LMFDB - Embedded newform 819.2.fy.a.50.15

Newspace parameters

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.fy (of order $12$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$84$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.15
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.15

$q$-expansion

$f(q)$	$=$	$q+(-0.548397 - 2.04664i) q^{2} +(-1.71570 + 0.237418i) q^{3} +(-2.15597 + 1.24475i) q^{4} +(0.530257 + 1.97895i) q^{5} +(1.42680 + 3.38123i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.733384 + 0.733384i) q^{8} +(2.88726 - 0.814679i) q^{9} +O(q^{10})$	\(q+(-0.548397 - 2.04664i) q^{2} +(-1.71570 + 0.237418i) q^{3} +(-2.15597 + 1.24475i) q^{4} +(0.530257 + 1.97895i) q^{5} +(1.42680 + 3.38123i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.733384 + 0.733384i) q^{8} +(2.88726 - 0.814679i) q^{9} +(3.75941 - 2.17049i) q^{10} +(0.0834806 - 0.0223685i) q^{11} +(3.40347 - 2.64748i) q^{12} +(-0.572885 - 3.55975i) q^{13} +(-1.83497 - 1.05942i) q^{14} +(-1.37960 - 3.26939i) q^{15} +(-1.39070 + 2.40877i) q^{16} +(-1.73263 + 3.00100i) q^{17} +(-3.25072 - 5.46244i) q^{18} +(-7.99159 + 2.14134i) q^{19} +(-3.60650 - 3.60650i) q^{20} +(-1.04530 + 1.38106i) q^{21} +(-0.0915609 - 0.158588i) q^{22} -2.60559 q^{23} +(-1.43239 - 1.08415i) q^{24} +(0.695075 - 0.401302i) q^{25} +(-6.97137 + 3.12465i) q^{26} +(-4.76027 + 2.08324i) q^{27} +(-0.644328 + 2.40467i) q^{28} +(7.84036 + 4.52663i) q^{29} +(-5.93471 + 4.61647i) q^{30} +(-0.614844 + 0.164747i) q^{31} +(7.69619 + 2.06219i) q^{32} +(-0.137917 + 0.0581976i) q^{33} +(7.09215 + 1.90033i) q^{34} +(1.77427 + 1.02438i) q^{35} +(-5.21077 + 5.35033i) q^{36} +(-6.94250 - 1.86024i) q^{37} +(8.76512 + 15.1816i) q^{38} +(1.82805 + 5.97145i) q^{39} +(-1.06244 + 1.84021i) q^{40} +(0.725760 - 0.725760i) q^{41} +(3.39979 + 1.38199i) q^{42} +7.34418i q^{43} +(-0.152138 + 0.152138i) q^{44} +(3.14320 + 5.28175i) q^{45} +(1.42890 + 5.33272i) q^{46} +(-2.14484 + 8.00464i) q^{47} +(1.81415 - 4.46291i) q^{48} -1.00000i q^{49} +(-1.20250 - 1.20250i) q^{50} +(2.26018 - 5.56018i) q^{51} +(5.66611 + 6.96159i) q^{52} -6.66554i q^{53} +(6.87416 + 8.60013i) q^{54} +(0.0885323 + 0.153342i) q^{55} +1.03716 q^{56} +(13.2028 - 5.57125i) q^{57} +(4.96478 - 18.5288i) q^{58} +(-2.80217 + 10.4579i) q^{59} +(7.04393 + 5.33143i) q^{60} -13.5427 q^{61} +(0.674357 + 1.16802i) q^{62} +(1.46554 - 2.61767i) q^{63} -11.3195i q^{64} +(6.74077 - 3.02129i) q^{65} +(0.194743 + 0.250352i) q^{66} +(-4.35616 - 4.35616i) q^{67} -8.62673i q^{68} +(4.47042 - 0.618616i) q^{69} +(1.12353 - 4.19307i) q^{70} +(4.03420 + 15.0559i) q^{71} +(2.71494 + 1.52000i) q^{72} +(-0.701151 + 0.701151i) q^{73} +15.2290i q^{74} +(-1.09727 + 0.853538i) q^{75} +(14.5642 - 14.5642i) q^{76} +(0.0432127 - 0.0748466i) q^{77} +(11.2189 - 7.01609i) q^{78} +(-1.21564 - 2.10555i) q^{79} +(-5.50425 - 1.47486i) q^{80} +(7.67260 - 4.70439i) q^{81} +(-1.88338 - 1.08737i) q^{82} +(0.700439 + 0.187682i) q^{83} +(0.534563 - 4.27867i) q^{84} +(-6.85755 - 1.83748i) q^{85} +(15.0309 - 4.02752i) q^{86} +(-14.5264 - 5.90491i) q^{87} +(0.0776280 + 0.0448185i) q^{88} +(-2.28784 + 8.53834i) q^{89} +(9.08615 - 9.32950i) q^{90} +(-2.92221 - 2.11203i) q^{91} +(5.61757 - 3.24330i) q^{92} +(1.01577 - 0.428632i) q^{93} +17.5589 q^{94} +(-8.47519 - 14.6795i) q^{95} +(-13.6940 - 1.71088i) q^{96} +(1.72304 + 1.72304i) q^{97} +(-2.04664 + 0.548397i) q^{98} +(0.222807 - 0.132594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) $ 336 * q - 12 * q^6 + 36 * q^8	$ 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) $ 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.548397	−	2.04664i	−0.387775	−	1.44720i	−0.833746	−	0.552149i	$-0.813808\pi$
$2$	−0.548397	−	2.04664i	−0.387775	−	1.44720i	0.445970	−	0.895048i	$-0.352859\pi$
$3$	−1.71570	+	0.237418i	−0.990561	+	0.137074i
$3$	−1.71570	+	0.237418i	−0.990561	+	0.137074i
$4$	−2.15597	+	1.24475i	−1.07798	+	0.622374i
$5$	0.530257	+	1.97895i	0.237138	+	0.885011i	0.977173	+	0.212443i	$0.0681421\pi$
$5$	0.530257	+	1.97895i	0.237138	+	0.885011i	−0.740035	+	0.672568i	$0.765191\pi$
$6$	1.42680	+	3.38123i	0.582487	+	1.38038i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.733384	+	0.733384i	0.259290	+	0.259290i
$9$	2.88726	−	0.814679i	0.962422	−	0.271560i
$10$	3.75941	−	2.17049i	1.18883	−	0.686371i
$11$	0.0834806	−	0.0223685i	0.0251703	−	0.00674437i	−0.246212	−	0.969216i	$-0.579186\pi$
$11$	0.0834806	−	0.0223685i	0.0251703	−	0.00674437i	0.271382	+	0.962472i	$0.412519\pi$
$12$	3.40347	−	2.64748i	0.982496	−	0.764262i
$13$	−0.572885	−	3.55975i	−0.158890	−	0.987296i
$13$	−0.572885	−	3.55975i	−0.158890	−	0.987296i
$14$	−1.83497	−	1.05942i	−0.490417	−	0.283142i
$15$	−1.37960	−	3.26939i	−0.356211	−	0.844152i
$16$	−1.39070	+	2.40877i	−0.347676	+	0.602192i
$17$	−1.73263	+	3.00100i	−0.420224	+	0.727849i	−0.995961	−	0.0897856i	$-0.971382\pi$
$17$	−1.73263	+	3.00100i	−0.420224	+	0.727849i	0.575737	+	0.817635i	$0.304715\pi$
$18$	−3.25072	−	5.46244i	−0.766203	−	1.28751i
$19$	−7.99159	+	2.14134i	−1.83340	+	0.491257i	−0.998270	−	0.0588015i	$-0.981272\pi$
$19$	−7.99159	+	2.14134i	−1.83340	+	0.491257i	−0.835126	+	0.550058i	$0.814605\pi$
$20$	−3.60650	−	3.60650i	−0.806438	−	0.806438i
$21$	−1.04530	+	1.38106i	−0.228104	+	0.301373i
$22$	−0.0915609	−	0.158588i	−0.0195209	−	0.0338111i
$23$	−2.60559			−0.543304			−0.271652	−	0.962396i	$-0.587570\pi$
$23$	−2.60559			−0.543304			−0.271652	+	0.962396i	$0.587570\pi$
$24$	−1.43239	−	1.08415i	−0.292385	−	0.221301i
$25$	0.695075	−	0.401302i	0.139015	−	0.0802604i
$26$	−6.97137	+	3.12465i	−1.36720	+	0.612794i
$27$	−4.76027	+	2.08324i	−0.916114	+	0.400919i
$28$	−0.644328	+	2.40467i	−0.121767	+	0.454439i
$29$	7.84036	+	4.52663i	1.45592	+	0.840575i	0.998807	−	0.0488344i	$-0.0155507\pi$
$29$	7.84036	+	4.52663i	1.45592	+	0.840575i	0.457112	+	0.889409i	$0.348884\pi$
$30$	−5.93471	+	4.61647i	−1.08352	+	0.842849i
$31$	−0.614844	+	0.164747i	−0.110429	+	0.0295894i	−0.313610	−	0.949552i	$-0.601539\pi$
$31$	−0.614844	+	0.164747i	−0.110429	+	0.0295894i	0.203181	+	0.979141i	$0.434872\pi$
$32$	7.69619	+	2.06219i	1.36051	+	0.364547i
$33$	−0.137917	+	0.0581976i	−0.0240083	+	0.0101309i
$34$	7.09215	+	1.90033i	1.21629	+	0.325905i
$35$	1.77427	+	1.02438i	0.299907	+	0.173151i
$36$	−5.21077	+	5.35033i	−0.868462	+	0.891722i
$37$	−6.94250	−	1.86024i	−1.14134	−	0.305821i	−0.361850	−	0.932236i	$-0.617855\pi$
$37$	−6.94250	−	1.86024i	−1.14134	−	0.305821i	−0.779490	+	0.626415i	$0.784521\pi$
$38$	8.76512	+	15.1816i	1.42189	+	2.46279i
$39$	1.82805	+	5.97145i	0.292722	+	0.956197i
$40$	−1.06244	+	1.84021i	−0.167987	+	0.290962i
$41$	0.725760	−	0.725760i	0.113345	−	0.113345i	−0.648160	−	0.761504i	$-0.724461\pi$
$41$	0.725760	−	0.725760i	0.113345	−	0.113345i	0.761504	+	0.648160i	$0.224461\pi$
$42$	3.39979	+	1.38199i	0.524599	+	0.213246i
$43$			7.34418i			1.11998i	0.828501	+	0.559988i	$0.189194\pi$
$43$			7.34418i			1.11998i	−0.828501	+	0.559988i	$0.810806\pi$
$44$	−0.152138	+	0.152138i	−0.0229357	+	0.0229357i
$45$	3.14320	+	5.28175i	0.468560	+	0.787357i
$46$	1.42890	+	5.33272i	0.210680	+	0.786267i
$47$	−2.14484	+	8.00464i	−0.312856	+	1.16760i	0.613112	+	0.789996i	$0.289917\pi$
$47$	−2.14484	+	8.00464i	−0.312856	+	1.16760i	−0.925969	+	0.377600i	$0.876749\pi$
$48$	1.81415	−	4.46291i	0.261849	−	0.644165i
$49$		−	1.00000i		−	0.142857i
$50$	−1.20250	−	1.20250i	−0.170059	−	0.170059i
$51$	2.26018	−	5.56018i	0.316488	−	0.778581i
$52$	5.66611	+	6.96159i	0.785748	+	0.965399i
$53$		−	6.66554i		−	0.915582i	−0.889060	−	0.457791i	$-0.848641\pi$
$53$		−	6.66554i		−	0.915582i	0.889060	−	0.457791i	$-0.151359\pi$
$54$	6.87416	+	8.60013i	0.935454	+	1.17033i
$55$	0.0885323	+	0.153342i	0.0119377	+	0.0206767i
$56$	1.03716			0.138596
$57$	13.2028	−	5.57125i	1.74875	−	0.737930i
$58$	4.96478	−	18.5288i	0.651908	−	2.43295i
$59$	−2.80217	+	10.4579i	−0.364812	+	1.36150i	0.502863	+	0.864366i	$0.332280\pi$
$59$	−2.80217	+	10.4579i	−0.364812	+	1.36150i	−0.867675	+	0.497131i	$0.834387\pi$
$60$	7.04393	+	5.33143i	0.909368	+	0.688285i
$61$	−13.5427			−1.73397			−0.866984	−	0.498337i	$-0.833944\pi$
$61$	−13.5427			−1.73397			−0.866984	+	0.498337i	$0.833944\pi$
$62$	0.674357	+	1.16802i	0.0856434	+	0.148339i
$63$	1.46554	−	2.61767i	0.184641	−	0.329795i
$64$		−	11.3195i		−	1.41493i
$65$	6.74077	−	3.02129i	0.836089	−	0.374745i
$66$	0.194743	+	0.250352i	0.0239712	+	0.0308162i
$67$	−4.35616	−	4.35616i	−0.532190	−	0.532190i	0.389033	−	0.921224i	$-0.372809\pi$
$67$	−4.35616	−	4.35616i	−0.532190	−	0.532190i	−0.921224	+	0.389033i	$0.872809\pi$
$68$		−	8.62673i		−	1.04614i
$69$	4.47042	−	0.618616i	0.538175	−	0.0744726i
$70$	1.12353	−	4.19307i	0.134288	−	0.501168i
$71$	4.03420	+	15.0559i	0.478772	+	1.78680i	0.606603	+	0.795005i	$0.292532\pi$
$71$	4.03420	+	15.0559i	0.478772	+	1.78680i	−0.127831	+	0.991796i	$0.540802\pi$
$72$	2.71494	+	1.52000i	0.319959	+	0.179134i
$73$	−0.701151	+	0.701151i	−0.0820635	+	0.0820635i	−0.746947	−	0.664884i	$-0.768481\pi$
$73$	−0.701151	+	0.701151i	−0.0820635	+	0.0820635i	0.664884	+	0.746947i	$0.268481\pi$
$74$			15.2290i			1.77033i
$75$	−1.09727	+	0.853538i	−0.126701	+	0.0985581i
$76$	14.5642	−	14.5642i	1.67062	−	1.67062i
$77$	0.0432127	−	0.0748466i	0.00492455	−	0.00852956i
$78$	11.2189	−	7.01609i	1.27030	−	0.794416i
$79$	−1.21564	−	2.10555i	−0.136770	−	0.236892i	0.789502	−	0.613748i	$-0.210339\pi$
$79$	−1.21564	−	2.10555i	−0.136770	−	0.236892i	−0.926272	+	0.376855i	$0.877005\pi$
$80$	−5.50425	−	1.47486i	−0.615394	−	0.164894i
$81$	7.67260	−	4.70439i	0.852511	−	0.522710i
$82$	−1.88338	−	1.08737i	−0.207984	−	0.120080i
$83$	0.700439	+	0.187682i	0.0768831	+	0.0206008i	0.297056	−	0.954860i	$-0.403995\pi$
$83$	0.700439	+	0.187682i	0.0768831	+	0.0206008i	−0.220172	+	0.975461i	$0.570662\pi$
$84$	0.534563	−	4.27867i	0.0583256	−	0.466841i
$85$	−6.85755	−	1.83748i	−0.743806	−	0.199302i
$86$	15.0309	−	4.02752i	1.62083	−	0.434299i
$87$	−14.5264	−	5.90491i	−1.55740	−	0.633073i
$88$	0.0776280	+	0.0448185i	0.00827517	+	0.00477767i
$89$	−2.28784	+	8.53834i	−0.242511	+	0.905062i	0.732108	+	0.681189i	$0.238537\pi$
$89$	−2.28784	+	8.53834i	−0.242511	+	0.905062i	−0.974618	+	0.223873i	$0.928130\pi$
$90$	9.08615	−	9.32950i	0.957764	−	0.983416i
$91$	−2.92221	−	2.11203i	−0.306331	−	0.221401i
$92$	5.61757	−	3.24330i	0.585672	−	0.338138i
$93$	1.01577	−	0.428632i	0.105331	−	0.0444471i
$94$	17.5589			1.81106
$95$	−8.47519	−	14.6795i	−0.869536	−	1.50608i
$96$	−13.6940	−	1.71088i	−1.39764	−	0.174616i
$97$	1.72304	+	1.72304i	0.174948	+	0.174948i	0.789149	−	0.614201i	$-0.210522\pi$
$97$	1.72304	+	1.72304i	0.174948	+	0.174948i	−0.614201	+	0.789149i	$0.710522\pi$
$98$	−2.04664	+	0.548397i	−0.206742	+	0.0553964i
$99$	0.222807	−	0.132594i	0.0223930	−	0.0133262i
$100$	−0.999038	+	1.73039i	−0.0999038	+	0.173039i
$101$	−2.93154	+	5.07757i	−0.291699	+	0.505237i	−0.974212	−	0.225637i	$-0.927554\pi$
$101$	−2.93154	+	5.07757i	−0.291699	+	0.505237i	0.682513	+	0.730874i	$0.260887\pi$
$102$	−12.6192	−	1.57660i	−1.24949	−	0.156107i
$103$	16.1099	+	9.30104i	1.58735	+	0.916458i	0.993741	+	0.111707i	$0.0356317\pi$
$103$	16.1099	+	9.30104i	1.58735	+	0.916458i	0.593611	+	0.804752i	$0.297702\pi$
$104$	2.19052	−	3.03080i	0.214798	−	0.297195i
$105$	−3.28733	−	1.33628i	−0.320811	−	0.130408i
$106$	−13.6420	+	3.65536i	−1.32503	+	0.355040i
$107$	−9.04871	+	5.22427i	−0.874772	+	0.505050i	−0.868931	−	0.494933i	$-0.835192\pi$
$107$	−9.04871	+	5.22427i	−0.874772	+	0.505050i	−0.00584063	+	0.999983i	$0.501859\pi$
$108$	7.66987	−	10.4167i	0.738033	−	1.00235i
$109$	11.3609	+	11.3609i	1.08818	+	1.08818i	0.995716	+	0.0924621i	$0.0294737\pi$
$109$	11.3609	+	11.3609i	1.08818	+	1.08818i	0.0924621	+	0.995716i	$0.470526\pi$
$110$	0.265287	−	0.265287i	0.0252941	−	0.0252941i
$111$	12.3529	+	1.54333i	1.17249	+	0.146487i
$112$	0.719881	+	2.68663i	0.0680224	+	0.253863i
$113$	4.51163	−	2.60479i	0.424419	−	0.245038i	−0.272547	−	0.962142i	$-0.587866\pi$
$113$	4.51163	−	2.60479i	0.424419	−	0.245038i	0.696966	+	0.717104i	$0.254533\pi$
$114$	−18.6427	−	23.9662i	−1.74605	−	2.24464i
$115$	−1.38163	−	5.15633i	−0.128838	−	0.480830i
$116$	−22.5381			−2.09261
$117$	−4.55412	−	9.81122i	−0.421029	−	0.907047i
$118$	22.9402			2.11182
$119$	0.896874	+	3.34718i	0.0822163	+	0.306835i
$120$	1.38594	−	3.40949i	0.126518	−	0.311243i
$121$	−9.51981	+	5.49627i	−0.865437	+	0.499660i
$122$	7.42678	+	27.7171i	0.672389	+	2.50939i
$123$	−1.07288	+	1.41750i	−0.0967382	+	0.127811i
$124$	1.12051	−	1.12051i	0.100625	−	0.100625i
$125$	8.40616	+	8.40616i	0.751870	+	0.751870i
$126$	−6.16114	−	1.56392i	−0.548878	−	0.139325i
$127$	2.16887	−	1.25220i	0.192456	−	0.111115i	−0.400676	−	0.916220i	$-0.631225\pi$
$127$	2.16887	−	1.25220i	0.192456	−	0.111115i	0.593132	+	0.805105i	$0.297891\pi$
$128$	−7.77452	+	2.08318i	−0.687177	+	0.184129i
$129$	−1.74364	−	12.6004i	−0.153519	−	1.10940i
$130$	−9.88012	−	12.1391i	−0.866544	−	1.06467i
$131$	−9.19939	−	5.31127i	−0.803754	−	0.464048i	0.0410279	−	0.999158i	$-0.486937\pi$
$131$	−9.19939	−	5.31127i	−0.803754	−	0.464048i	−0.844782	+	0.535110i	$0.820270\pi$
$132$	0.224903	−	0.297144i	0.0195753	−	0.0258630i
$133$	−4.13675	+	7.16506i	−0.358702	+	0.621290i
$134$	−6.52662	+	11.3044i	−0.563814	+	0.976554i
$135$	−6.64677	−	8.31566i	−0.572063	−	0.715698i
$136$	−3.47156	+	0.930203i	−0.297684	+	0.0797642i
$137$	−11.0691	−	11.0691i	−0.945700	−	0.945700i	0.0528998	−	0.998600i	$-0.483154\pi$
$137$	−11.0691	−	11.0691i	−0.945700	−	0.945700i	−0.998600	+	0.0528998i	$0.983154\pi$
$138$	−3.71765	−	8.81012i	−0.316468	−	0.749967i
$139$	−7.48794	−	12.9695i	−0.635119	−	1.10006i	−0.986490	−	0.163822i	$-0.947618\pi$
$139$	−7.48794	−	12.9695i	−0.635119	−	1.10006i	0.351371	−	0.936236i	$-0.385715\pi$
$140$	−5.10036			−0.431059
$141$	1.77945	−	14.2428i	0.149857	−	1.19946i
$142$	28.6016	−	16.5132i	2.40020	−	1.38575i
$143$	−0.127451	−	0.284355i	−0.0106580	−	0.0237790i
$144$	−2.05296	+	8.08773i	−0.171080	+	0.673978i
$145$	−4.80056	+	17.9159i	−0.398665	+	1.48784i
$146$	1.81952	+	1.05050i	0.150584	+	0.0869398i
$147$	0.237418	+	1.71570i	0.0195819	+	0.141509i
$148$	17.2833	−	4.63105i	1.42068	−	0.380670i
$149$	1.57199	+	0.421215i	0.128783	+	0.0345073i	0.322635	−	0.946524i	$-0.395431\pi$
$149$	1.57199	+	0.421215i	0.128783	+	0.0345073i	−0.193852	+	0.981031i	$0.562098\pi$
$150$	2.34863	+	1.77763i	0.191764	+	0.145143i
$151$	−2.84530	−	0.762397i	−0.231548	−	0.0620430i	0.141179	−	0.989984i	$-0.454911\pi$
$151$	−2.84530	−	0.762397i	−0.231548	−	0.0620430i	−0.372727	+	0.927941i	$0.621577\pi$
$152$	−7.43132	−	4.29048i	−0.602760	−	0.348004i
$153$	−2.55771	+	10.0762i	−0.206778	+	0.814614i
$154$	−0.176882	−	0.0473954i	−0.0142536	−	0.00381923i
$155$	−0.652050	−	1.12938i	−0.0523739	−	0.0907143i
$156$	−11.3742	−	10.5988i	−0.910662	−	0.848582i
$157$	11.0887	−	19.2061i	0.884972	−	1.53282i	0.0392267	−	0.999230i	$-0.487511\pi$
$157$	11.0887	−	19.2061i	0.884972	−	1.53282i	0.845746	−	0.533586i	$-0.179156\pi$
$158$	−3.64265	+	3.64265i	−0.289794	+	0.289794i
$159$	1.58252	+	11.4361i	0.125502	+	0.906940i
$160$			16.3238i			1.29051i
$161$	−1.84243	+	1.84243i	−0.145204	+	0.145204i
$162$	−13.8358	−	13.1232i	−1.08705	−	1.03106i
$163$	−4.38406	−	16.3615i	−0.343386	−	1.28153i	−0.894487	−	0.447095i	$-0.852459\pi$
$163$	−4.38406	−	16.3615i	−0.343386	−	1.28153i	0.551101	−	0.834439i	$-0.314208\pi$
$164$	−0.661325	+	2.46810i	−0.0516408	+	0.192726i
$165$	−0.188301	−	0.242071i	−0.0146592	−	0.0188452i
$166$		−	1.53647i		−	0.119253i
$167$	−13.5522	−	13.5522i	−1.04870	−	1.04870i	−0.998752	−	0.0499467i	$-0.984095\pi$
$167$	−13.5522	−	13.5522i	−1.04870	−	1.04870i	−0.0499467	−	0.998752i	$-0.515905\pi$
$168$	−1.77946	+	0.246241i	−0.137288	+	0.0189979i
$169$	−12.3436	+	4.07865i	−0.949508	+	0.313743i
$170$			15.0426i			1.15372i
$171$	−21.3293	+	12.6932i	−1.63109	+	0.970672i
$172$	−9.14164	−	15.8338i	−0.697044	−	1.20731i
$173$	1.26511			0.0961845			0.0480923	−	0.998843i	$-0.484686\pi$
$173$	1.26511			0.0961845			0.0480923	+	0.998843i	$0.484686\pi$
$174$	−4.11900	+	32.9687i	−0.312261	+	2.49935i
$175$	0.207729	−	0.775256i	0.0157028	−	0.0586038i
$176$	−0.0622160	+	0.232193i	−0.00468971	+	0.0175022i
$177$	2.32481	−	18.6079i	0.174743	−	1.39865i
$178$	18.7296			1.40384
$179$	5.61976	+	9.73371i	0.420041	+	0.727532i	0.995943	−	0.0899867i	$-0.0286825\pi$
$179$	5.61976	+	9.73371i	0.420041	+	0.727532i	−0.575902	+	0.817519i	$0.695349\pi$
$180$	−13.3511	−	7.47479i	−0.995130	−	0.557138i
$181$			11.0144i			0.818695i	0.912378	+	0.409348i	$0.134244\pi$
$181$			11.0144i			0.818695i	−0.912378	+	0.409348i	$0.865756\pi$
$182$	−2.72004	+	7.13896i	−0.201623	+	0.529175i
$183$	23.2353	−	3.21529i	1.71760	−	0.237681i
$184$	−1.91090	−	1.91090i	−0.140873	−	0.140873i
$185$		−	14.7252i		−	1.08262i
$186$	−1.43431	−	1.84387i	−0.105168	−	0.135199i
$187$	−0.0775127	+	0.289281i	−0.00566829	+	0.0211544i
$188$	−5.33956	−	19.9275i	−0.389427	−	1.45336i
$189$	−1.89295	+	4.83909i	−0.137692	+	0.351992i
$190$	−25.3959	+	25.3959i	−1.84241	+	1.84241i
$191$		−	0.576642i		−	0.0417244i	−0.999782	−	0.0208622i	$-0.993359\pi$
$191$		−	0.576642i		−	0.0417244i	0.999782	−	0.0208622i	$-0.00664112\pi$
$192$	2.68745	+	19.4208i	0.193950	+	1.40158i
$193$	−12.7514	+	12.7514i	−0.917869	+	0.917869i	−0.996874	−	0.0790052i	$-0.974826\pi$
$193$	−12.7514	+	12.7514i	−0.917869	+	0.917869i	0.0790052	+	0.996874i	$0.474826\pi$
$194$	2.58153	−	4.47135i	0.185343	−	0.321024i
$195$	−10.8478	+	6.78401i	−0.776830	+	0.485813i
$196$	1.24475	+	2.15597i	0.0889105	+	0.153998i
$197$	−9.57625	−	2.56595i	−0.682279	−	0.182816i	−0.0989995	−	0.995087i	$-0.531564\pi$
$197$	−9.57625	−	2.56595i	−0.682279	−	0.182816i	−0.583280	+	0.812271i	$0.698231\pi$
$198$	−0.393559	−	0.383293i	−0.0279690	−	0.0272395i
$199$	2.63953	+	1.52394i	0.187112	+	0.108029i	0.590630	−	0.806943i	$-0.298879\pi$
$199$	2.63953	+	1.52394i	0.187112	+	0.108029i	−0.403518	+	0.914972i	$0.632213\pi$
$200$	0.804065	+	0.215449i	0.0568560	+	0.0152345i
$201$	8.50811	+	6.43965i	0.600116	+	0.454218i
$202$	11.9996	+	3.21529i	0.844291	+	0.226227i
$203$	8.74479	−	2.34316i	0.613764	−	0.164457i
$204$	2.04815	+	14.8009i	0.143399	+	1.03627i
$205$	1.82108	+	1.05140i	0.127190	+	0.0734329i
$206$	10.2013	−	38.0718i	0.710760	−	2.65259i
$207$	−7.52304	+	2.12272i	−0.522887	+	0.147539i
$208$	9.37132	+	3.57061i	0.649784	+	0.247577i
$209$	−0.619244	+	0.357520i	−0.0428340	+	0.0247302i
$210$	−0.932130	+	7.46081i	−0.0643231	+	0.514845i
$211$	−9.03074			−0.621702			−0.310851	−	0.950459i	$-0.600614\pi$
$211$	−9.03074			−0.621702			−0.310851	+	0.950459i	$0.600614\pi$
$212$	8.29691	+	14.3707i	0.569834	+	0.986981i
$213$	−10.4960	−	24.8736i	−0.719176	−	1.70431i
$214$	15.6545	+	15.6545i	1.07012	+	1.07012i
$215$	−14.5337	+	3.89430i	−0.991192	+	0.265589i
$216$	−5.01891	−	1.96329i	−0.341494	−	0.133585i
$217$	−0.318267	+	0.551254i	−0.0216054	+	0.0374216i
$218$	17.0215	−	29.4820i	1.15284	−	1.99678i
$219$	1.03650	−	1.36943i	0.0700402	−	0.0925376i
$220$	−0.381745	−	0.220401i	−0.0257372	−	0.0148594i
$221$	11.6754	+	4.44849i	0.785372	+	0.299238i
$222$	−3.61564	−	26.1284i	−0.242666	−	1.75362i
$223$	1.33888	−	0.358751i	0.0896579	−	0.0240238i	−0.213711	−	0.976897i	$-0.568555\pi$
$223$	1.33888	−	0.358751i	0.0896579	−	0.0240238i	0.303369	+	0.952873i	$0.401888\pi$
$224$	6.90022	−	3.98384i	0.461040	−	0.266182i
$225$	1.67993	−	1.72493i	0.111996	−	0.114995i
$226$	−7.80525	−	7.80525i	−0.519197	−	0.519197i
$227$	−19.8536	+	19.8536i	−1.31773	+	1.31773i	−0.402163	+	0.915568i	$0.631741\pi$
$227$	−19.8536	+	19.8536i	−1.31773	+	1.31773i	−0.915568	+	0.402163i	$0.868259\pi$
$228$	−21.5300	+	28.4456i	−1.42586	+	1.88385i
$229$	−4.30327	−	16.0600i	−0.284368	−	1.06128i	−0.949300	−	0.314372i	$-0.898206\pi$
$229$	−4.30327	−	16.0600i	−0.284368	−	1.06128i	0.664932	−	0.746904i	$-0.268461\pi$
$230$	−9.79549	+	5.65543i	−0.645895	+	0.372908i
$231$	−0.0563702	+	0.138674i	−0.00370888	+	0.00912408i
$232$	2.43023	+	9.06975i	0.159553	+	0.595458i
$233$	8.85947			0.580403			0.290202	−	0.956966i	$-0.406278\pi$
$233$	8.85947			0.580403			0.290202	+	0.956966i	$0.406278\pi$
$234$	−17.5826	+	14.7011i	−1.14941	+	0.961042i
$235$	−16.9781			−1.10753
$236$	−6.97600	−	26.0348i	−0.454099	−	1.69472i
$237$	2.58557	+	3.32387i	0.167951	+	0.215909i
$238$	6.35864	−	3.67117i	0.412170	−	0.237966i
$239$	−2.16902	−	8.09489i	−0.140302	−	0.523615i	−0.999920	−	0.0126765i	$-0.995965\pi$
$239$	−2.16902	−	8.09489i	−0.140302	−	0.523615i	0.859618	−	0.510938i	$-0.170702\pi$
$240$	9.79382	+	1.22361i	0.632188	+	0.0789836i
$241$	0.922859	−	0.922859i	0.0594466	−	0.0594466i	−0.676759	−	0.736205i	$-0.736616\pi$
$241$	0.922859	−	0.922859i	0.0594466	−	0.0594466i	0.736205	+	0.676759i	$0.236616\pi$
$242$	16.4695	+	16.4695i	1.05870	+	1.05870i
$243$	−12.0470	+	9.89294i	−0.772814	+	0.634632i
$244$	29.1976	−	16.8573i	1.86919	−	1.07918i
$245$	1.97895	−	0.530257i	0.126430	−	0.0338769i
$246$	3.48947	+	1.41845i	0.222481	+	0.0904371i
$247$	12.2009	+	27.2213i	0.776324	+	1.73205i
$248$	−0.571739	−	0.330094i	−0.0363055	−	0.0209610i
$249$	−1.24630	−	0.155709i	−0.0789813	−	0.00986767i
$250$	12.5945	−	21.8143i	0.796547	−	1.37966i
$251$	10.6646	−	18.4717i	0.673146	−	1.16592i	−0.303861	−	0.952717i	$-0.598276\pi$
$251$	10.6646	−	18.4717i	0.673146	−	1.16592i	0.977007	−	0.213207i	$-0.0683910\pi$
$252$	0.0986833	+	7.46783i	0.00621646	+	0.470429i
$253$	−0.217516	+	0.0582833i	−0.0136751	+	0.00366424i
$254$	−3.75221	−	3.75221i	−0.235434	−	0.235434i
$255$	12.2018	+	1.52445i	0.764104	+	0.0954648i
$256$	−2.79241	−	4.83660i	−0.174526	−	0.302287i
$257$	19.1467			1.19434			0.597169	−	0.802116i	$-0.296292\pi$
$257$	19.1467			1.19434			0.597169	+	0.802116i	$0.296292\pi$
$258$	−24.8324	+	10.4786i	−1.54600	+	0.652372i
$259$	−6.22447	+	3.59370i	−0.386770	+	0.223302i
$260$	−10.7721	+	14.9043i	−0.668059	+	0.924328i
$261$	26.3250	+	6.68222i	1.62947	+	0.413619i
$262$	−5.82537	+	21.7406i	−0.359892	+	1.34314i
$263$	−8.33457	−	4.81197i	−0.513932	−	0.296719i	0.220517	−	0.975383i	$-0.429226\pi$
$263$	−8.33457	−	4.81197i	−0.513932	−	0.296719i	−0.734448	+	0.678665i	$0.762559\pi$
$264$	−0.143827	−	0.0584649i	−0.00885195	−	0.00359827i
$265$	13.1907	−	3.53445i	0.810300	−	0.217119i
$266$	16.9329	+	4.53716i	1.03822	+	0.278191i
$267$	1.89809	−	15.1924i	0.116161	−	0.929761i
$268$	14.8141	+	3.96942i	0.904913	+	0.242471i
$269$	0.0205416	+	0.0118597i	0.00125244	+	0.000723098i	0.500626	−	0.865664i	$-0.333103\pi$
$269$	0.0205416	+	0.0118597i	0.00125244	+	0.000723098i	−0.499374	+	0.866387i	$0.666436\pi$
$270$	−13.3741	+	18.1639i	−0.813923	+	1.10542i
$271$	−11.1441	−	2.98605i	−0.676955	−	0.181389i	−0.0960691	−	0.995375i	$-0.530627\pi$
$271$	−11.1441	−	2.98605i	−0.676955	−	0.181389i	−0.580886	+	0.813985i	$0.697294\pi$
$272$	−4.81914	−	8.34700i	−0.292203	−	0.506111i
$273$	5.51508	+	2.92983i	0.333788	+	0.177321i
$274$	−16.5843	+	28.7249i	−1.00189	+	1.73533i
$275$	0.0490487	−	0.0490487i	0.00295775	−	0.00295775i
$276$	−8.86805	+	6.89826i	−0.533794	+	0.415226i
$277$		−	10.8472i		−	0.651745i	−0.945414	−	0.325873i	$-0.894342\pi$
$277$		−	10.8472i		−	0.651745i	0.945414	−	0.325873i	$-0.105658\pi$
$278$	−22.4376	+	22.4376i	−1.34572	+	1.34572i
$279$	−1.64100	+	0.976568i	−0.0982442	+	0.0584656i
$280$	0.549962	+	2.05248i	0.0328665	+	0.122659i
$281$	6.88843	−	25.7080i	0.410929	−	1.53361i	−0.381923	−	0.924194i	$-0.624738\pi$
$281$	6.88843	−	25.7080i	0.410929	−	1.53361i	0.792852	−	0.609414i	$-0.208595\pi$
$282$	−30.1258	+	4.16880i	−1.79396	+	0.248248i
$283$			1.76822i			0.105110i	0.998618	+	0.0525550i	$0.0167365\pi$
$283$			1.76822i			0.105110i	−0.998618	+	0.0525550i	$0.983264\pi$
$284$	−27.4383	−	27.4383i	−1.62817	−	1.62817i
$285$	18.0261	+	23.1734i	1.06777	+	1.37267i
$286$	−0.512080	+	0.416787i	−0.0302799	+	0.0246451i
$287$		−	1.02638i		−	0.0605852i
$288$	23.9010	−	0.315838i	1.40838	−	0.0186109i
$289$	2.49600	+	4.32320i	0.146824	+	0.254306i
$290$	39.3001			2.30778
$291$	−3.36530	−	2.54713i	−0.197277	−	0.149316i
$292$	0.638901	−	2.38441i	0.0373889	−	0.139537i
$293$	2.61100	−	9.74439i	0.152536	−	0.569273i	−0.846767	−	0.531963i	$-0.821454\pi$
$293$	2.61100	−	9.74439i	0.152536	−	0.569273i	0.999304	−	0.0373100i	$-0.0118789\pi$
$294$	3.38123	−	1.42680i	0.197197	−	0.0832125i
$295$	−22.1814			−1.29145
$296$	−3.72725	−	6.45578i	−0.216642	−	0.375235i
$297$	−0.350791	+	0.280390i	−0.0203549	+	0.0162699i
$298$		−	3.44831i		−	0.199755i
$299$	1.49271	+	9.27526i	0.0863254	+	0.536402i
$300$	1.30323	−	3.20602i	0.0752418	−	0.185099i
$301$	5.19312	+	5.19312i	0.299326	+	0.299326i
$302$			6.24142i			0.359154i
$303$	3.82413	−	9.40759i	0.219691	−	0.540452i
$304$	5.95594	−	22.2279i	0.341596	−	1.27486i
$305$	−7.18112	−	26.8003i	−0.411190	−	1.53458i
$306$	22.0251	−	0.291049i	1.25909	−	0.0166382i
$307$	0.510076	−	0.510076i	0.0291116	−	0.0291116i	−0.692401	−	0.721513i	$-0.743447\pi$
$307$	0.510076	−	0.510076i	0.0291116	−	0.0291116i	0.721513	+	0.692401i	$0.243447\pi$
$308$			0.215156i			0.0122596i
$309$	−29.8480	−	12.1330i	−1.69799	−	0.690224i
$310$	−1.95387	+	1.95387i	−0.110972	+	0.110972i
$311$	1.51475	−	2.62362i	0.0858935	−	0.148772i	−0.819878	−	0.572538i	$-0.805959\pi$
$311$	1.51475	−	2.62362i	0.0858935	−	0.148772i	0.905772	+	0.423766i	$0.139292\pi$
$312$	−3.03870	+	5.72003i	−0.172033	+	0.323833i
$313$	0.812409	+	1.40713i	0.0459201	+	0.0795359i	0.888072	−	0.459705i	$-0.152045\pi$
$313$	0.812409	+	1.40713i	0.0459201	+	0.0795359i	−0.842152	+	0.539241i	$0.818711\pi$
$314$	−45.3891	−	12.1620i	−2.56146	−	0.686340i
$315$	5.95734	+	1.51219i	0.335658	+	0.0852020i
$316$	5.24174	+	3.02632i	0.294871	+	0.170244i
$317$	−11.6958	−	3.13389i	−0.656904	−	0.176017i	−0.0850554	−	0.996376i	$-0.527107\pi$
$317$	−11.6958	−	3.13389i	−0.656904	−	0.176017i	−0.571848	+	0.820359i	$0.693773\pi$
$318$	22.5377	−	9.51037i	1.26385	−	0.533315i
$319$	0.755772	+	0.202508i	0.0423151	+	0.0113383i
$320$	22.4006	−	6.00222i	1.25223	−	0.335534i
$321$	14.2845	−	11.1116i	0.797286	−	0.620190i
$322$	4.78119	+	2.76042i	0.266445	+	0.153832i
$323$	7.42029	−	27.6929i	0.412876	−	1.54087i
$324$	−10.6861	+	19.6929i	−0.593671	+	1.09405i
$325$	−1.82673	−	2.24439i	−0.101329	−	0.124496i
$326$	−31.0820	+	17.9452i	−1.72147	+	0.993894i
$327$	−22.1892	−	16.7947i	−1.22707	−	0.928746i
$328$	1.06452			0.0587783
$329$	4.14350	+	7.17676i	0.228439	+	0.395668i
$330$	−0.392169	+	0.518137i	−0.0215882	+	0.0285225i
$331$	−19.2226	−	19.2226i	−1.05657	−	1.05657i	−0.998301	−	0.0582690i	$-0.981442\pi$
$331$	−19.2226	−	19.2226i	−1.05657	−	1.05657i	−0.0582690	−	0.998301i	$-0.518558\pi$
$332$	−1.74374	+	0.467233i	−0.0957001	+	0.0256428i
$333$	−21.5603	+	0.284908i	−1.18150	+	0.0156129i
$334$	−20.3045	+	35.1685i	−1.11101	+	1.92433i
$335$	6.31073	−	10.9305i	0.344792	−	0.597197i
$336$	−1.87296	−	4.43855i	−0.102178	−	0.242143i
$337$	4.80437	+	2.77380i	0.261711	+	0.151099i	0.625115	−	0.780533i	$-0.285052\pi$
$337$	4.80437	+	2.77380i	0.261711	+	0.151099i	−0.363404	+	0.931632i	$0.618386\pi$
$338$	15.1168	+	23.0263i	0.822243	+	1.25246i
$339$	−7.12219	+	5.54019i	−0.386824	+	0.300902i
$340$	17.0718	−	4.57438i	0.925850	−	0.248081i
$341$	−0.0476424	+	0.0275063i	−0.00257998	+	0.00148955i
$342$	37.6754	+	36.6927i	2.03725	+	1.98411i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−5.38610	+	5.38610i	−0.290399	+	0.290399i
$345$	3.59468	+	8.51869i	0.193531	+	0.458631i
$346$	−0.693782	−	2.58923i	−0.0372980	−	0.139198i
$347$	6.85407	−	3.95720i	0.367946	−	0.212434i	−0.304615	−	0.952476i	$-0.598528\pi$
$347$	6.85407	−	3.95720i	0.367946	−	0.212434i	0.672561	+	0.740042i	$0.265194\pi$
$348$	38.6686	−	5.35095i	2.07285	−	0.286841i
$349$	2.85617	+	10.6594i	0.152887	+	0.570584i	0.999277	+	0.0380194i	$0.0121049\pi$
$349$	2.85617	+	10.6594i	0.152887	+	0.570584i	−0.846390	+	0.532564i	$0.821228\pi$
$350$	−1.70059			−0.0909004
$351$	10.1429	+	15.7519i	0.541387	+	0.840774i
$352$	0.688611			0.0367031
$353$	4.57750	+	17.0835i	0.243636	+	0.909262i	0.974064	+	0.226272i	$0.0726539\pi$
$353$	4.57750	+	17.0835i	0.243636	+	0.909262i	−0.730428	+	0.682989i	$0.760679\pi$
$354$	−39.3586	+	5.44643i	−2.09188	+	0.289475i
$355$	−27.6555	+	15.9669i	−1.46780	+	0.847437i
$356$	−5.69557	−	21.2561i	−0.301864	−	1.12657i
$357$	−2.33345	−	5.52983i	−0.123499	−	0.292669i
$358$	16.8396	−	16.8396i	0.890000	−	0.890000i
$359$	13.3372	+	13.3372i	0.703911	+	0.703911i	0.965248	−	0.261337i	$-0.0841634\pi$
$359$	13.3372	+	13.3372i	0.703911	+	0.703911i	−0.261337	+	0.965248i	$0.584163\pi$
$360$	−1.56838	+	6.17872i	−0.0826609	+	0.325647i
$361$	42.8257	−	24.7254i	2.25398	−	1.30134i
$362$	22.5426	−	6.04027i	1.18481	−	0.317470i
$363$	15.0282	−	11.6901i	0.788778	−	0.613573i
$364$	8.92913	+	0.916048i	0.468014	+	0.0480140i
$365$	−1.75933	−	1.01575i	−0.0920875	−	0.0531667i
$366$	−19.3227	−	45.7911i	−1.01001	−	2.39354i
$367$	9.52163	−	16.4919i	0.497025	−	0.860873i	−0.502969	−	0.864304i	$-0.667759\pi$
$367$	9.52163	−	16.4919i	0.497025	−	0.860873i	0.999994	+	0.00343174i	$0.00109236\pi$
$368$	3.62361	−	6.27627i	0.188894	−	0.327173i
$369$	1.50420	−	2.68672i	0.0783055	−	0.139865i
$370$	−30.1373	+	8.07527i	−1.56676	+	0.419813i
$371$	−4.71325	−	4.71325i	−0.244700	−	0.244700i
$372$	−1.65644	+	2.18850i	−0.0858823	+	0.113468i
$373$	6.76062	+	11.7097i	0.350051	+	0.606307i	0.986258	−	0.165212i	$-0.0528308\pi$
$373$	6.76062	+	11.7097i	0.350051	+	0.606307i	−0.636207	+	0.771519i	$0.719497\pi$
$374$	0.634564			0.0328125
$375$	−16.4183	−	12.4267i	−0.847835	−	0.641712i
$376$	−7.44346	+	4.29748i	−0.383867	+	0.221626i
$377$	11.6220	−	30.5029i	0.598566	−	1.57098i
$378$	10.9420	+	1.22045i	0.562795	+	0.0627731i
$379$	−5.19090	+	19.3727i	−0.266639	+	0.995108i	0.694601	+	0.719395i	$0.255581\pi$
$379$	−5.19090	+	19.3727i	−0.266639	+	0.995108i	−0.961240	+	0.275714i	$0.911086\pi$
$380$	36.5444	+	21.0989i	1.87469	+	1.08235i
$381$	−3.42384	+	2.66333i	−0.175409	+	0.136447i
$382$	−1.18018	+	0.316229i	−0.0603833	+	0.0161797i
$383$	17.5580	+	4.70466i	0.897174	+	0.240397i	0.677802	−	0.735244i	$-0.262933\pi$
$383$	17.5580	+	4.70466i	0.897174	+	0.240397i	0.219372	+	0.975641i	$0.429599\pi$
$384$	12.8442	−	5.41993i	0.655452	−	0.276584i
$385$	0.171031	+	0.0458277i	0.00871656	+	0.00233559i
$386$	33.0905	+	19.1048i	1.68426	+	0.972410i
$387$	5.98314	+	21.2046i	0.304140	+	1.07789i
$388$	−5.85955	−	1.57006i	−0.297474	−	0.0797078i
$389$	14.0735	+	24.3759i	0.713553	+	1.23591i	0.963515	+	0.267654i	$0.0862484\pi$
$389$	14.0735	+	24.3759i	0.713553	+	1.23591i	−0.249962	+	0.968256i	$0.580418\pi$
$390$	19.8334	+	18.4813i	1.00430	+	0.935839i
$391$	4.51452	−	7.81938i	0.228309	−	0.395443i
$392$	0.733384	−	0.733384i	0.0370415	−	0.0370415i
$393$	17.0444	+	6.92845i	0.859776	+	0.349494i
$394$			21.0063i			1.05828i
$395$	3.52216	−	3.52216i	0.177219	−	0.177219i
$396$	−0.315319	+	0.563206i	−0.0158454	+	0.0283022i
$397$	−3.48836	−	13.0187i	−0.175076	−	0.653391i	−0.996539	−	0.0831296i	$-0.973508\pi$
$397$	−3.48836	−	13.0187i	−0.175076	−	0.653391i	0.821463	−	0.570262i	$-0.193158\pi$
$398$	1.67144	−	6.23791i	0.0837818	−	0.312678i
$399$	5.39631	−	13.2752i	0.270153	−	0.664594i
$400$			2.23237i			0.111618i
$401$	−19.9817	−	19.9817i	−0.997840	−	0.997840i	0.00215756	−	0.999998i	$-0.499313\pi$
$401$	−19.9817	−	19.9817i	−0.997840	−	0.997840i	−0.999998	+	0.00215756i	$0.999313\pi$
$402$	8.51385	−	20.9446i	0.424632	−	1.04462i
$403$	0.938693	+	2.09431i	0.0467596	+	0.104325i
$404$		−	14.5961i		−	0.726182i
$405$	13.3782	+	12.6891i	0.664767	+	0.630527i
$406$	−9.59123	−	16.6125i	−0.476005	−	0.824464i
$407$	−0.621175			−0.0307905
$408$	5.73532	−	2.42016i	0.283941	−	0.119816i
$409$	3.11780	−	11.6358i	0.154165	−	0.575352i	−0.845010	−	0.534750i	$-0.820406\pi$
$409$	3.11780	−	11.6358i	0.154165	−	0.575352i	0.999175	−	0.0406022i	$-0.0129276\pi$
$410$	1.15317	−	4.30368i	0.0569509	−	0.212544i
$411$	21.6194	+	16.3633i	1.06640	+	0.807143i
$412$	−46.3098			−2.28152
$413$	5.41338	+	9.37626i	0.266375	+	0.461375i
$414$	8.47007	+	14.2329i	0.416281	+	0.699509i
$415$			1.48565i			0.0729277i
$416$	2.93184	−	28.5779i	0.143745	−	1.40115i
$417$	15.9263	+	20.4740i	0.779912	+	1.00262i
$418$	1.07131	+	1.07131i	0.0523994	+	0.0523994i
$419$		−	9.37605i		−	0.458050i	−0.973421	−	0.229025i	$-0.926446\pi$
$419$		−	9.37605i		−	0.458050i	0.973421	−	0.229025i	$-0.0735538\pi$
$420$	8.75070	−	1.21092i	0.426991	−	0.0590869i
$421$	2.09747	−	7.82785i	0.102224	−	0.381506i	−0.895791	−	0.444475i	$-0.853390\pi$
$421$	2.09747	−	7.82785i	0.102224	−	0.381506i	0.998015	+	0.0629690i	$0.0200569\pi$
$422$	4.95243	+	18.4827i	0.241081	+	0.899725i
$423$	0.328496	+	24.8589i	0.0159720	+	1.20868i
$424$	4.88840	−	4.88840i	0.237401	−	0.237401i
$425$			2.78123i			0.134909i
$426$	−45.1513	+	35.1222i	−2.18759	+	1.70168i
$427$	−9.57615	+	9.57615i	−0.463422	+	0.463422i
$428$	13.0058	−	22.5267i	0.628659	−	1.08887i
$429$	0.286179	+	0.457609i	0.0138169	+	0.0220936i
$430$	15.9405	+	27.6097i	0.768719	+	1.33146i
$431$	−13.0314	−	3.49175i	−0.627699	−	0.168191i	−0.0690737	−	0.997612i	$-0.522004\pi$
$431$	−13.0314	−	3.49175i	−0.627699	−	0.168191i	−0.558625	+	0.829420i	$0.688671\pi$
$432$	1.60209	−	14.3635i	0.0770804	−	0.691066i
$433$	11.9734	+	6.91287i	0.575407	+	0.332211i	0.759306	−	0.650734i	$-0.225539\pi$
$433$	11.9734	+	6.91287i	0.575407	+	0.332211i	−0.183899	+	0.982945i	$0.558872\pi$
$434$	1.30276	+	0.349073i	0.0625344	+	0.0167560i
$435$	3.98275	−	31.8781i	0.190958	−	1.52844i
$436$	−38.6352	−	10.3523i	−1.85029	−	0.495784i
$437$	20.8228	−	5.57946i	0.996091	−	0.266902i
$438$	−3.37115	−	1.37035i	−0.161080	−	0.0654781i
$439$	30.4267	+	17.5669i	1.45219	+	0.838421i	0.998605	−	0.0527926i	$-0.0168122\pi$
$439$	30.4267	+	17.5669i	1.45219	+	0.838421i	0.453583	+	0.891214i	$0.350146\pi$
$440$	−0.0475307	+	0.177387i	−0.00226594	+	0.00845659i
$441$	−0.814679	−	2.88726i	−0.0387942	−	0.137489i
$442$	2.70173	−	26.3349i	0.128508	−	1.25262i
$443$	−0.747115	+	0.431347i	−0.0354965	+	0.0204939i	−0.517643	−	0.855597i	$-0.673191\pi$
$443$	−0.747115	+	0.431347i	−0.0354965	+	0.0204939i	0.482147	+	0.876090i	$0.339857\pi$
$444$	−28.5535	+	12.0489i	−1.35509	+	0.571814i
$445$	−18.1100			−0.858499
$446$	−1.46847	−	2.54347i	−0.0695342	−	0.120437i
$447$	−2.79708	−	0.349458i	−0.132297	−	0.0165288i
$448$	−8.00407	−	8.00407i	−0.378157	−	0.378157i
$449$	7.15037	−	1.91594i	0.337447	−	0.0904186i	−0.0861165	−	0.996285i	$-0.527446\pi$
$449$	7.15037	−	1.91594i	0.337447	−	0.0904186i	0.423563	+	0.905866i	$0.360779\pi$
$450$	−4.45158	−	2.49228i	−0.209850	−	0.117487i
$451$	0.0443526	−	0.0768210i	0.00208848	−	0.00361736i
$452$	−6.48461	+	11.2317i	−0.305011	+	0.528294i
$453$	5.06270	+	0.632518i	0.237866	+	0.0297183i
$454$	51.5210	+	29.7456i	2.41800	+	1.39603i
$455$	2.63007	−	6.90282i	0.123300	−	0.323609i
$456$	13.7686	+	5.59684i	0.644772	+	0.262096i
$457$	29.3481	−	7.86379i	1.37284	−	0.367853i	0.504328	−	0.863512i	$-0.331740\pi$
$457$	29.3481	−	7.86379i	1.37284	−	0.367853i	0.868517	+	0.495660i	$0.165074\pi$
$458$	−30.5093	+	17.6145i	−1.42560	+	0.823073i
$459$	1.99598	−	17.8950i	0.0931644	−	0.835268i
$460$	9.39708	+	9.39708i	0.438141	+	0.438141i
$461$	−28.0420	+	28.0420i	−1.30605	+	1.30605i	−0.381803	+	0.924244i	$0.624697\pi$
$461$	−28.0420	+	28.0420i	−1.30605	+	1.30605i	−0.924244	+	0.381803i	$0.875303\pi$
$462$	0.314730	+	0.0393213i	0.0146425	+	0.00182939i
$463$	−2.38186	−	8.88921i	−0.110694	−	0.413117i	0.888235	−	0.459390i	$-0.151932\pi$
$463$	−2.38186	−	8.88921i	−0.110694	−	0.413117i	−0.998929	+	0.0462736i	$0.985265\pi$
$464$	−21.8072	+	12.5904i	−1.01238	+	0.584495i
$465$	1.38686	+	1.78288i	0.0643141	+	0.0826790i
$466$	−4.85851	−	18.1322i	−0.225066	−	0.839958i
$467$	3.70856			0.171612			0.0858059	−	0.996312i	$-0.472654\pi$
$467$	3.70856			0.171612			0.0858059	+	0.996312i	$0.472654\pi$
$468$	22.0310	+	15.4839i	1.01838	+	0.715744i
$469$	−6.16055			−0.284468
$470$	9.31071	+	34.7480i	0.429471	+	1.60281i
$471$	−14.4650	+	35.5847i	−0.666510	+	1.63965i
$472$	−9.72469	+	5.61455i	−0.447615	+	0.258431i
$473$	0.164279	+	0.613096i	0.00755354	+	0.0281902i
$474$	5.38487	−	7.11454i	0.247335	−	0.326781i
$475$	−4.69543	+	4.69543i	−0.215441	+	0.215441i
$476$	−6.10002	−	6.10002i	−0.279594	−	0.279594i
$477$	−5.43027	−	19.2452i	−0.248635	−	0.881176i
$478$	−15.3779	+	8.87842i	−0.703367	+	0.406089i
$479$	10.8052	−	2.89525i	0.493703	−	0.132287i	−0.00337279	−	0.999994i	$-0.501074\pi$
$479$	10.8052	−	2.89525i	0.493703	−	0.132287i	0.497076	+	0.867707i	$0.334407\pi$
$480$	−3.87558	−	28.0068i	−0.176895	−	1.27833i
$481$	−2.64472	+	25.7792i	−0.120589	+	1.17543i
$482$	−2.39486	−	1.38267i	−0.109083	−	0.0629790i
$483$	2.72364	−	3.59849i	0.123930	−	0.163737i
$484$	13.6829	−	23.6995i	0.621951	−	1.07725i
$485$	−2.49614	+	4.32344i	−0.113344	+	0.196318i
$486$	26.8539	+	19.2306i	1.21812	+	0.872319i
$487$	8.01878	−	2.14863i	0.363366	−	0.0973636i	−0.0725166	−	0.997367i	$-0.523103\pi$
$487$	8.01878	−	2.14863i	0.363366	−	0.0973636i	0.435882	+	0.900004i	$0.356436\pi$
$488$	−9.93201	−	9.93201i	−0.449601	−	0.449601i
$489$	11.4063	+	27.0306i	0.515809	+	1.22237i
$490$	−2.17049	−	3.75941i	−0.0980529	−	0.169833i
$491$	9.75343			0.440166			0.220083	−	0.975481i	$-0.429367\pi$
$491$	9.75343			0.440166			0.220083	+	0.975481i	$0.429367\pi$
$492$	0.548665	−	4.39153i	0.0247357	−	0.197986i
$493$	−27.1689	+	15.6859i	−1.22362	+	0.706459i
$494$	49.0214	−	39.8990i	2.20558	−	1.79514i
$495$	0.380541	+	0.370615i	0.0171040	+	0.0166579i
$496$	0.458228	−	1.71013i	0.0205751	−	0.0767872i
$497$	13.4987	+	7.79348i	0.605500	+	0.349585i
$498$	0.364787	+	2.63613i	0.0163465	+	0.118128i
$499$	22.7070	−	6.08433i	1.01651	−	0.272372i	0.288160	−	0.957582i	$-0.406956\pi$
$499$	22.7070	−	6.08433i	1.01651	−	0.272372i	0.728345	+	0.685210i	$0.240290\pi$
$500$	−28.5869	−	7.65985i	−1.27845	−	0.342559i
$501$	26.4690	+	20.0340i	1.18255	+	0.895051i
$502$	−43.6535	−	11.6969i	−1.94835	−	0.522059i
$503$	5.99942	+	3.46376i	0.267501	+	0.154442i	0.627751	−	0.778414i	$-0.283975\pi$
$503$	5.99942	+	3.46376i	0.267501	+	0.154442i	−0.360251	+	0.932856i	$0.617309\pi$
$504$	2.99456	−	0.844953i	0.133388	−	0.0376372i
$505$	−11.6027	−	3.10893i	−0.516313	−	0.138346i
$506$	0.238571	+	0.413216i	0.0106058	+	0.0183697i
$507$	20.2096	−	9.92835i	0.897540	−	0.440934i
$508$	−3.11734	+	5.39939i	−0.138310	+	0.239559i
$509$	9.02272	−	9.02272i	0.399925	−	0.399925i	−0.478282	−	0.878207i	$-0.658740\pi$
$509$	9.02272	−	9.02272i	0.399925	−	0.399925i	0.878207	+	0.478282i	$0.158740\pi$
$510$	−3.57140	−	25.8087i	−0.158144	−	1.14283i
$511$			0.991577i			0.0438648i
$512$	−19.7501	+	19.7501i	−0.872841	+	0.872841i
$513$	33.5812	−	26.8417i	1.48264	−	1.18509i
$514$	−10.5000	−	39.1865i	−0.463134	−	1.72844i
$515$	−9.86388	+	36.8125i	−0.434654	+	1.62215i
$516$	19.4436	+	24.9957i	0.855955	+	1.10037i
$517$			0.716208i			0.0314988i
$518$	10.7685	+	10.7685i	0.473141	+	0.473141i
$519$	−2.17055	+	0.300360i	−0.0952766	+	0.0131844i
$520$	7.15933	+	2.72781i	0.313957	+	0.119622i
$521$			25.8029i			1.13045i	0.824938	+	0.565223i	$0.191210\pi$
$521$			25.8029i			1.13045i	−0.824938	+	0.565223i	$0.808790\pi$
$522$	−0.760390	−	57.5423i	−0.0332814	−	2.51856i
$523$	13.9549	+	24.1706i	0.610206	+	1.05691i	0.991205	+	0.132332i	$0.0422465\pi$
$523$	13.9549	+	24.1706i	0.610206	+	1.05691i	−0.381000	+	0.924575i	$0.624420\pi$
$524$	26.4447			1.15524
$525$	−0.172341	+	1.37943i	−0.00752159	+	0.0602031i
$526$	−5.27773	+	19.6968i	−0.230120	+	0.858820i
$527$	0.570890	−	2.13059i	0.0248684	−	0.0928100i
$528$	0.0516172	−	0.413146i	0.00224635	−	0.0179799i
$529$	−16.2109			−0.704821
$530$	−14.4675	−	25.0585i	−0.628429	−	1.08847i
$531$	0.429172	+	32.4775i	0.0186245	+	1.40940i
$532$		−	20.5968i		−	0.892986i
$533$	−2.99930	−	2.16774i	−0.129914	−	0.0938954i
$534$	−32.1344	+	4.44675i	−1.39059	+	0.192430i
$535$	−15.1367	−	15.1367i	−0.654416	−	0.654416i
$536$		−	6.38948i		−	0.275983i
$537$	−11.9528	−	15.3659i	−0.515801	−	0.663088i
$538$	0.0130076	−	0.0485451i	0.000560799	−	0.00209293i
$539$	−0.0223685	−	0.0834806i	−0.000963482	−	0.00359576i
$540$	24.6811	+	9.65471i	1.06211	+	0.415473i
$541$	−17.9177	+	17.9177i	−0.770342	+	0.770342i	−0.978166	−	0.207824i	$-0.933362\pi$
$541$	−17.9177	+	17.9177i	−0.770342	+	0.770342i	0.207824	+	0.978166i	$0.433362\pi$
$542$			24.4455i			1.05002i
$543$	−2.61503	−	18.8975i	−0.112222	−	0.810968i
$544$	−19.5233	+	19.5233i	−0.837053	+	0.837053i
$545$	−16.4584	+	28.5068i	−0.705002	+	1.22110i
$546$	2.97186	−	12.8941i	0.127184	−	0.551817i
$547$	7.23721	+	12.5352i	0.309441	+	0.535967i	0.978240	−	0.207476i	$-0.0665249\pi$
$547$	7.23721	+	12.5352i	0.309441	+	0.535967i	−0.668800	+	0.743443i	$0.733192\pi$
$548$	37.6429	+	10.0864i	1.60803	+	0.430869i
$549$	−39.1014	+	11.0330i	−1.66881	+	0.470875i
$550$	−0.127283	−	0.0734871i	−0.00542739	−	0.00313350i
$551$	−72.3500	−	19.3861i	−3.08221	−	0.825877i
$552$	3.73222	+	2.82485i	0.158854	+	0.120234i
$553$	−2.34843	−	0.629260i	−0.0998654	−	0.0267589i
$554$	−22.2004	+	5.94857i	−0.943203	+	0.252731i
$555$	3.49604	+	25.2641i	0.148399	+	1.07240i
$556$	32.2875	+	18.6412i	1.36929	+	0.790562i
$557$	−6.40654	+	23.9095i	−0.271454	+	1.01308i	0.686727	+	0.726916i	$0.259047\pi$
$557$	−6.40654	+	23.9095i	−0.271454	+	1.01308i	−0.958181	+	0.286164i	$0.907620\pi$
$558$	2.89861	+	2.82300i	0.122708	+	0.119507i
$559$	26.1434	−	4.20737i	1.10575	−	0.177953i
$560$	−4.93498	+	2.84921i	−0.208541	+	0.120401i
$561$	0.0643080	−	0.514724i	0.00271508	−	0.0217316i
$562$	−56.3927			−2.37878
$563$	−16.3754	−	28.3630i	−0.690140	−	1.19536i	−0.971792	−	0.235841i	$-0.924216\pi$
$563$	−16.3754	−	28.3630i	−0.690140	−	1.19536i	0.281652	−	0.959517i	$-0.409118\pi$
$564$	13.8922	+	32.9219i	0.584969	+	1.38626i
$565$	7.54706	+	7.54706i	0.317507	+	0.317507i
$566$	3.61892	−	0.969687i	0.152115	−	0.0407590i
$567$	2.09884	−	8.75185i	0.0881431	−	0.367543i
$568$	−8.08310	+	14.0003i	−0.339159	+	0.587441i
$569$	−14.1869	+	24.5725i	−0.594747	+	1.03013i	0.398835	+	0.917023i	$0.369415\pi$
$569$	−14.1869	+	24.5725i	−0.594747	+	1.03013i	−0.993582	+	0.113110i	$0.963919\pi$
$570$	37.5423	−	49.6012i	1.57247	−	2.07756i
$571$	−28.9705	−	16.7261i	−1.21238	−	0.699966i	−0.249100	−	0.968478i	$-0.580135\pi$
$571$	−28.9705	−	16.7261i	−1.21238	−	0.699966i	−0.963276	+	0.268512i	$0.913468\pi$
$572$	0.628730	+	0.454415i	0.0262885	+	0.0190001i
$573$	0.136905	+	0.989346i	0.00571931	+	0.0413305i
$574$	−2.10063	+	0.562863i	−0.0876788	+	0.0234935i
$575$	−1.81108	+	1.04563i	−0.0755274	+	0.0436058i
$576$	−9.22172	−	32.6823i	−0.384238	−	1.36176i
$577$	5.90389	+	5.90389i	0.245782	+	0.245782i	0.819237	−	0.573455i	$-0.194397\pi$
$577$	5.90389	+	5.90389i	0.245782	+	0.245782i	−0.573455	+	0.819237i	$0.694397\pi$
$578$	7.47926	−	7.47926i	0.311096	−	0.311096i
$579$	18.8502	−	24.9051i	0.783389	−	1.03502i
$580$	−11.9510	−	44.6016i	−0.496237	−	1.85198i
$581$	0.627996	−	0.362574i	0.0260537	−	0.0150421i
$582$	−3.36756	+	8.28441i	−0.139590	+	0.343400i
$583$	−0.149098	−	0.556443i	−0.00617502	−	0.0230455i
$584$	−1.02843			−0.0425565
$585$	17.0010	−	14.2148i	0.702905	−	0.587711i
$586$	−21.3752			−0.883000
$587$	1.99661	+	7.45144i	0.0824088	+	0.307554i	0.994811	−	0.101741i	$-0.0324413\pi$
$587$	1.99661	+	7.45144i	0.0824088	+	0.307554i	−0.912402	+	0.409295i	$0.865775\pi$
$588$	−2.64748	−	3.40347i	−0.109180	−	0.140357i
$589$	4.56080	−	2.63318i	0.187925	−	0.108498i
$590$	12.1642	+	45.3974i	0.500793	+	1.86898i
$591$	17.0392	+	2.12882i	0.700899	+	0.0875681i
$592$	14.1358	−	14.1358i	0.580980	−	0.580980i
$593$	−16.6688	−	16.6688i	−0.684505	−	0.684505i	0.276507	−	0.961012i	$-0.410823\pi$
$593$	−16.6688	−	16.6688i	−0.684505	−	0.684505i	−0.961012	+	0.276507i	$0.910823\pi$
$594$	0.766231	+	0.564179i	0.0314388	+	0.0231485i
$595$	−6.14831	+	3.54973i	−0.252056	+	0.145525i
$596$	−3.91347	+	1.04861i	−0.160302	+	0.0429528i
$597$	−4.89046	−	1.98794i	−0.200153	−	0.0813612i
$598$	18.1646	−	8.14156i	0.742804	−	0.332933i
$599$	−6.73726	−	3.88976i	−0.275277	−	0.158931i	0.356006	−	0.934484i	$-0.384138\pi$
$599$	−6.73726	−	3.88976i	−0.275277	−	0.158931i	−0.631283	+	0.775552i	$0.717471\pi$
$600$	−1.43069	−	0.178746i	−0.0584075	−	0.00729726i
$601$	−20.8155	+	36.0535i	−0.849083	+	1.47065i	0.0329453	+	0.999457i	$0.489511\pi$
$601$	−20.8155	+	36.0535i	−0.849083	+	1.47065i	−0.882028	+	0.471197i	$0.843822\pi$
$602$	7.78058	−	13.4764i	0.317113	−	0.549255i
$603$	−16.1263	−	9.02853i	−0.656713	−	0.367670i
$604$	7.08337	−	1.89798i	0.288218	−	0.0772278i
$605$	−15.9248	−	15.9248i	−0.647433	−	0.647433i
$606$	−21.3511	−	2.66755i	−0.867331	−	0.108362i
$607$	−21.2440	−	36.7957i	−0.862267	−	1.49349i	−0.869736	−	0.493518i	$-0.835711\pi$
$607$	−21.2440	−	36.7957i	−0.862267	−	1.49349i	0.00746854	−	0.999972i	$-0.497623\pi$
$608$	−65.9207			−2.67344
$609$	−14.4471	+	6.09633i	−0.585427	+	0.247036i
$610$	−50.9126	+	29.3944i	−2.06139	+	1.19014i
$611$	29.7232	+	3.04934i	1.20247	+	0.123363i
$612$	−7.02801	−	24.9077i	−0.284091	−	1.00683i
$613$	8.42018	−	31.4245i	0.340088	−	1.26922i	−0.558159	−	0.829734i	$-0.688492\pi$
$613$	8.42018	−	31.4245i	0.340088	−	1.26922i	0.898247	−	0.439491i	$-0.144841\pi$
$614$	−1.32367	−	0.764221i	−0.0534190	−	0.0308414i
$615$	−3.37405	−	1.37153i	−0.136055	−	0.0553055i
$616$	0.0865828	−	0.0231998i	0.00348852	−	0.000934746i
$617$	31.1444	+	8.34512i	1.25383	+	0.335962i	0.823814	−	0.566861i	$-0.191842\pi$
$617$	31.1444	+	8.34512i	1.25383	+	0.335962i	0.430013	+	0.902823i	$0.358509\pi$
$618$	−8.46346	+	67.7419i	−0.340450	+	2.72498i
$619$	−14.2879	−	3.82843i	−0.574279	−	0.153878i	−0.0400205	−	0.999199i	$-0.512742\pi$
$619$	−14.2879	−	3.82843i	−0.574279	−	0.153878i	−0.534258	+	0.845321i	$0.679409\pi$
$620$	2.81160	+	1.62328i	0.112916	+	0.0651923i
$621$	12.4033	−	5.42806i	0.497728	−	0.217821i
$622$	−6.20030	−	1.66137i	−0.248609	−	0.0666147i
$623$	4.41977	+	7.65527i	0.177074	+	0.306702i
$624$	−16.9261	−	3.90117i	−0.677587	−	0.156172i
$625$	−10.1714	+	17.6174i	−0.406856	+	0.704696i
$626$	2.43438	−	2.43438i	0.0972975	−	0.0972975i
$627$	0.977555	−	0.760418i	0.0390398	−	0.0303682i
$628$			55.2104i			2.20313i
$629$	17.6113	−	17.6113i	0.702210	−	0.702210i
$630$	−0.172076	−	13.0218i	−0.00685569	−	0.518802i
$631$	−5.50144	−	20.5317i	−0.219009	−	0.817353i	−0.984717	−	0.174164i	$-0.944278\pi$
$631$	−5.50144	−	20.5317i	−0.219009	−	0.817353i	0.765708	−	0.643189i	$-0.222389\pi$
$632$	0.652644	−	2.43570i	0.0259608	−	0.0968870i
$633$	15.4941	−	2.14406i	0.615834	−	0.0852189i
$634$			25.6558i			1.01892i
$635$	3.62809	+	3.62809i	0.143976	+	0.143976i
$636$	−17.6469	−	22.6859i	−0.699744	−	0.899556i
$637$	−3.55975	+	0.572885i	−0.141042	+	0.0226985i
$638$		−	1.65785i		−	0.0656350i
$639$	23.9135	+	40.1837i	0.946003	+	1.58964i
$640$	−8.24499	−	14.2807i	−0.325912	−	0.564496i
$641$	23.0797			0.911593			0.455796	−	0.890084i	$-0.349355\pi$
$641$	23.0797			0.911593			0.455796	+	0.890084i	$0.349355\pi$
$642$	−30.5752	−	23.1418i	−1.20670	−	0.913334i
$643$	−9.03967	+	33.7365i	−0.356490	+	1.33044i	0.522110	+	0.852878i	$0.325145\pi$
$643$	−9.03967	+	33.7365i	−0.356490	+	1.33044i	−0.878599	+	0.477559i	$0.841522\pi$
$644$	1.67886	−	6.26558i	0.0661563	−	0.246899i
$645$	24.0110	−	10.1320i	0.945430	−	0.398948i
$646$	−60.7468			−2.39005
$647$	−11.8814	−	20.5792i	−0.467106	−	0.809051i	0.532188	−	0.846626i	$-0.321370\pi$
$647$	−11.8814	−	20.5792i	−0.467106	−	0.809051i	−0.999294	+	0.0375755i	$0.988037\pi$
$648$	9.07708	+	2.17684i	0.356581	+	0.0855143i
$649$			0.935708i			0.0367298i
$650$	−3.59170	+	4.96949i	−0.140878	+	0.194919i
$651$	0.415173	−	1.02135i	0.0162719	−	0.0400299i
$652$	29.8178	+	29.8178i	1.16776	+	1.16776i
$653$		−	12.9458i		−	0.506607i	−0.967387	−	0.253303i	$-0.918483\pi$
$653$		−	12.9458i		−	0.506607i	0.967387	−	0.253303i	$-0.0815171\pi$
$654$	−22.2042	+	54.6236i	−0.868252	+	2.13595i
$655$	5.63267	−	21.0214i	0.220087	−	0.821375i
$656$	0.738871	+	2.75750i	0.0288481	+	0.107662i
$657$	−1.45320	+	2.59562i	−0.0566946	+	0.101265i
$658$	12.4160	−	12.4160i	0.484026	−	0.484026i
$659$		−	0.449994i		−	0.0175293i	−0.999962	−	0.00876465i	$-0.997210\pi$
$659$		−	0.449994i		−	0.0175293i	0.999962	−	0.00876465i	$-0.00278991\pi$
$660$	0.707288	+	0.287508i	0.0275311	+	0.0111912i
$661$	−13.1111	+	13.1111i	−0.509964	+	0.509964i	−0.914515	−	0.404551i	$-0.867428\pi$
$661$	−13.1111	+	13.1111i	−0.509964	+	0.509964i	0.404551	+	0.914515i	$0.367428\pi$
$662$	−28.8002	+	49.8835i	−1.11935	+	1.93878i
$663$	−21.0877	−	4.86032i	−0.818976	−	0.188759i
$664$	0.376047	+	0.651333i	0.0145935	+	0.0252766i
$665$	−16.3728	−	4.38708i	−0.634910	−	0.170124i
$666$	12.4067	+	43.9701i	0.480751	+	1.70381i
$667$	−20.4288	−	11.7946i	−0.791006	−	0.456688i
$668$	46.0870	+	12.3490i	1.78316	+	0.477797i
$669$	−2.21194	+	0.933384i	−0.0855186	+	0.0360867i
$670$	−25.8316	−	6.92156i	−0.997963	−	0.267403i
$671$	−1.13055	+	0.302931i	−0.0436445	+	0.0116945i
$672$	−10.8929	+	8.47333i	−0.420202	+	0.326866i
$673$	16.8688	+	9.73923i	0.650246	+	0.375420i	0.788551	−	0.614970i	$-0.210832\pi$
$673$	16.8688	+	9.73923i	0.650246	+	0.375420i	−0.138304	+	0.990390i	$0.544165\pi$
$674$	3.04229	−	11.3540i	0.117185	−	0.437339i
$675$	−2.47274	+	3.35831i	−0.0951757	+	0.129261i
$676$	21.5355	−	24.1581i	0.828288	−	0.929158i
$677$	35.3932	−	20.4342i	1.36027	−	0.785352i	0.370610	−	0.928789i	$-0.379149\pi$
$677$	35.3932	−	20.4342i	1.36027	−	0.785352i	0.989659	+	0.143437i	$0.0458154\pi$
$678$	15.2446	+	11.5384i	0.585465	+	0.443128i
$679$	2.43674			0.0935135
$680$	−3.68164	−	6.37679i	−0.141184	−	0.244539i
$681$	29.3493	−	38.7765i	1.12467	−	1.48592i
$682$	0.0824226	+	0.0824226i	0.00315613	+	0.00315613i
$683$	−22.6149	+	6.05965i	−0.865336	+	0.231866i	−0.664070	−	0.747670i	$-0.731172\pi$
$683$	−22.6149	+	6.05965i	−0.865336	+	0.231866i	−0.201266	+	0.979537i	$0.564506\pi$
$684$	30.1855	−	53.9157i	1.15417	−	2.06152i
$685$	16.0357	−	27.7747i	0.612694	−	1.06122i
$686$	−1.05942	+	1.83497i	−0.0404489	+	0.0700595i
$687$	11.1961	+	26.5325i	0.427157	+	1.01228i
$688$	−17.6904	−	10.2136i	−0.674441	−	0.389389i
$689$	−23.7276	+	3.81859i	−0.903951	+	0.145477i
$690$	15.4634	−	12.0287i	0.588683	−	0.457923i
$691$	13.8622	−	3.71437i	0.527344	−	0.141301i	0.0146825	−	0.999892i	$-0.495326\pi$
$691$	13.8622	−	3.71437i	0.527344	−	0.141301i	0.512662	+	0.858591i	$0.328660\pi$
$692$	−2.72753	+	1.57474i	−0.103685	+	0.0598627i
$693$	0.0637906	−	0.251307i	0.00242321	−	0.00954634i
$694$	−11.8577	−	11.8577i	−0.450113	−	0.450113i
$695$	21.6954	−	21.6954i	0.822953	−	0.822953i
$696$	−6.32288	−	14.9840i	−0.239668	−	0.567967i
$697$	0.920533	+	3.43548i	0.0348677	+	0.130128i
$698$	20.2497	−	11.6911i	0.766461	−	0.442516i
$699$	−15.2002	+	2.10340i	−0.574925	+	0.0795580i
$700$	0.517140	+	1.92999i	0.0195461	+	0.0729469i
$701$	−41.2404			−1.55763			−0.778815	−	0.627254i	$-0.784179\pi$
$701$	−41.2404			−1.55763			−0.778815	+	0.627254i	$0.784179\pi$
$702$	26.6762	−	29.3972i	1.00683	−	1.10952i
$703$	59.4650			2.24276
$704$	−0.253200	−	0.944955i	−0.00954283	−	0.0356143i
$705$	29.1293	−	4.03090i	1.09707	−	0.151813i
$706$	32.4535	−	18.7370i	1.22140	−	0.705178i
$707$	1.51747	+	5.66329i	0.0570705	+	0.212990i
$708$	18.1499	+	43.0117i	0.682114	+	1.61648i
$709$	−7.94801	+	7.94801i	−0.298494	+	0.298494i	−0.840424	−	0.541930i	$-0.817694\pi$
$709$	−7.94801	+	7.94801i	−0.298494	+	0.298494i	0.541930	+	0.840424i	$0.317694\pi$
$710$	47.8449	+	47.8449i	1.79559	+	1.79559i
$711$	−5.22521	−	5.08891i	−0.195961	−	0.190849i
$712$	−7.93974	+	4.58401i	−0.297554	+	0.171793i
$713$	1.60203	−	0.429264i	0.0599966	−	0.0160760i
$714$	−10.0379	+	7.80828i	−0.375660	+	0.292218i
$715$	0.495141	−	0.403000i	0.0185172	−	0.0150713i
$716$	−24.2320	−	13.9904i	−0.905593	−	0.522844i
$717$	5.64326	+	13.3734i	0.210752	+	0.499440i
$718$	19.9824	−	34.6106i	0.745738	−	1.29166i
$719$	−3.86793	+	6.69946i	−0.144250	+	0.249848i	−0.929093	−	0.369847i	$-0.879410\pi$
$719$	−3.86793	+	6.69946i	−0.144250	+	0.249848i	0.784843	+	0.619694i	$0.212743\pi$
$720$	−17.0938	+	0.225885i	−0.637047	+	0.00841823i
$721$	17.9682	−	4.81457i	0.669172	−	0.179304i
$722$	−74.0896	−	74.0896i	−2.75733	−	2.75733i
$723$	−1.36425	+	1.80245i	−0.0507369	+	0.0670340i
$724$	−13.7102	−	23.7467i	−0.509534	−	0.882539i
$725$	7.26619			0.269859
$726$	−32.1670	−	24.3466i	−1.19383	−	0.903589i
$727$	−3.23257	+	1.86633i	−0.119889	+	0.0692182i	−0.558745	−	0.829339i	$-0.688717\pi$
$727$	−3.23257	+	1.86633i	−0.119889	+	0.0692182i	0.438856	+	0.898557i	$0.355384\pi$
$728$	−0.594174	−	3.69203i	−0.0220216	−	0.136836i
$729$	18.3203	−	19.8335i	0.678528	−	0.734574i
$730$	−1.11407	+	4.15776i	−0.0412335	+	0.153885i
$731$	−22.0399	−	12.7247i	−0.815174	−	0.470641i
$732$	−46.0922	+	35.8541i	−1.70362	+	1.32521i
$733$	−1.97821	+	0.530060i	−0.0730668	+	0.0195782i	−0.295167	−	0.955446i	$-0.595375\pi$
$733$	−1.97821	+	0.530060i	−0.0730668	+	0.0195782i	0.222100	+	0.975024i	$0.428709\pi$
$734$	−38.9748	−	10.4433i	−1.43859	−	0.385468i
$735$	−3.26939	+	1.37960i	−0.120593	+	0.0508873i
$736$	−20.0532	−	5.37323i	−0.739169	−	0.198060i
$737$	−0.461096	−	0.266214i	−0.0169847	−	0.00980612i
$738$	−6.32366	−	1.60517i	−0.232777	−	0.0590872i
$739$	47.9705	+	12.8537i	1.76462	+	0.472829i	0.987646	−	0.156701i	$-0.0500857\pi$
$739$	47.9705	+	12.8537i	1.76462	+	0.472829i	0.776976	+	0.629530i	$0.216752\pi$
$740$	18.3292	+	31.7471i	0.673794	+	1.16705i
$741$	−27.3959	−	43.8069i	−1.00641	−	1.60929i
$742$	−7.06161	+	12.2311i	−0.259240	+	0.449017i
$743$	−31.7511	+	31.7511i	−1.16483	+	1.16483i	−0.181429	+	0.983404i	$0.558072\pi$
$743$	−31.7511	+	31.7511i	−1.16483	+	1.16483i	−0.983404	+	0.181429i	$0.941928\pi$
$744$	1.05930	+	0.430601i	0.0388360	+	0.0157866i
$745$			3.33424i			0.122157i
$746$	20.2582	−	20.2582i	0.741704	−	0.741704i
$747$	2.17525	−	0.0287448i	0.0795883	−	0.00105172i
$748$	−0.192967	−	0.720164i	−0.00705559	−	0.0263318i
$749$	−2.70428	+	10.0925i	−0.0988124	+	0.368773i
$750$	−16.4293	+	40.4171i	−0.599914	+	1.47582i
$751$			11.2554i			0.410714i	0.978687	+	0.205357i	$0.0658355\pi$
$751$			11.2554i			0.410714i	−0.978687	+	0.205357i	$0.934164\pi$
$752$	−16.2985	−	16.2985i	−0.594345	−	0.594345i
$753$	−13.9118	+	34.2239i	−0.506975	+	1.24719i
$754$	−68.8022	−	7.05848i	−2.50563	−	0.257055i
$755$		−	6.03497i		−	0.219635i
$756$	−1.94231	−	12.7891i	−0.0706412	−	0.465137i
$757$	19.5734	+	33.9020i	0.711406	+	1.23219i	0.964330	+	0.264705i	$0.0852745\pi$
$757$	19.5734	+	33.9020i	0.711406	+	1.23219i	−0.252924	+	0.967486i	$0.581392\pi$
$758$	42.4957			1.54351
$759$	0.359356	−	0.151639i	0.0130438	−	0.00550416i
$760$	4.55011	−	16.9812i	0.165050	−	0.615974i
$761$	5.43654	−	20.2895i	0.197075	−	0.735492i	−0.794645	−	0.607074i	$-0.792343\pi$
$761$	5.43654	−	20.2895i	0.197075	−	0.735492i	0.991720	−	0.128419i	$-0.0409901\pi$
$762$	7.32851	+	5.54683i	0.265484	+	0.200940i
$763$	16.0668			0.581656
$764$	0.717774	+	1.24322i	0.0259681	+	0.0449781i
$765$	−21.2965	+	0.281422i	−0.769977	+	0.0101748i
$766$		−	38.5151i		−	1.39161i
$767$	38.8327	+	3.98388i	1.40217	+	0.143850i
$768$	5.93924	+	7.63519i	0.214314	+	0.275511i
$769$	13.9345	+	13.9345i	0.502493	+	0.502493i	0.912212	−	0.409719i	$-0.134373\pi$
$769$	13.9345	+	13.9345i	0.502493	+	0.502493i	−0.409719	+	0.912212i	$0.634373\pi$
$770$		−	0.375172i		−	0.0135203i
$771$	−32.8500	+	4.54578i	−1.18306	+	0.163712i
$772$	11.6193	−	43.3640i	0.418189	−	1.56070i
$773$	−11.6929	−	43.6386i	−0.420565	−	1.56957i	−0.773421

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.fy (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.548397 - 2.04664i) q^{2} +(-1.71570 + 0.237418i) q^{3} +(-2.15597 + 1.24475i) q^{4} +(0.530257 + 1.97895i) q^{5} +(1.42680 + 3.38123i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.733384 + 0.733384i) q^{8} +(2.88726 - 0.814679i) q^{9} +O(q^{10})\)	\(q+(-0.548397 - 2.04664i) q^{2} +(-1.71570 + 0.237418i) q^{3} +(-2.15597 + 1.24475i) q^{4} +(0.530257 + 1.97895i) q^{5} +(1.42680 + 3.38123i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.733384 + 0.733384i) q^{8} +(2.88726 - 0.814679i) q^{9} +(3.75941 - 2.17049i) q^{10} +(0.0834806 - 0.0223685i) q^{11} +(3.40347 - 2.64748i) q^{12} +(-0.572885 - 3.55975i) q^{13} +(-1.83497 - 1.05942i) q^{14} +(-1.37960 - 3.26939i) q^{15} +(-1.39070 + 2.40877i) q^{16} +(-1.73263 + 3.00100i) q^{17} +(-3.25072 - 5.46244i) q^{18} +(-7.99159 + 2.14134i) q^{19} +(-3.60650 - 3.60650i) q^{20} +(-1.04530 + 1.38106i) q^{21} +(-0.0915609 - 0.158588i) q^{22} -2.60559 q^{23} +(-1.43239 - 1.08415i) q^{24} +(0.695075 - 0.401302i) q^{25} +(-6.97137 + 3.12465i) q^{26} +(-4.76027 + 2.08324i) q^{27} +(-0.644328 + 2.40467i) q^{28} +(7.84036 + 4.52663i) q^{29} +(-5.93471 + 4.61647i) q^{30} +(-0.614844 + 0.164747i) q^{31} +(7.69619 + 2.06219i) q^{32} +(-0.137917 + 0.0581976i) q^{33} +(7.09215 + 1.90033i) q^{34} +(1.77427 + 1.02438i) q^{35} +(-5.21077 + 5.35033i) q^{36} +(-6.94250 - 1.86024i) q^{37} +(8.76512 + 15.1816i) q^{38} +(1.82805 + 5.97145i) q^{39} +(-1.06244 + 1.84021i) q^{40} +(0.725760 - 0.725760i) q^{41} +(3.39979 + 1.38199i) q^{42} +7.34418i q^{43} +(-0.152138 + 0.152138i) q^{44} +(3.14320 + 5.28175i) q^{45} +(1.42890 + 5.33272i) q^{46} +(-2.14484 + 8.00464i) q^{47} +(1.81415 - 4.46291i) q^{48} -1.00000i q^{49} +(-1.20250 - 1.20250i) q^{50} +(2.26018 - 5.56018i) q^{51} +(5.66611 + 6.96159i) q^{52} -6.66554i q^{53} +(6.87416 + 8.60013i) q^{54} +(0.0885323 + 0.153342i) q^{55} +1.03716 q^{56} +(13.2028 - 5.57125i) q^{57} +(4.96478 - 18.5288i) q^{58} +(-2.80217 + 10.4579i) q^{59} +(7.04393 + 5.33143i) q^{60} -13.5427 q^{61} +(0.674357 + 1.16802i) q^{62} +(1.46554 - 2.61767i) q^{63} -11.3195i q^{64} +(6.74077 - 3.02129i) q^{65} +(0.194743 + 0.250352i) q^{66} +(-4.35616 - 4.35616i) q^{67} -8.62673i q^{68} +(4.47042 - 0.618616i) q^{69} +(1.12353 - 4.19307i) q^{70} +(4.03420 + 15.0559i) q^{71} +(2.71494 + 1.52000i) q^{72} +(-0.701151 + 0.701151i) q^{73} +15.2290i q^{74} +(-1.09727 + 0.853538i) q^{75} +(14.5642 - 14.5642i) q^{76} +(0.0432127 - 0.0748466i) q^{77} +(11.2189 - 7.01609i) q^{78} +(-1.21564 - 2.10555i) q^{79} +(-5.50425 - 1.47486i) q^{80} +(7.67260 - 4.70439i) q^{81} +(-1.88338 - 1.08737i) q^{82} +(0.700439 + 0.187682i) q^{83} +(0.534563 - 4.27867i) q^{84} +(-6.85755 - 1.83748i) q^{85} +(15.0309 - 4.02752i) q^{86} +(-14.5264 - 5.90491i) q^{87} +(0.0776280 + 0.0448185i) q^{88} +(-2.28784 + 8.53834i) q^{89} +(9.08615 - 9.32950i) q^{90} +(-2.92221 - 2.11203i) q^{91} +(5.61757 - 3.24330i) q^{92} +(1.01577 - 0.428632i) q^{93} +17.5589 q^{94} +(-8.47519 - 14.6795i) q^{95} +(-13.6940 - 1.71088i) q^{96} +(1.72304 + 1.72304i) q^{97} +(-2.04664 + 0.548397i) q^{98} +(0.222807 - 0.132594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q - 12 q^{6} + 36 q^{8}+O(q^{10}) \) 336 * q - 12 * q^6 + 36 * q^8	\( 336 q - 12 q^{6} + 36 q^{8} - 12 q^{11} + 4 q^{15} + 168 q^{16} - 4 q^{18} - 4 q^{21} + 8 q^{24} - 96 q^{26} + 24 q^{27} - 120 q^{30} - 72 q^{32} + 36 q^{33} + 72 q^{38} + 8 q^{39} - 48 q^{41} - 76 q^{45} + 24 q^{48} - 24 q^{50} - 36 q^{52} + 72 q^{54} + 32 q^{57} + 36 q^{58} - 72 q^{59} + 4 q^{60} + 36 q^{62} - 8 q^{63} - 72 q^{65} - 20 q^{66} - 48 q^{71} - 176 q^{72} - 60 q^{75} - 124 q^{78} - 12 q^{79} - 96 q^{80} - 20 q^{81} - 156 q^{83} - 12 q^{84} - 108 q^{85} - 24 q^{87} + 60 q^{89} - 72 q^{92} + 20 q^{93} + 96 q^{94} + 88 q^{96} - 96 q^{97} + 108 q^{99}+O(q^{100}) \) 336 * q - 12 * q^6 + 36 * q^8 - 12 * q^11 + 4 * q^15 + 168 * q^16 - 4 * q^18 - 4 * q^21 + 8 * q^24 - 96 * q^26 + 24 * q^27 - 120 * q^30 - 72 * q^32 + 36 * q^33 + 72 * q^38 + 8 * q^39 - 48 * q^41 - 76 * q^45 + 24 * q^48 - 24 * q^50 - 36 * q^52 + 72 * q^54 + 32 * q^57 + 36 * q^58 - 72 * q^59 + 4 * q^60 + 36 * q^62 - 8 * q^63 - 72 * q^65 - 20 * q^66 - 48 * q^71 - 176 * q^72 - 60 * q^75 - 124 * q^78 - 12 * q^79 - 96 * q^80 - 20 * q^81 - 156 * q^83 - 12 * q^84 - 108 * q^85 - 24 * q^87 + 60 * q^89 - 72 * q^92 + 20 * q^93 + 96 * q^94 + 88 * q^96 - 96 * q^97 + 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more