LMFDB - Embedded newform 552.2.q.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	552.193
Dual form			552.2.q.a.409.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{3} +(-0.494929 - 3.44231i) q^{5} +(0.813772 - 1.78191i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{3} +(-0.494929 - 3.44231i) q^{5} +(0.813772 - 1.78191i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-4.59332 - 1.34872i) q^{11} +(1.11537 + 2.44232i) q^{13} +(-2.27741 + 2.62828i) q^{15} +(-0.657735 - 0.422701i) q^{17} +(1.64177 - 1.05510i) q^{19} +(-1.87959 + 0.551896i) q^{21} +(-4.35337 + 2.01202i) q^{23} +(-6.80708 + 1.99874i) q^{25} +(0.841254 - 0.540641i) q^{27} +(4.69732 + 3.01878i) q^{29} +(-4.53151 + 5.22964i) q^{31} +(1.98869 + 4.35463i) q^{33} +(-6.53665 - 1.91933i) q^{35} +(1.36865 - 9.51916i) q^{37} +(1.11537 - 2.44232i) q^{39} +(-1.09875 - 7.64196i) q^{41} +(-4.35629 - 5.02742i) q^{43} +3.47771 q^{45} -9.53389 q^{47} +(2.07104 + 2.39011i) q^{49} +(0.111269 + 0.773893i) q^{51} +(2.18629 - 4.78731i) q^{53} +(-2.36935 + 16.4792i) q^{55} +(-1.87253 - 0.549824i) q^{57} +(-4.02082 - 8.80436i) q^{59} +(1.63680 - 1.88897i) q^{61} +(1.64796 + 1.05908i) q^{63} +(7.85519 - 5.04822i) q^{65} +(6.98906 - 2.05217i) q^{67} +(4.37143 + 1.97246i) q^{69} +(12.3486 - 3.62588i) q^{71} +(1.04034 - 0.668588i) q^{73} +(5.96823 + 3.83555i) q^{75} +(-6.14122 + 7.08735i) q^{77} +(2.10629 + 4.61213i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-0.238762 + 1.66063i) q^{83} +(-1.12953 + 2.47333i) q^{85} +(-0.794645 - 5.52688i) q^{87} +(-0.717979 - 0.828591i) q^{89} +5.25965 q^{91} +6.91980 q^{93} +(-4.44456 - 5.12929i) q^{95} +(2.17166 + 15.1042i) q^{97} +(1.98869 - 4.35463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$	$1$

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
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$3$	−0.654861	−	0.755750i	−0.378084	−	0.436332i
$4$		0			0
$5$	−0.494929	−	3.44231i	−0.221339	−	1.53945i	−0.732981	−	0.680249i	$-0.761872\pi$
$5$	−0.494929	−	3.44231i	−0.221339	−	1.53945i	0.511642	−	0.859199i	$-0.329037\pi$
$6$		0			0
$7$	0.813772	−	1.78191i	0.307577	−	0.673499i	−0.691215	−	0.722650i	$-0.742924\pi$
$7$	0.813772	−	1.78191i	0.307577	−	0.673499i	0.998791	+	0.0491503i	$0.0156513\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−4.59332	−	1.34872i	−1.38494	−	0.406655i	−0.497454	−	0.867491i	$-0.665732\pi$
$11$	−4.59332	−	1.34872i	−1.38494	−	0.406655i	−0.887485	+	0.460836i	$0.847550\pi$
$12$		0			0
$13$	1.11537	+	2.44232i	0.309348	+	0.677377i	0.998902	−	0.0468573i	$-0.0149206\pi$
$13$	1.11537	+	2.44232i	0.309348	+	0.677377i	−0.689554	+	0.724234i	$0.742193\pi$
$14$		0			0
$15$	−2.27741	+	2.62828i	−0.588026	+	0.678618i
$16$		0			0
$17$	−0.657735	−	0.422701i	−0.159524	−	0.102520i	0.458443	−	0.888724i	$-0.348407\pi$
$17$	−0.657735	−	0.422701i	−0.159524	−	0.102520i	−0.617967	+	0.786204i	$0.712044\pi$
$18$		0			0
$19$	1.64177	−	1.05510i	0.376649	−	0.242058i	−0.338595	−	0.940932i	$-0.609952\pi$
$19$	1.64177	−	1.05510i	0.376649	−	0.242058i	0.715244	+	0.698875i	$0.246315\pi$
$20$		0			0
$21$	−1.87959	+	0.551896i	−0.410159	+	0.120434i
$22$		0			0
$23$	−4.35337	+	2.01202i	−0.907739	+	0.419534i
$23$	−4.35337	+	2.01202i	−0.907739	+	0.419534i
$24$		0			0
$25$	−6.80708	+	1.99874i	−1.36142	+	0.399748i
$26$		0			0
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$		0			0
$29$	4.69732	+	3.01878i	0.872270	+	0.560574i	0.898446	−	0.439083i	$-0.144697\pi$
$29$	4.69732	+	3.01878i	0.872270	+	0.560574i	−0.0261761	+	0.999657i	$0.508333\pi$
$30$		0			0
$31$	−4.53151	+	5.22964i	−0.813883	+	0.939271i	−0.999056	−	0.0434353i	$-0.986170\pi$
$31$	−4.53151	+	5.22964i	−0.813883	+	0.939271i	0.185174	+	0.982706i	$0.440715\pi$
$32$		0			0
$33$	1.98869	+	4.35463i	0.346187	+	0.758043i
$34$		0			0
$35$	−6.53665	−	1.91933i	−1.10490	−	0.324427i
$36$		0			0
$37$	1.36865	−	9.51916i	0.225004	−	1.56494i	−0.493705	−	0.869629i	$-0.664358\pi$
$37$	1.36865	−	9.51916i	0.225004	−	1.56494i	0.718710	−	0.695310i	$-0.244733\pi$
$38$		0			0
$39$	1.11537	−	2.44232i	0.178602	−	0.391084i
$40$		0			0
$41$	−1.09875	−	7.64196i	−0.171596	−	1.19347i	−0.875514	−	0.483193i	$-0.839477\pi$
$41$	−1.09875	−	7.64196i	−0.171596	−	1.19347i	0.703919	−	0.710281i	$-0.251432\pi$
$42$		0			0
$43$	−4.35629	−	5.02742i	−0.664328	−	0.766675i	0.319150	−	0.947704i	$-0.396603\pi$
$43$	−4.35629	−	5.02742i	−0.664328	−	0.766675i	−0.983478	+	0.181029i	$0.942057\pi$
$44$		0			0
$45$	3.47771			0.518426
$46$		0			0
$47$	−9.53389			−1.39066			−0.695330	−	0.718690i	$-0.744742\pi$
$47$	−9.53389			−1.39066			−0.695330	+	0.718690i	$0.744742\pi$
$48$		0			0
$49$	2.07104	+	2.39011i	0.295863	+	0.341444i
$50$		0			0
$51$	0.111269	+	0.773893i	0.0155808	+	0.108367i
$52$		0			0
$53$	2.18629	−	4.78731i	0.300310	−	0.657588i	−0.697975	−	0.716122i	$-0.745915\pi$
$53$	2.18629	−	4.78731i	0.300310	−	0.657588i	0.998285	+	0.0585343i	$0.0186427\pi$
$54$		0			0
$55$	−2.36935	+	16.4792i	−0.319483	+	2.22205i
$56$		0			0
$57$	−1.87253	−	0.549824i	−0.248022	−	0.0728260i
$58$		0			0
$59$	−4.02082	−	8.80436i	−0.523466	−	1.14623i	−0.968111	−	0.250524i	$-0.919397\pi$
$59$	−4.02082	−	8.80436i	−0.523466	−	1.14623i	0.444645	−	0.895707i	$-0.353330\pi$
$60$		0			0
$61$	1.63680	−	1.88897i	0.209571	−	0.241858i	−0.641226	−	0.767352i	$-0.721574\pi$
$61$	1.63680	−	1.88897i	0.209571	−	0.241858i	0.850797	+	0.525494i	$0.176119\pi$
$62$		0			0
$63$	1.64796	+	1.05908i	0.207624	+	0.133432i
$64$		0			0
$65$	7.85519	−	5.04822i	0.974316	−	0.626155i
$66$		0			0
$67$	6.98906	−	2.05217i	0.853850	−	0.250713i	0.174617	−	0.984636i	$-0.444131\pi$
$67$	6.98906	−	2.05217i	0.853850	−	0.250713i	0.679232	+	0.733923i	$0.262313\pi$
$68$		0			0
$69$	4.37143	+	1.97246i	0.526258	+	0.237457i
$70$		0			0
$71$	12.3486	−	3.62588i	1.46551	−	0.430313i	0.550874	−	0.834589i	$-0.314295\pi$
$71$	12.3486	−	3.62588i	1.46551	−	0.430313i	0.914637	+	0.404276i	$0.132476\pi$
$72$		0			0
$73$	1.04034	−	0.668588i	0.121763	−	0.0782523i	−0.478342	−	0.878174i	$-0.658762\pi$
$73$	1.04034	−	0.668588i	0.121763	−	0.0782523i	0.600105	+	0.799922i	$0.295126\pi$
$74$		0			0
$75$	5.96823	+	3.83555i	0.689152	+	0.442891i
$76$		0			0
$77$	−6.14122	+	7.08735i	−0.699857	+	0.807678i
$78$		0			0
$79$	2.10629	+	4.61213i	0.236976	+	0.518906i	0.990334	−	0.138706i	$-0.0442942\pi$
$79$	2.10629	+	4.61213i	0.236976	+	0.518906i	−0.753357	+	0.657611i	$0.771567\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−0.238762	+	1.66063i	−0.0262075	+	0.182277i	−0.998720	−	0.0505716i	$-0.983896\pi$
$83$	−0.238762	+	1.66063i	−0.0262075	+	0.182277i	0.972513	+	0.232849i	$0.0748048\pi$
$84$		0			0
$85$	−1.12953	+	2.47333i	−0.122515	+	0.268271i
$86$		0			0
$87$	−0.794645	−	5.52688i	−0.0851949	−	0.592544i
$88$		0			0
$89$	−0.717979	−	0.828591i	−0.0761056	−	0.0878305i	0.716420	−	0.697669i	$-0.245780\pi$
$89$	−0.717979	−	0.828591i	−0.0761056	−	0.0878305i	−0.792525	+	0.609839i	$0.791234\pi$
$90$		0			0
$91$	5.25965			0.551361
$92$		0			0
$93$	6.91980			0.717550
$94$		0			0
$95$	−4.44456	−	5.12929i	−0.456002	−	0.526255i
$96$		0			0
$97$	2.17166	+	15.1042i	0.220498	+	1.53360i	0.736161	+	0.676807i	$0.236637\pi$
$97$	2.17166	+	15.1042i	0.220498	+	1.53360i	−0.515662	+	0.856792i	$0.672454\pi$
$98$		0			0
$99$	1.98869	−	4.35463i	0.199871	−	0.437656i
$100$		0			0
$101$	−1.81783	+	12.6433i	−0.180881	+	1.25805i	0.673805	+	0.738909i	$0.264659\pi$
$101$	−1.81783	+	12.6433i	−0.180881	+	1.25805i	−0.854686	+	0.519145i	$0.826250\pi$
$102$		0			0
$103$	−1.67581	−	0.492063i	−0.165123	−	0.0484844i	0.198126	−	0.980177i	$-0.436514\pi$
$103$	−1.67581	−	0.492063i	−0.165123	−	0.0484844i	−0.363249	+	0.931692i	$0.618333\pi$
$104$		0			0
$105$	2.83006	+	6.19697i	0.276186	+	0.604762i
$106$		0			0
$107$	9.76717	−	11.2719i	0.944228	−	1.08970i	−0.0516206	−	0.998667i	$-0.516439\pi$
$107$	9.76717	−	11.2719i	0.944228	−	1.08970i	0.995848	−	0.0910299i	$-0.0290159\pi$
$108$		0			0
$109$	−15.9426	−	10.2457i	−1.52703	−	0.981362i	−0.990505	−	0.137476i	$-0.956101\pi$
$109$	−15.9426	−	10.2457i	−1.52703	−	0.981362i	−0.536523	−	0.843885i	$-0.680263\pi$
$110$		0			0
$111$	−8.09037	+	5.19937i	−0.767904	+	0.493502i
$112$		0			0
$113$	19.1673	−	5.62801i	1.80310	−	0.529439i	0.805132	−	0.593096i	$-0.202094\pi$
$113$	19.1673	−	5.62801i	1.80310	−	0.529439i	0.997972	+	0.0636565i	$0.0202762\pi$
$114$		0			0
$115$	9.08059	+	13.9898i	0.846770	+	1.30456i
$116$		0			0
$117$	−2.57619	+	0.756438i	−0.238169	+	0.0699327i
$118$		0			0
$119$	−1.28846	+	0.828044i	−0.118113	+	0.0759066i
$120$		0			0
$121$	10.0258	+	6.44318i	0.911435	+	0.585743i
$122$		0			0
$123$	−5.05588	+	5.83480i	−0.455873	+	0.526106i
$124$		0			0
$125$	3.02584	+	6.62567i	0.270640	+	0.592618i
$126$		0			0
$127$	4.56653	+	1.34085i	0.405214	+	0.118982i	0.477987	−	0.878367i	$-0.341367\pi$
$127$	4.56653	+	1.34085i	0.405214	+	0.118982i	−0.0727728	+	0.997349i	$0.523185\pi$
$128$		0			0
$129$	−0.946712	+	6.58452i	−0.0833533	+	0.579735i
$130$		0			0
$131$	6.33856	−	13.8795i	0.553802	−	1.21266i	−0.401181	−	0.915999i	$-0.631400\pi$
$131$	6.33856	−	13.8795i	0.553802	−	1.21266i	0.954983	−	0.296659i	$-0.0958726\pi$
$132$		0			0
$133$	−0.544073	−	3.78411i	−0.0471771	−	0.328124i
$134$		0			0
$135$	−2.27741	−	2.62828i	−0.196009	−	0.226206i
$136$		0			0
$137$	−9.87094			−0.843331			−0.421666	−	0.906751i	$-0.638554\pi$
$137$	−9.87094			−0.843331			−0.421666	+	0.906751i	$0.638554\pi$
$138$		0			0
$139$	0.680822			0.0577466			0.0288733	−	0.999583i	$-0.490808\pi$
$139$	0.680822			0.0577466			0.0288733	+	0.999583i	$0.490808\pi$
$140$		0			0
$141$	6.24337	+	7.20523i	0.525786	+	0.606790i
$142$		0			0
$143$	−1.82924	−	12.7227i	−0.152969	−	1.06392i
$144$		0			0
$145$	8.06675	−	17.6637i	0.669907	−	1.46689i
$146$		0			0
$147$	0.450080	−	3.13038i	0.0371220	−	0.258189i
$148$		0			0
$149$	−15.1664	−	4.45325i	−1.24248	−	0.364824i	−0.406532	−	0.913636i	$-0.633262\pi$
$149$	−15.1664	−	4.45325i	−1.24248	−	0.364824i	−0.835946	+	0.548812i	$0.815080\pi$
$150$		0			0
$151$	−1.68618	−	3.69222i	−0.137219	−	0.300468i	0.828530	−	0.559944i	$-0.189177\pi$
$151$	−1.68618	−	3.69222i	−0.137219	−	0.300468i	−0.965750	+	0.259476i	$0.916450\pi$
$152$		0			0
$153$	0.512003	−	0.590883i	0.0413930	−	0.0477701i
$154$		0			0
$155$	20.2448	+	13.0105i	1.62610	+	1.04503i
$156$		0			0
$157$	11.7845	−	7.57341i	0.940502	−	0.604424i	0.0219647	−	0.999759i	$-0.493008\pi$
$157$	11.7845	−	7.57341i	0.940502	−	0.604424i	0.918537	+	0.395335i	$0.129371\pi$
$158$		0			0
$159$	−5.04972	+	1.48273i	−0.400469	+	0.117588i
$160$		0			0
$161$	0.0425884	+	9.39464i	0.00335643	+	0.740401i
$162$		0			0
$163$	9.85476	−	2.89362i	0.771885	−	0.226646i	0.128006	−	0.991773i	$-0.459142\pi$
$163$	9.85476	−	2.89362i	0.771885	−	0.226646i	0.643879	+	0.765128i	$0.277324\pi$
$164$		0			0
$165$	14.0057	−	9.00093i	1.09034	−	0.700721i
$166$		0			0
$167$	−7.02980	−	4.51778i	−0.543983	−	0.349596i	0.239612	−	0.970869i	$-0.422980\pi$
$167$	−7.02980	−	4.51778i	−0.543983	−	0.349596i	−0.783595	+	0.621272i	$0.786616\pi$
$168$		0			0
$169$	3.79232	−	4.37657i	0.291717	−	0.336659i
$170$		0			0
$171$	0.810716	+	1.77522i	0.0619970	+	0.135755i
$172$		0			0
$173$	15.6187	+	4.58606i	1.18747	+	0.348672i	0.815049	−	0.579393i	$-0.196710\pi$
$173$	15.6187	+	4.58606i	1.18747	+	0.348672i	0.372419	+	0.928065i	$0.378528\pi$
$174$		0			0
$175$	−1.97783	+	13.7561i	−0.149510	+	1.03987i
$176$		0			0
$177$	−4.02082	+	8.80436i	−0.302223	+	0.661777i
$178$		0			0
$179$	3.05754	+	21.2657i	0.228532	+	1.58947i	0.704301	+	0.709901i	$0.251261\pi$
$179$	3.05754	+	21.2657i	0.228532	+	1.58947i	−0.475769	+	0.879570i	$0.657830\pi$
$180$		0			0
$181$	−3.70044	−	4.27054i	−0.275052	−	0.317427i	0.601370	−	0.798970i	$-0.294622\pi$
$181$	−3.70044	−	4.27054i	−0.275052	−	0.317427i	−0.876422	+	0.481544i	$0.840076\pi$
$182$		0			0
$183$	−2.49947			−0.184766
$184$		0			0
$185$	−33.4453			−2.45895
$186$		0			0
$187$	2.45108	+	2.82870i	0.179241	+	0.206855i
$188$		0			0
$189$	−0.278786	−	1.93900i	−0.0202787	−	0.141041i
$190$		0			0
$191$	−4.11208	+	9.00419i	−0.297539	+	0.651520i	−0.998070	−	0.0621021i	$-0.980220\pi$
$191$	−4.11208	+	9.00419i	−0.297539	+	0.651520i	0.700530	+	0.713623i	$0.252947\pi$
$192$		0			0
$193$	0.968890	−	6.73878i	0.0697422	−	0.485068i	−0.924777	−	0.380510i	$-0.875748\pi$
$193$	0.968890	−	6.73878i	0.0697422	−	0.485068i	0.994519	−	0.104557i	$-0.0333426\pi$
$194$		0			0
$195$	−8.95925	−	2.63067i	−0.641585	−	0.188386i
$196$		0			0
$197$	−5.54636	−	12.1448i	−0.395162	−	0.865283i	−0.997738	−	0.0672221i	$-0.978586\pi$
$197$	−5.54636	−	12.1448i	−0.395162	−	0.865283i	0.602576	−	0.798061i	$-0.294141\pi$
$198$		0			0
$199$	1.09992	−	1.26938i	0.0779714	−	0.0899837i	−0.715423	−	0.698691i	$-0.753766\pi$
$199$	1.09992	−	1.26938i	0.0779714	−	0.0899837i	0.793395	+	0.608707i	$0.208312\pi$
$200$		0			0
$201$	−6.12779	−	3.93809i	−0.432221	−	0.277772i
$202$		0			0
$203$	9.20175	−	5.91361i	0.645836	−	0.415054i
$204$		0			0
$205$	−25.7622	+	7.56446i	−1.79931	+	0.528325i
$206$		0			0
$207$	−1.37199	−	4.59539i	−0.0953598	−	0.319402i
$208$		0			0
$209$	−8.96424	+	2.63214i	−0.620070	+	0.182069i
$210$		0			0
$211$	15.2729	−	9.81529i	1.05143	−	0.675713i	0.103642	−	0.994615i	$-0.466950\pi$
$211$	15.2729	−	9.81529i	1.05143	−	0.675713i	0.947788	+	0.318902i	$0.103314\pi$
$212$		0			0
$213$	−10.8269	−	6.95801i	−0.741845	−	0.476755i
$214$		0			0
$215$	−15.1499	+	17.4839i	−1.03321	+	1.19239i
$216$		0			0
$217$	5.63114	+	12.3305i	0.382267	+	0.837047i
$218$		0			0
$219$	−1.18656	−	0.348407i	−0.0801806	−	0.0235431i
$220$		0			0
$221$	0.298752	−	2.07786i	0.0200962	−	0.139772i
$222$		0			0
$223$	5.90563	−	12.9315i	0.395470	−	0.865959i	−0.602239	−	0.798316i	$-0.705725\pi$
$223$	5.90563	−	12.9315i	0.395470	−	0.865959i	0.997710	−	0.0676436i	$-0.0215481\pi$
$224$		0			0
$225$	−1.00965	−	7.02224i	−0.0673097	−	0.468150i
$226$		0			0
$227$	−5.50271	−	6.35046i	−0.365228	−	0.421495i	0.543157	−	0.839631i	$-0.317229\pi$
$227$	−5.50271	−	6.35046i	−0.365228	−	0.421495i	−0.908384	+	0.418136i	$0.862683\pi$
$228$		0			0
$229$	−8.54683			−0.564790			−0.282395	−	0.959298i	$-0.591129\pi$
$229$	−8.54683			−0.564790			−0.282395	+	0.959298i	$0.591129\pi$
$230$		0			0
$231$	9.37790			0.617021
$232$		0			0
$233$	2.83509	+	3.27187i	0.185733	+	0.214347i	0.840978	−	0.541069i	$-0.181980\pi$
$233$	2.83509	+	3.27187i	0.185733	+	0.214347i	−0.655245	+	0.755416i	$0.727435\pi$
$234$		0			0
$235$	4.71860	+	32.8186i	0.307808	+	2.14085i
$236$		0			0
$237$	2.10629	−	4.61213i	0.136818	−	0.299590i
$238$		0			0
$239$	0.369517	−	2.57005i	0.0239021	−	0.166243i	−0.974374	−	0.224933i	$-0.927784\pi$
$239$	0.369517	−	2.57005i	0.0239021	−	0.166243i	0.998276	+	0.0586909i	$0.0186926\pi$
$240$		0			0
$241$	−19.3249	−	5.67431i	−1.24483	−	0.365515i	−0.408001	−	0.912981i	$-0.633774\pi$
$241$	−19.3249	−	5.67431i	−1.24483	−	0.365515i	−0.836827	+	0.547467i	$0.815592\pi$
$242$		0			0
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$		0			0
$245$	7.20247	−	8.31210i	0.460149	−	0.531040i
$246$		0			0
$247$	4.40808	+	2.83290i	0.280480	+	0.180253i
$248$		0			0
$249$	1.41137	−	0.907034i	0.0894421	−	0.0574810i
$250$		0			0
$251$	−18.8229	+	5.52689i	−1.18809	+	0.348854i	−0.815287	−	0.579057i	$-0.803421\pi$
$251$	−18.8229	+	5.52689i	−1.18809	+	0.348854i	−0.372801	+	0.927911i	$0.621603\pi$
$252$		0			0
$253$	22.7101	−	3.37036i	1.42777	−	0.211893i
$254$		0			0
$255$	2.60891	−	0.766045i	0.163376	−	0.0479716i
$256$		0			0
$257$	19.3919	−	12.4624i	1.20963	−	0.777383i	0.229035	−	0.973418i	$-0.426443\pi$
$257$	19.3919	−	12.4624i	1.20963	−	0.777383i	0.980597	+	0.196035i	$0.0628065\pi$
$258$		0			0
$259$	−15.8485	−	10.1852i	−0.984780	−	0.632879i
$260$		0			0
$261$	−3.65655	+	4.21989i	−0.226335	+	0.261205i
$262$		0			0
$263$	3.72845	+	8.16418i	0.229906	+	0.503425i	0.989065	−	0.147481i	$-0.0471166\pi$
$263$	3.72845	+	8.16418i	0.229906	+	0.503425i	−0.759159	+	0.650906i	$0.774389\pi$
$264$		0			0
$265$	−17.5615	−	5.15651i	−1.07879	−	0.316762i
$266$		0			0
$267$	−0.156032	+	1.08522i	−0.00954898	+	0.0664146i
$268$		0			0
$269$	−11.5144	+	25.2129i	−0.702043	+	1.53726i	0.135433	+	0.990786i	$0.456757\pi$
$269$	−11.5144	+	25.2129i	−0.702043	+	1.53726i	−0.837476	+	0.546474i	$0.815970\pi$
$270$		0			0
$271$	−1.15665	−	8.04471i	−0.0702617	−	0.488681i	−0.994320	−	0.106430i	$-0.966058\pi$
$271$	−1.15665	−	8.04471i	−0.0702617	−	0.488681i	0.924058	−	0.382251i	$-0.124851\pi$
$272$		0			0
$273$	−3.44434	−	3.97498i	−0.208461	−	0.240577i
$274$		0			0
$275$	33.9629			2.04804
$276$		0			0
$277$	−30.4776			−1.83122			−0.915611	−	0.402064i	$-0.868293\pi$
$277$	−30.4776			−1.83122			−0.915611	+	0.402064i	$0.868293\pi$
$278$		0			0
$279$	−4.53151	−	5.22964i	−0.271294	−	0.313090i
$280$		0			0
$281$	0.207093	+	1.44036i	0.0123541	+	0.0859247i	0.995066	−	0.0992184i	$-0.0316342\pi$
$281$	0.207093	+	1.44036i	0.0123541	+	0.0859247i	−0.982712	+	0.185143i	$0.940725\pi$
$282$		0			0
$283$	5.84591	−	12.8008i	0.347503	−	0.760926i	−0.652492	−	0.757796i	$-0.726276\pi$
$283$	5.84591	−	12.8008i	0.347503	−	0.760926i	0.999995	−	0.00313032i	$-0.000996413\pi$
$284$		0			0
$285$	−0.965895	+	6.71795i	−0.0572147	+	0.397937i
$286$		0			0
$287$	−14.5114	−	4.26094i	−0.856582	−	0.251515i
$288$		0			0
$289$	−6.80812	−	14.9077i	−0.400477	−	0.876923i
$290$		0			0
$291$	9.99286	−	11.5324i	0.585792	−	0.676040i
$292$		0			0
$293$	16.1328	+	10.3679i	0.942490	+	0.605702i	0.919100	−	0.394025i	$-0.128918\pi$
$293$	16.1328	+	10.3679i	0.942490	+	0.605702i	0.0233905	+	0.999726i	$0.492554\pi$
$294$		0			0
$295$	−28.3173	+	18.1984i	−1.64870	+	1.05955i
$296$		0			0
$297$	−4.59332	+	1.34872i	−0.266532	+	0.0782608i
$298$		0			0
$299$	−9.76959	−	8.38816i	−0.564990	−	0.485100i
$300$		0			0
$301$	−12.5034	+	3.67134i	−0.720687	+	0.211613i
$302$		0			0
$303$	10.7456	−	6.90577i	0.617318	−	0.396726i
$304$		0			0
$305$	−7.31253	−	4.69948i	−0.418714	−	0.269091i
$306$		0			0
$307$	8.30818	−	9.58815i	0.474173	−	0.547225i	−0.467395	−	0.884049i	$-0.654807\pi$
$307$	8.30818	−	9.58815i	0.474173	−	0.547225i	0.941568	+	0.336824i	$0.109353\pi$
$308$		0			0
$309$	0.725548	+	1.58873i	0.0412750	+	0.0903796i
$310$		0			0
$311$	14.6484	+	4.30116i	0.830636	+	0.243897i	0.669290	−	0.743001i	$-0.266598\pi$
$311$	14.6484	+	4.30116i	0.830636	+	0.243897i	0.161346	+	0.986898i	$0.448417\pi$
$312$		0			0
$313$	1.45255	−	10.1027i	0.0821033	−	0.571041i	−0.906695	−	0.421786i	$-0.861403\pi$
$313$	1.45255	−	10.1027i	0.0821033	−	0.571041i	0.988799	−	0.149255i	$-0.0476875\pi$
$314$		0			0
$315$	2.83006	−	6.19697i	0.159456	−	0.349160i
$316$		0			0
$317$	4.60658	+	32.0395i	0.258731	+	1.79952i	0.541897	+	0.840445i	$0.317706\pi$
$317$	4.60658	+	32.0395i	0.258731	+	1.79952i	−0.283165	+	0.959071i	$0.591384\pi$
$318$		0			0
$319$	−17.5048	−	20.2016i	−0.980081	−	1.13107i
$320$		0			0
$321$	−14.9149			−0.832467
$322$		0			0
$323$	−1.52585			−0.0849003
$324$		0			0
$325$	−12.4740	−	14.3957i	−0.691931	−	0.798531i
$326$		0			0
$327$	2.69702	+	18.7582i	0.149145	+	1.03733i
$328$		0			0
$329$	−7.75841	+	16.9885i	−0.427735	+	0.936609i
$330$		0			0
$331$	−0.975639	+	6.78572i	−0.0536259	+	0.372977i	0.945282	+	0.326254i	$0.105787\pi$
$331$	−0.975639	+	6.78572i	−0.0536259	+	0.372977i	−0.998908	+	0.0467222i	$0.985122\pi$
$332$		0			0
$333$	9.22749	+	2.70943i	0.505663	+	0.148476i
$334$		0			0
$335$	−10.5233	−	23.0428i	−0.574950	−	1.25896i
$336$		0			0
$337$	−8.14053	+	9.39467i	−0.443443	+	0.511761i	−0.932835	−	0.360303i	$-0.882673\pi$
$337$	−8.14053	+	9.39467i	−0.443443	+	0.511761i	0.489392	+	0.872064i	$0.337219\pi$
$338$		0			0
$339$	−16.8053	−	10.8001i	−0.912736	−	0.586580i
$340$		0			0
$341$	27.8680	−	17.9097i	1.50914	−	0.969863i
$342$		0			0
$343$	19.1014	−	5.60868i	1.03138	−	0.302840i
$344$		0			0
$345$	4.62628	−	16.0240i	0.249071	−	0.862705i
$346$		0			0
$347$	19.0237	−	5.58587i	1.02125	−	0.299865i	0.272100	−	0.962269i	$-0.412282\pi$
$347$	19.0237	−	5.58587i	1.02125	−	0.299865i	0.749147	+	0.662404i	$0.230464\pi$
$348$		0			0
$349$	−23.4108	+	15.0452i	−1.25315	+	0.805350i	−0.987331	−	0.158673i	$-0.949278\pi$
$349$	−23.4108	+	15.0452i	−1.25315	+	0.805350i	−0.265818	+	0.964023i	$0.585642\pi$
$350$		0			0
$351$	2.25873	+	1.45159i	0.120562	+	0.0774804i
$352$		0			0
$353$	15.2040	−	17.5464i	0.809227	−	0.933898i	−0.189622	−	0.981857i	$-0.560726\pi$
$353$	15.2040	−	17.5464i	0.809227	−	0.933898i	0.998849	+	0.0479592i	$0.0152717\pi$
$354$		0			0
$355$	−18.5931	−	40.7132i	−0.986819	−	2.16083i
$356$		0			0
$357$	1.46956	+	0.431501i	0.0777772	+	0.0228374i
$358$		0			0
$359$	−2.16766	+	15.0764i	−0.114405	+	0.795702i	0.849143	+	0.528164i	$0.177119\pi$
$359$	−2.16766	+	15.0764i	−0.114405	+	0.795702i	−0.963547	+	0.267538i	$0.913790\pi$
$360$		0			0
$361$	−6.31071	+	13.8185i	−0.332142	+	0.727291i
$362$		0			0
$363$	−1.69606	−	11.7964i	−0.0890201	−	0.619148i
$364$		0			0
$365$	−2.81638	−	3.25028i	−0.147416	−	0.170127i
$366$		0			0
$367$	16.0454			0.837561			0.418781	−	0.908087i	$-0.362458\pi$
$367$	16.0454			0.837561			0.418781	+	0.908087i	$0.362458\pi$
$368$		0			0
$369$	7.72054			0.401915
$370$		0			0
$371$	−6.75142	−	7.79156i	−0.350516	−	0.404517i
$372$		0			0
$373$	4.42909	+	30.8050i	0.229329	+	1.59502i	0.700944	+	0.713216i	$0.252762\pi$
$373$	4.42909	+	30.8050i	0.229329	+	1.59502i	−0.471615	+	0.881805i	$0.656329\pi$
$374$		0			0
$375$	3.02584	−	6.62567i	0.156254	−	0.342148i
$376$		0			0
$377$	−2.13358	+	14.8394i	−0.109885	+	0.764268i
$378$		0			0
$379$	13.9795	+	4.10475i	0.718078	+	0.210847i	0.620303	−	0.784362i	$-0.287009\pi$
$379$	13.9795	+	4.10475i	0.718078	+	0.210847i	0.0977744	+	0.995209i	$0.468828\pi$
$380$		0			0
$381$	−1.97709	−	4.32923i	−0.101290	−	0.221793i
$382$		0			0
$383$	−14.9813	+	17.2893i	−0.765508	+	0.883444i	−0.995975	−	0.0896368i	$-0.971429\pi$
$383$	−14.9813	+	17.2893i	−0.765508	+	0.883444i	0.230466	+	0.973080i	$0.425975\pi$
$384$		0			0
$385$	27.4363	+	17.6322i	1.39828	+	0.898623i
$386$		0			0
$387$	5.59622	−	3.59647i	0.284472	−	0.182819i
$388$		0			0
$389$	4.30401	−	1.26377i	0.218222	−	0.0640757i	−0.170794	−	0.985307i	$-0.554633\pi$
$389$	4.30401	−	1.26377i	0.218222	−	0.0640757i	0.389016	+	0.921231i	$0.372815\pi$
$390$		0			0
$391$	3.71384	+	0.516797i	0.187817	+	0.0261355i
$392$		0			0
$393$	−14.6403	+	4.29878i	−0.738506	+	0.216845i
$394$		0			0
$395$	14.8339	−	9.53319i	0.746376	−	0.479667i
$396$		0			0
$397$	−11.3871	−	7.31802i	−0.571500	−	0.367281i	0.222747	−	0.974876i	$-0.428498\pi$
$397$	−11.3871	−	7.31802i	−0.571500	−	0.367281i	−0.794246	+	0.607596i	$0.792134\pi$
$398$		0			0
$399$	−2.50355	+	2.88925i	−0.125334	+	0.144643i
$400$		0			0
$401$	−3.64291	−	7.97686i	−0.181918	−	0.398346i	0.796600	−	0.604507i	$-0.206630\pi$
$401$	−3.64291	−	7.97686i	−0.181918	−	0.398346i	−0.978518	+	0.206162i	$0.933903\pi$
$402$		0			0
$403$	−17.8267	−	5.23440i	−0.888013	−	0.260744i
$404$		0			0
$405$	−0.494929	+	3.44231i	−0.0245932	+	0.171050i
$406$		0			0
$407$	−19.1253	+	41.8786i	−0.948008	+	2.07585i
$408$		0			0
$409$	−3.39717	−	23.6278i	−0.167979	−	1.16832i	−0.883053	−	0.469272i	$-0.844516\pi$
$409$	−3.39717	−	23.6278i	−0.167979	−	1.16832i	0.715074	−	0.699049i	$-0.246393\pi$
$410$		0			0
$411$	6.46409	+	7.45996i	0.318850	+	0.367973i
$412$		0			0
$413$	−18.9606			−0.932992
$414$		0			0
$415$	5.83456			0.286407
$416$		0			0
$417$	−0.445844	−	0.514531i	−0.0218331	−	0.0251967i
$418$		0			0
$419$	4.29284	+	29.8574i	0.209719	+	1.45863i	0.774074	+	0.633095i	$0.218216\pi$
$419$	4.29284	+	29.8574i	0.209719	+	1.45863i	−0.564355	+	0.825532i	$0.690875\pi$
$420$		0			0
$421$	6.65925	−	14.5817i	0.324552	−	0.710670i	−0.675081	−	0.737743i	$-0.735892\pi$
$421$	6.65925	−	14.5817i	0.324552	−	0.710670i	0.999633	+	0.0270734i	$0.00861880\pi$
$422$		0			0
$423$	1.35681	−	9.43685i	0.0659705	−	0.458835i
$424$		0			0
$425$	5.32212	+	1.56272i	0.258161	+	0.0758028i
$426$		0			0
$427$	−2.03400	−	4.45383i	−0.0984320	−	0.215536i
$428$		0			0
$429$	−8.41726	+	9.71403i	−0.406389	+	0.468998i
$430$		0			0
$431$	24.9902	+	16.0602i	1.20373	+	0.773593i	0.979598	−	0.200965i	$-0.0644078\pi$
$431$	24.9902	+	16.0602i	1.20373	+	0.773593i	0.224135	+	0.974558i	$0.428044\pi$
$432$		0			0
$433$	29.3774	−	18.8797i	1.41179	−	0.907301i	0.411796	−	0.911276i	$-0.364902\pi$
$433$	29.3774	−	18.8797i	1.41179	−	0.907301i	0.999992	+	0.00397513i	$0.00126533\pi$
$434$		0			0
$435$	−18.6319	+	5.47083i	−0.893333	+	0.262306i
$436$		0			0
$437$	−5.02436	+	7.89653i	−0.240348	+	0.377742i
$438$		0			0
$439$	−35.9865	+	10.5666i	−1.71754	+	0.504316i	−0.984428	−	0.175791i	$-0.943752\pi$
$439$	−35.9865	+	10.5666i	−1.71754	+	0.504316i	−0.733114	+	0.680106i	$0.761934\pi$
$440$		0			0
$441$	−2.66052	+	1.70981i	−0.126691	+	0.0814196i
$442$		0			0
$443$	−3.96214	−	2.54631i	−0.188247	−	0.120979i	0.443123	−	0.896461i	$-0.353871\pi$
$443$	−3.96214	−	2.54631i	−0.188247	−	0.120979i	−0.631370	+	0.775482i	$0.717507\pi$
$444$		0			0
$445$	−2.49692	+	2.88160i	−0.118365	+	0.136601i
$446$		0			0
$447$	6.56632	+	14.3782i	0.310576	+	0.680067i
$448$		0			0
$449$	−28.6039	−	8.39886i	−1.34990	−	0.396367i	−0.474709	−	0.880143i	$-0.657447\pi$
$449$	−28.6039	−	8.39886i	−1.34990	−	0.396367i	−0.875192	+	0.483776i	$0.839265\pi$
$450$		0			0
$451$	−5.25997	+	36.5839i	−0.247682	+	1.72267i
$452$		0			0
$453$	−1.68618	+	3.69222i	−0.0792236	+	0.173476i
$454$		0			0
$455$	−2.60316	−	18.1054i	−0.122038	−	0.848792i
$456$		0			0
$457$	26.0773	+	30.0948i	1.21985	+	1.40778i	0.885057	+	0.465483i	$0.154119\pi$
$457$	26.0773	+	30.0948i	1.21985	+	1.40778i	0.334788	+	0.942293i	$0.391335\pi$
$458$		0			0
$459$	−0.781851			−0.0364937
$460$		0			0
$461$	−8.59838			−0.400467			−0.200233	−	0.979748i	$-0.564170\pi$
$461$	−8.59838			−0.400467			−0.200233	+	0.979748i	$0.564170\pi$
$462$		0			0
$463$	21.0242	+	24.2632i	0.977075	+	1.12760i	0.991811	+	0.127714i	$0.0407638\pi$
$463$	21.0242	+	24.2632i	0.977075	+	1.12760i	−0.0147358	+	0.999891i	$0.504691\pi$
$464$		0			0
$465$	−3.42481	−	23.8201i	−0.158822	−	1.10463i
$466$		0			0
$467$	−5.52919	+	12.1072i	−0.255860	+	0.560256i	−0.993354	−	0.115098i	$-0.963282\pi$
$467$	−5.52919	+	12.1072i	−0.255860	+	0.560256i	0.737494	+	0.675354i	$0.236009\pi$
$468$		0			0
$469$	2.03071	−	14.1239i	0.0937694	−	0.652181i
$470$		0			0
$471$	−13.4408	−	3.94657i	−0.619318	−	0.181848i
$472$		0			0
$473$	13.2292	+	28.9680i	0.608281	+	1.33195i
$474$		0			0
$475$	−9.06681	+	10.4637i	−0.416014	+	0.480106i
$476$		0			0
$477$	4.42744	+	2.84534i	0.202719	+	0.130279i
$478$		0			0
$479$	12.3565	−	7.94102i	0.564582	−	0.362835i	−0.227003	−	0.973894i	$-0.572893\pi$
$479$	12.3565	−	7.94102i	0.564582	−	0.362835i	0.791585	+	0.611059i	$0.209256\pi$
$480$		0			0
$481$	24.7754	−	7.27470i	1.12966	−	0.331698i
$482$		0			0
$483$	7.07210	−	6.18436i	0.321792	−	0.281398i
$484$		0			0
$485$	50.9185	−	14.9510i	2.31209	−	0.678891i
$486$		0			0
$487$	32.8637	−	21.1202i	1.48919	−	0.957047i	0.492987	−	0.870037i	$-0.335905\pi$
$487$	32.8637	−	21.1202i	1.48919	−	0.957047i	0.996207	−	0.0870105i	$-0.0277314\pi$
$488$		0			0
$489$	−8.64035	−	5.55282i	−0.390730	−	0.251107i
$490$		0			0
$491$	−11.6753	+	13.4741i	−0.526901	+	0.608076i	−0.955345	−	0.295492i	$-0.904516\pi$
$491$	−11.6753	+	13.4741i	−0.526901	+	0.608076i	0.428444	+	0.903568i	$0.359062\pi$
$492$		0			0
$493$	−1.81355	−	3.97112i	−0.0816781	−	0.178850i
$494$		0			0
$495$	−15.9742	−	4.69046i	−0.717989	−	0.210820i
$496$		0			0
$497$	3.58796	−	24.9548i	0.160942	−	1.11937i
$498$		0			0
$499$	−0.0869976	+	0.190498i	−0.00389455	+	0.00852787i	−0.911569	−	0.411147i	$-0.865128\pi$
$499$	−0.0869976	+	0.190498i	−0.00389455	+	0.00852787i	0.907675	+	0.419674i	$0.137856\pi$
$500$		0			0
$501$	1.18923	+	8.27129i	0.0531310	+	0.369534i
$502$		0			0
$503$	25.8003	+	29.7752i	1.15038	+	1.32761i	0.936467	+	0.350756i	$0.114075\pi$
$503$	25.8003	+	29.7752i	1.15038	+	1.32761i	0.213912	+	0.976853i	$0.431379\pi$
$504$		0			0
$505$	44.4218			1.97674
$506$		0			0
$507$	−5.79103			−0.257189
$508$		0			0
$509$	2.50672	+	2.89291i	0.111109	+	0.128226i	0.808579	−	0.588387i	$-0.200237\pi$
$509$	2.50672	+	2.89291i	0.111109	+	0.128226i	−0.697471	+	0.716613i	$0.745691\pi$
$510$		0			0
$511$	−0.344763	−	2.39788i	−0.0152514	−	0.106076i
$512$		0			0
$513$	0.810716	−	1.77522i	0.0357940	−	0.0783779i
$514$		0			0
$515$	−0.864425	+	6.01220i	−0.0380911	+	0.264929i
$516$		0			0
$517$	43.7922	+	12.8586i	1.92598	+	0.565519i
$518$		0			0
$519$	−6.76216	−	14.8071i	−0.296826	−	0.649958i
$520$		0			0
$521$	3.37200	−	3.89150i	0.147730	−	0.170490i	−0.677062	−	0.735926i	$-0.736747\pi$
$521$	3.37200	−	3.89150i	0.147730	−	0.170490i	0.824792	+	0.565437i	$0.191292\pi$
$522$		0			0
$523$	4.96011	+	3.18767i	0.216891	+	0.139387i	0.644575	−	0.764541i	$-0.277034\pi$
$523$	4.96011	+	3.18767i	0.216891	+	0.139387i	−0.427685	+	0.903928i	$0.640671\pi$
$524$		0			0
$525$	11.6914	−	7.51360i	0.510254	−	0.327921i
$526$		0			0
$527$	5.19110	−	1.52424i	0.226128	−	0.0663971i
$528$		0			0
$529$	14.9036	−	17.5181i	0.647982	−	0.761656i
$530$		0			0
$531$	9.28697	−	2.72690i	0.403020	−	0.118337i
$532$		0			0
$533$	17.4386	−	11.2071i	0.755349	−	0.485433i
$534$		0			0
$535$	−43.6355	−	28.0428i	−1.88653	−	1.21240i
$536$		0			0
$537$	14.0693	−	16.2368i	0.607134	−	0.700669i
$538$		0			0
$539$	−6.28937	−	13.7718i	−0.270902	−	0.593193i
$540$		0			0
$541$	30.5769	+	8.97820i	1.31461	+	0.386003i	0.862543	−	0.505983i	$-0.168870\pi$
$541$	30.5769	+	8.97820i	1.31461	+	0.386003i	0.452062	+	0.891986i	$0.350688\pi$
$542$		0			0
$543$	−0.804183	+	5.59322i	−0.0345108	+	0.240028i
$544$		0			0
$545$	−27.3784	+	59.9504i	−1.17276	+	2.56799i
$546$		0			0
$547$	−3.81241	−	26.5159i	−0.163007	−	1.13374i	−0.892926	−	0.450204i	$-0.851351\pi$
$547$	−3.81241	−	26.5159i	−0.163007	−	1.13374i	0.729919	−	0.683534i	$-0.239558\pi$
$548$		0			0
$549$	1.63680	+	1.88897i	0.0698571	+	0.0806194i
$550$		0			0
$551$	10.8971			0.464231
$552$		0			0
$553$	9.93246			0.422371
$554$		0			0
$555$	21.9020	+	25.2763i	0.929688	+	1.07292i
$556$		0			0
$557$	−4.70231	−	32.7053i	−0.199243	−	1.38577i	−0.806487	−	0.591251i	$-0.798634\pi$
$557$	−4.70231	−	32.7053i	−0.199243	−	1.38577i	0.607244	−	0.794515i	$-0.292275\pi$
$558$		0			0
$559$	7.41970	−	16.2469i	0.313820	−	0.687169i
$560$		0			0
$561$	0.532671	−	3.70481i	0.0224894	−	0.156417i
$562$		0			0
$563$	−33.8498	−	9.93918i	−1.42660	−	0.418887i	−0.524866	−	0.851185i	$-0.675885\pi$
$563$	−33.8498	−	9.93918i	−1.42660	−	0.418887i	−0.901731	+	0.432298i	$0.857703\pi$
$564$		0			0
$565$	−28.8598	−	63.1942i	−1.21414	−	2.65860i
$566$		0			0
$567$	−1.28283	+	1.48047i	−0.0538738	+	0.0621737i
$568$		0			0
$569$	17.6815	+	11.3632i	0.741248	+	0.476371i	0.855969	−	0.517027i	$-0.172961\pi$
$569$	17.6815	+	11.3632i	0.741248	+	0.476371i	−0.114721	+	0.993398i	$0.536598\pi$
$570$		0			0
$571$	26.9868	−	17.3433i	1.12936	−	0.725796i	0.163935	−	0.986471i	$-0.447581\pi$
$571$	26.9868	−	17.3433i	1.12936	−	0.725796i	0.965427	+	0.260675i	$0.0839451\pi$
$572$		0			0
$573$	9.49775	−	2.78879i	0.396774	−	0.116503i
$574$		0			0
$575$	25.6122	−	22.3972i	1.06810	−	0.934027i
$576$		0			0
$577$	−5.27905	+	1.55007i	−0.219770	+	0.0645303i	−0.389764	−	0.920915i	$-0.627443\pi$
$577$	−5.27905	+	1.55007i	−0.219770	+	0.0645303i	0.169994	+	0.985445i	$0.445625\pi$
$578$		0			0
$579$	−5.72732	+	3.68072i	−0.238019	+	0.152966i
$580$		0			0
$581$	2.76479	+	1.77682i	0.114703	+	0.0737150i
$582$		0			0
$583$	−16.4991	+	19.0410i	−0.683322	+	0.788596i
$584$		0			0
$585$	3.87893	+	8.49367i	0.160374	+	0.351170i
$586$		0			0
$587$	−20.5343	−	6.02940i	−0.847540	−	0.248860i	−0.171004	−	0.985270i	$-0.554701\pi$
$587$	−20.5343	−	6.02940i	−0.847540	−	0.248860i	−0.676535	+	0.736410i	$0.736519\pi$
$588$		0			0
$589$	−1.92190	+	13.3671i	−0.0791904	+	0.550782i
$590$		0			0
$591$	−5.54636	+	12.1448i	−0.228147	+	0.499572i
$592$		0			0
$593$	1.64447	+	11.4376i	0.0675304	+	0.469685i	0.995324	+	0.0965910i	$0.0307939\pi$
$593$	1.64447	+	11.4376i	0.0675304	+	0.469685i	−0.927794	+	0.373094i	$0.878297\pi$
$594$		0			0
$595$	3.48808	+	4.02546i	0.142997	+	0.165028i
$596$		0			0
$597$	−1.67963			−0.0687425
$598$		0			0
$599$	45.0442			1.84046			0.920229	−	0.391380i	$-0.128002\pi$
$599$	45.0442			1.84046			0.920229	+	0.391380i	$0.128002\pi$
$600$		0			0
$601$	4.03014	+	4.65103i	0.164393	+	0.189719i	0.831969	−	0.554822i	$-0.187214\pi$
$601$	4.03014	+	4.65103i	0.164393	+	0.189719i	−0.667576	+	0.744541i	$0.732668\pi$
$602$		0			0
$603$	1.03664	+	7.20998i	0.0422152	+	0.293613i
$604$		0			0
$605$	17.2174	−	37.7008i	0.699985	−	1.53275i
$606$		0			0
$607$	−4.59487	+	31.9580i	−0.186500	+	1.29714i	0.654484	+	0.756076i	$0.272886\pi$
$607$	−4.59487	+	31.9580i	−0.186500	+	1.29714i	−0.840984	+	0.541060i	$0.818023\pi$
$608$		0			0
$609$	−10.4951	−	3.08163i	−0.425282	−	0.124874i
$610$		0			0
$611$	−10.6338	−	23.2848i	−0.430198	−	0.942002i
$612$		0			0
$613$	−17.2368	+	19.8923i	−0.696186	+	0.803442i	−0.988232	−	0.152963i	$-0.951119\pi$
$613$	−17.2368	+	19.8923i	−0.696186	+	0.803442i	0.292046	+	0.956404i	$0.405664\pi$
$614$		0			0
$615$	22.5875	+	14.5161i	0.910815	+	0.585345i
$616$		0			0
$617$	−19.8534	+	12.7590i	−0.799269	+	0.513659i	−0.875377	−	0.483440i	$-0.839387\pi$
$617$	−19.8534	+	12.7590i	−0.799269	+	0.513659i	0.0761081	+	0.997100i	$0.475751\pi$
$618$		0			0
$619$	−22.1359	+	6.49968i	−0.889716	+	0.261244i	−0.694480	−	0.719512i	$-0.744366\pi$
$619$	−22.1359	+	6.49968i	−0.889716	+	0.261244i	−0.195236	+	0.980756i	$0.562547\pi$
$620$		0			0
$621$	−2.57451	+	4.04622i	−0.103311	+	0.162369i
$622$		0			0
$623$	−2.06075	+	0.605090i	−0.0825621	+	0.0242424i
$624$		0			0
$625$	−8.53114	+	5.48263i	−0.341246	+	0.219305i
$626$		0			0
$627$	7.85957	+	5.05104i	0.313881	+	0.201719i
$628$		0			0
$629$	−4.92396	+	5.68255i	−0.196331	+	0.226578i
$630$		0			0
$631$	−11.3572	−	24.8688i	−0.452123	−	0.990011i	−0.989213	−	0.146486i	$-0.953204\pi$
$631$	−11.3572	−	24.8688i	−0.452123	−	0.990011i	0.537090	−	0.843525i	$-0.319524\pi$
$632$		0			0
$633$	−17.4195	−	5.11483i	−0.692364	−	0.203296i
$634$		0			0
$635$	2.35553	−	16.3830i	0.0934762	−	0.650141i
$636$		0			0
$637$	−3.52743	+	7.72399i	−0.139762	+	0.306036i
$638$		0			0
$639$	1.83158	+	12.7389i	0.0724563	+	0.503945i
$640$		0			0
$641$	−6.48055	−	7.47895i	−0.255966	−	0.295401i	0.613193	−	0.789933i	$-0.289885\pi$
$641$	−6.48055	−	7.47895i	−0.255966	−	0.295401i	−0.869159	+	0.494532i	$0.835339\pi$
$642$		0			0
$643$	−7.28869			−0.287438			−0.143719	−	0.989619i	$-0.545906\pi$
$643$	−7.28869			−0.287438			−0.143719	+	0.989619i	$0.545906\pi$
$644$		0			0
$645$	23.1345			0.910921
$646$		0			0
$647$	−11.6533	−	13.4486i	−0.458137	−	0.528718i	0.478937	−	0.877849i	$-0.341022\pi$
$647$	−11.6533	−	13.4486i	−0.458137	−	0.528718i	−0.937074	+	0.349131i	$0.886477\pi$
$648$		0			0
$649$	6.59428	+	45.8643i	0.258848	+	1.80033i
$650$		0			0
$651$	5.63114	−	12.3305i	0.220702	−	0.483269i
$652$		0			0
$653$	−3.86489	+	26.8809i	−0.151245	+	1.05193i	0.762892	+	0.646525i	$0.223779\pi$
$653$	−3.86489	+	26.8809i	−0.151245	+	1.05193i	−0.914137	+	0.405405i	$0.867131\pi$
$654$		0			0
$655$	−50.9147	−	14.9499i	−1.98940	−	0.584141i
$656$		0			0
$657$	0.513726	+	1.12490i	0.0200424	+	0.0438867i
$658$		0			0
$659$	−8.40134	+	9.69566i	−0.327270	+	0.377689i	−0.895410	−	0.445242i	$-0.853118\pi$
$659$	−8.40134	+	9.69566i	−0.327270	+	0.377689i	0.568140	+	0.822932i	$0.307663\pi$
$660$		0			0
$661$	24.1159	+	15.4984i	0.938001	+	0.602816i	0.917827	−	0.396980i	$-0.129942\pi$
$661$	24.1159	+	15.4984i	0.938001	+	0.602816i	0.0201733	+	0.999796i	$0.493578\pi$
$662$		0			0
$663$	−1.76599	+	1.13493i	−0.0685852	+	0.0440770i
$664$		0			0
$665$	−12.7568	+	3.74574i	−0.494688	+	0.145253i
$666$		0			0
$667$	−26.5230	−	3.69079i	−1.02697	−	0.142908i
$668$		0			0
$669$	−13.6404	+	4.00517i	−0.527367	+	0.154849i
$670$		0			0
$671$	−10.0661	+	6.46907i	−0.388596	+	0.249736i
$672$		0			0
$673$	22.8250	+	14.6687i	0.879839	+	0.565438i	0.900748	−	0.434343i	$-0.143019\pi$
$673$	22.8250	+	14.6687i	0.879839	+	0.565438i	−0.0209084	+	0.999781i	$0.506656\pi$
$674$		0			0
$675$	−4.64588	+	5.36163i	−0.178820	+	0.206369i
$676$		0			0
$677$	−4.04075	−	8.84802i	−0.155299	−	0.340057i	0.815950	−	0.578122i	$-0.196214\pi$
$677$	−4.04075	−	8.84802i	−0.155299	−	0.340057i	−0.971249	+	0.238065i	$0.923487\pi$
$678$		0			0
$679$	28.6816	+	8.42167i	1.10070	+	0.323194i
$680$		0			0
$681$	−1.19585	+	8.31734i	−0.0458252	+	0.318721i
$682$		0			0
$683$	−4.92224	+	10.7782i	−0.188344	+	0.412416i	−0.980123	−	0.198392i	$-0.936428\pi$
$683$	−4.92224	+	10.7782i	−0.188344	+	0.412416i	0.791779	+	0.610808i	$0.209155\pi$
$684$		0			0
$685$	4.88542	+	33.9788i	0.186662	+	1.29826i
$686$		0			0
$687$	5.59698	+	6.45926i	0.213538	+	0.246436i
$688$		0			0
$689$	14.1307			0.538335
$690$		0			0
$691$	27.8293			1.05868			0.529338	−	0.848411i	$-0.322440\pi$
$691$	27.8293			1.05868			0.529338	+	0.848411i	$0.322440\pi$
$692$		0			0
$693$	−6.14122	−	7.08735i	−0.233286	−	0.269226i
$694$		0			0
$695$	−0.336959	−	2.34360i	−0.0127816	−	0.0888978i
$696$		0			0
$697$	−2.50757	+	5.49082i	−0.0949812	+	0.207980i
$698$		0			0
$699$	0.616124	−	4.28524i	0.0233040	−	0.162083i
$700$		0			0
$701$	38.5095	+	11.3074i	1.45448	+	0.427075i	0.911021	−	0.412359i	$-0.135295\pi$
$701$	38.5095	+	11.3074i	1.45448	+	0.427075i	0.543461	+	0.839434i	$0.317113\pi$
$702$		0			0
$703$	−7.79669	−	17.0724i	−0.294058	−	0.643897i
$704$		0			0
$705$	21.7126	−	25.0577i	0.817744	−	0.943727i
$706$		0			0
$707$	21.0499	+	13.5280i	0.791664	+	0.508772i
$708$		0			0
$709$	−18.2250	+	11.7125i	−0.684453	+	0.439871i	−0.836110	−	0.548562i	$-0.815175\pi$
$709$	−18.2250	+	11.7125i	−0.684453	+	0.439871i	0.151657	+	0.988433i	$0.451539\pi$
$710$		0			0
$711$	−4.86495	+	1.42848i	−0.182450	+	0.0535721i
$712$		0			0
$713$	9.20519	−	31.8840i	0.344737	−	1.19406i
$714$		0			0
$715$	−42.8901	+	12.5937i	−1.60400	+	0.470976i
$716$		0			0
$717$	−2.18429	+	1.40376i	−0.0815740	+	0.0524244i
$718$		0			0
$719$	−21.0447	−	13.5246i	−0.784835	−	0.504383i	0.0858003	−	0.996312i	$-0.472655\pi$
$719$	−21.0447	−	13.5246i	−0.784835	−	0.504383i	−0.870635	+	0.491930i	$0.836292\pi$
$720$		0			0
$721$	−2.24054	+	2.58572i	−0.0834422	+	0.0962974i
$722$		0			0
$723$	8.36678	+	18.3207i	0.311164	+	0.681354i
$724$		0			0
$725$	−38.0088	−	11.1604i	−1.41161	−	0.414486i
$726$		0			0
$727$	1.03915	−	7.22742i	0.0385398	−	0.268050i	−0.961436	−	0.275029i	$-0.911312\pi$
$727$	1.03915	−	7.22742i	0.0385398	−	0.268050i	0.999976	+	0.00697914i	$0.00222155\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	0.740187	+	5.14812i	0.0273768	+	0.190410i
$732$		0			0
$733$	−20.3213	−	23.4520i	−0.750583	−	0.866219i	0.244041	−	0.969765i	$-0.421527\pi$
$733$	−20.3213	−	23.4520i	−0.750583	−	0.866219i	−0.994625	+	0.103545i	$0.966981\pi$
$734$		0			0
$735$	−10.9985			−0.405685
$736$		0			0
$737$	−34.8708			−1.28448
$738$		0			0
$739$	15.8994	+	18.3489i	0.584868	+	0.674974i	0.968644	−	0.248452i	$-0.0799219\pi$
$739$	15.8994	+	18.3489i	0.584868	+	0.674974i	−0.383776	+	0.923426i	$0.625376\pi$
$740$		0			0
$741$	−0.745716	−	5.18657i	−0.0273945	−	0.190533i
$742$		0			0
$743$	5.71010	−	12.5034i	0.209483	−	0.458705i	−0.775501	−	0.631346i	$-0.782503\pi$
$743$	5.71010	−	12.5034i	0.209483	−	0.458705i	0.984985	+	0.172641i	$0.0552301\pi$
$744$		0			0
$745$	−7.82318	+	54.4114i	−0.286619	+	1.99348i
$746$		0			0
$747$	−1.60974	−	0.472663i	−0.0588974	−	0.0172938i
$748$		0			0
$749$	−12.1373	−	26.5770i	−0.443487	−	0.971102i
$750$		0			0
$751$	−11.9569	+	13.7990i	−0.436313	+	0.503533i	−0.930737	−	0.365688i	$-0.880834\pi$
$751$	−11.9569	+	13.7990i	−0.436313	+	0.503533i	0.494424	+	0.869221i	$0.335379\pi$
$752$		0			0
$753$	16.5033	+	10.6060i	0.601413	+	0.386505i
$754$		0			0
$755$	−11.8752	+	7.63174i	−0.432184	+	0.277747i
$756$		0			0
$757$	−4.23603	+	1.24381i	−0.153961	+	0.0452071i	−0.357805	−	0.933796i	$-0.616475\pi$
$757$	−4.23603	+	1.24381i	−0.153961	+	0.0452071i	0.203844	+	0.979003i	$0.434657\pi$
$758$		0			0
$759$	−17.4191	−	14.9560i	−0.632273	−	0.542869i
$760$		0			0
$761$	−23.1465	+	6.79641i	−0.839058	+	0.246370i	−0.672904	−	0.739730i	$-0.734953\pi$
$761$	−23.1465	+	6.79641i	−0.839058	+	0.246370i	−0.166155	+	0.986100i	$0.553135\pi$
$762$		0			0
$763$	−31.2306	+	20.0707i	−1.13062	+	0.726609i
$764$		0			0
$765$	−2.28741	−	1.47003i	−0.0827015	−	0.0531490i
$766$		0			0
$767$	17.0184	−	19.6402i	0.614497	−	0.709168i
$768$		0			0
$769$	−6.01490	−	13.1708i	−0.216903	−	0.474951i	0.769635	−	0.638484i	$-0.220438\pi$
$769$	−6.01490	−	13.1708i	−0.216903	−	0.474951i	−0.986538	+	0.163533i	$0.947711\pi$
$770$		0			0
$771$	−22.1174	−	6.49427i	−0.796540	−	0.233885i
$772$		0			0
$773$	1.03258	−	7.18173i	0.0371392	−	0.258309i	−0.962789	−	0.270253i	$-0.912893\pi$
$773$	1.03258	−	7.18173i	0.0371392	−	0.258309i	0.999929	+	0.0119436i	$0.00380186\pi$
$774$		0			0
$775$	20.3936	−	44.6559i	0.732561	−	1.60409i
$776$		0			0
$777$	2.68110	+	18.6474i	0.0961838	+	0.668973i
$778$		0			0
$779$	−9.86696	−	11.3871i	−0.353520	−	0.407984i
$780$		0			0
$781$	−61.6115			−2.20463
$782$		0			0
$783$	5.58371			0.199546
$784$		0			0
$785$	−31.9025	−	36.8174i	−1.13865	−	1.31407i
$786$		0			0
$787$	−0.885248	−	6.15704i	−0.0315557	−	0.219475i	0.967942	−	0.251175i	$-0.0808169\pi$
$787$	−0.885248	−	6.15704i	−0.0315557	−	0.219475i	−0.999497	+	0.0317002i	$0.989908\pi$
$788$		0			0
$789$	3.72845	−	8.16418i	0.132736	−	0.290652i
$790$		0			0
$791$	5.56915	−	38.7343i	0.198016	−	1.37723i
$792$		0			0
$793$	6.43911	+	1.89069i	0.228660	+	0.0671405i
$794$		0			0
$795$	7.60328	+	16.6489i	0.269661	+	0.590474i
$796$		0			0
$797$	17.9235	−	20.6848i	0.634882	−	0.732693i	−0.343579	−	0.939124i	$-0.611639\pi$
$797$	17.9235	−	20.6848i	0.634882	−	0.732693i	0.978461	+	0.206431i	$0.0661848\pi$
$798$		0			0
$799$	6.27077	+	4.02998i	0.221844	+	0.142570i
$800$		0			0
$801$	0.922337	−	0.592750i	0.0325892	−	0.0209438i
$802$		0			0
$803$	−5.68037	+	1.66791i	−0.200456	+	0.0588591i
$804$		0			0
$805$	32.3182	−	4.79628i	1.13907	−	0.169047i
$806$		0			0
$807$	26.5950	−	7.80899i	0.936187	−	0.274889i
$808$		0			0
$809$	23.5764	−	15.1517i	0.828903	−	0.532704i	−0.0560260	−	0.998429i	$-0.517843\pi$
$809$	23.5764	−	15.1517i	0.828903	−	0.532704i	0.884929	+	0.465726i	$0.154207\pi$
$810$		0			0
$811$	−13.1542	−	8.45371i	−0.461907	−	0.296850i	0.288914	−	0.957355i	$-0.406706\pi$
$811$	−13.1542	−	8.45371i	−0.461907	−	0.296850i	−0.750821	+	0.660505i	$0.770342\pi$
$812$		0			0
$813$	−5.32234	+	6.14230i	−0.186662	+	0.215420i
$814$		0			0
$815$	−14.8381	−	32.4910i	−0.519758	−	1.13811i
$816$		0			0
$817$	−12.4565	−	3.65756i	−0.435798	−	0.127962i
$818$		0			0
$819$	−0.748526	+	5.20612i	−0.0261556	+	0.181916i
$820$		0			0
$821$	−1.00611	+	2.20308i	−0.0351135	+	0.0768879i	−0.926376	−	0.376600i	$-0.877093\pi$
$821$	−1.00611	+	2.20308i	−0.0351135	+	0.0768879i	0.891262	+	0.453488i	$0.149820\pi$
$822$		0			0
$823$	1.15553	+	8.03688i	0.0402792	+	0.280148i	1.00000		0.000808517i	$-0.000257359\pi$
$823$	1.15553	+	8.03688i	0.0402792	+	0.280148i	−0.959720	+	0.280957i	$0.909348\pi$
$824$		0			0
$825$	−22.2409	−	25.6674i	−0.774330	−	0.893625i
$826$		0			0
$827$	18.6273			0.647733			0.323867	−	0.946103i	$-0.395017\pi$
$827$	18.6273			0.647733			0.323867	+	0.946103i	$0.395017\pi$
$828$		0			0
$829$	−18.3320			−0.636696			−0.318348	−	0.947974i	$-0.603128\pi$
$829$	−18.3320			−0.636696			−0.318348	+	0.947974i	$0.603128\pi$
$830$		0			0
$831$	19.9586	+	23.0335i	0.692356	+	0.799022i
$832$		0			0
$833$	−0.351895	−	2.44749i	−0.0121925	−	0.0848004i
$834$		0			0
$835$	−12.0723	+	26.4347i	−0.417781	+	0.914812i
$836$		0			0
$837$	−0.984790	+	6.84937i	−0.0340393	+	0.236749i
$838$		0			0
$839$	−46.6621	−	13.7012i	−1.61096	−	0.473019i	−0.652388	−	0.757885i	$-0.726233\pi$
$839$	−46.6621	−	13.7012i	−1.61096	−	0.473019i	−0.958567	+	0.284866i	$0.908051\pi$
$840$		0			0
$841$	0.904715	+	1.98105i	0.0311971	+	0.0683121i
$842$		0			0
$843$	0.952935	−	1.09975i	0.0328208	−	0.0378772i
$844$		0			0
$845$	−16.9424	−	10.8883i	−0.582838	−	0.374567i
$846$		0			0
$847$	19.6399	−	12.6218i	0.674834	−	0.433689i
$848$		0			0
$849$	−13.5024	+	3.96467i	−0.463402	+	0.136067i
$850$		0			0
$851$	13.1945	+	44.1941i	0.452301	+	1.51495i
$852$		0			0
$853$	27.1744	−	7.97913i	0.930434	−	0.273200i	0.218816	−	0.975766i	$-0.429781\pi$
$853$	27.1744	−	7.97913i	0.930434	−	0.273200i	0.711619	+	0.702566i	$0.247962\pi$
$854$		0			0
$855$	5.70961	−	3.66935i	0.195265	−	0.125489i
$856$		0			0
$857$	−11.4943	−	7.38694i	−0.392638	−	0.252333i	0.329394	−	0.944192i	$-0.393155\pi$
$857$	−11.4943	−	7.38694i	−0.392638	−	0.252333i	−0.722032	+	0.691859i	$0.756792\pi$
$858$		0			0
$859$	−20.4653	+	23.6182i	−0.698267	+	0.805843i	−0.988517	−	0.151108i	$-0.951716\pi$
$859$	−20.4653	+	23.6182i	−0.698267	+	0.805843i	0.290250	+	0.956951i	$0.406261\pi$
$860$		0			0
$861$	6.28276	+	13.7573i	0.214116	+	0.468848i
$862$		0			0
$863$	10.3217	+	3.03072i	0.351355	+	0.103167i	0.452647	−	0.891690i	$-0.350480\pi$
$863$	10.3217	+	3.03072i	0.351355	+	0.103167i	−0.101293	+	0.994857i	$0.532298\pi$
$864$		0			0
$865$	8.05650	−	56.0342i	0.273929	−	1.90522i
$866$		0			0
$867$	−6.80812	+	14.9077i	−0.231216	+	0.506292i
$868$		0			0
$869$	−3.45439	−	24.0258i	−0.117182	−	0.815020i
$870$		0			0
$871$	12.8074	+	14.7806i	0.433964	+	0.500821i
$872$		0			0
$873$	−15.2595			−0.516456
$874$		0			0
$875$	14.2687			0.482370
$876$		0			0
$877$	−16.2873	−	18.7966i	−0.549984	−	0.634715i	0.410896	−	0.911682i	$-0.365216\pi$
$877$	−16.2873	−	18.7966i	−0.549984	−	0.634715i	−0.960879	+	0.276967i	$0.910671\pi$
$878$		0			0
$879$	−2.72919	−	18.9819i	−0.0920533	−	0.640245i
$880$		0			0
$881$	14.6425	−	32.0627i	0.493320	−	1.08022i	−0.485264	−	0.874368i	$-0.661276\pi$
$881$	14.6425	−	32.0627i	0.493320	−	1.08022i	0.978583	−	0.205851i	$-0.0659963\pi$
$882$		0			0
$883$	7.54633	−	52.4859i	0.253954	−	1.76629i	−0.320014	−	0.947413i	$-0.603688\pi$
$883$	7.54633	−	52.4859i	0.253954	−	1.76629i	0.573969	−	0.818877i	$-0.305403\pi$
$884$		0			0
$885$	32.2974	+	9.48337i	1.08566	+	0.318780i
$886$		0			0
$887$	7.03606	+	15.4068i	0.236248	+	0.517310i	0.990206	−	0.139611i	$-0.0445854\pi$
$887$	7.03606	+	15.4068i	0.236248	+	0.517310i	−0.753959	+	0.656922i	$0.771858\pi$
$888$		0			0
$889$	6.10540	−	7.04601i	0.204769	−	0.236316i
$890$		0			0
$891$	4.02728	+	2.58818i	0.134919	+	0.0867072i
$892$		0			0
$893$	−15.6525	+	10.0592i	−0.523791	+	0.336620i
$894$		0			0
$895$	71.6898	−	21.0500i	2.39633	−	0.703625i
$896$		0			0
$897$	0.0583724	+	12.8764i	0.00194900	+	0.429932i
$898$		0			0
$899$	−37.0731	+	10.8856i	−1.23646	+	0.363056i
$900$		0			0
$901$	−3.46160	+	2.22463i	−0.115323	+	0.0741133i
$902$		0			0
$903$	10.9626	+	7.04526i	0.364814	+	0.234451i
$904$		0			0
$905$	−12.8691	+	14.8517i	−0.427782	+	0.493687i
$906$		0			0
$907$	−21.7905	−	47.7145i	−0.723541	−	1.58433i	−0.808874	−	0.587982i	$-0.799922\pi$
$907$	−21.7905	−	47.7145i	−0.723541	−	1.58433i	0.0853324	−	0.996353i	$-0.472805\pi$
$908$		0			0
$909$	−12.2559	−	3.59866i	−0.406502	−	0.119360i
$910$		0			0
$911$	−2.17598	+	15.1343i	−0.0720935	+	0.501421i	0.921497	+	0.388385i	$0.126967\pi$
$911$	−2.17598	+	15.1343i	−0.0720935	+	0.501421i	−0.993591	+	0.113036i	$0.963942\pi$
$912$		0			0
$913$	3.33643	−	7.30577i	0.110420	−	0.241786i
$914$		0			0
$915$	1.23706	+	8.60395i	0.0408960	+	0.284438i
$916$		0			0
$917$	−19.5739	−	22.5895i	−0.646388	−	0.745971i
$918$		0			0
$919$	−9.84503			−0.324758			−0.162379	−	0.986728i	$-0.551917\pi$
$919$	−9.84503			−0.324758			−0.162379	+	0.986728i	$0.551917\pi$
$920$		0			0
$921$	−12.6869			−0.418049
$922$		0			0
$923$	22.6288	+	26.1150i	0.744836	+	0.859587i
$924$		0			0
$925$	9.70981	+	67.5332i	0.319257	+	2.22048i
$926$		0			0
$927$	0.725548	−	1.58873i	0.0238301	−	0.0521807i
$928$		0			0
$929$	−2.25431	+	15.6790i	−0.0739614	+	0.514413i	0.918839	+	0.394632i	$0.129128\pi$
$929$	−2.25431	+	15.6790i	−0.0739614	+	0.514413i	−0.992800	+	0.119780i	$0.961781\pi$
$930$		0			0
$931$	5.92199	+	1.73885i	0.194086	+	0.0569886i
$932$		0			0
$933$	−6.34207	−	13.8872i	−0.207630	−	0.454647i
$934$		0			0
$935$	8.52415	−	9.83740i	0.278770	−	0.321717i
$936$		0			0
$937$	32.9205	+	21.1567i	1.07547	+	0.691160i	0.953506	−	0.301375i	$-0.0974456\pi$
$937$	32.9205	+	21.1567i	1.07547	+	0.691160i	0.121960	+	0.992535i	$0.461082\pi$
$938$		0			0
$939$	−8.58636	+	5.51812i	−0.280205	+	0.180077i
$940$		0			0
$941$	−58.2305	+	17.0980i	−1.89826	+	0.557379i	−0.907833	+	0.419331i	$0.862265\pi$
$941$	−58.2305	+	17.0980i	−1.89826	+	0.557379i	−0.990426	+	0.138048i	$0.955917\pi$
$942$		0			0
$943$	20.1590	+	31.0575i	0.656467	+	1.01137i
$944$		0			0
$945$	−6.53665	+	1.91933i	−0.212637	+	0.0624360i
$946$		0			0
$947$	−12.2892	+	7.89777i	−0.399344	+	0.256643i	−0.724864	−	0.688892i	$-0.758097\pi$
$947$	−12.2892	+	7.89777i	−0.399344	+	0.256643i	0.325519	+	0.945535i	$0.394461\pi$
$948$		0			0
$949$	2.79327	+	1.79513i	0.0906734	+	0.0582722i
$950$		0			0
$951$	21.1972	−	24.4628i	0.687365	−	0.793261i
$952$		0			0
$953$	−5.21305	−	11.4150i	−0.168867	−	0.369768i	0.806211	−	0.591628i	$-0.201514\pi$
$953$	−5.21305	−	11.4150i	−0.168867	−	0.369768i	−0.975079	+	0.221860i	$0.928787\pi$
$954$		0			0
$955$	33.0304	+	9.69860i	1.06884	+	0.313839i
$956$		0			0
$957$	−3.80416	+	26.4585i	−0.122971	+	0.855282i
$958$		0			0
$959$	−8.03269	+	17.5891i	−0.259389	+	0.567983i
$960$		0			0
$961$	−2.40279	−	16.7118i	−0.0775095	−	0.539090i
$962$		0			0
$963$	9.76717	+	11.2719i	0.314743	+	0.363232i
$964$		0			0
$965$	−23.6765			−0.762173
$966$		0			0
$967$	−56.9568			−1.83161			−0.915803	−	0.401628i	$-0.868444\pi$
$967$	−56.9568			−1.83161			−0.915803	+	0.401628i	$0.868444\pi$
$968$		0			0
$969$	0.999216	+	1.15316i	0.0320994	+	0.0370447i
$970$		0			0
$971$	1.12474	+	7.82272i	0.0360946	+	0.251043i	0.999878	−	0.0156443i	$-0.00497995\pi$
$971$	1.12474	+	7.82272i	0.0360946	+	0.251043i	−0.963783	+	0.266687i	$0.914071\pi$
$972$		0			0
$973$	0.554034	−	1.21316i	0.0177615	−	0.0388923i
$974$		0			0
$975$	−2.71085	+	18.8544i	−0.0868167	+	0.603824i
$976$		0			0
$977$	−44.7336	−	13.1350i	−1.43116	−	0.420225i	−0.527892	−	0.849311i	$-0.677017\pi$
$977$	−44.7336	−	13.1350i	−1.43116	−	0.420225i	−0.903264	+	0.429086i	$0.858836\pi$
$978$		0			0
$979$	2.18037	+	4.77434i	0.0696849	+	0.152589i
$980$		0			0
$981$	12.4103	−	14.3223i	0.396231	−	0.457274i
$982$		0			0
$983$	−2.95703	−	1.90037i	−0.0943147	−	0.0606124i	0.492633	−	0.870237i	$-0.336034\pi$
$983$	−2.95703	−	1.90037i	−0.0943147	−	0.0606124i	−0.586948	+	0.809625i	$0.699671\pi$
$984$		0			0
$985$	−39.0612	+	25.1031i	−1.24459	+	0.799852i
$986$		0			0
$987$	17.9198	−	5.26172i	0.570392	−	0.167482i
$988$		0			0
$989$	29.0798	+	13.1213i	0.924683	+	0.417233i
$990$		0			0
$991$	9.81971	−	2.88333i	0.311933	−	0.0915919i	−0.122019	−	0.992528i	$-0.538937\pi$
$991$	9.81971	−	2.88333i	0.311933	−	0.0915919i	0.433952	+	0.900936i	$0.357119\pi$
$992$		0			0
$993$	5.76721	−	3.70636i	0.183017	−	0.117618i
$994$		0			0
$995$	−4.91397	−	3.15802i	−0.155783	−	0.100116i
$996$		0			0
$997$	−3.95160	+	4.56038i	−0.125148	+	0.144429i	−0.814866	−	0.579650i	$-0.803189\pi$
$997$	−3.95160	+	4.56038i	−0.125148	+	0.144429i	0.689717	+	0.724079i	$0.257735\pi$
$998$		0			0
$999$	−3.99506	−	8.74797i	−0.126398	−	0.276774i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.193.1	✓	30
23.18	even	11	inner	552.2.q.a.409.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.193.1	✓	30	1.1	even	1	trivial
552.2.q.a.409.1	yes	30	23.18	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{3} +(-0.494929 - 3.44231i) q^{5} +(0.813772 - 1.78191i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{3} +(-0.494929 - 3.44231i) q^{5} +(0.813772 - 1.78191i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-4.59332 - 1.34872i) q^{11} +(1.11537 + 2.44232i) q^{13} +(-2.27741 + 2.62828i) q^{15} +(-0.657735 - 0.422701i) q^{17} +(1.64177 - 1.05510i) q^{19} +(-1.87959 + 0.551896i) q^{21} +(-4.35337 + 2.01202i) q^{23} +(-6.80708 + 1.99874i) q^{25} +(0.841254 - 0.540641i) q^{27} +(4.69732 + 3.01878i) q^{29} +(-4.53151 + 5.22964i) q^{31} +(1.98869 + 4.35463i) q^{33} +(-6.53665 - 1.91933i) q^{35} +(1.36865 - 9.51916i) q^{37} +(1.11537 - 2.44232i) q^{39} +(-1.09875 - 7.64196i) q^{41} +(-4.35629 - 5.02742i) q^{43} +3.47771 q^{45} -9.53389 q^{47} +(2.07104 + 2.39011i) q^{49} +(0.111269 + 0.773893i) q^{51} +(2.18629 - 4.78731i) q^{53} +(-2.36935 + 16.4792i) q^{55} +(-1.87253 - 0.549824i) q^{57} +(-4.02082 - 8.80436i) q^{59} +(1.63680 - 1.88897i) q^{61} +(1.64796 + 1.05908i) q^{63} +(7.85519 - 5.04822i) q^{65} +(6.98906 - 2.05217i) q^{67} +(4.37143 + 1.97246i) q^{69} +(12.3486 - 3.62588i) q^{71} +(1.04034 - 0.668588i) q^{73} +(5.96823 + 3.83555i) q^{75} +(-6.14122 + 7.08735i) q^{77} +(2.10629 + 4.61213i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-0.238762 + 1.66063i) q^{83} +(-1.12953 + 2.47333i) q^{85} +(-0.794645 - 5.52688i) q^{87} +(-0.717979 - 0.828591i) q^{89} +5.25965 q^{91} +6.91980 q^{93} +(-4.44456 - 5.12929i) q^{95} +(2.17166 + 15.1042i) q^{97} +(1.98869 - 4.35463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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