LMFDB - Embedded newform 324.2.m.a.25.8

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			25.8
Character	$\chi$	$=$	324.25
Dual form			324.2.m.a.13.8

$q$-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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{27}\right)$

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	−0.134331	−	0.990937i	$-0.542888\pi$
$5$	1.16819	−	3.90202i	0.522430	−	1.74504i	0.656760	−	0.754100i	$-0.271926\pi$
$6$		0			0
$7$	−1.69197	+	3.92242i	−0.639503	+	1.48253i	0.222138	+	0.975015i	$0.428696\pi$
$7$	−1.69197	+	3.92242i	−0.639503	+	1.48253i	−0.861641	+	0.507519i	$0.830563\pi$
$8$		0			0
$9$	1.54799	−	2.56977i	0.515998	−	0.856590i
$10$		0			0
$11$	0.707474	+	0.167674i	0.213311	+	0.0505557i	0.335882	−	0.941904i	$-0.390966\pi$
$11$	0.707474	+	0.167674i	0.213311	+	0.0505557i	−0.122571	+	0.992460i	$0.539114\pi$
$12$		0			0
$13$	3.48323	−	2.29095i	0.966073	−	0.635396i	0.0346753	−	0.999399i	$-0.488960\pi$
$13$	3.48323	−	2.29095i	0.966073	−	0.635396i	0.931398	+	0.364002i	$0.118590\pi$
$14$		0			0
$15$	−1.56315	−	6.87952i	−0.403603	−	1.77628i
$16$		0			0
$17$	−0.559183	−	0.203526i	−0.135622	−	0.0493623i	0.273318	−	0.961924i	$-0.411879\pi$
$17$	−0.559183	−	0.203526i	−0.135622	−	0.0493623i	−0.408939	+	0.912562i	$0.634101\pi$
$18$		0			0
$19$	−5.80091	+	2.11136i	−1.33082	+	0.484379i	−0.906910	−	0.421325i	$-0.861565\pi$
$19$	−5.80091	+	2.11136i	−1.33082	+	0.484379i	−0.423911	+	0.905704i	$0.639343\pi$
$20$		0			0
$21$	0.790682	+	7.35657i	0.172541	+	1.60533i
$22$		0			0
$23$	−0.314501	−	0.729095i	−0.0655780	−	0.152027i	0.882275	−	0.470734i	$-0.156011\pi$
$23$	−0.314501	−	0.729095i	−0.0655780	−	0.152027i	−0.947853	+	0.318707i	$0.896751\pi$
$24$		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	0.835362	+	0.549700i	$0.185258\pi$
$29$	−0.313243	+	5.37818i	−0.0581678	+	0.998703i	−0.893530	+	0.449003i	$0.851779\pi$
$30$		0			0
$31$	8.04246	+	0.940029i	1.44447	+	0.168834i	0.801929	−	0.597419i	$-0.203807\pi$
$31$	8.04246	+	0.940029i	1.44447	+	0.168834i	0.642539	+	0.766253i	$0.277881\pi$
$32$		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	−0.831828	−	0.555034i	$-0.812705\pi$
$37$	−2.61359	+	2.19306i	−0.429671	+	0.360537i	0.402157	+	0.915571i	$0.368261\pi$
$38$		0			0
$39$	3.30060	−	6.42262i	0.528519	−	1.02844i
$40$		0			0
$41$	4.93990	+	2.48091i	0.771482	+	0.387453i	0.790575	−	0.612365i	$-0.209782\pi$
$41$	4.93990	+	2.48091i	0.771482	+	0.387453i	−0.0190931	+	0.999818i	$0.506078\pi$
$42$		0			0
$43$	−2.81985	+	2.98887i	−0.430024	+	0.455798i	−0.905761	−	0.423789i	$-0.860700\pi$
$43$	−2.81985	+	2.98887i	−0.430024	+	0.455798i	0.475737	+	0.879587i	$0.342181\pi$
$44$		0			0
$45$	−8.21895	−	9.04227i	−1.22521	−	1.34794i
$46$		0			0
$47$	5.32740	−	0.622684i	0.777082	−	0.0908278i	0.281699	−	0.959503i	$-0.409102\pi$
$47$	5.32740	−	0.622684i	0.777082	−	0.0908278i	0.495383	+	0.868675i	$0.335028\pi$
$48$		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	0.912419	+	0.409257i	$0.134212\pi$
$53$	5.90152	+	10.2217i	0.810636	+	1.40406i	−0.101783	+	0.994807i	$0.532455\pi$
$54$		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	−0.950852	−	0.309647i	$-0.899789\pi$
$59$	−12.7629	+	3.02487i	−1.66159	+	0.393805i	−0.710743	+	0.703452i	$0.751641\pi$
$60$		0			0
$61$	3.87541	+	5.20558i	0.496195	+	0.666506i	0.977717	−	0.209928i	$-0.0673231\pi$
$61$	3.87541	+	5.20558i	0.496195	+	0.666506i	−0.481521	+	0.876434i	$0.659916\pi$
$62$		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	0.781067	+	0.624447i	$0.214676\pi$
$67$	0.636617	+	10.9303i	0.0777752	+	1.33535i	−0.703292	+	0.710901i	$0.748287\pi$
$68$		0			0
$69$	−1.09549	−	0.831486i	−0.131882	−	0.100099i
$70$		0			0
$71$	−1.83516	−	10.4077i	−0.217794	−	1.23517i	−0.875993	−	0.482324i	$-0.839793\pi$
$71$	−1.83516	−	10.4077i	−0.217794	−	1.23517i	0.658199	−	0.752844i	$-0.271318\pi$
$72$		0			0
$73$	−0.878501	+	4.98223i	−0.102821	+	0.583125i	0.889248	+	0.457426i	$0.151229\pi$
$73$	−0.878501	+	4.98223i	−0.102821	+	0.583125i	−0.992068	+	0.125699i	$0.959883\pi$
$74$		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	−0.615592	−	0.788065i	$-0.711083\pi$
$79$	−3.12040	+	1.56713i	−0.351073	+	0.176315i	0.264519	+	0.964380i	$0.414787\pi$
$80$		0			0
$81$	−4.20744	−	7.95597i	−0.467493	−	0.883997i
$82$		0			0
$83$	2.77942	−	1.39588i	0.305081	−	0.153217i	−0.289672	−	0.957126i	$-0.593546\pi$
$83$	2.77942	−	1.39588i	0.305081	−	0.153217i	0.594753	+	0.803909i	$0.297250\pi$
$84$		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	−0.941338	−	0.337465i	$-0.890431\pi$
$89$	0.553305	−	3.13795i	0.0586502	−	0.332622i	0.999988	+	0.00484315i	$0.00154163\pi$
$90$		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	0.936207	−	0.351449i	$-0.114311\pi$
$97$	−0.385156	−	1.28651i	−0.0391067	−	0.130626i	−0.975314	+	0.220823i	$0.929126\pi$
$98$		0			0
$99$	1.52605	−	1.55849i	0.153374	−	0.156634i
$100$		0			0
$101$	−0.572384	−	0.768845i	−0.0569543	−	0.0765029i	0.772733	−	0.634731i	$-0.218889\pi$
$101$	−0.572384	−	0.768845i	−0.0569543	−	0.0765029i	−0.829688	+	0.558228i	$0.811482\pi$
$102$		0			0
$103$	−4.39244	+	1.04103i	−0.432800	+	0.102575i	−0.441240	−	0.897389i	$-0.645461\pi$
$103$	−4.39244	+	1.04103i	−0.432800	+	0.102575i	0.00844068	+	0.999964i	$0.497313\pi$
$104$		0			0
$105$	29.6291	+	5.50860i	2.89151	+	0.537584i
$106$		0			0
$107$	6.38041	−	11.0512i	0.616817	−	1.06836i	−0.373246	−	0.927733i	$-0.621755\pi$
$107$	6.38041	−	11.0512i	0.616817	−	1.06836i	0.990063	−	0.140626i	$-0.0449115\pi$
$108$		0			0
$109$	−0.479926	−	0.831255i	−0.0459685	−	0.0796198i	0.842126	−	0.539281i	$-0.181304\pi$
$109$	−0.479926	−	0.831255i	−0.0459685	−	0.0796198i	−0.888094	+	0.459662i	$0.847971\pi$
$110$		0			0
$111$	−2.07261	+	5.53401i	−0.196724	+	0.525265i
$112$		0			0
$113$	−8.08790	−	8.57267i	−0.760845	−	0.806449i	0.224955	−	0.974369i	$-0.427776\pi$
$113$	−8.08790	−	8.57267i	−0.760845	−	0.806449i	−0.985801	+	0.167920i	$0.946295\pi$
$114$		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	0.662507	−	0.749056i	$-0.269493\pi$
$127$	0.449356	+	0.377055i	0.0398739	+	0.0334582i	−0.622633	+	0.782514i	$0.713937\pi$
$128$		0			0
$129$	−1.70558	+	6.90983i	−0.150168	+	0.608377i
$130$		0			0
$131$	−7.11777	−	0.831948i	−0.621882	−	0.0726876i	−0.200684	−	0.979656i	$-0.564316\pi$
$131$	−7.11777	−	0.831948i	−0.621882	−	0.0726876i	−0.421198	+	0.906968i	$0.638390\pi$
$132$		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	0.386408	−	0.922328i	$-0.373716\pi$
$137$	−3.59850	−	2.36677i	−0.307441	−	0.202207i	−0.693848	+	0.720121i	$0.744086\pi$
$138$		0			0
$139$	−1.87755	−	4.35265i	−0.159252	−	0.369187i	0.819844	−	0.572587i	$-0.194060\pi$
$139$	−1.87755	−	4.35265i	−0.159252	−	0.369187i	−0.979096	+	0.203400i	$0.934801\pi$
$140$		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	−0.838031	−	0.545623i	$-0.816293\pi$
$149$	−8.16567	+	5.37065i	−0.668958	+	0.439981i	0.169073	+	0.985604i	$0.445923\pi$
$150$		0			0
$151$	−7.33765	−	1.73905i	−0.597129	−	0.141522i	−0.0790731	−	0.996869i	$-0.525196\pi$
$151$	−7.33765	−	1.73905i	−0.597129	−	0.141522i	−0.518056	+	0.855347i	$0.673344\pi$
$152$		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	−0.745616	−	0.666376i	$-0.767845\pi$
$157$	3.05125	−	10.1919i	0.243516	−	0.813402i	0.989133	−	0.147026i	$-0.0469701\pi$
$158$		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	−0.730184	−	0.683250i	$-0.760566\pi$
$167$	3.29957	−	11.0213i	0.255328	−	0.852855i	0.985512	−	0.169605i	$-0.0542491\pi$
$168$		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	0.799036	−	0.601284i	$-0.205344\pi$
$173$	16.3521	+	3.87551i	1.24322	+	0.294650i	0.444189	+	0.895933i	$0.353492\pi$
$174$		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	0.841038	−	0.540975i	$-0.181945\pi$
$179$	15.2198	+	5.53954i	1.13758	+	0.414045i	0.296540	+	0.955020i	$0.404167\pi$
$180$		0			0
$181$	12.5339	−	4.56197i	0.931638	−	0.339088i	0.168779	−	0.985654i	$-0.446018\pi$
$181$	12.5339	−	4.56197i	0.931638	−	0.339088i	0.762858	+	0.646566i	$0.223795\pi$
$182$		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	−0.921064	−	0.389411i	$-0.872679\pi$
$191$	0.538713	−	9.24935i	0.0389799	−	0.669259i	0.960044	−	0.279849i	$-0.0902843\pi$
$192$		0			0
$193$	19.8566	+	2.32091i	1.42931	+	0.167063i	0.795279	−	0.606244i	$-0.207325\pi$
$193$	19.8566	+	2.32091i	1.42931	+	0.167063i	0.634032	+	0.773307i	$0.281399\pi$
$194$		0			0
$195$	−21.2055	−	20.3818i	−1.51856	−	1.45957i
$196$		0			0
$197$	−17.3877	−	14.5900i	−1.23882	−	1.03950i	−0.997615	−	0.0690242i	$-0.978011\pi$
$197$	−17.3877	−	14.5900i	−1.23882	−	1.03950i	−0.241210	−	0.970473i	$-0.577544\pi$
$198$		0			0
$199$	0.784385	−	0.658177i	0.0556036	−	0.0466569i	−0.614562	−	0.788868i	$-0.710667\pi$
$199$	0.784385	−	0.658177i	0.0556036	−	0.0466569i	0.670166	+	0.742211i	$0.266223\pi$
$200$		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	−0.993504	−	0.113797i	$-0.963699\pi$
$211$	−15.2426	−	16.1562i	−1.04934	−	1.11224i	−0.0558372	−	0.998440i	$-0.517783\pi$
$212$		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	0.761775	−	0.647842i	$-0.224328\pi$
$223$	−1.15480	−	1.55116i	−0.0773309	−	0.103873i	−0.839105	+	0.543969i	$0.816921\pi$
$224$		0			0
$225$	−31.3572	+	15.0255i	−2.09048	+	1.00170i
$226$		0			0
$227$	4.06304	+	13.5715i	0.269674	+	0.900772i	0.980352	+	0.197256i	$0.0632029\pi$
$227$	4.06304	+	13.5715i	0.269674	+	0.900772i	−0.710679	+	0.703517i	$0.751612\pi$
$228$		0			0
$229$	1.55727	+	26.7373i	0.102907	+	1.76685i	0.516403	+	0.856346i	$0.327271\pi$
$229$	1.55727	+	26.7373i	0.102907	+	1.76685i	−0.413495	+	0.910506i	$0.635692\pi$
$230$		0			0
$231$	−0.674121	+	5.33716i	−0.0443539	+	0.351159i
$232$		0			0
$233$	−2.77556	−	15.7410i	−0.181833	−	1.03122i	−0.929958	−	0.367667i	$-0.880157\pi$
$233$	−2.77556	−	15.7410i	−0.181833	−	1.03122i	0.748125	−	0.663558i	$-0.230954\pi$
$234$		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	−0.392360	−	0.919812i	$-0.628341\pi$
$239$	9.29649	−	12.4874i	0.601340	−	0.807740i	0.993700	+	0.112072i	$0.0357486\pi$
$240$		0			0
$241$	−24.4616	+	12.2851i	−1.57571	+	0.791353i	−0.999660	−	0.0260597i	$-0.991704\pi$
$241$	−24.4616	+	12.2851i	−1.57571	+	0.791353i	−0.576053	+	0.817413i	$0.695408\pi$
$242$		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	−0.938681	−	0.344787i	$-0.887951\pi$
$251$	0.971406	−	5.50912i	0.0613146	−	0.347732i	0.999996	−	0.00294566i	$-0.000937634\pi$
$252$		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	−0.486725	−	0.873555i	$-0.661809\pi$
$257$	−1.67854	−	28.8195i	−0.104705	−	1.79771i	0.382020	−	0.924154i	$-0.375228\pi$
$258$		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	−0.999955	−	0.00943789i	$-0.996996\pi$
$263$	−11.7122	−	15.7322i	−0.722206	−	0.970092i	0.277749	−	0.960654i	$-0.410412\pi$
$264$		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	0.147867	+	0.989007i	$0.452759\pi$
$269$	−12.8351	+	22.2311i	−0.782572	+	1.35545i	−0.930439	+	0.366447i	$0.880574\pi$
$270$		0			0
$271$	2.54720	+	4.41188i	0.154732	+	0.268003i	0.932961	−	0.359977i	$-0.117215\pi$
$271$	2.54720	+	4.41188i	0.154732	+	0.268003i	−0.778230	+	0.627980i	$0.783882\pi$
$272$		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	0.0888142	−	0.996048i	$-0.471692\pi$
$277$	6.73953	−	0.787738i	0.404939	−	0.0473306i	0.316125	+	0.948718i	$0.397618\pi$
$278$		0			0
$279$	14.8653	−	19.2121i	0.889964	−	1.15020i
$280$		0			0
$281$	−11.6342	+	12.3315i	−0.694038	+	0.735637i	−0.974539	−	0.224216i	$-0.928018\pi$
$281$	−11.6342	+	12.3315i	−0.694038	+	0.735637i	0.280501	+	0.959854i	$0.409499\pi$
$282$		0			0
$283$	−0.990582	−	0.497489i	−0.0588840	−	0.0295726i	0.419114	−	0.907934i	$-0.362341\pi$
$283$	−0.990582	−	0.497489i	−0.0588840	−	0.0295726i	−0.477998	+	0.878361i	$0.658637\pi$
$284$		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	0.388985	−	0.921244i	$-0.372826\pi$
$293$	9.50061	+	1.11046i	0.555032	+	0.0648739i	0.166047	+	0.986118i	$0.446900\pi$
$294$		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	0.696299	−	0.717752i	$-0.254829\pi$
$307$	13.4623	+	4.89986i	0.768332	+	0.279650i	0.0720335	+	0.997402i	$0.477051\pi$
$308$		0			0
$309$	−5.73668	+	5.31246i	−0.326348	+	0.302215i
$310$		0			0
$311$	−15.9597	+	10.4968i	−0.904990	+	0.595221i	−0.914434	−	0.404734i	$-0.867364\pi$
$311$	−15.9597	+	10.4968i	−0.904990	+	0.595221i	0.00944460	+	0.999955i	$0.496994\pi$
$312$		0			0
$313$	4.97721	+	1.17962i	0.281329	+	0.0666761i	0.368858	−	0.929486i	$-0.379749\pi$
$313$	4.97721	+	1.17962i	0.281329	+	0.0666761i	−0.0875291	+	0.996162i	$0.527897\pi$
$314$		0			0
$315$	49.3737	−	16.9389i	2.78189	−	0.954400i
$316$		0			0
$317$	1.38868	−	3.21932i	0.0779959	−	0.180815i	−0.874757	−	0.484563i	$-0.838979\pi$
$317$	1.38868	−	3.21932i	0.0779959	−	0.180815i	0.952752	+	0.303748i	$0.0982380\pi$
$318$		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	0.294533	+	0.955641i	$0.404836\pi$
$331$	−10.9651	+	25.4199i	−0.602696	+	1.39721i	−0.897229	+	0.441565i	$0.854423\pi$
$332$		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	−0.256946	−	0.966426i	$-0.582716\pi$
$337$	9.70509	−	6.38314i	0.528670	−	0.347712i	0.785616	+	0.618714i	$0.212346\pi$
$338$		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	−0.947229	−	0.320558i	$-0.896130\pi$
$347$	−9.87963	−	22.9036i	−0.530367	−	1.22953i	0.416862	−	0.908970i	$-0.363130\pi$
$348$		0			0
$349$	−7.53751	−	4.95750i	−0.403473	−	0.265369i	0.331513	−	0.943451i	$-0.392441\pi$
$349$	−7.53751	−	4.95750i	−0.403473	−	0.265369i	−0.734986	+	0.678082i	$0.762811\pi$
$350$		0			0
$351$	−11.3954	−	18.4240i	−0.608239	−	0.983398i
$352$		0			0
$353$	1.05449	−	18.1049i	0.0561249	−	0.963627i	−0.846280	−	0.532738i	$-0.821163\pi$
$353$	1.05449	−	18.1049i	0.0561249	−	0.963627i	0.902405	−	0.430889i	$-0.141800\pi$
$354$		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	0.781436	−	0.623986i	$-0.214488\pi$
$359$	5.73391	+	4.81132i	0.302624	+	0.253932i	−0.478811	+	0.877918i	$0.658932\pi$
$360$		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	−0.629742	−	0.776805i	$-0.716839\pi$
$367$	3.49361	−	3.70301i	0.182365	−	0.193295i	0.812107	+	0.583509i	$0.198321\pi$
$368$		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	0.997644	+	0.0686057i	$0.0218551\pi$
$373$	19.4701	+	20.6371i	1.00813	+	1.06855i	0.0104818	+	0.999945i	$0.496663\pi$
$374$		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	−0.820184	−	0.572099i	$-0.806129\pi$
$379$	1.66179	−	2.87830i	0.0853604	−	0.147849i	0.905545	+	0.424251i	$0.139462\pi$
$380$		0			0
$381$	0.998892	+	0.185712i	0.0511748	+	0.00951433i
$382$		0			0
$383$	12.7469	−	3.02106i	0.651334	−	0.154369i	0.108351	−	0.994113i	$-0.465443\pi$
$383$	12.7469	−	3.02106i	0.651334	−	0.154369i	0.542983	+	0.839744i	$0.317295\pi$
$384$		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	0.999980	−	0.00640260i	$-0.00203802\pi$
$389$	3.17523	+	10.6060i	0.160991	+	0.537746i	−0.838989	+	0.544148i	$0.816853\pi$
$390$		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	−0.515585	−	0.856838i	$-0.672425\pi$
$397$	5.21956	−	29.6016i	0.261962	−	1.48566i	0.777547	−	0.628824i	$-0.216464\pi$
$398$		0			0
$399$	−20.1190	−	41.0054i	−1.00721	−	2.05284i
$400$		0			0
$401$	2.59002	−	3.47899i	0.129339	−	0.173733i	−0.732736	−	0.680513i	$-0.761757\pi$
$401$	2.59002	−	3.47899i	0.129339	−	0.173733i	0.862075	+	0.506780i	$0.169164\pi$
$402$		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	−0.0673227	+	0.997731i	$0.521446\pi$
$409$	−20.3012	+	27.2693i	−1.00383	+	1.34838i	−0.936508	+	0.350647i	$0.885962\pi$
$410$		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	0.929225	+	0.369515i	$0.120476\pi$
$419$	1.00671	+	17.2846i	0.0491811	+	0.844407i	−0.880044	+	0.474893i	$0.842487\pi$
$420$		0			0
$421$	−3.75680	−	12.5486i	−0.183095	−	0.611580i	−0.999422	−	0.0339901i	$-0.989179\pi$
$421$	−3.75680	−	12.5486i	−0.183095	−	0.611580i	0.816327	−	0.577590i	$-0.196007\pi$
$422$		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	−0.864894	−	0.501955i	$-0.832614\pi$
$431$	0.0468879	−	0.0812122i	0.00225851	−	0.00391186i	0.867152	+	0.498043i	$0.165948\pi$
$432$		0			0
$433$	3.08387	+	5.34141i	0.148201	+	0.256692i	0.930563	−	0.366133i	$-0.119318\pi$
$433$	3.08387	+	5.34141i	0.148201	+	0.256692i	−0.782361	+	0.622825i	$0.785985\pi$
$434$		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	−0.430143	−	0.902761i	$-0.641537\pi$
$439$	−13.4200	+	1.56857i	−0.640501	+	0.0748638i	−0.210358	+	0.977624i	$0.567463\pi$
$440$		0			0
$441$	−32.9736	+	7.17082i	−1.57017	+	0.341468i
$442$		0			0
$443$	−6.46212	+	6.84944i	−0.307024	+	0.325427i	−0.862453	−	0.506137i	$-0.831073\pi$
$443$	−6.46212	+	6.84944i	−0.307024	+	0.325427i	0.555428	+	0.831564i	$0.312554\pi$
$444$		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	0.140336	−	0.990104i	$-0.455182\pi$
$449$	24.1512	−	20.2653i	1.13977	−	0.956378i	0.999431	+	0.0337257i	$0.0107373\pi$
$450$		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	−0.939648	−	0.342144i	$-0.888847\pi$
$457$	0.713303	−	12.2469i	0.0333669	−	0.572887i	0.973015	−	0.230744i	$-0.0741159\pi$
$458$		0			0
$459$	−1.13808	+	2.87501i	−0.0531210	+	0.134194i
$460$		0			0
$461$	21.3636	+	14.0511i	0.995002	+	0.654423i	0.938967	−	0.344006i	$-0.111784\pi$
$461$	21.3636	+	14.0511i	0.995002	+	0.654423i	0.0560342	+	0.998429i	$0.482154\pi$
$462$		0			0
$463$	4.79869	+	11.1246i	0.223014	+	0.517005i	0.992584	−	0.121557i	$-0.0387888\pi$
$463$	4.79869	+	11.1246i	0.223014	+	0.517005i	−0.769570	+	0.638562i	$0.779530\pi$
$464$		0			0
$465$	−6.10460	−	56.7977i	−0.283094	−	2.63393i
$466$		0			0
$467$	−22.0808	+	8.03674i	−1.02178	+	0.371896i	−0.797944	−	0.602732i	$-0.794079\pi$
$467$	−22.0808	+	8.03674i	−1.02178	+	0.371896i	−0.223832	+	0.974628i	$0.571857\pi$
$468$		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	−0.611095	−	0.791557i	$-0.709271\pi$
$479$	8.40473	−	19.4844i	0.384022	−	0.890263i	0.995117	−	0.0987053i	$-0.0314701\pi$
$480$		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	0.778329	+	0.627856i	$0.216068\pi$
$491$	−4.80769	+	16.0588i	−0.216968	+	0.724724i	−0.995297	+	0.0968676i	$0.969118\pi$
$492$		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	−0.567271	−	0.823531i	$-0.692001\pi$
$499$	−0.799176	+	0.525626i	−0.0357760	+	0.0235303i	0.531495	+	0.847061i	$0.321630\pi$
$500$		0			0
$501$	−4.41513	−	19.4313i	−0.197254	−	0.868127i
$502$		0			0
$503$	−29.3308	−	10.6755i	−1.30780	−	0.475999i	−0.408268	−	0.912862i	$-0.633867\pi$
$503$	−29.3308	−	10.6755i	−1.30780	−	0.475999i	−0.899528	+	0.436863i	$0.856089\pi$
$504$		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	0.993812	−	0.111076i	$-0.0354298\pi$
$509$	5.21211	+	12.0830i	0.231023	+	0.535571i	−0.762789	+	0.646647i	$0.776171\pi$
$510$		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	0.0709457	−	0.997480i	$-0.477398\pi$
$521$	−20.5214	−	17.2195i	−0.899061	−	0.754402i	−0.970007	+	0.243078i	$0.921843\pi$
$522$		0			0
$523$	−4.29256	+	3.60189i	−0.187701	+	0.157500i	−0.731796	−	0.681524i	$-0.761318\pi$
$523$	−4.29256	+	3.60189i	−0.187701	+	0.157500i	0.544095	+	0.839024i	$0.316873\pi$
$524$		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	−0.985281	−	0.170942i	$-0.945319\pi$
$541$	−8.01520	+	13.8827i	−0.344600	+	0.596865i	0.640681	+	0.767807i	$0.278652\pi$
$542$		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	0.730726	−	0.682671i	$-0.239182\pi$
$547$	−3.10689	−	4.17327i	−0.132841	−	0.178436i	−0.863566	+	0.504235i	$0.831775\pi$
$548$		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	0.999559	+	0.0296861i	$0.00945077\pi$
$557$	1.66230	+	9.42739i	0.0704341	+	0.399451i	−0.929125	+	0.369765i	$0.879438\pi$
$558$		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	−0.565786	−	0.824552i	$-0.691427\pi$
$563$	9.16824	−	12.3151i	0.386395	−	0.519019i	0.952182	+	0.305533i	$0.0988346\pi$
$564$		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	−0.415751	−	0.909478i	$-0.636481\pi$
$569$	1.56225	−	0.784594i	0.0654931	−	0.0328919i	0.481244	+	0.876587i	$0.340185\pi$
$570$		0			0
$571$	−24.6751	+	33.1444i	−1.03262	+	1.38705i	−0.113291	+	0.993562i	$0.536139\pi$
$571$	−24.6751	+	33.1444i	−1.03262	+	1.38705i	−0.919329	+	0.393489i	$0.871268\pi$
$572$		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	0.964665	+	0.263479i	$0.0848699\pi$
$577$	3.56208	+	20.2016i	0.148291	+	0.841003i	−0.816374	+	0.577524i	$0.804019\pi$
$578$		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	0.995034	−	0.0995378i	$-0.0317364\pi$
$587$	14.8833	+	19.9917i	0.614299	+	0.825146i	−0.380735	+	0.924684i	$0.624329\pi$
$588$		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	−0.981003	−	0.193992i	$-0.937857\pi$
$593$	−7.85339	+	13.6025i	−0.322500	+	0.558586i	0.658503	+	0.752578i	$0.271190\pi$
$594$		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	0.111138	−	0.993805i	$-0.464550\pi$
$599$	−21.7198	−	23.0217i	−0.887448	−	0.940640i	−0.998586	+	0.0531653i	$0.983069\pi$
$600$		0			0
$601$	6.83349	−	0.798720i	0.278744	−	0.0325805i	0.0244276	−	0.999702i	$-0.492224\pi$
$601$	6.83349	−	0.798720i	0.278744	−	0.0325805i	0.254316	+	0.967121i	$0.418150\pi$
$602$		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	0.541458	−	0.840728i	$-0.317873\pi$
$607$	4.69161	+	2.35621i	0.190426	+	0.0956357i	−0.351031	+	0.936364i	$0.614169\pi$
$608$		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	0.993418	−	0.114545i	$-0.0365409\pi$
$613$	26.0740	+	21.8787i	1.05312	+	0.883672i	0.0597007	+	0.998216i	$0.480985\pi$
$614$		0			0
$615$	9.34568	−	37.8622i	0.376854	−	1.52675i
$616$		0			0
$617$	8.94135	+	1.04509i	0.359965	+	0.0420739i	0.294154	−	0.955758i	$-0.404962\pi$
$617$	8.94135	+	1.04509i	0.359965	+	0.0420739i	0.0658117	+	0.997832i	$0.479036\pi$
$618$		0			0
$619$	2.19391	−	37.6679i	0.0881806	−	1.51400i	−0.606731	−	0.794907i	$-0.707519\pi$
$619$	2.19391	−	37.6679i	0.0881806	−	1.51400i	0.694912	−	0.719095i	$-0.255443\pi$
$620$		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	0.875912	−	0.482472i	$-0.160261\pi$
$631$	31.0674	+	11.3076i	1.23677	+	0.450148i	0.360860	+	0.932620i	$0.382483\pi$
$632$		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	−0.996880	−	0.0789263i	$-0.974851\pi$
$641$	−6.46547	+	14.9886i	−0.255371	+	0.592016i	0.741510	+	0.670942i	$0.234110\pi$
$642$		0			0
$643$	0.735889	−	2.45804i	0.0290206	−	0.0969357i	−0.942252	−	0.334904i	$-0.891296\pi$
$643$	0.735889	−	2.45804i	0.0290206	−	0.0969357i	0.971273	+	0.237968i	$0.0764814\pi$
$644$		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	0.160053	−	0.987108i	$-0.448834\pi$
$653$	14.5339	−	48.5466i	0.568756	−	1.89978i	0.408703	−	0.912668i	$-0.365981\pi$
$654$		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	0.736043	−	0.676934i	$-0.236692\pi$
$659$	27.9811	+	6.63164i	1.08999	+	0.258332i	0.353945	+	0.935266i	$0.384840\pi$
$660$		0			0
$661$	6.68574	−	4.39728i	0.260045	−	0.171034i	−0.412791	−	0.910826i	$-0.635446\pi$
$661$	6.68574	−	4.39728i	0.260045	−	0.171034i	0.672836	+	0.739791i	$0.265076\pi$
$662$		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	0.981589	+	0.191004i	$0.0611745\pi$
$673$	40.1005	+	26.3745i	1.54576	+	1.01666i	0.564171	+	0.825658i	$0.309196\pi$
$674$		0			0
$675$	−34.4833	+	49.3763i	−1.32726	+	1.90050i
$676$		0			0
$677$	−1.35311	+	23.2320i	−0.0520043	+	0.892880i	0.866920	+	0.498447i	$0.166096\pi$
$677$	−1.35311	+	23.2320i	−0.0520043	+	0.892880i	−0.918925	+	0.394433i	$0.870941\pi$
$678$		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	0.999490	−	0.0319308i	$-0.0101656\pi$
$683$	29.8350	+	25.0345i	1.14160	+	0.957919i	0.142114	+	0.989850i	$0.454610\pi$
$684$		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	−0.253350	−	0.967375i	$-0.581532\pi$
$691$	19.1137	−	20.2593i	0.727120	−	0.770702i	0.980469	+	0.196673i	$0.0630137\pi$
$692$		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	−0.971306	−	0.237835i	$-0.923562\pi$
$701$	−18.3117	−	31.7168i	−0.691624	−	1.19793i	0.279682	−	0.960093i	$-0.409771\pi$
$702$		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	0.877892	+	0.478858i	$0.158949\pi$
$709$	28.8864	+	38.8012i	1.08485	+	1.45721i	0.206959	+	0.978350i	$0.433643\pi$
$710$		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	0.982219	−	0.187738i	$-0.0601156\pi$
$719$	−0.133404	−	0.756569i	−0.00497511	−	0.0282153i	−0.987194	+	0.159523i	$0.949004\pi$
$720$		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	−0.0588472	−	0.998267i	$-0.518742\pi$
$727$	19.0559	−	9.57024i	0.706745	−	0.354941i	0.765592	+	0.643326i	$0.222446\pi$
$728$		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	−0.280324	−	0.959905i	$-0.590442\pi$
$733$	19.4839	−	26.1714i	0.719653	−	0.966662i	0.999977	−	0.00675660i	$-0.00215071\pi$
$734$		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	0.940372	−	0.340148i	$-0.110477\pi$
$739$	−1.62091	−	9.19262i	−0.0596260	−	0.338156i	−0.999998	+	0.00199189i	$0.999366\pi$
$740$		0			0
$741$	−5.58604	+	44.2258i	−0.205208	+	1.62468i
$742$		0			0
$743$	2.94253	+	50.5212i	0.107951	+	1.85344i	0.425196	+	0.905101i	$0.360205\pi$
$743$	2.94253	+	50.5212i	0.107951	+	1.85344i	−0.317245	+	0.948344i	$0.602758\pi$
$744$		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	−0.545262	−	0.838266i	$-0.683570\pi$
$751$	−17.9858	+	4.26272i	−0.656312	+	0.155549i	−0.111050	+	0.993815i	$0.535421\pi$
$752$		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	−0.878487	−	0.477767i	$-0.841446\pi$
$757$	−23.4692	−	40.6498i	−0.853001	−	1.47744i	0.0254855	−	0.999675i	$-0.491887\pi$
$758$		0			0
$759$	−0.635613	−	0.771940i	−0.0230713	−	0.0280197i
$760$		0			0
$761$	−7.18699	−	7.61777i	−0.260528	−	0.276144i	0.583885	−	0.811837i	$-0.301532\pi$
$761$	−7.18699	−	7.61777i	−0.260528	−	0.276144i	−0.844413	+	0.535693i	$0.820051\pi$
$762$		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	0.905803	−	0.423700i	$-0.139269\pi$
$769$	30.6939	+	15.4151i	1.10685	+	0.555881i	0.201048	+	0.979581i	$0.435565\pi$
$770$		0			0
$771$	−27.0871	−	42.0289i	−0.975517	−	1.51363i
$772$		0			0
$773$	5.15062	−	4.32188i	0.185255	−	0.155447i	−0.545444	−	0.838147i	$-0.683639\pi$
$773$	5.15062	−	4.32188i	0.185255	−	0.155447i	0.730699	+	0.682700i	$0.239194\pi$
$774$		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	0.845929	−	0.533296i	$-0.179047\pi$
$787$	−3.43623	−	7.96607i	−0.122488	−	0.283960i	−0.968417	+	0.249336i	$0.919788\pi$
$788$		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	−0.485781	−	0.874081i	$-0.661465\pi$
$797$	3.51215	−	2.30998i	0.124407	−	0.0818236i	0.610187	+	0.792257i	$0.291094\pi$
$798$		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	−0.282110	−	0.959382i	$-0.591034\pi$
$821$	−27.6440	−	6.55175i	−0.964783	−	0.228658i	−0.682673	+	0.730724i	$0.739183\pi$
$822$		0			0
$823$	−38.9795	+	25.6372i	−1.35874	+	0.893658i	−0.999220	−	0.0394790i	$-0.987430\pi$
$823$	−38.9795	+	25.6372i	−1.35874	+	0.893658i	−0.359521	+	0.933137i	$0.617060\pi$
$824$		0			0
$825$	−13.9434	−	4.31588i	−0.485449	−	0.150260i
$826$		0			0
$827$	14.3389	+	5.21892i	0.498611	+	0.181479i	0.579069	−	0.815279i	$-0.303416\pi$
$827$	14.3389	+	5.21892i	0.498611	+	0.181479i	−0.0804583	+	0.996758i	$0.525638\pi$
$828$		0			0
$829$	−7.71316	+	2.80736i	−0.267889	+	0.0975036i	−0.472472	−	0.881346i	$-0.656638\pi$
$829$	−7.71316	+	2.80736i	−0.267889	+	0.0975036i	0.204583	+	0.978849i	$0.434416\pi$
$830$		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	0.972928	+	0.231107i	$0.0742347\pi$
$839$	−0.586588	+	10.0713i	−0.0202513	+	0.347701i	−0.993180	+	0.116594i	$0.962802\pi$
$840$		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	−0.766033	−	0.642801i	$-0.777772\pi$
$853$	−2.33002	+	2.46968i	−0.0797784	+	0.0845601i	0.686255	+	0.727361i	$0.259254\pi$
$854$		0			0
$855$	66.7689	+	35.1003i	2.28345	+	1.20040i
$856$		0			0
$857$	−11.2528	+	1.31526i	−0.384389	+	0.0449286i	−0.306093	−	0.952002i	$-0.599022\pi$
$857$	−11.2528	+	1.31526i	−0.384389	+	0.0449286i	−0.0782955	+	0.996930i	$0.524948\pi$
$858$		0			0
$859$	16.6681	+	17.6671i	0.568707	+	0.602794i	0.946345	−	0.323159i	$-0.104745\pi$
$859$	16.6681	+	17.6671i	0.568707	+	0.602794i	−0.377638	+	0.925954i	$0.623263\pi$
$860$		0			0
$861$	−14.3451	+	38.3023i	−0.488879	+	1.30534i
$862$		0			0
$863$	3.23825	+	5.60881i	0.110231	+	0.190926i	0.915863	−	0.401490i	$-0.131508\pi$
$863$	3.23825	+	5.60881i	0.110231	+	0.190926i	−0.805632	+	0.592416i	$0.798174\pi$
$864$		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	0.992843	+	0.119428i	$0.0381059\pi$
$877$	0.609399	+	10.4630i	0.0205779	+	0.353310i	−0.972265	+	0.233882i	$0.924857\pi$
$878$		0			0
$879$	15.2729	−	6.42052i	0.515142	−	0.216559i
$880$		0			0
$881$	2.83886	+	16.1000i	0.0956438	+	0.542423i	0.994548	+	0.104278i	$0.0332532\pi$
$881$	2.83886	+	16.1000i	0.0956438	+	0.542423i	−0.898904	+	0.438145i	$0.855636\pi$
$882$		0			0
$883$	0.355227	−	2.01459i	0.0119543	−	0.0677964i	−0.978247	−	0.207443i	$-0.933486\pi$
$883$	0.355227	−	2.01459i	0.0119543	−	0.0677964i	0.990201	+	0.139647i	$0.0445968\pi$
$884$		0			0
$885$	40.7601	+	83.0746i	1.37013	+	2.79252i
$886$		0			0
$887$	−32.6176	+	43.8131i	−1.09519	+	1.47110i	−0.227646	+	0.973744i	$0.573103\pi$
$887$	−32.6176	+	43.8131i	−1.09519	+	1.47110i	−0.867547	+	0.497356i	$0.834304\pi$
$888$		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	0.999378	+	0.0352551i	$0.0112244\pi$
$907$	5.53489	+	18.4878i	0.183783	+	0.613878i	−0.815595	+	0.578623i	$0.803590\pi$
$908$		0			0
$909$	−2.86180	+	0.280729i	−0.0949199	+	0.00931118i
$910$		0			0
$911$	−21.3050	−	28.6176i	−0.705868	−	0.948145i	0.294103	−	0.955774i	$-0.404979\pi$
$911$	−21.3050	−	28.6176i	−0.705868	−	0.948145i	−0.999971	+	0.00762875i	$0.997572\pi$
$912$		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	0.988336	−	0.152287i	$-0.0486638\pi$
$919$	10.9826	+	19.0225i	0.362284	+	0.627494i	−0.626053	+	0.779781i	$0.715330\pi$
$920$		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	−0.985786	−	0.168008i	$-0.946266\pi$
$929$	−23.1871	+	24.5769i	−0.760743	+	0.806341i	0.225042	+	0.974349i	$0.427748\pi$
$930$		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	0.640713	−	0.767780i	$-0.278639\pi$
$937$	−0.126863	−	0.106451i	−0.00414443	−	0.00347759i	−0.644857	+	0.764303i	$0.723083\pi$
$938$		0			0
$939$	8.51063	−	2.46203i	0.277734	−	0.0803455i
$940$		0			0
$941$	−58.1030	−	6.79127i	−1.89410	−	0.221389i	−0.912062	−	0.410053i	$-0.865510\pi$
$941$	−58.1030	−	6.79127i	−1.89410	−	0.221389i	−0.982042	+	0.188664i	$0.939584\pi$
$942$		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	0.978099	−	0.208141i	$-0.0667413\pi$
$947$	36.1398	+	23.7695i	1.17439	+	0.772406i	0.196287	+	0.980547i	$0.437112\pi$
$948$		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	−0.322880	−	0.946440i	$-0.604651\pi$
$953$	1.17741	−	0.428543i	0.0381401	−	0.0138819i	0.361020	+	0.932558i	$0.382429\pi$
$954$		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	−0.669916	−	0.742437i	$-0.733670\pi$
$967$	9.25952	−	30.9290i	0.297766	−	0.994608i	0.967682	−	0.252172i	$-0.0811448\pi$
$968$		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	−0.489758	−	0.871858i	$-0.662915\pi$
$977$	12.4566	−	41.6080i	0.398523	−	1.33116i	0.888281	−	0.459300i	$-0.151900\pi$
$978$		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	0.417654	−	0.908606i	$-0.362853\pi$
$983$	12.0113	+	2.84673i	0.383101	+	0.0907966i	−0.0345528	+	0.999403i	$0.511001\pi$
$984$		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	−0.437084	−	0.899421i	$-0.643989\pi$
$991$	−6.10003	+	2.22023i	−0.193774	+	0.0705280i	0.243310	+	0.969948i	$0.421767\pi$
$992$		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	0.797437	−	0.603402i	$-0.206188\pi$
$997$	17.6580	+	11.6138i	0.559233	+	0.367814i	−0.238204	+	0.971215i	$0.576559\pi$
$998$		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.25.8	yes	162
3.2	odd	2		972.2.m.a.73.1		162
81.13	even	27	inner	324.2.m.a.13.8	✓	162
81.68	odd	54		972.2.m.a.253.1		162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.2.m.a.13.8	✓	162	81.13	even	27	inner
324.2.m.a.25.8	yes	162	1.1	even	1	trivial
972.2.m.a.73.1		162	3.2	odd	2
972.2.m.a.253.1		162	81.68	odd	54

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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