LMFDB - Embedded newform 552.2.q.a.193.3

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			193.3
Character	$\chi$	$=$	552.193
Dual form			552.2.q.a.409.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 - 0.755750i) q^{3} +(0.309108 + 2.14989i) q^{5} +(1.22533 - 2.68309i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 - 0.755750i) q^{3} +(0.309108 + 2.14989i) q^{5} +(1.22533 - 2.68309i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.937939 + 0.275404i) q^{11} +(-0.279364 - 0.611723i) q^{13} +(1.42236 - 1.64149i) q^{15} +(2.67663 + 1.72017i) q^{17} +(1.94736 - 1.25149i) q^{19} +(-2.83016 + 0.831010i) q^{21} +(4.76454 + 0.546970i) q^{23} +(0.270967 - 0.0795632i) q^{25} +(0.841254 - 0.540641i) q^{27} +(0.860066 + 0.552731i) q^{29} +(2.27610 - 2.62676i) q^{31} +(-0.406083 - 0.889198i) q^{33} +(6.14712 + 1.80496i) q^{35} +(-0.116960 + 0.813476i) q^{37} +(-0.279364 + 0.611723i) q^{39} +(-0.840457 - 5.84550i) q^{41} +(-0.0622611 - 0.0718531i) q^{43} -2.17200 q^{45} +12.2394 q^{47} +(-1.11352 - 1.28507i) q^{49} +(-0.452805 - 3.14933i) q^{51} +(-0.944392 + 2.06793i) q^{53} +(-0.302164 + 2.10160i) q^{55} +(-2.22106 - 0.652163i) q^{57} +(-2.17770 - 4.76851i) q^{59} +(1.64506 - 1.89850i) q^{61} +(2.48140 + 1.59470i) q^{63} +(1.22879 - 0.789693i) q^{65} +(-11.2677 + 3.30849i) q^{67} +(-2.70674 - 3.95899i) q^{69} +(-0.504755 + 0.148210i) q^{71} +(-7.15489 + 4.59817i) q^{73} +(-0.237576 - 0.152681i) q^{75} +(1.88821 - 2.17911i) q^{77} +(-5.51940 - 12.0858i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.46252 + 10.1721i) q^{83} +(-2.87081 + 6.28619i) q^{85} +(-0.145497 - 1.01196i) q^{87} +(-0.750602 - 0.866241i) q^{89} -1.98362 q^{91} -3.47570 q^{93} +(3.29252 + 3.79977i) q^{95} +(1.23761 + 8.60775i) q^{97} +(-0.406083 + 0.889198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.309108	+	2.14989i	0.138237	+	0.961462i	0.934361	+	0.356328i	$0.115971\pi$
$5$	0.309108	+	2.14989i	0.138237	+	0.961462i	−0.796124	+	0.605134i	$0.793120\pi$
$6$		0			0
$7$	1.22533	−	2.68309i	0.463130	−	1.01411i	−0.523633	−	0.851944i	$-0.675424\pi$
$7$	1.22533	−	2.68309i	0.463130	−	1.01411i	0.986763	−	0.162169i	$-0.0518489\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	0.937939	+	0.275404i	0.282799	+	0.0830373i	0.420056	−	0.907498i	$-0.362010\pi$
$11$	0.937939	+	0.275404i	0.282799	+	0.0830373i	−0.137257	+	0.990535i	$0.543829\pi$
$12$		0			0
$13$	−0.279364	−	0.611723i	−0.0774818	−	0.169661i	0.866927	−	0.498435i	$-0.166092\pi$
$13$	−0.279364	−	0.611723i	−0.0774818	−	0.169661i	−0.944409	+	0.328774i	$0.893365\pi$
$14$		0			0
$15$	1.42236	−	1.64149i	0.367251	−	0.423831i
$16$		0			0
$17$	2.67663	+	1.72017i	0.649178	+	0.417201i	0.823366	−	0.567511i	$-0.192094\pi$
$17$	2.67663	+	1.72017i	0.649178	+	0.417201i	−0.174188	+	0.984712i	$0.555730\pi$
$18$		0			0
$19$	1.94736	−	1.25149i	0.446755	−	0.287112i	−0.297856	−	0.954611i	$-0.596271\pi$
$19$	1.94736	−	1.25149i	0.446755	−	0.287112i	0.744611	+	0.667499i	$0.232635\pi$
$20$		0			0
$21$	−2.83016	+	0.831010i	−0.617592	+	0.181341i
$22$		0			0
$23$	4.76454	+	0.546970i	0.993475	+	0.114051i
$23$	4.76454	+	0.546970i	0.993475	+	0.114051i
$24$		0			0
$25$	0.270967	−	0.0795632i	0.0541935	−	0.0159126i
$26$		0			0
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$		0			0
$29$	0.860066	+	0.552731i	0.159710	+	0.102640i	0.618055	−	0.786135i	$-0.287921\pi$
$29$	0.860066	+	0.552731i	0.159710	+	0.102640i	−0.458344	+	0.888775i	$0.651557\pi$
$30$		0			0
$31$	2.27610	−	2.62676i	0.408799	−	0.471779i	−0.513593	−	0.858034i	$-0.671686\pi$
$31$	2.27610	−	2.62676i	0.408799	−	0.471779i	0.922392	+	0.386255i	$0.126231\pi$
$32$		0			0
$33$	−0.406083	−	0.889198i	−0.0706900	−	0.154790i
$34$		0			0
$35$	6.14712	+	1.80496i	1.03905	+	0.305093i
$36$		0			0
$37$	−0.116960	+	0.813476i	−0.0192281	+	0.133735i	−0.997174	−	0.0751224i	$-0.976065\pi$
$37$	−0.116960	+	0.813476i	−0.0192281	+	0.133735i	0.977946	+	0.208857i	$0.0669743\pi$
$38$		0			0
$39$	−0.279364	+	0.611723i	−0.0447341	+	0.0979541i
$40$		0			0
$41$	−0.840457	−	5.84550i	−0.131257	−	0.912914i	−0.943919	−	0.330178i	$-0.892891\pi$
$41$	−0.840457	−	5.84550i	−0.131257	−	0.912914i	0.812661	−	0.582736i	$-0.198018\pi$
$42$		0			0
$43$	−0.0622611	−	0.0718531i	−0.00949473	−	0.0109575i	0.750982	−	0.660322i	$-0.229580\pi$
$43$	−0.0622611	−	0.0718531i	−0.00949473	−	0.0109575i	−0.760477	+	0.649365i	$0.775035\pi$
$44$		0			0
$45$	−2.17200			−0.323783
$46$		0			0
$47$	12.2394			1.78530			0.892650	−	0.450750i	$-0.148843\pi$
$47$	12.2394			1.78530			0.892650	+	0.450750i	$0.148843\pi$
$48$		0			0
$49$	−1.11352	−	1.28507i	−0.159074	−	0.183581i
$50$		0			0
$51$	−0.452805	−	3.14933i	−0.0634054	−	0.440995i
$52$		0			0
$53$	−0.944392	+	2.06793i	−0.129722	+	0.284052i	−0.963337	−	0.268294i	$-0.913540\pi$
$53$	−0.944392	+	2.06793i	−0.129722	+	0.284052i	0.833615	+	0.552346i	$0.186267\pi$
$54$		0			0
$55$	−0.302164	+	2.10160i	−0.0407438	+	0.283380i
$56$		0			0
$57$	−2.22106	−	0.652163i	−0.294187	−	0.0863811i
$58$		0			0
$59$	−2.17770	−	4.76851i	−0.283513	−	0.620806i	0.713276	−	0.700883i	$-0.247211\pi$
$59$	−2.17770	−	4.76851i	−0.283513	−	0.620806i	−0.996789	+	0.0800769i	$0.974483\pi$
$60$		0			0
$61$	1.64506	−	1.89850i	0.210628	−	0.243078i	−0.640599	−	0.767876i	$-0.721314\pi$
$61$	1.64506	−	1.89850i	0.210628	−	0.243078i	0.851227	+	0.524798i	$0.175859\pi$
$62$		0			0
$63$	2.48140	+	1.59470i	0.312627	+	0.200913i
$64$		0			0
$65$	1.22879	−	0.789693i	0.152412	−	0.0979493i
$66$		0			0
$67$	−11.2677	+	3.30849i	−1.37656	+	0.404196i	−0.884572	−	0.466403i	$-0.845550\pi$
$67$	−11.2677	+	3.30849i	−1.37656	+	0.404196i	−0.491993	+	0.870599i	$0.663731\pi$
$68$		0			0
$69$	−2.70674	−	3.95899i	−0.325853	−	0.476606i
$70$		0			0
$71$	−0.504755	+	0.148210i	−0.0599034	+	0.0175892i	−0.311547	−	0.950231i	$-0.600847\pi$
$71$	−0.504755	+	0.148210i	−0.0599034	+	0.0175892i	0.251644	+	0.967820i	$0.419029\pi$
$72$		0			0
$73$	−7.15489	+	4.59817i	−0.837417	+	0.538175i	−0.887627	−	0.460564i	$-0.847647\pi$
$73$	−7.15489	+	4.59817i	−0.837417	+	0.538175i	0.0502101	+	0.998739i	$0.484011\pi$
$74$		0			0
$75$	−0.237576	−	0.152681i	−0.0274329	−	0.0176300i
$76$		0			0
$77$	1.88821	−	2.17911i	0.215182	−	0.248333i
$78$		0			0
$79$	−5.51940	−	12.0858i	−0.620981	−	1.35976i	−0.914804	−	0.403898i	$-0.867655\pi$
$79$	−5.51940	−	12.0858i	−0.620981	−	1.35976i	0.293823	−	0.955860i	$-0.405072\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	−1.46252	+	10.1721i	−0.160533	+	1.11653i	0.737099	+	0.675784i	$0.236195\pi$
$83$	−1.46252	+	10.1721i	−0.160533	+	1.11653i	−0.897632	+	0.440745i	$0.854714\pi$
$84$		0			0
$85$	−2.87081	+	6.28619i	−0.311383	+	0.681833i
$86$		0			0
$87$	−0.145497	−	1.01196i	−0.0155990	−	0.108493i
$88$		0			0
$89$	−0.750602	−	0.866241i	−0.0795637	−	0.0918214i	0.714572	−	0.699562i	$-0.246622\pi$
$89$	−0.750602	−	0.866241i	−0.0795637	−	0.0918214i	−0.794136	+	0.607741i	$0.792076\pi$
$90$		0			0
$91$	−1.98362			−0.207940
$92$		0			0
$93$	−3.47570			−0.360413
$94$		0			0
$95$	3.29252	+	3.79977i	0.337806	+	0.389848i
$96$		0			0
$97$	1.23761	+	8.60775i	0.125660	+	0.873984i	0.950965	+	0.309298i	$0.100094\pi$
$97$	1.23761	+	8.60775i	0.125660	+	0.873984i	−0.825305	+	0.564687i	$0.808997\pi$
$98$		0			0
$99$	−0.406083	+	0.889198i	−0.0408129	+	0.0893678i
$100$		0			0
$101$	−2.56165	+	17.8167i	−0.254894	+	1.77282i	0.313031	+	0.949743i	$0.398656\pi$
$101$	−2.56165	+	17.8167i	−0.254894	+	1.77282i	−0.567925	+	0.823081i	$0.692254\pi$
$102$		0			0
$103$	−13.8290	−	4.06056i	−1.36261	−	0.400099i	−0.482929	−	0.875659i	$-0.660427\pi$
$103$	−13.8290	−	4.06056i	−1.36261	−	0.400099i	−0.879683	+	0.475560i	$0.842245\pi$
$104$		0			0
$105$	−2.66141	−	5.82768i	−0.259727	−	0.568723i
$106$		0			0
$107$	−1.32194	+	1.52560i	−0.127797	+	0.147486i	−0.816042	−	0.577993i	$-0.803836\pi$
$107$	−1.32194	+	1.52560i	−0.127797	+	0.147486i	0.688245	+	0.725479i	$0.258382\pi$
$108$		0			0
$109$	10.2850	+	6.60980i	0.985129	+	0.633104i	0.930842	−	0.365422i	$-0.119075\pi$
$109$	10.2850	+	6.60980i	0.985129	+	0.633104i	0.0542865	+	0.998525i	$0.482712\pi$
$110$		0			0
$111$	0.691377	−	0.444321i	0.0656226	−	0.0421731i
$112$		0			0
$113$	−8.33561	+	2.44756i	−0.784148	+	0.230247i	−0.649212	−	0.760608i	$-0.724901\pi$
$113$	−8.33561	+	2.44756i	−0.784148	+	0.230247i	−0.134936	+	0.990854i	$0.543083\pi$
$114$		0			0
$115$	0.296829	+	10.4123i	0.0276795	+	0.970954i
$116$		0			0
$117$	0.645254	−	0.189464i	0.0596538	−	0.0175159i
$118$		0			0
$119$	7.89510	−	5.07387i	0.723743	−	0.465121i
$120$		0			0
$121$	−8.44991	−	5.43043i	−0.768173	−	0.493675i
$122$		0			0
$123$	−3.86736	+	4.46317i	−0.348708	+	0.402430i
$124$		0			0
$125$	4.76622	+	10.4366i	0.426304	+	0.933475i
$126$		0			0
$127$	2.26992	+	0.666509i	0.201423	+	0.0591431i	0.380888	−	0.924621i	$-0.375618\pi$
$127$	2.26992	+	0.666509i	0.201423	+	0.0591431i	−0.179465	+	0.983764i	$0.557437\pi$
$128$		0			0
$129$	−0.0135306	+	0.0941076i	−0.00119131	+	0.00828571i
$130$		0			0
$131$	−5.98169	+	13.0981i	−0.522622	+	1.14438i	0.445815	+	0.895125i	$0.352914\pi$
$131$	−5.98169	+	13.0981i	−0.522622	+	1.14438i	−0.968437	+	0.249258i	$0.919813\pi$
$132$		0			0
$133$	−0.971715	−	6.75843i	−0.0842584	−	0.586030i
$134$		0			0
$135$	1.42236	+	1.64149i	0.122417	+	0.141277i
$136$		0			0
$137$	−5.33172			−0.455520			−0.227760	−	0.973717i	$-0.573140\pi$
$137$	−5.33172			−0.455520			−0.227760	+	0.973717i	$0.573140\pi$
$138$		0			0
$139$	−8.03111			−0.681190			−0.340595	−	0.940210i	$-0.610629\pi$
$139$	−8.03111			−0.681190			−0.340595	+	0.940210i	$0.610629\pi$
$140$		0			0
$141$	−8.01511	−	9.24992i	−0.674994	−	0.778984i
$142$		0			0
$143$	−0.0935561	−	0.650697i	−0.00782355	−	0.0544140i
$144$		0			0
$145$	−0.922460	+	2.01990i	−0.0766061	+	0.167744i
$146$		0			0
$147$	−0.241991	+	1.68308i	−0.0199591	+	0.138818i
$148$		0			0
$149$	−7.08031	−	2.07897i	−0.580042	−	0.170316i	−0.0214666	−	0.999770i	$-0.506834\pi$
$149$	−7.08031	−	2.07897i	−0.580042	−	0.170316i	−0.558575	+	0.829454i	$0.688652\pi$
$150$		0			0
$151$	−9.64889	−	21.1281i	−0.785215	−	1.71938i	−0.689865	−	0.723938i	$-0.742330\pi$
$151$	−9.64889	−	21.1281i	−0.785215	−	1.71938i	−0.0953500	−	0.995444i	$-0.530397\pi$
$152$		0			0
$153$	−2.08358	+	2.40458i	−0.168448	+	0.194399i
$154$		0			0
$155$	6.35081	+	4.08142i	0.510109	+	0.327827i
$156$		0			0
$157$	20.0182	−	12.8649i	1.59763	−	1.02673i	0.629265	−	0.777191i	$-0.283356\pi$
$157$	20.0182	−	12.8649i	1.59763	−	1.02673i	0.968364	−	0.249542i	$-0.0802801\pi$
$158$		0			0
$159$	2.18128	−	0.640482i	0.172987	−	0.0507936i
$160$		0			0
$161$	7.30568	−	12.1135i	0.575768	−	0.954675i
$162$		0			0
$163$	−1.56575	+	0.459747i	−0.122639	+	0.0360101i	−0.342476	−	0.939526i	$-0.611266\pi$
$163$	−1.56575	+	0.459747i	−0.122639	+	0.0360101i	0.219837	+	0.975537i	$0.429447\pi$
$164$		0			0
$165$	1.78616	−	1.14789i	0.139052	−	0.0893634i
$166$		0			0
$167$	−11.5039	−	7.39312i	−0.890200	−	0.572097i	0.0136688	−	0.999907i	$-0.495649\pi$
$167$	−11.5039	−	7.39312i	−0.890200	−	0.572097i	−0.903869	+	0.427810i	$0.859285\pi$
$168$		0			0
$169$	8.21703	−	9.48296i	0.632079	−	0.729458i
$170$		0			0
$171$	0.961616	+	2.10564i	0.0735366	+	0.161023i
$172$		0			0
$173$	−11.9486	−	3.50843i	−0.908436	−	0.266741i	−0.206054	−	0.978541i	$-0.566062\pi$
$173$	−11.9486	−	3.50843i	−0.908436	−	0.266741i	−0.702382	+	0.711800i	$0.747880\pi$
$174$		0			0
$175$	0.118548	−	0.824520i	0.00896140	−	0.0623279i
$176$		0			0
$177$	−2.17770	+	4.76851i	−0.163686	+	0.358423i
$178$		0			0
$179$	−0.813411	−	5.65740i	−0.0607972	−	0.422854i	−0.997376	−	0.0723965i	$-0.976935\pi$
$179$	−0.813411	−	5.65740i	−0.0607972	−	0.422854i	0.936579	−	0.350457i	$-0.113974\pi$
$180$		0			0
$181$	−5.60507	−	6.46859i	−0.416621	−	0.480807i	0.508183	−	0.861249i	$-0.330317\pi$
$181$	−5.60507	−	6.46859i	−0.416621	−	0.480807i	−0.924805	+	0.380442i	$0.875772\pi$
$182$		0			0
$183$	−2.51207			−0.185698
$184$		0			0
$185$	−1.78504			−0.131239
$186$		0			0
$187$	2.03678	+	2.35056i	0.148944	+	0.171890i
$188$		0			0
$189$	−0.419778	−	2.91962i	−0.0305343	−	0.212371i
$190$		0			0
$191$	5.01197	−	10.9747i	0.362654	−	0.794101i	−0.637075	−	0.770802i	$-0.719856\pi$
$191$	5.01197	−	10.9747i	0.362654	−	0.794101i	0.999729	−	0.0232988i	$-0.00741692\pi$
$192$		0			0
$193$	−3.11649	+	21.6757i	−0.224330	+	1.56025i	0.497059	+	0.867717i	$0.334413\pi$
$193$	−3.11649	+	21.6757i	−0.224330	+	1.56025i	−0.721388	+	0.692531i	$0.756496\pi$
$194$		0			0
$195$	−1.40149	−	0.411516i	−0.100363	−	0.0294692i
$196$		0			0
$197$	−0.212295	−	0.464862i	−0.0151254	−	0.0331200i	0.901919	−	0.431906i	$-0.142159\pi$
$197$	−0.212295	−	0.464862i	−0.0151254	−	0.0331200i	−0.917044	+	0.398786i	$0.869432\pi$
$198$		0			0
$199$	−3.75468	+	4.33314i	−0.266162	+	0.307168i	−0.873061	−	0.487612i	$-0.837868\pi$
$199$	−3.75468	+	4.33314i	−0.266162	+	0.307168i	0.606898	+	0.794780i	$0.292414\pi$
$200$		0			0
$201$	9.87914	+	6.34894i	0.696821	+	0.447820i
$202$		0			0
$203$	2.53689	−	1.63036i	0.178055	−	0.114429i
$204$		0			0
$205$	12.3074	−	3.61379i	0.859588	−	0.252398i
$206$		0			0
$207$	−1.21947	+	4.63820i	−0.0847588	+	0.322377i
$208$		0			0
$209$	2.17117	−	0.637513i	0.150183	−	0.0440977i
$210$		0			0
$211$	−5.15965	+	3.31590i	−0.355205	+	0.228276i	−0.706058	−	0.708154i	$-0.749528\pi$
$211$	−5.15965	+	3.31590i	−0.355205	+	0.228276i	0.350853	+	0.936431i	$0.385892\pi$
$212$		0			0
$213$	0.442554	+	0.284412i	0.0303233	+	0.0194876i
$214$		0			0
$215$	0.135231	−	0.156065i	0.00922269	−	0.0106436i
$216$		0			0
$217$	−4.25886	−	9.32560i	−0.289110	−	0.633063i
$218$		0			0
$219$	8.16052	+	2.39615i	0.551437	+	0.161916i
$220$		0			0
$221$	0.304509	−	2.11791i	0.0204835	−	0.142466i
$222$		0			0
$223$	−1.67268	+	3.66266i	−0.112011	+	0.245270i	−0.957333	−	0.288987i	$-0.906681\pi$
$223$	−1.67268	+	3.66266i	−0.112011	+	0.245270i	0.845322	+	0.534257i	$0.179409\pi$
$224$		0			0
$225$	0.0401907	+	0.279532i	0.00267938	+	0.0186355i
$226$		0			0
$227$	6.88614	+	7.94703i	0.457049	+	0.527463i	0.936764	−	0.349962i	$-0.113805\pi$
$227$	6.88614	+	7.94703i	0.457049	+	0.527463i	−0.479715	+	0.877424i	$0.659260\pi$
$228$		0			0
$229$	29.1403			1.92564			0.962822	−	0.270138i	$-0.0870694\pi$
$229$	29.1403			1.92564			0.962822	+	0.270138i	$0.0870694\pi$
$230$		0			0
$231$	−2.88338			−0.189713
$232$		0			0
$233$	0.828321	+	0.955933i	0.0542651	+	0.0626253i	0.782233	−	0.622986i	$-0.214081\pi$
$233$	0.828321	+	0.955933i	0.0542651	+	0.0626253i	−0.727968	+	0.685611i	$0.759535\pi$
$234$		0			0
$235$	3.78330	+	26.3134i	0.246795	+	1.71650i
$236$		0			0
$237$	−5.51940	+	12.0858i	−0.358523	+	0.785057i
$238$		0			0
$239$	0.970639	−	6.75094i	0.0627854	−	0.436682i	−0.934047	−	0.357150i	$-0.883748\pi$
$239$	0.970639	−	6.75094i	0.0627854	−	0.436682i	0.996832	−	0.0795318i	$-0.0253425\pi$
$240$		0			0
$241$	24.2026	+	7.10652i	1.55903	+	0.457771i	0.943783	−	0.330567i	$-0.107240\pi$
$241$	24.2026	+	7.10652i	1.55903	+	0.457771i	0.615243	+	0.788338i	$0.289058\pi$
$242$		0			0
$243$	0.415415	+	0.909632i	0.0266489	+	0.0583529i
$244$		0			0
$245$	2.41857	−	2.79117i	0.154517	−	0.178322i
$246$		0			0
$247$	−1.30959	−	0.841622i	−0.0833272	−	0.0535511i
$248$		0			0
$249$	8.64529	−	5.55599i	0.547873	−	0.352096i
$250$		0			0
$251$	−20.6200	+	6.05457i	−1.30152	+	0.382161i	−0.857791	−	0.513999i	$-0.828164\pi$
$251$	−20.6200	+	6.05457i	−1.30152	+	0.382161i	−0.443731	+	0.896160i	$0.646345\pi$
$252$		0			0
$253$	4.31821	+	1.82520i	0.271483	+	0.114749i
$254$		0			0
$255$	6.63076	−	1.94697i	0.415234	−	0.121924i
$256$		0			0
$257$	24.6895	−	15.8670i	1.54009	−	0.989756i	0.552357	−	0.833608i	$-0.313729\pi$
$257$	24.6895	−	15.8670i	1.54009	−	0.989756i	0.987734	−	0.156148i	$-0.0499077\pi$
$258$		0			0
$259$	2.03932	+	1.31059i	0.126717	+	0.0814360i
$260$		0			0
$261$	−0.669505	+	0.772650i	−0.0414413	+	0.0478258i
$262$		0			0
$263$	1.70421	+	3.73170i	0.105086	+	0.230106i	0.954870	−	0.297026i	$-0.0959947\pi$
$263$	1.70421	+	3.73170i	0.105086	+	0.230106i	−0.849783	+	0.527132i	$0.823267\pi$
$264$		0			0
$265$	−4.73775	−	1.39113i	−0.291038	−	0.0854564i
$266$		0			0
$267$	−0.163122	+	1.13454i	−0.00998287	+	0.0694324i
$268$		0			0
$269$	2.57702	−	5.64290i	0.157124	−	0.344053i	−0.814655	−	0.579945i	$-0.803074\pi$
$269$	2.57702	−	5.64290i	0.157124	−	0.344053i	0.971779	+	0.235892i	$0.0758012\pi$
$270$		0			0
$271$	1.65916	+	11.5397i	0.100787	+	0.700986i	0.976083	+	0.217399i	$0.0697572\pi$
$271$	1.65916	+	11.5397i	0.100787	+	0.700986i	−0.875296	+	0.483587i	$0.839334\pi$
$272$		0			0
$273$	1.29899	+	1.49912i	0.0786187	+	0.0907308i
$274$		0			0
$275$	0.276063			0.0166472
$276$		0			0
$277$	−13.5634			−0.814946			−0.407473	−	0.913217i	$-0.633590\pi$
$277$	−13.5634			−0.814946			−0.407473	+	0.913217i	$0.633590\pi$
$278$		0			0
$279$	2.27610	+	2.62676i	0.136266	+	0.157260i
$280$		0			0
$281$	1.86942	+	13.0021i	0.111520	+	0.775641i	0.966442	+	0.256884i	$0.0826959\pi$
$281$	1.86942	+	13.0021i	0.111520	+	0.775641i	−0.854922	+	0.518757i	$0.826395\pi$
$282$		0			0
$283$	5.42477	−	11.8786i	0.322469	−	0.706109i	−0.677087	−	0.735903i	$-0.736758\pi$
$283$	5.42477	−	11.8786i	0.322469	−	0.706109i	0.999556	+	0.0297939i	$0.00948510\pi$
$284$		0			0
$285$	0.715533	−	4.97664i	0.0423845	−	0.294791i
$286$		0			0
$287$	−16.7138	−	4.90763i	−0.986587	−	0.289688i
$288$		0			0
$289$	−2.85668	−	6.25525i	−0.168040	−	0.367956i
$290$		0			0
$291$	5.69484	−	6.57220i	0.333837	−	0.385269i
$292$		0			0
$293$	−8.79488	−	5.65212i	−0.513802	−	0.330201i	0.257914	−	0.966168i	$-0.416965\pi$
$293$	−8.79488	−	5.65212i	−0.513802	−	0.330201i	−0.771716	+	0.635967i	$0.780601\pi$
$294$		0			0
$295$	9.57864	−	6.15582i	0.557690	−	0.358405i
$296$		0			0
$297$	0.937939	−	0.275404i	0.0544247	−	0.0159805i
$298$		0			0
$299$	−0.996448	−	3.06738i	−0.0576261	−	0.177391i
$300$		0			0
$301$	−0.269078	+	0.0790086i	−0.0155094	+	0.00455398i
$302$		0			0
$303$	15.1425	−	9.73146i	0.869911	−	0.559058i
$304$		0			0
$305$	4.59007	+	2.94986i	0.262827	+	0.168909i
$306$		0			0
$307$	−15.9366	+	18.3919i	−0.909552	+	1.04968i	0.0890076	+	0.996031i	$0.471630\pi$
$307$	−15.9366	+	18.3919i	−0.909552	+	1.04968i	−0.998560	+	0.0536484i	$0.982915\pi$
$308$		0			0
$309$	5.98731	+	13.1104i	0.340606	+	0.745823i
$310$		0			0
$311$	0.806820	+	0.236904i	0.0457506	+	0.0134336i	0.304528	−	0.952503i	$-0.401501\pi$
$311$	0.806820	+	0.236904i	0.0457506	+	0.0134336i	−0.258777	+	0.965937i	$0.583320\pi$
$312$		0			0
$313$	−0.108671	+	0.755823i	−0.00614245	+	0.0427217i	−0.992662	−	0.120921i	$-0.961415\pi$
$313$	−0.108671	+	0.755823i	−0.00614245	+	0.0427217i	0.986520	+	0.163643i	$0.0523244\pi$
$314$		0			0
$315$	−2.66141	+	5.82768i	−0.149953	+	0.328352i
$316$		0			0
$317$	−2.95526	−	20.5543i	−0.165984	−	1.15444i	−0.887082	−	0.461611i	$-0.847272\pi$
$317$	−2.95526	−	20.5543i	−0.165984	−	1.15444i	0.721098	−	0.692833i	$-0.243638\pi$
$318$		0			0
$319$	0.654465	+	0.755293i	0.0366430	+	0.0422883i
$320$		0			0
$321$	2.01866			0.112671
$322$		0			0
$323$	7.36514			0.409807
$324$		0			0
$325$	−0.124369	−	0.143530i	−0.00689877	−	0.00796160i
$326$		0			0
$327$	−1.73992	−	12.1014i	−0.0962178	−	0.669210i
$328$		0			0
$329$	14.9973	−	32.8394i	0.826826	−	1.81050i
$330$		0			0
$331$	2.43453	−	16.9325i	0.133814	−	0.930695i	−0.806705	−	0.590954i	$-0.798752\pi$
$331$	2.43453	−	16.9325i	0.133814	−	0.930695i	0.940519	−	0.339741i	$-0.110339\pi$
$332$		0			0
$333$	−0.788551	−	0.231540i	−0.0432123	−	0.0126883i
$334$		0			0
$335$	−10.5958	−	23.2016i	−0.578912	−	1.26764i
$336$		0			0
$337$	−0.585436	+	0.675629i	−0.0318907	+	0.0368038i	−0.771471	−	0.636265i	$-0.780479\pi$
$337$	−0.585436	+	0.675629i	−0.0318907	+	0.0368038i	0.739580	+	0.673068i	$0.235024\pi$
$338$		0			0
$339$	7.30840	+	4.69682i	0.396938	+	0.255096i
$340$		0			0
$341$	2.85826	−	1.83689i	0.154783	−	0.0994732i
$342$		0			0
$343$	14.9987	−	4.40403i	0.809856	−	0.237795i
$344$		0			0
$345$	7.67473	−	7.04295i	0.413194	−	0.379180i
$346$		0			0
$347$	−19.0461	+	5.59244i	−1.02245	+	0.300218i	−0.749637	−	0.661849i	$-0.769772\pi$
$347$	−19.0461	+	5.59244i	−1.02245	+	0.300218i	−0.272812	+	0.962067i	$0.587954\pi$
$348$		0			0
$349$	24.7301	−	15.8931i	1.32377	−	0.850737i	0.328189	−	0.944612i	$-0.393562\pi$
$349$	24.7301	−	15.8931i	1.32377	−	0.850737i	0.995584	+	0.0938748i	$0.0299253\pi$
$350$		0			0
$351$	−0.565739	−	0.363578i	−0.0301969	−	0.0194064i
$352$		0			0
$353$	−18.0720	+	20.8561i	−0.961873	+	1.11006i	0.0319949	+	0.999488i	$0.489814\pi$
$353$	−18.0720	+	20.8561i	−0.961873	+	1.11006i	−0.993868	+	0.110573i	$0.964731\pi$
$354$		0			0
$355$	−0.474659	−	1.03936i	−0.0251923	−	0.0551634i
$356$		0			0
$357$	−9.00477	−	2.64404i	−0.476583	−	0.139937i
$358$		0			0
$359$	−3.17045	+	22.0510i	−0.167330	+	1.16381i	0.717044	+	0.697028i	$0.245494\pi$
$359$	−3.17045	+	22.0510i	−0.167330	+	1.16381i	−0.884374	+	0.466778i	$0.845415\pi$
$360$		0			0
$361$	−5.66691	+	12.4088i	−0.298258	+	0.653095i
$362$		0			0
$363$	1.42947	+	9.94219i	0.0750277	+	0.521829i
$364$		0			0
$365$	−12.0972	−	13.9609i	−0.633197	−	0.730748i
$366$		0			0
$367$	33.1515			1.73049			0.865246	−	0.501348i	$-0.167162\pi$
$367$	33.1515			1.73049			0.865246	+	0.501348i	$0.167162\pi$
$368$		0			0
$369$	5.90561			0.307434
$370$		0			0
$371$	4.39125	+	5.06778i	0.227983	+	0.263106i
$372$		0			0
$373$	3.87462	+	26.9485i	0.200620	+	1.39534i	0.802450	+	0.596719i	$0.203529\pi$
$373$	3.87462	+	26.9485i	0.200620	+	1.39534i	−0.601830	+	0.798624i	$0.705562\pi$
$374$		0			0
$375$	4.76622	−	10.4366i	0.246127	−	0.538942i
$376$		0			0
$377$	0.0978462	−	0.680536i	0.00503934	−	0.0350494i
$378$		0			0
$379$	−25.1101	−	7.37300i	−1.28982	−	0.378725i	−0.436308	−	0.899798i	$-0.643714\pi$
$379$	−25.1101	−	7.37300i	−1.28982	−	0.378725i	−0.853513	+	0.521072i	$0.825532\pi$
$380$		0			0
$381$	−0.982769	−	2.15196i	−0.0503488	−	0.110248i
$382$		0			0
$383$	−8.54891	+	9.86596i	−0.436829	+	0.504127i	−0.930890	−	0.365300i	$-0.880966\pi$
$383$	−8.54891	+	9.86596i	−0.436829	+	0.504127i	0.494061	+	0.869427i	$0.335512\pi$
$384$		0			0
$385$	5.26853	+	3.38588i	0.268509	+	0.172560i
$386$		0			0
$387$	0.0799824	−	0.0514016i	0.00406574	−	0.00261289i
$388$		0			0
$389$	3.16627	−	0.929699i	0.160536	−	0.0471376i	−0.200477	−	0.979698i	$-0.564249\pi$
$389$	3.16627	−	0.929699i	0.160536	−	0.0471376i	0.361013	+	0.932561i	$0.382431\pi$
$390$		0			0
$391$	11.8120	+	9.65983i	0.597360	+	0.488519i
$392$		0			0
$393$	13.8160	−	4.05675i	0.696926	−	0.204636i
$394$		0			0
$395$	24.2771	−	15.6019i	1.22151	−	0.785019i
$396$		0			0
$397$	−14.5874	−	9.37474i	−0.732120	−	0.470505i	0.120714	−	0.992687i	$-0.461482\pi$
$397$	−14.5874	−	9.37474i	−0.732120	−	0.470505i	−0.852834	+	0.522183i	$0.825118\pi$
$398$		0			0
$399$	−4.47134	+	5.16020i	−0.223847	+	0.258333i
$400$		0			0
$401$	7.03302	+	15.4002i	0.351212	+	0.769048i	0.999968	+	0.00805052i	$0.00256259\pi$
$401$	7.03302	+	15.4002i	0.351212	+	0.769048i	−0.648755	+	0.760997i	$0.724710\pi$
$402$		0			0
$403$	−2.24271	−	0.658518i	−0.111717	−	0.0328031i
$404$		0			0
$405$	0.309108	−	2.14989i	0.0153597	−	0.106829i
$406$		0			0
$407$	−0.333736	+	0.730780i	−0.0165427	+	0.0362234i
$408$		0			0
$409$	2.60838	+	18.1417i	0.128976	+	0.897047i	0.946856	+	0.321658i	$0.104240\pi$
$409$	2.60838	+	18.1417i	0.128976	+	0.897047i	−0.817880	+	0.575389i	$0.804851\pi$
$410$		0			0
$411$	3.49154	+	4.02945i	0.172225	+	0.198758i
$412$		0			0
$413$	−15.4627			−0.760871
$414$		0			0
$415$	−22.3209			−1.09569
$416$		0			0
$417$	5.25926	+	6.06951i	0.257547	+	0.297225i
$418$		0			0
$419$	3.24388	+	22.5617i	0.158474	+	1.10221i	0.901447	+	0.432889i	$0.142506\pi$
$419$	3.24388	+	22.5617i	0.158474	+	1.10221i	−0.742973	+	0.669321i	$0.766585\pi$
$420$		0			0
$421$	6.74587	−	14.7714i	0.328773	−	0.719914i	−0.670994	−	0.741462i	$-0.734133\pi$
$421$	6.74587	−	14.7714i	0.328773	−	0.719914i	0.999768	+	0.0215490i	$0.00685979\pi$
$422$		0			0
$423$	−1.74185	+	12.1148i	−0.0846916	+	0.589043i
$424$		0			0
$425$	0.862141	+	0.253147i	0.0418200	+	0.0122795i
$426$		0			0
$427$	−3.07811	−	6.74012i	−0.148960	−	0.326177i
$428$		0			0
$429$	−0.430498	+	0.496821i	−0.0207846	+	0.0239867i
$430$		0			0
$431$	−4.60751	−	2.96107i	−0.221936	−	0.142630i	0.424949	−	0.905217i	$-0.360292\pi$
$431$	−4.60751	−	2.96107i	−0.221936	−	0.142630i	−0.646885	+	0.762588i	$0.723929\pi$
$432$		0			0
$433$	−9.65238	+	6.20321i	−0.463864	+	0.298107i	−0.751620	−	0.659597i	$-0.770727\pi$
$433$	−9.65238	+	6.20321i	−0.463864	+	0.298107i	0.287756	+	0.957704i	$0.407091\pi$
$434$		0			0
$435$	2.13062	−	0.625608i	0.102156	−	0.0299956i
$436$		0			0
$437$	9.96280	−	4.89763i	0.476585	−	0.234286i
$438$		0			0
$439$	24.6967	−	7.25161i	1.17871	−	0.346101i	0.367034	−	0.930208i	$-0.380373\pi$
$439$	24.6967	−	7.25161i	1.17871	−	0.346101i	0.811677	+	0.584107i	$0.198555\pi$
$440$		0			0
$441$	1.43046	−	0.919301i	0.0681171	−	0.0437762i
$442$		0			0
$443$	−23.8436	−	15.3233i	−1.13284	−	0.728034i	−0.166692	−	0.986009i	$-0.553308\pi$
$443$	−23.8436	−	15.3233i	−1.13284	−	0.728034i	−0.966152	+	0.257975i	$0.916945\pi$
$444$		0			0
$445$	1.63031	−	1.88148i	0.0772841	−	0.0891906i
$446$		0			0
$447$	3.06544	+	6.71238i	0.144990	+	0.317484i
$448$		0			0
$449$	−26.4294	−	7.76038i	−1.24728	−	0.366235i	−0.409535	−	0.912294i	$-0.634309\pi$
$449$	−26.4294	−	7.76038i	−1.24728	−	0.366235i	−0.837746	+	0.546059i	$0.816127\pi$
$450$		0			0
$451$	0.821577	−	5.71419i	0.0386865	−	0.269071i
$452$		0			0
$453$	−9.64889	+	21.1281i	−0.453344	+	0.992685i
$454$		0			0
$455$	−0.613153	−	4.26457i	−0.0287451	−	0.199926i
$456$		0			0
$457$	−20.5013	−	23.6597i	−0.959010	−	1.10676i	−0.994218	−	0.107376i	$-0.965755\pi$
$457$	−20.5013	−	23.6597i	−0.959010	−	1.10676i	0.0352085	−	0.999380i	$-0.488790\pi$
$458$		0			0
$459$	3.18172			0.148510
$460$		0			0
$461$	−38.3280			−1.78511			−0.892556	−	0.450937i	$-0.851090\pi$
$461$	−38.3280			−1.78511			−0.892556	+	0.450937i	$0.851090\pi$
$462$		0			0
$463$	9.16661	+	10.5788i	0.426008	+	0.491640i	0.927658	−	0.373431i	$-0.121819\pi$
$463$	9.16661	+	10.5788i	0.426008	+	0.491640i	−0.501649	+	0.865071i	$0.667273\pi$
$464$		0			0
$465$	−1.07437	−	7.47238i	−0.0498225	−	0.346523i
$466$		0			0
$467$	3.16045	−	6.92043i	0.146248	−	0.320239i	−0.822304	−	0.569048i	$-0.807312\pi$
$467$	3.16045	−	6.92043i	0.146248	−	0.320239i	0.968553	+	0.248809i	$0.0800391\pi$
$468$		0			0
$469$	−4.92960	+	34.2861i	−0.227628	+	1.58319i
$470$		0			0
$471$	−22.8318	−	6.70403i	−1.05203	−	0.308905i
$472$		0			0
$473$	−0.0386085	−	0.0845408i	−0.00177522	−	0.00388719i
$474$		0			0
$475$	0.428098	−	0.494052i	0.0196425	−	0.0226686i
$476$		0			0
$477$	−1.91248	−	1.22908i	−0.0875665	−	0.0562756i
$478$		0			0
$479$	9.51139	−	6.11260i	0.434587	−	0.279292i	−0.305001	−	0.952352i	$-0.598657\pi$
$479$	9.51139	−	6.11260i	0.434587	−	0.279292i	0.739588	+	0.673060i	$0.235020\pi$
$480$		0			0
$481$	0.530297	−	0.155709i	0.0241794	−	0.00709973i
$482$		0			0
$483$	−13.9389	+	2.41137i	−0.634244	+	0.109721i
$484$		0			0
$485$	−18.1232	+	5.32145i	−0.822932	+	0.241635i
$486$		0			0
$487$	−1.67651	+	1.07743i	−0.0759698	+	0.0488228i	−0.578074	−	0.815984i	$-0.696196\pi$
$487$	−1.67651	+	1.07743i	−0.0759698	+	0.0488228i	0.502105	+	0.864807i	$0.332559\pi$
$488$		0			0
$489$	1.37280	+	0.882247i	0.0620803	+	0.0398966i
$490$		0			0
$491$	−23.2440	+	26.8250i	−1.04899	+	1.21060i	−0.0719774	+	0.997406i	$0.522931\pi$
$491$	−23.2440	+	26.8250i	−1.04899	+	1.21060i	−0.977011	+	0.213190i	$0.931615\pi$
$492$		0			0
$493$	1.35129	+	2.95891i	0.0608590	+	0.133263i
$494$		0			0
$495$	−2.03721	−	0.598177i	−0.0915656	−	0.0268861i
$496$		0			0
$497$	−0.220830	+	1.53591i	−0.00990559	+	0.0688949i
$498$		0			0
$499$	13.0140	−	28.4966i	0.582585	−	1.27568i	−0.357236	−	0.934014i	$-0.616281\pi$
$499$	13.0140	−	28.4966i	0.582585	−	1.27568i	0.939821	−	0.341668i	$-0.110992\pi$
$500$		0			0
$501$	1.94612	+	13.5355i	0.0869461	+	0.604724i
$502$		0			0
$503$	−13.8659	−	16.0021i	−0.618249	−	0.713497i	0.357125	−	0.934057i	$-0.383757\pi$
$503$	−13.8659	−	16.0021i	−0.618249	−	0.713497i	−0.975373	+	0.220560i	$0.929212\pi$
$504$		0			0
$505$	−39.0957			−1.73974
$506$		0			0
$507$	−12.5478			−0.557265
$508$		0			0
$509$	−4.54335	−	5.24330i	−0.201380	−	0.232405i	0.646072	−	0.763276i	$-0.276410\pi$
$509$	−4.54335	−	5.24330i	−0.201380	−	0.232405i	−0.847453	+	0.530871i	$0.821865\pi$
$510$		0			0
$511$	3.57023	+	24.8315i	0.157937	+	1.09848i
$512$		0			0
$513$	0.961616	−	2.10564i	0.0424564	−	0.0929665i
$514$		0			0
$515$	4.45512	−	30.9861i	0.196316	−	1.36541i
$516$		0			0
$517$	11.4798	+	3.37078i	0.504882	+	0.148247i
$518$		0			0
$519$	5.17318	+	11.3277i	0.227077	+	0.497230i
$520$		0			0
$521$	10.0784	−	11.6311i	0.441542	−	0.509567i	−0.490736	−	0.871308i	$-0.663272\pi$
$521$	10.0784	−	11.6311i	0.441542	−	0.509567i	0.932279	+	0.361741i	$0.117818\pi$
$522$		0			0
$523$	16.0160	+	10.2929i	0.700332	+	0.450076i	0.841745	−	0.539875i	$-0.181528\pi$
$523$	16.0160	+	10.2929i	0.700332	+	0.450076i	−0.141413	+	0.989951i	$0.545165\pi$
$524$		0			0
$525$	−0.700763	+	0.450353i	−0.0305838	+	0.0196550i
$526$		0			0
$527$	10.6107	−	3.11559i	0.462210	−	0.135717i
$528$		0			0
$529$	22.4016	+	5.21212i	0.973985	+	0.226614i
$530$		0			0
$531$	5.02989	−	1.47691i	0.218279	−	0.0640924i
$532$		0			0
$533$	−3.34103	+	2.14715i	−0.144716	+	0.0930035i
$534$		0			0
$535$	−3.68851	−	2.37046i	−0.159468	−	0.102484i
$536$		0			0
$537$	−3.74290	+	4.31954i	−0.161518	+	0.186402i
$538$		0			0
$539$	−0.690500	−	1.51198i	−0.0297420	−	0.0651258i
$540$		0			0
$541$	−2.99980	−	0.880820i	−0.128971	−	0.0378694i	0.216610	−	0.976258i	$-0.430500\pi$
$541$	−2.99980	−	0.880820i	−0.128971	−	0.0378694i	−0.345581	+	0.938389i	$0.612318\pi$
$542$		0			0
$543$	−1.21810	+	8.47205i	−0.0522736	+	0.363571i
$544$		0			0
$545$	−11.0312	+	24.1549i	−0.472524	+	1.03468i
$546$		0			0
$547$	−1.92337	−	13.3773i	−0.0822374	−	0.571974i	−0.988725	−	0.149742i	$-0.952156\pi$
$547$	−1.92337	−	13.3773i	−0.0822374	−	0.571974i	0.906488	−	0.422232i	$-0.138753\pi$
$548$		0			0
$549$	1.64506	+	1.89850i	0.0702094	+	0.0810259i
$550$		0			0
$551$	2.36660			0.100820
$552$		0			0
$553$	−39.1903			−1.66654
$554$		0			0
$555$	1.16895	+	1.34904i	0.0496193	+	0.0572638i
$556$		0			0
$557$	2.09968	+	14.6036i	0.0889664	+	0.618775i	0.984710	+	0.174203i	$0.0557350\pi$
$557$	2.09968	+	14.6036i	0.0889664	+	0.618775i	−0.895743	+	0.444572i	$0.853356\pi$
$558$		0			0
$559$	−0.0265607	+	0.0581597i	−0.00112340	+	0.00245990i
$560$		0			0
$561$	0.442634	−	3.07858i	0.0186880	−	0.129978i
$562$		0			0
$563$	−23.6852	−	6.95461i	−0.998213	−	0.293102i	−0.258491	−	0.966014i	$-0.583225\pi$
$563$	−23.6852	−	6.95461i	−0.998213	−	0.293102i	−0.739723	+	0.672912i	$0.765043\pi$
$564$		0			0
$565$	−7.83859	−	17.1641i	−0.329772	−	0.722100i
$566$		0			0
$567$	−1.93161	+	2.22919i	−0.0811198	+	0.0936172i
$568$		0			0
$569$	−4.17039	−	2.68015i	−0.174832	−	0.112358i	0.450298	−	0.892878i	$-0.351318\pi$
$569$	−4.17039	−	2.68015i	−0.174832	−	0.112358i	−0.625130	+	0.780521i	$0.714954\pi$
$570$		0			0
$571$	−9.29876	+	5.97595i	−0.389141	+	0.250086i	−0.720552	−	0.693401i	$-0.756112\pi$
$571$	−9.29876	+	5.97595i	−0.389141	+	0.250086i	0.331411	+	0.943486i	$0.392475\pi$
$572$		0			0
$573$	−11.5763	+	3.39910i	−0.483605	+	0.141999i
$574$		0			0
$575$	1.33455	−	0.230871i	0.0556547	−	0.00962798i
$576$		0			0
$577$	−39.7724	+	11.6782i	−1.65575	+	0.486171i	−0.970291	−	0.241941i	$-0.922216\pi$
$577$	−39.7724	+	11.6782i	−1.65575	+	0.486171i	−0.685457	+	0.728113i	$0.740398\pi$
$578$		0			0
$579$	18.4222	−	11.8392i	0.765602	−	0.492022i
$580$		0			0
$581$	25.5005	+	16.3882i	1.05794	+	0.679896i
$582$		0			0
$583$	−1.45530	+	1.67950i	−0.0602723	+	0.0695579i
$584$		0			0
$585$	0.606780	+	1.32866i	0.0250873	+	0.0549335i
$586$		0			0
$587$	−20.6771	−	6.07135i	−0.853435	−	0.250591i	−0.174380	−	0.984678i	$-0.555792\pi$
$587$	−20.6771	−	6.07135i	−0.853435	−	0.250591i	−0.679055	+	0.734087i	$0.737610\pi$
$588$		0			0
$589$	1.14502	−	7.96376i	0.0471795	−	0.328141i
$590$		0			0
$591$	−0.212295	+	0.464862i	−0.00873266	+	0.0191218i
$592$		0			0
$593$	6.09137	+	42.3664i	0.250143	+	1.73978i	0.597341	+	0.801988i	$0.296224\pi$
$593$	6.09137	+	42.3664i	0.250143	+	1.73978i	−0.347198	+	0.937792i	$0.612867\pi$
$594$		0			0
$595$	13.3487	+	15.4053i	0.547245	+	0.631554i
$596$		0			0
$597$	5.73356			0.234659
$598$		0			0
$599$	33.4614			1.36720			0.683599	−	0.729858i	$-0.260414\pi$
$599$	33.4614			1.36720			0.683599	+	0.729858i	$0.260414\pi$
$600$		0			0
$601$	−14.0042	−	16.1617i	−0.571242	−	0.659248i	0.394457	−	0.918915i	$-0.370933\pi$
$601$	−14.0042	−	16.1617i	−0.571242	−	0.659248i	−0.965698	+	0.259667i	$0.916387\pi$
$602$		0			0
$603$	−1.67125	−	11.6238i	−0.0680587	−	0.473359i
$604$		0			0
$605$	9.06291	−	19.8450i	0.368459	−	0.806814i
$606$		0			0
$607$	−3.57889	+	24.8917i	−0.145263	+	1.01032i	0.778579	+	0.627547i	$0.215941\pi$
$607$	−3.57889	+	24.8917i	−0.145263	+	1.01032i	−0.923841	+	0.382776i	$0.874968\pi$
$608$		0			0
$609$	−2.89345	−	0.849594i	−0.117249	−	0.0344273i
$610$		0			0
$611$	−3.41925	−	7.48712i	−0.138328	−	0.302897i
$612$		0			0
$613$	−12.1161	+	13.9827i	−0.489364	+	0.564756i	−0.945696	−	0.325054i	$-0.894618\pi$
$613$	−12.1161	+	13.9827i	−0.489364	+	0.564756i	0.456332	+	0.889810i	$0.349163\pi$
$614$		0			0
$615$	−10.7908	−	6.93480i	−0.435126	−	0.279638i
$616$		0			0
$617$	−14.9925	+	9.63508i	−0.603575	+	0.387894i	−0.806443	−	0.591312i	$-0.798610\pi$
$617$	−14.9925	+	9.63508i	−0.603575	+	0.387894i	0.202868	+	0.979206i	$0.434974\pi$
$618$		0			0
$619$	45.4831	−	13.3550i	1.82812	−	0.536784i	0.828393	−	0.560147i	$-0.189256\pi$
$619$	45.4831	−	13.3550i	1.82812	−	0.536784i	0.999727	+	0.0233629i	$0.00743732\pi$
$620$		0			0
$621$	4.30390	−	2.11576i	0.172710	−	0.0849026i
$622$		0			0
$623$	−3.24394	+	0.952505i	−0.129966	+	0.0381613i
$624$		0			0
$625$	−19.7764	+	12.7095i	−0.791055	+	0.508380i
$626$		0			0
$627$	−1.90361	−	1.22338i	−0.0760230	−	0.0488570i
$628$		0			0
$629$	−1.71237	+	1.97618i	−0.0682768	+	0.0787956i
$630$		0			0
$631$	−8.96045	−	19.6207i	−0.356710	−	0.781086i	−0.999882	−	0.0153643i	$-0.995109\pi$
$631$	−8.96045	−	19.6207i	−0.356710	−	0.781086i	0.643172	−	0.765722i	$-0.277618\pi$
$632$		0			0
$633$	5.88484	+	1.72795i	0.233902	+	0.0686797i
$634$		0			0
$635$	−0.731273	+	5.08612i	−0.0290197	+	0.201836i
$636$		0			0
$637$	−0.475029	+	1.04017i	−0.0188213	+	0.0412130i
$638$		0			0
$639$	−0.0748668	−	0.520710i	−0.00296168	−	0.0205990i
$640$		0			0
$641$	2.12174	+	2.44862i	0.0838039	+	0.0967148i	0.796103	−	0.605161i	$-0.206891\pi$
$641$	2.12174	+	2.44862i	0.0838039	+	0.0967148i	−0.712299	+	0.701876i	$0.752346\pi$
$642$		0			0
$643$	20.3122			0.801037			0.400518	−	0.916289i	$-0.368830\pi$
$643$	20.3122			0.801037			0.400518	+	0.916289i	$0.368830\pi$
$644$		0			0
$645$	−0.206504			−0.00813108
$646$		0			0
$647$	14.2587	+	16.4554i	0.560567	+	0.646928i	0.963312	−	0.268384i	$-0.0864895\pi$
$647$	14.2587	+	16.4554i	0.560567	+	0.646928i	−0.402746	+	0.915312i	$0.631944\pi$
$648$		0			0
$649$	−0.729289	−	5.07231i	−0.0286271	−	0.199106i
$650$		0			0
$651$	−4.25886	+	9.32560i	−0.166918	+	0.365499i
$652$		0			0
$653$	−3.24869	+	22.5951i	−0.127131	+	0.884216i	0.822034	+	0.569438i	$0.192839\pi$
$653$	−3.24869	+	22.5951i	−0.127131	+	0.884216i	−0.949165	+	0.314778i	$0.898070\pi$
$654$		0			0
$655$	−30.0084	−	8.81127i	−1.17253	−	0.344285i
$656$		0			0
$657$	−3.53312	−	7.73645i	−0.137840	−	0.301828i
$658$		0			0
$659$	23.0339	−	26.5826i	0.897275	−	1.03551i	−0.101896	−	0.994795i	$-0.532491\pi$
$659$	23.0339	−	26.5826i	0.897275	−	1.03551i	0.999171	−	0.0407151i	$-0.0129636\pi$
$660$		0			0
$661$	9.10669	+	5.85251i	0.354209	+	0.227636i	0.705629	−	0.708582i	$-0.250665\pi$
$661$	9.10669	+	5.85251i	0.354209	+	0.227636i	−0.351420	+	0.936218i	$0.614301\pi$
$662$		0			0
$663$	−1.80002	+	1.15680i	−0.0699070	+	0.0449265i
$664$		0			0
$665$	14.2295	−	4.17817i	0.551798	−	0.162022i
$666$		0			0
$667$	3.79549	+	3.10394i	0.146962	+	0.120185i
$668$		0			0
$669$	3.86343	−	1.13440i	0.149369	−	0.0438586i
$670$		0			0
$671$	2.06582	−	1.32762i	0.0797500	−	0.0512522i
$672$		0			0
$673$	−10.4759	−	6.73244i	−0.403816	−	0.259516i	0.322931	−	0.946423i	$-0.395332\pi$
$673$	−10.4759	−	6.73244i	−0.403816	−	0.259516i	−0.726746	+	0.686906i	$0.758968\pi$
$674$		0			0
$675$	0.184937	−	0.213429i	0.00711823	−	0.00821488i
$676$		0			0
$677$	18.3259	+	40.1281i	0.704320	+	1.54225i	0.834653	+	0.550776i	$0.185668\pi$
$677$	18.3259	+	40.1281i	0.704320	+	1.54225i	−0.130332	+	0.991470i	$0.541604\pi$
$678$		0			0
$679$	24.6118	+	7.22668i	0.944515	+	0.277335i
$680$		0			0
$681$	1.49650	−	10.4084i	0.0573460	−	0.398850i
$682$		0			0
$683$	1.36931	−	2.99837i	0.0523951	−	0.114729i	−0.881624	−	0.471953i	$-0.843549\pi$
$683$	1.36931	−	2.99837i	0.0523951	−	0.114729i	0.934019	+	0.357223i	$0.116277\pi$
$684$		0			0
$685$	−1.64808	−	11.4626i	−0.0629699	−	0.437965i
$686$		0			0
$687$	−19.0828	−	22.0227i	−0.728055	−	0.840220i
$688$		0			0
$689$	1.52883			0.0582438
$690$		0			0
$691$	−22.0810			−0.839999			−0.420000	−	0.907524i	$-0.637970\pi$
$691$	−22.0810			−0.839999			−0.420000	+	0.907524i	$0.637970\pi$
$692$		0			0
$693$	1.88821	+	2.17911i	0.0717273	+	0.0827777i
$694$		0			0
$695$	−2.48248	−	17.2660i	−0.0941659	−	0.654938i
$696$		0			0
$697$	7.80564	−	17.0920i	0.295660	−	0.647405i
$698$		0			0
$699$	0.180011	−	1.25201i	0.00680865	−	0.0473552i
$700$		0			0
$701$	−24.2284	−	7.11411i	−0.915095	−	0.268696i	−0.209911	−	0.977721i	$-0.567317\pi$
$701$	−24.2284	−	7.11411i	−0.915095	−	0.268696i	−0.705184	+	0.709024i	$0.749136\pi$
$702$		0			0
$703$	0.790296	+	1.73051i	0.0298066	+	0.0652673i
$704$		0			0
$705$	17.4088	−	20.0909i	0.655654	−	0.756665i
$706$		0			0
$707$	44.6648	+	28.7043i	1.67979	+	1.07954i
$708$		0			0
$709$	25.9806	−	16.6967i	0.975723	−	0.627059i	0.0474165	−	0.998875i	$-0.484901\pi$
$709$	25.9806	−	16.6967i	0.975723	−	0.627059i	0.928306	+	0.371816i	$0.121265\pi$
$710$		0			0
$711$	12.7483	−	3.74323i	0.478097	−	0.140382i
$712$		0			0
$713$	12.2813	−	11.2703i	0.459938	−	0.422077i
$714$		0			0
$715$	1.37001	−	0.402271i	0.0512355	−	0.0150441i
$716$		0			0
$717$	−5.73765	+	3.68737i	−0.214277	+	0.137707i
$718$		0			0
$719$	−6.89096	−	4.42855i	−0.256989	−	0.165157i	0.405802	−	0.913961i	$-0.366992\pi$
$719$	−6.89096	−	4.42855i	−0.256989	−	0.165157i	−0.662792	+	0.748804i	$0.730628\pi$
$720$		0			0
$721$	−27.8399	+	32.1289i	−1.03681	+	1.19654i
$722$		0			0
$723$	−10.4786	−	22.9449i	−0.389702	−	0.853329i
$724$		0			0
$725$	0.277027	+	0.0813424i	0.0102885	+	0.00302098i
$726$		0			0
$727$	0.850874	−	5.91796i	0.0315572	−	0.219485i	−0.967940	−	0.251180i	$-0.919181\pi$
$727$	0.850874	−	5.91796i	0.0315572	−	0.219485i	0.999498	+	0.0316950i	$0.0100905\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	−0.0430506	−	0.299424i	−0.00159228	−	0.0110746i
$732$		0			0
$733$	−8.95598	−	10.3357i	−0.330797	−	0.381760i	0.565849	−	0.824509i	$-0.308549\pi$
$733$	−8.95598	−	10.3357i	−0.330797	−	0.381760i	−0.896645	+	0.442749i	$0.854003\pi$
$734$		0			0
$735$	−3.69325			−0.136228
$736$		0			0
$737$	−11.4796			−0.422855
$738$		0			0
$739$	−4.84752	−	5.59434i	−0.178319	−	0.205791i	0.659553	−	0.751658i	$-0.270746\pi$
$739$	−4.84752	−	5.59434i	−0.178319	−	0.205791i	−0.837872	+	0.545867i	$0.816200\pi$
$740$		0			0
$741$	0.221543	+	1.54087i	0.00813859	+	0.0566052i
$742$		0			0
$743$	−11.1966	+	24.5171i	−0.410764	+	0.899447i	0.585301	+	0.810816i	$0.300976\pi$
$743$	−11.1966	+	24.5171i	−0.410764	+	0.899447i	−0.996065	+	0.0886308i	$0.971751\pi$
$744$		0			0
$745$	2.28098	−	15.8645i	0.0835685	−	0.581232i
$746$		0			0
$747$	−9.86039	−	2.89527i	−0.360773	−	0.105932i
$748$		0			0
$749$	2.47352	+	5.41625i	0.0903805	+	0.197906i
$750$		0			0
$751$	−20.6432	+	23.8235i	−0.753281	+	0.869333i	−0.994882	−	0.101043i	$-0.967782\pi$
$751$	−20.6432	+	23.8235i	−0.753281	+	0.869333i	0.241601	+	0.970376i	$0.422327\pi$
$752$		0			0
$753$	18.0790	+	11.6186i	0.658834	+	0.423407i
$754$		0			0
$755$	42.4407	−	27.2750i	1.54457	−	0.992637i
$756$		0			0
$757$	27.4184	−	8.05077i	0.996539	−	0.292610i	0.257504	−	0.966277i	$-0.417100\pi$
$757$	27.4184	−	8.05077i	0.996539	−	0.292610i	0.739035	+	0.673667i	$0.235282\pi$
$758$		0			0
$759$	−1.44843	−	4.45873i	−0.0525748	−	0.161842i
$760$		0			0
$761$	49.4650	−	14.5242i	1.79311	−	0.526504i	0.796195	−	0.605040i	$-0.206843\pi$
$761$	49.4650	−	14.5242i	1.79311	−	0.526504i	0.996911	+	0.0785364i	$0.0250247\pi$
$762$		0			0
$763$	30.3372	−	19.4965i	1.09828	−	0.705822i
$764$		0			0
$765$	−5.81365	−	3.73620i	−0.210193	−	0.135083i
$766$		0			0
$767$	−2.30863	+	2.66430i	−0.0833598	+	0.0962024i
$768$		0			0
$769$	−14.3996	−	31.5307i	−0.519262	−	1.13703i	−0.969718	−	0.244227i	$-0.921466\pi$
$769$	−14.3996	−	31.5307i	−0.519262	−	1.13703i	0.450456	−	0.892799i	$-0.351261\pi$
$770$		0			0
$771$	−28.1597	−	8.26843i	−1.01415	−	0.297780i
$772$		0			0
$773$	1.31614	−	9.15394i	0.0473382	−	0.329244i	−0.952367	−	0.304955i	$-0.901359\pi$
$773$	1.31614	−	9.15394i	0.0473382	−	0.329244i	0.999705	−	0.0242893i	$-0.00773229\pi$
$774$		0			0
$775$	0.407755	−	0.892858i	0.0146470	−	0.0320724i
$776$		0			0
$777$	−0.344991	−	2.39946i	−0.0123765	−	0.0860803i
$778$		0			0
$779$	−8.95227	−	10.3315i	−0.320749	−	0.370164i
$780$		0			0
$781$	−0.514247			−0.0184012
$782$		0			0
$783$	1.02236			0.0365363
$784$		0			0
$785$	33.8460	+	39.0604i	1.20802	+	1.39413i
$786$		0			0
$787$	6.20893	+	43.1841i	0.221324	+	1.53935i	0.733037	+	0.680189i	$0.238102\pi$
$787$	6.20893	+	43.1841i	0.221324	+	1.53935i	−0.511713	+	0.859157i	$0.670989\pi$
$788$		0			0
$789$	1.70421	−	3.73170i	0.0606715	−	0.132852i
$790$		0			0
$791$	−3.64683	+	25.3642i	−0.129666	+	0.901848i
$792$		0			0
$793$	−1.62093	−	0.475947i	−0.0575608	−	0.0169014i
$794$		0			0
$795$	2.05122	+	4.49155i	0.0727493	+	0.159299i
$796$		0			0
$797$	32.0490	−	36.9865i	1.13523	−	1.31013i	0.190726	−	0.981643i	$-0.438916\pi$
$797$	32.0490	−	36.9865i	1.13523	−	1.31013i	0.944509	−	0.328487i	$-0.106539\pi$
$798$		0			0
$799$	32.7604	+	21.0538i	1.15898	+	0.744830i
$800$		0			0
$801$	0.964246	−	0.619683i	0.0340700	−	0.0218954i
$802$		0			0
$803$	−7.97720	+	2.34232i	−0.281509	+	0.0826586i
$804$		0			0
$805$	28.3009	+	11.9621i	0.997476	+	0.421608i
$806$		0			0
$807$	−5.95221	+	1.74773i	−0.209528	+	0.0615229i
$808$		0			0
$809$	13.2708	−	8.52865i	0.466578	−	0.299851i	−0.286148	−	0.958185i	$-0.592375\pi$
$809$	13.2708	−	8.52865i	0.466578	−	0.299851i	0.752726	+	0.658334i	$0.228739\pi$
$810$		0			0
$811$	19.9183	+	12.8007i	0.699427	+	0.449494i	0.841426	−	0.540372i	$-0.181717\pi$
$811$	19.9183	+	12.8007i	0.699427	+	0.449494i	−0.141999	+	0.989867i	$0.545353\pi$
$812$		0			0
$813$	7.63459	−	8.81079i	0.267757	−	0.309008i
$814$		0			0
$815$	−1.47239	−	3.22409i	−0.0515757	−	0.112935i
$816$		0			0
$817$	−0.211168	−	0.0620046i	−0.00738785	−	0.00216927i
$818$		0			0
$819$	0.282298	−	1.96343i	0.00986431	−	0.0686078i
$820$		0			0
$821$	−6.48708	+	14.2047i	−0.226401	+	0.495749i	−0.988408	−	0.151820i	$-0.951487\pi$
$821$	−6.48708	+	14.2047i	−0.226401	+	0.495749i	0.762007	+	0.647568i	$0.224214\pi$
$822$		0			0
$823$	−5.56708	−	38.7199i	−0.194056	−	1.34969i	−0.821135	−	0.570734i	$-0.806659\pi$
$823$	−5.56708	−	38.7199i	−0.194056	−	1.34969i	0.627079	−	0.778956i	$-0.284250\pi$
$824$		0			0
$825$	−0.180783	−	0.208634i	−0.00629405	−	0.00726372i
$826$		0			0
$827$	42.2053			1.46762			0.733810	−	0.679354i	$-0.237740\pi$
$827$	42.2053			1.46762			0.733810	+	0.679354i	$0.237740\pi$
$828$		0			0
$829$	6.82107			0.236906			0.118453	−	0.992960i	$-0.462207\pi$
$829$	6.82107			0.236906			0.118453	+	0.992960i	$0.462207\pi$
$830$		0			0
$831$	8.88214	+	10.2505i	0.308118	+	0.355587i
$832$		0			0
$833$	−0.769946	−	5.35509i	−0.0266771	−	0.185543i
$834$		0			0
$835$	12.3385	−	27.0175i	0.426990	−	0.934979i
$836$		0			0
$837$	0.494643	−	3.44032i	0.0170974	−	0.118915i
$838$		0			0
$839$	−39.1402	−	11.4926i	−1.35127	−	0.396768i	−0.475592	−	0.879666i	$-0.657766\pi$
$839$	−39.1402	−	11.4926i	−1.35127	−	0.396768i	−0.875677	+	0.482898i	$0.839584\pi$
$840$		0			0
$841$	−11.6128	−	25.4286i	−0.400443	−	0.876847i
$842$		0			0
$843$	8.60213	−	9.92739i	0.296273	−	0.341917i
$844$		0			0
$845$	22.9273	+	14.7345i	0.788723	+	0.506882i
$846$		0			0
$847$	−24.9242	+	16.0178i	−0.856406	+	0.550379i
$848$		0			0
$849$	−12.5297	+	3.67906i	−0.430019	+	0.126265i
$850$		0			0
$851$	−1.00221	+	3.81187i	−0.0343553	+	0.130669i
$852$		0			0
$853$	−44.5198	+	13.0722i	−1.52433	+	0.447583i	−0.933309	−	0.359074i	$-0.883092\pi$
$853$	−44.5198	+	13.0722i	−1.52433	+	0.447583i	−0.591019	+	0.806658i	$0.701274\pi$
$854$		0			0
$855$	−4.22967	+	2.71824i	−0.144652	+	0.0929620i
$856$		0			0
$857$	17.8205	+	11.4525i	0.608737	+	0.391211i	0.808383	−	0.588657i	$-0.200343\pi$
$857$	17.8205	+	11.4525i	0.608737	+	0.391211i	−0.199646	+	0.979868i	$0.563979\pi$
$858$		0			0
$859$	−12.7789	+	14.7477i	−0.436012	+	0.503184i	−0.930648	−	0.365916i	$-0.880756\pi$
$859$	−12.7789	+	14.7477i	−0.436012	+	0.503184i	0.494636	+	0.869100i	$0.335301\pi$
$860$		0			0
$861$	7.23630	+	15.8453i	0.246613	+	0.540006i
$862$		0			0
$863$	−18.8599	−	5.53777i	−0.641999	−	0.188508i	−0.0555012	−	0.998459i	$-0.517676\pi$
$863$	−18.8599	−	5.53777i	−0.641999	−	0.188508i	−0.586498	+	0.809951i	$0.699494\pi$
$864$		0			0
$865$	3.84934	−	26.7727i	0.130881	−	0.910300i
$866$		0			0
$867$	−2.85668	+	6.25525i	−0.0970178	+	0.212439i
$868$		0			0
$869$	−1.84838	−	12.8558i	−0.0627022	−	0.436103i
$870$		0			0
$871$	5.17166	+	5.96842i	0.175235	+	0.202232i
$872$		0			0
$873$	−8.69626			−0.294324
$874$		0			0
$875$	33.8424			1.14408
$876$		0			0
$877$	−29.0546	−	33.5308i	−0.981105	−	1.13226i	−0.991209	−	0.132307i	$-0.957762\pi$
$877$	−29.0546	−	33.5308i	−0.981105	−	1.13226i	0.0101034	−	0.999949i	$-0.496784\pi$
$878$		0			0
$879$	1.48783	+	10.3481i	0.0501832	+	0.349032i
$880$		0			0
$881$	22.9277	−	50.2046i	0.772454	−	1.69144i	0.0512787	−	0.998684i	$-0.483670\pi$
$881$	22.9277	−	50.2046i	0.772454	−	1.69144i	0.721175	−	0.692753i	$-0.243602\pi$
$882$		0			0
$883$	−1.08931	+	7.57633i	−0.0366583	+	0.254964i	−0.999907	−	0.0136476i	$-0.995656\pi$
$883$	−1.08931	+	7.57633i	−0.0366583	+	0.254964i	0.963249	+	0.268612i	$0.0865648\pi$
$884$		0			0
$885$	−10.9249	−	3.20785i	−0.367237	−	0.107831i
$886$		0			0
$887$	22.2915	+	48.8115i	0.748474	+	1.63893i	0.769088	+	0.639143i	$0.220711\pi$
$887$	22.2915	+	48.8115i	0.748474	+	1.63893i	−0.0206140	+	0.999788i	$0.506562\pi$
$888$		0			0
$889$	4.56970	−	5.27371i	0.153263	−	0.176875i
$890$		0			0
$891$	−0.822356	−	0.528496i	−0.0275500	−	0.0177053i
$892$		0			0
$893$	23.8345	−	15.3175i	0.797592	−	0.512581i
$894$		0			0
$895$	11.9114	−	3.49749i	0.398153	−	0.116908i
$896$		0			0
$897$	−1.66564	+	2.76177i	−0.0556140	+	0.0922129i
$898$		0			0
$899$	3.40948	−	1.00111i	0.113713	−	0.0333890i
$900$		0			0
$901$	−6.08497	+	3.91057i	−0.202720	+	0.130280i
$902$		0			0
$903$	0.235920	+	0.151616i	0.00785091	+	0.00504548i
$904$		0			0
$905$	12.1742	−	14.0498i	0.404685	−	0.467031i
$906$		0			0
$907$	−6.25027	−	13.6862i	−0.207537	−	0.454442i	0.777027	−	0.629467i	$-0.216727\pi$
$907$	−6.25027	−	13.6862i	−0.207537	−	0.454442i	−0.984564	+	0.175025i	$0.943999\pi$
$908$		0			0
$909$	−17.2707	−	5.07115i	−0.572834	−	0.168199i
$910$		0			0
$911$	−4.91285	+	34.1696i	−0.162770	+	1.13209i	0.730612	+	0.682792i	$0.239235\pi$
$911$	−4.91285	+	34.1696i	−0.162770	+	1.13209i	−0.893382	+	0.449297i	$0.851674\pi$
$912$		0			0
$913$	−4.17318	+	9.13800i	−0.138112	+	0.302424i
$914$		0			0
$915$	−0.776502	−	5.40069i	−0.0256704	−	0.178541i
$916$		0			0
$917$	27.8138	+	32.0988i	0.918491	+	1.06000i
$918$		0			0
$919$	−9.56477			−0.315513			−0.157756	−	0.987478i	$-0.550426\pi$
$919$	−9.56477			−0.315513			−0.157756	+	0.987478i	$0.550426\pi$
$920$		0			0
$921$	24.3359			0.801896
$922$		0			0
$923$	0.231674	+	0.267366i	0.00762564	+	0.00880045i
$924$		0			0
$925$	0.0330304	+	0.229731i	0.00108603	+	0.00755352i
$926$		0			0
$927$	5.98731	−	13.1104i	0.196649	−	0.430601i
$928$		0			0
$929$	−0.837989	+	5.82834i	−0.0274935	+	0.191222i	−0.998940	−	0.0460385i	$-0.985340\pi$
$929$	−0.837989	+	5.82834i	−0.0274935	+	0.191222i	0.971446	+	0.237260i	$0.0762494\pi$
$930$		0			0
$931$	−3.77668	−	1.10893i	−0.123776	−	0.0363438i
$932$		0			0
$933$	−0.349315	−	0.764893i	−0.0114361	−	0.0250415i
$934$		0			0
$935$	−4.42388	+	5.10543i	−0.144676	+	0.166965i
$936$		0			0
$937$	30.3781	+	19.5228i	0.992408	+	0.637782i	0.932783	−	0.360439i	$-0.117373\pi$
$937$	30.3781	+	19.5228i	0.992408	+	0.637782i	0.0596253	+	0.998221i	$0.481009\pi$
$938$		0			0
$939$	0.642378	−	0.412831i	0.0209632	−	0.0134722i
$940$		0			0
$941$	−29.4610	+	8.65052i	−0.960400	+	0.281999i	−0.724111	−	0.689684i	$-0.757750\pi$
$941$	−29.4610	+	8.65052i	−0.960400	+	0.281999i	−0.236289	+	0.971683i	$0.575931\pi$
$942$		0			0
$943$	−0.807070	−	28.3108i	−0.0262818	−	0.921928i
$944$		0			0
$945$	6.14712	−	1.80496i	0.199966	−	0.0587152i
$946$		0			0
$947$	−11.9548	+	7.68286i	−0.388478	+	0.249659i	−0.720271	−	0.693693i	$-0.755983\pi$
$947$	−11.9548	+	7.68286i	−0.388478	+	0.249659i	0.331794	+	0.943352i	$0.392346\pi$
$948$		0			0
$949$	4.81163	+	3.09225i	0.156192	+	0.100379i
$950$		0			0
$951$	−13.5986	+	15.6936i	−0.440965	+	0.508901i
$952$		0			0
$953$	−10.8250	−	23.7034i	−0.350656	−	0.767829i	−0.999973	−	0.00731156i	$-0.997673\pi$
$953$	−10.8250	−	23.7034i	−0.350656	−	0.767829i	0.649318	−	0.760517i	$-0.275055\pi$
$954$		0			0
$955$	25.1437	+	7.38285i	0.813630	+	0.238903i
$956$		0			0
$957$	0.142229	−	0.989224i	0.00459761	−	0.0319771i
$958$		0			0
$959$	−6.53310	+	14.3055i	−0.210965	+	0.461948i
$960$		0			0
$961$	2.69253	+	18.7270i	0.0868559	+	0.604096i
$962$		0			0
$963$	−1.32194	−	1.52560i	−0.0425990	−	0.0491619i
$964$		0			0
$965$	−47.5637			−1.53113
$966$		0			0
$967$	5.39917			0.173626			0.0868128	−	0.996225i	$-0.472332\pi$
$967$	5.39917			0.173626			0.0868128	+	0.996225i	$0.472332\pi$
$968$		0			0
$969$	−4.82314	−	5.56620i	−0.154942	−	0.178812i
$970$		0			0
$971$	−2.78761	−	19.3883i	−0.0894588	−	0.622199i	−0.984391	−	0.175997i	$-0.943685\pi$
$971$	−2.78761	−	19.3883i	−0.0894588	−	0.622199i	0.894932	−	0.446203i	$-0.147224\pi$
$972$		0			0
$973$	−9.84073	+	21.5482i	−0.315479	+	0.690803i
$974$		0			0
$975$	−0.0270280	+	0.187984i	−0.000865590	+	0.00602031i
$976$		0			0
$977$	34.3274	+	10.0794i	1.09823	+	0.322470i	0.780150	−	0.625593i	$-0.215143\pi$
$977$	34.3274	+	10.0794i	1.09823	+	0.322470i	0.318082	+	0.948063i	$0.396961\pi$
$978$		0			0
$979$	−0.465453	−	1.01920i	−0.0148759	−	0.0325738i
$980$		0			0
$981$	−8.00623	+	9.23968i	−0.255619	+	0.295000i
$982$		0			0
$983$	26.2976	+	16.9004i	0.838762	+	0.539040i	0.888051	−	0.459745i	$-0.152059\pi$
$983$	26.2976	+	16.9004i	0.838762	+	0.539040i	−0.0492890	+	0.998785i	$0.515696\pi$
$984$		0			0
$985$	0.933781	−	0.600105i	0.0297527	−	0.0191209i
$986$		0			0
$987$	−34.6395	+	10.1711i	−1.10259	+	0.323749i
$988$		0			0
$989$	−0.257344	−	0.376402i	−0.00818306	−	0.0119689i
$990$		0			0
$991$	−24.9227	+	7.31797i	−0.791696	+	0.232463i	−0.652487	−	0.757800i	$-0.726274\pi$
$991$	−24.9227	+	7.31797i	−0.791696	+	0.232463i	−0.139209	+	0.990263i	$0.544456\pi$
$992$		0			0
$993$	−14.3910	+	9.24854i	−0.456685	+	0.293494i
$994$		0			0
$995$	−10.4764	−	6.73276i	−0.332124	−	0.213443i
$996$		0			0
$997$	19.0643	−	22.0014i	0.603773	−	0.696791i	−0.368769	−	0.929521i	$-0.620221\pi$
$997$	19.0643	−	22.0014i	0.603773	−	0.696791i	0.972541	+	0.232730i	$0.0747660\pi$
$998$		0			0
$999$	0.341405	+	0.747573i	0.0108016	+	0.0236522i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.193.3	✓	30
23.18	even	11	inner	552.2.q.a.409.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.193.3	✓	30	1.1	even	1	trivial
552.2.q.a.409.3	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)

\(f(q)\)	\(=\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.309108 + 2.14989i) q^{5} +(1.22533 - 2.68309i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 - 0.755750i) q^{3} +(0.309108 + 2.14989i) q^{5} +(1.22533 - 2.68309i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(0.937939 + 0.275404i) q^{11} +(-0.279364 - 0.611723i) q^{13} +(1.42236 - 1.64149i) q^{15} +(2.67663 + 1.72017i) q^{17} +(1.94736 - 1.25149i) q^{19} +(-2.83016 + 0.831010i) q^{21} +(4.76454 + 0.546970i) q^{23} +(0.270967 - 0.0795632i) q^{25} +(0.841254 - 0.540641i) q^{27} +(0.860066 + 0.552731i) q^{29} +(2.27610 - 2.62676i) q^{31} +(-0.406083 - 0.889198i) q^{33} +(6.14712 + 1.80496i) q^{35} +(-0.116960 + 0.813476i) q^{37} +(-0.279364 + 0.611723i) q^{39} +(-0.840457 - 5.84550i) q^{41} +(-0.0622611 - 0.0718531i) q^{43} -2.17200 q^{45} +12.2394 q^{47} +(-1.11352 - 1.28507i) q^{49} +(-0.452805 - 3.14933i) q^{51} +(-0.944392 + 2.06793i) q^{53} +(-0.302164 + 2.10160i) q^{55} +(-2.22106 - 0.652163i) q^{57} +(-2.17770 - 4.76851i) q^{59} +(1.64506 - 1.89850i) q^{61} +(2.48140 + 1.59470i) q^{63} +(1.22879 - 0.789693i) q^{65} +(-11.2677 + 3.30849i) q^{67} +(-2.70674 - 3.95899i) q^{69} +(-0.504755 + 0.148210i) q^{71} +(-7.15489 + 4.59817i) q^{73} +(-0.237576 - 0.152681i) q^{75} +(1.88821 - 2.17911i) q^{77} +(-5.51940 - 12.0858i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(-1.46252 + 10.1721i) q^{83} +(-2.87081 + 6.28619i) q^{85} +(-0.145497 - 1.01196i) q^{87} +(-0.750602 - 0.866241i) q^{89} -1.98362 q^{91} -3.47570 q^{93} +(3.29252 + 3.79977i) q^{95} +(1.23761 + 8.60775i) q^{97} +(-0.406083 + 0.889198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 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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