LMFDB - Embedded newform 567.2.e.g.487.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(163,567)]

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([0, 2]))

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

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

chi := DirichletCharacter("567.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: 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			487.6
Root			$-0.776749 + 1.18180i$ of defining polynomial
Character	$\chi$	$=$	567.487
Dual form			567.2.e.g.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

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

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

Coefficient data

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

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

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

$2$	0.635098	+	1.10002i	0.449082	+	0.777833i	0.998327	−	0.0578286i	$-0.0184177\pi$
$2$	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
$5$	−0.776749	−	1.34537i	−0.347373	−	0.601667i	0.638409	−	0.769697i	$-0.279593\pi$
$5$	−0.776749	−	1.34537i	−0.347373	−	0.601667i	−0.985782	+	0.168030i	$0.946259\pi$
$6$		0			0
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$8$	3.03145			1.07178
$9$		0			0
$10$	0.986623	−	1.70888i	0.311998	−	0.540396i
$11$	1.60500	−	2.77995i	0.483927	−	0.838185i	−0.515903	−	0.856647i	$-0.672544\pi$
$11$	1.60500	−	2.77995i	0.483927	−	0.838185i	0.999830	+	0.0184616i	$0.00587686\pi$
$12$		0			0
$13$	4.78669			1.32759			0.663795	−	0.747915i	$-0.268945\pi$
$13$	4.78669			1.32759			0.663795	+	0.747915i	$0.268945\pi$
$14$	−3.35166	−	0.245346i	−0.895768	−	0.0655714i
$15$		0			0
$16$	1.53867	+	2.66505i	0.384667	+	0.666263i
$17$	1.05918	−	1.83456i	0.256889	−	0.444945i	−0.708518	−	0.705693i	$-0.750636\pi$
$17$	1.05918	−	1.83456i	0.256889	−	0.444945i	0.965407	+	0.260748i	$0.0839691\pi$
$18$		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	$0.644924\pi$
$20$	−0.600584			−0.134295
$21$		0			0
$22$	4.07734			0.869291
$23$	−1.85379	−	3.21086i	−0.386542	−	0.669510i	0.605440	−	0.795891i	$-0.292997\pi$
$23$	−1.85379	−	3.21086i	−0.386542	−	0.669510i	−0.991982	+	0.126381i	$0.959664\pi$
$24$		0			0
$25$	1.29332	−	2.24010i	0.258665	−	0.448020i
$26$	3.04002	+	5.26547i	0.596197	+	1.03264i
$27$		0			0
$28$	0.445391	+	0.920788i	0.0841709	+	0.174013i
$29$	7.37944			1.37033			0.685164	−	0.728389i	$-0.259731\pi$
$29$	7.37944			1.37033			0.685164	+	0.728389i	$0.259731\pi$
$30$		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
$34$	2.69074			0.461457
$35$	4.09920	+	0.300067i	0.692891	+	0.0507206i
$36$		0			0
$37$	0.0932782	+	0.161563i	0.0153348	+	0.0265607i	0.873591	−	0.486661i	$-0.161785\pi$
$37$	0.0932782	+	0.161563i	0.0153348	+	0.0265607i	−0.858256	+	0.513222i	$0.828452\pi$
$38$	−3.08914	+	5.35054i	−0.501124	+	0.867972i
$39$		0			0
$40$	−2.35468	−	4.07842i	−0.372307	−	0.644855i
$41$	−10.7972			−1.68624			−0.843120	−	0.537726i	$-0.819284\pi$
$41$	−10.7972			−1.68624			−0.843120	+	0.537726i	$0.819284\pi$
$42$		0			0
$43$	4.86916			0.742539			0.371270	−	0.928525i	$-0.378923\pi$
$43$	4.86916			0.742539			0.371270	+	0.928525i	$0.378923\pi$
$44$	−0.620496	−	1.07473i	−0.0935433	−	0.162022i
$45$		0			0
$46$	2.35468	−	4.07842i	0.347178	−	0.601330i
$47$	−0.885937	−	1.53449i	−0.129227	−	0.223828i	0.794150	−	0.607722i	$-0.207916\pi$
$47$	−0.885937	−	1.53449i	−0.129227	−	0.223828i	−0.923377	+	0.383893i	$0.874583\pi$
$48$		0			0
$49$	−2.57990	−	6.50724i	−0.368557	−	0.929605i
$50$	3.28555			0.464647
$51$		0			0
$52$	0.925270	−	1.60261i	0.128312	−	0.222243i
$53$	−0.834432	+	1.44528i	−0.114618	+	0.198524i	−0.917627	−	0.397443i	$-0.869898\pi$
$53$	−0.834432	+	1.44528i	−0.114618	+	0.198524i	0.803009	+	0.595967i	$0.203231\pi$
$54$		0			0
$55$	−4.98674			−0.672411
$56$	−4.50663	+	6.63462i	−0.602223	+	0.886589i
$57$		0			0
$58$	4.68667	+	8.11755i	0.615390	+	1.06589i
$59$	−2.91297	+	5.04541i	−0.379236	+	0.656857i	−0.990951	−	0.134221i	$-0.957147\pi$
$59$	−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	$0.897913\pi$
$68$	−0.409481	−	0.709241i	−0.0496568	−	0.0860081i
$69$		0			0
$70$	2.27331	+	4.69978i	0.271713	+	0.561732i
$71$	−13.8101			−1.63895			−0.819477	−	0.573112i	$-0.805736\pi$
$71$	−13.8101			−1.63895			−0.819477	+	0.573112i	$0.805736\pi$
$72$		0			0
$73$	−5.93201	+	10.2745i	−0.694290	+	1.20255i	0.276130	+	0.961120i	$0.410948\pi$
$73$	−5.93201	+	10.2745i	−0.694290	+	1.20255i	−0.970420	+	0.241425i	$0.922385\pi$
$74$	−0.118482	+	0.205216i	−0.0137732	+	0.0238559i
$75$		0			0
$76$	1.88044			0.215701
$77$	3.69814	+	7.64544i	0.421443	+	0.871278i
$78$		0			0
$79$	0.654632	+	1.13386i	0.0736518	+	0.127569i	0.900499	−	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
$83$	−0.346488			−0.0380320			−0.0190160	−	0.999819i	$-0.506053\pi$
$83$	−0.346488			−0.0380320			−0.0190160	+	0.999819i	$0.506053\pi$
$84$		0			0
$85$	−3.29087			−0.356945
$86$	3.09239	+	5.35618i	0.333461	+	0.577572i
$87$		0			0
$88$	4.86549	−	8.42727i	0.518663	−	0.898350i
$89$	8.70319	+	15.0744i	0.922537	+	1.59788i	0.795476	+	0.605985i	$0.207221\pi$
$89$	8.70319	+	15.0744i	0.922537	+	1.59788i	0.127061	+	0.991895i	$0.459446\pi$
$90$		0			0
$91$	−7.11601	+	10.4761i	−0.745960	+	1.09820i
$92$	−1.43335			−0.149437
$93$		0			0
$94$	1.12531	−	1.94910i	0.116067	−	0.201035i
$95$	3.77813	−	6.54391i	0.387628	−	0.671391i
$96$		0			0
$97$	−10.5683			−1.07304			−0.536522	−	0.843886i	$-0.680262\pi$
$97$	−10.5683			−1.07304			−0.536522	+	0.843886i	$0.680262\pi$
$98$	5.51961	−	6.97068i	0.557565	−	0.704145i
$99$		0			0
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.01697	−	1.76144i	0.101192	−	0.175270i	−0.810984	−	0.585068i	$-0.801068\pi$
$101$	1.01697	−	1.76144i	0.101192	−	0.175270i	0.912176	+	0.409798i	$0.134401\pi$
$102$		0			0
$103$	−9.99080	−	17.3046i	−0.984423	−	1.70507i	−0.644472	−	0.764628i	$-0.722923\pi$
$103$	−9.99080	−	17.3046i	−0.984423	−	1.70507i	−0.339951	−	0.940443i	$-0.610410\pi$
$104$	14.5106			1.42288
$105$		0			0
$106$	−2.11979			−0.205892
$107$	−8.45322	−	14.6414i	−0.817204	−	1.41544i	−0.907735	−	0.419545i	$-0.862190\pi$
$107$	−8.45322	−	14.6414i	−0.817204	−	1.41544i	0.0905308	−	0.995894i	$-0.471144\pi$
$108$		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
$112$	−8.12014	−	0.594406i	−0.767281	−	0.0561661i
$113$	8.58471			0.807582			0.403791	−	0.914851i	$-0.367692\pi$
$113$	8.58471			0.807582			0.403791	+	0.914851i	$0.367692\pi$
$114$		0			0
$115$	−2.87986	+	4.98806i	−0.268548	+	0.465139i
$116$	1.42645	−	2.47068i	0.132442	−	0.229397i
$117$		0			0
$118$	−7.40009			−0.681233
$119$	2.44050	+	5.04541i	0.223720	+	0.462512i
$120$		0			0
$121$	0.347932	+	0.602636i	0.0316302	+	0.0547851i
$122$	4.36776	−	7.56518i	0.395438	−	0.684919i
$123$		0			0
$124$	1.06396	+	1.84283i	0.0955465	+	0.165491i
$125$	−11.7858			−1.05416
$126$		0			0
$127$	1.95162			0.173178			0.0865892	−	0.996244i	$-0.472403\pi$
$127$	1.95162			0.173178			0.0865892	+	0.996244i	$0.472403\pi$
$128$	3.49244	+	6.04908i	0.308691	+	0.534668i
$129$		0			0
$130$	4.72266	−	8.17989i	0.414205	−	0.717424i
$131$	5.87214	+	10.1708i	0.513051	+	0.888630i	0.999885	+	0.0151361i	$0.00481816\pi$
$131$	5.87214	+	10.1708i	0.513051	+	0.888630i	−0.486834	+	0.873494i	$0.661849\pi$
$132$		0			0
$133$	−12.8347	−	0.939515i	−1.11291	−	0.0814663i
$134$	−15.5439			−1.34278
$135$		0			0
$136$	3.21086	−	5.56137i	0.275329	−	0.476883i
$137$	8.06604	−	13.9708i	0.689128	−	1.19361i	−0.282992	−	0.959122i	$-0.591327\pi$
$137$	8.06604	−	13.9708i	0.689128	−	1.19361i	0.972120	−	0.234483i	$-0.0753398\pi$
$138$		0			0
$139$	13.4425			1.14018			0.570091	−	0.821582i	$-0.306908\pi$
$139$	13.4425			1.14018			0.570091	+	0.821582i	$0.306908\pi$
$140$	0.892842	−	1.31443i	0.0754589	−	0.111090i
$141$		0			0
$142$	−8.77075	−	15.1914i	−0.736025	−	1.27483i
$143$	7.68265	−	13.3067i	0.642456	−	1.11277i
$144$		0			0
$145$	−5.73197	−	9.92806i	−0.476014	−	0.824481i
$146$	−15.0696			−1.24717
$147$		0			0
$148$	0.0721229			0.00592846
$149$	1.60587	+	2.78145i	0.131558	+	0.227865i	0.924277	−	0.381722i	$-0.124669\pi$
$149$	1.60587	+	2.78145i	0.131558	+	0.227865i	−0.792719	+	0.609587i	$0.791335\pi$
$150$		0			0
$151$	−8.51610	+	14.7503i	−0.693030	+	1.20036i	0.277810	+	0.960636i	$0.410391\pi$
$151$	−8.51610	+	14.7503i	−0.693030	+	1.20036i	−0.970840	+	0.239727i	$0.922942\pi$
$152$	7.37253	+	12.7696i	0.597991	+	1.03575i
$153$		0			0
$154$	−6.06147	+	8.92364i	−0.488447	+	0.719088i
$155$	8.55073			0.686811
$156$		0			0
$157$	−4.71709	+	8.17024i	−0.376465	+	0.652056i	−0.990545	−	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
$160$	−3.34636			−0.264553
$161$	9.78315	+	0.716140i	0.771021	+	0.0564398i
$162$		0			0
$163$	−1.83874	−	3.18478i	−0.144021	−	0.249452i	0.784986	−	0.619513i	$-0.212670\pi$
$163$	−1.83874	−	3.18478i	−0.144021	−	0.249452i	−0.929007	+	0.370062i	$0.879337\pi$
$164$	−2.08710	+	3.61497i	−0.162976	+	0.282282i
$165$		0			0
$166$	−0.220054	−	0.381144i	−0.0170795	−	0.0295825i
$167$	1.61017			0.124599			0.0622994	−	0.998058i	$-0.480157\pi$
$167$	1.61017			0.124599			0.0622994	+	0.998058i	$0.480157\pi$
$168$		0			0
$169$	9.91241			0.762493
$170$	−2.09003	−	3.62003i	−0.160298	−	0.277644i
$171$		0			0
$172$	0.941210	−	1.63022i	0.0717666	−	0.124303i
$173$	−8.09213	−	14.0160i	−0.615233	−	1.06562i	−0.990344	−	0.138635i	$-0.955728\pi$
$173$	−8.09213	−	14.0160i	−0.615233	−	1.06562i	0.375110	−	0.926980i	$-0.377605\pi$
$174$		0			0
$175$	2.97999	+	6.16075i	0.225266	+	0.465709i
$176$	9.87827			0.744603
$177$		0			0
$178$	−11.0548	+	19.1474i	−0.828590	+	1.43516i
$179$	−8.70319	+	15.0744i	−0.650507	+	1.12671i	0.332493	+	0.943106i	$0.392110\pi$
$179$	−8.70319	+	15.0744i	−0.650507	+	1.12671i	−0.983000	+	0.183606i	$0.941223\pi$
$180$		0			0
$181$	8.89591			0.661228			0.330614	−	0.943766i	$-0.392744\pi$
$181$	8.89591			0.661228			0.330614	+	0.943766i	$0.392744\pi$
$182$	−16.0433	−	1.17439i	−1.18921	−	0.0870519i
$183$		0			0
$184$	−5.61967	−	9.73356i	−0.414288	−	0.717568i
$185$	0.144907	−	0.250987i	0.0106538	−	0.0184529i
$186$		0			0
$187$	−3.39998	−	5.88893i	−0.248631	−	0.430642i
$188$	−0.685009			−0.0499594
$189$		0			0
$190$	9.59793			0.696307
$191$	7.39609	+	12.8104i	0.535163	+	0.926929i	0.999155	+	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	$0.187550\pi$
$194$	−6.71188	−	11.6253i	−0.481885	−	0.834649i
$195$		0			0
$196$	−2.67736	−	0.394085i	−0.191240	−	0.0281489i
$197$	−7.71970			−0.550006			−0.275003	−	0.961443i	$-0.588679\pi$
$197$	−7.71970			−0.550006			−0.275003	+	0.961443i	$0.588679\pi$
$198$		0			0
$199$	−1.10665	+	1.91678i	−0.0784487	+	0.135877i	−0.902581	−	0.430521i	$-0.858330\pi$
$199$	−1.10665	+	1.91678i	−0.0784487	+	0.135877i	0.824132	+	0.566398i	$0.191663\pi$
$200$	3.92065	−	6.79076i	0.277232	−	0.480179i
$201$		0			0
$202$	2.58350			0.181774
$203$	−10.9704	+	16.1506i	−0.769974	+	1.13355i
$204$		0			0
$205$	8.38671	+	14.5262i	0.585753	+	1.01455i
$206$	12.6903	−	21.9802i	0.884174	−	1.53143i
$207$		0			0
$208$	7.36513	+	12.7568i	0.510680	+	0.884524i
$209$	15.6136			1.08001
$210$		0			0
$211$	−1.81344			−0.124843			−0.0624213	−	0.998050i	$-0.519882\pi$
$211$	−1.81344			−0.124843			−0.0624213	+	0.998050i	$0.519882\pi$
$212$	0.322592	+	0.558746i	0.0221557	+	0.0383749i
$213$		0			0
$214$	10.7373	−	18.5975i	0.733983	−	1.27130i
$215$	−3.78211	−	6.55081i	−0.257938	−	0.446761i
$216$		0			0
$217$	−6.34119	−	13.1096i	−0.430468	−	0.889937i
$218$	13.5900			0.920428
$219$		0			0
$220$	−0.963939	+	1.66959i	−0.0649887	+	0.112564i
$221$	5.06997	−	8.78145i	0.341043	−	0.590704i
$222$		0			0
$223$	9.50616			0.636580			0.318290	−	0.947993i	$-0.396891\pi$
$223$	9.50616			0.636580			0.318290	+	0.947993i	$0.396891\pi$
$224$	2.48165	+	5.13049i	0.165812	+	0.342795i
$225$		0			0
$226$	5.45213	+	9.44337i	0.362671	+	0.628164i
$227$	−5.41646	+	9.38158i	−0.359503	+	0.622678i	−0.987878	−	0.155233i	$-0.950387\pi$
$227$	−5.41646	+	9.38158i	−0.359503	+	0.622678i	0.628375	+	0.777911i	$0.283720\pi$
$228$		0			0
$229$	−6.25983	−	10.8423i	−0.413661	−	0.716482i	0.581626	−	0.813456i	$-0.302417\pi$
$229$	−6.25983	−	10.8423i	−0.413661	−	0.716482i	−0.995287	+	0.0969747i	$0.969083\pi$
$230$	−7.31597			−0.482401
$231$		0			0
$232$	22.3704			1.46869
$233$	7.64044	+	13.2336i	0.500542	+	0.866964i	1.00000		0.000625732i	$0.000199177\pi$
$233$	7.64044	+	13.2336i	0.500542	+	0.866964i	−0.499458	+	0.866338i	$0.666467\pi$
$234$		0			0
$235$	−1.37630	+	2.38382i	−0.0897800	+	0.155504i
$236$	1.12616	+	1.95056i	0.0733066	+	0.126971i
$237$		0			0
$238$	−4.00011	+	5.88893i	−0.259289	+	0.381723i
$239$	−10.7158			−0.693149			−0.346574	−	0.938023i	$-0.612655\pi$
$239$	−10.7158			−0.693149			−0.346574	+	0.938023i	$0.612655\pi$
$240$		0			0
$241$	7.50011	−	12.9906i	0.483125	−	0.836796i	−0.516688	−	0.856174i	$-0.672835\pi$
$241$	7.50011	−	12.9906i	0.483125	−	0.836796i	0.999812	+	0.0193775i	$0.00616845\pi$
$242$	−0.441942	+	0.765467i	−0.0284091	+	0.0492061i
$243$		0			0
$244$	−2.65877			−0.170210
$245$	−6.75069	+	8.52540i	−0.431286	+	0.544668i
$246$		0			0
$247$	11.6413	+	20.1633i	0.740718	+	1.28296i
$248$	−8.34283	+	14.4502i	−0.529770	+	0.917589i
$249$		0			0
$250$	−7.48516	−	12.9647i	−0.473403	−	0.819958i
$251$	16.5665			1.04567			0.522833	−	0.852435i	$-0.324875\pi$
$251$	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
$257$	−11.2886	−	19.5524i	−0.704163	−	1.21965i	−0.966993	−	0.254804i	$-0.917989\pi$
$257$	−11.2886	−	19.5524i	−0.704163	−	1.21965i	0.262829	−	0.964842i	$-0.415344\pi$
$258$		0			0
$259$	−0.492265	−	0.0360344i	−0.0305878	−	0.00223907i
$260$	−2.87481			−0.178288
$261$		0			0
$262$	−7.45877	+	12.9190i	−0.460804	+	0.798136i
$263$	−11.1730	+	19.3523i	−0.688959	+	1.19331i	0.283216	+	0.959056i	$0.408599\pi$
$263$	−11.1730	+	19.3523i	−0.688959	+	1.19331i	−0.972175	+	0.234256i	$0.924735\pi$
$264$		0			0
$265$	2.59258			0.159261
$266$	−7.11779	−	14.7151i	−0.436419	−	0.902241i
$267$		0			0
$268$	2.36549	+	4.09715i	0.144495	+	0.250273i
$269$	−13.9475	+	24.1577i	−0.850392	+	1.47292i	0.0304623	+	0.999536i	$0.490302\pi$
$269$	−13.9475	+	24.1577i	−0.850392	+	1.47292i	−0.880855	+	0.473387i	$0.843031\pi$
$270$		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	$0.930290\pi$
$272$	6.51892			0.395267
$273$		0			0
$274$	20.4909			1.23790
$275$	−4.15157	−	7.19074i	−0.250349	−	0.433618i
$276$		0			0
$277$	4.35728	−	7.54704i	0.261804	−	0.453458i	−0.704917	−	0.709289i	$-0.749016\pi$
$277$	4.35728	−	7.54704i	0.261804	−	0.453458i	0.966721	+	0.255832i	$0.0823493\pi$
$278$	8.53733	+	14.7871i	0.512035	+	0.886871i
$279$		0			0
$280$	12.4265	+	0.909639i	0.742627	+	0.0543613i
$281$	−6.20641			−0.370243			−0.185122	−	0.982716i	$-0.559268\pi$
$281$	−6.20641			−0.370243			−0.185122	+	0.982716i	$0.559268\pi$
$282$		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
$286$	19.5170			1.15406
$287$	16.0514	−	23.6307i	0.947483	−	1.39488i
$288$		0			0
$289$	6.25627	+	10.8362i	0.368016	+	0.637422i
$290$	7.28073	−	12.6106i	0.427539	−	0.740519i
$291$		0			0
$292$	2.29332	+	3.97215i	0.134207	+	0.232453i
$293$	−14.4968			−0.846913			−0.423456	−	0.905916i	$-0.639183\pi$
$293$	−14.4968			−0.846913			−0.423456	+	0.905916i	$0.639183\pi$
$294$		0			0
$295$	9.05058			0.526945
$296$	0.282768	+	0.489769i	0.0164356	+	0.0284672i
$297$		0			0
$298$	−2.03977	+	3.53299i	−0.118161	+	0.204661i
$299$	−8.87352	−	15.3694i	−0.513169	−	0.888834i
$300$		0			0
$301$	−7.23860	+	10.6566i	−0.417226	+	0.614237i
$302$	−21.6342			−1.24491
$303$		0			0
$304$	−7.48413	+	12.9629i	−0.429244	+	0.743473i
$305$	−5.34193	+	9.25249i	−0.305878	+	0.529796i
$306$		0			0
$307$	22.2776			1.27145			0.635725	−	0.771916i	$-0.280701\pi$
$307$	22.2776			1.27145			0.635725	+	0.771916i	$0.280701\pi$
$308$	3.27459	+	0.239705i	0.186587	+	0.0136584i
$309$		0			0
$310$	5.43055	+	9.40599i	0.308435	+	0.534225i
$311$	−8.70027	+	15.0693i	−0.493347	+	0.854502i	−0.999971	−	0.00766509i	$-0.997560\pi$
$311$	−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
$320$	−6.90590	−	11.9614i	−0.386052	−	0.668661i
$321$		0			0
$322$	5.42549	+	11.2165i	0.302351	+	0.625072i
$323$	10.3038			0.573317
$324$		0			0
$325$	6.19074	−	10.7227i	0.343400	−	0.594787i
$326$	2.33556	−	4.04530i	0.129354	−	0.224049i
$327$		0			0
$328$	−32.7312			−1.80728
$329$	4.67543	+	0.342248i	0.257765	+	0.0188687i
$330$		0			0
$331$	8.31616	+	14.4040i	0.457098	+	0.791716i	0.998806	−	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
$335$	19.0107			1.03867
$336$		0			0
$337$	15.9095			0.866645			0.433322	−	0.901239i	$-0.357341\pi$
$337$	15.9095			0.866645			0.433322	+	0.901239i	$0.357341\pi$
$338$	6.29535	+	10.9039i	0.342422	+	0.593092i
$339$		0			0
$340$	−0.636127	+	1.10180i	−0.0344988	+	0.0597537i
$341$	8.83422	+	15.3013i	0.478400	+	0.828613i
$342$		0			0
$343$	18.0770	+	4.02745i	0.976069	+	0.217462i
$344$	14.7606			0.795839
$345$		0			0
$346$	10.2786	−	17.8031i	0.552581	−	0.957098i
$347$	−3.14462	+	5.44665i	−0.168812	+	0.292391i	−0.938003	−	0.346628i	$-0.887326\pi$
$347$	−3.14462	+	5.44665i	−0.168812	+	0.292391i	0.769190	+	0.639020i	$0.220660\pi$
$348$		0			0
$349$	1.61955			0.0866927			0.0433463	−	0.999060i	$-0.486198\pi$
$349$	1.61955			0.0866927			0.0433463	+	0.999060i	$0.486198\pi$
$350$	−4.88437	+	7.19074i	−0.261081	+	0.384361i
$351$		0			0
$352$	−3.45731	−	5.98823i	−0.184275	−	0.319174i
$353$	−16.2559	+	28.1560i	−0.865213	+	1.49859i	0.00162266	+	0.999999i	$0.499483\pi$
$353$	−16.2559	+	28.1560i	−0.865213	+	1.49859i	−0.866836	+	0.498594i	$0.833850\pi$
$354$		0			0
$355$	10.7270	+	18.5796i	0.569328	+	0.986104i
$356$	6.72933			0.356654
$357$		0			0
$358$	−22.1095			−1.16852
$359$	−5.59588	−	9.69235i	−0.295339	−	0.511543i	0.679724	−	0.733468i	$-0.262099\pi$
$359$	−5.59588	−	9.69235i	−0.295339	−	0.511543i	−0.975064	+	0.221925i	$0.928766\pi$
$360$		0			0
$361$	−2.32938	+	4.03461i	−0.122599	+	0.212348i
$362$	5.64978	+	9.78570i	0.296946	+	0.514325i
$363$		0			0
$364$	2.13195	+	4.40753i	0.111744	+	0.231017i
$365$	18.4307			0.964709
$366$		0			0
$367$	2.59339	−	4.49188i	0.135374	−	0.234474i	−0.790366	−	0.612634i	$-0.790110\pi$
$367$	2.59339	−	4.49188i	0.135374	−	0.234474i	0.925740	+	0.378160i	$0.123443\pi$
$368$	5.70474	−	9.88089i	0.297380	−	0.515077i
$369$		0			0
$370$	0.368122			0.0191377
$371$	−1.92264	−	3.97482i	−0.0998187	−	0.206362i
$372$		0			0
$373$	−16.4322	−	28.4614i	−0.850825	−	1.47367i	−0.880464	−	0.474112i	$-0.842769\pi$
$373$	−16.4322	−	28.4614i	−0.850825	−	1.47367i	0.0296389	−	0.999561i	$-0.490564\pi$
$374$	4.31864	−	7.48010i	0.223312	−	0.386787i
$375$		0			0
$376$	−2.68568	−	4.65173i	−0.138503	−	0.239895i
$377$	35.3231			1.81923
$378$		0			0
$379$	13.9362			0.715856			0.357928	−	0.933749i	$-0.383483\pi$
$379$	13.9362			0.715856			0.357928	+	0.933749i	$0.383483\pi$
$380$	−1.46063	−	2.52988i	−0.0749286	−	0.129780i
$381$		0			0
$382$	−9.39449	+	16.2717i	−0.480664	+	0.832534i
$383$	0.857601	+	1.48541i	0.0438214	+	0.0759008i	0.887104	−	0.461569i	$-0.152713\pi$
$383$	0.857601	+	1.48541i	0.0438214	+	0.0759008i	−0.843283	+	0.537470i	$0.819380\pi$
$384$		0			0
$385$	7.41340	−	10.9139i	0.377822	−	0.556226i
$386$	−2.31376			−0.117768
$387$		0			0
$388$	−2.04285	+	3.53832i	−0.103710	+	0.179631i
$389$	1.57428	−	2.72673i	0.0798191	−	0.138251i	−0.823353	−	0.567530i	$-0.807899\pi$
$389$	1.57428	−	2.72673i	0.0798191	−	0.138251i	0.903172	+	0.429279i	$0.141232\pi$
$390$		0			0
$391$	−7.85400			−0.397194
$392$	−7.82085	−	19.7264i	−0.395012	−	0.996332i
$393$		0			0
$394$	−4.90277	−	8.49184i	−0.246998	−	0.427813i
$395$	1.01697	−	1.76144i	0.0511693	−	0.0886277i
$396$		0			0
$397$	−13.7172	−	23.7590i	−0.688449	−	1.19243i	−0.972340	−	0.233572i	$-0.924959\pi$
$397$	−13.7172	−	23.7590i	−0.688449	−	1.19243i	0.283891	−	0.958857i	$-0.408375\pi$
$398$	−2.81134			−0.140920
$399$		0			0
$400$	7.95998			0.397999
$401$	−14.5185	−	25.1468i	−0.725020	−	1.25577i	−0.958966	−	0.283522i	$-0.908497\pi$
$401$	−14.5185	−	25.1468i	−0.725020	−	1.25577i	0.233946	−	0.972250i	$-0.424836\pi$
$402$		0			0
$403$	−13.1734	+	22.8170i	−0.656214	+	1.13660i
$404$	−0.393161	−	0.680975i	−0.0195605	−	0.0338798i
$405$		0			0
$406$	−24.7333	−	1.81051i	−1.22750	−	0.0898543i
$407$	0.598847			0.0296837
$408$		0			0
$409$	13.8650	−	24.0149i	0.685581	−	1.18746i	−0.287673	−	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
$412$	−7.72491			−0.380579
$413$	−6.71188	−	13.8759i	−0.330270	−	0.682791i
$414$		0			0
$415$	0.269134	+	0.466153i	0.0132113	+	0.0228826i
$416$	5.15546	−	8.92952i	0.252767	−	0.437806i
$417$		0			0
$418$	9.91614	+	17.1753i	0.485014	+	0.840070i
$419$	30.3598			1.48317			0.741586	−	0.670857i	$-0.234074\pi$
$419$	30.3598			1.48317			0.741586	+	0.670857i	$0.234074\pi$
$420$		0			0
$421$	−27.7735			−1.35360			−0.676799	−	0.736168i	$-0.736633\pi$
$421$	−27.7735			−1.35360			−0.676799	+	0.736168i	$0.736633\pi$
$422$	−1.15171	−	1.99483i	−0.0560646	−	0.0971067i
$423$		0			0
$424$	−2.52954	+	4.38129i	−0.122845	+	0.212774i
$425$	−2.73973	−	4.74535i	−0.132896	−	0.230183i
$426$		0			0
$427$	18.1471	+	1.32839i	0.878197	+	0.0642853i
$428$	−6.53605			−0.315932
$429$		0			0
$430$	4.80402	−	8.32081i	0.231671	−	0.401265i
$431$	3.62965	−	6.28673i	0.174834	−	0.302821i	−0.765270	−	0.643710i	$-0.777394\pi$
$431$	3.62965	−	6.28673i	0.174834	−	0.302821i	0.940104	+	0.340888i	$0.110728\pi$
$432$		0			0
$433$	15.0375			0.722658			0.361329	−	0.932438i	$-0.382323\pi$
$433$	15.0375			0.722658			0.361329	+	0.932438i	$0.382323\pi$
$434$	10.3936	−	15.3013i	0.498907	−	0.734487i
$435$		0			0
$436$	−2.06814	−	3.58213i	−0.0990460	−	0.171553i
$437$	9.01688	−	15.6177i	0.431336	−	0.747096i
$438$		0			0
$439$	−0.770595	−	1.33471i	−0.0367785	−	0.0637022i	0.847050	−	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
$446$	6.03735	+	10.4570i	0.285877	+	0.495153i
$447$		0			0
$448$	−13.2172	+	19.4583i	−0.624456	+	0.919319i
$449$	−26.4527			−1.24838			−0.624190	−	0.781272i	$-0.714571\pi$
$449$	−26.4527			−1.24838			−0.624190	+	0.781272i	$0.714571\pi$
$450$		0			0
$451$	−17.3295	+	30.0156i	−0.816016	+	1.41338i
$452$	1.65943	−	2.87422i	0.0780530	−	0.135192i
$453$		0			0
$454$	−13.7599			−0.645786
$455$	19.6216	+	1.43633i	0.919875	+	0.0673361i
$456$		0			0
$457$	3.24681	+	5.62363i	0.151879	+	0.263063i	0.931918	−	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
$461$	−15.5916			−0.726175			−0.363088	−	0.931755i	$-0.618277\pi$
$461$	−15.5916			−0.726175			−0.363088	+	0.931755i	$0.618277\pi$
$462$		0			0
$463$	7.65585			0.355797			0.177899	−	0.984049i	$-0.443070\pi$
$463$	7.65585			0.355797			0.177899	+	0.984049i	$0.443070\pi$
$464$	11.3545	+	19.6666i	0.527120	+	0.912999i
$465$		0			0
$466$	−9.70486	+	16.8093i	−0.449569	+	0.778676i
$467$	−20.8137	−	36.0503i	−0.963142	−	1.66821i	−0.714526	−	0.699608i	$-0.753358\pi$
$467$	−20.8137	−	36.0503i	−0.963142	−	1.66821i	−0.248615	−	0.968602i	$-0.579976\pi$
$468$		0			0
$469$	−14.0983	−	29.1464i	−0.650998	−	1.34585i
$470$	−3.49635			−0.161274
$471$		0			0
$472$	−8.83053	+	15.2949i	−0.406458	+	0.704006i
$473$	7.81501	−	13.5360i	0.359335	−	0.622386i
$474$		0			0
$475$	12.5815			0.577280
$476$	2.16099	+	0.158187i	0.0990486	+	0.00725050i
$477$		0			0
$478$	−6.80560	−	11.7876i	−0.311281	−	0.539154i
$479$	1.15789	−	2.00553i	0.0529055	−	0.0916350i	−0.838360	−	0.545117i	$-0.816485\pi$
$479$	1.15789	−	2.00553i	0.0529055	−	0.0916350i	0.891265	+	0.453482i	$0.149818\pi$
$480$		0			0
$481$	0.446494	+	0.773350i	0.0203584	+	0.0352617i
$482$	19.0532			0.867851
$483$		0			0
$484$	0.269022			0.0122283
$485$	8.20888	+	14.2182i	0.372746	+	0.645615i
$486$		0			0
$487$	−9.06396	+	15.6992i	−0.410727	+	0.711401i	−0.994969	−	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
$490$	−13.6655	−	2.01144i	−0.617344	−	0.0908677i
$491$	21.5944			0.974542			0.487271	−	0.873251i	$-0.337992\pi$
$491$	21.5944			0.974542			0.487271	+	0.873251i	$0.337992\pi$
$492$		0			0
$493$	7.81616	−	13.5380i	0.352022	−	0.609720i
$494$	−14.7867	+	25.6114i	−0.665287	+	1.15231i
$495$		0			0
$496$	−16.9382			−0.760549
$497$	20.5304	−	30.2247i	0.920913	−	1.35576i
$498$		0			0
$499$	−13.5827	−	23.5259i	−0.608045	−	1.05316i	−0.991562	−	0.129631i	$-0.958621\pi$
$499$	−13.5827	−	23.5259i	−0.608045	−	1.05316i	0.383518	−	0.923534i	$-0.374713\pi$
$500$	−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
$509$	20.7297	+	35.9049i	0.918829	+	1.59146i	0.801197	+	0.598401i	$0.204197\pi$
$509$	20.7297	+	35.9049i	0.918829	+	1.59146i	0.117632	+	0.993057i	$0.462470\pi$
$510$		0			0
$511$	−13.6682	−	28.2572i	−0.604644	−	1.25002i
$512$	25.2864			1.11751
$513$		0			0
$514$	14.3387	−	24.8354i	0.632455	−	1.09544i
$515$	−15.5207	+	26.8826i	−0.683923	+	1.18459i
$516$		0			0
$517$	−5.68773			−0.250146
$518$	−0.272998	−	0.564387i	−0.0119948	−	0.0247978i
$519$		0			0
$520$	−11.2711	−	19.5221i	−0.494271	−	0.856102i
$521$	−1.65221	+	2.86171i	−0.0723846	+	0.125374i	−0.899946	−	0.436002i	$-0.856394\pi$
$521$	−1.65221	+	2.86171i	−0.0723846	+	0.125374i	0.827561	+	0.561375i	$0.189728\pi$
$522$		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	$0.815998\pi$
$524$	4.54035			0.198346
$525$		0			0
$526$	−28.3839			−1.23760
$527$	5.82992	+	10.0977i	0.253955	+	0.439864i
$528$		0			0
$529$	4.62693	−	8.01408i	0.201171	−	0.348438i
$530$	1.64654	+	2.85189i	0.0715211	+	0.123878i
$531$		0			0
$532$	−2.79550	+	4.11552i	−0.121200	+	0.178430i
$533$	−51.6829			−2.23863
$534$		0			0
$535$	−13.1321	+	22.7454i	−0.567748	+	0.983369i
$536$	−18.5485	+	32.1269i	−0.801173	+	1.38767i
$537$		0			0
$538$	−35.4321			−1.52758
$539$	−22.2305	−	3.27214i	−0.957536	−	0.140941i
$540$		0			0
$541$	11.2397	+	19.4677i	0.483233	+	0.836984i	0.999815	−	0.0192542i	$-0.00612919\pi$
$541$	11.2397	+	19.4677i	0.483233	+	0.836984i	−0.516582	+	0.856238i	$0.672796\pi$
$542$	6.27114	−	10.8619i	0.269369	−	0.466560i
$543$		0			0
$544$	−2.28156	−	3.95178i	−0.0978212	−	0.169431i
$545$	−16.6210			−0.711966
$546$		0			0
$547$	−14.5545			−0.622307			−0.311154	−	0.950360i	$-0.600715\pi$
$547$	−14.5545			−0.622307			−0.311154	+	0.950360i	$0.600715\pi$
$548$	−3.11834	−	5.40112i	−0.133209	−	0.230725i
$549$		0			0
$550$	5.27331	−	9.13365i	0.224855	−	0.389460i
$551$	17.9469	+	31.0849i	0.764564	+	1.32426i
$552$		0			0
$553$	−3.45474	−	0.252892i	−0.146911	−	0.0107541i
$554$	11.0692			0.470286
$555$		0			0
$556$	2.59845	−	4.50065i	0.110199	−	0.190870i
$557$	−7.77331	+	13.4638i	−0.329366	+	0.570478i	−0.982386	−	0.186862i	$-0.940168\pi$
$557$	−7.77331	+	13.4638i	−0.329366	+	0.570478i	0.653021	+	0.757340i	$0.273502\pi$
$558$		0			0
$559$	23.3071			0.985787
$560$	5.50762	+	11.3863i	0.232739	+	0.481158i
$561$		0			0
$562$	−3.94168	−	6.82719i	−0.166270	−	0.287988i
$563$	7.36914	−	12.7637i	0.310572	−	0.537927i	−0.667914	−	0.744238i	$-0.732813\pi$
$563$	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	$0.253379\pi$
$572$	−2.97012	−	5.14440i	−0.124187	−	0.215098i
$573$		0			0
$574$	36.1885	+	2.64905i	1.51048	+	0.110569i
$575$	−9.59019			−0.399939
$576$		0			0
$577$	5.26279	−	9.11542i	0.219093	−	0.379480i	−0.735438	−	0.677592i	$-0.763024\pi$
$577$	5.26279	−	9.11542i	0.219093	−	0.379480i	0.954531	+	0.298112i	$0.0963569\pi$
$578$	−7.94669	+	13.7641i	−0.330539	+	0.572510i
$579$		0			0
$580$	−4.43197			−0.184028
$581$	0.515097	−	0.758321i	0.0213698	−	0.0314605i
$582$		0			0
$583$	2.67853	+	4.63935i	0.110933	+	0.192142i
$584$	−17.9826	+	31.1468i	−0.744126	+	1.28886i
$585$		0			0
$586$	−9.20690	−	15.9468i	−0.380334	−	0.658757i
$587$	−6.20018			−0.255909			−0.127954	−	0.991780i	$-0.540841\pi$
$587$	−6.20018			−0.255909			−0.127954	+	0.991780i	$0.540841\pi$
$588$		0			0
$589$	−26.7725			−1.10314
$590$	5.74801	+	9.95585i	0.236642	+	0.409876i
$591$		0			0
$592$	−0.287048	+	0.497182i	−0.0117976	+	0.0204341i
$593$	−18.7629	−	32.4984i	−0.770502	−	1.33455i	−0.937288	−	0.348555i	$-0.886673\pi$
$593$	−18.7629	−	32.4984i	−0.770502	−	1.33455i	0.166787	−	0.985993i	$-0.446661\pi$
$594$		0			0
$595$	4.89229	−	7.20239i	0.200564	−	0.295269i
$596$	1.24166			0.0508605
$597$		0			0
$598$	11.2711	−	19.5221i	0.460910	−	0.798319i
$599$	17.5460	−	30.3905i	0.716909	−	1.24172i	−0.245309	−	0.969445i	$-0.578889\pi$
$599$	17.5460	−	30.3905i	0.716909	−	1.24172i	0.962218	−	0.272279i	$-0.0877773\pi$
$600$		0			0
$601$	26.2342			1.07012			0.535058	−	0.844815i	$-0.320290\pi$
$601$	26.2342			1.07012			0.535058	+	0.844815i	$0.320290\pi$
$602$	−16.3197	−	1.19463i	−0.665143	−	0.0486894i
$603$		0			0
$604$	3.29233	+	5.70249i	0.133963	+	0.232031i
$605$	0.540512	−	0.936194i	0.0219749	−	0.0380617i
$606$		0			0
$607$	1.10933	+	1.92142i	0.0450263	+	0.0779879i	0.887660	−	0.460499i	$-0.152329\pi$
$607$	1.10933	+	1.92142i	0.0450263	+	0.0779879i	−0.842634	+	0.538487i	$0.818996\pi$
$608$	10.4775			0.424919
$609$		0			0
$610$	−13.5706			−0.549457
$611$	−4.24071	−	7.34512i	−0.171561	−	0.297152i
$612$		0			0
$613$	−7.43312	+	12.8745i	−0.300221	+	0.519998i	−0.976186	−	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
$616$	11.2107	+	23.1768i	0.451694	+	0.933819i
$617$	−23.2046			−0.934181			−0.467091	−	0.884210i	$-0.654698\pi$
$617$	−23.2046			−0.934181			−0.467091	+	0.884210i	$0.654698\pi$
$618$		0			0
$619$	4.15562	−	7.19775i	0.167029	−	0.289302i	−0.770345	−	0.637627i	$-0.779916\pi$
$619$	4.15562	−	7.19775i	0.167029	−	0.289302i	0.937374	+	0.348325i	$0.113249\pi$
$620$	1.65286	−	2.86284i	0.0663805	−	0.114974i
$621$		0			0
$622$	−22.1021			−0.886214
$623$	−45.9301	−	3.36215i	−1.84015	−	0.134701i
$624$		0			0
$625$	2.68802	+	4.65578i	0.107521	+	0.186231i
$626$	−0.127048	+	0.220054i	−0.00507786	+	0.00879511i
$627$		0			0
$628$	1.82363	+	3.15862i	0.0727708	+	0.126043i
$629$	0.395194			0.0157574
$630$		0			0
$631$	−24.5415			−0.976982			−0.488491	−	0.872569i	$-0.662452\pi$
$631$	−24.5415			−0.976982			−0.488491	+	0.872569i	$0.662452\pi$
$632$	1.98448	+	3.43723i	0.0789386	+	0.136726i
$633$		0			0
$634$	5.22947	−	9.05771i	0.207689	−	0.359728i
$635$	−1.51592	−	2.62565i	−0.0601574	−	0.104196i
$636$		0			0
$637$	−12.3492	−	31.1481i	−0.489293	−	1.23413i
$638$	30.0885			1.19121
$639$		0			0
$640$	5.42549	−	9.39723i	0.214461	−	0.371458i
$641$	3.98762	−	6.90677i	0.157502	−	0.272801i	−0.776465	−	0.630160i	$-0.782989\pi$
$641$	3.98762	−	6.90677i	0.157502	−	0.272801i	0.933967	+	0.357359i	$0.116323\pi$
$642$		0			0
$643$	−3.12279			−0.123151			−0.0615755	−	0.998102i	$-0.519612\pi$
$643$	−3.12279			−0.123151			−0.0615755	+	0.998102i	$0.519612\pi$
$644$	2.13086	−	3.13703i	0.0839675	−	0.123616i
$645$		0			0
$646$	6.54391	+	11.3344i	0.257467	+	0.445945i
$647$	−6.13273	+	10.6222i	−0.241102	+	0.417602i	−0.961029	−	0.276449i	$-0.910842\pi$
$647$	−6.13273	+	10.6222i	−0.241102	+	0.417602i	0.719926	+	0.694051i	$0.244176\pi$
$648$		0			0
$649$	9.35065	+	16.1958i	0.367045	+	0.635741i
$650$	15.7269			0.616860
$651$		0			0
$652$	−1.42171			−0.0556786
$653$	8.25476	+	14.2977i	0.323034	+	0.559511i	0.981112	−	0.193438i	$-0.0619640\pi$
$653$	8.25476	+	14.2977i	0.323034	+	0.559511i	−0.658079	+	0.752949i	$0.728631\pi$
$654$		0			0
$655$	9.12235	−	15.8004i	0.356440	−	0.617372i
$656$	−16.6133	−	28.7751i	−0.648641	−	1.12348i
$657$		0			0
$658$	2.59288	+	5.36044i	0.101081	+	0.208972i
$659$	−10.7388			−0.418324			−0.209162	−	0.977881i	$-0.567074\pi$
$659$	−10.7388			−0.418324			−0.209162	+	0.977881i	$0.567074\pi$
$660$		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
$664$	−1.05036			−0.0407619
$665$	8.70532	+	17.9971i	0.337578	+	0.697898i
$666$		0			0
$667$	−13.6799	−	23.6943i	−0.529689	−	0.917448i
$668$	0.311247	−	0.539095i	0.0120425	−	0.0208582i
$669$		0			0
$670$	12.0737	+	20.9122i	0.466447	+	0.807909i
$671$	−22.0761			−0.852240
$672$		0			0
$673$	40.8986			1.57653			0.788264	−	0.615338i	$-0.210980\pi$
$673$	40.8986			1.57653			0.788264	+	0.615338i	$0.210980\pi$
$674$	10.1041	+	17.5008i	0.389195	+	0.674105i
$675$		0			0
$676$	1.91607	−	3.31874i	0.0736951	−	0.127644i
$677$	−10.6250	−	18.4031i	−0.408353	−	0.707288i	0.586353	−	0.810056i	$-0.300563\pi$
$677$	−10.6250	−	18.4031i	−0.408353	−	0.707288i	−0.994705	+	0.102768i	$0.967230\pi$
$678$		0			0
$679$	15.7110	−	23.1296i	0.602933	−	0.887634i
$680$	−9.97612			−0.382567
$681$		0			0
$682$	−11.2212	+	19.4357i	−0.429682	+	0.744231i
$683$	20.6708	−	35.8029i	0.790948	−	1.36996i	−0.134433	−	0.990923i	$-0.542921\pi$
$683$	20.6708	−	35.8029i	0.790948	−	1.36996i	0.925381	−	0.379039i	$-0.123745\pi$
$684$		0			0
$685$	−25.0612			−0.957537
$686$	7.05042	+	22.4430i	0.269186	+	0.856877i
$687$		0			0
$688$	7.49202	+	12.9766i	0.285631	+	0.494727i
$689$	−3.99417	+	6.91810i	−0.152166	+	0.263559i
$690$		0			0
$691$	0.760183	+	1.31668i	0.0289187	+	0.0500887i	0.880123	−	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
$698$	1.02858	+	1.78154i	0.0389321	+	0.0674325i
$699$		0			0
$700$	2.63869	+	0.193156i	0.0997331	+	0.00730060i
$701$	32.5344			1.22881			0.614404	−	0.788991i	$-0.289396\pi$
$701$	32.5344			1.22881			0.614404	+	0.788991i	$0.289396\pi$
$702$		0			0
$703$	−0.453708	+	0.785845i	−0.0171119	+	0.0296387i
$704$	14.2697	−	24.7159i	0.537811	−	0.931515i
$705$		0			0
$706$	−41.2963			−1.55421
$707$	2.34323	+	4.84433i	0.0881264	+	0.182190i
$708$		0			0
$709$	−11.2810	−	19.5394i	−0.423669	−	0.733816i	0.572626	−	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
$713$	20.4072			0.764255
$714$		0			0
$715$	−23.8700			−0.892686
$716$	3.36466	+	5.82777i	0.125743	+	0.217794i
$717$		0			0
$718$	7.10787	−	12.3112i	0.265263	−	0.459450i
$719$	−3.25084	−	5.63062i	−0.121236	−	0.209987i	0.799019	−	0.601305i	$-0.205352\pi$
$719$	−3.25084	−	5.63062i	−0.121236	−	0.209987i	−0.920255	+	0.391319i	$0.872019\pi$
$720$		0			0
$721$	52.7253	+	3.85956i	1.96359	+	0.143738i
$722$	−5.91755			−0.220228
$723$		0			0
$724$	1.71958	−	2.97841i	0.0639078	−	0.110692i
$725$	9.54400	−	16.5307i	0.354455	−	0.613934i
$726$		0			0
$727$	−7.83215			−0.290478			−0.145239	−	0.989397i	$-0.546395\pi$
$727$	−7.83215			−0.290478			−0.145239	+	0.989397i	$0.546395\pi$
$728$	−21.5718	+	31.7579i	−0.799505	+	1.17703i
$729$		0			0
$730$	11.7053	+	20.2742i	0.433234	+	0.750383i
$731$	5.15732	−	8.93274i	0.190750	−	0.330389i
$732$		0			0
$733$	3.74780	+	6.49138i	0.138428	+	0.239764i	0.926902	−	0.375304i	$-0.122462\pi$
$733$	3.74780	+	6.49138i	0.138428	+	0.239764i	−0.788474	+	0.615068i	$0.789128\pi$
$734$	6.58823			0.243176
$735$		0			0
$736$	−7.98643			−0.294384
$737$	19.6410	+	34.0192i	0.723486	+	1.25311i
$738$		0			0
$739$	−12.0480	+	20.8678i	−0.443194	+	0.767634i	−0.997924	−	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
$742$	3.15132	−	4.63935i	0.115689	−	0.170316i
$743$	−19.2882			−0.707616			−0.353808	−	0.935318i	$-0.615113\pi$
$743$	−19.2882			−0.707616			−0.353808	+	0.935318i	$0.615113\pi$
$744$		0			0
$745$	2.49472	−	4.32098i	0.0913994	−	0.158308i
$746$	20.8721	−	36.1515i	0.764181	−	1.32360i
$747$		0			0
$748$	−2.62887			−0.0961210
$749$	44.6109	+	3.26558i	1.63005	+	0.119322i
$750$		0			0
$751$	16.6045	+	28.7598i	0.605906	+	1.04946i	0.991908	+	0.126961i	$0.0405225\pi$
$751$	16.6045	+	28.7598i	0.605906	+	1.04946i	−0.386002	+	0.922498i	$0.626144\pi$
$752$	2.72633	−	4.72214i	0.0994190	−	0.172199i
$753$		0			0
$754$	22.4336	+	38.8562i	0.816985	+	1.41506i
$755$	26.4595			0.962959
$756$		0			0
$757$	9.70935			0.352892			0.176446	−	0.984310i	$-0.443540\pi$
$757$	9.70935			0.352892			0.176446	+	0.984310i	$0.443540\pi$
$758$	8.85088	+	15.3302i	0.321478	+	0.556817i
$759$		0			0
$760$	11.4532	−	19.8375i	0.415452	−	0.719583i
$761$	1.36305	+	2.36086i	0.0494104	+	0.0855813i	0.889673	−	0.456599i	$-0.150932\pi$
$761$	1.36305	+	2.36086i	0.0494104	+	0.0855813i	−0.840262	+	0.542180i	$0.817599\pi$
$762$		0			0
$763$	12.3261	+	25.4826i	0.446234	+	0.922532i
$764$	5.71868			0.206894
$765$		0			0
$766$	−1.08932	+	1.88676i	−0.0393588	+	0.0681714i
$767$	−13.9435	+	24.1508i	−0.503470	+	0.872036i
$768$		0			0
$769$	50.0460			1.80470			0.902352	−	0.430999i	$-0.141839\pi$
$769$	50.0460			1.80470			0.902352	+	0.430999i	$0.141839\pi$
$770$	16.7138	+	1.22347i	0.602324	+	0.0440910i
$771$		0			0
$772$	0.352112	+	0.609877i	0.0126728	+	0.0219499i
$773$	9.52030	−	16.4896i	0.342421	−	0.593091i	−0.642461	−	0.766319i	$-0.722086\pi$
$773$	9.52030	−	16.4896i	0.342421	−	0.593091i	0.984882	+	0.173228i	$0.0554197\pi$
$774$		0			0
$775$	7.11868	+	12.3299i	0.255711	+	0.442904i
$776$	−32.0372			−1.15007
$777$		0			0
$778$	3.99928			0.143381
$779$	−26.2589	−	45.4818i	−0.940824	−	1.62956i
$780$		0			0
$781$	−22.1652	+	38.3912i	−0.793133	+	1.37375i
$782$	−4.98806	−	8.63957i	−0.178373	−	0.308950i
$783$		0			0
$784$	13.3725	−	16.8881i	0.477590	−	0.603145i
$785$	14.6560			0.523094
$786$		0			0
$787$	16.6011	−	28.7540i	0.591766	−	1.02497i	−0.402228	−	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
$790$	2.58350			0.0919168
$791$	−12.7622	+	18.7885i	−0.453773	+	0.668041i
$792$		0			0
$793$	−16.4597	−	28.5091i	−0.584502	−	1.01239i
$794$	17.4236	−	30.1785i	0.618340	−	1.07100i
$795$		0			0
$796$	0.427834	+	0.741030i	0.0151642	+	0.0262651i
$797$	−2.08944			−0.0740118			−0.0370059	−	0.999315i	$-0.511782\pi$
$797$	−2.08944			−0.0740118			−0.0370059	+	0.999315i	$0.511782\pi$
$798$		0			0
$799$	−3.75347			−0.132788
$800$	−2.78592	−	4.82536i	−0.0984972	−	0.170602i
$801$		0			0
$802$	18.4414	−	31.9414i	0.651187	−	1.12789i
$803$	19.0418	+	32.9814i	0.671970	+	1.16389i
$804$		0			0
$805$	−6.63558	−	13.7182i	−0.233873	−	0.483503i
$806$	−33.4656			−1.17878
$807$		0			0
$808$	3.08289	−	5.33973i	0.108456	−	0.187851i
$809$	0.241404	−	0.418125i	0.00848732	−	0.0147005i	−0.861751	−	0.507332i	$-0.830632\pi$
$809$	0.241404	−	0.418125i	0.00848732	−	0.0147005i	0.870238	+	0.492632i	$0.163965\pi$
$810$		0			0
$811$	17.1671			0.602820			0.301410	−	0.953495i	$-0.402543\pi$
$811$	17.1671			0.602820			0.301410	+	0.953495i	$0.402543\pi$
$812$	3.28673	+	6.79490i	0.115342	+	0.238454i
$813$		0			0
$814$	0.380327	+	0.658745i	0.0133304	+	0.0230890i
$815$	−2.85647	+	4.94755i	−0.100058	+	0.173305i
$816$		0			0
$817$	11.8419	+	20.5107i	0.414294	+	0.717578i
$818$	35.2226			1.23153
$819$		0			0
$820$	6.48462			0.226453
$821$	−6.41086	−	11.1039i	−0.223741	−	0.387530i	0.732200	−	0.681089i	$-0.238493\pi$
$821$	−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	$0.307679\pi$
$824$	−30.2866	−	52.4580i	−1.05509	−	1.82746i
$825$		0			0
$826$	11.0011	−	16.1958i	0.382779	−	0.563524i
$827$	−0.527165			−0.0183313			−0.00916567	−	0.999958i	$-0.502918\pi$
$827$	−0.527165			−0.0183313			−0.00916567	+	0.999958i	$0.502918\pi$
$828$		0			0
$829$	23.1015	−	40.0130i	0.802348	−	1.38971i	−0.115718	−	0.993282i	$-0.536917\pi$
$829$	23.1015	−	40.0130i	0.802348	−	1.38971i	0.918067	−	0.396426i	$-0.129750\pi$
$830$	−0.341853	+	0.592106i	−0.0118659	+	0.0205523i
$831$		0			0
$832$	42.5574			1.47541
$833$	−14.6705	−	2.15937i	−0.508302	−	0.0748177i
$834$		0			0
$835$	−1.25070	−	2.16627i	−0.0432822	−	0.0749669i
$836$	3.01811	−	5.22752i	0.104383	−	0.180797i
$837$		0			0
$838$	19.2815	+	33.3965i	0.666067	+	1.15366i
$839$	10.8258			0.373747			0.186874	−	0.982384i	$-0.440165\pi$
$839$	10.8258			0.373747			0.186874	+	0.982384i	$0.440165\pi$
$840$		0			0
$841$	25.4561			0.877797
$842$	−17.6389	−	30.5515i	−0.607877	−	1.05287i
$843$		0			0
$844$	−0.350540	+	0.607152i	−0.0120661	+	0.0208990i
$845$	−7.69945	−	13.3358i	−0.264869	−	0.458767i
$846$		0			0
$847$	−1.83617	−	0.134410i	−0.0630916	−	0.00461839i
$848$	−5.13566			−0.176359
$849$		0			0
$850$	3.47999	−	6.02752i	0.119363	−	0.206742i
$851$	0.345836	−	0.599006i	0.0118551	−	0.0205337i
$852$		0			0
$853$	−43.1922			−1.47887			−0.739437	−	0.673226i	$-0.764908\pi$
$853$	−43.1922			−1.47887			−0.739437	+	0.673226i	$0.764908\pi$
$854$	10.0639	+	20.8058i	0.344380	+	0.711961i
$855$		0			0
$856$	−25.6255	−	44.3847i	−0.875863	−	1.51704i
$857$	0.787226	−	1.36352i	0.0268911	−	0.0465768i	−0.852267	−	0.523108i	$-0.824773\pi$
$857$	0.787226	−	1.36352i	0.0268911	−	0.0465768i	0.879158	+	0.476531i	$0.158106\pi$
$858$		0			0
$859$	−3.41090	−	5.90786i	−0.116378	−	0.201573i	0.801951	−	0.597389i	$-0.203795\pi$
$859$	−3.41090	−	5.90786i	−0.116378	−	0.201573i	−0.918330	+	0.395816i	$0.870462\pi$
$860$	−2.92434			−0.0997190
$861$		0			0
$862$	9.22073			0.314059
$863$	4.51387	+	7.81825i	0.153654	+	0.266136i	0.932568	−	0.360994i	$-0.117563\pi$
$863$	4.51387	+	7.81825i	0.153654	+	0.266136i	−0.778914	+	0.627131i	$0.784229\pi$
$864$		0			0
$865$	−12.5711	+	21.7738i	−0.427430	+	0.740331i
$866$	9.55032	+	16.5416i	0.324533	+	0.562108i
$867$		0			0
$868$	−5.61493	−	0.411021i	−0.190583	−	0.0139509i
$869$	4.20274			0.142568
$870$		0			0
$871$	−29.2882	+	50.7287i	−0.992394	+	1.71888i
$872$	16.2169	−	28.0885i	0.549174	−	0.951196i
$873$		0			0
$874$	22.9064			0.774821
$875$	17.5211	−	25.7944i	0.592321	−	0.872011i
$876$		0			0
$877$	−4.83460	−	8.37377i	−0.163253	−	0.282762i	0.772781	−	0.634673i	$-0.218865\pi$
$877$	−4.83460	−	8.37377i	−0.163253	−	0.282762i	−0.936033	+	0.351911i	$0.885532\pi$
$878$	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
$887$	20.7612	+	35.9594i	0.697091	+	1.20740i	0.969471	+	0.245208i	$0.0788562\pi$
$887$	20.7612	+	35.9594i	0.697091	+	1.20740i	−0.272379	+	0.962190i	$0.587810\pi$
$888$		0			0
$889$	−2.90133	+	4.27131i	−0.0973074	+	0.143255i
$890$	34.3471			1.15132
$891$		0			0
$892$	1.83755	−	3.18272i	0.0615256	−	0.106565i
$893$	4.30922	−	7.46380i	0.144203	−	0.249766i
$894$		0			0
$895$	27.0408			0.903873
$896$	−18.4309	−	1.34917i	−0.615734	−	0.0450726i
$897$		0			0
$898$	−16.8001	−	29.0986i	−0.560626	−	0.971032i
$899$	−20.3089	+	35.1760i	−0.677339	+	1.17319i
$900$		0			0
$901$	1.76763	+	3.06162i	0.0588883	+	0.101997i
$902$	−44.0238			−1.46583
$903$		0			0
$904$	26.0241			0.865550
$905$	−6.90989	−	11.9683i	−0.229692	−	0.397839i
$906$		0			0
$907$	2.32180	−	4.02148i	0.0770942	−	0.133531i	−0.824901	−	0.565277i	$-0.808769\pi$
$907$	2.32180	−	4.02148i	0.0770942	−	0.133531i	0.901995	+	0.431746i	$0.142102\pi$
$908$	2.09401	+	3.62693i	0.0694921	+	0.120364i
$909$		0			0
$910$	10.8817	+	22.4964i	0.360723	+	0.745749i
$911$	1.34811			0.0446648			0.0223324	−	0.999751i	$-0.492891\pi$
$911$	1.34811			0.0446648			0.0223324	+	0.999751i	$0.492891\pi$
$912$		0			0
$913$	−0.556114	+	0.963217i	−0.0184047	+	0.0318778i
$914$	−4.12408	+	7.14312i	−0.136413	+	0.236273i
$915$		0			0
$916$	−4.84011			−0.159922
$917$	−30.9895	−	2.26848i	−1.02336	−	0.0749116i
$918$		0			0
$919$	20.2472	+	35.0692i	0.667893	+	1.15682i	0.978492	+	0.206284i	$0.0661370\pi$
$919$	20.2472	+	35.0692i	0.667893	+	1.15682i	−0.310599	+	0.950541i	$0.600530\pi$
$920$	−8.73015	+	15.1211i	−0.287824	+	0.498527i
$921$		0			0
$922$	−9.90223	−	17.1512i	−0.326112	−	0.564843i
$923$	−66.1045			−2.17586
$924$		0			0
$925$	0.482555			0.0158663
$926$	4.86221	+	8.42160i	0.159782	+	0.276751i
$927$		0			0
$928$	7.94795	−	13.7663i	0.260904	−	0.451900i
$929$	11.1569	+	19.3243i	0.366046	+	0.634011i	0.988944	−	0.148293i	$-0.0473778\pi$
$929$	11.1569	+	19.3243i	0.366046	+	0.634011i	−0.622897	+	0.782304i	$0.714044\pi$
$930$		0			0
$931$	21.1365	−	26.6932i	0.692722	−	0.874834i
$932$	5.90760			0.193510
$933$		0			0
$934$	26.4375	−	45.7910i	0.865060	−	1.49833i
$935$	−5.28186	+	9.14844i	−0.172735	+	0.299186i
$936$		0			0
$937$	−1.13943			−0.0372235			−0.0186117	−	0.999827i	$-0.505925\pi$
$937$	−1.13943			−0.0372235			−0.0186117	+	0.999827i	$0.505925\pi$
$938$	23.1079	−	34.0192i	0.754498	−	1.11077i
$939$		0			0
$940$	0.532080	+	0.921589i	0.0173545	+	0.0300589i
$941$	23.5938	−	40.8656i	0.769134	−	1.33218i	−0.168898	−	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
$950$	7.99050	+	13.8400i	0.259246	+	0.449027i
$951$		0			0
$952$	7.39825	+	15.2949i	0.239779	+	0.495711i
$953$	56.2821			1.82316			0.911579	−	0.411125i	$-0.134864\pi$
$953$	56.2821			1.82316			0.911579	+	0.411125i	$0.134864\pi$
$954$		0			0
$955$	11.4898	−	19.9009i	0.371802	−	0.643979i
$956$	−2.07137	+	3.58772i	−0.0669930	+	0.116035i
$957$		0			0
$958$	2.94150			0.0950356
$959$	18.5853	+	38.4226i	0.600149	+	1.24073i
$960$		0			0
$961$	0.352001	+	0.609683i	0.0113549	+	0.0196672i
$962$	−0.567135	+	0.982306i	−0.0182852	+	0.0316708i
$963$		0			0
$964$	−2.89955	−	5.02217i	−0.0933883	−	0.161753i
$965$	2.82982			0.0910951
$966$		0			0
$967$	−58.5977			−1.88438			−0.942188	−	0.335084i	$-0.891235\pi$
$967$	−58.5977			−1.88438			−0.942188	+	0.335084i	$0.891235\pi$
$968$	1.05474	+	1.82686i	0.0339006	+	0.0587176i
$969$		0			0
$970$	−10.4269	+	18.0599i	−0.334787	+	0.579868i
$971$	−3.04991	−	5.28260i	−0.0978763	−	0.169527i	0.812929	−	0.582363i	$-0.197872\pi$
$971$	−3.04991	−	5.28260i	−0.0978763	−	0.169527i	−0.910805	+	0.412836i	$0.864538\pi$
$972$		0			0
$973$	−19.9840	+	29.4203i	−0.640657	+	0.943171i
$974$	−23.0260			−0.737801
$975$		0			0
$976$	10.5819	−	18.3283i	0.338718	−	0.586676i
$977$	−2.57988	+	4.46849i	−0.0825377	+	0.142960i	−0.904339	−	0.426814i	$-0.859636\pi$
$977$	−2.57988	+	4.46849i	−0.0825377	+	0.142960i	0.821802	+	0.569774i	$0.192969\pi$
$978$		0			0
$979$	55.8746			1.78576
$980$	1.54945	+	3.90814i	0.0494953	+	0.124841i
$981$		0			0
$982$	13.7146	+	23.7543i	0.437649	+	0.758031i
$983$	31.0536	−	53.7864i	0.990455	−	1.71552i	0.375857	−	0.926678i	$-0.377348\pi$
$983$	31.0536	−	53.7864i	0.990455	−	1.71552i	0.614598	−	0.788841i	$-0.289318\pi$
$984$		0			0
$985$	5.99626	+	10.3858i	0.191057	+	0.330920i
$986$	19.8561			0.632348
$987$		0			0
$988$	9.00108			0.286362
$989$	−9.02639	−	15.6342i	−0.287022	−	0.497138i
$990$		0			0
$991$	10.8163	−	18.7343i	0.343590	−	0.595116i	−0.641506	−	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
$994$	46.2866	+	3.38824i	1.46812	+	0.107469i
$995$	3.43837			0.109004
$996$		0			0
$997$	20.3681	−	35.2786i	0.645064	−	1.11728i	−0.339223	−	0.940706i	$-0.610164\pi$
$997$	20.3681	−	35.2786i	0.645064	−	1.11728i	0.984287	−	0.176578i	$-0.0565027\pi$
$998$	17.2527	−	29.8825i	0.546124	−	0.945915i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.g.163.3	✓	16	21.2	odd	6	inner
567.2.e.g.163.6	yes	16	7.2	even	3	inner
567.2.e.g.487.3	yes	16	3.2	odd	2	inner
567.2.e.g.487.6	yes	16	1.1	even	1	trivial
567.2.g.l.109.3		16	9.2	odd	6
567.2.g.l.109.6		16	9.7	even	3
567.2.g.l.541.3		16	63.23	odd	6
567.2.g.l.541.6		16	63.58	even	3
567.2.h.l.298.3		16	9.4	even	3
567.2.h.l.298.6		16	9.5	odd	6
567.2.h.l.352.3		16	63.16	even	3
567.2.h.l.352.6		16	63.2	odd	6
3969.2.a.bf.1.3		8	7.3	odd	6
3969.2.a.bf.1.6		8	21.17	even	6
3969.2.a.bg.1.3		8	7.4	even	3
3969.2.a.bg.1.6		8	21.11	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.e (of order \(3\), degree \(2\), minimal)

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

Introduction

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