LMFDB - Embedded newform 336.2.u.a.139.7

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			139.7
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.7

$q$-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} +(2.50681 + 2.77775i) 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} +(2.12218 - 1.57998i) 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} +(-0.227317 - 5.28662i) 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} +(-0.502609 + 0.374196i) 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} +(-3.73675 - 0.191582i) 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} +(-4.51824 + 5.96536i) 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} +(0.884996 + 0.0453735i) 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} +(-7.55428 + 5.62422i) 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} +(3.89894 + 3.57747i) 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} +(-9.56366 - 12.8456i) 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} +(-5.49742 - 8.23276i) 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	−0.668668	−	0.743562i	$-0.733135\pi$
$5$	0.167468	−	0.167468i	0.0748940	−	0.0748940i	0.743562	+	0.668668i	$0.233135\pi$
$6$	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	$0.0670956\pi$
$13$	4.28014	+	4.28014i	1.18710	+	1.18710i	0.209230	+	0.977867i	$0.432904\pi$
$14$	2.50681	+	2.77775i	0.669974	+	0.742385i
$15$			0.236836i			0.0611507i
$16$	−3.71941	+	1.47174i	−0.929851	+	0.367936i
$17$			7.14268i			1.73235i	0.499737	+	0.866177i	$0.333430\pi$
$17$			7.14268i			1.73235i	−0.499737	+	0.866177i	$0.666570\pi$
$18$	−0.901509	+	1.08962i	−0.212488	+	0.256827i
$19$	−3.61962	+	3.61962i	−0.830398	+	0.830398i	−0.987571	−	0.157173i	$-0.949762\pi$
$19$	−3.61962	+	3.61962i	−0.830398	+	0.830398i	0.157173	+	0.987571i	$0.449762\pi$
$20$	0.391737	+	0.266283i	0.0875951	+	0.0595426i
$21$	2.12218	−	1.57998i	0.463098	−	0.344780i
$22$	−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
$28$	−0.227317	−	5.28662i	−0.0429588	−	0.999077i
$29$	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	$-0.420765\pi$
$31$	2.74337			0.492723			0.246361	+	0.969178i	$0.420765\pi$
$32$	5.37954	+	1.74943i	0.950978	+	0.309259i
$33$			3.55968i			0.619660i
$34$	6.43919	−	7.78284i	1.10431	−	1.33475i
$35$	−0.502609	+	0.374196i	−0.0849564	+	0.0632506i
$36$	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	$-0.237729\pi$
$41$	9.39766			1.46767			0.733834	+	0.679328i	$0.237729\pi$
$42$	−3.73675	−	0.191582i	−0.576593	−	0.0295618i
$43$	−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	$-0.518571\pi$
$47$	−0.799500			−0.116619			−0.0583095	+	0.998299i	$0.518571\pi$
$48$	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
$56$	−4.51824	+	5.96536i	−0.603776	+	0.797154i
$57$		−	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	$-0.995725\pi$
$59$	−7.78362	−	7.78362i	−1.01334	−	1.01334i	−0.0134315	−	0.999910i	$-0.504275\pi$
$60$	−0.465290	+	0.0887099i	−0.0600687	+	0.0114524i
$61$	−8.08940	−	8.08940i	−1.03574	−	1.03574i	−0.999337	−	0.0364049i	$-0.988409\pi$
$61$	−8.08940	−	8.08940i	−1.03574	−	1.03574i	−0.0364049	−	0.999337i	$-0.511591\pi$
$62$	−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
$70$	0.884996	+	0.0453735i	0.105777	+	0.00542317i
$71$	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	$-0.272513\pi$
$73$	11.1990			1.31074			0.655370	+	0.755308i	$0.272513\pi$
$74$	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
$77$	−7.55428	+	5.62422i	−0.860891	+	0.640939i
$78$	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	−0.999230	−	0.0392297i	$-0.987510\pi$
$83$	−8.74602	+	8.74602i	−0.960001	+	0.960001i	0.0392297	+	0.999230i	$0.487510\pi$
$84$	3.89894	+	3.57747i	0.425409	+	0.390334i
$85$	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	$-0.630945\pi$
$89$	−7.54477			−0.799744			−0.399872	+	0.916571i	$0.630945\pi$
$90$	0.0315033	+	0.333451i	0.00332074	+	0.0351489i
$91$	−9.56366	−	12.8456i	−1.00254	−	1.34659i
$92$	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	$0.263309\pi$
$97$			14.4984i			1.47209i	−0.676932	+	0.736045i	$0.736691\pi$
$98$	−5.49742	−	8.23276i	−0.555323	−	0.831635i
$99$	−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	−0.445150	−	0.895456i	$-0.646850\pi$
$101$	4.52552	−	4.52552i	0.450306	−	0.450306i	0.895456	+	0.445150i	$0.146850\pi$
$102$	0.950103	+	10.0565i	0.0940742	+	0.995741i
$103$		−	6.94145i		−	0.683962i	−0.939707	−	0.341981i	$-0.888902\pi$
$103$		−	6.94145i		−	0.683962i	0.939707	−	0.341981i	$-0.111098\pi$
$104$	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
$112$	10.3010	−	2.42676i	0.973354	−	0.229307i
$113$	−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
$126$	2.77775	−	2.50681i	0.247462	−	0.223325i
$127$			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	−0.715886	−	0.698217i	$-0.753977\pi$
$131$	−0.202227	+	0.202227i	−0.0176686	+	0.0176686i	0.698217	+	0.715886i	$0.253977\pi$
$132$	−6.99338	+	1.33332i	−0.608696	+	0.116051i
$133$	10.8633	−	8.08779i	0.941966	−	0.701300i
$134$	−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	0.615873	−	0.787845i	$-0.288803\pi$
$139$	−2.02752	−	2.02752i	−0.171972	−	0.171972i	−0.787845	+	0.615873i	$0.788803\pi$
$140$	−0.923408	−	0.847272i	−0.0780422	−	0.0716075i
$141$	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
$147$	−6.16126	+	3.32248i	−0.508172	+	0.274033i
$148$	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
$154$	13.3016	+	0.681971i	1.07187	+	0.0549548i
$155$	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	0.0536685	−	0.998559i	$-0.482909\pi$
$157$	−11.8394	−	11.8394i	−0.944890	−	0.944890i	−0.998559	+	0.0536685i	$0.982909\pi$
$158$	−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	$0.108833\pi$
$167$			8.66571i			0.670573i	−0.942116	+	0.335287i	$0.891167\pi$
$168$	−1.02326	−	7.41302i	−0.0789464	−	0.571927i
$169$			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	0.500505	−	0.865734i	$-0.333148\pi$
$173$	−4.80384	−	4.80384i	−0.365229	−	0.365229i	−0.865734	+	0.500505i	$0.833148\pi$
$174$	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	−0.602153	−	0.798380i	$-0.705690\pi$
$181$	2.63997	−	2.63997i	0.196227	−	0.196227i	0.798380	+	0.602153i	$0.205690\pi$
$182$	−1.15965	+	22.6186i	−0.0859592	+	1.67661i
$183$	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
$189$	−1.57998	−	2.12218i	−0.114927	−	0.154366i
$190$	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
$196$	−1.43179	+	13.9266i	−0.102271	+	0.994757i
$197$	−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	$0.106048\pi$
$199$			9.22666i			0.654060i	−0.945014	+	0.327030i	$0.893952\pi$
$200$	12.2528	+	6.73846i	0.866403	+	0.476481i
$201$	−14.0909			−0.993892
$202$	−9.01092	+	0.851320i	−0.634006	+	0.0598987i
$203$	−0.219760	+	0.163613i	−0.0154241	+	0.0114834i
$204$	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
$210$	−0.657870	+	0.593702i	−0.0453974	+	0.0409694i
$211$	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	$-0.491102\pi$
$223$	0.834795			0.0559020			0.0279510	+	0.999609i	$0.491102\pi$
$224$	−13.4120	−	6.64220i	−0.896126	−	0.443801i
$225$	4.94391			0.329594
$226$	8.37456	+	6.92875i	0.557067	+	0.460894i
$227$	3.92781	−	3.92781i	0.260698	−	0.260698i	−0.564640	−	0.825337i	$-0.690985\pi$
$227$	3.92781	−	3.92781i	0.260698	−	0.260698i	0.825337	+	0.564640i	$0.190985\pi$
$228$	10.0567	−	1.91736i	0.666020	−	0.126980i
$229$	−1.17563	+	1.17563i	−0.0776881	+	0.0776881i	−0.744883	−	0.667195i	$-0.767495\pi$
$229$	−1.17563	+	1.17563i	−0.0776881	+	0.0776881i	0.667195	+	0.744883i	$0.267495\pi$
$230$	−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
$238$	−19.8406	+	17.9053i	−1.28607	+	1.16063i
$239$			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	$-0.857682\pi$
$241$		−	13.4240i		−	0.864716i	0.901702	−	0.432358i	$-0.142318\pi$
$242$	−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
$245$	1.45921	−	0.786881i	0.0932253	−	0.0502720i
$246$	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	0.520261	−	0.854007i	$-0.325835\pi$
$251$	−5.28753	−	5.28753i	−0.333746	−	0.333746i	−0.854007	+	0.520261i	$0.825835\pi$
$252$	−5.28662	+	0.227317i	−0.333026	+	0.0143196i
$253$	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	$-0.995780\pi$
$257$		−	0.425017i		−	0.0265118i	0.999912	−	0.0132559i	$-0.00421961\pi$
$258$	−4.21229	+	5.09125i	−0.262246	+	0.316968i
$259$	1.09554	+	1.47150i	0.0680736	+	0.0914345i
$260$	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
$266$	−19.1281	−	0.980694i	−1.17282	−	0.0601302i
$267$	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	0.0643617	−	0.997927i	$-0.479499\pi$
$269$	−15.3116	−	15.3116i	−0.933565	−	0.933565i	−0.997927	+	0.0643617i	$0.979499\pi$
$270$	−0.258062	−	0.213509i	−0.0157051	−	0.0129938i
$271$	20.1296			1.22278			0.611392	−	0.791328i	$-0.290610\pi$
$271$	20.1296			1.22278			0.611392	+	0.791328i	$0.290610\pi$
$272$	−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
$280$	0.242345	+	1.75567i	0.0144829	+	0.104921i
$281$		−	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	0.358336	−	0.933593i	$-0.383344\pi$
$283$	−9.67731	−	9.67731i	−0.575256	−	0.575256i	−0.933593	+	0.358336i	$0.883344\pi$
$284$	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	−0.910150	−	0.414279i	$-0.864034\pi$
$293$	−8.48795	+	8.48795i	−0.495871	+	0.495871i	0.414279	+	0.910150i	$0.364034\pi$
$294$	9.70870	+	1.93418i	0.566223	+	0.112804i
$295$	−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
$301$	9.91587	−	7.38243i	0.571541	−	0.425516i
$302$	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	−0.917049	−	0.398774i	$-0.869436\pi$
$307$	−9.08093	+	9.08093i	−0.518276	+	0.518276i	0.398774	+	0.917049i	$0.369436\pi$
$308$	−13.8790	−	12.7346i	−0.790827	−	0.725622i
$309$	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	$0.167429\pi$
$311$			17.7083i			1.00415i	−0.864825	+	0.502074i	$0.832571\pi$
$312$	−8.25017	+	15.0016i	−0.467074	+	0.849298i
$313$	−14.1377			−0.799112			−0.399556	−	0.916709i	$-0.630836\pi$
$313$	−14.1377			−0.799112			−0.399556	+	0.916709i	$0.630836\pi$
$314$	2.22718	+	23.5739i	0.125687	+	1.33035i
$315$	0.374196	+	0.502609i	0.0210835	+	0.0283188i
$316$	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
$322$	14.1072	+	15.6319i	0.786161	+	0.871130i
$323$	−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
$336$	−5.56794	+	8.99989i	−0.303756	+	0.490984i
$337$	−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	0.869129	−	0.494585i	$-0.164680\pi$
$349$	6.99706	+	6.99706i	0.374544	+	0.374544i	−0.494585	+	0.869129i	$0.664680\pi$
$350$	−13.7329	+	12.3934i	−0.734057	+	0.662458i
$351$			6.05303i			0.323087i
$352$	17.9441	−	9.13725i	0.956426	−	0.487017i
$353$		−	27.6603i		−	1.47221i	−0.676869	−	0.736104i	$-0.736663\pi$
$353$		−	27.6603i		−	1.47221i	0.676869	−	0.736104i	$-0.263337\pi$
$354$	−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
$357$	11.2853	+	15.1581i	0.597281	+	0.802250i
$358$	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
$364$	21.6545	−	23.6004i	1.13500	−	1.23700i
$365$	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	$-0.496584\pi$
$367$	0.411143			0.0214615			0.0107307	+	0.999942i	$0.496584\pi$
$368$	−20.9311	+	8.28227i	−1.09111	+	0.431743i
$369$		−	9.39766i		−	0.489223i
$370$	0.178937	+	0.148045i	0.00930251	+	0.00769650i
$371$	10.4595	+	14.0489i	0.543031	+	0.729383i
$372$	−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
$378$	−0.191582	+	3.73675i	−0.00985393	+	0.192198i
$379$	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	$-0.240621\pi$
$383$	28.4801			1.45527			0.727633	+	0.685967i	$0.240621\pi$
$384$	−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
$392$	14.1151	−	13.8840i	0.712918	−	0.701247i
$393$		−	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	0.622232	−	0.782833i	$-0.286226\pi$
$397$	−3.19995	−	3.19995i	−0.160601	−	0.160601i	−0.782833	+	0.622232i	$0.786226\pi$
$398$	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
$406$	0.386955	+	0.0198391i	0.0192042	+	0.000984597i
$407$	−2.46824			−0.122346
$408$	−19.4012	+	5.63337i	−0.960504	+	0.278893i
$409$	9.89111			0.489084			0.244542	−	0.969639i	$-0.421362\pi$
$409$	9.89111			0.489084			0.244542	+	0.969639i	$0.421362\pi$
$410$	−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
$413$	17.3920	+	23.3604i	0.855802	+	1.14949i
$414$	−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	−0.264978	−	0.964254i	$-0.585365\pi$
$419$	14.3138	−	14.3138i	0.699276	−	0.699276i	0.964254	+	0.264978i	$0.0853648\pi$
$420$	1.25206	−	0.0538367i	0.0610943	−	0.00262696i
$421$	−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
$427$	18.0752	+	24.2781i	0.874720	+	1.17490i
$428$	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	$-0.965670\pi$
$433$		−	4.47978i		−	0.215285i	0.994190	−	0.107642i	$-0.0343301\pi$
$434$	6.87710	+	7.62038i	0.330111	+	0.365790i
$435$	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	$0.00130161\pi$
$439$			0.171353i			0.00817822i	−0.999992	+	0.00408911i	$0.998698\pi$
$440$	−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
$448$	8.62602	+	19.3285i	0.407541	+	0.913187i
$449$	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	0.985025	−	0.172412i	$-0.0551561\pi$
$461$	17.4475	+	17.4475i	0.812613	+	0.812613i	−0.172412	+	0.985025i	$0.555156\pi$
$462$	−9.88789	+	8.92344i	−0.460026	+	0.415156i
$463$		−	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	−0.889186	−	0.457545i	$-0.848729\pi$
$467$	−9.32784	+	9.32784i	−0.431641	+	0.431641i	0.457545	+	0.889186i	$0.348729\pi$
$468$	10.0120	+	6.80563i	0.462804	+	0.314590i
$469$	−22.2633	−	29.9034i	−1.02802	−	1.38081i
$470$	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
$476$	37.7606	−	1.62365i	1.73075	−	0.0744198i
$477$	−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	$-0.816937\pi$
$479$	−36.7307			−1.67827			−0.839134	+	0.543925i	$0.816937\pi$
$480$	−0.414328	+	1.27407i	−0.0189114	+	0.0581530i
$481$		−	4.19710i		−	0.191371i
$482$	−12.1019	+	14.6271i	−0.551225	+	0.666247i
$483$	11.9427	−	8.89139i	0.543409	−	0.404572i
$484$	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
$490$	−2.29937	−	0.458083i	−0.103875	−	0.0206941i
$491$	−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	$-0.784484\pi$
$503$		−	28.1022i		−	1.25301i	0.779416	−	0.626507i	$-0.215516\pi$
$504$	5.96536	+	4.51824i	0.265718	+	0.201259i
$505$		−	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	0.813205	−	0.581978i	$-0.197721\pi$
$509$	5.21671	+	5.21671i	0.231227	+	0.231227i	−0.581978	+	0.813205i	$0.697721\pi$
$510$	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
$518$	0.132841	−	2.59102i	0.00583670	−	0.113843i
$519$	6.79365			0.298208
$520$	1.95394	−	3.55291i	0.0856857	−	0.155805i
$521$	19.5127			0.854867			0.427433	−	0.904047i	$-0.359418\pi$
$521$	19.5127			0.854867			0.427433	+	0.904047i	$0.359418\pi$
$522$	0.0137745	+	0.145798i	0.000602893	+	0.00638140i
$523$	21.8246	+	21.8246i	0.954322	+	0.954322i	0.999001	−	0.0446791i	$-0.0142265\pi$
$523$	21.8246	+	21.8246i	0.954322	+	0.954322i	−0.0446791	+	0.999001i	$0.514227\pi$
$524$	−0.473044	−	0.321551i	−0.0206650	−	0.0140470i
$525$	7.81128	+	10.4919i	0.340912	+	0.457903i
$526$	−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
$532$	19.9584	+	18.3128i	0.865304	+	0.793958i
$533$	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
$539$	21.9321	−	11.8269i	0.944682	−	0.509422i
$540$	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
$546$	−15.1738	−	16.8138i	−0.649379	−	0.719564i
$547$	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
$560$	1.31869	−	2.13150i	0.0557247	−	0.0900721i
$561$	−25.4256			−1.07347
$562$	−4.03611	+	4.87831i	−0.170253	+	0.205779i
$563$	17.0537	−	17.0537i	0.718726	−	0.718726i	−0.249618	−	0.968344i	$-0.580305\pi$
$563$	17.0537	−	17.0537i	0.718726	−	0.718726i	0.968344	+	0.249618i	$0.0803051\pi$
$564$	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
$574$	23.5582	+	26.1044i	0.983299	+	1.08958i
$575$			27.8220i			1.16026i
$576$	−6.75593	+	4.28455i	−0.281497	+	0.178523i
$577$		−	13.7657i		−	0.573074i	−0.958069	−	0.286537i	$-0.907496\pi$
$577$		−	13.7657i		−	0.573074i	0.958069	−	0.286537i	$-0.0925042\pi$
$578$	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
$581$	26.2487	−	19.5424i	1.08898	−	0.810754i
$582$	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	0.456442	−	0.889753i	$-0.349124\pi$
$587$	−10.4983	−	10.4983i	−0.433312	−	0.433312i	−0.889753	+	0.456442i	$0.849124\pi$
$588$	−8.83516	−	10.8600i	−0.364356	−	0.447860i
$589$	−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	$-0.890627\pi$
$593$		−	16.4073i		−	0.673768i	0.941546	−	0.336884i	$-0.109373\pi$
$594$	−3.87871	−	3.20908i	−0.159145	−	0.131670i
$595$	−2.67276	−	3.58997i	−0.109572	−	0.147175i
$596$	−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	$-0.175131\pi$
$601$	41.7949			1.70485			0.852425	+	0.522849i	$0.175131\pi$
$602$	−17.4599	−	0.895165i	−0.711613	−	0.0364842i
$603$	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	$-0.836418\pi$
$607$	−42.9099			−1.74166			−0.870830	+	0.491584i	$0.836418\pi$
$608$	−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
$616$	3.64248	+	26.3880i	0.146760	+	1.06320i
$617$		−	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	0.278219	−	0.960518i	$-0.410256\pi$
$619$	−16.9754	−	16.9754i	−0.682298	−	0.682298i	−0.960518	+	0.278219i	$0.910256\pi$
$620$	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
$630$	0.0453735	−	0.884996i	0.00180772	−	0.0352591i
$631$	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
$637$	20.1110	+	37.2943i	0.796828	+	1.47765i
$638$	−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	$-0.383270\pi$
$643$	32.7634	−	32.7634i	1.29206	−	1.29206i	0.933509	−	0.358555i	$-0.116730\pi$
$644$	−1.27923	−	29.7506i	−0.0504088	−	1.17234i
$645$	−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	$0.110386\pi$
$647$			17.2904i			0.679756i	−0.940469	+	0.339878i	$0.889614\pi$
$648$	−1.36298	+	2.47836i	−0.0535430	+	0.0973592i
$649$	−39.1839			−1.53810
$650$	42.1336	−	3.98064i	1.65262	−	0.156133i
$651$	5.82192	−	4.33446i	0.228179	−	0.169881i
$652$	−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
$658$	−2.00420	−	2.22081i	−0.0781317	−	0.0865762i
$659$	−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	−0.647128	−	0.762381i	$-0.724030\pi$
$661$	2.96315	−	2.96315i	0.115253	−	0.115253i	0.762381	+	0.647128i	$0.224030\pi$
$662$	−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
$672$	14.1804	−	4.78696i	0.547023	−	0.184661i
$673$	−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	−0.548402	−	0.836215i	$-0.684764\pi$
$677$	7.48867	−	7.48867i	0.287813	−	0.287813i	0.836215	+	0.548402i	$0.184764\pi$
$678$	−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
$686$	11.2349	+	23.6596i	0.428949	+	0.903328i
$687$		−	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	−0.575592	−	0.817737i	$-0.695229\pi$
$691$	6.36522	−	6.36522i	0.242144	−	0.242144i	0.817737	+	0.575592i	$0.195229\pi$
$692$	7.63834	−	11.2370i	0.290366	−	0.427168i
$693$	5.62422	+	7.55428i	0.213646	+	0.286964i
$694$	−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
$700$	26.1366	−	1.12383i	0.987869	−	0.0424769i
$701$	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
$707$	−13.5821	+	10.1120i	−0.510807	+	0.380299i
$708$	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
$714$	1.36841	−	26.6904i	0.0512115	−	0.998863i
$715$	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	$-0.679940\pi$
$719$	−28.7270			−1.07134			−0.535668	+	0.844429i	$0.679940\pi$
$720$	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	$-0.554797\pi$
$727$		−	53.1288i		−	1.97044i	0.171302	−	0.985219i	$-0.445203\pi$
$728$	−44.8712	+	6.19384i	−1.66304	+	0.229559i
$729$			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	0.989486	−	0.144627i	$-0.0461981\pi$
$733$	22.8737	+	22.8737i	0.844860	+	0.844860i	−0.144627	+	0.989486i	$0.546198\pi$
$734$	−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
$742$	1.26828	−	24.7374i	0.0465600	−	0.908138i
$743$	−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
$749$	−5.62494	+	4.18781i	−0.205531	+	0.153019i
$750$	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
$756$	3.57747	−	3.89894i	0.130111	−	0.141803i
$757$	−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	$-0.602849\pi$
$761$	−17.5182			−0.635034			−0.317517	+	0.948253i	$0.602849\pi$
$762$	0.430862	+	4.56052i	0.0156085	+	0.165210i
$763$	−37.8969	+	28.2145i	−1.37196	+	1.02143i
$764$	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	$-0.806459\pi$
$769$		−	31.6824i		−	1.14250i	0.820777	−	0.571249i	$-0.193541\pi$
$770$	2.34180	−	2.11339i	0.0843928	−	0.0761612i
$771$	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	$0.597654\pi$
$773$	−34.9011	+	34.9011i	−1.25531	+	1.25531i	−0.953308	+	0.301998i	$0.902346\pi$
$774$	−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
$784$	−27.8967	+	2.40347i	−0.996309	+	0.0858383i
$785$	−3.96546			−0.141533
$786$	−0.257824	+	0.311624i	−0.00919628	+	0.0111152i
$787$	−20.4440	+	20.4440i	−0.728749	+	0.728749i	−0.970371	−	0.241622i	$-0.922321\pi$
$787$	−20.4440	+	20.4440i	−0.728749	+	0.728749i	0.241622	+	0.970371i	$0.422321\pi$
$788$	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	0.539301	−	0.842113i	$-0.318689\pi$
$797$	−8.54875	−	8.54875i	−0.302812	−	0.302812i	−0.842113	+	0.539301i	$0.818689\pi$
$798$	14.2191	−	12.8322i	0.503350	−	0.454254i
$799$		−	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
$805$	−2.82845	+	2.10580i	−0.0996896	+	0.0742196i
$806$	−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	0.664515	−	0.747275i	$-0.268638\pi$
$811$	−2.35686	−	2.35686i	−0.0827606	−	0.0827606i	−0.747275	+	0.664515i	$0.768638\pi$
$812$	−0.403750	−	0.370460i	−0.0141689	−	0.0130006i
$813$	−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
$819$	−12.8456	+	9.56366i	−0.448863	+	0.334181i
$820$	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
$826$	2.10888	−	41.1330i	0.0733774	−	1.43120i
$827$	−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	0.525197	−	0.850981i	$-0.323992\pi$
$829$	−9.38010	−	9.38010i	−0.325784	−	0.325784i	−0.850981	+	0.525197i	$0.823992\pi$
$830$	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	$0.118007\pi$
$839$			20.9881i			0.724591i	−0.932063	+	0.362296i	$0.881993\pi$
$840$	−1.41281	−	1.07008i	−0.0487465	−	0.0369213i
$841$			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	$0.506557\pi$
$853$	−29.8015	+	29.8015i	−1.02038	+	1.02038i	−0.999788	+	0.0205966i	$0.993443\pi$
$854$	2.19173	−	42.7490i	0.0749994	−	1.46284i
$855$	1.21234			0.0414612
$856$	−2.09046	−	7.19952i	−0.0714505	−	0.246074i
$857$	51.8982			1.77281			0.886405	−	0.462910i	$-0.153195\pi$
$857$	51.8982			1.77281			0.886405	+	0.462910i	$0.153195\pi$
$858$	30.3367	−	2.86611i	1.03568	−	0.0978473i
$859$	−10.4965	−	10.4965i	−0.358138	−	0.358138i	0.504988	−	0.863126i	$-0.331497\pi$
$859$	−10.4965	−	10.4965i	−0.358138	−	0.358138i	−0.863126	+	0.504988i	$0.831497\pi$
$860$	−2.17406	+	0.414495i	−0.0741349	+	0.0141342i
$861$	19.9436	−	14.8481i	0.679675	−	0.506023i
$862$	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
$868$	−0.623612	−	14.5031i	−0.0211668	−	0.492268i
$869$	−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
$875$	−3.72097	−	4.99790i	−0.125792	−	0.168960i
$876$	−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	$-0.875049\pi$
$881$		−	22.7089i		−	0.765081i	0.923939	−	0.382541i	$-0.124951\pi$
$882$	−8.23276	+	5.49742i	−0.277212	+	0.185108i
$883$	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	$-0.812919\pi$
$887$		−	33.0274i		−	1.10895i	0.832200	−	0.554475i	$-0.187081\pi$
$888$	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
$896$	8.02572	−	28.8373i	0.268120	−	0.963385i
$897$	−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
$910$	3.59370	+	3.98211i	0.119130	+	0.132006i
$911$		−	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
$917$	0.606927	−	0.451861i	0.0200425	−	0.0149218i
$918$	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
$924$	18.8186	−	0.809173i	0.619088	−	0.0266198i
$925$	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	$0.161538\pi$
$929$			29.6249i			0.971963i	−0.873969	+	0.485981i	$0.838462\pi$
$930$	0.585734	−	0.707958i	0.0192070	−	0.0232149i
$931$	−31.5390	+	17.0075i	−1.03365	+	0.557398i
$932$	−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	$-0.351716\pi$
$937$	27.4992			0.898361			0.449181	+	0.893441i	$0.351716\pi$
$938$	−2.69956	+	52.6540i	−0.0881437	+	1.71921i
$939$	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	0.995886	−	0.0906204i	$-0.0288850\pi$
$941$	27.7697	+	27.7697i	0.905265	+	0.905265i	−0.0906204	+	0.995886i	$0.528885\pi$
$942$	−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
$952$	−42.6086	−	32.2724i	−1.38095	−	1.04595i
$953$			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
$966$	−21.0287	−	1.07814i	−0.676586	−	0.0346884i
$967$	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	0.996896	−	0.0787312i	$-0.0250869\pi$
$971$	28.6108	+	28.6108i	0.918165	+	0.918165i	−0.0787312	+	0.996896i	$0.525087\pi$
$972$	1.65405	+	1.12433i	0.0530536	+	0.0360631i
$973$	4.53034	+	6.08502i	0.145236	+	0.195077i
$974$	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
$980$	2.09248	+	2.57204i	0.0668418	+	0.0821608i
$981$	−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	$0.170799\pi$
$983$			32.0551i			1.02240i	−0.859462	+	0.511200i	$0.829201\pi$
$984$	7.41186	+	25.5263i	0.236282	+	0.813749i
$985$	−3.64941			−0.116280
$986$	−0.0983868	−	1.04139i	−0.00313327	−	0.0331646i
$987$	−1.69669	+	1.26319i	−0.0540061	+	0.0402079i
$988$	−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
$994$	0.589985	+	0.653751i	0.0187132	+	0.0207357i
$995$	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	−0.790756	−	0.612131i	$-0.790313\pi$
$997$	−5.64016	+	5.64016i	−0.178626	+	0.178626i	0.612131	+	0.790756i	$0.290313\pi$
$998$	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.139.7	✓	64
4.3	odd	2		1344.2.u.a.1231.25		64
7.6	odd	2	inner	336.2.u.a.139.8	yes	64
16.3	odd	4	inner	336.2.u.a.307.8	yes	64
16.13	even	4		1344.2.u.a.559.8		64
28.27	even	2		1344.2.u.a.1231.8		64
112.13	odd	4		1344.2.u.a.559.25		64
112.83	even	4	inner	336.2.u.a.307.7	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.7	✓	64	1.1	even	1	trivial
336.2.u.a.139.8	yes	64	7.6	odd	2	inner
336.2.u.a.307.7	yes	64	112.83	even	4	inner
336.2.u.a.307.8	yes	64	16.3	odd	4	inner
1344.2.u.a.559.8		64	16.13	even	4
1344.2.u.a.559.25		64	112.13	odd	4
1344.2.u.a.1231.8		64	28.27	even	2
1344.2.u.a.1231.25		64	4.3	odd	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} +(2.50681 + 2.77775i) 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} +(2.12218 - 1.57998i) 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} +(-0.227317 - 5.28662i) 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} +(-0.502609 + 0.374196i) 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} +(-3.73675 - 0.191582i) 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} +(-4.51824 + 5.96536i) 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} +(0.884996 + 0.0453735i) 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} +(-7.55428 + 5.62422i) 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} +(3.89894 + 3.57747i) 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} +(-9.56366 - 12.8456i) 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} +(-5.49742 - 8.23276i) 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

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