LMFDB - Embedded newform 324.2.m.a.13.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(13,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("324.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.m (of order $27$, degree $18$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$9$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			13.8
Character	$\chi$	$=$	324.13
Dual form			324.2.m.a.25.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50798 + 0.852058i) q^{3} +(1.16819 + 3.90202i) q^{5} +(-1.69197 - 3.92242i) q^{7} +(1.54799 + 2.56977i) q^{9} +O(q^{10})$	\(q+(1.50798 + 0.852058i) q^{3} +(1.16819 + 3.90202i) q^{5} +(-1.69197 - 3.92242i) q^{7} +(1.54799 + 2.56977i) q^{9} +(0.707474 - 0.167674i) q^{11} +(3.48323 + 2.29095i) q^{13} +(-1.56315 + 6.87952i) q^{15} +(-0.559183 + 0.203526i) q^{17} +(-5.80091 - 2.11136i) q^{19} +(0.790682 - 7.35657i) q^{21} +(-0.314501 + 0.729095i) q^{23} +(-9.68365 + 6.36904i) q^{25} +(0.144744 + 5.19414i) q^{27} +(-0.313243 - 5.37818i) q^{29} +(8.04246 - 0.940029i) q^{31} +(1.20972 + 0.349960i) q^{33} +(13.3288 - 11.1842i) q^{35} +(-2.61359 - 2.19306i) q^{37} +(3.30060 + 6.42262i) q^{39} +(4.93990 - 2.48091i) q^{41} +(-2.81985 - 2.98887i) q^{43} +(-8.21895 + 9.04227i) q^{45} +(5.32740 + 0.622684i) q^{47} +(-7.71891 + 8.18157i) q^{49} +(-1.01665 - 0.169544i) q^{51} +(5.90152 - 10.2217i) q^{53} +(1.48073 + 2.56470i) q^{55} +(-6.94865 - 8.12660i) q^{57} +(-12.7629 - 3.02487i) q^{59} +(3.87541 - 5.20558i) q^{61} +(7.46056 - 10.4198i) q^{63} +(-4.87028 + 16.2679i) q^{65} +(0.636617 - 10.9303i) q^{67} +(-1.09549 + 0.831486i) q^{69} +(-1.83516 + 10.4077i) q^{71} +(-0.878501 - 4.98223i) q^{73} +(-20.0295 + 1.35333i) q^{75} +(-1.85471 - 2.49131i) q^{77} +(-3.12040 - 1.56713i) q^{79} +(-4.20744 + 7.95597i) q^{81} +(2.77942 + 1.39588i) q^{83} +(-1.44739 - 1.94419i) q^{85} +(4.11016 - 8.37708i) q^{87} +(0.553305 + 3.13795i) q^{89} +(3.09258 - 17.5389i) q^{91} +(12.9288 + 5.43510i) q^{93} +(1.46201 - 25.1017i) q^{95} +(-0.385156 + 1.28651i) q^{97} +(1.52605 + 1.55849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q+O(q^{10}) $ 162 * q	$ 162 q + 27 q^{21} + 27 q^{23} + 27 q^{27} + 27 q^{29} + 27 q^{33} + 27 q^{35} - 18 q^{41} - 54 q^{45} - 54 q^{47} - 63 q^{51} - 54 q^{53} - 54 q^{57} - 63 q^{59} - 54 q^{63} - 90 q^{65} + 27 q^{67} - 90 q^{69} - 72 q^{71} - 90 q^{75} - 144 q^{77} + 54 q^{79} - 72 q^{81} - 72 q^{83} + 54 q^{85} - 144 q^{87} - 99 q^{89} - 90 q^{93} - 126 q^{95} + 27 q^{97} - 90 q^{99}+O(q^{100}) $ 162 * q + 27 * q^21 + 27 * q^23 + 27 * q^27 + 27 * q^29 + 27 * q^33 + 27 * q^35 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 - 90 * q^65 + 27 * q^67 - 90 * q^69 - 72 * q^71 - 90 * q^75 - 144 * q^77 + 54 * q^79 - 72 * q^81 - 72 * q^83 + 54 * q^85 - 144 * q^87 - 99 * q^89 - 90 * q^93 - 126 * q^95 + 27 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{4}{27}\right)$

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
$3$	1.50798	+	0.852058i	0.870631	+	0.491936i
$3$	1.50798	+	0.852058i	0.870631	+	0.491936i
$4$		0			0
$5$	1.16819	+	3.90202i	0.522430	+	1.74504i	0.656760	+	0.754100i	$0.271926\pi$
$5$	1.16819	+	3.90202i	0.522430	+	1.74504i	−0.134331	+	0.990937i	$0.542888\pi$
$6$		0			0
$7$	−1.69197	−	3.92242i	−0.639503	−	1.48253i	−0.861641	−	0.507519i	$-0.830563\pi$
$7$	−1.69197	−	3.92242i	−0.639503	−	1.48253i	0.222138	−	0.975015i	$-0.428696\pi$
$8$		0			0
$9$	1.54799	+	2.56977i	0.515998	+	0.856590i
$10$		0			0
$11$	0.707474	−	0.167674i	0.213311	−	0.0505557i	−0.122571	−	0.992460i	$-0.539114\pi$
$11$	0.707474	−	0.167674i	0.213311	−	0.0505557i	0.335882	+	0.941904i	$0.390966\pi$
$12$		0			0
$13$	3.48323	+	2.29095i	0.966073	+	0.635396i	0.931398	−	0.364002i	$-0.118590\pi$
$13$	3.48323	+	2.29095i	0.966073	+	0.635396i	0.0346753	+	0.999399i	$0.488960\pi$
$14$		0			0
$15$	−1.56315	+	6.87952i	−0.403603	+	1.77628i
$16$		0			0
$17$	−0.559183	+	0.203526i	−0.135622	+	0.0493623i	−0.408939	−	0.912562i	$-0.634101\pi$
$17$	−0.559183	+	0.203526i	−0.135622	+	0.0493623i	0.273318	+	0.961924i	$0.411879\pi$
$18$		0			0
$19$	−5.80091	−	2.11136i	−1.33082	−	0.484379i	−0.423911	−	0.905704i	$-0.639343\pi$
$19$	−5.80091	−	2.11136i	−1.33082	−	0.484379i	−0.906910	+	0.421325i	$0.861565\pi$
$20$		0			0
$21$	0.790682	−	7.35657i	0.172541	−	1.60533i
$22$		0			0
$23$	−0.314501	+	0.729095i	−0.0655780	+	0.152027i	−0.947853	−	0.318707i	$-0.896751\pi$
$23$	−0.314501	+	0.729095i	−0.0655780	+	0.152027i	0.882275	+	0.470734i	$0.156011\pi$
$24$		0			0
$25$	−9.68365	+	6.36904i	−1.93673	+	1.27381i
$26$		0			0
$27$	0.144744	+	5.19414i	0.0278559	+	0.999612i
$28$		0			0
$29$	−0.313243	−	5.37818i	−0.0581678	−	0.998703i	−0.893530	−	0.449003i	$-0.851779\pi$
$29$	−0.313243	−	5.37818i	−0.0581678	−	0.998703i	0.835362	−	0.549700i	$-0.185258\pi$
$30$		0			0
$31$	8.04246	−	0.940029i	1.44447	−	0.168834i	0.642539	−	0.766253i	$-0.277881\pi$
$31$	8.04246	−	0.940029i	1.44447	−	0.168834i	0.801929	+	0.597419i	$0.203807\pi$
$32$		0			0
$33$	1.20972	+	0.349960i	0.210586	+	0.0609202i
$34$		0			0
$35$	13.3288	−	11.1842i	2.25298	−	1.89047i
$36$		0			0
$37$	−2.61359	−	2.19306i	−0.429671	−	0.360537i	0.402157	−	0.915571i	$-0.368261\pi$
$37$	−2.61359	−	2.19306i	−0.429671	−	0.360537i	−0.831828	+	0.555034i	$0.812705\pi$
$38$		0			0
$39$	3.30060	+	6.42262i	0.528519	+	1.02844i
$40$		0			0
$41$	4.93990	−	2.48091i	0.771482	−	0.387453i	−0.0190931	−	0.999818i	$-0.506078\pi$
$41$	4.93990	−	2.48091i	0.771482	−	0.387453i	0.790575	+	0.612365i	$0.209782\pi$
$42$		0			0
$43$	−2.81985	−	2.98887i	−0.430024	−	0.455798i	0.475737	−	0.879587i	$-0.342181\pi$
$43$	−2.81985	−	2.98887i	−0.430024	−	0.455798i	−0.905761	+	0.423789i	$0.860700\pi$
$44$		0			0
$45$	−8.21895	+	9.04227i	−1.22521	+	1.34794i
$46$		0			0
$47$	5.32740	+	0.622684i	0.777082	+	0.0908278i	0.495383	−	0.868675i	$-0.335028\pi$
$47$	5.32740	+	0.622684i	0.777082	+	0.0908278i	0.281699	+	0.959503i	$0.409102\pi$
$48$		0			0
$49$	−7.71891	+	8.18157i	−1.10270	+	1.16880i
$50$		0			0
$51$	−1.01665	−	0.169544i	−0.142360	−	0.0237409i
$52$		0			0
$53$	5.90152	−	10.2217i	0.810636	−	1.40406i	−0.101783	−	0.994807i	$-0.532455\pi$
$53$	5.90152	−	10.2217i	0.810636	−	1.40406i	0.912419	−	0.409257i	$-0.134212\pi$
$54$		0			0
$55$	1.48073	+	2.56470i	0.199662	+	0.345824i
$56$		0			0
$57$	−6.94865	−	8.12660i	−0.920371	−	1.07639i
$58$		0			0
$59$	−12.7629	−	3.02487i	−1.66159	−	0.393805i	−0.710743	−	0.703452i	$-0.751641\pi$
$59$	−12.7629	−	3.02487i	−1.66159	−	0.393805i	−0.950852	+	0.309647i	$0.899789\pi$
$60$		0			0
$61$	3.87541	−	5.20558i	0.496195	−	0.666506i	−0.481521	−	0.876434i	$-0.659916\pi$
$61$	3.87541	−	5.20558i	0.496195	−	0.666506i	0.977717	+	0.209928i	$0.0673231\pi$
$62$		0			0
$63$	7.46056	−	10.4198i	0.939942	−	1.31278i
$64$		0			0
$65$	−4.87028	+	16.2679i	−0.604084	+	2.01778i
$66$		0			0
$67$	0.636617	−	10.9303i	0.0777752	−	1.33535i	−0.703292	−	0.710901i	$-0.748287\pi$
$67$	0.636617	−	10.9303i	0.0777752	−	1.33535i	0.781067	−	0.624447i	$-0.214676\pi$
$68$		0			0
$69$	−1.09549	+	0.831486i	−0.131882	+	0.100099i
$70$		0			0
$71$	−1.83516	+	10.4077i	−0.217794	+	1.23517i	0.658199	+	0.752844i	$0.271318\pi$
$71$	−1.83516	+	10.4077i	−0.217794	+	1.23517i	−0.875993	+	0.482324i	$0.839793\pi$
$72$		0			0
$73$	−0.878501	−	4.98223i	−0.102821	−	0.583125i	−0.992068	−	0.125699i	$-0.959883\pi$
$73$	−0.878501	−	4.98223i	−0.102821	−	0.583125i	0.889248	−	0.457426i	$-0.151229\pi$
$74$		0			0
$75$	−20.0295	+	1.35333i	−2.31281	+	0.156269i
$76$		0			0
$77$	−1.85471	−	2.49131i	−0.211364	−	0.283911i
$78$		0			0
$79$	−3.12040	−	1.56713i	−0.351073	−	0.176315i	0.264519	−	0.964380i	$-0.414787\pi$
$79$	−3.12040	−	1.56713i	−0.351073	−	0.176315i	−0.615592	+	0.788065i	$0.711083\pi$
$80$		0			0
$81$	−4.20744	+	7.95597i	−0.467493	+	0.883997i
$82$		0			0
$83$	2.77942	+	1.39588i	0.305081	+	0.153217i	0.594753	−	0.803909i	$-0.297250\pi$
$83$	2.77942	+	1.39588i	0.305081	+	0.153217i	−0.289672	+	0.957126i	$0.593546\pi$
$84$		0			0
$85$	−1.44739	−	1.94419i	−0.156992	−	0.210877i
$86$		0			0
$87$	4.11016	−	8.37708i	0.440655	−	0.898117i
$88$		0			0
$89$	0.553305	+	3.13795i	0.0586502	+	0.332622i	0.999988	−	0.00484315i	$-0.00154163\pi$
$89$	0.553305	+	3.13795i	0.0586502	+	0.332622i	−0.941338	+	0.337465i	$0.890431\pi$
$90$		0			0
$91$	3.09258	−	17.5389i	0.324190	−	1.83857i
$92$		0			0
$93$	12.9288	+	5.43510i	1.34065	+	0.563594i
$94$		0			0
$95$	1.46201	−	25.1017i	0.149999	−	2.57538i
$96$		0			0
$97$	−0.385156	+	1.28651i	−0.0391067	+	0.130626i	−0.975314	−	0.220823i	$-0.929126\pi$
$97$	−0.385156	+	1.28651i	−0.0391067	+	0.130626i	0.936207	+	0.351449i	$0.114311\pi$
$98$		0			0
$99$	1.52605	+	1.55849i	0.153374	+	0.156634i
$100$		0			0
$101$	−0.572384	+	0.768845i	−0.0569543	+	0.0765029i	−0.829688	−	0.558228i	$-0.811482\pi$
$101$	−0.572384	+	0.768845i	−0.0569543	+	0.0765029i	0.772733	+	0.634731i	$0.218889\pi$
$102$		0			0
$103$	−4.39244	−	1.04103i	−0.432800	−	0.102575i	0.00844068	−	0.999964i	$-0.497313\pi$
$103$	−4.39244	−	1.04103i	−0.432800	−	0.102575i	−0.441240	+	0.897389i	$0.645461\pi$
$104$		0			0
$105$	29.6291	−	5.50860i	2.89151	−	0.537584i
$106$		0			0
$107$	6.38041	+	11.0512i	0.616817	+	1.06836i	0.990063	+	0.140626i	$0.0449115\pi$
$107$	6.38041	+	11.0512i	0.616817	+	1.06836i	−0.373246	+	0.927733i	$0.621755\pi$
$108$		0			0
$109$	−0.479926	+	0.831255i	−0.0459685	+	0.0796198i	−0.888094	−	0.459662i	$-0.847971\pi$
$109$	−0.479926	+	0.831255i	−0.0459685	+	0.0796198i	0.842126	+	0.539281i	$0.181304\pi$
$110$		0			0
$111$	−2.07261	−	5.53401i	−0.196724	−	0.525265i
$112$		0			0
$113$	−8.08790	+	8.57267i	−0.760845	+	0.806449i	−0.985801	−	0.167920i	$-0.946295\pi$
$113$	−8.08790	+	8.57267i	−0.760845	+	0.806449i	0.224955	+	0.974369i	$0.427776\pi$
$114$		0			0
$115$	−3.21234	−	0.375469i	−0.299552	−	0.0350126i
$116$		0			0
$117$	−0.495217	+	12.4975i	−0.0457828	+	1.15539i
$118$		0			0
$119$	1.74443	+	1.84899i	0.159912	+	0.169497i
$120$		0			0
$121$	−9.35755	+	4.69954i	−0.850687	+	0.427231i
$122$		0			0
$123$	9.56313	+	0.467925i	0.862279	+	0.0421914i
$124$		0			0
$125$	−20.5634	−	17.2548i	−1.83925	−	1.54331i
$126$		0			0
$127$	0.449356	−	0.377055i	0.0398739	−	0.0334582i	−0.622633	−	0.782514i	$-0.713937\pi$
$127$	0.449356	−	0.377055i	0.0398739	−	0.0334582i	0.662507	+	0.749056i	$0.269493\pi$
$128$		0			0
$129$	−1.70558	−	6.90983i	−0.150168	−	0.608377i
$130$		0			0
$131$	−7.11777	+	0.831948i	−0.621882	+	0.0726876i	−0.421198	−	0.906968i	$-0.638390\pi$
$131$	−7.11777	+	0.831948i	−0.621882	+	0.0726876i	−0.200684	+	0.979656i	$0.564316\pi$
$132$		0			0
$133$	1.53331	+	26.3259i	0.132955	+	2.28275i
$134$		0			0
$135$	−20.0985	+	6.63252i	−1.72981	+	0.570836i
$136$		0			0
$137$	−3.59850	+	2.36677i	−0.307441	+	0.202207i	−0.693848	−	0.720121i	$-0.744086\pi$
$137$	−3.59850	+	2.36677i	−0.307441	+	0.202207i	0.386408	+	0.922328i	$0.373716\pi$
$138$		0			0
$139$	−1.87755	+	4.35265i	−0.159252	+	0.369187i	−0.979096	−	0.203400i	$-0.934801\pi$
$139$	−1.87755	+	4.35265i	−0.159252	+	0.369187i	0.819844	+	0.572587i	$0.194060\pi$
$140$		0			0
$141$	7.50304	+	5.47825i	0.631870	+	0.461352i
$142$		0			0
$143$	2.84843	+	1.03674i	0.238197	+	0.0866968i
$144$		0			0
$145$	20.6198	−	7.50501i	1.71238	−	0.623257i
$146$		0			0
$147$	−18.6111	+	5.76066i	−1.53502	+	0.475131i
$148$		0			0
$149$	−8.16567	−	5.37065i	−0.668958	−	0.439981i	0.169073	−	0.985604i	$-0.445923\pi$
$149$	−8.16567	−	5.37065i	−0.668958	−	0.439981i	−0.838031	+	0.545623i	$0.816293\pi$
$150$		0			0
$151$	−7.33765	+	1.73905i	−0.597129	+	0.141522i	−0.518056	−	0.855347i	$-0.673344\pi$
$151$	−7.33765	+	1.73905i	−0.597129	+	0.141522i	−0.0790731	+	0.996869i	$0.525196\pi$
$152$		0			0
$153$	−1.38863	−	1.12192i	−0.112264	−	0.0907015i
$154$		0			0
$155$	13.0631	+	30.2837i	1.04925	+	2.43245i
$156$		0			0
$157$	3.05125	+	10.1919i	0.243516	+	0.813402i	0.989133	+	0.147026i	$0.0469701\pi$
$157$	3.05125	+	10.1919i	0.243516	+	0.813402i	−0.745616	+	0.666376i	$0.767845\pi$
$158$		0			0
$159$	17.6089	−	10.3857i	1.39648	−	0.823640i
$160$		0			0
$161$	3.39194			0.267322
$162$		0			0
$163$	0.393109			0.0307906			0.0153953	−	0.999881i	$-0.495099\pi$
$163$	0.393109			0.0307906			0.0153953	+	0.999881i	$0.495099\pi$
$164$		0			0
$165$	0.0476336	+	5.12918i	0.00370827	+	0.399306i
$166$		0			0
$167$	3.29957	+	11.0213i	0.255328	+	0.852855i	0.985512	+	0.169605i	$0.0542491\pi$
$167$	3.29957	+	11.0213i	0.255328	+	0.852855i	−0.730184	+	0.683250i	$0.760566\pi$
$168$		0			0
$169$	1.73536	+	4.02302i	0.133489	+	0.309463i
$170$		0			0
$171$	−3.55406	−	18.1754i	−0.271786	−	1.38991i
$172$		0			0
$173$	16.3521	−	3.87551i	1.24322	−	0.294650i	0.444189	−	0.895933i	$-0.353492\pi$
$173$	16.3521	−	3.87551i	1.24322	−	0.294650i	0.799036	+	0.601284i	$0.205344\pi$
$174$		0			0
$175$	41.3664	+	27.2071i	3.12701	+	2.05667i
$176$		0			0
$177$	−16.6689	−	15.4362i	−1.25291	−	1.16026i
$178$		0			0
$179$	15.2198	−	5.53954i	1.13758	−	0.414045i	0.296540	−	0.955020i	$-0.404167\pi$
$179$	15.2198	−	5.53954i	1.13758	−	0.414045i	0.841038	+	0.540975i	$0.181945\pi$
$180$		0			0
$181$	12.5339	+	4.56197i	0.931638	+	0.339088i	0.762858	−	0.646566i	$-0.223795\pi$
$181$	12.5339	+	4.56197i	0.931638	+	0.339088i	0.168779	+	0.985654i	$0.446018\pi$
$182$		0			0
$183$	10.2795	−	4.54782i	0.759882	−	0.336185i
$184$		0			0
$185$	5.50420	−	12.7602i	0.404677	−	0.938146i
$186$		0			0
$187$	−0.361481	+	0.237750i	−0.0264341	+	0.0173860i
$188$		0			0
$189$	20.1287	−	9.35604i	1.46414	−	0.680552i
$190$		0			0
$191$	0.538713	+	9.24935i	0.0389799	+	0.669259i	0.960044	+	0.279849i	$0.0902843\pi$
$191$	0.538713	+	9.24935i	0.0389799	+	0.669259i	−0.921064	+	0.389411i	$0.872679\pi$
$192$		0			0
$193$	19.8566	−	2.32091i	1.42931	−	0.167063i	0.634032	−	0.773307i	$-0.281399\pi$
$193$	19.8566	−	2.32091i	1.42931	−	0.167063i	0.795279	+	0.606244i	$0.207325\pi$
$194$		0			0
$195$	−21.2055	+	20.3818i	−1.51856	+	1.45957i
$196$		0			0
$197$	−17.3877	+	14.5900i	−1.23882	+	1.03950i	−0.241210	+	0.970473i	$0.577544\pi$
$197$	−17.3877	+	14.5900i	−1.23882	+	1.03950i	−0.997615	+	0.0690242i	$0.978011\pi$
$198$		0			0
$199$	0.784385	+	0.658177i	0.0556036	+	0.0466569i	0.670166	−	0.742211i	$-0.266223\pi$
$199$	0.784385	+	0.658177i	0.0556036	+	0.0466569i	−0.614562	+	0.788868i	$0.710667\pi$
$200$		0			0
$201$	10.2733	−	15.9402i	0.724619	−	1.12434i
$202$		0			0
$203$	−20.5655	+	10.3284i	−1.44341	+	0.724909i
$204$		0			0
$205$	15.4513	+	16.3774i	1.07916	+	1.14385i
$206$		0			0
$207$	−2.36045	+	0.320439i	−0.164063	+	0.0222720i
$208$		0			0
$209$	−4.45802	−	0.521067i	−0.308367	−	0.0360430i
$210$		0			0
$211$	−15.2426	+	16.1562i	−1.04934	+	1.11224i	−0.0558372	+	0.998440i	$0.517783\pi$
$211$	−15.2426	+	16.1562i	−1.04934	+	1.11224i	−0.993504	+	0.113797i	$0.963699\pi$
$212$		0			0
$213$	−11.6354	+	14.1309i	−0.797242	+	0.968236i
$214$		0			0
$215$	8.36851	−	14.4947i	0.570728	−	0.988529i
$216$		0			0
$217$	−17.2947	−	29.9554i	−1.17404	−	2.03350i
$218$		0			0
$219$	2.92039	−	8.26162i	0.197342	−	0.558269i
$220$		0			0
$221$	−2.41403	−	0.572136i	−0.162385	−	0.0384860i
$222$		0			0
$223$	−1.15480	+	1.55116i	−0.0773309	+	0.103873i	−0.839105	−	0.543969i	$-0.816921\pi$
$223$	−1.15480	+	1.55116i	−0.0773309	+	0.103873i	0.761775	+	0.647842i	$0.224328\pi$
$224$		0			0
$225$	−31.3572	−	15.0255i	−2.09048	−	1.00170i
$226$		0			0
$227$	4.06304	−	13.5715i	0.269674	−	0.900772i	−0.710679	−	0.703517i	$-0.751612\pi$
$227$	4.06304	−	13.5715i	0.269674	−	0.900772i	0.980352	−	0.197256i	$-0.0632029\pi$
$228$		0			0
$229$	1.55727	−	26.7373i	0.102907	−	1.76685i	−0.413495	−	0.910506i	$-0.635692\pi$
$229$	1.55727	−	26.7373i	0.102907	−	1.76685i	0.516403	−	0.856346i	$-0.327271\pi$
$230$		0			0
$231$	−0.674121	−	5.33716i	−0.0443539	−	0.351159i
$232$		0			0
$233$	−2.77556	+	15.7410i	−0.181833	+	1.03122i	0.748125	+	0.663558i	$0.230954\pi$
$233$	−2.77556	+	15.7410i	−0.181833	+	1.03122i	−0.929958	+	0.367667i	$0.880157\pi$
$234$		0			0
$235$	3.79368	+	21.5150i	0.247473	+	1.40349i
$236$		0			0
$237$	−3.37022	−	5.02196i	−0.218919	−	0.326211i
$238$		0			0
$239$	9.29649	+	12.4874i	0.601340	+	0.807740i	0.993700	−	0.112072i	$-0.0357486\pi$
$239$	9.29649	+	12.4874i	0.601340	+	0.807740i	−0.392360	+	0.919812i	$0.628341\pi$
$240$		0			0
$241$	−24.4616	−	12.2851i	−1.57571	−	0.791353i	−0.576053	−	0.817413i	$-0.695408\pi$
$241$	−24.4616	−	12.2851i	−1.57571	−	0.791353i	−0.999660	+	0.0260597i	$0.991704\pi$
$242$		0			0
$243$	−13.1237	+	8.41244i	−0.841884	+	0.539658i
$244$		0			0
$245$	−40.9418	−	20.5617i	−2.61567	−	1.31364i
$246$		0			0
$247$	−15.3689	−	20.6440i	−0.977898	−	1.31354i
$248$		0			0
$249$	3.00193	+	4.47317i	0.190240	+	0.283476i
$250$		0			0
$251$	0.971406	+	5.50912i	0.0613146	+	0.347732i	0.999996	+	0.00294566i	$0.000937634\pi$
$251$	0.971406	+	5.50912i	0.0613146	+	0.347732i	−0.938681	+	0.344787i	$0.887951\pi$
$252$		0			0
$253$	−0.100251	+	0.568549i	−0.00630270	+	0.0357444i
$254$		0			0
$255$	−0.526076	−	4.16505i	−0.0329442	−	0.260826i
$256$		0			0
$257$	−1.67854	+	28.8195i	−0.104705	+	1.79771i	0.382020	+	0.924154i	$0.375228\pi$
$257$	−1.67854	+	28.8195i	−0.104705	+	1.79771i	−0.486725	+	0.873555i	$0.661809\pi$
$258$		0			0
$259$	−4.17999	+	13.9622i	−0.259732	+	0.867566i
$260$		0			0
$261$	13.3358	−	9.13035i	0.825465	−	0.565154i
$262$		0			0
$263$	−11.7122	+	15.7322i	−0.722206	+	0.970092i	0.277749	+	0.960654i	$0.410412\pi$
$263$	−11.7122	+	15.7322i	−0.722206	+	0.970092i	−0.999955	+	0.00943789i	$0.996996\pi$
$264$		0			0
$265$	46.7795	+	11.0869i	2.87364	+	0.681066i
$266$		0			0
$267$	−1.83934	+	5.20340i	−0.112566	+	0.318443i
$268$		0			0
$269$	−12.8351	−	22.2311i	−0.782572	−	1.35545i	−0.930439	−	0.366447i	$-0.880574\pi$
$269$	−12.8351	−	22.2311i	−0.782572	−	1.35545i	0.147867	−	0.989007i	$-0.452759\pi$
$270$		0			0
$271$	2.54720	−	4.41188i	0.154732	−	0.268003i	−0.778230	−	0.627980i	$-0.783882\pi$
$271$	2.54720	−	4.41188i	0.154732	−	0.268003i	0.932961	+	0.359977i	$0.117215\pi$
$272$		0			0
$273$	19.6077	−	23.8132i	1.18671	−	1.44124i
$274$		0			0
$275$	−5.78301	+	6.12963i	−0.348728	+	0.369631i
$276$		0			0
$277$	6.73953	+	0.787738i	0.404939	+	0.0473306i	0.316125	−	0.948718i	$-0.397618\pi$
$277$	6.73953	+	0.787738i	0.404939	+	0.0473306i	0.0888142	+	0.996048i	$0.471692\pi$
$278$		0			0
$279$	14.8653	+	19.2121i	0.889964	+	1.15020i
$280$		0			0
$281$	−11.6342	−	12.3315i	−0.694038	−	0.735637i	0.280501	−	0.959854i	$-0.409499\pi$
$281$	−11.6342	−	12.3315i	−0.694038	−	0.735637i	−0.974539	+	0.224216i	$0.928018\pi$
$282$		0			0
$283$	−0.990582	+	0.497489i	−0.0588840	+	0.0295726i	−0.477998	−	0.878361i	$-0.658637\pi$
$283$	−0.990582	+	0.497489i	−0.0588840	+	0.0295726i	0.419114	+	0.907934i	$0.362341\pi$
$284$		0			0
$285$	23.5928	−	36.6071i	1.39752	−	2.16842i
$286$		0			0
$287$	−18.0893	−	15.1787i	−1.06778	−	0.895971i
$288$		0			0
$289$	−12.7515	+	10.6998i	−0.750088	+	0.629398i
$290$		0			0
$291$	−1.67699	+	1.61186i	−0.0983070	+	0.0944887i
$292$		0			0
$293$	9.50061	−	1.11046i	0.555032	−	0.0648739i	0.166047	−	0.986118i	$-0.446900\pi$
$293$	9.50061	−	1.11046i	0.555032	−	0.0648739i	0.388985	+	0.921244i	$0.372826\pi$
$294$		0			0
$295$	−3.10640	−	53.3349i	−0.180862	−	3.10528i
$296$		0			0
$297$	0.973326	+	3.65045i	0.0564781	+	0.211820i
$298$		0			0
$299$	−2.76580	+	1.81910i	−0.159950	+	0.105201i
$300$		0			0
$301$	−6.95250	+	16.1177i	−0.400735	+	0.929009i
$302$		0			0
$303$	−1.51824	+	0.671696i	−0.0872208	+	0.0385880i
$304$		0			0
$305$	24.8395	+	9.04083i	1.42230	+	0.517676i
$306$		0			0
$307$	13.4623	−	4.89986i	0.768332	−	0.279650i	0.0720335	−	0.997402i	$-0.477051\pi$
$307$	13.4623	−	4.89986i	0.768332	−	0.279650i	0.696299	+	0.717752i	$0.254829\pi$
$308$		0			0
$309$	−5.73668	−	5.31246i	−0.326348	−	0.302215i
$310$		0			0
$311$	−15.9597	−	10.4968i	−0.904990	−	0.595221i	0.00944460	−	0.999955i	$-0.496994\pi$
$311$	−15.9597	−	10.4968i	−0.904990	−	0.595221i	−0.914434	+	0.404734i	$0.867364\pi$
$312$		0			0
$313$	4.97721	−	1.17962i	0.281329	−	0.0666761i	−0.0875291	−	0.996162i	$-0.527897\pi$
$313$	4.97721	−	1.17962i	0.281329	−	0.0666761i	0.368858	+	0.929486i	$0.379749\pi$
$314$		0			0
$315$	49.3737	+	16.9389i	2.78189	+	0.954400i
$316$		0			0
$317$	1.38868	+	3.21932i	0.0779959	+	0.180815i	0.952752	−	0.303748i	$-0.0982380\pi$
$317$	1.38868	+	3.21932i	0.0779959	+	0.180815i	−0.874757	+	0.484563i	$0.838979\pi$
$318$		0			0
$319$	−1.12339	−	3.75240i	−0.0628980	−	0.210094i
$320$		0			0
$321$	0.205251	+	22.1014i	0.0114560	+	1.23358i
$322$		0			0
$323$	3.67349			0.204398
$324$		0			0
$325$	−48.3215			−2.68040
$326$		0			0
$327$	−1.43200	+	0.844590i	−0.0791895	+	0.0467059i
$328$		0			0
$329$	−6.57135	−	21.9499i	−0.362291	−	1.21013i
$330$		0			0
$331$	−10.9651	−	25.4199i	−0.602696	−	1.39721i	−0.897229	−	0.441565i	$-0.854423\pi$
$331$	−10.9651	−	25.4199i	−0.602696	−	1.39721i	0.294533	−	0.955641i	$-0.404836\pi$
$332$		0			0
$333$	1.58985	−	10.1112i	0.0871230	−	0.554088i
$334$		0			0
$335$	43.3939	−	10.2845i	2.37086	−	0.561905i
$336$		0			0
$337$	9.70509	+	6.38314i	0.528670	+	0.347712i	0.785616	−	0.618714i	$-0.212346\pi$
$337$	9.70509	+	6.38314i	0.528670	+	0.347712i	−0.256946	+	0.966426i	$0.582716\pi$
$338$		0			0
$339$	−19.5008	+	6.03603i	−1.05914	+	0.327832i
$340$		0			0
$341$	5.53221	−	2.01356i	0.299586	−	0.109040i
$342$		0			0
$343$	17.0525	+	6.20661i	0.920749	+	0.335125i
$344$		0			0
$345$	−4.52421	−	3.30330i	−0.243575	−	0.177844i
$346$		0			0
$347$	−9.87963	+	22.9036i	−0.530367	+	1.22953i	0.416862	+	0.908970i	$0.363130\pi$
$347$	−9.87963	+	22.9036i	−0.530367	+	1.22953i	−0.947229	+	0.320558i	$0.896130\pi$
$348$		0			0
$349$	−7.53751	+	4.95750i	−0.403473	+	0.265369i	−0.734986	−	0.678082i	$-0.762811\pi$
$349$	−7.53751	+	4.95750i	−0.403473	+	0.265369i	0.331513	+	0.943451i	$0.392441\pi$
$350$		0			0
$351$	−11.3954	+	18.4240i	−0.608239	+	0.983398i
$352$		0			0
$353$	1.05449	+	18.1049i	0.0561249	+	0.963627i	0.902405	+	0.430889i	$0.141800\pi$
$353$	1.05449	+	18.1049i	0.0561249	+	0.963627i	−0.846280	+	0.532738i	$0.821163\pi$
$354$		0			0
$355$	−42.7549	+	4.99733i	−2.26920	+	0.265231i
$356$		0			0
$357$	1.05512	+	4.27459i	0.0558427	+	0.226235i
$358$		0			0
$359$	5.73391	−	4.81132i	0.302624	−	0.253932i	−0.478811	−	0.877918i	$-0.658932\pi$
$359$	5.73391	−	4.81132i	0.302624	−	0.253932i	0.781436	+	0.623986i	$0.214488\pi$
$360$		0			0
$361$	14.6379	+	12.2827i	0.770416	+	0.646456i
$362$		0			0
$363$	−18.1153	−	0.886382i	−0.950805	−	0.0465230i
$364$		0			0
$365$	18.4145	−	9.24810i	0.963858	−	0.484068i
$366$		0			0
$367$	3.49361	+	3.70301i	0.182365	+	0.193295i	0.812107	−	0.583509i	$-0.198321\pi$
$367$	3.49361	+	3.70301i	0.182365	+	0.193295i	−0.629742	+	0.776805i	$0.716839\pi$
$368$		0			0
$369$	14.0223	+	8.85397i	0.729971	+	0.460919i
$370$		0			0
$371$	−50.0791	−	5.85340i	−2.59998	−	0.303894i
$372$		0			0
$373$	19.4701	−	20.6371i	1.00813	−	1.06855i	0.0104818	−	0.999945i	$-0.496663\pi$
$373$	19.4701	−	20.6371i	1.00813	−	1.06855i	0.997644	−	0.0686057i	$-0.0218551\pi$
$374$		0			0
$375$	−16.3071	−	43.5410i	−0.842096	−	2.24845i
$376$		0			0
$377$	11.2301	−	19.4511i	0.578378	−	1.00178i
$378$		0			0
$379$	1.66179	+	2.87830i	0.0853604	+	0.147849i	0.905545	−	0.424251i	$-0.139462\pi$
$379$	1.66179	+	2.87830i	0.0853604	+	0.147849i	−0.820184	+	0.572099i	$0.806129\pi$
$380$		0			0
$381$	0.998892	−	0.185712i	0.0511748	−	0.00951433i
$382$		0			0
$383$	12.7469	+	3.02106i	0.651334	+	0.154369i	0.542983	−	0.839744i	$-0.317295\pi$
$383$	12.7469	+	3.02106i	0.651334	+	0.154369i	0.108351	+	0.994113i	$0.465443\pi$
$384$		0			0
$385$	7.55448	−	10.1474i	0.385012	−	0.517161i
$386$		0			0
$387$	3.31560	−	11.8731i	0.168541	−	0.603545i
$388$		0			0
$389$	3.17523	−	10.6060i	0.160991	−	0.537746i	−0.838989	−	0.544148i	$-0.816853\pi$
$389$	3.17523	−	10.6060i	0.160991	−	0.537746i	0.999980	+	0.00640260i	$0.00203802\pi$
$390$		0			0
$391$	0.0274738	−	0.471707i	0.00138941	−	0.0238552i
$392$		0			0
$393$	−11.4423	−	4.81020i	−0.577188	−	0.242642i
$394$		0			0
$395$	2.46974	−	14.0066i	0.124266	−	0.704747i
$396$		0			0
$397$	5.21956	+	29.6016i	0.261962	+	1.48566i	0.777547	+	0.628824i	$0.216464\pi$
$397$	5.21956	+	29.6016i	0.261962	+	1.48566i	−0.515585	+	0.856838i	$0.672425\pi$
$398$		0			0
$399$	−20.1190	+	41.0054i	−1.00721	+	2.05284i
$400$		0			0
$401$	2.59002	+	3.47899i	0.129339	+	0.173733i	0.862075	−	0.506780i	$-0.169164\pi$
$401$	2.59002	+	3.47899i	0.129339	+	0.173733i	−0.732736	+	0.680513i	$0.761757\pi$
$402$		0			0
$403$	30.1673	+	15.1506i	1.50274	+	0.754704i
$404$		0			0
$405$	−35.9594	−	7.12343i	−1.78684	−	0.353966i
$406$		0			0
$407$	−2.21676	−	1.11330i	−0.109881	−	0.0551843i
$408$		0			0
$409$	−20.3012	−	27.2693i	−1.00383	−	1.34838i	−0.936508	−	0.350647i	$-0.885962\pi$
$409$	−20.3012	−	27.2693i	−1.00383	−	1.34838i	−0.0673227	−	0.997731i	$-0.521446\pi$
$410$		0			0
$411$	−7.44308	+	0.502905i	−0.367140	+	0.0248065i
$412$		0			0
$413$	9.72965	+	55.1796i	0.478765	+	2.71521i
$414$		0			0
$415$	−2.19985	+	12.4760i	−0.107987	+	0.612422i
$416$		0			0
$417$	−6.54001	+	4.96391i	−0.320266	+	0.243084i
$418$		0			0
$419$	1.00671	−	17.2846i	0.0491811	−	0.844407i	−0.880044	−	0.474893i	$-0.842487\pi$
$419$	1.00671	−	17.2846i	0.0491811	−	0.844407i	0.929225	−	0.369515i	$-0.120476\pi$
$420$		0			0
$421$	−3.75680	+	12.5486i	−0.183095	+	0.611580i	0.816327	+	0.577590i	$0.196007\pi$
$421$	−3.75680	+	12.5486i	−0.183095	+	0.611580i	−0.999422	+	0.0339901i	$0.989179\pi$
$422$		0			0
$423$	6.64663	+	14.6541i	0.323170	+	0.712507i
$424$		0			0
$425$	4.11867	−	5.53233i	0.199785	−	0.268358i
$426$		0			0
$427$	−26.9755	−	6.39331i	−1.30544	−	0.309394i
$428$		0			0
$429$	3.41200	+	3.99041i	0.164733	+	0.192659i
$430$		0			0
$431$	0.0468879	+	0.0812122i	0.00225851	+	0.00391186i	0.867152	−	0.498043i	$-0.165948\pi$
$431$	0.0468879	+	0.0812122i	0.00225851	+	0.00391186i	−0.864894	+	0.501955i	$0.832614\pi$
$432$		0			0
$433$	3.08387	−	5.34141i	0.148201	−	0.256692i	−0.782361	−	0.622825i	$-0.785985\pi$
$433$	3.08387	−	5.34141i	0.148201	−	0.256692i	0.930563	+	0.366133i	$0.119318\pi$
$434$		0			0
$435$	37.4890	+	6.25193i	1.79746	+	0.299757i
$436$		0			0
$437$	3.36377	−	3.56539i	0.160911	−	0.170556i
$438$		0			0
$439$	−13.4200	−	1.56857i	−0.640501	−	0.0748638i	−0.210358	−	0.977624i	$-0.567463\pi$
$439$	−13.4200	−	1.56857i	−0.640501	−	0.0748638i	−0.430143	+	0.902761i	$0.641537\pi$
$440$		0			0
$441$	−32.9736	−	7.17082i	−1.57017	−	0.341468i
$442$		0			0
$443$	−6.46212	−	6.84944i	−0.307024	−	0.325427i	0.555428	−	0.831564i	$-0.312554\pi$
$443$	−6.46212	−	6.84944i	−0.307024	−	0.325427i	−0.862453	+	0.506137i	$0.831073\pi$
$444$		0			0
$445$	−11.5980	+	5.82472i	−0.549797	+	0.276118i
$446$		0			0
$447$	−7.73754	−	15.0564i	−0.365973	−	0.712145i
$448$		0			0
$449$	24.1512	+	20.2653i	1.13977	+	0.956378i	0.999431	−	0.0337257i	$-0.0107373\pi$
$449$	24.1512	+	20.2653i	1.13977	+	0.956378i	0.140336	+	0.990104i	$0.455182\pi$
$450$		0			0
$451$	3.07886	−	2.58347i	0.144978	−	0.121651i
$452$		0			0
$453$	−12.5468	−	3.62965i	−0.589499	−	0.170536i
$454$		0			0
$455$	72.0498	−	8.42141i	3.37774	−	0.394802i
$456$		0			0
$457$	0.713303	+	12.2469i	0.0333669	+	0.572887i	0.973015	+	0.230744i	$0.0741159\pi$
$457$	0.713303	+	12.2469i	0.0333669	+	0.572887i	−0.939648	+	0.342144i	$0.888847\pi$
$458$		0			0
$459$	−1.13808	−	2.87501i	−0.0531210	−	0.134194i
$460$		0			0
$461$	21.3636	−	14.0511i	0.995002	−	0.654423i	0.0560342	−	0.998429i	$-0.482154\pi$
$461$	21.3636	−	14.0511i	0.995002	−	0.654423i	0.938967	+	0.344006i	$0.111784\pi$
$462$		0			0
$463$	4.79869	−	11.1246i	0.223014	−	0.517005i	−0.769570	−	0.638562i	$-0.779530\pi$
$463$	4.79869	−	11.1246i	0.223014	−	0.517005i	0.992584	+	0.121557i	$0.0387888\pi$
$464$		0			0
$465$	−6.10460	+	56.7977i	−0.283094	+	2.63393i
$466$		0			0
$467$	−22.0808	−	8.03674i	−1.02178	−	0.371896i	−0.223832	−	0.974628i	$-0.571857\pi$
$467$	−22.0808	−	8.03674i	−1.02178	−	0.371896i	−0.797944	+	0.602732i	$0.794079\pi$
$468$		0			0
$469$	−43.9503	+	15.9966i	−2.02944	+	0.738654i
$470$		0			0
$471$	−4.08287	+	17.9690i	−0.188129	+	0.827967i
$472$		0			0
$473$	−2.49613	−	1.64173i	−0.114772	−	0.0754869i
$474$		0			0
$475$	69.6214	−	16.5006i	3.19445	−	0.757098i
$476$		0			0
$477$	35.4030	−	0.657617i	1.62099	−	0.0301102i
$478$		0			0
$479$	8.40473	+	19.4844i	0.384022	+	0.890263i	0.995117	+	0.0987053i	$0.0314701\pi$
$479$	8.40473	+	19.4844i	0.384022	+	0.890263i	−0.611095	+	0.791557i	$0.709271\pi$
$480$		0			0
$481$	−4.07952	−	13.6265i	−0.186010	−	0.621316i
$482$		0			0
$483$	5.11497	+	2.89013i	0.232739	+	0.131505i
$484$		0			0
$485$	−5.46993			−0.248377
$486$		0			0
$487$	13.4623			0.610036			0.305018	−	0.952347i	$-0.401338\pi$
$487$	13.4623			0.610036			0.305018	+	0.952347i	$0.401338\pi$
$488$		0			0
$489$	0.592799	+	0.334952i	0.0268073	+	0.0151470i
$490$		0			0
$491$	−4.80769	−	16.0588i	−0.216968	−	0.724724i	−0.995297	−	0.0968676i	$-0.969118\pi$
$491$	−4.80769	−	16.0588i	−0.216968	−	0.724724i	0.778329	−	0.627856i	$-0.216068\pi$
$492$		0			0
$493$	1.26976	+	2.94363i	0.0571871	+	0.132575i
$494$		0			0
$495$	−4.29853	+	7.77528i	−0.193205	+	0.349473i
$496$		0			0
$497$	43.9284	−	10.4112i	1.97046	−	0.467007i
$498$		0			0
$499$	−0.799176	−	0.525626i	−0.0357760	−	0.0235303i	0.531495	−	0.847061i	$-0.321630\pi$
$499$	−0.799176	−	0.525626i	−0.0357760	−	0.0235303i	−0.567271	+	0.823531i	$0.692001\pi$
$500$		0			0
$501$	−4.41513	+	19.4313i	−0.197254	+	0.868127i
$502$		0			0
$503$	−29.3308	+	10.6755i	−1.30780	+	0.475999i	−0.899528	−	0.436863i	$-0.856089\pi$
$503$	−29.3308	+	10.6755i	−1.30780	+	0.475999i	−0.408268	+	0.912862i	$0.633867\pi$
$504$		0			0
$505$	−3.66870	−	1.33530i	−0.163255	−	0.0594200i
$506$		0			0
$507$	−0.810962	+	7.54525i	−0.0360161	+	0.335096i
$508$		0			0
$509$	5.21211	−	12.0830i	0.231023	−	0.535571i	−0.762789	−	0.646647i	$-0.776171\pi$
$509$	5.21211	−	12.0830i	0.231023	−	0.535571i	0.993812	+	0.111076i	$0.0354298\pi$
$510$		0			0
$511$	−18.0560	+	11.8756i	−0.798749	+	0.525346i
$512$		0			0
$513$	10.1270	−	30.4363i	0.447120	−	1.34380i
$514$		0			0
$515$	−1.06909	−	18.3555i	−0.0471095	−	0.808839i
$516$		0			0
$517$	3.87341	−	0.452736i	0.170352	−	0.0199113i
$518$		0			0
$519$	27.9607	+	8.08873i	1.22734	+	0.355056i
$520$		0			0
$521$	−20.5214	+	17.2195i	−0.899061	+	0.754402i	−0.970007	−	0.243078i	$-0.921843\pi$
$521$	−20.5214	+	17.2195i	−0.899061	+	0.754402i	0.0709457	+	0.997480i	$0.477398\pi$
$522$		0			0
$523$	−4.29256	−	3.60189i	−0.187701	−	0.157500i	0.544095	−	0.839024i	$-0.316873\pi$
$523$	−4.29256	−	3.60189i	−0.187701	−	0.157500i	−0.731796	+	0.681524i	$0.761318\pi$
$524$		0			0
$525$	39.1976	+	76.2743i	1.71072	+	3.32888i
$526$		0			0
$527$	−4.30589	+	2.16250i	−0.187567	+	0.0941999i
$528$		0			0
$529$	15.3509	+	16.2710i	0.667430	+	0.707434i
$530$		0			0
$531$	−11.9837	−	37.4803i	−0.520049	−	1.62651i
$532$		0			0
$533$	22.8904	+	2.67551i	0.991495	+	0.115889i
$534$		0			0
$535$	−35.6684	+	37.8063i	−1.54208	+	1.63451i
$536$		0			0
$537$	27.6711	+	4.61463i	1.19410	+	0.199136i
$538$		0			0
$539$	−4.08909	+	7.08251i	−0.176129	+	0.305065i
$540$		0			0
$541$	−8.01520	−	13.8827i	−0.344600	−	0.596865i	0.640681	−	0.767807i	$-0.278652\pi$
$541$	−8.01520	−	13.8827i	−0.344600	−	0.596865i	−0.985281	+	0.170942i	$0.945319\pi$
$542$		0			0
$543$	15.0138	+	17.5590i	0.644303	+	0.753527i
$544$		0			0
$545$	−3.80422	−	0.901616i	−0.162955	−	0.0386210i
$546$		0			0
$547$	−3.10689	+	4.17327i	−0.132841	+	0.178436i	−0.863566	−	0.504235i	$-0.831775\pi$
$547$	−3.10689	+	4.17327i	−0.132841	+	0.178436i	0.730726	+	0.682671i	$0.239182\pi$
$548$		0			0
$549$	19.3762	+	1.90071i	0.826958	+	0.0811205i
$550$		0			0
$551$	−9.53818	+	31.8597i	−0.406340	+	1.35727i
$552$		0			0
$553$	−0.867304	+	14.8910i	−0.0368815	+	0.633231i
$554$		0			0
$555$	19.1726	−	14.5521i	0.813832	−	0.617704i
$556$		0			0
$557$	1.66230	−	9.42739i	0.0704341	−	0.399451i	−0.929125	−	0.369765i	$-0.879438\pi$
$557$	1.66230	−	9.42739i	0.0704341	−	0.399451i	0.999559	−	0.0296861i	$-0.00945077\pi$
$558$		0			0
$559$	−2.97483	−	16.8711i	−0.125822	−	0.713570i
$560$		0			0
$561$	−0.747683	+	0.0505185i	−0.0315672	+	0.00213289i
$562$		0			0
$563$	9.16824	+	12.3151i	0.386395	+	0.519019i	0.952182	−	0.305533i	$-0.0988346\pi$
$563$	9.16824	+	12.3151i	0.386395	+	0.519019i	−0.565786	+	0.824552i	$0.691427\pi$
$564$		0			0
$565$	−42.8989	−	21.5446i	−1.80477	−	0.906390i
$566$		0			0
$567$	38.3255	+	3.04209i	1.60952	+	0.127756i
$568$		0			0
$569$	1.56225	+	0.784594i	0.0654931	+	0.0328919i	0.481244	−	0.876587i	$-0.340185\pi$
$569$	1.56225	+	0.784594i	0.0654931	+	0.0328919i	−0.415751	+	0.909478i	$0.636481\pi$
$570$		0			0
$571$	−24.6751	−	33.1444i	−1.03262	−	1.38705i	−0.919329	−	0.393489i	$-0.871268\pi$
$571$	−24.6751	−	33.1444i	−1.03262	−	1.38705i	−0.113291	−	0.993562i	$-0.536139\pi$
$572$		0			0
$573$	−7.06862	+	14.4068i	−0.295296	+	0.601854i
$574$		0			0
$575$	−1.59812	−	9.06337i	−0.0666461	−	0.377969i
$576$		0			0
$577$	3.56208	−	20.2016i	0.148291	−	0.841003i	−0.816374	−	0.577524i	$-0.804019\pi$
$577$	3.56208	−	20.2016i	0.148291	−	0.841003i	0.964665	−	0.263479i	$-0.0848699\pi$
$578$		0			0
$579$	31.9209	+	13.4191i	1.32659	+	0.557680i
$580$		0			0
$581$	0.772528	−	13.2638i	0.0320499	−	0.550275i
$582$		0			0
$583$	2.46125	−	8.22115i	0.101935	−	0.340485i
$584$		0			0
$585$	−49.3439	+	12.6671i	−2.04012	+	0.523718i
$586$		0			0
$587$	14.8833	−	19.9917i	0.614299	−	0.825146i	−0.380735	−	0.924684i	$-0.624329\pi$
$587$	14.8833	−	19.9917i	0.614299	−	0.825146i	0.995034	+	0.0995378i	$0.0317364\pi$
$588$		0			0
$589$	−48.6383	−	11.5275i	−2.00411	−	0.474982i
$590$		0			0
$591$	−38.6519	+	7.18609i	−1.58993	+	0.295596i
$592$		0			0
$593$	−7.85339	−	13.6025i	−0.322500	−	0.558586i	0.658503	−	0.752578i	$-0.271190\pi$
$593$	−7.85339	−	13.6025i	−0.322500	−	0.558586i	−0.981003	+	0.193992i	$0.937857\pi$
$594$		0			0
$595$	−5.17697	+	8.96678i	−0.212235	+	0.367602i
$596$		0			0
$597$	0.622030	+	1.66086i	0.0254580	+	0.0679744i
$598$		0			0
$599$	−21.7198	+	23.0217i	−0.887448	+	0.940640i	−0.998586	−	0.0531653i	$-0.983069\pi$
$599$	−21.7198	+	23.0217i	−0.887448	+	0.940640i	0.111138	+	0.993805i	$0.464550\pi$
$600$		0			0
$601$	6.83349	+	0.798720i	0.278744	+	0.0325805i	0.254316	−	0.967121i	$-0.418150\pi$
$601$	6.83349	+	0.798720i	0.278744	+	0.0325805i	0.0244276	+	0.999702i	$0.492224\pi$
$602$		0			0
$603$	29.0738	−	15.2841i	1.18398	−	0.622415i
$604$		0			0
$605$	−29.2691	−	31.0234i	−1.18996	−	1.26128i
$606$		0			0
$607$	4.69161	−	2.35621i	0.190426	−	0.0956357i	−0.351031	−	0.936364i	$-0.614169\pi$
$607$	4.69161	−	2.35621i	0.190426	−	0.0956357i	0.541458	+	0.840728i	$0.317873\pi$
$608$		0			0
$609$	−39.8126	−	1.94804i	−1.61329	−	0.0789384i
$610$		0			0
$611$	17.1300	+	14.3738i	0.693006	+	0.581501i
$612$		0			0
$613$	26.0740	−	21.8787i	1.05312	−	0.883672i	0.0597007	−	0.998216i	$-0.480985\pi$
$613$	26.0740	−	21.8787i	1.05312	−	0.883672i	0.993418	+	0.114545i	$0.0365409\pi$
$614$		0			0
$615$	9.34568	+	37.8622i	0.376854	+	1.52675i
$616$		0			0
$617$	8.94135	−	1.04509i	0.359965	−	0.0420739i	0.0658117	−	0.997832i	$-0.479036\pi$
$617$	8.94135	−	1.04509i	0.359965	−	0.0420739i	0.294154	+	0.955758i	$0.404962\pi$
$618$		0			0
$619$	2.19391	+	37.6679i	0.0881806	+	1.51400i	0.694912	+	0.719095i	$0.255443\pi$
$619$	2.19391	+	37.6679i	0.0881806	+	1.51400i	−0.606731	+	0.794907i	$0.707519\pi$
$620$		0			0
$621$	−3.83254	−	1.52803i	−0.153795	−	0.0613177i
$622$		0			0
$623$	11.3722	−	7.47959i	0.455616	−	0.299664i
$624$		0			0
$625$	20.3528	−	47.1832i	0.814113	−	1.88733i
$626$		0			0
$627$	−6.27861	−	4.58425i	−0.250743	−	0.183077i
$628$		0			0
$629$	1.90782	+	0.694389i	0.0760697	+	0.0276871i
$630$		0			0
$631$	31.0674	−	11.3076i	1.23677	−	0.450148i	0.360860	−	0.932620i	$-0.382483\pi$
$631$	31.0674	−	11.3076i	1.23677	−	0.450148i	0.875912	+	0.482472i	$0.160261\pi$
$632$		0			0
$633$	−36.7514	+	11.3756i	−1.46074	+	0.452139i
$634$		0			0
$635$	1.99621	+	1.31293i	0.0792171	+	0.0521019i
$636$		0			0
$637$	−45.6303	+	10.8146i	−1.80794	+	0.428489i
$638$		0			0
$639$	−29.5862	+	11.3951i	−1.17041	+	0.450784i
$640$		0			0
$641$	−6.46547	−	14.9886i	−0.255371	−	0.592016i	0.741510	−	0.670942i	$-0.234110\pi$
$641$	−6.46547	−	14.9886i	−0.255371	−	0.592016i	−0.996880	+	0.0789263i	$0.974851\pi$
$642$		0			0
$643$	0.735889	+	2.45804i	0.0290206	+	0.0969357i	0.971273	−	0.237968i	$-0.0764814\pi$
$643$	0.735889	+	2.45804i	0.0290206	+	0.0969357i	−0.942252	+	0.334904i	$0.891296\pi$
$644$		0			0
$645$	24.9698	−	14.7272i	0.983187	−	0.579883i
$646$		0			0
$647$	−30.4497			−1.19710			−0.598551	−	0.801085i	$-0.704256\pi$
$647$	−30.4497			−1.19710			−0.598551	+	0.801085i	$0.704256\pi$
$648$		0			0
$649$	−9.53665			−0.374346
$650$		0			0
$651$	−0.556354	−	59.9082i	−0.0218052	−	2.34799i
$652$		0			0
$653$	14.5339	+	48.5466i	0.568756	+	1.89978i	0.408703	+	0.912668i	$0.365981\pi$
$653$	14.5339	+	48.5466i	0.568756	+	1.89978i	0.160053	+	0.987108i	$0.448834\pi$
$654$		0			0
$655$	−11.5612	−	26.8018i	−0.451732	−	1.04723i
$656$		0			0
$657$	11.4433	−	9.97000i	0.446444	−	0.388967i
$658$		0			0
$659$	27.9811	−	6.63164i	1.08999	−	0.258332i	0.353945	−	0.935266i	$-0.384840\pi$
$659$	27.9811	−	6.63164i	1.08999	−	0.258332i	0.736043	+	0.676934i	$0.236692\pi$
$660$		0			0
$661$	6.68574	+	4.39728i	0.260045	+	0.171034i	0.672836	−	0.739791i	$-0.265076\pi$
$661$	6.68574	+	4.39728i	0.260045	+	0.171034i	−0.412791	+	0.910826i	$0.635446\pi$
$662$		0			0
$663$	−3.15281	−	2.91966i	−0.122445	−	0.113390i
$664$		0			0
$665$	−100.933	+	36.7367i	−3.91402	+	1.42459i
$666$		0			0
$667$	4.01972	+	1.46306i	0.155644	+	0.0566498i
$668$		0			0
$669$	−3.06309	+	1.35516i	−0.118426	+	0.0523936i
$670$		0			0
$671$	1.86891	−	4.33262i	0.0721484	−	0.167259i
$672$		0			0
$673$	40.1005	−	26.3745i	1.54576	−	1.01666i	0.564171	−	0.825658i	$-0.309196\pi$
$673$	40.1005	−	26.3745i	1.54576	−	1.01666i	0.981589	−	0.191004i	$-0.0611745\pi$
$674$		0			0
$675$	−34.4833	−	49.3763i	−1.32726	−	1.90050i
$676$		0			0
$677$	−1.35311	−	23.2320i	−0.0520043	−	0.892880i	−0.918925	−	0.394433i	$-0.870941\pi$
$677$	−1.35311	−	23.2320i	−0.0520043	−	0.892880i	0.866920	−	0.498447i	$-0.166096\pi$
$678$		0			0
$679$	5.69791	−	0.665990i	0.218666	−	0.0255583i
$680$		0			0
$681$	17.6907	−	17.0036i	0.677909	−	0.651578i
$682$		0			0
$683$	29.8350	−	25.0345i	1.14160	−	0.957919i	0.142114	−	0.989850i	$-0.454610\pi$
$683$	29.8350	−	25.0345i	1.14160	−	0.957919i	0.999490	+	0.0319308i	$0.0101656\pi$
$684$		0			0
$685$	−13.4389	−	11.2766i	−0.513474	−	0.430856i
$686$		0			0
$687$	25.1301	−	38.9924i	0.958773	−	1.48765i
$688$		0			0
$689$	43.9739	−	22.0845i	1.67527	−	0.841353i
$690$		0			0
$691$	19.1137	+	20.2593i	0.727120	+	0.770702i	0.980469	−	0.196673i	$-0.0630137\pi$
$691$	19.1137	+	20.2593i	0.727120	+	0.770702i	−0.253350	+	0.967375i	$0.581532\pi$
$692$		0			0
$693$	3.53101	−	8.62270i	0.134132	−	0.327549i
$694$		0			0
$695$	−19.1774	−	2.24152i	−0.727442	−	0.0850257i
$696$		0			0
$697$	−2.25738	+	2.39268i	−0.0855043	+	0.0906292i
$698$		0			0
$699$	−17.5977	+	21.3721i	−0.665606	+	0.808366i
$700$		0			0
$701$	−18.3117	+	31.7168i	−0.691624	+	1.19793i	0.279682	+	0.960093i	$0.409771\pi$
$701$	−18.3117	+	31.7168i	−0.691624	+	1.19793i	−0.971306	+	0.237835i	$0.923562\pi$
$702$		0			0
$703$	10.5309	+	18.2400i	0.397179	+	0.687933i
$704$		0			0
$705$	−12.6113	+	35.6766i	−0.474969	+	1.34366i
$706$		0			0
$707$	3.98418	+	0.944269i	0.149841	+	0.0355129i
$708$		0			0
$709$	28.8864	−	38.8012i	1.08485	−	1.45721i	0.206959	−	0.978350i	$-0.433643\pi$
$709$	28.8864	−	38.8012i	1.08485	−	1.45721i	0.877892	−	0.478858i	$-0.158949\pi$
$710$		0			0
$711$	−0.803209	−	10.4446i	−0.0301227	−	0.391704i
$712$		0			0
$713$	−1.84399	+	6.15936i	−0.0690580	+	0.230670i
$714$		0			0
$715$	−0.717892	+	12.3257i	−0.0268476	+	0.460956i
$716$		0			0
$717$	3.37894	+	26.7518i	0.126189	+	0.999065i
$718$		0			0
$719$	−0.133404	+	0.756569i	−0.00497511	+	0.0282153i	−0.987194	−	0.159523i	$-0.949004\pi$
$719$	−0.133404	+	0.756569i	−0.00497511	+	0.0282153i	0.982219	+	0.187738i	$0.0601156\pi$
$720$		0			0
$721$	3.34851	+	18.9903i	0.124705	+	0.707237i
$722$		0			0
$723$	−26.4200	−	39.3684i	−0.982570	−	1.46413i
$724$		0			0
$725$	37.2872	+	50.0854i	1.38481	+	1.86012i
$726$		0			0
$727$	19.0559	+	9.57024i	0.706745	+	0.354941i	0.765592	−	0.643326i	$-0.222446\pi$
$727$	19.0559	+	9.57024i	0.706745	+	0.354941i	−0.0588472	+	0.998267i	$0.518742\pi$
$728$		0			0
$729$	−26.9581	+	1.50364i	−0.998448	+	0.0556903i
$730$		0			0
$731$	2.18513	+	1.09741i	0.0808199	+	0.0405893i
$732$		0			0
$733$	19.4839	+	26.1714i	0.719653	+	0.966662i	0.999977	+	0.00675660i	$0.00215071\pi$
$733$	19.4839	+	26.1714i	0.719653	+	0.966662i	−0.280324	+	0.959905i	$0.590442\pi$
$734$		0			0
$735$	−44.2195	−	65.8914i	−1.63106	−	2.43044i
$736$		0			0
$737$	−1.38234	−	7.83964i	−0.0509192	−	0.288777i
$738$		0			0
$739$	−1.62091	+	9.19262i	−0.0596260	+	0.338156i	−0.999998	−	0.00199189i	$-0.999366\pi$
$739$	−1.62091	+	9.19262i	−0.0596260	+	0.338156i	0.940372	+	0.340148i	$0.110477\pi$
$740$		0			0
$741$	−5.58604	−	44.2258i	−0.205208	−	1.62468i
$742$		0			0
$743$	2.94253	−	50.5212i	0.107951	−	1.85344i	−0.317245	−	0.948344i	$-0.602758\pi$
$743$	2.94253	−	50.5212i	0.107951	−	1.85344i	0.425196	−	0.905101i	$-0.360205\pi$
$744$		0			0
$745$	11.4173	−	38.1365i	0.418299	−	1.39721i
$746$		0			0
$747$	0.715437	+	9.30327i	0.0261765	+	0.340389i
$748$		0			0
$749$	32.5519	−	43.7248i	1.18942	−	1.59767i
$750$		0			0
$751$	−17.9858	−	4.26272i	−0.656312	−	0.155549i	−0.111050	−	0.993815i	$-0.535421\pi$
$751$	−17.9858	−	4.26272i	−0.656312	−	0.155549i	−0.545262	+	0.838266i	$0.683570\pi$
$752$		0			0
$753$	−3.22923	+	9.13532i	−0.117680	+	0.332910i
$754$		0			0
$755$	−15.3576	−	26.6001i	−0.558919	−	0.968077i
$756$		0			0
$757$	−23.4692	+	40.6498i	−0.853001	+	1.47744i	0.0254855	+	0.999675i	$0.491887\pi$
$757$	−23.4692	+	40.6498i	−0.853001	+	1.47744i	−0.878487	+	0.477767i	$0.841446\pi$
$758$		0			0
$759$	−0.635613	+	0.771940i	−0.0230713	+	0.0280197i
$760$		0			0
$761$	−7.18699	+	7.61777i	−0.260528	+	0.276144i	−0.844413	−	0.535693i	$-0.820051\pi$
$761$	−7.18699	+	7.61777i	−0.260528	+	0.276144i	0.583885	+	0.811837i	$0.301532\pi$
$762$		0			0
$763$	4.07255	+	0.476012i	0.147436	+	0.0172328i
$764$		0			0
$765$	2.75556	−	6.72906i	0.0996274	−	0.243290i
$766$		0			0
$767$	−37.5264	−	39.7757i	−1.35500	−	1.43622i
$768$		0			0
$769$	30.6939	−	15.4151i	1.10685	−	0.555881i	0.201048	−	0.979581i	$-0.435565\pi$
$769$	30.6939	−	15.4151i	1.10685	−	0.555881i	0.905803	+	0.423700i	$0.139269\pi$
$770$		0			0
$771$	−27.0871	+	42.0289i	−0.975517	+	1.51363i
$772$		0			0
$773$	5.15062	+	4.32188i	0.185255	+	0.155447i	0.730699	−	0.682700i	$-0.239194\pi$
$773$	5.15062	+	4.32188i	0.185255	+	0.155447i	−0.545444	+	0.838147i	$0.683639\pi$
$774$		0			0
$775$	−71.8933	+	60.3256i	−2.58248	+	2.16696i
$776$		0			0
$777$	−18.1999	+	17.4930i	−0.652918	+	0.627558i
$778$		0			0
$779$	−33.8940	+	3.96164i	−1.21438	+	0.141941i
$780$		0			0
$781$	0.446779	+	7.67089i	0.0159870	+	0.274486i
$782$		0			0
$783$	27.8897	−	2.40549i	0.996695	−	0.0859651i
$784$		0			0
$785$	−36.2045	+	23.8121i	−1.29220	+	0.849890i
$786$		0			0
$787$	−3.43623	+	7.96607i	−0.122488	+	0.283960i	−0.968417	−	0.249336i	$-0.919788\pi$
$787$	−3.43623	+	7.96607i	−0.122488	+	0.283960i	0.845929	+	0.533296i	$0.179047\pi$
$788$		0			0
$789$	−31.0666	+	13.7444i	−1.10600	+	0.489313i
$790$		0			0
$791$	47.3100	+	17.2194i	1.68215	+	0.612253i
$792$		0			0
$793$	25.4247	−	9.25382i	0.902857	−	0.328613i
$794$		0			0
$795$	61.0957	+	56.5777i	2.16684	+	2.00661i
$796$		0			0
$797$	3.51215	+	2.30998i	0.124407	+	0.0818236i	0.610187	−	0.792257i	$-0.291094\pi$
$797$	3.51215	+	2.30998i	0.124407	+	0.0818236i	−0.485781	+	0.874081i	$0.661465\pi$
$798$		0			0
$799$	−3.10573	+	0.736071i	−0.109873	+	0.0260403i
$800$		0			0
$801$	−7.20730	+	6.27939i	−0.254657	+	0.221871i
$802$		0			0
$803$	−1.45691	−	3.37749i	−0.0514132	−	0.119189i
$804$		0			0
$805$	3.96242	+	13.2354i	0.139657	+	0.466487i
$806$		0			0
$807$	−0.412893	−	44.4603i	−0.0145345	−	1.56508i
$808$		0			0
$809$	52.0039			1.82836			0.914179	−	0.405310i	$-0.132836\pi$
$809$	52.0039			1.82836			0.914179	+	0.405310i	$0.132836\pi$
$810$		0			0
$811$	0.00958830			0.000336691			0.000168345	−	1.00000i	$-0.499946\pi$
$811$	0.00958830			0.000336691			0.000168345		1.00000i	$0.499946\pi$
$812$		0			0
$813$	7.60031	−	4.48266i	0.266554	−	0.157214i
$814$		0			0
$815$	0.459225	+	1.53392i	0.0160859	+	0.0537308i
$816$		0			0
$817$	10.0471	+	23.2919i	0.351505	+	0.814881i
$818$		0			0
$819$	49.8582	−	19.2028i	1.74219	−	0.671002i
$820$		0			0
$821$	−27.6440	+	6.55175i	−0.964783	+	0.228658i	−0.682673	−	0.730724i	$-0.739183\pi$
$821$	−27.6440	+	6.55175i	−0.964783	+	0.228658i	−0.282110	+	0.959382i	$0.591034\pi$
$822$		0			0
$823$	−38.9795	−	25.6372i	−1.35874	−	0.893658i	−0.359521	−	0.933137i	$-0.617060\pi$
$823$	−38.9795	−	25.6372i	−1.35874	−	0.893658i	−0.999220	+	0.0394790i	$0.987430\pi$
$824$		0			0
$825$	−13.9434	+	4.31588i	−0.485449	+	0.150260i
$826$		0			0
$827$	14.3389	−	5.21892i	0.498611	−	0.181479i	−0.0804583	−	0.996758i	$-0.525638\pi$
$827$	14.3389	−	5.21892i	0.498611	−	0.181479i	0.579069	+	0.815279i	$0.303416\pi$
$828$		0			0
$829$	−7.71316	−	2.80736i	−0.267889	−	0.0975036i	0.204583	−	0.978849i	$-0.434416\pi$
$829$	−7.71316	−	2.80736i	−0.267889	−	0.0975036i	−0.472472	+	0.881346i	$0.656638\pi$
$830$		0			0
$831$	9.49186	+	6.93036i	0.329269	+	0.240412i
$832$		0			0
$833$	2.65112	−	6.14599i	0.0918559	−	0.212946i
$834$		0			0
$835$	−39.1509	+	25.7499i	−1.35487	+	0.891113i
$836$		0			0
$837$	6.04673	+	41.6376i	0.209006	+	1.43920i
$838$		0			0
$839$	−0.586588	−	10.0713i	−0.0202513	−	0.347701i	−0.993180	−	0.116594i	$-0.962802\pi$
$839$	−0.586588	−	10.0713i	−0.0202513	−	0.347701i	0.972928	−	0.231107i	$-0.0742347\pi$
$840$		0			0
$841$	−0.0227953	+	0.00266438i	−0.000786044	+	9.18753e-5i
$842$		0			0
$843$	−7.03692	−	28.5087i	−0.242365	−	0.981891i
$844$		0			0
$845$	−13.6707	+	11.4711i	−0.470285	+	0.394616i
$846$		0			0
$847$	34.2662	+	28.7528i	1.17740	+	0.987957i
$848$		0			0
$849$	−1.91766	−	0.0938315i	−0.0658141	−	0.00322029i
$850$		0			0
$851$	2.42092	−	1.21583i	0.0829882	−	0.0416782i
$852$		0			0
$853$	−2.33002	−	2.46968i	−0.0797784	−	0.0845601i	0.686255	−	0.727361i	$-0.259254\pi$
$853$	−2.33002	−	2.46968i	−0.0797784	−	0.0845601i	−0.766033	+	0.642801i	$0.777772\pi$
$854$		0			0
$855$	66.7689	−	35.1003i	2.28345	−	1.20040i
$856$		0			0
$857$	−11.2528	−	1.31526i	−0.384389	−	0.0449286i	−0.0782955	−	0.996930i	$-0.524948\pi$
$857$	−11.2528	−	1.31526i	−0.384389	−	0.0449286i	−0.306093	+	0.952002i	$0.599022\pi$
$858$		0			0
$859$	16.6681	−	17.6671i	0.568707	−	0.602794i	−0.377638	−	0.925954i	$-0.623263\pi$
$859$	16.6681	−	17.6671i	0.568707	−	0.602794i	0.946345	+	0.323159i	$0.104745\pi$
$860$		0			0
$861$	−14.3451	−	38.3023i	−0.488879	−	1.30534i
$862$		0			0
$863$	3.23825	−	5.60881i	0.110231	−	0.190926i	−0.805632	−	0.592416i	$-0.798174\pi$
$863$	3.23825	−	5.60881i	0.110231	−	0.190926i	0.915863	+	0.401490i	$0.131508\pi$
$864$		0			0
$865$	34.2246	+	59.2787i	1.16367	+	2.01554i
$866$		0			0
$867$	−28.3458	+	5.27000i	−0.962674	+	0.178979i
$868$		0			0
$869$	−2.47037	−	0.585489i	−0.0838016	−	0.0198613i
$870$		0			0
$871$	27.2583	−	36.6142i	0.923612	−	1.24063i
$872$		0			0
$873$	−3.90226	+	1.00175i	−0.132071	+	0.0339040i
$874$		0			0
$875$	−32.8878	+	109.853i	−1.11181	+	3.71370i
$876$		0			0
$877$	0.609399	−	10.4630i	0.0205779	−	0.353310i	−0.972265	−	0.233882i	$-0.924857\pi$
$877$	0.609399	−	10.4630i	0.0205779	−	0.353310i	0.992843	−	0.119428i	$-0.0381059\pi$
$878$		0			0
$879$	15.2729	+	6.42052i	0.515142	+	0.216559i
$880$		0			0
$881$	2.83886	−	16.1000i	0.0956438	−	0.542423i	−0.898904	−	0.438145i	$-0.855636\pi$
$881$	2.83886	−	16.1000i	0.0956438	−	0.542423i	0.994548	−	0.104278i	$-0.0332532\pi$
$882$		0			0
$883$	0.355227	+	2.01459i	0.0119543	+	0.0677964i	0.990201	−	0.139647i	$-0.0445968\pi$
$883$	0.355227	+	2.01459i	0.0119543	+	0.0677964i	−0.978247	+	0.207443i	$0.933486\pi$
$884$		0			0
$885$	40.7601	−	83.0746i	1.37013	−	2.79252i
$886$		0			0
$887$	−32.6176	−	43.8131i	−1.09519	−	1.47110i	−0.867547	−	0.497356i	$-0.834304\pi$
$887$	−32.6176	−	43.8131i	−1.09519	−	1.47110i	−0.227646	−	0.973744i	$-0.573103\pi$
$888$		0			0
$889$	−2.23926	−	1.12460i	−0.0751024	−	0.0377178i
$890$		0			0
$891$	−1.64264	+	6.33412i	−0.0550305	+	0.212201i
$892$		0			0
$893$	−29.5891	−	14.8602i	−0.990161	−	0.497278i
$894$		0			0
$895$	39.3949	+	52.9166i	1.31683	+	1.76881i
$896$		0			0
$897$	−5.72074	+	0.386532i	−0.191010	+	0.0129059i
$898$		0			0
$899$	−7.57489	−	42.9593i	−0.252637	−	1.43277i
$900$		0			0
$901$	−1.21964	+	6.91694i	−0.0406322	+	0.230437i
$902$		0			0
$903$	−24.2174	+	18.3812i	−0.805906	+	0.611688i
$904$		0			0
$905$	−3.15893	+	54.2368i	−0.105006	+	1.80289i
$906$		0			0
$907$	5.53489	−	18.4878i	0.183783	−	0.613878i	−0.815595	−	0.578623i	$-0.803590\pi$
$907$	5.53489	−	18.4878i	0.183783	−	0.613878i	0.999378	−	0.0352551i	$-0.0112244\pi$
$908$		0			0
$909$	−2.86180	−	0.280729i	−0.0949199	−	0.00931118i
$910$		0			0
$911$	−21.3050	+	28.6176i	−0.705868	+	0.948145i	−0.999971	−	0.00762875i	$-0.997572\pi$
$911$	−21.3050	+	28.6176i	−0.705868	+	0.948145i	0.294103	+	0.955774i	$0.404979\pi$
$912$		0			0
$913$	2.20042	+	0.521509i	0.0728232	+	0.0172594i
$914$		0			0
$915$	29.7541	+	34.7981i	0.983639	+	1.15039i
$916$		0			0
$917$	15.3063	+	26.5112i	0.505457	+	0.875477i
$918$		0			0
$919$	10.9826	−	19.0225i	0.362284	−	0.627494i	−0.626053	−	0.779781i	$-0.715330\pi$
$919$	10.9826	−	19.0225i	0.362284	−	0.627494i	0.988336	+	0.152287i	$0.0486638\pi$
$920$		0			0
$921$	24.4758	+	4.08175i	0.806504	+	0.134498i
$922$		0			0
$923$	−30.2359	+	32.0482i	−0.995226	+	1.05488i
$924$		0			0
$925$	39.2767	+	4.59079i	1.29141	+	0.150944i
$926$		0			0
$927$	−4.12426	−	12.8991i	−0.135458	−	0.423661i
$928$		0			0
$929$	−23.1871	−	24.5769i	−0.760743	−	0.806341i	0.225042	−	0.974349i	$-0.427748\pi$
$929$	−23.1871	−	24.5769i	−0.760743	−	0.806341i	−0.985786	+	0.168008i	$0.946266\pi$
$930$		0			0
$931$	62.0509	−	31.1632i	2.03364	−	1.02133i
$932$		0			0
$933$	−15.1229	−	29.4276i	−0.495102	−	0.963415i
$934$		0			0
$935$	−1.34998	−	1.13277i	−0.0441492	−	0.0370456i
$936$		0			0
$937$	−0.126863	+	0.106451i	−0.00414443	+	0.00347759i	−0.644857	−	0.764303i	$-0.723083\pi$
$937$	−0.126863	+	0.106451i	−0.00414443	+	0.00347759i	0.640713	+	0.767780i	$0.278639\pi$
$938$		0			0
$939$	8.51063	+	2.46203i	0.277734	+	0.0803455i
$940$		0			0
$941$	−58.1030	+	6.79127i	−1.89410	+	0.221389i	−0.982042	−	0.188664i	$-0.939584\pi$
$941$	−58.1030	+	6.79127i	−1.89410	+	0.221389i	−0.912062	+	0.410053i	$0.865510\pi$
$942$		0			0
$943$	0.255217	+	4.38190i	0.00831100	+	0.142694i
$944$		0			0
$945$	60.0215	+	67.6128i	1.95250	+	2.19944i
$946$		0			0
$947$	36.1398	−	23.7695i	1.17439	−	0.772406i	0.196287	−	0.980547i	$-0.437112\pi$
$947$	36.1398	−	23.7695i	1.17439	−	0.772406i	0.978099	+	0.208141i	$0.0667413\pi$
$948$		0			0
$949$	8.35404	−	19.3668i	0.271183	−	0.628674i
$950$		0			0
$951$	−0.648951	+	6.03789i	−0.0210437	+	0.195792i
$952$		0			0
$953$	1.17741	+	0.428543i	0.0381401	+	0.0138819i	0.361020	−	0.932558i	$-0.382429\pi$
$953$	1.17741	+	0.428543i	0.0381401	+	0.0138819i	−0.322880	+	0.946440i	$0.604651\pi$
$954$		0			0
$955$	−35.4618	+	12.9070i	−1.14752	+	0.417662i
$956$		0			0
$957$	1.50321	−	6.61573i	0.0485919	−	0.213856i
$958$		0			0
$959$	15.3720	+	10.1103i	0.496388	+	0.326479i
$960$		0			0
$961$	33.6331	−	7.97119i	1.08494	−	0.257135i
$962$		0			0
$963$	−18.5222	+	33.5033i	−0.596869	+	1.07963i
$964$		0			0
$965$	32.2525	+	74.7697i	1.03824	+	2.40692i
$966$		0			0
$967$	9.25952	+	30.9290i	0.297766	+	0.994608i	0.967682	+	0.252172i	$0.0811448\pi$
$967$	9.25952	+	30.9290i	0.297766	+	0.994608i	−0.669916	+	0.742437i	$0.733670\pi$
$968$		0			0
$969$	5.53954	+	3.13003i	0.177956	+	0.100551i
$970$		0			0
$971$	55.6470			1.78580			0.892898	−	0.450259i	$-0.148668\pi$
$971$	55.6470			1.78580			0.892898	+	0.450259i	$0.148668\pi$
$972$		0			0
$973$	20.2496			0.649173
$974$		0			0
$975$	−72.8678	−	41.1728i	−2.33364	−	1.31858i
$976$		0			0
$977$	12.4566	+	41.6080i	0.398523	+	1.33116i	0.888281	+	0.459300i	$0.151900\pi$
$977$	12.4566	+	41.6080i	0.398523	+	1.33116i	−0.489758	+	0.871858i	$0.662915\pi$
$978$		0			0
$979$	0.917603	+	2.12724i	0.0293267	+	0.0679869i
$980$		0			0
$981$	−2.87906	+	0.0534790i	−0.0919212	+	0.00170745i
$982$		0			0
$983$	12.0113	−	2.84673i	0.383101	−	0.0907966i	−0.0345528	−	0.999403i	$-0.511001\pi$
$983$	12.0113	−	2.84673i	0.383101	−	0.0907966i	0.417654	+	0.908606i	$0.362853\pi$
$984$		0			0
$985$	−77.2428	−	50.8034i	−2.46116	−	1.61873i
$986$		0			0
$987$	8.79310	−	38.6991i	0.279888	−	1.23180i
$988$		0			0
$989$	3.06602	−	1.11594i	0.0974937	−	0.0354848i
$990$		0			0
$991$	−6.10003	−	2.22023i	−0.193774	−	0.0705280i	0.243310	−	0.969948i	$-0.421767\pi$
$991$	−6.10003	−	2.22023i	−0.193774	−	0.0705280i	−0.437084	+	0.899421i	$0.643989\pi$
$992$		0			0
$993$	5.12416	−	47.6756i	0.162610	−	1.51294i
$994$		0			0
$995$	−1.65191	+	3.82956i	−0.0523691	+	0.121405i
$996$		0			0
$997$	17.6580	−	11.6138i	0.559233	−	0.367814i	−0.238204	−	0.971215i	$-0.576559\pi$
$997$	17.6580	−	11.6138i	0.559233	−	0.367814i	0.797437	+	0.603402i	$0.206188\pi$
$998$		0			0
$999$	11.0127	−	13.8928i	0.348428	−	0.439547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.m.a.13.8	✓	162
3.2	odd	2		972.2.m.a.253.1		162
81.25	even	27	inner	324.2.m.a.25.8	yes	162
81.56	odd	54		972.2.m.a.73.1		162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.m.a.13.8	✓	162	1.1	even	1	trivial
324.2.m.a.25.8	yes	162	81.25	even	27	inner
972.2.m.a.73.1		162	81.56	odd	54
972.2.m.a.253.1		162	3.2	odd	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.m (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50798 + 0.852058i) q^{3} +(1.16819 + 3.90202i) q^{5} +(-1.69197 - 3.92242i) q^{7} +(1.54799 + 2.56977i) q^{9} +O(q^{10})\)	\(q+(1.50798 + 0.852058i) q^{3} +(1.16819 + 3.90202i) q^{5} +(-1.69197 - 3.92242i) q^{7} +(1.54799 + 2.56977i) q^{9} +(0.707474 - 0.167674i) q^{11} +(3.48323 + 2.29095i) q^{13} +(-1.56315 + 6.87952i) q^{15} +(-0.559183 + 0.203526i) q^{17} +(-5.80091 - 2.11136i) q^{19} +(0.790682 - 7.35657i) q^{21} +(-0.314501 + 0.729095i) q^{23} +(-9.68365 + 6.36904i) q^{25} +(0.144744 + 5.19414i) q^{27} +(-0.313243 - 5.37818i) q^{29} +(8.04246 - 0.940029i) q^{31} +(1.20972 + 0.349960i) q^{33} +(13.3288 - 11.1842i) q^{35} +(-2.61359 - 2.19306i) q^{37} +(3.30060 + 6.42262i) q^{39} +(4.93990 - 2.48091i) q^{41} +(-2.81985 - 2.98887i) q^{43} +(-8.21895 + 9.04227i) q^{45} +(5.32740 + 0.622684i) q^{47} +(-7.71891 + 8.18157i) q^{49} +(-1.01665 - 0.169544i) q^{51} +(5.90152 - 10.2217i) q^{53} +(1.48073 + 2.56470i) q^{55} +(-6.94865 - 8.12660i) q^{57} +(-12.7629 - 3.02487i) q^{59} +(3.87541 - 5.20558i) q^{61} +(7.46056 - 10.4198i) q^{63} +(-4.87028 + 16.2679i) q^{65} +(0.636617 - 10.9303i) q^{67} +(-1.09549 + 0.831486i) q^{69} +(-1.83516 + 10.4077i) q^{71} +(-0.878501 - 4.98223i) q^{73} +(-20.0295 + 1.35333i) q^{75} +(-1.85471 - 2.49131i) q^{77} +(-3.12040 - 1.56713i) q^{79} +(-4.20744 + 7.95597i) q^{81} +(2.77942 + 1.39588i) q^{83} +(-1.44739 - 1.94419i) q^{85} +(4.11016 - 8.37708i) q^{87} +(0.553305 + 3.13795i) q^{89} +(3.09258 - 17.5389i) q^{91} +(12.9288 + 5.43510i) q^{93} +(1.46201 - 25.1017i) q^{95} +(-0.385156 + 1.28651i) q^{97} +(1.52605 + 1.55849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q+O(q^{10}) \) 162 * q	\( 162 q + 27 q^{21} + 27 q^{23} + 27 q^{27} + 27 q^{29} + 27 q^{33} + 27 q^{35} - 18 q^{41} - 54 q^{45} - 54 q^{47} - 63 q^{51} - 54 q^{53} - 54 q^{57} - 63 q^{59} - 54 q^{63} - 90 q^{65} + 27 q^{67} - 90 q^{69} - 72 q^{71} - 90 q^{75} - 144 q^{77} + 54 q^{79} - 72 q^{81} - 72 q^{83} + 54 q^{85} - 144 q^{87} - 99 q^{89} - 90 q^{93} - 126 q^{95} + 27 q^{97} - 90 q^{99}+O(q^{100}) \) 162 * q + 27 * q^21 + 27 * q^23 + 27 * q^27 + 27 * q^29 + 27 * q^33 + 27 * q^35 - 18 * q^41 - 54 * q^45 - 54 * q^47 - 63 * q^51 - 54 * q^53 - 54 * q^57 - 63 * q^59 - 54 * q^63 - 90 * q^65 + 27 * q^67 - 90 * q^69 - 72 * q^71 - 90 * q^75 - 144 * q^77 + 54 * q^79 - 72 * q^81 - 72 * q^83 + 54 * q^85 - 144 * q^87 - 99 * q^89 - 90 * q^93 - 126 * q^95 + 27 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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