LMFDB - Embedded newform 729.2.i.a.685.25

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			685.25
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.25

$q$-expansion

$f(q)$	$=$	$q+(2.50078 + 0.696141i) q^{2} +(4.05698 + 2.44840i) q^{4} +(-0.716991 + 0.0278225i) q^{5} +(2.72859 + 0.426743i) q^{7} +(4.87841 + 5.17082i) q^{8} +O(q^{10})$	\(q+(2.50078 + 0.696141i) q^{2} +(4.05698 + 2.44840i) q^{4} +(-0.716991 + 0.0278225i) q^{5} +(2.72859 + 0.426743i) q^{7} +(4.87841 + 5.17082i) q^{8} +(-1.81241 - 0.429549i) q^{10} +(-0.742549 - 5.43642i) q^{11} +(-1.59335 + 2.32316i) q^{13} +(6.52653 + 2.96667i) q^{14} +(4.18351 + 7.94221i) q^{16} +(1.84965 - 0.928931i) q^{17} +(0.137773 + 2.36548i) q^{19} +(-2.97694 - 1.64260i) q^{20} +(1.92756 - 14.1122i) q^{22} +(-2.77393 + 7.18467i) q^{23} +(-4.47166 + 0.347565i) q^{25} +(-5.60187 + 4.70052i) q^{26} +(10.0250 + 8.41196i) q^{28} +(-2.18645 - 1.56278i) q^{29} +(4.19476 - 4.80666i) q^{31} +(1.92322 + 8.87856i) q^{32} +(5.27225 - 1.03544i) q^{34} +(-1.96824 - 0.230055i) q^{35} +(-3.11994 - 4.19081i) q^{37} +(-1.30216 + 6.01146i) q^{38} +(-3.64164 - 3.57170i) q^{40} +(-1.92690 + 7.48070i) q^{41} +(-5.74986 - 5.21772i) q^{43} +(10.2980 - 23.8735i) q^{44} +(-11.9386 + 16.0363i) q^{46} +(-1.85151 - 2.12160i) q^{47} +(0.597340 + 0.191529i) q^{49} +(-11.4246 - 2.24372i) q^{50} +(-12.1522 + 5.52385i) q^{52} +(0.472455 - 2.67943i) q^{53} +(0.683655 + 3.87720i) q^{55} +(11.1046 + 16.1908i) q^{56} +(-4.37993 - 5.43026i) q^{58} +(13.5827 - 5.54915i) q^{59} +(-3.82711 + 2.30967i) q^{61} +(13.8363 - 9.10028i) q^{62} +(-0.327284 + 5.61924i) q^{64} +(1.07778 - 1.71001i) q^{65} +(5.06095 - 3.61735i) q^{67} +(9.77840 + 0.760038i) q^{68} +(-4.76200 - 1.94549i) q^{70} +(-1.07858 - 3.60272i) q^{71} +(15.1890 - 3.59985i) q^{73} +(-4.88491 - 12.6522i) q^{74} +(-5.23269 + 9.93401i) q^{76} +(0.293846 - 15.1506i) q^{77} +(-10.6039 + 10.4002i) q^{79} +(-3.22051 - 5.57809i) q^{80} +(-10.0264 + 17.3662i) q^{82} +(1.27729 + 4.95875i) q^{83} +(-1.30034 + 0.717497i) q^{85} +(-10.7469 - 17.0511i) q^{86} +(24.4883 - 30.3607i) q^{88} +(-2.89132 + 9.65769i) q^{89} +(-5.33898 + 5.65899i) q^{91} +(-28.8447 + 22.3564i) q^{92} +(-3.15330 - 6.59457i) q^{94} +(-0.164596 - 1.69219i) q^{95} +(-5.23621 - 0.203189i) q^{97} +(1.36049 + 0.894806i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.50078	+	0.696141i	1.76832	+	0.492246i	0.990650	−	0.136425i	$-0.0435612\pi$
$2$	2.50078	+	0.696141i	1.76832	+	0.492246i	0.777671	+	0.628671i	$0.216401\pi$
$3$		0			0
$3$		0			0
$4$	4.05698	+	2.44840i	2.02849	+	1.22420i
$5$	−0.716991	+	0.0278225i	−0.320648	+	0.0124426i	−0.198597	−	0.980081i	$-0.563638\pi$
$5$	−0.716991	+	0.0278225i	−0.320648	+	0.0124426i	−0.122051	+	0.992524i	$0.538947\pi$
$6$		0			0
$7$	2.72859	+	0.426743i	1.03131	+	0.161294i	0.647458	−	0.762101i	$-0.275832\pi$
$7$	2.72859	+	0.426743i	1.03131	+	0.161294i	0.383851	+	0.923395i	$0.374598\pi$
$8$	4.87841	+	5.17082i	1.72478	+	1.82816i
$9$		0			0
$10$	−1.81241	−	0.429549i	−0.573134	−	0.135835i
$11$	−0.742549	−	5.43642i	−0.223887	−	1.63914i	−0.668710	−	0.743523i	$-0.733153\pi$
$11$	−0.742549	−	5.43642i	−0.223887	−	1.63914i	0.444823	−	0.895618i	$-0.353267\pi$
$12$		0			0
$13$	−1.59335	+	2.32316i	−0.441915	+	0.644328i	−0.980101	−	0.198498i	$-0.936394\pi$
$13$	−1.59335	+	2.32316i	−0.441915	+	0.644328i	0.538186	+	0.842826i	$0.319110\pi$
$14$	6.52653	+	2.96667i	1.74429	+	0.792877i
$15$		0			0
$16$	4.18351	+	7.94221i	1.04588	+	1.98555i
$17$	1.84965	−	0.928931i	0.448607	−	0.225299i	−0.210128	−	0.977674i	$-0.567388\pi$
$17$	1.84965	−	0.928931i	0.448607	−	0.225299i	0.658735	+	0.752375i	$0.271092\pi$
$18$		0			0
$19$	0.137773	+	2.36548i	0.0316074	+	0.542678i	0.976530	+	0.215383i	$0.0690999\pi$
$19$	0.137773	+	2.36548i	0.0316074	+	0.542678i	−0.944922	+	0.327295i	$0.893863\pi$
$20$	−2.97694	−	1.64260i	−0.665663	−	0.367297i
$21$		0			0
$22$	1.92756	−	14.1122i	0.410957	−	3.00874i
$23$	−2.77393	+	7.18467i	−0.578405	+	1.49811i	0.266846	+	0.963739i	$0.414018\pi$
$23$	−2.77393	+	7.18467i	−0.578405	+	1.49811i	−0.845252	+	0.534368i	$0.820550\pi$
$24$		0			0
$25$	−4.47166	+	0.347565i	−0.894333	+	0.0695130i
$26$	−5.60187	+	4.70052i	−1.09862	+	0.921848i
$27$		0			0
$28$	10.0250	+	8.41196i	1.89454	+	1.58971i
$29$	−2.18645	−	1.56278i	−0.406014	−	0.290202i	0.360090	−	0.932917i	$-0.382746\pi$
$29$	−2.18645	−	1.56278i	−0.406014	−	0.290202i	−0.766105	+	0.642716i	$0.777808\pi$
$30$		0			0
$31$	4.19476	−	4.80666i	0.753401	−	0.863301i	−0.240830	−	0.970567i	$-0.577420\pi$
$31$	4.19476	−	4.80666i	0.753401	−	0.863301i	0.994230	+	0.107266i	$0.0342096\pi$
$32$	1.92322	+	8.87856i	0.339980	+	1.56952i
$33$		0			0
$34$	5.27225	−	1.03544i	0.904184	−	0.177576i
$35$	−1.96824	−	0.230055i	−0.332694	−	0.0388863i
$36$		0			0
$37$	−3.11994	−	4.19081i	−0.512916	−	0.688965i	0.467927	−	0.883767i	$-0.345001\pi$
$37$	−3.11994	−	4.19081i	−0.512916	−	0.688965i	−0.980843	+	0.194802i	$0.937594\pi$
$38$	−1.30216	+	6.01146i	−0.211239	+	0.975187i
$39$		0			0
$40$	−3.64164	−	3.57170i	−0.575794	−	0.564735i
$41$	−1.92690	+	7.48070i	−0.300932	+	1.16829i	0.621903	+	0.783094i	$0.286360\pi$
$41$	−1.92690	+	7.48070i	−0.300932	+	1.16829i	−0.922835	+	0.385195i	$0.874134\pi$
$42$		0			0
$43$	−5.74986	−	5.21772i	−0.876846	−	0.795695i	0.103160	−	0.994665i	$-0.467105\pi$
$43$	−5.74986	−	5.21772i	−0.876846	−	0.795695i	−0.980006	+	0.198970i	$0.936240\pi$
$44$	10.2980	−	23.8735i	1.55248	−	3.59906i
$45$		0			0
$46$	−11.9386	+	16.0363i	−1.76024	+	2.36442i
$47$	−1.85151	−	2.12160i	−0.270071	−	0.309467i	0.602341	−	0.798239i	$-0.294235\pi$
$47$	−1.85151	−	2.12160i	−0.270071	−	0.309467i	−0.872411	+	0.488773i	$0.837445\pi$
$48$		0			0
$49$	0.597340	+	0.191529i	0.0853342	+	0.0273613i
$50$	−11.4246	−	2.24372i	−1.61569	−	0.317310i
$51$		0			0
$52$	−12.1522	+	5.52385i	−1.68521	+	0.766020i
$53$	0.472455	−	2.67943i	0.0648968	−	0.368048i	−0.935013	−	0.354613i	$-0.884612\pi$
$53$	0.472455	−	2.67943i	0.0648968	−	0.368048i	0.999910	−	0.0134343i	$-0.00427641\pi$
$54$		0			0
$55$	0.683655	+	3.87720i	0.0921841	+	0.522802i
$56$	11.1046	+	16.1908i	1.48391	+	2.16359i
$57$		0			0
$58$	−4.37993	−	5.43026i	−0.575113	−	0.713029i
$59$	13.5827	−	5.54915i	1.76832	−	0.722438i	0.772106	−	0.635494i	$-0.219203\pi$
$59$	13.5827	−	5.54915i	1.76832	−	0.722438i	0.996213	−	0.0869440i	$-0.0277101\pi$
$60$		0			0
$61$	−3.82711	+	2.30967i	−0.490011	+	0.295723i	−0.740097	−	0.672501i	$-0.765220\pi$
$61$	−3.82711	+	2.30967i	−0.490011	+	0.295723i	0.250086	+	0.968224i	$0.419541\pi$
$62$	13.8363	−	9.10028i	1.75721	−	1.15574i
$63$		0			0
$64$	−0.327284	+	5.61924i	−0.0409105	+	0.702406i
$65$	1.07778	−	1.71001i	0.133682	−	0.212101i
$66$		0			0
$67$	5.06095	−	3.61735i	0.618293	−	0.441929i	−0.228727	−	0.973491i	$-0.573456\pi$
$67$	5.06095	−	3.61735i	0.618293	−	0.441929i	0.847020	+	0.531561i	$0.178394\pi$
$68$	9.77840	+	0.760038i	1.18581	+	0.0921681i
$69$		0			0
$70$	−4.76200	−	1.94549i	−0.569168	−	0.232531i
$71$	−1.07858	−	3.60272i	−0.128004	−	0.427564i	0.869829	−	0.493353i	$-0.164229\pi$
$71$	−1.07858	−	3.60272i	−0.128004	−	0.427564i	−0.997834	+	0.0657886i	$0.979044\pi$
$72$		0			0
$73$	15.1890	−	3.59985i	1.77773	−	0.421331i	0.795039	−	0.606558i	$-0.207450\pi$
$73$	15.1890	−	3.59985i	1.77773	−	0.421331i	0.982696	+	0.185228i	$0.0593023\pi$
$74$	−4.88491	−	12.6522i	−0.567860	−	1.47079i
$75$		0			0
$76$	−5.23269	+	9.93401i	−0.600230	+	1.13951i
$77$	0.293846	−	15.1506i	0.0334868	−	1.72657i
$78$		0			0
$79$	−10.6039	+	10.4002i	−1.19303	+	1.17012i	−0.211797	+	0.977314i	$0.567931\pi$
$79$	−10.6039	+	10.4002i	−1.19303	+	1.17012i	−0.981237	+	0.192805i	$0.938241\pi$
$80$	−3.22051	−	5.57809i	−0.360064	−	0.623650i
$81$		0			0
$82$	−10.0264	+	17.3662i	−1.10723	+	1.91778i
$83$	1.27729	+	4.95875i	0.140201	+	0.544293i	0.999463	+	0.0327581i	$0.0104291\pi$
$83$	1.27729	+	4.95875i	0.140201	+	0.544293i	−0.859262	+	0.511535i	$0.829077\pi$
$84$		0			0
$85$	−1.30034	+	0.717497i	−0.141042	+	0.0778235i
$86$	−10.7469	−	17.0511i	−1.15887	−	1.83867i
$87$		0			0
$88$	24.4883	−	30.3607i	2.61046	−	3.23646i
$89$	−2.89132	+	9.65769i	−0.306479	+	1.02371i	0.656542	+	0.754289i	$0.272018\pi$
$89$	−2.89132	+	9.65769i	−0.306479	+	1.02371i	−0.963022	+	0.269423i	$0.913167\pi$
$90$		0			0
$91$	−5.33898	+	5.65899i	−0.559677	+	0.593223i
$92$	−28.8447	+	22.3564i	−3.00727	+	2.33081i
$93$		0			0
$94$	−3.15330	−	6.59457i	−0.325238	−	0.680178i
$95$	−0.164596	−	1.69219i	−0.0168872	−	0.173615i
$96$		0			0
$97$	−5.23621	−	0.203189i	−0.531657	−	0.0206307i	−0.228450	−	0.973556i	$-0.573366\pi$
$97$	−5.23621	−	0.203189i	−0.531657	−	0.0206307i	−0.303207	+	0.952925i	$0.598057\pi$
$98$	1.36049	+	0.894806i	0.137430	+	0.0903891i
$99$		0			0
$100$	−18.9924	−	9.53835i	−1.89924	−	0.953835i
$101$	−0.285905	−	14.7412i	−0.0284486	−	1.46680i	−0.693743	−	0.720223i	$-0.744040\pi$
$101$	−0.285905	−	14.7412i	−0.0284486	−	1.46680i	0.665294	−	0.746581i	$-0.268306\pi$
$102$		0			0
$103$	−9.61327	−	7.45085i	−0.947224	−	0.734154i	0.0168305	−	0.999858i	$-0.494642\pi$
$103$	−9.61327	−	7.45085i	−0.947224	−	0.734154i	−0.964055	+	0.265704i	$0.914396\pi$
$104$	−19.7856	+	3.09442i	−1.94014	+	0.303432i
$105$		0			0
$106$	3.04677	−	6.37178i	0.295928	−	0.618882i
$107$	9.91721	+	3.60957i	0.958733	+	0.348950i	0.773537	−	0.633751i	$-0.218486\pi$
$107$	9.91721	+	3.60957i	0.958733	+	0.348950i	0.185196	+	0.982702i	$0.440708\pi$
$108$		0			0
$109$	−2.70858	+	0.985841i	−0.259435	+	0.0944264i	−0.468463	−	0.883483i	$-0.655192\pi$
$109$	−2.70858	+	0.985841i	−0.259435	+	0.0944264i	0.209029	+	0.977910i	$0.432970\pi$
$110$	−0.989404	+	10.1720i	−0.0943360	+	0.969859i
$111$		0			0
$112$	8.02580	+	23.4563i	0.758367	+	2.21641i
$113$	−11.5808	+	10.5090i	−1.08943	+	0.988603i	−0.999973	−	0.00738734i	$-0.997649\pi$
$113$	−11.5808	+	10.5090i	−1.08943	+	0.988603i	−0.0894556	+	0.995991i	$0.528513\pi$
$114$		0			0
$115$	1.78899	−	5.22852i	0.166824	−	0.487562i
$116$	−5.04408	−	11.6935i	−0.468331	−	1.08571i
$117$		0			0
$118$	37.8304	−	4.42174i	3.48257	−	0.407055i
$119$	5.44336	−	1.74534i	0.498992	−	0.159995i
$120$		0			0
$121$	−18.4062	+	5.12371i	−1.67329	+	0.465792i
$122$	−11.1786	+	3.11178i	−1.01207	+	0.281728i
$123$		0			0
$124$	28.7867	−	9.23007i	2.58512	−	0.828885i
$125$	6.75986	−	0.790115i	0.604621	−	0.0706700i
$126$		0			0
$127$	−1.70274	−	3.94739i	−0.151094	−	0.350274i	0.825812	−	0.563945i	$-0.190717\pi$
$127$	−1.70274	−	3.94739i	−0.151094	−	0.350274i	−0.976906	+	0.213671i	$0.931458\pi$
$128$	1.15165	−	3.36582i	0.101792	−	0.297499i
$129$		0			0
$130$	3.88570	−	3.52609i	0.340799	−	0.309258i
$131$	1.74554	+	5.10154i	0.152509	+	0.445723i	0.995781	−	0.0917635i	$-0.0292504\pi$
$131$	1.74554	+	5.10154i	0.152509	+	0.445723i	−0.843272	+	0.537487i	$0.819374\pi$
$132$		0			0
$133$	−0.633525	+	6.51320i	−0.0549335	+	0.564766i
$134$	15.1745	−	5.52308i	1.31088	−	0.477121i
$135$		0			0
$136$	13.8267	+	5.03251i	1.18563	+	0.431534i
$137$	3.83504	−	8.02030i	0.327649	−	0.685220i	−0.670756	−	0.741678i	$-0.734030\pi$
$137$	3.83504	−	8.02030i	0.327649	−	0.685220i	0.998405	+	0.0564580i	$0.0179807\pi$
$138$		0			0
$139$	−1.72835	+	0.270310i	−0.146597	+	0.0229274i	−0.227392	−	0.973803i	$-0.573020\pi$
$139$	−1.72835	+	0.270310i	−0.146597	+	0.0229274i	0.0807944	+	0.996731i	$0.474254\pi$
$140$	−7.42186	−	5.75237i	−0.627262	−	0.486164i
$141$		0			0
$142$	−0.189304	−	9.76048i	−0.0158861	−	0.819081i
$143$	13.8128	+	6.93705i	1.15508	+	0.580105i
$144$		0			0
$145$	1.61115	+	1.05967i	0.133799	+	0.0880007i
$146$	40.4904	+	1.57121i	3.35101	+	0.130034i
$147$		0			0
$148$	−2.39677	−	24.6409i	−0.197013	−	2.02547i
$149$	−6.41565	−	13.4172i	−0.525591	−	1.09918i	−0.978237	−	0.207490i	$-0.933471\pi$
$149$	−6.41565	−	13.4172i	−0.525591	−	1.09918i	0.452647	−	0.891690i	$-0.350480\pi$
$150$		0			0
$151$	−0.205920	+	0.159600i	−0.0167575	+	0.0129881i	−0.620945	−	0.783854i	$-0.713251\pi$
$151$	−0.205920	+	0.159600i	−0.0167575	+	0.0129881i	0.604187	+	0.796842i	$0.293498\pi$
$152$	−11.5593	+	12.2522i	−0.937585	+	0.993782i
$153$		0			0
$154$	11.2818	−	37.6839i	0.909114	−	3.03665i
$155$	−2.87387	+	3.56304i	−0.230835	+	0.286190i
$156$		0			0
$157$	6.09261	+	9.66658i	0.486243	+	0.771477i	0.996048	−	0.0888128i	$-0.0283073\pi$
$157$	6.09261	+	9.66658i	0.486243	+	0.771477i	−0.509805	+	0.860290i	$0.670283\pi$
$158$	−33.7581	+	18.6270i	−2.68565	+	1.48188i
$159$		0			0
$160$	−1.62595	−	6.31233i	−0.128543	−	0.499034i
$161$	−10.6349	+	18.4202i	−0.838150	+	1.45172i
$162$		0			0
$163$	6.91859	+	11.9833i	0.541906	+	0.938608i	0.998795	+	0.0490843i	$0.0156303\pi$
$163$	6.91859	+	11.9833i	0.541906	+	0.938608i	−0.456889	+	0.889524i	$0.651036\pi$
$164$	−26.1332	+	25.6312i	−2.04066	+	2.00146i
$165$		0			0
$166$	−0.257758	+	13.2899i	−0.0200059	+	1.03150i
$167$	1.10341	−	2.09478i	0.0853847	−	0.162099i	−0.838349	−	0.545133i	$-0.816479\pi$
$167$	1.10341	−	2.09478i	0.0853847	−	0.162099i	0.923734	+	0.383035i	$0.125121\pi$
$168$		0			0
$169$	1.82401	+	4.72429i	0.140308	+	0.363407i
$170$	−3.75135	+	0.889086i	−0.287715	+	0.0681898i
$171$		0			0
$172$	−10.5520	−	35.2461i	−0.804583	−	2.68749i
$173$	11.8268	+	4.83178i	0.899174	+	0.367353i	0.780190	−	0.625543i	$-0.215123\pi$
$173$	11.8268	+	4.83178i	0.899174	+	0.367353i	0.118984	+	0.992896i	$0.462036\pi$
$174$		0			0
$175$	−12.3496	−	0.959890i	−0.933545	−	0.0725609i
$176$	40.0707	−	28.6408i	3.02044	−	2.15888i
$177$		0			0
$178$	−13.9537	+	22.1390i	−1.04587	+	1.65939i
$179$	−1.14619	+	19.6793i	−0.0856702	+	1.47090i	0.632244	+	0.774769i	$0.282134\pi$
$179$	−1.14619	+	19.6793i	−0.0856702	+	1.47090i	−0.717914	+	0.696131i	$0.754903\pi$
$180$		0			0
$181$	1.97173	−	1.29683i	0.146557	−	0.0963923i	−0.474113	−	0.880464i	$-0.657231\pi$
$181$	1.97173	−	1.29683i	0.146557	−	0.0963923i	0.620670	+	0.784072i	$0.286861\pi$
$182$	−17.2911	+	10.4352i	−1.28170	+	0.773510i
$183$		0			0
$184$	−50.6830	+	20.7063i	−3.73640	+	1.52649i
$185$	2.35357	+	2.91797i	0.173038	+	0.214533i
$186$		0			0
$187$	−6.42352	−	9.36572i	−0.469734	−	0.684889i
$188$	−2.31703	−	13.1405i	−0.168987	−	0.958370i
$189$		0			0
$190$	0.766386	−	4.34639i	0.0555995	−	0.315320i
$191$	−7.11757	+	3.23533i	−0.515010	+	0.234101i	−0.654416	−	0.756135i	$-0.727085\pi$
$191$	−7.11757	+	3.23533i	−0.515010	+	0.234101i	0.139406	+	0.990235i	$0.455481\pi$
$192$		0			0
$193$	21.7180	+	4.26528i	1.56330	+	0.307022i	0.898150	−	0.439690i	$-0.144912\pi$
$193$	21.7180	+	4.26528i	1.56330	+	0.307022i	0.665148	+	0.746711i	$0.268368\pi$
$194$	−12.9532	−	4.15328i	−0.929985	−	0.298188i
$195$		0			0
$196$	1.95445	+	2.23956i	0.139604	+	0.159968i
$197$	4.17704	−	5.61074i	0.297602	−	0.399749i	−0.628021	−	0.778197i	$-0.716135\pi$
$197$	4.17704	−	5.61074i	0.297602	−	0.399749i	0.925623	+	0.378448i	$0.123542\pi$
$198$		0			0
$199$	−8.65869	+	20.0731i	−0.613798	+	1.42294i	0.273556	+	0.961856i	$0.411800\pi$
$199$	−8.65869	+	20.0731i	−0.613798	+	1.42294i	−0.887354	+	0.461088i	$0.847459\pi$
$200$	−23.6118	−	21.4266i	−1.66961	−	1.51509i
$201$		0			0
$202$	9.54696	−	37.0636i	0.671722	−	2.60779i
$203$	−5.29902	−	5.19724i	−0.371918	−	0.364775i
$204$		0			0
$205$	1.17344	−	5.41721i	0.0819567	−	0.378354i
$206$	−18.8539	−	25.3252i	−1.31361	−	1.76449i
$207$		0			0
$208$	−25.1168	−	2.93573i	−1.74154	−	0.203556i
$209$	12.7574	−	2.50548i	0.882449	−	0.173307i
$210$		0			0
$211$	−0.214265	−	0.989155i	−0.0147506	−	0.0680963i	0.969365	−	0.245623i	$-0.0789927\pi$
$211$	−0.214265	−	0.989155i	−0.0147506	−	0.0680963i	−0.984116	+	0.177527i	$0.943190\pi$
$212$	8.47705	−	9.71362i	0.582206	−	0.667134i
$213$		0			0
$214$	22.2880	+	15.9305i	1.52358	+	1.08899i
$215$	4.26777	+	3.58108i	0.291059	+	0.244228i
$216$		0			0
$217$	13.4970	−	11.3253i	0.916234	−	0.768812i
$218$	−7.45985	+	0.579825i	−0.505245	+	0.0392707i
$219$		0			0
$220$	−6.71936	+	17.4036i	−0.453019	+	1.17335i
$221$	−0.789088	+	5.77715i	−0.0530798	+	0.388613i
$222$		0			0
$223$	7.24949	+	4.00010i	0.485462	+	0.267866i	0.706907	−	0.707306i	$-0.250090\pi$
$223$	7.24949	+	4.00010i	0.485462	+	0.267866i	−0.221446	+	0.975173i	$0.571078\pi$
$224$	1.45880	+	25.0466i	0.0974702	+	1.67350i
$225$		0			0
$226$	−36.2768	+	18.2189i	−2.41310	+	1.21190i
$227$	7.28381	+	13.8280i	0.483443	+	0.917795i	0.998172	+	0.0604413i	$0.0192508\pi$
$227$	7.28381	+	13.8280i	0.483443	+	0.917795i	−0.514728	+	0.857353i	$0.672107\pi$
$228$		0			0
$229$	14.8675	+	6.75812i	0.982474	+	0.446589i	0.839632	−	0.543156i	$-0.182771\pi$
$229$	14.8675	+	6.75812i	0.982474	+	0.446589i	0.142842	+	0.989745i	$0.454376\pi$
$230$	8.11367	−	11.8300i	0.534999	−	0.780048i
$231$		0			0
$232$	−2.58556	−	18.9296i	−0.169750	−	1.24279i
$233$	−3.93408	−	0.932394i	−0.257730	−	0.0610832i	0.0997195	−	0.995016i	$-0.468205\pi$
$233$	−3.93408	−	0.932394i	−0.257730	−	0.0610832i	−0.357450	+	0.933932i	$0.616354\pi$
$234$		0			0
$235$	1.38654	+	1.46965i	0.0904482	+	0.0958695i
$236$	68.6913	+	10.7431i	4.47142	+	0.699318i
$237$		0			0
$238$	14.8277	−	0.575381i	0.961135	−	0.0372964i
$239$	−1.80319	−	1.08823i	−0.116639	−	0.0703918i	0.457180	−	0.889374i	$-0.348860\pi$
$239$	−1.80319	−	1.08823i	−0.116639	−	0.0703918i	−0.573819	+	0.818982i	$0.694539\pi$
$240$		0			0
$241$	10.2946	+	2.86570i	0.663135	+	0.184596i	0.583356	−	0.812216i	$-0.301739\pi$
$241$	10.2946	+	2.86570i	0.663135	+	0.184596i	0.0797786	+	0.996813i	$0.474579\pi$
$242$	−49.5967			−3.18820
$243$		0			0
$244$	−21.1815			−1.35601
$245$	−0.433616	−	0.120705i	−0.0277027	−	0.00771157i
$246$		0			0
$247$	−5.71490	−	3.44896i	−0.363630	−	0.219452i
$248$	45.3181	−	1.75855i	2.87770	−	0.111668i
$249$		0			0
$250$	17.4550	+	2.72991i	1.10395	+	0.172655i
$251$	0.0568054	+	0.0602102i	0.00358552	+	0.00380043i	0.729164	−	0.684339i	$-0.239909\pi$
$251$	0.0568054	+	0.0602102i	0.00358552	+	0.00380043i	−0.725578	+	0.688140i	$0.758428\pi$
$252$		0			0
$253$	41.1187	+	9.74530i	2.58511	+	0.612682i
$254$	−1.51024	−	11.0569i	−0.0947610	−	0.693773i
$255$		0			0
$256$	11.5904	−	16.8993i	0.724403	−	1.05621i
$257$	13.3475	+	6.06716i	0.832591	+	0.378459i	0.784306	−	0.620374i	$-0.213019\pi$
$257$	13.3475	+	6.06716i	0.832591	+	0.378459i	0.0482854	+	0.998834i	$0.484624\pi$
$258$		0			0
$259$	−6.72464	−	12.7664i	−0.417849	−	0.793266i
$260$	8.55932	−	4.29865i	0.530827	−	0.266591i
$261$		0			0
$262$	0.813834	+	13.9730i	0.0502788	+	0.863254i
$263$	−3.68237	−	2.03185i	−0.227065	−	0.125289i	0.365502	−	0.930811i	$-0.380897\pi$
$263$	−3.68237	−	2.03185i	−0.227065	−	0.125289i	−0.592566	+	0.805522i	$0.701885\pi$
$264$		0			0
$265$	−0.264198	+	1.93427i	−0.0162295	+	0.118821i
$266$	−6.11842	+	15.8471i	−0.375144	+	0.971648i
$267$		0			0
$268$	29.3889	−	2.28428i	1.79521	−	0.139535i
$269$	−7.28444	+	6.11237i	−0.444140	+	0.372678i	−0.837256	−	0.546811i	$-0.815842\pi$
$269$	−7.28444	+	6.11237i	−0.444140	+	0.372678i	0.393116	+	0.919489i	$0.371397\pi$
$270$		0			0
$271$	−8.14726	−	6.83637i	−0.494911	−	0.415280i	0.360871	−	0.932616i	$-0.382479\pi$
$271$	−8.14726	−	6.83637i	−0.494911	−	0.415280i	−0.855782	+	0.517336i	$0.826924\pi$
$272$	15.1158	+	10.8041i	0.916531	+	0.655097i
$273$		0			0
$274$	15.1739	−	17.3873i	0.916687	−	1.05041i
$275$	5.20994	+	24.0517i	0.314171	+	1.45038i
$276$		0			0
$277$	−10.9000	+	2.14069i	−0.654918	+	0.128622i	−0.509124	−	0.860693i	$-0.670030\pi$
$277$	−10.9000	+	2.14069i	−0.654918	+	0.128622i	−0.145794	+	0.989315i	$0.546574\pi$
$278$	−4.51042	−	0.527192i	−0.270517	−	0.0316189i
$279$		0			0
$280$	−8.41234	−	11.2997i	−0.502733	−	0.675288i
$281$	−0.187335	+	0.864836i	−0.0111755	+	0.0515918i	−0.982581	−	0.185834i	$-0.940501\pi$
$281$	−0.187335	+	0.864836i	−0.0111755	+	0.0515918i	0.971406	+	0.237426i	$0.0763037\pi$
$282$		0			0
$283$	0.451104	+	0.442440i	0.0268154	+	0.0263003i	0.713502	−	0.700654i	$-0.247108\pi$
$283$	0.451104	+	0.442440i	0.0268154	+	0.0263003i	−0.686686	+	0.726954i	$0.740935\pi$
$284$	4.44511	−	17.2570i	0.263769	−	1.02401i
$285$		0			0
$286$	29.7137	+	26.9637i	1.75701	+	1.59440i
$287$	−8.45006	+	19.5895i	−0.498792	+	1.15633i
$288$		0			0
$289$	−7.59339	+	10.1997i	−0.446670	+	0.599982i
$290$	3.29145	+	3.77159i	0.193281	+	0.221475i
$291$		0			0
$292$	70.4352	+	22.5841i	4.12191	+	1.32164i
$293$	2.50934	+	0.492819i	0.146597	+	0.0287908i	0.265473	−	0.964118i	$-0.414472\pi$
$293$	2.50934	+	0.492819i	0.146597	+	0.0287908i	−0.118875	+	0.992909i	$0.537929\pi$
$294$		0			0
$295$	−9.58429	+	4.35659i	−0.558019	+	0.253651i
$296$	6.44954	−	36.5772i	0.374872	−	2.12600i
$297$		0			0
$298$	−6.70390	−	38.0197i	−0.388347	−	2.20242i
$299$	−12.2713	−	17.8920i	−0.709667	−	1.03472i
$300$		0			0
$301$	−13.4624	−	16.6907i	−0.775958	−	0.962037i
$302$	−0.626065	+	0.255776i	−0.0360260	+	0.0147182i
$303$		0			0
$304$	−18.2107	+	10.9902i	−1.04446	+	0.630333i
$305$	2.67974	−	1.76249i	0.153441	−	0.100920i
$306$		0			0
$307$	−1.30463	+	22.3996i	−0.0744590	+	1.27841i	0.729605	+	0.683869i	$0.239704\pi$
$307$	−1.30463	+	22.3996i	−0.0744590	+	1.27841i	−0.804064	+	0.594543i	$0.797333\pi$
$308$	38.2869	−	60.7463i	2.18160	−	3.46134i
$309$		0			0
$310$	−9.66730	+	6.90977i	−0.549066	+	0.392449i
$311$	−1.51385	−	0.117665i	−0.0858423	−	0.00667219i	0.0344994	−	0.999405i	$-0.489016\pi$
$311$	−1.51385	−	0.117665i	−0.0858423	−	0.00667219i	−0.120342	+	0.992733i	$0.538399\pi$
$312$		0			0
$313$	6.38492	+	2.60853i	0.360897	+	0.147443i	0.551394	−	0.834245i	$-0.314096\pi$
$313$	6.38492	+	2.60853i	0.360897	+	0.147443i	−0.190497	+	0.981688i	$0.561010\pi$
$314$	8.50700	+	28.4153i	0.480078	+	1.60357i
$315$		0			0
$316$	−68.4838	+	16.2310i	−3.85252	+	0.913063i
$317$	−3.14331	−	8.14137i	−0.176546	−	0.457265i	0.816160	−	0.577826i	$-0.196099\pi$
$317$	−3.14331	−	8.14137i	−0.176546	−	0.457265i	−0.992706	+	0.120561i	$0.961531\pi$
$318$		0			0
$319$	−6.87239	+	13.0469i	−0.384780	+	0.730487i
$320$	0.0783179	−	4.03805i	0.00437811	−	0.225734i
$321$		0			0
$322$	−39.4188	+	38.6616i	−2.19672	+	2.15453i
$323$	2.45220	+	4.24733i	0.136444	+	0.236328i
$324$		0			0
$325$	6.31747	−	10.9422i	0.350430	−	0.606962i
$326$	8.95980	+	34.7841i	0.496237	+	1.92651i
$327$		0			0
$328$	−48.0816	+	26.5303i	−2.65486	+	1.46489i
$329$	−4.14663	−	6.57908i	−0.228611	−	0.362716i
$330$		0			0
$331$	16.1132	−	19.9772i	0.885659	−	1.09805i	−0.108919	−	0.994051i	$-0.534739\pi$
$331$	16.1132	−	19.9772i	0.885659	−	1.09805i	0.994578	−	0.103995i	$-0.0331625\pi$
$332$	−6.95905	+	23.2448i	−0.381927	+	1.27573i
$333$		0			0
$334$	4.21766	−	4.47046i	0.230780	−	0.244613i
$335$	−3.52801	+	2.73441i	−0.192756	+	0.149397i
$336$		0			0
$337$	−5.48737	−	11.4759i	−0.298916	−	0.625130i	0.696833	−	0.717233i	$-0.254592\pi$
$337$	−5.48737	−	11.4759i	−0.298916	−	0.625130i	−0.995749	+	0.0921029i	$0.970641\pi$
$338$	1.27267	+	13.0842i	0.0692242	+	0.711687i
$339$		0			0
$340$	−7.03217	−	0.272880i	−0.381373	−	0.0147990i
$341$	−29.2458	−	19.2353i	−1.58375	−	1.04165i
$342$		0			0
$343$	−15.7278	−	7.89880i	−0.849222	−	0.426495i
$344$	−1.07032	−	55.1857i	−0.0577080	−	2.97541i
$345$		0			0
$346$	26.2127	+	20.3163i	1.40920	+	1.09221i
$347$	28.2924	−	4.42485i	1.51881	−	0.237538i	0.660564	−	0.750770i	$-0.270317\pi$
$347$	28.2924	−	4.42485i	1.51881	−	0.237538i	0.858250	+	0.513232i	$0.171552\pi$
$348$		0			0
$349$	2.30048	−	4.81104i	0.123142	−	0.257529i	−0.831360	−	0.555734i	$-0.812437\pi$
$349$	2.30048	−	4.81104i	0.123142	−	0.257529i	0.954502	+	0.298205i	$0.0963879\pi$
$350$	−30.2156	−	10.9976i	−1.61509	−	0.587845i
$351$		0			0
$352$	46.8395	−	17.0482i	2.49655	−	0.908671i
$353$	2.08407	−	21.4261i	0.110924	−	1.14040i	−0.760321	−	0.649547i	$-0.774958\pi$
$353$	2.08407	−	21.4261i	0.110924	−	1.14040i	0.871245	−	0.490849i	$-0.163313\pi$
$354$		0			0
$355$	0.873571	+	2.55311i	0.0463643	+	0.135505i
$356$	−35.3759	+	32.1019i	−1.87492	+	1.70140i
$357$		0			0
$358$	−16.5659	+	48.4158i	−0.875538	+	2.55886i
$359$	7.24796	+	16.8027i	0.382533	+	0.886811i	0.995326	+	0.0965676i	$0.0307864\pi$
$359$	7.24796	+	16.8027i	0.382533	+	0.886811i	−0.612794	+	0.790243i	$0.709954\pi$
$360$		0			0
$361$	13.2950	−	1.55397i	0.699738	−	0.0817877i
$362$	5.83364	−	1.87048i	0.306609	−	0.0983104i
$363$		0			0
$364$	−35.5156	+	9.88644i	−1.86152	+	0.518190i
$365$	−10.7902	+	3.00366i	−0.564784	+	0.157219i
$366$		0			0
$367$	−27.5680	+	8.83932i	−1.43904	+	0.461409i	−0.919517	−	0.393050i	$-0.871420\pi$
$367$	−27.5680	+	8.83932i	−1.43904	+	0.461409i	−0.519520	+	0.854459i	$0.673889\pi$
$368$	−68.6669	+	8.02601i	−3.57951	+	0.418385i
$369$		0			0
$370$	3.85445	+	8.93563i	0.200383	+	0.464541i
$371$	2.43256	−	7.10943i	0.126292	−	0.369103i
$372$		0			0
$373$	8.90247	−	8.07856i	0.460952	−	0.418292i	−0.408157	−	0.912912i	$-0.633828\pi$
$373$	8.90247	−	8.07856i	0.460952	−	0.418292i	0.869110	+	0.494620i	$0.164693\pi$
$374$	−9.54398	−	27.8933i	−0.493507	−	1.44233i
$375$		0			0
$376$	1.93795	−	19.9238i	0.0999420	−	1.02749i
$377$	7.11437	−	2.58942i	0.366409	−	0.133362i
$378$		0			0
$379$	−6.02404	−	2.19257i	−0.309434	−	0.112625i	0.182635	−	0.983181i	$-0.441537\pi$
$379$	−6.02404	−	2.19257i	−0.309434	−	0.112625i	−0.492069	+	0.870556i	$0.663759\pi$
$380$	3.47540	−	7.26818i	0.178284	−	0.372850i
$381$		0			0
$382$	−20.0518	+	3.13604i	−1.02594	+	0.160454i
$383$	−16.7401	−	12.9745i	−0.855377	−	0.662968i	0.0874792	−	0.996166i	$-0.472119\pi$
$383$	−16.7401	−	12.9745i	−0.855377	−	0.662968i	−0.942857	+	0.333199i	$0.891872\pi$
$384$		0			0
$385$	0.210843	+	10.8710i	0.0107456	+	0.554039i
$386$	51.3429	+	25.7854i	2.61328	+	1.31244i
$387$		0			0
$388$	−20.7457	−	13.6447i	−1.05320	−	0.692704i
$389$	−30.7701	−	1.19402i	−1.56011	−	0.0605392i	−0.755820	−	0.654780i	$-0.772761\pi$
$389$	−30.7701	−	1.19402i	−1.56011	−	0.0605392i	−0.804287	+	0.594241i	$0.797453\pi$
$390$		0			0
$391$	1.54325	+	15.8660i	0.0780453	+	0.802376i
$392$	1.92371	+	4.02309i	0.0971619	+	0.203197i
$393$		0			0
$394$	14.3517	−	11.1234i	0.723030	−	0.560391i
$395$	7.31355	−	7.75191i	0.367984	−	0.390041i
$396$		0			0
$397$	4.87408	−	16.2806i	0.244623	−	0.817097i	−0.744194	−	0.667963i	$-0.767166\pi$
$397$	4.87408	−	16.2806i	0.244623	−	0.817097i	0.988817	−	0.149134i	$-0.0476486\pi$
$398$	−35.6272	+	44.1708i	−1.78583	+	2.21408i
$399$		0			0
$400$	−21.4677	−	34.0608i	−1.07339	−	1.70304i
$401$	26.8353	−	14.8071i	1.34009	−	0.739432i	0.359067	−	0.933312i	$-0.383095\pi$
$401$	26.8353	−	14.8071i	1.34009	−	0.739432i	0.981025	+	0.193880i	$0.0621073\pi$
$402$		0			0
$403$	4.48292	+	17.4038i	0.223310	+	0.866943i
$404$	34.9324	−	60.5047i	1.73795	−	3.01022i
$405$		0			0
$406$	−9.63370	−	16.6861i	−0.478112	−	0.828115i
$407$	−20.4663	+	20.0732i	−1.01448	+	0.994992i
$408$		0			0
$409$	0.400958	−	20.6733i	0.0198261	−	1.02223i	−0.849381	−	0.527780i	$-0.823025\pi$
$409$	0.400958	−	20.6733i	0.0198261	−	1.02223i	0.869207	−	0.494448i	$-0.164630\pi$
$410$	6.70566	−	12.7304i	0.331169	−	0.628709i
$411$		0			0
$412$	−20.7582	−	53.7651i	−1.02268	−	2.64881i
$413$	39.4297	−	9.34501i	1.94021	−	0.459838i
$414$		0			0
$415$	−1.05377	−	3.51984i	−0.0517275	−	0.172782i
$416$	−23.6906	−	9.67869i	−1.16153	−	0.474537i
$417$		0			0
$418$	33.6477	+	2.61531i	1.64576	+	0.127919i
$419$	−11.6463	+	8.32426i	−0.568958	+	0.406667i	−0.829262	−	0.558860i	$-0.811239\pi$
$419$	−11.6463	+	8.32426i	−0.568958	+	0.406667i	0.260304	+	0.965527i	$0.416177\pi$
$420$		0			0
$421$	5.06672	−	8.03889i	0.246937	−	0.391792i	−0.699525	−	0.714608i	$-0.746605\pi$
$421$	5.06672	−	8.03889i	0.246937	−	0.391792i	0.946462	+	0.322817i	$0.104630\pi$
$422$	0.152762	−	2.62282i	0.00743634	−	0.127677i
$423$		0			0
$424$	16.1597	−	10.6284i	0.784783	−	0.516160i
$425$	−7.94817	+	4.79674i	−0.385543	+	0.232676i
$426$		0			0
$427$	−11.4282	+	4.66895i	−0.553051	+	0.225946i
$428$	31.3962	+	38.9252i	1.51759	+	1.88152i
$429$		0			0
$430$	8.17983	+	11.9265i	0.394466	+	0.575146i
$431$	6.59007	+	37.3742i	0.317433	+	1.80025i	0.558242	+	0.829678i	$0.311476\pi$
$431$	6.59007	+	37.3742i	0.317433	+	1.80025i	−0.240810	+	0.970572i	$0.577413\pi$
$432$		0			0
$433$	−0.184493	+	1.04631i	−0.00886615	+	0.0502824i	−0.988920	−	0.148450i	$-0.952571\pi$
$433$	−0.184493	+	1.04631i	−0.00886615	+	0.0502824i	0.980054	+	0.198733i	$0.0636826\pi$
$434$	41.6370	−	18.9263i	1.99864	−	0.908494i
$435$		0			0
$436$	−13.4024	−	2.63214i	−0.641857	−	0.126057i
$437$	−17.3773	−	5.57182i	−0.831271	−	0.266536i
$438$		0			0
$439$	15.6362	+	17.9171i	0.746276	+	0.855137i	0.993501	−	0.113821i	$-0.0363090\pi$
$439$	15.6362	+	17.9171i	0.746276	+	0.855137i	−0.247226	+	0.968958i	$0.579519\pi$
$440$	−16.7131	+	22.4496i	−0.796768	+	1.07024i
$441$		0			0
$442$	−5.99505	+	13.8981i	−0.285156	+	0.661065i
$443$	−0.0321116	−	0.0291397i	−0.00152567	−	0.00138447i	0.671245	−	0.741236i	$-0.265760\pi$
$443$	−0.0321116	−	0.0291397i	−0.00152567	−	0.00138447i	−0.672770	+	0.739851i	$0.734896\pi$
$444$		0			0
$445$	1.80435	−	7.00491i	0.0855344	−	0.332065i
$446$	15.3448	+	15.0501i	0.726596	+	0.712641i
$447$		0			0
$448$	−3.29100	+	15.1929i	−0.155485	+	0.717798i
$449$	−14.3005	−	19.2089i	−0.674883	−	0.906525i	0.324340	−	0.945941i	$-0.394858\pi$
$449$	−14.3005	−	19.2089i	−0.674883	−	0.906525i	−0.999223	+	0.0394152i	$0.987450\pi$
$450$		0			0
$451$	42.0991	+	4.92067i	1.98237	+	0.231705i
$452$	−72.7132	+	14.2804i	−3.42014	+	0.671694i
$453$		0			0
$454$	8.58902	+	39.6513i	0.403103	+	1.86093i
$455$	3.67055	−	4.20598i	0.172078	−	0.197180i
$456$		0			0
$457$	−18.3101	−	13.0873i	−0.856511	−	0.612197i	0.0661502	−	0.997810i	$-0.478928\pi$
$457$	−18.3101	−	13.0873i	−0.856511	−	0.612197i	−0.922661	+	0.385613i	$0.873990\pi$
$458$	32.4759	+	27.2505i	1.51750	+	1.27333i
$459$		0			0
$460$	20.0594	−	16.8318i	0.935274	−	0.784788i
$461$	−1.06014	+	0.0824003i	−0.0493755	+	0.00383776i	−0.102156	−	0.994768i	$-0.532574\pi$
$461$	−1.06014	+	0.0824003i	−0.0493755	+	0.00383776i	0.0527809	+	0.998606i	$0.483191\pi$
$462$		0			0
$463$	−1.42369	+	3.68745i	−0.0661645	+	0.171370i	−0.962023	−	0.272970i	$-0.911994\pi$
$463$	−1.42369	+	3.68745i	−0.0661645	+	0.171370i	0.895858	+	0.444340i	$0.146562\pi$
$464$	3.26489	−	23.9032i	0.151568	−	1.10968i
$465$		0			0
$466$	−9.18921	−	5.07039i	−0.425682	−	0.234881i
$467$	1.44736	+	24.8502i	0.0669759	+	1.14993i	0.849597	+	0.527433i	$0.176845\pi$
$467$	1.44736	+	24.8502i	0.0669759	+	1.14993i	−0.782621	+	0.622499i	$0.786117\pi$
$468$		0			0
$469$	15.3529	−	7.71052i	0.708932	−	0.356039i
$470$	2.44437	+	4.64051i	0.112750	+	0.214051i
$471$		0			0
$472$	94.9557	+	43.1627i	4.37069	+	1.98672i
$473$	−24.0962	+	35.1331i	−1.10794	+	1.61542i
$474$		0			0
$475$	−1.43823	−	10.5297i	−0.0659907	−	0.483137i
$476$	26.3569	+	6.24669i	1.20807	+	0.286317i
$477$		0			0
$478$	−3.75183	−	3.97671i	−0.171605	−	0.181890i
$479$	26.5448	+	4.15153i	1.21286	+	0.189688i	0.728418	−	0.685133i	$-0.240256\pi$
$479$	26.5448	+	4.15153i	1.21286	+	0.189688i	0.484445	+	0.874822i	$0.339022\pi$
$480$		0			0
$481$	14.7071	−	0.570701i	0.670585	−	0.0260217i
$482$	23.7497	+	14.3330i	1.08177	+	0.652851i
$483$		0			0
$484$	−87.2184	−	24.2789i	−3.96447	−	1.10359i
$485$	3.75997			0.170731
$486$		0			0
$487$	0.611056			0.0276896			0.0138448	−	0.999904i	$-0.495593\pi$
$487$	0.611056			0.0276896			0.0138448	+	0.999904i	$0.495593\pi$
$488$	−30.6131	−	8.52174i	−1.38579	−	0.385761i
$489$		0			0
$490$	−1.00035	−	0.603715i	−0.0451913	−	0.0272731i
$491$	−8.44663	+	0.327768i	−0.381191	+	0.0147919i	−0.228659	−	0.973507i	$-0.573434\pi$
$491$	−8.44663	+	0.327768i	−0.381191	+	0.0147919i	−0.152532	+	0.988299i	$0.548743\pi$
$492$		0			0
$493$	−5.49590	−	0.859543i	−0.247523	−	0.0387119i
$494$	−11.8908	−	12.6035i	−0.534991	−	0.567057i
$495$		0			0
$496$	55.7243	+	13.2069i	2.50209	+	0.593007i
$497$	−1.40557	−	10.2906i	−0.0630486	−	0.461597i
$498$		0			0
$499$	−8.93784	+	13.0317i	−0.400113	+	0.583379i	−0.971423	−	0.237356i	$-0.923719\pi$
$499$	−8.93784	+	13.0317i	−0.400113	+	0.583379i	0.571310	+	0.820734i	$0.306435\pi$
$500$	29.3591	+	13.3454i	1.31298	+	0.596823i
$501$		0			0
$502$	0.100143	+	0.190117i	0.00446961	+	0.00848535i
$503$	−16.2244	+	8.14819i	−0.723409	+	0.363310i	−0.772097	−	0.635504i	$-0.780792\pi$
$503$	−16.2244	+	8.14819i	−0.723409	+	0.363310i	0.0486881	+	0.998814i	$0.484496\pi$
$504$		0			0
$505$	0.615128	+	10.5613i	0.0273729	+	0.469974i
$506$	96.0448	+	52.9953i	4.26971	+	2.35593i
$507$		0			0
$508$	2.75682	−	20.1835i	0.122314	−	0.895497i
$509$	9.75933	−	25.2773i	0.432574	−	1.12040i	−0.529669	−	0.848205i	$-0.677684\pi$
$509$	9.75933	−	25.2773i	0.432574	−	1.12040i	0.962243	−	0.272191i	$-0.0877484\pi$
$510$		0			0
$511$	42.9806	−	3.34072i	1.90135	−	0.147785i
$512$	35.2993	−	29.6196i	1.56002	−	1.30901i
$513$		0			0
$514$	29.1555	+	24.4644i	1.28599	+	1.07908i
$515$	7.09993	+	5.07472i	0.312860	+	0.223619i
$516$		0			0
$517$	−10.1591	+	11.6410i	−0.446795	+	0.511970i
$518$	−7.92965	−	36.6073i	−0.348409	−	1.60843i
$519$		0			0
$520$	14.1000	−	2.76915i	0.618327	−	0.121435i
$521$	−35.5321	−	4.15310i	−1.55669	−	0.181951i	−0.706225	−	0.707987i	$-0.749603\pi$
$521$	−35.5321	−	4.15310i	−1.55669	−	0.181951i	−0.850462	+	0.526036i	$0.823678\pi$
$522$		0			0
$523$	−3.58627	−	4.81720i	−0.156817	−	0.210641i	0.716770	−	0.697309i	$-0.245620\pi$
$523$	−3.58627	−	4.81720i	−0.156817	−	0.210641i	−0.873587	+	0.486668i	$0.838212\pi$
$524$	−5.40897	+	24.9706i	−0.236292	+	1.09085i
$525$		0			0
$526$	−7.79436	−	7.64466i	−0.339850	−	0.333323i
$527$	3.29380	−	12.7873i	0.143480	−	0.557024i
$528$		0			0
$529$	−26.8923	−	24.4034i	−1.16923	−	1.06102i
$530$	−2.00723	+	4.65327i	−0.0871883	+	0.202125i
$531$		0			0
$532$	−18.5171	+	24.8728i	−0.802819	+	1.07837i
$533$	−14.3086	−	16.3959i	−0.619775	−	0.710184i
$534$		0			0
$535$	−7.21098	−	2.31211i	−0.311758	−	0.0999611i
$536$	43.3940	+	8.52231i	1.87434	+	0.368108i
$537$		0			0
$538$	−22.4719	+	10.2147i	−0.968832	+	0.440388i
$539$	0.597679	−	3.38961i	0.0257439	−	0.146001i
$540$		0			0
$541$	7.34936	+	41.6803i	0.315974	+	1.79198i	0.566706	+	0.823920i	$0.308217\pi$
$541$	7.34936	+	41.6803i	0.315974	+	1.79198i	−0.250732	+	0.968056i	$0.580671\pi$
$542$	−15.6155	−	22.7679i	−0.670742	−	0.977966i
$543$		0			0
$544$	11.8049	+	14.6357i	0.506129	+	0.627502i
$545$	1.91459	−	0.782198i	0.0820122	−	0.0335057i
$546$		0			0
$547$	0.513877	−	0.310126i	0.0219718	−	0.0132600i	−0.505671	−	0.862726i	$-0.668755\pi$
$547$	0.513877	−	0.310126i	0.0219718	−	0.0132600i	0.527643	+	0.849466i	$0.323076\pi$
$548$	35.1956	−	23.1485i	1.50348	−	0.988854i
$549$		0			0
$550$	−3.71448	+	63.7751i	−0.158386	+	2.71938i
$551$	3.39549	−	5.38732i	0.144653	−	0.229507i
$552$		0			0
$553$	−33.3719	+	23.8528i	−1.41912	+	1.01433i
$554$	−28.7488	−	2.23453i	−1.22142	−	0.0949362i
$555$		0			0
$556$	−7.67372	−	3.13506i	−0.325438	−	0.132956i
$557$	−6.30067	−	21.0457i	−0.266968	−	0.891735i	−0.981391	−	0.192021i	$-0.938496\pi$
$557$	−6.30067	−	21.0457i	−0.266968	−	0.891735i	0.714423	−	0.699714i	$-0.246689\pi$
$558$		0			0
$559$	21.2831	−	5.04419i	0.900180	−	0.213347i
$560$	−6.40703	−	16.5946i	−0.270747	−	0.701251i
$561$		0			0
$562$	−1.07053	+	2.03236i	−0.0451577	+	0.0857298i
$563$	−0.472020	+	24.3372i	−0.0198933	+	1.02569i	0.848315	+	0.529492i	$0.177617\pi$
$563$	−0.472020	+	24.3372i	−0.0198933	+	1.02569i	−0.868208	+	0.496200i	$0.834728\pi$
$564$		0			0
$565$	8.01093	−	7.85706i	0.337022	−	0.330549i
$566$	0.820114	+	1.42048i	0.0344720	+	0.0597072i
$567$		0			0
$568$	13.3672	−	23.1527i	0.560876	−	0.971466i
$569$	5.73637	+	22.2699i	0.240481	+	0.933605i	0.968695	+	0.248255i	$0.0798570\pi$
$569$	5.73637	+	22.2699i	0.240481	+	0.933605i	−0.728214	+	0.685350i	$0.759649\pi$
$570$		0			0
$571$	29.4529	−	16.2514i	1.23257	−	0.680101i	0.273116	−	0.961981i	$-0.411946\pi$
$571$	29.4529	−	16.2514i	1.23257	−	0.680101i	0.959450	+	0.281880i	$0.0909580\pi$
$572$	39.0536	+	61.9627i	1.63291	+	2.59079i
$573$		0			0
$574$	−34.7688	+	43.1066i	−1.45122	+	1.79923i
$575$	9.90696	−	33.0916i	0.413149	−	1.38001i
$576$		0			0
$577$	−7.73031	+	8.19365i	−0.321817	+	0.341106i	−0.868004	−	0.496557i	$-0.834597\pi$
$577$	−7.73031	+	8.19365i	−0.321817	+	0.341106i	0.546187	+	0.837663i	$0.316079\pi$
$578$	−26.0899	+	20.2212i	−1.08519	+	0.841089i
$579$		0			0
$580$	3.94190	+	8.24378i	0.163678	+	0.342304i
$581$	1.36909	+	14.0754i	0.0567993	+	0.583948i
$582$		0			0
$583$	−14.9173	−	0.578860i	−0.617812	−	0.0239739i
$584$	92.7122	+	60.9778i	3.83646	+	2.52328i
$585$		0			0
$586$	5.93226	+	2.97929i	0.245059	+	0.123073i
$587$	−0.664659	−	34.2696i	−0.0274334	−	1.41446i	−0.720435	−	0.693523i	$-0.756058\pi$
$587$	−0.664659	−	34.2696i	−0.0274334	−	1.41446i	0.693001	−	0.720936i	$-0.256288\pi$
$588$		0			0
$589$	11.9480	+	9.26037i	0.492307	+	0.381567i
$590$	−27.0011	+	4.22289i	−1.11162	+	0.173854i
$591$		0			0
$592$	20.2320	−	42.3116i	0.831528	−	1.73899i
$593$	23.4470	+	8.53401i	0.962853	+	0.350450i	0.775151	−	0.631776i	$-0.217674\pi$
$593$	23.4470	+	8.53401i	0.962853	+	0.350450i	0.187702	+	0.982226i	$0.439896\pi$
$594$		0			0
$595$	−3.85428	+	1.40284i	−0.158010	+	0.0575109i
$596$	6.82249	−	70.1414i	0.279460	−	2.87310i
$597$		0			0
$598$	−18.2325	−	53.2865i	−0.745582	−	2.17905i
$599$	14.3871	−	13.0556i	0.587839	−	0.533436i	−0.322892	−	0.946436i	$-0.604655\pi$
$599$	14.3871	−	13.0556i	0.587839	−	0.533436i	0.910731	+	0.413000i	$0.135519\pi$
$600$		0			0
$601$	9.76326	−	28.5342i	0.398252	−	1.16393i	−0.546871	−	0.837217i	$-0.684181\pi$
$601$	9.76326	−	28.5342i	0.398252	−	1.16393i	0.945122	−	0.326717i	$-0.105942\pi$
$602$	−22.0474	−	51.1116i	−0.898585	−	2.08315i
$603$		0			0
$604$	−1.22618	+	0.143319i	−0.0498924	+	0.00583158i
$605$	13.0545	−	4.18576i	0.530741	−	0.170175i
$606$		0			0
$607$	−26.1915	+	7.29091i	−1.06308	+	0.295929i	−0.755199	−	0.655495i	$-0.772460\pi$
$607$	−26.1915	+	7.29091i	−1.06308	+	0.295929i	−0.307882	+	0.951424i	$0.599620\pi$
$608$	−20.7371	+	5.77255i	−0.840999	+	0.234108i
$609$		0			0
$610$	7.92840	−	2.54214i	0.321011	−	0.102928i
$611$	7.87891	−	0.920912i	0.318746	−	0.0372561i
$612$		0			0
$613$	−8.56402	−	19.8536i	−0.345898	−	0.801881i	−0.999004	−	0.0446148i	$-0.985794\pi$
$613$	−8.56402	−	19.8536i	−0.345898	−	0.801881i	0.653107	−	0.757266i	$-0.273465\pi$
$614$	−18.8559	+	55.1083i	−0.760960	+	2.22399i
$615$		0			0
$616$	79.7745	−	72.3915i	3.21421	−	2.91674i
$617$	−0.946650	−	2.76669i	−0.0381107	−	0.111383i	0.925452	−	0.378864i	$-0.123685\pi$
$617$	−0.946650	−	2.76669i	−0.0381107	−	0.111383i	−0.963563	+	0.267481i	$0.913809\pi$
$618$		0			0
$619$	1.90826	−	19.6186i	0.0766994	−	0.788538i	−0.875532	−	0.483160i	$-0.839489\pi$
$619$	1.90826	−	19.6186i	0.0766994	−	0.788538i	0.952231	−	0.305378i	$-0.0987828\pi$
$620$	−20.3830	+	7.41879i	−0.818600	+	0.297946i
$621$		0			0
$622$	−3.70389	−	1.34811i	−0.148513	−	0.0540541i
$623$	−12.0106	+	25.1180i	−0.481193	+	1.00633i
$624$		0			0
$625$	17.3316	−	2.71062i	0.693266	−	0.108425i
$626$	14.1514	+	10.9682i	0.565604	+	0.438376i
$627$		0			0
$628$	1.04993	+	54.1342i	0.0418969	+	2.16019i
$629$	−9.66379	−	4.85334i	−0.385321	−	0.193515i
$630$		0			0
$631$	25.8599	+	17.0083i	1.02947	+	0.677091i	0.947569	−	0.319550i	$-0.103532\pi$
$631$	25.8599	+	17.0083i	1.02947	+	0.677091i	0.0818971	+	0.996641i	$0.473902\pi$
$632$	−105.508	−	4.09419i	−4.19688	−	0.162858i
$633$		0			0
$634$	−2.19319	−	22.5480i	−0.0871029	−	0.895496i
$635$	1.33067	+	2.78287i	0.0528062	+	0.110435i
$636$		0			0
$637$	−1.39672	+	1.08254i	−0.0553402	+	0.0428919i
$638$	−26.2689	+	27.8434i	−1.03999	+	1.10233i
$639$		0			0
$640$	−0.732075	+	2.44530i	−0.0289378	+	0.0966590i
$641$	6.96954	−	8.64087i	0.275280	−	0.341294i	−0.621788	−	0.783185i	$-0.713594\pi$
$641$	6.96954	−	8.64087i	0.275280	−	0.341294i	0.897069	+	0.441891i	$0.145692\pi$
$642$		0			0
$643$	−18.5069	−	29.3631i	−0.729840	−	1.15797i	−0.981742	−	0.190217i	$-0.939081\pi$
$643$	−18.5069	−	29.3631i	−0.729840	−	1.15797i	0.251903	−	0.967753i	$-0.418944\pi$
$644$	−88.2458	+	48.6920i	−3.47737	+	1.91873i
$645$		0			0
$646$	3.17568	+	12.3287i	0.124945	+	0.485068i
$647$	5.20638	−	9.01771i	0.204684	−	0.354523i	−0.745348	−	0.666676i	$-0.767717\pi$
$647$	5.20638	−	9.01771i	0.204684	−	0.354523i	0.950032	+	0.312153i	$0.101050\pi$
$648$		0			0
$649$	−40.2533	−	69.7208i	−1.58008	−	2.73678i
$650$	23.4159	−	22.9662i	0.918448	−	0.900807i
$651$		0			0
$652$	−1.27145	+	65.5556i	−0.0497938	+	2.56736i
$653$	15.6354	−	29.6832i	0.611862	−	1.16159i	−0.361511	−	0.932368i	$-0.617739\pi$
$653$	15.6354	−	29.6832i	0.611862	−	1.16159i	0.973374	−	0.229224i	$-0.0736190\pi$
$654$		0			0
$655$	−1.39347	−	3.60919i	−0.0544475	−	0.141023i
$656$	−67.4745	+	15.9918i	−2.63444	+	0.624373i
$657$		0			0
$658$	−5.78987	−	19.3395i	−0.225713	−	0.753932i
$659$	−40.1912	−	16.4199i	−1.56563	−	0.639629i	−0.580938	−	0.813948i	$-0.697314\pi$
$659$	−40.1912	−	16.4199i	−1.56563	−	0.639629i	−0.984689	+	0.174319i	$0.944228\pi$
$660$		0			0
$661$	39.3467	+	3.05827i	1.53041	+	0.118953i	0.814880	−	0.579630i	$-0.196803\pi$
$661$	39.3467	+	3.05827i	1.53041	+	0.118953i	0.715529	+	0.698583i	$0.246186\pi$
$662$	54.2025	−	38.7416i	2.10664	−	1.50574i
$663$		0			0
$664$	−19.4096	+	30.7954i	−0.753239	+	1.19509i
$665$	0.273018	−	4.68753i	0.0105872	−	0.181775i
$666$		0			0
$667$	17.2932	−	11.3739i	0.669594	−	0.440399i
$668$	9.60538	−	5.79687i	0.371643	−	0.224288i
$669$		0			0
$670$	−10.7263	+	4.38219i	−0.414394	+	0.169299i
$671$	15.3982	+	19.0907i	0.594439	+	0.736989i
$672$		0			0
$673$	−15.0153	−	21.8929i	−0.578799	−	0.843910i	0.419150	−	0.907917i	$-0.362328\pi$
$673$	−15.0153	−	21.8929i	−0.578799	−	0.843910i	−0.997949	+	0.0640071i	$0.979612\pi$
$674$	−5.73392	−	32.5187i	−0.220862	−	1.25257i
$675$		0			0
$676$	−4.16700	+	23.6322i	−0.160269	+	0.908933i
$677$	2.89958	−	1.31802i	0.111440	−	0.0506556i	−0.357315	−	0.933984i	$-0.616308\pi$
$677$	2.89958	−	1.31802i	0.111440	−	0.0506556i	0.468755	+	0.883328i	$0.344703\pi$
$678$		0			0
$679$	−14.2008	−	2.78894i	−0.544975	−	0.107030i
$680$	−10.0536	−	3.22357i	−0.385539	−	0.123618i
$681$		0			0
$682$	−59.7470	−	68.4625i	−2.28783	−	2.62157i
$683$	4.00094	−	5.37420i	0.153092	−	0.205638i	−0.718960	−	0.695051i	$-0.755382\pi$
$683$	4.00094	−	5.37420i	0.153092	−	0.205638i	0.872052	+	0.489413i	$0.162789\pi$
$684$		0			0
$685$	−2.52654	+	5.85718i	−0.0965342	+	0.223791i
$686$	−33.8332	−	30.7020i	−1.29176	−	1.17221i
$687$		0			0
$688$	17.3856	−	67.4950i	0.662819	−	2.57322i
$689$	5.47195	+	5.36685i	0.208465	+	0.204461i
$690$		0			0
$691$	−8.30575	+	38.3436i	−0.315966	+	1.45866i	0.492601	+	0.870255i	$0.336046\pi$
$691$	−8.30575	+	38.3436i	−0.315966	+	1.45866i	−0.808566	+	0.588405i	$0.799756\pi$
$692$	36.1509	+	48.5591i	1.37425	+	1.84594i
$693$		0			0
$694$	73.8334	+	8.62989i	2.80268	+	0.327586i
$695$	1.23169	−	0.241897i	0.0467208	−	0.00917566i
$696$		0			0
$697$	3.38495	+	15.6267i	0.128214	+	0.591903i
$698$	9.10216	−	10.4299i	0.344522	−	0.394778i
$699$		0			0
$700$	−47.7520	−	34.1311i	−1.80486	−	1.29003i
$701$	−17.0474	−	14.3045i	−0.643872	−	0.540273i	0.261332	−	0.965249i	$-0.415838\pi$
$701$	−17.0474	−	14.3045i	−0.643872	−	0.540273i	−0.905205	+	0.424976i	$0.860283\pi$
$702$		0			0
$703$	9.48342	−	7.95754i	0.357674	−	0.300124i
$704$	30.7916	−	2.39331i	1.16050	−	0.0902013i
$705$		0			0
$706$	20.1274	−	52.1313i	0.757504	−	1.96199i
$707$	5.51059	−	40.3446i	0.207247	−	1.51732i
$708$		0			0
$709$	3.18490	+	1.75735i	0.119611	+	0.0659988i	0.541790	−	0.840514i	$-0.317747\pi$
$709$	3.18490	+	1.75735i	0.119611	+	0.0659988i	−0.422179	+	0.906513i	$0.638734\pi$
$710$	0.407290	+	6.99290i	0.0152853	+	0.262439i
$711$		0			0
$712$	−64.0432	+	32.1637i	−2.40012	+	1.20539i
$713$	22.8983	+	43.4713i	0.857547	+	1.62801i
$714$		0			0
$715$	−10.0967	−	4.58949i	−0.377593	−	0.171637i
$716$	−52.8329	+	77.0322i	−1.97446	+	2.87883i
$717$		0			0
$718$	6.42857	+	47.0654i	0.239912	+	1.75647i
$719$	−30.7263	−	7.28228i	−1.14590	−	0.271583i	−0.386551	−	0.922268i	$-0.626334\pi$
$719$	−30.7263	−	7.28228i	−1.14590	−	0.271583i	−0.759348	+	0.650685i	$0.774482\pi$
$720$		0			0
$721$	−23.0511	−	24.4327i	−0.858466	−	0.909921i
$722$	34.3298	+	5.36908i	1.27762	+	0.199817i
$723$		0			0
$724$	11.1744	−	0.433618i	0.415294	−	0.0161153i
$725$	10.3203	+	6.22830i	0.383285	+	0.231313i
$726$		0			0
$727$	33.4868	+	9.32168i	1.24196	+	0.345722i	0.826004	−	0.563665i	$-0.190609\pi$
$727$	33.4868	+	9.32168i	1.24196	+	0.345722i	0.415952	+	0.909387i	$0.363449\pi$
$728$	−55.3073			−2.04983
$729$		0			0
$730$	−29.0749			−1.07611
$731$	−15.4822	−	4.30975i	−0.572628	−	0.159402i
$732$		0			0
$733$	21.3000	+	12.8546i	0.786732	+	0.474795i	0.852300	−	0.523053i	$-0.175207\pi$
$733$	21.3000	+	12.8546i	0.786732	+	0.474795i	−0.0655684	+	0.997848i	$0.520886\pi$
$734$	−75.0950	+	2.91403i	−2.77181	+	0.107559i
$735$		0			0
$736$	−69.1244	−	10.8109i	−2.54796	−	0.398493i
$737$	−23.4234	−	24.8274i	−0.862813	−	0.914528i
$738$		0			0
$739$	−32.4436	−	7.68926i	−1.19346	−	0.282854i	−0.414568	−	0.910018i	$-0.636067\pi$
$739$	−32.4436	−	7.68926i	−1.19346	−	0.282854i	−0.778887	+	0.627164i	$0.784216\pi$
$740$	2.40403	+	17.6006i	0.0883739	+	0.647011i
$741$		0			0
$742$	11.0325	−	16.0858i	0.405015	−	0.590527i
$743$	−23.9698	−	10.8956i	−0.879366	−	0.399721i	−0.0773363	−	0.997005i	$-0.524641\pi$
$743$	−23.9698	−	10.8956i	−0.879366	−	0.399721i	−0.802030	+	0.597284i	$0.796246\pi$
$744$		0			0
$745$	4.97326	+	9.44151i	0.182206	+	0.345910i
$746$	27.8870	−	14.0054i	1.02101	−	0.512773i
$747$		0			0
$748$	−3.12906	−	53.7239i	−0.114410	−	1.96434i
$749$	25.5196	+	14.0811i	0.932466	+	0.514513i
$750$		0			0
$751$	1.80047	−	13.1818i	0.0657001	−	0.481010i	−0.928317	−	0.371789i	$-0.878745\pi$
$751$	1.80047	−	13.1818i	0.0657001	−	0.481010i	0.994017	−	0.109221i	$-0.0348357\pi$
$752$	9.10433	−	23.5808i	0.332001	−	0.859904i
$753$		0			0
$754$	19.5941	−	1.52298i	0.713576	−	0.0554635i
$755$	0.143202	−	0.120161i	0.00521166	−	0.00437310i
$756$		0			0
$757$	−21.4671	−	18.0131i	−0.780236	−	0.654696i	0.163072	−	0.986614i	$-0.447860\pi$
$757$	−21.4671	−	18.0131i	−0.780236	−	0.654696i	−0.943308	+	0.331918i	$0.892304\pi$
$758$	−13.5385	−	9.67672i	−0.491740	−	0.351474i
$759$		0			0
$760$	7.94704	−	9.10630i	0.288270	−	0.330320i
$761$	−2.82492	−	13.0413i	−0.102403	−	0.472746i	−0.999521	−	0.0309541i	$-0.990145\pi$
$761$	−2.82492	−	13.0413i	−0.102403	−	0.472746i	0.897118	−	0.441792i	$-0.145657\pi$
$762$		0			0
$763$	−7.81128	+	1.53409i	−0.282787	+	0.0555377i
$764$	−36.7972	−	4.30098i	−1.33128	−	0.155604i
$765$		0			0
$766$	−32.8312	−	44.1000i	−1.18624	−	1.59340i
$767$	−8.75044	+	40.3965i	−0.315960	+	1.45863i
$768$		0			0
$769$	−11.0718	−	10.8591i	−0.399259	−	0.391591i	0.472656	−	0.881247i	$-0.343295\pi$
$769$	−11.0718	−	10.8591i	−0.399259	−	0.391591i	−0.871916	+	0.489656i	$0.837122\pi$
$770$	−7.04049	+	27.3329i	−0.253722	+	0.985008i
$771$		0			0
$772$	77.6665	+	70.4786i	2.79528	+	2.53658i
$773$	3.30278	−	7.65670i	0.118793	−	0.275392i	−0.848437	−	0.529297i	$-0.822456\pi$
$773$	3.30278	−	7.65670i	0.118793	−	0.275392i	0.967229	+	0.253905i	$0.0817150\pi$
$774$		0			0
$775$	−17.0869	+	22.9517i	−0.613780	+	0.824450i
$776$	−24.4938	−	28.0667i	−0.879275	−	1.00754i
$777$		0			0
$778$	−76.1182	−	24.4063i	−2.72897	−	0.875009i
$779$	−17.9609	−	3.52741i	−0.643516	−	0.126382i
$780$		0			0
$781$	−18.7850	+	8.53883i	−0.672180	+	0.305543i
$782$	−7.18562	+	40.7517i	−0.256957	+	1.45728i
$783$		0			0
$784$	0.977814	+	5.54546i	0.0349219	+	0.198052i
$785$	−4.63729	−	6.76133i	−0.165512	−	0.241322i
$786$		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)

\(f(q)\)	\(=\)	\(q+(2.50078 + 0.696141i) q^{2} +(4.05698 + 2.44840i) q^{4} +(-0.716991 + 0.0278225i) q^{5} +(2.72859 + 0.426743i) q^{7} +(4.87841 + 5.17082i) q^{8} +O(q^{10})\)	\(q+(2.50078 + 0.696141i) q^{2} +(4.05698 + 2.44840i) q^{4} +(-0.716991 + 0.0278225i) q^{5} +(2.72859 + 0.426743i) q^{7} +(4.87841 + 5.17082i) q^{8} +(-1.81241 - 0.429549i) q^{10} +(-0.742549 - 5.43642i) q^{11} +(-1.59335 + 2.32316i) q^{13} +(6.52653 + 2.96667i) q^{14} +(4.18351 + 7.94221i) q^{16} +(1.84965 - 0.928931i) q^{17} +(0.137773 + 2.36548i) q^{19} +(-2.97694 - 1.64260i) q^{20} +(1.92756 - 14.1122i) q^{22} +(-2.77393 + 7.18467i) q^{23} +(-4.47166 + 0.347565i) q^{25} +(-5.60187 + 4.70052i) q^{26} +(10.0250 + 8.41196i) q^{28} +(-2.18645 - 1.56278i) q^{29} +(4.19476 - 4.80666i) q^{31} +(1.92322 + 8.87856i) q^{32} +(5.27225 - 1.03544i) q^{34} +(-1.96824 - 0.230055i) q^{35} +(-3.11994 - 4.19081i) q^{37} +(-1.30216 + 6.01146i) q^{38} +(-3.64164 - 3.57170i) q^{40} +(-1.92690 + 7.48070i) q^{41} +(-5.74986 - 5.21772i) q^{43} +(10.2980 - 23.8735i) q^{44} +(-11.9386 + 16.0363i) q^{46} +(-1.85151 - 2.12160i) q^{47} +(0.597340 + 0.191529i) q^{49} +(-11.4246 - 2.24372i) q^{50} +(-12.1522 + 5.52385i) q^{52} +(0.472455 - 2.67943i) q^{53} +(0.683655 + 3.87720i) q^{55} +(11.1046 + 16.1908i) q^{56} +(-4.37993 - 5.43026i) q^{58} +(13.5827 - 5.54915i) q^{59} +(-3.82711 + 2.30967i) q^{61} +(13.8363 - 9.10028i) q^{62} +(-0.327284 + 5.61924i) q^{64} +(1.07778 - 1.71001i) q^{65} +(5.06095 - 3.61735i) q^{67} +(9.77840 + 0.760038i) q^{68} +(-4.76200 - 1.94549i) q^{70} +(-1.07858 - 3.60272i) q^{71} +(15.1890 - 3.59985i) q^{73} +(-4.88491 - 12.6522i) q^{74} +(-5.23269 + 9.93401i) q^{76} +(0.293846 - 15.1506i) q^{77} +(-10.6039 + 10.4002i) q^{79} +(-3.22051 - 5.57809i) q^{80} +(-10.0264 + 17.3662i) q^{82} +(1.27729 + 4.95875i) q^{83} +(-1.30034 + 0.717497i) q^{85} +(-10.7469 - 17.0511i) q^{86} +(24.4883 - 30.3607i) q^{88} +(-2.89132 + 9.65769i) q^{89} +(-5.33898 + 5.65899i) q^{91} +(-28.8447 + 22.3564i) q^{92} +(-3.15330 - 6.59457i) q^{94} +(-0.164596 - 1.69219i) q^{95} +(-5.23621 - 0.203189i) q^{97} +(1.36049 + 0.894806i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 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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