LMFDB - Embedded newform 567.2.g.j.541.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(109,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

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

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

Newform invariants

comment:select newform

sage:traces = [8,-1,0,-5,4,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1767277521.3
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + x^{6} - 10x^{5} + 38x^{4} - 40x^{3} + 64x^{2} - 38x + 7 $ x^8 - 2x^7 + x^6 - 10x^5 + 38x^4 - 40x^3 + 64x^2 - 38x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.3
Root			$2.11692 + 0.978886i$ of defining polynomial
Character	$\chi$	$=$	567.541
Dual form			567.2.g.j.109.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.186423 + 0.322894i) q^{2} +(0.930493 - 1.61166i) q^{4} +1.42143 q^{5} +(-1.03335 + 2.43561i) q^{7} +1.43955 q^{8} +(0.264988 + 0.458972i) q^{10} +3.76381 q^{11} +(-0.930493 - 1.61166i) q^{13} +(-0.979083 + 0.120389i) q^{14} +(-1.59262 - 2.75850i) q^{16} +(3.76718 + 6.52496i) q^{17} +(0.837872 - 1.45124i) q^{19} +(1.32264 - 2.29087i) q^{20} +(0.701659 + 1.21531i) q^{22} -0.511859 q^{23} -2.97952 q^{25} +(0.346930 - 0.600901i) q^{26} +(2.96385 + 3.93173i) q^{28} +(4.36099 - 7.55345i) q^{29} +(1.46665 - 2.54031i) q^{31} +(2.03335 - 3.52187i) q^{32} +(-1.40458 + 2.43280i) q^{34} +(-1.46884 + 3.46206i) q^{35} +(-2.16551 + 3.75077i) q^{37} +0.624794 q^{38} +2.04623 q^{40} +(-3.42025 - 5.92405i) q^{41} +(2.26837 - 3.92892i) q^{43} +(3.50220 - 6.06598i) q^{44} +(-0.0954222 - 0.165276i) q^{46} +(3.71978 + 6.44284i) q^{47} +(-4.86436 - 5.03368i) q^{49} +(-0.555451 - 0.962069i) q^{50} -3.46327 q^{52} +(0.416437 + 0.721290i) q^{53} +5.35001 q^{55} +(-1.48756 + 3.50618i) q^{56} +3.25195 q^{58} +(-6.51126 + 11.2778i) q^{59} +(5.15189 + 8.92333i) q^{61} +1.09367 q^{62} -4.85423 q^{64} +(-1.32264 - 2.29087i) q^{65} +(-3.25813 + 5.64324i) q^{67} +14.0214 q^{68} +(-1.39170 + 0.171126i) q^{70} -4.11854 q^{71} +(-2.84737 - 4.93179i) q^{73} -1.61480 q^{74} +(-1.55927 - 2.70073i) q^{76} +(-3.88934 + 9.16716i) q^{77} +(-0.132152 - 0.228895i) q^{79} +(-2.26381 - 3.92103i) q^{80} +(1.27523 - 2.20876i) q^{82} +(-3.95023 + 6.84200i) q^{83} +(5.35481 + 9.27480i) q^{85} +1.69150 q^{86} +5.41819 q^{88} +(0.398321 - 0.689912i) q^{89} +(4.88690 - 0.600901i) q^{91} +(-0.476282 + 0.824944i) q^{92} +(-1.38690 + 2.40218i) q^{94} +(1.19098 - 2.06284i) q^{95} +(6.43999 - 11.1544i) q^{97} +(0.718516 - 2.50907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8} + 7 q^{10} + 10 q^{11} + 5 q^{13} + 7 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + 8 q^{20} + 7 q^{22} - 24 q^{23} + 16 q^{25} - q^{26} + 5 q^{28} + 10 q^{29}+ \cdots + 11 q^{98}+O(q^{100}) $ 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8 + 7 * q^10 + 10 * q^11 + 5 * q^13 + 7 * q^14 + q^16 - 6 * q^17 + 8 * q^19 + 8 * q^20 + 7 * q^22 - 24 * q^23 + 16 * q^25 - q^26 + 5 * q^28 + 10 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 - 40 * q^38 - 36 * q^40 + 5 * q^41 + 7 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 2 * q^49 - 38 * q^50 - 50 * q^52 + 12 * q^53 - 52 * q^55 - 33 * q^56 - 14 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 + 102 * q^68 - 46 * q^70 - 18 * q^71 + 6 * q^73 - 5 * q^76 - 16 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 - 9 * q^83 + 9 * q^85 - 44 * q^86 + 36 * q^88 + 22 * q^89 + 13 * q^91 + 36 * q^92 + 15 * q^94 + 16 * q^95 + 9 * q^97 + 11 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.186423	+	0.322894i	0.131821	+	0.228320i	0.924378	−	0.381477i	$-0.124584\pi$
$2$	0.186423	+	0.322894i	0.131821	+	0.228320i	−0.792558	+	0.609797i	$0.791251\pi$
$3$		0			0
$3$		0			0
$4$	0.930493	−	1.61166i	0.465247	−	0.805831i
$5$	1.42143			0.635685			0.317843	−	0.948144i	$-0.397042\pi$
$5$	1.42143			0.635685			0.317843	+	0.948144i	$0.397042\pi$
$6$		0			0
$7$	−1.03335	+	2.43561i	−0.390571	+	0.920573i
$7$	−1.03335	+	2.43561i	−0.390571	+	0.920573i
$8$	1.43955			0.508958
$9$		0			0
$10$	0.264988	+	0.458972i	0.0837965	+	0.145140i
$11$	3.76381			1.13483			0.567415	−	0.823432i	$-0.307943\pi$
$11$	3.76381			1.13483			0.567415	+	0.823432i	$0.307943\pi$
$12$		0			0
$13$	−0.930493	−	1.61166i	−0.258072	−	0.446994i	0.707653	−	0.706560i	$-0.249754\pi$
$13$	−0.930493	−	1.61166i	−0.258072	−	0.446994i	−0.965725	+	0.259566i	$0.916421\pi$
$14$	−0.979083	+	0.120389i	−0.261671	+	0.0321754i
$15$		0			0
$16$	−1.59262	−	2.75850i	−0.398155	−	0.689625i
$17$	3.76718	+	6.52496i	0.913676	+	1.58253i	0.808828	+	0.588046i	$0.200103\pi$
$17$	3.76718	+	6.52496i	0.913676	+	1.58253i	0.104849	+	0.994488i	$0.466564\pi$
$18$		0			0
$19$	0.837872	−	1.45124i	0.192221	−	0.332937i	−0.753765	−	0.657144i	$-0.771764\pi$
$19$	0.837872	−	1.45124i	0.192221	−	0.332937i	0.945986	+	0.324208i	$0.105098\pi$
$20$	1.32264	−	2.29087i	0.295750	−	0.512255i
$21$		0			0
$22$	0.701659	+	1.21531i	0.149594	+	0.259105i
$23$	−0.511859			−0.106730			−0.0533650	−	0.998575i	$-0.516995\pi$
$23$	−0.511859			−0.106730			−0.0533650	+	0.998575i	$0.516995\pi$
$24$		0			0
$25$	−2.97952			−0.595905
$26$	0.346930	−	0.600901i	0.0680386	−	0.117846i
$27$		0			0
$28$	2.96385	+	3.93173i	0.560114	+	0.743027i
$29$	4.36099	−	7.55345i	0.809815	−	1.40264i	−0.103177	−	0.994663i	$-0.532901\pi$
$29$	4.36099	−	7.55345i	0.809815	−	1.40264i	0.912992	−	0.407977i	$-0.133766\pi$
$30$		0			0
$31$	1.46665	−	2.54031i	0.263418	−	0.456253i	−0.703730	−	0.710467i	$-0.748484\pi$
$31$	1.46665	−	2.54031i	0.263418	−	0.456253i	0.967148	+	0.254215i	$0.0818170\pi$
$32$	2.03335	−	3.52187i	0.359449	−	0.622585i
$33$		0			0
$34$	−1.40458	+	2.43280i	−0.240883	+	0.417222i
$35$	−1.46884	+	3.46206i	−0.248280	+	0.585194i
$36$		0			0
$37$	−2.16551	+	3.75077i	−0.356007	+	0.616622i	−0.987290	−	0.158931i	$-0.949195\pi$
$37$	−2.16551	+	3.75077i	−0.356007	+	0.616622i	0.631283	+	0.775553i	$0.282529\pi$
$38$	0.624794			0.101355
$39$		0			0
$40$	2.04623			0.323537
$41$	−3.42025	−	5.92405i	−0.534154	−	0.925182i	−0.999204	−	0.0398973i	$-0.987297\pi$
$41$	−3.42025	−	5.92405i	−0.534154	−	0.925182i	0.465050	−	0.885285i	$-0.346036\pi$
$42$		0			0
$43$	2.26837	−	3.92892i	0.345922	−	0.599155i	−0.639598	−	0.768709i	$-0.720899\pi$
$43$	2.26837	−	3.92892i	0.345922	−	0.599155i	0.985521	+	0.169554i	$0.0542327\pi$
$44$	3.50220	−	6.06598i	0.527976	−	0.914481i
$45$		0			0
$46$	−0.0954222	−	0.165276i	−0.0140692	−	0.0243686i
$47$	3.71978	+	6.44284i	0.542585	+	0.939785i	0.998755	+	0.0498920i	$0.0158877\pi$
$47$	3.71978	+	6.44284i	0.542585	+	0.939785i	−0.456170	+	0.889893i	$0.650779\pi$
$48$		0			0
$49$	−4.86436	−	5.03368i	−0.694909	−	0.719098i
$50$	−0.555451	−	0.962069i	−0.0785526	−	0.136057i
$51$		0			0
$52$	−3.46327			−0.480269
$53$	0.416437	+	0.721290i	0.0572020	+	0.0990768i	0.893208	−	0.449643i	$-0.148449\pi$
$53$	0.416437	+	0.721290i	0.0572020	+	0.0990768i	−0.836006	+	0.548720i	$0.815115\pi$
$54$		0			0
$55$	5.35001			0.721395
$56$	−1.48756	+	3.50618i	−0.198784	+	0.468533i
$57$		0			0
$58$	3.25195			0.427002
$59$	−6.51126	+	11.2778i	−0.847693	+	1.46825i	0.0355684	+	0.999367i	$0.488676\pi$
$59$	−6.51126	+	11.2778i	−0.847693	+	1.46825i	−0.883262	+	0.468880i	$0.844658\pi$
$60$		0			0
$61$	5.15189	+	8.92333i	0.659632	+	1.14252i	0.980711	+	0.195463i	$0.0626211\pi$
$61$	5.15189	+	8.92333i	0.659632	+	1.14252i	−0.321079	+	0.947052i	$0.604046\pi$
$62$	1.09367			0.138896
$63$		0			0
$64$	−4.85423			−0.606779
$65$	−1.32264	−	2.29087i	−0.164053	−	0.284148i
$66$		0			0
$67$	−3.25813	+	5.64324i	−0.398043	+	0.689432i	−0.993484	−	0.113967i	$-0.963644\pi$
$67$	−3.25813	+	5.64324i	−0.398043	+	0.689432i	0.595441	+	0.803399i	$0.296977\pi$
$68$	14.0214			1.70034
$69$		0			0
$70$	−1.39170	+	0.171126i	−0.166340	+	0.0204534i
$71$	−4.11854			−0.488780			−0.244390	−	0.969677i	$-0.578588\pi$
$71$	−4.11854			−0.488780			−0.244390	+	0.969677i	$0.578588\pi$
$72$		0			0
$73$	−2.84737	−	4.93179i	−0.333259	−	0.577222i	0.649889	−	0.760029i	$-0.274815\pi$
$73$	−2.84737	−	4.93179i	−0.333259	−	0.577222i	−0.983149	+	0.182806i	$0.941482\pi$
$74$	−1.61480			−0.187716
$75$		0			0
$76$	−1.55927	−	2.70073i	−0.178860	−	0.309795i
$77$	−3.88934	+	9.16716i	−0.443232	+	1.04469i
$78$		0			0
$79$	−0.132152	−	0.228895i	−0.0148683	−	0.0257527i	0.858496	−	0.512821i	$-0.171400\pi$
$79$	−0.132152	−	0.228895i	−0.0148683	−	0.0257527i	−0.873364	+	0.487068i	$0.838066\pi$
$80$	−2.26381	−	3.92103i	−0.253101	−	0.438384i
$81$		0			0
$82$	1.27523	−	2.20876i	0.140825	−	0.243916i
$83$	−3.95023	+	6.84200i	−0.433594	+	0.751007i	−0.997180	−	0.0750507i	$-0.976088\pi$
$83$	−3.95023	+	6.84200i	−0.433594	+	0.751007i	0.563586	+	0.826058i	$0.309421\pi$
$84$		0			0
$85$	5.35481	+	9.27480i	0.580810	+	1.00599i
$86$	1.69150			0.182399
$87$		0			0
$88$	5.41819			0.577581
$89$	0.398321	−	0.689912i	0.0422219	−	0.0731305i	−0.844142	−	0.536119i	$-0.819890\pi$
$89$	0.398321	−	0.689912i	0.0422219	−	0.0731305i	0.886364	+	0.462989i	$0.153223\pi$
$90$		0			0
$91$	4.88690	−	0.600901i	0.512286	−	0.0629915i
$92$	−0.476282	+	0.824944i	−0.0496558	+	0.0860063i
$93$		0			0
$94$	−1.38690	+	2.40218i	−0.143048	+	0.247766i
$95$	1.19098	−	2.06284i	0.122192	−	0.211643i
$96$		0			0
$97$	6.43999	−	11.1544i	0.653882	−	1.13256i	−0.328291	−	0.944577i	$-0.606473\pi$
$97$	6.43999	−	11.1544i	0.653882	−	1.13256i	0.982173	−	0.187980i	$-0.0601941\pi$
$98$	0.718516	−	2.50907i	0.0725811	−	0.253454i
$99$		0			0
$100$	−2.77243	+	4.80198i	−0.277243	+	0.480198i
$101$	−12.8586			−1.27948			−0.639741	−	0.768591i	$-0.720958\pi$
$101$	−12.8586			−1.27948			−0.639741	+	0.768591i	$0.720958\pi$
$102$		0			0
$103$	−19.7558			−1.94660			−0.973301	−	0.229534i	$-0.926280\pi$
$103$	−19.7558			−1.94660			−0.973301	+	0.229534i	$0.926280\pi$
$104$	−1.33949	−	2.32007i	−0.131348	−	0.227502i
$105$		0			0
$106$	−0.155267	+	0.268930i	−0.0150808	+	0.0261208i
$107$	−3.61530	+	6.26188i	−0.349504	+	0.605358i	−0.986161	−	0.165788i	$-0.946983\pi$
$107$	−3.61530	+	6.26188i	−0.349504	+	0.605358i	0.636658	+	0.771147i	$0.280316\pi$
$108$		0			0
$109$	−4.88410	−	8.45951i	−0.467812	−	0.810274i	0.531512	−	0.847051i	$-0.321624\pi$
$109$	−4.88410	−	8.45951i	−0.467812	−	0.810274i	−0.999323	+	0.0367769i	$0.988291\pi$
$110$	0.997363	+	1.72748i	0.0950948	+	0.164709i
$111$		0			0
$112$	8.36436	−	1.02849i	0.790358	−	0.0971836i
$113$	−8.45361	−	14.6421i	−0.795248	−	1.37741i	−0.922681	−	0.385564i	$-0.874007\pi$
$113$	−8.45361	−	14.6421i	−0.795248	−	1.37741i	0.127433	−	0.991847i	$-0.459326\pi$
$114$		0			0
$115$	−0.727575			−0.0678467
$116$	−8.11574	−	14.0569i	−0.753527	−	1.30515i
$117$		0			0
$118$	−4.85538			−0.446974
$119$	−19.7851	+	2.43280i	−1.81369	+	0.223014i
$120$		0			0
$121$	3.16625			0.287841
$122$	−1.92086	+	3.32702i	−0.173906	+	0.301215i
$123$		0			0
$124$	−2.72941	−	4.72748i	−0.245108	−	0.424540i
$125$	−11.3424			−1.01449
$126$		0			0
$127$	−16.1715			−1.43499			−0.717495	−	0.696563i	$-0.754711\pi$
$127$	−16.1715			−1.43499			−0.717495	+	0.696563i	$0.754711\pi$
$128$	−4.97164	−	8.61114i	−0.439435	−	0.761125i
$129$		0			0
$130$	0.493139	−	0.854141i	0.0432511	−	0.0749131i
$131$	13.6216			1.19012			0.595060	−	0.803681i	$-0.297128\pi$
$131$	13.6216			1.19012			0.595060	+	0.803681i	$0.297128\pi$
$132$		0			0
$133$	2.66883	+	3.54037i	0.231416	+	0.306989i
$134$	−2.42956			−0.209882
$135$		0			0
$136$	5.42306	+	9.39301i	0.465023	+	0.805444i
$137$	6.51186			0.556346			0.278173	−	0.960531i	$-0.410271\pi$
$137$	6.51186			0.556346			0.278173	+	0.960531i	$0.410271\pi$
$138$		0			0
$139$	8.95361	+	15.5081i	0.759435	+	1.31538i	0.943139	+	0.332399i	$0.107858\pi$
$139$	8.95361	+	15.5081i	0.759435	+	1.31538i	−0.183704	+	0.982982i	$0.558809\pi$
$140$	4.21291	+	5.58870i	0.356056	+	0.472331i
$141$		0			0
$142$	−0.767789	−	1.32985i	−0.0644314	−	0.111598i
$143$	−3.50220	−	6.06598i	−0.292868	−	0.507263i
$144$		0			0
$145$	6.19886	−	10.7367i	0.514787	−	0.891638i
$146$	1.06163	−	1.83880i	0.0878611	−	0.152180i
$147$		0			0
$148$	4.02998	+	6.98012i	0.331262	+	0.573763i
$149$	−19.9692			−1.63594			−0.817970	−	0.575261i	$-0.804901\pi$
$149$	−19.9692			−1.63594			−0.817970	+	0.575261i	$0.804901\pi$
$150$		0			0
$151$	6.31865			0.514205			0.257102	−	0.966384i	$-0.417232\pi$
$151$	6.31865			0.514205			0.257102	+	0.966384i	$0.417232\pi$
$152$	1.20616	−	2.08913i	0.0978325	−	0.169451i
$153$		0			0
$154$	−3.68508	+	0.453123i	−0.296952	+	0.0365137i
$155$	2.08474	−	3.61088i	0.167451	−	0.290033i
$156$		0			0
$157$	3.24789	−	5.62551i	0.259210	−	0.448964i	−0.706821	−	0.707393i	$-0.749871\pi$
$157$	3.24789	−	5.62551i	0.259210	−	0.448964i	0.966030	+	0.258428i	$0.0832046\pi$
$158$	0.0492724	−	0.0853424i	0.00391990	−	0.00678947i
$159$		0			0
$160$	2.89028	−	5.00611i	0.228497	−	0.395768i
$161$	0.528931	−	1.24669i	0.0416856	−	0.0982528i
$162$		0			0
$163$	9.61631	−	16.6559i	0.753208	−	1.30459i	−0.193053	−	0.981188i	$-0.561839\pi$
$163$	9.61631	−	16.6559i	0.753208	−	1.30459i	0.946260	−	0.323406i	$-0.104828\pi$
$164$	−12.7301			−0.994053
$165$		0			0
$166$	−2.94565			−0.228627
$167$	5.18862	+	8.98695i	0.401507	+	0.695431i	0.993908	−	0.110212i	$-0.0351531\pi$
$167$	5.18862	+	8.98695i	0.401507	+	0.695431i	−0.592401	+	0.805644i	$0.701820\pi$
$168$		0			0
$169$	4.76837	−	8.25905i	0.366797	−	0.635312i
$170$	−1.99652	+	3.45807i	−0.153126	+	0.265222i
$171$		0			0
$172$	−4.22140	−	7.31167i	−0.321878	−	0.557510i
$173$	6.61005	+	11.4490i	0.502553	+	0.870448i	0.999996	+	0.00295062i	$0.000939214\pi$
$173$	6.61005	+	11.4490i	0.502553	+	0.870448i	−0.497443	+	0.867497i	$0.665727\pi$
$174$		0			0
$175$	3.07890	−	7.25695i	0.232743	−	0.548574i
$176$	−5.99432	−	10.3825i	−0.451839	−	0.782608i
$177$		0			0
$178$	0.297024			0.0222629
$179$	5.74745	+	9.95487i	0.429584	+	0.744062i	0.996836	−	0.0794823i	$-0.0253267\pi$
$179$	5.74745	+	9.95487i	0.429584	+	0.744062i	−0.567252	+	0.823544i	$0.691993\pi$
$180$		0			0
$181$	−13.7040			−1.01861			−0.509306	−	0.860586i	$-0.670098\pi$
$181$	−13.7040			−1.01861			−0.509306	+	0.860586i	$0.670098\pi$
$182$	1.10506	+	1.46593i	0.0819122	+	0.108662i
$183$		0			0
$184$	−0.736848			−0.0543211
$185$	−3.07812	+	5.33147i	−0.226308	+	0.391977i
$186$		0			0
$187$	14.1790	+	24.5587i	1.03687	+	1.79591i
$188$	13.8449			1.00974
$189$		0			0
$190$	0.888103			0.0644298
$191$	3.87167	+	6.70592i	0.280144	+	0.485223i	0.971420	−	0.237367i	$-0.0762845\pi$
$191$	3.87167	+	6.70592i	0.280144	+	0.485223i	−0.691276	+	0.722591i	$0.742951\pi$
$192$		0			0
$193$	−7.91002	+	13.7005i	−0.569375	+	0.986187i	0.427252	+	0.904132i	$0.359482\pi$
$193$	−7.91002	+	13.7005i	−0.569375	+	0.986187i	−0.996628	+	0.0820547i	$0.973852\pi$
$194$	4.80224			0.344781
$195$		0			0
$196$	−12.6388	+	3.15590i	−0.902775	+	0.225421i
$197$	−3.64966			−0.260028			−0.130014	−	0.991512i	$-0.541502\pi$
$197$	−3.64966			−0.260028			−0.130014	+	0.991512i	$0.541502\pi$
$198$		0			0
$199$	10.3582	+	17.9409i	0.734272	+	1.27180i	0.955042	+	0.296471i	$0.0958098\pi$
$199$	10.3582	+	17.9409i	0.734272	+	1.27180i	−0.220770	+	0.975326i	$0.570857\pi$
$200$	−4.28918			−0.303291
$201$		0			0
$202$	−2.39714	−	4.15197i	−0.168662	−	0.292131i
$203$	13.8908	+	18.4270i	0.974943	+	1.29332i
$204$		0			0
$205$	−4.86167	−	8.42066i	−0.339554	−	0.588124i
$206$	−3.68294	−	6.37904i	−0.256602	−	0.444449i
$207$		0			0
$208$	−2.96385	+	5.13353i	−0.205506	+	0.355946i
$209$	3.15359	−	5.46218i	0.218138	−	0.377827i
$210$		0			0
$211$	−9.92695	−	17.1940i	−0.683400	−	1.18368i	−0.973937	−	0.226819i	$-0.927167\pi$
$211$	−9.92695	−	17.1940i	−0.683400	−	1.18368i	0.290537	−	0.956864i	$-0.406166\pi$
$212$	1.54997			0.106452
$213$		0			0
$214$	−2.69589			−0.184287
$215$	3.22433	−	5.58471i	0.219898	−	0.380874i
$216$		0			0
$217$	4.67163	+	6.19721i	0.317131	+	0.420694i
$218$	1.82101	−	3.15409i	0.123335	−	0.213622i
$219$		0			0
$220$	4.97814	−	8.62240i	0.335626	−	0.581322i
$221$	7.01068	−	12.1429i	0.471589	−	0.816817i
$222$		0			0
$223$	−8.03599	+	13.9187i	−0.538130	+	0.932068i	0.460875	+	0.887465i	$0.347536\pi$
$223$	−8.03599	+	13.9187i	−0.538130	+	0.932068i	−0.999005	+	0.0446029i	$0.985798\pi$
$224$	6.47672	+	8.59178i	0.432744	+	0.574063i
$225$		0			0
$226$	3.15189	−	5.45923i	0.209661	−	0.363143i
$227$	0.857745			0.0569305			0.0284653	−	0.999595i	$-0.490938\pi$
$227$	0.857745			0.0569305			0.0284653	+	0.999595i	$0.490938\pi$
$228$		0			0
$229$	5.75584			0.380357			0.190178	−	0.981750i	$-0.439093\pi$
$229$	5.75584			0.380357			0.190178	+	0.981750i	$0.439093\pi$
$230$	−0.135636	−	0.234929i	−0.00894360	−	0.0154908i
$231$		0			0
$232$	6.27786	−	10.8736i	0.412162	−	0.713885i
$233$	−3.69430	+	6.39872i	−0.242022	+	0.419194i	−0.961290	−	0.275539i	$-0.911144\pi$
$233$	−3.69430	+	6.39872i	−0.242022	+	0.419194i	0.719268	+	0.694732i	$0.244477\pi$
$234$		0			0
$235$	5.28742	+	9.15808i	0.344913	+	0.597407i
$236$	12.1174	+	20.9879i	0.788773	+	1.36619i
$237$		0			0
$238$	−4.47392	−	5.93494i	−0.290001	−	0.384705i
$239$	−6.90052	−	11.9520i	−0.446357	−	0.773114i	0.551788	−	0.833984i	$-0.313946\pi$
$239$	−6.90052	−	11.9520i	−0.446357	−	0.773114i	−0.998146	+	0.0608706i	$0.980612\pi$
$240$		0			0
$241$	−19.7558			−1.27259			−0.636293	−	0.771448i	$-0.719533\pi$
$241$	−19.7558			−1.27259			−0.636293	+	0.771448i	$0.719533\pi$
$242$	0.590260	+	1.02236i	0.0379434	+	0.0657198i
$243$		0			0
$244$	19.1752			1.22757
$245$	−6.91438	−	7.15505i	−0.441743	−	0.457120i
$246$		0			0
$247$	−3.11854			−0.198428
$248$	2.11131	−	3.65690i	0.134069	−	0.232214i
$249$		0			0
$250$	−2.11448	−	3.66238i	−0.133731	−	0.231629i
$251$	9.45207			0.596609			0.298305	−	0.954471i	$-0.403579\pi$
$251$	9.45207			0.596609			0.298305	+	0.954471i	$0.403579\pi$
$252$		0			0
$253$	−1.92654			−0.121121
$254$	−3.01474	−	5.22168i	−0.189162	−	0.327637i
$255$		0			0
$256$	−3.00058	+	5.19715i	−0.187536	+	0.324822i
$257$	7.47327			0.466169			0.233085	−	0.972456i	$-0.425118\pi$
$257$	7.47327			0.466169			0.233085	+	0.972456i	$0.425118\pi$
$258$		0			0
$259$	−6.89766	−	9.15018i	−0.428600	−	0.568565i
$260$	−4.92281			−0.305300
$261$		0			0
$262$	2.53937	+	4.39831i	0.156883	+	0.271729i
$263$	25.8112			1.59159			0.795793	−	0.605569i	$-0.207054\pi$
$263$	25.8112			1.59159			0.795793	+	0.605569i	$0.207054\pi$
$264$		0			0
$265$	0.591938	+	1.02527i	0.0363625	+	0.0629816i
$266$	−0.645632	+	1.52175i	−0.0395863	+	0.0933046i
$267$		0			0
$268$	6.06333	+	10.5020i	0.370377	+	0.641511i
$269$	3.24349	+	5.61790i	0.197759	+	0.342529i	0.947802	−	0.318861i	$-0.103300\pi$
$269$	3.24349	+	5.61790i	0.197759	+	0.342529i	−0.750042	+	0.661390i	$0.769967\pi$
$270$		0			0
$271$	9.11980	−	15.7959i	0.553988	−	0.959536i	−0.443993	−	0.896030i	$-0.646439\pi$
$271$	9.11980	−	15.7959i	0.553988	−	0.959536i	0.997981	−	0.0635055i	$-0.0202280\pi$
$272$	11.9994	−	20.7836i	0.727570	−	1.26019i
$273$		0			0
$274$	1.21396	+	2.10264i	0.0733379	+	0.127025i
$275$	−11.2143			−0.676251
$276$		0			0
$277$	−3.04656			−0.183050			−0.0915249	−	0.995803i	$-0.529174\pi$
$277$	−3.04656			−0.183050			−0.0915249	+	0.995803i	$0.529174\pi$
$278$	−3.33831	+	5.78213i	−0.200219	+	0.346789i
$279$		0			0
$280$	−2.11448	+	4.98381i	−0.126364	+	0.297840i
$281$	14.2723	−	24.7203i	0.851412	−	1.47469i	−0.0285227	−	0.999593i	$-0.509080\pi$
$281$	14.2723	−	24.7203i	0.851412	−	1.47469i	0.879934	−	0.475095i	$-0.157586\pi$
$282$		0			0
$283$	4.77043	−	8.26262i	0.283572	−	0.491162i	−0.688690	−	0.725056i	$-0.741814\pi$
$283$	4.77043	−	8.26262i	0.283572	−	0.491162i	0.972262	+	0.233895i	$0.0751470\pi$
$284$	−3.83227	+	6.63769i	−0.227403	+	0.393874i
$285$		0			0
$286$	1.30578	−	2.26167i	0.0772123	−	0.133736i
$287$	17.9630	−	2.20876i	1.06032	−	0.130379i
$288$		0			0
$289$	−19.8834	+	34.4390i	−1.16961	+	2.02582i
$290$	4.62243			0.271439
$291$		0			0
$292$	−10.5978			−0.620191
$293$	−6.31533	−	10.9385i	−0.368946	−	0.639033i	0.620455	−	0.784242i	$-0.286948\pi$
$293$	−6.31533	−	10.9385i	−0.368946	−	0.639033i	−0.989401	+	0.145209i	$0.953615\pi$
$294$		0			0
$295$	−9.25533	+	16.0307i	−0.538866	+	0.933343i
$296$	−3.11736	+	5.39942i	−0.181193	+	0.313835i
$297$		0			0
$298$	−3.72271	−	6.44793i	−0.215651	−	0.373518i
$299$	0.476282	+	0.824944i	0.0275441	+	0.0477077i
$300$		0			0
$301$	7.22529	+	9.58481i	0.416459	+	0.552459i
$302$	1.17794	+	2.04025i	0.0677829	+	0.117403i
$303$		0			0
$304$	−5.33765			−0.306135
$305$	7.32308	+	12.6839i	0.419318	+	0.726280i
$306$		0			0
$307$	−10.9319			−0.623918			−0.311959	−	0.950096i	$-0.600985\pi$
$307$	−10.9319			−0.623918			−0.311959	+	0.950096i	$0.600985\pi$
$308$	11.1553	+	14.7983i	0.635635	+	0.843210i
$309$		0			0
$310$	1.55457			0.0882939
$311$	2.38028	−	4.12277i	0.134973	−	0.233781i	−0.790614	−	0.612315i	$-0.790238\pi$
$311$	2.38028	−	4.12277i	0.134973	−	0.233781i	0.925587	+	0.378534i	$0.123572\pi$
$312$		0			0
$313$	−3.60550	−	6.24490i	−0.203795	−	0.352983i	0.745953	−	0.665998i	$-0.231994\pi$
$313$	−3.60550	−	6.24490i	−0.203795	−	0.352983i	−0.949748	+	0.313015i	$0.898661\pi$
$314$	2.42192			0.136677
$315$		0			0
$316$	−0.491868			−0.0276697
$317$	−3.64459	−	6.31261i	−0.204700	−	0.354552i	0.745337	−	0.666688i	$-0.232289\pi$
$317$	−3.64459	−	6.31261i	−0.204700	−	0.354552i	−0.950037	+	0.312137i	$0.898955\pi$
$318$		0			0
$319$	16.4139	−	28.4297i	0.919003	−	1.59176i
$320$	−6.89997			−0.385720
$321$		0			0
$322$	0.501152	−	0.0616225i	0.0279281	−	0.00343408i
$323$	12.6257			0.702511
$324$		0			0
$325$	2.77243	+	4.80198i	0.153786	+	0.266366i
$326$	7.17080			0.397154
$327$		0			0
$328$	−4.92363	−	8.52798i	−0.271862	−	0.470879i
$329$	−19.5361	+	2.40218i	−1.07706	+	0.132437i
$330$		0			0
$331$	0.609557	+	1.05578i	0.0335043	+	0.0580311i	0.882291	−	0.470704i	$-0.156000\pi$
$331$	0.609557	+	1.05578i	0.0335043	+	0.0580311i	−0.848787	+	0.528735i	$0.822667\pi$
$332$	7.35132	+	12.7329i	0.403456	+	0.698807i
$333$		0			0
$334$	−1.93455	+	3.35074i	−0.105854	+	0.183345i
$335$	−4.63121	+	8.02150i	−0.253030	+	0.438261i
$336$		0			0
$337$	7.45698	+	12.9159i	0.406208	+	0.703573i	0.994461	−	0.105104i	$-0.0335176\pi$
$337$	7.45698	+	12.9159i	0.406208	+	0.703573i	−0.588253	+	0.808677i	$0.700184\pi$
$338$	3.55573			0.193406
$339$		0			0
$340$	19.9304			1.08088
$341$	5.52018	−	9.56123i	0.298934	−	0.517769i
$342$		0			0
$343$	17.2867	−	6.64611i	0.933393	−	0.358856i
$344$	3.26543	−	5.65589i	0.176060	−	0.304945i
$345$		0			0
$346$	−2.46453	+	4.26869i	−0.132494	+	0.229486i
$347$	2.57914	−	4.46720i	0.138456	−	0.239812i	−0.788457	−	0.615090i	$-0.789120\pi$
$347$	2.57914	−	4.46720i	0.138456	−	0.239812i	0.926912	+	0.375278i	$0.122453\pi$
$348$		0			0
$349$	12.2253	−	21.1749i	0.654408	−	1.13347i	−0.327634	−	0.944805i	$-0.606251\pi$
$349$	12.2253	−	21.1749i	0.654408	−	1.13347i	0.982042	−	0.188663i	$-0.0604154\pi$
$350$	2.91720	−	0.358703i	0.155931	−	0.0191735i
$351$		0			0
$352$	7.65315	−	13.2556i	0.407914	−	0.706528i
$353$	14.9095			0.793551			0.396775	−	0.917916i	$-0.370129\pi$
$353$	14.9095			0.793551			0.396775	+	0.917916i	$0.370129\pi$
$354$		0			0
$355$	−5.85423			−0.310710
$356$	−0.741269	−	1.28392i	−0.0392872	−	0.0680474i
$357$		0			0
$358$	−2.14291	+	3.71163i	−0.113256	+	0.196166i
$359$	1.07390	−	1.86005i	0.0566783	−	0.0981697i	−0.836294	−	0.548281i	$-0.815282\pi$
$359$	1.07390	−	1.86005i	0.0566783	−	0.0981697i	0.892972	+	0.450111i	$0.148616\pi$
$360$		0			0
$361$	8.09594	+	14.0226i	0.426102	+	0.738031i
$362$	−2.55474	−	4.42494i	−0.134274	−	0.232570i
$363$		0			0
$364$	3.57878	−	8.43516i	0.187579	−	0.442123i
$365$	−4.04735	−	7.01022i	−0.211848	−	0.366932i
$366$		0			0
$367$	−15.8610			−0.827937			−0.413968	−	0.910291i	$-0.635858\pi$
$367$	−15.8610			−0.827937			−0.413968	+	0.910291i	$0.635858\pi$
$368$	0.815198	+	1.41196i	0.0424951	+	0.0736037i
$369$		0			0
$370$	−2.29533			−0.119329
$371$	−2.18711	+	0.268930i	−0.113549	+	0.0139621i
$372$		0			0
$373$	11.7368			0.607711			0.303855	−	0.952718i	$-0.401726\pi$
$373$	11.7368			0.607711			0.303855	+	0.952718i	$0.401726\pi$
$374$	−5.28656	+	9.15659i	−0.273362	+	0.473476i
$375$		0			0
$376$	5.35481	+	9.27480i	0.276153	+	0.478311i
$377$	−16.2315			−0.835963
$378$		0			0
$379$	18.9400			0.972885			0.486442	−	0.873713i	$-0.338294\pi$
$379$	18.9400			0.972885			0.486442	+	0.873713i	$0.338294\pi$
$380$	−2.21640	−	3.83891i	−0.113699	−	0.196932i
$381$		0			0
$382$	−1.44353	+	2.50027i	−0.0738576	+	0.127925i
$383$	29.6812			1.51664			0.758319	−	0.651884i	$-0.226021\pi$
$383$	29.6812			1.51664			0.758319	+	0.651884i	$0.226021\pi$
$384$		0			0
$385$	−5.52845	+	13.0305i	−0.281756	+	0.664097i
$386$	−5.89843			−0.300222
$387$		0			0
$388$	−11.9847	−	20.7582i	−0.608433	−	1.05384i
$389$	−1.27819			−0.0648066			−0.0324033	−	0.999475i	$-0.510316\pi$
$389$	−1.27819			−0.0648066			−0.0324033	+	0.999475i	$0.510316\pi$
$390$		0			0
$391$	−1.92827	−	3.33986i	−0.0975167	−	0.168904i
$392$	−7.00250	−	7.24625i	−0.353680	−	0.365991i
$393$		0			0
$394$	−0.680380	−	1.17845i	−0.0342771	−	0.0593696i
$395$	−0.187846	−	0.325359i	−0.00945156	−	0.0163706i
$396$		0			0
$397$	3.21734	−	5.57259i	0.161473	−	0.279680i	−0.773924	−	0.633279i	$-0.781709\pi$
$397$	3.21734	−	5.57259i	0.161473	−	0.279680i	0.935397	+	0.353598i	$0.115042\pi$
$398$	−3.86200	+	6.68918i	−0.193585	+	0.335299i
$399$		0			0
$400$	4.74525	+	8.21902i	0.237263	+	0.410951i
$401$	27.6910			1.38282			0.691412	−	0.722461i	$-0.256989\pi$
$401$	27.6910			1.38282			0.691412	+	0.722461i	$0.256989\pi$
$402$		0			0
$403$	−5.45882			−0.271923
$404$	−11.9649	+	20.7237i	−0.595274	+	1.03105i
$405$		0			0
$406$	−3.36041	+	7.92047i	−0.166774	+	0.393086i
$407$	−8.15054	+	14.1172i	−0.404008	+	0.699762i
$408$		0			0
$409$	6.01362	−	10.4159i	0.297354	−	0.515033i	−0.678176	−	0.734900i	$-0.737229\pi$
$409$	6.01362	−	10.4159i	0.297354	−	0.515033i	0.975530	+	0.219867i	$0.0705625\pi$
$410$	1.81265	−	3.13960i	0.0895205	−	0.155054i
$411$		0			0
$412$	−18.3827	+	31.8397i	−0.905650	+	1.56863i
$413$	−20.7399	−	27.5128i	−1.02054	−	1.35382i
$414$		0			0
$415$	−5.61500	+	9.72546i	−0.275629	+	0.477404i
$416$	−7.56808			−0.371056
$417$		0			0
$418$	2.35160			0.115021
$419$	9.00950	+	15.6049i	0.440143	+	0.762350i	0.997700	−	0.0677891i	$-0.0215945\pi$
$419$	9.00950	+	15.6049i	0.440143	+	0.762350i	−0.557557	+	0.830139i	$0.688261\pi$
$420$		0			0
$421$	8.62861	−	14.9452i	0.420533	−	0.728384i	−0.575459	−	0.817831i	$-0.695177\pi$
$421$	8.62861	−	14.9452i	0.420533	−	0.728384i	0.995992	+	0.0894466i	$0.0285098\pi$
$422$	3.70122	−	6.41070i	0.180173	−	0.312068i
$423$		0			0
$424$	0.599482	+	1.03833i	0.0291134	+	0.0504260i
$425$	−11.2244	−	19.4413i	−0.544464	−	0.943039i
$426$		0			0
$427$	−27.0575	+	3.32702i	−1.30940	+	0.161006i
$428$	6.72801	+	11.6533i	0.325211	+	0.563282i
$429$		0			0
$430$	2.40436			0.115948
$431$	−4.28368	−	7.41955i	−0.206338	−	0.357387i	0.744220	−	0.667934i	$-0.232821\pi$
$431$	−4.28368	−	7.41955i	−0.206338	−	0.357387i	−0.950558	+	0.310547i	$0.899488\pi$
$432$		0			0
$433$	1.58971			0.0763967			0.0381984	−	0.999270i	$-0.487838\pi$
$433$	1.58971			0.0763967			0.0381984	+	0.999270i	$0.487838\pi$
$434$	−1.13014	+	2.66374i	−0.0542486	+	0.127864i
$435$		0			0
$436$	−18.1785			−0.870592
$437$	−0.428873	+	0.742829i	−0.0205158	+	0.0355343i
$438$		0			0
$439$	−11.2218	−	19.4367i	−0.535588	−	0.927665i	−0.999135	−	0.0415927i	$-0.986757\pi$
$439$	−11.2218	−	19.4367i	−0.535588	−	0.927665i	0.463547	−	0.886072i	$-0.346577\pi$
$440$	7.70161			0.367160
$441$		0			0
$442$	5.22780			0.248661
$443$	12.1605	+	21.0626i	0.577763	+	1.00072i	0.995735	+	0.0922553i	$0.0294076\pi$
$443$	12.1605	+	21.0626i	0.577763	+	1.00072i	−0.417972	+	0.908460i	$0.637259\pi$
$444$		0			0
$445$	0.566187	−	0.980665i	0.0268398	−	0.0464880i
$446$	−5.99237			−0.283747
$447$		0			0
$448$	5.01613	−	11.8230i	0.236990	−	0.558584i
$449$	12.9016			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$449$	12.9016			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$450$		0			0
$451$	−12.8732	−	22.2970i	−0.606174	−	1.04992i
$452$	−31.4641			−1.47995
$453$		0			0
$454$	0.159903	+	0.276960i	0.00750463	+	0.0129984i
$455$	6.94641	−	0.854141i	0.325653	−	0.0400428i
$456$		0			0
$457$	−0.593880	−	1.02863i	−0.0277806	−	0.0481173i	0.851801	−	0.523866i	$-0.175511\pi$
$457$	−0.593880	−	1.02863i	−0.0277806	−	0.0481173i	−0.879581	+	0.475748i	$0.842177\pi$
$458$	1.07302	+	1.85853i	0.0501389	+	0.0868432i
$459$		0			0
$460$	−0.677003	+	1.17260i	−0.0315654	+	0.0546729i
$461$	−8.08370	+	14.0014i	−0.376495	+	0.652109i	−0.990550	−	0.137155i	$-0.956204\pi$
$461$	−8.08370	+	14.0014i	−0.376495	+	0.652109i	0.614054	+	0.789264i	$0.289538\pi$
$462$		0			0
$463$	0.265564	+	0.459970i	0.0123418	+	0.0213766i	0.872130	−	0.489274i	$-0.162738\pi$
$463$	0.265564	+	0.459970i	0.0123418	+	0.0213766i	−0.859789	+	0.510650i	$0.829405\pi$
$464$	−27.7816			−1.28973
$465$		0			0
$466$	−2.75481			−0.127614
$467$	10.7393	−	18.6011i	0.496958	−	0.860756i	−0.503036	−	0.864265i	$-0.667784\pi$
$467$	10.7393	−	18.6011i	0.496958	−	0.860756i	0.999994	+	0.00350930i	$0.00111705\pi$
$468$		0			0
$469$	−10.3779	−	13.7670i	−0.479208	−	0.635700i
$470$	−1.97139	+	3.41455i	−0.0909335	+	0.157501i
$471$		0			0
$472$	−9.37329	+	16.2350i	−0.431440	+	0.747277i
$473$	8.53769	−	14.7877i	0.392563	−	0.679940i
$474$		0			0
$475$	−2.49646	+	4.32399i	−0.114545	+	0.198398i
$476$	−14.4890	+	34.1505i	−0.664103	+	1.56529i
$477$		0			0
$478$	2.57283	−	4.45627i	0.117678	−	0.203825i
$479$	−28.3529			−1.29548			−0.647739	−	0.761862i	$-0.724285\pi$
$479$	−28.3529			−1.29548			−0.647739	+	0.761862i	$0.724285\pi$
$480$		0			0
$481$	8.05995			0.367502
$482$	−3.68294	−	6.37904i	−0.167753	−	0.290557i
$483$		0			0
$484$	2.94617	−	5.10292i	0.133917	−	0.231951i
$485$	9.15403	−	15.8552i	0.415663	−	0.719950i
$486$		0			0
$487$	−3.93513	−	6.81584i	−0.178318	−	0.308855i	0.762987	−	0.646414i	$-0.223732\pi$
$487$	−3.93513	−	6.81584i	−0.178318	−	0.308855i	−0.941304	+	0.337559i	$0.890399\pi$
$488$	7.41641	+	12.8456i	0.335725	+	0.581493i
$489$		0			0
$490$	1.02132	−	3.56647i	0.0461387	−	0.161117i
$491$	14.1592	+	24.5244i	0.638994	+	1.10677i	0.985654	+	0.168779i	$0.0539825\pi$
$491$	14.1592	+	24.5244i	0.638994	+	1.10677i	−0.346660	+	0.937991i	$0.612684\pi$
$492$		0			0
$493$	65.7146			2.95963
$494$	−0.581366	−	1.00696i	−0.0261569	−	0.0453051i
$495$		0			0
$496$	−9.34325			−0.419524
$497$	4.25590	−	10.0311i	0.190903	−	0.449958i
$498$		0			0
$499$	6.84187			0.306284			0.153142	−	0.988204i	$-0.451061\pi$
$499$	6.84187			0.306284			0.153142	+	0.988204i	$0.451061\pi$
$500$	−10.5540	+	18.2801i	−0.471989	+	0.817509i
$501$		0			0
$502$	1.76208	+	3.05201i	0.0786455	+	0.136218i
$503$	−30.5760			−1.36332			−0.681658	−	0.731671i	$-0.738741\pi$
$503$	−30.5760			−1.36332			−0.681658	+	0.731671i	$0.738741\pi$
$504$		0			0
$505$	−18.2777			−0.813347
$506$	−0.359151	−	0.622067i	−0.0159662	−	0.0276543i
$507$		0			0
$508$	−15.0475	+	26.0630i	−0.667624	+	1.15636i
$509$	−34.1123			−1.51200			−0.756001	−	0.654570i	$-0.772850\pi$
$509$	−34.1123			−1.51200			−0.756001	+	0.654570i	$0.772850\pi$
$510$		0			0
$511$	14.9542	−	1.83880i	0.661537	−	0.0813435i
$512$	−22.1241			−0.977756
$513$		0			0
$514$	1.39319	+	2.41307i	0.0614508	+	0.106436i
$515$	−28.0816			−1.23743
$516$		0			0
$517$	14.0005	+	24.2496i	0.615742	+	1.06650i
$518$	1.66866	−	3.93301i	0.0733165	−	0.172807i
$519$		0			0
$520$	−1.90400	−	3.29783i	−0.0834960	−	0.144619i
$521$	7.37216	+	12.7690i	0.322980	+	0.559418i	0.981102	−	0.193494i	$-0.0619819\pi$
$521$	7.37216	+	12.7690i	0.322980	+	0.559418i	−0.658121	+	0.752912i	$0.728649\pi$
$522$		0			0
$523$	−2.03953	+	3.53257i	−0.0891825	+	0.154469i	−0.907166	−	0.420773i	$-0.861759\pi$
$523$	−2.03953	+	3.53257i	−0.0891825	+	0.154469i	0.817983	+	0.575242i	$0.195092\pi$
$524$	12.6748	−	21.9533i	0.553699	−	0.959036i
$525$		0			0
$526$	4.81179	+	8.33427i	0.209804	+	0.363391i
$527$	22.1005			0.962714
$528$		0			0
$529$	−22.7380			−0.988609
$530$	−0.220701	+	0.382266i	−0.00958666	+	0.0166046i
$531$		0			0
$532$	8.18920	−	1.00696i	0.355047	−	0.0436571i
$533$	−6.36505	+	11.0246i	−0.275701	+	0.477528i
$534$		0			0
$535$	−5.13891	+	8.90085i	−0.222174	+	0.384817i
$536$	−4.69024	+	8.12373i	−0.202588	+	0.350892i
$537$		0			0
$538$	−1.20932	+	2.09461i	−0.0521376	+	0.0903049i
$539$	−18.3085	−	18.9458i	−0.788604	−	0.816054i
$540$		0			0
$541$	−1.90052	+	3.29179i	−0.0817096	+	0.141525i	−0.903984	−	0.427565i	$-0.859371\pi$
$541$	−1.90052	+	3.29179i	−0.0817096	+	0.141525i	0.822275	+	0.569091i	$0.192705\pi$
$542$	6.80055			0.292109
$543$		0			0
$544$	30.6401			1.31368
$545$	−6.94243	−	12.0246i	−0.297381	−	0.515079i
$546$		0			0
$547$	5.23891	−	9.07406i	0.224000	−	0.387979i	−0.732019	−	0.681284i	$-0.761422\pi$
$547$	5.23891	−	9.07406i	0.224000	−	0.387979i	0.956019	+	0.293305i	$0.0947553\pi$
$548$	6.05924	−	10.4949i	0.258838	−	0.448320i
$549$		0			0
$550$	−2.09061	−	3.62104i	−0.0891439	−	0.154402i
$551$	−7.30790	−	12.6576i	−0.311327	−	0.539234i
$552$		0			0
$553$	0.694058	−	0.0853424i	0.0295143	−	0.00362913i
$554$	−0.567947	−	0.983714i	−0.0241298	−	0.0417940i
$555$		0			0
$556$	33.3251			1.41330
$557$	−17.4975	−	30.3065i	−0.741392	−	1.28413i	−0.951862	−	0.306528i	$-0.900833\pi$
$557$	−17.4975	−	30.3065i	−0.741392	−	1.28413i	0.210470	−	0.977600i	$-0.432501\pi$
$558$		0			0
$559$	−8.44279			−0.357092
$560$	11.8894	−	1.46194i	0.502419	−	0.0617782i
$561$		0			0
$562$	10.6427			0.448935
$563$	14.5322	−	25.1705i	0.612458	−	1.06081i	−0.378367	−	0.925656i	$-0.623514\pi$
$563$	14.5322	−	25.1705i	0.612458	−	1.06081i	0.990825	−	0.135153i	$-0.0431525\pi$
$564$		0			0
$565$	−12.0163	−	20.8128i	−0.505528	−	0.875599i
$566$	3.55726			0.149523
$567$		0			0
$568$	−5.92884			−0.248769
$569$	−11.0163	−	19.0808i	−0.461829	−	0.799911i	0.537224	−	0.843440i	$-0.319473\pi$
$569$	−11.0163	−	19.0808i	−0.461829	−	0.799911i	−0.999052	+	0.0435292i	$0.986140\pi$
$570$		0			0
$571$	−1.01413	+	1.75653i	−0.0424402	+	0.0735086i	−0.886465	−	0.462795i	$-0.846847\pi$
$571$	−1.01413	+	1.75653i	−0.0424402	+	0.0735086i	0.844025	+	0.536304i	$0.180180\pi$
$572$	−13.0351			−0.545024
$573$		0			0
$574$	4.06191	+	5.38838i	0.169541	+	0.224906i
$575$	1.52510			0.0636009
$576$		0			0
$577$	2.47060	+	4.27921i	0.102852	+	0.178146i	0.912859	−	0.408275i	$-0.133870\pi$
$577$	2.47060	+	4.27921i	0.102852	+	0.178146i	−0.810006	+	0.586421i	$0.800536\pi$
$578$	−14.8268			−0.616715
$579$		0			0
$580$	−11.5360	−	19.9809i	−0.479006	−	0.829663i
$581$	−12.5824	−	16.6914i	−0.522008	−	0.692476i
$582$		0			0
$583$	1.56739	+	2.71480i	0.0649146	+	0.112435i
$584$	−4.09894	−	7.09956i	−0.169615	−	0.293782i
$585$		0			0
$586$	2.35464	−	4.07836i	0.0972694	−	0.168476i
$587$	−16.2491	+	28.1443i	−0.670674	+	1.16164i	0.307039	+	0.951697i	$0.400662\pi$
$587$	−16.2491	+	28.1443i	−0.670674	+	1.16164i	−0.977713	+	0.209945i	$0.932672\pi$
$588$		0			0
$589$	−2.45773	−	4.25690i	−0.101269	−	0.175403i
$590$	−6.90161			−0.284135
$591$		0			0
$592$	13.7953			0.566984
$593$	7.77361	−	13.4643i	0.319224	−	0.552912i	−0.661103	−	0.750296i	$-0.729911\pi$
$593$	7.77361	−	13.4643i	0.319224	−	0.552912i	0.980326	+	0.197384i	$0.0632445\pi$
$594$		0			0
$595$	−28.1232	+	3.45807i	−1.15294	+	0.141767i
$596$	−18.5812	+	32.1836i	−0.761116	+	1.31829i
$597$		0			0
$598$	−0.177579	+	0.307577i	−0.00726176	+	0.0125777i
$599$	−11.9942	+	20.7745i	−0.490068	+	0.848822i	−0.999935	−	0.0114309i	$-0.996361\pi$
$599$	−11.9942	+	20.7745i	−0.490068	+	0.848822i	0.509867	+	0.860253i	$0.329695\pi$
$600$		0			0
$601$	0.443533	−	0.768221i	0.0180921	−	0.0313364i	−0.856838	−	0.515586i	$-0.827574\pi$
$601$	0.443533	−	0.768221i	0.0180921	−	0.0313364i	0.874930	+	0.484250i	$0.160907\pi$
$602$	−1.74792	+	4.11983i	−0.0712397	+	0.167912i
$603$		0			0
$604$	5.87946	−	10.1835i	0.239232	−	0.414362i
$605$	4.50061			0.182976
$606$		0			0
$607$	−11.7206			−0.475725			−0.237862	−	0.971299i	$-0.576447\pi$
$607$	−11.7206			−0.475725			−0.237862	+	0.971299i	$0.576447\pi$
$608$	−3.40738	−	5.90175i	−0.138187	−	0.239348i
$609$		0			0
$610$	−2.73038	+	4.72915i	−0.110550	+	0.191478i
$611$	6.92245	−	11.9900i	0.280052	−	0.485065i
$612$		0			0
$613$	4.83845	+	8.38044i	0.195423	+	0.338483i	0.947039	−	0.321118i	$-0.104059\pi$
$613$	4.83845	+	8.38044i	0.195423	+	0.338483i	−0.751616	+	0.659601i	$0.770725\pi$
$614$	−2.03796	−	3.52985i	−0.0822454	−	0.142453i
$615$		0			0
$616$	−5.59891	+	13.1966i	−0.225586	+	0.531706i
$617$	4.64513	+	8.04561i	0.187006	+	0.323904i	0.944251	−	0.329227i	$-0.106788\pi$
$617$	4.64513	+	8.04561i	0.187006	+	0.323904i	−0.757245	+	0.653131i	$0.773455\pi$
$618$		0			0
$619$	−30.2696			−1.21664			−0.608319	−	0.793693i	$-0.708156\pi$
$619$	−30.2696			−1.21664			−0.608319	+	0.793693i	$0.708156\pi$
$620$	−3.87968	−	6.71980i	−0.155812	−	0.269874i
$621$		0			0
$622$	1.77496			0.0711692
$623$	1.26875	+	1.68307i	0.0508313	+	0.0674310i
$624$		0			0
$625$	−1.22483			−0.0489932
$626$	1.34429	−	2.32838i	0.0537288	−	0.0930609i
$627$		0			0
$628$	−6.04427	−	10.4690i	−0.241193	−	0.417758i
$629$	−32.6314			−1.30110
$630$		0			0
$631$	30.5921			1.21785			0.608926	−	0.793227i	$-0.291600\pi$
$631$	30.5921			1.21785			0.608926	+	0.793227i	$0.291600\pi$
$632$	−0.190240	−	0.329506i	−0.00756735	−	0.0131070i
$633$		0			0
$634$	1.35887	−	2.35363i	0.0539675	−	0.0934745i
$635$	−22.9868			−0.912202
$636$		0			0
$637$	−3.58634	+	12.5235i	−0.142096	+	0.496200i
$638$	12.2397			0.484575
$639$		0			0
$640$	−7.06687	−	12.2402i	−0.279343	−	0.483836i
$641$	32.8876			1.29898			0.649491	−	0.760369i	$-0.274982\pi$
$641$	32.8876			1.29898			0.649491	+	0.760369i	$0.274982\pi$
$642$		0			0
$643$	−2.68598	−	4.65226i	−0.105925	−	0.183467i	0.808191	−	0.588921i	$-0.200447\pi$
$643$	−2.68598	−	4.65226i	−0.105925	−	0.183467i	−0.914116	+	0.405453i	$0.867114\pi$
$644$	−1.51707	−	2.01249i	−0.0597810	−	0.0793033i
$645$		0			0
$646$	2.35371	+	4.07675i	0.0926056	+	0.160398i
$647$	−6.93041	−	12.0038i	−0.272463	−	0.471919i	0.697029	−	0.717043i	$-0.254505\pi$
$647$	−6.93041	−	12.0038i	−0.272463	−	0.471919i	−0.969492	+	0.245124i	$0.921171\pi$
$648$		0			0
$649$	−24.5071	+	42.4476i	−0.961988	+	1.66621i
$650$	−1.03369	+	1.79040i	−0.0405445	+	0.0702252i
$651$		0			0
$652$	−17.8958	−	30.9965i	−0.700855	−	1.21392i
$653$	33.2740			1.30211			0.651056	−	0.759030i	$-0.274326\pi$
$653$	33.2740			1.30211			0.651056	+	0.759030i	$0.274326\pi$
$654$		0			0
$655$	19.3622			0.756542
$656$	−10.8943	+	18.8695i	−0.425352	+	0.736732i
$657$		0			0
$658$	−4.41762	−	5.86025i	−0.172217	−	0.228456i
$659$	−6.39450	+	11.0756i	−0.249094	+	0.431444i	−0.963275	−	0.268517i	$-0.913466\pi$
$659$	−6.39450	+	11.0756i	−0.249094	+	0.431444i	0.714180	+	0.699962i	$0.246800\pi$
$660$		0			0
$661$	−20.5502	+	35.5940i	−0.799309	+	1.38444i	0.120757	+	0.992682i	$0.461468\pi$
$661$	−20.5502	+	35.5940i	−0.799309	+	1.38444i	−0.920066	+	0.391762i	$0.871866\pi$
$662$	−0.227271	+	0.393644i	−0.00883312	+	0.0152994i
$663$		0			0
$664$	−5.68656	+	9.84941i	−0.220681	+	0.382231i
$665$	3.79356	+	5.03240i	0.147108	+	0.195148i
$666$		0			0
$667$	−2.23221	+	3.86630i	−0.0864316	+	0.149704i
$668$	19.3119			0.747200
$669$		0			0
$670$	−3.45346			−0.133419
$671$	19.3907	+	33.5857i	0.748570	+	1.29656i
$672$		0			0
$673$	−14.3446	+	24.8455i	−0.552943	+	0.957725i	0.445118	+	0.895472i	$0.353162\pi$
$673$	−14.3446	+	24.8455i	−0.552943	+	0.957725i	−0.998060	+	0.0622526i	$0.980172\pi$
$674$	−2.78030	+	4.81563i	−0.107093	+	0.185491i
$675$		0			0
$676$	−8.87386	−	15.3700i	−0.341302	−	0.591153i
$677$	−24.7561	−	42.8788i	−0.951454	−	1.64797i	−0.742281	−	0.670088i	$-0.766256\pi$
$677$	−24.7561	−	42.8788i	−0.951454	−	1.64797i	−0.209173	−	0.977879i	$-0.567077\pi$
$678$		0			0
$679$	20.5129	+	27.2117i	0.787214	+	1.04429i
$680$	7.70852	+	13.3515i	0.295608	+	0.512009i
$681$		0			0
$682$	4.11635			0.157623
$683$	16.2536	+	28.1520i	0.621926	+	1.07721i	0.989127	+	0.147065i	$0.0469827\pi$
$683$	16.2536	+	28.1520i	0.621926	+	1.07721i	−0.367201	+	0.930142i	$0.619684\pi$
$684$		0			0
$685$	9.25618			0.353661
$686$	5.36862	+	4.34277i	0.204975	+	0.165808i
$687$		0			0
$688$	−14.4506			−0.550923
$689$	0.774984	−	1.34231i	0.0295245	−	0.0511380i
$690$		0			0
$691$	7.08644	+	12.2741i	0.269581	+	0.466928i	0.968754	−	0.248025i	$-0.0797815\pi$
$691$	7.08644	+	12.2741i	0.269581	+	0.466928i	−0.699173	+	0.714953i	$0.746448\pi$
$692$	24.6024			0.935244
$693$		0			0
$694$	1.92324			0.0730053
$695$	12.7270	+	22.0438i	0.482762	+	0.836167i
$696$		0			0
$697$	25.7695	−	44.6340i	0.976088	−	1.69063i
$698$	9.11633			0.345058
$699$		0			0
$700$	−8.83085	−	11.7147i	−0.333775	−	0.442773i
$701$	28.1485			1.06316			0.531578	−	0.847010i	$-0.321599\pi$
$701$	28.1485			1.06316			0.531578	+	0.847010i	$0.321599\pi$
$702$		0			0
$703$	3.62883	+	6.28532i	0.136864	+	0.237055i
$704$	−18.2704			−0.688591
$705$		0			0
$706$	2.77946	+	4.81417i	0.104606	+	0.181184i
$707$	13.2875	−	31.3186i	0.499728	−	1.17786i
$708$		0			0
$709$	−12.2335	−	21.1890i	−0.459438	−	0.795769i	0.539494	−	0.841990i	$-0.318616\pi$
$709$	−12.2335	−	21.1890i	−0.459438	−	0.795769i	−0.998931	+	0.0462204i	$0.985282\pi$
$710$	−1.09136	−	1.89029i	−0.0409581	−	0.0709415i
$711$		0			0
$712$	0.573403	−	0.993163i	0.0214892	−	0.0372204i
$713$	−0.750717	+	1.30028i	−0.0281146	+	0.0486959i
$714$		0			0
$715$	−4.97814	−	8.62240i	−0.186172	−	0.322459i
$716$	21.3918			0.799451
$717$		0			0
$718$	0.800798			0.0298855
$719$	−8.27732	+	14.3367i	−0.308692	+	0.534670i	−0.978076	−	0.208246i	$-0.933225\pi$
$719$	−8.27732	+	14.3367i	−0.308692	+	0.534670i	0.669385	+	0.742916i	$0.266558\pi$
$720$		0			0
$721$	20.4148	−	48.1175i	0.760285	−	1.79199i
$722$	−3.01854	+	5.22826i	−0.112338	+	0.194576i
$723$		0			0
$724$	−12.7515	+	22.0862i	−0.473905	+	0.820828i
$725$	−12.9937	+	22.5057i	−0.482572	+	0.835840i
$726$		0			0
$727$	17.1191	−	29.6511i	0.634911	−	1.09970i	−0.351623	−	0.936142i	$-0.614370\pi$
$727$	17.1191	−	29.6511i	0.634911	−	1.09970i	0.986534	−	0.163556i	$-0.0522964\pi$
$728$	7.03495	−	0.865027i	0.260732	−	0.0320600i
$729$		0			0
$730$	1.50904	−	2.61373i	0.0558520	−	0.0967384i
$731$	34.1814			1.26424
$732$		0			0
$733$	−12.2889			−0.453901			−0.226951	−	0.973906i	$-0.572876\pi$
$733$	−12.2889			−0.453901			−0.226951	+	0.973906i	$0.572876\pi$
$734$	−2.95685	−	5.12141i	−0.109139	−	0.189035i
$735$		0			0
$736$	−1.04079	+	1.80270i	−0.0383640	+	0.0664485i
$737$	−12.2630	+	21.2401i	−0.451712	+	0.782388i
$738$		0			0
$739$	21.6496	+	37.4982i	0.796394	+	1.37939i	0.921950	+	0.387308i	$0.126595\pi$
$739$	21.6496	+	37.4982i	0.796394	+	1.37939i	−0.125557	+	0.992086i	$0.540072\pi$
$740$	5.72835	+	9.92179i	0.210578	+	0.364732i
$741$		0			0
$742$	−0.494562	−	0.656068i	−0.0181559	−	0.0240850i
$743$	11.9739	+	20.7394i	0.439281	+	0.760856i	0.997634	−	0.0687469i	$-0.0219001\pi$
$743$	11.9739	+	20.7394i	0.439281	+	0.760856i	−0.558354	+	0.829603i	$0.688567\pi$
$744$		0			0
$745$	−28.3849			−1.03994
$746$	2.18802	+	3.78975i	0.0801089	+	0.138753i
$747$		0			0
$748$	52.7737			1.92960
$749$	−11.5156	−	15.2762i	−0.420771	−	0.558179i
$750$		0			0
$751$	−2.90298			−0.105931			−0.0529656	−	0.998596i	$-0.516867\pi$
$751$	−2.90298			−0.105931			−0.0529656	+	0.998596i	$0.516867\pi$
$752$	11.8484	−	20.5220i	0.432066	−	0.748361i
$753$		0			0
$754$	−3.02592	−	5.24104i	−0.110197	−	0.190867i
$755$	8.98156			0.326872
$756$		0			0
$757$	−8.99407			−0.326895			−0.163448	−	0.986552i	$-0.552261\pi$
$757$	−8.99407			−0.326895			−0.163448	+	0.986552i	$0.552261\pi$
$758$	3.53086	+	6.11562i	0.128246	+	0.222129i
$759$		0			0
$760$	1.71448	−	2.96956i	0.0621906	−	0.107717i
$761$	−38.0509			−1.37934			−0.689672	−	0.724122i	$-0.742245\pi$
$761$	−38.0509			−1.37934			−0.689672	+	0.724122i	$0.742245\pi$
$762$		0			0
$763$	25.6510	−	3.15409i	0.928630	−	0.114186i
$764$	14.4102			0.521344
$765$		0			0
$766$	5.53325	+	9.58386i	0.199924	+	0.346279i
$767$	24.2347			0.875065
$768$		0			0
$769$	−11.4065	−	19.7567i	−0.411330	−	0.712445i	0.583705	−	0.811966i	$-0.301602\pi$
$769$	−11.4065	−	19.7567i	−0.411330	−	0.712445i	−0.995035	+	0.0995210i	$0.968269\pi$
$770$	−5.23810	+	0.644084i	−0.188768	+	0.0232112i
$771$		0			0
$772$	14.7204	+	25.4965i	0.529800	+	0.917640i
$773$	3.06443	+	5.30775i	0.110220	+	0.190906i	0.915859	−	0.401500i	$-0.131511\pi$
$773$	3.06443	+	5.30775i	0.110220	+	0.190906i	−0.805639	+	0.592407i	$0.798178\pi$
$774$		0			0
$775$	−4.36991	+	7.56890i	−0.156972	+	0.271883i
$776$	9.27070	−	16.0573i	0.332799	−	0.576424i
$777$		0			0
$778$	−0.238283	−	0.412718i	−0.00854285	−	0.0147967i
$779$	−11.4629			−0.410703
$780$		0			0
$781$	−15.5014			−0.554683
$782$	0.718946	−	1.24525i	0.0257095	−	0.0445301i
$783$		0			0
$784$	−6.13833	+	21.4351i	−0.219226	+	0.765539i
$785$	4.61666	−	7.99629i	0.164776	−	0.285400i
$786$		0			0
$787$	23.2314	−	40.2379i	0.828109	−	1.43433i	−0.0714114	−	0.997447i	$-0.522750\pi$
$787$	23.2314	−	40.2379i	0.828109	−	1.43433i	0.899520	−	0.436879i	$-0.143916\pi$
$788$	−3.39599	+	5.88202i	−0.120977	+	0.209538i
$789$		0			0
$790$	0.0700376	−	0.121309i	0.00249182	−	0.00431597i
$791$	44.3979	−	5.45923i	1.57861	−	0.194108i
$792$		0			0
$793$	9.58760	−	16.6062i	0.340465	−	0.589704i
$794$	2.39914			0.0851422
$795$		0			0
$796$	38.5529			1.36647
$797$	3.81939	+	6.61538i	0.135290	+	0.234329i	0.925708	−	0.378239i	$-0.123470\pi$
$797$	3.81939	+	6.61538i	0.135290	+	0.234329i	−0.790418	+	0.612568i	$0.790137\pi$
$798$		0			0
$799$	−28.0262	+	48.5427i	−0.991494	+	1.71732i
$800$	−6.05842	+	10.4935i	−0.214198	+	0.371001i
$801$		0			0
$802$	5.16223	+	8.94125i	0.182285	+	0.315727i
$803$	−10.7170	−	18.5623i	−0.378193	−	0.655050i
$804$		0			0
$805$	0.751841	−	1.77209i	0.0264989	−	0.0624578i
$806$	−1.01765	−	1.76262i	−0.0358451	−	0.0620856i
$807$		0			0
$808$	−18.5107			−0.651202
$809$	13.8316	+	23.9570i	0.486293	+	0.842285i	0.999876	−	0.0157553i	$-0.00501528\pi$
$809$	13.8316	+	23.9570i	0.486293	+	0.842285i	−0.513582	+	0.858040i	$0.671682\pi$
$810$		0			0
$811$	−34.0746			−1.19652			−0.598261	−	0.801301i	$-0.704141\pi$
$811$	−34.0746			−1.19652			−0.598261	+	0.801301i	$0.704141\pi$
$812$	42.6234	−	5.24104i	1.49579	−	0.183924i
$813$		0			0
$814$	−6.07779			−0.213026
$815$	13.6690	−	23.6753i	0.478803	−	0.829311i
$816$		0			0
$817$	−3.80120	−	6.58387i	−0.132987	−	0.230340i
$818$	4.48430			0.156790
$819$		0			0
$820$	−18.0950			−0.631905
$821$	3.63723	+	6.29987i	0.126940	+	0.219867i	0.922490	−	0.386022i	$-0.126151\pi$
$821$	3.63723	+	6.29987i	0.126940	+	0.219867i	−0.795549	+	0.605889i	$0.792818\pi$
$822$		0			0
$823$	2.83101	−	4.90345i	0.0986828	−	0.170924i	−0.812457	−	0.583021i	$-0.801870\pi$
$823$	2.83101	−	4.90345i	0.0986828	−	0.170924i	0.911140	+	0.412098i	$0.135204\pi$
$824$	−28.4396			−0.990739
$825$		0			0
$826$	5.01733	−	11.8258i	0.174575	−	0.411472i
$827$	−35.3143			−1.22800			−0.614000	−	0.789306i	$-0.710440\pi$
$827$	−35.3143			−1.22800			−0.614000	+	0.789306i	$0.710440\pi$
$828$		0			0
$829$	−14.8684	−	25.7529i	−0.516402	−	0.894434i	−0.999819	−	0.0190438i	$-0.993938\pi$
$829$	−14.8684	−	25.7529i	−0.516402	−	0.894434i	0.483417	−	0.875390i	$-0.339396\pi$
$830$	−4.18705			−0.145335
$831$		0			0
$832$	4.51683	+	7.82338i	0.156593	+	0.271227i
$833$	14.5196	−	50.7026i	0.503074	−	1.75674i
$834$		0			0
$835$	7.37529	+	12.7744i	0.255232	+	0.442075i
$836$	−5.86879	−	10.1650i	−0.202976	−	0.351565i
$837$		0			0
$838$	−3.35915	+	5.81822i	−0.116040	+	0.200987i
$839$	2.62529	−	4.54714i	0.0906351	−	0.156985i	−0.817143	−	0.576434i	$-0.804444\pi$
$839$	2.62529	−	4.54714i	0.0906351	−	0.156985i	0.907779	+	0.419450i	$0.137777\pi$
$840$		0			0
$841$	−23.5364	−	40.7662i	−0.811600	−	1.40573i
$842$	6.43428			0.221740
$843$		0			0
$844$	−36.9478			−1.27180
$845$	6.77792	−	11.7397i	0.233168	−	0.403858i
$846$		0			0
$847$	−3.27185	+	7.71173i	−0.112422	+	0.264978i
$848$	1.32645	−	2.29748i	0.0455506	−	0.0788959i
$849$		0			0
$850$	4.18497	−	7.24858i	0.143543	−	0.248624i
$851$	1.10843	−	1.91986i	0.0379966	−	0.0658121i
$852$		0			0
$853$	−11.2458	+	19.4782i	−0.385048	+	0.666922i	−0.991776	−	0.127987i	$-0.959148\pi$
$853$	−11.2458	+	19.4782i	−0.385048	+	0.666922i	0.606728	+	0.794910i	$0.292482\pi$
$854$	−6.11840	−	8.11645i	−0.209367	−	0.277739i
$855$		0			0
$856$	−5.20440	+	9.01429i	−0.177883	+	0.308102i
$857$	55.2956			1.88886			0.944432	−	0.328708i	$-0.106613\pi$
$857$	55.2956			1.88886			0.944432	+	0.328708i	$0.106613\pi$
$858$		0			0
$859$	51.2704			1.74932			0.874662	−	0.484734i	$-0.161083\pi$
$859$	51.2704			1.74932			0.874662	+	0.484734i	$0.161083\pi$
$860$	−6.00044	−	10.3931i	−0.204613	−	0.354401i
$861$		0			0
$862$	1.59715	−	2.76635i	0.0543992	−	0.0942221i
$863$	−14.5908	+	25.2719i	−0.496675	+	0.860267i	−0.999993	−	0.00383494i	$-0.998779\pi$
$863$	−14.5908	+	25.2719i	−0.496675	+	0.860267i	0.503317	+	0.864102i	$0.332113\pi$
$864$		0			0
$865$	9.39576	+	16.2739i	0.319466	+	0.553330i
$866$	0.296359	+	0.513308i	0.0100707	+	0.0174429i
$867$		0			0
$868$	14.3347	−	1.76262i	0.486552	−	0.0598272i
$869$	−0.497396	−	0.861516i	−0.0168730	−	0.0292249i
$870$		0			0
$871$	12.1267			0.410896
$872$	−7.03091	−	12.1779i	−0.238097	−	0.412396i
$873$		0			0
$874$	−0.319806			−0.0108176
$875$	11.7207	−	27.6256i	0.396231	−	0.933914i
$876$		0			0
$877$	17.9605			0.606484			0.303242	−	0.952914i	$-0.401931\pi$
$877$	17.9605			0.606484			0.303242	+	0.952914i	$0.401931\pi$
$878$	4.18400	−	7.24690i	0.141203	−	0.244571i
$879$		0			0
$880$	−8.52053	−	14.7580i	−0.287227	−	0.497492i
$881$	45.7619			1.54176			0.770880	−	0.636981i	$-0.219817\pi$
$881$	45.7619			1.54176			0.770880	+	0.636981i	$0.219817\pi$
$882$		0			0
$883$	40.8060			1.37323			0.686615	−	0.727021i	$-0.259096\pi$
$883$	40.8060			1.37323			0.686615	+	0.727021i	$0.259096\pi$
$884$	−13.0468	−	22.5977i	−0.438811	−	0.760042i
$885$		0			0
$886$	−4.53399	+	7.85310i	−0.152322	+	0.263830i
$887$	−38.8683			−1.30507			−0.652535	−	0.757759i	$-0.726294\pi$
$887$	−38.8683			−1.30507			−0.652535	+	0.757759i	$0.726294\pi$
$888$		0			0
$889$	16.7109	−	39.3875i	0.560465	−	1.32101i
$890$	0.422200			0.0141522
$891$		0			0
$892$	14.9549	+	25.9026i	0.500726	+	0.867283i
$893$	12.4668			0.417185
$894$		0			0
$895$	8.16962	+	14.1502i	0.273080	+	0.472989i
$896$	26.1108	−	3.21063i	0.872301	−	0.107259i
$897$		0			0
$898$	2.40515	+	4.16585i	0.0802610	+	0.139016i
$899$	−12.7921	−	22.1565i	−0.426639	−	0.738960i
$900$		0			0
$901$	−3.13759	+	5.43447i	−0.104528	+	0.181048i
$902$	4.79971	−	8.31334i	0.159813	−	0.276804i
$903$		0			0
$904$	−12.1694	−	21.0780i	−0.404748	−	0.701045i
$905$	−19.4794			−0.647516
$906$		0			0
$907$	−28.0570			−0.931617			−0.465809	−	0.884886i	$-0.654236\pi$
$907$	−28.0570			−0.931617			−0.465809	+	0.884886i	$0.654236\pi$
$908$	0.798126	−	1.38239i	0.0264867	−	0.0458764i
$909$		0			0
$910$	1.57077	+	2.08372i	0.0520704	+	0.0690747i
$911$	6.19194	−	10.7248i	0.205148	−	0.355327i	−0.745032	−	0.667029i	$-0.767566\pi$
$911$	6.19194	−	10.7248i	0.205148	−	0.355327i	0.950180	+	0.311702i	$0.100899\pi$
$912$		0			0
$913$	−14.8679	+	25.7520i	−0.492056	+	0.852266i
$914$	0.221426	−	0.383520i	0.00732411	−	0.0126857i
$915$		0			0
$916$	5.35577	−	9.27647i	0.176960	−	0.306503i
$917$	−14.0759	+	33.1767i	−0.464826	+	1.09559i
$918$		0			0
$919$	27.3029	−	47.2901i	0.900641	−	1.55996i	0.0739762	−	0.997260i	$-0.476431\pi$
$919$	27.3029	−	47.2901i	0.900641	−	1.55996i	0.826664	−	0.562695i	$-0.190236\pi$
$920$	−1.04738			−0.0345311
$921$		0			0
$922$	−6.02794			−0.198520
$923$	3.83227	+	6.63769i	0.126141	+	0.218482i
$924$		0			0
$925$	6.45217	−	11.1755i	0.212146	−	0.367448i
$926$	−0.0990144	+	0.171498i	−0.00325381	+	0.00563577i
$927$		0			0
$928$	−17.7348	−	30.7177i	−0.582175	−	1.00836i
$929$	−6.40356	−	11.0913i	−0.210094	−	0.363894i	0.741650	−	0.670787i	$-0.234044\pi$
$929$	−6.40356	−	11.0913i	−0.210094	−	0.363894i	−0.951744	+	0.306894i	$0.900710\pi$
$930$		0			0
$931$	−11.3808	+	2.84176i	−0.372990	+	0.0931350i
$932$	6.87504	+	11.9079i	0.225199	+	0.390057i
$933$		0			0
$934$	8.00824			0.262037
$935$	20.1545	+	34.9086i	0.659121	+	1.14163i
$936$		0			0
$937$	37.9601			1.24010			0.620051	−	0.784562i	$-0.287112\pi$
$937$	37.9601			1.24010			0.620051	+	0.784562i	$0.287112\pi$
$938$	2.51059	−	5.91744i	0.0819736	−	0.193211i
$939$		0			0
$940$	19.6796			0.641879
$941$	9.13487	−	15.8221i	0.297788	−	0.515784i	−0.677841	−	0.735208i	$-0.737084\pi$
$941$	9.13487	−	15.8221i	0.297788	−	0.515784i	0.975630	+	0.219424i	$0.0704177\pi$
$942$		0			0
$943$	1.75069	+	3.03228i	0.0570103	+	0.0987447i
$944$	41.4798			1.35005
$945$		0			0
$946$	6.36648			0.206992
$947$	20.7760	+	35.9850i	0.675128	+	1.16936i	0.976431	+	0.215828i	$0.0692451\pi$
$947$	20.7760	+	35.9850i	0.675128	+	1.16936i	−0.301303	+	0.953528i	$0.597422\pi$
$948$		0			0
$949$	−5.29892	+	9.17799i	−0.172010	+	0.297930i
$950$	−1.86159			−0.0603978
$951$		0			0
$952$	−28.4816	+	3.50214i	−0.923094	+	0.113505i
$953$	26.0298			0.843186			0.421593	−	0.906785i	$-0.361471\pi$
$953$	26.0298			0.843186			0.421593	+	0.906785i	$0.361471\pi$
$954$		0			0
$955$	5.50332	+	9.53203i	0.178083	+	0.308449i
$956$	−25.6835			−0.830665
$957$		0			0
$958$	−5.28563	−	9.15498i	−0.170771	−	0.295784i
$959$	−6.72905	+	15.8603i	−0.217292	+	0.512157i
$960$		0			0
$961$	11.1979	+	19.3953i	0.361222	+	0.625655i
$962$	1.50256	+	2.60251i	0.0484444	+	0.0839082i
$963$		0			0
$964$	−18.3827	+	31.8397i	−0.592066	+	1.02549i
$965$	−11.2436	+	19.4744i	−0.361943	+	0.626904i
$966$		0			0
$967$	7.32535	+	12.6879i	0.235567	+	0.408015i	0.959437	−	0.281922i	$-0.0909718\pi$
$967$	7.32535	+	12.6879i	0.235567	+	0.408015i	−0.723870	+	0.689936i	$0.757638\pi$
$968$	4.55797			0.146499
$969$		0			0
$970$	6.82608			0.219172
$971$	−19.5007	+	33.7762i	−0.625808	+	1.08393i	0.362576	+	0.931954i	$0.381897\pi$
$971$	−19.5007	+	33.7762i	−0.625808	+	1.08393i	−0.988384	+	0.151977i	$0.951436\pi$
$972$		0			0
$973$	−47.0239	+	5.78213i	−1.50752	+	0.185366i
$974$	1.46720	−	2.54126i	0.0470120	−	0.0814271i
$975$		0			0
$976$	16.4100	−	28.4230i	0.525272	−	0.909797i
$977$	−9.55342	+	16.5470i	−0.305641	+	0.529386i	−0.977404	−	0.211380i	$-0.932204\pi$
$977$	−9.55342	+	16.5470i	−0.305641	+	0.529386i	0.671763	+	0.740766i	$0.265537\pi$
$978$		0			0
$979$	1.49920	−	2.59669i	0.0479147	−	0.0829907i
$980$	−17.9653	+	4.48591i	−0.573881	+	0.143297i
$981$		0			0
$982$	−5.27918	+	9.14381i	−0.168465	+	0.291791i
$983$	12.8877			0.411055			0.205527	−	0.978651i	$-0.434109\pi$
$983$	12.8877			0.411055			0.205527	+	0.978651i	$0.434109\pi$
$984$		0			0
$985$	−5.18776			−0.165296
$986$	12.2507	+	21.2188i	0.390141	+	0.675745i
$987$		0			0
$988$	−2.90178	+	5.02602i	−0.0923178	+	0.159899i
$989$	−1.16108	+	2.01106i	−0.0369203	+	0.0639479i
$990$		0			0
$991$	1.48644	+	2.57459i	0.0472184	+	0.0817846i	0.888669	−	0.458550i	$-0.151631\pi$
$991$	1.48644	+	2.57459i	0.0472184	+	0.0817846i	−0.841450	+	0.540335i	$0.818298\pi$
$992$	−5.96442	−	10.3307i	−0.189371	−	0.327999i
$993$		0			0
$994$	4.03239	−	0.495828i	0.127900	−	0.0157267i
$995$	14.7235	+	25.5018i	0.466766	+	0.808462i
$996$		0			0
$997$	13.6689			0.432898			0.216449	−	0.976294i	$-0.430553\pi$
$997$	13.6689			0.432898			0.216449	+	0.976294i	$0.430553\pi$
$998$	1.27548	+	2.20920i	0.0403746	+	0.0699309i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.g.j.541.3		8
3.2	odd	2		567.2.g.k.541.2		8
7.4	even	3		567.2.h.k.298.2		8
9.2	odd	6		567.2.e.d.163.2	yes	8
9.4	even	3		567.2.h.k.352.2		8
9.5	odd	6		567.2.h.j.352.3		8
9.7	even	3		567.2.e.c.163.3	✓	8
21.11	odd	6		567.2.h.j.298.3		8
63.2	odd	6		3969.2.a.s.1.3		4
63.4	even	3	inner	567.2.g.j.109.3		8
63.11	odd	6		567.2.e.d.487.2	yes	8
63.16	even	3		3969.2.a.x.1.2		4
63.25	even	3		567.2.e.c.487.3	yes	8
63.32	odd	6		567.2.g.k.109.2		8
63.47	even	6		3969.2.a.t.1.3		4
63.61	odd	6		3969.2.a.w.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.3	✓	8	9.7	even	3
567.2.e.c.487.3	yes	8	63.25	even	3
567.2.e.d.163.2	yes	8	9.2	odd	6
567.2.e.d.487.2	yes	8	63.11	odd	6
567.2.g.j.109.3		8	63.4	even	3	inner
567.2.g.j.541.3		8	1.1	even	1	trivial
567.2.g.k.109.2		8	63.32	odd	6
567.2.g.k.541.2		8	3.2	odd	2
567.2.h.j.298.3		8	21.11	odd	6
567.2.h.j.352.3		8	9.5	odd	6
567.2.h.k.298.2		8	7.4	even	3
567.2.h.k.352.2		8	9.4	even	3
3969.2.a.s.1.3		4	63.2	odd	6
3969.2.a.t.1.3		4	63.47	even	6
3969.2.a.w.1.2		4	63.61	odd	6
3969.2.a.x.1.2		4	63.16	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)

\(f(q)\)	\(=\)	\(q+(0.186423 + 0.322894i) q^{2} +(0.930493 - 1.61166i) q^{4} +1.42143 q^{5} +(-1.03335 + 2.43561i) q^{7} +1.43955 q^{8} +(0.264988 + 0.458972i) q^{10} +3.76381 q^{11} +(-0.930493 - 1.61166i) q^{13} +(-0.979083 + 0.120389i) q^{14} +(-1.59262 - 2.75850i) q^{16} +(3.76718 + 6.52496i) q^{17} +(0.837872 - 1.45124i) q^{19} +(1.32264 - 2.29087i) q^{20} +(0.701659 + 1.21531i) q^{22} -0.511859 q^{23} -2.97952 q^{25} +(0.346930 - 0.600901i) q^{26} +(2.96385 + 3.93173i) q^{28} +(4.36099 - 7.55345i) q^{29} +(1.46665 - 2.54031i) q^{31} +(2.03335 - 3.52187i) q^{32} +(-1.40458 + 2.43280i) q^{34} +(-1.46884 + 3.46206i) q^{35} +(-2.16551 + 3.75077i) q^{37} +0.624794 q^{38} +2.04623 q^{40} +(-3.42025 - 5.92405i) q^{41} +(2.26837 - 3.92892i) q^{43} +(3.50220 - 6.06598i) q^{44} +(-0.0954222 - 0.165276i) q^{46} +(3.71978 + 6.44284i) q^{47} +(-4.86436 - 5.03368i) q^{49} +(-0.555451 - 0.962069i) q^{50} -3.46327 q^{52} +(0.416437 + 0.721290i) q^{53} +5.35001 q^{55} +(-1.48756 + 3.50618i) q^{56} +3.25195 q^{58} +(-6.51126 + 11.2778i) q^{59} +(5.15189 + 8.92333i) q^{61} +1.09367 q^{62} -4.85423 q^{64} +(-1.32264 - 2.29087i) q^{65} +(-3.25813 + 5.64324i) q^{67} +14.0214 q^{68} +(-1.39170 + 0.171126i) q^{70} -4.11854 q^{71} +(-2.84737 - 4.93179i) q^{73} -1.61480 q^{74} +(-1.55927 - 2.70073i) q^{76} +(-3.88934 + 9.16716i) q^{77} +(-0.132152 - 0.228895i) q^{79} +(-2.26381 - 3.92103i) q^{80} +(1.27523 - 2.20876i) q^{82} +(-3.95023 + 6.84200i) q^{83} +(5.35481 + 9.27480i) q^{85} +1.69150 q^{86} +5.41819 q^{88} +(0.398321 - 0.689912i) q^{89} +(4.88690 - 0.600901i) q^{91} +(-0.476282 + 0.824944i) q^{92} +(-1.38690 + 2.40218i) q^{94} +(1.19098 - 2.06284i) q^{95} +(6.43999 - 11.1544i) q^{97} +(0.718516 - 2.50907i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} - 5 q^{4} + 4 q^{5} - 2 q^{7} - 6 q^{8} + 7 q^{10} + 10 q^{11} + 5 q^{13} + 7 q^{14} + q^{16} - 6 q^{17} + 8 q^{19} + 8 q^{20} + 7 q^{22} - 24 q^{23} + 16 q^{25} - q^{26} + 5 q^{28} + 10 q^{29}+ \cdots + 11 q^{98}+O(q^{100}) \) 8 * q - q^2 - 5 * q^4 + 4 * q^5 - 2 * q^7 - 6 * q^8 + 7 * q^10 + 10 * q^11 + 5 * q^13 + 7 * q^14 + q^16 - 6 * q^17 + 8 * q^19 + 8 * q^20 + 7 * q^22 - 24 * q^23 + 16 * q^25 - q^26 + 5 * q^28 + 10 * q^29 + 18 * q^31 + 10 * q^32 + 23 * q^35 - 40 * q^38 - 36 * q^40 + 5 * q^41 + 7 * q^43 - 13 * q^44 - 12 * q^46 + 21 * q^47 + 2 * q^49 - 38 * q^50 - 50 * q^52 + 12 * q^53 - 52 * q^55 - 33 * q^56 - 14 * q^58 - 6 * q^59 + 20 * q^61 + 36 * q^62 - 46 * q^64 - 8 * q^65 + 5 * q^67 + 102 * q^68 - 46 * q^70 - 18 * q^71 + 6 * q^73 - 5 * q^76 - 16 * q^77 + 10 * q^79 + 2 * q^80 + 35 * q^82 - 9 * q^83 + 9 * q^85 - 44 * q^86 + 36 * q^88 + 22 * q^89 + 13 * q^91 + 36 * q^92 + 15 * q^94 + 16 * q^95 + 9 * q^97 + 11 * q^98

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