LMFDB - Embedded newform 729.2.i.a.685.20

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			685.20
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.20

$q$-expansion

$f(q)$	$=$	$q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +O(q^{10})$	\(q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +(-1.43545 - 0.340207i) q^{10} +(-0.568431 - 4.16165i) q^{11} +(1.68656 - 2.45906i) q^{13} +(-0.215331 - 0.0978801i) q^{14} +(-1.94408 - 3.69075i) q^{16} +(6.87645 - 3.45348i) q^{17} +(0.307437 + 5.27850i) q^{19} +(-0.0802008 - 0.0442529i) q^{20} +(0.821725 - 6.01609i) q^{22} +(2.81598 - 7.29357i) q^{23} +(-3.94671 + 0.306763i) q^{25} +(3.30209 - 2.77079i) q^{26} +(-0.0112509 - 0.00944061i) q^{28} +(-7.18377 - 5.13465i) q^{29} +(1.77271 - 2.03130i) q^{31} +(-0.107416 - 0.495887i) q^{32} +(10.9153 - 2.14369i) q^{34} +(0.165845 + 0.0193845i) q^{35} +(2.96555 + 3.98343i) q^{37} +(-1.61816 + 7.47028i) q^{38} +(2.01186 + 1.97321i) q^{40} +(-2.73505 + 10.6181i) q^{41} +(0.972771 + 0.882743i) q^{43} +(0.149331 - 0.346189i) q^{44} +(6.74917 - 9.06571i) q^{46} +(2.91535 + 3.34063i) q^{47} +(-6.64024 - 2.12911i) q^{49} +(-5.61531 - 1.10281i) q^{50} +(0.243663 - 0.110759i) q^{52} +(1.30702 - 7.41249i) q^{53} +(0.744313 + 4.22121i) q^{55} +(0.255561 + 0.372617i) q^{56} +(-8.01392 - 9.93570i) q^{58} +(-9.14555 + 3.73637i) q^{59} +(-1.32732 + 0.801042i) q^{61} +(3.25624 - 2.14166i) q^{62} +(-0.442450 + 7.59658i) q^{64} +(-1.62251 + 2.57428i) q^{65} +(5.87992 - 4.20272i) q^{67} +(0.688629 + 0.0535245i) q^{68} +(0.223450 + 0.0912892i) q^{70} +(1.31059 + 4.37768i) q^{71} +(3.87220 - 0.917728i) q^{73} +(2.58572 + 6.69718i) q^{74} +(-0.221187 + 0.419914i) q^{76} +(-0.0133270 + 0.687135i) q^{77} +(7.95096 - 7.79825i) q^{79} +(2.12845 + 3.68659i) q^{80} +(-7.92530 + 13.7270i) q^{82} +(-1.44424 - 5.60690i) q^{83} +(-6.87536 + 3.79367i) q^{85} +(1.01252 + 1.60647i) q^{86} +(-7.28191 + 9.02815i) q^{88} +(-1.18082 + 3.94420i) q^{89} +(-0.334818 + 0.354886i) q^{91} +(0.554681 - 0.429910i) q^{92} +(2.76500 + 5.78252i) q^{94} +(-0.522366 - 5.37039i) q^{95} +(5.41592 + 0.210162i) q^{97} +(-8.42214 - 5.53933i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.39265	+	0.387670i	0.984752	+	0.274124i	0.722877	−	0.690977i	$-0.242820\pi$
$2$	1.39265	+	0.387670i	0.984752	+	0.274124i	0.261875	+	0.965102i	$0.415659\pi$
$3$		0			0
$3$		0			0
$4$	0.0768505	+	0.0463795i	0.0384253	+	0.0231898i
$5$	−1.01971	+	0.0395696i	−0.456030	+	0.0176961i	−0.265768	−	0.964037i	$-0.585625\pi$
$5$	−1.01971	+	0.0395696i	−0.456030	+	0.0176961i	−0.190263	+	0.981733i	$0.560934\pi$
$6$		0			0
$7$	−0.161658	−	0.0252828i	−0.0611009	−	0.00955601i	0.123894	−	0.992295i	$-0.460462\pi$
$7$	−0.161658	−	0.0252828i	−0.0611009	−	0.00955601i	−0.184995	+	0.982739i	$0.559227\pi$
$8$	−1.89502	−	2.00860i	−0.669990	−	0.710148i
$9$		0			0
$10$	−1.43545	−	0.340207i	−0.453928	−	0.107583i
$11$	−0.568431	−	4.16165i	−0.171388	−	1.25479i	−0.852547	−	0.522650i	$-0.824943\pi$
$11$	−0.568431	−	4.16165i	−0.171388	−	1.25479i	0.681159	−	0.732136i	$-0.261476\pi$
$12$		0			0
$13$	1.68656	−	2.45906i	0.467768	−	0.682022i	−0.516983	−	0.855996i	$-0.672945\pi$
$13$	1.68656	−	2.45906i	0.467768	−	0.682022i	0.984750	+	0.173974i	$0.0556609\pi$
$14$	−0.215331	−	0.0978801i	−0.0575497	−	0.0261595i
$15$		0			0
$16$	−1.94408	−	3.69075i	−0.486021	−	0.922688i
$17$	6.87645	−	3.45348i	1.66778	−	0.837593i	0.672553	−	0.740049i	$-0.265198\pi$
$17$	6.87645	−	3.45348i	1.66778	−	0.837593i	0.995231	−	0.0975436i	$-0.0310985\pi$
$18$		0			0
$19$	0.307437	+	5.27850i	0.0705310	+	1.21097i	0.828995	+	0.559255i	$0.188913\pi$
$19$	0.307437	+	5.27850i	0.0705310	+	1.21097i	−0.758464	+	0.651714i	$0.774050\pi$
$20$	−0.0802008	−	0.0442529i	−0.0179334	−	0.00989526i
$21$		0			0
$22$	0.821725	−	6.01609i	0.175192	−	1.28263i
$23$	2.81598	−	7.29357i	0.587172	−	1.52081i	−0.246834	−	0.969058i	$-0.579390\pi$
$23$	2.81598	−	7.29357i	0.587172	−	1.52081i	0.834006	−	0.551756i	$-0.186042\pi$
$24$		0			0
$25$	−3.94671	+	0.306763i	−0.789342	+	0.0613525i
$26$	3.30209	−	2.77079i	0.647594	−	0.543396i
$27$		0			0
$28$	−0.0112509	−	0.00944061i	−0.00212622	−	0.00178411i
$29$	−7.18377	−	5.13465i	−1.33399	−	0.953481i	−0.999940	−	0.0109259i	$-0.996522\pi$
$29$	−7.18377	−	5.13465i	−1.33399	−	0.953481i	−0.334052	−	0.942555i	$-0.608416\pi$
$30$		0			0
$31$	1.77271	−	2.03130i	0.318388	−	0.364832i	−0.571826	−	0.820375i	$-0.693765\pi$
$31$	1.77271	−	2.03130i	0.318388	−	0.364832i	0.890214	+	0.455543i	$0.150555\pi$
$32$	−0.107416	−	0.495887i	−0.0189886	−	0.0876613i
$33$		0			0
$34$	10.9153	−	2.14369i	1.87196	−	0.367641i
$35$	0.165845	+	0.0193845i	0.0280330	+	0.00327658i
$36$		0			0
$37$	2.96555	+	3.98343i	0.487534	+	0.654871i	0.976015	−	0.217703i	$-0.0698564\pi$
$37$	2.96555	+	3.98343i	0.487534	+	0.654871i	−0.488481	+	0.872574i	$0.662449\pi$
$38$	−1.61816	+	7.47028i	−0.262501	+	1.21184i
$39$		0			0
$40$	2.01186	+	1.97321i	0.318102	+	0.311993i
$41$	−2.73505	+	10.6181i	−0.427143	+	1.65827i	0.286741	+	0.958008i	$0.407428\pi$
$41$	−2.73505	+	10.6181i	−0.427143	+	1.65827i	−0.713884	+	0.700264i	$0.753066\pi$
$42$		0			0
$43$	0.972771	+	0.882743i	0.148346	+	0.134617i	0.742802	−	0.669512i	$-0.233497\pi$
$43$	0.972771	+	0.882743i	0.148346	+	0.134617i	−0.594455	+	0.804129i	$0.702632\pi$
$44$	0.149331	−	0.346189i	0.0225125	−	0.0521899i
$45$		0			0
$46$	6.74917	−	9.06571i	0.995111	−	1.33667i
$47$	2.91535	+	3.34063i	0.425248	+	0.487280i	0.925579	−	0.378554i	$-0.123579\pi$
$47$	2.91535	+	3.34063i	0.425248	+	0.487280i	−0.500331	+	0.865834i	$0.666788\pi$
$48$		0			0
$49$	−6.64024	−	2.12911i	−0.948606	−	0.304158i
$50$	−5.61531	−	1.10281i	−0.794125	−	0.155961i
$51$		0			0
$52$	0.243663	−	0.110759i	0.0337900	−	0.0153594i
$53$	1.30702	−	7.41249i	0.179533	−	1.01818i	−0.753247	−	0.657738i	$-0.771514\pi$
$53$	1.30702	−	7.41249i	0.179533	−	1.01818i	0.932780	−	0.360446i	$-0.117375\pi$
$54$		0			0
$55$	0.744313	+	4.22121i	0.100363	+	0.569187i
$56$	0.255561	+	0.372617i	0.0341508	+	0.0497931i
$57$		0			0
$58$	−8.01392	−	9.93570i	−1.05228	−	1.30462i
$59$	−9.14555	+	3.73637i	−1.19065	+	0.486434i	−0.884946	−	0.465693i	$-0.845805\pi$
$59$	−9.14555	+	3.73637i	−1.19065	+	0.486434i	−0.305703	+	0.952127i	$0.598892\pi$
$60$		0			0
$61$	−1.32732	+	0.801042i	−0.169946	+	0.102563i	−0.599121	−	0.800658i	$-0.704483\pi$
$61$	−1.32732	+	0.801042i	−0.169946	+	0.102563i	0.429175	+	0.903221i	$0.358804\pi$
$62$	3.25624	−	2.14166i	0.413542	−	0.271991i
$63$		0			0
$64$	−0.442450	+	7.59658i	−0.0553063	+	0.949572i
$65$	−1.62251	+	2.57428i	−0.201247	+	0.319300i
$66$		0			0
$67$	5.87992	−	4.20272i	0.718347	−	0.513443i	−0.162580	−	0.986695i	$-0.551982\pi$
$67$	5.87992	−	4.20272i	0.718347	−	0.513443i	0.880927	+	0.473252i	$0.156920\pi$
$68$	0.688629	+	0.0535245i	0.0835086	+	0.00649080i
$69$		0			0
$70$	0.223450	+	0.0912892i	0.0267073	+	0.0109111i
$71$	1.31059	+	4.37768i	0.155539	+	0.519535i	0.999867	−	0.0162905i	$-0.00518564\pi$
$71$	1.31059	+	4.37768i	0.155539	+	0.519535i	−0.844329	+	0.535826i	$0.820000\pi$
$72$		0			0
$73$	3.87220	−	0.917728i	0.453207	−	0.107412i	0.00232814	−	0.999997i	$-0.499259\pi$
$73$	3.87220	−	0.917728i	0.453207	−	0.107412i	0.450878	+	0.892585i	$0.351111\pi$
$74$	2.58572	+	6.69718i	0.300584	+	0.778531i
$75$		0			0
$76$	−0.221187	+	0.419914i	−0.0253719	+	0.0481674i
$77$	−0.0133270	+	0.687135i	−0.00151875	+	0.0783063i
$78$		0			0
$79$	7.95096	−	7.79825i	0.894553	−	0.877372i	−0.0984881	−	0.995138i	$-0.531401\pi$
$79$	7.95096	−	7.79825i	0.894553	−	0.877372i	0.993041	+	0.117767i	$0.0375735\pi$
$80$	2.12845	+	3.68659i	0.237968	+	0.412173i
$81$		0			0
$82$	−7.92530	+	13.7270i	−0.875203	+	1.51590i
$83$	−1.44424	−	5.60690i	−0.158526	−	0.615437i	−0.997462	−	0.0712058i	$-0.977315\pi$
$83$	−1.44424	−	5.60690i	−0.158526	−	0.615437i	0.838935	−	0.544231i	$-0.183179\pi$
$84$		0			0
$85$	−6.87536	+	3.79367i	−0.745738	+	0.411481i
$86$	1.01252	+	1.60647i	0.109182	+	0.173230i
$87$		0			0
$88$	−7.28191	+	9.02815i	−0.776254	+	0.962404i
$89$	−1.18082	+	3.94420i	−0.125166	+	0.418084i	−0.997487	−	0.0708497i	$-0.977429\pi$
$89$	−1.18082	+	3.94420i	−0.125166	+	0.418084i	0.872321	+	0.488934i	$0.162614\pi$
$90$		0			0
$91$	−0.334818	+	0.354886i	−0.0350984	+	0.0372022i
$92$	0.554681	−	0.429910i	0.0578295	−	0.0448213i
$93$		0			0
$94$	2.76500	+	5.78252i	0.285188	+	0.596421i
$95$	−0.522366	−	5.37039i	−0.0535936	−	0.550991i
$96$		0			0
$97$	5.41592	+	0.210162i	0.549903	+	0.0213388i	0.312230	−	0.950006i	$-0.398924\pi$
$97$	5.41592	+	0.210162i	0.549903	+	0.0213388i	0.237673	+	0.971345i	$0.423615\pi$
$98$	−8.42214	−	5.53933i	−0.850764	−	0.559556i
$99$		0			0
$100$	−0.317534	−	0.159472i	−0.0317534	−	0.0159472i
$101$	0.0115083	+	0.593364i	0.00114512	+	0.0590420i	0.999949	+	0.0101381i	$0.00322711\pi$
$101$	0.0115083	+	0.593364i	0.00114512	+	0.0590420i	−0.998803	+	0.0489039i	$0.984427\pi$
$102$		0			0
$103$	10.7641	+	8.34284i	1.06062	+	0.822045i	0.984558	−	0.175058i	$-0.0560113\pi$
$103$	10.7641	+	8.34284i	1.06062	+	0.822045i	0.0760649	+	0.997103i	$0.475764\pi$
$104$	−8.13534	+	1.27234i	−0.797735	+	0.124764i
$105$		0			0
$106$	4.69383	−	9.81630i	0.455905	−	0.953444i
$107$	7.79161	+	2.83591i	0.753243	+	0.274158i	0.689970	−	0.723838i	$-0.257624\pi$
$107$	7.79161	+	2.83591i	0.753243	+	0.274158i	0.0632735	+	0.997996i	$0.479846\pi$
$108$		0			0
$109$	−2.51418	+	0.915087i	−0.240815	+	0.0876494i	−0.459608	−	0.888122i	$-0.652010\pi$
$109$	−2.51418	+	0.915087i	−0.240815	+	0.0876494i	0.218793	+	0.975771i	$0.429788\pi$
$110$	−0.599871	+	6.16721i	−0.0571954	+	0.588020i
$111$		0			0
$112$	0.220964	+	0.645791i	0.0208791	+	0.0610215i
$113$	4.14789	−	3.76401i	0.390201	−	0.354088i	−0.453166	−	0.891426i	$-0.649706\pi$
$113$	4.14789	−	3.76401i	0.390201	−	0.354088i	0.843367	+	0.537338i	$0.180570\pi$
$114$		0			0
$115$	−2.58289	+	7.54878i	−0.240856	+	0.703928i
$116$	−0.313934	−	0.727780i	−0.0291480	−	0.0675727i
$117$		0			0
$118$	−14.1850	+	1.65799i	−1.30584	+	0.152631i
$119$	−1.19895	+	0.384426i	−0.109907	+	0.0352403i
$120$		0			0
$121$	−6.39916	+	1.78133i	−0.581742	+	0.161939i
$122$	−2.15903	+	0.601008i	−0.195470	+	0.0544127i
$123$		0			0
$124$	0.230444	−	0.0738889i	0.0206945	−	0.00663542i
$125$	9.08029	−	1.06133i	0.812166	−	0.0949286i
$126$		0			0
$127$	4.23580	+	9.81969i	0.375866	+	0.871356i	0.996206	+	0.0870232i	$0.0277354\pi$
$127$	4.23580	+	9.81969i	0.375866	+	0.871356i	−0.620340	+	0.784333i	$0.713005\pi$
$128$	−3.88966	+	11.3680i	−0.343801	+	1.00480i
$129$		0			0
$130$	−3.25755	+	2.95607i	−0.285706	+	0.259265i
$131$	−2.05573	−	6.00810i	−0.179610	−	0.524930i	0.819210	−	0.573494i	$-0.194412\pi$
$131$	−2.05573	−	6.00810i	−0.179610	−	0.524930i	−0.998820	+	0.0485634i	$0.984536\pi$
$132$		0			0
$133$	0.0837556	−	0.861083i	0.00726253	−	0.0746653i
$134$	9.81794	−	3.57344i	0.848141	−	0.308698i
$135$		0			0
$136$	−19.9677	−	7.26763i	−1.71221	−	0.623194i
$137$	−2.27819	+	4.76442i	−0.194639	+	0.407052i	−0.976230	−	0.216739i	$-0.930458\pi$
$137$	−2.27819	+	4.76442i	−0.194639	+	0.407052i	0.781591	+	0.623791i	$0.214408\pi$
$138$		0			0
$139$	−2.26702	+	0.354556i	−0.192286	+	0.0300730i	−0.249929	−	0.968264i	$-0.580407\pi$
$139$	−2.26702	+	0.354556i	−0.192286	+	0.0300730i	0.0576423	+	0.998337i	$0.481642\pi$
$140$	0.0118462	+	0.00918153i	0.00100119	+	0.000775981i
$141$		0			0
$142$	0.128097	+	6.60465i	0.0107497	+	0.554250i
$143$	−11.1925	−	5.62107i	−0.935961	−	0.470057i
$144$		0			0
$145$	7.52857	+	4.95162i	0.625214	+	0.411210i
$146$	5.74839	+	0.223064i	0.475740	+	0.0184609i
$147$		0			0
$148$	0.0431547	+	0.443669i	0.00354730	+	0.0364694i
$149$	4.16744	+	8.71547i	0.341410	+	0.713999i	0.999232	−	0.0391743i	$-0.0124728\pi$
$149$	4.16744	+	8.71547i	0.341410	+	0.713999i	−0.657822	+	0.753173i	$0.728522\pi$
$150$		0			0
$151$	3.54973	−	2.75125i	0.288873	−	0.223894i	−0.457848	−	0.889030i	$-0.651380\pi$
$151$	3.54973	−	2.75125i	0.288873	−	0.223894i	0.746722	+	0.665137i	$0.231627\pi$
$152$	10.0198	−	10.6204i	0.812712	−	0.861425i
$153$		0			0
$154$	−0.284942	+	0.951772i	−0.0229613	+	0.0766960i
$155$	−1.72728	+	2.14149i	−0.138738	+	0.172009i
$156$		0			0
$157$	−6.04980	−	9.59867i	−0.482827	−	0.766057i	0.512896	−	0.858451i	$-0.328573\pi$
$157$	−6.04980	−	9.59867i	−0.482827	−	0.766057i	−0.995723	+	0.0923939i	$0.970548\pi$
$158$	14.0961	−	7.77787i	1.12142	−	0.618774i
$159$		0			0
$160$	0.129156	+	0.501413i	0.0102107	+	0.0396402i
$161$	−0.639627	+	1.10787i	−0.0504096	+	0.0873121i
$162$		0			0
$163$	5.36363	+	9.29008i	0.420112	+	0.727656i	0.995950	−	0.0899083i	$-0.0286574\pi$
$163$	5.36363	+	9.29008i	0.420112	+	0.727656i	−0.575838	+	0.817564i	$0.695324\pi$
$164$	−0.702653	+	0.689158i	−0.0548680	+	0.0538142i
$165$		0			0
$166$	0.162304	−	8.36833i	0.0125972	−	0.649509i
$167$	2.38746	−	4.53248i	0.184747	−	0.350734i	−0.774835	−	0.632164i	$-0.782167\pi$
$167$	2.38746	−	4.53248i	0.184747	−	0.350734i	0.959582	+	0.281430i	$0.0908088\pi$
$168$		0			0
$169$	1.47980	+	3.83277i	0.113831	+	0.294828i
$170$	−11.0457	+	2.61787i	−0.847164	+	0.200782i
$171$		0			0
$172$	0.0338168	+	0.112956i	0.00257850	+	0.00861281i
$173$	18.0422	+	7.37104i	1.37172	+	0.560410i	0.939869	−	0.341535i	$-0.110947\pi$
$173$	18.0422	+	7.37104i	1.37172	+	0.560410i	0.431852	+	0.901945i	$0.357860\pi$
$174$		0			0
$175$	0.645773	+	0.0501934i	0.0488158	+	0.00379427i
$176$	−14.2546	+	10.1885i	−1.07448	+	0.767990i
$177$		0			0
$178$	−3.17351	+	5.03512i	−0.237865	+	0.377398i
$179$	0.113114	−	1.94209i	0.00845452	−	0.145159i	−0.991439	−	0.130570i	$-0.958319\pi$
$179$	0.113114	−	1.94209i	0.00845452	−	0.145159i	0.999894	−	0.0145883i	$-0.00464376\pi$
$180$		0			0
$181$	13.2848	−	8.73752i	0.987449	−	0.649455i	0.0504274	−	0.998728i	$-0.483942\pi$
$181$	13.2848	−	8.73752i	0.987449	−	0.649455i	0.937021	+	0.349273i	$0.113571\pi$
$182$	−0.603862	+	0.364433i	−0.0447613	+	0.0270136i
$183$		0			0
$184$	−19.9862	+	8.16526i	−1.47340	+	0.601951i
$185$	−3.18164	−	3.94461i	−0.233919	−	0.290014i
$186$		0			0
$187$	−18.2810	−	26.6543i	−1.33684	−	1.94916i
$188$	0.0691098	+	0.391941i	0.00504035	+	0.0285853i
$189$		0			0
$190$	1.35447	−	7.68158i	0.0982636	−	0.557281i
$191$	−5.41212	+	2.46011i	−0.391607	+	0.178007i	−0.599929	−	0.800053i	$-0.704805\pi$
$191$	−5.41212	+	2.46011i	−0.391607	+	0.178007i	0.208322	+	0.978060i	$0.433200\pi$
$192$		0			0
$193$	−23.9668	−	4.70693i	−1.72517	−	0.338812i	−0.770717	−	0.637178i	$-0.780102\pi$
$193$	−23.9668	−	4.70693i	−1.72517	−	0.338812i	−0.954452	+	0.298366i	$0.903559\pi$
$194$	7.46101	+	2.39228i	0.535669	+	0.171755i
$195$		0			0
$196$	−0.411559	−	0.471594i	−0.0293971	−	0.0336853i
$197$	−16.1596	+	21.7060i	−1.15132	+	1.54649i	−0.362371	+	0.932034i	$0.618033\pi$
$197$	−16.1596	+	21.7060i	−1.15132	+	1.54649i	−0.788949	+	0.614458i	$0.789375\pi$
$198$		0			0
$199$	1.00671	−	2.33383i	0.0713641	−	0.165440i	−0.878800	−	0.477189i	$-0.841656\pi$
$199$	1.00671	−	2.33383i	0.0713641	−	0.165440i	0.950164	+	0.311749i	$0.100915\pi$
$200$	8.09525	+	7.34605i	0.572421	+	0.519444i
$201$		0			0
$202$	−0.214003	+	0.830810i	−0.0150572	+	0.0584556i
$203$	1.03149	+	1.01168i	0.0723967	+	0.0710062i
$204$		0			0
$205$	2.36882	−	10.9357i	0.165445	−	0.763781i
$206$	11.7564	+	15.7916i	0.819108	+	1.10025i
$207$		0			0
$208$	−12.3546	−	1.44405i	−0.856638	−	0.100127i
$209$	21.7925	−	4.27991i	1.50742	−	0.296047i
$210$		0			0
$211$	−5.07006	−	23.4060i	−0.349038	−	1.61134i	−0.727763	−	0.685828i	$-0.759440\pi$
$211$	−5.07006	−	23.4060i	−0.349038	−	1.61134i	0.378726	−	0.925509i	$-0.376362\pi$
$212$	0.444233	−	0.509034i	0.0305100	−	0.0349606i
$213$		0			0
$214$	9.75158	+	6.97001i	0.666604	+	0.476460i
$215$	−1.02688	−	0.861654i	−0.0700326	−	0.0587643i
$216$		0			0
$217$	−0.337929	+	0.283556i	−0.0229401	+	0.0192490i
$218$	−3.85612	+	0.299722i	−0.261170	+	0.0202997i
$219$		0			0
$220$	−0.138577	+	0.358923i	−0.00934284	+	0.0241986i
$221$	3.10521	−	22.7341i	0.208879	−	1.52926i
$222$		0			0
$223$	15.1723	+	8.37173i	1.01601	+	0.560612i	0.901486	−	0.432808i	$-0.142477\pi$
$223$	15.1723	+	8.37173i	1.01601	+	0.560612i	0.114527	+	0.993420i	$0.463465\pi$
$224$	0.00482720	+	0.0828798i	0.000322531	+	0.00553764i
$225$		0			0
$226$	7.23576	−	3.63393i	0.481315	−	0.241726i
$227$	−7.95218	−	15.0968i	−0.527805	−	1.00201i	−0.993146	−	0.116881i	$-0.962710\pi$
$227$	−7.95218	−	15.0968i	−0.527805	−	1.00201i	0.465341	−	0.885131i	$-0.345932\pi$
$228$		0			0
$229$	19.3311	+	8.78705i	1.27743	+	0.580664i	0.933583	−	0.358360i	$-0.116664\pi$
$229$	19.3311	+	8.78705i	1.27743	+	0.580664i	0.343849	+	0.939025i	$0.388269\pi$
$230$	−6.52350	+	9.51150i	−0.430147	+	0.627170i
$231$		0			0
$232$	3.29990	+	24.1596i	0.216649	+	1.58615i
$233$	6.53641	+	1.54916i	0.428214	+	0.101489i	0.439071	−	0.898452i	$-0.355308\pi$
$233$	6.53641	+	1.54916i	0.428214	+	0.101489i	−0.0108566	+	0.999941i	$0.503456\pi$
$234$		0			0
$235$	−3.10502	−	3.29113i	−0.202549	−	0.214689i
$236$	−0.876131	−	0.137024i	−0.0570313	−	0.00891953i
$237$		0			0
$238$	−1.81874	+	0.0705755i	−0.117892	+	0.00457473i
$239$	−0.468903	−	0.282985i	−0.0303308	−	0.0183048i	0.501453	−	0.865185i	$-0.332799\pi$
$239$	−0.468903	−	0.282985i	−0.0303308	−	0.0183048i	−0.531784	+	0.846880i	$0.678478\pi$
$240$		0			0
$241$	7.70182	+	2.14395i	0.496118	+	0.138104i	0.507189	−	0.861835i	$-0.330685\pi$
$241$	7.70182	+	2.14395i	0.496118	+	0.138104i	−0.0110712	+	0.999939i	$0.503524\pi$
$242$	−9.60236			−0.617263
$243$		0			0
$244$	−0.139157			−0.00890863
$245$	6.85540	+	1.90833i	0.437975	+	0.121919i
$246$		0			0
$247$	13.4987	+	8.14649i	0.858900	+	0.518349i
$248$	−7.43938	+	0.288682i	−0.472401	+	0.0183313i
$249$		0			0
$250$	13.0571	+	2.04210i	0.825804	+	0.129153i
$251$	−1.78971	−	1.89698i	−0.112966	−	0.119737i	0.668423	−	0.743781i	$-0.266970\pi$
$251$	−1.78971	−	1.89698i	−0.112966	−	0.119737i	−0.781388	+	0.624045i	$0.785488\pi$
$252$		0			0
$253$	−31.9540	−	7.57323i	−2.00893	−	0.476125i
$254$	2.09218	+	15.3175i	0.131275	+	0.961104i
$255$		0			0
$256$	−1.21605	+	1.77305i	−0.0760032	+	0.110815i
$257$	−27.3862	−	12.4485i	−1.70830	−	0.776519i	−0.997308	−	0.0733207i	$-0.976640\pi$
$257$	−27.3862	−	12.4485i	−1.70830	−	0.776519i	−0.710994	−	0.703198i	$-0.751755\pi$
$258$		0			0
$259$	−0.378692	−	0.718930i	−0.0235308	−	0.0446721i
$260$	−0.244084	+	0.122584i	−0.0151375	+	0.00760232i
$261$		0			0
$262$	−0.533749	−	9.16412i	−0.0329752	−	0.566161i
$263$	14.2684	+	7.87295i	0.879825	+	0.485467i	0.857619	−	0.514286i	$-0.171943\pi$
$263$	14.2684	+	7.87295i	0.879825	+	0.485467i	0.0222067	+	0.999753i	$0.492931\pi$
$264$		0			0
$265$	−1.03948	+	7.61034i	−0.0638548	+	0.467499i
$266$	0.450459	−	1.16672i	0.0276194	−	0.0715360i
$267$		0			0
$268$	0.646795	−	0.0502729i	0.0395093	−	0.00307090i
$269$	−7.73321	+	6.48893i	−0.471502	+	0.395637i	−0.847342	−	0.531047i	$-0.821799\pi$
$269$	−7.73321	+	6.48893i	−0.471502	+	0.395637i	0.375840	+	0.926685i	$0.377354\pi$
$270$		0			0
$271$	5.17989	+	4.34645i	0.314656	+	0.264028i	0.786413	−	0.617701i	$-0.211936\pi$
$271$	5.17989	+	4.34645i	0.314656	+	0.264028i	−0.471757	+	0.881729i	$0.656380\pi$
$272$	−26.1144	−	18.6654i	−1.58342	−	1.13176i
$273$		0			0
$274$	−5.01974	+	5.75198i	−0.303254	+	0.347490i
$275$	3.52007	+	16.2505i	0.212268	+	0.979940i
$276$		0			0
$277$	−20.0846	+	3.94449i	−1.20677	+	0.237001i	−0.755356	−	0.655314i	$-0.772536\pi$
$277$	−20.0846	+	3.94449i	−1.20677	+	0.237001i	−0.451412	+	0.892316i	$0.649079\pi$
$278$	−3.29462	−	0.385086i	−0.197598	−	0.0230959i
$279$		0			0
$280$	−0.275344	−	0.369851i	−0.0164549	−	0.0221028i
$281$	4.06776	−	18.7789i	0.242662	−	1.12025i	−0.679568	−	0.733613i	$-0.737833\pi$
$281$	4.06776	−	18.7789i	0.242662	−	1.12025i	0.922230	−	0.386641i	$-0.126365\pi$
$282$		0			0
$283$	17.0525	+	16.7250i	1.01367	+	0.994197i	0.999984	−	0.00570916i	$-0.00181729\pi$
$283$	17.0525	+	16.7250i	1.01367	+	0.994197i	0.0136829	+	0.999906i	$0.495644\pi$
$284$	−0.102315	+	0.397212i	−0.00607128	+	0.0235702i
$285$		0			0
$286$	−13.4081	−	12.1672i	−0.792835	−	0.719460i
$287$	0.710598	−	1.64735i	0.0419453	−	0.0972401i
$288$		0			0
$289$	25.2073	−	33.8593i	1.48278	−	1.99172i
$290$	8.56506	+	9.81448i	0.502958	+	0.576326i
$291$		0			0
$292$	0.340144	+	0.109063i	0.0199054	+	0.00638242i
$293$	1.23529	+	0.242602i	0.0721662	+	0.0141730i	0.228665	−	0.973505i	$-0.426564\pi$
$293$	1.23529	+	0.242602i	0.0721662	+	0.0141730i	−0.156499	+	0.987678i	$0.550021\pi$
$294$		0			0
$295$	9.17801	−	4.17192i	0.534364	−	0.242898i
$296$	2.38134	−	13.5053i	0.138413	−	0.784978i
$297$		0			0
$298$	2.42506	+	13.7532i	0.140480	+	0.796701i
$299$	−13.1860	−	19.2257i	−0.762568	−	1.11185i
$300$		0			0
$301$	−0.134938	−	0.167297i	−0.00777769	−	0.00964282i
$302$	6.01011	−	2.45540i	0.345843	−	0.141293i
$303$		0			0
$304$	18.8839	−	11.3965i	1.08307	−	0.653635i
$305$	1.32179	−	0.869356i	0.0756856	−	0.0497792i
$306$		0			0
$307$	1.18915	−	20.4169i	0.0678682	−	1.16525i	−0.776724	−	0.629842i	$-0.783120\pi$
$307$	1.18915	−	20.4169i	0.0678682	−	1.16525i	0.844592	−	0.535411i	$-0.179843\pi$
$308$	−0.0328932	+	0.0521886i	−0.00187426	+	0.00297372i
$309$		0			0
$310$	−3.23569	+	2.31273i	−0.183775	+	0.131354i
$311$	26.4427	+	2.05529i	1.49943	+	0.116545i	0.800795	−	0.598938i	$-0.204411\pi$
$311$	26.4427	+	2.05529i	1.49943	+	0.116545i	0.698630	+	0.715483i	$0.253793\pi$
$312$		0			0
$313$	−5.58110	−	2.28013i	−0.315463	−	0.128881i	0.214938	−	0.976628i	$-0.431045\pi$
$313$	−5.58110	−	2.28013i	−0.315463	−	0.128881i	−0.530401	+	0.847747i	$0.677959\pi$
$314$	−4.70414	−	15.7129i	−0.265470	−	0.886731i
$315$		0			0
$316$	0.972714	−	0.230538i	0.0547195	−	0.0129688i
$317$	−2.02480	−	5.24435i	−0.113724	−	0.294552i	0.864323	−	0.502937i	$-0.167747\pi$
$317$	−2.02480	−	5.24435i	−0.113724	−	0.294552i	−0.978047	+	0.208385i	$0.933179\pi$
$318$		0			0
$319$	−17.2852	+	32.8150i	−0.967783	+	1.83729i
$320$	0.150580	−	7.76385i	0.00841766	−	0.434012i
$321$		0			0
$322$	−1.32026	+	1.29490i	−0.0735754	+	0.0721622i
$323$	20.3433	+	35.2356i	1.13193	+	1.96056i
$324$		0			0
$325$	−5.90202	+	10.2226i	−0.327385	+	0.567047i
$326$	3.86817	+	15.0172i	0.214238	+	0.831723i
$327$		0			0
$328$	26.5105	−	14.6279i	1.46380	−	0.807690i
$329$	−0.386829	−	0.613746i	−0.0213266	−	0.0338369i
$330$		0			0
$331$	−6.62023	+	8.20779i	−0.363881	+	0.451141i	−0.926903	−	0.375300i	$-0.877540\pi$
$331$	−6.62023	+	8.20779i	−0.363881	+	0.451141i	0.563023	+	0.826441i	$0.309638\pi$
$332$	0.149054	−	0.497876i	0.00818042	−	0.0273245i
$333$		0			0
$334$	5.08200	−	5.38661i	0.278075	−	0.294742i
$335$	−5.82954	+	4.51824i	−0.318502	+	0.246858i
$336$		0			0
$337$	1.94346	+	4.06439i	0.105867	+	0.221402i	0.948283	−	0.317425i	$-0.102818\pi$
$337$	1.94346	+	4.06439i	0.105867	+	0.221402i	−0.842416	+	0.538827i	$0.818868\pi$
$338$	0.574986	+	5.91138i	0.0312751	+	0.321537i
$339$		0			0
$340$	−0.704324	−	0.0273310i	−0.0381973	−	0.00148223i
$341$	−9.46122	−	6.22274i	−0.512354	−	0.336980i
$342$		0			0
$343$	2.04315	+	1.02611i	0.110320	+	0.0554046i
$344$	−0.0703402	−	3.62672i	−0.00379249	−	0.195540i
$345$		0			0
$346$	22.2689	+	17.2597i	1.19718	+	0.927887i
$347$	17.1174	−	2.67711i	0.918908	−	0.143715i	0.322660	−	0.946515i	$-0.395423\pi$
$347$	17.1174	−	2.67711i	0.918908	−	0.143715i	0.596248	+	0.802800i	$0.296658\pi$
$348$		0			0
$349$	−4.88284	+	10.2116i	−0.261372	+	0.546614i	−0.990459	−	0.137807i	$-0.955995\pi$
$349$	−4.88284	+	10.2116i	−0.261372	+	0.546614i	0.729087	+	0.684421i	$0.239945\pi$
$350$	0.879876	+	0.320249i	0.0470314	+	0.0171180i
$351$		0			0
$352$	−2.00265	+	0.728906i	−0.106742	+	0.0388508i
$353$	2.60842	−	26.8169i	0.138832	−	1.42732i	−0.624355	−	0.781140i	$-0.714638\pi$
$353$	2.60842	−	26.8169i	0.138832	−	1.42732i	0.763187	−	0.646177i	$-0.223633\pi$
$354$		0			0
$355$	−1.50965	−	4.41213i	−0.0801240	−	0.234171i
$356$	−0.273676	+	0.248348i	−0.0145048	+	0.0131624i
$357$		0			0
$358$	0.910418	−	2.66080i	0.0481171	−	0.140628i
$359$	9.25644	+	21.4588i	0.488536	+	1.13255i	0.967076	+	0.254488i	$0.0819070\pi$
$359$	9.25644	+	21.4588i	0.488536	+	1.13255i	−0.478540	+	0.878066i	$0.658834\pi$
$360$		0			0
$361$	−8.89647	+	1.03985i	−0.468235	+	0.0547288i
$362$	21.8883	−	7.01820i	1.15042	−	0.368868i
$363$		0			0
$364$	−0.0421903	+	0.0117445i	−0.00221137	+	0.000615578i
$365$	−3.91222	+	1.08904i	−0.204775	+	0.0570031i
$366$		0			0
$367$	16.3887	−	5.25483i	0.855484	−	0.274300i	0.154953	−	0.987922i	$-0.450477\pi$
$367$	16.3887	−	5.25483i	0.855484	−	0.274300i	0.700531	+	0.713622i	$0.252947\pi$
$368$	−32.3932	+	3.78623i	−1.68861	+	0.197371i
$369$		0			0
$370$	−2.90170	−	6.72689i	−0.150852	−	0.349715i
$371$	−0.398699	+	1.16524i	−0.0206994	+	0.0604963i
$372$		0			0
$373$	−2.69016	+	2.44119i	−0.139291	+	0.126400i	−0.738675	−	0.674062i	$-0.764548\pi$
$373$	−2.69016	+	2.44119i	−0.139291	+	0.126400i	0.599384	+	0.800462i	$0.295412\pi$
$374$	−15.1259	−	44.2071i	−0.782142	−	2.28590i
$375$		0			0
$376$	1.18534	−	12.1863i	0.0611291	−	0.628462i
$377$	−24.7423	+	9.00546i	−1.27429	+	0.463805i
$378$		0			0
$379$	29.5533	+	10.7565i	1.51805	+	0.552526i	0.960661	−	0.277724i	$-0.0895802\pi$
$379$	29.5533	+	10.7565i	1.51805	+	0.552526i	0.557391	+	0.830250i	$0.311802\pi$
$380$	0.208932	−	0.436945i	0.0107180	−	0.0224148i
$381$		0			0
$382$	−8.49090	+	1.32795i	−0.434432	+	0.0679439i
$383$	0.0366957	+	0.0284413i	0.00187506	+	0.00145328i	0.613538	−	0.789665i	$-0.289746\pi$
$383$	0.0366957	+	0.0284413i	0.00187506	+	0.00145328i	−0.611663	+	0.791119i	$0.709499\pi$
$384$		0			0
$385$	−0.0135999	−	0.701209i	−0.000693117	−	0.0357369i
$386$	−31.5526	−	15.8463i	−1.60599	−	0.806557i
$387$		0			0
$388$	0.406469	+	0.267339i	0.0206353	+	0.0135721i
$389$	−27.4190	−	1.06398i	−1.39020	−	0.0539461i	−0.667243	−	0.744840i	$-0.732526\pi$
$389$	−27.4190	−	1.06398i	−1.39020	−	0.0539461i	−0.722956	+	0.690894i	$0.757217\pi$
$390$		0			0
$391$	−5.82427	−	59.8788i	−0.294546	−	3.02820i
$392$	8.30684	+	17.3723i	0.419559	+	0.877433i
$393$		0			0
$394$	−30.9194	+	23.9643i	−1.55770	+	1.20731i
$395$	−7.79914	+	8.26661i	−0.392417	+	0.415938i
$396$		0			0
$397$	−6.43740	+	21.5024i	−0.323084	+	1.07918i	0.630032	+	0.776569i	$0.283042\pi$
$397$	−6.43740	+	21.5024i	−0.323084	+	1.07918i	−0.953116	+	0.302606i	$0.902143\pi$
$398$	2.30675	−	2.85993i	0.115627	−	0.143355i
$399$		0			0
$400$	8.80493	+	13.9700i	0.440246	+	0.698498i
$401$	−4.97522	+	2.74521i	−0.248451	+	0.137089i	−0.602451	−	0.798156i	$-0.705809\pi$
$401$	−4.97522	+	2.74521i	−0.248451	+	0.137089i	0.354000	+	0.935245i	$0.384821\pi$
$402$		0			0
$403$	−2.00531	−	7.78511i	−0.0998919	−	0.387804i
$404$	−0.0266355	+	0.0461341i	−0.00132517	+	0.00229526i
$405$		0			0
$406$	1.04431	+	1.80880i	0.0518282	+	0.0897691i
$407$	14.8919	−	14.6059i	0.738166	−	0.723988i
$408$		0			0
$409$	0.117282	−	6.04703i	0.00579922	−	0.299006i	−0.985671	−	0.168677i	$-0.946051\pi$
$409$	0.117282	−	6.04703i	0.00579922	−	0.299006i	0.991471	−	0.130330i	$-0.0416036\pi$
$410$	7.53837	−	14.3112i	0.372294	−	0.706782i
$411$		0			0
$412$	0.440293	+	1.14039i	0.0216917	+	0.0561829i
$413$	1.57292	−	0.372788i	0.0773981	−	0.0183437i
$414$		0			0
$415$	1.69458	+	5.66029i	0.0831836	+	0.277853i
$416$	−1.40058	−	0.572201i	−0.0686692	−	0.0280544i
$417$		0			0
$418$	32.0085	+	2.48790i	1.56559	+	0.121687i
$419$	6.05958	−	4.33113i	0.296030	−	0.211589i	−0.423772	−	0.905769i	$-0.639294\pi$
$419$	6.05958	−	4.33113i	0.296030	−	0.211589i	0.719802	+	0.694179i	$0.244233\pi$
$420$		0			0
$421$	−8.47127	+	13.4406i	−0.412864	+	0.655054i	−0.986444	−	0.164095i	$-0.947529\pi$
$421$	−8.47127	+	13.4406i	−0.412864	+	0.655054i	0.573580	+	0.819150i	$0.305554\pi$
$422$	2.01300	−	34.5619i	0.0979914	−	1.68245i
$423$		0			0
$424$	−17.3656	+	11.4215i	−0.843346	+	0.554677i
$425$	−26.0800	+	15.7393i	−1.26506	+	0.763470i
$426$		0			0
$427$	0.234824	−	0.0959363i	0.0113639	−	0.00464268i
$428$	0.467261	+	0.579313i	0.0225859	+	0.0280021i
$429$		0			0
$430$	−1.09604	−	1.59807i	−0.0528560	−	0.0770659i
$431$	−4.23951	−	24.0435i	−0.204210	−	1.15813i	−0.898678	−	0.438609i	$-0.855471\pi$
$431$	−4.23951	−	24.0435i	−0.204210	−	1.15813i	0.694468	−	0.719524i	$-0.255640\pi$
$432$		0			0
$433$	3.18938	−	18.0879i	0.153272	−	0.869249i	−0.807077	−	0.590447i	$-0.798952\pi$
$433$	3.18938	−	18.0879i	0.153272	−	0.869249i	0.960349	−	0.278802i	$-0.0899373\pi$
$434$	−0.580543	+	0.263889i	−0.0278670	+	0.0126671i
$435$		0			0
$436$	−0.235657	−	0.0462816i	−0.0112859	−	0.00221649i
$437$	39.3648	+	12.6218i	1.88307	+	0.603783i
$438$		0			0
$439$	18.1744	+	20.8256i	0.867419	+	0.993952i	0.999996	+	0.00277887i	$0.000884543\pi$
$439$	18.1744	+	20.8256i	0.867419	+	0.993952i	−0.132577	+	0.991173i	$0.542325\pi$
$440$	7.06823	−	9.49428i	0.336965	−	0.452622i
$441$		0			0
$442$	13.1378	−	30.4569i	0.624902	−	1.44869i
$443$	−3.08554	−	2.79998i	−0.146599	−	0.133031i	0.595409	−	0.803423i	$-0.296990\pi$
$443$	−3.08554	−	2.79998i	−0.146599	−	0.133031i	−0.742007	+	0.670392i	$0.766126\pi$
$444$		0			0
$445$	1.04803	−	4.06868i	0.0496812	−	0.192874i
$446$	17.8842	+	17.5407i	0.846843	+	0.830578i
$447$		0			0
$448$	0.263588	−	1.21686i	0.0124534	−	0.0574912i
$449$	2.94564	+	3.95668i	0.139013	+	0.186727i	0.866178	−	0.499736i	$-0.166570\pi$
$449$	2.94564	+	3.95668i	0.139013	+	0.186727i	−0.727165	+	0.686463i	$0.759162\pi$
$450$		0			0
$451$	45.7436	+	5.34666i	2.15398	+	0.251765i
$452$	0.493341	−	0.0968889i	0.0232048	−	0.00455727i
$453$		0			0
$454$	−5.22200	−	24.1074i	−0.245081	−	1.13142i
$455$	0.327376	−	0.375131i	0.0153476	−	0.0175864i
$456$		0			0
$457$	−1.77444	−	1.26829i	−0.0830049	−	0.0593283i	0.539232	−	0.842157i	$-0.318714\pi$
$457$	−1.77444	−	1.26829i	−0.0830049	−	0.0593283i	−0.622237	+	0.782829i	$0.713776\pi$
$458$	23.5149	+	19.7314i	1.09878	+	0.921986i
$459$		0			0
$460$	−0.548605	+	0.460335i	−0.0255789	+	0.0214632i
$461$	−5.22069	+	0.405784i	−0.243152	+	0.0188992i	−0.198490	−	0.980103i	$-0.563604\pi$
$461$	−5.22069	+	0.405784i	−0.243152	+	0.0188992i	−0.0446617	+	0.999002i	$0.514221\pi$
$462$		0			0
$463$	−8.37633	+	21.6952i	−0.389281	+	1.00826i	0.590294	+	0.807188i	$0.299012\pi$
$463$	−8.37633	+	21.6952i	−0.389281	+	1.00826i	−0.979576	+	0.201076i	$0.935556\pi$
$464$	−4.98487	+	36.4957i	−0.231417	+	1.69427i
$465$		0			0
$466$	8.50236	+	4.69140i	0.393864	+	0.217325i
$467$	−1.60319	−	27.5257i	−0.0741869	−	1.27374i	−0.805869	−	0.592094i	$-0.798302\pi$
$467$	−1.60319	−	27.5257i	−0.0741869	−	1.27374i	0.731682	−	0.681646i	$-0.238736\pi$
$468$		0			0
$469$	−1.05679	+	0.530741i	−0.0487981	+	0.0245073i
$470$	−3.04833	−	5.78711i	−0.140609	−	0.266939i
$471$		0			0
$472$	24.8359	+	11.2893i	1.14316	+	0.519631i
$473$	3.12072	−	4.55011i	0.143491	−	0.209214i
$474$		0			0
$475$	−2.83261	−	20.7384i	−0.129969	−	0.951543i
$476$	−0.109969	−	0.0260631i	−0.00504042	−	0.00119460i
$477$		0			0
$478$	−0.543313	−	0.575878i	−0.0248506	−	0.0263401i
$479$	−19.5183	−	3.05261i	−0.891815	−	0.139477i	−0.308021	−	0.951379i	$-0.599667\pi$
$479$	−19.5183	−	3.05261i	−0.891815	−	0.139477i	−0.583793	+	0.811902i	$0.698432\pi$
$480$		0			0
$481$	14.7971	−	0.574194i	0.674689	−	0.0261810i
$482$	9.89479	+	5.97153i	0.450695	+	0.271996i
$483$		0			0
$484$	−0.574396	−	0.159894i	−0.0261089	−	0.00726791i
$485$	−5.53101			−0.251150
$486$		0			0
$487$	7.01353			0.317813			0.158907	−	0.987294i	$-0.449203\pi$
$487$	7.01353			0.317813			0.158907	+	0.987294i	$0.449203\pi$
$488$	4.12427	+	1.14807i	0.186697	+	0.0519706i
$489$		0			0
$490$	8.80737	+	5.31527i	0.397876	+	0.240120i
$491$	4.77417	−	0.185259i	0.215455	−	0.00836064i	0.0691782	−	0.997604i	$-0.477962\pi$
$491$	4.77417	−	0.185259i	0.215455	−	0.00836064i	0.146277	+	0.989244i	$0.453271\pi$
$492$		0			0
$493$	−67.1313	−	10.4991i	−3.02344	−	0.472857i
$494$	15.6408	+	16.5782i	0.703711	+	0.745890i
$495$		0			0
$496$	−10.9433	−	2.59361i	−0.491369	−	0.116457i
$497$	−0.101187	−	0.740822i	−0.00453887	−	0.0332304i
$498$		0			0
$499$	−17.1968	+	25.0735i	−0.769833	+	1.12244i	0.219334	+	0.975650i	$0.429612\pi$
$499$	−17.1968	+	25.0735i	−0.769833	+	1.12244i	−0.989167	+	0.146795i	$0.953104\pi$
$500$	0.747049	+	0.339576i	0.0334091	+	0.0151863i
$501$		0			0
$502$	−1.75704	−	3.33565i	−0.0784204	−	0.148877i
$503$	34.8506	−	17.5026i	1.55391	−	0.780403i	0.555227	−	0.831699i	$-0.312631\pi$
$503$	34.8506	−	17.5026i	1.55391	−	0.780403i	0.998684	+	0.0512958i	$0.0163351\pi$
$504$		0			0
$505$	−0.0352144	−	0.604607i	−0.00156702	−	0.0269047i
$506$	−41.5648	−	22.9345i	−1.84778	−	1.01956i
$507$		0			0
$508$	−0.129909	+	0.951102i	−0.00576378	+	0.0421983i
$509$	−11.4930	+	29.7675i	−0.509417	+	1.31942i	0.404877	+	0.914371i	$0.367314\pi$
$509$	−11.4930	+	29.7675i	−0.509417	+	1.31942i	−0.914294	+	0.405051i	$0.867254\pi$
$510$		0			0
$511$	−0.649174	+	0.0504578i	−0.0287178	+	0.00223212i
$512$	16.0272	−	13.4484i	0.708307	−	0.594340i
$513$		0			0
$514$	−33.3134	−	27.9533i	−1.46939	−	1.23297i
$515$	−11.3065	−	8.08139i	−0.498223	−	0.356109i
$516$		0			0
$517$	12.2453	−	14.0316i	0.538550	−	0.617109i
$518$	−0.248678	−	1.14802i	−0.0109263	−	0.0504413i
$519$		0			0
$520$	8.24538	−	1.61934i	0.361584	−	0.0710127i
$521$	−19.7568	−	2.30923i	−0.865559	−	0.101169i	−0.328287	−	0.944578i	$-0.606471\pi$
$521$	−19.7568	−	2.30923i	−0.865559	−	0.101169i	−0.537272	+	0.843409i	$0.680545\pi$
$522$		0			0
$523$	−12.1586	−	16.3319i	−0.531660	−	0.714143i	0.452433	−	0.891798i	$-0.350556\pi$
$523$	−12.1586	−	16.3319i	−0.531660	−	0.714143i	−0.984093	+	0.177655i	$0.943149\pi$
$524$	0.120669	−	0.557069i	0.00527144	−	0.0243357i
$525$		0			0
$526$	16.8187	+	16.4957i	0.733331	+	0.719246i
$527$	5.17489	−	20.0901i	0.225422	−	0.875140i
$528$		0			0
$529$	−28.2339	−	25.6209i	−1.22756	−	1.11395i
$530$	−4.39794	+	10.1956i	−0.191034	+	0.442867i
$531$		0			0
$532$	0.0463733	−	0.0622901i	0.00201054	−	0.00270062i
$533$	21.4978	+	24.6338i	0.931174	+	1.06701i
$534$		0			0
$535$	−8.05744	−	2.58351i	−0.348353	−	0.111695i
$536$	−19.5841	−	3.84620i	−0.845905	−	0.166130i
$537$		0			0
$538$	−13.2852	+	6.03887i	−0.572766	+	0.260354i
$539$	−5.08609	+	28.8446i	−0.219073	+	1.24243i
$540$		0			0
$541$	−4.09510	−	23.2245i	−0.176062	−	0.998497i	−0.936911	−	0.349568i	$-0.886328\pi$
$541$	−4.09510	−	23.2245i	−0.176062	−	0.998497i	0.760849	−	0.648929i	$-0.224783\pi$
$542$	5.52879	+	8.06117i	0.237482	+	0.346257i
$543$		0			0
$544$	−2.45118	−	3.03898i	−0.105093	−	0.130295i
$545$	2.52754	−	1.03261i	0.108268	−	0.0442323i
$546$		0			0
$547$	12.0551	−	7.27526i	0.515437	−	0.311068i	−0.235016	−	0.971991i	$-0.575514\pi$
$547$	12.0551	−	7.27526i	0.515437	−	0.311068i	0.750453	+	0.660924i	$0.229835\pi$
$548$	−0.396051	+	0.260487i	−0.0169185	+	0.0111275i
$549$		0			0
$550$	−1.39760	+	23.9958i	−0.0595938	+	1.02319i
$551$	24.8947	−	39.4981i	1.06055	−	1.68267i
$552$		0			0
$553$	−1.48250	+	1.05962i	−0.0630422	+	0.0450598i
$554$	−29.5000	−	2.29292i	−1.25333	−	0.0974169i
$555$		0			0
$556$	−0.190666	−	0.0778956i	−0.00808604	−	0.00330351i
$557$	−5.12433	−	17.1165i	−0.217125	−	0.725248i	−0.995269	−	0.0971615i	$-0.969024\pi$
$557$	−5.12433	−	17.1165i	−0.217125	−	0.725248i	0.778144	−	0.628086i	$-0.216162\pi$
$558$		0			0
$559$	3.81136	−	0.903309i	0.161203	−	0.0382059i
$560$	−0.250874	−	0.649779i	−0.0106013	−	0.0274582i
$561$		0			0
$562$	12.9450	−	24.5754i	0.546051	−	1.03665i
$563$	−0.595337	+	30.6954i	−0.0250905	+	1.29366i	0.749843	+	0.661616i	$0.230129\pi$
$563$	−0.595337	+	30.6954i	−0.0250905	+	1.29366i	−0.774934	+	0.632043i	$0.782217\pi$
$564$		0			0
$565$	−4.08073	+	4.00235i	−0.171677	+	0.168380i
$566$	17.2644	+	29.9028i	0.725676	+	1.25691i
$567$		0			0
$568$	6.30942	−	10.9282i	0.264737	−	0.458538i
$569$	3.90030	+	15.1419i	0.163509	+	0.634781i	0.996655	+	0.0817272i	$0.0260436\pi$
$569$	3.90030	+	15.1419i	0.163509	+	0.634781i	−0.833146	+	0.553053i	$0.813463\pi$
$570$		0			0
$571$	6.30704	−	3.48007i	0.263941	−	0.145637i	−0.345623	−	0.938374i	$-0.612332\pi$
$571$	6.30704	−	3.48007i	0.263941	−	0.145637i	0.609564	+	0.792737i	$0.291345\pi$
$572$	−0.599444	−	0.951083i	−0.0250640	−	0.0397668i
$573$		0			0
$574$	1.62824	−	2.01871i	0.0679616	−	0.0842592i
$575$	−8.87646	+	29.6494i	−0.370174	+	1.23647i
$576$		0			0
$577$	−3.70448	+	3.92651i	−0.154219	+	0.163463i	−0.799877	−	0.600164i	$-0.795102\pi$
$577$	−3.70448	+	3.92651i	−0.154219	+	0.163463i	0.645657	+	0.763627i	$0.276583\pi$
$578$	48.2312	−	37.3820i	2.00615	−	1.55489i
$579$		0			0
$580$	0.348921	+	0.729706i	0.0144881	+	0.0302994i
$581$	0.0917150	+	0.942913i	0.00380498	+	0.0391186i
$582$		0			0
$583$	−31.5911	−	1.22588i	−1.30837	−	0.0507708i
$584$	−9.18123	−	6.03859i	−0.379922	−	0.249879i
$585$		0			0
$586$	1.62627	+	0.816744i	0.0671807	+	0.0337394i
$587$	−0.165929	−	8.55524i	−0.00684861	−	0.353113i	−0.987524	−	0.157470i	$-0.949666\pi$
$587$	−0.165929	−	8.55524i	−0.00684861	−	0.353113i	0.980675	−	0.195643i	$-0.0626794\pi$
$588$		0			0
$589$	11.2672	+	8.73274i	0.464257	+	0.359826i
$590$	14.3991	−	2.25198i	0.592801	−	0.0927123i
$591$		0			0
$592$	8.93656	−	18.6892i	0.367291	−	0.768123i
$593$	−18.5728	−	6.75993i	−0.762691	−	0.277597i	−0.0687553	−	0.997634i	$-0.521903\pi$
$593$	−18.5728	−	6.75993i	−0.762691	−	0.277597i	−0.693936	+	0.720037i	$0.744125\pi$
$594$		0			0
$595$	1.20737	−	0.439447i	0.0494974	−	0.0180156i
$596$	−0.0839491	+	0.863072i	−0.00343869	+	0.0353528i
$597$		0			0
$598$	−10.9103	−	31.8865i	−0.446155	−	1.30394i
$599$	25.6370	−	23.2644i	1.04750	−	0.950556i	0.0486658	−	0.998815i	$-0.484503\pi$
$599$	25.6370	−	23.2644i	1.04750	−	0.950556i	0.998835	+	0.0482590i	$0.0153673\pi$
$600$		0			0
$601$	6.76430	−	19.7694i	0.275921	−	0.806411i	−0.717973	−	0.696071i	$-0.754930\pi$
$601$	6.76430	−	19.7694i	0.275921	−	0.806411i	0.993894	−	0.110339i	$-0.0351938\pi$
$602$	−0.123065	−	0.285297i	−0.00501576	−	0.0116278i
$603$		0			0
$604$	0.400401	−	0.0468001i	0.0162921	−	0.00190427i
$605$	6.45483	−	2.06966i	0.262426	−	0.0841436i
$606$		0			0
$607$	−38.8176	+	10.8056i	−1.57556	+	0.438586i	−0.942139	−	0.335224i	$-0.891188\pi$
$607$	−38.8176	+	10.8056i	−1.57556	+	0.438586i	−0.633418	+	0.773810i	$0.718349\pi$
$608$	2.58451	−	0.719449i	0.104816	−	0.0291775i
$609$		0			0
$610$	2.17782	−	0.698289i	0.0881772	−	0.0282729i
$611$	13.1317	−	1.53488i	0.531253	−	0.0620946i
$612$		0			0
$613$	−5.08719	−	11.7934i	−0.205470	−	0.476332i	0.784056	−	0.620690i	$-0.213148\pi$
$613$	−5.08719	−	11.7934i	−0.205470	−	0.476332i	−0.989526	+	0.144358i	$0.953888\pi$
$614$	9.57108	−	27.9725i	0.386257	−	1.12888i
$615$		0			0
$616$	1.40543	−	1.27536i	0.0566266	−	0.0513859i
$617$	8.49476	+	24.8269i	0.341986	+	0.999493i	0.974392	+	0.224856i	$0.0721910\pi$
$617$	8.49476	+	24.8269i	0.341986	+	0.999493i	−0.632406	+	0.774637i	$0.717932\pi$
$618$		0			0
$619$	−2.03774	+	20.9498i	−0.0819036	+	0.842043i	0.860918	+	0.508744i	$0.169890\pi$
$619$	−2.03774	+	20.9498i	−0.0819036	+	0.842043i	−0.942821	+	0.333299i	$0.891838\pi$
$620$	−0.232064	+	0.0844642i	−0.00931990	+	0.00339216i
$621$		0			0
$622$	36.0286	+	13.1133i	1.44461	+	0.525797i
$623$	0.290609	−	0.607756i	0.0116430	−	0.0243492i
$624$		0			0
$625$	10.3381	−	1.61684i	0.413522	−	0.0646737i
$626$	−6.88858	−	5.33905i	−0.275323	−	0.213391i
$627$		0			0
$628$	−0.0197489	−	1.01825i	−0.000788068	−	0.0406326i
$629$	34.1492	+	17.1504i	1.36162	+	0.683830i
$630$		0			0
$631$	7.75911	+	5.10324i	0.308885	+	0.203157i	0.694481	−	0.719511i	$-0.255634\pi$
$631$	7.75911	+	5.10324i	0.308885	+	0.203157i	−0.385596	+	0.922668i	$0.626004\pi$
$632$	−30.7308	−	1.19249i	−1.22240	−	0.0474349i
$633$		0			0
$634$	−0.786750	−	8.08850i	−0.0312458	−	0.321235i
$635$	−4.70787	−	9.84567i	−0.186826	−	0.390714i
$636$		0			0
$637$	−16.4348	+	12.7379i	−0.651170	+	0.504695i
$638$	−36.7936	+	38.9989i	−1.45667	+	1.54398i
$639$		0			0
$640$	3.51652	−	11.7460i	0.139003	−	0.464301i
$641$	−14.2164	+	17.6255i	−0.561513	+	0.696166i	−0.976953	−	0.213454i	$-0.931529\pi$
$641$	−14.2164	+	17.6255i	−0.561513	+	0.696166i	0.415441	+	0.909620i	$0.363627\pi$
$642$		0			0
$643$	−13.9295	−	22.1006i	−0.549324	−	0.871562i	0.450450	−	0.892802i	$-0.351264\pi$
$643$	−13.9295	−	22.1006i	−0.549324	−	0.871562i	−0.999774	+	0.0212393i	$0.993239\pi$
$644$	−0.100538	+	0.0554745i	−0.00396175	+	0.00218600i
$645$		0			0
$646$	14.6713	+	56.9573i	0.577233	+	2.24095i
$647$	−11.0603	+	19.1570i	−0.434824	+	0.753138i	−0.997281	−	0.0736887i	$-0.976523\pi$
$647$	−11.0603	+	19.1570i	−0.434824	+	0.753138i	0.562457	+	0.826827i	$0.309856\pi$
$648$		0			0
$649$	20.7481	+	35.9368i	0.814434	+	1.41064i
$650$	−12.1824	+	11.9485i	−0.477835	+	0.468657i
$651$		0			0
$652$	−0.0186717	+	0.962710i	−0.000731242	+	0.0377026i
$653$	−16.2094	+	30.7729i	−0.634325	+	1.20424i	0.331110	+	0.943592i	$0.392577\pi$
$653$	−16.2094	+	30.7729i	−0.634325	+	1.20424i	−0.965435	+	0.260644i	$0.916065\pi$
$654$		0			0
$655$	2.33400	+	6.04520i	0.0911968	+	0.236206i
$656$	44.5060	−	10.5481i	1.73767	−	0.411835i
$657$		0			0
$658$	−0.300786	−	1.00470i	−0.0117259	−	0.0391671i
$659$	−12.8659	−	5.25631i	−0.501185	−	0.204757i	0.113487	−	0.993540i	$-0.463798\pi$
$659$	−12.8659	−	5.25631i	−0.501185	−	0.204757i	−0.614672	+	0.788783i	$0.710712\pi$
$660$		0			0
$661$	−29.6294	−	2.30298i	−1.15245	−	0.0895755i	−0.512986	−	0.858397i	$-0.671461\pi$
$661$	−29.6294	−	2.30298i	−1.15245	−	0.0895755i	−0.639464	+	0.768821i	$0.720844\pi$
$662$	−12.4016	+	8.86411i	−0.482001	+	0.344514i
$663$		0			0
$664$	−8.52515	+	13.5261i	−0.330840	+	0.524913i
$665$	−0.0513341	+	0.881373i	−0.00199065	+	0.0341782i
$666$		0			0
$667$	−57.6792	+	37.9362i	−2.23335	+	1.46890i
$668$	0.393692	−	0.237594i	0.0152324	−	0.00919279i
$669$		0			0
$670$	−9.87010	+	4.03238i	−0.381315	+	0.155784i
$671$	4.08815	+	5.06851i	0.157821	+	0.195668i
$672$		0			0
$673$	−6.06444	−	8.84217i	−0.233767	−	0.340840i	0.689991	−	0.723818i	$-0.257615\pi$
$673$	−6.06444	−	8.84217i	−0.233767	−	0.340840i	−0.923758	+	0.382978i	$0.874899\pi$
$674$	1.13091	+	6.41370i	0.0435609	+	0.247046i
$675$		0			0
$676$	−0.0640389	+	0.363183i	−0.00246303	+	0.0139686i
$677$	−44.5865	+	20.2671i	−1.71360	+	0.778926i	−0.716951	+	0.697124i	$0.754463\pi$
$677$	−44.5865	+	20.2671i	−1.71360	+	0.778926i	−0.996649	+	0.0818027i	$0.973932\pi$
$678$		0			0
$679$	−0.870212	−	0.170904i	−0.0333957	−	0.00655870i
$680$	20.6489	+	6.62080i	0.791849	+	0.253896i
$681$		0			0
$682$	−10.7638	−	12.3339i	−0.412167	−	0.472291i
$683$	0.762977	−	1.02486i	0.0291945	−	0.0392150i	−0.787286	−	0.616588i	$-0.788515\pi$
$683$	0.762977	−	1.02486i	0.0291945	−	0.0392150i	0.816481	+	0.577373i	$0.195922\pi$
$684$		0			0
$685$	2.13457	−	4.94850i	0.0815579	−	0.189072i
$686$	2.44760	+	2.22108i	0.0934497	+	0.0848011i
$687$		0			0
$688$	1.36684	−	5.30638i	0.0521102	−	0.202304i
$689$	−16.0234	−	15.7157i	−0.610443	−	0.598719i
$690$		0			0
$691$	−3.28010	+	15.1426i	−0.124781	+	0.576053i	0.871538	+	0.490328i	$0.163123\pi$
$691$	−3.28010	+	15.1426i	−0.124781	+	0.576053i	−0.996319	+	0.0857249i	$0.972679\pi$
$692$	1.04468	+	1.40325i	0.0397129	+	0.0533437i
$693$		0			0
$694$	24.8763	+	2.90762i	0.944292	+	0.110372i
$695$	2.29769	−	0.451251i	0.0871562	−	0.0171169i
$696$		0			0
$697$	17.8621	+	82.4604i	0.676574	+	3.12341i
$698$	−10.7588	+	12.3282i	−0.407227	+	0.466631i
$699$		0			0
$700$	0.0473000	+	0.0338080i	0.00178777	+	0.00127782i
$701$	−9.42749	−	7.91060i	−0.356071	−	0.298779i	0.447151	−	0.894458i	$-0.352439\pi$
$701$	−9.42749	−	7.91060i	−0.356071	−	0.298779i	−0.803223	+	0.595679i	$0.796883\pi$
$702$		0			0
$703$	−20.1148	+	16.8783i	−0.758643	+	0.636577i
$704$	31.8658	−	2.47681i	1.20099	−	0.0933482i
$705$		0			0
$706$	14.0287	−	36.3353i	0.527978	−	1.36750i
$707$	0.0131415	−	0.0962129i	0.000494238	−	0.00361846i
$708$		0			0
$709$	6.49473	+	3.58364i	0.243915	+	0.134586i	0.600360	−	0.799730i	$-0.295024\pi$
$709$	6.49473	+	3.58364i	0.243915	+	0.134586i	−0.356446	+	0.934316i	$0.616011\pi$
$710$	−0.391966	−	6.72979i	−0.0147102	−	0.252565i
$711$		0			0
$712$	10.1600	−	5.10254i	0.380762	−	0.191226i
$713$	−9.82350	−	18.6495i	−0.367893	−	0.698428i
$714$		0			0
$715$	11.6355	+	5.28900i	0.435145	+	0.197798i
$716$	0.0987660	−	0.144004i	0.00369106	−	0.00538169i
$717$		0			0
$718$	4.57202	+	33.4731i	0.170626	+	1.24920i
$719$	11.9143	+	2.82373i	0.444327	+	0.105307i	0.446688	−	0.894690i	$-0.352603\pi$
$719$	11.9143	+	2.82373i	0.444327	+	0.105307i	−0.00236092	+	0.999997i	$0.500752\pi$
$720$		0			0
$721$	−1.52918	−	1.62083i	−0.0569496	−	0.0603630i
$722$	−12.7928	−	2.00075i	−0.476098	−	0.0744604i
$723$		0			0
$724$	1.42618	−	0.0553424i	0.0530037	−	0.00205678i
$725$	29.9274	+	18.0613i	1.11148	+	0.670779i
$726$		0			0
$727$	−1.89340	−	0.527063i	−0.0702222	−	0.0195477i	0.232883	−	0.972505i	$-0.425184\pi$
$727$	−1.89340	−	0.527063i	−0.0702222	−	0.0195477i	−0.303106	+	0.952957i	$0.598023\pi$
$728$	1.34731			0.0499346
$729$		0			0
$730$	−5.87055			−0.217279
$731$	9.73775	+	2.71069i	0.360164	+	0.100258i
$732$		0			0
$733$	27.6454	+	16.6841i	1.02111	+	0.616240i	0.925330	−	0.379163i	$-0.123788\pi$
$733$	27.6454	+	16.6841i	1.02111	+	0.616240i	0.0957752	+	0.995403i	$0.469467\pi$
$734$	24.8609	−	0.964715i	0.917632	−	0.0356083i
$735$		0			0
$736$	−3.91927	−	0.612962i	−0.144466	−	0.0225941i
$737$	−20.8326	−	22.0812i	−0.767378	−	0.813373i
$738$		0			0
$739$	−19.1572	−	4.54034i	−0.704709	−	0.167019i	−0.137390	−	0.990517i	$-0.543871\pi$
$739$	−19.1572	−	4.54034i	−0.704709	−	0.167019i	−0.567319	+	0.823498i	$0.692019\pi$
$740$	−0.0615613	−	0.450709i	−0.00226304	−	0.0165684i
$741$		0			0
$742$	−1.00698	+	1.46821i	−0.0369673	+	0.0538996i
$743$	24.0075	+	10.9127i	0.880749	+	0.400350i	0.802548	−	0.596588i	$-0.203477\pi$
$743$	24.0075	+	10.9127i	0.880749	+	0.400350i	0.0782014	+	0.996938i	$0.475082\pi$
$744$		0			0
$745$	−4.59447	−	8.72239i	−0.168328	−	0.319564i
$746$	−4.69282	+	2.35683i	−0.171817	+	0.0862895i
$747$		0			0
$748$	−0.168688	−	2.89626i	−0.00616785	−	0.105898i
$749$	−1.18787	−	0.655441i	−0.0434040	−	0.0239493i
$750$		0			0
$751$	−4.96942	+	36.3826i	−0.181337	+	1.32762i	0.644887	+	0.764278i	$0.276904\pi$
$751$	−4.96942	+	36.3826i	−0.181337	+	1.32762i	−0.826224	+	0.563342i	$0.809515\pi$
$752$	6.66173	−	17.2543i	0.242928	−	0.629200i
$753$		0			0
$754$	−37.9485	+	2.94959i	−1.38200	+	0.107418i
$755$	−3.51085	+	2.94595i	−0.127773	+	0.107214i
$756$		0			0
$757$	4.11994	+	3.45704i	0.149742	+	0.125648i	0.714581	−	0.699553i	$-0.246617\pi$
$757$	4.11994	+	3.45704i	0.149742	+	0.125648i	−0.564839	+	0.825201i	$0.691062\pi$
$758$	36.9874	+	26.4370i	1.34344	+	0.960236i
$759$		0			0
$760$	−9.79708	+	11.2262i	−0.355378	+	0.407218i
$761$	8.10676	+	37.4250i	0.293870	+	1.35665i	0.850535	+	0.525918i	$0.176278\pi$
$761$	8.10676	+	37.4250i	0.293870	+	1.35665i	−0.556665	+	0.830737i	$0.687919\pi$
$762$		0			0
$763$	0.429573	−	0.0843653i	0.0155516	−	0.00305423i
$764$	−0.530023	−	0.0619508i	−0.0191756	−	0.00224130i
$765$		0			0
$766$	0.0400784	+	0.0538346i	0.00144809	+	0.00194512i
$767$	−6.23655	+	28.7911i	−0.225189	+	1.03959i
$768$		0			0
$769$	−5.43973	−	5.33525i	−0.196162	−	0.192394i	0.595497	−	0.803357i	$-0.296955\pi$
$769$	−5.43973	−	5.33525i	−0.196162	−	0.192394i	−0.791659	+	0.610963i	$0.790782\pi$
$770$	0.252898	−	0.981811i	0.00911382	−	0.0353820i
$771$		0			0
$772$	−1.62356	−	1.47330i	−0.0584331	−	0.0530252i
$773$	−3.21805	+	7.46027i	−0.115745	+	0.268327i	−0.966234	−	0.257665i	$-0.917047\pi$
$773$	−3.21805	+	7.46027i	−0.115745	+	0.268327i	0.850489	+	0.525993i	$0.176306\pi$
$774$		0			0
$775$	−6.37324	+	8.56075i	−0.228934	+	0.307511i
$776$	−9.84113	−	11.2767i	−0.353276	−	0.404809i
$777$		0			0
$778$	−37.7726	−	12.1113i	−1.35421	−	0.434211i
$779$	−56.8886	−	11.1726i	−2.03824	−	0.400298i
$780$		0			0
$781$	17.4734	−	7.94264i	0.625248	−	0.284210i
$782$	15.1021	−	85.6480i	0.540049	−	3.06277i
$783$		0			0
$784$	5.05118	+	28.6467i	0.180399	+	1.02309i
$785$	6.54889	+	9.54852i	0.233740	+	0.340801i
$786$		0

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)

\(f(q)\)	\(=\)	\(q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +O(q^{10})\)	\(q+(1.39265 + 0.387670i) q^{2} +(0.0768505 + 0.0463795i) q^{4} +(-1.01971 + 0.0395696i) q^{5} +(-0.161658 - 0.0252828i) q^{7} +(-1.89502 - 2.00860i) q^{8} +(-1.43545 - 0.340207i) q^{10} +(-0.568431 - 4.16165i) q^{11} +(1.68656 - 2.45906i) q^{13} +(-0.215331 - 0.0978801i) q^{14} +(-1.94408 - 3.69075i) q^{16} +(6.87645 - 3.45348i) q^{17} +(0.307437 + 5.27850i) q^{19} +(-0.0802008 - 0.0442529i) q^{20} +(0.821725 - 6.01609i) q^{22} +(2.81598 - 7.29357i) q^{23} +(-3.94671 + 0.306763i) q^{25} +(3.30209 - 2.77079i) q^{26} +(-0.0112509 - 0.00944061i) q^{28} +(-7.18377 - 5.13465i) q^{29} +(1.77271 - 2.03130i) q^{31} +(-0.107416 - 0.495887i) q^{32} +(10.9153 - 2.14369i) q^{34} +(0.165845 + 0.0193845i) q^{35} +(2.96555 + 3.98343i) q^{37} +(-1.61816 + 7.47028i) q^{38} +(2.01186 + 1.97321i) q^{40} +(-2.73505 + 10.6181i) q^{41} +(0.972771 + 0.882743i) q^{43} +(0.149331 - 0.346189i) q^{44} +(6.74917 - 9.06571i) q^{46} +(2.91535 + 3.34063i) q^{47} +(-6.64024 - 2.12911i) q^{49} +(-5.61531 - 1.10281i) q^{50} +(0.243663 - 0.110759i) q^{52} +(1.30702 - 7.41249i) q^{53} +(0.744313 + 4.22121i) q^{55} +(0.255561 + 0.372617i) q^{56} +(-8.01392 - 9.93570i) q^{58} +(-9.14555 + 3.73637i) q^{59} +(-1.32732 + 0.801042i) q^{61} +(3.25624 - 2.14166i) q^{62} +(-0.442450 + 7.59658i) q^{64} +(-1.62251 + 2.57428i) q^{65} +(5.87992 - 4.20272i) q^{67} +(0.688629 + 0.0535245i) q^{68} +(0.223450 + 0.0912892i) q^{70} +(1.31059 + 4.37768i) q^{71} +(3.87220 - 0.917728i) q^{73} +(2.58572 + 6.69718i) q^{74} +(-0.221187 + 0.419914i) q^{76} +(-0.0133270 + 0.687135i) q^{77} +(7.95096 - 7.79825i) q^{79} +(2.12845 + 3.68659i) q^{80} +(-7.92530 + 13.7270i) q^{82} +(-1.44424 - 5.60690i) q^{83} +(-6.87536 + 3.79367i) q^{85} +(1.01252 + 1.60647i) q^{86} +(-7.28191 + 9.02815i) q^{88} +(-1.18082 + 3.94420i) q^{89} +(-0.334818 + 0.354886i) q^{91} +(0.554681 - 0.429910i) q^{92} +(2.76500 + 5.78252i) q^{94} +(-0.522366 - 5.37039i) q^{95} +(5.41592 + 0.210162i) q^{97} +(-8.42214 - 5.53933i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more