LMFDB - Embedded newform 357.2.bl.a.10.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [357,2,Mod(10,357)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("357.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(357, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([0, 8, 9])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$357 = 3 \cdot 7 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$ , degree $16$ , minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.12
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.12

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0465376 - 0.00612679i) q^{2} +(0.442289 + 0.896873i) q^{3} +(-1.92972 + 0.517068i) q^{4} +(3.21502 - 2.81950i) q^{5} +(0.0260780 + 0.0390285i) q^{6} +(-1.10998 + 2.40166i) q^{7} +(-0.173369 + 0.0718118i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(0.132345 - 0.150910i) q^{10} +(4.91158 - 0.321922i) q^{11} +(-1.31724 - 1.50202i) q^{12} +(1.03125 + 1.03125i) q^{13} +(-0.0369411 + 0.118568i) q^{14} +(3.95070 + 1.63643i) q^{15} +(3.45266 - 1.99339i) q^{16} +(-0.291724 - 4.11277i) q^{17} +(-0.0234696 + 0.0406505i) q^{18} +(0.850832 + 6.46271i) q^{19} +(-4.74623 + 7.10323i) q^{20} +(-2.64491 + 0.0667189i) q^{21} +(0.226601 - 0.0450737i) q^{22} +(1.46554 + 0.722724i) q^{23} +(-0.141085 - 0.123728i) q^{24} +(1.73416 - 13.1723i) q^{25} +(0.0543104 + 0.0416738i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(0.900126 - 5.20847i) q^{28} +(0.861607 + 4.33159i) q^{29} +(0.193882 + 0.0519505i) q^{30} +(-1.49981 + 0.739625i) q^{31} +(0.446216 - 0.342394i) q^{32} +(2.46106 + 4.26268i) q^{33} +(-0.0387742 - 0.189611i) q^{34} +(3.20287 + 10.8509i) q^{35} +(0.764524 - 1.84572i) q^{36} +(-0.176565 + 2.69387i) q^{37} +(0.0791914 + 0.295546i) q^{38} +(-0.468792 + 1.38102i) q^{39} +(-0.354912 + 0.719690i) q^{40} +(-1.05257 + 5.29161i) q^{41} +(-0.122679 + 0.0193098i) q^{42} +(-1.09261 - 2.63780i) q^{43} +(-9.31153 + 3.16084i) q^{44} +(0.279677 + 4.26705i) q^{45} +(0.0726307 + 0.0246548i) q^{46} +(1.79389 - 6.69489i) q^{47} +(3.31489 + 2.21494i) q^{48} +(-4.53591 - 5.33156i) q^{49} -0.623630i q^{50} +(3.55961 - 2.08067i) q^{51} +(-2.52326 - 1.45681i) q^{52} +(-4.64889 - 6.05855i) q^{53} +(-0.0468387 - 0.00306997i) q^{54} +(14.8832 - 14.8832i) q^{55} +(0.0199681 - 0.496082i) q^{56} +(-5.41992 + 3.62147i) q^{57} +(0.0666359 + 0.196303i) q^{58} +(-12.8463 - 1.69125i) q^{59} +(-8.46990 - 1.11508i) q^{60} +(-3.52562 - 10.3862i) q^{61} +(-0.0652661 + 0.0436094i) q^{62} +(-1.22965 - 2.34264i) q^{63} +(-5.61950 + 5.61950i) q^{64} +(6.22312 + 0.407885i) q^{65} +(0.140648 + 0.183296i) q^{66} +(4.96385 + 2.86588i) q^{67} +(2.68953 + 7.78567i) q^{68} +1.63406i q^{69} +(0.215535 + 0.485354i) q^{70} +(-6.57290 - 4.39187i) q^{71} +(0.0485682 - 0.181259i) q^{72} +(-6.39100 - 2.16945i) q^{73} +(0.00828783 + 0.126448i) q^{74} +(12.5808 - 4.27062i) q^{75} +(-4.98353 - 12.0313i) q^{76} +(-4.67858 + 12.1532i) q^{77} +(-0.0133552 + 0.0671413i) q^{78} +(-2.81281 + 5.70382i) q^{79} +(5.48000 - 16.1436i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(-0.0165633 + 0.252708i) q^{82} +(1.84547 - 4.45535i) q^{83} +(5.06945 - 1.49635i) q^{84} +(-12.5338 - 12.4001i) q^{85} +(-0.0670088 - 0.116063i) q^{86} +(-3.50381 + 2.68856i) q^{87} +(-0.828397 + 0.408520i) q^{88} +(-2.45040 - 0.656582i) q^{89} +(0.0391588 + 0.196865i) q^{90} +(-3.62138 + 1.33205i) q^{91} +(-3.20178 - 0.636874i) q^{92} +(-1.32670 - 1.01801i) q^{93} +(0.0424652 - 0.322555i) q^{94} +(20.9570 + 18.3788i) q^{95} +(0.504440 + 0.248762i) q^{96} +(1.27306 - 0.253227i) q^{97} +(-0.243756 - 0.220327i) q^{98} +(-2.73458 + 4.09259i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100})$ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$ .

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.0465376	−	0.00612679i	0.0329071	−	0.00433230i	−0.114055	−	0.993474i	$-0.536384\pi$
$2$	0.0465376	−	0.00612679i	0.0329071	−	0.00433230i	0.146962	+	0.989142i	$0.453051\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	−1.92972	+	0.517068i	−0.964862	+	0.258534i
$5$	3.21502	−	2.81950i	1.43780	−	1.26092i	0.525875	−	0.850562i	$-0.323738\pi$
$5$	3.21502	−	2.81950i	1.43780	−	1.26092i	0.911926	−	0.410356i	$-0.134595\pi$
$6$	0.0260780	+	0.0390285i	0.0106463	+	0.0159333i
$7$	−1.10998	+	2.40166i	−0.419531	+	0.907741i
$7$	−1.10998	+	2.40166i	−0.419531	+	0.907741i
$8$	−0.173369	+	0.0718118i	−0.0612952	+	0.0253893i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	0.132345	−	0.150910i	0.0418511	−	0.0477221i
$11$	4.91158	−	0.321922i	1.48090	−	0.0970630i	0.696604	−	0.717456i	$-0.254693\pi$
$11$	4.91158	−	0.321922i	1.48090	−	0.0970630i	0.784291	+	0.620393i	$0.213027\pi$
$12$	−1.31724	−	1.50202i	−0.380254	−	0.433597i
$13$	1.03125	+	1.03125i	0.286018	+	0.286018i	0.835504	−	0.549485i	$-0.185176\pi$
$13$	1.03125	+	1.03125i	0.286018	+	0.286018i	−0.549485	+	0.835504i	$0.685176\pi$
$14$	−0.0369411	+	0.118568i	−0.00987294	+	0.0316886i
$15$	3.95070	+	1.63643i	1.02007	+	0.422525i
$16$	3.45266	−	1.99339i	0.863164	−	0.498348i
$17$	−0.291724	−	4.11277i	−0.0707535	−	0.997494i
$17$	−0.291724	−	4.11277i	−0.0707535	−	0.997494i
$18$	−0.0234696	+	0.0406505i	−0.00553183	+	0.00958142i
$19$	0.850832	+	6.46271i	0.195194	+	1.48265i	0.755930	+	0.654653i	$0.227185\pi$
$19$	0.850832	+	6.46271i	0.195194	+	1.48265i	−0.560736	+	0.827995i	$0.689482\pi$
$20$	−4.74623	+	7.10323i	−1.06129	+	1.58833i
$21$	−2.64491	+	0.0667189i	−0.577167	+	0.0145593i
$22$	0.226601	−	0.0450737i	0.0483114	−	0.00960974i
$23$	1.46554	+	0.722724i	0.305586	+	0.150698i	0.588616	−	0.808413i	$-0.299673\pi$
$23$	1.46554	+	0.722724i	0.305586	+	0.150698i	−0.283030	+	0.959111i	$0.591340\pi$
$24$	−0.141085	−	0.123728i	−0.0287989	−	0.0252560i
$25$	1.73416	−	13.1723i	0.346832	−	2.63445i
$26$	0.0543104	+	0.0416738i	0.0106511	+	0.00817291i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	0.900126	−	5.20847i	0.170108	−	0.984307i
$29$	0.861607	+	4.33159i	0.159996	+	0.804356i	0.974533	+	0.224244i	$0.0719912\pi$
$29$	0.861607	+	4.33159i	0.159996	+	0.804356i	−0.814537	+	0.580112i	$0.803009\pi$
$30$	0.193882	+	0.0519505i	0.0353979	+	0.00948483i
$31$	−1.49981	+	0.739625i	−0.269374	+	0.132841i	−0.571960	−	0.820282i	$-0.693817\pi$
$31$	−1.49981	+	0.739625i	−0.269374	+	0.132841i	0.302586	+	0.953122i	$0.402150\pi$
$32$	0.446216	−	0.342394i	0.0788806	−	0.0605272i
$33$	2.46106	+	4.26268i	0.428415	+	0.742037i
$34$	−0.0387742	−	0.189611i	−0.00664973	−	0.0325181i
$35$	3.20287	+	10.8509i	0.541384	+	1.83414i
$36$	0.764524	−	1.84572i	0.127421	−	0.307621i
$37$	−0.176565	+	2.69387i	−0.0290272	+	0.442869i	0.958466	+	0.285207i	$0.0920623\pi$
$37$	−0.176565	+	2.69387i	−0.0290272	+	0.442869i	−0.987493	+	0.157662i	$0.949604\pi$
$38$	0.0791914	+	0.295546i	0.0128465	+	0.0479439i
$39$	−0.468792	+	1.38102i	−0.0750667	+	0.221139i
$40$	−0.354912	+	0.719690i	−0.0561165	+	0.113793i
$41$	−1.05257	+	5.29161i	−0.164383	+	0.826411i	0.807303	+	0.590137i	$0.200926\pi$
$41$	−1.05257	+	5.29161i	−0.164383	+	0.826411i	−0.971687	+	0.236274i	$0.924074\pi$
$42$	−0.122679	+	0.0193098i	−0.0189298	+	0.00297956i
$43$	−1.09261	−	2.63780i	−0.166622	−	0.402261i	0.818410	−	0.574635i	$-0.194856\pi$
$43$	−1.09261	−	2.63780i	−0.166622	−	0.402261i	−0.985031	+	0.172375i	$0.944856\pi$
$44$	−9.31153	+	3.16084i	−1.40377	+	0.476514i
$45$	0.279677	+	4.26705i	0.0416918	+	0.636094i
$46$	0.0726307	+	0.0246548i	0.0107088	+	0.00363515i
$47$	1.79389	−	6.69489i	0.261666	−	0.976550i	−0.702594	−	0.711591i	$-0.747975\pi$
$47$	1.79389	−	6.69489i	0.261666	−	0.976550i	0.964260	−	0.264959i	$-0.0853585\pi$
$48$	3.31489	+	2.21494i	0.478463	+	0.319699i
$49$	−4.53591	−	5.33156i	−0.647987	−	0.761651i
$50$		−	0.623630i		−	0.0881946i
$51$	3.55961	−	2.08067i	0.498445	−	0.291352i
$52$	−2.52326	−	1.45681i	−0.349914	−	0.202023i
$53$	−4.64889	−	6.05855i	−0.638574	−	0.832205i	0.356189	−	0.934414i	$-0.384076\pi$
$53$	−4.64889	−	6.05855i	−0.638574	−	0.832205i	−0.994763	+	0.102209i	$0.967409\pi$
$54$	−0.0468387	−	0.00306997i	−0.00637394	−	0.000417770i
$55$	14.8832	−	14.8832i	2.00684	−	2.00684i
$56$	0.0199681	−	0.496082i	0.00266834	−	0.0662918i
$57$	−5.41992	+	3.62147i	−0.717885	+	0.479676i
$58$	0.0666359	+	0.196303i	0.00874972	+	0.0257758i
$59$	−12.8463	−	1.69125i	−1.67245	−	0.220182i	−0.766102	−	0.642719i	$-0.777806\pi$
$59$	−12.8463	−	1.69125i	−1.67245	−	0.220182i	−0.906345	+	0.422538i	$0.861139\pi$
$60$	−8.46990	−	1.11508i	−1.09346	−	0.143957i
$61$	−3.52562	−	10.3862i	−0.451410	−	1.32981i	−0.899929	−	0.436037i	$-0.856382\pi$
$61$	−3.52562	−	10.3862i	−0.451410	−	1.32981i	0.448519	−	0.893773i	$-0.351952\pi$
$62$	−0.0652661	+	0.0436094i	−0.00828881	+	0.00553840i
$63$	−1.22965	−	2.34264i	−0.154922	−	0.295145i
$64$	−5.61950	+	5.61950i	−0.702437	+	0.702437i
$65$	6.22312	+	0.407885i	0.771883	+	0.0505919i
$66$	0.140648	+	0.183296i	0.0173126	+	0.0225622i
$67$	4.96385	+	2.86588i	0.606431	+	0.350123i	0.771567	−	0.636148i	$-0.219473\pi$
$67$	4.96385	+	2.86588i	0.606431	+	0.350123i	−0.165137	+	0.986271i	$0.552807\pi$
$68$	2.68953	+	7.78567i	0.326153	+	0.944151i
$69$			1.63406i			0.196717i
$70$	0.215535	+	0.485354i	0.0257614	+	0.0580109i
$71$	−6.57290	−	4.39187i	−0.780059	−	0.521219i	0.100624	−	0.994925i	$-0.467916\pi$
$71$	−6.57290	−	4.39187i	−0.780059	−	0.521219i	−0.880683	+	0.473705i	$0.842916\pi$
$72$	0.0485682	−	0.181259i	0.00572382	−	0.0213616i
$73$	−6.39100	−	2.16945i	−0.748010	−	0.253915i	−0.0786999	−	0.996898i	$-0.525077\pi$
$73$	−6.39100	−	2.16945i	−0.748010	−	0.253915i	−0.669310	+	0.742983i	$0.733410\pi$
$74$	0.00828783	+	0.126448i	0.000963441	+	0.0146993i
$75$	12.5808	−	4.27062i	1.45271	−	0.493129i
$76$	−4.98353	−	12.0313i	−0.571650	−	1.38009i
$77$	−4.67858	+	12.1532i	−0.533174	+	1.38499i
$78$	−0.0133552	+	0.0671413i	−0.00151218	+	0.00760226i
$79$	−2.81281	+	5.70382i	−0.316466	+	0.641730i	−0.995745	−	0.0921503i	$-0.970626\pi$
$79$	−2.81281	+	5.70382i	−0.316466	+	0.641730i	0.679279	+	0.733880i	$0.262293\pi$
$80$	5.48000	−	16.1436i	0.612682	−	1.80490i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	−0.0165633	+	0.252708i	−0.00182911	+	0.0279069i
$83$	1.84547	−	4.45535i	0.202566	−	0.489038i	−0.789651	−	0.613556i	$-0.789738\pi$
$83$	1.84547	−	4.45535i	0.202566	−	0.489038i	0.992217	+	0.124518i	$0.0397384\pi$
$84$	5.06945	−	1.49635i	0.553122	−	0.163265i
$85$	−12.5338	−	12.4001i	−1.35949	−	1.34498i
$86$	−0.0670088	−	0.116063i	−0.00722575	−	0.0125154i
$87$	−3.50381	+	2.68856i	−0.375647	+	0.288244i
$88$	−0.828397	+	0.408520i	−0.0883074	+	0.0435484i
$89$	−2.45040	−	0.656582i	−0.259742	−	0.0695975i	0.126598	−	0.991954i	$-0.459594\pi$
$89$	−2.45040	−	0.656582i	−0.259742	−	0.0695975i	−0.386340	+	0.922357i	$0.626261\pi$
$90$	0.0391588	+	0.196865i	0.00412770	+	0.0207514i
$91$	−3.62138	+	1.33205i	−0.379624	+	0.139637i
$92$	−3.20178	−	0.636874i	−0.333809	−	0.0663987i
$93$	−1.32670	−	1.01801i	−0.137572	−	0.105563i
$94$	0.0424652	−	0.322555i	0.00437995	−	0.0332690i
$95$	20.9570	+	18.3788i	2.15015	+	1.88563i
$96$	0.504440	+	0.248762i	0.0514842	+	0.0253892i
$97$	1.27306	−	0.253227i	0.129259	−	0.0257113i	−0.130037	−	0.991509i	$-0.541509\pi$
$97$	1.27306	−	0.253227i	0.129259	−	0.0257113i	0.259296	+	0.965798i	$0.416509\pi$
$98$	−0.243756	−	0.220327i	−0.0246230	−	0.0222564i
$99$	−2.73458	+	4.09259i	−0.274836	+	0.411321i
$100$	3.46450	+	26.3155i	0.346450	+	2.63155i
$101$	0.408484	−	0.707516i	0.0406457	−	0.0704005i	−0.844987	−	0.534787i	$-0.820392\pi$
$101$	0.408484	−	0.707516i	0.0406457	−	0.0704005i	0.885633	+	0.464387i	$0.153725\pi$
$102$	0.152908	−	0.118638i	0.0151401	−	0.0117470i
$103$	1.37843	−	0.795839i	0.135821	−	0.0784163i	−0.430550	−	0.902567i	$-0.641680\pi$
$103$	1.37843	−	0.795839i	0.135821	−	0.0784163i	0.566371	+	0.824151i	$0.308347\pi$
$104$	−0.252844	−	0.104731i	−0.0247934	−	0.0102697i
$105$	−8.31532	+	7.67182i	−0.811493	+	0.748693i
$106$	−0.253467	−	0.253467i	−0.0246189	−	0.0246189i
$107$	4.59274	+	5.23702i	0.443997	+	0.506281i	0.929941	−	0.367708i	$-0.119858\pi$
$107$	4.59274	+	5.23702i	0.443997	+	0.506281i	−0.485944	+	0.873990i	$0.661524\pi$
$108$	1.99352	−	0.130662i	0.191826	−	0.0125730i
$109$	−10.8812	+	12.4077i	−1.04223	+	1.18844i	−0.0605010	+	0.998168i	$0.519270\pi$
$109$	−10.8812	+	12.4077i	−1.04223	+	1.18844i	−0.981732	+	0.190271i	$0.939063\pi$
$110$	0.601440	−	0.783812i	0.0573451	−	0.0747336i
$111$	−2.49415	+	1.03311i	−0.236734	+	0.0980584i
$112$	0.955080	+	10.5047i	0.0902466	+	0.992602i
$113$	2.00555	+	3.00151i	0.188666	+	0.282359i	0.913729	−	0.406324i	$-0.133189\pi$
$113$	2.00555	+	3.00151i	0.188666	+	0.282359i	−0.725063	+	0.688682i	$0.758189\pi$
$114$	−0.230042	+	0.201741i	−0.0215454	+	0.0188948i
$115$	6.74946	−	1.80851i	0.629390	−	0.168645i
$116$	−3.90239	−	7.91326i	−0.362328	−	0.734728i
$117$	−1.44594	+	0.190361i	−0.133677	+	0.0175989i
$118$	−0.608198			−0.0559892
$119$	10.2013	+	3.86445i	0.935149	+	0.354254i
$120$	−0.802444			−0.0732527
$121$	13.1140	−	1.72650i	1.19219	−	0.156954i
$122$	−0.227708	−	0.461746i	−0.0206157	−	0.0418045i
$123$	−5.21144	+	1.39640i	−0.469900	+	0.125909i
$124$	2.51179	−	2.20278i	0.225565	−	0.197815i
$125$	−19.6851	−	29.4609i	−1.76069	−	2.63506i
$126$	−0.0715779	−	0.101487i	−0.00637667	−	0.00904118i
$127$	−0.235317	+	0.0974717i	−0.0208810	+	0.00864921i	−0.393100	−	0.919496i	$-0.628597\pi$
$127$	−0.235317	+	0.0974717i	−0.0208810	+	0.00864921i	0.372218	+	0.928145i	$0.378597\pi$
$128$	−0.911876	+	1.18838i	−0.0805992	+	0.105039i
$129$	1.88252	−	2.14660i	0.165747	−	0.188998i
$130$	0.292108	−	0.0191458i	0.0256196	−	0.00167920i
$131$	−3.72825	−	4.25126i	−0.325739	−	0.371434i	0.565672	−	0.824630i	$-0.308617\pi$
$131$	−3.72825	−	4.25126i	−0.325739	−	0.371434i	−0.891411	+	0.453197i	$0.850284\pi$
$132$	−6.95325	−	6.95325i	−0.605203	−	0.605203i
$133$	−16.4656	−	5.13004i	−1.42775	−	0.444831i
$134$	0.248564	+	0.102959i	0.0214727	+	0.00889428i
$135$	−3.70330	+	2.13810i	−0.318729	+	0.184019i
$136$	0.345922	+	0.692078i	0.0296625	+	0.0593452i
$137$	3.00318	−	5.20166i	0.256579	−	0.444408i	−0.708744	−	0.705466i	$-0.750738\pi$
$137$	3.00318	−	5.20166i	0.256579	−	0.444408i	0.965323	+	0.261058i	$0.0840712\pi$
$138$	0.0100115	+	0.0760450i	0.000852237	+	0.00647338i
$139$	5.80142	−	8.68244i	0.492070	−	0.736435i	−0.499457	−	0.866339i	$-0.666467\pi$
$139$	5.80142	−	8.68244i	0.492070	−	0.736435i	0.991527	+	0.129904i	$0.0414670\pi$
$140$	−11.7913	−	19.2832i	−0.996549	−	1.62973i
$141$	6.79788	−	1.35218i	0.572485	−	0.113874i
$142$	−0.332795	−	0.164116i	−0.0279275	−	0.0137723i
$143$	5.39706	+	4.73310i	0.451325	+	0.395802i
$144$	−0.520380	+	3.95268i	−0.0433650	+	0.329390i
$145$	14.9830	+	11.4969i	1.24427	+	0.954761i
$146$	−0.310714	−	0.0618048i	−0.0257148	−	0.00511500i
$147$	2.77555	−	6.42622i	0.228923	−	0.530026i
$148$	−1.05219	−	5.28971i	−0.0864894	−	0.434812i
$149$	2.42533	+	0.649867i	0.198691	+	0.0532391i	0.356792	−	0.934184i	$-0.383870\pi$
$149$	2.42533	+	0.649867i	0.198691	+	0.0532391i	−0.158101	+	0.987423i	$0.550537\pi$
$150$	0.559317	−	0.275824i	0.0456680	−	0.0225210i
$151$	−10.1941	+	7.82224i	−0.829588	+	0.636565i	−0.933722	−	0.357998i	$-0.883459\pi$
$151$	−10.1941	+	7.82224i	−0.829588	+	0.636565i	0.104135	+	0.994563i	$0.466793\pi$
$152$	−0.611607	−	1.05933i	−0.0496079	−	0.0859233i
$153$	3.44047	+	2.27226i	0.278146	+	0.183701i
$154$	−0.143270	+	0.594248i	−0.0115450	+	0.0478858i
$155$	−2.73655	+	6.60662i	−0.219805	+	0.530657i
$156$	0.190559	−	2.90738i	0.0152570	−	0.232776i
$157$	4.93990	+	18.4360i	0.394247	+	1.47135i	0.823059	+	0.567956i	$0.192266\pi$
$157$	4.93990	+	18.4360i	0.394247	+	1.47135i	−0.428811	+	0.903394i	$0.641068\pi$
$158$	−0.0959554	+	0.282676i	−0.00763381	+	0.0224885i
$159$	3.37759	−	6.84908i	0.267861	−	0.543168i
$160$	0.469216	−	2.35891i	0.0370948	−	0.186488i
$161$	−3.36245	+	2.71752i	−0.264998	+	0.214170i
$162$	−0.0179628	−	0.0433661i	−0.00141129	−	0.00340717i
$163$	−11.8729	+	4.03031i	−0.929957	+	0.315678i	−0.744997	−	0.667068i	$-0.767549\pi$
$163$	−11.8729	+	4.03031i	−0.929957	+	0.315678i	−0.184961	+	0.982746i	$0.559216\pi$
$164$	−0.704959	−	10.7556i	−0.0550480	−	0.839871i
$165$	19.9309	+	6.76565i	1.55162	+	0.526705i
$166$	0.0585866	−	0.218648i	0.00454720	−	0.0169704i
$167$	10.4005	+	6.94939i	0.804815	+	0.537760i	0.888578	−	0.458726i	$-0.151694\pi$
$167$	10.4005	+	6.94939i	0.804815	+	0.537760i	−0.0837631	+	0.996486i	$0.526694\pi$
$168$	0.453754	−	0.201503i	0.0350079	−	0.0155463i
$169$		−	10.8730i		−	0.836387i
$170$	−0.659268	−	0.500280i	−0.0505636	−	0.0383697i
$171$	−5.64517	−	3.25924i	−0.431697	−	0.249240i
$172$	3.47236	+	4.52527i	0.264765	+	0.345048i
$173$	20.6609	+	1.35419i	1.57082	+	0.102957i	0.825754	−	0.564031i	$-0.190750\pi$
$173$	20.6609	+	1.35419i	1.57082	+	0.102957i	0.745068	+	0.666988i	$0.232417\pi$
$174$	−0.146586	+	0.146586i	−0.0111127	+	0.0111127i
$175$	29.7104	+	18.7857i	2.24589	+	1.42007i
$176$	16.3163	−	10.9022i	1.22989	−	0.821783i
$177$	−4.16494	−	12.2695i	−0.313056	−	0.922234i
$178$	−0.118058	−	0.0155427i	−0.00884885	−	0.00116497i
$179$	−10.4134	−	1.37095i	−0.778333	−	0.102469i	−0.269116	−	0.963108i	$-0.586731\pi$
$179$	−10.4134	−	1.37095i	−0.778333	−	0.102469i	−0.509217	+	0.860638i	$0.670065\pi$
$180$	−2.74605	−	8.08961i	−0.204679	−	0.602964i
$181$	−0.813298	+	0.543429i	−0.0604520	+	0.0403927i	−0.585429	−	0.810724i	$-0.699074\pi$
$181$	−0.813298	+	0.543429i	−0.0604520	+	0.0403927i	0.524977	+	0.851116i	$0.324074\pi$
$182$	−0.160369	+	0.0841780i	−0.0118874	+	0.00623969i
$183$	7.75571	−	7.75571i	0.573319	−	0.573319i
$184$	−0.305979	−	0.0200549i	−0.0225571	−	0.00147847i
$185$	7.02769	+	9.15866i	0.516686	+	0.673358i
$186$	−0.0679786	−	0.0392474i	−0.00498443	−	0.00287776i
$187$	−2.75682	−	20.1063i	−0.201598	−	1.47032i
$188$			13.8469i			1.00989i
$189$	1.55719	−	2.13896i	0.113269	−	0.155587i
$190$	1.08789	+	0.726907i	0.0789241	+	0.0527354i
$191$	−5.21502	+	19.4627i	−0.377345	+	1.40827i	0.472542	+	0.881308i	$0.343336\pi$
$191$	−5.21502	+	19.4627i	−0.377345	+	1.40827i	−0.849888	+	0.526964i	$0.823330\pi$
$192$	−7.52541	−	2.55453i	−0.543100	−	0.184358i
$193$	0.0852700	+	1.30097i	0.00613787	+	0.0936458i	0.999829	−	0.0185082i	$-0.00589168\pi$
$193$	0.0852700	+	1.30097i	0.00613787	+	0.0936458i	−0.993691	+	0.112154i	$0.964225\pi$
$194$	0.0576936	−	0.0195843i	0.00414216	−	0.00140607i
$195$	2.38659	+	5.76175i	0.170908	+	0.412607i
$196$	11.5098	+	7.94306i	0.822131	+	0.567362i
$197$	−0.361829	+	1.81904i	−0.0257793	+	0.129601i	−0.991532	−	0.129863i	$-0.958546\pi$
$197$	−0.361829	+	1.81904i	−0.0257793	+	0.129601i	0.965753	+	0.259465i	$0.0835461\pi$
$198$	−0.102186	+	0.207213i	−0.00726207	+	0.0147260i
$199$	7.73429	−	22.7845i	0.548269	−	1.61515i	−0.220335	−	0.975424i	$-0.570715\pi$
$199$	7.73429	−	22.7845i	0.548269	−	1.61515i	0.768604	−	0.639724i	$-0.220951\pi$
$200$	0.645274	+	2.40819i	0.0456277	+	0.170285i
$201$	−0.374875	+	5.71949i	−0.0264416	+	0.403421i
$202$	0.0146751	−	0.0354288i	0.00103254	−	0.00249276i
$203$	−11.3594	−	2.73867i	−0.797270	−	0.192217i
$204$	−5.79321	+	5.85568i	−0.405606	+	0.409980i
$205$	11.5357	+	19.9803i	0.805685	+	1.39549i
$206$	0.0592730	−	0.0454818i	0.00412975	−	0.00316887i
$207$	−1.46554	+	0.722724i	−0.101862	+	0.0502328i
$208$	5.61626	+	1.50487i	0.389418	+	0.104344i
$209$	6.25941	+	31.4682i	0.432973	+	2.17670i
$210$	−0.339972	+	0.407974i	−0.0234603	+	0.0281529i
$211$	15.9999	+	3.18258i	1.10148	+	0.219098i	0.712168	−	0.702009i	$-0.247713\pi$
$211$	15.9999	+	3.18258i	1.10148	+	0.219098i	0.389310	+	0.921107i	$0.372713\pi$
$212$	12.1037	+	9.28753i	0.831288	+	0.637870i
$213$	1.03183	−	7.83753i	0.0706998	−	0.537019i
$214$	0.245821	+	0.215579i	0.0168040	+	0.0147367i
$215$	−10.9500	−	5.39996i	−0.746786	−	0.368274i
$216$	0.184048	−	0.0366093i	0.0125229	−	0.00249095i
$217$	−0.111572	−	4.42300i	−0.00757400	−	0.300253i
$218$	−0.430367	+	0.644090i	−0.0291481	+	0.0436233i
$219$	−0.880945	−	6.69144i	−0.0595287	−	0.452165i
$220$	−21.0248	+	36.4160i	−1.41749	+	2.45516i
$221$	3.94047	−	4.54215i	0.265065	−	0.305538i
$222$	−0.109742	+	0.0633596i	−0.00736540	+	0.00425242i
$223$	18.5464	+	7.68217i	1.24196	+	0.514436i	0.904326	−	0.426842i	$-0.140374\pi$
$223$	18.5464	+	7.68217i	1.24196	+	0.514436i	0.337633	+	0.941278i	$0.390374\pi$
$224$	0.327023	+	1.45171i	0.0218501	+	0.0969962i
$225$	9.39456	+	9.39456i	0.626304	+	0.626304i
$226$	0.111723	+	0.127396i	0.00743171	+	0.00847424i
$227$	−24.5915	+	1.61181i	−1.63220	+	0.106980i	−0.853733	−	0.520711i	$-0.825667\pi$
$227$	−24.5915	+	1.61181i	−1.63220	+	0.106980i	−0.778463	+	0.627690i	$0.784000\pi$
$228$	8.58639	−	9.79090i	0.568648	−	0.648418i
$229$	−12.1436	+	15.8258i	−0.802468	+	1.04580i	0.195412	+	0.980721i	$0.437396\pi$
$229$	−12.1436	+	15.8258i	−0.802468	+	1.04580i	−0.997880	+	0.0650759i	$0.979271\pi$
$230$	0.303023	−	0.125516i	0.0199808	−	0.00827630i
$231$	−12.9692	+	1.17915i	−0.853310	+	0.0775823i
$232$	−0.460435	−	0.689090i	−0.0302291	−	0.0452410i
$233$	9.50688	−	8.33731i	0.622816	−	0.546195i	−0.288721	−	0.957413i	$-0.593230\pi$
$233$	9.50688	−	8.33731i	0.622816	−	0.546195i	0.911537	+	0.411218i	$0.134897\pi$
$234$	−0.0661241	+	0.0177179i	−0.00432267	+	0.00115826i
$235$	−13.1088	−	26.5821i	−0.855126	−	1.73402i
$236$	25.6643	−	3.37877i	1.67060	−	0.219939i
$237$	−6.35968			−0.413105
$238$	0.498420	+	0.117341i	0.0323077	+	0.00760611i
$239$	11.5615			0.747852			0.373926	−	0.927459i	$-0.378011\pi$
$239$	11.5615			0.747852			0.373926	+	0.927459i	$0.378011\pi$
$240$	16.9025	−	2.22525i	1.09105	−	0.143639i
$241$	−7.87766	−	15.9743i	−0.507444	−	1.02900i	−0.988346	−	0.152221i	$-0.951357\pi$
$241$	−7.87766	−	15.9743i	−0.507444	−	1.02900i	0.480902	−	0.876774i	$-0.340309\pi$
$242$	0.599718	−	0.160694i	0.0385514	−	0.0103298i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	12.1738	+	18.2194i	0.779349	+	1.16638i
$245$	−29.6154	−	4.35209i	−1.89206	−	0.278045i
$246$	−0.233972	+	0.0969146i	−0.0149175	+	0.00617905i
$247$	−5.78727	+	7.54212i	−0.368235	+	0.479894i
$248$	0.206907	−	0.235932i	0.0131386	−	0.0149817i
$249$	4.81211	−	0.315402i	0.304955	−	0.0199878i
$250$	−1.09660	−	1.25043i	−0.0693550	−	0.0790842i
$251$	−4.73079	−	4.73079i	−0.298605	−	0.298605i	0.541862	−	0.840467i	$-0.317719\pi$
$251$	−4.73079	−	4.73079i	−0.298605	−	0.298605i	−0.840467	+	0.541862i	$0.817719\pi$
$252$	3.58419	+	3.88483i	0.225783	+	0.244721i
$253$	7.43077	+	3.07793i	0.467168	+	0.193508i
$254$	−0.0103539	+	0.00597784i	−0.000649663	+	0.000375083i
$255$	5.57776	−	16.7257i	0.349293	−	1.04740i
$256$	7.91201	−	13.7040i	0.494501	−	0.856501i
$257$	−0.811035	−	6.16042i	−0.0505910	−	0.384277i	−0.997944	−	0.0640867i	$-0.979587\pi$
$257$	−0.811035	−	6.16042i	−0.0505910	−	0.384277i	0.947353	−	0.320190i	$-0.103747\pi$
$258$	0.0744562	−	0.111432i	0.00463544	−	0.00693743i
$259$	−6.27376	−	3.41417i	−0.389832	−	0.212146i
$260$	−12.2198	+	2.43067i	−0.757840	+	0.150744i
$261$	−3.96099	−	1.95335i	−0.245179	−	0.120909i
$262$	−0.199550	−	0.175001i	−0.0123283	−	0.0108116i
$263$	−0.951121	+	7.22448i	−0.0586486	+	0.445480i	0.936776	+	0.349930i	$0.113795\pi$
$263$	−0.951121	+	7.22448i	−0.0586486	+	0.445480i	−0.995425	+	0.0955507i	$0.969539\pi$
$264$	−0.732781	−	0.562283i	−0.0450996	−	0.0346061i
$265$	−32.0283	−	6.37083i	−1.96748	−	0.391357i
$266$	−0.797701	−	0.137859i	−0.0489102	−	0.00845265i
$267$	−0.494912	−	2.48809i	−0.0302881	−	0.152269i
$268$	−11.0607	−	2.96371i	−0.675640	−	0.181037i
$269$	−13.3805	+	6.59854i	−0.815825	+	0.402320i	−0.801808	−	0.597581i	$-0.796128\pi$
$269$	−13.3805	+	6.59854i	−0.815825	+	0.402320i	−0.0140168	+	0.999902i	$0.504462\pi$
$270$	−0.159243	+	0.122191i	−0.00969122	+	0.00743634i
$271$	−7.15017	−	12.3844i	−0.434342	−	0.752302i	0.562900	−	0.826525i	$-0.309686\pi$
$271$	−7.15017	−	12.3844i	−0.434342	−	0.752302i	−0.997242	+	0.0742232i	$0.976352\pi$
$272$	−9.20559	−	13.6185i	−0.558171	−	0.825741i
$273$	−2.79638	−	2.65877i	−0.169245	−	0.160916i
$274$	0.107891	−	0.260473i	0.00651796	−	0.0157357i
$275$	4.27702	−	65.2548i	0.257914	−	3.93501i
$276$	−0.844917	−	3.15327i	−0.0508581	−	0.189805i
$277$	0.649980	−	1.91478i	0.0390535	−	0.115048i	−0.925655	−	0.378370i	$-0.876485\pi$
$277$	0.649980	−	1.91478i	0.0390535	−	0.115048i	0.964708	+	0.263322i	$0.0848181\pi$
$278$	0.216789	−	0.439604i	0.0130021	−	0.0263657i
$279$	0.326243	−	1.64014i	0.0195317	−	0.0981924i
$280$	−1.33450	−	1.65121i	−0.0797519	−	0.0986789i
$281$	7.99983	+	19.3133i	0.477230	+	1.15214i	0.960903	+	0.276886i	$0.0893025\pi$
$281$	7.99983	+	19.3133i	0.477230	+	1.15214i	−0.483673	+	0.875249i	$0.660697\pi$
$282$	0.308073	−	0.104577i	0.0183455	−	0.00622744i
$283$	−0.571121	−	8.71362i	−0.0339496	−	0.517971i	−0.980639	−	0.195824i	$-0.937262\pi$
$283$	−0.571121	−	8.71362i	−0.0339496	−	0.517971i	0.946690	−	0.322147i	$-0.104405\pi$
$284$	14.9548	+	5.07646i	0.887402	+	0.301233i
$285$	−7.21441	+	26.9245i	−0.427345	+	1.59487i
$286$	0.280165	+	0.187200i	0.0165665	+	0.0110694i
$287$	−11.5403	−	8.40146i	−0.681203	−	0.495923i
$288$			0.562443i			0.0331423i
$289$	−16.8298	+	2.39959i	−0.989988	+	0.141152i
$290$	0.767711	+	0.443238i	0.0450816	+	0.0260278i
$291$	0.790172	+	1.02977i	0.0463207	+	0.0603663i
$292$	13.4546	+	0.881862i	0.787372	+	0.0516071i
$293$	7.99630	−	7.99630i	0.467149	−	0.467149i	−0.433841	−	0.900990i	$-0.642842\pi$
$293$	7.99630	−	7.99630i	0.467149	−	0.467149i	0.900990	+	0.433841i	$0.142842\pi$
$294$	0.0897953	−	0.316066i	0.00523697	−	0.0184334i
$295$	−46.0696	+	30.7827i	−2.68228	+	1.79224i
$296$	−0.162840	−	0.479712i	−0.00946491	−	0.0278827i
$297$	−4.88000	−	0.642465i	−0.283167	−	0.0372796i
$298$	0.116851	+	0.0153837i	0.00676899	+	0.000891154i
$299$	0.766031	+	2.25666i	0.0443007	+	0.130506i
$300$	−22.0693	+	14.7463i	−1.27417	+	0.851376i
$301$	7.54786	+	0.303813i	0.435051	+	0.0175115i
$302$	−0.426486	+	0.426486i	−0.0245415	+	0.0245415i
$303$	0.815220	+	0.0534323i	0.0468331	+	0.00306961i
$304$	15.8203	+	20.6175i	0.907359	+	1.18249i
$305$	−40.6187	−	23.4512i	−2.32582	−	1.34281i
$306$	0.174033	+	0.0846663i	0.00994880	+	0.00484005i
$307$			5.08527i			0.290231i	0.989415	+	0.145116i	$0.0463554\pi$
$307$			5.08527i			0.290231i	−0.989415	+	0.145116i	$0.953645\pi$
$308$	2.74432	−	25.8715i	0.156372	−	1.47417i
$309$	1.32343	+	0.884288i	0.0752874	+	0.0503054i
$310$	−0.0868752	+	0.324223i	−0.00493418	+	0.0184146i
$311$	−7.88731	−	2.67738i	−0.447248	−	0.151820i	0.0887233	−	0.996056i	$-0.471721\pi$
$311$	−7.88731	−	2.67738i	−0.447248	−	0.151820i	−0.535972	+	0.844236i	$0.680055\pi$
$312$	−0.0178993	−	0.273090i	−0.00101335	−	0.0154607i
$313$	−1.89925	+	0.644708i	−0.107352	+	0.0364411i	−0.374599	−	0.927187i	$-0.622219\pi$
$313$	−1.89925	+	0.644708i	−0.107352	+	0.0364411i	0.267247	+	0.963628i	$0.413886\pi$
$314$	0.342845	+	0.827700i	0.0193478	+	0.0467098i
$315$	−10.5584	−	4.06463i	−0.594900	−	0.229016i
$316$	2.47869	−	12.4612i	0.139437	−	0.700998i
$317$	8.19169	−	16.6111i	0.460091	−	0.932972i	−0.535965	−	0.844240i	$-0.680052\pi$
$317$	8.19169	−	16.6111i	0.460091	−	0.932972i	0.996056	−	0.0887316i	$-0.0282813\pi$
$318$	0.115222	−	0.339434i	0.00646134	−	0.0190345i
$319$	5.62628	+	20.9976i	0.315011	+	1.17564i
$320$	−2.22264	+	33.9110i	−0.124249	+	1.89568i
$321$	−2.66562	+	6.43538i	−0.148780	+	0.359188i
$322$	−0.139831	+	0.147068i	−0.00779246	+	0.00819577i
$323$	26.3314	−	5.38461i	1.46512	−	0.299608i
$324$	0.998898	+	1.73014i	0.0554944	+	0.0961190i
$325$	15.3723	−	11.7956i	0.852702	−	0.654301i
$326$	−0.527844	+	0.260304i	−0.0292346	+	0.0144169i
$327$	−15.9407	−	4.27131i	−0.881525	−	0.236204i
$328$	−0.197518	−	0.992988i	−0.0109061	−	0.0548286i
$329$	14.0877	+	11.7395i	0.776678	+	0.647218i
$330$	0.968990	+	0.192744i	0.0533412	+	0.0106102i
$331$	6.22219	+	4.77445i	0.342002	+	0.262428i	0.765453	−	0.643491i	$-0.222515\pi$
$331$	6.22219	+	4.77445i	0.342002	+	0.262428i	−0.423451	+	0.905919i	$0.639181\pi$
$332$	−1.25752	+	9.55183i	−0.0690155	+	0.524225i
$333$	−2.02970	−	1.78000i	−0.111227	−	0.0975434i
$334$	0.526592	+	0.259686i	0.0288138	+	0.0142094i
$335$	24.0392	−	4.78170i	1.31340	−	0.261252i
$336$	−8.99897	+	5.50270i	−0.490934	+	0.300197i
$337$	18.7136	−	28.0068i	1.01939	−	1.52563i	0.178855	−	0.983875i	$-0.442761\pi$
$337$	18.7136	−	28.0068i	1.01939	−	1.52563i	0.840537	−	0.541754i	$-0.182239\pi$
$338$	−0.0666168	−	0.506005i	−0.00362348	−	0.0275230i
$339$	−1.80495	+	3.12626i	−0.0980312	+	0.169795i
$340$	30.5986	+	17.4480i	1.65944	+	0.946249i
$341$	−7.12834	+	4.11555i	−0.386021	+	0.222869i
$342$	−0.282681	−	0.117090i	−0.0152856	−	0.00633152i
$343$	17.8393	−	4.97580i	0.963233	−	0.268668i
$344$	0.378850	+	0.378850i	0.0204262	+	0.0204262i
$345$	4.60721	+	5.25352i	0.248044	+	0.282840i
$346$	0.969807	−	0.0635645i	0.0521372	−	0.00341725i
$347$	−2.59025	+	2.95361i	−0.139052	+	0.158558i	−0.817174	−	0.576391i	$-0.804461\pi$
$347$	−2.59025	+	2.95361i	−0.139052	+	0.158558i	0.678122	+	0.734949i	$0.262794\pi$
$348$	5.37121	−	6.99989i	0.287927	−	0.375234i
$349$	−5.77728	+	2.39303i	−0.309251	+	0.128096i	−0.531911	−	0.846800i	$-0.678526\pi$
$349$	−5.77728	+	2.39303i	−0.309251	+	0.128096i	0.222660	+	0.974896i	$0.428526\pi$
$350$	1.49775	+	0.692214i	0.0800578	+	0.0370004i
$351$	−0.810251	−	1.21263i	−0.0432480	−	0.0647252i
$352$	2.08140	−	1.82534i	0.110939	−	0.0972909i
$353$	25.9668	−	6.95777i	1.38207	−	0.370325i	0.510198	−	0.860057i	$-0.329572\pi$
$353$	25.9668	−	6.95777i	1.38207	−	0.370325i	0.871873	+	0.489732i	$0.162905\pi$
$354$	−0.268999	−	0.545477i	−0.0142972	−	0.0289918i
$355$	−33.5149	+	4.41232i	−1.77878	+	0.234181i
$356$	5.06808			0.268608
$357$	1.04598	+	10.8584i	0.0553594	+	0.574690i
$358$	−0.493013			−0.0260566
$359$	−12.5220	+	1.64855i	−0.660885	+	0.0870072i	−0.453506	−	0.891253i	$-0.649827\pi$
$359$	−12.5220	+	1.64855i	−0.660885	+	0.0870072i	−0.207380	+	0.978261i	$0.566494\pi$
$360$	−0.354912	−	0.719690i	−0.0187055	−	0.0379310i
$361$	−22.6901	+	6.07980i	−1.19422	+	0.319989i
$362$	−0.0345195	+	0.0302728i	−0.00181430	+	0.00159110i
$363$	7.34864	+	10.9980i	0.385704	+	0.577246i
$364$	6.29951	−	4.44299i	0.330184	−	0.232876i
$365$	−26.6640	+	11.0446i	−1.39566	+	0.578099i
$366$	0.313415	−	0.408450i	0.0163824	−	0.0213500i
$367$	5.36206	−	6.11425i	0.279897	−	0.319161i	−0.594760	−	0.803903i	$-0.702753\pi$
$367$	5.36206	−	6.11425i	0.279897	−	0.319161i	0.874657	+	0.484742i	$0.161086\pi$
$368$	6.50068	−	0.426077i	0.338871	−	0.0222108i
$369$	−3.55735	−	4.05639i	−0.185188	−	0.211167i
$370$	0.383165	+	0.383165i	0.0199198	+	0.0199198i
$371$	19.7107	−	4.44019i	1.02333	−	0.230523i
$372$	3.08654	+	1.27849i	0.160030	+	0.0662865i
$373$	−20.6489	+	11.9217i	−1.06916	+	0.617281i	−0.927952	−	0.372699i	$-0.878432\pi$
$373$	−20.6489	+	11.9217i	−1.06916	+	0.617281i	−0.141209	+	0.989980i	$0.545099\pi$
$374$	−0.251483	−	0.918808i	−0.0130039	−	0.0475104i
$375$	17.7161	−	30.6852i	0.914857	−	1.58458i
$376$	0.169767	+	1.28951i	0.00875507	+	0.0665014i
$377$	−3.57843	+	5.35550i	−0.184299	+	0.275823i
$378$	0.0593628	−	0.109083i	0.00305329	−	0.00561062i
$379$	−22.4977	+	4.47507i	−1.15563	+	0.229869i	−0.735454	−	0.677575i	$-0.763031\pi$
$379$	−22.4977	+	4.47507i	−1.15563	+	0.229869i	−0.420174	+	0.907444i	$0.638031\pi$
$380$	−49.9444	−	24.6298i	−2.56209	−	1.26348i
$381$	−0.191498	−	0.167939i	−0.00981074	−	0.00860378i
$382$	−0.123450	+	0.937699i	−0.00631627	+	0.0479769i
$383$	1.15392	+	0.885432i	0.0589624	+	0.0452434i	0.637822	−	0.770184i	$-0.279835\pi$
$383$	1.15392	+	0.885432i	0.0589624	+	0.0452434i	−0.578860	+	0.815427i	$0.696502\pi$
$384$	−1.46914	−	0.292230i	−0.0749716	−	0.0149128i
$385$	19.2243	+	52.2642i	0.979761	+	2.66363i
$386$	0.0119390	+	0.0600215i	0.000607680	+	0.00305502i
$387$	2.75785	+	0.738963i	0.140189	+	0.0375636i
$388$	−2.32571	+	1.14692i	−0.118070	+	0.0582258i
$389$	−16.7368	+	12.8426i	−0.848590	+	0.651146i	−0.938681	−	0.344787i	$-0.887951\pi$
$389$	−16.7368	+	12.8426i	−0.848590	+	0.651146i	0.0900905	+	0.995934i	$0.471284\pi$
$390$	0.146367	+	0.253516i	0.00741160	+	0.0128373i
$391$	2.54487	−	6.23827i	0.128699	−	0.315483i
$392$	1.16926	+	0.598595i	0.0590563	+	0.0302336i
$393$	2.16387	−	5.22405i	0.109153	−	0.263518i
$394$	−0.00569380	+	0.0868706i	−0.000286850	+	0.00437648i
$395$	7.03865	+	26.2686i	0.354153	+	1.32172i
$396$	3.16084	−	9.31153i	0.158838	−	0.467922i
$397$	11.8724	−	24.0748i	0.595857	−	1.20828i	−0.364942	−	0.931030i	$-0.618911\pi$
$397$	11.8724	−	24.0748i	0.595857	−	1.20828i	0.960798	−	0.277248i	$-0.0894222\pi$
$398$	0.220339	−	1.10772i	0.0110446	−	0.0555250i
$399$	−2.68156	−	17.0365i	−0.134246	−	0.852893i
$400$	−20.2700	−	48.9361i	−1.01350	−	2.44681i
$401$	1.97981	−	0.672055i	0.0988670	−	0.0335608i	−0.271568	−	0.962419i	$-0.587542\pi$
$401$	1.97981	−	0.672055i	0.0988670	−	0.0335608i	0.370435	+	0.928859i	$0.379209\pi$
$402$	0.0175963	+	0.268468i	0.000877625	+	0.0133900i
$403$	−2.30943	−	0.783945i	−0.115041	−	0.0390511i
$404$	−0.422428	+	1.57652i	−0.0210166	+	0.0784350i
$405$	−3.55553	−	2.37573i	−0.176676	−	0.118051i
$406$	−0.545416	−	0.0578549i	−0.0270686	−	0.00287129i
$407$			13.2880i			0.658660i
$408$	−0.467709	+	0.616346i	−0.0231550	+	0.0305137i
$409$	−25.6289	−	14.7969i	−1.26727	−	0.731658i	−0.292798	−	0.956174i	$-0.594586\pi$
$409$	−25.6289	−	14.7969i	−1.26727	−	0.731658i	−0.974470	+	0.224517i	$0.927920\pi$
$410$	0.659257	+	0.859161i	0.0325584	+	0.0424309i
$411$	5.99350	+	0.392835i	0.295638	+	0.0193771i
$412$	−2.24849	+	2.24849i	−0.110775	+	0.110775i
$413$	18.3209	−	28.9752i	0.901512	−	1.42578i
$414$	−0.0637747	+	0.0426129i	−0.00313436	+	0.00209431i
$415$	−6.62863	−	19.5273i	−0.325387	−	0.958559i
$416$	0.813257	+	0.107067i	0.0398732	+	0.00524941i
$417$	10.3529	+	1.36299i	0.506986	+	0.0667459i
$418$	0.484097	+	1.42610i	0.0236780	+	0.0697530i
$419$	11.9375	−	7.97641i	0.583187	−	0.389673i	−0.228692	−	0.973499i	$-0.573445\pi$
$419$	11.9375	−	7.97641i	0.583187	−	0.389673i	0.811879	+	0.583826i	$0.198445\pi$
$420$	12.0794	−	19.1041i	0.589416	−	0.932183i
$421$	−5.42244	+	5.42244i	−0.264273	+	0.264273i	−0.826788	−	0.562514i	$-0.809834\pi$
$421$	−5.42244	+	5.42244i	−0.264273	+	0.264273i	0.562514	+	0.826788i	$0.309834\pi$
$422$	0.764096	+	0.0500815i	0.0371956	+	0.00243793i
$423$	4.21936	+	5.49878i	0.205152	+	0.267360i
$424$	1.24105	+	0.716519i	0.0602706	+	0.0347973i
$425$	−54.6804	−	3.28954i	−2.65239	−	0.159566i
$426$		−	0.371062i		−	0.0179780i
$427$	28.8573	+	3.06104i	1.39650	+	0.148134i
$428$	−11.5706	−	7.73123i	−0.559287	−	0.373703i
$429$	−1.85793	+	6.93388i	−0.0897015	+	0.334771i
$430$	−0.542673	−	0.184213i	−0.0261700	−	0.00888352i
$431$	−0.285724	−	4.35930i	−0.0137628	−	0.209980i	−0.999202	−	0.0399501i	$-0.987280\pi$
$431$	−0.285724	−	4.35930i	−0.0137628	−	0.209980i	0.985439	−	0.170030i	$-0.0543866\pi$
$432$	−3.77521	+	1.28151i	−0.181635	+	0.0616567i
$433$	−10.5913	−	25.5697i	−0.508987	−	1.22880i	−0.944468	−	0.328604i	$-0.893422\pi$
$433$	−10.5913	−	25.5697i	−0.508987	−	1.22880i	0.435481	−	0.900198i	$-0.356578\pi$
$434$	−0.0322911	−	0.205152i	−0.00155002	−	0.00984762i
$435$	−3.68441	+	18.5228i	−0.176654	+	0.888098i
$436$	14.5822	−	29.5697i	0.698359	−	1.41613i
$437$	−3.42383	+	10.0863i	−0.163784	+	0.482492i
$438$	−0.0819941	−	0.306006i	−0.00391783	−	0.0146215i
$439$	−2.25322	+	34.3775i	−0.107540	+	1.64075i	0.514304	+	0.857608i	$0.328050\pi$
$439$	−2.25322	+	34.3775i	−0.107540	+	1.64075i	−0.621845	+	0.783141i	$0.713617\pi$
$440$	−1.51149	+	3.64906i	−0.0720576	+	0.173962i
$441$	6.99110	−	0.352931i	0.332909	−	0.0168062i
$442$	0.155551	−	0.235523i	0.00739882	−	0.0112027i
$443$	20.6074	+	35.6931i	0.979089	+	1.69583i	0.665723	+	0.746199i	$0.268123\pi$
$443$	20.6074	+	35.6931i	0.979089	+	1.69583i	0.313366	+	0.949632i	$0.398543\pi$
$444$	4.27883	−	3.28326i	0.203064	−	0.155817i
$445$	−9.72930	+	4.79796i	−0.461213	+	0.227445i
$446$	0.910172	+	0.243880i	0.0430979	+	0.0115480i
$447$	0.489851	+	2.46265i	0.0231691	+	0.116479i
$448$	−7.25860	−	19.7336i	−0.342937	−	0.932325i
$449$	23.9356	+	4.76109i	1.12959	+	0.224690i	0.724291	−	0.689494i	$-0.242167\pi$
$449$	23.9356	+	4.76109i	1.12959	+	0.224690i	0.405300	+	0.914184i	$0.367167\pi$
$450$	0.494759	+	0.379642i	0.0233232	+	0.0178965i
$451$	−3.46628	+	26.3290i	−0.163221	+	1.23978i
$452$	−5.42214	−	4.75509i	−0.255036	−	0.223661i
$453$	−11.5243	−	5.68316i	−0.541459	−	0.267018i
$454$	−1.13456	+	0.225677i	−0.0532473	+	0.0105915i
$455$	−7.88711	+	14.4931i	−0.369753	+	0.679445i
$456$	0.679581	−	1.01706i	0.0318243	−	0.0476284i
$457$	0.182555	+	1.38664i	0.00853956	+	0.0648644i	0.995184	−	0.0980241i	$-0.0312522\pi$
$457$	0.182555	+	1.38664i	0.00853956	+	0.0648644i	−0.986644	+	0.162889i	$0.947919\pi$
$458$	−0.468170	+	0.810895i	−0.0218762	+	0.0378906i
$459$	−0.516243	+	4.09066i	−0.0240962	+	0.190936i
$460$	−12.0895	+	6.97986i	−0.563674	+	0.325437i
$461$	−19.1351	−	7.92601i	−0.891209	−	0.369151i	−0.110375	−	0.993890i	$-0.535205\pi$
$461$	−19.1351	−	7.92601i	−0.891209	−	0.369151i	−0.780834	+	0.624739i	$0.785205\pi$
$462$	−0.596331	+	0.134334i	−0.0277438	+	0.00624980i
$463$	−10.3370	−	10.3370i	−0.480400	−	0.480400i	0.424860	−	0.905259i	$-0.360323\pi$
$463$	−10.3370	−	10.3370i	−0.480400	−	0.480400i	−0.905259	+	0.424860i	$0.860323\pi$
$464$	11.6094	+	13.2380i	0.538952	+	0.614558i
$465$	−7.13565	+	0.467695i	−0.330908	+	0.0216888i
$466$	0.391346	−	0.446245i	0.0181288	−	0.0206719i
$467$	10.4910	−	13.6722i	0.485468	−	0.632674i	−0.484824	−	0.874612i	$-0.661116\pi$
$467$	10.4910	−	13.6722i	0.485468	−	0.632674i	0.970292	+	0.241938i	$0.0777830\pi$
$468$	2.69183	−	1.11499i	0.124430	−	0.0515405i
$469$	−12.3926	+	8.74040i	−0.572237	+	0.403594i
$470$	−0.772916	−	1.15675i	−0.0356520	−	0.0533570i
$471$	−14.3499	+	12.5845i	−0.661206	+	0.579862i
$472$	2.34860	−	0.629306i	0.108103	−	0.0289662i
$473$	−6.21561	−	12.6040i	−0.285794	−	0.579533i
$474$	−0.295964	+	0.0389644i	−0.0135941	+	0.00178969i
$475$	86.6039			3.97366
$476$	−21.6838	−	2.18258i	−0.993876	−	0.100038i
$477$	7.63663			0.349657
$478$	0.538045	−	0.0708349i	0.0246096	−	0.00323991i
$479$	4.73598	+	9.60362i	0.216392	+	0.438800i	0.977819	−	0.209450i	$-0.0671675\pi$
$479$	4.73598	+	9.60362i	0.216392	+	0.438800i	−0.761427	+	0.648251i	$0.775501\pi$
$480$	2.32317	−	0.622491i	0.106038	−	0.0284127i
$481$	−2.96014	+	2.59598i	−0.134971	+	0.118366i
$482$	−0.464479	−	0.695141i	−0.0211564	−	0.0316628i
$483$	−3.92444	−	1.81376i	−0.178568	−	0.0825290i
$484$	−24.4138	+	10.1125i	−1.10972	+	0.459660i
$485$	3.37894	−	4.40351i	0.153430	−	0.199953i
$486$	0.0309491	−	0.0352907i	0.00140388	−	0.00160082i
$487$	−30.8218	+	2.02017i	−1.39667	+	0.0915427i	−0.745053	−	0.667005i	$-0.767576\pi$
$487$	−30.8218	+	2.02017i	−1.39667	+	0.0915427i	−0.651618	+	0.758548i	$0.725909\pi$
$488$	1.35708	+	1.54746i	0.0614322	+	0.0700500i
$489$	−8.86592	−	8.86592i	−0.400931	−	0.400931i
$490$	−1.40489	−	0.0210886i	−0.0634666	−	0.000952687i
$491$	16.8276	+	6.97020i	0.759417	+	0.314561i	0.728577	−	0.684963i	$-0.240182\pi$
$491$	16.8276	+	6.97020i	0.759417	+	0.314561i	0.0308397	+	0.999524i	$0.490182\pi$
$492$	9.33460	−	5.38933i	0.420836	−	0.242970i
$493$	17.5635	−	4.80722i	0.791020	−	0.216506i
$494$	−0.223117	+	0.386450i	−0.0100385	+	0.0173872i
$495$	2.74731	+	20.8679i	0.123482	+	0.937942i
$496$	−3.70397	+	5.54339i	−0.166313	+	0.248905i
$497$	17.8435	−	10.9110i	0.800391	−	0.489424i
$498$	0.222012	−	0.0441609i	0.00994858	−	0.00197890i
$499$	10.2083	+	5.03417i	0.456985	+	0.225360i	0.656187	−	0.754598i	$-0.272168\pi$
$499$	10.2083	+	5.03417i	0.456985	+	0.225360i	−0.199202	+	0.979959i	$0.563835\pi$
$500$	53.2201	+	46.6728i	2.38007	+	2.08727i
$501$	−1.63270	+	12.4016i	−0.0729435	+	0.554061i
$502$	−0.249144	−	0.191175i	−0.0111199	−	0.00853256i
$503$	−30.7458	−	6.11571i	−1.37089	−	0.272686i	−0.545905	−	0.837847i	$-0.683814\pi$
$503$	−30.7458	−	6.11571i	−1.37089	−	0.272686i	−0.824981	+	0.565161i	$0.808814\pi$
$504$	0.381413	+	0.317837i	0.0169895	+	0.0141576i
$505$	−0.681553	−	3.42640i	−0.0303287	−	0.152473i
$506$	0.364668	+	0.0977125i	0.0162115	+	0.00434385i
$507$	9.75172	−	4.80902i	0.433089	−	0.213576i
$508$	0.403698	−	0.309768i	0.0179112	−	0.0137438i
$509$	11.1507	+	19.3136i	0.494246	+	0.856060i	0.999978	−	0.00663091i	$-0.00211070\pi$
$509$	11.1507	+	19.3136i	0.494246	+	0.856060i	−0.505732	+	0.862691i	$0.668777\pi$
$510$	0.157101	−	0.812548i	0.00695653	−	0.0359802i
$511$	12.3041	−	12.9409i	0.544303	−	0.572474i
$512$	1.43070	−	3.45402i	0.0632287	−	0.152648i
$513$	0.426329	−	6.50452i	0.0188229	−	0.287182i
$514$	−0.0754873	−	0.281722i	−0.00332960	−	0.0124262i
$515$	2.18782	−	6.44512i	0.0964071	−	0.284006i
$516$	−2.52280	+	5.11574i	−0.111060	+	0.225208i
$517$	6.65560	−	33.4600i	0.292713	−	1.47157i
$518$	−0.312884	−	0.120449i	−0.0137473	−	0.00529225i
$519$	7.92356	+	19.1292i	0.347806	+	0.839678i
$520$	−1.10819	+	0.376179i	−0.0485972	+	0.0164965i
$521$	−0.636325	−	9.70844i	−0.0278779	−	0.425335i	−0.988872	−	0.148767i	$-0.952470\pi$
$521$	−0.636325	−	9.70844i	−0.0278779	−	0.425335i	0.960994	−	0.276568i	$-0.0891970\pi$
$522$	−0.196303	−	0.0666359i	−0.00859195	−	0.00291657i
$523$	9.90946	−	36.9826i	0.433310	−	1.61714i	−0.311767	−	0.950159i	$-0.600921\pi$
$523$	9.90946	−	36.9826i	0.433310	−	1.61714i	0.745077	−	0.666978i	$-0.232413\pi$
$524$	9.39268	+	6.27599i	0.410321	+	0.274168i
$525$	−3.70786	+	34.9551i	−0.161824	+	1.52557i
$526$			0.342037i			0.0149135i
$527$	3.47944	+	5.95262i	0.151567	+	0.259300i
$528$	16.9944	+	9.81171i	0.739585	+	0.427000i
$529$	−12.3760	−	16.1288i	−0.538089	−	0.701251i
$530$	−1.52955	−	0.100252i	−0.0664396	−	0.00435468i
$531$	9.16210	−	9.16210i	0.397601	−	0.397601i
$532$	34.4267	+	1.38572i	1.49259	+	0.0600788i
$533$	−6.54246	+	4.37153i	−0.283385	+	0.189352i
$534$	−0.0382761	−	0.112758i	−0.00165637	−	0.00487950i
$535$	29.5315	+	3.88790i	1.27676	+	0.168088i
$536$	−1.06638	−	0.140392i	−0.0460607	−	0.00606400i
$537$	−3.37616	−	9.94583i	−0.145692	−	0.429194i
$538$	−0.582270	+	0.389060i	−0.0251034	+	0.0167736i
$539$	−23.9948	−	24.7261i	−1.03353	−	1.06503i
$540$	6.04080	−	6.04080i	0.259955	−	0.259955i
$541$	19.0025	+	1.24549i	0.816980	+	0.0535477i	0.468162	−	0.883643i	$-0.344916\pi$
$541$	19.0025	+	1.24549i	0.816980	+	0.0535477i	0.348818	+	0.937190i	$0.386583\pi$
$542$	−0.408629	−	0.532535i	−0.0175521	−	0.0228743i
$543$	−0.847099	−	0.489073i	−0.0363525	−	0.0209881i
$544$	−1.53836	−	1.73530i	−0.0659566	−	0.0744004i
$545$			70.5705i			3.02291i
$546$	−0.146426	−	0.106600i	−0.00626647	−	0.00456206i
$547$	26.7232	+	17.8558i	1.14260	+	0.763461i	0.974958	−	0.222387i	$-0.0713850\pi$
$547$	26.7232	+	17.8558i	1.14260	+	0.763461i	0.167641	+	0.985848i	$0.446385\pi$
$548$	−3.10570	+	11.5906i	−0.132669	+	0.495127i
$549$	10.3862	+	3.52562i	0.443270	+	0.150470i
$550$	−0.200760	−	3.06301i	−0.00856044	−	0.130607i
$551$	−27.2607	+	9.25377i	−1.16135	+	0.394224i
$552$	−0.117344	−	0.283295i	−0.00499451	−	0.0120578i
$553$	−10.5765	−	13.0865i	−0.449757	−	0.556495i
$554$	0.0185171	−	0.0930915i	0.000786714	−	0.00395508i
$555$	−5.10589	+	10.3537i	−0.216733	+	0.439491i
$556$	−6.70572	+	19.7544i	−0.284386	+	0.837774i
$557$	10.4978	+	39.1784i	0.444807	+	1.66004i	0.716445	+	0.697643i	$0.245768\pi$
$557$	10.4978	+	39.1784i	0.444807	+	1.66004i	−0.271638	+	0.962399i	$0.587565\pi$
$558$	0.00513381	−	0.0783268i	0.000217332	−	0.00331584i
$559$	1.59348	−	3.84700i	0.0673970	−	0.162711i
$560$	32.6886	+	31.0800i	1.38135	+	1.31337i
$561$	16.8135	−	11.3653i	0.709865	−	0.479843i
$562$	0.490622	+	0.849782i	0.0206956	+	0.0358459i
$563$	9.49356	−	7.28467i	0.400106	−	0.307012i	−0.389036	−	0.921222i	$-0.627192\pi$
$563$	9.49356	−	7.28467i	0.400106	−	0.307012i	0.789142	+	0.614210i	$0.210525\pi$
$564$	−12.4189	+	6.12431i	−0.522928	+	0.257880i
$565$	14.9106	+	3.99529i	0.627295	+	0.168083i
$566$	−0.0799652	−	0.402012i	−0.00336119	−	0.0168978i
$567$	2.60710	+	0.450559i	0.109488	+	0.0189217i
$568$	1.45493	+	0.289403i	0.0610473	+	0.0121431i
$569$	−12.6351	−	9.69528i	−0.529692	−	0.406447i	0.308992	−	0.951065i	$-0.400008\pi$
$569$	−12.6351	−	9.69528i	−0.529692	−	0.406447i	−0.838685	+	0.544617i	$0.816675\pi$
$570$	−0.170780	+	1.29720i	−0.00715320	+	0.0543339i
$571$	16.2965	+	14.2917i	0.681988	+	0.598088i	0.928625	−	0.371020i	$-0.120992\pi$
$571$	16.2965	+	14.2917i	0.681988	+	0.598088i	−0.246636	+	0.969108i	$0.579325\pi$
$572$	−12.8622	−	6.34292i	−0.537795	−	0.265211i
$573$	−19.7621	+	3.93093i	−0.825574	+	0.164217i
$574$	−0.588532	−	0.320279i	−0.0245649	−	0.0133682i
$575$	12.0614	−	18.0511i	0.502995	−	0.752785i
$576$	−1.03731	−	7.87918i	−0.0432214	−	0.328299i
$577$	10.0915	−	17.4789i	0.420113	−	0.727658i	−0.575837	−	0.817565i	$-0.695324\pi$
$577$	10.0915	−	17.4789i	0.420113	−	0.727658i	0.995950	+	0.0899070i	$0.0286570\pi$
$578$	−0.768517	+	0.214784i	−0.0319661	+	0.00893383i
$579$	−1.12909	+	0.651880i	−0.0469233	+	0.0270912i
$580$	−34.8577	−	14.4385i	−1.44739	−	0.599527i
$581$	8.65180	+	9.37751i	0.358937	+	0.389045i
$582$	0.0430819	+	0.0430819i	0.00178580	+	0.00178580i
$583$	−24.7837	−	28.2604i	−1.02644	−	1.17043i
$584$	1.26379	−	0.0828334i	0.0522962	−	0.00342767i
$585$	−4.11199	+	4.68883i	−0.170010	+	0.193859i
$586$	0.323137	−	0.421120i	0.0133487	−	0.0173963i
$587$	−15.4861	+	6.41455i	−0.639179	+	0.264757i	−0.678648	−	0.734464i	$-0.737434\pi$
$587$	−15.4861	+	6.41455i	−0.639179	+	0.264757i	0.0394683	+	0.999221i	$0.487434\pi$
$588$	−2.03325	+	13.8360i	−0.0838498	+	0.570586i
$589$	−6.05607	−	9.06355i	−0.249536	−	0.373457i
$590$	−1.95537	+	1.71481i	−0.0805013	+	0.0705978i
$591$	−1.79148	+	0.480026i	−0.0736916	+	0.0197456i
$592$	4.76031	+	9.65296i	0.195648	+	0.396734i
$593$	25.9838	−	3.42084i	1.06703	−	0.140477i	0.423498	−	0.905897i	$-0.360802\pi$
$593$	25.9838	−	3.42084i	1.06703	−	0.140477i	0.643531	+	0.765420i	$0.277469\pi$
$594$	−0.231040			−0.00947969
$595$	43.6931	−	16.3382i	1.79124	−	0.669799i
$596$	−5.01625			−0.205474
$597$	23.8556	−	3.14064i	0.976343	−	0.128538i
$598$	0.0494753	+	0.100326i	0.00202320	+	0.00410264i
$599$	38.5843	−	10.3386i	1.57651	−	0.422425i	0.638667	−	0.769483i	$-0.279486\pi$
$599$	38.5843	−	10.3386i	1.57651	−	0.422425i	0.937844	+	0.347058i	$0.112819\pi$
$600$	−1.87445	+	1.64385i	−0.0765240	+	0.0671097i
$601$	−2.81159	−	4.20785i	−0.114687	−	0.171642i	0.769685	−	0.638424i	$-0.220413\pi$
$601$	−2.81159	−	4.20785i	−0.114687	−	0.171642i	−0.884372	+	0.466782i	$0.845413\pi$
$602$	0.353121	−	0.0321055i	0.0143921	−	0.00130852i
$603$	−5.29545	+	2.19345i	−0.215648	+	0.0893241i
$604$	15.6272	−	20.3658i	0.635864	−	0.828674i
$605$	37.2941	−	42.5257i	1.51622	−	1.72892i
$606$	0.0382657	−	0.00250807i	0.00155444	−	0.000101883i
$607$	18.4852	+	21.0783i	0.750289	+	0.855541i	0.993429	−	0.114450i	$-0.0365107\pi$
$607$	18.4852	+	21.0783i	0.750289	+	0.855541i	−0.243140	+	0.969991i	$0.578177\pi$
$608$	2.59245	+	2.59245i	0.105138	+	0.105138i
$609$	−2.56787	−	11.3992i	−0.104055	−	0.461918i
$610$	−2.03398	−	0.842501i	−0.0823533	−	0.0341119i
$611$	8.75409	−	5.05418i	0.354153	−	0.204470i
$612$	−7.81407	−	2.60587i	−0.315865	−	0.105336i
$613$	3.28127	−	5.68333i	0.132529	−	0.229548i	−0.792122	−	0.610363i	$-0.791023\pi$
$613$	3.28127	−	5.68333i	0.132529	−	0.229548i	0.924651	+	0.380816i	$0.124357\pi$
$614$	0.0311564	+	0.236656i	0.00125737	+	0.00955066i
$615$	−12.8177	+	19.1831i	−0.516861	+	0.773537i
$616$	−0.0616250	−	2.44297i	−0.00248294	−	0.0984302i
$617$	−26.3693	+	5.24518i	−1.06159	+	0.211163i	−0.694845	−	0.719159i	$-0.744527\pi$
$617$	−26.3693	+	5.24518i	−1.06159	+	0.211163i	−0.366743	+	0.930322i	$0.619527\pi$
$618$	0.0670072	+	0.0330443i	0.00269542	+	0.00132924i
$619$	−4.36519	−	3.82817i	−0.175452	−	0.153867i	0.567116	−	0.823638i	$-0.308059\pi$
$619$	−4.36519	−	3.82817i	−0.175452	−	0.153867i	−0.742568	+	0.669771i	$0.766392\pi$
$620$	1.86472	−	14.1639i	0.0748889	−	0.568838i
$621$	−1.29638	−	0.994750i	−0.0520221	−	0.0399179i
$622$	−0.383460	−	0.0762750i	−0.0153754	−	0.00305835i
$623$	4.29676	−	5.15622i	0.172146	−	0.206580i
$624$	1.13433	+	5.70266i	0.0454095	+	0.228289i
$625$	−82.1868	−	22.0219i	−3.28747	−	0.880875i
$626$	−0.0844365	+	0.0416395i	−0.00337476	+	0.00166425i
$627$	−25.4545	+	19.5319i	−1.01655	+	0.780030i
$628$	−19.0653	−	33.0221i	−0.760788	−	1.31772i
$629$	11.1308	−	0.0596931i	0.443813	−	0.00238012i
$630$	−0.516267	−	0.124469i	−0.0205686	−	0.00495896i
$631$	−1.60907	+	3.88463i	−0.0640560	+	0.154645i	−0.952666	−	0.304018i	$-0.901672\pi$
$631$	−1.60907	+	3.88463i	−0.0640560	+	0.154645i	0.888610	+	0.458663i	$0.151672\pi$
$632$	0.0780530	−	1.19086i	0.00310478	−	0.0473698i
$633$	4.22221	+	15.7575i	0.167818	+	0.626304i
$634$	0.279449	−	0.823229i	0.0110983	−	0.0326946i
$635$	−0.481729	+	0.976850i	−0.0191168	+	0.0387651i
$636$	−2.97638	+	14.9633i	−0.118021	+	0.593333i
$637$	0.820517	−	10.1759i	0.0325101	−	0.403183i
$638$	0.390481	+	0.942705i	0.0154593	+	0.0373221i
$639$	7.48563	−	2.54103i	0.296127	−	0.100522i
$640$	0.418934	+	6.39169i	0.0165598	+	0.252654i
$641$	10.0968	+	3.42740i	0.398799	+	0.135374i	0.513632	−	0.858011i	$-0.328300\pi$
$641$	10.0968	+	3.42740i	0.398799	+	0.135374i	−0.114832	+	0.993385i	$0.536633\pi$
$642$	−0.0846234	+	0.315819i	−0.00333982	+	0.0124644i
$643$	19.4500	+	12.9961i	0.767034	+	0.512515i	0.876457	−	0.481480i	$-0.159901\pi$
$643$	19.4500	+	12.9961i	0.767034	+	0.512515i	−0.109424	+	0.993995i	$0.534901\pi$
$644$	5.08345	−	6.98267i	0.200316	−	0.275156i
$645$		−	12.2091i		−	0.480734i
$646$	1.19241	−	0.411914i	0.0469148	−	0.0162065i
$647$	−11.5198	−	6.65094i	−0.452889	−	0.261476i	0.256161	−	0.966634i	$-0.417542\pi$
$647$	−11.5198	−	6.65094i	−0.452889	−	0.261476i	−0.709050	+	0.705159i	$0.750876\pi$
$648$	0.114236	+	0.148875i	0.00448762	+	0.00584838i
$649$	−63.6401	−	4.17119i	−2.49809	−	0.163734i
$650$	0.643121	−	0.643121i	0.0252253	−	0.0252253i
$651$	3.91752	−	2.05631i	0.153540	−	0.0805931i
$652$	20.8275	−	13.9165i	0.815667	−	0.545011i
$653$	−0.423763	−	1.24837i	−0.0165831	−	0.0488524i	0.938323	−	0.345759i	$-0.112378\pi$
$653$	−0.423763	−	1.24837i	−0.0165831	−	0.0488524i	−0.954907	+	0.296906i	$0.904045\pi$
$654$	−0.768013	−	0.101111i	−0.0300317	−	0.00395375i
$655$	−23.9728	−	3.15608i	−0.936695	−	0.123318i
$656$	6.91410	+	20.3683i	0.269950	+	0.795248i
$657$	5.61174	−	3.74964i	0.218935	−	0.146287i
$658$	0.727531	+	0.460015i	0.0283621	+	0.0179332i
$659$	24.1650	−	24.1650i	0.941334	−	0.941334i	−0.0570377	−	0.998372i	$-0.518166\pi$
$659$	24.1650	−	24.1650i	0.941334	−	0.941334i	0.998372	+	0.0570377i	$0.0181655\pi$
$660$	−41.9595	−	2.75017i	−1.63327	−	0.107050i
$661$	16.2230	+	21.1423i	0.631003	+	0.822339i	0.993992	−	0.109454i	$-0.0349103\pi$
$661$	16.2230	+	21.1423i	0.631003	+	0.822339i	−0.362989	+	0.931794i	$0.618244\pi$
$662$	0.318818	+	0.184070i	0.0123912	+	0.00715406i
$663$	5.81656	+	1.52516i	0.225896	+	0.0592322i
$664$			0.904946i			0.0351187i
$665$	−67.4014	+	29.9316i	−2.61371	+	1.16070i
$666$	−0.105363	−	0.0704014i	−0.00408274	−	0.00272800i
$667$	−1.86783	+	6.97082i	−0.0723225	+	0.269911i
$668$	−23.6634	−	8.03264i	−0.915564	−	0.310792i
$669$	1.31293	+	20.0315i	0.0507610	+	0.774462i
$670$	1.08943	−	0.369812i	0.0420884	−	0.0142871i
$671$	−20.6599	−	49.8774i	−0.797566	−	1.92550i
$672$	−1.15736	+	0.935371i	−0.0446460	+	0.0360827i
$673$	−3.44289	+	17.3086i	−0.132714	+	0.667196i	0.855951	+	0.517057i	$0.172972\pi$
$673$	−3.44289	+	17.3086i	−0.132714	+	0.667196i	−0.988665	+	0.150140i	$0.952028\pi$
$674$	0.699292	−	1.41802i	0.0269357	−	0.0546203i
$675$	−4.27062	+	12.5808i	−0.164376	+	0.484237i
$676$	5.62209	+	20.9819i	0.216234	+	0.806998i
$677$	2.35347	−	35.9071i	0.0904514	−	1.38002i	−0.675613	−	0.737257i	$-0.736121\pi$
$677$	2.35347	−	35.9071i	0.0904514	−	1.38002i	0.766064	−	0.642764i	$-0.222213\pi$
$678$	−0.0648439	+	0.156547i	−0.00249032	+	0.00601215i
$679$	−0.804899	+	3.33852i	−0.0308892	+	0.128121i
$680$	3.06346	+	1.24972i	0.117478	+	0.0479246i
$681$	−12.3221	−	21.3426i	−0.472185	−	0.817849i
$682$	−0.306521	+	0.235202i	−0.0117373	+	0.00900633i
$683$	10.7166	−	5.28486i	0.410061	−	0.202220i	−0.225546	−	0.974233i	$-0.572417\pi$
$683$	10.7166	−	5.28486i	0.410061	−	0.202220i	0.635607	+	0.772013i	$0.280750\pi$
$684$	12.5789	+	3.37049i	0.480965	+	0.128874i
$685$	−5.01079	−	25.1909i	−0.191452	−	0.962496i
$686$	0.799714	−	0.340860i	0.0305332	−	0.0130141i
$687$	−19.5647	−	3.89165i	−0.746439	−	0.148476i
$688$	−9.03059	−	6.92941i	−0.344288	−	0.264181i
$689$	1.45372	−	11.0421i	0.0553822	−	0.420670i
$690$	0.246596	+	0.216259i	0.00938775	+	0.00823283i
$691$	−8.87106	−	4.37472i	−0.337471	−	0.166422i	0.265655	−	0.964068i	$-0.414412\pi$
$691$	−8.87106	−	4.37472i	−0.337471	−	0.166422i	−0.603126	+	0.797646i	$0.706078\pi$
$692$	−40.5701	+	8.06990i	−1.54224	+	0.306771i
$693$	−6.79368	−	11.1102i	−0.258070	−	0.422041i
$694$	−0.102448	+	0.153324i	−0.00388886	+	0.00582009i
$695$	−5.82843	−	44.2713i	−0.221085	−	1.67931i
$696$	0.414381	−	0.717728i	0.0157071	−	0.0272054i
$697$	22.0702	+	2.78528i	0.835970	+	0.105500i
$698$	−0.254199	+	0.146762i	−0.00962159	+	0.00555503i
$699$	11.6823	+	4.83896i	0.441865	+	0.183026i
$700$	−67.0463	−	20.8890i	−2.53411	−	0.789530i
$701$	16.7907	+	16.7907i	0.634176	+	0.634176i	0.949113	−	0.314936i	$-0.101983\pi$
$701$	16.7907	+	16.7907i	0.634176	+	0.634176i	−0.314936	+	0.949113i	$0.601983\pi$
$702$	−0.0451367	−	0.0514685i	−0.00170357	−	0.00194255i
$703$	−17.5599	+	1.15094i	−0.662284	+	0.0434084i
$704$	−25.7915	+	29.4096i	−0.972056	+	1.10842i
$705$	18.0429	−	23.5139i	0.679533	−	0.885585i
$706$	1.16580	−	0.482891i	0.0438755	−	0.0181738i
$707$	1.24580	+	1.76636i	0.0468532	+	0.0664310i
$708$	14.3814	+	21.5232i	0.540485	+	0.808893i
$709$	18.9819	−	16.6467i	0.712879	−	0.625178i	−0.224099	−	0.974566i	$-0.571944\pi$
$709$	18.9819	−	16.6467i	0.712879	−	0.625178i	0.936978	+	0.349388i	$0.113610\pi$
$710$	−1.53267	+	0.410677i	−0.0575200	+	0.0154124i
$711$	−2.81281	−	5.70382i	−0.105489	−	0.213910i
$712$	0.471973	−	0.0621364i	0.0176879	−	0.00232866i
$713$	−2.73258			−0.102336
$714$	0.115205	+	0.498918i	0.00431144	+	0.0186715i
$715$	30.6966			1.14799
$716$	20.8038	−	2.73887i	0.777475	−	0.102357i
$717$	5.11352	+	10.3692i	0.190968	+	0.387245i
$718$	−0.572643	+	0.153439i	−0.0213709	+	0.00572630i
$719$	−15.6944	+	13.7636i	−0.585301	+	0.513295i	−0.899996	−	0.435898i	$-0.856431\pi$
$719$	−15.6944	+	13.7636i	−0.585301	+	0.513295i	0.314696	+	0.949193i	$0.398098\pi$
$720$	9.47153	+	14.1751i	0.352983	+	0.528277i
$721$	0.381305	+	4.19388i	0.0142005	+	0.156188i
$722$	−1.01869	+	0.421957i	−0.0379119	+	0.0157036i
$723$	10.8427	−	14.1305i	0.403245	−	0.525519i
$724$	1.28845	−	1.46920i	0.0478849	−	0.0546023i
$725$	58.5510	−	3.83763i	2.17453	−	0.142526i
$726$	0.409371	+	0.466798i	0.0151932	+	0.0173245i
$727$	20.0362	+	20.0362i	0.743102	+	0.743102i	0.973174	−	0.230072i	$-0.0738961\pi$
$727$	20.0362	+	20.0362i	0.743102	+	0.743102i	−0.230072	+	0.973174i	$0.573896\pi$
$728$	0.532179	−	0.490995i	0.0197239	−	0.0181975i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	−1.17321	+	0.677352i	−0.0434224	+	0.0250699i
$731$	−10.5299	+	5.26318i	−0.389463	+	0.194666i
$732$	−10.9562	+	18.9766i	−0.404951	+	0.701396i
$733$	3.21077	+	24.3882i	0.118592	+	0.900799i	0.942531	+	0.334119i	$0.108439\pi$
$733$	3.21077	+	24.3882i	0.118592	+	0.900799i	−0.823938	+	0.566679i	$0.808228\pi$
$734$	0.212077	−	0.317395i	0.00782789	−	0.0117153i
$735$	−9.19527	−	28.4861i	−0.339173	−	1.05073i
$736$	0.901403	−	0.179300i	0.0332262	−	0.00660910i
$737$	25.3029	+	12.4780i	0.932044	+	0.459633i
$738$	−0.190403	−	0.166979i	−0.00700885	−	0.00614659i
$739$	−3.59899	+	27.3371i	−0.132391	+	1.00561i	0.788292	+	0.615301i	$0.210965\pi$
$739$	−3.59899	+	27.3371i	−0.132391	+	1.00561i	−0.920684	+	0.390310i	$0.872368\pi$
$740$	−18.2971	−	14.0399i	−0.672616	−	0.516117i
$741$	−9.32397	−	1.85465i	−0.342524	−	0.0681323i
$742$	0.890084	−	0.327399i	0.0326760	−	0.0120192i
$743$	1.29374	+	6.50406i	0.0474627	+	0.238611i	0.997233	−	0.0743361i	$-0.0236838\pi$
$743$	1.29374	+	6.50406i	0.0474627	+	0.238611i	−0.949771	+	0.312947i	$0.898684\pi$
$744$	0.303114	+	0.0812191i	0.0111127	+	0.00297764i
$745$	9.62980	−	4.74889i	0.352808	−	0.173986i
$746$	−0.887911	+	0.681318i	−0.0325087	+	0.0249448i
$747$	2.41122	+	4.17635i	0.0882219	+	0.152805i
$748$	15.7162	+	37.3741i	0.574641	+	1.36653i
$749$	−17.6753	+	5.21723i	−0.645843	+	0.190633i
$750$	0.636464	−	1.53656i	0.0232404	−	0.0561073i
$751$	−3.05199	+	46.5643i	−0.111369	+	1.69916i	0.467708	+	0.883883i	$0.345080\pi$
$751$	−3.05199	+	46.5643i	−0.111369	+	1.69916i	−0.579077	+	0.815273i	$0.696587\pi$
$752$	−7.15186	−	26.6911i	−0.260801	−	0.973324i
$753$	2.15054	−	6.33529i	0.0783701	−	0.230871i
$754$	−0.133720	+	0.271157i	−0.00486978	+	0.00987494i
$755$	−10.7196	+	53.8910i	−0.390126	+	1.96130i
$756$	−1.89895	+	4.93278i	−0.0690642	+	0.179403i
$757$	15.5655	+	37.5784i	0.565737	+	1.36581i	0.905118	+	0.425161i	$0.139783\pi$
$757$	15.5655	+	37.5784i	0.565737	+	1.36581i	−0.339381	+	0.940649i	$0.610217\pi$
$758$	−1.01957	+	0.346097i	−0.0370325	+	0.0125708i
$759$	0.526038	+	8.02579i	0.0190940	+	0.291318i
$760$	−4.95312	−	1.68136i	−0.179668	−	0.0609892i
$761$	−7.22185	+	26.9523i	−0.261792	+	0.977021i	0.702393	+	0.711789i	$0.252115\pi$
$761$	−7.22185	+	26.9523i	−0.261792	+	0.977021i	−0.964185	+	0.265231i	$0.914552\pi$
$762$	−0.00994078	−	0.00664222i	−0.000360117	−	0.000240622i
$763$	−17.7211	−	39.9052i	−0.641545	−	1.44466i
$764$		−	40.2542i		−	1.45634i
$765$	17.4678	−	2.39505i	0.631550	−	0.0865932i
$766$	0.0591254	+	0.0341361i	0.00213629	+	0.00123339i
$767$	−11.5037	−	14.9919i	−0.415375	−	0.541327i
$768$	15.7901	+	1.03494i	0.569778	+	0.0373452i
$769$	1.07261	−	1.07261i	0.0386791	−	0.0386791i	−0.687503	−	0.726182i	$-0.741293\pi$
$769$	1.07261	−	1.07261i	0.0386791	−	0.0386791i	0.726182	+	0.687503i	$0.241293\pi$
$770$	1.21486	+	2.31447i	0.0437807	+	0.0834076i
$771$	5.16640	−	3.45208i	0.186064	−	0.124324i
$772$	−0.837236	−	2.46642i	−0.0301328	−	0.0887684i
$773$	−13.2310	−	1.74189i	−0.475886	−	0.0626516i	−0.111232	−	0.993795i	$-0.535480\pi$
$773$	−13.2310	−	1.74189i	−0.475886	−	0.0626516i	−0.364654	+	0.931143i	$0.618813\pi$
$774$	0.132871	+	0.0174928i	0.00477595	+	0.000628766i
$775$	7.14162	+	21.0385i	0.256535	+	0.755726i
$776$	−0.202524	+	0.135322i	−0.00727019	+	0.00485779i
$777$	0.287267	−	7.13681i	0.0103057	−	0.256032i
$778$	−0.700207	+	0.700207i	−0.0251036	+	0.0251036i
$779$	−35.0937	−	2.30016i	−1.25736	−	0.0824119i
$780$	−7.58468	−	9.88455i	−0.271575	−	0.353924i
$781$	−33.6971	−	19.4550i	−1.20578	−	0.696156i
$782$	0.0802114	−	0.305906i	0.00286835	−	0.0109392i
$783$		−	4.41645i		−	0.157831i
$784$	−26.2888	−	9.36620i	−0.938887	−	0.334507i
$785$	67.8620	+	45.3440i	2.42210	+	1.61840i
$786$	0.0686948	−	0.256372i	0.00245026	−	0.00914450i
$787$	−11.1278	−	3.77739i	−0.396664	−	0.134649i	0.115978	−	0.993252i	$-0.463000\pi$
$787$	−11.1278	−	3.77739i	−0.396664	−	0.134649i	−0.512642	+	0.858602i	$0.671333\pi$
$788$	−0.242336	−	3.69733i	−0.00863287	−	0.131712i
$789$	−6.90011	+	2.34227i	−0.245650	+	0.0833870i
$790$	0.488504	+	1.17935i	0.0173802	+	0.0419595i
$791$	−9.43472	+	1.48503i	−0.335460	+	0.0528016i
$792$	0.180195	−	0.905903i	0.00640296	−	0.0321899i
$793$	7.07495	−	14.3466i	0.251239	−	0.509462i
$794$	0.405010	−	1.19312i	0.0143733	−	0.0423423i
$795$	−8.45194	−	31.5431i	−0.299759	−	1.11872i
$796$	−3.14392	+	47.9669i	−0.111433	+	1.70014i
$797$	3.23675	−	7.81420i	0.114651	−	0.276793i	−0.856129	−	0.516762i	$-0.827137\pi$
$797$	3.23675	−	7.81420i	0.114651	−	0.276793i	0.970781	+	0.239969i	$0.0771372\pi$
$798$	−0.229173	−	0.776409i	−0.00811262	−	0.0274846i
$799$	−28.0579	−	5.42480i	−0.992617	−	0.191916i
$800$	−3.73629	−	6.47144i	−0.132098	−	0.228800i
$801$	2.01261	−	1.54433i	0.0711120	−	0.0545662i
$802$	0.0880181	−	0.0434057i	0.00310803	−	0.00153271i
$803$	−32.0883	−	8.59803i	−1.13237	−	0.303418i
$804$	−2.23396	−	11.2309i	−0.0787856	−	0.396082i
$805$	−3.14831	+	18.2173i	−0.110963	+	0.642075i
$806$	−0.112278	−	0.0223335i	−0.00395484	−	0.000786666i
$807$	−11.8361	−	9.08217i	−0.416651	−	0.319707i
$808$	−0.0200106	+	0.151995i	−0.000703969	+	0.00534718i
$809$	14.8669	+	13.0379i	0.522693	+	0.458390i	0.879575	−	0.475760i	$-0.157827\pi$
$809$	14.8669	+	13.0379i	0.522693	+	0.458390i	−0.356882	+	0.934149i	$0.616160\pi$
$810$	−0.180022	−	0.0887768i	−0.00632531	−	0.00311930i
$811$	−13.4865	+	2.68264i	−0.473576	+	0.0942002i	−0.426107	−	0.904673i	$-0.640115\pi$
$811$	−13.4865	+	2.68264i	−0.473576	+	0.0942002i	−0.0474687	+	0.998873i	$0.515115\pi$
$812$	23.3365	−	0.588673i	0.818950	−	0.0206584i
$813$	7.94484	−	11.8903i	0.278638	−	0.417011i
$814$	0.0814126	+	0.618390i	0.00285351	+	0.0216746i
$815$	−26.8082	+	46.4331i	−0.939050	+	1.62648i
$816$	8.14251	−	14.2795i	0.285045	−	0.499884i
$817$	16.1177	−	9.30556i	0.563887	−	0.325560i
$818$	−1.28337	−	0.531587i	−0.0448718	−	0.0185865i
$819$	1.14777	−	3.68394i	0.0401064	−	0.128727i
$820$	−32.5918	−	32.5918i	−1.13816	−	1.13816i
$821$	5.87908	+	6.70381i	0.205181	+	0.233964i	0.845274	−	0.534333i	$-0.179437\pi$
$821$	5.87908	+	6.70381i	0.205181	+	0.233964i	−0.640092	+	0.768298i	$0.721104\pi$
$822$	0.281330	−	0.0184394i	0.00981252	−	0.000643146i
$823$	−1.01521	+	1.15762i	−0.0353880	+	0.0403523i	−0.769263	−	0.638932i	$-0.779376\pi$
$823$	−1.01521	+	1.15762i	−0.0353880	+	0.0403523i	0.733875	+	0.679284i	$0.237710\pi$
$824$	−0.181827	+	0.236962i	−0.00633424	+	0.00825495i
$825$	60.4169	−	25.0255i	2.10345	−	0.871276i
$826$	0.675085	−	1.46068i	0.0234892	−	0.0508237i
$827$	−4.40542	−	6.59318i	−0.153192	−	0.229267i	0.746934	−	0.664899i	$-0.231525\pi$
$827$	−4.40542	−	6.59318i	−0.153192	−	0.229267i	−0.900125	+	0.435631i	$0.856525\pi$
$828$	2.45439	−	2.15244i	0.0852959	−	0.0748025i
$829$	−3.86271	+	1.03501i	−0.134157	+	0.0359473i	−0.325273	−	0.945620i	$-0.605456\pi$
$829$	−3.86271	+	1.03501i	−0.134157	+	0.0359473i	0.191116	+	0.981568i	$0.438789\pi$
$830$	−0.428121	−	0.868143i	−0.0148603	−	0.0301337i
$831$	2.00479	−	0.263936i	0.0695454	−	0.00915583i
$832$	−11.5903			−0.401820
$833$	−20.6043	+	20.2105i	−0.713895	+	0.700253i
$834$	0.490152			0.0169726
$835$	53.0316	−	6.98174i	1.83523	−	0.241613i
$836$	−28.3501	−	57.4884i	−0.980509	−	1.98828i
$837$	1.61529	−	0.432815i	0.0558325	−	0.0149603i
$838$	0.506675	−	0.444342i	0.0175028	−	0.0153495i
$839$	−3.70363	−	5.54288i	−0.127864	−	0.191361i	0.762014	−	0.647560i	$-0.224211\pi$
$839$	−3.70363	−	5.54288i	−0.127864	−	0.191361i	−0.889878	+	0.456199i	$0.849211\pi$
$840$	0.890693	−	1.92719i	0.0307318	−	0.0664945i
$841$	8.77220	−	3.63357i	0.302490	−	0.125295i
$842$	−0.219125	+	0.285569i	−0.00755155	+	0.00984137i
$843$	−13.7833	+	15.7169i	−0.474724	+	0.541318i
$844$	−32.5210	+	2.13154i	−1.11942	+	0.0733706i
$845$	−30.6565	−	34.9570i	−1.05461	−	1.20256i
$846$	0.230049	+	0.230049i	0.00790924	+	0.00790924i
$847$	−10.4098	+	33.4118i	−0.357685	+	1.14804i
$848$	−28.1281	−	11.6510i	−0.965922	−	0.400098i
$849$	7.56241	−	4.36616i	0.259541	−	0.149846i
$850$	−2.56485	+	0.181928i	−0.0879736	+	0.00624008i
$851$	−2.20569	+	3.82036i	−0.0756099	+	0.130960i
$852$	2.06139	+	15.6578i	0.0706219	+	0.536427i
$853$	−26.2068	+	39.2213i	−0.897305	+	1.34291i	0.0417447	+	0.999128i	$0.486708\pi$
$853$	−26.2068	+	39.2213i	−0.897305	+	1.34291i	−0.939049	+	0.343783i	$0.888292\pi$
$854$	1.36171	−	0.0343496i	0.0465966	−	0.00117542i
$855$	−27.3387	+	5.43801i	−0.934965	+	0.185976i
$856$	−1.17232	−	0.578123i	−0.0400690	−	0.0197599i
$857$	−32.7653	−	28.7344i	−1.11924	−	0.981547i	−0.119304	−	0.992858i	$-0.538066\pi$
$857$	−32.7653	−	28.7344i	−1.11924	−	0.981547i	−0.999936	+	0.0113106i	$0.996400\pi$
$858$	−0.0439810	+	0.334069i	−0.00150149	+	0.0114049i
$859$	29.8743	+	22.9233i	1.01930	+	0.782134i	0.976186	−	0.216937i	$-0.0696065\pi$
$859$	29.8743	+	22.9233i	1.01930	+	0.782134i	0.0431107	+	0.999070i	$0.486273\pi$
$860$	23.9227	+	4.75852i	0.815757	+	0.162264i
$861$	2.43089	−	14.0661i	0.0828446	−	0.479370i
$862$	−0.0400055	−	0.201121i	−0.00136259	−	0.00685021i
$863$	−22.3773	−	5.99598i	−0.761732	−	0.204105i	−0.143016	−	0.989720i	$-0.545680\pi$
$863$	−22.3773	−	5.99598i	−0.761732	−	0.204105i	−0.618716	+	0.785615i	$0.712347\pi$
$864$	−0.504440	+	0.248762i	−0.0171614	+	0.00846306i
$865$	70.2435	−	53.8997i	2.38835	−	1.83265i
$866$	−0.649555	−	1.12506i	−0.0220728	−	0.0382312i
$867$	−9.59576	−	14.0329i	−0.325889	−	0.476581i
$868$	2.50229	+	8.47747i	0.0849334	+	0.287744i
$869$	−11.9792	+	28.9202i	−0.406365	+	0.981052i
$870$	−0.0579783	+	0.884578i	−0.00196565	+	0.0299900i
$871$	2.16354	+	8.07444i	0.0733087	+	0.273592i
$872$	0.995451	−	2.93251i	0.0337102	−	0.0993072i
$873$	−0.574090	+	1.16414i	−0.0194300	+	0.0394002i
$874$	−0.0975403	+	0.490368i	−0.00329935	+	0.0165869i
$875$	92.6049	−	14.5761i	3.13062	−	0.492761i
$876$	5.15991	+	12.4571i	0.174337	+	0.420887i
$877$	20.9008	−	7.09486i	0.705769	−	0.239576i	0.0545991	−	0.998508i	$-0.482612\pi$
$877$	20.9008	−	7.09486i	0.705769	−	0.239576i	0.651170	+	0.758932i	$0.274279\pi$
$878$	0.105764	+	1.61365i	0.00356937	+	0.0544581i
$879$	10.7083	+	3.63499i	0.361183	+	0.122605i
$880$	21.7185	−	81.0544i	0.732129	−	2.73234i
$881$	35.1034	+	23.4554i	1.18266	+	0.790231i	0.981898	−	0.189408i	$-0.0606568\pi$
$881$	35.1034	+	23.4554i	1.18266	+	0.790231i	0.200766	+	0.979639i	$0.435657\pi$
$882$	0.323187	−	0.0592576i	0.0108823	−	0.00199531i
$883$			9.89325i			0.332934i	0.986047	+	0.166467i	$0.0532360\pi$
$883$			9.89325i			0.332934i	−0.986047	+	0.166467i	$0.946764\pi$
$884$	−5.25542	+	10.8026i	−0.176759	+	0.363331i
$885$	−47.9843	−	27.7037i	−1.61297	−	0.931251i
$886$	1.17771	+	1.53482i	0.0395658	+	0.0515631i
$887$	−21.8433	−	1.43168i	−0.733425	−	0.0480712i	−0.305886	−	0.952068i	$-0.598953\pi$
$887$	−21.8433	−	1.43168i	−0.733425	−	0.0480712i	−0.427539	+	0.903997i	$0.640619\pi$
$888$	0.358218	−	0.358218i	0.0120210	−	0.0120210i
$889$	0.0271031	−	0.673343i	0.000909007	−	0.0225832i
$890$	−0.423382	+	0.282895i	−0.0141918	+	0.00948266i
$891$	−1.58216	−	4.66090i	−0.0530044	−	0.156146i
$892$	−39.7616	−	5.23472i	−1.33132	−	0.175271i
$893$	44.7934	+	5.89717i	1.49896	+	0.197341i
$894$	0.0378846	+	0.111604i	0.00126705	+	0.00373261i
$895$	−37.3446	+	24.9529i	−1.24829	+	0.834083i
$896$	−1.84192	−	3.50908i	−0.0615342	−	0.117230i
$897$	−1.68513	+	1.68513i	−0.0562647	+	0.0562647i
$898$	1.14308	+	0.0749211i	0.0381449	+	0.00250015i
$899$	−4.49600	−	5.85930i	−0.149950	−	0.195419i
$900$	−22.9865	−	13.2713i	−0.766218	−	0.442376i
$901$	−23.5612	+	20.8872i	−0.784938	+	0.695855i
$902$			1.24653i			0.0415047i
$903$	3.06585	+	6.90384i	0.102025	+	0.229746i
$904$	−0.563244	−	0.376348i	−0.0187332	−	0.0125171i
$905$	−1.08258	+	4.04023i	−0.0359860	+	0.134302i
$906$	−0.571133	−	0.193874i	−0.0189746	−	0.00644102i
$907$	−2.39253	−	36.5030i	−0.0794427	−	1.21206i	−0.832469	−	0.554071i	$-0.813074\pi$
$907$	−2.39253	−	36.5030i	−0.0794427	−	1.21206i	0.753027	−	0.657990i	$-0.228593\pi$
$908$	46.6214	−	15.8258i	1.54719	−	0.525199i
$909$	0.312640	+	0.754781i	0.0103696	+	0.0250345i
$910$	−0.278251	+	0.722795i	−0.00922394	+	0.0239604i
$911$	4.98842	−	25.0785i	0.165274	−	0.830888i	−0.805815	−	0.592168i	$-0.798272\pi$
$911$	4.98842	−	25.0785i	0.165274	−	0.830888i	0.971089	−	0.238720i	$-0.0767277\pi$
$912$	−11.4941	+	23.3077i	−0.380608	+	0.771796i
$913$	7.62987	−	22.4769i	0.252512	−	0.743876i
$914$	0.0169913	+	0.0634125i	0.000562023	+	0.00209750i
$915$	3.06756	−	46.8020i	0.101411	−	1.54723i
$916$	15.2507	−	36.8184i	0.503897	−	1.21651i
$917$	14.3483	−	4.23519i	0.473823	−	0.139858i
$918$	0.00103789	+	0.193532i	3.42556e−5	+	0.00638752i
$919$	−25.4515	−	44.0832i	−0.839566	−	1.45417i	−0.890258	−	0.455457i	$-0.849476\pi$
$919$	−25.4515	−	44.0832i	−0.839566	−	1.45417i	0.0506914	−	0.998714i	$-0.483858\pi$
$920$	−1.04027	+	0.798231i	−0.0342968	+	0.0263169i
$921$	−4.56084	+	2.24916i	−0.150285	+	0.0741122i
$922$	−0.939061	−	0.251621i	−0.0309263	−	0.00828669i
$923$	−2.24919	−	11.3075i	−0.0740331	−	0.372190i
$924$	24.4173	−	8.98139i	0.803269	−	0.295466i
$925$	35.1781	+	6.99736i	1.15665	+	0.230072i
$926$	−0.544390	−	0.417725i	−0.0178898	−	0.0137273i
$927$	−0.207756	+	1.57806i	−0.00682359	+	0.0518303i
$928$	1.86757	+	1.63782i	0.0613060	+	0.0537639i
$929$	35.8183	+	17.6636i	1.17516	+	0.579526i	0.921732	−	0.387828i	$-0.126775\pi$
$929$	35.8183	+	17.6636i	1.17516	+	0.579526i	0.253430	+	0.967354i	$0.418441\pi$
$930$	−0.329211	+	0.0654840i	−0.0107952	+	0.00214731i
$931$	30.5970	−	33.8505i	1.00278	−	1.10941i
$932$	−14.0347	+	21.0044i	−0.459722	+	0.688022i
$933$	−1.08720	−	8.25809i	−0.0355933	−	0.270358i
$934$	0.404461	−	0.700548i	0.0132344	−	0.0229226i
$935$	−65.5528	−	56.8693i	−2.14381	−	1.85982i
$936$	0.237010	−	0.136838i	0.00774693	−	0.00447269i
$937$	6.52008	+	2.70071i	0.213002	+	0.0882282i	0.486633	−	0.873606i	$-0.338225\pi$
$937$	6.52008	+	2.70071i	0.213002	+	0.0882282i	−0.273631	+	0.961835i	$0.588225\pi$
$938$	−0.523172	+	0.482684i	−0.0170822	+	0.0157602i
$939$	−1.41824	−	1.41824i	−0.0462824	−	0.0462824i
$940$	39.0412	+	44.5179i	1.27338	+	1.45201i
$941$	−7.40676	+	0.485465i	−0.241453	+	0.0158257i	−0.185649	−	0.982616i	$-0.559439\pi$
$941$	−7.40676	+	0.485465i	−0.241453	+	0.0158257i	−0.0558040	+	0.998442i	$0.517772\pi$
$942$	−0.590705	+	0.673570i	−0.0192462	+	0.0219461i
$943$	−5.36695	+	6.99435i	−0.174772	+	0.227767i
$944$	−47.7252	+	19.7684i	−1.55332	+	0.643408i
$945$	−1.02441	−	11.2673i	−0.0333242	−	0.366525i
$946$	−0.366482	−	0.548479i	−0.0119154	−	0.0178326i
$947$	−27.5438	+	24.1553i	−0.895054	+	0.784941i	−0.977342	−	0.211667i	$-0.932111\pi$
$947$	−27.5438	+	24.1553i	−0.895054	+	0.784941i	0.0822878	+	0.996609i	$0.473777\pi$
$948$	12.2724	−	3.28838i	0.398590	−	0.106802i
$949$	−4.35349	−	8.82800i	−0.141320	−	0.286569i
$950$	4.03034	−	0.530604i	0.130761	−	0.0172151i
$951$	18.5211			0.600589
$952$	−2.04610	+	0.0625951i	−0.0663144	+	0.00202872i
$953$	−40.0941			−1.29878			−0.649388	−	0.760458i	$-0.724975\pi$
$953$	−40.0941			−1.29878			−0.649388	+	0.760458i	$0.724975\pi$
$954$	0.355390	−	0.0467880i	0.0115062	−	0.00151482i
$955$	38.1087	+	77.2767i	1.23317	+	2.50062i
$956$	−22.3105	+	5.97808i	−0.721573	+	0.193345i
$957$	−16.3437	+	14.3330i	−0.528317	+	0.463321i
$958$	0.279241	+	0.417913i	0.00902185	+	0.0135022i
$959$	9.15915	+	12.9863i	0.295765	+	0.419351i
$960$	−31.3969	+	13.0050i	−1.01333	+	0.419735i
$961$	−17.1692	+	22.3754i	−0.553846	+	0.721786i
$962$	−0.121853	+	0.138947i	−0.00392870	+	0.00447982i
$963$	−6.95069	+	0.455572i	−0.223983	+	0.0146806i
$964$	23.4615	+	26.7527i	0.755644	+	0.861647i
$965$	3.94222	+	3.94222i	0.126905	+	0.126905i
$966$	−0.193747	−	0.0603639i	−0.00623369	−	0.00194218i
$967$	46.8240	+	19.3951i	1.50576	+	0.623705i	0.974677	−	0.223617i	$-0.0717863\pi$
$967$	46.8240	+	19.3951i	1.50576	+	0.623705i	0.531080	+	0.847322i	$0.321786\pi$
$968$	−2.14959	+	1.24106i	−0.0690903	+	0.0398893i
$969$	16.4754	+	21.2344i	0.529266	+	0.682147i
$970$	0.130268	−	0.225631i	0.00418266	−	0.00724458i
$971$	6.10530	+	46.3743i	0.195928	+	1.48822i	0.753144	+	0.657855i	$0.228536\pi$
$971$	6.10530	+	46.3743i	0.195928	+	1.48822i	−0.557216	+	0.830368i	$0.688130\pi$
$972$	−1.10992	+	1.66111i	−0.0356006	+	0.0532800i
$973$	14.4128	+	23.5703i	0.462053	+	0.755629i
$974$	−1.42200	+	0.282853i	−0.0455637	+	0.00906319i
$975$	17.3781	+	8.56994i	0.556546	+	0.274458i
$976$	−32.8764	−	28.8319i	−1.05235	−	0.922886i
$977$	−4.38251	+	33.2885i	−0.140209	+	1.06499i	0.766203	+	0.642599i	$0.222144\pi$
$977$	−4.38251	+	33.2885i	−0.140209	+	1.06499i	−0.906412	+	0.422395i	$0.861190\pi$
$978$	−0.466918	−	0.358279i	−0.0149304	−	0.0114565i
$979$	−12.2467	−	2.43602i	−0.391405	−	0.0778554i
$980$	59.3998	−	6.91482i	1.89746	−	0.220886i
$981$	−3.21959	−	16.1860i	−0.102794	−	0.516778i
$982$	0.825819	+	0.221278i	0.0263530	+	0.00706125i
$983$	−2.57336	+	1.26904i	−0.0820775	+	0.0404762i	−0.482864	−	0.875695i	$-0.660404\pi$
$983$	−2.57336	+	1.26904i	−0.0820775	+	0.0404762i	0.400787	+	0.916171i	$0.368737\pi$
$984$	0.803224	−	0.616335i	0.0256058	−	0.0196481i
$985$	3.96549	+	6.86843i	0.126351	+	0.218846i
$986$	0.787910	−	0.331324i	0.0250922	−	0.0105515i
$987$	−4.29800	+	17.8271i	−0.136807	+	0.567442i
$988$	7.26805	−	17.5466i	0.231227	−	0.558232i
$989$	0.305135	−	4.65546i	0.00970272	−	0.148035i
$990$	0.255706	+	0.954310i	0.00812689	+	0.0303299i
$991$	−14.9439	+	44.0234i	−0.474710	+	1.39845i	0.401206	+	0.915988i	$0.368591\pi$
$991$	−14.9439	+	44.0234i	−0.474710	+	1.39845i	−0.875916	+	0.482463i	$0.839742\pi$
$992$	−0.415997	+	0.843559i	−0.0132079	+	0.0267830i
$993$	−1.53007	+	7.69220i	−0.0485554	+	0.244104i
$994$	0.763545	−	0.617094i	0.0242182	−	0.0195730i
$995$	−39.3749	−	95.0593i	−1.24827	−	3.01358i
$996$	−9.12296	+	3.09683i	−0.289072	+	0.0981267i
$997$	1.91349	+	29.1943i	0.0606010	+	0.924592i	0.914611	+	0.404335i	$0.132497\pi$
$997$	1.91349	+	29.1943i	0.0606010	+	0.924592i	−0.854010	+	0.520257i	$0.825836\pi$
$998$	0.505912	+	0.171734i	0.0160144	+	0.00543615i
$999$	0.698720	−	2.60766i	0.0221065	−	0.0825026i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.12	✓	384
7.5	odd	6	inner	357.2.bl.a.61.13	yes	384
17.12	odd	16	inner	357.2.bl.a.199.13	yes	384
119.12	even	48	inner	357.2.bl.a.250.12	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.12	✓	384	1.1	even	1	trivial
357.2.bl.a.61.13	yes	384	7.5	odd	6	inner
357.2.bl.a.199.13	yes	384	17.12	odd	16	inner
357.2.bl.a.250.12	yes	384	119.12	even	48	inner

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	357.2.bl.a.10.12

Level	$357$
Weight	$2$
Character	357.10
Analytic conductor	$2.851$
Analytic rank	$0$
Dimension	$384$
Inner twists	$4$