4106i	0.184456	−	1.04610i	0.926653	−	0.375919i	$-0.122673\pi$
$278$		0			0
$279$	22.6077	+	18.5061i	1.35349	+	1.10793i
$280$		0			0
$281$	12.2941	−	4.47467i	0.733402	−	0.266936i	0.0517977	−	0.998658i	$-0.483505\pi$
$281$	12.2941	−	4.47467i	0.733402	−	0.266936i	0.681604	+	0.731721i	$0.261283\pi$
$282$		0			0
$283$	15.2400	−	12.7879i	0.905923	−	0.760160i	−0.0654159	−	0.997858i	$-0.520837\pi$
$283$	15.2400	−	12.7879i	0.905923	−	0.760160i	0.971339	+	0.237698i	$0.0763930\pi$
$284$		0			0
$285$	−0.326322	−	0.185765i	−0.0193297	−	0.0110038i
$286$		0			0
$287$	−0.137421	−	0.238020i	−0.00811171	−	0.0140499i
$288$		0			0
$289$	6.31309	−	10.9346i	0.371358	−	0.643211i
$290$		0			0
$291$	−3.52029	−	4.14387i	−0.206363	−	0.242918i
$292$		0			0
$293$	0.558677	+	3.16841i	0.0326382	+	0.185101i	0.996768	−	0.0803294i	$-0.0255972\pi$
$293$	0.558677	+	3.16841i	0.0326382	+	0.185101i	−0.964130	+	0.265430i	$0.914486\pi$
$294$		0			0
$295$	32.6607	+	27.4056i	1.90158	+	1.59561i
$296$		0			0
$297$	0.501608	+	0.0790377i	0.0291062	+	0.00458623i
$298$		0			0
$299$	4.47573	+	3.75558i	0.258838	+	0.217191i
$300$		0			0
$301$	0.537490	+	3.04826i	0.0309804	+	0.175699i
$302$		0			0
$303$	−27.3553	+	4.99525i	−1.57152	+	0.286969i
$304$		0			0
$305$	6.31163	−	10.9321i	0.361403	−	0.625968i
$306$		0			0
$307$	−10.3963	−	18.0069i	−0.593348	−	1.02771i	−0.993778	−	0.111381i	$-0.964472\pi$
$307$	−10.3963	−	18.0069i	−0.593348	−	1.02771i	0.400430	−	0.916327i	$-0.368861\pi$
$308$		0			0
$309$	−0.0503320	−	8.27399i	−0.00286329	−	0.470691i
$310$		0			0
$311$	−6.80734	+	5.71204i	−0.386009	+	0.323900i	−0.815056	−	0.579382i	$-0.803294\pi$
$311$	−6.80734	+	5.71204i	−0.386009	+	0.323900i	0.429047	+	0.903282i	$0.358849\pi$
$312$		0			0
$313$	10.2159	−	3.71828i	0.577436	−	0.210169i	−0.0367588	−	0.999324i	$-0.511703\pi$
$313$	10.2159	−	3.71828i	0.577436	−	0.210169i	0.614194	+	0.789155i	$0.289481\pi$
$314$		0			0
$315$	−0.570961	−	3.02258i	−0.0321700	−	0.170303i
$316$		0			0
$317$	−4.65746	+	26.4138i	−0.261589	+	1.48354i	0.516987	+	0.855993i	$0.327054\pi$
$317$	−4.65746	+	26.4138i	−0.261589	+	1.48354i	−0.778576	+	0.627551i	$0.784057\pi$
$318$		0			0
$319$	0.650086	+	0.236612i	0.0363979	+	0.0132477i
$320$		0			0
$321$	3.55952	+	9.59763i	0.198673	+	0.535687i
$322$		0			0
$323$	−0.147288			−0.00819531
$324$		0			0
$325$	−4.14752			−0.230063
$326$		0			0
$327$	−6.44784	−	17.3855i	−0.356566	−	0.961421i
$328$		0			0
$329$	−1.71232	−	0.623232i	−0.0944030	−	0.0343599i
$330$		0			0
$331$	4.09405	−	23.2185i	0.225029	−	1.27621i	−0.637599	−	0.770368i	$-0.720072\pi$
$331$	4.09405	−	23.2185i	0.225029	−	1.27621i	0.862629	−	0.505837i	$-0.168816\pi$
$332$		0			0
$333$	−12.7179	−	4.45449i	−0.696939	−	0.244105i
$334$		0			0
$335$	−35.8877	+	13.0621i	−1.96076	+	0.713657i
$336$		0			0
$337$	−11.1354	+	9.34371i	−0.606584	+	0.508984i	−0.893554	−	0.448955i	$-0.851796\pi$
$337$	−11.1354	+	9.34371i	−0.606584	+	0.508984i	0.286970	+	0.957939i	$0.407352\pi$
$338$		0			0
$339$	−0.0609180	−	10.0142i	−0.00330861	−	0.543896i
$340$		0			0
$341$	0.475861	+	0.824215i	0.0257693	+	0.0446337i
$342$		0			0
$343$	2.31316	−	4.00652i	0.124899	−	0.216332i
$344$		0			0
$345$	−33.0692	+	6.03864i	−1.78039	+	0.325109i
$346$		0			0
$347$	−5.04724	−	28.6243i	−0.270950	−	1.53663i	−0.751540	−	0.659688i	$-0.770688\pi$
$347$	−5.04724	−	28.6243i	−0.270950	−	1.53663i	0.480590	−	0.876946i	$-0.340423\pi$
$348$		0			0
$349$	−18.5479	−	15.5636i	−0.992849	−	0.833099i	−0.00687094	−	0.999976i	$-0.502187\pi$
$349$	−18.5479	−	15.5636i	−0.992849	−	0.833099i	−0.985978	+	0.166878i	$0.946632\pi$
$350$		0			0
$351$	4.72596	−	0.922539i	0.252253	−	0.0492415i
$352$		0			0
$353$	8.25585	+	6.92748i	0.439414	+	0.368712i	0.835490	−	0.549505i	$-0.185184\pi$
$353$	8.25585	+	6.92748i	0.439414	+	0.368712i	−0.396076	+	0.918218i	$0.629628\pi$
$354$		0			0
$355$	−3.12205	−	17.7060i	−0.165701	−	0.939738i
$356$		0			0
$357$	−0.781181	−	0.919557i	−0.0413445	−	0.0486681i
$358$		0			0
$359$	15.9754	−	27.6703i	0.843152	−	1.46038i	−0.0440654	−	0.999029i	$-0.514031\pi$
$359$	15.9754	−	27.6703i	0.843152	−	1.46038i	0.887217	−	0.461353i	$-0.152636\pi$
$360$		0			0
$361$	9.49752	+	16.4502i	0.499869	+	0.865799i
$362$		0			0
$363$	−16.5433	−	9.41755i	−0.868296	−	0.494293i
$364$		0			0
$365$	9.78109	−	8.20730i	0.511965	−	0.429590i
$366$		0			0
$367$	4.89218	−	1.78061i	0.255370	−	0.0929470i	−0.211163	−	0.977451i	$-0.567725\pi$
$367$	4.89218	−	1.78061i	0.255370	−	0.0929470i	0.466533	+	0.884504i	$0.345503\pi$
$368$		0			0
$369$	−0.400155	+	2.44282i	−0.0208312	+	0.127168i
$370$		0			0
$371$	−0.499652	+	2.83367i	−0.0259407	+	0.147117i
$372$		0			0
$373$	−23.3419	−	8.49577i	−1.20860	−	0.439894i	−0.342382	−	0.939561i	$-0.611234\pi$
$373$	−23.3419	−	8.49577i	−1.20860	−	0.439894i	−0.866218	+	0.499667i	$0.833456\pi$
$374$		0			0
$375$	−1.78385	+	2.15236i	−0.0921175	+	0.111147i
$376$		0			0
$377$	6.56004			0.337859
$378$		0			0
$379$	−27.2176			−1.39808			−0.699038	−	0.715084i	$-0.746388\pi$
$379$	−27.2176			−1.39808			−0.699038	+	0.715084i	$0.746388\pi$
$380$		0			0
$381$	−5.57149	−	0.947495i	−0.285436	−	0.0485417i
$382$		0			0
$383$	−10.9645	−	3.99075i	−0.560259	−	0.203918i	0.0463398	−	0.998926i	$-0.485244\pi$
$383$	−10.9645	−	3.99075i	−0.560259	−	0.203918i	−0.606599	+	0.795008i	$0.707467\pi$
$384$		0			0
$385$	0.0173999	−	0.0986799i	0.000886782	−	0.00502919i
$386$		0			0
$387$	13.6441	−	24.3106i	0.693570	−	1.23578i
$388$		0			0
$389$	7.81324	−	2.84379i	0.396147	−	0.144186i	−0.136262	−	0.990673i	$-0.543509\pi$
$389$	7.81324	−	2.84379i	0.396147	−	0.144186i	0.532409	+	0.846487i	$0.321287\pi$
$390$		0			0
$391$	−10.1010	+	8.47576i	−0.510830	+	0.428638i
$392$		0			0
$393$	21.6432	−	12.6719i	1.09176	−	0.639213i
$394$		0			0
$395$	−9.67156	−	16.7516i	−0.486629	−	0.842866i
$396$		0			0
$397$	5.05659	−	8.75827i	0.253783	−	0.439565i	−0.710781	−	0.703413i	$-0.751658\pi$
$397$	5.05659	−	8.75827i	0.253783	−	0.439565i	0.964564	+	0.263848i	$0.0849918\pi$
$398$		0			0
$399$	0.0136642	−	0.0382647i	0.000684066	−	0.00191563i
$400$		0			0
$401$	2.67186	+	15.1529i	0.133426	+	0.756699i	0.975943	+	0.218028i	$0.0699624\pi$
$401$	2.67186	+	15.1529i	0.133426	+	0.756699i	−0.842516	+	0.538671i	$0.818927\pi$
$402$		0			0
$403$	6.91330	+	5.80094i	0.344376	+	0.288966i
$404$		0			0
$405$	−13.2643	+	24.3226i	−0.659110	+	1.20860i
$406$		0			0
$407$	−0.336268	−	0.282162i	−0.0166682	−	0.0139863i
$408$		0			0
$409$	−6.56680	−	37.2422i	−0.324707	−	1.84151i	−0.511724	−	0.859150i	$-0.670993\pi$
$409$	−6.56680	−	37.2422i	−0.324707	−	1.84151i	0.187017	−	0.982357i	$-0.440118\pi$
$410$		0			0
$411$	11.1100	−	31.1120i	0.548016	−	1.53464i
$412$		0			0
$413$	−2.30675	+	3.99540i	−0.113508	+	0.196601i
$414$		0			0
$415$	−22.9473	−	39.7459i	−1.12644	−	1.95105i
$416$		0			0
$417$	4.55878	−	2.66912i	0.223244	−	0.130707i
$418$		0			0
$419$	21.1838	−	17.7753i	1.03490	−	0.868380i	0.0434699	−	0.999055i	$-0.486159\pi$
$419$	21.1838	−	17.7753i	1.03490	−	0.868380i	0.991425	+	0.130674i	$0.0417143\pi$
$420$		0			0
$421$	5.14169	−	1.87142i	0.250591	−	0.0912075i	−0.213671	−	0.976906i	$-0.568542\pi$
$421$	5.14169	−	1.87142i	0.250591	−	0.0912075i	0.464262	+	0.885698i	$0.346320\pi$
$422$		0			0
$423$	8.37819	+	14.1121i	0.407361	+	0.686155i
$424$		0			0
$425$	1.62540	−	9.21810i	0.0788435	−	0.447144i
$426$		0			0
$427$	1.28356	+	0.467178i	0.0621158	+	0.0226083i
$428$		0			0
$429$	0.154635	+	0.0262974i	0.00746583	+	0.00126965i
$430$		0			0
$431$	22.4164			1.07976			0.539879	−	0.841743i	$-0.318470\pi$
$431$	22.4164			1.07976			0.539879	+	0.841743i	$0.318470\pi$
$432$		0			0
$433$	−38.6486			−1.85733			−0.928667	−	0.370914i	$-0.879044\pi$
$433$	−38.6486			−1.85733			−0.928667	+	0.370914i	$0.879044\pi$
$434$		0			0
$435$	−24.0848	+	29.0603i	−1.15478	+	1.39334i
$436$		0			0
$437$	−0.417256	−	0.151869i	−0.0199600	−	0.00726486i
$438$		0			0
$439$	0.129035	−	0.731792i	0.00615849	−	0.0349265i	−0.981574	−	0.191084i	$-0.938800\pi$
$439$	0.129035	−	0.731792i	0.00615849	−	0.0349265i	0.987732	+	0.156158i	$0.0499108\pi$
$440$		0			0
$441$	−19.3333	+	7.30433i	−0.920635	+	0.347825i
$442$		0			0
$443$	−17.9081	+	6.51802i	−0.850840	+	0.309680i	−0.730383	−	0.683038i	$-0.760658\pi$
$443$	−17.9081	+	6.51802i	−0.850840	+	0.309680i	−0.120457	+	0.992719i	$0.538436\pi$
$444$		0			0
$445$	−5.11858	+	4.29500i	−0.242644	+	0.203603i
$446$		0			0
$447$	−25.0131	−	14.2391i	−1.18308	−	0.673488i
$448$		0			0
$449$	16.7956	+	29.0909i	0.792635	+	1.37288i	0.924330	+	0.381594i	$0.124625\pi$
$449$	16.7956	+	29.0909i	0.792635	+	1.37288i	−0.131695	+	0.991290i	$0.542042\pi$
$450$		0			0
$451$	−0.0403179	+	0.0698326i	−0.00189849	+	0.00328829i
$452$		0			0
$453$	16.1951	+	19.0639i	0.760912	+	0.895698i
$454$		0			0
$455$	−0.164994	−	0.935729i	−0.00773505	−	0.0438676i
$456$		0			0
$457$	−20.9248	−	17.5580i	−0.978822	−	0.821329i	0.00508919	−	0.999987i	$-0.498380\pi$
$457$	−20.9248	−	17.5580i	−0.978822	−	0.821329i	−0.983911	+	0.178658i	$0.942824\pi$
$458$		0			0
$459$	0.198305	+	10.8653i	0.00925609	+	0.507147i
$460$		0			0
$461$	6.47834	+	5.43597i	0.301726	+	0.253179i	0.781062	−	0.624453i	$-0.214678\pi$
$461$	6.47834	+	5.43597i	0.301726	+	0.253179i	−0.479336	+	0.877631i	$0.659122\pi$
$462$		0			0
$463$	3.61095	+	20.4787i	0.167815	+	0.951726i	0.946114	+	0.323833i	$0.104972\pi$
$463$	3.61095	+	20.4787i	0.167815	+	0.951726i	−0.778299	+	0.627893i	$0.783917\pi$
$464$		0			0
$465$	−51.0793	+	9.32739i	−2.36875	+	0.432547i
$466$		0			0
$467$	−6.73820	+	11.6709i	−0.311807	+	0.540065i	−0.978754	−	0.205040i	$-0.934267\pi$
$467$	−6.73820	+	11.6709i	−0.311807	+	0.540065i	0.666947	+	0.745105i	$0.267601\pi$
$468$		0			0
$469$	−2.06628	−	3.57890i	−0.0954119	−	0.165258i
$470$		0			0
$471$	−0.142915	−	23.4936i	−0.00658519	−	1.08253i
$472$		0			0
$473$	0.695662	−	0.583730i	0.0319866	−	0.0268399i
$474$		0			0
$475$	0.296197	−	0.107807i	0.0135905	−	0.00494653i
$476$		0			0
$477$	19.6481	−	16.8983i	0.899624	−	0.773719i
$478$		0			0
$479$	1.31308	−	7.44684i	0.0599961	−	0.340255i	−0.940003	−	0.341165i	$-0.889179\pi$
$479$	1.31308	−	7.44684i	0.0599961	−	0.340255i	1.00000		0.000909967i	$0.000289652\pi$
$480$		0			0
$481$	−3.91145	−	1.42365i	−0.178347	−	0.0649130i
$482$		0			0
$483$	−1.26487	−	3.41052i	−0.0575538	−	0.155184i
$484$		0			0
$485$	9.66334			0.438790
$486$		0			0
$487$	−1.89534			−0.0858860			−0.0429430	−	0.999078i	$-0.513673\pi$
$487$	−1.89534			−0.0858860			−0.0429430	+	0.999078i	$0.513673\pi$
$488$		0			0
$489$	−5.68039	−	15.3162i	−0.256876	−	0.692622i
$490$		0			0
$491$	−7.10930	−	2.58757i	−0.320838	−	0.116776i	0.176580	−	0.984286i	$-0.443496\pi$
$491$	−7.10930	−	2.58757i	−0.320838	−	0.116776i	−0.497419	+	0.867511i	$0.665719\pi$
$492$		0			0
$493$	−2.57086	+	14.5801i	−0.115786	+	0.656653i
$494$		0			0
$495$	−0.684226	+	0.588467i	−0.0307537	+	0.0264496i
$496$		0			0
$497$	1.82816	−	0.665395i	0.0820041	−	0.0298471i
$498$		0			0
$499$	21.7824	−	18.2776i	0.975116	−	0.818220i	−0.00822925	−	0.999966i	$-0.502619\pi$
$499$	21.7824	−	18.2776i	0.975116	−	0.818220i	0.983345	+	0.181747i	$0.0581750\pi$
$500$		0			0
$501$	−0.0291114	−	4.78557i	−0.00130060	−	0.213803i
$502$		0			0
$503$	4.34878	+	7.53231i	0.193902	+	0.335849i	0.946540	−	0.322586i	$-0.104552\pi$
$503$	4.34878	+	7.53231i	0.193902	+	0.335849i	−0.752638	+	0.658435i	$0.771219\pi$
$504$		0			0
$505$	24.7104	−	42.7996i	1.09960	−	1.90456i
$506$		0			0
$507$	−20.6872	+	3.77761i	−0.918751	+	0.167770i
$508$		0			0
$509$	4.39133	+	24.9045i	0.194642	+	1.10387i	0.912927	+	0.408123i	$0.133817\pi$
$509$	4.39133	+	24.9045i	0.194642	+	1.10387i	−0.718285	+	0.695749i	$0.755072\pi$
$510$		0			0
$511$	1.05839	+	0.888095i	0.0468204	+	0.0392870i
$512$		0			0
$513$	−0.313527	+	0.188726i	−0.0138426	+	0.00833246i
$514$		0			0
$515$	11.2647	+	9.45225i	0.496384	+	0.416516i
$516$		0			0
$517$	0.0928351	+	0.526494i	0.00408288	+	0.0231552i
$518$		0			0
$519$	10.5207	+	12.3843i	0.461808	+	0.543611i
$520$		0			0
$521$	−1.19117	+	2.06317i	−0.0521863	+	0.0903892i	−0.890938	−	0.454124i	$-0.849952\pi$
$521$	−1.19117	+	2.06317i	−0.0521863	+	0.0903892i	0.838752	+	0.544513i	$0.183286\pi$
$522$		0			0
$523$	15.7971	+	27.3615i	0.690761	+	1.19643i	0.971589	+	0.236675i	$0.0760576\pi$
$523$	15.7971	+	27.3615i	0.690761	+	1.19643i	−0.280828	+	0.959758i	$0.590609\pi$
$524$		0			0
$525$	2.24403	+	1.27746i	0.0979376	+	0.0557527i
$526$		0			0
$527$	−15.6022	+	13.0918i	−0.679643	+	0.570289i
$528$		0			0
$529$	−15.7419	+	5.72958i	−0.684430	+	0.249112i
$530$		0			0
$531$	38.8699	−	14.6854i	1.68681	−	0.637294i
$532$		0			0
$533$	−0.132776	+	0.753009i	−0.00575116	+	0.0326165i
$534$		0			0
$535$	−17.0954	−	6.22222i	−0.739099	−	0.269010i
$536$		0			0
$537$	−6.39698	+	7.71850i	−0.276050	+	0.333078i
$538$		0			0
$539$	−0.673236			−0.0289983
$540$		0			0
$541$	−39.1910			−1.68495			−0.842477	−	0.538732i	$-0.818903\pi$
$541$	−39.1910			−1.68495			−0.842477	+	0.538732i	$0.818903\pi$
$542$		0			0
$543$	23.0639	+	3.92228i	0.989767	+	0.168321i
$544$		0			0
$545$	30.9673	+	11.2712i	1.32649	+	0.482803i
$546$		0			0
$547$	−2.73073	+	15.4868i	−0.116758	+	0.662166i	0.869107	+	0.494624i	$0.164694\pi$
$547$	−2.73073	+	15.4868i	−0.116758	+	0.662166i	−0.985865	+	0.167542i	$0.946417\pi$
$548$		0			0
$549$	−6.28033	−	10.5785i	−0.268038	−	0.451480i
$550$		0			0
$551$	−0.468489	+	0.170516i	−0.0199583	+	0.00726422i
$552$		0			0
$553$	1.60339	−	1.34540i	0.0681830	−	0.0572124i
$554$		0			0
$555$	20.6673	−	12.1005i	0.877278	−	0.513637i
$556$		0			0
$557$	5.08750	+	8.81182i	0.215564	+	0.373369i	0.953447	−	0.301561i	$-0.0975075\pi$
$557$	5.08750	+	8.81182i	0.215564	+	0.373369i	−0.737883	+	0.674929i	$0.764174\pi$
$558$		0			0
$559$	4.30562	−	7.45755i	0.182108	−	0.315421i
$560$		0			0
$561$	−0.119048	+	0.333378i	−0.00502622	+	0.0140752i
$562$		0			0
$563$	−2.71490	−	15.3970i	−0.114420	−	0.648906i	−0.987036	−	0.160499i	$-0.948690\pi$
$563$	−2.71490	−	15.3970i	−0.114420	−	0.648906i	0.872616	−	0.488406i	$-0.162422\pi$
$564$		0			0
$565$	13.6340	+	11.4403i	0.573585	+	0.481295i
$566$		0			0
$567$	−2.84115	−	0.956475i	−0.119317	−	0.0401682i
$568$		0			0
$569$	33.2876	+	27.9316i	1.39549	+	1.17095i	0.963061	+	0.269284i	$0.0867871\pi$
$569$	33.2876	+	27.9316i	1.39549	+	1.17095i	0.432427	+	0.901669i	$0.357657\pi$
$570$		0			0
$571$	−5.41229	−	30.6946i	−0.226497	−	1.28453i	−0.859802	−	0.510627i	$-0.829413\pi$
$571$	−5.41229	−	30.6946i	−0.226497	−	1.28453i	0.633305	−	0.773902i	$-0.281698\pi$
$572$		0			0
$573$	8.61986	−	24.1387i	0.360100	−	1.00841i
$574$		0			0
$575$	14.1094	−	24.4383i	0.588405	−	1.01915i
$576$		0			0
$577$	−0.920067	−	1.59360i	−0.0383029	−	0.0663426i	0.846238	−	0.532804i	$-0.178862\pi$
$577$	−0.920067	−	1.59360i	−0.0383029	−	0.0663426i	−0.884541	+	0.466462i	$0.845529\pi$
$578$		0			0
$579$	−15.9611	+	9.34508i	−0.663322	+	0.388368i
$580$		0			0
$581$	3.80430	−	3.19218i	0.157829	−	0.132434i
$582$		0			0
$583$	0.793282	−	0.288731i	0.0328544	−	0.0119580i
$584$		0			0
$585$	−4.18836	+	7.46267i	−0.173167	+	0.308544i
$586$		0			0
$587$	−1.10216	+	6.25069i	−0.0454912	+	0.257994i	−0.999068	−	0.0431553i	$-0.986259\pi$
$587$	−1.10216	+	6.25069i	−0.0454912	+	0.257994i	0.953577	+	0.301149i	$0.0973701\pi$
$588$		0			0
$589$	−0.644501	−	0.234579i	−0.0265562	−	0.00966566i
$590$		0			0
$591$	−21.0997	−	3.58824i	−0.867925	−	0.147601i
$592$		0			0
$593$	19.5902			0.804472			0.402236	−	0.915536i	$-0.368233\pi$
$593$	19.5902			0.804472			0.402236	+	0.915536i	$0.368233\pi$
$594$		0			0
$595$	2.14437			0.0879106
$596$		0			0
$597$	6.13475	−	7.40210i	0.251079	−	0.302948i
$598$		0			0
$599$	−36.9383	−	13.4445i	−1.50926	−	0.549325i	−0.550820	−	0.834624i	$-0.685685\pi$
$599$	−36.9383	−	13.4445i	−1.50926	−	0.549325i	−0.958439	+	0.285299i	$0.907907\pi$
$600$		0			0
$601$	4.90024	−	27.7907i	0.199885	−	1.13360i	−0.705403	−	0.708807i	$-0.749234\pi$
$601$	4.90024	−	27.7907i	0.199885	−	1.13360i	0.905288	−	0.424798i	$-0.139655\pi$
$602$		0			0
$603$	−6.01677	+	36.7305i	−0.245022	+	1.49578i
$604$		0			0
$605$	31.7912	−	11.5710i	1.29250	−	0.470430i
$606$		0			0
$607$	25.6678	−	21.5378i	1.04182	−	0.874194i	0.0496139	−	0.998768i	$-0.484201\pi$
$607$	25.6678	−	21.5378i	1.04182	−	0.874194i	0.992210	+	0.124574i	$0.0397565\pi$
$608$		0			0
$609$	−3.54934	−	2.02052i	−0.143826	−	0.0818757i
$610$		0			0
$611$	2.53474	+	4.39030i	0.102545	+	0.177612i
$612$		0			0
$613$	16.8676	−	29.2156i	0.681278	−	1.18001i	−0.293313	−	0.956016i	$-0.594758\pi$
$613$	16.8676	−	29.2156i	0.681278	−	1.18001i	0.974591	−	0.223992i	$-0.0719088\pi$
$614$		0			0
$615$	−2.84828	−	3.35281i	−0.114854	−	0.135198i
$616$		0			0
$617$	−0.464372	−	2.63359i	−0.0186949	−	0.106024i	0.974032	−	0.226408i	$-0.0726984\pi$
$617$	−0.464372	−	2.63359i	−0.0186949	−	0.106024i	−0.992727	+	0.120384i	$0.961587\pi$
$618$		0			0
$619$	−22.4711	−	18.8555i	−0.903191	−	0.757867i	0.0676204	−	0.997711i	$-0.478459\pi$
$619$	−22.4711	−	18.8555i	−0.903191	−	0.757867i	−0.970811	+	0.239844i	$0.922904\pi$
$620$		0			0
$621$	−10.6414	+	30.9850i	−0.427025	+	1.24338i
$622$		0			0
$623$	−0.553871	−	0.464753i	−0.0221904	−	0.0186199i
$624$		0			0
$625$	−4.74870	−	26.9312i	−0.189948	−	1.07725i
$626$		0			0
$627$	−0.0117269	+	0.00214140i	−0.000468326	+	8.55191e-5i
$628$		0			0
$629$	4.69704	−	8.13550i	0.187283	−	0.324384i
$630$		0			0
$631$	−6.64926	−	11.5168i	−0.264703	−	0.458478i	0.702783	−	0.711404i	$-0.251940\pi$
$631$	−6.64926	−	11.5168i	−0.264703	−	0.458478i	−0.967486	+	0.252926i	$0.918607\pi$
$632$		0			0
$633$	0.263326	+	43.2876i	0.0104663	+	1.72053i
$634$		0			0
$635$	7.69416	−	6.45616i	0.305333	−	0.256205i
$636$		0			0
$637$	−5.99894	+	2.18344i	−0.237687	+	0.0865109i
$638$		0			0
$639$	−16.5370	−	5.79214i	−0.654196	−	0.229134i
$640$		0			0
$641$	4.52695	−	25.6736i	0.178804	−	1.01405i	−0.754857	−	0.655889i	$-0.772294\pi$
$641$	4.52695	−	25.6736i	0.178804	−	1.01405i	0.933661	−	0.358158i	$-0.116595\pi$
$642$		0			0
$643$	−4.18214	−	1.52217i	−0.164928	−	0.0600287i	0.258237	−	0.966082i	$-0.416858\pi$
$643$	−4.18214	−	1.52217i	−0.164928	−	0.0600287i	−0.423164	+	0.906053i	$0.639081\pi$
$644$		0			0
$645$	17.2284	+	46.4534i	0.678367	+	1.82910i
$646$		0			0
$647$	25.3237			0.995578			0.497789	−	0.867298i	$-0.334145\pi$
$647$	25.3237			0.995578			0.497789	+	0.867298i	$0.334145\pi$
$648$		0			0
$649$	1.35355			0.0531314
$650$		0			0
$651$	−1.95375	−	5.26795i	−0.0765734	−	0.206467i
$652$		0			0
$653$	12.8225	+	4.66701i	0.501784	+	0.182634i	0.580496	−	0.814263i	$-0.302859\pi$
$653$	12.8225	+	4.66701i	0.501784	+	0.182634i	−0.0787124	+	0.996897i	$0.525081\pi$
$654$		0			0
$655$	−7.74003	+	43.8959i	−0.302428	+	1.71515i
$656$		0			0
$657$	−2.30975	−	12.2274i	−0.0901120	−	0.477038i
$658$		0			0
$659$	25.2443	−	9.18818i	0.983379	−	0.357921i	0.200226	−	0.979750i	$-0.435832\pi$
$659$	25.2443	−	9.18818i	0.983379	−	0.357921i	0.783153	+	0.621829i	$0.213610\pi$
$660$		0			0
$661$	27.2171	−	22.8378i	1.05862	−	0.888289i	0.0646483	−	0.997908i	$-0.479407\pi$
$661$	27.2171	−	22.8378i	1.05862	−	0.888289i	0.993974	+	0.109619i	$0.0349630\pi$
$662$		0			0
$663$	0.0204194	+	3.35670i	0.000793022	+	0.130363i
$664$		0			0
$665$	0.0361056	+	0.0625368i	0.00140012	+	0.00242507i
$666$		0			0
$667$	−22.3166	+	38.6535i	−0.864102	+	1.49667i
$668$		0			0
$669$	−29.9509	+	5.46922i	−1.15797	+	0.211452i
$670$		0			0
$671$	−0.0695896	−	0.394662i	−0.00268648	−	0.0152358i
$672$		0			0
$673$	−5.75031	−	4.82508i	−0.221658	−	0.185993i	0.525196	−	0.850981i	$-0.323992\pi$
$673$	−5.75031	−	4.82508i	−0.221658	−	0.185993i	−0.746854	+	0.664988i	$0.768437\pi$
$674$		0			0
$675$	−8.35161	−	21.7050i	−0.321453	−	0.835427i
$676$		0			0
$677$	−8.47757	−	7.11352i	−0.325819	−	0.273395i	0.465175	−	0.885219i	$-0.345992\pi$
$677$	−8.47757	−	7.11352i	−0.325819	−	0.273395i	−0.790994	+	0.611824i	$0.790436\pi$
$678$		0			0
$679$	0.181575	+	1.02976i	0.00696821	+	0.0395187i
$680$		0			0
$681$	−3.16672	−	3.72766i	−0.121349	−	0.142844i
$682$		0			0
$683$	−16.9052	+	29.2807i	−0.646861	+	1.12040i	0.337008	+	0.941502i	$0.390585\pi$
$683$	−16.9052	+	29.2807i	−0.646861	+	1.12040i	−0.983868	+	0.178894i	$0.942748\pi$
$684$		0			0
$685$	29.3565	+	50.8470i	1.12166	+	1.94276i
$686$		0			0
$687$	35.3764	+	20.1386i	1.34969	+	0.768337i
$688$		0			0
$689$	6.13221	−	5.14554i	0.233619	−	0.196029i
$690$		0			0
$691$	−7.63368	+	2.77843i	−0.290399	+	0.105697i	−0.483112	−	0.875559i	$-0.660494\pi$
$691$	−7.63368	+	2.77843i	−0.290399	+	0.105697i	0.192713	+	0.981255i	$0.438271\pi$
$692$		0			0
$693$	−0.0755660	−	0.0618565i	−0.00287051	−	0.00234973i
$694$		0			0
$695$	−1.63030	+	9.24592i	−0.0618410	+	0.350718i
$696$		0			0
$697$	−1.62157	−	0.590204i	−0.0614214	−	0.0223556i
$698$		0			0
$699$	19.4193	−	23.4310i	0.734505	−	0.886242i
$700$		0			0
$701$	2.64774			0.100004			0.0500019	−	0.998749i	$-0.484077\pi$
$701$	2.64774			0.100004			0.0500019	+	0.998749i	$0.484077\pi$
$702$		0			0
$703$	0.316344			0.0119311
$704$		0			0
$705$	−28.7547	−	4.89007i	−1.08296	−	0.184171i
$706$		0			0
$707$	5.02520	+	1.82902i	0.188992	+	0.0687875i
$708$		0			0
$709$	5.65574	−	32.0753i	0.212406	−	1.20461i	−0.672946	−	0.739692i	$-0.734971\pi$
$709$	5.65574	−	32.0753i	0.212406	−	1.20461i	0.885352	−	0.464922i	$-0.153918\pi$
$710$		0			0
$711$	−18.8499	+	0.229343i	−0.706928	+	0.00860104i
$712$		0			0
$713$	−57.6990	+	21.0007i	−2.16084	+	0.786483i
$714$		0			0
$715$	−0.213548	+	0.179188i	−0.00798626	+	0.00670127i
$716$		0			0
$717$	−23.6944	+	13.8728i	−0.884882	+	0.518089i
$718$		0			0
$719$	6.00980	+	10.4093i	0.224128	+	0.388201i	0.956057	−	0.293179i	$-0.0947133\pi$
$719$	6.00980	+	10.4093i	0.224128	+	0.388201i	−0.731930	+	0.681380i	$0.761380\pi$
$720$		0			0
$721$	−0.795603	+	1.37802i	−0.0296298	+	0.0513203i
$722$		0			0
$723$	−10.3332	+	28.9368i	−0.384296	+	1.07617i
$724$		0			0
$725$	−5.50183	−	31.2024i	−0.204333	−	1.15883i
$726$		0			0
$727$	11.3727	+	9.54283i	0.421790	+	0.353924i	0.828844	−	0.559480i	$-0.188999\pi$
$727$	11.3727	+	9.54283i	0.421790	+	0.353924i	−0.407054	+	0.913404i	$0.633444\pi$
$728$		0			0
$729$	14.3443	+	22.8745i	0.531269	+	0.847203i
$730$		0			0
$731$	14.8875	+	12.4921i	0.550633	+	0.462036i
$732$		0			0
$733$	2.45253	+	13.9090i	0.0905861	+	0.513740i	0.996011	+	0.0892326i	$0.0284414\pi$
$733$	2.45253	+	13.9090i	0.0905861	+	0.513740i	−0.905425	+	0.424507i	$0.860447\pi$
$734$		0			0
$735$	12.3523	−	34.5910i	0.455623	−	1.27591i
$736$		0			0
$737$	−0.606224	+	1.05001i	−0.0223305	+	0.0386776i
$738$		0			0
$739$	18.6568	+	32.3145i	0.686300	+	1.18871i	0.973026	+	0.230694i	$0.0740997\pi$
$739$	18.6568	+	32.3145i	0.686300	+	1.18871i	−0.286726	+	0.958013i	$0.592567\pi$
$740$		0			0
$741$	−0.0975485	+	0.0571136i	−0.00358353	+	0.00209812i
$742$		0			0
$743$	−26.2069	+	21.9902i	−0.961437	+	0.806742i	−0.981186	−	0.193063i	$-0.938158\pi$
$743$	−26.2069	+	21.9902i	−0.961437	+	0.806742i	0.0197490	+	0.999805i	$0.493713\pi$
$744$		0			0
$745$	48.0676	−	17.4952i	1.76106	−	0.640973i
$746$		0			0
$747$	−44.7245	+	0.544153i	−1.63638	+	0.0199095i
$748$		0			0
$749$	0.341840	−	1.93867i	0.0124905	−	0.0708374i
$750$		0			0
$751$	27.3393	+	9.95070i	0.997626	+	0.363106i	0.788669	−	0.614818i	$-0.210771\pi$
$751$	27.3393	+	9.95070i	0.997626	+	0.363106i	0.208958	+	0.977925i	$0.432993\pi$
$752$		0			0
$753$	43.6977	+	7.43129i	1.59243	+	0.270811i
$754$		0			0
$755$	−44.4562			−1.61793
$756$		0			0
$757$	−22.3705			−0.813070			−0.406535	−	0.913635i	$-0.633263\pi$
$757$	−22.3705			−0.813070			−0.406535	+	0.913635i	$0.633263\pi$
$758$		0			0
$759$	−0.681002	+	0.821686i	−0.0247188	+	0.0298253i
$760$		0			0
$761$	−3.32069	−	1.20863i	−0.120375	−	0.0438129i	0.281130	−	0.959670i	$-0.409291\pi$
$761$	−3.32069	−	1.20863i	−0.120375	−	0.0438129i	−0.401505	+	0.915857i	$0.631513\pi$
$762$		0			0
$763$	−0.619221	+	3.51178i	−0.0224173	+	0.127135i
$764$		0			0
$765$	−14.9448	−	12.2335i	−0.540331	−	0.442302i
$766$		0			0
$767$	12.0609	−	4.38982i	0.435495	−	0.158507i
$768$		0			0
$769$	−13.8620	+	11.6316i	−0.499876	+	0.419445i	−0.857550	−	0.514401i	$-0.828014\pi$
$769$	−13.8620	+	11.6316i	−0.499876	+	0.419445i	0.357674	+	0.933846i	$0.383570\pi$
$770$		0			0
$771$	15.9625	+	9.08691i	0.574874	+	0.327257i
$772$		0			0
$773$	−12.6595	−	21.9269i	−0.455330	−	0.788654i	0.543377	−	0.839489i	$-0.317145\pi$
$773$	−12.6595	−	21.9269i	−0.455330	−	0.788654i	−0.998707	+	0.0508344i	$0.983812\pi$
$774$		0			0
$775$	21.7937	−	37.7478i	0.782854	−	1.35594i
$776$		0			0
$777$	1.67782	+	1.97502i	0.0601913	+	0.0708534i
$778$		0			0
$779$	−0.0100908	−	0.0572278i	−0.000361541	−	0.00205040i
$780$		0			0
$781$	−0.437246	−	0.366893i	−0.0156459	−	0.0131285i
$782$		0			0
$783$	13.2095	+	34.3303i	0.472071	+	1.22687i
$784$		0			0
$785$	31.9857	+	26.8392i	1.14162	+	0.957931i
$786$		0			0
$787$	−2.54013	−	14.4058i	−0.0905459	−	0.513511i	−0.996022	−	0.0891131i	$-0.971597\pi$
$787$	−2.54013	−	14.4058i	−0.0905459	−	0.513511i	0.905476	−	0.424398i	$-0.139514\pi$
$788$		0			0
$789$	−39.4612	+	7.20584i	−1.40485	+	0.256535i
$790$		0			0
$791$	−0.962935	+	1.66785i	−0.0342380	+	0.0593020i
$792$		0			0
$793$	−1.90005	−	3.29099i	−0.0674728	−	0.116866i
$794$		0			0
$795$	0.280170	+	46.0566i	0.00993660	+	1.63346i
$796$		0			0
$797$	−5.74716	+	4.82244i	−0.203575	+	0.170820i	−0.738875	−	0.673842i	$-0.764643\pi$
$797$	−5.74716	+	4.82244i	−0.203575	+	0.170820i	0.535300	+	0.844662i	$0.320198\pi$
$798$		0			0
$799$	−10.7510	+	3.91306i	−0.380344	+	0.138434i
$800$		0			0
$801$	1.20873	+	6.39880i	0.0427083	+	0.226090i
$802$		0			0
$803$	0.0703892	−	0.399197i	0.00248398	−	0.0140874i
$804$		0			0
$805$	6.07485	+	2.21106i	0.214110	+	0.0779298i
$806$		0			0
$807$	3.41762	+	9.21503i	0.120306	+	0.324384i
$808$		0			0
$809$	−29.1354			−1.02435			−0.512173	−	0.858882i	$-0.671159\pi$
$809$	−29.1354			−1.02435			−0.512173	+	0.858882i	$0.671159\pi$
$810$		0			0
$811$	37.0684			1.30165			0.650823	−	0.759229i	$-0.274424\pi$
$811$	37.0684			1.30165			0.650823	+	0.759229i	$0.274424\pi$
$812$		0			0
$813$	−19.4078	−	52.3297i	−0.680660	−	1.83528i
$814$		0			0
$815$	27.2814	+	9.92961i	0.955625	+	0.347819i
$816$		0			0
$817$	−0.113643	+	0.644501i	−0.00397586	+	0.0225482i
$818$		0			0
$819$	−0.873951	−	0.306103i	−0.0305383	−	0.0106961i
$820$		0			0
$821$	−9.72069	+	3.53804i	−0.339254	+	0.123478i	−0.506029	−	0.862517i	$-0.668887\pi$
$821$	−9.72069	+	3.53804i	−0.339254	+	0.123478i	0.166774	+	0.985995i	$0.446665\pi$
$822$		0			0
$823$	−25.1697	+	21.1199i	−0.877360	+	0.736192i	−0.965634	−	0.259904i	$-0.916309\pi$
$823$	−25.1697	+	21.1199i	−0.877360	+	0.736192i	0.0882747	+	0.996096i	$0.471865\pi$
$824$		0			0
$825$	−0.00460839	−	0.757565i	−0.000160444	−	0.0263750i
$826$		0			0
$827$	18.4009	+	31.8712i	0.639861	+	1.10827i	0.985463	+	0.169890i	$0.0543413\pi$
$827$	18.4009	+	31.8712i	0.639861	+	1.10827i	−0.345602	+	0.938381i	$0.612325\pi$
$828$		0			0
$829$	17.9054	−	31.0130i	0.621880	−	1.07713i	−0.367255	−	0.930120i	$-0.619702\pi$
$829$	17.9054	−	31.0130i	0.621880	−	1.07713i	0.989135	−	0.147008i	$-0.0469642\pi$
$830$		0			0
$831$	30.1231	−	5.50066i	1.04496	−	0.190816i
$832$		0			0
$833$	−2.50184	−	14.1887i	−0.0866837	−	0.491608i
$834$		0			0
$835$	6.51539	+	5.46706i	0.225474	+	0.189195i
$836$		0			0
$837$	−16.4369	+	47.8600i	−0.568143	+	1.65428i
$838$		0			0
$839$	19.9870	+	16.7711i	0.690027	+	0.579001i	0.918917	−	0.394451i	$-0.129065\pi$
$839$	19.9870	+	16.7711i	0.690027	+	0.579001i	−0.228890	+	0.973452i	$0.573510\pi$
$840$		0			0
$841$	3.66632	+	20.7927i	0.126425	+	0.716991i
$842$		0			0
$843$	14.6712	+	17.2700i	0.505304	+	0.594812i
$844$		0			0
$845$	18.6870	−	32.3668i	0.642852	−	1.11345i
$846$		0			0
$847$	1.83041	+	3.17037i	0.0628938	+	0.108935i
$848$		0			0
$849$	29.9458	+	17.0472i	1.02774	+	0.585058i
$850$		0			0
$851$	21.6949	−	18.2042i	0.743692	−	0.624031i
$852$		0			0
$853$	−20.0619	+	7.30193i	−0.686906	+	0.250013i	−0.661810	−	0.749672i	$-0.730211\pi$
$853$	−20.0619	+	7.30193i	−0.686906	+	0.250013i	−0.0250961	+	0.999685i	$0.507989\pi$
$854$		0			0
$855$	0.105136	−	0.641819i	0.00359556	−	0.0219497i
$856$		0			0
$857$	4.46145	−	25.3022i	0.152400	−	0.864306i	−0.808724	−	0.588189i	$-0.799841\pi$
$857$	4.46145	−	25.3022i	0.152400	−	0.864306i	0.961124	−	0.276117i	$-0.0890477\pi$
$858$		0			0
$859$	6.92252	+	2.51959i	0.236193	+	0.0859673i	0.457405	−	0.889259i	$-0.348779\pi$
$859$	6.92252	+	2.51959i	0.236193	+	0.0859673i	−0.221212	+	0.975226i	$0.571001\pi$
$860$		0			0
$861$	0.303769	−	0.366523i	0.0103524	−	0.0124911i
$862$		0			0
$863$	14.4586			0.492176			0.246088	−	0.969247i	$-0.420855\pi$
$863$	14.4586			0.492176			0.246088	+	0.969247i	$0.420855\pi$
$864$		0			0
$865$	−28.8797			−0.981940
$866$		0			0
$867$	21.5596	+	3.66646i	0.732204	+	0.124520i
$868$		0			0
$869$	−0.577052	−	0.210030i	−0.0195751	−	0.00712477i
$870$		0			0
$871$	−1.99643	+	11.3223i	−0.0676465	+	0.383643i
$872$		0			0
$873$	4.60926	−	8.21262i	0.156000	−	0.277955i
$874$		0			0
$875$	0.505181	−	0.183871i	0.0170782	−	0.00621597i
$876$		0			0
$877$	3.35388	−	2.81424i	0.113252	−	0.0950301i	−0.584403	−	0.811464i	$-0.698671\pi$
$877$	3.35388	−	2.81424i	0.113252	−	0.0950301i	0.697655	+	0.716434i	$0.254227\pi$
$878$		0			0
$879$	−4.80890	+	2.81556i	−0.162200	+	0.0949665i
$880$		0			0
$881$	−2.66740	−	4.62007i	−0.0898669	−	0.155654i	0.817588	−	0.575804i	$-0.195311\pi$
$881$	−2.66740	−	4.62007i	−0.0898669	−	0.155654i	−0.907455	+	0.420150i	$0.861977\pi$
$882$		0			0
$883$	−13.5393	+	23.4508i	−0.455635	+	0.789184i	−0.998724	−	0.0504914i	$-0.983921\pi$
$883$	−13.5393	+	23.4508i	−0.455635	+	0.789184i	0.543089	+	0.839675i	$0.317255\pi$
$884$		0			0
$885$	−24.8345	+	69.5457i	−0.834803	+	2.33775i
$886$		0			0
$887$	−5.99487	−	33.9986i	−0.201288	−	1.14156i	−0.903175	−	0.429273i	$-0.858770\pi$
$887$	−5.99487	−	33.9986i	−0.201288	−	1.14156i	0.701887	−	0.712289i	$-0.252341\pi$
$888$		0			0
$889$	0.832568	+	0.698607i	0.0279234	+	0.0234305i
$890$		0			0
$891$	0.173757	+	0.862195i	0.00582109	+	0.0288846i
$892$		0			0
$893$	−0.295137	−	0.247649i	−0.00987639	−	0.00828727i
$894$		0			0
$895$	−3.09379	−	17.5457i	−0.103414	−	0.586490i
$896$		0			0
$897$	−3.40325	+	9.53035i	−0.113631	+	0.318209i
$898$		0			0
$899$	−34.4706	+	59.7049i	−1.14966	+	1.99127i
$900$		0			0
$901$	9.03305	+	15.6457i	0.300935	+	0.521234i
$902$		0			0
$903$	−4.62653	+	2.70879i	−0.153961	+	0.0901428i
$904$		0			0
$905$	−31.8510	+	26.7261i	−1.05876	+	0.888407i
$906$		0			0
$907$	−13.9575	+	5.08010i	−0.463450	+	0.168682i	−0.563183	−	0.826332i	$-0.690423\pi$
$907$	−13.9575	+	5.08010i	−0.463450	+	0.168682i	0.0997331	+	0.995014i	$0.468201\pi$
$908$		0			0
$909$	−24.5878	−	41.4154i	−0.815526	−	1.37366i
$910$		0			0
$911$	2.28045	−	12.9331i	0.0755548	−	0.428492i	−0.923443	−	0.383735i	$-0.874637\pi$
$911$	2.28045	−	12.9331i	0.0755548	−	0.428492i	0.998998	−	0.0447571i	$-0.0142514\pi$
$912$		0			0
$913$	−1.36915	−	0.498329i	−0.0453122	−	0.0164923i
$914$		0			0
$915$	21.5547	+	3.66562i	0.712575	+	0.121182i
$916$		0			0
$917$	−4.82315			−0.159275
$918$		0			0
$919$	27.3820			0.903250			0.451625	−	0.892208i	$-0.350844\pi$
$919$	27.3820			0.903250			0.451625	+	0.892208i	$0.350844\pi$
$920$		0			0
$921$	22.9810	−	27.7285i	0.757250	−	0.913685i
$922$		0			0
$923$	−5.08603	−	1.85116i	−0.167409	−	0.0609318i
$924$		0			0
$925$	−3.49103	+	19.7986i	−0.114784	+	0.650974i
$926$		0			0
$927$	13.4063	−	5.06504i	0.440321	−	0.166358i
$928$		0			0
$929$	−23.7384	+	8.64007i	−0.778832	+	0.283472i	−0.700685	−	0.713470i	$-0.747122\pi$
$929$	−23.7384	+	8.64007i	−0.778832	+	0.283472i	−0.0781462	+	0.996942i	$0.524900\pi$
$930$		0			0
$931$	0.371663	−	0.311862i	0.0121808	−	0.0102209i
$932$		0			0
$933$	−13.3761	−	7.61458i	−0.437914	−	0.249290i
$934$		0			0
$935$	−0.314567	−	0.544847i	−0.0102875	−	0.0178184i
$936$		0			0
$937$	16.0584	−	27.8140i	0.524605	−	0.908643i	−0.474984	−	0.879994i	$-0.657546\pi$
$937$	16.0584	−	27.8140i	0.524605	−	0.908643i	0.999590	−	0.0286488i	$-0.00912046\pi$
$938$		0			0
$939$	12.1912	+	14.3507i	0.397845	+	0.468318i
$940$		0			0
$941$	−0.719414	−	4.08000i	−0.0234522	−	0.133004i	0.970834	−	0.239754i	$-0.0770668\pi$
$941$	−0.719414	−	4.08000i	−0.0234522	−	0.133004i	−0.994286	+	0.106750i	$0.965956\pi$
$942$		0			0
$943$	−3.98524	−	3.34401i	−0.129777	−	0.108896i
$944$		0			0
$945$	4.56466	−	2.74767i	0.148489	−	0.0893819i
$946$		0			0
$947$	−1.15127	−	0.966033i	−0.0374113	−	0.0313918i	0.623890	−	0.781512i	$-0.285551\pi$
$947$	−1.15127	−	0.966033i	−0.0374113	−	0.0313918i	−0.661302	+	0.750120i	$0.729996\pi$
$948$		0			0
$949$	−0.667463	−	3.78537i	−0.0216668	−	0.122878i
$950$		0			0
$951$	−45.7000	+	8.34510i	−1.48193	+	0.270609i
$952$		0			0
$953$	−13.8407	+	23.9729i	−0.448346	+	0.776558i	−0.998279	−	0.0586513i	$-0.981320\pi$
$953$	−13.8407	+	23.9729i	−0.448346	+	0.776558i	0.549933	+	0.835209i	$0.314653\pi$
$954$		0			0
$955$	22.7767	+	39.4504i	0.737037	+	1.27659i
$956$		0			0
$957$	0.00728899	+	1.19822i	0.000235620	+	0.0387331i
$958$		0			0
$959$	−4.86684	+	4.08377i	−0.157159	+	0.131872i
$960$		0			0
$961$	−59.9925	+	21.8355i	−1.93524	+	0.704370i
$962$		0			0
$963$	−13.4423	+	11.5610i	−0.433173	+	0.372549i
$964$		0			0
$965$	5.70800	−	32.3717i	0.183747	−	1.04208i
$966$		0			0
$967$	−25.2872	−	9.20379i	−0.813182	−	0.295974i	−0.0982442	−	0.995162i	$-0.531323\pi$
$967$	−25.2872	−	9.20379i	−0.813182	−	0.295974i	−0.714937	+	0.699188i	$0.753545\pi$
$968$		0			0
$969$	−0.0887093	−	0.239190i	−0.00284975	−	0.00768388i
$970$		0			0
$971$	−0.449240			−0.0144168			−0.00720839	−	0.999974i	$-0.502295\pi$
$971$	−0.449240			−0.0144168			−0.00720839	+	0.999974i	$0.502295\pi$
$972$		0			0
$973$	−1.01591			−0.0325687
$974$		0			0
$975$	−2.49800	−	6.73542i	−0.0799999	−	0.215706i
$976$		0			0
$977$	−15.8034	−	5.75198i	−0.505597	−	0.184022i	0.0766127	−	0.997061i	$-0.475590\pi$
$977$	−15.8034	−	5.75198i	−0.505597	−	0.184022i	−0.582210	+	0.813039i	$0.697812\pi$
$978$		0			0
$979$	−0.0368357	+	0.208906i	−0.00117727	+	0.00667665i
$980$		0			0
$981$	24.3500	−	20.9421i	0.777434	−	0.668630i
$982$		0			0
$983$	28.7692	−	10.4711i	0.917596	−	0.333978i	0.160314	−	0.987066i	$-0.448749\pi$
$983$	28.7692	−	10.4711i	0.917596	−	0.333978i	0.757282	+	0.653089i	$0.226527\pi$
$984$		0			0
$985$	29.1384	−	24.4500i	0.928426	−	0.779042i
$986$		0			0
$987$	−0.0191991	−	3.15610i	−0.000611113	−	0.100460i
$988$		0			0
$989$	29.2946	+	50.7397i	0.931513	+	1.61343i
$990$		0			0
$991$	8.39924	−	14.5479i	0.266811	−	0.462129i	−0.701226	−	0.712939i	$-0.747364\pi$
$991$	8.39924	−	14.5479i	0.266811	−	0.462129i	0.968036	+	0.250810i	$0.0806969\pi$
$992$		0			0
$993$	40.1718	−	7.33561i	1.27481	−	0.232789i
$994$		0			0
$995$	2.96697	+	16.8265i	0.0940591	+	0.533436i
$996$		0			0
$997$	18.7023	+	15.6931i	0.592309	+	0.497006i	0.888963	−	0.457979i	$-0.151426\pi$
$997$	18.7023	+	15.6931i	0.592309	+	0.497006i	−0.296654	+	0.954985i	$0.595871\pi$
$998$		0			0
$999$	−0.425918	−	23.3363i	−0.0134755	−	0.738329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.a.97.6	yes	48
4.3	odd	2	inner	864.2.y.a.97.3	✓	48
27.22	even	9	inner	864.2.y.a.481.6	yes	48
108.103	odd	18	inner	864.2.y.a.481.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.a.97.3	✓	48	4.3	odd	2	inner
864.2.y.a.97.6	yes	48	1.1	even	1	trivial
864.2.y.a.481.3	yes	48	108.103	odd	18	inner
864.2.y.a.481.6	yes	48	27.22	even	9	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.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.602286 + 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(0.0578408 - 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +O(q^{10})\)	\(q+(0.602286 + 1.62396i) q^{3} +(-2.89262 - 1.05283i) q^{5} +(0.0578408 - 0.328031i) q^{7} +(-2.27450 + 1.95618i) q^{9} +(-0.0918319 + 0.0334241i) q^{11} +(-0.709877 + 0.595658i) q^{13} +(-0.0324330 - 5.33160i) q^{15} +(-1.04568 - 1.81118i) q^{17} +(0.0352132 - 0.0609911i) q^{19} +(0.567547 - 0.103638i) q^{21} +(-1.09484 - 6.20915i) q^{23} +(3.42857 + 2.87691i) q^{25} +(-4.54666 - 2.51553i) q^{27} +(-5.42290 - 4.55035i) q^{29} +(-1.69111 - 9.59077i) q^{31} +(-0.109589 - 0.129001i) q^{33} +(-0.512672 + 0.887973i) q^{35} +(2.24591 + 3.89004i) q^{37} +(-1.39487 - 0.794057i) q^{39} +(0.632082 - 0.530380i) q^{41} +(-8.73217 + 3.17825i) q^{43} +(8.63879 - 3.26382i) q^{45} +(0.949958 - 5.38748i) q^{47} +(6.47359 + 2.35619i) q^{49} +(2.31148 - 2.78900i) q^{51} -8.63841 q^{53} +0.300825 q^{55} +(0.120256 + 0.0204508i) q^{57} +(-13.0152 - 4.73715i) q^{59} +(-0.712093 + 4.03848i) q^{61} +(0.510129 + 0.859255i) q^{63} +(2.68053 - 0.975633i) q^{65} +(9.50406 - 7.97485i) q^{67} +(9.42401 - 5.51766i) q^{69} +(2.92034 + 5.05819i) q^{71} +(-2.07395 + 3.59218i) q^{73} +(-2.60702 + 7.30060i) q^{75} +(0.00565252 + 0.0320570i) q^{77} +(4.81366 + 4.03914i) q^{79} +(1.34673 - 8.89867i) q^{81} +(11.4212 + 9.58350i) q^{83} +(1.11791 + 6.33997i) q^{85} +(4.12346 - 11.5472i) q^{87} +(1.08533 - 1.87984i) q^{89} +(0.154335 + 0.267315i) q^{91} +(14.5565 - 8.52268i) q^{93} +(-0.166072 + 0.139351i) q^{95} +(-2.94990 + 1.07368i) q^{97} +(0.143489 - 0.255663i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{9}+O(q^{10}) \) 48 * q - 12 * q^9	\( 48 q - 12 q^{9} - 12 q^{17} - 48 q^{21} + 24 q^{25} + 6 q^{29} - 6 q^{33} + 30 q^{37} - 12 q^{41} + 30 q^{45} - 6 q^{49} - 36 q^{53} - 6 q^{57} - 12 q^{61} - 60 q^{65} - 78 q^{69} + 48 q^{73} - 12 q^{77} - 36 q^{81} + 102 q^{85} - 66 q^{89} + 36 q^{93} + 6 q^{97}+O(q^{100}) \) 48 * q - 12 * q^9 - 12 * q^17 - 48 * q^21 + 24 * q^25 + 6 * q^29 - 6 * q^33 + 30 * q^37 - 12 * q^41 + 30 * q^45 - 6 * q^49 - 36 * q^53 - 6 * q^57 - 12 * q^61 - 60 * q^65 - 78 * q^69 + 48 * q^73 - 12 * q^77 - 36 * q^81 + 102 * q^85 - 66 * q^89 + 36 * q^93 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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