LMFDB - Embedded newform 336.2.u.a.139.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, degree $2$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.8
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08962 - 0.901509i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.374563 + 1.96461i) q^{4} +(-0.167468 + 0.167468i) q^{5} +(-1.40794 + 0.133018i) q^{6} +(-2.61783 + 0.383395i) q^{7} +(1.36298 - 2.47836i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.08962 - 0.901509i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.374563 + 1.96461i) q^{4} +(-0.167468 + 0.167468i) q^{5} +(-1.40794 + 0.133018i) q^{6} +(-2.61783 + 0.383395i) q^{7} +(1.36298 - 2.47836i) q^{8} -1.00000i q^{9} +(0.333451 - 0.0315033i) q^{10} +(2.51707 - 2.51707i) q^{11} +(1.65405 + 1.12433i) q^{12} +(-4.28014 - 4.28014i) q^{13} +(3.19808 + 1.94224i) q^{14} +0.236836i q^{15} +(-3.71941 + 1.47174i) q^{16} -7.14268i q^{17} +(-0.901509 + 1.08962i) q^{18} +(3.61962 - 3.61962i) q^{19} +(-0.391737 - 0.266283i) q^{20} +(-1.57998 + 2.12218i) q^{21} +(-5.01182 + 0.473500i) q^{22} +5.62753 q^{23} +(-0.788692 - 2.71624i) q^{24} +4.94391i q^{25} +(0.805160 + 8.52232i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.73376 - 4.99941i) q^{28} +(0.0732236 - 0.0732236i) q^{29} +(0.213509 - 0.258062i) q^{30} -2.74337 q^{31} +(5.37954 + 1.74943i) q^{32} -3.55968i q^{33} +(-6.43919 + 7.78284i) q^{34} +(0.374196 - 0.502609i) q^{35} +(1.96461 - 0.374563i) q^{36} +(-0.490300 - 0.490300i) q^{37} +(-7.20715 + 0.680906i) q^{38} -6.05303 q^{39} +(0.186790 + 0.643303i) q^{40} -9.39766 q^{41} +(3.63475 - 0.888016i) q^{42} +(-3.30395 + 3.30395i) q^{43} +(5.88787 + 4.00227i) q^{44} +(0.167468 + 0.167468i) q^{45} +(-6.13189 - 5.07327i) q^{46} +0.799500 q^{47} +(-1.58934 + 3.67070i) q^{48} +(6.70602 - 2.00732i) q^{49} +(4.45698 - 5.38700i) q^{50} +(-5.05064 - 5.05064i) q^{51} +(6.80563 - 10.0120i) q^{52} +(-4.68107 - 4.68107i) q^{53} +(0.133018 + 1.40794i) q^{54} +0.843058i q^{55} +(-2.61786 + 7.01048i) q^{56} -5.11892i q^{57} +(-0.145798 + 0.0137745i) q^{58} +(7.78362 + 7.78362i) q^{59} +(-0.465290 + 0.0887099i) q^{60} +(8.08940 + 8.08940i) q^{61} +(2.98924 + 2.47317i) q^{62} +(0.383395 + 2.61783i) q^{63} +(-4.28455 - 6.75593i) q^{64} +1.43357 q^{65} +(-3.20908 + 3.87871i) q^{66} +(9.96374 + 9.96374i) q^{67} +(14.0326 - 2.67538i) q^{68} +(3.97926 - 3.97926i) q^{69} +(-0.860839 + 0.210314i) q^{70} +0.235353 q^{71} +(-2.47836 - 1.36298i) q^{72} -11.1990 q^{73} +(0.0922330 + 0.976253i) q^{74} +(3.49587 + 3.49587i) q^{75} +(8.46693 + 5.75538i) q^{76} +(-5.62422 + 7.55428i) q^{77} +(6.59553 + 5.45686i) q^{78} -0.211784i q^{79} +(0.376412 - 0.869352i) q^{80} -1.00000 q^{81} +(10.2399 + 8.47208i) q^{82} +(8.74602 - 8.74602i) q^{83} +(-4.76107 - 2.30916i) q^{84} +(1.19617 + 1.19617i) q^{85} +(6.57860 - 0.621523i) q^{86} -0.103554i q^{87} +(-2.80749 - 9.66894i) q^{88} +7.54477 q^{89} +(-0.0315033 - 0.333451i) q^{90} +(12.8456 + 9.56366i) q^{91} +(2.10786 + 11.0559i) q^{92} +(-1.93985 + 1.93985i) q^{93} +(-0.871155 - 0.720757i) q^{94} +1.21234i q^{95} +(5.04095 - 2.56688i) q^{96} -14.4984i q^{97} +(-9.11666 - 3.85830i) q^{98} +(-2.51707 - 2.51707i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.08962	−	0.901509i	−0.770481	−	0.637463i
$2$	−1.08962	−	0.901509i	−0.770481	−	0.637463i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	0.374563	+	1.96461i	0.187281	+	0.982306i
$5$	−0.167468	+	0.167468i	−0.0748940	+	0.0748940i	−0.743562	−	0.668668i	$-0.766865\pi$
$5$	−0.167468	+	0.167468i	−0.0748940	+	0.0748940i	0.668668	+	0.743562i	$0.266865\pi$
$6$	−1.40794	+	0.133018i	−0.574791	+	0.0543042i
$7$	−2.61783	+	0.383395i	−0.989445	+	0.144910i
$7$	−2.61783	+	0.383395i	−0.989445	+	0.144910i
$8$	1.36298	−	2.47836i	0.481887	−	0.876233i
$9$		−	1.00000i		−	0.333333i
$10$	0.333451	−	0.0315033i	0.105447	−	0.00996223i
$11$	2.51707	−	2.51707i	0.758925	−	0.758925i	−0.217201	−	0.976127i	$-0.569693\pi$
$11$	2.51707	−	2.51707i	0.758925	−	0.758925i	0.976127	+	0.217201i	$0.0696928\pi$
$12$	1.65405	+	1.12433i	0.477482	+	0.324568i
$13$	−4.28014	−	4.28014i	−1.18710	−	1.18710i	−0.977867	−	0.209230i	$-0.932904\pi$
$13$	−4.28014	−	4.28014i	−1.18710	−	1.18710i	−0.209230	−	0.977867i	$-0.567096\pi$
$14$	3.19808	+	1.94224i	0.854723	+	0.519084i
$15$			0.236836i			0.0611507i
$16$	−3.71941	+	1.47174i	−0.929851	+	0.367936i
$17$		−	7.14268i		−	1.73235i	−0.499737	−	0.866177i	$-0.666570\pi$
$17$		−	7.14268i		−	1.73235i	0.499737	−	0.866177i	$-0.333430\pi$
$18$	−0.901509	+	1.08962i	−0.212488	+	0.256827i
$19$	3.61962	−	3.61962i	0.830398	−	0.830398i	−0.157173	−	0.987571i	$-0.550238\pi$
$19$	3.61962	−	3.61962i	0.830398	−	0.830398i	0.987571	+	0.157173i	$0.0502381\pi$
$20$	−0.391737	−	0.266283i	−0.0875951	−	0.0595426i
$21$	−1.57998	+	2.12218i	−0.344780	+	0.463098i
$22$	−5.01182	+	0.473500i	−1.06852	+	0.100950i
$23$	5.62753			1.17342			0.586711	−	0.809797i	$-0.300423\pi$
$23$	5.62753			1.17342			0.586711	+	0.809797i	$0.300423\pi$
$24$	−0.788692	−	2.71624i	−0.160991	−	0.554450i
$25$			4.94391i			0.988782i
$26$	0.805160	+	8.52232i	0.157905	+	1.67136i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.73376	−	4.99941i	−0.327651	−	0.944799i
$29$	0.0732236	−	0.0732236i	0.0135973	−	0.0135973i	−0.700275	−	0.713873i	$-0.746939\pi$
$29$	0.0732236	−	0.0732236i	0.0135973	−	0.0135973i	0.713873	+	0.700275i	$0.246939\pi$
$30$	0.213509	−	0.258062i	0.0389813	−	0.0471154i
$31$	−2.74337			−0.492723			−0.246361	−	0.969178i	$-0.579235\pi$
$31$	−2.74337			−0.492723			−0.246361	+	0.969178i	$0.579235\pi$
$32$	5.37954	+	1.74943i	0.950978	+	0.309259i
$33$		−	3.55968i		−	0.619660i
$34$	−6.43919	+	7.78284i	−1.10431	+	1.33475i
$35$	0.374196	−	0.502609i	0.0632506	−	0.0849564i
$36$	1.96461	−	0.374563i	0.327435	−	0.0624272i
$37$	−0.490300	−	0.490300i	−0.0806049	−	0.0806049i	0.665655	−	0.746260i	$-0.268152\pi$
$37$	−0.490300	−	0.490300i	−0.0806049	−	0.0806049i	−0.746260	+	0.665655i	$0.768152\pi$
$38$	−7.20715	+	0.680906i	−1.16915	+	0.110458i
$39$	−6.05303			−0.969260
$40$	0.186790	+	0.643303i	0.0295341	+	0.101715i
$41$	−9.39766			−1.46767			−0.733834	−	0.679328i	$-0.762271\pi$
$41$	−9.39766			−1.46767			−0.733834	+	0.679328i	$0.762271\pi$
$42$	3.63475	−	0.888016i	0.560855	−	0.137024i
$43$	−3.30395	+	3.30395i	−0.503847	+	0.503847i	−0.912631	−	0.408784i	$-0.865953\pi$
$43$	−3.30395	+	3.30395i	−0.503847	+	0.503847i	0.408784	+	0.912631i	$0.365953\pi$
$44$	5.88787	+	4.00227i	0.887630	+	0.603365i
$45$	0.167468	+	0.167468i	0.0249647	+	0.0249647i
$46$	−6.13189	−	5.07327i	−0.904098	−	0.748013i
$47$	0.799500			0.116619			0.0583095	−	0.998299i	$-0.481429\pi$
$47$	0.799500			0.116619			0.0583095	+	0.998299i	$0.481429\pi$
$48$	−1.58934	+	3.67070i	−0.229401	+	0.529819i
$49$	6.70602	−	2.00732i	0.958002	−	0.286761i
$50$	4.45698	−	5.38700i	0.630312	−	0.761837i
$51$	−5.05064	−	5.05064i	−0.707231	−	0.707231i
$52$	6.80563	−	10.0120i	0.943771	−	1.38841i
$53$	−4.68107	−	4.68107i	−0.642994	−	0.642994i	0.308296	−	0.951290i	$-0.400241\pi$
$53$	−4.68107	−	4.68107i	−0.642994	−	0.642994i	−0.951290	+	0.308296i	$0.900241\pi$
$54$	0.133018	+	1.40794i	0.0181014	+	0.191597i
$55$			0.843058i			0.113678i
$56$	−2.61786	+	7.01048i	−0.349826	+	0.936815i
$57$		−	5.11892i		−	0.678017i
$58$	−0.145798	+	0.0137745i	−0.0191442	+	0.00180868i
$59$	7.78362	+	7.78362i	1.01334	+	1.01334i	0.999910	+	0.0134315i	$0.00427550\pi$
$59$	7.78362	+	7.78362i	1.01334	+	1.01334i	0.0134315	+	0.999910i	$0.495725\pi$
$60$	−0.465290	+	0.0887099i	−0.0600687	+	0.0114524i
$61$	8.08940	+	8.08940i	1.03574	+	1.03574i	0.999337	+	0.0364049i	$0.0115906\pi$
$61$	8.08940	+	8.08940i	1.03574	+	1.03574i	0.0364049	+	0.999337i	$0.488409\pi$
$62$	2.98924	+	2.47317i	0.379634	+	0.314093i
$63$	0.383395	+	2.61783i	0.0483033	+	0.329815i
$64$	−4.28455	−	6.75593i	−0.535569	−	0.844491i
$65$	1.43357			0.177813
$66$	−3.20908	+	3.87871i	−0.395010	+	0.477436i
$67$	9.96374	+	9.96374i	1.21726	+	1.21726i	0.968586	+	0.248678i	$0.0799963\pi$
$67$	9.96374	+	9.96374i	1.21726	+	1.21726i	0.248678	+	0.968586i	$0.420004\pi$
$68$	14.0326	−	2.67538i	1.70170	−	0.324438i
$69$	3.97926	−	3.97926i	0.479047	−	0.479047i
$70$	−0.860839	+	0.210314i	−0.102890	+	0.0251373i
$71$	0.235353			0.0279312			0.0139656	−	0.999902i	$-0.495554\pi$
$71$	0.235353			0.0279312			0.0139656	+	0.999902i	$0.495554\pi$
$72$	−2.47836	−	1.36298i	−0.292078	−	0.160629i
$73$	−11.1990			−1.31074			−0.655370	−	0.755308i	$-0.727487\pi$
$73$	−11.1990			−1.31074			−0.655370	+	0.755308i	$0.727487\pi$
$74$	0.0922330	+	0.976253i	0.0107219	+	0.113487i
$75$	3.49587	+	3.49587i	0.403668	+	0.403668i
$76$	8.46693	+	5.75538i	0.971223	+	0.660187i
$77$	−5.62422	+	7.55428i	−0.640939	+	0.860891i
$78$	6.59553	+	5.45686i	0.746796	+	0.617867i
$79$		−	0.211784i		−	0.0238276i	−0.999929	−	0.0119138i	$-0.996208\pi$
$79$		−	0.211784i		−	0.0238276i	0.999929	−	0.0119138i	$-0.00379236\pi$
$80$	0.376412	−	0.869352i	0.0420841	−	0.0971965i
$81$	−1.00000			−0.111111
$82$	10.2399	+	8.47208i	1.13081	+	0.935585i
$83$	8.74602	−	8.74602i	0.960001	−	0.960001i	−0.0392297	−	0.999230i	$-0.512490\pi$
$83$	8.74602	−	8.74602i	0.960001	−	0.960001i	0.999230	+	0.0392297i	$0.0124904\pi$
$84$	−4.76107	−	2.30916i	−0.519475	−	0.251950i
$85$	1.19617	+	1.19617i	0.129743	+	0.129743i
$86$	6.57860	−	0.621523i	0.709388	−	0.0670206i
$87$		−	0.103554i		−	0.0111021i
$88$	−2.80749	−	9.66894i	−0.299279	−	1.03071i
$89$	7.54477			0.799744			0.399872	−	0.916571i	$-0.369055\pi$
$89$	7.54477			0.799744			0.399872	+	0.916571i	$0.369055\pi$
$90$	−0.0315033	−	0.333451i	−0.00332074	−	0.0351489i
$91$	12.8456	+	9.56366i	1.34659	+	1.00254i
$92$	2.10786	+	11.0559i	0.219760	+	1.15266i
$93$	−1.93985	+	1.93985i	−0.201153	+	0.201153i
$94$	−0.871155	−	0.720757i	−0.0898528	−	0.0743404i
$95$			1.21234i			0.124384i
$96$	5.04095	−	2.56688i	0.514489	−	0.261981i
$97$		−	14.4984i		−	1.47209i	−0.676932	−	0.736045i	$-0.736691\pi$
$97$		−	14.4984i		−	1.47209i	0.676932	−	0.736045i	$-0.263309\pi$
$98$	−9.11666	−	3.85830i	−0.920922	−	0.389748i
$99$	−2.51707	−	2.51707i	−0.252975	−	0.252975i
$100$	−9.71287	+	1.85180i	−0.971287	+	0.185180i
$101$	−4.52552	+	4.52552i	−0.450306	+	0.450306i	−0.895456	−	0.445150i	$-0.853150\pi$
$101$	−4.52552	+	4.52552i	−0.450306	+	0.450306i	0.445150	+	0.895456i	$0.353150\pi$
$102$	0.950103	+	10.0565i	0.0940742	+	0.995741i
$103$			6.94145i			0.683962i	0.939707	+	0.341981i	$0.111098\pi$
$103$			6.94145i			0.683962i	−0.939707	+	0.341981i	$0.888902\pi$
$104$	−16.4415	+	4.77397i	−1.61222	+	0.468126i
$105$	−0.0908017	−	0.619994i	−0.00886134	−	0.0605053i
$106$	0.880581	+	9.32063i	0.0855296	+	0.905300i
$107$	1.87422	−	1.87422i	0.181187	−	0.181187i	−0.610686	−	0.791873i	$-0.709106\pi$
$107$	1.87422	−	1.87422i	0.181187	−	0.181187i	0.791873	+	0.610686i	$0.209106\pi$
$108$	1.12433	−	1.65405i	0.108189	−	0.159161i
$109$	12.6272	−	12.6272i	1.20946	−	1.20946i	0.238261	−	0.971201i	$-0.423423\pi$
$109$	12.6272	−	12.6272i	1.20946	−	1.20946i	0.971201	−	0.238261i	$-0.0765772\pi$
$110$	0.760025	−	0.918617i	0.0724655	−	0.0875867i
$111$	−0.693389			−0.0658136
$112$	9.17249	−	5.27877i	0.866719	−	0.498797i
$113$	−7.68573			−0.723012			−0.361506	−	0.932370i	$-0.617737\pi$
$113$	−7.68573			−0.723012			−0.361506	+	0.932370i	$0.617737\pi$
$114$	−4.61475	+	5.57770i	−0.432211	+	0.522399i
$115$	−0.942432	+	0.942432i	−0.0878822	+	0.0878822i
$116$	0.171283	+	0.116429i	0.0159032	+	0.0108102i
$117$	−4.28014	+	4.28014i	−0.395699	+	0.395699i
$118$	−1.46422	−	15.4982i	−0.134792	−	1.42673i
$119$	2.73847	+	18.6983i	0.251035	+	1.71407i
$120$	0.586964	+	0.322803i	0.0535823	+	0.0294677i
$121$		−	1.67129i		−	0.151935i
$122$	−1.52174	−	16.1071i	−0.137772	−	1.45827i
$123$	−6.64515	+	6.64515i	−0.599173	+	0.599173i
$124$	−1.02756	−	5.38965i	−0.0922779	−	0.484005i
$125$	−1.66529	−	1.66529i	−0.148948	−	0.148948i
$126$	1.94224	−	3.19808i	0.173028	−	0.284908i
$127$			3.23913i			0.287427i	0.989619	+	0.143713i	$0.0459043\pi$
$127$			3.23913i			0.287427i	−0.989619	+	0.143713i	$0.954096\pi$
$128$	−1.42198	+	11.2240i	−0.125686	+	0.992070i
$129$			4.67248i			0.411389i
$130$	−1.56206	−	1.29238i	−0.137001	−	0.113349i
$131$	0.202227	−	0.202227i	0.0176686	−	0.0176686i	−0.698217	−	0.715886i	$-0.746023\pi$
$131$	0.202227	−	0.202227i	0.0176686	−	0.0176686i	0.715886	+	0.698217i	$0.246023\pi$
$132$	6.99338	−	1.33332i	0.608696	−	0.116051i
$133$	−8.08779	+	10.8633i	−0.701300	+	0.941966i
$134$	−1.87433	−	19.8391i	−0.161918	−	1.71384i
$135$	0.236836			0.0203836
$136$	−17.7021	−	9.73535i	−1.51795	−	0.834799i
$137$		−	15.9858i		−	1.36576i	−0.730533	−	0.682878i	$-0.760728\pi$
$137$		−	15.9858i		−	1.36576i	0.730533	−	0.682878i	$-0.239272\pi$
$138$	−7.92325	+	0.748561i	−0.674472	+	0.0637217i
$139$	2.02752	+	2.02752i	0.171972	+	0.171972i	0.787845	−	0.615873i	$-0.211197\pi$
$139$	2.02752	+	2.02752i	0.171972	+	0.171972i	−0.615873	+	0.787845i	$0.711197\pi$
$140$	1.12759	+	0.546891i	0.0952989	+	0.0462207i
$141$	0.565332	−	0.565332i	0.0476095	−	0.0476095i
$142$	−0.256446	−	0.212173i	−0.0215205	−	0.0178051i
$143$	−21.5468			−1.80183
$144$	1.47174	+	3.71941i	0.122645	+	0.309950i
$145$			0.0245252i			0.00203671i
$146$	12.2027	+	10.0960i	1.00990	+	0.835549i
$147$	3.32248	−	6.16126i	0.274033	−	0.508172i
$148$	0.779602	−	1.14690i	0.0640829	−	0.0942745i
$149$	6.61834	+	6.61834i	0.542195	+	0.542195i	0.924172	−	0.381977i	$-0.124757\pi$
$149$	6.61834	+	6.61834i	0.542195	+	0.542195i	−0.381977	+	0.924172i	$0.624757\pi$
$150$	−0.657627	−	6.96075i	−0.0536950	−	0.568343i
$151$	−5.60636			−0.456239			−0.228120	−	0.973633i	$-0.573258\pi$
$151$	−5.60636			−0.456239			−0.228120	+	0.973633i	$0.573258\pi$
$152$	−4.03725	−	13.9042i	−0.327464	−	1.12778i
$153$	−7.14268			−0.577451
$154$	12.9385	−	3.16105i	1.04262	−	0.254725i
$155$	0.459426	−	0.459426i	0.0369020	−	0.0369020i
$156$	−2.26724	−	11.8919i	−0.181524	−	0.952110i
$157$	11.8394	+	11.8394i	0.944890	+	0.944890i	0.998559	−	0.0536685i	$-0.0170914\pi$
$157$	11.8394	+	11.8394i	0.944890	+	0.944890i	−0.0536685	+	0.998559i	$0.517091\pi$
$158$	−0.190925	+	0.230765i	−0.0151892	+	0.0183587i
$159$	−6.62003			−0.525003
$160$	−1.19388	+	0.607928i	−0.0943842	+	0.0480609i
$161$	−14.7319	+	2.15757i	−1.16104	+	0.170040i
$162$	1.08962	+	0.901509i	0.0856090	+	0.0708292i
$163$	0.641460	+	0.641460i	0.0502430	+	0.0502430i	0.731782	−	0.681539i	$-0.238689\pi$
$163$	0.641460	+	0.641460i	0.0502430	+	0.0502430i	−0.681539	+	0.731782i	$0.738689\pi$
$164$	−3.52002	−	18.4628i	−0.274867	−	1.44170i
$165$	0.596132	+	0.596132i	0.0464088	+	0.0464088i
$166$	−17.4145	+	1.64526i	−1.35163	+	0.127697i
$167$		−	8.66571i		−	0.670573i	−0.942116	−	0.335287i	$-0.891167\pi$
$167$		−	8.66571i		−	0.670573i	0.942116	−	0.335287i	$-0.108833\pi$
$168$	3.10605	+	6.80826i	0.239637	+	0.525269i
$169$			23.6391i			1.81839i
$170$	−0.225018	−	2.38174i	−0.0172581	−	0.182671i
$171$	−3.61962	−	3.61962i	−0.276799	−	0.276799i
$172$	−7.72851	−	5.25344i	−0.589293	−	0.400571i
$173$	4.80384	+	4.80384i	0.365229	+	0.365229i	0.865734	−	0.500505i	$-0.166852\pi$
$173$	4.80384	+	4.80384i	0.365229	+	0.365229i	−0.500505	+	0.865734i	$0.666852\pi$
$174$	−0.0933547	+	0.112835i	−0.00707720	+	0.00855398i
$175$	−1.89547	−	12.9423i	−0.143284	−	0.978345i
$176$	−5.65753	+	13.0665i	−0.426452	+	0.984923i
$177$	11.0077			0.827390
$178$	−8.22097	−	6.80168i	−0.616188	−	0.509808i
$179$	−3.03426	−	3.03426i	−0.226792	−	0.226792i	0.584559	−	0.811351i	$-0.301267\pi$
$179$	−3.03426	−	3.03426i	−0.226792	−	0.226792i	−0.811351	+	0.584559i	$0.801267\pi$
$180$	−0.266283	+	0.391737i	−0.0198475	+	0.0291984i
$181$	−2.63997	+	2.63997i	−0.196227	+	0.196227i	−0.798380	−	0.602153i	$-0.794310\pi$
$181$	−2.63997	+	2.63997i	−0.196227	+	0.196227i	0.602153	+	0.798380i	$0.294310\pi$
$182$	−5.37519	−	22.0013i	−0.398435	−	1.63084i
$183$	11.4401			0.845680
$184$	7.67023	−	13.9471i	0.565457	−	1.02819i
$185$	0.164219			0.0120736
$186$	3.86250	−	0.364916i	0.283213	−	0.0267569i
$187$	−17.9786	−	17.9786i	−1.31473	−	1.31473i
$188$	0.299463	+	1.57071i	0.0218406	+	0.114556i
$189$	2.12218	+	1.57998i	0.154366	+	0.114927i
$190$	1.09294	−	1.32100i	0.0792900	−	0.0958352i
$191$		−	12.4428i		−	0.900328i	−0.892946	−	0.450164i	$-0.851366\pi$
$191$		−	12.4428i		−	0.900328i	0.892946	−	0.450164i	$-0.148634\pi$
$192$	−7.80680	−	1.74753i	−0.563407	−	0.126117i
$193$	6.00200			0.432034			0.216017	−	0.976390i	$-0.430693\pi$
$193$	6.00200			0.432034			0.216017	+	0.976390i	$0.430693\pi$
$194$	−13.0704	+	15.7978i	−0.938403	+	1.13422i
$195$	1.01369	−	1.01369i	0.0725918	−	0.0725918i
$196$	6.45544	+	12.4229i	0.461103	+	0.887347i
$197$	−10.8958	−	10.8958i	−0.776297	−	0.776297i	0.202902	−	0.979199i	$-0.434963\pi$
$197$	−10.8958	−	10.8958i	−0.776297	−	0.776297i	−0.979199	+	0.202902i	$0.934963\pi$
$198$	0.473500	+	5.01182i	0.0336502	+	0.356175i
$199$		−	9.22666i		−	0.654060i	−0.945014	−	0.327030i	$-0.893952\pi$
$199$		−	9.22666i		−	0.654060i	0.945014	−	0.327030i	$-0.106048\pi$
$200$	12.2528	+	6.73846i	0.866403	+	0.476481i
$201$	14.0909			0.993892
$202$	9.01092	−	0.851320i	0.634006	−	0.0598987i
$203$	−0.163613	+	0.219760i	−0.0114834	+	0.0154241i
$204$	8.03076	−	11.8143i	0.562266	−	0.827168i
$205$	1.57381	−	1.57381i	0.109920	−	0.109920i
$206$	6.25778	−	7.56358i	0.436000	−	0.526979i
$207$		−	5.62753i		−	0.391140i
$208$	22.2188	+	9.62030i	1.54060	+	0.667048i
$209$		−	18.2217i		−	1.26042i
$210$	−0.459991	+	0.757420i	−0.0317424	+	0.0522669i
$211$	7.53917	+	7.53917i	0.519018	+	0.519018i	0.917274	−	0.398256i	$-0.130385\pi$
$211$	7.53917	+	7.53917i	0.519018	+	0.519018i	−0.398256	+	0.917274i	$0.630385\pi$
$212$	7.44313	−	10.9498i	0.511196	−	0.752038i
$213$	0.166420	−	0.166420i	0.0114029	−	0.0114029i
$214$	−3.73182	+	0.352569i	−0.255102	+	0.0241011i
$215$		−	1.10661i		−	0.0754702i
$216$	−2.71624	+	0.788692i	−0.184817	+	0.0536637i
$217$	7.18165	−	1.05179i	0.487522	−	0.0714004i
$218$	−25.1423	+	2.37536i	−1.70285	+	0.160880i
$219$	−7.91887	+	7.91887i	−0.535108	+	0.535108i
$220$	−1.65628	+	0.315778i	−0.111667	+	0.0212898i
$221$	−30.5716	+	30.5716i	−2.05647	+	2.05647i
$222$	0.755534	+	0.625097i	0.0507081	+	0.0419537i
$223$	−0.834795			−0.0559020			−0.0279510	−	0.999609i	$-0.508898\pi$
$223$	−0.834795			−0.0559020			−0.0279510	+	0.999609i	$0.508898\pi$
$224$	−14.7534	−	2.51721i	−0.985755	−	0.168188i
$225$	4.94391			0.329594
$226$	8.37456	+	6.92875i	0.557067	+	0.460894i
$227$	−3.92781	+	3.92781i	−0.260698	+	0.260698i	−0.825337	−	0.564640i	$-0.809015\pi$
$227$	−3.92781	+	3.92781i	−0.260698	+	0.260698i	0.564640	+	0.825337i	$0.309015\pi$
$228$	10.0567	−	1.91736i	0.666020	−	0.126980i
$229$	1.17563	−	1.17563i	0.0776881	−	0.0776881i	−0.667195	−	0.744883i	$-0.732505\pi$
$229$	1.17563	−	1.17563i	0.0776881	−	0.0776881i	0.744883	+	0.667195i	$0.232505\pi$
$230$	1.87651	−	0.177286i	0.123733	−	0.0116899i
$231$	1.36476	+	9.31861i	0.0897948	+	0.613119i
$232$	−0.0816721	−	0.281277i	−0.00536203	−	0.0184668i
$233$			10.6073i			0.694905i	0.937698	+	0.347452i	$0.112953\pi$
$233$			10.6073i			0.694905i	−0.937698	+	0.347452i	$0.887047\pi$
$234$	8.52232	−	0.805160i	0.557122	−	0.0526349i
$235$	−0.133891	+	0.133891i	−0.00873407	+	0.00873407i
$236$	−12.3763	+	18.2073i	−0.805631	+	1.18519i
$237$	−0.149754	−	0.149754i	−0.00972756	−	0.00972756i
$238$	13.8728	−	22.8429i	0.899238	−	1.48068i
$239$			7.16271i			0.463317i	0.972797	+	0.231659i	$0.0744152\pi$
$239$			7.16271i			0.463317i	−0.972797	+	0.231659i	$0.925585\pi$
$240$	−0.348561	−	0.880888i	−0.0224995	−	0.0568611i
$241$			13.4240i			0.864716i	0.901702	+	0.432358i	$0.142318\pi$
$241$			13.4240i			0.864716i	−0.901702	+	0.432358i	$0.857682\pi$
$242$	−1.50668	+	1.82108i	−0.0968532	+	0.117063i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−12.8626	+	18.9225i	−0.823441	+	1.21139i
$245$	−0.786881	+	1.45921i	−0.0502720	+	0.0932253i
$246$	13.2314	−	1.25006i	0.843602	−	0.0797006i
$247$	−30.9849			−1.97152
$248$	−3.73916	+	6.79905i	−0.237437	+	0.431740i
$249$		−	12.3687i		−	0.783837i
$250$	0.313266	+	3.31581i	0.0198127	+	0.209710i
$251$	5.28753	+	5.28753i	0.333746	+	0.333746i	0.854007	−	0.520261i	$-0.174165\pi$
$251$	5.28753	+	5.28753i	0.333746	+	0.333746i	−0.520261	+	0.854007i	$0.674165\pi$
$252$	−4.99941	+	1.73376i	−0.314933	+	0.109217i
$253$	14.1649	−	14.1649i	0.890539	−	0.890539i
$254$	2.92011	−	3.52944i	0.183224	−	0.221457i
$255$	1.69164			0.105935
$256$	11.6680	−	10.9480i	0.729247	−	0.684251i
$257$			0.425017i			0.0265118i	0.999912	+	0.0132559i	$0.00421961\pi$
$257$			0.425017i			0.0265118i	−0.999912	+	0.0132559i	$0.995780\pi$
$258$	4.21229	−	5.09125i	0.262246	−	0.316968i
$259$	1.47150	+	1.09554i	0.0914345	+	0.0680736i
$260$	0.536963	+	2.81641i	0.0333010	+	0.174667i
$261$	−0.0732236	−	0.0732236i	−0.00453243	−	0.00453243i
$262$	−0.402660	+	0.0380420i	−0.0248764	+	0.00235024i
$263$	26.6012			1.64030			0.820151	−	0.572147i	$-0.193889\pi$
$263$	26.6012			1.64030			0.820151	+	0.572147i	$0.193889\pi$
$264$	−8.82216	−	4.85178i	−0.542967	−	0.298606i
$265$	1.56786			0.0963128
$266$	18.6060	−	4.54568i	1.14081	−	0.278714i
$267$	5.33496	−	5.33496i	0.326494	−	0.326494i
$268$	−15.8428	+	23.3069i	−0.967756	+	1.42370i
$269$	15.3116	+	15.3116i	0.933565	+	0.933565i	0.997927	−	0.0643617i	$-0.0205011\pi$
$269$	15.3116	+	15.3116i	0.933565	+	0.933565i	−0.0643617	+	0.997927i	$0.520501\pi$
$270$	−0.258062	−	0.213509i	−0.0157051	−	0.0129938i
$271$	−20.1296			−1.22278			−0.611392	−	0.791328i	$-0.709390\pi$
$271$	−20.1296			−1.22278			−0.611392	+	0.791328i	$0.709390\pi$
$272$	10.5122	+	26.5665i	0.637395	+	1.61083i
$273$	15.8458	−	2.32070i	0.959029	−	0.140455i
$274$	−14.4113	+	17.4185i	−0.870619	+	1.05229i
$275$	12.4442	+	12.4442i	0.750412	+	0.750412i
$276$	9.30820	+	6.32723i	0.560288	+	0.380854i
$277$	16.8102	+	16.8102i	1.01003	+	1.01003i	0.999949	+	0.0100769i	$0.00320764\pi$
$277$	16.8102	+	16.8102i	1.01003	+	1.01003i	0.0100769	+	0.999949i	$0.496792\pi$
$278$	−0.381407	−	4.03706i	−0.0228753	−	0.242127i
$279$			2.74337i			0.164241i
$280$	−0.735624	−	1.61244i	−0.0439619	−	0.0963617i
$281$		−	4.47706i		−	0.267079i	−0.991044	−	0.133539i	$-0.957366\pi$
$281$		−	4.47706i		−	0.267079i	0.991044	−	0.133539i	$-0.0426343\pi$
$282$	−1.12565	+	0.106348i	−0.0670316	+	0.00633291i
$283$	9.67731	+	9.67731i	0.575256	+	0.575256i	0.933593	−	0.358336i	$-0.116656\pi$
$283$	9.67731	+	9.67731i	0.575256	+	0.575256i	−0.358336	+	0.933593i	$0.616656\pi$
$284$	0.0881544	+	0.462377i	0.00523100	+	0.0274370i
$285$	0.857255	+	0.857255i	0.0507794	+	0.0507794i
$286$	23.4779	+	19.4246i	1.38828	+	1.14860i
$287$	24.6014	−	3.60302i	1.45218	−	0.212680i
$288$	1.74943	−	5.37954i	0.103086	−	0.316993i
$289$	−34.0179			−2.00105
$290$	0.0221097	−	0.0267233i	0.00129833	−	0.00156925i
$291$	−10.2519	−	10.2519i	−0.600978	−	0.600978i
$292$	−4.19472	−	22.0016i	−0.245477	−	1.28755i
$293$	8.48795	−	8.48795i	0.495871	−	0.495871i	−0.414279	−	0.910150i	$-0.635966\pi$
$293$	8.48795	−	8.48795i	0.495871	−	0.495871i	0.910150	+	0.414279i	$0.135966\pi$
$294$	−9.17469	+	3.71822i	−0.535078	+	0.216851i
$295$	−2.60702			−0.151786
$296$	−1.88341	+	0.546870i	−0.109471	+	0.0317862i
$297$	−3.55968			−0.206553
$298$	−1.24501	−	13.1780i	−0.0721216	−	0.763380i
$299$	−24.0866	−	24.0866i	−1.39296	−	1.39296i
$300$	−5.55861	+	8.17746i	−0.320926	+	0.472126i
$301$	7.38243	−	9.91587i	0.425516	−	0.571541i
$302$	6.10883	+	5.05419i	0.351524	+	0.290836i
$303$			6.40005i			0.367673i
$304$	−8.13569	+	18.7900i	−0.466614	+	1.07768i
$305$	−2.70943			−0.155142
$306$	7.78284	+	6.43919i	0.444915	+	0.368104i
$307$	9.08093	−	9.08093i	0.518276	−	0.518276i	−0.398774	−	0.917049i	$-0.630564\pi$
$307$	9.08093	−	9.08093i	0.518276	−	0.518276i	0.917049	+	0.398774i	$0.130564\pi$
$308$	−16.9479	−	8.21985i	−0.965694	−	0.468370i
$309$	4.90835	+	4.90835i	0.279226	+	0.279226i
$310$	−0.914779	+	0.0864251i	−0.0519559	+	0.00490862i
$311$		−	17.7083i		−	1.00415i	−0.864825	−	0.502074i	$-0.832571\pi$
$311$		−	17.7083i		−	1.00415i	0.864825	−	0.502074i	$-0.167429\pi$
$312$	−8.25017	+	15.0016i	−0.467074	+	0.849298i
$313$	14.1377			0.799112			0.399556	−	0.916709i	$-0.369164\pi$
$313$	14.1377			0.799112			0.399556	+	0.916709i	$0.369164\pi$
$314$	−2.22718	−	23.5739i	−0.125687	−	1.33035i
$315$	−0.502609	−	0.374196i	−0.0283188	−	0.0210835i
$316$	0.416074	−	0.0793264i	0.0234060	−	0.00446246i
$317$	6.54573	−	6.54573i	0.367645	−	0.367645i	−0.498973	−	0.866618i	$-0.666289\pi$
$317$	6.54573	−	6.54573i	0.367645	−	0.367645i	0.866618	+	0.498973i	$0.166289\pi$
$318$	7.21335	+	5.96802i	0.404504	+	0.334670i
$319$		−	0.368618i		−	0.0206386i
$320$	1.84893	+	0.413877i	0.103358	+	0.0231364i
$321$		−	2.65054i		−	0.147939i
$322$	17.9973	+	10.9300i	1.00295	+	0.609105i
$323$	−25.8538	−	25.8538i	−1.43854	−	1.43854i
$324$	−0.374563	−	1.96461i	−0.0208091	−	0.109145i
$325$	21.1606	−	21.1606i	1.17378	−	1.17378i
$326$	−0.120669	−	1.27723i	−0.00668321	−	0.0707394i
$327$		−	17.8575i		−	0.987521i
$328$	−12.8089	+	23.2908i	−0.707251	+	1.28602i
$329$	−2.09295	+	0.306525i	−0.115388	+	0.0168993i
$330$	−0.112142	−	1.18698i	−0.00617319	−	0.0653410i
$331$	9.17452	−	9.17452i	0.504277	−	0.504277i	−0.408487	−	0.912764i	$-0.633944\pi$
$331$	9.17452	−	9.17452i	0.504277	−	0.504277i	0.912764	+	0.408487i	$0.133944\pi$
$332$	20.4585	+	13.9066i	1.12280	+	0.763224i
$333$	−0.490300	+	0.490300i	−0.0268683	+	0.0268683i
$334$	−7.81222	+	9.44237i	−0.427466	+	0.516664i
$335$	−3.33722			−0.182332
$336$	2.75328	−	10.2186i	0.150204	−	0.557469i
$337$	−6.41647			−0.349528			−0.174764	−	0.984610i	$-0.555916\pi$
$337$	−6.41647			−0.349528			−0.174764	+	0.984610i	$0.555916\pi$
$338$	21.3109	−	25.7578i	1.15916	−	1.40104i
$339$	−5.43463	+	5.43463i	−0.295169	+	0.295169i
$340$	−1.90197	+	2.79805i	−0.103149	+	0.151746i
$341$	−6.90524	+	6.90524i	−0.373940	+	0.373940i
$342$	0.680906	+	7.20715i	0.0368192	+	0.389718i
$343$	−16.7856	+	7.82588i	−0.906336	+	0.422558i
$344$	3.68515	+	12.6916i	0.198690	+	0.684285i
$345$			1.33280i			0.0717555i
$346$	−0.903676	−	9.56509i	−0.0485819	−	0.514222i
$347$	4.80880	−	4.80880i	0.258150	−	0.258150i	−0.566151	−	0.824301i	$-0.691568\pi$
$347$	4.80880	−	4.80880i	0.258150	−	0.258150i	0.824301	+	0.566151i	$0.191568\pi$
$348$	0.203443	−	0.0387874i	0.0109057	−	0.00207922i
$349$	−6.99706	−	6.99706i	−0.374544	−	0.374544i	0.494585	−	0.869129i	$-0.335320\pi$
$349$	−6.99706	−	6.99706i	−0.374544	−	0.374544i	−0.869129	+	0.494585i	$0.835320\pi$
$350$	−9.60224	+	15.8110i	−0.513261	+	0.845135i
$351$			6.05303i			0.323087i
$352$	17.9441	−	9.13725i	0.956426	−	0.487017i
$353$			27.6603i			1.47221i	0.676869	+	0.736104i	$0.263337\pi$
$353$			27.6603i			1.47221i	−0.676869	+	0.736104i	$0.736663\pi$
$354$	−11.9943	−	9.92354i	−0.637488	−	0.527430i
$355$	−0.0394141	+	0.0394141i	−0.00209188	+	0.00209188i
$356$	2.82599	+	14.8226i	0.149777	+	0.785594i
$357$	15.1581	+	11.2853i	0.802250	+	0.597281i
$358$	0.570792	+	6.04162i	0.0301673	+	0.319310i
$359$	29.1366			1.53777			0.768884	−	0.639388i	$-0.220812\pi$
$359$	29.1366			1.53777			0.768884	+	0.639388i	$0.220812\pi$
$360$	0.643303	−	0.186790i	0.0339050	−	0.00984472i
$361$		−	7.20331i		−	0.379121i
$362$	5.25652	−	0.496618i	0.276277	−	0.0261017i
$363$	−1.18178	−	1.18178i	−0.0620274	−	0.0620274i
$364$	−13.9774	+	28.8189i	−0.732614	+	1.51052i
$365$	1.87547	−	1.87547i	0.0981666	−	0.0981666i
$366$	−12.4655	−	10.3134i	−0.651580	−	0.539090i
$367$	−0.411143			−0.0214615			−0.0107307	−	0.999942i	$-0.503416\pi$
$367$	−0.411143			−0.0214615			−0.0107307	+	0.999942i	$0.503416\pi$
$368$	−20.9311	+	8.28227i	−1.09111	+	0.431743i
$369$			9.39766i			0.489223i
$370$	−0.178937	−	0.148045i	−0.00930251	−	0.00769650i
$371$	14.0489	+	10.4595i	0.729383	+	0.543031i
$372$	−4.53765	−	3.08446i	−0.235266	−	0.159922i
$373$	−13.7349	−	13.7349i	−0.711165	−	0.711165i	0.255614	−	0.966779i	$-0.417722\pi$
$373$	−13.7349	−	13.7349i	−0.711165	−	0.711165i	−0.966779	+	0.255614i	$0.917722\pi$
$374$	3.38206	+	35.7978i	0.174882	+	1.85106i
$375$	−2.35507			−0.121615
$376$	1.08971	−	1.98145i	0.0561973	−	0.102186i
$377$	−0.626814			−0.0322826
$378$	−0.888016	−	3.63475i	−0.0456746	−	0.186952i
$379$	5.47899	−	5.47899i	0.281437	−	0.281437i	−0.552245	−	0.833682i	$-0.686229\pi$
$379$	5.47899	−	5.47899i	0.281437	−	0.281437i	0.833682	+	0.552245i	$0.186229\pi$
$380$	−2.38178	+	0.454098i	−0.122183	+	0.0232948i
$381$	2.29041	+	2.29041i	0.117341	+	0.117341i
$382$	−11.2173	+	13.5580i	−0.573926	+	0.693685i
$383$	−28.4801			−1.45527			−0.727633	−	0.685967i	$-0.759379\pi$
$383$	−28.4801			−1.45527			−0.727633	+	0.685967i	$0.759379\pi$
$384$	6.93107	+	8.94205i	0.353700	+	0.456322i
$385$	−0.323225	−	2.20698i	−0.0164731	−	0.112478i
$386$	−6.53993	−	5.41086i	−0.332874	−	0.275406i
$387$	3.30395	+	3.30395i	0.167949	+	0.167949i
$388$	28.4838	−	5.43057i	1.44604	−	0.275695i
$389$	−8.44152	−	8.44152i	−0.428002	−	0.428002i	0.459945	−	0.887947i	$-0.347869\pi$
$389$	−8.44152	−	8.44152i	−0.428002	−	0.428002i	−0.887947	+	0.459945i	$0.847869\pi$
$390$	−2.01839	+	0.190691i	−0.102205	+	0.00965599i
$391$		−	40.1956i		−	2.03278i
$392$	4.16531	−	19.3559i	0.210380	−	0.977620i
$393$		−	0.285992i		−	0.0144264i
$394$	2.04968	+	21.6951i	0.103261	+	1.09298i
$395$	0.0354671	+	0.0354671i	0.00178454	+	0.00178454i
$396$	4.00227	−	5.88787i	0.201122	−	0.295877i
$397$	3.19995	+	3.19995i	0.160601	+	0.160601i	0.782833	−	0.622232i	$-0.213774\pi$
$397$	3.19995	+	3.19995i	0.160601	+	0.160601i	−0.622232	+	0.782833i	$0.713774\pi$
$398$	−8.31792	+	10.0536i	−0.416939	+	0.503941i
$399$	1.96257	+	13.4004i	0.0982514	+	0.670861i
$400$	−7.27616	−	18.3884i	−0.363808	−	0.919420i
$401$	19.1019			0.953904			0.476952	−	0.878929i	$-0.341742\pi$
$401$	19.1019			0.953904			0.476952	+	0.878929i	$0.341742\pi$
$402$	−15.3537	−	12.7030i	−0.765775	−	0.633570i
$403$	11.7420	+	11.7420i	0.584909	+	0.584909i
$404$	−10.5860	−	7.19580i	−0.526673	−	0.358005i
$405$	0.167468	−	0.167468i	0.00832156	−	0.00832156i
$406$	0.376393	−	0.0919575i	0.0186800	−	0.00456377i
$407$	−2.46824			−0.122346
$408$	−19.4012	+	5.63337i	−0.960504	+	0.278893i
$409$	−9.89111			−0.489084			−0.244542	−	0.969639i	$-0.578638\pi$
$409$	−9.89111			−0.489084			−0.244542	+	0.969639i	$0.578638\pi$
$410$	−3.13366	+	0.296058i	−0.154761	+	0.0146213i
$411$	−11.3036	−	11.3036i	−0.557567	−	0.557567i
$412$	−13.6373	+	2.60001i	−0.671860	+	0.128093i
$413$	−23.3604	−	17.3920i	−1.14949	−	0.855802i
$414$	−5.07327	+	6.13189i	−0.249338	+	0.301366i
$415$			2.92936i			0.143797i
$416$	−15.5374	−	30.5130i	−0.761782	−	1.49602i
$417$	2.86734			0.140414
$418$	−16.4270	+	19.8548i	−0.803471	+	0.971130i
$419$	−14.3138	+	14.3138i	−0.699276	+	0.699276i	−0.964254	−	0.264978i	$-0.914635\pi$
$419$	−14.3138	+	14.3138i	−0.699276	+	0.699276i	0.264978	+	0.964254i	$0.414635\pi$
$420$	1.18404	−	0.410617i	0.0577751	−	0.0200361i
$421$	−16.6566	−	16.6566i	−0.811792	−	0.811792i	0.173110	−	0.984902i	$-0.444618\pi$
$421$	−16.6566	−	16.6566i	−0.811792	−	0.811792i	−0.984902	+	0.173110i	$0.944618\pi$
$422$	−1.41823	−	15.0115i	−0.0690386	−	0.730748i
$423$		−	0.799500i		−	0.0388730i
$424$	−17.9816	+	5.22116i	−0.873264	+	0.253562i
$425$	35.3128			1.71292
$426$	−0.331364	+	0.0313061i	−0.0160546	+	0.00151679i
$427$	−24.2781	−	18.0752i	−1.17490	−	0.874720i
$428$	4.38412	+	2.98010i	0.211915	+	0.144049i
$429$	−15.2359	+	15.2359i	−0.735596	+	0.735596i
$430$	−0.997620	+	1.20579i	−0.0481095	+	0.0581484i
$431$			15.3363i			0.738721i	0.929286	+	0.369361i	$0.120423\pi$
$431$			15.3363i			0.738721i	−0.929286	+	0.369361i	$0.879577\pi$
$432$	3.67070	+	1.58934i	0.176606	+	0.0764671i
$433$			4.47978i			0.215285i	0.994190	+	0.107642i	$0.0343301\pi$
$433$			4.47978i			0.215285i	−0.994190	+	0.107642i	$0.965670\pi$
$434$	−8.77350	−	5.32826i	−0.421142	−	0.255765i
$435$	0.0173420	+	0.0173420i	0.000831484	+	0.000831484i
$436$	29.5371	+	20.0778i	1.41457	+	0.961552i
$437$	20.3695	−	20.3695i	0.974406	−	0.974406i
$438$	15.7675	−	1.48966i	0.753402	−	0.0711788i
$439$		−	0.171353i		−	0.00817822i	−0.999992	−	0.00408911i	$-0.998698\pi$
$439$		−	0.171353i		−	0.00817822i	0.999992	−	0.00408911i	$-0.00130161\pi$
$440$	2.08940	+	1.14907i	0.0996084	+	0.0547800i
$441$	−2.00732	−	6.70602i	−0.0955869	−	0.319334i
$442$	60.8722	−	5.75100i	2.89540	−	0.273547i
$443$	−0.195944	+	0.195944i	−0.00930960	+	0.00930960i	−0.711746	−	0.702437i	$-0.752095\pi$
$443$	−0.195944	+	0.195944i	−0.00930960	+	0.00930960i	0.702437	+	0.711746i	$0.252095\pi$
$444$	−0.259718	−	1.36224i	−0.0123257	−	0.0646491i
$445$	−1.26351	+	1.26351i	−0.0598961	+	0.0598961i
$446$	0.909613	+	0.752575i	0.0430714	+	0.0356355i
$447$	9.35974			0.442701
$448$	13.8064	+	16.0432i	0.652291	+	0.757968i
$449$	24.7162			1.16643			0.583215	−	0.812318i	$-0.301794\pi$
$449$	24.7162			1.16643			0.583215	+	0.812318i	$0.301794\pi$
$450$	−5.38700	−	4.45698i	−0.253946	−	0.210104i
$451$	−23.6546	+	23.6546i	−1.11385	+	1.11385i
$452$	−2.87879	−	15.0995i	−0.135407	−	0.710220i
$453$	−3.96430	+	3.96430i	−0.186259	+	0.186259i
$454$	7.82078	−	0.738881i	0.367048	−	0.0346774i
$455$	−3.75284	+	0.549625i	−0.175936	+	0.0257668i
$456$	−12.6865	−	6.97700i	−0.594101	−	0.326728i
$457$			23.1197i			1.08149i	0.841186	+	0.540746i	$0.181858\pi$
$457$			23.1197i			1.08149i	−0.841186	+	0.540746i	$0.818142\pi$
$458$	−2.34085	+	0.221155i	−0.109381	+	0.0103339i
$459$	−5.05064	+	5.05064i	−0.235744	+	0.235744i
$460$	−2.20451	−	1.49851i	−0.102786	−	0.0698685i
$461$	−17.4475	−	17.4475i	−0.812613	−	0.812613i	0.172412	−	0.985025i	$-0.444844\pi$
$461$	−17.4475	−	17.4475i	−0.812613	−	0.812613i	−0.985025	+	0.172412i	$0.944844\pi$
$462$	6.91373	−	11.3841i	0.321656	−	0.529638i
$463$		−	31.6552i		−	1.47114i	−0.677448	−	0.735570i	$-0.736914\pi$
$463$		−	31.6552i		−	1.47114i	0.677448	−	0.735570i	$-0.263086\pi$
$464$	−0.164582	+	0.380115i	−0.00764053	+	0.0176464i
$465$		−	0.649727i		−	0.0301304i
$466$	9.56254	−	11.5579i	0.442976	−	0.535411i
$467$	9.32784	−	9.32784i	0.431641	−	0.431641i	−0.457545	−	0.889186i	$-0.651271\pi$
$467$	9.32784	−	9.32784i	0.431641	−	0.431641i	0.889186	+	0.457545i	$0.151271\pi$
$468$	−10.0120	−	6.80563i	−0.462804	−	0.314590i
$469$	−29.9034	−	22.2633i	−1.38081	−	1.02802i
$470$	0.266594	−	0.0251869i	0.0122971	−	0.00116179i
$471$	16.7435			0.771500
$472$	29.8996	−	8.68169i	1.37624	−	0.399607i
$473$			16.6325i			0.764765i
$474$	0.0281710	+	0.298180i	0.00129394	+	0.0136959i
$475$	17.8951	+	17.8951i	0.821082	+	0.821082i
$476$	−35.7092	+	12.3837i	−1.63673	+	0.567607i
$477$	−4.68107	+	4.68107i	−0.214331	+	0.214331i
$478$	6.45725	−	7.80466i	0.295348	−	0.356977i
$479$	36.7307			1.67827			0.839134	−	0.543925i	$-0.183063\pi$
$479$	36.7307			1.67827			0.839134	+	0.543925i	$0.183063\pi$
$480$	−0.414328	+	1.27407i	−0.0189114	+	0.0581530i
$481$			4.19710i			0.191371i
$482$	12.1019	−	14.6271i	0.551225	−	0.666247i
$483$	−8.89139	+	11.9427i	−0.404572	+	0.543409i
$484$	3.28344	−	0.626003i	0.149247	−	0.0284547i
$485$	2.42802	+	2.42802i	0.110251	+	0.110251i
$486$	1.40794	−	0.133018i	0.0638656	−	0.00603380i
$487$	−23.4740			−1.06371			−0.531854	−	0.846836i	$-0.678505\pi$
$487$	−23.4740			−1.06371			−0.531854	+	0.846836i	$0.678505\pi$
$488$	31.0742	−	9.02275i	1.40666	−	0.408441i
$489$	0.907161			0.0410233
$490$	2.17289	−	0.880607i	0.0981613	−	0.0397818i
$491$	−19.6670	+	19.6670i	−0.887559	+	0.887559i	−0.994288	−	0.106730i	$-0.965962\pi$
$491$	−19.6670	+	19.6670i	−0.887559	+	0.887559i	0.106730	+	0.994288i	$0.465962\pi$
$492$	−15.5442	−	10.5661i	−0.700786	−	0.476358i
$493$	−0.523013	−	0.523013i	−0.0235553	−	0.0235553i
$494$	33.7619	+	27.9332i	1.51902	+	1.25677i
$495$	0.843058			0.0378926
$496$	10.2037	−	4.03753i	0.458159	−	0.181290i
$497$	−0.616113	+	0.0902332i	−0.0276364	+	0.00404751i
$498$	−11.1505	+	13.4773i	−0.499667	+	0.603932i
$499$	−23.7424	−	23.7424i	−1.06286	−	1.06286i	−0.997887	−	0.0649694i	$-0.979305\pi$
$499$	−23.7424	−	23.7424i	−1.06286	−	1.06286i	−0.0649694	−	0.997887i	$-0.520695\pi$
$500$	2.64789	−	3.89540i	0.118417	−	0.174208i
$501$	−6.12758	−	6.12758i	−0.273760	−	0.273760i
$502$	−0.994666	−	10.5282i	−0.0443941	−	0.469895i
$503$			28.1022i			1.25301i	0.779416	+	0.626507i	$0.215516\pi$
$503$			28.1022i			1.25301i	−0.779416	+	0.626507i	$0.784484\pi$
$504$	7.01048	+	2.61786i	0.312272	+	0.116609i
$505$		−	1.51576i		−	0.0674505i
$506$	−28.2042	+	2.66463i	−1.25383	+	0.118457i
$507$	16.7154	+	16.7154i	0.742356	+	0.742356i
$508$	−6.36364	+	1.21326i	−0.282341	+	0.0538297i
$509$	−5.21671	−	5.21671i	−0.231227	−	0.231227i	0.581978	−	0.813205i	$-0.302279\pi$
$509$	−5.21671	−	5.21671i	−0.231227	−	0.231227i	−0.813205	+	0.581978i	$0.802279\pi$
$510$	−1.84325	−	1.52503i	−0.0816206	−	0.0675294i
$511$	29.3170	−	4.29364i	1.29691	−	0.189939i
$512$	−22.5834	+	1.41046i	−0.998055	+	0.0623340i
$513$	−5.11892			−0.226006
$514$	0.383157	−	0.463109i	0.0169003	−	0.0204269i
$515$	−1.16247	−	1.16247i	−0.0512246	−	0.0512246i
$516$	−9.17962	+	1.75014i	−0.404110	+	0.0770456i
$517$	2.01240	−	2.01240i	0.0885052	−	0.0885052i
$518$	−0.615741	−	2.52030i	−0.0270541	−	0.110736i
$519$	6.79365			0.298208
$520$	1.95394	−	3.55291i	0.0856857	−	0.155805i
$521$	−19.5127			−0.854867			−0.427433	−	0.904047i	$-0.640582\pi$
$521$	−19.5127			−0.854867			−0.427433	+	0.904047i	$0.640582\pi$
$522$	0.0137745	+	0.145798i	0.000602893	+	0.00638140i
$523$	−21.8246	−	21.8246i	−0.954322	−	0.954322i	0.0446791	−	0.999001i	$-0.485773\pi$
$523$	−21.8246	−	21.8246i	−0.954322	−	0.954322i	−0.999001	+	0.0446791i	$0.985773\pi$
$524$	0.473044	+	0.321551i	0.0206650	+	0.0140470i
$525$	−10.4919	−	7.81128i	−0.457903	−	0.340912i
$526$	−28.9854	−	23.9813i	−1.26382	−	1.04563i
$527$			19.5950i			0.853570i
$528$	5.23892	+	13.2399i	0.227995	+	0.576192i
$529$	8.66909			0.376917
$530$	−1.70838	−	1.41344i	−0.0742072	−	0.0613959i
$531$	7.78362	−	7.78362i	0.337780	−	0.337780i
$532$	−24.3715	−	11.8204i	−1.05664	−	0.512479i
$533$	40.2233	+	40.2233i	1.74226	+	1.74226i
$534$	−10.6226	+	1.00359i	−0.459686	+	0.0434295i
$535$			0.627743i			0.0271397i
$536$	38.2742	−	11.1133i	1.65319	−	0.480023i
$537$	−4.29110			−0.185174
$538$	−2.88035	−	30.4874i	−0.124181	−	1.31441i
$539$	11.8269	−	21.9321i	0.509422	−	0.944682i
$540$	0.0887099	+	0.465290i	0.00381746	+	0.0200229i
$541$	20.4164	−	20.4164i	0.877769	−	0.877769i	−0.115534	−	0.993303i	$-0.536858\pi$
$541$	20.4164	−	20.4164i	0.877769	−	0.877769i	0.993303	+	0.115534i	$0.0368580\pi$
$542$	21.9337	+	18.1470i	0.942132	+	0.779480i
$543$			3.73348i			0.160219i
$544$	12.4956	−	38.4243i	0.535745	−	1.64743i
$545$			4.22929i			0.181163i
$546$	−19.3581	−	11.7564i	−0.828449	−	0.503128i
$547$	17.2377	+	17.2377i	0.737030	+	0.737030i	0.972002	−	0.234972i	$-0.0754998\pi$
$547$	17.2377	+	17.2377i	0.737030	+	0.737030i	−0.234972	+	0.972002i	$0.575500\pi$
$548$	31.4058	−	5.98767i	1.34159	−	0.255781i
$549$	8.08940	−	8.08940i	0.345247	−	0.345247i
$550$	−2.34094	−	24.7780i	−0.0998180	−	1.05654i
$551$		−	0.530083i		−	0.0225823i
$552$	−4.43839	−	15.2857i	−0.188910	−	0.650604i
$553$	0.0811970	+	0.554414i	0.00345285	+	0.0235761i
$554$	−3.16226	−	33.4713i	−0.134351	−	1.42206i
$555$	0.116121	−	0.116121i	0.00492904	−	0.00492904i
$556$	−3.22385	+	4.74272i	−0.136722	+	0.201136i
$557$	22.7060	−	22.7060i	0.962084	−	0.962084i	−0.0372230	−	0.999307i	$-0.511851\pi$
$557$	22.7060	−	22.7060i	0.962084	−	0.962084i	0.999307	+	0.0372230i	$0.0118512\pi$
$558$	2.47317	−	2.98924i	0.104698	−	0.126545i
$559$	28.2827			1.19623
$560$	−0.652075	+	2.42013i	−0.0275552	+	0.102269i
$561$	−25.4256			−1.07347
$562$	−4.03611	+	4.87831i	−0.170253	+	0.205779i
$563$	−17.0537	+	17.0537i	−0.718726	+	0.718726i	−0.968344	−	0.249618i	$-0.919695\pi$
$563$	−17.0537	+	17.0537i	−0.718726	+	0.718726i	0.249618	+	0.968344i	$0.419695\pi$
$564$	1.32241	+	0.898906i	0.0556835	+	0.0378508i
$565$	1.28711	−	1.28711i	0.0541493	−	0.0541493i
$566$	−1.82045	−	19.2688i	−0.0765193	−	0.809929i
$567$	2.61783	−	0.383395i	0.109938	−	0.0161011i
$568$	0.320782	−	0.583290i	0.0134597	−	0.0244743i
$569$		−	22.0290i		−	0.923502i	−0.887009	−	0.461751i	$-0.847221\pi$
$569$		−	22.0290i		−	0.923502i	0.887009	−	0.461751i	$-0.152779\pi$
$570$	−0.161263	−	1.70691i	−0.00675456	−	0.0714946i
$571$	5.13880	−	5.13880i	0.215052	−	0.215052i	−0.591357	−	0.806410i	$-0.701408\pi$
$571$	5.13880	−	5.13880i	0.215052	−	0.215052i	0.806410	+	0.591357i	$0.201408\pi$
$572$	−8.07064	−	42.3311i	−0.337450	−	1.76995i
$573$	−8.79837	−	8.79837i	−0.367557	−	0.367557i
$574$	−30.0545	−	18.2525i	−1.25445	−	0.761844i
$575$			27.8220i			1.16026i
$576$	−6.75593	+	4.28455i	−0.281497	+	0.178523i
$577$			13.7657i			0.573074i	0.958069	+	0.286537i	$0.0925042\pi$
$577$			13.7657i			0.573074i	−0.958069	+	0.286537i	$0.907496\pi$
$578$	37.0667	+	30.6674i	1.54177	+	1.27560i
$579$	4.24406	−	4.24406i	0.176377	−	0.176377i
$580$	−0.0481826	+	0.00918625i	−0.00200067	+	0.000381438i
$581$	−19.5424	+	26.2487i	−0.810754	+	1.08898i
$582$	1.92854	+	20.4129i	0.0799408	+	0.846144i
$583$	−23.5652			−0.975969
$584$	−15.2640	+	27.7551i	−0.631629	+	1.14851i
$585$		−	1.43357i		−	0.0592709i
$586$	−16.9006	+	1.59671i	−0.698159	+	0.0659597i
$587$	10.4983	+	10.4983i	0.433312	+	0.433312i	0.889753	−	0.456442i	$-0.150876\pi$
$587$	10.4983	+	10.4983i	0.433312	+	0.433312i	−0.456442	+	0.889753i	$0.650876\pi$
$588$	13.3490	+	4.21960i	0.550502	+	0.174013i
$589$	−9.92994	+	9.92994i	−0.409156	+	0.409156i
$590$	2.84067	+	2.35025i	0.116949	+	0.0967582i
$591$	−15.4091			−0.633844
$592$	2.54522	+	1.10203i	0.104608	+	0.0452931i
$593$			16.4073i			0.673768i	0.941546	+	0.336884i	$0.109373\pi$
$593$			16.4073i			0.673768i	−0.941546	+	0.336884i	$0.890627\pi$
$594$	3.87871	+	3.20908i	0.159145	+	0.131670i
$595$	−3.58997	−	2.67276i	−0.147175	−	0.109572i
$596$	−10.5235	+	15.4814i	−0.431059	+	0.634145i
$597$	−6.52423	−	6.52423i	−0.267019	−	0.267019i
$598$	4.53106	+	47.9596i	0.185289	+	1.96121i
$599$	−21.9084			−0.895154			−0.447577	−	0.894245i	$-0.647713\pi$
$599$	−21.9084			−0.895154			−0.447577	+	0.894245i	$0.647713\pi$
$600$	13.4288	−	3.89922i	0.548230	−	0.159185i
$601$	−41.7949			−1.70485			−0.852425	−	0.522849i	$-0.824869\pi$
$601$	−41.7949			−1.70485			−0.852425	+	0.522849i	$0.824869\pi$
$602$	−16.9833	+	4.14924i	−0.692189	+	0.169111i
$603$	9.96374	−	9.96374i	0.405755	−	0.405755i
$604$	−2.09994	−	11.0143i	−0.0854452	−	0.448167i
$605$	0.279888	+	0.279888i	0.0113791	+	0.0113791i
$606$	5.76971	−	6.97365i	0.234378	−	0.283285i
$607$	42.9099			1.74166			0.870830	−	0.491584i	$-0.163582\pi$
$607$	42.9099			1.74166			0.870830	+	0.491584i	$0.163582\pi$
$608$	25.8042	−	13.1396i	1.04650	−	0.532882i
$609$	0.0397021	+	0.271086i	0.00160881	+	0.0109850i
$610$	2.95227	+	2.44258i	0.119534	+	0.0988972i
$611$	−3.42197	−	3.42197i	−0.138438	−	0.138438i
$612$	−2.67538	−	14.0326i	−0.108146	−	0.567234i
$613$	−3.30257	−	3.30257i	−0.133390	−	0.133390i	0.637260	−	0.770649i	$-0.280068\pi$
$613$	−3.30257	−	3.30257i	−0.133390	−	0.133390i	−0.770649	+	0.637260i	$0.780068\pi$
$614$	−18.0813	+	1.70826i	−0.729703	+	0.0689399i
$615$		−	2.22570i		−	0.0897490i
$616$	11.0565	+	24.2352i	0.445481	+	0.976464i
$617$		−	20.7360i		−	0.834800i	−0.908723	−	0.417400i	$-0.862941\pi$
$617$		−	20.7360i		−	0.834800i	0.908723	−	0.417400i	$-0.137059\pi$
$618$	−0.923336	−	9.77318i	−0.0371420	−	0.393135i
$619$	16.9754	+	16.9754i	0.682298	+	0.682298i	0.960518	−	0.278219i	$-0.0897442\pi$
$619$	16.9754	+	16.9754i	0.682298	+	0.682298i	−0.278219	+	0.960518i	$0.589744\pi$
$620$	1.07468	+	0.730510i	0.0431601	+	0.0293380i
$621$	−3.97926	−	3.97926i	−0.159682	−	0.159682i
$622$	−15.9642	+	19.2954i	−0.640107	+	0.773677i
$623$	−19.7509	+	2.89263i	−0.791303	+	0.115891i
$624$	22.5137	−	8.90849i	0.901268	−	0.356625i
$625$	−24.1618			−0.966471
$626$	−15.4048	−	12.7453i	−0.615700	−	0.509404i
$627$	−12.8847	−	12.8847i	−0.514564	−	0.514564i
$628$	−18.8253	+	27.6945i	−0.751211	+	1.10513i
$629$	−3.50206	+	3.50206i	−0.139636	+	0.139636i
$630$	0.210314	+	0.860839i	0.00837911	+	0.0342966i
$631$	41.1032			1.63629			0.818146	−	0.575010i	$-0.195002\pi$
$631$	41.1032			1.63629			0.818146	+	0.575010i	$0.195002\pi$
$632$	−0.524877	−	0.288658i	−0.0208785	−	0.0114822i
$633$	10.6620			0.423776
$634$	−13.0334	+	1.23135i	−0.517624	+	0.0489033i
$635$	−0.542451	−	0.542451i	−0.0215265	−	0.0215265i
$636$	−2.47962	−	13.0058i	−0.0983232	−	0.515713i
$637$	−37.2943	−	20.1110i	−1.47765	−	0.796828i
$638$	−0.332312	+	0.401655i	−0.0131564	+	0.0159017i
$639$		−	0.235353i		−	0.00931041i
$640$	−1.64152	−	2.11780i	−0.0648870	−	0.0837133i
$641$	−7.71535			−0.304738			−0.152369	−	0.988324i	$-0.548690\pi$
$641$	−7.71535			−0.304738			−0.152369	+	0.988324i	$0.548690\pi$
$642$	−2.38949	+	2.88810i	−0.0943056	+	0.113984i
$643$	−32.7634	+	32.7634i	−1.29206	+	1.29206i	−0.358555	+	0.933509i	$0.616730\pi$
$643$	−32.7634	+	32.7634i	−1.29206	+	1.29206i	−0.933509	+	0.358555i	$0.883270\pi$
$644$	−9.75681	−	28.1343i	−0.384472	−	1.10865i
$645$	−0.782492	−	0.782492i	−0.0308106	−	0.0308106i
$646$	4.86350	+	51.4783i	0.191352	+	2.02539i
$647$		−	17.2904i		−	0.679756i	−0.940469	−	0.339878i	$-0.889614\pi$
$647$		−	17.2904i		−	0.679756i	0.940469	−	0.339878i	$-0.110386\pi$
$648$	−1.36298	+	2.47836i	−0.0535430	+	0.0973592i
$649$	39.1839			1.53810
$650$	−42.1336	+	3.98064i	−1.65262	+	0.156133i
$651$	4.33446	−	5.82192i	0.169881	−	0.228179i
$652$	−1.01995	+	1.50049i	−0.0399445	+	0.0587636i
$653$	2.03773	−	2.03773i	0.0797425	−	0.0797425i	−0.666111	−	0.745853i	$-0.732042\pi$
$653$	2.03773	−	2.03773i	0.0797425	−	0.0797425i	0.745853	+	0.666111i	$0.232042\pi$
$654$	−16.0987	+	19.4580i	−0.629509	+	0.760866i
$655$			0.0677331i			0.00264655i
$656$	34.9537	−	13.8309i	1.36471	−	0.540007i
$657$			11.1990i			0.436914i
$658$	2.55687	+	1.55282i	0.0996770	+	0.0605351i
$659$	−17.0779	−	17.0779i	−0.665259	−	0.665259i	0.291356	−	0.956615i	$-0.405894\pi$
$659$	−17.0779	−	17.0779i	−0.665259	−	0.665259i	−0.956615	+	0.291356i	$0.905894\pi$
$660$	−0.947880	+	1.39446i	−0.0368962	+	0.0542792i
$661$	−2.96315	+	2.96315i	−0.115253	+	0.115253i	−0.762381	−	0.647128i	$-0.775970\pi$
$661$	−2.96315	+	2.96315i	−0.115253	+	0.115253i	0.647128	+	0.762381i	$0.275970\pi$
$662$	−18.2677	+	1.72587i	−0.709994	+	0.0670778i
$663$			43.2348i			1.67910i
$664$	−9.75513	−	33.5965i	−0.378572	−	1.30380i
$665$	−0.464806	−	3.17370i	−0.0180244	−	0.123071i
$666$	0.976253	−	0.0922330i	0.0378290	−	0.00357396i
$667$	0.412068	−	0.412068i	0.0159553	−	0.0159553i
$668$	17.0248	−	3.24586i	0.658708	−	0.125586i
$669$	−0.590289	+	0.590289i	−0.0228219	+	0.0228219i
$670$	3.63631	+	3.00853i	0.140483	+	0.116230i
$671$	40.7232			1.57210
$672$	−12.2122	+	8.65231i	−0.471095	+	0.333770i
$673$	−8.94408			−0.344769			−0.172384	−	0.985030i	$-0.555147\pi$
$673$	−8.94408			−0.344769			−0.172384	+	0.985030i	$0.555147\pi$
$674$	6.99155	+	5.78451i	0.269304	+	0.222811i
$675$	3.49587	−	3.49587i	0.134556	−	0.134556i
$676$	−46.4417	+	8.85434i	−1.78622	+	0.340552i
$677$	−7.48867	+	7.48867i	−0.287813	+	0.287813i	−0.836215	−	0.548402i	$-0.815236\pi$
$677$	−7.48867	+	7.48867i	−0.287813	+	0.287813i	0.548402	+	0.836215i	$0.315236\pi$
$678$	10.8211	−	1.02234i	0.415581	−	0.0392626i
$679$	5.55862	+	37.9543i	0.213320	+	1.45655i
$680$	4.59490	−	1.33418i	0.176207	−	0.0511636i
$681$			5.55476i			0.212859i
$682$	13.7493	−	1.29898i	0.526486	−	0.0497406i
$683$	19.2209	−	19.2209i	0.735467	−	0.735467i	−0.236230	−	0.971697i	$-0.575912\pi$
$683$	19.2209	−	19.2209i	0.735467	−	0.735467i	0.971697	+	0.236230i	$0.0759119\pi$
$684$	5.75538	−	8.46693i	0.220062	−	0.323741i
$685$	2.67710	+	2.67710i	0.102287	+	0.102287i
$686$	25.3451	+	6.60508i	0.967680	+	0.252183i
$687$		−	1.66260i		−	0.0634321i
$688$	7.42616	−	17.1513i	0.283120	−	0.653886i
$689$			40.0712i			1.52659i
$690$	1.20153	−	1.45225i	0.0457415	−	0.0552863i
$691$	−6.36522	+	6.36522i	−0.242144	+	0.242144i	−0.817737	−	0.575592i	$-0.804771\pi$
$691$	−6.36522	+	6.36522i	−0.242144	+	0.242144i	0.575592	+	0.817737i	$0.304771\pi$
$692$	−7.63834	+	11.2370i	−0.290366	+	0.427168i
$693$	7.55428	+	5.62422i	0.286964	+	0.213646i
$694$	−9.57496	+	0.904609i	−0.363460	+	0.0343385i
$695$	−0.679089			−0.0257593
$696$	−0.256644	−	0.141142i	−0.00972806	−	0.00534998i
$697$			67.1245i			2.54252i
$698$	1.31625	+	13.9321i	0.0498210	+	0.527337i
$699$	7.50047	+	7.50047i	0.283694	+	0.283694i
$700$	24.7166	−	8.57157i	0.934200	−	0.323975i
$701$	2.92182	−	2.92182i	0.110356	−	0.110356i	−0.649773	−	0.760128i	$-0.725136\pi$
$701$	2.92182	−	2.92182i	0.110356	−	0.110356i	0.760128	+	0.649773i	$0.225136\pi$
$702$	5.45686	−	6.59553i	0.205956	−	0.248932i
$703$	−3.54940			−0.133868
$704$	−27.7897	−	6.22063i	−1.04736	−	0.234449i
$705$			0.189350i			0.00713134i
$706$	24.9360	−	30.1393i	0.938478	−	1.13431i
$707$	10.1120	−	13.5821i	0.380299	−	0.510807i
$708$	4.12308	+	21.6259i	0.154955	+	0.812750i
$709$	20.3789	+	20.3789i	0.765346	+	0.765346i	0.977283	−	0.211937i	$-0.0679773\pi$
$709$	20.3789	+	20.3789i	0.765346	+	0.765346i	−0.211937	+	0.977283i	$0.567977\pi$
$710$	0.0784787	−	0.00741440i	0.00294525	−	0.000278257i
$711$	−0.211784			−0.00794252
$712$	10.2834	−	18.6987i	0.385387	−	0.700763i
$713$	−15.4384			−0.578171
$714$	−6.34282	−	25.9619i	−0.237374	−	0.971599i
$715$	3.60840	−	3.60840i	0.134947	−	0.134947i
$716$	4.82463	−	7.09768i	0.180305	−	0.265253i
$717$	5.06480	+	5.06480i	0.189148	+	0.189148i
$718$	−31.7479	−	26.2669i	−1.18482	−	0.980271i
$719$	28.7270			1.07134			0.535668	−	0.844429i	$-0.320060\pi$
$719$	28.7270			1.07134			0.535668	+	0.844429i	$0.320060\pi$
$720$	−0.869352	−	0.376412i	−0.0323988	−	0.0140280i
$721$	−2.66132	−	18.1715i	−0.0991128	−	0.676742i
$722$	−6.49385	+	7.84890i	−0.241676	+	0.292106i
$723$	9.49221	+	9.49221i	0.353019	+	0.353019i
$724$	−6.17534	−	4.19768i	−0.229505	−	0.156005i
$725$	0.362011	+	0.362011i	0.0134447	+	0.0134447i
$726$	0.222311	+	2.35308i	0.00825074	+	0.0873311i
$727$			53.1288i			1.97044i	0.171302	+	0.985219i	$0.445203\pi$
$727$			53.1288i			1.97044i	−0.171302	+	0.985219i	$0.554797\pi$
$728$	41.2106	−	18.8010i	1.52737	−	0.696812i
$729$			1.00000i			0.0370370i
$730$	−3.73431	+	0.352805i	−0.138213	+	0.0130579i
$731$	23.5990	+	23.5990i	0.872841	+	0.872841i
$732$	4.28505	+	22.4755i	0.158380	+	0.830717i
$733$	−22.8737	−	22.8737i	−0.844860	−	0.844860i	0.144627	−	0.989486i	$-0.453802\pi$
$733$	−22.8737	−	22.8737i	−0.844860	−	0.844860i	−0.989486	+	0.144627i	$0.953802\pi$
$734$	0.447991	+	0.370649i	0.0165357	+	0.0136809i
$735$	0.475406	+	1.58822i	0.0175356	+	0.0585825i
$736$	30.2735	+	9.84498i	1.11590	+	0.362891i
$737$	50.1589			1.84763
$738$	8.47208	−	10.2399i	0.311862	−	0.376937i
$739$	17.1191	+	17.1191i	0.629735	+	0.629735i	0.948001	−	0.318266i	$-0.103101\pi$
$739$	17.1191	+	17.1191i	0.629735	+	0.629735i	−0.318266	+	0.948001i	$0.603101\pi$
$740$	0.0615105	+	0.322627i	0.00226117	+	0.0118600i
$741$	−21.9097	+	21.9097i	−0.804871	+	0.804871i
$742$	−5.87870	−	24.0622i	−0.215814	−	0.883350i
$743$	−52.4170			−1.92299			−0.961496	−	0.274818i	$-0.911382\pi$
$743$	−52.4170			−1.92299			−0.961496	+	0.274818i	$0.911382\pi$
$744$	2.16367	+	7.45164i	0.0793240	+	0.273190i
$745$	−2.21672			−0.0812143
$746$	2.58374	+	27.3480i	0.0945975	+	1.00128i
$747$	−8.74602	−	8.74602i	−0.320000	−	0.320000i
$748$	28.5869	−	42.0552i	1.04524	−	1.53769i
$749$	−4.18781	+	5.62494i	−0.153019	+	0.205531i
$750$	2.56614	+	2.12312i	0.0937023	+	0.0775253i
$751$		−	5.04763i		−	0.184191i	−0.995750	−	0.0920953i	$-0.970644\pi$
$751$		−	5.04763i		−	0.184191i	0.995750	−	0.0920953i	$-0.0293564\pi$
$752$	−2.97367	+	1.17666i	−0.108438	+	0.0429083i
$753$	7.47769			0.272502
$754$	0.682992	+	0.565079i	0.0248731	+	0.0205789i
$755$	0.938887	−	0.938887i	0.0341696	−	0.0341696i
$756$	−2.30916	+	4.76107i	−0.0839833	+	0.173158i
$757$	−19.3984	−	19.3984i	−0.705045	−	0.705045i	0.260444	−	0.965489i	$-0.416131\pi$
$757$	−19.3984	−	19.3984i	−0.705045	−	0.705045i	−0.965489	+	0.260444i	$0.916131\pi$
$758$	−10.9094	+	1.03068i	−0.396247	+	0.0374361i
$759$		−	20.0322i		−	0.727122i
$760$	3.00462	+	1.65240i	0.108989	+	0.0599389i
$761$	17.5182			0.635034			0.317517	−	0.948253i	$-0.397151\pi$
$761$	17.5182			0.635034			0.317517	+	0.948253i	$0.397151\pi$
$762$	−0.430862	−	4.56052i	−0.0156085	−	0.165210i
$763$	−28.2145	+	37.8969i	−1.02143	+	1.37196i
$764$	24.4452	−	4.66060i	0.884397	−	0.168615i
$765$	1.19617	−	1.19617i	0.0432476	−	0.0432476i
$766$	31.0326	+	25.6751i	1.12125	+	0.927678i
$767$		−	66.6299i		−	2.40587i
$768$	0.509075	−	15.9919i	0.0183697	−	0.577058i
$769$			31.6824i			1.14250i	0.820777	+	0.571249i	$0.193541\pi$
$769$			31.6824i			1.14250i	−0.820777	+	0.571249i	$0.806459\pi$
$770$	−1.63742	+	2.69617i	−0.0590084	+	0.0971631i
$771$	0.300532	+	0.300532i	0.0108234	+	0.0108234i
$772$	2.24813	+	11.7916i	0.0809119	+	0.424389i
$773$	34.9011	−	34.9011i	1.25531	−	1.25531i	0.301998	−	0.953308i	$-0.402346\pi$
$773$	34.9011	−	34.9011i	1.25531	−	1.25531i	0.953308	−	0.301998i	$-0.0976537\pi$
$774$	−0.621523	−	6.57860i	−0.0223402	−	0.236463i
$775$		−	13.5629i		−	0.487195i
$776$	−35.9323	−	19.7611i	−1.28989	−	0.709382i
$777$	1.81517	−	0.265842i	0.0651189	−	0.00953704i
$778$	1.58798	+	16.8082i	0.0569318	+	0.602603i
$779$	−34.0160	+	34.0160i	−1.21875	+	1.21875i
$780$	2.37120	+	1.61182i	0.0849024	+	0.0577123i
$781$	0.592400	−	0.592400i	0.0211977	−	0.0211977i
$782$	−36.2367	+	43.7981i	−1.29582	+	1.56622i
$783$	−0.103554			−0.00370071
$784$	−21.9881	+	17.3356i	−0.785290	+	0.619128i
$785$	−3.96546			−0.141533
$786$	−0.257824	+	0.311624i	−0.00919628	+	0.0111152i
$787$	20.4440	−	20.4440i	0.728749	−	0.728749i	−0.241622	−	0.970371i	$-0.577679\pi$
$787$	20.4440	−	20.4440i	0.728749	−	0.728749i	0.970371	+	0.241622i	$0.0776793\pi$
$788$	17.3249	−	25.4873i	0.617175	−	0.907947i
$789$	18.8099	−	18.8099i	0.669651	−	0.669651i
$790$	−0.00667190	−	0.0706197i	−0.000237376	−	0.00251254i
$791$	20.1199	−	2.94667i	0.715381	−	0.104772i
$792$	−9.66894	+	2.80749i	−0.343571	+	0.0997597i
$793$		−	69.2475i		−	2.45905i
$794$	−0.601959	−	6.37152i	−0.0213627	−	0.226117i
$795$	1.10864	−	1.10864i	0.0393195	−	0.0393195i
$796$	18.1268	−	3.45596i	0.642488	−	0.122493i
$797$	8.54875	+	8.54875i	0.302812	+	0.302812i	0.842113	−	0.539301i	$-0.181311\pi$
$797$	8.54875	+	8.54875i	0.302812	+	0.302812i	−0.539301	+	0.842113i	$0.681311\pi$
$798$	9.94214	−	16.3707i	0.351948	−	0.579517i
$799$		−	5.71057i		−	0.202026i
$800$	−8.64903	+	26.5960i	−0.305789	+	0.940310i
$801$		−	7.54477i		−	0.266581i
$802$	−20.8139	−	17.2205i	−0.734965	−	0.608079i
$803$	−28.1886	+	28.1886i	−0.994755	+	0.994755i
$804$	5.27791	+	27.6831i	0.186138	+	0.976307i
$805$	2.10580	−	2.82845i	0.0742196	−	0.0996896i
$806$	−2.20885	−	23.3798i	−0.0778033	−	0.823520i
$807$	21.6539			0.762253
$808$	5.04767	+	17.3841i	0.177576	+	0.611570i
$809$		−	13.2816i		−	0.466956i	−0.972362	−	0.233478i	$-0.924989\pi$
$809$		−	13.2816i		−	0.466956i	0.972362	−	0.233478i	$-0.0750108\pi$
$810$	−0.333451	+	0.0315033i	−0.0117163	+	0.00110691i
$811$	2.35686	+	2.35686i	0.0827606	+	0.0827606i	0.747275	−	0.664515i	$-0.231362\pi$
$811$	2.35686	+	2.35686i	0.0827606	+	0.0827606i	−0.664515	+	0.747275i	$0.731362\pi$
$812$	−0.493027	−	0.239122i	−0.0173019	−	0.00839154i
$813$	−14.2338	+	14.2338i	−0.499200	+	0.499200i
$814$	2.68946	+	2.22514i	0.0942654	+	0.0779912i
$815$	−0.214848			−0.00752580
$816$	26.2186	+	11.3521i	0.917834	+	0.397404i
$817$			23.9181i			0.836787i
$818$	10.7776	+	8.91692i	0.376830	+	0.311773i
$819$	9.56366	−	12.8456i	0.334181	−	0.448863i
$820$	3.68142	+	2.50243i	0.128561	+	0.0873888i
$821$	2.18290	+	2.18290i	0.0761836	+	0.0761836i	0.744172	−	0.667988i	$-0.232844\pi$
$821$	2.18290	+	2.18290i	0.0761836	+	0.0761836i	−0.667988	+	0.744172i	$0.732844\pi$
$822$	2.12639	+	22.5070i	0.0741663	+	0.785024i
$823$	9.24257			0.322176			0.161088	−	0.986940i	$-0.448500\pi$
$823$	9.24257			0.322176			0.161088	+	0.986940i	$0.448500\pi$
$824$	17.2034	+	9.46108i	0.599310	+	0.329592i
$825$	17.5987			0.612708
$826$	9.77502	+	40.0103i	0.340116	+	1.39214i
$827$	−25.0240	+	25.0240i	−0.870171	+	0.870171i	−0.992491	−	0.122319i	$-0.960967\pi$
$827$	−25.0240	+	25.0240i	−0.870171	+	0.870171i	0.122319	+	0.992491i	$0.460967\pi$
$828$	11.0559	−	2.10786i	0.384220	−	0.0732533i
$829$	9.38010	+	9.38010i	0.325784	+	0.325784i	0.850981	−	0.525197i	$-0.176008\pi$
$829$	9.38010	+	9.38010i	0.325784	+	0.325784i	−0.525197	+	0.850981i	$0.676008\pi$
$830$	2.64084	−	3.19190i	0.0916650	−	0.110793i
$831$	23.7732			0.824683
$832$	−10.5778	+	47.2548i	−0.366720	+	1.63826i
$833$	−14.3377	−	47.8989i	−0.496771	−	1.65960i
$834$	−3.12432	−	2.58493i	−0.108187	−	0.0895089i
$835$	1.45123	+	1.45123i	0.0502219	+	0.0502219i
$836$	35.7985	−	6.82517i	1.23812	−	0.236053i
$837$	1.93985	+	1.93985i	0.0670511	+	0.0670511i
$838$	28.5007	−	2.69265i	0.984542	−	0.0930161i
$839$		−	20.9881i		−	0.724591i	−0.932063	−	0.362296i	$-0.881993\pi$
$839$		−	20.9881i		−	0.724591i	0.932063	−	0.362296i	$-0.118007\pi$
$840$	−1.66033	−	0.620002i	−0.0572869	−	0.0213921i
$841$			28.9893i			0.999630i
$842$	3.13336	+	33.1655i	0.107983	+	1.14296i
$843$	−3.16576	−	3.16576i	−0.109034	−	0.109034i
$844$	−11.9877	+	17.6354i	−0.412632	+	0.607037i
$845$	−3.95880	−	3.95880i	−0.136187	−	0.136187i
$846$	−0.720757	+	0.871155i	−0.0247801	+	0.0299509i
$847$	0.640765	+	4.37514i	0.0220169	+	0.150332i
$848$	24.3001	+	10.5215i	0.834469	+	0.361309i
$849$	13.6858			0.469695
$850$	−38.4776	−	31.8348i	−1.31977	−	1.09192i
$851$	−2.75918	−	2.75918i	−0.0945835	−	0.0945835i
$852$	0.389285	+	0.264615i	0.0133367	+	0.00906557i
$853$	29.8015	−	29.8015i	1.02038	−	1.02038i	0.0205966	−	0.999788i	$-0.493443\pi$
$853$	29.8015	−	29.8015i	1.02038	−	1.02038i	0.999788	−	0.0205966i	$-0.00655656\pi$
$854$	10.1590	+	41.5821i	0.347635	+	1.42291i
$855$	1.21234			0.0414612
$856$	−2.09046	−	7.19952i	−0.0714505	−	0.246074i
$857$	−51.8982			−1.77281			−0.886405	−	0.462910i	$-0.846805\pi$
$857$	−51.8982			−1.77281			−0.886405	+	0.462910i	$0.846805\pi$
$858$	30.3367	−	2.86611i	1.03568	−	0.0978473i
$859$	10.4965	+	10.4965i	0.358138	+	0.358138i	0.863126	−	0.504988i	$-0.168503\pi$
$859$	10.4965	+	10.4965i	0.358138	+	0.358138i	−0.504988	+	0.863126i	$0.668503\pi$
$860$	2.17406	−	0.414495i	0.0741349	−	0.0141342i
$861$	14.8481	−	19.9436i	0.506023	−	0.679675i
$862$	13.8258	−	16.7108i	0.470908	−	0.569171i
$863$			21.5284i			0.732836i	0.930450	+	0.366418i	$0.119416\pi$
$863$			21.5284i			0.732836i	−0.930450	+	0.366418i	$0.880584\pi$
$864$	−2.56688	−	5.04095i	−0.0873269	−	0.171496i
$865$	−1.60898			−0.0547070
$866$	4.03857	−	4.88128i	0.137236	−	0.165873i
$867$	−24.0543	+	24.0543i	−0.816925	+	0.816925i
$868$	4.75635	+	13.7152i	0.161441	+	0.465524i
$869$	−0.533075	−	0.533075i	−0.0180833	−	0.0180833i
$870$	−0.00326229	−	0.0345302i	−0.000110602	−	0.00117068i
$871$		−	85.2923i		−	2.89002i
$872$	−14.0841	−	48.5052i	−0.476946	−	1.64259i
$873$	−14.4984			−0.490697
$874$	−40.5584	+	3.83182i	−1.37191	+	0.129613i
$875$	4.99790	+	3.72097i	0.168960	+	0.125792i
$876$	−18.5236	−	12.5914i	−0.625855	−	0.425424i
$877$	−6.07418	+	6.07418i	−0.205110	+	0.205110i	−0.802185	−	0.597075i	$-0.796329\pi$
$877$	−6.07418	+	6.07418i	−0.205110	+	0.205110i	0.597075	+	0.802185i	$0.296329\pi$
$878$	−0.154476	+	0.186710i	−0.00521331	+	0.00630116i
$879$		−	12.0038i		−	0.404877i
$880$	−1.24076	−	3.13567i	−0.0418261	−	0.105704i
$881$			22.7089i			0.765081i	0.923939	+	0.382541i	$0.124951\pi$
$881$			22.7089i			0.765081i	−0.923939	+	0.382541i	$0.875049\pi$
$882$	−3.85830	+	9.11666i	−0.129916	+	0.306974i
$883$	27.9984	+	27.9984i	0.942222	+	0.942222i	0.998420	−	0.0561975i	$-0.0178976\pi$
$883$	27.9984	+	27.9984i	0.942222	+	0.942222i	−0.0561975	+	0.998420i	$0.517898\pi$
$884$	−71.5124	−	48.6104i	−2.40522	−	1.63495i
$885$	−1.84344	+	1.84344i	−0.0619665	+	0.0619665i
$886$	0.390151	−	0.0368602i	0.0131074	−	0.00123834i
$887$			33.0274i			1.10895i	0.832200	+	0.554475i	$0.187081\pi$
$887$			33.0274i			1.10895i	−0.832200	+	0.554475i	$0.812919\pi$
$888$	−0.945078	+	1.71847i	−0.0317147	+	0.0576681i
$889$	−1.24187	−	8.47948i	−0.0416509	−	0.284393i
$890$	2.51581	−	0.237685i	0.0843303	−	0.00796724i
$891$	−2.51707	+	2.51707i	−0.0843250	+	0.0843250i
$892$	−0.312683	−	1.64005i	−0.0104694	−	0.0549129i
$893$	2.89389	−	2.89389i	0.0968402	−	0.0968402i
$894$	−10.1986	−	8.43789i	−0.341092	−	0.282205i
$895$	1.01628			0.0339707
$896$	−0.580740	−	29.9276i	−0.0194012	−	0.999812i
$897$	−34.0636			−1.13735
$898$	−26.9314	−	22.2819i	−0.898712	−	0.743556i
$899$	−0.200879	+	0.200879i	−0.00669969	+	0.00669969i
$900$	1.85180	+	9.71287i	0.0617268	+	0.323762i
$901$	−33.4354	+	33.4354i	−1.11389	+	1.11389i
$902$	47.0994	−	4.44979i	1.56824	−	0.148162i
$903$	−1.79141	−	12.2317i	−0.0596144	−	0.407047i
$904$	−10.4755	+	19.0480i	−0.348410	+	0.633527i
$905$		−	0.884220i		−	0.0293925i
$906$	7.89345	−	0.745746i	0.262242	−	0.0247757i
$907$	6.57527	−	6.57527i	0.218328	−	0.218328i	−0.589465	−	0.807794i	$-0.700662\pi$
$907$	6.57527	−	6.57527i	0.218328	−	0.218328i	0.807794	+	0.589465i	$0.200662\pi$
$908$	−9.18783	−	6.24541i	−0.304909	−	0.207261i
$909$	4.52552	+	4.52552i	0.150102	+	0.150102i
$910$	4.58468	+	2.78434i	0.151981	+	0.0922998i
$911$		−	12.7400i		−	0.422095i	−0.977476	−	0.211047i	$-0.932313\pi$
$911$		−	12.7400i		−	0.422095i	0.977476	−	0.211047i	$-0.0676875\pi$
$912$	7.53372	+	19.0393i	0.249467	+	0.630455i
$913$		−	44.0287i		−	1.45714i
$914$	20.8426	−	25.1917i	0.689411	−	0.833269i
$915$	−1.91586	+	1.91586i	−0.0633364	+	0.0633364i
$916$	2.75002	+	1.86932i	0.0908631	+	0.0617640i
$917$	−0.451861	+	0.606927i	−0.0149218	+	0.0200425i
$918$	10.0565	−	0.950103i	0.331914	−	0.0313581i
$919$	22.9394			0.756700			0.378350	−	0.925663i	$-0.376492\pi$
$919$	22.9394			0.756700			0.378350	+	0.925663i	$0.376492\pi$
$920$	1.05117	+	3.62021i	0.0346560	+	0.119355i
$921$		−	12.8424i		−	0.423170i
$922$	3.28215	+	34.7404i	0.108092	+	1.14411i
$923$	−1.00734	−	1.00734i	−0.0331571	−	0.0331571i
$924$	−17.7963	+	6.17164i	−0.585454	+	0.203032i
$925$	2.42400	−	2.42400i	0.0797006	−	0.0797006i
$926$	−28.5374	+	34.4923i	−0.937798	+	1.13349i
$927$	6.94145			0.227987
$928$	0.522009	−	0.265810i	0.0171358	−	0.00872564i
$929$		−	29.6249i		−	0.971963i	−0.873969	−	0.485981i	$-0.838462\pi$
$929$		−	29.6249i		−	0.971963i	0.873969	−	0.485981i	$-0.161538\pi$
$930$	−0.585734	+	0.707958i	−0.0192070	+	0.0232149i
$931$	17.0075	−	31.5390i	0.557398	−	1.03365i
$932$	−20.8392	+	3.97309i	−0.682609	+	0.130143i
$933$	−12.5217	−	12.5217i	−0.409942	−	0.409942i
$934$	−18.5730	+	1.75471i	−0.607727	+	0.0574159i
$935$	6.02169			0.196930
$936$	4.77397	+	16.4415i	0.156042	+	0.537407i
$937$	−27.4992			−0.898361			−0.449181	−	0.893441i	$-0.648284\pi$
$937$	−27.4992			−0.898361			−0.449181	+	0.893441i	$0.648284\pi$
$938$	12.5129	+	51.2168i	0.408561	+	1.67229i
$939$	9.99689	−	9.99689i	0.326236	−	0.326236i
$940$	−0.313194	−	0.212893i	−0.0102153	−	0.00694380i
$941$	−27.7697	−	27.7697i	−0.905265	−	0.905265i	0.0906204	−	0.995886i	$-0.471115\pi$
$941$	−27.7697	−	27.7697i	−0.905265	−	0.905265i	−0.995886	+	0.0906204i	$0.971115\pi$
$942$	−18.2441	−	15.0944i	−0.594426	−	0.491803i
$943$	−52.8856			−1.72219
$944$	−40.4059	−	17.4950i	−1.31510	−	0.569412i
$945$	−0.619994	+	0.0908017i	−0.0201684	+	0.00295378i
$946$	14.9944	−	18.1232i	0.487509	−	0.589236i
$947$	−9.00930	−	9.00930i	−0.292763	−	0.292763i	0.545408	−	0.838171i	$-0.316375\pi$
$947$	−9.00930	−	9.00930i	−0.292763	−	0.292763i	−0.838171	+	0.545408i	$0.816375\pi$
$948$	0.238116	−	0.350301i	0.00773365	−	0.0113772i
$949$	47.9331	+	47.9331i	1.55598	+	1.55598i
$950$	−3.36634	−	35.6315i	−0.109218	−	1.15604i
$951$		−	9.25707i		−	0.300181i
$952$	50.0736	+	18.6985i	1.62289	+	0.606023i
$953$			19.0905i			0.618402i	0.950997	+	0.309201i	$0.100062\pi$
$953$			19.0905i			0.618402i	−0.950997	+	0.309201i	$0.899938\pi$
$954$	9.32063	−	0.880581i	0.301767	−	0.0285099i
$955$	2.08377	+	2.08377i	0.0674291	+	0.0674291i
$956$	−14.0720	+	2.68289i	−0.455119	+	0.0867707i
$957$	−0.260652	−	0.260652i	−0.00842569	−	0.00842569i
$958$	−40.0226	−	33.1130i	−1.29307	−	1.06983i
$959$	6.12887	+	41.8479i	0.197911	+	1.35134i
$960$	1.60005	−	1.01474i	0.0516412	−	0.0327504i
$961$	−23.4739			−0.757224
$962$	3.78373	−	4.57327i	0.121992	−	0.147448i
$963$	−1.87422	−	1.87422i	−0.0603958	−	0.0603958i
$964$	−26.3730	+	5.02814i	−0.849416	+	0.161945i
$965$	−1.00514	+	1.00514i	−0.0323567	+	0.0323567i
$966$	20.4547	−	4.99734i	0.658119	−	0.160787i
$967$	26.0264			0.836951			0.418476	−	0.908228i	$-0.362565\pi$
$967$	26.0264			0.836951			0.418476	+	0.908228i	$0.362565\pi$
$968$	−4.14206	−	2.27794i	−0.133131	−	0.0732158i
$969$	−36.5628			−1.17457
$970$	−0.456748	−	4.83451i	−0.0146653	−	0.155227i
$971$	−28.6108	−	28.6108i	−0.918165	−	0.918165i	0.0787312	−	0.996896i	$-0.474913\pi$
$971$	−28.6108	−	28.6108i	−0.918165	−	0.918165i	−0.996896	+	0.0787312i	$0.974913\pi$
$972$	−1.65405	−	1.12433i	−0.0530536	−	0.0360631i
$973$	−6.08502	−	4.53034i	−0.195077	−	0.145236i
$974$	25.5778	+	21.1620i	0.819567	+	0.678075i
$975$		−	29.9256i		−	0.958387i
$976$	−41.9933	−	18.1823i	−1.34417	−	0.582000i
$977$	−56.1767			−1.79725			−0.898626	−	0.438716i	$-0.855433\pi$
$977$	−56.1767			−1.79725			−0.898626	+	0.438716i	$0.855433\pi$
$978$	−0.988465	−	0.817814i	−0.0316076	−	0.0261508i
$979$	18.9907	−	18.9907i	0.606946	−	0.606946i
$980$	−3.16151	−	0.999352i	−0.100991	−	0.0319231i
$981$	−12.6272	−	12.6272i	−0.403154	−	0.403154i
$982$	39.1596	−	3.69966i	1.24963	−	0.118061i
$983$		−	32.0551i		−	1.02240i	−0.859462	−	0.511200i	$-0.829201\pi$
$983$		−	32.0551i		−	1.02240i	0.859462	−	0.511200i	$-0.170799\pi$
$984$	7.41186	+	25.5263i	0.236282	+	0.813749i
$985$	3.64941			0.116280
$986$	0.0983868	+	1.04139i	0.00313327	+	0.0331646i
$987$	−1.26319	+	1.69669i	−0.0402079	+	0.0540061i
$988$	−11.6058	−	60.8734i	−0.369230	−	1.93664i
$989$	−18.5931	+	18.5931i	−0.591225	+	0.591225i
$990$	−0.918617	−	0.760025i	−0.0291956	−	0.0241552i
$991$			54.6720i			1.73671i	0.495940	+	0.868357i	$0.334823\pi$
$991$			54.6720i			1.73671i	−0.495940	+	0.868357i	$0.665177\pi$
$992$	−14.7581	−	4.79933i	−0.468569	−	0.152379i
$993$		−	12.9747i		−	0.411740i
$994$	0.752677	+	0.457111i	0.0238735	+	0.0144987i
$995$	1.54517	+	1.54517i	0.0489852	+	0.0489852i
$996$	24.2998	−	4.63287i	0.769968	−	0.146798i
$997$	5.64016	−	5.64016i	0.178626	−	0.178626i	−0.612131	−	0.790756i	$-0.709687\pi$
$997$	5.64016	−	5.64016i	0.178626	−	0.178626i	0.790756	+	0.612131i	$0.209687\pi$
$998$	4.46632	+	47.2743i	0.141379	+	1.49644i
$999$			0.693389i			0.0219379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.8	yes	64
4.3	odd	2		1344.2.u.a.1231.8		64
7.6	odd	2	inner	336.2.u.a.139.7	✓	64
16.3	odd	4	inner	336.2.u.a.307.7	yes	64
16.13	even	4		1344.2.u.a.559.25		64
28.27	even	2		1344.2.u.a.1231.25		64
112.13	odd	4		1344.2.u.a.559.8		64
112.83	even	4	inner	336.2.u.a.307.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.7	✓	64	7.6	odd	2	inner
336.2.u.a.139.8	yes	64	1.1	even	1	trivial
336.2.u.a.307.7	yes	64	16.3	odd	4	inner
336.2.u.a.307.8	yes	64	112.83	even	4	inner
1344.2.u.a.559.8		64	112.13	odd	4
1344.2.u.a.559.25		64	16.13	even	4
1344.2.u.a.1231.8		64	4.3	odd	2
1344.2.u.a.1231.25		64	28.27	even	2

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08962 - 0.901509i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.374563 + 1.96461i) q^{4} +(-0.167468 + 0.167468i) q^{5} +(-1.40794 + 0.133018i) q^{6} +(-2.61783 + 0.383395i) q^{7} +(1.36298 - 2.47836i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.08962 - 0.901509i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.374563 + 1.96461i) q^{4} +(-0.167468 + 0.167468i) q^{5} +(-1.40794 + 0.133018i) q^{6} +(-2.61783 + 0.383395i) q^{7} +(1.36298 - 2.47836i) q^{8} -1.00000i q^{9} +(0.333451 - 0.0315033i) q^{10} +(2.51707 - 2.51707i) q^{11} +(1.65405 + 1.12433i) q^{12} +(-4.28014 - 4.28014i) q^{13} +(3.19808 + 1.94224i) q^{14} +0.236836i q^{15} +(-3.71941 + 1.47174i) q^{16} -7.14268i q^{17} +(-0.901509 + 1.08962i) q^{18} +(3.61962 - 3.61962i) q^{19} +(-0.391737 - 0.266283i) q^{20} +(-1.57998 + 2.12218i) q^{21} +(-5.01182 + 0.473500i) q^{22} +5.62753 q^{23} +(-0.788692 - 2.71624i) q^{24} +4.94391i q^{25} +(0.805160 + 8.52232i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.73376 - 4.99941i) q^{28} +(0.0732236 - 0.0732236i) q^{29} +(0.213509 - 0.258062i) q^{30} -2.74337 q^{31} +(5.37954 + 1.74943i) q^{32} -3.55968i q^{33} +(-6.43919 + 7.78284i) q^{34} +(0.374196 - 0.502609i) q^{35} +(1.96461 - 0.374563i) q^{36} +(-0.490300 - 0.490300i) q^{37} +(-7.20715 + 0.680906i) q^{38} -6.05303 q^{39} +(0.186790 + 0.643303i) q^{40} -9.39766 q^{41} +(3.63475 - 0.888016i) q^{42} +(-3.30395 + 3.30395i) q^{43} +(5.88787 + 4.00227i) q^{44} +(0.167468 + 0.167468i) q^{45} +(-6.13189 - 5.07327i) q^{46} +0.799500 q^{47} +(-1.58934 + 3.67070i) q^{48} +(6.70602 - 2.00732i) q^{49} +(4.45698 - 5.38700i) q^{50} +(-5.05064 - 5.05064i) q^{51} +(6.80563 - 10.0120i) q^{52} +(-4.68107 - 4.68107i) q^{53} +(0.133018 + 1.40794i) q^{54} +0.843058i q^{55} +(-2.61786 + 7.01048i) q^{56} -5.11892i q^{57} +(-0.145798 + 0.0137745i) q^{58} +(7.78362 + 7.78362i) q^{59} +(-0.465290 + 0.0887099i) q^{60} +(8.08940 + 8.08940i) q^{61} +(2.98924 + 2.47317i) q^{62} +(0.383395 + 2.61783i) q^{63} +(-4.28455 - 6.75593i) q^{64} +1.43357 q^{65} +(-3.20908 + 3.87871i) q^{66} +(9.96374 + 9.96374i) q^{67} +(14.0326 - 2.67538i) q^{68} +(3.97926 - 3.97926i) q^{69} +(-0.860839 + 0.210314i) q^{70} +0.235353 q^{71} +(-2.47836 - 1.36298i) q^{72} -11.1990 q^{73} +(0.0922330 + 0.976253i) q^{74} +(3.49587 + 3.49587i) q^{75} +(8.46693 + 5.75538i) q^{76} +(-5.62422 + 7.55428i) q^{77} +(6.59553 + 5.45686i) q^{78} -0.211784i q^{79} +(0.376412 - 0.869352i) q^{80} -1.00000 q^{81} +(10.2399 + 8.47208i) q^{82} +(8.74602 - 8.74602i) q^{83} +(-4.76107 - 2.30916i) q^{84} +(1.19617 + 1.19617i) q^{85} +(6.57860 - 0.621523i) q^{86} -0.103554i q^{87} +(-2.80749 - 9.66894i) q^{88} +7.54477 q^{89} +(-0.0315033 - 0.333451i) q^{90} +(12.8456 + 9.56366i) q^{91} +(2.10786 + 11.0559i) q^{92} +(-1.93985 + 1.93985i) q^{93} +(-0.871155 - 0.720757i) q^{94} +1.21234i q^{95} +(5.04095 - 2.56688i) q^{96} -14.4984i q^{97} +(-9.11666 - 3.85830i) q^{98} +(-2.51707 - 2.51707i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more