LMFDB - Embedded newform 567.2.e.g.163.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(163,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.163"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 14x^{12} - 39x^{10} + 77x^{8} - 156x^{6} + 224x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 14x^12 - 39x^10 + 77x^8 - 156x^6 + 224x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.3
Root			$0.776749 + 1.18180i$ of defining polynomial
Character	$\chi$	$=$	567.163
Dual form			567.2.e.g.487.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.635098 + 1.10002i) q^{2} +(0.193301 + 0.334806i) q^{4} +(0.776749 - 1.34537i) q^{5} +(-1.48662 - 2.18860i) q^{7} -3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} +(-1.60500 - 2.77995i) q^{11} +4.78669 q^{13} +(3.35166 - 0.245346i) q^{14} +(1.53867 - 2.66505i) q^{16} +(-1.05918 - 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +0.600584 q^{20} +4.07734 q^{22} +(1.85379 - 3.21086i) q^{23} +(1.29332 + 2.24010i) q^{25} +(-3.04002 + 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} -7.37944 q^{29} +(-2.75209 - 4.76676i) q^{31} +(-1.07704 - 1.86549i) q^{32} +2.69074 q^{34} +(-4.09920 + 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +(3.08914 + 5.35054i) q^{38} +(-2.35468 + 4.07842i) q^{40} +10.7972 q^{41} +4.86916 q^{43} +(0.620496 - 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} +(0.885937 - 1.53449i) q^{47} +(-2.57990 + 6.50724i) q^{49} -3.28555 q^{50} +(0.925270 + 1.60261i) q^{52} +(0.834432 + 1.44528i) q^{53} -4.98674 q^{55} +(4.50663 + 6.63462i) q^{56} +(4.68667 - 8.11755i) q^{58} +(2.91297 + 5.04541i) q^{59} +(-3.43865 + 5.95591i) q^{61} +6.99139 q^{62} +8.89078 q^{64} +(3.71806 - 6.43986i) q^{65} +(-6.11868 - 10.5979i) q^{67} +(0.409481 - 0.709241i) q^{68} +(2.27331 - 4.69978i) q^{70} +13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +(0.118482 + 0.205216i) q^{74} +1.88044 q^{76} +(-3.69814 + 7.64544i) q^{77} +(0.654632 - 1.13386i) q^{79} +(-2.39032 - 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +0.346488 q^{83} -3.29087 q^{85} +(-3.09239 + 5.35618i) q^{86} +(4.86549 + 8.42727i) q^{88} +(-8.70319 + 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +1.43335 q^{92} +(1.12531 + 1.94910i) q^{94} +(-3.77813 - 6.54391i) q^{95} -10.5683 q^{97} +(-5.51961 - 6.97068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.635098	+	1.10002i	−0.449082	+	0.777833i	−0.998327	−	0.0578286i	$-0.981582\pi$
$2$	−0.635098	+	1.10002i	−0.449082	+	0.777833i	0.549244	+	0.835662i	$0.314916\pi$
$3$		0			0
$3$		0			0
$4$	0.193301	+	0.334806i	0.0966503	+	0.167403i
$5$	0.776749	−	1.34537i	0.347373	−	0.601667i	−0.638409	−	0.769697i	$-0.720407\pi$
$5$	0.776749	−	1.34537i	0.347373	−	0.601667i	0.985782	+	0.168030i	$0.0537406\pi$
$6$		0			0
$7$	−1.48662	−	2.18860i	−0.561891	−	0.827211i
$7$	−1.48662	−	2.18860i	−0.561891	−	0.827211i
$8$	−3.03145			−1.07178
$9$		0			0
$10$	0.986623	+	1.70888i	0.311998	+	0.540396i
$11$	−1.60500	−	2.77995i	−0.483927	−	0.838185i	0.515903	−	0.856647i	$-0.327456\pi$
$11$	−1.60500	−	2.77995i	−0.483927	−	0.838185i	−0.999830	+	0.0184616i	$0.994123\pi$
$12$		0			0
$13$	4.78669			1.32759			0.663795	−	0.747915i	$-0.268945\pi$
$13$	4.78669			1.32759			0.663795	+	0.747915i	$0.268945\pi$
$14$	3.35166	−	0.245346i	0.895768	−	0.0655714i
$15$		0			0
$16$	1.53867	−	2.66505i	0.384667	−	0.666263i
$17$	−1.05918	−	1.83456i	−0.256889	−	0.444945i	0.708518	−	0.705693i	$-0.249364\pi$
$17$	−1.05918	−	1.83456i	−0.256889	−	0.444945i	−0.965407	+	0.260748i	$0.916031\pi$
$18$		0			0
$19$	2.43201	−	4.21237i	0.557942	−	0.966384i	−0.439726	−	0.898132i	$-0.644924\pi$
$19$	2.43201	−	4.21237i	0.557942	−	0.966384i	0.997668	−	0.0682523i	$-0.0217423\pi$
$20$	0.600584			0.134295
$21$		0			0
$22$	4.07734			0.869291
$23$	1.85379	−	3.21086i	0.386542	−	0.669510i	−0.605440	−	0.795891i	$-0.707003\pi$
$23$	1.85379	−	3.21086i	0.386542	−	0.669510i	0.991982	+	0.126381i	$0.0403362\pi$
$24$		0			0
$25$	1.29332	+	2.24010i	0.258665	+	0.448020i
$26$	−3.04002	+	5.26547i	−0.596197	+	1.03264i
$27$		0			0
$28$	0.445391	−	0.920788i	0.0841709	−	0.174013i
$29$	−7.37944			−1.37033			−0.685164	−	0.728389i	$-0.740269\pi$
$29$	−7.37944			−1.37033			−0.685164	+	0.728389i	$0.740269\pi$
$30$		0			0
$31$	−2.75209	−	4.76676i	−0.494290	−	0.856135i	0.505688	−	0.862716i	$-0.331239\pi$
$31$	−2.75209	−	4.76676i	−0.494290	−	0.856135i	−0.999978	+	0.00658088i	$0.997905\pi$
$32$	−1.07704	−	1.86549i	−0.190396	−	0.329775i
$33$		0			0
$34$	2.69074			0.461457
$35$	−4.09920	+	0.300067i	−0.692891	+	0.0507206i
$36$		0			0
$37$	0.0932782	−	0.161563i	0.0153348	−	0.0265607i	−0.858256	−	0.513222i	$-0.828452\pi$
$37$	0.0932782	−	0.161563i	0.0153348	−	0.0265607i	0.873591	+	0.486661i	$0.161785\pi$
$38$	3.08914	+	5.35054i	0.501124	+	0.867972i
$39$		0			0
$40$	−2.35468	+	4.07842i	−0.372307	+	0.644855i
$41$	10.7972			1.68624			0.843120	−	0.537726i	$-0.180716\pi$
$41$	10.7972			1.68624			0.843120	+	0.537726i	$0.180716\pi$
$42$		0			0
$43$	4.86916			0.742539			0.371270	−	0.928525i	$-0.378923\pi$
$43$	4.86916			0.742539			0.371270	+	0.928525i	$0.378923\pi$
$44$	0.620496	−	1.07473i	0.0935433	−	0.162022i
$45$		0			0
$46$	2.35468	+	4.07842i	0.347178	+	0.601330i
$47$	0.885937	−	1.53449i	0.129227	−	0.223828i	−0.794150	−	0.607722i	$-0.792084\pi$
$47$	0.885937	−	1.53449i	0.129227	−	0.223828i	0.923377	+	0.383893i	$0.125417\pi$
$48$		0			0
$49$	−2.57990	+	6.50724i	−0.368557	+	0.929605i
$50$	−3.28555			−0.464647
$51$		0			0
$52$	0.925270	+	1.60261i	0.128312	+	0.222243i
$53$	0.834432	+	1.44528i	0.114618	+	0.198524i	0.917627	−	0.397443i	$-0.130102\pi$
$53$	0.834432	+	1.44528i	0.114618	+	0.198524i	−0.803009	+	0.595967i	$0.796769\pi$
$54$		0			0
$55$	−4.98674			−0.672411
$56$	4.50663	+	6.63462i	0.602223	+	0.886589i
$57$		0			0
$58$	4.68667	−	8.11755i	0.615390	−	1.06589i
$59$	2.91297	+	5.04541i	0.379236	+	0.656857i	0.990951	−	0.134221i	$-0.0428534\pi$
$59$	2.91297	+	5.04541i	0.379236	+	0.656857i	−0.611715	+	0.791078i	$0.709520\pi$
$60$		0			0
$61$	−3.43865	+	5.95591i	−0.440274	+	0.762576i	−0.997710	−	0.0676438i	$-0.978452\pi$
$61$	−3.43865	+	5.95591i	−0.440274	+	0.762576i	0.557436	+	0.830220i	$0.311785\pi$
$62$	6.99139			0.887907
$63$		0			0
$64$	8.89078			1.11135
$65$	3.71806	−	6.43986i	0.461168	−	0.798766i
$66$		0			0
$67$	−6.11868	−	10.5979i	−0.747516	−	1.29474i	−0.949010	−	0.315246i	$-0.897913\pi$
$67$	−6.11868	−	10.5979i	−0.747516	−	1.29474i	0.201494	−	0.979490i	$-0.435420\pi$
$68$	0.409481	−	0.709241i	0.0496568	−	0.0860081i
$69$		0			0
$70$	2.27331	−	4.69978i	0.271713	−	0.561732i
$71$	13.8101			1.63895			0.819477	−	0.573112i	$-0.194264\pi$
$71$	13.8101			1.63895			0.819477	+	0.573112i	$0.194264\pi$
$72$		0			0
$73$	−5.93201	−	10.2745i	−0.694290	−	1.20255i	−0.970420	−	0.241425i	$-0.922385\pi$
$73$	−5.93201	−	10.2745i	−0.694290	−	1.20255i	0.276130	−	0.961120i	$-0.410948\pi$
$74$	0.118482	+	0.205216i	0.0137732	+	0.0238559i
$75$		0			0
$76$	1.88044			0.215701
$77$	−3.69814	+	7.64544i	−0.421443	+	0.871278i
$78$		0			0
$79$	0.654632	−	1.13386i	0.0736518	−	0.127569i	−0.826847	−	0.562426i	$-0.809868\pi$
$79$	0.654632	−	1.13386i	0.0736518	−	0.127569i	0.900499	+	0.434858i	$0.143201\pi$
$80$	−2.39032	−	4.14015i	−0.267246	−	0.462883i
$81$		0			0
$82$	−6.85728	+	11.8772i	−0.757260	+	1.31161i
$83$	0.346488			0.0380320			0.0190160	−	0.999819i	$-0.493947\pi$
$83$	0.346488			0.0380320			0.0190160	+	0.999819i	$0.493947\pi$
$84$		0			0
$85$	−3.29087			−0.356945
$86$	−3.09239	+	5.35618i	−0.333461	+	0.577572i
$87$		0			0
$88$	4.86549	+	8.42727i	0.518663	+	0.898350i
$89$	−8.70319	+	15.0744i	−0.922537	+	1.59788i	−0.127061	+	0.991895i	$0.540554\pi$
$89$	−8.70319	+	15.0744i	−0.922537	+	1.59788i	−0.795476	+	0.605985i	$0.792779\pi$
$90$		0			0
$91$	−7.11601	−	10.4761i	−0.745960	−	1.09820i
$92$	1.43335			0.149437
$93$		0			0
$94$	1.12531	+	1.94910i	0.116067	+	0.201035i
$95$	−3.77813	−	6.54391i	−0.387628	−	0.671391i
$96$		0			0
$97$	−10.5683			−1.07304			−0.536522	−	0.843886i	$-0.680262\pi$
$97$	−10.5683			−1.07304			−0.536522	+	0.843886i	$0.680262\pi$
$98$	−5.51961	−	6.97068i	−0.557565	−	0.704145i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−1.01697	−	1.76144i	−0.101192	−	0.175270i	0.810984	−	0.585068i	$-0.198932\pi$
$101$	−1.01697	−	1.76144i	−0.101192	−	0.175270i	−0.912176	+	0.409798i	$0.865599\pi$
$102$		0			0
$103$	−9.99080	+	17.3046i	−0.984423	+	1.70507i	−0.339951	+	0.940443i	$0.610410\pi$
$103$	−9.99080	+	17.3046i	−0.984423	+	1.70507i	−0.644472	+	0.764628i	$0.722923\pi$
$104$	−14.5106			−1.42288
$105$		0			0
$106$	−2.11979			−0.205892
$107$	8.45322	−	14.6414i	0.817204	−	1.41544i	−0.0905308	−	0.995894i	$-0.528856\pi$
$107$	8.45322	−	14.6414i	0.817204	−	1.41544i	0.907735	−	0.419545i	$-0.137810\pi$
$108$		0			0
$109$	5.34955	+	9.26569i	0.512394	+	0.887492i	0.999897	+	0.0143707i	$0.00457451\pi$
$109$	5.34955	+	9.26569i	0.512394	+	0.887492i	−0.487503	+	0.873121i	$0.662092\pi$
$110$	3.16707	−	5.48552i	0.301968	−	0.523024i
$111$		0			0
$112$	−8.12014	+	0.594406i	−0.767281	+	0.0561661i
$113$	−8.58471			−0.807582			−0.403791	−	0.914851i	$-0.632308\pi$
$113$	−8.58471			−0.807582			−0.403791	+	0.914851i	$0.632308\pi$
$114$		0			0
$115$	−2.87986	−	4.98806i	−0.268548	−	0.465139i
$116$	−1.42645	−	2.47068i	−0.132442	−	0.229397i
$117$		0			0
$118$	−7.40009			−0.681233
$119$	−2.44050	+	5.04541i	−0.223720	+	0.462512i
$120$		0			0
$121$	0.347932	−	0.602636i	0.0316302	−	0.0547851i
$122$	−4.36776	−	7.56518i	−0.395438	−	0.684919i
$123$		0			0
$124$	1.06396	−	1.84283i	0.0955465	−	0.165491i
$125$	11.7858			1.05416
$126$		0			0
$127$	1.95162			0.173178			0.0865892	−	0.996244i	$-0.472403\pi$
$127$	1.95162			0.173178			0.0865892	+	0.996244i	$0.472403\pi$
$128$	−3.49244	+	6.04908i	−0.308691	+	0.534668i
$129$		0			0
$130$	4.72266	+	8.17989i	0.414205	+	0.717424i
$131$	−5.87214	+	10.1708i	−0.513051	+	0.888630i	0.486834	+	0.873494i	$0.338151\pi$
$131$	−5.87214	+	10.1708i	−0.513051	+	0.888630i	−0.999885	+	0.0151361i	$0.995182\pi$
$132$		0			0
$133$	−12.8347	+	0.939515i	−1.11291	+	0.0814663i
$134$	15.5439			1.34278
$135$		0			0
$136$	3.21086	+	5.56137i	0.275329	+	0.476883i
$137$	−8.06604	−	13.9708i	−0.689128	−	1.19361i	−0.972120	−	0.234483i	$-0.924660\pi$
$137$	−8.06604	−	13.9708i	−0.689128	−	1.19361i	0.282992	−	0.959122i	$-0.408673\pi$
$138$		0			0
$139$	13.4425			1.14018			0.570091	−	0.821582i	$-0.306908\pi$
$139$	13.4425			1.14018			0.570091	+	0.821582i	$0.306908\pi$
$140$	−0.892842	−	1.31443i	−0.0754589	−	0.111090i
$141$		0			0
$142$	−8.77075	+	15.1914i	−0.736025	+	1.27483i
$143$	−7.68265	−	13.3067i	−0.642456	−	1.11277i
$144$		0			0
$145$	−5.73197	+	9.92806i	−0.476014	+	0.824481i
$146$	15.0696			1.24717
$147$		0			0
$148$	0.0721229			0.00592846
$149$	−1.60587	+	2.78145i	−0.131558	+	0.227865i	−0.924277	−	0.381722i	$-0.875331\pi$
$149$	−1.60587	+	2.78145i	−0.131558	+	0.227865i	0.792719	+	0.609587i	$0.208665\pi$
$150$		0			0
$151$	−8.51610	−	14.7503i	−0.693030	−	1.20036i	−0.970840	−	0.239727i	$-0.922942\pi$
$151$	−8.51610	−	14.7503i	−0.693030	−	1.20036i	0.277810	−	0.960636i	$-0.410391\pi$
$152$	−7.37253	+	12.7696i	−0.597991	+	1.03575i
$153$		0			0
$154$	−6.06147	−	8.92364i	−0.488447	−	0.719088i
$155$	−8.55073			−0.686811
$156$		0			0
$157$	−4.71709	−	8.17024i	−0.376465	−	0.652056i	0.614080	−	0.789243i	$-0.289527\pi$
$157$	−4.71709	−	8.17024i	−0.376465	−	0.652056i	−0.990545	+	0.137188i	$0.956194\pi$
$158$	0.831511	+	1.44022i	0.0661515	+	0.114578i
$159$		0			0
$160$	−3.34636			−0.264553
$161$	−9.78315	+	0.716140i	−0.771021	+	0.0564398i
$162$		0			0
$163$	−1.83874	+	3.18478i	−0.144021	+	0.249452i	−0.929007	−	0.370062i	$-0.879337\pi$
$163$	−1.83874	+	3.18478i	−0.144021	+	0.249452i	0.784986	+	0.619513i	$0.212670\pi$
$164$	2.08710	+	3.61497i	0.162976	+	0.282282i
$165$		0			0
$166$	−0.220054	+	0.381144i	−0.0170795	+	0.0295825i
$167$	−1.61017			−0.124599			−0.0622994	−	0.998058i	$-0.519843\pi$
$167$	−1.61017			−0.124599			−0.0622994	+	0.998058i	$0.519843\pi$
$168$		0			0
$169$	9.91241			0.762493
$170$	2.09003	−	3.62003i	0.160298	−	0.277644i
$171$		0			0
$172$	0.941210	+	1.63022i	0.0717666	+	0.124303i
$173$	8.09213	−	14.0160i	0.615233	−	1.06562i	−0.375110	−	0.926980i	$-0.622395\pi$
$173$	8.09213	−	14.0160i	0.615233	−	1.06562i	0.990344	−	0.138635i	$-0.0442716\pi$
$174$		0			0
$175$	2.97999	−	6.16075i	0.225266	−	0.465709i
$176$	−9.87827			−0.744603
$177$		0			0
$178$	−11.0548	−	19.1474i	−0.828590	−	1.43516i
$179$	8.70319	+	15.0744i	0.650507	+	1.12671i	0.983000	+	0.183606i	$0.0587770\pi$
$179$	8.70319	+	15.0744i	0.650507	+	1.12671i	−0.332493	+	0.943106i	$0.607890\pi$
$180$		0			0
$181$	8.89591			0.661228			0.330614	−	0.943766i	$-0.392744\pi$
$181$	8.89591			0.661228			0.330614	+	0.943766i	$0.392744\pi$
$182$	16.0433	−	1.17439i	1.18921	−	0.0870519i
$183$		0			0
$184$	−5.61967	+	9.73356i	−0.414288	+	0.717568i
$185$	−0.144907	−	0.250987i	−0.0106538	−	0.0184529i
$186$		0			0
$187$	−3.39998	+	5.88893i	−0.248631	+	0.430642i
$188$	0.685009			0.0499594
$189$		0			0
$190$	9.59793			0.696307
$191$	−7.39609	+	12.8104i	−0.535163	+	0.926929i	0.463993	+	0.885839i	$0.346416\pi$
$191$	−7.39609	+	12.8104i	−0.535163	+	0.926929i	−0.999155	+	0.0410898i	$0.986917\pi$
$192$		0			0
$193$	−0.910790	−	1.57753i	−0.0655601	−	0.113553i	0.831382	−	0.555701i	$-0.187550\pi$
$193$	−0.910790	−	1.57753i	−0.0655601	−	0.113553i	−0.896942	+	0.442148i	$0.854217\pi$
$194$	6.71188	−	11.6253i	0.481885	−	0.834649i
$195$		0			0
$196$	−2.67736	+	0.394085i	−0.191240	+	0.0281489i
$197$	7.71970			0.550006			0.275003	−	0.961443i	$-0.411321\pi$
$197$	7.71970			0.550006			0.275003	+	0.961443i	$0.411321\pi$
$198$		0			0
$199$	−1.10665	−	1.91678i	−0.0784487	−	0.135877i	0.824132	−	0.566398i	$-0.191663\pi$
$199$	−1.10665	−	1.91678i	−0.0784487	−	0.135877i	−0.902581	+	0.430521i	$0.858330\pi$
$200$	−3.92065	−	6.79076i	−0.277232	−	0.480179i
$201$		0			0
$202$	2.58350			0.181774
$203$	10.9704	+	16.1506i	0.769974	+	1.13355i
$204$		0			0
$205$	8.38671	−	14.5262i	0.585753	−	1.01455i
$206$	−12.6903	−	21.9802i	−0.884174	−	1.53143i
$207$		0			0
$208$	7.36513	−	12.7568i	0.510680	−	0.884524i
$209$	−15.6136			−1.08001
$210$		0			0
$211$	−1.81344			−0.124843			−0.0624213	−	0.998050i	$-0.519882\pi$
$211$	−1.81344			−0.124843			−0.0624213	+	0.998050i	$0.519882\pi$
$212$	−0.322592	+	0.558746i	−0.0221557	+	0.0383749i
$213$		0			0
$214$	10.7373	+	18.5975i	0.733983	+	1.27130i
$215$	3.78211	−	6.55081i	0.257938	−	0.446761i
$216$		0			0
$217$	−6.34119	+	13.1096i	−0.430468	+	0.889937i
$218$	−13.5900			−0.920428
$219$		0			0
$220$	−0.963939	−	1.66959i	−0.0649887	−	0.112564i
$221$	−5.06997	−	8.78145i	−0.341043	−	0.590704i
$222$		0			0
$223$	9.50616			0.636580			0.318290	−	0.947993i	$-0.396891\pi$
$223$	9.50616			0.636580			0.318290	+	0.947993i	$0.396891\pi$
$224$	−2.48165	+	5.13049i	−0.165812	+	0.342795i
$225$		0			0
$226$	5.45213	−	9.44337i	0.362671	−	0.628164i
$227$	5.41646	+	9.38158i	0.359503	+	0.622678i	0.987878	−	0.155233i	$-0.0496129\pi$
$227$	5.41646	+	9.38158i	0.359503	+	0.622678i	−0.628375	+	0.777911i	$0.716280\pi$
$228$		0			0
$229$	−6.25983	+	10.8423i	−0.413661	+	0.716482i	−0.995287	−	0.0969747i	$-0.969083\pi$
$229$	−6.25983	+	10.8423i	−0.413661	+	0.716482i	0.581626	+	0.813456i	$0.302417\pi$
$230$	7.31597			0.482401
$231$		0			0
$232$	22.3704			1.46869
$233$	−7.64044	+	13.2336i	−0.500542	+	0.866964i	0.499458	+	0.866338i	$0.333533\pi$
$233$	−7.64044	+	13.2336i	−0.500542	+	0.866964i	−1.00000		0.000625732i	$0.999801\pi$
$234$		0			0
$235$	−1.37630	−	2.38382i	−0.0897800	−	0.155504i
$236$	−1.12616	+	1.95056i	−0.0733066	+	0.126971i
$237$		0			0
$238$	−4.00011	−	5.88893i	−0.259289	−	0.381723i
$239$	10.7158			0.693149			0.346574	−	0.938023i	$-0.387345\pi$
$239$	10.7158			0.693149			0.346574	+	0.938023i	$0.387345\pi$
$240$		0			0
$241$	7.50011	+	12.9906i	0.483125	+	0.836796i	0.999812	−	0.0193775i	$-0.00616845\pi$
$241$	7.50011	+	12.9906i	0.483125	+	0.836796i	−0.516688	+	0.856174i	$0.672835\pi$
$242$	0.441942	+	0.765467i	0.0284091	+	0.0492061i
$243$		0			0
$244$	−2.65877			−0.170210
$245$	6.75069	+	8.52540i	0.431286	+	0.544668i
$246$		0			0
$247$	11.6413	−	20.1633i	0.740718	−	1.28296i
$248$	8.34283	+	14.4502i	0.529770	+	0.917589i
$249$		0			0
$250$	−7.48516	+	12.9647i	−0.473403	+	0.819958i
$251$	−16.5665			−1.04567			−0.522833	−	0.852435i	$-0.675125\pi$
$251$	−16.5665			−1.04567			−0.522833	+	0.852435i	$0.675125\pi$
$252$		0			0
$253$	−11.9013			−0.748231
$254$	−1.23947	+	2.14683i	−0.0777714	+	0.134704i
$255$		0			0
$256$	4.45470	+	7.71576i	0.278419	+	0.482235i
$257$	11.2886	−	19.5524i	0.704163	−	1.21965i	−0.262829	−	0.964842i	$-0.584656\pi$
$257$	11.2886	−	19.5524i	0.704163	−	1.21965i	0.966993	−	0.254804i	$-0.0820111\pi$
$258$		0			0
$259$	−0.492265	+	0.0360344i	−0.0305878	+	0.00223907i
$260$	2.87481			0.178288
$261$		0			0
$262$	−7.45877	−	12.9190i	−0.460804	−	0.798136i
$263$	11.1730	+	19.3523i	0.688959	+	1.19331i	0.972175	+	0.234256i	$0.0752653\pi$
$263$	11.1730	+	19.3523i	0.688959	+	1.19331i	−0.283216	+	0.959056i	$0.591401\pi$
$264$		0			0
$265$	2.59258			0.159261
$266$	7.11779	−	14.7151i	0.436419	−	0.902241i
$267$		0			0
$268$	2.36549	−	4.09715i	0.144495	−	0.250273i
$269$	13.9475	+	24.1577i	0.850392	+	1.47292i	0.880855	+	0.473387i	$0.156969\pi$
$269$	13.9475	+	24.1577i	0.850392	+	1.47292i	−0.0304623	+	0.999536i	$0.509698\pi$
$270$		0			0
$271$	−4.93714	+	8.55138i	−0.299910	+	0.519459i	−0.976115	−	0.217254i	$-0.930290\pi$
$271$	−4.93714	+	8.55138i	−0.299910	+	0.519459i	0.676205	+	0.736713i	$0.263623\pi$
$272$	−6.51892			−0.395267
$273$		0			0
$274$	20.4909			1.23790
$275$	4.15157	−	7.19074i	0.250349	−	0.433618i
$276$		0			0
$277$	4.35728	+	7.54704i	0.261804	+	0.453458i	0.966721	−	0.255832i	$-0.0823493\pi$
$277$	4.35728	+	7.54704i	0.261804	+	0.453458i	−0.704917	+	0.709289i	$0.749016\pi$
$278$	−8.53733	+	14.7871i	−0.512035	+	0.886871i
$279$		0			0
$280$	12.4265	−	0.909639i	0.742627	−	0.0543613i
$281$	6.20641			0.370243			0.185122	−	0.982716i	$-0.440732\pi$
$281$	6.20641			0.370243			0.185122	+	0.982716i	$0.440732\pi$
$282$		0			0
$283$	−9.82943	−	17.0251i	−0.584299	−	1.01204i	−0.994962	−	0.100248i	$-0.968036\pi$
$283$	−9.82943	−	17.0251i	−0.584299	−	1.01204i	0.410664	−	0.911787i	$-0.365297\pi$
$284$	2.66949	+	4.62370i	0.158405	+	0.274366i
$285$		0			0
$286$	19.5170			1.15406
$287$	−16.0514	−	23.6307i	−0.947483	−	1.39488i
$288$		0			0
$289$	6.25627	−	10.8362i	0.368016	−	0.637422i
$290$	−7.28073	−	12.6106i	−0.427539	−	0.740519i
$291$		0			0
$292$	2.29332	−	3.97215i	0.134207	−	0.232453i
$293$	14.4968			0.846913			0.423456	−	0.905916i	$-0.360817\pi$
$293$	14.4968			0.846913			0.423456	+	0.905916i	$0.360817\pi$
$294$		0			0
$295$	9.05058			0.526945
$296$	−0.282768	+	0.489769i	−0.0164356	+	0.0284672i
$297$		0			0
$298$	−2.03977	−	3.53299i	−0.118161	−	0.204661i
$299$	8.87352	−	15.3694i	0.513169	−	0.888834i
$300$		0			0
$301$	−7.23860	−	10.6566i	−0.417226	−	0.614237i
$302$	21.6342			1.24491
$303$		0			0
$304$	−7.48413	−	12.9629i	−0.429244	−	0.743473i
$305$	5.34193	+	9.25249i	0.305878	+	0.529796i
$306$		0			0
$307$	22.2776			1.27145			0.635725	−	0.771916i	$-0.280701\pi$
$307$	22.2776			1.27145			0.635725	+	0.771916i	$0.280701\pi$
$308$	−3.27459	+	0.239705i	−0.186587	+	0.0136584i
$309$		0			0
$310$	5.43055	−	9.40599i	0.308435	−	0.534225i
$311$	8.70027	+	15.0693i	0.493347	+	0.854502i	0.999971	−	0.00766509i	$-0.00243990\pi$
$311$	8.70027	+	15.0693i	0.493347	+	0.854502i	−0.506623	+	0.862167i	$0.669107\pi$
$312$		0			0
$313$	0.100022	−	0.173244i	0.00565360	−	0.00979232i	−0.863185	−	0.504888i	$-0.831534\pi$
$313$	0.100022	−	0.173244i	0.00565360	−	0.00979232i	0.868838	+	0.495096i	$0.164867\pi$
$314$	11.9833			0.676254
$315$		0			0
$316$	0.506163			0.0284739
$317$	4.11706	−	7.13096i	0.231237	−	0.400514i	−0.726935	−	0.686706i	$-0.759056\pi$
$317$	4.11706	−	7.13096i	0.231237	−	0.400514i	0.958172	+	0.286192i	$0.0923894\pi$
$318$		0			0
$319$	11.8440	+	20.5144i	0.663138	+	1.14859i
$320$	6.90590	−	11.9614i	0.386052	−	0.668661i
$321$		0			0
$322$	5.42549	−	11.2165i	0.302351	−	0.625072i
$323$	−10.3038			−0.573317
$324$		0			0
$325$	6.19074	+	10.7227i	0.343400	+	0.594787i
$326$	−2.33556	−	4.04530i	−0.129354	−	0.224049i
$327$		0			0
$328$	−32.7312			−1.80728
$329$	−4.67543	+	0.342248i	−0.257765	+	0.0188687i
$330$		0			0
$331$	8.31616	−	14.4040i	0.457098	−	0.791716i	−0.541708	−	0.840566i	$-0.682222\pi$
$331$	8.31616	−	14.4040i	0.457098	−	0.791716i	0.998806	+	0.0488501i	$0.0155557\pi$
$332$	0.0669762	+	0.116006i	0.00367580	+	0.00636667i
$333$		0			0
$334$	1.02262	−	1.77122i	0.0559551	−	0.0969170i
$335$	−19.0107			−1.03867
$336$		0			0
$337$	15.9095			0.866645			0.433322	−	0.901239i	$-0.357341\pi$
$337$	15.9095			0.866645			0.433322	+	0.901239i	$0.357341\pi$
$338$	−6.29535	+	10.9039i	−0.342422	+	0.593092i
$339$		0			0
$340$	−0.636127	−	1.10180i	−0.0344988	−	0.0597537i
$341$	−8.83422	+	15.3013i	−0.478400	+	0.828613i
$342$		0			0
$343$	18.0770	−	4.02745i	0.976069	−	0.217462i
$344$	−14.7606			−0.795839
$345$		0			0
$346$	10.2786	+	17.8031i	0.552581	+	0.957098i
$347$	3.14462	+	5.44665i	0.168812	+	0.292391i	0.938003	−	0.346628i	$-0.112674\pi$
$347$	3.14462	+	5.44665i	0.168812	+	0.292391i	−0.769190	+	0.639020i	$0.779340\pi$
$348$		0			0
$349$	1.61955			0.0866927			0.0433463	−	0.999060i	$-0.486198\pi$
$349$	1.61955			0.0866927			0.0433463	+	0.999060i	$0.486198\pi$
$350$	4.88437	+	7.19074i	0.261081	+	0.384361i
$351$		0			0
$352$	−3.45731	+	5.98823i	−0.184275	+	0.319174i
$353$	16.2559	+	28.1560i	0.865213	+	1.49859i	0.866836	+	0.498594i	$0.166150\pi$
$353$	16.2559	+	28.1560i	0.865213	+	1.49859i	−0.00162266	+	0.999999i	$0.500517\pi$
$354$		0			0
$355$	10.7270	−	18.5796i	0.569328	−	0.986104i
$356$	−6.72933			−0.356654
$357$		0			0
$358$	−22.1095			−1.16852
$359$	5.59588	−	9.69235i	0.295339	−	0.511543i	−0.679724	−	0.733468i	$-0.737901\pi$
$359$	5.59588	−	9.69235i	0.295339	−	0.511543i	0.975064	+	0.221925i	$0.0712340\pi$
$360$		0			0
$361$	−2.32938	−	4.03461i	−0.122599	−	0.212348i
$362$	−5.64978	+	9.78570i	−0.296946	+	0.514325i
$363$		0			0
$364$	2.13195	−	4.40753i	0.111744	−	0.231017i
$365$	−18.4307			−0.964709
$366$		0			0
$367$	2.59339	+	4.49188i	0.135374	+	0.234474i	0.925740	−	0.378160i	$-0.123443\pi$
$367$	2.59339	+	4.49188i	0.135374	+	0.234474i	−0.790366	+	0.612634i	$0.790110\pi$
$368$	−5.70474	−	9.88089i	−0.297380	−	0.515077i
$369$		0			0
$370$	0.368122			0.0191377
$371$	1.92264	−	3.97482i	0.0998187	−	0.206362i
$372$		0			0
$373$	−16.4322	+	28.4614i	−0.850825	+	1.47367i	0.0296389	+	0.999561i	$0.490564\pi$
$373$	−16.4322	+	28.4614i	−0.850825	+	1.47367i	−0.880464	+	0.474112i	$0.842769\pi$
$374$	−4.31864	−	7.48010i	−0.223312	−	0.386787i
$375$		0			0
$376$	−2.68568	+	4.65173i	−0.138503	+	0.239895i
$377$	−35.3231			−1.81923
$378$		0			0
$379$	13.9362			0.715856			0.357928	−	0.933749i	$-0.383483\pi$
$379$	13.9362			0.715856			0.357928	+	0.933749i	$0.383483\pi$
$380$	1.46063	−	2.52988i	0.0749286	−	0.129780i
$381$		0			0
$382$	−9.39449	−	16.2717i	−0.480664	−	0.832534i
$383$	−0.857601	+	1.48541i	−0.0438214	+	0.0759008i	−0.887104	−	0.461569i	$-0.847287\pi$
$383$	−0.857601	+	1.48541i	−0.0438214	+	0.0759008i	0.843283	+	0.537470i	$0.180620\pi$
$384$		0			0
$385$	7.41340	+	10.9139i	0.377822	+	0.556226i
$386$	2.31376			0.117768
$387$		0			0
$388$	−2.04285	−	3.53832i	−0.103710	−	0.179631i
$389$	−1.57428	−	2.72673i	−0.0798191	−	0.138251i	0.823353	−	0.567530i	$-0.192101\pi$
$389$	−1.57428	−	2.72673i	−0.0798191	−	0.138251i	−0.903172	+	0.429279i	$0.858768\pi$
$390$		0			0
$391$	−7.85400			−0.397194
$392$	7.82085	−	19.7264i	0.395012	−	0.996332i
$393$		0			0
$394$	−4.90277	+	8.49184i	−0.246998	+	0.427813i
$395$	−1.01697	−	1.76144i	−0.0511693	−	0.0886277i
$396$		0			0
$397$	−13.7172	+	23.7590i	−0.688449	+	1.19243i	0.283891	+	0.958857i	$0.408375\pi$
$397$	−13.7172	+	23.7590i	−0.688449	+	1.19243i	−0.972340	+	0.233572i	$0.924959\pi$
$398$	2.81134			0.140920
$399$		0			0
$400$	7.95998			0.397999
$401$	14.5185	−	25.1468i	0.725020	−	1.25577i	−0.233946	−	0.972250i	$-0.575164\pi$
$401$	14.5185	−	25.1468i	0.725020	−	1.25577i	0.958966	−	0.283522i	$-0.0915029\pi$
$402$		0			0
$403$	−13.1734	−	22.8170i	−0.656214	−	1.13660i
$404$	0.393161	−	0.680975i	0.0195605	−	0.0338798i
$405$		0			0
$406$	−24.7333	+	1.81051i	−1.22750	+	0.0898543i
$407$	−0.598847			−0.0296837
$408$		0			0
$409$	13.8650	+	24.0149i	0.685581	+	1.18746i	0.973254	+	0.229732i	$0.0737851\pi$
$409$	13.8650	+	24.0149i	0.685581	+	1.18746i	−0.287673	+	0.957729i	$0.592882\pi$
$410$	10.6528	+	18.4511i	0.526103	+	0.911237i
$411$		0			0
$412$	−7.72491			−0.380579
$413$	6.71188	−	13.8759i	0.330270	−	0.682791i
$414$		0			0
$415$	0.269134	−	0.466153i	0.0132113	−	0.0228826i
$416$	−5.15546	−	8.92952i	−0.252767	−	0.437806i
$417$		0			0
$418$	9.91614	−	17.1753i	0.485014	−	0.840070i
$419$	−30.3598			−1.48317			−0.741586	−	0.670857i	$-0.765926\pi$
$419$	−30.3598			−1.48317			−0.741586	+	0.670857i	$0.765926\pi$
$420$		0			0
$421$	−27.7735			−1.35360			−0.676799	−	0.736168i	$-0.736633\pi$
$421$	−27.7735			−1.35360			−0.676799	+	0.736168i	$0.736633\pi$
$422$	1.15171	−	1.99483i	0.0560646	−	0.0971067i
$423$		0			0
$424$	−2.52954	−	4.38129i	−0.122845	−	0.212774i
$425$	2.73973	−	4.74535i	0.132896	−	0.230183i
$426$		0			0
$427$	18.1471	−	1.32839i	0.878197	−	0.0642853i
$428$	6.53605			0.315932
$429$		0			0
$430$	4.80402	+	8.32081i	0.231671	+	0.401265i
$431$	−3.62965	−	6.28673i	−0.174834	−	0.302821i	0.765270	−	0.643710i	$-0.222606\pi$
$431$	−3.62965	−	6.28673i	−0.174834	−	0.302821i	−0.940104	+	0.340888i	$0.889272\pi$
$432$		0			0
$433$	15.0375			0.722658			0.361329	−	0.932438i	$-0.382323\pi$
$433$	15.0375			0.722658			0.361329	+	0.932438i	$0.382323\pi$
$434$	−10.3936	−	15.3013i	−0.498907	−	0.734487i
$435$		0			0
$436$	−2.06814	+	3.58213i	−0.0990460	+	0.171553i
$437$	−9.01688	−	15.6177i	−0.431336	−	0.747096i
$438$		0			0
$439$	−0.770595	+	1.33471i	−0.0367785	+	0.0637022i	−0.883829	−	0.467811i	$-0.845043\pi$
$439$	−0.770595	+	1.33471i	−0.0367785	+	0.0637022i	0.847050	+	0.531513i	$0.178376\pi$
$440$	15.1170			0.720677
$441$		0			0
$442$	12.8797			0.612626
$443$	−10.1689	+	17.6131i	−0.483141	+	0.836824i	−0.999813	−	0.0193593i	$-0.993837\pi$
$443$	−10.1689	+	17.6131i	−0.483141	+	0.836824i	0.516672	+	0.856183i	$0.327171\pi$
$444$		0			0
$445$	13.5204	+	23.4180i	0.640928	+	1.11012i
$446$	−6.03735	+	10.4570i	−0.285877	+	0.495153i
$447$		0			0
$448$	−13.2172	−	19.4583i	−0.624456	−	0.919319i
$449$	26.4527			1.24838			0.624190	−	0.781272i	$-0.285429\pi$
$449$	26.4527			1.24838			0.624190	+	0.781272i	$0.285429\pi$
$450$		0			0
$451$	−17.3295	−	30.0156i	−0.816016	−	1.41338i
$452$	−1.65943	−	2.87422i	−0.0780530	−	0.135192i
$453$		0			0
$454$	−13.7599			−0.645786
$455$	−19.6216	+	1.43633i	−0.919875	+	0.0673361i
$456$		0			0
$457$	3.24681	−	5.62363i	0.151879	−	0.263063i	−0.780039	−	0.625731i	$-0.784801\pi$
$457$	3.24681	−	5.62363i	0.151879	−	0.263063i	0.931918	+	0.362668i	$0.118134\pi$
$458$	−7.95121	−	13.7719i	−0.371536	−	0.643518i
$459$		0			0
$460$	1.11336	−	1.92839i	0.0519105	−	0.0899116i
$461$	15.5916			0.726175			0.363088	−	0.931755i	$-0.381723\pi$
$461$	15.5916			0.726175			0.363088	+	0.931755i	$0.381723\pi$
$462$		0			0
$463$	7.65585			0.355797			0.177899	−	0.984049i	$-0.443070\pi$
$463$	7.65585			0.355797			0.177899	+	0.984049i	$0.443070\pi$
$464$	−11.3545	+	19.6666i	−0.527120	+	0.912999i
$465$		0			0
$466$	−9.70486	−	16.8093i	−0.449569	−	0.778676i
$467$	20.8137	−	36.0503i	0.963142	−	1.66821i	0.248615	−	0.968602i	$-0.420024\pi$
$467$	20.8137	−	36.0503i	0.963142	−	1.66821i	0.714526	−	0.699608i	$-0.246642\pi$
$468$		0			0
$469$	−14.0983	+	29.1464i	−0.650998	+	1.34585i
$470$	3.49635			0.161274
$471$		0			0
$472$	−8.83053	−	15.2949i	−0.406458	−	0.704006i
$473$	−7.81501	−	13.5360i	−0.359335	−	0.622386i
$474$		0			0
$475$	12.5815			0.577280
$476$	−2.16099	+	0.158187i	−0.0990486	+	0.00725050i
$477$		0			0
$478$	−6.80560	+	11.7876i	−0.311281	+	0.539154i
$479$	−1.15789	−	2.00553i	−0.0529055	−	0.0916350i	0.838360	−	0.545117i	$-0.183515\pi$
$479$	−1.15789	−	2.00553i	−0.0529055	−	0.0916350i	−0.891265	+	0.453482i	$0.850182\pi$
$480$		0			0
$481$	0.446494	−	0.773350i	0.0203584	−	0.0352617i
$482$	−19.0532			−0.867851
$483$		0			0
$484$	0.269022			0.0122283
$485$	−8.20888	+	14.2182i	−0.372746	+	0.645615i
$486$		0			0
$487$	−9.06396	−	15.6992i	−0.410727	−	0.711401i	0.584242	−	0.811579i	$-0.301392\pi$
$487$	−9.06396	−	15.6992i	−0.410727	−	0.711401i	−0.994969	+	0.100179i	$0.968058\pi$
$488$	10.4241	−	18.0551i	0.471876	−	0.817314i
$489$		0			0
$490$	−13.6655	+	2.01144i	−0.617344	+	0.0908677i
$491$	−21.5944			−0.974542			−0.487271	−	0.873251i	$-0.662008\pi$
$491$	−21.5944			−0.974542			−0.487271	+	0.873251i	$0.662008\pi$
$492$		0			0
$493$	7.81616	+	13.5380i	0.352022	+	0.609720i
$494$	14.7867	+	25.6114i	0.665287	+	1.15231i
$495$		0			0
$496$	−16.9382			−0.760549
$497$	−20.5304	−	30.2247i	−0.920913	−	1.35576i
$498$		0			0
$499$	−13.5827	+	23.5259i	−0.608045	+	1.05316i	0.383518	+	0.923534i	$0.374713\pi$
$499$	−13.5827	+	23.5259i	−0.608045	+	1.05316i	−0.991562	+	0.129631i	$0.958621\pi$
$500$	2.27821	+	3.94597i	0.101885	+	0.176469i
$501$		0			0
$502$	10.5213	−	18.2235i	0.469590	−	0.813354i
$503$	−11.8850			−0.529927			−0.264964	−	0.964258i	$-0.585360\pi$
$503$	−11.8850			−0.529927			−0.264964	+	0.964258i	$0.585360\pi$
$504$		0			0
$505$	−3.15972			−0.140606
$506$	7.55852	−	13.0917i	0.336017	−	0.581999i
$507$		0			0
$508$	0.377250	+	0.653415i	0.0167377	+	0.0289906i
$509$	−20.7297	+	35.9049i	−0.918829	+	1.59146i	−0.117632	+	0.993057i	$0.537530\pi$
$509$	−20.7297	+	35.9049i	−0.918829	+	1.59146i	−0.801197	+	0.598401i	$0.795803\pi$
$510$		0			0
$511$	−13.6682	+	28.2572i	−0.604644	+	1.25002i
$512$	−25.2864			−1.11751
$513$		0			0
$514$	14.3387	+	24.8354i	0.632455	+	1.09544i
$515$	15.5207	+	26.8826i	0.683923	+	1.18459i
$516$		0			0
$517$	−5.68773			−0.250146
$518$	0.272998	−	0.564387i	0.0119948	−	0.0247978i
$519$		0			0
$520$	−11.2711	+	19.5221i	−0.494271	+	0.856102i
$521$	1.65221	+	2.86171i	0.0723846	+	0.125374i	0.899946	−	0.436002i	$-0.143606\pi$
$521$	1.65221	+	2.86171i	0.0723846	+	0.125374i	−0.827561	+	0.561375i	$0.810272\pi$
$522$		0			0
$523$	1.24483	−	2.15611i	0.0544327	−	0.0942803i	−0.837525	−	0.546399i	$-0.815998\pi$
$523$	1.24483	−	2.15611i	0.0544327	−	0.0942803i	0.891958	+	0.452119i	$0.149332\pi$
$524$	−4.54035			−0.198346
$525$		0			0
$526$	−28.3839			−1.23760
$527$	−5.82992	+	10.0977i	−0.253955	+	0.439864i
$528$		0			0
$529$	4.62693	+	8.01408i	0.201171	+	0.348438i
$530$	−1.64654	+	2.85189i	−0.0715211	+	0.123878i
$531$		0			0
$532$	−2.79550	−	4.11552i	−0.121200	−	0.178430i
$533$	51.6829			2.23863
$534$		0			0
$535$	−13.1321	−	22.7454i	−0.567748	−	0.983369i
$536$	18.5485	+	32.1269i	0.801173	+	1.38767i
$537$		0			0
$538$	−35.4321			−1.52758
$539$	22.2305	−	3.27214i	0.957536	−	0.140941i
$540$		0			0
$541$	11.2397	−	19.4677i	0.483233	−	0.836984i	−0.516582	−	0.856238i	$-0.672796\pi$
$541$	11.2397	−	19.4677i	0.483233	−	0.836984i	0.999815	+	0.0192542i	$0.00612919\pi$
$542$	−6.27114	−	10.8619i	−0.269369	−	0.466560i
$543$		0			0
$544$	−2.28156	+	3.95178i	−0.0978212	+	0.169431i
$545$	16.6210			0.711966
$546$		0			0
$547$	−14.5545			−0.622307			−0.311154	−	0.950360i	$-0.600715\pi$
$547$	−14.5545			−0.622307			−0.311154	+	0.950360i	$0.600715\pi$
$548$	3.11834	−	5.40112i	0.133209	−	0.230725i
$549$		0			0
$550$	5.27331	+	9.13365i	0.224855	+	0.389460i
$551$	−17.9469	+	31.0849i	−0.764564	+	1.32426i
$552$		0			0
$553$	−3.45474	+	0.252892i	−0.146911	+	0.0107541i
$554$	−11.0692			−0.470286
$555$		0			0
$556$	2.59845	+	4.50065i	0.110199	+	0.190870i
$557$	7.77331	+	13.4638i	0.329366	+	0.570478i	0.982386	−	0.186862i	$-0.0598318\pi$
$557$	7.77331	+	13.4638i	0.329366	+	0.570478i	−0.653021	+	0.757340i	$0.726498\pi$
$558$		0			0
$559$	23.3071			0.985787
$560$	−5.50762	+	11.3863i	−0.232739	+	0.481158i
$561$		0			0
$562$	−3.94168	+	6.82719i	−0.166270	+	0.287988i
$563$	−7.36914	−	12.7637i	−0.310572	−	0.537927i	0.667914	−	0.744238i	$-0.267187\pi$
$563$	−7.36914	−	12.7637i	−0.310572	−	0.537927i	−0.978486	+	0.206312i	$0.933854\pi$
$564$		0			0
$565$	−6.66816	+	11.5496i	−0.280532	+	0.485895i
$566$	24.9706			1.04959
$567$		0			0
$568$	−41.8646			−1.75660
$569$	6.48539	−	11.2330i	0.271882	−	0.470913i	−0.697462	−	0.716622i	$-0.745687\pi$
$569$	6.48539	−	11.2330i	0.271882	−	0.470913i	0.969344	+	0.245709i	$0.0790207\pi$
$570$		0			0
$571$	−6.42929	−	11.1359i	−0.269058	−	0.466021i	0.699561	−	0.714573i	$-0.253379\pi$
$571$	−6.42929	−	11.1359i	−0.269058	−	0.466021i	−0.968619	+	0.248551i	$0.920046\pi$
$572$	2.97012	−	5.14440i	0.124187	−	0.215098i
$573$		0			0
$574$	36.1885	−	2.64905i	1.51048	−	0.110569i
$575$	9.59019			0.399939
$576$		0			0
$577$	5.26279	+	9.11542i	0.219093	+	0.379480i	0.954531	−	0.298112i	$-0.0963569\pi$
$577$	5.26279	+	9.11542i	0.219093	+	0.379480i	−0.735438	+	0.677592i	$0.763024\pi$
$578$	7.94669	+	13.7641i	0.330539	+	0.572510i
$579$		0			0
$580$	−4.43197			−0.184028
$581$	−0.515097	−	0.758321i	−0.0213698	−	0.0314605i
$582$		0			0
$583$	2.67853	−	4.63935i	0.110933	−	0.192142i
$584$	17.9826	+	31.1468i	0.744126	+	1.28886i
$585$		0			0
$586$	−9.20690	+	15.9468i	−0.380334	+	0.658757i
$587$	6.20018			0.255909			0.127954	−	0.991780i	$-0.459159\pi$
$587$	6.20018			0.255909			0.127954	+	0.991780i	$0.459159\pi$
$588$		0			0
$589$	−26.7725			−1.10314
$590$	−5.74801	+	9.95585i	−0.236642	+	0.409876i
$591$		0			0
$592$	−0.287048	−	0.497182i	−0.0117976	−	0.0204341i
$593$	18.7629	−	32.4984i	0.770502	−	1.33455i	−0.166787	−	0.985993i	$-0.553339\pi$
$593$	18.7629	−	32.4984i	0.770502	−	1.33455i	0.937288	−	0.348555i	$-0.113327\pi$
$594$		0			0
$595$	4.89229	+	7.20239i	0.200564	+	0.295269i
$596$	−1.24166			−0.0508605
$597$		0			0
$598$	11.2711	+	19.5221i	0.460910	+	0.798319i
$599$	−17.5460	−	30.3905i	−0.716909	−	1.24172i	−0.962218	−	0.272279i	$-0.912223\pi$
$599$	−17.5460	−	30.3905i	−0.716909	−	1.24172i	0.245309	−	0.969445i	$-0.421111\pi$
$600$		0			0
$601$	26.2342			1.07012			0.535058	−	0.844815i	$-0.320290\pi$
$601$	26.2342			1.07012			0.535058	+	0.844815i	$0.320290\pi$
$602$	16.3197	−	1.19463i	0.665143	−	0.0486894i
$603$		0			0
$604$	3.29233	−	5.70249i	0.133963	−	0.232031i
$605$	−0.540512	−	0.936194i	−0.0219749	−	0.0380617i
$606$		0			0
$607$	1.10933	−	1.92142i	0.0450263	−	0.0779879i	−0.842634	−	0.538487i	$-0.818996\pi$
$607$	1.10933	−	1.92142i	0.0450263	−	0.0779879i	0.887660	+	0.460499i	$0.152329\pi$
$608$	−10.4775			−0.424919
$609$		0			0
$610$	−13.5706			−0.549457
$611$	4.24071	−	7.34512i	0.171561	−	0.297152i
$612$		0			0
$613$	−7.43312	−	12.8745i	−0.300221	−	0.519998i	0.675965	−	0.736934i	$-0.263727\pi$
$613$	−7.43312	−	12.8745i	−0.300221	−	0.519998i	−0.976186	+	0.216936i	$0.930394\pi$
$614$	−14.1485	+	24.5059i	−0.570986	+	0.988976i
$615$		0			0
$616$	11.2107	−	23.1768i	0.451694	−	0.933819i
$617$	23.2046			0.934181			0.467091	−	0.884210i	$-0.345302\pi$
$617$	23.2046			0.934181			0.467091	+	0.884210i	$0.345302\pi$
$618$		0			0
$619$	4.15562	+	7.19775i	0.167029	+	0.289302i	0.937374	−	0.348325i	$-0.113249\pi$
$619$	4.15562	+	7.19775i	0.167029	+	0.289302i	−0.770345	+	0.637627i	$0.779916\pi$
$620$	−1.65286	−	2.86284i	−0.0663805	−	0.114974i
$621$		0			0
$622$	−22.1021			−0.886214
$623$	45.9301	−	3.36215i	1.84015	−	0.134701i
$624$		0			0
$625$	2.68802	−	4.65578i	0.107521	−	0.186231i
$626$	0.127048	+	0.220054i	0.00507786	+	0.00879511i
$627$		0			0
$628$	1.82363	−	3.15862i	0.0727708	−	0.126043i
$629$	−0.395194			−0.0157574
$630$		0			0
$631$	−24.5415			−0.976982			−0.488491	−	0.872569i	$-0.662452\pi$
$631$	−24.5415			−0.976982			−0.488491	+	0.872569i	$0.662452\pi$
$632$	−1.98448	+	3.43723i	−0.0789386	+	0.136726i
$633$		0			0
$634$	5.22947	+	9.05771i	0.207689	+	0.359728i
$635$	1.51592	−	2.62565i	0.0601574	−	0.104196i
$636$		0			0
$637$	−12.3492	+	31.1481i	−0.489293	+	1.23413i
$638$	−30.0885			−1.19121
$639$		0			0
$640$	5.42549	+	9.39723i	0.214461	+	0.371458i
$641$	−3.98762	−	6.90677i	−0.157502	−	0.272801i	0.776465	−	0.630160i	$-0.217011\pi$
$641$	−3.98762	−	6.90677i	−0.157502	−	0.272801i	−0.933967	+	0.357359i	$0.883677\pi$
$642$		0			0
$643$	−3.12279			−0.123151			−0.0615755	−	0.998102i	$-0.519612\pi$
$643$	−3.12279			−0.123151			−0.0615755	+	0.998102i	$0.519612\pi$
$644$	−2.13086	−	3.13703i	−0.0839675	−	0.123616i
$645$		0			0
$646$	6.54391	−	11.3344i	0.257467	−	0.445945i
$647$	6.13273	+	10.6222i	0.241102	+	0.417602i	0.961029	−	0.276449i	$-0.0891577\pi$
$647$	6.13273	+	10.6222i	0.241102	+	0.417602i	−0.719926	+	0.694051i	$0.755824\pi$
$648$		0			0
$649$	9.35065	−	16.1958i	0.367045	−	0.635741i
$650$	−15.7269			−0.616860
$651$		0			0
$652$	−1.42171			−0.0556786
$653$	−8.25476	+	14.2977i	−0.323034	+	0.559511i	−0.981112	−	0.193438i	$-0.938036\pi$
$653$	−8.25476	+	14.2977i	−0.323034	+	0.559511i	0.658079	+	0.752949i	$0.271369\pi$
$654$		0			0
$655$	9.12235	+	15.8004i	0.356440	+	0.617372i
$656$	16.6133	−	28.7751i	0.648641	−	1.12348i
$657$		0			0
$658$	2.59288	−	5.36044i	0.101081	−	0.208972i
$659$	10.7388			0.418324			0.209162	−	0.977881i	$-0.432926\pi$
$659$	10.7388			0.418324			0.209162	+	0.977881i	$0.432926\pi$
$660$		0			0
$661$	6.68817	+	11.5843i	0.260140	+	0.450575i	0.966279	−	0.257498i	$-0.0828980\pi$
$661$	6.68817	+	11.5843i	0.260140	+	0.450575i	−0.706139	+	0.708073i	$0.749565\pi$
$662$	10.5632	+	18.2959i	0.410549	+	0.711092i
$663$		0			0
$664$	−1.05036			−0.0407619
$665$	−8.70532	+	17.9971i	−0.337578	+	0.697898i
$666$		0			0
$667$	−13.6799	+	23.6943i	−0.529689	+	0.917448i
$668$	−0.311247	−	0.539095i	−0.0120425	−	0.0208582i
$669$		0			0
$670$	12.0737	−	20.9122i	0.466447	−	0.807909i
$671$	22.0761			0.852240
$672$		0			0
$673$	40.8986			1.57653			0.788264	−	0.615338i	$-0.210980\pi$
$673$	40.8986			1.57653			0.788264	+	0.615338i	$0.210980\pi$
$674$	−10.1041	+	17.5008i	−0.389195	+	0.674105i
$675$		0			0
$676$	1.91607	+	3.31874i	0.0736951	+	0.127644i
$677$	10.6250	−	18.4031i	0.408353	−	0.707288i	−0.586353	−	0.810056i	$-0.699437\pi$
$677$	10.6250	−	18.4031i	0.408353	−	0.707288i	0.994705	+	0.102768i	$0.0327700\pi$
$678$		0			0
$679$	15.7110	+	23.1296i	0.602933	+	0.887634i
$680$	9.97612			0.382567
$681$		0			0
$682$	−11.2212	−	19.4357i	−0.429682	−	0.744231i
$683$	−20.6708	−	35.8029i	−0.790948	−	1.36996i	−0.925381	−	0.379039i	$-0.876255\pi$
$683$	−20.6708	−	35.8029i	−0.790948	−	1.36996i	0.134433	−	0.990923i	$-0.457079\pi$
$684$		0			0
$685$	−25.0612			−0.957537
$686$	−7.05042	+	22.4430i	−0.269186	+	0.856877i
$687$		0			0
$688$	7.49202	−	12.9766i	0.285631	−	0.494727i
$689$	3.99417	+	6.91810i	0.152166	+	0.263559i
$690$		0			0
$691$	0.760183	−	1.31668i	0.0289187	−	0.0500887i	−0.851204	−	0.524835i	$-0.824127\pi$
$691$	0.760183	−	1.31668i	0.0289187	−	0.0500887i	0.880123	+	0.474747i	$0.157460\pi$
$692$	6.25685			0.237850
$693$		0			0
$694$	−7.98858			−0.303242
$695$	10.4415	−	18.0852i	0.396068	−	0.686009i
$696$		0			0
$697$	−11.4362	−	19.8081i	−0.433177	−	0.750284i
$698$	−1.02858	+	1.78154i	−0.0389321	+	0.0674325i
$699$		0			0
$700$	2.63869	−	0.193156i	0.0997331	−	0.00730060i
$701$	−32.5344			−1.22881			−0.614404	−	0.788991i	$-0.710604\pi$
$701$	−32.5344			−1.22881			−0.614404	+	0.788991i	$0.710604\pi$
$702$		0			0
$703$	−0.453708	−	0.785845i	−0.0171119	−	0.0296387i
$704$	−14.2697	−	24.7159i	−0.537811	−	0.931515i
$705$		0			0
$706$	−41.2963			−1.55421
$707$	−2.34323	+	4.84433i	−0.0881264	+	0.182190i
$708$		0			0
$709$	−11.2810	+	19.5394i	−0.423669	+	0.733816i	−0.996295	−	0.0860007i	$-0.972591\pi$
$709$	−11.2810	+	19.5394i	−0.423669	+	0.733816i	0.572626	+	0.819816i	$0.305925\pi$
$710$	13.6253	+	23.5998i	0.511350	+	0.885684i
$711$		0			0
$712$	26.3833	−	45.6972i	0.988756	−	1.71258i
$713$	−20.4072			−0.764255
$714$		0			0
$715$	−23.8700			−0.892686
$716$	−3.36466	+	5.82777i	−0.125743	+	0.217794i
$717$		0			0
$718$	7.10787	+	12.3112i	0.265263	+	0.459450i
$719$	3.25084	−	5.63062i	0.121236	−	0.209987i	−0.799019	−	0.601305i	$-0.794648\pi$
$719$	3.25084	−	5.63062i	0.121236	−	0.209987i	0.920255	+	0.391319i	$0.127981\pi$
$720$		0			0
$721$	52.7253	−	3.85956i	1.96359	−	0.143738i
$722$	5.91755			0.220228
$723$		0			0
$724$	1.71958	+	2.97841i	0.0639078	+	0.110692i
$725$	−9.54400	−	16.5307i	−0.354455	−	0.613934i
$726$		0			0
$727$	−7.83215			−0.290478			−0.145239	−	0.989397i	$-0.546395\pi$
$727$	−7.83215			−0.290478			−0.145239	+	0.989397i	$0.546395\pi$
$728$	21.5718	+	31.7579i	0.799505	+	1.17703i
$729$		0			0
$730$	11.7053	−	20.2742i	0.433234	−	0.750383i
$731$	−5.15732	−	8.93274i	−0.190750	−	0.330389i
$732$		0			0
$733$	3.74780	−	6.49138i	0.138428	−	0.239764i	−0.788474	−	0.615068i	$-0.789128\pi$
$733$	3.74780	−	6.49138i	0.138428	−	0.239764i	0.926902	+	0.375304i	$0.122462\pi$
$734$	−6.58823			−0.243176
$735$		0			0
$736$	−7.98643			−0.294384
$737$	−19.6410	+	34.0192i	−0.723486	+	1.25311i
$738$		0			0
$739$	−12.0480	−	20.8678i	−0.443194	−	0.767634i	0.554731	−	0.832030i	$-0.312821\pi$
$739$	−12.0480	−	20.8678i	−0.443194	−	0.767634i	−0.997924	+	0.0643961i	$0.979488\pi$
$740$	0.0560213	−	0.0970318i	0.00205939	−	0.00356696i
$741$		0			0
$742$	3.15132	+	4.63935i	0.115689	+	0.170316i
$743$	19.2882			0.707616			0.353808	−	0.935318i	$-0.384887\pi$
$743$	19.2882			0.707616			0.353808	+	0.935318i	$0.384887\pi$
$744$		0			0
$745$	2.49472	+	4.32098i	0.0913994	+	0.158308i
$746$	−20.8721	−	36.1515i	−0.764181	−	1.32360i
$747$		0			0
$748$	−2.62887			−0.0961210
$749$	−44.6109	+	3.26558i	−1.63005	+	0.119322i
$750$		0			0
$751$	16.6045	−	28.7598i	0.605906	−	1.04946i	−0.386002	−	0.922498i	$-0.626144\pi$
$751$	16.6045	−	28.7598i	0.605906	−	1.04946i	0.991908	−	0.126961i	$-0.0405225\pi$
$752$	−2.72633	−	4.72214i	−0.0994190	−	0.172199i
$753$		0			0
$754$	22.4336	−	38.8562i	0.816985	−	1.41506i
$755$	−26.4595			−0.962959
$756$		0			0
$757$	9.70935			0.352892			0.176446	−	0.984310i	$-0.443540\pi$
$757$	9.70935			0.352892			0.176446	+	0.984310i	$0.443540\pi$
$758$	−8.85088	+	15.3302i	−0.321478	+	0.556817i
$759$		0			0
$760$	11.4532	+	19.8375i	0.415452	+	0.719583i
$761$	−1.36305	+	2.36086i	−0.0494104	+	0.0855813i	−0.889673	−	0.456599i	$-0.849068\pi$
$761$	−1.36305	+	2.36086i	−0.0494104	+	0.0855813i	0.840262	+	0.542180i	$0.182401\pi$
$762$		0			0
$763$	12.3261	−	25.4826i	0.446234	−	0.922532i
$764$	−5.71868			−0.206894
$765$		0			0
$766$	−1.08932	−	1.88676i	−0.0393588	−	0.0681714i
$767$	13.9435	+	24.1508i	0.503470	+	0.872036i
$768$		0			0
$769$	50.0460			1.80470			0.902352	−	0.430999i	$-0.141839\pi$
$769$	50.0460			1.80470			0.902352	+	0.430999i	$0.141839\pi$
$770$	−16.7138	+	1.22347i	−0.602324	+	0.0440910i
$771$		0			0
$772$	0.352112	−	0.609877i	0.0126728	−	0.0219499i
$773$	−9.52030	−	16.4896i	−0.342421	−	0.593091i	0.642461	−	0.766319i	$-0.277914\pi$
$773$	−9.52030	−	16.4896i	−0.342421	−	0.593091i	−0.984882	+	0.173228i	$0.944580\pi$
$774$		0			0
$775$	7.11868	−	12.3299i	0.255711	−	0.442904i
$776$	32.0372			1.15007
$777$		0			0
$778$	3.99928			0.143381
$779$	26.2589	−	45.4818i	0.940824	−	1.62956i
$780$		0			0
$781$	−22.1652	−	38.3912i	−0.793133	−	1.37375i
$782$	4.98806	−	8.63957i	0.178373	−	0.308950i
$783$		0			0
$784$	13.3725	+	16.8881i	0.477590	+	0.603145i
$785$	−14.6560			−0.523094
$786$		0			0
$787$	16.6011	+	28.7540i	0.591766	+	1.02497i	0.993995	+	0.109430i	$0.0349025\pi$
$787$	16.6011	+	28.7540i	0.591766	+	1.02497i	−0.402228	+	0.915539i	$0.631764\pi$
$788$	1.49222	+	2.58460i	0.0531582	+	0.0920727i
$789$		0			0
$790$	2.58350			0.0919168
$791$	12.7622	+	18.7885i	0.453773	+	0.668041i
$792$		0			0
$793$	−16.4597	+	28.5091i	−0.584502	+	1.01239i
$794$	−17.4236	−	30.1785i	−0.618340	−	1.07100i
$795$		0			0
$796$	0.427834	−	0.741030i	0.0151642	−	0.0262651i
$797$	2.08944			0.0740118			0.0370059	−	0.999315i	$-0.488218\pi$
$797$	2.08944			0.0740118			0.0370059	+	0.999315i	$0.488218\pi$
$798$		0			0
$799$	−3.75347			−0.132788
$800$	2.78592	−	4.82536i	0.0984972	−	0.170602i
$801$		0			0
$802$	18.4414	+	31.9414i	0.651187	+	1.12789i
$803$	−19.0418	+	32.9814i	−0.671970	+	1.16389i
$804$		0			0
$805$	−6.63558	+	13.7182i	−0.233873	+	0.483503i
$806$	33.4656			1.17878
$807$		0			0
$808$	3.08289	+	5.33973i	0.108456	+	0.187851i
$809$	−0.241404	−	0.418125i	−0.00848732	−	0.0147005i	0.861751	−	0.507332i	$-0.169368\pi$
$809$	−0.241404	−	0.418125i	−0.00848732	−	0.0147005i	−0.870238	+	0.492632i	$0.836035\pi$
$810$		0			0
$811$	17.1671			0.602820			0.301410	−	0.953495i	$-0.402543\pi$
$811$	17.1671			0.602820			0.301410	+	0.953495i	$0.402543\pi$
$812$	−3.28673	+	6.79490i	−0.115342	+	0.238454i
$813$		0			0
$814$	0.380327	−	0.658745i	0.0133304	−	0.0230890i
$815$	2.85647	+	4.94755i	0.100058	+	0.173305i
$816$		0			0
$817$	11.8419	−	20.5107i	0.414294	−	0.717578i
$818$	−35.2226			−1.23153
$819$		0			0
$820$	6.48462			0.226453
$821$	6.41086	−	11.1039i	0.223741	−	0.387530i	−0.732200	−	0.681089i	$-0.761507\pi$
$821$	6.41086	−	11.1039i	0.223741	−	0.387530i	0.955941	+	0.293559i	$0.0948398\pi$
$822$		0			0
$823$	−12.2973	−	21.2995i	−0.428655	−	0.742453i	0.568099	−	0.822961i	$-0.307679\pi$
$823$	−12.2973	−	21.2995i	−0.428655	−	0.742453i	−0.996754	+	0.0805075i	$0.974346\pi$
$824$	30.2866	−	52.4580i	1.05509	−	1.82746i
$825$		0			0
$826$	11.0011	+	16.1958i	0.382779	+	0.563524i
$827$	0.527165			0.0183313			0.00916567	−	0.999958i	$-0.497082\pi$
$827$	0.527165			0.0183313			0.00916567	+	0.999958i	$0.497082\pi$
$828$		0			0
$829$	23.1015	+	40.0130i	0.802348	+	1.38971i	0.918067	+	0.396426i	$0.129750\pi$
$829$	23.1015	+	40.0130i	0.802348	+	1.38971i	−0.115718	+	0.993282i	$0.536917\pi$
$830$	0.341853	+	0.592106i	0.0118659	+	0.0205523i
$831$		0			0
$832$	42.5574			1.47541
$833$	14.6705	−	2.15937i	0.508302	−	0.0748177i
$834$		0			0
$835$	−1.25070	+	2.16627i	−0.0432822	+	0.0749669i
$836$	−3.01811	−	5.22752i	−0.104383	−	0.180797i
$837$		0			0
$838$	19.2815	−	33.3965i	0.666067	−	1.15366i
$839$	−10.8258			−0.373747			−0.186874	−	0.982384i	$-0.559835\pi$
$839$	−10.8258			−0.373747			−0.186874	+	0.982384i	$0.559835\pi$
$840$		0			0
$841$	25.4561			0.877797
$842$	17.6389	−	30.5515i	0.607877	−	1.05287i
$843$		0			0
$844$	−0.350540	−	0.607152i	−0.0120661	−	0.0208990i
$845$	7.69945	−	13.3358i	0.264869	−	0.458767i
$846$		0			0
$847$	−1.83617	+	0.134410i	−0.0630916	+	0.00461839i
$848$	5.13566			0.176359
$849$		0			0
$850$	3.47999	+	6.02752i	0.119363	+	0.206742i
$851$	−0.345836	−	0.599006i	−0.0118551	−	0.0205337i
$852$		0			0
$853$	−43.1922			−1.47887			−0.739437	−	0.673226i	$-0.764908\pi$
$853$	−43.1922			−1.47887			−0.739437	+	0.673226i	$0.764908\pi$
$854$	−10.0639	+	20.8058i	−0.344380	+	0.711961i
$855$		0			0
$856$	−25.6255	+	44.3847i	−0.875863	+	1.51704i
$857$	−0.787226	−	1.36352i	−0.0268911	−	0.0465768i	0.852267	−	0.523108i	$-0.175227\pi$
$857$	−0.787226	−	1.36352i	−0.0268911	−	0.0465768i	−0.879158	+	0.476531i	$0.841894\pi$
$858$		0			0
$859$	−3.41090	+	5.90786i	−0.116378	+	0.201573i	−0.918330	−	0.395816i	$-0.870462\pi$
$859$	−3.41090	+	5.90786i	−0.116378	+	0.201573i	0.801951	+	0.597389i	$0.203795\pi$
$860$	2.92434			0.0997190
$861$		0			0
$862$	9.22073			0.314059
$863$	−4.51387	+	7.81825i	−0.153654	+	0.266136i	−0.932568	−	0.360994i	$-0.882437\pi$
$863$	−4.51387	+	7.81825i	−0.153654	+	0.266136i	0.778914	+	0.627131i	$0.215771\pi$
$864$		0			0
$865$	−12.5711	−	21.7738i	−0.427430	−	0.740331i
$866$	−9.55032	+	16.5416i	−0.324533	+	0.562108i
$867$		0			0
$868$	−5.61493	+	0.411021i	−0.190583	+	0.0139509i
$869$	−4.20274			−0.142568
$870$		0			0
$871$	−29.2882	−	50.7287i	−0.992394	−	1.71888i
$872$	−16.2169	−	28.0885i	−0.549174	−	0.951196i
$873$		0			0
$874$	22.9064			0.774821
$875$	−17.5211	−	25.7944i	−0.592321	−	0.872011i
$876$		0			0
$877$	−4.83460	+	8.37377i	−0.163253	+	0.282762i	−0.936033	−	0.351911i	$-0.885532\pi$
$877$	−4.83460	+	8.37377i	−0.163253	+	0.282762i	0.772781	+	0.634673i	$0.218865\pi$
$878$	−0.978807	−	1.69534i	−0.0330331	−	0.0572151i
$879$		0			0
$880$	−7.67293	+	13.2899i	−0.258655	+	0.448003i
$881$	−21.4721			−0.723415			−0.361707	−	0.932292i	$-0.617806\pi$
$881$	−21.4721			−0.723415			−0.361707	+	0.932292i	$0.617806\pi$
$882$		0			0
$883$	−26.5380			−0.893076			−0.446538	−	0.894765i	$-0.647343\pi$
$883$	−26.5380			−0.893076			−0.446538	+	0.894765i	$0.647343\pi$
$884$	1.96006	−	3.39492i	0.0659238	−	0.114183i
$885$		0			0
$886$	−12.9165	−	22.3721i	−0.433940	−	0.751606i
$887$	−20.7612	+	35.9594i	−0.697091	+	1.20740i	0.272379	+	0.962190i	$0.412190\pi$
$887$	−20.7612	+	35.9594i	−0.697091	+	1.20740i	−0.969471	+	0.245208i	$0.921144\pi$
$888$		0			0
$889$	−2.90133	−	4.27131i	−0.0973074	−	0.143255i
$890$	−34.3471			−1.15132
$891$		0			0
$892$	1.83755	+	3.18272i	0.0615256	+	0.106565i
$893$	−4.30922	−	7.46380i	−0.144203	−	0.249766i
$894$		0			0
$895$	27.0408			0.903873
$896$	18.4309	−	1.34917i	0.615734	−	0.0450726i
$897$		0			0
$898$	−16.8001	+	29.0986i	−0.560626	+	0.971032i
$899$	20.3089	+	35.1760i	0.677339	+	1.17319i
$900$		0			0
$901$	1.76763	−	3.06162i	0.0588883	−	0.101997i
$902$	44.0238			1.46583
$903$		0			0
$904$	26.0241			0.865550
$905$	6.90989	−	11.9683i	0.229692	−	0.397839i
$906$		0			0
$907$	2.32180	+	4.02148i	0.0770942	+	0.133531i	0.901995	−	0.431746i	$-0.142102\pi$
$907$	2.32180	+	4.02148i	0.0770942	+	0.133531i	−0.824901	+	0.565277i	$0.808769\pi$
$908$	−2.09401	+	3.62693i	−0.0694921	+	0.120364i
$909$		0			0
$910$	10.8817	−	22.4964i	0.360723	−	0.745749i
$911$	−1.34811			−0.0446648			−0.0223324	−	0.999751i	$-0.507109\pi$
$911$	−1.34811			−0.0446648			−0.0223324	+	0.999751i	$0.507109\pi$
$912$		0			0
$913$	−0.556114	−	0.963217i	−0.0184047	−	0.0318778i
$914$	4.12408	+	7.14312i	0.136413	+	0.236273i
$915$		0			0
$916$	−4.84011			−0.159922
$917$	30.9895	−	2.26848i	1.02336	−	0.0749116i
$918$		0			0
$919$	20.2472	−	35.0692i	0.667893	−	1.15682i	−0.310599	−	0.950541i	$-0.600530\pi$
$919$	20.2472	−	35.0692i	0.667893	−	1.15682i	0.978492	−	0.206284i	$-0.0661370\pi$
$920$	8.73015	+	15.1211i	0.287824	+	0.498527i
$921$		0			0
$922$	−9.90223	+	17.1512i	−0.326112	+	0.564843i
$923$	66.1045			2.17586
$924$		0			0
$925$	0.482555			0.0158663
$926$	−4.86221	+	8.42160i	−0.159782	+	0.276751i
$927$		0			0
$928$	7.94795	+	13.7663i	0.260904	+	0.451900i
$929$	−11.1569	+	19.3243i	−0.366046	+	0.634011i	−0.988944	−	0.148293i	$-0.952622\pi$
$929$	−11.1569	+	19.3243i	−0.366046	+	0.634011i	0.622897	+	0.782304i	$0.285956\pi$
$930$		0			0
$931$	21.1365	+	26.6932i	0.692722	+	0.874834i
$932$	−5.90760			−0.193510
$933$		0			0
$934$	26.4375	+	45.7910i	0.865060	+	1.49833i
$935$	5.28186	+	9.14844i	0.172735	+	0.299186i
$936$		0			0
$937$	−1.13943			−0.0372235			−0.0186117	−	0.999827i	$-0.505925\pi$
$937$	−1.13943			−0.0372235			−0.0186117	+	0.999827i	$0.505925\pi$
$938$	−23.1079	−	34.0192i	−0.754498	−	1.11077i
$939$		0			0
$940$	0.532080	−	0.921589i	0.0173545	−	0.0300589i
$941$	−23.5938	−	40.8656i	−0.769134	−	1.33218i	−0.938033	−	0.346546i	$-0.887354\pi$
$941$	−23.5938	−	40.8656i	−0.769134	−	1.33218i	0.168898	−	0.985633i	$-0.445979\pi$
$942$		0			0
$943$	20.0157	−	34.6683i	0.651802	−	1.12895i
$944$	17.9284			0.583519
$945$		0			0
$946$	19.8532			0.645483
$947$	−12.3230	+	21.3441i	−0.400444	+	0.693590i	−0.993779	−	0.111366i	$-0.964477\pi$
$947$	−12.3230	+	21.3441i	−0.400444	+	0.693590i	0.593335	+	0.804955i	$0.297811\pi$
$948$		0			0
$949$	−28.3947	−	49.1811i	−0.921731	−	1.59649i
$950$	−7.99050	+	13.8400i	−0.259246	+	0.449027i
$951$		0			0
$952$	7.39825	−	15.2949i	0.239779	−	0.495711i
$953$	−56.2821			−1.82316			−0.911579	−	0.411125i	$-0.865136\pi$
$953$	−56.2821			−1.82316			−0.911579	+	0.411125i	$0.865136\pi$
$954$		0			0
$955$	11.4898	+	19.9009i	0.371802	+	0.643979i
$956$	2.07137	+	3.58772i	0.0669930	+	0.116035i
$957$		0			0
$958$	2.94150			0.0950356
$959$	−18.5853	+	38.4226i	−0.600149	+	1.24073i
$960$		0			0
$961$	0.352001	−	0.609683i	0.0113549	−	0.0196672i
$962$	0.567135	+	0.982306i	0.0182852	+	0.0316708i
$963$		0			0
$964$	−2.89955	+	5.02217i	−0.0933883	+	0.161753i
$965$	−2.82982			−0.0910951
$966$		0			0
$967$	−58.5977			−1.88438			−0.942188	−	0.335084i	$-0.891235\pi$
$967$	−58.5977			−1.88438			−0.942188	+	0.335084i	$0.891235\pi$
$968$	−1.05474	+	1.82686i	−0.0339006	+	0.0587176i
$969$		0			0
$970$	−10.4269	−	18.0599i	−0.334787	−	0.579868i
$971$	3.04991	−	5.28260i	0.0978763	−	0.169527i	−0.812929	−	0.582363i	$-0.802128\pi$
$971$	3.04991	−	5.28260i	0.0978763	−	0.169527i	0.910805	+	0.412836i	$0.135462\pi$
$972$		0			0
$973$	−19.9840	−	29.4203i	−0.640657	−	0.943171i
$974$	23.0260			0.737801
$975$		0			0
$976$	10.5819	+	18.3283i	0.338718	+	0.586676i
$977$	2.57988	+	4.46849i	0.0825377	+	0.142960i	0.904339	−	0.426814i	$-0.140364\pi$
$977$	2.57988	+	4.46849i	0.0825377	+	0.142960i	−0.821802	+	0.569774i	$0.807031\pi$
$978$		0			0
$979$	55.8746			1.78576
$980$	−1.54945	+	3.90814i	−0.0494953	+	0.124841i
$981$		0			0
$982$	13.7146	−	23.7543i	0.437649	−	0.758031i
$983$	−31.0536	−	53.7864i	−0.990455	−	1.71552i	−0.614598	−	0.788841i	$-0.710682\pi$
$983$	−31.0536	−	53.7864i	−0.990455	−	1.71552i	−0.375857	−	0.926678i	$-0.622652\pi$
$984$		0			0
$985$	5.99626	−	10.3858i	0.191057	−	0.330920i
$986$	−19.8561			−0.632348
$987$		0			0
$988$	9.00108			0.286362
$989$	9.02639	−	15.6342i	0.287022	−	0.497138i
$990$		0			0
$991$	10.8163	+	18.7343i	0.343590	+	0.595116i	0.985097	−	0.172002i	$-0.0550235\pi$
$991$	10.8163	+	18.7343i	0.343590	+	0.595116i	−0.641506	+	0.767118i	$0.721690\pi$
$992$	−5.92823	+	10.2680i	−0.188221	+	0.326009i
$993$		0			0
$994$	46.2866	−	3.38824i	1.46812	−	0.107469i
$995$	−3.43837			−0.109004
$996$		0			0
$997$	20.3681	+	35.2786i	0.645064	+	1.11728i	0.984287	+	0.176578i	$0.0565027\pi$
$997$	20.3681	+	35.2786i	0.645064	+	1.11728i	−0.339223	+	0.940706i	$0.610164\pi$
$998$	−17.2527	−	29.8825i	−0.546124	−	0.945915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.e.g.163.3	✓	16
3.2	odd	2	inner	567.2.e.g.163.6	yes	16
7.2	even	3		3969.2.a.bg.1.6		8
7.4	even	3	inner	567.2.e.g.487.3	yes	16
7.5	odd	6		3969.2.a.bf.1.6		8
9.2	odd	6		567.2.h.l.352.3		16
9.4	even	3		567.2.g.l.541.3		16
9.5	odd	6		567.2.g.l.541.6		16
9.7	even	3		567.2.h.l.352.6		16
21.2	odd	6		3969.2.a.bg.1.3		8
21.5	even	6		3969.2.a.bf.1.3		8
21.11	odd	6	inner	567.2.e.g.487.6	yes	16
63.4	even	3		567.2.h.l.298.6		16
63.11	odd	6		567.2.g.l.109.6		16
63.25	even	3		567.2.g.l.109.3		16
63.32	odd	6		567.2.h.l.298.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.3	✓	16	1.1	even	1	trivial
567.2.e.g.163.6	yes	16	3.2	odd	2	inner
567.2.e.g.487.3	yes	16	7.4	even	3	inner
567.2.e.g.487.6	yes	16	21.11	odd	6	inner
567.2.g.l.109.3		16	63.25	even	3
567.2.g.l.109.6		16	63.11	odd	6
567.2.g.l.541.3		16	9.4	even	3
567.2.g.l.541.6		16	9.5	odd	6
567.2.h.l.298.3		16	63.32	odd	6
567.2.h.l.298.6		16	63.4	even	3
567.2.h.l.352.3		16	9.2	odd	6
567.2.h.l.352.6		16	9.7	even	3
3969.2.a.bf.1.3		8	21.5	even	6
3969.2.a.bf.1.6		8	7.5	odd	6
3969.2.a.bg.1.3		8	21.2	odd	6
3969.2.a.bg.1.6		8	7.2	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.635098 + 1.10002i) q^{2} +(0.193301 + 0.334806i) q^{4} +(0.776749 - 1.34537i) q^{5} +(-1.48662 - 2.18860i) q^{7} -3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} +(-1.60500 - 2.77995i) q^{11} +4.78669 q^{13} +(3.35166 - 0.245346i) q^{14} +(1.53867 - 2.66505i) q^{16} +(-1.05918 - 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +0.600584 q^{20} +4.07734 q^{22} +(1.85379 - 3.21086i) q^{23} +(1.29332 + 2.24010i) q^{25} +(-3.04002 + 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} -7.37944 q^{29} +(-2.75209 - 4.76676i) q^{31} +(-1.07704 - 1.86549i) q^{32} +2.69074 q^{34} +(-4.09920 + 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +(3.08914 + 5.35054i) q^{38} +(-2.35468 + 4.07842i) q^{40} +10.7972 q^{41} +4.86916 q^{43} +(0.620496 - 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} +(0.885937 - 1.53449i) q^{47} +(-2.57990 + 6.50724i) q^{49} -3.28555 q^{50} +(0.925270 + 1.60261i) q^{52} +(0.834432 + 1.44528i) q^{53} -4.98674 q^{55} +(4.50663 + 6.63462i) q^{56} +(4.68667 - 8.11755i) q^{58} +(2.91297 + 5.04541i) q^{59} +(-3.43865 + 5.95591i) q^{61} +6.99139 q^{62} +8.89078 q^{64} +(3.71806 - 6.43986i) q^{65} +(-6.11868 - 10.5979i) q^{67} +(0.409481 - 0.709241i) q^{68} +(2.27331 - 4.69978i) q^{70} +13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +(0.118482 + 0.205216i) q^{74} +1.88044 q^{76} +(-3.69814 + 7.64544i) q^{77} +(0.654632 - 1.13386i) q^{79} +(-2.39032 - 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +0.346488 q^{83} -3.29087 q^{85} +(-3.09239 + 5.35618i) q^{86} +(4.86549 + 8.42727i) q^{88} +(-8.70319 + 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +1.43335 q^{92} +(1.12531 + 1.94910i) q^{94} +(-3.77813 - 6.54391i) q^{95} -10.5683 q^{97} +(-5.51961 - 6.97068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} + 6 q^{7} - 14 q^{10} + 12 q^{13} - 6 q^{16} - 24 q^{19} + 4 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} - 36 q^{40} + 20 q^{43} + 36 q^{46} - 14 q^{49} - 34 q^{52} + 8 q^{55} + 22 q^{58} - 36 q^{61}+ \cdots + 28 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 + 6 * q^7 - 14 * q^10 + 12 * q^13 - 6 * q^16 - 24 * q^19 + 4 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 - 36 * q^40 + 20 * q^43 + 36 * q^46 - 14 * q^49 - 34 * q^52 + 8 * q^55 + 22 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 - 58 * q^70 - 32 * q^73 + 116 * q^76 + 32 * q^79 + 2 * q^82 + 60 * q^85 + 72 * q^88 - 22 * q^91 - 54 * q^94 + 28 * q^97

Introduction

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