LMFDB - Embedded newform 567.2.g.l.541.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(109,567)] 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([2, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.109"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.g (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,-6,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == 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			541.6
Root			$-0.776749 + 1.18180i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.l.109.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.635098 + 1.10002i) q^{2} +(0.193301 - 0.334806i) q^{4} +1.55350 q^{5} +(2.63869 - 0.193156i) q^{7} +3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} -3.21001 q^{11} +(-2.39335 - 4.14540i) q^{13} +(1.88830 + 2.77995i) q^{14} +(1.53867 + 2.66505i) q^{16} +(1.05918 + 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +(0.300292 - 0.520121i) q^{20} +(-2.03867 - 3.53108i) q^{22} +3.70758 q^{23} -2.58665 q^{25} +(3.04002 - 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} +(-3.68972 + 6.39078i) q^{29} +(-2.75209 + 4.76676i) q^{31} +(1.07704 - 1.86549i) q^{32} +(-1.34537 + 2.33025i) q^{34} +(4.09920 - 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +6.17827 q^{38} +4.70935 q^{40} +(5.39860 + 9.35065i) q^{41} +(-2.43458 + 4.21681i) q^{43} +(-0.620496 + 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} +(-0.885937 - 1.53449i) q^{47} +(6.92538 - 1.01936i) q^{49} +(-1.64277 - 2.84537i) q^{50} -1.85054 q^{52} +(-0.834432 - 1.44528i) q^{53} -4.98674 q^{55} +(7.99907 - 0.585543i) q^{56} -9.37334 q^{58} +(-2.91297 + 5.04541i) q^{59} +(-3.43865 - 5.95591i) q^{61} -6.99139 q^{62} +8.89078 q^{64} +(-3.71806 - 6.43986i) q^{65} +(-6.11868 + 10.5979i) q^{67} +0.818961 q^{68} +(2.93347 + 4.31864i) q^{70} -13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +0.236963 q^{74} +(-0.940219 - 1.62851i) q^{76} +(-8.47021 + 0.620031i) q^{77} +(0.654632 + 1.13386i) q^{79} +(2.39032 + 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +(0.173244 - 0.300067i) q^{83} +(1.64544 + 2.84998i) q^{85} -6.18478 q^{86} -9.73098 q^{88} +(8.70319 - 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +(0.716677 - 1.24132i) q^{92} +(1.12531 - 1.94910i) q^{94} +(3.77813 - 6.54391i) q^{95} +(5.28413 - 9.15238i) q^{97} +(5.51961 + 6.97068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) $ 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.635098	+	1.10002i	0.449082	+	0.777833i	0.998327	−	0.0578286i	$-0.0184177\pi$
$2$	0.635098	+	1.10002i	0.449082	+	0.777833i	−0.549244	+	0.835662i	$0.685084\pi$
$3$		0			0
$3$		0			0
$4$	0.193301	−	0.334806i	0.0966503	−	0.167403i
$5$	1.55350			0.694745			0.347373	−	0.937727i	$-0.387074\pi$
$5$	1.55350			0.694745			0.347373	+	0.937727i	$0.387074\pi$
$6$		0			0
$7$	2.63869	−	0.193156i	0.997331	−	0.0730060i
$7$	2.63869	−	0.193156i	0.997331	−	0.0730060i
$8$	3.03145			1.07178
$9$		0			0
$10$	0.986623	+	1.70888i	0.311998	+	0.540396i
$11$	−3.21001			−0.967853			−0.483927	−	0.875109i	$-0.660790\pi$
$11$	−3.21001			−0.967853			−0.483927	+	0.875109i	$0.660790\pi$
$12$		0			0
$13$	−2.39335	−	4.14540i	−0.663795	−	1.14973i	−0.979611	−	0.200905i	$-0.935612\pi$
$13$	−2.39335	−	4.14540i	−0.663795	−	1.14973i	0.315816	−	0.948820i	$-0.397722\pi$
$14$	1.88830	+	2.77995i	0.504670	+	0.742972i
$15$		0			0
$16$	1.53867	+	2.66505i	0.384667	+	0.666263i
$17$	1.05918	+	1.83456i	0.256889	+	0.444945i	0.965407	−	0.260748i	$-0.0839691\pi$
$17$	1.05918	+	1.83456i	0.256889	+	0.444945i	−0.708518	+	0.705693i	$0.750636\pi$
$18$		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	$-0.0217423\pi$
$20$	0.300292	−	0.520121i	0.0671473	−	0.116303i
$21$		0			0
$22$	−2.03867	−	3.53108i	−0.434646	−	0.752828i
$23$	3.70758			0.773084			0.386542	−	0.922272i	$-0.373670\pi$
$23$	3.70758			0.773084			0.386542	+	0.922272i	$0.373670\pi$
$24$		0			0
$25$	−2.58665			−0.517329
$26$	3.04002	−	5.26547i	0.596197	−	1.03264i
$27$		0			0
$28$	0.445391	−	0.920788i	0.0841709	−	0.174013i
$29$	−3.68972	+	6.39078i	−0.685164	+	1.18674i	0.288222	+	0.957564i	$0.406936\pi$
$29$	−3.68972	+	6.39078i	−0.685164	+	1.18674i	−0.973385	+	0.229175i	$0.926397\pi$
$30$		0			0
$31$	−2.75209	+	4.76676i	−0.494290	+	0.856135i	−0.999978	−	0.00658088i	$-0.997905\pi$
$31$	−2.75209	+	4.76676i	−0.494290	+	0.856135i	0.505688	+	0.862716i	$0.331239\pi$
$32$	1.07704	−	1.86549i	0.190396	−	0.329775i
$33$		0			0
$34$	−1.34537	+	2.33025i	−0.230729	+	0.399634i
$35$	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	$0.161785\pi$
$38$	6.17827			1.00225
$39$		0			0
$40$	4.70935			0.744614
$41$	5.39860	+	9.35065i	0.843120	+	1.46033i	0.887244	+	0.461300i	$0.152617\pi$
$41$	5.39860	+	9.35065i	0.843120	+	1.46033i	−0.0441242	+	0.999026i	$0.514050\pi$
$42$		0			0
$43$	−2.43458	+	4.21681i	−0.371270	+	0.643058i	−0.989761	−	0.142734i	$-0.954411\pi$
$43$	−2.43458	+	4.21681i	−0.371270	+	0.643058i	0.618491	+	0.785792i	$0.287744\pi$
$44$	−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	$-0.207916\pi$
$47$	−0.885937	−	1.53449i	−0.129227	−	0.223828i	−0.923377	+	0.383893i	$0.874583\pi$
$48$		0			0
$49$	6.92538	−	1.01936i	0.989340	−	0.145622i
$50$	−1.64277	−	2.84537i	−0.232323	−	0.402396i
$51$		0			0
$52$	−1.85054			−0.256624
$53$	−0.834432	−	1.44528i	−0.114618	−	0.198524i	0.803009	−	0.595967i	$-0.203231\pi$
$53$	−0.834432	−	1.44528i	−0.114618	−	0.198524i	−0.917627	+	0.397443i	$0.869898\pi$
$54$		0			0
$55$	−4.98674			−0.672411
$56$	7.99907	−	0.585543i	1.06892	−	0.0782464i
$57$		0			0
$58$	−9.37334			−1.23078
$59$	−2.91297	+	5.04541i	−0.379236	+	0.656857i	−0.990951	−	0.134221i	$-0.957147\pi$
$59$	−2.91297	+	5.04541i	−0.379236	+	0.656857i	0.611715	+	0.791078i	$0.290480\pi$
$60$		0			0
$61$	−3.43865	−	5.95591i	−0.440274	−	0.762576i	0.557436	−	0.830220i	$-0.311785\pi$
$61$	−3.43865	−	5.95591i	−0.440274	−	0.762576i	−0.997710	+	0.0676438i	$0.978452\pi$
$62$	−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	0.201494	+	0.979490i	$0.435420\pi$
$67$	−6.11868	+	10.5979i	−0.747516	+	1.29474i	−0.949010	+	0.315246i	$0.897913\pi$
$68$	0.818961			0.0993136
$69$		0			0
$70$	2.93347	+	4.31864i	0.350617	+	0.516176i
$71$	−13.8101			−1.63895			−0.819477	−	0.573112i	$-0.805736\pi$
$71$	−13.8101			−1.63895			−0.819477	+	0.573112i	$0.805736\pi$
$72$		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	$-0.410948\pi$
$74$	0.236963			0.0275464
$75$		0			0
$76$	−0.940219	−	1.62851i	−0.107851	−	0.186803i
$77$	−8.47021	+	0.620031i	−0.965270	+	0.0706591i
$78$		0			0
$79$	0.654632	+	1.13386i	0.0736518	+	0.127569i	0.900499	−	0.434858i	$-0.143201\pi$
$79$	0.654632	+	1.13386i	0.0736518	+	0.127569i	−0.826847	+	0.562426i	$0.809868\pi$
$80$	2.39032	+	4.14015i	0.267246	+	0.462883i
$81$		0			0
$82$	−6.85728	+	11.8772i	−0.757260	+	1.31161i
$83$	0.173244	−	0.300067i	0.0190160	−	0.0329366i	−0.856361	−	0.516378i	$-0.827280\pi$
$83$	0.173244	−	0.300067i	0.0190160	−	0.0329366i	0.875377	+	0.483441i	$0.160613\pi$
$84$		0			0
$85$	1.64544	+	2.84998i	0.178473	+	0.309123i
$86$	−6.18478			−0.666922
$87$		0			0
$88$	−9.73098			−1.03733
$89$	8.70319	−	15.0744i	0.922537	−	1.59788i	0.127061	−	0.991895i	$-0.459446\pi$
$89$	8.70319	−	15.0744i	0.922537	−	1.59788i	0.795476	−	0.605985i	$-0.207221\pi$
$90$		0			0
$91$	−7.11601	−	10.4761i	−0.745960	−	1.09820i
$92$	0.716677	−	1.24132i	0.0747187	−	0.129417i
$93$		0			0
$94$	1.12531	−	1.94910i	0.116067	−	0.201035i
$95$	3.77813	−	6.54391i	0.387628	−	0.671391i
$96$		0			0
$97$	5.28413	−	9.15238i	0.536522	−	0.929283i	−0.462566	−	0.886585i	$-0.653071\pi$
$97$	5.28413	−	9.15238i	0.536522	−	0.929283i	0.999088	−	0.0426982i	$-0.0135954\pi$
$98$	5.51961	+	6.97068i	0.557565	+	0.704145i
$99$		0			0
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−2.03394			−0.202384			−0.101192	−	0.994867i	$-0.532266\pi$
$101$	−2.03394			−0.202384			−0.101192	+	0.994867i	$0.532266\pi$
$102$		0			0
$103$	19.9816			1.96885			0.984423	−	0.175816i	$-0.0562562\pi$
$103$	19.9816			1.96885			0.984423	+	0.175816i	$0.0562562\pi$
$104$	−7.25531	−	12.5666i	−0.711442	−	1.23225i
$105$		0			0
$106$	1.05989	−	1.83579i	0.102946	−	0.178307i
$107$	−8.45322	+	14.6414i	−0.817204	+	1.41544i	0.0905308	+	0.995894i	$0.471144\pi$
$107$	−8.45322	+	14.6414i	−0.817204	+	1.41544i	−0.907735	+	0.419545i	$0.862190\pi$
$108$		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
$112$	4.57484	+	6.73505i	0.432282	+	0.636402i
$113$	−4.29236	−	7.43458i	−0.403791	−	0.699386i	0.590389	−	0.807119i	$-0.298974\pi$
$113$	−4.29236	−	7.43458i	−0.403791	−	0.699386i	−0.994180	+	0.107733i	$0.965641\pi$
$114$		0			0
$115$	5.75971			0.537096
$116$	1.42645	+	2.47068i	0.132442	+	0.229397i
$117$		0			0
$118$	−7.40009			−0.681233
$119$	3.14921	+	4.63624i	0.288687	+	0.425003i
$120$		0			0
$121$	−0.695865			−0.0632604
$122$	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
$131$	−11.7443			−1.02610			−0.513051	−	0.858358i	$-0.671485\pi$
$131$	−11.7443			−1.02610			−0.513051	+	0.858358i	$0.671485\pi$
$132$		0			0
$133$	5.60369	−	11.5849i	0.485902	−	1.00454i
$134$	−15.5439			−1.34278
$135$		0			0
$136$	3.21086	+	5.56137i	0.275329	+	0.476883i
$137$	−16.1321			−1.37826			−0.689128	−	0.724639i	$-0.742006\pi$
$137$	−16.1321			−1.37826			−0.689128	+	0.724639i	$0.742006\pi$
$138$		0			0
$139$	−6.72127	−	11.6416i	−0.570091	−	0.987426i	−0.996556	−	0.0829220i	$-0.973575\pi$
$139$	−6.72127	−	11.6416i	−0.570091	−	0.987426i	0.426465	−	0.904504i	$-0.359759\pi$
$140$	0.691913	−	1.43044i	0.0584773	−	0.120894i
$141$		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
$146$	7.53482	−	13.0507i	0.623586	−	1.08008i
$147$		0			0
$148$	−0.0360614	−	0.0624602i	−0.00296423	−	0.00513420i
$149$	−3.21174			−0.263116			−0.131558	−	0.991308i	$-0.541998\pi$
$149$	−3.21174			−0.263116			−0.131558	+	0.991308i	$0.541998\pi$
$150$		0			0
$151$	17.0322			1.38606			0.693030	−	0.720909i	$-0.256275\pi$
$151$	17.0322			1.38606			0.693030	+	0.720909i	$0.256275\pi$
$152$	7.37253	−	12.7696i	0.597991	−	1.03575i
$153$		0			0
$154$	−6.06147	−	8.92364i	−0.488447	−	0.719088i
$155$	−4.27536	+	7.40515i	−0.343406	+	0.594796i
$156$		0			0
$157$	−4.71709	+	8.17024i	−0.376465	+	0.652056i	−0.990545	−	0.137188i	$-0.956194\pi$
$157$	−4.71709	+	8.17024i	−0.376465	+	0.652056i	0.614080	+	0.789243i	$0.289527\pi$
$158$	−0.831511	+	1.44022i	−0.0661515	+	0.114578i
$159$		0			0
$160$	1.67318	−	2.89803i	0.132276	−	0.229110i
$161$	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	$0.212670\pi$
$164$	4.17421			0.325951
$165$		0			0
$166$	0.440107			0.0341590
$167$	−0.805085	−	1.39445i	−0.0622994	−	0.107906i	0.833193	−	0.552982i	$-0.186510\pi$
$167$	−0.805085	−	1.39445i	−0.0622994	−	0.107906i	−0.895493	+	0.445076i	$0.853177\pi$
$168$		0			0
$169$	−4.95620	+	8.58440i	−0.381246	+	0.660338i
$170$	−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	−0.990344	−	0.138635i	$-0.955728\pi$
$173$	−8.09213	−	14.0160i	−0.615233	−	1.06562i	0.375110	−	0.926980i	$-0.377605\pi$
$174$		0			0
$175$	−6.82536	+	0.499626i	−0.515949	+	0.0377682i
$176$	−4.93914	−	8.55483i	−0.372301	−	0.644845i
$177$		0			0
$178$	22.1095			1.65718
$179$	−8.70319	−	15.0744i	−0.650507	−	1.12671i	−0.983000	−	0.183606i	$-0.941223\pi$
$179$	−8.70319	−	15.0744i	−0.650507	−	1.12671i	0.332493	−	0.943106i	$-0.392110\pi$
$180$		0			0
$181$	8.89591			0.661228			0.330614	−	0.943766i	$-0.392744\pi$
$181$	8.89591			0.661228			0.330614	+	0.943766i	$0.392744\pi$
$182$	7.00461	−	14.4811i	0.519217	−	1.07341i
$183$		0			0
$184$	11.2393			0.828576
$185$	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	0.999155	+	0.0410898i	$0.0130830\pi$
$191$	7.39609	+	12.8104i	0.535163	+	0.926929i	−0.463993	+	0.885839i	$0.653584\pi$
$192$		0			0
$193$	−0.910790	+	1.57753i	−0.0655601	+	0.113553i	−0.896942	−	0.442148i	$-0.854217\pi$
$193$	−0.910790	+	1.57753i	−0.0655601	+	0.113553i	0.831382	+	0.555701i	$0.187550\pi$
$194$	13.4238			0.963770
$195$		0			0
$196$	0.997393	−	2.51570i	0.0712423	−	0.179693i
$197$	−7.71970			−0.550006			−0.275003	−	0.961443i	$-0.588679\pi$
$197$	−7.71970			−0.550006			−0.275003	+	0.961443i	$0.588679\pi$
$198$		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	$0.858330\pi$
$200$	−7.84129			−0.554463
$201$		0			0
$202$	−1.29175	−	2.23738i	−0.0908872	−	0.157421i
$203$	−8.50161	+	17.5760i	−0.596696	+	1.23359i
$204$		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
$209$	−7.80678	+	13.5217i	−0.540006	+	0.935318i
$210$		0			0
$211$	0.906722	+	1.57049i	0.0624213	+	0.108117i	0.895547	−	0.444967i	$-0.146784\pi$
$211$	0.906722	+	1.57049i	0.0624213	+	0.108117i	−0.833126	+	0.553083i	$0.813451\pi$
$212$	−0.645185			−0.0443115
$213$		0			0
$214$	−21.4745			−1.46797
$215$	−3.78211	+	6.55081i	−0.257938	+	0.446761i
$216$		0			0
$217$	−6.34119	+	13.1096i	−0.430468	+	0.889937i
$218$	−6.79498	+	11.7692i	−0.460214	+	0.797114i
$219$		0			0
$220$	−0.963939	+	1.66959i	−0.0649887	+	0.112564i
$221$	5.06997	−	8.78145i	0.341043	−	0.590704i
$222$		0			0
$223$	−4.75308	+	8.23258i	−0.318290	+	0.551294i	−0.980131	−	0.198350i	$-0.936442\pi$
$223$	−4.75308	+	8.23258i	−0.318290	+	0.551294i	0.661841	+	0.749644i	$0.269775\pi$
$224$	2.48165	−	5.13049i	0.165812	−	0.342795i
$225$		0			0
$226$	5.45213	−	9.44337i	0.362671	−	0.628164i
$227$	10.8329			0.719006			0.359503	−	0.933144i	$-0.382946\pi$
$227$	10.8329			0.719006			0.359503	+	0.933144i	$0.382946\pi$
$228$		0			0
$229$	12.5197			0.827322			0.413661	−	0.910431i	$-0.364250\pi$
$229$	12.5197			0.827322			0.413661	+	0.910431i	$0.364250\pi$
$230$	3.65798	+	6.33581i	0.241200	+	0.417771i
$231$		0			0
$232$	−11.1852	+	19.3733i	−0.734345	+	1.27192i
$233$	7.64044	−	13.2336i	0.500542	−	0.866964i	−0.499458	−	0.866338i	$-0.666467\pi$
$233$	7.64044	−	13.2336i	0.500542	−	0.866964i	1.00000		0.000625732i	$-0.000199177\pi$
$234$		0			0
$235$	−1.37630	−	2.38382i	−0.0897800	−	0.155504i
$236$	1.12616	+	1.95056i	0.0733066	+	0.126971i
$237$		0			0
$238$	−3.09991	+	6.40867i	−0.200937	+	0.415412i
$239$	5.35791	+	9.28017i	0.346574	+	0.600284i	0.985638	−	0.168869i	$-0.0540115\pi$
$239$	5.35791	+	9.28017i	0.346574	+	0.600284i	−0.639064	+	0.769153i	$0.720678\pi$
$240$		0			0
$241$	−15.0002			−0.966249			−0.483125	−	0.875552i	$-0.660498\pi$
$241$	−15.0002			−0.966249			−0.483125	+	0.875552i	$0.660498\pi$
$242$	−0.441942	−	0.765467i	−0.0284091	−	0.0492061i
$243$		0			0
$244$	−2.65877			−0.170210
$245$	10.7586	−	1.58357i	0.687339	−	0.101170i
$246$		0			0
$247$	−23.2826			−1.48144
$248$	−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	$-0.324875\pi$
$251$	16.5665			1.04567			0.522833	+	0.852435i	$0.324875\pi$
$252$		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
$257$	22.5772			1.40833			0.704163	−	0.710038i	$-0.251322\pi$
$257$	22.5772			1.40833			0.704163	+	0.710038i	$0.251322\pi$
$258$		0			0
$259$	0.214926	−	0.444331i	0.0133548	−	0.0276094i
$260$	−2.87481			−0.178288
$261$		0			0
$262$	−7.45877	−	12.9190i	−0.460804	−	0.798136i
$263$	22.3461			1.37792			0.688959	−	0.724800i	$-0.258068\pi$
$263$	22.3461			1.37792			0.688959	+	0.724800i	$0.258068\pi$
$264$		0			0
$265$	−1.29629	−	2.24524i	−0.0796303	−	0.137924i
$266$	16.3025	−	1.19337i	0.999573	−	0.0731702i
$267$		0			0
$268$	2.36549	+	4.09715i	0.144495	+	0.250273i
$269$	−13.9475	−	24.1577i	−0.850392	−	1.47292i	−0.880855	−	0.473387i	$-0.843031\pi$
$269$	−13.9475	−	24.1577i	−0.850392	−	1.47292i	0.0304623	−	0.999536i	$-0.490302\pi$
$270$		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	$0.263623\pi$
$272$	−3.25946	+	5.64555i	−0.197634	+	0.342312i
$273$		0			0
$274$	−10.2455	−	17.7457i	−0.618951	−	1.07205i
$275$	8.30315			0.500699
$276$		0			0
$277$	−8.71457			−0.523608			−0.261804	−	0.965121i	$-0.584317\pi$
$277$	−8.71457			−0.523608			−0.261804	+	0.965121i	$0.584317\pi$
$278$	8.53733	−	14.7871i	0.512035	−	0.886871i
$279$		0			0
$280$	12.4265	−	0.909639i	0.742627	−	0.0543613i
$281$	3.10321	−	5.37491i	0.185122	−	0.320640i	−0.758496	−	0.651678i	$-0.774065\pi$
$281$	3.10321	−	5.37491i	0.185122	−	0.320640i	0.943618	+	0.331038i	$0.107399\pi$
$282$		0			0
$283$	−9.82943	+	17.0251i	−0.584299	+	1.01204i	0.410664	+	0.911787i	$0.365297\pi$
$283$	−9.82943	+	17.0251i	−0.584299	+	1.01204i	−0.994962	+	0.100248i	$0.968036\pi$
$284$	−2.66949	+	4.62370i	−0.158405	+	0.274366i
$285$		0			0
$286$	−9.75848	+	16.9022i	−0.577031	+	0.999447i
$287$	16.0514	+	23.6307i	0.947483	+	1.39488i
$288$		0			0
$289$	6.25627	−	10.8362i	0.368016	−	0.637422i
$290$	−14.5615			−0.855078
$291$		0			0
$292$	−4.58665			−0.268413
$293$	7.24841	+	12.5546i	0.423456	+	0.733448i	0.996275	−	0.0862342i	$-0.0274833\pi$
$293$	7.24841	+	12.5546i	0.423456	+	0.733448i	−0.572818	+	0.819682i	$0.694150\pi$
$294$		0			0
$295$	−4.52529	+	7.83804i	−0.263473	+	0.456348i
$296$	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
$301$	−5.60960	+	11.5971i	−0.323332	+	0.668447i
$302$	10.8171	+	18.7358i	0.622455	+	1.07812i
$303$		0			0
$304$	14.9683			0.858488
$305$	−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	$0.280701\pi$
$308$	−1.42971	+	2.95573i	−0.0814651	+	0.168419i
$309$		0			0
$310$	−10.8611			−0.616869
$311$	−8.70027	+	15.0693i	−0.493347	+	0.854502i	−0.999971	−	0.00766509i	$-0.997560\pi$
$311$	−8.70027	+	15.0693i	−0.493347	+	0.854502i	0.506623	+	0.862167i	$0.330893\pi$
$312$		0			0
$313$	0.100022	+	0.173244i	0.00565360	+	0.00979232i	0.868838	−	0.495096i	$-0.164867\pi$
$313$	0.100022	+	0.173244i	0.00565360	+	0.00979232i	−0.863185	+	0.504888i	$0.831534\pi$
$314$	−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	$-0.240944\pi$
$317$	−4.11706	−	7.13096i	−0.231237	−	0.400514i	−0.958172	+	0.286192i	$0.907611\pi$
$318$		0			0
$319$	11.8440	−	20.5144i	0.663138	−	1.14859i
$320$	13.8118			0.772103
$321$		0			0
$322$	7.00103	+	10.3069i	0.390152	+	0.574379i
$323$	10.3038			0.573317
$324$		0			0
$325$	6.19074	+	10.7227i	0.343400	+	0.594787i
$326$	−4.67111			−0.258709
$327$		0			0
$328$	16.3656	+	28.3461i	0.903639	+	1.56515i
$329$	−2.63411	−	3.87792i	−0.145223	−	0.213797i
$330$		0			0
$331$	8.31616	+	14.4040i	0.457098	+	0.791716i	0.998806	−	0.0488501i	$-0.0155557\pi$
$331$	8.31616	+	14.4040i	0.457098	+	0.791716i	−0.541708	+	0.840566i	$0.682222\pi$
$332$	−0.0669762	−	0.116006i	−0.00367580	−	0.00636667i
$333$		0			0
$334$	1.02262	−	1.77122i	0.0559551	−	0.0969170i
$335$	−9.50536	+	16.4638i	−0.519333	+	0.899511i
$336$		0			0
$337$	−7.95474	−	13.7780i	−0.433322	−	0.750536i	0.563835	−	0.825888i	$-0.309326\pi$
$337$	−7.95474	−	13.7780i	−0.433322	−	0.750536i	−0.997157	+	0.0753513i	$0.975992\pi$
$338$	−12.5907			−0.684844
$339$		0			0
$340$	1.27225			0.0689977
$341$	8.83422	−	15.3013i	0.478400	−	0.828613i
$342$		0			0
$343$	18.0770	−	4.02745i	0.976069	−	0.217462i
$344$	−7.38031	+	12.7831i	−0.397919	+	0.689217i
$345$		0			0
$346$	10.2786	−	17.8031i	0.552581	−	0.957098i
$347$	−3.14462	+	5.44665i	−0.168812	+	0.292391i	−0.938003	−	0.346628i	$-0.887326\pi$
$347$	−3.14462	+	5.44665i	−0.168812	+	0.292391i	0.769190	+	0.639020i	$0.220660\pi$
$348$		0			0
$349$	−0.809776	+	1.40257i	−0.0433463	+	0.0750781i	−0.886885	−	0.461991i	$-0.847135\pi$
$349$	−0.809776	+	1.40257i	−0.0433463	+	0.0750781i	0.843538	+	0.537069i	$0.180469\pi$
$350$	−4.88437	−	7.19074i	−0.261081	−	0.384361i
$351$		0			0
$352$	−3.45731	+	5.98823i	−0.184275	+	0.319174i
$353$	32.5118			1.73043			0.865213	−	0.501405i	$-0.167183\pi$
$353$	32.5118			1.73043			0.865213	+	0.501405i	$0.167183\pi$
$354$		0			0
$355$	−21.4539			−1.13866
$356$	−3.36466	−	5.82777i	−0.178327	−	0.308871i
$357$		0			0
$358$	11.0548	−	19.1474i	0.584262	−	1.01197i
$359$	−5.59588	+	9.69235i	−0.295339	+	0.511543i	−0.975064	−	0.221925i	$-0.928766\pi$
$359$	−5.59588	+	9.69235i	−0.295339	+	0.511543i	0.679724	+	0.733468i	$0.262099\pi$
$360$		0			0
$361$	−2.32938	−	4.03461i	−0.122599	−	0.212348i
$362$	5.64978	+	9.78570i	0.296946	+	0.514325i
$363$		0			0
$364$	−4.88300	+	0.357443i	−0.255939	+	0.0187351i
$365$	−9.21537	−	15.9615i	−0.482354	−	0.835462i
$366$		0			0
$367$	−5.18678			−0.270748			−0.135374	−	0.990795i	$-0.543224\pi$
$367$	−5.18678			−0.270748			−0.135374	+	0.990795i	$0.543224\pi$
$368$	5.70474	+	9.88089i	0.297380	+	0.515077i
$369$		0			0
$370$	0.368122			0.0191377
$371$	−2.48097	−	3.65247i	−0.128806	−	0.189627i
$372$		0			0
$373$	32.8643			1.70165			0.850825	−	0.525448i	$-0.176102\pi$
$373$	32.8643			1.70165			0.850825	+	0.525448i	$0.176102\pi$
$374$	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
$383$	−1.71520			−0.0876427			−0.0438214	−	0.999039i	$-0.513953\pi$
$383$	−1.71520			−0.0876427			−0.0438214	+	0.999039i	$0.513953\pi$
$384$		0			0
$385$	−13.1585	+	0.963217i	−0.670617	+	0.0490901i
$386$	−2.31376			−0.117768
$387$		0			0
$388$	−2.04285	−	3.53832i	−0.103710	−	0.179631i
$389$	−3.14856			−0.159638			−0.0798191	−	0.996809i	$-0.525434\pi$
$389$	−3.14856			−0.159638			−0.0798191	+	0.996809i	$0.525434\pi$
$390$		0			0
$391$	3.92700	+	6.80176i	0.198597	+	0.343980i
$392$	20.9940	−	3.09013i	1.06036	−	0.156075i
$393$		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	$0.924959\pi$
$398$	1.40567	−	2.43469i	0.0704598	−	0.122040i
$399$		0			0
$400$	−3.97999	−	6.89355i	−0.199000	−	0.344677i
$401$	29.0370			1.45004			0.725020	−	0.688728i	$-0.241830\pi$
$401$	29.0370			1.45004			0.725020	+	0.688728i	$0.241830\pi$
$402$		0			0
$403$	26.3468			1.31243
$404$	−0.393161	+	0.680975i	−0.0195605	+	0.0338798i
$405$		0			0
$406$	−24.7333	+	1.81051i	−1.22750	+	0.0898543i
$407$	−0.299423	+	0.518617i	−0.0148419	+	0.0257069i
$408$		0			0
$409$	13.8650	−	24.0149i	0.685581	−	1.18746i	−0.287673	−	0.957729i	$-0.592882\pi$
$409$	13.8650	−	24.0149i	0.685581	−	1.18746i	0.973254	−	0.229732i	$-0.0737851\pi$
$410$	−10.6528	+	18.4511i	−0.526103	+	0.911237i
$411$		0			0
$412$	3.86246	−	6.68997i	0.190290	−	0.329591i
$413$	−6.71188	+	13.8759i	−0.330270	+	0.682791i
$414$		0			0
$415$	0.269134	−	0.466153i	0.0132113	−	0.0228826i
$416$	−10.3109			−0.505534
$417$		0			0
$418$	−19.8323			−0.970029
$419$	−15.1799	−	26.2924i	−0.741586	−	1.28447i	−0.951773	−	0.306804i	$-0.900740\pi$
$419$	−15.1799	−	26.2924i	−0.741586	−	1.28447i	0.210186	−	0.977661i	$-0.432593\pi$
$420$		0			0
$421$	13.8868	−	24.0526i	0.676799	−	1.17225i	−0.299140	−	0.954209i	$-0.596700\pi$
$421$	13.8868	−	24.0526i	0.676799	−	1.17225i	0.975940	−	0.218041i	$-0.0699668\pi$
$422$	−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
$427$	−10.2239	−	15.0516i	−0.494771	−	0.728399i
$428$	3.26802	+	5.66038i	0.157966	+	0.273605i
$429$		0			0
$430$	−9.60805			−0.463341
$431$	3.62965	+	6.28673i	0.174834	+	0.302821i	0.940104	−	0.340888i	$-0.110728\pi$
$431$	3.62965	+	6.28673i	0.174834	+	0.302821i	−0.765270	+	0.643710i	$0.777394\pi$
$432$		0			0
$433$	15.0375			0.722658			0.361329	−	0.932438i	$-0.382323\pi$
$433$	15.0375			0.722658			0.361329	+	0.932438i	$0.382323\pi$
$434$	−18.4481	+	1.35043i	−0.885538	+	0.0648226i
$435$		0			0
$436$	4.13628			0.198092
$437$	9.01688	−	15.6177i	0.431336	−	0.747096i
$438$		0			0
$439$	−0.770595	−	1.33471i	−0.0367785	−	0.0637022i	0.847050	−	0.531513i	$-0.178376\pi$
$439$	−0.770595	−	1.33471i	−0.0367785	−	0.0637022i	−0.883829	+	0.467811i	$0.845043\pi$
$440$	−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	$-0.00616265\pi$
$443$	10.1689	+	17.6131i	0.483141	+	0.836824i	−0.516672	+	0.856183i	$0.672829\pi$
$444$		0			0
$445$	13.5204	−	23.4180i	0.640928	−	1.11012i
$446$	−12.0747			−0.571753
$447$		0			0
$448$	23.4600	−	1.71731i	1.10838	−	0.0811351i
$449$	−26.4527			−1.24838			−0.624190	−	0.781272i	$-0.714571\pi$
$449$	−26.4527			−1.24838			−0.624190	+	0.781272i	$0.714571\pi$
$450$		0			0
$451$	−17.3295	−	30.0156i	−0.816016	−	1.41338i
$452$	−3.31886			−0.156106
$453$		0			0
$454$	6.87997	+	11.9165i	0.322893	+	0.559267i
$455$	−11.0547	−	16.2746i	−0.518252	−	0.762967i
$456$		0			0
$457$	3.24681	+	5.62363i	0.151879	+	0.263063i	0.931918	−	0.362668i	$-0.118134\pi$
$457$	3.24681	+	5.62363i	0.151879	+	0.263063i	−0.780039	+	0.625731i	$0.784801\pi$
$458$	7.95121	+	13.7719i	0.371536	+	0.643518i
$459$		0			0
$460$	1.11336	−	1.92839i	0.0519105	−	0.0899116i
$461$	7.79582	−	13.5028i	0.363088	−	0.628886i	−0.625380	−	0.780321i	$-0.715056\pi$
$461$	7.79582	−	13.5028i	0.363088	−	0.628886i	0.988467	+	0.151434i	$0.0483892\pi$
$462$		0			0
$463$	−3.82792	−	6.63016i	−0.177899	−	0.308130i	0.763262	−	0.646089i	$-0.223597\pi$
$463$	−3.82792	−	6.63016i	−0.177899	−	0.308130i	−0.941161	+	0.337960i	$0.890263\pi$
$464$	−22.7090			−1.05424
$465$		0			0
$466$	19.4097			0.899138
$467$	−20.8137	+	36.0503i	−0.963142	+	1.66821i	−0.248615	+	0.968602i	$0.579976\pi$
$467$	−20.8137	+	36.0503i	−0.963142	+	1.66821i	−0.714526	+	0.699608i	$0.753358\pi$
$468$		0			0
$469$	−14.0983	+	29.1464i	−0.650998	+	1.34585i
$470$	1.74817	−	3.02792i	0.0806372	−	0.139668i
$471$		0			0
$472$	−8.83053	+	15.2949i	−0.406458	+	0.704006i
$473$	7.81501	−	13.5360i	0.359335	−	0.622386i
$474$		0			0
$475$	−6.29076	+	10.8959i	−0.288640	+	0.499939i
$476$	2.16099	−	0.158187i	0.0990486	−	0.00725050i
$477$		0			0
$478$	−6.80560	+	11.7876i	−0.311281	+	0.539154i
$479$	−2.31579			−0.105811			−0.0529055	−	0.998600i	$-0.516848\pi$
$479$	−2.31579			−0.105811			−0.0529055	+	0.998600i	$0.516848\pi$
$480$		0			0
$481$	−0.892987			−0.0407167
$482$	−9.52662	−	16.5006i	−0.433925	−	0.751581i
$483$		0			0
$484$	−0.134511	+	0.232980i	−0.00611414	+	0.0105900i
$485$	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
$490$	8.57470	+	10.8289i	0.387366	+	0.489202i
$491$	−10.7972	−	18.7013i	−0.487271	−	0.843978i	0.512622	−	0.858614i	$-0.328674\pi$
$491$	−10.7972	−	18.7013i	−0.487271	−	0.843978i	−0.999893	+	0.0146364i	$0.995341\pi$
$492$		0			0
$493$	−15.6323			−0.704045
$494$	−14.7867	−	25.6114i	−0.665287	−	1.15231i
$495$		0			0
$496$	−16.9382			−0.760549
$497$	−36.4405	+	2.66750i	−1.63458	+	0.119654i
$498$		0			0
$499$	27.1654			1.21609			0.608045	−	0.793903i	$-0.291954\pi$
$499$	27.1654			1.21609			0.608045	+	0.793903i	$0.291954\pi$
$500$	−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	$-0.414640\pi$
$503$	11.8850			0.529927			0.264964	+	0.964258i	$0.414640\pi$
$504$		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
$509$	−41.4595			−1.83766			−0.918829	−	0.394656i	$-0.870864\pi$
$509$	−41.4595			−1.83766			−0.918829	+	0.394656i	$0.870864\pi$
$510$		0			0
$511$	−17.6373	−	25.9656i	−0.780230	−	1.14865i
$512$	25.2864			1.11751
$513$		0			0
$514$	14.3387	+	24.8354i	0.632455	+	1.09544i
$515$	31.0414			1.36785
$516$		0			0
$517$	2.84386	+	4.92572i	0.125073	+	0.216633i
$518$	0.625273	−	0.0457708i	0.0274729	−	0.00201105i
$519$		0			0
$520$	−11.2711	−	19.5221i	−0.494271	−	0.856102i
$521$	−1.65221	−	2.86171i	−0.0723846	−	0.125374i	0.827561	−	0.561375i	$-0.189728\pi$
$521$	−1.65221	−	2.86171i	−0.0723846	−	0.125374i	−0.899946	+	0.436002i	$0.856394\pi$
$522$		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	$0.149332\pi$
$524$	−2.27017	+	3.93206i	−0.0991730	+	0.171773i
$525$		0			0
$526$	14.1920	+	24.5812i	0.618798	+	1.07179i
$527$	−11.6598			−0.507911
$528$		0			0
$529$	−9.25386			−0.402342
$530$	1.64654	−	2.85189i	0.0715211	−	0.123878i
$531$		0			0
$532$	−2.79550	−	4.11552i	−0.121200	−	0.178430i
$533$	25.8414	−	44.7587i	1.11932	−	1.93871i
$534$		0			0
$535$	−13.1321	+	22.7454i	−0.567748	+	0.983369i
$536$	−18.5485	+	32.1269i	−0.801173	+	1.38767i
$537$		0			0
$538$	17.7160	−	30.6851i	0.763792	−	1.32293i
$539$	−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	$0.00612919\pi$
$542$	−12.5423			−0.538737
$543$		0			0
$544$	4.56312			0.195642
$545$	8.31051	+	14.3942i	0.355983	+	0.616581i
$546$		0			0
$547$	7.27727	−	12.6046i	0.311154	−	0.538934i	−0.667459	−	0.744647i	$-0.732618\pi$
$547$	7.27727	−	12.6046i	0.311154	−	0.538934i	0.978612	+	0.205713i	$0.0659513\pi$
$548$	−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
$553$	1.94638	+	2.86545i	0.0827686	+	0.121851i
$554$	−5.53461	−	9.58622i	−0.235143	−	0.407279i
$555$		0			0
$556$	−5.19690			−0.220398
$557$	−7.77331	−	13.4638i	−0.329366	−	0.570478i	0.653021	−	0.757340i	$-0.273502\pi$
$557$	−7.77331	−	13.4638i	−0.329366	−	0.570478i	−0.982386	+	0.186862i	$0.940168\pi$
$558$		0			0
$559$	23.3071			0.985787
$560$	7.10701	+	10.4629i	0.300326	+	0.442137i
$561$		0			0
$562$	7.88336			0.332539
$563$	7.36914	−	12.7637i	0.310572	−	0.537927i	−0.667914	−	0.744238i	$-0.732813\pi$
$563$	7.36914	−	12.7637i	0.310572	−	0.537927i	0.978486	+	0.206312i	$0.0661461\pi$
$564$		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	$-0.254313\pi$
$569$	−6.48539	−	11.2330i	−0.271882	−	0.470913i	−0.969344	+	0.245709i	$0.920979\pi$
$570$		0			0
$571$	−6.42929	+	11.1359i	−0.269058	+	0.466021i	−0.968619	−	0.248551i	$-0.920046\pi$
$571$	−6.42929	+	11.1359i	−0.269058	+	0.466021i	0.699561	+	0.714573i	$0.253379\pi$
$572$	5.94024			0.248374
$573$		0			0
$574$	−15.8001	+	32.6647i	−0.659484	+	1.36340i
$575$	−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	$0.763024\pi$
$578$	15.8934			0.661078
$579$		0			0
$580$	2.21599	+	3.83820i	0.0920138	+	0.159373i
$581$	0.399177	−	0.825247i	0.0165607	−	0.0342370i
$582$		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
$587$	3.10009	−	5.36951i	0.127954	−	0.221624i	−0.794930	−	0.606702i	$-0.792492\pi$
$587$	3.10009	−	5.36951i	0.127954	−	0.221624i	0.922884	+	0.385078i	$0.125826\pi$
$588$		0			0
$589$	13.3862	+	23.1857i	0.551571	+	0.955348i
$590$	−11.4960			−0.473284
$591$		0			0
$592$	0.574097			0.0235952
$593$	−18.7629	+	32.4984i	−0.770502	+	1.33455i	0.166787	+	0.985993i	$0.446661\pi$
$593$	−18.7629	+	32.4984i	−0.770502	+	1.33455i	−0.937288	+	0.348555i	$0.886673\pi$
$594$		0			0
$595$	4.89229	+	7.20239i	0.200564	+	0.295269i
$596$	−0.620832	+	1.07531i	−0.0254302	+	0.0440465i
$597$		0			0
$598$	11.2711	−	19.5221i	0.460910	−	0.798319i
$599$	17.5460	−	30.3905i	0.716909	−	1.24172i	−0.245309	−	0.969445i	$-0.578889\pi$
$599$	17.5460	−	30.3905i	0.716909	−	1.24172i	0.962218	−	0.272279i	$-0.0877773\pi$
$600$		0			0
$601$	−13.1171	+	22.7195i	−0.535058	+	0.926748i	0.464102	+	0.885782i	$0.346377\pi$
$601$	−13.1171	+	22.7195i	−0.535058	+	0.926748i	−0.999161	+	0.0409662i	$0.986956\pi$
$602$	−16.3197	+	1.19463i	−0.665143	+	0.0486894i
$603$		0			0
$604$	3.29233	−	5.70249i	0.133963	−	0.232031i
$605$	−1.08102			−0.0439499
$606$		0			0
$607$	−2.21866			−0.0900527			−0.0450263	−	0.998986i	$-0.514337\pi$
$607$	−2.21866			−0.0900527			−0.0450263	+	0.998986i	$0.514337\pi$
$608$	−5.23876	−	9.07379i	−0.212460	−	0.367991i
$609$		0			0
$610$	6.78530	−	11.7525i	0.274729	−	0.475844i
$611$	−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
$616$	−25.6770	+	1.87960i	−1.03456	+	0.0757311i
$617$	11.6023	+	20.0958i	0.467091	+	0.809024i	0.999293	−	0.0375925i	$-0.0119689\pi$
$617$	11.6023	+	20.0958i	0.467091	+	0.809024i	−0.532203	+	0.846617i	$0.678636\pi$
$618$		0			0
$619$	−8.31125			−0.334057			−0.167029	−	0.985952i	$-0.553417\pi$
$619$	−8.31125			−0.334057			−0.167029	+	0.985952i	$0.553417\pi$
$620$	1.65286	+	2.86284i	0.0663805	+	0.114974i
$621$		0			0
$622$	−22.1021			−0.886214
$623$	20.0533	−	41.4577i	0.803420	−	1.66097i
$624$		0			0
$625$	−5.37603			−0.215041
$626$	−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
$635$	3.03184			0.120315
$636$		0			0
$637$	−20.8005	−	26.2688i	−0.824145	−	1.04081i
$638$	30.0885			1.19121
$639$		0			0
$640$	5.42549	+	9.39723i	0.214461	+	0.371458i
$641$	−7.97525			−0.315003			−0.157502	−	0.987519i	$-0.550344\pi$
$641$	−7.97525			−0.315003			−0.157502	+	0.987519i	$0.550344\pi$
$642$		0			0
$643$	1.56140	+	2.70442i	0.0615755	+	0.106652i	0.895170	−	0.445725i	$-0.147054\pi$
$643$	1.56140	+	2.70442i	0.0615755	+	0.106652i	−0.833594	+	0.552377i	$0.813721\pi$
$644$	1.65132	−	3.41389i	0.0650711	−	0.134526i
$645$		0			0
$646$	6.54391	+	11.3344i	0.257467	+	0.445945i
$647$	−6.13273	−	10.6222i	−0.241102	−	0.417602i	0.719926	−	0.694051i	$-0.244176\pi$
$647$	−6.13273	−	10.6222i	−0.241102	−	0.417602i	−0.961029	+	0.276449i	$0.910842\pi$
$648$		0			0
$649$	9.35065	−	16.1958i	0.367045	−	0.635741i
$650$	−7.86345	+	13.6199i	−0.308430	+	0.534216i
$651$		0			0
$652$	0.710857	+	1.23124i	0.0278393	+	0.0482191i
$653$	−16.5095			−0.646067			−0.323034	−	0.946387i	$-0.604703\pi$
$653$	−16.5095			−0.646067			−0.323034	+	0.946387i	$0.604703\pi$
$654$		0			0
$655$	−18.2447			−0.712879
$656$	−16.6133	+	28.7751i	−0.648641	+	1.12348i
$657$		0			0
$658$	2.59288	−	5.36044i	0.101081	−	0.208972i
$659$	5.36940	−	9.30007i	0.209162	−	0.362279i	−0.742289	−	0.670080i	$-0.766260\pi$
$659$	5.36940	−	9.30007i	0.209162	−	0.362279i	0.951451	+	0.307801i	$0.0995931\pi$
$660$		0			0
$661$	6.68817	−	11.5843i	0.260140	−	0.450575i	−0.706139	−	0.708073i	$-0.749565\pi$
$661$	6.68817	−	11.5843i	0.260140	−	0.450575i	0.966279	+	0.257498i	$0.0828980\pi$
$662$	−10.5632	+	18.2959i	−0.410549	+	0.711092i
$663$		0			0
$664$	0.525180	−	0.909639i	0.0203810	−	0.0353008i
$665$	8.70532	−	17.9971i	0.337578	−	0.697898i
$666$		0			0
$667$	−13.6799	+	23.6943i	−0.529689	+	0.917448i
$668$	−0.622494			−0.0240850
$669$		0			0
$670$	−24.1473			−0.932893
$671$	11.0381	+	19.1185i	0.426120	+	0.738062i
$672$		0			0
$673$	−20.4493	+	35.4193i	−0.788264	+	1.36531i	0.138766	+	0.990325i	$0.455686\pi$
$673$	−20.4493	+	35.4193i	−0.788264	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$674$	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	$-0.300563\pi$
$677$	−10.6250	−	18.4031i	−0.408353	−	0.707288i	−0.994705	+	0.102768i	$0.967230\pi$
$678$		0			0
$679$	12.1753	−	25.1710i	0.467247	−	0.965972i
$680$	4.98806	+	8.63957i	0.191283	+	0.331312i
$681$		0			0
$682$	22.4424			0.859364
$683$	20.6708	+	35.8029i	0.790948	+	1.36996i	0.925381	+	0.379039i	$0.123745\pi$
$683$	20.6708	+	35.8029i	0.790948	+	1.36996i	−0.134433	+	0.990923i	$0.542921\pi$
$684$		0			0
$685$	−25.0612			−0.957537
$686$	15.9110	+	17.3273i	0.607484	+	0.661561i
$687$		0			0
$688$	−14.9840			−0.571261
$689$	−3.99417	+	6.91810i	−0.152166	+	0.263559i
$690$		0			0
$691$	0.760183	+	1.31668i	0.0289187	+	0.0500887i	0.880123	−	0.474747i	$-0.157460\pi$
$691$	0.760183	+	1.31668i	0.0289187	+	0.0500887i	−0.851204	+	0.524835i	$0.824127\pi$
$692$	−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
$698$	−2.05715			−0.0778643
$699$		0			0
$700$	−1.15207	+	2.38175i	−0.0435441	+	0.0900217i
$701$	32.5344			1.22881			0.614404	−	0.788991i	$-0.289396\pi$
$701$	32.5344			1.22881			0.614404	+	0.788991i	$0.289396\pi$
$702$		0			0
$703$	−0.453708	−	0.785845i	−0.0171119	−	0.0296387i
$704$	−28.5395			−1.07562
$705$		0			0
$706$	20.6482	+	35.7637i	0.777104	+	1.34598i
$707$	−5.36693	+	0.392867i	−0.201844	+	0.0147753i
$708$		0			0
$709$	−11.2810	−	19.5394i	−0.423669	−	0.733816i	0.572626	−	0.819816i	$-0.305925\pi$
$709$	−11.2810	−	19.5394i	−0.423669	−	0.733816i	−0.996295	+	0.0860007i	$0.972591\pi$
$710$	−13.6253	−	23.5998i	−0.511350	−	0.885684i
$711$		0			0
$712$	26.3833	−	45.6972i	0.988756	−	1.71258i
$713$	−10.2036	+	17.6731i	−0.382127	+	0.661864i
$714$		0			0
$715$	11.9350	+	20.6720i	0.446343	+	0.773089i
$716$	−6.72933			−0.251487
$717$		0			0
$718$	−14.2157			−0.530527
$719$	−3.25084	+	5.63062i	−0.121236	+	0.209987i	−0.920255	−	0.391319i	$-0.872019\pi$
$719$	−3.25084	+	5.63062i	−0.121236	+	0.209987i	0.799019	+	0.601305i	$0.205352\pi$
$720$		0			0
$721$	52.7253	−	3.85956i	1.96359	−	0.143738i
$722$	2.95878	−	5.12475i	0.110114	−	0.190723i
$723$		0			0
$724$	1.71958	−	2.97841i	0.0639078	−	0.110692i
$725$	9.54400	−	16.5307i	0.354455	−	0.613934i
$726$		0			0
$727$	3.91607	−	6.78284i	0.145239	−	0.251562i	−0.784223	−	0.620479i	$-0.786938\pi$
$727$	3.91607	−	6.78284i	0.145239	−	0.251562i	0.929462	+	0.368918i	$0.120272\pi$
$728$	−21.5718	−	31.7579i	−0.799505	−	1.17703i
$729$		0			0
$730$	11.7053	−	20.2742i	0.433234	−	0.750383i
$731$	−10.3146			−0.381501
$732$		0			0
$733$	−7.49560			−0.276856			−0.138428	−	0.990372i	$-0.544205\pi$
$733$	−7.49560			−0.276856			−0.138428	+	0.990372i	$0.544205\pi$
$734$	−3.29411	−	5.70557i	−0.121588	−	0.210597i
$735$		0			0
$736$	3.99321	−	6.91645i	0.147192	−	0.254944i
$737$	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
$742$	2.44214	−	5.04880i	0.0896536	−	0.185347i
$743$	9.64411	+	16.7041i	0.353808	+	0.612814i	0.986913	−	0.161252i	$-0.0515533\pi$
$743$	9.64411	+	16.7041i	0.353808	+	0.612814i	−0.633105	+	0.774066i	$0.718220\pi$
$744$		0			0
$745$	−4.98943			−0.182799
$746$	20.8721	+	36.1515i	0.764181	+	1.32360i
$747$		0			0
$748$	−2.62887			−0.0961210
$749$	−19.4774	+	40.2669i	−0.711688	+	1.47132i
$750$		0			0
$751$	−33.2089			−1.21181			−0.605906	−	0.795536i	$-0.707189\pi$
$751$	−33.2089			−1.21181			−0.605906	+	0.795536i	$0.707189\pi$
$752$	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
$761$	−2.72609			−0.0988207			−0.0494104	−	0.998779i	$-0.515734\pi$
$761$	−2.72609			−0.0988207			−0.0494104	+	0.998779i	$0.515734\pi$
$762$		0			0
$763$	15.9055	+	23.4160i	0.575819	+	0.847716i
$764$	5.71868			0.206894
$765$		0			0
$766$	−1.08932	−	1.88676i	−0.0393588	−	0.0681714i
$767$	27.8870			1.00694
$768$		0			0
$769$	−25.0230	−	43.3411i	−0.902352	−	1.56292i	−0.824432	−	0.565960i	$-0.808506\pi$
$769$	−25.0230	−	43.3411i	−0.902352	−	1.56292i	−0.0779198	−	0.996960i	$-0.524828\pi$
$770$	−9.41647	−	13.8629i	−0.339346	−	0.499583i
$771$		0			0
$772$	0.352112	+	0.609877i	0.0126728	+	0.0219499i
$773$	9.52030	+	16.4896i	0.342421	+	0.593091i	0.984882	−	0.173228i	$-0.0554197\pi$
$773$	9.52030	+	16.4896i	0.342421	+	0.593091i	−0.642461	+	0.766319i	$0.722086\pi$
$774$		0			0
$775$	7.11868	−	12.3299i	0.255711	−	0.442904i
$776$	16.0186	−	27.7450i	0.575033	−	0.995987i
$777$		0			0
$778$	−1.99964	−	3.46348i	−0.0716906	−	0.124172i
$779$	52.5179			1.88165
$780$		0			0
$781$	44.3304			1.58627
$782$	−4.98806	+	8.63957i	−0.178373	+	0.308950i
$783$		0			0
$784$	13.3725	+	16.8881i	0.477590	+	0.603145i
$785$	−7.32798	+	12.6924i	−0.261547	+	0.453013i
$786$		0			0
$787$	16.6011	−	28.7540i	0.591766	−	1.02497i	−0.402228	−	0.915539i	$-0.631764\pi$
$787$	16.6011	−	28.7540i	0.591766	−	1.02497i	0.993995	−	0.109430i	$-0.0349025\pi$
$788$	−1.49222	+	2.58460i	−0.0531582	+	0.0920727i
$789$		0			0
$790$	−1.29175	+	2.23738i	−0.0459584	+	0.0796023i
$791$	−12.7622	−	18.7885i	−0.453773	−	0.668041i
$792$		0			0
$793$	−16.4597	+	28.5091i	−0.584502	+	1.01239i
$794$	−34.8472			−1.23668
$795$		0			0
$796$	−0.855668			−0.0303283
$797$	1.04472	+	1.80951i	0.0370059	+	0.0640961i	0.883935	−	0.467609i	$-0.154885\pi$
$797$	1.04472	+	1.80951i	0.0370059	+	0.0640961i	−0.846929	+	0.531706i	$0.821551\pi$
$798$		0			0
$799$	1.87674	−	3.25060i	0.0663942	−	0.114998i
$800$	−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
$805$	15.1981	−	1.11252i	0.535663	−	0.0392113i
$806$	16.7328	+	28.9821i	0.589388	+	1.02085i
$807$		0			0
$808$	−6.16578			−0.216912
$809$	0.241404	+	0.418125i	0.00848732	+	0.0147005i	0.870238	−	0.492632i	$-0.163965\pi$
$809$	0.241404	+	0.418125i	0.00848732	+	0.0147005i	−0.861751	+	0.507332i	$0.830632\pi$
$810$		0			0
$811$	17.1671			0.602820			0.301410	−	0.953495i	$-0.402543\pi$
$811$	17.1671			0.602820			0.301410	+	0.953495i	$0.402543\pi$
$812$	4.24119	+	6.24384i	0.148836	+	0.219116i
$813$		0			0
$814$	−0.760653			−0.0266609
$815$	−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	$-0.238493\pi$
$821$	−6.41086	−	11.1039i	−0.223741	−	0.387530i	−0.955941	+	0.293559i	$0.905160\pi$
$822$		0			0
$823$	−12.2973	+	21.2995i	−0.428655	+	0.742453i	−0.996754	−	0.0805075i	$-0.974346\pi$
$823$	−12.2973	+	21.2995i	−0.428655	+	0.742453i	0.568099	+	0.822961i	$0.307679\pi$
$824$	60.5733			2.11017
$825$		0			0
$826$	−19.5266	+	1.42937i	−0.679416	+	0.0497342i
$827$	−0.527165			−0.0183313			−0.00916567	−	0.999958i	$-0.502918\pi$
$827$	−0.527165			−0.0183313			−0.00916567	+	0.999958i	$0.502918\pi$
$828$		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	$0.536917\pi$
$830$	0.683706			0.0237318
$831$		0			0
$832$	−21.2787	−	36.8558i	−0.737707	−	1.27775i
$833$	9.20530	+	11.6253i	0.318945	+	0.402793i
$834$		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
$839$	−5.41289	+	9.37540i	−0.186874	+	0.323675i	−0.944206	−	0.329355i	$-0.893169\pi$
$839$	−5.41289	+	9.37540i	−0.186874	+	0.323675i	0.757333	+	0.653029i	$0.226502\pi$
$840$		0			0
$841$	−12.7281	−	22.0456i	−0.438898	−	0.760194i
$842$	35.2778			1.21575
$843$		0			0
$844$	0.701079			0.0241321
$845$	−7.69945	+	13.3358i	−0.264869	+	0.458767i
$846$		0			0
$847$	−1.83617	+	0.134410i	−0.0630916	+	0.00461839i
$848$	2.56783	−	4.44761i	0.0881796	−	0.152732i
$849$		0			0
$850$	3.47999	−	6.02752i	0.119363	−	0.206742i
$851$	0.345836	−	0.599006i	0.0118551	−	0.0205337i
$852$		0			0
$853$	21.5961	−	37.4056i	0.739437	−	1.28074i	−0.213313	−	0.976984i	$-0.568425\pi$
$853$	21.5961	−	37.4056i	0.739437	−	1.28074i	0.952749	−	0.303758i	$-0.0982414\pi$
$854$	10.0639	−	20.8058i	0.344380	−	0.711961i
$855$		0			0
$856$	−25.6255	+	44.3847i	−0.875863	+	1.51704i
$857$	−1.57445			−0.0537822			−0.0268911	−	0.999638i	$-0.508561\pi$
$857$	−1.57445			−0.0537822			−0.0268911	+	0.999638i	$0.508561\pi$
$858$		0			0
$859$	6.82180			0.232757			0.116378	−	0.993205i	$-0.462871\pi$
$859$	6.82180			0.232757			0.116378	+	0.993205i	$0.462871\pi$
$860$	1.46217	+	2.53255i	0.0498595	+	0.0863592i
$861$		0			0
$862$	−4.61037	+	7.98539i	−0.157030	+	0.271983i
$863$	4.51387	−	7.81825i	0.153654	−	0.266136i	−0.778914	−	0.627131i	$-0.784229\pi$
$863$	4.51387	−	7.81825i	0.153654	−	0.266136i	0.932568	+	0.360994i	$0.117563\pi$
$864$		0			0
$865$	−12.5711	−	21.7738i	−0.427430	−	0.740331i
$866$	9.55032	+	16.5416i	0.324533	+	0.562108i
$867$		0			0
$868$	3.16342	+	4.65716i	0.107373	+	0.158074i
$869$	−2.10137	−	3.63968i	−0.0712841	−	0.123468i
$870$		0			0
$871$	58.5765			1.98479
$872$	16.2169	+	28.0885i	0.549174	+	0.951196i
$873$		0			0
$874$	22.9064			0.774821
$875$	−31.0992	+	2.27650i	−1.05134	+	0.0769598i
$876$		0			0
$877$	9.66920			0.326506			0.163253	−	0.986584i	$-0.447801\pi$
$877$	9.66920			0.326506			0.163253	+	0.986584i	$0.447801\pi$
$878$	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	$-0.382194\pi$
$881$	21.4721			0.723415			0.361707	+	0.932292i	$0.382194\pi$
$882$		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
$887$	−41.5223			−1.39418			−0.697091	−	0.716982i	$-0.745523\pi$
$887$	−41.5223			−1.39418			−0.697091	+	0.716982i	$0.745523\pi$
$888$		0			0
$889$	5.14973	−	0.376967i	0.172716	−	0.0126431i
$890$	34.3471			1.15132
$891$		0			0
$892$	1.83755	+	3.18272i	0.0615256	+	0.106565i
$893$	−8.61845			−0.288405
$894$		0			0
$895$	−13.5204	−	23.4180i	−0.451937	−	0.782777i
$896$	10.3839	+	15.2871i	0.346901	+	0.510705i
$897$		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
$902$	22.0119	−	38.1258i	0.732917	−	1.26945i
$903$		0			0
$904$	−13.0121	−	22.5376i	−0.432775	−	0.749588i
$905$	13.8198			0.459385
$906$		0			0
$907$	−4.64361			−0.154188			−0.0770942	−	0.997024i	$-0.524564\pi$
$907$	−4.64361			−0.154188			−0.0770942	+	0.997024i	$0.524564\pi$
$908$	2.09401	−	3.62693i	0.0694921	−	0.120364i
$909$		0			0
$910$	10.8817	−	22.4964i	0.360723	−	0.745749i
$911$	−0.674054	+	1.16750i	−0.0223324	+	0.0386808i	−0.876976	−	0.480535i	$-0.840443\pi$
$911$	−0.674054	+	1.16750i	−0.0223324	+	0.0386808i	0.854643	+	0.519216i	$0.173776\pi$
$912$		0			0
$913$	−0.556114	+	0.963217i	−0.0184047	+	0.0318778i
$914$	−4.12408	+	7.14312i	−0.136413	+	0.236273i
$915$		0			0
$916$	2.42006	−	4.19166i	0.0799609	−	0.138496i
$917$	−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	$-0.0661370\pi$
$920$	17.4603			0.575649
$921$		0			0
$922$	19.8045			0.652225
$923$	33.0523	+	57.2482i	1.08793	+	1.88435i
$924$		0			0
$925$	−0.241278	+	0.417905i	−0.00793316	+	0.0137406i
$926$	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	$-0.0473778\pi$
$929$	11.1569	+	19.3243i	0.366046	+	0.634011i	−0.622897	+	0.782304i	$0.714044\pi$
$930$		0			0
$931$	12.5487	−	31.6514i	0.411267	−	1.03733i
$932$	−2.95380	−	5.11613i	−0.0967550	−	0.167585i
$933$		0			0
$934$	−52.8749			−1.73012
$935$	−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	$0.505925\pi$
$938$	−41.0154	+	3.00239i	−1.33920	+	0.0980314i
$939$		0			0
$940$	−1.06416			−0.0347090
$941$	23.5938	−	40.8656i	0.769134	−	1.33218i	−0.168898	−	0.985633i	$-0.554021\pi$
$941$	23.5938	−	40.8656i	0.769134	−	1.33218i	0.938033	−	0.346546i	$-0.112646\pi$
$942$		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	$-0.0355225\pi$
$947$	12.3230	+	21.3441i	0.400444	+	0.693590i	−0.593335	+	0.804955i	$0.702189\pi$
$948$		0			0
$949$	−28.3947	+	49.1811i	−0.921731	+	1.59649i
$950$	−15.9810			−0.518492
$951$		0			0
$952$	9.54667	+	14.0545i	0.309409	+	0.455510i
$953$	56.2821			1.82316			0.911579	−	0.411125i	$-0.134864\pi$
$953$	56.2821			1.82316			0.911579	+	0.411125i	$0.134864\pi$
$954$		0			0
$955$	11.4898	+	19.9009i	0.371802	+	0.643979i
$956$	4.14275			0.133986
$957$		0			0
$958$	−1.47075	−	2.54742i	−0.0475178	−	0.0823033i
$959$	−42.5676	+	3.11601i	−1.37458	+	0.100621i
$960$		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
$965$	−1.41491	+	2.45070i	−0.0455476	+	0.0788907i
$966$		0			0
$967$	29.2989	+	50.7471i	0.942188	+	1.63192i	0.761285	+	0.648417i	$0.224569\pi$
$967$	29.2989	+	50.7471i	0.942188	+	1.63192i	0.180903	+	0.983501i	$0.442098\pi$
$968$	−2.10948			−0.0678013
$969$		0			0
$970$	20.8538			0.669574
$971$	−3.04991	+	5.28260i	−0.0978763	+	0.169527i	−0.910805	−	0.412836i	$-0.864538\pi$
$971$	−3.04991	+	5.28260i	−0.0978763	+	0.169527i	0.812929	+	0.582363i	$0.197872\pi$
$972$		0			0
$973$	−19.9840	−	29.4203i	−0.640657	−	0.943171i
$974$	11.5130	−	19.9411i	0.368901	−	0.638955i
$975$		0			0
$976$	10.5819	−	18.3283i	0.338718	−	0.586676i
$977$	−2.57988	+	4.46849i	−0.0825377	+	0.142960i	−0.904339	−	0.426814i	$-0.859636\pi$
$977$	−2.57988	+	4.46849i	−0.0825377	+	0.142960i	0.821802	+	0.569774i	$0.192969\pi$
$978$		0			0
$979$	−27.9373	+	48.3888i	−0.892880	+	1.54651i
$980$	1.54945	−	3.90814i	0.0494953	−	0.124841i
$981$		0			0
$982$	13.7146	−	23.7543i	0.437649	−	0.758031i
$983$	−62.1071			−1.98091			−0.990455	−	0.137837i	$-0.955985\pi$
$983$	−62.1071			−1.98091			−0.990455	+	0.137837i	$0.955985\pi$
$984$		0			0
$985$	−11.9925			−0.382114
$986$	−9.92806	−	17.1959i	−0.316174	−	0.547629i
$987$		0			0
$988$	−4.50054	+	7.79516i	−0.143181	+	0.247997i
$989$	−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
$994$	−26.0776	−	38.3912i	−0.827131	−	1.21770i
$995$	−1.71919	−	2.97772i	−0.0545018	−	0.0944000i
$996$		0			0
$997$	−40.7362			−1.29013			−0.645064	−	0.764128i	$-0.723169\pi$
$997$	−40.7362			−1.29013			−0.645064	+	0.764128i	$0.723169\pi$
$998$	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.g.l.541.6		16
3.2	odd	2	inner	567.2.g.l.541.3		16
7.4	even	3		567.2.h.l.298.3		16
9.2	odd	6		567.2.e.g.163.3	✓	16
9.4	even	3		567.2.h.l.352.3		16
9.5	odd	6		567.2.h.l.352.6		16
9.7	even	3		567.2.e.g.163.6	yes	16
21.11	odd	6		567.2.h.l.298.6		16
63.2	odd	6		3969.2.a.bg.1.6		8
63.4	even	3	inner	567.2.g.l.109.6		16
63.11	odd	6		567.2.e.g.487.3	yes	16
63.16	even	3		3969.2.a.bg.1.3		8
63.25	even	3		567.2.e.g.487.6	yes	16
63.32	odd	6	inner	567.2.g.l.109.3		16
63.47	even	6		3969.2.a.bf.1.6		8
63.61	odd	6		3969.2.a.bf.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.3	✓	16	9.2	odd	6
567.2.e.g.163.6	yes	16	9.7	even	3
567.2.e.g.487.3	yes	16	63.11	odd	6
567.2.e.g.487.6	yes	16	63.25	even	3
567.2.g.l.109.3		16	63.32	odd	6	inner
567.2.g.l.109.6		16	63.4	even	3	inner
567.2.g.l.541.3		16	3.2	odd	2	inner
567.2.g.l.541.6		16	1.1	even	1	trivial
567.2.h.l.298.3		16	7.4	even	3
567.2.h.l.298.6		16	21.11	odd	6
567.2.h.l.352.3		16	9.4	even	3
567.2.h.l.352.6		16	9.5	odd	6
3969.2.a.bf.1.3		8	63.61	odd	6
3969.2.a.bf.1.6		8	63.47	even	6
3969.2.a.bg.1.3		8	63.16	even	3
3969.2.a.bg.1.6		8	63.2	odd	6

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.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.635098 + 1.10002i) q^{2} +(0.193301 - 0.334806i) q^{4} +1.55350 q^{5} +(2.63869 - 0.193156i) q^{7} +3.03145 q^{8} +(0.986623 + 1.70888i) q^{10} -3.21001 q^{11} +(-2.39335 - 4.14540i) q^{13} +(1.88830 + 2.77995i) q^{14} +(1.53867 + 2.66505i) q^{16} +(1.05918 + 1.83456i) q^{17} +(2.43201 - 4.21237i) q^{19} +(0.300292 - 0.520121i) q^{20} +(-2.03867 - 3.53108i) q^{22} +3.70758 q^{23} -2.58665 q^{25} +(3.04002 - 5.26547i) q^{26} +(0.445391 - 0.920788i) q^{28} +(-3.68972 + 6.39078i) q^{29} +(-2.75209 + 4.76676i) q^{31} +(1.07704 - 1.86549i) q^{32} +(-1.34537 + 2.33025i) q^{34} +(4.09920 - 0.300067i) q^{35} +(0.0932782 - 0.161563i) q^{37} +6.17827 q^{38} +4.70935 q^{40} +(5.39860 + 9.35065i) q^{41} +(-2.43458 + 4.21681i) q^{43} +(-0.620496 + 1.07473i) q^{44} +(2.35468 + 4.07842i) q^{46} +(-0.885937 - 1.53449i) q^{47} +(6.92538 - 1.01936i) q^{49} +(-1.64277 - 2.84537i) q^{50} -1.85054 q^{52} +(-0.834432 - 1.44528i) q^{53} -4.98674 q^{55} +(7.99907 - 0.585543i) q^{56} -9.37334 q^{58} +(-2.91297 + 5.04541i) q^{59} +(-3.43865 - 5.95591i) q^{61} -6.99139 q^{62} +8.89078 q^{64} +(-3.71806 - 6.43986i) q^{65} +(-6.11868 + 10.5979i) q^{67} +0.818961 q^{68} +(2.93347 + 4.31864i) q^{70} -13.8101 q^{71} +(-5.93201 - 10.2745i) q^{73} +0.236963 q^{74} +(-0.940219 - 1.62851i) q^{76} +(-8.47021 + 0.620031i) q^{77} +(0.654632 + 1.13386i) q^{79} +(2.39032 + 4.14015i) q^{80} +(-6.85728 + 11.8772i) q^{82} +(0.173244 - 0.300067i) q^{83} +(1.64544 + 2.84998i) q^{85} -6.18478 q^{86} -9.73098 q^{88} +(8.70319 - 15.0744i) q^{89} +(-7.11601 - 10.4761i) q^{91} +(0.716677 - 1.24132i) q^{92} +(1.12531 - 1.94910i) q^{94} +(3.77813 - 6.54391i) q^{95} +(5.28413 - 9.15238i) q^{97} +(5.51961 + 6.97068i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{4} - 14 q^{10} - 6 q^{13} - 6 q^{16} - 24 q^{19} - 2 q^{22} - 26 q^{28} - 20 q^{31} + 4 q^{37} + 72 q^{40} - 10 q^{43} + 36 q^{46} + 4 q^{49} + 68 q^{52} + 8 q^{55} - 44 q^{58} - 36 q^{61} + 76 q^{64}+ \cdots - 14 q^{97}+O(q^{100}) \) 16 * q - 6 * q^4 - 14 * q^10 - 6 * q^13 - 6 * q^16 - 24 * q^19 - 2 * q^22 - 26 * q^28 - 20 * q^31 + 4 * q^37 + 72 * q^40 - 10 * q^43 + 36 * q^46 + 4 * q^49 + 68 * q^52 + 8 * q^55 - 44 * q^58 - 36 * q^61 + 76 * q^64 + 18 * q^67 + 104 * q^70 - 32 * q^73 - 58 * q^76 + 32 * q^79 + 2 * q^82 - 30 * q^85 - 144 * q^88 - 22 * q^91 - 54 * q^94 - 14 * q^97

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