LMFDB - Embedded newform 729.2.i.a.685.10

Newspace parameters

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			685.10
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.10

$q$-expansion

$f(q)$	$=$	$q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +O(q^{10})$	\(q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +(2.72264 + 0.645278i) q^{10} +(0.602874 + 4.41382i) q^{11} +(3.10343 - 4.52491i) q^{13} +(-0.825572 - 0.375269i) q^{14} +(-0.546251 - 1.03703i) q^{16} +(-1.67001 + 0.838712i) q^{17} +(0.0797307 + 1.36892i) q^{19} +(2.29394 + 1.26574i) q^{20} +(0.615847 - 4.50880i) q^{22} +(3.01412 - 7.80676i) q^{23} +(2.49528 - 0.193948i) q^{25} +(-4.29366 + 3.60281i) q^{26} +(-0.650480 - 0.545818i) q^{28} +(-6.07359 - 4.34114i) q^{29} +(-3.66393 + 4.19840i) q^{31} +(-1.02526 - 4.73314i) q^{32} +(1.87322 - 0.367888i) q^{34} +(-2.41524 - 0.282301i) q^{35} +(-5.28091 - 7.09349i) q^{37} +(0.296544 - 1.36900i) q^{38} +(-5.90597 - 5.79254i) q^{40} +(0.508525 - 1.97421i) q^{41} +(3.65414 + 3.31596i) q^{43} +(1.68771 - 3.91254i) q^{44} +(-5.10480 + 6.85694i) q^{46} +(-3.30800 - 3.79054i) q^{47} +(-5.91526 - 1.89665i) q^{49} +(-2.50874 - 0.492700i) q^{50} +(-4.77780 + 2.17178i) q^{52} +(1.25461 - 7.11526i) q^{53} +(-2.11890 - 12.0169i) q^{55} +(1.51647 + 2.21106i) q^{56} +(4.78780 + 5.93594i) q^{58} +(0.734578 - 0.300108i) q^{59} +(5.51875 - 3.33058i) q^{61} +(4.75579 - 3.12794i) q^{62} +(-0.423953 + 7.27899i) q^{64} +(-8.01370 + 12.7146i) q^{65} +(4.19634 - 2.99937i) q^{67} +(1.78213 + 0.138518i) q^{68} +(2.29950 + 0.939450i) q^{70} +(1.74374 + 5.82449i) q^{71} +(0.740362 - 0.175469i) q^{73} +(3.25373 + 8.42737i) q^{74} +(0.611261 - 1.16045i) q^{76} +(-0.0766886 + 3.95404i) q^{77} +(4.92388 - 4.82930i) q^{79} +(1.60527 + 2.78040i) q^{80} +(-1.04126 + 1.80352i) q^{82} +(0.337095 + 1.30868i) q^{83} +(4.48185 - 2.47298i) q^{85} +(-2.68766 - 4.26426i) q^{86} +(-8.44660 + 10.4721i) q^{88} +(5.30103 - 17.7067i) q^{89} +(3.34271 - 3.54307i) q^{91} +(-6.32662 + 4.90350i) q^{92} +(2.21701 + 4.63648i) q^{94} +(-0.363622 - 3.73836i) q^{95} +(16.1419 + 0.626379i) q^{97} +(5.30163 + 3.48694i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{81}\right)$

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 $

$2$	−0.984101	−	0.273943i	−0.695864	−	0.193707i	−0.0978602	−	0.995200i	$-0.531200\pi$
$2$	−0.984101	−	0.273943i	−0.695864	−	0.193707i	−0.598004	+	0.801493i	$0.704039\pi$
$3$		0			0
$3$		0			0
$4$	−0.818925	−	0.494224i	−0.409462	−	0.247112i
$5$	−2.73706	+	0.106211i	−1.22405	+	0.0474988i	−0.642677	−	0.766137i	$-0.722176\pi$
$5$	−2.73706	+	0.106211i	−1.22405	+	0.0474988i	−0.581375	+	0.813636i	$0.697485\pi$
$6$		0			0
$7$	0.877096	+	0.137175i	0.331511	+	0.0518474i	0.318084	−	0.948062i	$-0.396961\pi$
$7$	0.877096	+	0.137175i	0.331511	+	0.0518474i	0.0134269	+	0.999910i	$0.495726\pi$
$8$	2.07253	+	2.19675i	0.732750	+	0.776670i
$9$		0			0
$10$	2.72264	+	0.645278i	0.860975	+	0.204055i
$11$	0.602874	+	4.41382i	0.181773	+	1.33082i	0.824997	+	0.565138i	$0.191177\pi$
$11$	0.602874	+	4.41382i	0.181773	+	1.33082i	−0.643223	+	0.765679i	$0.722403\pi$
$12$		0			0
$13$	3.10343	−	4.52491i	0.860737	−	1.25499i	−0.104741	−	0.994500i	$-0.533401\pi$
$13$	3.10343	−	4.52491i	0.860737	−	1.25499i	0.965478	−	0.260486i	$-0.0838827\pi$
$14$	−0.825572	−	0.375269i	−0.220643	−	0.100295i
$15$		0			0
$16$	−0.546251	−	1.03703i	−0.136563	−	0.259258i
$17$	−1.67001	+	0.838712i	−0.405037	+	0.203417i	−0.639641	−	0.768674i	$-0.720917\pi$
$17$	−1.67001	+	0.838712i	−0.405037	+	0.203417i	0.234604	+	0.972091i	$0.424621\pi$
$18$		0			0
$19$	0.0797307	+	1.36892i	0.0182915	+	0.314053i	0.995027	+	0.0996053i	$0.0317580\pi$
$19$	0.0797307	+	1.36892i	0.0182915	+	0.314053i	−0.976736	+	0.214447i	$0.931205\pi$
$20$	2.29394	+	1.26574i	0.512941	+	0.283029i
$21$		0			0
$22$	0.615847	−	4.50880i	0.131299	−	0.961278i
$23$	3.01412	−	7.80676i	0.628487	−	1.62782i	−0.141630	−	0.989920i	$-0.545234\pi$
$23$	3.01412	−	7.80676i	0.628487	−	1.62782i	0.770117	−	0.637903i	$-0.220198\pi$
$24$		0			0
$25$	2.49528	−	0.193948i	0.499056	−	0.0387897i
$26$	−4.29366	+	3.60281i	−0.842056	+	0.706569i
$27$		0			0
$28$	−0.650480	−	0.545818i	−0.122929	−	0.103150i
$29$	−6.07359	−	4.34114i	−1.12784	−	0.806130i	−0.144787	−	0.989463i	$-0.546250\pi$
$29$	−6.07359	−	4.34114i	−1.12784	−	0.806130i	−0.983051	+	0.183333i	$0.941311\pi$
$30$		0			0
$31$	−3.66393	+	4.19840i	−0.658061	+	0.754054i	−0.981346	−	0.192247i	$-0.938422\pi$
$31$	−3.66393	+	4.19840i	−0.658061	+	0.754054i	0.323286	+	0.946301i	$0.395213\pi$
$32$	−1.02526	−	4.73314i	−0.181243	−	0.836710i
$33$		0			0
$34$	1.87322	−	0.367888i	0.321254	−	0.0630923i
$35$	−2.41524	−	0.282301i	−0.408250	−	0.0477175i
$36$		0			0
$37$	−5.28091	−	7.09349i	−0.868175	−	1.16616i	−0.984922	−	0.173000i	$-0.944654\pi$
$37$	−5.28091	−	7.09349i	−0.868175	−	1.16616i	0.116746	−	0.993162i	$-0.462754\pi$
$38$	0.296544	−	1.36900i	0.0481058	−	0.222081i
$39$		0			0
$40$	−5.90597	−	5.79254i	−0.933816	−	0.915880i
$41$	0.508525	−	1.97421i	0.0794182	−	0.308320i	−0.916332	−	0.400420i	$-0.868864\pi$
$41$	0.508525	−	1.97421i	0.0794182	−	0.308320i	0.995750	+	0.0920999i	$0.0293579\pi$
$42$		0			0
$43$	3.65414	+	3.31596i	0.557252	+	0.505679i	0.901255	−	0.433290i	$-0.142647\pi$
$43$	3.65414	+	3.31596i	0.557252	+	0.505679i	−0.344003	+	0.938969i	$0.611783\pi$
$44$	1.68771	−	3.91254i	0.254431	−	0.589838i
$45$		0			0
$46$	−5.10480	+	6.85694i	−0.752662	+	1.01100i
$47$	−3.30800	−	3.79054i	−0.482521	−	0.552908i	0.459624	−	0.888114i	$-0.347984\pi$
$47$	−3.30800	−	3.79054i	−0.482521	−	0.552908i	−0.942145	+	0.335206i	$0.891194\pi$
$48$		0			0
$49$	−5.91526	−	1.89665i	−0.845036	−	0.270950i
$50$	−2.50874	−	0.492700i	−0.354789	−	0.0696782i
$51$		0			0
$52$	−4.77780	+	2.17178i	−0.662561	+	0.301171i
$53$	1.25461	−	7.11526i	0.172334	−	0.977356i	−0.768842	−	0.639439i	$-0.779167\pi$
$53$	1.25461	−	7.11526i	0.172334	−	0.977356i	0.941176	−	0.337917i	$-0.109722\pi$
$54$		0			0
$55$	−2.11890	−	12.0169i	−0.285712	−	1.62036i
$56$	1.51647	+	2.21106i	0.202647	+	0.295466i
$57$		0			0
$58$	4.78780	+	5.93594i	0.628669	+	0.779427i
$59$	0.734578	−	0.300108i	0.0956340	−	0.0390708i	−0.329878	−	0.944024i	$-0.607008\pi$
$59$	0.734578	−	0.300108i	0.0956340	−	0.0390708i	0.425512	+	0.904953i	$0.360094\pi$
$60$		0			0
$61$	5.51875	−	3.33058i	0.706603	−	0.426437i	−0.117353	−	0.993090i	$-0.537441\pi$
$61$	5.51875	−	3.33058i	0.706603	−	0.426437i	0.823957	+	0.566653i	$0.191762\pi$
$62$	4.75579	−	3.12794i	0.603986	−	0.397248i
$63$		0			0
$64$	−0.423953	+	7.27899i	−0.0529941	+	0.909874i
$65$	−8.01370	+	12.7146i	−0.993977	+	1.57705i
$66$		0			0
$67$	4.19634	−	2.99937i	0.512665	−	0.366431i	−0.295542	−	0.955330i	$-0.595500\pi$
$67$	4.19634	−	2.99937i	0.512665	−	0.366431i	0.808207	+	0.588899i	$0.200438\pi$
$68$	1.78213	+	0.138518i	0.216114	+	0.0167977i
$69$		0			0
$70$	2.29950	+	0.939450i	0.274843	+	0.112286i
$71$	1.74374	+	5.82449i	0.206944	+	0.691240i	0.996943	+	0.0781325i	$0.0248957\pi$
$71$	1.74374	+	5.82449i	0.206944	+	0.691240i	−0.789999	+	0.613108i	$0.789919\pi$
$72$		0			0
$73$	0.740362	−	0.175469i	0.0866529	−	0.0205371i	−0.187061	−	0.982348i	$-0.559896\pi$
$73$	0.740362	−	0.175469i	0.0866529	−	0.0205371i	0.273714	+	0.961811i	$0.411748\pi$
$74$	3.25373	+	8.42737i	0.378238	+	0.979662i
$75$		0			0
$76$	0.611261	−	1.16045i	0.0701164	−	0.133113i
$77$	−0.0766886	+	3.95404i	−0.00873947	+	0.450605i
$78$		0			0
$79$	4.92388	−	4.82930i	0.553979	−	0.543339i	−0.368378	−	0.929676i	$-0.620087\pi$
$79$	4.92388	−	4.82930i	0.553979	−	0.543339i	0.922358	+	0.386337i	$0.126260\pi$
$80$	1.60527	+	2.78040i	0.179474	+	0.310859i
$81$		0			0
$82$	−1.04126	+	1.80352i	−0.114988	+	0.199165i
$83$	0.337095	+	1.30868i	0.0370010	+	0.143647i	0.984223	−	0.176931i	$-0.0566169\pi$
$83$	0.337095	+	1.30868i	0.0370010	+	0.143647i	−0.947222	+	0.320577i	$0.896123\pi$
$84$		0			0
$85$	4.48185	−	2.47298i	0.486125	−	0.268232i
$86$	−2.68766	−	4.26426i	−0.289818	−	0.459827i
$87$		0			0
$88$	−8.44660	+	10.4721i	−0.900411	+	1.11633i
$89$	5.30103	−	17.7067i	0.561908	−	1.87690i	0.0884671	−	0.996079i	$-0.471803\pi$
$89$	5.30103	−	17.7067i	0.561908	−	1.87690i	0.473441	−	0.880825i	$-0.343012\pi$
$90$		0			0
$91$	3.34271	−	3.54307i	0.350412	−	0.371415i
$92$	−6.32662	+	4.90350i	−0.659596	+	0.511225i
$93$		0			0
$94$	2.21701	+	4.63648i	0.228667	+	0.478216i
$95$	−0.363622	−	3.73836i	−0.0373069	−	0.383548i
$96$		0			0
$97$	16.1419	+	0.626379i	1.63896	+	0.0635992i	0.841669	−	0.539994i	$-0.181574\pi$
$97$	16.1419	+	0.626379i	1.63896	+	0.0635992i	0.797292	+	0.603593i	$0.206265\pi$
$98$	5.30163	+	3.48694i	0.535546	+	0.352234i
$99$		0			0
$100$	−2.13930	−	1.07440i	−0.213930	−	0.107440i
$101$	−0.297597	−	15.3440i	−0.0296121	−	1.52679i	−0.660447	−	0.750873i	$-0.729633\pi$
$101$	−0.297597	−	15.3440i	−0.0296121	−	1.52679i	0.630835	−	0.775917i	$-0.282712\pi$
$102$		0			0
$103$	−10.2106	−	7.91381i	−1.00608	−	0.779771i	−0.0305271	−	0.999534i	$-0.509719\pi$
$103$	−10.2106	−	7.91381i	−1.00608	−	0.779771i	−0.975553	+	0.219763i	$0.929472\pi$
$104$	16.3721	−	2.56055i	1.60542	−	0.251082i
$105$		0			0
$106$	−3.18384	+	6.65844i	−0.309242	+	0.646725i
$107$	−8.67791	−	3.15850i	−0.838925	−	0.305344i	−0.113409	−	0.993548i	$-0.536177\pi$
$107$	−8.67791	−	3.15850i	−0.838925	−	0.305344i	−0.725517	+	0.688205i	$0.758399\pi$
$108$		0			0
$109$	−14.6358	+	5.32701i	−1.40186	+	0.510235i	−0.928730	−	0.370758i	$-0.879098\pi$
$109$	−14.6358	+	5.32701i	−1.40186	+	0.510235i	−0.473129	+	0.880993i	$0.656876\pi$
$110$	−1.20673	+	12.4063i	−0.115057	+	1.18289i
$111$		0			0
$112$	−0.336859	−	0.984508i	−0.0318302	−	0.0930273i
$113$	−4.01096	+	3.63975i	−0.377319	+	0.342399i	−0.838494	−	0.544910i	$-0.816564\pi$
$113$	−4.01096	+	3.63975i	−0.377319	+	0.342399i	0.461175	+	0.887309i	$0.347428\pi$
$114$		0			0
$115$	−7.42068	+	21.6877i	−0.691982	+	2.02239i
$116$	2.82832	+	6.55678i	0.262603	+	0.608782i
$117$		0			0
$118$	−0.805112	+	0.0941040i	−0.0741165	+	0.00866298i
$119$	−1.57981	+	0.506546i	−0.144821	+	0.0464350i
$120$		0			0
$121$	−8.52126	+	2.37206i	−0.774660	+	0.215641i
$122$	−6.34339	+	1.76580i	−0.574304	+	0.159868i
$123$		0			0
$124$	5.07543	−	1.62737i	0.455787	−	0.146142i
$125$	6.79388	−	0.794091i	0.607663	−	0.0710256i
$126$		0			0
$127$	−1.42268	−	3.29814i	−0.126242	−	0.292663i	0.843360	−	0.537349i	$-0.180574\pi$
$127$	−1.42268	−	3.29814i	−0.126242	−	0.292663i	−0.969602	+	0.244686i	$0.921315\pi$
$128$	−0.724389	+	2.11711i	−0.0640276	+	0.187128i
$129$		0			0
$130$	11.3694	−	10.3171i	0.997159	−	0.904874i
$131$	−2.11285	−	6.17504i	−0.184601	−	0.539516i	0.814577	−	0.580055i	$-0.196969\pi$
$131$	−2.11285	−	6.17504i	−0.184601	−	0.539516i	−0.999178	+	0.0405392i	$0.987092\pi$
$132$		0			0
$133$	−0.117851	+	1.21161i	−0.0102190	+	0.105060i
$134$	−4.95128	+	1.80212i	−0.427725	+	0.155679i
$135$		0			0
$136$	−5.30360	−	1.93035i	−0.454780	−	0.165526i
$137$	−1.93773	+	4.05243i	−0.165552	+	0.346222i	−0.968179	−	0.250259i	$-0.919484\pi$
$137$	−1.93773	+	4.05243i	−0.165552	+	0.346222i	0.802627	+	0.596481i	$0.203435\pi$
$138$		0			0
$139$	−9.45164	+	1.47821i	−0.801678	+	0.125380i	−0.542069	−	0.840334i	$-0.682359\pi$
$139$	−9.45164	+	1.47821i	−0.801678	+	0.125380i	−0.259609	+	0.965714i	$0.583594\pi$
$140$	1.83838	+	1.42485i	0.155371	+	0.120422i
$141$		0			0
$142$	−0.120435	−	6.20957i	−0.0101066	−	0.521096i
$143$	21.8431	+	10.9700i	1.82661	+	0.917360i
$144$		0			0
$145$	17.0849	+	11.2369i	1.41882	+	0.933175i
$146$	−0.776659	−	0.0301379i	−0.0642768	−	0.00249423i
$147$		0			0
$148$	0.818895	+	8.41898i	0.0673128	+	0.692036i
$149$	−0.334935	−	0.700458i	−0.0274390	−	0.0573837i	0.887992	−	0.459860i	$-0.152100\pi$
$149$	−0.334935	−	0.700458i	−0.0274390	−	0.0573837i	−0.915431	+	0.402476i	$0.868150\pi$
$150$		0			0
$151$	18.0411	−	13.9829i	1.46816	−	1.13791i	0.506993	−	0.861950i	$-0.330757\pi$
$151$	18.0411	−	13.9829i	1.46816	−	1.13791i	0.961169	−	0.275961i	$-0.0889961\pi$
$152$	−2.84195	+	3.01229i	−0.230512	+	0.244329i
$153$		0			0
$154$	1.15865	−	3.87017i	0.0933668	−	0.311867i
$155$	9.58249	−	11.8804i	0.769684	−	0.954259i
$156$		0			0
$157$	−4.81328	−	7.63679i	−0.384141	−	0.609482i	0.597123	−	0.802150i	$-0.296311\pi$
$157$	−4.81328	−	7.63679i	−0.384141	−	0.609482i	−0.981264	+	0.192668i	$0.938286\pi$
$158$	−6.16854	+	3.40366i	−0.490743	+	0.270780i
$159$		0			0
$160$	3.30892	+	12.8460i	0.261593	+	1.01557i
$161$	3.71456	−	6.43382i	0.292749	−	0.507056i
$162$		0			0
$163$	2.19502	+	3.80188i	0.171927	+	0.297787i	0.939094	−	0.343662i	$-0.111667\pi$
$163$	2.19502	+	3.80188i	0.171927	+	0.297787i	−0.767166	+	0.641448i	$0.778334\pi$
$164$	−1.39215	+	1.36541i	−0.108708	+	0.106620i
$165$		0			0
$166$	0.0267694	−	1.38022i	0.00207770	−	0.107126i
$167$	0.728491	−	1.38301i	0.0563723	−	0.107020i	−0.854956	−	0.518700i	$-0.826416\pi$
$167$	0.728491	−	1.38301i	0.0563723	−	0.107020i	0.911328	+	0.411680i	$0.135058\pi$
$168$		0			0
$169$	−6.16125	−	15.9580i	−0.473942	−	1.22754i
$170$	−5.08805	+	1.20589i	−0.390236	+	0.0924875i
$171$		0			0
$172$	−1.35364	−	4.52149i	−0.103214	−	0.344760i
$173$	2.36083	+	0.964505i	0.179491	+	0.0733300i	0.466164	−	0.884698i	$-0.345636\pi$
$173$	2.36083	+	0.964505i	0.179491	+	0.0733300i	−0.286673	+	0.958028i	$0.592549\pi$
$174$		0			0
$175$	2.21520	+	0.172179i	0.167454	+	0.0130155i
$176$	4.24795	−	3.03625i	0.320201	−	0.228866i
$177$		0			0
$178$	−10.0674	+	15.9730i	−0.754581	+	1.19722i
$179$	−1.18057	+	20.2696i	−0.0882400	+	1.51502i	0.606107	+	0.795383i	$0.292730\pi$
$179$	−1.18057	+	20.2696i	−0.0882400	+	1.51502i	−0.694347	+	0.719640i	$0.744307\pi$
$180$		0			0
$181$	−8.40142	+	5.52570i	−0.624473	+	0.410722i	−0.821929	−	0.569589i	$-0.807102\pi$
$181$	−8.40142	+	5.52570i	−0.624473	+	0.410722i	0.197456	+	0.980312i	$0.436732\pi$
$182$	−4.26017	+	2.57102i	−0.315784	+	0.190577i
$183$		0			0
$184$	23.3964	−	9.55848i	1.72481	−	0.704660i
$185$	15.2076	+	18.8544i	1.11808	+	1.38621i
$186$		0			0
$187$	−4.70873	−	6.86549i	−0.344336	−	0.502055i
$188$	0.835624	+	4.73906i	0.0609442	+	0.345632i
$189$		0			0
$190$	−0.666258	+	3.77854i	−0.0483355	+	0.274124i
$191$	14.2941	−	6.49747i	1.03429	−	0.470141i	0.176583	−	0.984286i	$-0.443496\pi$
$191$	14.2941	−	6.49747i	1.03429	−	0.470141i	0.857703	+	0.514145i	$0.171891\pi$
$192$		0			0
$193$	19.1167	+	3.75440i	1.37605	+	0.270248i	0.825428	−	0.564507i	$-0.190934\pi$
$193$	19.1167	+	3.75440i	1.37605	+	0.270248i	0.550622	+	0.834755i	$0.314390\pi$
$194$	−15.7137	−	5.03838i	−1.12817	−	0.361735i
$195$		0			0
$196$	3.90678	+	4.47667i	0.279056	+	0.319762i
$197$	−10.9788	+	14.7471i	−0.782208	+	1.05069i	0.215044	+	0.976604i	$0.431011\pi$
$197$	−10.9788	+	14.7471i	−0.782208	+	1.05069i	−0.997252	+	0.0740839i	$0.976397\pi$
$198$		0			0
$199$	−9.41644	+	21.8298i	−0.667514	+	1.54747i	0.160667	+	0.987009i	$0.448636\pi$
$199$	−9.41644	+	21.8298i	−0.667514	+	1.54747i	−0.828180	+	0.560462i	$0.810624\pi$
$200$	5.59760	+	5.07955i	0.395810	+	0.359178i
$201$		0			0
$202$	−3.91053	+	15.1816i	−0.275144	+	1.06817i
$203$	−4.73163	−	4.64075i	−0.332095	−	0.325717i
$204$		0			0
$205$	−1.18218	+	5.45756i	−0.0825672	+	0.381173i
$206$	7.88032	+	10.5851i	0.549048	+	0.737500i
$207$		0			0
$208$	−6.38773	−	0.746619i	−0.442909	−	0.0517687i
$209$	−5.99411	+	1.17721i	−0.414622	+	0.0814290i
$210$		0			0
$211$	1.54557	+	7.13514i	0.106401	+	0.491203i	0.999172	+	0.0406915i	$0.0129561\pi$
$211$	1.54557	+	7.13514i	0.106401	+	0.491203i	−0.892770	+	0.450512i	$0.851241\pi$
$212$	−4.54396	+	5.20680i	−0.312081	+	0.357605i
$213$		0			0
$214$	7.67469	+	5.48554i	0.524631	+	0.374983i
$215$	−10.3538	−	8.68789i	−0.706125	−	0.592509i
$216$		0			0
$217$	−3.78953	+	3.17979i	−0.257250	+	0.215859i
$218$	15.8624	−	1.23293i	1.07434	−	0.0835043i
$219$		0			0
$220$	−4.20381	+	10.8881i	−0.283421	+	0.734078i
$221$	−1.38767	+	10.1595i	−0.0933448	+	0.683405i
$222$		0			0
$223$	−0.168498	−	0.0929734i	−0.0112835	−	0.00622596i	0.477461	−	0.878653i	$-0.341557\pi$
$223$	−0.168498	−	0.0929734i	−0.0112835	−	0.00622596i	−0.488744	+	0.872427i	$0.662545\pi$
$224$	−0.249984	−	4.29206i	−0.0167028	−	0.286775i
$225$		0			0
$226$	4.94427	−	2.48311i	0.328888	−	0.165174i
$227$	−1.92124	−	3.64739i	−0.127517	−	0.242085i	0.812684	−	0.582704i	$-0.198005\pi$
$227$	−1.92124	−	3.64739i	−0.127517	−	0.242085i	−0.940201	+	0.340619i	$0.889363\pi$
$228$		0			0
$229$	−10.8316	−	4.92358i	−0.715774	−	0.325359i	0.0226056	−	0.999744i	$-0.492804\pi$
$229$	−10.8316	−	4.92358i	−0.715774	−	0.325359i	−0.738380	+	0.674385i	$0.764409\pi$
$230$	13.2439	−	19.3101i	0.873277	−	1.27327i
$231$		0			0
$232$	−3.05128	−	22.3394i	−0.200327	−	1.46665i
$233$	17.7434	+	4.20527i	1.16241	+	0.275496i	0.766163	−	0.642647i	$-0.222164\pi$
$233$	17.7434	+	4.20527i	1.16241	+	0.275496i	0.396248	+	0.918143i	$0.370312\pi$
$234$		0			0
$235$	9.45680	+	10.0236i	0.616893	+	0.653869i
$236$	−0.749885	−	0.117280i	−0.0488134	−	0.00763427i
$237$		0			0
$238$	1.69346	−	0.0657139i	0.109771	−	0.00425960i
$239$	1.47571	+	0.890596i	0.0954558	+	0.0576078i	0.563624	−	0.826032i	$-0.309407\pi$
$239$	1.47571	+	0.890596i	0.0954558	+	0.0576078i	−0.468168	+	0.883639i	$0.655086\pi$
$240$		0			0
$241$	−5.30942	−	1.47798i	−0.342010	−	0.0952049i	0.0929091	−	0.995675i	$-0.470383\pi$
$241$	−5.30942	−	1.47798i	−0.342010	−	0.0952049i	−0.434919	+	0.900470i	$0.643223\pi$
$242$	9.03559			0.580830
$243$		0			0
$244$	−6.16549			−0.394705
$245$	16.3919	+	4.56299i	1.04724	+	0.291519i
$246$		0			0
$247$	6.44170	+	3.88759i	0.409876	+	0.247361i
$248$	−16.8164	+	0.652555i	−1.06785	+	0.0414373i
$249$		0			0
$250$	−6.90340	−	1.07967i	−0.436609	−	0.0682844i
$251$	−11.5955	−	12.2905i	−0.731902	−	0.775771i	0.249368	−	0.968409i	$-0.419777\pi$
$251$	−11.5955	−	12.2905i	−0.731902	−	0.775771i	−0.981270	+	0.192638i	$0.938296\pi$
$252$		0			0
$253$	36.2748	+	8.59728i	2.28058	+	0.540506i
$254$	0.496556	+	3.63544i	0.0311567	+	0.228107i
$255$		0			0
$256$	9.54089	−	13.9110i	0.596306	−	0.869435i
$257$	5.82991	+	2.65002i	0.363660	+	0.165304i	0.587302	−	0.809368i	$-0.300190\pi$
$257$	5.82991	+	2.65002i	0.363660	+	0.165304i	−0.223643	+	0.974671i	$0.571795\pi$
$258$		0			0
$259$	−3.65881	−	6.94608i	−0.227347	−	0.431608i
$260$	12.8465	−	6.45174i	0.796704	−	0.400120i
$261$		0			0
$262$	0.387648	+	6.65566i	0.0239490	+	0.411188i
$263$	−19.7700	−	10.9087i	−1.21907	−	0.672656i	−0.262721	−	0.964872i	$-0.584620\pi$
$263$	−19.7700	−	10.9087i	−1.21907	−	0.672656i	−0.956352	+	0.292216i	$0.905607\pi$
$264$		0			0
$265$	−2.67824	+	19.6082i	−0.164523	+	1.20452i
$266$	0.447891	−	1.16007i	0.0274619	−	0.0711282i
$267$		0			0
$268$	−4.91885	+	0.382323i	−0.300466	+	0.0233541i
$269$	12.2734	−	10.2986i	0.748321	−	0.627916i	−0.186737	−	0.982410i	$-0.559791\pi$
$269$	12.2734	−	10.2986i	0.748321	−	0.627916i	0.935058	+	0.354494i	$0.115347\pi$
$270$		0			0
$271$	−11.5105	−	9.65850i	−0.699216	−	0.586712i	0.222334	−	0.974970i	$-0.428632\pi$
$271$	−11.5105	−	9.65850i	−0.699216	−	0.586712i	−0.921550	+	0.388259i	$0.873077\pi$
$272$	1.78202	+	1.27371i	0.108051	+	0.0772299i
$273$		0			0
$274$	3.01706	−	3.45717i	0.182267	−	0.208855i
$275$	2.36039	+	10.8968i	0.142337	+	0.657101i
$276$		0			0
$277$	−16.6503	+	3.27000i	−1.00042	+	0.196475i	−0.666002	−	0.745950i	$-0.731996\pi$
$277$	−16.6503	+	3.27000i	−1.00042	+	0.196475i	−0.334415	+	0.942426i	$0.608539\pi$
$278$	9.70631	+	1.13451i	0.582146	+	0.0680431i
$279$		0			0
$280$	−4.38551	−	5.89076i	−0.262084	−	0.352040i
$281$	−0.402812	+	1.85959i	−0.0240297	+	0.110934i	−0.987773	−	0.155896i	$-0.950174\pi$
$281$	−0.402812	+	1.85959i	−0.0240297	+	0.110934i	0.963744	+	0.266829i	$0.0859760\pi$
$282$		0			0
$283$	−1.39461	−	1.36782i	−0.0829007	−	0.0813085i	0.657586	−	0.753380i	$-0.271578\pi$
$283$	−1.39461	−	1.36782i	−0.0829007	−	0.0813085i	−0.740487	+	0.672071i	$0.765405\pi$
$284$	1.45061	−	5.63162i	0.0860780	−	0.334175i
$285$		0			0
$286$	−18.4907	−	16.7794i	−1.09338	−	0.992186i
$287$	0.716838	−	1.66182i	0.0423136	−	0.0980940i
$288$		0			0
$289$	−8.06619	+	10.8348i	−0.474482	+	0.637340i
$290$	−13.7350	−	15.7385i	−0.806546	−	0.924199i
$291$		0			0
$292$	−0.693022	−	0.222209i	−0.0405560	−	0.0130038i
$293$	−9.70882	−	1.90675i	−0.567196	−	0.111394i	−0.0991096	−	0.995077i	$-0.531599\pi$
$293$	−9.70882	−	1.90675i	−0.567196	−	0.111394i	−0.468086	+	0.883683i	$0.655056\pi$
$294$		0			0
$295$	−1.97871	+	0.899436i	−0.115205	+	0.0523672i
$296$	4.63781	−	26.3023i	0.269567	−	1.52879i
$297$		0			0
$298$	0.137724	+	0.781074i	0.00797816	+	0.0452464i
$299$	−25.9708	−	37.8664i	−1.50193	−	2.18987i
$300$		0			0
$301$	2.75017	+	3.40967i	0.158517	+	0.196530i
$302$	−21.5847	+	8.81834i	−1.24206	+	0.507438i
$303$		0			0
$304$	1.37606	−	0.830459i	0.0789227	−	0.0476301i
$305$	−14.7514	+	9.70217i	−0.844664	+	0.555545i
$306$		0			0
$307$	−0.0274664	+	0.471580i	−0.00156759	+	0.0269145i	−0.999001	−	0.0446823i	$-0.985772\pi$
$307$	−0.0274664	+	0.471580i	−0.00156759	+	0.0269145i	0.997434	+	0.0715968i	$0.0228095\pi$
$308$	2.01698	−	3.20016i	0.114928	−	0.182346i
$309$		0			0
$310$	−12.6847	+	9.06648i	−0.720442	+	0.514941i
$311$	14.1884	+	1.10281i	0.804549	+	0.0625345i	0.473179	−	0.880966i	$-0.343106\pi$
$311$	14.1884	+	1.10281i	0.804549	+	0.0625345i	0.331370	+	0.943501i	$0.392489\pi$
$312$		0			0
$313$	−4.48719	−	1.83322i	−0.253631	−	0.103620i	0.247819	−	0.968806i	$-0.420286\pi$
$313$	−4.48719	−	1.83322i	−0.253631	−	0.103620i	−0.501450	+	0.865187i	$0.667200\pi$
$314$	2.64471	+	8.83393i	0.149249	+	0.498528i
$315$		0			0
$316$	−6.41904	+	1.52134i	−0.361099	+	0.0855821i
$317$	5.61316	+	14.5384i	0.315266	+	0.816560i	0.996430	+	0.0844286i	$0.0269065\pi$
$317$	5.61316	+	14.5384i	0.315266	+	0.816560i	−0.681163	+	0.732132i	$0.738526\pi$
$318$		0			0
$319$	15.4994	−	29.4249i	0.867801	−	1.64748i
$320$	0.387281	−	19.9681i	0.0216497	−	1.11625i
$321$		0			0
$322$	−5.41800	+	5.31394i	−0.301934	+	0.296134i
$323$	−1.28128	−	2.21925i	−0.0712925	−	0.123482i
$324$		0			0
$325$	6.86633	−	11.8928i	0.380875	−	0.659695i
$326$	−1.11862	−	4.34275i	−0.0619546	−	0.240523i
$327$		0			0
$328$	5.39080	−	2.97452i	0.297657	−	0.164240i
$329$	−2.38146	−	3.77845i	−0.131294	−	0.208312i
$330$		0			0
$331$	20.7687	−	25.7491i	1.14155	−	1.41530i	0.246607	−	0.969115i	$-0.420684\pi$
$331$	20.7687	−	25.7491i	1.14155	−	1.41530i	0.894942	−	0.446183i	$-0.147217\pi$
$332$	0.370727	−	1.23831i	0.0203463	−	0.0679613i
$333$		0			0
$334$	−1.09577	+	1.16145i	−0.0599580	+	0.0635518i
$335$	−11.1671	+	8.65515i	−0.610124	+	0.472881i
$336$		0			0
$337$	−12.6722	−	26.5017i	−0.690301	−	1.44364i	−0.886335	−	0.463044i	$-0.846757\pi$
$337$	−12.6722	−	26.5017i	−0.690301	−	1.44364i	0.196035	−	0.980597i	$-0.437193\pi$
$338$	1.69169	+	17.3921i	0.0920161	+	0.946008i
$339$		0			0
$340$	−4.89251	−	0.189851i	−0.265333	−	0.0102961i
$341$	−20.7398	−	13.6408i	−1.12313	−	0.738691i
$342$		0			0
$343$	−10.4814	−	5.26395i	−0.565941	−	0.284226i
$344$	0.288979	+	14.8997i	0.0155807	+	0.803337i
$345$		0			0
$346$	−2.05907	−	1.59590i	−0.110697	−	0.0857963i
$347$	3.11755	−	0.487576i	0.167359	−	0.0261745i	−0.0702841	−	0.997527i	$-0.522391\pi$
$347$	3.11755	−	0.487576i	0.167359	−	0.0261745i	0.237643	+	0.971353i	$0.423625\pi$
$348$		0			0
$349$	−9.35966	+	19.5741i	−0.501011	+	1.04778i	0.483965	+	0.875087i	$0.339196\pi$
$349$	−9.35966	+	19.5741i	−0.501011	+	1.04778i	−0.984976	+	0.172689i	$0.944754\pi$
$350$	−2.13281	−	0.776281i	−0.114004	−	0.0414940i
$351$		0			0
$352$	20.2731	−	7.37882i	1.08056	−	0.393292i
$353$	−1.06172	+	10.9154i	−0.0565097	+	0.580971i	0.923715	+	0.383081i	$0.125137\pi$
$353$	−1.06172	+	10.9154i	−0.0565097	+	0.580971i	−0.980224	+	0.197889i	$0.936591\pi$
$354$		0			0
$355$	−5.39135	−	15.7568i	−0.286143	−	0.836285i
$356$	−13.0922	+	11.8805i	−0.693886	+	0.629668i
$357$		0			0
$358$	6.71453	−	19.6239i	0.354874	−	1.03716i
$359$	−0.245387	−	0.568871i	−0.0129510	−	0.0300239i	0.911618	−	0.411039i	$-0.134834\pi$
$359$	−0.245387	−	0.568871i	−0.0129510	−	0.0300239i	−0.924569	+	0.381015i	$0.875575\pi$
$360$		0			0
$361$	17.0039	−	1.98747i	0.894944	−	0.104604i
$362$	9.78158	−	3.13634i	0.514108	−	0.164842i
$363$		0			0
$364$	−4.48850	+	1.24946i	−0.235261	+	0.0654895i
$365$	−2.00778	+	0.558905i	−0.105092	+	0.0292544i
$366$		0			0
$367$	34.7752	−	11.1502i	1.81525	−	0.582037i	0.815257	−	0.579099i	$-0.196596\pi$
$367$	34.7752	−	11.1502i	1.81525	−	0.582037i	0.999996	−	0.00293835i	$-0.000935308\pi$
$368$	−9.74232	+	1.13871i	−0.507854	+	0.0593596i
$369$		0			0
$370$	−9.80074	−	22.7207i	−0.509516	−	1.18119i
$371$	2.07645	−	6.06866i	0.107804	−	0.315069i
$372$		0			0
$373$	−8.58167	+	7.78745i	−0.444342	+	0.403219i	−0.863224	−	0.504822i	$-0.831558\pi$
$373$	−8.58167	+	7.78745i	−0.444342	+	0.403219i	0.418881	+	0.908041i	$0.362422\pi$
$374$	2.75311	+	8.04626i	0.142360	+	0.416062i
$375$		0			0
$376$	1.47097	−	15.1229i	0.0758594	−	0.779903i
$377$	−38.4923	+	14.0100i	−1.98245	+	0.721554i
$378$		0			0
$379$	−14.3131	−	5.20955i	−0.735215	−	0.267596i	−0.0528444	−	0.998603i	$-0.516829\pi$
$379$	−14.3131	−	5.20955i	−0.735215	−	0.267596i	−0.682371	+	0.731006i	$0.739051\pi$
$380$	−1.54981	+	3.24115i	−0.0795035	+	0.166267i
$381$		0			0
$382$	−15.8468	+	2.47839i	−0.810792	+	0.126806i
$383$	11.2959	+	8.75500i	0.577195	+	0.447360i	0.858901	−	0.512141i	$-0.171147\pi$
$383$	11.2959	+	8.75500i	0.577195	+	0.447360i	−0.281707	+	0.959501i	$0.590900\pi$
$384$		0			0
$385$	−0.210060	−	10.8306i	−0.0107056	−	0.551979i
$386$	−17.7843	−	8.93159i	−0.905195	−	0.454606i
$387$		0			0
$388$	−12.9094	−	8.49066i	−0.655377	−	0.431048i
$389$	−17.0236	−	0.660592i	−0.863130	−	0.0334934i	−0.396592	−	0.917995i	$-0.629807\pi$
$389$	−17.0236	−	0.660592i	−0.863130	−	0.0334934i	−0.466537	+	0.884501i	$0.654499\pi$
$390$		0			0
$391$	1.51401	+	15.5654i	0.0765667	+	0.787174i
$392$	−8.09308	−	16.9252i	−0.408762	−	0.854853i
$393$		0			0
$394$	14.8441	−	11.5051i	0.747837	−	0.579617i
$395$	−12.9640	+	13.7411i	−0.652292	+	0.691389i
$396$		0			0
$397$	7.51986	−	25.1181i	0.377411	−	1.26064i	−0.532710	−	0.846298i	$-0.678826\pi$
$397$	7.51986	−	25.1181i	0.377411	−	1.26064i	0.910121	−	0.414343i	$-0.135989\pi$
$398$	15.2468	−	18.9031i	0.764255	−	0.947527i
$399$		0			0
$400$	−1.56418	−	2.48174i	−0.0782089	−	0.124087i
$401$	4.11300	−	2.26946i	0.205394	−	0.113331i	−0.377081	−	0.926180i	$-0.623072\pi$
$401$	4.11300	−	2.26946i	0.205394	−	0.113331i	0.582475	+	0.812849i	$0.302085\pi$
$402$		0			0
$403$	7.62663	+	29.6084i	0.379909	+	1.47490i
$404$	−7.33968	+	12.7127i	−0.365163	+	0.632480i
$405$		0			0
$406$	3.38510	+	5.86316i	0.167999	+	0.290984i
$407$	28.1256	−	27.5854i	1.39414	−	1.36736i
$408$		0			0
$409$	−0.419979	+	21.6540i	−0.0207666	+	1.07072i	0.834017	+	0.551738i	$0.186035\pi$
$409$	−0.419979	+	21.6540i	−0.0207666	+	1.07072i	−0.854784	+	0.518984i	$0.826310\pi$
$410$	2.65845	−	5.04694i	0.131291	−	0.249251i
$411$		0			0
$412$	4.45052	+	11.5271i	0.219261	+	0.567901i
$413$	0.685463	−	0.162458i	0.0337294	−	0.00799402i
$414$		0			0
$415$	−1.06165	−	3.54615i	−0.0521142	−	0.174074i
$416$	−24.5989	−	10.0498i	−1.20606	−	0.492730i
$417$		0			0
$418$	6.22130	+	0.483558i	0.304294	+	0.0236516i
$419$	10.0218	−	7.16316i	0.489597	−	0.349943i	−0.309744	−	0.950820i	$-0.600243\pi$
$419$	10.0218	−	7.16316i	0.489597	−	0.349943i	0.799342	+	0.600877i	$0.205182\pi$
$420$		0			0
$421$	−15.6312	+	24.8006i	−0.761818	+	1.20871i	0.211079	+	0.977469i	$0.432302\pi$
$421$	−15.6312	+	24.8006i	−0.761818	+	1.20871i	−0.972897	+	0.231238i	$0.925722\pi$
$422$	0.433627	−	7.44510i	0.0211087	−	0.362422i
$423$		0			0
$424$	18.2307	−	11.9905i	0.885361	−	0.582311i
$425$	−4.00448	+	2.41671i	−0.194246	+	0.117228i
$426$		0			0
$427$	5.29735	−	2.16420i	0.256357	−	0.104733i
$428$	5.54555	+	6.87540i	0.268054	+	0.332335i
$429$		0			0
$430$	7.80921	+	11.3861i	0.376594	+	0.549087i
$431$	1.43533	+	8.14018i	0.0691376	+	0.392099i	0.999665	+	0.0258768i	$0.00823777\pi$
$431$	1.43533	+	8.14018i	0.0691376	+	0.392099i	−0.930528	+	0.366222i	$0.880651\pi$
$432$		0			0
$433$	2.78198	−	15.7774i	0.133694	−	0.758214i	−0.842067	−	0.539373i	$-0.818661\pi$
$433$	2.78198	−	15.7774i	0.133694	−	0.758214i	0.975761	−	0.218841i	$-0.0702275\pi$
$434$	4.60036	−	2.09112i	0.220824	−	0.100377i
$435$		0			0
$436$	14.6184	+	2.87096i	0.700094	+	0.137494i
$437$	10.9272	+	3.50366i	0.522718	+	0.167603i
$438$		0			0
$439$	−22.9254	−	26.2696i	−1.09417	−	1.25378i	−0.965026	−	0.262155i	$-0.915567\pi$
$439$	−22.9254	−	26.2696i	−1.09417	−	1.25378i	−0.129145	−	0.991626i	$-0.541223\pi$
$440$	22.0066	−	29.5601i	1.04913	−	1.40922i
$441$		0			0
$442$	4.14875	−	9.61787i	0.197336	−	0.457476i
$443$	23.7838	+	21.5827i	1.13000	+	1.02542i	0.999422	+	0.0339855i	$0.0108200\pi$
$443$	23.7838	+	21.5827i	1.13000	+	1.02542i	0.130581	+	0.991438i	$0.458316\pi$
$444$		0			0
$445$	−12.6286	+	49.0274i	−0.598655	+	2.32412i
$446$	0.140350	+	0.137654i	0.00664575	+	0.00651811i
$447$		0			0
$448$	−1.37035	+	6.32622i	−0.0647427	+	0.298886i
$449$	−13.3958	−	17.9937i	−0.632187	−	0.849174i	0.364441	−	0.931226i	$-0.381260\pi$
$449$	−13.3958	−	17.9937i	−0.632187	−	0.849174i	−0.996628	+	0.0820520i	$0.973853\pi$
$450$		0			0
$451$	9.02040	+	1.05433i	0.424754	+	0.0496466i
$452$	5.08352	−	0.998372i	0.239109	−	0.0469595i
$453$		0			0
$454$	0.891518	+	4.11570i	0.0418410	+	0.193160i
$455$	−8.77291	+	10.0526i	−0.411280	+	0.471275i
$456$		0			0
$457$	−9.89787	−	7.07457i	−0.463003	−	0.330934i	0.325951	−	0.945387i	$-0.394315\pi$
$457$	−9.89787	−	7.07457i	−0.463003	−	0.330934i	−0.788954	+	0.614452i	$0.789377\pi$
$458$	9.31063	+	7.81255i	0.435057	+	0.365056i
$459$		0			0
$460$	16.7956	−	14.0932i	0.783098	−	0.657097i
$461$	−14.3194	+	1.11299i	−0.666921	+	0.0518372i	−0.406490	−	0.913655i	$-0.633247\pi$
$461$	−14.3194	+	1.11299i	−0.666921	+	0.0518372i	−0.260431	+	0.965492i	$0.583865\pi$
$462$		0			0
$463$	−6.32862	+	16.3915i	−0.294116	+	0.761779i	0.704526	+	0.709678i	$0.251160\pi$
$463$	−6.32862	+	16.3915i	−0.294116	+	0.761779i	−0.998642	+	0.0521007i	$0.983408\pi$
$464$	−1.18420	+	8.66986i	−0.0549750	+	0.402488i
$465$		0			0
$466$	−16.3093	−	8.99910i	−0.755515	−	0.416875i
$467$	−0.619940	−	10.6440i	−0.0286874	−	0.492543i	−0.981799	−	0.189924i	$-0.939176\pi$
$467$	−0.619940	−	10.6440i	−0.0286874	−	0.492543i	0.953111	−	0.302620i	$-0.0978611\pi$
$468$		0			0
$469$	4.09203	−	2.05510i	0.188953	−	0.0948955i
$470$	−6.56054	−	12.4549i	−0.302615	−	0.574501i
$471$		0			0
$472$	2.18170	+	0.991705i	0.100421	+	0.0456469i
$473$	−12.4331	+	18.1278i	−0.571672	+	0.833519i
$474$		0			0
$475$	0.464451	+	3.40038i	0.0213105	+	0.156020i
$476$	1.54409	+	0.365957i	0.0707734	+	0.0167736i
$477$		0			0
$478$	−1.20827	−	1.28070i	−0.0552652	−	0.0585777i
$479$	28.4548	+	4.45025i	1.30013	+	0.203337i	0.766426	−	0.642332i	$-0.222033\pi$
$479$	28.4548	+	4.45025i	1.30013	+	0.203337i	0.533707	+	0.845670i	$0.320799\pi$
$480$		0			0
$481$	−48.4863	+	1.88149i	−2.21079	+	0.0857886i
$482$	4.82012	+	2.90896i	0.219550	+	0.132499i
$483$		0			0
$484$	8.15060	+	2.26887i	0.370482	+	0.103131i
$485$	−44.2479			−2.00920
$486$		0			0
$487$	33.0583			1.49801			0.749006	−	0.662563i	$-0.230531\pi$
$487$	33.0583			1.49801			0.749006	+	0.662563i	$0.230531\pi$
$488$	18.7543	+	5.22060i	0.848965	+	0.236326i
$489$		0			0
$490$	−14.8813	−	8.98089i	−0.672267	−	0.405715i
$491$	−0.230994	+	0.00896363i	−0.0104246	+	0.000404523i	−0.0439872	−	0.999032i	$-0.514006\pi$
$491$	−0.230994	+	0.00896363i	−0.0104246	+	0.000404523i	0.0335625	+	0.999437i	$0.489315\pi$
$492$		0			0
$493$	13.7839	+	2.15577i	0.620798	+	0.0970910i
$494$	−5.27430	−	5.59044i	−0.237302	−	0.251526i
$495$		0			0
$496$	6.35529	+	1.50623i	0.285361	+	0.0676318i
$497$	0.730450	+	5.34784i	0.0327651	+	0.239883i
$498$		0			0
$499$	−7.57199	+	11.0402i	−0.338969	+	0.494229i	−0.956265	−	0.292502i	$-0.905512\pi$
$499$	−7.57199	+	11.0402i	−0.338969	+	0.494229i	0.617296	+	0.786731i	$0.288228\pi$
$500$	−5.95614	−	2.70740i	−0.266366	−	0.121078i
$501$		0			0
$502$	8.04424	+	15.2716i	0.359032	+	0.681605i
$503$	−27.1474	+	13.6339i	−1.21044	+	0.607907i	−0.935423	−	0.353532i	$-0.884981\pi$
$503$	−27.1474	+	13.6339i	−1.21044	+	0.607907i	−0.275020	+	0.961439i	$0.588684\pi$
$504$		0			0
$505$	2.44424	+	41.9660i	0.108767	+	1.86746i
$506$	−33.3429	−	18.3978i	−1.48227	−	0.817882i
$507$		0			0
$508$	−0.464952	+	3.40405i	−0.0206289	+	0.151030i
$509$	−9.06128	+	23.4693i	−0.401634	+	1.04026i	0.573610	+	0.819128i	$0.305542\pi$
$509$	−9.06128	+	23.4693i	−0.401634	+	1.04026i	−0.975244	+	0.221130i	$0.929025\pi$
$510$		0			0
$511$	0.673439	−	0.0523438i	0.0297912	−	0.00231555i
$512$	−9.77179	+	8.19951i	−0.431856	+	0.362370i
$513$		0			0
$514$	−5.01126	−	4.20495i	−0.221037	−	0.185472i
$515$	28.7876	+	20.5761i	1.26853	+	0.906693i
$516$		0			0
$517$	14.7365	−	16.8861i	0.648109	−	0.742651i
$518$	1.69781	+	7.83794i	0.0745973	+	0.344379i
$519$		0			0
$520$	−44.5395	+	8.74727i	−1.95319	+	0.383593i
$521$	24.3092	+	2.84134i	1.06500	+	0.124481i	0.630501	−	0.776189i	$-0.282850\pi$
$521$	24.3092	+	2.84134i	1.06500	+	0.124481i	0.434504	+	0.900670i	$0.356924\pi$
$522$		0			0
$523$	−0.991286	−	1.33153i	−0.0433459	−	0.0582236i	0.779922	−	0.625877i	$-0.215259\pi$
$523$	−0.991286	−	1.33153i	−0.0433459	−	0.0582236i	−0.823268	+	0.567653i	$0.807851\pi$
$524$	−1.32158	+	6.10112i	−0.0577337	+	0.266528i
$525$		0			0
$526$	16.4674	+	16.1511i	0.718011	+	0.704220i
$527$	2.59756	−	10.0844i	0.113152	−	0.439281i
$528$		0			0
$529$	−34.8281	−	31.6048i	−1.51427	−	1.37412i
$530$	8.00718	−	18.5627i	0.347810	−	0.806314i
$531$		0			0
$532$	0.695320	−	0.933976i	0.0301459	−	0.0404930i
$533$	−7.35498	−	8.42787i	−0.318579	−	0.365052i
$534$		0			0
$535$	24.0875	+	7.72334i	1.04139	+	0.333909i
$536$	15.2859	+	3.00206i	0.660251	+	0.129669i
$537$		0			0
$538$	−14.8995	+	6.77264i	−0.642362	+	0.291989i
$539$	4.80532	−	27.2523i	0.206980	−	1.17384i
$540$		0			0
$541$	−5.48009	−	31.0791i	−0.235607	−	1.33620i	−0.841331	−	0.540520i	$-0.818227\pi$
$541$	−5.48009	−	31.0791i	−0.235607	−	1.33620i	0.605724	−	0.795675i	$-0.292884\pi$
$542$	8.68166	+	12.6582i	0.372909	+	0.543715i
$543$		0			0
$544$	5.68195	+	7.04451i	0.243611	+	0.302031i
$545$	39.4934	−	16.1348i	1.69171	−	0.691141i
$546$		0			0
$547$	−4.68567	+	2.82781i	−0.200345	+	0.120909i	−0.613323	−	0.789832i	$-0.710168\pi$
$547$	−4.68567	+	2.82781i	−0.200345	+	0.120909i	0.412978	+	0.910741i	$0.364489\pi$
$548$	3.58967	−	2.36096i	0.153343	−	0.100855i
$549$		0			0
$550$	0.662235	−	11.3701i	0.0282378	−	0.484824i
$551$	5.45844	−	8.66041i	0.232537	−	0.368946i
$552$		0			0
$553$	4.98117	−	3.56033i	0.211821	−	0.151401i
$554$	17.2813	+	1.34321i	0.734213	+	0.0570675i
$555$		0			0
$556$	8.47075	+	3.46068i	0.359240	+	0.146766i
$557$	4.62603	+	15.4520i	0.196011	+	0.654723i	0.998327	+	0.0578228i	$0.0184158\pi$
$557$	4.62603	+	15.4520i	0.196011	+	0.654723i	−0.802316	+	0.596900i	$0.796399\pi$
$558$		0			0
$559$	26.3448	−	6.24384i	1.11427	−	0.264086i
$560$	1.02657	+	2.65888i	0.0433805	+	0.112358i
$561$		0			0
$562$	0.905828	−	1.71967i	0.0382100	−	0.0725400i
$563$	−0.361837	+	18.6562i	−0.0152496	+	0.786265i	0.911652	+	0.410962i	$0.134807\pi$
$563$	−0.361837	+	18.6562i	−0.0152496	+	0.786265i	−0.926902	+	0.375303i	$0.877539\pi$
$564$		0			0
$565$	10.5917	−	10.3882i	0.445595	−	0.437037i
$566$	0.997728	+	1.72812i	0.0419376	+	0.0726381i
$567$		0			0
$568$	−9.18103	+	15.9020i	−0.385228	+	0.667234i
$569$	3.73219	+	14.4892i	0.156461	+	0.607420i	0.997763	+	0.0668540i	$0.0212962\pi$
$569$	3.73219	+	14.4892i	0.156461	+	0.607420i	−0.841301	+	0.540566i	$0.818210\pi$
$570$		0			0
$571$	21.2431	−	11.7215i	0.888996	−	0.490527i	0.0282729	−	0.999600i	$-0.490999\pi$
$571$	21.2431	−	11.7215i	0.888996	−	0.490527i	0.860723	+	0.509073i	$0.170012\pi$
$572$	−12.4662	−	19.7790i	−0.521239	−	0.827003i
$573$		0			0
$574$	−1.16068	+	1.43902i	−0.0484460	+	0.0600637i
$575$	6.00695	−	20.0646i	0.250507	−	0.836753i
$576$		0			0
$577$	−15.8788	+	16.8305i	−0.661043	+	0.700665i	−0.967969	−	0.251068i	$-0.919218\pi$
$577$	−15.8788	+	16.8305i	−0.661043	+	0.700665i	0.306926	+	0.951733i	$0.400700\pi$
$578$	10.9061	−	8.45283i	0.453632	−	0.351591i
$579$		0			0
$580$	−8.43770	−	17.6459i	−0.350356	−	0.732708i
$581$	0.116146	+	1.19408i	0.00481853	+	0.0495389i
$582$		0			0
$583$	32.1618	+	1.24803i	1.33201	+	0.0516879i
$584$	1.91989	+	1.26273i	0.0794455	+	0.0522521i
$585$		0			0
$586$	9.03212	+	4.53610i	0.373113	+	0.187385i
$587$	0.0869337	+	4.48228i	0.00358814	+	0.185003i	0.997318	+	0.0731935i	$0.0233191\pi$
$587$	0.0869337	+	4.48228i	0.00358814	+	0.185003i	−0.993730	+	0.111810i	$0.964335\pi$
$588$		0			0
$589$	−6.03941	−	4.68090i	−0.248850	−	0.192873i
$590$	2.19365	−	0.343080i	0.0903110	−	0.0141244i
$591$		0			0
$592$	−4.47147	+	9.35129i	−0.183776	+	0.384336i
$593$	22.8131	+	8.30328i	0.936820	+	0.340975i	0.764909	−	0.644138i	$-0.222784\pi$
$593$	22.8131	+	8.30328i	0.936820	+	0.340975i	0.171911	+	0.985113i	$0.445006\pi$
$594$		0			0
$595$	4.27025	−	1.55424i	0.175063	−	0.0637177i
$596$	−0.0718960	+	0.739155i	−0.00294497	+	0.0302770i
$597$		0			0
$598$	15.1847	+	44.3788i	0.620947	+	1.81479i
$599$	25.2859	−	22.9458i	1.03315	−	0.937538i	0.0350692	−	0.999385i	$-0.488835\pi$
$599$	25.2859	−	22.9458i	1.03315	−	0.937538i	0.998086	+	0.0618468i	$0.0196990\pi$
$600$		0			0
$601$	−2.60915	+	7.62553i	−0.106430	+	0.311052i	−0.986493	−	0.163804i	$-0.947623\pi$
$601$	−2.60915	+	7.62553i	−0.106430	+	0.311052i	0.880063	+	0.474856i	$0.157500\pi$
$602$	−1.77238	−	4.10885i	−0.0722370	−	0.167464i
$603$		0			0
$604$	−21.6850	+	2.53461i	−0.882348	+	0.103132i
$605$	23.0713	−	7.39752i	0.937982	−	0.300752i
$606$		0			0
$607$	25.7893	−	7.17895i	1.04676	−	0.291385i	0.298233	−	0.954493i	$-0.403603\pi$
$607$	25.7893	−	7.17895i	1.04676	−	0.291385i	0.748523	+	0.663109i	$0.230763\pi$
$608$	6.39757	−	1.78088i	0.259456	−	0.0722244i
$609$		0			0
$610$	17.1747	−	5.50686i	0.695385	−	0.222966i
$611$	−27.4180	+	3.20471i	−1.10921	+	0.129649i
$612$		0			0
$613$	18.8407	+	43.6777i	0.760969	+	1.76412i	0.635606	+	0.772014i	$0.280750\pi$
$613$	18.8407	+	43.6777i	0.760969	+	1.76412i	0.125363	+	0.992111i	$0.459990\pi$
$614$	0.156216	−	0.456558i	0.00630435	−	0.0184252i
$615$		0			0
$616$	−8.84500	+	8.02641i	−0.356375	+	0.323393i
$617$	5.52097	+	16.1356i	0.222266	+	0.649596i	0.999785	+	0.0207372i	$0.00660132\pi$
$617$	5.52097	+	16.1356i	0.222266	+	0.649596i	−0.777519	+	0.628859i	$0.783522\pi$
$618$		0			0
$619$	2.37339	−	24.4005i	0.0953944	−	0.980741i	−0.818423	−	0.574616i	$-0.805151\pi$
$619$	2.37339	−	24.4005i	0.0953944	−	0.980741i	0.913818	−	0.406125i	$-0.133120\pi$
$620$	−13.7189	+	4.99328i	−0.550965	+	0.200535i
$621$		0			0
$622$	−13.6607	−	4.97208i	−0.547743	−	0.199362i
$623$	7.07843	−	14.8033i	0.283591	−	0.593081i
$624$		0			0
$625$	−30.8747	+	4.82871i	−1.23499	+	0.193148i
$626$	3.91365	+	3.03331i	0.156421	+	0.121235i
$627$		0			0
$628$	0.167433	+	8.63279i	0.00668129	+	0.344486i
$629$	14.7686	+	7.41705i	0.588861	+	0.295737i
$630$		0			0
$631$	−2.29673	−	1.51058i	−0.0914314	−	0.0601354i	0.502970	−	0.864304i	$-0.332241\pi$
$631$	−2.29673	−	1.51058i	−0.0914314	−	0.0601354i	−0.594401	+	0.804168i	$0.702611\pi$
$632$	20.8137	+	0.807666i	0.827924	+	0.0321272i
$633$		0			0
$634$	−1.54120	−	15.8450i	−0.0612091	−	0.629284i
$635$	4.24426	+	8.87612i	0.168428	+	0.352238i
$636$		0			0
$637$	−26.9398	+	20.8799i	−1.06739	+	0.827292i
$638$	−23.3137	+	24.7111i	−0.923000	+	0.978322i
$639$		0			0
$640$	1.75784	−	5.87160i	0.0694848	−	0.232095i
$641$	−9.15349	+	11.3486i	−0.361541	+	0.448241i	−0.926171	−	0.377103i	$-0.876920\pi$
$641$	−9.15349	+	11.3486i	−0.361541	+	0.448241i	0.564630	+	0.825344i	$0.309019\pi$
$642$		0			0
$643$	1.22908	+	1.95007i	0.0484703	+	0.0769034i	0.869347	−	0.494202i	$-0.164540\pi$
$643$	1.22908	+	1.95007i	0.0484703	+	0.0769034i	−0.820877	+	0.571105i	$0.806515\pi$
$644$	−6.22169	+	3.43298i	−0.245169	+	0.135279i
$645$		0			0
$646$	0.652964	+	2.53496i	0.0256905	+	0.0997367i
$647$	14.6670	−	25.4040i	0.576618	−	0.998732i	−0.419245	−	0.907873i	$-0.637705\pi$
$647$	14.6670	−	25.4040i	0.576618	−	0.998732i	0.995864	−	0.0908594i	$-0.0289614\pi$
$648$		0			0
$649$	1.76748	+	3.06137i	0.0693797	+	0.120169i
$650$	−10.0151	+	9.82275i	−0.392825	+	0.385280i
$651$		0			0
$652$	0.0814257	−	4.19829i	0.00318888	−	0.164418i
$653$	−21.8381	+	41.4586i	−0.854592	+	1.62240i	−0.0740872	+	0.997252i	$0.523604\pi$
$653$	−21.8381	+	41.4586i	−0.854592	+	1.62240i	−0.780504	+	0.625150i	$0.785038\pi$
$654$		0			0
$655$	6.43887	+	16.6771i	0.251587	+	0.651627i
$656$	−2.32510	+	0.551060i	−0.0907801	+	0.0215153i
$657$		0			0
$658$	1.30852	+	4.37076i	0.0510114	+	0.170390i
$659$	−40.2567	−	16.4467i	−1.56818	−	0.640672i	−0.583042	−	0.812442i	$-0.698138\pi$
$659$	−40.2567	−	16.4467i	−1.56818	−	0.640672i	−0.985137	+	0.171771i	$0.945051\pi$
$660$		0			0
$661$	−10.5438	−	0.819526i	−0.410105	−	0.0318759i	−0.129217	−	0.991616i	$-0.541246\pi$
$661$	−10.5438	−	0.819526i	−0.410105	−	0.0318759i	−0.280888	+	0.959741i	$0.590629\pi$
$662$	−27.4922	+	19.6503i	−1.06852	+	0.763730i
$663$		0			0
$664$	−2.17622	+	3.45280i	−0.0844536	+	0.133995i
$665$	0.193880	−	3.32878i	0.00751833	−	0.129085i
$666$		0			0
$667$	−52.1968	+	34.3304i	−2.02107	+	1.32928i
$668$	−1.28009	+	0.772540i	−0.0495283	+	0.0298905i
$669$		0			0
$670$	13.3606	−	5.45839i	0.516164	−	0.210876i
$671$	18.0277	+	22.3508i	0.695952	+	0.862845i
$672$		0			0
$673$	−17.2692	−	25.1791i	−0.665677	−	0.970582i	−0.999608	−	0.0279840i	$-0.991091\pi$
$673$	−17.2692	−	25.1791i	−0.665677	−	0.970582i	0.333931	−	0.942598i	$-0.391625\pi$
$674$	5.21079	+	29.5518i	0.200712	+	1.13829i
$675$		0			0
$676$	−2.84124	+	16.1135i	−0.109278	+	0.619749i
$677$	9.41592	−	4.28006i	0.361883	−	0.164496i	−0.224613	−	0.974448i	$-0.572112\pi$
$677$	9.41592	−	4.28006i	0.361883	−	0.164496i	0.586496	+	0.809952i	$0.300507\pi$
$678$		0			0
$679$	14.0721	+	2.76366i	0.540036	+	0.106060i
$680$	14.7213	+	4.72020i	0.564537	+	0.181011i
$681$		0			0
$682$	16.6733	+	19.1055i	0.638453	+	0.731586i
$683$	−11.6548	+	15.6552i	−0.445960	+	0.599029i	−0.967086	−	0.254452i	$-0.918105\pi$
$683$	−11.6548	+	15.6552i	−0.445960	+	0.599029i	0.521125	+	0.853480i	$0.325512\pi$
$684$		0			0
$685$	4.87329	−	11.2976i	0.186199	−	0.431658i
$686$	8.87271	+	8.05155i	0.338762	+	0.307410i
$687$		0			0
$688$	1.44267	−	5.60081i	0.0550015	−	0.213529i
$689$	−28.3023	−	27.7587i	−1.07823	−	1.05752i
$690$		0			0
$691$	−4.30928	+	19.8939i	−0.163933	+	0.756799i	0.819141	+	0.573592i	$0.194450\pi$
$691$	−4.30928	+	19.8939i	−0.163933	+	0.756799i	−0.983074	+	0.183207i	$0.941352\pi$
$692$	−1.45666	−	1.95664i	−0.0553739	−	0.0743801i
$693$		0			0
$694$	−3.20155	−	0.374208i	−0.121529	−	0.0142047i
$695$	25.7128	−	5.04982i	0.975341	−	0.191551i
$696$		0			0
$697$	0.806554	+	3.72347i	0.0305504	+	0.141036i
$698$	14.5730	−	16.6988i	0.551597	−	0.632060i
$699$		0			0
$700$	−1.72899	−	1.23581i	−0.0653497	−	0.0467091i
$701$	0.925503	+	0.776590i	0.0349558	+	0.0293314i	0.660098	−	0.751179i	$-0.270515\pi$
$701$	0.925503	+	0.776590i	0.0349558	+	0.0293314i	−0.625142	+	0.780511i	$0.714959\pi$
$702$		0			0
$703$	9.28939	−	7.79472i	0.350356	−	0.293984i
$704$	−32.3837	+	2.51706i	−1.22051	+	0.0948654i
$705$		0			0
$706$	4.03505	−	10.4510i	0.151861	−	0.393330i
$707$	1.84380	−	13.4990i	0.0693433	−	0.507683i
$708$		0			0
$709$	22.0574	+	12.1708i	0.828383	+	0.457082i	0.839828	−	0.542852i	$-0.182656\pi$
$709$	22.0574	+	12.1708i	0.828383	+	0.457082i	−0.0114455	+	0.999934i	$0.503643\pi$
$710$	0.989159	+	16.9832i	0.0371225	+	0.637369i
$711$		0			0
$712$	49.8838	−	25.0526i	1.86947	−	0.938885i
$713$	21.7324	+	41.2579i	0.813883	+	1.54512i
$714$		0			0
$715$	−60.9512	−	27.7057i	−2.27945	−	1.03614i
$716$	10.9845	−	16.0158i	0.410511	−	0.598540i
$717$		0			0
$718$	0.0856472	+	0.627049i	0.00319633	+	0.0234013i
$719$	16.3701	+	3.87979i	0.610502	+	0.144692i	0.524225	−	0.851580i	$-0.324355\pi$
$719$	16.3701	+	3.87979i	0.610502	+	0.144692i	0.0862768	+	0.996271i	$0.472503\pi$
$720$		0			0
$721$	−7.87010	−	8.34181i	−0.293098	−	0.310665i
$722$	−17.2780	−	2.70224i	−0.643022	−	0.100567i
$723$		0			0
$724$	9.61107	−	0.372953i	0.357193	−	0.0138607i
$725$	−15.9973	−	9.65440i	−0.594123	−	0.358555i
$726$		0			0
$727$	15.5314	+	4.32345i	0.576026	+	0.160348i	0.543921	−	0.839137i	$-0.316939\pi$
$727$	15.5314	+	4.32345i	0.576026	+	0.160348i	0.0321055	+	0.999484i	$0.489779\pi$
$728$	14.7111			0.545231
$729$		0			0
$730$	2.12897			0.0787966
$731$	−8.88360	−	2.47292i	−0.328572	−	0.0914642i
$732$		0			0
$733$	18.1838	+	10.9740i	0.671632	+	0.405332i	0.811110	−	0.584893i	$-0.198864\pi$
$733$	18.1838	+	10.9740i	0.671632	+	0.405332i	−0.139478	+	0.990225i	$0.544543\pi$
$734$	−37.2769	+	1.44651i	−1.37591	+	0.0533917i
$735$		0			0
$736$	−40.0408	−	6.26227i	−1.47592	−	0.230830i
$737$	15.7685	+	16.7137i	0.580841	+	0.615655i
$738$		0			0
$739$	−4.47861	−	1.06145i	−0.164748	−	0.0390461i	0.147414	−	0.989075i	$-0.452905\pi$
$739$	−4.47861	−	1.06145i	−0.164748	−	0.0390461i	−0.312162	+	0.950029i	$0.601053\pi$
$740$	−3.13555	−	22.9563i	−0.115265	−	0.843891i
$741$		0			0
$742$	−3.70591	+	5.40334i	−0.136048	+	0.198363i
$743$	9.03661	+	4.10764i	0.331521	+	0.150695i	0.572654	−	0.819797i	$-0.305914\pi$
$743$	9.03661	+	4.10764i	0.331521	+	0.150695i	−0.241133	+	0.970492i	$0.577519\pi$
$744$		0			0
$745$	0.991136	+	1.88162i	0.0363124	+	0.0689374i
$746$	10.5785	−	5.31275i	0.387308	−	0.194514i
$747$		0			0
$748$	0.463005	+	7.94949i	0.0169291	+	0.290662i
$749$	−7.17809	−	3.96070i	−0.262282	−	0.144721i
$750$		0			0
$751$	−2.19869	+	16.0972i	−0.0802313	+	0.587397i	0.906154	+	0.422947i	$0.139005\pi$
$751$	−2.19869	+	16.0972i	−0.0802313	+	0.587397i	−0.986386	+	0.164450i	$0.947415\pi$
$752$	−2.12392	+	5.50109i	−0.0774513	+	0.200604i
$753$		0			0
$754$	41.7182	−	3.24260i	1.51929	−	0.118088i
$755$	−47.8945	+	40.1882i	−1.74306	+	1.46260i
$756$		0			0
$757$	40.0675	+	33.6207i	1.45628	+	1.22196i	0.927833	+	0.372997i	$0.121670\pi$
$757$	40.0675	+	33.6207i	1.45628	+	1.22196i	0.528447	+	0.848967i	$0.322775\pi$
$758$	12.6584	+	9.04769i	0.459774	+	0.328627i
$759$		0			0
$760$	7.45865	−	8.54667i	0.270554	−	0.310020i
$761$	−8.78357	−	40.5495i	−0.318404	−	1.46992i	−0.803420	−	0.595413i	$-0.796989\pi$
$761$	−8.78357	−	40.5495i	−0.318404	−	1.46992i	0.485016	−	0.874505i	$-0.338814\pi$
$762$		0			0
$763$	−13.5678	+	2.66462i	−0.491186	+	0.0964658i
$764$	−14.9170	−	1.74355i	−0.539678	−	0.0630794i
$765$		0			0
$766$	−8.71795	−	11.7102i	−0.314992	−	0.423108i
$767$	0.921750	−	4.25527i	0.0332824	−	0.153649i
$768$		0			0
$769$	−15.5633	−	15.2643i	−0.561225	−	0.550446i	0.363248	−	0.931692i	$-0.381668\pi$
$769$	−15.5633	−	15.2643i	−0.561225	−	0.550446i	−0.924473	+	0.381247i	$0.875495\pi$
$770$	−2.76025	+	10.7160i	−0.0994726	+	0.386176i
$771$		0			0
$772$	−13.7996	−	12.5225i	−0.496660	−	0.450695i
$773$	15.5539	−	36.0580i	0.559435	−	1.29692i	−0.370377	−	0.928881i	$-0.620772\pi$
$773$	15.5539	−	36.0580i	0.559435	−	1.29692i	0.929812	−	0.368034i	$-0.119969\pi$
$774$		0			0
$775$	−8.32825	+	11.1868i	−0.299159	+	0.401841i
$776$	32.0786	+	36.7580i	1.15155	+	1.31953i
$777$		0			0
$778$	16.5719	+	5.31358i	0.594133	+	0.190501i
$779$	2.74309	+	0.538726i	0.0982815	+	0.0193019i
$780$		0			0
$781$	−24.6570	+	11.2080i	−0.882297	+	0.401053i
$782$	2.77409	−	15.7326i	0.0992012	−	0.562598i
$783$		0			0
$784$	1.26433	+	7.17035i	0.0451545	+	0.256084i
$785$	13.9854	+	20.3912i	0.499159	+	0.727792i
$786$		0			0
$787$	−28

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +O(q^{10})\)	\(q+(-0.984101 - 0.273943i) q^{2} +(-0.818925 - 0.494224i) q^{4} +(-2.73706 + 0.106211i) q^{5} +(0.877096 + 0.137175i) q^{7} +(2.07253 + 2.19675i) q^{8} +(2.72264 + 0.645278i) q^{10} +(0.602874 + 4.41382i) q^{11} +(3.10343 - 4.52491i) q^{13} +(-0.825572 - 0.375269i) q^{14} +(-0.546251 - 1.03703i) q^{16} +(-1.67001 + 0.838712i) q^{17} +(0.0797307 + 1.36892i) q^{19} +(2.29394 + 1.26574i) q^{20} +(0.615847 - 4.50880i) q^{22} +(3.01412 - 7.80676i) q^{23} +(2.49528 - 0.193948i) q^{25} +(-4.29366 + 3.60281i) q^{26} +(-0.650480 - 0.545818i) q^{28} +(-6.07359 - 4.34114i) q^{29} +(-3.66393 + 4.19840i) q^{31} +(-1.02526 - 4.73314i) q^{32} +(1.87322 - 0.367888i) q^{34} +(-2.41524 - 0.282301i) q^{35} +(-5.28091 - 7.09349i) q^{37} +(0.296544 - 1.36900i) q^{38} +(-5.90597 - 5.79254i) q^{40} +(0.508525 - 1.97421i) q^{41} +(3.65414 + 3.31596i) q^{43} +(1.68771 - 3.91254i) q^{44} +(-5.10480 + 6.85694i) q^{46} +(-3.30800 - 3.79054i) q^{47} +(-5.91526 - 1.89665i) q^{49} +(-2.50874 - 0.492700i) q^{50} +(-4.77780 + 2.17178i) q^{52} +(1.25461 - 7.11526i) q^{53} +(-2.11890 - 12.0169i) q^{55} +(1.51647 + 2.21106i) q^{56} +(4.78780 + 5.93594i) q^{58} +(0.734578 - 0.300108i) q^{59} +(5.51875 - 3.33058i) q^{61} +(4.75579 - 3.12794i) q^{62} +(-0.423953 + 7.27899i) q^{64} +(-8.01370 + 12.7146i) q^{65} +(4.19634 - 2.99937i) q^{67} +(1.78213 + 0.138518i) q^{68} +(2.29950 + 0.939450i) q^{70} +(1.74374 + 5.82449i) q^{71} +(0.740362 - 0.175469i) q^{73} +(3.25373 + 8.42737i) q^{74} +(0.611261 - 1.16045i) q^{76} +(-0.0766886 + 3.95404i) q^{77} +(4.92388 - 4.82930i) q^{79} +(1.60527 + 2.78040i) q^{80} +(-1.04126 + 1.80352i) q^{82} +(0.337095 + 1.30868i) q^{83} +(4.48185 - 2.47298i) q^{85} +(-2.68766 - 4.26426i) q^{86} +(-8.44660 + 10.4721i) q^{88} +(5.30103 - 17.7067i) q^{89} +(3.34271 - 3.54307i) q^{91} +(-6.32662 + 4.90350i) q^{92} +(2.21701 + 4.63648i) q^{94} +(-0.363622 - 3.73836i) q^{95} +(16.1419 + 0.626379i) q^{97} +(5.30163 + 3.48694i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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