LMFDB - Embedded newform 216.2.q.a.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.q (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	216.25
Dual form			216.2.q.a.121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.56946 - 0.732664i) q^{3} +(0.407020 - 0.341530i) q^{5} +(0.507439 - 0.184693i) q^{7} +(1.92641 - 2.29977i) q^{9} +O(q^{10})$	\(q+(1.56946 - 0.732664i) q^{3} +(0.407020 - 0.341530i) q^{5} +(0.507439 - 0.184693i) q^{7} +(1.92641 - 2.29977i) q^{9} +(-1.49166 - 1.25165i) q^{11} +(0.696168 + 3.94816i) q^{13} +(0.388574 - 0.834226i) q^{15} +(0.0114999 + 0.0199184i) q^{17} +(1.25366 - 2.17140i) q^{19} +(0.661088 - 0.661651i) q^{21} +(-6.43593 - 2.34249i) q^{23} +(-0.819219 + 4.64602i) q^{25} +(1.33845 - 5.02081i) q^{27} +(-1.03716 + 5.88202i) q^{29} +(3.81218 + 1.38752i) q^{31} +(-3.25813 - 0.871529i) q^{33} +(0.143460 - 0.248479i) q^{35} +(3.58546 + 6.21019i) q^{37} +(3.98528 + 5.68642i) q^{39} +(-1.30857 - 7.42125i) q^{41} +(-4.23124 - 3.55043i) q^{43} +(-0.00135669 - 1.59398i) q^{45} +(-10.4739 + 3.81218i) q^{47} +(-5.13893 + 4.31207i) q^{49} +(0.0326421 + 0.0228356i) q^{51} +2.91189 q^{53} -1.03461 q^{55} +(0.376659 - 4.32643i) q^{57} +(-3.02267 + 2.53632i) q^{59} +(-9.15728 + 3.33298i) q^{61} +(0.552783 - 1.52279i) q^{63} +(1.63177 + 1.36922i) q^{65} +(1.88380 + 10.6835i) q^{67} +(-11.8172 + 1.03894i) q^{69} +(2.30083 + 3.98515i) q^{71} +(8.36375 - 14.4864i) q^{73} +(2.11824 + 7.89195i) q^{75} +(-0.988096 - 0.359638i) q^{77} +(2.23867 - 12.6961i) q^{79} +(-1.57792 - 8.86060i) q^{81} +(-0.334381 + 1.89637i) q^{83} +(0.0114834 + 0.00417962i) q^{85} +(2.68177 + 9.99148i) q^{87} +(3.68793 - 6.38768i) q^{89} +(1.08246 + 1.87488i) q^{91} +(6.99964 - 0.615391i) q^{93} +(-0.231335 - 1.31196i) q^{95} +(-2.32754 - 1.95304i) q^{97} +(-5.75205 + 1.01929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q - 3 * q^7 + 6 * q^9	$ 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) $ 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{9}\right)$

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
$3$	1.56946	−	0.732664i	0.906128	−	0.423004i
$3$	1.56946	−	0.732664i	0.906128	−	0.423004i
$4$		0			0
$5$	0.407020	−	0.341530i	0.182025	−	0.152737i	−0.547223	−	0.836987i	$-0.684315\pi$
$5$	0.407020	−	0.341530i	0.182025	−	0.152737i	0.729247	+	0.684250i	$0.239870\pi$
$6$		0			0
$7$	0.507439	−	0.184693i	0.191794	−	0.0698073i	−0.244337	−	0.969690i	$-0.578570\pi$
$7$	0.507439	−	0.184693i	0.191794	−	0.0698073i	0.436132	+	0.899883i	$0.356348\pi$
$8$		0			0
$9$	1.92641	−	2.29977i	0.642135	−	0.766591i
$10$		0			0
$11$	−1.49166	−	1.25165i	−0.449752	−	0.377386i	0.389592	−	0.920988i	$-0.372616\pi$
$11$	−1.49166	−	1.25165i	−0.449752	−	0.377386i	−0.839344	+	0.543601i	$0.817060\pi$
$12$		0			0
$13$	0.696168	+	3.94816i	0.193082	+	1.09502i	0.915124	+	0.403173i	$0.132093\pi$
$13$	0.696168	+	3.94816i	0.193082	+	1.09502i	−0.722041	+	0.691850i	$0.756796\pi$
$14$		0			0
$15$	0.388574	−	0.834226i	0.100329	−	0.215396i
$16$		0			0
$17$	0.0114999	+	0.0199184i	0.00278914	+	0.00483093i	0.867417	−	0.497583i	$-0.165779\pi$
$17$	0.0114999	+	0.0199184i	0.00278914	+	0.00483093i	−0.864627	+	0.502414i	$0.832446\pi$
$18$		0			0
$19$	1.25366	−	2.17140i	0.287609	−	0.498153i	−0.685630	−	0.727951i	$-0.740473\pi$
$19$	1.25366	−	2.17140i	0.287609	−	0.498153i	0.973238	+	0.229797i	$0.0738064\pi$
$20$		0			0
$21$	0.661088	−	0.661651i	0.144261	−	0.144384i
$22$		0			0
$23$	−6.43593	−	2.34249i	−1.34199	−	0.488443i	−0.431548	−	0.902090i	$-0.642032\pi$
$23$	−6.43593	−	2.34249i	−1.34199	−	0.488443i	−0.910437	+	0.413647i	$0.864255\pi$
$24$		0			0
$25$	−0.819219	+	4.64602i	−0.163844	+	0.929204i
$26$		0			0
$27$	1.33845	−	5.02081i	0.257586	−	0.966255i
$28$		0			0
$29$	−1.03716	+	5.88202i	−0.192595	+	1.09226i	0.723206	+	0.690632i	$0.242668\pi$
$29$	−1.03716	+	5.88202i	−0.192595	+	1.09226i	−0.915802	+	0.401631i	$0.868443\pi$
$30$		0			0
$31$	3.81218	+	1.38752i	0.684687	+	0.249206i	0.660859	−	0.750510i	$-0.270192\pi$
$31$	3.81218	+	1.38752i	0.684687	+	0.249206i	0.0238283	+	0.999716i	$0.492414\pi$
$32$		0			0
$33$	−3.25813	−	0.871529i	−0.567168	−	0.151714i
$34$		0			0
$35$	0.143460	−	0.248479i	0.0242491	−	0.0420007i
$36$		0			0
$37$	3.58546	+	6.21019i	0.589445	+	1.02095i	0.994305	+	0.106571i	$0.0339870\pi$
$37$	3.58546	+	6.21019i	0.589445	+	1.02095i	−0.404860	+	0.914379i	$0.632680\pi$
$38$		0			0
$39$	3.98528	+	5.68642i	0.638156	+	0.910557i
$40$		0			0
$41$	−1.30857	−	7.42125i	−0.204364	−	1.15901i	−0.898438	−	0.439101i	$-0.855297\pi$
$41$	−1.30857	−	7.42125i	−0.204364	−	1.15901i	0.694074	−	0.719904i	$-0.255814\pi$
$42$		0			0
$43$	−4.23124	−	3.55043i	−0.645258	−	0.541435i	0.260370	−	0.965509i	$-0.416155\pi$
$43$	−4.23124	−	3.55043i	−0.645258	−	0.541435i	−0.905628	+	0.424073i	$0.860600\pi$
$44$		0			0
$45$	−0.00135669	−	1.59398i	−0.000202244	−	0.237616i
$46$		0			0
$47$	−10.4739	+	3.81218i	−1.52777	+	0.556063i	−0.963074	−	0.269236i	$-0.913229\pi$
$47$	−10.4739	+	3.81218i	−1.52777	+	0.556063i	−0.564697	+	0.825299i	$0.691007\pi$
$48$		0			0
$49$	−5.13893	+	4.31207i	−0.734133	+	0.616010i
$50$		0			0
$51$	0.0326421	+	0.0228356i	0.00457081	+	0.00319762i
$52$		0			0
$53$	2.91189			0.399979			0.199990	−	0.979798i	$-0.435909\pi$
$53$	2.91189			0.399979			0.199990	+	0.979798i	$0.435909\pi$
$54$		0			0
$55$	−1.03461			−0.139507
$56$		0			0
$57$	0.376659	−	4.32643i	0.0498897	−	0.573050i
$58$		0			0
$59$	−3.02267	+	2.53632i	−0.393518	+	0.330201i	−0.817982	−	0.575244i	$-0.804907\pi$
$59$	−3.02267	+	2.53632i	−0.393518	+	0.330201i	0.424464	+	0.905445i	$0.360463\pi$
$60$		0			0
$61$	−9.15728	+	3.33298i	−1.17247	+	0.426744i	−0.853537	−	0.521033i	$-0.825547\pi$
$61$	−9.15728	+	3.33298i	−1.17247	+	0.426744i	−0.318934	+	0.947777i	$0.603325\pi$
$62$		0			0
$63$	0.552783	−	1.52279i	0.0696441	−	0.191853i
$64$		0			0
$65$	1.63177	+	1.36922i	0.202396	+	0.169831i
$66$		0			0
$67$	1.88380	+	10.6835i	0.230142	+	1.30520i	0.852606	+	0.522554i	$0.175021\pi$
$67$	1.88380	+	10.6835i	0.230142	+	1.30520i	−0.622464	+	0.782648i	$0.713868\pi$
$68$		0			0
$69$	−11.8172	+	1.03894i	−1.42262	+	0.125073i
$70$		0			0
$71$	2.30083	+	3.98515i	0.273058	+	0.472950i	0.969643	−	0.244524i	$-0.0786317\pi$
$71$	2.30083	+	3.98515i	0.273058	+	0.472950i	−0.696586	+	0.717474i	$0.745298\pi$
$72$		0			0
$73$	8.36375	−	14.4864i	0.978903	−	1.69551i	0.312500	−	0.949918i	$-0.398834\pi$
$73$	8.36375	−	14.4864i	0.978903	−	1.69551i	0.666403	−	0.745592i	$-0.267833\pi$
$74$		0			0
$75$	2.11824	+	7.89195i	0.244594	+	0.911284i
$76$		0			0
$77$	−0.988096	−	0.359638i	−0.112604	−	0.0409845i
$78$		0			0
$79$	2.23867	−	12.6961i	0.251870	−	1.42842i	−0.552112	−	0.833770i	$-0.686178\pi$
$79$	2.23867	−	12.6961i	0.251870	−	1.42842i	0.803981	−	0.594655i	$-0.202711\pi$
$80$		0			0
$81$	−1.57792	−	8.86060i	−0.175324	−	0.984511i
$82$		0			0
$83$	−0.334381	+	1.89637i	−0.0367031	+	0.208153i	−0.997644	−	0.0685990i	$-0.978147\pi$
$83$	−0.334381	+	1.89637i	−0.0367031	+	0.208153i	0.960941	+	0.276752i	$0.0892582\pi$
$84$		0			0
$85$	0.0114834	+	0.00417962i	0.00124555	+	0.000453344i
$86$		0			0
$87$	2.68177	+	9.99148i	0.287515	+	1.07120i
$88$		0			0
$89$	3.68793	−	6.38768i	0.390920	−	0.677093i	−0.601651	−	0.798759i	$-0.705490\pi$
$89$	3.68793	−	6.38768i	0.390920	−	0.677093i	0.992571	+	0.121666i	$0.0388236\pi$
$90$		0			0
$91$	1.08246	+	1.87488i	0.113473	+	0.196540i
$92$		0			0
$93$	6.99964	−	0.615391i	0.725829	−	0.0638131i
$94$		0			0
$95$	−0.231335	−	1.31196i	−0.0237344	−	0.134605i
$96$		0			0
$97$	−2.32754	−	1.95304i	−0.236326	−	0.198301i	0.516931	−	0.856027i	$-0.327074\pi$
$97$	−2.32754	−	1.95304i	−0.236326	−	0.198301i	−0.753258	+	0.657726i	$0.771519\pi$
$98$		0			0
$99$	−5.75205	+	1.01929i	−0.578103	+	0.102443i
$100$		0			0
$101$	6.66762	−	2.42681i	0.663453	−	0.241477i	0.0117264	−	0.999931i	$-0.496267\pi$
$101$	6.66762	−	2.42681i	0.663453	−	0.241477i	0.651726	+	0.758454i	$0.274045\pi$
$102$		0			0
$103$	3.05315	−	2.56190i	0.300836	−	0.252431i	−0.479856	−	0.877347i	$-0.659311\pi$
$103$	3.05315	−	2.56190i	0.300836	−	0.252431i	0.780692	+	0.624916i	$0.214867\pi$
$104$		0			0
$105$	0.0431021	−	0.495086i	0.00420634	−	0.0483155i
$106$		0			0
$107$	20.5414			1.98581			0.992906	−	0.118902i	$-0.0379374\pi$
$107$	20.5414			1.98581			0.992906	+	0.118902i	$0.0379374\pi$
$108$		0			0
$109$	−0.610824			−0.0585063			−0.0292532	−	0.999572i	$-0.509313\pi$
$109$	−0.610824			−0.0585063			−0.0292532	+	0.999572i	$0.509313\pi$
$110$		0			0
$111$	10.1772	+	7.11971i	0.965978	+	0.675773i
$112$		0			0
$113$	11.5871	−	9.72271i	1.09002	−	0.914636i	0.0933066	−	0.995637i	$-0.470256\pi$
$113$	11.5871	−	9.72271i	1.09002	−	0.914636i	0.996714	+	0.0810016i	$0.0258119\pi$
$114$		0			0
$115$	−3.41958	+	1.24463i	−0.318878	+	0.116062i
$116$		0			0
$117$	10.4210	+	6.00474i	0.963420	+	0.555138i
$118$		0			0
$119$	0.00951429	+	0.00798344i	0.000872174	+	0.000731841i
$120$		0			0
$121$	−1.25171	−	7.09882i	−0.113792	−	0.645347i
$122$		0			0
$123$	−7.49103	−	10.6886i	−0.675444	−	0.963760i
$124$		0			0
$125$	2.58163	+	4.47152i	0.230908	+	0.399945i
$126$		0			0
$127$	8.46911	−	14.6689i	0.751512	−	1.30166i	−0.195578	−	0.980688i	$-0.562658\pi$
$127$	8.46911	−	14.6689i	0.751512	−	1.30166i	0.947090	−	0.320969i	$-0.104008\pi$
$128$		0			0
$129$	−9.24203	−	2.47218i	−0.813715	−	0.217663i
$130$		0			0
$131$	3.35430	+	1.22086i	0.293066	+	0.106667i	0.484369	−	0.874864i	$-0.339049\pi$
$131$	3.35430	+	1.22086i	0.293066	+	0.106667i	−0.191303	+	0.981531i	$0.561271\pi$
$132$		0			0
$133$	0.235114	−	1.33340i	0.0203869	−	0.115620i
$134$		0			0
$135$	−1.16998	−	2.50069i	−0.100696	−	0.215225i
$136$		0			0
$137$	−3.21117	+	18.2114i	−0.274349	+	1.55591i	0.466675	+	0.884429i	$0.345452\pi$
$137$	−3.21117	+	18.2114i	−0.274349	+	1.55591i	−0.741023	+	0.671479i	$0.765659\pi$
$138$		0			0
$139$	3.67080	+	1.33606i	0.311354	+	0.113323i	0.492971	−	0.870046i	$-0.335911\pi$
$139$	3.67080	+	1.33606i	0.311354	+	0.113323i	−0.181617	+	0.983369i	$0.558133\pi$
$140$		0			0
$141$	−13.6453	+	13.6569i	−1.14914	+	1.15012i
$142$		0			0
$143$	3.90327	−	6.76066i	0.326408	−	0.565355i
$144$		0			0
$145$	1.58674	+	2.74832i	0.131772	+	0.228235i
$146$		0			0
$147$	−4.90604	+	10.5327i	−0.404643	+	0.868725i
$148$		0			0
$149$	−1.99257	−	11.3005i	−0.163238	−	0.925769i	−0.950862	−	0.309613i	$-0.899800\pi$
$149$	−1.99257	−	11.3005i	−0.163238	−	0.925769i	0.787624	−	0.616156i	$-0.211311\pi$
$150$		0			0
$151$	−8.53371	−	7.16063i	−0.694463	−	0.582724i	0.225729	−	0.974190i	$-0.427524\pi$
$151$	−8.53371	−	7.16063i	−0.694463	−	0.582724i	−0.920192	+	0.391466i	$0.871968\pi$
$152$		0			0
$153$	0.0679613	+	0.0119238i	0.00549435	+	0.000963981i
$154$		0			0
$155$	2.02551	−	0.737225i	0.162693	−	0.0592153i
$156$		0			0
$157$	−0.0493091	+	0.0413752i	−0.00393529	+	0.00330210i	−0.644753	−	0.764391i	$-0.723040\pi$
$157$	−0.0493091	+	0.0413752i	−0.00393529	+	0.00330210i	0.640818	+	0.767693i	$0.278595\pi$
$158$		0			0
$159$	4.57010	−	2.13344i	0.362432	−	0.169193i
$160$		0			0
$161$	−3.69849			−0.291482
$162$		0			0
$163$	−22.7447			−1.78150			−0.890750	−	0.454494i	$-0.849820\pi$
$163$	−22.7447			−1.78150			−0.890750	+	0.454494i	$0.849820\pi$
$164$		0			0
$165$	−1.62378	+	0.758021i	−0.126411	+	0.0590119i
$166$		0			0
$167$	−8.55520	+	7.17866i	−0.662021	+	0.555502i	−0.910692	−	0.413087i	$-0.864451\pi$
$167$	−8.55520	+	7.17866i	−0.662021	+	0.555502i	0.248671	+	0.968588i	$0.420006\pi$
$168$		0			0
$169$	−2.88733	+	1.05090i	−0.222103	+	0.0808388i
$170$		0			0
$171$	−2.57867	−	7.06613i	−0.197196	−	0.540360i
$172$		0			0
$173$	5.20576	+	4.36815i	0.395787	+	0.332105i	0.818862	−	0.573990i	$-0.194605\pi$
$173$	5.20576	+	4.36815i	0.395787	+	0.332105i	−0.423076	+	0.906094i	$0.639050\pi$
$174$		0			0
$175$	0.442383	+	2.50888i	0.0334410	+	0.189653i
$176$		0			0
$177$	−2.88568	+	6.19525i	−0.216901	+	0.465664i
$178$		0			0
$179$	3.76377	+	6.51905i	0.281318	+	0.487257i	0.971710	−	0.236179i	$-0.0758952\pi$
$179$	3.76377	+	6.51905i	0.281318	+	0.487257i	−0.690392	+	0.723436i	$0.742562\pi$
$180$		0			0
$181$	6.74838	−	11.6885i	0.501603	−	0.868802i	−0.498395	−	0.866950i	$-0.666077\pi$
$181$	6.74838	−	11.6885i	0.501603	−	0.868802i	0.999998	−	0.00185197i	$-0.000589500\pi$
$182$		0			0
$183$	−11.9300	+	11.9402i	−0.881893	+	0.882644i
$184$		0			0
$185$	3.58032	+	1.30313i	0.263230	+	0.0958080i
$186$		0			0
$187$	0.00777695	−	0.0441053i	0.000568707	−	0.00322530i
$188$		0			0
$189$	−0.248123	−	2.79496i	−0.0180483	−	0.203303i
$190$		0			0
$191$	3.69323	−	20.9454i	0.267233	−	1.51555i	−0.495367	−	0.868684i	$-0.664966\pi$
$191$	3.69323	−	20.9454i	0.267233	−	1.51555i	0.762600	−	0.646870i	$-0.223922\pi$
$192$		0			0
$193$	−10.1549	−	3.69607i	−0.730963	−	0.266049i	−0.0503903	−	0.998730i	$-0.516047\pi$
$193$	−10.1549	−	3.69607i	−0.730963	−	0.266049i	−0.680572	+	0.732681i	$0.738269\pi$
$194$		0			0
$195$	3.56417	+	0.953392i	0.255236	+	0.0682738i
$196$		0			0
$197$	−8.72052	+	15.1044i	−0.621312	+	1.07614i	0.367930	+	0.929853i	$0.380067\pi$
$197$	−8.72052	+	15.1044i	−0.621312	+	1.07614i	−0.989242	+	0.146290i	$0.953267\pi$
$198$		0			0
$199$	4.94919	+	8.57226i	0.350839	+	0.607671i	0.986397	−	0.164382i	$-0.0525631\pi$
$199$	4.94919	+	8.57226i	0.350839	+	0.607671i	−0.635558	+	0.772053i	$0.719230\pi$
$200$		0			0
$201$	10.7840	+	15.3872i	0.760644	+	1.08533i
$202$		0			0
$203$	0.560071	+	3.17632i	0.0393093	+	0.222934i
$204$		0			0
$205$	−3.06719	−	2.57368i	−0.214222	−	0.179754i
$206$		0			0
$207$	−17.7854	+	10.2886i	−1.23617	+	0.715108i
$208$		0			0
$209$	−4.58786	+	1.66984i	−0.317349	+	0.115505i
$210$		0			0
$211$	−9.43861	+	7.91994i	−0.649781	+	0.545231i	−0.907004	−	0.421121i	$-0.861637\pi$
$211$	−9.43861	+	7.91994i	−0.649781	+	0.545231i	0.257224	+	0.966352i	$0.417192\pi$
$212$		0			0
$213$	6.53083	+	4.56879i	0.447485	+	0.313049i
$214$		0			0
$215$	−2.93477			−0.200150
$216$		0			0
$217$	2.19071			0.148715
$218$		0			0
$219$	2.51287	−	28.8637i	0.169804	−	1.95043i
$220$		0			0
$221$	−0.0706353	+	0.0592700i	−0.00475144	+	0.00398693i
$222$		0			0
$223$	9.23512	−	3.36131i	0.618430	−	0.225090i	−0.0137579	−	0.999905i	$-0.504379\pi$
$223$	9.23512	−	3.36131i	0.618430	−	0.225090i	0.632188	+	0.774815i	$0.282157\pi$
$224$		0			0
$225$	9.10665	+	10.8341i	0.607110	+	0.722276i
$226$		0			0
$227$	8.62308	+	7.23563i	0.572334	+	0.480245i	0.882420	−	0.470463i	$-0.155913\pi$
$227$	8.62308	+	7.23563i	0.572334	+	0.480245i	−0.310085	+	0.950709i	$0.600358\pi$
$228$		0			0
$229$	−1.46437	−	8.30488i	−0.0967685	−	0.548802i	−0.994191	−	0.107630i	$-0.965674\pi$
$229$	−1.46437	−	8.30488i	−0.0967685	−	0.548802i	0.897423	−	0.441172i	$-0.145437\pi$
$230$		0			0
$231$	−1.81427	+	0.159506i	−0.119370	+	0.0104947i
$232$		0			0
$233$	−6.66670	−	11.5471i	−0.436750	−	0.756474i	0.560686	−	0.828028i	$-0.310537\pi$
$233$	−6.66670	−	11.5471i	−0.436750	−	0.756474i	−0.997437	+	0.0715546i	$0.977204\pi$
$234$		0			0
$235$	−2.96110	+	5.12877i	−0.193161	+	0.334564i
$236$		0			0
$237$	−5.78849	−	21.5662i	−0.376003	−	1.40088i
$238$		0			0
$239$	−1.14161	−	0.415513i	−0.0738449	−	0.0268773i	0.304834	−	0.952406i	$-0.401399\pi$
$239$	−1.14161	−	0.415513i	−0.0738449	−	0.0268773i	−0.378678	+	0.925528i	$0.623621\pi$
$240$		0			0
$241$	−2.93753	+	16.6596i	−0.189223	+	1.07314i	0.731185	+	0.682179i	$0.238967\pi$
$241$	−2.93753	+	16.6596i	−0.189223	+	1.07314i	−0.920408	+	0.390958i	$0.872144\pi$
$242$		0			0
$243$	−8.96832	−	12.7503i	−0.575318	−	0.817930i
$244$		0			0
$245$	−0.618942	+	3.51020i	−0.0395428	+	0.224258i
$246$		0			0
$247$	9.44579	+	3.43799i	0.601021	+	0.218754i
$248$		0			0
$249$	0.864604	+	3.22126i	0.0547920	+	0.204139i
$250$		0			0
$251$	4.37020	−	7.56941i	0.275845	−	0.477777i	−0.694503	−	0.719490i	$-0.744376\pi$
$251$	4.37020	−	7.56941i	0.275845	−	0.477777i	0.970348	+	0.241713i	$0.0777092\pi$
$252$		0			0
$253$	6.66824	+	11.5497i	0.419228	+	0.726125i
$254$		0			0
$255$	0.0210850	−	0.00185374i	0.00132040	−	0.000116086i
$256$		0			0
$257$	3.44075	+	19.5135i	0.214628	+	1.21722i	0.881551	+	0.472089i	$0.156500\pi$
$257$	3.44075	+	19.5135i	0.214628	+	1.21722i	−0.666923	+	0.745127i	$0.732389\pi$
$258$		0			0
$259$	2.96638	+	2.48909i	0.184322	+	0.154664i
$260$		0			0
$261$	11.5293	+	13.7164i	0.713647	+	0.849023i
$262$		0			0
$263$	−16.6335	+	6.05410i	−1.02567	+	0.373312i	−0.799429	−	0.600761i	$-0.794864\pi$
$263$	−16.6335	+	6.05410i	−1.02567	+	0.373312i	−0.226237	+	0.974072i	$0.572642\pi$
$264$		0			0
$265$	1.18520	−	0.994498i	0.0728061	−	0.0610915i
$266$		0			0
$267$	1.10803	−	12.7272i	0.0678104	−	0.778894i
$268$		0			0
$269$	−16.9166			−1.03142			−0.515711	−	0.856763i	$-0.672472\pi$
$269$	−16.9166			−1.03142			−0.515711	+	0.856763i	$0.672472\pi$
$270$		0			0
$271$	−23.1866			−1.40848			−0.704242	−	0.709960i	$-0.748713\pi$
$271$	−23.1866			−1.40848			−0.704242	+	0.709960i	$0.748713\pi$
$272$		0			0
$273$	3.07253	+	2.14946i	0.185958	+	0.130091i
$274$		0			0
$275$	7.03718	−	5.90490i	0.424358	−	0.356079i
$276$		0			0
$277$	13.7744	−	5.01349i	0.827626	−	0.301231i	0.106742	−	0.994287i	$-0.465958\pi$
$277$	13.7744	−	5.01349i	0.827626	−	0.301231i	0.720884	+	0.693056i	$0.243736\pi$
$278$		0			0
$279$	10.5348	−	6.09422i	0.630701	−	0.364851i
$280$		0			0
$281$	−16.4506	−	13.8037i	−0.981361	−	0.823459i	0.00293356	−	0.999996i	$-0.499066\pi$
$281$	−16.4506	−	13.8037i	−0.981361	−	0.823459i	−0.984294	+	0.176536i	$0.943511\pi$
$282$		0			0
$283$	0.691736	+	3.92303i	0.0411194	+	0.233200i	0.998440	−	0.0558268i	$-0.0177795\pi$
$283$	0.691736	+	3.92303i	0.0411194	+	0.233200i	−0.957321	+	0.289027i	$0.906668\pi$
$284$		0			0
$285$	−1.32430	−	1.88958i	−0.0784447	−	0.111929i
$286$		0			0
$287$	−2.03467	−	3.52415i	−0.120103	−	0.208024i
$288$		0			0
$289$	8.49974	−	14.7220i	0.499984	−	0.865998i
$290$		0			0
$291$	−5.08391	−	1.35991i	−0.298024	−	0.0797194i
$292$		0			0
$293$	−19.9946	−	7.27742i	−1.16809	−	0.425152i	−0.316112	−	0.948722i	$-0.602377\pi$
$293$	−19.9946	−	7.27742i	−1.16809	−	0.425152i	−0.851982	+	0.523570i	$0.824600\pi$
$294$		0			0
$295$	−0.364056	+	2.06466i	−0.0211962	+	0.120209i
$296$		0			0
$297$	−8.28081	+	5.81405i	−0.480501	+	0.337366i
$298$		0			0
$299$	4.76804	−	27.0409i	0.275743	−	1.56381i
$300$		0			0
$301$	−2.80284	−	1.02015i	−0.161553	−	0.0588004i
$302$		0			0
$303$	8.68652	−	8.69391i	0.499027	−	0.499452i
$304$		0			0
$305$	−2.58888	+	4.48408i	−0.148239	+	0.256757i
$306$		0			0
$307$	16.6925	+	28.9123i	0.952691	+	1.65011i	0.739565	+	0.673085i	$0.235031\pi$
$307$	16.6925	+	28.9123i	0.952691	+	1.65011i	0.213127	+	0.977025i	$0.431635\pi$
$308$		0			0
$309$	2.91478	−	6.25773i	0.165816	−	0.355990i
$310$		0			0
$311$	1.40854	+	7.98820i	0.0798707	+	0.452969i	0.998346	+	0.0574910i	$0.0183101\pi$
$311$	1.40854	+	7.98820i	0.0798707	+	0.452969i	−0.918475	+	0.395478i	$0.870579\pi$
$312$		0			0
$313$	24.3700	+	20.4488i	1.37747	+	1.15584i	0.970137	+	0.242557i	$0.0779860\pi$
$313$	24.3700	+	20.4488i	1.37747	+	1.15584i	0.407334	+	0.913279i	$0.366458\pi$
$314$		0			0
$315$	−0.295085	−	0.808597i	−0.0166261	−	0.0455593i
$316$		0			0
$317$	26.9610	−	9.81300i	1.51428	−	0.551153i	0.554569	−	0.832138i	$-0.312883\pi$
$317$	26.9610	−	9.81300i	1.51428	−	0.551153i	0.959712	+	0.280985i	$0.0906610\pi$
$318$		0			0
$319$	8.90931	−	7.47580i	0.498825	−	0.418564i
$320$		0			0
$321$	32.2389	−	15.0499i	1.79940	−	0.840006i
$322$		0			0
$323$	0.0576678			0.00320872
$324$		0			0
$325$	−18.9136			−1.04914
$326$		0			0
$327$	−0.958664	+	0.447529i	−0.0530142	+	0.0247484i
$328$		0			0
$329$	−4.61077	+	3.86890i	−0.254200	+	0.213299i
$330$		0			0
$331$	2.12514	−	0.773487i	0.116808	−	0.0425147i	−0.282955	−	0.959133i	$-0.591315\pi$
$331$	2.12514	−	0.773487i	0.116808	−	0.0425147i	0.399763	+	0.916619i	$0.369092\pi$
$332$		0			0
$333$	21.1891	+	3.71761i	1.16115	+	0.203724i
$334$		0			0
$335$	4.41549	+	3.70504i	0.241244	+	0.202428i
$336$		0			0
$337$	−1.36067	−	7.71672i	−0.0741202	−	0.420356i	−0.999178	−	0.0405308i	$-0.987095\pi$
$337$	−1.36067	−	7.71672i	−0.0741202	−	0.420356i	0.925058	−	0.379826i	$-0.124016\pi$
$338$		0			0
$339$	11.0620	−	23.7488i	0.600803	−	1.28986i
$340$		0			0
$341$	−3.94977	−	6.84121i	−0.213892	−	0.370472i
$342$		0			0
$343$	−3.70131	+	6.41085i	−0.199852	+	0.346153i
$344$		0			0
$345$	−4.45500	+	4.45880i	−0.239849	+	0.240053i
$346$		0			0
$347$	12.4412	+	4.52822i	0.667878	+	0.243088i	0.653634	−	0.756811i	$-0.273244\pi$
$347$	12.4412	+	4.52822i	0.667878	+	0.243088i	0.0142441	+	0.999899i	$0.495466\pi$
$348$		0			0
$349$	1.63948	−	9.29794i	0.0877592	−	0.497707i	−0.908968	−	0.416866i	$-0.863128\pi$
$349$	1.63948	−	9.29794i	0.0877592	−	0.497707i	0.996727	−	0.0808409i	$-0.0257606\pi$
$350$		0			0
$351$	20.7548	+	1.78911i	1.10781	+	0.0954956i
$352$		0			0
$353$	−3.58649	+	20.3400i	−0.190890	+	1.08259i	0.727262	+	0.686360i	$0.240793\pi$
$353$	−3.58649	+	20.3400i	−0.190890	+	1.08259i	−0.918151	+	0.396230i	$0.870318\pi$
$354$		0			0
$355$	2.29753	+	0.836232i	0.121940	+	0.0443826i
$356$		0			0
$357$	0.0207815	+	0.00555890i	0.00109987	+	0.000294208i
$358$		0			0
$359$	−3.88171	+	6.72332i	−0.204869	+	0.354843i	−0.950091	−	0.311973i	$-0.899010\pi$
$359$	−3.88171	+	6.72332i	−0.204869	+	0.354843i	0.745222	+	0.666816i	$0.232343\pi$
$360$		0			0
$361$	6.35668	+	11.0101i	0.334562	+	0.579479i
$362$		0			0
$363$	−7.16557	−	10.2242i	−0.376095	−	0.536633i
$364$		0			0
$365$	−1.54334	−	8.75274i	−0.0807823	−	0.458139i
$366$		0			0
$367$	20.9844	+	17.6080i	1.09537	+	0.919128i	0.997105	−	0.0760318i	$-0.0242250\pi$
$367$	20.9844	+	17.6080i	1.09537	+	0.919128i	0.0982688	+	0.995160i	$0.468669\pi$
$368$		0			0
$369$	−19.5880	−	11.2869i	−1.01971	−	0.587575i
$370$		0			0
$371$	1.47761	−	0.537806i	0.0767136	−	0.0279215i
$372$		0			0
$373$	24.1285	−	20.2462i	1.24933	−	1.04831i	0.252589	−	0.967574i	$-0.418718\pi$
$373$	24.1285	−	20.2462i	1.24933	−	1.04831i	0.996736	−	0.0807346i	$-0.0257266\pi$
$374$		0			0
$375$	7.32789	+	5.12640i	0.378411	+	0.264726i
$376$		0			0
$377$	−23.9452			−1.23324
$378$		0			0
$379$	−11.1373			−0.572085			−0.286042	−	0.958217i	$-0.592340\pi$
$379$	−11.1373			−0.572085			−0.286042	+	0.958217i	$0.592340\pi$
$380$		0			0
$381$	2.54452	−	29.2273i	0.130360	−	1.49736i
$382$		0			0
$383$	−7.96026	+	6.67945i	−0.406750	+	0.341304i	−0.823096	−	0.567902i	$-0.807755\pi$
$383$	−7.96026	+	6.67945i	−0.406750	+	0.341304i	0.416346	+	0.909206i	$0.363311\pi$
$384$		0			0
$385$	−0.525002	+	0.191085i	−0.0267566	+	0.00973859i
$386$		0			0
$387$	−16.3163	+	2.89132i	−0.829402	+	0.146974i
$388$		0			0
$389$	−18.8995	−	15.8585i	−0.958241	−	0.804060i	0.0224250	−	0.999749i	$-0.492861\pi$
$389$	−18.8995	−	15.8585i	−0.958241	−	0.804060i	−0.980666	+	0.195689i	$0.937306\pi$
$390$		0			0
$391$	−0.0273540	−	0.155132i	−0.00138335	−	0.00784536i
$392$		0			0
$393$	6.15891	−	0.541476i	0.310676	−	0.0273139i
$394$		0			0
$395$	−3.42492	−	5.93214i	−0.172327	−	0.298478i
$396$		0			0
$397$	−7.98926	+	13.8378i	−0.400970	+	0.694500i	−0.993843	−	0.110796i	$-0.964660\pi$
$397$	−7.98926	+	13.8378i	−0.400970	+	0.694500i	0.592873	+	0.805296i	$0.297993\pi$
$398$		0			0
$399$	−0.607930	−	2.26497i	−0.0304346	−	0.113390i
$400$		0			0
$401$	24.5701	+	8.94277i	1.22697	+	0.446581i	0.872559	−	0.488509i	$-0.162459\pi$
$401$	24.5701	+	8.94277i	1.22697	+	0.446581i	0.354411	+	0.935090i	$0.384681\pi$
$402$		0			0
$403$	−2.82424	+	16.0170i	−0.140685	+	0.797865i
$404$		0			0
$405$	−3.66840	−	3.06753i	−0.182284	−	0.152427i
$406$		0			0
$407$	2.42471	−	13.7512i	0.120188	−	0.681622i
$408$		0			0
$409$	−10.6899	−	3.89081i	−0.528582	−	0.192388i	0.0639233	−	0.997955i	$-0.479639\pi$
$409$	−10.6899	−	3.89081i	−0.528582	−	0.192388i	−0.592505	+	0.805567i	$0.701861\pi$
$410$		0			0
$411$	8.30307	+	30.9348i	0.409560	+	1.52590i
$412$		0			0
$413$	−1.06538	+	1.84529i	−0.0524240	+	0.0908010i
$414$		0			0
$415$	0.511567	+	0.886060i	0.0251118	+	0.0434950i
$416$		0			0
$417$	6.74006	−	0.592570i	0.330062	−	0.0290183i
$418$		0			0
$419$	3.46560	+	19.6544i	0.169306	+	0.960181i	0.944513	+	0.328474i	$0.106534\pi$
$419$	3.46560	+	19.6544i	0.169306	+	0.960181i	−0.775207	+	0.631707i	$0.782355\pi$
$420$		0			0
$421$	−13.1460	−	11.0308i	−0.640698	−	0.537610i	0.263534	−	0.964650i	$-0.415112\pi$
$421$	−13.1460	−	11.0308i	−0.640698	−	0.537610i	−0.904233	+	0.427040i	$0.859556\pi$
$422$		0			0
$423$	−11.4098	+	31.4313i	−0.554763	+	1.52824i
$424$		0			0
$425$	−0.101962	+	0.0371112i	−0.00494590	+	0.00180016i
$426$		0			0
$427$	−4.03119	+	3.38257i	−0.195083	+	0.163694i
$428$		0			0
$429$	1.17273	−	13.4704i	0.0566199	−	0.650356i
$430$		0			0
$431$	−27.2090			−1.31061			−0.655305	−	0.755364i	$-0.727460\pi$
$431$	−27.2090			−1.31061			−0.655305	+	0.755364i	$0.727460\pi$
$432$		0			0
$433$	−12.8378			−0.616946			−0.308473	−	0.951233i	$-0.599818\pi$
$433$	−12.8378			−0.616946			−0.308473	+	0.951233i	$0.599818\pi$
$434$		0			0
$435$	4.50392	+	3.15082i	0.215946	+	0.151070i
$436$		0			0
$437$	−13.1549	+	11.0383i	−0.629286	+	0.528034i
$438$		0			0
$439$	0.00559152	−	0.00203515i	0.000266869	−	9.71322e-5i	−0.341887	−	0.939741i	$-0.611066\pi$
$439$	0.00559152	−	0.00203515i	0.000266869	−	9.71322e-5i	0.342154	+	0.939644i	$0.388844\pi$
$440$		0			0
$441$	0.0171293	+	20.1252i	0.000815680	+	0.958342i
$442$		0			0
$443$	4.14128	+	3.47494i	0.196758	+	0.165100i	0.735844	−	0.677151i	$-0.236786\pi$
$443$	4.14128	+	3.47494i	0.196758	+	0.165100i	−0.539086	+	0.842251i	$0.681230\pi$
$444$		0			0
$445$	−0.680526	−	3.85945i	−0.0322600	−	0.182956i
$446$		0			0
$447$	−11.4067	−	16.2757i	−0.539519	−	0.769815i
$448$		0			0
$449$	−11.0666	−	19.1679i	−0.522266	−	0.904591i	−0.999664	−	0.0259043i	$-0.991753\pi$
$449$	−11.0666	−	19.1679i	−0.522266	−	0.904591i	0.477398	−	0.878687i	$-0.341580\pi$
$450$		0			0
$451$	−7.33687	+	12.7078i	−0.345480	+	0.598389i
$452$		0			0
$453$	−18.6396	−	4.98598i	−0.875767	−	0.234262i
$454$		0			0
$455$	1.08091	+	0.393419i	0.0506738	+	0.0184438i
$456$		0			0
$457$	0.909089	−	5.15570i	0.0425254	−	0.241174i	−0.956134	−	0.292928i	$-0.905370\pi$
$457$	0.909089	−	5.15570i	0.0425254	−	0.241174i	0.998660	+	0.0517547i	$0.0164814\pi$
$458$		0			0
$459$	0.115399	−	0.0310789i	0.00538635	−	0.00145064i
$460$		0			0
$461$	4.77901	−	27.1031i	0.222581	−	1.26232i	−0.644675	−	0.764457i	$-0.723007\pi$
$461$	4.77901	−	27.1031i	0.222581	−	1.26232i	0.867256	−	0.497862i	$-0.165882\pi$
$462$		0			0
$463$	−18.3576	−	6.68163i	−0.853152	−	0.310522i	−0.121827	−	0.992551i	$-0.538875\pi$
$463$	−18.3576	−	6.68163i	−0.853152	−	0.310522i	−0.731325	+	0.682029i	$0.761098\pi$
$464$		0			0
$465$	2.63882	−	2.64106i	0.122372	−	0.122476i
$466$		0			0
$467$	−14.9293	+	25.8582i	−0.690844	+	1.19658i	0.280718	+	0.959790i	$0.409428\pi$
$467$	−14.9293	+	25.8582i	−0.690844	+	1.19658i	−0.971562	+	0.236787i	$0.923906\pi$
$468$		0			0
$469$	2.92909	+	5.07333i	0.135253	+	0.234264i
$470$		0			0
$471$	−0.0470744	+	0.101064i	−0.00216908	+	0.00465677i
$472$		0			0
$473$	1.86766	+	10.5921i	0.0858753	+	0.487023i
$474$		0			0
$475$	9.06134	+	7.60337i	0.415763	+	0.348867i
$476$		0			0
$477$	5.60949	−	6.69669i	0.256841	−	0.306620i
$478$		0			0
$479$	3.36367	−	1.22428i	0.153690	−	0.0559387i	−0.264029	−	0.964515i	$-0.585052\pi$
$479$	3.36367	−	1.22428i	0.153690	−	0.0559387i	0.417720	+	0.908576i	$0.362829\pi$
$480$		0			0
$481$	−22.0228	+	18.4793i	−1.00415	+	0.842583i
$482$		0			0
$483$	−5.80463	+	2.70975i	−0.264120	+	0.123298i
$484$		0			0
$485$	−1.61438			−0.0733051
$486$		0			0
$487$	6.26631			0.283954			0.141977	−	0.989870i	$-0.454654\pi$
$487$	6.26631			0.283954			0.141977	+	0.989870i	$0.454654\pi$
$488$		0			0
$489$	−35.6968	+	16.6642i	−1.61427	+	0.753581i
$490$		0			0
$491$	2.83119	−	2.37565i	0.127770	−	0.107212i	−0.576663	−	0.816982i	$-0.695646\pi$
$491$	2.83119	−	2.37565i	0.127770	−	0.107212i	0.704433	+	0.709770i	$0.251201\pi$
$492$		0			0
$493$	−0.129088	+	0.0469841i	−0.00581382	+	0.00211606i
$494$		0			0
$495$	−1.99308	+	2.37937i	−0.0895822	+	0.106945i
$496$		0			0
$497$	1.90356	+	1.59727i	0.0853862	+	0.0716475i
$498$		0			0
$499$	−4.73894	−	26.8759i	−0.212144	−	1.20313i	−0.885794	−	0.464078i	$-0.846386\pi$
$499$	−4.73894	−	26.8759i	−0.212144	−	1.20313i	0.673650	−	0.739050i	$-0.264725\pi$
$500$		0			0
$501$	−8.16748	+	17.5347i	−0.364896	+	0.783393i
$502$		0			0
$503$	4.35623	+	7.54521i	0.194235	+	0.336424i	0.946649	−	0.322265i	$-0.104444\pi$
$503$	4.35623	+	7.54521i	0.194235	+	0.336424i	−0.752415	+	0.658690i	$0.771111\pi$
$504$		0			0
$505$	1.88502	−	3.26495i	0.0838823	−	0.145288i
$506$		0			0
$507$	−3.76160	+	3.76480i	−0.167058	+	0.167201i
$508$		0			0
$509$	15.1415	+	5.51106i	0.671135	+	0.244273i	0.655037	−	0.755597i	$-0.272653\pi$
$509$	15.1415	+	5.51106i	0.671135	+	0.244273i	0.0160987	+	0.999870i	$0.494875\pi$
$510$		0			0
$511$	1.56855	−	8.89572i	0.0693888	−	0.393523i
$512$		0			0
$513$	−9.22422	−	9.20070i	−0.407259	−	0.406221i
$514$		0			0
$515$	0.367727	−	2.08548i	0.0162040	−	0.0918974i
$516$		0			0
$517$	20.3949	+	7.42315i	0.896968	+	0.326470i
$518$		0			0
$519$	11.3706	+	3.04156i	0.499115	+	0.133510i
$520$		0			0
$521$	4.12681	−	7.14785i	0.180799	−	0.313153i	−0.761354	−	0.648337i	$-0.775465\pi$
$521$	4.12681	−	7.14785i	0.180799	−	0.313153i	0.942153	+	0.335184i	$0.108798\pi$
$522$		0			0
$523$	−11.3557	−	19.6687i	−0.496552	−	0.860053i	0.503440	−	0.864030i	$-0.332067\pi$
$523$	−11.3557	−	19.6687i	−0.496552	−	0.860053i	−0.999992	+	0.00397719i	$0.998734\pi$
$524$		0			0
$525$	2.53247	+	3.61346i	0.110526	+	0.157704i
$526$		0			0
$527$	0.0162025	+	0.0918888i	0.000705791	+	0.00400274i
$528$		0			0
$529$	18.3150	+	15.3681i	0.796303	+	0.668178i
$530$		0			0
$531$	0.0100753	+	11.8374i	0.000437230	+	0.513701i
$532$		0			0
$533$	28.3893	−	10.3329i	1.22968	−	0.447566i
$534$		0			0
$535$	8.36075	−	7.01550i	0.361467	−	0.303307i
$536$		0			0
$537$	10.6834	+	7.47380i	0.461021	+	0.322518i
$538$		0			0
$539$	13.0627			0.562651
$540$		0			0
$541$	−30.5412			−1.31307			−0.656535	−	0.754296i	$-0.727979\pi$
$541$	−30.5412			−1.31307			−0.656535	+	0.754296i	$0.727979\pi$
$542$		0			0
$543$	2.02753	−	23.2890i	0.0870098	−	0.999426i
$544$		0			0
$545$	−0.248617	+	0.208615i	−0.0106496	+	0.00893607i
$546$		0			0
$547$	7.98634	−	2.90679i	0.341471	−	0.124285i	−0.165592	−	0.986194i	$-0.552953\pi$
$547$	7.98634	−	2.90679i	0.341471	−	0.124285i	0.507063	+	0.861909i	$0.330731\pi$
$548$		0			0
$549$	−9.97555	+	27.4804i	−0.425746	+	1.17283i
$550$		0			0
$551$	11.4720	+	9.62612i	0.488722	+	0.410087i
$552$		0			0
$553$	−1.20889	−	6.85598i	−0.0514074	−	0.291546i
$554$		0			0
$555$	6.57392	−	0.577963i	0.279047	−	0.0245331i
$556$		0			0
$557$	22.6254	+	39.1884i	0.958670	+	1.66046i	0.725738	+	0.687971i	$0.241498\pi$
$557$	22.6254	+	39.1884i	0.958670	+	1.66046i	0.232932	+	0.972493i	$0.425168\pi$
$558$		0			0
$559$	11.0720	−	19.1773i	0.468297	−	0.811114i
$560$		0			0
$561$	−0.0201088	−	0.0749194i	−0.000848993	−	0.00316310i
$562$		0			0
$563$	−7.44046	−	2.70811i	−0.313578	−	0.114133i	0.180437	−	0.983587i	$-0.442249\pi$
$563$	−7.44046	−	2.70811i	−0.313578	−	0.114133i	−0.494015	+	0.869454i	$0.664471\pi$
$564$		0			0
$565$	1.39557	−	7.91467i	0.0587121	−	0.332973i
$566$		0			0
$567$	−2.43719	−	4.20479i	−0.102352	−	0.176584i
$568$		0			0
$569$	−1.95131	+	11.0664i	−0.0818030	+	0.463928i	0.916198	+	0.400726i	$0.131242\pi$
$569$	−1.95131	+	11.0664i	−0.0818030	+	0.463928i	−0.998001	+	0.0632016i	$0.979869\pi$
$570$		0			0
$571$	−17.9192	−	6.52205i	−0.749895	−	0.272939i	−0.0613332	−	0.998117i	$-0.519535\pi$
$571$	−17.9192	−	6.52205i	−0.749895	−	0.272939i	−0.688561	+	0.725178i	$0.741757\pi$
$572$		0			0
$573$	−9.54954	−	35.5788i	−0.398938	−	1.48633i
$574$		0			0
$575$	16.1557	−	27.9825i	0.673739	−	1.16695i
$576$		0			0
$577$	−3.61313	−	6.25813i	−0.150417	−	0.260529i	0.780964	−	0.624576i	$-0.214728\pi$
$577$	−3.61313	−	6.25813i	−0.150417	−	0.260529i	−0.931381	+	0.364047i	$0.881395\pi$
$578$		0			0
$579$	−18.6456	+	1.63928i	−0.774885	+	0.0681260i
$580$		0			0
$581$	0.180568	+	1.02405i	0.00749120	+	0.0424847i
$582$		0			0
$583$	−4.34354	−	3.64467i	−0.179891	−	0.150947i
$584$		0			0
$585$	6.29234	−	1.11503i	0.260156	−	0.0461009i
$586$		0			0
$587$	−16.9995	+	6.18732i	−0.701645	+	0.255378i	−0.668113	−	0.744060i	$-0.732898\pi$
$587$	−16.9995	+	6.18732i	−0.701645	+	0.255378i	−0.0335319	+	0.999438i	$0.510676\pi$
$588$		0			0
$589$	7.79202	−	6.53828i	0.321065	−	0.269405i
$590$		0			0
$591$	−2.62006	+	30.0949i	−0.107775	+	1.23794i
$592$		0			0
$593$	40.6651			1.66992			0.834958	−	0.550313i	$-0.185492\pi$
$593$	40.6651			1.66992			0.834958	+	0.550313i	$0.185492\pi$
$594$		0			0
$595$	0.00659909			0.000270536
$596$		0			0
$597$	14.0481	+	9.82771i	0.574952	+	0.402221i
$598$		0			0
$599$	17.5898	−	14.7596i	0.718701	−	0.603062i	−0.208325	−	0.978060i	$-0.566801\pi$
$599$	17.5898	−	14.7596i	0.718701	−	0.603062i	0.927026	+	0.374998i	$0.122357\pi$
$600$		0			0
$601$	15.3025	−	5.56964i	0.624200	−	0.227190i	−0.0105049	−	0.999945i	$-0.503344\pi$
$601$	15.3025	−	5.56964i	0.624200	−	0.227190i	0.634705	+	0.772755i	$0.281122\pi$
$602$		0			0
$603$	28.1987	+	16.2485i	1.14834	+	0.661691i
$604$		0			0
$605$	−2.93393	−	2.46186i	−0.119281	−	0.100089i
$606$		0			0
$607$	−4.82780	−	27.3798i	−0.195954	−	1.11131i	−0.911053	−	0.412288i	$-0.864730\pi$
$607$	−4.82780	−	27.3798i	−0.195954	−	1.11131i	0.715099	−	0.699023i	$-0.246382\pi$
$608$		0			0
$609$	3.20619	+	4.57477i	0.129921	+	0.185379i
$610$		0			0
$611$	−22.3427	−	38.6986i	−0.903887	−	1.56558i
$612$		0			0
$613$	−12.1824	+	21.1005i	−0.492041	+	0.852239i	−0.999958	−	0.00916648i	$-0.997082\pi$
$613$	−12.1824	+	21.1005i	−0.492041	+	0.852239i	0.507917	+	0.861406i	$0.330416\pi$
$614$		0			0
$615$	−6.69948	−	1.79206i	−0.270149	−	0.0722630i
$616$		0			0
$617$	16.1430	+	5.87558i	0.649894	+	0.236542i	0.645867	−	0.763450i	$-0.276496\pi$
$617$	16.1430	+	5.87558i	0.649894	+	0.236542i	0.00402677	+	0.999992i	$0.498718\pi$
$618$		0			0
$619$	0.409119	−	2.32023i	0.0164439	−	0.0932580i	−0.975481	−	0.220082i	$-0.929367\pi$
$619$	0.409119	−	2.32023i	0.0164439	−	0.0932580i	0.991925	+	0.126824i	$0.0404785\pi$
$620$		0			0
$621$	−20.3754	+	29.1783i	−0.817636	+	1.17088i
$622$		0			0
$623$	0.691642	−	3.92250i	0.0277101	−	0.157152i
$624$		0			0
$625$	−19.5880	−	7.12944i	−0.783519	−	0.285178i
$626$		0			0
$627$	−5.97702	+	5.98211i	−0.238699	+	0.238903i
$628$		0			0
$629$	−0.0824648	+	0.142833i	−0.00328809	+	0.00569513i
$630$		0			0
$631$	−1.65693	−	2.86989i	−0.0659614	−	0.114249i	0.831159	−	0.556035i	$-0.187678\pi$
$631$	−1.65693	−	2.86989i	−0.0659614	−	0.114249i	−0.897120	+	0.441787i	$0.854345\pi$
$632$		0			0
$633$	−9.01086	+	19.3454i	−0.358150	+	0.768909i
$634$		0			0
$635$	−1.56279	−	8.86300i	−0.0620172	−	0.351717i
$636$		0			0
$637$	−20.6023	−	17.2874i	−0.816294	−	0.684952i
$638$		0			0
$639$	13.5973	+	2.38563i	0.537899	+	0.0943742i
$640$		0			0
$641$	31.1070	−	11.3220i	1.22865	−	0.447192i	0.355516	−	0.934670i	$-0.384305\pi$
$641$	31.1070	−	11.3220i	1.22865	−	0.447192i	0.873135	+	0.487478i	$0.162083\pi$
$642$		0			0
$643$	24.7924	−	20.8033i	0.977719	−	0.820403i	−0.00602498	−	0.999982i	$-0.501918\pi$
$643$	24.7924	−	20.8033i	0.977719	−	0.820403i	0.983744	+	0.179578i	$0.0574734\pi$
$644$		0			0
$645$	−4.60601	+	2.15020i	−0.181361	+	0.0846642i
$646$		0			0
$647$	−42.1528			−1.65720			−0.828599	−	0.559842i	$-0.810862\pi$
$647$	−42.1528			−1.65720			−0.828599	+	0.559842i	$0.810862\pi$
$648$		0			0
$649$	7.68337			0.301599
$650$		0			0
$651$	3.43824	−	1.60506i	0.134755	−	0.0629072i
$652$		0			0
$653$	1.84096	−	1.54475i	0.0720424	−	0.0604507i	−0.606055	−	0.795422i	$-0.707249\pi$
$653$	1.84096	−	1.54475i	0.0720424	−	0.0604507i	0.678098	+	0.734972i	$0.262805\pi$
$654$		0			0
$655$	1.78223	−	0.648677i	0.0696373	−	0.0253459i
$656$		0			0
$657$	−17.2036	−	47.1415i	−0.671175	−	1.83917i
$658$		0			0
$659$	32.9073	+	27.6125i	1.28188	+	1.07563i	0.992981	+	0.118271i	$0.0377351\pi$
$659$	32.9073	+	27.6125i	1.28188	+	1.07563i	0.288904	+	0.957358i	$0.406709\pi$
$660$		0			0
$661$	3.82263	+	21.6792i	0.148683	+	0.843224i	0.964336	+	0.264682i	$0.0852670\pi$
$661$	3.82263	+	21.6792i	0.148683	+	0.843224i	−0.815653	+	0.578542i	$0.803622\pi$
$662$		0			0
$663$	−0.0674342	+	0.144774i	−0.00261893	+	0.00562255i
$664$		0			0
$665$	−0.359699	−	0.623016i	−0.0139485	−	0.0241595i
$666$		0			0
$667$	20.4536	−	35.4267i	0.791968	−	1.37173i
$668$		0			0
$669$	12.0314	−	12.0417i	0.465162	−	0.465558i
$670$		0			0
$671$	17.8313	+	6.49005i	0.688368	+	0.250545i
$672$		0			0
$673$	−2.61712	+	14.8424i	−0.100883	+	0.572134i	0.891903	+	0.452228i	$0.149371\pi$
$673$	−2.61712	+	14.8424i	−0.100883	+	0.572134i	−0.992785	+	0.119906i	$0.961741\pi$
$674$		0			0
$675$	22.2303	+	10.3316i	0.855645	+	0.397665i
$676$		0			0
$677$	−1.44744	+	8.20885i	−0.0556297	+	0.315492i	−0.999907	−	0.0136602i	$-0.995652\pi$
$677$	−1.44744	+	8.20885i	−0.0556297	+	0.315492i	0.944277	+	0.329152i	$0.106763\pi$
$678$		0			0
$679$	−1.54180	−	0.561169i	−0.0591689	−	0.0215357i
$680$		0			0
$681$	18.8349	+	5.03820i	0.721753	+	0.193064i
$682$		0			0
$683$	−13.8381	+	23.9683i	−0.529501	+	0.917123i	0.469907	+	0.882716i	$0.344288\pi$
$683$	−13.8381	+	23.9683i	−0.529501	+	0.917123i	−0.999408	+	0.0344069i	$0.989046\pi$
$684$		0			0
$685$	4.91274	+	8.50912i	0.187706	+	0.325117i
$686$		0			0
$687$	−8.38296	−	11.9613i	−0.319830	−	0.456351i
$688$		0			0
$689$	2.02716	+	11.4966i	0.0772288	+	0.437986i
$690$		0			0
$691$	−30.1167	−	25.2709i	−1.14569	−	0.961350i	−0.146082	−	0.989272i	$-0.546666\pi$
$691$	−30.1167	−	25.2709i	−1.14569	−	0.961350i	−0.999610	+	0.0279223i	$0.991111\pi$
$692$		0			0
$693$	−2.73056	+	1.57959i	−0.103725	+	0.0600037i
$694$		0			0
$695$	1.95039	−	0.709886i	0.0739827	−	0.0269275i
$696$		0			0
$697$	0.132771	−	0.111408i	0.00502907	−	0.00421989i
$698$		0			0
$699$	−18.9232	−	13.2382i	−0.715743	−	0.500715i
$700$		0			0
$701$	45.9501			1.73551			0.867755	−	0.496992i	$-0.165562\pi$
$701$	45.9501			1.73551			0.867755	+	0.496992i	$0.165562\pi$
$702$		0			0
$703$	17.9797			0.678119
$704$		0			0
$705$	−0.889655	+	10.2189i	−0.0335063	+	0.384866i
$706$		0			0
$707$	2.93520	−	2.46292i	0.110389	−	0.0926277i
$708$		0			0
$709$	3.62722	−	1.32020i	0.136223	−	0.0495812i	−0.273009	−	0.962012i	$-0.588019\pi$
$709$	3.62722	−	1.32020i	0.136223	−	0.0495812i	0.409232	+	0.912430i	$0.365797\pi$
$710$		0			0
$711$	−24.8856	−	29.6063i	−0.933283	−	1.11032i
$712$		0			0
$713$	−21.2847	−	17.8600i	−0.797117	−	0.668861i
$714$		0			0
$715$	−0.720262	−	4.08481i	−0.0269363	−	0.152763i
$716$		0			0
$717$	−2.09615	+	0.184288i	−0.0782821	+	0.00688237i
$718$		0			0
$719$	20.2879	+	35.1397i	0.756612	+	1.31049i	0.944569	+	0.328313i	$0.106480\pi$
$719$	20.2879	+	35.1397i	0.756612	+	1.31049i	−0.187957	+	0.982177i	$0.560187\pi$
$720$		0			0
$721$	1.07612	−	1.86390i	0.0400770	−	0.0694153i
$722$		0			0
$723$	7.59554	+	28.2987i	0.282481	+	1.05244i
$724$		0			0
$725$	−26.4783	−	9.63732i	−0.983380	−	0.357921i
$726$		0			0
$727$	0.107065	−	0.607198i	0.00397083	−	0.0225197i	−0.982758	−	0.184897i	$-0.940805\pi$
$727$	0.107065	−	0.607198i	0.00397083	−	0.0225197i	0.986729	+	0.162377i	$0.0519161\pi$
$728$		0			0
$729$	−23.4171	−	13.4403i	−0.867299	−	0.497787i
$730$		0			0
$731$	0.0220601	−	0.125109i	0.000815923	−	0.00462733i
$732$		0			0
$733$	27.8770	+	10.1464i	1.02966	+	0.374766i	0.800952	−	0.598729i	$-0.204327\pi$
$733$	27.8770	+	10.1464i	1.02966	+	0.374766i	0.228709	+	0.973495i	$0.426549\pi$
$734$		0			0
$735$	1.60039	+	5.96259i	0.0590313	+	0.219933i
$736$		0			0
$737$	10.5621	−	18.2940i	0.389059	−	0.673869i
$738$		0			0
$739$	−5.07983	−	8.79853i	−0.186865	−	0.323659i	0.757339	−	0.653022i	$-0.226499\pi$
$739$	−5.07983	−	8.79853i	−0.186865	−	0.323659i	−0.944203	+	0.329363i	$0.893166\pi$
$740$		0			0
$741$	17.3437	−	1.52481i	0.637136	−	0.0560154i
$742$		0			0
$743$	−3.58215	−	20.3154i	−0.131416	−	0.745298i	−0.977289	−	0.211913i	$-0.932031\pi$
$743$	−3.58215	−	20.3154i	−0.131416	−	0.745298i	0.845872	−	0.533385i	$-0.179080\pi$
$744$		0			0
$745$	−4.67046	−	3.91898i	−0.171112	−	0.143580i
$746$		0			0
$747$	3.71706	+	4.42217i	0.136000	+	0.161799i
$748$		0			0
$749$	10.4235	−	3.79385i	0.380867	−	0.138624i
$750$		0			0
$751$	−36.3706	+	30.5186i	−1.32718	+	1.11364i	−0.342454	+	0.939534i	$0.611258\pi$
$751$	−36.3706	+	30.5186i	−1.32718	+	1.11364i	−0.984727	+	0.174103i	$0.944297\pi$
$752$		0			0
$753$	1.31302	−	15.0818i	0.0478490	−	0.549610i
$754$		0			0
$755$	−5.91896			−0.215413
$756$		0			0
$757$	8.19040			0.297685			0.148843	−	0.988861i	$-0.452445\pi$
$757$	8.19040			0.297685			0.148843	+	0.988861i	$0.452445\pi$
$758$		0			0
$759$	18.9276	+	13.2412i	0.687028	+	0.480627i
$760$		0			0
$761$	16.7935	−	14.0914i	0.608764	−	0.510813i	−0.285485	−	0.958383i	$-0.592155\pi$
$761$	16.7935	−	14.0914i	0.608764	−	0.510813i	0.894249	+	0.447570i	$0.147710\pi$
$762$		0			0
$763$	−0.309956	+	0.112815i	−0.0112212	+	0.00408417i
$764$		0			0
$765$	0.0317339	−	0.0183576i	0.00114734	−	0.000663721i
$766$		0			0
$767$	−12.1181	−	10.1683i	−0.437559	−	0.367155i
$768$		0			0
$769$	6.40139	+	36.3041i	0.230840	+	1.30916i	0.851200	+	0.524842i	$0.175875\pi$
$769$	6.40139	+	36.3041i	0.230840	+	1.30916i	−0.620360	+	0.784317i	$0.713013\pi$
$770$		0			0
$771$	19.6969	+	28.1047i	0.709368	+	1.01216i
$772$		0			0
$773$	2.99433	+	5.18633i	0.107699	+	0.186539i	0.914838	−	0.403822i	$-0.132319\pi$
$773$	2.99433	+	5.18633i	0.107699	+	0.186539i	−0.807139	+	0.590362i	$0.798985\pi$
$774$		0			0
$775$	−9.56944	+	16.5748i	−0.343745	+	0.595383i
$776$		0			0
$777$	6.47928	+	1.73316i	0.232443	+	0.0621769i
$778$		0			0
$779$	−17.7550	−	6.46229i	−0.636139	−	0.231536i
$780$		0			0
$781$	1.55596	−	8.82430i	0.0556767	−	0.315758i
$782$		0			0
$783$	28.1443	+	13.0802i	1.00580	+	0.467448i
$784$		0			0
$785$	−0.00593888	+	0.0336811i	−0.000211968	+	0.00120213i
$786$		0			0
$787$	8.66285	+	3.15302i	0.308797	+	0.112393i	0.491770	−	0.870725i	$-0.336350\pi$
$787$	8.66285	+	3.15302i	0.308797	+	0.112393i	−0.182973	+	0.983118i	$0.558572\pi$
$788$		0			0
$789$	−21.6700	+	21.6884i	−0.771472	+	0.772129i
$790$		0			0
$791$	4.08402	−	7.07374i	0.145211	−	0.251513i
$792$		0			0
$793$	−19.5341	−	33.8341i	−0.693678	−	1.20149i
$794$		0			0
$795$	1.13149	−	2.42918i	0.0401296	−	0.0861540i
$796$		0			0
$797$	5.43271	+	30.8104i	0.192436	+	1.09136i	0.916023	+	0.401127i	$0.131381\pi$
$797$	5.43271	+	30.8104i	0.192436	+	1.09136i	−0.723586	+	0.690234i	$0.757508\pi$
$798$		0			0
$799$	−0.196381	−	0.164783i	−0.00694746	−	0.00582961i
$800$		0			0
$801$	−7.58578	−	20.7867i	−0.268030	−	0.734461i
$802$		0			0
$803$	−30.6078	+	11.1403i	−1.08013	+	0.393134i
$804$		0			0
$805$	−1.50536	+	1.26314i	−0.0530569	+	0.0445200i
$806$		0			0
$807$	−26.5499	+	12.3942i	−0.934600	+	0.436296i
$808$		0			0
$809$	−20.2213			−0.710942			−0.355471	−	0.934687i	$-0.615680\pi$
$809$	−20.2213			−0.710942			−0.355471	+	0.934687i	$0.615680\pi$
$810$		0			0
$811$	52.9994			1.86106			0.930529	−	0.366217i	$-0.119347\pi$
$811$	52.9994			1.86106			0.930529	+	0.366217i	$0.119347\pi$
$812$		0			0
$813$	−36.3904	+	16.9880i	−1.27627	+	0.595794i
$814$		0			0
$815$	−9.25752	+	7.76798i	−0.324277	+	0.272101i
$816$		0			0
$817$	−13.0139	+	4.73668i	−0.455300	+	0.165715i
$818$		0			0
$819$	6.39705	+	1.12236i	0.223531	+	0.0392184i
$820$		0			0
$821$	−16.1506	−	13.5520i	−0.563660	−	0.472967i	0.315875	−	0.948801i	$-0.397702\pi$
$821$	−16.1506	−	13.5520i	−0.563660	−	0.472967i	−0.879535	+	0.475834i	$0.842146\pi$
$822$		0			0
$823$	−0.882347	−	5.00404i	−0.0307567	−	0.174430i	0.965560	−	0.260181i	$-0.0837822\pi$
$823$	−0.882347	−	5.00404i	−0.0307567	−	0.174430i	−0.996317	+	0.0857510i	$0.972671\pi$
$824$		0			0
$825$	6.71826	−	14.4234i	0.233900	−	0.502158i
$826$		0			0
$827$	−11.1938	−	19.3883i	−0.389248	−	0.674198i	0.603100	−	0.797665i	$-0.293932\pi$
$827$	−11.1938	−	19.3883i	−0.389248	−	0.674198i	−0.992349	+	0.123468i	$0.960599\pi$
$828$		0			0
$829$	−26.7151	+	46.2719i	−0.927853	+	1.60709i	−0.140945	+	0.990017i	$0.545014\pi$
$829$	−26.7151	+	46.2719i	−0.927853	+	1.60709i	−0.786908	+	0.617070i	$0.788319\pi$
$830$		0			0
$831$	17.9452	−	17.9605i	0.622513	−	0.623043i
$832$		0			0
$833$	−0.144987	−	0.0527709i	−0.00502350	−	0.00182840i
$834$		0			0
$835$	−1.03040	+	5.84371i	−0.0356586	+	0.202230i
$836$		0			0
$837$	12.0689	−	17.2831i	0.417162	−	0.597391i
$838$		0			0
$839$	−9.45716	+	53.6342i	−0.326498	+	1.85166i	0.172438	+	0.985020i	$0.444836\pi$
$839$	−9.45716	+	53.6342i	−0.326498	+	1.85166i	−0.498935	+	0.866639i	$0.666275\pi$
$840$		0			0
$841$	−6.27134	−	2.28258i	−0.216253	−	0.0787097i
$842$		0			0
$843$	−35.9320	−	9.61157i	−1.23756	−	0.331040i
$844$		0			0
$845$	−0.816287	+	1.41385i	−0.0280811	+	0.0486379i
$846$		0			0
$847$	−1.94627	−	3.37104i	−0.0668746	−	0.115830i
$848$		0			0
$849$	3.95991	+	5.65023i	0.135904	+	0.193915i
$850$		0			0
$851$	−8.52846	−	48.3673i	−0.292352	−	1.65801i
$852$		0			0
$853$	−4.87229	−	4.08833i	−0.166824	−	0.139982i	0.555554	−	0.831481i	$-0.312506\pi$
$853$	−4.87229	−	4.08833i	−0.166824	−	0.139982i	−0.722378	+	0.691499i	$0.756951\pi$
$854$		0			0
$855$	−3.46286	−	1.99536i	−0.118427	−	0.0682398i
$856$		0			0
$857$	−43.5806	+	15.8620i	−1.48868	+	0.541837i	−0.953103	−	0.302647i	$-0.902130\pi$
$857$	−43.5806	+	15.8620i	−1.48868	+	0.541837i	−0.535581	+	0.844484i	$0.679907\pi$
$858$		0			0
$859$	−13.5397	+	11.3612i	−0.461969	+	0.387638i	−0.843855	−	0.536571i	$-0.819719\pi$
$859$	−13.5397	+	11.3612i	−0.461969	+	0.387638i	0.381886	+	0.924210i	$0.375275\pi$
$860$		0			0
$861$	−5.77536	−	4.04029i	−0.196824	−	0.137693i
$862$		0			0
$863$	31.5490			1.07394			0.536970	−	0.843601i	$-0.319569\pi$
$863$	31.5490			1.07394			0.536970	+	0.843601i	$0.319569\pi$
$864$		0			0
$865$	3.61070			0.122768
$866$		0			0
$867$	2.55373	−	29.3330i	0.0867291	−	0.996201i
$868$		0			0
$869$	−19.2304	+	16.1362i	−0.652347	+	0.547384i
$870$		0			0
$871$	−40.8689	+	14.8751i	−1.38479	+	0.504022i
$872$		0			0
$873$	−8.97535	+	1.59047i	−0.303770	+	0.0538294i
$874$		0			0
$875$	2.13588	+	1.79222i	0.0722059	+	0.0605880i
$876$		0			0
$877$	3.30962	+	18.7698i	0.111758	+	0.633811i	0.988304	+	0.152494i	$0.0487305\pi$
$877$	3.30962	+	18.7698i	0.111758	+	0.633811i	−0.876546	+	0.481317i	$0.840158\pi$
$878$		0			0
$879$	−36.7125	+	3.22768i	−1.23828	+	0.108867i
$880$		0			0
$881$	−3.14816	−	5.45278i	−0.106064	−	0.183709i	0.808108	−	0.589034i	$-0.200492\pi$
$881$	−3.14816	−	5.45278i	−0.106064	−	0.183709i	−0.914173	+	0.405325i	$0.867158\pi$
$882$		0			0
$883$	2.93909	−	5.09065i	0.0989081	−	0.171314i	−0.812325	−	0.583205i	$-0.801798\pi$
$883$	2.93909	−	5.09065i	0.0989081	−	0.171314i	0.911233	+	0.411891i	$0.135132\pi$
$884$		0			0
$885$	0.941334	+	3.50714i	0.0316426	+	0.117891i
$886$		0			0
$887$	−16.1671	−	5.88433i	−0.542837	−	0.197576i	0.0560243	−	0.998429i	$-0.482158\pi$
$887$	−16.1671	−	5.88433i	−0.542837	−	0.197576i	−0.598861	+	0.800853i	$0.704380\pi$
$888$		0			0
$889$	1.58831	−	9.00778i	0.0532703	−	0.302111i
$890$		0			0
$891$	−8.73664	+	15.1920i	−0.292689	+	0.508950i
$892$		0			0
$893$	−4.85289	+	27.5221i	−0.162396	+	0.920992i
$894$		0			0
$895$	3.75838	+	1.36794i	0.125629	+	0.0457251i
$896$		0			0
$897$	−12.3286	−	45.9329i	−0.411642	−	1.53366i
$898$		0			0
$899$	−12.1152	+	20.9842i	−0.404066	+	0.699862i
$900$		0			0
$901$	0.0334865	+	0.0580003i	0.00111560	+	0.00193227i
$902$		0			0
$903$	−5.14636	+	0.452455i	−0.171260	+	0.0150568i
$904$		0			0
$905$	−1.24526	−	7.06224i	−0.0413939	−	0.234757i
$906$		0			0
$907$	33.3013	+	27.9431i	1.10575	+	0.927836i	0.997798	−	0.0663202i	$-0.0211259\pi$
$907$	33.3013	+	27.9431i	1.10575	+	0.927836i	0.107953	+	0.994156i	$0.465570\pi$
$908$		0			0
$909$	7.26342	−	20.0090i	0.240912	−	0.663658i
$910$		0			0
$911$	−14.5792	+	5.30638i	−0.483029	+	0.175808i	−0.572045	−	0.820222i	$-0.693850\pi$
$911$	−14.5792	+	5.30638i	−0.483029	+	0.175808i	0.0890165	+	0.996030i	$0.471628\pi$
$912$		0			0
$913$	2.87237	−	2.41020i	0.0950615	−	0.0797661i
$914$		0			0
$915$	−0.777824	+	8.93436i	−0.0257141	+	0.295361i
$916$		0			0
$917$	1.92759			0.0636545
$918$		0			0
$919$	23.3953			0.771741			0.385870	−	0.922553i	$-0.373901\pi$
$919$	23.3953			0.771741			0.385870	+	0.922553i	$0.373901\pi$
$920$		0			0
$921$	47.3812	+	33.1466i	1.56126	+	1.09222i
$922$		0			0
$923$	−14.1322	+	11.8584i	−0.465169	+	0.390323i
$924$		0			0
$925$	−31.7899	+	11.5706i	−1.04525	+	0.380439i
$926$		0			0
$927$	−0.0101769	−	11.9568i	−0.000334253	−	0.392713i
$928$		0			0
$929$	−16.2649	−	13.6479i	−0.533636	−	0.447773i	0.335719	−	0.941962i	$-0.391021\pi$
$929$	−16.2649	−	13.6479i	−0.533636	−	0.447773i	−0.869355	+	0.494189i	$0.835465\pi$
$930$		0			0
$931$	2.92077	+	16.5645i	0.0957245	+	0.542880i
$932$		0			0
$933$	8.06331	+	11.5052i	0.263981	+	0.376662i
$934$		0			0
$935$	−0.0118979	−	0.0206078i	−0.000389103	−	0.000673947i
$936$		0			0
$937$	12.4208	−	21.5135i	0.405771	−	0.702816i	−0.588640	−	0.808395i	$-0.700336\pi$
$937$	12.4208	−	21.5135i	0.405771	−	0.702816i	0.994411	+	0.105579i	$0.0336697\pi$
$938$		0			0
$939$	53.2298	+	14.2386i	1.73709	+	0.464659i
$940$		0			0
$941$	−52.6657	−	19.1687i	−1.71685	−	0.624883i	−0.719293	−	0.694707i	$-0.755534\pi$
$941$	−52.6657	−	19.1687i	−1.71685	−	0.624883i	−0.997559	+	0.0698233i	$0.977756\pi$
$942$		0			0
$943$	−8.96235	+	50.8280i	−0.291854	+	1.65519i
$944$		0			0
$945$	−1.05555	−	1.05286i	−0.0343372	−	0.0342496i
$946$		0			0
$947$	5.37737	−	30.4966i	0.174741	−	0.991007i	−0.763701	−	0.645570i	$-0.776620\pi$
$947$	5.37737	−	30.4966i	0.174741	−	0.991007i	0.938442	−	0.345436i	$-0.112269\pi$
$948$		0			0
$949$	63.0174	+	22.9365i	2.04563	+	0.744549i
$950$		0			0
$951$	35.1246	−	35.1545i	1.13899	−	1.13996i
$952$		0			0
$953$	24.2754	−	42.0462i	0.786357	−	1.36201i	−0.141828	−	0.989891i	$-0.545298\pi$
$953$	24.2754	−	42.0462i	0.786357	−	1.36201i	0.928185	−	0.372119i	$-0.121369\pi$
$954$		0			0
$955$	−5.65025	−	9.78653i	−0.182838	−	0.316685i
$956$		0			0
$957$	8.50555	−	18.2605i	0.274945	−	0.590278i
$958$		0			0
$959$	1.73405	+	9.83428i	0.0559954	+	0.317566i
$960$		0			0
$961$	−11.1399	−	9.34749i	−0.359352	−	0.301532i
$962$		0			0
$963$	39.5711	−	47.2406i	1.27516	−	1.52231i
$964$		0			0
$965$	−5.39554	+	1.96382i	−0.173689	+	0.0632175i
$966$		0			0
$967$	−1.21828	+	1.02226i	−0.0391772	+	0.0328736i	−0.662166	−	0.749357i	$-0.730363\pi$
$967$	−1.21828	+	1.02226i	−0.0391772	+	0.0328736i	0.622989	+	0.782231i	$0.285918\pi$
$968$		0			0
$969$	0.0905072	−	0.0422511i	0.00290751	−	0.00135730i
$970$		0			0
$971$	−5.28775			−0.169692			−0.0848460	−	0.996394i	$-0.527040\pi$
$971$	−5.28775			−0.169692			−0.0848460	+	0.996394i	$0.527040\pi$
$972$		0			0
$973$	2.10947			0.0676266
$974$		0			0
$975$	−29.6841	+	13.8573i	−0.950651	+	0.443788i
$976$		0			0
$977$	−3.44926	+	2.89428i	−0.110352	+	0.0925961i	−0.696294	−	0.717757i	$-0.745169\pi$
$977$	−3.44926	+	2.89428i	−0.110352	+	0.0925961i	0.585942	+	0.810353i	$0.300725\pi$
$978$		0			0
$979$	−13.4963	+	4.91224i	−0.431343	+	0.156996i
$980$		0			0
$981$	−1.17670	+	1.40476i	−0.0375690	+	0.0448504i
$982$		0			0
$983$	46.2595	+	38.8163i	1.47545	+	1.23805i	0.910886	+	0.412659i	$0.135400\pi$
$983$	46.2595	+	38.8163i	1.47545	+	1.23805i	0.564563	+	0.825390i	$0.309045\pi$
$984$		0			0
$985$	1.60918	+	9.12610i	0.0512727	+	0.290782i
$986$		0			0
$987$	−4.40182	+	9.45023i	−0.140111	+	0.300804i
$988$		0			0
$989$	18.9151	+	32.7620i	0.601466	+	1.04177i
$990$		0			0
$991$	−9.23926	+	16.0029i	−0.293495	+	0.508348i	−0.974634	−	0.223806i	$-0.928152\pi$
$991$	−9.23926	+	16.0029i	−0.293495	+	0.508348i	0.681139	+	0.732154i	$0.261485\pi$
$992$		0			0
$993$	2.76861	−	2.77097i	0.0878592	−	0.0879340i
$994$		0			0
$995$	4.94210	+	1.79878i	0.156675	+	0.0570251i
$996$		0			0
$997$	10.0734	−	57.1292i	0.319028	−	1.80930i	−0.229658	−	0.973271i	$-0.573761\pi$
$997$	10.0734	−	57.1292i	0.319028	−	1.80930i	0.548686	−	0.836028i	$-0.315128\pi$
$998$		0			0
$999$	35.9792	−	9.68984i	1.13833	−	0.306573i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.a.25.4	✓	24
3.2	odd	2		648.2.q.a.73.2		24
4.3	odd	2		432.2.u.e.241.1		24
27.11	odd	18		5832.2.a.i.1.5		12
27.13	even	9	inner	216.2.q.a.121.4	yes	24
27.14	odd	18		648.2.q.a.577.2		24
27.16	even	9		5832.2.a.h.1.8		12
108.67	odd	18		432.2.u.e.337.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.25.4	✓	24	1.1	even	1	trivial
216.2.q.a.121.4	yes	24	27.13	even	9	inner
432.2.u.e.241.1		24	4.3	odd	2
432.2.u.e.337.1		24	108.67	odd	18
648.2.q.a.73.2		24	3.2	odd	2
648.2.q.a.577.2		24	27.14	odd	18
5832.2.a.h.1.8		12	27.16	even	9
5832.2.a.i.1.5		12	27.11	odd	18

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.56946 - 0.732664i) q^{3} +(0.407020 - 0.341530i) q^{5} +(0.507439 - 0.184693i) q^{7} +(1.92641 - 2.29977i) q^{9} +O(q^{10})\)	\(q+(1.56946 - 0.732664i) q^{3} +(0.407020 - 0.341530i) q^{5} +(0.507439 - 0.184693i) q^{7} +(1.92641 - 2.29977i) q^{9} +(-1.49166 - 1.25165i) q^{11} +(0.696168 + 3.94816i) q^{13} +(0.388574 - 0.834226i) q^{15} +(0.0114999 + 0.0199184i) q^{17} +(1.25366 - 2.17140i) q^{19} +(0.661088 - 0.661651i) q^{21} +(-6.43593 - 2.34249i) q^{23} +(-0.819219 + 4.64602i) q^{25} +(1.33845 - 5.02081i) q^{27} +(-1.03716 + 5.88202i) q^{29} +(3.81218 + 1.38752i) q^{31} +(-3.25813 - 0.871529i) q^{33} +(0.143460 - 0.248479i) q^{35} +(3.58546 + 6.21019i) q^{37} +(3.98528 + 5.68642i) q^{39} +(-1.30857 - 7.42125i) q^{41} +(-4.23124 - 3.55043i) q^{43} +(-0.00135669 - 1.59398i) q^{45} +(-10.4739 + 3.81218i) q^{47} +(-5.13893 + 4.31207i) q^{49} +(0.0326421 + 0.0228356i) q^{51} +2.91189 q^{53} -1.03461 q^{55} +(0.376659 - 4.32643i) q^{57} +(-3.02267 + 2.53632i) q^{59} +(-9.15728 + 3.33298i) q^{61} +(0.552783 - 1.52279i) q^{63} +(1.63177 + 1.36922i) q^{65} +(1.88380 + 10.6835i) q^{67} +(-11.8172 + 1.03894i) q^{69} +(2.30083 + 3.98515i) q^{71} +(8.36375 - 14.4864i) q^{73} +(2.11824 + 7.89195i) q^{75} +(-0.988096 - 0.359638i) q^{77} +(2.23867 - 12.6961i) q^{79} +(-1.57792 - 8.86060i) q^{81} +(-0.334381 + 1.89637i) q^{83} +(0.0114834 + 0.00417962i) q^{85} +(2.68177 + 9.99148i) q^{87} +(3.68793 - 6.38768i) q^{89} +(1.08246 + 1.87488i) q^{91} +(6.99964 - 0.615391i) q^{93} +(-0.231335 - 1.31196i) q^{95} +(-2.32754 - 1.95304i) q^{97} +(-5.75205 + 1.01929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q - 3 * q^7 + 6 * q^9	\( 24 q - 3 q^{7} + 6 q^{9} + 6 q^{11} + 12 q^{13} - 3 q^{15} + 6 q^{17} + 9 q^{19} - 18 q^{21} + 24 q^{23} - 24 q^{25} - 9 q^{29} - 27 q^{31} + 21 q^{33} - 18 q^{35} + 15 q^{37} - 15 q^{39} - 6 q^{41} + 39 q^{43} - 69 q^{45} - 36 q^{47} + 3 q^{49} - 36 q^{51} - 18 q^{53} - 54 q^{55} + 27 q^{57} - 30 q^{59} + 12 q^{61} + 18 q^{63} - 18 q^{65} + 54 q^{67} - 57 q^{69} + 36 q^{73} - 51 q^{75} - 24 q^{77} - 45 q^{79} + 18 q^{81} + 33 q^{83} - 57 q^{85} + 90 q^{87} + 9 q^{89} + 39 q^{91} + 42 q^{93} + 87 q^{95} + 57 q^{97} - 24 q^{99}+O(q^{100}) \) 24 * q - 3 * q^7 + 6 * q^9 + 6 * q^11 + 12 * q^13 - 3 * q^15 + 6 * q^17 + 9 * q^19 - 18 * q^21 + 24 * q^23 - 24 * q^25 - 9 * q^29 - 27 * q^31 + 21 * q^33 - 18 * q^35 + 15 * q^37 - 15 * q^39 - 6 * q^41 + 39 * q^43 - 69 * q^45 - 36 * q^47 + 3 * q^49 - 36 * q^51 - 18 * q^53 - 54 * q^55 + 27 * q^57 - 30 * q^59 + 12 * q^61 + 18 * q^63 - 18 * q^65 + 54 * q^67 - 57 * q^69 + 36 * q^73 - 51 * q^75 - 24 * q^77 - 45 * q^79 + 18 * q^81 + 33 * q^83 - 57 * q^85 + 90 * q^87 + 9 * q^89 + 39 * q^91 + 42 * q^93 + 87 * q^95 + 57 * q^97 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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