LMFDB - Embedded newform 804.2.s.b.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(5,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 5]))

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

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

chi := DirichletCharacter("804.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$20$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	804.5
Dual form			804.2.s.b.161.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56138 + 0.749732i) q^{3} +(-3.06595 + 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(1.87580 - 2.34123i) q^{9} +O(q^{10})$	\(q+(-1.56138 + 0.749732i) q^{3} +(-3.06595 + 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(1.87580 - 2.34123i) q^{9} +(-4.86665 + 1.42898i) q^{11} +(-2.95958 - 4.60520i) q^{13} +(4.11216 - 3.70426i) q^{15} +(4.50325 + 0.647469i) q^{17} +(1.29471 + 1.49418i) q^{19} +(-1.30819 - 0.356899i) q^{21} +(2.56007 - 1.16914i) q^{23} +(4.38332 - 2.81699i) q^{25} +(-1.17354 + 5.06190i) q^{27} +4.91969i q^{29} +(3.39701 - 5.28586i) q^{31} +(6.52733 - 5.87985i) q^{33} +(-2.27555 - 1.03921i) q^{35} +3.77494 q^{37} +(8.07369 + 4.97156i) q^{39} +(-0.190364 + 1.32401i) q^{41} +(8.46946 + 1.21772i) q^{43} +(-3.64344 + 8.86676i) q^{45} +(-1.21808 + 0.556280i) q^{47} +(-0.908978 - 6.32208i) q^{49} +(-7.51670 + 2.36528i) q^{51} +(-1.69585 - 11.7949i) q^{53} +(13.6344 - 8.76233i) q^{55} +(-3.14176 - 1.36229i) q^{57} +(4.76970 - 7.42180i) q^{59} +(3.83621 - 13.0649i) q^{61} +(2.31016 - 0.423536i) q^{63} +(13.2197 + 11.4549i) q^{65} +(1.21150 + 8.09520i) q^{67} +(-3.12069 + 3.74484i) q^{69} +(4.49276 - 0.645961i) q^{71} +(2.01307 + 0.591090i) q^{73} +(-4.73203 + 7.68470i) q^{75} +(-3.61204 - 1.64956i) q^{77} +(2.99859 + 4.66590i) q^{79} +(-1.96272 - 8.78338i) q^{81} +(1.16155 + 3.95589i) q^{83} +(-14.3896 + 2.06891i) q^{85} +(-3.68845 - 7.68150i) q^{87} +(-14.3613 - 6.55861i) q^{89} +(0.609916 - 4.24206i) q^{91} +(-1.34105 + 10.8001i) q^{93} +(-5.31463 - 3.41551i) q^{95} +3.09130i q^{97} +(-5.78331 + 14.0744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 10 q^{9}+O(q^{10}) $ 200 * q - 10 * q^9	$ 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) $ 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$-1$	$e\left(\frac{5}{22}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.56138	+	0.749732i	−0.901462	+	0.432858i
$3$	−1.56138	+	0.749732i	−0.901462	+	0.432858i
$4$		0			0
$5$	−3.06595	+	0.900243i	−1.37113	+	0.402601i	−0.882674	−	0.469986i	$-0.844259\pi$
$5$	−3.06595	+	0.900243i	−1.37113	+	0.402601i	−0.488459	+	0.872587i	$0.662441\pi$
$6$		0			0
$7$	0.591666	+	0.512682i	0.223629	+	0.193775i	0.759468	−	0.650545i	$-0.225459\pi$
$7$	0.591666	+	0.512682i	0.223629	+	0.193775i	−0.535839	+	0.844320i	$0.680005\pi$
$8$		0			0
$9$	1.87580	−	2.34123i	0.625268	−	0.780410i
$10$		0			0
$11$	−4.86665	+	1.42898i	−1.46735	+	0.430852i	−0.915236	−	0.402917i	$-0.867996\pi$
$11$	−4.86665	+	1.42898i	−1.46735	+	0.430852i	−0.552112	+	0.833770i	$0.686178\pi$
$12$		0			0
$13$	−2.95958	−	4.60520i	−0.820840	−	1.27725i	−0.958019	−	0.286705i	$-0.907440\pi$
$13$	−2.95958	−	4.60520i	−0.820840	−	1.27725i	0.137179	−	0.990546i	$-0.456196\pi$
$14$		0			0
$15$	4.11216	−	3.70426i	1.06176	−	0.956435i
$16$		0			0
$17$	4.50325	+	0.647469i	1.09220	+	0.157034i	0.664794	−	0.747027i	$-0.268519\pi$
$17$	4.50325	+	0.647469i	1.09220	+	0.157034i	0.427403	+	0.904061i	$0.359428\pi$
$18$		0			0
$19$	1.29471	+	1.49418i	0.297027	+	0.342787i	0.884572	−	0.466404i	$-0.154451\pi$
$19$	1.29471	+	1.49418i	0.297027	+	0.342787i	−0.587545	+	0.809192i	$0.699905\pi$
$20$		0			0
$21$	−1.30819	−	0.356899i	−0.285470	−	0.0778817i
$22$		0			0
$23$	2.56007	−	1.16914i	0.533812	−	0.243784i	−0.130224	−	0.991485i	$-0.541570\pi$
$23$	2.56007	−	1.16914i	0.533812	−	0.243784i	0.664036	+	0.747701i	$0.268842\pi$
$24$		0			0
$25$	4.38332	−	2.81699i	0.876664	−	0.563398i
$26$		0			0
$27$	−1.17354	+	5.06190i	−0.225849	+	0.974162i
$28$		0			0
$29$			4.91969i			0.913564i	0.889579	+	0.456782i	$0.150998\pi$
$29$			4.91969i			0.913564i	−0.889579	+	0.456782i	$0.849002\pi$
$30$		0			0
$31$	3.39701	−	5.28586i	0.610122	−	0.949368i	−0.389477	−	0.921036i	$-0.627344\pi$
$31$	3.39701	−	5.28586i	0.610122	−	0.949368i	0.999599	−	0.0283318i	$-0.00901950\pi$
$32$		0			0
$33$	6.52733	−	5.87985i	1.13626	−	1.02355i
$34$		0			0
$35$	−2.27555	−	1.03921i	−0.384639	−	0.175659i
$36$		0			0
$37$	3.77494			0.620596			0.310298	−	0.950639i	$-0.399571\pi$
$37$	3.77494			0.620596			0.310298	+	0.950639i	$0.399571\pi$
$38$		0			0
$39$	8.07369	+	4.97156i	1.29282	+	0.796087i
$40$		0			0
$41$	−0.190364	+	1.32401i	−0.0297299	+	0.206776i	−0.999272	−	0.0381483i	$-0.987854\pi$
$41$	−0.190364	+	1.32401i	−0.0297299	+	0.206776i	0.969542	+	0.244924i	$0.0787632\pi$
$42$		0			0
$43$	8.46946	+	1.21772i	1.29158	+	0.185701i	0.753643	−	0.657284i	$-0.228295\pi$
$43$	8.46946	+	1.21772i	1.29158	+	0.185701i	0.537937	+	0.842985i	$0.319204\pi$
$44$		0			0
$45$	−3.64344	+	8.86676i	−0.543132	+	1.32178i
$46$		0			0
$47$	−1.21808	+	0.556280i	−0.177676	+	0.0811417i	−0.502267	−	0.864713i	$-0.667501\pi$
$47$	−1.21808	+	0.556280i	−0.177676	+	0.0811417i	0.324591	+	0.945854i	$0.394773\pi$
$48$		0			0
$49$	−0.908978	−	6.32208i	−0.129854	−	0.903154i
$50$		0			0
$51$	−7.51670	+	2.36528i	−1.05255	+	0.331206i
$52$		0			0
$53$	−1.69585	−	11.7949i	−0.232943	−	1.62016i	−0.685259	−	0.728299i	$-0.740311\pi$
$53$	−1.69585	−	11.7949i	−0.232943	−	1.62016i	0.452316	−	0.891858i	$-0.350598\pi$
$54$		0			0
$55$	13.6344	−	8.76233i	1.83847	−	1.18151i
$56$		0			0
$57$	−3.14176	−	1.36229i	−0.416137	−	0.180439i
$58$		0			0
$59$	4.76970	−	7.42180i	0.620963	−	0.966237i	−0.378216	−	0.925717i	$-0.623462\pi$
$59$	4.76970	−	7.42180i	0.620963	−	0.966237i	0.999179	−	0.0405193i	$-0.0129012\pi$
$60$		0			0
$61$	3.83621	−	13.0649i	0.491176	−	1.67279i	−0.224590	−	0.974453i	$-0.572104\pi$
$61$	3.83621	−	13.0649i	0.491176	−	1.67279i	0.715766	−	0.698340i	$-0.246078\pi$
$62$		0			0
$63$	2.31016	−	0.423536i	0.291052	−	0.0533605i
$64$		0			0
$65$	13.2197	+	11.4549i	1.63970	+	1.42081i
$66$		0			0
$67$	1.21150	+	8.09520i	0.148008	+	0.988986i
$67$	1.21150	+	8.09520i	0.148008	+	0.988986i
$68$		0			0
$69$	−3.12069	+	3.74484i	−0.375687	+	0.450826i
$70$		0			0
$71$	4.49276	−	0.645961i	0.533192	−	0.0766614i	0.129540	−	0.991574i	$-0.458650\pi$
$71$	4.49276	−	0.645961i	0.533192	−	0.0766614i	0.403652	+	0.914913i	$0.367741\pi$
$72$		0			0
$73$	2.01307	+	0.591090i	0.235612	+	0.0691818i	0.397407	−	0.917643i	$-0.369910\pi$
$73$	2.01307	+	0.591090i	0.235612	+	0.0691818i	−0.161795	+	0.986824i	$0.551728\pi$
$74$		0			0
$75$	−4.73203	+	7.68470i	−0.546408	+	0.887353i
$76$		0			0
$77$	−3.61204	−	1.64956i	−0.411630	−	0.187985i
$78$		0			0
$79$	2.99859	+	4.66590i	0.337368	+	0.524955i	0.967942	−	0.251175i	$-0.0808168\pi$
$79$	2.99859	+	4.66590i	0.337368	+	0.524955i	−0.630574	+	0.776129i	$0.717180\pi$
$80$		0			0
$81$	−1.96272	−	8.78338i	−0.218080	−	0.975931i
$82$		0			0
$83$	1.16155	+	3.95589i	0.127497	+	0.434215i	0.998356	−	0.0573178i	$-0.0182548\pi$
$83$	1.16155	+	3.95589i	0.127497	+	0.434215i	−0.870859	+	0.491533i	$0.836437\pi$
$84$		0			0
$85$	−14.3896	+	2.06891i	−1.56077	+	0.224405i
$86$		0			0
$87$	−3.68845	−	7.68150i	−0.395443	−	0.823543i
$88$		0			0
$89$	−14.3613	−	6.55861i	−1.52230	−	0.695211i	−0.533685	−	0.845683i	$-0.679193\pi$
$89$	−14.3613	−	6.55861i	−1.52230	−	0.695211i	−0.988614	+	0.150472i	$0.951921\pi$
$90$		0			0
$91$	0.609916	−	4.24206i	0.0639366	−	0.444689i
$92$		0			0
$93$	−1.34105	+	10.8001i	−0.139060	+	1.11992i
$94$		0			0
$95$	−5.31463	−	3.41551i	−0.545270	−	0.350424i
$96$		0			0
$97$			3.09130i			0.313874i	0.987609	+	0.156937i	$0.0501619\pi$
$97$			3.09130i			0.313874i	−0.987609	+	0.156937i	$0.949838\pi$
$98$		0			0
$99$	−5.78331	+	14.0744i	−0.581245	+	1.41453i
$100$		0			0
$101$	2.16124	+	2.49420i	0.215051	+	0.248182i	0.853018	−	0.521882i	$-0.174770\pi$
$101$	2.16124	+	2.49420i	0.215051	+	0.248182i	−0.637967	+	0.770064i	$0.720224\pi$
$102$		0			0
$103$	−4.11999	−	2.64776i	−0.405955	−	0.260891i	0.321691	−	0.946845i	$-0.395749\pi$
$103$	−4.11999	−	2.64776i	−0.405955	−	0.260891i	−0.727645	+	0.685954i	$0.759385\pi$
$104$		0			0
$105$	4.33213	−	0.0834544i	0.422773	−	0.00814432i
$106$		0			0
$107$	−3.05837	+	10.4159i	−0.295664	+	1.00694i	0.668958	+	0.743300i	$0.266741\pi$
$107$	−3.05837	+	10.4159i	−0.295664	+	1.00694i	−0.964622	+	0.263638i	$0.915077\pi$
$108$		0			0
$109$	3.72176	+	5.79117i	0.356480	+	0.554693i	0.972460	−	0.233068i	$-0.0748765\pi$
$109$	3.72176	+	5.79117i	0.356480	+	0.554693i	−0.615981	+	0.787761i	$0.711240\pi$
$110$		0			0
$111$	−5.89411	+	2.83019i	−0.559444	+	0.268630i
$112$		0			0
$113$	−13.7712	−	4.04358i	−1.29548	−	0.380388i	−0.439896	−	0.898049i	$-0.644985\pi$
$113$	−13.7712	−	4.04358i	−1.29548	−	0.380388i	−0.855586	+	0.517661i	$0.826803\pi$
$114$		0			0
$115$	−6.79652	+	5.88922i	−0.633779	+	0.549173i
$116$		0			0
$117$	−16.3334	−	1.70939i	−1.51003	−	0.158033i
$118$		0			0
$119$	2.33247	+	2.69182i	0.213817	+	0.246758i
$120$		0			0
$121$	12.3885	−	7.96159i	1.12622	−	0.723781i
$122$		0			0
$123$	−0.695424	−	2.21001i	−0.0627043	−	0.199270i
$124$		0			0
$125$	−0.440399	+	0.508248i	−0.0393905	+	0.0454590i
$126$		0			0
$127$	−9.03409	+	10.4259i	−0.801646	+	0.925149i	−0.998470	−	0.0552898i	$-0.982392\pi$
$127$	−9.03409	+	10.4259i	−0.801646	+	0.925149i	0.196824	+	0.980439i	$0.436937\pi$
$128$		0			0
$129$	−14.1370	+	4.44849i	−1.24469	+	0.391668i
$130$		0			0
$131$	14.8926	−	6.80123i	1.30117	−	0.594226i	0.360253	−	0.932854i	$-0.382690\pi$
$131$	14.8926	−	6.80123i	1.30117	−	0.594226i	0.940920	+	0.338628i	$0.109963\pi$
$132$		0			0
$133$			1.54783i			0.134214i
$134$		0			0
$135$	−0.958911	−	16.5760i	−0.0825299	−	1.42663i
$136$		0			0
$137$	−6.25736	−	13.7017i	−0.534603	−	1.17062i	−0.963609	−	0.267315i	$-0.913863\pi$
$137$	−6.25736	−	13.7017i	−0.534603	−	1.17062i	0.429006	−	0.903301i	$-0.358864\pi$
$138$		0			0
$139$	−1.64168	−	5.59103i	−0.139245	−	0.474225i	0.860111	−	0.510107i	$-0.170394\pi$
$139$	−1.64168	−	5.59103i	−0.139245	−	0.474225i	−0.999356	+	0.0358817i	$0.988576\pi$
$140$		0			0
$141$	1.48483	−	1.78180i	0.125045	−	0.150055i
$142$		0			0
$143$	20.9839	+	18.1827i	1.75477	+	1.52051i
$144$		0			0
$145$	−4.42892	−	15.0835i	−0.367801	−	1.25262i
$146$		0			0
$147$	6.15912	+	9.18967i	0.507996	+	0.757951i
$148$		0			0
$149$	15.6118	−	13.5277i	1.27897	−	1.10823i	0.290492	−	0.956877i	$-0.406181\pi$
$149$	15.6118	−	13.5277i	1.27897	−	1.10823i	0.988479	−	0.151358i	$-0.0483645\pi$
$150$		0			0
$151$	−0.471751	+	3.28110i	−0.0383906	+	0.267012i	−0.999972	−	0.00750825i	$-0.997610\pi$
$151$	−0.471751	+	3.28110i	−0.0383906	+	0.267012i	0.961581	+	0.274521i	$0.0885191\pi$
$152$		0			0
$153$	9.96308	−	9.32861i	0.805467	−	0.754173i
$154$		0			0
$155$	−5.65651	+	19.2643i	−0.454342	+	1.54735i
$156$		0			0
$157$	−8.02015	−	17.5617i	−0.640077	−	1.40157i	−0.899977	−	0.435938i	$-0.856417\pi$
$157$	−8.02015	−	17.5617i	−0.640077	−	1.40157i	0.259899	−	0.965636i	$-0.416311\pi$
$158$		0			0
$159$	11.4909	+	17.1449i	0.911287	+	1.35968i
$160$		0			0
$161$	2.11411	+	0.620757i	0.166615	+	0.0489225i
$162$		0			0
$163$	−18.4910			−1.44833			−0.724165	−	0.689627i	$-0.757775\pi$
$163$	−18.4910			−1.44833			−0.724165	+	0.689627i	$0.757775\pi$
$164$		0			0
$165$	−14.7191	+	23.9035i	−1.14588	+	1.86088i
$166$		0			0
$167$	4.74561	−	4.11209i	0.367226	−	0.318203i	−0.451627	−	0.892207i	$-0.649156\pi$
$167$	4.74561	−	4.11209i	0.367226	−	0.318203i	0.818853	+	0.574004i	$0.194611\pi$
$168$		0			0
$169$	−7.04833	+	15.4337i	−0.542179	+	1.18721i
$170$		0			0
$171$	5.92683	−	0.228435i	0.453236	−	0.0174688i
$172$		0			0
$173$	11.1237	−	17.3088i	0.845718	−	1.31596i	−0.101325	−	0.994853i	$-0.532308\pi$
$173$	11.1237	−	17.3088i	0.845718	−	1.31596i	0.947042	−	0.321109i	$-0.104056\pi$
$174$		0			0
$175$	4.03768	+	0.580531i	0.305220	+	0.0438840i
$176$		0			0
$177$	−1.88295	+	15.1642i	−0.141531	+	1.13981i
$178$		0			0
$179$	9.19948	−	20.1440i	0.687601	−	1.50564i	−0.166782	−	0.985994i	$-0.553338\pi$
$179$	9.19948	−	20.1440i	0.687601	−	1.50564i	0.854384	−	0.519643i	$-0.173935\pi$
$180$		0			0
$181$	0.297134	+	0.650633i	0.0220858	+	0.0483612i	0.920353	−	0.391088i	$-0.127901\pi$
$181$	0.297134	+	0.650633i	0.0220858	+	0.0483612i	−0.898268	+	0.439449i	$0.855174\pi$
$182$		0			0
$183$	3.80542	+	23.2754i	0.281305	+	1.72057i
$184$		0			0
$185$	−11.5738	+	3.39836i	−0.850919	+	0.249853i
$186$		0			0
$187$	−22.8409	+	3.28403i	−1.67029	+	0.240152i
$188$		0			0
$189$	−3.28949	+	2.39330i	−0.239275	+	0.174087i
$190$		0			0
$191$	−7.89553	+	17.2888i	−0.571300	+	1.25097i	0.374802	+	0.927105i	$0.377711\pi$
$191$	−7.89553	+	17.2888i	−0.571300	+	1.25097i	−0.946102	+	0.323868i	$0.895016\pi$
$192$		0			0
$193$	0.0158178	+	0.0101655i	0.00113859	+	0.000731725i	0.541210	−	0.840887i	$-0.317966\pi$
$193$	0.0158178	+	0.0101655i	0.00113859	+	0.000731725i	−0.540071	+	0.841619i	$0.681603\pi$
$194$		0			0
$195$	−29.2291	−	7.97426i	−2.09314	−	0.571049i
$196$		0			0
$197$	1.71963	+	11.9603i	0.122518	+	0.852135i	0.954687	+	0.297612i	$0.0961901\pi$
$197$	1.71963	+	11.9603i	0.122518	+	0.852135i	−0.832168	+	0.554523i	$0.812901\pi$
$198$		0			0
$199$	5.58649	−	6.44716i	0.396016	−	0.457027i	−0.522366	−	0.852721i	$-0.674951\pi$
$199$	5.58649	−	6.44716i	0.396016	−	0.457027i	0.918382	+	0.395694i	$0.129496\pi$
$200$		0			0
$201$	−7.96083	−	11.7314i	−0.561514	−	0.827467i
$202$		0			0
$203$	−2.52223	+	2.91081i	−0.177026	+	0.204299i
$204$		0			0
$205$	−0.608287	−	4.23073i	−0.0424846	−	0.295487i
$206$		0			0
$207$	2.06495	−	8.18680i	0.143524	−	0.569022i
$208$		0			0
$209$	−8.43604	−	5.42151i	−0.583533	−	0.375014i
$210$		0			0
$211$	0.888906	−	1.94643i	0.0611948	−	0.133998i	−0.876564	−	0.481286i	$-0.840170\pi$
$211$	0.888906	−	1.94643i	0.0611948	−	0.133998i	0.937759	+	0.347288i	$0.112897\pi$
$212$		0			0
$213$	−6.53059	+	4.37695i	−0.447469	+	0.299904i
$214$		0			0
$215$	−27.0631	+	3.89109i	−1.84569	+	0.265370i
$216$		0			0
$217$	4.71986	−	1.38588i	0.320405	−	0.0940794i
$218$		0			0
$219$	−3.58632	+	0.586346i	−0.242341	+	0.0396216i
$220$		0			0
$221$	−10.3460	−	22.6546i	−0.695947	−	1.52391i
$222$		0			0
$223$	−0.873755	+	1.91326i	−0.0585110	+	0.128121i	−0.936629	−	0.350323i	$-0.886072\pi$
$223$	−0.873755	+	1.91326i	−0.0585110	+	0.128121i	0.878118	+	0.478444i	$0.158799\pi$
$224$		0			0
$225$	1.62703	−	15.5465i	0.108469	−	1.03643i
$226$		0			0
$227$	−12.1107	−	1.74126i	−0.803815	−	0.115571i	−0.271853	−	0.962339i	$-0.587636\pi$
$227$	−12.1107	−	1.74126i	−0.803815	−	0.115571i	−0.531963	+	0.846768i	$0.678545\pi$
$228$		0			0
$229$	−2.95346	+	4.59567i	−0.195170	+	0.303691i	−0.925021	−	0.379916i	$-0.875953\pi$
$229$	−2.95346	+	4.59567i	−0.195170	+	0.303691i	0.729851	+	0.683606i	$0.239589\pi$
$230$		0			0
$231$	6.87649	−	0.132469i	0.452440	−	0.00871583i
$232$		0			0
$233$	−11.4074	+	24.9786i	−0.747320	+	1.63640i	0.0238023	+	0.999717i	$0.492423\pi$
$233$	−11.4074	+	24.9786i	−0.747320	+	1.63640i	−0.771123	+	0.636687i	$0.780304\pi$
$234$		0			0
$235$	3.23379	−	2.80209i	0.210949	−	0.182788i
$236$		0			0
$237$	−8.18011	−	5.03709i	−0.531355	−	0.327194i
$238$		0			0
$239$	19.7308			1.27628			0.638139	−	0.769921i	$-0.279705\pi$
$239$	19.7308			1.27628			0.638139	+	0.769921i	$0.279705\pi$
$240$		0			0
$241$	24.5144	+	7.19807i	1.57911	+	0.463668i	0.949636	−	0.313354i	$-0.101453\pi$
$241$	24.5144	+	7.19807i	1.57911	+	0.463668i	0.629473	+	0.777023i	$0.283271\pi$
$242$		0			0
$243$	9.64972	+	12.2427i	0.619030	+	0.785367i
$244$		0			0
$245$	8.47828	+	18.5648i	0.541658	+	1.18606i
$246$		0			0
$247$	3.04917	−	10.3845i	0.194014	−	0.660752i
$248$		0			0
$249$	−4.77948	−	5.30579i	−0.302887	−	0.336241i
$250$		0			0
$251$	1.52185	−	10.5847i	0.0960585	−	0.668102i	−0.883720	−	0.468016i	$-0.844969\pi$
$251$	1.52185	−	10.5847i	0.0960585	−	0.668102i	0.979778	−	0.200086i	$-0.0641220\pi$
$252$		0			0
$253$	−10.7883	+	9.34809i	−0.678253	+	0.587710i
$254$		0			0
$255$	20.9165	−	14.0187i	1.30984	−	0.877884i
$256$		0			0
$257$	1.85895	+	6.33100i	0.115958	+	0.394917i	0.996934	−	0.0782437i	$-0.0249312\pi$
$257$	1.85895	+	6.33100i	0.115958	+	0.394917i	−0.880976	+	0.473161i	$0.843113\pi$
$258$		0			0
$259$	2.23350	+	1.93534i	0.138783	+	0.120256i
$260$		0			0
$261$	11.5181	+	9.22838i	0.712954	+	0.571222i
$262$		0			0
$263$	−5.30404	−	18.0639i	−0.327061	−	1.11387i	−0.944845	−	0.327519i	$-0.893787\pi$
$263$	−5.30404	−	18.0639i	−0.327061	−	1.11387i	0.617784	−	0.786348i	$-0.288031\pi$
$264$		0			0
$265$	15.8177	+	34.6359i	0.971673	+	2.12767i
$266$		0			0
$267$	27.3407	−	0.526693i	1.67322	−	0.0322331i
$268$		0			0
$269$		−	6.99643i		−	0.426580i	−0.976989	−	0.213290i	$-0.931582\pi$
$269$		−	6.99643i		−	0.426580i	0.976989	−	0.213290i	$-0.0684179\pi$
$270$		0			0
$271$	19.7238	−	9.00755i	1.19813	−	0.547170i	0.286464	−	0.958091i	$-0.407520\pi$
$271$	19.7238	−	9.00755i	1.19813	−	0.547170i	0.911671	+	0.410921i	$0.134793\pi$
$272$		0			0
$273$	2.22810	+	7.08074i	0.134851	+	0.428546i
$274$		0			0
$275$	−17.3067	+	19.9729i	−1.04363	+	1.20441i
$276$		0			0
$277$	2.37514	−	2.74106i	0.142708	−	0.164694i	−0.679896	−	0.733309i	$-0.737975\pi$
$277$	2.37514	−	2.74106i	0.142708	−	0.164694i	0.822604	+	0.568615i	$0.192520\pi$
$278$		0			0
$279$	−6.00328	−	17.8684i	−0.359407	−	1.06975i
$280$		0			0
$281$	3.31710	−	2.13177i	0.197882	−	0.127171i	−0.437948	−	0.899000i	$-0.644295\pi$
$281$	3.31710	−	2.13177i	0.197882	−	0.127171i	0.635829	+	0.771830i	$0.280658\pi$
$282$		0			0
$283$	−7.98123	−	9.21083i	−0.474435	−	0.547527i	0.467205	−	0.884149i	$-0.345261\pi$
$283$	−7.98123	−	9.21083i	−0.474435	−	0.547527i	−0.941640	+	0.336622i	$0.890716\pi$
$284$		0			0
$285$	10.8589	+	1.34835i	0.643224	+	0.0798693i
$286$		0			0
$287$	−0.791429	+	0.685777i	−0.0467166	+	0.0404802i
$288$		0			0
$289$	3.54863	+	1.04197i	0.208743	+	0.0612924i
$290$		0			0
$291$	−2.31765	−	4.82669i	−0.135863	−	0.282945i
$292$		0			0
$293$	−0.657398	−	1.02293i	−0.0384056	−	0.0597603i	0.821520	−	0.570180i	$-0.193126\pi$
$293$	−0.657398	−	1.02293i	−0.0384056	−	0.0597603i	−0.859926	+	0.510420i	$0.829490\pi$
$294$		0			0
$295$	−7.94223	+	27.0487i	−0.462414	+	1.57484i
$296$		0			0
$297$	−1.52210	−	26.3114i	−0.0883213	−	1.52674i
$298$		0			0
$299$	−12.9609	−	8.32945i	−0.749547	−	0.481704i
$300$		0			0
$301$	4.38678	+	5.06262i	0.252850	+	0.291805i
$302$		0			0
$303$	−5.24449	−	2.27404i	−0.301288	−	0.130640i
$304$		0			0
$305$			43.5099i			2.49137i
$306$		0			0
$307$	12.7095	+	8.16791i	0.725370	+	0.466167i	0.850501	−	0.525973i	$-0.176299\pi$
$307$	12.7095	+	8.16791i	0.725370	+	0.466167i	−0.125131	+	0.992140i	$0.539935\pi$
$308$		0			0
$309$	8.41797	+	1.04526i	0.478882	+	0.0594629i
$310$		0			0
$311$	1.95696	−	13.6110i	0.110969	−	0.771807i	−0.856011	−	0.516957i	$-0.827065\pi$
$311$	1.95696	−	13.6110i	0.110969	−	0.771807i	0.966981	−	0.254850i	$-0.0820261\pi$
$312$		0			0
$313$	−8.14747	−	3.72083i	−0.460522	−	0.210314i	0.171624	−	0.985163i	$-0.445099\pi$
$313$	−8.14747	−	3.72083i	−0.460522	−	0.210314i	−0.632146	+	0.774849i	$0.717826\pi$
$314$		0			0
$315$	−6.70153	+	3.37824i	−0.377588	+	0.190342i
$316$		0			0
$317$	19.4743	−	2.79998i	1.09379	−	0.157263i	0.428273	−	0.903649i	$-0.359122\pi$
$317$	19.4743	−	2.79998i	1.09379	−	0.157263i	0.665513	+	0.746387i	$0.268213\pi$
$318$		0			0
$319$	−7.03012	−	23.9424i	−0.393611	−	1.34052i
$320$		0			0
$321$	−3.03382	−	18.5560i	−0.169332	−	1.03570i
$322$		0			0
$323$	4.86297	+	7.56692i	0.270583	+	0.421035i
$324$		0			0
$325$	−25.9456	−	11.8489i	−1.43920	−	0.657261i
$326$		0			0
$327$	−10.1529	−	6.25188i	−0.561456	−	0.345730i
$328$		0			0
$329$	−1.00589	−	0.295357i	−0.0554567	−	0.0162835i
$330$		0			0
$331$	25.6433	−	3.68695i	1.40948	−	0.202653i	0.604809	−	0.796371i	$-0.293249\pi$
$331$	25.6433	−	3.68695i	1.40948	−	0.202653i	0.804673	+	0.593718i	$0.202340\pi$
$332$		0			0
$333$	7.08104	−	8.83800i	0.388039	−	0.484319i
$334$		0			0
$335$	−11.0020	−	23.7288i	−0.601105	−	1.29644i
$336$		0			0
$337$	11.4752	+	9.94335i	0.625096	+	0.541649i	0.908784	−	0.417268i	$-0.137012\pi$
$337$	11.4752	+	9.94335i	0.625096	+	0.541649i	−0.283687	+	0.958917i	$0.591558\pi$
$338$		0			0
$339$	24.5336	−	4.01112i	1.33248	−	0.217854i
$340$		0			0
$341$	−8.97870	+	30.5786i	−0.486224	+	1.65593i
$342$		0			0
$343$	5.66622	−	8.81682i	0.305947	−	0.476063i
$344$		0			0
$345$	6.19661	−	14.2909i	0.333614	−	0.769395i
$346$		0			0
$347$	27.2097	−	17.4866i	1.46069	−	0.938731i	0.462041	−	0.886859i	$-0.347117\pi$
$347$	27.2097	−	17.4866i	1.46069	−	0.938731i	0.998654	−	0.0518726i	$-0.0165190\pi$
$348$		0			0
$349$	2.47093	+	17.1857i	0.132266	+	0.919931i	0.942591	+	0.333950i	$0.108382\pi$
$349$	2.47093	+	17.1857i	0.132266	+	0.919931i	−0.810325	+	0.585981i	$0.800709\pi$
$350$		0			0
$351$	26.7842	−	9.57668i	1.42964	−	0.511166i
$352$		0			0
$353$	3.94534	+	27.4404i	0.209989	+	1.46051i	0.773183	+	0.634183i	$0.218663\pi$
$353$	3.94534	+	27.4404i	0.209989	+	1.46051i	−0.563194	+	0.826325i	$0.690428\pi$
$354$		0			0
$355$	−13.1930	+	6.02505i	−0.700213	+	0.319777i
$356$		0			0
$357$	−5.66001	−	2.45421i	−0.299560	−	0.129891i
$358$		0			0
$359$	1.35152	+	0.194319i	0.0713305	+	0.0102558i	0.177888	−	0.984051i	$-0.443074\pi$
$359$	1.35152	+	0.194319i	0.0713305	+	0.0102558i	−0.106557	+	0.994307i	$0.533983\pi$
$360$		0			0
$361$	2.14770	−	14.9376i	0.113037	−	0.786187i
$362$		0			0
$363$	−13.3740	+	21.7191i	−0.701955	+	1.13996i
$364$		0			0
$365$	−6.70408			−0.350908
$366$		0			0
$367$	−28.9579	−	13.2246i	−1.51159	−	0.690320i	−0.524636	−	0.851327i	$-0.675798\pi$
$367$	−28.9579	−	13.2246i	−1.51159	−	0.690320i	−0.986953	+	0.161007i	$0.948526\pi$
$368$		0			0
$369$	2.74273	+	2.92928i	0.142781	+	0.152492i
$370$		0			0
$371$	5.04366	−	7.84809i	0.261854	−	0.407452i
$372$		0			0
$373$		−	8.07461i		−	0.418088i	−0.977906	−	0.209044i	$-0.932965\pi$
$373$		−	8.07461i		−	0.418088i	0.977906	−	0.209044i	$-0.0670351\pi$
$374$		0			0
$375$	0.306580	−	1.12375i	0.0158317	−	0.0580301i
$376$		0			0
$377$	22.6561	−	14.5602i	1.16685	−	0.749889i
$378$		0			0
$379$	−23.4477	+	10.7082i	−1.20443	+	0.550044i	−0.913554	−	0.406717i	$-0.866674\pi$
$379$	−23.4477	+	10.7082i	−1.20443	+	0.550044i	−0.290875	+	0.956761i	$0.593946\pi$
$380$		0			0
$381$	6.28901	−	23.0519i	0.322196	−	1.18099i
$382$		0			0
$383$	−11.4000	−	13.1564i	−0.582515	−	0.672259i	0.385628	−	0.922654i	$-0.373985\pi$
$383$	−11.4000	−	13.1564i	−0.582515	−	0.672259i	−0.968144	+	0.250396i	$0.919439\pi$
$384$		0			0
$385$	12.5593	+	1.80576i	0.640082	+	0.0920299i
$386$		0			0
$387$	18.7380	−	17.5447i	0.952507	−	0.891849i
$388$		0			0
$389$	−11.8584	−	18.4520i	−0.601245	−	0.935555i	−0.999830	−	0.0184238i	$-0.994135\pi$
$389$	−11.8584	−	18.4520i	−0.601245	−	0.935555i	0.398586	−	0.917131i	$-0.369501\pi$
$390$		0			0
$391$	12.2856	−	3.60738i	0.621310	−	0.182433i
$392$		0			0
$393$	−18.1539	+	21.7848i	−0.915743	+	1.09890i
$394$		0			0
$395$	−13.3940	−	11.6059i	−0.673923	−	0.583958i
$396$		0			0
$397$	21.6056	−	6.34398i	1.08436	−	0.318395i	0.309736	−	0.950823i	$-0.399759\pi$
$397$	21.6056	−	6.34398i	1.08436	−	0.318395i	0.774620	+	0.632427i	$0.217941\pi$
$398$		0			0
$399$	−1.16046	−	2.41674i	−0.0580954	−	0.120989i
$400$		0			0
$401$	23.7844			1.18774			0.593868	−	0.804563i	$-0.297600\pi$
$401$	23.7844			1.18774			0.593868	+	0.804563i	$0.297600\pi$
$402$		0			0
$403$	−34.3962			−1.71339
$404$		0			0
$405$	13.9248	+	25.1624i	0.691927	+	1.25033i
$406$		0			0
$407$	−18.3713	+	5.39430i	−0.910631	+	0.267385i
$408$		0			0
$409$	−17.0685	−	14.7899i	−0.843983	−	0.731316i	0.121273	−	0.992619i	$-0.461302\pi$
$409$	−17.0685	−	14.7899i	−0.843983	−	0.731316i	−0.965257	+	0.261303i	$0.915848\pi$
$410$		0			0
$411$	20.0427	+	16.7022i	0.988635	+	0.823860i
$412$		0			0
$413$	6.62709	−	1.94589i	0.326098	−	0.0957510i
$414$		0			0
$415$	−7.12252	−	11.0829i	−0.349631	−	0.544036i
$416$		0			0
$417$	6.75505	+	7.49890i	0.330796	+	0.367223i
$418$		0			0
$419$	−3.62622	−	0.521372i	−0.177153	−	0.0254707i	0.0531675	−	0.998586i	$-0.483068\pi$
$419$	−3.62622	−	0.521372i	−0.177153	−	0.0254707i	−0.230320	+	0.973115i	$0.573977\pi$
$420$		0			0
$421$	5.73664	+	6.62044i	0.279587	+	0.322660i	0.878123	−	0.478436i	$-0.158796\pi$
$421$	5.73664	+	6.62044i	0.279587	+	0.322660i	−0.598536	+	0.801096i	$0.704251\pi$
$422$		0			0
$423$	−0.982506	+	3.89528i	−0.0477711	+	0.189395i
$424$		0			0
$425$	21.5631	−	9.84753i	1.04596	−	0.477675i
$426$		0			0
$427$	8.96791	−	5.76332i	0.433987	−	0.278907i
$428$		0			0
$429$	−46.3960	−	12.6577i	−2.24002	−	0.611121i
$430$		0			0
$431$			18.3086i			0.881892i	0.897534	+	0.440946i	$0.145357\pi$
$431$			18.3086i			0.881892i	−0.897534	+	0.440946i	$0.854643\pi$
$432$		0			0
$433$	−21.6063	+	33.6201i	−1.03833	+	1.61568i	−0.284424	+	0.958698i	$0.591802\pi$
$433$	−21.6063	+	33.6201i	−1.03833	+	1.61568i	−0.753909	+	0.656979i	$0.771834\pi$
$434$		0			0
$435$	18.2238	+	20.2306i	0.873764	+	0.969981i
$436$		0			0
$437$	5.06146	+	2.31149i	0.242122	+	0.110574i
$438$		0			0
$439$	31.7813			1.51684			0.758418	−	0.651768i	$-0.225972\pi$
$439$	31.7813			1.51684			0.758418	+	0.651768i	$0.225972\pi$
$440$		0			0
$441$	−16.5065	−	9.73085i	−0.786024	−	0.463374i
$442$		0			0
$443$	0.346201	−	2.40788i	0.0164485	−	0.114402i	−0.979943	−	0.199278i	$-0.936140\pi$
$443$	0.346201	−	2.40788i	0.0164485	−	0.114402i	0.996392	+	0.0848761i	$0.0270494\pi$
$444$		0			0
$445$	49.9354	+	7.17963i	2.36717	+	0.340347i
$446$		0			0
$447$	−14.2338	+	32.8266i	−0.673236	+	1.55264i
$448$		0			0
$449$	37.8266	−	17.2748i	1.78515	−	0.815250i	0.812504	−	0.582956i	$-0.198104\pi$
$449$	37.8266	−	17.2748i	1.78515	−	0.815250i	0.972646	−	0.232294i	$-0.0746232\pi$
$450$		0			0
$451$	−0.965547	−	6.71553i	−0.0454658	−	0.316222i
$452$		0			0
$453$	−1.72336	−	5.47673i	−0.0809707	−	0.257319i
$454$		0			0
$455$	1.94892	+	13.5550i	0.0913665	+	0.635468i
$456$		0			0
$457$	6.94117	−	4.46082i	0.324694	−	0.208668i	−0.368131	−	0.929774i	$-0.620002\pi$
$457$	6.94117	−	4.46082i	0.324694	−	0.208668i	0.692825	+	0.721106i	$0.256366\pi$
$458$		0			0
$459$	−8.56218	+	22.0351i	−0.399648	+	1.02851i
$460$		0			0
$461$	17.1945	−	26.7552i	0.800828	−	1.24611i	−0.164837	−	0.986321i	$-0.552710\pi$
$461$	17.1945	−	26.7552i	0.800828	−	1.24611i	0.965665	−	0.259791i	$-0.0836538\pi$
$462$		0			0
$463$	−1.35839	+	4.62626i	−0.0631298	+	0.215000i	−0.985017	−	0.172458i	$-0.944829\pi$
$463$	−1.35839	+	4.62626i	−0.0631298	+	0.215000i	0.921887	+	0.387459i	$0.126647\pi$
$464$		0			0
$465$	−5.61111	−	34.3197i	−0.260209	−	1.59154i
$466$		0			0
$467$	−1.76214	−	1.52691i	−0.0815423	−	0.0706568i	0.613136	−	0.789977i	$-0.289908\pi$
$467$	−1.76214	−	1.52691i	−0.0815423	−	0.0706568i	−0.694678	+	0.719321i	$0.744453\pi$
$468$		0			0
$469$	−3.43346	+	5.41077i	−0.158542	+	0.249846i
$470$		0			0
$471$	25.6890	+	21.4075i	1.18369	+	0.986403i
$472$		0			0
$473$	−42.9579	+	6.17642i	−1.97521	+	0.283992i
$474$		0			0
$475$	9.88421	+	2.90226i	0.453518	+	0.133165i
$476$		0			0
$477$	−30.7957	−	18.1546i	−1.41004	−	0.831241i
$478$		0			0
$479$	5.85237	+	2.67269i	0.267402	+	0.122118i	0.544604	−	0.838693i	$-0.316680\pi$
$479$	5.85237	+	2.67269i	0.267402	+	0.122118i	−0.277202	+	0.960812i	$0.589407\pi$
$480$		0			0
$481$	−11.1722	−	17.3843i	−0.509410	−	0.792657i
$482$		0			0
$483$	−3.76632	+	0.615775i	−0.171374	+	0.0280187i
$484$		0			0
$485$	−2.78292	−	9.47776i	−0.126366	−	0.430363i
$486$		0			0
$487$	−14.0502	+	2.02011i	−0.636675	+	0.0915400i	−0.453091	−	0.891464i	$-0.649679\pi$
$487$	−14.0502	+	2.02011i	−0.636675	+	0.0915400i	−0.183583	+	0.983004i	$0.558770\pi$
$488$		0			0
$489$	28.8715	−	13.8633i	1.30561	−	0.626921i
$490$		0			0
$491$	−16.6419	−	7.60010i	−0.751038	−	0.342988i	0.00284517	−	0.999996i	$-0.499094\pi$
$491$	−16.6419	−	7.60010i	−0.751038	−	0.342988i	−0.753883	+	0.657008i	$0.771822\pi$
$492$		0			0
$493$	−3.18535	+	22.1546i	−0.143461	+	0.997792i
$494$		0			0
$495$	5.06093	−	48.3578i	0.227472	−	2.17352i
$496$		0			0
$497$	2.98938	+	1.92116i	0.134092	+	0.0861758i
$498$		0			0
$499$			39.6955i			1.77702i	0.458862	+	0.888508i	$0.348257\pi$
$499$			39.6955i			1.77702i	−0.458862	+	0.888508i	$0.651743\pi$
$500$		0			0
$501$	−4.32672	+	9.97846i	−0.193304	+	0.445805i
$502$		0			0
$503$	0.907942	+	1.04782i	0.0404831	+	0.0467200i	0.775630	−	0.631188i	$-0.217432\pi$
$503$	0.907942	+	1.04782i	0.0404831	+	0.0467200i	−0.735147	+	0.677908i	$0.762887\pi$
$504$		0			0
$505$	−8.87162	−	5.70144i	−0.394782	−	0.253711i
$506$		0			0
$507$	−0.566020	−	29.3822i	−0.0251378	−	1.30491i
$508$		0			0
$509$	−6.46433	+	22.0155i	−0.286526	+	0.975819i	0.682915	+	0.730498i	$0.260712\pi$
$509$	−6.46433	+	22.0155i	−0.286526	+	0.975819i	−0.969442	+	0.245322i	$0.921106\pi$
$510$		0			0
$511$	0.888023	+	1.38179i	0.0392838	+	0.0611268i
$512$		0			0
$513$	−9.08276	+	4.80021i	−0.401014	+	0.211934i
$514$		0			0
$515$	15.0153	+	4.40889i	0.661653	+	0.194279i
$516$		0			0
$517$	5.13307	−	4.44783i	0.225752	−	0.195615i
$518$		0			0
$519$	−4.39132	+	35.3653i	−0.192758	+	1.55237i
$520$		0			0
$521$	−24.3956	−	28.1540i	−1.06879	−	1.23345i	−0.971210	−	0.238224i	$-0.923435\pi$
$521$	−24.3956	−	28.1540i	−1.06879	−	1.23345i	−0.0975814	−	0.995228i	$-0.531111\pi$
$522$		0			0
$523$	−13.5444	+	8.70448i	−0.592257	+	0.380621i	−0.802167	−	0.597100i	$-0.796319\pi$
$523$	−13.5444	+	8.70448i	−0.592257	+	0.380621i	0.209909	+	0.977721i	$0.432683\pi$
$524$		0			0
$525$	−6.73959	+	2.12075i	−0.294140	+	0.0925571i
$526$		0			0
$527$	18.7200	−	21.6041i	0.815457	−	0.941087i
$528$		0			0
$529$	−9.87474	+	11.3961i	−0.429336	+	0.495481i
$530$		0			0
$531$	−8.42912	−	25.0888i	−0.365793	−	1.08876i
$532$		0			0
$533$	6.66074	−	3.04186i	0.288509	−	0.131757i
$534$		0			0
$535$		−	34.6877i		−	1.49968i
$536$		0			0
$537$	0.738769	+	38.3496i	0.0318803	+	1.65491i
$538$		0			0
$539$	13.4578	+	29.4684i	0.579667	+	1.26929i
$540$		0			0
$541$	−4.89120	−	16.6579i	−0.210289	−	0.716179i	−0.995312	−	0.0967127i	$-0.969167\pi$
$541$	−4.89120	−	16.6579i	−0.210289	−	0.716179i	0.785023	−	0.619466i	$-0.212651\pi$
$542$		0			0
$543$	−0.951740	−	0.793114i	−0.0408431	−	0.0340358i
$544$		0			0
$545$	−16.6242	−	14.4049i	−0.712101	−	0.617039i
$546$		0			0
$547$	9.47920	+	32.2832i	0.405301	+	1.38033i	0.869209	+	0.494446i	$0.164629\pi$
$547$	9.47920	+	32.2832i	0.405301	+	1.38033i	−0.463907	+	0.885884i	$0.653553\pi$
$548$		0			0
$549$	−23.3920	−	33.4887i	−0.998348	−	1.42926i
$550$		0			0
$551$	−7.35088	+	6.36957i	−0.313158	+	0.271353i
$552$		0			0
$553$	−0.617956	+	4.29798i	−0.0262781	+	0.182769i
$554$		0			0
$555$	15.5232	−	13.9833i	0.658921	−	0.593560i
$556$		0			0
$557$	−11.2361	+	38.2666i	−0.476088	+	1.62141i	0.275168	+	0.961396i	$0.411267\pi$
$557$	−11.2361	+	38.2666i	−0.476088	+	1.62141i	−0.751256	+	0.660011i	$0.770552\pi$
$558$		0			0
$559$	−19.4582	−	42.6075i	−0.822993	−	1.80210i
$560$		0			0
$561$	33.2012	−	22.2522i	1.40175	−	0.939488i
$562$		0			0
$563$	28.2902	+	8.30676i	1.19229	+	0.350088i	0.816901	−	0.576778i	$-0.195690\pi$
$563$	28.2902	+	8.30676i	1.19229	+	0.350088i	0.375391	+	0.926867i	$0.377509\pi$
$564$		0			0
$565$	45.8618			1.92942
$566$		0			0
$567$	3.34180	−	6.20308i	0.140343	−	0.260505i
$568$		0			0
$569$	4.57891	−	3.96765i	0.191958	−	0.166332i	−0.553579	−	0.832796i	$-0.686738\pi$
$569$	4.57891	−	3.96765i	0.191958	−	0.166332i	0.745537	+	0.666464i	$0.232193\pi$
$570$		0			0
$571$	−4.09520	+	8.96724i	−0.171379	+	0.375267i	−0.975759	−	0.218848i	$-0.929770\pi$
$571$	−4.09520	+	8.96724i	−0.171379	+	0.375267i	0.804380	+	0.594115i	$0.202498\pi$
$572$		0			0
$573$	−0.634055	−	32.9139i	−0.0264880	−	1.37500i
$574$		0			0
$575$	7.92814	−	12.3364i	0.330626	−	0.514464i
$576$		0			0
$577$	17.6365	+	2.53574i	0.734217	+	0.105564i	0.499273	−	0.866445i	$-0.333600\pi$
$577$	17.6365	+	2.53574i	0.734217	+	0.105564i	0.234943	+	0.972009i	$0.424510\pi$
$578$		0			0
$579$	−0.0323189	−	0.00401304i	−0.00134313	−	0.000166776i
$580$		0			0
$581$	−1.34086	+	2.93607i	−0.0556282	+	0.121809i
$582$		0			0
$583$	25.1078	+	54.9784i	1.03986	+	2.27697i
$584$		0			0
$585$	51.6162	−	9.46315i	2.13407	−	0.391253i
$586$		0			0
$587$	−31.0273	+	9.11042i	−1.28063	+	0.376027i	−0.850135	−	0.526565i	$-0.823480\pi$
$587$	−31.0273	+	9.11042i	−1.28063	+	0.376027i	−0.430497	+	0.902592i	$0.641662\pi$
$588$		0			0
$589$	12.2962	−	1.76792i	0.506654	−	0.0728459i
$590$		0			0
$591$	−11.6520	−	17.3853i	−0.479299	−	0.715134i
$592$		0			0
$593$	0.791302	−	1.73271i	0.0324949	−	0.0711538i	−0.892689	−	0.450674i	$-0.851184\pi$
$593$	0.791302	−	1.73271i	0.0324949	−	0.0711538i	0.925183	+	0.379520i	$0.123911\pi$
$594$		0			0
$595$	−9.57452	−	6.15317i	−0.392517	−	0.252255i
$596$		0			0
$597$	−3.88899	+	14.2548i	−0.159166	+	0.583411i
$598$		0			0
$599$	1.67155	+	11.6259i	0.0682976	+	0.475021i	0.995052	+	0.0993532i	$0.0316774\pi$
$599$	1.67155	+	11.6259i	0.0682976	+	0.475021i	−0.926755	+	0.375667i	$0.877414\pi$
$600$		0			0
$601$	2.88118	−	3.32506i	0.117526	−	0.135632i	−0.693938	−	0.720035i	$-0.744126\pi$
$601$	2.88118	−	3.32506i	0.117526	−	0.135632i	0.811464	+	0.584403i	$0.198671\pi$
$602$		0			0
$603$	21.2253	+	12.3486i	0.864359	+	0.502875i
$604$		0			0
$605$	−30.8150	+	35.5624i	−1.25281	+	1.44582i
$606$		0			0
$607$	−4.10078	−	28.5216i	−0.166446	−	1.15766i	−0.886158	−	0.463383i	$-0.846635\pi$
$607$	−4.10078	−	28.5216i	−0.166446	−	1.15766i	0.719713	−	0.694272i	$-0.244274\pi$
$608$		0			0
$609$	1.75583	−	6.43588i	0.0711499	−	0.260795i
$610$		0			0
$611$	6.16679	+	3.96316i	0.249482	+	0.160332i
$612$		0			0
$613$	−2.51281	+	5.50228i	−0.101491	+	0.222235i	−0.953565	−	0.301186i	$-0.902617\pi$
$613$	−2.51281	+	5.50228i	−0.101491	+	0.222235i	0.852074	+	0.523421i	$0.175345\pi$
$614$		0			0
$615$	4.12168	+	6.14971i	0.166202	+	0.247980i
$616$		0			0
$617$	14.1110	−	2.02885i	0.568087	−	0.0816785i	0.147714	−	0.989030i	$-0.452808\pi$
$617$	14.1110	−	2.02885i	0.568087	−	0.0816785i	0.420373	+	0.907352i	$0.361899\pi$
$618$		0			0
$619$	−29.7888	+	8.74678i	−1.19731	+	0.351563i	−0.818825	−	0.574044i	$-0.805374\pi$
$619$	−29.7888	+	8.74678i	−1.19731	+	0.351563i	−0.378488	+	0.925606i	$0.623556\pi$
$620$		0			0
$621$	2.91373	+	14.3309i	0.116924	+	0.575077i
$622$		0			0
$623$	−5.13464	−	11.2433i	−0.205715	−	0.450453i
$624$		0			0
$625$	−9.92983	+	21.7433i	−0.397193	+	0.869732i
$626$		0			0
$627$	17.2365	+	2.14026i	0.688361	+	0.0854739i
$628$		0			0
$629$	16.9995	+	2.44416i	0.677813	+	0.0974549i
$630$		0			0
$631$	7.97701	−	12.4125i	0.317560	−	0.494132i	−0.645375	−	0.763865i	$-0.723299\pi$
$631$	7.97701	−	12.4125i	0.317560	−	0.494132i	0.962935	+	0.269733i	$0.0869354\pi$
$632$		0			0
$633$	0.0713841	+	3.70556i	0.00283726	+	0.147283i
$634$		0			0
$635$	18.3122	−	40.0981i	0.726697	−	1.59125i
$636$		0			0
$637$	−26.4242	+	22.8967i	−1.04697	+	0.907201i
$638$		0			0
$639$	6.91519	−	11.7303i	0.273561	−	0.464042i
$640$		0			0
$641$	22.0231			0.869862			0.434931	−	0.900464i	$-0.356773\pi$
$641$	22.0231			0.869862			0.434931	+	0.900464i	$0.356773\pi$
$642$		0			0
$643$	−0.988101	−	0.290133i	−0.0389669	−	0.0114417i	0.262191	−	0.965016i	$-0.415555\pi$
$643$	−0.988101	−	0.290133i	−0.0389669	−	0.0114417i	−0.301158	+	0.953574i	$0.597373\pi$
$644$		0			0
$645$	39.3385	−	26.3656i	1.54895	−	1.03814i
$646$		0			0
$647$	−18.3102	−	40.0937i	−0.719847	−	1.57625i	−0.814118	−	0.580699i	$-0.802779\pi$
$647$	−18.3102	−	40.0937i	−0.719847	−	1.57625i	0.0942711	−	0.995547i	$-0.469948\pi$
$648$		0			0
$649$	−12.6069	+	42.9351i	−0.494863	+	1.68535i
$650$		0			0
$651$	−6.33045	+	5.70251i	−0.248110	+	0.223499i
$652$		0			0
$653$	3.35191	−	23.3131i	0.131171	−	0.912311i	−0.812861	−	0.582457i	$-0.802091\pi$
$653$	3.35191	−	23.3131i	0.131171	−	0.912311i	0.944032	−	0.329854i	$-0.107000\pi$
$654$		0			0
$655$	−39.5372	+	34.2592i	−1.54485	+	1.33862i
$656$		0			0
$657$	5.16000	−	3.60428i	0.201311	−	0.140617i
$658$		0			0
$659$	−2.20150	−	7.49761i	−0.0857582	−	0.292066i	0.905436	−	0.424483i	$-0.139544\pi$
$659$	−2.20150	−	7.49761i	−0.0857582	−	0.292066i	−0.991194	+	0.132418i	$0.957726\pi$
$660$		0			0
$661$	−37.9559	−	32.8889i	−1.47631	−	1.27923i	−0.878634	−	0.477496i	$-0.841545\pi$
$661$	−37.9559	−	32.8889i	−1.47631	−	1.27923i	−0.597678	−	0.801736i	$-0.703910\pi$
$662$		0			0
$663$	33.1389	+	27.6156i	1.28701	+	1.07250i
$664$		0			0
$665$	−1.39342	−	4.74555i	−0.0540345	−	0.184025i
$666$		0			0
$667$	5.75183	+	12.5948i	0.222712	+	0.487671i
$668$		0			0
$669$	−0.0701674	−	3.64240i	−0.00271283	−	0.140823i
$670$		0			0
$671$			69.0642i			2.66620i
$672$		0			0
$673$	44.5977	−	20.3671i	1.71911	−	0.785093i	0.723626	−	0.690192i	$-0.242474\pi$
$673$	44.5977	−	20.3671i	1.71911	−	0.785093i	0.995487	−	0.0949009i	$-0.0302534\pi$
$674$		0			0
$675$	9.11528	+	25.4938i	0.350847	+	0.981256i
$676$		0			0
$677$	11.8582	−	13.6851i	0.455746	−	0.525959i	−0.480646	−	0.876915i	$-0.659598\pi$
$677$	11.8582	−	13.6851i	0.455746	−	0.525959i	0.936392	+	0.350955i	$0.114143\pi$
$678$		0			0
$679$	−1.58485	+	1.82902i	−0.0608210	+	0.0701912i
$680$		0			0
$681$	20.2149	−	6.36102i	0.774635	−	0.243755i
$682$		0			0
$683$	−3.07753	+	1.97781i	−0.117759	+	0.0756788i	−0.598194	−	0.801351i	$-0.704115\pi$
$683$	−3.07753	+	1.97781i	−0.117759	+	0.0756788i	0.480436	+	0.877030i	$0.340479\pi$
$684$		0			0
$685$	31.5196	+	36.3756i	1.20430	+	1.38984i
$686$		0			0
$687$	1.16595	−	9.38989i	0.0444836	−	0.358247i
$688$		0			0
$689$	−49.2989	+	42.7178i	−1.87814	+	1.62742i
$690$		0			0
$691$	−22.9206	−	6.73010i	−0.871942	−	0.256025i	−0.185001	−	0.982738i	$-0.559229\pi$
$691$	−22.9206	−	6.73010i	−0.871942	−	0.256025i	−0.686941	+	0.726713i	$0.741047\pi$
$692$		0			0
$693$	−10.6375	+	5.36236i	−0.404085	+	0.203699i
$694$		0			0
$695$	10.0666	+	15.6639i	0.381847	+	0.594166i
$696$		0			0
$697$	−1.71451	+	5.83910i	−0.0649419	+	0.221172i
$698$		0			0
$699$	−0.916074	−	47.5535i	−0.0346491	−	1.79864i
$700$		0			0
$701$	−7.15827	−	4.60034i	−0.270364	−	0.173752i	0.398433	−	0.917197i	$-0.369554\pi$
$701$	−7.15827	−	4.60034i	−0.270364	−	0.173752i	−0.668797	+	0.743445i	$0.733190\pi$
$702$		0			0
$703$	4.88745	+	5.64042i	0.184334	+	0.212732i
$704$		0			0
$705$	−2.94835	+	6.79960i	−0.111041	+	0.256088i
$706$		0			0
$707$			2.58376i			0.0971722i
$708$		0			0
$709$	3.78525	+	2.43263i	0.142158	+	0.0913595i	0.609787	−	0.792566i	$-0.291255\pi$
$709$	3.78525	+	2.43263i	0.142158	+	0.0913595i	−0.467629	+	0.883925i	$0.654891\pi$
$710$		0			0
$711$	16.5487	+	1.73192i	0.620625	+	0.0649521i
$712$		0			0
$713$	2.51666	−	17.5038i	0.0942497	−	0.655521i
$714$		0			0
$715$	−80.7045	−	36.8565i	−3.01818	−	1.37835i
$716$		0			0
$717$	−30.8072	+	14.7928i	−1.15052	+	0.552447i
$718$		0			0
$719$	−43.8824	+	6.30933i	−1.63654	+	0.235298i	−0.898344	−	0.439292i	$-0.855229\pi$
$719$	−43.8824	+	6.30933i	−1.63654	+	0.235298i	−0.738192	+	0.674591i	$0.764320\pi$
$720$		0			0
$721$	−1.08020	−	3.67883i	−0.0402288	−	0.137007i
$722$		0			0
$723$	−43.6728	+	7.14030i	−1.62421	+	0.265550i
$724$		0			0
$725$	13.8587	+	21.5646i	0.514700	+	0.800888i
$726$		0			0
$727$	10.1784	+	4.64832i	0.377496	+	0.172397i	0.595122	−	0.803636i	$-0.297104\pi$
$727$	10.1784	+	4.64832i	0.377496	+	0.172397i	−0.217626	+	0.976032i	$0.569831\pi$
$728$		0			0
$729$	−24.2456	−	11.8807i	−0.897985	−	0.440027i
$730$		0			0
$731$	37.3516	+	10.9674i	1.38150	+	0.405645i
$732$		0			0
$733$	0.719942	−	0.103512i	0.0265917	−	0.00382330i	−0.129006	−	0.991644i	$-0.541179\pi$
$733$	0.719942	−	0.103512i	0.0265917	−	0.00382330i	0.155598	+	0.987820i	$0.450270\pi$
$734$		0			0
$735$	−27.1565	−	22.6303i	−1.00168	−	0.834732i
$736$		0			0
$737$	−17.4638	−	37.6653i	−0.643286	−	1.38742i
$738$		0			0
$739$	−3.91386	−	3.39138i	−0.143974	−	0.124754i	0.579896	−	0.814690i	$-0.303093\pi$
$739$	−3.91386	−	3.39138i	−0.143974	−	0.124754i	−0.723870	+	0.689936i	$0.757639\pi$
$740$		0			0
$741$	3.02470	+	18.5002i	0.111115	+	0.679623i
$742$		0			0
$743$	−9.27006	+	31.5709i	−0.340085	+	1.15822i	0.594977	+	0.803742i	$0.297161\pi$
$743$	−9.27006	+	31.5709i	−0.340085	+	1.15822i	−0.935063	+	0.354482i	$0.884657\pi$
$744$		0			0
$745$	−35.6868	+	55.5297i	−1.30746	+	2.03445i
$746$		0			0
$747$	11.4405	+	4.70101i	0.418586	+	0.172001i
$748$		0			0
$749$	−7.14955	+	4.59474i	−0.261239	+	0.167888i
$750$		0			0
$751$	−4.72629	−	32.8721i	−0.172465	−	1.19952i	−0.873655	−	0.486546i	$-0.838257\pi$
$751$	−4.72629	−	32.8721i	−0.172465	−	1.19952i	0.701190	−	0.712974i	$-0.252652\pi$
$752$		0			0
$753$	5.55951	+	17.6677i	0.202600	+	0.643848i
$754$		0			0
$755$	−1.50742	−	10.4844i	−0.0548608	−	0.381565i
$756$		0			0
$757$	36.8168	−	16.8137i	1.33813	−	0.611103i	0.387626	−	0.921817i	$-0.373295\pi$
$757$	36.8168	−	16.8137i	1.33813	−	0.611103i	0.950504	+	0.310713i	$0.100568\pi$
$758$		0			0
$759$	9.83601	−	22.6842i	0.357025	−	0.823385i
$760$		0			0
$761$	−38.6217	−	5.55295i	−1.40003	−	0.201294i	−0.599401	−	0.800449i	$-0.704594\pi$
$761$	−38.6217	−	5.55295i	−1.40003	−	0.201294i	−0.800633	+	0.599155i	$0.795503\pi$
$762$		0			0
$763$	−0.766987	+	5.33451i	−0.0277668	+	0.193122i
$764$		0			0
$765$	−22.1483	+	37.5702i	−0.800772	+	1.35835i
$766$		0			0
$767$	−48.2952			−1.74384
$768$		0			0
$769$	4.79533	+	2.18995i	0.172924	+	0.0789717i	0.499996	−	0.866028i	$-0.333335\pi$
$769$	4.79533	+	2.18995i	0.172924	+	0.0789717i	−0.327072	+	0.944999i	$0.606062\pi$
$770$		0			0
$771$	−7.64907	−	8.49137i	−0.275475	−	0.305809i
$772$		0			0
$773$	9.21678	−	14.3416i	0.331505	−	0.515831i	−0.634989	−	0.772521i	$-0.718995\pi$
$773$	9.21678	−	14.3416i	0.331505	−	0.515831i	0.966494	+	0.256690i	$0.0826319\pi$
$774$		0			0
$775$		−	32.7390i		−	1.17602i
$776$		0			0
$777$	−4.93833	−	1.34727i	−0.177162	−	0.0483331i
$778$		0			0
$779$	−2.22477	+	1.42978i	−0.0797108	+	0.0512270i
$780$		0			0
$781$	−20.9416	+	9.56370i	−0.749349	+	0.342216i
$782$		0			0
$783$	−24.9030	−	5.77348i	−0.889959	−	0.206327i
$784$		0			0
$785$	40.3991	+	46.6231i	1.44191	+	1.66405i
$786$		0			0
$787$	−52.9999	−	7.62023i	−1.88924	−	0.271632i	−0.902106	−	0.431516i	$-0.857979\pi$
$787$	−52.9999	−	7.62023i	−1.88924	−	0.271632i	−0.987136	+	0.159884i	$0.948888\pi$
$788$		0			0
$789$	21.8247	+	24.2280i	0.776979	+	0.862538i
$790$		0			0
$791$	−6.07486	−	9.45267i	−0.215997	−	0.336098i
$792$		0			0
$793$	−71.5202	+	21.0002i	−2.53976	+	0.745739i
$794$		0			0
$795$	−50.6650	−	42.2207i	−1.79690	−	1.49741i
$796$		0			0
$797$	6.18085	+	5.35574i	0.218937	+	0.189710i	0.757423	−	0.652924i	$-0.226458\pi$
$797$	6.18085	+	5.35574i	0.218937	+	0.189710i	−0.538486	+	0.842634i	$0.681004\pi$
$798$		0			0
$799$	−5.84550	+	1.71639i	−0.206799	+	0.0607216i
$800$		0			0
$801$	−42.2943	+	21.3206i	−1.49439	+	0.753325i
$802$		0			0
$803$	−10.6415			−0.375532
$804$		0			0
$805$	−7.04057			−0.248147
$806$		0			0
$807$	5.24545	+	10.9241i	0.184648	+	0.384546i
$808$		0			0
$809$	−13.7255	+	4.03018i	−0.482564	+	0.141693i	−0.513961	−	0.857814i	$-0.671822\pi$
$809$	−13.7255	+	4.03018i	−0.482564	+	0.141693i	0.0313975	+	0.999507i	$0.490004\pi$
$810$		0			0
$811$	−30.0175	−	26.0103i	−1.05406	−	0.913345i	−0.0576744	−	0.998335i	$-0.518369\pi$
$811$	−30.0175	−	26.0103i	−1.05406	−	0.913345i	−0.996382	+	0.0849906i	$0.972914\pi$
$812$		0			0
$813$	−24.0430	+	28.8517i	−0.843226	+	1.01187i
$814$		0			0
$815$	56.6925	−	16.6464i	1.98585	−	0.583099i
$816$		0			0
$817$	9.14600	+	14.2315i	0.319978	+	0.497896i
$818$		0			0
$819$	−8.78756	−	9.38523i	−0.307062	−	0.327946i
$820$		0			0
$821$	−34.5249	−	4.96393i	−1.20493	−	0.173242i	−0.489547	−	0.871977i	$-0.662838\pi$
$821$	−34.5249	−	4.96393i	−1.20493	−	0.173242i	−0.715381	+	0.698735i	$0.753747\pi$
$822$		0			0
$823$	−3.85918	−	4.45373i	−0.134522	−	0.155247i	0.684491	−	0.729021i	$-0.260024\pi$
$823$	−3.85918	−	4.45373i	−0.134522	−	0.155247i	−0.819014	+	0.573774i	$0.805479\pi$
$824$		0			0
$825$	12.0479	−	44.1607i	0.419453	−	1.53748i
$826$		0			0
$827$	−33.6965	+	15.3887i	−1.17174	+	0.535117i	−0.903648	−	0.428276i	$-0.859121\pi$
$827$	−33.6965	+	15.3887i	−1.17174	+	0.535117i	−0.268095	+	0.963393i	$0.586394\pi$
$828$		0			0
$829$	26.0769	−	16.7586i	0.905687	−	0.582050i	−0.00278462	−	0.999996i	$-0.500886\pi$
$829$	26.0769	−	16.7586i	0.905687	−	0.582050i	0.908472	+	0.417946i	$0.137250\pi$
$830$		0			0
$831$	−1.65343	+	6.06055i	−0.0573570	+	0.210238i
$832$		0			0
$833$		−	29.0584i		−	1.00681i
$834$		0			0
$835$	−10.8479	+	16.8796i	−0.375407	+	0.584144i
$836$		0			0
$837$	22.7699	+	23.3985i	0.787043	+	0.808771i
$838$		0			0
$839$	12.4517	+	5.68652i	0.429882	+	0.196320i	0.618592	−	0.785712i	$-0.287703\pi$
$839$	12.4517	+	5.68652i	0.429882	+	0.196320i	−0.188710	+	0.982033i	$0.560431\pi$
$840$		0			0
$841$	4.79665			0.165402
$842$		0			0
$843$	−3.58099	+	5.81544i	−0.123336	+	0.200294i
$844$		0			0
$845$	7.71572	−	53.6640i	0.265429	−	1.84610i
$846$		0			0
$847$	11.4116	+	1.64074i	0.392107	+	0.0563765i
$848$		0			0
$849$	19.3674	+	8.39781i	0.664687	+	0.288212i
$850$		0			0
$851$	9.66411	−	4.41345i	0.331281	−	0.151291i
$852$		0			0
$853$	4.30316	+	29.9291i	0.147337	+	1.02475i	0.920555	+	0.390613i	$0.127737\pi$
$853$	4.30316	+	29.9291i	0.147337	+	1.02475i	−0.773218	+	0.634140i	$0.781354\pi$
$854$		0			0
$855$	−17.9657	+	6.03596i	−0.614414	+	0.206425i
$856$		0			0
$857$	1.43579	+	9.98613i	0.0490456	+	0.341120i	0.999539	+	0.0303737i	$0.00966972\pi$
$857$	1.43579	+	9.98613i	0.0490456	+	0.341120i	−0.950493	+	0.310746i	$0.899421\pi$
$858$		0			0
$859$	−25.4650	+	16.3654i	−0.868855	+	0.558379i	−0.897402	−	0.441213i	$-0.854548\pi$
$859$	−25.4650	+	16.3654i	−0.868855	+	0.558379i	0.0285476	+	0.999592i	$0.490912\pi$
$860$		0			0
$861$	0.721571	−	1.66412i	0.0245911	−	0.0567130i
$862$		0			0
$863$	−5.05620	+	7.86760i	−0.172115	+	0.267816i	−0.916585	−	0.399840i	$-0.869066\pi$
$863$	−5.05620	+	7.86760i	−0.172115	+	0.267816i	0.744470	+	0.667656i	$0.232702\pi$
$864$		0			0
$865$	−18.5225	+	63.0818i	−0.629784	+	2.14485i
$866$		0			0
$867$	−6.32194	+	1.03361i	−0.214704	+	0.0351032i
$868$		0			0
$869$	−21.2605	−	18.4224i	−0.721214	−	0.624936i
$870$		0			0
$871$	33.6945	−	29.5376i	1.14169	−	1.00084i
$872$		0			0
$873$	7.23744	+	5.79867i	0.244950	+	0.196255i
$874$		0			0
$875$	−0.521138	+	0.0749284i	−0.0176177	+	0.00253304i
$876$		0			0
$877$	41.1969	+	12.0965i	1.39112	+	0.408469i	0.889625	−	0.456691i	$-0.150966\pi$
$877$	41.1969	+	12.0965i	1.39112	+	0.408469i	0.501494	+	0.865161i	$0.332784\pi$
$878$		0			0
$879$	1.79337	+	1.10431i	0.0604889	+	0.0372475i
$880$		0			0
$881$	−9.51440	−	4.34508i	−0.320548	−	0.146389i	0.248642	−	0.968596i	$-0.420016\pi$
$881$	−9.51440	−	4.34508i	−0.320548	−	0.146389i	−0.569190	+	0.822206i	$0.692743\pi$
$882$		0			0
$883$	25.8555	+	40.2319i	0.870106	+	1.35391i	0.934491	+	0.355986i	$0.115855\pi$
$883$	25.8555	+	40.2319i	0.870106	+	1.35391i	−0.0643854	+	0.997925i	$0.520509\pi$
$884$		0			0
$885$	−7.87848	−	48.1879i	−0.264832	−	1.61982i
$886$		0			0
$887$	15.8490	+	53.9766i	0.532156	+	1.81236i	0.581461	+	0.813574i	$0.302481\pi$
$887$	15.8490	+	53.9766i	0.532156	+	1.81236i	−0.0493046	+	0.998784i	$0.515701\pi$
$888$		0			0
$889$	−10.6903	+	1.53704i	−0.358542	+	0.0515506i
$890$		0			0
$891$	22.1031	+	39.9409i	0.740481	+	1.33807i
$892$		0			0
$893$	−2.40824	−	1.09981i	−0.0805888	−	0.0368037i
$894$		0			0
$895$	−10.0706	+	70.0423i	−0.336622	+	2.34126i
$896$		0			0
$897$	26.4817	+	3.28824i	0.884198	+	0.109791i
$898$		0			0
$899$	26.0048	+	16.7123i	0.867308	+	0.557385i
$900$		0			0
$901$		−	54.2134i		−	1.80611i
$902$		0			0
$903$	−10.6450	−	4.61575i	−0.354245	−	0.153603i
$904$		0			0
$905$	−1.49673	−	1.72731i	−0.0497529	−	0.0574179i
$906$		0			0
$907$	10.8640	+	6.98187i	0.360733	+	0.231829i	0.708435	−	0.705776i	$-0.249401\pi$
$907$	10.8640	+	6.98187i	0.360733	+	0.231829i	−0.347702	+	0.937605i	$0.613038\pi$
$908$		0			0
$909$	9.89355	−	0.381321i	0.328148	−	0.0126476i
$910$		0			0
$911$	11.1851	−	38.0930i	0.370580	−	1.26208i	−0.537494	−	0.843267i	$-0.680629\pi$
$911$	11.1851	−	38.0930i	0.370580	−	1.26208i	0.908074	−	0.418810i	$-0.137553\pi$
$912$		0			0
$913$	−11.3057	−	17.5921i	−0.374166	−	0.582213i
$914$		0			0
$915$	−32.6208	−	67.9354i	−1.07841	−	2.24588i
$916$		0			0
$917$	12.2983	+	3.61111i	0.406126	+	0.119249i
$918$		0			0
$919$	3.39100	−	2.93832i	0.111859	−	0.0969263i	−0.597136	−	0.802140i	$-0.703695\pi$
$919$	3.39100	−	2.93832i	0.111859	−	0.0969263i	0.708994	+	0.705214i	$0.249149\pi$
$920$		0			0
$921$	−25.9681	−	3.22447i	−0.855678	−	0.106250i
$922$		0			0
$923$	−16.2714	−	18.7783i	−0.535581	−	0.618094i
$924$		0			0
$925$	16.5468	−	10.6340i	0.544054	−	0.349642i
$926$		0			0
$927$	−13.9273	+	4.67917i	−0.457433	+	0.153684i
$928$		0			0
$929$	4.69962	−	5.42365i	0.154190	−	0.177944i	−0.673399	−	0.739279i	$-0.735166\pi$
$929$	4.69962	−	5.42365i	0.154190	−	0.177944i	0.827589	+	0.561335i	$0.189712\pi$
$930$		0			0
$931$	8.26943	−	9.54343i	0.271020	−	0.312773i
$932$		0			0
$933$	7.14902	+	22.7191i	0.234048	+	0.743789i
$934$		0			0
$935$	67.0726	−	30.6310i	2.19351	−	1.00174i
$936$		0			0
$937$		−	43.5815i		−	1.42374i	−0.702309	−	0.711872i	$-0.747847\pi$
$937$		−	43.5815i		−	1.42374i	0.702309	−	0.711872i	$-0.252153\pi$
$938$		0			0
$939$	15.5109	−	0.298803i	0.506179	−	0.00975107i
$940$		0			0
$941$	18.3337	+	40.1452i	0.597662	+	1.30870i	0.930700	+	0.365783i	$0.119199\pi$
$941$	18.3337	+	40.1452i	0.597662	+	1.30870i	−0.333038	+	0.942913i	$0.608074\pi$
$942$		0			0
$943$	1.06062	+	3.61213i	0.0345384	+	0.117627i
$944$		0			0
$945$	7.93084	−	10.2991i	0.257990	−	0.335028i
$946$		0			0
$947$	25.1500	+	21.7926i	0.817265	+	0.708164i	0.959512	−	0.281667i	$-0.0908874\pi$
$947$	25.1500	+	21.7926i	0.817265	+	0.708164i	−0.142247	+	0.989831i	$0.545433\pi$
$948$		0			0
$949$	−3.23575	−	11.0199i	−0.105037	−	0.357723i
$950$		0			0
$951$	−28.3075	+	18.9723i	−0.917934	+	0.615220i
$952$		0			0
$953$	1.80134	−	1.56087i	0.0583511	−	0.0505615i	−0.625197	−	0.780467i	$-0.714981\pi$
$953$	1.80134	−	1.56087i	0.0583511	−	0.0505615i	0.683548	+	0.729905i	$0.260436\pi$
$954$		0			0
$955$	8.64315	−	60.1144i	0.279686	−	1.94526i
$956$		0			0
$957$	28.9270	+	32.1124i	0.935079	+	1.03805i
$958$		0			0
$959$	3.32235	−	11.3149i	0.107284	−	0.365376i
$960$		0			0
$961$	−3.52272	−	7.71368i	−0.113636	−	0.248828i
$962$		0			0
$963$	18.6490	+	26.6985i	0.600956	+	0.860346i
$964$		0			0
$965$	−0.0576478	−	0.0169269i	−0.00185575	−	0.000544897i
$966$		0			0
$967$	−26.8692			−0.864054			−0.432027	−	0.901861i	$-0.642201\pi$
$967$	−26.8692			−0.864054			−0.432027	+	0.901861i	$0.642201\pi$
$968$		0			0
$969$	−13.2661	−	8.16891i	−0.426168	−	0.262423i
$970$		0			0
$971$	0.810892	−	0.702642i	0.0260228	−	0.0225489i	−0.641752	−	0.766912i	$-0.721792\pi$
$971$	0.810892	−	0.702642i	0.0260228	−	0.0225489i	0.667775	+	0.744363i	$0.267247\pi$
$972$		0			0
$973$	1.89510	−	4.14968i	0.0607540	−	0.133033i
$974$		0			0
$975$	49.3944	−	0.951537i	1.58189	−	0.0304736i
$976$		0			0
$977$	−8.18397	+	12.7345i	−0.261828	+	0.407413i	−0.947132	−	0.320845i	$-0.896033\pi$
$977$	−8.18397	+	12.7345i	−0.261828	+	0.407413i	0.685303	+	0.728258i	$0.259670\pi$
$978$		0			0
$979$	79.2637	+	11.3964i	2.53328	+	0.364230i
$980$		0			0
$981$	20.5397	+	2.14960i	0.655783	+	0.0686316i
$982$		0			0
$983$	18.0171	−	39.4519i	0.574656	−	1.25832i	−0.369625	−	0.929181i	$-0.620514\pi$
$983$	18.0171	−	39.4519i	0.574656	−	1.25832i	0.944281	−	0.329140i	$-0.106759\pi$
$984$		0			0
$985$	−16.0394	−	35.1215i	−0.511059	−	1.11906i
$986$		0			0
$987$	1.79202	−	0.292986i	0.0570405	−	0.00932585i
$988$		0			0
$989$	23.1061	−	6.78456i	0.734731	−	0.215737i
$990$		0			0
$991$	26.2272	−	3.77091i	0.833136	−	0.119787i	0.287470	−	0.957790i	$-0.407186\pi$
$991$	26.2272	−	3.77091i	0.833136	−	0.119787i	0.545666	+	0.838003i	$0.316277\pi$
$992$		0			0
$993$	−37.2746	+	24.9823i	−1.18288	+	0.792790i
$994$		0			0
$995$	−11.3239	+	24.7958i	−0.358991	+	0.786081i
$996$		0			0
$997$	8.95887	+	5.75751i	0.283730	+	0.182342i	0.674763	−	0.738034i	$-0.264246\pi$
$997$	8.95887	+	5.75751i	0.283730	+	0.182342i	−0.391033	+	0.920377i	$0.627882\pi$
$998$		0			0
$999$	−4.43006	+	19.1083i	−0.140161	+	0.604561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.s.b.5.4	yes	200
3.2	odd	2	inner	804.2.s.b.5.2	✓	200
67.27	odd	22	inner	804.2.s.b.161.2	yes	200
201.161	even	22	inner	804.2.s.b.161.4	yes	200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.s.b.5.2	✓	200	3.2	odd	2	inner
804.2.s.b.5.4	yes	200	1.1	even	1	trivial
804.2.s.b.161.2	yes	200	67.27	odd	22	inner
804.2.s.b.161.4	yes	200	201.161	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56138 + 0.749732i) q^{3} +(-3.06595 + 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(1.87580 - 2.34123i) q^{9} +O(q^{10})\)	\(q+(-1.56138 + 0.749732i) q^{3} +(-3.06595 + 0.900243i) q^{5} +(0.591666 + 0.512682i) q^{7} +(1.87580 - 2.34123i) q^{9} +(-4.86665 + 1.42898i) q^{11} +(-2.95958 - 4.60520i) q^{13} +(4.11216 - 3.70426i) q^{15} +(4.50325 + 0.647469i) q^{17} +(1.29471 + 1.49418i) q^{19} +(-1.30819 - 0.356899i) q^{21} +(2.56007 - 1.16914i) q^{23} +(4.38332 - 2.81699i) q^{25} +(-1.17354 + 5.06190i) q^{27} +4.91969i q^{29} +(3.39701 - 5.28586i) q^{31} +(6.52733 - 5.87985i) q^{33} +(-2.27555 - 1.03921i) q^{35} +3.77494 q^{37} +(8.07369 + 4.97156i) q^{39} +(-0.190364 + 1.32401i) q^{41} +(8.46946 + 1.21772i) q^{43} +(-3.64344 + 8.86676i) q^{45} +(-1.21808 + 0.556280i) q^{47} +(-0.908978 - 6.32208i) q^{49} +(-7.51670 + 2.36528i) q^{51} +(-1.69585 - 11.7949i) q^{53} +(13.6344 - 8.76233i) q^{55} +(-3.14176 - 1.36229i) q^{57} +(4.76970 - 7.42180i) q^{59} +(3.83621 - 13.0649i) q^{61} +(2.31016 - 0.423536i) q^{63} +(13.2197 + 11.4549i) q^{65} +(1.21150 + 8.09520i) q^{67} +(-3.12069 + 3.74484i) q^{69} +(4.49276 - 0.645961i) q^{71} +(2.01307 + 0.591090i) q^{73} +(-4.73203 + 7.68470i) q^{75} +(-3.61204 - 1.64956i) q^{77} +(2.99859 + 4.66590i) q^{79} +(-1.96272 - 8.78338i) q^{81} +(1.16155 + 3.95589i) q^{83} +(-14.3896 + 2.06891i) q^{85} +(-3.68845 - 7.68150i) q^{87} +(-14.3613 - 6.55861i) q^{89} +(0.609916 - 4.24206i) q^{91} +(-1.34105 + 10.8001i) q^{93} +(-5.31463 - 3.41551i) q^{95} +3.09130i q^{97} +(-5.78331 + 14.0744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 10 q^{9}+O(q^{10}) \) 200 * q - 10 * q^9	\( 200 q - 10 q^{9} + 2 q^{15} + 6 q^{19} - 10 q^{21} - 20 q^{25} - 44 q^{31} - 5 q^{33} + 78 q^{39} - 22 q^{43} - 22 q^{45} - 16 q^{49} + 36 q^{55} + 66 q^{57} + 176 q^{61} + 132 q^{63} + 46 q^{67} - 26 q^{73} - 165 q^{75} - 44 q^{79} + 42 q^{81} - 66 q^{87} - 20 q^{91} + 84 q^{93} - 55 q^{99}+O(q^{100}) \) 200 * q - 10 * q^9 + 2 * q^15 + 6 * q^19 - 10 * q^21 - 20 * q^25 - 44 * q^31 - 5 * q^33 + 78 * q^39 - 22 * q^43 - 22 * q^45 - 16 * q^49 + 36 * q^55 + 66 * q^57 + 176 * q^61 + 132 * q^63 + 46 * q^67 - 26 * q^73 - 165 * q^75 - 44 * q^79 + 42 * q^81 - 66 * q^87 - 20 * q^91 + 84 * q^93 - 55 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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