LMFDB - Embedded newform 567.2.g.j.109.3

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			109.3
Root			$2.11692 - 0.978886i$ of defining polynomial
Character	$\chi$	$=$	567.109
Dual form			567.2.g.j.541.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.186423 - 0.322894i) q^{2} +(0.930493 + 1.61166i) q^{4} +1.42143 q^{5} +(-1.03335 - 2.43561i) q^{7} +1.43955 q^{8} +(0.264988 - 0.458972i) q^{10} +3.76381 q^{11} +(-0.930493 + 1.61166i) q^{13} +(-0.979083 - 0.120389i) q^{14} +(-1.59262 + 2.75850i) q^{16} +(3.76718 - 6.52496i) q^{17} +(0.837872 + 1.45124i) q^{19} +(1.32264 + 2.29087i) q^{20} +(0.701659 - 1.21531i) q^{22} -0.511859 q^{23} -2.97952 q^{25} +(0.346930 + 0.600901i) q^{26} +(2.96385 - 3.93173i) q^{28} +(4.36099 + 7.55345i) q^{29} +(1.46665 + 2.54031i) q^{31} +(2.03335 + 3.52187i) q^{32} +(-1.40458 - 2.43280i) q^{34} +(-1.46884 - 3.46206i) q^{35} +(-2.16551 - 3.75077i) q^{37} +0.624794 q^{38} +2.04623 q^{40} +(-3.42025 + 5.92405i) q^{41} +(2.26837 + 3.92892i) q^{43} +(3.50220 + 6.06598i) q^{44} +(-0.0954222 + 0.165276i) q^{46} +(3.71978 - 6.44284i) q^{47} +(-4.86436 + 5.03368i) q^{49} +(-0.555451 + 0.962069i) q^{50} -3.46327 q^{52} +(0.416437 - 0.721290i) q^{53} +5.35001 q^{55} +(-1.48756 - 3.50618i) q^{56} +3.25195 q^{58} +(-6.51126 - 11.2778i) q^{59} +(5.15189 - 8.92333i) q^{61} +1.09367 q^{62} -4.85423 q^{64} +(-1.32264 + 2.29087i) q^{65} +(-3.25813 - 5.64324i) q^{67} +14.0214 q^{68} +(-1.39170 - 0.171126i) q^{70} -4.11854 q^{71} +(-2.84737 + 4.93179i) q^{73} -1.61480 q^{74} +(-1.55927 + 2.70073i) q^{76} +(-3.88934 - 9.16716i) q^{77} +(-0.132152 + 0.228895i) q^{79} +(-2.26381 + 3.92103i) q^{80} +(1.27523 + 2.20876i) q^{82} +(-3.95023 - 6.84200i) q^{83} +(5.35481 - 9.27480i) q^{85} +1.69150 q^{86} +5.41819 q^{88} +(0.398321 + 0.689912i) q^{89} +(4.88690 + 0.600901i) q^{91} +(-0.476282 - 0.824944i) q^{92} +(-1.38690 - 2.40218i) q^{94} +(1.19098 + 2.06284i) q^{95} +(6.43999 + 11.1544i) q^{97} +(0.718516 + 2.50907i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.186423	−	0.322894i	0.131821	−	0.228320i	−0.792558	−	0.609797i	$-0.791251\pi$
$2$	0.186423	−	0.322894i	0.131821	−	0.228320i	0.924378	+	0.381477i	$0.124584\pi$
$3$		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	−0.965725	−	0.259566i	$-0.916421\pi$
$13$	−0.930493	+	1.61166i	−0.258072	+	0.446994i	0.707653	+	0.706560i	$0.249754\pi$
$14$	−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	0.104849	−	0.994488i	$-0.466564\pi$
$17$	3.76718	−	6.52496i	0.913676	−	1.58253i	0.808828	−	0.588046i	$-0.200103\pi$
$18$		0			0
$19$	0.837872	+	1.45124i	0.192221	+	0.332937i	0.945986	−	0.324208i	$-0.105098\pi$
$19$	0.837872	+	1.45124i	0.192221	+	0.332937i	−0.753765	+	0.657144i	$0.771764\pi$
$20$	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	0.912992	+	0.407977i	$0.133766\pi$
$29$	4.36099	+	7.55345i	0.809815	+	1.40264i	−0.103177	+	0.994663i	$0.532901\pi$
$30$		0			0
$31$	1.46665	+	2.54031i	0.263418	+	0.456253i	0.967148	−	0.254215i	$-0.0818170\pi$
$31$	1.46665	+	2.54031i	0.263418	+	0.456253i	−0.703730	+	0.710467i	$0.748484\pi$
$32$	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	0.631283	−	0.775553i	$-0.282529\pi$
$37$	−2.16551	−	3.75077i	−0.356007	−	0.616622i	−0.987290	+	0.158931i	$0.949195\pi$
$38$	0.624794			0.101355
$39$		0			0
$40$	2.04623			0.323537
$41$	−3.42025	+	5.92405i	−0.534154	+	0.925182i	0.465050	+	0.885285i	$0.346036\pi$
$41$	−3.42025	+	5.92405i	−0.534154	+	0.925182i	−0.999204	+	0.0398973i	$0.987297\pi$
$42$		0			0
$43$	2.26837	+	3.92892i	0.345922	+	0.599155i	0.985521	−	0.169554i	$-0.0542327\pi$
$43$	2.26837	+	3.92892i	0.345922	+	0.599155i	−0.639598	+	0.768709i	$0.720899\pi$
$44$	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	−0.456170	−	0.889893i	$-0.650779\pi$
$47$	3.71978	−	6.44284i	0.542585	−	0.939785i	0.998755	−	0.0498920i	$-0.0158877\pi$
$48$		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	−0.836006	−	0.548720i	$-0.815115\pi$
$53$	0.416437	−	0.721290i	0.0572020	−	0.0990768i	0.893208	+	0.449643i	$0.148449\pi$
$54$		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	−0.883262	−	0.468880i	$-0.844658\pi$
$59$	−6.51126	−	11.2778i	−0.847693	−	1.46825i	0.0355684	−	0.999367i	$-0.488676\pi$
$60$		0			0
$61$	5.15189	−	8.92333i	0.659632	−	1.14252i	−0.321079	−	0.947052i	$-0.604046\pi$
$61$	5.15189	−	8.92333i	0.659632	−	1.14252i	0.980711	−	0.195463i	$-0.0626211\pi$
$62$	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	0.595441	−	0.803399i	$-0.296977\pi$
$67$	−3.25813	−	5.64324i	−0.398043	−	0.689432i	−0.993484	+	0.113967i	$0.963644\pi$
$68$	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	−0.983149	−	0.182806i	$-0.941482\pi$
$73$	−2.84737	+	4.93179i	−0.333259	+	0.577222i	0.649889	+	0.760029i	$0.274815\pi$
$74$	−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	−0.873364	−	0.487068i	$-0.838066\pi$
$79$	−0.132152	+	0.228895i	−0.0148683	+	0.0257527i	0.858496	+	0.512821i	$0.171400\pi$
$80$	−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	0.563586	−	0.826058i	$-0.309421\pi$
$83$	−3.95023	−	6.84200i	−0.433594	−	0.751007i	−0.997180	+	0.0750507i	$0.976088\pi$
$84$		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	0.886364	−	0.462989i	$-0.153223\pi$
$89$	0.398321	+	0.689912i	0.0422219	+	0.0731305i	−0.844142	+	0.536119i	$0.819890\pi$
$90$		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	0.982173	+	0.187980i	$0.0601941\pi$
$97$	6.43999	+	11.1544i	0.653882	+	1.13256i	−0.328291	+	0.944577i	$0.606473\pi$
$98$	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	0.636658	−	0.771147i	$-0.280316\pi$
$107$	−3.61530	−	6.26188i	−0.349504	−	0.605358i	−0.986161	+	0.165788i	$0.946983\pi$
$108$		0			0
$109$	−4.88410	+	8.45951i	−0.467812	+	0.810274i	−0.999323	−	0.0367769i	$-0.988291\pi$
$109$	−4.88410	+	8.45951i	−0.467812	+	0.810274i	0.531512	+	0.847051i	$0.321624\pi$
$110$	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	0.127433	+	0.991847i	$0.459326\pi$
$113$	−8.45361	+	14.6421i	−0.795248	+	1.37741i	−0.922681	+	0.385564i	$0.874007\pi$
$114$		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	−0.183704	−	0.982982i	$-0.558809\pi$
$139$	8.95361	−	15.5081i	0.759435	−	1.31538i	0.943139	−	0.332399i	$-0.107858\pi$
$140$	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	0.966030	−	0.258428i	$-0.0832046\pi$
$157$	3.24789	+	5.62551i	0.259210	+	0.448964i	−0.706821	+	0.707393i	$0.749871\pi$
$158$	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	0.946260	+	0.323406i	$0.104828\pi$
$163$	9.61631	+	16.6559i	0.753208	+	1.30459i	−0.193053	+	0.981188i	$0.561839\pi$
$164$	−12.7301			−0.994053
$165$		0			0
$166$	−2.94565			−0.228627
$167$	5.18862	−	8.98695i	0.401507	−	0.695431i	−0.592401	−	0.805644i	$-0.701820\pi$
$167$	5.18862	−	8.98695i	0.401507	−	0.695431i	0.993908	+	0.110212i	$0.0351531\pi$
$168$		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	−0.497443	−	0.867497i	$-0.665727\pi$
$173$	6.61005	−	11.4490i	0.502553	−	0.870448i	0.999996	−	0.00295062i	$-0.000939214\pi$
$174$		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	−0.567252	−	0.823544i	$-0.691993\pi$
$179$	5.74745	−	9.95487i	0.429584	−	0.744062i	0.996836	+	0.0794823i	$0.0253267\pi$
$180$		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	−0.691276	−	0.722591i	$-0.742951\pi$
$191$	3.87167	−	6.70592i	0.280144	−	0.485223i	0.971420	+	0.237367i	$0.0762845\pi$
$192$		0			0
$193$	−7.91002	−	13.7005i	−0.569375	−	0.986187i	−0.996628	−	0.0820547i	$-0.973852\pi$
$193$	−7.91002	−	13.7005i	−0.569375	−	0.986187i	0.427252	−	0.904132i	$-0.359482\pi$
$194$	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	−0.220770	−	0.975326i	$-0.570857\pi$
$199$	10.3582	−	17.9409i	0.734272	−	1.27180i	0.955042	−	0.296471i	$-0.0958098\pi$
$200$	−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	0.290537	+	0.956864i	$0.406166\pi$
$211$	−9.92695	+	17.1940i	−0.683400	+	1.18368i	−0.973937	+	0.226819i	$0.927167\pi$
$212$	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	−0.999005	−	0.0446029i	$-0.985798\pi$
$223$	−8.03599	−	13.9187i	−0.538130	−	0.932068i	0.460875	−	0.887465i	$-0.347536\pi$
$224$	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	0.719268	−	0.694732i	$-0.244477\pi$
$233$	−3.69430	−	6.39872i	−0.242022	−	0.419194i	−0.961290	+	0.275539i	$0.911144\pi$
$234$		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	−0.998146	−	0.0608706i	$-0.980612\pi$
$239$	−6.90052	+	11.9520i	−0.446357	+	0.773114i	0.551788	+	0.833984i	$0.313946\pi$
$240$		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	−0.750042	−	0.661390i	$-0.769967\pi$
$269$	3.24349	−	5.61790i	0.197759	−	0.342529i	0.947802	+	0.318861i	$0.103300\pi$
$270$		0			0
$271$	9.11980	+	15.7959i	0.553988	+	0.959536i	0.997981	+	0.0635055i	$0.0202280\pi$
$271$	9.11980	+	15.7959i	0.553988	+	0.959536i	−0.443993	+	0.896030i	$0.646439\pi$
$272$	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	0.879934	+	0.475095i	$0.157586\pi$
$281$	14.2723	+	24.7203i	0.851412	+	1.47469i	−0.0285227	+	0.999593i	$0.509080\pi$
$282$		0			0
$283$	4.77043	+	8.26262i	0.283572	+	0.491162i	0.972262	−	0.233895i	$-0.0751470\pi$
$283$	4.77043	+	8.26262i	0.283572	+	0.491162i	−0.688690	+	0.725056i	$0.741814\pi$
$284$	−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	−0.989401	−	0.145209i	$-0.953615\pi$
$293$	−6.31533	+	10.9385i	−0.368946	+	0.639033i	0.620455	+	0.784242i	$0.286948\pi$
$294$		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	0.925587	−	0.378534i	$-0.123572\pi$
$311$	2.38028	+	4.12277i	0.134973	+	0.233781i	−0.790614	+	0.612315i	$0.790238\pi$
$312$		0			0
$313$	−3.60550	+	6.24490i	−0.203795	+	0.352983i	−0.949748	−	0.313015i	$-0.898661\pi$
$313$	−3.60550	+	6.24490i	−0.203795	+	0.352983i	0.745953	+	0.665998i	$0.231994\pi$
$314$	2.42192			0.136677
$315$		0			0
$316$	−0.491868			−0.0276697
$317$	−3.64459	+	6.31261i	−0.204700	+	0.354552i	−0.950037	−	0.312137i	$-0.898955\pi$
$317$	−3.64459	+	6.31261i	−0.204700	+	0.354552i	0.745337	+	0.666688i	$0.232289\pi$
$318$		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	−0.848787	−	0.528735i	$-0.822667\pi$
$331$	0.609557	−	1.05578i	0.0335043	−	0.0580311i	0.882291	+	0.470704i	$0.156000\pi$
$332$	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	−0.588253	−	0.808677i	$-0.700184\pi$
$337$	7.45698	−	12.9159i	0.406208	−	0.703573i	0.994461	+	0.105104i	$0.0335176\pi$
$338$	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	0.926912	−	0.375278i	$-0.122453\pi$
$347$	2.57914	+	4.46720i	0.138456	+	0.239812i	−0.788457	+	0.615090i	$0.789120\pi$
$348$		0			0
$349$	12.2253	+	21.1749i	0.654408	+	1.13347i	0.982042	+	0.188663i	$0.0604154\pi$
$349$	12.2253	+	21.1749i	0.654408	+	1.13347i	−0.327634	+	0.944805i	$0.606251\pi$
$350$	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	0.892972	−	0.450111i	$-0.148616\pi$
$359$	1.07390	+	1.86005i	0.0566783	+	0.0981697i	−0.836294	+	0.548281i	$0.815282\pi$
$360$		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	0.935397	−	0.353598i	$-0.115042\pi$
$397$	3.21734	+	5.57259i	0.161473	+	0.279680i	−0.773924	+	0.633279i	$0.781709\pi$
$398$	−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	0.975530	−	0.219867i	$-0.0705625\pi$
$409$	6.01362	+	10.4159i	0.297354	+	0.515033i	−0.678176	+	0.734900i	$0.737229\pi$
$410$	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	−0.557557	−	0.830139i	$-0.688261\pi$
$419$	9.00950	−	15.6049i	0.440143	−	0.762350i	0.997700	+	0.0677891i	$0.0215945\pi$
$420$		0			0
$421$	8.62861	+	14.9452i	0.420533	+	0.728384i	0.995992	−	0.0894466i	$-0.0285098\pi$
$421$	8.62861	+	14.9452i	0.420533	+	0.728384i	−0.575459	+	0.817831i	$0.695177\pi$
$422$	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	−0.950558	−	0.310547i	$-0.899488\pi$
$431$	−4.28368	+	7.41955i	−0.206338	+	0.357387i	0.744220	+	0.667934i	$0.232821\pi$
$432$		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	0.463547	+	0.886072i	$0.346577\pi$
$439$	−11.2218	+	19.4367i	−0.535588	+	0.927665i	−0.999135	+	0.0415927i	$0.986757\pi$
$440$	7.70161			0.367160
$441$		0			0
$442$	5.22780			0.248661
$443$	12.1605	−	21.0626i	0.577763	−	1.00072i	−0.417972	−	0.908460i	$-0.637259\pi$
$443$	12.1605	−	21.0626i	0.577763	−	1.00072i	0.995735	−	0.0922553i	$-0.0294076\pi$
$444$		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	−0.879581	−	0.475748i	$-0.842177\pi$
$457$	−0.593880	+	1.02863i	−0.0277806	+	0.0481173i	0.851801	+	0.523866i	$0.175511\pi$
$458$	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	0.614054	−	0.789264i	$-0.289538\pi$
$461$	−8.08370	−	14.0014i	−0.376495	−	0.652109i	−0.990550	+	0.137155i	$0.956204\pi$
$462$		0			0
$463$	0.265564	−	0.459970i	0.0123418	−	0.0213766i	−0.859789	−	0.510650i	$-0.829405\pi$
$463$	0.265564	−	0.459970i	0.0123418	−	0.0213766i	0.872130	+	0.489274i	$0.162738\pi$
$464$	−27.7816			−1.28973
$465$		0			0
$466$	−2.75481			−0.127614
$467$	10.7393	+	18.6011i	0.496958	+	0.860756i	0.999994	−	0.00350930i	$-0.00111705\pi$
$467$	10.7393	+	18.6011i	0.496958	+	0.860756i	−0.503036	+	0.864265i	$0.667784\pi$
$468$		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	−0.941304	−	0.337559i	$-0.890399\pi$
$487$	−3.93513	+	6.81584i	−0.178318	+	0.308855i	0.762987	+	0.646414i	$0.223732\pi$
$488$	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	−0.346660	−	0.937991i	$-0.612684\pi$
$491$	14.1592	−	24.5244i	0.638994	−	1.10677i	0.985654	−	0.168779i	$-0.0539825\pi$
$492$		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	−0.658121	−	0.752912i	$-0.728649\pi$
$521$	7.37216	−	12.7690i	0.322980	−	0.559418i	0.981102	+	0.193494i	$0.0619819\pi$
$522$		0			0
$523$	−2.03953	−	3.53257i	−0.0891825	−	0.154469i	0.817983	−	0.575242i	$-0.195092\pi$
$523$	−2.03953	−	3.53257i	−0.0891825	−	0.154469i	−0.907166	+	0.420773i	$0.861759\pi$
$524$	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	0.822275	−	0.569091i	$-0.192705\pi$
$541$	−1.90052	−	3.29179i	−0.0817096	−	0.141525i	−0.903984	+	0.427565i	$0.859371\pi$
$542$	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	0.956019	−	0.293305i	$-0.0947553\pi$
$547$	5.23891	+	9.07406i	0.224000	+	0.387979i	−0.732019	+	0.681284i	$0.761422\pi$
$548$	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	0.210470	+	0.977600i	$0.432501\pi$
$557$	−17.4975	+	30.3065i	−0.741392	+	1.28413i	−0.951862	+	0.306528i	$0.900833\pi$
$558$		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	0.990825	+	0.135153i	$0.0431525\pi$
$563$	14.5322	+	25.1705i	0.612458	+	1.06081i	−0.378367	+	0.925656i	$0.623514\pi$
$564$		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	−0.999052	−	0.0435292i	$-0.986140\pi$
$569$	−11.0163	+	19.0808i	−0.461829	+	0.799911i	0.537224	+	0.843440i	$0.319473\pi$
$570$		0			0
$571$	−1.01413	−	1.75653i	−0.0424402	−	0.0735086i	0.844025	−	0.536304i	$-0.180180\pi$
$571$	−1.01413	−	1.75653i	−0.0424402	−	0.0735086i	−0.886465	+	0.462795i	$0.846847\pi$
$572$	−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	−0.810006	−	0.586421i	$-0.800536\pi$
$577$	2.47060	−	4.27921i	0.102852	−	0.178146i	0.912859	+	0.408275i	$0.133870\pi$
$578$	−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	−0.977713	−	0.209945i	$-0.932672\pi$
$587$	−16.2491	−	28.1443i	−0.670674	−	1.16164i	0.307039	−	0.951697i	$-0.400662\pi$
$588$		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	0.980326	−	0.197384i	$-0.0632445\pi$
$593$	7.77361	+	13.4643i	0.319224	+	0.552912i	−0.661103	+	0.750296i	$0.729911\pi$
$594$		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	0.509867	−	0.860253i	$-0.329695\pi$
$599$	−11.9942	−	20.7745i	−0.490068	−	0.848822i	−0.999935	+	0.0114309i	$0.996361\pi$
$600$		0			0
$601$	0.443533	+	0.768221i	0.0180921	+	0.0313364i	0.874930	−	0.484250i	$-0.160907\pi$
$601$	0.443533	+	0.768221i	0.0180921	+	0.0313364i	−0.856838	+	0.515586i	$0.827574\pi$
$602$	−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	−0.751616	−	0.659601i	$-0.770725\pi$
$613$	4.83845	−	8.38044i	0.195423	−	0.338483i	0.947039	+	0.321118i	$0.104059\pi$
$614$	−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	−0.757245	−	0.653131i	$-0.773455\pi$
$617$	4.64513	−	8.04561i	0.187006	−	0.323904i	0.944251	+	0.329227i	$0.106788\pi$
$618$		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	−0.914116	−	0.405453i	$-0.867114\pi$
$643$	−2.68598	+	4.65226i	−0.105925	+	0.183467i	0.808191	+	0.588921i	$0.200447\pi$
$644$	−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	−0.969492	−	0.245124i	$-0.921171\pi$
$647$	−6.93041	+	12.0038i	−0.272463	+	0.471919i	0.697029	+	0.717043i	$0.254505\pi$
$648$		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	0.714180	−	0.699962i	$-0.246800\pi$
$659$	−6.39450	−	11.0756i	−0.249094	−	0.431444i	−0.963275	+	0.268517i	$0.913466\pi$
$660$		0			0
$661$	−20.5502	−	35.5940i	−0.799309	−	1.38444i	−0.920066	−	0.391762i	$-0.871866\pi$
$661$	−20.5502	−	35.5940i	−0.799309	−	1.38444i	0.120757	−	0.992682i	$-0.461468\pi$
$662$	−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	−0.998060	−	0.0622526i	$-0.980172\pi$
$673$	−14.3446	−	24.8455i	−0.552943	−	0.957725i	0.445118	−	0.895472i	$-0.353162\pi$
$674$	−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	−0.209173	+	0.977879i	$0.567077\pi$
$677$	−24.7561	+	42.8788i	−0.951454	+	1.64797i	−0.742281	+	0.670088i	$0.766256\pi$
$678$		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	−0.367201	−	0.930142i	$-0.619684\pi$
$683$	16.2536	−	28.1520i	0.621926	−	1.07721i	0.989127	−	0.147065i	$-0.0469827\pi$
$684$		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	−0.699173	−	0.714953i	$-0.746448\pi$
$691$	7.08644	−	12.2741i	0.269581	−	0.466928i	0.968754	+	0.248025i	$0.0797815\pi$
$692$	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	−0.998931	−	0.0462204i	$-0.985282\pi$
$709$	−12.2335	+	21.1890i	−0.459438	+	0.795769i	0.539494	+	0.841990i	$0.318616\pi$
$710$	−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	0.669385	−	0.742916i	$-0.266558\pi$
$719$	−8.27732	−	14.3367i	−0.308692	−	0.534670i	−0.978076	+	0.208246i	$0.933225\pi$
$720$		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	0.986534	+	0.163556i	$0.0522964\pi$
$727$	17.1191	+	29.6511i	0.634911	+	1.09970i	−0.351623	+	0.936142i	$0.614370\pi$
$728$	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	−0.125557	−	0.992086i	$-0.540072\pi$
$739$	21.6496	−	37.4982i	0.796394	−	1.37939i	0.921950	−	0.387308i	$-0.126595\pi$
$740$	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	−0.558354	−	0.829603i	$-0.688567\pi$
$743$	11.9739	−	20.7394i	0.439281	−	0.760856i	0.997634	+	0.0687469i	$0.0219001\pi$
$744$		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	−0.995035	−	0.0995210i	$-0.968269\pi$
$769$	−11.4065	+	19.7567i	−0.411330	+	0.712445i	0.583705	+	0.811966i	$0.301602\pi$
$770$	−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	−0.805639	−	0.592407i	$-0.798178\pi$
$773$	3.06443	−	5.30775i	0.110220	−	0.190906i	0.915859	+	0.401500i	$0.131511\pi$
$774$		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	0.899520	+	0.436879i	$0.143916\pi$
$787$	23.2314	+	40.2379i	0.828109	+	1.43433i	−0.0714114	+	0.997447i	$0.522750\pi$
$788$	−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	−0.790418	−	0.612568i	$-0.790137\pi$
$797$	3.81939	−	6.61538i	0.135290	−	0.234329i	0.925708	+	0.378239i	$0.123470\pi$
$798$		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	−0.513582	−	0.858040i	$-0.671682\pi$
$809$	13.8316	−	23.9570i	0.486293	−	0.842285i	0.999876	+	0.0157553i	$0.00501528\pi$
$810$		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	−0.795549	−	0.605889i	$-0.792818\pi$
$821$	3.63723	−	6.29987i	0.126940	−	0.219867i	0.922490	+	0.386022i	$0.126151\pi$
$822$		0			0
$823$	2.83101	+	4.90345i	0.0986828	+	0.170924i	0.911140	−	0.412098i	$-0.135204\pi$
$823$	2.83101	+	4.90345i	0.0986828	+	0.170924i	−0.812457	+	0.583021i	$0.801870\pi$
$824$	−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	0.483417	+	0.875390i	$0.339396\pi$
$829$	−14.8684	+	25.7529i	−0.516402	+	0.894434i	−0.999819	+	0.0190438i	$0.993938\pi$
$830$	−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	0.907779	−	0.419450i	$-0.137777\pi$
$839$	2.62529	+	4.54714i	0.0906351	+	0.156985i	−0.817143	+	0.576434i	$0.804444\pi$
$840$		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	0.606728	−	0.794910i	$-0.292482\pi$
$853$	−11.2458	−	19.4782i	−0.385048	−	0.666922i	−0.991776	+	0.127987i	$0.959148\pi$
$854$	−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	0.503317	−	0.864102i	$-0.332113\pi$
$863$	−14.5908	−	25.2719i	−0.496675	−	0.860267i	−0.999993	+	0.00383494i	$0.998779\pi$
$864$		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	0.950180	−	0.311702i	$-0.100899\pi$
$911$	6.19194	+	10.7248i	0.205148	+	0.355327i	−0.745032	+	0.667029i	$0.767566\pi$
$912$		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	0.826664	+	0.562695i	$0.190236\pi$
$919$	27.3029	+	47.2901i	0.900641	+	1.55996i	0.0739762	+	0.997260i	$0.476431\pi$
$920$	−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	−0.951744	−	0.306894i	$-0.900710\pi$
$929$	−6.40356	+	11.0913i	−0.210094	+	0.363894i	0.741650	+	0.670787i	$0.234044\pi$
$930$		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	0.975630	−	0.219424i	$-0.0704177\pi$
$941$	9.13487	+	15.8221i	0.297788	+	0.515784i	−0.677841	+	0.735208i	$0.737084\pi$
$942$		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	−0.301303	−	0.953528i	$-0.597422\pi$
$947$	20.7760	−	35.9850i	0.675128	−	1.16936i	0.976431	−	0.215828i	$-0.0692451\pi$
$948$		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	−0.723870	−	0.689936i	$-0.757638\pi$
$967$	7.32535	−	12.6879i	0.235567	−	0.408015i	0.959437	+	0.281922i	$0.0909718\pi$
$968$	4.55797			0.146499
$969$		0			0
$970$	6.82608			0.219172
$971$	−19.5007	−	33.7762i	−0.625808	−	1.08393i	−0.988384	−	0.151977i	$-0.951436\pi$
$971$	−19.5007	−	33.7762i	−0.625808	−	1.08393i	0.362576	−	0.931954i	$-0.381897\pi$
$972$		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	0.671763	−	0.740766i	$-0.265537\pi$
$977$	−9.55342	−	16.5470i	−0.305641	−	0.529386i	−0.977404	+	0.211380i	$0.932204\pi$
$978$		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	−0.841450	−	0.540335i	$-0.818298\pi$
$991$	1.48644	−	2.57459i	0.0472184	−	0.0817846i	0.888669	+	0.458550i	$0.151631\pi$
$992$	−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.109.3		8
3.2	odd	2		567.2.g.k.109.2		8
7.2	even	3		567.2.h.k.352.2		8
9.2	odd	6		567.2.h.j.298.3		8
9.4	even	3		567.2.e.c.487.3	yes	8
9.5	odd	6		567.2.e.d.487.2	yes	8
9.7	even	3		567.2.h.k.298.2		8
21.2	odd	6		567.2.h.j.352.3		8
63.2	odd	6		567.2.g.k.541.2		8
63.4	even	3		3969.2.a.x.1.2		4
63.16	even	3	inner	567.2.g.j.541.3		8
63.23	odd	6		567.2.e.d.163.2	yes	8
63.31	odd	6		3969.2.a.w.1.2		4
63.32	odd	6		3969.2.a.s.1.3		4
63.58	even	3		567.2.e.c.163.3	✓	8
63.59	even	6		3969.2.a.t.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
567.2.e.c.163.3	✓	8	63.58	even	3
567.2.e.c.487.3	yes	8	9.4	even	3
567.2.e.d.163.2	yes	8	63.23	odd	6
567.2.e.d.487.2	yes	8	9.5	odd	6
567.2.g.j.109.3		8	1.1	even	1	trivial
567.2.g.j.541.3		8	63.16	even	3	inner
567.2.g.k.109.2		8	3.2	odd	2
567.2.g.k.541.2		8	63.2	odd	6
567.2.h.j.298.3		8	9.2	odd	6
567.2.h.j.352.3		8	21.2	odd	6
567.2.h.k.298.2		8	9.7	even	3
567.2.h.k.352.2		8	7.2	even	3
3969.2.a.s.1.3		4	63.32	odd	6
3969.2.a.t.1.3		4	63.59	even	6
3969.2.a.w.1.2		4	63.31	odd	6
3969.2.a.x.1.2		4	63.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

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