LMFDB - Embedded newform 567.2.g.l.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(109,567)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.52751779461$
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			109.3
Root			$0.776749 + 1.18180i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.l.541.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.635098 + 1.10002i) q^{2} +(0.193301 + 0.334806i) q^{4} -1.55350 q^{5} +(2.63869 + 0.193156i) q^{7} -3.03145 q^{8} +(0.986623 - 1.70888i) q^{10} +3.21001 q^{11} +(-2.39335 + 4.14540i) q^{13} +(-1.88830 + 2.77995i) q^{14} +(1.53867 - 2.66505i) q^{16} +(-1.05918 + 1.83456i) q^{17} +(2.43201 + 4.21237i) q^{19} +(-0.300292 - 0.520121i) q^{20} +(-2.03867 + 3.53108i) q^{22} -3.70758 q^{23} -2.58665 q^{25} +(-3.04002 - 5.26547i) q^{26} +(0.445391 + 0.920788i) q^{28} +(3.68972 + 6.39078i) q^{29} +(-2.75209 - 4.76676i) q^{31} +(-1.07704 - 1.86549i) q^{32} +(-1.34537 - 2.33025i) q^{34} +(-4.09920 - 0.300067i) q^{35} +(0.0932782 + 0.161563i) q^{37} -6.17827 q^{38} +4.70935 q^{40} +(-5.39860 + 9.35065i) q^{41} +(-2.43458 - 4.21681i) q^{43} +(0.620496 + 1.07473i) q^{44} +(2.35468 - 4.07842i) q^{46} +(0.885937 - 1.53449i) q^{47} +(6.92538 + 1.01936i) q^{49} +(1.64277 - 2.84537i) q^{50} -1.85054 q^{52} +(0.834432 - 1.44528i) q^{53} -4.98674 q^{55} +(-7.99907 - 0.585543i) q^{56} -9.37334 q^{58} +(2.91297 + 5.04541i) q^{59} +(-3.43865 + 5.95591i) q^{61} +6.99139 q^{62} +8.89078 q^{64} +(3.71806 - 6.43986i) q^{65} +(-6.11868 - 10.5979i) q^{67} -0.818961 q^{68} +(2.93347 - 4.31864i) q^{70} +13.8101 q^{71} +(-5.93201 + 10.2745i) q^{73} -0.236963 q^{74} +(-0.940219 + 1.62851i) q^{76} +(8.47021 + 0.620031i) q^{77} +(0.654632 - 1.13386i) q^{79} +(-2.39032 + 4.14015i) q^{80} +(-6.85728 - 11.8772i) q^{82} +(-0.173244 - 0.300067i) q^{83} +(1.64544 - 2.84998i) q^{85} +6.18478 q^{86} -9.73098 q^{88} +(-8.70319 - 15.0744i) q^{89} +(-7.11601 + 10.4761i) q^{91} +(-0.716677 - 1.24132i) q^{92} +(1.12531 + 1.94910i) q^{94} +(-3.77813 - 6.54391i) q^{95} +(5.28413 + 9.15238i) q^{97} +(-5.51961 + 6.97068i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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	$-0.981582\pi$
$2$	−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
$5$	−1.55350			−0.694745			−0.347373	−	0.937727i	$-0.612926\pi$
$5$	−1.55350			−0.694745			−0.347373	+	0.937727i	$0.612926\pi$
$6$		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	$-0.339210\pi$
$11$	3.21001			0.967853			0.483927	+	0.875109i	$0.339210\pi$
$12$		0			0
$13$	−2.39335	+	4.14540i	−0.663795	+	1.14973i	0.315816	+	0.948820i	$0.397722\pi$
$13$	−2.39335	+	4.14540i	−0.663795	+	1.14973i	−0.979611	+	0.200905i	$0.935612\pi$
$14$	−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	$-0.916031\pi$
$17$	−1.05918	+	1.83456i	−0.256889	+	0.444945i	0.708518	+	0.705693i	$0.249364\pi$
$18$		0			0
$19$	2.43201	+	4.21237i	0.557942	+	0.966384i	0.997668	+	0.0682523i	$0.0217423\pi$
$19$	2.43201	+	4.21237i	0.557942	+	0.966384i	−0.439726	+	0.898132i	$0.644924\pi$
$20$	−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	$-0.626330\pi$
$23$	−3.70758			−0.773084			−0.386542	+	0.922272i	$0.626330\pi$
$24$		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	0.973385	+	0.229175i	$0.0736027\pi$
$29$	3.68972	+	6.39078i	0.685164	+	1.18674i	−0.288222	+	0.957564i	$0.593064\pi$
$30$		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
$34$	−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	0.873591	−	0.486661i	$-0.161785\pi$
$37$	0.0932782	+	0.161563i	0.0153348	+	0.0265607i	−0.858256	+	0.513222i	$0.828452\pi$
$38$	−6.17827			−1.00225
$39$		0			0
$40$	4.70935			0.744614
$41$	−5.39860	+	9.35065i	−0.843120	+	1.46033i	0.0441242	+	0.999026i	$0.485950\pi$
$41$	−5.39860	+	9.35065i	−0.843120	+	1.46033i	−0.887244	+	0.461300i	$0.847383\pi$
$42$		0			0
$43$	−2.43458	−	4.21681i	−0.371270	−	0.643058i	0.618491	−	0.785792i	$-0.287744\pi$
$43$	−2.43458	−	4.21681i	−0.371270	−	0.643058i	−0.989761	+	0.142734i	$0.954411\pi$
$44$	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
$49$	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	$-0.796769\pi$
$53$	0.834432	−	1.44528i	0.114618	−	0.198524i	0.917627	+	0.397443i	$0.130102\pi$
$54$		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	$-0.0428534\pi$
$59$	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	$-0.435420\pi$
$68$	−0.818961			−0.0993136
$69$		0			0
$70$	2.93347	−	4.31864i	0.350617	−	0.516176i
$71$	13.8101			1.63895			0.819477	−	0.573112i	$-0.194264\pi$
$71$	13.8101			1.63895			0.819477	+	0.573112i	$0.194264\pi$
$72$		0			0
$73$	−5.93201	+	10.2745i	−0.694290	+	1.20255i	0.276130	+	0.961120i	$0.410948\pi$
$73$	−5.93201	+	10.2745i	−0.694290	+	1.20255i	−0.970420	+	0.241425i	$0.922385\pi$
$74$	−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	−0.826847	−	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
$83$	−0.173244	−	0.300067i	−0.0190160	−	0.0329366i	0.856361	−	0.516378i	$-0.172720\pi$
$83$	−0.173244	−	0.300067i	−0.0190160	−	0.0329366i	−0.875377	+	0.483441i	$0.839387\pi$
$84$		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	−0.795476	−	0.605985i	$-0.792779\pi$
$89$	−8.70319	−	15.0744i	−0.922537	−	1.59788i	−0.127061	−	0.991895i	$-0.540554\pi$
$90$		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	0.999088	+	0.0426982i	$0.0135954\pi$
$97$	5.28413	+	9.15238i	0.536522	+	0.929283i	−0.462566	+	0.886585i	$0.653071\pi$
$98$	−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	$-0.467734\pi$
$101$	2.03394			0.202384			0.101192	+	0.994867i	$0.467734\pi$
$102$		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	0.907735	+	0.419545i	$0.137810\pi$
$107$	8.45322	+	14.6414i	0.817204	+	1.41544i	−0.0905308	+	0.995894i	$0.528856\pi$
$108$		0			0
$109$	5.34955	−	9.26569i	0.512394	−	0.887492i	−0.487503	−	0.873121i	$-0.662092\pi$
$109$	5.34955	−	9.26569i	0.512394	−	0.887492i	0.999897	−	0.0143707i	$-0.00457451\pi$
$110$	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	$-0.701026\pi$
$113$	4.29236	−	7.43458i	0.403791	−	0.699386i	0.994180	+	0.107733i	$0.0343590\pi$
$114$		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	$-0.328515\pi$
$131$	11.7443			1.02610			0.513051	+	0.858358i	$0.328515\pi$
$132$		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	$-0.257994\pi$
$137$	16.1321			1.37826			0.689128	+	0.724639i	$0.257994\pi$
$138$		0			0
$139$	−6.72127	+	11.6416i	−0.570091	+	0.987426i	0.426465	+	0.904504i	$0.359759\pi$
$139$	−6.72127	+	11.6416i	−0.570091	+	0.987426i	−0.996556	+	0.0829220i	$0.973575\pi$
$140$	−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	$-0.458002\pi$
$149$	3.21174			0.263116			0.131558	+	0.991308i	$0.458002\pi$
$150$		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	0.614080	−	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
$160$	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	0.784986	−	0.619513i	$-0.212670\pi$
$163$	−1.83874	−	3.18478i	−0.144021	−	0.249452i	−0.929007	+	0.370062i	$0.879337\pi$
$164$	−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	$-0.813490\pi$
$167$	0.805085	−	1.39445i	0.0622994	−	0.107906i	0.895493	+	0.445076i	$0.146823\pi$
$168$		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	−0.375110	−	0.926980i	$-0.622395\pi$
$173$	8.09213	−	14.0160i	0.615233	−	1.06562i	0.990344	−	0.138635i	$-0.0442716\pi$
$174$		0			0
$175$	−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	−0.332493	−	0.943106i	$-0.607890\pi$
$179$	8.70319	−	15.0744i	0.650507	−	1.12671i	0.983000	−	0.183606i	$-0.0587770\pi$
$180$		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	0.463993	+	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	$0.854217\pi$
$194$	−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	$-0.411321\pi$
$197$	7.71970			0.550006			0.275003	+	0.961443i	$0.411321\pi$
$198$		0			0
$199$	−1.10665	+	1.91678i	−0.0784487	+	0.135877i	−0.902581	−	0.430521i	$-0.858330\pi$
$199$	−1.10665	+	1.91678i	−0.0784487	+	0.135877i	0.824132	+	0.566398i	$0.191663\pi$
$200$	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	−0.833126	−	0.553083i	$-0.813451\pi$
$211$	0.906722	−	1.57049i	0.0624213	−	0.108117i	0.895547	+	0.444967i	$0.146784\pi$
$212$	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	0.661841	−	0.749644i	$-0.269775\pi$
$223$	−4.75308	−	8.23258i	−0.318290	−	0.551294i	−0.980131	+	0.198350i	$0.936442\pi$
$224$	−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	$-0.617054\pi$
$227$	−10.8329			−0.719006			−0.359503	+	0.933144i	$0.617054\pi$
$228$		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	−1.00000		0.000625732i	$-0.999801\pi$
$233$	−7.64044	−	13.2336i	−0.500542	−	0.866964i	0.499458	−	0.866338i	$-0.333533\pi$
$234$		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	$-0.945988\pi$
$239$	−5.35791	+	9.28017i	−0.346574	+	0.600284i	0.639064	+	0.769153i	$0.279322\pi$
$240$		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	$-0.675125\pi$
$251$	−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
$257$	−22.5772			−1.40833			−0.704163	−	0.710038i	$-0.748678\pi$
$257$	−22.5772			−1.40833			−0.704163	+	0.710038i	$0.748678\pi$
$258$		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	$-0.741932\pi$
$263$	−22.3461			−1.37792			−0.688959	+	0.724800i	$0.741932\pi$
$264$		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	−0.0304623	−	0.999536i	$-0.509698\pi$
$269$	13.9475	−	24.1577i	0.850392	−	1.47292i	0.880855	−	0.473387i	$-0.156969\pi$
$270$		0			0
$271$	−4.93714	−	8.55138i	−0.299910	−	0.519459i	0.676205	−	0.736713i	$-0.263623\pi$
$271$	−4.93714	−	8.55138i	−0.299910	−	0.519459i	−0.976115	+	0.217254i	$0.930290\pi$
$272$	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	$-0.225935\pi$
$281$	−3.10321	−	5.37491i	−0.185122	−	0.320640i	−0.943618	+	0.331038i	$0.892601\pi$
$282$		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
$286$	−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	$-0.972517\pi$
$293$	−7.24841	+	12.5546i	−0.423456	+	0.733448i	0.572818	+	0.819682i	$0.305850\pi$
$294$		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	$-0.00243990\pi$
$311$	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
$320$	−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	−0.541708	−	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
$335$	9.50536	+	16.4638i	0.519333	+	0.899511i
$336$		0			0
$337$	−7.95474	+	13.7780i	−0.433322	+	0.750536i	−0.997157	−	0.0753513i	$-0.975992\pi$
$337$	−7.95474	+	13.7780i	−0.433322	+	0.750536i	0.563835	+	0.825888i	$0.309326\pi$
$338$	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	$-0.112674\pi$
$347$	3.14462	+	5.44665i	0.168812	+	0.292391i	−0.769190	+	0.639020i	$0.779340\pi$
$348$		0			0
$349$	−0.809776	−	1.40257i	−0.0433463	−	0.0750781i	0.843538	−	0.537069i	$-0.180469\pi$
$349$	−0.809776	−	1.40257i	−0.0433463	−	0.0750781i	−0.886885	+	0.461991i	$0.847135\pi$
$350$	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	$-0.832817\pi$
$353$	−32.5118			−1.73043			−0.865213	+	0.501405i	$0.832817\pi$
$354$		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	$-0.0712340\pi$
$359$	5.59588	+	9.69235i	0.295339	+	0.511543i	−0.679724	+	0.733468i	$0.737901\pi$
$360$		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	$-0.486047\pi$
$383$	1.71520			0.0876427			0.0438214	+	0.999039i	$0.486047\pi$
$384$		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	$-0.474566\pi$
$389$	3.14856			0.159638			0.0798191	+	0.996809i	$0.474566\pi$
$390$		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	−0.972340	−	0.233572i	$-0.924959\pi$
$397$	−13.7172	−	23.7590i	−0.688449	−	1.19243i	0.283891	−	0.958857i	$-0.408375\pi$
$398$	−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	$-0.758170\pi$
$401$	−29.0370			−1.45004			−0.725020	+	0.688728i	$0.758170\pi$
$402$		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	0.973254	+	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
$412$	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	−0.210186	−	0.977661i	$-0.567407\pi$
$419$	15.1799	−	26.2924i	0.741586	−	1.28447i	0.951773	−	0.306804i	$-0.0992596\pi$
$420$		0			0
$421$	13.8868	+	24.0526i	0.676799	+	1.17225i	0.975940	+	0.218041i	$0.0699668\pi$
$421$	13.8868	+	24.0526i	0.676799	+	1.17225i	−0.299140	+	0.954209i	$0.596700\pi$
$422$	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	$-0.889272\pi$
$431$	−3.62965	+	6.28673i	−0.174834	+	0.302821i	0.765270	+	0.643710i	$0.222606\pi$
$432$		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	−0.883829	−	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
$446$	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	$-0.285429\pi$
$449$	26.4527			1.24838			0.624190	+	0.781272i	$0.285429\pi$
$450$		0			0
$451$	−17.3295	+	30.0156i	−0.816016	+	1.41338i
$452$	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	−0.780039	−	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
$461$	−7.79582	−	13.5028i	−0.363088	−	0.628886i	0.625380	−	0.780321i	$-0.284944\pi$
$461$	−7.79582	−	13.5028i	−0.363088	−	0.628886i	−0.988467	+	0.151434i	$0.951611\pi$
$462$		0			0
$463$	−3.82792	+	6.63016i	−0.177899	+	0.308130i	−0.941161	−	0.337960i	$-0.890263\pi$
$463$	−3.82792	+	6.63016i	−0.177899	+	0.308130i	0.763262	+	0.646089i	$0.223597\pi$
$464$	22.7090			1.05424
$465$		0			0
$466$	19.4097			0.899138
$467$	20.8137	+	36.0503i	0.963142	+	1.66821i	0.714526	+	0.699608i	$0.246642\pi$
$467$	20.8137	+	36.0503i	0.963142	+	1.66821i	0.248615	+	0.968602i	$0.420024\pi$
$468$		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	$-0.483152\pi$
$479$	2.31579			0.105811			0.0529055	+	0.998600i	$0.483152\pi$
$480$		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	−0.994969	−	0.100179i	$-0.968058\pi$
$487$	−9.06396	+	15.6992i	−0.410727	+	0.711401i	0.584242	+	0.811579i	$0.301392\pi$
$488$	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	$-0.671326\pi$
$491$	10.7972	−	18.7013i	0.487271	−	0.843978i	0.999893	+	0.0146364i	$0.00465909\pi$
$492$		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	$-0.585360\pi$
$503$	−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
$509$	41.4595			1.83766			0.918829	−	0.394656i	$-0.129136\pi$
$509$	41.4595			1.83766			0.918829	+	0.394656i	$0.129136\pi$
$510$		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	$-0.810272\pi$
$521$	1.65221	−	2.86171i	0.0723846	−	0.125374i	0.899946	+	0.436002i	$0.143606\pi$
$522$		0			0
$523$	1.24483	+	2.15611i	0.0544327	+	0.0942803i	0.891958	−	0.452119i	$-0.149332\pi$
$523$	1.24483	+	2.15611i	0.0544327	+	0.0942803i	−0.837525	+	0.546399i	$0.815998\pi$
$524$	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	0.999815	−	0.0192542i	$-0.00612919\pi$
$541$	11.2397	+	19.4677i	0.483233	+	0.836984i	−0.516582	+	0.856238i	$0.672796\pi$
$542$	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	0.978612	−	0.205713i	$-0.0659513\pi$
$547$	7.27727	+	12.6046i	0.311154	+	0.538934i	−0.667459	+	0.744647i	$0.732618\pi$
$548$	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	$-0.726498\pi$
$557$	7.77331	−	13.4638i	0.329366	−	0.570478i	0.982386	+	0.186862i	$0.0598318\pi$
$558$		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	$-0.267187\pi$
$563$	−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	$0.920046\pi$
$572$	−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	−0.735438	−	0.677592i	$-0.763024\pi$
$577$	5.26279	−	9.11542i	0.219093	−	0.379480i	0.954531	+	0.298112i	$0.0963569\pi$
$578$	−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	$-0.207508\pi$
$587$	−3.10009	−	5.36951i	−0.127954	−	0.221624i	−0.922884	+	0.385078i	$0.874174\pi$
$588$		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	0.937288	+	0.348555i	$0.113327\pi$
$593$	18.7629	+	32.4984i	0.770502	+	1.33455i	−0.166787	+	0.985993i	$0.553339\pi$
$594$		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	−0.962218	−	0.272279i	$-0.912223\pi$
$599$	−17.5460	−	30.3905i	−0.716909	−	1.24172i	0.245309	−	0.969445i	$-0.421111\pi$
$600$		0			0
$601$	−13.1171	−	22.7195i	−0.535058	−	0.926748i	−0.999161	−	0.0409662i	$-0.986956\pi$
$601$	−13.1171	−	22.7195i	−0.535058	−	0.926748i	0.464102	−	0.885782i	$-0.346377\pi$
$602$	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	−0.976186	−	0.216936i	$-0.930394\pi$
$613$	−7.43312	+	12.8745i	−0.300221	+	0.519998i	0.675965	+	0.736934i	$0.263727\pi$
$614$	−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	$-0.988031\pi$
$617$	−11.6023	+	20.0958i	−0.467091	+	0.809024i	0.532203	+	0.846617i	$0.321364\pi$
$618$		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	$-0.449656\pi$
$641$	7.97525			0.315003			0.157502	+	0.987519i	$0.449656\pi$
$642$		0			0
$643$	1.56140	−	2.70442i	0.0615755	−	0.106652i	−0.833594	−	0.552377i	$-0.813721\pi$
$643$	1.56140	−	2.70442i	0.0615755	−	0.106652i	0.895170	+	0.445725i	$0.147054\pi$
$644$	−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	$-0.755824\pi$
$647$	6.13273	−	10.6222i	0.241102	−	0.417602i	0.961029	+	0.276449i	$0.0891577\pi$
$648$		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	$-0.395297\pi$
$653$	16.5095			0.646067			0.323034	+	0.946387i	$0.395297\pi$
$654$		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	$-0.233740\pi$
$659$	−5.36940	−	9.30007i	−0.209162	−	0.362279i	−0.951451	+	0.307801i	$0.900407\pi$
$660$		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
$664$	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	−0.927030	−	0.374987i	$-0.877647\pi$
$673$	−20.4493	−	35.4193i	−0.788264	−	1.36531i	0.138766	−	0.990325i	$-0.455686\pi$
$674$	−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
$679$	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	0.134433	+	0.990923i	$0.457079\pi$
$683$	−20.6708	+	35.8029i	−0.790948	+	1.36996i	−0.925381	+	0.379039i	$0.876255\pi$
$684$		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	−0.851204	−	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
$698$	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	$-0.710604\pi$
$701$	−32.5344			−1.22881			−0.614404	+	0.788991i	$0.710604\pi$
$702$		0			0
$703$	−0.453708	+	0.785845i	−0.0171119	+	0.0296387i
$704$	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	−0.996295	−	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
$713$	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	$-0.127981\pi$
$719$	3.25084	+	5.63062i	0.121236	+	0.209987i	−0.799019	+	0.601305i	$0.794648\pi$
$720$		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	0.929462	−	0.368918i	$-0.120272\pi$
$727$	3.91607	+	6.78284i	0.145239	+	0.251562i	−0.784223	+	0.620479i	$0.786938\pi$
$728$	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	−0.997924	−	0.0643961i	$-0.979488\pi$
$739$	−12.0480	+	20.8678i	−0.443194	+	0.767634i	0.554731	+	0.832030i	$0.312821\pi$
$740$	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	$-0.948447\pi$
$743$	−9.64411	+	16.7041i	−0.353808	+	0.612814i	0.633105	+	0.774066i	$0.281780\pi$
$744$		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	$-0.484266\pi$
$761$	2.72609			0.0988207			0.0494104	+	0.998779i	$0.484266\pi$
$762$		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	−0.0779198	+	0.996960i	$0.524828\pi$
$769$	−25.0230	+	43.3411i	−0.902352	+	1.56292i	−0.824432	+	0.565960i	$0.808506\pi$
$770$	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	$-0.944580\pi$
$773$	−9.52030	+	16.4896i	−0.342421	+	0.593091i	0.642461	+	0.766319i	$0.277914\pi$
$774$		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	0.993995	+	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
$790$	−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	$-0.845115\pi$
$797$	−1.04472	+	1.80951i	−0.0370059	+	0.0640961i	0.846929	+	0.531706i	$0.178449\pi$
$798$		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	$-0.836035\pi$
$809$	−0.241404	+	0.418125i	−0.00848732	+	0.0147005i	0.861751	+	0.507332i	$0.169368\pi$
$810$		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	$-0.761507\pi$
$821$	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	$0.974346\pi$
$824$	−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	$-0.497082\pi$
$827$	0.527165			0.0183313			0.00916567	+	0.999958i	$0.497082\pi$
$828$		0			0
$829$	23.1015	−	40.0130i	0.802348	−	1.38971i	−0.115718	−	0.993282i	$-0.536917\pi$
$829$	23.1015	−	40.0130i	0.802348	−	1.38971i	0.918067	−	0.396426i	$-0.129750\pi$
$830$	−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	$-0.106831\pi$
$839$	5.41289	+	9.37540i	0.186874	+	0.323675i	−0.757333	+	0.653029i	$0.773498\pi$
$840$		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	0.952749	+	0.303758i	$0.0982414\pi$
$853$	21.5961	+	37.4056i	0.739437	+	1.28074i	−0.213313	+	0.976984i	$0.568425\pi$
$854$	−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	$-0.491439\pi$
$857$	1.57445			0.0537822			0.0268911	+	0.999638i	$0.491439\pi$
$858$		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	$-0.215771\pi$
$863$	−4.51387	−	7.81825i	−0.153654	−	0.266136i	−0.932568	+	0.360994i	$0.882437\pi$
$864$		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	$-0.617806\pi$
$881$	−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
$887$	41.5223			1.39418			0.697091	−	0.716982i	$-0.254477\pi$
$887$	41.5223			1.39418			0.697091	+	0.716982i	$0.254477\pi$
$888$		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	$-0.159557\pi$
$911$	0.674054	+	1.16750i	0.0223324	+	0.0386808i	−0.854643	+	0.519216i	$0.826224\pi$
$912$		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	0.978492	+	0.206284i	$0.0661370\pi$
$919$	20.2472	+	35.0692i	0.667893	+	1.15682i	−0.310599	+	0.950541i	$0.600530\pi$
$920$	−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	$-0.952622\pi$
$929$	−11.1569	+	19.3243i	−0.366046	+	0.634011i	0.622897	+	0.782304i	$0.285956\pi$
$930$		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	−0.938033	−	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
$950$	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	$-0.865136\pi$
$953$	−56.2821			−1.82316			−0.911579	+	0.411125i	$0.865136\pi$
$954$		0			0
$955$	11.4898	−	19.9009i	0.371802	−	0.643979i
$956$	−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	0.180903	−	0.983501i	$-0.442098\pi$
$967$	29.2989	−	50.7471i	0.942188	−	1.63192i	0.761285	−	0.648417i	$-0.224569\pi$
$968$	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	$-0.135462\pi$
$971$	3.04991	+	5.28260i	0.0978763	+	0.169527i	−0.812929	+	0.582363i	$0.802128\pi$
$972$		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	$-0.140364\pi$
$977$	2.57988	+	4.46849i	0.0825377	+	0.142960i	−0.821802	+	0.569774i	$0.807031\pi$
$978$		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	$-0.0440150\pi$
$983$	62.1071			1.98091			0.990455	+	0.137837i	$0.0440150\pi$
$984$		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	−0.641506	−	0.767118i	$-0.721690\pi$
$991$	10.8163	−	18.7343i	0.343590	−	0.595116i	0.985097	+	0.172002i	$0.0550235\pi$
$992$	−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.109.3		16
3.2	odd	2	inner	567.2.g.l.109.6		16
7.2	even	3		567.2.h.l.352.6		16
9.2	odd	6		567.2.h.l.298.3		16
9.4	even	3		567.2.e.g.487.3	yes	16
9.5	odd	6		567.2.e.g.487.6	yes	16
9.7	even	3		567.2.h.l.298.6		16
21.2	odd	6		567.2.h.l.352.3		16
63.2	odd	6	inner	567.2.g.l.541.6		16
63.4	even	3		3969.2.a.bg.1.6		8
63.16	even	3	inner	567.2.g.l.541.3		16
63.23	odd	6		567.2.e.g.163.6	yes	16
63.31	odd	6		3969.2.a.bf.1.6		8
63.32	odd	6		3969.2.a.bg.1.3		8
63.58	even	3		567.2.e.g.163.3	✓	16
63.59	even	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	63.58	even	3
567.2.e.g.163.6	yes	16	63.23	odd	6
567.2.e.g.487.3	yes	16	9.4	even	3
567.2.e.g.487.6	yes	16	9.5	odd	6
567.2.g.l.109.3		16	1.1	even	1	trivial
567.2.g.l.109.6		16	3.2	odd	2	inner
567.2.g.l.541.3		16	63.16	even	3	inner
567.2.g.l.541.6		16	63.2	odd	6	inner
567.2.h.l.298.3		16	9.2	odd	6
567.2.h.l.298.6		16	9.7	even	3
567.2.h.l.352.3		16	21.2	odd	6
567.2.h.l.352.6		16	7.2	even	3
3969.2.a.bf.1.3		8	63.59	even	6
3969.2.a.bf.1.6		8	63.31	odd	6
3969.2.a.bg.1.3		8	63.32	odd	6
3969.2.a.bg.1.6		8	63.4	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.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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