LMFDB - Embedded newform 729.2.i.a.685.17

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			685.17
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.17

$q$-expansion

$f(q)$	$=$	$q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +O(q^{10})$	\(q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +(2.18685 + 0.518294i) q^{10} +(-0.767098 - 5.61615i) q^{11} +(-3.39021 + 4.94305i) q^{13} +(-4.16188 - 1.89181i) q^{14} +(-0.781868 - 1.48434i) q^{16} +(-1.18240 + 0.593821i) q^{17} +(-0.383327 - 6.58146i) q^{19} +(-1.49207 - 0.823287i) q^{20} +(0.832318 - 6.09365i) q^{22} +(0.756746 - 1.96002i) q^{23} +(-0.707484 + 0.0549900i) q^{25} +(-4.98201 + 4.18040i) q^{26} +(2.65549 + 2.22822i) q^{28} +(3.30770 + 2.36420i) q^{29} +(0.0367254 - 0.0420827i) q^{31} +(0.911413 + 4.20755i) q^{32} +(-1.40872 + 0.276663i) q^{34} +(-8.66837 - 1.01319i) q^{35} +(-2.13975 - 2.87418i) q^{37} +(1.51435 - 6.99101i) q^{38} +(-4.52909 - 4.44210i) q^{40} +(0.587714 - 2.28165i) q^{41} +(2.40574 + 2.18309i) q^{43} +(-1.84710 + 4.28206i) q^{44} +(1.36132 - 1.82858i) q^{46} +(-0.143743 - 0.164711i) q^{47} +(10.2395 + 3.28317i) q^{49} +(-0.755519 - 0.148379i) q^{50} +(4.48933 - 2.04065i) q^{52} +(1.06035 - 6.01354i) q^{53} +(-2.03878 - 11.5625i) q^{55} +(7.29891 + 10.6421i) q^{56} +(2.76955 + 3.43370i) q^{58} +(-0.683778 + 0.279354i) q^{59} +(11.3205 - 6.83197i) q^{61} +(0.0506333 - 0.0333020i) q^{62} +(-0.466700 + 8.01293i) q^{64} +(-6.61994 + 10.5032i) q^{65} +(-4.99078 + 3.56720i) q^{67} +(1.08530 + 0.0843564i) q^{68} +(-8.76606 - 3.58133i) q^{70} +(-3.11481 - 10.4042i) q^{71} +(-1.60703 + 0.380872i) q^{73} +(-1.40032 - 3.62693i) q^{74} +(-2.52778 + 4.79887i) q^{76} +(-0.463123 + 23.8785i) q^{77} +(-0.413794 + 0.405846i) q^{79} +(-1.73750 - 3.00944i) q^{80} +(1.27822 - 2.21395i) q^{82} +(0.994054 + 3.85915i) q^{83} +(-2.39959 + 1.32404i) q^{85} +(1.87945 + 2.98195i) q^{86} +(-10.8991 + 13.5127i) q^{88} +(2.78199 - 9.29248i) q^{89} +(17.3311 - 18.3698i) q^{91} +(-1.36625 + 1.05893i) q^{92} +(-0.102325 - 0.213994i) q^{94} +(-1.32200 - 13.5913i) q^{95} +(-6.85532 - 0.266018i) q^{97} +(9.74785 + 6.41126i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.04528	+	0.290973i	0.739124	+	0.205749i	0.617218	−	0.786792i	$-0.288260\pi$
$2$	1.04528	+	0.290973i	0.739124	+	0.205749i	0.121906	+	0.992542i	$0.461099\pi$
$3$		0			0
$3$		0			0
$4$	−0.704391	−	0.425102i	−0.352195	−	0.212551i
$5$	2.06977	−	0.0803163i	0.925627	−	0.0359186i	0.428448	−	0.903566i	$-0.359060\pi$
$5$	2.06977	−	0.0803163i	0.925627	−	0.0359186i	0.497179	+	0.867648i	$0.334369\pi$
$6$		0			0
$7$	−4.16283	−	0.651054i	−1.57340	−	0.246075i	−0.693224	−	0.720722i	$-0.743810\pi$
$7$	−4.16283	−	0.651054i	−1.57340	−	0.246075i	−0.880177	+	0.474646i	$0.842576\pi$
$8$	−2.10177	−	2.22774i	−0.743087	−	0.787626i
$9$		0			0
$10$	2.18685	+	0.518294i	0.691544	+	0.163899i
$11$	−0.767098	−	5.61615i	−0.231289	−	1.69333i	−0.630272	−	0.776374i	$-0.717057\pi$
$11$	−0.767098	−	5.61615i	−0.231289	−	1.69333i	0.398983	−	0.916958i	$-0.369363\pi$
$12$		0			0
$13$	−3.39021	+	4.94305i	−0.940275	+	1.37095i	−0.0116516	+	0.999932i	$0.503709\pi$
$13$	−3.39021	+	4.94305i	−0.940275	+	1.37095i	−0.928624	+	0.371023i	$0.879007\pi$
$14$	−4.16188	−	1.89181i	−1.11231	−	0.505606i
$15$		0			0
$16$	−0.781868	−	1.48434i	−0.195467	−	0.371085i
$17$	−1.18240	+	0.593821i	−0.286773	+	0.144023i	−0.586371	−	0.810043i	$-0.699444\pi$
$17$	−1.18240	+	0.593821i	−0.286773	+	0.144023i	0.299598	+	0.954066i	$0.403148\pi$
$18$		0			0
$19$	−0.383327	−	6.58146i	−0.0879412	−	1.50989i	−0.697175	−	0.716901i	$-0.745560\pi$
$19$	−0.383327	−	6.58146i	−0.0879412	−	1.50989i	0.609234	−	0.792991i	$-0.291477\pi$
$20$	−1.49207	−	0.823287i	−0.333636	−	0.184093i
$21$		0			0
$22$	0.832318	−	6.09365i	0.177451	−	1.29917i
$23$	0.756746	−	1.96002i	0.157792	−	0.408692i	−0.831332	−	0.555777i	$-0.812421\pi$
$23$	0.756746	−	1.96002i	0.157792	−	0.408692i	0.989124	+	0.147084i	$0.0469889\pi$
$24$		0			0
$25$	−0.707484	+	0.0549900i	−0.141497	+	0.0109980i
$26$	−4.98201	+	4.18040i	−0.977053	+	0.819845i
$27$		0			0
$28$	2.65549	+	2.22822i	0.501841	+	0.421094i
$29$	3.30770	+	2.36420i	0.614224	+	0.439021i	0.845580	−	0.533848i	$-0.179255\pi$
$29$	3.30770	+	2.36420i	0.614224	+	0.439021i	−0.231356	+	0.972869i	$0.574316\pi$
$30$		0			0
$31$	0.0367254	−	0.0420827i	0.00659609	−	0.00755828i	−0.750128	−	0.661292i	$-0.770008\pi$
$31$	0.0367254	−	0.0420827i	0.00659609	−	0.00755828i	0.756724	+	0.653734i	$0.226798\pi$
$32$	0.911413	+	4.20755i	0.161117	+	0.743797i
$33$		0			0
$34$	−1.40872	+	0.276663i	−0.241593	+	0.0474474i
$35$	−8.66837	−	1.01319i	−1.46522	−	0.171260i
$36$		0			0
$37$	−2.13975	−	2.87418i	−0.351772	−	0.472512i	0.590655	−	0.806924i	$-0.298870\pi$
$37$	−2.13975	−	2.87418i	−0.351772	−	0.472512i	−0.942427	+	0.334413i	$0.891462\pi$
$38$	1.51435	−	6.99101i	0.245660	−	1.13409i
$39$		0			0
$40$	−4.52909	−	4.44210i	−0.716112	−	0.702358i
$41$	0.587714	−	2.28165i	0.0917856	−	0.356333i	−0.905966	−	0.423350i	$-0.860854\pi$
$41$	0.587714	−	2.28165i	0.0917856	−	0.356333i	0.997752	+	0.0670163i	$0.0213480\pi$
$42$		0			0
$43$	2.40574	+	2.18309i	0.366872	+	0.332919i	0.834501	−	0.551006i	$-0.185756\pi$
$43$	2.40574	+	2.18309i	0.366872	+	0.332919i	−0.467629	+	0.883925i	$0.654892\pi$
$44$	−1.84710	+	4.28206i	−0.278461	+	0.645544i
$45$		0			0
$46$	1.36132	−	1.82858i	0.200716	−	0.269609i
$47$	−0.143743	−	0.164711i	−0.0209670	−	0.0240255i	0.742857	−	0.669451i	$-0.233470\pi$
$47$	−0.143743	−	0.164711i	−0.0209670	−	0.0240255i	−0.763824	+	0.645425i	$0.776680\pi$
$48$		0			0
$49$	10.2395	+	3.28317i	1.46279	+	0.469025i
$50$	−0.755519	−	0.148379i	−0.106847	−	0.0209840i
$51$		0			0
$52$	4.48933	−	2.04065i	0.622558	−	0.282987i
$53$	1.06035	−	6.01354i	0.145650	−	0.826024i	−0.821193	−	0.570651i	$-0.806691\pi$
$53$	1.06035	−	6.01354i	0.145650	−	0.826024i	0.966843	−	0.255372i	$-0.0821981\pi$
$54$		0			0
$55$	−2.03878	−	11.5625i	−0.274909	−	1.55909i
$56$	7.29891	+	10.6421i	0.975358	+	1.42211i
$57$		0			0
$58$	2.76955	+	3.43370i	0.363660	+	0.450867i
$59$	−0.683778	+	0.279354i	−0.0890204	+	0.0363688i	−0.422273	−	0.906469i	$-0.638768\pi$
$59$	−0.683778	+	0.279354i	−0.0890204	+	0.0363688i	0.333252	+	0.942838i	$0.391854\pi$
$60$		0			0
$61$	11.3205	−	6.83197i	1.44944	−	0.874745i	0.449616	−	0.893222i	$-0.351561\pi$
$61$	11.3205	−	6.83197i	1.44944	−	0.874745i	0.999829	+	0.0184776i	$0.00588194\pi$
$62$	0.0506333	−	0.0333020i	0.00643043	−	0.00422936i
$63$		0			0
$64$	−0.466700	+	8.01293i	−0.0583375	+	1.00162i
$65$	−6.61994	+	10.5032i	−0.821102	+	1.30277i
$66$		0			0
$67$	−4.99078	+	3.56720i	−0.609721	+	0.435802i	−0.843982	−	0.536371i	$-0.819795\pi$
$67$	−4.99078	+	3.56720i	−0.609721	+	0.435802i	0.234261	+	0.972174i	$0.424733\pi$
$68$	1.08530	+	0.0843564i	0.131612	+	0.0102297i
$69$		0			0
$70$	−8.76606	−	3.58133i	−1.04774	−	0.428051i
$71$	−3.11481	−	10.4042i	−0.369660	−	1.23475i	−0.917355	−	0.398071i	$-0.869680\pi$
$71$	−3.11481	−	10.4042i	−0.369660	−	1.23475i	0.547695	−	0.836678i	$-0.315505\pi$
$72$		0			0
$73$	−1.60703	+	0.380872i	−0.188088	+	0.0445777i	−0.323580	−	0.946201i	$-0.604887\pi$
$73$	−1.60703	+	0.380872i	−0.188088	+	0.0445777i	0.135492	+	0.990778i	$0.456738\pi$
$74$	−1.40032	−	3.62693i	−0.162784	−	0.421622i
$75$		0			0
$76$	−2.52778	+	4.79887i	−0.289956	+	0.550469i
$77$	−0.463123	+	23.8785i	−0.0527777	+	2.72121i
$78$		0			0
$79$	−0.413794	+	0.405846i	−0.0465555	+	0.0456613i	−0.723123	−	0.690720i	$-0.757294\pi$
$79$	−0.413794	+	0.405846i	−0.0465555	+	0.0456613i	0.676567	+	0.736381i	$0.263467\pi$
$80$	−1.73750	−	3.00944i	−0.194258	−	0.336465i
$81$		0			0
$82$	1.27822	−	2.21395i	0.141156	−	0.244490i
$83$	0.994054	+	3.85915i	0.109112	+	0.423597i	0.999500	−	0.0316034i	$-0.0100614\pi$
$83$	0.994054	+	3.85915i	0.109112	+	0.423597i	−0.890389	+	0.455201i	$0.849568\pi$
$84$		0			0
$85$	−2.39959	+	1.32404i	−0.260272	+	0.143612i
$86$	1.87945	+	2.98195i	0.202666	+	0.321552i
$87$		0			0
$88$	−10.8991	+	13.5127i	−1.16185	+	1.44046i
$89$	2.78199	−	9.29248i	0.294890	−	0.985001i	−0.674253	−	0.738501i	$-0.735534\pi$
$89$	2.78199	−	9.29248i	0.294890	−	0.985001i	0.969143	−	0.246500i	$-0.0792806\pi$
$90$		0			0
$91$	17.3311	−	18.3698i	1.81679	−	1.92568i
$92$	−1.36625	+	1.05893i	−0.142442	+	0.110401i
$93$		0			0
$94$	−0.102325	−	0.213994i	−0.0105540	−	0.0220718i
$95$	−1.32200	−	13.5913i	−0.135634	−	1.39444i
$96$		0			0
$97$	−6.85532	−	0.266018i	−0.696052	−	0.0270100i	−0.311678	−	0.950188i	$-0.600891\pi$
$97$	−6.85532	−	0.266018i	−0.696052	−	0.0270100i	−0.384374	+	0.923178i	$0.625583\pi$
$98$	9.74785	+	6.41126i	0.984681	+	0.647635i
$99$		0			0
$100$	0.521721	+	0.262018i	0.0521721	+	0.0262018i
$101$	−0.0139667	−	0.720121i	−0.00138974	−	0.0716547i	−0.999865	−	0.0164485i	$-0.994764\pi$
$101$	−0.0139667	−	0.720121i	−0.00138974	−	0.0716547i	0.998475	−	0.0552062i	$-0.0175816\pi$
$102$		0			0
$103$	9.02470	+	6.99467i	0.889231	+	0.689206i	0.951102	−	0.308878i	$-0.0999536\pi$
$103$	9.02470	+	6.99467i	0.889231	+	0.689206i	−0.0618710	+	0.998084i	$0.519707\pi$
$104$	18.1373	−	2.83662i	1.77851	−	0.278153i
$105$		0			0
$106$	2.85814	−	5.97730i	0.277607	−	0.580567i
$107$	−5.54390	−	2.01781i	−0.535949	−	0.195069i	0.0598438	−	0.998208i	$-0.480940\pi$
$107$	−5.54390	−	2.01781i	−0.535949	−	0.195069i	−0.595793	+	0.803138i	$0.703162\pi$
$108$		0			0
$109$	1.37106	−	0.499023i	0.131323	−	0.0477978i	−0.275523	−	0.961295i	$-0.588851\pi$
$109$	1.37106	−	0.499023i	0.131323	−	0.0477978i	0.406846	+	0.913497i	$0.366629\pi$
$110$	1.23328	−	12.6793i	0.117589	−	1.20892i
$111$		0			0
$112$	2.28839	+	6.68809i	0.216233	+	0.631965i
$113$	−9.69927	+	8.80161i	−0.912430	+	0.827986i	−0.985558	−	0.169336i	$-0.945838\pi$
$113$	−9.69927	+	8.80161i	−0.912430	+	0.827986i	0.0731282	+	0.997323i	$0.476702\pi$
$114$		0			0
$115$	1.40886	−	4.11756i	0.131377	−	0.383965i
$116$	−1.32489	−	3.07143i	−0.123012	−	0.285175i
$117$		0			0
$118$	−0.796024	+	0.0930419i	−0.0732799	+	0.00856520i
$119$	5.30872	−	1.70217i	0.486649	−	0.156038i
$120$		0			0
$121$	−20.3556	+	5.66637i	−1.85051	+	0.515125i
$122$	13.8210	−	3.84735i	1.25130	−	0.348323i
$123$		0			0
$124$	−0.0437585	+	0.0140306i	−0.00392963	+	0.00125998i
$125$	−11.7465	+	1.37297i	−1.05064	+	0.122802i
$126$		0			0
$127$	7.70782	+	17.8687i	0.683958	+	1.58559i	0.805222	+	0.592973i	$0.202046\pi$
$127$	7.70782	+	17.8687i	0.683958	+	1.58559i	−0.121264	+	0.992620i	$0.538695\pi$
$128$	−0.0319456	+	0.0933645i	−0.00282362	+	0.00825234i
$129$		0			0
$130$	−9.97585	+	9.05260i	−0.874940	+	0.793965i
$131$	−1.13479	−	3.31655i	−0.0991470	−	0.289768i	0.885416	−	0.464800i	$-0.153874\pi$
$131$	−1.13479	−	3.31655i	−0.0991470	−	0.289768i	−0.984563	+	0.175032i	$0.943997\pi$
$132$		0			0
$133$	−2.68917	+	27.6471i	−0.233180	+	2.39730i
$134$	−6.25472	+	2.27653i	−0.540325	+	0.196662i
$135$		0			0
$136$	3.80800	+	1.38600i	0.326533	+	0.118848i
$137$	10.0360	−	20.9886i	0.857437	−	1.79318i	0.328549	−	0.944487i	$-0.393440\pi$
$137$	10.0360	−	20.9886i	0.857437	−	1.79318i	0.528888	−	0.848691i	$-0.322609\pi$
$138$		0			0
$139$	19.9394	−	3.11847i	1.69124	−	0.264505i	0.765711	−	0.643185i	$-0.222387\pi$
$139$	19.9394	−	3.11847i	1.69124	−	0.264505i	0.925528	+	0.378680i	$0.123622\pi$
$140$	5.67521	+	4.39862i	0.479643	+	0.371751i
$141$		0			0
$142$	−0.228504	−	11.7816i	−0.0191756	−	0.988690i
$143$	30.3615	+	15.2481i	2.53896	+	1.27511i
$144$		0			0
$145$	7.03604	+	4.62768i	0.584312	+	0.384308i
$146$	−1.79061	−	0.0694840i	−0.148192	−	0.00575054i
$147$		0			0
$148$	0.285399	+	2.93415i	0.0234596	+	0.241186i
$149$	8.61731	+	18.0216i	0.705957	+	1.47638i	0.871610	+	0.490200i	$0.163076\pi$
$149$	8.61731	+	18.0216i	0.705957	+	1.47638i	−0.165653	+	0.986184i	$0.552973\pi$
$150$		0			0
$151$	−1.59151	+	1.23351i	−0.129515	+	0.100382i	−0.675299	−	0.737544i	$-0.735985\pi$
$151$	−1.59151	+	1.23351i	−0.129515	+	0.100382i	0.545783	+	0.837926i	$0.316232\pi$
$152$	−13.8561	+	14.6867i	−1.12388	+	1.19125i
$153$		0			0
$154$	−7.43209	+	24.8249i	−0.598895	+	2.00045i
$155$	0.0726332	−	0.0900510i	0.00583404	−	0.00723307i
$156$		0			0
$157$	−3.43534	−	5.45054i	−0.274170	−	0.435000i	0.680464	−	0.732781i	$-0.261778\pi$
$157$	−3.43534	−	5.45054i	−0.274170	−	0.435000i	−0.954634	+	0.297781i	$0.903753\pi$
$158$	−0.550621	+	0.303820i	−0.0438050	+	0.0241706i
$159$		0			0
$160$	2.22435	+	8.63545i	0.175850	+	0.682692i
$161$	−4.42628	+	7.66654i	−0.348840	+	0.604208i
$162$		0			0
$163$	−1.47948	−	2.56253i	−0.115882	−	0.200713i	0.802250	−	0.596988i	$-0.203636\pi$
$163$	−1.47948	−	2.56253i	−0.115882	−	0.200713i	−0.918132	+	0.396275i	$0.870303\pi$
$164$	−1.38391	+	1.35733i	−0.108065	+	0.105990i
$165$		0			0
$166$	−0.0838472	+	4.32314i	−0.00650780	+	0.335541i
$167$	2.71931	−	5.16249i	0.210427	−	0.399485i	−0.756707	−	0.653755i	$-0.773193\pi$
$167$	2.71931	−	5.16249i	0.210427	−	0.399485i	0.967134	+	0.254269i	$0.0818349\pi$
$168$		0			0
$169$	−8.25789	−	21.3885i	−0.635222	−	1.64527i
$170$	−2.89350	+	0.685772i	−0.221921	+	0.0525963i
$171$		0			0
$172$	−0.766544	−	2.56044i	−0.0584484	−	0.195231i
$173$	7.73215	+	3.15893i	0.587865	+	0.240169i	0.652561	−	0.757736i	$-0.273694\pi$
$173$	7.73215	+	3.15893i	0.587865	+	0.240169i	−0.0646967	+	0.997905i	$0.520608\pi$
$174$		0			0
$175$	2.98094	+	0.231697i	0.225338	+	0.0175146i
$176$	−7.73650	+	5.52972i	−0.583161	+	0.416818i
$177$		0			0
$178$	5.61182	−	8.90375i	0.420623	−	0.667364i
$179$	−0.253842	+	4.35830i	−0.0189730	+	0.325755i	0.975445	+	0.220243i	$0.0706850\pi$
$179$	−0.253842	+	4.35830i	−0.0189730	+	0.325755i	−0.994418	+	0.105512i	$0.966352\pi$
$180$		0			0
$181$	−11.1262	+	7.31784i	−0.827006	+	0.543930i	−0.890991	−	0.454020i	$-0.849989\pi$
$181$	−11.1262	+	7.31784i	−0.827006	+	0.543930i	0.0639852	+	0.997951i	$0.479619\pi$
$182$	23.4609	−	14.1587i	1.73904	−	1.04952i
$183$		0			0
$184$	−5.95692	+	2.43367i	−0.439150	+	0.179413i
$185$	−4.65962	−	5.77702i	−0.342582	−	0.424735i
$186$		0			0
$187$	4.24200	+	6.18499i	0.310206	+	0.452291i
$188$	0.0312321	+	0.177126i	0.00227783	+	0.0129182i
$189$		0			0
$190$	2.57285	−	14.5914i	0.186654	−	1.05857i
$191$	−0.339837	+	0.154475i	−0.0245898	+	0.0111774i	−0.426068	−	0.904691i	$-0.640102\pi$
$191$	−0.339837	+	0.154475i	−0.0245898	+	0.0111774i	0.401478	+	0.915869i	$0.368497\pi$
$192$		0			0
$193$	−19.8836	−	3.90502i	−1.43125	−	0.281089i	−0.583774	−	0.811916i	$-0.698425\pi$
$193$	−19.8836	−	3.90502i	−1.43125	−	0.281089i	−0.847480	+	0.530827i	$0.821881\pi$
$194$	−7.08832	−	2.27278i	−0.508911	−	0.163176i
$195$		0			0
$196$	−5.81694	−	6.66548i	−0.415496	−	0.476105i
$197$	7.82208	−	10.5069i	0.557300	−	0.748584i	−0.430791	−	0.902452i	$-0.641766\pi$
$197$	7.82208	−	10.5069i	0.557300	−	0.748584i	0.988091	+	0.153868i	$0.0491730\pi$
$198$		0			0
$199$	4.41653	−	10.2387i	0.313080	−	0.725800i	−0.686920	−	0.726733i	$-0.741038\pi$
$199$	4.41653	−	10.2387i	0.313080	−	0.725800i	1.00000		0.000933098i	$0.000297014\pi$
$200$	1.60947	+	1.46052i	0.113807	+	0.103274i
$201$		0			0
$202$	0.194937	−	0.756791i	0.0137157	−	0.0532476i
$203$	−12.2302	−	11.9952i	−0.858388	−	0.841901i
$204$		0			0
$205$	1.03318	−	4.76968i	0.0721603	−	0.333129i
$206$	7.39807	+	9.93734i	0.515448	+	0.692367i
$207$		0			0
$208$	9.98786	+	1.16741i	0.692533	+	0.0809455i
$209$	−36.6684	+	7.20145i	−2.53641	+	0.498134i
$210$		0			0
$211$	−3.03033	−	13.9896i	−0.208617	−	0.963082i	−0.954779	−	0.297318i	$-0.903908\pi$
$211$	−3.03033	−	13.9896i	−0.208617	−	0.963082i	0.746162	−	0.665765i	$-0.231895\pi$
$212$	−3.30327	+	3.78513i	−0.226869	+	0.259964i
$213$		0			0
$214$	−5.20779	−	3.72231i	−0.355997	−	0.254452i
$215$	5.15466	+	4.32527i	0.351545	+	0.294981i
$216$		0			0
$217$	−0.180280	+	0.151273i	−0.0122382	+	0.0102691i
$218$	1.57834	−	0.122678i	0.106899	−	0.00830881i
$219$		0			0
$220$	−3.47914	+	9.01121i	−0.234564	+	0.607536i
$221$	1.07328	−	7.85782i	0.0721968	−	0.528574i
$222$		0			0
$223$	−2.77245	−	1.52977i	−0.185657	−	0.102441i	0.387561	−	0.921844i	$-0.373318\pi$
$223$	−2.77245	−	1.52977i	−0.185657	−	0.102441i	−0.573218	+	0.819403i	$0.694305\pi$
$224$	−1.05471	−	18.1087i	−0.0704708	−	1.20994i
$225$		0			0
$226$	−12.6995	+	6.37792i	−0.844757	+	0.424253i
$227$	−9.57731	−	18.1821i	−0.635668	−	1.20679i	−0.964920	−	0.262544i	$-0.915439\pi$
$227$	−9.57731	−	18.1821i	−0.635668	−	1.20679i	0.329252	−	0.944242i	$-0.393203\pi$
$228$		0			0
$229$	20.5994	+	9.36356i	1.36124	+	0.618761i	0.955436	−	0.295197i	$-0.0953853\pi$
$229$	20.5994	+	9.36356i	1.36124	+	0.618761i	0.405808	+	0.913958i	$0.366990\pi$
$230$	2.67076	−	3.89406i	0.176105	−	0.256767i
$231$		0			0
$232$	−1.68518	−	12.3377i	−0.110637	−	0.810010i
$233$	0.992700	+	0.235274i	0.0650339	+	0.0154133i	0.263004	−	0.964795i	$-0.415287\pi$
$233$	0.992700	+	0.235274i	0.0650339	+	0.0154133i	−0.197970	+	0.980208i	$0.563435\pi$
$234$		0			0
$235$	−0.310742	−	0.329368i	−0.0202706	−	0.0214856i
$236$	0.600401	+	0.0939010i	0.0390828	+	0.00611243i
$237$		0			0
$238$	6.04438	−	0.234549i	0.391799	−	0.0152036i
$239$	−5.61958	−	3.39143i	−0.363501	−	0.219374i	0.323173	−	0.946340i	$-0.395251\pi$
$239$	−5.61958	−	3.39143i	−0.363501	−	0.219374i	−0.686673	+	0.726966i	$0.740930\pi$
$240$		0			0
$241$	−12.4054	−	3.45327i	−0.799101	−	0.222445i	−0.155530	−	0.987831i	$-0.549708\pi$
$241$	−12.4054	−	3.45327i	−0.799101	−	0.222445i	−0.643571	+	0.765386i	$0.722548\pi$
$242$	−22.9261			−1.47374
$243$		0			0
$244$	−10.8784			−0.696415
$245$	21.4571	+	5.97300i	1.37084	+	0.381601i
$246$		0			0
$247$	33.8321	+	20.4177i	2.15268	+	1.29915i
$248$	−0.170938	+	0.00663316i	−0.0108546	+	0.000421206i
$249$		0			0
$250$	−12.6779	−	1.98278i	−0.801819	−	0.125402i
$251$	−9.51765	−	10.0881i	−0.600749	−	0.636757i	0.353619	−	0.935389i	$-0.384951\pi$
$251$	−9.51765	−	10.0881i	−0.600749	−	0.636757i	−0.954368	+	0.298633i	$0.903469\pi$
$252$		0			0
$253$	−11.5883	−	2.74647i	−0.728548	−	0.172669i
$254$	2.85750	+	20.9206i	0.179295	+	1.31267i
$255$		0			0
$256$	9.01914	−	13.1502i	0.563696	−	0.821889i
$257$	7.86924	+	3.57701i	0.490870	+	0.223128i	0.643923	−	0.765090i	$-0.277306\pi$
$257$	7.86924	+	3.57701i	0.490870	+	0.223128i	−0.153053	+	0.988218i	$0.548911\pi$
$258$		0			0
$259$	7.03615	+	13.3578i	0.437205	+	0.830013i
$260$	9.12797	−	4.58424i	0.566093	−	0.284302i
$261$		0			0
$262$	−0.221145	−	3.79691i	−0.0136624	−	0.234574i
$263$	−18.7578	−	10.3501i	−1.15665	−	0.638214i	−0.215603	−	0.976481i	$-0.569172\pi$
$263$	−18.7578	−	10.3501i	−1.15665	−	0.638214i	−0.941050	+	0.338267i	$0.890159\pi$
$264$		0			0
$265$	1.71169	−	12.5318i	0.105148	−	0.769822i
$266$	−10.8555	+	28.1164i	−0.665593	+	1.72393i
$267$		0			0
$268$	5.03188	−	0.391109i	0.307371	−	0.0238908i
$269$	19.5545	−	16.4082i	1.19226	−	1.00042i	0.192442	−	0.981308i	$-0.438359\pi$
$269$	19.5545	−	16.4082i	1.19226	−	1.00042i	0.999817	−	0.0191163i	$-0.00608526\pi$
$270$		0			0
$271$	−10.0479	−	8.43121i	−0.610368	−	0.512160i	0.284391	−	0.958708i	$-0.408209\pi$
$271$	−10.0479	−	8.43121i	−0.610368	−	0.512160i	−0.894759	+	0.446549i	$0.852653\pi$
$272$	1.80591	+	1.29079i	0.109499	+	0.0782654i
$273$		0			0
$274$	16.5976	−	19.0187i	1.00270	−	1.14896i
$275$	0.851542	+	3.93115i	0.0513499	+	0.237057i
$276$		0			0
$277$	−22.4112	+	4.40141i	−1.34656	+	0.264455i	−0.813471	−	0.581606i	$-0.802425\pi$
$277$	−22.4112	+	4.40141i	−1.34656	+	0.264455i	−0.533086	+	0.846061i	$0.678968\pi$
$278$	21.7496	+	2.54217i	1.30446	+	0.152469i
$279$		0			0
$280$	15.9618	+	21.4404i	0.953898	+	1.28131i
$281$	−4.89552	+	22.6002i	−0.292042	+	1.34822i	0.561623	+	0.827393i	$0.310177\pi$
$281$	−4.89552	+	22.6002i	−0.292042	+	1.34822i	−0.853665	+	0.520823i	$0.825625\pi$
$282$		0			0
$283$	3.92356	+	3.84820i	0.233231	+	0.228752i	0.807429	−	0.589965i	$-0.200859\pi$
$283$	3.92356	+	3.84820i	0.233231	+	0.228752i	−0.574197	+	0.818717i	$0.694686\pi$
$284$	−2.22880	+	8.65272i	−0.132255	+	0.513444i
$285$		0			0
$286$	27.2995	+	24.7729i	1.61425	+	1.46485i
$287$	−3.93203	+	9.11547i	−0.232100	+	0.538069i
$288$		0			0
$289$	−9.10626	+	12.2318i	−0.535662	+	0.719520i
$290$	6.00810	+	6.88452i	0.352808	+	0.404273i
$291$		0			0
$292$	1.29388	+	0.414867i	0.0757188	+	0.0242783i
$293$	7.07478	+	1.38944i	0.413313	+	0.0811720i	0.395047	−	0.918661i	$-0.370728\pi$
$293$	7.07478	+	1.38944i	0.413313	+	0.0811720i	0.0182666	+	0.999833i	$0.494185\pi$
$294$		0			0
$295$	−1.39282	+	0.633116i	−0.0810934	+	0.0368615i
$296$	−1.90568	+	10.8077i	−0.110765	+	0.628182i
$297$		0			0
$298$	3.76370	+	21.3450i	0.218025	+	1.23648i
$299$	7.12295	+	10.3855i	0.411931	+	0.600610i
$300$		0			0
$301$	−8.59337	−	10.6541i	−0.495314	−	0.614093i
$302$	−2.02249	+	0.826278i	−0.116381	+	0.0475470i
$303$		0			0
$304$	−9.46941	+	5.71482i	−0.543108	+	0.327767i
$305$	22.8821	−	15.0498i	1.31023	−	0.861750i
$306$		0			0
$307$	0.144842	−	2.48685i	0.00826659	−	0.141932i	−0.991649	−	0.128964i	$-0.958835\pi$
$307$	0.144842	−	2.48685i	0.00826659	−	0.141932i	0.999916	−	0.0129682i	$-0.00412803\pi$
$308$	10.4770	−	16.6229i	0.596983	−	0.947178i
$309$		0			0
$310$	0.102124	−	0.0729941i	0.00580027	−	0.00414579i
$311$	−21.2432	−	1.65115i	−1.20459	−	0.0936282i	−0.540542	−	0.841317i	$-0.681781\pi$
$311$	−21.2432	−	1.65115i	−1.20459	−	0.0936282i	−0.664049	+	0.747689i	$0.731163\pi$
$312$		0			0
$313$	11.5247	+	4.70836i	0.651415	+	0.266132i	0.679725	−	0.733467i	$-0.262099\pi$
$313$	11.5247	+	4.70836i	0.651415	+	0.266132i	−0.0283100	+	0.999599i	$0.509013\pi$
$314$	−2.00493	−	6.69693i	−0.113145	−	0.377930i
$315$		0			0
$316$	0.463999	−	0.109970i	0.0261020	−	0.00618628i
$317$	−7.79162	−	20.1808i	−0.437621	−	1.13347i	−0.959813	−	0.280639i	$-0.909454\pi$
$317$	−7.79162	−	20.1808i	−0.437621	−	1.13347i	0.522193	−	0.852828i	$-0.325114\pi$
$318$		0			0
$319$	10.7404	−	20.3901i	0.601345	−	1.14163i
$320$	−0.322391	+	16.6224i	−0.0180222	+	0.929219i
$321$		0			0
$322$	−6.85746	+	6.72575i	−0.382151	+	0.374811i
$323$	4.36146	+	7.55426i	0.242678	+	0.420331i
$324$		0			0
$325$	2.12670	−	3.68356i	0.117968	−	0.204327i
$326$	−0.800839	−	3.10905i	−0.0443544	−	0.172194i
$327$		0			0
$328$	−6.31816	+	3.48621i	−0.348862	+	0.192494i
$329$	0.491140	+	0.779247i	0.0270774	+	0.0429613i
$330$		0			0
$331$	21.5273	−	26.6897i	1.18325	−	1.46700i	0.331183	−	0.943566i	$-0.392552\pi$
$331$	21.5273	−	26.6897i	1.18325	−	1.46700i	0.852067	−	0.523433i	$-0.175349\pi$
$332$	0.940332	−	3.14093i	0.0516074	−	0.172381i
$333$		0			0
$334$	4.34459	−	4.60500i	0.237725	−	0.251974i
$335$	−10.0432	+	7.78410i	−0.548721	+	0.425291i
$336$		0			0
$337$	−6.61256	−	13.8290i	−0.360209	−	0.753313i	0.639673	−	0.768647i	$-0.279070\pi$
$337$	−6.61256	−	13.8290i	−0.360209	−	0.753313i	−0.999882	+	0.0153334i	$0.995119\pi$
$338$	−2.40832	−	24.7597i	−0.130996	−	1.34675i
$339$		0			0
$340$	2.25310	+	0.0874304i	0.122191	+	0.00474158i
$341$	−0.264515	−	0.173974i	−0.0143243	−	0.00942122i
$342$		0			0
$343$	−14.1310	−	7.09687i	−0.763004	−	0.383195i
$344$	−0.192936	−	9.94773i	−0.0104024	−	0.536345i
$345$		0			0
$346$	7.16310	+	5.55182i	0.385090	+	0.298468i
$347$	3.84583	−	0.601476i	0.206455	−	0.0322889i	−0.0504457	−	0.998727i	$-0.516064\pi$
$347$	3.84583	−	0.601476i	0.206455	−	0.0322889i	0.256900	+	0.966438i	$0.417299\pi$
$348$		0			0
$349$	8.63417	−	18.0568i	0.462176	−	0.966560i	−0.530716	−	0.847549i	$-0.678077\pi$
$349$	8.63417	−	18.0568i	0.462176	−	0.966560i	0.992893	−	0.119011i	$-0.0379723\pi$
$350$	3.04849	+	1.10956i	0.162949	+	0.0593085i
$351$		0			0
$352$	22.9311	−	8.34623i	1.22223	−	0.444856i
$353$	1.45659	−	14.9750i	0.0775263	−	0.797040i	−0.873273	−	0.487232i	$-0.838007\pi$
$353$	1.45659	−	14.9750i	0.0775263	−	0.797040i	0.950799	−	0.309809i	$-0.100265\pi$
$354$		0			0
$355$	−7.28255	−	21.2840i	−0.386517	−	1.12964i
$356$	−5.90985	+	5.36291i	−0.313222	+	0.284233i
$357$		0			0
$358$	−1.53348	+	4.48178i	−0.0810472	+	0.236869i
$359$	5.07641	+	11.7684i	0.267922	+	0.621114i	0.998065	−	0.0621809i	$-0.0198056\pi$
$359$	5.07641	+	11.7684i	0.267922	+	0.621114i	−0.730142	+	0.683295i	$0.760546\pi$
$360$		0			0
$361$	−24.2972	+	2.83994i	−1.27880	+	0.149470i
$362$	−13.7593	+	4.41175i	−0.723173	+	0.231876i
$363$		0			0
$364$	−20.0169	+	5.57208i	−1.04917	+	0.292056i
$365$	−3.29558	+	0.917387i	−0.172498	+	0.0480182i
$366$		0			0
$367$	3.32897	−	1.06739i	0.173771	−	0.0557174i	−0.217167	−	0.976134i	$-0.569682\pi$
$367$	3.32897	−	1.06739i	0.173771	−	0.0557174i	0.390938	+	0.920417i	$0.372151\pi$
$368$	−3.50101	+	0.409209i	−0.182503	+	0.0213315i
$369$		0			0
$370$	−3.18964	−	7.39442i	−0.165822	−	0.384418i
$371$	−8.32920	+	24.3430i	−0.432430	+	1.26383i
$372$		0			0
$373$	17.4903	−	15.8716i	0.905614	−	0.821801i	−0.0789405	−	0.996879i	$-0.525154\pi$
$373$	17.4903	−	15.8716i	0.905614	−	0.821801i	0.984554	+	0.175078i	$0.0560179\pi$
$374$	2.63441	+	7.69935i	0.136222	+	0.398124i
$375$		0			0
$376$	−0.0648197	+	0.666405i	−0.00334282	+	0.0343672i
$377$	−22.9001	+	8.33497i	−1.17942	+	0.429273i
$378$		0			0
$379$	−7.89684	−	2.87422i	−0.405634	−	0.147639i	0.131142	−	0.991364i	$-0.458136\pi$
$379$	−7.89684	−	2.87422i	−0.405634	−	0.147639i	−0.536776	+	0.843725i	$0.680358\pi$
$380$	−4.84649	+	10.1356i	−0.248620	+	0.519944i
$381$		0			0
$382$	−0.400173	+	0.0625859i	−0.0204746	+	0.00320217i
$383$	−25.2875	−	19.5993i	−1.29213	−	1.00148i	−0.998968	−	0.0454146i	$-0.985539\pi$
$383$	−25.2875	−	19.5993i	−1.29213	−	1.00148i	−0.293163	−	0.956063i	$-0.594708\pi$
$384$		0			0
$385$	0.959277	+	49.4601i	0.0488893	+	2.52072i
$386$	−19.6477	−	9.86744i	−1.00004	−	0.502239i
$387$		0			0
$388$	4.71574	+	3.10159i	0.239405	+	0.157459i
$389$	1.16611	+	0.0452504i	0.0591241	+	0.00229428i	0.0683204	−	0.997663i	$-0.478236\pi$
$389$	1.16611	+	0.0452504i	0.0591241	+	0.00229428i	−0.00919635	+	0.999958i	$0.502927\pi$
$390$		0			0
$391$	0.269129	+	2.76689i	0.0136104	+	0.139928i
$392$	−14.2070	−	29.7115i	−0.717564	−	1.50066i
$393$		0			0
$394$	11.2335	−	8.70660i	0.565934	−	0.438632i
$395$	−0.823861	+	0.873241i	−0.0414529	+	0.0439375i
$396$		0			0
$397$	3.72068	−	12.4279i	0.186736	−	0.623740i	−0.812436	−	0.583050i	$-0.801859\pi$
$397$	3.72068	−	12.4279i	0.186736	−	0.623740i	0.999172	−	0.0406903i	$-0.0129557\pi$
$398$	7.59569	−	9.41717i	0.380737	−	0.472040i
$399$		0			0
$400$	0.634783	+	1.00715i	0.0317391	+	0.0503576i
$401$	29.1695	−	16.0950i	1.45666	−	0.803748i	0.460195	−	0.887818i	$-0.347779\pi$
$401$	29.1695	−	16.0950i	1.45666	−	0.803748i	0.996460	+	0.0840692i	$0.0267917\pi$
$402$		0			0
$403$	0.0835098	+	0.324205i	0.00415992	+	0.0161498i
$404$	−0.296287	+	0.513183i	−0.0147408	+	0.0255318i
$405$		0			0
$406$	−9.29363	−	16.0970i	−0.461235	−	0.798882i
$407$	−14.5004	+	14.2219i	−0.718759	+	0.704954i
$408$		0			0
$409$	−0.477971	+	24.6441i	−0.0236342	+	1.21857i	0.780897	+	0.624660i	$0.214763\pi$
$409$	−0.477971	+	24.6441i	−0.0236342	+	1.21857i	−0.804531	+	0.593911i	$0.797583\pi$
$410$	2.46781	−	4.68502i	0.121876	−	0.231377i
$411$		0			0
$412$	−3.38347	−	8.76340i	−0.166691	−	0.431742i
$413$	3.02833	−	0.717726i	0.149014	−	0.0353170i
$414$		0			0
$415$	2.36741	+	7.90771i	0.116212	+	0.388174i
$416$	−23.8880	−	9.75933i	−1.17121	−	0.478490i
$417$		0			0
$418$	−40.4242	−	3.14202i	−1.97721	−	0.153681i
$419$	10.4789	−	7.48988i	0.511929	−	0.365905i	−0.295997	−	0.955189i	$-0.595652\pi$
$419$	10.4789	−	7.48988i	0.511929	−	0.365905i	0.807926	+	0.589284i	$0.200590\pi$
$420$		0			0
$421$	10.3082	−	16.3551i	0.502390	−	0.797096i	−0.495030	−	0.868876i	$-0.664843\pi$
$421$	10.3082	−	16.3551i	0.502390	−	0.797096i	0.997421	+	0.0717793i	$0.0228677\pi$
$422$	0.903050	−	15.5048i	0.0439598	−	0.754760i
$423$		0			0
$424$	−15.6252	+	10.2769i	−0.758829	+	0.499089i
$425$	0.803872	−	0.485139i	0.0389935	−	0.0235327i
$426$		0			0
$427$	−51.5734	+	21.0700i	−2.49581	+	1.01965i
$428$	3.04729	+	3.77805i	0.147296	+	0.182619i
$429$		0			0
$430$	4.12952	+	6.02099i	0.199143	+	0.290358i
$431$	−1.76488	−	10.0091i	−0.0850111	−	0.482122i	−0.997354	−	0.0726954i	$-0.976840\pi$
$431$	−1.76488	−	10.0091i	−0.0850111	−	0.482122i	0.912343	−	0.409427i	$-0.134271\pi$
$432$		0			0
$433$	2.65017	−	15.0299i	0.127359	−	0.722290i	−0.852519	−	0.522696i	$-0.824926\pi$
$433$	2.65017	−	15.0299i	0.127359	−	0.722290i	0.979879	−	0.199594i	$-0.0639624\pi$
$434$	−0.232459	+	0.105666i	−0.0111584	+	0.00507211i
$435$		0			0
$436$	−1.17789	−	0.231331i	−0.0564109	−	0.0110787i
$437$	−13.1899	−	4.22917i	−0.630958	−	0.202308i
$438$		0			0
$439$	12.4563	+	14.2733i	0.594506	+	0.681228i	0.969300	−	0.245880i	$-0.0790769\pi$
$439$	12.4563	+	14.2733i	0.594506	+	0.681228i	−0.374795	+	0.927108i	$0.622287\pi$
$440$	−21.4732	+	28.8436i	−1.02370	+	1.37506i
$441$		0			0
$442$	3.40829	−	7.90132i	0.162116	−	0.375827i
$443$	17.9719	+	16.3086i	0.853870	+	0.774846i	0.976023	−	0.217665i	$-0.0698441\pi$
$443$	17.9719	+	16.3086i	0.853870	+	0.774846i	−0.122153	+	0.992511i	$0.538980\pi$
$444$		0			0
$445$	5.01172	−	19.4567i	0.237578	−	0.922336i
$446$	−2.45286	−	2.40575i	−0.116146	−	0.113915i
$447$		0			0
$448$	7.15964	−	33.0526i	0.338261	−	1.56159i
$449$	5.12488	+	6.88390i	0.241858	+	0.324871i	0.906433	−	0.422350i	$-0.138795\pi$
$449$	5.12488	+	6.88390i	0.241858	+	0.324871i	−0.664575	+	0.747222i	$0.731387\pi$
$450$		0			0
$451$	−13.2649	−	1.55045i	−0.624620	−	0.0730076i
$452$	10.5737	−	2.07660i	0.497343	−	0.0976749i
$453$		0			0
$454$	−4.72046	−	21.7921i	−0.221542	−	1.02275i
$455$	34.3958	−	39.4132i	1.61250	−	1.84772i
$456$		0			0
$457$	7.74455	+	5.53547i	0.362275	+	0.258938i	0.748033	−	0.663661i	$-0.230998\pi$
$457$	7.74455	+	5.53547i	0.362275	+	0.258938i	−0.385758	+	0.922600i	$0.626060\pi$
$458$	18.8075	+	15.7814i	0.878819	+	0.737416i
$459$		0			0
$460$	−2.74277	+	2.30146i	−0.127883	+	0.107306i
$461$	−9.89019	+	0.768726i	−0.460632	+	0.0358032i	−0.305712	−	0.952124i	$-0.598895\pi$
$461$	−9.89019	+	0.768726i	−0.460632	+	0.0358032i	−0.154920	+	0.987927i	$0.549512\pi$
$462$		0			0
$463$	2.55690	−	6.62255i	0.118829	−	0.307776i	−0.860689	−	0.509131i	$-0.829967\pi$
$463$	2.55690	−	6.62255i	0.118829	−	0.307776i	0.979518	+	0.201355i	$0.0645346\pi$
$464$	0.923093	−	6.75824i	0.0428535	−	0.313743i
$465$		0			0
$466$	0.969190	+	0.534776i	0.0448969	+	0.0247730i
$467$	−0.0967509	−	1.66115i	−0.00447710	−	0.0768688i	0.995329	−	0.0965361i	$-0.0307763\pi$
$467$	−0.0967509	−	1.66115i	−0.00447710	−	0.0768688i	−0.999807	+	0.0196673i	$0.993739\pi$
$468$		0			0
$469$	23.0982	−	11.6003i	1.06658	−	0.535654i
$470$	−0.228975	−	0.434699i	−0.0105618	−	0.0200512i
$471$		0			0
$472$	2.05947	+	0.936145i	0.0947949	+	0.0430896i
$473$	10.4151	−	15.1856i	0.478889	−	0.698237i
$474$		0			0
$475$	0.633112	+	4.63520i	0.0290492	+	0.212678i
$476$	−4.46301	−	1.05775i	−0.204562	−	0.0484820i
$477$		0			0
$478$	−4.88721	−	5.18015i	−0.223536	−	0.236934i
$479$	−14.1069	−	2.20627i	−0.644559	−	0.100807i	−0.176212	−	0.984352i	$-0.556385\pi$
$479$	−14.1069	−	2.20627i	−0.644559	−	0.100807i	−0.468346	+	0.883545i	$0.655150\pi$
$480$		0			0
$481$	21.4614	−	0.832800i	0.978555	−	0.0379724i
$482$	−11.9623	−	7.21927i	−0.544867	−	0.328829i
$483$		0			0
$484$	16.7471	+	4.66187i	0.761231	+	0.211903i
$485$	−14.2103			−0.645255
$486$		0			0
$487$	−16.7491			−0.758976			−0.379488	−	0.925197i	$-0.623900\pi$
$487$	−16.7491			−0.758976			−0.379488	+	0.925197i	$0.623900\pi$
$488$	−39.0130	−	10.8600i	−1.76604	−	0.491609i
$489$		0			0
$490$	20.6907	+	12.4869i	0.934710	+	0.564100i
$491$	−12.5492	+	0.486965i	−0.566336	+	0.0219764i	−0.320354	−	0.947298i	$-0.603802\pi$
$491$	−12.5492	+	0.486965i	−0.566336	+	0.0219764i	−0.245982	+	0.969274i	$0.579111\pi$
$492$		0			0
$493$	−5.31492	−	0.831238i	−0.239372	−	0.0374371i
$494$	29.4229	+	31.1865i	1.32380	+	1.40315i
$495$		0			0
$496$	−0.0911794	−	0.0216099i	−0.00409408	−	0.000970314i
$497$	6.19272	+	45.3387i	0.277781	+	2.03372i
$498$		0			0
$499$	−18.2355	+	26.5880i	−0.816334	+	1.19024i	0.162726	+	0.986671i	$0.447971\pi$
$499$	−18.2355	+	26.5880i	−0.816334	+	1.19024i	−0.979060	+	0.203572i	$0.934745\pi$
$500$	8.85778	+	4.02635i	0.396132	+	0.180064i
$501$		0			0
$502$	−7.01323	−	13.3143i	−0.313016	−	0.594246i
$503$	36.7503	−	18.4567i	1.63861	−	0.822942i	0.640107	−	0.768285i	$-0.278890\pi$
$503$	36.7503	−	18.4567i	1.63861	−	0.822942i	0.998505	−	0.0546568i	$-0.0174065\pi$
$504$		0			0
$505$	−0.0867453	−	1.48936i	−0.00386012	−	0.0662756i
$506$	−11.3138	−	6.24270i	−0.502961	−	0.277522i
$507$		0			0
$508$	2.16672	−	15.8632i	0.0961325	−	0.703814i
$509$	−5.36061	+	13.8843i	−0.237605	+	0.615412i	−0.999478	−	0.0323146i	$-0.989712\pi$
$509$	−5.36061	+	13.8843i	−0.237605	+	0.615412i	0.761873	+	0.647727i	$0.224280\pi$
$510$		0			0
$511$	6.93774	−	0.539244i	0.306908	−	0.0238547i
$512$	13.4051	−	11.2482i	0.592426	−	0.497104i
$513$		0			0
$514$	7.18474	+	6.02872i	0.316905	+	0.265915i
$515$	19.2408	+	13.7525i	0.847852	+	0.606008i
$516$		0			0
$517$	−0.814775	+	0.933629i	−0.0358338	+	0.0410610i
$518$	3.46798	+	16.0100i	0.152374	+	0.703437i
$519$		0			0
$520$	37.3121	−	7.32785i	1.63624	−	0.321348i
$521$	−33.9224	−	3.96497i	−1.48617	−	0.173708i	−0.666053	−	0.745905i	$-0.732017\pi$
$521$	−33.9224	−	3.96497i	−1.48617	−	0.173708i	−0.820117	+	0.572196i	$0.806092\pi$
$522$		0			0
$523$	13.1600	+	17.6769i	0.575446	+	0.772958i	0.990600	−	0.136793i	$-0.0436796\pi$
$523$	13.1600	+	17.6769i	0.575446	+	0.772958i	−0.415154	+	0.909751i	$0.636272\pi$
$524$	−0.610536	+	2.81855i	−0.0266714	+	0.123129i
$525$		0			0
$526$	−16.5955	−	16.2767i	−0.723598	−	0.709700i
$527$	−0.0184344	+	0.0715667i	−0.000803015	+	0.00311750i
$528$		0			0
$529$	13.7635	+	12.4897i	0.598413	+	0.543031i
$530$	5.43561	−	12.6012i	0.236108	−	0.547360i
$531$		0			0
$532$	13.6470	−	18.3312i	0.591674	−	0.794757i
$533$	9.28582	+	10.6404i	0.402213	+	0.460885i
$534$		0			0
$535$	−11.6366	−	3.73114i	−0.503096	−	0.161311i
$536$	18.4363	+	3.62076i	0.796325	+	0.156393i
$537$		0			0
$538$	25.2143	−	11.4613i	1.08706	−	0.494131i
$539$	10.5841	−	60.0252i	0.455888	−	2.58547i
$540$		0			0
$541$	2.13348	+	12.0996i	0.0917254	+	0.520200i	0.995702	+	0.0926180i	$0.0295235\pi$
$541$	2.13348	+	12.0996i	0.0917254	+	0.520200i	−0.903976	+	0.427582i	$0.859365\pi$
$542$	−8.04963	−	11.7367i	−0.345761	−	0.504132i
$543$		0			0
$544$	−3.57618	−	4.43377i	−0.153328	−	0.190096i
$545$	2.79768	−	1.14298i	0.119840	−	0.0489599i
$546$		0			0
$547$	−25.8445	+	15.5972i	−1.10503	+	0.666890i	−0.947222	−	0.320580i	$-0.896122\pi$
$547$	−25.8445	+	15.5972i	−1.10503	+	0.666890i	−0.157810	+	0.987470i	$0.550443\pi$
$548$	−15.9916	+	10.5178i	−0.683127	+	0.449300i
$549$		0			0
$550$	−0.253762	+	4.35693i	−0.0108205	+	0.185780i
$551$	14.2920	−	22.6758i	0.608858	−	0.966020i
$552$		0			0
$553$	1.98678	−	1.42007i	0.0844865	−	0.0603873i
$554$	−24.7066	−	1.92035i	−1.04968	−	0.0815879i
$555$		0			0
$556$	−15.3708	−	6.27966i	−0.651867	−	0.266317i
$557$	11.1259	+	37.1631i	0.471420	+	1.57465i	0.781477	+	0.623934i	$0.214467\pi$
$557$	11.1259	+	37.1631i	0.471420	+	1.57465i	−0.310057	+	0.950718i	$0.600348\pi$
$558$		0			0
$559$	−18.9471	+	4.49055i	−0.801377	+	0.189930i
$560$	5.27360	+	13.6590i	0.222850	+	0.577197i
$561$		0			0
$562$	−11.6932	+	22.1991i	−0.493250	+	0.936411i
$563$	−0.657827	+	33.9174i	−0.0277241	+	1.42945i	0.685276	+	0.728283i	$0.259682\pi$
$563$	−0.657827	+	33.9174i	−0.0277241	+	1.42945i	−0.713000	+	0.701164i	$0.752664\pi$
$564$		0			0
$565$	−19.3683	+	18.9963i	−0.814830	+	0.799180i
$566$	2.98149	+	5.16409i	0.125321	+	0.217063i
$567$		0			0
$568$	−16.6312	+	28.8062i	−0.697831	+	1.20868i
$569$	8.09955	+	31.4444i	0.339551	+	1.31822i	0.879251	+	0.476359i	$0.158044\pi$
$569$	8.09955	+	31.4444i	0.339551	+	1.31822i	−0.539700	+	0.841857i	$0.681462\pi$
$570$		0			0
$571$	3.13375	−	1.72913i	0.131143	−	0.0723617i	−0.416184	−	0.909280i	$-0.636633\pi$
$571$	3.13375	−	1.72913i	0.131143	−	0.0723617i	0.547327	+	0.836919i	$0.315645\pi$
$572$	−14.9044	−	23.6474i	−0.623183	−	0.988746i
$573$		0			0
$574$	−6.76243	+	8.38410i	−0.282258	+	0.349945i
$575$	−0.427604	+	1.42830i	−0.0178323	+	0.0595641i
$576$		0			0
$577$	−13.8841	+	14.7163i	−0.578002	+	0.612646i	−0.948727	−	0.316096i	$-0.897628\pi$
$577$	−13.8841	+	14.7163i	−0.578002	+	0.612646i	0.370725	+	0.928743i	$0.379109\pi$
$578$	−13.0777	+	10.1360i	−0.543962	+	0.421602i
$579$		0			0
$580$	−2.98889	−	6.25073i	−0.124107	−	0.259547i
$581$	−1.62556	−	16.7122i	−0.0674394	−	0.693338i
$582$		0			0
$583$	−34.5863	−	1.34211i	−1.43242	−	0.0555844i
$584$	4.22608	+	2.77954i	0.174876	+	0.115018i
$585$		0			0
$586$	6.99083	+	3.51093i	0.288789	+	0.145035i
$587$	−0.0773927	−	3.99035i	−0.00319434	−	0.164699i	−0.998012	−	0.0630241i	$-0.979925\pi$
$587$	−0.0773927	−	3.99035i	−0.00319434	−	0.164699i	0.994818	−	0.101675i	$-0.0324202\pi$
$588$		0			0
$589$	−0.291044	−	0.225576i	−0.0119922	−	0.00929469i
$590$	−1.64011	+	0.256509i	−0.0675223	+	0.0105603i
$591$		0			0
$592$	−2.59326	+	5.42333i	−0.106582	+	0.222898i
$593$	1.42711	+	0.519426i	0.0586044	+	0.0213303i	0.371156	−	0.928571i	$-0.378962\pi$
$593$	1.42711	+	0.519426i	0.0586044	+	0.0213303i	−0.312552	+	0.949901i	$0.601184\pi$
$594$		0			0
$595$	10.8511	−	3.94947i	0.444851	−	0.161913i
$596$	1.59105	−	16.3575i	0.0651721	−	0.670027i
$597$		0			0
$598$	4.42356	+	12.9283i	0.180893	+	0.528679i
$599$	−21.9036	+	19.8764i	−0.894955	+	0.812129i	−0.982927	−	0.183994i	$-0.941097\pi$
$599$	−21.9036	+	19.8764i	−0.894955	+	0.812129i	0.0879721	+	0.996123i	$0.471961\pi$
$600$		0			0
$601$	3.63929	−	10.6362i	0.148450	−	0.433861i	−0.846719	−	0.532041i	$-0.821425\pi$
$601$	3.63929	−	10.6362i	0.148450	−	0.433861i	0.995169	+	0.0981794i	$0.0313019\pi$
$602$	−5.88241	−	13.6370i	−0.239749	−	0.555801i
$603$		0			0
$604$	1.64541	−	0.192321i	0.0669509	−	0.00782543i
$605$	−41.6762	+	13.3630i	−1.69438	+	0.543281i
$606$		0			0
$607$	16.0875	−	4.47826i	0.652971	−	0.181767i	0.0741827	−	0.997245i	$-0.476365\pi$
$607$	16.0875	−	4.47826i	0.652971	−	0.181767i	0.578788	+	0.815478i	$0.303526\pi$
$608$	27.3425	−	7.61130i	1.10888	−	0.308679i
$609$		0			0
$610$	28.2973	−	9.07316i	1.14572	−	0.367362i
$611$	1.30149	−	0.152122i	0.0526527	−	0.00615422i
$612$		0			0
$613$	15.3124	+	35.4980i	0.618460	+	1.43375i	0.882998	+	0.469377i	$0.155522\pi$
$613$	15.3124	+	35.4980i	0.618460	+	1.43375i	−0.264537	+	0.964375i	$0.585219\pi$
$614$	0.875007	−	2.55731i	0.0353124	−	0.103204i
$615$		0			0
$616$	54.1685	−	49.1553i	2.18251	−	1.98052i
$617$	−11.6928	−	34.1735i	−0.470735	−	1.37577i	−0.884989	−	0.465613i	$-0.845834\pi$
$617$	−11.6928	−	34.1735i	−0.470735	−	1.37577i	0.414254	−	0.910161i	$-0.364043\pi$
$618$		0			0
$619$	−1.86745	+	19.1991i	−0.0750593	+	0.771677i	0.879943	+	0.475079i	$0.157581\pi$
$619$	−1.86745	+	19.1991i	−0.0750593	+	0.771677i	−0.955002	+	0.296598i	$0.904148\pi$
$620$	−0.0894430	+	0.0325546i	−0.00359212	+	0.00130742i
$621$		0			0
$622$	−21.7246	−	7.90712i	−0.871078	−	0.317047i
$623$	−17.6308	+	36.8718i	−0.706364	+	1.47724i
$624$		0			0
$625$	−20.6968	+	3.23691i	−0.827870	+	0.129477i
$626$	10.6765	+	8.27494i	0.426720	+	0.330733i
$627$		0			0
$628$	0.102787	+	5.29968i	0.00410165	+	0.211480i
$629$	4.23677	+	2.12779i	0.168931	+	0.0848404i
$630$		0			0
$631$	13.4371	+	8.83774i	0.534924	+	0.351825i	0.788053	−	0.615608i	$-0.211089\pi$
$631$	13.4371	+	8.83774i	0.534924	+	0.351825i	−0.253129	+	0.967433i	$0.581460\pi$
$632$	1.77382	+	0.0688323i	0.0705588	+	0.00273800i
$633$		0			0
$634$	−2.27234	−	23.3617i	−0.0902462	−	0.927813i
$635$	17.3885	+	36.3650i	0.690043	+	1.44310i
$636$		0			0
$637$	−50.9430	+	39.4838i	−2.01844	+	1.56441i
$638$	17.1597	−	18.1882i	0.679358	−	0.720077i
$639$		0			0
$640$	−0.0586212	+	0.195808i	−0.00231721	+	0.00774001i
$641$	10.0323	−	12.4382i	0.396254	−	0.491278i	−0.540462	−	0.841369i	$-0.681750\pi$
$641$	10.0323	−	12.4382i	0.396254	−	0.491278i	0.936716	+	0.350091i	$0.113849\pi$
$642$		0			0
$643$	−14.8800	−	23.6088i	−0.586812	−	0.931040i	−0.999794	−	0.0203010i	$-0.993538\pi$
$643$	−14.8800	−	23.6088i	−0.586812	−	0.931040i	0.412982	−	0.910739i	$-0.364487\pi$
$644$	6.37689	−	3.51862i	0.251285	−	0.138653i
$645$		0			0
$646$	2.36085	+	9.16538i	0.0928864	+	0.360607i
$647$	0.401769	−	0.695885i	0.0157952	−	0.0273581i	−0.858020	−	0.513617i	$-0.828305\pi$
$647$	0.401769	−	0.695885i	0.0157952	−	0.0273581i	0.873815	+	0.486259i	$0.161639\pi$
$648$		0			0
$649$	2.09342	+	3.62591i	0.0821739	+	0.142329i
$650$	3.29481	−	3.23153i	0.129233	−	0.126751i
$651$		0			0
$652$	−0.0472064	+	2.43395i	−0.00184875	+	0.0953208i
$653$	−6.20800	+	11.7856i	−0.242938	+	0.461206i	−0.975650	−	0.219332i	$-0.929612\pi$
$653$	−6.20800	+	11.7856i	−0.242938	+	0.461206i	0.732712	+	0.680539i	$0.238254\pi$
$654$		0			0
$655$	−2.61512	−	6.77334i	−0.102181	−	0.264656i
$656$	−3.84625	+	0.911579i	−0.150171	+	0.0355912i
$657$		0			0
$658$	0.286638	+	0.957439i	0.0111743	+	0.0373249i
$659$	21.5026	+	8.78478i	0.837623	+	0.342207i	0.756093	−	0.654464i	$-0.227106\pi$
$659$	21.5026	+	8.78478i	0.837623	+	0.342207i	0.0815298	+	0.996671i	$0.474019\pi$
$660$		0			0
$661$	−8.29399	−	0.644660i	−0.322599	−	0.0250744i	−0.0848279	−	0.996396i	$-0.527034\pi$
$661$	−8.29399	−	0.644660i	−0.322599	−	0.0250744i	−0.237771	+	0.971321i	$0.576417\pi$
$662$	30.2681	−	21.6343i	1.17640	−	0.840842i
$663$		0			0
$664$	6.50793	−	10.3255i	0.252557	−	0.400709i
$665$	−3.34544	+	57.4389i	−0.129730	+	2.22739i
$666$		0			0
$667$	7.13697	−	4.69406i	0.276344	−	0.181755i
$668$	−4.11004	+	2.48042i	−0.159022	+	0.0959705i
$669$		0			0
$670$	−12.7630	+	5.21424i	−0.493076	+	0.201444i
$671$	−47.0533	−	58.3370i	−1.81647	−	2.25207i
$672$		0			0
$673$	5.55884	+	8.10498i	0.214277	+	0.312424i	0.916884	−	0.399155i	$-0.130696\pi$
$673$	5.55884	+	8.10498i	0.214277	+	0.312424i	−0.702606	+	0.711579i	$0.747980\pi$
$674$	−2.88810	−	16.3792i	−0.111246	−	0.630905i
$675$		0			0
$676$	−3.27550	+	18.5763i	−0.125981	+	0.714472i
$677$	43.0634	−	19.5747i	1.65506	−	0.752318i	0.655067	−	0.755571i	$-0.272640\pi$
$677$	43.0634	−	19.5747i	1.65506	−	0.752318i	0.999995	+	0.00325290i	$0.00103543\pi$
$678$		0			0
$679$	28.3643	+	5.57057i	1.08852	+	0.213779i
$680$	7.99299	+	2.56285i	0.306517	+	0.0982808i
$681$		0			0
$682$	−0.225870	−	0.258818i	−0.00864901	−	0.00991066i
$683$	0.281656	−	0.378329i	0.0107773	−	0.0144764i	−0.796702	−	0.604372i	$-0.793424\pi$
$683$	0.281656	−	0.378329i	0.0107773	−	0.0144764i	0.807479	+	0.589896i	$0.200831\pi$
$684$		0			0
$685$	19.0865	−	44.2476i	0.729259	−	1.69061i
$686$	−12.7059	−	11.5300i	−0.485113	−	0.440216i
$687$		0			0
$688$	1.35948	−	5.27783i	0.0518297	−	0.201215i
$689$	26.1304	+	25.6285i	0.995490	+	0.976370i
$690$		0			0
$691$	4.95733	−	22.8856i	0.188586	−	0.870608i	−0.780745	−	0.624849i	$-0.785160\pi$
$691$	4.95733	−	22.8856i	0.188586	−	0.870608i	0.969331	−	0.245759i	$-0.0790371\pi$
$692$	−4.10359	−	5.51208i	−0.155995	−	0.209538i
$693$		0			0
$694$	4.19498	+	0.490322i	0.159239	+	0.0186124i
$695$	41.0194	−	8.05596i	1.55596	−	0.305580i
$696$		0			0
$697$	0.659980	+	3.04681i	0.0249985	+	0.115406i
$698$	14.2792	−	16.3621i	0.540475	−	0.619315i
$699$		0			0
$700$	−2.00125	−	1.43041i	−0.0756401	−	0.0540643i
$701$	23.2425	+	19.5028i	0.877859	+	0.736611i	0.965738	−	0.259520i	$-0.0835644\pi$
$701$	23.2425	+	19.5028i	0.877859	+	0.736611i	−0.0878790	+	0.996131i	$0.528009\pi$
$702$		0			0
$703$	−18.0961	+	15.1844i	−0.682506	+	0.572691i
$704$	45.3598	−	3.52564i	1.70956	−	0.132878i
$705$		0			0
$706$	5.87988	−	15.2293i	0.221292	−	0.573161i
$707$	−0.410697	+	3.00683i	−0.0154458	+	0.113084i
$708$		0			0
$709$	38.8710	+	21.4481i	1.45983	+	0.805501i	0.996730	−	0.0808040i	$-0.0257488\pi$
$709$	38.8710	+	21.4481i	1.45983	+	0.805501i	0.463102	+	0.886305i	$0.346736\pi$
$710$	−1.41920	−	24.3668i	−0.0532618	−	0.914470i
$711$		0			0
$712$	−26.5483	+	13.3331i	−0.994941	+	0.499678i
$713$	−0.0546911	−	0.103829i	−0.00204820	−	0.00388841i
$714$		0			0
$715$	64.0659	+	29.1215i	2.39593	+	1.08908i
$716$	2.03153	−	2.96204i	0.0759217	−	0.110696i
$717$		0			0
$718$	1.88196	+	13.7784i	0.0702342	+	0.514205i
$719$	20.0540	+	4.75288i	0.747887	+	0.177252i	0.586850	−	0.809696i	$-0.300368\pi$
$719$	20.0540	+	4.75288i	0.747887	+	0.177252i	0.161037	+	0.986948i	$0.448516\pi$
$720$		0			0
$721$	−33.0144	−	34.9932i	−1.22952	−	1.30321i
$722$	−26.2237	−	4.10131i	−0.975945	−	0.152635i
$723$		0			0
$724$	10.9480	−	0.424834i	0.406881	−	0.0157888i
$725$	−2.47015	−	1.49074i	−0.0917391	−	0.0553648i
$726$		0			0
$727$	26.5964	+	7.40362i	0.986407	+	0.274585i	0.723567	−	0.690254i	$-0.242501\pi$
$727$	26.5964	+	7.40362i	0.986407	+	0.274585i	0.262840	+	0.964839i	$0.415341\pi$
$728$	−77.3491			−2.86675
$729$		0			0
$730$	−3.71173			−0.137377
$731$	−4.14090	−	1.15270i	−0.153157	−	0.0426341i
$732$		0			0
$733$	−35.2240	−	21.2578i	−1.30103	−	0.785174i	−0.314577	−	0.949232i	$-0.601863\pi$
$733$	−35.2240	−	21.2578i	−1.30103	−	0.785174i	−0.986451	+	0.164058i	$0.947542\pi$
$734$	3.79029	−	0.147080i	0.139902	−	0.00542884i
$735$		0			0
$736$	8.93659	+	1.39766i	0.329407	+	0.0515183i
$737$	23.8623	+	25.2926i	0.878980	+	0.931664i
$738$		0			0
$739$	−12.0514	−	2.85623i	−0.443318	−	0.105068i	0.00289380	−	0.999996i	$-0.499079\pi$
$739$	−12.0514	−	2.85623i	−0.443318	−	0.105068i	−0.446211	+	0.894928i	$0.647227\pi$
$740$	0.826369	+	6.05009i	0.0303779	+	0.222406i
$741$		0			0
$742$	−15.7895	+	23.0217i	−0.579651	+	0.845152i
$743$	0.790351	+	0.359258i	0.0289952	+	0.0131799i	0.428256	−	0.903658i	$-0.359128\pi$
$743$	0.790351	+	0.359258i	0.0289952	+	0.0131799i	−0.399261	+	0.916837i	$0.630733\pi$
$744$		0			0
$745$	19.2832	+	36.6083i	0.706483	+	1.34123i
$746$	22.9005	−	11.5011i	0.838446	−	0.421083i
$747$		0			0
$748$	−0.358775	−	6.15993i	−0.0131181	−	0.225229i
$749$	21.7646	+	12.0092i	0.795261	+	0.438806i
$750$		0			0
$751$	−4.73604	+	34.6739i	−0.172821	+	1.26527i	0.676124	+	0.736788i	$0.263658\pi$
$751$	−4.73604	+	34.6739i	−0.172821	+	1.26527i	−0.848944	+	0.528482i	$0.822761\pi$
$752$	−0.132099	+	0.342145i	−0.00481715	+	0.0124767i
$753$		0			0
$754$	−26.3623	+	2.04904i	−0.960059	+	0.0746217i
$755$	−3.19498	+	2.68091i	−0.116277	+	0.0975681i
$756$		0			0
$757$	−12.3117	−	10.3308i	−0.447477	−	0.375478i	0.391021	−	0.920382i	$-0.372122\pi$
$757$	−12.3117	−	10.3308i	−0.447477	−	0.375478i	−0.838499	+	0.544904i	$0.816566\pi$
$758$	−7.41809	−	5.30213i	−0.269437	−	0.192582i
$759$		0			0
$760$	−27.4994	+	31.5108i	−0.997508	+	1.14302i
$761$	2.69287	+	12.4317i	0.0976163	+	0.450647i	0.999813	+	0.0193228i	$0.00615102\pi$
$761$	2.69287	+	12.4317i	0.0976163	+	0.450647i	−0.902197	+	0.431324i	$0.858047\pi$
$762$		0			0
$763$	−6.03236	+	1.18472i	−0.218386	+	0.0428896i
$764$	0.305046	+	0.0356548i	0.0110362	+	0.00128994i
$765$		0			0
$766$	−20.7296	−	27.8447i	−0.748992	−	1.00607i
$767$	0.937291	−	4.32702i	0.0338436	−	0.156240i
$768$		0			0
$769$	37.3292	+	36.6122i	1.34612	+	1.32027i	0.906571	+	0.422053i	$0.138690\pi$
$769$	37.3292	+	36.6122i	1.34612	+	1.32027i	0.439553	+	0.898217i	$0.355137\pi$
$770$	−13.3888	+	51.9787i	−0.482501	+	1.87318i
$771$		0			0
$772$	12.3458	+	11.2032i	0.444335	+	0.403213i
$773$	−9.20251	+	21.3338i	−0.330991	+	0.767324i	0.668725	+	0.743510i	$0.266840\pi$
$773$	−9.20251	+	21.3338i	−0.330991	+	0.767324i	−0.999716	+	0.0238141i	$0.992419\pi$
$774$		0			0
$775$	−0.0236685	+	0.0317924i	−0.000850199	+	0.00114202i
$776$	13.8157	+	15.8310i	0.495953	+	0.568299i
$777$		0			0
$778$	1.20574	+	0.386606i	0.0432280	+	0.0138605i
$779$	−15.2419	−	2.99341i	−0.546097	−	0.107250i
$780$		0			0
$781$	−56.0421	+	25.4742i	−2.00534	+	0.911540i
$782$	−0.523776	+	2.97048i	−0.0187302	+	0.106224i
$783$		0			0
$784$	−3.13261	−	17.7659i	−0.111879	−	0.634498i
$785$	−7.54812	−	11.0054i	−0.269404	−	0.392801i
$786$		0			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)

\(f(q)\)	\(=\)	\(q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +O(q^{10})\)	\(q+(1.04528 + 0.290973i) q^{2} +(-0.704391 - 0.425102i) q^{4} +(2.06977 - 0.0803163i) q^{5} +(-4.16283 - 0.651054i) q^{7} +(-2.10177 - 2.22774i) q^{8} +(2.18685 + 0.518294i) q^{10} +(-0.767098 - 5.61615i) q^{11} +(-3.39021 + 4.94305i) q^{13} +(-4.16188 - 1.89181i) q^{14} +(-0.781868 - 1.48434i) q^{16} +(-1.18240 + 0.593821i) q^{17} +(-0.383327 - 6.58146i) q^{19} +(-1.49207 - 0.823287i) q^{20} +(0.832318 - 6.09365i) q^{22} +(0.756746 - 1.96002i) q^{23} +(-0.707484 + 0.0549900i) q^{25} +(-4.98201 + 4.18040i) q^{26} +(2.65549 + 2.22822i) q^{28} +(3.30770 + 2.36420i) q^{29} +(0.0367254 - 0.0420827i) q^{31} +(0.911413 + 4.20755i) q^{32} +(-1.40872 + 0.276663i) q^{34} +(-8.66837 - 1.01319i) q^{35} +(-2.13975 - 2.87418i) q^{37} +(1.51435 - 6.99101i) q^{38} +(-4.52909 - 4.44210i) q^{40} +(0.587714 - 2.28165i) q^{41} +(2.40574 + 2.18309i) q^{43} +(-1.84710 + 4.28206i) q^{44} +(1.36132 - 1.82858i) q^{46} +(-0.143743 - 0.164711i) q^{47} +(10.2395 + 3.28317i) q^{49} +(-0.755519 - 0.148379i) q^{50} +(4.48933 - 2.04065i) q^{52} +(1.06035 - 6.01354i) q^{53} +(-2.03878 - 11.5625i) q^{55} +(7.29891 + 10.6421i) q^{56} +(2.76955 + 3.43370i) q^{58} +(-0.683778 + 0.279354i) q^{59} +(11.3205 - 6.83197i) q^{61} +(0.0506333 - 0.0333020i) q^{62} +(-0.466700 + 8.01293i) q^{64} +(-6.61994 + 10.5032i) q^{65} +(-4.99078 + 3.56720i) q^{67} +(1.08530 + 0.0843564i) q^{68} +(-8.76606 - 3.58133i) q^{70} +(-3.11481 - 10.4042i) q^{71} +(-1.60703 + 0.380872i) q^{73} +(-1.40032 - 3.62693i) q^{74} +(-2.52778 + 4.79887i) q^{76} +(-0.463123 + 23.8785i) q^{77} +(-0.413794 + 0.405846i) q^{79} +(-1.73750 - 3.00944i) q^{80} +(1.27822 - 2.21395i) q^{82} +(0.994054 + 3.85915i) q^{83} +(-2.39959 + 1.32404i) q^{85} +(1.87945 + 2.98195i) q^{86} +(-10.8991 + 13.5127i) q^{88} +(2.78199 - 9.29248i) q^{89} +(17.3311 - 18.3698i) q^{91} +(-1.36625 + 1.05893i) q^{92} +(-0.102325 - 0.213994i) q^{94} +(-1.32200 - 13.5913i) q^{95} +(-6.85532 - 0.266018i) q^{97} +(9.74785 + 6.41126i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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

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