LMFDB - Embedded newform 800.2.be.a.529.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(209,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 7]))

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

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

chi := DirichletCharacter("800.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			529.13
Character	$\chi$	$=$	800.529
Dual form			800.2.be.a.369.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.235999 - 0.171463i) q^{3} +(2.21228 - 0.325311i) q^{5} -0.234809i q^{7} +(-0.900755 - 2.77224i) q^{9} +O(q^{10})$	\(q+(-0.235999 - 0.171463i) q^{3} +(2.21228 - 0.325311i) q^{5} -0.234809i q^{7} +(-0.900755 - 2.77224i) q^{9} +(-5.50105 - 1.78740i) q^{11} +(-0.580270 - 1.78589i) q^{13} +(-0.577875 - 0.302552i) q^{15} +(-2.42773 - 3.34149i) q^{17} +(-1.59154 - 2.19056i) q^{19} +(-0.0402612 + 0.0554147i) q^{21} +(2.32295 + 0.754772i) q^{23} +(4.78835 - 1.43935i) q^{25} +(-0.533191 + 1.64099i) q^{27} +(-3.89100 + 5.35551i) q^{29} +(4.28302 - 3.11180i) q^{31} +(0.991770 + 1.36505i) q^{33} +(-0.0763858 - 0.519463i) q^{35} +(-0.624829 - 1.92303i) q^{37} +(-0.169271 + 0.520963i) q^{39} +(2.13805 + 6.58023i) q^{41} -8.04419 q^{43} +(-2.89456 - 5.83994i) q^{45} +(6.18554 - 8.51367i) q^{47} +6.94486 q^{49} +1.20486i q^{51} +(-3.06610 - 2.22765i) q^{53} +(-12.7513 - 2.16467i) q^{55} +0.789862i q^{57} +(6.66931 - 2.16699i) q^{59} +(-1.54958 - 0.503489i) q^{61} +(-0.650947 + 0.211505i) q^{63} +(-1.86468 - 3.76211i) q^{65} +(9.01003 - 6.54617i) q^{67} +(-0.418799 - 0.576427i) q^{69} +(-2.21139 - 1.60667i) q^{71} +(-14.3832 - 4.67339i) q^{73} +(-1.37684 - 0.481340i) q^{75} +(-0.419697 + 1.29170i) q^{77} +(10.3770 + 7.53932i) q^{79} +(-6.66742 + 4.84416i) q^{81} +(2.55253 - 1.85452i) q^{83} +(-6.45784 - 6.60253i) q^{85} +(1.83655 - 0.596730i) q^{87} +(3.51258 - 10.8106i) q^{89} +(-0.419342 + 0.136252i) q^{91} -1.54435 q^{93} +(-4.23354 - 4.32839i) q^{95} +(4.11921 - 5.66961i) q^{97} +16.8602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9}+O(q^{10}) $ 112 * q - 30 * q^9	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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
$3$	−0.235999	−	0.171463i	−0.136254	−	0.0989945i	0.517570	−	0.855641i	$-0.326837\pi$
$3$	−0.235999	−	0.171463i	−0.136254	−	0.0989945i	−0.653825	+	0.756646i	$0.726837\pi$
$4$		0			0
$5$	2.21228	−	0.325311i	0.989361	−	0.145483i
$5$	2.21228	−	0.325311i	0.989361	−	0.145483i
$6$		0			0
$7$		−	0.234809i		−	0.0887494i	−0.999015	−	0.0443747i	$-0.985870\pi$
$7$		−	0.234809i		−	0.0887494i	0.999015	−	0.0443747i	$-0.0141296\pi$
$8$		0			0
$9$	−0.900755	−	2.77224i	−0.300252	−	0.924080i
$10$		0			0
$11$	−5.50105	−	1.78740i	−1.65863	−	0.538921i	−0.678045	−	0.735021i	$-0.737172\pi$
$11$	−5.50105	−	1.78740i	−1.65863	−	0.538921i	−0.980584	+	0.196099i	$0.937172\pi$
$12$		0			0
$13$	−0.580270	−	1.78589i	−0.160938	−	0.495316i	0.837776	−	0.546014i	$-0.183855\pi$
$13$	−0.580270	−	1.78589i	−0.160938	−	0.495316i	−0.998714	+	0.0506981i	$0.983855\pi$
$14$		0			0
$15$	−0.577875	−	0.302552i	−0.149207	−	0.0781185i
$16$		0			0
$17$	−2.42773	−	3.34149i	−0.588811	−	0.810429i	0.405815	−	0.913955i	$-0.366988\pi$
$17$	−2.42773	−	3.34149i	−0.588811	−	0.810429i	−0.994627	+	0.103526i	$0.966988\pi$
$18$		0			0
$19$	−1.59154	−	2.19056i	−0.365124	−	0.502550i	0.586443	−	0.809990i	$-0.300528\pi$
$19$	−1.59154	−	2.19056i	−0.365124	−	0.502550i	−0.951567	+	0.307440i	$0.900528\pi$
$20$		0			0
$21$	−0.0402612	+	0.0554147i	−0.00878571	+	0.0120925i
$22$		0			0
$23$	2.32295	+	0.754772i	0.484369	+	0.157381i	0.541014	−	0.841013i	$-0.318041\pi$
$23$	2.32295	+	0.754772i	0.484369	+	0.157381i	−0.0566456	+	0.998394i	$0.518041\pi$
$24$		0			0
$25$	4.78835	−	1.43935i	0.957669	−	0.287871i
$26$		0			0
$27$	−0.533191	+	1.64099i	−0.102613	+	0.315809i
$28$		0			0
$29$	−3.89100	+	5.35551i	−0.722541	+	0.994493i	0.276894	+	0.960900i	$0.410695\pi$
$29$	−3.89100	+	5.35551i	−0.722541	+	0.994493i	−0.999436	+	0.0335922i	$0.989305\pi$
$30$		0			0
$31$	4.28302	−	3.11180i	0.769253	−	0.558895i	−0.132482	−	0.991185i	$-0.542295\pi$
$31$	4.28302	−	3.11180i	0.769253	−	0.558895i	0.901734	+	0.432291i	$0.142295\pi$
$32$		0			0
$33$	0.991770	+	1.36505i	0.172645	+	0.237625i
$34$		0			0
$35$	−0.0763858	−	0.519463i	−0.0129116	−	0.0878052i
$36$		0			0
$37$	−0.624829	−	1.92303i	−0.102721	−	0.316144i	0.886468	−	0.462791i	$-0.153152\pi$
$37$	−0.624829	−	1.92303i	−0.102721	−	0.316144i	−0.989189	+	0.146647i	$0.953152\pi$
$38$		0			0
$39$	−0.169271	+	0.520963i	−0.0271051	+	0.0834208i
$40$		0			0
$41$	2.13805	+	6.58023i	0.333907	+	1.02766i	0.967258	+	0.253795i	$0.0816787\pi$
$41$	2.13805	+	6.58023i	0.333907	+	1.02766i	−0.633352	+	0.773864i	$0.718321\pi$
$42$		0			0
$43$	−8.04419			−1.22673			−0.613364	−	0.789801i	$-0.710184\pi$
$43$	−8.04419			−1.22673			−0.613364	+	0.789801i	$0.710184\pi$
$44$		0			0
$45$	−2.89456	−	5.83994i	−0.431495	−	0.870567i
$46$		0			0
$47$	6.18554	−	8.51367i	0.902254	−	1.24185i	−0.0674892	−	0.997720i	$-0.521499\pi$
$47$	6.18554	−	8.51367i	0.902254	−	1.24185i	0.969743	−	0.244126i	$-0.0785012\pi$
$48$		0			0
$49$	6.94486			0.992124
$50$		0			0
$51$			1.20486i			0.168714i
$52$		0			0
$53$	−3.06610	−	2.22765i	−0.421161	−	0.305991i	0.356944	−	0.934126i	$-0.383819\pi$
$53$	−3.06610	−	2.22765i	−0.421161	−	0.305991i	−0.778105	+	0.628135i	$0.783819\pi$
$54$		0			0
$55$	−12.7513	−	2.16467i	−1.71939	−	0.291885i
$56$		0			0
$57$			0.789862i			0.104620i
$58$		0			0
$59$	6.66931	−	2.16699i	0.868270	−	0.282118i	0.159192	−	0.987248i	$-0.449111\pi$
$59$	6.66931	−	2.16699i	0.868270	−	0.282118i	0.709078	+	0.705130i	$0.249111\pi$
$60$		0			0
$61$	−1.54958	−	0.503489i	−0.198403	−	0.0644651i	0.208130	−	0.978101i	$-0.433262\pi$
$61$	−1.54958	−	0.503489i	−0.198403	−	0.0644651i	−0.406533	+	0.913636i	$0.633262\pi$
$62$		0			0
$63$	−0.650947	+	0.211505i	−0.0820116	+	0.0266472i
$64$		0			0
$65$	−1.86468	−	3.76211i	−0.231286	−	0.466632i
$66$		0			0
$67$	9.01003	−	6.54617i	1.10075	−	0.799742i	0.119569	−	0.992826i	$-0.461849\pi$
$67$	9.01003	−	6.54617i	1.10075	−	0.799742i	0.981182	+	0.193084i	$0.0618489\pi$
$68$		0			0
$69$	−0.418799	−	0.576427i	−0.0504174	−	0.0693936i
$70$		0			0
$71$	−2.21139	−	1.60667i	−0.262443	−	0.190676i	0.448780	−	0.893642i	$-0.351859\pi$
$71$	−2.21139	−	1.60667i	−0.262443	−	0.190676i	−0.711223	+	0.702966i	$0.751859\pi$
$72$		0			0
$73$	−14.3832	−	4.67339i	−1.68343	−	0.546979i	−0.697857	−	0.716237i	$-0.745863\pi$
$73$	−14.3832	−	4.67339i	−1.68343	−	0.546979i	−0.985572	+	0.169258i	$0.945863\pi$
$74$		0			0
$75$	−1.37684	−	0.481340i	−0.158984	−	0.0555803i
$76$		0			0
$77$	−0.419697	+	1.29170i	−0.0478290	+	0.147202i
$78$		0			0
$79$	10.3770	+	7.53932i	1.16750	+	0.848240i	0.990708	−	0.136008i	$-0.0434272\pi$
$79$	10.3770	+	7.53932i	1.16750	+	0.848240i	0.176795	+	0.984248i	$0.443427\pi$
$80$		0			0
$81$	−6.66742	+	4.84416i	−0.740824	+	0.538240i
$82$		0			0
$83$	2.55253	−	1.85452i	0.280176	−	0.203560i	−0.438818	−	0.898576i	$-0.644603\pi$
$83$	2.55253	−	1.85452i	0.280176	−	0.203560i	0.718994	+	0.695016i	$0.244603\pi$
$84$		0			0
$85$	−6.45784	−	6.60253i	−0.700451	−	0.716145i
$86$		0			0
$87$	1.83655	−	0.596730i	0.196899	−	0.0639762i
$88$		0			0
$89$	3.51258	−	10.8106i	0.372333	−	1.14592i	−0.572927	−	0.819606i	$-0.694192\pi$
$89$	3.51258	−	10.8106i	0.372333	−	1.14592i	0.945260	−	0.326317i	$-0.105808\pi$
$90$		0			0
$91$	−0.419342	+	0.136252i	−0.0439590	+	0.0142831i
$92$		0			0
$93$	−1.54435			−0.160141
$94$		0			0
$95$	−4.23354	−	4.32839i	−0.434352	−	0.444084i
$96$		0			0
$97$	4.11921	−	5.66961i	0.418243	−	0.575661i	−0.546962	−	0.837157i	$-0.684216\pi$
$97$	4.11921	−	5.66961i	0.418243	−	0.575661i	0.965205	+	0.261496i	$0.0842158\pi$
$98$		0			0
$99$			16.8602i			1.69452i
$100$		0			0
$101$			10.9484i			1.08941i	0.838628	+	0.544704i	$0.183358\pi$
$101$			10.9484i			1.08941i	−0.838628	+	0.544704i	$0.816642\pi$
$102$		0			0
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	−0.999908	−	0.0135350i	$-0.995692\pi$
$103$	−6.88143	+	9.47147i	−0.678047	+	0.933252i	0.321861	+	0.946787i	$0.395692\pi$
$104$		0			0
$105$	−0.0710419	+	0.135690i	−0.00693298	+	0.0132420i
$106$		0			0
$107$	−0.352640			−0.0340910			−0.0170455	−	0.999855i	$-0.505426\pi$
$107$	−0.352640			−0.0340910			−0.0170455	+	0.999855i	$0.505426\pi$
$108$		0			0
$109$	9.24706	−	3.00455i	0.885708	−	0.287784i	0.169382	−	0.985550i	$-0.445823\pi$
$109$	9.24706	−	3.00455i	0.885708	−	0.287784i	0.716325	+	0.697767i	$0.245823\pi$
$110$		0			0
$111$	−0.182270	+	0.560968i	−0.0173003	+	0.0532448i
$112$		0			0
$113$	−0.311428	+	0.101189i	−0.0292967	+	0.00951907i	−0.323629	−	0.946184i	$-0.604903\pi$
$113$	−0.311428	+	0.101189i	−0.0292967	+	0.00951907i	0.294332	+	0.955703i	$0.404903\pi$
$114$		0			0
$115$	5.38455	+	0.914086i	0.502112	+	0.0852389i
$116$		0			0
$117$	−4.42822	+	3.21729i	−0.409389	+	0.297439i
$118$		0			0
$119$	−0.784611	+	0.570053i	−0.0719252	+	0.0522567i
$120$		0			0
$121$	18.1676	+	13.1995i	1.65160	+	1.19995i
$122$		0			0
$123$	0.623691	−	1.91953i	0.0562364	−	0.173078i
$124$		0			0
$125$	10.1249	−	4.74195i	0.905600	−	0.424133i
$126$		0			0
$127$	8.78610	+	2.85478i	0.779640	+	0.253320i	0.671687	−	0.740835i	$-0.265570\pi$
$127$	8.78610	+	2.85478i	0.779640	+	0.253320i	0.107954	+	0.994156i	$0.465570\pi$
$128$		0			0
$129$	1.89842	+	1.37928i	0.167147	+	0.121439i
$130$		0			0
$131$	4.46019	+	6.13893i	0.389689	+	0.536361i	0.958119	−	0.286371i	$-0.0924490\pi$
$131$	4.46019	+	6.13893i	0.389689	+	0.536361i	−0.568430	+	0.822732i	$0.692449\pi$
$132$		0			0
$133$	−0.514364	+	0.373707i	−0.0446010	+	0.0324045i
$134$		0			0
$135$	−0.645735	+	3.80379i	−0.0555760	+	0.327378i
$136$		0			0
$137$	−12.5733	+	4.08531i	−1.07421	+	0.349032i	−0.792125	−	0.610358i	$-0.791025\pi$
$137$	−12.5733	+	4.08531i	−1.07421	+	0.349032i	−0.282083	+	0.959390i	$0.591025\pi$
$138$		0			0
$139$	2.15160	+	0.699096i	0.182496	+	0.0592965i	0.398839	−	0.917021i	$-0.369413\pi$
$139$	2.15160	+	0.699096i	0.182496	+	0.0592965i	−0.216343	+	0.976317i	$0.569413\pi$
$140$		0			0
$141$	−2.91957	+	0.948625i	−0.245872	+	0.0798886i
$142$		0			0
$143$			10.8614i			0.908278i
$144$		0			0
$145$	−6.86578	+	13.1137i	−0.570172	+	1.08903i
$146$		0			0
$147$	−1.63898	−	1.19079i	−0.135181	−	0.0982148i
$148$		0			0
$149$			15.3980i			1.26145i	0.776004	+	0.630727i	$0.217243\pi$
$149$			15.3980i			1.26145i	−0.776004	+	0.630727i	$0.782757\pi$
$150$		0			0
$151$	−0.300063			−0.0244187			−0.0122094	−	0.999925i	$-0.503886\pi$
$151$	−0.300063			−0.0244187			−0.0122094	+	0.999925i	$0.503886\pi$
$152$		0			0
$153$	−7.07661	+	9.74011i	−0.572110	+	0.787441i
$154$		0			0
$155$	8.46293	−	8.27747i	0.679759	−	0.664862i
$156$		0			0
$157$	20.8929			1.66744			0.833719	−	0.552189i	$-0.186207\pi$
$157$	20.8929			1.66744			0.833719	+	0.552189i	$0.186207\pi$
$158$		0			0
$159$	0.341636	+	1.05145i	0.0270935	+	0.0833852i
$160$		0			0
$161$	0.177227	−	0.545449i	0.0139675	−	0.0429874i
$162$		0			0
$163$	−3.86624	−	11.8991i	−0.302827	−	0.932006i	−0.980479	−	0.196624i	$-0.937002\pi$
$163$	−3.86624	−	11.8991i	−0.302827	−	0.932006i	0.677652	−	0.735383i	$-0.262998\pi$
$164$		0			0
$165$	2.63814	+	2.69725i	0.205379	+	0.209980i
$166$		0			0
$167$	−12.6676	−	17.4355i	−0.980251	−	1.34920i	−0.936694	−	0.350149i	$-0.886131\pi$
$167$	−12.6676	−	17.4355i	−0.980251	−	1.34920i	−0.0435571	−	0.999051i	$-0.513869\pi$
$168$		0			0
$169$	7.66454	−	5.56862i	0.589580	−	0.428355i
$170$		0			0
$171$	−4.63918	+	6.38529i	−0.354767	+	0.488295i
$172$		0			0
$173$	−0.492423	+	1.51552i	−0.0374382	+	0.115223i	−0.968029	−	0.250838i	$-0.919294\pi$
$173$	−0.492423	+	1.51552i	−0.0374382	+	0.115223i	0.930591	+	0.366061i	$0.119294\pi$
$174$		0			0
$175$	−0.337973	−	1.12435i	−0.0255484	−	0.0849926i
$176$		0			0
$177$	−1.94551	−	0.632135i	−0.146234	−	0.0475142i
$178$		0			0
$179$	−6.51305	+	8.96444i	−0.486808	+	0.670034i	−0.979795	−	0.200003i	$-0.935905\pi$
$179$	−6.51305	+	8.96444i	−0.486808	+	0.670034i	0.492987	+	0.870037i	$0.335905\pi$
$180$		0			0
$181$	−11.7991	−	16.2401i	−0.877020	−	1.20711i	−0.977237	−	0.212149i	$-0.931954\pi$
$181$	−11.7991	−	16.2401i	−0.877020	−	1.20711i	0.100217	−	0.994966i	$-0.468046\pi$
$182$		0			0
$183$	0.279369	+	0.384519i	0.0206516	+	0.0284245i
$184$		0			0
$185$	−2.00788	−	4.05101i	−0.147622	−	0.297836i
$186$		0			0
$187$	7.38250	+	22.7210i	0.539862	+	1.66152i
$188$		0			0
$189$	0.385320	+	0.125198i	0.0280279	+	0.00910682i
$190$		0			0
$191$	5.85762	+	18.0279i	0.423842	+	1.30445i	0.904099	+	0.427324i	$0.140544\pi$
$191$	5.85762	+	18.0279i	0.423842	+	1.30445i	−0.480256	+	0.877128i	$0.659456\pi$
$192$		0			0
$193$			2.63353i			0.189566i	0.995498	+	0.0947828i	$0.0302157\pi$
$193$			2.63353i			0.189566i	−0.995498	+	0.0947828i	$0.969784\pi$
$194$		0			0
$195$	−0.205000	+	1.20758i	−0.0146804	+	0.0864766i
$196$		0			0
$197$	20.4204	+	14.8363i	1.45489	+	1.05704i	0.984658	+	0.174498i	$0.0558303\pi$
$197$	20.4204	+	14.8363i	1.45489	+	1.05704i	0.470233	+	0.882542i	$0.344170\pi$
$198$		0			0
$199$	−3.97231			−0.281589			−0.140795	−	0.990039i	$-0.544966\pi$
$199$	−3.97231			−0.281589			−0.140795	+	0.990039i	$0.544966\pi$
$200$		0			0
$201$	−3.24879			−0.229152
$202$		0			0
$203$	1.25752	+	0.913642i	0.0882607	+	0.0641251i
$204$		0			0
$205$	6.87057	+	13.8618i	0.479861	+	0.968147i
$206$		0			0
$207$		−	7.11964i		−	0.494849i
$208$		0			0
$209$	4.83972	+	14.8951i	0.334770	+	1.03032i
$210$		0			0
$211$	−13.9414	−	4.52984i	−0.959766	−	0.311847i	−0.213088	−	0.977033i	$-0.568352\pi$
$211$	−13.9414	−	4.52984i	−0.959766	−	0.311847i	−0.746678	+	0.665186i	$0.768352\pi$
$212$		0			0
$213$	0.246401	+	0.758344i	0.0168831	+	0.0519609i
$214$		0			0
$215$	−17.7960	+	2.61686i	−1.21368	+	0.178468i
$216$		0			0
$217$	−0.730677	−	1.00569i	−0.0496016	−	0.0682708i
$218$		0			0
$219$	2.59311	+	3.56911i	0.175226	+	0.241178i
$220$		0			0
$221$	−4.55877	+	6.27461i	−0.306656	+	0.422076i
$222$		0			0
$223$	16.2169	+	5.26920i	1.08597	+	0.352852i	0.796686	−	0.604393i	$-0.206584\pi$
$223$	16.2169	+	5.26920i	1.08597	+	0.352852i	0.289280	+	0.957245i	$0.406584\pi$
$224$		0			0
$225$	−8.30336	−	11.9779i	−0.553557	−	0.798529i
$226$		0			0
$227$	4.52341	−	13.9216i	0.300229	−	0.924011i	−0.681185	−	0.732111i	$-0.738535\pi$
$227$	4.52341	−	13.9216i	0.300229	−	0.924011i	0.981414	−	0.191900i	$-0.0614649\pi$
$228$		0			0
$229$	3.58252	−	4.93092i	0.236740	−	0.325844i	−0.674072	−	0.738665i	$-0.735456\pi$
$229$	3.58252	−	4.93092i	0.236740	−	0.325844i	0.910812	+	0.412821i	$0.135456\pi$
$230$		0			0
$231$	0.320527	−	0.232876i	0.0210891	−	0.0153221i
$232$		0			0
$233$	4.19480	+	5.77365i	0.274811	+	0.378244i	0.924006	−	0.382377i	$-0.124894\pi$
$233$	4.19480	+	5.77365i	0.274811	+	0.378244i	−0.649196	+	0.760621i	$0.724894\pi$
$234$		0			0
$235$	10.9146	−	20.8468i	0.711987	−	1.35990i
$236$		0			0
$237$	−1.15624	−	3.55855i	−0.0751060	−	0.231153i
$238$		0			0
$239$	1.65706	−	5.09989i	0.107186	−	0.329885i	−0.883051	−	0.469276i	$-0.844515\pi$
$239$	1.65706	−	5.09989i	0.107186	−	0.329885i	0.990237	+	0.139392i	$0.0445148\pi$
$240$		0			0
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	0.930501	−	0.366289i	$-0.119372\pi$
$241$	−0.583541	−	1.79595i	−0.0375892	−	0.115688i	−0.968090	+	0.250601i	$0.919372\pi$
$242$		0			0
$243$	7.58043			0.486285
$244$		0			0
$245$	15.3640	−	2.25924i	0.981568	−	0.144337i
$246$		0			0
$247$	−2.98858	+	4.11342i	−0.190159	+	0.261731i
$248$		0			0
$249$	−0.920377			−0.0583265
$250$		0			0
$251$			4.55040i			0.287219i	0.989634	+	0.143609i	$0.0458709\pi$
$251$			4.55040i			0.287219i	−0.989634	+	0.143609i	$0.954129\pi$
$252$		0			0
$253$	−11.4296	−	8.30408i	−0.718572	−	0.522073i
$254$		0			0
$255$	0.391952	+	2.66547i	0.0245450	+	0.166919i
$256$		0			0
$257$		−	6.99079i		−	0.436074i	−0.975941	−	0.218037i	$-0.930035\pi$
$257$		−	6.99079i		−	0.436074i	0.975941	−	0.218037i	$-0.0699653\pi$
$258$		0			0
$259$	−0.451544	+	0.146716i	−0.0280576	+	0.00911646i
$260$		0			0
$261$	18.3516	+	5.96279i	1.13593	+	0.369088i
$262$		0			0
$263$	−21.5131	+	6.99005i	−1.32656	+	0.431025i	−0.884742	−	0.466081i	$-0.845665\pi$
$263$	−21.5131	+	6.99005i	−1.32656	+	0.431025i	−0.441816	+	0.897106i	$0.645665\pi$
$264$		0			0
$265$	−7.50773	−	3.93075i	−0.461196	−	0.241464i
$266$		0			0
$267$	−2.68259	+	1.94902i	−0.164172	+	0.119278i
$268$		0			0
$269$	−3.68963	−	5.07835i	−0.224961	−	0.309632i	0.681585	−	0.731739i	$-0.261291\pi$
$269$	−3.68963	−	5.07835i	−0.224961	−	0.309632i	−0.906546	+	0.422106i	$0.861291\pi$
$270$		0			0
$271$	2.75055	+	1.99839i	0.167084	+	0.121393i	0.668185	−	0.743995i	$-0.267072\pi$
$271$	2.75055	+	1.99839i	0.167084	+	0.121393i	−0.501101	+	0.865389i	$0.667072\pi$
$272$		0			0
$273$	0.122327	+	0.0397464i	0.00740355	+	0.00240556i
$274$		0			0
$275$	−28.9136	−	0.640726i	−1.74356	−	0.0386372i
$276$		0			0
$277$	7.95552	−	24.4846i	0.478001	−	1.47114i	−0.363867	−	0.931451i	$-0.618544\pi$
$277$	7.95552	−	24.4846i	0.478001	−	1.47114i	0.841868	−	0.539684i	$-0.181456\pi$
$278$		0			0
$279$	−12.4846	−	9.07059i	−0.747433	−	0.543042i
$280$		0			0
$281$	−3.16034	+	2.29612i	−0.188530	+	0.136975i	−0.678047	−	0.735019i	$-0.737173\pi$
$281$	−3.16034	+	2.29612i	−0.188530	+	0.136975i	0.489517	+	0.871994i	$0.337173\pi$
$282$		0			0
$283$	1.03911	−	0.754960i	0.0617689	−	0.0448777i	−0.556472	−	0.830866i	$-0.687845\pi$
$283$	1.03911	−	0.754960i	0.0617689	−	0.0448777i	0.618241	+	0.785988i	$0.287845\pi$
$284$		0			0
$285$	0.256951	+	1.74739i	0.0152204	+	0.103507i
$286$		0			0
$287$	1.54510	−	0.502032i	0.0912041	−	0.0296340i
$288$		0			0
$289$	−0.0183581	+	0.0565005i	−0.00107989	+	0.00332356i
$290$		0			0
$291$	−1.94426	+	0.631729i	−0.113975	+	0.0370326i
$292$		0			0
$293$	−8.55020			−0.499508			−0.249754	−	0.968309i	$-0.580350\pi$
$293$	−8.55020			−0.499508			−0.249754	+	0.968309i	$0.580350\pi$
$294$		0			0
$295$	14.0494	−	6.96358i	0.817989	−	0.405435i
$296$		0			0
$297$	5.86622	−	8.07416i	0.340393	−	0.468510i
$298$		0			0
$299$		−	4.58650i		−	0.265244i
$300$		0			0
$301$			1.88885i			0.108871i
$302$		0			0
$303$	1.87725	−	2.58382i	0.107845	−	0.148436i
$304$		0			0
$305$	−3.59189	−	0.609762i	−0.205671	−	0.0349149i
$306$		0			0
$307$	11.0920			0.633052			0.316526	−	0.948584i	$-0.397483\pi$
$307$	11.0920			0.633052			0.316526	+	0.948584i	$0.397483\pi$
$308$		0			0
$309$	3.24802	−	1.05535i	0.184774	−	0.0600366i
$310$		0			0
$311$	−9.28886	+	28.5882i	−0.526723	+	1.62109i	0.234160	+	0.972198i	$0.424766\pi$
$311$	−9.28886	+	28.5882i	−0.526723	+	1.62109i	−0.760883	+	0.648889i	$0.775234\pi$
$312$		0			0
$313$	0.0349980	−	0.0113715i	0.00197820	−	0.000642758i	−0.308028	−	0.951377i	$-0.599669\pi$
$313$	0.0349980	−	0.0113715i	0.00197820	−	0.000642758i	0.310006	+	0.950735i	$0.399669\pi$
$314$		0			0
$315$	−1.37127	+	0.679668i	−0.0772623	+	0.0382950i
$316$		0			0
$317$	−13.1594	+	9.56085i	−0.739104	+	0.536991i	−0.892431	−	0.451185i	$-0.851002\pi$
$317$	−13.1594	+	9.56085i	−0.739104	+	0.536991i	0.153326	+	0.988176i	$0.451002\pi$
$318$		0			0
$319$	30.9770	−	22.5061i	1.73438	−	1.26010i
$320$		0			0
$321$	0.0832228	+	0.0604649i	0.00464505	+	0.00337482i
$322$		0			0
$323$	−3.45591	+	10.6362i	−0.192292	+	0.591814i
$324$		0			0
$325$	−5.34905	−	7.71623i	−0.296712	−	0.428019i
$326$		0			0
$327$	−2.69747	−	0.876461i	−0.149170	−	0.0484684i
$328$		0			0
$329$	−1.99909	−	1.45242i	−0.110213	−	0.0800746i
$330$		0			0
$331$	13.3539	+	18.3800i	0.733995	+	1.01026i	0.998942	+	0.0459939i	$0.0146455\pi$
$331$	13.3539	+	18.3800i	0.733995	+	1.01026i	−0.264947	+	0.964263i	$0.585355\pi$
$332$		0			0
$333$	−4.76827	+	3.46435i	−0.261300	+	0.189845i
$334$		0			0
$335$	17.8032	−	17.4130i	0.972691	−	0.951375i
$336$		0			0
$337$	17.8926	−	5.81367i	0.974674	−	0.316691i	0.221972	−	0.975053i	$-0.428751\pi$
$337$	17.8926	−	5.81367i	0.974674	−	0.316691i	0.752701	+	0.658362i	$0.228751\pi$
$338$		0			0
$339$	0.0908470	+	0.0295180i	0.00493413	+	0.00160320i
$340$		0			0
$341$	−29.1231	+	9.46267i	−1.57711	+	0.512433i
$342$		0			0
$343$		−	3.27438i		−	0.176800i
$344$		0			0
$345$	−1.11402	−	1.13898i	−0.0599766	−	0.0613204i
$346$		0			0
$347$	−23.8972	−	17.3624i	−1.28287	−	0.932060i	−0.283235	−	0.959051i	$-0.591408\pi$
$347$	−23.8972	−	17.3624i	−1.28287	−	0.932060i	−0.999636	+	0.0269903i	$0.991408\pi$
$348$		0			0
$349$			15.7634i			0.843797i	0.906643	+	0.421898i	$0.138636\pi$
$349$			15.7634i			0.843797i	−0.906643	+	0.421898i	$0.861364\pi$
$350$		0			0
$351$	3.24002			0.172940
$352$		0			0
$353$	−4.79864	+	6.60477i	−0.255406	+	0.351536i	−0.917395	−	0.397977i	$-0.869712\pi$
$353$	−4.79864	+	6.60477i	−0.255406	+	0.351536i	0.661989	+	0.749513i	$0.269712\pi$
$354$		0			0
$355$	−5.41486	−	2.83500i	−0.287391	−	0.150466i
$356$		0			0
$357$	0.282911			0.0149732
$358$		0			0
$359$	9.42480	+	29.0065i	0.497422	+	1.53091i	0.813148	+	0.582056i	$0.197752\pi$
$359$	9.42480	+	29.0065i	0.497422	+	1.53091i	−0.315727	+	0.948850i	$0.602248\pi$
$360$		0			0
$361$	3.60574	−	11.0973i	0.189776	−	0.584071i
$362$		0			0
$363$	−2.02430	−	6.23015i	−0.106248	−	0.326998i
$364$		0			0
$365$	−33.3400	−	5.65983i	−1.74509	−	0.296249i
$366$		0			0
$367$	4.40881	+	6.06821i	0.230138	+	0.316758i	0.908432	−	0.418033i	$-0.137280\pi$
$367$	4.40881	+	6.06821i	0.230138	+	0.316758i	−0.678294	+	0.734791i	$0.737280\pi$
$368$		0			0
$369$	16.3161	−	11.8543i	0.849383	−	0.617113i
$370$		0			0
$371$	−0.523072	+	0.719947i	−0.0271565	+	0.0373778i
$372$		0			0
$373$	3.94238	−	12.1334i	0.204129	−	0.628243i	−0.795619	−	0.605797i	$-0.792854\pi$
$373$	3.94238	−	12.1334i	0.204129	−	0.628243i	0.999748	−	0.0224465i	$-0.00714553\pi$
$374$		0			0
$375$	−3.20254	−	0.616956i	−0.165379	−	0.0318595i
$376$		0			0
$377$	11.8222	+	3.84125i	0.608872	+	0.197834i
$378$		0			0
$379$	7.20040	−	9.91051i	0.369860	−	0.509069i	−0.583003	−	0.812470i	$-0.698122\pi$
$379$	7.20040	−	9.91051i	0.369860	−	0.509069i	0.952863	+	0.303402i	$0.0981224\pi$
$380$		0			0
$381$	−1.58402	−	2.18022i	−0.0811519	−	0.111696i
$382$		0			0
$383$	−15.8262	−	21.7829i	−0.808681	−	1.11305i	−0.991525	−	0.129912i	$-0.958530\pi$
$383$	−15.8262	−	21.7829i	−0.808681	−	1.11305i	0.182844	−	0.983142i	$-0.441470\pi$
$384$		0			0
$385$	−0.508285	+	2.99412i	−0.0259046	+	0.152595i
$386$		0			0
$387$	7.24584	+	22.3004i	0.368327	+	1.13359i
$388$		0			0
$389$	−9.06656	−	2.94590i	−0.459693	−	0.149363i	0.0700104	−	0.997546i	$-0.477697\pi$
$389$	−9.06656	−	2.94590i	−0.459693	−	0.149363i	−0.529703	+	0.848183i	$0.677697\pi$
$390$		0			0
$391$	−3.11744	−	9.59449i	−0.157656	−	0.485214i
$392$		0			0
$393$		−	2.21354i		−	0.111658i
$394$		0			0
$395$	25.4094	+	13.3033i	1.27849	+	0.669363i
$396$		0			0
$397$	−18.8253	−	13.6774i	−0.944816	−	0.686449i	0.00475885	−	0.999989i	$-0.498485\pi$
$397$	−18.8253	−	13.6774i	−0.944816	−	0.686449i	−0.949575	+	0.313539i	$0.898485\pi$
$398$		0			0
$399$	0.185467			0.00928495
$400$		0			0
$401$	12.2917			0.613820			0.306910	−	0.951739i	$-0.400705\pi$
$401$	12.2917			0.613820			0.306910	+	0.951739i	$0.400705\pi$
$402$		0			0
$403$	−8.04262	−	5.84330i	−0.400631	−	0.291076i
$404$		0			0
$405$	−13.1743	+	12.8856i	−0.654637	+	0.640291i
$406$		0			0
$407$			11.6955i			0.579724i
$408$		0			0
$409$	9.76563	+	30.0555i	0.482879	+	1.48615i	0.835029	+	0.550206i	$0.185451\pi$
$409$	9.76563	+	30.0555i	0.482879	+	1.48615i	−0.352150	+	0.935944i	$0.614549\pi$
$410$		0			0
$411$	3.66777	+	1.19173i	0.180918	+	0.0587837i
$412$		0			0
$413$	−0.508829	−	1.56601i	−0.0250378	−	0.0770585i
$414$		0			0
$415$	5.04361	−	4.93308i	0.247581	−	0.242155i
$416$		0			0
$417$	−0.387905	−	0.533906i	−0.0189958	−	0.0261455i
$418$		0			0
$419$	−5.07417	−	6.98399i	−0.247889	−	0.341190i	0.666881	−	0.745164i	$-0.267629\pi$
$419$	−5.07417	−	6.98399i	−0.247889	−	0.341190i	−0.914771	+	0.403973i	$0.867629\pi$
$420$		0			0
$421$	7.53026	−	10.3645i	0.367002	−	0.505135i	−0.585081	−	0.810975i	$-0.698937\pi$
$421$	7.53026	−	10.3645i	0.367002	−	0.505135i	0.952083	+	0.305840i	$0.0989371\pi$
$422$		0			0
$423$	−29.1736	−	9.47907i	−1.41847	−	0.460888i
$424$		0			0
$425$	−16.4344	−	12.5058i	−0.797186	−	0.606622i
$426$		0			0
$427$	−0.118224	+	0.363855i	−0.00572124	+	0.0176082i
$428$		0			0
$429$	1.86234	−	2.56329i	0.0899145	−	0.123757i
$430$		0			0
$431$	24.3298	−	17.6766i	1.17193	−	0.851454i	0.180688	−	0.983541i	$-0.442168\pi$
$431$	24.3298	−	17.6766i	1.17193	−	0.851454i	0.991238	+	0.132087i	$0.0421677\pi$
$432$		0			0
$433$	−0.945079	−	1.30079i	−0.0454176	−	0.0625120i	0.785704	−	0.618602i	$-0.212301\pi$
$433$	−0.945079	−	1.30079i	−0.0454176	−	0.0625120i	−0.831122	+	0.556090i	$0.812301\pi$
$434$		0			0
$435$	3.86883	−	1.91758i	0.185496	−	0.0919410i
$436$		0			0
$437$	−2.04369	−	6.28982i	−0.0977628	−	0.300883i
$438$		0			0
$439$	11.7350	−	36.1165i	0.560079	−	1.72374i	−0.122061	−	0.992523i	$-0.538950\pi$
$439$	11.7350	−	36.1165i	0.560079	−	1.72374i	0.682139	−	0.731222i	$-0.261050\pi$
$440$		0			0
$441$	−6.25562	−	19.2528i	−0.297887	−	0.916801i
$442$		0			0
$443$	−19.5670			−0.929654			−0.464827	−	0.885402i	$-0.653883\pi$
$443$	−19.5670			−0.929654			−0.464827	+	0.885402i	$0.653883\pi$
$444$		0			0
$445$	4.25400	−	25.0588i	0.201659	−	1.18790i
$446$		0			0
$447$	2.64020	−	3.63392i	0.124877	−	0.171879i
$448$		0			0
$449$	−33.2573			−1.56951			−0.784755	−	0.619806i	$-0.787211\pi$
$449$	−33.2573			−1.56951			−0.784755	+	0.619806i	$0.787211\pi$
$450$		0			0
$451$		−	40.0197i		−	1.88445i
$452$		0			0
$453$	0.0708145	+	0.0514498i	0.00332716	+	0.00241732i
$454$		0			0
$455$	−0.883377	+	0.437845i	−0.0414133	+	0.0205265i
$456$		0			0
$457$		−	15.5897i		−	0.729254i	−0.931154	−	0.364627i	$-0.881197\pi$
$457$		−	15.5897i		−	0.729254i	0.931154	−	0.364627i	$-0.118803\pi$
$458$		0			0
$459$	6.77780	−	2.20224i	0.316361	−	0.102792i
$460$		0			0
$461$	−5.51241	−	1.79109i	−0.256739	−	0.0834194i	0.177820	−	0.984063i	$-0.443096\pi$
$461$	−5.51241	−	1.79109i	−0.256739	−	0.0834194i	−0.434558	+	0.900644i	$0.643096\pi$
$462$		0			0
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	−0.0343111	−	0.999411i	$-0.510924\pi$
$463$	11.3046	−	3.67309i	0.525370	−	0.170703i	0.559681	+	0.828708i	$0.310924\pi$
$464$		0			0
$465$	−3.41653	+	0.502393i	−0.158438	+	0.0232979i
$466$		0			0
$467$	20.1818	−	14.6630i	0.933903	−	0.678521i	−0.0130420	−	0.999915i	$-0.504152\pi$
$467$	20.1818	−	14.6630i	0.933903	−	0.678521i	0.946945	+	0.321394i	$0.104152\pi$
$468$		0			0
$469$	−1.53710	−	2.11564i	−0.0709767	−	0.0976910i
$470$		0			0
$471$	−4.93072	−	3.58238i	−0.227196	−	0.165067i
$472$		0			0
$473$	44.2515	+	14.3782i	2.03468	+	0.661109i
$474$		0			0
$475$	−10.7738	−	8.19839i	−0.494337	−	0.376168i
$476$		0			0
$477$	−3.41377	+	10.5065i	−0.156306	+	0.481060i
$478$		0			0
$479$	−12.4287	−	9.02994i	−0.567880	−	0.412589i	0.266455	−	0.963847i	$-0.414148\pi$
$479$	−12.4287	−	9.02994i	−0.567880	−	0.412589i	−0.834334	+	0.551259i	$0.814148\pi$
$480$		0			0
$481$	−3.07174	+	2.23175i	−0.140059	+	0.101759i
$482$		0			0
$483$	−0.135350	+	0.0983377i	−0.00615865	+	0.00447452i
$484$		0			0
$485$	7.26846	−	13.8828i	0.330044	−	0.630384i
$486$		0			0
$487$	−21.4527	+	6.97042i	−0.972117	+	0.315860i	−0.751670	−	0.659539i	$-0.770751\pi$
$487$	−21.4527	+	6.97042i	−0.972117	+	0.315860i	−0.220447	+	0.975399i	$0.570751\pi$
$488$		0			0
$489$	−1.12782	+	3.47109i	−0.0510020	+	0.156968i
$490$		0			0
$491$	7.25634	−	2.35773i	0.327474	−	0.106403i	−0.140666	−	0.990057i	$-0.544924\pi$
$491$	7.25634	−	2.35773i	0.327474	−	0.106403i	0.468140	+	0.883654i	$0.344924\pi$
$492$		0			0
$493$	27.3417			1.23141
$494$		0			0
$495$	5.48481	+	37.2995i	0.246524	+	1.67649i
$496$		0			0
$497$	−0.377259	+	0.519253i	−0.0169224	+	0.0232917i
$498$		0			0
$499$			26.9689i			1.20729i	0.797252	+	0.603647i	$0.206286\pi$
$499$			26.9689i			1.20729i	−0.797252	+	0.603647i	$0.793714\pi$
$500$		0			0
$501$			6.28680i			0.280874i
$502$		0			0
$503$	18.0952	−	24.9059i	0.806825	−	1.11050i	−0.184980	−	0.982742i	$-0.559222\pi$
$503$	18.0952	−	24.9059i	0.806825	−	1.11050i	0.991805	−	0.127757i	$-0.0407778\pi$
$504$		0			0
$505$	3.56163	+	24.2209i	0.158491	+	1.07782i
$506$		0			0
$507$	−2.76364			−0.122738
$508$		0			0
$509$	3.29675	−	1.07118i	0.146126	−	0.0474792i	−0.235041	−	0.971986i	$-0.575522\pi$
$509$	3.29675	−	1.07118i	0.146126	−	0.0474792i	0.381167	+	0.924506i	$0.375522\pi$
$510$		0			0
$511$	−1.09735	+	3.37731i	−0.0485441	+	0.149403i
$512$		0			0
$513$	4.44330	−	1.44371i	0.196176	−	0.0637416i
$514$		0			0
$515$	−12.1425	+	23.1921i	−0.535061	+	1.02197i
$516$		0			0
$517$	−49.2443	+	35.7781i	−2.16576	+	1.57352i
$518$		0			0
$519$	0.376068	−	0.273229i	0.0165076	−	0.0119934i
$520$		0			0
$521$	−32.2980	−	23.4659i	−1.41500	−	1.02806i	−0.992571	−	0.121663i	$-0.961177\pi$
$521$	−32.2980	−	23.4659i	−1.41500	−	1.02806i	−0.422430	−	0.906395i	$-0.638823\pi$
$522$		0			0
$523$	1.93267	−	5.94816i	0.0845099	−	0.260095i	−0.899868	−	0.436162i	$-0.856338\pi$
$523$	1.93267	−	5.94816i	0.0845099	−	0.260095i	0.984378	+	0.176067i	$0.0563375\pi$
$524$		0			0
$525$	−0.113023	+	0.323295i	−0.00493272	+	0.0141098i
$526$		0			0
$527$	−20.7960	−	6.75704i	−0.905890	−	0.294341i
$528$		0			0
$529$	−13.7810	−	10.0125i	−0.599173	−	0.435325i
$530$		0			0
$531$	−12.0148	−	16.5370i	−0.521399	−	0.717644i
$532$		0			0
$533$	10.5109	−	7.63661i	0.455277	−	0.330778i
$534$		0			0
$535$	−0.780138	+	0.114718i	−0.0337283	+	0.00495967i
$536$		0			0
$537$	3.07415	−	0.998852i	0.132659	−	0.0431036i
$538$		0			0
$539$	−38.2040	−	12.4132i	−1.64556	−	0.534676i
$540$		0			0
$541$	19.5034	−	6.33705i	0.838518	−	0.272451i	0.141889	−	0.989883i	$-0.454682\pi$
$541$	19.5034	−	6.33705i	0.838518	−	0.272451i	0.696629	+	0.717432i	$0.254682\pi$
$542$		0			0
$543$			5.85576i			0.251295i
$544$		0			0
$545$	19.4797	−	9.65507i	0.834417	−	0.413578i
$546$		0			0
$547$	−17.9423	−	13.0358i	−0.767157	−	0.557372i	0.133940	−	0.990989i	$-0.457237\pi$
$547$	−17.9423	−	13.0358i	−0.767157	−	0.557372i	−0.901097	+	0.433617i	$0.857237\pi$
$548$		0			0
$549$			4.74932i			0.202696i
$550$		0			0
$551$	17.9243			0.763599
$552$		0			0
$553$	1.77030	−	2.43661i	0.0752808	−	0.103615i
$554$		0			0
$555$	−0.220742	+	1.30031i	−0.00936998	+	0.0551952i
$556$		0			0
$557$	36.8641			1.56198			0.780991	−	0.624543i	$-0.214715\pi$
$557$	36.8641			1.56198			0.780991	+	0.624543i	$0.214715\pi$
$558$		0			0
$559$	4.66780	+	14.3660i	0.197427	+	0.607617i
$560$		0			0
$561$	2.15356	−	6.62797i	0.0909233	−	0.279833i
$562$		0			0
$563$	12.7139	+	39.1294i	0.535828	+	1.64911i	0.741854	+	0.670561i	$0.233947\pi$
$563$	12.7139	+	39.1294i	0.535828	+	1.64911i	−0.206027	+	0.978546i	$0.566053\pi$
$564$		0			0
$565$	−0.656048	+	0.325169i	−0.0276001	+	0.0136800i
$566$		0			0
$567$	1.13745	+	1.56557i	0.0477685	+	0.0657477i
$568$		0			0
$569$	−2.43983	+	1.77264i	−0.102283	+	0.0743130i	−0.637751	−	0.770242i	$-0.720135\pi$
$569$	−2.43983	+	1.77264i	−0.102283	+	0.0743130i	0.535468	+	0.844555i	$0.320135\pi$
$570$		0			0
$571$	−8.11104	+	11.1639i	−0.339436	+	0.467194i	−0.944277	−	0.329153i	$-0.893237\pi$
$571$	−8.11104	+	11.1639i	−0.339436	+	0.467194i	0.604840	+	0.796347i	$0.293237\pi$
$572$		0			0
$573$	1.70873	−	5.25893i	0.0713833	−	0.219695i
$574$		0			0
$575$	12.2095	+	0.270562i	0.509170	+	0.0112832i
$576$		0			0
$577$	12.5473	+	4.07686i	0.522351	+	0.169722i	0.558312	−	0.829631i	$-0.311449\pi$
$577$	12.5473	+	4.07686i	0.522351	+	0.169722i	−0.0359612	+	0.999353i	$0.511449\pi$
$578$		0			0
$579$	0.451554	−	0.621511i	0.0187659	−	0.0258291i
$580$		0			0
$581$	−0.435458	−	0.599356i	−0.0180658	−	0.0248655i
$582$		0			0
$583$	12.8850	+	17.7347i	0.533644	+	0.734498i
$584$		0			0
$585$	−8.74984	+	8.55809i	−0.361761	+	0.353833i
$586$		0			0
$587$	8.38908	+	25.8189i	0.346254	+	1.06566i	0.960909	+	0.276865i	$0.0892954\pi$
$587$	8.38908	+	25.8189i	0.346254	+	1.06566i	−0.614655	+	0.788796i	$0.710705\pi$
$588$		0			0
$589$	−13.6332	−	4.42969i	−0.561745	−	0.182522i
$590$		0			0
$591$	−2.27531	−	7.00269i	−0.0935939	−	0.288052i
$592$		0			0
$593$		−	10.5301i		−	0.432420i	−0.976347	−	0.216210i	$-0.930630\pi$
$593$		−	10.5301i		−	0.432420i	0.976347	−	0.216210i	$-0.0693696\pi$
$594$		0			0
$595$	−1.55033	+	1.51636i	−0.0635574	+	0.0621646i
$596$		0			0
$597$	0.937461	+	0.681105i	0.0383677	+	0.0278758i
$598$		0			0
$599$	−20.1787			−0.824481			−0.412241	−	0.911075i	$-0.635254\pi$
$599$	−20.1787			−0.824481			−0.412241	+	0.911075i	$0.635254\pi$
$600$		0			0
$601$	11.7592			0.479669			0.239834	−	0.970814i	$-0.422907\pi$
$601$	11.7592			0.479669			0.239834	+	0.970814i	$0.422907\pi$
$602$		0			0
$603$	−26.2634	−	19.0815i	−1.06953	−	0.777058i
$604$		0			0
$605$	44.4856	+	23.2909i	1.80860	+	0.946909i
$606$		0			0
$607$			35.8362i			1.45455i	0.686347	+	0.727274i	$0.259213\pi$
$607$			35.8362i			1.45455i	−0.686347	+	0.727274i	$0.740787\pi$
$608$		0			0
$609$	−0.140118	−	0.431238i	−0.00567785	−	0.0174746i
$610$		0			0
$611$	−18.7937	−	6.10645i	−0.760313	−	0.247041i
$612$		0			0
$613$	3.94986	+	12.1564i	0.159533	+	0.490994i	0.998592	−	0.0530477i	$-0.0168935\pi$
$613$	3.94986	+	12.1564i	0.159533	+	0.490994i	−0.839059	+	0.544041i	$0.816894\pi$
$614$		0			0
$615$	0.755337	−	4.44942i	0.0304581	−	0.179418i
$616$		0			0
$617$	−9.18527	−	12.6424i	−0.369785	−	0.508965i	0.583057	−	0.812431i	$-0.301856\pi$
$617$	−9.18527	−	12.6424i	−0.369785	−	0.508965i	−0.952842	+	0.303466i	$0.901856\pi$
$618$		0			0
$619$	−20.9771	−	28.8724i	−0.843139	−	1.16048i	−0.985333	−	0.170643i	$-0.945416\pi$
$619$	−20.9771	−	28.8724i	−0.843139	−	1.16048i	0.142194	−	0.989839i	$-0.454584\pi$
$620$		0			0
$621$	−2.47715	+	3.40951i	−0.0994048	+	0.136819i
$622$		0			0
$623$	−2.53843	−	0.824786i	−0.101700	−	0.0330444i
$624$		0			0
$625$	20.8565	−	13.7843i	0.834261	−	0.551370i
$626$		0			0
$627$	1.41180	−	4.34507i	0.0563818	−	0.173525i
$628$		0			0
$629$	−4.90885	+	6.75645i	−0.195729	+	0.269397i
$630$		0			0
$631$	−36.4157	+	26.4575i	−1.44969	+	1.05326i	−0.463781	+	0.885950i	$0.653508\pi$
$631$	−36.4157	+	26.4575i	−1.44969	+	1.05326i	−0.985905	+	0.167308i	$0.946492\pi$
$632$		0			0
$633$	2.51346	+	3.45948i	0.0999010	+	0.137502i
$634$		0			0
$635$	20.3660	+	3.45735i	0.808199	+	0.137201i
$636$		0			0
$637$	−4.02989	−	12.4027i	−0.159670	−	0.491414i
$638$		0			0
$639$	−2.46214	+	7.57770i	−0.0974009	+	0.299769i
$640$		0			0
$641$	4.02897	+	12.3999i	0.159135	+	0.489766i	0.998556	−	0.0537145i	$-0.0171061\pi$
$641$	4.02897	+	12.3999i	0.159135	+	0.489766i	−0.839422	+	0.543481i	$0.817106\pi$
$642$		0			0
$643$	34.5558			1.36275			0.681375	−	0.731935i	$-0.261382\pi$
$643$	34.5558			1.36275			0.681375	+	0.731935i	$0.261382\pi$
$644$		0			0
$645$	4.64853	+	2.43378i	0.183036	+	0.0958301i
$646$		0			0
$647$	−5.64166	+	7.76508i	−0.221797	+	0.305277i	−0.905386	−	0.424590i	$-0.860418\pi$
$647$	−5.64166	+	7.76508i	−0.221797	+	0.305277i	0.683589	+	0.729867i	$0.260418\pi$
$648$		0			0
$649$	−40.5615			−1.59218
$650$		0			0
$651$			0.362627i			0.0142125i
$652$		0			0
$653$	19.7759	+	14.3680i	0.773889	+	0.562263i	0.903139	−	0.429349i	$-0.141257\pi$
$653$	19.7759	+	14.3680i	0.773889	+	0.562263i	−0.129250	+	0.991612i	$0.541257\pi$
$654$		0			0
$655$	11.8642	+	12.1301i	0.463574	+	0.473961i
$656$		0			0
$657$			44.0833i			1.71985i
$658$		0			0
$659$	41.1516	−	13.3710i	1.60304	−	0.520859i	0.635184	−	0.772361i	$-0.280924\pi$
$659$	41.1516	−	13.3710i	1.60304	−	0.520859i	0.967857	+	0.251502i	$0.0809245\pi$
$660$		0			0
$661$	33.1551	+	10.7728i	1.28958	+	0.419012i	0.871946	−	0.489602i	$-0.162858\pi$
$661$	33.1551	+	10.7728i	1.28958	+	0.419012i	0.417639	+	0.908613i	$0.362858\pi$
$662$		0			0
$663$	2.15173	−	0.699141i	0.0835664	−	0.0271524i
$664$		0			0
$665$	−1.01635	+	0.994073i	−0.0394122	+	0.0385485i
$666$		0			0
$667$	−13.0808	+	9.50375i	−0.506490	+	0.367987i
$668$		0			0
$669$	−2.92371	−	4.02414i	−0.113037	−	0.155582i
$670$		0			0
$671$	7.62437	+	5.53943i	0.294336	+	0.213847i
$672$		0			0
$673$	−10.2698	−	3.33688i	−0.395874	−	0.128627i	0.104314	−	0.994544i	$-0.466735\pi$
$673$	−10.2698	−	3.33688i	−0.395874	−	0.128627i	−0.500187	+	0.865917i	$0.666735\pi$
$674$		0			0
$675$	−0.191132	+	8.62510i	−0.00735668	+	0.331980i
$676$		0			0
$677$	12.9196	−	39.7626i	0.496542	−	1.52820i	−0.317997	−	0.948092i	$-0.603010\pi$
$677$	12.9196	−	39.7626i	0.496542	−	1.52820i	0.814539	−	0.580109i	$-0.196990\pi$
$678$		0			0
$679$	−1.33127	−	0.967228i	−0.0510896	−	0.0371188i
$680$		0			0
$681$	−3.45457	+	2.50989i	−0.132380	+	0.0961794i
$682$		0			0
$683$	−16.0534	+	11.6635i	−0.614267	+	0.446291i	−0.850914	−	0.525305i	$-0.823951\pi$
$683$	−16.0534	+	11.6635i	−0.614267	+	0.446291i	0.236647	+	0.971596i	$0.423951\pi$
$684$		0			0
$685$	−26.4866	+	13.1281i	−1.01200	+	0.501598i
$686$		0			0
$687$	−1.69095	+	0.549422i	−0.0645136	+	0.0209617i
$688$		0			0
$689$	−2.19917	+	6.76834i	−0.0837815	+	0.257853i
$690$		0			0
$691$	15.2658	−	4.96017i	0.580740	−	0.188694i	−0.00389213	−	0.999992i	$-0.501239\pi$
$691$	15.2658	−	4.96017i	0.580740	−	0.188694i	0.584632	+	0.811299i	$0.301239\pi$
$692$		0			0
$693$	3.95893			0.150387
$694$		0			0
$695$	4.98735	+	0.846657i	0.189181	+	0.0321155i
$696$		0			0
$697$	16.7971	−	23.1193i	0.636237	−	0.875705i
$698$		0			0
$699$		−	2.08183i		−	0.0787422i
$700$		0			0
$701$		−	15.2259i		−	0.575073i	−0.957770	−	0.287537i	$-0.907164\pi$
$701$		−	15.2259i		−	0.575073i	0.957770	−	0.287537i	$-0.0928363\pi$
$702$		0			0
$703$	−3.21807	+	4.42930i	−0.121372	+	0.167054i
$704$		0			0
$705$	−6.15030	+	3.04839i	−0.231634	+	0.114809i
$706$		0			0
$707$	2.57079			0.0966843
$708$		0			0
$709$	35.0361	−	11.3839i	1.31581	−	0.427532i	0.434754	−	0.900549i	$-0.356835\pi$
$709$	35.0361	−	11.3839i	1.31581	−	0.427532i	0.881053	+	0.473018i	$0.156835\pi$
$710$		0			0
$711$	11.5537	−	35.5586i	0.433297	−	1.33355i
$712$		0			0
$713$	12.2979	−	3.99584i	0.460561	−	0.149645i
$714$		0			0
$715$	3.53333	+	24.0285i	0.132139	+	0.898614i
$716$		0			0
$717$	−1.26551	+	0.919446i	−0.0472613	+	0.0343373i
$718$		0			0
$719$	−17.8070	+	12.9375i	−0.664088	+	0.482488i	−0.868041	−	0.496492i	$-0.834621\pi$
$719$	−17.8070	+	12.9375i	−0.664088	+	0.482488i	0.203953	+	0.978981i	$0.434621\pi$
$720$		0			0
$721$	2.22399	+	1.61582i	0.0828256	+	0.0601763i
$722$		0			0
$723$	−0.170225	+	0.523900i	−0.00633075	+	0.0194840i
$724$		0			0
$725$	−10.9230	+	31.2446i	−0.405670	+	1.16039i
$726$		0			0
$727$	37.4888	+	12.1809i	1.39038	+	0.451763i	0.906069	−	0.423131i	$-0.139069\pi$
$727$	37.4888	+	12.1809i	1.39038	+	0.451763i	0.484315	+	0.874894i	$0.339069\pi$
$728$		0			0
$729$	18.2133	+	13.2327i	0.674566	+	0.490101i
$730$		0			0
$731$	19.5291	+	26.8795i	0.722311	+	0.994176i
$732$		0			0
$733$	−20.6186	+	14.9803i	−0.761565	+	0.553309i	−0.899390	−	0.437147i	$-0.855989\pi$
$733$	−20.6186	+	14.9803i	−0.761565	+	0.553309i	0.137825	+	0.990457i	$0.455989\pi$
$734$		0			0
$735$	−4.01326	−	2.10118i	−0.148031	−	0.0775032i
$736$		0			0
$737$	−61.2653	+	19.9063i	−2.25674	+	0.733258i
$738$		0			0
$739$	8.47753	+	2.75452i	0.311851	+	0.101327i	0.460761	−	0.887524i	$-0.347576\pi$
$739$	8.47753	+	2.75452i	0.311851	+	0.101327i	−0.148910	+	0.988851i	$0.547576\pi$
$740$		0			0
$741$	1.41060	−	0.458333i	0.0518198	−	0.0168373i
$742$		0			0
$743$		−	21.5410i		−	0.790261i	−0.918625	−	0.395130i	$-0.870699\pi$
$743$		−	21.5410i		−	0.790261i	0.918625	−	0.395130i	$-0.129301\pi$
$744$		0			0
$745$	5.00914	+	34.0647i	0.183521	+	1.24803i
$746$		0			0
$747$	−7.44038	−	5.40575i	−0.272229	−	0.197786i
$748$		0			0
$749$			0.0828031i			0.00302556i
$750$		0			0
$751$	−31.4361			−1.14712			−0.573561	−	0.819163i	$-0.694438\pi$
$751$	−31.4361			−1.14712			−0.573561	+	0.819163i	$0.694438\pi$
$752$		0			0
$753$	0.780227	−	1.07389i	0.0284331	−	0.0391347i
$754$		0			0
$755$	−0.663822	+	0.0976135i	−0.0241589	+	0.00355252i
$756$		0			0
$757$	−3.46461			−0.125924			−0.0629618	−	0.998016i	$-0.520055\pi$
$757$	−3.46461			−0.125924			−0.0629618	+	0.998016i	$0.520055\pi$
$758$		0			0
$759$	1.27353	+	3.91951i	0.0462261	+	0.142269i
$760$		0			0
$761$	−6.25196	+	19.2415i	−0.226633	+	0.697505i	0.771488	+	0.636243i	$0.219513\pi$
$761$	−6.25196	+	19.2415i	−0.226633	+	0.697505i	−0.998122	+	0.0612621i	$0.980487\pi$
$762$		0			0
$763$	−0.705496	−	2.17129i	−0.0255407	−	0.0786061i
$764$		0			0
$765$	−12.4869	+	23.8499i	−0.451463	+	0.862296i
$766$		0			0
$767$	−7.73999	−	10.6532i	−0.279475	−	0.384664i
$768$		0			0
$769$	−6.10205	+	4.43340i	−0.220046	+	0.159872i	−0.692347	−	0.721565i	$-0.743423\pi$
$769$	−6.10205	+	4.43340i	−0.220046	+	0.159872i	0.472302	+	0.881437i	$0.343423\pi$
$770$		0			0
$771$	−1.19867	+	1.64982i	−0.0431689	+	0.0594169i
$772$		0			0
$773$	−7.63507	+	23.4983i	−0.274614	+	0.845176i	0.714707	+	0.699424i	$0.246560\pi$
$773$	−7.63507	+	23.4983i	−0.274614	+	0.845176i	−0.989321	+	0.145752i	$0.953440\pi$
$774$		0			0
$775$	16.0296	−	21.0651i	0.575800	−	0.756682i
$776$		0			0
$777$	0.131720	+	0.0427985i	0.00472544	+	0.00153539i
$778$		0			0
$779$	11.0116	−	15.1562i	0.394533	−	0.543027i
$780$		0			0
$781$	9.29319	+	12.7910i	0.332536	+	0.457697i
$782$		0			0
$783$	−6.71371	−	9.24062i	−0.239928	−	0.330233i
$784$		0			0
$785$	46.2210	−	6.79669i	1.64970	−	0.242584i
$786$		0			0
$787$	−2.96732	−	9.13248i	−0.105774	−	0.325538i	0.884138	−	0.467227i	$-0.154747\pi$
$787$	−2.96732	−	9.13248i	−0.105774	−	0.325538i	−0.989911	+	0.141689i	$0.954747\pi$
$788$		0			0
$789$	6.27562	+	2.03907i	0.223418	+	0.0725930i
$790$		0			0
$791$	0.0237601	+	0.0731261i	0.000844812	+	0.00260007i
$792$		0			0
$793$			3.05953i			0.108647i
$794$		0			0
$795$	1.09784	+	2.21496i	0.0389364	+	0.0785564i
$796$		0			0
$797$	−25.7837	−	18.7330i	−0.913306	−	0.663556i	0.0285428	−	0.999593i	$-0.490913\pi$
$797$	−25.7837	−	18.7330i	−0.913306	−	0.663556i	−0.941849	+	0.336037i	$0.890913\pi$
$798$		0			0
$799$	−43.4651			−1.53769
$800$		0			0
$801$	−33.1336			−1.17072
$802$		0			0
$803$	70.7696	+	51.4171i	2.49740	+	1.81447i
$804$		0			0
$805$	0.214636	−	1.26434i	0.00756491	−	0.0445621i
$806$		0			0
$807$			1.83112i			0.0644586i
$808$		0			0
$809$	−1.35706	−	4.17661i	−0.0477118	−	0.146842i	0.924362	−	0.381516i	$-0.124598\pi$
$809$	−1.35706	−	4.17661i	−0.0477118	−	0.146842i	−0.972074	+	0.234674i	$0.924598\pi$
$810$		0			0
$811$	36.8697	+	11.9797i	1.29467	+	0.420664i	0.873725	−	0.486421i	$-0.161698\pi$
$811$	36.8697	+	11.9797i	1.29467	+	0.420664i	0.420947	+	0.907085i	$0.361698\pi$
$812$		0			0
$813$	−0.306476	−	0.943236i	−0.0107486	−	0.0330807i
$814$		0			0
$815$	−12.4241	−	25.0663i	−0.435197	−	0.878034i
$816$		0			0
$817$	12.8026	+	17.6213i	0.447907	+	0.616492i
$818$		0			0
$819$	0.755449	+	1.03979i	0.0263975	+	0.0363331i
$820$		0			0
$821$	25.5877	−	35.2185i	0.893017	−	1.22913i	−0.0796254	−	0.996825i	$-0.525372\pi$
$821$	25.5877	−	35.2185i	0.893017	−	1.22913i	0.972642	−	0.232308i	$-0.0746276\pi$
$822$		0			0
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	0.385771	−	0.922594i	$-0.373935\pi$
$823$	4.46326	+	1.45020i	0.155580	+	0.0505509i	−0.230192	+	0.973145i	$0.573935\pi$
$824$		0			0
$825$	6.71373	+	5.10884i	0.233742	+	0.177867i
$826$		0			0
$827$	−3.61552	+	11.1274i	−0.125724	+	0.386938i	−0.994032	−	0.109087i	$-0.965207\pi$
$827$	−3.61552	+	11.1274i	−0.125724	+	0.386938i	0.868308	+	0.496025i	$0.165207\pi$
$828$		0			0
$829$	−0.462729	+	0.636892i	−0.0160712	+	0.0221202i	−0.816977	−	0.576670i	$-0.804352\pi$
$829$	−0.462729	+	0.636892i	−0.0160712	+	0.0221202i	0.800906	+	0.598790i	$0.204352\pi$
$830$		0			0
$831$	−6.07571	+	4.41426i	−0.210764	+	0.153129i
$832$		0			0
$833$	−16.8603	−	23.2062i	−0.584174	−	0.804046i
$834$		0			0
$835$	−33.6963	−	34.4513i	−1.16611	−	1.19224i
$836$		0			0
$837$	2.82277	+	8.68759i	0.0975692	+	0.300287i
$838$		0			0
$839$	−10.8077	+	33.2628i	−0.373124	+	1.14836i	0.571611	+	0.820524i	$0.306318\pi$
$839$	−10.8077	+	33.2628i	−0.373124	+	1.14836i	−0.944736	+	0.327833i	$0.893682\pi$
$840$		0			0
$841$	−4.58005	−	14.0959i	−0.157933	−	0.486067i
$842$		0			0
$843$	1.13954			0.0392478
$844$		0			0
$845$	15.1446	−	14.8127i	0.520989	−	0.509572i
$846$		0			0
$847$	3.09936	−	4.26591i	0.106495	−	0.146578i
$848$		0			0
$849$	−0.374678			−0.0128589
$850$		0			0
$851$		−	4.93870i		−	0.169296i
$852$		0			0
$853$	9.00501	+	6.54252i	0.308326	+	0.224012i	0.731178	−	0.682187i	$-0.238971\pi$
$853$	9.00501	+	6.54252i	0.308326	+	0.224012i	−0.422852	+	0.906199i	$0.638971\pi$
$854$		0			0
$855$	−8.18596	+	15.6352i	−0.279954	+	0.534713i
$856$		0			0
$857$			53.1600i			1.81591i	0.419068	+	0.907955i	$0.362357\pi$
$857$			53.1600i			1.81591i	−0.419068	+	0.907955i	$0.637643\pi$
$858$		0			0
$859$	32.6009	−	10.5927i	1.11233	−	0.361417i	0.305493	−	0.952194i	$-0.401179\pi$
$859$	32.6009	−	10.5927i	1.11233	−	0.361417i	0.806835	+	0.590777i	$0.201179\pi$
$860$		0			0
$861$	−0.450722	−	0.146448i	−0.0153606	−	0.00499095i
$862$		0			0
$863$	37.8328	−	12.2926i	1.28784	−	0.418446i	0.416508	−	0.909132i	$-0.363254\pi$
$863$	37.8328	−	12.2926i	1.28784	−	0.418446i	0.871336	+	0.490686i	$0.163254\pi$
$864$		0			0
$865$	−0.596361	+	3.51295i	−0.0202769	+	0.119444i
$866$		0			0
$867$	0.0140203	−	0.0101863i	0.000476154	−	0.000345946i
$868$		0			0
$869$	−43.6085	−	60.0220i	−1.47932	−	2.03611i
$870$		0			0
$871$	−16.9190	−	12.2923i	−0.573277	−	0.416510i
$872$		0			0
$873$	−19.4279	−	6.31251i	−0.657535	−	0.213646i
$874$		0			0
$875$	−1.11345	−	2.37742i	−0.0376416	−	0.0803715i
$876$		0			0
$877$	−12.4831	+	38.4191i	−0.421525	+	1.29732i	0.484758	+	0.874649i	$0.338908\pi$
$877$	−12.4831	+	38.4191i	−0.421525	+	1.29732i	−0.906283	+	0.422672i	$0.861092\pi$
$878$		0			0
$879$	2.01784	+	1.46605i	0.0680601	+	0.0494486i
$880$		0			0
$881$	26.2858	−	19.0977i	0.885591	−	0.643419i	−0.0491339	−	0.998792i	$-0.515646\pi$
$881$	26.2858	−	19.0977i	0.885591	−	0.643419i	0.934725	+	0.355373i	$0.115646\pi$
$882$		0			0
$883$	31.0584	−	22.5652i	1.04520	−	0.759380i	0.0739039	−	0.997265i	$-0.476454\pi$
$883$	31.0584	−	22.5652i	1.04520	−	0.759380i	0.971293	+	0.237885i	$0.0764542\pi$
$884$		0			0
$885$	−4.50965	−	0.765563i	−0.151590	−	0.0257341i
$886$		0			0
$887$	14.5493	−	4.72737i	0.488519	−	0.158729i	−0.0543921	−	0.998520i	$-0.517322\pi$
$887$	14.5493	−	4.72737i	0.488519	−	0.158729i	0.542911	+	0.839790i	$0.317322\pi$
$888$		0			0
$889$	0.670327	−	2.06305i	0.0224821	−	0.0691926i
$890$		0			0
$891$	45.3363	−	14.7306i	1.51882	−	0.493495i
$892$		0			0
$893$	−28.4943			−0.953524
$894$		0			0
$895$	−11.4924	+	21.9506i	−0.384150	+	0.733728i
$896$		0			0
$897$	−0.786416	+	1.08241i	−0.0262577	+	0.0361406i
$898$		0			0
$899$			35.0457i			1.16884i
$900$		0			0
$901$			15.6535i			0.521492i
$902$		0			0
$903$	0.323868	−	0.445767i	0.0107777	−	0.0148342i
$904$		0			0
$905$	−31.3859	−	32.0892i	−1.04330	−	1.06668i
$906$		0			0
$907$	−31.6503			−1.05093			−0.525465	−	0.850815i	$-0.676109\pi$
$907$	−31.6503			−1.05093			−0.525465	+	0.850815i	$0.676109\pi$
$908$		0			0
$909$	30.3516	−	9.86184i	1.00670	−	0.327096i
$910$		0			0
$911$	1.64977	−	5.07747i	0.0546593	−	0.168224i	−0.920000	−	0.391918i	$-0.871812\pi$
$911$	1.64977	−	5.07747i	0.0546593	−	0.168224i	0.974659	+	0.223694i	$0.0718116\pi$
$912$		0			0
$913$	−17.3564	+	5.63942i	−0.574411	+	0.186638i
$914$		0			0
$915$	0.743131	+	0.759781i	0.0245671	+	0.0251176i
$916$		0			0
$917$	1.44148	−	1.04729i	0.0476017	−	0.0345847i
$918$		0			0
$919$	−11.6067	+	8.43275i	−0.382869	+	0.278171i	−0.762527	−	0.646956i	$-0.776042\pi$
$919$	−11.6067	+	8.43275i	−0.382869	+	0.278171i	0.379658	+	0.925127i	$0.376042\pi$
$920$		0			0
$921$	−2.61770	−	1.90187i	−0.0862561	−	0.0626687i
$922$		0			0
$923$	−1.58612	+	4.88158i	−0.0522078	+	0.160679i
$924$		0			0
$925$	−5.75982	−	8.30877i	−0.189382	−	0.273191i
$926$		0			0
$927$	32.4557	+	10.5455i	1.06598	+	0.346359i
$928$		0			0
$929$	5.50414	+	3.99899i	0.180585	+	0.131203i	0.674405	−	0.738361i	$-0.264400\pi$
$929$	5.50414	+	3.99899i	0.180585	+	0.131203i	−0.493820	+	0.869564i	$0.664400\pi$
$930$		0			0
$931$	−11.0530	−	15.2132i	−0.362248	−	0.498592i
$932$		0			0
$933$	7.09400	−	5.15409i	0.232247	−	0.168737i
$934$		0			0
$935$	23.7235	+	47.8636i	0.775842	+	1.56531i
$936$		0			0
$937$	−15.8759	+	5.15839i	−0.518643	+	0.168517i	−0.556629	−	0.830761i	$-0.687906\pi$
$937$	−15.8759	+	5.15839i	−0.518643	+	0.168517i	0.0379863	+	0.999278i	$0.487906\pi$
$938$		0			0
$939$	−0.0102093	−	0.00331721i	−0.000333168	−	0.000108253i
$940$		0			0
$941$	−10.5188	+	3.41775i	−0.342902	+	0.111416i	−0.475405	−	0.879767i	$-0.657699\pi$
$941$	−10.5188	+	3.41775i	−0.342902	+	0.111416i	0.132503	+	0.991183i	$0.457699\pi$
$942$		0			0
$943$			16.8993i			0.550316i
$944$		0			0
$945$	0.893163	+	0.151624i	0.0290546	+	0.00493234i
$946$		0			0
$947$	−16.0299	−	11.6464i	−0.520901	−	0.378457i	0.296042	−	0.955175i	$-0.404333\pi$
$947$	−16.0299	−	11.6464i	−0.520901	−	0.378457i	−0.816943	+	0.576718i	$0.804333\pi$
$948$		0			0
$949$			28.3986i			0.921858i
$950$		0			0
$951$	4.74494			0.153865
$952$		0			0
$953$	28.4871	−	39.2091i	0.922787	−	1.27011i	−0.0398210	−	0.999207i	$-0.512679\pi$
$953$	28.4871	−	39.2091i	0.922787	−	1.27011i	0.962608	−	0.270900i	$-0.0873212\pi$
$954$		0			0
$955$	18.8233	+	37.9771i	0.609109	+	1.22891i
$956$		0			0
$957$	−11.1695			−0.361060
$958$		0			0
$959$	0.959267	+	2.95232i	0.0309764	+	0.0953354i
$960$		0			0
$961$	−0.918548	+	2.82700i	−0.0296306	+	0.0911936i
$962$		0			0
$963$	0.317642	+	0.977603i	0.0102359	+	0.0315028i
$964$		0			0
$965$	0.856715	+	5.82610i	0.0275786	+	0.187549i
$966$		0			0
$967$	−11.5880	−	15.9495i	−0.372645	−	0.512901i	0.580973	−	0.813923i	$-0.302672\pi$
$967$	−11.5880	−	15.9495i	−0.372645	−	0.512901i	−0.953617	+	0.301022i	$0.902672\pi$
$968$		0			0
$969$	2.63931	−	1.91757i	0.0847870	−	0.0616013i
$970$		0			0
$971$	1.31463	−	1.80943i	0.0421885	−	0.0580675i	−0.787402	−	0.616440i	$-0.788574\pi$
$971$	1.31463	−	1.80943i	0.0421885	−	0.0580675i	0.829590	+	0.558373i	$0.188574\pi$
$972$		0			0
$973$	0.164154	−	0.505214i	0.00526253	−	0.0161964i
$974$		0			0
$975$	−0.0606783	+	2.73819i	−0.00194326	+	0.0876923i
$976$		0			0
$977$	11.4440	+	3.71838i	0.366126	+	0.118962i	0.486301	−	0.873791i	$-0.338346\pi$
$977$	11.4440	+	3.71838i	0.366126	+	0.118962i	−0.120175	+	0.992753i	$0.538346\pi$
$978$		0			0
$979$	−38.6458	+	53.1914i	−1.23512	+	1.70000i
$980$		0			0
$981$	−16.6587	−	22.9287i	−0.531870	−	0.732057i
$982$		0			0
$983$	27.2305	+	37.4796i	0.868518	+	1.19541i	0.979471	+	0.201587i	$0.0646099\pi$
$983$	27.2305	+	37.4796i	0.868518	+	1.19541i	−0.110952	+	0.993826i	$0.535390\pi$
$984$		0			0
$985$	50.0019	+	26.1790i	1.59319	+	0.834132i
$986$		0			0
$987$	0.222746	+	0.685540i	0.00709007	+	0.0218210i
$988$		0			0
$989$	−18.6862	−	6.07153i	−0.594188	−	0.193063i
$990$		0			0
$991$	−18.8475	−	58.0065i	−0.598710	−	1.84264i	−0.535319	−	0.844650i	$-0.679809\pi$
$991$	−18.8475	−	58.0065i	−0.598710	−	1.84264i	−0.0633902	−	0.997989i	$-0.520191\pi$
$992$		0			0
$993$		−	6.62737i		−	0.210313i
$994$		0			0
$995$	−8.78784	+	1.29223i	−0.278593	+	0.0409665i
$996$		0			0
$997$	26.2826	+	19.0954i	0.832378	+	0.604758i	0.920231	−	0.391375i	$-0.128001\pi$
$997$	26.2826	+	19.0954i	0.832378	+	0.604758i	−0.0878532	+	0.996133i	$0.528001\pi$
$998$		0			0
$999$	3.48883			0.110382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.529.13		112
4.3	odd	2		200.2.o.a.29.12	yes	112
8.3	odd	2		200.2.o.a.29.6	✓	112
8.5	even	2	inner	800.2.be.a.529.16		112
20.3	even	4		1000.2.t.b.101.7		224
20.7	even	4		1000.2.t.b.101.50		224
20.19	odd	2		1000.2.o.a.149.17		112
25.19	even	10	inner	800.2.be.a.369.16		112
40.3	even	4		1000.2.t.b.101.39		224
40.19	odd	2		1000.2.o.a.149.23		112
40.27	even	4		1000.2.t.b.101.18		224
100.19	odd	10		200.2.o.a.69.6	yes	112
100.31	odd	10		1000.2.o.a.349.23		112
100.67	even	20		1000.2.t.b.901.18		224
100.83	even	20		1000.2.t.b.901.39		224
200.19	odd	10		200.2.o.a.69.12	yes	112
200.67	even	20		1000.2.t.b.901.50		224
200.69	even	10	inner	800.2.be.a.369.13		112
200.83	even	20		1000.2.t.b.901.7		224
200.131	odd	10		1000.2.o.a.349.17		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.6	✓	112	8.3	odd	2
200.2.o.a.29.12	yes	112	4.3	odd	2
200.2.o.a.69.6	yes	112	100.19	odd	10
200.2.o.a.69.12	yes	112	200.19	odd	10
800.2.be.a.369.13		112	200.69	even	10	inner
800.2.be.a.369.16		112	25.19	even	10	inner
800.2.be.a.529.13		112	1.1	even	1	trivial
800.2.be.a.529.16		112	8.5	even	2	inner
1000.2.o.a.149.17		112	20.19	odd	2
1000.2.o.a.149.23		112	40.19	odd	2
1000.2.o.a.349.17		112	200.131	odd	10
1000.2.o.a.349.23		112	100.31	odd	10
1000.2.t.b.101.7		224	20.3	even	4
1000.2.t.b.101.18		224	40.27	even	4
1000.2.t.b.101.39		224	40.3	even	4
1000.2.t.b.101.50		224	20.7	even	4
1000.2.t.b.901.7		224	200.83	even	20
1000.2.t.b.901.18		224	100.67	even	20
1000.2.t.b.901.39		224	100.83	even	20
1000.2.t.b.901.50		224	200.67	even	20

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.235999 - 0.171463i) q^{3} +(2.21228 - 0.325311i) q^{5} -0.234809i q^{7} +(-0.900755 - 2.77224i) q^{9} +O(q^{10})\)	\(q+(-0.235999 - 0.171463i) q^{3} +(2.21228 - 0.325311i) q^{5} -0.234809i q^{7} +(-0.900755 - 2.77224i) q^{9} +(-5.50105 - 1.78740i) q^{11} +(-0.580270 - 1.78589i) q^{13} +(-0.577875 - 0.302552i) q^{15} +(-2.42773 - 3.34149i) q^{17} +(-1.59154 - 2.19056i) q^{19} +(-0.0402612 + 0.0554147i) q^{21} +(2.32295 + 0.754772i) q^{23} +(4.78835 - 1.43935i) q^{25} +(-0.533191 + 1.64099i) q^{27} +(-3.89100 + 5.35551i) q^{29} +(4.28302 - 3.11180i) q^{31} +(0.991770 + 1.36505i) q^{33} +(-0.0763858 - 0.519463i) q^{35} +(-0.624829 - 1.92303i) q^{37} +(-0.169271 + 0.520963i) q^{39} +(2.13805 + 6.58023i) q^{41} -8.04419 q^{43} +(-2.89456 - 5.83994i) q^{45} +(6.18554 - 8.51367i) q^{47} +6.94486 q^{49} +1.20486i q^{51} +(-3.06610 - 2.22765i) q^{53} +(-12.7513 - 2.16467i) q^{55} +0.789862i q^{57} +(6.66931 - 2.16699i) q^{59} +(-1.54958 - 0.503489i) q^{61} +(-0.650947 + 0.211505i) q^{63} +(-1.86468 - 3.76211i) q^{65} +(9.01003 - 6.54617i) q^{67} +(-0.418799 - 0.576427i) q^{69} +(-2.21139 - 1.60667i) q^{71} +(-14.3832 - 4.67339i) q^{73} +(-1.37684 - 0.481340i) q^{75} +(-0.419697 + 1.29170i) q^{77} +(10.3770 + 7.53932i) q^{79} +(-6.66742 + 4.84416i) q^{81} +(2.55253 - 1.85452i) q^{83} +(-6.45784 - 6.60253i) q^{85} +(1.83655 - 0.596730i) q^{87} +(3.51258 - 10.8106i) q^{89} +(-0.419342 + 0.136252i) q^{91} -1.54435 q^{93} +(-4.23354 - 4.32839i) q^{95} +(4.11921 - 5.66961i) q^{97} +16.8602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9}+O(q^{10}) \) 112 * q - 30 * q^9	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79} - 6 q^{81} + 10 q^{87} + 24 q^{89} + 86 q^{95} - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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