LMFDB - Embedded newform 729.2.i.a.685.22

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			685.22
Character	$\chi$	$=$	729.685
Dual form			729.2.i.a.613.22

$q$-expansion

$f(q)$	$=$	$q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +O(q^{10})$	\(q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +(-5.46724 - 1.29576i) q^{10} +(-0.589047 - 4.31259i) q^{11} +(1.84548 - 2.69078i) q^{13} +(-4.68860 - 2.13123i) q^{14} +(-2.14553 - 4.07318i) q^{16} +(-4.70279 + 2.36183i) q^{17} +(0.0335399 + 0.575858i) q^{19} +(-4.20780 - 2.32177i) q^{20} +(1.12221 - 8.21604i) q^{22} +(-2.84305 + 7.36370i) q^{23} +(3.68691 - 0.286569i) q^{25} +(4.76183 - 3.99565i) q^{26} +(-3.37456 - 2.83159i) q^{28} +(0.495027 + 0.353824i) q^{29} +(5.02592 - 5.75907i) q^{31} +(-1.55794 - 7.19223i) q^{32} +(-9.83791 + 1.93210i) q^{34} +(7.91895 + 0.925592i) q^{35} +(1.86718 + 2.50805i) q^{37} +(-0.232651 + 1.07404i) q^{38} +(1.48612 + 1.45758i) q^{40} +(2.17856 - 8.45769i) q^{41} +(0.623280 + 0.565596i) q^{43} +(2.80928 - 6.51263i) q^{44} +(-8.98013 + 12.0624i) q^{46} +(-5.83765 - 6.68920i) q^{47} +(0.293432 + 0.0940850i) q^{49} +(6.91316 + 1.35770i) q^{50} +(4.84027 - 2.20017i) q^{52} +(-2.35120 + 13.3343i) q^{53} +(2.22912 + 12.6419i) q^{55} +(1.07921 + 1.57353i) q^{56} +(0.727777 + 0.902301i) q^{58} +(-6.01839 + 2.45878i) q^{59} +(4.92623 - 2.97299i) q^{61} +(12.1666 - 8.00212i) q^{62} +(0.279822 - 4.80436i) q^{64} +(-5.13097 + 8.14083i) q^{65} +(-7.89248 + 5.64120i) q^{67} +(-8.54964 - 0.664531i) q^{68} +(14.0611 + 5.74460i) q^{70} +(-0.635585 - 2.12300i) q^{71} +(-5.07940 + 1.20384i) q^{73} +(2.14554 + 5.55709i) q^{74} +(-0.438064 + 0.831643i) q^{76} +(-0.228172 + 11.7645i) q^{77} +(8.20313 - 8.04557i) q^{79} +(6.78872 + 11.7584i) q^{80} +(8.31948 - 14.4098i) q^{82} +(-3.22782 - 12.5312i) q^{83} +(13.5891 - 7.49816i) q^{85} +(0.854969 + 1.35650i) q^{86} +(-1.92873 + 2.39125i) q^{88} +(-1.18058 + 3.94341i) q^{89} +(-6.05307 + 6.41588i) q^{91} +(-10.1665 + 7.87962i) q^{92} +(-7.29657 - 15.2595i) q^{94} +(-0.164697 - 1.69323i) q^{95} +(-4.78397 - 0.185640i) q^{97} +(0.490480 + 0.322594i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.83535	+	0.510904i	1.29779	+	0.361263i	0.847107	−	0.531423i	$-0.178342\pi$
$2$	1.83535	+	0.510904i	1.29779	+	0.361263i	0.450679	+	0.892686i	$0.351182\pi$
$3$		0			0
$3$		0			0
$4$	1.39514	+	0.841972i	0.697571	+	0.420986i
$5$	−2.94702	+	0.114358i	−1.31795	+	0.0511424i	−0.688123	−	0.725594i	$-0.741565\pi$
$5$	−2.94702	+	0.114358i	−1.31795	+	0.0511424i	−0.629826	+	0.776736i	$0.716874\pi$
$6$		0			0
$7$	−2.67089	−	0.417720i	−1.00950	−	0.157883i	−0.371919	−	0.928265i	$-0.621300\pi$
$7$	−2.67089	−	0.417720i	−1.00950	−	0.157883i	−0.637583	+	0.770382i	$0.720066\pi$
$8$	−0.484358	−	0.513389i	−0.171246	−	0.181510i
$9$		0			0
$10$	−5.46724	−	1.29576i	−1.72889	−	0.409755i
$11$	−0.589047	−	4.31259i	−0.177604	−	1.30029i	−0.836461	−	0.548026i	$-0.815379\pi$
$11$	−0.589047	−	4.31259i	−0.177604	−	1.30029i	0.658857	−	0.752268i	$-0.271040\pi$
$12$		0			0
$13$	1.84548	−	2.69078i	0.511845	−	0.746288i	−0.479505	−	0.877539i	$-0.659184\pi$
$13$	1.84548	−	2.69078i	0.511845	−	0.746288i	0.991349	+	0.131252i	$0.0418996\pi$
$14$	−4.68860	−	2.13123i	−1.25308	−	0.569595i
$15$		0			0
$16$	−2.14553	−	4.07318i	−0.536382	−	1.01830i
$17$	−4.70279	+	2.36183i	−1.14059	+	0.572827i	−0.915822	−	0.401584i	$-0.868460\pi$
$17$	−4.70279	+	2.36183i	−1.14059	+	0.572827i	−0.224771	+	0.974412i	$0.572163\pi$
$18$		0			0
$19$	0.0335399	+	0.575858i	0.00769459	+	0.132111i	0.999968	+	0.00803807i	$0.00255862\pi$
$19$	0.0335399	+	0.575858i	0.00769459	+	0.132111i	−0.992273	+	0.124073i	$0.960404\pi$
$20$	−4.20780	−	2.32177i	−0.940893	−	0.519163i
$21$		0			0
$22$	1.12221	−	8.21604i	0.239256	−	1.75167i
$23$	−2.84305	+	7.36370i	−0.592818	+	1.53544i	0.233573	+	0.972339i	$0.424958\pi$
$23$	−2.84305	+	7.36370i	−0.592818	+	1.53544i	−0.826390	+	0.563098i	$0.809610\pi$
$24$		0			0
$25$	3.68691	−	0.286569i	0.737382	−	0.0573138i
$26$	4.76183	−	3.99565i	0.933871	−	0.783611i
$27$		0			0
$28$	−3.37456	−	2.83159i	−0.637732	−	0.535121i
$29$	0.495027	+	0.353824i	0.0919242	+	0.0657035i	0.626525	−	0.779401i	$-0.284476\pi$
$29$	0.495027	+	0.353824i	0.0919242	+	0.0657035i	−0.534601	+	0.845104i	$0.679538\pi$
$30$		0			0
$31$	5.02592	−	5.75907i	0.902682	−	1.03436i	−0.0965560	−	0.995328i	$-0.530783\pi$
$31$	5.02592	−	5.75907i	0.902682	−	1.03436i	0.999238	−	0.0390313i	$-0.0124272\pi$
$32$	−1.55794	−	7.19223i	−0.275407	−	1.27142i
$33$		0			0
$34$	−9.83791	+	1.93210i	−1.68719	+	0.331353i
$35$	7.91895	+	0.925592i	1.33855	+	0.156454i
$36$		0			0
$37$	1.86718	+	2.50805i	0.306962	+	0.412321i	0.928658	−	0.370937i	$-0.120964\pi$
$37$	1.86718	+	2.50805i	0.306962	+	0.412321i	−0.621696	+	0.783259i	$0.713556\pi$
$38$	−0.232651	+	1.07404i	−0.0377409	+	0.174232i
$39$		0			0
$40$	1.48612	+	1.45758i	0.234977	+	0.230464i
$41$	2.17856	−	8.45769i	0.340234	−	1.32087i	−0.538124	−	0.842866i	$-0.680867\pi$
$41$	2.17856	−	8.45769i	0.340234	−	1.32087i	0.878358	−	0.478003i	$-0.158639\pi$
$42$		0			0
$43$	0.623280	+	0.565596i	0.0950492	+	0.0862526i	0.718147	−	0.695891i	$-0.244990\pi$
$43$	0.623280	+	0.565596i	0.0950492	+	0.0862526i	−0.623098	+	0.782144i	$0.714126\pi$
$44$	2.80928	−	6.51263i	0.423514	−	0.981816i
$45$		0			0
$46$	−8.98013	+	12.0624i	−1.32405	+	1.77851i
$47$	−5.83765	−	6.68920i	−0.851508	−	0.975720i	0.148405	−	0.988927i	$-0.452586\pi$
$47$	−5.83765	−	6.68920i	−0.851508	−	0.975720i	−0.999913	+	0.0132066i	$0.995796\pi$
$48$		0			0
$49$	0.293432	+	0.0940850i	0.0419188	+	0.0134407i
$50$	6.91316	+	1.35770i	0.977669	+	0.192008i
$51$		0			0
$52$	4.84027	−	2.20017i	0.671224	−	0.305109i
$53$	−2.35120	+	13.3343i	−0.322963	+	1.83161i	0.200660	+	0.979661i	$0.435691\pi$
$53$	−2.35120	+	13.3343i	−0.322963	+	1.83161i	−0.523622	+	0.851950i	$0.675420\pi$
$54$		0			0
$55$	2.22912	+	12.6419i	0.300574	+	1.70464i
$56$	1.07921	+	1.57353i	0.144216	+	0.210272i
$57$		0			0
$58$	0.727777	+	0.902301i	0.0955617	+	0.118478i
$59$	−6.01839	+	2.45878i	−0.783528	+	0.320107i	−0.734427	−	0.678687i	$-0.762549\pi$
$59$	−6.01839	+	2.45878i	−0.783528	+	0.320107i	−0.0491009	+	0.998794i	$0.515636\pi$
$60$		0			0
$61$	4.92623	−	2.97299i	0.630739	−	0.380653i	−0.164999	−	0.986294i	$-0.552762\pi$
$61$	4.92623	−	2.97299i	0.630739	−	0.380653i	0.795738	+	0.605641i	$0.207083\pi$
$62$	12.1666	−	8.00212i	1.54516	−	1.01627i
$63$		0			0
$64$	0.279822	−	4.80436i	0.0349778	−	0.600545i
$65$	−5.13097	+	8.14083i	−0.636418	+	1.00975i
$66$		0			0
$67$	−7.89248	+	5.64120i	−0.964220	+	0.689183i	−0.950500	−	0.310723i	$-0.899429\pi$
$67$	−7.89248	+	5.64120i	−0.964220	+	0.689183i	−0.0137191	+	0.999906i	$0.504367\pi$
$68$	−8.54964	−	0.664531i	−1.03680	−	0.0805862i
$69$		0			0
$70$	14.0611	+	5.74460i	1.68063	+	0.686611i
$71$	−0.635585	−	2.12300i	−0.0754300	−	0.251954i	0.911955	−	0.410290i	$-0.134572\pi$
$71$	−0.635585	−	2.12300i	−0.0754300	−	0.251954i	−0.987385	+	0.158336i	$0.949387\pi$
$72$		0			0
$73$	−5.07940	+	1.20384i	−0.594499	+	0.140899i	−0.516841	−	0.856081i	$-0.672892\pi$
$73$	−5.07940	+	1.20384i	−0.594499	+	0.140899i	−0.0776577	+	0.996980i	$0.524744\pi$
$74$	2.14554	+	5.55709i	0.249414	+	0.645999i
$75$		0			0
$76$	−0.438064	+	0.831643i	−0.0502493	+	0.0953960i
$77$	−0.228172	+	11.7645i	−0.0260027	+	1.34069i
$78$		0			0
$79$	8.20313	−	8.04557i	0.922924	−	0.905198i	−0.0728211	−	0.997345i	$-0.523200\pi$
$79$	8.20313	−	8.04557i	0.922924	−	0.905198i	0.995745	+	0.0921472i	$0.0293730\pi$
$80$	6.78872	+	11.7584i	0.759002	+	1.31463i
$81$		0			0
$82$	8.31948	−	14.4098i	0.918732	−	1.59129i
$83$	−3.22782	−	12.5312i	−0.354300	−	1.37548i	−0.858909	−	0.512128i	$-0.828857\pi$
$83$	−3.22782	−	12.5312i	−0.354300	−	1.37548i	0.504609	−	0.863348i	$-0.331637\pi$
$84$		0			0
$85$	13.5891	−	7.49816i	1.47395	−	0.813290i
$86$	0.854969	+	1.35650i	0.0921937	+	0.146275i
$87$		0			0
$88$	−1.92873	+	2.39125i	−0.205603	+	0.254908i
$89$	−1.18058	+	3.94341i	−0.125141	+	0.418001i	−0.997484	−	0.0708941i	$-0.977415\pi$
$89$	−1.18058	+	3.94341i	−0.125141	+	0.418001i	0.872343	+	0.488895i	$0.162600\pi$
$90$		0			0
$91$	−6.05307	+	6.41588i	−0.634534	+	0.672567i
$92$	−10.1665	+	7.87962i	−1.05993	+	0.821508i
$93$		0			0
$94$	−7.29657	−	15.2595i	−0.752583	−	1.57389i
$95$	−0.164697	−	1.69323i	−0.0168975	−	0.173722i
$96$		0			0
$97$	−4.78397	−	0.185640i	−0.485738	−	0.0188489i	−0.205257	−	0.978708i	$-0.565803\pi$
$97$	−4.78397	−	0.185640i	−0.485738	−	0.0188489i	−0.280482	+	0.959859i	$0.590494\pi$
$98$	0.490480	+	0.322594i	0.0495460	+	0.0325869i
$99$		0			0
$100$	5.38504	+	2.70447i	0.538504	+	0.270447i
$101$	−0.178798	−	9.21880i	−0.0177911	−	0.917305i	−0.897300	−	0.441422i	$-0.854474\pi$
$101$	−0.178798	−	9.21880i	−0.0177911	−	0.917305i	0.879509	−	0.475883i	$-0.157871\pi$
$102$		0			0
$103$	4.98182	+	3.86120i	0.490874	+	0.380456i	0.827754	−	0.561092i	$-0.189619\pi$
$103$	4.98182	+	3.86120i	0.490874	+	0.380456i	−0.336880	+	0.941548i	$0.609372\pi$
$104$	−2.27529	+	0.355849i	−0.223110	+	0.0348938i
$105$		0			0
$106$	−11.1278	+	23.2719i	−1.08083	+	2.26037i
$107$	8.46716	+	3.08179i	0.818551	+	0.297928i	0.717151	−	0.696918i	$-0.245446\pi$
$107$	8.46716	+	3.08179i	0.818551	+	0.297928i	0.101400	+	0.994846i	$0.467668\pi$
$108$		0			0
$109$	9.81756	−	3.57330i	0.940352	−	0.342260i	0.174047	−	0.984737i	$-0.444315\pi$
$109$	9.81756	−	3.57330i	0.940352	−	0.342260i	0.766305	+	0.642477i	$0.222093\pi$
$110$	−2.36761	+	24.3412i	−0.225743	+	2.32084i
$111$		0			0
$112$	4.02902	+	11.7753i	0.380706	+	1.11266i
$113$	6.12995	−	5.56264i	0.576658	−	0.523289i	−0.330652	−	0.943753i	$-0.607269\pi$
$113$	6.12995	−	5.56264i	0.576658	−	0.523289i	0.907309	+	0.420464i	$0.138133\pi$
$114$		0			0
$115$	7.53645	−	22.0261i	0.702778	−	2.05395i
$116$	0.392723	+	0.910434i	0.0364634	+	0.0845317i
$117$		0			0
$118$	−12.3020	+	1.43790i	−1.13249	+	0.132370i
$119$	13.5472	−	4.34374i	1.24187	−	0.398190i
$120$		0			0
$121$	−7.65436	+	2.13074i	−0.695851	+	0.193703i
$122$	10.5603	−	2.93965i	0.956080	−	0.266143i
$123$		0			0
$124$	11.8608	−	3.80303i	1.06514	−	0.341522i
$125$	3.81386	−	0.445777i	0.341122	−	0.0398715i
$126$		0			0
$127$	−3.31800	−	7.69199i	−0.294425	−	0.682553i	0.705226	−	0.708983i	$-0.250846\pi$
$127$	−3.31800	−	7.69199i	−0.294425	−	0.682553i	−0.999651	+	0.0264293i	$0.991586\pi$
$128$	−1.79660	+	5.25076i	−0.158799	+	0.464106i
$129$		0			0
$130$	−13.5763	+	12.3198i	−1.19072	+	1.08052i
$131$	−1.47113	−	4.29953i	−0.128533	−	0.375652i	0.863051	−	0.505117i	$-0.168551\pi$
$131$	−1.47113	−	4.29953i	−0.128533	−	0.375652i	−0.991584	+	0.129465i	$0.958674\pi$
$132$		0			0
$133$	0.150966	−	1.55206i	0.0130904	−	0.134581i
$134$	−17.3675	+	6.32127i	−1.50033	+	0.546075i
$135$		0			0
$136$	3.49037	+	1.27039i	0.299296	+	0.108935i
$137$	−2.02186	+	4.22836i	−0.172739	+	0.361253i	−0.970270	−	0.242025i	$-0.922188\pi$
$137$	−2.02186	+	4.22836i	−0.172739	+	0.361253i	0.797531	+	0.603278i	$0.206139\pi$
$138$		0			0
$139$	2.85495	−	0.446507i	0.242154	−	0.0378722i	−0.0322771	−	0.999479i	$-0.510276\pi$
$139$	2.85495	−	0.446507i	0.242154	−	0.0378722i	0.274431	+	0.961607i	$0.411510\pi$
$140$	10.2687	+	7.95887i	0.867866	+	0.672647i
$141$		0			0
$142$	−0.0818694	−	4.22116i	−0.00687033	−	0.354232i
$143$	−12.6913	−	6.37381i	−1.06130	−	0.533005i
$144$		0			0
$145$	−1.49932	−	0.986118i	−0.124512	−	0.0818927i
$146$	−9.93751	−	0.385621i	−0.822434	−	0.0319142i
$147$		0			0
$148$	0.493264	+	5.07120i	0.0405461	+	0.416850i
$149$	−7.64332	−	15.9846i	−0.626165	−	1.30951i	−0.933727	−	0.357985i	$-0.883464\pi$
$149$	−7.64332	−	15.9846i	−0.626165	−	1.30951i	0.307562	−	0.951528i	$-0.400487\pi$
$150$		0			0
$151$	−0.737056	+	0.571262i	−0.0599808	+	0.0464886i	−0.642150	−	0.766579i	$-0.721957\pi$
$151$	−0.737056	+	0.571262i	−0.0599808	+	0.0464886i	0.582169	+	0.813068i	$0.302204\pi$
$152$	0.279394	−	0.296140i	0.0226618	−	0.0240202i
$153$		0			0
$154$	−6.42931	+	21.4754i	−0.518088	+	1.73054i
$155$	−14.1529	+	17.5469i	−1.13679	+	1.40940i
$156$		0			0
$157$	−0.553431	−	0.878077i	−0.0441686	−	0.0700782i	0.823176	−	0.567786i	$-0.192200\pi$
$157$	−0.553431	−	0.878077i	−0.0441686	−	0.0700782i	−0.867345	+	0.497708i	$0.834175\pi$
$158$	19.1661	−	10.5754i	1.52477	−	0.841334i
$159$		0			0
$160$	5.41376	+	21.0175i	0.427995	+	1.66158i
$161$	10.6694	−	18.4800i	0.840870	−	1.45643i
$162$		0			0
$163$	−3.52004	−	6.09689i	−0.275711	−	0.477545i	0.694603	−	0.719393i	$-0.255580\pi$
$163$	−3.52004	−	6.09689i	−0.275711	−	0.477545i	−0.970314	+	0.241848i	$0.922247\pi$
$164$	10.1605	−	9.96538i	0.793404	−	0.778166i
$165$		0			0
$166$	0.478051	−	24.6482i	0.0371039	−	1.91307i
$167$	7.51784	−	14.2723i	0.581748	−	1.10442i	−0.400405	−	0.916338i	$-0.631131\pi$
$167$	7.51784	−	14.2723i	0.581748	−	1.10442i	0.982153	−	0.188083i	$-0.0602275\pi$
$168$		0			0
$169$	0.847826	+	2.19592i	0.0652174	+	0.168917i
$170$	28.7716	−	6.81899i	2.20668	−	0.522993i
$171$		0			0
$172$	0.393347	+	1.31387i	0.0299924	+	0.100182i
$173$	16.1339	+	6.59141i	1.22663	+	0.501135i	0.896603	−	0.442835i	$-0.146027\pi$
$173$	16.1339	+	6.59141i	1.22663	+	0.501135i	0.330031	+	0.943970i	$0.392941\pi$
$174$		0			0
$175$	−9.96703	−	0.774699i	−0.753437	−	0.0585618i
$176$	−16.3021	+	11.6521i	−1.22882	+	0.878308i
$177$		0			0
$178$	−4.18148	+	6.63437i	−0.313415	+	0.497267i
$179$	−1.21144	+	20.7996i	−0.0905472	+	1.55464i	0.581141	+	0.813803i	$0.302606\pi$
$179$	−1.21144	+	20.7996i	−0.0905472	+	1.55464i	−0.671689	+	0.740834i	$0.734431\pi$
$180$		0			0
$181$	−12.3454	+	8.11973i	−0.917630	+	0.603534i	−0.918050	−	0.396465i	$-0.870237\pi$
$181$	−12.3454	+	8.11973i	−0.917630	+	0.603534i	0.000420068		1.00000i	$0.499866\pi$
$182$	−14.3874	+	8.68283i	−1.06646	+	0.643614i
$183$		0			0
$184$	5.15750	−	2.10707i	0.380216	−	0.155335i
$185$	−5.78943	−	7.17777i	−0.425647	−	0.527720i
$186$		0			0
$187$	12.9558	+	18.8899i	0.947418	+	1.38137i
$188$	−2.51222	−	14.2475i	−0.183223	−	1.03911i
$189$		0			0
$190$	0.562803	−	3.19181i	0.0408300	−	0.231558i
$191$	19.2046	−	8.72954i	1.38959	−	0.631647i	0.427411	−	0.904057i	$-0.359426\pi$
$191$	19.2046	−	8.72954i	1.38959	−	0.631647i	0.962181	+	0.272410i	$0.0878207\pi$
$192$		0			0
$193$	−14.3546	−	2.81916i	−1.03327	−	0.202927i	−0.352796	−	0.935700i	$-0.614769\pi$
$193$	−14.3546	−	2.81916i	−1.03327	−	0.202927i	−0.680473	+	0.732773i	$0.738226\pi$
$194$	−8.68539	−	2.78486i	−0.623575	−	0.199941i
$195$		0			0
$196$	0.330161	+	0.378323i	0.0235830	+	0.0270231i
$197$	12.6636	−	17.0101i	0.902242	−	1.21192i	−0.0744395	−	0.997226i	$-0.523717\pi$
$197$	12.6636	−	17.0101i	0.902242	−	1.21192i	0.976681	−	0.214695i	$-0.0688758\pi$
$198$		0			0
$199$	3.50981	−	8.13666i	0.248804	−	0.576793i	−0.747348	−	0.664433i	$-0.768673\pi$
$199$	3.50981	−	8.13666i	0.248804	−	0.576793i	0.996152	+	0.0876400i	$0.0279325\pi$
$200$	−1.93290	−	1.75402i	−0.136677	−	0.124028i
$201$		0			0
$202$	4.38176	−	17.0110i	0.308300	−	1.19689i
$203$	−1.17436	−	1.15181i	−0.0824242	−	0.0808411i
$204$		0			0
$205$	−5.45306	+	25.1741i	−0.380858	+	1.75824i
$206$	7.17067	+	9.63188i	0.499604	+	0.671085i
$207$		0			0
$208$	−14.9196	−	1.74385i	−1.03449	−	0.120914i
$209$	2.46368	−	0.483852i	0.170417	−	0.0334687i
$210$		0			0
$211$	0.809358	+	3.73641i	0.0557185	+	0.257225i	0.996694	−	0.0812502i	$-0.0258913\pi$
$211$	0.809358	+	3.73641i	0.0557185	+	0.257225i	−0.940975	+	0.338475i	$0.890089\pi$
$212$	−14.5074	+	16.6236i	−0.996372	+	1.14172i
$213$		0			0
$214$	13.9657	+	9.98206i	0.954674	+	0.682360i
$215$	−1.90150	−	1.59555i	−0.129681	−	0.108815i
$216$		0			0
$217$	−15.8294	+	13.2824i	−1.07457	+	0.901669i
$218$	19.8442	−	1.54242i	1.34402	−	0.104466i
$219$		0			0
$220$	−7.53423	+	19.5141i	−0.507958	+	1.31564i
$221$	−2.32375	+	17.0129i	−0.156312	+	1.14441i
$222$		0			0
$223$	−21.8674	−	12.0659i	−1.46435	−	0.807992i	−0.467249	−	0.884126i	$-0.654755\pi$
$223$	−21.8674	−	12.0659i	−1.46435	−	0.807992i	−0.997098	+	0.0761338i	$0.975742\pi$
$224$	1.15674	+	19.8604i	0.0772879	+	1.32698i
$225$		0			0
$226$	14.0926	−	7.07755i	0.937423	−	0.470792i
$227$	−0.567868	−	1.07807i	−0.0376907	−	0.0715541i	0.865193	−	0.501439i	$-0.167196\pi$
$227$	−0.567868	−	1.07807i	−0.0376907	−	0.0715541i	−0.902884	+	0.429885i	$0.858554\pi$
$228$		0			0
$229$	−14.2095	−	6.45902i	−0.938991	−	0.426824i	−0.114961	−	0.993370i	$-0.536674\pi$
$229$	−14.2095	−	6.45902i	−0.938991	−	0.426824i	−0.824030	+	0.566546i	$0.808279\pi$
$230$	25.0852	−	36.5752i	1.65407	−	2.41169i
$231$		0			0
$232$	−0.0581207	−	0.425519i	−0.00381581	−	0.0279367i
$233$	−11.3621	−	2.69288i	−0.744359	−	0.176416i	−0.159099	−	0.987263i	$-0.550859\pi$
$233$	−11.3621	−	2.69288i	−0.744359	−	0.176416i	−0.585259	+	0.810846i	$0.699007\pi$
$234$		0			0
$235$	17.9686	+	19.0457i	1.17215	+	1.24240i
$236$	−10.4667	−	1.63697i	−0.681327	−	0.106558i
$237$		0			0
$238$	27.0831	−	1.05095i	1.75553	−	0.0681227i
$239$	0.622167	+	0.375480i	0.0402447	+	0.0242878i	0.536679	−	0.843787i	$-0.319679\pi$
$239$	0.622167	+	0.375480i	0.0402447	+	0.0242878i	−0.496434	+	0.868074i	$0.665358\pi$
$240$		0			0
$241$	−16.6418	−	4.63256i	−1.07199	−	0.298410i	−0.313164	−	0.949699i	$-0.601389\pi$
$241$	−16.6418	−	4.63256i	−1.07199	−	0.298410i	−0.758829	+	0.651289i	$0.774228\pi$
$242$	−15.1370			−0.973044
$243$		0			0
$244$	9.37596			0.600235
$245$	−0.875509	−	0.243715i	−0.0559342	−	0.0155704i
$246$		0			0
$247$	1.61140	+	0.972487i	0.102531	+	0.0618779i
$248$	−5.39098	+	0.209195i	−0.342328	+	0.0132839i
$249$		0			0
$250$	7.22751	+	1.13036i	0.457108	+	0.0714904i
$251$	−21.0933	−	22.3575i	−1.33139	−	1.41120i	−0.842344	−	0.538940i	$-0.818825\pi$
$251$	−21.0933	−	22.3575i	−1.33139	−	1.41120i	−0.489050	−	0.872256i	$-0.662657\pi$
$252$		0			0
$253$	33.4313	+	7.92336i	2.10181	+	0.498137i
$254$	−2.15981	−	15.8126i	−0.135519	−	0.992173i
$255$		0			0
$256$	−11.4240	+	16.6566i	−0.713999	+	1.04104i
$257$	8.91225	+	4.05111i	0.555931	+	0.252702i	0.672015	−	0.740538i	$-0.265429\pi$
$257$	8.91225	+	4.05111i	0.555931	+	0.252702i	−0.116084	+	0.993239i	$0.537034\pi$
$258$		0			0
$259$	−3.93936	−	7.47869i	−0.244780	−	0.464703i
$260$	−14.0128	+	7.03748i	−0.869036	+	0.436446i
$261$		0			0
$262$	−0.503382	−	8.64273i	−0.0310990	−	0.533950i
$263$	7.05204	+	3.89115i	0.434847	+	0.239939i	0.685403	−	0.728163i	$-0.259626\pi$
$263$	7.05204	+	3.89115i	0.434847	+	0.239939i	−0.250556	+	0.968102i	$0.580614\pi$
$264$		0			0
$265$	5.40416	−	39.5655i	0.331975	−	2.43049i
$266$	1.07003	−	2.77145i	0.0656078	−	0.169928i
$267$		0			0
$268$	−15.7609	+	1.22503i	−0.962748	+	0.0748307i
$269$	−21.6606	+	18.1754i	−1.32067	+	1.10818i	−0.334510	+	0.942392i	$0.608571\pi$
$269$	−21.6606	+	18.1754i	−1.32067	+	1.10818i	−0.986162	+	0.165784i	$0.946985\pi$
$270$		0			0
$271$	−20.5231	−	17.2209i	−1.24669	−	1.04610i	−0.996971	−	0.0777801i	$-0.975217\pi$
$271$	−20.5231	−	17.2209i	−1.24669	−	1.04610i	−0.249721	−	0.968318i	$-0.580339\pi$
$272$	19.7101	+	14.0879i	1.19510	+	0.854206i
$273$		0			0
$274$	−5.87109	+	6.72753i	−0.354686	+	0.406425i
$275$	−3.40762	−	15.7313i	−0.205487	−	0.948634i
$276$		0			0
$277$	2.98501	−	0.586237i	0.179352	−	0.0352236i	−0.102230	−	0.994761i	$-0.532598\pi$
$277$	2.98501	−	0.586237i	0.179352	−	0.0352236i	0.281582	+	0.959537i	$0.409141\pi$
$278$	5.46795	+	0.639112i	0.327946	+	0.0383314i
$279$		0			0
$280$	−3.36041	−	4.51382i	−0.200823	−	0.269752i
$281$	−0.347356	+	1.60358i	−0.0207215	+	0.0956613i	−0.986524	−	0.163620i	$-0.947683\pi$
$281$	−0.347356	+	1.60358i	−0.0207215	+	0.0956613i	0.965802	+	0.259281i	$0.0834855\pi$
$282$		0			0
$283$	16.1852	+	15.8743i	0.962108	+	0.943629i	0.998447	−	0.0557106i	$-0.0177424\pi$
$283$	16.1852	+	15.8743i	0.962108	+	0.943629i	−0.0363389	+	0.999340i	$0.511570\pi$
$284$	0.900777	−	3.49703i	0.0534513	−	0.207511i
$285$		0			0
$286$	−20.0365	−	18.1822i	−1.18478	−	1.07513i
$287$	−9.35164	+	21.6795i	−0.552010	+	1.27970i
$288$		0			0
$289$	6.38626	−	8.57824i	0.375663	−	0.504602i
$290$	−2.24796	−	2.57588i	−0.132005	−	0.151261i
$291$		0			0
$292$	−8.10008	−	2.59719i	−0.474021	−	0.151989i
$293$	−9.76298	−	1.91739i	−0.570359	−	0.112015i	−0.100785	−	0.994908i	$-0.532136\pi$
$293$	−9.76298	−	1.91739i	−0.570359	−	0.112015i	−0.469574	+	0.882893i	$0.655592\pi$
$294$		0			0
$295$	17.4552	−	7.93435i	1.01628	−	0.461956i
$296$	0.383226	−	2.17338i	0.0222746	−	0.126325i
$297$		0			0
$298$	−5.86153	−	33.2424i	−0.339549	−	1.92568i
$299$	14.5673	+	21.2396i	0.842447	+	1.22832i
$300$		0			0
$301$	−1.42845	−	1.77100i	−0.0823345	−	0.102079i
$302$	−1.64461	+	0.671899i	−0.0946369	+	0.0386634i
$303$		0			0
$304$	2.27361	−	1.37213i	0.130401	−	0.0786972i
$305$	−14.1777	+	9.32484i	−0.811814	+	0.533939i
$306$		0			0
$307$	0.854376	−	14.6691i	0.0487618	−	0.837208i	−0.881925	−	0.471390i	$-0.843752\pi$
$307$	0.854376	−	14.6691i	0.0487618	−	0.837208i	0.930686	−	0.365818i	$-0.119211\pi$
$308$	−10.2237	+	16.2210i	−0.582551	+	0.924279i
$309$		0			0
$310$	−34.9403	+	24.9738i	−1.98447	+	1.41842i
$311$	6.07999	+	0.472574i	0.344764	+	0.0267972i	0.248708	−	0.968579i	$-0.419994\pi$
$311$	6.07999	+	0.472574i	0.344764	+	0.0267972i	0.0960569	+	0.995376i	$0.469377\pi$
$312$		0			0
$313$	−12.2888	−	5.02051i	−0.694602	−	0.283776i	0.00327429	−	0.999995i	$-0.498958\pi$
$313$	−12.2888	−	5.02051i	−0.694602	−	0.283776i	−0.697876	+	0.716219i	$0.745871\pi$
$314$	−0.567124	−	1.89433i	−0.0320047	−	0.106903i
$315$		0			0
$316$	18.2187	−	4.31791i	1.02488	−	0.242901i
$317$	−6.55288	−	16.9724i	−0.368046	−	0.953264i	−0.985955	−	0.167014i	$-0.946588\pi$
$317$	−6.55288	−	16.9724i	−0.368046	−	0.953264i	0.617908	−	0.786250i	$-0.287980\pi$
$318$		0			0
$319$	1.23430	−	2.34327i	0.0691077	−	0.131198i
$320$	−0.275226	+	14.1906i	−0.0153856	+	0.793277i
$321$		0			0
$322$	29.0237	−	28.4662i	1.61742	−	1.58636i
$323$	−1.51781	−	2.62892i	−0.0844531	−	0.146277i
$324$		0			0
$325$	6.03303	−	10.4495i	0.334652	−	0.579635i
$326$	−3.34557	−	12.9883i	−0.185294	−	0.719355i
$327$		0			0
$328$	−5.39729	+	2.97810i	−0.298015	+	0.164438i
$329$	12.7975	+	20.3046i	0.705549	+	1.11943i
$330$		0			0
$331$	−2.43120	+	3.01422i	−0.133631	+	0.165676i	−0.840760	−	0.541408i	$-0.817891\pi$
$331$	−2.43120	+	3.01422i	−0.133631	+	0.165676i	0.707129	+	0.707085i	$0.249990\pi$
$332$	6.04764	−	20.2005i	0.331907	−	1.10865i
$333$		0			0
$334$	21.0896	−	22.3537i	1.15397	−	1.22314i
$335$	22.6142	−	17.5273i	1.23555	−	0.957620i
$336$		0			0
$337$	11.7344	+	24.5405i	0.639215	+	1.33680i	0.925532	+	0.378669i	$0.123618\pi$
$337$	11.7344	+	24.5405i	0.639215	+	1.33680i	−0.286318	+	0.958135i	$0.592431\pi$
$338$	0.434149	+	4.46344i	0.0236146	+	0.242779i
$339$		0			0
$340$	25.2720	+	0.980669i	1.37057	+	0.0531842i
$341$	−27.7970	−	18.2824i	−1.50529	−	0.990046i
$342$		0			0
$343$	16.1662	+	8.11899i	0.872895	+	0.438384i
$344$	−0.0115194	−	0.593936i	−0.000621083	−	0.0320229i
$345$		0			0
$346$	26.2436	+	20.3404i	1.41087	+	1.09350i
$347$	16.8812	−	2.64017i	0.906231	−	0.141732i	0.315806	−	0.948824i	$-0.397725\pi$
$347$	16.8812	−	2.64017i	0.906231	−	0.141732i	0.590426	+	0.807092i	$0.298960\pi$
$348$		0			0
$349$	−14.5995	+	30.5323i	−0.781493	+	1.63435i	−0.00848026	+	0.999964i	$0.502699\pi$
$349$	−14.5995	+	30.5323i	−0.781493	+	1.63435i	−0.773013	+	0.634390i	$0.781251\pi$
$350$	−17.8972	−	6.51404i	−0.956644	−	0.348190i
$351$		0			0
$352$	−30.0994	+	10.9553i	−1.60431	+	0.583919i
$353$	−1.57672	+	16.2101i	−0.0839205	+	0.862779i	0.854996	+	0.518634i	$0.173559\pi$
$353$	−1.57672	+	16.2101i	−0.0839205	+	0.862779i	−0.938917	+	0.344144i	$0.888169\pi$
$354$		0			0
$355$	2.11586	+	6.18385i	0.112298	+	0.328205i
$356$	−4.96732	+	4.50760i	−0.263268	+	0.238903i
$357$		0			0
$358$	−12.8500	+	37.5556i	−0.679144	+	1.98487i
$359$	2.97661	+	6.90056i	0.157099	+	0.364198i	0.978528	−	0.206114i	$-0.0660818\pi$
$359$	2.97661	+	6.90056i	0.157099	+	0.364198i	−0.821429	+	0.570311i	$0.806823\pi$
$360$		0			0
$361$	18.5410	−	2.16714i	0.975844	−	0.114060i
$362$	−26.8066	+	8.59518i	−1.40892	+	0.451753i
$363$		0			0
$364$	−13.8469	+	3.85454i	−0.725774	+	0.202033i
$365$	14.8314	−	4.12862i	0.776313	−	0.216102i
$366$		0			0
$367$	4.11329	−	1.31887i	0.214712	−	0.0688446i	−0.196023	−	0.980599i	$-0.562803\pi$
$367$	4.11329	−	1.31887i	0.214712	−	0.0688446i	0.410735	+	0.911755i	$0.365272\pi$
$368$	36.0935	−	4.21873i	1.88150	−	0.219916i
$369$		0			0
$370$	−6.95846	−	16.1315i	−0.361753	−	0.838638i
$371$	11.8498	−	34.6324i	0.615212	−	1.79802i
$372$		0			0
$373$	−8.37068	+	7.59598i	−0.433417	+	0.393305i	−0.859299	−	0.511474i	$-0.829100\pi$
$373$	−8.37068	+	7.59598i	−0.433417	+	0.393305i	0.425882	+	0.904779i	$0.359964\pi$
$374$	14.1274	+	41.2887i	0.730508	+	2.13499i
$375$		0			0
$376$	−0.606654	+	6.23695i	−0.0312858	+	0.321646i
$377$	1.86563	−	0.679032i	0.0960846	−	0.0349719i
$378$		0			0
$379$	−4.04003	−	1.47045i	−0.207522	−	0.0755319i	0.236168	−	0.971712i	$-0.424109\pi$
$379$	−4.04003	−	1.47045i	−0.207522	−	0.0755319i	−0.443690	+	0.896180i	$0.646331\pi$
$380$	1.19588	−	2.50097i	0.0613473	−	0.128297i
$381$		0			0
$382$	39.7070	−	6.21006i	2.03158	−	0.317734i
$383$	12.1682	+	9.43104i	0.621765	+	0.481904i	0.874107	−	0.485734i	$-0.161448\pi$
$383$	12.1682	+	9.43104i	0.621765	+	0.481904i	−0.252342	+	0.967638i	$0.581201\pi$
$384$		0			0
$385$	−0.672936	−	34.6964i	−0.0342960	−	1.76829i
$386$	−24.9054	−	12.5080i	−1.26765	−	0.636639i
$387$		0			0
$388$	−6.51801	−	4.28696i	−0.330902	−	0.217637i
$389$	−18.5472	−	0.719717i	−0.940381	−	0.0364911i	−0.435976	−	0.899958i	$-0.643597\pi$
$389$	−18.5472	−	0.719717i	−0.940381	−	0.0364911i	−0.504405	+	0.863467i	$0.668288\pi$
$390$		0			0
$391$	−4.02151	−	41.3447i	−0.203376	−	2.09089i
$392$	−0.0938236	−	0.196215i	−0.00473881	−	0.00991037i
$393$		0			0
$394$	31.9326	−	24.7496i	1.60874	−	1.24687i
$395$	−23.2547	+	24.6486i	−1.17007	+	1.24021i
$396$		0			0
$397$	−0.00656058	+	0.0219139i	−0.000329266	+	0.00109983i	−0.958154	−	0.286253i	$-0.907590\pi$
$397$	−0.00656058	+	0.0219139i	−0.000329266	+	0.00109983i	0.957825	+	0.287353i	$0.0927753\pi$
$398$	10.5988	−	13.1404i	0.531269	−	0.658670i
$399$		0			0
$400$	−9.07761	−	14.4026i	−0.453880	−	0.720130i
$401$	−1.61439	+	0.890782i	−0.0806187	+	0.0444835i	−0.522910	−	0.852388i	$-0.675154\pi$
$401$	−1.61439	+	0.890782i	−0.0806187	+	0.0444835i	0.442291	+	0.896872i	$0.354166\pi$
$402$		0			0
$403$	−6.22112	−	24.1519i	−0.309896	−	1.20309i
$404$	7.51252	−	13.0121i	0.373762	−	0.647375i
$405$		0			0
$406$	−1.56690	−	2.71395i	−0.0777641	−	0.134691i
$407$	9.71634	−	9.52972i	0.481621	−	0.472371i
$408$		0			0
$409$	−0.235192	+	12.1265i	−0.0116295	+	0.599615i	0.947988	+	0.318306i	$0.103114\pi$
$409$	−0.235192	+	12.1265i	−0.0116295	+	0.599615i	−0.959617	+	0.281308i	$0.909232\pi$
$410$	−22.8698	+	43.4173i	−1.12946	+	2.14423i
$411$		0			0
$412$	3.69932	+	9.58148i	0.182252	+	0.472046i
$413$	17.1016	−	4.05314i	0.841513	−	0.199442i
$414$		0			0
$415$	10.9455	+	36.5606i	0.537294	+	1.79469i
$416$	−22.2278	−	9.08107i	−1.08981	−	0.445236i
$417$		0			0
$418$	4.76891	+	0.370669i	0.233255	+	0.0181300i
$419$	−19.7120	+	14.0893i	−0.962996	+	0.688308i	−0.950210	−	0.311610i	$-0.899132\pi$
$419$	−19.7120	+	14.0893i	−0.962996	+	0.688308i	−0.0127860	+	0.999918i	$0.504070\pi$
$420$		0			0
$421$	−3.18020	+	5.04574i	−0.154994	+	0.245914i	−0.914500	−	0.404586i	$-0.867416\pi$
$421$	−3.18020	+	5.04574i	−0.154994	+	0.245914i	0.759506	+	0.650500i	$0.225440\pi$
$422$	−0.423494	+	7.27111i	−0.0206154	+	0.353952i
$423$		0			0
$424$	7.98452	−	5.25150i	0.387763	−	0.255036i
$425$	−16.6619	+	10.0555i	−0.808221	+	0.487764i
$426$		0			0
$427$	−14.3993	+	5.88276i	−0.696831	+	0.284687i
$428$	9.21810	+	11.4286i	0.445574	+	0.552424i
$429$		0			0
$430$	−2.67474	−	3.89987i	−0.128987	−	0.188068i
$431$	−5.12465	−	29.0633i	−0.246846	−	1.39993i	−0.816167	−	0.577817i	$-0.803905\pi$
$431$	−5.12465	−	29.0633i	−0.246846	−	1.39993i	0.569321	−	0.822116i	$-0.307206\pi$
$432$		0			0
$433$	−1.65067	+	9.36143i	−0.0793262	+	0.449881i	0.919111	+	0.393999i	$0.128908\pi$
$433$	−1.65067	+	9.36143i	−0.0793262	+	0.449881i	−0.998437	+	0.0558830i	$0.982203\pi$
$434$	−35.8384	+	16.2905i	−1.72030	+	0.781971i
$435$		0			0
$436$	16.7055	+	3.28085i	0.800049	+	0.157124i
$437$	−4.33580	−	1.39022i	−0.207410	−	0.0665032i
$438$		0			0
$439$	−0.0529657	−	0.0606920i	−0.00252791	−	0.00289667i	0.752171	−	0.658968i	$-0.229007\pi$
$439$	−0.0529657	−	0.0606920i	−0.00252791	−	0.00289667i	−0.754698	+	0.656072i	$0.772217\pi$
$440$	5.41054	−	7.26762i	0.257938	−	0.346470i
$441$		0			0
$442$	−12.9568	+	30.0373i	−0.616293	+	1.42873i
$443$	−25.2756	−	22.9364i	−1.20088	−	1.08974i	−0.993773	−	0.111422i	$-0.964459\pi$
$443$	−25.2756	−	22.9364i	−1.20088	−	1.08974i	−0.207107	−	0.978318i	$-0.566405\pi$
$444$		0			0
$445$	3.02824	−	11.7563i	0.143552	−	0.557304i
$446$	−33.9697	−	33.3172i	−1.60851	−	1.57762i
$447$		0			0
$448$	−2.75425	+	12.7150i	−0.130126	+	0.600729i
$449$	20.9958	+	28.2023i	0.990854	+	1.33095i	0.943251	+	0.332081i	$0.107751\pi$
$449$	20.9958	+	28.2023i	0.990854	+	1.33095i	0.0476032	+	0.998866i	$0.484842\pi$
$450$		0			0
$451$	−37.7578	−	4.41325i	−1.77795	−	0.207812i
$452$	13.2357	−	2.59941i	0.622557	−	0.122266i
$453$		0			0
$454$	−0.491445	−	2.26876i	−0.0230646	−	0.106478i
$455$	17.1048	−	19.6000i	0.801887	−	0.918861i
$456$		0			0
$457$	−8.24919	−	5.89617i	−0.385881	−	0.275811i	0.371962	−	0.928248i	$-0.378685\pi$
$457$	−8.24919	−	5.89617i	−0.385881	−	0.275811i	−0.757843	+	0.652437i	$0.773747\pi$
$458$	−22.7795	−	19.1142i	−1.06441	−	0.893149i
$459$		0			0
$460$	29.0598	−	24.3841i	1.35492	−	1.13691i
$461$	17.2190	−	1.33836i	0.801968	−	0.0623339i	0.330035	−	0.943969i	$-0.392939\pi$
$461$	17.2190	−	1.33836i	0.801968	−	0.0623339i	0.471932	+	0.881635i	$0.343557\pi$
$462$		0			0
$463$	8.94970	−	23.1803i	0.415928	−	1.07728i	−0.553705	−	0.832713i	$-0.686786\pi$
$463$	8.94970	−	23.1803i	0.415928	−	1.07728i	0.969632	−	0.244567i	$-0.0786457\pi$
$464$	0.379096	−	2.77547i	0.0175991	−	0.128848i
$465$		0			0
$466$	−19.4777	−	10.7473i	−0.902286	−	0.497860i
$467$	0.391271	+	6.71786i	0.0181059	+	0.310866i	0.995187	+	0.0979970i	$0.0312436\pi$
$467$	0.391271	+	6.71786i	0.0181059	+	0.310866i	−0.977081	+	0.212869i	$0.931719\pi$
$468$		0			0
$469$	23.4364	−	11.7702i	1.08219	−	0.543497i
$470$	23.2482	+	44.1356i	1.07236	+	2.03582i
$471$		0			0
$472$	4.17737	+	1.89885i	0.192279	+	0.0874015i
$473$	2.07204	−	3.02111i	0.0952726	−	0.138911i
$474$		0			0
$475$	0.288682	+	2.11353i	0.0132456	+	0.0969752i
$476$	22.5576	+	5.34624i	1.03392	+	0.245045i
$477$		0			0
$478$	0.950059	+	1.00700i	0.0434547	+	0.0460593i
$479$	11.5631	+	1.80843i	0.528330	+	0.0826293i	0.413058	−	0.910705i	$-0.364461\pi$
$479$	11.5631	+	1.80843i	0.528330	+	0.0826293i	0.115272	+	0.993334i	$0.463226\pi$
$480$		0			0
$481$	10.1945	−	0.395591i	0.464827	−	0.0180374i
$482$	−28.1767	−	17.0047i	−1.28341	−	0.774544i
$483$		0			0
$484$	−12.4729	−	3.47208i	−0.566952	−	0.157822i
$485$	14.1197			0.641142
$486$		0			0
$487$	12.2482			0.555018			0.277509	−	0.960723i	$-0.410491\pi$
$487$	12.2482			0.555018			0.277509	+	0.960723i	$0.410491\pi$
$488$	−3.91236	−	1.08908i	−0.177104	−	0.0493003i
$489$		0			0
$490$	−1.48235	−	0.894602i	−0.0669657	−	0.0404140i
$491$	−10.6518	+	0.413338i	−0.480709	+	0.0186537i	−0.277991	−	0.960584i	$-0.589669\pi$
$491$	−10.6518	+	0.413338i	−0.480709	+	0.0186537i	−0.202717	+	0.979237i	$0.564977\pi$
$492$		0			0
$493$	−3.16368	−	0.494790i	−0.142485	−	0.0222842i
$494$	2.46064	+	2.60812i	0.110709	+	0.117345i
$495$		0			0
$496$	−34.2410	−	8.11526i	−1.53746	−	0.364386i
$497$	0.810758	+	5.93580i	0.0363675	+	0.266257i
$498$		0			0
$499$	−1.94472	+	2.83548i	−0.0870578	+	0.126933i	−0.865758	−	0.500463i	$-0.833163\pi$
$499$	−1.94472	+	2.83548i	−0.0870578	+	0.126933i	0.778700	+	0.627396i	$0.215879\pi$
$500$	5.69621	+	2.58925i	0.254742	+	0.115795i
$501$		0			0
$502$	−27.2909	−	51.8105i	−1.21805	−	2.31241i
$503$	12.8559	−	6.45647i	0.573216	−	0.287880i	−0.138483	−	0.990365i	$-0.544223\pi$
$503$	12.8559	−	6.45647i	0.573216	−	0.287880i	0.711698	+	0.702485i	$0.247926\pi$
$504$		0			0
$505$	1.58117	+	27.1476i	0.0703610	+	1.20805i
$506$	57.3099	+	31.6223i	2.54774	+	1.40578i
$507$		0			0
$508$	1.84736	−	13.5251i	0.0819634	−	0.600078i
$509$	4.00720	−	10.3789i	0.177616	−	0.460037i	−0.815274	−	0.579076i	$-0.803413\pi$
$509$	4.00720	−	10.3789i	0.177616	−	0.460037i	0.992890	+	0.119039i	$0.0379814\pi$
$510$		0			0
$511$	14.0694	−	1.09356i	0.622393	−	0.0483762i
$512$	−20.9744	+	17.5996i	−0.926945	+	0.777799i
$513$		0			0
$514$	14.2873	+	11.9885i	0.630187	+	0.528790i
$515$	−15.1231	−	10.8094i	−0.666404	−	0.476317i
$516$		0			0
$517$	−25.4091	+	29.1156i	−1.11749	+	1.28050i
$518$	−3.40920	−	15.7386i	−0.149792	−	0.691515i
$519$		0			0
$520$	6.66464	−	1.30889i	0.292264	−	0.0573987i
$521$	17.5572	+	2.05214i	0.769193	+	0.0899058i	0.491633	−	0.870802i	$-0.336400\pi$
$521$	17.5572	+	2.05214i	0.769193	+	0.0899058i	0.277560	+	0.960708i	$0.410474\pi$
$522$		0			0
$523$	5.66315	+	7.60693i	0.247632	+	0.332628i	0.908508	−	0.417867i	$-0.137222\pi$
$523$	5.66315	+	7.60693i	0.247632	+	0.332628i	−0.660876	+	0.750495i	$0.729815\pi$
$524$	1.56765	−	7.23710i	0.0684833	−	0.316154i
$525$		0			0
$526$	10.9549	+	10.7445i	0.477658	+	0.468483i
$527$	−10.0339	+	38.9540i	−0.437084	+	1.69686i
$528$		0			0
$529$	−29.1086	−	26.4146i	−1.26559	−	1.14846i
$530$	30.1327	−	69.8554i	1.30888	−	3.03432i
$531$		0			0
$532$	1.51741	−	2.03824i	0.0657882	−	0.0883689i
$533$	−18.7373	−	21.4705i	−0.811601	−	0.929992i
$534$		0			0
$535$	−25.3053	−	8.11383i	−1.09405	−	0.350792i
$536$	6.71891	+	1.31955i	0.290213	+	0.0569959i
$537$		0			0
$538$	−49.0407	+	22.2917i	−2.11429	+	0.961065i
$539$	0.232905	−	1.32087i	0.0100319	−	0.0568939i
$540$		0			0
$541$	2.32999	+	13.2140i	0.100174	+	0.568114i	0.993039	+	0.117789i	$0.0375808\pi$
$541$	2.32999	+	13.2140i	0.100174	+	0.568114i	−0.892865	+	0.450325i	$0.851308\pi$
$542$	−28.8688	−	42.0918i	−1.24002	−	1.80800i
$543$		0			0
$544$	24.3134	+	30.1439i	1.04243	+	1.29241i
$545$	−28.5240	+	11.6533i	−1.22183	+	0.499173i
$546$		0			0
$547$	3.42671	−	2.06803i	0.146515	−	0.0884225i	−0.441547	−	0.897238i	$-0.645570\pi$
$547$	3.42671	−	2.06803i	0.146515	−	0.0884225i	0.588062	+	0.808816i	$0.299891\pi$
$548$	−6.38093	+	4.19681i	−0.272580	+	0.179279i
$549$		0			0
$550$	1.78303	−	30.6134i	0.0760285	−	1.30536i
$551$	−0.187149	+	0.296933i	−0.00797283	+	0.0126498i
$552$		0			0
$553$	−25.2705	+	18.0622i	−1.07461	+	0.768085i
$554$	5.77804	+	0.449105i	0.245485	+	0.0190806i
$555$		0			0
$556$	4.35901	+	1.78085i	0.184863	+	0.0755250i
$557$	−0.834823	−	2.78850i	−0.0353726	−	0.118153i	0.938480	−	0.345334i	$-0.112234\pi$
$557$	−0.834823	−	2.78850i	−0.0353726	−	0.118153i	−0.973853	+	0.227181i	$0.927049\pi$
$558$		0			0
$559$	2.67214	−	0.633310i	0.113020	−	0.0267862i
$560$	−13.2202	−	34.2412i	−0.558656	−	1.44695i
$561$		0			0
$562$	−1.45679	+	2.76565i	−0.0614511	+	0.116662i
$563$	0.609188	−	31.4096i	0.0256742	−	1.32375i	−0.736524	−	0.676411i	$-0.763534\pi$
$563$	0.609188	−	31.4096i	0.0256742	−	1.32375i	0.762198	−	0.647344i	$-0.224120\pi$
$564$		0			0
$565$	−17.4290	+	17.0942i	−0.733243	+	0.719160i
$566$	21.5951	+	37.4039i	0.907712	+	1.57220i
$567$		0			0
$568$	−0.782075	+	1.35459i	−0.0328151	+	0.0568375i
$569$	0.922457	+	3.58120i	0.0386714	+	0.150132i	0.984812	−	0.173625i	$-0.0555480\pi$
$569$	0.922457	+	3.58120i	0.0386714	+	0.150132i	−0.946140	+	0.323756i	$0.895054\pi$
$570$		0			0
$571$	−28.9327	+	15.9644i	−1.21080	+	0.668089i	−0.954414	−	0.298487i	$-0.903518\pi$
$571$	−28.9327	+	15.9644i	−1.21080	+	0.668089i	−0.256382	+	0.966576i	$0.582531\pi$
$572$	−12.3396	−	19.5781i	−0.515944	−	0.818601i
$573$		0			0
$574$	−28.2396	+	35.0117i	−1.17870	+	1.46136i
$575$	−8.37187	+	27.9640i	−0.349131	+	1.16618i
$576$		0			0
$577$	−24.2426	+	25.6956i	−1.00923	+	1.06972i	−0.0116702	+	0.999932i	$0.503715\pi$
$577$	−24.2426	+	25.6956i	−1.00923	+	1.06972i	−0.997562	+	0.0697914i	$0.977767\pi$
$578$	16.1037	−	12.4813i	0.669824	−	0.519153i
$579$		0			0
$580$	−1.26148	−	2.63816i	−0.0523801	−	0.109544i
$581$	3.38664	+	34.8178i	0.140502	+	1.44448i
$582$		0			0
$583$	58.8905	+	2.28522i	2.43899	+	0.0946441i
$584$	3.07828	+	2.02462i	0.127380	+	0.0837794i
$585$		0			0
$586$	−16.9388	−	8.50701i	−0.699737	−	0.351421i
$587$	−0.719307	−	37.0873i	−0.0296890	−	1.53076i	−0.658134	−	0.752901i	$-0.728654\pi$
$587$	−0.719307	−	37.0873i	−0.0296890	−	1.53076i	0.628445	−	0.777854i	$-0.283692\pi$
$588$		0			0
$589$	3.48497	+	2.70106i	0.143596	+	0.111295i
$590$	36.0900	−	5.64437i	1.48580	−	0.232375i
$591$		0			0
$592$	6.20968	−	12.9864i	0.255216	−	0.533739i
$593$	−14.2684	−	5.19326i	−0.585932	−	0.213262i	0.0320074	−	0.999488i	$-0.489810\pi$
$593$	−14.2684	−	5.19326i	−0.585932	−	0.213262i	−0.617939	+	0.786226i	$0.712032\pi$
$594$		0			0
$595$	−39.4272	+	14.3503i	−1.61636	+	0.588306i
$596$	2.79512	−	28.7363i	0.114492	−	1.17708i
$597$		0			0
$598$	15.8846	+	46.4245i	0.649570	+	1.89844i
$599$	28.9497	−	26.2705i	1.18285	−	1.07338i	0.187005	−	0.982359i	$-0.440122\pi$
$599$	28.9497	−	26.2705i	1.18285	−	1.07338i	0.995849	−	0.0910237i	$-0.0290139\pi$
$600$		0			0
$601$	6.72378	−	19.6510i	0.274269	−	0.801581i	−0.719932	−	0.694044i	$-0.755827\pi$
$601$	6.72378	−	19.6510i	0.274269	−	0.801581i	0.994201	−	0.107537i	$-0.0342963\pi$
$602$	−1.71689	−	3.98020i	−0.0699753	−	0.162221i
$603$		0			0
$604$	−1.50928	+	0.176410i	−0.0614119	+	0.00717802i
$605$	22.3139	−	7.15467i	0.907190	−	0.290879i
$606$		0			0
$607$	13.9219	−	3.87544i	0.565074	−	0.157299i	0.0261568	−	0.999658i	$-0.491673\pi$
$607$	13.9219	−	3.87544i	0.565074	−	0.157299i	0.538917	+	0.842359i	$0.318834\pi$
$608$	4.08945	−	1.13838i	0.165849	−	0.0461673i
$609$		0			0
$610$	−30.7851	+	9.87086i	−1.24645	+	0.399659i
$611$	−28.7724	+	3.36301i	−1.16401	+	0.136053i
$612$		0			0
$613$	−2.13026	−	4.93849i	−0.0860403	−	0.199464i	0.869764	−	0.493468i	$-0.164271\pi$
$613$	−2.13026	−	4.93849i	−0.0860403	−	0.199464i	−0.955804	+	0.294005i	$0.905012\pi$
$614$	9.06256	−	26.4863i	0.365735	−	1.06890i
$615$		0			0
$616$	6.15029	−	5.58109i	0.247802	−	0.224868i
$617$	7.87738	+	23.0225i	0.317131	+	0.926851i	0.983449	+	0.181183i	$0.0579928\pi$
$617$	7.87738	+	23.0225i	0.317131	+	0.926851i	−0.666318	+	0.745668i	$0.732131\pi$
$618$		0			0
$619$	3.30867	−	34.0161i	0.132987	−	1.36722i	−0.656903	−	0.753975i	$-0.728134\pi$
$619$	3.30867	−	34.0161i	0.132987	−	1.36722i	0.789890	−	0.613249i	$-0.210138\pi$
$620$	−34.5193	+	12.5640i	−1.38633	+	0.504582i
$621$		0			0
$622$	10.9174	+	3.97362i	0.437750	+	0.159328i
$623$	4.80044	−	10.0393i	0.192326	−	0.402215i
$624$		0			0
$625$	−29.4566	+	4.60694i	−1.17827	+	0.184277i
$626$	−19.9891	−	15.4927i	−0.798927	−	0.619215i
$627$		0			0
$628$	−0.0327972	−	1.69102i	−0.00130875	−	0.0674788i
$629$	−14.7045	−	7.38489i	−0.586307	−	0.294455i
$630$		0			0
$631$	5.94167	+	3.90790i	0.236534	+	0.155571i	0.662243	−	0.749289i	$-0.269605\pi$
$631$	5.94167	+	3.90790i	0.236534	+	0.155571i	−0.425709	+	0.904860i	$0.639975\pi$
$632$	−8.10376	−	0.314463i	−0.322350	−	0.0125087i
$633$		0			0
$634$	−3.35555	−	34.4981i	−0.133266	−	1.37009i
$635$	10.6579	+	22.2890i	0.422944	+	0.884513i
$636$		0			0
$637$	0.794684	−	0.615927i	0.0314865	−	0.0244039i
$638$	3.46256	−	3.67010i	0.137084	−	0.145301i
$639$		0			0
$640$	4.69416	−	15.6796i	0.185553	−	0.619790i
$641$	−18.5297	+	22.9732i	−0.731878	+	0.907386i	−0.998406	−	0.0564412i	$-0.982025\pi$
$641$	−18.5297	+	22.9732i	−0.731878	+	0.907386i	0.266528	+	0.963827i	$0.414123\pi$
$642$		0			0
$643$	−4.62450	−	7.33727i	−0.182373	−	0.289354i	0.742337	−	0.670026i	$-0.233717\pi$
$643$	−4.62450	−	7.33727i	−0.182373	−	0.289354i	−0.924710	+	0.380673i	$0.875693\pi$
$644$	30.4451	−	16.7989i	1.19970	−	0.661968i
$645$		0			0
$646$	−1.44258	−	5.60044i	−0.0567575	−	0.220346i
$647$	22.2567	−	38.5498i	0.875002	−	1.51555i	0.0182408	−	0.999834i	$-0.494193\pi$
$647$	22.2567	−	38.5498i	0.875002	−	1.51555i	0.856761	−	0.515714i	$-0.172473\pi$
$648$		0			0
$649$	14.1488	+	24.5065i	0.555391	+	0.961965i
$650$	16.4114	−	16.0962i	0.643708	−	0.631344i
$651$		0			0
$652$	0.222456	−	11.4698i	0.00871206	−	0.449192i
$653$	−16.6696	+	31.6464i	−0.652330	+	1.23842i	0.305803	+	0.952095i	$0.401075\pi$
$653$	−16.6696	+	31.6464i	−0.652330	+	1.23842i	−0.958133	+	0.286323i	$0.907567\pi$
$654$		0			0
$655$	4.82713	+	12.5026i	0.188612	+	0.488516i
$656$	−39.1239	+	9.27252i	−1.52753	+	0.362031i
$657$		0			0
$658$	13.1141	+	43.8043i	0.511243	+	1.70767i
$659$	26.7663	+	10.9352i	1.04267	+	0.425977i	0.833858	−	0.551979i	$-0.186127\pi$
$659$	26.7663	+	10.9352i	1.04267	+	0.425977i	0.208810	+	0.977956i	$0.433041\pi$
$660$		0			0
$661$	37.7591	+	2.93487i	1.46866	+	0.114153i	0.786744	−	0.617279i	$-0.211765\pi$
$661$	37.7591	+	2.93487i	1.46866	+	0.114153i	0.681914	+	0.731432i	$0.261148\pi$
$662$	−6.00208	+	4.29003i	−0.233277	+	0.166737i
$663$		0			0
$664$	−4.86995	+	7.72670i	−0.188991	+	0.299854i
$665$	−0.267409	+	4.59124i	−0.0103697	+	0.178041i
$666$		0			0
$667$	−4.01284	+	2.63929i	−0.155378	+	0.102194i
$668$	22.5053	−	13.5820i	0.870757	−	0.525504i
$669$		0			0
$670$	50.4597	−	20.6151i	1.94943	−	0.796429i
$671$	−15.7231	−	19.4936i	−0.606983	−	0.752541i
$672$		0			0
$673$	−17.8691	−	26.0538i	−0.688803	−	1.00430i	−0.998569	−	0.0534860i	$-0.982967\pi$
$673$	−17.8691	−	26.0538i	−0.688803	−	1.00430i	0.309766	−	0.950813i	$-0.399749\pi$
$674$	8.99892	+	51.0354i	0.346625	+	1.96581i
$675$		0			0
$676$	−0.666070	+	3.77747i	−0.0256181	+	0.145287i
$677$	−13.4713	+	6.12347i	−0.517745	+	0.235344i	−0.655600	−	0.755108i	$-0.727584\pi$
$677$	−13.4713	+	6.12347i	−0.517745	+	0.235344i	0.137855	+	0.990452i	$0.455979\pi$
$678$		0			0
$679$	12.6999	+	2.49418i	0.487378	+	0.0957179i
$680$	−10.4315	−	3.34472i	−0.400029	−	0.128264i
$681$		0			0
$682$	−41.6766	−	47.7561i	−1.59588	−	1.82867i
$683$	−6.33715	+	8.51226i	−0.242484	+	0.325713i	−0.906659	−	0.421865i	$-0.861376\pi$
$683$	−6.33715	+	8.51226i	−0.242484	+	0.325713i	0.664175	+	0.747577i	$0.268783\pi$
$684$		0			0
$685$	5.47492	−	12.6923i	0.209186	−	0.484947i
$686$	25.5226	+	23.1606i	0.974459	+	0.884274i
$687$		0			0
$688$	0.966513	−	3.75223i	0.0368479	−	0.143053i
$689$	31.5406	+	30.9348i	1.20160	+	1.17852i
$690$		0			0
$691$	−0.0718770	+	0.331821i	−0.00273433	+	0.0126231i	−0.978681	−	0.205388i	$-0.934154\pi$
$691$	−0.0718770	+	0.331821i	−0.00273433	+	0.0126231i	0.975946	+	0.218011i	$0.0699569\pi$
$692$	16.9592	+	22.7802i	0.644693	+	0.865973i
$693$		0			0
$694$	32.3318	+	3.77904i	1.22730	+	0.143450i
$695$	−8.36256	+	1.64235i	−0.317210	+	0.0622980i
$696$		0			0
$697$	9.73030	+	44.9201i	0.368561	+	1.70147i
$698$	−42.3942	+	48.5783i	−1.60464	+	1.83872i
$699$		0			0
$700$	−13.2531	−	9.47278i	−0.500922	−	0.358037i
$701$	28.5457	+	23.9527i	1.07816	+	0.904681i	0.995767	−	0.0919188i	$-0.0293000\pi$
$701$	28.5457	+	23.9527i	1.07816	+	0.904681i	0.0823907	+	0.996600i	$0.473744\pi$
$702$		0			0
$703$	−1.38166	+	1.15935i	−0.0521102	+	0.0437257i
$704$	−20.8841	+	1.62324i	−0.787098	+	0.0611781i
$705$		0			0
$706$	−11.1757	+	28.9457i	−0.420601	+	1.08938i
$707$	−3.37332	+	24.6971i	−0.126867	+	0.928830i
$708$		0			0
$709$	23.5431	+	12.9905i	0.884181	+	0.487870i	0.859096	−	0.511815i	$-0.171027\pi$
$709$	23.5431	+	12.9905i	0.884181	+	0.487870i	0.0250850	+	0.999685i	$0.492014\pi$
$710$	0.723995	+	12.4305i	0.0271710	+	0.466509i
$711$		0			0
$712$	2.59633	−	1.30393i	0.0973015	−	0.0488667i
$713$	28.1190	+	53.3827i	1.05307	+	1.99920i
$714$		0			0
$715$	38.1304	+	17.3324i	1.42600	+	0.648196i
$716$	−19.2028	+	27.9984i	−0.717643	+	1.04635i
$717$		0			0
$718$	1.93759	+	14.1857i	0.0723103	+	0.529405i
$719$	37.6978	+	8.93455i	1.40589	+	0.333203i	0.862407	−	0.506216i	$-0.168956\pi$
$719$	37.6978	+	8.93455i	1.40589	+	0.333203i	0.543486	+	0.839418i	$0.317104\pi$
$720$		0			0
$721$	−11.6930	−	12.3939i	−0.435470	−	0.461572i
$722$	35.1364	+	5.49524i	1.30764	+	0.204512i
$723$		0			0
$724$	−24.0602	+	0.933646i	−0.894191	+	0.0346987i
$725$	1.92652	+	1.16266i	0.0715490	+	0.0431800i
$726$		0			0
$727$	14.1793	+	3.94709i	0.525883	+	0.146390i	0.520932	−	0.853598i	$-0.325585\pi$
$727$	14.1793	+	3.94709i	0.525883	+	0.146390i	0.00495097	+	0.999988i	$0.498424\pi$
$728$	6.22569			0.230740
$729$		0			0
$730$	29.3302			1.08556
$731$	−4.26699	−	1.18780i	−0.157820	−	0.0439323i
$732$		0			0
$733$	−7.82473	−	4.72225i	−0.289013	−	0.174420i	0.364780	−	0.931094i	$-0.381144\pi$
$733$	−7.82473	−	4.72225i	−0.289013	−	0.174420i	−0.653793	+	0.756674i	$0.726823\pi$
$734$	8.22313	−	0.319095i	0.303521	−	0.0117780i
$735$		0			0
$736$	57.3907	+	8.97574i	2.11545	+	0.330850i
$737$	28.9772	+	30.7141i	1.06739	+	1.13137i
$738$		0			0
$739$	27.9445	+	6.62296i	1.02795	+	0.243630i	0.709795	−	0.704408i	$-0.248787\pi$
$739$	27.9445	+	6.62296i	1.02795	+	0.243630i	0.318159	+	0.948037i	$0.396936\pi$
$740$	−2.03359	−	14.8885i	−0.0747564	−	0.547313i
$741$		0			0
$742$	39.4423	−	57.5083i	1.44797	−	2.11120i
$743$	28.0396	+	12.7456i	1.02867	+	0.467590i	0.855774	−	0.517349i	$-0.173081\pi$
$743$	28.0396	+	12.7456i	1.02867	+	0.467590i	0.172900	+	0.984939i	$0.444686\pi$
$744$		0			0
$745$	24.3530	+	46.2331i	0.892226	+	1.69385i
$746$	−19.2439	+	9.66466i	−0.704570	+	0.353848i
$747$		0			0
$748$	2.17030	+	37.2625i	0.0793539	+	1.36245i
$749$	−21.3275	−	11.7680i	−0.779291	−	0.429994i
$750$		0			0
$751$	5.24462	−	38.3974i	0.191379	−	1.40114i	−0.604943	−	0.796269i	$-0.706804\pi$
$751$	5.24462	−	38.3974i	0.191379	−	1.40114i	0.796322	−	0.604873i	$-0.206776\pi$
$752$	−14.7215	+	38.1296i	−0.536838	+	1.39045i
$753$		0			0
$754$	3.77099	−	0.293105i	0.137331	−	0.0106742i
$755$	2.10679	−	1.76781i	0.0766741	−	0.0643372i
$756$		0			0
$757$	6.10708	+	5.12445i	0.221966	+	0.186251i	0.746989	−	0.664837i	$-0.231499\pi$
$757$	6.10708	+	5.12445i	0.221966	+	0.186251i	−0.525023	+	0.851088i	$0.675943\pi$
$758$	−6.66359	−	4.76285i	−0.242033	−	0.172995i
$759$		0			0
$760$	−0.789515	+	0.904684i	−0.0286387	+	0.0328163i
$761$	3.81026	+	17.5901i	0.138122	+	0.637641i	0.992930	+	0.118698i	$0.0378720\pi$
$761$	3.81026	+	17.5901i	0.138122	+	0.637641i	−0.854809	+	0.518943i	$0.826326\pi$
$762$		0			0
$763$	−27.7143	+	5.44291i	−1.00332	+	0.197046i
$764$	34.1431	+	3.99075i	1.23525	+	0.144380i
$765$		0			0
$766$	17.5145	+	23.5260i	0.632823	+	0.850029i
$767$	−4.49079	+	20.7318i	−0.162153	+	0.748582i
$768$		0			0
$769$	34.9971	+	34.3249i	1.26203	+	1.23779i	0.958541	+	0.284953i	$0.0919781\pi$
$769$	34.9971	+	34.3249i	1.26203	+	1.23779i	0.303487	+	0.952836i	$0.401849\pi$
$770$	16.4914	−	64.0237i	0.594310	−	2.30725i
$771$		0			0
$772$	−17.6531	−	16.0193i	−0.635349	−	0.576548i
$773$	−4.60233	+	10.6694i	−0.165534	+	0.383752i	−0.980712	−	0.195460i	$-0.937380\pi$
$773$	−4.60233	+	10.6694i	−0.165534	+	0.383752i	0.815177	+	0.579211i	$0.196639\pi$
$774$		0			0
$775$	16.8797	−	22.6734i	0.606338	−	0.814453i
$776$	2.22185	+	2.54595i	0.0797596	+	0.0913944i
$777$		0			0
$778$	−33.6729	−	10.7968i	−1.20723	−	0.387083i
$779$	4.94350	+	0.970871i	0.177119	+	0.0347851i
$780$		0			0
$781$	−8.78124	+	3.99156i	−0.314217	+	0.142829i
$782$	13.7423	−	77.9364i	0.491424	−	2.78700i
$783$		0			0
$784$	−0.246340	−	1.39706i	−0.00879785	−	0.0498951i
$785$	1.73139	+	2.52443i	0.0617959	+	0.0901006i
$786$		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)

\(f(q)\)	\(=\)	\(q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +O(q^{10})\)	\(q+(1.83535 + 0.510904i) q^{2} +(1.39514 + 0.841972i) q^{4} +(-2.94702 + 0.114358i) q^{5} +(-2.67089 - 0.417720i) q^{7} +(-0.484358 - 0.513389i) q^{8} +(-5.46724 - 1.29576i) q^{10} +(-0.589047 - 4.31259i) q^{11} +(1.84548 - 2.69078i) q^{13} +(-4.68860 - 2.13123i) q^{14} +(-2.14553 - 4.07318i) q^{16} +(-4.70279 + 2.36183i) q^{17} +(0.0335399 + 0.575858i) q^{19} +(-4.20780 - 2.32177i) q^{20} +(1.12221 - 8.21604i) q^{22} +(-2.84305 + 7.36370i) q^{23} +(3.68691 - 0.286569i) q^{25} +(4.76183 - 3.99565i) q^{26} +(-3.37456 - 2.83159i) q^{28} +(0.495027 + 0.353824i) q^{29} +(5.02592 - 5.75907i) q^{31} +(-1.55794 - 7.19223i) q^{32} +(-9.83791 + 1.93210i) q^{34} +(7.91895 + 0.925592i) q^{35} +(1.86718 + 2.50805i) q^{37} +(-0.232651 + 1.07404i) q^{38} +(1.48612 + 1.45758i) q^{40} +(2.17856 - 8.45769i) q^{41} +(0.623280 + 0.565596i) q^{43} +(2.80928 - 6.51263i) q^{44} +(-8.98013 + 12.0624i) q^{46} +(-5.83765 - 6.68920i) q^{47} +(0.293432 + 0.0940850i) q^{49} +(6.91316 + 1.35770i) q^{50} +(4.84027 - 2.20017i) q^{52} +(-2.35120 + 13.3343i) q^{53} +(2.22912 + 12.6419i) q^{55} +(1.07921 + 1.57353i) q^{56} +(0.727777 + 0.902301i) q^{58} +(-6.01839 + 2.45878i) q^{59} +(4.92623 - 2.97299i) q^{61} +(12.1666 - 8.00212i) q^{62} +(0.279822 - 4.80436i) q^{64} +(-5.13097 + 8.14083i) q^{65} +(-7.89248 + 5.64120i) q^{67} +(-8.54964 - 0.664531i) q^{68} +(14.0611 + 5.74460i) q^{70} +(-0.635585 - 2.12300i) q^{71} +(-5.07940 + 1.20384i) q^{73} +(2.14554 + 5.55709i) q^{74} +(-0.438064 + 0.831643i) q^{76} +(-0.228172 + 11.7645i) q^{77} +(8.20313 - 8.04557i) q^{79} +(6.78872 + 11.7584i) q^{80} +(8.31948 - 14.4098i) q^{82} +(-3.22782 - 12.5312i) q^{83} +(13.5891 - 7.49816i) q^{85} +(0.854969 + 1.35650i) q^{86} +(-1.92873 + 2.39125i) q^{88} +(-1.18058 + 3.94341i) q^{89} +(-6.05307 + 6.41588i) q^{91} +(-10.1665 + 7.87962i) q^{92} +(-7.29657 - 15.2595i) q^{94} +(-0.164697 - 1.69323i) q^{95} +(-4.78397 - 0.185640i) q^{97} +(0.490480 + 0.322594i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more