LMFDB - Embedded newform 216.2.q.b.25.5

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			25.5
Character	$\chi$	$=$	216.25
Dual form			216.2.q.b.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59356 + 0.678655i) q^{3} +(1.47310 - 1.23608i) q^{5} +(-0.495883 + 0.180487i) q^{7} +(2.07886 + 2.16295i) q^{9} +O(q^{10})$	\(q+(1.59356 + 0.678655i) q^{3} +(1.47310 - 1.23608i) q^{5} +(-0.495883 + 0.180487i) q^{7} +(2.07886 + 2.16295i) q^{9} +(-1.04540 - 0.877191i) q^{11} +(-0.231701 - 1.31404i) q^{13} +(3.18634 - 0.970035i) q^{15} +(-1.45161 - 2.51426i) q^{17} +(-4.12432 + 7.14353i) q^{19} +(-0.912707 - 0.0489173i) q^{21} +(4.64302 + 1.68992i) q^{23} +(-0.226106 + 1.28231i) q^{25} +(1.84488 + 4.85761i) q^{27} +(1.56047 - 8.84985i) q^{29} +(-7.35856 - 2.67830i) q^{31} +(-1.07059 - 2.10732i) q^{33} +(-0.507389 + 0.878824i) q^{35} +(0.567200 + 0.982419i) q^{37} +(0.522552 - 2.25125i) q^{39} +(-0.675320 - 3.82993i) q^{41} +(-1.69457 - 1.42191i) q^{43} +(5.73593 + 0.616616i) q^{45} +(-6.47466 + 2.35658i) q^{47} +(-5.14899 + 4.32051i) q^{49} +(-0.606910 - 4.99177i) q^{51} -8.26669 q^{53} -2.62425 q^{55} +(-11.4203 + 8.58465i) q^{57} +(1.66426 - 1.39648i) q^{59} +(7.98814 - 2.90745i) q^{61} +(-1.42125 - 0.697365i) q^{63} +(-1.96558 - 1.64931i) q^{65} +(-0.319056 - 1.80946i) q^{67} +(6.25204 + 5.84399i) q^{69} +(3.51403 + 6.08647i) q^{71} +(-2.42368 + 4.19794i) q^{73} +(-1.23056 + 1.88999i) q^{75} +(0.676715 + 0.246304i) q^{77} +(1.99680 - 11.3244i) q^{79} +(-0.356716 + 8.99293i) q^{81} +(2.49258 - 14.1361i) q^{83} +(-5.24619 - 1.90946i) q^{85} +(8.49269 - 13.0437i) q^{87} +(-7.50092 + 12.9920i) q^{89} +(0.352064 + 0.609793i) q^{91} +(-9.90866 - 9.26194i) q^{93} +(2.75442 + 15.6211i) q^{95} +(14.2467 + 11.9544i) q^{97} +(-0.275905 - 4.08469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) $ 30 * q + 3 * q^7 - 6 * q^9	$ 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) $ 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * 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
$3$	1.59356	+	0.678655i	0.920041	+	0.391821i
$3$	1.59356	+	0.678655i	0.920041	+	0.391821i
$4$		0			0
$5$	1.47310	−	1.23608i	0.658790	−	0.552790i	−0.250934	−	0.968004i	$-0.580738\pi$
$5$	1.47310	−	1.23608i	0.658790	−	0.552790i	0.909724	+	0.415214i	$0.136293\pi$
$6$		0			0
$7$	−0.495883	+	0.180487i	−0.187426	+	0.0682176i	−0.434028	−	0.900899i	$-0.642908\pi$
$7$	−0.495883	+	0.180487i	−0.187426	+	0.0682176i	0.246602	+	0.969117i	$0.420686\pi$
$8$		0			0
$9$	2.07886	+	2.16295i	0.692952	+	0.720984i
$10$		0			0
$11$	−1.04540	−	0.877191i	−0.315199	−	0.264483i	0.471438	−	0.881899i	$-0.343735\pi$
$11$	−1.04540	−	0.877191i	−0.315199	−	0.264483i	−0.786637	+	0.617416i	$0.788180\pi$
$12$		0			0
$13$	−0.231701	−	1.31404i	−0.0642623	−	0.364450i	−0.999933	−	0.0115753i	$-0.996315\pi$
$13$	−0.231701	−	1.31404i	−0.0642623	−	0.364450i	0.935671	−	0.352874i	$-0.114796\pi$
$14$		0			0
$15$	3.18634	−	0.970035i	0.822709	−	0.250462i
$16$		0			0
$17$	−1.45161	−	2.51426i	−0.352067	−	0.609799i	0.634544	−	0.772887i	$-0.281188\pi$
$17$	−1.45161	−	2.51426i	−0.352067	−	0.609799i	−0.986612	+	0.163088i	$0.947855\pi$
$18$		0			0
$19$	−4.12432	+	7.14353i	−0.946184	+	1.63884i	−0.192821	+	0.981234i	$0.561764\pi$
$19$	−4.12432	+	7.14353i	−0.946184	+	1.63884i	−0.753363	+	0.657605i	$0.771570\pi$
$20$		0			0
$21$	−0.912707	−	0.0489173i	−0.199169	−	0.0106746i
$22$		0			0
$23$	4.64302	+	1.68992i	0.968136	+	0.352373i	0.777217	−	0.629233i	$-0.216631\pi$
$23$	4.64302	+	1.68992i	0.968136	+	0.352373i	0.190919	+	0.981606i	$0.438853\pi$
$24$		0			0
$25$	−0.226106	+	1.28231i	−0.0452213	+	0.256463i
$26$		0			0
$27$	1.84488	+	4.85761i	0.355048	+	0.934848i
$28$		0			0
$29$	1.56047	−	8.84985i	0.289771	−	1.64338i	−0.397954	−	0.917405i	$-0.630280\pi$
$29$	1.56047	−	8.84985i	0.289771	−	1.64338i	0.687726	−	0.725970i	$-0.258609\pi$
$30$		0			0
$31$	−7.35856	−	2.67830i	−1.32164	−	0.481036i	−0.417654	−	0.908606i	$-0.637148\pi$
$31$	−7.35856	−	2.67830i	−1.32164	−	0.481036i	−0.903982	+	0.427570i	$0.859370\pi$
$32$		0			0
$33$	−1.07059	−	2.10732i	−0.186366	−	0.366837i
$34$		0			0
$35$	−0.507389	+	0.878824i	−0.0857645	+	0.148548i
$36$		0			0
$37$	0.567200	+	0.982419i	0.0932471	+	0.161509i	0.908876	−	0.417067i	$-0.136942\pi$
$37$	0.567200	+	0.982419i	0.0932471	+	0.161509i	−0.815629	+	0.578576i	$0.803609\pi$
$38$		0			0
$39$	0.522552	−	2.25125i	0.0836752	−	0.360488i
$40$		0			0
$41$	−0.675320	−	3.82993i	−0.105467	−	0.598135i	−0.991033	−	0.133620i	$-0.957340\pi$
$41$	−0.675320	−	3.82993i	−0.105467	−	0.598135i	0.885565	−	0.464515i	$-0.153771\pi$
$42$		0			0
$43$	−1.69457	−	1.42191i	−0.258420	−	0.216840i	0.504368	−	0.863489i	$-0.331725\pi$
$43$	−1.69457	−	1.42191i	−0.258420	−	0.216840i	−0.762788	+	0.646649i	$0.776170\pi$
$44$		0			0
$45$	5.73593	+	0.616616i	0.855063	+	0.0919196i
$46$		0			0
$47$	−6.47466	+	2.35658i	−0.944426	+	0.343743i	−0.767912	−	0.640555i	$-0.778704\pi$
$47$	−6.47466	+	2.35658i	−0.944426	+	0.343743i	−0.176514	+	0.984298i	$0.556482\pi$
$48$		0			0
$49$	−5.14899	+	4.32051i	−0.735569	+	0.617216i
$50$		0			0
$51$	−0.606910	−	4.99177i	−0.0849844	−	0.698988i
$52$		0			0
$53$	−8.26669			−1.13552			−0.567759	−	0.823195i	$-0.692189\pi$
$53$	−8.26669			−1.13552			−0.567759	+	0.823195i	$0.692189\pi$
$54$		0			0
$55$	−2.62425			−0.353853
$56$		0			0
$57$	−11.4203	+	8.58465i	−1.51266	+	1.13706i
$58$		0			0
$59$	1.66426	−	1.39648i	0.216668	−	0.181806i	−0.527993	−	0.849249i	$-0.677055\pi$
$59$	1.66426	−	1.39648i	0.216668	−	0.181806i	0.744662	+	0.667442i	$0.232611\pi$
$60$		0			0
$61$	7.98814	−	2.90745i	1.02278	−	0.372260i	0.224451	−	0.974485i	$-0.427941\pi$
$61$	7.98814	−	2.90745i	1.02278	−	0.372260i	0.798326	+	0.602225i	$0.205719\pi$
$62$		0			0
$63$	−1.42125	−	0.697365i	−0.179061	−	0.0878598i
$64$		0			0
$65$	−1.96558	−	1.64931i	−0.243800	−	0.204572i
$66$		0			0
$67$	−0.319056	−	1.80946i	−0.0389789	−	0.221060i	0.959096	−	0.283081i	$-0.0913566\pi$
$67$	−0.319056	−	1.80946i	−0.0389789	−	0.221060i	−0.998075	+	0.0620209i	$0.980245\pi$
$68$		0			0
$69$	6.25204	+	5.84399i	0.752658	+	0.703534i
$70$		0			0
$71$	3.51403	+	6.08647i	0.417038	+	0.722332i	0.995640	−	0.0932786i	$-0.0297347\pi$
$71$	3.51403	+	6.08647i	0.417038	+	0.722332i	−0.578602	+	0.815610i	$0.696401\pi$
$72$		0			0
$73$	−2.42368	+	4.19794i	−0.283671	+	0.491332i	−0.972286	−	0.233795i	$-0.924886\pi$
$73$	−2.42368	+	4.19794i	−0.283671	+	0.491332i	0.688615	+	0.725127i	$0.258219\pi$
$74$		0			0
$75$	−1.23056	+	1.88999i	−0.142093	+	0.218237i
$76$		0			0
$77$	0.676715	+	0.246304i	0.0771189	+	0.0280690i
$78$		0			0
$79$	1.99680	−	11.3244i	0.224658	−	1.27410i	−0.638680	−	0.769472i	$-0.720519\pi$
$79$	1.99680	−	11.3244i	0.224658	−	1.27410i	0.863338	−	0.504626i	$-0.168370\pi$
$80$		0			0
$81$	−0.356716	+	8.99293i	−0.0396352	+	0.999214i
$82$		0			0
$83$	2.49258	−	14.1361i	0.273596	−	1.55164i	−0.469789	−	0.882779i	$-0.655670\pi$
$83$	2.49258	−	14.1361i	0.273596	−	1.55164i	0.743385	−	0.668864i	$-0.233219\pi$
$84$		0			0
$85$	−5.24619	−	1.90946i	−0.569029	−	0.207110i
$86$		0			0
$87$	8.49269	−	13.0437i	0.910511	−	1.39843i
$88$		0			0
$89$	−7.50092	+	12.9920i	−0.795096	+	1.37715i	0.127682	+	0.991815i	$0.459246\pi$
$89$	−7.50092	+	12.9920i	−0.795096	+	1.37715i	−0.922778	+	0.385332i	$0.874087\pi$
$90$		0			0
$91$	0.352064	+	0.609793i	0.0369063	+	0.0639236i
$92$		0			0
$93$	−9.90866	−	9.26194i	−1.02748	−	0.960419i
$94$		0			0
$95$	2.75442	+	15.6211i	0.282598	+	1.60269i
$96$		0			0
$97$	14.2467	+	11.9544i	1.44654	+	1.21379i	0.935060	+	0.354491i	$0.115346\pi$
$97$	14.2467	+	11.9544i	1.44654	+	1.21379i	0.511477	+	0.859297i	$0.329099\pi$
$98$		0			0
$99$	−0.275905	−	4.08469i	−0.0277295	−	0.410527i
$100$		0			0
$101$	11.6766	−	4.24995i	1.16187	−	0.422886i	0.312104	−	0.950048i	$-0.398966\pi$
$101$	11.6766	−	4.24995i	1.16187	−	0.422886i	0.849765	+	0.527162i	$0.176744\pi$
$102$		0			0
$103$	5.42807	−	4.55469i	0.534843	−	0.448787i	−0.334927	−	0.942244i	$-0.608712\pi$
$103$	5.42807	−	4.55469i	0.534843	−	0.448787i	0.869770	+	0.493457i	$0.164267\pi$
$104$		0			0
$105$	−1.40497	+	1.05612i	−0.137111	+	0.103066i
$106$		0			0
$107$	1.45108			0.140282			0.0701408	−	0.997537i	$-0.477655\pi$
$107$	1.45108			0.140282			0.0701408	+	0.997537i	$0.477655\pi$
$108$		0			0
$109$	18.3965			1.76207			0.881033	−	0.473056i	$-0.156849\pi$
$109$	18.3965			1.76207			0.881033	+	0.473056i	$0.156849\pi$
$110$		0			0
$111$	0.237143	+	1.95048i	0.0225086	+	0.185131i
$112$		0			0
$113$	6.14775	−	5.15857i	0.578332	−	0.485278i	−0.306067	−	0.952010i	$-0.599013\pi$
$113$	6.14775	−	5.15857i	0.578332	−	0.485278i	0.884399	+	0.466732i	$0.154569\pi$
$114$		0			0
$115$	8.92849	−	3.24970i	0.832586	−	0.303037i
$116$		0			0
$117$	2.36054	−	3.23286i	0.218232	−	0.298878i
$118$		0			0
$119$	1.17362	+	0.984785i	0.107586	+	0.0902751i
$120$		0			0
$121$	−1.58674	−	8.99886i	−0.144249	−	0.818078i
$122$		0			0
$123$	1.52304	−	6.56153i	0.137328	−	0.591633i
$124$		0			0
$125$	6.05944	+	10.4953i	0.541973	+	0.938725i
$126$		0			0
$127$	−9.43607	+	16.3438i	−0.837316	+	1.45027i	0.0548149	+	0.998497i	$0.482543\pi$
$127$	−9.43607	+	16.3438i	−0.837316	+	1.45027i	−0.892131	+	0.451777i	$0.850790\pi$
$128$		0			0
$129$	−1.73541	−	3.41593i	−0.152794	−	0.300756i
$130$		0			0
$131$	10.5753	+	3.84910i	0.923969	+	0.336297i	0.759816	−	0.650138i	$-0.225289\pi$
$131$	10.5753	+	3.84910i	0.923969	+	0.336297i	0.164153	+	0.986435i	$0.447511\pi$
$132$		0			0
$133$	0.755868	−	4.28674i	0.0655421	−	0.371708i
$134$		0			0
$135$	8.72208	+	4.87533i	0.750677	+	0.419602i
$136$		0			0
$137$	−3.29666	+	18.6963i	−0.281652	+	1.59733i	0.435351	+	0.900261i	$0.356624\pi$
$137$	−3.29666	+	18.6963i	−0.281652	+	1.59733i	−0.717003	+	0.697070i	$0.754487\pi$
$138$		0			0
$139$	7.58087	+	2.75921i	0.643001	+	0.234033i	0.642880	−	0.765967i	$-0.277739\pi$
$139$	7.58087	+	2.75921i	0.643001	+	0.234033i	0.000120846		1.00000i	$0.499962\pi$
$140$		0			0
$141$	−11.9171	−	0.638704i	−1.00360	−	0.0537886i
$142$		0			0
$143$	−0.910447	+	1.57694i	−0.0761354	+	0.131870i
$144$		0			0
$145$	−8.64037	−	14.9656i	−0.717544	−	1.24282i
$146$		0			0
$147$	−11.1373	+	3.39061i	−0.918593	+	0.279652i
$148$		0			0
$149$	−0.0923465	−	0.523723i	−0.00756532	−	0.0429050i	0.980791	−	0.195059i	$-0.0624900\pi$
$149$	−0.0923465	−	0.523723i	−0.00756532	−	0.0429050i	−0.988357	+	0.152154i	$0.951379\pi$
$150$		0			0
$151$	−7.42414	−	6.22959i	−0.604168	−	0.506957i	0.288614	−	0.957445i	$-0.406805\pi$
$151$	−7.42414	−	6.22959i	−0.604168	−	0.506957i	−0.892782	+	0.450488i	$0.851250\pi$
$152$		0			0
$153$	2.42054	−	8.36656i	0.195689	−	0.676396i
$154$		0			0
$155$	−14.1505	+	5.15035i	−1.13659	+	0.413686i
$156$		0			0
$157$	−3.45033	+	2.89517i	−0.275366	+	0.231060i	−0.770003	−	0.638040i	$-0.779745\pi$
$157$	−3.45033	+	2.89517i	−0.275366	+	0.231060i	0.494637	+	0.869100i	$0.335301\pi$
$158$		0			0
$159$	−13.1735	−	5.61023i	−1.04472	−	0.444920i
$160$		0			0
$161$	−2.60740			−0.205492
$162$		0			0
$163$	22.4835			1.76105			0.880524	−	0.474002i	$-0.157191\pi$
$163$	22.4835			1.76105			0.880524	+	0.474002i	$0.157191\pi$
$164$		0			0
$165$	−4.18189	−	1.78096i	−0.325560	−	0.138647i
$166$		0			0
$167$	−5.87285	+	4.92791i	−0.454455	+	0.381333i	−0.841086	−	0.540902i	$-0.818083\pi$
$167$	−5.87285	+	4.92791i	−0.454455	+	0.381333i	0.386631	+	0.922234i	$0.373639\pi$
$168$		0			0
$169$	10.5430	−	3.83733i	0.810999	−	0.295179i
$170$		0			0
$171$	−24.0250	+	5.92967i	−1.83724	+	0.453453i
$172$		0			0
$173$	−8.96660	−	7.52387i	−0.681718	−	0.572029i	0.234790	−	0.972046i	$-0.424560\pi$
$173$	−8.96660	−	7.52387i	−0.681718	−	0.572029i	−0.916508	+	0.400017i	$0.869004\pi$
$174$		0			0
$175$	−0.119318	−	0.676686i	−0.00901960	−	0.0511527i
$176$		0			0
$177$	3.59983	−	1.09592i	0.270580	−	0.0823741i
$178$		0			0
$179$	−7.19958	−	12.4700i	−0.538122	−	0.932054i	−0.999005	−	0.0445934i	$-0.985801\pi$
$179$	−7.19958	−	12.4700i	−0.538122	−	0.932054i	0.460884	−	0.887461i	$-0.347533\pi$
$180$		0			0
$181$	−4.91109	+	8.50625i	−0.365038	+	0.632265i	−0.988782	−	0.149364i	$-0.952277\pi$
$181$	−4.91109	+	8.50625i	−0.365038	+	0.632265i	0.623744	+	0.781629i	$0.285611\pi$
$182$		0			0
$183$	14.7027	+	0.788005i	1.08686	+	0.0582510i
$184$		0			0
$185$	2.04989	+	0.746098i	0.150711	+	0.0548542i
$186$		0			0
$187$	−0.687982	+	3.90174i	−0.0503103	+	0.285324i
$188$		0			0
$189$	−1.79158	−	2.07583i	−0.130318	−	0.150995i
$190$		0			0
$191$	0.0726668	−	0.412114i	0.00525799	−	0.0298195i	−0.982066	−	0.188538i	$-0.939625\pi$
$191$	0.0726668	−	0.412114i	0.00525799	−	0.0298195i	0.987324	+	0.158719i	$0.0507362\pi$
$192$		0			0
$193$	−9.05092	−	3.29426i	−0.651499	−	0.237126i	−0.00493736	−	0.999988i	$-0.501572\pi$
$193$	−9.05092	−	3.29426i	−0.651499	−	0.237126i	−0.646562	+	0.762861i	$0.723794\pi$
$194$		0			0
$195$	−2.01295	−	3.96223i	−0.144150	−	0.283741i
$196$		0			0
$197$	−4.26846	+	7.39319i	−0.304115	+	0.526743i	−0.977064	−	0.212946i	$-0.931694\pi$
$197$	−4.26846	+	7.39319i	−0.304115	+	0.526743i	0.672949	+	0.739689i	$0.265027\pi$
$198$		0			0
$199$	−5.02358	−	8.70110i	−0.356112	−	0.616804i	0.631196	−	0.775624i	$-0.282565\pi$
$199$	−5.02358	−	8.70110i	−0.356112	−	0.616804i	−0.987308	+	0.158819i	$0.949231\pi$
$200$		0			0
$201$	0.719562	−	3.10000i	0.0507540	−	0.218657i
$202$		0			0
$203$	0.823471	+	4.67013i	0.0577963	+	0.327779i
$204$		0			0
$205$	−5.72890	−	4.80712i	−0.400124	−	0.335744i
$206$		0			0
$207$	5.99695	+	13.5557i	0.416817	+	0.942187i
$208$		0			0
$209$	10.5778	−	3.85000i	0.731681	−	0.266310i
$210$		0			0
$211$	12.7816	−	10.7250i	0.879922	−	0.738343i	−0.0862407	−	0.996274i	$-0.527485\pi$
$211$	12.7816	−	10.7250i	0.879922	−	0.738343i	0.966163	+	0.257932i	$0.0830410\pi$
$212$		0			0
$213$	1.46919	+	12.0840i	0.100668	+	0.827980i
$214$		0			0
$215$	−4.25386			−0.290111
$216$		0			0
$217$	4.13238			0.280524
$218$		0			0
$219$	−6.71124	+	5.04482i	−0.453503	+	0.340898i
$220$		0			0
$221$	−2.96751	+	2.49004i	−0.199616	+	0.167498i
$222$		0			0
$223$	−13.4373	+	4.89078i	−0.899828	+	0.327511i	−0.750184	−	0.661229i	$-0.770035\pi$
$223$	−13.4373	+	4.89078i	−0.899828	+	0.327511i	−0.149644	+	0.988740i	$0.547813\pi$
$224$		0			0
$225$	−3.24362	+	2.17669i	−0.216241	+	0.145112i
$226$		0			0
$227$	−3.60664	−	3.02633i	−0.239381	−	0.200865i	0.515202	−	0.857068i	$-0.327717\pi$
$227$	−3.60664	−	3.02633i	−0.239381	−	0.200865i	−0.754584	+	0.656204i	$0.772161\pi$
$228$		0			0
$229$	−1.83128	−	10.3857i	−0.121015	−	0.686308i	−0.983595	−	0.180389i	$-0.942264\pi$
$229$	−1.83128	−	10.3857i	−0.121015	−	0.686308i	0.862581	−	0.505919i	$-0.168847\pi$
$230$		0			0
$231$	0.911230	+	0.851756i	0.0599545	+	0.0560414i
$232$		0			0
$233$	−3.09913	−	5.36784i	−0.203030	−	0.351659i	0.746473	−	0.665416i	$-0.231746\pi$
$233$	−3.09913	−	5.36784i	−0.203030	−	0.351659i	−0.949503	+	0.313757i	$0.898412\pi$
$234$		0			0
$235$	−6.62489	+	11.4747i	−0.432160	+	0.748524i
$236$		0			0
$237$	10.8674	−	16.6910i	0.705914	−	1.08420i
$238$		0			0
$239$	0.169808	+	0.0618049i	0.0109839	+	0.00399783i	0.347506	−	0.937678i	$-0.387029\pi$
$239$	0.169808	+	0.0618049i	0.0109839	+	0.00399783i	−0.336522	+	0.941675i	$0.609251\pi$
$240$		0			0
$241$	−1.68285	+	9.54390i	−0.108402	+	0.614777i	0.881405	+	0.472361i	$0.156598\pi$
$241$	−1.68285	+	9.54390i	−0.108402	+	0.614777i	−0.989807	+	0.142416i	$0.954513\pi$
$242$		0			0
$243$	−6.67154	+	14.0887i	−0.427980	+	0.903788i
$244$		0			0
$245$	−2.24448	+	12.7291i	−0.143395	+	0.813231i
$246$		0			0
$247$	10.3425	+	3.76437i	0.658079	+	0.239521i
$248$		0			0
$249$	13.5656	−	20.8352i	0.859687	−	1.32037i
$250$		0			0
$251$	9.36265	−	16.2166i	0.590965	−	1.02358i	−0.403138	−	0.915139i	$-0.632080\pi$
$251$	9.36265	−	16.2166i	0.590965	−	1.02358i	0.994103	−	0.108442i	$-0.0345863\pi$
$252$		0			0
$253$	−3.37141	−	5.83945i	−0.211958	−	0.367123i
$254$		0			0
$255$	−7.06425	−	6.60318i	−0.442380	−	0.413507i
$256$		0			0
$257$	−2.86002	−	16.2200i	−0.178403	−	1.01177i	−0.934142	−	0.356901i	$-0.883833\pi$
$257$	−2.86002	−	16.2200i	−0.178403	−	1.01177i	0.755740	−	0.654872i	$-0.227278\pi$
$258$		0			0
$259$	−0.458579	−	0.384793i	−0.0284947	−	0.0239099i
$260$		0			0
$261$	22.3858	−	15.0223i	1.38564	−	0.929860i
$262$		0			0
$263$	−3.34146	+	1.21619i	−0.206044	+	0.0749937i	−0.442980	−	0.896531i	$-0.646079\pi$
$263$	−3.34146	+	1.21619i	−0.206044	+	0.0749937i	0.236937	+	0.971525i	$0.423857\pi$
$264$		0			0
$265$	−12.1777	+	10.2183i	−0.748067	+	0.627703i
$266$		0			0
$267$	−20.7702	+	15.6129i	−1.27112	+	0.955497i
$268$		0			0
$269$	6.41273			0.390991			0.195496	−	0.980705i	$-0.437368\pi$
$269$	6.41273			0.390991			0.195496	+	0.980705i	$0.437368\pi$
$270$		0			0
$271$	0.263089			0.0159815			0.00799076	−	0.999968i	$-0.497456\pi$
$271$	0.263089			0.0159815			0.00799076	+	0.999968i	$0.497456\pi$
$272$		0			0
$273$	0.147196	+	1.21067i	0.00890870	+	0.0732731i
$274$		0			0
$275$	1.36120	−	1.14219i	0.0820837	−	0.0688764i
$276$		0			0
$277$	−28.1521	+	10.2465i	−1.69150	+	0.615655i	−0.994813	−	0.101722i	$-0.967565\pi$
$277$	−28.1521	+	10.2465i	−1.69150	+	0.615655i	−0.696685	+	0.717377i	$0.745343\pi$
$278$		0			0
$279$	−9.50436	−	21.4840i	−0.569011	−	1.28621i
$280$		0			0
$281$	11.8164	+	9.91510i	0.704905	+	0.591485i	0.923164	−	0.384405i	$-0.125593\pi$
$281$	11.8164	+	9.91510i	0.704905	+	0.591485i	−0.218260	+	0.975891i	$0.570038\pi$
$282$		0			0
$283$	3.79501	+	21.5226i	0.225590	+	1.27938i	0.861554	+	0.507666i	$0.169492\pi$
$283$	3.79501	+	21.5226i	0.225590	+	1.27938i	−0.635964	+	0.771719i	$0.719397\pi$
$284$		0			0
$285$	−6.21200	+	26.7624i	−0.367967	+	1.58527i
$286$		0			0
$287$	1.02613	+	1.77731i	0.0605706	+	0.104911i
$288$		0			0
$289$	4.28565	−	7.42296i	0.252097	−	0.436645i
$290$		0			0
$291$	14.5901	+	28.7187i	0.855285	+	1.68352i
$292$		0			0
$293$	−13.3267	−	4.85052i	−0.778553	−	0.283370i	−0.0779839	−	0.996955i	$-0.524848\pi$
$293$	−13.3267	−	4.85052i	−0.778553	−	0.283370i	−0.700569	+	0.713584i	$0.747070\pi$
$294$		0			0
$295$	0.725464	−	4.11431i	0.0422382	−	0.239544i
$296$		0			0
$297$	2.33243	−	6.69644i	0.135341	−	0.388567i
$298$		0			0
$299$	1.14483	−	6.49268i	0.0662075	−	0.375481i
$300$		0			0
$301$	1.09695	+	0.399255i	0.0632269	+	0.0230127i
$302$		0			0
$303$	21.4916	+	1.15186i	1.23466	+	0.0661728i
$304$		0			0
$305$	8.17350	−	14.1569i	0.468013	−	0.810623i
$306$		0			0
$307$	0.769684	+	1.33313i	0.0439282	+	0.0760859i	0.887154	−	0.461474i	$-0.152679\pi$
$307$	0.769684	+	1.33313i	0.0439282	+	0.0760859i	−0.843225	+	0.537560i	$0.819346\pi$
$308$		0			0
$309$	11.7410	−	3.57438i	0.667922	−	0.203339i
$310$		0			0
$311$	−2.08494	−	11.8243i	−0.118226	−	0.670493i	−0.985102	−	0.171969i	$-0.944987\pi$
$311$	−2.08494	−	11.8243i	−0.118226	−	0.670493i	0.866876	−	0.498523i	$-0.166124\pi$
$312$		0			0
$313$	−1.60383	−	1.34578i	−0.0906541	−	0.0760678i	0.596334	−	0.802736i	$-0.296623\pi$
$313$	−1.60383	−	1.34578i	−0.0906541	−	0.0760678i	−0.686988	+	0.726668i	$0.741068\pi$
$314$		0			0
$315$	−2.95564	+	0.729490i	−0.166532	+	0.0411021i
$316$		0			0
$317$	23.2299	−	8.45498i	1.30472	−	0.474879i	0.406189	−	0.913789i	$-0.366858\pi$
$317$	23.2299	−	8.45498i	1.30472	−	0.474879i	0.898531	+	0.438910i	$0.144635\pi$
$318$		0			0
$319$	−9.39431	+	7.88276i	−0.525981	+	0.441350i
$320$		0			0
$321$	2.31239	+	0.984785i	0.129065	+	0.0549654i
$322$		0			0
$323$	23.9476			1.33248
$324$		0			0
$325$	1.73740			0.0963738
$326$		0			0
$327$	29.3159	+	12.4849i	1.62117	+	0.690415i
$328$		0			0
$329$	2.78534	−	2.33718i	0.153561	−	0.128853i
$330$		0			0
$331$	8.08653	−	2.94326i	0.444476	−	0.161776i	−0.110080	−	0.993923i	$-0.535111\pi$
$331$	8.08653	−	2.94326i	0.444476	−	0.161776i	0.554555	+	0.832147i	$0.312888\pi$
$332$		0			0
$333$	−0.945798	+	3.26913i	−0.0518294	+	0.179147i
$334$		0			0
$335$	−2.70663	−	2.27113i	−0.147879	−	0.124085i
$336$		0			0
$337$	4.37964	+	24.8382i	0.238574	+	1.35302i	0.834954	+	0.550320i	$0.185494\pi$
$337$	4.37964	+	24.8382i	0.238574	+	1.35302i	−0.596380	+	0.802702i	$0.703395\pi$
$338$		0			0
$339$	13.2977	−	4.04829i	0.722231	−	0.219873i
$340$		0			0
$341$	5.34323	+	9.25474i	0.289352	+	0.501173i
$342$		0			0
$343$	3.62048	−	6.27085i	0.195487	−	0.338594i
$344$		0			0
$345$	16.4335	+	0.880767i	0.884750	+	0.0474189i
$346$		0			0
$347$	−30.9882	−	11.2788i	−1.66353	−	0.605476i	−0.672621	−	0.739988i	$-0.734831\pi$
$347$	−30.9882	−	11.2788i	−1.66353	−	0.605476i	−0.990912	+	0.134511i	$0.957054\pi$
$348$		0			0
$349$	−3.20075	+	18.1524i	−0.171332	+	0.971674i	0.770960	+	0.636883i	$0.219777\pi$
$349$	−3.20075	+	18.1524i	−0.171332	+	0.971674i	−0.942293	+	0.334791i	$0.891334\pi$
$350$		0			0
$351$	5.95565	−	3.54977i	0.317889	−	0.189473i
$352$		0			0
$353$	−2.40564	+	13.6431i	−0.128039	+	0.726148i	0.851417	+	0.524490i	$0.175744\pi$
$353$	−2.40564	+	13.6431i	−0.128039	+	0.726148i	−0.979456	+	0.201658i	$0.935367\pi$
$354$		0			0
$355$	12.6999	+	4.62237i	0.674039	+	0.245330i
$356$		0			0
$357$	1.20190	+	2.36580i	0.0636115	+	0.125211i
$358$		0			0
$359$	12.8677	−	22.2876i	0.679133	−	1.17629i	−0.296110	−	0.955154i	$-0.595689\pi$
$359$	12.8677	−	22.2876i	0.679133	−	1.17629i	0.975242	−	0.221138i	$-0.0709773\pi$
$360$		0			0
$361$	−24.5200	−	42.4700i	−1.29053	−	2.23526i
$362$		0			0
$363$	3.57855	−	15.4171i	0.187825	−	0.809186i
$364$		0			0
$365$	1.61865	+	9.17985i	0.0847242	+	0.480495i
$366$		0			0
$367$	6.39271	+	5.36412i	0.333697	+	0.280005i	0.794204	−	0.607651i	$-0.207888\pi$
$367$	6.39271	+	5.36412i	0.333697	+	0.280005i	−0.460507	+	0.887656i	$0.652332\pi$
$368$		0			0
$369$	6.88006	−	9.42256i	0.358162	−	0.490519i
$370$		0			0
$371$	4.09931	−	1.49203i	0.212826	−	0.0774622i
$372$		0			0
$373$	9.87503	−	8.28614i	0.511310	−	0.429040i	−0.350280	−	0.936645i	$-0.613914\pi$
$373$	9.87503	−	8.28614i	0.511310	−	0.429040i	0.861590	+	0.507605i	$0.169469\pi$
$374$		0			0
$375$	2.53342	+	20.8371i	0.130825	+	1.07602i
$376$		0			0
$377$	−11.9906			−0.617549
$378$		0			0
$379$	−1.08906			−0.0559412			−0.0279706	−	0.999609i	$-0.508904\pi$
$379$	−1.08906			−0.0559412			−0.0279706	+	0.999609i	$0.508904\pi$
$380$		0			0
$381$	−26.1287	+	19.6409i	−1.33861	+	1.00623i
$382$		0			0
$383$	0.730597	−	0.613044i	0.0373318	−	0.0313251i	−0.623931	−	0.781480i	$-0.714465\pi$
$383$	0.730597	−	0.613044i	0.0373318	−	0.0313251i	0.661263	+	0.750154i	$0.270021\pi$
$384$		0			0
$385$	1.30132	−	0.473642i	0.0663214	−	0.0241390i
$386$		0			0
$387$	−0.447238	−	6.62123i	−0.0227344	−	0.336576i
$388$		0			0
$389$	−8.59462	−	7.21175i	−0.435765	−	0.365650i	0.398357	−	0.917230i	$-0.369581\pi$
$389$	−8.59462	−	7.21175i	−0.435765	−	0.365650i	−0.834122	+	0.551580i	$0.814025\pi$
$390$		0			0
$391$	−2.49095	−	14.1269i	−0.125973	−	0.714427i
$392$		0			0
$393$	14.2402	+	13.3107i	0.718321	+	0.671438i
$394$		0			0
$395$	−11.0564	−	19.1502i	−0.556307	−	0.963552i
$396$		0			0
$397$	−12.3592	+	21.4068i	−0.620293	+	1.07438i	0.369138	+	0.929374i	$0.379653\pi$
$397$	−12.3592	+	21.4068i	−0.620293	+	1.07438i	−0.989431	+	0.145004i	$0.953680\pi$
$398$		0			0
$399$	4.11374	−	6.31820i	0.205945	−	0.316306i
$400$		0			0
$401$	3.99274	+	1.45324i	0.199388	+	0.0725712i	0.439784	−	0.898104i	$-0.355055\pi$
$401$	3.99274	+	1.45324i	0.199388	+	0.0725712i	−0.240396	+	0.970675i	$0.577277\pi$
$402$		0			0
$403$	−1.81441	+	10.2900i	−0.0903822	+	0.512583i
$404$		0			0
$405$	10.5905	+	13.6884i	0.526245	+	0.680182i
$406$		0			0
$407$	0.268821	−	1.52456i	0.0133250	−	0.0755696i
$408$		0			0
$409$	0.952016	+	0.346506i	0.0470742	+	0.0171336i	0.365450	−	0.930831i	$-0.380915\pi$
$409$	0.952016	+	0.346506i	0.0470742	+	0.0171336i	−0.318376	+	0.947965i	$0.603137\pi$
$410$		0			0
$411$	−17.9417	+	27.5563i	−0.885000	+	1.35925i
$412$		0			0
$413$	−0.573233	+	0.992869i	−0.0282070	+	0.0488559i
$414$		0			0
$415$	−13.8015	−	23.9049i	−0.677490	−	1.17345i
$416$		0			0
$417$	10.2080	+	9.54176i	0.499888	+	0.467262i
$418$		0			0
$419$	−6.08021	−	34.4826i	−0.297038	−	1.68458i	−0.658803	−	0.752315i	$-0.728937\pi$
$419$	−6.08021	−	34.4826i	−0.297038	−	1.68458i	0.361766	−	0.932269i	$-0.382174\pi$
$420$		0			0
$421$	−12.0000	−	10.0692i	−0.584845	−	0.490743i	0.301689	−	0.953406i	$-0.402450\pi$
$421$	−12.0000	−	10.0692i	−0.584845	−	0.490743i	−0.886534	+	0.462663i	$0.846894\pi$
$422$		0			0
$423$	−18.5571	−	9.10537i	−0.902275	−	0.442718i
$424$		0			0
$425$	3.55229	−	1.29293i	0.172311	−	0.0627162i
$426$		0			0
$427$	−3.43643	+	2.88351i	−0.166301	+	0.139543i
$428$		0			0
$429$	−2.52105	+	1.89507i	−0.121717	+	0.0914947i
$430$		0			0
$431$	−2.79246			−0.134508			−0.0672540	−	0.997736i	$-0.521424\pi$
$431$	−2.79246			−0.134508			−0.0672540	+	0.997736i	$0.521424\pi$
$432$		0			0
$433$	13.1756			0.633177			0.316589	−	0.948563i	$-0.397463\pi$
$433$	13.1756			0.633177			0.316589	+	0.948563i	$0.397463\pi$
$434$		0			0
$435$	−3.61249	−	29.7123i	−0.173205	−	1.42460i
$436$		0			0
$437$	−31.2213	+	26.1978i	−1.49352	+	1.25321i
$438$		0			0
$439$	−26.2025	+	9.53693i	−1.25058	+	0.455173i	−0.880596	−	0.473867i	$-0.842858\pi$
$439$	−26.2025	+	9.53693i	−1.25058	+	0.455173i	−0.369980	+	0.929040i	$0.620636\pi$
$440$		0			0
$441$	−20.0491	−	2.15528i	−0.954717	−	0.102633i
$442$		0			0
$443$	18.3034	+	15.3584i	0.869619	+	0.729697i	0.964018	−	0.265837i	$-0.0856483\pi$
$443$	18.3034	+	15.3584i	0.869619	+	0.729697i	−0.0943985	+	0.995534i	$0.530093\pi$
$444$		0			0
$445$	5.00948	+	28.4102i	0.237472	+	1.34677i
$446$		0			0
$447$	0.208267	−	0.897254i	0.00985071	−	0.0424387i
$448$		0			0
$449$	−4.24255	−	7.34831i	−0.200218	−	0.346788i	0.748380	−	0.663270i	$-0.230832\pi$
$449$	−4.24255	−	7.34831i	−0.200218	−	0.346788i	−0.948599	+	0.316482i	$0.897498\pi$
$450$		0			0
$451$	−2.65361	+	4.59618i	−0.124953	+	0.216426i
$452$		0			0
$453$	−7.60306	−	14.9656i	−0.357223	−	0.703147i
$454$		0			0
$455$	1.27238	+	0.463107i	0.0596499	+	0.0217108i
$456$		0			0
$457$	−0.0328029	+	0.186034i	−0.00153445	+	0.00870231i	−0.985565	−	0.169295i	$-0.945851\pi$
$457$	−0.0328029	+	0.186034i	−0.00153445	+	0.00870231i	0.984031	+	0.177998i	$0.0569619\pi$
$458$		0			0
$459$	9.53528	−	11.6899i	0.445069	−	0.545637i
$460$		0			0
$461$	−2.16513	+	12.2791i	−0.100840	+	0.571893i	0.891960	+	0.452114i	$0.149330\pi$
$461$	−2.16513	+	12.2791i	−0.100840	+	0.571893i	−0.992801	+	0.119780i	$0.961781\pi$
$462$		0			0
$463$	6.04249	+	2.19929i	0.280818	+	0.102210i	0.478590	−	0.878039i	$-0.341148\pi$
$463$	6.04249	+	2.19929i	0.280818	+	0.102210i	−0.197771	+	0.980248i	$0.563370\pi$
$464$		0			0
$465$	−26.0449	−	1.39590i	−1.20780	−	0.0647333i
$466$		0			0
$467$	−10.2352	+	17.7278i	−0.473627	+	0.820347i	−0.999544	−	0.0301893i	$-0.990389\pi$
$467$	−10.2352	+	17.7278i	−0.473627	+	0.820347i	0.525917	+	0.850536i	$0.323722\pi$
$468$		0			0
$469$	0.484797	+	0.839694i	0.0223859	+	0.0387734i
$470$		0			0
$471$	−7.46312	+	2.27204i	−0.343882	+	0.104690i
$472$		0			0
$473$	0.524207	+	2.97292i	0.0241030	+	0.136695i
$474$		0			0
$475$	−8.22771	−	6.90387i	−0.377513	−	0.316771i
$476$		0			0
$477$	−17.1853	−	17.8805i	−0.786859	−	0.818690i
$478$		0			0
$479$	−35.9108	+	13.0705i	−1.64081	+	0.597204i	−0.987180	−	0.159613i	$-0.948975\pi$
$479$	−35.9108	+	13.0705i	−1.64081	+	0.597204i	−0.653626	+	0.756818i	$0.726753\pi$
$480$		0			0
$481$	1.15952	−	0.972953i	0.0528695	−	0.0443628i
$482$		0			0
$483$	−4.15505	−	1.76952i	−0.189061	−	0.0805162i
$484$		0			0
$485$	35.7634			1.62393
$486$		0			0
$487$	23.7637			1.07684			0.538418	−	0.842678i	$-0.319022\pi$
$487$	23.7637			1.07684			0.538418	+	0.842678i	$0.319022\pi$
$488$		0			0
$489$	35.8288	+	15.2586i	1.62024	+	0.690016i
$490$		0			0
$491$	−0.0261889	+	0.0219751i	−0.00118189	+	0.000991721i	−0.643378	−	0.765548i	$-0.722468\pi$
$491$	−0.0261889	+	0.0219751i	−0.00118189	+	0.000991721i	0.642196	+	0.766540i	$0.278023\pi$
$492$		0			0
$493$	−24.5161	+	8.92311i	−1.10415	+	0.401877i
$494$		0			0
$495$	−5.45543	−	5.67612i	−0.245203	−	0.255122i
$496$		0			0
$497$	−2.84108	−	2.38395i	−0.127440	−	0.106935i
$498$		0			0
$499$	−2.12908	−	12.0746i	−0.0953109	−	0.540535i	−0.994652	−	0.103287i	$-0.967064\pi$
$499$	−2.12908	−	12.0746i	−0.0953109	−	0.540535i	0.899341	−	0.437249i	$-0.144047\pi$
$500$		0			0
$501$	−12.7031	+	3.86727i	−0.567532	+	0.172777i
$502$		0			0
$503$	10.6749	+	18.4895i	0.475971	+	0.824406i	0.999621	−	0.0275274i	$-0.00876335\pi$
$503$	10.6749	+	18.4895i	0.475971	+	0.824406i	−0.523650	+	0.851934i	$0.675430\pi$
$504$		0			0
$505$	11.9476	−	20.6938i	0.531660	−	0.920863i
$506$		0			0
$507$	19.4051	+	1.04003i	0.861810	+	0.0461894i
$508$		0			0
$509$	−33.0302	−	12.0220i	−1.46404	−	0.532866i	−0.517563	−	0.855645i	$-0.673161\pi$
$509$	−33.0302	−	12.0220i	−1.46404	−	0.532866i	−0.946474	+	0.322779i	$0.895383\pi$
$510$		0			0
$511$	0.444191	−	2.51913i	0.0196499	−	0.111440i
$512$		0			0
$513$	−42.3094	−	6.85539i	−1.86801	−	0.302673i
$514$		0			0
$515$	2.36613	−	13.4190i	0.104264	−	0.591313i
$516$		0			0
$517$	8.83575	+	3.21595i	0.388596	+	0.141437i
$518$		0			0
$519$	−9.18269	−	18.0749i	−0.403075	−	0.793402i
$520$		0			0
$521$	13.8600	−	24.0062i	0.607218	−	1.05173i	−0.384479	−	0.923134i	$-0.625619\pi$
$521$	13.8600	−	24.0062i	0.607218	−	1.05173i	0.991697	−	0.128599i	$-0.0410479\pi$
$522$		0			0
$523$	−11.8061	−	20.4488i	−0.516245	−	0.894163i	−0.999822	−	0.0188613i	$-0.993996\pi$
$523$	−11.8061	−	20.4488i	−0.516245	−	0.894163i	0.483577	−	0.875302i	$-0.339337\pi$
$524$		0			0
$525$	0.269096	−	1.15932i	0.0117443	−	0.0505967i
$526$		0			0
$527$	3.94782	+	22.3892i	0.171970	+	0.975290i
$528$		0			0
$529$	1.08274	+	0.908529i	0.0470758	+	0.0395013i
$530$		0			0
$531$	6.48028	+	0.696634i	0.281220	+	0.0302313i
$532$		0			0
$533$	−4.87622	+	1.77480i	−0.211213	+	0.0768751i
$534$		0			0
$535$	2.13759	−	1.79365i	0.0924161	−	0.0775463i
$536$		0			0
$537$	−3.01010	−	24.7577i	−0.129895	−	1.06838i
$538$		0			0
$539$	9.17264			0.395094
$540$		0			0
$541$	4.54086			0.195227			0.0976135	−	0.995224i	$-0.468879\pi$
$541$	4.54086			0.195227			0.0976135	+	0.995224i	$0.468879\pi$
$542$		0			0
$543$	−13.5989	+	10.2223i	−0.583585	+	0.438680i
$544$		0			0
$545$	27.0999	−	22.7395i	1.16083	−	0.974052i
$546$		0			0
$547$	1.88744	−	0.686973i	0.0807012	−	0.0293728i	−0.301354	−	0.953512i	$-0.597439\pi$
$547$	1.88744	−	0.686973i	0.0807012	−	0.0293728i	0.382055	+	0.924139i	$0.375216\pi$
$548$		0			0
$549$	22.8949	+	11.2338i	0.977129	+	0.479447i
$550$		0			0
$551$	56.7833	+	47.6469i	2.41905	+	2.02982i
$552$		0			0
$553$	1.05373	+	5.97599i	0.0448091	+	0.254125i
$554$		0			0
$555$	2.76027	+	2.58012i	0.117167	+	0.109520i
$556$		0			0
$557$	−10.6716	−	18.4838i	−0.452171	−	0.783183i	0.546350	−	0.837557i	$-0.316017\pi$
$557$	−10.6716	−	18.4838i	−0.452171	−	0.783183i	−0.998521	+	0.0543742i	$0.982684\pi$
$558$		0			0
$559$	−1.47582	+	2.55620i	−0.0624206	+	0.108116i
$560$		0			0
$561$	−3.74428	+	5.75075i	−0.158083	+	0.242797i
$562$		0			0
$563$	9.80247	+	3.56781i	0.413125	+	0.150365i	0.540217	−	0.841526i	$-0.318342\pi$
$563$	9.80247	+	3.56781i	0.413125	+	0.150365i	−0.127092	+	0.991891i	$0.540564\pi$
$564$		0			0
$565$	2.67985	−	15.1982i	0.112742	−	0.639392i
$566$		0			0
$567$	−1.44621	−	4.52382i	−0.0607353	−	0.189983i
$568$		0			0
$569$	−5.76020	+	32.6677i	−0.241480	+	1.36950i	0.587048	+	0.809552i	$0.300290\pi$
$569$	−5.76020	+	32.6677i	−0.241480	+	1.36950i	−0.828527	+	0.559948i	$0.810821\pi$
$570$		0			0
$571$	5.20011	+	1.89269i	0.217618	+	0.0792065i	0.448529	−	0.893769i	$-0.351948\pi$
$571$	5.20011	+	1.89269i	0.217618	+	0.0792065i	−0.230911	+	0.972975i	$0.574170\pi$
$572$		0			0
$573$	0.395482	−	0.607412i	0.0165215	−	0.0253750i
$574$		0			0
$575$	−3.21682	+	5.57170i	−0.134151	+	0.232356i
$576$		0			0
$577$	17.2935	+	29.9532i	0.719938	+	1.24697i	0.961024	+	0.276465i	$0.0891630\pi$
$577$	17.2935	+	29.9532i	0.719938	+	1.24697i	−0.241086	+	0.970504i	$0.577504\pi$
$578$		0			0
$579$	−12.1875	−	11.3921i	−0.506495	−	0.473437i
$580$		0			0
$581$	1.31536	+	7.45975i	0.0545701	+	0.309483i
$582$		0			0
$583$	8.64196	+	7.25147i	0.357914	+	0.300325i
$584$		0			0
$585$	−0.518763	−	7.68013i	−0.0214482	−	0.317534i
$586$		0			0
$587$	−23.3103	+	8.48424i	−0.962117	+	0.350182i	−0.774863	−	0.632129i	$-0.782181\pi$
$587$	−23.3103	+	8.48424i	−0.962117	+	0.350182i	−0.187255	+	0.982311i	$0.559959\pi$
$588$		0			0
$589$	49.4816	−	41.5200i	2.03885	−	1.71080i
$590$		0			0
$591$	−11.8195	+	8.88467i	−0.486188	+	0.365466i
$592$		0			0
$593$	−31.9466			−1.31189			−0.655944	−	0.754809i	$-0.727729\pi$
$593$	−31.9466			−1.31189			−0.655944	+	0.754809i	$0.727729\pi$
$594$		0			0
$595$	2.94613			0.120780
$596$		0			0
$597$	−2.10033	−	17.2750i	−0.0859607	−	0.707018i
$598$		0			0
$599$	−17.7549	+	14.8981i	−0.725446	+	0.608722i	−0.928886	−	0.370366i	$-0.879232\pi$
$599$	−17.7549	+	14.8981i	−0.725446	+	0.608722i	0.203440	+	0.979087i	$0.434788\pi$
$600$		0			0
$601$	21.8157	−	7.94025i	0.889879	−	0.323890i	0.143689	−	0.989623i	$-0.454103\pi$
$601$	21.8157	−	7.94025i	0.889879	−	0.323890i	0.746190	+	0.665733i	$0.231881\pi$
$602$		0			0
$603$	3.25049	−	4.45170i	0.132370	−	0.181287i
$604$		0			0
$605$	−13.4607	−	11.2949i	−0.547256	−	0.459202i
$606$		0			0
$607$	−0.0554097	−	0.314244i	−0.00224901	−	0.0127548i	0.983663	−	0.180022i	$-0.0576169\pi$
$607$	−0.0554097	−	0.314244i	−0.00224901	−	0.0127548i	−0.985912	+	0.167267i	$0.946506\pi$
$608$		0			0
$609$	−1.85716	+	8.00098i	−0.0752559	+	0.324216i
$610$		0			0
$611$	4.59684	+	7.96195i	0.185968	+	0.322106i
$612$		0			0
$613$	7.07232	−	12.2496i	0.285648	−	0.494758i	−0.687118	−	0.726546i	$-0.741124\pi$
$613$	7.07232	−	12.2496i	0.285648	−	0.494758i	0.972766	+	0.231788i	$0.0744577\pi$
$614$		0			0
$615$	−5.86697	−	11.5484i	−0.236579	−	0.465675i
$616$		0			0
$617$	24.6544	+	8.97348i	0.992551	+	0.361259i	0.786707	−	0.617326i	$-0.211784\pi$
$617$	24.6544	+	8.97348i	0.992551	+	0.361259i	0.205843	+	0.978585i	$0.434006\pi$
$618$		0			0
$619$	−3.63980	+	20.6424i	−0.146296	+	0.829686i	0.820021	+	0.572333i	$0.193962\pi$
$619$	−3.63980	+	20.6424i	−0.146296	+	0.829686i	−0.966317	+	0.257353i	$0.917150\pi$
$620$		0			0
$621$	0.356835	+	25.6717i	0.0143193	+	1.03017i
$622$		0			0
$623$	1.37470	−	7.79632i	0.0550763	−	0.312353i
$624$		0			0
$625$	15.7813	+	5.74391i	0.631251	+	0.229757i
$626$		0			0
$627$	19.4691	+	1.04347i	0.777523	+	0.0416720i
$628$		0			0
$629$	1.64671	−	2.85218i	0.0656585	−	0.113724i
$630$		0			0
$631$	4.35176	+	7.53747i	0.173241	+	0.300062i	0.939551	−	0.342409i	$-0.111243\pi$
$631$	4.35176	+	7.53747i	0.173241	+	0.300062i	−0.766310	+	0.642471i	$0.777909\pi$
$632$		0			0
$633$	27.6468	−	8.41669i	1.09886	−	0.334533i
$634$		0			0
$635$	6.30187	+	35.7397i	0.250082	+	1.41829i
$636$		0			0
$637$	6.87036	+	5.76492i	0.272214	+	0.228414i
$638$		0			0
$639$	−5.85959	+	20.2536i	−0.231802	+	0.801219i
$640$		0			0
$641$	−3.34559	+	1.21770i	−0.132143	+	0.0480961i	−0.407245	−	0.913319i	$-0.633511\pi$
$641$	−3.34559	+	1.21770i	−0.132143	+	0.0480961i	0.275102	+	0.961415i	$0.411288\pi$
$642$		0			0
$643$	−14.9101	+	12.5111i	−0.587999	+	0.493390i	−0.887563	−	0.460687i	$-0.847603\pi$
$643$	−14.9101	+	12.5111i	−0.587999	+	0.493390i	0.299564	+	0.954076i	$0.403159\pi$
$644$		0			0
$645$	−6.77878	−	2.88690i	−0.266914	−	0.113672i
$646$		0			0
$647$	−14.4926			−0.569763			−0.284882	−	0.958563i	$-0.591954\pi$
$647$	−14.4926			−0.569763			−0.284882	+	0.958563i	$0.591954\pi$
$648$		0			0
$649$	−2.96479			−0.116378
$650$		0			0
$651$	6.58519	+	2.80446i	0.258094	+	0.109916i
$652$		0			0
$653$	8.75778	−	7.34865i	0.342719	−	0.287575i	−0.455140	−	0.890420i	$-0.650411\pi$
$653$	8.75778	−	7.34865i	0.342719	−	0.287575i	0.797858	+	0.602845i	$0.205966\pi$
$654$		0			0
$655$	20.3363	−	7.40179i	0.794603	−	0.289212i
$656$		0			0
$657$	−14.1184	+	3.48461i	−0.550813	+	0.135948i
$658$		0			0
$659$	20.0290	+	16.8063i	0.780218	+	0.654681i	0.943304	−	0.331931i	$-0.107700\pi$
$659$	20.0290	+	16.8063i	0.780218	+	0.654681i	−0.163086	+	0.986612i	$0.552145\pi$
$660$		0			0
$661$	−7.21799	−	40.9353i	−0.280747	−	1.59220i	−0.720092	−	0.693878i	$-0.755901\pi$
$661$	−7.21799	−	40.9353i	−0.280747	−	1.59220i	0.439345	−	0.898318i	$-0.355211\pi$
$662$		0			0
$663$	−6.41878	+	1.95410i	−0.249285	+	0.0758911i
$664$		0			0
$665$	−4.18527	−	7.24911i	−0.162298	−	0.281108i
$666$		0			0
$667$	22.2008	−	38.4529i	0.859619	−	1.48890i
$668$		0			0
$669$	−24.7323	−	1.32555i	−0.956204	−	0.0512486i
$670$		0			0
$671$	−10.9012	−	3.96770i	−0.420835	−	0.153171i
$672$		0			0
$673$	3.37128	−	19.1195i	0.129953	−	0.737002i	−0.848289	−	0.529534i	$-0.822367\pi$
$673$	3.37128	−	19.1195i	0.129953	−	0.737002i	0.978242	−	0.207468i	$-0.0665222\pi$
$674$		0			0
$675$	−6.64612	+	1.26738i	−0.255809	+	0.0487814i
$676$		0			0
$677$	3.31320	−	18.7901i	0.127337	−	0.722162i	−0.852556	−	0.522636i	$-0.824949\pi$
$677$	3.31320	−	18.7901i	0.127337	−	0.722162i	0.979893	−	0.199526i	$-0.0639403\pi$
$678$		0			0
$679$	−9.22233	−	3.35665i	−0.353920	−	0.128817i
$680$		0			0
$681$	−3.69356	−	7.27030i	−0.141538	−	0.278599i
$682$		0			0
$683$	−11.2474	+	19.4811i	−0.430371	+	0.745424i	−0.996905	−	0.0786138i	$-0.974951\pi$
$683$	−11.2474	+	19.4811i	−0.430371	+	0.745424i	0.566534	+	0.824038i	$0.308284\pi$
$684$		0			0
$685$	18.2537	+	31.6164i	0.697439	+	1.20800i
$686$		0			0
$687$	4.13006	−	17.7931i	0.157572	−	0.678848i
$688$		0			0
$689$	1.91540	+	10.8628i	0.0729710	+	0.413839i
$690$		0			0
$691$	−14.4541	−	12.1284i	−0.549859	−	0.461386i	0.325034	−	0.945702i	$-0.394624\pi$
$691$	−14.4541	−	12.1284i	−0.549859	−	0.461386i	−0.874893	+	0.484316i	$0.839069\pi$
$692$		0			0
$693$	0.874050	+	1.97573i	0.0332024	+	0.0750519i
$694$		0			0
$695$	14.5780	−	5.30595i	0.552974	−	0.201266i
$696$		0			0
$697$	−8.64916	+	7.25751i	−0.327610	+	0.274898i
$698$		0			0
$699$	−1.29573	−	10.6572i	−0.0490089	−	0.403093i
$700$		0			0
$701$	46.9150			1.77196			0.885978	−	0.463727i	$-0.153488\pi$
$701$	46.9150			1.77196			0.885978	+	0.463727i	$0.153488\pi$
$702$		0			0
$703$	−9.35726			−0.352916
$704$		0			0
$705$	−18.3445	+	13.7895i	−0.690893	+	0.519343i
$706$		0			0
$707$	−5.02319	+	4.21496i	−0.188916	+	0.158520i
$708$		0			0
$709$	17.0836	−	6.21792i	0.641588	−	0.233519i	−0.000679379	−	1.00000i	$-0.500216\pi$
$709$	17.0836	−	6.21792i	0.641588	−	0.233519i	0.642267	+	0.766481i	$0.277994\pi$
$710$		0			0
$711$	28.6453	−	19.2229i	1.07428	−	0.720914i
$712$		0			0
$713$	−29.6398	−	24.8708i	−1.11002	−	0.931417i
$714$		0			0
$715$	0.608041	+	3.44837i	0.0227394	+	0.128962i
$716$		0			0
$717$	0.228654	+	0.213730i	0.00853924	+	0.00798191i
$718$		0			0
$719$	12.6194	+	21.8575i	0.470626	+	0.815148i	0.999436	−	0.0335927i	$-0.0106949\pi$
$719$	12.6194	+	21.8575i	0.470626	+	0.815148i	−0.528810	+	0.848740i	$0.677362\pi$
$720$		0			0
$721$	−1.86963	+	3.23829i	−0.0696285	+	0.120600i
$722$		0			0
$723$	−9.15873	+	14.0667i	−0.340617	+	0.523146i
$724$		0			0
$725$	10.9954	+	4.00201i	0.408360	+	0.148631i
$726$		0			0
$727$	−0.237158	+	1.34499i	−0.00879571	+	0.0498829i	−0.988890	−	0.148651i	$-0.952507\pi$
$727$	−0.237158	+	1.34499i	−0.00879571	+	0.0498829i	0.980094	+	0.198534i	$0.0636180\pi$
$728$		0			0
$729$	−20.1928	+	17.9234i	−0.747882	+	0.663831i
$730$		0			0
$731$	−1.11521	+	6.32466i	−0.0412475	+	0.233926i
$732$		0			0
$733$	37.2132	+	13.5445i	1.37450	+	0.500278i	0.920507	−	0.390726i	$-0.127776\pi$
$733$	37.2132	+	13.5445i	1.37450	+	0.500278i	0.453995	+	0.891004i	$0.349998\pi$
$734$		0			0
$735$	−12.2154	+	18.7613i	−0.450570	+	0.692021i
$736$		0			0
$737$	−1.25370	+	2.17147i	−0.0461806	+	0.0799871i
$738$		0			0
$739$	4.92991	+	8.53886i	0.181350	+	0.314107i	0.942340	−	0.334656i	$-0.108620\pi$
$739$	4.92991	+	8.53886i	0.181350	+	0.314107i	−0.760991	+	0.648763i	$0.775287\pi$
$740$		0			0
$741$	13.9267	+	13.0177i	0.511610	+	0.478218i
$742$		0			0
$743$	−7.77297	−	44.0827i	−0.285163	−	1.61724i	−0.704704	−	0.709501i	$-0.748920\pi$
$743$	−7.77297	−	44.0827i	−0.285163	−	1.61724i	0.419542	−	0.907736i	$-0.362191\pi$
$744$		0			0
$745$	−0.783397	−	0.657348i	−0.0287014	−	0.0240834i
$746$		0			0
$747$	35.7575	−	23.9957i	1.30830	−	0.877955i
$748$		0			0
$749$	−0.719569	+	0.261902i	−0.0262925	+	0.00956967i
$750$		0			0
$751$	−11.0845	+	9.30097i	−0.404478	+	0.339397i	−0.822221	−	0.569168i	$-0.807265\pi$
$751$	−11.0845	+	9.30097i	−0.404478	+	0.339397i	0.417744	+	0.908565i	$0.362821\pi$
$752$		0			0
$753$	25.9254	−	19.4881i	0.944774	−	0.710185i
$754$		0			0
$755$	−18.6367			−0.678260
$756$		0			0
$757$	−17.6905			−0.642972			−0.321486	−	0.946914i	$-0.604182\pi$
$757$	−17.6905			−0.642972			−0.321486	+	0.946914i	$0.604182\pi$
$758$		0			0
$759$	−1.40956	−	11.5935i	−0.0511640	−	0.420818i
$760$		0			0
$761$	−27.4931	+	23.0695i	−0.996625	+	0.836267i	−0.986513	−	0.163681i	$-0.947663\pi$
$761$	−27.4931	+	23.0695i	−0.996625	+	0.836267i	−0.0101115	+	0.999949i	$0.503219\pi$
$762$		0			0
$763$	−9.12251	+	3.32032i	−0.330257	+	0.120204i
$764$		0			0
$765$	−6.77601	−	15.3167i	−0.244987	−	0.553778i
$766$		0			0
$767$	−2.22065	−	1.86334i	−0.0801829	−	0.0672815i
$768$		0			0
$769$	4.16898	+	23.6435i	0.150337	+	0.852605i	0.962926	+	0.269767i	$0.0869468\pi$
$769$	4.16898	+	23.6435i	0.150337	+	0.852605i	−0.812588	+	0.582838i	$0.801942\pi$
$770$		0			0
$771$	6.45014	−	27.7884i	0.232296	−	1.00077i
$772$		0			0
$773$	22.5380	+	39.0369i	0.810634	+	1.40406i	0.912421	+	0.409253i	$0.134211\pi$
$773$	22.5380	+	39.0369i	0.810634	+	1.40406i	−0.101787	+	0.994806i	$0.532456\pi$
$774$		0			0
$775$	5.09823	−	8.83040i	0.183134	−	0.317197i
$776$		0			0
$777$	−0.469630	−	0.924407i	−0.0168479	−	0.0331629i
$778$		0			0
$779$	30.1445	+	10.9717i	1.08004	+	0.393102i
$780$		0			0
$781$	1.66545	−	9.44525i	0.0595946	−	0.337978i
$782$		0			0
$783$	45.8680	−	8.74677i	1.63919	−	0.312584i
$784$		0			0
$785$	−1.50402	+	8.52974i	−0.0536809	+	0.304439i
$786$		0			0
$787$	−42.0352	−	15.2996i	−1.49839	−	0.545371i	−0.542749	−	0.839895i	$-0.682617\pi$
$787$	−42.0352	−	15.2996i	−1.49839	−	0.545371i	−0.955644	+	0.294524i	$0.904839\pi$
$788$		0			0
$789$	−6.15019	−	0.329625i	−0.218953	−	0.0117350i
$790$		0			0
$791$	−2.11751	+	3.66764i	−0.0752900	+	0.130406i
$792$		0			0
$793$	−5.67137	−	9.82310i	−0.201396	−	0.348829i
$794$		0			0
$795$	−26.3405	+	8.01898i	−0.934200	+	0.284404i
$796$		0			0
$797$	−5.06364	−	28.7173i	−0.179363	−	1.01722i	−0.932986	−	0.359912i	$-0.882807\pi$
$797$	−5.06364	−	28.7173i	−0.179363	−	1.01722i	0.753623	−	0.657307i	$-0.228305\pi$
$798$		0			0
$799$	15.3238	+	12.8582i	0.542116	+	0.454889i
$800$		0			0
$801$	−43.6944	+	10.7843i	−1.54386	+	0.381045i
$802$		0			0
$803$	6.21611	−	2.26248i	0.219362	−	0.0798411i
$804$		0			0
$805$	−3.84096	+	3.22295i	−0.135376	+	0.113594i
$806$		0			0
$807$	10.2191	+	4.35203i	0.359728	+	0.153199i
$808$		0			0
$809$	−17.9470			−0.630983			−0.315491	−	0.948928i	$-0.602169\pi$
$809$	−17.9470			−0.630983			−0.315491	+	0.948928i	$0.602169\pi$
$810$		0			0
$811$	−36.1342			−1.26884			−0.634422	−	0.772987i	$-0.718762\pi$
$811$	−36.1342			−1.26884			−0.634422	+	0.772987i	$0.718762\pi$
$812$		0			0
$813$	0.419248	+	0.178547i	0.0147037	+	0.00626190i
$814$		0			0
$815$	33.1205	−	27.7914i	1.16016	−	0.973490i
$816$		0			0
$817$	17.1464	−	6.24079i	0.599878	−	0.218338i
$818$		0			0
$819$	−0.587062	+	2.02917i	−0.0205136	+	0.0709049i
$820$		0			0
$821$	−25.4948	−	21.3927i	−0.889776	−	0.746611i	0.0783890	−	0.996923i	$-0.475022\pi$
$821$	−25.4948	−	21.3927i	−0.889776	−	0.746611i	−0.968165	+	0.250312i	$0.919467\pi$
$822$		0			0
$823$	3.19979	+	18.1469i	0.111538	+	0.632562i	0.988406	+	0.151832i	$0.0485172\pi$
$823$	3.19979	+	18.1469i	0.111538	+	0.632562i	−0.876869	+	0.480730i	$0.840372\pi$
$824$		0			0
$825$	2.94431	−	0.896352i	0.102508	−	0.0312070i
$826$		0			0
$827$	−9.29674	−	16.1024i	−0.323279	−	0.559936i	0.657883	−	0.753120i	$-0.271452\pi$
$827$	−9.29674	−	16.1024i	−0.323279	−	0.559936i	−0.981163	+	0.193184i	$0.938119\pi$
$828$		0			0
$829$	−26.1723	+	45.3318i	−0.909003	+	1.57444i	−0.0935514	+	0.995614i	$0.529822\pi$
$829$	−26.1723	+	45.3318i	−0.909003	+	1.57444i	−0.815452	+	0.578825i	$0.803511\pi$
$830$		0			0
$831$	−51.8159	−	2.77712i	−1.79747	−	0.0963372i
$832$		0			0
$833$	18.3372	+	6.67421i	0.635348	+	0.231248i
$834$		0			0
$835$	−2.56002	+	14.5186i	−0.0885931	+	0.502436i
$836$		0			0
$837$	−0.565537	−	40.6862i	−0.0195478	−	1.40632i
$838$		0			0
$839$	7.04237	−	39.9393i	0.243130	−	1.37886i	−0.581667	−	0.813427i	$-0.697599\pi$
$839$	7.04237	−	39.9393i	0.243130	−	1.37886i	0.824797	−	0.565429i	$-0.191289\pi$
$840$		0			0
$841$	−48.6337	−	17.7012i	−1.67702	−	0.610387i
$842$		0			0
$843$	12.1011	+	23.8195i	0.416785	+	0.820388i
$844$		0			0
$845$	10.7876	−	18.6847i	0.371105	−	0.642773i
$846$		0			0
$847$	2.41101	+	4.17600i	0.0828434	+	0.143489i
$848$		0			0
$849$	−8.55883	+	36.8730i	−0.293738	+	1.26548i
$850$		0			0
$851$	0.973309	+	5.51991i	0.0333646	+	0.189220i
$852$		0			0
$853$	−18.5062	−	15.5286i	−0.633642	−	0.531689i	0.268416	−	0.963303i	$-0.413500\pi$
$853$	−18.5062	−	15.5286i	−0.633642	−	0.531689i	−0.902058	+	0.431614i	$0.857944\pi$
$854$		0			0
$855$	−28.0616	+	38.4317i	−0.959688	+	1.31434i
$856$		0			0
$857$	−2.84802	+	1.03659i	−0.0972864	+	0.0354094i	−0.390205	−	0.920728i	$-0.627596\pi$
$857$	−2.84802	+	1.03659i	−0.0972864	+	0.0354094i	0.292918	+	0.956137i	$0.405374\pi$
$858$		0			0
$859$	−26.5879	+	22.3099i	−0.907167	+	0.761203i	−0.971578	−	0.236720i	$-0.923928\pi$
$859$	−26.5879	+	22.3099i	−0.907167	+	0.761203i	0.0644111	+	0.997923i	$0.479483\pi$
$860$		0			0
$861$	0.429020	+	3.52864i	0.0146209	+	0.120256i
$862$		0			0
$863$	−56.1958			−1.91293			−0.956463	−	0.291853i	$-0.905728\pi$
$863$	−56.1958			−1.91293			−0.956463	+	0.291853i	$0.905728\pi$
$864$		0			0
$865$	−22.5088			−0.765321
$866$		0			0
$867$	11.8671	−	8.92045i	0.403026	−	0.302954i
$868$		0			0
$869$	−12.0211	+	10.0869i	−0.407789	+	0.342176i
$870$		0			0
$871$	−2.30378	+	0.838506i	−0.0780605	+	0.0284117i
$872$		0			0
$873$	3.76006	+	55.6665i	0.127259	+	1.88403i
$874$		0			0
$875$	−4.89903	−	4.11078i	−0.165618	−	0.138970i
$876$		0			0
$877$	−5.91607	−	33.5517i	−0.199772	−	1.13296i	−0.905458	−	0.424436i	$-0.860472\pi$
$877$	−5.91607	−	33.5517i	−0.199772	−	1.13296i	0.705686	−	0.708524i	$-0.250639\pi$
$878$		0			0
$879$	−17.9450	−	16.7738i	−0.605271	−	0.565766i
$880$		0			0
$881$	−17.9660	−	31.1180i	−0.605290	−	1.04839i	−0.992006	−	0.126194i	$-0.959724\pi$
$881$	−17.9660	−	31.1180i	−0.605290	−	1.04839i	0.386716	−	0.922199i	$-0.373609\pi$
$882$		0			0
$883$	3.22767	−	5.59049i	0.108620	−	0.188135i	−0.806592	−	0.591109i	$-0.798690\pi$
$883$	3.22767	−	5.59049i	0.108620	−	0.188135i	0.915211	+	0.402974i	$0.132024\pi$
$884$		0			0
$885$	3.94827	−	6.06406i	0.132719	−	0.203841i
$886$		0			0
$887$	−31.8568	−	11.5949i	−1.06965	−	0.389320i	−0.253603	−	0.967308i	$-0.581616\pi$
$887$	−31.8568	−	11.5949i	−1.06965	−	0.389320i	−0.816045	+	0.577989i	$0.803838\pi$
$888$		0			0
$889$	1.72936	−	9.80768i	0.0580008	−	0.328939i
$890$		0			0
$891$	8.26143	−	9.08826i	0.276768	−	0.304468i
$892$		0			0
$893$	9.86924	−	55.9712i	0.330262	−	1.87301i
$894$		0			0
$895$	−26.0196	−	9.47036i	−0.869739	−	0.316559i
$896$		0			0
$897$	6.23064	−	9.56951i	0.208035	−	0.319517i
$898$		0			0
$899$	−35.1853	+	60.9428i	−1.17350	+	2.03255i
$900$		0			0
$901$	12.0000	+	20.7847i	0.399779	+	0.692437i
$902$		0			0
$903$	1.47709	+	1.38068i	0.0491545	+	0.0459463i
$904$		0			0
$905$	3.27986	+	18.6010i	0.109026	+	0.618319i
$906$		0			0
$907$	30.4159	+	25.5220i	1.00994	+	0.847444i	0.988331	−	0.152322i	$-0.0486751\pi$
$907$	30.4159	+	25.5220i	1.00994	+	0.847444i	0.0216139	+	0.999766i	$0.493120\pi$
$908$		0			0
$909$	33.4665	+	16.4210i	1.11001	+	0.544649i
$910$		0			0
$911$	41.7700	−	15.2030i	1.38390	−	0.503699i	0.460543	−	0.887638i	$-0.347655\pi$
$911$	41.7700	−	15.2030i	1.38390	−	0.503699i	0.923359	+	0.383939i	$0.125433\pi$
$912$		0			0
$913$	−15.0058	+	12.5914i	−0.496620	+	0.416714i
$914$		0			0
$915$	22.6326	−	17.0129i	0.748211	−	0.562429i
$916$		0			0
$917$	−5.93883			−0.196117
$918$		0			0
$919$	−1.03441			−0.0341221			−0.0170611	−	0.999854i	$-0.505431\pi$
$919$	−1.03441			−0.0341221			−0.0170611	+	0.999854i	$0.505431\pi$
$920$		0			0
$921$	0.321800	+	2.64677i	0.0106037	+	0.0872142i
$922$		0			0
$923$	7.18368	−	6.02783i	0.236454	−	0.198408i
$924$		0			0
$925$	−1.38802	+	0.505197i	−0.0456377	+	0.0166108i
$926$		0			0
$927$	21.1357	+	2.27210i	0.694189	+	0.0746256i
$928$		0			0
$929$	1.31025	+	1.09943i	0.0429880	+	0.0360712i	0.664029	−	0.747707i	$-0.268845\pi$
$929$	1.31025	+	1.09943i	0.0429880	+	0.0360712i	−0.621041	+	0.783778i	$0.713290\pi$
$930$		0			0
$931$	−9.62765	−	54.6011i	−0.315534	−	1.78948i
$932$		0			0
$933$	4.70212	−	20.2576i	0.153941	−	0.663204i
$934$		0			0
$935$	3.80939	+	6.59805i	0.124580	+	0.215779i
$936$		0			0
$937$	−19.8504	+	34.3820i	−0.648486	+	1.12321i	0.334999	+	0.942218i	$0.391264\pi$
$937$	−19.8504	+	34.3820i	−0.648486	+	1.12321i	−0.983485	+	0.180992i	$0.942069\pi$
$938$		0			0
$939$	−1.64249	−	3.23302i	−0.0536005	−	0.105506i
$940$		0			0
$941$	3.80422	+	1.38462i	0.124014	+	0.0451374i	0.403282	−	0.915076i	$-0.367869\pi$
$941$	3.80422	+	1.38462i	0.124014	+	0.0451374i	−0.279268	+	0.960213i	$0.590092\pi$
$942$		0			0
$943$	3.33675	−	18.9237i	0.108660	−	0.616239i
$944$		0			0
$945$	−5.20506	−	0.843376i	−0.169321	−	0.0274350i
$946$		0			0
$947$	−1.27986	+	7.25844i	−0.0415898	+	0.235868i	−0.998516	−	0.0544648i	$-0.982655\pi$
$947$	−1.27986	+	7.25844i	−0.0415898	+	0.235868i	0.956926	+	0.290332i	$0.0937658\pi$
$948$		0			0
$949$	6.07785	+	2.21216i	0.197295	+	0.0718096i
$950$		0			0
$951$	42.7562	+	2.29155i	1.38646	+	0.0743087i
$952$		0			0
$953$	−17.4357	+	30.1995i	−0.564797	+	0.978257i	0.432272	+	0.901743i	$0.357712\pi$
$953$	−17.4357	+	30.1995i	−0.564797	+	0.978257i	−0.997069	+	0.0765136i	$0.975621\pi$
$954$		0			0
$955$	−0.402359	−	0.696906i	−0.0130200	−	0.0225514i
$956$		0			0
$957$	−20.3201	+	6.18615i	−0.656854	+	0.199970i
$958$		0			0
$959$	−1.73967	−	9.86617i	−0.0561769	−	0.318595i
$960$		0			0
$961$	23.2278	+	19.4904i	0.749283	+	0.628723i
$962$		0			0
$963$	3.01660	+	3.13863i	0.0972085	+	0.101141i
$964$		0			0
$965$	−17.4049	+	6.33485i	−0.560282	+	0.203926i
$966$		0			0
$967$	13.5633	−	11.3809i	0.436165	−	0.365986i	−0.398107	−	0.917339i	$-0.630333\pi$
$967$	13.5633	−	11.3809i	0.436165	−	0.365986i	0.834272	+	0.551353i	$0.185888\pi$
$968$		0			0
$969$	38.1620	+	16.2522i	1.22594	+	0.522095i
$970$		0			0
$971$	50.7783			1.62955			0.814777	−	0.579775i	$-0.196859\pi$
$971$	50.7783			1.62955			0.814777	+	0.579775i	$0.196859\pi$
$972$		0			0
$973$	−4.25723			−0.136480
$974$		0			0
$975$	2.76865	+	1.17910i	0.0886678	+	0.0377613i
$976$		0			0
$977$	32.2580	−	27.0677i	1.03203	−	0.865972i	0.0409350	−	0.999162i	$-0.486966\pi$
$977$	32.2580	−	27.0677i	1.03203	−	0.865972i	0.991091	+	0.133190i	$0.0425219\pi$
$978$		0			0
$979$	19.2379	−	7.00202i	0.614845	−	0.223785i
$980$		0			0
$981$	38.2437	+	39.7907i	1.22103	+	1.27042i
$982$		0			0
$983$	−45.1644	−	37.8974i	−1.44052	−	1.20874i	−0.939151	−	0.343506i	$-0.888385\pi$
$983$	−45.1644	−	37.8974i	−1.44052	−	1.20874i	−0.501369	−	0.865234i	$-0.667170\pi$
$984$		0			0
$985$	2.85069	+	16.1670i	0.0908304	+	0.515125i
$986$		0			0
$987$	6.02474	−	1.83415i	0.191770	−	0.0583815i
$988$		0			0
$989$	−5.46500	−	9.46565i	−0.173777	−	0.300990i
$990$		0			0
$991$	3.33936	−	5.78394i	0.106078	−	0.183733i	−0.808100	−	0.589045i	$-0.799504\pi$
$991$	3.33936	−	5.78394i	0.106078	−	0.183733i	0.914178	+	0.405312i	$0.132837\pi$
$992$		0			0
$993$	14.8838	+	0.797710i	0.472323	+	0.0253146i
$994$		0			0
$995$	−18.1554	−	6.60804i	−0.575566	−	0.209489i
$996$		0			0
$997$	−0.447272	+	2.53660i	−0.0141652	+	0.0803351i	−0.991071	−	0.133336i	$-0.957431\pi$
$997$	−0.447272	+	2.53660i	−0.0141652	+	0.0803351i	0.976906	+	0.213671i	$0.0685421\pi$
$998$		0			0
$999$	−3.72580	+	4.56769i	−0.117879	+	0.144515i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.q.b.25.5	✓	30
3.2	odd	2		648.2.q.b.73.2		30
4.3	odd	2		432.2.u.f.241.1		30
27.11	odd	18		5832.2.a.l.1.5		15
27.13	even	9	inner	216.2.q.b.121.5	yes	30
27.14	odd	18		648.2.q.b.577.2		30
27.16	even	9		5832.2.a.k.1.11		15
108.67	odd	18		432.2.u.f.337.1		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.b.25.5	✓	30	1.1	even	1	trivial
216.2.q.b.121.5	yes	30	27.13	even	9	inner
432.2.u.f.241.1		30	4.3	odd	2
432.2.u.f.337.1		30	108.67	odd	18
648.2.q.b.73.2		30	3.2	odd	2
648.2.q.b.577.2		30	27.14	odd	18
5832.2.a.k.1.11		15	27.16	even	9
5832.2.a.l.1.5		15	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)

\(f(q)\)	\(=\)	\(q+(1.59356 + 0.678655i) q^{3} +(1.47310 - 1.23608i) q^{5} +(-0.495883 + 0.180487i) q^{7} +(2.07886 + 2.16295i) q^{9} +O(q^{10})\)	\(q+(1.59356 + 0.678655i) q^{3} +(1.47310 - 1.23608i) q^{5} +(-0.495883 + 0.180487i) q^{7} +(2.07886 + 2.16295i) q^{9} +(-1.04540 - 0.877191i) q^{11} +(-0.231701 - 1.31404i) q^{13} +(3.18634 - 0.970035i) q^{15} +(-1.45161 - 2.51426i) q^{17} +(-4.12432 + 7.14353i) q^{19} +(-0.912707 - 0.0489173i) q^{21} +(4.64302 + 1.68992i) q^{23} +(-0.226106 + 1.28231i) q^{25} +(1.84488 + 4.85761i) q^{27} +(1.56047 - 8.84985i) q^{29} +(-7.35856 - 2.67830i) q^{31} +(-1.07059 - 2.10732i) q^{33} +(-0.507389 + 0.878824i) q^{35} +(0.567200 + 0.982419i) q^{37} +(0.522552 - 2.25125i) q^{39} +(-0.675320 - 3.82993i) q^{41} +(-1.69457 - 1.42191i) q^{43} +(5.73593 + 0.616616i) q^{45} +(-6.47466 + 2.35658i) q^{47} +(-5.14899 + 4.32051i) q^{49} +(-0.606910 - 4.99177i) q^{51} -8.26669 q^{53} -2.62425 q^{55} +(-11.4203 + 8.58465i) q^{57} +(1.66426 - 1.39648i) q^{59} +(7.98814 - 2.90745i) q^{61} +(-1.42125 - 0.697365i) q^{63} +(-1.96558 - 1.64931i) q^{65} +(-0.319056 - 1.80946i) q^{67} +(6.25204 + 5.84399i) q^{69} +(3.51403 + 6.08647i) q^{71} +(-2.42368 + 4.19794i) q^{73} +(-1.23056 + 1.88999i) q^{75} +(0.676715 + 0.246304i) q^{77} +(1.99680 - 11.3244i) q^{79} +(-0.356716 + 8.99293i) q^{81} +(2.49258 - 14.1361i) q^{83} +(-5.24619 - 1.90946i) q^{85} +(8.49269 - 13.0437i) q^{87} +(-7.50092 + 12.9920i) q^{89} +(0.352064 + 0.609793i) q^{91} +(-9.90866 - 9.26194i) q^{93} +(2.75442 + 15.6211i) q^{95} +(14.2467 + 11.9544i) q^{97} +(-0.275905 - 4.08469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{7} - 6 q^{9}+O(q^{10}) \) 30 * q + 3 * q^7 - 6 * q^9	\( 30 q + 3 q^{7} - 6 q^{9} - 3 q^{11} - 12 q^{13} + 15 q^{15} + 6 q^{17} - 9 q^{19} + 30 q^{21} - 12 q^{23} + 24 q^{25} - 15 q^{27} - 9 q^{29} + 27 q^{31} - 30 q^{33} - 18 q^{35} - 15 q^{37} - 21 q^{39} - 15 q^{41} - 30 q^{43} + 15 q^{45} - 18 q^{47} + 15 q^{49} - 6 q^{51} - 18 q^{53} + 54 q^{55} - 72 q^{57} - 12 q^{59} + 6 q^{61} - 54 q^{63} - 54 q^{65} - 45 q^{67} + 9 q^{69} - 36 q^{73} + 69 q^{75} + 12 q^{77} + 45 q^{79} - 30 q^{81} - 3 q^{83} + 57 q^{85} - 60 q^{87} + 36 q^{89} - 39 q^{91} + 30 q^{93} + 51 q^{95} - 84 q^{97} + 162 q^{99}+O(q^{100}) \) 30 * q + 3 * q^7 - 6 * q^9 - 3 * q^11 - 12 * q^13 + 15 * q^15 + 6 * q^17 - 9 * q^19 + 30 * q^21 - 12 * q^23 + 24 * q^25 - 15 * q^27 - 9 * q^29 + 27 * q^31 - 30 * q^33 - 18 * q^35 - 15 * q^37 - 21 * q^39 - 15 * q^41 - 30 * q^43 + 15 * q^45 - 18 * q^47 + 15 * q^49 - 6 * q^51 - 18 * q^53 + 54 * q^55 - 72 * q^57 - 12 * q^59 + 6 * q^61 - 54 * q^63 - 54 * q^65 - 45 * q^67 + 9 * q^69 - 36 * q^73 + 69 * q^75 + 12 * q^77 + 45 * q^79 - 30 * q^81 - 3 * q^83 + 57 * q^85 - 60 * q^87 + 36 * q^89 - 39 * q^91 + 30 * q^93 + 51 * q^95 - 84 * q^97 + 162 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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