LMFDB - Embedded newform 819.2.fy.a.50.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(50,819)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("819.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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			50.20
Character	$\chi$	$=$	819.50
Dual form			819.2.fy.a.344.20

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.445095 - 1.66112i) q^{2} +(-0.117775 - 1.72804i) q^{3} +(-0.829146 + 0.478708i) q^{4} +(0.109473 + 0.408558i) q^{5} +(-2.81806 + 0.964781i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.26780 - 1.26780i) q^{8} +(-2.97226 + 0.407041i) q^{9} +O(q^{10})$	\(q+(-0.445095 - 1.66112i) q^{2} +(-0.117775 - 1.72804i) q^{3} +(-0.829146 + 0.478708i) q^{4} +(0.109473 + 0.408558i) q^{5} +(-2.81806 + 0.964781i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.26780 - 1.26780i) q^{8} +(-2.97226 + 0.407041i) q^{9} +(0.629936 - 0.363694i) q^{10} +(-1.76817 + 0.473779i) q^{11} +(0.924880 + 1.37642i) q^{12} +(-2.15901 - 2.88768i) q^{13} +(1.48932 + 0.859857i) q^{14} +(0.693112 - 0.237291i) q^{15} +(-2.49909 + 4.32856i) q^{16} +(-2.15452 + 3.73173i) q^{17} +(1.99908 + 4.75609i) q^{18} +(4.53676 - 1.21562i) q^{19} +(-0.286349 - 0.286349i) q^{20} +(1.30519 + 1.13863i) q^{21} +(1.57400 + 2.72625i) q^{22} -4.30244 q^{23} +(-2.04150 + 2.34014i) q^{24} +(4.17519 - 2.41055i) q^{25} +(-3.83580 + 4.87166i) q^{26} +(1.05344 + 5.08825i) q^{27} +(0.247797 - 0.924793i) q^{28} +(-1.13458 - 0.655051i) q^{29} +(-0.702669 - 1.04572i) q^{30} +(-4.95087 + 1.32658i) q^{31} +(4.83886 + 1.29657i) q^{32} +(1.02696 + 2.99967i) q^{33} +(7.15780 + 1.91793i) q^{34} +(-0.366303 - 0.211485i) q^{35} +(2.26958 - 1.76034i) q^{36} +(-3.74125 - 1.00247i) q^{37} +(-4.03858 - 6.99502i) q^{38} +(-4.73575 + 4.07096i) q^{39} +(0.379181 - 0.656761i) q^{40} +(-8.27380 + 8.27380i) q^{41} +(1.31046 - 2.67487i) q^{42} +3.63005i q^{43} +(1.23927 - 1.23927i) q^{44} +(-0.491681 - 1.16978i) q^{45} +(1.91499 + 7.14685i) q^{46} +(0.633089 - 2.36272i) q^{47} +(7.77426 + 3.80874i) q^{48} -1.00000i q^{49} +(-5.86256 - 5.86256i) q^{50} +(6.70233 + 3.28359i) q^{51} +(3.17249 + 1.36077i) q^{52} -4.21863i q^{53} +(7.98329 - 4.01464i) q^{54} +(-0.387132 - 0.670532i) q^{55} +1.79295 q^{56} +(-2.63496 - 7.69655i) q^{57} +(-0.583119 + 2.17623i) q^{58} +(1.42549 - 5.32001i) q^{59} +(-0.461098 + 0.528547i) q^{60} +1.27059 q^{61} +(4.40721 + 7.63352i) q^{62} +(1.81388 - 2.38953i) q^{63} +1.38137i q^{64} +(0.943430 - 1.19820i) q^{65} +(4.52570 - 3.04103i) q^{66} +(1.39844 + 1.39844i) q^{67} -4.12553i q^{68} +(0.506721 + 7.43479i) q^{69} +(-0.188262 + 0.702602i) q^{70} +(0.366964 + 1.36953i) q^{71} +(4.28429 + 3.25219i) q^{72} +(11.9975 - 11.9975i) q^{73} +6.66085i q^{74} +(-4.65726 - 6.93100i) q^{75} +(-3.17971 + 3.17971i) q^{76} +(0.915271 - 1.58530i) q^{77} +(8.87019 + 6.05466i) q^{78} +(0.664649 + 1.15121i) q^{79} +(-2.04205 - 0.547165i) q^{80} +(8.66863 - 2.41966i) q^{81} +(17.4264 + 10.0611i) q^{82} +(-16.7010 - 4.47501i) q^{83} +(-1.62726 - 0.319287i) q^{84} +(-1.76049 - 0.471721i) q^{85} +(6.02994 - 1.61572i) q^{86} +(-0.998329 + 2.03775i) q^{87} +(2.84235 + 1.64103i) q^{88} +(4.25797 - 15.8910i) q^{89} +(-1.72429 + 1.33740i) q^{90} +(3.56855 + 0.515244i) q^{91} +(3.56735 - 2.05961i) q^{92} +(2.87548 + 8.39907i) q^{93} -4.20654 q^{94} +(0.993304 + 1.72045i) q^{95} +(1.67063 - 8.51446i) q^{96} +(-11.3675 - 11.3675i) q^{97} +(-1.66112 + 0.445095i) q^{98} +(5.06260 - 2.12791i) 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 $

$2$	−0.445095	−	1.66112i	−0.314729	−	1.17459i	−0.924241	−	0.381809i	$-0.875301\pi$
$2$	−0.445095	−	1.66112i	−0.314729	−	1.17459i	0.609512	−	0.792777i	$-0.291366\pi$
$3$	−0.117775	−	1.72804i	−0.0679976	−	0.997685i
$3$	−0.117775	−	1.72804i	−0.0679976	−	0.997685i
$4$	−0.829146	+	0.478708i	−0.414573	+	0.239354i
$5$	0.109473	+	0.408558i	0.0489577	+	0.182713i	0.986075	−	0.166303i	$-0.0531828\pi$
$5$	0.109473	+	0.408558i	0.0489577	+	0.182713i	−0.937117	+	0.349015i	$0.886516\pi$
$6$	−2.81806	+	0.964781i	−1.15047	+	0.393870i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.26780	−	1.26780i	−0.448237	−	0.448237i
$9$	−2.97226	+	0.407041i	−0.990753	+	0.135680i
$10$	0.629936	−	0.363694i	0.199203	−	0.115010i
$11$	−1.76817	+	0.473779i	−0.533122	+	0.142850i	−0.515330	−	0.856992i	$-0.672331\pi$
$11$	−1.76817	+	0.473779i	−0.533122	+	0.142850i	−0.0177927	+	0.999842i	$0.505664\pi$
$12$	0.924880	+	1.37642i	0.266990	+	0.397338i
$13$	−2.15901	−	2.88768i	−0.598802	−	0.800897i
$13$	−2.15901	−	2.88768i	−0.598802	−	0.800897i
$14$	1.48932	+	0.859857i	0.398036	+	0.229806i
$15$	0.693112	−	0.237291i	0.178961	−	0.0612684i
$16$	−2.49909	+	4.32856i	−0.624773	+	1.08214i
$17$	−2.15452	+	3.73173i	−0.522547	+	0.905077i	0.477109	+	0.878844i	$0.341685\pi$
$17$	−2.15452	+	3.73173i	−0.522547	+	0.905077i	−0.999656	+	0.0262334i	$0.991649\pi$
$18$	1.99908	+	4.75609i	0.471188	+	1.12102i
$19$	4.53676	−	1.21562i	1.04080	−	0.278883i	0.302358	−	0.953194i	$-0.402226\pi$
$19$	4.53676	−	1.21562i	1.04080	−	0.278883i	0.738447	+	0.674312i	$0.235560\pi$
$20$	−0.286349	−	0.286349i	−0.0640295	−	0.0640295i
$21$	1.30519	+	1.13863i	0.284816	+	0.248470i
$22$	1.57400	+	2.72625i	0.335579	+	0.581239i
$23$	−4.30244			−0.897120			−0.448560	−	0.893753i	$-0.648063\pi$
$23$	−4.30244			−0.897120			−0.448560	+	0.893753i	$0.648063\pi$
$24$	−2.04150	+	2.34014i	−0.416720	+	0.477678i
$25$	4.17519	−	2.41055i	0.835038	−	0.482110i
$26$	−3.83580	+	4.87166i	−0.752262	+	0.955411i
$27$	1.05344	+	5.08825i	0.202735	+	0.979234i
$28$	0.247797	−	0.924793i	0.0468293	−	0.174769i
$29$	−1.13458	−	0.655051i	−0.210686	−	0.121640i	0.390944	−	0.920414i	$-0.372149\pi$
$29$	−1.13458	−	0.655051i	−0.210686	−	0.121640i	−0.601630	+	0.798775i	$0.705482\pi$
$30$	−0.702669	−	1.04572i	−0.128289	−	0.190922i
$31$	−4.95087	+	1.32658i	−0.889202	+	0.238261i	−0.674373	−	0.738391i	$-0.735586\pi$
$31$	−4.95087	+	1.32658i	−0.889202	+	0.238261i	−0.214829	+	0.976652i	$0.568919\pi$
$32$	4.83886	+	1.29657i	0.855398	+	0.229203i
$33$	1.02696	+	2.99967i	0.178770	+	0.522175i
$34$	7.15780	+	1.91793i	1.22755	+	0.328922i
$35$	−0.366303	−	0.211485i	−0.0619165	−	0.0357475i
$36$	2.26958	−	1.76034i	0.378264	−	0.293390i
$37$	−3.74125	−	1.00247i	−0.615058	−	0.164804i	−0.0621779	−	0.998065i	$-0.519805\pi$
$37$	−3.74125	−	1.00247i	−0.615058	−	0.164804i	−0.552880	+	0.833261i	$0.686471\pi$
$38$	−4.03858	−	6.99502i	−0.655144	−	1.13474i
$39$	−4.73575	+	4.07096i	−0.758326	+	0.651875i
$40$	0.379181	−	0.656761i	0.0599538	−	0.103843i
$41$	−8.27380	+	8.27380i	−1.29215	+	1.29215i	−0.358697	+	0.933454i	$0.616779\pi$
$41$	−8.27380	+	8.27380i	−1.29215	+	1.29215i	−0.933454	+	0.358697i	$0.883221\pi$
$42$	1.31046	−	2.67487i	0.202209	−	0.412741i
$43$			3.63005i			0.553578i	0.960931	+	0.276789i	$0.0892703\pi$
$43$			3.63005i			0.553578i	−0.960931	+	0.276789i	$0.910730\pi$
$44$	1.23927	−	1.23927i	0.186827	−	0.186827i
$45$	−0.491681	−	1.16978i	−0.0732955	−	0.174380i
$46$	1.91499	+	7.14685i	0.282350	+	1.05374i
$47$	0.633089	−	2.36272i	0.0923456	−	0.344638i	−0.904258	−	0.426986i	$-0.859575\pi$
$47$	0.633089	−	2.36272i	0.0923456	−	0.344638i	0.996604	+	0.0823480i	$0.0262419\pi$
$48$	7.77426	+	3.80874i	1.12212	+	0.549744i
$49$		−	1.00000i		−	0.142857i
$50$	−5.86256	−	5.86256i	−0.829091	−	0.829091i
$51$	6.70233	+	3.28359i	0.938515	+	0.459794i
$52$	3.17249	+	1.36077i	0.439945	+	0.188705i
$53$		−	4.21863i		−	0.579474i	−0.957106	−	0.289737i	$-0.906432\pi$
$53$		−	4.21863i		−	0.579474i	0.957106	−	0.289737i	$-0.0935678\pi$
$54$	7.98329	−	4.01464i	1.08639	−	0.546324i
$55$	−0.387132	−	0.670532i	−0.0522009	−	0.0904146i
$56$	1.79295			0.239593
$57$	−2.63496	−	7.69655i	−0.349010	−	1.01943i
$58$	−0.583119	+	2.17623i	−0.0765673	+	0.285753i
$59$	1.42549	−	5.32001i	0.185583	−	0.692606i	−0.808922	−	0.587916i	$-0.799948\pi$
$59$	1.42549	−	5.32001i	0.185583	−	0.692606i	0.994505	−	0.104690i	$-0.0333850\pi$
$60$	−0.461098	+	0.528547i	−0.0595275	+	0.0682352i
$61$	1.27059			0.162683			0.0813413	−	0.996686i	$-0.474080\pi$
$61$	1.27059			0.162683			0.0813413	+	0.996686i	$0.474080\pi$
$62$	4.40721	+	7.63352i	0.559716	+	0.969457i
$63$	1.81388	−	2.38953i	0.228528	−	0.301052i
$64$			1.38137i			0.172671i
$65$	0.943430	−	1.19820i	0.117018	−	0.148619i
$66$	4.52570	−	3.04103i	0.557075	−	0.374325i
$67$	1.39844	+	1.39844i	0.170847	+	0.170847i	0.787351	−	0.616505i	$-0.211452\pi$
$67$	1.39844	+	1.39844i	0.170847	+	0.170847i	−0.616505	+	0.787351i	$0.711452\pi$
$68$		−	4.12553i		−	0.500294i
$69$	0.506721	+	7.43479i	0.0610020	+	0.895044i
$70$	−0.188262	+	0.702602i	−0.0225016	+	0.0839771i
$71$	0.366964	+	1.36953i	0.0435506	+	0.162533i	0.984276	−	0.176635i	$-0.0565212\pi$
$71$	0.366964	+	1.36953i	0.0435506	+	0.162533i	−0.940726	+	0.339168i	$0.889854\pi$
$72$	4.28429	+	3.25219i	0.504909	+	0.383275i
$73$	11.9975	−	11.9975i	1.40420	−	1.40420i	0.618097	−	0.786102i	$-0.287904\pi$
$73$	11.9975	−	11.9975i	1.40420	−	1.40420i	0.786102	−	0.618097i	$-0.212096\pi$
$74$			6.66085i			0.774308i
$75$	−4.65726	−	6.93100i	−0.537774	−	0.800323i
$76$	−3.17971	+	3.17971i	−0.364738	+	0.364738i
$77$	0.915271	−	1.58530i	0.104305	−	0.180661i
$78$	8.87019	+	6.05466i	1.00435	+	0.685556i
$79$	0.664649	+	1.15121i	0.0747788	+	0.129521i	0.900990	−	0.433840i	$-0.142842\pi$
$79$	0.664649	+	1.15121i	0.0747788	+	0.129521i	−0.826211	+	0.563360i	$0.809508\pi$
$80$	−2.04205	−	0.547165i	−0.228308	−	0.0611749i
$81$	8.66863	−	2.41966i	0.963182	−	0.268852i
$82$	17.4264	+	10.0611i	1.92442	+	1.11106i
$83$	−16.7010	−	4.47501i	−1.83317	−	0.491196i	−0.834922	−	0.550369i	$-0.814487\pi$
$83$	−16.7010	−	4.47501i	−1.83317	−	0.491196i	−0.998248	+	0.0591723i	$0.981154\pi$
$84$	−1.62726	−	0.319287i	−0.177549	−	0.0348370i
$85$	−1.76049	−	0.471721i	−0.190952	−	0.0511654i
$86$	6.02994	−	1.61572i	0.650225	−	0.174227i
$87$	−0.998329	+	2.03775i	−0.107032	+	0.218470i
$88$	2.84235	+	1.64103i	0.302995	+	0.174935i
$89$	4.25797	−	15.8910i	0.451344	−	1.68444i	−0.247275	−	0.968945i	$-0.579535\pi$
$89$	4.25797	−	15.8910i	0.451344	−	1.68444i	0.698619	−	0.715494i	$-0.253798\pi$
$90$	−1.72429	+	1.33740i	−0.181757	+	0.140975i
$91$	3.56855	+	0.515244i	0.374085	+	0.0540122i
$92$	3.56735	−	2.05961i	0.371922	−	0.214729i
$93$	2.87548	+	8.39907i	0.298173	+	0.870943i
$94$	−4.20654			−0.433871
$95$	0.993304	+	1.72045i	0.101911	+	0.176515i
$96$	1.67063	−	8.51446i	0.170508	−	0.869003i
$97$	−11.3675	−	11.3675i	−1.15419	−	1.15419i	−0.985703	−	0.168489i	$-0.946111\pi$
$97$	−11.3675	−	11.3675i	−1.15419	−	1.15419i	−0.168489	−	0.985703i	$-0.553889\pi$
$98$	−1.66112	+	0.445095i	−0.167798	+	0.0449614i
$99$	5.06260	−	2.12791i	0.508811	−	0.213863i
$100$	−2.30790	+	3.99739i	−0.230790	+	0.399739i
$101$	−0.246435	+	0.426837i	−0.0245212	+	0.0424719i	−0.878026	−	0.478614i	$-0.841139\pi$
$101$	−0.246435	+	0.426837i	−0.0245212	+	0.0424719i	0.853504	+	0.521086i	$0.174473\pi$
$102$	2.47125	−	12.5949i	0.244690	−	1.24708i
$103$	−5.06020	−	2.92151i	−0.498596	−	0.287865i	0.229537	−	0.973300i	$-0.426279\pi$
$103$	−5.06020	−	2.92151i	−0.498596	−	0.287865i	−0.728134	+	0.685435i	$0.759612\pi$
$104$	−0.923805	+	6.39821i	−0.0905865	+	0.627396i
$105$	−0.322314	+	0.657894i	−0.0314546	+	0.0642039i
$106$	−7.00764	+	1.87769i	−0.680642	+	0.182377i
$107$	4.76146	−	2.74903i	0.460308	−	0.265759i	−0.251866	−	0.967762i	$-0.581044\pi$
$107$	4.76146	−	2.74903i	0.460308	−	0.265759i	0.712174	+	0.702003i	$0.247711\pi$
$108$	−3.30924	−	3.71461i	−0.318432	−	0.357439i
$109$	9.05314	+	9.05314i	0.867133	+	0.867133i	0.992154	−	0.125021i	$-0.0398997\pi$
$109$	9.05314	+	9.05314i	0.867133	+	0.867133i	−0.125021	+	0.992154i	$0.539900\pi$
$110$	−0.941522	+	0.941522i	−0.0897706	+	0.0897706i
$111$	−1.29168	+	6.58311i	−0.122600	+	0.624841i
$112$	−1.29363	−	4.82788i	−0.122236	−	0.456192i
$113$	−11.7567	+	6.78775i	−1.10598	+	0.638538i	−0.937785	−	0.347216i	$-0.887127\pi$
$113$	−11.7567	+	6.78775i	−1.10598	+	0.638538i	−0.168194	+	0.985754i	$0.553794\pi$
$114$	−11.6120	+	7.80268i	−1.08757	+	0.730787i
$115$	−0.470999	−	1.75779i	−0.0439209	−	0.163915i
$116$	1.25431			0.116460
$117$	7.59254	+	7.70411i	0.701931	+	0.712245i
$118$	−9.47163			−0.871934
$119$	−1.11526	−	4.16220i	−0.102236	−	0.381549i
$120$	−1.17957	−	0.577891i	−0.107679	−	0.0527540i
$121$	−6.62433	+	3.82456i	−0.602212	+	0.347687i
$122$	−0.565534	−	2.11060i	−0.0512010	−	0.191085i
$123$	15.2719	+	13.3230i	1.37702	+	1.20130i
$124$	3.46995	−	3.46995i	0.311611	−	0.311611i
$125$	2.93734	+	2.93734i	0.262724	+	0.262724i
$126$	−4.77663	−	1.94950i	−0.425536	−	0.173676i
$127$	−2.96335	+	1.71089i	−0.262955	+	0.151817i	−0.625682	−	0.780078i	$-0.715179\pi$
$127$	−2.96335	+	1.71089i	−0.262955	+	0.151817i	0.362727	+	0.931896i	$0.381846\pi$
$128$	11.9723	−	3.20798i	1.05821	−	0.283548i
$129$	6.27288	−	0.427531i	0.552296	−	0.0376420i
$130$	−2.41027	−	1.03383i	−0.211395	−	0.0906731i
$131$	−9.86699	−	5.69671i	−0.862083	−	0.497724i	0.00262622	−	0.999997i	$-0.499164\pi$
$131$	−9.86699	−	5.69671i	−0.862083	−	0.497724i	−0.864709	+	0.502273i	$0.832497\pi$
$132$	−2.28746	−	1.99555i	−0.199098	−	0.173690i
$133$	−2.34840	+	4.06755i	−0.203632	+	0.352701i
$134$	1.70053	−	2.94541i	0.146904	−	0.254445i
$135$	−1.96352	+	0.987417i	−0.168993	+	0.0849833i
$136$	7.46261	−	1.99960i	0.639913	−	0.171464i
$137$	−9.52343	−	9.52343i	−0.813642	−	0.813642i	0.171536	−	0.985178i	$-0.445127\pi$
$137$	−9.52343	−	9.52343i	−0.813642	−	0.813642i	−0.985178	+	0.171536i	$0.945127\pi$
$138$	12.1245	−	4.15091i	1.03211	−	0.353349i
$139$	5.15106	+	8.92190i	0.436907	+	0.756745i	0.997449	−	0.0713806i	$-0.0227405\pi$
$139$	5.15106	+	8.92190i	0.436907	+	0.756745i	−0.560542	+	0.828126i	$0.689407\pi$
$140$	0.404958			0.0342252
$141$	−4.15744	−	0.815734i	−0.350120	−	0.0686972i
$142$	2.11161	−	1.21914i	0.177203	−	0.102308i
$143$	5.18561	+	4.08300i	0.433643	+	0.341438i
$144$	5.66605	−	13.8828i	0.472171	−	1.15690i
$145$	0.143420	−	0.535252i	0.0119104	−	0.0444503i
$146$	−25.2692	−	14.5892i	−2.09130	−	1.20741i
$147$	−1.72804	+	0.117775i	−0.142526	+	0.00971395i
$148$	3.58193	−	0.959776i	0.294433	−	0.0788931i
$149$	−12.5417	−	3.36054i	−1.02746	−	0.275306i	−0.294550	−	0.955636i	$-0.595170\pi$
$149$	−12.5417	−	3.36054i	−1.02746	−	0.275306i	−0.732906	+	0.680330i	$0.761836\pi$
$150$	−9.44028	+	10.8212i	−0.770795	+	0.883548i
$151$	−10.5812	−	2.83522i	−0.861084	−	0.230727i	−0.198856	−	0.980029i	$-0.563723\pi$
$151$	−10.5812	−	2.83522i	−0.861084	−	0.230727i	−0.662229	+	0.749302i	$0.730389\pi$
$152$	−7.29290	−	4.21056i	−0.591532	−	0.341521i
$153$	4.88481	−	11.9686i	0.394913	−	0.967607i
$154$	−3.04074	−	0.814764i	−0.245030	−	0.0656556i
$155$	−1.08397	−	1.87749i	−0.0870666	−	0.150804i
$156$	1.97783	−	5.64246i	0.158353	−	0.451758i
$157$	5.58294	−	9.66994i	0.445567	−	0.771745i	−0.552524	−	0.833497i	$-0.686335\pi$
$157$	5.58294	−	9.66994i	0.445567	−	0.771745i	0.998092	+	0.0617516i	$0.0196686\pi$
$158$	1.61645	−	1.61645i	0.128598	−	0.128598i
$159$	−7.28997	+	0.496851i	−0.578133	+	0.0394028i
$160$			2.11889i			0.167513i
$161$	3.04228	−	3.04228i	0.239765	−	0.239765i
$162$	−7.87771	−	13.3226i	−0.618931	−	1.04672i
$163$	1.68239	+	6.27875i	0.131775	+	0.491789i	0.999990	−	0.00439745i	$-0.00139976\pi$
$163$	1.68239	+	6.27875i	0.131775	+	0.491789i	−0.868216	+	0.496187i	$0.834733\pi$
$164$	2.89946	−	10.8209i	0.226410	−	0.844973i
$165$	−1.11311	+	0.747953i	−0.0866558	+	0.0582280i
$166$			29.7341i			2.30781i
$167$	−11.7930	−	11.7930i	−0.912566	−	0.912566i	0.0839072	−	0.996474i	$-0.473260\pi$
$167$	−11.7930	−	11.7930i	−0.912566	−	0.912566i	−0.996474	+	0.0839072i	$0.973260\pi$
$168$	−0.211165	−	3.09829i	−0.0162917	−	0.239038i
$169$	−3.67734	+	12.4690i	−0.282873	+	0.959157i
$170$			3.13434i			0.240393i
$171$	−12.9896	+	5.45979i	−0.993341	+	0.417521i
$172$	−1.73773	−	3.00984i	−0.132501	−	0.229498i
$173$	8.03213			0.610672			0.305336	−	0.952245i	$-0.401231\pi$
$173$	8.03213			0.610672			0.305336	+	0.952245i	$0.401231\pi$
$174$	3.82929	+	0.751348i	0.290298	+	0.0569596i
$175$	−1.24779	+	4.65682i	−0.0943242	+	0.352023i
$176$	2.36804	−	8.83763i	0.178497	−	0.666161i
$177$	−9.36109	−	1.83674i	−0.703622	−	0.138058i
$178$	−28.2919			−2.12057
$179$	3.79430	+	6.57192i	0.283599	+	0.491208i	0.972269	−	0.233867i	$-0.0751382\pi$
$179$	3.79430	+	6.57192i	0.283599	+	0.491208i	−0.688669	+	0.725076i	$0.741805\pi$
$180$	0.967658	+	0.734547i	0.0721250	+	0.0547499i
$181$			1.35355i			0.100608i	0.998734	+	0.0503042i	$0.0160191\pi$
$181$			1.35355i			0.100608i	−0.998734	+	0.0503042i	$0.983981\pi$
$182$	−0.732461	−	6.15710i	−0.0542936	−	0.456395i
$183$	−0.149644	−	2.19564i	−0.0110620	−	0.162306i
$184$	5.45465	+	5.45465i	0.402122	+	0.402122i
$185$		−	1.63826i		−	0.120447i
$186$	12.6720	−	8.51489i	0.929154	−	0.624342i
$187$	2.04153	−	7.61909i	0.149291	−	0.557163i
$188$	0.606130	+	2.26211i	0.0442065	+	0.164981i
$189$	−4.34283	−	2.85304i	−0.315894	−	0.207528i
$190$	2.41576	−	2.41576i	0.175257	−	0.175257i
$191$			15.4909i			1.12089i	0.828193	+	0.560443i	$0.189369\pi$
$191$			15.4909i			1.12089i	−0.828193	+	0.560443i	$0.810631\pi$
$192$	2.38706	−	0.162691i	0.172271	−	0.0117412i
$193$	7.48212	−	7.48212i	0.538575	−	0.538575i	−0.384535	−	0.923110i	$-0.625638\pi$
$193$	7.48212	−	7.48212i	0.538575	−	0.538575i	0.923110	+	0.384535i	$0.125638\pi$
$194$	−13.8231	+	23.9423i	−0.992441	+	1.71896i
$195$	−2.18166	−	1.48917i	−0.156232	−	0.106641i
$196$	0.478708	+	0.829146i	0.0341934	+	0.0592247i
$197$	−2.67832	−	0.717655i	−0.190823	−	0.0511308i	0.162142	−	0.986767i	$-0.448160\pi$
$197$	−2.67832	−	0.717655i	−0.190823	−	0.0511308i	−0.352965	+	0.935637i	$0.614826\pi$
$198$	−5.78804	−	7.46245i	−0.411338	−	0.530333i
$199$	−19.3036	−	11.1449i	−1.36839	−	0.790043i	−0.377671	−	0.925940i	$-0.623275\pi$
$199$	−19.3036	−	11.1449i	−1.36839	−	0.790043i	−0.990723	+	0.135897i	$0.956608\pi$
$200$	−8.34943	−	2.23722i	−0.590394	−	0.158196i
$201$	2.25186	−	2.58127i	0.158834	−	0.182069i
$202$	0.818713	+	0.219373i	0.0576044	+	0.0154351i
$203$	1.26546	−	0.339079i	0.0888179	−	0.0237987i
$204$	−7.12910	+	0.485886i	−0.499137	+	0.0340188i
$205$	−4.28608	−	2.47457i	−0.299353	−	0.172832i
$206$	−2.60069	+	9.70592i	−0.181199	+	0.676244i
$207$	12.7880	−	1.75127i	0.888824	−	0.121722i
$208$	17.8950	−	2.12883i	1.24080	−	0.147608i
$209$	−7.44582	+	4.29885i	−0.515038	+	0.297357i
$210$	1.23630	+	0.242575i	0.0853127	+	0.0167393i
$211$	−9.63964			−0.663620			−0.331810	−	0.943346i	$-0.607659\pi$
$211$	−9.63964			−0.663620			−0.331810	+	0.943346i	$0.607659\pi$
$212$	2.01949	+	3.49786i	0.138699	+	0.240234i
$213$	2.32338	−	0.795426i	0.159196	−	0.0545017i
$214$	−6.68576	−	6.68576i	−0.457029	−	0.457029i
$215$	−1.48309	+	0.397392i	−0.101146	+	0.0271019i
$216$	5.11534	−	7.78646i	0.348055	−	0.529802i
$217$	2.56276	−	4.43883i	0.173971	−	0.301327i
$218$	11.0088	−	19.0678i	0.745611	−	1.29144i
$219$	−22.1452	−	19.3191i	−1.49643	−	1.30547i
$220$	0.641978	+	0.370646i	0.0432822	+	0.0249890i
$221$	15.4276	−	1.83530i	1.03778	−	0.123456i
$222$	11.5102	−	0.784483i	0.772515	−	0.0526511i
$223$	−18.2542	+	4.89120i	−1.22239	+	0.327539i	−0.811613	−	0.584196i	$-0.801410\pi$
$223$	−18.2542	+	4.89120i	−1.22239	+	0.327539i	−0.410779	+	0.911735i	$0.634743\pi$
$224$	−4.33840	+	2.50478i	−0.289872	+	0.167358i
$225$	−11.4286	+	8.86425i	−0.761904	+	0.590950i
$226$	16.5081	+	16.5081i	1.09810	+	1.09810i
$227$	−1.43230	+	1.43230i	−0.0950653	+	0.0950653i	−0.753040	−	0.657975i	$-0.771413\pi$
$227$	−1.43230	+	1.43230i	−0.0950653	+	0.0950653i	0.657975	+	0.753040i	$0.271413\pi$
$228$	5.86917	+	5.12019i	0.388695	+	0.339093i
$229$	−0.947542	−	3.53628i	−0.0626153	−	0.233684i	0.927525	−	0.373760i	$-0.121932\pi$
$229$	−0.947542	−	3.53628i	−0.0626153	−	0.233684i	−0.990141	+	0.140077i	$0.955265\pi$
$230$	−2.71026	+	1.56477i	−0.178709	+	0.103178i
$231$	−2.84725	−	1.39492i	−0.187335	−	0.0917788i
$232$	0.607951	+	2.26890i	0.0399139	+	0.148961i
$233$	22.5692			1.47856			0.739280	−	0.673398i	$-0.235166\pi$
$233$	22.5692			1.47856			0.739280	+	0.673398i	$0.235166\pi$
$234$	9.41802	−	16.0412i	0.615675	−	1.04864i
$235$	1.03461			0.0674908
$236$	1.36479	+	5.09346i	0.0888402	+	0.331556i
$237$	1.91105	−	1.28412i	0.124136	−	0.0834128i
$238$	−6.41751	+	3.70515i	−0.415985	+	0.240169i
$239$	−2.00007	−	7.46437i	−0.129374	−	0.482830i	0.870584	−	0.492020i	$-0.163741\pi$
$239$	−2.00007	−	7.46437i	−0.129374	−	0.482830i	−0.999958	+	0.00919006i	$0.997075\pi$
$240$	−0.705021	+	3.59319i	−0.0455089	+	0.231939i
$241$	8.41246	−	8.41246i	0.541894	−	0.541894i	−0.382190	−	0.924084i	$-0.624830\pi$
$241$	8.41246	−	8.41246i	0.541894	−	0.541894i	0.924084	+	0.382190i	$0.124830\pi$
$242$	9.30149	+	9.30149i	0.597923	+	0.597923i
$243$	−5.20223	−	14.6948i	−0.333723	−	0.942671i
$244$	−1.05351	+	0.608242i	−0.0674439	+	0.0389387i
$245$	0.408558	−	0.109473i	0.0261018	−	0.00699396i
$246$	15.3336	−	31.2985i	0.977637	−	1.99552i
$247$	−13.3052	−	10.4762i	−0.846592	−	0.666582i
$248$	7.95858	+	4.59489i	0.505370	+	0.291776i
$249$	−5.76605	+	29.3870i	−0.365408	+	1.86233i
$250$	3.57187	−	6.18666i	0.225905	−	0.391279i
$251$	−9.44542	+	16.3599i	−0.596189	+	1.03263i	0.397189	+	0.917737i	$0.369986\pi$
$251$	−9.44542	+	16.3599i	−0.596189	+	1.03263i	−0.993378	+	0.114893i	$0.963347\pi$
$252$	−0.360089	+	2.84959i	−0.0226835	+	0.179507i
$253$	7.60743	−	2.03840i	0.478275	−	0.128153i
$254$	4.16096	+	4.16096i	0.261082	+	0.261082i
$255$	−0.607812	+	3.09775i	−0.0380627	+	0.193989i
$256$	−9.27628	−	16.0670i	−0.579767	−	1.00419i
$257$	18.1255			1.13064			0.565318	−	0.824873i	$-0.308754\pi$
$257$	18.1255			1.13064			0.565318	+	0.824873i	$0.308754\pi$
$258$	−3.50220	−	10.2297i	−0.218038	−	0.636873i
$259$	3.35431	−	1.93661i	0.208427	−	0.120335i
$260$	−0.208652	+	1.44511i	−0.0129401	+	0.0896221i
$261$	3.63890	+	1.48516i	0.225242	+	0.0919290i
$262$	−5.07115	+	18.9258i	−0.313297	+	1.16924i
$263$	15.1635	+	8.75463i	0.935019	+	0.539834i	0.888396	−	0.459079i	$-0.151820\pi$
$263$	15.1635	+	8.75463i	0.935019	+	0.539834i	0.0466239	+	0.998913i	$0.485154\pi$
$264$	2.50101	−	5.10497i	0.153927	−	0.314189i
$265$	1.72356	−	0.461825i	0.105877	−	0.0283697i
$266$	7.80194	+	2.09052i	0.478367	+	0.128178i
$267$	−27.9617	−	5.48639i	−1.71123	−	0.335762i
$268$	−1.82896	−	0.490068i	−0.111721	−	0.0299357i
$269$	22.2322	+	12.8357i	1.35552	+	0.782609i	0.989016	−	0.147808i	$-0.0472217\pi$
$269$	22.2322	+	12.8357i	1.35552	+	0.782609i	0.366503	+	0.930417i	$0.380555\pi$
$270$	2.51417	+	2.82214i	0.153007	+	0.171750i
$271$	−23.9498	−	6.41732i	−1.45484	−	0.389824i	−0.557139	−	0.830419i	$-0.688101\pi$
$271$	−23.9498	−	6.41732i	−1.45484	−	0.389824i	−0.897706	+	0.440595i	$0.854768\pi$
$272$	−10.7687	−	18.6519i	−0.652947	−	1.13094i
$273$	0.470076	−	6.22728i	0.0284503	−	0.376892i
$274$	−11.5807	+	20.0584i	−0.699615	+	1.21177i
$275$	−6.24037	+	6.24037i	−0.376308	+	0.376308i
$276$	−3.97924	−	5.92196i	−0.239522	−	0.356460i
$277$		−	26.1013i		−	1.56827i	−0.620588	−	0.784137i	$-0.713106\pi$
$277$		−	26.1013i		−	1.56827i	0.620588	−	0.784137i	$-0.286894\pi$
$278$	12.5276	−	12.5276i	0.751355	−	0.751355i
$279$	14.1753	−	5.95815i	0.848652	−	0.356705i
$280$	0.196279	+	0.732522i	0.0117299	+	0.0437766i
$281$	−2.50890	+	9.36336i	−0.149669	+	0.558571i	0.849834	+	0.527050i	$0.176702\pi$
$281$	−2.50890	+	9.36336i	−0.149669	+	0.558571i	−0.999503	+	0.0315213i	$0.989965\pi$
$282$	0.495426	+	7.26907i	0.0295022	+	0.432867i
$283$			1.22611i			0.0728845i	0.999336	+	0.0364423i	$0.0116025\pi$
$283$			1.22611i			0.0728845i	−0.999336	+	0.0364423i	$0.988398\pi$
$284$	−0.959871	−	0.959871i	−0.0569579	−	0.0569579i
$285$	2.85603	−	1.91910i	0.169176	−	0.113678i
$286$	4.47425	−	10.4312i	0.264568	−	0.616811i
$287$		−	11.7009i		−	0.690684i
$288$	−14.9101	−	1.88412i	−0.878586	−	0.111023i
$289$	−0.783873	−	1.35771i	−0.0461102	−	0.0798652i
$290$	−0.952951			−0.0559592
$291$	−18.3047	+	20.9823i	−1.07304	+	1.23000i
$292$	−4.20438	+	15.6910i	−0.246043	+	0.918244i
$293$	4.86948	−	18.1731i	0.284478	−	1.06169i	−0.664742	−	0.747073i	$-0.731459\pi$
$293$	4.86948	−	18.1731i	0.284478	−	1.06169i	0.949220	−	0.314613i	$-0.101875\pi$
$294$	0.964781	+	2.81806i	0.0562672	+	0.164352i
$295$	2.32958			0.135634
$296$	3.47225	+	6.01411i	0.201820	+	0.349563i
$297$	−4.27337	−	8.49777i	−0.247966	−	0.493091i
$298$			22.3290i			1.29348i
$299$	9.28901	+	12.4240i	0.537197	+	0.718501i
$300$	7.17948	+	3.51735i	0.414507	+	0.203074i
$301$	−2.56683	−	2.56683i	−0.147950	−	0.147950i
$302$			18.8385i			1.08403i
$303$	0.766617	+	0.375578i	0.0440410	+	0.0215764i
$304$	−6.07591	+	22.6756i	−0.348477	+	1.30053i
$305$	0.139095	+	0.519110i	0.00796457	+	0.0297242i
$306$	−22.0555	−	2.78705i	−1.26083	−	0.159325i
$307$	12.2224	−	12.2224i	0.697569	−	0.697569i	−0.266317	−	0.963886i	$-0.585807\pi$
$307$	12.2224	−	12.2224i	0.697569	−	0.697569i	0.963886	+	0.266317i	$0.0858068\pi$
$308$			1.75259i			0.0998630i
$309$	−4.45252	+	9.08832i	−0.253295	+	0.517016i
$310$	−2.63626	+	2.63626i	−0.149730	+	0.149730i
$311$	7.51423	−	13.0150i	0.426093	−	0.738015i	−0.570429	−	0.821347i	$-0.693223\pi$
$311$	7.51423	−	13.0150i	0.426093	−	0.738015i	0.996522	+	0.0833324i	$0.0265563\pi$
$312$	11.1652	+	0.842822i	0.632104	+	0.0477154i
$313$	5.45090	+	9.44123i	0.308103	+	0.533650i	0.977947	−	0.208852i	$-0.0669725\pi$
$313$	5.45090	+	9.44123i	0.308103	+	0.533650i	−0.669844	+	0.742501i	$0.733639\pi$
$314$	−18.5478	−	4.96988i	−1.04671	−	0.280466i
$315$	1.17483	+	0.479488i	0.0661942	+	0.0270161i
$316$	−1.10218	−	0.636345i	−0.0620026	−	0.0357972i
$317$	−5.87956	−	1.57542i	−0.330229	−	0.0884845i	0.0898952	−	0.995951i	$-0.471347\pi$
$317$	−5.87956	−	1.57542i	−0.330229	−	0.0884845i	−0.420124	+	0.907467i	$0.638013\pi$
$318$	4.07006	+	11.8883i	0.228237	+	0.666665i
$319$	2.31648	+	0.620698i	0.129698	+	0.0347524i
$320$	−0.564368	+	0.151222i	−0.0315492	+	0.00845357i
$321$	−5.31122	−	7.90424i	−0.296444	−	0.441171i
$322$	−6.40769	−	3.69948i	−0.357086	−	0.206164i
$323$	−5.23815	+	19.5491i	−0.291459	+	1.08774i
$324$	−6.02925	+	6.15600i	−0.334959	+	0.342000i
$325$	−15.9752	−	6.85220i	−0.886143	−	0.380092i
$326$	9.68091	−	5.58927i	0.536176	−	0.309561i
$327$	14.5780	−	16.7104i	0.806163	−	0.924089i
$328$	20.9791			1.15838
$329$	1.22303	+	2.11836i	0.0674281	+	0.116789i
$330$	1.73788	+	1.51610i	0.0956670	+	0.0834586i
$331$	9.25600	+	9.25600i	0.508756	+	0.508756i	0.914144	−	0.405389i	$-0.132864\pi$
$331$	9.25600	+	9.25600i	0.508756	+	0.508756i	−0.405389	+	0.914144i	$0.632864\pi$
$332$	15.9898	−	4.28445i	0.877553	−	0.235140i
$333$	11.5280	+	1.45674i	0.631731	+	0.0798289i
$334$	−14.3405	+	24.8385i	−0.784676	+	1.35910i
$335$	−0.418253	+	0.724435i	−0.0228516	+	0.0395801i
$336$	−8.19042	+	2.80404i	−0.446824	+	0.152973i
$337$	26.4625	+	15.2782i	1.44151	+	0.832254i	0.997950	−	0.0639929i	$-0.0203835\pi$
$337$	26.4625	+	15.2782i	1.44151	+	0.832254i	0.443556	+	0.896247i	$0.353717\pi$
$338$	22.3493	+	0.558588i	1.21564	+	0.0303832i
$339$	13.1142	+	19.5167i	0.712264	+	1.06000i
$340$	1.68552	−	0.451633i	0.0914101	−	0.0244933i
$341$	8.12546	−	4.69124i	0.440018	−	0.254045i
$342$	14.8510	+	19.1471i	0.803048	+	1.03536i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	4.60220	−	4.60220i	0.248134	−	0.248134i
$345$	−2.98207	+	1.02093i	−0.160549	+	0.0549651i
$346$	−3.57506	−	13.3423i	−0.192196	−	0.717287i
$347$	−14.5388	+	8.39400i	−0.780485	+	0.450613i	−0.836602	−	0.547811i	$-0.815461\pi$
$347$	−14.5388	+	8.39400i	−0.780485	+	0.450613i	0.0561169	+	0.998424i	$0.482128\pi$
$348$	−0.147727	−	2.16750i	−0.00791900	−	0.116190i
$349$	−7.65571	−	28.5715i	−0.409801	−	1.52940i	−0.795026	−	0.606575i	$-0.792543\pi$
$349$	−7.65571	−	28.5715i	−0.409801	−	1.52940i	0.385226	−	0.922822i	$-0.374124\pi$
$350$	8.29091			0.443168
$351$	12.4188	−	14.0276i	0.662867	−	0.748737i
$352$	−9.17020			−0.488773
$353$	−1.93915	−	7.23700i	−0.103210	−	0.385187i	0.894926	−	0.446215i	$-0.147228\pi$
$353$	−1.93915	−	7.23700i	−0.103210	−	0.385187i	−0.998136	+	0.0610289i	$0.980562\pi$
$354$	1.11552	+	16.3674i	0.0592895	+	0.869916i
$355$	−0.519359	+	0.299852i	−0.0275647	+	0.0159145i
$356$	4.07665	+	15.2143i	0.216062	+	0.806354i
$357$	−7.06111	+	2.41742i	−0.373714	+	0.127943i
$358$	9.22790	−	9.22790i	0.487709	−	0.487709i
$359$	−0.948751	−	0.948751i	−0.0500732	−	0.0500732i	0.681627	−	0.731700i	$-0.261273\pi$
$359$	−0.948751	−	0.948751i	−0.0500732	−	0.0500732i	−0.731700	+	0.681627i	$0.761273\pi$
$360$	−0.859696	+	2.10641i	−0.0453100	+	0.111017i
$361$	2.65001	−	1.52998i	0.139474	−	0.0805253i
$362$	2.24840	−	0.602456i	0.118173	−	0.0316644i
$363$	7.38918	+	10.9967i	0.387831	+	0.577176i
$364$	−3.20550	+	1.28108i	−0.168014	+	0.0671468i
$365$	6.21506	+	3.58827i	0.325311	+	0.187818i
$366$	−3.58060	+	1.22584i	−0.187161	+	0.0640758i
$367$	7.60971	−	13.1804i	0.397224	−	0.688012i	−0.596159	−	0.802867i	$-0.703307\pi$
$367$	7.60971	−	13.1804i	0.397224	−	0.688012i	0.993382	+	0.114855i	$0.0366404\pi$
$368$	10.7522	−	18.6233i	0.560497	−	0.970809i
$369$	21.2241	−	27.9597i	1.10488	−	1.45552i
$370$	−2.72134	+	0.729181i	−0.141476	+	0.0379083i
$371$	2.98302	+	2.98302i	0.154871	+	0.154871i
$372$	−6.40490	−	5.58755i	−0.332078	−	0.289701i
$373$	−16.5758	−	28.7101i	−0.858262	−	1.48655i	−0.873586	−	0.486671i	$-0.838211\pi$
$373$	−16.5758	−	28.7101i	−0.858262	−	1.48655i	0.0153238	−	0.999883i	$-0.495122\pi$
$374$	−13.5649			−0.701422
$375$	4.72991	−	5.42180i	0.244251	−	0.279980i
$376$	−3.79810	+	2.19284i	−0.195872	+	0.113087i
$377$	0.557999	+	4.69056i	0.0287384	+	0.241576i
$378$	−2.80625	+	8.48382i	−0.144338	+	0.436360i
$379$	−3.37802	+	12.6069i	−0.173517	+	0.647575i	0.823282	+	0.567632i	$0.192140\pi$
$379$	−3.37802	+	12.6069i	−0.173517	+	0.647575i	−0.996799	+	0.0799430i	$0.974526\pi$
$380$	−1.64719	−	0.951005i	−0.0844990	−	0.0487855i
$381$	3.30550	+	4.91929i	0.169346	+	0.252023i
$382$	25.7323	−	6.89494i	1.31658	−	0.352776i
$383$	−21.5066	−	5.76266i	−1.09893	−	0.294458i	−0.336603	−	0.941647i	$-0.609278\pi$
$383$	−21.5066	−	5.76266i	−1.09893	−	0.294458i	−0.762330	+	0.647188i	$0.775945\pi$
$384$	−6.95356	−	20.3109i	−0.354848	−	1.03648i
$385$	0.747882	+	0.200394i	0.0381156	+	0.0102130i
$386$	−15.7589	−	9.09842i	−0.802108	−	0.463097i
$387$	−1.47758	−	10.7894i	−0.0751097	−	0.548459i
$388$	14.8670	+	3.98360i	0.754758	+	0.202237i
$389$	2.80564	+	4.85951i	0.142252	+	0.246387i	0.928344	−	0.371722i	$-0.121232\pi$
$389$	2.80564	+	4.85951i	0.142252	+	0.246387i	−0.786093	+	0.618109i	$0.787899\pi$
$390$	−1.50264	+	4.28681i	−0.0760889	+	0.217071i
$391$	9.26967	−	16.0555i	0.468787	−	0.811963i
$392$	−1.26780	+	1.26780i	−0.0640338	+	0.0640338i
$393$	−8.68207	+	17.7215i	−0.437952	+	0.893932i
$394$			4.76843i			0.240230i
$395$	−0.397573	+	0.397573i	−0.0200041	+	0.0200041i
$396$	−3.17899	+	4.18786i	−0.159750	+	0.210448i
$397$	1.13432	+	4.23332i	0.0569297	+	0.212464i	0.988531	−	0.151017i	$-0.0482547\pi$
$397$	1.13432	+	4.23332i	0.0569297	+	0.212464i	−0.931602	+	0.363481i	$0.881588\pi$
$398$	−9.92109	+	37.0260i	−0.497300	+	1.85595i
$399$	7.30548	+	3.57908i	0.365732	+	0.179178i
$400$			24.0967i			1.20484i
$401$	15.7265	+	15.7265i	0.785342	+	0.785342i	0.980727	−	0.195385i	$-0.0625956\pi$
$401$	15.7265	+	15.7265i	0.785342	+	0.785342i	−0.195385	+	0.980727i	$0.562596\pi$
$402$	−5.29008	−	2.59170i	−0.263845	−	0.129262i
$403$	14.5197	+	11.4324i	0.723279	+	0.569489i
$404$		−	0.471881i		−	0.0234769i
$405$	1.93755	+	3.27675i	0.0962777	+	0.162823i
$406$	−1.12650	−	1.95115i	−0.0559072	−	0.0968342i
$407$	7.09011			0.351443
$408$	−4.33430	−	12.6602i	−0.214580	−	0.626773i
$409$	2.70594	−	10.0987i	0.133800	−	0.499349i	−0.866200	−	0.499698i	$-0.833444\pi$
$409$	2.70594	−	10.0987i	0.133800	−	0.499349i	1.00000		0.000348673i	$0.000110986\pi$
$410$	−2.20284	+	8.22110i	−0.108790	+	0.406011i
$411$	−15.3353	+	17.5785i	−0.756433	+	0.867084i
$412$	5.59419			0.275606
$413$	2.75384	+	4.76979i	0.135508	+	0.234706i
$414$	−8.60091	−	20.4628i	−0.422712	−	1.00569i
$415$		−	7.31320i		−	0.358991i
$416$	−6.70308	−	16.7724i	−0.328646	−	0.822333i
$417$	14.8107	−	9.95203i	0.725285	−	0.487353i
$418$	10.4550	+	10.4550i	0.511370	+	0.511370i
$419$			9.91487i			0.484373i	0.970230	+	0.242186i	$0.0778646\pi$
$419$			9.91487i			0.484373i	−0.970230	+	0.242186i	$0.922135\pi$
$420$	−0.0476941	−	0.699785i	−0.00232723	−	0.0341460i
$421$	−8.42147	+	31.4293i	−0.410437	+	1.53177i	0.383365	+	0.923597i	$0.374765\pi$
$421$	−8.42147	+	31.4293i	−0.410437	+	1.53177i	−0.793802	+	0.608176i	$0.791902\pi$
$422$	4.29055	+	16.0126i	0.208861	+	0.779479i
$423$	−0.919979	+	7.28031i	−0.0447309	+	0.353981i
$424$	−5.34840	+	5.34840i	−0.259741	+	0.259741i
$425$			20.7743i			1.00770i
$426$	−2.35542	−	3.50537i	−0.114121	−	0.169836i
$427$	−0.898444	+	0.898444i	−0.0434788	+	0.0434788i
$428$	−2.63197	+	4.55870i	−0.127221	+	0.220353i
$429$	6.44486	−	9.44183i	0.311161	−	0.455856i
$430$	1.32023	+	2.28670i	0.0636670	+	0.110274i
$431$	33.3117	+	8.92585i	1.60457	+	0.429943i	0.946419	−	0.322943i	$-0.104672\pi$
$431$	33.3117	+	8.92585i	1.60457	+	0.429943i	0.658151	+	0.752886i	$0.271339\pi$
$432$	−24.6574	−	8.15611i	−1.18633	−	0.392411i
$433$	−15.4673	−	8.93002i	−0.743309	−	0.429150i	0.0799624	−	0.996798i	$-0.474520\pi$
$433$	−15.4673	−	8.93002i	−0.743309	−	0.429150i	−0.823271	+	0.567648i	$0.807853\pi$
$434$	−8.51408	−	2.28134i	−0.408689	−	0.109508i
$435$	−0.941829	−	0.184797i	−0.0451573	−	0.00886033i
$436$	−11.8402	−	3.17257i	−0.567042	−	0.151938i
$437$	−19.5191	+	5.23014i	−0.933727	+	0.250191i
$438$	−22.2346	+	45.3845i	−1.06241	+	2.16856i
$439$	30.5329	+	17.6282i	1.45726	+	0.841347i	0.998876	−	0.0474098i	$-0.0150967\pi$
$439$	30.5329	+	17.6282i	1.45726	+	0.841347i	0.458380	+	0.888756i	$0.348430\pi$
$440$	−0.359296	+	1.34091i	−0.0171288	+	0.0639255i
$441$	0.407041	+	2.97226i	0.0193829	+	0.141536i
$442$	−9.91542	−	24.8102i	−0.471628	−	1.18010i
$443$	30.2435	−	17.4611i	1.43691	−	0.829603i	0.439280	−	0.898350i	$-0.355234\pi$
$443$	30.2435	−	17.4611i	1.43691	−	0.829603i	0.997634	+	0.0687476i	$0.0219003\pi$
$444$	−2.08040	−	6.07669i	−0.0987313	−	0.288387i
$445$	6.95851			0.329865
$446$	16.2497	+	28.1453i	0.769446	+	1.33272i
$447$	−4.33005	+	22.0684i	−0.204804	+	1.04380i
$448$	−0.976774	−	0.976774i	−0.0461482	−	0.0461482i
$449$	31.8517	−	8.53464i	1.50318	−	0.402775i	0.589014	−	0.808123i	$-0.299516\pi$
$449$	31.8517	−	8.53464i	1.50318	−	0.402775i	0.914162	+	0.405348i	$0.132850\pi$
$450$	19.8113	+	15.0387i	0.933915	+	0.708932i
$451$	10.7095	−	18.5494i	0.504291	−	0.873458i
$452$	6.49870	−	11.2561i	0.305673	−	0.529441i
$453$	−3.65318	+	18.6186i	−0.171641	+	0.874780i
$454$	3.01673	+	1.74171i	0.141582	+	0.0817425i
$455$	0.180152	+	1.51436i	0.00844564	+	0.0709944i
$456$	−6.41710	+	13.0983i	−0.300508	+	0.613386i
$457$	−7.55305	+	2.02383i	−0.353317	+	0.0946710i	−0.431112	−	0.902298i	$-0.641879\pi$
$457$	−7.55305	+	2.02383i	−0.353317	+	0.0946710i	0.0777952	+	0.996969i	$0.475212\pi$
$458$	−5.45242	+	3.14795i	−0.254775	+	0.147094i
$459$	−21.2576	−	7.03154i	−0.992221	−	0.328204i
$460$	1.23200	+	1.23200i	0.0574422	+	0.0574422i
$461$	18.6624	−	18.6624i	0.869194	−	0.869194i	−0.123189	−	0.992383i	$-0.539312\pi$
$461$	18.6624	−	18.6624i	0.869194	−	0.869194i	0.992383	+	0.123189i	$0.0393121\pi$
$462$	−1.04982	+	5.35049i	−0.0488422	+	0.248927i
$463$	5.09570	+	19.0174i	0.236817	+	0.883814i	0.977321	+	0.211762i	$0.0679202\pi$
$463$	5.09570	+	19.0174i	0.236817	+	0.883814i	−0.740504	+	0.672052i	$0.765413\pi$
$464$	5.67085	−	3.27407i	0.263263	−	0.151995i
$465$	−3.11672	+	2.09427i	−0.144534	+	0.0971194i
$466$	−10.0454	−	37.4901i	−0.465346	−	1.73670i
$467$	−30.5226			−1.41242			−0.706209	−	0.708004i	$-0.749596\pi$
$467$	−30.5226			−1.41242			−0.706209	+	0.708004i	$0.749596\pi$
$468$	−9.98335	−	2.75323i	−0.461480	−	0.127268i
$469$	−1.97770			−0.0913215
$470$	−0.460501	−	1.71861i	−0.0212413	−	0.0792738i
$471$	−17.3676	−	8.50868i	−0.800257	−	0.392059i
$472$	−8.55198	+	4.93749i	−0.393637	+	0.227266i
$473$	−1.71984	−	6.41854i	−0.0790784	−	0.295125i
$474$	−2.98368	−	2.60292i	−0.137045	−	0.119556i
$475$	16.0115	−	16.0115i	0.734660	−	0.734660i
$476$	2.91719	+	2.91719i	0.133709	+	0.133709i
$477$	1.71716	+	12.5389i	0.0786233	+	0.574115i
$478$	−11.5090	+	6.64470i	−0.526408	+	0.303922i
$479$	−18.0156	+	4.82726i	−0.823152	+	0.220563i	−0.645724	−	0.763571i	$-0.723444\pi$
$479$	−18.0156	+	4.82726i	−0.823152	+	0.220563i	−0.177428	+	0.984134i	$0.556778\pi$
$480$	3.66154	−	0.249553i	0.167126	−	0.0113905i
$481$	5.18261	+	12.9679i	0.236307	+	0.591283i
$482$	−17.7184	−	10.2297i	−0.807052	−	0.465952i
$483$	−5.61550	−	4.89889i	−0.255514	−	0.222907i
$484$	3.66169	−	6.34224i	0.166441	−	0.288284i
$485$	3.39984	−	5.88870i	0.154379	−	0.267392i
$486$	−22.0943	+	15.1821i	−1.00222	+	0.688673i
$487$	2.26846	−	0.607833i	0.102794	−	0.0275435i	−0.207055	−	0.978329i	$-0.566388\pi$
$487$	2.26846	−	0.607833i	0.102794	−	0.0275435i	0.309849	+	0.950786i	$0.399721\pi$
$488$	−1.61086	−	1.61086i	−0.0729203	−	0.0729203i
$489$	10.6518	−	3.64671i	0.481691	−	0.164910i
$490$	−0.363694	−	0.629936i	−0.0164300	−	0.0284576i
$491$	−4.57603			−0.206513			−0.103257	−	0.994655i	$-0.532926\pi$
$491$	−4.57603			−0.206513			−0.103257	+	0.994655i	$0.532926\pi$
$492$	−19.0405	−	3.73595i	−0.858412	−	0.168430i
$493$	4.88894	−	2.82263i	0.220187	−	0.127125i
$494$	−11.4800	+	26.7644i	−0.516511	+	1.20419i
$495$	1.42359	+	1.83542i	0.0639857	+	0.0824958i
$496$	6.63050	−	24.7454i	0.297718	−	1.11110i
$497$	−1.22789	−	0.708920i	−0.0550782	−	0.0317994i
$498$	51.3817	−	3.50194i	2.30247	−	0.156926i
$499$	−6.34774	+	1.70087i	−0.284164	+	0.0761415i	−0.398086	−	0.917348i	$-0.630325\pi$
$499$	−6.34774	+	1.70087i	−0.284164	+	0.0761415i	0.113922	+	0.993490i	$0.463659\pi$
$500$	−3.84162	−	1.02936i	−0.171802	−	0.0460343i
$501$	−18.9898	+	21.7676i	−0.848402	+	0.972507i
$502$	31.3799	+	8.40821i	1.40055	+	0.375277i
$503$	−7.86936	−	4.54338i	−0.350877	−	0.202579i	0.314194	−	0.949359i	$-0.398266\pi$
$503$	−7.86936	−	4.54338i	−0.350877	−	0.202579i	−0.665072	+	0.746780i	$0.731599\pi$
$504$	−5.32910	+	0.729804i	−0.237377	+	0.0325080i
$505$	−0.201366	−	0.0539557i	−0.00896065	−	0.00240100i
$506$	−6.77205	−	11.7295i	−0.301054	−	0.521441i
$507$	21.9801	+	4.88606i	0.976172	+	0.216997i
$508$	1.63803	−	2.83716i	0.0726760	−	0.125879i
$509$	−15.9947	+	15.9947i	−0.708955	+	0.708955i	−0.966315	−	0.257361i	$-0.917147\pi$
$509$	−15.9947	+	15.9947i	−0.708955	+	0.708955i	0.257361	+	0.966315i	$0.417147\pi$
$510$	5.41626	−	0.369147i	0.239836	−	0.0163461i
$511$			16.9670i			0.750576i
$512$	−5.03159	+	5.03159i	−0.222367	+	0.222367i
$513$	10.9646	+	21.8036i	0.484099	+	0.962652i
$514$	−8.06755	−	30.1085i	−0.355844	−	1.32803i
$515$	0.639651	−	2.38721i	0.0281864	−	0.105193i
$516$	−4.99647	+	3.35736i	−0.219958	+	0.147800i
$517$			4.47763i			0.196926i
$518$	−4.70993	−	4.70993i	−0.206942	−	0.206942i
$519$	−0.945987	−	13.8799i	−0.0415242	−	0.609258i
$520$	−2.71517	+	0.323002i	−0.119068	+	0.0141646i
$521$		−	3.38176i		−	0.148157i	−0.997252	−	0.0740787i	$-0.976398\pi$
$521$		−	3.38176i		−	0.148157i	0.997252	−	0.0740787i	$-0.0236016\pi$
$522$	0.847365	−	6.70567i	0.0370881	−	0.293499i
$523$	4.38025	+	7.58681i	0.191535	+	0.331748i	0.945759	−	0.324869i	$-0.105320\pi$
$523$	4.38025	+	7.58681i	0.191535	+	0.331748i	−0.754224	+	0.656617i	$0.771987\pi$
$524$	10.9082			0.476529
$525$	8.19414	+	1.60778i	0.357622	+	0.0701692i
$526$	7.79328	−	29.0849i	0.339803	−	1.26816i
$527$	5.71628	−	21.3335i	0.249005	−	0.929300i
$528$	−15.5507	−	3.05121i	−0.676757	−	0.132787i
$529$	−4.48904			−0.195176
$530$	−1.53429	−	2.65747i	−0.0666453	−	0.115433i
$531$	−2.07147	+	16.3927i	−0.0898940	+	0.711382i
$532$		−	4.49679i		−	0.194961i
$533$	41.7553	+	6.02883i	1.80862	+	0.261138i
$534$	3.33209	+	48.8896i	0.144194	+	2.11566i
$535$	1.64439	+	1.64439i	0.0710931	+	0.0710931i
$536$		−	3.54590i		−	0.153160i
$537$	10.9097	−	7.33072i	0.470787	−	0.316344i
$538$	11.4262	−	42.6433i	0.492620	−	1.83848i
$539$	0.473779	+	1.76817i	0.0204071	+	0.0761603i
$540$	1.15536	−	1.75867i	0.0497188	−	0.0756809i
$541$	28.2497	−	28.2497i	1.21455	−	1.21455i	0.245037	−	0.969514i	$-0.421200\pi$
$541$	28.2497	−	28.2497i	1.21455	−	1.21455i	0.969514	−	0.245037i	$-0.0788001\pi$
$542$			42.6397i			1.83153i
$543$	2.33899	−	0.159414i	0.100375	−	0.00684113i
$544$	−15.2638	+	15.2638i	−0.654432	+	0.654432i
$545$	−2.70766	+	4.68980i	−0.115983	+	0.200889i
$546$	−10.5535	+	1.99088i	−0.451647	+	0.0852017i
$547$	15.2866	+	26.4772i	0.653608	+	1.13208i	0.982241	+	0.187625i	$0.0600789\pi$
$547$	15.2866	+	26.4772i	0.653608	+	1.13208i	−0.328632	+	0.944458i	$0.606588\pi$
$548$	12.4553	+	3.33738i	0.532062	+	0.142566i
$549$	−3.77653	+	0.517184i	−0.161178	+	0.0220729i
$550$	13.1435	+	7.58842i	0.560442	+	0.323571i
$551$	−5.94362	−	1.59259i	−0.253207	−	0.0678465i
$552$	8.78344	−	10.0683i	0.373848	−	0.428535i
$553$	−1.28400	−	0.344047i	−0.0546013	−	0.0146304i
$554$	−43.3572	+	11.6175i	−1.84207	+	0.493582i
$555$	−2.83098	+	0.192947i	−0.120169	+	0.00819013i
$556$	−8.54196	−	4.93171i	−0.362260	−	0.209151i
$557$	−5.15327	+	19.2323i	−0.218351	+	0.814897i	0.766609	+	0.642114i	$0.221943\pi$
$557$	−5.15327	+	19.2323i	−0.218351	+	0.814897i	−0.984960	+	0.172783i	$0.944724\pi$
$558$	−16.2065	−	20.8949i	−0.686077	−	0.884550i
$559$	10.4824	−	7.83732i	0.443359	−	0.331483i
$560$	1.83085	−	1.05704i	0.0773675	−	0.0446682i
$561$	−13.4065	−	2.63051i	−0.566025	−	0.111060i
$562$	16.6703			0.703195
$563$	21.2845	+	36.8659i	0.897037	+	1.55371i	0.831264	+	0.555879i	$0.187618\pi$
$563$	21.2845	+	36.8659i	0.897037	+	1.55371i	0.0657732	+	0.997835i	$0.479049\pi$
$564$	3.83763	−	1.31384i	0.161593	−	0.0553225i
$565$	−4.06023	−	4.06023i	−0.170815	−	0.170815i
$566$	2.03671	−	0.545734i	0.0856091	−	0.0229389i
$567$	−4.41869	+	7.84061i	−0.185568	+	0.329275i
$568$	1.27106	−	2.20153i	0.0533323	−	0.0923743i
$569$	21.3130	−	36.9152i	0.893486	−	1.54756i	0.0578197	−	0.998327i	$-0.481585\pi$
$569$	21.3130	−	36.9152i	0.893486	−	1.54756i	0.835667	−	0.549237i	$-0.185082\pi$
$570$	−4.45905	−	3.89001i	−0.186769	−	0.162935i
$571$	−21.9806	−	12.6905i	−0.919858	−	0.531080i	−0.0362681	−	0.999342i	$-0.511547\pi$
$571$	−21.9806	−	12.6905i	−0.919858	−	0.531080i	−0.883590	+	0.468262i	$0.844880\pi$
$572$	−6.25419	−	0.903011i	−0.261501	−	0.0377568i
$573$	26.7690	−	1.82445i	1.11829	−	0.0762175i
$574$	−19.4366	+	5.20802i	−0.811268	+	0.217379i
$575$	−17.9635	+	10.3712i	−0.749130	+	0.432510i
$576$	−0.562274	−	4.10578i	−0.0234281	−	0.171074i
$577$	−14.5017	−	14.5017i	−0.603712	−	0.603712i	0.337584	−	0.941296i	$-0.390390\pi$
$577$	−14.5017	−	14.5017i	−0.603712	−	0.603712i	−0.941296	+	0.337584i	$0.890390\pi$
$578$	−1.90641	+	1.90641i	−0.0792963	+	0.0792963i
$579$	−13.8106	−	12.0482i	−0.573950	−	0.500707i
$580$	0.137313	+	0.512459i	0.00570161	+	0.0212787i
$581$	14.9737	−	8.64506i	0.621213	−	0.358657i
$582$	43.0013	+	21.0671i	1.78246	+	0.873259i
$583$	1.99870	+	7.45925i	0.0827777	+	0.308930i
$584$	−30.4209			−1.25883
$585$	−2.31640	+	3.94538i	−0.0957713	+	0.163121i
$586$	−32.3551			−1.33658
$587$	−3.03392	−	11.3228i	−0.125223	−	0.467340i	0.874624	−	0.484802i	$-0.161108\pi$
$587$	−3.03392	−	11.3228i	−0.125223	−	0.467340i	−0.999848	+	0.0174614i	$0.994442\pi$
$588$	1.37642	−	0.924880i	0.0567626	−	0.0381414i
$589$	−20.8483	+	12.0368i	−0.859039	+	0.495967i
$590$	−1.03689	−	3.86971i	−0.0426879	−	0.159313i
$591$	−0.924697	+	4.71278i	−0.0380369	+	0.193858i
$592$	13.6890	−	13.6890i	0.562613	−	0.562613i
$593$	19.2431	+	19.2431i	0.790220	+	0.790220i	0.981530	−	0.191310i	$-0.0612735\pi$
$593$	19.2431	+	19.2431i	0.790220	+	0.790220i	−0.191310	+	0.981530i	$0.561273\pi$
$594$	−12.2137	+	10.8809i	−0.501135	+	0.446448i
$595$	1.57841	−	0.911296i	0.0647085	−	0.0373595i
$596$	12.0076	−	3.21743i	0.491851	−	0.131791i
$597$	−16.9854	+	34.6700i	−0.695167	+	1.41895i
$598$	16.5033	−	20.9600i	0.674870	−	0.857118i
$599$	−9.94572	−	5.74216i	−0.406371	−	0.234618i	0.282858	−	0.959162i	$-0.408717\pi$
$599$	−9.94572	−	5.74216i	−0.406371	−	0.234618i	−0.689229	+	0.724543i	$0.742051\pi$
$600$	−2.88266	+	14.6917i	−0.117684	+	0.599784i
$601$	−8.98033	+	15.5544i	−0.366315	+	0.634477i	−0.988986	−	0.148007i	$-0.952714\pi$
$601$	−8.98033	+	15.5544i	−0.366315	+	0.634477i	0.622671	+	0.782484i	$0.286047\pi$
$602$	−3.12133	+	5.40629i	−0.127216	+	0.220344i
$603$	−4.72575	−	3.58731i	−0.192448	−	0.146086i
$604$	10.1306	−	2.71448i	0.412208	−	0.110451i
$605$	−2.28774	−	2.28774i	−0.0930097	−	0.0930097i
$606$	0.282662	−	1.44061i	0.0114824	−	0.0585207i
$607$	−5.22293	−	9.04638i	−0.211992	−	0.367181i	0.740346	−	0.672226i	$-0.234662\pi$
$607$	−5.22293	−	9.04638i	−0.211992	−	0.367181i	−0.952338	+	0.305045i	$0.901328\pi$
$608$	23.5289			0.954223
$609$	−0.734983	−	2.14683i	−0.0297830	−	0.0869941i
$610$	0.800392	−	0.462106i	0.0324069	−	0.0187101i
$611$	−8.18962	+	3.27298i	−0.331317	+	0.132411i
$612$	1.67926	+	12.2622i	0.0678802	+	0.495668i
$613$	−2.40610	+	8.97968i	−0.0971814	+	0.362686i	−0.997341	−	0.0728740i	$-0.976783\pi$
$613$	−2.40610	+	8.97968i	−0.0971814	+	0.362686i	0.900160	+	0.435560i	$0.143450\pi$
$614$	−25.7429	−	14.8627i	−1.03890	−	0.599809i
$615$	−3.77137	+	7.69797i	−0.152076	+	0.310412i
$616$	−3.17023	+	0.849460i	−0.127732	+	0.0342257i
$617$	−34.4040	−	9.21854i	−1.38505	−	0.371124i	−0.512100	−	0.858926i	$-0.671132\pi$
$617$	−34.4040	−	9.21854i	−1.38505	−	0.371124i	−0.872955	+	0.487801i	$0.837799\pi$
$618$	17.0785	+	3.35099i	0.687000	+	0.134797i
$619$	−20.0634	−	5.37597i	−0.806415	−	0.216078i	−0.168017	−	0.985784i	$-0.553736\pi$
$619$	−20.0634	−	5.37597i	−0.806415	−	0.216078i	−0.638399	+	0.769706i	$0.720403\pi$
$620$	1.79754	+	1.03781i	0.0721910	+	0.0416795i
$621$	−4.53237	−	21.8919i	−0.181878	−	0.878490i
$622$	−24.9640	−	6.68909i	−1.00097	−	0.268208i
$623$	8.22577	+	14.2474i	0.329558	+	0.570812i
$624$	−5.78630	−	30.6727i	−0.231637	−	1.22789i
$625$	11.1742	−	19.3543i	0.446969	−	0.774173i
$626$	13.2568	−	13.2568i	0.529849	−	0.529849i
$627$	8.30552	+	12.3604i	0.331691	+	0.493626i
$628$			10.6904i			0.426593i
$629$	11.8015	−	11.8015i	0.470557	−	0.470557i
$630$	0.273574	−	2.16495i	0.0108995	−	0.0862535i
$631$	−10.7169	−	39.9959i	−0.426631	−	1.59221i	−0.760335	−	0.649532i	$-0.774965\pi$
$631$	−10.7169	−	39.9959i	−0.426631	−	1.59221i	0.333703	−	0.942678i	$-0.391702\pi$
$632$	0.616859	−	2.30215i	0.0245373	−	0.0915745i
$633$	1.13531	+	16.6577i	0.0451246	+	0.662084i
$634$			10.4678i			0.415731i
$635$	−1.02340	−	1.02340i	−0.0406126	−	0.0406126i
$636$	5.80661	−	3.90173i	0.230247	−	0.154714i
$637$	−2.88768	+	2.15901i	−0.114414	+	0.0855431i
$638$		−	4.12421i		−	0.163279i
$639$	−1.64817	−	3.92122i	−0.0652005	−	0.155121i
$640$	2.62129	+	4.54020i	0.103616	+	0.179467i
$641$	0.379502			0.0149894			0.00749471	−	0.999972i	$-0.497614\pi$
$641$	0.379502			0.0149894			0.00749471	+	0.999972i	$0.497614\pi$
$642$	−10.7659	+	12.3407i	−0.424894	+	0.487048i
$643$	11.7066	−	43.6895i	0.461662	−	1.72294i	−0.206065	−	0.978538i	$-0.566066\pi$
$643$	11.7066	−	43.6895i	0.461662	−	1.72294i	0.667727	−	0.744406i	$-0.267267\pi$
$644$	−1.06613	+	3.97886i	−0.0420115	+	0.156789i
$645$	0.861380	+	2.51603i	0.0339168	+	0.0990686i
$646$	34.8047			1.36937
$647$	−19.2008	−	33.2568i	−0.754863	−	1.30746i	−0.945443	−	0.325789i	$-0.894370\pi$
$647$	−19.2008	−	33.2568i	−0.754863	−	1.30746i	0.190580	−	0.981672i	$-0.438963\pi$
$648$	−14.0578	−	7.92247i	−0.552242	−	0.311224i
$649$			10.0820i			0.395754i
$650$	−4.27184	+	29.5865i	−0.167555	+	1.16048i
$651$	−7.97231	−	3.90577i	−0.312460	−	0.153079i
$652$	−4.40063	−	4.40063i	−0.172342	−	0.172342i
$653$		−	8.83056i		−	0.345567i	−0.984960	−	0.172783i	$-0.944724\pi$
$653$		−	8.83056i		−	0.345567i	0.984960	−	0.172783i	$-0.0552760\pi$
$654$	−34.2466	−	16.7780i	−1.33915	−	0.656070i
$655$	1.24727	−	4.65487i	0.0487348	−	0.181881i
$656$	−15.1366	−	56.4906i	−0.590986	−	2.20559i
$657$	−30.7761	+	40.5431i	−1.20069	+	1.58174i
$658$	2.97447	−	2.97447i	0.115957	−	0.115957i
$659$		−	15.6896i		−	0.611180i	−0.952163	−	0.305590i	$-0.901146\pi$
$659$		−	15.6896i		−	0.611180i	0.952163	−	0.305590i	$-0.0988537\pi$
$660$	0.564883	−	1.15302i	0.0219881	−	0.0448812i
$661$	−13.3679	+	13.3679i	−0.519950	+	0.519950i	−0.917556	−	0.397607i	$-0.869841\pi$
$661$	−13.3679	+	13.3679i	−0.519950	+	0.519950i	0.397607	+	0.917556i	$0.369841\pi$
$662$	11.2555	−	19.4951i	0.437457	−	0.757698i
$663$	−4.98848	−	26.4435i	−0.193736	−	1.02698i
$664$	15.5001	+	26.8470i	0.601522	+	1.04187i
$665$	−1.91892	−	0.514172i	−0.0744124	−	0.0199387i
$666$	−2.71124	−	19.7978i	−0.105058	−	0.767147i
$667$	4.88146	+	2.81831i	0.189011	+	0.109126i
$668$	15.4235	+	4.13271i	0.596752	+	0.159899i
$669$	10.6021	+	30.9680i	0.409901	+	1.19729i
$670$	1.38953	+	0.372324i	0.0536824	+	0.0143841i
$671$	−2.24662	+	0.601980i	−0.0867297	+	0.0232392i
$672$	4.83932	+	7.20194i	0.186681	+	0.277821i
$673$	25.6390	+	14.8027i	0.988311	+	0.570601i	0.904769	−	0.425903i	$-0.140043\pi$
$673$	25.6390	+	14.8027i	0.988311	+	0.570601i	0.0835417	+	0.996504i	$0.473377\pi$
$674$	13.6004	−	50.7576i	0.523870	−	1.95511i
$675$	16.6638	+	18.7050i	0.641390	+	0.719957i
$676$	−2.91998	−	12.0990i	−0.112307	−	0.465348i
$677$	24.0346	−	13.8764i	0.923725	−	0.533313i	0.0389034	−	0.999243i	$-0.487614\pi$
$677$	24.0346	−	13.8764i	0.923725	−	0.533313i	0.884822	+	0.465930i	$0.154280\pi$
$678$	26.5824	−	30.4709i	1.02089	−	1.17023i
$679$	16.0760			0.616942
$680$	1.63390	+	2.83001i	0.0626574	+	0.108526i
$681$	2.64377	+	2.30639i	0.101309	+	0.0883810i
$682$	−11.4093	−	11.4093i	−0.436884	−	0.436884i
$683$	12.7334	−	3.41190i	0.487230	−	0.130553i	−0.00683732	−	0.999977i	$-0.502176\pi$
$683$	12.7334	−	3.41190i	0.487230	−	0.130553i	0.494067	+	0.869424i	$0.335510\pi$
$684$	8.15665	−	10.7452i	0.311877	−	0.410853i
$685$	2.84832	−	4.93343i	0.108829	−	0.188497i
$686$	0.859857	−	1.48932i	0.0328295	−	0.0568623i
$687$	−5.99923	+	2.05388i	−0.228885	+	0.0783603i
$688$	−15.7129	−	9.07184i	−0.599048	−	0.345861i
$689$	−12.1820	+	9.10807i	−0.464099	+	0.346990i
$690$	3.02319	+	4.49915i	0.115091	+	0.171280i
$691$	43.7001	−	11.7094i	1.66243	−	0.445447i	0.699375	−	0.714755i	$-0.253462\pi$
$691$	43.7001	−	11.7094i	1.66243	−	0.445447i	0.963054	+	0.269308i	$0.0867949\pi$
$692$	−6.65981	+	3.84504i	−0.253168	+	0.146167i
$693$	−2.07514	+	5.08446i	−0.0788280	+	0.193143i
$694$	20.4146	+	20.4146i	0.774926	+	0.774926i
$695$	−3.08121	+	3.08121i	−0.116877	+	0.116877i
$696$	3.84916	−	1.31779i	0.145902	−	0.0499505i
$697$	−13.0496	−	48.7016i	−0.494287	−	1.84471i
$698$	−44.0531	+	25.4340i	−1.66743	+	0.962693i
$699$	−2.65810	−	39.0006i	−0.100539	−	1.47514i
$700$	−1.19466	−	4.45851i	−0.0451537	−	0.168516i
$701$	−0.238335			−0.00900181			−0.00450090	−	0.999990i	$-0.501433\pi$
$701$	−0.238335			−0.00900181			−0.00450090	+	0.999990i	$0.501433\pi$
$702$	−28.8290	−	14.3855i	−1.08808	−	0.542945i
$703$	−18.1918			−0.686117
$704$	−0.654463	−	2.44249i	−0.0246660	−	0.0920547i
$705$	−0.121852	−	1.78786i	−0.00458921	−	0.0673346i
$706$	−11.1584	+	6.44230i	−0.419952	+	0.242459i
$707$	−0.127564	−	0.476075i	−0.00479754	−	0.0179046i
$708$	8.64098	−	2.95830i	0.324748	−	0.111180i
$709$	−20.9235	+	20.9235i	−0.785799	+	0.785799i	−0.980802	−	0.195004i	$-0.937528\pi$
$709$	−20.9235	+	20.9235i	−0.785799	+	0.785799i	0.195004	+	0.980802i	$0.437528\pi$
$710$	0.729253	+	0.729253i	0.0273684	+	0.0273684i
$711$	−2.44410	−	3.15114i	−0.0916607	−	0.118177i
$712$	−25.5449	+	14.7484i	−0.957336	+	0.552718i
$713$	21.3008	−	5.70753i	0.797721	−	0.213749i
$714$	7.15848	+	10.6533i	0.267899	+	0.398692i
$715$	−1.10046	+	2.56560i	−0.0411548	+	0.0959480i
$716$	−6.29206	−	3.63272i	−0.235145	−	0.135761i
$717$	−12.6632	+	4.33533i	−0.472915	+	0.161906i
$718$	−1.15370	+	1.99827i	−0.0430558	+	0.0745748i
$719$	18.7649	−	32.5017i	0.699812	−	1.21211i	−0.268720	−	0.963218i	$-0.586601\pi$
$719$	18.7649	−	32.5017i	0.699812	−	1.21211i	0.968531	−	0.248891i	$-0.0800661\pi$
$720$	6.29221	+	0.795118i	0.234497	+	0.0296323i
$721$	5.64392	−	1.51228i	0.210190	−	0.0563204i
$722$	−3.72098	−	3.72098i	−0.138481	−	0.138481i
$723$	−15.5279	−	13.5463i	−0.577488	−	0.503793i
$724$	−0.647953	−	1.12229i	−0.0240810	−	0.0417095i
$725$	−6.31612			−0.234575
$726$	14.9779	−	17.1689i	0.555881	−	0.637196i
$727$	−20.6713	+	11.9346i	−0.766655	+	0.442628i	−0.831680	−	0.555255i	$-0.812621\pi$
$727$	−20.6713	+	11.9346i	−0.766655	+	0.442628i	0.0650254	+	0.997884i	$0.479287\pi$
$728$	−3.87099	−	5.17745i	−0.143468	−	0.191889i
$729$	−24.7805	+	10.7204i	−0.917797	+	0.397050i
$730$	3.19424	−	11.9211i	0.118224	−	0.441218i
$731$	−13.5464	−	7.82100i	−0.501031	−	0.289270i
$732$	1.17515	+	1.74887i	0.0434346	+	0.0646400i
$733$	41.7437	−	11.1852i	1.54184	−	0.413134i	0.614978	−	0.788544i	$-0.289165\pi$
$733$	41.7437	−	11.1852i	1.54184	−	0.413134i	0.926859	+	0.375410i	$0.122498\pi$
$734$	−25.2812	−	6.77408i	−0.933147	−	0.250036i
$735$	−0.237291	−	0.693112i	−0.00875263	−	0.0255658i
$736$	−20.8189	−	5.57841i	−0.767395	−	0.205623i
$737$	−3.13523	−	1.81013i	−0.115488	−	0.0666769i
$738$	−55.8910	−	22.8110i	−2.05737	−	0.839684i
$739$	−34.1238	−	9.14344i	−1.25526	−	0.336347i	−0.430896	−	0.902402i	$-0.641802\pi$
$739$	−34.1238	−	9.14344i	−1.25526	−	0.336347i	−0.824368	+	0.566055i	$0.808469\pi$
$740$	0.784248	+	1.35836i	0.0288295	+	0.0499342i
$741$	−16.5362	+	24.2259i	−0.607473	+	0.889959i
$742$	3.62742	−	6.28288i	0.133167	−	0.230652i
$743$	−0.627756	+	0.627756i	−0.0230301	+	0.0230301i	−0.718528	−	0.695498i	$-0.755184\pi$
$743$	−0.627756	+	0.627756i	−0.0230301	+	0.0230301i	0.695498	+	0.718528i	$0.255184\pi$
$744$	7.00284	−	14.2939i	0.256736	−	0.524041i
$745$		−	5.49189i		−	0.201207i
$746$	−40.3130	+	40.3130i	−1.47596	+	1.47596i
$747$	51.4611	+	6.50290i	1.88286	+	0.237929i
$748$	1.95459	+	7.29463i	0.0714669	+	0.266718i
$749$	−1.42300	+	5.31072i	−0.0519954	+	0.194049i
$750$	−11.1115	−	5.44371i	−0.405734	−	0.198776i
$751$			5.16347i			0.188418i	0.995552	+	0.0942088i	$0.0300321\pi$
$751$			5.16347i			0.188418i	−0.995552	+	0.0942088i	$0.969968\pi$
$752$	8.64502	+	8.64502i	0.315252	+	0.315252i
$753$	29.3831	+	14.3953i	1.07078	+	0.524593i
$754$	7.54321	−	3.01465i	0.274707	−	0.109787i
$755$		−	4.63340i		−	0.168627i
$756$	4.96661	+	0.286638i	0.180634	+	0.0104249i
$757$	−18.8636	−	32.6728i	−0.685610	−	1.18751i	−0.973245	−	0.229771i	$-0.926202\pi$
$757$	−18.8636	−	32.6728i	−0.685610	−	1.18751i	0.287635	−	0.957740i	$-0.407131\pi$
$758$	22.4451			0.815244
$759$	−4.41841	−	12.9059i	−0.160378	−	0.468454i
$760$	0.921883	−	3.44051i	0.0334402	−	0.124801i
$761$	−1.38059	+	5.15242i	−0.0500463	+	0.186775i	−0.986424	−	0.164219i	$-0.947490\pi$
$761$	−1.38059	+	5.15242i	−0.0500463	+	0.186775i	0.936378	+	0.350994i	$0.114156\pi$
$762$	6.70026	−	7.68038i	0.242725	−	0.278231i
$763$	−12.8031			−0.463502
$764$	−7.41564	−	12.8443i	−0.268288	−	0.464689i
$765$	5.42463	+	0.685486i	0.196128	+	0.0247838i
$766$			38.2898i			1.38347i
$767$	−18.4401	+	7.36960i	−0.665834	+	0.266101i
$768$	−26.6719	+	17.9221i	−0.962439	+	0.646708i
$769$	37.9361	+	37.9361i	1.36801	+	1.36801i	0.863270	+	0.504742i	$0.168412\pi$
$769$	37.9361	+	37.9361i	1.36801	+	1.36801i	0.504742	+	0.863270i	$0.331588\pi$
$770$		−	1.33151i		−	0.0479844i
$771$	−2.13473	−	31.3216i	−0.0768805	−	1.12802i
$772$	−2.62202	+	9.78553i	−0.0943687	+	0.352189i
$773$	10.8391	+	40.4521i	0.389856	+	1.45496i	0.830368	+	0.557215i	$0.188130\pi$
$773$	10.8391	+	40.4521i	0.389856	+	1.45496i	−0.440512	+	0.897747i	$0.645203\pi$
$774$	−17.2649	+	7.25676i	−0.620573	+	0.260839i
$775$	−17.4730	+	17.4730i	−0.627650	+	0.627650i
$776$			28.8235i			1.03470i
$777$	−3.74161	−	5.56831i	−0.134229	−	0.199762i
$778$	6.82344	−	6.82344i	0.244632	−	0.244632i
$779$	−27.4785	+	47.5941i	−0.984518	+	1.70524i
$780$	2.52179	+	0.190361i	0.0902945	+	0.00681603i
$781$	−1.29771	−	2.24770i	−0.0464356	−	0.0804289i
$782$	−30.7960	−	8.25176i	−1.10126	−	0.295082i
$783$	2.13784	−	6.46309i	0.0764003	−	0.230972i
$784$	4.32856	+	2.49909i	0.154591	+	0.0892533i
$785$	4.56191	+	1.22236i	0.162822	+	0.0436279i
$786$	33.3018	+	6.53417i	1.18784	+	0.233066i
$787$	28.7724	+	7.70955i	1.02563	+	0.274816i	0.732145	−	0.681149i	$-0.238519\pi$
$787$	28.7724	+	7.70955i	1.02563	+	0.274816i	0.293482	+	0.955965i	$0.405186\pi$
$788$	2.56427	−	0.687094i	0.0913483	−	0.0244767i
$789$	13.3425	−	27.2342i	0.475005	−	0.969563i
$790$	0.837372	+	0.483457i	0.0297924	+	0.0172006i
$791$	3.51360	−	13.1129i	0.124929	−	0.466242i
$792$	−9.11616	−	3.72061i	−0.323929	−	0.132206i
$793$	−2.74322	−	3.66906i	−0.0974147	−	0.130292i
$794$	6.52717	−	3.76846i	0.231640	−	0.133738i
$795$	−1.00105	−	2.92398i	−0.0355034	−	0.103703i
$796$	21.3407			0.756399
$797$	18.2772	+	31.6570i	0.647411	+	1.12135i	0.983739	+	0.179603i	$0.0574814\pi$
$797$	18.2772	+	31.6570i	0.647411	+	1.12135i	−0.336328	+	0.941745i	$0.609185\pi$
$798$	2.69363	−	13.7283i	0.0953536	−	0.485976i
$799$	7.45304	+	7.45304i	0.263669	+	0.263669i
$800$	23.3286	−	6.25088i	0.824791	−	0.221002i
$801$	−6.18751	+	48.9652i	−0.218625	+	1.73010i
$802$	19.1237	−	33.1232i	0.675282	−	1.16962i
$803$	−15.5294	+	26.8977i	−0.548020	+	0.949199i
$804$	−0.631452	+	3.21823i	−0.0222696	+	0.113498i
$805$	1.57599	+	0.909901i	0.0555465	+	0.0320698i
$806$	12.5279	−	29.2074i	0.441276	−	1.02879i
$807$	19.5623	−	39.9298i	0.688626	−	1.40560i
$808$	0.853577	−	0.228715i	0.0300287	−	0.00804618i
$809$	26.3436	−	15.2095i	0.926191	−	0.534737i	0.0405863	−	0.999176i	$-0.487077\pi$
$809$	26.3436	−	15.2095i	0.926191	−	0.534737i	0.885605	+	0.464439i	$0.153744\pi$
$810$	4.58067	−	4.67696i	0.160948	−	0.164332i
$811$	−10.3377	−	10.3377i	−0.363005	−	0.363005i	0.501913	−	0.864918i	$-0.332630\pi$
$811$	−10.3377	−	10.3377i	−0.363005	−	0.363005i	−0.864918	+	0.501913i	$0.832630\pi$
$812$	−0.886932	+	0.886932i	−0.0311252	+	0.0311252i
$813$	−8.26871	+	42.1420i	−0.289996	+	1.47798i
$814$	−3.15577	−	11.7775i	−0.110610	−	0.412801i
$815$	−2.38106	+	1.37470i	−0.0834047	+	0.0481537i
$816$	−30.9630	+	20.8054i	−1.08392	+	0.728336i
$817$	4.41277	+	16.4687i	0.154383	+	0.576166i
$818$	−17.9795			−0.628640
$819$	−10.8164	−	0.0788916i	−0.377954	−	0.00275669i
$820$	4.73839			0.165472
$821$	−7.75707	−	28.9498i	−0.270723	−	1.01035i	−0.958653	−	0.284577i	$-0.908147\pi$
$821$	−7.75707	−	28.9498i	−0.270723	−	1.01035i	0.687930	−	0.725777i	$-0.258520\pi$
$822$	36.0256	+	17.6495i	1.25654	+	0.615599i
$823$	−8.32356	+	4.80561i	−0.290141	+	0.167513i	−0.638006	−	0.770032i	$-0.720240\pi$
$823$	−8.32356	+	4.80561i	−0.290141	+	0.167513i	0.347864	+	0.937545i	$0.386907\pi$
$824$	2.71144	+	10.1192i	0.0944576	+	0.352521i
$825$	11.5186	+	10.0487i	0.401026	+	0.349849i
$826$	6.69746	−	6.69746i	0.233034	−	0.233034i
$827$	4.40529	+	4.40529i	0.153187	+	0.153187i	0.779540	−	0.626353i	$-0.215453\pi$
$827$	4.40529	+	4.40529i	0.153187	+	0.153187i	−0.626353	+	0.779540i	$0.715453\pi$
$828$	−9.76474	+	7.57375i	−0.339348	+	0.263206i
$829$	−13.4276	+	7.75242i	−0.466360	+	0.269253i	−0.714715	−	0.699416i	$-0.753443\pi$
$829$	−13.4276	+	7.75242i	−0.466360	+	0.269253i	0.248355	+	0.968669i	$0.420110\pi$
$830$	−12.1481	+	3.25507i	−0.421666	+	0.112985i
$831$	−45.1041	+	3.07409i	−1.56464	+	0.106639i
$832$	3.98894	−	2.98239i	0.138292	−	0.103396i
$833$	3.73173	+	2.15452i	0.129297	+	0.0746495i
$834$	−23.1237	−	20.1728i	−0.800707	−	0.698526i
$835$	3.52710	−	6.10911i	0.122060	−	0.211415i
$836$	4.11578	−	7.12875i	0.142347	−	0.246553i
$837$	−11.9654	−	23.7938i	−0.413586	−	0.822433i
$838$	16.4697	−	4.41305i	0.568938	−	0.152446i
$839$	−20.5014	−	20.5014i	−0.707787	−	0.707787i	0.258283	−	0.966069i	$-0.416843\pi$
$839$	−20.5014	−	20.5014i	−0.707787	−	0.707787i	−0.966069	+	0.258283i	$0.916843\pi$
$840$	1.24271	−	0.425451i	0.0428777	−	0.0146795i
$841$	−13.6418	−	23.6283i	−0.470407	−	0.814770i
$842$	55.9561			1.92838
$843$	16.4758	+	3.23272i	0.567455	+	0.111341i
$844$	7.99267	−	4.61457i	0.275119	−	0.158840i
$845$	−5.49690	−	0.137387i	−0.189099	−	0.00472625i
$846$	12.5029	−	1.71224i	0.429859	−	0.0588679i
$847$	1.97974	−	7.38848i	0.0680246	−	0.253871i
$848$	18.2606	+	10.5428i	0.627071	+	0.362040i
$849$	2.11876	−	0.144405i	0.0727158	−	0.00495597i
$850$	34.5084	−	9.24651i	1.18363	−	0.317153i
$851$	16.0965	+	4.31304i	0.551781	+	0.147849i
$852$	−1.54565	+	1.77175i	−0.0529531	+	0.0606991i
$853$	−4.72612	−	1.26636i	−0.161819	−	0.0433594i	0.177000	−	0.984211i	$-0.443361\pi$
$853$	−4.72612	−	1.26636i	−0.161819	−	0.0433594i	−0.338819	+	0.940852i	$0.610027\pi$
$854$	1.89231	+	1.09253i	0.0647536	+	0.0373855i
$855$	−3.65265	−	4.70931i	−0.124918	−	0.161055i
$856$	−9.52184	−	2.55137i	−0.325450	−	0.0872040i
$857$	8.99984	+	15.5882i	0.307429	+	0.532482i	0.977799	−	0.209545i	$-0.0671982\pi$
$857$	8.99984	+	15.5882i	0.307429	+	0.532482i	−0.670371	+	0.742027i	$0.733865\pi$
$858$	−18.5525	−	6.50315i	−0.633374	−	0.222014i
$859$	−20.0247	+	34.6839i	−0.683235	+	1.18340i	0.290753	+	0.956798i	$0.406094\pi$
$859$	−20.0247	+	34.6839i	−0.683235	+	1.18340i	−0.973988	+	0.226600i	$0.927239\pi$
$860$	1.03946	−	1.03946i	0.0354453	−	0.0354453i
$861$	−20.2197	+	1.37808i	−0.689085	+	0.0469648i
$862$		−	59.3075i		−	2.02002i
$863$	−32.0430	+	32.0430i	−1.09075	+	1.09075i	−0.0953068	+	0.995448i	$0.530383\pi$
$863$	−32.0430	+	32.0430i	−1.09075	+	1.09075i	−0.995448	+	0.0953068i	$0.969617\pi$
$864$	−1.49980	+	25.9872i	−0.0510241	+	0.884102i
$865$	0.879299	+	3.28159i	0.0298971	+	0.111577i
$866$	−7.94941	+	29.6676i	−0.270132	+	1.00815i
$867$	−2.25386	+	1.51447i	−0.0765449	+	0.0514341i
$868$			4.90725i			0.166563i
$869$	−1.72063	−	1.72063i	−0.0583683	−	0.0583683i
$870$	0.112234	+	1.64674i	0.00380509	+	0.0558297i
$871$	1.01900	−	7.05750i	0.0345273	−	0.239134i
$872$		−	22.9552i		−	0.777362i
$873$	38.4141	+	29.1601i	1.30012	+	0.986918i
$874$	17.3757	+	30.0956i	0.587743	+	1.01800i
$875$	−4.15403			−0.140432
$876$	27.6098	+	5.41734i	0.932849	+	0.183035i
$877$	−4.79322	+	17.8886i	−0.161856	+	0.604054i	0.836565	+	0.547868i	$0.184560\pi$
$877$	−4.79322	+	17.8886i	−0.161856	+	0.604054i	−0.998420	+	0.0561855i	$0.982106\pi$
$878$	15.6924	−	58.5649i	0.529593	−	1.97647i
$879$	−31.9774	−	6.27431i	−1.07857	−	0.211627i
$880$	3.86992			0.130455
$881$	−5.42487	−	9.39614i	−0.182768	−	0.316564i	0.760054	−	0.649860i	$-0.225173\pi$
$881$	−5.42487	−	9.39614i	−0.182768	−	0.316564i	−0.942822	+	0.333296i	$0.891839\pi$
$882$	4.75609	−	1.99908i	0.160146	−	0.0673125i
$883$			24.6301i			0.828870i	0.910079	+	0.414435i	$0.136021\pi$
$883$			24.6301i			0.828870i	−0.910079	+	0.414435i	$0.863979\pi$
$884$	−11.9132	+	8.90707i	−0.400684	+	0.299577i
$885$	−0.274368	−	4.02562i	−0.00922276	−	0.135320i
$886$	−42.4662	−	42.4662i	−1.42668	−	1.42668i
$887$			22.0391i			0.739999i	0.929032	+	0.370000i	$0.120642\pi$
$887$			22.0391i			0.739999i	−0.929032	+	0.370000i	$0.879358\pi$
$888$	9.98368	−	6.70850i	0.335031	−	0.225123i
$889$	0.885623	−	3.30519i	0.0297028	−	0.110852i
$890$	−3.09720	−	11.5589i	−0.103818	−	0.387455i
$891$	−14.1812	+	8.38539i	−0.475088	+	0.280921i
$892$	12.7940	−	12.7940i	0.428373	−	0.428373i
$893$		−	11.4887i		−	0.384455i
$894$	38.5854	−	2.62980i	1.29049	−	0.0879537i
$895$	−2.26964	+	2.26964i	−0.0758656	+	0.0758656i
$896$	−6.19734	+	10.7341i	−0.207038	+	0.358601i
$897$	20.3752	−	17.5150i	0.680310	−	0.584810i
$898$	−28.3541	−	49.1107i	−0.946188	−	1.63884i
$899$	6.48614	+	1.73796i	0.216325	+	0.0579641i
$900$	5.23256	−	12.8207i	0.174419	−	0.427357i
$901$	15.7428	+	9.08911i	0.524469	+	0.302802i
$902$	−35.5795	−	9.53349i	−1.18467	−	0.317431i
$903$	−4.13329	+	4.73791i	−0.137547	+	0.157668i
$904$	23.5108	+	6.29969i	0.781956	+	0.209525i
$905$	−0.553002	+	0.148176i	−0.0183824	+	0.00492555i
$906$	32.5537	−	2.21871i	1.08153	−	0.0737118i
$907$	−17.3645	−	10.0254i	−0.576580	−	0.332889i	0.183193	−	0.983077i	$-0.441357\pi$
$907$	−17.3645	−	10.0254i	−0.576580	−	0.332889i	−0.759773	+	0.650188i	$0.774690\pi$
$908$	0.501934	−	1.87324i	0.0166573	−	0.0621657i
$909$	0.558727	−	1.36898i	0.0185318	−	0.0454062i
$910$	2.43535	−	0.973287i	0.0807310	−	0.0322642i
$911$	15.8873	−	9.17255i	0.526370	−	0.303900i	−0.213167	−	0.977016i	$-0.568378\pi$
$911$	15.8873	−	9.17255i	0.526370	−	0.303900i	0.739537	+	0.673116i	$0.235044\pi$
$912$	39.9000	+	7.82880i	1.32122	+	0.259237i
$913$	31.6503			1.04747
$914$	6.72365	+	11.6457i	0.222398	+	0.385205i
$915$	0.880662	−	0.301501i	0.0291138	−	0.00996730i
$916$	2.47849	+	2.47849i	0.0818917	+	0.0818917i
$917$	11.0052	−	2.94883i	0.363424	−	0.0973791i
$918$	−2.21855	+	38.4411i	−0.0732230	+	1.26874i
$919$	7.02078	−	12.1603i	0.231594	−	0.401133i	−0.726683	−	0.686973i	$-0.758939\pi$
$919$	7.02078	−	12.1603i	0.231594	−	0.401133i	0.958277	+	0.285840i	$0.0922725\pi$
$920$	−1.63140	+	2.82567i	−0.0537858	+	0.0931597i
$921$	−22.5603	−	19.6813i	−0.743387	−	0.648521i
$922$	−39.3069	−	22.6939i	−1.29451	−	0.747383i
$923$	3.16248	−	4.01650i	0.104094	−	0.132205i
$924$	3.02855	−	0.206412i	0.0996319	−	0.00679045i
$925$	−18.0369	+	4.83298i	−0.593051	+	0.158907i
$926$	29.3221	−	16.9291i	0.963583	−	0.556325i
$927$	16.2294	+	6.62376i	0.533043	+	0.217553i
$928$	−4.64076	−	4.64076i	−0.152340	−	0.152340i
$929$	8.42849	−	8.42849i	0.276530	−	0.276530i	−0.555192	−	0.831722i	$-0.687355\pi$
$929$	8.42849	−	8.42849i	0.276530	−	0.276530i	0.831722	+	0.555192i	$0.187355\pi$
$930$	4.86606	+	4.24509i	0.159564	+	0.139202i
$931$	−1.21562	−	4.53676i	−0.0398404	−	0.148686i
$932$	−18.7132	+	10.8041i	−0.612971	+	0.353899i
$933$	−23.3755	−	11.4521i	−0.765280	−	0.374924i
$934$	13.5854	+	50.7016i	0.444529	+	1.65901i
$935$	3.33633			0.109110
$936$	0.141448	−	19.3932i	0.00462338	−	0.633885i
$937$	−21.1577			−0.691193			−0.345596	−	0.938383i	$-0.612323\pi$
$937$	−21.1577			−0.691193			−0.345596	+	0.938383i	$0.612323\pi$
$938$	0.880262	+	3.28518i	0.0287416	+	0.107265i
$939$	15.6729	−	10.5313i	0.511465	−	0.343677i
$940$	−0.857846	+	0.495278i	−0.0279799	+	0.0161542i
$941$	−3.19537	−	11.9253i	−0.104166	−	0.388754i	0.894083	−	0.447901i	$-0.147828\pi$
$941$	−3.19537	−	11.9253i	−0.104166	−	0.388754i	−0.998249	+	0.0591477i	$0.981162\pi$
$942$	−6.40368	+	32.6368i	−0.208643	+	1.06336i
$943$	35.5975	−	35.5975i	1.15921	−	1.15921i
$944$	19.4655	+	19.4655i	0.633549	+	0.633549i
$945$	0.690209	−	2.08663i	0.0224525	−	0.0678780i
$946$	−9.89644	+	5.71371i	−0.321761	+	0.185769i
$947$	−12.4189	+	3.32763i	−0.403560	+	0.108133i	−0.454889	−	0.890548i	$-0.650321\pi$
$947$	−12.4189	+	3.32763i	−0.403560	+	0.108133i	0.0513290	+	0.998682i	$0.483654\pi$
$948$	−0.969821	+	1.97956i	−0.0314983	+	0.0642932i
$949$	−60.5475	−	8.74214i	−1.96546	−	0.283782i
$950$	−33.7237	−	19.4704i	−1.09414	−	0.631702i
$951$	−2.02993	+	10.3457i	−0.0658250	+	0.335481i
$952$	−3.86293	+	6.69079i	−0.125198	+	0.216850i
$953$	2.54489	−	4.40788i	0.0824371	−	0.142785i	−0.821859	−	0.569691i	$-0.807063\pi$
$953$	2.54489	−	4.40788i	0.0824371	−	0.142785i	0.904296	+	0.426905i	$0.140396\pi$
$954$	20.0642	−	8.43338i	0.649603	−	0.273041i
$955$	−6.32895	+	1.69584i	−0.204800	+	0.0548760i
$956$	5.23161	+	5.23161i	0.169202	+	0.169202i
$957$	0.799769	−	4.07607i	0.0258529	−	0.131761i
$958$	16.0373	+	27.7774i	0.518141	+	0.897446i
$959$	13.4682			0.434910
$960$	0.327787	+	0.957442i	0.0105793	+	0.0309013i
$961$	−4.09549	+	2.36453i	−0.132113	+	0.0762753i
$962$	19.2344	−	14.3808i	0.620141	−	0.463657i
$963$	−13.0333	+	10.1089i	−0.419993	+	0.325756i
$964$	−2.94805	+	11.0023i	−0.0949503	+	0.354359i
$965$	3.87597	+	2.23779i	0.124772	+	0.0720371i
$966$	−5.63819	+	11.5085i	−0.181406	+	0.370279i
$967$	57.9231	−	15.5204i	1.86268	−	0.499104i	0.862702	−	0.505713i	$-0.168771\pi$
$967$	57.9231	−	15.5204i	1.86268	−	0.499104i	0.999978	+	0.00660950i	$0.00210388\pi$
$968$	13.2472	+	3.54956i	0.425780	+	0.114087i
$969$	34.3985	+	6.74935i	1.10504	+	0.216820i
$970$	−11.2951	−	3.02650i	−0.362663	−	0.0971752i
$971$	−5.13037	−	2.96202i	−0.164642	−	0.0950558i	0.415415	−	0.909632i	$-0.363636\pi$
$971$	−5.13037	−	2.96202i	−0.164642	−	0.0950558i	−0.580057	+	0.814576i	$0.696970\pi$
$972$	11.3479	+	9.69378i	0.363985	+	0.310928i
$973$	−9.95108	−	2.66638i	−0.319017	−	0.0854804i
$974$	−2.01936	−	3.49764i	−0.0647045	−	0.112072i
$975$	−9.95941	+	28.4128i	−0.318956	+	0.909937i
$976$	−3.17533	+	5.49983i	−0.101640	+	0.176045i
$977$	19.6895	−	19.6895i	0.629922	−	0.629922i	−0.318126	−	0.948048i	$-0.603054\pi$
$977$	19.6895	−	19.6895i	0.629922	−	0.629922i	0.948048	+	0.318126i	$0.103054\pi$
$978$	−10.7987	−	16.0707i	−0.345303	−	0.513885i
$979$			30.1152i			0.962486i
$980$	−0.286349	+	0.286349i	−0.00914707	+	0.00914707i
$981$	−30.5933	−	23.2233i	−0.976768	−	0.741462i
$982$	2.03677	+	7.60131i	0.0649958	+	0.242568i
$983$	9.37099	−	34.9730i	0.298888	−	1.11547i	−0.639192	−	0.769047i	$-0.720731\pi$
$983$	9.37099	−	34.9730i	0.298888	−	1.11547i	0.938080	−	0.346419i	$-0.112602\pi$
$984$	−2.47082	−	36.2528i	−0.0787670	−	1.15570i
$985$		−	1.17281i		−	0.0373689i
$986$	−6.86477	−	6.86477i	−0.218619	−	0.218619i
$987$	3.51657	−	2.36295i	0.111934	−	0.0752134i
$988$	16.0470	+	2.31695i	0.510524	+	0.0737119i
$989$		−	15.6181i		−	0.496626i
$990$	2.41521	−	3.18168i	0.0767603	−	0.101121i
$991$	23.4732	+	40.6568i	0.745651	+	1.29151i	0.949890	+	0.312584i	$0.101195\pi$
$991$	23.4732	+	40.6568i	0.745651	+	1.29151i	−0.204239	+	0.978921i	$0.565472\pi$
$992$	−25.6766			−0.815232
$993$	14.9046	−	17.0849i	0.472984	−	0.542172i
$994$	−0.631073	+	2.35520i	−0.0200164	+	0.0747023i
$995$	2.44013	−	9.10669i	0.0773573	−	0.288702i
$996$	−9.28690	−	27.1264i	−0.294267	−	0.859533i
$997$	−25.8169			−0.817629			−0.408814	−	0.912618i	$-0.634058\pi$
$997$	−25.8169			−0.817629			−0.408814	+	0.912618i	$0.634058\pi$
$998$	5.65069	+	9.78729i	0.178870	+	0.309811i
$999$	1.15959	−	20.0925i	0.0366880	−	0.635697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.fy.a.50.20	yes	336
9.2	odd	6		819.2.ew.a.596.65	✓	336
13.6	odd	12		819.2.ew.a.617.65	yes	336
117.110	even	12	inner	819.2.fy.a.344.20	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
819.2.ew.a.596.65	✓	336	9.2	odd	6
819.2.ew.a.617.65	yes	336	13.6	odd	12
819.2.fy.a.50.20	yes	336	1.1	even	1	trivial
819.2.fy.a.344.20	yes	336	117.110	even	12	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.445095 - 1.66112i) q^{2} +(-0.117775 - 1.72804i) q^{3} +(-0.829146 + 0.478708i) q^{4} +(0.109473 + 0.408558i) q^{5} +(-2.81806 + 0.964781i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.26780 - 1.26780i) q^{8} +(-2.97226 + 0.407041i) q^{9} +O(q^{10})\)	\(q+(-0.445095 - 1.66112i) q^{2} +(-0.117775 - 1.72804i) q^{3} +(-0.829146 + 0.478708i) q^{4} +(0.109473 + 0.408558i) q^{5} +(-2.81806 + 0.964781i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.26780 - 1.26780i) q^{8} +(-2.97226 + 0.407041i) q^{9} +(0.629936 - 0.363694i) q^{10} +(-1.76817 + 0.473779i) q^{11} +(0.924880 + 1.37642i) q^{12} +(-2.15901 - 2.88768i) q^{13} +(1.48932 + 0.859857i) q^{14} +(0.693112 - 0.237291i) q^{15} +(-2.49909 + 4.32856i) q^{16} +(-2.15452 + 3.73173i) q^{17} +(1.99908 + 4.75609i) q^{18} +(4.53676 - 1.21562i) q^{19} +(-0.286349 - 0.286349i) q^{20} +(1.30519 + 1.13863i) q^{21} +(1.57400 + 2.72625i) q^{22} -4.30244 q^{23} +(-2.04150 + 2.34014i) q^{24} +(4.17519 - 2.41055i) q^{25} +(-3.83580 + 4.87166i) q^{26} +(1.05344 + 5.08825i) q^{27} +(0.247797 - 0.924793i) q^{28} +(-1.13458 - 0.655051i) q^{29} +(-0.702669 - 1.04572i) q^{30} +(-4.95087 + 1.32658i) q^{31} +(4.83886 + 1.29657i) q^{32} +(1.02696 + 2.99967i) q^{33} +(7.15780 + 1.91793i) q^{34} +(-0.366303 - 0.211485i) q^{35} +(2.26958 - 1.76034i) q^{36} +(-3.74125 - 1.00247i) q^{37} +(-4.03858 - 6.99502i) q^{38} +(-4.73575 + 4.07096i) q^{39} +(0.379181 - 0.656761i) q^{40} +(-8.27380 + 8.27380i) q^{41} +(1.31046 - 2.67487i) q^{42} +3.63005i q^{43} +(1.23927 - 1.23927i) q^{44} +(-0.491681 - 1.16978i) q^{45} +(1.91499 + 7.14685i) q^{46} +(0.633089 - 2.36272i) q^{47} +(7.77426 + 3.80874i) q^{48} -1.00000i q^{49} +(-5.86256 - 5.86256i) q^{50} +(6.70233 + 3.28359i) q^{51} +(3.17249 + 1.36077i) q^{52} -4.21863i q^{53} +(7.98329 - 4.01464i) q^{54} +(-0.387132 - 0.670532i) q^{55} +1.79295 q^{56} +(-2.63496 - 7.69655i) q^{57} +(-0.583119 + 2.17623i) q^{58} +(1.42549 - 5.32001i) q^{59} +(-0.461098 + 0.528547i) q^{60} +1.27059 q^{61} +(4.40721 + 7.63352i) q^{62} +(1.81388 - 2.38953i) q^{63} +1.38137i q^{64} +(0.943430 - 1.19820i) q^{65} +(4.52570 - 3.04103i) q^{66} +(1.39844 + 1.39844i) q^{67} -4.12553i q^{68} +(0.506721 + 7.43479i) q^{69} +(-0.188262 + 0.702602i) q^{70} +(0.366964 + 1.36953i) q^{71} +(4.28429 + 3.25219i) q^{72} +(11.9975 - 11.9975i) q^{73} +6.66085i q^{74} +(-4.65726 - 6.93100i) q^{75} +(-3.17971 + 3.17971i) q^{76} +(0.915271 - 1.58530i) q^{77} +(8.87019 + 6.05466i) q^{78} +(0.664649 + 1.15121i) q^{79} +(-2.04205 - 0.547165i) q^{80} +(8.66863 - 2.41966i) q^{81} +(17.4264 + 10.0611i) q^{82} +(-16.7010 - 4.47501i) q^{83} +(-1.62726 - 0.319287i) q^{84} +(-1.76049 - 0.471721i) q^{85} +(6.02994 - 1.61572i) q^{86} +(-0.998329 + 2.03775i) q^{87} +(2.84235 + 1.64103i) q^{88} +(4.25797 - 15.8910i) q^{89} +(-1.72429 + 1.33740i) q^{90} +(3.56855 + 0.515244i) q^{91} +(3.56735 - 2.05961i) q^{92} +(2.87548 + 8.39907i) q^{93} -4.20654 q^{94} +(0.993304 + 1.72045i) q^{95} +(1.67063 - 8.51446i) q^{96} +(-11.3675 - 11.3675i) q^{97} +(-1.66112 + 0.445095i) q^{98} +(5.06260 - 2.12791i) 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